1,1,67,0,0.461333," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^4,x, algorithm=""fricas"")","\frac{{\left(24 i \, a^{4} x^{4} + 30 \, a^{3} x^{3} - 32 i \, a^{2} x^{2} - 45 \, a x + 64 i\right)} \sqrt{a^{2} x^{2} + 1} - 45 \, \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right)}{120 \, a^{5}}"," ",0,"1/120*((24*I*a^4*x^4 + 30*a^3*x^3 - 32*I*a^2*x^2 - 45*a*x + 64*I)*sqrt(a^2*x^2 + 1) - 45*log(-a*x + sqrt(a^2*x^2 + 1)))/a^5","A",0
2,1,59,0,0.467616," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^3,x, algorithm=""fricas"")","\frac{{\left(6 i \, a^{3} x^{3} + 8 \, a^{2} x^{2} - 9 i \, a x - 16\right)} \sqrt{a^{2} x^{2} + 1} - 9 i \, \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right)}{24 \, a^{4}}"," ",0,"1/24*((6*I*a^3*x^3 + 8*a^2*x^2 - 9*I*a*x - 16)*sqrt(a^2*x^2 + 1) - 9*I*log(-a*x + sqrt(a^2*x^2 + 1)))/a^4","A",0
3,1,51,0,0.426839," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^2,x, algorithm=""fricas"")","\frac{\sqrt{a^{2} x^{2} + 1} {\left(2 i \, a^{2} x^{2} + 3 \, a x - 4 i\right)} + 3 \, \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right)}{6 \, a^{3}}"," ",0,"1/6*(sqrt(a^2*x^2 + 1)*(2*I*a^2*x^2 + 3*a*x - 4*I) + 3*log(-a*x + sqrt(a^2*x^2 + 1)))/a^3","A",0
4,1,43,0,0.431309," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x,x, algorithm=""fricas"")","\frac{\sqrt{a^{2} x^{2} + 1} {\left(i \, a x + 2\right)} + i \, \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right)}{2 \, a^{2}}"," ",0,"1/2*(sqrt(a^2*x^2 + 1)*(I*a*x + 2) + I*log(-a*x + sqrt(a^2*x^2 + 1)))/a^2","A",0
5,1,37,0,0.446271," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{i \, \sqrt{a^{2} x^{2} + 1} - \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right)}{a}"," ",0,"(I*sqrt(a^2*x^2 + 1) - log(-a*x + sqrt(a^2*x^2 + 1)))/a","A",0
6,1,58,0,0.425106," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/x,x, algorithm=""fricas"")","-\log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) - i \, \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right)"," ",0,"-log(-a*x + sqrt(a^2*x^2 + 1) + 1) - I*log(-a*x + sqrt(a^2*x^2 + 1)) + log(-a*x + sqrt(a^2*x^2 + 1) - 1)","B",0
7,1,66,0,0.453888," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{-i \, a x \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) + i \, a x \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) - a x - \sqrt{a^{2} x^{2} + 1}}{x}"," ",0,"(-I*a*x*log(-a*x + sqrt(a^2*x^2 + 1) + 1) + I*a*x*log(-a*x + sqrt(a^2*x^2 + 1) - 1) - a*x - sqrt(a^2*x^2 + 1))/x","B",0
8,1,83,0,1.197833," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{a^{2} x^{2} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) - a^{2} x^{2} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) - 2 i \, a^{2} x^{2} + \sqrt{a^{2} x^{2} + 1} {\left(-2 i \, a x - 1\right)}}{2 \, x^{2}}"," ",0,"1/2*(a^2*x^2*log(-a*x + sqrt(a^2*x^2 + 1) + 1) - a^2*x^2*log(-a*x + sqrt(a^2*x^2 + 1) - 1) - 2*I*a^2*x^2 + sqrt(a^2*x^2 + 1)*(-2*I*a*x - 1))/x^2","A",0
9,1,92,0,0.411375," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^4,x, algorithm=""fricas"")","\frac{3 i \, a^{3} x^{3} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) - 3 i \, a^{3} x^{3} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + 4 \, a^{3} x^{3} + {\left(4 \, a^{2} x^{2} - 3 i \, a x - 2\right)} \sqrt{a^{2} x^{2} + 1}}{6 \, x^{3}}"," ",0,"1/6*(3*I*a^3*x^3*log(-a*x + sqrt(a^2*x^2 + 1) + 1) - 3*I*a^3*x^3*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + 4*a^3*x^3 + (4*a^2*x^2 - 3*I*a*x - 2)*sqrt(a^2*x^2 + 1))/x^3","A",0
10,1,101,0,0.466935," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{9 \, a^{4} x^{4} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) - 9 \, a^{4} x^{4} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) - 16 i \, a^{4} x^{4} - {\left(16 i \, a^{3} x^{3} + 9 \, a^{2} x^{2} - 8 i \, a x - 6\right)} \sqrt{a^{2} x^{2} + 1}}{24 \, x^{4}}"," ",0,"-1/24*(9*a^4*x^4*log(-a*x + sqrt(a^2*x^2 + 1) + 1) - 9*a^4*x^4*log(-a*x + sqrt(a^2*x^2 + 1) - 1) - 16*I*a^4*x^4 - (16*I*a^3*x^3 + 9*a^2*x^2 - 8*I*a*x - 6)*sqrt(a^2*x^2 + 1))/x^4","A",0
11,1,46,0,0.444563," ","integrate((1+I*a*x)^2/(a^2*x^2+1)*x^3,x, algorithm=""fricas"")","-\frac{3 \, a^{4} x^{4} - 8 i \, a^{3} x^{3} - 12 \, a^{2} x^{2} + 24 i \, a x + 24 \, \log\left(\frac{a x + i}{a}\right)}{12 \, a^{4}}"," ",0,"-1/12*(3*a^4*x^4 - 8*I*a^3*x^3 - 12*a^2*x^2 + 24*I*a*x + 24*log((a*x + I)/a))/a^4","A",0
12,1,37,0,0.463534," ","integrate((1+I*a*x)^2/(a^2*x^2+1)*x^2,x, algorithm=""fricas"")","-\frac{a^{3} x^{3} - 3 i \, a^{2} x^{2} - 6 \, a x + 6 i \, \log\left(\frac{a x + i}{a}\right)}{3 \, a^{3}}"," ",0,"-1/3*(a^3*x^3 - 3*I*a^2*x^2 - 6*a*x + 6*I*log((a*x + I)/a))/a^3","A",0
13,1,29,0,0.379564," ","integrate((1+I*a*x)^2/(a^2*x^2+1)*x,x, algorithm=""fricas"")","-\frac{a^{2} x^{2} - 4 i \, a x - 4 \, \log\left(\frac{a x + i}{a}\right)}{2 \, a^{2}}"," ",0,"-1/2*(a^2*x^2 - 4*I*a*x - 4*log((a*x + I)/a))/a^2","A",0
14,1,21,0,0.416631," ","integrate((1+I*a*x)^2/(a^2*x^2+1),x, algorithm=""fricas"")","-\frac{a x - 2 i \, \log\left(\frac{a x + i}{a}\right)}{a}"," ",0,"-(a*x - 2*I*log((a*x + I)/a))/a","A",0
15,1,15,0,0.390915," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/x,x, algorithm=""fricas"")","\log\left(x\right) - 2 \, \log\left(\frac{a x + i}{a}\right)"," ",0,"log(x) - 2*log((a*x + I)/a)","A",0
16,1,26,0,0.395673," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/x^2,x, algorithm=""fricas"")","\frac{2 i \, a x \log\left(x\right) - 2 i \, a x \log\left(\frac{a x + i}{a}\right) - 1}{x}"," ",0,"(2*I*a*x*log(x) - 2*I*a*x*log((a*x + I)/a) - 1)/x","A",0
17,1,39,0,0.420837," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/x^3,x, algorithm=""fricas"")","-\frac{4 \, a^{2} x^{2} \log\left(x\right) - 4 \, a^{2} x^{2} \log\left(\frac{a x + i}{a}\right) + 4 i \, a x + 1}{2 \, x^{2}}"," ",0,"-1/2*(4*a^2*x^2*log(x) - 4*a^2*x^2*log((a*x + I)/a) + 4*I*a*x + 1)/x^2","A",0
18,1,47,0,0.405107," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/x^4,x, algorithm=""fricas"")","\frac{-6 i \, a^{3} x^{3} \log\left(x\right) + 6 i \, a^{3} x^{3} \log\left(\frac{a x + i}{a}\right) + 6 \, a^{2} x^{2} - 3 i \, a x - 1}{3 \, x^{3}}"," ",0,"1/3*(-6*I*a^3*x^3*log(x) + 6*I*a^3*x^3*log((a*x + I)/a) + 6*a^2*x^2 - 3*I*a*x - 1)/x^3","A",0
19,1,88,0,0.416087," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^3,x, algorithm=""fricas"")","\frac{32 i \, a x - 51 \, {\left(-i \, a x + 1\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + {\left(-2 i \, a^{4} x^{4} - 6 \, a^{3} x^{3} + 11 i \, a^{2} x^{2} + 29 \, a x + 80 i\right)} \sqrt{a^{2} x^{2} + 1} - 32}{8 \, a^{5} x + 8 i \, a^{4}}"," ",0,"(32*I*a*x - 51*(-I*a*x + 1)*log(-a*x + sqrt(a^2*x^2 + 1)) + (-2*I*a^4*x^4 - 6*a^3*x^3 + 11*I*a^2*x^2 + 29*a*x + 80*I)*sqrt(a^2*x^2 + 1) - 32)/(8*a^5*x + 8*I*a^4)","A",0
20,1,81,0,0.409751," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^2,x, algorithm=""fricas"")","-\frac{24 \, a x + {\left(33 \, a x + 33 i\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) - {\left(-2 i \, a^{3} x^{3} - 7 \, a^{2} x^{2} + 19 i \, a x - 52\right)} \sqrt{a^{2} x^{2} + 1} + 24 i}{6 \, a^{4} x + 6 i \, a^{3}}"," ",0,"-(24*a*x + (33*a*x + 33*I)*log(-a*x + sqrt(a^2*x^2 + 1)) - (-2*I*a^3*x^3 - 7*a^2*x^2 + 19*I*a*x - 52)*sqrt(a^2*x^2 + 1) + 24*I)/(6*a^4*x + 6*I*a^3)","A",0
21,1,72,0,0.438743," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x,x, algorithm=""fricas"")","\frac{-8 i \, a x - 9 \, {\left(i \, a x - 1\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + \sqrt{a^{2} x^{2} + 1} {\left(-i \, a^{2} x^{2} - 5 \, a x - 14 i\right)} + 8}{2 \, a^{3} x + 2 i \, a^{2}}"," ",0,"(-8*I*a*x - 9*(I*a*x - 1)*log(-a*x + sqrt(a^2*x^2 + 1)) + sqrt(a^2*x^2 + 1)*(-I*a^2*x^2 - 5*a*x - 14*I) + 8)/(2*a^3*x + 2*I*a^2)","A",0
22,1,60,0,0.419299," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{4 \, a x + {\left(3 \, a x + 3 i\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + \sqrt{a^{2} x^{2} + 1} {\left(-i \, a x + 5\right)} + 4 i}{a^{2} x + i \, a}"," ",0,"(4*a*x + (3*a*x + 3*I)*log(-a*x + sqrt(a^2*x^2 + 1)) + sqrt(a^2*x^2 + 1)*(-I*a*x + 5) + 4*I)/(a^2*x + I*a)","A",0
23,1,100,0,0.446982," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x,x, algorithm=""fricas"")","\frac{4 i \, a x - {\left(a x + i\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) + {\left(i \, a x - 1\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + {\left(a x + i\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + 4 i \, \sqrt{a^{2} x^{2} + 1} - 4}{a x + i}"," ",0,"(4*I*a*x - (a*x + I)*log(-a*x + sqrt(a^2*x^2 + 1) + 1) + (I*a*x - 1)*log(-a*x + sqrt(a^2*x^2 + 1)) + (a*x + I)*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + 4*I*sqrt(a^2*x^2 + 1) - 4)/(a*x + I)","B",0
24,1,109,0,0.441021," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x^2,x, algorithm=""fricas"")","-\frac{5 \, a^{2} x^{2} + 5 i \, a x + 3 \, {\left(i \, a^{2} x^{2} - a x\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) + 3 \, {\left(-i \, a^{2} x^{2} + a x\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + \sqrt{a^{2} x^{2} + 1} {\left(5 \, a x + i\right)}}{a x^{2} + i \, x}"," ",0,"-(5*a^2*x^2 + 5*I*a*x + 3*(I*a^2*x^2 - a*x)*log(-a*x + sqrt(a^2*x^2 + 1) + 1) + 3*(-I*a^2*x^2 + a*x)*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + sqrt(a^2*x^2 + 1)*(5*a*x + I))/(a*x^2 + I*x)","B",0
25,1,131,0,0.482878," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{-14 i \, a^{3} x^{3} + 14 \, a^{2} x^{2} + {\left(9 \, a^{3} x^{3} + 9 i \, a^{2} x^{2}\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) - {\left(9 \, a^{3} x^{3} + 9 i \, a^{2} x^{2}\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + \sqrt{a^{2} x^{2} + 1} {\left(-14 i \, a^{2} x^{2} + 5 \, a x - i\right)}}{2 \, a x^{3} + 2 i \, x^{2}}"," ",0,"(-14*I*a^3*x^3 + 14*a^2*x^2 + (9*a^3*x^3 + 9*I*a^2*x^2)*log(-a*x + sqrt(a^2*x^2 + 1) + 1) - (9*a^3*x^3 + 9*I*a^2*x^2)*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + sqrt(a^2*x^2 + 1)*(-14*I*a^2*x^2 + 5*a*x - I))/(2*a*x^3 + 2*I*x^2)","A",0
26,1,139,0,0.460665," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x^4,x, algorithm=""fricas"")","\frac{52 \, a^{4} x^{4} + 52 i \, a^{3} x^{3} - 33 \, {\left(-i \, a^{4} x^{4} + a^{3} x^{3}\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) - 33 \, {\left(i \, a^{4} x^{4} - a^{3} x^{3}\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + {\left(52 \, a^{3} x^{3} + 19 i \, a^{2} x^{2} + 7 \, a x - 2 i\right)} \sqrt{a^{2} x^{2} + 1}}{6 \, a x^{4} + 6 i \, x^{3}}"," ",0,"(52*a^4*x^4 + 52*I*a^3*x^3 - 33*(-I*a^4*x^4 + a^3*x^3)*log(-a*x + sqrt(a^2*x^2 + 1) + 1) - 33*(I*a^4*x^4 - a^3*x^3)*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + (52*a^3*x^3 + 19*I*a^2*x^2 + 7*a*x - 2*I)*sqrt(a^2*x^2 + 1))/(6*a*x^4 + 6*I*x^3)","A",0
27,1,70,0,0.421435," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2*x^3,x, algorithm=""fricas"")","\frac{3 \, a^{5} x^{5} - 13 i \, a^{4} x^{4} - 32 \, a^{3} x^{3} + 96 i \, a^{2} x^{2} - 144 \, a x + {\left(192 \, a x + 192 i\right)} \log\left(\frac{a x + i}{a}\right) + 48 i}{12 \, a^{5} x + 12 i \, a^{4}}"," ",0,"(3*a^5*x^5 - 13*I*a^4*x^4 - 32*a^3*x^3 + 96*I*a^2*x^2 - 144*a*x + (192*a*x + 192*I)*log((a*x + I)/a) + 48*I)/(12*a^5*x + 12*I*a^4)","A",0
28,1,62,0,0.851338," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2*x^2,x, algorithm=""fricas"")","\frac{a^{4} x^{4} - 5 i \, a^{3} x^{3} - 18 \, a^{2} x^{2} - 24 i \, a x - 36 \, {\left(-i \, a x + 1\right)} \log\left(\frac{a x + i}{a}\right) - 12}{3 \, a^{4} x + 3 i \, a^{3}}"," ",0,"(a^4*x^4 - 5*I*a^3*x^3 - 18*a^2*x^2 - 24*I*a*x - 36*(-I*a*x + 1)*log((a*x + I)/a) - 12)/(3*a^4*x + 3*I*a^3)","A",0
29,1,54,0,0.420845," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2*x,x, algorithm=""fricas"")","\frac{a^{3} x^{3} - 7 i \, a^{2} x^{2} + 8 \, a x - {\left(16 \, a x + 16 i\right)} \log\left(\frac{a x + i}{a}\right) - 8 i}{2 \, a^{3} x + 2 i \, a^{2}}"," ",0,"(a^3*x^3 - 7*I*a^2*x^2 + 8*a*x - (16*a*x + 16*I)*log((a*x + I)/a) - 8*I)/(2*a^3*x + 2*I*a^2)","A",0
30,1,43,0,0.522379," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2,x, algorithm=""fricas"")","\frac{a^{2} x^{2} + i \, a x - 4 \, {\left(i \, a x - 1\right)} \log\left(\frac{a x + i}{a}\right) + 4}{a^{2} x + i \, a}"," ",0,"(a^2*x^2 + I*a*x - 4*(I*a*x - 1)*log((a*x + I)/a) + 4)/(a^2*x + I*a)","A",0
31,1,18,0,0.535631," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/x,x, algorithm=""fricas"")","\frac{{\left(a x + i\right)} \log\left(x\right) + 4 i}{a x + i}"," ",0,"((a*x + I)*log(x) + 4*I)/(a*x + I)","A",0
32,1,60,0,0.418967," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/x^2,x, algorithm=""fricas"")","-\frac{5 \, a x + 4 \, {\left(-i \, a^{2} x^{2} + a x\right)} \log\left(x\right) + 4 \, {\left(i \, a^{2} x^{2} - a x\right)} \log\left(\frac{a x + i}{a}\right) + i}{a x^{2} + i \, x}"," ",0,"-(5*a*x + 4*(-I*a^2*x^2 + a*x)*log(x) + 4*(I*a^2*x^2 - a*x)*log((a*x + I)/a) + I)/(a*x^2 + I*x)","A",0
33,1,78,0,0.468662," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/x^3,x, algorithm=""fricas"")","\frac{-16 i \, a^{2} x^{2} + 7 \, a x - {\left(16 \, a^{3} x^{3} + 16 i \, a^{2} x^{2}\right)} \log\left(x\right) + {\left(16 \, a^{3} x^{3} + 16 i \, a^{2} x^{2}\right)} \log\left(\frac{a x + i}{a}\right) - i}{2 \, a x^{3} + 2 i \, x^{2}}"," ",0,"(-16*I*a^2*x^2 + 7*a*x - (16*a^3*x^3 + 16*I*a^2*x^2)*log(x) + (16*a^3*x^3 + 16*I*a^2*x^2)*log((a*x + I)/a) - I)/(2*a*x^3 + 2*I*x^2)","A",0
34,1,86,0,0.465660," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/x^4,x, algorithm=""fricas"")","\frac{36 \, a^{3} x^{3} + 18 i \, a^{2} x^{2} + 5 \, a x - 36 \, {\left(i \, a^{4} x^{4} - a^{3} x^{3}\right)} \log\left(x\right) - 36 \, {\left(-i \, a^{4} x^{4} + a^{3} x^{3}\right)} \log\left(\frac{a x + i}{a}\right) - i}{3 \, a x^{4} + 3 i \, x^{3}}"," ",0,"(36*a^3*x^3 + 18*I*a^2*x^2 + 5*a*x - 36*(I*a^4*x^4 - a^3*x^3)*log(x) - 36*(-I*a^4*x^4 + a^3*x^3)*log((a*x + I)/a) - I)/(3*a*x^4 + 3*I*x^3)","A",0
35,1,59,0,0.457273," ","integrate(x^3/(1+I*a*x)*(a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(-6 i \, a^{3} x^{3} + 8 \, a^{2} x^{2} + 9 i \, a x - 16\right)} \sqrt{a^{2} x^{2} + 1} + 9 i \, \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right)}{24 \, a^{4}}"," ",0,"1/24*((-6*I*a^3*x^3 + 8*a^2*x^2 + 9*I*a*x - 16)*sqrt(a^2*x^2 + 1) + 9*I*log(-a*x + sqrt(a^2*x^2 + 1)))/a^4","A",0
36,1,51,0,0.571033," ","integrate(x^2/(1+I*a*x)*(a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} x^{2} + 1} {\left(-2 i \, a^{2} x^{2} + 3 \, a x + 4 i\right)} + 3 \, \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right)}{6 \, a^{3}}"," ",0,"1/6*(sqrt(a^2*x^2 + 1)*(-2*I*a^2*x^2 + 3*a*x + 4*I) + 3*log(-a*x + sqrt(a^2*x^2 + 1)))/a^3","A",0
37,1,43,0,0.543940," ","integrate(x/(1+I*a*x)*(a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} x^{2} + 1} {\left(-i \, a x + 2\right)} - i \, \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right)}{2 \, a^{2}}"," ",0,"1/2*(sqrt(a^2*x^2 + 1)*(-I*a*x + 2) - I*log(-a*x + sqrt(a^2*x^2 + 1)))/a^2","A",0
38,1,37,0,0.442010," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{-i \, \sqrt{a^{2} x^{2} + 1} - \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right)}{a}"," ",0,"(-I*sqrt(a^2*x^2 + 1) - log(-a*x + sqrt(a^2*x^2 + 1)))/a","A",0
39,1,58,0,0.464200," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x,x, algorithm=""fricas"")","-\log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) + i \, \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right)"," ",0,"-log(-a*x + sqrt(a^2*x^2 + 1) + 1) + I*log(-a*x + sqrt(a^2*x^2 + 1)) + log(-a*x + sqrt(a^2*x^2 + 1) - 1)","B",0
40,1,66,0,0.486986," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{i \, a x \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) - i \, a x \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) - a x - \sqrt{a^{2} x^{2} + 1}}{x}"," ",0,"(I*a*x*log(-a*x + sqrt(a^2*x^2 + 1) + 1) - I*a*x*log(-a*x + sqrt(a^2*x^2 + 1) - 1) - a*x - sqrt(a^2*x^2 + 1))/x","B",0
41,1,83,0,0.438432," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{a^{2} x^{2} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) - a^{2} x^{2} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + 2 i \, a^{2} x^{2} + \sqrt{a^{2} x^{2} + 1} {\left(2 i \, a x - 1\right)}}{2 \, x^{2}}"," ",0,"1/2*(a^2*x^2*log(-a*x + sqrt(a^2*x^2 + 1) + 1) - a^2*x^2*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + 2*I*a^2*x^2 + sqrt(a^2*x^2 + 1)*(2*I*a*x - 1))/x^2","A",0
42,1,92,0,0.445897," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^4,x, algorithm=""fricas"")","\frac{-3 i \, a^{3} x^{3} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) + 3 i \, a^{3} x^{3} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + 4 \, a^{3} x^{3} + {\left(4 \, a^{2} x^{2} + 3 i \, a x - 2\right)} \sqrt{a^{2} x^{2} + 1}}{6 \, x^{3}}"," ",0,"1/6*(-3*I*a^3*x^3*log(-a*x + sqrt(a^2*x^2 + 1) + 1) + 3*I*a^3*x^3*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + 4*a^3*x^3 + (4*a^2*x^2 + 3*I*a*x - 2)*sqrt(a^2*x^2 + 1))/x^3","A",0
43,1,101,0,0.460427," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{9 \, a^{4} x^{4} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) - 9 \, a^{4} x^{4} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + 16 i \, a^{4} x^{4} - {\left(-16 i \, a^{3} x^{3} + 9 \, a^{2} x^{2} + 8 i \, a x - 6\right)} \sqrt{a^{2} x^{2} + 1}}{24 \, x^{4}}"," ",0,"-1/24*(9*a^4*x^4*log(-a*x + sqrt(a^2*x^2 + 1) + 1) - 9*a^4*x^4*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + 16*I*a^4*x^4 - (-16*I*a^3*x^3 + 9*a^2*x^2 + 8*I*a*x - 6)*sqrt(a^2*x^2 + 1))/x^4","A",0
44,1,46,0,0.405674," ","integrate(x^3/(1+I*a*x)^2*(a^2*x^2+1),x, algorithm=""fricas"")","-\frac{3 \, a^{4} x^{4} + 8 i \, a^{3} x^{3} - 12 \, a^{2} x^{2} - 24 i \, a x + 24 \, \log\left(\frac{a x - i}{a}\right)}{12 \, a^{4}}"," ",0,"-1/12*(3*a^4*x^4 + 8*I*a^3*x^3 - 12*a^2*x^2 - 24*I*a*x + 24*log((a*x - I)/a))/a^4","A",0
45,1,37,0,0.469056," ","integrate(x^2/(1+I*a*x)^2*(a^2*x^2+1),x, algorithm=""fricas"")","-\frac{a^{3} x^{3} + 3 i \, a^{2} x^{2} - 6 \, a x - 6 i \, \log\left(\frac{a x - i}{a}\right)}{3 \, a^{3}}"," ",0,"-1/3*(a^3*x^3 + 3*I*a^2*x^2 - 6*a*x - 6*I*log((a*x - I)/a))/a^3","A",0
46,1,29,0,0.401242," ","integrate(x/(1+I*a*x)^2*(a^2*x^2+1),x, algorithm=""fricas"")","-\frac{a^{2} x^{2} + 4 i \, a x - 4 \, \log\left(\frac{a x - i}{a}\right)}{2 \, a^{2}}"," ",0,"-1/2*(a^2*x^2 + 4*I*a*x - 4*log((a*x - I)/a))/a^2","A",0
47,1,21,0,0.438673," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1),x, algorithm=""fricas"")","-\frac{a x + 2 i \, \log\left(\frac{a x - i}{a}\right)}{a}"," ",0,"-(a*x + 2*I*log((a*x - I)/a))/a","A",0
48,1,15,0,0.407812," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/x,x, algorithm=""fricas"")","\log\left(x\right) - 2 \, \log\left(\frac{a x - i}{a}\right)"," ",0,"log(x) - 2*log((a*x - I)/a)","A",0
49,1,26,0,0.421623," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/x^2,x, algorithm=""fricas"")","\frac{-2 i \, a x \log\left(x\right) + 2 i \, a x \log\left(\frac{a x - i}{a}\right) - 1}{x}"," ",0,"(-2*I*a*x*log(x) + 2*I*a*x*log((a*x - I)/a) - 1)/x","A",0
50,1,39,0,0.399525," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/x^3,x, algorithm=""fricas"")","-\frac{4 \, a^{2} x^{2} \log\left(x\right) - 4 \, a^{2} x^{2} \log\left(\frac{a x - i}{a}\right) - 4 i \, a x + 1}{2 \, x^{2}}"," ",0,"-1/2*(4*a^2*x^2*log(x) - 4*a^2*x^2*log((a*x - I)/a) - 4*I*a*x + 1)/x^2","A",0
51,1,47,0,0.422402," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/x^4,x, algorithm=""fricas"")","\frac{6 i \, a^{3} x^{3} \log\left(x\right) - 6 i \, a^{3} x^{3} \log\left(\frac{a x - i}{a}\right) + 6 \, a^{2} x^{2} + 3 i \, a x - 1}{3 \, x^{3}}"," ",0,"1/3*(6*I*a^3*x^3*log(x) - 6*I*a^3*x^3*log((a*x - I)/a) + 6*a^2*x^2 + 3*I*a*x - 1)/x^3","A",0
52,1,88,0,0.408982," ","integrate(x^3/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{-32 i \, a x - 51 \, {\left(i \, a x + 1\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + {\left(2 i \, a^{4} x^{4} - 6 \, a^{3} x^{3} - 11 i \, a^{2} x^{2} + 29 \, a x - 80 i\right)} \sqrt{a^{2} x^{2} + 1} - 32}{8 \, a^{5} x - 8 i \, a^{4}}"," ",0,"(-32*I*a*x - 51*(I*a*x + 1)*log(-a*x + sqrt(a^2*x^2 + 1)) + (2*I*a^4*x^4 - 6*a^3*x^3 - 11*I*a^2*x^2 + 29*a*x - 80*I)*sqrt(a^2*x^2 + 1) - 32)/(8*a^5*x - 8*I*a^4)","A",0
53,1,81,0,0.411489," ","integrate(x^2/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","-\frac{24 \, a x + {\left(33 \, a x - 33 i\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) - {\left(2 i \, a^{3} x^{3} - 7 \, a^{2} x^{2} - 19 i \, a x - 52\right)} \sqrt{a^{2} x^{2} + 1} - 24 i}{6 \, a^{4} x - 6 i \, a^{3}}"," ",0,"-(24*a*x + (33*a*x - 33*I)*log(-a*x + sqrt(a^2*x^2 + 1)) - (2*I*a^3*x^3 - 7*a^2*x^2 - 19*I*a*x - 52)*sqrt(a^2*x^2 + 1) - 24*I)/(6*a^4*x - 6*I*a^3)","A",0
54,1,72,0,0.420309," ","integrate(x/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{8 i \, a x - 9 \, {\left(-i \, a x - 1\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + \sqrt{a^{2} x^{2} + 1} {\left(i \, a^{2} x^{2} - 5 \, a x + 14 i\right)} + 8}{2 \, a^{3} x - 2 i \, a^{2}}"," ",0,"(8*I*a*x - 9*(-I*a*x - 1)*log(-a*x + sqrt(a^2*x^2 + 1)) + sqrt(a^2*x^2 + 1)*(I*a^2*x^2 - 5*a*x + 14*I) + 8)/(2*a^3*x - 2*I*a^2)","A",0
55,1,60,0,0.486938," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{4 \, a x + {\left(3 \, a x - 3 i\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + \sqrt{a^{2} x^{2} + 1} {\left(i \, a x + 5\right)} - 4 i}{a^{2} x - i \, a}"," ",0,"(4*a*x + (3*a*x - 3*I)*log(-a*x + sqrt(a^2*x^2 + 1)) + sqrt(a^2*x^2 + 1)*(I*a*x + 5) - 4*I)/(a^2*x - I*a)","A",0
56,1,100,0,0.437145," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x,x, algorithm=""fricas"")","\frac{-4 i \, a x - {\left(a x - i\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) + {\left(-i \, a x - 1\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + {\left(a x - i\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) - 4 i \, \sqrt{a^{2} x^{2} + 1} - 4}{a x - i}"," ",0,"(-4*I*a*x - (a*x - I)*log(-a*x + sqrt(a^2*x^2 + 1) + 1) + (-I*a*x - 1)*log(-a*x + sqrt(a^2*x^2 + 1)) + (a*x - I)*log(-a*x + sqrt(a^2*x^2 + 1) - 1) - 4*I*sqrt(a^2*x^2 + 1) - 4)/(a*x - I)","B",0
57,1,109,0,0.408839," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^2,x, algorithm=""fricas"")","-\frac{5 \, a^{2} x^{2} - 5 i \, a x + 3 \, {\left(-i \, a^{2} x^{2} - a x\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) + 3 \, {\left(i \, a^{2} x^{2} + a x\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + \sqrt{a^{2} x^{2} + 1} {\left(5 \, a x - i\right)}}{a x^{2} - i \, x}"," ",0,"-(5*a^2*x^2 - 5*I*a*x + 3*(-I*a^2*x^2 - a*x)*log(-a*x + sqrt(a^2*x^2 + 1) + 1) + 3*(I*a^2*x^2 + a*x)*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + sqrt(a^2*x^2 + 1)*(5*a*x - I))/(a*x^2 - I*x)","B",0
58,1,131,0,0.438630," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{14 i \, a^{3} x^{3} + 14 \, a^{2} x^{2} + {\left(9 \, a^{3} x^{3} - 9 i \, a^{2} x^{2}\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) - {\left(9 \, a^{3} x^{3} - 9 i \, a^{2} x^{2}\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + \sqrt{a^{2} x^{2} + 1} {\left(14 i \, a^{2} x^{2} + 5 \, a x + i\right)}}{2 \, a x^{3} - 2 i \, x^{2}}"," ",0,"(14*I*a^3*x^3 + 14*a^2*x^2 + (9*a^3*x^3 - 9*I*a^2*x^2)*log(-a*x + sqrt(a^2*x^2 + 1) + 1) - (9*a^3*x^3 - 9*I*a^2*x^2)*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + sqrt(a^2*x^2 + 1)*(14*I*a^2*x^2 + 5*a*x + I))/(2*a*x^3 - 2*I*x^2)","A",0
59,1,139,0,0.555655," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^4,x, algorithm=""fricas"")","\frac{52 \, a^{4} x^{4} - 52 i \, a^{3} x^{3} - 33 \, {\left(i \, a^{4} x^{4} + a^{3} x^{3}\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) - 33 \, {\left(-i \, a^{4} x^{4} - a^{3} x^{3}\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + {\left(52 \, a^{3} x^{3} - 19 i \, a^{2} x^{2} + 7 \, a x + 2 i\right)} \sqrt{a^{2} x^{2} + 1}}{6 \, a x^{4} - 6 i \, x^{3}}"," ",0,"(52*a^4*x^4 - 52*I*a^3*x^3 - 33*(I*a^4*x^4 + a^3*x^3)*log(-a*x + sqrt(a^2*x^2 + 1) + 1) - 33*(-I*a^4*x^4 - a^3*x^3)*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + (52*a^3*x^3 - 19*I*a^2*x^2 + 7*a*x + 2*I)*sqrt(a^2*x^2 + 1))/(6*a*x^4 - 6*I*x^3)","A",0
60,1,146,0,0.479145," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^5,x, algorithm=""fricas"")","\frac{-80 i \, a^{5} x^{5} - 80 \, a^{4} x^{4} - 51 \, {\left(a^{5} x^{5} - i \, a^{4} x^{4}\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} + 1\right) + 51 \, {\left(a^{5} x^{5} - i \, a^{4} x^{4}\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1} - 1\right) + {\left(-80 i \, a^{4} x^{4} - 29 \, a^{3} x^{3} - 11 i \, a^{2} x^{2} + 6 \, a x + 2 i\right)} \sqrt{a^{2} x^{2} + 1}}{8 \, a x^{5} - 8 i \, x^{4}}"," ",0,"(-80*I*a^5*x^5 - 80*a^4*x^4 - 51*(a^5*x^5 - I*a^4*x^4)*log(-a*x + sqrt(a^2*x^2 + 1) + 1) + 51*(a^5*x^5 - I*a^4*x^4)*log(-a*x + sqrt(a^2*x^2 + 1) - 1) + (-80*I*a^4*x^4 - 29*a^3*x^3 - 11*I*a^2*x^2 + 6*a*x + 2*I)*sqrt(a^2*x^2 + 1))/(8*a*x^5 - 8*I*x^4)","A",0
61,1,244,0,0.611291," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x^2,x, algorithm=""fricas"")","-\frac{12 \, a^{3} \sqrt{\frac{9 i}{64 \, a^{6}}} \log\left(\frac{8}{3} i \, a^{3} \sqrt{\frac{9 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 12 \, a^{3} \sqrt{\frac{9 i}{64 \, a^{6}}} \log\left(-\frac{8}{3} i \, a^{3} \sqrt{\frac{9 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 12 \, a^{3} \sqrt{-\frac{9 i}{64 \, a^{6}}} \log\left(\frac{8}{3} i \, a^{3} \sqrt{-\frac{9 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 12 \, a^{3} \sqrt{-\frac{9 i}{64 \, a^{6}}} \log\left(-\frac{8}{3} i \, a^{3} \sqrt{-\frac{9 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(8 \, a^{3} x^{3} - 2 i \, a^{2} x^{2} - a x - 11 i\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{24 \, a^{3}}"," ",0,"-1/24*(12*a^3*sqrt(9/64*I/a^6)*log(8/3*I*a^3*sqrt(9/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 12*a^3*sqrt(9/64*I/a^6)*log(-8/3*I*a^3*sqrt(9/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 12*a^3*sqrt(-9/64*I/a^6)*log(8/3*I*a^3*sqrt(-9/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 12*a^3*sqrt(-9/64*I/a^6)*log(-8/3*I*a^3*sqrt(-9/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (8*a^3*x^3 - 2*I*a^2*x^2 - a*x - 11*I)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^3","A",0
62,1,236,0,0.524001," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x,x, algorithm=""fricas"")","-\frac{2 \, a^{2} \sqrt{\frac{i}{16 \, a^{4}}} \log\left(4 \, a^{2} \sqrt{\frac{i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 2 \, a^{2} \sqrt{\frac{i}{16 \, a^{4}}} \log\left(-4 \, a^{2} \sqrt{\frac{i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 2 \, a^{2} \sqrt{-\frac{i}{16 \, a^{4}}} \log\left(4 \, a^{2} \sqrt{-\frac{i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 2 \, a^{2} \sqrt{-\frac{i}{16 \, a^{4}}} \log\left(-4 \, a^{2} \sqrt{-\frac{i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(2 \, a^{2} x^{2} - i \, a x + 3\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{4 \, a^{2}}"," ",0,"-1/4*(2*a^2*sqrt(1/16*I/a^4)*log(4*a^2*sqrt(1/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 2*a^2*sqrt(1/16*I/a^4)*log(-4*a^2*sqrt(1/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 2*a^2*sqrt(-1/16*I/a^4)*log(4*a^2*sqrt(-1/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 2*a^2*sqrt(-1/16*I/a^4)*log(-4*a^2*sqrt(-1/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (2*a^2*x^2 - I*a*x + 3)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^2","A",0
63,1,209,0,0.461317," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{a \sqrt{\frac{i}{a^{2}}} \log\left(i \, a \sqrt{\frac{i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - a \sqrt{\frac{i}{a^{2}}} \log\left(-i \, a \sqrt{\frac{i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + a \sqrt{-\frac{i}{a^{2}}} \log\left(i \, a \sqrt{-\frac{i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - a \sqrt{-\frac{i}{a^{2}}} \log\left(-i \, a \sqrt{-\frac{i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(2 \, a x + 2 i\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, a}"," ",0,"1/2*(a*sqrt(I/a^2)*log(I*a*sqrt(I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - a*sqrt(I/a^2)*log(-I*a*sqrt(I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + a*sqrt(-I/a^2)*log(I*a*sqrt(-I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - a*sqrt(-I/a^2)*log(-I*a*sqrt(-I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (2*a*x + 2*I)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a","A",0
64,1,243,0,0.431533," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{4 i} \log\left(\frac{1}{2} \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \frac{1}{2} \, \sqrt{4 i} \log\left(-\frac{1}{2} \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + \frac{1}{2} \, \sqrt{-4 i} \log\left(\frac{1}{2} \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \frac{1}{2} \, \sqrt{-4 i} \log\left(-\frac{1}{2} \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - i \, \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + i \, \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right)"," ",0,"1/2*sqrt(4*I)*log(1/2*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 1/2*sqrt(4*I)*log(-1/2*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 1/2*sqrt(-4*I)*log(1/2*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 1/2*sqrt(-4*I)*log(-1/2*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - I*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + I*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1)","A",0
65,1,151,0,0.448263," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^2,x, algorithm=""fricas"")","\frac{-i \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + i \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - 2 \, {\left(-i \, a x + 1\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, x}"," ",0,"1/2*(-I*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + I*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - 2*(-I*a*x + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x","B",0
66,1,175,0,0.505603," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^3,x, algorithm=""fricas"")","\frac{a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + i \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - i \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - {\left(6 \, a^{2} x^{2} + 2 i \, a x + 4\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{8 \, x^{2}}"," ",0,"1/8*(a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + I*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - I*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - (6*a^2*x^2 + 2*I*a*x + 4)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^2","A",0
67,1,183,0,0.434893," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^4,x, algorithm=""fricas"")","\frac{9 i \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - 9 \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + 9 \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 9 i \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) + {\left(-22 i \, a^{3} x^{3} + 2 \, a^{2} x^{2} - 4 i \, a x - 16\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{48 \, x^{3}}"," ",0,"1/48*(9*I*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - 9*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + 9*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 9*I*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) + (-22*I*a^3*x^3 + 2*a^2*x^2 - 4*I*a*x - 16)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^3","A",0
68,1,192,0,0.434008," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{33 \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + 33 i \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - 33 i \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 33 \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - {\left(166 \, a^{4} x^{4} + 50 i \, a^{3} x^{3} + 4 \, a^{2} x^{2} - 16 i \, a x - 96\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{384 \, x^{4}}"," ",0,"-1/384*(33*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + 33*I*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - 33*I*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 33*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - (166*a^4*x^4 + 50*I*a^3*x^3 + 4*a^2*x^2 - 16*I*a*x - 96)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^4","A",0
69,1,199,0,0.450952," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^6,x, algorithm=""fricas"")","\frac{-465 i \, a^{5} x^{5} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + 465 \, a^{5} x^{5} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - 465 \, a^{5} x^{5} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + 465 i \, a^{5} x^{5} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) + {\left(1222 i \, a^{5} x^{5} - 146 \, a^{4} x^{4} + 196 i \, a^{3} x^{3} + 16 \, a^{2} x^{2} - 96 i \, a x - 768\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{3840 \, x^{5}}"," ",0,"1/3840*(-465*I*a^5*x^5*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + 465*a^5*x^5*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - 465*a^5*x^5*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + 465*I*a^5*x^5*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) + (1222*I*a^5*x^5 - 146*a^4*x^4 + 196*I*a^3*x^3 + 16*a^2*x^2 - 96*I*a*x - 768)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^5","A",0
70,1,254,0,0.449959," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^3,x, algorithm=""fricas"")","\frac{32 \, a^{4} \sqrt{\frac{15129 i}{4096 \, a^{8}}} \log\left(\frac{64}{123} i \, a^{4} \sqrt{\frac{15129 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 32 \, a^{4} \sqrt{\frac{15129 i}{4096 \, a^{8}}} \log\left(-\frac{64}{123} i \, a^{4} \sqrt{\frac{15129 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 32 \, a^{4} \sqrt{-\frac{15129 i}{4096 \, a^{8}}} \log\left(\frac{64}{123} i \, a^{4} \sqrt{-\frac{15129 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 32 \, a^{4} \sqrt{-\frac{15129 i}{4096 \, a^{8}}} \log\left(-\frac{64}{123} i \, a^{4} \sqrt{-\frac{15129 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(16 i \, a^{3} x^{3} + 24 \, a^{2} x^{2} - 30 i \, a x - 63\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{64 \, a^{4}}"," ",0,"1/64*(32*a^4*sqrt(15129/4096*I/a^8)*log(64/123*I*a^4*sqrt(15129/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 32*a^4*sqrt(15129/4096*I/a^8)*log(-64/123*I*a^4*sqrt(15129/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 32*a^4*sqrt(-15129/4096*I/a^8)*log(64/123*I*a^4*sqrt(-15129/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 32*a^4*sqrt(-15129/4096*I/a^8)*log(-64/123*I*a^4*sqrt(-15129/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (16*I*a^3*x^3 + 24*a^2*x^2 - 30*I*a*x - 63)*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^4","A",0
71,1,247,0,0.483576," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^2,x, algorithm=""fricas"")","-\frac{12 \, a^{3} \sqrt{\frac{289 i}{64 \, a^{6}}} \log\left(\frac{8}{17} \, a^{3} \sqrt{\frac{289 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 12 \, a^{3} \sqrt{\frac{289 i}{64 \, a^{6}}} \log\left(-\frac{8}{17} \, a^{3} \sqrt{\frac{289 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 12 \, a^{3} \sqrt{-\frac{289 i}{64 \, a^{6}}} \log\left(\frac{8}{17} \, a^{3} \sqrt{-\frac{289 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 12 \, a^{3} \sqrt{-\frac{289 i}{64 \, a^{6}}} \log\left(-\frac{8}{17} \, a^{3} \sqrt{-\frac{289 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \sqrt{a^{2} x^{2} + 1} {\left(8 i \, a^{2} x^{2} + 14 \, a x - 23 i\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{24 \, a^{3}}"," ",0,"-1/24*(12*a^3*sqrt(289/64*I/a^6)*log(8/17*a^3*sqrt(289/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 12*a^3*sqrt(289/64*I/a^6)*log(-8/17*a^3*sqrt(289/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 12*a^3*sqrt(-289/64*I/a^6)*log(8/17*a^3*sqrt(-289/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 12*a^3*sqrt(-289/64*I/a^6)*log(-8/17*a^3*sqrt(-289/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - sqrt(a^2*x^2 + 1)*(8*I*a^2*x^2 + 14*a*x - 23*I)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^3","A",0
72,1,239,0,0.445683," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x,x, algorithm=""fricas"")","-\frac{2 \, a^{2} \sqrt{\frac{81 i}{16 \, a^{4}}} \log\left(\frac{4}{9} i \, a^{2} \sqrt{\frac{81 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 2 \, a^{2} \sqrt{\frac{81 i}{16 \, a^{4}}} \log\left(-\frac{4}{9} i \, a^{2} \sqrt{\frac{81 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 2 \, a^{2} \sqrt{-\frac{81 i}{16 \, a^{4}}} \log\left(\frac{4}{9} i \, a^{2} \sqrt{-\frac{81 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 2 \, a^{2} \sqrt{-\frac{81 i}{16 \, a^{4}}} \log\left(-\frac{4}{9} i \, a^{2} \sqrt{-\frac{81 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \sqrt{a^{2} x^{2} + 1} {\left(2 i \, a x + 5\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{4 \, a^{2}}"," ",0,"-1/4*(2*a^2*sqrt(81/16*I/a^4)*log(4/9*I*a^2*sqrt(81/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 2*a^2*sqrt(81/16*I/a^4)*log(-4/9*I*a^2*sqrt(81/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 2*a^2*sqrt(-81/16*I/a^4)*log(4/9*I*a^2*sqrt(-81/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 2*a^2*sqrt(-81/16*I/a^4)*log(-4/9*I*a^2*sqrt(-81/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - sqrt(a^2*x^2 + 1)*(2*I*a*x + 5)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^2","A",0
73,1,215,0,0.511218," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{a \sqrt{\frac{9 i}{a^{2}}} \log\left(\frac{1}{3} \, a \sqrt{\frac{9 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - a \sqrt{\frac{9 i}{a^{2}}} \log\left(-\frac{1}{3} \, a \sqrt{\frac{9 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - a \sqrt{-\frac{9 i}{a^{2}}} \log\left(\frac{1}{3} \, a \sqrt{-\frac{9 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + a \sqrt{-\frac{9 i}{a^{2}}} \log\left(-\frac{1}{3} \, a \sqrt{-\frac{9 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 2 i \, \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, a}"," ",0,"1/2*(a*sqrt(9*I/a^2)*log(1/3*a*sqrt(9*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - a*sqrt(9*I/a^2)*log(-1/3*a*sqrt(9*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - a*sqrt(-9*I/a^2)*log(1/3*a*sqrt(-9*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + a*sqrt(-9*I/a^2)*log(-1/3*a*sqrt(-9*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 2*I*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a","A",0
74,1,243,0,0.533665," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x,x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{4 i} \log\left(\frac{1}{2} i \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \frac{1}{2} \, \sqrt{4 i} \log\left(-\frac{1}{2} i \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \frac{1}{2} \, \sqrt{-4 i} \log\left(\frac{1}{2} i \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + \frac{1}{2} \, \sqrt{-4 i} \log\left(-\frac{1}{2} i \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + i \, \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - i \, \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right)"," ",0,"1/2*sqrt(4*I)*log(1/2*I*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 1/2*sqrt(4*I)*log(-1/2*I*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 1/2*sqrt(-4*I)*log(1/2*I*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 1/2*sqrt(-4*I)*log(-1/2*I*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + I*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - I*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1)","A",0
75,1,157,0,0.742914," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^2,x, algorithm=""fricas"")","\frac{-3 i \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - 3 \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + 3 \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + 3 i \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - 2 \, \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, x}"," ",0,"1/2*(-3*I*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - 3*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + 3*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + 3*I*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - 2*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x","B",0
76,1,179,0,1.187827," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^3,x, algorithm=""fricas"")","\frac{9 \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - 9 i \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + 9 i \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 9 \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - 2 \, \sqrt{a^{2} x^{2} + 1} {\left(5 i \, a x + 2\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{8 \, x^{2}}"," ",0,"1/8*(9*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - 9*I*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + 9*I*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 9*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - 2*sqrt(a^2*x^2 + 1)*(5*I*a*x + 2)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^2","A",0
77,1,186,0,0.490996," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^4,x, algorithm=""fricas"")","\frac{51 i \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + 51 \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - 51 \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 51 i \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) + {\left(46 \, a^{2} x^{2} - 28 i \, a x - 16\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{48 \, x^{3}}"," ",0,"1/48*(51*I*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + 51*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - 51*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 51*I*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) + (46*a^2*x^2 - 28*I*a*x - 16)*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^3","A",0
78,1,195,0,0.440418," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^5,x, algorithm=""fricas"")","-\frac{123 \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - 123 i \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + 123 i \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 123 \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - {\left(126 i \, a^{3} x^{3} + 60 \, a^{2} x^{2} - 48 i \, a x - 32\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{128 \, x^{4}}"," ",0,"-1/128*(123*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - 123*I*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + 123*I*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 123*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - (126*I*a^3*x^3 + 60*a^2*x^2 - 48*I*a*x - 32)*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^4","A",0
79,1,251,0,0.559443," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^3,x, algorithm=""fricas"")","-\frac{96 \, a^{4} \sqrt{\frac{225625 i}{4096 \, a^{8}}} \log\left(\frac{64}{475} \, a^{4} \sqrt{\frac{225625 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 96 \, a^{4} \sqrt{\frac{225625 i}{4096 \, a^{8}}} \log\left(-\frac{64}{475} \, a^{4} \sqrt{\frac{225625 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 96 \, a^{4} \sqrt{-\frac{225625 i}{4096 \, a^{8}}} \log\left(\frac{64}{475} \, a^{4} \sqrt{-\frac{225625 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 96 \, a^{4} \sqrt{-\frac{225625 i}{4096 \, a^{8}}} \log\left(-\frac{64}{475} \, a^{4} \sqrt{-\frac{225625 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(48 \, a^{4} x^{4} - 136 i \, a^{3} x^{3} - 226 \, a^{2} x^{2} + 521 i \, a x - 2467\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{192 \, a^{4}}"," ",0,"-1/192*(96*a^4*sqrt(225625/4096*I/a^8)*log(64/475*a^4*sqrt(225625/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 96*a^4*sqrt(225625/4096*I/a^8)*log(-64/475*a^4*sqrt(225625/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 96*a^4*sqrt(-225625/4096*I/a^8)*log(64/475*a^4*sqrt(-225625/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 96*a^4*sqrt(-225625/4096*I/a^8)*log(-64/475*a^4*sqrt(-225625/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (48*a^4*x^4 - 136*I*a^3*x^3 - 226*a^2*x^2 + 521*I*a*x - 2467)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^4","A",0
80,1,244,0,0.523536," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^2,x, algorithm=""fricas"")","\frac{12 \, a^{3} \sqrt{\frac{3025 i}{64 \, a^{6}}} \log\left(\frac{8}{55} i \, a^{3} \sqrt{\frac{3025 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 12 \, a^{3} \sqrt{\frac{3025 i}{64 \, a^{6}}} \log\left(-\frac{8}{55} i \, a^{3} \sqrt{\frac{3025 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 12 \, a^{3} \sqrt{-\frac{3025 i}{64 \, a^{6}}} \log\left(\frac{8}{55} i \, a^{3} \sqrt{-\frac{3025 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 12 \, a^{3} \sqrt{-\frac{3025 i}{64 \, a^{6}}} \log\left(-\frac{8}{55} i \, a^{3} \sqrt{-\frac{3025 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(8 \, a^{3} x^{3} - 26 i \, a^{2} x^{2} - 61 \, a x - 287 i\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{24 \, a^{3}}"," ",0,"1/24*(12*a^3*sqrt(3025/64*I/a^6)*log(8/55*I*a^3*sqrt(3025/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 12*a^3*sqrt(3025/64*I/a^6)*log(-8/55*I*a^3*sqrt(3025/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 12*a^3*sqrt(-3025/64*I/a^6)*log(8/55*I*a^3*sqrt(-3025/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 12*a^3*sqrt(-3025/64*I/a^6)*log(-8/55*I*a^3*sqrt(-3025/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (8*a^3*x^3 - 26*I*a^2*x^2 - 61*a*x - 287*I)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^3","A",0
81,1,236,0,0.798623," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x,x, algorithm=""fricas"")","\frac{2 \, a^{2} \sqrt{\frac{625 i}{16 \, a^{4}}} \log\left(\frac{4}{25} \, a^{2} \sqrt{\frac{625 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 2 \, a^{2} \sqrt{\frac{625 i}{16 \, a^{4}}} \log\left(-\frac{4}{25} \, a^{2} \sqrt{\frac{625 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 2 \, a^{2} \sqrt{-\frac{625 i}{16 \, a^{4}}} \log\left(\frac{4}{25} \, a^{2} \sqrt{-\frac{625 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 2 \, a^{2} \sqrt{-\frac{625 i}{16 \, a^{4}}} \log\left(-\frac{4}{25} \, a^{2} \sqrt{-\frac{625 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(2 \, a^{2} x^{2} - 9 i \, a x + 43\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{4 \, a^{2}}"," ",0,"1/4*(2*a^2*sqrt(625/16*I/a^4)*log(4/25*a^2*sqrt(625/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 2*a^2*sqrt(625/16*I/a^4)*log(-4/25*a^2*sqrt(625/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 2*a^2*sqrt(-625/16*I/a^4)*log(4/25*a^2*sqrt(-625/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 2*a^2*sqrt(-625/16*I/a^4)*log(-4/25*a^2*sqrt(-625/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (2*a^2*x^2 - 9*I*a*x + 43)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^2","A",0
82,1,209,0,0.423568," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""fricas"")","-\frac{a \sqrt{\frac{25 i}{a^{2}}} \log\left(\frac{1}{5} i \, a \sqrt{\frac{25 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - a \sqrt{\frac{25 i}{a^{2}}} \log\left(-\frac{1}{5} i \, a \sqrt{\frac{25 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + a \sqrt{-\frac{25 i}{a^{2}}} \log\left(\frac{1}{5} i \, a \sqrt{-\frac{25 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - a \sqrt{-\frac{25 i}{a^{2}}} \log\left(-\frac{1}{5} i \, a \sqrt{-\frac{25 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(2 \, a x + 18 i\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, a}"," ",0,"-1/2*(a*sqrt(25*I/a^2)*log(1/5*I*a*sqrt(25*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - a*sqrt(25*I/a^2)*log(-1/5*I*a*sqrt(25*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + a*sqrt(-25*I/a^2)*log(1/5*I*a*sqrt(-25*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - a*sqrt(-25*I/a^2)*log(-1/5*I*a*sqrt(-25*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (2*a*x + 18*I)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a","A",0
83,1,267,0,0.729465," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x,x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{4 i} \log\left(\frac{1}{2} \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + \frac{1}{2} \, \sqrt{4 i} \log\left(-\frac{1}{2} \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \frac{1}{2} \, \sqrt{-4 i} \log\left(\frac{1}{2} \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + \frac{1}{2} \, \sqrt{-4 i} \log\left(-\frac{1}{2} \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 8 \, \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - i \, \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + i \, \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right)"," ",0,"-1/2*sqrt(4*I)*log(1/2*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 1/2*sqrt(4*I)*log(-1/2*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 1/2*sqrt(-4*I)*log(1/2*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 1/2*sqrt(-4*I)*log(-1/2*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 8*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - I*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + I*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1)","A",0
84,1,152,0,0.417447," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^2,x, algorithm=""fricas"")","\frac{-5 i \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + 5 \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - 5 \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + 5 i \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - 2 \, {\left(-9 i \, a x + 1\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, x}"," ",0,"1/2*(-5*I*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + 5*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - 5*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + 5*I*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - 2*(-9*I*a*x + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x","A",0
85,1,176,0,1.007020," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^3,x, algorithm=""fricas"")","\frac{25 \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + 25 i \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - 25 i \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 25 \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - {\left(86 \, a^{2} x^{2} + 18 i \, a x + 4\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{8 \, x^{2}}"," ",0,"1/8*(25*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + 25*I*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - 25*I*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 25*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - (86*a^2*x^2 + 18*I*a*x + 4)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^2","A",0
86,1,183,0,0.727533," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^4,x, algorithm=""fricas"")","\frac{165 i \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - 165 \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + 165 \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 165 i \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) + {\left(-574 i \, a^{3} x^{3} + 122 \, a^{2} x^{2} - 52 i \, a x - 16\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{48 \, x^{3}}"," ",0,"1/48*(165*I*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - 165*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + 165*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 165*I*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) + (-574*I*a^3*x^3 + 122*a^2*x^2 - 52*I*a*x - 16)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^3","A",0
87,1,192,0,0.518667," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^5,x, algorithm=""fricas"")","-\frac{1425 \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + 1425 i \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - 1425 i \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 1425 \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - {\left(4934 \, a^{4} x^{4} + 1042 i \, a^{3} x^{3} + 452 \, a^{2} x^{2} - 272 i \, a x - 96\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{384 \, x^{4}}"," ",0,"-1/384*(1425*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + 1425*I*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - 1425*I*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 1425*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - (4934*a^4*x^4 + 1042*I*a^3*x^3 + 452*a^2*x^2 - 272*I*a*x - 96)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^4","A",0
88,1,255,0,0.541011," ","integrate(x^3/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{96 \, a^{4} \sqrt{\frac{121 i}{4096 \, a^{8}}} \log\left(\frac{64}{11} i \, a^{4} \sqrt{\frac{121 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 96 \, a^{4} \sqrt{\frac{121 i}{4096 \, a^{8}}} \log\left(-\frac{64}{11} i \, a^{4} \sqrt{\frac{121 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 96 \, a^{4} \sqrt{-\frac{121 i}{4096 \, a^{8}}} \log\left(\frac{64}{11} i \, a^{4} \sqrt{-\frac{121 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 96 \, a^{4} \sqrt{-\frac{121 i}{4096 \, a^{8}}} \log\left(-\frac{64}{11} i \, a^{4} \sqrt{-\frac{121 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(-48 i \, a^{3} x^{3} + 56 \, a^{2} x^{2} + 58 i \, a x - 83\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{192 \, a^{4}}"," ",0,"-1/192*(96*a^4*sqrt(121/4096*I/a^8)*log(64/11*I*a^4*sqrt(121/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 96*a^4*sqrt(121/4096*I/a^8)*log(-64/11*I*a^4*sqrt(121/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 96*a^4*sqrt(-121/4096*I/a^8)*log(64/11*I*a^4*sqrt(-121/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 96*a^4*sqrt(-121/4096*I/a^8)*log(-64/11*I*a^4*sqrt(-121/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (-48*I*a^3*x^3 + 56*a^2*x^2 + 58*I*a*x - 83)*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^4","A",0
89,1,247,0,0.451653," ","integrate(x^2/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{12 \, a^{3} \sqrt{\frac{9 i}{64 \, a^{6}}} \log\left(\frac{8}{3} \, a^{3} \sqrt{\frac{9 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 12 \, a^{3} \sqrt{\frac{9 i}{64 \, a^{6}}} \log\left(-\frac{8}{3} \, a^{3} \sqrt{\frac{9 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 12 \, a^{3} \sqrt{-\frac{9 i}{64 \, a^{6}}} \log\left(\frac{8}{3} \, a^{3} \sqrt{-\frac{9 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 12 \, a^{3} \sqrt{-\frac{9 i}{64 \, a^{6}}} \log\left(-\frac{8}{3} \, a^{3} \sqrt{-\frac{9 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \sqrt{a^{2} x^{2} + 1} {\left(-8 i \, a^{2} x^{2} + 10 \, a x + 11 i\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{24 \, a^{3}}"," ",0,"-1/24*(12*a^3*sqrt(9/64*I/a^6)*log(8/3*a^3*sqrt(9/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 12*a^3*sqrt(9/64*I/a^6)*log(-8/3*a^3*sqrt(9/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 12*a^3*sqrt(-9/64*I/a^6)*log(8/3*a^3*sqrt(-9/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 12*a^3*sqrt(-9/64*I/a^6)*log(-8/3*a^3*sqrt(-9/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - sqrt(a^2*x^2 + 1)*(-8*I*a^2*x^2 + 10*a*x + 11*I)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^3","A",0
90,1,238,0,0.497138," ","integrate(x/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, a^{2} \sqrt{\frac{i}{16 \, a^{4}}} \log\left(4 i \, a^{2} \sqrt{\frac{i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 2 \, a^{2} \sqrt{\frac{i}{16 \, a^{4}}} \log\left(-4 i \, a^{2} \sqrt{\frac{i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 2 \, a^{2} \sqrt{-\frac{i}{16 \, a^{4}}} \log\left(4 i \, a^{2} \sqrt{-\frac{i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 2 \, a^{2} \sqrt{-\frac{i}{16 \, a^{4}}} \log\left(-4 i \, a^{2} \sqrt{-\frac{i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + \sqrt{a^{2} x^{2} + 1} {\left(-2 i \, a x + 3\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{4 \, a^{2}}"," ",0,"1/4*(2*a^2*sqrt(1/16*I/a^4)*log(4*I*a^2*sqrt(1/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 2*a^2*sqrt(1/16*I/a^4)*log(-4*I*a^2*sqrt(1/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 2*a^2*sqrt(-1/16*I/a^4)*log(4*I*a^2*sqrt(-1/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 2*a^2*sqrt(-1/16*I/a^4)*log(-4*I*a^2*sqrt(-1/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + sqrt(a^2*x^2 + 1)*(-2*I*a*x + 3)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^2","A",0
91,1,213,0,0.421338," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{a \sqrt{\frac{i}{a^{2}}} \log\left(a \sqrt{\frac{i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - a \sqrt{\frac{i}{a^{2}}} \log\left(-a \sqrt{\frac{i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - a \sqrt{-\frac{i}{a^{2}}} \log\left(a \sqrt{-\frac{i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + a \sqrt{-\frac{i}{a^{2}}} \log\left(-a \sqrt{-\frac{i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 2 i \, \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, a}"," ",0,"1/2*(a*sqrt(I/a^2)*log(a*sqrt(I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - a*sqrt(I/a^2)*log(-a*sqrt(I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - a*sqrt(-I/a^2)*log(a*sqrt(-I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + a*sqrt(-I/a^2)*log(-a*sqrt(-I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 2*I*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a","A",0
92,1,243,0,0.469042," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x,x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{4 i} \log\left(\frac{1}{2} i \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + \frac{1}{2} \, \sqrt{4 i} \log\left(-\frac{1}{2} i \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + \frac{1}{2} \, \sqrt{-4 i} \log\left(\frac{1}{2} i \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \frac{1}{2} \, \sqrt{-4 i} \log\left(-\frac{1}{2} i \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + i \, \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - i \, \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right)"," ",0,"-1/2*sqrt(4*I)*log(1/2*I*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 1/2*sqrt(4*I)*log(-1/2*I*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 1/2*sqrt(-4*I)*log(1/2*I*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 1/2*sqrt(-4*I)*log(-1/2*I*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + I*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - I*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1)","A",0
93,1,156,0,0.457800," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^2,x, algorithm=""fricas"")","\frac{i \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - i \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - 2 \, \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, x}"," ",0,"1/2*(I*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - I*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - 2*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x","B",0
94,1,178,0,0.442891," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^3,x, algorithm=""fricas"")","\frac{a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - i \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + i \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - 2 \, \sqrt{a^{2} x^{2} + 1} {\left(-3 i \, a x + 2\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{8 \, x^{2}}"," ",0,"1/8*(a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - I*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + I*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - 2*sqrt(a^2*x^2 + 1)*(-3*I*a*x + 2)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^2","A",0
95,1,186,0,0.488574," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^4,x, algorithm=""fricas"")","\frac{-9 i \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - 9 \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + 9 \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + 9 i \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) + {\left(22 \, a^{2} x^{2} + 20 i \, a x - 16\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{48 \, x^{3}}"," ",0,"1/48*(-9*I*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - 9*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + 9*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + 9*I*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) + (22*a^2*x^2 + 20*I*a*x - 16)*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^3","A",0
96,1,195,0,0.462916," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{33 \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - 33 i \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + 33 i \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 33 \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - {\left(-166 i \, a^{3} x^{3} + 116 \, a^{2} x^{2} + 112 i \, a x - 96\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{384 \, x^{4}}"," ",0,"-1/384*(33*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - 33*I*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + 33*I*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 33*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - (-166*I*a^3*x^3 + 116*a^2*x^2 + 112*I*a*x - 96)*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^4","A",0
97,1,251,0,0.432190," ","integrate(x^3/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""fricas"")","-\frac{32 \, a^{4} \sqrt{\frac{15129 i}{4096 \, a^{8}}} \log\left(\frac{64}{123} \, a^{4} \sqrt{\frac{15129 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 32 \, a^{4} \sqrt{\frac{15129 i}{4096 \, a^{8}}} \log\left(-\frac{64}{123} \, a^{4} \sqrt{\frac{15129 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 32 \, a^{4} \sqrt{-\frac{15129 i}{4096 \, a^{8}}} \log\left(\frac{64}{123} \, a^{4} \sqrt{-\frac{15129 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 32 \, a^{4} \sqrt{-\frac{15129 i}{4096 \, a^{8}}} \log\left(-\frac{64}{123} \, a^{4} \sqrt{-\frac{15129 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(16 \, a^{4} x^{4} + 40 i \, a^{3} x^{3} - 54 \, a^{2} x^{2} - 93 i \, a x + 63\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{64 \, a^{4}}"," ",0,"-1/64*(32*a^4*sqrt(15129/4096*I/a^8)*log(64/123*a^4*sqrt(15129/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 32*a^4*sqrt(15129/4096*I/a^8)*log(-64/123*a^4*sqrt(15129/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 32*a^4*sqrt(-15129/4096*I/a^8)*log(64/123*a^4*sqrt(-15129/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 32*a^4*sqrt(-15129/4096*I/a^8)*log(-64/123*a^4*sqrt(-15129/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (16*a^4*x^4 + 40*I*a^3*x^3 - 54*a^2*x^2 - 93*I*a*x + 63)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^4","A",0
98,1,243,0,0.448576," ","integrate(x^2/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""fricas"")","-\frac{12 \, a^{3} \sqrt{\frac{289 i}{64 \, a^{6}}} \log\left(\frac{8}{17} i \, a^{3} \sqrt{\frac{289 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 12 \, a^{3} \sqrt{\frac{289 i}{64 \, a^{6}}} \log\left(-\frac{8}{17} i \, a^{3} \sqrt{\frac{289 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 12 \, a^{3} \sqrt{-\frac{289 i}{64 \, a^{6}}} \log\left(\frac{8}{17} i \, a^{3} \sqrt{-\frac{289 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 12 \, a^{3} \sqrt{-\frac{289 i}{64 \, a^{6}}} \log\left(-\frac{8}{17} i \, a^{3} \sqrt{-\frac{289 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(8 \, a^{3} x^{3} + 22 i \, a^{2} x^{2} - 37 \, a x - 23 i\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{24 \, a^{3}}"," ",0,"-1/24*(12*a^3*sqrt(289/64*I/a^6)*log(8/17*I*a^3*sqrt(289/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 12*a^3*sqrt(289/64*I/a^6)*log(-8/17*I*a^3*sqrt(289/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 12*a^3*sqrt(-289/64*I/a^6)*log(8/17*I*a^3*sqrt(-289/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 12*a^3*sqrt(-289/64*I/a^6)*log(-8/17*I*a^3*sqrt(-289/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (8*a^3*x^3 + 22*I*a^2*x^2 - 37*a*x - 23*I)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^3","A",0
99,1,236,0,0.476738," ","integrate(x/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{2 \, a^{2} \sqrt{\frac{81 i}{16 \, a^{4}}} \log\left(\frac{4}{9} \, a^{2} \sqrt{\frac{81 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 2 \, a^{2} \sqrt{\frac{81 i}{16 \, a^{4}}} \log\left(-\frac{4}{9} \, a^{2} \sqrt{\frac{81 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 2 \, a^{2} \sqrt{-\frac{81 i}{16 \, a^{4}}} \log\left(\frac{4}{9} \, a^{2} \sqrt{-\frac{81 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - 2 \, a^{2} \sqrt{-\frac{81 i}{16 \, a^{4}}} \log\left(-\frac{4}{9} \, a^{2} \sqrt{-\frac{81 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(2 \, a^{2} x^{2} + 7 i \, a x - 5\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{4 \, a^{2}}"," ",0,"1/4*(2*a^2*sqrt(81/16*I/a^4)*log(4/9*a^2*sqrt(81/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 2*a^2*sqrt(81/16*I/a^4)*log(-4/9*a^2*sqrt(81/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 2*a^2*sqrt(-81/16*I/a^4)*log(4/9*a^2*sqrt(-81/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 2*a^2*sqrt(-81/16*I/a^4)*log(-4/9*a^2*sqrt(-81/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (2*a^2*x^2 + 7*I*a*x - 5)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a^2","A",0
100,1,210,0,0.508234," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{a \sqrt{\frac{9 i}{a^{2}}} \log\left(\frac{1}{3} i \, a \sqrt{\frac{9 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - a \sqrt{\frac{9 i}{a^{2}}} \log\left(-\frac{1}{3} i \, a \sqrt{\frac{9 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + a \sqrt{-\frac{9 i}{a^{2}}} \log\left(\frac{1}{3} i \, a \sqrt{-\frac{9 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - a \sqrt{-\frac{9 i}{a^{2}}} \log\left(-\frac{1}{3} i \, a \sqrt{-\frac{9 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(2 \, a x + 2 i\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, a}"," ",0,"1/2*(a*sqrt(9*I/a^2)*log(1/3*I*a*sqrt(9*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - a*sqrt(9*I/a^2)*log(-1/3*I*a*sqrt(9*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + a*sqrt(-9*I/a^2)*log(1/3*I*a*sqrt(-9*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - a*sqrt(-9*I/a^2)*log(-1/3*I*a*sqrt(-9*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (2*a*x + 2*I)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/a","A",0
101,1,243,0,0.632480," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x,x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{4 i} \log\left(\frac{1}{2} \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + \frac{1}{2} \, \sqrt{4 i} \log\left(-\frac{1}{2} \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \frac{1}{2} \, \sqrt{-4 i} \log\left(\frac{1}{2} \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + \frac{1}{2} \, \sqrt{-4 i} \log\left(-\frac{1}{2} \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - i \, \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + i \, \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right)"," ",0,"-1/2*sqrt(4*I)*log(1/2*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 1/2*sqrt(4*I)*log(-1/2*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - 1/2*sqrt(-4*I)*log(1/2*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 1/2*sqrt(-4*I)*log(-1/2*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - I*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + I*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1)","A",0
102,1,152,0,1.110866," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^2,x, algorithm=""fricas"")","\frac{3 i \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - 3 \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + 3 \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 3 i \, a x \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - 2 \, {\left(-i \, a x + 1\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, x}"," ",0,"1/2*(3*I*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - 3*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + 3*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 3*I*a*x*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - 2*(-I*a*x + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x","B",0
103,1,175,0,0.418273," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^3,x, algorithm=""fricas"")","\frac{9 \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + 9 i \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - 9 i \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 9 \, a^{2} x^{2} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) + {\left(10 \, a^{2} x^{2} + 14 i \, a x - 4\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{8 \, x^{2}}"," ",0,"1/8*(9*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + 9*I*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - 9*I*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 9*a^2*x^2*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) + (10*a^2*x^2 + 14*I*a*x - 4)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^2","A",0
104,1,183,0,0.420936," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^4,x, algorithm=""fricas"")","\frac{-51 i \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + 51 \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - 51 \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + 51 i \, a^{3} x^{3} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) + {\left(-46 i \, a^{3} x^{3} + 74 \, a^{2} x^{2} + 44 i \, a x - 16\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{48 \, x^{3}}"," ",0,"1/48*(-51*I*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + 51*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - 51*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + 51*I*a^3*x^3*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) + (-46*I*a^3*x^3 + 74*a^2*x^2 + 44*I*a*x - 16)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^3","A",0
105,1,191,0,0.498983," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^5,x, algorithm=""fricas"")","-\frac{123 \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + 123 i \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - 123 i \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 123 \, a^{4} x^{4} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) + {\left(126 \, a^{4} x^{4} + 186 i \, a^{3} x^{3} - 108 \, a^{2} x^{2} - 80 i \, a x + 32\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{128 \, x^{4}}"," ",0,"-1/128*(123*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + 123*I*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - 123*I*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 123*a^4*x^4*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) + (126*a^4*x^4 + 186*I*a^3*x^3 - 108*a^2*x^2 - 80*I*a*x + 32)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/x^4","A",0
106,1,306,0,0.426296," ","integrate(x^3/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""fricas"")","\frac{{\left(96 \, a^{5} x - 96 i \, a^{4}\right)} \sqrt{\frac{225625 i}{4096 \, a^{8}}} \log\left(\frac{64}{475} i \, a^{4} \sqrt{\frac{225625 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(96 \, a^{5} x - 96 i \, a^{4}\right)} \sqrt{\frac{225625 i}{4096 \, a^{8}}} \log\left(-\frac{64}{475} i \, a^{4} \sqrt{\frac{225625 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(96 \, a^{5} x - 96 i \, a^{4}\right)} \sqrt{-\frac{225625 i}{4096 \, a^{8}}} \log\left(\frac{64}{475} i \, a^{4} \sqrt{-\frac{225625 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(96 \, a^{5} x - 96 i \, a^{4}\right)} \sqrt{-\frac{225625 i}{4096 \, a^{8}}} \log\left(-\frac{64}{475} i \, a^{4} \sqrt{-\frac{225625 i}{4096 \, a^{8}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(48 i \, a^{4} x^{4} - 136 \, a^{3} x^{3} - 226 i \, a^{2} x^{2} + 521 \, a x - 2467 i\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{192 \, a^{5} x - 192 i \, a^{4}}"," ",0,"((96*a^5*x - 96*I*a^4)*sqrt(225625/4096*I/a^8)*log(64/475*I*a^4*sqrt(225625/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (96*a^5*x - 96*I*a^4)*sqrt(225625/4096*I/a^8)*log(-64/475*I*a^4*sqrt(225625/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (96*a^5*x - 96*I*a^4)*sqrt(-225625/4096*I/a^8)*log(64/475*I*a^4*sqrt(-225625/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (96*a^5*x - 96*I*a^4)*sqrt(-225625/4096*I/a^8)*log(-64/475*I*a^4*sqrt(-225625/4096*I/a^8) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (48*I*a^4*x^4 - 136*a^3*x^3 - 226*I*a^2*x^2 + 521*a*x - 2467*I)*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/(192*a^5*x - 192*I*a^4)","A",0
107,1,298,0,0.423194," ","integrate(x^2/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""fricas"")","\frac{{\left(12 \, a^{4} x - 12 i \, a^{3}\right)} \sqrt{\frac{3025 i}{64 \, a^{6}}} \log\left(\frac{8}{55} \, a^{3} \sqrt{\frac{3025 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(12 \, a^{4} x - 12 i \, a^{3}\right)} \sqrt{\frac{3025 i}{64 \, a^{6}}} \log\left(-\frac{8}{55} \, a^{3} \sqrt{\frac{3025 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(12 \, a^{4} x - 12 i \, a^{3}\right)} \sqrt{-\frac{3025 i}{64 \, a^{6}}} \log\left(\frac{8}{55} \, a^{3} \sqrt{-\frac{3025 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(12 \, a^{4} x - 12 i \, a^{3}\right)} \sqrt{-\frac{3025 i}{64 \, a^{6}}} \log\left(-\frac{8}{55} \, a^{3} \sqrt{-\frac{3025 i}{64 \, a^{6}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(8 i \, a^{3} x^{3} - 26 \, a^{2} x^{2} - 61 i \, a x - 287\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{24 \, a^{4} x - 24 i \, a^{3}}"," ",0,"((12*a^4*x - 12*I*a^3)*sqrt(3025/64*I/a^6)*log(8/55*a^3*sqrt(3025/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (12*a^4*x - 12*I*a^3)*sqrt(3025/64*I/a^6)*log(-8/55*a^3*sqrt(3025/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (12*a^4*x - 12*I*a^3)*sqrt(-3025/64*I/a^6)*log(8/55*a^3*sqrt(-3025/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (12*a^4*x - 12*I*a^3)*sqrt(-3025/64*I/a^6)*log(-8/55*a^3*sqrt(-3025/64*I/a^6) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (8*I*a^3*x^3 - 26*a^2*x^2 - 61*I*a*x - 287)*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/(24*a^4*x - 24*I*a^3)","A",0
108,1,292,0,0.651948," ","integrate(x/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{3} x - 2 i \, a^{2}\right)} \sqrt{\frac{625 i}{16 \, a^{4}}} \log\left(\frac{4}{25} i \, a^{2} \sqrt{\frac{625 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(2 \, a^{3} x - 2 i \, a^{2}\right)} \sqrt{\frac{625 i}{16 \, a^{4}}} \log\left(-\frac{4}{25} i \, a^{2} \sqrt{\frac{625 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(2 \, a^{3} x - 2 i \, a^{2}\right)} \sqrt{-\frac{625 i}{16 \, a^{4}}} \log\left(\frac{4}{25} i \, a^{2} \sqrt{-\frac{625 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(2 \, a^{3} x - 2 i \, a^{2}\right)} \sqrt{-\frac{625 i}{16 \, a^{4}}} \log\left(-\frac{4}{25} i \, a^{2} \sqrt{-\frac{625 i}{16 \, a^{4}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \sqrt{a^{2} x^{2} + 1} {\left(2 i \, a^{2} x^{2} - 9 \, a x + 43 i\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{4 \, a^{3} x - 4 i \, a^{2}}"," ",0,"-((2*a^3*x - 2*I*a^2)*sqrt(625/16*I/a^4)*log(4/25*I*a^2*sqrt(625/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (2*a^3*x - 2*I*a^2)*sqrt(625/16*I/a^4)*log(-4/25*I*a^2*sqrt(625/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (2*a^3*x - 2*I*a^2)*sqrt(-625/16*I/a^4)*log(4/25*I*a^2*sqrt(-625/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (2*a^3*x - 2*I*a^2)*sqrt(-625/16*I/a^4)*log(-4/25*I*a^2*sqrt(-625/16*I/a^4) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - sqrt(a^2*x^2 + 1)*(2*I*a^2*x^2 - 9*a*x + 43*I)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/(4*a^3*x - 4*I*a^2)","A",0
109,1,262,0,0.579952," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(a^{2} x - i \, a\right)} \sqrt{\frac{25 i}{a^{2}}} \log\left(\frac{1}{5} \, a \sqrt{\frac{25 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(a^{2} x - i \, a\right)} \sqrt{\frac{25 i}{a^{2}}} \log\left(-\frac{1}{5} \, a \sqrt{\frac{25 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(a^{2} x - i \, a\right)} \sqrt{-\frac{25 i}{a^{2}}} \log\left(\frac{1}{5} \, a \sqrt{-\frac{25 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + {\left(a^{2} x - i \, a\right)} \sqrt{-\frac{25 i}{a^{2}}} \log\left(-\frac{1}{5} \, a \sqrt{-\frac{25 i}{a^{2}}} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + 2 \, \sqrt{a^{2} x^{2} + 1} {\left(-i \, a x - 9\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, a^{2} x - 2 i \, a}"," ",0,"-((a^2*x - I*a)*sqrt(25*I/a^2)*log(1/5*a*sqrt(25*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (a^2*x - I*a)*sqrt(25*I/a^2)*log(-1/5*a*sqrt(25*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (a^2*x - I*a)*sqrt(-25*I/a^2)*log(1/5*a*sqrt(-25*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + (a^2*x - I*a)*sqrt(-25*I/a^2)*log(-1/5*a*sqrt(-25*I/a^2) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + 2*sqrt(a^2*x^2 + 1)*(-I*a*x - 9)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/(2*a^2*x - 2*I*a)","A",0
110,1,330,0,0.560142," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x,x, algorithm=""fricas"")","\frac{\sqrt{4 i} {\left(a x - i\right)} \log\left(\frac{1}{2} i \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \sqrt{4 i} {\left(a x - i\right)} \log\left(-\frac{1}{2} i \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - \sqrt{-4 i} {\left(a x - i\right)} \log\left(\frac{1}{2} i \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) + \sqrt{-4 i} {\left(a x - i\right)} \log\left(-\frac{1}{2} i \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}\right) - {\left(2 \, a x - 2 i\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - 2 \, {\left(-i \, a x - 1\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - 2 \, {\left(i \, a x + 1\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + {\left(2 \, a x - 2 i\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right) - 16 i \, \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{2 \, a x - 2 i}"," ",0,"(sqrt(4*I)*(a*x - I)*log(1/2*I*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - sqrt(4*I)*(a*x - I)*log(-1/2*I*sqrt(4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - sqrt(-4*I)*(a*x - I)*log(1/2*I*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) + sqrt(-4*I)*(a*x - I)*log(-1/2*I*sqrt(-4*I) + sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))) - (2*a*x - 2*I)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - 2*(-I*a*x - 1)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - 2*(I*a*x + 1)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + (2*a*x - 2*I)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1) - 16*I*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)))/(2*a*x - 2*I)","A",0
111,1,213,0,0.618024," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^2,x, algorithm=""fricas"")","-\frac{\sqrt{a^{2} x^{2} + 1} {\left(18 \, a x - 2 i\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 5 \, {\left(-i \, a^{2} x^{2} - a x\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - {\left(5 \, a^{2} x^{2} - 5 i \, a x\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + {\left(5 \, a^{2} x^{2} - 5 i \, a x\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + 5 \, {\left(i \, a^{2} x^{2} + a x\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right)}{2 \, a x^{2} - 2 i \, x}"," ",0,"-(sqrt(a^2*x^2 + 1)*(18*a*x - 2*I)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 5*(-I*a^2*x^2 - a*x)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - (5*a^2*x^2 - 5*I*a*x)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + (5*a^2*x^2 - 5*I*a*x)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + 5*(I*a^2*x^2 + a*x)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1))/(2*a*x^2 - 2*I*x)","B",0
112,1,238,0,0.635659," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^3,x, algorithm=""fricas"")","\frac{\sqrt{a^{2} x^{2} + 1} {\left(86 i \, a^{2} x^{2} + 18 \, a x + 4 i\right)} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + {\left(25 \, a^{3} x^{3} - 25 i \, a^{2} x^{2}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - 25 \, {\left(i \, a^{3} x^{3} + a^{2} x^{2}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) - 25 \, {\left(-i \, a^{3} x^{3} - a^{2} x^{2}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - {\left(25 \, a^{3} x^{3} - 25 i \, a^{2} x^{2}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right)}{8 \, a x^{3} - 8 i \, x^{2}}"," ",0,"(sqrt(a^2*x^2 + 1)*(86*I*a^2*x^2 + 18*a*x + 4*I)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + (25*a^3*x^3 - 25*I*a^2*x^2)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - 25*(I*a^3*x^3 + a^2*x^2)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) - 25*(-I*a^3*x^3 - a^2*x^2)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - (25*a^3*x^3 - 25*I*a^2*x^2)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1))/(8*a*x^3 - 8*I*x^2)","B",0
113,1,246,0,0.749705," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^4,x, algorithm=""fricas"")","\frac{{\left(574 \, a^{3} x^{3} - 122 i \, a^{2} x^{2} + 52 \, a x + 16 i\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 165 \, {\left(i \, a^{4} x^{4} + a^{3} x^{3}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) - {\left(165 \, a^{4} x^{4} - 165 i \, a^{3} x^{3}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + {\left(165 \, a^{4} x^{4} - 165 i \, a^{3} x^{3}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) - 165 \, {\left(-i \, a^{4} x^{4} - a^{3} x^{3}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right)}{48 \, a x^{4} - 48 i \, x^{3}}"," ",0,"((574*a^3*x^3 - 122*I*a^2*x^2 + 52*a*x + 16*I)*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 165*(I*a^4*x^4 + a^3*x^3)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) - (165*a^4*x^4 - 165*I*a^3*x^3)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + (165*a^4*x^4 - 165*I*a^3*x^3)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) - 165*(-I*a^4*x^4 - a^3*x^3)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1))/(48*a*x^4 - 48*I*x^3)","A",0
114,1,252,0,0.540622," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^5,x, algorithm=""fricas"")","\frac{{\left(-4934 i \, a^{4} x^{4} - 1042 \, a^{3} x^{3} - 452 i \, a^{2} x^{2} + 272 \, a x + 96 i\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1425 \, {\left(a^{5} x^{5} - i \, a^{4} x^{4}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + 1\right) + {\left(1425 i \, a^{5} x^{5} + 1425 \, a^{4} x^{4}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} + i\right) + {\left(-1425 i \, a^{5} x^{5} - 1425 \, a^{4} x^{4}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - i\right) + 1425 \, {\left(a^{5} x^{5} - i \, a^{4} x^{4}\right)} \log\left(\sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}} - 1\right)}{384 \, a x^{5} - 384 i \, x^{4}}"," ",0,"((-4934*I*a^4*x^4 - 1042*a^3*x^3 - 452*I*a^2*x^2 + 272*a*x + 96*I)*sqrt(a^2*x^2 + 1)*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1425*(a^5*x^5 - I*a^4*x^4)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + 1) + (1425*I*a^5*x^5 + 1425*a^4*x^4)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) + I) + (-1425*I*a^5*x^5 - 1425*a^4*x^4)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - I) + 1425*(a^5*x^5 - I*a^4*x^4)*log(sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)) - 1))/(384*a*x^5 - 384*I*x^4)","A",0
115,1,208,0,0.627885," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)*x^2,x, algorithm=""fricas"")","-\frac{19}{324} \, {\left(-i \, \sqrt{3} + 1\right)} \log\left(\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - \frac{19}{324} \, {\left(-i \, \sqrt{3} - 1\right)} \log\left(\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - \frac{19}{324} \, {\left(i \, \sqrt{3} + 1\right)} \log\left(-\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - \frac{19}{324} \, {\left(i \, \sqrt{3} - 1\right)} \log\left(-\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + \frac{1}{324} \, {\left(108 \, x^{3} - 18 i \, x^{2} - 6 \, x - 132 i\right)} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{19}{162} \, \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + i\right) + \frac{19}{162} \, \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - i\right)"," ",0,"-19/324*(-I*sqrt(3) + 1)*log(1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2*I) - 19/324*(-I*sqrt(3) - 1)*log(1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2*I) - 19/324*(I*sqrt(3) + 1)*log(-1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2*I) - 19/324*(I*sqrt(3) - 1)*log(-1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2*I) + 1/324*(108*x^3 - 18*I*x^2 - 6*x - 132*I)*(I*sqrt(x^2 + 1)/(x + I))^(1/3) - 19/162*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) + I) + 19/162*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) - I)","A",0
116,1,195,0,0.474876," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)*x,x, algorithm=""fricas"")","-\frac{1}{36} \, {\left(\sqrt{3} + i\right)} \log\left(\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - \frac{1}{36} \, {\left(\sqrt{3} - i\right)} \log\left(\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + \frac{1}{36} \, {\left(\sqrt{3} - i\right)} \log\left(-\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + \frac{1}{36} \, {\left(\sqrt{3} + i\right)} \log\left(-\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + \frac{1}{6} \, {\left(3 \, x^{2} - i \, x + 4\right)} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{18} i \, \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + i\right) + \frac{1}{18} i \, \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - i\right)"," ",0,"-1/36*(sqrt(3) + I)*log(1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2*I) - 1/36*(sqrt(3) - I)*log(1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2*I) + 1/36*(sqrt(3) - I)*log(-1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2*I) + 1/36*(sqrt(3) + I)*log(-1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2*I) + 1/6*(3*x^2 - I*x + 4)*(I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/18*I*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) + I) + 1/18*I*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) - I)","A",0
117,1,198,0,0.440451," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(-i \, \sqrt{3} + 1\right)} \log\left(\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + \frac{1}{6} \, {\left(-i \, \sqrt{3} - 1\right)} \log\left(\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + \frac{1}{6} \, {\left(i \, \sqrt{3} + 1\right)} \log\left(-\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + \frac{1}{6} \, {\left(i \, \sqrt{3} - 1\right)} \log\left(-\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + \frac{1}{6} \, {\left(6 \, x + 6 i\right)} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{3} \, \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + i\right) - \frac{1}{3} \, \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - i\right)"," ",0,"1/6*(-I*sqrt(3) + 1)*log(1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2*I) + 1/6*(-I*sqrt(3) - 1)*log(1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2*I) + 1/6*(I*sqrt(3) + 1)*log(-1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2*I) + 1/6*(I*sqrt(3) - 1)*log(-1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2*I) + 1/6*(6*x + 6*I)*(I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/3*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) + I) - 1/3*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) - I)","A",0
118,1,339,0,0.504820," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x,x, algorithm=""fricas"")","\frac{1}{2} \, {\left(\sqrt{3} + i\right)} \log\left(\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) + \frac{1}{2} \, {\left(\sqrt{3} - i\right)} \log\left(\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) + \frac{1}{2} \, {\left(-i \, \sqrt{3} - 1\right)} \log\left(\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2}\right) + \frac{1}{2} \, {\left(-i \, \sqrt{3} + 1\right)} \log\left(\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2}\right) + \frac{1}{2} \, {\left(i \, \sqrt{3} - 1\right)} \log\left(-\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2}\right) + \frac{1}{2} \, {\left(i \, \sqrt{3} + 1\right)} \log\left(-\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2}\right) - \frac{1}{2} \, {\left(\sqrt{3} - i\right)} \log\left(-\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2} i\right) - \frac{1}{2} \, {\left(\sqrt{3} + i\right)} \log\left(-\frac{1}{2} \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2} i\right) - \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + 1\right) + i \, \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + i\right) - i \, \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - i\right) + \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - 1\right)"," ",0,"1/2*(sqrt(3) + I)*log(1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2*I) + 1/2*(sqrt(3) - I)*log(1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2*I) + 1/2*(-I*sqrt(3) - 1)*log(1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2) + 1/2*(-I*sqrt(3) + 1)*log(1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2) + 1/2*(I*sqrt(3) - 1)*log(-1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2) + 1/2*(I*sqrt(3) + 1)*log(-1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2) - 1/2*(sqrt(3) - I)*log(-1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2*I) - 1/2*(sqrt(3) + I)*log(-1/2*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2*I) - log((I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1) + I*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) + I) - I*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) - I) + log((I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1)","A",0
119,1,211,0,3.168658," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^2,x, algorithm=""fricas"")","\frac{{\left(\sqrt{3} x - i \, x\right)} \log\left(\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2}\right) + {\left(\sqrt{3} x + i \, x\right)} \log\left(\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2}\right) - {\left(\sqrt{3} x + i \, x\right)} \log\left(-\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2}\right) - {\left(\sqrt{3} x - i \, x\right)} \log\left(-\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2}\right) - 2 i \, x \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + 1\right) + 2 i \, x \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - 1\right) - 6 \, {\left(-i \, x + 1\right)} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}}}{6 \, x}"," ",0,"1/6*((sqrt(3)*x - I*x)*log(1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2) + (sqrt(3)*x + I*x)*log(1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2) - (sqrt(3)*x + I*x)*log(-1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2) - (sqrt(3)*x - I*x)*log(-1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2) - 2*I*x*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1) + 2*I*x*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1) - 6*(-I*x + 1)*(I*sqrt(x^2 + 1)/(x + I))^(1/3))/x","A",0
120,1,234,0,2.272790," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^3,x, algorithm=""fricas"")","\frac{2 \, x^{2} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + 1\right) - 2 \, x^{2} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - 1\right) + {\left(i \, \sqrt{3} x^{2} + x^{2}\right)} \log\left(\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2}\right) + {\left(i \, \sqrt{3} x^{2} - x^{2}\right)} \log\left(\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2}\right) + {\left(-i \, \sqrt{3} x^{2} + x^{2}\right)} \log\left(-\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2}\right) + {\left(-i \, \sqrt{3} x^{2} - x^{2}\right)} \log\left(-\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2}\right) - 6 \, {\left(4 \, x^{2} + i \, x + 3\right)} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}}}{36 \, x^{2}}"," ",0,"1/36*(2*x^2*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1) - 2*x^2*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1) + (I*sqrt(3)*x^2 + x^2)*log(1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2) + (I*sqrt(3)*x^2 - x^2)*log(1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2) + (-I*sqrt(3)*x^2 + x^2)*log(-1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2) + (-I*sqrt(3)*x^2 - x^2)*log(-1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2) - 6*(4*x^2 + I*x + 3)*(I*sqrt(x^2 + 1)/(x + I))^(1/3))/x^2","A",0
121,1,244,0,1.956789," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^4,x, algorithm=""fricas"")","\frac{38 i \, x^{3} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + 1\right) - 38 i \, x^{3} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - 1\right) - {\left(19 \, \sqrt{3} x^{3} - 19 i \, x^{3}\right)} \log\left(\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2}\right) - {\left(19 \, \sqrt{3} x^{3} + 19 i \, x^{3}\right)} \log\left(\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2}\right) + {\left(19 \, \sqrt{3} x^{3} + 19 i \, x^{3}\right)} \log\left(-\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + \frac{1}{2}\right) + {\left(19 \, \sqrt{3} x^{3} - 19 i \, x^{3}\right)} \log\left(-\frac{1}{2} i \, \sqrt{3} + \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} - \frac{1}{2}\right) + {\left(-132 i \, x^{3} + 6 \, x^{2} - 18 i \, x - 108\right)} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}}}{324 \, x^{3}}"," ",0,"1/324*(38*I*x^3*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1) - 38*I*x^3*log((I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1) - (19*sqrt(3)*x^3 - 19*I*x^3)*log(1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2) - (19*sqrt(3)*x^3 + 19*I*x^3)*log(1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2) + (19*sqrt(3)*x^3 + 19*I*x^3)*log(-1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) + 1/2) + (19*sqrt(3)*x^3 - 19*I*x^3)*log(-1/2*I*sqrt(3) + (I*sqrt(x^2 + 1)/(x + I))^(1/3) - 1/2) + (-132*I*x^3 + 6*x^2 - 18*I*x - 108)*(I*sqrt(x^2 + 1)/(x + I))^(1/3))/x^3","A",0
122,1,121,0,1.535971," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3)*x^2,x, algorithm=""fricas"")","-\frac{1}{81} \, {\left(11 \, \sqrt{3} + 11 i\right)} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} + \frac{1}{2} i \, \sqrt{3} - \frac{1}{2}\right) + \frac{1}{81} \, {\left(11 \, \sqrt{3} - 11 i\right)} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} - \frac{1}{2} i \, \sqrt{3} - \frac{1}{2}\right) + \frac{1}{81} \, {\left(27 \, x^{3} - 9 i \, x^{2} - 6 \, x - 42 i\right)} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} + \frac{22}{81} i \, \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} + 1\right)"," ",0,"-1/81*(11*sqrt(3) + 11*I)*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) + 1/2*I*sqrt(3) - 1/2) + 1/81*(11*sqrt(3) - 11*I)*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) - 1/2*I*sqrt(3) - 1/2) + 1/81*(27*x^3 - 9*I*x^2 - 6*x - 42*I)*(I*sqrt(x^2 + 1)/(x + I))^(2/3) + 22/81*I*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) + 1)","A",0
123,1,116,0,0.624436," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3)*x,x, algorithm=""fricas"")","-\frac{1}{9} \, {\left(i \, \sqrt{3} - 1\right)} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} + \frac{1}{2} i \, \sqrt{3} - \frac{1}{2}\right) - \frac{1}{9} \, {\left(-i \, \sqrt{3} - 1\right)} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} - \frac{1}{2} i \, \sqrt{3} - \frac{1}{2}\right) + \frac{1}{6} \, {\left(3 \, x^{2} - 2 i \, x + 5\right)} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} - \frac{2}{9} \, \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} + 1\right)"," ",0,"-1/9*(I*sqrt(3) - 1)*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) + 1/2*I*sqrt(3) - 1/2) - 1/9*(-I*sqrt(3) - 1)*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) - 1/2*I*sqrt(3) - 1/2) + 1/6*(3*x^2 - 2*I*x + 5)*(I*sqrt(x^2 + 1)/(x + I))^(2/3) - 2/9*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) + 1)","A",0
124,1,107,0,0.634157," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(\sqrt{3} + i\right)} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} + \frac{1}{2} i \, \sqrt{3} - \frac{1}{2}\right) - \frac{1}{3} \, {\left(\sqrt{3} - i\right)} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} - \frac{1}{2} i \, \sqrt{3} - \frac{1}{2}\right) + \frac{1}{3} \, {\left(3 \, x + 3 i\right)} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} - \frac{2}{3} i \, \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} + 1\right)"," ",0,"1/3*(sqrt(3) + I)*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) + 1/2*I*sqrt(3) - 1/2) - 1/3*(sqrt(3) - I)*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) - 1/2*I*sqrt(3) - 1/2) + 1/3*(3*x + 3*I)*(I*sqrt(x^2 + 1)/(x + I))^(2/3) - 2/3*I*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) + 1)","A",0
125,1,147,0,0.506799," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x,x, algorithm=""fricas"")","\frac{1}{2} \, {\left(i \, \sqrt{3} - 1\right)} \log\left(\frac{\sqrt{3} {\left(i \, x - 1\right)} + x + 2 i \, \sqrt{x^{2} + 1} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + i}{2 \, x + 2 i}\right) + \frac{1}{2} \, {\left(-i \, \sqrt{3} - 1\right)} \log\left(\frac{\sqrt{3} {\left(-i \, x + 1\right)} + x + 2 i \, \sqrt{x^{2} + 1} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + i}{2 \, x + 2 i}\right) + \log\left(-\frac{x - i \, \sqrt{x^{2} + 1} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{1}{3}} + i}{x + i}\right)"," ",0,"1/2*(I*sqrt(3) - 1)*log((sqrt(3)*(I*x - 1) + x + 2*I*sqrt(x^2 + 1)*(I*sqrt(x^2 + 1)/(x + I))^(1/3) + I)/(2*x + 2*I)) + 1/2*(-I*sqrt(3) - 1)*log((sqrt(3)*(-I*x + 1) + x + 2*I*sqrt(x^2 + 1)*(I*sqrt(x^2 + 1)/(x + I))^(1/3) + I)/(2*x + 2*I)) + log(-(x - I*sqrt(x^2 + 1)*(I*sqrt(x^2 + 1)/(x + I))^(1/3) + I)/(x + I))","A",0
126,1,120,0,0.629172," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x^2,x, algorithm=""fricas"")","\frac{{\left(\sqrt{3} x - i \, x\right)} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} + \frac{1}{2} i \, \sqrt{3} + \frac{1}{2}\right) - {\left(\sqrt{3} x + i \, x\right)} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} - \frac{1}{2} i \, \sqrt{3} + \frac{1}{2}\right) + 2 i \, x \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} - 1\right) - 3 \, {\left(-i \, x + 1\right)} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}}}{3 \, x}"," ",0,"1/3*((sqrt(3)*x - I*x)*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) + 1/2*I*sqrt(3) + 1/2) - (sqrt(3)*x + I*x)*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) - 1/2*I*sqrt(3) + 1/2) + 2*I*x*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) - 1) - 3*(-I*x + 1)*(I*sqrt(x^2 + 1)/(x + I))^(2/3))/x","A",0
127,1,138,0,0.640431," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x^3,x, algorithm=""fricas"")","-\frac{4 \, x^{2} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} - 1\right) + 2 \, {\left(-i \, \sqrt{3} x^{2} - x^{2}\right)} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} + \frac{1}{2} i \, \sqrt{3} + \frac{1}{2}\right) + 2 \, {\left(i \, \sqrt{3} x^{2} - x^{2}\right)} \log\left(\left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}} - \frac{1}{2} i \, \sqrt{3} + \frac{1}{2}\right) + 3 \, {\left(5 \, x^{2} + 2 i \, x + 3\right)} \left(\frac{i \, \sqrt{x^{2} + 1}}{x + i}\right)^{\frac{2}{3}}}{18 \, x^{2}}"," ",0,"-1/18*(4*x^2*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) - 1) + 2*(-I*sqrt(3)*x^2 - x^2)*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) + 1/2*I*sqrt(3) + 1/2) + 2*(I*sqrt(3)*x^2 - x^2)*log((I*sqrt(x^2 + 1)/(x + I))^(2/3) - 1/2*I*sqrt(3) + 1/2) + 3*(5*x^2 + 2*I*x + 3)*(I*sqrt(x^2 + 1)/(x + I))^(2/3))/x^2","A",0
128,1,435,0,0.652429," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x^2,x, algorithm=""fricas"")","\frac{96 i \, a^{3} \left(\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} \log\left(\frac{128}{11} \, a^{3} \left(\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - 96 \, a^{3} \left(\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} \log\left(\frac{128}{11} i \, a^{3} \left(\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + 96 \, a^{3} \left(\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} \log\left(-\frac{128}{11} i \, a^{3} \left(\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - 96 i \, a^{3} \left(\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} \log\left(-\frac{128}{11} \, a^{3} \left(\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + 96 i \, a^{3} \left(-\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} \log\left(\frac{128}{11} \, a^{3} \left(-\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - 96 \, a^{3} \left(-\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} \log\left(\frac{128}{11} i \, a^{3} \left(-\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + 96 \, a^{3} \left(-\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} \log\left(-\frac{128}{11} i \, a^{3} \left(-\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - 96 i \, a^{3} \left(-\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} \log\left(-\frac{128}{11} \, a^{3} \left(-\frac{14641 i}{268435456 \, a^{12}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + {\left(32 \, a^{3} x^{3} - 4 i \, a^{2} x^{2} - a x - 37 i\right)} \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}}{96 \, a^{3}}"," ",0,"1/96*(96*I*a^3*(14641/268435456*I/a^12)^(1/4)*log(128/11*a^3*(14641/268435456*I/a^12)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - 96*a^3*(14641/268435456*I/a^12)^(1/4)*log(128/11*I*a^3*(14641/268435456*I/a^12)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + 96*a^3*(14641/268435456*I/a^12)^(1/4)*log(-128/11*I*a^3*(14641/268435456*I/a^12)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - 96*I*a^3*(14641/268435456*I/a^12)^(1/4)*log(-128/11*a^3*(14641/268435456*I/a^12)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + 96*I*a^3*(-14641/268435456*I/a^12)^(1/4)*log(128/11*a^3*(-14641/268435456*I/a^12)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - 96*a^3*(-14641/268435456*I/a^12)^(1/4)*log(128/11*I*a^3*(-14641/268435456*I/a^12)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + 96*a^3*(-14641/268435456*I/a^12)^(1/4)*log(-128/11*I*a^3*(-14641/268435456*I/a^12)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - 96*I*a^3*(-14641/268435456*I/a^12)^(1/4)*log(-128/11*a^3*(-14641/268435456*I/a^12)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + (32*a^3*x^3 - 4*I*a^2*x^2 - a*x - 37*I)*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4))/a^3","A",0
129,1,428,0,0.900777," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x,x, algorithm=""fricas"")","-\frac{8 \, a^{2} \left(\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} \log\left(32 \, a^{2} \left(\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + 8 i \, a^{2} \left(\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} \log\left(32 i \, a^{2} \left(\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - 8 i \, a^{2} \left(\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} \log\left(-32 i \, a^{2} \left(\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - 8 \, a^{2} \left(\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} \log\left(-32 \, a^{2} \left(\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + 8 \, a^{2} \left(-\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} \log\left(32 \, a^{2} \left(-\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + 8 i \, a^{2} \left(-\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} \log\left(32 i \, a^{2} \left(-\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - 8 i \, a^{2} \left(-\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} \log\left(-32 i \, a^{2} \left(-\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - 8 \, a^{2} \left(-\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} \log\left(-32 \, a^{2} \left(-\frac{i}{1048576 \, a^{8}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - {\left(4 \, a^{2} x^{2} - i \, a x + 5\right)} \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}}{8 \, a^{2}}"," ",0,"-1/8*(8*a^2*(1/1048576*I/a^8)^(1/4)*log(32*a^2*(1/1048576*I/a^8)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + 8*I*a^2*(1/1048576*I/a^8)^(1/4)*log(32*I*a^2*(1/1048576*I/a^8)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - 8*I*a^2*(1/1048576*I/a^8)^(1/4)*log(-32*I*a^2*(1/1048576*I/a^8)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - 8*a^2*(1/1048576*I/a^8)^(1/4)*log(-32*a^2*(1/1048576*I/a^8)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + 8*a^2*(-1/1048576*I/a^8)^(1/4)*log(32*a^2*(-1/1048576*I/a^8)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + 8*I*a^2*(-1/1048576*I/a^8)^(1/4)*log(32*I*a^2*(-1/1048576*I/a^8)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - 8*I*a^2*(-1/1048576*I/a^8)^(1/4)*log(-32*I*a^2*(-1/1048576*I/a^8)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - 8*a^2*(-1/1048576*I/a^8)^(1/4)*log(-32*a^2*(-1/1048576*I/a^8)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - (4*a^2*x^2 - I*a*x + 5)*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4))/a^2","A",0
130,1,383,0,0.675104," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4),x, algorithm=""fricas"")","\frac{-i \, a \left(\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} \log\left(4 \, a \left(\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + a \left(\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} \log\left(4 i \, a \left(\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - a \left(\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} \log\left(-4 i \, a \left(\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + i \, a \left(\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} \log\left(-4 \, a \left(\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - i \, a \left(-\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} \log\left(4 \, a \left(-\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + a \left(-\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} \log\left(4 i \, a \left(-\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - a \left(-\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} \log\left(-4 i \, a \left(-\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + i \, a \left(-\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} \log\left(-4 \, a \left(-\frac{i}{256 \, a^{4}}\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + {\left(a x + i\right)} \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}}{a}"," ",0,"(-I*a*(1/256*I/a^4)^(1/4)*log(4*a*(1/256*I/a^4)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + a*(1/256*I/a^4)^(1/4)*log(4*I*a*(1/256*I/a^4)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - a*(1/256*I/a^4)^(1/4)*log(-4*I*a*(1/256*I/a^4)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + I*a*(1/256*I/a^4)^(1/4)*log(-4*a*(1/256*I/a^4)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - I*a*(-1/256*I/a^4)^(1/4)*log(4*a*(-1/256*I/a^4)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + a*(-1/256*I/a^4)^(1/4)*log(4*I*a*(-1/256*I/a^4)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - a*(-1/256*I/a^4)^(1/4)*log(-4*I*a*(-1/256*I/a^4)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + I*a*(-1/256*I/a^4)^(1/4)*log(-4*a*(-1/256*I/a^4)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + (a*x + I)*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4))/a","A",0
131,1,509,0,0.631848," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x,x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{4 i} \log\left(\frac{1}{2} \, \sqrt{4 i} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + \frac{1}{2} \, \sqrt{4 i} \log\left(-\frac{1}{2} \, \sqrt{4 i} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - \frac{1}{2} \, \sqrt{-4 i} \log\left(\frac{1}{2} \, \sqrt{-4 i} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + \frac{1}{2} \, \sqrt{-4 i} \log\left(-\frac{1}{2} \, \sqrt{-4 i} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + i^{\frac{1}{4}} \log\left(i^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + i \, i^{\frac{1}{4}} \log\left(i \, i^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - i \, i^{\frac{1}{4}} \log\left(-i \, i^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - i^{\frac{1}{4}} \log\left(-i^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + \left(-i\right)^{\frac{1}{4}} \log\left(\left(-i\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) + i \, \left(-i\right)^{\frac{1}{4}} \log\left(i \, \left(-i\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - i \, \left(-i\right)^{\frac{1}{4}} \log\left(-i \, \left(-i\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - \left(-i\right)^{\frac{1}{4}} \log\left(-\left(-i\right)^{\frac{1}{4}} + \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}\right) - \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} + 1\right) - i \, \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} + i\right) + i \, \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} - i\right) + \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} - 1\right)"," ",0,"-1/2*sqrt(4*I)*log(1/2*sqrt(4*I) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + 1/2*sqrt(4*I)*log(-1/2*sqrt(4*I) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - 1/2*sqrt(-4*I)*log(1/2*sqrt(-4*I) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + 1/2*sqrt(-4*I)*log(-1/2*sqrt(-4*I) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + I^(1/4)*log(I^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + I*I^(1/4)*log(I*I^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - I*I^(1/4)*log(-I*I^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - I^(1/4)*log(-I^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + (-I)^(1/4)*log((-I)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) + I*(-I)^(1/4)*log(I*(-I)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - I*(-I)^(1/4)*log(-I*(-I)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - (-I)^(1/4)*log(-(-I)^(1/4) + (I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4)) - log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) + 1) - I*log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) + I) + I*log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) - I) + log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) - 1)","A",0
132,1,345,0,0.541969," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x^2,x, algorithm=""fricas"")","\frac{-i \, a x \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} + 1\right) + a x \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} + i\right) - a x \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} - i\right) + i \, a x \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} - 1\right) + \sqrt{i \, a^{2}} x \log\left(\frac{a \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} + i \, \sqrt{i \, a^{2}}}{a}\right) - \sqrt{i \, a^{2}} x \log\left(\frac{a \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} - i \, \sqrt{i \, a^{2}}}{a}\right) + \sqrt{-i \, a^{2}} x \log\left(\frac{a \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} + i \, \sqrt{-i \, a^{2}}}{a}\right) - \sqrt{-i \, a^{2}} x \log\left(\frac{a \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} - i \, \sqrt{-i \, a^{2}}}{a}\right) - 4 \, {\left(-i \, a x + 1\right)} \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}}{4 \, x}"," ",0,"1/4*(-I*a*x*log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) + 1) + a*x*log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) + I) - a*x*log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) - I) + I*a*x*log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) - 1) + sqrt(I*a^2)*x*log((a*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) + I*sqrt(I*a^2))/a) - sqrt(I*a^2)*x*log((a*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) - I*sqrt(I*a^2))/a) + sqrt(-I*a^2)*x*log((a*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) + I*sqrt(-I*a^2))/a) - sqrt(-I*a^2)*x*log((a*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) - I*sqrt(-I*a^2))/a) - 4*(-I*a*x + 1)*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4))/x","A",0
133,1,381,0,0.495559," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x^3,x, algorithm=""fricas"")","\frac{a^{2} x^{2} \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} + 1\right) + i \, a^{2} x^{2} \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} + i\right) - i \, a^{2} x^{2} \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} - i\right) - a^{2} x^{2} \log\left(\left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} - 1\right) + \sqrt{i \, a^{4}} x^{2} \log\left(\frac{a^{2} \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} + \sqrt{i \, a^{4}}}{a^{2}}\right) - \sqrt{i \, a^{4}} x^{2} \log\left(\frac{a^{2} \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} - \sqrt{i \, a^{4}}}{a^{2}}\right) + \sqrt{-i \, a^{4}} x^{2} \log\left(\frac{a^{2} \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} + \sqrt{-i \, a^{4}}}{a^{2}}\right) - \sqrt{-i \, a^{4}} x^{2} \log\left(\frac{a^{2} \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}} - \sqrt{-i \, a^{4}}}{a^{2}}\right) - {\left(20 \, a^{2} x^{2} + 4 i \, a x + 16\right)} \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}}{32 \, x^{2}}"," ",0,"1/32*(a^2*x^2*log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) + 1) + I*a^2*x^2*log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) + I) - I*a^2*x^2*log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) - I) - a^2*x^2*log((I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) - 1) + sqrt(I*a^4)*x^2*log((a^2*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) + sqrt(I*a^4))/a^2) - sqrt(I*a^4)*x^2*log((a^2*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) - sqrt(I*a^4))/a^2) + sqrt(-I*a^4)*x^2*log((a^2*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) + sqrt(-I*a^4))/a^2) - sqrt(-I*a^4)*x^2*log((a^2*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4) - sqrt(-I*a^4))/a^2) - (20*a^2*x^2 + 4*I*a*x + 16)*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4))/x^2","A",0
134,0,0,0,0.588825," ","integrate((1+I*a*x)^6/(a^2*x^2+1)^3*x^m,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{3} x^{3} - 3 i \, a^{2} x^{2} - 3 \, a x + i\right)} x^{m}}{a^{3} x^{3} + 3 i \, a^{2} x^{2} - 3 \, a x - i}, x\right)"," ",0,"integral(-(a^3*x^3 - 3*I*a^2*x^2 - 3*a*x + I)*x^m/(a^3*x^3 + 3*I*a^2*x^2 - 3*a*x - I), x)","F",0
135,0,0,0,0.570342," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{2} - 2 i \, a x - 1\right)} x^{m}}{a^{2} x^{2} + 2 i \, a x - 1}, x\right)"," ",0,"integral((a^2*x^2 - 2*I*a*x - 1)*x^m/(a^2*x^2 + 2*I*a*x - 1), x)","F",0
136,0,0,0,0.634059," ","integrate((1+I*a*x)^2/(a^2*x^2+1)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a x - i\right)} x^{m}}{a x + i}, x\right)"," ",0,"integral(-(a*x - I)*x^m/(a*x + I), x)","F",0
137,0,0,0,0.461791," ","integrate(x^m/(1+I*a*x)^2*(a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a x + i\right)} x^{m}}{a x - i}, x\right)"," ",0,"integral(-(a*x + I)*x^m/(a*x - I), x)","F",0
138,0,0,0,0.427785," ","integrate(x^m/(1+I*a*x)^4*(a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{2} + 2 i \, a x - 1\right)} x^{m}}{a^{2} x^{2} - 2 i \, a x - 1}, x\right)"," ",0,"integral((a^2*x^2 + 2*I*a*x - 1)*x^m/(a^2*x^2 - 2*I*a*x - 1), x)","F",0
139,0,0,0,0.460332," ","integrate(x^m/(1+I*a*x)^6*(a^2*x^2+1)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{3} x^{3} + 3 i \, a^{2} x^{2} - 3 \, a x - i\right)} x^{m}}{a^{3} x^{3} - 3 i \, a^{2} x^{2} - 3 \, a x + i}, x\right)"," ",0,"integral(-(a^3*x^3 + 3*I*a^2*x^2 - 3*a*x - I)*x^m/(a^3*x^3 - 3*I*a^2*x^2 - 3*a*x + I), x)","F",0
140,0,0,0,0.469290," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} x^{2} + 1} {\left(-i \, a x - 1\right)} x^{m}}{a^{2} x^{2} + 2 i \, a x - 1}, x\right)"," ",0,"integral(sqrt(a^2*x^2 + 1)*(-I*a*x - 1)*x^m/(a^2*x^2 + 2*I*a*x - 1), x)","F",0
141,0,0,0,0.463636," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \sqrt{a^{2} x^{2} + 1} x^{m}}{a x + i}, x\right)"," ",0,"integral(I*sqrt(a^2*x^2 + 1)*x^m/(a*x + I), x)","F",0
142,0,0,0,0.485599," ","integrate(x^m/(1+I*a*x)*(a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{i \, \sqrt{a^{2} x^{2} + 1} x^{m}}{a x - i}, x\right)"," ",0,"integral(-I*sqrt(a^2*x^2 + 1)*x^m/(a*x - I), x)","F",0
143,0,0,0,0.468248," ","integrate(x^m/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} x^{2} + 1} {\left(i \, a x - 1\right)} x^{m}}{a^{2} x^{2} - 2 i \, a x - 1}, x\right)"," ",0,"integral(sqrt(a^2*x^2 + 1)*(I*a*x - 1)*x^m/(a^2*x^2 - 2*I*a*x - 1), x)","F",0
144,0,0,0,0.492620," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a x - i\right)} x^{m} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{a x + i}, x\right)"," ",0,"integral(-(a*x - I)*x^m*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))/(a*x + I), x)","F",0
145,0,0,0,0.455316," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \sqrt{a^{2} x^{2} + 1} x^{m} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{a x + i}, x\right)"," ",0,"integral(I*sqrt(a^2*x^2 + 1)*x^m*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))/(a*x + I), x)","F",0
146,0,0,0,0.605308," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}, x\right)"," ",0,"integral(x^m*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I)), x)","F",0
147,0,0,0,0.451261," ","integrate(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{i \, \sqrt{a^{2} x^{2} + 1} x^{m} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{a x - i}, x\right)"," ",0,"integral(-I*sqrt(a^2*x^2 + 1)*x^m*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))/(a*x - I), x)","F",0
148,0,0,0,0.438541," ","integrate(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a x + i\right)} x^{m} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{a x - i}, x\right)"," ",0,"integral(-(a*x + I)*x^m*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))/(a*x - I), x)","F",0
149,0,0,0,0.534625," ","integrate(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} x^{2} + 1} {\left(i \, a x - 1\right)} x^{m} \sqrt{\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}}}{a^{2} x^{2} - 2 i \, a x - 1}, x\right)"," ",0,"integral(sqrt(a^2*x^2 + 1)*(I*a*x - 1)*x^m*sqrt(I*sqrt(a^2*x^2 + 1)/(a*x + I))/(a^2*x^2 - 2*I*a*x - 1), x)","F",0
150,0,0,0,0.454275," ","integrate(exp(2/3*arctan(x))*x^m,x, algorithm=""fricas"")","{\rm integral}\left(x^{m} e^{\left(\frac{2}{3} \, \arctan\left(x\right)\right)}, x\right)"," ",0,"integral(x^m*e^(2/3*arctan(x)), x)","F",0
151,0,0,0,0.466091," ","integrate(exp(1/3*arctan(x))*x^m,x, algorithm=""fricas"")","{\rm integral}\left(x^{m} e^{\left(\frac{1}{3} \, \arctan\left(x\right)\right)}, x\right)"," ",0,"integral(x^m*e^(1/3*arctan(x)), x)","F",0
152,0,0,0,0.473753," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \left(\frac{i \, \sqrt{a^{2} x^{2} + 1}}{a x + i}\right)^{\frac{1}{4}}, x\right)"," ",0,"integral(x^m*(I*sqrt(a^2*x^2 + 1)/(a*x + I))^(1/4), x)","F",0
153,0,0,0,0.447344," ","integrate(exp(I*n*arctan(a*x))*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\left(-\frac{a x + i}{a x - i}\right)^{\frac{1}{2} \, n}}, x\right)"," ",0,"integral(x^m/(-(a*x + I)/(a*x - I))^(1/2*n), x)","F",0
154,0,0,0,0.438774," ","integrate(exp(I*n*arctan(a*x))*x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\left(-\frac{a x + i}{a x - i}\right)^{\frac{1}{2} \, n}}, x\right)"," ",0,"integral(x^3/(-(a*x + I)/(a*x - I))^(1/2*n), x)","F",0
155,0,0,0,0.453027," ","integrate(exp(I*n*arctan(a*x))*x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\left(-\frac{a x + i}{a x - i}\right)^{\frac{1}{2} \, n}}, x\right)"," ",0,"integral(x^2/(-(a*x + I)/(a*x - I))^(1/2*n), x)","F",0
156,0,0,0,0.473000," ","integrate(exp(I*n*arctan(a*x))*x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\left(-\frac{a x + i}{a x - i}\right)^{\frac{1}{2} \, n}}, x\right)"," ",0,"integral(x/(-(a*x + I)/(a*x - I))^(1/2*n), x)","F",0
157,0,0,0,0.446609," ","integrate(exp(I*n*arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\left(-\frac{a x + i}{a x - i}\right)^{\frac{1}{2} \, n}}, x\right)"," ",0,"integral(1/((-(a*x + I)/(a*x - I))^(1/2*n)), x)","F",0
158,0,0,0,0.449712," ","integrate(exp(I*n*arctan(a*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x \left(-\frac{a x + i}{a x - i}\right)^{\frac{1}{2} \, n}}, x\right)"," ",0,"integral(1/(x*(-(a*x + I)/(a*x - I))^(1/2*n)), x)","F",0
159,0,0,0,0.528691," ","integrate(exp(I*n*arctan(a*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{2} \left(-\frac{a x + i}{a x - i}\right)^{\frac{1}{2} \, n}}, x\right)"," ",0,"integral(1/(x^2*(-(a*x + I)/(a*x - I))^(1/2*n)), x)","F",0
160,0,0,0,0.600256," ","integrate(exp(I*n*arctan(a*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{3} \left(-\frac{a x + i}{a x - i}\right)^{\frac{1}{2} \, n}}, x\right)"," ",0,"integral(1/(x^3*(-(a*x + I)/(a*x - I))^(1/2*n)), x)","F",0
161,0,0,0,0.470819," ","integrate(exp(I*n*arctan(a*x))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{4} \left(-\frac{a x + i}{a x - i}\right)^{\frac{1}{2} \, n}}, x\right)"," ",0,"integral(1/(x^4*(-(a*x + I)/(a*x - I))^(1/2*n)), x)","F",0
162,1,175,0,0.493606," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x^4,x, algorithm=""fricas"")","\frac{186 i \, a^{5} - 1345 \, a^{4} - 1730 i \, a^{3} + 1320 \, a^{2} - {\left(960 \, a^{4} + 1920 i \, a^{3} - 2880 \, a^{2} - 1440 i \, a + 360\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(192 i \, b^{4} x^{4} - 48 \, {\left(4 i \, a - 5\right)} b^{3} x^{3} + {\left(192 i \, a^{2} - 560 \, a - 256 i\right)} b^{2} x^{2} + 192 i \, a^{4} - 2000 \, a^{3} + {\left(-192 i \, a^{3} + 1040 \, a^{2} + 928 i \, a - 360\right)} b x - 2656 i \, a^{2} + 2200 \, a + 512 i\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 300 i \, a}{960 \, b^{5}}"," ",0,"1/960*(186*I*a^5 - 1345*a^4 - 1730*I*a^3 + 1320*a^2 - (960*a^4 + 1920*I*a^3 - 2880*a^2 - 1440*I*a + 360)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (192*I*b^4*x^4 - 48*(4*I*a - 5)*b^3*x^3 + (192*I*a^2 - 560*a - 256*I)*b^2*x^2 + 192*I*a^4 - 2000*a^3 + (-192*I*a^3 + 1040*a^2 + 928*I*a - 360)*b*x - 2656*I*a^2 + 2200*a + 512*I)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 300*I*a)/b^5","A",0
163,1,137,0,0.628145," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x^3,x, algorithm=""fricas"")","\frac{-45 i \, a^{4} + 224 \, a^{3} + 192 i \, a^{2} + {\left(192 \, a^{3} + 288 i \, a^{2} - 288 \, a - 72 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(48 i \, b^{3} x^{3} - 16 \, {\left(3 i \, a - 4\right)} b^{2} x^{2} - 48 i \, a^{3} + {\left(48 i \, a^{2} - 160 \, a - 72 i\right)} b x + 352 \, a^{2} + 312 i \, a - 128\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} - 72 \, a}{192 \, b^{4}}"," ",0,"1/192*(-45*I*a^4 + 224*a^3 + 192*I*a^2 + (192*a^3 + 288*I*a^2 - 288*a - 72*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (48*I*b^3*x^3 - 16*(3*I*a - 4)*b^2*x^2 - 48*I*a^3 + (48*I*a^2 - 160*a - 72*I)*b*x + 352*a^2 + 312*I*a - 128)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 72*a)/b^4","A",0
164,1,106,0,0.476459," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x^2,x, algorithm=""fricas"")","\frac{7 i \, a^{3} - 21 \, a^{2} - 12 \, {\left(2 \, a^{2} + 2 i \, a - 1\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(8 i \, b^{2} x^{2} - 4 \, {\left(2 i \, a - 3\right)} b x + 8 i \, a^{2} - 36 \, a - 16 i\right)} - 9 i \, a}{24 \, b^{3}}"," ",0,"1/24*(7*I*a^3 - 21*a^2 - 12*(2*a^2 + 2*I*a - 1)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(8*I*b^2*x^2 - 4*(2*I*a - 3)*b*x + 8*I*a^2 - 36*a - 16*I) - 9*I*a)/b^3","A",0
165,1,77,0,0.432485," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x,x, algorithm=""fricas"")","\frac{-3 i \, a^{2} + {\left(8 \, a + 4 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(4 i \, b x - 4 i \, a + 8\right)} + 4 \, a}{8 \, b^{2}}"," ",0,"1/8*(-3*I*a^2 + (8*a + 4*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(4*I*b*x - 4*I*a + 8) + 4*a)/b^2","A",0
166,1,60,0,0.436003," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{i \, a + 2 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} - 2 \, \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}{2 \, b}"," ",0,"1/2*(I*a + 2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)))/b","A",0
167,1,155,0,0.468104," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-\frac{4 \, a - 4 i}{a + i}} \log\left(-b x + \frac{1}{2} \, {\left(i \, a - 1\right)} \sqrt{-\frac{4 \, a - 4 i}{a + i}} + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) - \frac{1}{2} \, \sqrt{-\frac{4 \, a - 4 i}{a + i}} \log\left(-b x + \frac{1}{2} \, {\left(-i \, a + 1\right)} \sqrt{-\frac{4 \, a - 4 i}{a + i}} + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) - i \, \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)"," ",0,"1/2*sqrt(-(4*a - 4*I)/(a + I))*log(-b*x + 1/2*(I*a - 1)*sqrt(-(4*a - 4*I)/(a + I)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 1/2*sqrt(-(4*a - 4*I)/(a + I))*log(-b*x + 1/2*(-I*a + 1)*sqrt(-(4*a - 4*I)/(a + I)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - I*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))","B",0
168,1,227,0,0.496218," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a + i\right)} \sqrt{\frac{b^{2}}{a^{4} + 2 i \, a^{3} + 2 i \, a - 1}} x \log\left(-\frac{b^{2} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b + {\left(a^{3} + i \, a^{2} + a + i\right)} \sqrt{\frac{b^{2}}{a^{4} + 2 i \, a^{3} + 2 i \, a - 1}}}{b}\right) - 2 \, {\left(a + i\right)} \sqrt{\frac{b^{2}}{a^{4} + 2 i \, a^{3} + 2 i \, a - 1}} x \log\left(-\frac{b^{2} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b - {\left(a^{3} + i \, a^{2} + a + i\right)} \sqrt{\frac{b^{2}}{a^{4} + 2 i \, a^{3} + 2 i \, a - 1}}}{b}\right) + 2 i \, b x + 2 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(2 \, a + 2 i\right)} x}"," ",0,"-(2*(a + I)*sqrt(b^2/(a^4 + 2*I*a^3 + 2*I*a - 1))*x*log(-(b^2*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b + (a^3 + I*a^2 + a + I)*sqrt(b^2/(a^4 + 2*I*a^3 + 2*I*a - 1)))/b) - 2*(a + I)*sqrt(b^2/(a^4 + 2*I*a^3 + 2*I*a - 1))*x*log(-(b^2*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b - (a^3 + I*a^2 + a + I)*sqrt(b^2/(a^4 + 2*I*a^3 + 2*I*a - 1)))/b) + 2*I*b*x + 2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((2*a + 2*I)*x)","B",0
169,1,455,0,0.450369," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{{\left(i \, a + 2\right)} b^{2} x^{2} + \sqrt{\frac{{\left(4 \, a^{2} - 4 i \, a - 1\right)} b^{4}}{a^{8} + 2 i \, a^{7} + 2 \, a^{6} + 6 i \, a^{5} + 6 i \, a^{3} - 2 \, a^{2} + 2 i \, a - 1}} {\left(a^{3} + i \, a^{2} + a + i\right)} x^{2} \log\left(-\frac{{\left(2 \, a - i\right)} b^{3} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a - i\right)} b^{2} + {\left(a^{5} + i \, a^{4} + 2 \, a^{3} + 2 i \, a^{2} + a + i\right)} \sqrt{\frac{{\left(4 \, a^{2} - 4 i \, a - 1\right)} b^{4}}{a^{8} + 2 i \, a^{7} + 2 \, a^{6} + 6 i \, a^{5} + 6 i \, a^{3} - 2 \, a^{2} + 2 i \, a - 1}}}{{\left(2 \, a - i\right)} b^{2}}\right) - \sqrt{\frac{{\left(4 \, a^{2} - 4 i \, a - 1\right)} b^{4}}{a^{8} + 2 i \, a^{7} + 2 \, a^{6} + 6 i \, a^{5} + 6 i \, a^{3} - 2 \, a^{2} + 2 i \, a - 1}} {\left(a^{3} + i \, a^{2} + a + i\right)} x^{2} \log\left(-\frac{{\left(2 \, a - i\right)} b^{3} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a - i\right)} b^{2} - {\left(a^{5} + i \, a^{4} + 2 \, a^{3} + 2 i \, a^{2} + a + i\right)} \sqrt{\frac{{\left(4 \, a^{2} - 4 i \, a - 1\right)} b^{4}}{a^{8} + 2 i \, a^{7} + 2 \, a^{6} + 6 i \, a^{5} + 6 i \, a^{3} - 2 \, a^{2} + 2 i \, a - 1}}}{{\left(2 \, a - i\right)} b^{2}}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left({\left(i \, a + 2\right)} b x - i \, a^{2} - i\right)}}{{\left(2 \, a^{3} + 2 i \, a^{2} + 2 \, a + 2 i\right)} x^{2}}"," ",0,"((I*a + 2)*b^2*x^2 + sqrt((4*a^2 - 4*I*a - 1)*b^4/(a^8 + 2*I*a^7 + 2*a^6 + 6*I*a^5 + 6*I*a^3 - 2*a^2 + 2*I*a - 1))*(a^3 + I*a^2 + a + I)*x^2*log(-((2*a - I)*b^3*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a - I)*b^2 + (a^5 + I*a^4 + 2*a^3 + 2*I*a^2 + a + I)*sqrt((4*a^2 - 4*I*a - 1)*b^4/(a^8 + 2*I*a^7 + 2*a^6 + 6*I*a^5 + 6*I*a^3 - 2*a^2 + 2*I*a - 1)))/((2*a - I)*b^2)) - sqrt((4*a^2 - 4*I*a - 1)*b^4/(a^8 + 2*I*a^7 + 2*a^6 + 6*I*a^5 + 6*I*a^3 - 2*a^2 + 2*I*a - 1))*(a^3 + I*a^2 + a + I)*x^2*log(-((2*a - I)*b^3*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a - I)*b^2 - (a^5 + I*a^4 + 2*a^3 + 2*I*a^2 + a + I)*sqrt((4*a^2 - 4*I*a - 1)*b^4/(a^8 + 2*I*a^7 + 2*a^6 + 6*I*a^5 + 6*I*a^3 - 2*a^2 + 2*I*a - 1)))/((2*a - I)*b^2)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*((I*a + 2)*b*x - I*a^2 - I))/((2*a^3 + 2*I*a^2 + 2*a + 2*I)*x^2)","B",0
170,1,700,0,0.567637," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x^4,x, algorithm=""fricas"")","\frac{{\left(-2 i \, a^{2} - 9 \, a + 4 i\right)} b^{3} x^{3} - \sqrt{\frac{{\left(4 \, a^{4} - 8 i \, a^{3} - 8 \, a^{2} + 4 i \, a + 1\right)} b^{6}}{a^{12} + 2 i \, a^{11} + 4 \, a^{10} + 10 i \, a^{9} + 5 \, a^{8} + 20 i \, a^{7} + 20 i \, a^{5} - 5 \, a^{4} + 10 i \, a^{3} - 4 \, a^{2} + 2 i \, a - 1}} {\left(3 \, a^{5} + 3 i \, a^{4} + 6 \, a^{3} + 6 i \, a^{2} + 3 \, a + 3 i\right)} x^{3} \log\left(-\frac{{\left(2 \, a^{2} - 2 i \, a - 1\right)} b^{4} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a^{2} - 2 i \, a - 1\right)} b^{3} + {\left(a^{7} + i \, a^{6} + 3 \, a^{5} + 3 i \, a^{4} + 3 \, a^{3} + 3 i \, a^{2} + a + i\right)} \sqrt{\frac{{\left(4 \, a^{4} - 8 i \, a^{3} - 8 \, a^{2} + 4 i \, a + 1\right)} b^{6}}{a^{12} + 2 i \, a^{11} + 4 \, a^{10} + 10 i \, a^{9} + 5 \, a^{8} + 20 i \, a^{7} + 20 i \, a^{5} - 5 \, a^{4} + 10 i \, a^{3} - 4 \, a^{2} + 2 i \, a - 1}}}{{\left(2 \, a^{2} - 2 i \, a - 1\right)} b^{3}}\right) + \sqrt{\frac{{\left(4 \, a^{4} - 8 i \, a^{3} - 8 \, a^{2} + 4 i \, a + 1\right)} b^{6}}{a^{12} + 2 i \, a^{11} + 4 \, a^{10} + 10 i \, a^{9} + 5 \, a^{8} + 20 i \, a^{7} + 20 i \, a^{5} - 5 \, a^{4} + 10 i \, a^{3} - 4 \, a^{2} + 2 i \, a - 1}} {\left(3 \, a^{5} + 3 i \, a^{4} + 6 \, a^{3} + 6 i \, a^{2} + 3 \, a + 3 i\right)} x^{3} \log\left(-\frac{{\left(2 \, a^{2} - 2 i \, a - 1\right)} b^{4} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a^{2} - 2 i \, a - 1\right)} b^{3} - {\left(a^{7} + i \, a^{6} + 3 \, a^{5} + 3 i \, a^{4} + 3 \, a^{3} + 3 i \, a^{2} + a + i\right)} \sqrt{\frac{{\left(4 \, a^{4} - 8 i \, a^{3} - 8 \, a^{2} + 4 i \, a + 1\right)} b^{6}}{a^{12} + 2 i \, a^{11} + 4 \, a^{10} + 10 i \, a^{9} + 5 \, a^{8} + 20 i \, a^{7} + 20 i \, a^{5} - 5 \, a^{4} + 10 i \, a^{3} - 4 \, a^{2} + 2 i \, a - 1}}}{{\left(2 \, a^{2} - 2 i \, a - 1\right)} b^{3}}\right) + {\left({\left(-2 i \, a^{2} - 9 \, a + 4 i\right)} b^{2} x^{2} - 2 i \, a^{4} + {\left(2 i \, a^{3} + 3 \, a^{2} + 2 i \, a + 3\right)} b x - 4 i \, a^{2} - 2 i\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(6 \, a^{5} + 6 i \, a^{4} + 12 \, a^{3} + 12 i \, a^{2} + 6 \, a + 6 i\right)} x^{3}}"," ",0,"((-2*I*a^2 - 9*a + 4*I)*b^3*x^3 - sqrt((4*a^4 - 8*I*a^3 - 8*a^2 + 4*I*a + 1)*b^6/(a^12 + 2*I*a^11 + 4*a^10 + 10*I*a^9 + 5*a^8 + 20*I*a^7 + 20*I*a^5 - 5*a^4 + 10*I*a^3 - 4*a^2 + 2*I*a - 1))*(3*a^5 + 3*I*a^4 + 6*a^3 + 6*I*a^2 + 3*a + 3*I)*x^3*log(-((2*a^2 - 2*I*a - 1)*b^4*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a^2 - 2*I*a - 1)*b^3 + (a^7 + I*a^6 + 3*a^5 + 3*I*a^4 + 3*a^3 + 3*I*a^2 + a + I)*sqrt((4*a^4 - 8*I*a^3 - 8*a^2 + 4*I*a + 1)*b^6/(a^12 + 2*I*a^11 + 4*a^10 + 10*I*a^9 + 5*a^8 + 20*I*a^7 + 20*I*a^5 - 5*a^4 + 10*I*a^3 - 4*a^2 + 2*I*a - 1)))/((2*a^2 - 2*I*a - 1)*b^3)) + sqrt((4*a^4 - 8*I*a^3 - 8*a^2 + 4*I*a + 1)*b^6/(a^12 + 2*I*a^11 + 4*a^10 + 10*I*a^9 + 5*a^8 + 20*I*a^7 + 20*I*a^5 - 5*a^4 + 10*I*a^3 - 4*a^2 + 2*I*a - 1))*(3*a^5 + 3*I*a^4 + 6*a^3 + 6*I*a^2 + 3*a + 3*I)*x^3*log(-((2*a^2 - 2*I*a - 1)*b^4*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a^2 - 2*I*a - 1)*b^3 - (a^7 + I*a^6 + 3*a^5 + 3*I*a^4 + 3*a^3 + 3*I*a^2 + a + I)*sqrt((4*a^4 - 8*I*a^3 - 8*a^2 + 4*I*a + 1)*b^6/(a^12 + 2*I*a^11 + 4*a^10 + 10*I*a^9 + 5*a^8 + 20*I*a^7 + 20*I*a^5 - 5*a^4 + 10*I*a^3 - 4*a^2 + 2*I*a - 1)))/((2*a^2 - 2*I*a - 1)*b^3)) + ((-2*I*a^2 - 9*a + 4*I)*b^2*x^2 - 2*I*a^4 + (2*I*a^3 + 3*a^2 + 2*I*a + 3)*b*x - 4*I*a^2 - 2*I)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((6*a^5 + 6*I*a^4 + 12*a^3 + 12*I*a^2 + 6*a + 6*I)*x^3)","B",0
171,1,105,0,0.478404," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x^4,x, algorithm=""fricas"")","-\frac{6 \, b^{5} x^{5} - 15 i \, b^{4} x^{4} + 20 \, {\left(i \, a - 1\right)} b^{3} x^{3} - {\left(30 i \, a^{2} - 60 \, a - 30 i\right)} b^{2} x^{2} - {\left(-60 i \, a^{3} + 180 \, a^{2} + 180 i \, a - 60\right)} b x - {\left(60 i \, a^{4} - 240 \, a^{3} - 360 i \, a^{2} + 240 \, a + 60 i\right)} \log\left(\frac{b x + a + i}{b}\right)}{30 \, b^{5}}"," ",0,"-1/30*(6*b^5*x^5 - 15*I*b^4*x^4 + 20*(I*a - 1)*b^3*x^3 - (30*I*a^2 - 60*a - 30*I)*b^2*x^2 - (-60*I*a^3 + 180*a^2 + 180*I*a - 60)*b*x - (60*I*a^4 - 240*a^3 - 360*I*a^2 + 240*a + 60*I)*log((b*x + a + I)/b))/b^5","A",0
172,1,77,0,0.472814," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x^3,x, algorithm=""fricas"")","-\frac{3 \, b^{4} x^{4} - 8 i \, b^{3} x^{3} + 12 \, {\left(i \, a - 1\right)} b^{2} x^{2} - {\left(24 i \, a^{2} - 48 \, a - 24 i\right)} b x - {\left(-24 i \, a^{3} + 72 \, a^{2} + 72 i \, a - 24\right)} \log\left(\frac{b x + a + i}{b}\right)}{12 \, b^{4}}"," ",0,"-1/12*(3*b^4*x^4 - 8*I*b^3*x^3 + 12*(I*a - 1)*b^2*x^2 - (24*I*a^2 - 48*a - 24*I)*b*x - (-24*I*a^3 + 72*a^2 + 72*I*a - 24)*log((b*x + a + I)/b))/b^4","A",0
173,1,53,0,0.413733," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x^2,x, algorithm=""fricas"")","-\frac{b^{3} x^{3} - 3 i \, b^{2} x^{2} + 6 \, {\left(i \, a - 1\right)} b x - {\left(6 i \, a^{2} - 12 \, a - 6 i\right)} \log\left(\frac{b x + a + i}{b}\right)}{3 \, b^{3}}"," ",0,"-1/3*(b^3*x^3 - 3*I*b^2*x^2 + 6*(I*a - 1)*b*x - (6*I*a^2 - 12*a - 6*I)*log((b*x + a + I)/b))/b^3","A",0
174,1,35,0,0.501522," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x,x, algorithm=""fricas"")","-\frac{b^{2} x^{2} - 4 i \, b x + 4 \, {\left(i \, a - 1\right)} \log\left(\frac{b x + a + i}{b}\right)}{2 \, b^{2}}"," ",0,"-1/2*(b^2*x^2 - 4*I*b*x + 4*(I*a - 1)*log((b*x + a + I)/b))/b^2","A",0
175,1,22,0,0.583695," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2),x, algorithm=""fricas"")","-\frac{b x - 2 i \, \log\left(\frac{b x + a + i}{b}\right)}{b}"," ",0,"-(b*x - 2*I*log((b*x + a + I)/b))/b","A",0
176,1,27,0,0.629481," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x,x, algorithm=""fricas"")","-\frac{{\left(a - i\right)} \log\left(x\right) + 2 i \, \log\left(\frac{b x + a + i}{b}\right)}{a + i}"," ",0,"-((a - I)*log(x) + 2*I*log((b*x + a + I)/b))/(a + I)","A",0
177,1,40,0,0.502133," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x^2,x, algorithm=""fricas"")","\frac{-2 i \, b x \log\left(x\right) + 2 i \, b x \log\left(\frac{b x + a + i}{b}\right) + a^{2} + 1}{{\left(a^{2} + 2 i \, a - 1\right)} x}"," ",0,"(-2*I*b*x*log(x) + 2*I*b*x*log((b*x + a + I)/b) + a^2 + 1)/((a^2 + 2*I*a - 1)*x)","A",0
178,1,70,0,0.428432," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x^3,x, algorithm=""fricas"")","\frac{4 i \, b^{2} x^{2} \log\left(x\right) - 4 i \, b^{2} x^{2} \log\left(\frac{b x + a + i}{b}\right) + a^{3} - 4 \, {\left(-i \, a + 1\right)} b x + i \, a^{2} + a + i}{{\left(2 \, a^{3} + 6 i \, a^{2} - 6 \, a - 2 i\right)} x^{2}}"," ",0,"(4*I*b^2*x^2*log(x) - 4*I*b^2*x^2*log((b*x + a + I)/b) + a^3 - 4*(-I*a + 1)*b*x + I*a^2 + a + I)/((2*a^3 + 6*I*a^2 - 6*a - 2*I)*x^2)","A",0
179,1,94,0,0.513103," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x^4,x, algorithm=""fricas"")","\frac{-6 i \, b^{3} x^{3} \log\left(x\right) + 6 i \, b^{3} x^{3} \log\left(\frac{b x + a + i}{b}\right) - 6 \, {\left(i \, a - 1\right)} b^{2} x^{2} + a^{4} + 2 i \, a^{3} + {\left(3 i \, a^{2} - 6 \, a - 3 i\right)} b x + 2 i \, a - 1}{{\left(3 \, a^{4} + 12 i \, a^{3} - 18 \, a^{2} - 12 i \, a + 3\right)} x^{3}}"," ",0,"(-6*I*b^3*x^3*log(x) + 6*I*b^3*x^3*log((b*x + a + I)/b) - 6*(I*a - 1)*b^2*x^2 + a^4 + 2*I*a^3 + (3*I*a^2 - 6*a - 3*I)*b*x + 2*I*a - 1)/((3*a^4 + 12*I*a^3 - 18*a^2 - 12*I*a + 3)*x^3)","A",0
180,1,263,0,0.496379," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x^4,x, algorithm=""fricas"")","\frac{-62 i \, a^{6} + 2687 \, a^{5} + 11575 i \, a^{4} - 20350 \, a^{3} + {\left(-62 i \, a^{5} + 2625 \, a^{4} + 8950 i \, a^{3} - 11400 \, a^{2} - 6340 i \, a + 1280\right)} b x - 17740 i \, a^{2} + {\left(960 \, a^{5} + 6720 i \, a^{4} - 16320 \, a^{3} + {\left(960 \, a^{4} + 5760 i \, a^{3} - 10560 \, a^{2} - 8160 i \, a + 2280\right)} b x - 18720 i \, a^{2} + 10440 \, a + 2280 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(-64 i \, b^{5} x^{5} - 176 \, b^{4} x^{4} + {\left(256 \, a + 272 i\right)} b^{3} x^{3} - 64 i \, a^{5} - 8 \, {\left(52 \, a^{2} + 118 i \, a - 61\right)} b^{2} x^{2} + 3344 \, a^{4} + 13552 i \, a^{3} + {\left(896 \, a^{3} + 3376 i \, a^{2} - 3664 \, a - 1304 i\right)} b x - 20792 \, a^{2} - 14104 i \, a + 3584\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 7620 \, a + 1280 i}{320 \, b^{6} x + {\left(320 \, a + 320 i\right)} b^{5}}"," ",0,"(-62*I*a^6 + 2687*a^5 + 11575*I*a^4 - 20350*a^3 + (-62*I*a^5 + 2625*a^4 + 8950*I*a^3 - 11400*a^2 - 6340*I*a + 1280)*b*x - 17740*I*a^2 + (960*a^5 + 6720*I*a^4 - 16320*a^3 + (960*a^4 + 5760*I*a^3 - 10560*a^2 - 8160*I*a + 2280)*b*x - 18720*I*a^2 + 10440*a + 2280*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-64*I*b^5*x^5 - 176*b^4*x^4 + (256*a + 272*I)*b^3*x^3 - 64*I*a^5 - 8*(52*a^2 + 118*I*a - 61)*b^2*x^2 + 3344*a^4 + 13552*I*a^3 + (896*a^3 + 3376*I*a^2 - 3664*a - 1304*I)*b*x - 20792*a^2 - 14104*I*a + 3584)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 7620*a + 1280*I)/(320*b^6*x + (320*a + 320*I)*b^5)","A",0
181,1,217,0,0.514977," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x^3,x, algorithm=""fricas"")","\frac{15 i \, a^{5} - 495 \, a^{4} - 1664 i \, a^{3} + {\left(15 i \, a^{4} - 480 \, a^{3} - 1184 i \, a^{2} + 968 \, a + 256 i\right)} b x + 2152 \, a^{2} - {\left(192 \, a^{4} + 1056 i \, a^{3} + {\left(192 \, a^{3} + 864 i \, a^{2} - 1056 \, a - 408 i\right)} b x - 1920 \, a^{2} - 1464 i \, a + 408\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(-16 i \, b^{4} x^{4} - 48 \, b^{3} x^{3} + {\left(80 \, a + 88 i\right)} b^{2} x^{2} + 16 i \, a^{4} - 624 \, a^{3} - 8 \, {\left(22 \, a^{2} + 54 i \, a - 29\right)} b x - 1864 i \, a^{2} + 1896 \, a + 640 i\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1224 i \, a - 256}{64 \, b^{5} x + {\left(64 \, a + 64 i\right)} b^{4}}"," ",0,"(15*I*a^5 - 495*a^4 - 1664*I*a^3 + (15*I*a^4 - 480*a^3 - 1184*I*a^2 + 968*a + 256*I)*b*x + 2152*a^2 - (192*a^4 + 1056*I*a^3 + (192*a^3 + 864*I*a^2 - 1056*a - 408*I)*b*x - 1920*a^2 - 1464*I*a + 408)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-16*I*b^4*x^4 - 48*b^3*x^3 + (80*a + 88*I)*b^2*x^2 + 16*I*a^4 - 624*a^3 - 8*(22*a^2 + 54*I*a - 29)*b*x - 1864*I*a^2 + 1896*a + 640*I)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1224*I*a - 256)/(64*b^5*x + (64*a + 64*I)*b^4)","A",0
182,1,174,0,0.459226," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x^2,x, algorithm=""fricas"")","\frac{-7 i \, a^{4} + 166 \, a^{3} + {\left(-7 i \, a^{3} + 159 \, a^{2} + 249 i \, a - 96\right)} b x + 408 i \, a^{2} + {\left(72 \, a^{3} + 12 \, {\left(6 \, a^{2} + 18 i \, a - 11\right)} b x + 288 i \, a^{2} - 348 \, a - 132 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(-8 i \, b^{3} x^{3} - 28 \, b^{2} x^{2} - 8 i \, a^{3} + {\left(64 \, a + 76 i\right)} b x + 212 \, a^{2} + 412 i \, a - 208\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} - 345 \, a - 96 i}{24 \, b^{4} x + {\left(24 \, a + 24 i\right)} b^{3}}"," ",0,"(-7*I*a^4 + 166*a^3 + (-7*I*a^3 + 159*a^2 + 249*I*a - 96)*b*x + 408*I*a^2 + (72*a^3 + 12*(6*a^2 + 18*I*a - 11)*b*x + 288*I*a^2 - 348*a - 132*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-8*I*b^3*x^3 - 28*b^2*x^2 - 8*I*a^3 + (64*a + 76*I)*b*x + 212*a^2 + 412*I*a - 208)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 345*a - 96*I)/(24*b^4*x + (24*a + 24*I)*b^3)","A",0
183,1,137,0,0.505504," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x,x, algorithm=""fricas"")","\frac{3 i \, a^{3} + {\left(3 i \, a^{2} - 44 \, a - 32 i\right)} b x - 47 \, a^{2} - {\left({\left(24 \, a + 36 i\right)} b x + 24 \, a^{2} + 60 i \, a - 36\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(-4 i \, b^{2} x^{2} + 4 i \, a^{2} - 20 \, b x - 60 \, a - 56 i\right)} - 76 i \, a + 32}{8 \, b^{3} x + {\left(8 \, a + 8 i\right)} b^{2}}"," ",0,"(3*I*a^3 + (3*I*a^2 - 44*a - 32*I)*b*x - 47*a^2 - ((24*a + 36*I)*b*x + 24*a^2 + 60*I*a - 36)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(-4*I*b^2*x^2 + 4*I*a^2 - 20*b*x - 60*a - 56*I) - 76*I*a + 32)/(8*b^3*x + (8*a + 8*I)*b^2)","A",0
184,1,102,0,0.520431," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(-i \, a + 8\right)} b x - i \, a^{2} + {\left(6 \, b x + 6 \, a + 6 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(-2 i \, b x - 2 i \, a + 10\right)} + 9 \, a + 8 i}{2 \, b^{2} x + {\left(2 \, a + 2 i\right)} b}"," ",0,"((-I*a + 8)*b*x - I*a^2 + (6*b*x + 6*a + 6*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(-2*I*b*x - 2*I*a + 10) + 9*a + 8*I)/(2*b^2*x + (2*a + 2*I)*b)","A",0
185,1,381,0,0.511857," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x,x, algorithm=""fricas"")","-\frac{{\left({\left(a + i\right)} b x + a^{2} + 2 i \, a - 1\right)} \sqrt{-\frac{4 \, a^{3} - 12 i \, a^{2} - 12 \, a + 4 i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}} \log\left(-\frac{{\left(2 \, a - 2 i\right)} b x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a - 2 i\right)} - {\left(i \, a^{2} - 2 \, a - i\right)} \sqrt{-\frac{4 \, a^{3} - 12 i \, a^{2} - 12 \, a + 4 i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}}}{2 \, a - 2 i}\right) - {\left({\left(a + i\right)} b x + a^{2} + 2 i \, a - 1\right)} \sqrt{-\frac{4 \, a^{3} - 12 i \, a^{2} - 12 \, a + 4 i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}} \log\left(-\frac{{\left(2 \, a - 2 i\right)} b x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a - 2 i\right)} - {\left(-i \, a^{2} + 2 \, a + i\right)} \sqrt{-\frac{4 \, a^{3} - 12 i \, a^{2} - 12 \, a + 4 i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}}}{2 \, a - 2 i}\right) + 8 \, b x + {\left(2 \, {\left(-i \, a + 1\right)} b x - 2 i \, a^{2} + 4 \, a + 2 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + 8 \, a + 8 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 8 i}{{\left(2 \, a + 2 i\right)} b x + 2 \, a^{2} + 4 i \, a - 2}"," ",0,"-(((a + I)*b*x + a^2 + 2*I*a - 1)*sqrt(-(4*a^3 - 12*I*a^2 - 12*a + 4*I)/(a^3 + 3*I*a^2 - 3*a - I))*log(-((2*a - 2*I)*b*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a - 2*I) - (I*a^2 - 2*a - I)*sqrt(-(4*a^3 - 12*I*a^2 - 12*a + 4*I)/(a^3 + 3*I*a^2 - 3*a - I)))/(2*a - 2*I)) - ((a + I)*b*x + a^2 + 2*I*a - 1)*sqrt(-(4*a^3 - 12*I*a^2 - 12*a + 4*I)/(a^3 + 3*I*a^2 - 3*a - I))*log(-((2*a - 2*I)*b*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a - 2*I) - (-I*a^2 + 2*a + I)*sqrt(-(4*a^3 - 12*I*a^2 - 12*a + 4*I)/(a^3 + 3*I*a^2 - 3*a - I)))/(2*a - 2*I)) + 8*b*x + (2*(-I*a + 1)*b*x - 2*I*a^2 + 4*a + 2*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + 8*a + 8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 8*I)/((2*a + 2*I)*b*x + 2*a^2 + 4*I*a - 2)","B",0
186,1,404,0,0.471387," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(-i \, a - 5\right)} b^{2} x^{2} - {\left(2 i \, a^{2} + 8 \, a + 10 i\right)} b x - {\left({\left(a^{2} + 2 i \, a - 1\right)} b x^{2} + {\left(a^{3} + 3 i \, a^{2} - 3 \, a - i\right)} x\right)} \sqrt{\frac{{\left(36 \, a - 36 i\right)} b^{2}}{a^{5} + 5 i \, a^{4} - 10 \, a^{3} - 10 i \, a^{2} + 5 \, a + i}} \log\left(-\frac{6 \, b^{2} x + {\left(a^{3} + 3 i \, a^{2} - 3 \, a - i\right)} \sqrt{\frac{{\left(36 \, a - 36 i\right)} b^{2}}{a^{5} + 5 i \, a^{4} - 10 \, a^{3} - 10 i \, a^{2} + 5 \, a + i}} - 6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b}{6 \, b}\right) + {\left({\left(a^{2} + 2 i \, a - 1\right)} b x^{2} + {\left(a^{3} + 3 i \, a^{2} - 3 \, a - i\right)} x\right)} \sqrt{\frac{{\left(36 \, a - 36 i\right)} b^{2}}{a^{5} + 5 i \, a^{4} - 10 \, a^{3} - 10 i \, a^{2} + 5 \, a + i}} \log\left(-\frac{6 \, b^{2} x - {\left(a^{3} + 3 i \, a^{2} - 3 \, a - i\right)} \sqrt{\frac{{\left(36 \, a - 36 i\right)} b^{2}}{a^{5} + 5 i \, a^{4} - 10 \, a^{3} - 10 i \, a^{2} + 5 \, a + i}} - 6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b}{6 \, b}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, {\left(-i \, a - 5\right)} b x - 2 i \, a^{2} - 2 i\right)}}{2 \, {\left(a^{2} + 2 i \, a - 1\right)} b x^{2} + {\left(2 \, a^{3} + 6 i \, a^{2} - 6 \, a - 2 i\right)} x}"," ",0,"-(2*(-I*a - 5)*b^2*x^2 - (2*I*a^2 + 8*a + 10*I)*b*x - ((a^2 + 2*I*a - 1)*b*x^2 + (a^3 + 3*I*a^2 - 3*a - I)*x)*sqrt((36*a - 36*I)*b^2/(a^5 + 5*I*a^4 - 10*a^3 - 10*I*a^2 + 5*a + I))*log(-1/6*(6*b^2*x + (a^3 + 3*I*a^2 - 3*a - I)*sqrt((36*a - 36*I)*b^2/(a^5 + 5*I*a^4 - 10*a^3 - 10*I*a^2 + 5*a + I)) - 6*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b)/b) + ((a^2 + 2*I*a - 1)*b*x^2 + (a^3 + 3*I*a^2 - 3*a - I)*x)*sqrt((36*a - 36*I)*b^2/(a^5 + 5*I*a^4 - 10*a^3 - 10*I*a^2 + 5*a + I))*log(-1/6*(6*b^2*x - (a^3 + 3*I*a^2 - 3*a - I)*sqrt((36*a - 36*I)*b^2/(a^5 + 5*I*a^4 - 10*a^3 - 10*I*a^2 + 5*a + I)) - 6*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b)/b) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*(-I*a - 5)*b*x - 2*I*a^2 - 2*I))/(2*(a^2 + 2*I*a - 1)*b*x^2 + (2*a^3 + 6*I*a^2 - 6*a - 2*I)*x)","B",0
187,1,580,0,0.558564," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{{\left(-i \, a - 14\right)} b^{3} x^{3} + {\left(-i \, a^{2} - 13 \, a - 14 i\right)} b^{2} x^{2} - 3 \, {\left({\left(a^{3} + 3 i \, a^{2} - 3 \, a - i\right)} b x^{3} + {\left(a^{4} + 4 i \, a^{3} - 6 \, a^{2} - 4 i \, a + 1\right)} x^{2}\right)} \sqrt{\frac{{\left(4 \, a^{2} - 12 i \, a - 9\right)} b^{4}}{a^{8} + 6 i \, a^{7} - 14 \, a^{6} - 14 i \, a^{5} - 14 i \, a^{3} + 14 \, a^{2} + 6 i \, a - 1}} \log\left(-\frac{{\left(6 \, a - 9 i\right)} b^{3} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(6 \, a - 9 i\right)} b^{2} + 3 \, {\left(a^{5} + 3 i \, a^{4} - 2 \, a^{3} + 2 i \, a^{2} - 3 \, a - i\right)} \sqrt{\frac{{\left(4 \, a^{2} - 12 i \, a - 9\right)} b^{4}}{a^{8} + 6 i \, a^{7} - 14 \, a^{6} - 14 i \, a^{5} - 14 i \, a^{3} + 14 \, a^{2} + 6 i \, a - 1}}}{{\left(6 \, a - 9 i\right)} b^{2}}\right) + 3 \, {\left({\left(a^{3} + 3 i \, a^{2} - 3 \, a - i\right)} b x^{3} + {\left(a^{4} + 4 i \, a^{3} - 6 \, a^{2} - 4 i \, a + 1\right)} x^{2}\right)} \sqrt{\frac{{\left(4 \, a^{2} - 12 i \, a - 9\right)} b^{4}}{a^{8} + 6 i \, a^{7} - 14 \, a^{6} - 14 i \, a^{5} - 14 i \, a^{3} + 14 \, a^{2} + 6 i \, a - 1}} \log\left(-\frac{{\left(6 \, a - 9 i\right)} b^{3} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(6 \, a - 9 i\right)} b^{2} - 3 \, {\left(a^{5} + 3 i \, a^{4} - 2 \, a^{3} + 2 i \, a^{2} - 3 \, a - i\right)} \sqrt{\frac{{\left(4 \, a^{2} - 12 i \, a - 9\right)} b^{4}}{a^{8} + 6 i \, a^{7} - 14 \, a^{6} - 14 i \, a^{5} - 14 i \, a^{3} + 14 \, a^{2} + 6 i \, a - 1}}}{{\left(6 \, a - 9 i\right)} b^{2}}\right) + {\left({\left(-i \, a - 14\right)} b^{2} x^{2} + i \, a^{3} - {\left(5 \, a + 5 i\right)} b x - a^{2} + i \, a - 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(2 \, a^{3} + 6 i \, a^{2} - 6 \, a - 2 i\right)} b x^{3} + {\left(2 \, a^{4} + 8 i \, a^{3} - 12 \, a^{2} - 8 i \, a + 2\right)} x^{2}}"," ",0,"((-I*a - 14)*b^3*x^3 + (-I*a^2 - 13*a - 14*I)*b^2*x^2 - 3*((a^3 + 3*I*a^2 - 3*a - I)*b*x^3 + (a^4 + 4*I*a^3 - 6*a^2 - 4*I*a + 1)*x^2)*sqrt((4*a^2 - 12*I*a - 9)*b^4/(a^8 + 6*I*a^7 - 14*a^6 - 14*I*a^5 - 14*I*a^3 + 14*a^2 + 6*I*a - 1))*log(-((6*a - 9*I)*b^3*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(6*a - 9*I)*b^2 + 3*(a^5 + 3*I*a^4 - 2*a^3 + 2*I*a^2 - 3*a - I)*sqrt((4*a^2 - 12*I*a - 9)*b^4/(a^8 + 6*I*a^7 - 14*a^6 - 14*I*a^5 - 14*I*a^3 + 14*a^2 + 6*I*a - 1)))/((6*a - 9*I)*b^2)) + 3*((a^3 + 3*I*a^2 - 3*a - I)*b*x^3 + (a^4 + 4*I*a^3 - 6*a^2 - 4*I*a + 1)*x^2)*sqrt((4*a^2 - 12*I*a - 9)*b^4/(a^8 + 6*I*a^7 - 14*a^6 - 14*I*a^5 - 14*I*a^3 + 14*a^2 + 6*I*a - 1))*log(-((6*a - 9*I)*b^3*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(6*a - 9*I)*b^2 - 3*(a^5 + 3*I*a^4 - 2*a^3 + 2*I*a^2 - 3*a - I)*sqrt((4*a^2 - 12*I*a - 9)*b^4/(a^8 + 6*I*a^7 - 14*a^6 - 14*I*a^5 - 14*I*a^3 + 14*a^2 + 6*I*a - 1)))/((6*a - 9*I)*b^2)) + ((-I*a - 14)*b^2*x^2 + I*a^3 - (5*a + 5*I)*b*x - a^2 + I*a - 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((2*a^3 + 6*I*a^2 - 6*a - 2*I)*b*x^3 + (2*a^4 + 8*I*a^3 - 12*a^2 - 8*I*a + 2)*x^2)","B",0
188,1,853,0,0.546209," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x^4,x, algorithm=""fricas"")","\frac{{\left(2 i \, a^{2} + 51 \, a - 52 i\right)} b^{4} x^{4} + {\left(2 i \, a^{3} + 49 \, a^{2} - i \, a + 52\right)} b^{3} x^{3} + \sqrt{\frac{{\left(36 \, a^{4} - 216 i \, a^{3} - 456 \, a^{2} + 396 i \, a + 121\right)} b^{6}}{a^{12} + 6 i \, a^{11} - 12 \, a^{10} - 2 i \, a^{9} - 27 \, a^{8} - 36 i \, a^{7} - 36 i \, a^{5} + 27 \, a^{4} - 2 i \, a^{3} + 12 \, a^{2} + 6 i \, a - 1}} {\left({\left(3 \, a^{5} + 9 i \, a^{4} - 6 \, a^{3} + 6 i \, a^{2} - 9 \, a - 3 i\right)} b x^{4} + {\left(3 \, a^{6} + 12 i \, a^{5} - 15 \, a^{4} - 15 \, a^{2} - 12 i \, a + 3\right)} x^{3}\right)} \log\left(-\frac{{\left(6 \, a^{2} - 18 i \, a - 11\right)} b^{4} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(6 \, a^{2} - 18 i \, a - 11\right)} b^{3} + {\left(a^{7} + 3 i \, a^{6} - a^{5} + 5 i \, a^{4} - 5 \, a^{3} + i \, a^{2} - 3 \, a - i\right)} \sqrt{\frac{{\left(36 \, a^{4} - 216 i \, a^{3} - 456 \, a^{2} + 396 i \, a + 121\right)} b^{6}}{a^{12} + 6 i \, a^{11} - 12 \, a^{10} - 2 i \, a^{9} - 27 \, a^{8} - 36 i \, a^{7} - 36 i \, a^{5} + 27 \, a^{4} - 2 i \, a^{3} + 12 \, a^{2} + 6 i \, a - 1}}}{{\left(6 \, a^{2} - 18 i \, a - 11\right)} b^{3}}\right) - \sqrt{\frac{{\left(36 \, a^{4} - 216 i \, a^{3} - 456 \, a^{2} + 396 i \, a + 121\right)} b^{6}}{a^{12} + 6 i \, a^{11} - 12 \, a^{10} - 2 i \, a^{9} - 27 \, a^{8} - 36 i \, a^{7} - 36 i \, a^{5} + 27 \, a^{4} - 2 i \, a^{3} + 12 \, a^{2} + 6 i \, a - 1}} {\left({\left(3 \, a^{5} + 9 i \, a^{4} - 6 \, a^{3} + 6 i \, a^{2} - 9 \, a - 3 i\right)} b x^{4} + {\left(3 \, a^{6} + 12 i \, a^{5} - 15 \, a^{4} - 15 \, a^{2} - 12 i \, a + 3\right)} x^{3}\right)} \log\left(-\frac{{\left(6 \, a^{2} - 18 i \, a - 11\right)} b^{4} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(6 \, a^{2} - 18 i \, a - 11\right)} b^{3} - {\left(a^{7} + 3 i \, a^{6} - a^{5} + 5 i \, a^{4} - 5 \, a^{3} + i \, a^{2} - 3 \, a - i\right)} \sqrt{\frac{{\left(36 \, a^{4} - 216 i \, a^{3} - 456 \, a^{2} + 396 i \, a + 121\right)} b^{6}}{a^{12} + 6 i \, a^{11} - 12 \, a^{10} - 2 i \, a^{9} - 27 \, a^{8} - 36 i \, a^{7} - 36 i \, a^{5} + 27 \, a^{4} - 2 i \, a^{3} + 12 \, a^{2} + 6 i \, a - 1}}}{{\left(6 \, a^{2} - 18 i \, a - 11\right)} b^{3}}\right) + {\left({\left(2 i \, a^{2} + 51 \, a - 52 i\right)} b^{3} x^{3} + 2 i \, a^{5} + {\left(16 \, a^{2} - 3 i \, a + 19\right)} b^{2} x^{2} - 2 \, a^{4} + 4 i \, a^{3} - {\left(7 \, a^{3} + 7 i \, a^{2} + 7 \, a + 7 i\right)} b x - 4 \, a^{2} + 2 i \, a - 2\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(6 \, a^{5} + 18 i \, a^{4} - 12 \, a^{3} + 12 i \, a^{2} - 18 \, a - 6 i\right)} b x^{4} + {\left(6 \, a^{6} + 24 i \, a^{5} - 30 \, a^{4} - 30 \, a^{2} - 24 i \, a + 6\right)} x^{3}}"," ",0,"((2*I*a^2 + 51*a - 52*I)*b^4*x^4 + (2*I*a^3 + 49*a^2 - I*a + 52)*b^3*x^3 + sqrt((36*a^4 - 216*I*a^3 - 456*a^2 + 396*I*a + 121)*b^6/(a^12 + 6*I*a^11 - 12*a^10 - 2*I*a^9 - 27*a^8 - 36*I*a^7 - 36*I*a^5 + 27*a^4 - 2*I*a^3 + 12*a^2 + 6*I*a - 1))*((3*a^5 + 9*I*a^4 - 6*a^3 + 6*I*a^2 - 9*a - 3*I)*b*x^4 + (3*a^6 + 12*I*a^5 - 15*a^4 - 15*a^2 - 12*I*a + 3)*x^3)*log(-((6*a^2 - 18*I*a - 11)*b^4*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(6*a^2 - 18*I*a - 11)*b^3 + (a^7 + 3*I*a^6 - a^5 + 5*I*a^4 - 5*a^3 + I*a^2 - 3*a - I)*sqrt((36*a^4 - 216*I*a^3 - 456*a^2 + 396*I*a + 121)*b^6/(a^12 + 6*I*a^11 - 12*a^10 - 2*I*a^9 - 27*a^8 - 36*I*a^7 - 36*I*a^5 + 27*a^4 - 2*I*a^3 + 12*a^2 + 6*I*a - 1)))/((6*a^2 - 18*I*a - 11)*b^3)) - sqrt((36*a^4 - 216*I*a^3 - 456*a^2 + 396*I*a + 121)*b^6/(a^12 + 6*I*a^11 - 12*a^10 - 2*I*a^9 - 27*a^8 - 36*I*a^7 - 36*I*a^5 + 27*a^4 - 2*I*a^3 + 12*a^2 + 6*I*a - 1))*((3*a^5 + 9*I*a^4 - 6*a^3 + 6*I*a^2 - 9*a - 3*I)*b*x^4 + (3*a^6 + 12*I*a^5 - 15*a^4 - 15*a^2 - 12*I*a + 3)*x^3)*log(-((6*a^2 - 18*I*a - 11)*b^4*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(6*a^2 - 18*I*a - 11)*b^3 - (a^7 + 3*I*a^6 - a^5 + 5*I*a^4 - 5*a^3 + I*a^2 - 3*a - I)*sqrt((36*a^4 - 216*I*a^3 - 456*a^2 + 396*I*a + 121)*b^6/(a^12 + 6*I*a^11 - 12*a^10 - 2*I*a^9 - 27*a^8 - 36*I*a^7 - 36*I*a^5 + 27*a^4 - 2*I*a^3 + 12*a^2 + 6*I*a - 1)))/((6*a^2 - 18*I*a - 11)*b^3)) + ((2*I*a^2 + 51*a - 52*I)*b^3*x^3 + 2*I*a^5 + (16*a^2 - 3*I*a + 19)*b^2*x^2 - 2*a^4 + 4*I*a^3 - (7*a^3 + 7*I*a^2 + 7*a + 7*I)*b*x - 4*a^2 + 2*I*a - 2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((6*a^5 + 18*I*a^4 - 12*a^3 + 12*I*a^2 - 18*a - 6*I)*b*x^4 + (6*a^6 + 24*I*a^5 - 30*a^4 - 30*a^2 - 24*I*a + 6)*x^3)","B",0
189,1,175,0,0.468138," ","integrate(x^4/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{-186 i \, a^{5} - 1345 \, a^{4} + 1730 i \, a^{3} + 1320 \, a^{2} - {\left(960 \, a^{4} - 1920 i \, a^{3} - 2880 \, a^{2} + 1440 i \, a + 360\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(-192 i \, b^{4} x^{4} - 48 \, {\left(-4 i \, a - 5\right)} b^{3} x^{3} + {\left(-192 i \, a^{2} - 560 \, a + 256 i\right)} b^{2} x^{2} - 192 i \, a^{4} - 2000 \, a^{3} + {\left(192 i \, a^{3} + 1040 \, a^{2} - 928 i \, a - 360\right)} b x + 2656 i \, a^{2} + 2200 \, a - 512 i\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} - 300 i \, a}{960 \, b^{5}}"," ",0,"1/960*(-186*I*a^5 - 1345*a^4 + 1730*I*a^3 + 1320*a^2 - (960*a^4 - 1920*I*a^3 - 2880*a^2 + 1440*I*a + 360)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-192*I*b^4*x^4 - 48*(-4*I*a - 5)*b^3*x^3 + (-192*I*a^2 - 560*a + 256*I)*b^2*x^2 - 192*I*a^4 - 2000*a^3 + (192*I*a^3 + 1040*a^2 - 928*I*a - 360)*b*x + 2656*I*a^2 + 2200*a - 512*I)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 300*I*a)/b^5","A",0
190,1,137,0,0.515320," ","integrate(x^3/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{45 i \, a^{4} + 224 \, a^{3} - 192 i \, a^{2} + {\left(192 \, a^{3} - 288 i \, a^{2} - 288 \, a + 72 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(-48 i \, b^{3} x^{3} - 16 \, {\left(-3 i \, a - 4\right)} b^{2} x^{2} + 48 i \, a^{3} + {\left(-48 i \, a^{2} - 160 \, a + 72 i\right)} b x + 352 \, a^{2} - 312 i \, a - 128\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} - 72 \, a}{192 \, b^{4}}"," ",0,"1/192*(45*I*a^4 + 224*a^3 - 192*I*a^2 + (192*a^3 - 288*I*a^2 - 288*a + 72*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-48*I*b^3*x^3 - 16*(-3*I*a - 4)*b^2*x^2 + 48*I*a^3 + (-48*I*a^2 - 160*a + 72*I)*b*x + 352*a^2 - 312*I*a - 128)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 72*a)/b^4","A",0
191,1,106,0,0.446515," ","integrate(x^2/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{-7 i \, a^{3} - 21 \, a^{2} - 12 \, {\left(2 \, a^{2} - 2 i \, a - 1\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(-8 i \, b^{2} x^{2} - 4 \, {\left(-2 i \, a - 3\right)} b x - 8 i \, a^{2} - 36 \, a + 16 i\right)} + 9 i \, a}{24 \, b^{3}}"," ",0,"1/24*(-7*I*a^3 - 21*a^2 - 12*(2*a^2 - 2*I*a - 1)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(-8*I*b^2*x^2 - 4*(-2*I*a - 3)*b*x - 8*I*a^2 - 36*a + 16*I) + 9*I*a)/b^3","A",0
192,1,77,0,0.469081," ","integrate(x/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{3 i \, a^{2} + {\left(8 \, a - 4 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(-4 i \, b x + 4 i \, a + 8\right)} + 4 \, a}{8 \, b^{2}}"," ",0,"1/8*(3*I*a^2 + (8*a - 4*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(-4*I*b*x + 4*I*a + 8) + 4*a)/b^2","A",0
193,1,60,0,0.550736," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{-i \, a - 2 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} - 2 \, \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}{2 \, b}"," ",0,"1/2*(-I*a - 2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)))/b","A",0
194,1,155,0,0.471032," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x,x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-\frac{4 \, a + 4 i}{a - i}} \log\left(-b x + \frac{1}{2} \, {\left(i \, a + 1\right)} \sqrt{-\frac{4 \, a + 4 i}{a - i}} + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + \frac{1}{2} \, \sqrt{-\frac{4 \, a + 4 i}{a - i}} \log\left(-b x + \frac{1}{2} \, {\left(-i \, a - 1\right)} \sqrt{-\frac{4 \, a + 4 i}{a - i}} + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + i \, \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)"," ",0,"-1/2*sqrt(-(4*a + 4*I)/(a - I))*log(-b*x + 1/2*(I*a + 1)*sqrt(-(4*a + 4*I)/(a - I)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + 1/2*sqrt(-(4*a + 4*I)/(a - I))*log(-b*x + 1/2*(-I*a - 1)*sqrt(-(4*a + 4*I)/(a - I)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + I*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))","B",0
195,1,227,0,0.489265," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a - i\right)} \sqrt{\frac{b^{2}}{a^{4} - 2 i \, a^{3} - 2 i \, a - 1}} x \log\left(-\frac{b^{2} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b + {\left(a^{3} - i \, a^{2} + a - i\right)} \sqrt{\frac{b^{2}}{a^{4} - 2 i \, a^{3} - 2 i \, a - 1}}}{b}\right) - 2 \, {\left(a - i\right)} \sqrt{\frac{b^{2}}{a^{4} - 2 i \, a^{3} - 2 i \, a - 1}} x \log\left(-\frac{b^{2} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b - {\left(a^{3} - i \, a^{2} + a - i\right)} \sqrt{\frac{b^{2}}{a^{4} - 2 i \, a^{3} - 2 i \, a - 1}}}{b}\right) - 2 i \, b x - 2 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(2 \, a - 2 i\right)} x}"," ",0,"-(2*(a - I)*sqrt(b^2/(a^4 - 2*I*a^3 - 2*I*a - 1))*x*log(-(b^2*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b + (a^3 - I*a^2 + a - I)*sqrt(b^2/(a^4 - 2*I*a^3 - 2*I*a - 1)))/b) - 2*(a - I)*sqrt(b^2/(a^4 - 2*I*a^3 - 2*I*a - 1))*x*log(-(b^2*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b - (a^3 - I*a^2 + a - I)*sqrt(b^2/(a^4 - 2*I*a^3 - 2*I*a - 1)))/b) - 2*I*b*x - 2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((2*a - 2*I)*x)","B",0
196,1,455,0,0.521739," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{{\left(-i \, a + 2\right)} b^{2} x^{2} + \sqrt{\frac{{\left(4 \, a^{2} + 4 i \, a - 1\right)} b^{4}}{a^{8} - 2 i \, a^{7} + 2 \, a^{6} - 6 i \, a^{5} - 6 i \, a^{3} - 2 \, a^{2} - 2 i \, a - 1}} {\left(a^{3} - i \, a^{2} + a - i\right)} x^{2} \log\left(-\frac{{\left(2 \, a + i\right)} b^{3} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a + i\right)} b^{2} + {\left(a^{5} - i \, a^{4} + 2 \, a^{3} - 2 i \, a^{2} + a - i\right)} \sqrt{\frac{{\left(4 \, a^{2} + 4 i \, a - 1\right)} b^{4}}{a^{8} - 2 i \, a^{7} + 2 \, a^{6} - 6 i \, a^{5} - 6 i \, a^{3} - 2 \, a^{2} - 2 i \, a - 1}}}{{\left(2 \, a + i\right)} b^{2}}\right) - \sqrt{\frac{{\left(4 \, a^{2} + 4 i \, a - 1\right)} b^{4}}{a^{8} - 2 i \, a^{7} + 2 \, a^{6} - 6 i \, a^{5} - 6 i \, a^{3} - 2 \, a^{2} - 2 i \, a - 1}} {\left(a^{3} - i \, a^{2} + a - i\right)} x^{2} \log\left(-\frac{{\left(2 \, a + i\right)} b^{3} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a + i\right)} b^{2} - {\left(a^{5} - i \, a^{4} + 2 \, a^{3} - 2 i \, a^{2} + a - i\right)} \sqrt{\frac{{\left(4 \, a^{2} + 4 i \, a - 1\right)} b^{4}}{a^{8} - 2 i \, a^{7} + 2 \, a^{6} - 6 i \, a^{5} - 6 i \, a^{3} - 2 \, a^{2} - 2 i \, a - 1}}}{{\left(2 \, a + i\right)} b^{2}}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left({\left(-i \, a + 2\right)} b x + i \, a^{2} + i\right)}}{{\left(2 \, a^{3} - 2 i \, a^{2} + 2 \, a - 2 i\right)} x^{2}}"," ",0,"((-I*a + 2)*b^2*x^2 + sqrt((4*a^2 + 4*I*a - 1)*b^4/(a^8 - 2*I*a^7 + 2*a^6 - 6*I*a^5 - 6*I*a^3 - 2*a^2 - 2*I*a - 1))*(a^3 - I*a^2 + a - I)*x^2*log(-((2*a + I)*b^3*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a + I)*b^2 + (a^5 - I*a^4 + 2*a^3 - 2*I*a^2 + a - I)*sqrt((4*a^2 + 4*I*a - 1)*b^4/(a^8 - 2*I*a^7 + 2*a^6 - 6*I*a^5 - 6*I*a^3 - 2*a^2 - 2*I*a - 1)))/((2*a + I)*b^2)) - sqrt((4*a^2 + 4*I*a - 1)*b^4/(a^8 - 2*I*a^7 + 2*a^6 - 6*I*a^5 - 6*I*a^3 - 2*a^2 - 2*I*a - 1))*(a^3 - I*a^2 + a - I)*x^2*log(-((2*a + I)*b^3*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a + I)*b^2 - (a^5 - I*a^4 + 2*a^3 - 2*I*a^2 + a - I)*sqrt((4*a^2 + 4*I*a - 1)*b^4/(a^8 - 2*I*a^7 + 2*a^6 - 6*I*a^5 - 6*I*a^3 - 2*a^2 - 2*I*a - 1)))/((2*a + I)*b^2)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*((-I*a + 2)*b*x + I*a^2 + I))/((2*a^3 - 2*I*a^2 + 2*a - 2*I)*x^2)","B",0
197,1,700,0,0.520577," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x^4,x, algorithm=""fricas"")","\frac{{\left(2 i \, a^{2} - 9 \, a - 4 i\right)} b^{3} x^{3} - \sqrt{\frac{{\left(4 \, a^{4} + 8 i \, a^{3} - 8 \, a^{2} - 4 i \, a + 1\right)} b^{6}}{a^{12} - 2 i \, a^{11} + 4 \, a^{10} - 10 i \, a^{9} + 5 \, a^{8} - 20 i \, a^{7} - 20 i \, a^{5} - 5 \, a^{4} - 10 i \, a^{3} - 4 \, a^{2} - 2 i \, a - 1}} {\left(3 \, a^{5} - 3 i \, a^{4} + 6 \, a^{3} - 6 i \, a^{2} + 3 \, a - 3 i\right)} x^{3} \log\left(-\frac{{\left(2 \, a^{2} + 2 i \, a - 1\right)} b^{4} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a^{2} + 2 i \, a - 1\right)} b^{3} + {\left(a^{7} - i \, a^{6} + 3 \, a^{5} - 3 i \, a^{4} + 3 \, a^{3} - 3 i \, a^{2} + a - i\right)} \sqrt{\frac{{\left(4 \, a^{4} + 8 i \, a^{3} - 8 \, a^{2} - 4 i \, a + 1\right)} b^{6}}{a^{12} - 2 i \, a^{11} + 4 \, a^{10} - 10 i \, a^{9} + 5 \, a^{8} - 20 i \, a^{7} - 20 i \, a^{5} - 5 \, a^{4} - 10 i \, a^{3} - 4 \, a^{2} - 2 i \, a - 1}}}{{\left(2 \, a^{2} + 2 i \, a - 1\right)} b^{3}}\right) + \sqrt{\frac{{\left(4 \, a^{4} + 8 i \, a^{3} - 8 \, a^{2} - 4 i \, a + 1\right)} b^{6}}{a^{12} - 2 i \, a^{11} + 4 \, a^{10} - 10 i \, a^{9} + 5 \, a^{8} - 20 i \, a^{7} - 20 i \, a^{5} - 5 \, a^{4} - 10 i \, a^{3} - 4 \, a^{2} - 2 i \, a - 1}} {\left(3 \, a^{5} - 3 i \, a^{4} + 6 \, a^{3} - 6 i \, a^{2} + 3 \, a - 3 i\right)} x^{3} \log\left(-\frac{{\left(2 \, a^{2} + 2 i \, a - 1\right)} b^{4} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a^{2} + 2 i \, a - 1\right)} b^{3} - {\left(a^{7} - i \, a^{6} + 3 \, a^{5} - 3 i \, a^{4} + 3 \, a^{3} - 3 i \, a^{2} + a - i\right)} \sqrt{\frac{{\left(4 \, a^{4} + 8 i \, a^{3} - 8 \, a^{2} - 4 i \, a + 1\right)} b^{6}}{a^{12} - 2 i \, a^{11} + 4 \, a^{10} - 10 i \, a^{9} + 5 \, a^{8} - 20 i \, a^{7} - 20 i \, a^{5} - 5 \, a^{4} - 10 i \, a^{3} - 4 \, a^{2} - 2 i \, a - 1}}}{{\left(2 \, a^{2} + 2 i \, a - 1\right)} b^{3}}\right) + {\left({\left(2 i \, a^{2} - 9 \, a - 4 i\right)} b^{2} x^{2} + 2 i \, a^{4} + {\left(-2 i \, a^{3} + 3 \, a^{2} - 2 i \, a + 3\right)} b x + 4 i \, a^{2} + 2 i\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(6 \, a^{5} - 6 i \, a^{4} + 12 \, a^{3} - 12 i \, a^{2} + 6 \, a - 6 i\right)} x^{3}}"," ",0,"((2*I*a^2 - 9*a - 4*I)*b^3*x^3 - sqrt((4*a^4 + 8*I*a^3 - 8*a^2 - 4*I*a + 1)*b^6/(a^12 - 2*I*a^11 + 4*a^10 - 10*I*a^9 + 5*a^8 - 20*I*a^7 - 20*I*a^5 - 5*a^4 - 10*I*a^3 - 4*a^2 - 2*I*a - 1))*(3*a^5 - 3*I*a^4 + 6*a^3 - 6*I*a^2 + 3*a - 3*I)*x^3*log(-((2*a^2 + 2*I*a - 1)*b^4*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a^2 + 2*I*a - 1)*b^3 + (a^7 - I*a^6 + 3*a^5 - 3*I*a^4 + 3*a^3 - 3*I*a^2 + a - I)*sqrt((4*a^4 + 8*I*a^3 - 8*a^2 - 4*I*a + 1)*b^6/(a^12 - 2*I*a^11 + 4*a^10 - 10*I*a^9 + 5*a^8 - 20*I*a^7 - 20*I*a^5 - 5*a^4 - 10*I*a^3 - 4*a^2 - 2*I*a - 1)))/((2*a^2 + 2*I*a - 1)*b^3)) + sqrt((4*a^4 + 8*I*a^3 - 8*a^2 - 4*I*a + 1)*b^6/(a^12 - 2*I*a^11 + 4*a^10 - 10*I*a^9 + 5*a^8 - 20*I*a^7 - 20*I*a^5 - 5*a^4 - 10*I*a^3 - 4*a^2 - 2*I*a - 1))*(3*a^5 - 3*I*a^4 + 6*a^3 - 6*I*a^2 + 3*a - 3*I)*x^3*log(-((2*a^2 + 2*I*a - 1)*b^4*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a^2 + 2*I*a - 1)*b^3 - (a^7 - I*a^6 + 3*a^5 - 3*I*a^4 + 3*a^3 - 3*I*a^2 + a - I)*sqrt((4*a^4 + 8*I*a^3 - 8*a^2 - 4*I*a + 1)*b^6/(a^12 - 2*I*a^11 + 4*a^10 - 10*I*a^9 + 5*a^8 - 20*I*a^7 - 20*I*a^5 - 5*a^4 - 10*I*a^3 - 4*a^2 - 2*I*a - 1)))/((2*a^2 + 2*I*a - 1)*b^3)) + ((2*I*a^2 - 9*a - 4*I)*b^2*x^2 + 2*I*a^4 + (-2*I*a^3 + 3*a^2 - 2*I*a + 3)*b*x + 4*I*a^2 + 2*I)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((6*a^5 - 6*I*a^4 + 12*a^3 - 12*I*a^2 + 6*a - 6*I)*x^3)","B",0
198,1,105,0,0.461812," ","integrate(x^4/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x, algorithm=""fricas"")","-\frac{6 \, b^{5} x^{5} + 15 i \, b^{4} x^{4} + 20 \, {\left(-i \, a - 1\right)} b^{3} x^{3} - {\left(-30 i \, a^{2} - 60 \, a + 30 i\right)} b^{2} x^{2} - {\left(60 i \, a^{3} + 180 \, a^{2} - 180 i \, a - 60\right)} b x - {\left(-60 i \, a^{4} - 240 \, a^{3} + 360 i \, a^{2} + 240 \, a - 60 i\right)} \log\left(\frac{b x + a - i}{b}\right)}{30 \, b^{5}}"," ",0,"-1/30*(6*b^5*x^5 + 15*I*b^4*x^4 + 20*(-I*a - 1)*b^3*x^3 - (-30*I*a^2 - 60*a + 30*I)*b^2*x^2 - (60*I*a^3 + 180*a^2 - 180*I*a - 60)*b*x - (-60*I*a^4 - 240*a^3 + 360*I*a^2 + 240*a - 60*I)*log((b*x + a - I)/b))/b^5","A",0
199,1,77,0,0.438915," ","integrate(x^3/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x, algorithm=""fricas"")","-\frac{3 \, b^{4} x^{4} + 8 i \, b^{3} x^{3} + 12 \, {\left(-i \, a - 1\right)} b^{2} x^{2} - {\left(-24 i \, a^{2} - 48 \, a + 24 i\right)} b x - {\left(24 i \, a^{3} + 72 \, a^{2} - 72 i \, a - 24\right)} \log\left(\frac{b x + a - i}{b}\right)}{12 \, b^{4}}"," ",0,"-1/12*(3*b^4*x^4 + 8*I*b^3*x^3 + 12*(-I*a - 1)*b^2*x^2 - (-24*I*a^2 - 48*a + 24*I)*b*x - (24*I*a^3 + 72*a^2 - 72*I*a - 24)*log((b*x + a - I)/b))/b^4","A",0
200,1,53,0,0.527178," ","integrate(x^2/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x, algorithm=""fricas"")","-\frac{b^{3} x^{3} + 3 i \, b^{2} x^{2} + 6 \, {\left(-i \, a - 1\right)} b x - {\left(-6 i \, a^{2} - 12 \, a + 6 i\right)} \log\left(\frac{b x + a - i}{b}\right)}{3 \, b^{3}}"," ",0,"-1/3*(b^3*x^3 + 3*I*b^2*x^2 + 6*(-I*a - 1)*b*x - (-6*I*a^2 - 12*a + 6*I)*log((b*x + a - I)/b))/b^3","A",0
201,1,35,0,0.441758," ","integrate(x/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x, algorithm=""fricas"")","-\frac{b^{2} x^{2} + 4 i \, b x + 4 \, {\left(-i \, a - 1\right)} \log\left(\frac{b x + a - i}{b}\right)}{2 \, b^{2}}"," ",0,"-1/2*(b^2*x^2 + 4*I*b*x + 4*(-I*a - 1)*log((b*x + a - I)/b))/b^2","A",0
202,1,22,0,0.507815," ","integrate(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x, algorithm=""fricas"")","-\frac{b x + 2 i \, \log\left(\frac{b x + a - i}{b}\right)}{b}"," ",0,"-(b*x + 2*I*log((b*x + a - I)/b))/b","A",0
203,1,27,0,0.443083," ","integrate(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x,x, algorithm=""fricas"")","-\frac{{\left(a + i\right)} \log\left(x\right) - 2 i \, \log\left(\frac{b x + a - i}{b}\right)}{a - i}"," ",0,"-((a + I)*log(x) - 2*I*log((b*x + a - I)/b))/(a - I)","A",0
204,1,40,0,0.452834," ","integrate(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x^2,x, algorithm=""fricas"")","\frac{2 i \, b x \log\left(x\right) - 2 i \, b x \log\left(\frac{b x + a - i}{b}\right) + a^{2} + 1}{{\left(a^{2} - 2 i \, a - 1\right)} x}"," ",0,"(2*I*b*x*log(x) - 2*I*b*x*log((b*x + a - I)/b) + a^2 + 1)/((a^2 - 2*I*a - 1)*x)","A",0
205,1,70,0,0.461604," ","integrate(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x^3,x, algorithm=""fricas"")","\frac{-4 i \, b^{2} x^{2} \log\left(x\right) + 4 i \, b^{2} x^{2} \log\left(\frac{b x + a - i}{b}\right) + a^{3} - 4 \, {\left(i \, a + 1\right)} b x - i \, a^{2} + a - i}{{\left(2 \, a^{3} - 6 i \, a^{2} - 6 \, a + 2 i\right)} x^{2}}"," ",0,"(-4*I*b^2*x^2*log(x) + 4*I*b^2*x^2*log((b*x + a - I)/b) + a^3 - 4*(I*a + 1)*b*x - I*a^2 + a - I)/((2*a^3 - 6*I*a^2 - 6*a + 2*I)*x^2)","A",0
206,1,94,0,0.433846," ","integrate(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x^4,x, algorithm=""fricas"")","\frac{6 i \, b^{3} x^{3} \log\left(x\right) - 6 i \, b^{3} x^{3} \log\left(\frac{b x + a - i}{b}\right) - 6 \, {\left(-i \, a - 1\right)} b^{2} x^{2} + a^{4} - 2 i \, a^{3} + {\left(-3 i \, a^{2} - 6 \, a + 3 i\right)} b x - 2 i \, a - 1}{{\left(3 \, a^{4} - 12 i \, a^{3} - 18 \, a^{2} + 12 i \, a + 3\right)} x^{3}}"," ",0,"(6*I*b^3*x^3*log(x) - 6*I*b^3*x^3*log((b*x + a - I)/b) - 6*(-I*a - 1)*b^2*x^2 + a^4 - 2*I*a^3 + (-3*I*a^2 - 6*a + 3*I)*b*x - 2*I*a - 1)/((3*a^4 - 12*I*a^3 - 18*a^2 + 12*I*a + 3)*x^3)","A",0
207,1,263,0,0.503599," ","integrate(x^4/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{62 i \, a^{6} + 2687 \, a^{5} - 11575 i \, a^{4} - 20350 \, a^{3} + {\left(62 i \, a^{5} + 2625 \, a^{4} - 8950 i \, a^{3} - 11400 \, a^{2} + 6340 i \, a + 1280\right)} b x + 17740 i \, a^{2} + {\left(960 \, a^{5} - 6720 i \, a^{4} - 16320 \, a^{3} + {\left(960 \, a^{4} - 5760 i \, a^{3} - 10560 \, a^{2} + 8160 i \, a + 2280\right)} b x + 18720 i \, a^{2} + 10440 \, a - 2280 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(64 i \, b^{5} x^{5} - 176 \, b^{4} x^{4} + {\left(256 \, a - 272 i\right)} b^{3} x^{3} + 64 i \, a^{5} - 8 \, {\left(52 \, a^{2} - 118 i \, a - 61\right)} b^{2} x^{2} + 3344 \, a^{4} - 13552 i \, a^{3} + {\left(896 \, a^{3} - 3376 i \, a^{2} - 3664 \, a + 1304 i\right)} b x - 20792 \, a^{2} + 14104 i \, a + 3584\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 7620 \, a - 1280 i}{320 \, b^{6} x + {\left(320 \, a - 320 i\right)} b^{5}}"," ",0,"(62*I*a^6 + 2687*a^5 - 11575*I*a^4 - 20350*a^3 + (62*I*a^5 + 2625*a^4 - 8950*I*a^3 - 11400*a^2 + 6340*I*a + 1280)*b*x + 17740*I*a^2 + (960*a^5 - 6720*I*a^4 - 16320*a^3 + (960*a^4 - 5760*I*a^3 - 10560*a^2 + 8160*I*a + 2280)*b*x + 18720*I*a^2 + 10440*a - 2280*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (64*I*b^5*x^5 - 176*b^4*x^4 + (256*a - 272*I)*b^3*x^3 + 64*I*a^5 - 8*(52*a^2 - 118*I*a - 61)*b^2*x^2 + 3344*a^4 - 13552*I*a^3 + (896*a^3 - 3376*I*a^2 - 3664*a + 1304*I)*b*x - 20792*a^2 + 14104*I*a + 3584)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 7620*a - 1280*I)/(320*b^6*x + (320*a - 320*I)*b^5)","A",0
208,1,217,0,0.438852," ","integrate(x^3/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{-15 i \, a^{5} - 495 \, a^{4} + 1664 i \, a^{3} + {\left(-15 i \, a^{4} - 480 \, a^{3} + 1184 i \, a^{2} + 968 \, a - 256 i\right)} b x + 2152 \, a^{2} - {\left(192 \, a^{4} - 1056 i \, a^{3} + {\left(192 \, a^{3} - 864 i \, a^{2} - 1056 \, a + 408 i\right)} b x - 1920 \, a^{2} + 1464 i \, a + 408\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(16 i \, b^{4} x^{4} - 48 \, b^{3} x^{3} + {\left(80 \, a - 88 i\right)} b^{2} x^{2} - 16 i \, a^{4} - 624 \, a^{3} - 8 \, {\left(22 \, a^{2} - 54 i \, a - 29\right)} b x + 1864 i \, a^{2} + 1896 \, a - 640 i\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} - 1224 i \, a - 256}{64 \, b^{5} x + {\left(64 \, a - 64 i\right)} b^{4}}"," ",0,"(-15*I*a^5 - 495*a^4 + 1664*I*a^3 + (-15*I*a^4 - 480*a^3 + 1184*I*a^2 + 968*a - 256*I)*b*x + 2152*a^2 - (192*a^4 - 1056*I*a^3 + (192*a^3 - 864*I*a^2 - 1056*a + 408*I)*b*x - 1920*a^2 + 1464*I*a + 408)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (16*I*b^4*x^4 - 48*b^3*x^3 + (80*a - 88*I)*b^2*x^2 - 16*I*a^4 - 624*a^3 - 8*(22*a^2 - 54*I*a - 29)*b*x + 1864*I*a^2 + 1896*a - 640*I)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 1224*I*a - 256)/(64*b^5*x + (64*a - 64*I)*b^4)","A",0
209,1,174,0,0.441312," ","integrate(x^2/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{7 i \, a^{4} + 166 \, a^{3} + {\left(7 i \, a^{3} + 159 \, a^{2} - 249 i \, a - 96\right)} b x - 408 i \, a^{2} + {\left(72 \, a^{3} + 12 \, {\left(6 \, a^{2} - 18 i \, a - 11\right)} b x - 288 i \, a^{2} - 348 \, a + 132 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + {\left(8 i \, b^{3} x^{3} - 28 \, b^{2} x^{2} + 8 i \, a^{3} + {\left(64 \, a - 76 i\right)} b x + 212 \, a^{2} - 412 i \, a - 208\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} - 345 \, a + 96 i}{24 \, b^{4} x + {\left(24 \, a - 24 i\right)} b^{3}}"," ",0,"(7*I*a^4 + 166*a^3 + (7*I*a^3 + 159*a^2 - 249*I*a - 96)*b*x - 408*I*a^2 + (72*a^3 + 12*(6*a^2 - 18*I*a - 11)*b*x - 288*I*a^2 - 348*a + 132*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (8*I*b^3*x^3 - 28*b^2*x^2 + 8*I*a^3 + (64*a - 76*I)*b*x + 212*a^2 - 412*I*a - 208)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 345*a + 96*I)/(24*b^4*x + (24*a - 24*I)*b^3)","A",0
210,1,137,0,0.477528," ","integrate(x/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{-3 i \, a^{3} + {\left(-3 i \, a^{2} - 44 \, a + 32 i\right)} b x - 47 \, a^{2} - {\left({\left(24 \, a - 36 i\right)} b x + 24 \, a^{2} - 60 i \, a - 36\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(4 i \, b^{2} x^{2} - 4 i \, a^{2} - 20 \, b x - 60 \, a + 56 i\right)} + 76 i \, a + 32}{8 \, b^{3} x + {\left(8 \, a - 8 i\right)} b^{2}}"," ",0,"(-3*I*a^3 + (-3*I*a^2 - 44*a + 32*I)*b*x - 47*a^2 - ((24*a - 36*I)*b*x + 24*a^2 - 60*I*a - 36)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(4*I*b^2*x^2 - 4*I*a^2 - 20*b*x - 60*a + 56*I) + 76*I*a + 32)/(8*b^3*x + (8*a - 8*I)*b^2)","A",0
211,1,102,0,0.470859," ","integrate(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(i \, a + 8\right)} b x + i \, a^{2} + {\left(6 \, b x + 6 \, a - 6 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 i \, b x + 2 i \, a + 10\right)} + 9 \, a - 8 i}{2 \, b^{2} x + {\left(2 \, a - 2 i\right)} b}"," ",0,"((I*a + 8)*b*x + I*a^2 + (6*b*x + 6*a - 6*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*I*b*x + 2*I*a + 10) + 9*a - 8*I)/(2*b^2*x + (2*a - 2*I)*b)","A",0
212,1,381,0,0.493033," ","integrate(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x,x, algorithm=""fricas"")","\frac{{\left({\left(a - i\right)} b x + a^{2} - 2 i \, a - 1\right)} \sqrt{-\frac{4 \, a^{3} + 12 i \, a^{2} - 12 \, a - 4 i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}} \log\left(-\frac{{\left(2 \, a + 2 i\right)} b x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a + 2 i\right)} - {\left(i \, a^{2} + 2 \, a - i\right)} \sqrt{-\frac{4 \, a^{3} + 12 i \, a^{2} - 12 \, a - 4 i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}}}{2 \, a + 2 i}\right) - {\left({\left(a - i\right)} b x + a^{2} - 2 i \, a - 1\right)} \sqrt{-\frac{4 \, a^{3} + 12 i \, a^{2} - 12 \, a - 4 i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}} \log\left(-\frac{{\left(2 \, a + 2 i\right)} b x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, a + 2 i\right)} - {\left(-i \, a^{2} - 2 \, a + i\right)} \sqrt{-\frac{4 \, a^{3} + 12 i \, a^{2} - 12 \, a - 4 i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}}}{2 \, a + 2 i}\right) - 8 \, b x - {\left(2 \, {\left(i \, a + 1\right)} b x + 2 i \, a^{2} + 4 \, a - 2 i\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right) - 8 \, a - 8 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 8 i}{{\left(2 \, a - 2 i\right)} b x + 2 \, a^{2} - 4 i \, a - 2}"," ",0,"(((a - I)*b*x + a^2 - 2*I*a - 1)*sqrt(-(4*a^3 + 12*I*a^2 - 12*a - 4*I)/(a^3 - 3*I*a^2 - 3*a + I))*log(-((2*a + 2*I)*b*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a + 2*I) - (I*a^2 + 2*a - I)*sqrt(-(4*a^3 + 12*I*a^2 - 12*a - 4*I)/(a^3 - 3*I*a^2 - 3*a + I)))/(2*a + 2*I)) - ((a - I)*b*x + a^2 - 2*I*a - 1)*sqrt(-(4*a^3 + 12*I*a^2 - 12*a - 4*I)/(a^3 - 3*I*a^2 - 3*a + I))*log(-((2*a + 2*I)*b*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*a + 2*I) - (-I*a^2 - 2*a + I)*sqrt(-(4*a^3 + 12*I*a^2 - 12*a - 4*I)/(a^3 - 3*I*a^2 - 3*a + I)))/(2*a + 2*I)) - 8*b*x - (2*(I*a + 1)*b*x + 2*I*a^2 + 4*a - 2*I)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 8*a - 8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 8*I)/((2*a - 2*I)*b*x + 2*a^2 - 4*I*a - 2)","B",0
213,1,404,0,0.460949," ","integrate(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(i \, a - 5\right)} b^{2} x^{2} - {\left(-2 i \, a^{2} + 8 \, a - 10 i\right)} b x - {\left({\left(a^{2} - 2 i \, a - 1\right)} b x^{2} + {\left(a^{3} - 3 i \, a^{2} - 3 \, a + i\right)} x\right)} \sqrt{\frac{{\left(36 \, a + 36 i\right)} b^{2}}{a^{5} - 5 i \, a^{4} - 10 \, a^{3} + 10 i \, a^{2} + 5 \, a - i}} \log\left(-\frac{6 \, b^{2} x + {\left(a^{3} - 3 i \, a^{2} - 3 \, a + i\right)} \sqrt{\frac{{\left(36 \, a + 36 i\right)} b^{2}}{a^{5} - 5 i \, a^{4} - 10 \, a^{3} + 10 i \, a^{2} + 5 \, a - i}} - 6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b}{6 \, b}\right) + {\left({\left(a^{2} - 2 i \, a - 1\right)} b x^{2} + {\left(a^{3} - 3 i \, a^{2} - 3 \, a + i\right)} x\right)} \sqrt{\frac{{\left(36 \, a + 36 i\right)} b^{2}}{a^{5} - 5 i \, a^{4} - 10 \, a^{3} + 10 i \, a^{2} + 5 \, a - i}} \log\left(-\frac{6 \, b^{2} x - {\left(a^{3} - 3 i \, a^{2} - 3 \, a + i\right)} \sqrt{\frac{{\left(36 \, a + 36 i\right)} b^{2}}{a^{5} - 5 i \, a^{4} - 10 \, a^{3} + 10 i \, a^{2} + 5 \, a - i}} - 6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b}{6 \, b}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 \, {\left(i \, a - 5\right)} b x + 2 i \, a^{2} + 2 i\right)}}{2 \, {\left(a^{2} - 2 i \, a - 1\right)} b x^{2} + {\left(2 \, a^{3} - 6 i \, a^{2} - 6 \, a + 2 i\right)} x}"," ",0,"-(2*(I*a - 5)*b^2*x^2 - (-2*I*a^2 + 8*a - 10*I)*b*x - ((a^2 - 2*I*a - 1)*b*x^2 + (a^3 - 3*I*a^2 - 3*a + I)*x)*sqrt((36*a + 36*I)*b^2/(a^5 - 5*I*a^4 - 10*a^3 + 10*I*a^2 + 5*a - I))*log(-1/6*(6*b^2*x + (a^3 - 3*I*a^2 - 3*a + I)*sqrt((36*a + 36*I)*b^2/(a^5 - 5*I*a^4 - 10*a^3 + 10*I*a^2 + 5*a - I)) - 6*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b)/b) + ((a^2 - 2*I*a - 1)*b*x^2 + (a^3 - 3*I*a^2 - 3*a + I)*x)*sqrt((36*a + 36*I)*b^2/(a^5 - 5*I*a^4 - 10*a^3 + 10*I*a^2 + 5*a - I))*log(-1/6*(6*b^2*x - (a^3 - 3*I*a^2 - 3*a + I)*sqrt((36*a + 36*I)*b^2/(a^5 - 5*I*a^4 - 10*a^3 + 10*I*a^2 + 5*a - I)) - 6*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b)/b) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*(I*a - 5)*b*x + 2*I*a^2 + 2*I))/(2*(a^2 - 2*I*a - 1)*b*x^2 + (2*a^3 - 6*I*a^2 - 6*a + 2*I)*x)","B",0
214,1,580,0,0.486193," ","integrate(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{{\left(i \, a - 14\right)} b^{3} x^{3} + {\left(i \, a^{2} - 13 \, a + 14 i\right)} b^{2} x^{2} - 3 \, {\left({\left(a^{3} - 3 i \, a^{2} - 3 \, a + i\right)} b x^{3} + {\left(a^{4} - 4 i \, a^{3} - 6 \, a^{2} + 4 i \, a + 1\right)} x^{2}\right)} \sqrt{\frac{{\left(4 \, a^{2} + 12 i \, a - 9\right)} b^{4}}{a^{8} - 6 i \, a^{7} - 14 \, a^{6} + 14 i \, a^{5} + 14 i \, a^{3} + 14 \, a^{2} - 6 i \, a - 1}} \log\left(-\frac{{\left(6 \, a + 9 i\right)} b^{3} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(6 \, a + 9 i\right)} b^{2} + 3 \, {\left(a^{5} - 3 i \, a^{4} - 2 \, a^{3} - 2 i \, a^{2} - 3 \, a + i\right)} \sqrt{\frac{{\left(4 \, a^{2} + 12 i \, a - 9\right)} b^{4}}{a^{8} - 6 i \, a^{7} - 14 \, a^{6} + 14 i \, a^{5} + 14 i \, a^{3} + 14 \, a^{2} - 6 i \, a - 1}}}{{\left(6 \, a + 9 i\right)} b^{2}}\right) + 3 \, {\left({\left(a^{3} - 3 i \, a^{2} - 3 \, a + i\right)} b x^{3} + {\left(a^{4} - 4 i \, a^{3} - 6 \, a^{2} + 4 i \, a + 1\right)} x^{2}\right)} \sqrt{\frac{{\left(4 \, a^{2} + 12 i \, a - 9\right)} b^{4}}{a^{8} - 6 i \, a^{7} - 14 \, a^{6} + 14 i \, a^{5} + 14 i \, a^{3} + 14 \, a^{2} - 6 i \, a - 1}} \log\left(-\frac{{\left(6 \, a + 9 i\right)} b^{3} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(6 \, a + 9 i\right)} b^{2} - 3 \, {\left(a^{5} - 3 i \, a^{4} - 2 \, a^{3} - 2 i \, a^{2} - 3 \, a + i\right)} \sqrt{\frac{{\left(4 \, a^{2} + 12 i \, a - 9\right)} b^{4}}{a^{8} - 6 i \, a^{7} - 14 \, a^{6} + 14 i \, a^{5} + 14 i \, a^{3} + 14 \, a^{2} - 6 i \, a - 1}}}{{\left(6 \, a + 9 i\right)} b^{2}}\right) + {\left({\left(i \, a - 14\right)} b^{2} x^{2} - i \, a^{3} - {\left(5 \, a - 5 i\right)} b x - a^{2} - i \, a - 1\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(2 \, a^{3} - 6 i \, a^{2} - 6 \, a + 2 i\right)} b x^{3} + {\left(2 \, a^{4} - 8 i \, a^{3} - 12 \, a^{2} + 8 i \, a + 2\right)} x^{2}}"," ",0,"((I*a - 14)*b^3*x^3 + (I*a^2 - 13*a + 14*I)*b^2*x^2 - 3*((a^3 - 3*I*a^2 - 3*a + I)*b*x^3 + (a^4 - 4*I*a^3 - 6*a^2 + 4*I*a + 1)*x^2)*sqrt((4*a^2 + 12*I*a - 9)*b^4/(a^8 - 6*I*a^7 - 14*a^6 + 14*I*a^5 + 14*I*a^3 + 14*a^2 - 6*I*a - 1))*log(-((6*a + 9*I)*b^3*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(6*a + 9*I)*b^2 + 3*(a^5 - 3*I*a^4 - 2*a^3 - 2*I*a^2 - 3*a + I)*sqrt((4*a^2 + 12*I*a - 9)*b^4/(a^8 - 6*I*a^7 - 14*a^6 + 14*I*a^5 + 14*I*a^3 + 14*a^2 - 6*I*a - 1)))/((6*a + 9*I)*b^2)) + 3*((a^3 - 3*I*a^2 - 3*a + I)*b*x^3 + (a^4 - 4*I*a^3 - 6*a^2 + 4*I*a + 1)*x^2)*sqrt((4*a^2 + 12*I*a - 9)*b^4/(a^8 - 6*I*a^7 - 14*a^6 + 14*I*a^5 + 14*I*a^3 + 14*a^2 - 6*I*a - 1))*log(-((6*a + 9*I)*b^3*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(6*a + 9*I)*b^2 - 3*(a^5 - 3*I*a^4 - 2*a^3 - 2*I*a^2 - 3*a + I)*sqrt((4*a^2 + 12*I*a - 9)*b^4/(a^8 - 6*I*a^7 - 14*a^6 + 14*I*a^5 + 14*I*a^3 + 14*a^2 - 6*I*a - 1)))/((6*a + 9*I)*b^2)) + ((I*a - 14)*b^2*x^2 - I*a^3 - (5*a - 5*I)*b*x - a^2 - I*a - 1)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((2*a^3 - 6*I*a^2 - 6*a + 2*I)*b*x^3 + (2*a^4 - 8*I*a^3 - 12*a^2 + 8*I*a + 2)*x^2)","B",0
215,1,853,0,0.529302," ","integrate(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x^4,x, algorithm=""fricas"")","\frac{{\left(-2 i \, a^{2} + 51 \, a + 52 i\right)} b^{4} x^{4} + {\left(-2 i \, a^{3} + 49 \, a^{2} + i \, a + 52\right)} b^{3} x^{3} + \sqrt{\frac{{\left(36 \, a^{4} + 216 i \, a^{3} - 456 \, a^{2} - 396 i \, a + 121\right)} b^{6}}{a^{12} - 6 i \, a^{11} - 12 \, a^{10} + 2 i \, a^{9} - 27 \, a^{8} + 36 i \, a^{7} + 36 i \, a^{5} + 27 \, a^{4} + 2 i \, a^{3} + 12 \, a^{2} - 6 i \, a - 1}} {\left({\left(3 \, a^{5} - 9 i \, a^{4} - 6 \, a^{3} - 6 i \, a^{2} - 9 \, a + 3 i\right)} b x^{4} + {\left(3 \, a^{6} - 12 i \, a^{5} - 15 \, a^{4} - 15 \, a^{2} + 12 i \, a + 3\right)} x^{3}\right)} \log\left(-\frac{{\left(6 \, a^{2} + 18 i \, a - 11\right)} b^{4} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(6 \, a^{2} + 18 i \, a - 11\right)} b^{3} + {\left(a^{7} - 3 i \, a^{6} - a^{5} - 5 i \, a^{4} - 5 \, a^{3} - i \, a^{2} - 3 \, a + i\right)} \sqrt{\frac{{\left(36 \, a^{4} + 216 i \, a^{3} - 456 \, a^{2} - 396 i \, a + 121\right)} b^{6}}{a^{12} - 6 i \, a^{11} - 12 \, a^{10} + 2 i \, a^{9} - 27 \, a^{8} + 36 i \, a^{7} + 36 i \, a^{5} + 27 \, a^{4} + 2 i \, a^{3} + 12 \, a^{2} - 6 i \, a - 1}}}{{\left(6 \, a^{2} + 18 i \, a - 11\right)} b^{3}}\right) - \sqrt{\frac{{\left(36 \, a^{4} + 216 i \, a^{3} - 456 \, a^{2} - 396 i \, a + 121\right)} b^{6}}{a^{12} - 6 i \, a^{11} - 12 \, a^{10} + 2 i \, a^{9} - 27 \, a^{8} + 36 i \, a^{7} + 36 i \, a^{5} + 27 \, a^{4} + 2 i \, a^{3} + 12 \, a^{2} - 6 i \, a - 1}} {\left({\left(3 \, a^{5} - 9 i \, a^{4} - 6 \, a^{3} - 6 i \, a^{2} - 9 \, a + 3 i\right)} b x^{4} + {\left(3 \, a^{6} - 12 i \, a^{5} - 15 \, a^{4} - 15 \, a^{2} + 12 i \, a + 3\right)} x^{3}\right)} \log\left(-\frac{{\left(6 \, a^{2} + 18 i \, a - 11\right)} b^{4} x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(6 \, a^{2} + 18 i \, a - 11\right)} b^{3} - {\left(a^{7} - 3 i \, a^{6} - a^{5} - 5 i \, a^{4} - 5 \, a^{3} - i \, a^{2} - 3 \, a + i\right)} \sqrt{\frac{{\left(36 \, a^{4} + 216 i \, a^{3} - 456 \, a^{2} - 396 i \, a + 121\right)} b^{6}}{a^{12} - 6 i \, a^{11} - 12 \, a^{10} + 2 i \, a^{9} - 27 \, a^{8} + 36 i \, a^{7} + 36 i \, a^{5} + 27 \, a^{4} + 2 i \, a^{3} + 12 \, a^{2} - 6 i \, a - 1}}}{{\left(6 \, a^{2} + 18 i \, a - 11\right)} b^{3}}\right) + {\left({\left(-2 i \, a^{2} + 51 \, a + 52 i\right)} b^{3} x^{3} - 2 i \, a^{5} + {\left(16 \, a^{2} + 3 i \, a + 19\right)} b^{2} x^{2} - 2 \, a^{4} - 4 i \, a^{3} - {\left(7 \, a^{3} - 7 i \, a^{2} + 7 \, a - 7 i\right)} b x - 4 \, a^{2} - 2 i \, a - 2\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{{\left(6 \, a^{5} - 18 i \, a^{4} - 12 \, a^{3} - 12 i \, a^{2} - 18 \, a + 6 i\right)} b x^{4} + {\left(6 \, a^{6} - 24 i \, a^{5} - 30 \, a^{4} - 30 \, a^{2} + 24 i \, a + 6\right)} x^{3}}"," ",0,"((-2*I*a^2 + 51*a + 52*I)*b^4*x^4 + (-2*I*a^3 + 49*a^2 + I*a + 52)*b^3*x^3 + sqrt((36*a^4 + 216*I*a^3 - 456*a^2 - 396*I*a + 121)*b^6/(a^12 - 6*I*a^11 - 12*a^10 + 2*I*a^9 - 27*a^8 + 36*I*a^7 + 36*I*a^5 + 27*a^4 + 2*I*a^3 + 12*a^2 - 6*I*a - 1))*((3*a^5 - 9*I*a^4 - 6*a^3 - 6*I*a^2 - 9*a + 3*I)*b*x^4 + (3*a^6 - 12*I*a^5 - 15*a^4 - 15*a^2 + 12*I*a + 3)*x^3)*log(-((6*a^2 + 18*I*a - 11)*b^4*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(6*a^2 + 18*I*a - 11)*b^3 + (a^7 - 3*I*a^6 - a^5 - 5*I*a^4 - 5*a^3 - I*a^2 - 3*a + I)*sqrt((36*a^4 + 216*I*a^3 - 456*a^2 - 396*I*a + 121)*b^6/(a^12 - 6*I*a^11 - 12*a^10 + 2*I*a^9 - 27*a^8 + 36*I*a^7 + 36*I*a^5 + 27*a^4 + 2*I*a^3 + 12*a^2 - 6*I*a - 1)))/((6*a^2 + 18*I*a - 11)*b^3)) - sqrt((36*a^4 + 216*I*a^3 - 456*a^2 - 396*I*a + 121)*b^6/(a^12 - 6*I*a^11 - 12*a^10 + 2*I*a^9 - 27*a^8 + 36*I*a^7 + 36*I*a^5 + 27*a^4 + 2*I*a^3 + 12*a^2 - 6*I*a - 1))*((3*a^5 - 9*I*a^4 - 6*a^3 - 6*I*a^2 - 9*a + 3*I)*b*x^4 + (3*a^6 - 12*I*a^5 - 15*a^4 - 15*a^2 + 12*I*a + 3)*x^3)*log(-((6*a^2 + 18*I*a - 11)*b^4*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(6*a^2 + 18*I*a - 11)*b^3 - (a^7 - 3*I*a^6 - a^5 - 5*I*a^4 - 5*a^3 - I*a^2 - 3*a + I)*sqrt((36*a^4 + 216*I*a^3 - 456*a^2 - 396*I*a + 121)*b^6/(a^12 - 6*I*a^11 - 12*a^10 + 2*I*a^9 - 27*a^8 + 36*I*a^7 + 36*I*a^5 + 27*a^4 + 2*I*a^3 + 12*a^2 - 6*I*a - 1)))/((6*a^2 + 18*I*a - 11)*b^3)) + ((-2*I*a^2 + 51*a + 52*I)*b^3*x^3 - 2*I*a^5 + (16*a^2 + 3*I*a + 19)*b^2*x^2 - 2*a^4 - 4*I*a^3 - (7*a^3 - 7*I*a^2 + 7*a - 7*I)*b*x - 4*a^2 - 2*I*a - 2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))/((6*a^5 - 18*I*a^4 - 12*a^3 - 12*I*a^2 - 18*a + 6*I)*b*x^4 + (6*a^6 - 24*I*a^5 - 30*a^4 - 30*a^2 + 24*I*a + 6)*x^3)","B",0
216,1,554,0,0.507888," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)*x^2,x, algorithm=""fricas"")","\frac{3 \, b^{3} \sqrt{\frac{64 i \, a^{4} - 64 \, a^{3} - 64 i \, a^{2} + 24 \, a + 9 i}{b^{6}}} \log\left(\frac{i \, b^{3} \sqrt{\frac{64 i \, a^{4} - 64 \, a^{3} - 64 i \, a^{2} + 24 \, a + 9 i}{b^{6}}} + {\left(8 \, a^{2} + 4 i \, a - 3\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, a^{2} + 4 i \, a - 3}\right) - 3 \, b^{3} \sqrt{\frac{64 i \, a^{4} - 64 \, a^{3} - 64 i \, a^{2} + 24 \, a + 9 i}{b^{6}}} \log\left(\frac{-i \, b^{3} \sqrt{\frac{64 i \, a^{4} - 64 \, a^{3} - 64 i \, a^{2} + 24 \, a + 9 i}{b^{6}}} + {\left(8 \, a^{2} + 4 i \, a - 3\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, a^{2} + 4 i \, a - 3}\right) + 3 \, b^{3} \sqrt{\frac{-64 i \, a^{4} + 64 \, a^{3} + 64 i \, a^{2} - 24 \, a - 9 i}{b^{6}}} \log\left(\frac{i \, b^{3} \sqrt{\frac{-64 i \, a^{4} + 64 \, a^{3} + 64 i \, a^{2} - 24 \, a - 9 i}{b^{6}}} + {\left(8 \, a^{2} + 4 i \, a - 3\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, a^{2} + 4 i \, a - 3}\right) - 3 \, b^{3} \sqrt{\frac{-64 i \, a^{4} + 64 \, a^{3} + 64 i \, a^{2} - 24 \, a - 9 i}{b^{6}}} \log\left(\frac{-i \, b^{3} \sqrt{\frac{-64 i \, a^{4} + 64 \, a^{3} + 64 i \, a^{2} - 24 \, a - 9 i}{b^{6}}} + {\left(8 \, a^{2} + 4 i \, a - 3\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, a^{2} + 4 i \, a - 3}\right) + 2 \, {\left(8 \, b^{3} x^{3} - 2 i \, b^{2} x^{2} + 8 \, a^{3} + {\left(8 i \, a - 1\right)} b x + 34 i \, a^{2} - 37 \, a - 11 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{48 \, b^{3}}"," ",0,"1/48*(3*b^3*sqrt((64*I*a^4 - 64*a^3 - 64*I*a^2 + 24*a + 9*I)/b^6)*log((I*b^3*sqrt((64*I*a^4 - 64*a^3 - 64*I*a^2 + 24*a + 9*I)/b^6) + (8*a^2 + 4*I*a - 3)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(8*a^2 + 4*I*a - 3)) - 3*b^3*sqrt((64*I*a^4 - 64*a^3 - 64*I*a^2 + 24*a + 9*I)/b^6)*log((-I*b^3*sqrt((64*I*a^4 - 64*a^3 - 64*I*a^2 + 24*a + 9*I)/b^6) + (8*a^2 + 4*I*a - 3)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(8*a^2 + 4*I*a - 3)) + 3*b^3*sqrt((-64*I*a^4 + 64*a^3 + 64*I*a^2 - 24*a - 9*I)/b^6)*log((I*b^3*sqrt((-64*I*a^4 + 64*a^3 + 64*I*a^2 - 24*a - 9*I)/b^6) + (8*a^2 + 4*I*a - 3)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(8*a^2 + 4*I*a - 3)) - 3*b^3*sqrt((-64*I*a^4 + 64*a^3 + 64*I*a^2 - 24*a - 9*I)/b^6)*log((-I*b^3*sqrt((-64*I*a^4 + 64*a^3 + 64*I*a^2 - 24*a - 9*I)/b^6) + (8*a^2 + 4*I*a - 3)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(8*a^2 + 4*I*a - 3)) + 2*(8*b^3*x^3 - 2*I*b^2*x^2 + 8*a^3 + (8*I*a - 1)*b*x + 34*I*a^2 - 37*a - 11*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b^3","A",0
217,1,415,0,0.496548," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)*x,x, algorithm=""fricas"")","-\frac{b^{2} \sqrt{\frac{16 i \, a^{2} - 8 \, a - i}{b^{4}}} \log\left(\frac{i \, b^{2} \sqrt{\frac{16 i \, a^{2} - 8 \, a - i}{b^{4}}} + {\left(4 \, a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{4 \, a + i}\right) - b^{2} \sqrt{\frac{16 i \, a^{2} - 8 \, a - i}{b^{4}}} \log\left(\frac{-i \, b^{2} \sqrt{\frac{16 i \, a^{2} - 8 \, a - i}{b^{4}}} + {\left(4 \, a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{4 \, a + i}\right) + b^{2} \sqrt{\frac{-16 i \, a^{2} + 8 \, a + i}{b^{4}}} \log\left(\frac{i \, b^{2} \sqrt{\frac{-16 i \, a^{2} + 8 \, a + i}{b^{4}}} + {\left(4 \, a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{4 \, a + i}\right) - b^{2} \sqrt{\frac{-16 i \, a^{2} + 8 \, a + i}{b^{4}}} \log\left(\frac{-i \, b^{2} \sqrt{\frac{-16 i \, a^{2} + 8 \, a + i}{b^{4}}} + {\left(4 \, a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{4 \, a + i}\right) - 2 \, {\left(2 \, b^{2} x^{2} - 2 \, a^{2} - i \, b x - 5 i \, a + 3\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, b^{2}}"," ",0,"-1/8*(b^2*sqrt((16*I*a^2 - 8*a - I)/b^4)*log((I*b^2*sqrt((16*I*a^2 - 8*a - I)/b^4) + (4*a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(4*a + I)) - b^2*sqrt((16*I*a^2 - 8*a - I)/b^4)*log((-I*b^2*sqrt((16*I*a^2 - 8*a - I)/b^4) + (4*a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(4*a + I)) + b^2*sqrt((-16*I*a^2 + 8*a + I)/b^4)*log((I*b^2*sqrt((-16*I*a^2 + 8*a + I)/b^4) + (4*a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(4*a + I)) - b^2*sqrt((-16*I*a^2 + 8*a + I)/b^4)*log((-I*b^2*sqrt((-16*I*a^2 + 8*a + I)/b^4) + (4*a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(4*a + I)) - 2*(2*b^2*x^2 - 2*a^2 - I*b*x - 5*I*a + 3)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b^2","A",0
218,1,257,0,0.446243," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{b \sqrt{\frac{i}{b^{2}}} \log\left(i \, b \sqrt{\frac{i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - b \sqrt{\frac{i}{b^{2}}} \log\left(-i \, b \sqrt{\frac{i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + b \sqrt{-\frac{i}{b^{2}}} \log\left(i \, b \sqrt{-\frac{i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - b \sqrt{-\frac{i}{b^{2}}} \log\left(-i \, b \sqrt{-\frac{i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + {\left(2 \, b x + 2 \, a + 2 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{2 \, b}"," ",0,"1/2*(b*sqrt(I/b^2)*log(I*b*sqrt(I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - b*sqrt(I/b^2)*log(-I*b*sqrt(I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + b*sqrt(-I/b^2)*log(I*b*sqrt(-I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - b*sqrt(-I/b^2)*log(-I*b*sqrt(-I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + (2*b*x + 2*a + 2*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b","A",0
219,1,414,0,0.492748," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{4 i} \log\left(\frac{1}{2} \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - \frac{1}{2} \, \sqrt{4 i} \log\left(-\frac{1}{2} \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + \frac{1}{2} \, \sqrt{-4 i} \log\left(\frac{1}{2} \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - \frac{1}{2} \, \sqrt{-4 i} \log\left(-\frac{1}{2} \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - \left(-\frac{a - i}{a + i}\right)^{\frac{1}{4}} \log\left(\sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + \left(-\frac{a - i}{a + i}\right)^{\frac{1}{4}}\right) - i \, \left(-\frac{a - i}{a + i}\right)^{\frac{1}{4}} \log\left(\sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + i \, \left(-\frac{a - i}{a + i}\right)^{\frac{1}{4}}\right) + i \, \left(-\frac{a - i}{a + i}\right)^{\frac{1}{4}} \log\left(\sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} - i \, \left(-\frac{a - i}{a + i}\right)^{\frac{1}{4}}\right) + \left(-\frac{a - i}{a + i}\right)^{\frac{1}{4}} \log\left(\sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} - \left(-\frac{a - i}{a + i}\right)^{\frac{1}{4}}\right)"," ",0,"1/2*sqrt(4*I)*log(1/2*sqrt(4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - 1/2*sqrt(4*I)*log(-1/2*sqrt(4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + 1/2*sqrt(-4*I)*log(1/2*sqrt(-4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - 1/2*sqrt(-4*I)*log(-1/2*sqrt(-4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - (-(a - I)/(a + I))^(1/4)*log(sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (-(a - I)/(a + I))^(1/4)) - I*(-(a - I)/(a + I))^(1/4)*log(sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + I*(-(a - I)/(a + I))^(1/4)) + I*(-(a - I)/(a + I))^(1/4)*log(sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) - I*(-(a - I)/(a + I))^(1/4)) + (-(a - I)/(a + I))^(1/4)*log(sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) - (-(a - I)/(a + I))^(1/4))","A",0
220,1,612,0,0.605404," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x^2,x, algorithm=""fricas"")","\frac{\left(-\frac{b^{4}}{16 \, a^{8} + 32 i \, a^{7} + 32 \, a^{6} + 96 i \, a^{5} + 96 i \, a^{3} - 32 \, a^{2} + 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(-i \, a + 1\right)} x \log\left(\frac{b \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + 2 \, \left(-\frac{b^{4}}{16 \, a^{8} + 32 i \, a^{7} + 32 \, a^{6} + 96 i \, a^{5} + 96 i \, a^{3} - 32 \, a^{2} + 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(a^{2} + 1\right)}}{b}\right) + \left(-\frac{b^{4}}{16 \, a^{8} + 32 i \, a^{7} + 32 \, a^{6} + 96 i \, a^{5} + 96 i \, a^{3} - 32 \, a^{2} + 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(i \, a - 1\right)} x \log\left(\frac{b \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} - 2 \, \left(-\frac{b^{4}}{16 \, a^{8} + 32 i \, a^{7} + 32 \, a^{6} + 96 i \, a^{5} + 96 i \, a^{3} - 32 \, a^{2} + 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(a^{2} + 1\right)}}{b}\right) + \left(-\frac{b^{4}}{16 \, a^{8} + 32 i \, a^{7} + 32 \, a^{6} + 96 i \, a^{5} + 96 i \, a^{3} - 32 \, a^{2} + 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(a + i\right)} x \log\left(\frac{b \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + \left(-\frac{b^{4}}{16 \, a^{8} + 32 i \, a^{7} + 32 \, a^{6} + 96 i \, a^{5} + 96 i \, a^{3} - 32 \, a^{2} + 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(2 i \, a^{2} + 2 i\right)}}{b}\right) - \left(-\frac{b^{4}}{16 \, a^{8} + 32 i \, a^{7} + 32 \, a^{6} + 96 i \, a^{5} + 96 i \, a^{3} - 32 \, a^{2} + 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(a + i\right)} x \log\left(\frac{b \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + \left(-\frac{b^{4}}{16 \, a^{8} + 32 i \, a^{7} + 32 \, a^{6} + 96 i \, a^{5} + 96 i \, a^{3} - 32 \, a^{2} + 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(-2 i \, a^{2} - 2 i\right)}}{b}\right) - {\left(b x + a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{{\left(a + i\right)} x}"," ",0,"((-b^4/(16*a^8 + 32*I*a^7 + 32*a^6 + 96*I*a^5 + 96*I*a^3 - 32*a^2 + 32*I*a - 16))^(1/4)*(-I*a + 1)*x*log((b*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + 2*(-b^4/(16*a^8 + 32*I*a^7 + 32*a^6 + 96*I*a^5 + 96*I*a^3 - 32*a^2 + 32*I*a - 16))^(1/4)*(a^2 + 1))/b) + (-b^4/(16*a^8 + 32*I*a^7 + 32*a^6 + 96*I*a^5 + 96*I*a^3 - 32*a^2 + 32*I*a - 16))^(1/4)*(I*a - 1)*x*log((b*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) - 2*(-b^4/(16*a^8 + 32*I*a^7 + 32*a^6 + 96*I*a^5 + 96*I*a^3 - 32*a^2 + 32*I*a - 16))^(1/4)*(a^2 + 1))/b) + (-b^4/(16*a^8 + 32*I*a^7 + 32*a^6 + 96*I*a^5 + 96*I*a^3 - 32*a^2 + 32*I*a - 16))^(1/4)*(a + I)*x*log((b*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (-b^4/(16*a^8 + 32*I*a^7 + 32*a^6 + 96*I*a^5 + 96*I*a^3 - 32*a^2 + 32*I*a - 16))^(1/4)*(2*I*a^2 + 2*I))/b) - (-b^4/(16*a^8 + 32*I*a^7 + 32*a^6 + 96*I*a^5 + 96*I*a^3 - 32*a^2 + 32*I*a - 16))^(1/4)*(a + I)*x*log((b*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (-b^4/(16*a^8 + 32*I*a^7 + 32*a^6 + 96*I*a^5 + 96*I*a^3 - 32*a^2 + 32*I*a - 16))^(1/4)*(-2*I*a^2 - 2*I))/b) - (b*x + a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/((a + I)*x)","B",0
221,1,561,0,0.478102," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)*x^2,x, algorithm=""fricas"")","\frac{3 \, b^{3} \sqrt{\frac{576 i \, a^{4} - 1728 \, a^{3} - 2112 i \, a^{2} + 1224 \, a + 289 i}{b^{6}}} \log\left(\frac{b^{3} \sqrt{\frac{576 i \, a^{4} - 1728 \, a^{3} - 2112 i \, a^{2} + 1224 \, a + 289 i}{b^{6}}} + {\left(24 \, a^{2} + 36 i \, a - 17\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{24 \, a^{2} + 36 i \, a - 17}\right) - 3 \, b^{3} \sqrt{\frac{576 i \, a^{4} - 1728 \, a^{3} - 2112 i \, a^{2} + 1224 \, a + 289 i}{b^{6}}} \log\left(-\frac{b^{3} \sqrt{\frac{576 i \, a^{4} - 1728 \, a^{3} - 2112 i \, a^{2} + 1224 \, a + 289 i}{b^{6}}} - {\left(24 \, a^{2} + 36 i \, a - 17\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{24 \, a^{2} + 36 i \, a - 17}\right) - 3 \, b^{3} \sqrt{\frac{-576 i \, a^{4} + 1728 \, a^{3} + 2112 i \, a^{2} - 1224 \, a - 289 i}{b^{6}}} \log\left(\frac{b^{3} \sqrt{\frac{-576 i \, a^{4} + 1728 \, a^{3} + 2112 i \, a^{2} - 1224 \, a - 289 i}{b^{6}}} + {\left(24 \, a^{2} + 36 i \, a - 17\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{24 \, a^{2} + 36 i \, a - 17}\right) + 3 \, b^{3} \sqrt{\frac{-576 i \, a^{4} + 1728 \, a^{3} + 2112 i \, a^{2} - 1224 \, a - 289 i}{b^{6}}} \log\left(-\frac{b^{3} \sqrt{\frac{-576 i \, a^{4} + 1728 \, a^{3} + 2112 i \, a^{2} - 1224 \, a - 289 i}{b^{6}}} - {\left(24 \, a^{2} + 36 i \, a - 17\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{24 \, a^{2} + 36 i \, a - 17}\right) + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(8 i \, b^{2} x^{2} - 2 \, {\left(4 i \, a - 7\right)} b x + 8 i \, a^{2} - 46 \, a - 23 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{48 \, b^{3}}"," ",0,"1/48*(3*b^3*sqrt((576*I*a^4 - 1728*a^3 - 2112*I*a^2 + 1224*a + 289*I)/b^6)*log((b^3*sqrt((576*I*a^4 - 1728*a^3 - 2112*I*a^2 + 1224*a + 289*I)/b^6) + (24*a^2 + 36*I*a - 17)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(24*a^2 + 36*I*a - 17)) - 3*b^3*sqrt((576*I*a^4 - 1728*a^3 - 2112*I*a^2 + 1224*a + 289*I)/b^6)*log(-(b^3*sqrt((576*I*a^4 - 1728*a^3 - 2112*I*a^2 + 1224*a + 289*I)/b^6) - (24*a^2 + 36*I*a - 17)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(24*a^2 + 36*I*a - 17)) - 3*b^3*sqrt((-576*I*a^4 + 1728*a^3 + 2112*I*a^2 - 1224*a - 289*I)/b^6)*log((b^3*sqrt((-576*I*a^4 + 1728*a^3 + 2112*I*a^2 - 1224*a - 289*I)/b^6) + (24*a^2 + 36*I*a - 17)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(24*a^2 + 36*I*a - 17)) + 3*b^3*sqrt((-576*I*a^4 + 1728*a^3 + 2112*I*a^2 - 1224*a - 289*I)/b^6)*log(-(b^3*sqrt((-576*I*a^4 + 1728*a^3 + 2112*I*a^2 - 1224*a - 289*I)/b^6) - (24*a^2 + 36*I*a - 17)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(24*a^2 + 36*I*a - 17)) + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(8*I*b^2*x^2 - 2*(4*I*a - 7)*b*x + 8*I*a^2 - 46*a - 23*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b^3","A",0
222,1,421,0,0.462526," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)*x,x, algorithm=""fricas"")","-\frac{b^{2} \sqrt{\frac{144 i \, a^{2} - 216 \, a - 81 i}{b^{4}}} \log\left(\frac{b^{2} \sqrt{\frac{144 i \, a^{2} - 216 \, a - 81 i}{b^{4}}} + {\left(12 \, a + 9 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{12 \, a + 9 i}\right) - b^{2} \sqrt{\frac{144 i \, a^{2} - 216 \, a - 81 i}{b^{4}}} \log\left(-\frac{b^{2} \sqrt{\frac{144 i \, a^{2} - 216 \, a - 81 i}{b^{4}}} - {\left(12 \, a + 9 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{12 \, a + 9 i}\right) - b^{2} \sqrt{\frac{-144 i \, a^{2} + 216 \, a + 81 i}{b^{4}}} \log\left(\frac{b^{2} \sqrt{\frac{-144 i \, a^{2} + 216 \, a + 81 i}{b^{4}}} + {\left(12 \, a + 9 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{12 \, a + 9 i}\right) + b^{2} \sqrt{\frac{-144 i \, a^{2} + 216 \, a + 81 i}{b^{4}}} \log\left(-\frac{b^{2} \sqrt{\frac{-144 i \, a^{2} + 216 \, a + 81 i}{b^{4}}} - {\left(12 \, a + 9 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{12 \, a + 9 i}\right) - 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 i \, b x - 2 i \, a + 5\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, b^{2}}"," ",0,"-1/8*(b^2*sqrt((144*I*a^2 - 216*a - 81*I)/b^4)*log((b^2*sqrt((144*I*a^2 - 216*a - 81*I)/b^4) + (12*a + 9*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(12*a + 9*I)) - b^2*sqrt((144*I*a^2 - 216*a - 81*I)/b^4)*log(-(b^2*sqrt((144*I*a^2 - 216*a - 81*I)/b^4) - (12*a + 9*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(12*a + 9*I)) - b^2*sqrt((-144*I*a^2 + 216*a + 81*I)/b^4)*log((b^2*sqrt((-144*I*a^2 + 216*a + 81*I)/b^4) + (12*a + 9*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(12*a + 9*I)) + b^2*sqrt((-144*I*a^2 + 216*a + 81*I)/b^4)*log(-(b^2*sqrt((-144*I*a^2 + 216*a + 81*I)/b^4) - (12*a + 9*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(12*a + 9*I)) - 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*I*b*x - 2*I*a + 5)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b^2","A",0
223,1,268,0,0.460558," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{b \sqrt{\frac{9 i}{b^{2}}} \log\left(\frac{1}{3} \, b \sqrt{\frac{9 i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - b \sqrt{\frac{9 i}{b^{2}}} \log\left(-\frac{1}{3} \, b \sqrt{\frac{9 i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - b \sqrt{-\frac{9 i}{b^{2}}} \log\left(\frac{1}{3} \, b \sqrt{-\frac{9 i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + b \sqrt{-\frac{9 i}{b^{2}}} \log\left(-\frac{1}{3} \, b \sqrt{-\frac{9 i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + 2 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{2 \, b}"," ",0,"1/2*(b*sqrt(9*I/b^2)*log(1/3*b*sqrt(9*I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - b*sqrt(9*I/b^2)*log(-1/3*b*sqrt(9*I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - b*sqrt(-9*I/b^2)*log(1/3*b*sqrt(-9*I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + b*sqrt(-9*I/b^2)*log(-1/3*b*sqrt(-9*I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + 2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b","A",0
224,1,690,0,0.513845," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x,x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{4 i} \log\left(\frac{1}{2} i \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - \frac{1}{2} \, \sqrt{4 i} \log\left(-\frac{1}{2} i \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - \frac{1}{2} \, \sqrt{-4 i} \log\left(\frac{1}{2} i \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + \frac{1}{2} \, \sqrt{-4 i} \log\left(-\frac{1}{2} i \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - \left(-\frac{a^{3} - 3 i \, a^{2} - 3 \, a + i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a^{2} + 2 i \, a - 1\right)} \left(-\frac{a^{3} - 3 i \, a^{2} - 3 \, a + i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}\right)^{\frac{3}{4}} + {\left(a^{2} - 2 i \, a - 1\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{a^{2} - 2 i \, a - 1}\right) + \left(-\frac{a^{3} - 3 i \, a^{2} - 3 \, a + i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(a^{2} + 2 i \, a - 1\right)} \left(-\frac{a^{3} - 3 i \, a^{2} - 3 \, a + i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}\right)^{\frac{3}{4}} - {\left(a^{2} - 2 i \, a - 1\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{a^{2} - 2 i \, a - 1}\right) + i \, \left(-\frac{a^{3} - 3 i \, a^{2} - 3 \, a + i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}\right)^{\frac{1}{4}} \log\left(\frac{{\left(i \, a^{2} - 2 \, a - i\right)} \left(-\frac{a^{3} - 3 i \, a^{2} - 3 \, a + i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}\right)^{\frac{3}{4}} + {\left(a^{2} - 2 i \, a - 1\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{a^{2} - 2 i \, a - 1}\right) - i \, \left(-\frac{a^{3} - 3 i \, a^{2} - 3 \, a + i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}\right)^{\frac{1}{4}} \log\left(\frac{{\left(-i \, a^{2} + 2 \, a + i\right)} \left(-\frac{a^{3} - 3 i \, a^{2} - 3 \, a + i}{a^{3} + 3 i \, a^{2} - 3 \, a - i}\right)^{\frac{3}{4}} + {\left(a^{2} - 2 i \, a - 1\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{a^{2} - 2 i \, a - 1}\right)"," ",0,"1/2*sqrt(4*I)*log(1/2*I*sqrt(4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - 1/2*sqrt(4*I)*log(-1/2*I*sqrt(4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - 1/2*sqrt(-4*I)*log(1/2*I*sqrt(-4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + 1/2*sqrt(-4*I)*log(-1/2*I*sqrt(-4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - (-(a^3 - 3*I*a^2 - 3*a + I)/(a^3 + 3*I*a^2 - 3*a - I))^(1/4)*log(((a^2 + 2*I*a - 1)*(-(a^3 - 3*I*a^2 - 3*a + I)/(a^3 + 3*I*a^2 - 3*a - I))^(3/4) + (a^2 - 2*I*a - 1)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(a^2 - 2*I*a - 1)) + (-(a^3 - 3*I*a^2 - 3*a + I)/(a^3 + 3*I*a^2 - 3*a - I))^(1/4)*log(-((a^2 + 2*I*a - 1)*(-(a^3 - 3*I*a^2 - 3*a + I)/(a^3 + 3*I*a^2 - 3*a - I))^(3/4) - (a^2 - 2*I*a - 1)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(a^2 - 2*I*a - 1)) + I*(-(a^3 - 3*I*a^2 - 3*a + I)/(a^3 + 3*I*a^2 - 3*a - I))^(1/4)*log(((I*a^2 - 2*a - I)*(-(a^3 - 3*I*a^2 - 3*a + I)/(a^3 + 3*I*a^2 - 3*a - I))^(3/4) + (a^2 - 2*I*a - 1)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(a^2 - 2*I*a - 1)) - I*(-(a^3 - 3*I*a^2 - 3*a + I)/(a^3 + 3*I*a^2 - 3*a - I))^(1/4)*log(((-I*a^2 + 2*a + I)*(-(a^3 - 3*I*a^2 - 3*a + I)/(a^3 + 3*I*a^2 - 3*a - I))^(3/4) + (a^2 - 2*I*a - 1)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(a^2 - 2*I*a - 1))","B",0
225,1,711,0,0.479214," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x^2,x, algorithm=""fricas"")","\frac{3 \, \left(-\frac{b^{4}}{16 \, a^{8} + 96 i \, a^{7} - 224 \, a^{6} - 224 i \, a^{5} - 224 i \, a^{3} + 224 \, a^{2} + 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(-i \, a + 1\right)} x \log\left(\frac{b^{3} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + {\left(8 \, a^{6} + 32 i \, a^{5} - 40 \, a^{4} - 40 \, a^{2} - 32 i \, a + 8\right)} \left(-\frac{b^{4}}{16 \, a^{8} + 96 i \, a^{7} - 224 \, a^{6} - 224 i \, a^{5} - 224 i \, a^{3} + 224 \, a^{2} + 96 i \, a - 16}\right)^{\frac{3}{4}}}{b^{3}}\right) + 3 \, \left(-\frac{b^{4}}{16 \, a^{8} + 96 i \, a^{7} - 224 \, a^{6} - 224 i \, a^{5} - 224 i \, a^{3} + 224 \, a^{2} + 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(i \, a - 1\right)} x \log\left(\frac{b^{3} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} - {\left(8 \, a^{6} + 32 i \, a^{5} - 40 \, a^{4} - 40 \, a^{2} - 32 i \, a + 8\right)} \left(-\frac{b^{4}}{16 \, a^{8} + 96 i \, a^{7} - 224 \, a^{6} - 224 i \, a^{5} - 224 i \, a^{3} + 224 \, a^{2} + 96 i \, a - 16}\right)^{\frac{3}{4}}}{b^{3}}\right) - 3 \, \left(-\frac{b^{4}}{16 \, a^{8} + 96 i \, a^{7} - 224 \, a^{6} - 224 i \, a^{5} - 224 i \, a^{3} + 224 \, a^{2} + 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(a + i\right)} x \log\left(\frac{b^{3} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + {\left(8 i \, a^{6} - 32 \, a^{5} - 40 i \, a^{4} - 40 i \, a^{2} + 32 \, a + 8 i\right)} \left(-\frac{b^{4}}{16 \, a^{8} + 96 i \, a^{7} - 224 \, a^{6} - 224 i \, a^{5} - 224 i \, a^{3} + 224 \, a^{2} + 96 i \, a - 16}\right)^{\frac{3}{4}}}{b^{3}}\right) + 3 \, \left(-\frac{b^{4}}{16 \, a^{8} + 96 i \, a^{7} - 224 \, a^{6} - 224 i \, a^{5} - 224 i \, a^{3} + 224 \, a^{2} + 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(a + i\right)} x \log\left(\frac{b^{3} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + {\left(-8 i \, a^{6} + 32 \, a^{5} + 40 i \, a^{4} + 40 i \, a^{2} - 32 \, a - 8 i\right)} \left(-\frac{b^{4}}{16 \, a^{8} + 96 i \, a^{7} - 224 \, a^{6} - 224 i \, a^{5} - 224 i \, a^{3} + 224 \, a^{2} + 96 i \, a - 16}\right)^{\frac{3}{4}}}{b^{3}}\right) - i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{{\left(a + i\right)} x}"," ",0,"(3*(-b^4/(16*a^8 + 96*I*a^7 - 224*a^6 - 224*I*a^5 - 224*I*a^3 + 224*a^2 + 96*I*a - 16))^(1/4)*(-I*a + 1)*x*log((b^3*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (8*a^6 + 32*I*a^5 - 40*a^4 - 40*a^2 - 32*I*a + 8)*(-b^4/(16*a^8 + 96*I*a^7 - 224*a^6 - 224*I*a^5 - 224*I*a^3 + 224*a^2 + 96*I*a - 16))^(3/4))/b^3) + 3*(-b^4/(16*a^8 + 96*I*a^7 - 224*a^6 - 224*I*a^5 - 224*I*a^3 + 224*a^2 + 96*I*a - 16))^(1/4)*(I*a - 1)*x*log((b^3*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) - (8*a^6 + 32*I*a^5 - 40*a^4 - 40*a^2 - 32*I*a + 8)*(-b^4/(16*a^8 + 96*I*a^7 - 224*a^6 - 224*I*a^5 - 224*I*a^3 + 224*a^2 + 96*I*a - 16))^(3/4))/b^3) - 3*(-b^4/(16*a^8 + 96*I*a^7 - 224*a^6 - 224*I*a^5 - 224*I*a^3 + 224*a^2 + 96*I*a - 16))^(1/4)*(a + I)*x*log((b^3*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (8*I*a^6 - 32*a^5 - 40*I*a^4 - 40*I*a^2 + 32*a + 8*I)*(-b^4/(16*a^8 + 96*I*a^7 - 224*a^6 - 224*I*a^5 - 224*I*a^3 + 224*a^2 + 96*I*a - 16))^(3/4))/b^3) + 3*(-b^4/(16*a^8 + 96*I*a^7 - 224*a^6 - 224*I*a^5 - 224*I*a^3 + 224*a^2 + 96*I*a - 16))^(1/4)*(a + I)*x*log((b^3*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (-8*I*a^6 + 32*a^5 + 40*I*a^4 + 40*I*a^2 - 32*a - 8*I)*(-b^4/(16*a^8 + 96*I*a^7 - 224*a^6 - 224*I*a^5 - 224*I*a^3 + 224*a^2 + 96*I*a - 16))^(3/4))/b^3) - I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/((a + I)*x)","B",0
226,1,561,0,0.481486," ","integrate(x^2/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{3 \, b^{3} \sqrt{\frac{64 i \, a^{4} + 64 \, a^{3} - 64 i \, a^{2} - 24 \, a + 9 i}{b^{6}}} \log\left(\frac{b^{3} \sqrt{\frac{64 i \, a^{4} + 64 \, a^{3} - 64 i \, a^{2} - 24 \, a + 9 i}{b^{6}}} + {\left(8 \, a^{2} - 4 i \, a - 3\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, a^{2} - 4 i \, a - 3}\right) - 3 \, b^{3} \sqrt{\frac{64 i \, a^{4} + 64 \, a^{3} - 64 i \, a^{2} - 24 \, a + 9 i}{b^{6}}} \log\left(-\frac{b^{3} \sqrt{\frac{64 i \, a^{4} + 64 \, a^{3} - 64 i \, a^{2} - 24 \, a + 9 i}{b^{6}}} - {\left(8 \, a^{2} - 4 i \, a - 3\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, a^{2} - 4 i \, a - 3}\right) - 3 \, b^{3} \sqrt{\frac{-64 i \, a^{4} - 64 \, a^{3} + 64 i \, a^{2} + 24 \, a - 9 i}{b^{6}}} \log\left(\frac{b^{3} \sqrt{\frac{-64 i \, a^{4} - 64 \, a^{3} + 64 i \, a^{2} + 24 \, a - 9 i}{b^{6}}} + {\left(8 \, a^{2} - 4 i \, a - 3\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, a^{2} - 4 i \, a - 3}\right) + 3 \, b^{3} \sqrt{\frac{-64 i \, a^{4} - 64 \, a^{3} + 64 i \, a^{2} + 24 \, a - 9 i}{b^{6}}} \log\left(-\frac{b^{3} \sqrt{\frac{-64 i \, a^{4} - 64 \, a^{3} + 64 i \, a^{2} + 24 \, a - 9 i}{b^{6}}} - {\left(8 \, a^{2} - 4 i \, a - 3\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, a^{2} - 4 i \, a - 3}\right) + 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(-8 i \, b^{2} x^{2} - 2 \, {\left(-4 i \, a - 5\right)} b x - 8 i \, a^{2} - 26 \, a + 11 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{48 \, b^{3}}"," ",0,"1/48*(3*b^3*sqrt((64*I*a^4 + 64*a^3 - 64*I*a^2 - 24*a + 9*I)/b^6)*log((b^3*sqrt((64*I*a^4 + 64*a^3 - 64*I*a^2 - 24*a + 9*I)/b^6) + (8*a^2 - 4*I*a - 3)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(8*a^2 - 4*I*a - 3)) - 3*b^3*sqrt((64*I*a^4 + 64*a^3 - 64*I*a^2 - 24*a + 9*I)/b^6)*log(-(b^3*sqrt((64*I*a^4 + 64*a^3 - 64*I*a^2 - 24*a + 9*I)/b^6) - (8*a^2 - 4*I*a - 3)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(8*a^2 - 4*I*a - 3)) - 3*b^3*sqrt((-64*I*a^4 - 64*a^3 + 64*I*a^2 + 24*a - 9*I)/b^6)*log((b^3*sqrt((-64*I*a^4 - 64*a^3 + 64*I*a^2 + 24*a - 9*I)/b^6) + (8*a^2 - 4*I*a - 3)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(8*a^2 - 4*I*a - 3)) + 3*b^3*sqrt((-64*I*a^4 - 64*a^3 + 64*I*a^2 + 24*a - 9*I)/b^6)*log(-(b^3*sqrt((-64*I*a^4 - 64*a^3 + 64*I*a^2 + 24*a - 9*I)/b^6) - (8*a^2 - 4*I*a - 3)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(8*a^2 - 4*I*a - 3)) + 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(-8*I*b^2*x^2 - 2*(-4*I*a - 5)*b*x - 8*I*a^2 - 26*a + 11*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b^3","A",0
227,1,421,0,0.445293," ","integrate(x/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x, algorithm=""fricas"")","-\frac{b^{2} \sqrt{\frac{16 i \, a^{2} + 8 \, a - i}{b^{4}}} \log\left(\frac{b^{2} \sqrt{\frac{16 i \, a^{2} + 8 \, a - i}{b^{4}}} + {\left(4 \, a - i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{4 \, a - i}\right) - b^{2} \sqrt{\frac{16 i \, a^{2} + 8 \, a - i}{b^{4}}} \log\left(-\frac{b^{2} \sqrt{\frac{16 i \, a^{2} + 8 \, a - i}{b^{4}}} - {\left(4 \, a - i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{4 \, a - i}\right) - b^{2} \sqrt{\frac{-16 i \, a^{2} - 8 \, a + i}{b^{4}}} \log\left(\frac{b^{2} \sqrt{\frac{-16 i \, a^{2} - 8 \, a + i}{b^{4}}} + {\left(4 \, a - i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{4 \, a - i}\right) + b^{2} \sqrt{\frac{-16 i \, a^{2} - 8 \, a + i}{b^{4}}} \log\left(-\frac{b^{2} \sqrt{\frac{-16 i \, a^{2} - 8 \, a + i}{b^{4}}} - {\left(4 \, a - i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{4 \, a - i}\right) - 2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(-2 i \, b x + 2 i \, a + 3\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, b^{2}}"," ",0,"-1/8*(b^2*sqrt((16*I*a^2 + 8*a - I)/b^4)*log((b^2*sqrt((16*I*a^2 + 8*a - I)/b^4) + (4*a - I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(4*a - I)) - b^2*sqrt((16*I*a^2 + 8*a - I)/b^4)*log(-(b^2*sqrt((16*I*a^2 + 8*a - I)/b^4) - (4*a - I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(4*a - I)) - b^2*sqrt((-16*I*a^2 - 8*a + I)/b^4)*log((b^2*sqrt((-16*I*a^2 - 8*a + I)/b^4) + (4*a - I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(4*a - I)) + b^2*sqrt((-16*I*a^2 - 8*a + I)/b^4)*log(-(b^2*sqrt((-16*I*a^2 - 8*a + I)/b^4) - (4*a - I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(4*a - I)) - 2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(-2*I*b*x + 2*I*a + 3)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b^2","A",0
228,1,266,0,0.477589," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{b \sqrt{\frac{i}{b^{2}}} \log\left(b \sqrt{\frac{i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - b \sqrt{\frac{i}{b^{2}}} \log\left(-b \sqrt{\frac{i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - b \sqrt{-\frac{i}{b^{2}}} \log\left(b \sqrt{-\frac{i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + b \sqrt{-\frac{i}{b^{2}}} \log\left(-b \sqrt{-\frac{i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - 2 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{2 \, b}"," ",0,"1/2*(b*sqrt(I/b^2)*log(b*sqrt(I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - b*sqrt(I/b^2)*log(-b*sqrt(I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - b*sqrt(-I/b^2)*log(b*sqrt(-I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + b*sqrt(-I/b^2)*log(-b*sqrt(-I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - 2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b","A",0
229,1,470,0,0.542755," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x,x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{4 i} \log\left(\frac{1}{2} i \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + \frac{1}{2} \, \sqrt{4 i} \log\left(-\frac{1}{2} i \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + \frac{1}{2} \, \sqrt{-4 i} \log\left(\frac{1}{2} i \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - \frac{1}{2} \, \sqrt{-4 i} \log\left(-\frac{1}{2} i \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + \left(-\frac{a + i}{a - i}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a - i\right)} \left(-\frac{a + i}{a - i}\right)^{\frac{3}{4}} + {\left(a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{a + i}\right) - \left(-\frac{a + i}{a - i}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(a - i\right)} \left(-\frac{a + i}{a - i}\right)^{\frac{3}{4}} - {\left(a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{a + i}\right) - i \, \left(-\frac{a + i}{a - i}\right)^{\frac{1}{4}} \log\left(\frac{{\left(i \, a + 1\right)} \left(-\frac{a + i}{a - i}\right)^{\frac{3}{4}} + {\left(a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{a + i}\right) + i \, \left(-\frac{a + i}{a - i}\right)^{\frac{1}{4}} \log\left(\frac{{\left(-i \, a - 1\right)} \left(-\frac{a + i}{a - i}\right)^{\frac{3}{4}} + {\left(a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{a + i}\right)"," ",0,"-1/2*sqrt(4*I)*log(1/2*I*sqrt(4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + 1/2*sqrt(4*I)*log(-1/2*I*sqrt(4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + 1/2*sqrt(-4*I)*log(1/2*I*sqrt(-4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - 1/2*sqrt(-4*I)*log(-1/2*I*sqrt(-4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + (-(a + I)/(a - I))^(1/4)*log(((a - I)*(-(a + I)/(a - I))^(3/4) + (a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(a + I)) - (-(a + I)/(a - I))^(1/4)*log(-((a - I)*(-(a + I)/(a - I))^(3/4) - (a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(a + I)) - I*(-(a + I)/(a - I))^(1/4)*log(((I*a + 1)*(-(a + I)/(a - I))^(3/4) + (a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(a + I)) + I*(-(a + I)/(a - I))^(1/4)*log(((-I*a - 1)*(-(a + I)/(a - I))^(3/4) + (a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(a + I))","A",0
230,1,728,0,0.469338," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x^2,x, algorithm=""fricas"")","\frac{\left(-\frac{b^{4}}{16 \, a^{8} - 32 i \, a^{7} + 32 \, a^{6} - 96 i \, a^{5} - 96 i \, a^{3} - 32 \, a^{2} - 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(-i \, a - 1\right)} x \log\left(\frac{b^{3} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + {\left(8 \, a^{6} - 16 i \, a^{5} + 8 \, a^{4} - 32 i \, a^{3} - 8 \, a^{2} - 16 i \, a - 8\right)} \left(-\frac{b^{4}}{16 \, a^{8} - 32 i \, a^{7} + 32 \, a^{6} - 96 i \, a^{5} - 96 i \, a^{3} - 32 \, a^{2} - 32 i \, a - 16}\right)^{\frac{3}{4}}}{b^{3}}\right) + \left(-\frac{b^{4}}{16 \, a^{8} - 32 i \, a^{7} + 32 \, a^{6} - 96 i \, a^{5} - 96 i \, a^{3} - 32 \, a^{2} - 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(i \, a + 1\right)} x \log\left(\frac{b^{3} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} - {\left(8 \, a^{6} - 16 i \, a^{5} + 8 \, a^{4} - 32 i \, a^{3} - 8 \, a^{2} - 16 i \, a - 8\right)} \left(-\frac{b^{4}}{16 \, a^{8} - 32 i \, a^{7} + 32 \, a^{6} - 96 i \, a^{5} - 96 i \, a^{3} - 32 \, a^{2} - 32 i \, a - 16}\right)^{\frac{3}{4}}}{b^{3}}\right) - \left(-\frac{b^{4}}{16 \, a^{8} - 32 i \, a^{7} + 32 \, a^{6} - 96 i \, a^{5} - 96 i \, a^{3} - 32 \, a^{2} - 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(a - i\right)} x \log\left(\frac{b^{3} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + {\left(8 i \, a^{6} + 16 \, a^{5} + 8 i \, a^{4} + 32 \, a^{3} - 8 i \, a^{2} + 16 \, a - 8 i\right)} \left(-\frac{b^{4}}{16 \, a^{8} - 32 i \, a^{7} + 32 \, a^{6} - 96 i \, a^{5} - 96 i \, a^{3} - 32 \, a^{2} - 32 i \, a - 16}\right)^{\frac{3}{4}}}{b^{3}}\right) + \left(-\frac{b^{4}}{16 \, a^{8} - 32 i \, a^{7} + 32 \, a^{6} - 96 i \, a^{5} - 96 i \, a^{3} - 32 \, a^{2} - 32 i \, a - 16}\right)^{\frac{1}{4}} {\left(a - i\right)} x \log\left(\frac{b^{3} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + {\left(-8 i \, a^{6} - 16 \, a^{5} - 8 i \, a^{4} - 32 \, a^{3} + 8 i \, a^{2} - 16 \, a + 8 i\right)} \left(-\frac{b^{4}}{16 \, a^{8} - 32 i \, a^{7} + 32 \, a^{6} - 96 i \, a^{5} - 96 i \, a^{3} - 32 \, a^{2} - 32 i \, a - 16}\right)^{\frac{3}{4}}}{b^{3}}\right) + i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{{\left(a - i\right)} x}"," ",0,"((-b^4/(16*a^8 - 32*I*a^7 + 32*a^6 - 96*I*a^5 - 96*I*a^3 - 32*a^2 - 32*I*a - 16))^(1/4)*(-I*a - 1)*x*log((b^3*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (8*a^6 - 16*I*a^5 + 8*a^4 - 32*I*a^3 - 8*a^2 - 16*I*a - 8)*(-b^4/(16*a^8 - 32*I*a^7 + 32*a^6 - 96*I*a^5 - 96*I*a^3 - 32*a^2 - 32*I*a - 16))^(3/4))/b^3) + (-b^4/(16*a^8 - 32*I*a^7 + 32*a^6 - 96*I*a^5 - 96*I*a^3 - 32*a^2 - 32*I*a - 16))^(1/4)*(I*a + 1)*x*log((b^3*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) - (8*a^6 - 16*I*a^5 + 8*a^4 - 32*I*a^3 - 8*a^2 - 16*I*a - 8)*(-b^4/(16*a^8 - 32*I*a^7 + 32*a^6 - 96*I*a^5 - 96*I*a^3 - 32*a^2 - 32*I*a - 16))^(3/4))/b^3) - (-b^4/(16*a^8 - 32*I*a^7 + 32*a^6 - 96*I*a^5 - 96*I*a^3 - 32*a^2 - 32*I*a - 16))^(1/4)*(a - I)*x*log((b^3*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (8*I*a^6 + 16*a^5 + 8*I*a^4 + 32*a^3 - 8*I*a^2 + 16*a - 8*I)*(-b^4/(16*a^8 - 32*I*a^7 + 32*a^6 - 96*I*a^5 - 96*I*a^3 - 32*a^2 - 32*I*a - 16))^(3/4))/b^3) + (-b^4/(16*a^8 - 32*I*a^7 + 32*a^6 - 96*I*a^5 - 96*I*a^3 - 32*a^2 - 32*I*a - 16))^(1/4)*(a - I)*x*log((b^3*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (-8*I*a^6 - 16*a^5 - 8*I*a^4 - 32*a^3 + 8*I*a^2 - 16*a + 8*I)*(-b^4/(16*a^8 - 32*I*a^7 + 32*a^6 - 96*I*a^5 - 96*I*a^3 - 32*a^2 - 32*I*a - 16))^(3/4))/b^3) + I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/((a - I)*x)","B",0
231,1,555,0,0.471532," ","integrate(x^2/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{3 \, b^{3} \sqrt{\frac{576 i \, a^{4} + 1728 \, a^{3} - 2112 i \, a^{2} - 1224 \, a + 289 i}{b^{6}}} \log\left(\frac{i \, b^{3} \sqrt{\frac{576 i \, a^{4} + 1728 \, a^{3} - 2112 i \, a^{2} - 1224 \, a + 289 i}{b^{6}}} + {\left(24 \, a^{2} - 36 i \, a - 17\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{24 \, a^{2} - 36 i \, a - 17}\right) - 3 \, b^{3} \sqrt{\frac{576 i \, a^{4} + 1728 \, a^{3} - 2112 i \, a^{2} - 1224 \, a + 289 i}{b^{6}}} \log\left(\frac{-i \, b^{3} \sqrt{\frac{576 i \, a^{4} + 1728 \, a^{3} - 2112 i \, a^{2} - 1224 \, a + 289 i}{b^{6}}} + {\left(24 \, a^{2} - 36 i \, a - 17\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{24 \, a^{2} - 36 i \, a - 17}\right) + 3 \, b^{3} \sqrt{\frac{-576 i \, a^{4} - 1728 \, a^{3} + 2112 i \, a^{2} + 1224 \, a - 289 i}{b^{6}}} \log\left(\frac{i \, b^{3} \sqrt{\frac{-576 i \, a^{4} - 1728 \, a^{3} + 2112 i \, a^{2} + 1224 \, a - 289 i}{b^{6}}} + {\left(24 \, a^{2} - 36 i \, a - 17\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{24 \, a^{2} - 36 i \, a - 17}\right) - 3 \, b^{3} \sqrt{\frac{-576 i \, a^{4} - 1728 \, a^{3} + 2112 i \, a^{2} + 1224 \, a - 289 i}{b^{6}}} \log\left(\frac{-i \, b^{3} \sqrt{\frac{-576 i \, a^{4} - 1728 \, a^{3} + 2112 i \, a^{2} + 1224 \, a - 289 i}{b^{6}}} + {\left(24 \, a^{2} - 36 i \, a - 17\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{24 \, a^{2} - 36 i \, a - 17}\right) - 2 \, {\left(8 \, b^{3} x^{3} + 22 i \, b^{2} x^{2} + 8 \, a^{3} - {\left(40 i \, a + 37\right)} b x - 38 i \, a^{2} + 23 \, a - 23 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{48 \, b^{3}}"," ",0,"1/48*(3*b^3*sqrt((576*I*a^4 + 1728*a^3 - 2112*I*a^2 - 1224*a + 289*I)/b^6)*log((I*b^3*sqrt((576*I*a^4 + 1728*a^3 - 2112*I*a^2 - 1224*a + 289*I)/b^6) + (24*a^2 - 36*I*a - 17)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(24*a^2 - 36*I*a - 17)) - 3*b^3*sqrt((576*I*a^4 + 1728*a^3 - 2112*I*a^2 - 1224*a + 289*I)/b^6)*log((-I*b^3*sqrt((576*I*a^4 + 1728*a^3 - 2112*I*a^2 - 1224*a + 289*I)/b^6) + (24*a^2 - 36*I*a - 17)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(24*a^2 - 36*I*a - 17)) + 3*b^3*sqrt((-576*I*a^4 - 1728*a^3 + 2112*I*a^2 + 1224*a - 289*I)/b^6)*log((I*b^3*sqrt((-576*I*a^4 - 1728*a^3 + 2112*I*a^2 + 1224*a - 289*I)/b^6) + (24*a^2 - 36*I*a - 17)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(24*a^2 - 36*I*a - 17)) - 3*b^3*sqrt((-576*I*a^4 - 1728*a^3 + 2112*I*a^2 + 1224*a - 289*I)/b^6)*log((-I*b^3*sqrt((-576*I*a^4 - 1728*a^3 + 2112*I*a^2 + 1224*a - 289*I)/b^6) + (24*a^2 - 36*I*a - 17)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(24*a^2 - 36*I*a - 17)) - 2*(8*b^3*x^3 + 22*I*b^2*x^2 + 8*a^3 - (40*I*a + 37)*b*x - 38*I*a^2 + 23*a - 23*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b^3","A",0
232,1,415,0,0.625933," ","integrate(x/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x, algorithm=""fricas"")","-\frac{b^{2} \sqrt{\frac{144 i \, a^{2} + 216 \, a - 81 i}{b^{4}}} \log\left(\frac{i \, b^{2} \sqrt{\frac{144 i \, a^{2} + 216 \, a - 81 i}{b^{4}}} + {\left(12 \, a - 9 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{12 \, a - 9 i}\right) - b^{2} \sqrt{\frac{144 i \, a^{2} + 216 \, a - 81 i}{b^{4}}} \log\left(\frac{-i \, b^{2} \sqrt{\frac{144 i \, a^{2} + 216 \, a - 81 i}{b^{4}}} + {\left(12 \, a - 9 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{12 \, a - 9 i}\right) + b^{2} \sqrt{\frac{-144 i \, a^{2} - 216 \, a + 81 i}{b^{4}}} \log\left(\frac{i \, b^{2} \sqrt{\frac{-144 i \, a^{2} - 216 \, a + 81 i}{b^{4}}} + {\left(12 \, a - 9 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{12 \, a - 9 i}\right) - b^{2} \sqrt{\frac{-144 i \, a^{2} - 216 \, a + 81 i}{b^{4}}} \log\left(\frac{-i \, b^{2} \sqrt{\frac{-144 i \, a^{2} - 216 \, a + 81 i}{b^{4}}} + {\left(12 \, a - 9 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{12 \, a - 9 i}\right) + 2 \, {\left(2 \, b^{2} x^{2} - 2 \, a^{2} + 7 i \, b x + 3 i \, a - 5\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{8 \, b^{2}}"," ",0,"-1/8*(b^2*sqrt((144*I*a^2 + 216*a - 81*I)/b^4)*log((I*b^2*sqrt((144*I*a^2 + 216*a - 81*I)/b^4) + (12*a - 9*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(12*a - 9*I)) - b^2*sqrt((144*I*a^2 + 216*a - 81*I)/b^4)*log((-I*b^2*sqrt((144*I*a^2 + 216*a - 81*I)/b^4) + (12*a - 9*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(12*a - 9*I)) + b^2*sqrt((-144*I*a^2 - 216*a + 81*I)/b^4)*log((I*b^2*sqrt((-144*I*a^2 - 216*a + 81*I)/b^4) + (12*a - 9*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(12*a - 9*I)) - b^2*sqrt((-144*I*a^2 - 216*a + 81*I)/b^4)*log((-I*b^2*sqrt((-144*I*a^2 - 216*a + 81*I)/b^4) + (12*a - 9*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/(12*a - 9*I)) + 2*(2*b^2*x^2 - 2*a^2 + 7*I*b*x + 3*I*a - 5)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b^2","A",0
233,1,258,0,0.484785," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{b \sqrt{\frac{9 i}{b^{2}}} \log\left(\frac{1}{3} i \, b \sqrt{\frac{9 i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - b \sqrt{\frac{9 i}{b^{2}}} \log\left(-\frac{1}{3} i \, b \sqrt{\frac{9 i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + b \sqrt{-\frac{9 i}{b^{2}}} \log\left(\frac{1}{3} i \, b \sqrt{-\frac{9 i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - b \sqrt{-\frac{9 i}{b^{2}}} \log\left(-\frac{1}{3} i \, b \sqrt{-\frac{9 i}{b^{2}}} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - {\left(2 \, b x + 2 \, a + 2 i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{2 \, b}"," ",0,"1/2*(b*sqrt(9*I/b^2)*log(1/3*I*b*sqrt(9*I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - b*sqrt(9*I/b^2)*log(-1/3*I*b*sqrt(9*I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + b*sqrt(-9*I/b^2)*log(1/3*I*b*sqrt(-9*I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - b*sqrt(-9*I/b^2)*log(-1/3*I*b*sqrt(-9*I/b^2) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - (2*b*x + 2*a + 2*I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/b","A",0
234,1,629,0,0.540285," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x,x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{4 i} \log\left(\frac{1}{2} \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + \frac{1}{2} \, \sqrt{4 i} \log\left(-\frac{1}{2} \, \sqrt{4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) - \frac{1}{2} \, \sqrt{-4 i} \log\left(\frac{1}{2} \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + \frac{1}{2} \, \sqrt{-4 i} \log\left(-\frac{1}{2} \, \sqrt{-4 i} + \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}\right) + \left(-\frac{a^{3} + 3 i \, a^{2} - 3 \, a - i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + {\left(a - i\right)} \left(-\frac{a^{3} + 3 i \, a^{2} - 3 \, a - i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}\right)^{\frac{1}{4}}}{a + i}\right) - \left(-\frac{a^{3} + 3 i \, a^{2} - 3 \, a - i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} - {\left(a - i\right)} \left(-\frac{a^{3} + 3 i \, a^{2} - 3 \, a - i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}\right)^{\frac{1}{4}}}{a + i}\right) + i \, \left(-\frac{a^{3} + 3 i \, a^{2} - 3 \, a - i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + {\left(i \, a + 1\right)} \left(-\frac{a^{3} + 3 i \, a^{2} - 3 \, a - i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}\right)^{\frac{1}{4}}}{a + i}\right) - i \, \left(-\frac{a^{3} + 3 i \, a^{2} - 3 \, a - i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + {\left(-i \, a - 1\right)} \left(-\frac{a^{3} + 3 i \, a^{2} - 3 \, a - i}{a^{3} - 3 i \, a^{2} - 3 \, a + i}\right)^{\frac{1}{4}}}{a + i}\right)"," ",0,"-1/2*sqrt(4*I)*log(1/2*sqrt(4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + 1/2*sqrt(4*I)*log(-1/2*sqrt(4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) - 1/2*sqrt(-4*I)*log(1/2*sqrt(-4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + 1/2*sqrt(-4*I)*log(-1/2*sqrt(-4*I) + sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I))) + (-(a^3 + 3*I*a^2 - 3*a - I)/(a^3 - 3*I*a^2 - 3*a + I))^(1/4)*log(((a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (a - I)*(-(a^3 + 3*I*a^2 - 3*a - I)/(a^3 - 3*I*a^2 - 3*a + I))^(1/4))/(a + I)) - (-(a^3 + 3*I*a^2 - 3*a - I)/(a^3 - 3*I*a^2 - 3*a + I))^(1/4)*log(((a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) - (a - I)*(-(a^3 + 3*I*a^2 - 3*a - I)/(a^3 - 3*I*a^2 - 3*a + I))^(1/4))/(a + I)) + I*(-(a^3 + 3*I*a^2 - 3*a - I)/(a^3 - 3*I*a^2 - 3*a + I))^(1/4)*log(((a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (I*a + 1)*(-(a^3 + 3*I*a^2 - 3*a - I)/(a^3 - 3*I*a^2 - 3*a + I))^(1/4))/(a + I)) - I*(-(a^3 + 3*I*a^2 - 3*a - I)/(a^3 - 3*I*a^2 - 3*a + I))^(1/4)*log(((a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (-I*a - 1)*(-(a^3 + 3*I*a^2 - 3*a - I)/(a^3 - 3*I*a^2 - 3*a + I))^(1/4))/(a + I))","B",0
235,1,626,0,0.504443," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x^2,x, algorithm=""fricas"")","\frac{3 \, \left(-\frac{b^{4}}{16 \, a^{8} - 96 i \, a^{7} - 224 \, a^{6} + 224 i \, a^{5} + 224 i \, a^{3} + 224 \, a^{2} - 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(-i \, a - 1\right)} x \log\left(\frac{b \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + 2 \, \left(-\frac{b^{4}}{16 \, a^{8} - 96 i \, a^{7} - 224 \, a^{6} + 224 i \, a^{5} + 224 i \, a^{3} + 224 \, a^{2} - 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(a^{2} - 2 i \, a - 1\right)}}{b}\right) + 3 \, \left(-\frac{b^{4}}{16 \, a^{8} - 96 i \, a^{7} - 224 \, a^{6} + 224 i \, a^{5} + 224 i \, a^{3} + 224 \, a^{2} - 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(i \, a + 1\right)} x \log\left(\frac{b \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} - 2 \, \left(-\frac{b^{4}}{16 \, a^{8} - 96 i \, a^{7} - 224 \, a^{6} + 224 i \, a^{5} + 224 i \, a^{3} + 224 \, a^{2} - 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(a^{2} - 2 i \, a - 1\right)}}{b}\right) + 3 \, \left(-\frac{b^{4}}{16 \, a^{8} - 96 i \, a^{7} - 224 \, a^{6} + 224 i \, a^{5} + 224 i \, a^{3} + 224 \, a^{2} - 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(a - i\right)} x \log\left(\frac{b \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + \left(-\frac{b^{4}}{16 \, a^{8} - 96 i \, a^{7} - 224 \, a^{6} + 224 i \, a^{5} + 224 i \, a^{3} + 224 \, a^{2} - 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(2 i \, a^{2} + 4 \, a - 2 i\right)}}{b}\right) - 3 \, \left(-\frac{b^{4}}{16 \, a^{8} - 96 i \, a^{7} - 224 \, a^{6} + 224 i \, a^{5} + 224 i \, a^{3} + 224 \, a^{2} - 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(a - i\right)} x \log\left(\frac{b \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}} + \left(-\frac{b^{4}}{16 \, a^{8} - 96 i \, a^{7} - 224 \, a^{6} + 224 i \, a^{5} + 224 i \, a^{3} + 224 \, a^{2} - 96 i \, a - 16}\right)^{\frac{1}{4}} {\left(-2 i \, a^{2} - 4 \, a + 2 i\right)}}{b}\right) + {\left(b x + a + i\right)} \sqrt{\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b x + a + i}}}{{\left(a - i\right)} x}"," ",0,"(3*(-b^4/(16*a^8 - 96*I*a^7 - 224*a^6 + 224*I*a^5 + 224*I*a^3 + 224*a^2 - 96*I*a - 16))^(1/4)*(-I*a - 1)*x*log((b*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + 2*(-b^4/(16*a^8 - 96*I*a^7 - 224*a^6 + 224*I*a^5 + 224*I*a^3 + 224*a^2 - 96*I*a - 16))^(1/4)*(a^2 - 2*I*a - 1))/b) + 3*(-b^4/(16*a^8 - 96*I*a^7 - 224*a^6 + 224*I*a^5 + 224*I*a^3 + 224*a^2 - 96*I*a - 16))^(1/4)*(I*a + 1)*x*log((b*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) - 2*(-b^4/(16*a^8 - 96*I*a^7 - 224*a^6 + 224*I*a^5 + 224*I*a^3 + 224*a^2 - 96*I*a - 16))^(1/4)*(a^2 - 2*I*a - 1))/b) + 3*(-b^4/(16*a^8 - 96*I*a^7 - 224*a^6 + 224*I*a^5 + 224*I*a^3 + 224*a^2 - 96*I*a - 16))^(1/4)*(a - I)*x*log((b*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (-b^4/(16*a^8 - 96*I*a^7 - 224*a^6 + 224*I*a^5 + 224*I*a^3 + 224*a^2 - 96*I*a - 16))^(1/4)*(2*I*a^2 + 4*a - 2*I))/b) - 3*(-b^4/(16*a^8 - 96*I*a^7 - 224*a^6 + 224*I*a^5 + 224*I*a^3 + 224*a^2 - 96*I*a - 16))^(1/4)*(a - I)*x*log((b*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)) + (-b^4/(16*a^8 - 96*I*a^7 - 224*a^6 + 224*I*a^5 + 224*I*a^3 + 224*a^2 - 96*I*a - 16))^(1/4)*(-2*I*a^2 - 4*a + 2*I))/b) + (b*x + a + I)*sqrt(I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(b*x + a + I)))/((a - I)*x)","B",0
236,0,0,0,0.505940," ","integrate(exp(n*arctan(b*x+a))*x^m,x, algorithm=""fricas"")","{\rm integral}\left(x^{m} e^{\left(n \arctan\left(b x + a\right)\right)}, x\right)"," ",0,"integral(x^m*e^(n*arctan(b*x + a)), x)","F",0
237,0,0,0,0.437491," ","integrate(exp(n*arctan(b*x+a))*x^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{3} e^{\left(n \arctan\left(b x + a\right)\right)}, x\right)"," ",0,"integral(x^3*e^(n*arctan(b*x + a)), x)","F",0
238,0,0,0,0.485530," ","integrate(exp(n*arctan(b*x+a))*x^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} e^{\left(n \arctan\left(b x + a\right)\right)}, x\right)"," ",0,"integral(x^2*e^(n*arctan(b*x + a)), x)","F",0
239,0,0,0,0.457100," ","integrate(exp(n*arctan(b*x+a))*x,x, algorithm=""fricas"")","{\rm integral}\left(x e^{\left(n \arctan\left(b x + a\right)\right)}, x\right)"," ",0,"integral(x*e^(n*arctan(b*x + a)), x)","F",0
240,0,0,0,0.433150," ","integrate(exp(n*arctan(b*x+a)),x, algorithm=""fricas"")","{\rm integral}\left(e^{\left(n \arctan\left(b x + a\right)\right)}, x\right)"," ",0,"integral(e^(n*arctan(b*x + a)), x)","F",0
241,0,0,0,0.604903," ","integrate(exp(n*arctan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(n \arctan\left(b x + a\right)\right)}}{x}, x\right)"," ",0,"integral(e^(n*arctan(b*x + a))/x, x)","F",0
242,0,0,0,0.488555," ","integrate(exp(n*arctan(b*x+a))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(n \arctan\left(b x + a\right)\right)}}{x^{2}}, x\right)"," ",0,"integral(e^(n*arctan(b*x + a))/x^2, x)","F",0
243,0,0,0,0.459331," ","integrate(exp(n*arctan(b*x+a))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(n \arctan\left(b x + a\right)\right)}}{x^{3}}, x\right)"," ",0,"integral(e^(n*arctan(b*x + a))/x^3, x)","F",0
244,0,0,0,0.519127," ","integrate(exp(arctan(a*x))*(a^2*c*x^2+c)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{p} e^{\left(\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^p*e^(arctan(a*x)), x)","F",0
245,0,0,0,0.446832," ","integrate(exp(arctan(a*x))*(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} e^{\left(\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*e^(arctan(a*x)), x)","F",0
246,0,0,0,0.469019," ","integrate(exp(arctan(a*x))*(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} e^{\left(\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*e^(arctan(a*x)), x)","F",0
247,0,0,0,0.472398," ","integrate(exp(arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(e^{\left(\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral(e^(arctan(a*x)), x)","F",0
248,1,12,0,0.432886," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{e^{\left(\arctan\left(a x\right)\right)}}{a c}"," ",0,"e^(arctan(a*x))/(a*c)","A",0
249,1,39,0,0.531698," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} x^{2} + 2 \, a x + 3\right)} e^{\left(\arctan\left(a x\right)\right)}}{5 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)}}"," ",0,"1/5*(2*a^2*x^2 + 2*a*x + 3)*e^(arctan(a*x))/(a^3*c^2*x^2 + a*c^2)","A",0
250,1,66,0,0.543648," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{{\left(24 \, a^{4} x^{4} + 24 \, a^{3} x^{3} + 60 \, a^{2} x^{2} + 44 \, a x + 41\right)} e^{\left(\arctan\left(a x\right)\right)}}{85 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"1/85*(24*a^4*x^4 + 24*a^3*x^3 + 60*a^2*x^2 + 44*a*x + 41)*e^(arctan(a*x))/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
251,1,93,0,0.468130," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^4,x, algorithm=""fricas"")","\frac{{\left(144 \, a^{6} x^{6} + 144 \, a^{5} x^{5} + 504 \, a^{4} x^{4} + 408 \, a^{3} x^{3} + 606 \, a^{2} x^{2} + 366 \, a x + 263\right)} e^{\left(\arctan\left(a x\right)\right)}}{629 \, {\left(a^{7} c^{4} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{3} c^{4} x^{2} + a c^{4}\right)}}"," ",0,"1/629*(144*a^6*x^6 + 144*a^5*x^5 + 504*a^4*x^4 + 408*a^3*x^3 + 606*a^2*x^2 + 366*a*x + 263)*e^(arctan(a*x))/(a^7*c^4*x^6 + 3*a^5*c^4*x^4 + 3*a^3*c^4*x^2 + a*c^4)","A",0
252,1,120,0,0.515290," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^5,x, algorithm=""fricas"")","\frac{{\left(8064 \, a^{8} x^{8} + 8064 \, a^{7} x^{7} + 36288 \, a^{6} x^{6} + 30912 \, a^{5} x^{5} + 62160 \, a^{4} x^{4} + 43344 \, a^{3} x^{3} + 48664 \, a^{2} x^{2} + 25528 \, a x + 15357\right)} e^{\left(\arctan\left(a x\right)\right)}}{40885 \, {\left(a^{9} c^{5} x^{8} + 4 \, a^{7} c^{5} x^{6} + 6 \, a^{5} c^{5} x^{4} + 4 \, a^{3} c^{5} x^{2} + a c^{5}\right)}}"," ",0,"1/40885*(8064*a^8*x^8 + 8064*a^7*x^7 + 36288*a^6*x^6 + 30912*a^5*x^5 + 62160*a^4*x^4 + 43344*a^3*x^3 + 48664*a^2*x^2 + 25528*a*x + 15357)*e^(arctan(a*x))/(a^9*c^5*x^8 + 4*a^7*c^5*x^6 + 6*a^5*c^5*x^4 + 4*a^3*c^5*x^2 + a*c^5)","A",0
253,0,0,0,0.506159," ","integrate(exp(arctan(a*x))*(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} e^{\left(\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*e^(arctan(a*x)), x)","F",0
254,0,0,0,0.533006," ","integrate(exp(arctan(a*x))*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} e^{\left(\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*e^(arctan(a*x)), x)","F",0
255,0,0,0,0.643888," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(\arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(e^(arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
256,1,42,0,0.508216," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(a x + 1\right)} e^{\left(\arctan\left(a x\right)\right)}}{2 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)}}"," ",0,"1/2*sqrt(a^2*c*x^2 + c)*(a*x + 1)*e^(arctan(a*x))/(a^3*c^2*x^2 + a*c^2)","A",0
257,1,70,0,0.477065," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + 6 \, a x + 4\right)} \sqrt{a^{2} c x^{2} + c} e^{\left(\arctan\left(a x\right)\right)}}{10 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"1/10*(3*a^3*x^3 + 3*a^2*x^2 + 6*a*x + 4)*sqrt(a^2*c*x^2 + c)*e^(arctan(a*x))/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
258,1,97,0,0.657989," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","\frac{{\left(6 \, a^{5} x^{5} + 6 \, a^{4} x^{4} + 18 \, a^{3} x^{3} + 14 \, a^{2} x^{2} + 17 \, a x + 9\right)} \sqrt{a^{2} c x^{2} + c} e^{\left(\arctan\left(a x\right)\right)}}{26 \, {\left(a^{7} c^{4} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{3} c^{4} x^{2} + a c^{4}\right)}}"," ",0,"1/26*(6*a^5*x^5 + 6*a^4*x^4 + 18*a^3*x^3 + 14*a^2*x^2 + 17*a*x + 9)*sqrt(a^2*c*x^2 + c)*e^(arctan(a*x))/(a^7*c^4*x^6 + 3*a^5*c^4*x^4 + 3*a^3*c^4*x^2 + a*c^4)","A",0
259,0,0,0,0.677242," ","integrate(exp(2*arctan(a*x))*(a^2*c*x^2+c)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{p} e^{\left(2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^p*e^(2*arctan(a*x)), x)","F",0
260,0,0,0,0.520726," ","integrate(exp(2*arctan(a*x))*(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} e^{\left(2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*e^(2*arctan(a*x)), x)","F",0
261,0,0,0,0.501488," ","integrate(exp(2*arctan(a*x))*(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} e^{\left(2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*e^(2*arctan(a*x)), x)","F",0
262,0,0,0,0.551773," ","integrate(exp(2*arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(e^{\left(2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral(e^(2*arctan(a*x)), x)","F",0
263,1,15,0,0.559502," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{e^{\left(2 \, \arctan\left(a x\right)\right)}}{2 \, a c}"," ",0,"1/2*e^(2*arctan(a*x))/(a*c)","A",0
264,1,40,0,0.477497," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} + 2 \, a x + 3\right)} e^{\left(2 \, \arctan\left(a x\right)\right)}}{8 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)}}"," ",0,"1/8*(a^2*x^2 + 2*a*x + 3)*e^(2*arctan(a*x))/(a^3*c^2*x^2 + a*c^2)","A",0
265,1,68,0,0.564814," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{4} x^{4} + 6 \, a^{3} x^{3} + 12 \, a^{2} x^{2} + 14 \, a x + 13\right)} e^{\left(2 \, \arctan\left(a x\right)\right)}}{40 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"1/40*(3*a^4*x^4 + 6*a^3*x^3 + 12*a^2*x^2 + 14*a*x + 13)*e^(2*arctan(a*x))/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
266,1,95,0,0.483199," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^4,x, algorithm=""fricas"")","\frac{{\left(9 \, a^{6} x^{6} + 18 \, a^{5} x^{5} + 45 \, a^{4} x^{4} + 60 \, a^{3} x^{3} + 75 \, a^{2} x^{2} + 66 \, a x + 47\right)} e^{\left(2 \, \arctan\left(a x\right)\right)}}{160 \, {\left(a^{7} c^{4} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{3} c^{4} x^{2} + a c^{4}\right)}}"," ",0,"1/160*(9*a^6*x^6 + 18*a^5*x^5 + 45*a^4*x^4 + 60*a^3*x^3 + 75*a^2*x^2 + 66*a*x + 47)*e^(2*arctan(a*x))/(a^7*c^4*x^6 + 3*a^5*c^4*x^4 + 3*a^3*c^4*x^2 + a*c^4)","A",0
267,0,0,0,0.477625," ","integrate(exp(2*arctan(a*x))*(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} e^{\left(2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*e^(2*arctan(a*x)), x)","F",0
268,0,0,0,0.450338," ","integrate(exp(2*arctan(a*x))*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} e^{\left(2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*e^(2*arctan(a*x)), x)","F",0
269,0,0,0,0.500745," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(2 \, \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(e^(2*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
270,1,44,0,0.474600," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(a x + 2\right)} e^{\left(2 \, \arctan\left(a x\right)\right)}}{5 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)}}"," ",0,"1/5*sqrt(a^2*c*x^2 + c)*(a*x + 2)*e^(2*arctan(a*x))/(a^3*c^2*x^2 + a*c^2)","A",0
271,1,72,0,0.428168," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(6 \, a^{3} x^{3} + 12 \, a^{2} x^{2} + 21 \, a x + 22\right)} \sqrt{a^{2} c x^{2} + c} e^{\left(2 \, \arctan\left(a x\right)\right)}}{65 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"1/65*(6*a^3*x^3 + 12*a^2*x^2 + 21*a*x + 22)*sqrt(a^2*c*x^2 + c)*e^(2*arctan(a*x))/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
272,1,99,0,0.420898," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","\frac{{\left(24 \, a^{5} x^{5} + 48 \, a^{4} x^{4} + 108 \, a^{3} x^{3} + 136 \, a^{2} x^{2} + 149 \, a x + 114\right)} \sqrt{a^{2} c x^{2} + c} e^{\left(2 \, \arctan\left(a x\right)\right)}}{377 \, {\left(a^{7} c^{4} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{3} c^{4} x^{2} + a c^{4}\right)}}"," ",0,"1/377*(24*a^5*x^5 + 48*a^4*x^4 + 108*a^3*x^3 + 136*a^2*x^2 + 149*a*x + 114)*sqrt(a^2*c*x^2 + c)*e^(2*arctan(a*x))/(a^7*c^4*x^6 + 3*a^5*c^4*x^4 + 3*a^3*c^4*x^2 + a*c^4)","A",0
273,0,0,0,0.457289," ","integrate((a^2*c*x^2+c)^p/exp(arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{p} e^{\left(-\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^p*e^(-arctan(a*x)), x)","F",0
274,0,0,0,0.457759," ","integrate((a^2*c*x^2+c)^2/exp(arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} e^{\left(-\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*e^(-arctan(a*x)), x)","F",0
275,0,0,0,0.531713," ","integrate((a^2*c*x^2+c)/exp(arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} e^{\left(-\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*e^(-arctan(a*x)), x)","F",0
276,0,0,0,0.488551," ","integrate(exp(-arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(e^{\left(-\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral(e^(-arctan(a*x)), x)","F",0
277,1,15,0,0.471016," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c),x, algorithm=""fricas"")","-\frac{e^{\left(-\arctan\left(a x\right)\right)}}{a c}"," ",0,"-e^(-arctan(a*x))/(a*c)","A",0
278,1,41,0,0.568696," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} x^{2} - 2 \, a x + 3\right)} e^{\left(-\arctan\left(a x\right)\right)}}{5 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)}}"," ",0,"-1/5*(2*a^2*x^2 - 2*a*x + 3)*e^(-arctan(a*x))/(a^3*c^2*x^2 + a*c^2)","A",0
279,1,68,0,0.456766," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{{\left(24 \, a^{4} x^{4} - 24 \, a^{3} x^{3} + 60 \, a^{2} x^{2} - 44 \, a x + 41\right)} e^{\left(-\arctan\left(a x\right)\right)}}{85 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"-1/85*(24*a^4*x^4 - 24*a^3*x^3 + 60*a^2*x^2 - 44*a*x + 41)*e^(-arctan(a*x))/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
280,1,95,0,0.455666," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^4,x, algorithm=""fricas"")","-\frac{{\left(144 \, a^{6} x^{6} - 144 \, a^{5} x^{5} + 504 \, a^{4} x^{4} - 408 \, a^{3} x^{3} + 606 \, a^{2} x^{2} - 366 \, a x + 263\right)} e^{\left(-\arctan\left(a x\right)\right)}}{629 \, {\left(a^{7} c^{4} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{3} c^{4} x^{2} + a c^{4}\right)}}"," ",0,"-1/629*(144*a^6*x^6 - 144*a^5*x^5 + 504*a^4*x^4 - 408*a^3*x^3 + 606*a^2*x^2 - 366*a*x + 263)*e^(-arctan(a*x))/(a^7*c^4*x^6 + 3*a^5*c^4*x^4 + 3*a^3*c^4*x^2 + a*c^4)","A",0
281,0,0,0,0.462725," ","integrate((a^2*c*x^2+c)^(3/2)/exp(arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} e^{\left(-\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*e^(-arctan(a*x)), x)","F",0
282,0,0,0,0.457445," ","integrate((a^2*c*x^2+c)^(1/2)/exp(arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} e^{\left(-\arctan\left(a x\right)\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*e^(-arctan(a*x)), x)","F",0
283,0,0,0,0.439174," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(-\arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(e^(-arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
284,1,44,0,0.428087," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(a x - 1\right)} e^{\left(-\arctan\left(a x\right)\right)}}{2 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)}}"," ",0,"1/2*sqrt(a^2*c*x^2 + c)*(a*x - 1)*e^(-arctan(a*x))/(a^3*c^2*x^2 + a*c^2)","A",0
285,1,72,0,0.417781," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} x^{3} - 3 \, a^{2} x^{2} + 6 \, a x - 4\right)} \sqrt{a^{2} c x^{2} + c} e^{\left(-\arctan\left(a x\right)\right)}}{10 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"1/10*(3*a^3*x^3 - 3*a^2*x^2 + 6*a*x - 4)*sqrt(a^2*c*x^2 + c)*e^(-arctan(a*x))/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
286,1,99,0,0.415199," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","\frac{{\left(6 \, a^{5} x^{5} - 6 \, a^{4} x^{4} + 18 \, a^{3} x^{3} - 14 \, a^{2} x^{2} + 17 \, a x - 9\right)} \sqrt{a^{2} c x^{2} + c} e^{\left(-\arctan\left(a x\right)\right)}}{26 \, {\left(a^{7} c^{4} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{3} c^{4} x^{2} + a c^{4}\right)}}"," ",0,"1/26*(6*a^5*x^5 - 6*a^4*x^4 + 18*a^3*x^3 - 14*a^2*x^2 + 17*a*x - 9)*sqrt(a^2*c*x^2 + c)*e^(-arctan(a*x))/(a^7*c^4*x^6 + 3*a^5*c^4*x^4 + 3*a^3*c^4*x^2 + a*c^4)","A",0
287,0,0,0,0.472778," ","integrate((a^2*c*x^2+c)^p/exp(2*arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{p} e^{\left(-2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^p*e^(-2*arctan(a*x)), x)","F",0
288,0,0,0,0.412857," ","integrate((a^2*c*x^2+c)^2/exp(2*arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} e^{\left(-2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*e^(-2*arctan(a*x)), x)","F",0
289,0,0,0,0.409246," ","integrate((a^2*c*x^2+c)/exp(2*arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} e^{\left(-2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*e^(-2*arctan(a*x)), x)","F",0
290,0,0,0,0.447816," ","integrate(exp(-2*arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(e^{\left(-2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral(e^(-2*arctan(a*x)), x)","F",0
291,1,15,0,0.441452," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c),x, algorithm=""fricas"")","-\frac{e^{\left(-2 \, \arctan\left(a x\right)\right)}}{2 \, a c}"," ",0,"-1/2*e^(-2*arctan(a*x))/(a*c)","A",0
292,1,40,0,0.474880," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} x^{2} - 2 \, a x + 3\right)} e^{\left(-2 \, \arctan\left(a x\right)\right)}}{8 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)}}"," ",0,"-1/8*(a^2*x^2 - 2*a*x + 3)*e^(-2*arctan(a*x))/(a^3*c^2*x^2 + a*c^2)","A",0
293,1,68,0,0.443238," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{4} x^{4} - 6 \, a^{3} x^{3} + 12 \, a^{2} x^{2} - 14 \, a x + 13\right)} e^{\left(-2 \, \arctan\left(a x\right)\right)}}{40 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"-1/40*(3*a^4*x^4 - 6*a^3*x^3 + 12*a^2*x^2 - 14*a*x + 13)*e^(-2*arctan(a*x))/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
294,1,95,0,0.490620," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^4,x, algorithm=""fricas"")","-\frac{{\left(9 \, a^{6} x^{6} - 18 \, a^{5} x^{5} + 45 \, a^{4} x^{4} - 60 \, a^{3} x^{3} + 75 \, a^{2} x^{2} - 66 \, a x + 47\right)} e^{\left(-2 \, \arctan\left(a x\right)\right)}}{160 \, {\left(a^{7} c^{4} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{3} c^{4} x^{2} + a c^{4}\right)}}"," ",0,"-1/160*(9*a^6*x^6 - 18*a^5*x^5 + 45*a^4*x^4 - 60*a^3*x^3 + 75*a^2*x^2 - 66*a*x + 47)*e^(-2*arctan(a*x))/(a^7*c^4*x^6 + 3*a^5*c^4*x^4 + 3*a^3*c^4*x^2 + a*c^4)","A",0
295,0,0,0,0.531473," ","integrate((a^2*c*x^2+c)^(3/2)/exp(2*arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} e^{\left(-2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*e^(-2*arctan(a*x)), x)","F",0
296,0,0,0,0.436417," ","integrate((a^2*c*x^2+c)^(1/2)/exp(2*arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} e^{\left(-2 \, \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*e^(-2*arctan(a*x)), x)","F",0
297,0,0,0,0.477576," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(-2 \, \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(e^(-2*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
298,1,44,0,0.428931," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(a x - 2\right)} e^{\left(-2 \, \arctan\left(a x\right)\right)}}{5 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)}}"," ",0,"1/5*sqrt(a^2*c*x^2 + c)*(a*x - 2)*e^(-2*arctan(a*x))/(a^3*c^2*x^2 + a*c^2)","A",0
299,1,72,0,0.506786," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(6 \, a^{3} x^{3} - 12 \, a^{2} x^{2} + 21 \, a x - 22\right)} \sqrt{a^{2} c x^{2} + c} e^{\left(-2 \, \arctan\left(a x\right)\right)}}{65 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"1/65*(6*a^3*x^3 - 12*a^2*x^2 + 21*a*x - 22)*sqrt(a^2*c*x^2 + c)*e^(-2*arctan(a*x))/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
300,1,99,0,0.503177," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","\frac{{\left(24 \, a^{5} x^{5} - 48 \, a^{4} x^{4} + 108 \, a^{3} x^{3} - 136 \, a^{2} x^{2} + 149 \, a x - 114\right)} \sqrt{a^{2} c x^{2} + c} e^{\left(-2 \, \arctan\left(a x\right)\right)}}{377 \, {\left(a^{7} c^{4} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{3} c^{4} x^{2} + a c^{4}\right)}}"," ",0,"1/377*(24*a^5*x^5 - 48*a^4*x^4 + 108*a^3*x^3 - 136*a^2*x^2 + 149*a*x - 114)*sqrt(a^2*c*x^2 + c)*e^(-2*arctan(a*x))/(a^7*c^4*x^6 + 3*a^5*c^4*x^4 + 3*a^3*c^4*x^2 + a*c^4)","A",0
301,1,53,0,0.508261," ","integrate((1+I*a*x)^5/(a^2*x^2+1)^3,x, algorithm=""fricas"")","-\frac{4 \, a x - {\left(i \, a^{2} x^{2} - 2 \, a x - i\right)} \log\left(\frac{a x + i}{a}\right) + 2 i}{a^{3} x^{2} + 2 i \, a^{2} x - a}"," ",0,"-(4*a*x - (I*a^2*x^2 - 2*a*x - I)*log((a*x + I)/a) + 2*I)/(a^3*x^2 + 2*I*a^2*x - a)","A",0
302,1,86,0,0.433186," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^(5/2),x, algorithm=""fricas"")","-\frac{8 \, a^{2} x^{2} + 16 i \, a x + {\left(3 \, a^{2} x^{2} + 6 i \, a x - 3\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + \sqrt{a^{2} x^{2} + 1} {\left(8 \, a x + 4 i\right)} - 8}{3 \, a^{3} x^{2} + 6 i \, a^{2} x - 3 \, a}"," ",0,"-(8*a^2*x^2 + 16*I*a*x + (3*a^2*x^2 + 6*I*a*x - 3)*log(-a*x + sqrt(a^2*x^2 + 1)) + sqrt(a^2*x^2 + 1)*(8*a*x + 4*I) - 8)/(3*a^3*x^2 + 6*I*a^2*x - 3*a)","A",0
303,1,31,0,0.411296," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^2,x, algorithm=""fricas"")","\frac{{\left(-i \, a x + 1\right)} \log\left(\frac{a x + i}{a}\right) + 2}{a^{2} x + i \, a}"," ",0,"((-I*a*x + 1)*log((a*x + I)/a) + 2)/(a^2*x + I*a)","A",0
304,1,54,0,0.431877," ","integrate((1+I*a*x)^2/(a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{2 \, a x + {\left(a x + i\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + 2 \, \sqrt{a^{2} x^{2} + 1} + 2 i}{a^{2} x + i \, a}"," ",0,"(2*a*x + (a*x + I)*log(-a*x + sqrt(a^2*x^2 + 1)) + 2*sqrt(a^2*x^2 + 1) + 2*I)/(a^2*x + I*a)","A",0
305,1,15,0,0.430896," ","integrate((1+I*a*x)/(a^2*x^2+1),x, algorithm=""fricas"")","\frac{i \, \log\left(\frac{a x + i}{a}\right)}{a}"," ",0,"I*log((a*x + I)/a)/a","A",0
306,1,15,0,0.391703," ","integrate(1/(1+I*a*x),x, algorithm=""fricas"")","-\frac{i \, \log\left(\frac{a x - i}{a}\right)}{a}"," ",0,"-I*log((a*x - I)/a)/a","A",0
307,1,54,0,0.483377," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, a x + {\left(a x - i\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + 2 \, \sqrt{a^{2} x^{2} + 1} - 2 i}{a^{2} x - i \, a}"," ",0,"(2*a*x + (a*x - I)*log(-a*x + sqrt(a^2*x^2 + 1)) + 2*sqrt(a^2*x^2 + 1) - 2*I)/(a^2*x - I*a)","A",0
308,1,31,0,0.511338," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1),x, algorithm=""fricas"")","\frac{{\left(i \, a x + 1\right)} \log\left(\frac{a x - i}{a}\right) + 2}{a^{2} x - i \, a}"," ",0,"((I*a*x + 1)*log((a*x - I)/a) + 2)/(a^2*x - I*a)","A",0
309,1,86,0,0.476289," ","integrate(1/(1+I*a*x)^4*(a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","-\frac{8 \, a^{2} x^{2} - 16 i \, a x + {\left(3 \, a^{2} x^{2} - 6 i \, a x - 3\right)} \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right) + \sqrt{a^{2} x^{2} + 1} {\left(8 \, a x - 4 i\right)} - 8}{3 \, a^{3} x^{2} - 6 i \, a^{2} x - 3 \, a}"," ",0,"-(8*a^2*x^2 - 16*I*a*x + (3*a^2*x^2 - 6*I*a*x - 3)*log(-a*x + sqrt(a^2*x^2 + 1)) + sqrt(a^2*x^2 + 1)*(8*a*x - 4*I) - 8)/(3*a^3*x^2 - 6*I*a^2*x - 3*a)","A",0
310,1,366,0,0.601797," ","integrate((1+I*a*x)^5/(a^2*x^2+1)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{-4 i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a x^{2} + {\left(i \, a^{4} c x^{4} - 2 \, a^{3} c x^{3} - 2 \, a c x - i \, c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{{\left(i \, a^{6} x^{2} - 2 \, a^{5} x - 2 i \, a^{4}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} + {\left(i \, a^{9} c x^{4} - 2 \, a^{8} c x^{3} + i \, a^{7} c x^{2} - 2 \, a^{6} c x\right)} \sqrt{\frac{1}{a^{2} c}}}{8 \, a^{3} x^{3} + 8 i \, a^{2} x^{2} + 8 \, a x + 8 i}\right) + {\left(-i \, a^{4} c x^{4} + 2 \, a^{3} c x^{3} + 2 \, a c x + i \, c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{{\left(i \, a^{6} x^{2} - 2 \, a^{5} x - 2 i \, a^{4}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} + {\left(-i \, a^{9} c x^{4} + 2 \, a^{8} c x^{3} - i \, a^{7} c x^{2} + 2 \, a^{6} c x\right)} \sqrt{\frac{1}{a^{2} c}}}{8 \, a^{3} x^{3} + 8 i \, a^{2} x^{2} + 8 \, a x + 8 i}\right)}{2 \, a^{4} c x^{4} + 4 i \, a^{3} c x^{3} + 4 i \, a c x - 2 \, c}"," ",0,"(-4*I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a*x^2 + (I*a^4*c*x^4 - 2*a^3*c*x^3 - 2*a*c*x - I*c)*sqrt(1/(a^2*c))*log(((I*a^6*x^2 - 2*a^5*x - 2*I*a^4)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1) + (I*a^9*c*x^4 - 2*a^8*c*x^3 + I*a^7*c*x^2 - 2*a^6*c*x)*sqrt(1/(a^2*c)))/(8*a^3*x^3 + 8*I*a^2*x^2 + 8*a*x + 8*I)) + (-I*a^4*c*x^4 + 2*a^3*c*x^3 + 2*a*c*x + I*c)*sqrt(1/(a^2*c))*log(((I*a^6*x^2 - 2*a^5*x - 2*I*a^4)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1) + (-I*a^9*c*x^4 + 2*a^8*c*x^3 - I*a^7*c*x^2 + 2*a^6*c*x)*sqrt(1/(a^2*c)))/(8*a^3*x^3 + 8*I*a^2*x^2 + 8*a*x + 8*I)))/(2*a^4*c*x^4 + 4*I*a^3*c*x^3 + 4*I*a*c*x - 2*c)","B",0
311,1,187,0,0.612953," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} c x^{2} + 6 i \, a^{2} c x - 3 \, a c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{2 \, {\left(a^{2} c x + \sqrt{a^{2} c x^{2} + c} a^{2} c \sqrt{\frac{1}{a^{2} c}}\right)}}{x}\right) - {\left(3 \, a^{3} c x^{2} + 6 i \, a^{2} c x - 3 \, a c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{2 \, {\left(a^{2} c x - \sqrt{a^{2} c x^{2} + c} a^{2} c \sqrt{\frac{1}{a^{2} c}}\right)}}{x}\right) - \sqrt{a^{2} c x^{2} + c} {\left(16 \, a x + 8 i\right)}}{6 \, a^{3} c x^{2} + 12 i \, a^{2} c x - 6 \, a c}"," ",0,"((3*a^3*c*x^2 + 6*I*a^2*c*x - 3*a*c)*sqrt(1/(a^2*c))*log(2*(a^2*c*x + sqrt(a^2*c*x^2 + c)*a^2*c*sqrt(1/(a^2*c)))/x) - (3*a^3*c*x^2 + 6*I*a^2*c*x - 3*a*c)*sqrt(1/(a^2*c))*log(2*(a^2*c*x - sqrt(a^2*c*x^2 + c)*a^2*c*sqrt(1/(a^2*c)))/x) - sqrt(a^2*c*x^2 + c)*(16*a*x + 8*I))/(6*a^3*c*x^2 + 12*I*a^2*c*x - 6*a*c)","B",0
312,1,360,0,0.570752," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(-i \, a^{3} c x^{3} + a^{2} c x^{2} - i \, a c x + c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{{\left(i \, a^{6} x^{2} - 2 \, a^{5} x - 2 i \, a^{4}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} + {\left(i \, a^{9} c x^{4} - 2 \, a^{8} c x^{3} + i \, a^{7} c x^{2} - 2 \, a^{6} c x\right)} \sqrt{\frac{1}{a^{2} c}}}{8 \, a^{3} x^{3} + 8 i \, a^{2} x^{2} + 8 \, a x + 8 i}\right) + {\left(i \, a^{3} c x^{3} - a^{2} c x^{2} + i \, a c x - c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{{\left(i \, a^{6} x^{2} - 2 \, a^{5} x - 2 i \, a^{4}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} + {\left(-i \, a^{9} c x^{4} + 2 \, a^{8} c x^{3} - i \, a^{7} c x^{2} + 2 \, a^{6} c x\right)} \sqrt{\frac{1}{a^{2} c}}}{8 \, a^{3} x^{3} + 8 i \, a^{2} x^{2} + 8 \, a x + 8 i}\right) + 4 i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} x}{2 \, a^{3} c x^{3} + 2 i \, a^{2} c x^{2} + 2 \, a c x + 2 i \, c}"," ",0,"((-I*a^3*c*x^3 + a^2*c*x^2 - I*a*c*x + c)*sqrt(1/(a^2*c))*log(((I*a^6*x^2 - 2*a^5*x - 2*I*a^4)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1) + (I*a^9*c*x^4 - 2*a^8*c*x^3 + I*a^7*c*x^2 - 2*a^6*c*x)*sqrt(1/(a^2*c)))/(8*a^3*x^3 + 8*I*a^2*x^2 + 8*a*x + 8*I)) + (I*a^3*c*x^3 - a^2*c*x^2 + I*a*c*x - c)*sqrt(1/(a^2*c))*log(((I*a^6*x^2 - 2*a^5*x - 2*I*a^4)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1) + (-I*a^9*c*x^4 + 2*a^8*c*x^3 - I*a^7*c*x^2 + 2*a^6*c*x)*sqrt(1/(a^2*c)))/(8*a^3*x^3 + 8*I*a^2*x^2 + 8*a*x + 8*I)) + 4*I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*x)/(2*a^3*c*x^3 + 2*I*a^2*c*x^2 + 2*a*c*x + 2*I*c)","B",0
313,1,152,0,0.433882," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a^{2} c x + i \, a c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{2 \, {\left(a^{2} c x + \sqrt{a^{2} c x^{2} + c} a^{2} c \sqrt{\frac{1}{a^{2} c}}\right)}}{x}\right) - {\left(a^{2} c x + i \, a c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{2 \, {\left(a^{2} c x - \sqrt{a^{2} c x^{2} + c} a^{2} c \sqrt{\frac{1}{a^{2} c}}\right)}}{x}\right) - 4 \, \sqrt{a^{2} c x^{2} + c}}{2 \, {\left(a^{2} c x + i \, a c\right)}}"," ",0,"-1/2*((a^2*c*x + I*a*c)*sqrt(1/(a^2*c))*log(2*(a^2*c*x + sqrt(a^2*c*x^2 + c)*a^2*c*sqrt(1/(a^2*c)))/x) - (a^2*c*x + I*a*c)*sqrt(1/(a^2*c))*log(2*(a^2*c*x - sqrt(a^2*c*x^2 + c)*a^2*c*sqrt(1/(a^2*c)))/x) - 4*sqrt(a^2*c*x^2 + c))/(a^2*c*x + I*a*c)","B",0
314,1,255,0,0.479370," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} i \, \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{{\left(i \, a^{6} x^{2} - 2 \, a^{5} x - 2 i \, a^{4}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} + {\left(i \, a^{9} c x^{4} - 2 \, a^{8} c x^{3} + i \, a^{7} c x^{2} - 2 \, a^{6} c x\right)} \sqrt{\frac{1}{a^{2} c}}}{8 \, a^{3} x^{3} + 8 i \, a^{2} x^{2} + 8 \, a x + 8 i}\right) - \frac{1}{2} i \, \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{{\left(i \, a^{6} x^{2} - 2 \, a^{5} x - 2 i \, a^{4}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} + {\left(-i \, a^{9} c x^{4} + 2 \, a^{8} c x^{3} - i \, a^{7} c x^{2} + 2 \, a^{6} c x\right)} \sqrt{\frac{1}{a^{2} c}}}{8 \, a^{3} x^{3} + 8 i \, a^{2} x^{2} + 8 \, a x + 8 i}\right)"," ",0,"1/2*I*sqrt(1/(a^2*c))*log(((I*a^6*x^2 - 2*a^5*x - 2*I*a^4)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1) + (I*a^9*c*x^4 - 2*a^8*c*x^3 + I*a^7*c*x^2 - 2*a^6*c*x)*sqrt(1/(a^2*c)))/(8*a^3*x^3 + 8*I*a^2*x^2 + 8*a*x + 8*I)) - 1/2*I*sqrt(1/(a^2*c))*log(((I*a^6*x^2 - 2*a^5*x - 2*I*a^4)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1) + (-I*a^9*c*x^4 + 2*a^8*c*x^3 - I*a^7*c*x^2 + 2*a^6*c*x)*sqrt(1/(a^2*c)))/(8*a^3*x^3 + 8*I*a^2*x^2 + 8*a*x + 8*I))","B",0
315,1,255,0,0.538926," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} i \, \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{{\left(-i \, a^{6} x^{2} - 2 \, a^{5} x + 2 i \, a^{4}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} + {\left(i \, a^{9} c x^{4} + 2 \, a^{8} c x^{3} + i \, a^{7} c x^{2} + 2 \, a^{6} c x\right)} \sqrt{\frac{1}{a^{2} c}}}{8 \, a^{3} x^{3} - 8 i \, a^{2} x^{2} + 8 \, a x - 8 i}\right) - \frac{1}{2} i \, \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{{\left(-i \, a^{6} x^{2} - 2 \, a^{5} x + 2 i \, a^{4}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} + {\left(-i \, a^{9} c x^{4} - 2 \, a^{8} c x^{3} - i \, a^{7} c x^{2} - 2 \, a^{6} c x\right)} \sqrt{\frac{1}{a^{2} c}}}{8 \, a^{3} x^{3} - 8 i \, a^{2} x^{2} + 8 \, a x - 8 i}\right)"," ",0,"1/2*I*sqrt(1/(a^2*c))*log(((-I*a^6*x^2 - 2*a^5*x + 2*I*a^4)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1) + (I*a^9*c*x^4 + 2*a^8*c*x^3 + I*a^7*c*x^2 + 2*a^6*c*x)*sqrt(1/(a^2*c)))/(8*a^3*x^3 - 8*I*a^2*x^2 + 8*a*x - 8*I)) - 1/2*I*sqrt(1/(a^2*c))*log(((-I*a^6*x^2 - 2*a^5*x + 2*I*a^4)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1) + (-I*a^9*c*x^4 - 2*a^8*c*x^3 - I*a^7*c*x^2 - 2*a^6*c*x)*sqrt(1/(a^2*c)))/(8*a^3*x^3 - 8*I*a^2*x^2 + 8*a*x - 8*I))","B",0
316,1,152,0,0.547389," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a^{2} c x - i \, a c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{2 \, {\left(a^{2} c x + \sqrt{a^{2} c x^{2} + c} a^{2} c \sqrt{\frac{1}{a^{2} c}}\right)}}{x}\right) - {\left(a^{2} c x - i \, a c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{2 \, {\left(a^{2} c x - \sqrt{a^{2} c x^{2} + c} a^{2} c \sqrt{\frac{1}{a^{2} c}}\right)}}{x}\right) - 4 \, \sqrt{a^{2} c x^{2} + c}}{2 \, {\left(a^{2} c x - i \, a c\right)}}"," ",0,"-1/2*((a^2*c*x - I*a*c)*sqrt(1/(a^2*c))*log(2*(a^2*c*x + sqrt(a^2*c*x^2 + c)*a^2*c*sqrt(1/(a^2*c)))/x) - (a^2*c*x - I*a*c)*sqrt(1/(a^2*c))*log(2*(a^2*c*x - sqrt(a^2*c*x^2 + c)*a^2*c*sqrt(1/(a^2*c)))/x) - 4*sqrt(a^2*c*x^2 + c))/(a^2*c*x - I*a*c)","B",0
317,1,360,0,0.621121," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(-i \, a^{3} c x^{3} - a^{2} c x^{2} - i \, a c x - c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{{\left(-i \, a^{6} x^{2} - 2 \, a^{5} x + 2 i \, a^{4}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} + {\left(i \, a^{9} c x^{4} + 2 \, a^{8} c x^{3} + i \, a^{7} c x^{2} + 2 \, a^{6} c x\right)} \sqrt{\frac{1}{a^{2} c}}}{8 \, a^{3} x^{3} - 8 i \, a^{2} x^{2} + 8 \, a x - 8 i}\right) + {\left(i \, a^{3} c x^{3} + a^{2} c x^{2} + i \, a c x + c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{{\left(-i \, a^{6} x^{2} - 2 \, a^{5} x + 2 i \, a^{4}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} + {\left(-i \, a^{9} c x^{4} - 2 \, a^{8} c x^{3} - i \, a^{7} c x^{2} - 2 \, a^{6} c x\right)} \sqrt{\frac{1}{a^{2} c}}}{8 \, a^{3} x^{3} - 8 i \, a^{2} x^{2} + 8 \, a x - 8 i}\right) - 4 i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} x}{2 \, a^{3} c x^{3} - 2 i \, a^{2} c x^{2} + 2 \, a c x - 2 i \, c}"," ",0,"((-I*a^3*c*x^3 - a^2*c*x^2 - I*a*c*x - c)*sqrt(1/(a^2*c))*log(((-I*a^6*x^2 - 2*a^5*x + 2*I*a^4)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1) + (I*a^9*c*x^4 + 2*a^8*c*x^3 + I*a^7*c*x^2 + 2*a^6*c*x)*sqrt(1/(a^2*c)))/(8*a^3*x^3 - 8*I*a^2*x^2 + 8*a*x - 8*I)) + (I*a^3*c*x^3 + a^2*c*x^2 + I*a*c*x + c)*sqrt(1/(a^2*c))*log(((-I*a^6*x^2 - 2*a^5*x + 2*I*a^4)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1) + (-I*a^9*c*x^4 - 2*a^8*c*x^3 - I*a^7*c*x^2 - 2*a^6*c*x)*sqrt(1/(a^2*c)))/(8*a^3*x^3 - 8*I*a^2*x^2 + 8*a*x - 8*I)) - 4*I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*x)/(2*a^3*c*x^3 - 2*I*a^2*c*x^2 + 2*a*c*x - 2*I*c)","B",0
318,1,187,0,0.506366," ","integrate(1/(1+I*a*x)^4*(a^2*x^2+1)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} c x^{2} - 6 i \, a^{2} c x - 3 \, a c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{2 \, {\left(a^{2} c x + \sqrt{a^{2} c x^{2} + c} a^{2} c \sqrt{\frac{1}{a^{2} c}}\right)}}{x}\right) - {\left(3 \, a^{3} c x^{2} - 6 i \, a^{2} c x - 3 \, a c\right)} \sqrt{\frac{1}{a^{2} c}} \log\left(\frac{2 \, {\left(a^{2} c x - \sqrt{a^{2} c x^{2} + c} a^{2} c \sqrt{\frac{1}{a^{2} c}}\right)}}{x}\right) - \sqrt{a^{2} c x^{2} + c} {\left(16 \, a x - 8 i\right)}}{6 \, a^{3} c x^{2} - 12 i \, a^{2} c x - 6 \, a c}"," ",0,"((3*a^3*c*x^2 - 6*I*a^2*c*x - 3*a*c)*sqrt(1/(a^2*c))*log(2*(a^2*c*x + sqrt(a^2*c*x^2 + c)*a^2*c*sqrt(1/(a^2*c)))/x) - (3*a^3*c*x^2 - 6*I*a^2*c*x - 3*a*c)*sqrt(1/(a^2*c))*log(2*(a^2*c*x - sqrt(a^2*c*x^2 + c)*a^2*c*sqrt(1/(a^2*c)))/x) - sqrt(a^2*c*x^2 + c)*(16*a*x - 8*I))/(6*a^3*c*x^2 - 12*I*a^2*c*x - 6*a*c)","B",0
319,1,35,0,0.421850," ","integrate((1+I*a*x)^5/(a^2*x^2+1)^4,x, algorithm=""fricas"")","\frac{-3 i \, a x - 1}{6 \, a^{4} x^{3} + 18 i \, a^{3} x^{2} - 18 \, a^{2} x - 6 i \, a}"," ",0,"(-3*I*a*x - 1)/(6*a^4*x^3 + 18*I*a^3*x^2 - 18*a^2*x - 6*I*a)","A",0
320,1,76,0,0.435287," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^(7/2),x, algorithm=""fricas"")","-\frac{a^{3} x^{3} + 3 i \, a^{2} x^{2} - 3 \, a x + {\left(a^{2} x^{2} + 3 i \, a x + 4\right)} \sqrt{a^{2} x^{2} + 1} - i}{15 \, a^{4} x^{3} + 45 i \, a^{3} x^{2} - 45 \, a^{2} x - 15 i \, a}"," ",0,"-(a^3*x^3 + 3*I*a^2*x^2 - 3*a*x + (a^2*x^2 + 3*I*a*x + 4)*sqrt(a^2*x^2 + 1) - I)/(15*a^4*x^3 + 45*I*a^3*x^2 - 45*a^2*x - 15*I*a)","A",0
321,1,22,0,0.381288," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^3,x, algorithm=""fricas"")","\frac{i}{2 \, a^{3} x^{2} + 4 i \, a^{2} x - 2 \, a}"," ",0,"I/(2*a^3*x^2 + 4*I*a^2*x - 2*a)","A",0
322,1,51,0,0.472717," ","integrate((1+I*a*x)^2/(a^2*x^2+1)^(5/2),x, algorithm=""fricas"")","\frac{a^{2} x^{2} + 2 i \, a x + \sqrt{a^{2} x^{2} + 1} {\left(a x + 2 i\right)} - 1}{3 \, a^{3} x^{2} + 6 i \, a^{2} x - 3 \, a}"," ",0,"(a^2*x^2 + 2*I*a*x + sqrt(a^2*x^2 + 1)*(a*x + 2*I) - 1)/(3*a^3*x^2 + 6*I*a^2*x - 3*a)","A",0
323,1,49,0,0.451752," ","integrate((1+I*a*x)/(a^2*x^2+1)^2,x, algorithm=""fricas"")","\frac{{\left(i \, a x - 1\right)} \log\left(\frac{a x + i}{a}\right) + {\left(-i \, a x + 1\right)} \log\left(\frac{a x - i}{a}\right) + 2}{4 \, a^{2} x + 4 i \, a}"," ",0,"((I*a*x - 1)*log((a*x + I)/a) + (-I*a*x + 1)*log((a*x - I)/a) + 2)/(4*a^2*x + 4*I*a)","B",0
324,1,49,0,0.561518," ","integrate(1/(1+I*a*x)/(a^2*x^2+1),x, algorithm=""fricas"")","\frac{{\left(i \, a x + 1\right)} \log\left(\frac{a x + i}{a}\right) + {\left(-i \, a x - 1\right)} \log\left(\frac{a x - i}{a}\right) + 2}{4 \, a^{2} x - 4 i \, a}"," ",0,"((I*a*x + 1)*log((a*x + I)/a) + (-I*a*x - 1)*log((a*x - I)/a) + 2)/(4*a^2*x - 4*I*a)","B",0
325,1,51,0,0.504410," ","integrate(1/(1+I*a*x)^2/(a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{a^{2} x^{2} - 2 i \, a x + \sqrt{a^{2} x^{2} + 1} {\left(a x - 2 i\right)} - 1}{3 \, a^{3} x^{2} - 6 i \, a^{2} x - 3 \, a}"," ",0,"(a^2*x^2 - 2*I*a*x + sqrt(a^2*x^2 + 1)*(a*x - 2*I) - 1)/(3*a^3*x^2 - 6*I*a^2*x - 3*a)","A",0
326,1,22,0,0.367659," ","integrate(1/(1+I*a*x)^3,x, algorithm=""fricas"")","-\frac{i}{2 \, a^{3} x^{2} - 4 i \, a^{2} x - 2 \, a}"," ",0,"-I/(2*a^3*x^2 - 4*I*a^2*x - 2*a)","A",0
327,1,76,0,0.459481," ","integrate(1/(1+I*a*x)^4*(a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{a^{3} x^{3} - 3 i \, a^{2} x^{2} - 3 \, a x + {\left(a^{2} x^{2} - 3 i \, a x + 4\right)} \sqrt{a^{2} x^{2} + 1} + i}{15 \, a^{4} x^{3} - 45 i \, a^{3} x^{2} - 45 \, a^{2} x + 15 i \, a}"," ",0,"-(a^3*x^3 - 3*I*a^2*x^2 - 3*a*x + (a^2*x^2 - 3*I*a*x + 4)*sqrt(a^2*x^2 + 1) + I)/(15*a^4*x^3 - 45*I*a^3*x^2 - 45*a^2*x + 15*I*a)","A",0
328,1,101,0,0.494479," ","integrate((1+I*a*x)^5/(a^2*x^2+1)^(5/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(i \, a^{2} x^{3} - 3 \, a x^{2} - 6 i \, x\right)} \sqrt{a^{2} x^{2} + 1}}{6 \, a^{5} c^{2} x^{5} + 18 i \, a^{4} c^{2} x^{4} - 12 \, a^{3} c^{2} x^{3} + 12 i \, a^{2} c^{2} x^{2} - 18 \, a c^{2} x - 6 i \, c^{2}}"," ",0,"sqrt(a^2*c*x^2 + c)*(I*a^2*x^3 - 3*a*x^2 - 6*I*x)*sqrt(a^2*x^2 + 1)/(6*a^5*c^2*x^5 + 18*I*a^4*c^2*x^4 - 12*a^3*c^2*x^3 + 12*I*a^2*c^2*x^2 - 18*a*c^2*x - 6*I*c^2)","A",0
329,1,67,0,0.515527," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{a^{2} c x^{2} + c} {\left(a^{2} x^{2} + 3 i \, a x + 4\right)}}{15 \, a^{4} c^{2} x^{3} + 45 i \, a^{3} c^{2} x^{2} - 45 \, a^{2} c^{2} x - 15 i \, a c^{2}}"," ",0,"-sqrt(a^2*c*x^2 + c)*(a^2*x^2 + 3*I*a*x + 4)/(15*a^4*c^2*x^3 + 45*I*a^3*c^2*x^2 - 45*a^2*c^2*x - 15*I*a*c^2)","A",0
330,1,71,0,0.480186," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} {\left(i \, a x^{2} - 2 \, x\right)}}{2 \, a^{4} c^{2} x^{4} + 4 i \, a^{3} c^{2} x^{3} + 4 i \, a c^{2} x - 2 \, c^{2}}"," ",0,"sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*(I*a*x^2 - 2*x)/(2*a^4*c^2*x^4 + 4*I*a^3*c^2*x^3 + 4*I*a*c^2*x - 2*c^2)","A",0
331,1,47,0,0.554688," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(a x + 2 i\right)}}{3 \, a^{3} c^{2} x^{2} + 6 i \, a^{2} c^{2} x - 3 \, a c^{2}}"," ",0,"sqrt(a^2*c*x^2 + c)*(a*x + 2*I)/(3*a^3*c^2*x^2 + 6*I*a^2*c^2*x - 3*a*c^2)","A",0
332,1,317,0,0.479422," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(-i \, a^{3} c^{2} x^{3} + a^{2} c^{2} x^{2} - i \, a c^{2} x + c^{2}\right)} \sqrt{\frac{1}{a^{2} c^{3}}} \log\left(\frac{8 \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{6} x + {\left(4 i \, a^{10} c^{2} x^{4} - 4 i \, a^{6} c^{2}\right)} \sqrt{\frac{1}{a^{2} c^{3}}}}{2 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)}}\right) + {\left(i \, a^{3} c^{2} x^{3} - a^{2} c^{2} x^{2} + i \, a c^{2} x - c^{2}\right)} \sqrt{\frac{1}{a^{2} c^{3}}} \log\left(\frac{8 \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{6} x + {\left(-4 i \, a^{10} c^{2} x^{4} + 4 i \, a^{6} c^{2}\right)} \sqrt{\frac{1}{a^{2} c^{3}}}}{2 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)}}\right) + 4 i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} x}{2 \, {\left(4 \, a^{3} c^{2} x^{3} + 4 i \, a^{2} c^{2} x^{2} + 4 \, a c^{2} x + 4 i \, c^{2}\right)}}"," ",0,"1/2*((-I*a^3*c^2*x^3 + a^2*c^2*x^2 - I*a*c^2*x + c^2)*sqrt(1/(a^2*c^3))*log(1/2*(8*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^6*x + (4*I*a^10*c^2*x^4 - 4*I*a^6*c^2)*sqrt(1/(a^2*c^3)))/(a^4*x^4 + 2*a^2*x^2 + 1)) + (I*a^3*c^2*x^3 - a^2*c^2*x^2 + I*a*c^2*x - c^2)*sqrt(1/(a^2*c^3))*log(1/2*(8*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^6*x + (-4*I*a^10*c^2*x^4 + 4*I*a^6*c^2)*sqrt(1/(a^2*c^3)))/(a^4*x^4 + 2*a^2*x^2 + 1)) + 4*I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*x)/(4*a^3*c^2*x^3 + 4*I*a^2*c^2*x^2 + 4*a*c^2*x + 4*I*c^2)","B",0
333,1,317,0,0.477301," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(-i \, a^{3} c^{2} x^{3} - a^{2} c^{2} x^{2} - i \, a c^{2} x - c^{2}\right)} \sqrt{\frac{1}{a^{2} c^{3}}} \log\left(\frac{8 \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{6} x + {\left(4 i \, a^{10} c^{2} x^{4} - 4 i \, a^{6} c^{2}\right)} \sqrt{\frac{1}{a^{2} c^{3}}}}{2 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)}}\right) + {\left(i \, a^{3} c^{2} x^{3} + a^{2} c^{2} x^{2} + i \, a c^{2} x + c^{2}\right)} \sqrt{\frac{1}{a^{2} c^{3}}} \log\left(\frac{8 \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{6} x + {\left(-4 i \, a^{10} c^{2} x^{4} + 4 i \, a^{6} c^{2}\right)} \sqrt{\frac{1}{a^{2} c^{3}}}}{2 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)}}\right) - 4 i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} x}{2 \, {\left(4 \, a^{3} c^{2} x^{3} - 4 i \, a^{2} c^{2} x^{2} + 4 \, a c^{2} x - 4 i \, c^{2}\right)}}"," ",0,"1/2*((-I*a^3*c^2*x^3 - a^2*c^2*x^2 - I*a*c^2*x - c^2)*sqrt(1/(a^2*c^3))*log(1/2*(8*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^6*x + (4*I*a^10*c^2*x^4 - 4*I*a^6*c^2)*sqrt(1/(a^2*c^3)))/(a^4*x^4 + 2*a^2*x^2 + 1)) + (I*a^3*c^2*x^3 + a^2*c^2*x^2 + I*a*c^2*x + c^2)*sqrt(1/(a^2*c^3))*log(1/2*(8*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^6*x + (-4*I*a^10*c^2*x^4 + 4*I*a^6*c^2)*sqrt(1/(a^2*c^3)))/(a^4*x^4 + 2*a^2*x^2 + 1)) - 4*I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*x)/(4*a^3*c^2*x^3 - 4*I*a^2*c^2*x^2 + 4*a*c^2*x - 4*I*c^2)","B",0
334,1,47,0,0.455548," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(a x - 2 i\right)}}{3 \, a^{3} c^{2} x^{2} - 6 i \, a^{2} c^{2} x - 3 \, a c^{2}}"," ",0,"sqrt(a^2*c*x^2 + c)*(a*x - 2*I)/(3*a^3*c^2*x^2 - 6*I*a^2*c^2*x - 3*a*c^2)","A",0
335,1,71,0,0.540031," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} {\left(-i \, a x^{2} - 2 \, x\right)}}{2 \, a^{4} c^{2} x^{4} - 4 i \, a^{3} c^{2} x^{3} - 4 i \, a c^{2} x - 2 \, c^{2}}"," ",0,"sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*(-I*a*x^2 - 2*x)/(2*a^4*c^2*x^4 - 4*I*a^3*c^2*x^3 - 4*I*a*c^2*x - 2*c^2)","A",0
336,1,67,0,0.719984," ","integrate(1/(1+I*a*x)^4*(a^2*x^2+1)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 3 i \, a x + 4\right)}}{15 \, a^{4} c^{2} x^{3} - 45 i \, a^{3} c^{2} x^{2} - 45 \, a^{2} c^{2} x + 15 i \, a c^{2}}"," ",0,"-sqrt(a^2*c*x^2 + c)*(a^2*x^2 - 3*I*a*x + 4)/(15*a^4*c^2*x^3 - 45*I*a^3*c^2*x^2 - 45*a^2*c^2*x + 15*I*a*c^2)","A",0
337,0,0,0,0.606301," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} e^{\left(n \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*e^(n*arctan(a*x)), x)","F",0
338,0,0,0,0.478236," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} e^{\left(n \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*e^(n*arctan(a*x)), x)","F",0
339,0,0,0,0.410059," ","integrate(exp(n*arctan(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(e^{\left(n \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral(e^(n*arctan(a*x)), x)","F",0
340,0,0,0,0.528685," ","integrate(exp(n*arctan(a*x))*x^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^3*e^(n*arctan(a*x))/(a^2*c*x^2 + c), x)","F",0
341,0,0,0,0.473454," ","integrate(exp(n*arctan(a*x))*x^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^2*e^(n*arctan(a*x))/(a^2*c*x^2 + c), x)","F",0
342,0,0,0,0.429000," ","integrate(exp(n*arctan(a*x))*x/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x*e^(n*arctan(a*x))/(a^2*c*x^2 + c), x)","F",0
343,1,17,0,0.423099," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{e^{\left(n \arctan\left(a x\right)\right)}}{a c n}"," ",0,"e^(n*arctan(a*x))/(a*c*n)","A",0
344,0,0,0,0.455062," ","integrate(exp(n*arctan(a*x))/x/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{3} + c x}, x\right)"," ",0,"integral(e^(n*arctan(a*x))/(a^2*c*x^3 + c*x), x)","F",0
345,0,0,0,0.462497," ","integrate(exp(n*arctan(a*x))/x^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{4} + c x^{2}}, x\right)"," ",0,"integral(e^(n*arctan(a*x))/(a^2*c*x^4 + c*x^2), x)","F",0
346,0,0,0,0.485446," ","integrate(exp(n*arctan(a*x))/x^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{5} + c x^{3}}, x\right)"," ",0,"integral(e^(n*arctan(a*x))/(a^2*c*x^5 + c*x^3), x)","F",0
347,1,298,0,0.454681," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^4,x, algorithm=""fricas"")","\frac{{\left(720 \, a^{6} x^{6} + 720 \, a^{5} n x^{5} + n^{6} + 360 \, {\left(a^{4} n^{2} + 6 \, a^{4}\right)} x^{4} + 50 \, n^{4} + 120 \, {\left(a^{3} n^{3} + 16 \, a^{3} n\right)} x^{3} + 30 \, {\left(a^{2} n^{4} + 28 \, a^{2} n^{2} + 72 \, a^{2}\right)} x^{2} + 544 \, n^{2} + 6 \, {\left(a n^{5} + 40 \, a n^{3} + 264 \, a n\right)} x + 720\right)} e^{\left(n \arctan\left(a x\right)\right)}}{a c^{4} n^{7} + 56 \, a c^{4} n^{5} + 784 \, a c^{4} n^{3} + {\left(a^{7} c^{4} n^{7} + 56 \, a^{7} c^{4} n^{5} + 784 \, a^{7} c^{4} n^{3} + 2304 \, a^{7} c^{4} n\right)} x^{6} + 2304 \, a c^{4} n + 3 \, {\left(a^{5} c^{4} n^{7} + 56 \, a^{5} c^{4} n^{5} + 784 \, a^{5} c^{4} n^{3} + 2304 \, a^{5} c^{4} n\right)} x^{4} + 3 \, {\left(a^{3} c^{4} n^{7} + 56 \, a^{3} c^{4} n^{5} + 784 \, a^{3} c^{4} n^{3} + 2304 \, a^{3} c^{4} n\right)} x^{2}}"," ",0,"(720*a^6*x^6 + 720*a^5*n*x^5 + n^6 + 360*(a^4*n^2 + 6*a^4)*x^4 + 50*n^4 + 120*(a^3*n^3 + 16*a^3*n)*x^3 + 30*(a^2*n^4 + 28*a^2*n^2 + 72*a^2)*x^2 + 544*n^2 + 6*(a*n^5 + 40*a*n^3 + 264*a*n)*x + 720)*e^(n*arctan(a*x))/(a*c^4*n^7 + 56*a*c^4*n^5 + 784*a*c^4*n^3 + (a^7*c^4*n^7 + 56*a^7*c^4*n^5 + 784*a^7*c^4*n^3 + 2304*a^7*c^4*n)*x^6 + 2304*a*c^4*n + 3*(a^5*c^4*n^7 + 56*a^5*c^4*n^5 + 784*a^5*c^4*n^3 + 2304*a^5*c^4*n)*x^4 + 3*(a^3*c^4*n^7 + 56*a^3*c^4*n^5 + 784*a^3*c^4*n^3 + 2304*a^3*c^4*n)*x^2)","A",0
348,0,0,0,0.455358," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} e^{\left(n \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*e^(n*arctan(a*x)), x)","F",0
349,0,0,0,0.541943," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} e^{\left(n \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*e^(n*arctan(a*x)), x)","F",0
350,0,0,0,0.441956," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
351,0,0,0,0.576883," ","integrate(exp(n*arctan(a*x))*x^2*(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{4} + c x^{2}\right)} \sqrt{a^{2} c x^{2} + c} e^{\left(n \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^4 + c*x^2)*sqrt(a^2*c*x^2 + c)*e^(n*arctan(a*x)), x)","F",0
352,0,0,0,0.451201," ","integrate(exp(n*arctan(a*x))*x^2*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{2} e^{\left(n \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2*e^(n*arctan(a*x)), x)","F",0
353,0,0,0,0.515779," ","integrate(exp(n*arctan(a*x))*x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^3*e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
354,0,0,0,0.486510," ","integrate(exp(n*arctan(a*x))*x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^2*e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
355,0,0,0,0.427705," ","integrate(exp(n*arctan(a*x))*x/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x*e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
356,0,0,0,0.577600," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
357,0,0,0,0.442070," ","integrate(exp(n*arctan(a*x))/x/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{3} + c x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*e^(n*arctan(a*x))/(a^2*c*x^3 + c*x), x)","F",0
358,0,0,0,0.445982," ","integrate(exp(n*arctan(a*x))/x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{4} + c x^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*e^(n*arctan(a*x))/(a^2*c*x^4 + c*x^2), x)","F",0
359,0,0,0,0.457445," ","integrate(exp(n*arctan(a*x))/x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{5} + c x^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*e^(n*arctan(a*x))/(a^2*c*x^5 + c*x^3), x)","F",0
360,0,0,0,0.452861," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{1}{3}} e^{\left(n \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(1/3)*e^(n*arctan(a*x)), x)","F",0
361,0,0,0,0.450859," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(e^(n*arctan(a*x))/(a^2*c*x^2 + c)^(1/3), x)","F",0
362,0,0,0,0.477108," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral(e^(n*arctan(a*x))/(a^2*c*x^2 + c)^(2/3), x)","F",0
363,0,0,0,0.450243," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{2}{3}} e^{\left(n \arctan\left(a x\right)\right)}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(2/3)*e^(n*arctan(a*x))/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
364,0,0,0,0.509480," ","integrate(exp(n*arctan(a*x))*x^m*(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} x^{m} e^{\left(n \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m*e^(n*arctan(a*x)), x)","F",0
365,0,0,0,0.488979," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^m*e^(n*arctan(a*x))/(a^2*c*x^2 + c), x)","F",0
366,0,0,0,0.488245," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(x^m*e^(n*arctan(a*x))/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
367,0,0,0,0.481406," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(x^m*e^(n*arctan(a*x))/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
368,0,0,0,0.483386," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^m*e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
369,0,0,0,0.487501," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*e^(n*arctan(a*x))/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
370,0,0,0,0.504793," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*e^(n*arctan(a*x))/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
371,0,0,0,0.429673," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{p} e^{\left(n \arctan\left(a x\right)\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^p*e^(n*arctan(a*x)), x)","F",0
372,1,42,0,0.628546," ","integrate((a^2*c*x^2+c)^p/exp(2*I*p*arctan(a*x)),x, algorithm=""fricas"")","\frac{{\left(a x + i\right)} {\left(a^{2} c x^{2} + c\right)}^{p} \left(-\frac{a x + i}{a x - i}\right)^{p}}{2 \, a p + a}"," ",0,"(a*x + I)*(a^2*c*x^2 + c)^p*(-(a*x + I)/(a*x - I))^p/(2*a*p + a)","A",0
373,1,44,0,0.443887," ","integrate(exp(2*I*p*arctan(a*x))*(a^2*c*x^2+c)^p,x, algorithm=""fricas"")","\frac{{\left(a x - i\right)} {\left(a^{2} c x^{2} + c\right)}^{p}}{{\left(2 \, a p + a\right)} \left(-\frac{a x + i}{a x - i}\right)^{p}}"," ",0,"(a*x - I)*(a^2*c*x^2 + c)^p/((2*a*p + a)*(-(a*x + I)/(a*x - I))^p)","A",0
374,1,78,0,0.469481," ","integrate(exp(I*n*arctan(a*x))*x^2*(a^2*c*x^2+c)^(-1-1/2*n^2),x, algorithm=""fricas"")","-\frac{{\left(a^{3} n x^{3} + i \, a^{2} x^{2} + a n x + i\right)} {\left(a^{2} c x^{2} + c\right)}^{-\frac{1}{2} \, n^{2} - 1}}{{\left(a^{3} n^{3} - a^{3} n\right)} \left(-\frac{a x + i}{a x - i}\right)^{\frac{1}{2} \, n}}"," ",0,"-(a^3*n*x^3 + I*a^2*x^2 + a*n*x + I)*(a^2*c*x^2 + c)^(-1/2*n^2 - 1)/((a^3*n^3 - a^3*n)*(-(a*x + I)/(a*x - I))^(1/2*n))","A",0
375,1,379,0,1.341023," ","integrate((1+I*a*x)^6/(a^2*x^2+1)^3*x^2/(a^2*c*x^2+c)^19,x, algorithm=""fricas"")","\frac{6 \, a x + i}{210 \, a^{39} c^{19} x^{36} + 1260 i \, a^{38} c^{19} x^{35} + 14700 i \, a^{36} c^{19} x^{33} - 22050 \, a^{35} c^{19} x^{32} + 70560 i \, a^{34} c^{19} x^{31} - 188160 \, a^{33} c^{19} x^{30} + 151200 i \, a^{32} c^{19} x^{29} - 819000 \, a^{31} c^{19} x^{28} - 58800 i \, a^{30} c^{19} x^{27} - 2257920 \, a^{29} c^{19} x^{26} - 1375920 i \, a^{28} c^{19} x^{25} - 4204200 \, a^{27} c^{19} x^{24} - 4586400 i \, a^{26} c^{19} x^{23} - 5241600 \, a^{25} c^{19} x^{22} - 9129120 i \, a^{24} c^{19} x^{21} - 3783780 \, a^{23} c^{19} x^{20} - 12612600 i \, a^{22} c^{19} x^{19} - 12612600 i \, a^{20} c^{19} x^{17} + 3783780 \, a^{19} c^{19} x^{16} - 9129120 i \, a^{18} c^{19} x^{15} + 5241600 \, a^{17} c^{19} x^{14} - 4586400 i \, a^{16} c^{19} x^{13} + 4204200 \, a^{15} c^{19} x^{12} - 1375920 i \, a^{14} c^{19} x^{11} + 2257920 \, a^{13} c^{19} x^{10} - 58800 i \, a^{12} c^{19} x^{9} + 819000 \, a^{11} c^{19} x^{8} + 151200 i \, a^{10} c^{19} x^{7} + 188160 \, a^{9} c^{19} x^{6} + 70560 i \, a^{8} c^{19} x^{5} + 22050 \, a^{7} c^{19} x^{4} + 14700 i \, a^{6} c^{19} x^{3} + 1260 i \, a^{4} c^{19} x - 210 \, a^{3} c^{19}}"," ",0,"(6*a*x + I)/(210*a^39*c^19*x^36 + 1260*I*a^38*c^19*x^35 + 14700*I*a^36*c^19*x^33 - 22050*a^35*c^19*x^32 + 70560*I*a^34*c^19*x^31 - 188160*a^33*c^19*x^30 + 151200*I*a^32*c^19*x^29 - 819000*a^31*c^19*x^28 - 58800*I*a^30*c^19*x^27 - 2257920*a^29*c^19*x^26 - 1375920*I*a^28*c^19*x^25 - 4204200*a^27*c^19*x^24 - 4586400*I*a^26*c^19*x^23 - 5241600*a^25*c^19*x^22 - 9129120*I*a^24*c^19*x^21 - 3783780*a^23*c^19*x^20 - 12612600*I*a^22*c^19*x^19 - 12612600*I*a^20*c^19*x^17 + 3783780*a^19*c^19*x^16 - 9129120*I*a^18*c^19*x^15 + 5241600*a^17*c^19*x^14 - 4586400*I*a^16*c^19*x^13 + 4204200*a^15*c^19*x^12 - 1375920*I*a^14*c^19*x^11 + 2257920*a^13*c^19*x^10 - 58800*I*a^12*c^19*x^9 + 819000*a^11*c^19*x^8 + 151200*I*a^10*c^19*x^7 + 188160*a^9*c^19*x^6 + 70560*I*a^8*c^19*x^5 + 22050*a^7*c^19*x^4 + 14700*I*a^6*c^19*x^3 + 1260*I*a^4*c^19*x - 210*a^3*c^19)","B",0
376,1,171,0,0.409685," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2*x^2/(a^2*c*x^2+c)^9,x, algorithm=""fricas"")","-\frac{4 \, a x + i}{60 \, a^{19} c^{9} x^{16} + 240 i \, a^{18} c^{9} x^{15} + 1200 i \, a^{16} c^{9} x^{13} - 1200 \, a^{15} c^{9} x^{12} + 2160 i \, a^{14} c^{9} x^{11} - 3840 \, a^{13} c^{9} x^{10} + 1200 i \, a^{12} c^{9} x^{9} - 5400 \, a^{11} c^{9} x^{8} - 1200 i \, a^{10} c^{9} x^{7} - 3840 \, a^{9} c^{9} x^{6} - 2160 i \, a^{8} c^{9} x^{5} - 1200 \, a^{7} c^{9} x^{4} - 1200 i \, a^{6} c^{9} x^{3} - 240 i \, a^{4} c^{9} x + 60 \, a^{3} c^{9}}"," ",0,"-(4*a*x + I)/(60*a^19*c^9*x^16 + 240*I*a^18*c^9*x^15 + 1200*I*a^16*c^9*x^13 - 1200*a^15*c^9*x^12 + 2160*I*a^14*c^9*x^11 - 3840*a^13*c^9*x^10 + 1200*I*a^12*c^9*x^9 - 5400*a^11*c^9*x^8 - 1200*I*a^10*c^9*x^7 - 3840*a^9*c^9*x^6 - 2160*I*a^8*c^9*x^5 - 1200*a^7*c^9*x^4 - 1200*I*a^6*c^9*x^3 - 240*I*a^4*c^9*x + 60*a^3*c^9)","B",0
377,1,49,0,0.536995," ","integrate((1+I*a*x)^2/(a^2*x^2+1)*x^2/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{2 \, a x + i}{6 \, a^{7} c^{3} x^{4} + 12 i \, a^{6} c^{3} x^{3} + 12 i \, a^{4} c^{3} x - 6 \, a^{3} c^{3}}"," ",0,"(2*a*x + I)/(6*a^7*c^3*x^4 + 12*I*a^6*c^3*x^3 + 12*I*a^4*c^3*x - 6*a^3*c^3)","A",0
378,1,49,0,0.522063," ","integrate(x^2/(1+I*a*x)^2*(a^2*x^2+1)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{2 \, a x - i}{6 \, a^{7} c^{3} x^{4} - 12 i \, a^{6} c^{3} x^{3} - 12 i \, a^{4} c^{3} x - 6 \, a^{3} c^{3}}"," ",0,"(2*a*x - I)/(6*a^7*c^3*x^4 - 12*I*a^6*c^3*x^3 - 12*I*a^4*c^3*x - 6*a^3*c^3)","A",0
379,1,171,0,0.513898," ","integrate(x^2/(1+I*a*x)^4*(a^2*x^2+1)^2/(a^2*c*x^2+c)^9,x, algorithm=""fricas"")","-\frac{4 \, a x - i}{60 \, a^{19} c^{9} x^{16} - 240 i \, a^{18} c^{9} x^{15} - 1200 i \, a^{16} c^{9} x^{13} - 1200 \, a^{15} c^{9} x^{12} - 2160 i \, a^{14} c^{9} x^{11} - 3840 \, a^{13} c^{9} x^{10} - 1200 i \, a^{12} c^{9} x^{9} - 5400 \, a^{11} c^{9} x^{8} + 1200 i \, a^{10} c^{9} x^{7} - 3840 \, a^{9} c^{9} x^{6} + 2160 i \, a^{8} c^{9} x^{5} - 1200 \, a^{7} c^{9} x^{4} + 1200 i \, a^{6} c^{9} x^{3} + 240 i \, a^{4} c^{9} x + 60 \, a^{3} c^{9}}"," ",0,"-(4*a*x - I)/(60*a^19*c^9*x^16 - 240*I*a^18*c^9*x^15 - 1200*I*a^16*c^9*x^13 - 1200*a^15*c^9*x^12 - 2160*I*a^14*c^9*x^11 - 3840*a^13*c^9*x^10 - 1200*I*a^12*c^9*x^9 - 5400*a^11*c^9*x^8 + 1200*I*a^10*c^9*x^7 - 3840*a^9*c^9*x^6 + 2160*I*a^8*c^9*x^5 - 1200*a^7*c^9*x^4 + 1200*I*a^6*c^9*x^3 + 240*I*a^4*c^9*x + 60*a^3*c^9)","B",0
380,1,497,0,0.611351," ","integrate((1+I*a*x)^5/(a^2*x^2+1)^(5/2)*x^2/(a^2*c*x^2+c)^(27/2),x, algorithm=""fricas"")","\frac{{\left(i \, a^{22} x^{25} - 5 \, a^{21} x^{24} - 40 \, a^{19} x^{22} - 50 i \, a^{18} x^{21} - 126 \, a^{17} x^{20} - 280 i \, a^{16} x^{19} - 160 \, a^{15} x^{18} - 765 i \, a^{14} x^{17} + 105 \, a^{13} x^{16} - 1248 i \, a^{12} x^{15} + 720 \, a^{11} x^{14} - 1260 i \, a^{10} x^{13} + 1260 \, a^{9} x^{12} - 720 i \, a^{8} x^{11} + 1248 \, a^{7} x^{10} - 105 i \, a^{6} x^{9} + 765 \, a^{5} x^{8} + 160 i \, a^{4} x^{7} + 280 \, a^{3} x^{6} + 126 i \, a^{2} x^{5} + 50 \, a x^{4} + 40 i \, x^{3}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1}}{120 \, a^{27} c^{14} x^{27} + 600 i \, a^{26} c^{14} x^{26} + 120 \, a^{25} c^{14} x^{25} + 5400 i \, a^{24} c^{14} x^{24} - 6000 \, a^{23} c^{14} x^{23} + 19920 i \, a^{22} c^{14} x^{22} - 39600 \, a^{21} c^{14} x^{21} + 34320 i \, a^{20} c^{14} x^{20} - 125400 \, a^{19} c^{14} x^{19} + 6600 i \, a^{18} c^{14} x^{18} - 241560 \, a^{17} c^{14} x^{17} - 99000 i \, a^{16} c^{14} x^{16} - 300960 \, a^{15} c^{14} x^{15} - 237600 i \, a^{14} c^{14} x^{14} - 237600 \, a^{13} c^{14} x^{13} - 300960 i \, a^{12} c^{14} x^{12} - 99000 \, a^{11} c^{14} x^{11} - 241560 i \, a^{10} c^{14} x^{10} + 6600 \, a^{9} c^{14} x^{9} - 125400 i \, a^{8} c^{14} x^{8} + 34320 \, a^{7} c^{14} x^{7} - 39600 i \, a^{6} c^{14} x^{6} + 19920 \, a^{5} c^{14} x^{5} - 6000 i \, a^{4} c^{14} x^{4} + 5400 \, a^{3} c^{14} x^{3} + 120 i \, a^{2} c^{14} x^{2} + 600 \, a c^{14} x + 120 i \, c^{14}}"," ",0,"(I*a^22*x^25 - 5*a^21*x^24 - 40*a^19*x^22 - 50*I*a^18*x^21 - 126*a^17*x^20 - 280*I*a^16*x^19 - 160*a^15*x^18 - 765*I*a^14*x^17 + 105*a^13*x^16 - 1248*I*a^12*x^15 + 720*a^11*x^14 - 1260*I*a^10*x^13 + 1260*a^9*x^12 - 720*I*a^8*x^11 + 1248*a^7*x^10 - 105*I*a^6*x^9 + 765*a^5*x^8 + 160*I*a^4*x^7 + 280*a^3*x^6 + 126*I*a^2*x^5 + 50*a*x^4 + 40*I*x^3)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)/(120*a^27*c^14*x^27 + 600*I*a^26*c^14*x^26 + 120*a^25*c^14*x^25 + 5400*I*a^24*c^14*x^24 - 6000*a^23*c^14*x^23 + 19920*I*a^22*c^14*x^22 - 39600*a^21*c^14*x^21 + 34320*I*a^20*c^14*x^20 - 125400*a^19*c^14*x^19 + 6600*I*a^18*c^14*x^18 - 241560*a^17*c^14*x^17 - 99000*I*a^16*c^14*x^16 - 300960*a^15*c^14*x^15 - 237600*I*a^14*c^14*x^14 - 237600*a^13*c^14*x^13 - 300960*I*a^12*c^14*x^12 - 99000*a^11*c^14*x^11 - 241560*I*a^10*c^14*x^10 + 6600*a^9*c^14*x^9 - 125400*I*a^8*c^14*x^8 + 34320*a^7*c^14*x^7 - 39600*I*a^6*c^14*x^6 + 19920*a^5*c^14*x^5 - 6000*I*a^4*c^14*x^4 + 5400*a^3*c^14*x^3 + 120*I*a^2*c^14*x^2 + 600*a*c^14*x + 120*I*c^14)","B",0
381,1,193,0,0.492856," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^2/(a^2*c*x^2+c)^(11/2),x, algorithm=""fricas"")","\frac{{\left(i \, a^{6} x^{9} - 3 \, a^{5} x^{8} - 8 \, a^{3} x^{6} - 6 i \, a^{2} x^{5} - 6 \, a x^{4} - 8 i \, x^{3}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1}}{24 \, a^{11} c^{6} x^{11} + 72 i \, a^{10} c^{6} x^{10} + 24 \, a^{9} c^{6} x^{9} + 264 i \, a^{8} c^{6} x^{8} - 144 \, a^{7} c^{6} x^{7} + 336 i \, a^{6} c^{6} x^{6} - 336 \, a^{5} c^{6} x^{5} + 144 i \, a^{4} c^{6} x^{4} - 264 \, a^{3} c^{6} x^{3} - 24 i \, a^{2} c^{6} x^{2} - 72 \, a c^{6} x - 24 i \, c^{6}}"," ",0,"(I*a^6*x^9 - 3*a^5*x^8 - 8*a^3*x^6 - 6*I*a^2*x^5 - 6*a*x^4 - 8*I*x^3)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)/(24*a^11*c^6*x^11 + 72*I*a^10*c^6*x^10 + 24*a^9*c^6*x^9 + 264*I*a^8*c^6*x^8 - 144*a^7*c^6*x^7 + 336*I*a^6*c^6*x^6 - 336*a^5*c^6*x^5 + 144*I*a^4*c^6*x^4 - 264*a^3*c^6*x^3 - 24*I*a^2*c^6*x^2 - 72*a*c^6*x - 24*I*c^6)","B",0
382,0,0,0,0.651468," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(-3 i \, a^{5} c^{2} x^{3} + 3 \, a^{4} c^{2} x^{2} - 3 i \, a^{3} c^{2} x + 3 \, a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(\frac{i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} + i \, a^{2} x^{3} + i \, x}{a^{3} x^{3} + i \, a^{2} x^{2} + a x + i}\right) + {\left(3 i \, a^{5} c^{2} x^{3} - 3 \, a^{4} c^{2} x^{2} + 3 i \, a^{3} c^{2} x - 3 \, a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(\frac{-i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} + i \, a^{2} x^{3} + i \, x}{a^{3} x^{3} + i \, a^{2} x^{2} + a x + i}\right) + {\left(i \, a^{5} c^{2} x^{3} - a^{4} c^{2} x^{2} + i \, a^{3} c^{2} x - a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(\frac{i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} - i \, a^{2} x^{3} - i \, x}{a^{3} x^{3} - i \, a^{2} x^{2} + a x - i}\right) + {\left(-i \, a^{5} c^{2} x^{3} + a^{4} c^{2} x^{2} - i \, a^{3} c^{2} x + a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(\frac{-i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} - i \, a^{2} x^{3} - i \, x}{a^{3} x^{3} - i \, a^{2} x^{2} + a x - i}\right) + {\left(4 i \, a^{5} c^{2} x^{3} - 4 \, a^{4} c^{2} x^{2} + 4 i \, a^{3} c^{2} x - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(\frac{\sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} + a^{2} x^{3} + x}{a^{2} x^{2} + 1}\right) + {\left(-4 i \, a^{5} c^{2} x^{3} + 4 \, a^{4} c^{2} x^{2} - 4 i \, a^{3} c^{2} x + 4 \, a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(-\frac{\sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} - a^{2} x^{3} - x}{a^{2} x^{2} + 1}\right) - 4 i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} x + 2 \, {\left(4 \, a^{5} c^{2} x^{3} + 4 i \, a^{4} c^{2} x^{2} + 4 \, a^{3} c^{2} x + 4 i \, a^{2} c^{2}\right)} {\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} {\left(2 i \, a x + 1\right)}}{2 \, {\left(a^{6} c^{2} x^{4} + 2 \, a^{4} c^{2} x^{2} + a^{2} c^{2}\right)}}, x\right)}{2 \, {\left(4 \, a^{5} c^{2} x^{3} + 4 i \, a^{4} c^{2} x^{2} + 4 \, a^{3} c^{2} x + 4 i \, a^{2} c^{2}\right)}}"," ",0,"1/2*((-3*I*a^5*c^2*x^3 + 3*a^4*c^2*x^2 - 3*I*a^3*c^2*x + 3*a^2*c^2)*sqrt(1/(a^6*c^3))*log((I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) + I*a^2*x^3 + I*x)/(a^3*x^3 + I*a^2*x^2 + a*x + I)) + (3*I*a^5*c^2*x^3 - 3*a^4*c^2*x^2 + 3*I*a^3*c^2*x - 3*a^2*c^2)*sqrt(1/(a^6*c^3))*log((-I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) + I*a^2*x^3 + I*x)/(a^3*x^3 + I*a^2*x^2 + a*x + I)) + (I*a^5*c^2*x^3 - a^4*c^2*x^2 + I*a^3*c^2*x - a^2*c^2)*sqrt(1/(a^6*c^3))*log((I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) - I*a^2*x^3 - I*x)/(a^3*x^3 - I*a^2*x^2 + a*x - I)) + (-I*a^5*c^2*x^3 + a^4*c^2*x^2 - I*a^3*c^2*x + a^2*c^2)*sqrt(1/(a^6*c^3))*log((-I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) - I*a^2*x^3 - I*x)/(a^3*x^3 - I*a^2*x^2 + a*x - I)) + (4*I*a^5*c^2*x^3 - 4*a^4*c^2*x^2 + 4*I*a^3*c^2*x - 4*a^2*c^2)*sqrt(1/(a^6*c^3))*log((sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) + a^2*x^3 + x)/(a^2*x^2 + 1)) + (-4*I*a^5*c^2*x^3 + 4*a^4*c^2*x^2 - 4*I*a^3*c^2*x + 4*a^2*c^2)*sqrt(1/(a^6*c^3))*log(-(sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) - a^2*x^3 - x)/(a^2*x^2 + 1)) - 4*I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*x + 2*(4*a^5*c^2*x^3 + 4*I*a^4*c^2*x^2 + 4*a^3*c^2*x + 4*I*a^2*c^2)*integral(1/2*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*(2*I*a*x + 1)/(a^6*c^2*x^4 + 2*a^4*c^2*x^2 + a^2*c^2), x))/(4*a^5*c^2*x^3 + 4*I*a^4*c^2*x^2 + 4*a^3*c^2*x + 4*I*a^2*c^2)","F",0
383,0,0,0,0.592171," ","integrate(x^2/(1+I*a*x)*(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(i \, a^{5} c^{2} x^{3} + a^{4} c^{2} x^{2} + i \, a^{3} c^{2} x + a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(\frac{i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} + i \, a^{2} x^{3} + i \, x}{a^{3} x^{3} + i \, a^{2} x^{2} + a x + i}\right) + {\left(-i \, a^{5} c^{2} x^{3} - a^{4} c^{2} x^{2} - i \, a^{3} c^{2} x - a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(\frac{-i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} + i \, a^{2} x^{3} + i \, x}{a^{3} x^{3} + i \, a^{2} x^{2} + a x + i}\right) + {\left(-3 i \, a^{5} c^{2} x^{3} - 3 \, a^{4} c^{2} x^{2} - 3 i \, a^{3} c^{2} x - 3 \, a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(\frac{i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} - i \, a^{2} x^{3} - i \, x}{a^{3} x^{3} - i \, a^{2} x^{2} + a x - i}\right) + {\left(3 i \, a^{5} c^{2} x^{3} + 3 \, a^{4} c^{2} x^{2} + 3 i \, a^{3} c^{2} x + 3 \, a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(\frac{-i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} - i \, a^{2} x^{3} - i \, x}{a^{3} x^{3} - i \, a^{2} x^{2} + a x - i}\right) + {\left(-4 i \, a^{5} c^{2} x^{3} - 4 \, a^{4} c^{2} x^{2} - 4 i \, a^{3} c^{2} x - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(\frac{\sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} + a^{2} x^{3} + x}{a^{2} x^{2} + 1}\right) + {\left(4 i \, a^{5} c^{2} x^{3} + 4 \, a^{4} c^{2} x^{2} + 4 i \, a^{3} c^{2} x + 4 \, a^{2} c^{2}\right)} \sqrt{\frac{1}{a^{6} c^{3}}} \log\left(-\frac{\sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} a^{3} c x \sqrt{\frac{1}{a^{6} c^{3}}} - a^{2} x^{3} - x}{a^{2} x^{2} + 1}\right) + 4 i \, \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} x + 2 \, {\left(4 \, a^{5} c^{2} x^{3} - 4 i \, a^{4} c^{2} x^{2} + 4 \, a^{3} c^{2} x - 4 i \, a^{2} c^{2}\right)} {\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1} {\left(-2 i \, a x + 1\right)}}{2 \, {\left(a^{6} c^{2} x^{4} + 2 \, a^{4} c^{2} x^{2} + a^{2} c^{2}\right)}}, x\right)}{2 \, {\left(4 \, a^{5} c^{2} x^{3} - 4 i \, a^{4} c^{2} x^{2} + 4 \, a^{3} c^{2} x - 4 i \, a^{2} c^{2}\right)}}"," ",0,"1/2*((I*a^5*c^2*x^3 + a^4*c^2*x^2 + I*a^3*c^2*x + a^2*c^2)*sqrt(1/(a^6*c^3))*log((I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) + I*a^2*x^3 + I*x)/(a^3*x^3 + I*a^2*x^2 + a*x + I)) + (-I*a^5*c^2*x^3 - a^4*c^2*x^2 - I*a^3*c^2*x - a^2*c^2)*sqrt(1/(a^6*c^3))*log((-I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) + I*a^2*x^3 + I*x)/(a^3*x^3 + I*a^2*x^2 + a*x + I)) + (-3*I*a^5*c^2*x^3 - 3*a^4*c^2*x^2 - 3*I*a^3*c^2*x - 3*a^2*c^2)*sqrt(1/(a^6*c^3))*log((I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) - I*a^2*x^3 - I*x)/(a^3*x^3 - I*a^2*x^2 + a*x - I)) + (3*I*a^5*c^2*x^3 + 3*a^4*c^2*x^2 + 3*I*a^3*c^2*x + 3*a^2*c^2)*sqrt(1/(a^6*c^3))*log((-I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) - I*a^2*x^3 - I*x)/(a^3*x^3 - I*a^2*x^2 + a*x - I)) + (-4*I*a^5*c^2*x^3 - 4*a^4*c^2*x^2 - 4*I*a^3*c^2*x - 4*a^2*c^2)*sqrt(1/(a^6*c^3))*log((sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) + a^2*x^3 + x)/(a^2*x^2 + 1)) + (4*I*a^5*c^2*x^3 + 4*a^4*c^2*x^2 + 4*I*a^3*c^2*x + 4*a^2*c^2)*sqrt(1/(a^6*c^3))*log(-(sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*a^3*c*x*sqrt(1/(a^6*c^3)) - a^2*x^3 - x)/(a^2*x^2 + 1)) + 4*I*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*x + 2*(4*a^5*c^2*x^3 - 4*I*a^4*c^2*x^2 + 4*a^3*c^2*x - 4*I*a^2*c^2)*integral(1/2*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*(-2*I*a*x + 1)/(a^6*c^2*x^4 + 2*a^4*c^2*x^2 + a^2*c^2), x))/(4*a^5*c^2*x^3 - 4*I*a^4*c^2*x^2 + 4*a^3*c^2*x - 4*I*a^2*c^2)","F",0
384,1,193,0,0.496579," ","integrate(x^2/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(11/2),x, algorithm=""fricas"")","\frac{{\left(-i \, a^{6} x^{9} - 3 \, a^{5} x^{8} - 8 \, a^{3} x^{6} + 6 i \, a^{2} x^{5} - 6 \, a x^{4} + 8 i \, x^{3}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1}}{24 \, a^{11} c^{6} x^{11} - 72 i \, a^{10} c^{6} x^{10} + 24 \, a^{9} c^{6} x^{9} - 264 i \, a^{8} c^{6} x^{8} - 144 \, a^{7} c^{6} x^{7} - 336 i \, a^{6} c^{6} x^{6} - 336 \, a^{5} c^{6} x^{5} - 144 i \, a^{4} c^{6} x^{4} - 264 \, a^{3} c^{6} x^{3} + 24 i \, a^{2} c^{6} x^{2} - 72 \, a c^{6} x + 24 i \, c^{6}}"," ",0,"(-I*a^6*x^9 - 3*a^5*x^8 - 8*a^3*x^6 + 6*I*a^2*x^5 - 6*a*x^4 + 8*I*x^3)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)/(24*a^11*c^6*x^11 - 72*I*a^10*c^6*x^10 + 24*a^9*c^6*x^9 - 264*I*a^8*c^6*x^8 - 144*a^7*c^6*x^7 - 336*I*a^6*c^6*x^6 - 336*a^5*c^6*x^5 - 144*I*a^4*c^6*x^4 - 264*a^3*c^6*x^3 + 24*I*a^2*c^6*x^2 - 72*a*c^6*x + 24*I*c^6)","B",0
385,1,497,0,0.658814," ","integrate(x^2/(1+I*a*x)^5*(a^2*x^2+1)^(5/2)/(a^2*c*x^2+c)^(27/2),x, algorithm=""fricas"")","\frac{{\left(-i \, a^{22} x^{25} - 5 \, a^{21} x^{24} - 40 \, a^{19} x^{22} + 50 i \, a^{18} x^{21} - 126 \, a^{17} x^{20} + 280 i \, a^{16} x^{19} - 160 \, a^{15} x^{18} + 765 i \, a^{14} x^{17} + 105 \, a^{13} x^{16} + 1248 i \, a^{12} x^{15} + 720 \, a^{11} x^{14} + 1260 i \, a^{10} x^{13} + 1260 \, a^{9} x^{12} + 720 i \, a^{8} x^{11} + 1248 \, a^{7} x^{10} + 105 i \, a^{6} x^{9} + 765 \, a^{5} x^{8} - 160 i \, a^{4} x^{7} + 280 \, a^{3} x^{6} - 126 i \, a^{2} x^{5} + 50 \, a x^{4} - 40 i \, x^{3}\right)} \sqrt{a^{2} c x^{2} + c} \sqrt{a^{2} x^{2} + 1}}{120 \, a^{27} c^{14} x^{27} - 600 i \, a^{26} c^{14} x^{26} + 120 \, a^{25} c^{14} x^{25} - 5400 i \, a^{24} c^{14} x^{24} - 6000 \, a^{23} c^{14} x^{23} - 19920 i \, a^{22} c^{14} x^{22} - 39600 \, a^{21} c^{14} x^{21} - 34320 i \, a^{20} c^{14} x^{20} - 125400 \, a^{19} c^{14} x^{19} - 6600 i \, a^{18} c^{14} x^{18} - 241560 \, a^{17} c^{14} x^{17} + 99000 i \, a^{16} c^{14} x^{16} - 300960 \, a^{15} c^{14} x^{15} + 237600 i \, a^{14} c^{14} x^{14} - 237600 \, a^{13} c^{14} x^{13} + 300960 i \, a^{12} c^{14} x^{12} - 99000 \, a^{11} c^{14} x^{11} + 241560 i \, a^{10} c^{14} x^{10} + 6600 \, a^{9} c^{14} x^{9} + 125400 i \, a^{8} c^{14} x^{8} + 34320 \, a^{7} c^{14} x^{7} + 39600 i \, a^{6} c^{14} x^{6} + 19920 \, a^{5} c^{14} x^{5} + 6000 i \, a^{4} c^{14} x^{4} + 5400 \, a^{3} c^{14} x^{3} - 120 i \, a^{2} c^{14} x^{2} + 600 \, a c^{14} x - 120 i \, c^{14}}"," ",0,"(-I*a^22*x^25 - 5*a^21*x^24 - 40*a^19*x^22 + 50*I*a^18*x^21 - 126*a^17*x^20 + 280*I*a^16*x^19 - 160*a^15*x^18 + 765*I*a^14*x^17 + 105*a^13*x^16 + 1248*I*a^12*x^15 + 720*a^11*x^14 + 1260*I*a^10*x^13 + 1260*a^9*x^12 + 720*I*a^8*x^11 + 1248*a^7*x^10 + 105*I*a^6*x^9 + 765*a^5*x^8 - 160*I*a^4*x^7 + 280*a^3*x^6 - 126*I*a^2*x^5 + 50*a*x^4 - 40*I*x^3)*sqrt(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)/(120*a^27*c^14*x^27 - 600*I*a^26*c^14*x^26 + 120*a^25*c^14*x^25 - 5400*I*a^24*c^14*x^24 - 6000*a^23*c^14*x^23 - 19920*I*a^22*c^14*x^22 - 39600*a^21*c^14*x^21 - 34320*I*a^20*c^14*x^20 - 125400*a^19*c^14*x^19 - 6600*I*a^18*c^14*x^18 - 241560*a^17*c^14*x^17 + 99000*I*a^16*c^14*x^16 - 300960*a^15*c^14*x^15 + 237600*I*a^14*c^14*x^14 - 237600*a^13*c^14*x^13 + 300960*I*a^12*c^14*x^12 - 99000*a^11*c^14*x^11 + 241560*I*a^10*c^14*x^10 + 6600*a^9*c^14*x^9 + 125400*I*a^8*c^14*x^8 + 34320*a^7*c^14*x^7 + 39600*I*a^6*c^14*x^6 + 19920*a^5*c^14*x^5 + 6000*I*a^4*c^14*x^4 + 5400*a^3*c^14*x^3 - 120*I*a^2*c^14*x^2 + 600*a*c^14*x - 120*I*c^14)","B",0
