1,1,113,0,0.0878502,"\int e^{i \tan ^{-1}(a x)} x^4 \, dx","Int[E^(I*ArcTan[a*x])*x^4,x]","\frac{i x^4 \sqrt{a^2 x^2+1}}{5 a}+\frac{x^3 \sqrt{a^2 x^2+1}}{4 a^2}-\frac{4 i x^2 \sqrt{a^2 x^2+1}}{15 a^3}+\frac{(-45 a x+64 i) \sqrt{a^2 x^2+1}}{120 a^5}+\frac{3 \sinh ^{-1}(a x)}{8 a^5}","\frac{i x^4 \sqrt{a^2 x^2+1}}{5 a}+\frac{x^3 \sqrt{a^2 x^2+1}}{4 a^2}-\frac{4 i x^2 \sqrt{a^2 x^2+1}}{15 a^3}+\frac{(-45 a x+64 i) \sqrt{a^2 x^2+1}}{120 a^5}+\frac{3 \sinh ^{-1}(a x)}{8 a^5}",1,"(((-4*I)/15)*x^2*Sqrt[1 + a^2*x^2])/a^3 + (x^3*Sqrt[1 + a^2*x^2])/(4*a^2) + ((I/5)*x^4*Sqrt[1 + a^2*x^2])/a + ((64*I - 45*a*x)*Sqrt[1 + a^2*x^2])/(120*a^5) + (3*ArcSinh[a*x])/(8*a^5)","A",6,4,14,0.2857,1,"{5060, 833, 780, 215}"
2,1,90,0,0.0642709,"\int e^{i \tan ^{-1}(a x)} x^3 \, dx","Int[E^(I*ArcTan[a*x])*x^3,x]","\frac{i x^3 \sqrt{a^2 x^2+1}}{4 a}+\frac{x^2 \sqrt{a^2 x^2+1}}{3 a^2}-\frac{(16+9 i a x) \sqrt{a^2 x^2+1}}{24 a^4}+\frac{3 i \sinh ^{-1}(a x)}{8 a^4}","\frac{i x^3 \sqrt{a^2 x^2+1}}{4 a}+\frac{x^2 \sqrt{a^2 x^2+1}}{3 a^2}-\frac{(16+9 i a x) \sqrt{a^2 x^2+1}}{24 a^4}+\frac{3 i \sinh ^{-1}(a x)}{8 a^4}",1,"(x^2*Sqrt[1 + a^2*x^2])/(3*a^2) + ((I/4)*x^3*Sqrt[1 + a^2*x^2])/a - ((16 + (9*I)*a*x)*Sqrt[1 + a^2*x^2])/(24*a^4) + (((3*I)/8)*ArcSinh[a*x])/a^4","A",5,4,14,0.2857,1,"{5060, 833, 780, 215}"
3,1,75,0,0.0471978,"\int e^{i \tan ^{-1}(a x)} x^2 \, dx","Int[E^(I*ArcTan[a*x])*x^2,x]","\frac{i \left(a^2 x^2+1\right)^{3/2}}{3 a^3}+\frac{x \sqrt{a^2 x^2+1}}{2 a^2}-\frac{i \sqrt{a^2 x^2+1}}{a^3}-\frac{\sinh ^{-1}(a x)}{2 a^3}","\frac{i \left(a^2 x^2+1\right)^{3/2}}{3 a^3}+\frac{x \sqrt{a^2 x^2+1}}{2 a^2}-\frac{i \sqrt{a^2 x^2+1}}{a^3}-\frac{\sinh ^{-1}(a x)}{2 a^3}",1,"((-I)*Sqrt[1 + a^2*x^2])/a^3 + (x*Sqrt[1 + a^2*x^2])/(2*a^2) + ((I/3)*(1 + a^2*x^2)^(3/2))/a^3 - ArcSinh[a*x]/(2*a^3)","A",7,5,14,0.3571,1,"{5060, 797, 641, 195, 215}"
4,1,42,0,0.019259,"\int e^{i \tan ^{-1}(a x)} x \, dx","Int[E^(I*ArcTan[a*x])*x,x]","\frac{(2+i a x) \sqrt{a^2 x^2+1}}{2 a^2}-\frac{i \sinh ^{-1}(a x)}{2 a^2}","\frac{(2+i a x) \sqrt{a^2 x^2+1}}{2 a^2}-\frac{i \sinh ^{-1}(a x)}{2 a^2}",1,"((2 + I*a*x)*Sqrt[1 + a^2*x^2])/(2*a^2) - ((I/2)*ArcSinh[a*x])/a^2","A",3,3,12,0.2500,1,"{5060, 780, 215}"
5,1,29,0,0.0090885,"\int e^{i \tan ^{-1}(a x)} \, dx","Int[E^(I*ArcTan[a*x]),x]","\frac{\sinh ^{-1}(a x)}{a}+\frac{i \sqrt{a^2 x^2+1}}{a}","\frac{\sinh ^{-1}(a x)}{a}+\frac{i \sqrt{a^2 x^2+1}}{a}",1,"(I*Sqrt[1 + a^2*x^2])/a + ArcSinh[a*x]/a","A",3,3,10,0.3000,1,"{5059, 641, 215}"
6,1,25,0,0.0365401,"\int \frac{e^{i \tan ^{-1}(a x)}}{x} \, dx","Int[E^(I*ArcTan[a*x])/x,x]","-\tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)+i \sinh ^{-1}(a x)","-\tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)+i \sinh ^{-1}(a x)",1,"I*ArcSinh[a*x] - ArcTanh[Sqrt[1 + a^2*x^2]]","A",6,6,14,0.4286,1,"{5060, 844, 215, 266, 63, 208}"
7,1,38,0,0.0382376,"\int \frac{e^{i \tan ^{-1}(a x)}}{x^2} \, dx","Int[E^(I*ArcTan[a*x])/x^2,x]","-\frac{\sqrt{a^2 x^2+1}}{x}-i a \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","-\frac{\sqrt{a^2 x^2+1}}{x}-i a \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-(Sqrt[1 + a^2*x^2]/x) - I*a*ArcTanh[Sqrt[1 + a^2*x^2]]","A",5,5,14,0.3571,1,"{5060, 807, 266, 63, 208}"
8,1,63,0,0.0502899,"\int \frac{e^{i \tan ^{-1}(a x)}}{x^3} \, dx","Int[E^(I*ArcTan[a*x])/x^3,x]","-\frac{i a \sqrt{a^2 x^2+1}}{x}-\frac{\sqrt{a^2 x^2+1}}{2 x^2}+\frac{1}{2} a^2 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","-\frac{i a \sqrt{a^2 x^2+1}}{x}-\frac{\sqrt{a^2 x^2+1}}{2 x^2}+\frac{1}{2} a^2 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-Sqrt[1 + a^2*x^2]/(2*x^2) - (I*a*Sqrt[1 + a^2*x^2])/x + (a^2*ArcTanh[Sqrt[1 + a^2*x^2]])/2","A",6,6,14,0.4286,1,"{5060, 835, 807, 266, 63, 208}"
9,1,90,0,0.0694304,"\int \frac{e^{i \tan ^{-1}(a x)}}{x^4} \, dx","Int[E^(I*ArcTan[a*x])/x^4,x]","\frac{2 a^2 \sqrt{a^2 x^2+1}}{3 x}-\frac{i a \sqrt{a^2 x^2+1}}{2 x^2}-\frac{\sqrt{a^2 x^2+1}}{3 x^3}+\frac{1}{2} i a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","\frac{2 a^2 \sqrt{a^2 x^2+1}}{3 x}-\frac{i a \sqrt{a^2 x^2+1}}{2 x^2}-\frac{\sqrt{a^2 x^2+1}}{3 x^3}+\frac{1}{2} i a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-Sqrt[1 + a^2*x^2]/(3*x^3) - ((I/2)*a*Sqrt[1 + a^2*x^2])/x^2 + (2*a^2*Sqrt[1 + a^2*x^2])/(3*x) + (I/2)*a^3*ArcTanh[Sqrt[1 + a^2*x^2]]","A",7,6,14,0.4286,1,"{5060, 835, 807, 266, 63, 208}"
10,1,113,0,0.0904184,"\int \frac{e^{i \tan ^{-1}(a x)}}{x^5} \, dx","Int[E^(I*ArcTan[a*x])/x^5,x]","\frac{2 i a^3 \sqrt{a^2 x^2+1}}{3 x}+\frac{3 a^2 \sqrt{a^2 x^2+1}}{8 x^2}-\frac{i a \sqrt{a^2 x^2+1}}{3 x^3}-\frac{\sqrt{a^2 x^2+1}}{4 x^4}-\frac{3}{8} a^4 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","\frac{2 i a^3 \sqrt{a^2 x^2+1}}{3 x}+\frac{3 a^2 \sqrt{a^2 x^2+1}}{8 x^2}-\frac{i a \sqrt{a^2 x^2+1}}{3 x^3}-\frac{\sqrt{a^2 x^2+1}}{4 x^4}-\frac{3}{8} a^4 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-Sqrt[1 + a^2*x^2]/(4*x^4) - ((I/3)*a*Sqrt[1 + a^2*x^2])/x^3 + (3*a^2*Sqrt[1 + a^2*x^2])/(8*x^2) + (((2*I)/3)*a^3*Sqrt[1 + a^2*x^2])/x - (3*a^4*ArcTanh[Sqrt[1 + a^2*x^2]])/8","A",8,6,14,0.4286,1,"{5060, 835, 807, 266, 63, 208}"
11,1,48,0,0.0361756,"\int e^{2 i \tan ^{-1}(a x)} x^3 \, dx","Int[E^((2*I)*ArcTan[a*x])*x^3,x]","\frac{x^2}{a^2}-\frac{2 i x}{a^3}-\frac{2 \log (a x+i)}{a^4}+\frac{2 i x^3}{3 a}-\frac{x^4}{4}","\frac{x^2}{a^2}-\frac{2 i x}{a^3}-\frac{2 \log (a x+i)}{a^4}+\frac{2 i x^3}{3 a}-\frac{x^4}{4}",1,"((-2*I)*x)/a^3 + x^2/a^2 + (((2*I)/3)*x^3)/a - x^4/4 - (2*Log[I + a*x])/a^4","A",3,2,14,0.1429,1,"{5062, 77}"
12,1,39,0,0.0284318,"\int e^{2 i \tan ^{-1}(a x)} x^2 \, dx","Int[E^((2*I)*ArcTan[a*x])*x^2,x]","\frac{2 x}{a^2}-\frac{2 i \log (a x+i)}{a^3}+\frac{i x^2}{a}-\frac{x^3}{3}","\frac{2 x}{a^2}-\frac{2 i \log (a x+i)}{a^3}+\frac{i x^2}{a}-\frac{x^3}{3}",1,"(2*x)/a^2 + (I*x^2)/a - x^3/3 - ((2*I)*Log[I + a*x])/a^3","A",3,2,14,0.1429,1,"{5062, 77}"
13,1,29,0,0.0194471,"\int e^{2 i \tan ^{-1}(a x)} x \, dx","Int[E^((2*I)*ArcTan[a*x])*x,x]","\frac{2 \log (a x+i)}{a^2}+\frac{2 i x}{a}-\frac{x^2}{2}","\frac{2 \log (a x+i)}{a^2}+\frac{2 i x}{a}-\frac{x^2}{2}",1,"((2*I)*x)/a - x^2/2 + (2*Log[I + a*x])/a^2","A",3,2,12,0.1667,1,"{5062, 77}"
14,1,19,0,0.0091863,"\int e^{2 i \tan ^{-1}(a x)} \, dx","Int[E^((2*I)*ArcTan[a*x]),x]","-x+\frac{2 i \log (a x+i)}{a}","-x+\frac{2 i \log (a x+i)}{a}",1,"-x + ((2*I)*Log[I + a*x])/a","A",3,2,10,0.2000,1,"{5061, 43}"
15,1,13,0,0.0194988,"\int \frac{e^{2 i \tan ^{-1}(a x)}}{x} \, dx","Int[E^((2*I)*ArcTan[a*x])/x,x]","\log (x)-2 \log (a x+i)","\log (x)-2 \log (a x+i)",1,"Log[x] - 2*Log[I + a*x]","A",3,2,14,0.1429,1,"{5062, 72}"
16,1,26,0,0.0236566,"\int \frac{e^{2 i \tan ^{-1}(a x)}}{x^2} \, dx","Int[E^((2*I)*ArcTan[a*x])/x^2,x]","2 i a \log (x)-2 i a \log (a x+i)-\frac{1}{x}","2 i a \log (x)-2 i a \log (a x+i)-\frac{1}{x}",1,"-x^(-1) + (2*I)*a*Log[x] - (2*I)*a*Log[I + a*x]","A",3,2,14,0.1429,1,"{5062, 77}"
17,1,36,0,0.0268669,"\int \frac{e^{2 i \tan ^{-1}(a x)}}{x^3} \, dx","Int[E^((2*I)*ArcTan[a*x])/x^3,x]","-2 a^2 \log (x)+2 a^2 \log (a x+i)-\frac{2 i a}{x}-\frac{1}{2 x^2}","-2 a^2 \log (x)+2 a^2 \log (a x+i)-\frac{2 i a}{x}-\frac{1}{2 x^2}",1,"-1/(2*x^2) - ((2*I)*a)/x - 2*a^2*Log[x] + 2*a^2*Log[I + a*x]","A",3,2,14,0.1429,1,"{5062, 77}"
18,1,48,0,0.0304261,"\int \frac{e^{2 i \tan ^{-1}(a x)}}{x^4} \, dx","Int[E^((2*I)*ArcTan[a*x])/x^4,x]","\frac{2 a^2}{x}-2 i a^3 \log (x)+2 i a^3 \log (a x+i)-\frac{i a}{x^2}-\frac{1}{3 x^3}","\frac{2 a^2}{x}-2 i a^3 \log (x)+2 i a^3 \log (a x+i)-\frac{i a}{x^2}-\frac{1}{3 x^3}",1,"-1/(3*x^3) - (I*a)/x^2 + (2*a^2)/x - (2*I)*a^3*Log[x] + (2*I)*a^3*Log[I + a*x]","A",3,2,14,0.1429,1,"{5062, 77}"
19,1,137,0,0.6213675,"\int e^{3 i \tan ^{-1}(a x)} x^3 \, dx","Int[E^((3*I)*ArcTan[a*x])*x^3,x]","-\frac{i x^3 \sqrt{a^2 x^2+1}}{4 a}-\frac{x^2 \sqrt{a^2 x^2+1}}{a^2}-\frac{9 i (-3 a x+2 i) \sqrt{a^2 x^2+1}}{8 a^4}+\frac{27 \sqrt{a^2 x^2+1}}{4 a^4}+\frac{(1+i a x)^3}{a^4 \sqrt{a^2 x^2+1}}-\frac{51 i \sinh ^{-1}(a x)}{8 a^4}","-\frac{i x^3 \sqrt{a^2 x^2+1}}{4 a}-\frac{x^2 \sqrt{a^2 x^2+1}}{a^2}-\frac{9 i (-3 a x+2 i) \sqrt{a^2 x^2+1}}{8 a^4}+\frac{27 \sqrt{a^2 x^2+1}}{4 a^4}+\frac{(1+i a x)^3}{a^4 \sqrt{a^2 x^2+1}}-\frac{51 i \sinh ^{-1}(a x)}{8 a^4}",1,"(1 + I*a*x)^3/(a^4*Sqrt[1 + a^2*x^2]) + (27*Sqrt[1 + a^2*x^2])/(4*a^4) - (x^2*Sqrt[1 + a^2*x^2])/a^2 - ((I/4)*x^3*Sqrt[1 + a^2*x^2])/a - (((9*I)/8)*(2*I - 3*a*x)*Sqrt[1 + a^2*x^2])/a^4 - (((51*I)/8)*ArcSinh[a*x])/a^4","A",14,11,14,0.7857,1,"{5060, 1633, 1593, 12, 852, 1635, 1815, 27, 743, 641, 215}"
20,1,102,0,0.5684566,"\int e^{3 i \tan ^{-1}(a x)} x^2 \, dx","Int[E^((3*I)*ArcTan[a*x])*x^2,x]","\frac{i (1+i a x)^3}{a^3 \sqrt{a^2 x^2+1}}+\frac{i (3+i a x)^2 \sqrt{a^2 x^2+1}}{3 a^3}+\frac{(-3 a x+28 i) \sqrt{a^2 x^2+1}}{6 a^3}+\frac{11 \sinh ^{-1}(a x)}{2 a^3}","\frac{i (1+i a x)^3}{a^3 \sqrt{a^2 x^2+1}}+\frac{i (3+i a x)^2 \sqrt{a^2 x^2+1}}{3 a^3}+\frac{(-3 a x+28 i) \sqrt{a^2 x^2+1}}{6 a^3}+\frac{11 \sinh ^{-1}(a x)}{2 a^3}",1,"(I*(1 + I*a*x)^3)/(a^3*Sqrt[1 + a^2*x^2]) + ((28*I - 3*a*x)*Sqrt[1 + a^2*x^2])/(6*a^3) + ((I/3)*(3 + I*a*x)^2*Sqrt[1 + a^2*x^2])/a^3 + (11*ArcSinh[a*x])/(2*a^3)","A",10,9,14,0.6429,1,"{5060, 1633, 1593, 12, 852, 1635, 1654, 780, 215}"
21,1,92,0,0.3256474,"\int e^{3 i \tan ^{-1}(a x)} x \, dx","Int[E^((3*I)*ArcTan[a*x])*x,x]","-\frac{\left(a^2 x^2+1\right)^{5/2}}{a^2 (1-i a x)^3}-\frac{3 \left(a^2 x^2+1\right)^{3/2}}{2 a^2 (1-i a x)}-\frac{9 \sqrt{a^2 x^2+1}}{2 a^2}+\frac{9 i \sinh ^{-1}(a x)}{2 a^2}","-\frac{\left(a^2 x^2+1\right)^{5/2}}{a^2 (1-i a x)^3}-\frac{3 \left(a^2 x^2+1\right)^{3/2}}{2 a^2 (1-i a x)}-\frac{9 \sqrt{a^2 x^2+1}}{2 a^2}+\frac{9 i \sinh ^{-1}(a x)}{2 a^2}",1,"(-9*Sqrt[1 + a^2*x^2])/(2*a^2) - (3*(1 + a^2*x^2)^(3/2))/(2*a^2*(1 - I*a*x)) - (1 + a^2*x^2)^(5/2)/(a^2*(1 - I*a*x)^3) + (((9*I)/2)*ArcSinh[a*x])/a^2","A",9,7,12,0.5833,1,"{5060, 1633, 1593, 12, 793, 665, 215}"
22,1,60,0,0.0448873,"\int e^{3 i \tan ^{-1}(a x)} \, dx","Int[E^((3*I)*ArcTan[a*x]),x]","-\frac{2 i (1+i a x)^2}{a \sqrt{a^2 x^2+1}}-\frac{3 i \sqrt{a^2 x^2+1}}{a}-\frac{3 \sinh ^{-1}(a x)}{a}","-\frac{2 i (1+i a x)^2}{a \sqrt{a^2 x^2+1}}-\frac{3 i \sqrt{a^2 x^2+1}}{a}-\frac{3 \sinh ^{-1}(a x)}{a}",1,"((-2*I)*(1 + I*a*x)^2)/(a*Sqrt[1 + a^2*x^2]) - ((3*I)*Sqrt[1 + a^2*x^2])/a - (3*ArcSinh[a*x])/a","A",5,5,10,0.5000,1,"{5059, 853, 669, 641, 215}"
23,1,51,0,0.6631977,"\int \frac{e^{3 i \tan ^{-1}(a x)}}{x} \, dx","Int[E^((3*I)*ArcTan[a*x])/x,x]","\frac{4 i \sqrt{a^2 x^2+1}}{a x+i}-\tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-i \sinh ^{-1}(a x)","\frac{4 i \sqrt{a^2 x^2+1}}{a x+i}-\tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-i \sinh ^{-1}(a x)",1,"((4*I)*Sqrt[1 + a^2*x^2])/(I + a*x) - I*ArcSinh[a*x] - ArcTanh[Sqrt[1 + a^2*x^2]]","A",8,7,14,0.5000,1,"{5060, 6742, 215, 266, 63, 208, 651}"
24,1,63,0,0.5597413,"\int \frac{e^{3 i \tan ^{-1}(a x)}}{x^2} \, dx","Int[E^((3*I)*ArcTan[a*x])/x^2,x]","-\frac{4 a \sqrt{a^2 x^2+1}}{a x+i}-\frac{\sqrt{a^2 x^2+1}}{x}-3 i a \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","-\frac{4 a \sqrt{a^2 x^2+1}}{a x+i}-\frac{\sqrt{a^2 x^2+1}}{x}-3 i a \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-(Sqrt[1 + a^2*x^2]/x) - (4*a*Sqrt[1 + a^2*x^2])/(I + a*x) - (3*I)*a*ArcTanh[Sqrt[1 + a^2*x^2]]","A",8,7,14,0.5000,1,"{5060, 6742, 264, 266, 63, 208, 651}"
25,1,92,0,0.6014642,"\int \frac{e^{3 i \tan ^{-1}(a x)}}{x^3} \, dx","Int[E^((3*I)*ArcTan[a*x])/x^3,x]","-\frac{4 i a^2 \sqrt{a^2 x^2+1}}{a x+i}-\frac{3 i a \sqrt{a^2 x^2+1}}{x}-\frac{\sqrt{a^2 x^2+1}}{2 x^2}+\frac{9}{2} a^2 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","-\frac{4 i a^2 \sqrt{a^2 x^2+1}}{a x+i}-\frac{3 i a \sqrt{a^2 x^2+1}}{x}-\frac{\sqrt{a^2 x^2+1}}{2 x^2}+\frac{9}{2} a^2 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-Sqrt[1 + a^2*x^2]/(2*x^2) - ((3*I)*a*Sqrt[1 + a^2*x^2])/x - ((4*I)*a^2*Sqrt[1 + a^2*x^2])/(I + a*x) + (9*a^2*ArcTanh[Sqrt[1 + a^2*x^2]])/2","A",12,8,14,0.5714,1,"{5060, 6742, 266, 51, 63, 208, 264, 651}"
26,1,117,0,0.61597,"\int \frac{e^{3 i \tan ^{-1}(a x)}}{x^4} \, dx","Int[E^((3*I)*ArcTan[a*x])/x^4,x]","\frac{4 a^3 \sqrt{a^2 x^2+1}}{a x+i}+\frac{14 a^2 \sqrt{a^2 x^2+1}}{3 x}-\frac{3 i a \sqrt{a^2 x^2+1}}{2 x^2}-\frac{\sqrt{a^2 x^2+1}}{3 x^3}+\frac{11}{2} i a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","\frac{4 a^3 \sqrt{a^2 x^2+1}}{a x+i}+\frac{14 a^2 \sqrt{a^2 x^2+1}}{3 x}-\frac{3 i a \sqrt{a^2 x^2+1}}{2 x^2}-\frac{\sqrt{a^2 x^2+1}}{3 x^3}+\frac{11}{2} i a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-Sqrt[1 + a^2*x^2]/(3*x^3) - (((3*I)/2)*a*Sqrt[1 + a^2*x^2])/x^2 + (14*a^2*Sqrt[1 + a^2*x^2])/(3*x) + (4*a^3*Sqrt[1 + a^2*x^2])/(I + a*x) + ((11*I)/2)*a^3*ArcTanh[Sqrt[1 + a^2*x^2]]","A",14,9,14,0.6429,1,"{5060, 6742, 271, 264, 266, 51, 63, 208, 651}"
27,1,65,0,0.0445987,"\int e^{4 i \tan ^{-1}(a x)} x^3 \, dx","Int[E^((4*I)*ArcTan[a*x])*x^3,x]","-\frac{4 x^2}{a^2}+\frac{12 i x}{a^3}+\frac{4 i}{a^4 (a x+i)}+\frac{16 \log (a x+i)}{a^4}-\frac{4 i x^3}{3 a}+\frac{x^4}{4}","-\frac{4 x^2}{a^2}+\frac{12 i x}{a^3}+\frac{4 i}{a^4 (a x+i)}+\frac{16 \log (a x+i)}{a^4}-\frac{4 i x^3}{3 a}+\frac{x^4}{4}",1,"((12*I)*x)/a^3 - (4*x^2)/a^2 - (((4*I)/3)*x^3)/a + x^4/4 + (4*I)/(a^4*(I + a*x)) + (16*Log[I + a*x])/a^4","A",3,2,14,0.1429,1,"{5062, 88}"
28,1,53,0,0.0399861,"\int e^{4 i \tan ^{-1}(a x)} x^2 \, dx","Int[E^((4*I)*ArcTan[a*x])*x^2,x]","-\frac{8 x}{a^2}-\frac{4}{a^3 (a x+i)}+\frac{12 i \log (a x+i)}{a^3}-\frac{2 i x^2}{a}+\frac{x^3}{3}","-\frac{8 x}{a^2}-\frac{4}{a^3 (a x+i)}+\frac{12 i \log (a x+i)}{a^3}-\frac{2 i x^2}{a}+\frac{x^3}{3}",1,"(-8*x)/a^2 - ((2*I)*x^2)/a + x^3/3 - 4/(a^3*(I + a*x)) + ((12*I)*Log[I + a*x])/a^3","A",3,2,14,0.1429,1,"{5062, 88}"
29,1,45,0,0.0262917,"\int e^{4 i \tan ^{-1}(a x)} x \, dx","Int[E^((4*I)*ArcTan[a*x])*x,x]","-\frac{4 i}{a^2 (a x+i)}-\frac{8 \log (a x+i)}{a^2}-\frac{4 i x}{a}+\frac{x^2}{2}","-\frac{4 i}{a^2 (a x+i)}-\frac{8 \log (a x+i)}{a^2}-\frac{4 i x}{a}+\frac{x^2}{2}",1,"((-4*I)*x)/a + x^2/2 - (4*I)/(a^2*(I + a*x)) - (8*Log[I + a*x])/a^2","A",3,2,12,0.1667,1,"{5062, 77}"
30,1,31,0,0.0140897,"\int e^{4 i \tan ^{-1}(a x)} \, dx","Int[E^((4*I)*ArcTan[a*x]),x]","\frac{4}{a (a x+i)}-\frac{4 i \log (a x+i)}{a}+x","\frac{4}{a (a x+i)}-\frac{4 i \log (a x+i)}{a}+x",1,"x + 4/(a*(I + a*x)) - ((4*I)*Log[I + a*x])/a","A",3,2,10,0.2000,1,"{5061, 43}"
31,1,16,0,0.0215648,"\int \frac{e^{4 i \tan ^{-1}(a x)}}{x} \, dx","Int[E^((4*I)*ArcTan[a*x])/x,x]","\log (x)+\frac{4 i}{a x+i}","\log (x)+\frac{4 i}{a x+i}",1,"(4*I)/(I + a*x) + Log[x]","A",3,2,14,0.1429,1,"{5062, 88}"
32,1,38,0,0.030845,"\int \frac{e^{4 i \tan ^{-1}(a x)}}{x^2} \, dx","Int[E^((4*I)*ArcTan[a*x])/x^2,x]","-\frac{4 a}{a x+i}+4 i a \log (x)-4 i a \log (a x+i)-\frac{1}{x}","-\frac{4 a}{a x+i}+4 i a \log (x)-4 i a \log (a x+i)-\frac{1}{x}",1,"-x^(-1) - (4*a)/(I + a*x) + (4*I)*a*Log[x] - (4*I)*a*Log[I + a*x]","A",3,2,14,0.1429,1,"{5062, 88}"
33,1,52,0,0.0353444,"\int \frac{e^{4 i \tan ^{-1}(a x)}}{x^3} \, dx","Int[E^((4*I)*ArcTan[a*x])/x^3,x]","-\frac{4 i a^2}{a x+i}-8 a^2 \log (x)+8 a^2 \log (a x+i)-\frac{4 i a}{x}-\frac{1}{2 x^2}","-\frac{4 i a^2}{a x+i}-8 a^2 \log (x)+8 a^2 \log (a x+i)-\frac{4 i a}{x}-\frac{1}{2 x^2}",1,"-1/(2*x^2) - ((4*I)*a)/x - ((4*I)*a^2)/(I + a*x) - 8*a^2*Log[x] + 8*a^2*Log[I + a*x]","A",3,2,14,0.1429,1,"{5062, 88}"
34,1,62,0,0.0390173,"\int \frac{e^{4 i \tan ^{-1}(a x)}}{x^4} \, dx","Int[E^((4*I)*ArcTan[a*x])/x^4,x]","\frac{4 a^3}{a x+i}+\frac{8 a^2}{x}-12 i a^3 \log (x)+12 i a^3 \log (a x+i)-\frac{2 i a}{x^2}-\frac{1}{3 x^3}","\frac{4 a^3}{a x+i}+\frac{8 a^2}{x}-12 i a^3 \log (x)+12 i a^3 \log (a x+i)-\frac{2 i a}{x^2}-\frac{1}{3 x^3}",1,"-1/(3*x^3) - ((2*I)*a)/x^2 + (8*a^2)/x + (4*a^3)/(I + a*x) - (12*I)*a^3*Log[x] + (12*I)*a^3*Log[I + a*x]","A",3,2,14,0.1429,1,"{5062, 88}"
35,1,90,0,0.0664229,"\int e^{-i \tan ^{-1}(a x)} x^3 \, dx","Int[x^3/E^(I*ArcTan[a*x]),x]","-\frac{i x^3 \sqrt{a^2 x^2+1}}{4 a}+\frac{x^2 \sqrt{a^2 x^2+1}}{3 a^2}-\frac{(16-9 i a x) \sqrt{a^2 x^2+1}}{24 a^4}-\frac{3 i \sinh ^{-1}(a x)}{8 a^4}","-\frac{i x^3 \sqrt{a^2 x^2+1}}{4 a}+\frac{x^2 \sqrt{a^2 x^2+1}}{3 a^2}-\frac{(16-9 i a x) \sqrt{a^2 x^2+1}}{24 a^4}-\frac{3 i \sinh ^{-1}(a x)}{8 a^4}",1,"(x^2*Sqrt[1 + a^2*x^2])/(3*a^2) - ((I/4)*x^3*Sqrt[1 + a^2*x^2])/a - ((16 - (9*I)*a*x)*Sqrt[1 + a^2*x^2])/(24*a^4) - (((3*I)/8)*ArcSinh[a*x])/a^4","A",5,4,14,0.2857,1,"{5060, 833, 780, 215}"
36,1,75,0,0.0473174,"\int e^{-i \tan ^{-1}(a x)} x^2 \, dx","Int[x^2/E^(I*ArcTan[a*x]),x]","-\frac{i \left(a^2 x^2+1\right)^{3/2}}{3 a^3}+\frac{x \sqrt{a^2 x^2+1}}{2 a^2}+\frac{i \sqrt{a^2 x^2+1}}{a^3}-\frac{\sinh ^{-1}(a x)}{2 a^3}","-\frac{i \left(a^2 x^2+1\right)^{3/2}}{3 a^3}+\frac{x \sqrt{a^2 x^2+1}}{2 a^2}+\frac{i \sqrt{a^2 x^2+1}}{a^3}-\frac{\sinh ^{-1}(a x)}{2 a^3}",1,"(I*Sqrt[1 + a^2*x^2])/a^3 + (x*Sqrt[1 + a^2*x^2])/(2*a^2) - ((I/3)*(1 + a^2*x^2)^(3/2))/a^3 - ArcSinh[a*x]/(2*a^3)","A",7,5,14,0.3571,1,"{5060, 797, 641, 195, 215}"
37,1,42,0,0.0199573,"\int e^{-i \tan ^{-1}(a x)} x \, dx","Int[x/E^(I*ArcTan[a*x]),x]","\frac{\sqrt{a^2 x^2+1} (2-i a x)}{2 a^2}+\frac{i \sinh ^{-1}(a x)}{2 a^2}","\frac{\sqrt{a^2 x^2+1} (2-i a x)}{2 a^2}+\frac{i \sinh ^{-1}(a x)}{2 a^2}",1,"((2 - I*a*x)*Sqrt[1 + a^2*x^2])/(2*a^2) + ((I/2)*ArcSinh[a*x])/a^2","A",3,3,12,0.2500,1,"{5060, 780, 215}"
38,1,29,0,0.0094273,"\int e^{-i \tan ^{-1}(a x)} \, dx","Int[E^((-I)*ArcTan[a*x]),x]","\frac{\sinh ^{-1}(a x)}{a}-\frac{i \sqrt{a^2 x^2+1}}{a}","\frac{\sinh ^{-1}(a x)}{a}-\frac{i \sqrt{a^2 x^2+1}}{a}",1,"((-I)*Sqrt[1 + a^2*x^2])/a + ArcSinh[a*x]/a","A",3,3,10,0.3000,1,"{5059, 641, 215}"
39,1,25,0,0.036575,"\int \frac{e^{-i \tan ^{-1}(a x)}}{x} \, dx","Int[1/(E^(I*ArcTan[a*x])*x),x]","-\tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-i \sinh ^{-1}(a x)","-\tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-i \sinh ^{-1}(a x)",1,"(-I)*ArcSinh[a*x] - ArcTanh[Sqrt[1 + a^2*x^2]]","A",6,6,14,0.4286,1,"{5060, 844, 215, 266, 63, 208}"
40,1,38,0,0.0369982,"\int \frac{e^{-i \tan ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^(I*ArcTan[a*x])*x^2),x]","-\frac{\sqrt{a^2 x^2+1}}{x}+i a \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","-\frac{\sqrt{a^2 x^2+1}}{x}+i a \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-(Sqrt[1 + a^2*x^2]/x) + I*a*ArcTanh[Sqrt[1 + a^2*x^2]]","A",5,5,14,0.3571,1,"{5060, 807, 266, 63, 208}"
41,1,63,0,0.05137,"\int \frac{e^{-i \tan ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^(I*ArcTan[a*x])*x^3),x]","\frac{i a \sqrt{a^2 x^2+1}}{x}-\frac{\sqrt{a^2 x^2+1}}{2 x^2}+\frac{1}{2} a^2 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","\frac{i a \sqrt{a^2 x^2+1}}{x}-\frac{\sqrt{a^2 x^2+1}}{2 x^2}+\frac{1}{2} a^2 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-Sqrt[1 + a^2*x^2]/(2*x^2) + (I*a*Sqrt[1 + a^2*x^2])/x + (a^2*ArcTanh[Sqrt[1 + a^2*x^2]])/2","A",6,6,14,0.4286,1,"{5060, 835, 807, 266, 63, 208}"
42,1,90,0,0.0695705,"\int \frac{e^{-i \tan ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^(I*ArcTan[a*x])*x^4),x]","\frac{2 a^2 \sqrt{a^2 x^2+1}}{3 x}+\frac{i a \sqrt{a^2 x^2+1}}{2 x^2}-\frac{\sqrt{a^2 x^2+1}}{3 x^3}-\frac{1}{2} i a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","\frac{2 a^2 \sqrt{a^2 x^2+1}}{3 x}+\frac{i a \sqrt{a^2 x^2+1}}{2 x^2}-\frac{\sqrt{a^2 x^2+1}}{3 x^3}-\frac{1}{2} i a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-Sqrt[1 + a^2*x^2]/(3*x^3) + ((I/2)*a*Sqrt[1 + a^2*x^2])/x^2 + (2*a^2*Sqrt[1 + a^2*x^2])/(3*x) - (I/2)*a^3*ArcTanh[Sqrt[1 + a^2*x^2]]","A",7,6,14,0.4286,1,"{5060, 835, 807, 266, 63, 208}"
43,1,113,0,0.0891088,"\int \frac{e^{-i \tan ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^(I*ArcTan[a*x])*x^5),x]","-\frac{2 i a^3 \sqrt{a^2 x^2+1}}{3 x}+\frac{3 a^2 \sqrt{a^2 x^2+1}}{8 x^2}+\frac{i a \sqrt{a^2 x^2+1}}{3 x^3}-\frac{\sqrt{a^2 x^2+1}}{4 x^4}-\frac{3}{8} a^4 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","-\frac{2 i a^3 \sqrt{a^2 x^2+1}}{3 x}+\frac{3 a^2 \sqrt{a^2 x^2+1}}{8 x^2}+\frac{i a \sqrt{a^2 x^2+1}}{3 x^3}-\frac{\sqrt{a^2 x^2+1}}{4 x^4}-\frac{3}{8} a^4 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-Sqrt[1 + a^2*x^2]/(4*x^4) + ((I/3)*a*Sqrt[1 + a^2*x^2])/x^3 + (3*a^2*Sqrt[1 + a^2*x^2])/(8*x^2) - (((2*I)/3)*a^3*Sqrt[1 + a^2*x^2])/x - (3*a^4*ArcTanh[Sqrt[1 + a^2*x^2]])/8","A",8,6,14,0.4286,1,"{5060, 835, 807, 266, 63, 208}"
44,1,49,0,0.0352147,"\int e^{-2 i \tan ^{-1}(a x)} x^3 \, dx","Int[x^3/E^((2*I)*ArcTan[a*x]),x]","\frac{x^2}{a^2}+\frac{2 i x}{a^3}-\frac{2 \log (-a x+i)}{a^4}-\frac{2 i x^3}{3 a}-\frac{x^4}{4}","\frac{x^2}{a^2}+\frac{2 i x}{a^3}-\frac{2 \log (-a x+i)}{a^4}-\frac{2 i x^3}{3 a}-\frac{x^4}{4}",1,"((2*I)*x)/a^3 + x^2/a^2 - (((2*I)/3)*x^3)/a - x^4/4 - (2*Log[I - a*x])/a^4","A",3,2,14,0.1429,1,"{5062, 77}"
45,1,40,0,0.0297327,"\int e^{-2 i \tan ^{-1}(a x)} x^2 \, dx","Int[x^2/E^((2*I)*ArcTan[a*x]),x]","\frac{2 x}{a^2}+\frac{2 i \log (-a x+i)}{a^3}-\frac{i x^2}{a}-\frac{x^3}{3}","\frac{2 x}{a^2}+\frac{2 i \log (-a x+i)}{a^3}-\frac{i x^2}{a}-\frac{x^3}{3}",1,"(2*x)/a^2 - (I*x^2)/a - x^3/3 + ((2*I)*Log[I - a*x])/a^3","A",3,2,14,0.1429,1,"{5062, 77}"
46,1,30,0,0.0210554,"\int e^{-2 i \tan ^{-1}(a x)} x \, dx","Int[x/E^((2*I)*ArcTan[a*x]),x]","\frac{2 \log (-a x+i)}{a^2}-\frac{2 i x}{a}-\frac{x^2}{2}","\frac{2 \log (-a x+i)}{a^2}-\frac{2 i x}{a}-\frac{x^2}{2}",1,"((-2*I)*x)/a - x^2/2 + (2*Log[I - a*x])/a^2","A",3,2,12,0.1667,1,"{5062, 77}"
47,1,20,0,0.0101968,"\int e^{-2 i \tan ^{-1}(a x)} \, dx","Int[E^((-2*I)*ArcTan[a*x]),x]","-x-\frac{2 i \log (-a x+i)}{a}","-x-\frac{2 i \log (-a x+i)}{a}",1,"-x - ((2*I)*Log[I - a*x])/a","A",3,2,10,0.2000,1,"{5061, 43}"
48,1,14,0,0.0200594,"\int \frac{e^{-2 i \tan ^{-1}(a x)}}{x} \, dx","Int[1/(E^((2*I)*ArcTan[a*x])*x),x]","\log (x)-2 \log (-a x+i)","\log (x)-2 \log (-a x+i)",1,"Log[x] - 2*Log[I - a*x]","A",3,2,14,0.1429,1,"{5062, 72}"
49,1,27,0,0.0255769,"\int \frac{e^{-2 i \tan ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^((2*I)*ArcTan[a*x])*x^2),x]","-2 i a \log (x)+2 i a \log (-a x+i)-\frac{1}{x}","-2 i a \log (x)+2 i a \log (-a x+i)-\frac{1}{x}",1,"-x^(-1) - (2*I)*a*Log[x] + (2*I)*a*Log[I - a*x]","A",3,2,14,0.1429,1,"{5062, 77}"
50,1,37,0,0.0271134,"\int \frac{e^{-2 i \tan ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^((2*I)*ArcTan[a*x])*x^3),x]","-2 a^2 \log (x)+2 a^2 \log (-a x+i)+\frac{2 i a}{x}-\frac{1}{2 x^2}","-2 a^2 \log (x)+2 a^2 \log (-a x+i)+\frac{2 i a}{x}-\frac{1}{2 x^2}",1,"-1/(2*x^2) + ((2*I)*a)/x - 2*a^2*Log[x] + 2*a^2*Log[I - a*x]","A",3,2,14,0.1429,1,"{5062, 77}"
51,1,49,0,0.0317706,"\int \frac{e^{-2 i \tan ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^((2*I)*ArcTan[a*x])*x^4),x]","\frac{2 a^2}{x}+2 i a^3 \log (x)-2 i a^3 \log (-a x+i)+\frac{i a}{x^2}-\frac{1}{3 x^3}","\frac{2 a^2}{x}+2 i a^3 \log (x)-2 i a^3 \log (-a x+i)+\frac{i a}{x^2}-\frac{1}{3 x^3}",1,"-1/(3*x^3) + (I*a)/x^2 + (2*a^2)/x + (2*I)*a^3*Log[x] - (2*I)*a^3*Log[I - a*x]","A",3,2,14,0.1429,1,"{5062, 77}"
52,1,137,0,0.6243603,"\int e^{-3 i \tan ^{-1}(a x)} x^3 \, dx","Int[x^3/E^((3*I)*ArcTan[a*x]),x]","\frac{i x^3 \sqrt{a^2 x^2+1}}{4 a}-\frac{x^2 \sqrt{a^2 x^2+1}}{a^2}-\frac{9 i (3 a x+2 i) \sqrt{a^2 x^2+1}}{8 a^4}+\frac{27 \sqrt{a^2 x^2+1}}{4 a^4}+\frac{(1-i a x)^3}{a^4 \sqrt{a^2 x^2+1}}+\frac{51 i \sinh ^{-1}(a x)}{8 a^4}","\frac{i x^3 \sqrt{a^2 x^2+1}}{4 a}-\frac{x^2 \sqrt{a^2 x^2+1}}{a^2}-\frac{9 i (3 a x+2 i) \sqrt{a^2 x^2+1}}{8 a^4}+\frac{27 \sqrt{a^2 x^2+1}}{4 a^4}+\frac{(1-i a x)^3}{a^4 \sqrt{a^2 x^2+1}}+\frac{51 i \sinh ^{-1}(a x)}{8 a^4}",1,"(1 - I*a*x)^3/(a^4*Sqrt[1 + a^2*x^2]) + (27*Sqrt[1 + a^2*x^2])/(4*a^4) - (x^2*Sqrt[1 + a^2*x^2])/a^2 + ((I/4)*x^3*Sqrt[1 + a^2*x^2])/a - (((9*I)/8)*(2*I + 3*a*x)*Sqrt[1 + a^2*x^2])/a^4 + (((51*I)/8)*ArcSinh[a*x])/a^4","A",14,11,14,0.7857,1,"{5060, 1633, 1593, 12, 852, 1635, 1815, 27, 743, 641, 215}"
53,1,102,0,0.5743553,"\int e^{-3 i \tan ^{-1}(a x)} x^2 \, dx","Int[x^2/E^((3*I)*ArcTan[a*x]),x]","-\frac{i (1-i a x)^3}{a^3 \sqrt{a^2 x^2+1}}-\frac{i (3-i a x)^2 \sqrt{a^2 x^2+1}}{3 a^3}-\frac{(3 a x+28 i) \sqrt{a^2 x^2+1}}{6 a^3}+\frac{11 \sinh ^{-1}(a x)}{2 a^3}","-\frac{i (1-i a x)^3}{a^3 \sqrt{a^2 x^2+1}}-\frac{i (3-i a x)^2 \sqrt{a^2 x^2+1}}{3 a^3}-\frac{(3 a x+28 i) \sqrt{a^2 x^2+1}}{6 a^3}+\frac{11 \sinh ^{-1}(a x)}{2 a^3}",1,"((-I)*(1 - I*a*x)^3)/(a^3*Sqrt[1 + a^2*x^2]) - ((I/3)*(3 - I*a*x)^2*Sqrt[1 + a^2*x^2])/a^3 - ((28*I + 3*a*x)*Sqrt[1 + a^2*x^2])/(6*a^3) + (11*ArcSinh[a*x])/(2*a^3)","A",10,9,14,0.6429,1,"{5060, 1633, 1593, 12, 852, 1635, 1654, 780, 215}"
54,1,92,0,0.3236442,"\int e^{-3 i \tan ^{-1}(a x)} x \, dx","Int[x/E^((3*I)*ArcTan[a*x]),x]","-\frac{\left(a^2 x^2+1\right)^{5/2}}{a^2 (1+i a x)^3}-\frac{3 \left(a^2 x^2+1\right)^{3/2}}{2 a^2 (1+i a x)}-\frac{9 \sqrt{a^2 x^2+1}}{2 a^2}-\frac{9 i \sinh ^{-1}(a x)}{2 a^2}","-\frac{\left(a^2 x^2+1\right)^{5/2}}{a^2 (1+i a x)^3}-\frac{3 \left(a^2 x^2+1\right)^{3/2}}{2 a^2 (1+i a x)}-\frac{9 \sqrt{a^2 x^2+1}}{2 a^2}-\frac{9 i \sinh ^{-1}(a x)}{2 a^2}",1,"(-9*Sqrt[1 + a^2*x^2])/(2*a^2) - (3*(1 + a^2*x^2)^(3/2))/(2*a^2*(1 + I*a*x)) - (1 + a^2*x^2)^(5/2)/(a^2*(1 + I*a*x)^3) - (((9*I)/2)*ArcSinh[a*x])/a^2","A",9,7,12,0.5833,1,"{5060, 1633, 1593, 12, 793, 665, 215}"
55,1,60,0,0.0441652,"\int e^{-3 i \tan ^{-1}(a x)} \, dx","Int[E^((-3*I)*ArcTan[a*x]),x]","\frac{2 i (1-i a x)^2}{a \sqrt{a^2 x^2+1}}+\frac{3 i \sqrt{a^2 x^2+1}}{a}-\frac{3 \sinh ^{-1}(a x)}{a}","\frac{2 i (1-i a x)^2}{a \sqrt{a^2 x^2+1}}+\frac{3 i \sqrt{a^2 x^2+1}}{a}-\frac{3 \sinh ^{-1}(a x)}{a}",1,"((2*I)*(1 - I*a*x)^2)/(a*Sqrt[1 + a^2*x^2]) + ((3*I)*Sqrt[1 + a^2*x^2])/a - (3*ArcSinh[a*x])/a","A",5,5,10,0.5000,1,"{5059, 853, 669, 641, 215}"
56,1,52,0,0.5720479,"\int \frac{e^{-3 i \tan ^{-1}(a x)}}{x} \, dx","Int[1/(E^((3*I)*ArcTan[a*x])*x),x]","\frac{4 i \sqrt{a^2 x^2+1}}{-a x+i}-\tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)+i \sinh ^{-1}(a x)","\frac{4 i \sqrt{a^2 x^2+1}}{-a x+i}-\tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)+i \sinh ^{-1}(a x)",1,"((4*I)*Sqrt[1 + a^2*x^2])/(I - a*x) + I*ArcSinh[a*x] - ArcTanh[Sqrt[1 + a^2*x^2]]","A",8,7,14,0.5000,1,"{5060, 6742, 215, 266, 63, 208, 651}"
57,1,64,0,0.5521665,"\int \frac{e^{-3 i \tan ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^((3*I)*ArcTan[a*x])*x^2),x]","\frac{4 a \sqrt{a^2 x^2+1}}{-a x+i}-\frac{\sqrt{a^2 x^2+1}}{x}+3 i a \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","\frac{4 a \sqrt{a^2 x^2+1}}{-a x+i}-\frac{\sqrt{a^2 x^2+1}}{x}+3 i a \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-(Sqrt[1 + a^2*x^2]/x) + (4*a*Sqrt[1 + a^2*x^2])/(I - a*x) + (3*I)*a*ArcTanh[Sqrt[1 + a^2*x^2]]","A",8,7,14,0.5000,1,"{5060, 6742, 264, 266, 63, 208, 651}"
58,1,93,0,0.5931308,"\int \frac{e^{-3 i \tan ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^((3*I)*ArcTan[a*x])*x^3),x]","-\frac{4 i a^2 \sqrt{a^2 x^2+1}}{-a x+i}+\frac{3 i a \sqrt{a^2 x^2+1}}{x}-\frac{\sqrt{a^2 x^2+1}}{2 x^2}+\frac{9}{2} a^2 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","-\frac{4 i a^2 \sqrt{a^2 x^2+1}}{-a x+i}+\frac{3 i a \sqrt{a^2 x^2+1}}{x}-\frac{\sqrt{a^2 x^2+1}}{2 x^2}+\frac{9}{2} a^2 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-Sqrt[1 + a^2*x^2]/(2*x^2) + ((3*I)*a*Sqrt[1 + a^2*x^2])/x - ((4*I)*a^2*Sqrt[1 + a^2*x^2])/(I - a*x) + (9*a^2*ArcTanh[Sqrt[1 + a^2*x^2]])/2","A",12,8,14,0.5714,1,"{5060, 6742, 266, 51, 63, 208, 264, 651}"
59,1,118,0,0.6038941,"\int \frac{e^{-3 i \tan ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^((3*I)*ArcTan[a*x])*x^4),x]","-\frac{4 a^3 \sqrt{a^2 x^2+1}}{-a x+i}+\frac{14 a^2 \sqrt{a^2 x^2+1}}{3 x}+\frac{3 i a \sqrt{a^2 x^2+1}}{2 x^2}-\frac{\sqrt{a^2 x^2+1}}{3 x^3}-\frac{11}{2} i a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","-\frac{4 a^3 \sqrt{a^2 x^2+1}}{-a x+i}+\frac{14 a^2 \sqrt{a^2 x^2+1}}{3 x}+\frac{3 i a \sqrt{a^2 x^2+1}}{2 x^2}-\frac{\sqrt{a^2 x^2+1}}{3 x^3}-\frac{11}{2} i a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-Sqrt[1 + a^2*x^2]/(3*x^3) + (((3*I)/2)*a*Sqrt[1 + a^2*x^2])/x^2 + (14*a^2*Sqrt[1 + a^2*x^2])/(3*x) - (4*a^3*Sqrt[1 + a^2*x^2])/(I - a*x) - ((11*I)/2)*a^3*ArcTanh[Sqrt[1 + a^2*x^2]]","A",14,9,14,0.6429,1,"{5060, 6742, 271, 264, 266, 51, 63, 208, 651}"
60,1,139,0,0.6622253,"\int \frac{e^{-3 i \tan ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^((3*I)*ArcTan[a*x])*x^5),x]","\frac{4 i a^4 \sqrt{a^2 x^2+1}}{-a x+i}-\frac{6 i a^3 \sqrt{a^2 x^2+1}}{x}+\frac{19 a^2 \sqrt{a^2 x^2+1}}{8 x^2}+\frac{i a \sqrt{a^2 x^2+1}}{x^3}-\frac{\sqrt{a^2 x^2+1}}{4 x^4}-\frac{51}{8} a^4 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)","\frac{4 i a^4 \sqrt{a^2 x^2+1}}{-a x+i}-\frac{6 i a^3 \sqrt{a^2 x^2+1}}{x}+\frac{19 a^2 \sqrt{a^2 x^2+1}}{8 x^2}+\frac{i a \sqrt{a^2 x^2+1}}{x^3}-\frac{\sqrt{a^2 x^2+1}}{4 x^4}-\frac{51}{8} a^4 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)",1,"-Sqrt[1 + a^2*x^2]/(4*x^4) + (I*a*Sqrt[1 + a^2*x^2])/x^3 + (19*a^2*Sqrt[1 + a^2*x^2])/(8*x^2) - ((6*I)*a^3*Sqrt[1 + a^2*x^2])/x + ((4*I)*a^4*Sqrt[1 + a^2*x^2])/(I - a*x) - (51*a^4*ArcTanh[Sqrt[1 + a^2*x^2]])/8","A",19,9,14,0.6429,1,"{5060, 6742, 266, 51, 63, 208, 271, 264, 651}"
61,1,339,0,0.2276052,"\int e^{\frac{1}{2} i \tan ^{-1}(a x)} x^2 \, dx","Int[E^((I/2)*ArcTan[a*x])*x^2,x]","\frac{x (1-i a x)^{3/4} (1+i a x)^{5/4}}{3 a^2}-\frac{i (1-i a x)^{3/4} (1+i a x)^{5/4}}{12 a^3}-\frac{3 i (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{8 a^3}-\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}-\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}","\frac{x (1-i a x)^{3/4} (1+i a x)^{5/4}}{3 a^2}-\frac{i (1-i a x)^{3/4} (1+i a x)^{5/4}}{12 a^3}-\frac{3 i (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{8 a^3}-\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}-\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}",1,"(((-3*I)/8)*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/a^3 - ((I/12)*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(5/4))/a^3 + (x*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(5/4))/(3*a^2) + (((3*I)/8)*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) - (((3*I)/8)*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) - (((3*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) + (((3*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3)","A",15,12,16,0.7500,1,"{5062, 90, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
62,1,295,0,0.1786096,"\int e^{\frac{1}{2} i \tan ^{-1}(a x)} x \, dx","Int[E^((I/2)*ArcTan[a*x])*x,x]","\frac{(1-i a x)^{3/4} (1+i a x)^{5/4}}{2 a^2}+\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 a^2}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}+\frac{\tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}","\frac{(1-i a x)^{3/4} (1+i a x)^{5/4}}{2 a^2}+\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 a^2}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}+\frac{\tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}",1,"((1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(4*a^2) + ((1 - I*a*x)^(3/4)*(1 + I*a*x)^(5/4))/(2*a^2) - ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/(4*Sqrt[2]*a^2) + ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/(4*Sqrt[2]*a^2) + Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/(8*Sqrt[2]*a^2) - Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/(8*Sqrt[2]*a^2)","A",14,11,14,0.7857,1,"{5062, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
63,1,268,0,0.1469857,"\int e^{\frac{1}{2} i \tan ^{-1}(a x)} \, dx","Int[E^((I/2)*ArcTan[a*x]),x]","\frac{i (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{a}+\frac{i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}+\frac{i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}","\frac{i (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{a}+\frac{i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}+\frac{i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}",1,"(I*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/a - (I*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) + (I*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) + ((I/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) - ((I/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a)","A",13,10,12,0.8333,1,"{5061, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
64,1,267,0,0.1739589,"\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x} \, dx","Int[E^((I/2)*ArcTan[a*x])/x,x]","-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"-2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] - 2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2] + Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2]","A",17,14,16,0.8750,1,"{5062, 105, 63, 331, 297, 1162, 617, 204, 1165, 628, 93, 212, 206, 203}"
65,1,92,0,0.0338023,"\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x^2} \, dx","Int[E^((I/2)*ArcTan[a*x])/x^2,x]","-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{x}-i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{x}-i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"-(((1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x) - I*a*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - I*a*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",6,6,16,0.3750,1,"{5062, 94, 93, 212, 206, 203}"
66,1,132,0,0.0426426,"\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x^3} \, dx","Int[E^((I/2)*ArcTan[a*x])/x^3,x]","\frac{1}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{1}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{(1-i a x)^{3/4} (1+i a x)^{5/4}}{2 x^2}-\frac{i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 x}","\frac{1}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{1}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{(1-i a x)^{3/4} (1+i a x)^{5/4}}{2 x^2}-\frac{i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 x}",1,"((-I/4)*a*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x - ((1 - I*a*x)^(3/4)*(1 + I*a*x)^(5/4))/(2*x^2) + (a^2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4 + (a^2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4","A",7,7,16,0.4375,1,"{5062, 96, 94, 93, 212, 206, 203}"
67,1,170,0,0.0628448,"\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x^4} \, dx","Int[E^((I/2)*ArcTan[a*x])/x^4,x]","\frac{11 a^2 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{24 x}+\frac{3}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{3}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{5 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{12 x^2}-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{3 x^3}","\frac{11 a^2 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{24 x}+\frac{3}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{3}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{5 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{12 x^2}-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{3 x^3}",1,"-((1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(3*x^3) - (((5*I)/12)*a*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x^2 + (11*a^2*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(24*x) + ((3*I)/8)*a^3*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + ((3*I)/8)*a^3*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",9,8,16,0.5000,1,"{5062, 99, 151, 12, 93, 212, 206, 203}"
68,1,202,0,0.0790615,"\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x^5} \, dx","Int[E^((I/2)*ArcTan[a*x])/x^5,x]","\frac{29 a^2 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{96 x^2}+\frac{83 i a^3 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{192 x}-\frac{11}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{11}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{7 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{24 x^3}-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 x^4}","\frac{29 a^2 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{96 x^2}+\frac{83 i a^3 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{192 x}-\frac{11}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{11}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{7 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{24 x^3}-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 x^4}",1,"-((1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(4*x^4) - (((7*I)/24)*a*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x^3 + (29*a^2*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(96*x^2) + (((83*I)/192)*a^3*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x - (11*a^4*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64 - (11*a^4*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64","A",10,8,16,0.5000,1,"{5062, 99, 151, 12, 93, 212, 206, 203}"
69,1,240,0,0.1019767,"\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x^6} \, dx","Int[E^((I/2)*ArcTan[a*x])/x^6,x]","\frac{269 i a^3 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{960 x^2}+\frac{11 a^2 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{48 x^3}-\frac{611 a^4 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{1920 x}-\frac{31}{128} i a^5 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{31}{128} i a^5 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{9 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{40 x^4}-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{5 x^5}","\frac{269 i a^3 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{960 x^2}+\frac{11 a^2 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{48 x^3}-\frac{611 a^4 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{1920 x}-\frac{31}{128} i a^5 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{31}{128} i a^5 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{9 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{40 x^4}-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{5 x^5}",1,"-((1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(5*x^5) - (((9*I)/40)*a*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x^4 + (11*a^2*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(48*x^3) + (((269*I)/960)*a^3*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x^2 - (611*a^4*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(1920*x) - ((31*I)/128)*a^5*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - ((31*I)/128)*a^5*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",11,8,16,0.5000,1,"{5062, 99, 151, 12, 93, 212, 206, 203}"
70,1,337,0,0.2145258,"\int e^{\frac{3}{2} i \tan ^{-1}(a x)} x^3 \, dx","Int[E^(((3*I)/2)*ArcTan[a*x])*x^3,x]","\frac{x^2 \sqrt[4]{1-i a x} (1+i a x)^{7/4}}{4 a^2}-\frac{\sqrt[4]{1-i a x} (1+i a x)^{7/4} (11+4 i a x)}{32 a^4}-\frac{41 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{64 a^4}+\frac{123 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{123 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}+\frac{123 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}-\frac{123 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}","\frac{x^2 \sqrt[4]{1-i a x} (1+i a x)^{7/4}}{4 a^2}-\frac{\sqrt[4]{1-i a x} (1+i a x)^{7/4} (11+4 i a x)}{32 a^4}-\frac{41 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{64 a^4}+\frac{123 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{123 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}+\frac{123 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}-\frac{123 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}",1,"(-41*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(64*a^4) + (x^2*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(7/4))/(4*a^2) - ((1 - I*a*x)^(1/4)*(1 + I*a*x)^(7/4)*(11 + (4*I)*a*x))/(32*a^4) + (123*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(64*Sqrt[2]*a^4) - (123*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (123*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(128*Sqrt[2]*a^4) - (123*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(128*Sqrt[2]*a^4)","A",15,12,16,0.7500,1,"{5062, 100, 147, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
71,1,339,0,0.209741,"\int e^{\frac{3}{2} i \tan ^{-1}(a x)} x^2 \, dx","Int[E^(((3*I)/2)*ArcTan[a*x])*x^2,x]","\frac{x \sqrt[4]{1-i a x} (1+i a x)^{7/4}}{3 a^2}-\frac{i \sqrt[4]{1-i a x} (1+i a x)^{7/4}}{4 a^3}-\frac{17 i \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{24 a^3}+\frac{17 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}-\frac{17 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{17 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}-\frac{17 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}","\frac{x \sqrt[4]{1-i a x} (1+i a x)^{7/4}}{3 a^2}-\frac{i \sqrt[4]{1-i a x} (1+i a x)^{7/4}}{4 a^3}-\frac{17 i \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{24 a^3}+\frac{17 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}-\frac{17 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{17 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}-\frac{17 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}",1,"(((-17*I)/24)*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/a^3 - ((I/4)*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(7/4))/a^3 + (x*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(7/4))/(3*a^2) + (((17*I)/8)*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) - (((17*I)/8)*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) + (((17*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) - (((17*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3)","A",15,12,16,0.7500,1,"{5062, 90, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
72,1,295,0,0.1770456,"\int e^{\frac{3}{2} i \tan ^{-1}(a x)} x \, dx","Int[E^(((3*I)/2)*ArcTan[a*x])*x,x]","\frac{\sqrt[4]{1-i a x} (1+i a x)^{7/4}}{2 a^2}+\frac{3 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{4 a^2}-\frac{9 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{9 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}-\frac{9 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}+\frac{9 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}","\frac{\sqrt[4]{1-i a x} (1+i a x)^{7/4}}{2 a^2}+\frac{3 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{4 a^2}-\frac{9 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{9 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}-\frac{9 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}+\frac{9 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}",1,"(3*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(4*a^2) + ((1 - I*a*x)^(1/4)*(1 + I*a*x)^(7/4))/(2*a^2) - (9*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(4*Sqrt[2]*a^2) + (9*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(4*Sqrt[2]*a^2) - (9*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(8*Sqrt[2]*a^2) + (9*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(8*Sqrt[2]*a^2)","A",14,11,14,0.7857,1,"{5062, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
73,1,268,0,0.1426547,"\int e^{\frac{3}{2} i \tan ^{-1}(a x)} \, dx","Int[E^(((3*I)/2)*ArcTan[a*x]),x]","\frac{i \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{a}-\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}+\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}+\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}","\frac{i \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{a}-\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}+\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}+\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}",1,"(I*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/a - ((3*I)*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) + ((3*I)*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) - (((3*I)/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) + (((3*I)/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a)","A",13,10,12,0.8333,1,"{5061, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
74,1,267,0,0.1660977,"\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a x)}}{x} \, dx","Int[E^(((3*I)/2)*ArcTan[a*x])/x,x]","\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}+2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}+2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] - 2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2]","A",17,14,16,0.8750,1,"{5062, 105, 63, 240, 211, 1165, 628, 1162, 617, 204, 93, 298, 203, 206}"
75,1,92,0,0.0318131,"\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a x)}}{x^2} \, dx","Int[E^(((3*I)/2)*ArcTan[a*x])/x^2,x]","-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{x}+3 i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-3 i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{x}+3 i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-3 i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"-(((1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/x) + (3*I)*a*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - (3*I)*a*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",6,6,16,0.3750,1,"{5062, 94, 93, 298, 203, 206}"
76,1,132,0,0.0423317,"\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a x)}}{x^3} \, dx","Int[E^(((3*I)/2)*ArcTan[a*x])/x^3,x]","-\frac{9}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{9}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{\sqrt[4]{1-i a x} (1+i a x)^{7/4}}{2 x^2}-\frac{3 i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{4 x}","-\frac{9}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{9}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{\sqrt[4]{1-i a x} (1+i a x)^{7/4}}{2 x^2}-\frac{3 i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{4 x}",1,"(((-3*I)/4)*a*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/x - ((1 - I*a*x)^(1/4)*(1 + I*a*x)^(7/4))/(2*x^2) - (9*a^2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4 + (9*a^2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4","A",7,7,16,0.4375,1,"{5062, 96, 94, 93, 298, 203, 206}"
77,1,170,0,0.0632094,"\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a x)}}{x^4} \, dx","Int[E^(((3*I)/2)*ArcTan[a*x])/x^4,x]","\frac{23 a^2 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{24 x}-\frac{17}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{17}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{7 i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{12 x^2}-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{3 x^3}","\frac{23 a^2 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{24 x}-\frac{17}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{17}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{7 i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{12 x^2}-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{3 x^3}",1,"-((1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(3*x^3) - (((7*I)/12)*a*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/x^2 + (23*a^2*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(24*x) - ((17*I)/8)*a^3*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + ((17*I)/8)*a^3*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",9,8,16,0.5000,1,"{5062, 99, 151, 12, 93, 298, 203, 206}"
78,1,202,0,0.0805202,"\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a x)}}{x^5} \, dx","Int[E^(((3*I)/2)*ArcTan[a*x])/x^5,x]","\frac{15 a^2 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{32 x^2}+\frac{63 i a^3 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{64 x}+\frac{123}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{123}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{3 i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{8 x^3}-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{4 x^4}","\frac{15 a^2 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{32 x^2}+\frac{63 i a^3 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{64 x}+\frac{123}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{123}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{3 i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{8 x^3}-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{4 x^4}",1,"-((1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(4*x^4) - (((3*I)/8)*a*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/x^3 + (15*a^2*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(32*x^2) + (((63*I)/64)*a^3*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/x + (123*a^4*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64 - (123*a^4*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64","A",10,8,16,0.5000,1,"{5062, 99, 151, 12, 93, 298, 203, 206}"
79,1,373,0,0.255284,"\int e^{\frac{5}{2} i \tan ^{-1}(a x)} x^3 \, dx","Int[E^(((5*I)/2)*ArcTan[a*x])*x^3,x]","-\frac{17 x^2 (1-i a x)^{3/4} (1+i a x)^{5/4}}{4 a^2}-\frac{i (-452 a x+521 i) (1-i a x)^{3/4} (1+i a x)^{5/4}}{96 a^4}+\frac{475 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{64 a^4}+\frac{475 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{475 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{475 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}+\frac{475 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}-\frac{4 i x^3 (1+i a x)^{5/4}}{a \sqrt[4]{1-i a x}}","-\frac{17 x^2 (1-i a x)^{3/4} (1+i a x)^{5/4}}{4 a^2}-\frac{i (-452 a x+521 i) (1-i a x)^{3/4} (1+i a x)^{5/4}}{96 a^4}+\frac{475 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{64 a^4}+\frac{475 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{475 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{475 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}+\frac{475 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}-\frac{4 i x^3 (1+i a x)^{5/4}}{a \sqrt[4]{1-i a x}}",1,"(475*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(64*a^4) - ((4*I)*x^3*(1 + I*a*x)^(5/4))/(a*(1 - I*a*x)^(1/4)) - (17*x^2*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(5/4))/(4*a^2) - ((I/96)*(521*I - 452*a*x)*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(5/4))/a^4 - (475*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (475*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (475*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(128*Sqrt[2]*a^4) - (475*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(128*Sqrt[2]*a^4)","A",16,13,16,0.8125,1,"{5062, 97, 153, 147, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
80,1,371,0,0.2444224,"\int e^{\frac{5}{2} i \tan ^{-1}(a x)} x^2 \, dx","Int[E^(((5*I)/2)*ArcTan[a*x])*x^2,x]","\frac{i (1-i a x)^{3/4} (1+i a x)^{9/4}}{3 a^3}+\frac{2 i (1+i a x)^{9/4}}{a^3 \sqrt[4]{1-i a x}}+\frac{11 i (1-i a x)^{3/4} (1+i a x)^{5/4}}{4 a^3}+\frac{55 i (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{8 a^3}+\frac{55 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}-\frac{55 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}-\frac{55 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}+\frac{55 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}","\frac{i (1-i a x)^{3/4} (1+i a x)^{9/4}}{3 a^3}+\frac{2 i (1+i a x)^{9/4}}{a^3 \sqrt[4]{1-i a x}}+\frac{11 i (1-i a x)^{3/4} (1+i a x)^{5/4}}{4 a^3}+\frac{55 i (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{8 a^3}+\frac{55 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}-\frac{55 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}-\frac{55 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}+\frac{55 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}",1,"(((55*I)/8)*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/a^3 + (((11*I)/4)*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(5/4))/a^3 + ((2*I)*(1 + I*a*x)^(9/4))/(a^3*(1 - I*a*x)^(1/4)) + ((I/3)*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(9/4))/a^3 - (((55*I)/8)*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) + (((55*I)/8)*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) + (((55*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) - (((55*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3)","A",16,12,16,0.7500,1,"{5062, 89, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
81,1,324,0,0.2095907,"\int e^{\frac{5}{2} i \tan ^{-1}(a x)} x \, dx","Int[E^(((5*I)/2)*ArcTan[a*x])*x,x]","-\frac{2 (1+i a x)^{9/4}}{a^2 \sqrt[4]{1-i a x}}-\frac{5 (1-i a x)^{3/4} (1+i a x)^{5/4}}{2 a^2}-\frac{25 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 a^2}-\frac{25 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{25 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{25 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}-\frac{25 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}","-\frac{2 (1+i a x)^{9/4}}{a^2 \sqrt[4]{1-i a x}}-\frac{5 (1-i a x)^{3/4} (1+i a x)^{5/4}}{2 a^2}-\frac{25 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 a^2}-\frac{25 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{25 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{25 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}-\frac{25 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}",1,"(-25*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(4*a^2) - (5*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(5/4))/(2*a^2) - (2*(1 + I*a*x)^(9/4))/(a^2*(1 - I*a*x)^(1/4)) + (25*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(4*Sqrt[2]*a^2) - (25*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(4*Sqrt[2]*a^2) - (25*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(8*Sqrt[2]*a^2) + (25*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(8*Sqrt[2]*a^2)","A",15,11,14,0.7857,1,"{5062, 78, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
82,1,299,0,0.1782782,"\int e^{\frac{5}{2} i \tan ^{-1}(a x)} \, dx","Int[E^(((5*I)/2)*ArcTan[a*x]),x]","-\frac{4 i (1+i a x)^{5/4}}{a \sqrt[4]{1-i a x}}-\frac{5 i (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{a}-\frac{5 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}+\frac{5 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}+\frac{5 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}-\frac{5 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}","-\frac{4 i (1+i a x)^{5/4}}{a \sqrt[4]{1-i a x}}-\frac{5 i (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{a}-\frac{5 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}+\frac{5 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}+\frac{5 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}-\frac{5 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}",1,"((-5*I)*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/a - ((4*I)*(1 + I*a*x)^(5/4))/(a*(1 - I*a*x)^(1/4)) + ((5*I)*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) - ((5*I)*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) - (((5*I)/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) + (((5*I)/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a)","A",14,11,12,0.9167,1,"{5061, 47, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
83,1,293,0,0.218881,"\int \frac{e^{\frac{5}{2} i \tan ^{-1}(a x)}}{x} \, dx","Int[E^(((5*I)/2)*ArcTan[a*x])/x,x]","\frac{8 \sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","\frac{8 \sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"(8*(1 + I*a*x)^(1/4))/(1 - I*a*x)^(1/4) - 2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] - 2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2]","A",19,16,16,1.000,1,"{5062, 98, 21, 105, 63, 331, 297, 1162, 617, 204, 1165, 628, 93, 212, 206, 203}"
84,1,121,0,0.0381298,"\int \frac{e^{\frac{5}{2} i \tan ^{-1}(a x)}}{x^2} \, dx","Int[E^(((5*I)/2)*ArcTan[a*x])/x^2,x]","-\frac{(1+i a x)^{5/4}}{x \sqrt[4]{1-i a x}}+\frac{10 i a \sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}-5 i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-5 i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","-\frac{(1+i a x)^{5/4}}{x \sqrt[4]{1-i a x}}+\frac{10 i a \sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}-5 i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-5 i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"((10*I)*a*(1 + I*a*x)^(1/4))/(1 - I*a*x)^(1/4) - (1 + I*a*x)^(5/4)/(x*(1 - I*a*x)^(1/4)) - (5*I)*a*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - (5*I)*a*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",7,6,16,0.3750,1,"{5062, 94, 93, 212, 206, 203}"
85,1,163,0,0.0505436,"\int \frac{e^{\frac{5}{2} i \tan ^{-1}(a x)}}{x^3} \, dx","Int[E^(((5*I)/2)*ArcTan[a*x])/x^3,x]","-\frac{25 a^2 \sqrt[4]{1+i a x}}{2 \sqrt[4]{1-i a x}}+\frac{25}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{25}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{(1+i a x)^{9/4}}{2 x^2 \sqrt[4]{1-i a x}}-\frac{5 i a (1+i a x)^{5/4}}{4 x \sqrt[4]{1-i a x}}","-\frac{25 a^2 \sqrt[4]{1+i a x}}{2 \sqrt[4]{1-i a x}}+\frac{25}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{25}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{(1+i a x)^{9/4}}{2 x^2 \sqrt[4]{1-i a x}}-\frac{5 i a (1+i a x)^{5/4}}{4 x \sqrt[4]{1-i a x}}",1,"(-25*a^2*(1 + I*a*x)^(1/4))/(2*(1 - I*a*x)^(1/4)) - (((5*I)/4)*a*(1 + I*a*x)^(5/4))/(x*(1 - I*a*x)^(1/4)) - (1 + I*a*x)^(9/4)/(2*x^2*(1 - I*a*x)^(1/4)) + (25*a^2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4 + (25*a^2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4","A",8,7,16,0.4375,1,"{5062, 96, 94, 93, 212, 206, 203}"
86,1,203,0,0.0819834,"\int \frac{e^{\frac{5}{2} i \tan ^{-1}(a x)}}{x^4} \, dx","Int[E^(((5*I)/2)*ArcTan[a*x])/x^4,x]","-\frac{287 i a^3 \sqrt[4]{1+i a x}}{24 \sqrt[4]{1-i a x}}+\frac{61 a^2 \sqrt[4]{1+i a x}}{24 x \sqrt[4]{1-i a x}}+\frac{55}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{55}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{13 i a \sqrt[4]{1+i a x}}{12 x^2 \sqrt[4]{1-i a x}}-\frac{\sqrt[4]{1+i a x}}{3 x^3 \sqrt[4]{1-i a x}}","-\frac{287 i a^3 \sqrt[4]{1+i a x}}{24 \sqrt[4]{1-i a x}}+\frac{61 a^2 \sqrt[4]{1+i a x}}{24 x \sqrt[4]{1-i a x}}+\frac{55}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{55}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{13 i a \sqrt[4]{1+i a x}}{12 x^2 \sqrt[4]{1-i a x}}-\frac{\sqrt[4]{1+i a x}}{3 x^3 \sqrt[4]{1-i a x}}",1,"(((-287*I)/24)*a^3*(1 + I*a*x)^(1/4))/(1 - I*a*x)^(1/4) - (1 + I*a*x)^(1/4)/(3*x^3*(1 - I*a*x)^(1/4)) - (((13*I)/12)*a*(1 + I*a*x)^(1/4))/(x^2*(1 - I*a*x)^(1/4)) + (61*a^2*(1 + I*a*x)^(1/4))/(24*x*(1 - I*a*x)^(1/4)) + ((55*I)/8)*a^3*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + ((55*I)/8)*a^3*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",10,9,16,0.5625,1,"{5062, 98, 151, 155, 12, 93, 212, 206, 203}"
87,1,233,0,0.0996443,"\int \frac{e^{\frac{5}{2} i \tan ^{-1}(a x)}}{x^5} \, dx","Int[E^(((5*I)/2)*ArcTan[a*x])/x^5,x]","\frac{113 a^2 \sqrt[4]{1+i a x}}{96 x^2 \sqrt[4]{1-i a x}}+\frac{2467 a^4 \sqrt[4]{1+i a x}}{192 \sqrt[4]{1-i a x}}+\frac{521 i a^3 \sqrt[4]{1+i a x}}{192 x \sqrt[4]{1-i a x}}-\frac{475}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{475}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{17 i a \sqrt[4]{1+i a x}}{24 x^3 \sqrt[4]{1-i a x}}-\frac{\sqrt[4]{1+i a x}}{4 x^4 \sqrt[4]{1-i a x}}","\frac{113 a^2 \sqrt[4]{1+i a x}}{96 x^2 \sqrt[4]{1-i a x}}+\frac{2467 a^4 \sqrt[4]{1+i a x}}{192 \sqrt[4]{1-i a x}}+\frac{521 i a^3 \sqrt[4]{1+i a x}}{192 x \sqrt[4]{1-i a x}}-\frac{475}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{475}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{17 i a \sqrt[4]{1+i a x}}{24 x^3 \sqrt[4]{1-i a x}}-\frac{\sqrt[4]{1+i a x}}{4 x^4 \sqrt[4]{1-i a x}}",1,"(2467*a^4*(1 + I*a*x)^(1/4))/(192*(1 - I*a*x)^(1/4)) - (1 + I*a*x)^(1/4)/(4*x^4*(1 - I*a*x)^(1/4)) - (((17*I)/24)*a*(1 + I*a*x)^(1/4))/(x^3*(1 - I*a*x)^(1/4)) + (113*a^2*(1 + I*a*x)^(1/4))/(96*x^2*(1 - I*a*x)^(1/4)) + (((521*I)/192)*a^3*(1 + I*a*x)^(1/4))/(x*(1 - I*a*x)^(1/4)) - (475*a^4*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64 - (475*a^4*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64","A",11,9,16,0.5625,1,"{5062, 98, 151, 155, 12, 93, 212, 206, 203}"
88,1,337,0,0.2132593,"\int e^{-\frac{1}{2} i \tan ^{-1}(a x)} x^3 \, dx","Int[x^3/E^((I/2)*ArcTan[a*x]),x]","\frac{x^2 (1-i a x)^{5/4} (1+i a x)^{3/4}}{4 a^2}-\frac{(1-i a x)^{5/4} (1+i a x)^{3/4} (25-4 i a x)}{96 a^4}-\frac{11 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{64 a^4}-\frac{11 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}+\frac{11 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{11 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}+\frac{11 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}","\frac{x^2 (1-i a x)^{5/4} (1+i a x)^{3/4}}{4 a^2}-\frac{(1-i a x)^{5/4} (1+i a x)^{3/4} (25-4 i a x)}{96 a^4}-\frac{11 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{64 a^4}-\frac{11 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}+\frac{11 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{11 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}+\frac{11 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}",1,"(-11*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(64*a^4) + (x^2*(1 - I*a*x)^(5/4)*(1 + I*a*x)^(3/4))/(4*a^2) - ((1 - I*a*x)^(5/4)*(1 + I*a*x)^(3/4)*(25 - (4*I)*a*x))/(96*a^4) - (11*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (11*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(64*Sqrt[2]*a^4) - (11*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(128*Sqrt[2]*a^4) + (11*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(128*Sqrt[2]*a^4)","A",15,12,16,0.7500,1,"{5062, 100, 147, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
89,1,339,0,0.2157203,"\int e^{-\frac{1}{2} i \tan ^{-1}(a x)} x^2 \, dx","Int[x^2/E^((I/2)*ArcTan[a*x]),x]","\frac{x (1+i a x)^{3/4} (1-i a x)^{5/4}}{3 a^2}+\frac{i (1+i a x)^{3/4} (1-i a x)^{5/4}}{12 a^3}+\frac{3 i (1+i a x)^{3/4} \sqrt[4]{1-i a x}}{8 a^3}+\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}-\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}-\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}","\frac{x (1+i a x)^{3/4} (1-i a x)^{5/4}}{3 a^2}+\frac{i (1+i a x)^{3/4} (1-i a x)^{5/4}}{12 a^3}+\frac{3 i (1+i a x)^{3/4} \sqrt[4]{1-i a x}}{8 a^3}+\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}-\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}-\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}",1,"(((3*I)/8)*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/a^3 + ((I/12)*(1 - I*a*x)^(5/4)*(1 + I*a*x)^(3/4))/a^3 + (x*(1 - I*a*x)^(5/4)*(1 + I*a*x)^(3/4))/(3*a^2) + (((3*I)/8)*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) - (((3*I)/8)*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) + (((3*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) - (((3*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3)","A",15,12,16,0.7500,1,"{5062, 90, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
90,1,295,0,0.172965,"\int e^{-\frac{1}{2} i \tan ^{-1}(a x)} x \, dx","Int[x/E^((I/2)*ArcTan[a*x]),x]","\frac{(1+i a x)^{3/4} (1-i a x)^{5/4}}{2 a^2}+\frac{(1+i a x)^{3/4} \sqrt[4]{1-i a x}}{4 a^2}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}-\frac{\tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}","\frac{(1+i a x)^{3/4} (1-i a x)^{5/4}}{2 a^2}+\frac{(1+i a x)^{3/4} \sqrt[4]{1-i a x}}{4 a^2}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}-\frac{\tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}",1,"((1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(4*a^2) + ((1 - I*a*x)^(5/4)*(1 + I*a*x)^(3/4))/(2*a^2) + ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/(4*Sqrt[2]*a^2) - ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/(4*Sqrt[2]*a^2) + Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/(8*Sqrt[2]*a^2) - Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/(8*Sqrt[2]*a^2)","A",14,11,14,0.7857,1,"{5062, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
91,1,268,0,0.1463622,"\int e^{-\frac{1}{2} i \tan ^{-1}(a x)} \, dx","Int[E^((-I/2)*ArcTan[a*x]),x]","-\frac{i \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{a}-\frac{i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}+\frac{i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}+\frac{i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}","-\frac{i \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{a}-\frac{i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}+\frac{i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}+\frac{i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}",1,"((-I)*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/a - (I*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) + (I*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) - ((I/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) + ((I/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a)","A",13,10,12,0.8333,1,"{5061, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
92,1,267,0,0.1609569,"\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a x)}}{x} \, dx","Int[1/(E^((I/2)*ArcTan[a*x])*x),x]","-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}+2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}+2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] - 2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2] + Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2]","A",17,14,16,0.8750,1,"{5062, 105, 63, 240, 211, 1165, 628, 1162, 617, 204, 93, 298, 203, 206}"
93,1,92,0,0.0351591,"\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^((I/2)*ArcTan[a*x])*x^2),x]","-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{x}-i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{x}-i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"-(((1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/x) - I*a*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + I*a*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",6,6,16,0.3750,1,"{5062, 94, 93, 298, 203, 206}"
94,1,132,0,0.0431289,"\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^((I/2)*ArcTan[a*x])*x^3),x]","-\frac{1}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{1}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{(1-i a x)^{5/4} (1+i a x)^{3/4}}{2 x^2}+\frac{i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{4 x}","-\frac{1}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{1}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{(1-i a x)^{5/4} (1+i a x)^{3/4}}{2 x^2}+\frac{i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{4 x}",1,"((I/4)*a*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/x - ((1 - I*a*x)^(5/4)*(1 + I*a*x)^(3/4))/(2*x^2) - (a^2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4 + (a^2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4","A",7,7,16,0.4375,1,"{5062, 96, 94, 93, 298, 203, 206}"
95,1,170,0,0.0690398,"\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^((I/2)*ArcTan[a*x])*x^4),x]","\frac{11 a^2 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{24 x}+\frac{3}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{3}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{5 i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{12 x^2}-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{3 x^3}","\frac{11 a^2 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{24 x}+\frac{3}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{3}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{5 i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{12 x^2}-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{3 x^3}",1,"-((1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(3*x^3) + (((5*I)/12)*a*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/x^2 + (11*a^2*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(24*x) + ((3*I)/8)*a^3*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - ((3*I)/8)*a^3*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",9,8,16,0.5000,1,"{5062, 99, 151, 12, 93, 298, 203, 206}"
96,1,202,0,0.0807455,"\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^((I/2)*ArcTan[a*x])*x^5),x]","\frac{29 a^2 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{96 x^2}-\frac{83 i a^3 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{192 x}+\frac{11}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{11}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{7 i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{24 x^3}-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{4 x^4}","\frac{29 a^2 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{96 x^2}-\frac{83 i a^3 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{192 x}+\frac{11}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{11}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{7 i a \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{24 x^3}-\frac{\sqrt[4]{1-i a x} (1+i a x)^{3/4}}{4 x^4}",1,"-((1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(4*x^4) + (((7*I)/24)*a*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/x^3 + (29*a^2*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(96*x^2) - (((83*I)/192)*a^3*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/x + (11*a^4*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64 - (11*a^4*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64","A",10,8,16,0.5000,1,"{5062, 99, 151, 12, 93, 298, 203, 206}"
97,1,337,0,0.2169796,"\int e^{-\frac{3}{2} i \tan ^{-1}(a x)} x^3 \, dx","Int[x^3/E^(((3*I)/2)*ArcTan[a*x]),x]","\frac{x^2 (1-i a x)^{7/4} \sqrt[4]{1+i a x}}{4 a^2}-\frac{(1-i a x)^{7/4} \sqrt[4]{1+i a x} (11-4 i a x)}{32 a^4}-\frac{41 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{64 a^4}+\frac{123 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{123 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{123 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}+\frac{123 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}","\frac{x^2 (1-i a x)^{7/4} \sqrt[4]{1+i a x}}{4 a^2}-\frac{(1-i a x)^{7/4} \sqrt[4]{1+i a x} (11-4 i a x)}{32 a^4}-\frac{41 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{64 a^4}+\frac{123 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{123 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{123 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}+\frac{123 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}",1,"(-41*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(64*a^4) + (x^2*(1 - I*a*x)^(7/4)*(1 + I*a*x)^(1/4))/(4*a^2) - ((1 - I*a*x)^(7/4)*(1 + I*a*x)^(1/4)*(11 - (4*I)*a*x))/(32*a^4) - (123*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (123*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (123*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(128*Sqrt[2]*a^4) - (123*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(128*Sqrt[2]*a^4)","A",15,12,16,0.7500,1,"{5062, 100, 147, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
98,1,339,0,0.2193175,"\int e^{-\frac{3}{2} i \tan ^{-1}(a x)} x^2 \, dx","Int[x^2/E^(((3*I)/2)*ArcTan[a*x]),x]","\frac{x \sqrt[4]{1+i a x} (1-i a x)^{7/4}}{3 a^2}+\frac{i \sqrt[4]{1+i a x} (1-i a x)^{7/4}}{4 a^3}+\frac{17 i \sqrt[4]{1+i a x} (1-i a x)^{3/4}}{24 a^3}-\frac{17 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{17 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{17 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}-\frac{17 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}","\frac{x \sqrt[4]{1+i a x} (1-i a x)^{7/4}}{3 a^2}+\frac{i \sqrt[4]{1+i a x} (1-i a x)^{7/4}}{4 a^3}+\frac{17 i \sqrt[4]{1+i a x} (1-i a x)^{3/4}}{24 a^3}-\frac{17 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{17 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{17 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}-\frac{17 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}",1,"(((17*I)/24)*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/a^3 + ((I/4)*(1 - I*a*x)^(7/4)*(1 + I*a*x)^(1/4))/a^3 + (x*(1 - I*a*x)^(7/4)*(1 + I*a*x)^(1/4))/(3*a^2) + (((17*I)/8)*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) - (((17*I)/8)*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) - (((17*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) + (((17*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3)","A",15,12,16,0.7500,1,"{5062, 90, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
99,1,295,0,0.1775151,"\int e^{-\frac{3}{2} i \tan ^{-1}(a x)} x \, dx","Int[x/E^(((3*I)/2)*ArcTan[a*x]),x]","\frac{\sqrt[4]{1+i a x} (1-i a x)^{7/4}}{2 a^2}+\frac{3 \sqrt[4]{1+i a x} (1-i a x)^{3/4}}{4 a^2}-\frac{9 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{9 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{9 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}-\frac{9 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}","\frac{\sqrt[4]{1+i a x} (1-i a x)^{7/4}}{2 a^2}+\frac{3 \sqrt[4]{1+i a x} (1-i a x)^{3/4}}{4 a^2}-\frac{9 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{9 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{9 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}-\frac{9 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}",1,"(3*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(4*a^2) + ((1 - I*a*x)^(7/4)*(1 + I*a*x)^(1/4))/(2*a^2) + (9*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(4*Sqrt[2]*a^2) - (9*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(4*Sqrt[2]*a^2) - (9*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(8*Sqrt[2]*a^2) + (9*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(8*Sqrt[2]*a^2)","A",14,11,14,0.7857,1,"{5062, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
100,1,268,0,0.1504133,"\int e^{-\frac{3}{2} i \tan ^{-1}(a x)} \, dx","Int[E^(((-3*I)/2)*ArcTan[a*x]),x]","-\frac{i (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{a}+\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}+\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}","-\frac{i (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{a}+\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{3 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}+\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}",1,"((-I)*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/a - ((3*I)*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) + ((3*I)*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) + (((3*I)/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) - (((3*I)/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a)","A",13,10,12,0.8333,1,"{5061, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
101,1,267,0,0.1680999,"\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a x)}}{x} \, dx","Int[1/(E^(((3*I)/2)*ArcTan[a*x])*x),x]","\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"-2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] - 2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2]","A",17,14,16,0.8750,1,"{5062, 105, 63, 331, 297, 1162, 617, 204, 1165, 628, 93, 212, 206, 203}"
102,1,92,0,0.0317273,"\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^(((3*I)/2)*ArcTan[a*x])*x^2),x]","-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{x}+3 i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+3 i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{x}+3 i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+3 i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"-(((1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x) + (3*I)*a*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + (3*I)*a*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",6,6,16,0.3750,1,"{5062, 94, 93, 212, 206, 203}"
103,1,132,0,0.0425153,"\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^(((3*I)/2)*ArcTan[a*x])*x^3),x]","\frac{9}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{9}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{(1-i a x)^{7/4} \sqrt[4]{1+i a x}}{2 x^2}+\frac{3 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 x}","\frac{9}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{9}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{(1-i a x)^{7/4} \sqrt[4]{1+i a x}}{2 x^2}+\frac{3 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 x}",1,"(((3*I)/4)*a*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x - ((1 - I*a*x)^(7/4)*(1 + I*a*x)^(1/4))/(2*x^2) + (9*a^2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4 + (9*a^2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4","A",7,7,16,0.4375,1,"{5062, 96, 94, 93, 212, 206, 203}"
104,1,170,0,0.0645408,"\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^(((3*I)/2)*ArcTan[a*x])*x^4),x]","\frac{23 a^2 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{24 x}-\frac{17}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{17}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{7 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{12 x^2}-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{3 x^3}","\frac{23 a^2 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{24 x}-\frac{17}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{17}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{7 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{12 x^2}-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{3 x^3}",1,"-((1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(3*x^3) + (((7*I)/12)*a*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x^2 + (23*a^2*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(24*x) - ((17*I)/8)*a^3*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - ((17*I)/8)*a^3*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",9,8,16,0.5000,1,"{5062, 99, 151, 12, 93, 212, 206, 203}"
105,1,202,0,0.0812171,"\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^(((3*I)/2)*ArcTan[a*x])*x^5),x]","\frac{15 a^2 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{32 x^2}-\frac{63 i a^3 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{64 x}-\frac{123}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{123}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{3 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{8 x^3}-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 x^4}","\frac{15 a^2 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{32 x^2}-\frac{63 i a^3 (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{64 x}-\frac{123}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{123}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{3 i a (1-i a x)^{3/4} \sqrt[4]{1+i a x}}{8 x^3}-\frac{(1-i a x)^{3/4} \sqrt[4]{1+i a x}}{4 x^4}",1,"-((1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(4*x^4) + (((3*I)/8)*a*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x^3 + (15*a^2*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/(32*x^2) - (((63*I)/64)*a^3*(1 - I*a*x)^(3/4)*(1 + I*a*x)^(1/4))/x - (123*a^4*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64 - (123*a^4*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64","A",10,8,16,0.5000,1,"{5062, 99, 151, 12, 93, 212, 206, 203}"
106,1,373,0,0.2544624,"\int e^{-\frac{5}{2} i \tan ^{-1}(a x)} x^3 \, dx","Int[x^3/E^(((5*I)/2)*ArcTan[a*x]),x]","-\frac{17 x^2 (1-i a x)^{5/4} (1+i a x)^{3/4}}{4 a^2}-\frac{i (1-i a x)^{5/4} (1+i a x)^{3/4} (452 a x+521 i)}{96 a^4}+\frac{475 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{64 a^4}+\frac{475 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{475 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}+\frac{475 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}-\frac{475 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}+\frac{4 i x^3 (1-i a x)^{5/4}}{a \sqrt[4]{1+i a x}}","-\frac{17 x^2 (1-i a x)^{5/4} (1+i a x)^{3/4}}{4 a^2}-\frac{i (1-i a x)^{5/4} (1+i a x)^{3/4} (452 a x+521 i)}{96 a^4}+\frac{475 \sqrt[4]{1-i a x} (1+i a x)^{3/4}}{64 a^4}+\frac{475 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}-\frac{475 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{128 \sqrt{2} a^4}+\frac{475 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}-\frac{475 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{64 \sqrt{2} a^4}+\frac{4 i x^3 (1-i a x)^{5/4}}{a \sqrt[4]{1+i a x}}",1,"((4*I)*x^3*(1 - I*a*x)^(5/4))/(a*(1 + I*a*x)^(1/4)) + (475*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(64*a^4) - (17*x^2*(1 - I*a*x)^(5/4)*(1 + I*a*x)^(3/4))/(4*a^2) - ((I/96)*(1 - I*a*x)^(5/4)*(1 + I*a*x)^(3/4)*(521*I + 452*a*x))/a^4 + (475*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(64*Sqrt[2]*a^4) - (475*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (475*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(128*Sqrt[2]*a^4) - (475*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(128*Sqrt[2]*a^4)","A",16,13,16,0.8125,1,"{5062, 97, 153, 147, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
107,1,371,0,0.2411324,"\int e^{-\frac{5}{2} i \tan ^{-1}(a x)} x^2 \, dx","Int[x^2/E^(((5*I)/2)*ArcTan[a*x]),x]","-\frac{i (1+i a x)^{3/4} (1-i a x)^{9/4}}{3 a^3}-\frac{2 i (1-i a x)^{9/4}}{a^3 \sqrt[4]{1+i a x}}-\frac{11 i (1+i a x)^{3/4} (1-i a x)^{5/4}}{4 a^3}-\frac{55 i (1+i a x)^{3/4} \sqrt[4]{1-i a x}}{8 a^3}-\frac{55 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{55 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}-\frac{55 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}+\frac{55 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}","-\frac{i (1+i a x)^{3/4} (1-i a x)^{9/4}}{3 a^3}-\frac{2 i (1-i a x)^{9/4}}{a^3 \sqrt[4]{1+i a x}}-\frac{11 i (1+i a x)^{3/4} (1-i a x)^{5/4}}{4 a^3}-\frac{55 i (1+i a x)^{3/4} \sqrt[4]{1-i a x}}{8 a^3}-\frac{55 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}+\frac{55 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{16 \sqrt{2} a^3}-\frac{55 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}+\frac{55 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{8 \sqrt{2} a^3}",1,"((-2*I)*(1 - I*a*x)^(9/4))/(a^3*(1 + I*a*x)^(1/4)) - (((55*I)/8)*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/a^3 - (((11*I)/4)*(1 - I*a*x)^(5/4)*(1 + I*a*x)^(3/4))/a^3 - ((I/3)*(1 - I*a*x)^(9/4)*(1 + I*a*x)^(3/4))/a^3 - (((55*I)/8)*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) + (((55*I)/8)*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) - (((55*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3) + (((55*I)/16)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a^3)","A",16,12,16,0.7500,1,"{5062, 89, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
108,1,324,0,0.2059367,"\int e^{-\frac{5}{2} i \tan ^{-1}(a x)} x \, dx","Int[x/E^(((5*I)/2)*ArcTan[a*x]),x]","-\frac{2 (1-i a x)^{9/4}}{a^2 \sqrt[4]{1+i a x}}-\frac{5 (1+i a x)^{3/4} (1-i a x)^{5/4}}{2 a^2}-\frac{25 (1+i a x)^{3/4} \sqrt[4]{1-i a x}}{4 a^2}-\frac{25 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{25 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}-\frac{25 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}+\frac{25 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}","-\frac{2 (1-i a x)^{9/4}}{a^2 \sqrt[4]{1+i a x}}-\frac{5 (1+i a x)^{3/4} (1-i a x)^{5/4}}{2 a^2}-\frac{25 (1+i a x)^{3/4} \sqrt[4]{1-i a x}}{4 a^2}-\frac{25 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}+\frac{25 \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{8 \sqrt{2} a^2}-\frac{25 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}+\frac{25 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{4 \sqrt{2} a^2}",1,"(-2*(1 - I*a*x)^(9/4))/(a^2*(1 + I*a*x)^(1/4)) - (25*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/(4*a^2) - (5*(1 - I*a*x)^(5/4)*(1 + I*a*x)^(3/4))/(2*a^2) - (25*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(4*Sqrt[2]*a^2) + (25*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(4*Sqrt[2]*a^2) - (25*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(8*Sqrt[2]*a^2) + (25*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(8*Sqrt[2]*a^2)","A",15,11,14,0.7857,1,"{5062, 78, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
109,1,299,0,0.1717215,"\int e^{-\frac{5}{2} i \tan ^{-1}(a x)} \, dx","Int[E^(((-5*I)/2)*ArcTan[a*x]),x]","\frac{4 i (1-i a x)^{5/4}}{a \sqrt[4]{1+i a x}}+\frac{5 i (1+i a x)^{3/4} \sqrt[4]{1-i a x}}{a}+\frac{5 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{5 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}+\frac{5 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}-\frac{5 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}","\frac{4 i (1-i a x)^{5/4}}{a \sqrt[4]{1+i a x}}+\frac{5 i (1+i a x)^{3/4} \sqrt[4]{1-i a x}}{a}+\frac{5 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}-\frac{5 i \log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{2 \sqrt{2} a}+\frac{5 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}-\frac{5 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)}{\sqrt{2} a}",1,"((4*I)*(1 - I*a*x)^(5/4))/(a*(1 + I*a*x)^(1/4)) + ((5*I)*(1 - I*a*x)^(1/4)*(1 + I*a*x)^(3/4))/a + ((5*I)*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) - ((5*I)*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) + (((5*I)/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a) - (((5*I)/2)*Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)])/(Sqrt[2]*a)","A",14,11,12,0.9167,1,"{5061, 47, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
110,1,293,0,0.2185364,"\int \frac{e^{-\frac{5}{2} i \tan ^{-1}(a x)}}{x} \, dx","Int[1/(E^(((5*I)/2)*ArcTan[a*x])*x),x]","\frac{8 \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}+2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","\frac{8 \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-i a x}}{\sqrt{1+i a x}}+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+1\right)}{\sqrt{2}}+2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"(8*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4) + 2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)] - 2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] - (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - I*a*x]/Sqrt[1 + I*a*x] + (Sqrt[2]*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4)]/Sqrt[2]","A",19,16,16,1.000,1,"{5062, 98, 21, 105, 63, 240, 211, 1165, 628, 1162, 617, 204, 93, 298, 203, 206}"
111,1,121,0,0.0392875,"\int \frac{e^{-\frac{5}{2} i \tan ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^(((5*I)/2)*ArcTan[a*x])*x^2),x]","-\frac{(1-i a x)^{5/4}}{x \sqrt[4]{1+i a x}}-\frac{10 i a \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-5 i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+5 i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)","-\frac{(1-i a x)^{5/4}}{x \sqrt[4]{1+i a x}}-\frac{10 i a \sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-5 i a \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+5 i a \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)",1,"((-10*I)*a*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4) - (1 - I*a*x)^(5/4)/(x*(1 + I*a*x)^(1/4)) - (5*I)*a*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] + (5*I)*a*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",7,6,16,0.3750,1,"{5062, 94, 93, 298, 203, 206}"
112,1,163,0,0.0504077,"\int \frac{e^{-\frac{5}{2} i \tan ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^(((5*I)/2)*ArcTan[a*x])*x^3),x]","-\frac{25 a^2 \sqrt[4]{1-i a x}}{2 \sqrt[4]{1+i a x}}-\frac{25}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{25}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{(1-i a x)^{9/4}}{2 x^2 \sqrt[4]{1+i a x}}+\frac{5 i a (1-i a x)^{5/4}}{4 x \sqrt[4]{1+i a x}}","-\frac{25 a^2 \sqrt[4]{1-i a x}}{2 \sqrt[4]{1+i a x}}-\frac{25}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{25}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{(1-i a x)^{9/4}}{2 x^2 \sqrt[4]{1+i a x}}+\frac{5 i a (1-i a x)^{5/4}}{4 x \sqrt[4]{1+i a x}}",1,"(-25*a^2*(1 - I*a*x)^(1/4))/(2*(1 + I*a*x)^(1/4)) + (((5*I)/4)*a*(1 - I*a*x)^(5/4))/(x*(1 + I*a*x)^(1/4)) - (1 - I*a*x)^(9/4)/(2*x^2*(1 + I*a*x)^(1/4)) - (25*a^2*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4 + (25*a^2*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/4","A",8,7,16,0.4375,1,"{5062, 96, 94, 93, 298, 203, 206}"
113,1,203,0,0.0789914,"\int \frac{e^{-\frac{5}{2} i \tan ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^(((5*I)/2)*ArcTan[a*x])*x^4),x]","\frac{287 i a^3 \sqrt[4]{1-i a x}}{24 \sqrt[4]{1+i a x}}+\frac{61 a^2 \sqrt[4]{1-i a x}}{24 x \sqrt[4]{1+i a x}}+\frac{55}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{55}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{13 i a \sqrt[4]{1-i a x}}{12 x^2 \sqrt[4]{1+i a x}}-\frac{\sqrt[4]{1-i a x}}{3 x^3 \sqrt[4]{1+i a x}}","\frac{287 i a^3 \sqrt[4]{1-i a x}}{24 \sqrt[4]{1+i a x}}+\frac{61 a^2 \sqrt[4]{1-i a x}}{24 x \sqrt[4]{1+i a x}}+\frac{55}{8} i a^3 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{55}{8} i a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{13 i a \sqrt[4]{1-i a x}}{12 x^2 \sqrt[4]{1+i a x}}-\frac{\sqrt[4]{1-i a x}}{3 x^3 \sqrt[4]{1+i a x}}",1,"(((287*I)/24)*a^3*(1 - I*a*x)^(1/4))/(1 + I*a*x)^(1/4) - (1 - I*a*x)^(1/4)/(3*x^3*(1 + I*a*x)^(1/4)) + (((13*I)/12)*a*(1 - I*a*x)^(1/4))/(x^2*(1 + I*a*x)^(1/4)) + (61*a^2*(1 - I*a*x)^(1/4))/(24*x*(1 + I*a*x)^(1/4)) + ((55*I)/8)*a^3*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)] - ((55*I)/8)*a^3*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]","A",10,9,16,0.5625,1,"{5062, 98, 151, 155, 12, 93, 298, 203, 206}"
114,1,233,0,0.0989286,"\int \frac{e^{-\frac{5}{2} i \tan ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^(((5*I)/2)*ArcTan[a*x])*x^5),x]","\frac{113 a^2 \sqrt[4]{1-i a x}}{96 x^2 \sqrt[4]{1+i a x}}+\frac{2467 a^4 \sqrt[4]{1-i a x}}{192 \sqrt[4]{1+i a x}}-\frac{521 i a^3 \sqrt[4]{1-i a x}}{192 x \sqrt[4]{1+i a x}}+\frac{475}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{475}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{17 i a \sqrt[4]{1-i a x}}{24 x^3 \sqrt[4]{1+i a x}}-\frac{\sqrt[4]{1-i a x}}{4 x^4 \sqrt[4]{1+i a x}}","\frac{113 a^2 \sqrt[4]{1-i a x}}{96 x^2 \sqrt[4]{1+i a x}}+\frac{2467 a^4 \sqrt[4]{1-i a x}}{192 \sqrt[4]{1+i a x}}-\frac{521 i a^3 \sqrt[4]{1-i a x}}{192 x \sqrt[4]{1+i a x}}+\frac{475}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)-\frac{475}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}\right)+\frac{17 i a \sqrt[4]{1-i a x}}{24 x^3 \sqrt[4]{1+i a x}}-\frac{\sqrt[4]{1-i a x}}{4 x^4 \sqrt[4]{1+i a x}}",1,"(2467*a^4*(1 - I*a*x)^(1/4))/(192*(1 + I*a*x)^(1/4)) - (1 - I*a*x)^(1/4)/(4*x^4*(1 + I*a*x)^(1/4)) + (((17*I)/24)*a*(1 - I*a*x)^(1/4))/(x^3*(1 + I*a*x)^(1/4)) + (113*a^2*(1 - I*a*x)^(1/4))/(96*x^2*(1 + I*a*x)^(1/4)) - (((521*I)/192)*a^3*(1 - I*a*x)^(1/4))/(x*(1 + I*a*x)^(1/4)) + (475*a^4*ArcTan[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64 - (475*a^4*ArcTanh[(1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/64","A",11,9,16,0.5625,1,"{5062, 98, 151, 155, 12, 93, 298, 203, 206}"
115,1,319,0,0.3841283,"\int e^{\frac{1}{3} i \tan ^{-1}(x)} x^2 \, dx","Int[E^((I/3)*ArcTan[x])*x^2,x]","\frac{1}{3} (1-i x)^{5/6} x (1+i x)^{7/6}-\frac{1}{18} i (1-i x)^{5/6} (1+i x)^{7/6}-\frac{19}{54} i (1-i x)^{5/6} \sqrt[6]{1+i x}-\frac{19 i \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}-\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{108 \sqrt{3}}+\frac{19 i \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}+\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{108 \sqrt{3}}+\frac{19}{162} i \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)-\frac{19}{162} i \tan ^{-1}\left(\sqrt{3}+\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)-\frac{19}{81} i \tan ^{-1}\left(\frac{\sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)","\frac{1}{3} (1-i x)^{5/6} x (1+i x)^{7/6}-\frac{1}{18} i (1-i x)^{5/6} (1+i x)^{7/6}-\frac{19}{54} i (1-i x)^{5/6} \sqrt[6]{1+i x}-\frac{19 i \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}-\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{108 \sqrt{3}}+\frac{19 i \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}+\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{108 \sqrt{3}}+\frac{19}{162} i \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)-\frac{19}{162} i \tan ^{-1}\left(\sqrt{3}+\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)-\frac{19}{81} i \tan ^{-1}\left(\frac{\sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)",1,"((-19*I)/54)*(1 - I*x)^(5/6)*(1 + I*x)^(1/6) - (I/18)*(1 - I*x)^(5/6)*(1 + I*x)^(7/6) + ((1 - I*x)^(5/6)*(1 + I*x)^(7/6)*x)/3 + ((19*I)/162)*ArcTan[Sqrt[3] - (2*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)] - ((19*I)/162)*ArcTan[Sqrt[3] + (2*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)] - ((19*I)/81)*ArcTan[(1 - I*x)^(1/6)/(1 + I*x)^(1/6)] - (((19*I)/108)*Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3) - (Sqrt[3]*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)])/Sqrt[3] + (((19*I)/108)*Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3) + (Sqrt[3]*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)])/Sqrt[3]","A",16,12,14,0.8571,1,"{5062, 90, 80, 50, 63, 331, 295, 634, 618, 204, 628, 203}"
116,1,278,0,0.338368,"\int e^{\frac{1}{3} i \tan ^{-1}(x)} x \, dx","Int[E^((I/3)*ArcTan[x])*x,x]","\frac{1}{2} (1-i x)^{5/6} (1+i x)^{7/6}+\frac{1}{6} (1-i x)^{5/6} \sqrt[6]{1+i x}+\frac{\log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}-\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{12 \sqrt{3}}-\frac{\log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}+\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{12 \sqrt{3}}-\frac{1}{18} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)+\frac{1}{18} \tan ^{-1}\left(\sqrt{3}+\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)+\frac{1}{9} \tan ^{-1}\left(\frac{\sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)","\frac{1}{2} (1-i x)^{5/6} (1+i x)^{7/6}+\frac{1}{6} (1-i x)^{5/6} \sqrt[6]{1+i x}+\frac{\log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}-\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{12 \sqrt{3}}-\frac{\log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}+\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{12 \sqrt{3}}-\frac{1}{18} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)+\frac{1}{18} \tan ^{-1}\left(\sqrt{3}+\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)+\frac{1}{9} \tan ^{-1}\left(\frac{\sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)",1,"((1 - I*x)^(5/6)*(1 + I*x)^(1/6))/6 + ((1 - I*x)^(5/6)*(1 + I*x)^(7/6))/2 - ArcTan[Sqrt[3] - (2*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)]/18 + ArcTan[Sqrt[3] + (2*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)]/18 + ArcTan[(1 - I*x)^(1/6)/(1 + I*x)^(1/6)]/9 + Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3) - (Sqrt[3]*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)]/(12*Sqrt[3]) - Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3) + (Sqrt[3]*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)]/(12*Sqrt[3])","A",15,11,12,0.9167,1,"{5062, 80, 50, 63, 331, 295, 634, 618, 204, 628, 203}"
117,1,262,0,0.310024,"\int e^{\frac{1}{3} i \tan ^{-1}(x)} \, dx","Int[E^((I/3)*ArcTan[x]),x]","i (1-i x)^{5/6} \sqrt[6]{1+i x}+\frac{i \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}-\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{2 \sqrt{3}}-\frac{i \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}+\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{2 \sqrt{3}}-\frac{1}{3} i \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)+\frac{1}{3} i \tan ^{-1}\left(\sqrt{3}+\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)+\frac{2}{3} i \tan ^{-1}\left(\frac{\sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)","i (1-i x)^{5/6} \sqrt[6]{1+i x}+\frac{i \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}-\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{2 \sqrt{3}}-\frac{i \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}+\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)}{2 \sqrt{3}}-\frac{1}{3} i \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)+\frac{1}{3} i \tan ^{-1}\left(\sqrt{3}+\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)+\frac{2}{3} i \tan ^{-1}\left(\frac{\sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)",1,"I*(1 - I*x)^(5/6)*(1 + I*x)^(1/6) - (I/3)*ArcTan[Sqrt[3] - (2*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)] + (I/3)*ArcTan[Sqrt[3] + (2*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)] + ((2*I)/3)*ArcTan[(1 - I*x)^(1/6)/(1 + I*x)^(1/6)] + ((I/2)*Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3) - (Sqrt[3]*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)])/Sqrt[3] - ((I/2)*Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3) + (Sqrt[3]*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)])/Sqrt[3]","A",14,10,10,1.000,1,"{5061, 50, 63, 331, 295, 634, 618, 204, 628, 203}"
118,1,430,0,0.4582255,"\int \frac{e^{\frac{1}{3} i \tan ^{-1}(x)}}{x} \, dx","Int[E^((I/3)*ArcTan[x])/x,x]","-\frac{1}{2} \sqrt{3} \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}-\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)+\frac{1}{2} \sqrt{3} \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}+\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)+\frac{1}{2} \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}-\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)-\frac{1}{2} \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}+\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)+\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)-\tan ^{-1}\left(\sqrt{3}+\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)-\sqrt{3} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)-2 \tan ^{-1}\left(\frac{\sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}\right)","-\frac{1}{2} \sqrt{3} \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}-\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)+\frac{1}{2} \sqrt{3} \log \left(\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}+\frac{\sqrt{3} \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}+1\right)+\frac{1}{2} \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}-\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)-\frac{1}{2} \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}+\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)+\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)-\tan ^{-1}\left(\sqrt{3}+\frac{2 \sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)-\sqrt{3} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)-2 \tan ^{-1}\left(\frac{\sqrt[6]{1-i x}}{\sqrt[6]{1+i x}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}\right)",1,"ArcTan[Sqrt[3] - (2*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)] - ArcTan[Sqrt[3] + (2*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)] + Sqrt[3]*ArcTan[(1 - (2*(1 + I*x)^(1/6))/(1 - I*x)^(1/6))/Sqrt[3]] - Sqrt[3]*ArcTan[(1 + (2*(1 + I*x)^(1/6))/(1 - I*x)^(1/6))/Sqrt[3]] - 2*ArcTan[(1 - I*x)^(1/6)/(1 + I*x)^(1/6)] - 2*ArcTanh[(1 + I*x)^(1/6)/(1 - I*x)^(1/6)] - (Sqrt[3]*Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3) - (Sqrt[3]*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)])/2 + (Sqrt[3]*Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3) + (Sqrt[3]*(1 - I*x)^(1/6))/(1 + I*x)^(1/6)])/2 + Log[1 - (1 + I*x)^(1/6)/(1 - I*x)^(1/6) + (1 + I*x)^(1/3)/(1 - I*x)^(1/3)]/2 - Log[1 + (1 + I*x)^(1/6)/(1 - I*x)^(1/6) + (1 + I*x)^(1/3)/(1 - I*x)^(1/3)]/2","A",25,13,14,0.9286,1,"{5062, 105, 63, 331, 295, 634, 618, 204, 628, 203, 93, 210, 206}"
119,1,253,0,0.1556454,"\int \frac{e^{\frac{1}{3} i \tan ^{-1}(x)}}{x^2} \, dx","Int[E^((I/3)*ArcTan[x])/x^2,x]","-\frac{(1-i x)^{5/6} \sqrt[6]{1+i x}}{x}+\frac{1}{6} i \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}-\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)-\frac{1}{6} i \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}+\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)+\frac{i \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{i \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2}{3} i \tanh ^{-1}\left(\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}\right)","-\frac{(1-i x)^{5/6} \sqrt[6]{1+i x}}{x}+\frac{1}{6} i \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}-\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)-\frac{1}{6} i \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}+\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)+\frac{i \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{i \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2}{3} i \tanh ^{-1}\left(\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}\right)",1,"-(((1 - I*x)^(5/6)*(1 + I*x)^(1/6))/x) + (I*ArcTan[(1 - (2*(1 + I*x)^(1/6))/(1 - I*x)^(1/6))/Sqrt[3]])/Sqrt[3] - (I*ArcTan[(1 + (2*(1 + I*x)^(1/6))/(1 - I*x)^(1/6))/Sqrt[3]])/Sqrt[3] - ((2*I)/3)*ArcTanh[(1 + I*x)^(1/6)/(1 - I*x)^(1/6)] + (I/6)*Log[1 - (1 + I*x)^(1/6)/(1 - I*x)^(1/6) + (1 + I*x)^(1/3)/(1 - I*x)^(1/3)] - (I/6)*Log[1 + (1 + I*x)^(1/6)/(1 - I*x)^(1/6) + (1 + I*x)^(1/3)/(1 - I*x)^(1/3)]","A",13,9,14,0.6429,1,"{5062, 94, 93, 210, 634, 618, 204, 628, 206}"
120,1,280,0,0.1761148,"\int \frac{e^{\frac{1}{3} i \tan ^{-1}(x)}}{x^3} \, dx","Int[E^((I/3)*ArcTan[x])/x^3,x]","-\frac{(1-i x)^{5/6} (1+i x)^{7/6}}{2 x^2}-\frac{i (1-i x)^{5/6} \sqrt[6]{1+i x}}{6 x}-\frac{1}{36} \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}-\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)+\frac{1}{36} \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}+\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{6 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1+\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{6 \sqrt{3}}+\frac{1}{9} \tanh ^{-1}\left(\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}\right)","-\frac{(1-i x)^{5/6} (1+i x)^{7/6}}{2 x^2}-\frac{i (1-i x)^{5/6} \sqrt[6]{1+i x}}{6 x}-\frac{1}{36} \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}-\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)+\frac{1}{36} \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}+\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{6 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1+\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{6 \sqrt{3}}+\frac{1}{9} \tanh ^{-1}\left(\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}\right)",1,"-((1 - I*x)^(5/6)*(1 + I*x)^(7/6))/(2*x^2) - ((I/6)*(1 - I*x)^(5/6)*(1 + I*x)^(1/6))/x - ArcTan[(1 - (2*(1 + I*x)^(1/6))/(1 - I*x)^(1/6))/Sqrt[3]]/(6*Sqrt[3]) + ArcTan[(1 + (2*(1 + I*x)^(1/6))/(1 - I*x)^(1/6))/Sqrt[3]]/(6*Sqrt[3]) + ArcTanh[(1 + I*x)^(1/6)/(1 - I*x)^(1/6)]/9 - Log[1 - (1 + I*x)^(1/6)/(1 - I*x)^(1/6) + (1 + I*x)^(1/3)/(1 - I*x)^(1/3)]/36 + Log[1 + (1 + I*x)^(1/6)/(1 - I*x)^(1/6) + (1 + I*x)^(1/3)/(1 - I*x)^(1/3)]/36","A",14,10,14,0.7143,1,"{5062, 96, 94, 93, 210, 634, 618, 204, 628, 206}"
121,1,319,0,0.2000217,"\int \frac{e^{\frac{1}{3} i \tan ^{-1}(x)}}{x^4} \, dx","Int[E^((I/3)*ArcTan[x])/x^4,x]","-\frac{7 i (1-i x)^{5/6} \sqrt[6]{1+i x}}{18 x^2}-\frac{(1-i x)^{5/6} \sqrt[6]{1+i x}}{3 x^3}+\frac{11 (1-i x)^{5/6} \sqrt[6]{1+i x}}{27 x}-\frac{19}{324} i \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}-\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)+\frac{19}{324} i \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}+\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)-\frac{19 i \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{54 \sqrt{3}}+\frac{19 i \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{54 \sqrt{3}}+\frac{19}{81} i \tanh ^{-1}\left(\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}\right)","-\frac{7 i (1-i x)^{5/6} \sqrt[6]{1+i x}}{18 x^2}-\frac{(1-i x)^{5/6} \sqrt[6]{1+i x}}{3 x^3}+\frac{11 (1-i x)^{5/6} \sqrt[6]{1+i x}}{27 x}-\frac{19}{324} i \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}-\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)+\frac{19}{324} i \log \left(\frac{\sqrt[3]{1+i x}}{\sqrt[3]{1-i x}}+\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}+1\right)-\frac{19 i \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{54 \sqrt{3}}+\frac{19 i \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}}{\sqrt{3}}\right)}{54 \sqrt{3}}+\frac{19}{81} i \tanh ^{-1}\left(\frac{\sqrt[6]{1+i x}}{\sqrt[6]{1-i x}}\right)",1,"-((1 - I*x)^(5/6)*(1 + I*x)^(1/6))/(3*x^3) - (((7*I)/18)*(1 - I*x)^(5/6)*(1 + I*x)^(1/6))/x^2 + (11*(1 - I*x)^(5/6)*(1 + I*x)^(1/6))/(27*x) - (((19*I)/54)*ArcTan[(1 - (2*(1 + I*x)^(1/6))/(1 - I*x)^(1/6))/Sqrt[3]])/Sqrt[3] + (((19*I)/54)*ArcTan[(1 + (2*(1 + I*x)^(1/6))/(1 - I*x)^(1/6))/Sqrt[3]])/Sqrt[3] + ((19*I)/81)*ArcTanh[(1 + I*x)^(1/6)/(1 - I*x)^(1/6)] - ((19*I)/324)*Log[1 - (1 + I*x)^(1/6)/(1 - I*x)^(1/6) + (1 + I*x)^(1/3)/(1 - I*x)^(1/3)] + ((19*I)/324)*Log[1 + (1 + I*x)^(1/6)/(1 - I*x)^(1/6) + (1 + I*x)^(1/3)/(1 - I*x)^(1/3)]","A",16,11,14,0.7857,1,"{5062, 99, 151, 12, 93, 210, 634, 618, 204, 628, 206}"
122,1,177,0,0.0546673,"\int e^{\frac{2}{3} i \tan ^{-1}(x)} x^2 \, dx","Int[E^(((2*I)/3)*ArcTan[x])*x^2,x]","\frac{1}{3} (1-i x)^{2/3} x (1+i x)^{4/3}-\frac{1}{9} i (1-i x)^{2/3} (1+i x)^{4/3}-\frac{11}{27} i (1-i x)^{2/3} \sqrt[3]{1+i x}+\frac{11}{27} i \log \left(1+\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}\right)+\frac{11}{81} i \log (1+i x)+\frac{22 i \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)}{27 \sqrt{3}}","\frac{1}{3} (1-i x)^{2/3} x (1+i x)^{4/3}-\frac{1}{9} i (1-i x)^{2/3} (1+i x)^{4/3}-\frac{11}{27} i (1-i x)^{2/3} \sqrt[3]{1+i x}+\frac{11}{27} i \log \left(1+\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}\right)+\frac{11}{81} i \log (1+i x)+\frac{22 i \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)}{27 \sqrt{3}}",1,"((-11*I)/27)*(1 - I*x)^(2/3)*(1 + I*x)^(1/3) - (I/9)*(1 - I*x)^(2/3)*(1 + I*x)^(4/3) + ((1 - I*x)^(2/3)*(1 + I*x)^(4/3)*x)/3 + (((22*I)/27)*ArcTan[1/Sqrt[3] - (2*(1 - I*x)^(1/3))/(Sqrt[3]*(1 + I*x)^(1/3))])/Sqrt[3] + ((11*I)/27)*Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3)] + ((11*I)/81)*Log[1 + I*x]","A",5,5,14,0.3571,1,"{5062, 90, 80, 50, 60}"
123,1,140,0,0.0359681,"\int e^{\frac{2}{3} i \tan ^{-1}(x)} x \, dx","Int[E^(((2*I)/3)*ArcTan[x])*x,x]","\frac{1}{2} (1-i x)^{2/3} (1+i x)^{4/3}+\frac{1}{3} (1-i x)^{2/3} \sqrt[3]{1+i x}-\frac{1}{3} \log \left(1+\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}\right)-\frac{1}{9} \log (1+i x)-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)}{3 \sqrt{3}}","\frac{1}{2} (1-i x)^{2/3} (1+i x)^{4/3}+\frac{1}{3} (1-i x)^{2/3} \sqrt[3]{1+i x}-\frac{1}{3} \log \left(1+\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}\right)-\frac{1}{9} \log (1+i x)-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)}{3 \sqrt{3}}",1,"((1 - I*x)^(2/3)*(1 + I*x)^(1/3))/3 + ((1 - I*x)^(2/3)*(1 + I*x)^(4/3))/2 - (2*ArcTan[1/Sqrt[3] - (2*(1 - I*x)^(1/3))/(Sqrt[3]*(1 + I*x)^(1/3))])/(3*Sqrt[3]) - Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3)]/3 - Log[1 + I*x]/9","A",4,4,12,0.3333,1,"{5062, 80, 50, 60}"
124,1,116,0,0.0205023,"\int e^{\frac{2}{3} i \tan ^{-1}(x)} \, dx","Int[E^(((2*I)/3)*ArcTan[x]),x]","i (1-i x)^{2/3} \sqrt[3]{1+i x}-i \log \left(1+\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}\right)-\frac{1}{3} i \log (1+i x)-\frac{2 i \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)}{\sqrt{3}}","i (1-i x)^{2/3} \sqrt[3]{1+i x}-i \log \left(1+\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}\right)-\frac{1}{3} i \log (1+i x)-\frac{2 i \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)}{\sqrt{3}}",1,"I*(1 - I*x)^(2/3)*(1 + I*x)^(1/3) - ((2*I)*ArcTan[1/Sqrt[3] - (2*(1 - I*x)^(1/3))/(Sqrt[3]*(1 + I*x)^(1/3))])/Sqrt[3] - I*Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3)] - (I/3)*Log[1 + I*x]","A",3,3,10,0.3000,1,"{5061, 50, 60}"
125,1,163,0,0.0403384,"\int \frac{e^{\frac{2}{3} i \tan ^{-1}(x)}}{x} \, dx","Int[E^(((2*I)/3)*ArcTan[x])/x,x]","\frac{3}{2} \log \left(1+\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}\right)+\frac{3}{2} \log \left(\sqrt[3]{1-i x}-\sqrt[3]{1+i x}\right)+\frac{1}{2} \log (1+i x)-\frac{\log (x)}{2}+\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)","\frac{3}{2} \log \left(1+\frac{\sqrt[3]{1-i x}}{\sqrt[3]{1+i x}}\right)+\frac{3}{2} \log \left(\sqrt[3]{1-i x}-\sqrt[3]{1+i x}\right)+\frac{1}{2} \log (1+i x)-\frac{\log (x)}{2}+\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)",1,"Sqrt[3]*ArcTan[1/Sqrt[3] - (2*(1 - I*x)^(1/3))/(Sqrt[3]*(1 + I*x)^(1/3))] + Sqrt[3]*ArcTan[1/Sqrt[3] + (2*(1 - I*x)^(1/3))/(Sqrt[3]*(1 + I*x)^(1/3))] + (3*Log[1 + (1 - I*x)^(1/3)/(1 + I*x)^(1/3)])/2 + (3*Log[(1 - I*x)^(1/3) - (1 + I*x)^(1/3)])/2 + Log[1 + I*x]/2 - Log[x]/2","A",4,4,14,0.2857,1,"{5062, 105, 60, 91}"
126,1,111,0,0.0292463,"\int \frac{e^{\frac{2}{3} i \tan ^{-1}(x)}}{x^2} \, dx","Int[E^(((2*I)/3)*ArcTan[x])/x^2,x]","-\frac{(1-i x)^{2/3} \sqrt[3]{1+i x}}{x}+i \log \left(\sqrt[3]{1-i x}-\sqrt[3]{1+i x}\right)-\frac{1}{3} i \log (x)+\frac{2 i \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)}{\sqrt{3}}","-\frac{(1-i x)^{2/3} \sqrt[3]{1+i x}}{x}+i \log \left(\sqrt[3]{1-i x}-\sqrt[3]{1+i x}\right)-\frac{1}{3} i \log (x)+\frac{2 i \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)}{\sqrt{3}}",1,"-(((1 - I*x)^(2/3)*(1 + I*x)^(1/3))/x) + ((2*I)*ArcTan[1/Sqrt[3] + (2*(1 - I*x)^(1/3))/(Sqrt[3]*(1 + I*x)^(1/3))])/Sqrt[3] + I*Log[(1 - I*x)^(1/3) - (1 + I*x)^(1/3)] - (I/3)*Log[x]","A",3,3,14,0.2143,1,"{5062, 94, 91}"
127,1,142,0,0.0398932,"\int \frac{e^{\frac{2}{3} i \tan ^{-1}(x)}}{x^3} \, dx","Int[E^(((2*I)/3)*ArcTan[x])/x^3,x]","-\frac{(1-i x)^{2/3} (1+i x)^{4/3}}{2 x^2}-\frac{i (1-i x)^{2/3} \sqrt[3]{1+i x}}{3 x}-\frac{1}{3} \log \left(\sqrt[3]{1-i x}-\sqrt[3]{1+i x}\right)+\frac{\log (x)}{9}-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)}{3 \sqrt{3}}","-\frac{(1-i x)^{2/3} (1+i x)^{4/3}}{2 x^2}-\frac{i (1-i x)^{2/3} \sqrt[3]{1+i x}}{3 x}-\frac{1}{3} \log \left(\sqrt[3]{1-i x}-\sqrt[3]{1+i x}\right)+\frac{\log (x)}{9}-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}+\frac{2 \sqrt[3]{1-i x}}{\sqrt{3} \sqrt[3]{1+i x}}\right)}{3 \sqrt{3}}",1,"-((1 - I*x)^(2/3)*(1 + I*x)^(4/3))/(2*x^2) - ((I/3)*(1 - I*x)^(2/3)*(1 + I*x)^(1/3))/x - (2*ArcTan[1/Sqrt[3] + (2*(1 - I*x)^(1/3))/(Sqrt[3]*(1 + I*x)^(1/3))])/(3*Sqrt[3]) - Log[(1 - I*x)^(1/3) - (1 + I*x)^(1/3)]/3 + Log[x]/9","A",4,4,14,0.2857,1,"{5062, 96, 94, 91}"
128,1,741,0,0.7333907,"\int e^{\frac{1}{4} i \tan ^{-1}(a x)} x^2 \, dx","Int[E^((I/4)*ArcTan[a*x])*x^2,x]","\frac{x (1-i a x)^{7/8} (1+i a x)^{9/8}}{3 a^2}-\frac{i (1-i a x)^{7/8} (1+i a x)^{9/8}}{24 a^3}-\frac{11 i (1-i a x)^{7/8} \sqrt[8]{1+i a x}}{32 a^3}-\frac{11 i \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{256 a^3}+\frac{11 i \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{256 a^3}-\frac{11 i \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{256 a^3}+\frac{11 i \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{256 a^3}+\frac{11 i \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{128 a^3}+\frac{11 i \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{128 a^3}-\frac{11 i \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{128 a^3}-\frac{11 i \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{128 a^3}","\frac{x (1-i a x)^{7/8} (1+i a x)^{9/8}}{3 a^2}-\frac{i (1-i a x)^{7/8} (1+i a x)^{9/8}}{24 a^3}-\frac{11 i (1-i a x)^{7/8} \sqrt[8]{1+i a x}}{32 a^3}-\frac{11 i \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{256 a^3}+\frac{11 i \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{256 a^3}-\frac{11 i \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{256 a^3}+\frac{11 i \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{256 a^3}+\frac{11 i \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{128 a^3}+\frac{11 i \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{128 a^3}-\frac{11 i \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{128 a^3}-\frac{11 i \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{128 a^3}",1,"(((-11*I)/32)*(1 - I*a*x)^(7/8)*(1 + I*a*x)^(1/8))/a^3 - ((I/24)*(1 - I*a*x)^(7/8)*(1 + I*a*x)^(9/8))/a^3 + (x*(1 - I*a*x)^(7/8)*(1 + I*a*x)^(9/8))/(3*a^2) + (((11*I)/128)*Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/a^3 + (((11*I)/128)*Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/a^3 - (((11*I)/128)*Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/a^3 - (((11*I)/128)*Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/a^3 - (((11*I)/256)*Sqrt[2 - Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) - (Sqrt[2 - Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/a^3 + (((11*I)/256)*Sqrt[2 - Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) + (Sqrt[2 - Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/a^3 - (((11*I)/256)*Sqrt[2 + Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) - (Sqrt[2 + Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/a^3 + (((11*I)/256)*Sqrt[2 + Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) + (Sqrt[2 + Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/a^3","A",27,13,16,0.8125,1,"{5062, 90, 80, 50, 63, 331, 299, 1122, 1169, 634, 618, 204, 628}"
129,1,689,0,0.4949306,"\int e^{\frac{1}{4} i \tan ^{-1}(a x)} x \, dx","Int[E^((I/4)*ArcTan[a*x])*x,x]","\frac{(1-i a x)^{7/8} (1+i a x)^{9/8}}{2 a^2}+\frac{(1-i a x)^{7/8} \sqrt[8]{1+i a x}}{8 a^2}+\frac{\sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{64 a^2}-\frac{\sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{64 a^2}+\frac{\sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{64 a^2}-\frac{\sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{64 a^2}-\frac{\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{32 a^2}-\frac{\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{32 a^2}+\frac{\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{32 a^2}+\frac{\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{32 a^2}","\frac{(1-i a x)^{7/8} (1+i a x)^{9/8}}{2 a^2}+\frac{(1-i a x)^{7/8} \sqrt[8]{1+i a x}}{8 a^2}+\frac{\sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{64 a^2}-\frac{\sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{64 a^2}+\frac{\sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{64 a^2}-\frac{\sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{64 a^2}-\frac{\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{32 a^2}-\frac{\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{32 a^2}+\frac{\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{32 a^2}+\frac{\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{32 a^2}",1,"((1 - I*a*x)^(7/8)*(1 + I*a*x)^(1/8))/(8*a^2) + ((1 - I*a*x)^(7/8)*(1 + I*a*x)^(9/8))/(2*a^2) - (Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/(32*a^2) - (Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/(32*a^2) + (Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/(32*a^2) + (Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/(32*a^2) + (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) - (Sqrt[2 - Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/(64*a^2) - (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) + (Sqrt[2 - Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/(64*a^2) + (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) - (Sqrt[2 + Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/(64*a^2) - (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) + (Sqrt[2 + Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/(64*a^2)","A",26,12,14,0.8571,1,"{5062, 80, 50, 63, 331, 299, 1122, 1169, 634, 618, 204, 628}"
130,1,674,0,0.4338523,"\int e^{\frac{1}{4} i \tan ^{-1}(a x)} \, dx","Int[E^((I/4)*ArcTan[a*x]),x]","\frac{i (1-i a x)^{7/8} \sqrt[8]{1+i a x}}{a}+\frac{i \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{8 a}-\frac{i \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{8 a}+\frac{i \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{8 a}-\frac{i \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{8 a}-\frac{i \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{4 a}-\frac{i \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{4 a}+\frac{i \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{4 a}+\frac{i \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{4 a}","\frac{i (1-i a x)^{7/8} \sqrt[8]{1+i a x}}{a}+\frac{i \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{8 a}-\frac{i \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{8 a}+\frac{i \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{8 a}-\frac{i \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{1+i a x}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}+1\right)}{8 a}-\frac{i \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{4 a}-\frac{i \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{4 a}+\frac{i \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2+\sqrt{2}}}\right)}{4 a}+\frac{i \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}+\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{1+i a x}}}{\sqrt{2-\sqrt{2}}}\right)}{4 a}",1,"(I*(1 - I*a*x)^(7/8)*(1 + I*a*x)^(1/8))/a - ((I/4)*Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/a - ((I/4)*Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/a + ((I/4)*Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/a + ((I/4)*Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/a + ((I/8)*Sqrt[2 - Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) - (Sqrt[2 - Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/a - ((I/8)*Sqrt[2 - Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) + (Sqrt[2 - Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/a + ((I/8)*Sqrt[2 + Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) - (Sqrt[2 + Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/a - ((I/8)*Sqrt[2 + Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) + (Sqrt[2 + Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/a","A",25,11,12,0.9167,1,"{5061, 50, 63, 331, 299, 1122, 1169, 634, 618, 204, 628}"
131,1,859,0,0.5458864,"\int \frac{e^{\frac{1}{4} i \tan ^{-1}(a x)}}{x} \, dx","Int[E^((I/4)*ArcTan[a*x])/x,x]","-2 \tan ^{-1}\left(\frac{\sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}\right)+\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}}{\sqrt{2+\sqrt{2}}}\right)+\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}}{\sqrt{2-\sqrt{2}}}\right)-\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)-\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}+1\right)-2 \tanh ^{-1}\left(\frac{\sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}\right)-\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{i a x+1}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+1\right)+\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{i a x+1}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+1\right)-\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{i a x+1}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+1\right)+\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{i a x+1}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+1\right)+\frac{\log \left(\frac{\sqrt[4]{i a x+1}}{\sqrt[4]{1-i a x}}-\frac{\sqrt{2} \sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt[4]{i a x+1}}{\sqrt[4]{1-i a x}}+\frac{\sqrt{2} \sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}+1\right)}{\sqrt{2}}","-2 \tan ^{-1}\left(\frac{\sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}\right)+\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}}{\sqrt{2+\sqrt{2}}}\right)+\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}}{\sqrt{2-\sqrt{2}}}\right)-\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)-\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}+1\right)-2 \tanh ^{-1}\left(\frac{\sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}\right)-\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{i a x+1}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+1\right)+\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{i a x+1}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+1\right)-\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{i a x+1}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+1\right)+\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-i a x}}{\sqrt[4]{i a x+1}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-i a x}}{\sqrt[8]{i a x+1}}+1\right)+\frac{\log \left(\frac{\sqrt[4]{i a x+1}}{\sqrt[4]{1-i a x}}-\frac{\sqrt{2} \sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt[4]{i a x+1}}{\sqrt[4]{1-i a x}}+\frac{\sqrt{2} \sqrt[8]{i a x+1}}{\sqrt[8]{1-i a x}}+1\right)}{\sqrt{2}}",1,"-2*ArcTan[(1 + I*a*x)^(1/8)/(1 - I*a*x)^(1/8)] + Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 + Sqrt[2]]] + Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 - Sqrt[2]]] - Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 + Sqrt[2]]] - Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + (2*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8))/Sqrt[2 - Sqrt[2]]] + Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8)] - 2*ArcTanh[(1 + I*a*x)^(1/8)/(1 - I*a*x)^(1/8)] - (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) - (Sqrt[2 - Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/2 + (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) + (Sqrt[2 - Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/2 - (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) - (Sqrt[2 + Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/2 + (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - I*a*x)^(1/4)/(1 + I*a*x)^(1/4) + (Sqrt[2 + Sqrt[2]]*(1 - I*a*x)^(1/8))/(1 + I*a*x)^(1/8)])/2 + Log[1 - (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8) + (1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]/Sqrt[2] - Log[1 + (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8) + (1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)]/Sqrt[2]","A",39,20,16,1.250,1,"{5062, 105, 63, 331, 299, 1122, 1169, 634, 618, 204, 628, 93, 214, 212, 206, 203, 211, 1165, 1162, 617}"
132,1,328,0,0.1321477,"\int \frac{e^{\frac{1}{4} i \tan ^{-1}(a x)}}{x^2} \, dx","Int[E^((I/4)*ArcTan[a*x])/x^2,x]","-\frac{(1-i a x)^{7/8} \sqrt[8]{1+i a x}}{x}+\frac{i a \log \left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}-\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}+1\right)}{4 \sqrt{2}}-\frac{i a \log \left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}+\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}+1\right)}{4 \sqrt{2}}-\frac{1}{2} i a \tan ^{-1}\left(\frac{\sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)+\frac{i a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)}{2 \sqrt{2}}-\frac{i a \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)}{2 \sqrt{2}}-\frac{1}{2} i a \tanh ^{-1}\left(\frac{\sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)","-\frac{(1-i a x)^{7/8} \sqrt[8]{1+i a x}}{x}+\frac{i a \log \left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}-\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}+1\right)}{4 \sqrt{2}}-\frac{i a \log \left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}+\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}+1\right)}{4 \sqrt{2}}-\frac{1}{2} i a \tan ^{-1}\left(\frac{\sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)+\frac{i a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)}{2 \sqrt{2}}-\frac{i a \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)}{2 \sqrt{2}}-\frac{1}{2} i a \tanh ^{-1}\left(\frac{\sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)",1,"-(((1 - I*a*x)^(7/8)*(1 + I*a*x)^(1/8))/x) - (I/2)*a*ArcTan[(1 + I*a*x)^(1/8)/(1 - I*a*x)^(1/8)] + ((I/2)*a*ArcTan[1 - (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8)])/Sqrt[2] - ((I/2)*a*ArcTan[1 + (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8)])/Sqrt[2] - (I/2)*a*ArcTanh[(1 + I*a*x)^(1/8)/(1 - I*a*x)^(1/8)] + ((I/4)*a*Log[1 - (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8) + (1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/Sqrt[2] - ((I/4)*a*Log[1 + (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8) + (1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/Sqrt[2]","A",16,13,16,0.8125,1,"{5062, 94, 93, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
133,1,364,0,0.1610887,"\int \frac{e^{\frac{1}{4} i \tan ^{-1}(a x)}}{x^3} \, dx","Int[E^((I/4)*ArcTan[a*x])/x^3,x]","-\frac{a^2 \log \left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}-\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}+1\right)}{32 \sqrt{2}}+\frac{a^2 \log \left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}+\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}+1\right)}{32 \sqrt{2}}+\frac{1}{16} a^2 \tan ^{-1}\left(\frac{\sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)-\frac{a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)}{16 \sqrt{2}}+\frac{a^2 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)}{16 \sqrt{2}}+\frac{1}{16} a^2 \tanh ^{-1}\left(\frac{\sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)-\frac{(1-i a x)^{7/8} (1+i a x)^{9/8}}{2 x^2}-\frac{i a (1-i a x)^{7/8} \sqrt[8]{1+i a x}}{8 x}","-\frac{a^2 \log \left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}-\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}+1\right)}{32 \sqrt{2}}+\frac{a^2 \log \left(\frac{\sqrt[4]{1+i a x}}{\sqrt[4]{1-i a x}}+\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}+1\right)}{32 \sqrt{2}}+\frac{1}{16} a^2 \tan ^{-1}\left(\frac{\sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)-\frac{a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)}{16 \sqrt{2}}+\frac{a^2 \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)}{16 \sqrt{2}}+\frac{1}{16} a^2 \tanh ^{-1}\left(\frac{\sqrt[8]{1+i a x}}{\sqrt[8]{1-i a x}}\right)-\frac{(1-i a x)^{7/8} (1+i a x)^{9/8}}{2 x^2}-\frac{i a (1-i a x)^{7/8} \sqrt[8]{1+i a x}}{8 x}",1,"((-I/8)*a*(1 - I*a*x)^(7/8)*(1 + I*a*x)^(1/8))/x - ((1 - I*a*x)^(7/8)*(1 + I*a*x)^(9/8))/(2*x^2) + (a^2*ArcTan[(1 + I*a*x)^(1/8)/(1 - I*a*x)^(1/8)])/16 - (a^2*ArcTan[1 - (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8)])/(16*Sqrt[2]) + (a^2*ArcTan[1 + (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8)])/(16*Sqrt[2]) + (a^2*ArcTanh[(1 + I*a*x)^(1/8)/(1 - I*a*x)^(1/8)])/16 - (a^2*Log[1 - (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8) + (1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/(32*Sqrt[2]) + (a^2*Log[1 + (Sqrt[2]*(1 + I*a*x)^(1/8))/(1 - I*a*x)^(1/8) + (1 + I*a*x)^(1/4)/(1 - I*a*x)^(1/4)])/(32*Sqrt[2])","A",17,14,16,0.8750,1,"{5062, 96, 94, 93, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
134,1,114,0,0.0950837,"\int e^{6 i \tan ^{-1}(a x)} x^m \, dx","Int[E^((6*I)*ArcTan[a*x])*x^m,x]","\frac{2 \left(2 m^2+4 m+3\right) x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,i a x)}{m+1}+\frac{4 i x^{m+1} \left(a \left(m^2+3 m+3\right) x+i (m+1)^2\right)}{(m+1) (1-i a x)^2}-\frac{(1+i a x)^2 x^{m+1}}{(m+1) (1-i a x)^2}","\frac{2 \left(2 m^2+4 m+3\right) x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,i a x)}{m+1}+\frac{4 i x^{m+1} \left(a \left(m^2+3 m+3\right) x+i (m+1)^2\right)}{(m+1) (1-i a x)^2}-\frac{(1+i a x)^2 x^{m+1}}{(m+1) (1-i a x)^2}",1,"-((x^(1 + m)*(1 + I*a*x)^2)/((1 + m)*(1 - I*a*x)^2)) + ((4*I)*x^(1 + m)*(I*(1 + m)^2 + a*(3 + 3*m + m^2)*x))/((1 + m)*(1 - I*a*x)^2) + (2*(3 + 4*m + 2*m^2)*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, I*a*x])/(1 + m)","A",4,4,14,0.2857,1,"{5062, 100, 145, 64}"
135,1,50,0,0.0420944,"\int e^{4 i \tan ^{-1}(a x)} x^m \, dx","Int[E^((4*I)*ArcTan[a*x])*x^m,x]","-4 x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,i a x)+\frac{4 x^{m+1}}{1-i a x}+\frac{x^{m+1}}{m+1}","-4 x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,i a x)+\frac{4 x^{m+1}}{1-i a x}+\frac{x^{m+1}}{m+1}",1,"x^(1 + m)/(1 + m) + (4*x^(1 + m))/(1 - I*a*x) - 4*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, I*a*x]","A",4,4,14,0.2857,1,"{5062, 89, 80, 64}"
136,1,39,0,0.0226873,"\int e^{2 i \tan ^{-1}(a x)} x^m \, dx","Int[E^((2*I)*ArcTan[a*x])*x^m,x]","-\frac{x^{m+1}}{m+1}+\frac{2 x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,i a x)}{m+1}","-\frac{x^{m+1}}{m+1}+\frac{2 x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,i a x)}{m+1}",1,"-(x^(1 + m)/(1 + m)) + (2*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, I*a*x])/(1 + m)","A",3,3,14,0.2143,1,"{5062, 80, 64}"
137,1,39,0,0.0231997,"\int e^{-2 i \tan ^{-1}(a x)} x^m \, dx","Int[x^m/E^((2*I)*ArcTan[a*x]),x]","-\frac{x^{m+1}}{m+1}+\frac{2 x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,-i a x)}{m+1}","-\frac{x^{m+1}}{m+1}+\frac{2 x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,-i a x)}{m+1}",1,"-(x^(1 + m)/(1 + m)) + (2*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (-I)*a*x])/(1 + m)","A",3,3,14,0.2143,1,"{5062, 80, 64}"
138,1,50,0,0.0390302,"\int e^{-4 i \tan ^{-1}(a x)} x^m \, dx","Int[x^m/E^((4*I)*ArcTan[a*x]),x]","-4 x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,-i a x)+\frac{4 x^{m+1}}{1+i a x}+\frac{x^{m+1}}{m+1}","-4 x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,-i a x)+\frac{4 x^{m+1}}{1+i a x}+\frac{x^{m+1}}{m+1}",1,"x^(1 + m)/(1 + m) + (4*x^(1 + m))/(1 + I*a*x) - 4*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (-I)*a*x]","A",4,4,14,0.2857,1,"{5062, 89, 80, 64}"
139,1,115,0,0.0897069,"\int e^{-6 i \tan ^{-1}(a x)} x^m \, dx","Int[x^m/E^((6*I)*ArcTan[a*x]),x]","\frac{2 \left(2 m^2+4 m+3\right) x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,-i a x)}{m+1}+\frac{4 i x^{m+1} \left(-a \left(m^2+3 m+3\right) x+i (m+1)^2\right)}{(m+1) (1+i a x)^2}-\frac{(1-i a x)^2 x^{m+1}}{(m+1) (1+i a x)^2}","\frac{2 \left(2 m^2+4 m+3\right) x^{m+1} \text{Hypergeometric2F1}(1,m+1,m+2,-i a x)}{m+1}+\frac{4 i x^{m+1} \left(-a \left(m^2+3 m+3\right) x+i (m+1)^2\right)}{(m+1) (1+i a x)^2}-\frac{(1-i a x)^2 x^{m+1}}{(m+1) (1+i a x)^2}",1,"-((x^(1 + m)*(1 - I*a*x)^2)/((1 + m)*(1 + I*a*x)^2)) + ((4*I)*x^(1 + m)*(I*(1 + m)^2 - a*(3 + 3*m + m^2)*x))/((1 + m)*(1 + I*a*x)^2) + (2*(3 + 4*m + 2*m^2)*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (-I)*a*x])/(1 + m)","A",4,4,14,0.2857,1,"{5062, 100, 145, 64}"
140,1,159,0,0.7742347,"\int e^{3 i \tan ^{-1}(a x)} x^m \, dx","Int[E^((3*I)*ArcTan[a*x])*x^m,x]","-\frac{3 x^{m+1} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}+\frac{4 x^{m+1} \text{Hypergeometric2F1}\left(\frac{3}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}-\frac{i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}+\frac{4 i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{3}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}","-\frac{3 x^{m+1} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}+\frac{4 x^{m+1} \text{Hypergeometric2F1}\left(\frac{3}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}-\frac{i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}+\frac{4 i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{3}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}",1,"(-3*x^(1 + m)*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(a^2*x^2)])/(1 + m) - (I*a*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(a^2*x^2)])/(2 + m) + (4*x^(1 + m)*Hypergeometric2F1[3/2, (1 + m)/2, (3 + m)/2, -(a^2*x^2)])/(1 + m) + ((4*I)*a*x^(2 + m)*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, -(a^2*x^2)])/(2 + m)","A",9,5,14,0.3571,1,"{5060, 6742, 364, 850, 808}"
141,1,79,0,0.0407399,"\int e^{i \tan ^{-1}(a x)} x^m \, dx","Int[E^(I*ArcTan[a*x])*x^m,x]","\frac{x^{m+1} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}+\frac{i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}","\frac{x^{m+1} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}+\frac{i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}",1,"(x^(1 + m)*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(a^2*x^2)])/(1 + m) + (I*a*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(a^2*x^2)])/(2 + m)","A",4,3,14,0.2143,1,"{5060, 808, 364}"
142,1,79,0,0.0403945,"\int e^{-i \tan ^{-1}(a x)} x^m \, dx","Int[x^m/E^(I*ArcTan[a*x]),x]","\frac{x^{m+1} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}-\frac{i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}","\frac{x^{m+1} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}-\frac{i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}",1,"(x^(1 + m)*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(a^2*x^2)])/(1 + m) - (I*a*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(a^2*x^2)])/(2 + m)","A",4,3,14,0.2143,1,"{5060, 808, 364}"
143,1,159,0,0.7049535,"\int e^{-3 i \tan ^{-1}(a x)} x^m \, dx","Int[x^m/E^((3*I)*ArcTan[a*x]),x]","-\frac{3 x^{m+1} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}+\frac{4 x^{m+1} \text{Hypergeometric2F1}\left(\frac{3}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}+\frac{i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}-\frac{4 i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{3}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}","-\frac{3 x^{m+1} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}+\frac{4 x^{m+1} \text{Hypergeometric2F1}\left(\frac{3}{2},\frac{m+1}{2},\frac{m+3}{2},-a^2 x^2\right)}{m+1}+\frac{i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}-\frac{4 i a x^{m+2} \text{Hypergeometric2F1}\left(\frac{3}{2},\frac{m+2}{2},\frac{m+4}{2},-a^2 x^2\right)}{m+2}",1,"(-3*x^(1 + m)*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(a^2*x^2)])/(1 + m) + (I*a*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(a^2*x^2)])/(2 + m) + (4*x^(1 + m)*Hypergeometric2F1[3/2, (1 + m)/2, (3 + m)/2, -(a^2*x^2)])/(1 + m) - ((4*I)*a*x^(2 + m)*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, -(a^2*x^2)])/(2 + m)","A",9,5,14,0.3571,1,"{5060, 6742, 364, 850, 808}"
144,1,36,0,0.0271013,"\int e^{\frac{5}{2} i \tan ^{-1}(a x)} x^m \, dx","Int[E^(((5*I)/2)*ArcTan[a*x])*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{5}{4},-\frac{5}{4};m+2;i a x,-i a x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;\frac{5}{4},-\frac{5}{4};m+2;i a x,-i a x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, 5/4, -5/4, 2 + m, I*a*x, (-I)*a*x])/(1 + m)","A",2,2,16,0.1250,1,"{5062, 133}"
145,1,36,0,0.0260395,"\int e^{\frac{3}{2} i \tan ^{-1}(a x)} x^m \, dx","Int[E^(((3*I)/2)*ArcTan[a*x])*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{3}{4},-\frac{3}{4};m+2;i a x,-i a x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;\frac{3}{4},-\frac{3}{4};m+2;i a x,-i a x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, 3/4, -3/4, 2 + m, I*a*x, (-I)*a*x])/(1 + m)","A",2,2,16,0.1250,1,"{5062, 133}"
146,1,36,0,0.0260548,"\int e^{\frac{1}{2} i \tan ^{-1}(a x)} x^m \, dx","Int[E^((I/2)*ArcTan[a*x])*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{1}{4},-\frac{1}{4};m+2;i a x,-i a x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;\frac{1}{4},-\frac{1}{4};m+2;i a x,-i a x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, 1/4, -1/4, 2 + m, I*a*x, (-I)*a*x])/(1 + m)","A",2,2,16,0.1250,1,"{5062, 133}"
147,1,36,0,0.0256764,"\int e^{-\frac{1}{2} i \tan ^{-1}(a x)} x^m \, dx","Int[x^m/E^((I/2)*ArcTan[a*x]),x]","\frac{x^{m+1} F_1\left(m+1;-\frac{1}{4},\frac{1}{4};m+2;i a x,-i a x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;-\frac{1}{4},\frac{1}{4};m+2;i a x,-i a x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, -1/4, 1/4, 2 + m, I*a*x, (-I)*a*x])/(1 + m)","A",2,2,16,0.1250,1,"{5062, 133}"
148,1,36,0,0.0254629,"\int e^{-\frac{3}{2} i \tan ^{-1}(a x)} x^m \, dx","Int[x^m/E^(((3*I)/2)*ArcTan[a*x]),x]","\frac{x^{m+1} F_1\left(m+1;-\frac{3}{4},\frac{3}{4};m+2;i a x,-i a x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;-\frac{3}{4},\frac{3}{4};m+2;i a x,-i a x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, -3/4, 3/4, 2 + m, I*a*x, (-I)*a*x])/(1 + m)","A",2,2,16,0.1250,1,"{5062, 133}"
149,1,36,0,0.0256187,"\int e^{-\frac{5}{2} i \tan ^{-1}(a x)} x^m \, dx","Int[x^m/E^(((5*I)/2)*ArcTan[a*x]),x]","\frac{x^{m+1} F_1\left(m+1;-\frac{5}{4},\frac{5}{4};m+2;i a x,-i a x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;-\frac{5}{4},\frac{5}{4};m+2;i a x,-i a x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, -5/4, 5/4, 2 + m, I*a*x, (-I)*a*x])/(1 + m)","A",2,2,16,0.1250,1,"{5062, 133}"
150,1,38,0,0.0232761,"\int e^{\frac{2}{3} \tan ^{-1}(x)} x^m \, dx","Int[E^((2*ArcTan[x])/3)*x^m,x]","\frac{x^{m+1} F_1\left(m+1;-\frac{i}{3},\frac{i}{3};m+2;i x,-i x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;-\frac{i}{3},\frac{i}{3};m+2;i x,-i x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, -I/3, I/3, 2 + m, I*x, (-I)*x])/(1 + m)","A",2,2,12,0.1667,1,"{5062, 133}"
151,1,38,0,0.023389,"\int e^{\frac{1}{3} \tan ^{-1}(x)} x^m \, dx","Int[E^(ArcTan[x]/3)*x^m,x]","\frac{x^{m+1} F_1\left(m+1;-\frac{i}{6},\frac{i}{6};m+2;i x,-i x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;-\frac{i}{6},\frac{i}{6};m+2;i x,-i x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, -I/6, I/6, 2 + m, I*x, (-I)*x])/(1 + m)","A",2,2,12,0.1667,1,"{5062, 133}"
152,1,36,0,0.0246622,"\int e^{\frac{1}{4} i \tan ^{-1}(a x)} x^m \, dx","Int[E^((I/4)*ArcTan[a*x])*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{1}{8},-\frac{1}{8};m+2;i a x,-i a x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;\frac{1}{8},-\frac{1}{8};m+2;i a x,-i a x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, 1/8, -1/8, 2 + m, I*a*x, (-I)*a*x])/(1 + m)","A",2,2,16,0.1250,1,"{5062, 133}"
153,1,40,0,0.0280571,"\int e^{i n \tan ^{-1}(a x)} x^m \, dx","Int[E^(I*n*ArcTan[a*x])*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{n}{2},-\frac{n}{2};m+2;i a x,-i a x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;\frac{n}{2},-\frac{n}{2};m+2;i a x,-i a x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, n/2, -n/2, 2 + m, I*a*x, (-I)*a*x])/(1 + m)","A",2,2,15,0.1333,1,"{5062, 133}"
154,1,171,0,0.1137633,"\int e^{i n \tan ^{-1}(a x)} x^3 \, dx","Int[E^(I*n*ArcTan[a*x])*x^3,x]","-\frac{2^{\frac{n}{2}-2} n \left(n^2+8\right) (1-i a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-i a x)\right)}{3 a^4 (2-n)}-\frac{(1+i a x)^{\frac{n+2}{2}} \left(2 i a n x+n^2+6\right) (1-i a x)^{1-\frac{n}{2}}}{24 a^4}+\frac{x^2 (1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{4 a^2}","-\frac{2^{\frac{n}{2}-2} n \left(n^2+8\right) (1-i a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-i a x)\right)}{3 a^4 (2-n)}-\frac{(1+i a x)^{\frac{n+2}{2}} \left(2 i a n x+n^2+6\right) (1-i a x)^{1-\frac{n}{2}}}{24 a^4}+\frac{x^2 (1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{4 a^2}",1,"(x^2*(1 - I*a*x)^(1 - n/2)*(1 + I*a*x)^((2 + n)/2))/(4*a^2) - ((1 - I*a*x)^(1 - n/2)*(1 + I*a*x)^((2 + n)/2)*(6 + n^2 + (2*I)*a*n*x))/(24*a^4) - (2^(-2 + n/2)*n*(8 + n^2)*(1 - I*a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - I*a*x)/2])/(3*a^4*(2 - n))","A",4,4,15,0.2667,1,"{5062, 100, 147, 69}"
155,1,159,0,0.0857674,"\int e^{i n \tan ^{-1}(a x)} x^2 \, dx","Int[E^(I*n*ArcTan[a*x])*x^2,x]","-\frac{i 2^{n/2} \left(n^2+2\right) (1-i a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-i a x)\right)}{3 a^3 (2-n)}-\frac{i n (1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{6 a^3}+\frac{x (1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{3 a^2}","-\frac{i 2^{n/2} \left(n^2+2\right) (1-i a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-i a x)\right)}{3 a^3 (2-n)}-\frac{i n (1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{6 a^3}+\frac{x (1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{3 a^2}",1,"((-I/6)*n*(1 - I*a*x)^(1 - n/2)*(1 + I*a*x)^((2 + n)/2))/a^3 + (x*(1 - I*a*x)^(1 - n/2)*(1 + I*a*x)^((2 + n)/2))/(3*a^2) - ((I/3)*2^(n/2)*(2 + n^2)*(1 - I*a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - I*a*x)/2])/(a^3*(2 - n))","A",4,4,15,0.2667,1,"{5062, 90, 80, 69}"
156,1,107,0,0.0458557,"\int e^{i n \tan ^{-1}(a x)} x \, dx","Int[E^(I*n*ArcTan[a*x])*x,x]","\frac{2^{n/2} n (1-i a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-i a x)\right)}{a^2 (2-n)}+\frac{(1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{2 a^2}","\frac{2^{n/2} n (1-i a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-i a x)\right)}{a^2 (2-n)}+\frac{(1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{2 a^2}",1,"((1 - I*a*x)^(1 - n/2)*(1 + I*a*x)^((2 + n)/2))/(2*a^2) + (2^(n/2)*n*(1 - I*a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - I*a*x)/2])/(a^2*(2 - n))","A",3,3,13,0.2308,1,"{5062, 80, 69}"
157,1,71,0,0.0127803,"\int e^{i n \tan ^{-1}(a x)} \, dx","Int[E^(I*n*ArcTan[a*x]),x]","\frac{i 2^{\frac{n}{2}+1} (1-i a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-i a x)\right)}{a (2-n)}","\frac{i 2^{\frac{n}{2}+1} (1-i a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-i a x)\right)}{a (2-n)}",1,"(I*2^(1 + n/2)*(1 - I*a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - I*a*x)/2])/(a*(2 - n))","A",2,2,11,0.1818,1,"{5061, 69}"
158,1,125,0,0.0503532,"\int \frac{e^{i n \tan ^{-1}(a x)}}{x} \, dx","Int[E^(I*n*ArcTan[a*x])/x,x]","\frac{2 (1-i a x)^{-n/2} (1+i a x)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{1-i a x}{i a x+1}\right)}{n}-\frac{2^{\frac{n}{2}+1} (1-i a x)^{-n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-i a x)\right)}{n}","\frac{2 (1-i a x)^{-n/2} (1+i a x)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{1-i a x}{i a x+1}\right)}{n}-\frac{2^{\frac{n}{2}+1} (1-i a x)^{-n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-i a x)\right)}{n}",1,"(2*(1 + I*a*x)^(n/2)*Hypergeometric2F1[1, -n/2, 1 - n/2, (1 - I*a*x)/(1 + I*a*x)])/(n*(1 - I*a*x)^(n/2)) - (2^(1 + n/2)*Hypergeometric2F1[-n/2, -n/2, 1 - n/2, (1 - I*a*x)/2])/(n*(1 - I*a*x)^(n/2))","A",4,4,15,0.2667,1,"{5062, 105, 69, 131}"
159,1,79,0,0.0307808,"\int \frac{e^{i n \tan ^{-1}(a x)}}{x^2} \, dx","Int[E^(I*n*ArcTan[a*x])/x^2,x]","-\frac{4 i a (1-i a x)^{1-\frac{n}{2}} (1+i a x)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-i a x}{i a x+1}\right)}{2-n}","-\frac{4 i a (1-i a x)^{1-\frac{n}{2}} (1+i a x)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-i a x}{i a x+1}\right)}{2-n}",1,"((-4*I)*a*(1 - I*a*x)^(1 - n/2)*(1 + I*a*x)^((-2 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (1 - I*a*x)/(1 + I*a*x)])/(2 - n)","A",2,2,15,0.1333,1,"{5062, 131}"
160,1,120,0,0.0492065,"\int \frac{e^{i n \tan ^{-1}(a x)}}{x^3} \, dx","Int[E^(I*n*ArcTan[a*x])/x^3,x]","\frac{2 a^2 n (1-i a x)^{1-\frac{n}{2}} (1+i a x)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-i a x}{i a x+1}\right)}{2-n}-\frac{(1-i a x)^{1-\frac{n}{2}} (1+i a x)^{\frac{n+2}{2}}}{2 x^2}","\frac{2 a^2 n (1-i a x)^{1-\frac{n}{2}} (1+i a x)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-i a x}{i a x+1}\right)}{2-n}-\frac{(1-i a x)^{1-\frac{n}{2}} (1+i a x)^{\frac{n+2}{2}}}{2 x^2}",1,"-((1 - I*a*x)^(1 - n/2)*(1 + I*a*x)^((2 + n)/2))/(2*x^2) + (2*a^2*n*(1 - I*a*x)^(1 - n/2)*(1 + I*a*x)^((-2 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (1 - I*a*x)/(1 + I*a*x)])/(2 - n)","A",3,3,15,0.2000,1,"{5062, 96, 131}"
161,1,171,0,0.0720683,"\int \frac{e^{i n \tan ^{-1}(a x)}}{x^4} \, dx","Int[E^(I*n*ArcTan[a*x])/x^4,x]","\frac{2 i a^3 \left(n^2+2\right) (1+i a x)^{\frac{n-2}{2}} (1-i a x)^{1-\frac{n}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-i a x}{i a x+1}\right)}{3 (2-n)}-\frac{i a n (1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{6 x^2}-\frac{(1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{3 x^3}","\frac{2 i a^3 \left(n^2+2\right) (1+i a x)^{\frac{n-2}{2}} (1-i a x)^{1-\frac{n}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-i a x}{i a x+1}\right)}{3 (2-n)}-\frac{i a n (1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{6 x^2}-\frac{(1+i a x)^{\frac{n+2}{2}} (1-i a x)^{1-\frac{n}{2}}}{3 x^3}",1,"-((1 - I*a*x)^(1 - n/2)*(1 + I*a*x)^((2 + n)/2))/(3*x^3) - ((I/6)*a*n*(1 - I*a*x)^(1 - n/2)*(1 + I*a*x)^((2 + n)/2))/x^2 + (((2*I)/3)*a^3*(2 + n^2)*(1 - I*a*x)^(1 - n/2)*(1 + I*a*x)^((-2 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (1 - I*a*x)/(1 + I*a*x)])/(2 - n)","A",5,5,15,0.3333,1,"{5062, 129, 151, 12, 131}"
162,1,276,0,0.2014351,"\int e^{i \tan ^{-1}(a+b x)} x^4 \, dx","Int[E^(I*ArcTan[a + b*x])*x^4,x]","\frac{\sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2} \left(-2 \left(-36 a^2-14 i a+13\right) b x-96 a^3-86 i a^2+114 a+19 i\right)}{120 b^5}+\frac{\left(8 i a^4-16 a^3-24 i a^2+12 a+3 i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^5}+\frac{\left(8 a^4+16 i a^3-24 a^2-12 i a+3\right) \sinh ^{-1}(a+b x)}{8 b^5}+\frac{x^3 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{5 b^2}-\frac{(8 a+i) x^2 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{20 b^3}","\frac{\sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2} \left(-2 \left(-36 a^2-14 i a+13\right) b x-96 a^3-86 i a^2+114 a+19 i\right)}{120 b^5}+\frac{\left(8 i a^4-16 a^3-24 i a^2+12 a+3 i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^5}+\frac{\left(8 a^4+16 i a^3-24 a^2-12 i a+3\right) \sinh ^{-1}(a+b x)}{8 b^5}+\frac{x^3 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{5 b^2}-\frac{(8 a+i) x^2 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{20 b^3}",1,"((3*I + 12*a - (24*I)*a^2 - 16*a^3 + (8*I)*a^4)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(8*b^5) - ((I + 8*a)*x^2*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(20*b^3) + (x^3*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(5*b^2) + (Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2)*(19*I + 114*a - (86*I)*a^2 - 96*a^3 - 2*(13 - (14*I)*a - 36*a^2)*b*x))/(120*b^5) + ((3 - (12*I)*a - 24*a^2 + (16*I)*a^3 + 8*a^4)*ArcSinh[a + b*x])/(8*b^5)","A",8,8,16,0.5000,1,"{5095, 100, 153, 147, 50, 53, 619, 215}"
163,1,201,0,0.1924152,"\int e^{i \tan ^{-1}(a+b x)} x^3 \, dx","Int[E^(I*ArcTan[a + b*x])*x^3,x]","-\frac{\sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2} \left(-18 a^2+2 (6 a+i) b x-10 i a+7\right)}{24 b^4}-\frac{\left(8 i a^3-12 a^2-12 i a+3\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^4}+\frac{\left(-8 a^3-12 i a^2+12 a+3 i\right) \sinh ^{-1}(a+b x)}{8 b^4}+\frac{x^2 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{4 b^2}","-\frac{\sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2} \left(-18 a^2+2 (6 a+i) b x-10 i a+7\right)}{24 b^4}-\frac{\left(8 i a^3-12 a^2-12 i a+3\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^4}+\frac{\left(-8 a^3-12 i a^2+12 a+3 i\right) \sinh ^{-1}(a+b x)}{8 b^4}+\frac{x^2 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{4 b^2}",1,"-((3 - (12*I)*a - 12*a^2 + (8*I)*a^3)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(8*b^4) + (x^2*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(4*b^2) - (Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2)*(7 - (10*I)*a - 18*a^2 + 2*(I + 6*a)*b*x))/(24*b^4) + ((3*I + 12*a - (12*I)*a^2 - 8*a^3)*ArcSinh[a + b*x])/(8*b^4)","A",7,7,16,0.4375,1,"{5095, 100, 147, 50, 53, 619, 215}"
164,1,171,0,0.1250076,"\int e^{i \tan ^{-1}(a+b x)} x^2 \, dx","Int[E^(I*ArcTan[a + b*x])*x^2,x]","-\frac{\left(-2 i a^2+2 a+i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 b^3}-\frac{\left(-2 a^2-2 i a+1\right) \sinh ^{-1}(a+b x)}{2 b^3}+\frac{x \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{3 b^2}-\frac{(4 a+i) \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{6 b^3}","-\frac{\left(-2 i a^2+2 a+i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 b^3}-\frac{\left(-2 a^2-2 i a+1\right) \sinh ^{-1}(a+b x)}{2 b^3}+\frac{x \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{3 b^2}-\frac{(4 a+i) \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{6 b^3}",1,"-((I + 2*a - (2*I)*a^2)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(2*b^3) - ((I + 4*a)*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(6*b^3) + (x*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(3*b^2) - ((1 - (2*I)*a - 2*a^2)*ArcSinh[a + b*x])/(2*b^3)","A",7,7,16,0.4375,1,"{5095, 90, 80, 50, 53, 619, 215}"
165,1,110,0,0.0753336,"\int e^{i \tan ^{-1}(a+b x)} x \, dx","Int[E^(I*ArcTan[a + b*x])*x,x]","\frac{\sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{2 b^2}+\frac{(1-2 i a) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 b^2}-\frac{(2 a+i) \sinh ^{-1}(a+b x)}{2 b^2}","\frac{\sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{2 b^2}+\frac{(1-2 i a) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 b^2}-\frac{(2 a+i) \sinh ^{-1}(a+b x)}{2 b^2}",1,"((1 - (2*I)*a)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(2*b^2) + (Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(2*b^2) - ((I + 2*a)*ArcSinh[a + b*x])/(2*b^2)","A",6,6,14,0.4286,1,"{5095, 80, 50, 53, 619, 215}"
166,1,52,0,0.0337835,"\int e^{i \tan ^{-1}(a+b x)} \, dx","Int[E^(I*ArcTan[a + b*x]),x]","\frac{\sinh ^{-1}(a+b x)}{b}+\frac{i \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{b}","\frac{\sinh ^{-1}(a+b x)}{b}+\frac{i \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{b}",1,"(I*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/b + ArcSinh[a + b*x]/b","A",5,5,12,0.4167,1,"{5093, 50, 53, 619, 215}"
167,1,89,0,0.0751899,"\int \frac{e^{i \tan ^{-1}(a+b x)}}{x} \, dx","Int[E^(I*ArcTan[a + b*x])/x,x]","i \sinh ^{-1}(a+b x)-\frac{2 \sqrt{-a+i} \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{\sqrt{a+i}}","i \sinh ^{-1}(a+b x)-\frac{2 \sqrt{-a+i} \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{\sqrt{a+i}}",1,"I*ArcSinh[a + b*x] - (2*Sqrt[I - a]*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/Sqrt[I + a]","A",7,7,16,0.4375,1,"{5095, 105, 53, 619, 215, 93, 208}"
168,1,130,0,0.0640981,"\int \frac{e^{i \tan ^{-1}(a+b x)}}{x^2} \, dx","Int[E^(I*ArcTan[a + b*x])/x^2,x]","\frac{2 i b \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{\sqrt{-a+i} (a+i)^{3/2}}-\frac{\sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{(1-i a) x}","\frac{2 i b \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{\sqrt{-a+i} (a+i)^{3/2}}-\frac{\sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{(1-i a) x}",1,"-((Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/((1 - I*a)*x)) + ((2*I)*b*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/(Sqrt[I - a]*(I + a)^(3/2))","A",4,4,16,0.2500,1,"{5095, 94, 93, 208}"
169,1,201,0,0.1377467,"\int \frac{e^{i \tan ^{-1}(a+b x)}}{x^3} \, dx","Int[E^(I*ArcTan[a + b*x])/x^3,x]","-\frac{\sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{2 \left(a^2+1\right) x^2}+\frac{(1+2 i a) b^2 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{3/2} (a+i)^{5/2}}-\frac{(1+2 i a) b \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 (-a+i) (a+i)^2 x}","-\frac{\sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{2 \left(a^2+1\right) x^2}+\frac{(1+2 i a) b^2 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{3/2} (a+i)^{5/2}}-\frac{(1+2 i a) b \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 (-a+i) (a+i)^2 x}",1,"-((1 + (2*I)*a)*b*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(2*(I - a)*(I + a)^2*x) - (Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(2*(1 + a^2)*x^2) + ((1 + (2*I)*a)*b^2*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/((I - a)^(3/2)*(I + a)^(5/2))","A",5,5,16,0.3125,1,"{5095, 96, 94, 93, 208}"
170,1,283,0,0.1832575,"\int \frac{e^{i \tan ^{-1}(a+b x)}}{x^4} \, dx","Int[E^(I*ArcTan[a + b*x])/x^4,x]","\frac{\left(-2 a^2+9 i a+4\right) b^2 \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{6 (1-i a) \left(a^2+1\right)^2 x}+\frac{\left(2 a-i \left(1-2 a^2\right)\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{5/2} (a+i)^{7/2}}-\frac{(-2 a+3 i) b \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{6 (1-i a) \left(a^2+1\right) x^2}-\frac{\sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{3 (1-i a) x^3}","\frac{\left(-2 a^2+9 i a+4\right) b^2 \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{6 (1-i a) \left(a^2+1\right)^2 x}+\frac{\left(2 a-i \left(1-2 a^2\right)\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{5/2} (a+i)^{7/2}}-\frac{(-2 a+3 i) b \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{6 (1-i a) \left(a^2+1\right) x^2}-\frac{\sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{3 (1-i a) x^3}",1,"-(Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(3*(1 - I*a)*x^3) - ((3*I - 2*a)*b*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(6*(1 - I*a)*(1 + a^2)*x^2) + ((4 + (9*I)*a - 2*a^2)*b^2*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(6*(1 - I*a)*(1 + a^2)^2*x) + ((2*a - I*(1 - 2*a^2))*b^3*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/((I - a)^(5/2)*(I + a)^(7/2))","A",7,6,16,0.3750,1,"{5095, 99, 151, 12, 93, 208}"
171,1,92,0,0.0828601,"\int e^{2 i \tan ^{-1}(a+b x)} x^4 \, dx","Int[E^((2*I)*ArcTan[a + b*x])*x^4,x]","\frac{2 (1-i a) x^3}{3 b^2}+\frac{i (a+i)^2 x^2}{b^3}-\frac{2 (1-i a)^3 x}{b^4}+\frac{2 i (a+i)^4 \log (a+b x+i)}{b^5}+\frac{i x^4}{2 b}-\frac{x^5}{5}","\frac{2 (1-i a) x^3}{3 b^2}+\frac{i (a+i)^2 x^2}{b^3}-\frac{2 (1-i a)^3 x}{b^4}+\frac{2 i (a+i)^4 \log (a+b x+i)}{b^5}+\frac{i x^4}{2 b}-\frac{x^5}{5}",1,"(-2*(1 - I*a)^3*x)/b^4 + (I*(I + a)^2*x^2)/b^3 + (2*(1 - I*a)*x^3)/(3*b^2) + ((I/2)*x^4)/b - x^5/5 + ((2*I)*(I + a)^4*Log[I + a + b*x])/b^5","A",3,2,16,0.1250,1,"{5095, 77}"
172,1,72,0,0.0586489,"\int e^{2 i \tan ^{-1}(a+b x)} x^3 \, dx","Int[E^((2*I)*ArcTan[a + b*x])*x^3,x]","\frac{(1-i a) x^2}{b^2}+\frac{2 i (a+i)^2 x}{b^3}-\frac{2 (1-i a)^3 \log (a+b x+i)}{b^4}+\frac{2 i x^3}{3 b}-\frac{x^4}{4}","\frac{(1-i a) x^2}{b^2}+\frac{2 i (a+i)^2 x}{b^3}-\frac{2 (1-i a)^3 \log (a+b x+i)}{b^4}+\frac{2 i x^3}{3 b}-\frac{x^4}{4}",1,"((2*I)*(I + a)^2*x)/b^3 + ((1 - I*a)*x^2)/b^2 + (((2*I)/3)*x^3)/b - x^4/4 - (2*(1 - I*a)^3*Log[I + a + b*x])/b^4","A",3,2,16,0.1250,1,"{5095, 77}"
173,1,54,0,0.0478082,"\int e^{2 i \tan ^{-1}(a+b x)} x^2 \, dx","Int[E^((2*I)*ArcTan[a + b*x])*x^2,x]","\frac{2 (1-i a) x}{b^2}+\frac{2 i (a+i)^2 \log (a+b x+i)}{b^3}+\frac{i x^2}{b}-\frac{x^3}{3}","\frac{2 (1-i a) x}{b^2}+\frac{2 i (a+i)^2 \log (a+b x+i)}{b^3}+\frac{i x^2}{b}-\frac{x^3}{3}",1,"(2*(1 - I*a)*x)/b^2 + (I*x^2)/b - x^3/3 + ((2*I)*(I + a)^2*Log[I + a + b*x])/b^3","A",3,2,16,0.1250,1,"{5095, 77}"
174,1,37,0,0.0300955,"\int e^{2 i \tan ^{-1}(a+b x)} x \, dx","Int[E^((2*I)*ArcTan[a + b*x])*x,x]","\frac{2 (1-i a) \log (a+b x+i)}{b^2}+\frac{2 i x}{b}-\frac{x^2}{2}","\frac{2 (1-i a) \log (a+b x+i)}{b^2}+\frac{2 i x}{b}-\frac{x^2}{2}",1,"((2*I)*x)/b - x^2/2 + (2*(1 - I*a)*Log[I + a + b*x])/b^2","A",3,2,14,0.1429,1,"{5095, 77}"
175,1,20,0,0.0118928,"\int e^{2 i \tan ^{-1}(a+b x)} \, dx","Int[E^((2*I)*ArcTan[a + b*x]),x]","-x+\frac{2 i \log (a+b x+i)}{b}","-x+\frac{2 i \log (a+b x+i)}{b}",1,"-x + ((2*I)*Log[I + a + b*x])/b","A",3,2,12,0.1667,1,"{5093, 43}"
176,1,38,0,0.0339896,"\int \frac{e^{2 i \tan ^{-1}(a+b x)}}{x} \, dx","Int[E^((2*I)*ArcTan[a + b*x])/x,x]","\frac{(-a+i) \log (x)}{a+i}-\frac{2 \log (a+b x+i)}{1-i a}","\frac{(-a+i) \log (x)}{a+i}-\frac{2 \log (a+b x+i)}{1-i a}",1,"((I - a)*Log[x])/(I + a) - (2*Log[I + a + b*x])/(1 - I*a)","A",3,2,16,0.1250,1,"{5095, 72}"
177,1,55,0,0.0413953,"\int \frac{e^{2 i \tan ^{-1}(a+b x)}}{x^2} \, dx","Int[E^((2*I)*ArcTan[a + b*x])/x^2,x]","-\frac{2 i b \log (x)}{(a+i)^2}+\frac{2 i b \log (a+b x+i)}{(a+i)^2}-\frac{-a+i}{(a+i) x}","-\frac{2 i b \log (x)}{(a+i)^2}+\frac{2 i b \log (a+b x+i)}{(a+i)^2}-\frac{-a+i}{(a+i) x}",1,"-((I - a)/((I + a)*x)) - ((2*I)*b*Log[x])/(I + a)^2 + ((2*I)*b*Log[I + a + b*x])/(I + a)^2","A",3,2,16,0.1250,1,"{5095, 77}"
178,1,76,0,0.0492248,"\int \frac{e^{2 i \tan ^{-1}(a+b x)}}{x^3} \, dx","Int[E^((2*I)*ArcTan[a + b*x])/x^3,x]","-\frac{2 b^2 \log (x)}{(1-i a)^3}+\frac{2 b^2 \log (a+b x+i)}{(1-i a)^3}+\frac{2 i b}{(a+i)^2 x}-\frac{-a+i}{2 (a+i) x^2}","-\frac{2 b^2 \log (x)}{(1-i a)^3}+\frac{2 b^2 \log (a+b x+i)}{(1-i a)^3}+\frac{2 i b}{(a+i)^2 x}-\frac{-a+i}{2 (a+i) x^2}",1,"-(I - a)/(2*(I + a)*x^2) + ((2*I)*b)/((I + a)^2*x) - (2*b^2*Log[x])/(1 - I*a)^3 + (2*b^2*Log[I + a + b*x])/(1 - I*a)^3","A",3,2,16,0.1250,1,"{5095, 77}"
179,1,93,0,0.0564335,"\int \frac{e^{2 i \tan ^{-1}(a+b x)}}{x^4} \, dx","Int[E^((2*I)*ArcTan[a + b*x])/x^4,x]","\frac{2 b^2}{(1-i a)^3 x}-\frac{2 i b^3 \log (x)}{(a+i)^4}+\frac{2 i b^3 \log (a+b x+i)}{(a+i)^4}+\frac{i b}{(a+i)^2 x^2}-\frac{-a+i}{3 (a+i) x^3}","\frac{2 b^2}{(1-i a)^3 x}-\frac{2 i b^3 \log (x)}{(a+i)^4}+\frac{2 i b^3 \log (a+b x+i)}{(a+i)^4}+\frac{i b}{(a+i)^2 x^2}-\frac{-a+i}{3 (a+i) x^3}",1,"-(I - a)/(3*(I + a)*x^3) + (I*b)/((I + a)^2*x^2) + (2*b^2)/((1 - I*a)^3*x) - ((2*I)*b^3*Log[x])/(I + a)^4 + ((2*I)*b^3*Log[I + a + b*x])/(I + a)^4","A",3,2,16,0.1250,1,"{5095, 77}"
180,1,324,0,0.2669297,"\int e^{3 i \tan ^{-1}(a+b x)} x^4 \, dx","Int[E^((3*I)*ArcTan[a + b*x])*x^4,x]","-\frac{i \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2} \left(2 \left(-52 i a^2+118 a+61 i\right) b x+112 i a^3-422 a^2-458 i a+163\right)}{40 b^5}-\frac{3 \left(8 i a^4-48 a^3-88 i a^2+68 a+19 i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^5}-\frac{3 \left(8 a^4+48 i a^3-88 a^2-68 i a+19\right) \sinh ^{-1}(a+b x)}{8 b^5}-\frac{11 x^3 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{5 b^2}+\frac{3 (16 a+17 i) x^2 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{20 b^3}-\frac{2 i x^4 (i a+i b x+1)^{3/2}}{b \sqrt{-i a-i b x+1}}","-\frac{i \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2} \left(2 \left(-52 i a^2+118 a+61 i\right) b x+112 i a^3-422 a^2-458 i a+163\right)}{40 b^5}-\frac{3 \left(8 i a^4-48 a^3-88 i a^2+68 a+19 i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^5}-\frac{3 \left(8 a^4+48 i a^3-88 a^2-68 i a+19\right) \sinh ^{-1}(a+b x)}{8 b^5}-\frac{11 x^3 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{5 b^2}+\frac{3 (16 a+17 i) x^2 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{20 b^3}-\frac{2 i x^4 (i a+i b x+1)^{3/2}}{b \sqrt{-i a-i b x+1}}",1,"(-3*(19*I + 68*a - (88*I)*a^2 - 48*a^3 + (8*I)*a^4)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(8*b^5) - ((2*I)*x^4*(1 + I*a + I*b*x)^(3/2))/(b*Sqrt[1 - I*a - I*b*x]) + (3*(17*I + 16*a)*x^2*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(20*b^3) - (11*x^3*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(5*b^2) - ((I/40)*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2)*(163 - (458*I)*a - 422*a^2 + (112*I)*a^3 + 2*(61*I + 118*a - (52*I)*a^2)*b*x))/b^5 - (3*(19 - (68*I)*a - 88*a^2 + (48*I)*a^3 + 8*a^4)*ArcSinh[a + b*x])/(8*b^5)","A",9,8,16,0.5000,1,"{5095, 97, 153, 147, 50, 53, 619, 215}"
181,1,249,0,0.2423325,"\int e^{3 i \tan ^{-1}(a+b x)} x^3 \, dx","Int[E^((3*I)*ArcTan[a + b*x])*x^3,x]","-\frac{i \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2} \left(-22 i a^2-2 (11-10 i a) b x+54 a+29 i\right)}{8 b^4}+\frac{3 \left(8 i a^3-36 a^2-44 i a+17\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^4}-\frac{3 \left(-8 a^3-36 i a^2+44 a+17 i\right) \sinh ^{-1}(a+b x)}{8 b^4}-\frac{9 x^2 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{4 b^2}-\frac{2 i x^3 (i a+i b x+1)^{3/2}}{b \sqrt{-i a-i b x+1}}","-\frac{i \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2} \left(-22 i a^2-2 (11-10 i a) b x+54 a+29 i\right)}{8 b^4}+\frac{3 \left(8 i a^3-36 a^2-44 i a+17\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^4}-\frac{3 \left(-8 a^3-36 i a^2+44 a+17 i\right) \sinh ^{-1}(a+b x)}{8 b^4}-\frac{9 x^2 \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{4 b^2}-\frac{2 i x^3 (i a+i b x+1)^{3/2}}{b \sqrt{-i a-i b x+1}}",1,"(3*(17 - (44*I)*a - 36*a^2 + (8*I)*a^3)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(8*b^4) - ((2*I)*x^3*(1 + I*a + I*b*x)^(3/2))/(b*Sqrt[1 - I*a - I*b*x]) - (9*x^2*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(4*b^2) - ((I/8)*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2)*(29*I + 54*a - (22*I)*a^2 - 2*(11 - (10*I)*a)*b*x))/b^4 - (3*(17*I + 44*a - (36*I)*a^2 - 8*a^3)*ArcSinh[a + b*x])/(8*b^4)","A",8,8,16,0.5000,1,"{5095, 97, 153, 147, 50, 53, 619, 215}"
182,1,227,0,0.1692393,"\int e^{3 i \tan ^{-1}(a+b x)} x^2 \, dx","Int[E^((3*I)*ArcTan[a + b*x])*x^2,x]","\frac{\left(-6 i a^2+18 a+11 i\right) \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{6 b^3}+\frac{\left(-6 i a^2+18 a+11 i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 b^3}+\frac{\left(-6 a^2-18 i a+11\right) \sinh ^{-1}(a+b x)}{2 b^3}+\frac{i \sqrt{-i a-i b x+1} (i a+i b x+1)^{5/2}}{3 b^3}-\frac{i (a+i)^2 (i a+i b x+1)^{5/2}}{b^3 \sqrt{-i a-i b x+1}}","\frac{\left(-6 i a^2+18 a+11 i\right) \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{6 b^3}+\frac{\left(-6 i a^2+18 a+11 i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 b^3}+\frac{\left(-6 a^2-18 i a+11\right) \sinh ^{-1}(a+b x)}{2 b^3}+\frac{i \sqrt{-i a-i b x+1} (i a+i b x+1)^{5/2}}{3 b^3}-\frac{i (a+i)^2 (i a+i b x+1)^{5/2}}{b^3 \sqrt{-i a-i b x+1}}",1,"((11*I + 18*a - (6*I)*a^2)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(2*b^3) + ((11*I + 18*a - (6*I)*a^2)*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(6*b^3) - (I*(I + a)^2*(1 + I*a + I*b*x)^(5/2))/(b^3*Sqrt[1 - I*a - I*b*x]) + ((I/3)*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(5/2))/b^3 + ((11 - (18*I)*a - 6*a^2)*ArcSinh[a + b*x])/(2*b^3)","A",8,7,16,0.4375,1,"{5095, 89, 80, 50, 53, 619, 215}"
183,1,163,0,0.1196577,"\int e^{3 i \tan ^{-1}(a+b x)} x \, dx","Int[E^((3*I)*ArcTan[a + b*x])*x,x]","-\frac{(1-i a) (i a+i b x+1)^{5/2}}{b^2 \sqrt{-i a-i b x+1}}-\frac{(3-2 i a) \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{2 b^2}-\frac{3 (3-2 i a) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 b^2}+\frac{3 (2 a+3 i) \sinh ^{-1}(a+b x)}{2 b^2}","-\frac{(1-i a) (i a+i b x+1)^{5/2}}{b^2 \sqrt{-i a-i b x+1}}-\frac{(3-2 i a) \sqrt{-i a-i b x+1} (i a+i b x+1)^{3/2}}{2 b^2}-\frac{3 (3-2 i a) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 b^2}+\frac{3 (2 a+3 i) \sinh ^{-1}(a+b x)}{2 b^2}",1,"(-3*(3 - (2*I)*a)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(2*b^2) - ((3 - (2*I)*a)*Sqrt[1 - I*a - I*b*x]*(1 + I*a + I*b*x)^(3/2))/(2*b^2) - ((1 - I*a)*(1 + I*a + I*b*x)^(5/2))/(b^2*Sqrt[1 - I*a - I*b*x]) + (3*(3*I + 2*a)*ArcSinh[a + b*x])/(2*b^2)","A",7,6,14,0.4286,1,"{5095, 78, 50, 53, 619, 215}"
184,1,94,0,0.0418089,"\int e^{3 i \tan ^{-1}(a+b x)} \, dx","Int[E^((3*I)*ArcTan[a + b*x]),x]","-\frac{2 i (i a+i b x+1)^{3/2}}{b \sqrt{-i a-i b x+1}}-\frac{3 i \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{b}-\frac{3 \sinh ^{-1}(a+b x)}{b}","-\frac{2 i (i a+i b x+1)^{3/2}}{b \sqrt{-i a-i b x+1}}-\frac{3 i \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{b}-\frac{3 \sinh ^{-1}(a+b x)}{b}",1,"((-3*I)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/b - ((2*I)*(1 + I*a + I*b*x)^(3/2))/(b*Sqrt[1 - I*a - I*b*x]) - (3*ArcSinh[a + b*x])/b","A",6,6,12,0.5000,1,"{5093, 47, 50, 53, 619, 215}"
185,1,134,0,0.0950191,"\int \frac{e^{3 i \tan ^{-1}(a+b x)}}{x} \, dx","Int[E^((3*I)*ArcTan[a + b*x])/x,x]","\frac{4 \sqrt{i a+i b x+1}}{(1-i a) \sqrt{-i a-i b x+1}}-i \sinh ^{-1}(a+b x)-\frac{2 (-a+i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(a+i)^{3/2}}","\frac{4 \sqrt{i a+i b x+1}}{(1-i a) \sqrt{-i a-i b x+1}}-i \sinh ^{-1}(a+b x)-\frac{2 (-a+i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(a+i)^{3/2}}",1,"(4*Sqrt[1 + I*a + I*b*x])/((1 - I*a)*Sqrt[1 - I*a - I*b*x]) - I*ArcSinh[a + b*x] - (2*(I - a)^(3/2)*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/(I + a)^(3/2)","A",8,8,16,0.5000,1,"{5095, 98, 157, 53, 619, 215, 93, 208}"
186,1,176,0,0.0833436,"\int \frac{e^{3 i \tan ^{-1}(a+b x)}}{x^2} \, dx","Int[E^((3*I)*ArcTan[a + b*x])/x^2,x]","-\frac{(i a+i b x+1)^{3/2}}{(1-i a) x \sqrt{-i a-i b x+1}}-\frac{6 i b \sqrt{i a+i b x+1}}{(a+i)^2 \sqrt{-i a-i b x+1}}+\frac{6 i \sqrt{-a+i} b \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(a+i)^{5/2}}","-\frac{(i a+i b x+1)^{3/2}}{(1-i a) x \sqrt{-i a-i b x+1}}-\frac{6 i b \sqrt{i a+i b x+1}}{(a+i)^2 \sqrt{-i a-i b x+1}}+\frac{6 i \sqrt{-a+i} b \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(a+i)^{5/2}}",1,"((-6*I)*b*Sqrt[1 + I*a + I*b*x])/((I + a)^2*Sqrt[1 - I*a - I*b*x]) - (1 + I*a + I*b*x)^(3/2)/((1 - I*a)*x*Sqrt[1 - I*a - I*b*x]) + ((6*I)*Sqrt[I - a]*b*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/(I + a)^(5/2)","A",5,4,16,0.2500,1,"{5095, 94, 93, 208}"
187,1,264,0,0.157934,"\int \frac{e^{3 i \tan ^{-1}(a+b x)}}{x^3} \, dx","Int[E^((3*I)*ArcTan[a + b*x])/x^3,x]","-\frac{(i a+i b x+1)^{5/2}}{2 \left(a^2+1\right) x^2 \sqrt{-i a-i b x+1}}+\frac{3 (-2 a+3 i) b^2 \sqrt{i a+i b x+1}}{(1+i a) (a+i)^3 \sqrt{-i a-i b x+1}}+\frac{3 (3+2 i a) b^2 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{\sqrt{-a+i} (a+i)^{7/2}}+\frac{(-2 a+3 i) b (i a+i b x+1)^{3/2}}{2 (1+i a) (a+i)^2 x \sqrt{-i a-i b x+1}}","-\frac{(i a+i b x+1)^{5/2}}{2 \left(a^2+1\right) x^2 \sqrt{-i a-i b x+1}}+\frac{3 (-2 a+3 i) b^2 \sqrt{i a+i b x+1}}{(1+i a) (a+i)^3 \sqrt{-i a-i b x+1}}+\frac{3 (3+2 i a) b^2 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{\sqrt{-a+i} (a+i)^{7/2}}+\frac{(-2 a+3 i) b (i a+i b x+1)^{3/2}}{2 (1+i a) (a+i)^2 x \sqrt{-i a-i b x+1}}",1,"(3*(3*I - 2*a)*b^2*Sqrt[1 + I*a + I*b*x])/((1 + I*a)*(I + a)^3*Sqrt[1 - I*a - I*b*x]) + ((3*I - 2*a)*b*(1 + I*a + I*b*x)^(3/2))/(2*(1 + I*a)*(I + a)^2*x*Sqrt[1 - I*a - I*b*x]) - (1 + I*a + I*b*x)^(5/2)/(2*(1 + a^2)*x^2*Sqrt[1 - I*a - I*b*x]) + (3*(3 + (2*I)*a)*b^2*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/(Sqrt[I - a]*(I + a)^(7/2))","A",6,5,16,0.3125,1,"{5095, 96, 94, 93, 208}"
188,1,338,0,0.269927,"\int \frac{e^{3 i \tan ^{-1}(a+b x)}}{x^4} \, dx","Int[E^((3*I)*ArcTan[a + b*x])/x^4,x]","\frac{\left(-2 a^2+51 i a+52\right) b^3 \sqrt{i a+i b x+1}}{6 (-a+i) (a+i)^4 \sqrt{-i a-i b x+1}}-\frac{\left(-6 i a^2-18 a+11 i\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{3/2} (a+i)^{9/2}}+\frac{(19+16 i a) b^2 \sqrt{i a+i b x+1}}{6 (-a+i) (a+i)^3 x \sqrt{-i a-i b x+1}}+\frac{7 i b \sqrt{i a+i b x+1}}{6 (a+i)^2 x^2 \sqrt{-i a-i b x+1}}-\frac{(-a+i) \sqrt{i a+i b x+1}}{3 (a+i) x^3 \sqrt{-i a-i b x+1}}","\frac{\left(-2 a^2+51 i a+52\right) b^3 \sqrt{i a+i b x+1}}{6 (-a+i) (a+i)^4 \sqrt{-i a-i b x+1}}-\frac{\left(-6 i a^2-18 a+11 i\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{3/2} (a+i)^{9/2}}+\frac{(19+16 i a) b^2 \sqrt{i a+i b x+1}}{6 (-a+i) (a+i)^3 x \sqrt{-i a-i b x+1}}+\frac{7 i b \sqrt{i a+i b x+1}}{6 (a+i)^2 x^2 \sqrt{-i a-i b x+1}}-\frac{(-a+i) \sqrt{i a+i b x+1}}{3 (a+i) x^3 \sqrt{-i a-i b x+1}}",1,"((52 + (51*I)*a - 2*a^2)*b^3*Sqrt[1 + I*a + I*b*x])/(6*(I - a)*(I + a)^4*Sqrt[1 - I*a - I*b*x]) - ((I - a)*Sqrt[1 + I*a + I*b*x])/(3*(I + a)*x^3*Sqrt[1 - I*a - I*b*x]) + (((7*I)/6)*b*Sqrt[1 + I*a + I*b*x])/((I + a)^2*x^2*Sqrt[1 - I*a - I*b*x]) + ((19 + (16*I)*a)*b^2*Sqrt[1 + I*a + I*b*x])/(6*(I - a)*(I + a)^3*x*Sqrt[1 - I*a - I*b*x]) - ((11*I - 18*a - (6*I)*a^2)*b^3*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/((I - a)^(3/2)*(I + a)^(9/2))","A",8,7,16,0.4375,1,"{5095, 98, 151, 152, 12, 93, 208}"
189,1,276,0,0.2247588,"\int e^{-i \tan ^{-1}(a+b x)} x^4 \, dx","Int[x^4/E^(I*ArcTan[a + b*x]),x]","-\frac{(-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1} \left(2 \left(-36 a^2+14 i a+13\right) b x+96 a^3-86 i a^2-114 a+19 i\right)}{120 b^5}-\frac{\left(8 i a^4+16 a^3-24 i a^2-12 a+3 i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^5}+\frac{\left(8 a^4-16 i a^3-24 a^2+12 i a+3\right) \sinh ^{-1}(a+b x)}{8 b^5}+\frac{x^3 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{5 b^2}+\frac{(-8 a+i) x^2 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{20 b^3}","-\frac{(-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1} \left(2 \left(-36 a^2+14 i a+13\right) b x+96 a^3-86 i a^2-114 a+19 i\right)}{120 b^5}-\frac{\left(8 i a^4+16 a^3-24 i a^2-12 a+3 i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^5}+\frac{\left(8 a^4-16 i a^3-24 a^2+12 i a+3\right) \sinh ^{-1}(a+b x)}{8 b^5}+\frac{x^3 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{5 b^2}+\frac{(-8 a+i) x^2 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{20 b^3}",1,"-((3*I - 12*a - (24*I)*a^2 + 16*a^3 + (8*I)*a^4)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(8*b^5) + ((I - 8*a)*x^2*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(20*b^3) + (x^3*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(5*b^2) - ((1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x]*(19*I - 114*a - (86*I)*a^2 + 96*a^3 + 2*(13 + (14*I)*a - 36*a^2)*b*x))/(120*b^5) + ((3 + (12*I)*a - 24*a^2 - (16*I)*a^3 + 8*a^4)*ArcSinh[a + b*x])/(8*b^5)","A",8,8,16,0.5000,1,"{5095, 100, 153, 147, 50, 53, 619, 215}"
190,1,201,0,0.1943443,"\int e^{-i \tan ^{-1}(a+b x)} x^3 \, dx","Int[x^3/E^(I*ArcTan[a + b*x]),x]","-\frac{(-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1} \left(-18 a^2-2 (-6 a+i) b x+10 i a+7\right)}{24 b^4}-\frac{\left(-8 i a^3-12 a^2+12 i a+3\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^4}-\frac{\left(8 a^3-12 i a^2-12 a+3 i\right) \sinh ^{-1}(a+b x)}{8 b^4}+\frac{x^2 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{4 b^2}","-\frac{(-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1} \left(-18 a^2-2 (-6 a+i) b x+10 i a+7\right)}{24 b^4}-\frac{\left(-8 i a^3-12 a^2+12 i a+3\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^4}-\frac{\left(8 a^3-12 i a^2-12 a+3 i\right) \sinh ^{-1}(a+b x)}{8 b^4}+\frac{x^2 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{4 b^2}",1,"-((3 + (12*I)*a - 12*a^2 - (8*I)*a^3)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(8*b^4) + (x^2*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(4*b^2) - ((1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x]*(7 + (10*I)*a - 18*a^2 - 2*(I - 6*a)*b*x))/(24*b^4) - ((3*I - 12*a - (12*I)*a^2 + 8*a^3)*ArcSinh[a + b*x])/(8*b^4)","A",7,7,16,0.4375,1,"{5095, 100, 147, 50, 53, 619, 215}"
191,1,171,0,0.1258678,"\int e^{-i \tan ^{-1}(a+b x)} x^2 \, dx","Int[x^2/E^(I*ArcTan[a + b*x]),x]","\frac{\left(-2 i a^2-2 a+i\right) \sqrt{i a+i b x+1} \sqrt{-i a-i b x+1}}{2 b^3}-\frac{\left(-2 a^2+2 i a+1\right) \sinh ^{-1}(a+b x)}{2 b^3}+\frac{x \sqrt{i a+i b x+1} (-i a-i b x+1)^{3/2}}{3 b^2}+\frac{(-4 a+i) \sqrt{i a+i b x+1} (-i a-i b x+1)^{3/2}}{6 b^3}","\frac{\left(-2 i a^2-2 a+i\right) \sqrt{i a+i b x+1} \sqrt{-i a-i b x+1}}{2 b^3}-\frac{\left(-2 a^2+2 i a+1\right) \sinh ^{-1}(a+b x)}{2 b^3}+\frac{x \sqrt{i a+i b x+1} (-i a-i b x+1)^{3/2}}{3 b^2}+\frac{(-4 a+i) \sqrt{i a+i b x+1} (-i a-i b x+1)^{3/2}}{6 b^3}",1,"((I - 2*a - (2*I)*a^2)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(2*b^3) + ((I - 4*a)*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(6*b^3) + (x*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(3*b^2) - ((1 + (2*I)*a - 2*a^2)*ArcSinh[a + b*x])/(2*b^3)","A",7,7,16,0.4375,1,"{5095, 90, 80, 50, 53, 619, 215}"
192,1,110,0,0.0759064,"\int e^{-i \tan ^{-1}(a+b x)} x \, dx","Int[x/E^(I*ArcTan[a + b*x]),x]","\frac{\sqrt{i a+i b x+1} (-i a-i b x+1)^{3/2}}{2 b^2}+\frac{(1+2 i a) \sqrt{i a+i b x+1} \sqrt{-i a-i b x+1}}{2 b^2}+\frac{(-2 a+i) \sinh ^{-1}(a+b x)}{2 b^2}","\frac{\sqrt{i a+i b x+1} (-i a-i b x+1)^{3/2}}{2 b^2}+\frac{(1+2 i a) \sqrt{i a+i b x+1} \sqrt{-i a-i b x+1}}{2 b^2}+\frac{(-2 a+i) \sinh ^{-1}(a+b x)}{2 b^2}",1,"((1 + (2*I)*a)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(2*b^2) + ((1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(2*b^2) + ((I - 2*a)*ArcSinh[a + b*x])/(2*b^2)","A",6,6,14,0.4286,1,"{5095, 80, 50, 53, 619, 215}"
193,1,52,0,0.0337881,"\int e^{-i \tan ^{-1}(a+b x)} \, dx","Int[E^((-I)*ArcTan[a + b*x]),x]","\frac{\sinh ^{-1}(a+b x)}{b}-\frac{i \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{b}","\frac{\sinh ^{-1}(a+b x)}{b}-\frac{i \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{b}",1,"((-I)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/b + ArcSinh[a + b*x]/b","A",5,5,12,0.4167,1,"{5093, 50, 53, 619, 215}"
194,1,89,0,0.0651262,"\int \frac{e^{-i \tan ^{-1}(a+b x)}}{x} \, dx","Int[1/(E^(I*ArcTan[a + b*x])*x),x]","-i \sinh ^{-1}(a+b x)-\frac{2 \sqrt{a+i} \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{\sqrt{-a+i}}","-i \sinh ^{-1}(a+b x)-\frac{2 \sqrt{a+i} \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{\sqrt{-a+i}}",1,"(-I)*ArcSinh[a + b*x] - (2*Sqrt[I + a]*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/Sqrt[I - a]","A",7,7,16,0.4375,1,"{5095, 105, 53, 619, 215, 93, 208}"
195,1,130,0,0.0635947,"\int \frac{e^{-i \tan ^{-1}(a+b x)}}{x^2} \, dx","Int[1/(E^(I*ArcTan[a + b*x])*x^2),x]","-\frac{\sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{(1+i a) x}-\frac{2 i b \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{3/2} \sqrt{a+i}}","-\frac{\sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{(1+i a) x}-\frac{2 i b \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{3/2} \sqrt{a+i}}",1,"-((Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/((1 + I*a)*x)) - ((2*I)*b*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/((I - a)^(3/2)*Sqrt[I + a])","A",4,4,16,0.2500,1,"{5095, 94, 93, 208}"
196,1,201,0,0.117133,"\int \frac{e^{-i \tan ^{-1}(a+b x)}}{x^3} \, dx","Int[1/(E^(I*ArcTan[a + b*x])*x^3),x]","-\frac{(-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{2 \left(a^2+1\right) x^2}+\frac{(1-2 i a) b^2 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{5/2} (a+i)^{3/2}}+\frac{(1-2 i a) b \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 (-a+i)^2 (a+i) x}","-\frac{(-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{2 \left(a^2+1\right) x^2}+\frac{(1-2 i a) b^2 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{5/2} (a+i)^{3/2}}+\frac{(1-2 i a) b \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{2 (-a+i)^2 (a+i) x}",1,"((1 - (2*I)*a)*b*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(2*(I - a)^2*(I + a)*x) - ((1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(2*(1 + a^2)*x^2) + ((1 - (2*I)*a)*b^2*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/((I - a)^(5/2)*(I + a)^(3/2))","A",5,5,16,0.3125,1,"{5095, 96, 94, 93, 208}"
197,1,282,0,0.1830093,"\int \frac{e^{-i \tan ^{-1}(a+b x)}}{x^4} \, dx","Int[1/(E^(I*ArcTan[a + b*x])*x^4),x]","\frac{\left(-2 a^2-9 i a+4\right) b^2 \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{6 (1+i a) \left(a^2+1\right)^2 x}+\frac{\left(-2 i a^2+2 a+i\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{7/2} (a+i)^{5/2}}+\frac{(3-2 i a) b \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{6 (-a+i)^2 (a+i) x^2}-\frac{\sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{3 (1+i a) x^3}","\frac{\left(-2 a^2-9 i a+4\right) b^2 \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{6 (1+i a) \left(a^2+1\right)^2 x}+\frac{\left(2 a+i \left(1-2 a^2\right)\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{7/2} (a+i)^{5/2}}+\frac{(3-2 i a) b \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{6 (-a+i)^2 (a+i) x^2}-\frac{\sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{3 (1+i a) x^3}",1,"-(Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(3*(1 + I*a)*x^3) + ((3 - (2*I)*a)*b*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(6*(I - a)^2*(I + a)*x^2) + ((4 - (9*I)*a - 2*a^2)*b^2*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(6*(1 + I*a)*(1 + a^2)^2*x) + ((I + 2*a - (2*I)*a^2)*b^3*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/((I - a)^(7/2)*(I + a)^(5/2))","A",7,6,16,0.3750,1,"{5095, 99, 151, 12, 93, 208}"
198,1,99,0,0.0856157,"\int e^{-2 i \tan ^{-1}(a+b x)} x^4 \, dx","Int[x^4/E^((2*I)*ArcTan[a + b*x]),x]","\frac{2 (1+i a) x^3}{3 b^2}-\frac{i (-a+i)^2 x^2}{b^3}-\frac{2 (1+i a)^3 x}{b^4}-\frac{2 i (-a+i)^4 \log (-a-b x+i)}{b^5}-\frac{i x^4}{2 b}-\frac{x^5}{5}","\frac{2 (1+i a) x^3}{3 b^2}-\frac{i (-a+i)^2 x^2}{b^3}-\frac{2 (1+i a)^3 x}{b^4}-\frac{2 i (-a+i)^4 \log (-a-b x+i)}{b^5}-\frac{i x^4}{2 b}-\frac{x^5}{5}",1,"(-2*(1 + I*a)^3*x)/b^4 - (I*(I - a)^2*x^2)/b^3 + (2*(1 + I*a)*x^3)/(3*b^2) - ((I/2)*x^4)/b - x^5/5 - ((2*I)*(I - a)^4*Log[I - a - b*x])/b^5","A",3,2,16,0.1250,1,"{5095, 77}"
199,1,77,0,0.0592766,"\int e^{-2 i \tan ^{-1}(a+b x)} x^3 \, dx","Int[x^3/E^((2*I)*ArcTan[a + b*x]),x]","\frac{(1+i a) x^2}{b^2}-\frac{2 i (-a+i)^2 x}{b^3}-\frac{2 (1+i a)^3 \log (-a-b x+i)}{b^4}-\frac{2 i x^3}{3 b}-\frac{x^4}{4}","\frac{(1+i a) x^2}{b^2}-\frac{2 i (-a+i)^2 x}{b^3}-\frac{2 (1+i a)^3 \log (-a-b x+i)}{b^4}-\frac{2 i x^3}{3 b}-\frac{x^4}{4}",1,"((-2*I)*(I - a)^2*x)/b^3 + ((1 + I*a)*x^2)/b^2 - (((2*I)/3)*x^3)/b - x^4/4 - (2*(1 + I*a)^3*Log[I - a - b*x])/b^4","A",3,2,16,0.1250,1,"{5095, 77}"
200,1,59,0,0.047512,"\int e^{-2 i \tan ^{-1}(a+b x)} x^2 \, dx","Int[x^2/E^((2*I)*ArcTan[a + b*x]),x]","\frac{2 (1+i a) x}{b^2}-\frac{2 i (-a+i)^2 \log (-a-b x+i)}{b^3}-\frac{i x^2}{b}-\frac{x^3}{3}","\frac{2 (1+i a) x}{b^2}-\frac{2 i (-a+i)^2 \log (-a-b x+i)}{b^3}-\frac{i x^2}{b}-\frac{x^3}{3}",1,"(2*(1 + I*a)*x)/b^2 - (I*x^2)/b - x^3/3 - ((2*I)*(I - a)^2*Log[I - a - b*x])/b^3","A",3,2,16,0.1250,1,"{5095, 77}"
201,1,40,0,0.0317712,"\int e^{-2 i \tan ^{-1}(a+b x)} x \, dx","Int[x/E^((2*I)*ArcTan[a + b*x]),x]","\frac{2 (1+i a) \log (-a-b x+i)}{b^2}-\frac{2 i x}{b}-\frac{x^2}{2}","\frac{2 (1+i a) \log (-a-b x+i)}{b^2}-\frac{2 i x}{b}-\frac{x^2}{2}",1,"((-2*I)*x)/b - x^2/2 + (2*(1 + I*a)*Log[I - a - b*x])/b^2","A",3,2,14,0.1429,1,"{5095, 77}"
202,1,23,0,0.0125188,"\int e^{-2 i \tan ^{-1}(a+b x)} \, dx","Int[E^((-2*I)*ArcTan[a + b*x]),x]","-x-\frac{2 i \log (-a-b x+i)}{b}","-x-\frac{2 i \log (-a-b x+i)}{b}",1,"-x - ((2*I)*Log[I - a - b*x])/b","A",3,2,12,0.1667,1,"{5093, 43}"
203,1,41,0,0.0356451,"\int \frac{e^{-2 i \tan ^{-1}(a+b x)}}{x} \, dx","Int[1/(E^((2*I)*ArcTan[a + b*x])*x),x]","\frac{(a+i) \log (x)}{-a+i}-\frac{2 \log (-a-b x+i)}{1+i a}","\frac{(a+i) \log (x)}{-a+i}-\frac{2 \log (-a-b x+i)}{1+i a}",1,"((I + a)*Log[x])/(I - a) - (2*Log[I - a - b*x])/(1 + I*a)","A",3,2,16,0.1250,1,"{5095, 72}"
204,1,62,0,0.0423323,"\int \frac{e^{-2 i \tan ^{-1}(a+b x)}}{x^2} \, dx","Int[1/(E^((2*I)*ArcTan[a + b*x])*x^2),x]","\frac{2 i b \log (x)}{(-a+i)^2}-\frac{2 i b \log (-a-b x+i)}{(-a+i)^2}-\frac{a+i}{(-a+i) x}","\frac{2 i b \log (x)}{(-a+i)^2}-\frac{2 i b \log (-a-b x+i)}{(-a+i)^2}-\frac{a+i}{(-a+i) x}",1,"-((I + a)/((I - a)*x)) + ((2*I)*b*Log[x])/(I - a)^2 - ((2*I)*b*Log[I - a - b*x])/(I - a)^2","A",3,2,16,0.1250,1,"{5095, 77}"
205,1,81,0,0.0516425,"\int \frac{e^{-2 i \tan ^{-1}(a+b x)}}{x^3} \, dx","Int[1/(E^((2*I)*ArcTan[a + b*x])*x^3),x]","-\frac{2 b^2 \log (x)}{(1+i a)^3}+\frac{2 b^2 \log (-a-b x+i)}{(1+i a)^3}-\frac{2 i b}{(-a+i)^2 x}-\frac{a+i}{2 (-a+i) x^2}","-\frac{2 b^2 \log (x)}{(1+i a)^3}+\frac{2 b^2 \log (-a-b x+i)}{(1+i a)^3}-\frac{2 i b}{(-a+i)^2 x}-\frac{a+i}{2 (-a+i) x^2}",1,"-(I + a)/(2*(I - a)*x^2) - ((2*I)*b)/((I - a)^2*x) - (2*b^2*Log[x])/(1 + I*a)^3 + (2*b^2*Log[I - a - b*x])/(1 + I*a)^3","A",3,2,16,0.1250,1,"{5095, 77}"
206,1,102,0,0.0606169,"\int \frac{e^{-2 i \tan ^{-1}(a+b x)}}{x^4} \, dx","Int[1/(E^((2*I)*ArcTan[a + b*x])*x^4),x]","\frac{2 b^2}{(1+i a)^3 x}+\frac{2 i b^3 \log (x)}{(-a+i)^4}-\frac{2 i b^3 \log (-a-b x+i)}{(-a+i)^4}-\frac{i b}{(-a+i)^2 x^2}-\frac{a+i}{3 (-a+i) x^3}","\frac{2 b^2}{(1+i a)^3 x}+\frac{2 i b^3 \log (x)}{(-a+i)^4}-\frac{2 i b^3 \log (-a-b x+i)}{(-a+i)^4}-\frac{i b}{(-a+i)^2 x^2}-\frac{a+i}{3 (-a+i) x^3}",1,"-(I + a)/(3*(I - a)*x^3) - (I*b)/((I - a)^2*x^2) + (2*b^2)/((1 + I*a)^3*x) + ((2*I)*b^3*Log[x])/(I - a)^4 - ((2*I)*b^3*Log[I - a - b*x])/(I - a)^4","A",3,2,16,0.1250,1,"{5095, 77}"
207,1,324,0,0.2812988,"\int e^{-3 i \tan ^{-1}(a+b x)} x^4 \, dx","Int[x^4/E^((3*I)*ArcTan[a + b*x]),x]","\frac{i (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1} \left(-2 \left(-52 i a^2-118 a+61 i\right) b x-112 i a^3-422 a^2+458 i a+163\right)}{40 b^5}+\frac{3 \left(8 i a^4+48 a^3-88 i a^2-68 a+19 i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^5}-\frac{3 \left(8 a^4-48 i a^3-88 a^2+68 i a+19\right) \sinh ^{-1}(a+b x)}{8 b^5}-\frac{11 x^3 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{5 b^2}-\frac{3 (-16 a+17 i) x^2 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{20 b^3}+\frac{2 i x^4 (-i a-i b x+1)^{3/2}}{b \sqrt{i a+i b x+1}}","\frac{i (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1} \left(-2 \left(-52 i a^2-118 a+61 i\right) b x-112 i a^3-422 a^2+458 i a+163\right)}{40 b^5}+\frac{3 \left(8 i a^4+48 a^3-88 i a^2-68 a+19 i\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^5}-\frac{3 \left(8 a^4-48 i a^3-88 a^2+68 i a+19\right) \sinh ^{-1}(a+b x)}{8 b^5}-\frac{11 x^3 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{5 b^2}-\frac{3 (-16 a+17 i) x^2 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{20 b^3}+\frac{2 i x^4 (-i a-i b x+1)^{3/2}}{b \sqrt{i a+i b x+1}}",1,"((2*I)*x^4*(1 - I*a - I*b*x)^(3/2))/(b*Sqrt[1 + I*a + I*b*x]) + (3*(19*I - 68*a - (88*I)*a^2 + 48*a^3 + (8*I)*a^4)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(8*b^5) - (3*(17*I - 16*a)*x^2*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(20*b^3) - (11*x^3*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(5*b^2) + ((I/40)*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x]*(163 + (458*I)*a - 422*a^2 - (112*I)*a^3 - 2*(61*I - 118*a - (52*I)*a^2)*b*x))/b^5 - (3*(19 + (68*I)*a - 88*a^2 - (48*I)*a^3 + 8*a^4)*ArcSinh[a + b*x])/(8*b^5)","A",9,8,16,0.5000,1,"{5095, 97, 153, 147, 50, 53, 619, 215}"
208,1,249,0,0.2455145,"\int e^{-3 i \tan ^{-1}(a+b x)} x^3 \, dx","Int[x^3/E^((3*I)*ArcTan[a + b*x]),x]","-\frac{i (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1} \left(-22 i a^2+2 (11+10 i a) b x-54 a+29 i\right)}{8 b^4}+\frac{3 \left(-8 i a^3-36 a^2+44 i a+17\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^4}+\frac{3 \left(8 a^3-36 i a^2-44 a+17 i\right) \sinh ^{-1}(a+b x)}{8 b^4}-\frac{9 x^2 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{4 b^2}+\frac{2 i x^3 (-i a-i b x+1)^{3/2}}{b \sqrt{i a+i b x+1}}","-\frac{i (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1} \left(-22 i a^2+2 (11+10 i a) b x-54 a+29 i\right)}{8 b^4}+\frac{3 \left(-8 i a^3-36 a^2+44 i a+17\right) \sqrt{-i a-i b x+1} \sqrt{i a+i b x+1}}{8 b^4}+\frac{3 \left(8 a^3-36 i a^2-44 a+17 i\right) \sinh ^{-1}(a+b x)}{8 b^4}-\frac{9 x^2 (-i a-i b x+1)^{3/2} \sqrt{i a+i b x+1}}{4 b^2}+\frac{2 i x^3 (-i a-i b x+1)^{3/2}}{b \sqrt{i a+i b x+1}}",1,"((2*I)*x^3*(1 - I*a - I*b*x)^(3/2))/(b*Sqrt[1 + I*a + I*b*x]) + (3*(17 + (44*I)*a - 36*a^2 - (8*I)*a^3)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(8*b^4) - (9*x^2*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(4*b^2) - ((I/8)*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x]*(29*I - 54*a - (22*I)*a^2 + 2*(11 + (10*I)*a)*b*x))/b^4 + (3*(17*I - 44*a - (36*I)*a^2 + 8*a^3)*ArcSinh[a + b*x])/(8*b^4)","A",8,8,16,0.5000,1,"{5095, 97, 153, 147, 50, 53, 619, 215}"
209,1,229,0,0.1682347,"\int e^{-3 i \tan ^{-1}(a+b x)} x^2 \, dx","Int[x^2/E^((3*I)*ArcTan[a + b*x]),x]","-\frac{\left(-6 i a^2-18 a+11 i\right) \sqrt{i a+i b x+1} (-i a-i b x+1)^{3/2}}{6 b^3}-\frac{\left(-6 i a^2-18 a+11 i\right) \sqrt{i a+i b x+1} \sqrt{-i a-i b x+1}}{2 b^3}+\frac{\left(-6 a^2+18 i a+11\right) \sinh ^{-1}(a+b x)}{2 b^3}-\frac{i \sqrt{i a+i b x+1} (-i a-i b x+1)^{5/2}}{3 b^3}+\frac{i (-a+i)^2 (-i a-i b x+1)^{5/2}}{b^3 \sqrt{i a+i b x+1}}","-\frac{\left(-6 i a^2-18 a+11 i\right) \sqrt{i a+i b x+1} (-i a-i b x+1)^{3/2}}{6 b^3}-\frac{\left(-6 i a^2-18 a+11 i\right) \sqrt{i a+i b x+1} \sqrt{-i a-i b x+1}}{2 b^3}+\frac{\left(-6 a^2+18 i a+11\right) \sinh ^{-1}(a+b x)}{2 b^3}-\frac{i \sqrt{i a+i b x+1} (-i a-i b x+1)^{5/2}}{3 b^3}+\frac{i (-a+i)^2 (-i a-i b x+1)^{5/2}}{b^3 \sqrt{i a+i b x+1}}",1,"(I*(I - a)^2*(1 - I*a - I*b*x)^(5/2))/(b^3*Sqrt[1 + I*a + I*b*x]) - ((11*I - 18*a - (6*I)*a^2)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(2*b^3) - ((11*I - 18*a - (6*I)*a^2)*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(6*b^3) - ((I/3)*(1 - I*a - I*b*x)^(5/2)*Sqrt[1 + I*a + I*b*x])/b^3 + ((11 + (18*I)*a - 6*a^2)*ArcSinh[a + b*x])/(2*b^3)","A",8,7,16,0.4375,1,"{5095, 89, 80, 50, 53, 619, 215}"
210,1,163,0,0.1190717,"\int e^{-3 i \tan ^{-1}(a+b x)} x \, dx","Int[x/E^((3*I)*ArcTan[a + b*x]),x]","-\frac{(1+i a) (-i a-i b x+1)^{5/2}}{b^2 \sqrt{i a+i b x+1}}-\frac{(3+2 i a) \sqrt{i a+i b x+1} (-i a-i b x+1)^{3/2}}{2 b^2}-\frac{3 (3+2 i a) \sqrt{i a+i b x+1} \sqrt{-i a-i b x+1}}{2 b^2}-\frac{3 (-2 a+3 i) \sinh ^{-1}(a+b x)}{2 b^2}","-\frac{(1+i a) (-i a-i b x+1)^{5/2}}{b^2 \sqrt{i a+i b x+1}}-\frac{(3+2 i a) \sqrt{i a+i b x+1} (-i a-i b x+1)^{3/2}}{2 b^2}-\frac{3 (3+2 i a) \sqrt{i a+i b x+1} \sqrt{-i a-i b x+1}}{2 b^2}-\frac{3 (-2 a+3 i) \sinh ^{-1}(a+b x)}{2 b^2}",1,"-(((1 + I*a)*(1 - I*a - I*b*x)^(5/2))/(b^2*Sqrt[1 + I*a + I*b*x])) - (3*(3 + (2*I)*a)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/(2*b^2) - ((3 + (2*I)*a)*(1 - I*a - I*b*x)^(3/2)*Sqrt[1 + I*a + I*b*x])/(2*b^2) - (3*(3*I - 2*a)*ArcSinh[a + b*x])/(2*b^2)","A",7,6,14,0.4286,1,"{5095, 78, 50, 53, 619, 215}"
211,1,94,0,0.0440134,"\int e^{-3 i \tan ^{-1}(a+b x)} \, dx","Int[E^((-3*I)*ArcTan[a + b*x]),x]","\frac{2 i (-i a-i b x+1)^{3/2}}{b \sqrt{i a+i b x+1}}+\frac{3 i \sqrt{i a+i b x+1} \sqrt{-i a-i b x+1}}{b}-\frac{3 \sinh ^{-1}(a+b x)}{b}","\frac{2 i (-i a-i b x+1)^{3/2}}{b \sqrt{i a+i b x+1}}+\frac{3 i \sqrt{i a+i b x+1} \sqrt{-i a-i b x+1}}{b}-\frac{3 \sinh ^{-1}(a+b x)}{b}",1,"((2*I)*(1 - I*a - I*b*x)^(3/2))/(b*Sqrt[1 + I*a + I*b*x]) + ((3*I)*Sqrt[1 - I*a - I*b*x]*Sqrt[1 + I*a + I*b*x])/b - (3*ArcSinh[a + b*x])/b","A",6,6,12,0.5000,1,"{5093, 47, 50, 53, 619, 215}"
212,1,134,0,0.0940627,"\int \frac{e^{-3 i \tan ^{-1}(a+b x)}}{x} \, dx","Int[1/(E^((3*I)*ArcTan[a + b*x])*x),x]","\frac{4 \sqrt{-i a-i b x+1}}{(1+i a) \sqrt{i a+i b x+1}}+i \sinh ^{-1}(a+b x)-\frac{2 (a+i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{3/2}}","\frac{4 \sqrt{-i a-i b x+1}}{(1+i a) \sqrt{i a+i b x+1}}+i \sinh ^{-1}(a+b x)-\frac{2 (a+i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{3/2}}",1,"(4*Sqrt[1 - I*a - I*b*x])/((1 + I*a)*Sqrt[1 + I*a + I*b*x]) + I*ArcSinh[a + b*x] - (2*(I + a)^(3/2)*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/(I - a)^(3/2)","A",8,8,16,0.5000,1,"{5095, 98, 157, 53, 619, 215, 93, 208}"
213,1,178,0,0.0854949,"\int \frac{e^{-3 i \tan ^{-1}(a+b x)}}{x^2} \, dx","Int[1/(E^((3*I)*ArcTan[a + b*x])*x^2),x]","-\frac{(-i a-i b x+1)^{3/2}}{(1+i a) x \sqrt{i a+i b x+1}}+\frac{6 i b \sqrt{-i a-i b x+1}}{(-a+i)^2 \sqrt{i a+i b x+1}}-\frac{6 i \sqrt{a+i} b \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{5/2}}","-\frac{(-i a-i b x+1)^{3/2}}{(1+i a) x \sqrt{i a+i b x+1}}+\frac{6 i b \sqrt{-i a-i b x+1}}{(-a+i)^2 \sqrt{i a+i b x+1}}-\frac{6 i \sqrt{a+i} b \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{5/2}}",1,"((6*I)*b*Sqrt[1 - I*a - I*b*x])/((I - a)^2*Sqrt[1 + I*a + I*b*x]) - (1 - I*a - I*b*x)^(3/2)/((1 + I*a)*x*Sqrt[1 + I*a + I*b*x]) - ((6*I)*Sqrt[I + a]*b*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/(I - a)^(5/2)","A",5,4,16,0.2500,1,"{5095, 94, 93, 208}"
214,1,264,0,0.1602935,"\int \frac{e^{-3 i \tan ^{-1}(a+b x)}}{x^3} \, dx","Int[1/(E^((3*I)*ArcTan[a + b*x])*x^3),x]","-\frac{(-i a-i b x+1)^{5/2}}{2 \left(a^2+1\right) x^2 \sqrt{i a+i b x+1}}-\frac{3 (2 a+3 i) b^2 \sqrt{-i a-i b x+1}}{(1+i a)^3 (a+i) \sqrt{i a+i b x+1}}+\frac{3 (3-2 i a) b^2 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{7/2} \sqrt{a+i}}+\frac{(3-2 i a) b (-i a-i b x+1)^{3/2}}{2 (-a+i)^2 (a+i) x \sqrt{i a+i b x+1}}","-\frac{(-i a-i b x+1)^{5/2}}{2 \left(a^2+1\right) x^2 \sqrt{i a+i b x+1}}-\frac{3 (2 a+3 i) b^2 \sqrt{-i a-i b x+1}}{(1+i a)^3 (a+i) \sqrt{i a+i b x+1}}+\frac{3 (3-2 i a) b^2 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{7/2} \sqrt{a+i}}+\frac{(3-2 i a) b (-i a-i b x+1)^{3/2}}{2 (-a+i)^2 (a+i) x \sqrt{i a+i b x+1}}",1,"(-3*(3*I + 2*a)*b^2*Sqrt[1 - I*a - I*b*x])/((1 + I*a)^3*(I + a)*Sqrt[1 + I*a + I*b*x]) + ((3 - (2*I)*a)*b*(1 - I*a - I*b*x)^(3/2))/(2*(I - a)^2*(I + a)*x*Sqrt[1 + I*a + I*b*x]) - (1 - I*a - I*b*x)^(5/2)/(2*(1 + a^2)*x^2*Sqrt[1 + I*a + I*b*x]) + (3*(3 - (2*I)*a)*b^2*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/((I - a)^(7/2)*Sqrt[I + a])","A",6,5,16,0.3125,1,"{5095, 96, 94, 93, 208}"
215,1,339,0,0.271053,"\int \frac{e^{-3 i \tan ^{-1}(a+b x)}}{x^4} \, dx","Int[1/(E^((3*I)*ArcTan[a + b*x])*x^4),x]","-\frac{\left(-2 a^2-51 i a+52\right) b^3 \sqrt{-i a-i b x+1}}{6 (-a+i)^4 (a+i) \sqrt{i a+i b x+1}}+\frac{\left(-6 i a^2+18 a+11 i\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{9/2} (a+i)^{3/2}}+\frac{(19-16 i a) b^2 \sqrt{-i a-i b x+1}}{6 (-a+i)^3 (a+i) x \sqrt{i a+i b x+1}}-\frac{7 i b \sqrt{-i a-i b x+1}}{6 (-a+i)^2 x^2 \sqrt{i a+i b x+1}}-\frac{(a+i) \sqrt{-i a-i b x+1}}{3 (-a+i) x^3 \sqrt{i a+i b x+1}}","-\frac{\left(-2 a^2-51 i a+52\right) b^3 \sqrt{-i a-i b x+1}}{6 (-a+i)^4 (a+i) \sqrt{i a+i b x+1}}+\frac{\left(-6 i a^2+18 a+11 i\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{a+i} \sqrt{i a+i b x+1}}{\sqrt{-a+i} \sqrt{-i a-i b x+1}}\right)}{(-a+i)^{9/2} (a+i)^{3/2}}+\frac{(19-16 i a) b^2 \sqrt{-i a-i b x+1}}{6 (-a+i)^3 (a+i) x \sqrt{i a+i b x+1}}-\frac{7 i b \sqrt{-i a-i b x+1}}{6 (-a+i)^2 x^2 \sqrt{i a+i b x+1}}-\frac{(a+i) \sqrt{-i a-i b x+1}}{3 (-a+i) x^3 \sqrt{i a+i b x+1}}",1,"-((52 - (51*I)*a - 2*a^2)*b^3*Sqrt[1 - I*a - I*b*x])/(6*(I - a)^4*(I + a)*Sqrt[1 + I*a + I*b*x]) - ((I + a)*Sqrt[1 - I*a - I*b*x])/(3*(I - a)*x^3*Sqrt[1 + I*a + I*b*x]) - (((7*I)/6)*b*Sqrt[1 - I*a - I*b*x])/((I - a)^2*x^2*Sqrt[1 + I*a + I*b*x]) + ((19 - (16*I)*a)*b^2*Sqrt[1 - I*a - I*b*x])/(6*(I - a)^3*(I + a)*x*Sqrt[1 + I*a + I*b*x]) + ((11*I + 18*a - (6*I)*a^2)*b^3*ArcTanh[(Sqrt[I + a]*Sqrt[1 + I*a + I*b*x])/(Sqrt[I - a]*Sqrt[1 - I*a - I*b*x])])/((I - a)^(9/2)*(I + a)^(3/2))","A",8,7,16,0.4375,1,"{5095, 98, 151, 152, 12, 93, 208}"
216,1,494,0,0.4054929,"\int e^{\frac{1}{2} i \tan ^{-1}(a+b x)} x^2 \, dx","Int[E^((I/2)*ArcTan[a + b*x])*x^2,x]","-\frac{\left(-8 i a^2+4 a+3 i\right) (-i a-i b x+1)^{3/4} \sqrt[4]{i a+i b x+1}}{8 b^3}-\frac{\left(-8 i a^2+4 a+3 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-8 i a^2+4 a+3 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-8 i a^2+4 a+3 i\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}-\frac{\left(-8 i a^2+4 a+3 i\right) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}+\frac{x (-i a-i b x+1)^{3/4} (i a+i b x+1)^{5/4}}{3 b^2}-\frac{(8 a+i) (-i a-i b x+1)^{3/4} (i a+i b x+1)^{5/4}}{12 b^3}","-\frac{\left(-8 i a^2+4 a+3 i\right) (-i a-i b x+1)^{3/4} \sqrt[4]{i a+i b x+1}}{8 b^3}-\frac{\left(-8 i a^2+4 a+3 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-8 i a^2+4 a+3 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-8 i a^2+4 a+3 i\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}-\frac{\left(-8 i a^2+4 a+3 i\right) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}+\frac{x (-i a-i b x+1)^{3/4} (i a+i b x+1)^{5/4}}{3 b^2}-\frac{(8 a+i) (-i a-i b x+1)^{3/4} (i a+i b x+1)^{5/4}}{12 b^3}",1,"-((3*I + 4*a - (8*I)*a^2)*(1 - I*a - I*b*x)^(3/4)*(1 + I*a + I*b*x)^(1/4))/(8*b^3) - ((I + 8*a)*(1 - I*a - I*b*x)^(3/4)*(1 + I*a + I*b*x)^(5/4))/(12*b^3) + (x*(1 - I*a - I*b*x)^(3/4)*(1 + I*a + I*b*x)^(5/4))/(3*b^2) + ((3*I + 4*a - (8*I)*a^2)*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^3) - ((3*I + 4*a - (8*I)*a^2)*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^3) - ((3*I + 4*a - (8*I)*a^2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(16*Sqrt[2]*b^3) + ((3*I + 4*a - (8*I)*a^2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(16*Sqrt[2]*b^3)","A",15,12,18,0.6667,1,"{5095, 90, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
217,1,410,0,0.3071941,"\int e^{\frac{1}{2} i \tan ^{-1}(a+b x)} x \, dx","Int[E^((I/2)*ArcTan[a + b*x])*x,x]","\frac{(-i a-i b x+1)^{3/4} (i a+i b x+1)^{5/4}}{2 b^2}+\frac{(1-4 i a) (-i a-i b x+1)^{3/4} \sqrt[4]{i a+i b x+1}}{4 b^2}+\frac{(1-4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}-\frac{(1-4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}-\frac{(1-4 i a) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}+\frac{(1-4 i a) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}","\frac{(-i a-i b x+1)^{3/4} (i a+i b x+1)^{5/4}}{2 b^2}+\frac{(1-4 i a) (-i a-i b x+1)^{3/4} \sqrt[4]{i a+i b x+1}}{4 b^2}+\frac{(1-4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}-\frac{(1-4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}-\frac{(1-4 i a) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}+\frac{(1-4 i a) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}",1,"((1 - (4*I)*a)*(1 - I*a - I*b*x)^(3/4)*(1 + I*a + I*b*x)^(1/4))/(4*b^2) + ((1 - I*a - I*b*x)^(3/4)*(1 + I*a + I*b*x)^(5/4))/(2*b^2) - ((1 - (4*I)*a)*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(4*Sqrt[2]*b^2) + ((1 - (4*I)*a)*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(4*Sqrt[2]*b^2) + ((1 - (4*I)*a)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^2) - ((1 - (4*I)*a)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^2)","A",14,11,16,0.6875,1,"{5095, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
218,1,338,0,0.1952119,"\int e^{\frac{1}{2} i \tan ^{-1}(a+b x)} \, dx","Int[E^((I/2)*ArcTan[a + b*x]),x]","\frac{i (-i a-i b x+1)^{3/4} \sqrt[4]{i a+i b x+1}}{b}+\frac{i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}+\frac{i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}","\frac{i (-i a-i b x+1)^{3/4} \sqrt[4]{i a+i b x+1}}{b}+\frac{i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}+\frac{i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}",1,"(I*(1 - I*a - I*b*x)^(3/4)*(1 + I*a + I*b*x)^(1/4))/b - (I*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) + (I*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) + ((I/2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) - ((I/2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b)","A",13,10,14,0.7143,1,"{5093, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
219,1,395,0,0.2455907,"\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a+b x)}}{x} \, dx","Int[E^((I/2)*ArcTan[a + b*x])/x,x]","-\frac{\log \left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}-\frac{\sqrt{2} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{1-i (a+b x)}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}+\frac{\sqrt{2} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{1-i (a+b x)}}+1\right)}{\sqrt{2}}-\frac{2 \sqrt[4]{-a+i} \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}\right)}{\sqrt[4]{a+i}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{1-i (a+b x)}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{1-i (a+b x)}}\right)-\frac{2 \sqrt[4]{-a+i} \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}\right)}{\sqrt[4]{a+i}}","-\frac{\log \left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}-\frac{\sqrt{2} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{1-i (a+b x)}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1+i (a+b x)}}{\sqrt{1-i (a+b x)}}+\frac{\sqrt{2} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{1-i (a+b x)}}+1\right)}{\sqrt{2}}-\frac{2 \sqrt[4]{-a+i} \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}\right)}{\sqrt[4]{a+i}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{1-i (a+b x)}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{1-i (a+b x)}}\right)-\frac{2 \sqrt[4]{-a+i} \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}\right)}{\sqrt[4]{a+i}}",1,"(-2*(I - a)^(1/4)*ArcTan[((I + a)^(1/4)*(1 + I*(a + b*x))^(1/4))/((I - a)^(1/4)*(1 - I*(a + b*x))^(1/4))])/(I + a)^(1/4) - Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 + I*(a + b*x))^(1/4))/(1 - I*(a + b*x))^(1/4)] + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 + I*(a + b*x))^(1/4))/(1 - I*(a + b*x))^(1/4)] - (2*(I - a)^(1/4)*ArcTanh[((I + a)^(1/4)*(1 + I*(a + b*x))^(1/4))/((I - a)^(1/4)*(1 - I*(a + b*x))^(1/4))])/(I + a)^(1/4) - Log[1 - (Sqrt[2]*(1 + I*(a + b*x))^(1/4))/(1 - I*(a + b*x))^(1/4) + Sqrt[1 + I*(a + b*x)]/Sqrt[1 - I*(a + b*x)]]/Sqrt[2] + Log[1 + (Sqrt[2]*(1 + I*(a + b*x))^(1/4))/(1 - I*(a + b*x))^(1/4) + Sqrt[1 + I*(a + b*x)]/Sqrt[1 - I*(a + b*x)]]/Sqrt[2]","A",15,12,18,0.6667,1,"{5094, 445, 481, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
220,1,205,0,0.1026953,"\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a+b x)}}{x^2} \, dx","Int[E^((I/2)*ArcTan[a + b*x])/x^2,x]","-\frac{\sqrt[4]{1+i (a+b x)} (a+b x+i)}{(a+i) x \sqrt[4]{1-i (a+b x)}}+\frac{i b \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}\right)}{(-a+i)^{3/4} (a+i)^{5/4}}+\frac{i b \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}\right)}{(-a+i)^{3/4} (a+i)^{5/4}}","-\frac{\sqrt[4]{1+i (a+b x)} (a+b x+i)}{(a+i) x \sqrt[4]{1-i (a+b x)}}+\frac{i b \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}\right)}{(-a+i)^{3/4} (a+i)^{5/4}}+\frac{i b \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}\right)}{(-a+i)^{3/4} (a+i)^{5/4}}",1,"-(((I + a + b*x)*(1 + I*(a + b*x))^(1/4))/((I + a)*x*(1 - I*(a + b*x))^(1/4))) + (I*b*ArcTan[((I + a)^(1/4)*(1 + I*(a + b*x))^(1/4))/((I - a)^(1/4)*(1 - I*(a + b*x))^(1/4))])/((I - a)^(3/4)*(I + a)^(5/4)) + (I*b*ArcTanh[((I + a)^(1/4)*(1 + I*(a + b*x))^(1/4))/((I - a)^(1/4)*(1 - I*(a + b*x))^(1/4))])/((I - a)^(3/4)*(I + a)^(5/4))","A",6,6,18,0.3333,1,"{5094, 263, 288, 212, 208, 205}"
221,1,494,0,0.3827753,"\int e^{\frac{3}{2} i \tan ^{-1}(a+b x)} x^2 \, dx","Int[E^(((3*I)/2)*ArcTan[a + b*x])*x^2,x]","-\frac{\left(-24 i a^2+36 a+17 i\right) \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{3/4}}{24 b^3}+\frac{\left(-24 i a^2+36 a+17 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}-\frac{\left(-24 i a^2+36 a+17 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-24 i a^2+36 a+17 i\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}-\frac{\left(-24 i a^2+36 a+17 i\right) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}+\frac{x \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{7/4}}{3 b^2}-\frac{(8 a+3 i) \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{7/4}}{12 b^3}","-\frac{\left(-24 i a^2+36 a+17 i\right) \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{3/4}}{24 b^3}+\frac{\left(-24 i a^2+36 a+17 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}-\frac{\left(-24 i a^2+36 a+17 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-24 i a^2+36 a+17 i\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}-\frac{\left(-24 i a^2+36 a+17 i\right) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}+\frac{x \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{7/4}}{3 b^2}-\frac{(8 a+3 i) \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{7/4}}{12 b^3}",1,"-((17*I + 36*a - (24*I)*a^2)*(1 - I*a - I*b*x)^(1/4)*(1 + I*a + I*b*x)^(3/4))/(24*b^3) - ((3*I + 8*a)*(1 - I*a - I*b*x)^(1/4)*(1 + I*a + I*b*x)^(7/4))/(12*b^3) + (x*(1 - I*a - I*b*x)^(1/4)*(1 + I*a + I*b*x)^(7/4))/(3*b^2) + ((17*I + 36*a - (24*I)*a^2)*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^3) - ((17*I + 36*a - (24*I)*a^2)*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^3) + ((17*I + 36*a - (24*I)*a^2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(16*Sqrt[2]*b^3) - ((17*I + 36*a - (24*I)*a^2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(16*Sqrt[2]*b^3)","A",15,12,18,0.6667,1,"{5095, 90, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
222,1,410,0,0.2921212,"\int e^{\frac{3}{2} i \tan ^{-1}(a+b x)} x \, dx","Int[E^(((3*I)/2)*ArcTan[a + b*x])*x,x]","\frac{\sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{7/4}}{2 b^2}+\frac{(3-4 i a) \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{3/4}}{4 b^2}-\frac{3 (3-4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}+\frac{3 (3-4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}-\frac{3 (3-4 i a) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}+\frac{3 (3-4 i a) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}","\frac{\sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{7/4}}{2 b^2}+\frac{(3-4 i a) \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{3/4}}{4 b^2}-\frac{3 (3-4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}+\frac{3 (3-4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}-\frac{3 (3-4 i a) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}+\frac{3 (3-4 i a) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}",1,"((3 - (4*I)*a)*(1 - I*a - I*b*x)^(1/4)*(1 + I*a + I*b*x)^(3/4))/(4*b^2) + ((1 - I*a - I*b*x)^(1/4)*(1 + I*a + I*b*x)^(7/4))/(2*b^2) - (3*(3 - (4*I)*a)*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(4*Sqrt[2]*b^2) + (3*(3 - (4*I)*a)*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(4*Sqrt[2]*b^2) - (3*(3 - (4*I)*a)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^2) + (3*(3 - (4*I)*a)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^2)","A",14,11,16,0.6875,1,"{5095, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
223,1,338,0,0.1974807,"\int e^{\frac{3}{2} i \tan ^{-1}(a+b x)} \, dx","Int[E^(((3*I)/2)*ArcTan[a + b*x]),x]","\frac{i \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{3/4}}{b}-\frac{3 i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}+\frac{3 i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}+\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}","\frac{i \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{3/4}}{b}-\frac{3 i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}+\frac{3 i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}+\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}",1,"(I*(1 - I*a - I*b*x)^(1/4)*(1 + I*a + I*b*x)^(3/4))/b - ((3*I)*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) + ((3*I)*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) - (((3*I)/2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) + (((3*I)/2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b)","A",13,10,14,0.7143,1,"{5093, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
224,1,427,0,0.2514179,"\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a+b x)}}{x} \, dx","Int[E^(((3*I)/2)*ArcTan[a + b*x])/x,x]","\frac{\log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{\sqrt{2}}+\frac{2 (-a+i)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(a+i)^{3/4}}+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)-\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)-\frac{2 (-a+i)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(a+i)^{3/4}}","\frac{\log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{\sqrt{2}}+\frac{2 (-a+i)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(a+i)^{3/4}}+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)-\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)-\frac{2 (-a+i)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(a+i)^{3/4}}",1,"(2*(I - a)^(3/4)*ArcTan[((I + a)^(1/4)*(1 + I*a + I*b*x)^(1/4))/((I - a)^(1/4)*(1 - I*a - I*b*x)^(1/4))])/(I + a)^(3/4) + Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)] - (2*(I - a)^(3/4)*ArcTanh[((I + a)^(1/4)*(1 + I*a + I*b*x)^(1/4))/((I - a)^(1/4)*(1 - I*a - I*b*x)^(1/4))])/(I + a)^(3/4) + Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)]/Sqrt[2]","A",17,14,18,0.7778,1,"{5095, 105, 63, 240, 211, 1165, 628, 1162, 617, 204, 93, 298, 205, 208}"
225,1,211,0,0.1078235,"\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a+b x)}}{x^2} \, dx","Int[E^(((3*I)/2)*ArcTan[a + b*x])/x^2,x]","-\frac{\sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{3/4}}{(1-i a) x}-\frac{3 i b \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{\sqrt[4]{-a+i} (a+i)^{7/4}}+\frac{3 i b \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{\sqrt[4]{-a+i} (a+i)^{7/4}}","-\frac{\sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{3/4}}{(1-i a) x}-\frac{3 i b \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{\sqrt[4]{-a+i} (a+i)^{7/4}}+\frac{3 i b \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{\sqrt[4]{-a+i} (a+i)^{7/4}}",1,"-(((1 - I*a - I*b*x)^(1/4)*(1 + I*a + I*b*x)^(3/4))/((1 - I*a)*x)) - ((3*I)*b*ArcTan[((I + a)^(1/4)*(1 + I*a + I*b*x)^(1/4))/((I - a)^(1/4)*(1 - I*a - I*b*x)^(1/4))])/((I - a)^(1/4)*(I + a)^(7/4)) + ((3*I)*b*ArcTanh[((I + a)^(1/4)*(1 + I*a + I*b*x)^(1/4))/((I - a)^(1/4)*(1 - I*a - I*b*x)^(1/4))])/((I - a)^(1/4)*(I + a)^(7/4))","A",6,6,18,0.3333,1,"{5095, 94, 93, 298, 205, 208}"
226,1,494,0,0.4012672,"\int e^{-\frac{1}{2} i \tan ^{-1}(a+b x)} x^2 \, dx","Int[x^2/E^((I/2)*ArcTan[a + b*x]),x]","\frac{\left(-8 i a^2-4 a+3 i\right) (i a+i b x+1)^{3/4} \sqrt[4]{-i a-i b x+1}}{8 b^3}+\frac{\left(-8 i a^2-4 a+3 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}-\frac{\left(-8 i a^2-4 a+3 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-8 i a^2-4 a+3 i\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}-\frac{\left(-8 i a^2-4 a+3 i\right) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}+\frac{x (i a+i b x+1)^{3/4} (-i a-i b x+1)^{5/4}}{3 b^2}+\frac{(-8 a+i) (i a+i b x+1)^{3/4} (-i a-i b x+1)^{5/4}}{12 b^3}","\frac{\left(-8 i a^2-4 a+3 i\right) (i a+i b x+1)^{3/4} \sqrt[4]{-i a-i b x+1}}{8 b^3}+\frac{\left(-8 i a^2-4 a+3 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}-\frac{\left(-8 i a^2-4 a+3 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-8 i a^2-4 a+3 i\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}-\frac{\left(-8 i a^2-4 a+3 i\right) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}+\frac{x (i a+i b x+1)^{3/4} (-i a-i b x+1)^{5/4}}{3 b^2}+\frac{(-8 a+i) (i a+i b x+1)^{3/4} (-i a-i b x+1)^{5/4}}{12 b^3}",1,"((3*I - 4*a - (8*I)*a^2)*(1 - I*a - I*b*x)^(1/4)*(1 + I*a + I*b*x)^(3/4))/(8*b^3) + ((I - 8*a)*(1 - I*a - I*b*x)^(5/4)*(1 + I*a + I*b*x)^(3/4))/(12*b^3) + (x*(1 - I*a - I*b*x)^(5/4)*(1 + I*a + I*b*x)^(3/4))/(3*b^2) + ((3*I - 4*a - (8*I)*a^2)*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^3) - ((3*I - 4*a - (8*I)*a^2)*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^3) + ((3*I - 4*a - (8*I)*a^2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(16*Sqrt[2]*b^3) - ((3*I - 4*a - (8*I)*a^2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(16*Sqrt[2]*b^3)","A",15,12,18,0.6667,1,"{5095, 90, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
227,1,410,0,0.3073341,"\int e^{-\frac{1}{2} i \tan ^{-1}(a+b x)} x \, dx","Int[x/E^((I/2)*ArcTan[a + b*x]),x]","\frac{(i a+i b x+1)^{3/4} (-i a-i b x+1)^{5/4}}{2 b^2}+\frac{(1+4 i a) (i a+i b x+1)^{3/4} \sqrt[4]{-i a-i b x+1}}{4 b^2}+\frac{(1+4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}-\frac{(1+4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}+\frac{(1+4 i a) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}-\frac{(1+4 i a) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}","\frac{(i a+i b x+1)^{3/4} (-i a-i b x+1)^{5/4}}{2 b^2}+\frac{(1+4 i a) (i a+i b x+1)^{3/4} \sqrt[4]{-i a-i b x+1}}{4 b^2}+\frac{(1+4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}-\frac{(1+4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}+\frac{(1+4 i a) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}-\frac{(1+4 i a) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}",1,"((1 + (4*I)*a)*(1 - I*a - I*b*x)^(1/4)*(1 + I*a + I*b*x)^(3/4))/(4*b^2) + ((1 - I*a - I*b*x)^(5/4)*(1 + I*a + I*b*x)^(3/4))/(2*b^2) + ((1 + (4*I)*a)*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(4*Sqrt[2]*b^2) - ((1 + (4*I)*a)*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(4*Sqrt[2]*b^2) + ((1 + (4*I)*a)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^2) - ((1 + (4*I)*a)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^2)","A",14,11,16,0.6875,1,"{5095, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
228,1,338,0,0.1972719,"\int e^{-\frac{1}{2} i \tan ^{-1}(a+b x)} \, dx","Int[E^((-I/2)*ArcTan[a + b*x]),x]","-\frac{i \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{3/4}}{b}-\frac{i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}+\frac{i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}+\frac{i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}","-\frac{i \sqrt[4]{-i a-i b x+1} (i a+i b x+1)^{3/4}}{b}-\frac{i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}+\frac{i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}+\frac{i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}",1,"((-I)*(1 - I*a - I*b*x)^(1/4)*(1 + I*a + I*b*x)^(3/4))/b - (I*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) + (I*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) - ((I/2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) + ((I/2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b)","A",13,10,14,0.7143,1,"{5093, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
229,1,395,0,0.2057748,"\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a+b x)}}{x} \, dx","Int[1/(E^((I/2)*ArcTan[a + b*x])*x),x]","-\frac{\log \left(\frac{\sqrt{1-i (a+b x)}}{\sqrt{1+i (a+b x)}}-\frac{\sqrt{2} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{1+i (a+b x)}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-i (a+b x)}}{\sqrt{1+i (a+b x)}}+\frac{\sqrt{2} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{1+i (a+b x)}}+1\right)}{\sqrt{2}}-\frac{2 \sqrt[4]{a+i} \tan ^{-1}\left(\frac{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}\right)}{\sqrt[4]{-a+i}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{1+i (a+b x)}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{1+i (a+b x)}}\right)-\frac{2 \sqrt[4]{a+i} \tanh ^{-1}\left(\frac{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}\right)}{\sqrt[4]{-a+i}}","-\frac{\log \left(\frac{\sqrt{1-i (a+b x)}}{\sqrt{1+i (a+b x)}}-\frac{\sqrt{2} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{1+i (a+b x)}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-i (a+b x)}}{\sqrt{1+i (a+b x)}}+\frac{\sqrt{2} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{1+i (a+b x)}}+1\right)}{\sqrt{2}}-\frac{2 \sqrt[4]{a+i} \tan ^{-1}\left(\frac{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}\right)}{\sqrt[4]{-a+i}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{1+i (a+b x)}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{1+i (a+b x)}}\right)-\frac{2 \sqrt[4]{a+i} \tanh ^{-1}\left(\frac{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}\right)}{\sqrt[4]{-a+i}}",1,"(-2*(I + a)^(1/4)*ArcTan[((I - a)^(1/4)*(1 - I*(a + b*x))^(1/4))/((I + a)^(1/4)*(1 + I*(a + b*x))^(1/4))])/(I - a)^(1/4) - Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - I*(a + b*x))^(1/4))/(1 + I*(a + b*x))^(1/4)] + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - I*(a + b*x))^(1/4))/(1 + I*(a + b*x))^(1/4)] - (2*(I + a)^(1/4)*ArcTanh[((I - a)^(1/4)*(1 - I*(a + b*x))^(1/4))/((I + a)^(1/4)*(1 + I*(a + b*x))^(1/4))])/(I - a)^(1/4) - Log[1 + Sqrt[1 - I*(a + b*x)]/Sqrt[1 + I*(a + b*x)] - (Sqrt[2]*(1 - I*(a + b*x))^(1/4))/(1 + I*(a + b*x))^(1/4)]/Sqrt[2] + Log[1 + Sqrt[1 - I*(a + b*x)]/Sqrt[1 + I*(a + b*x)] + (Sqrt[2]*(1 - I*(a + b*x))^(1/4))/(1 + I*(a + b*x))^(1/4)]/Sqrt[2]","A",14,11,18,0.6111,1,"{5094, 481, 211, 1165, 628, 1162, 617, 204, 212, 208, 205}"
230,1,210,0,0.1013429,"\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a+b x)}}{x^2} \, dx","Int[1/(E^((I/2)*ArcTan[a + b*x])*x^2),x]","-\frac{\sqrt[4]{1-i (a+b x)} (-a-b x+i)}{(-a+i) x \sqrt[4]{1+i (a+b x)}}-\frac{i b \tan ^{-1}\left(\frac{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}\right)}{(-a+i)^{5/4} (a+i)^{3/4}}-\frac{i b \tanh ^{-1}\left(\frac{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}\right)}{(-a+i)^{5/4} (a+i)^{3/4}}","-\frac{\sqrt[4]{1-i (a+b x)} (-a-b x+i)}{(-a+i) x \sqrt[4]{1+i (a+b x)}}-\frac{i b \tan ^{-1}\left(\frac{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}\right)}{(-a+i)^{5/4} (a+i)^{3/4}}-\frac{i b \tanh ^{-1}\left(\frac{\sqrt[4]{-a+i} \sqrt[4]{1-i (a+b x)}}{\sqrt[4]{a+i} \sqrt[4]{1+i (a+b x)}}\right)}{(-a+i)^{5/4} (a+i)^{3/4}}",1,"-(((I - a - b*x)*(1 - I*(a + b*x))^(1/4))/((I - a)*x*(1 + I*(a + b*x))^(1/4))) - (I*b*ArcTan[((I - a)^(1/4)*(1 - I*(a + b*x))^(1/4))/((I + a)^(1/4)*(1 + I*(a + b*x))^(1/4))])/((I - a)^(5/4)*(I + a)^(3/4)) - (I*b*ArcTanh[((I - a)^(1/4)*(1 - I*(a + b*x))^(1/4))/((I + a)^(1/4)*(1 + I*(a + b*x))^(1/4))])/((I - a)^(5/4)*(I + a)^(3/4))","A",5,5,18,0.2778,1,"{5094, 288, 212, 208, 205}"
231,1,494,0,0.3903441,"\int e^{-\frac{3}{2} i \tan ^{-1}(a+b x)} x^2 \, dx","Int[x^2/E^(((3*I)/2)*ArcTan[a + b*x]),x]","\frac{\left(-24 i a^2-36 a+17 i\right) \sqrt[4]{i a+i b x+1} (-i a-i b x+1)^{3/4}}{24 b^3}-\frac{\left(-24 i a^2-36 a+17 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-24 i a^2-36 a+17 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-24 i a^2-36 a+17 i\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}-\frac{\left(-24 i a^2-36 a+17 i\right) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}+\frac{x \sqrt[4]{i a+i b x+1} (-i a-i b x+1)^{7/4}}{3 b^2}+\frac{(-8 a+3 i) \sqrt[4]{i a+i b x+1} (-i a-i b x+1)^{7/4}}{12 b^3}","\frac{\left(-24 i a^2-36 a+17 i\right) \sqrt[4]{i a+i b x+1} (-i a-i b x+1)^{3/4}}{24 b^3}-\frac{\left(-24 i a^2-36 a+17 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-24 i a^2-36 a+17 i\right) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{16 \sqrt{2} b^3}+\frac{\left(-24 i a^2-36 a+17 i\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}-\frac{\left(-24 i a^2-36 a+17 i\right) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{8 \sqrt{2} b^3}+\frac{x \sqrt[4]{i a+i b x+1} (-i a-i b x+1)^{7/4}}{3 b^2}+\frac{(-8 a+3 i) \sqrt[4]{i a+i b x+1} (-i a-i b x+1)^{7/4}}{12 b^3}",1,"((17*I - 36*a - (24*I)*a^2)*(1 - I*a - I*b*x)^(3/4)*(1 + I*a + I*b*x)^(1/4))/(24*b^3) + ((3*I - 8*a)*(1 - I*a - I*b*x)^(7/4)*(1 + I*a + I*b*x)^(1/4))/(12*b^3) + (x*(1 - I*a - I*b*x)^(7/4)*(1 + I*a + I*b*x)^(1/4))/(3*b^2) + ((17*I - 36*a - (24*I)*a^2)*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^3) - ((17*I - 36*a - (24*I)*a^2)*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^3) - ((17*I - 36*a - (24*I)*a^2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(16*Sqrt[2]*b^3) + ((17*I - 36*a - (24*I)*a^2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(16*Sqrt[2]*b^3)","A",15,12,18,0.6667,1,"{5095, 90, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
232,1,410,0,0.2970404,"\int e^{-\frac{3}{2} i \tan ^{-1}(a+b x)} x \, dx","Int[x/E^(((3*I)/2)*ArcTan[a + b*x]),x]","\frac{\sqrt[4]{i a+i b x+1} (-i a-i b x+1)^{7/4}}{2 b^2}+\frac{(3+4 i a) \sqrt[4]{i a+i b x+1} (-i a-i b x+1)^{3/4}}{4 b^2}-\frac{3 (3+4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}+\frac{3 (3+4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}+\frac{3 (3+4 i a) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}-\frac{3 (3+4 i a) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}","\frac{\sqrt[4]{i a+i b x+1} (-i a-i b x+1)^{7/4}}{2 b^2}+\frac{(3+4 i a) \sqrt[4]{i a+i b x+1} (-i a-i b x+1)^{3/4}}{4 b^2}-\frac{3 (3+4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}+\frac{3 (3+4 i a) \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{8 \sqrt{2} b^2}+\frac{3 (3+4 i a) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}-\frac{3 (3+4 i a) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{4 \sqrt{2} b^2}",1,"((3 + (4*I)*a)*(1 - I*a - I*b*x)^(3/4)*(1 + I*a + I*b*x)^(1/4))/(4*b^2) + ((1 - I*a - I*b*x)^(7/4)*(1 + I*a + I*b*x)^(1/4))/(2*b^2) + (3*(3 + (4*I)*a)*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(4*Sqrt[2]*b^2) - (3*(3 + (4*I)*a)*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(4*Sqrt[2]*b^2) - (3*(3 + (4*I)*a)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^2) + (3*(3 + (4*I)*a)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(8*Sqrt[2]*b^2)","A",14,11,16,0.6875,1,"{5095, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
233,1,338,0,0.1968095,"\int e^{-\frac{3}{2} i \tan ^{-1}(a+b x)} \, dx","Int[E^(((-3*I)/2)*ArcTan[a + b*x]),x]","-\frac{i (-i a-i b x+1)^{3/4} \sqrt[4]{i a+i b x+1}}{b}+\frac{3 i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{3 i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}+\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}","-\frac{i (-i a-i b x+1)^{3/4} \sqrt[4]{i a+i b x+1}}{b}+\frac{3 i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{3 i \log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{2 \sqrt{2} b}-\frac{3 i \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}+\frac{3 i \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)}{\sqrt{2} b}",1,"((-I)*(1 - I*a - I*b*x)^(3/4)*(1 + I*a + I*b*x)^(1/4))/b - ((3*I)*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) + ((3*I)*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) + (((3*I)/2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b) - (((3*I)/2)*Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)])/(Sqrt[2]*b)","A",13,10,14,0.7143,1,"{5093, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
234,1,427,0,0.23995,"\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a+b x)}}{x} \, dx","Int[1/(E^(((3*I)/2)*ArcTan[a + b*x])*x),x]","\frac{\log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{\sqrt{2}}-\frac{2 (a+i)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(-a+i)^{3/4}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)-\frac{2 (a+i)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(-a+i)^{3/4}}","\frac{\log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{-i a-i b x+1}}{\sqrt{i a+i b x+1}}+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}+1\right)}{\sqrt{2}}-\frac{2 (a+i)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(-a+i)^{3/4}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)+\sqrt{2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt[4]{-i a-i b x+1}}{\sqrt[4]{i a+i b x+1}}\right)-\frac{2 (a+i)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(-a+i)^{3/4}}",1,"(-2*(I + a)^(3/4)*ArcTan[((I + a)^(1/4)*(1 + I*a + I*b*x)^(1/4))/((I - a)^(1/4)*(1 - I*a - I*b*x)^(1/4))])/(I - a)^(3/4) - Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)] + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)] - (2*(I + a)^(3/4)*ArcTanh[((I + a)^(1/4)*(1 + I*a + I*b*x)^(1/4))/((I - a)^(1/4)*(1 - I*a - I*b*x)^(1/4))])/(I - a)^(3/4) + Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] - (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - I*a - I*b*x]/Sqrt[1 + I*a + I*b*x] + (Sqrt[2]*(1 - I*a - I*b*x)^(1/4))/(1 + I*a + I*b*x)^(1/4)]/Sqrt[2]","A",17,14,18,0.7778,1,"{5095, 105, 63, 331, 297, 1162, 617, 204, 1165, 628, 93, 212, 208, 205}"
235,1,211,0,0.1181212,"\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a+b x)}}{x^2} \, dx","Int[1/(E^(((3*I)/2)*ArcTan[a + b*x])*x^2),x]","-\frac{(-i a-i b x+1)^{3/4} \sqrt[4]{i a+i b x+1}}{(1+i a) x}-\frac{3 i b \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(-a+i)^{7/4} \sqrt[4]{a+i}}-\frac{3 i b \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(-a+i)^{7/4} \sqrt[4]{a+i}}","-\frac{(-i a-i b x+1)^{3/4} \sqrt[4]{i a+i b x+1}}{(1+i a) x}-\frac{3 i b \tan ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(-a+i)^{7/4} \sqrt[4]{a+i}}-\frac{3 i b \tanh ^{-1}\left(\frac{\sqrt[4]{a+i} \sqrt[4]{i a+i b x+1}}{\sqrt[4]{-a+i} \sqrt[4]{-i a-i b x+1}}\right)}{(-a+i)^{7/4} \sqrt[4]{a+i}}",1,"-(((1 - I*a - I*b*x)^(3/4)*(1 + I*a + I*b*x)^(1/4))/((1 + I*a)*x)) - ((3*I)*b*ArcTan[((I + a)^(1/4)*(1 + I*a + I*b*x)^(1/4))/((I - a)^(1/4)*(1 - I*a - I*b*x)^(1/4))])/((I - a)^(7/4)*(I + a)^(1/4)) - ((3*I)*b*ArcTanh[((I + a)^(1/4)*(1 + I*a + I*b*x)^(1/4))/((I - a)^(1/4)*(1 - I*a - I*b*x)^(1/4))])/((I - a)^(7/4)*(I + a)^(1/4))","A",6,6,18,0.3333,1,"{5095, 94, 93, 212, 208, 205}"
236,1,140,0,0.0744353,"\int e^{n \tan ^{-1}(a+b x)} x^m \, dx","Int[E^(n*ArcTan[a + b*x])*x^m,x]","\frac{x^{m+1} (-i a-i b x+1)^{\frac{i n}{2}} (i a+i b x+1)^{-\frac{i n}{2}} \left(1-\frac{b x}{-a+i}\right)^{\frac{i n}{2}} \left(1+\frac{b x}{a+i}\right)^{-\frac{i n}{2}} F_1\left(m+1;-\frac{i n}{2},\frac{i n}{2};m+2;-\frac{b x}{a+i},\frac{b x}{i-a}\right)}{m+1}","\frac{x^{m+1} (-i a-i b x+1)^{\frac{i n}{2}} (i a+i b x+1)^{-\frac{i n}{2}} \left(1-\frac{b x}{-a+i}\right)^{\frac{i n}{2}} \left(1+\frac{b x}{a+i}\right)^{-\frac{i n}{2}} F_1\left(m+1;-\frac{i n}{2},\frac{i n}{2};m+2;-\frac{b x}{a+i},\frac{b x}{i-a}\right)}{m+1}",1,"(x^(1 + m)*(1 - I*a - I*b*x)^((I/2)*n)*(1 - (b*x)/(I - a))^((I/2)*n)*AppellF1[1 + m, (-I/2)*n, (I/2)*n, 2 + m, -((b*x)/(I + a)), (b*x)/(I - a)])/((1 + m)*(1 + I*a + I*b*x)^((I/2)*n)*(1 + (b*x)/(I + a))^((I/2)*n))","A",4,3,14,0.2143,1,"{5095, 135, 133}"
237,1,260,0,0.1856419,"\int e^{n \tan ^{-1}(a+b x)} x^3 \, dx","Int[E^(n*ArcTan[a + b*x])*x^3,x]","\frac{2^{-2-\frac{i n}{2}} \left(36 a^2 n+24 a^3-12 a \left(2-n^2\right)-n \left(8-n^2\right)\right) (-i a-i b x+1)^{1+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}+1,\frac{i n}{2};\frac{i n}{2}+2;\frac{1}{2} (-i a-i b x+1)\right)}{3 b^4 (-n+2 i)}-\frac{(-i a-i b x+1)^{1+\frac{i n}{2}} \left(-18 a^2+2 b x (6 a+n)-10 a n-n^2+6\right) (i a+i b x+1)^{1-\frac{i n}{2}}}{24 b^4}+\frac{x^2 (-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{1-\frac{i n}{2}}}{4 b^2}","\frac{2^{-2-\frac{i n}{2}} \left(36 a^2 n+24 a^3-12 a \left(2-n^2\right)-n \left(8-n^2\right)\right) (-i a-i b x+1)^{1+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}+1,\frac{i n}{2};\frac{i n}{2}+2;\frac{1}{2} (-i a-i b x+1)\right)}{3 b^4 (-n+2 i)}-\frac{(-i a-i b x+1)^{1+\frac{i n}{2}} \left(-18 a^2+2 b x (6 a+n)-10 a n-n^2+6\right) (i a+i b x+1)^{1-\frac{i n}{2}}}{24 b^4}+\frac{x^2 (-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{1-\frac{i n}{2}}}{4 b^2}",1,"(x^2*(1 - I*a - I*b*x)^(1 + (I/2)*n)*(1 + I*a + I*b*x)^(1 - (I/2)*n))/(4*b^2) - ((1 - I*a - I*b*x)^(1 + (I/2)*n)*(1 + I*a + I*b*x)^(1 - (I/2)*n)*(6 - 18*a^2 - 10*a*n - n^2 + 2*b*(6*a + n)*x))/(24*b^4) + (2^(-2 - (I/2)*n)*(24*a^3 + 36*a^2*n - 12*a*(2 - n^2) - n*(8 - n^2))*(1 - I*a - I*b*x)^(1 + (I/2)*n)*Hypergeometric2F1[1 + (I/2)*n, (I/2)*n, 2 + (I/2)*n, (1 - I*a - I*b*x)/2])/(3*b^4*(2*I - n))","A",4,4,14,0.2857,1,"{5095, 100, 147, 69}"
238,1,220,0,0.1390887,"\int e^{n \tan ^{-1}(a+b x)} x^2 \, dx","Int[E^(n*ArcTan[a + b*x])*x^2,x]","\frac{2^{-\frac{i n}{2}} \left(-6 a^2-6 a n-n^2+2\right) (-i a-i b x+1)^{1+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}+1,\frac{i n}{2};\frac{i n}{2}+2;\frac{1}{2} (-i a-i b x+1)\right)}{3 b^3 (-n+2 i)}-\frac{(4 a+n) (-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{1-\frac{i n}{2}}}{6 b^3}+\frac{x (-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{1-\frac{i n}{2}}}{3 b^2}","\frac{2^{-\frac{i n}{2}} \left(-6 a^2-6 a n-n^2+2\right) (-i a-i b x+1)^{1+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}+1,\frac{i n}{2};\frac{i n}{2}+2;\frac{1}{2} (-i a-i b x+1)\right)}{3 b^3 (-n+2 i)}-\frac{(4 a+n) (-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{1-\frac{i n}{2}}}{6 b^3}+\frac{x (-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{1-\frac{i n}{2}}}{3 b^2}",1,"-((4*a + n)*(1 - I*a - I*b*x)^(1 + (I/2)*n)*(1 + I*a + I*b*x)^(1 - (I/2)*n))/(6*b^3) + (x*(1 - I*a - I*b*x)^(1 + (I/2)*n)*(1 + I*a + I*b*x)^(1 - (I/2)*n))/(3*b^2) + ((2 - 6*a^2 - 6*a*n - n^2)*(1 - I*a - I*b*x)^(1 + (I/2)*n)*Hypergeometric2F1[1 + (I/2)*n, (I/2)*n, 2 + (I/2)*n, (1 - I*a - I*b*x)/2])/(3*2^((I/2)*n)*b^3*(2*I - n))","A",4,4,14,0.2857,1,"{5095, 90, 80, 69}"
239,1,147,0,0.0672028,"\int e^{n \tan ^{-1}(a+b x)} x \, dx","Int[E^(n*ArcTan[a + b*x])*x,x]","\frac{2^{-\frac{i n}{2}} (2 a+n) (-i a-i b x+1)^{1+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}+1,\frac{i n}{2};\frac{i n}{2}+2;\frac{1}{2} (-i a-i b x+1)\right)}{b^2 (-n+2 i)}+\frac{(-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{1-\frac{i n}{2}}}{2 b^2}","\frac{2^{-\frac{i n}{2}} (2 a+n) (-i a-i b x+1)^{1+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}+1,\frac{i n}{2};\frac{i n}{2}+2;\frac{1}{2} (-i a-i b x+1)\right)}{b^2 (-n+2 i)}+\frac{(-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{1-\frac{i n}{2}}}{2 b^2}",1,"((1 - I*a - I*b*x)^(1 + (I/2)*n)*(1 + I*a + I*b*x)^(1 - (I/2)*n))/(2*b^2) + ((2*a + n)*(1 - I*a - I*b*x)^(1 + (I/2)*n)*Hypergeometric2F1[1 + (I/2)*n, (I/2)*n, 2 + (I/2)*n, (1 - I*a - I*b*x)/2])/(2^((I/2)*n)*b^2*(2*I - n))","A",3,3,12,0.2500,1,"{5095, 80, 69}"
240,1,91,0,0.013713,"\int e^{n \tan ^{-1}(a+b x)} \, dx","Int[E^(n*ArcTan[a + b*x]),x]","-\frac{2^{1-\frac{i n}{2}} (-i a-i b x+1)^{1+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}+1,\frac{i n}{2};\frac{i n}{2}+2;\frac{1}{2} (-i a-i b x+1)\right)}{b (-n+2 i)}","-\frac{2^{1-\frac{i n}{2}} (-i a-i b x+1)^{1+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}+1,\frac{i n}{2};\frac{i n}{2}+2;\frac{1}{2} (-i a-i b x+1)\right)}{b (-n+2 i)}",1,"-((2^(1 - (I/2)*n)*(1 - I*a - I*b*x)^(1 + (I/2)*n)*Hypergeometric2F1[1 + (I/2)*n, (I/2)*n, 2 + (I/2)*n, (1 - I*a - I*b*x)/2])/(b*(2*I - n)))","A",2,2,10,0.2000,1,"{5093, 69}"
241,1,191,0,0.0742903,"\int \frac{e^{n \tan ^{-1}(a+b x)}}{x} \, dx","Int[E^(n*ArcTan[a + b*x])/x,x]","\frac{2 i (-i a-i b x+1)^{\frac{i n}{2}} (i a+i b x+1)^{-\frac{i n}{2}} \, _2F_1\left(1,\frac{i n}{2};\frac{i n}{2}+1;\frac{(i-a) (-i a-i b x+1)}{(a+i) (i a+i b x+1)}\right)}{n}-\frac{i 2^{1-\frac{i n}{2}} (-i a-i b x+1)^{\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2},\frac{i n}{2};\frac{i n}{2}+1;\frac{1}{2} (-i a-i b x+1)\right)}{n}","\frac{2 i (-i a-i b x+1)^{\frac{i n}{2}} (i a+i b x+1)^{-\frac{i n}{2}} \, _2F_1\left(1,\frac{i n}{2};\frac{i n}{2}+1;\frac{(i-a) (-i a-i b x+1)}{(a+i) (i a+i b x+1)}\right)}{n}-\frac{i 2^{1-\frac{i n}{2}} (-i a-i b x+1)^{\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2},\frac{i n}{2};\frac{i n}{2}+1;\frac{1}{2} (-i a-i b x+1)\right)}{n}",1,"((2*I)*(1 - I*a - I*b*x)^((I/2)*n)*Hypergeometric2F1[1, (I/2)*n, 1 + (I/2)*n, ((I - a)*(1 - I*a - I*b*x))/((I + a)*(1 + I*a + I*b*x))])/(n*(1 + I*a + I*b*x)^((I/2)*n)) - (I*2^(1 - (I/2)*n)*(1 - I*a - I*b*x)^((I/2)*n)*Hypergeometric2F1[(I/2)*n, (I/2)*n, 1 + (I/2)*n, (1 - I*a - I*b*x)/2])/n","A",4,4,14,0.2857,1,"{5095, 105, 69, 131}"
242,1,128,0,0.0428307,"\int \frac{e^{n \tan ^{-1}(a+b x)}}{x^2} \, dx","Int[E^(n*ArcTan[a + b*x])/x^2,x]","-\frac{4 b (-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{-1-\frac{i n}{2}} \, _2F_1\left(2,\frac{i n}{2}+1;\frac{i n}{2}+2;\frac{(i-a) (-i a-i b x+1)}{(a+i) (i a+i b x+1)}\right)}{(a+i)^2 (-n+2 i)}","-\frac{4 b (-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{-1-\frac{i n}{2}} \, _2F_1\left(2,\frac{i n}{2}+1;\frac{i n}{2}+2;\frac{(i-a) (-i a-i b x+1)}{(a+i) (i a+i b x+1)}\right)}{(a+i)^2 (-n+2 i)}",1,"(-4*b*(1 - I*a - I*b*x)^(1 + (I/2)*n)*(1 + I*a + I*b*x)^(-1 - (I/2)*n)*Hypergeometric2F1[2, 1 + (I/2)*n, 2 + (I/2)*n, ((I - a)*(1 - I*a - I*b*x))/((I + a)*(1 + I*a + I*b*x))])/((I + a)^2*(2*I - n))","A",2,2,14,0.1429,1,"{5095, 131}"
243,1,207,0,0.1087833,"\int \frac{e^{n \tan ^{-1}(a+b x)}}{x^3} \, dx","Int[E^(n*ArcTan[a + b*x])/x^3,x]","-\frac{(-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{1-\frac{i n}{2}}}{2 \left(a^2+1\right) x^2}-\frac{2 b^2 (2 a-n) (-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{-1-\frac{i n}{2}} \, _2F_1\left(2,\frac{i n}{2}+1;\frac{i n}{2}+2;\frac{(i-a) (-i a-i b x+1)}{(a+i) (i a+i b x+1)}\right)}{(-a+i) (a+i)^3 (-n+2 i)}","-\frac{(-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{1-\frac{i n}{2}}}{2 \left(a^2+1\right) x^2}-\frac{2 b^2 (2 a-n) (-i a-i b x+1)^{1+\frac{i n}{2}} (i a+i b x+1)^{-1-\frac{i n}{2}} \, _2F_1\left(2,\frac{i n}{2}+1;\frac{i n}{2}+2;\frac{(i-a) (-i a-i b x+1)}{(a+i) (i a+i b x+1)}\right)}{(-a+i) (a+i)^3 (-n+2 i)}",1,"-((1 - I*a - I*b*x)^(1 + (I/2)*n)*(1 + I*a + I*b*x)^(1 - (I/2)*n))/(2*(1 + a^2)*x^2) - (2*b^2*(2*a - n)*(1 - I*a - I*b*x)^(1 + (I/2)*n)*(1 + I*a + I*b*x)^(-1 - (I/2)*n)*Hypergeometric2F1[2, 1 + (I/2)*n, 2 + (I/2)*n, ((I - a)*(1 - I*a - I*b*x))/((I + a)*(1 + I*a + I*b*x))])/((I - a)*(I + a)^3*(2*I - n))","A",3,3,14,0.2143,1,"{5095, 96, 131}"
244,1,102,0,0.0751491,"\int e^{\tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^p \, dx","Int[E^ArcTan[a*x]*(c + a^2*c*x^2)^p,x]","\frac{i 2^{p+\left(1-\frac{i}{2}\right)} (1-i a x)^{p+\left(1+\frac{i}{2}\right)} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p \, _2F_1\left(\frac{i}{2}-p,p+\left(1+\frac{i}{2}\right);p+\left(2+\frac{i}{2}\right);\frac{1}{2} (1-i a x)\right)}{a (2 p+(2+i))}","\frac{i 2^{p+\left(1-\frac{i}{2}\right)} (1-i a x)^{p+\left(1+\frac{i}{2}\right)} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p \, _2F_1\left(\frac{i}{2}-p,p+\left(1+\frac{i}{2}\right);p+\left(2+\frac{i}{2}\right);\frac{1}{2} (1-i a x)\right)}{a (2 p+(2+i))}",1,"(I*2^((1 - I/2) + p)*(1 - I*a*x)^((1 + I/2) + p)*(c + a^2*c*x^2)^p*Hypergeometric2F1[I/2 - p, (1 + I/2) + p, (2 + I/2) + p, (1 - I*a*x)/2])/(a*((2 + I) + 2*p)*(1 + a^2*x^2)^p)","A",3,3,19,0.1579,1,"{5076, 5073, 69}"
245,1,63,0,0.0372467,"\int e^{\tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^2 \, dx","Int[E^ArcTan[a*x]*(c + a^2*c*x^2)^2,x]","\frac{\left(\frac{1}{37}+\frac{6 i}{37}\right) 2^{3-\frac{i}{2}} c^2 (1-i a x)^{3+\frac{i}{2}} \, _2F_1\left(-2+\frac{i}{2},3+\frac{i}{2};4+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}","\frac{\left(\frac{1}{37}+\frac{6 i}{37}\right) 2^{3-\frac{i}{2}} c^2 (1-i a x)^{3+\frac{i}{2}} \, _2F_1\left(-2+\frac{i}{2},3+\frac{i}{2};4+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}",1,"((1/37 + (6*I)/37)*2^(3 - I/2)*c^2*(1 - I*a*x)^(3 + I/2)*Hypergeometric2F1[-2 + I/2, 3 + I/2, 4 + I/2, (1 - I*a*x)/2])/a","A",2,2,19,0.1053,1,"{5073, 69}"
246,1,61,0,0.0261251,"\int e^{\tan ^{-1}(a x)} \left(c+a^2 c x^2\right) \, dx","Int[E^ArcTan[a*x]*(c + a^2*c*x^2),x]","\frac{\left(\frac{1}{17}+\frac{4 i}{17}\right) 2^{2-\frac{i}{2}} c (1-i a x)^{2+\frac{i}{2}} \, _2F_1\left(-1+\frac{i}{2},2+\frac{i}{2};3+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}","\frac{\left(\frac{1}{17}+\frac{4 i}{17}\right) 2^{2-\frac{i}{2}} c (1-i a x)^{2+\frac{i}{2}} \, _2F_1\left(-1+\frac{i}{2},2+\frac{i}{2};3+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}",1,"((1/17 + (4*I)/17)*2^(2 - I/2)*c*(1 - I*a*x)^(2 + I/2)*Hypergeometric2F1[-1 + I/2, 2 + I/2, 3 + I/2, (1 - I*a*x)/2])/a","A",2,2,17,0.1176,1,"{5073, 69}"
247,1,60,0,0.0113063,"\int e^{\tan ^{-1}(a x)} \, dx","Int[E^ArcTan[a*x],x]","\frac{\left(\frac{1}{5}+\frac{2 i}{5}\right) 2^{1-\frac{i}{2}} (1-i a x)^{1+\frac{i}{2}} \, _2F_1\left(\frac{i}{2},1+\frac{i}{2};2+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}","\frac{\left(\frac{1}{5}+\frac{2 i}{5}\right) 2^{1-\frac{i}{2}} (1-i a x)^{1+\frac{i}{2}} \, _2F_1\left(\frac{i}{2},1+\frac{i}{2};2+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}",1,"((1/5 + (2*I)/5)*2^(1 - I/2)*(1 - I*a*x)^(1 + I/2)*Hypergeometric2F1[I/2, 1 + I/2, 2 + I/2, (1 - I*a*x)/2])/a","A",2,2,6,0.3333,1,"{5061, 69}"
248,1,13,0,0.0258877,"\int \frac{e^{\tan ^{-1}(a x)}}{c+a^2 c x^2} \, dx","Int[E^ArcTan[a*x]/(c + a^2*c*x^2),x]","\frac{e^{\tan ^{-1}(a x)}}{a c}","\frac{e^{\tan ^{-1}(a x)}}{a c}",1,"E^ArcTan[a*x]/(a*c)","A",1,1,19,0.05263,1,"{5071}"
249,1,50,0,0.0504912,"\int \frac{e^{\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^2} \, dx","Int[E^ArcTan[a*x]/(c + a^2*c*x^2)^2,x]","\frac{(2 a x+1) e^{\tan ^{-1}(a x)}}{5 a c^2 \left(a^2 x^2+1\right)}+\frac{2 e^{\tan ^{-1}(a x)}}{5 a c^2}","\frac{(2 a x+1) e^{\tan ^{-1}(a x)}}{5 a c^2 \left(a^2 x^2+1\right)}+\frac{2 e^{\tan ^{-1}(a x)}}{5 a c^2}",1,"(2*E^ArcTan[a*x])/(5*a*c^2) + (E^ArcTan[a*x]*(1 + 2*a*x))/(5*a*c^2*(1 + a^2*x^2))","A",2,2,19,0.1053,1,"{5070, 5071}"
250,1,83,0,0.0777701,"\int \frac{e^{\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^3} \, dx","Int[E^ArcTan[a*x]/(c + a^2*c*x^2)^3,x]","\frac{12 (2 a x+1) e^{\tan ^{-1}(a x)}}{85 a c^3 \left(a^2 x^2+1\right)}+\frac{(4 a x+1) e^{\tan ^{-1}(a x)}}{17 a c^3 \left(a^2 x^2+1\right)^2}+\frac{24 e^{\tan ^{-1}(a x)}}{85 a c^3}","\frac{12 (2 a x+1) e^{\tan ^{-1}(a x)}}{85 a c^3 \left(a^2 x^2+1\right)}+\frac{(4 a x+1) e^{\tan ^{-1}(a x)}}{17 a c^3 \left(a^2 x^2+1\right)^2}+\frac{24 e^{\tan ^{-1}(a x)}}{85 a c^3}",1,"(24*E^ArcTan[a*x])/(85*a*c^3) + (E^ArcTan[a*x]*(1 + 4*a*x))/(17*a*c^3*(1 + a^2*x^2)^2) + (12*E^ArcTan[a*x]*(1 + 2*a*x))/(85*a*c^3*(1 + a^2*x^2))","A",3,2,19,0.1053,1,"{5070, 5071}"
251,1,116,0,0.1097428,"\int \frac{e^{\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^4} \, dx","Int[E^ArcTan[a*x]/(c + a^2*c*x^2)^4,x]","\frac{72 (2 a x+1) e^{\tan ^{-1}(a x)}}{629 a c^4 \left(a^2 x^2+1\right)}+\frac{30 (4 a x+1) e^{\tan ^{-1}(a x)}}{629 a c^4 \left(a^2 x^2+1\right)^2}+\frac{(6 a x+1) e^{\tan ^{-1}(a x)}}{37 a c^4 \left(a^2 x^2+1\right)^3}+\frac{144 e^{\tan ^{-1}(a x)}}{629 a c^4}","\frac{72 (2 a x+1) e^{\tan ^{-1}(a x)}}{629 a c^4 \left(a^2 x^2+1\right)}+\frac{30 (4 a x+1) e^{\tan ^{-1}(a x)}}{629 a c^4 \left(a^2 x^2+1\right)^2}+\frac{(6 a x+1) e^{\tan ^{-1}(a x)}}{37 a c^4 \left(a^2 x^2+1\right)^3}+\frac{144 e^{\tan ^{-1}(a x)}}{629 a c^4}",1,"(144*E^ArcTan[a*x])/(629*a*c^4) + (E^ArcTan[a*x]*(1 + 6*a*x))/(37*a*c^4*(1 + a^2*x^2)^3) + (30*E^ArcTan[a*x]*(1 + 4*a*x))/(629*a*c^4*(1 + a^2*x^2)^2) + (72*E^ArcTan[a*x]*(1 + 2*a*x))/(629*a*c^4*(1 + a^2*x^2))","A",4,2,19,0.1053,1,"{5070, 5071}"
252,1,149,0,0.1404648,"\int \frac{e^{\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^5} \, dx","Int[E^ArcTan[a*x]/(c + a^2*c*x^2)^5,x]","\frac{4032 (2 a x+1) e^{\tan ^{-1}(a x)}}{40885 a c^5 \left(a^2 x^2+1\right)}+\frac{336 (4 a x+1) e^{\tan ^{-1}(a x)}}{8177 a c^5 \left(a^2 x^2+1\right)^2}+\frac{56 (6 a x+1) e^{\tan ^{-1}(a x)}}{2405 a c^5 \left(a^2 x^2+1\right)^3}+\frac{(8 a x+1) e^{\tan ^{-1}(a x)}}{65 a c^5 \left(a^2 x^2+1\right)^4}+\frac{8064 e^{\tan ^{-1}(a x)}}{40885 a c^5}","\frac{4032 (2 a x+1) e^{\tan ^{-1}(a x)}}{40885 a c^5 \left(a^2 x^2+1\right)}+\frac{336 (4 a x+1) e^{\tan ^{-1}(a x)}}{8177 a c^5 \left(a^2 x^2+1\right)^2}+\frac{56 (6 a x+1) e^{\tan ^{-1}(a x)}}{2405 a c^5 \left(a^2 x^2+1\right)^3}+\frac{(8 a x+1) e^{\tan ^{-1}(a x)}}{65 a c^5 \left(a^2 x^2+1\right)^4}+\frac{8064 e^{\tan ^{-1}(a x)}}{40885 a c^5}",1,"(8064*E^ArcTan[a*x])/(40885*a*c^5) + (E^ArcTan[a*x]*(1 + 8*a*x))/(65*a*c^5*(1 + a^2*x^2)^4) + (56*E^ArcTan[a*x]*(1 + 6*a*x))/(2405*a*c^5*(1 + a^2*x^2)^3) + (336*E^ArcTan[a*x]*(1 + 4*a*x))/(8177*a*c^5*(1 + a^2*x^2)^2) + (4032*E^ArcTan[a*x]*(1 + 2*a*x))/(40885*a*c^5*(1 + a^2*x^2))","A",5,2,19,0.1053,1,"{5070, 5071}"
253,1,98,0,0.0749484,"\int e^{\tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^{3/2} \, dx","Int[E^ArcTan[a*x]*(c + a^2*c*x^2)^(3/2),x]","\frac{\left(\frac{1}{13}+\frac{5 i}{13}\right) 2^{\frac{3}{2}-\frac{i}{2}} c (1-i a x)^{\frac{5}{2}+\frac{i}{2}} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{3}{2}+\frac{i}{2},\frac{5}{2}+\frac{i}{2};\frac{7}{2}+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}","\frac{\left(\frac{1}{13}+\frac{5 i}{13}\right) 2^{\frac{3}{2}-\frac{i}{2}} c (1-i a x)^{\frac{5}{2}+\frac{i}{2}} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{3}{2}+\frac{i}{2},\frac{5}{2}+\frac{i}{2};\frac{7}{2}+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}",1,"((1/13 + (5*I)/13)*2^(3/2 - I/2)*c*(1 - I*a*x)^(5/2 + I/2)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[-3/2 + I/2, 5/2 + I/2, 7/2 + I/2, (1 - I*a*x)/2])/(a*Sqrt[1 + a^2*x^2])","A",3,3,21,0.1429,1,"{5076, 5073, 69}"
254,1,97,0,0.0695813,"\int e^{\tan ^{-1}(a x)} \sqrt{c+a^2 c x^2} \, dx","Int[E^ArcTan[a*x]*Sqrt[c + a^2*c*x^2],x]","\frac{\left(\frac{1}{5}+\frac{3 i}{5}\right) 2^{\frac{1}{2}-\frac{i}{2}} (1-i a x)^{\frac{3}{2}+\frac{i}{2}} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{1}{2}+\frac{i}{2},\frac{3}{2}+\frac{i}{2};\frac{5}{2}+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}","\frac{\left(\frac{1}{5}+\frac{3 i}{5}\right) 2^{\frac{1}{2}-\frac{i}{2}} (1-i a x)^{\frac{3}{2}+\frac{i}{2}} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{1}{2}+\frac{i}{2},\frac{3}{2}+\frac{i}{2};\frac{5}{2}+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}",1,"((1/5 + (3*I)/5)*2^(1/2 - I/2)*(1 - I*a*x)^(3/2 + I/2)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[-1/2 + I/2, 3/2 + I/2, 5/2 + I/2, (1 - I*a*x)/2])/(a*Sqrt[1 + a^2*x^2])","A",3,3,21,0.1429,1,"{5076, 5073, 69}"
255,1,93,0,0.0709474,"\int \frac{e^{\tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[E^ArcTan[a*x]/Sqrt[c + a^2*c*x^2],x]","\frac{(1+i) 2^{-\frac{1}{2}-\frac{i}{2}} (1-i a x)^{\frac{1}{2}+\frac{i}{2}} \sqrt{a^2 x^2+1} \, _2F_1\left(\frac{1}{2}+\frac{i}{2},\frac{1}{2}+\frac{i}{2};\frac{3}{2}+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 c x^2+c}}","\frac{(1+i) 2^{-\frac{1}{2}-\frac{i}{2}} (1-i a x)^{\frac{1}{2}+\frac{i}{2}} \sqrt{a^2 x^2+1} \, _2F_1\left(\frac{1}{2}+\frac{i}{2},\frac{1}{2}+\frac{i}{2};\frac{3}{2}+\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 c x^2+c}}",1,"((1 + I)*(1 - I*a*x)^(1/2 + I/2)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[1/2 + I/2, 1/2 + I/2, 3/2 + I/2, (1 - I*a*x)/2])/(2^(1/2 + I/2)*a*Sqrt[c + a^2*c*x^2])","A",3,3,21,0.1429,1,"{5076, 5073, 69}"
256,1,35,0,0.0361105,"\int \frac{e^{\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[E^ArcTan[a*x]/(c + a^2*c*x^2)^(3/2),x]","\frac{(a x+1) e^{\tan ^{-1}(a x)}}{2 a c \sqrt{a^2 c x^2+c}}","\frac{(a x+1) e^{\tan ^{-1}(a x)}}{2 a c \sqrt{a^2 c x^2+c}}",1,"(E^ArcTan[a*x]*(1 + a*x))/(2*a*c*Sqrt[c + a^2*c*x^2])","A",1,1,21,0.04762,1,"{5069}"
257,1,72,0,0.0730196,"\int \frac{e^{\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{5/2}} \, dx","Int[E^ArcTan[a*x]/(c + a^2*c*x^2)^(5/2),x]","\frac{3 (a x+1) e^{\tan ^{-1}(a x)}}{10 a c^2 \sqrt{a^2 c x^2+c}}+\frac{(3 a x+1) e^{\tan ^{-1}(a x)}}{10 a c \left(a^2 c x^2+c\right)^{3/2}}","\frac{3 (a x+1) e^{\tan ^{-1}(a x)}}{10 a c^2 \sqrt{a^2 c x^2+c}}+\frac{(3 a x+1) e^{\tan ^{-1}(a x)}}{10 a c \left(a^2 c x^2+c\right)^{3/2}}",1,"(E^ArcTan[a*x]*(1 + 3*a*x))/(10*a*c*(c + a^2*c*x^2)^(3/2)) + (3*E^ArcTan[a*x]*(1 + a*x))/(10*a*c^2*Sqrt[c + a^2*c*x^2])","A",2,2,21,0.09524,1,"{5070, 5069}"
258,1,108,0,0.1132766,"\int \frac{e^{\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{7/2}} \, dx","Int[E^ArcTan[a*x]/(c + a^2*c*x^2)^(7/2),x]","\frac{3 (a x+1) e^{\tan ^{-1}(a x)}}{13 a c^3 \sqrt{a^2 c x^2+c}}+\frac{(3 a x+1) e^{\tan ^{-1}(a x)}}{13 a c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{(5 a x+1) e^{\tan ^{-1}(a x)}}{26 a c \left(a^2 c x^2+c\right)^{5/2}}","\frac{3 (a x+1) e^{\tan ^{-1}(a x)}}{13 a c^3 \sqrt{a^2 c x^2+c}}+\frac{(3 a x+1) e^{\tan ^{-1}(a x)}}{13 a c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{(5 a x+1) e^{\tan ^{-1}(a x)}}{26 a c \left(a^2 c x^2+c\right)^{5/2}}",1,"(E^ArcTan[a*x]*(1 + 5*a*x))/(26*a*c*(c + a^2*c*x^2)^(5/2)) + (E^ArcTan[a*x]*(1 + 3*a*x))/(13*a*c^2*(c + a^2*c*x^2)^(3/2)) + (3*E^ArcTan[a*x]*(1 + a*x))/(13*a*c^3*Sqrt[c + a^2*c*x^2])","A",3,2,21,0.09524,1,"{5070, 5069}"
259,1,90,0,0.0703924,"\int e^{2 \tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^p \, dx","Int[E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^p,x]","\frac{i 2^{p-i} (1-i a x)^{p+(1+i)} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p \, _2F_1\left(i-p,p+(1+i);p+(2+i);\frac{1}{2} (1-i a x)\right)}{a (p+(1+i))}","\frac{i 2^{p-i} (1-i a x)^{p+(1+i)} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p \, _2F_1\left(i-p,p+(1+i);p+(2+i);\frac{1}{2} (1-i a x)\right)}{a (p+(1+i))}",1,"(I*2^(-I + p)*(1 - I*a*x)^((1 + I) + p)*(c + a^2*c*x^2)^p*Hypergeometric2F1[I - p, (1 + I) + p, (2 + I) + p, (1 - I*a*x)/2])/(a*((1 + I) + p)*(1 + a^2*x^2)^p)","A",3,3,21,0.1429,1,"{5076, 5073, 69}"
260,1,53,0,0.0389405,"\int e^{2 \tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^2 \, dx","Int[E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^2,x]","\frac{\left(\frac{1}{5}+\frac{3 i}{5}\right) 2^{1-i} c^2 (1-i a x)^{3+i} \, _2F_1\left(-2+i,3+i;4+i;\frac{1}{2} (1-i a x)\right)}{a}","\frac{\left(\frac{1}{5}+\frac{3 i}{5}\right) 2^{1-i} c^2 (1-i a x)^{3+i} \, _2F_1\left(-2+i,3+i;4+i;\frac{1}{2} (1-i a x)\right)}{a}",1,"((1/5 + (3*I)/5)*2^(1 - I)*c^2*(1 - I*a*x)^(3 + I)*Hypergeometric2F1[-2 + I, 3 + I, 4 + I, (1 - I*a*x)/2])/a","A",2,2,21,0.09524,1,"{5073, 69}"
261,1,51,0,0.0256805,"\int e^{2 \tan ^{-1}(a x)} \left(c+a^2 c x^2\right) \, dx","Int[E^(2*ArcTan[a*x])*(c + a^2*c*x^2),x]","\frac{\left(\frac{1}{5}+\frac{2 i}{5}\right) 2^{1-i} c (1-i a x)^{2+i} \, _2F_1\left(-1+i,2+i;3+i;\frac{1}{2} (1-i a x)\right)}{a}","\frac{\left(\frac{1}{5}+\frac{2 i}{5}\right) 2^{1-i} c (1-i a x)^{2+i} \, _2F_1\left(-1+i,2+i;3+i;\frac{1}{2} (1-i a x)\right)}{a}",1,"((1/5 + (2*I)/5)*2^(1 - I)*c*(1 - I*a*x)^(2 + I)*Hypergeometric2F1[-1 + I, 2 + I, 3 + I, (1 - I*a*x)/2])/a","A",2,2,19,0.1053,1,"{5073, 69}"
262,1,46,0,0.0121184,"\int e^{2 \tan ^{-1}(a x)} \, dx","Int[E^(2*ArcTan[a*x]),x]","\frac{(1+i) 2^{-1-i} (1-i a x)^{1+i} \, _2F_1\left(i,1+i;2+i;\frac{1}{2} (1-i a x)\right)}{a}","\frac{(1+i) 2^{-1-i} (1-i a x)^{1+i} \, _2F_1\left(i,1+i;2+i;\frac{1}{2} (1-i a x)\right)}{a}",1,"((1 + I)*(1 - I*a*x)^(1 + I)*Hypergeometric2F1[I, 1 + I, 2 + I, (1 - I*a*x)/2])/(2^(1 + I)*a)","A",2,2,8,0.2500,1,"{5061, 69}"
263,1,18,0,0.0281226,"\int \frac{e^{2 \tan ^{-1}(a x)}}{c+a^2 c x^2} \, dx","Int[E^(2*ArcTan[a*x])/(c + a^2*c*x^2),x]","\frac{e^{2 \tan ^{-1}(a x)}}{2 a c}","\frac{e^{2 \tan ^{-1}(a x)}}{2 a c}",1,"E^(2*ArcTan[a*x])/(2*a*c)","A",1,1,21,0.04762,1,"{5071}"
264,1,53,0,0.057281,"\int \frac{e^{2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^2} \, dx","Int[E^(2*ArcTan[a*x])/(c + a^2*c*x^2)^2,x]","\frac{(a x+1) e^{2 \tan ^{-1}(a x)}}{4 a c^2 \left(a^2 x^2+1\right)}+\frac{e^{2 \tan ^{-1}(a x)}}{8 a c^2}","\frac{(a x+1) e^{2 \tan ^{-1}(a x)}}{4 a c^2 \left(a^2 x^2+1\right)}+\frac{e^{2 \tan ^{-1}(a x)}}{8 a c^2}",1,"E^(2*ArcTan[a*x])/(8*a*c^2) + (E^(2*ArcTan[a*x])*(1 + a*x))/(4*a*c^2*(1 + a^2*x^2))","A",2,2,21,0.09524,1,"{5070, 5071}"
265,1,88,0,0.0894982,"\int \frac{e^{2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^3} \, dx","Int[E^(2*ArcTan[a*x])/(c + a^2*c*x^2)^3,x]","\frac{3 (a x+1) e^{2 \tan ^{-1}(a x)}}{20 a c^3 \left(a^2 x^2+1\right)}+\frac{(2 a x+1) e^{2 \tan ^{-1}(a x)}}{10 a c^3 \left(a^2 x^2+1\right)^2}+\frac{3 e^{2 \tan ^{-1}(a x)}}{40 a c^3}","\frac{3 (a x+1) e^{2 \tan ^{-1}(a x)}}{20 a c^3 \left(a^2 x^2+1\right)}+\frac{(2 a x+1) e^{2 \tan ^{-1}(a x)}}{10 a c^3 \left(a^2 x^2+1\right)^2}+\frac{3 e^{2 \tan ^{-1}(a x)}}{40 a c^3}",1,"(3*E^(2*ArcTan[a*x]))/(40*a*c^3) + (E^(2*ArcTan[a*x])*(1 + 2*a*x))/(10*a*c^3*(1 + a^2*x^2)^2) + (3*E^(2*ArcTan[a*x])*(1 + a*x))/(20*a*c^3*(1 + a^2*x^2))","A",3,2,21,0.09524,1,"{5070, 5071}"
266,1,123,0,0.1197639,"\int \frac{e^{2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^4} \, dx","Int[E^(2*ArcTan[a*x])/(c + a^2*c*x^2)^4,x]","\frac{9 (a x+1) e^{2 \tan ^{-1}(a x)}}{80 a c^4 \left(a^2 x^2+1\right)}+\frac{3 (2 a x+1) e^{2 \tan ^{-1}(a x)}}{40 a c^4 \left(a^2 x^2+1\right)^2}+\frac{(3 a x+1) e^{2 \tan ^{-1}(a x)}}{20 a c^4 \left(a^2 x^2+1\right)^3}+\frac{9 e^{2 \tan ^{-1}(a x)}}{160 a c^4}","\frac{9 (a x+1) e^{2 \tan ^{-1}(a x)}}{80 a c^4 \left(a^2 x^2+1\right)}+\frac{3 (2 a x+1) e^{2 \tan ^{-1}(a x)}}{40 a c^4 \left(a^2 x^2+1\right)^2}+\frac{(3 a x+1) e^{2 \tan ^{-1}(a x)}}{20 a c^4 \left(a^2 x^2+1\right)^3}+\frac{9 e^{2 \tan ^{-1}(a x)}}{160 a c^4}",1,"(9*E^(2*ArcTan[a*x]))/(160*a*c^4) + (E^(2*ArcTan[a*x])*(1 + 3*a*x))/(20*a*c^4*(1 + a^2*x^2)^3) + (3*E^(2*ArcTan[a*x])*(1 + 2*a*x))/(40*a*c^4*(1 + a^2*x^2)^2) + (9*E^(2*ArcTan[a*x])*(1 + a*x))/(80*a*c^4*(1 + a^2*x^2))","A",4,2,21,0.09524,1,"{5070, 5071}"
267,1,88,0,0.08045,"\int e^{2 \tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^{3/2} \, dx","Int[E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^(3/2),x]","\frac{\left(\frac{2}{29}+\frac{5 i}{29}\right) 2^{\frac{5}{2}-i} c (1-i a x)^{\frac{5}{2}+i} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{3}{2}+i,\frac{5}{2}+i;\frac{7}{2}+i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}","\frac{\left(\frac{2}{29}+\frac{5 i}{29}\right) 2^{\frac{5}{2}-i} c (1-i a x)^{\frac{5}{2}+i} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{3}{2}+i,\frac{5}{2}+i;\frac{7}{2}+i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}",1,"((2/29 + (5*I)/29)*2^(5/2 - I)*c*(1 - I*a*x)^(5/2 + I)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[-3/2 + I, 5/2 + I, 7/2 + I, (1 - I*a*x)/2])/(a*Sqrt[1 + a^2*x^2])","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
268,1,87,0,0.0744987,"\int e^{2 \tan ^{-1}(a x)} \sqrt{c+a^2 c x^2} \, dx","Int[E^(2*ArcTan[a*x])*Sqrt[c + a^2*c*x^2],x]","\frac{\left(\frac{2}{13}+\frac{3 i}{13}\right) 2^{\frac{3}{2}-i} (1-i a x)^{\frac{3}{2}+i} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{1}{2}+i,\frac{3}{2}+i;\frac{5}{2}+i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}","\frac{\left(\frac{2}{13}+\frac{3 i}{13}\right) 2^{\frac{3}{2}-i} (1-i a x)^{\frac{3}{2}+i} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{1}{2}+i,\frac{3}{2}+i;\frac{5}{2}+i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}",1,"((2/13 + (3*I)/13)*2^(3/2 - I)*(1 - I*a*x)^(3/2 + I)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[-1/2 + I, 3/2 + I, 5/2 + I, (1 - I*a*x)/2])/(a*Sqrt[1 + a^2*x^2])","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
269,1,87,0,0.0759546,"\int \frac{e^{2 \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[E^(2*ArcTan[a*x])/Sqrt[c + a^2*c*x^2],x]","\frac{\left(\frac{2}{5}+\frac{i}{5}\right) 2^{\frac{1}{2}-i} (1-i a x)^{\frac{1}{2}+i} \sqrt{a^2 x^2+1} \, _2F_1\left(\frac{1}{2}+i,\frac{1}{2}+i;\frac{3}{2}+i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 c x^2+c}}","\frac{\left(\frac{2}{5}+\frac{i}{5}\right) 2^{\frac{1}{2}-i} (1-i a x)^{\frac{1}{2}+i} \sqrt{a^2 x^2+1} \, _2F_1\left(\frac{1}{2}+i,\frac{1}{2}+i;\frac{3}{2}+i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 c x^2+c}}",1,"((2/5 + I/5)*2^(1/2 - I)*(1 - I*a*x)^(1/2 + I)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[1/2 + I, 1/2 + I, 3/2 + I, (1 - I*a*x)/2])/(a*Sqrt[c + a^2*c*x^2])","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
270,1,37,0,0.0397945,"\int \frac{e^{2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[E^(2*ArcTan[a*x])/(c + a^2*c*x^2)^(3/2),x]","\frac{(a x+2) e^{2 \tan ^{-1}(a x)}}{5 a c \sqrt{a^2 c x^2+c}}","\frac{(a x+2) e^{2 \tan ^{-1}(a x)}}{5 a c \sqrt{a^2 c x^2+c}}",1,"(E^(2*ArcTan[a*x])*(2 + a*x))/(5*a*c*Sqrt[c + a^2*c*x^2])","A",1,1,23,0.04348,1,"{5069}"
271,1,76,0,0.0811724,"\int \frac{e^{2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{5/2}} \, dx","Int[E^(2*ArcTan[a*x])/(c + a^2*c*x^2)^(5/2),x]","\frac{6 (a x+2) e^{2 \tan ^{-1}(a x)}}{65 a c^2 \sqrt{a^2 c x^2+c}}+\frac{(3 a x+2) e^{2 \tan ^{-1}(a x)}}{13 a c \left(a^2 c x^2+c\right)^{3/2}}","\frac{6 (a x+2) e^{2 \tan ^{-1}(a x)}}{65 a c^2 \sqrt{a^2 c x^2+c}}+\frac{(3 a x+2) e^{2 \tan ^{-1}(a x)}}{13 a c \left(a^2 c x^2+c\right)^{3/2}}",1,"(E^(2*ArcTan[a*x])*(2 + 3*a*x))/(13*a*c*(c + a^2*c*x^2)^(3/2)) + (6*E^(2*ArcTan[a*x])*(2 + a*x))/(65*a*c^2*Sqrt[c + a^2*c*x^2])","A",2,2,23,0.08696,1,"{5070, 5069}"
272,1,114,0,0.1253504,"\int \frac{e^{2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{7/2}} \, dx","Int[E^(2*ArcTan[a*x])/(c + a^2*c*x^2)^(7/2),x]","\frac{24 (a x+2) e^{2 \tan ^{-1}(a x)}}{377 a c^3 \sqrt{a^2 c x^2+c}}+\frac{20 (3 a x+2) e^{2 \tan ^{-1}(a x)}}{377 a c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{(5 a x+2) e^{2 \tan ^{-1}(a x)}}{29 a c \left(a^2 c x^2+c\right)^{5/2}}","\frac{24 (a x+2) e^{2 \tan ^{-1}(a x)}}{377 a c^3 \sqrt{a^2 c x^2+c}}+\frac{20 (3 a x+2) e^{2 \tan ^{-1}(a x)}}{377 a c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{(5 a x+2) e^{2 \tan ^{-1}(a x)}}{29 a c \left(a^2 c x^2+c\right)^{5/2}}",1,"(E^(2*ArcTan[a*x])*(2 + 5*a*x))/(29*a*c*(c + a^2*c*x^2)^(5/2)) + (20*E^(2*ArcTan[a*x])*(2 + 3*a*x))/(377*a*c^2*(c + a^2*c*x^2)^(3/2)) + (24*E^(2*ArcTan[a*x])*(2 + a*x))/(377*a*c^3*Sqrt[c + a^2*c*x^2])","A",3,2,23,0.08696,1,"{5070, 5069}"
273,1,101,0,0.0732523,"\int e^{-\tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^p \, dx","Int[(c + a^2*c*x^2)^p/E^ArcTan[a*x],x]","\frac{2^{p+\left(1+\frac{i}{2}\right)} (1-i a x)^{p+\left(1-\frac{i}{2}\right)} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p \, _2F_1\left(-p-\frac{i}{2},p+\left(1-\frac{i}{2}\right);p+\left(2-\frac{i}{2}\right);\frac{1}{2} (1-i a x)\right)}{a (-2 i p-(1+2 i))}","\frac{2^{p+\left(1+\frac{i}{2}\right)} (1-i a x)^{p+\left(1-\frac{i}{2}\right)} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p \, _2F_1\left(-p-\frac{i}{2},p+\left(1-\frac{i}{2}\right);p+\left(2-\frac{i}{2}\right);\frac{1}{2} (1-i a x)\right)}{a (-2 i p-(1+2 i))}",1,"(2^((1 + I/2) + p)*(1 - I*a*x)^((1 - I/2) + p)*(c + a^2*c*x^2)^p*Hypergeometric2F1[-I/2 - p, (1 - I/2) + p, (2 - I/2) + p, (1 - I*a*x)/2])/(a*((-1 - 2*I) - (2*I)*p)*(1 + a^2*x^2)^p)","A",3,3,21,0.1429,1,"{5076, 5073, 69}"
274,1,63,0,0.0366298,"\int e^{-\tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^2 \, dx","Int[(c + a^2*c*x^2)^2/E^ArcTan[a*x],x]","-\frac{\left(\frac{1}{37}-\frac{6 i}{37}\right) 2^{3+\frac{i}{2}} c^2 (1-i a x)^{3-\frac{i}{2}} \, _2F_1\left(-2-\frac{i}{2},3-\frac{i}{2};4-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}","-\frac{\left(\frac{1}{37}-\frac{6 i}{37}\right) 2^{3+\frac{i}{2}} c^2 (1-i a x)^{3-\frac{i}{2}} \, _2F_1\left(-2-\frac{i}{2},3-\frac{i}{2};4-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}",1,"((-1/37 + (6*I)/37)*2^(3 + I/2)*c^2*(1 - I*a*x)^(3 - I/2)*Hypergeometric2F1[-2 - I/2, 3 - I/2, 4 - I/2, (1 - I*a*x)/2])/a","A",2,2,21,0.09524,1,"{5073, 69}"
275,1,61,0,0.0259134,"\int e^{-\tan ^{-1}(a x)} \left(c+a^2 c x^2\right) \, dx","Int[(c + a^2*c*x^2)/E^ArcTan[a*x],x]","-\frac{\left(\frac{1}{17}-\frac{4 i}{17}\right) 2^{2+\frac{i}{2}} c (1-i a x)^{2-\frac{i}{2}} \, _2F_1\left(-1-\frac{i}{2},2-\frac{i}{2};3-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}","-\frac{\left(\frac{1}{17}-\frac{4 i}{17}\right) 2^{2+\frac{i}{2}} c (1-i a x)^{2-\frac{i}{2}} \, _2F_1\left(-1-\frac{i}{2},2-\frac{i}{2};3-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}",1,"((-1/17 + (4*I)/17)*2^(2 + I/2)*c*(1 - I*a*x)^(2 - I/2)*Hypergeometric2F1[-1 - I/2, 2 - I/2, 3 - I/2, (1 - I*a*x)/2])/a","A",2,2,19,0.1053,1,"{5073, 69}"
276,1,60,0,0.0113338,"\int e^{-\tan ^{-1}(a x)} \, dx","Int[E^(-ArcTan[a*x]),x]","-\frac{\left(\frac{1}{5}-\frac{2 i}{5}\right) 2^{1+\frac{i}{2}} (1-i a x)^{1-\frac{i}{2}} \, _2F_1\left(-\frac{i}{2},1-\frac{i}{2};2-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}","-\frac{\left(\frac{1}{5}-\frac{2 i}{5}\right) 2^{1+\frac{i}{2}} (1-i a x)^{1-\frac{i}{2}} \, _2F_1\left(-\frac{i}{2},1-\frac{i}{2};2-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a}",1,"((-1/5 + (2*I)/5)*2^(1 + I/2)*(1 - I*a*x)^(1 - I/2)*Hypergeometric2F1[-I/2, 1 - I/2, 2 - I/2, (1 - I*a*x)/2])/a","A",2,2,8,0.2500,1,"{5061, 69}"
277,1,16,0,0.0267153,"\int \frac{e^{-\tan ^{-1}(a x)}}{c+a^2 c x^2} \, dx","Int[1/(E^ArcTan[a*x]*(c + a^2*c*x^2)),x]","-\frac{e^{-\tan ^{-1}(a x)}}{a c}","-\frac{e^{-\tan ^{-1}(a x)}}{a c}",1,"-(1/(a*c*E^ArcTan[a*x]))","A",1,1,21,0.04762,1,"{5071}"
278,1,54,0,0.0539602,"\int \frac{e^{-\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^2} \, dx","Int[1/(E^ArcTan[a*x]*(c + a^2*c*x^2)^2),x]","-\frac{(1-2 a x) e^{-\tan ^{-1}(a x)}}{5 a c^2 \left(a^2 x^2+1\right)}-\frac{2 e^{-\tan ^{-1}(a x)}}{5 a c^2}","-\frac{(1-2 a x) e^{-\tan ^{-1}(a x)}}{5 a c^2 \left(a^2 x^2+1\right)}-\frac{2 e^{-\tan ^{-1}(a x)}}{5 a c^2}",1,"-2/(5*a*c^2*E^ArcTan[a*x]) - (1 - 2*a*x)/(5*a*c^2*E^ArcTan[a*x]*(1 + a^2*x^2))","A",2,2,21,0.09524,1,"{5070, 5071}"
279,1,89,0,0.0825961,"\int \frac{e^{-\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^3} \, dx","Int[1/(E^ArcTan[a*x]*(c + a^2*c*x^2)^3),x]","-\frac{(1-4 a x) e^{-\tan ^{-1}(a x)}}{17 a c^3 \left(a^2 x^2+1\right)^2}-\frac{12 (1-2 a x) e^{-\tan ^{-1}(a x)}}{85 a c^3 \left(a^2 x^2+1\right)}-\frac{24 e^{-\tan ^{-1}(a x)}}{85 a c^3}","-\frac{(1-4 a x) e^{-\tan ^{-1}(a x)}}{17 a c^3 \left(a^2 x^2+1\right)^2}-\frac{12 (1-2 a x) e^{-\tan ^{-1}(a x)}}{85 a c^3 \left(a^2 x^2+1\right)}-\frac{24 e^{-\tan ^{-1}(a x)}}{85 a c^3}",1,"-24/(85*a*c^3*E^ArcTan[a*x]) - (1 - 4*a*x)/(17*a*c^3*E^ArcTan[a*x]*(1 + a^2*x^2)^2) - (12*(1 - 2*a*x))/(85*a*c^3*E^ArcTan[a*x]*(1 + a^2*x^2))","A",3,2,21,0.09524,1,"{5070, 5071}"
280,1,124,0,0.1192765,"\int \frac{e^{-\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^4} \, dx","Int[1/(E^ArcTan[a*x]*(c + a^2*c*x^2)^4),x]","-\frac{(1-6 a x) e^{-\tan ^{-1}(a x)}}{37 a c^4 \left(a^2 x^2+1\right)^3}-\frac{72 (1-2 a x) e^{-\tan ^{-1}(a x)}}{629 a c^4 \left(a^2 x^2+1\right)}-\frac{30 (1-4 a x) e^{-\tan ^{-1}(a x)}}{629 a c^4 \left(a^2 x^2+1\right)^2}-\frac{144 e^{-\tan ^{-1}(a x)}}{629 a c^4}","-\frac{(1-6 a x) e^{-\tan ^{-1}(a x)}}{37 a c^4 \left(a^2 x^2+1\right)^3}-\frac{72 (1-2 a x) e^{-\tan ^{-1}(a x)}}{629 a c^4 \left(a^2 x^2+1\right)}-\frac{30 (1-4 a x) e^{-\tan ^{-1}(a x)}}{629 a c^4 \left(a^2 x^2+1\right)^2}-\frac{144 e^{-\tan ^{-1}(a x)}}{629 a c^4}",1,"-144/(629*a*c^4*E^ArcTan[a*x]) - (1 - 6*a*x)/(37*a*c^4*E^ArcTan[a*x]*(1 + a^2*x^2)^3) - (30*(1 - 4*a*x))/(629*a*c^4*E^ArcTan[a*x]*(1 + a^2*x^2)^2) - (72*(1 - 2*a*x))/(629*a*c^4*E^ArcTan[a*x]*(1 + a^2*x^2))","A",4,2,21,0.09524,1,"{5070, 5071}"
281,1,98,0,0.0764833,"\int e^{-\tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^{3/2} \, dx","Int[(c + a^2*c*x^2)^(3/2)/E^ArcTan[a*x],x]","-\frac{\left(\frac{1}{13}-\frac{5 i}{13}\right) 2^{\frac{3}{2}+\frac{i}{2}} c (1-i a x)^{\frac{5}{2}-\frac{i}{2}} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{3}{2}-\frac{i}{2},\frac{5}{2}-\frac{i}{2};\frac{7}{2}-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}","-\frac{\left(\frac{1}{13}-\frac{5 i}{13}\right) 2^{\frac{3}{2}+\frac{i}{2}} c (1-i a x)^{\frac{5}{2}-\frac{i}{2}} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{3}{2}-\frac{i}{2},\frac{5}{2}-\frac{i}{2};\frac{7}{2}-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}",1,"((-1/13 + (5*I)/13)*2^(3/2 + I/2)*c*(1 - I*a*x)^(5/2 - I/2)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[-3/2 - I/2, 5/2 - I/2, 7/2 - I/2, (1 - I*a*x)/2])/(a*Sqrt[1 + a^2*x^2])","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
282,1,97,0,0.0705675,"\int e^{-\tan ^{-1}(a x)} \sqrt{c+a^2 c x^2} \, dx","Int[Sqrt[c + a^2*c*x^2]/E^ArcTan[a*x],x]","-\frac{\left(\frac{1}{5}-\frac{3 i}{5}\right) 2^{\frac{1}{2}+\frac{i}{2}} (1-i a x)^{\frac{3}{2}-\frac{i}{2}} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{1}{2}-\frac{i}{2},\frac{3}{2}-\frac{i}{2};\frac{5}{2}-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}","-\frac{\left(\frac{1}{5}-\frac{3 i}{5}\right) 2^{\frac{1}{2}+\frac{i}{2}} (1-i a x)^{\frac{3}{2}-\frac{i}{2}} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{1}{2}-\frac{i}{2},\frac{3}{2}-\frac{i}{2};\frac{5}{2}-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}",1,"((-1/5 + (3*I)/5)*2^(1/2 + I/2)*(1 - I*a*x)^(3/2 - I/2)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[-1/2 - I/2, 3/2 - I/2, 5/2 - I/2, (1 - I*a*x)/2])/(a*Sqrt[1 + a^2*x^2])","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
283,1,93,0,0.0762926,"\int \frac{e^{-\tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[1/(E^ArcTan[a*x]*Sqrt[c + a^2*c*x^2]),x]","-\frac{(1-i) 2^{-\frac{1}{2}+\frac{i}{2}} (1-i a x)^{\frac{1}{2}-\frac{i}{2}} \sqrt{a^2 x^2+1} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},\frac{1}{2}-\frac{i}{2};\frac{3}{2}-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 c x^2+c}}","-\frac{(1-i) 2^{-\frac{1}{2}+\frac{i}{2}} (1-i a x)^{\frac{1}{2}-\frac{i}{2}} \sqrt{a^2 x^2+1} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},\frac{1}{2}-\frac{i}{2};\frac{3}{2}-\frac{i}{2};\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 c x^2+c}}",1,"((-1 + I)*(1 - I*a*x)^(1/2 - I/2)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[1/2 - I/2, 1/2 - I/2, 3/2 - I/2, (1 - I*a*x)/2])/(2^(1/2 - I/2)*a*Sqrt[c + a^2*c*x^2])","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
284,1,38,0,0.038571,"\int \frac{e^{-\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^ArcTan[a*x]*(c + a^2*c*x^2)^(3/2)),x]","-\frac{(1-a x) e^{-\tan ^{-1}(a x)}}{2 a c \sqrt{a^2 c x^2+c}}","-\frac{(1-a x) e^{-\tan ^{-1}(a x)}}{2 a c \sqrt{a^2 c x^2+c}}",1,"-(1 - a*x)/(2*a*c*E^ArcTan[a*x]*Sqrt[c + a^2*c*x^2])","A",1,1,23,0.04348,1,"{5069}"
285,1,77,0,0.0798143,"\int \frac{e^{-\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{5/2}} \, dx","Int[1/(E^ArcTan[a*x]*(c + a^2*c*x^2)^(5/2)),x]","-\frac{3 (1-a x) e^{-\tan ^{-1}(a x)}}{10 a c^2 \sqrt{a^2 c x^2+c}}-\frac{(1-3 a x) e^{-\tan ^{-1}(a x)}}{10 a c \left(a^2 c x^2+c\right)^{3/2}}","-\frac{3 (1-a x) e^{-\tan ^{-1}(a x)}}{10 a c^2 \sqrt{a^2 c x^2+c}}-\frac{(1-3 a x) e^{-\tan ^{-1}(a x)}}{10 a c \left(a^2 c x^2+c\right)^{3/2}}",1,"-(1 - 3*a*x)/(10*a*c*E^ArcTan[a*x]*(c + a^2*c*x^2)^(3/2)) - (3*(1 - a*x))/(10*a*c^2*E^ArcTan[a*x]*Sqrt[c + a^2*c*x^2])","A",2,2,23,0.08696,1,"{5070, 5069}"
286,1,115,0,0.123632,"\int \frac{e^{-\tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{7/2}} \, dx","Int[1/(E^ArcTan[a*x]*(c + a^2*c*x^2)^(7/2)),x]","-\frac{3 (1-a x) e^{-\tan ^{-1}(a x)}}{13 a c^3 \sqrt{a^2 c x^2+c}}-\frac{(1-3 a x) e^{-\tan ^{-1}(a x)}}{13 a c^2 \left(a^2 c x^2+c\right)^{3/2}}-\frac{(1-5 a x) e^{-\tan ^{-1}(a x)}}{26 a c \left(a^2 c x^2+c\right)^{5/2}}","-\frac{3 (1-a x) e^{-\tan ^{-1}(a x)}}{13 a c^3 \sqrt{a^2 c x^2+c}}-\frac{(1-3 a x) e^{-\tan ^{-1}(a x)}}{13 a c^2 \left(a^2 c x^2+c\right)^{3/2}}-\frac{(1-5 a x) e^{-\tan ^{-1}(a x)}}{26 a c \left(a^2 c x^2+c\right)^{5/2}}",1,"-(1 - 5*a*x)/(26*a*c*E^ArcTan[a*x]*(c + a^2*c*x^2)^(5/2)) - (1 - 3*a*x)/(13*a*c^2*E^ArcTan[a*x]*(c + a^2*c*x^2)^(3/2)) - (3*(1 - a*x))/(13*a*c^3*E^ArcTan[a*x]*Sqrt[c + a^2*c*x^2])","A",3,2,23,0.08696,1,"{5070, 5069}"
287,1,90,0,0.0675013,"\int e^{-2 \tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^p \, dx","Int[(c + a^2*c*x^2)^p/E^(2*ArcTan[a*x]),x]","\frac{i 2^{p+i} (1-i a x)^{p+(1-i)} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p \, _2F_1\left(-p-i,p+(1-i);p+(2-i);\frac{1}{2} (1-i a x)\right)}{a (p+(1-i))}","\frac{i 2^{p+i} (1-i a x)^{p+(1-i)} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p \, _2F_1\left(-p-i,p+(1-i);p+(2-i);\frac{1}{2} (1-i a x)\right)}{a (p+(1-i))}",1,"(I*2^(I + p)*(1 - I*a*x)^((1 - I) + p)*(c + a^2*c*x^2)^p*Hypergeometric2F1[-I - p, (1 - I) + p, (2 - I) + p, (1 - I*a*x)/2])/(a*((1 - I) + p)*(1 + a^2*x^2)^p)","A",3,3,21,0.1429,1,"{5076, 5073, 69}"
288,1,53,0,0.0368077,"\int e^{-2 \tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^2 \, dx","Int[(c + a^2*c*x^2)^2/E^(2*ArcTan[a*x]),x]","-\frac{\left(\frac{1}{5}-\frac{3 i}{5}\right) 2^{1+i} c^2 (1-i a x)^{3-i} \, _2F_1\left(-2-i,3-i;4-i;\frac{1}{2} (1-i a x)\right)}{a}","-\frac{\left(\frac{1}{5}-\frac{3 i}{5}\right) 2^{1+i} c^2 (1-i a x)^{3-i} \, _2F_1\left(-2-i,3-i;4-i;\frac{1}{2} (1-i a x)\right)}{a}",1,"((-1/5 + (3*I)/5)*2^(1 + I)*c^2*(1 - I*a*x)^(3 - I)*Hypergeometric2F1[-2 - I, 3 - I, 4 - I, (1 - I*a*x)/2])/a","A",2,2,21,0.09524,1,"{5073, 69}"
289,1,51,0,0.0258661,"\int e^{-2 \tan ^{-1}(a x)} \left(c+a^2 c x^2\right) \, dx","Int[(c + a^2*c*x^2)/E^(2*ArcTan[a*x]),x]","-\frac{\left(\frac{1}{5}-\frac{2 i}{5}\right) 2^{1+i} c (1-i a x)^{2-i} \, _2F_1\left(-1-i,2-i;3-i;\frac{1}{2} (1-i a x)\right)}{a}","-\frac{\left(\frac{1}{5}-\frac{2 i}{5}\right) 2^{1+i} c (1-i a x)^{2-i} \, _2F_1\left(-1-i,2-i;3-i;\frac{1}{2} (1-i a x)\right)}{a}",1,"((-1/5 + (2*I)/5)*2^(1 + I)*c*(1 - I*a*x)^(2 - I)*Hypergeometric2F1[-1 - I, 2 - I, 3 - I, (1 - I*a*x)/2])/a","A",2,2,19,0.1053,1,"{5073, 69}"
290,1,46,0,0.0108576,"\int e^{-2 \tan ^{-1}(a x)} \, dx","Int[E^(-2*ArcTan[a*x]),x]","-\frac{(1-i) 2^{-1+i} (1-i a x)^{1-i} \, _2F_1\left(-i,1-i;2-i;\frac{1}{2} (1-i a x)\right)}{a}","-\frac{(1-i) 2^{-1+i} (1-i a x)^{1-i} \, _2F_1\left(-i,1-i;2-i;\frac{1}{2} (1-i a x)\right)}{a}",1,"((-1 + I)*(1 - I*a*x)^(1 - I)*Hypergeometric2F1[-I, 1 - I, 2 - I, (1 - I*a*x)/2])/(2^(1 - I)*a)","A",2,2,8,0.2500,1,"{5061, 69}"
291,1,18,0,0.028431,"\int \frac{e^{-2 \tan ^{-1}(a x)}}{c+a^2 c x^2} \, dx","Int[1/(E^(2*ArcTan[a*x])*(c + a^2*c*x^2)),x]","-\frac{e^{-2 \tan ^{-1}(a x)}}{2 a c}","-\frac{e^{-2 \tan ^{-1}(a x)}}{2 a c}",1,"-1/(2*a*c*E^(2*ArcTan[a*x]))","A",1,1,21,0.04762,1,"{5071}"
292,1,54,0,0.057639,"\int \frac{e^{-2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^2} \, dx","Int[1/(E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^2),x]","-\frac{(1-a x) e^{-2 \tan ^{-1}(a x)}}{4 a c^2 \left(a^2 x^2+1\right)}-\frac{e^{-2 \tan ^{-1}(a x)}}{8 a c^2}","-\frac{(1-a x) e^{-2 \tan ^{-1}(a x)}}{4 a c^2 \left(a^2 x^2+1\right)}-\frac{e^{-2 \tan ^{-1}(a x)}}{8 a c^2}",1,"-1/(8*a*c^2*E^(2*ArcTan[a*x])) - (1 - a*x)/(4*a*c^2*E^(2*ArcTan[a*x])*(1 + a^2*x^2))","A",2,2,21,0.09524,1,"{5070, 5071}"
293,1,89,0,0.0875743,"\int \frac{e^{-2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^3} \, dx","Int[1/(E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^3),x]","-\frac{(1-2 a x) e^{-2 \tan ^{-1}(a x)}}{10 a c^3 \left(a^2 x^2+1\right)^2}-\frac{3 (1-a x) e^{-2 \tan ^{-1}(a x)}}{20 a c^3 \left(a^2 x^2+1\right)}-\frac{3 e^{-2 \tan ^{-1}(a x)}}{40 a c^3}","-\frac{(1-2 a x) e^{-2 \tan ^{-1}(a x)}}{10 a c^3 \left(a^2 x^2+1\right)^2}-\frac{3 (1-a x) e^{-2 \tan ^{-1}(a x)}}{20 a c^3 \left(a^2 x^2+1\right)}-\frac{3 e^{-2 \tan ^{-1}(a x)}}{40 a c^3}",1,"-3/(40*a*c^3*E^(2*ArcTan[a*x])) - (1 - 2*a*x)/(10*a*c^3*E^(2*ArcTan[a*x])*(1 + a^2*x^2)^2) - (3*(1 - a*x))/(20*a*c^3*E^(2*ArcTan[a*x])*(1 + a^2*x^2))","A",3,2,21,0.09524,1,"{5070, 5071}"
294,1,124,0,0.1207851,"\int \frac{e^{-2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^4} \, dx","Int[1/(E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^4),x]","-\frac{(1-3 a x) e^{-2 \tan ^{-1}(a x)}}{20 a c^4 \left(a^2 x^2+1\right)^3}-\frac{9 (1-a x) e^{-2 \tan ^{-1}(a x)}}{80 a c^4 \left(a^2 x^2+1\right)}-\frac{3 (1-2 a x) e^{-2 \tan ^{-1}(a x)}}{40 a c^4 \left(a^2 x^2+1\right)^2}-\frac{9 e^{-2 \tan ^{-1}(a x)}}{160 a c^4}","-\frac{(1-3 a x) e^{-2 \tan ^{-1}(a x)}}{20 a c^4 \left(a^2 x^2+1\right)^3}-\frac{9 (1-a x) e^{-2 \tan ^{-1}(a x)}}{80 a c^4 \left(a^2 x^2+1\right)}-\frac{3 (1-2 a x) e^{-2 \tan ^{-1}(a x)}}{40 a c^4 \left(a^2 x^2+1\right)^2}-\frac{9 e^{-2 \tan ^{-1}(a x)}}{160 a c^4}",1,"-9/(160*a*c^4*E^(2*ArcTan[a*x])) - (1 - 3*a*x)/(20*a*c^4*E^(2*ArcTan[a*x])*(1 + a^2*x^2)^3) - (3*(1 - 2*a*x))/(40*a*c^4*E^(2*ArcTan[a*x])*(1 + a^2*x^2)^2) - (9*(1 - a*x))/(80*a*c^4*E^(2*ArcTan[a*x])*(1 + a^2*x^2))","A",4,2,21,0.09524,1,"{5070, 5071}"
295,1,88,0,0.0792291,"\int e^{-2 \tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^{3/2} \, dx","Int[(c + a^2*c*x^2)^(3/2)/E^(2*ArcTan[a*x]),x]","-\frac{\left(\frac{2}{29}-\frac{5 i}{29}\right) 2^{\frac{5}{2}+i} c (1-i a x)^{\frac{5}{2}-i} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{3}{2}-i,\frac{5}{2}-i;\frac{7}{2}-i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}","-\frac{\left(\frac{2}{29}-\frac{5 i}{29}\right) 2^{\frac{5}{2}+i} c (1-i a x)^{\frac{5}{2}-i} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{3}{2}-i,\frac{5}{2}-i;\frac{7}{2}-i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}",1,"((-2/29 + (5*I)/29)*2^(5/2 + I)*c*(1 - I*a*x)^(5/2 - I)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[-3/2 - I, 5/2 - I, 7/2 - I, (1 - I*a*x)/2])/(a*Sqrt[1 + a^2*x^2])","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
296,1,87,0,0.0718009,"\int e^{-2 \tan ^{-1}(a x)} \sqrt{c+a^2 c x^2} \, dx","Int[Sqrt[c + a^2*c*x^2]/E^(2*ArcTan[a*x]),x]","-\frac{\left(\frac{2}{13}-\frac{3 i}{13}\right) 2^{\frac{3}{2}+i} (1-i a x)^{\frac{3}{2}-i} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{1}{2}-i,\frac{3}{2}-i;\frac{5}{2}-i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}","-\frac{\left(\frac{2}{13}-\frac{3 i}{13}\right) 2^{\frac{3}{2}+i} (1-i a x)^{\frac{3}{2}-i} \sqrt{a^2 c x^2+c} \, _2F_1\left(-\frac{1}{2}-i,\frac{3}{2}-i;\frac{5}{2}-i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 x^2+1}}",1,"((-2/13 + (3*I)/13)*2^(3/2 + I)*(1 - I*a*x)^(3/2 - I)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[-1/2 - I, 3/2 - I, 5/2 - I, (1 - I*a*x)/2])/(a*Sqrt[1 + a^2*x^2])","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
297,1,87,0,0.0746697,"\int \frac{e^{-2 \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[1/(E^(2*ArcTan[a*x])*Sqrt[c + a^2*c*x^2]),x]","-\frac{\left(\frac{2}{5}-\frac{i}{5}\right) 2^{\frac{1}{2}+i} (1-i a x)^{\frac{1}{2}-i} \sqrt{a^2 x^2+1} \, _2F_1\left(\frac{1}{2}-i,\frac{1}{2}-i;\frac{3}{2}-i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 c x^2+c}}","-\frac{\left(\frac{2}{5}-\frac{i}{5}\right) 2^{\frac{1}{2}+i} (1-i a x)^{\frac{1}{2}-i} \sqrt{a^2 x^2+1} \, _2F_1\left(\frac{1}{2}-i,\frac{1}{2}-i;\frac{3}{2}-i;\frac{1}{2} (1-i a x)\right)}{a \sqrt{a^2 c x^2+c}}",1,"((-2/5 + I/5)*2^(1/2 + I)*(1 - I*a*x)^(1/2 - I)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[1/2 - I, 1/2 - I, 3/2 - I, (1 - I*a*x)/2])/(a*Sqrt[c + a^2*c*x^2])","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
298,1,38,0,0.0392175,"\int \frac{e^{-2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^(3/2)),x]","-\frac{(2-a x) e^{-2 \tan ^{-1}(a x)}}{5 a c \sqrt{a^2 c x^2+c}}","-\frac{(2-a x) e^{-2 \tan ^{-1}(a x)}}{5 a c \sqrt{a^2 c x^2+c}}",1,"-(2 - a*x)/(5*a*c*E^(2*ArcTan[a*x])*Sqrt[c + a^2*c*x^2])","A",1,1,23,0.04348,1,"{5069}"
299,1,77,0,0.080294,"\int \frac{e^{-2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{5/2}} \, dx","Int[1/(E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^(5/2)),x]","-\frac{6 (2-a x) e^{-2 \tan ^{-1}(a x)}}{65 a c^2 \sqrt{a^2 c x^2+c}}-\frac{(2-3 a x) e^{-2 \tan ^{-1}(a x)}}{13 a c \left(a^2 c x^2+c\right)^{3/2}}","-\frac{6 (2-a x) e^{-2 \tan ^{-1}(a x)}}{65 a c^2 \sqrt{a^2 c x^2+c}}-\frac{(2-3 a x) e^{-2 \tan ^{-1}(a x)}}{13 a c \left(a^2 c x^2+c\right)^{3/2}}",1,"-(2 - 3*a*x)/(13*a*c*E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^(3/2)) - (6*(2 - a*x))/(65*a*c^2*E^(2*ArcTan[a*x])*Sqrt[c + a^2*c*x^2])","A",2,2,23,0.08696,1,"{5070, 5069}"
300,1,115,0,0.1249175,"\int \frac{e^{-2 \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{7/2}} \, dx","Int[1/(E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^(7/2)),x]","-\frac{24 (2-a x) e^{-2 \tan ^{-1}(a x)}}{377 a c^3 \sqrt{a^2 c x^2+c}}-\frac{20 (2-3 a x) e^{-2 \tan ^{-1}(a x)}}{377 a c^2 \left(a^2 c x^2+c\right)^{3/2}}-\frac{(2-5 a x) e^{-2 \tan ^{-1}(a x)}}{29 a c \left(a^2 c x^2+c\right)^{5/2}}","-\frac{24 (2-a x) e^{-2 \tan ^{-1}(a x)}}{377 a c^3 \sqrt{a^2 c x^2+c}}-\frac{20 (2-3 a x) e^{-2 \tan ^{-1}(a x)}}{377 a c^2 \left(a^2 c x^2+c\right)^{3/2}}-\frac{(2-5 a x) e^{-2 \tan ^{-1}(a x)}}{29 a c \left(a^2 c x^2+c\right)^{5/2}}",1,"-(2 - 5*a*x)/(29*a*c*E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^(5/2)) - (20*(2 - 3*a*x))/(377*a*c^2*E^(2*ArcTan[a*x])*(c + a^2*c*x^2)^(3/2)) - (24*(2 - a*x))/(377*a*c^3*E^(2*ArcTan[a*x])*Sqrt[c + a^2*c*x^2])","A",3,2,23,0.08696,1,"{5070, 5069}"
301,1,50,0,0.0427698,"\int \frac{e^{5 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx","Int[E^((5*I)*ArcTan[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{4 i}{a (1-i a x)}-\frac{2 i}{a (1-i a x)^2}+\frac{i \log (a x+i)}{a}","\frac{4 i}{a (1-i a x)}-\frac{2 i}{a (1-i a x)^2}+\frac{i \log (a x+i)}{a}",1,"(-2*I)/(a*(1 - I*a*x)^2) + (4*I)/(a*(1 - I*a*x)) + (I*Log[I + a*x])/a","A",3,2,24,0.08333,1,"{5073, 43}"
302,1,73,0,0.0388457,"\int \frac{e^{4 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx","Int[E^((4*I)*ArcTan[a*x])/Sqrt[1 + a^2*x^2],x]","-\frac{2 i (1+i a x)^{3/2}}{3 a (1-i a x)^{3/2}}+\frac{2 i \sqrt{1+i a x}}{a \sqrt{1-i a x}}+\frac{\sinh ^{-1}(a x)}{a}","-\frac{2 i (1+i a x)^{3/2}}{3 a (1-i a x)^{3/2}}+\frac{2 i \sqrt{1+i a x}}{a \sqrt{1-i a x}}+\frac{\sinh ^{-1}(a x)}{a}",1,"((2*I)*Sqrt[1 + I*a*x])/(a*Sqrt[1 - I*a*x]) - (((2*I)/3)*(1 + I*a*x)^(3/2))/(a*(1 - I*a*x)^(3/2)) + ArcSinh[a*x]/a","A",5,4,24,0.1667,1,"{5073, 47, 41, 215}"
303,1,30,0,0.0382867,"\int \frac{e^{3 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx","Int[E^((3*I)*ArcTan[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{2}{a (a x+i)}-\frac{i \log (a x+i)}{a}","\frac{2}{a (a x+i)}-\frac{i \log (a x+i)}{a}",1,"2/(a*(I + a*x)) - (I*Log[I + a*x])/a","A",3,2,24,0.08333,1,"{5073, 43}"
304,1,41,0,0.0346615,"\int \frac{e^{2 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx","Int[E^((2*I)*ArcTan[a*x])/Sqrt[1 + a^2*x^2],x]","-\frac{\sinh ^{-1}(a x)}{a}-\frac{2 i \sqrt{1+i a x}}{a \sqrt{1-i a x}}","-\frac{\sinh ^{-1}(a x)}{a}-\frac{2 i \sqrt{1+i a x}}{a \sqrt{1-i a x}}",1,"((-2*I)*Sqrt[1 + I*a*x])/(a*Sqrt[1 - I*a*x]) - ArcSinh[a*x]/a","A",4,4,24,0.1667,1,"{5073, 47, 41, 215}"
305,1,15,0,0.02944,"\int \frac{e^{i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx","Int[E^(I*ArcTan[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{i \log (a x+i)}{a}","\frac{i \log (a x+i)}{a}",1,"(I*Log[I + a*x])/a","A",2,2,24,0.08333,1,"{5073, 31}"
306,1,16,0,0.0315238,"\int \frac{e^{-i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx","Int[1/(E^(I*ArcTan[a*x])*Sqrt[1 + a^2*x^2]),x]","-\frac{i \log (-a x+i)}{a}","-\frac{i \log (-a x+i)}{a}",1,"((-I)*Log[I - a*x])/a","A",2,2,24,0.08333,1,"{5073, 31}"
307,1,41,0,0.0352676,"\int \frac{e^{-2 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx","Int[1/(E^((2*I)*ArcTan[a*x])*Sqrt[1 + a^2*x^2]),x]","-\frac{\sinh ^{-1}(a x)}{a}+\frac{2 i \sqrt{1-i a x}}{a \sqrt{1+i a x}}","-\frac{\sinh ^{-1}(a x)}{a}+\frac{2 i \sqrt{1-i a x}}{a \sqrt{1+i a x}}",1,"((2*I)*Sqrt[1 - I*a*x])/(a*Sqrt[1 + I*a*x]) - ArcSinh[a*x]/a","A",4,4,24,0.1667,1,"{5073, 47, 41, 215}"
308,1,32,0,0.0380563,"\int \frac{e^{-3 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx","Int[1/(E^((3*I)*ArcTan[a*x])*Sqrt[1 + a^2*x^2]),x]","\frac{i \log (-a x+i)}{a}-\frac{2}{a (-a x+i)}","\frac{i \log (-a x+i)}{a}-\frac{2}{a (-a x+i)}",1,"-2/(a*(I - a*x)) + (I*Log[I - a*x])/a","A",3,2,24,0.08333,1,"{5073, 43}"
309,1,73,0,0.0376806,"\int \frac{e^{-4 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx","Int[1/(E^((4*I)*ArcTan[a*x])*Sqrt[1 + a^2*x^2]),x]","\frac{2 i (1-i a x)^{3/2}}{3 a (1+i a x)^{3/2}}-\frac{2 i \sqrt{1-i a x}}{a \sqrt{1+i a x}}+\frac{\sinh ^{-1}(a x)}{a}","\frac{2 i (1-i a x)^{3/2}}{3 a (1+i a x)^{3/2}}-\frac{2 i \sqrt{1-i a x}}{a \sqrt{1+i a x}}+\frac{\sinh ^{-1}(a x)}{a}",1,"(((2*I)/3)*(1 - I*a*x)^(3/2))/(a*(1 + I*a*x)^(3/2)) - ((2*I)*Sqrt[1 - I*a*x])/(a*Sqrt[1 + I*a*x]) + ArcSinh[a*x]/a","A",5,4,24,0.1667,1,"{5073, 47, 41, 215}"
310,1,131,0,0.0831411,"\int \frac{e^{5 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[E^((5*I)*ArcTan[a*x])/Sqrt[c + a^2*c*x^2],x]","\frac{4 i \sqrt{a^2 x^2+1}}{a (1-i a x) \sqrt{a^2 c x^2+c}}-\frac{2 i \sqrt{a^2 x^2+1}}{a (1-i a x)^2 \sqrt{a^2 c x^2+c}}+\frac{i \sqrt{a^2 x^2+1} \log (a x+i)}{a \sqrt{a^2 c x^2+c}}","\frac{4 i \sqrt{a^2 x^2+1}}{a (1-i a x) \sqrt{a^2 c x^2+c}}-\frac{2 i \sqrt{a^2 x^2+1}}{a (1-i a x)^2 \sqrt{a^2 c x^2+c}}+\frac{i \sqrt{a^2 x^2+1} \log (a x+i)}{a \sqrt{a^2 c x^2+c}}",1,"((-2*I)*Sqrt[1 + a^2*x^2])/(a*(1 - I*a*x)^2*Sqrt[c + a^2*c*x^2]) + ((4*I)*Sqrt[1 + a^2*x^2])/(a*(1 - I*a*x)*Sqrt[c + a^2*c*x^2]) + (I*Sqrt[1 + a^2*x^2]*Log[I + a*x])/(a*Sqrt[c + a^2*c*x^2])","A",4,3,25,0.1200,1,"{5076, 5073, 43}"
311,1,96,0,0.0845581,"\int \frac{e^{4 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[E^((4*I)*ArcTan[a*x])/Sqrt[c + a^2*c*x^2],x]","-\frac{2 i c (1+i a x)^3}{3 a \left(a^2 c x^2+c\right)^{3/2}}+\frac{2 i (1+i a x)}{a \sqrt{a^2 c x^2+c}}+\frac{\tanh ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{a^2 c x^2+c}}\right)}{a \sqrt{c}}","-\frac{2 i c (1+i a x)^3}{3 a \left(a^2 c x^2+c\right)^{3/2}}+\frac{2 i (1+i a x)}{a \sqrt{a^2 c x^2+c}}+\frac{\tanh ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{a^2 c x^2+c}}\right)}{a \sqrt{c}}",1,"(((-2*I)/3)*c*(1 + I*a*x)^3)/(a*(c + a^2*c*x^2)^(3/2)) + ((2*I)*(1 + I*a*x))/(a*Sqrt[c + a^2*c*x^2]) + ArcTanh[(a*Sqrt[c]*x)/Sqrt[c + a^2*c*x^2]]/(a*Sqrt[c])","A",5,5,25,0.2000,1,"{5075, 669, 653, 217, 206}"
312,1,84,0,0.0767305,"\int \frac{e^{3 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[E^((3*I)*ArcTan[a*x])/Sqrt[c + a^2*c*x^2],x]","\frac{2 \sqrt{a^2 x^2+1}}{a (a x+i) \sqrt{a^2 c x^2+c}}-\frac{i \sqrt{a^2 x^2+1} \log (a x+i)}{a \sqrt{a^2 c x^2+c}}","\frac{2 \sqrt{a^2 x^2+1}}{a (a x+i) \sqrt{a^2 c x^2+c}}-\frac{i \sqrt{a^2 x^2+1} \log (a x+i)}{a \sqrt{a^2 c x^2+c}}",1,"(2*Sqrt[1 + a^2*x^2])/(a*(I + a*x)*Sqrt[c + a^2*c*x^2]) - (I*Sqrt[1 + a^2*x^2]*Log[I + a*x])/(a*Sqrt[c + a^2*c*x^2])","A",4,3,25,0.1200,1,"{5076, 5073, 43}"
313,1,63,0,0.0602542,"\int \frac{e^{2 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[E^((2*I)*ArcTan[a*x])/Sqrt[c + a^2*c*x^2],x]","-\frac{\tanh ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{a^2 c x^2+c}}\right)}{a \sqrt{c}}-\frac{2 i (1+i a x)}{a \sqrt{a^2 c x^2+c}}","-\frac{\tanh ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{a^2 c x^2+c}}\right)}{a \sqrt{c}}-\frac{2 i (1+i a x)}{a \sqrt{a^2 c x^2+c}}",1,"((-2*I)*(1 + I*a*x))/(a*Sqrt[c + a^2*c*x^2]) - ArcTanh[(a*Sqrt[c]*x)/Sqrt[c + a^2*c*x^2]]/(a*Sqrt[c])","A",4,4,25,0.1600,1,"{5075, 653, 217, 206}"
314,1,42,0,0.0648809,"\int \frac{e^{i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[E^(I*ArcTan[a*x])/Sqrt[c + a^2*c*x^2],x]","\frac{i \sqrt{a^2 x^2+1} \log (a x+i)}{a \sqrt{a^2 c x^2+c}}","\frac{i \sqrt{a^2 x^2+1} \log (a x+i)}{a \sqrt{a^2 c x^2+c}}",1,"(I*Sqrt[1 + a^2*x^2]*Log[I + a*x])/(a*Sqrt[c + a^2*c*x^2])","A",3,3,25,0.1200,1,"{5076, 5073, 31}"
315,1,43,0,0.0658911,"\int \frac{e^{-i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[1/(E^(I*ArcTan[a*x])*Sqrt[c + a^2*c*x^2]),x]","-\frac{i \sqrt{a^2 x^2+1} \log (-a x+i)}{a \sqrt{a^2 c x^2+c}}","-\frac{i \sqrt{a^2 x^2+1} \log (-a x+i)}{a \sqrt{a^2 c x^2+c}}",1,"((-I)*Sqrt[1 + a^2*x^2]*Log[I - a*x])/(a*Sqrt[c + a^2*c*x^2])","A",3,3,25,0.1200,1,"{5076, 5073, 31}"
316,1,63,0,0.0611335,"\int \frac{e^{-2 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[1/(E^((2*I)*ArcTan[a*x])*Sqrt[c + a^2*c*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{a^2 c x^2+c}}\right)}{a \sqrt{c}}+\frac{2 i (1-i a x)}{a \sqrt{a^2 c x^2+c}}","-\frac{\tanh ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{a^2 c x^2+c}}\right)}{a \sqrt{c}}+\frac{2 i (1-i a x)}{a \sqrt{a^2 c x^2+c}}",1,"((2*I)*(1 - I*a*x))/(a*Sqrt[c + a^2*c*x^2]) - ArcTanh[(a*Sqrt[c]*x)/Sqrt[c + a^2*c*x^2]]/(a*Sqrt[c])","A",4,4,25,0.1600,1,"{5074, 653, 217, 206}"
317,1,86,0,0.0755422,"\int \frac{e^{-3 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[1/(E^((3*I)*ArcTan[a*x])*Sqrt[c + a^2*c*x^2]),x]","\frac{i \sqrt{a^2 x^2+1} \log (-a x+i)}{a \sqrt{a^2 c x^2+c}}-\frac{2 \sqrt{a^2 x^2+1}}{a (-a x+i) \sqrt{a^2 c x^2+c}}","\frac{i \sqrt{a^2 x^2+1} \log (-a x+i)}{a \sqrt{a^2 c x^2+c}}-\frac{2 \sqrt{a^2 x^2+1}}{a (-a x+i) \sqrt{a^2 c x^2+c}}",1,"(-2*Sqrt[1 + a^2*x^2])/(a*(I - a*x)*Sqrt[c + a^2*c*x^2]) + (I*Sqrt[1 + a^2*x^2]*Log[I - a*x])/(a*Sqrt[c + a^2*c*x^2])","A",4,3,25,0.1200,1,"{5076, 5073, 43}"
318,1,96,0,0.0775118,"\int \frac{e^{-4 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[1/(E^((4*I)*ArcTan[a*x])*Sqrt[c + a^2*c*x^2]),x]","\frac{2 i c (1-i a x)^3}{3 a \left(a^2 c x^2+c\right)^{3/2}}-\frac{2 i (1-i a x)}{a \sqrt{a^2 c x^2+c}}+\frac{\tanh ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{a^2 c x^2+c}}\right)}{a \sqrt{c}}","\frac{2 i c (1-i a x)^3}{3 a \left(a^2 c x^2+c\right)^{3/2}}-\frac{2 i (1-i a x)}{a \sqrt{a^2 c x^2+c}}+\frac{\tanh ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{a^2 c x^2+c}}\right)}{a \sqrt{c}}",1,"(((2*I)/3)*c*(1 - I*a*x)^3)/(a*(c + a^2*c*x^2)^(3/2)) - ((2*I)*(1 - I*a*x))/(a*Sqrt[c + a^2*c*x^2]) + ArcTanh[(a*Sqrt[c]*x)/Sqrt[c + a^2*c*x^2]]/(a*Sqrt[c])","A",5,5,25,0.2000,1,"{5074, 669, 653, 217, 206}"
319,1,35,0,0.0384182,"\int \frac{e^{5 i \tan ^{-1}(a x)}}{\left(1+a^2 x^2\right)^{3/2}} \, dx","Int[E^((5*I)*ArcTan[a*x])/(1 + a^2*x^2)^(3/2),x]","-\frac{i}{2 a (a x+i)^2}-\frac{2}{3 a (a x+i)^3}","-\frac{i}{2 a (a x+i)^2}-\frac{2}{3 a (a x+i)^3}",1,"-2/(3*a*(I + a*x)^3) - (I/2)/(a*(I + a*x)^2)","A",3,2,24,0.08333,1,"{5073, 43}"
320,1,67,0,0.0385951,"\int \frac{e^{4 i \tan ^{-1}(a x)}}{\left(1+a^2 x^2\right)^{3/2}} \, dx","Int[E^((4*I)*ArcTan[a*x])/(1 + a^2*x^2)^(3/2),x]","-\frac{i (1+i a x)^{3/2}}{15 a (1-i a x)^{3/2}}-\frac{i (1+i a x)^{3/2}}{5 a (1-i a x)^{5/2}}","-\frac{i (1+i a x)^{3/2}}{15 a (1-i a x)^{3/2}}-\frac{i (1+i a x)^{3/2}}{5 a (1-i a x)^{5/2}}",1,"((-I/5)*(1 + I*a*x)^(3/2))/(a*(1 - I*a*x)^(5/2)) - ((I/15)*(1 + I*a*x)^(3/2))/(a*(1 - I*a*x)^(3/2))","A",3,3,24,0.1250,1,"{5073, 45, 37}"
321,1,19,0,0.0320956,"\int \frac{e^{3 i \tan ^{-1}(a x)}}{\left(1+a^2 x^2\right)^{3/2}} \, dx","Int[E^((3*I)*ArcTan[a*x])/(1 + a^2*x^2)^(3/2),x]","-\frac{i}{2 a (1-i a x)^2}","-\frac{i}{2 a (1-i a x)^2}",1,"(-I/2)/(a*(1 - I*a*x)^2)","A",2,2,24,0.08333,1,"{5073, 32}"
322,1,67,0,0.0389113,"\int \frac{e^{2 i \tan ^{-1}(a x)}}{\left(1+a^2 x^2\right)^{3/2}} \, dx","Int[E^((2*I)*ArcTan[a*x])/(1 + a^2*x^2)^(3/2),x]","-\frac{i \sqrt{1+i a x}}{3 a \sqrt{1-i a x}}-\frac{i \sqrt{1+i a x}}{3 a (1-i a x)^{3/2}}","-\frac{i \sqrt{1+i a x}}{3 a \sqrt{1-i a x}}-\frac{i \sqrt{1+i a x}}{3 a (1-i a x)^{3/2}}",1,"((-I/3)*Sqrt[1 + I*a*x])/(a*(1 - I*a*x)^(3/2)) - ((I/3)*Sqrt[1 + I*a*x])/(a*Sqrt[1 - I*a*x])","A",3,3,24,0.1250,1,"{5073, 45, 37}"
323,1,28,0,0.0422823,"\int \frac{e^{i \tan ^{-1}(a x)}}{\left(1+a^2 x^2\right)^{3/2}} \, dx","Int[E^(I*ArcTan[a*x])/(1 + a^2*x^2)^(3/2),x]","\frac{\tan ^{-1}(a x)}{2 a}+\frac{1}{2 a (a x+i)}","\frac{\tan ^{-1}(a x)}{2 a}+\frac{1}{2 a (a x+i)}",1,"1/(2*a*(I + a*x)) + ArcTan[a*x]/(2*a)","A",4,3,24,0.1250,1,"{5073, 44, 203}"
324,1,29,0,0.0412167,"\int \frac{e^{-i \tan ^{-1}(a x)}}{\left(1+a^2 x^2\right)^{3/2}} \, dx","Int[1/(E^(I*ArcTan[a*x])*(1 + a^2*x^2)^(3/2)),x]","\frac{\tan ^{-1}(a x)}{2 a}-\frac{1}{2 a (-a x+i)}","\frac{\tan ^{-1}(a x)}{2 a}-\frac{1}{2 a (-a x+i)}",1,"-1/(2*a*(I - a*x)) + ArcTan[a*x]/(2*a)","A",4,3,24,0.1250,1,"{5073, 44, 203}"
325,1,67,0,0.0403993,"\int \frac{e^{-2 i \tan ^{-1}(a x)}}{\left(1+a^2 x^2\right)^{3/2}} \, dx","Int[1/(E^((2*I)*ArcTan[a*x])*(1 + a^2*x^2)^(3/2)),x]","\frac{i \sqrt{1-i a x}}{3 a \sqrt{1+i a x}}+\frac{i \sqrt{1-i a x}}{3 a (1+i a x)^{3/2}}","\frac{i \sqrt{1-i a x}}{3 a \sqrt{1+i a x}}+\frac{i \sqrt{1-i a x}}{3 a (1+i a x)^{3/2}}",1,"((I/3)*Sqrt[1 - I*a*x])/(a*(1 + I*a*x)^(3/2)) + ((I/3)*Sqrt[1 - I*a*x])/(a*Sqrt[1 + I*a*x])","A",3,3,24,0.1250,1,"{5073, 45, 37}"
326,1,19,0,0.0323292,"\int \frac{e^{-3 i \tan ^{-1}(a x)}}{\left(1+a^2 x^2\right)^{3/2}} \, dx","Int[1/(E^((3*I)*ArcTan[a*x])*(1 + a^2*x^2)^(3/2)),x]","\frac{i}{2 a (1+i a x)^2}","\frac{i}{2 a (1+i a x)^2}",1,"(I/2)/(a*(1 + I*a*x)^2)","A",2,2,24,0.08333,1,"{5073, 32}"
327,1,67,0,0.0387899,"\int \frac{e^{-4 i \tan ^{-1}(a x)}}{\left(1+a^2 x^2\right)^{3/2}} \, dx","Int[1/(E^((4*I)*ArcTan[a*x])*(1 + a^2*x^2)^(3/2)),x]","\frac{i (1-i a x)^{3/2}}{15 a (1+i a x)^{3/2}}+\frac{i (1-i a x)^{3/2}}{5 a (1+i a x)^{5/2}}","\frac{i (1-i a x)^{3/2}}{15 a (1+i a x)^{3/2}}+\frac{i (1-i a x)^{3/2}}{5 a (1+i a x)^{5/2}}",1,"((I/5)*(1 - I*a*x)^(3/2))/(a*(1 + I*a*x)^(5/2)) + ((I/15)*(1 - I*a*x)^(3/2))/(a*(1 + I*a*x)^(3/2))","A",3,3,24,0.1250,1,"{5073, 45, 37}"
328,1,95,0,0.0799853,"\int \frac{e^{5 i \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[E^((5*I)*ArcTan[a*x])/(c + a^2*c*x^2)^(3/2),x]","-\frac{i \sqrt{a^2 x^2+1}}{2 a c (a x+i)^2 \sqrt{a^2 c x^2+c}}-\frac{2 \sqrt{a^2 x^2+1}}{3 a c (a x+i)^3 \sqrt{a^2 c x^2+c}}","-\frac{i \sqrt{a^2 x^2+1}}{2 a c (a x+i)^2 \sqrt{a^2 c x^2+c}}-\frac{2 \sqrt{a^2 x^2+1}}{3 a c (a x+i)^3 \sqrt{a^2 c x^2+c}}",1,"(-2*Sqrt[1 + a^2*x^2])/(3*a*c*(I + a*x)^3*Sqrt[c + a^2*c*x^2]) - ((I/2)*Sqrt[1 + a^2*x^2])/(a*c*(I + a*x)^2*Sqrt[c + a^2*c*x^2])","A",4,3,25,0.1200,1,"{5076, 5073, 43}"
329,1,69,0,0.0652056,"\int \frac{e^{4 i \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[E^((4*I)*ArcTan[a*x])/(c + a^2*c*x^2)^(3/2),x]","\frac{i c (1+i a x)^5}{15 a \left(a^2 c x^2+c\right)^{5/2}}-\frac{i c (1+i a x)^4}{3 a \left(a^2 c x^2+c\right)^{5/2}}","\frac{i c (1+i a x)^5}{15 a \left(a^2 c x^2+c\right)^{5/2}}-\frac{i c (1+i a x)^4}{3 a \left(a^2 c x^2+c\right)^{5/2}}",1,"((-I/3)*c*(1 + I*a*x)^4)/(a*(c + a^2*c*x^2)^(5/2)) + ((I/15)*c*(1 + I*a*x)^5)/(a*(c + a^2*c*x^2)^(5/2))","A",3,3,25,0.1200,1,"{5075, 659, 651}"
330,1,49,0,0.0688765,"\int \frac{e^{3 i \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[E^((3*I)*ArcTan[a*x])/(c + a^2*c*x^2)^(3/2),x]","-\frac{i \sqrt{a^2 x^2+1}}{2 a c (1-i a x)^2 \sqrt{a^2 c x^2+c}}","-\frac{i \sqrt{a^2 x^2+1}}{2 a c (1-i a x)^2 \sqrt{a^2 c x^2+c}}",1,"((-I/2)*Sqrt[1 + a^2*x^2])/(a*c*(1 - I*a*x)^2*Sqrt[c + a^2*c*x^2])","A",3,3,25,0.1200,1,"{5076, 5073, 32}"
331,1,54,0,0.0549454,"\int \frac{e^{2 i \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[E^((2*I)*ArcTan[a*x])/(c + a^2*c*x^2)^(3/2),x]","\frac{x}{3 c \sqrt{a^2 c x^2+c}}-\frac{2 i (1+i a x)}{3 a \left(a^2 c x^2+c\right)^{3/2}}","\frac{x}{3 c \sqrt{a^2 c x^2+c}}-\frac{2 i (1+i a x)}{3 a \left(a^2 c x^2+c\right)^{3/2}}",1,"(((-2*I)/3)*(1 + I*a*x))/(a*(c + a^2*c*x^2)^(3/2)) + x/(3*c*Sqrt[c + a^2*c*x^2])","A",3,3,25,0.1200,1,"{5075, 653, 191}"
332,1,88,0,0.0813627,"\int \frac{e^{i \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[E^(I*ArcTan[a*x])/(c + a^2*c*x^2)^(3/2),x]","\frac{\sqrt{a^2 x^2+1} \tan ^{-1}(a x)}{2 a c \sqrt{a^2 c x^2+c}}+\frac{\sqrt{a^2 x^2+1}}{2 a c (a x+i) \sqrt{a^2 c x^2+c}}","\frac{\sqrt{a^2 x^2+1} \tan ^{-1}(a x)}{2 a c \sqrt{a^2 c x^2+c}}+\frac{\sqrt{a^2 x^2+1}}{2 a c (a x+i) \sqrt{a^2 c x^2+c}}",1,"Sqrt[1 + a^2*x^2]/(2*a*c*(I + a*x)*Sqrt[c + a^2*c*x^2]) + (Sqrt[1 + a^2*x^2]*ArcTan[a*x])/(2*a*c*Sqrt[c + a^2*c*x^2])","A",5,4,25,0.1600,1,"{5076, 5073, 44, 203}"
333,1,89,0,0.0806776,"\int \frac{e^{-i \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^(I*ArcTan[a*x])*(c + a^2*c*x^2)^(3/2)),x]","\frac{\sqrt{a^2 x^2+1} \tan ^{-1}(a x)}{2 a c \sqrt{a^2 c x^2+c}}-\frac{\sqrt{a^2 x^2+1}}{2 a c (-a x+i) \sqrt{a^2 c x^2+c}}","\frac{\sqrt{a^2 x^2+1} \tan ^{-1}(a x)}{2 a c \sqrt{a^2 c x^2+c}}-\frac{\sqrt{a^2 x^2+1}}{2 a c (-a x+i) \sqrt{a^2 c x^2+c}}",1,"-Sqrt[1 + a^2*x^2]/(2*a*c*(I - a*x)*Sqrt[c + a^2*c*x^2]) + (Sqrt[1 + a^2*x^2]*ArcTan[a*x])/(2*a*c*Sqrt[c + a^2*c*x^2])","A",5,4,25,0.1600,1,"{5076, 5073, 44, 203}"
334,1,54,0,0.0548632,"\int \frac{e^{-2 i \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^((2*I)*ArcTan[a*x])*(c + a^2*c*x^2)^(3/2)),x]","\frac{x}{3 c \sqrt{a^2 c x^2+c}}+\frac{2 i (1-i a x)}{3 a \left(a^2 c x^2+c\right)^{3/2}}","\frac{x}{3 c \sqrt{a^2 c x^2+c}}+\frac{2 i (1-i a x)}{3 a \left(a^2 c x^2+c\right)^{3/2}}",1,"(((2*I)/3)*(1 - I*a*x))/(a*(c + a^2*c*x^2)^(3/2)) + x/(3*c*Sqrt[c + a^2*c*x^2])","A",3,3,25,0.1200,1,"{5074, 653, 191}"
335,1,49,0,0.0720498,"\int \frac{e^{-3 i \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^((3*I)*ArcTan[a*x])*(c + a^2*c*x^2)^(3/2)),x]","\frac{i \sqrt{a^2 x^2+1}}{2 a c (1+i a x)^2 \sqrt{a^2 c x^2+c}}","\frac{i \sqrt{a^2 x^2+1}}{2 a c (1+i a x)^2 \sqrt{a^2 c x^2+c}}",1,"((I/2)*Sqrt[1 + a^2*x^2])/(a*c*(1 + I*a*x)^2*Sqrt[c + a^2*c*x^2])","A",3,3,25,0.1200,1,"{5076, 5073, 32}"
336,1,69,0,0.0661462,"\int \frac{e^{-4 i \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^((4*I)*ArcTan[a*x])*(c + a^2*c*x^2)^(3/2)),x]","\frac{i c (1-i a x)^4}{3 a \left(a^2 c x^2+c\right)^{5/2}}-\frac{i c (1-i a x)^5}{15 a \left(a^2 c x^2+c\right)^{5/2}}","\frac{i c (1-i a x)^4}{3 a \left(a^2 c x^2+c\right)^{5/2}}-\frac{i c (1-i a x)^5}{15 a \left(a^2 c x^2+c\right)^{5/2}}",1,"((I/3)*c*(1 - I*a*x)^4)/(a*(c + a^2*c*x^2)^(5/2)) - ((I/15)*c*(1 - I*a*x)^5)/(a*(c + a^2*c*x^2)^(5/2))","A",3,3,25,0.1200,1,"{5074, 659, 651}"
337,1,86,0,0.052661,"\int e^{n \tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^2 \, dx","Int[E^(n*ArcTan[a*x])*(c + a^2*c*x^2)^2,x]","-\frac{c^2 2^{3-\frac{i n}{2}} (1-i a x)^{3+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}-2,\frac{i n}{2}+3;\frac{i n}{2}+4;\frac{1}{2} (1-i a x)\right)}{a (-n+6 i)}","-\frac{c^2 2^{3-\frac{i n}{2}} (1-i a x)^{3+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}-2,\frac{i n}{2}+3;\frac{i n}{2}+4;\frac{1}{2} (1-i a x)\right)}{a (-n+6 i)}",1,"-((2^(3 - (I/2)*n)*c^2*(1 - I*a*x)^(3 + (I/2)*n)*Hypergeometric2F1[-2 + (I/2)*n, 3 + (I/2)*n, 4 + (I/2)*n, (1 - I*a*x)/2])/(a*(6*I - n)))","A",2,2,21,0.09524,1,"{5073, 69}"
338,1,84,0,0.0390547,"\int e^{n \tan ^{-1}(a x)} \left(c+a^2 c x^2\right) \, dx","Int[E^(n*ArcTan[a*x])*(c + a^2*c*x^2),x]","-\frac{c 2^{2-\frac{i n}{2}} (1-i a x)^{2+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}-1,\frac{i n}{2}+2;\frac{i n}{2}+3;\frac{1}{2} (1-i a x)\right)}{a (-n+4 i)}","-\frac{c 2^{2-\frac{i n}{2}} (1-i a x)^{2+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}-1,\frac{i n}{2}+2;\frac{i n}{2}+3;\frac{1}{2} (1-i a x)\right)}{a (-n+4 i)}",1,"-((2^(2 - (I/2)*n)*c*(1 - I*a*x)^(2 + (I/2)*n)*Hypergeometric2F1[-1 + (I/2)*n, 2 + (I/2)*n, 3 + (I/2)*n, (1 - I*a*x)/2])/(a*(4*I - n)))","A",2,2,19,0.1053,1,"{5073, 69}"
339,1,81,0,0.0156714,"\int e^{n \tan ^{-1}(a x)} \, dx","Int[E^(n*ArcTan[a*x]),x]","-\frac{2^{1-\frac{i n}{2}} (1-i a x)^{1+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}+1,\frac{i n}{2};\frac{i n}{2}+2;\frac{1}{2} (1-i a x)\right)}{a (-n+2 i)}","-\frac{2^{1-\frac{i n}{2}} (1-i a x)^{1+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}+1,\frac{i n}{2};\frac{i n}{2}+2;\frac{1}{2} (1-i a x)\right)}{a (-n+2 i)}",1,"-((2^(1 - (I/2)*n)*(1 - I*a*x)^(1 + (I/2)*n)*Hypergeometric2F1[1 + (I/2)*n, (I/2)*n, 2 + (I/2)*n, (1 - I*a*x)/2])/(a*(2*I - n)))","A",2,2,8,0.2500,1,"{5061, 69}"
340,1,206,0,0.2267684,"\int \frac{e^{n \tan ^{-1}(a x)} x^3}{c+a^2 c x^2} \, dx","Int[(E^(n*ArcTan[a*x])*x^3)/(c + a^2*c*x^2),x]","\frac{2^{-1-\frac{i n}{2}} \left(2-n^2\right) (1-i a x)^{1+\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2}+1,\frac{i n}{2}+1;\frac{i n}{2}+2;\frac{1}{2} (1-i a x)\right)}{a^4 c (2+i n)}+\frac{i (1+i a x)^{-\frac{i n}{2}} \left(i a n^2 x-n^2-i n+2\right) (1-i a x)^{\frac{i n}{2}}}{2 a^4 c n}+\frac{x^2 (1+i a x)^{-\frac{i n}{2}} (1-i a x)^{\frac{i n}{2}}}{2 a^2 c}","\frac{i \left(n^2-2\right) e^{n \tan ^{-1}(a x)} \, _2F_1\left(1,-\frac{i n}{2};1-\frac{i n}{2};-e^{2 i \tan ^{-1}(a x)}\right)}{a^4 c n}+\frac{\left(-i n^2+n+2 i\right) e^{n \tan ^{-1}(a x)}}{2 a^4 c n}+\frac{x^2 e^{n \tan ^{-1}(a x)}}{2 a^2 c}-\frac{n x e^{n \tan ^{-1}(a x)}}{2 a^3 c}",1,"(x^2*(1 - I*a*x)^((I/2)*n))/(2*a^2*c*(1 + I*a*x)^((I/2)*n)) + ((I/2)*(1 - I*a*x)^((I/2)*n)*(2 - I*n - n^2 + I*a*n^2*x))/(a^4*c*n*(1 + I*a*x)^((I/2)*n)) + (2^(-1 - (I/2)*n)*(2 - n^2)*(1 - I*a*x)^(1 + (I/2)*n)*Hypergeometric2F1[1 + (I/2)*n, 1 + (I/2)*n, 2 + (I/2)*n, (1 - I*a*x)/2])/(a^4*c*(2 + I*n))","A",4,4,24,0.1667,0,"{5082, 100, 143, 69}"
341,1,164,0,0.1315966,"\int \frac{e^{n \tan ^{-1}(a x)} x^2}{c+a^2 c x^2} \, dx","Int[(E^(n*ArcTan[a*x])*x^2)/(c + a^2*c*x^2),x]","\frac{i 2^{1-\frac{i n}{2}} (1-i a x)^{\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2},\frac{i n}{2};\frac{i n}{2}+1;\frac{1}{2} (1-i a x)\right)}{a^3 c}+\frac{x (1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{a^2 c}-\frac{(1+i n) (1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{a^3 c n}","\frac{i 2^{1-\frac{i n}{2}} (1-i a x)^{\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2},\frac{i n}{2};\frac{i n}{2}+1;\frac{1}{2} (1-i a x)\right)}{a^3 c}+\frac{x (1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{a^2 c}-\frac{(1+i n) (1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{a^3 c n}",1,"-(((1 + I*n)*(1 - I*a*x)^((I/2)*n))/(a^3*c*n*(1 + I*a*x)^((I/2)*n))) + (x*(1 - I*a*x)^((I/2)*n))/(a^2*c*(1 + I*a*x)^((I/2)*n)) + (I*2^(1 - (I/2)*n)*(1 - I*a*x)^((I/2)*n)*Hypergeometric2F1[(I/2)*n, (I/2)*n, 1 + (I/2)*n, (1 - I*a*x)/2])/(a^3*c)","A",4,4,24,0.1667,1,"{5082, 90, 79, 69}"
342,1,122,0,0.0779773,"\int \frac{e^{n \tan ^{-1}(a x)} x}{c+a^2 c x^2} \, dx","Int[(E^(n*ArcTan[a*x])*x)/(c + a^2*c*x^2),x]","\frac{i (1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{a^2 c n}-\frac{i 2^{1-\frac{i n}{2}} (1-i a x)^{\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2},\frac{i n}{2};\frac{i n}{2}+1;\frac{1}{2} (1-i a x)\right)}{a^2 c n}","\frac{i (1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{a^2 c n}-\frac{i 2^{1-\frac{i n}{2}} (1-i a x)^{\frac{i n}{2}} \, _2F_1\left(\frac{i n}{2},\frac{i n}{2};\frac{i n}{2}+1;\frac{1}{2} (1-i a x)\right)}{a^2 c n}",1,"(I*(1 - I*a*x)^((I/2)*n))/(a^2*c*n*(1 + I*a*x)^((I/2)*n)) - (I*2^(1 - (I/2)*n)*(1 - I*a*x)^((I/2)*n)*Hypergeometric2F1[(I/2)*n, (I/2)*n, 1 + (I/2)*n, (1 - I*a*x)/2])/(a^2*c*n)","A",3,3,22,0.1364,1,"{5082, 79, 69}"
343,1,18,0,0.0303301,"\int \frac{e^{n \tan ^{-1}(a x)}}{c+a^2 c x^2} \, dx","Int[E^(n*ArcTan[a*x])/(c + a^2*c*x^2),x]","\frac{e^{n \tan ^{-1}(a x)}}{a c n}","\frac{e^{n \tan ^{-1}(a x)}}{a c n}",1,"E^(n*ArcTan[a*x])/(a*c*n)","A",1,1,21,0.04762,1,"{5071}"
344,1,132,0,0.0984313,"\int \frac{e^{n \tan ^{-1}(a x)}}{x \left(c+a^2 c x^2\right)} \, dx","Int[E^(n*ArcTan[a*x])/(x*(c + a^2*c*x^2)),x]","\frac{i (1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{c n}-\frac{2 (1-i a x)^{1+\frac{i n}{2}} (1+i a x)^{-1-\frac{i n}{2}} \, _2F_1\left(1,\frac{i n}{2}+1;\frac{i n}{2}+2;\frac{1-i a x}{i a x+1}\right)}{c (2+i n)}","\frac{i e^{n \tan ^{-1}(a x)}}{c n}-\frac{2 i e^{n \tan ^{-1}(a x)} \, _2F_1\left(1,-\frac{i n}{2};1-\frac{i n}{2};e^{2 i \tan ^{-1}(a x)}\right)}{c n}",1,"(I*(1 - I*a*x)^((I/2)*n))/(c*n*(1 + I*a*x)^((I/2)*n)) - (2*(1 - I*a*x)^(1 + (I/2)*n)*(1 + I*a*x)^(-1 - (I/2)*n)*Hypergeometric2F1[1, 1 + (I/2)*n, 2 + (I/2)*n, (1 - I*a*x)/(1 + I*a*x)])/(c*(2 + I*n))","B",3,3,24,0.1250,0,"{5082, 96, 131}"
345,1,180,0,0.1373012,"\int \frac{e^{n \tan ^{-1}(a x)}}{x^2 \left(c+a^2 c x^2\right)} \, dx","Int[E^(n*ArcTan[a*x])/(x^2*(c + a^2*c*x^2)),x]","-\frac{2 a n (1-i a x)^{1+\frac{i n}{2}} (1+i a x)^{-1-\frac{i n}{2}} \, _2F_1\left(1,\frac{i n}{2}+1;\frac{i n}{2}+2;\frac{1-i a x}{i a x+1}\right)}{c (2+i n)}-\frac{a (1-i n) (1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{c n}-\frac{(1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{c x}","-\frac{2 i a \, _2F_1\left(1,-\frac{i n}{2};1-\frac{i n}{2};\frac{2 i}{a x+i}-1\right) e^{n \tan ^{-1}(a x)}}{c}+\frac{i a (n+i) e^{n \tan ^{-1}(a x)}}{c n}-\frac{e^{n \tan ^{-1}(a x)}}{c x}",1,"-((a*(1 - I*n)*(1 - I*a*x)^((I/2)*n))/(c*n*(1 + I*a*x)^((I/2)*n))) - (1 - I*a*x)^((I/2)*n)/(c*x*(1 + I*a*x)^((I/2)*n)) - (2*a*n*(1 - I*a*x)^(1 + (I/2)*n)*(1 + I*a*x)^(-1 - (I/2)*n)*Hypergeometric2F1[1, 1 + (I/2)*n, 2 + (I/2)*n, (1 - I*a*x)/(1 + I*a*x)])/(c*(2 + I*n))","A",5,5,24,0.2083,0,"{5082, 129, 155, 12, 131}"
346,1,242,0,0.1828064,"\int \frac{e^{n \tan ^{-1}(a x)}}{x^3 \left(c+a^2 c x^2\right)} \, dx","Int[E^(n*ArcTan[a*x])/(x^3*(c + a^2*c*x^2)),x]","\frac{a^2 \left(2-n^2\right) (1-i a x)^{1+\frac{i n}{2}} (1+i a x)^{-1-\frac{i n}{2}} \, _2F_1\left(1,\frac{i n}{2}+1;\frac{i n}{2}+2;\frac{1-i a x}{i a x+1}\right)}{c (2+i n)}-\frac{a^2 \left(-i n^2+n+2 i\right) (1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{2 c n}-\frac{(1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{2 c x^2}-\frac{a n (1-i a x)^{\frac{i n}{2}} (1+i a x)^{-\frac{i n}{2}}}{2 c x}","-\frac{i a^2 \left(n^2-2\right) e^{n \tan ^{-1}(a x)} \, _2F_1\left(1,-\frac{i n}{2};1-\frac{i n}{2};e^{2 i \tan ^{-1}(a x)}\right)}{c n}+\frac{i a^2 \left(n^2+i n-2\right) e^{n \tan ^{-1}(a x)}}{2 c n}-\frac{e^{n \tan ^{-1}(a x)}}{2 c x^2}-\frac{a n e^{n \tan ^{-1}(a x)}}{2 c x}",1,"-(a^2*(2*I + n - I*n^2)*(1 - I*a*x)^((I/2)*n))/(2*c*n*(1 + I*a*x)^((I/2)*n)) - (1 - I*a*x)^((I/2)*n)/(2*c*x^2*(1 + I*a*x)^((I/2)*n)) - (a*n*(1 - I*a*x)^((I/2)*n))/(2*c*x*(1 + I*a*x)^((I/2)*n)) + (a^2*(2 - n^2)*(1 - I*a*x)^(1 + (I/2)*n)*(1 + I*a*x)^(-1 - (I/2)*n)*Hypergeometric2F1[1, 1 + (I/2)*n, 2 + (I/2)*n, (1 - I*a*x)/(1 + I*a*x)])/(c*(2 + I*n))","A",6,6,24,0.2500,0,"{5082, 129, 151, 155, 12, 131}"
347,1,181,0,0.1751169,"\int \frac{e^{n \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^4} \, dx","Int[E^(n*ArcTan[a*x])/(c + a^2*c*x^2)^4,x]","\frac{360 (2 a x+n) e^{n \tan ^{-1}(a x)}}{a c^4 \left(n^2+4\right) \left(n^2+16\right) \left(n^2+36\right) \left(a^2 x^2+1\right)}+\frac{30 (4 a x+n) e^{n \tan ^{-1}(a x)}}{a c^4 \left(n^2+16\right) \left(n^2+36\right) \left(a^2 x^2+1\right)^2}+\frac{(6 a x+n) e^{n \tan ^{-1}(a x)}}{a c^4 \left(n^2+36\right) \left(a^2 x^2+1\right)^3}+\frac{720 e^{n \tan ^{-1}(a x)}}{a c^4 n \left(n^2+4\right) \left(n^2+16\right) \left(n^2+36\right)}","\frac{360 (2 a x+n) e^{n \tan ^{-1}(a x)}}{a c^4 \left(n^2+4\right) \left(n^2+16\right) \left(n^2+36\right) \left(a^2 x^2+1\right)}+\frac{30 (4 a x+n) e^{n \tan ^{-1}(a x)}}{a c^4 \left(n^2+16\right) \left(n^2+36\right) \left(a^2 x^2+1\right)^2}+\frac{(6 a x+n) e^{n \tan ^{-1}(a x)}}{a c^4 \left(n^2+36\right) \left(a^2 x^2+1\right)^3}+\frac{720 e^{n \tan ^{-1}(a x)}}{a c^4 n \left(n^2+4\right) \left(n^2+16\right) \left(n^2+36\right)}",1,"(720*E^(n*ArcTan[a*x]))/(a*c^4*n*(4 + n^2)*(16 + n^2)*(36 + n^2)) + (E^(n*ArcTan[a*x])*(n + 6*a*x))/(a*c^4*(36 + n^2)*(1 + a^2*x^2)^3) + (30*E^(n*ArcTan[a*x])*(n + 4*a*x))/(a*c^4*(16 + n^2)*(36 + n^2)*(1 + a^2*x^2)^2) + (360*E^(n*ArcTan[a*x])*(n + 2*a*x))/(a*c^4*(4 + n^2)*(16 + n^2)*(36 + n^2)*(1 + a^2*x^2))","A",4,2,21,0.09524,1,"{5070, 5071}"
348,1,121,0,0.1038582,"\int e^{n \tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^{3/2} \, dx","Int[E^(n*ArcTan[a*x])*(c + a^2*c*x^2)^(3/2),x]","-\frac{c 2^{\frac{5}{2}-\frac{i n}{2}} \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (5+i n)} \, _2F_1\left(\frac{1}{2} (i n-3),\frac{1}{2} (i n+5);\frac{1}{2} (i n+7);\frac{1}{2} (1-i a x)\right)}{a (-n+5 i) \sqrt{a^2 x^2+1}}","-\frac{c 2^{\frac{5}{2}-\frac{i n}{2}} \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (5+i n)} \, _2F_1\left(\frac{1}{2} (i n-3),\frac{1}{2} (i n+5);\frac{1}{2} (i n+7);\frac{1}{2} (1-i a x)\right)}{a (-n+5 i) \sqrt{a^2 x^2+1}}",1,"-((2^(5/2 - (I/2)*n)*c*(1 - I*a*x)^((5 + I*n)/2)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[(-3 + I*n)/2, (5 + I*n)/2, (7 + I*n)/2, (1 - I*a*x)/2])/(a*(5*I - n)*Sqrt[1 + a^2*x^2]))","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
349,1,120,0,0.0966217,"\int e^{n \tan ^{-1}(a x)} \sqrt{c+a^2 c x^2} \, dx","Int[E^(n*ArcTan[a*x])*Sqrt[c + a^2*c*x^2],x]","-\frac{2^{\frac{3}{2}-\frac{i n}{2}} \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (3+i n)} \, _2F_1\left(\frac{1}{2} (i n-1),\frac{1}{2} (i n+3);\frac{1}{2} (i n+5);\frac{1}{2} (1-i a x)\right)}{a (-n+3 i) \sqrt{a^2 x^2+1}}","-\frac{2^{\frac{3}{2}-\frac{i n}{2}} \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (3+i n)} \, _2F_1\left(\frac{1}{2} (i n-1),\frac{1}{2} (i n+3);\frac{1}{2} (i n+5);\frac{1}{2} (1-i a x)\right)}{a (-n+3 i) \sqrt{a^2 x^2+1}}",1,"-((2^(3/2 - (I/2)*n)*(1 - I*a*x)^((3 + I*n)/2)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[(-1 + I*n)/2, (3 + I*n)/2, (5 + I*n)/2, (1 - I*a*x)/2])/(a*(3*I - n)*Sqrt[1 + a^2*x^2]))","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
350,1,120,0,0.0975418,"\int \frac{e^{n \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[E^(n*ArcTan[a*x])/Sqrt[c + a^2*c*x^2],x]","-\frac{2^{\frac{1}{2}-\frac{i n}{2}} \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} \, _2F_1\left(\frac{1}{2} (i n+1),\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1}{2} (1-i a x)\right)}{a (-n+i) \sqrt{a^2 c x^2+c}}","-\frac{2^{\frac{1}{2}-\frac{i n}{2}} \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} \, _2F_1\left(\frac{1}{2} (i n+1),\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1}{2} (1-i a x)\right)}{a (-n+i) \sqrt{a^2 c x^2+c}}",1,"-((2^(1/2 - (I/2)*n)*(1 - I*a*x)^((1 + I*n)/2)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[(1 + I*n)/2, (1 + I*n)/2, (3 + I*n)/2, (1 - I*a*x)/2])/(a*(I - n)*Sqrt[c + a^2*c*x^2]))","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
351,1,283,0,0.3105106,"\int e^{n \tan ^{-1}(a x)} x^2 \left(c+a^2 c x^2\right)^{3/2} \, dx","Int[E^(n*ArcTan[a*x])*x^2*(c + a^2*c*x^2)^(3/2),x]","\frac{c 2^{\frac{3}{2}-\frac{i n}{2}} \left(5-n^2\right) \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (5+i n)} \, _2F_1\left(\frac{1}{2} (i n-3),\frac{1}{2} (i n+5);\frac{1}{2} (i n+7);\frac{1}{2} (1-i a x)\right)}{15 a^3 (-n+5 i) \sqrt{a^2 x^2+1}}-\frac{c n \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (5+i n)} (1+i a x)^{\frac{1}{2} (5-i n)}}{30 a^3 \sqrt{a^2 x^2+1}}+\frac{c x \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (5+i n)} (1+i a x)^{\frac{1}{2} (5-i n)}}{6 a^2 \sqrt{a^2 x^2+1}}","\frac{c 2^{\frac{3}{2}-\frac{i n}{2}} \left(5-n^2\right) \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (5+i n)} \, _2F_1\left(\frac{1}{2} (i n-3),\frac{1}{2} (i n+5);\frac{1}{2} (i n+7);\frac{1}{2} (1-i a x)\right)}{15 a^3 (-n+5 i) \sqrt{a^2 x^2+1}}-\frac{c n \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (5+i n)} (1+i a x)^{\frac{1}{2} (5-i n)}}{30 a^3 \sqrt{a^2 x^2+1}}+\frac{c x \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (5+i n)} (1+i a x)^{\frac{1}{2} (5-i n)}}{6 a^2 \sqrt{a^2 x^2+1}}",1,"-(c*n*(1 - I*a*x)^((5 + I*n)/2)*(1 + I*a*x)^((5 - I*n)/2)*Sqrt[c + a^2*c*x^2])/(30*a^3*Sqrt[1 + a^2*x^2]) + (c*x*(1 - I*a*x)^((5 + I*n)/2)*(1 + I*a*x)^((5 - I*n)/2)*Sqrt[c + a^2*c*x^2])/(6*a^2*Sqrt[1 + a^2*x^2]) + (2^(3/2 - (I/2)*n)*c*(5 - n^2)*(1 - I*a*x)^((5 + I*n)/2)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[(-3 + I*n)/2, (5 + I*n)/2, (7 + I*n)/2, (1 - I*a*x)/2])/(15*a^3*(5*I - n)*Sqrt[1 + a^2*x^2])","A",5,5,26,0.1923,1,"{5085, 5082, 90, 80, 69}"
352,1,280,0,0.2889783,"\int e^{n \tan ^{-1}(a x)} x^2 \sqrt{c+a^2 c x^2} \, dx","Int[E^(n*ArcTan[a*x])*x^2*Sqrt[c + a^2*c*x^2],x]","\frac{2^{-\frac{1}{2}-\frac{i n}{2}} \left(3-n^2\right) \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (3+i n)} \, _2F_1\left(\frac{1}{2} (i n-1),\frac{1}{2} (i n+3);\frac{1}{2} (i n+5);\frac{1}{2} (1-i a x)\right)}{3 a^3 (-n+3 i) \sqrt{a^2 x^2+1}}-\frac{n \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (3+i n)} (1+i a x)^{\frac{1}{2} (3-i n)}}{12 a^3 \sqrt{a^2 x^2+1}}+\frac{x \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (3+i n)} (1+i a x)^{\frac{1}{2} (3-i n)}}{4 a^2 \sqrt{a^2 x^2+1}}","\frac{2^{-\frac{1}{2}-\frac{i n}{2}} \left(3-n^2\right) \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (3+i n)} \, _2F_1\left(\frac{1}{2} (i n-1),\frac{1}{2} (i n+3);\frac{1}{2} (i n+5);\frac{1}{2} (1-i a x)\right)}{3 a^3 (-n+3 i) \sqrt{a^2 x^2+1}}-\frac{n \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (3+i n)} (1+i a x)^{\frac{1}{2} (3-i n)}}{12 a^3 \sqrt{a^2 x^2+1}}+\frac{x \sqrt{a^2 c x^2+c} (1-i a x)^{\frac{1}{2} (3+i n)} (1+i a x)^{\frac{1}{2} (3-i n)}}{4 a^2 \sqrt{a^2 x^2+1}}",1,"-(n*(1 - I*a*x)^((3 + I*n)/2)*(1 + I*a*x)^((3 - I*n)/2)*Sqrt[c + a^2*c*x^2])/(12*a^3*Sqrt[1 + a^2*x^2]) + (x*(1 - I*a*x)^((3 + I*n)/2)*(1 + I*a*x)^((3 - I*n)/2)*Sqrt[c + a^2*c*x^2])/(4*a^2*Sqrt[1 + a^2*x^2]) + (2^(-1/2 - (I/2)*n)*(3 - n^2)*(1 - I*a*x)^((3 + I*n)/2)*Sqrt[c + a^2*c*x^2]*Hypergeometric2F1[(-1 + I*n)/2, (3 + I*n)/2, (5 + I*n)/2, (1 - I*a*x)/2])/(3*a^3*(3*I - n)*Sqrt[1 + a^2*x^2])","A",5,5,26,0.1923,1,"{5085, 5082, 90, 80, 69}"
353,1,322,0,0.3569036,"\int \frac{e^{n \tan ^{-1}(a x)} x^3}{\sqrt{c+a^2 c x^2}} \, dx","Int[(E^(n*ArcTan[a*x])*x^3)/Sqrt[c + a^2*c*x^2],x]","\frac{2^{-\frac{1}{2}-\frac{i n}{2}} n \left(5-n^2\right) \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (3+i n)} \, _2F_1\left(\frac{1}{2} (i n+1),\frac{1}{2} (i n+3);\frac{1}{2} (i n+5);\frac{1}{2} (1-i a x)\right)}{3 a^4 \left(4 n-i \left(3-n^2\right)\right) \sqrt{a^2 c x^2+c}}-\frac{\sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} \left(a (1+i n) n x-n^2-i n+4\right) (1+i a x)^{\frac{1}{2} (1-i n)}}{6 a^4 (1+i n) \sqrt{a^2 c x^2+c}}+\frac{x^2 \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{3 a^2 \sqrt{a^2 c x^2+c}}","\frac{2^{-\frac{1}{2}-\frac{i n}{2}} n \left(5-n^2\right) \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (3+i n)} \, _2F_1\left(\frac{1}{2} (i n+1),\frac{1}{2} (i n+3);\frac{1}{2} (i n+5);\frac{1}{2} (1-i a x)\right)}{3 a^4 \left(4 n-i \left(3-n^2\right)\right) \sqrt{a^2 c x^2+c}}-\frac{\sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} \left(a (1+i n) n x-n^2-i n+4\right) (1+i a x)^{\frac{1}{2} (1-i n)}}{6 a^4 (1+i n) \sqrt{a^2 c x^2+c}}+\frac{x^2 \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{3 a^2 \sqrt{a^2 c x^2+c}}",1,"(x^2*(1 - I*a*x)^((1 + I*n)/2)*(1 + I*a*x)^((1 - I*n)/2)*Sqrt[1 + a^2*x^2])/(3*a^2*Sqrt[c + a^2*c*x^2]) - ((1 - I*a*x)^((1 + I*n)/2)*(1 + I*a*x)^((1 - I*n)/2)*(4 - I*n - n^2 + a*(1 + I*n)*n*x)*Sqrt[1 + a^2*x^2])/(6*a^4*(1 + I*n)*Sqrt[c + a^2*c*x^2]) + (2^(-1/2 - (I/2)*n)*n*(5 - n^2)*(1 - I*a*x)^((3 + I*n)/2)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[(1 + I*n)/2, (3 + I*n)/2, (5 + I*n)/2, (1 - I*a*x)/2])/(3*a^4*(4*n - I*(3 - n^2))*Sqrt[c + a^2*c*x^2])","A",5,5,26,0.1923,1,"{5085, 5082, 100, 146, 69}"
354,1,291,0,0.3421688,"\int \frac{e^{n \tan ^{-1}(a x)} x^2}{\sqrt{c+a^2 c x^2}} \, dx","Int[(E^(n*ArcTan[a*x])*x^2)/Sqrt[c + a^2*c*x^2],x]","-\frac{i 2^{\frac{1}{2}-\frac{i n}{2}} \left(1-n^2\right) \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} \, _2F_1\left(\frac{1}{2} (i n-1),\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1}{2} (1-i a x)\right)}{a^3 \left(n^2+1\right) \sqrt{a^2 c x^2+c}}+\frac{x \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{2 a^2 \sqrt{a^2 c x^2+c}}-\frac{(1+i n) \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{2 a^3 (n+i) \sqrt{a^2 c x^2+c}}","-\frac{i 2^{\frac{1}{2}-\frac{i n}{2}} \left(1-n^2\right) \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} \, _2F_1\left(\frac{1}{2} (i n-1),\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1}{2} (1-i a x)\right)}{a^3 \left(n^2+1\right) \sqrt{a^2 c x^2+c}}+\frac{x \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{2 a^2 \sqrt{a^2 c x^2+c}}-\frac{(1+i n) \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{2 a^3 (n+i) \sqrt{a^2 c x^2+c}}",1,"-((1 + I*n)*(1 - I*a*x)^((1 + I*n)/2)*(1 + I*a*x)^((1 - I*n)/2)*Sqrt[1 + a^2*x^2])/(2*a^3*(I + n)*Sqrt[c + a^2*c*x^2]) + (x*(1 - I*a*x)^((1 + I*n)/2)*(1 + I*a*x)^((1 - I*n)/2)*Sqrt[1 + a^2*x^2])/(2*a^2*Sqrt[c + a^2*c*x^2]) - (I*2^(1/2 - (I/2)*n)*(1 - n^2)*(1 - I*a*x)^((1 + I*n)/2)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[(-1 + I*n)/2, (1 + I*n)/2, (3 + I*n)/2, (1 - I*a*x)/2])/(a^3*(1 + n^2)*Sqrt[c + a^2*c*x^2])","A",5,5,26,0.1923,1,"{5085, 5082, 90, 79, 69}"
355,1,202,0,0.1866345,"\int \frac{e^{n \tan ^{-1}(a x)} x}{\sqrt{c+a^2 c x^2}} \, dx","Int[(E^(n*ArcTan[a*x])*x)/Sqrt[c + a^2*c*x^2],x]","\frac{\sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{a^2 (1-i n) \sqrt{a^2 c x^2+c}}-\frac{i 2^{\frac{3}{2}-\frac{i n}{2}} n \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} \, _2F_1\left(\frac{1}{2} (i n-1),\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1}{2} (1-i a x)\right)}{a^2 \left(n^2+1\right) \sqrt{a^2 c x^2+c}}","\frac{\sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{a^2 (1-i n) \sqrt{a^2 c x^2+c}}-\frac{i 2^{\frac{3}{2}-\frac{i n}{2}} n \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} \, _2F_1\left(\frac{1}{2} (i n-1),\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1}{2} (1-i a x)\right)}{a^2 \left(n^2+1\right) \sqrt{a^2 c x^2+c}}",1,"((1 - I*a*x)^((1 + I*n)/2)*(1 + I*a*x)^((1 - I*n)/2)*Sqrt[1 + a^2*x^2])/(a^2*(1 - I*n)*Sqrt[c + a^2*c*x^2]) - (I*2^(3/2 - (I/2)*n)*n*(1 - I*a*x)^((1 + I*n)/2)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[(-1 + I*n)/2, (1 + I*n)/2, (3 + I*n)/2, (1 - I*a*x)/2])/(a^2*(1 + n^2)*Sqrt[c + a^2*c*x^2])","A",4,4,24,0.1667,1,"{5085, 5082, 79, 69}"
356,1,120,0,0.0833224,"\int \frac{e^{n \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[E^(n*ArcTan[a*x])/Sqrt[c + a^2*c*x^2],x]","-\frac{2^{\frac{1}{2}-\frac{i n}{2}} \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} \, _2F_1\left(\frac{1}{2} (i n+1),\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1}{2} (1-i a x)\right)}{a (-n+i) \sqrt{a^2 c x^2+c}}","-\frac{2^{\frac{1}{2}-\frac{i n}{2}} \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} \, _2F_1\left(\frac{1}{2} (i n+1),\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1}{2} (1-i a x)\right)}{a (-n+i) \sqrt{a^2 c x^2+c}}",1,"-((2^(1/2 - (I/2)*n)*(1 - I*a*x)^((1 + I*n)/2)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[(1 + I*n)/2, (1 + I*n)/2, (3 + I*n)/2, (1 - I*a*x)/2])/(a*(I - n)*Sqrt[c + a^2*c*x^2]))","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
357,1,121,0,0.2032023,"\int \frac{e^{n \tan ^{-1}(a x)}}{x \sqrt{c+a^2 c x^2}} \, dx","Int[E^(n*ArcTan[a*x])/(x*Sqrt[c + a^2*c*x^2]),x]","-\frac{2 \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (-1-i n)} \, _2F_1\left(1,\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1-i a x}{i a x+1}\right)}{(1+i n) \sqrt{a^2 c x^2+c}}","-\frac{2 \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (-1-i n)} \, _2F_1\left(1,\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1-i a x}{i a x+1}\right)}{(1+i n) \sqrt{a^2 c x^2+c}}",1,"(-2*(1 - I*a*x)^((1 + I*n)/2)*(1 + I*a*x)^((-1 - I*n)/2)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[1, (1 + I*n)/2, (3 + I*n)/2, (1 - I*a*x)/(1 + I*a*x)])/((1 + I*n)*Sqrt[c + a^2*c*x^2])","A",3,3,26,0.1154,1,"{5085, 5082, 131}"
358,1,196,0,0.2326389,"\int \frac{e^{n \tan ^{-1}(a x)}}{x^2 \sqrt{c+a^2 c x^2}} \, dx","Int[E^(n*ArcTan[a*x])/(x^2*Sqrt[c + a^2*c*x^2]),x]","-\frac{2 a n \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (-1-i n)} \, _2F_1\left(1,\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1-i a x}{i a x+1}\right)}{(1+i n) \sqrt{a^2 c x^2+c}}-\frac{\sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{x \sqrt{a^2 c x^2+c}}","-\frac{2 a n \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (-1-i n)} \, _2F_1\left(1,\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1-i a x}{i a x+1}\right)}{(1+i n) \sqrt{a^2 c x^2+c}}-\frac{\sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{x \sqrt{a^2 c x^2+c}}",1,"-(((1 - I*a*x)^((1 + I*n)/2)*(1 + I*a*x)^((1 - I*n)/2)*Sqrt[1 + a^2*x^2])/(x*Sqrt[c + a^2*c*x^2])) - (2*a*n*(1 - I*a*x)^((1 + I*n)/2)*(1 + I*a*x)^((-1 - I*n)/2)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[1, (1 + I*n)/2, (3 + I*n)/2, (1 - I*a*x)/(1 + I*a*x)])/((1 + I*n)*Sqrt[c + a^2*c*x^2])","A",4,4,26,0.1538,1,"{5085, 5082, 96, 131}"
359,1,281,0,0.2525304,"\int \frac{e^{n \tan ^{-1}(a x)}}{x^3 \sqrt{c+a^2 c x^2}} \, dx","Int[E^(n*ArcTan[a*x])/(x^3*Sqrt[c + a^2*c*x^2]),x]","\frac{a^2 \left(1-n^2\right) \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (-1-i n)} \, _2F_1\left(1,\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1-i a x}{i a x+1}\right)}{(1+i n) \sqrt{a^2 c x^2+c}}-\frac{a n \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{2 x \sqrt{a^2 c x^2+c}}-\frac{\sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{2 x^2 \sqrt{a^2 c x^2+c}}","\frac{a^2 \left(1-n^2\right) \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (-1-i n)} \, _2F_1\left(1,\frac{1}{2} (i n+1);\frac{1}{2} (i n+3);\frac{1-i a x}{i a x+1}\right)}{(1+i n) \sqrt{a^2 c x^2+c}}-\frac{a n \sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{2 x \sqrt{a^2 c x^2+c}}-\frac{\sqrt{a^2 x^2+1} (1-i a x)^{\frac{1}{2} (1+i n)} (1+i a x)^{\frac{1}{2} (1-i n)}}{2 x^2 \sqrt{a^2 c x^2+c}}",1,"-((1 - I*a*x)^((1 + I*n)/2)*(1 + I*a*x)^((1 - I*n)/2)*Sqrt[1 + a^2*x^2])/(2*x^2*Sqrt[c + a^2*c*x^2]) - (a*n*(1 - I*a*x)^((1 + I*n)/2)*(1 + I*a*x)^((1 - I*n)/2)*Sqrt[1 + a^2*x^2])/(2*x*Sqrt[c + a^2*c*x^2]) + (a^2*(1 - n^2)*(1 - I*a*x)^((1 + I*n)/2)*(1 + I*a*x)^((-1 - I*n)/2)*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[1, (1 + I*n)/2, (3 + I*n)/2, (1 - I*a*x)/(1 + I*a*x)])/((1 + I*n)*Sqrt[c + a^2*c*x^2])","A",6,6,26,0.2308,1,"{5085, 5082, 129, 151, 12, 131}"
360,1,120,0,0.106687,"\int e^{n \tan ^{-1}(a x)} \sqrt[3]{c+a^2 c x^2} \, dx","Int[E^(n*ArcTan[a*x])*(c + a^2*c*x^2)^(1/3),x]","-\frac{3\ 2^{\frac{4}{3}-\frac{i n}{2}} \sqrt[3]{a^2 c x^2+c} (1-i a x)^{\frac{1}{6} (8+3 i n)} \, _2F_1\left(\frac{1}{6} (3 i n-2),\frac{1}{6} (3 i n+8);\frac{1}{6} (3 i n+14);\frac{1}{2} (1-i a x)\right)}{a (-3 n+8 i) \sqrt[3]{a^2 x^2+1}}","-\frac{3\ 2^{\frac{4}{3}-\frac{i n}{2}} \sqrt[3]{a^2 c x^2+c} (1-i a x)^{\frac{1}{6} (8+3 i n)} \, _2F_1\left(\frac{1}{6} (3 i n-2),\frac{1}{6} (3 i n+8);\frac{1}{6} (3 i n+14);\frac{1}{2} (1-i a x)\right)}{a (-3 n+8 i) \sqrt[3]{a^2 x^2+1}}",1,"(-3*2^(4/3 - (I/2)*n)*(1 - I*a*x)^((8 + (3*I)*n)/6)*(c + a^2*c*x^2)^(1/3)*Hypergeometric2F1[(-2 + (3*I)*n)/6, (8 + (3*I)*n)/6, (14 + (3*I)*n)/6, (1 - I*a*x)/2])/(a*(8*I - 3*n)*(1 + a^2*x^2)^(1/3))","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
361,1,120,0,0.1088264,"\int \frac{e^{n \tan ^{-1}(a x)}}{\sqrt[3]{c+a^2 c x^2}} \, dx","Int[E^(n*ArcTan[a*x])/(c + a^2*c*x^2)^(1/3),x]","-\frac{3\ 2^{\frac{2}{3}-\frac{i n}{2}} \sqrt[3]{a^2 x^2+1} (1-i a x)^{\frac{1}{6} (4+3 i n)} \, _2F_1\left(\frac{1}{6} (3 i n+2),\frac{1}{6} (3 i n+4);\frac{1}{6} (3 i n+10);\frac{1}{2} (1-i a x)\right)}{a (-3 n+4 i) \sqrt[3]{a^2 c x^2+c}}","-\frac{3\ 2^{\frac{2}{3}-\frac{i n}{2}} \sqrt[3]{a^2 x^2+1} (1-i a x)^{\frac{1}{6} (4+3 i n)} \, _2F_1\left(\frac{1}{6} (3 i n+2),\frac{1}{6} (3 i n+4);\frac{1}{6} (3 i n+10);\frac{1}{2} (1-i a x)\right)}{a (-3 n+4 i) \sqrt[3]{a^2 c x^2+c}}",1,"(-3*2^(2/3 - (I/2)*n)*(1 - I*a*x)^((4 + (3*I)*n)/6)*(1 + a^2*x^2)^(1/3)*Hypergeometric2F1[(2 + (3*I)*n)/6, (4 + (3*I)*n)/6, (10 + (3*I)*n)/6, (1 - I*a*x)/2])/(a*(4*I - 3*n)*(c + a^2*c*x^2)^(1/3))","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
362,1,120,0,0.110613,"\int \frac{e^{n \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{2/3}} \, dx","Int[E^(n*ArcTan[a*x])/(c + a^2*c*x^2)^(2/3),x]","-\frac{3\ 2^{\frac{1}{3}-\frac{i n}{2}} \left(a^2 x^2+1\right)^{2/3} (1-i a x)^{\frac{1}{6} (2+3 i n)} \, _2F_1\left(\frac{1}{6} (3 i n+2),\frac{1}{6} (3 i n+4);\frac{1}{6} (3 i n+8);\frac{1}{2} (1-i a x)\right)}{a (-3 n+2 i) \left(a^2 c x^2+c\right)^{2/3}}","-\frac{3\ 2^{\frac{1}{3}-\frac{i n}{2}} \left(a^2 x^2+1\right)^{2/3} (1-i a x)^{\frac{1}{6} (2+3 i n)} \, _2F_1\left(\frac{1}{6} (3 i n+2),\frac{1}{6} (3 i n+4);\frac{1}{6} (3 i n+8);\frac{1}{2} (1-i a x)\right)}{a (-3 n+2 i) \left(a^2 c x^2+c\right)^{2/3}}",1,"(-3*2^(1/3 - (I/2)*n)*(1 - I*a*x)^((2 + (3*I)*n)/6)*(1 + a^2*x^2)^(2/3)*Hypergeometric2F1[(2 + (3*I)*n)/6, (4 + (3*I)*n)/6, (8 + (3*I)*n)/6, (1 - I*a*x)/2])/(a*(2*I - 3*n)*(c + a^2*c*x^2)^(2/3))","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
363,1,123,0,0.1191312,"\int \frac{e^{n \tan ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{4/3}} \, dx","Int[E^(n*ArcTan[a*x])/(c + a^2*c*x^2)^(4/3),x]","\frac{3\ 2^{-\frac{1}{3}-\frac{i n}{2}} \sqrt[3]{a^2 x^2+1} (1-i a x)^{\frac{1}{6} (-2+3 i n)} \, _2F_1\left(\frac{1}{6} (3 i n-2),\frac{1}{6} (3 i n+8);\frac{1}{6} (3 i n+4);\frac{1}{2} (1-i a x)\right)}{a c (3 n+2 i) \sqrt[3]{a^2 c x^2+c}}","\frac{3\ 2^{-\frac{1}{3}-\frac{i n}{2}} \sqrt[3]{a^2 x^2+1} (1-i a x)^{\frac{1}{6} (-2+3 i n)} \, _2F_1\left(\frac{1}{6} (3 i n-2),\frac{1}{6} (3 i n+8);\frac{1}{6} (3 i n+4);\frac{1}{2} (1-i a x)\right)}{a c (3 n+2 i) \sqrt[3]{a^2 c x^2+c}}",1,"(3*2^(-1/3 - (I/2)*n)*(1 - I*a*x)^((-2 + (3*I)*n)/6)*(1 + a^2*x^2)^(1/3)*Hypergeometric2F1[(-2 + (3*I)*n)/6, (8 + (3*I)*n)/6, (4 + (3*I)*n)/6, (1 - I*a*x)/2])/(a*c*(2*I + 3*n)*(c + a^2*c*x^2)^(1/3))","A",3,3,23,0.1304,1,"{5076, 5073, 69}"
364,1,49,0,0.0681657,"\int e^{n \tan ^{-1}(a x)} x^m \left(c+a^2 c x^2\right) \, dx","Int[E^(n*ArcTan[a*x])*x^m*(c + a^2*c*x^2),x]","\frac{c x^{m+1} F_1\left(m+1;-\frac{i n}{2}-1,\frac{i n}{2}-1;m+2;i a x,-i a x\right)}{m+1}","\frac{c x^{m+1} F_1\left(m+1;-\frac{i n}{2}-1,\frac{i n}{2}-1;m+2;i a x,-i a x\right)}{m+1}",1,"(c*x^(1 + m)*AppellF1[1 + m, -1 - (I/2)*n, -1 + (I/2)*n, 2 + m, I*a*x, (-I)*a*x])/(1 + m)","A",2,2,22,0.09091,1,"{5082, 133}"
365,1,51,0,0.0923885,"\int \frac{e^{n \tan ^{-1}(a x)} x^m}{c+a^2 c x^2} \, dx","Int[(E^(n*ArcTan[a*x])*x^m)/(c + a^2*c*x^2),x]","\frac{x^{m+1} F_1\left(m+1;1-\frac{i n}{2},\frac{i n}{2}+1;m+2;i a x,-i a x\right)}{c (m+1)}","\frac{x^{m+1} F_1\left(m+1;1-\frac{i n}{2},\frac{i n}{2}+1;m+2;i a x,-i a x\right)}{c (m+1)}",1,"(x^(1 + m)*AppellF1[1 + m, 1 - (I/2)*n, 1 + (I/2)*n, 2 + m, I*a*x, (-I)*a*x])/(c*(1 + m))","A",2,2,24,0.08333,1,"{5082, 133}"
366,1,51,0,0.0897596,"\int \frac{e^{n \tan ^{-1}(a x)} x^m}{\left(c+a^2 c x^2\right)^2} \, dx","Int[(E^(n*ArcTan[a*x])*x^m)/(c + a^2*c*x^2)^2,x]","\frac{x^{m+1} F_1\left(m+1;2-\frac{i n}{2},\frac{i n}{2}+2;m+2;i a x,-i a x\right)}{c^2 (m+1)}","\frac{x^{m+1} F_1\left(m+1;2-\frac{i n}{2},\frac{i n}{2}+2;m+2;i a x,-i a x\right)}{c^2 (m+1)}",1,"(x^(1 + m)*AppellF1[1 + m, 2 - (I/2)*n, 2 + (I/2)*n, 2 + m, I*a*x, (-I)*a*x])/(c^2*(1 + m))","A",2,2,24,0.08333,1,"{5082, 133}"
367,1,51,0,0.0891178,"\int \frac{e^{n \tan ^{-1}(a x)} x^m}{\left(c+a^2 c x^2\right)^3} \, dx","Int[(E^(n*ArcTan[a*x])*x^m)/(c + a^2*c*x^2)^3,x]","\frac{x^{m+1} F_1\left(m+1;3-\frac{i n}{2},\frac{i n}{2}+3;m+2;i a x,-i a x\right)}{c^3 (m+1)}","\frac{x^{m+1} F_1\left(m+1;3-\frac{i n}{2},\frac{i n}{2}+3;m+2;i a x,-i a x\right)}{c^3 (m+1)}",1,"(x^(1 + m)*AppellF1[1 + m, 3 - (I/2)*n, 3 + (I/2)*n, 2 + m, I*a*x, (-I)*a*x])/(c^3*(1 + m))","A",2,2,24,0.08333,1,"{5082, 133}"
368,1,79,0,0.1943922,"\int \frac{e^{n \tan ^{-1}(a x)} x^m}{\sqrt{c+a^2 c x^2}} \, dx","Int[(E^(n*ArcTan[a*x])*x^m)/Sqrt[c + a^2*c*x^2],x]","\frac{\sqrt{a^2 x^2+1} x^{m+1} F_1\left(m+1;\frac{1}{2} (1-i n),\frac{1}{2} (i n+1);m+2;i a x,-i a x\right)}{(m+1) \sqrt{a^2 c x^2+c}}","\frac{\sqrt{a^2 x^2+1} x^{m+1} F_1\left(m+1;\frac{1}{2} (1-i n),\frac{1}{2} (i n+1);m+2;i a x,-i a x\right)}{(m+1) \sqrt{a^2 c x^2+c}}",1,"(x^(1 + m)*Sqrt[1 + a^2*x^2]*AppellF1[1 + m, (1 - I*n)/2, (1 + I*n)/2, 2 + m, I*a*x, (-I)*a*x])/((1 + m)*Sqrt[c + a^2*c*x^2])","A",3,3,26,0.1154,1,"{5085, 5082, 133}"
369,1,82,0,0.2110707,"\int \frac{e^{n \tan ^{-1}(a x)} x^m}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(n*ArcTan[a*x])*x^m)/(c + a^2*c*x^2)^(3/2),x]","\frac{\sqrt{a^2 x^2+1} x^{m+1} F_1\left(m+1;\frac{1}{2} (3-i n),\frac{1}{2} (i n+3);m+2;i a x,-i a x\right)}{c (m+1) \sqrt{a^2 c x^2+c}}","\frac{\sqrt{a^2 x^2+1} x^{m+1} F_1\left(m+1;\frac{1}{2} (3-i n),\frac{1}{2} (i n+3);m+2;i a x,-i a x\right)}{c (m+1) \sqrt{a^2 c x^2+c}}",1,"(x^(1 + m)*Sqrt[1 + a^2*x^2]*AppellF1[1 + m, (3 - I*n)/2, (3 + I*n)/2, 2 + m, I*a*x, (-I)*a*x])/(c*(1 + m)*Sqrt[c + a^2*c*x^2])","A",3,3,26,0.1154,1,"{5085, 5082, 133}"
370,1,82,0,0.2142083,"\int \frac{e^{n \tan ^{-1}(a x)} x^m}{\left(c+a^2 c x^2\right)^{5/2}} \, dx","Int[(E^(n*ArcTan[a*x])*x^m)/(c + a^2*c*x^2)^(5/2),x]","\frac{\sqrt{a^2 x^2+1} x^{m+1} F_1\left(m+1;\frac{1}{2} (5-i n),\frac{1}{2} (i n+5);m+2;i a x,-i a x\right)}{c^2 (m+1) \sqrt{a^2 c x^2+c}}","\frac{\sqrt{a^2 x^2+1} x^{m+1} F_1\left(m+1;\frac{1}{2} (5-i n),\frac{1}{2} (i n+5);m+2;i a x,-i a x\right)}{c^2 (m+1) \sqrt{a^2 c x^2+c}}",1,"(x^(1 + m)*Sqrt[1 + a^2*x^2]*AppellF1[1 + m, (5 - I*n)/2, (5 + I*n)/2, 2 + m, I*a*x, (-I)*a*x])/(c^2*(1 + m)*Sqrt[c + a^2*c*x^2])","A",3,3,26,0.1154,1,"{5085, 5082, 133}"
371,1,115,0,0.0867331,"\int e^{n \tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^p \, dx","Int[E^(n*ArcTan[a*x])*(c + a^2*c*x^2)^p,x]","\frac{2^{-\frac{i n}{2}+p+1} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p (1-i a x)^{\frac{i n}{2}+p+1} \, _2F_1\left(\frac{i n}{2}-p,\frac{i n}{2}+p+1;\frac{i n}{2}+p+2;\frac{1}{2} (1-i a x)\right)}{a (n-2 i (p+1))}","\frac{2^{-\frac{i n}{2}+p+1} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p (1-i a x)^{\frac{i n}{2}+p+1} \, _2F_1\left(\frac{i n}{2}-p,\frac{i n}{2}+p+1;\frac{i n}{2}+p+2;\frac{1}{2} (1-i a x)\right)}{a (n-2 i (p+1))}",1,"(2^(1 - (I/2)*n + p)*(1 - I*a*x)^(1 + (I/2)*n + p)*(c + a^2*c*x^2)^p*Hypergeometric2F1[(I/2)*n - p, 1 + (I/2)*n + p, 2 + (I/2)*n + p, (1 - I*a*x)/2])/(a*(n - (2*I)*(1 + p))*(1 + a^2*x^2)^p)","A",3,3,21,0.1429,1,"{5076, 5073, 69}"
372,1,53,0,0.0649463,"\int e^{-2 i p \tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^p \, dx","Int[(c + a^2*c*x^2)^p/E^((2*I)*p*ArcTan[a*x]),x]","\frac{i (1-i a x)^{2 p+1} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p}{a (2 p+1)}","\frac{i (1-i a x)^{2 p+1} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p}{a (2 p+1)}",1,"(I*(1 - I*a*x)^(1 + 2*p)*(c + a^2*c*x^2)^p)/(a*(1 + 2*p)*(1 + a^2*x^2)^p)","A",3,3,24,0.1250,1,"{5076, 5073, 32}"
373,1,53,0,0.0610917,"\int e^{2 i p \tan ^{-1}(a x)} \left(c+a^2 c x^2\right)^p \, dx","Int[E^((2*I)*p*ArcTan[a*x])*(c + a^2*c*x^2)^p,x]","-\frac{i (1+i a x)^{2 p+1} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p}{a (2 p+1)}","-\frac{i (1+i a x)^{2 p+1} \left(a^2 x^2+1\right)^{-p} \left(a^2 c x^2+c\right)^p}{a (2 p+1)}",1,"((-I)*(1 + I*a*x)^(1 + 2*p)*(c + a^2*c*x^2)^p)/(a*(1 + 2*p)*(1 + a^2*x^2)^p)","A",3,3,24,0.1250,1,"{5076, 5073, 32}"
374,1,60,0,0.1119182,"\int e^{i n \tan ^{-1}(a x)} x^2 \left(c+a^2 c x^2\right)^{-1-\frac{n^2}{2}} \, dx","Int[E^(I*n*ArcTan[a*x])*x^2*(c + a^2*c*x^2)^(-1 - n^2/2),x]","\frac{i (1-i a n x) \left(a^2 c x^2+c\right)^{-\frac{n^2}{2}} e^{i n \tan ^{-1}(a x)}}{a^3 c n \left(1-n^2\right)}","\frac{i (1-i a n x) \left(a^2 c x^2+c\right)^{-\frac{n^2}{2}} e^{i n \tan ^{-1}(a x)}}{a^3 c n \left(1-n^2\right)}",1,"(I*E^(I*n*ArcTan[a*x])*(1 - I*a*n*x))/(a^3*c*n*(1 - n^2)*(c + a^2*c*x^2)^(n^2/2))","A",1,1,35,0.02857,1,"{5079}"
375,1,38,0,0.0785909,"\int \frac{e^{6 i \tan ^{-1}(a x)} x^2}{\left(c+a^2 c x^2\right)^{19}} \, dx","Int[(E^((6*I)*ArcTan[a*x])*x^2)/(c + a^2*c*x^2)^19,x]","-\frac{6 a x+i}{210 a^3 c^{19} (1-i a x)^{21} (1+i a x)^{15}}","-\frac{6 a x+i}{210 a^3 c^{19} (1-i a x)^{21} (1+i a x)^{15}}",1,"-(I + 6*a*x)/(210*a^3*c^19*(1 - I*a*x)^21*(1 + I*a*x)^15)","A",2,2,26,0.07692,1,"{5082, 81}"
376,1,38,0,0.0775599,"\int \frac{e^{4 i \tan ^{-1}(a x)} x^2}{\left(c+a^2 c x^2\right)^9} \, dx","Int[(E^((4*I)*ArcTan[a*x])*x^2)/(c + a^2*c*x^2)^9,x]","-\frac{4 a x+i}{60 a^3 c^9 (1-i a x)^{10} (1+i a x)^6}","-\frac{4 a x+i}{60 a^3 c^9 (1-i a x)^{10} (1+i a x)^6}",1,"-(I + 4*a*x)/(60*a^3*c^9*(1 - I*a*x)^10*(1 + I*a*x)^6)","A",2,2,26,0.07692,1,"{5082, 81}"
377,1,38,0,0.0767827,"\int \frac{e^{2 i \tan ^{-1}(a x)} x^2}{\left(c+a^2 c x^2\right)^3} \, dx","Int[(E^((2*I)*ArcTan[a*x])*x^2)/(c + a^2*c*x^2)^3,x]","-\frac{2 a x+i}{6 a^3 c^3 (1-i a x)^3 (1+i a x)}","-\frac{2 a x+i}{6 a^3 c^3 (1-i a x)^3 (1+i a x)}",1,"-(I + 2*a*x)/(6*a^3*c^3*(1 - I*a*x)^3*(1 + I*a*x))","A",2,2,26,0.07692,1,"{5082, 81}"
378,1,38,0,0.0774534,"\int \frac{e^{-2 i \tan ^{-1}(a x)} x^2}{\left(c+a^2 c x^2\right)^3} \, dx","Int[x^2/(E^((2*I)*ArcTan[a*x])*(c + a^2*c*x^2)^3),x]","\frac{-2 a x+i}{6 a^3 c^3 (1-i a x) (1+i a x)^3}","\frac{-2 a x+i}{6 a^3 c^3 (1-i a x) (1+i a x)^3}",1,"(I - 2*a*x)/(6*a^3*c^3*(1 - I*a*x)*(1 + I*a*x)^3)","A",2,2,26,0.07692,1,"{5082, 81}"
379,1,38,0,0.0775632,"\int \frac{e^{-4 i \tan ^{-1}(a x)} x^2}{\left(c+a^2 c x^2\right)^9} \, dx","Int[x^2/(E^((4*I)*ArcTan[a*x])*(c + a^2*c*x^2)^9),x]","\frac{-4 a x+i}{60 a^3 c^9 (1-i a x)^6 (1+i a x)^{10}}","\frac{-4 a x+i}{60 a^3 c^9 (1-i a x)^6 (1+i a x)^{10}}",1,"(I - 4*a*x)/(60*a^3*c^9*(1 - I*a*x)^6*(1 + I*a*x)^10)","A",2,2,26,0.07692,1,"{5082, 81}"
380,1,65,0,0.2013342,"\int \frac{e^{5 i \tan ^{-1}(a x)} x^2}{\left(c+a^2 c x^2\right)^{27/2}} \, dx","Int[(E^((5*I)*ArcTan[a*x])*x^2)/(c + a^2*c*x^2)^(27/2),x]","-\frac{(5 a x+i) \sqrt{a^2 x^2+1}}{120 a^3 c^{13} (1-i a x)^{15} (1+i a x)^{10} \sqrt{a^2 c x^2+c}}","-\frac{(5 a x+i) \sqrt{a^2 x^2+1}}{120 a^3 c^{13} (1-i a x)^{15} (1+i a x)^{10} \sqrt{a^2 c x^2+c}}",1,"-((I + 5*a*x)*Sqrt[1 + a^2*x^2])/(120*a^3*c^13*(1 - I*a*x)^15*(1 + I*a*x)^10*Sqrt[c + a^2*c*x^2])","A",3,3,28,0.1071,1,"{5085, 5082, 81}"
381,1,65,0,0.2039025,"\int \frac{e^{3 i \tan ^{-1}(a x)} x^2}{\left(c+a^2 c x^2\right)^{11/2}} \, dx","Int[(E^((3*I)*ArcTan[a*x])*x^2)/(c + a^2*c*x^2)^(11/2),x]","-\frac{(3 a x+i) \sqrt{a^2 x^2+1}}{24 a^3 c^5 (1-i a x)^6 (1+i a x)^3 \sqrt{a^2 c x^2+c}}","-\frac{(3 a x+i) \sqrt{a^2 x^2+1}}{24 a^3 c^5 (1-i a x)^6 (1+i a x)^3 \sqrt{a^2 c x^2+c}}",1,"-((I + 3*a*x)*Sqrt[1 + a^2*x^2])/(24*a^3*c^5*(1 - I*a*x)^6*(1 + I*a*x)^3*Sqrt[c + a^2*c*x^2])","A",3,3,28,0.1071,1,"{5085, 5082, 81}"
382,1,142,0,0.2188277,"\int \frac{e^{i \tan ^{-1}(a x)} x^2}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(I*ArcTan[a*x])*x^2)/(c + a^2*c*x^2)^(3/2),x]","-\frac{\sqrt{a^2 x^2+1}}{2 a^3 c (a x+i) \sqrt{a^2 c x^2+c}}+\frac{i \sqrt{a^2 x^2+1} \log (-a x+i)}{4 a^3 c \sqrt{a^2 c x^2+c}}+\frac{3 i \sqrt{a^2 x^2+1} \log (a x+i)}{4 a^3 c \sqrt{a^2 c x^2+c}}","-\frac{\sqrt{a^2 x^2+1}}{2 a^3 c (a x+i) \sqrt{a^2 c x^2+c}}+\frac{i \sqrt{a^2 x^2+1} \log (-a x+i)}{4 a^3 c \sqrt{a^2 c x^2+c}}+\frac{3 i \sqrt{a^2 x^2+1} \log (a x+i)}{4 a^3 c \sqrt{a^2 c x^2+c}}",1,"-Sqrt[1 + a^2*x^2]/(2*a^3*c*(I + a*x)*Sqrt[c + a^2*c*x^2]) + ((I/4)*Sqrt[1 + a^2*x^2]*Log[I - a*x])/(a^3*c*Sqrt[c + a^2*c*x^2]) + (((3*I)/4)*Sqrt[1 + a^2*x^2]*Log[I + a*x])/(a^3*c*Sqrt[c + a^2*c*x^2])","A",4,3,28,0.1071,1,"{5085, 5082, 88}"
383,1,143,0,0.2235908,"\int \frac{e^{-i \tan ^{-1}(a x)} x^2}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[x^2/(E^(I*ArcTan[a*x])*(c + a^2*c*x^2)^(3/2)),x]","\frac{\sqrt{a^2 x^2+1}}{2 a^3 c (-a x+i) \sqrt{a^2 c x^2+c}}-\frac{3 i \sqrt{a^2 x^2+1} \log (-a x+i)}{4 a^3 c \sqrt{a^2 c x^2+c}}-\frac{i \sqrt{a^2 x^2+1} \log (a x+i)}{4 a^3 c \sqrt{a^2 c x^2+c}}","\frac{\sqrt{a^2 x^2+1}}{2 a^3 c (-a x+i) \sqrt{a^2 c x^2+c}}-\frac{3 i \sqrt{a^2 x^2+1} \log (-a x+i)}{4 a^3 c \sqrt{a^2 c x^2+c}}-\frac{i \sqrt{a^2 x^2+1} \log (a x+i)}{4 a^3 c \sqrt{a^2 c x^2+c}}",1,"Sqrt[1 + a^2*x^2]/(2*a^3*c*(I - a*x)*Sqrt[c + a^2*c*x^2]) - (((3*I)/4)*Sqrt[1 + a^2*x^2]*Log[I - a*x])/(a^3*c*Sqrt[c + a^2*c*x^2]) - ((I/4)*Sqrt[1 + a^2*x^2]*Log[I + a*x])/(a^3*c*Sqrt[c + a^2*c*x^2])","A",4,3,28,0.1071,1,"{5085, 5082, 88}"
384,1,65,0,0.2082882,"\int \frac{e^{-3 i \tan ^{-1}(a x)} x^2}{\left(c+a^2 c x^2\right)^{11/2}} \, dx","Int[x^2/(E^((3*I)*ArcTan[a*x])*(c + a^2*c*x^2)^(11/2)),x]","\frac{(-3 a x+i) \sqrt{a^2 x^2+1}}{24 a^3 c^5 (1-i a x)^3 (1+i a x)^6 \sqrt{a^2 c x^2+c}}","\frac{(-3 a x+i) \sqrt{a^2 x^2+1}}{24 a^3 c^5 (1-i a x)^3 (1+i a x)^6 \sqrt{a^2 c x^2+c}}",1,"((I - 3*a*x)*Sqrt[1 + a^2*x^2])/(24*a^3*c^5*(1 - I*a*x)^3*(1 + I*a*x)^6*Sqrt[c + a^2*c*x^2])","A",3,3,28,0.1071,1,"{5085, 5082, 81}"
385,1,65,0,0.2089972,"\int \frac{e^{-5 i \tan ^{-1}(a x)} x^2}{\left(c+a^2 c x^2\right)^{27/2}} \, dx","Int[x^2/(E^((5*I)*ArcTan[a*x])*(c + a^2*c*x^2)^(27/2)),x]","\frac{(-5 a x+i) \sqrt{a^2 x^2+1}}{120 a^3 c^{13} (1-i a x)^{10} (1+i a x)^{15} \sqrt{a^2 c x^2+c}}","\frac{(-5 a x+i) \sqrt{a^2 x^2+1}}{120 a^3 c^{13} (1-i a x)^{10} (1+i a x)^{15} \sqrt{a^2 c x^2+c}}",1,"((I - 5*a*x)*Sqrt[1 + a^2*x^2])/(120*a^3*c^13*(1 - I*a*x)^10*(1 + I*a*x)^15*Sqrt[c + a^2*c*x^2])","A",3,3,28,0.1071,1,"{5085, 5082, 81}"