1,1,100,0,0.358780," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^4,x, algorithm=""maxima"")","\frac{i \, \sqrt{a^{2} x^{2} + 1} x^{4}}{5 \, a} + \frac{\sqrt{a^{2} x^{2} + 1} x^{3}}{4 \, a^{2}} - \frac{4 i \, \sqrt{a^{2} x^{2} + 1} x^{2}}{15 \, a^{3}} - \frac{3 \, \sqrt{a^{2} x^{2} + 1} x}{8 \, a^{4}} + \frac{3 \, \operatorname{arsinh}\left(a x\right)}{8 \, a^{5}} + \frac{8 i \, \sqrt{a^{2} x^{2} + 1}}{15 \, a^{5}}"," ",0,"1/5*I*sqrt(a^2*x^2 + 1)*x^4/a + 1/4*sqrt(a^2*x^2 + 1)*x^3/a^2 - 4/15*I*sqrt(a^2*x^2 + 1)*x^2/a^3 - 3/8*sqrt(a^2*x^2 + 1)*x/a^4 + 3/8*arcsinh(a*x)/a^5 + 8/15*I*sqrt(a^2*x^2 + 1)/a^5","A",0
2,1,81,0,0.317020," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^3,x, algorithm=""maxima"")","\frac{i \, \sqrt{a^{2} x^{2} + 1} x^{3}}{4 \, a} + \frac{\sqrt{a^{2} x^{2} + 1} x^{2}}{3 \, a^{2}} - \frac{3 i \, \sqrt{a^{2} x^{2} + 1} x}{8 \, a^{3}} + \frac{3 i \, \operatorname{arsinh}\left(a x\right)}{8 \, a^{4}} - \frac{2 \, \sqrt{a^{2} x^{2} + 1}}{3 \, a^{4}}"," ",0,"1/4*I*sqrt(a^2*x^2 + 1)*x^3/a + 1/3*sqrt(a^2*x^2 + 1)*x^2/a^2 - 3/8*I*sqrt(a^2*x^2 + 1)*x/a^3 + 3/8*I*arcsinh(a*x)/a^4 - 2/3*sqrt(a^2*x^2 + 1)/a^4","A",0
3,1,62,0,0.316710," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^2,x, algorithm=""maxima"")","\frac{i \, \sqrt{a^{2} x^{2} + 1} x^{2}}{3 \, a} + \frac{\sqrt{a^{2} x^{2} + 1} x}{2 \, a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)}{2 \, a^{3}} - \frac{2 i \, \sqrt{a^{2} x^{2} + 1}}{3 \, a^{3}}"," ",0,"1/3*I*sqrt(a^2*x^2 + 1)*x^2/a + 1/2*sqrt(a^2*x^2 + 1)*x/a^2 - 1/2*arcsinh(a*x)/a^3 - 2/3*I*sqrt(a^2*x^2 + 1)/a^3","A",0
4,1,42,0,0.331960," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x,x, algorithm=""maxima"")","\frac{i \, \sqrt{a^{2} x^{2} + 1} x}{2 \, a} - \frac{i \, \operatorname{arsinh}\left(a x\right)}{2 \, a^{2}} + \frac{\sqrt{a^{2} x^{2} + 1}}{a^{2}}"," ",0,"1/2*I*sqrt(a^2*x^2 + 1)*x/a - 1/2*I*arcsinh(a*x)/a^2 + sqrt(a^2*x^2 + 1)/a^2","A",0
5,1,25,0,0.319950," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(a x\right)}{a} + \frac{i \, \sqrt{a^{2} x^{2} + 1}}{a}"," ",0,"arcsinh(a*x)/a + I*sqrt(a^2*x^2 + 1)/a","A",0
6,1,18,0,0.312644," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","i \, \operatorname{arsinh}\left(a x\right) - \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right)"," ",0,"I*arcsinh(a*x) - arcsinh(1/(a*abs(x)))","A",0
7,1,29,0,0.339346," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","-i \, a \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right) - \frac{\sqrt{a^{2} x^{2} + 1}}{x}"," ",0,"-I*a*arcsinh(1/(a*abs(x))) - sqrt(a^2*x^2 + 1)/x","A",0
8,1,48,0,0.331490," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right) - \frac{i \, \sqrt{a^{2} x^{2} + 1} a}{x} - \frac{\sqrt{a^{2} x^{2} + 1}}{2 \, x^{2}}"," ",0,"1/2*a^2*arcsinh(1/(a*abs(x))) - I*sqrt(a^2*x^2 + 1)*a/x - 1/2*sqrt(a^2*x^2 + 1)/x^2","A",0
9,1,67,0,0.329113," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^4,x, algorithm=""maxima"")","\frac{1}{2} i \, a^{3} \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right) + \frac{2 \, \sqrt{a^{2} x^{2} + 1} a^{2}}{3 \, x} - \frac{i \, \sqrt{a^{2} x^{2} + 1} a}{2 \, x^{2}} - \frac{\sqrt{a^{2} x^{2} + 1}}{3 \, x^{3}}"," ",0,"1/2*I*a^3*arcsinh(1/(a*abs(x))) + 2/3*sqrt(a^2*x^2 + 1)*a^2/x - 1/2*I*sqrt(a^2*x^2 + 1)*a/x^2 - 1/3*sqrt(a^2*x^2 + 1)/x^3","A",0
10,1,86,0,0.332979," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^5,x, algorithm=""maxima"")","-\frac{3}{8} \, a^{4} \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right) + \frac{2 i \, \sqrt{a^{2} x^{2} + 1} a^{3}}{3 \, x} + \frac{3 \, \sqrt{a^{2} x^{2} + 1} a^{2}}{8 \, x^{2}} - \frac{i \, \sqrt{a^{2} x^{2} + 1} a}{3 \, x^{3}} - \frac{\sqrt{a^{2} x^{2} + 1}}{4 \, x^{4}}"," ",0,"-3/8*a^4*arcsinh(1/(a*abs(x))) + 2/3*I*sqrt(a^2*x^2 + 1)*a^3/x + 3/8*sqrt(a^2*x^2 + 1)*a^2/x^2 - 1/3*I*sqrt(a^2*x^2 + 1)*a/x^3 - 1/4*sqrt(a^2*x^2 + 1)/x^4","A",0
11,1,56,0,0.428858," ","integrate((1+I*a*x)^2/(a^2*x^2+1)*x^3,x, algorithm=""maxima"")","-\frac{3 \, a^{3} x^{4} - 8 i \, a^{2} x^{3} - 12 \, a x^{2} + 24 i \, x}{12 \, a^{3}} + \frac{2 i \, \arctan\left(a x\right)}{a^{4}} - \frac{\log\left(a^{2} x^{2} + 1\right)}{a^{4}}"," ",0,"-1/12*(3*a^3*x^4 - 8*I*a^2*x^3 - 12*a*x^2 + 24*I*x)/a^3 + 2*I*arctan(a*x)/a^4 - log(a^2*x^2 + 1)/a^4","A",0
12,1,47,0,0.432673," ","integrate((1+I*a*x)^2/(a^2*x^2+1)*x^2,x, algorithm=""maxima"")","-\frac{a^{2} x^{3} - 3 i \, a x^{2} - 6 \, x}{3 \, a^{2}} - \frac{2 \, \arctan\left(a x\right)}{a^{3}} - \frac{i \, \log\left(a^{2} x^{2} + 1\right)}{a^{3}}"," ",0,"-1/3*(a^2*x^3 - 3*I*a*x^2 - 6*x)/a^2 - 2*arctan(a*x)/a^3 - I*log(a^2*x^2 + 1)/a^3","A",0
13,1,38,0,0.441078," ","integrate((1+I*a*x)^2/(a^2*x^2+1)*x,x, algorithm=""maxima"")","-\frac{a x^{2} - 4 i \, x}{2 \, a} - \frac{2 i \, \arctan\left(a x\right)}{a^{2}} + \frac{\log\left(a^{2} x^{2} + 1\right)}{a^{2}}"," ",0,"-1/2*(a*x^2 - 4*I*x)/a - 2*I*arctan(a*x)/a^2 + log(a^2*x^2 + 1)/a^2","A",0
14,1,28,0,0.441118," ","integrate((1+I*a*x)^2/(a^2*x^2+1),x, algorithm=""maxima"")","-x + \frac{2 \, \arctan\left(a x\right)}{a} + \frac{i \, \log\left(a^{2} x^{2} + 1\right)}{a}"," ",0,"-x + 2*arctan(a*x)/a + I*log(a^2*x^2 + 1)/a","A",0
15,1,21,0,0.452689," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/x,x, algorithm=""maxima"")","2 i \, \arctan\left(a x\right) - \log\left(a^{2} x^{2} + 1\right) + \log\left(x\right)"," ",0,"2*I*arctan(a*x) - log(a^2*x^2 + 1) + log(x)","A",0
16,1,31,0,0.441979," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/x^2,x, algorithm=""maxima"")","-2 \, a \arctan\left(a x\right) - i \, a \log\left(a^{2} x^{2} + 1\right) + 2 i \, a \log\left(x\right) - \frac{1}{x}"," ",0,"-2*a*arctan(a*x) - I*a*log(a^2*x^2 + 1) + 2*I*a*log(x) - 1/x","A",0
17,1,42,0,0.429722," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/x^3,x, algorithm=""maxima"")","-2 i \, a^{2} \arctan\left(a x\right) + a^{2} \log\left(a^{2} x^{2} + 1\right) - 2 \, a^{2} \log\left(x\right) - \frac{4 i \, a x + 1}{2 \, x^{2}}"," ",0,"-2*I*a^2*arctan(a*x) + a^2*log(a^2*x^2 + 1) - 2*a^2*log(x) - 1/2*(4*I*a*x + 1)/x^2","A",0
18,1,51,0,0.416207," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/x^4,x, algorithm=""maxima"")","2 \, a^{3} \arctan\left(a x\right) + i \, a^{3} \log\left(a^{2} x^{2} + 1\right) - 2 i \, a^{3} \log\left(x\right) + \frac{6 \, a^{2} x^{2} - 3 i \, a x - 1}{3 \, x^{3}}"," ",0,"2*a^3*arctan(a*x) + I*a^3*log(a^2*x^2 + 1) - 2*I*a^3*log(x) + 1/3*(6*a^2*x^2 - 3*I*a*x - 1)/x^3","A",0
19,1,114,0,0.315941," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^3,x, algorithm=""maxima"")","-\frac{i \, a x^{5}}{4 \, \sqrt{a^{2} x^{2} + 1}} - \frac{x^{4}}{\sqrt{a^{2} x^{2} + 1}} + \frac{17 i \, x^{3}}{8 \, \sqrt{a^{2} x^{2} + 1} a} + \frac{5 \, x^{2}}{\sqrt{a^{2} x^{2} + 1} a^{2}} + \frac{51 i \, x}{8 \, \sqrt{a^{2} x^{2} + 1} a^{3}} - \frac{51 i \, \operatorname{arsinh}\left(a x\right)}{8 \, a^{4}} + \frac{10}{\sqrt{a^{2} x^{2} + 1} a^{4}}"," ",0,"-1/4*I*a*x^5/sqrt(a^2*x^2 + 1) - x^4/sqrt(a^2*x^2 + 1) + 17/8*I*x^3/(sqrt(a^2*x^2 + 1)*a) + 5*x^2/(sqrt(a^2*x^2 + 1)*a^2) + 51/8*I*x/(sqrt(a^2*x^2 + 1)*a^3) - 51/8*I*arcsinh(a*x)/a^4 + 10/(sqrt(a^2*x^2 + 1)*a^4)","A",0
20,1,95,0,0.318714," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^2,x, algorithm=""maxima"")","-\frac{i \, a x^{4}}{3 \, \sqrt{a^{2} x^{2} + 1}} - \frac{3 \, x^{3}}{2 \, \sqrt{a^{2} x^{2} + 1}} + \frac{13 i \, x^{2}}{3 \, \sqrt{a^{2} x^{2} + 1} a} - \frac{11 \, x}{2 \, \sqrt{a^{2} x^{2} + 1} a^{2}} + \frac{11 \, \operatorname{arsinh}\left(a x\right)}{2 \, a^{3}} + \frac{26 i}{3 \, \sqrt{a^{2} x^{2} + 1} a^{3}}"," ",0,"-1/3*I*a*x^4/sqrt(a^2*x^2 + 1) - 3/2*x^3/sqrt(a^2*x^2 + 1) + 13/3*I*x^2/(sqrt(a^2*x^2 + 1)*a) - 11/2*x/(sqrt(a^2*x^2 + 1)*a^2) + 11/2*arcsinh(a*x)/a^3 + 26/3*I/(sqrt(a^2*x^2 + 1)*a^3)","A",0
21,1,76,0,0.323266," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x,x, algorithm=""maxima"")","-\frac{i \, a x^{3}}{2 \, \sqrt{a^{2} x^{2} + 1}} - \frac{3 \, x^{2}}{\sqrt{a^{2} x^{2} + 1}} - \frac{9 i \, x}{2 \, \sqrt{a^{2} x^{2} + 1} a} + \frac{9 i \, \operatorname{arsinh}\left(a x\right)}{2 \, a^{2}} - \frac{7}{\sqrt{a^{2} x^{2} + 1} a^{2}}"," ",0,"-1/2*I*a*x^3/sqrt(a^2*x^2 + 1) - 3*x^2/sqrt(a^2*x^2 + 1) - 9/2*I*x/(sqrt(a^2*x^2 + 1)*a) + 9/2*I*arcsinh(a*x)/a^2 - 7/(sqrt(a^2*x^2 + 1)*a^2)","A",0
22,1,57,0,0.312083," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{i \, a x^{2}}{\sqrt{a^{2} x^{2} + 1}} + \frac{4 \, x}{\sqrt{a^{2} x^{2} + 1}} - \frac{3 \, \operatorname{arsinh}\left(a x\right)}{a} - \frac{5 i}{\sqrt{a^{2} x^{2} + 1} a}"," ",0,"-I*a*x^2/sqrt(a^2*x^2 + 1) + 4*x/sqrt(a^2*x^2 + 1) - 3*arcsinh(a*x)/a - 5*I/(sqrt(a^2*x^2 + 1)*a)","A",0
23,1,46,0,0.321424," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x,x, algorithm=""maxima"")","\frac{4 i \, a x}{\sqrt{a^{2} x^{2} + 1}} + \frac{4}{\sqrt{a^{2} x^{2} + 1}} - i \, \operatorname{arsinh}\left(a x\right) - \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right)"," ",0,"4*I*a*x/sqrt(a^2*x^2 + 1) + 4/sqrt(a^2*x^2 + 1) - I*arcsinh(a*x) - arcsinh(1/(a*abs(x)))","A",0
24,1,60,0,0.312995," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x^2,x, algorithm=""maxima"")","-\frac{5 \, a^{2} x}{\sqrt{a^{2} x^{2} + 1}} - 3 i \, a \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right) + \frac{4 i \, a}{\sqrt{a^{2} x^{2} + 1}} - \frac{1}{\sqrt{a^{2} x^{2} + 1} x}"," ",0,"-5*a^2*x/sqrt(a^2*x^2 + 1) - 3*I*a*arcsinh(1/(a*abs(x))) + 4*I*a/sqrt(a^2*x^2 + 1) - 1/(sqrt(a^2*x^2 + 1)*x)","A",0
25,1,81,0,0.311037," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x^3,x, algorithm=""maxima"")","-\frac{7 i \, a^{3} x}{\sqrt{a^{2} x^{2} + 1}} + \frac{9}{2} \, a^{2} \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right) - \frac{9 \, a^{2}}{2 \, \sqrt{a^{2} x^{2} + 1}} - \frac{3 i \, a}{\sqrt{a^{2} x^{2} + 1} x} - \frac{1}{2 \, \sqrt{a^{2} x^{2} + 1} x^{2}}"," ",0,"-7*I*a^3*x/sqrt(a^2*x^2 + 1) + 9/2*a^2*arcsinh(1/(a*abs(x))) - 9/2*a^2/sqrt(a^2*x^2 + 1) - 3*I*a/(sqrt(a^2*x^2 + 1)*x) - 1/2/(sqrt(a^2*x^2 + 1)*x^2)","A",0
26,1,100,0,0.312652," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x^4,x, algorithm=""maxima"")","\frac{26 \, a^{4} x}{3 \, \sqrt{a^{2} x^{2} + 1}} + \frac{11}{2} i \, a^{3} \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right) - \frac{11 i \, a^{3}}{2 \, \sqrt{a^{2} x^{2} + 1}} + \frac{13 \, a^{2}}{3 \, \sqrt{a^{2} x^{2} + 1} x} - \frac{3 i \, a}{2 \, \sqrt{a^{2} x^{2} + 1} x^{2}} - \frac{1}{3 \, \sqrt{a^{2} x^{2} + 1} x^{3}}"," ",0,"26/3*a^4*x/sqrt(a^2*x^2 + 1) + 11/2*I*a^3*arcsinh(1/(a*abs(x))) - 11/2*I*a^3/sqrt(a^2*x^2 + 1) + 13/3*a^2/(sqrt(a^2*x^2 + 1)*x) - 3/2*I*a/(sqrt(a^2*x^2 + 1)*x^2) - 1/3/(sqrt(a^2*x^2 + 1)*x^3)","A",0
27,1,77,0,0.415618," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2*x^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(-i \, a x - 1\right)}}{a^{6} x^{2} + a^{4}} + \frac{3 \, a^{3} x^{4} - 16 i \, a^{2} x^{3} - 48 \, a x^{2} + 144 i \, x}{12 \, a^{3}} - \frac{16 i \, \arctan\left(a x\right)}{a^{4}} + \frac{8 \, \log\left(a^{2} x^{2} + 1\right)}{a^{4}}"," ",0,"-4*(-I*a*x - 1)/(a^6*x^2 + a^4) + 1/12*(3*a^3*x^4 - 16*I*a^2*x^3 - 48*a*x^2 + 144*I*x)/a^3 - 16*I*arctan(a*x)/a^4 + 8*log(a^2*x^2 + 1)/a^4","A",0
28,1,68,0,0.420153," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2*x^2,x, algorithm=""maxima"")","-\frac{8 \, a x - 8 i}{2 \, {\left(a^{5} x^{2} + a^{3}\right)}} + \frac{a^{2} x^{3} - 6 i \, a x^{2} - 24 \, x}{3 \, a^{2}} + \frac{12 \, \arctan\left(a x\right)}{a^{3}} + \frac{6 i \, \log\left(a^{2} x^{2} + 1\right)}{a^{3}}"," ",0,"-1/2*(8*a*x - 8*I)/(a^5*x^2 + a^3) + 1/3*(a^2*x^3 - 6*I*a*x^2 - 24*x)/a^2 + 12*arctan(a*x)/a^3 + 6*I*log(a^2*x^2 + 1)/a^3","A",0
29,1,60,0,0.419088," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2*x,x, algorithm=""maxima"")","-\frac{4 \, {\left(i \, a x + 1\right)}}{a^{4} x^{2} + a^{2}} + \frac{a x^{2} - 8 i \, x}{2 \, a} + \frac{8 i \, \arctan\left(a x\right)}{a^{2}} - \frac{4 \, \log\left(a^{2} x^{2} + 1\right)}{a^{2}}"," ",0,"-4*(I*a*x + 1)/(a^4*x^2 + a^2) + 1/2*(a*x^2 - 8*I*x)/a + 8*I*arctan(a*x)/a^2 - 4*log(a^2*x^2 + 1)/a^2","A",0
30,1,45,0,0.425122," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2,x, algorithm=""maxima"")","x + \frac{8 \, a x - 8 i}{2 \, {\left(a^{3} x^{2} + a\right)}} - \frac{4 \, \arctan\left(a x\right)}{a} - \frac{2 i \, \log\left(a^{2} x^{2} + 1\right)}{a}"," ",0,"x + 1/2*(8*a*x - 8*I)/(a^3*x^2 + a) - 4*arctan(a*x)/a - 2*I*log(a^2*x^2 + 1)/a","A",0
31,1,22,0,0.423306," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/x,x, algorithm=""maxima"")","-\frac{4 \, {\left(-i \, a x - 1\right)}}{a^{2} x^{2} + 1} + \log\left(x\right)"," ",0,"-4*(-I*a*x - 1)/(a^2*x^2 + 1) + log(x)","A",0
32,1,53,0,0.423879," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/x^2,x, algorithm=""maxima"")","-4 \, a \arctan\left(a x\right) - 2 i \, a \log\left(a^{2} x^{2} + 1\right) + 4 i \, a \log\left(x\right) - \frac{10 \, a^{2} x^{2} - 8 i \, a x + 2}{2 \, {\left(a^{2} x^{3} + x\right)}}"," ",0,"-4*a*arctan(a*x) - 2*I*a*log(a^2*x^2 + 1) + 4*I*a*log(x) - 1/2*(10*a^2*x^2 - 8*I*a*x + 2)/(a^2*x^3 + x)","A",0
33,1,69,0,0.422934," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/x^3,x, algorithm=""maxima"")","-8 i \, a^{2} \arctan\left(a x\right) + 4 \, a^{2} \log\left(a^{2} x^{2} + 1\right) - 8 \, a^{2} \log\left(x\right) + \frac{-16 i \, a^{3} x^{3} - 9 \, a^{2} x^{2} - 8 i \, a x - 1}{2 \, {\left(a^{2} x^{4} + x^{2}\right)}}"," ",0,"-8*I*a^2*arctan(a*x) + 4*a^2*log(a^2*x^2 + 1) - 8*a^2*log(x) + 1/2*(-16*I*a^3*x^3 - 9*a^2*x^2 - 8*I*a*x - 1)/(a^2*x^4 + x^2)","A",0
34,1,77,0,0.418823," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/x^4,x, algorithm=""maxima"")","12 \, a^{3} \arctan\left(a x\right) + 6 i \, a^{3} \log\left(a^{2} x^{2} + 1\right) - 12 i \, a^{3} \log\left(x\right) + \frac{72 \, a^{4} x^{4} - 36 i \, a^{3} x^{3} + 46 \, a^{2} x^{2} - 12 i \, a x - 2}{6 \, {\left(a^{2} x^{5} + x^{3}\right)}}"," ",0,"12*a^3*arctan(a*x) + 6*I*a^3*log(a^2*x^2 + 1) - 12*I*a^3*log(x) + 1/6*(72*a^4*x^4 - 36*I*a^3*x^3 + 46*a^2*x^2 - 12*I*a*x - 2)/(a^2*x^5 + x^3)","A",0
35,1,76,0,0.426138," ","integrate(x^3/(1+I*a*x)*(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{i \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, a^{3}} + \frac{5 i \, \sqrt{a^{2} x^{2} + 1} x}{8 \, a^{3}} + \frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{3 \, a^{4}} - \frac{3 i \, \operatorname{arsinh}\left(a x\right)}{8 \, a^{4}} - \frac{\sqrt{a^{2} x^{2} + 1}}{a^{4}}"," ",0,"-1/4*I*(a^2*x^2 + 1)^(3/2)*x/a^3 + 5/8*I*sqrt(a^2*x^2 + 1)*x/a^3 + 1/3*(a^2*x^2 + 1)^(3/2)/a^4 - 3/8*I*arcsinh(a*x)/a^4 - sqrt(a^2*x^2 + 1)/a^4","A",0
36,1,59,0,0.437131," ","integrate(x^2/(1+I*a*x)*(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a^{2} x^{2} + 1} x}{2 \, a^{2}} - \frac{i \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{3 \, a^{3}} - \frac{\operatorname{arsinh}\left(a x\right)}{2 \, a^{3}} + \frac{i \, \sqrt{a^{2} x^{2} + 1}}{a^{3}}"," ",0,"1/2*sqrt(a^2*x^2 + 1)*x/a^2 - 1/3*I*(a^2*x^2 + 1)^(3/2)/a^3 - 1/2*arcsinh(a*x)/a^3 + I*sqrt(a^2*x^2 + 1)/a^3","A",0
37,1,42,0,0.427828," ","integrate(x/(1+I*a*x)*(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{i \, \sqrt{a^{2} x^{2} + 1} x}{2 \, a} + \frac{i \, \operatorname{arsinh}\left(a x\right)}{2 \, a^{2}} + \frac{\sqrt{a^{2} x^{2} + 1}}{a^{2}}"," ",0,"-1/2*I*sqrt(a^2*x^2 + 1)*x/a + 1/2*I*arcsinh(a*x)/a^2 + sqrt(a^2*x^2 + 1)/a^2","A",0
38,1,25,0,0.428463," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(a x\right)}{a} - \frac{i \, \sqrt{a^{2} x^{2} + 1}}{a}"," ",0,"arcsinh(a*x)/a - I*sqrt(a^2*x^2 + 1)/a","A",0
39,1,26,0,0.474180," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","-i \, a {\left(\frac{\operatorname{arsinh}\left(a x\right)}{a} - \frac{i \, \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right)}{a}\right)}"," ",0,"-I*a*(arcsinh(a*x)/a - I*arcsinh(1/(a*abs(x)))/a)","A",0
40,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} x^{2} + 1}}{{\left(i \, a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 + 1)/((I*a*x + 1)*x^2), x)","F",0
41,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} x^{2} + 1}}{{\left(i \, a x + 1\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 + 1)/((I*a*x + 1)*x^3), x)","F",0
42,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} x^{2} + 1}}{{\left(i \, a x + 1\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 + 1)/((I*a*x + 1)*x^4), x)","F",0
43,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} x^{2} + 1}}{{\left(i \, a x + 1\right)} x^{5}}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 + 1)/((I*a*x + 1)*x^5), x)","F",0
44,1,44,0,0.318807," ","integrate(x^3/(1+I*a*x)^2*(a^2*x^2+1),x, algorithm=""maxima"")","-\frac{i \, {\left(-3 i \, a^{3} x^{4} + 8 \, a^{2} x^{3} + 12 i \, a x^{2} - 24 \, x\right)}}{12 \, a^{3}} - \frac{2 \, \log\left(i \, a x + 1\right)}{a^{4}}"," ",0,"-1/12*I*(-3*I*a^3*x^4 + 8*a^2*x^3 + 12*I*a*x^2 - 24*x)/a^3 - 2*log(I*a*x + 1)/a^4","A",0
45,1,35,0,0.319452," ","integrate(x^2/(1+I*a*x)^2*(a^2*x^2+1),x, algorithm=""maxima"")","-\frac{a^{2} x^{3} + 3 i \, a x^{2} - 6 \, x}{3 \, a^{2}} + \frac{2 i \, \log\left(i \, a x + 1\right)}{a^{3}}"," ",0,"-1/3*(a^2*x^3 + 3*I*a*x^2 - 6*x)/a^2 + 2*I*log(I*a*x + 1)/a^3","A",0
46,1,28,0,0.329638," ","integrate(x/(1+I*a*x)^2*(a^2*x^2+1),x, algorithm=""maxima"")","\frac{i \, {\left(i \, a x^{2} - 4 \, x\right)}}{2 \, a} + \frac{2 \, \log\left(i \, a x + 1\right)}{a^{2}}"," ",0,"1/2*I*(I*a*x^2 - 4*x)/a + 2*log(I*a*x + 1)/a^2","A",0
47,1,16,0,0.326865," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1),x, algorithm=""maxima"")","-x - \frac{2 i \, \log\left(i \, a x + 1\right)}{a}"," ",0,"-x - 2*I*log(I*a*x + 1)/a","A",0
48,1,12,0,0.320181," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/x,x, algorithm=""maxima"")","-2 \, \log\left(i \, a x + 1\right) + \log\left(x\right)"," ",0,"-2*log(I*a*x + 1) + log(x)","A",0
49,1,34,0,0.327307," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/x^2,x, algorithm=""maxima"")","2 i \, a \log\left(i \, a x + 1\right) - 2 i \, a \log\left(x\right) - \frac{a x - i}{a x^{2} - i \, x}"," ",0,"2*I*a*log(I*a*x + 1) - 2*I*a*log(x) - (a*x - I)/(a*x^2 - I*x)","A",0
50,1,50,0,0.332106," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/x^3,x, algorithm=""maxima"")","2 \, a^{2} \log\left(i \, a x + 1\right) - 2 \, a^{2} \log\left(x\right) - \frac{4 \, a^{2} x^{2} - 3 i \, a x + 1}{2 i \, a x^{3} + 2 \, x^{2}}"," ",0,"2*a^2*log(I*a*x + 1) - 2*a^2*log(x) - (4*a^2*x^2 - 3*I*a*x + 1)/(2*I*a*x^3 + 2*x^2)","A",0
51,1,57,0,0.325813," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/x^4,x, algorithm=""maxima"")","-2 i \, a^{3} \log\left(i \, a x + 1\right) + 2 i \, a^{3} \log\left(x\right) + \frac{6 i \, a^{3} x^{3} + 3 \, a^{2} x^{2} + 2 i \, a x - 1}{3 i \, a x^{4} + 3 \, x^{3}}"," ",0,"-2*I*a^3*log(I*a*x + 1) + 2*I*a^3*log(x) + (6*I*a^3*x^3 + 3*a^2*x^2 + 2*I*a*x - 1)/(3*I*a*x^4 + 3*x^3)","A",0
52,1,216,0,0.454836," ","integrate(x^3/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{6} x^{2} - 2 i \, a^{5} x - a^{4}} + \frac{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{2 i \, a^{5} x + 2 \, a^{4}} + \frac{6 \, \sqrt{a^{2} x^{2} + 1}}{i \, a^{5} x + a^{4}} + \frac{i \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, a^{3}} + \frac{3 i \, \sqrt{a^{2} x^{2} + 1} x}{8 \, a^{3}} - \frac{3 i \, \sqrt{-a^{2} x^{2} + 4 i \, a x + 3} x}{2 \, a^{3}} - \frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{4}} + \frac{3 i \, \arcsin\left(i \, a x + 2\right)}{2 \, a^{4}} + \frac{63 i \, \operatorname{arsinh}\left(a x\right)}{8 \, a^{4}} + \frac{9 \, \sqrt{a^{2} x^{2} + 1}}{2 \, a^{4}} - \frac{3 \, \sqrt{-a^{2} x^{2} + 4 i \, a x + 3}}{a^{4}}"," ",0,"(a^2*x^2 + 1)^(3/2)/(a^6*x^2 - 2*I*a^5*x - a^4) + 3*(a^2*x^2 + 1)^(3/2)/(2*I*a^5*x + 2*a^4) + 6*sqrt(a^2*x^2 + 1)/(I*a^5*x + a^4) + 1/4*I*(a^2*x^2 + 1)^(3/2)*x/a^3 + 3/8*I*sqrt(a^2*x^2 + 1)*x/a^3 - 3/2*I*sqrt(-a^2*x^2 + 4*I*a*x + 3)*x/a^3 - (a^2*x^2 + 1)^(3/2)/a^4 + 3/2*I*arcsin(I*a*x + 2)/a^4 + 63/8*I*arcsinh(a*x)/a^4 + 9/2*sqrt(a^2*x^2 + 1)/a^4 - 3*sqrt(-a^2*x^2 + 4*I*a*x + 3)/a^4","A",0
53,1,181,0,0.440725," ","integrate(x^2/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{i \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{5} x^{2} - 2 i \, a^{4} x - a^{3}} - \frac{i \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{i \, a^{4} x + a^{3}} - \frac{6 i \, \sqrt{a^{2} x^{2} + 1}}{i \, a^{4} x + a^{3}} - \frac{\sqrt{-a^{2} x^{2} + 4 i \, a x + 3} x}{2 \, a^{2}} + \frac{i \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{3 \, a^{3}} + \frac{\arcsin\left(i \, a x + 2\right)}{2 \, a^{3}} + \frac{6 \, \operatorname{arsinh}\left(a x\right)}{a^{3}} - \frac{3 i \, \sqrt{a^{2} x^{2} + 1}}{a^{3}} + \frac{i \, \sqrt{-a^{2} x^{2} + 4 i \, a x + 3}}{a^{3}}"," ",0,"-I*(a^2*x^2 + 1)^(3/2)/(a^5*x^2 - 2*I*a^4*x - a^3) - I*(a^2*x^2 + 1)^(3/2)/(I*a^4*x + a^3) - 6*I*sqrt(a^2*x^2 + 1)/(I*a^4*x + a^3) - 1/2*sqrt(-a^2*x^2 + 4*I*a*x + 3)*x/a^2 + 1/3*I*(a^2*x^2 + 1)^(3/2)/a^3 + 1/2*arcsin(I*a*x + 2)/a^3 + 6*arcsinh(a*x)/a^3 - 3*I*sqrt(a^2*x^2 + 1)/a^3 + I*sqrt(-a^2*x^2 + 4*I*a*x + 3)/a^3","B",0
54,1,112,0,0.454178," ","integrate(x/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{4} x^{2} - 2 i \, a^{3} x - a^{2}} - \frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{2 i \, a^{3} x + 2 \, a^{2}} - \frac{6 \, \sqrt{a^{2} x^{2} + 1}}{i \, a^{3} x + a^{2}} - \frac{9 i \, \operatorname{arsinh}\left(a x\right)}{2 \, a^{2}} - \frac{3 \, \sqrt{a^{2} x^{2} + 1}}{2 \, a^{2}}"," ",0,"-(a^2*x^2 + 1)^(3/2)/(a^4*x^2 - 2*I*a^3*x - a^2) - (a^2*x^2 + 1)^(3/2)/(2*I*a^3*x + 2*a^2) - 6*sqrt(a^2*x^2 + 1)/(I*a^3*x + a^2) - 9/2*I*arcsinh(a*x)/a^2 - 3/2*sqrt(a^2*x^2 + 1)/a^2","A",0
55,1,65,0,0.453206," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{3} x^{2} - 2 i \, a^{2} x - a} - \frac{3 \, \operatorname{arsinh}\left(a x\right)}{a} + \frac{6 i \, \sqrt{a^{2} x^{2} + 1}}{i \, a^{2} x + a}"," ",0,"I*(a^2*x^2 + 1)^(3/2)/(a^3*x^2 - 2*I*a^2*x - a) - 3*arcsinh(a*x)/a + 6*I*sqrt(a^2*x^2 + 1)/(I*a^2*x + a)","A",0
56,0,0,0,0.000000," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(i \, a x + 1\right)}^{3} x}\,{d x}"," ",0,"integrate((a^2*x^2 + 1)^(3/2)/((I*a*x + 1)^3*x), x)","F",0
57,0,0,0,0.000000," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(i \, a x + 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate((a^2*x^2 + 1)^(3/2)/((I*a*x + 1)^3*x^2), x)","F",0
58,0,0,0,0.000000," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(i \, a x + 1\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate((a^2*x^2 + 1)^(3/2)/((I*a*x + 1)^3*x^3), x)","F",0
59,0,0,0,0.000000," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(i \, a x + 1\right)}^{3} x^{4}}\,{d x}"," ",0,"integrate((a^2*x^2 + 1)^(3/2)/((I*a*x + 1)^3*x^4), x)","F",0
60,0,0,0,0.000000," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(i \, a x + 1\right)}^{3} x^{5}}\,{d x}"," ",0,"integrate((a^2*x^2 + 1)^(3/2)/((I*a*x + 1)^3*x^5), x)","F",0
61,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x^2,x, algorithm=""maxima"")","\int x^{2} \sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(x^2*sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1)), x)","F",0
62,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x,x, algorithm=""maxima"")","\int x \sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(x*sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1)), x)","F",0
63,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1)), x)","F",0
64,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}{x}\,{d x}"," ",0,"integrate(sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1))/x, x)","F",0
65,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1))/x^2, x)","F",0
66,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1))/x^3, x)","F",0
67,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1))/x^4, x)","F",0
68,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1))/x^5, x)","F",0
69,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^6,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1))/x^6, x)","F",0
70,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^3,x, algorithm=""maxima"")","\int x^{3} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^3*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2), x)","F",0
71,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^2*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2), x)","F",0
72,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x,x, algorithm=""maxima"")","\int x \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2), x)","F",0
73,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2), x)","F",0
74,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2)/x, x)","F",0
75,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2)/x^2, x)","F",0
76,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2)/x^3, x)","F",0
77,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2)/x^4, x)","F",0
78,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{5}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2)/x^5, x)","F",0
79,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^3,x, algorithm=""maxima"")","\int x^{3} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x^3*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2), x)","F",0
80,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x^2*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2), x)","F",0
81,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x,x, algorithm=""maxima"")","\int x \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2), x)","F",0
82,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2), x)","F",0
83,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}{x}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2)/x, x)","F",0
84,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2)/x^2, x)","F",0
85,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2)/x^3, x)","F",0
86,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^4,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}{x^{4}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2)/x^4, x)","F",0
87,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^5,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}{x^{5}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2)/x^5, x)","F",0
88,0,0,0,0.000000," ","integrate(x^3/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(x^3/sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1)), x)","F",0
89,0,0,0,0.000000," ","integrate(x^2/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(x^2/sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1)), x)","F",0
90,0,0,0,0.000000," ","integrate(x/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(x/sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1)), x)","F",0
91,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1)), x)","F",0
92,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{1}{x \sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x*sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1))), x)","F",0
93,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{1}{x^{2} \sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^2*sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1))), x)","F",0
94,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{1}{x^{3} \sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^3*sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1))), x)","F",0
95,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{1}{x^{4} \sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^4*sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1))), x)","F",0
96,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{1}{x^{5} \sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^5*sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1))), x)","F",0
97,0,0,0,0.000000," ","integrate(x^3/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3/((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2), x)","F",0
98,0,0,0,0.000000," ","integrate(x^2/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2), x)","F",0
99,0,0,0,0.000000," ","integrate(x/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{x}{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2), x)","F",0
100,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(-3/2), x)","F",0
101,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x,x, algorithm=""maxima"")","\int \frac{1}{x \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2)), x)","F",0
102,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{1}{x^{2} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x^2*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2)), x)","F",0
103,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{1}{x^{3} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x^3*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2)), x)","F",0
104,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{1}{x^{4} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x^4*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2)), x)","F",0
105,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{1}{x^{5} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x^5*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2)), x)","F",0
106,0,0,0,0.000000," ","integrate(x^3/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^3/((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2), x)","F",0
107,0,0,0,0.000000," ","integrate(x^2/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^2/((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2), x)","F",0
108,0,0,0,0.000000," ","integrate(x/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \frac{x}{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x/((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2), x)","F",0
109,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(-5/2), x)","F",0
110,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x,x, algorithm=""maxima"")","\int \frac{1}{x \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2)), x)","F",0
111,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^2,x, algorithm=""maxima"")","\int \frac{1}{x^{2} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x^2*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2)), x)","F",0
112,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^3,x, algorithm=""maxima"")","\int \frac{1}{x^{3} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x^3*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2)), x)","F",0
113,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^4,x, algorithm=""maxima"")","\int \frac{1}{x^{4} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x^4*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2)), x)","F",0
114,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^5,x, algorithm=""maxima"")","\int \frac{1}{x^{5} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x^5*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2)), x)","F",0
115,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(x^2*((I*x + 1)/sqrt(x^2 + 1))^(1/3), x)","F",0
116,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)*x,x, algorithm=""maxima"")","\int x \left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(x*((I*x + 1)/sqrt(x^2 + 1))^(1/3), x)","F",0
117,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3),x, algorithm=""maxima"")","\int \left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(((I*x + 1)/sqrt(x^2 + 1))^(1/3), x)","F",0
118,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{1}{3}}}{x}\,{d x}"," ",0,"integrate(((I*x + 1)/sqrt(x^2 + 1))^(1/3)/x, x)","F",0
119,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{1}{3}}}{x^{2}}\,{d x}"," ",0,"integrate(((I*x + 1)/sqrt(x^2 + 1))^(1/3)/x^2, x)","F",0
120,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{1}{3}}}{x^{3}}\,{d x}"," ",0,"integrate(((I*x + 1)/sqrt(x^2 + 1))^(1/3)/x^3, x)","F",0
121,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^4,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{1}{3}}}{x^{4}}\,{d x}"," ",0,"integrate(((I*x + 1)/sqrt(x^2 + 1))^(1/3)/x^4, x)","F",0
122,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3)*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(x^2*((I*x + 1)/sqrt(x^2 + 1))^(2/3), x)","F",0
123,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3)*x,x, algorithm=""maxima"")","\int x \left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(x*((I*x + 1)/sqrt(x^2 + 1))^(2/3), x)","F",0
124,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3),x, algorithm=""maxima"")","\int \left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(((I*x + 1)/sqrt(x^2 + 1))^(2/3), x)","F",0
125,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{2}{3}}}{x}\,{d x}"," ",0,"integrate(((I*x + 1)/sqrt(x^2 + 1))^(2/3)/x, x)","F",0
126,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{2}{3}}}{x^{2}}\,{d x}"," ",0,"integrate(((I*x + 1)/sqrt(x^2 + 1))^(2/3)/x^2, x)","F",0
127,0,0,0,0.000000," ","integrate(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, x + 1}{\sqrt{x^{2} + 1}}\right)^{\frac{2}{3}}}{x^{3}}\,{d x}"," ",0,"integrate(((I*x + 1)/sqrt(x^2 + 1))^(2/3)/x^3, x)","F",0
128,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}\,{d x}"," ",0,"integrate(x^2*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(1/4), x)","F",0
129,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x,x, algorithm=""maxima"")","\int x \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}\,{d x}"," ",0,"integrate(x*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(1/4), x)","F",0
130,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4),x, algorithm=""maxima"")","\int \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(1/4), x)","F",0
131,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}}{x}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(1/4)/x, x)","F",0
132,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}}{x^{2}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(1/4)/x^2, x)","F",0
133,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}}{x^{3}}\,{d x}"," ",0,"integrate(((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(1/4)/x^3, x)","F",0
134,0,0,0,0.000000," ","integrate((1+I*a*x)^6/(a^2*x^2+1)^3*x^m,x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)}^{6} x^{m}}{{\left(a^{2} x^{2} + 1\right)}^{3}}\,{d x}"," ",0,"integrate((I*a*x + 1)^6*x^m/(a^2*x^2 + 1)^3, x)","F",0
135,0,0,0,0.000000," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2*x^m,x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)}^{4} x^{m}}{{\left(a^{2} x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((I*a*x + 1)^4*x^m/(a^2*x^2 + 1)^2, x)","F",0
136,0,0,0,0.000000," ","integrate((1+I*a*x)^2/(a^2*x^2+1)*x^m,x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)}^{2} x^{m}}{a^{2} x^{2} + 1}\,{d x}"," ",0,"integrate((I*a*x + 1)^2*x^m/(a^2*x^2 + 1), x)","F",0
137,0,0,0,0.000000," ","integrate(x^m/(1+I*a*x)^2*(a^2*x^2+1),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} + 1\right)} x^{m}}{{\left(i \, a x + 1\right)}^{2}}\,{d x}"," ",0,"integrate((a^2*x^2 + 1)*x^m/(I*a*x + 1)^2, x)","F",0
138,0,0,0,0.000000," ","integrate(x^m/(1+I*a*x)^4*(a^2*x^2+1)^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} + 1\right)}^{2} x^{m}}{{\left(i \, a x + 1\right)}^{4}}\,{d x}"," ",0,"integrate((a^2*x^2 + 1)^2*x^m/(I*a*x + 1)^4, x)","F",0
139,0,0,0,0.000000," ","integrate(x^m/(1+I*a*x)^6*(a^2*x^2+1)^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} + 1\right)}^{3} x^{m}}{{\left(i \, a x + 1\right)}^{6}}\,{d x}"," ",0,"integrate((a^2*x^2 + 1)^3*x^m/(I*a*x + 1)^6, x)","F",0
140,0,0,0,0.000000," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^m,x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)}^{3} x^{m}}{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*x + 1)^3*x^m/(a^2*x^2 + 1)^(3/2), x)","F",0
141,0,0,0,0.000000," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^m,x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)} x^{m}}{\sqrt{a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((I*a*x + 1)*x^m/sqrt(a^2*x^2 + 1), x)","F",0
142,0,0,0,0.000000," ","integrate(x^m/(1+I*a*x)*(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} x^{2} + 1} x^{m}}{i \, a x + 1}\,{d x}"," ",0,"integrate(sqrt(a^2*x^2 + 1)*x^m/(I*a*x + 1), x)","F",0
143,0,0,0,0.000000," ","integrate(x^m/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{m}}{{\left(i \, a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((a^2*x^2 + 1)^(3/2)*x^m/(I*a*x + 1)^3, x)","F",0
144,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^m,x, algorithm=""maxima"")","\int x^{m} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x^m*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2), x)","F",0
145,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^m,x, algorithm=""maxima"")","\int x^{m} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^m*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2), x)","F",0
146,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x^m,x, algorithm=""maxima"")","\int x^{m} \sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(x^m*sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1)), x)","F",0
147,0,0,0,0.000000," ","integrate(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\sqrt{\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(x^m/sqrt((I*a*x + 1)/sqrt(a^2*x^2 + 1)), x)","F",0
148,0,0,0,0.000000," ","integrate(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m/((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(3/2), x)","F",0
149,0,0,0,0.000000," ","integrate(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^m/((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(5/2), x)","F",0
150,0,0,0,0.000000," ","integrate(exp(2/3*arctan(x))*x^m,x, algorithm=""maxima"")","\int x^{m} e^{\left(\frac{2}{3} \, \arctan\left(x\right)\right)}\,{d x}"," ",0,"integrate(x^m*e^(2/3*arctan(x)), x)","F",0
151,0,0,0,0.000000," ","integrate(exp(1/3*arctan(x))*x^m,x, algorithm=""maxima"")","\int x^{m} e^{\left(\frac{1}{3} \, \arctan\left(x\right)\right)}\,{d x}"," ",0,"integrate(x^m*e^(1/3*arctan(x)), x)","F",0
152,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x^m,x, algorithm=""maxima"")","\int x^{m} \left(\frac{i \, a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}\,{d x}"," ",0,"integrate(x^m*((I*a*x + 1)/sqrt(a^2*x^2 + 1))^(1/4), x)","F",0
153,0,0,0,0.000000," ","integrate(exp(I*n*arctan(a*x))*x^m,x, algorithm=""maxima"")","\int x^{m} e^{\left(i \, n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(x^m*e^(I*n*arctan(a*x)), x)","F",0
154,0,0,0,0.000000," ","integrate(exp(I*n*arctan(a*x))*x^3,x, algorithm=""maxima"")","\int x^{3} e^{\left(i \, n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(x^3*e^(I*n*arctan(a*x)), x)","F",0
155,0,0,0,0.000000," ","integrate(exp(I*n*arctan(a*x))*x^2,x, algorithm=""maxima"")","\int x^{2} e^{\left(i \, n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(x^2*e^(I*n*arctan(a*x)), x)","F",0
156,0,0,0,0.000000," ","integrate(exp(I*n*arctan(a*x))*x,x, algorithm=""maxima"")","\int x e^{\left(i \, n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(x*e^(I*n*arctan(a*x)), x)","F",0
157,0,0,0,0.000000," ","integrate(exp(I*n*arctan(a*x)),x, algorithm=""maxima"")","\int e^{\left(i \, n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(e^(I*n*arctan(a*x)), x)","F",0
158,0,0,0,0.000000," ","integrate(exp(I*n*arctan(a*x))/x,x, algorithm=""maxima"")","\int \frac{e^{\left(i \, n \arctan\left(a x\right)\right)}}{x}\,{d x}"," ",0,"integrate(e^(I*n*arctan(a*x))/x, x)","F",0
159,0,0,0,0.000000," ","integrate(exp(I*n*arctan(a*x))/x^2,x, algorithm=""maxima"")","\int \frac{e^{\left(i \, n \arctan\left(a x\right)\right)}}{x^{2}}\,{d x}"," ",0,"integrate(e^(I*n*arctan(a*x))/x^2, x)","F",0
160,0,0,0,0.000000," ","integrate(exp(I*n*arctan(a*x))/x^3,x, algorithm=""maxima"")","\int \frac{e^{\left(i \, n \arctan\left(a x\right)\right)}}{x^{3}}\,{d x}"," ",0,"integrate(e^(I*n*arctan(a*x))/x^3, x)","F",0
161,0,0,0,0.000000," ","integrate(exp(I*n*arctan(a*x))/x^4,x, algorithm=""maxima"")","\int \frac{e^{\left(i \, n \arctan\left(a x\right)\right)}}{x^{4}}\,{d x}"," ",0,"integrate(e^(I*n*arctan(a*x))/x^4, x)","F",0
162,1,749,0,0.355533," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x^4,x, algorithm=""maxima"")","\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x^{4}}{5 \, b} - \frac{9 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a x^{3}}{20 \, b^{2}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(-i \, a - 1\right)} x^{3}}{4 \, b^{2}} + \frac{21 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2} x^{2}}{20 \, b^{3}} - \frac{7 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a {\left(i \, a + 1\right)} x^{2}}{12 \, b^{3}} - \frac{63 i \, a^{5} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{5}} + \frac{35 \, a^{4} {\left(i \, a + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{5}} - \frac{21 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{3} x}{8 \, b^{4}} + \frac{35 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2} {\left(i \, a + 1\right)} x}{24 \, b^{4}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(4 i \, a^{2} + 4 i\right)} x^{2}}{15 \, b^{3}} + \frac{35 i \, {\left(a^{2} + 1\right)} a^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{4 \, b^{5}} - \frac{15 \, {\left(a^{2} + 1\right)} a^{2} {\left(i \, a + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{4 \, b^{5}} + \frac{63 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{4}}{8 \, b^{5}} - \frac{35 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{3} {\left(i \, a + 1\right)}}{8 \, b^{5}} + \frac{161 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} a x}{120 \, b^{4}} - \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} {\left(i \, a + 1\right)} x}{8 \, b^{4}} - \frac{15 i \, {\left(a^{2} + 1\right)}^{2} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{5}} - \frac{3 \, {\left(a^{2} + 1\right)}^{2} {\left(-i \, a - 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{5}} - \frac{49 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} a^{2}}{8 \, b^{5}} + \frac{55 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} a {\left(i \, a + 1\right)}}{24 \, b^{5}} + \frac{8 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}}{15 \, b^{5}}"," ",0,"1/5*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x^4/b - 9/20*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*x^3/b^2 - 1/4*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(-I*a - 1)*x^3/b^2 + 21/20*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2*x^2/b^3 - 7/12*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*(I*a + 1)*x^2/b^3 - 63/8*I*a^5*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 + 35/8*a^4*(I*a + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 - 21/8*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^3*x/b^4 + 35/24*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2*(I*a + 1)*x/b^4 - 1/15*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(4*I*a^2 + 4*I)*x^2/b^3 + 35/4*I*(a^2 + 1)*a^3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 - 15/4*(a^2 + 1)*a^2*(I*a + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 + 63/8*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^4/b^5 - 35/8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^3*(I*a + 1)/b^5 + 161/120*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*a*x/b^4 - 3/8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*(I*a + 1)*x/b^4 - 15/8*I*(a^2 + 1)^2*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 - 3/8*(a^2 + 1)^2*(-I*a - 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 - 49/8*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*a^2/b^5 + 55/24*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*a*(I*a + 1)/b^5 + 8/15*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2/b^5","B",0
163,1,529,0,0.351948," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x^3,x, algorithm=""maxima"")","\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x^{3}}{4 \, b} - \frac{7 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a x^{2}}{12 \, b^{2}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(-i \, a - 1\right)} x^{2}}{3 \, b^{2}} + \frac{35 i \, a^{4} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{4}} - \frac{5 \, a^{3} {\left(i \, a + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{4}} + \frac{35 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2} x}{24 \, b^{3}} - \frac{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a {\left(i \, a + 1\right)} x}{6 \, b^{3}} - \frac{15 i \, {\left(a^{2} + 1\right)} a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{4 \, b^{4}} + \frac{3 \, {\left(a^{2} + 1\right)} a {\left(i \, a + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{4}} - \frac{35 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{3}}{8 \, b^{4}} + \frac{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2} {\left(i \, a + 1\right)}}{2 \, b^{4}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(3 i \, a^{2} + 3 i\right)} x}{8 \, b^{3}} + \frac{3 i \, {\left(a^{2} + 1\right)}^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{4}} + \frac{55 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} a}{24 \, b^{4}} - \frac{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} {\left(i \, a + 1\right)}}{3 \, b^{4}}"," ",0,"1/4*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x^3/b - 7/12*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*x^2/b^2 - 1/3*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(-I*a - 1)*x^2/b^2 + 35/8*I*a^4*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 - 5/2*a^3*(I*a + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 + 35/24*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2*x/b^3 - 5/6*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*(I*a + 1)*x/b^3 - 15/4*I*(a^2 + 1)*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 + 3/2*(a^2 + 1)*a*(I*a + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 - 35/8*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^3/b^4 + 5/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2*(I*a + 1)/b^4 - 1/8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(3*I*a^2 + 3*I)*x/b^3 + 3/8*I*(a^2 + 1)^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 + 55/24*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*a/b^4 - 2/3*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*(I*a + 1)/b^4","B",0
164,1,351,0,0.348157," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x^2,x, algorithm=""maxima"")","\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x^{2}}{3 \, b} - \frac{5 i \, a^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{3}} + \frac{3 \, a^{2} {\left(i \, a + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{3}} - \frac{5 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a x}{6 \, b^{2}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(-i \, a - 1\right)} x}{2 \, b^{2}} + \frac{3 i \, {\left(a^{2} + 1\right)} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{3}} - \frac{{\left(a^{2} + 1\right)} {\left(i \, a + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{3}} + \frac{5 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2}}{2 \, b^{3}} - \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a {\left(i \, a + 1\right)}}{2 \, b^{3}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(2 i \, a^{2} + 2 i\right)}}{3 \, b^{3}}"," ",0,"1/3*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x^2/b - 5/2*I*a^3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 + 3/2*a^2*(I*a + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 - 5/6*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*x/b^2 - 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(-I*a - 1)*x/b^2 + 3/2*I*(a^2 + 1)*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 - 1/2*(a^2 + 1)*(I*a + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 + 5/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2/b^3 - 3/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*(I*a + 1)/b^3 - 1/3*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(2*I*a^2 + 2*I)/b^3","B",0
165,1,209,0,0.331291," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x,x, algorithm=""maxima"")","\frac{3 i \, a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{2}} - \frac{a {\left(i \, a + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{2}} + \frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x}{2 \, b} - \frac{{\left(i \, a^{2} + i\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{2}} - \frac{3 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{2 \, b^{2}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(i \, a + 1\right)}}{b^{2}}"," ",0,"3/2*I*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^2 - a*(I*a + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^2 + 1/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x/b - 1/2*(I*a^2 + I)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^2 - 3/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b^2 + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(I*a + 1)/b^2","B",0
166,1,62,0,0.329371," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b} + \frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b}"," ",0,"arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b + I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/b","A",0
167,1,233,0,0.330911," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x,x, algorithm=""maxima"")","-\frac{i \, a \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{\sqrt{a^{2} + 1}} - \frac{\operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{\sqrt{a^{2} + 1}} + i \, \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)"," ",0,"-I*a*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/sqrt(a^2 + 1) - arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/sqrt(a^2 + 1) + I*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))","B",0
168,1,239,0,0.322150," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x^2,x, algorithm=""maxima"")","\frac{a {\left(i \, a + 1\right)} b \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{3}{2}}} - \frac{i \, b \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{\sqrt{a^{2} + 1}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(-i \, a - 1\right)}}{{\left(a^{2} + 1\right)} x}"," ",0,"a*(I*a + 1)*b*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) - I*b*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/sqrt(a^2 + 1) + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(-I*a - 1)/((a^2 + 1)*x)","B",0
169,1,424,0,0.343585," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x^3,x, algorithm=""maxima"")","-\frac{3 \, a^{2} {\left(i \, a + 1\right)} b^{2} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{5}{2}}} + \frac{i \, a b^{2} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{3}{2}}} - \frac{{\left(-i \, a - 1\right)} b^{2} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{3}{2}}} + \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a {\left(i \, a + 1\right)} b}{2 \, {\left(a^{2} + 1\right)}^{2} x} - \frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b}{{\left(a^{2} + 1\right)} x} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(i \, a + 1\right)}}{2 \, {\left(a^{2} + 1\right)} x^{2}}"," ",0,"-3/2*a^2*(I*a + 1)*b^2*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) + I*a*b^2*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) - 1/2*(-I*a - 1)*b^2*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) + 3/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*(I*a + 1)*b/((a^2 + 1)^2*x) - I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b/((a^2 + 1)*x) - 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(I*a + 1)/((a^2 + 1)*x^2)","B",0
170,1,644,0,0.351135," ","integrate((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x^4,x, algorithm=""maxima"")","\frac{5 \, a^{3} {\left(i \, a + 1\right)} b^{3} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{7}{2}}} - \frac{3 i \, a^{2} b^{3} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{5}{2}}} - \frac{3 \, a {\left(i \, a + 1\right)} b^{3} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{5}{2}}} + \frac{i \, b^{3} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{3}{2}}} - \frac{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2} {\left(i \, a + 1\right)} b^{2}}{2 \, {\left(a^{2} + 1\right)}^{3} x} + \frac{3 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a b^{2}}{2 \, {\left(a^{2} + 1\right)}^{2} x} - \frac{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(-i \, a - 1\right)} b^{2}}{3 \, {\left(a^{2} + 1\right)}^{2} x} + \frac{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a {\left(i \, a + 1\right)} b}{6 \, {\left(a^{2} + 1\right)}^{2} x^{2}} - \frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b}{2 \, {\left(a^{2} + 1\right)} x^{2}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(i \, a + 1\right)}}{3 \, {\left(a^{2} + 1\right)} x^{3}}"," ",0,"5/2*a^3*(I*a + 1)*b^3*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(7/2) - 3/2*I*a^2*b^3*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) - 3/2*a*(I*a + 1)*b^3*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) + 1/2*I*b^3*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) - 5/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2*(I*a + 1)*b^2/((a^2 + 1)^3*x) + 3/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*b^2/((a^2 + 1)^2*x) - 2/3*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(-I*a - 1)*b^2/((a^2 + 1)^2*x) + 5/6*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*(I*a + 1)*b/((a^2 + 1)^2*x^2) - 1/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b/((a^2 + 1)*x^2) - 1/3*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(I*a + 1)/((a^2 + 1)*x^3)","B",0
171,1,150,0,0.450573," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x^4,x, algorithm=""maxima"")","-\frac{6 \, b^{4} x^{5} - 15 i \, b^{3} x^{4} + 20 \, {\left(i \, a - 1\right)} b^{2} x^{3} - {\left(30 i \, a^{2} - 60 \, a - 30 i\right)} b x^{2} - {\left(-60 i \, a^{3} + 180 \, a^{2} + 180 i \, a - 60\right)} x}{30 \, b^{4}} + \frac{{\left(2 \, a^{4} + 8 i \, a^{3} - 12 \, a^{2} - 8 i \, a + 2\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{5}} + \frac{{\left(i \, a^{4} - 4 \, a^{3} - 6 i \, a^{2} + 4 \, a + i\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b^{5}}"," ",0,"-1/30*(6*b^4*x^5 - 15*I*b^3*x^4 + 20*(I*a - 1)*b^2*x^3 - (30*I*a^2 - 60*a - 30*I)*b*x^2 - (-60*I*a^3 + 180*a^2 + 180*I*a - 60)*x)/b^4 + (2*a^4 + 8*I*a^3 - 12*a^2 - 8*I*a + 2)*arctan((b^2*x + a*b)/b)/b^5 + (I*a^4 - 4*a^3 - 6*I*a^2 + 4*a + I)*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^5","B",0
172,1,118,0,0.428064," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x^3,x, algorithm=""maxima"")","-\frac{3 \, b^{3} x^{4} - 8 i \, b^{2} x^{3} + 12 \, {\left(i \, a - 1\right)} b x^{2} - {\left(24 i \, a^{2} - 48 \, a - 24 i\right)} x}{12 \, b^{3}} - \frac{{\left(2 \, a^{3} + 6 i \, a^{2} - 6 \, a - 2 i\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{4}} + \frac{{\left(-i \, a^{3} + 3 \, a^{2} + 3 i \, a - 1\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b^{4}}"," ",0,"-1/12*(3*b^3*x^4 - 8*I*b^2*x^3 + 12*(I*a - 1)*b*x^2 - (24*I*a^2 - 48*a - 24*I)*x)/b^3 - (2*a^3 + 6*I*a^2 - 6*a - 2*I)*arctan((b^2*x + a*b)/b)/b^4 + (-I*a^3 + 3*a^2 + 3*I*a - 1)*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^4","B",0
173,1,87,0,0.419757," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x^2,x, algorithm=""maxima"")","-\frac{b^{2} x^{3} - 3 i \, b x^{2} + 6 \, {\left(i \, a - 1\right)} x}{3 \, b^{2}} + \frac{2 \, {\left(a^{2} + 2 i \, a - 1\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{3}} + \frac{{\left(i \, a^{2} - 2 \, a - i\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b^{3}}"," ",0,"-1/3*(b^2*x^3 - 3*I*b*x^2 + 6*(I*a - 1)*x)/b^2 + 2*(a^2 + 2*I*a - 1)*arctan((b^2*x + a*b)/b)/b^3 + (I*a^2 - 2*a - I)*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^3","B",0
174,1,66,0,0.441458," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x,x, algorithm=""maxima"")","-\frac{b x^{2} - 4 i \, x}{2 \, b} - \frac{{\left(2 \, a + 2 i\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{2}} + \frac{{\left(-i \, a + 1\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b^{2}}"," ",0,"-1/2*(b*x^2 - 4*I*x)/b - (2*a + 2*I)*arctan((b^2*x + a*b)/b)/b^2 + (-I*a + 1)*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^2","B",0
175,1,46,0,0.422927," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2),x, algorithm=""maxima"")","-x + \frac{2 \, \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b} + \frac{i \, \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b}"," ",0,"-x + 2*arctan((b^2*x + a*b)/b)/b + I*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b","B",0
176,1,80,0,0.414865," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x,x, algorithm=""maxima"")","-\frac{{\left(2 \, a - 2 i\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{a^{2} + 1} - \frac{{\left(i \, a + 1\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{a^{2} + 1} - \frac{{\left(a^{2} - 2 i \, a - 1\right)} \log\left(x\right)}{a^{2} + 1}"," ",0,"-(2*a - 2*I)*arctan((b^2*x + a*b)/b)/(a^2 + 1) - (I*a + 1)*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^2 + 1) - (a^2 - 2*I*a - 1)*log(x)/(a^2 + 1)","B",0
177,1,125,0,0.421341," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{2} - 2 i \, a - 1\right)} b \arctan\left(\frac{b^{2} x + a b}{b}\right)}{a^{4} + 2 \, a^{2} + 1} + \frac{{\left(i \, a^{2} + 2 \, a - i\right)} b \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{a^{4} + 2 \, a^{2} + 1} + \frac{{\left(-2 i \, a^{2} - 4 \, a + 2 i\right)} b \log\left(x\right)}{a^{4} + 2 \, a^{2} + 1} + \frac{a^{2} - 2 i \, a - 1}{{\left(a^{2} + 1\right)} x}"," ",0,"2*(a^2 - 2*I*a - 1)*b*arctan((b^2*x + a*b)/b)/(a^4 + 2*a^2 + 1) + (I*a^2 + 2*a - I)*b*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^4 + 2*a^2 + 1) + (-2*I*a^2 - 4*a + 2*I)*b*log(x)/(a^4 + 2*a^2 + 1) + (a^2 - 2*I*a - 1)/((a^2 + 1)*x)","B",0
178,1,188,0,0.431945," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, a^{3} - 6 i \, a^{2} - 6 \, a + 2 i\right)} b^{2} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1} + \frac{{\left(-2 i \, a^{3} - 6 \, a^{2} + 6 i \, a + 2\right)} b^{2} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{2 \, {\left(a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1\right)}} + \frac{{\left(2 i \, a^{3} + 6 \, a^{2} - 6 i \, a - 2\right)} b^{2} \log\left(x\right)}{a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1} + \frac{a^{4} - 2 i \, a^{3} + {\left(4 i \, a^{2} + 8 \, a - 4 i\right)} b x - 2 i \, a - 1}{2 \, {\left(a^{4} + 2 \, a^{2} + 1\right)} x^{2}}"," ",0,"-(2*a^3 - 6*I*a^2 - 6*a + 2*I)*b^2*arctan((b^2*x + a*b)/b)/(a^6 + 3*a^4 + 3*a^2 + 1) + 1/2*(-2*I*a^3 - 6*a^2 + 6*I*a + 2)*b^2*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^6 + 3*a^4 + 3*a^2 + 1) + (2*I*a^3 + 6*a^2 - 6*I*a - 2)*b^2*log(x)/(a^6 + 3*a^4 + 3*a^2 + 1) + 1/2*(a^4 - 2*I*a^3 + (4*I*a^2 + 8*a - 4*I)*b*x - 2*I*a - 1)/((a^4 + 2*a^2 + 1)*x^2)","B",0
179,1,263,0,0.440462," ","integrate((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x^4,x, algorithm=""maxima"")","\frac{{\left(2 \, a^{4} - 8 i \, a^{3} - 12 \, a^{2} + 8 i \, a + 2\right)} b^{3} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{a^{8} + 4 \, a^{6} + 6 \, a^{4} + 4 \, a^{2} + 1} + \frac{{\left(i \, a^{4} + 4 \, a^{3} - 6 i \, a^{2} - 4 \, a + i\right)} b^{3} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{a^{8} + 4 \, a^{6} + 6 \, a^{4} + 4 \, a^{2} + 1} + \frac{{\left(-2 i \, a^{4} - 8 \, a^{3} + 12 i \, a^{2} + 8 \, a - 2 i\right)} b^{3} \log\left(x\right)}{a^{8} + 4 \, a^{6} + 6 \, a^{4} + 4 \, a^{2} + 1} + \frac{a^{6} - 2 i \, a^{5} - {\left(6 i \, a^{3} + 18 \, a^{2} - 18 i \, a - 6\right)} b^{2} x^{2} + a^{4} - 4 i \, a^{3} - {\left(-3 i \, a^{4} - 6 \, a^{3} - 6 \, a + 3 i\right)} b x - a^{2} - 2 i \, a - 1}{3 \, {\left(a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1\right)} x^{3}}"," ",0,"(2*a^4 - 8*I*a^3 - 12*a^2 + 8*I*a + 2)*b^3*arctan((b^2*x + a*b)/b)/(a^8 + 4*a^6 + 6*a^4 + 4*a^2 + 1) + (I*a^4 + 4*a^3 - 6*I*a^2 - 4*a + I)*b^3*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^8 + 4*a^6 + 6*a^4 + 4*a^2 + 1) + (-2*I*a^4 - 8*a^3 + 12*I*a^2 + 8*a - 2*I)*b^3*log(x)/(a^8 + 4*a^6 + 6*a^4 + 4*a^2 + 1) + 1/3*(a^6 - 2*I*a^5 - (6*I*a^3 + 18*a^2 - 18*I*a - 6)*b^2*x^2 + a^4 - 4*I*a^3 - (-3*I*a^4 - 6*a^3 - 6*a + 3*I)*b*x - a^2 - 2*I*a - 1)/((a^6 + 3*a^4 + 3*a^2 + 1)*x^3)","B",0
180,1,3117,0,0.408193," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x^4,x, algorithm=""maxima"")","-\frac{i \, b x^{6}}{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{11 i \, a x^{5}}{20 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{693 i \, a^{7} x}{4 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{33 i \, a^{2} x^{4}}{20 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{2415 i \, {\left(a^{2} + 1\right)} a^{5} x}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{231 i \, a^{3} x^{3}}{40 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{{\left(-2 i \, a^{2} - 2 i\right)} x^{4}}{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} x^{5}}{4 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{231 i \, {\left(a^{2} + 1\right)} a^{6}}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{315 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{6} x}{4 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} + \frac{35 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{5} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{2919 i \, {\left(a^{2} + 1\right)}^{2} a^{3} x}{20 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{15 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{231 i \, a^{4} x^{2}}{8 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{111 i \, {\left(a^{2} + 1\right)} a x^{3}}{40 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{3 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a x^{4}}{4 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} x^{4}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{189 i \, {\left(a^{2} + 1\right)}^{2} a^{4}}{5 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{945 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a^{4} x}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} - \frac{265 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} a^{3} x}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{653 i \, {\left(a^{2} + 1\right)}^{3} a x}{40 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{31 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} {\left(a^{2} + 1\right)} a^{2} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{819 i \, {\left(a^{2} + 1\right)} a^{2} x^{2}}{40 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{21 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{2} x^{3}}{8 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} - \frac{7 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a x^{3}}{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{{\left(i \, a^{3} + 3 \, a^{2} - 3 i \, a - 1\right)} x^{3}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{693 i \, a^{5} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{5}} - \frac{105 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a^{5}}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{5}} + \frac{35 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} a^{4}}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} - \frac{397 i \, {\left(a^{2} + 1\right)}^{3} a^{2}}{40 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{5 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} {\left(a^{2} + 1\right)} a^{3}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{169 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}^{2} a^{2} x}{4 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} + \frac{61 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)}^{2} a x}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{3 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} {\left(a^{2} + 1\right)}^{2} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{105 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{3} x^{2}}{8 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{5}} + \frac{35 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{2} x^{2}}{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} - \frac{8 i \, {\left(a^{2} + 1\right)}^{2} x^{2}}{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{5 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a x^{2}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{5 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} x^{3}}{8 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} - \frac{315 i \, {\left(a^{2} + 1\right)} a^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{4 \, b^{5}} + \frac{14 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}^{2} a^{3}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{5}} - \frac{231 i \, {\left(a^{2} + 1\right)} a^{4}}{4 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{5}} - \frac{29 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)}^{2} a^{2}}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} + \frac{3 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} {\left(a^{2} + 1\right)}^{2} a}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{15 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}^{3} x}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} + \frac{49 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a x^{2}}{8 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{5}} - \frac{4 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} x^{2}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} + \frac{315 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{4} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{7}} - \frac{35 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{6}} + \frac{105 i \, {\left(a^{2} + 1\right)}^{2} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{5}} + \frac{15 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{5}} - \frac{15 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}^{3} a}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{5}} + \frac{819 i \, {\left(a^{2} + 1\right)}^{2} a^{2}}{20 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{5}} - \frac{105 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{4 \, b^{7}} + \frac{15 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{6}} - \frac{3 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} {\left(a^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{5}} - \frac{105 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a^{3}}{4 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{7}} + \frac{35 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} a^{2}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{6}} - \frac{16 i \, {\left(a^{2} + 1\right)}^{3}}{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{5}} - \frac{5 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} {\left(a^{2} + 1\right)} a}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{5}} + \frac{15 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{7}} + \frac{49 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}^{2} a}{4 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{7}} - \frac{8 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)}^{2}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{6}}"," ",0,"-1/5*I*b*x^6/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 11/20*I*a*x^5/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 693/4*I*a^7*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 33/20*I*a^2*x^4/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + 2415/8*I*(a^2 + 1)*a^5*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 231/40*I*a^3*x^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 1/5*(-2*I*a^2 - 2*I)*x^4/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + 1/4*(-3*I*a*b^2 - 3*b^2)*x^5/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 231/8*I*(a^2 + 1)*a^6/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 315/4*(-3*I*a*b^2 - 3*b^2)*a^6*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) + 35*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^5*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 2919/20*I*(a^2 + 1)^2*a^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 15*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 231/8*I*a^4*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 111/40*I*(a^2 + 1)*a*x^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 3/4*(-3*I*a*b^2 - 3*b^2)*a*x^4/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + 1/3*(-3*I*a^2*b - 6*a*b + 3*I*b)*x^4/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 189/5*I*(a^2 + 1)^2*a^4/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + 945/8*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) - 265/6*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*a^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + 653/40*I*(a^2 + 1)^3*a*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 31/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*(a^2 + 1)*a^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 819/40*I*(a^2 + 1)*a^2*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + 21/8*(-3*I*a*b^2 - 3*b^2)*a^2*x^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) - 7/6*(-3*I*a^2*b - 6*a*b + 3*I*b)*a*x^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 1/2*(I*a^3 + 3*a^2 - 3*I*a - 1)*x^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 693/8*I*a^5*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 - 105/8*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a^5/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^5) + 35/6*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*a^4/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) - 397/40*I*(a^2 + 1)^3*a^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 5/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*(a^2 + 1)*a^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 169/4*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)^2*a^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) + 61/6*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)^2*a*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 3/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*(a^2 + 1)^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 105/8*(-3*I*a*b^2 - 3*b^2)*a^3*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^5) + 35/6*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^2*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) - 8/5*I*(a^2 + 1)^2*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 5/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 5/8*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*x^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) - 315/4*I*(a^2 + 1)*a^3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 + 14*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)^2*a^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^5) - 231/4*I*(a^2 + 1)*a^4/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^5) - 29/6*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)^2*a^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) + 3/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*(a^2 + 1)^2*a/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + 15/8*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) + 49/8*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^5) - 4/3*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) + 315/8*(-3*I*a*b^2 - 3*b^2)*a^4*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^7 - 35/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^6 + 105/8*I*(a^2 + 1)^2*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 + 15/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 - 15/8*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)^3*a/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^5) + 819/20*I*(a^2 + 1)^2*a^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^5) - 105/4*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^7 + 15/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^6 - 3/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*(a^2 + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 - 105/4*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^7) + 35/3*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*a^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^6) - 16/5*I*(a^2 + 1)^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^5) - 5*(-I*a^3 - 3*a^2 + 3*I*a + 1)*(a^2 + 1)*a/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^5) + 15/8*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^7 + 49/4*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)^2*a/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^7) - 8/3*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^6)","B",0
181,1,2321,0,0.370515," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x^3,x, algorithm=""maxima"")","-\frac{i \, b x^{5}}{4 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{315 i \, a^{6} x}{4 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{3 i \, a x^{4}}{4 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{945 i \, {\left(a^{2} + 1\right)} a^{4} x}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} - \frac{21 i \, a^{2} x^{3}}{8 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{105 i \, {\left(a^{2} + 1\right)} a^{5}}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{35 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{5} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{15 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{169 i \, {\left(a^{2} + 1\right)}^{2} a^{2} x}{4 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{6 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{3} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{105 i \, a^{3} x^{2}}{8 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{{\left(-5 i \, a^{2} - 5 i\right)} x^{3}}{8 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} x^{4}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{14 i \, {\left(a^{2} + 1\right)}^{2} a^{3}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{265 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a^{3} x}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{31 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} a^{2} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{15 i \, {\left(a^{2} + 1\right)}^{3} x}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} - \frac{5 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} {\left(a^{2} + 1\right)} a x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} - \frac{49 i \, {\left(a^{2} + 1\right)} a x^{2}}{8 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{7 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a x^{3}}{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} x^{3}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{315 i \, a^{4} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{4}} + \frac{35 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a^{4}}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} - \frac{5 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} a^{3}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{15 i \, {\left(a^{2} + 1\right)}^{3} a}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{{\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} {\left(a^{2} + 1\right)} a^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{61 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}^{2} a x}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{3 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)}^{2} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{35 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{2} x^{2}}{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} - \frac{5 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a x^{2}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{{\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} x^{2}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{105 i \, {\left(a^{2} + 1\right)} a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{4 \, b^{4}} - \frac{29 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}^{2} a^{2}}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} + \frac{105 i \, {\left(a^{2} + 1\right)} a^{3}}{4 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} + \frac{3 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)}^{2} a}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{4 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} x^{2}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} - \frac{35 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{6}} + \frac{15 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{5}} - \frac{15 i \, {\left(a^{2} + 1\right)}^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{8 \, b^{4}} - \frac{3 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{4}} - \frac{49 i \, {\left(a^{2} + 1\right)}^{2} a}{4 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} + \frac{15 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{6}} - \frac{3 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{5}} + \frac{35 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a^{2}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{6}} - \frac{5 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} a}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{5}} + \frac{2 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} {\left(a^{2} + 1\right)}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}} - \frac{8 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}^{2}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{6}}"," ",0,"-1/4*I*b*x^5/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 315/4*I*a^6*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + 3/4*I*a*x^4/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 945/8*I*(a^2 + 1)*a^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) - 21/8*I*a^2*x^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + 105/8*I*(a^2 + 1)*a^5/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 35*(-3*I*a*b^2 - 3*b^2)*a^5*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 15*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 169/4*I*(a^2 + 1)^2*a^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + 6*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + 105/8*I*a^3*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 1/8*(-5*I*a^2 - 5*I)*x^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + 1/3*(-3*I*a*b^2 - 3*b^2)*x^4/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 14*I*(a^2 + 1)^2*a^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 265/6*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + 31/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*a^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 15/8*I*(a^2 + 1)^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) - 5*(-I*a^3 - 3*a^2 + 3*I*a + 1)*(a^2 + 1)*a*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) - 49/8*I*(a^2 + 1)*a*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 7/6*(-3*I*a*b^2 - 3*b^2)*a*x^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + 1/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*x^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 315/8*I*a^4*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 + 35/6*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a^4/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) - 5/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*a^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + 15/8*I*(a^2 + 1)^3*a/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + (-I*a^3 - 3*a^2 + 3*I*a + 1)*(a^2 + 1)*a^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 61/6*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)^2*a*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 3/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 35/6*(-3*I*a*b^2 - 3*b^2)*a^2*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) - 5/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + (-I*a^3 - 3*a^2 + 3*I*a + 1)*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 105/4*I*(a^2 + 1)*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 - 29/6*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)^2*a^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) + 105/4*I*(a^2 + 1)*a^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) + 3/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)^2*a/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 4/3*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) - 35/2*(-3*I*a*b^2 - 3*b^2)*a^3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^6 + 15/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 - 15/8*I*(a^2 + 1)^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 - 3*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 - 49/4*I*(a^2 + 1)^2*a/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) + 15/2*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^6 - 3/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 + 35/3*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^6) - 5*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*a/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^5) + 2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*(a^2 + 1)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4) - 8/3*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^6)","B",0
182,1,1626,0,0.359443," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x^2,x, algorithm=""maxima"")","-\frac{35 i \, a^{5} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{i \, b x^{4}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{265 i \, {\left(a^{2} + 1\right)} a^{3} x}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{7 i \, a x^{3}}{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{35 i \, {\left(a^{2} + 1\right)} a^{4}}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} - \frac{61 i \, {\left(a^{2} + 1\right)}^{2} a x}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{2 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{15 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{6 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{3} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} - \frac{35 i \, a^{2} x^{2}}{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{29 i \, {\left(a^{2} + 1\right)}^{2} a^{2}}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{{\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} {\left(a^{2} + 1\right)} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{31 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a^{2} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{5 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} a x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} - \frac{{\left(-4 i \, a^{2} - 4 i\right)} x^{2}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} x^{3}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{35 i \, a^{3} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{3}} - \frac{5 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a^{3}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} a^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{{\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} {\left(a^{2} + 1\right)} a}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} - \frac{3 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}^{2} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{5 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a x^{2}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} x^{2}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{15 i \, {\left(a^{2} + 1\right)} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{3}} + \frac{3 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}^{2} a}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{35 i \, {\left(a^{2} + 1\right)} a^{2}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} + \frac{15 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{5}} - \frac{3 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{4}} + \frac{{\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{3}} + \frac{8 i \, {\left(a^{2} + 1\right)}^{2}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{3}} - \frac{3 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{5}} - \frac{5 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{5}} + \frac{2 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}}"," ",0,"-35*I*a^5*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 1/3*I*b*x^4/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 265/6*I*(a^2 + 1)*a^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + 7/6*I*a*x^3/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 35/6*I*(a^2 + 1)*a^4/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) - 61/6*I*(a^2 + 1)^2*a*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 15*(-3*I*a*b^2 - 3*b^2)*a^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 6*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) - 35/6*I*a^2*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + 29/6*I*(a^2 + 1)^2*a^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + (-I*a^3 - 3*a^2 + 3*I*a + 1)*(a^2 + 1)*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + 31/2*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 5*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*a*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) - 1/3*(-4*I*a^2 - 4*I)*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + 1/2*(-3*I*a*b^2 - 3*b^2)*x^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 35/2*I*a^3*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 - 5/2*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + (-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*a^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - (-I*a^3 - 3*a^2 + 3*I*a + 1)*(a^2 + 1)*a/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) - 3/2*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 5/2*(-3*I*a*b^2 - 3*b^2)*a*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + (-3*I*a^2*b - 6*a*b + 3*I*b)*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 15/2*I*(a^2 + 1)*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 + 3/2*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)^2*a/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 35/3*I*(a^2 + 1)*a^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) + 15/2*(-3*I*a*b^2 - 3*b^2)*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 - 3*(-3*I*a^2*b - 6*a*b + 3*I*b)*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 + (-I*a^3 - 3*a^2 + 3*I*a + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 + 8/3*I*(a^2 + 1)^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^3) - 3/2*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^5 - 5*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^5) + 2*(-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4)","B",0
183,1,1116,0,0.366319," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x,x, algorithm=""maxima"")","\frac{15 i \, a^{4} b x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{31 i \, {\left(a^{2} + 1\right)} a^{2} b x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{i \, b x^{3}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{5 i \, {\left(a^{2} + 1\right)} a^{3}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{2 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{6 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{3} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{3 i \, {\left(a^{2} + 1\right)}^{2} b x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{{\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{5 i \, a x^{2}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{3 i \, {\left(a^{2} + 1\right)}^{2} a}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{{\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{5 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} - \frac{15 i \, a^{2} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{2}} + \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} {\left(a^{2} + 1\right)} a}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} x^{2}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{{\left(-3 i \, a^{2} - 3 i\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{2 \, b^{2}} + \frac{5 i \, {\left(a^{2} + 1\right)} a}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - \frac{3 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{4}} + \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{3}} + \frac{i \, a^{3} + 3 \, a^{2} - 3 i \, a - 1}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} + \frac{2 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{4}}"," ",0,"15*I*a^4*b*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 31/2*I*(a^2 + 1)*a^2*b*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 1/2*I*b*x^3/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 5/2*I*(a^2 + 1)*a^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + 6*(-3*I*a*b^2 - 3*b^2)*a^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + 3/2*I*(a^2 + 1)^2*b*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + 5/2*I*a*x^2/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 3/2*I*(a^2 + 1)^2*a/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-I*a^3 - 3*a^2 + 3*I*a + 1)*a^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 5*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) - 15/2*I*a^2*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^2 + (-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - (-3*I*a^2*b - 6*a*b + 3*I*b)*(a^2 + 1)*a/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + (-3*I*a*b^2 - 3*b^2)*x^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 1/2*(-3*I*a^2 - 3*I)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^2 + 5*I*(a^2 + 1)*a/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - 3*(-3*I*a*b^2 - 3*b^2)*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^4 + (-3*I*a^2*b - 6*a*b + 3*I*b)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 + (I*a^3 + 3*a^2 - 3*I*a - 1)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) + 2*(-3*I*a*b^2 - 3*b^2)*(a^2 + 1)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^4)","B",0
184,1,740,0,0.344154," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2),x, algorithm=""maxima"")","-\frac{6 i \, a^{3} b^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{5 i \, {\left(a^{2} + 1\right)} a b^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{i \, {\left(a^{2} + 1\right)} a^{2} b}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{2 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a b x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{{\left(-4 i \, a^{3} - 12 \, a^{2} + 12 i \, a + 4\right)} b^{2} x}{4 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{i \, b x^{2}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{{\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{3 i \, a \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b} - \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} {\left(a^{2} + 1\right)} a}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{-2 i \, a^{2} - 2 i}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b} + \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)}{b^{3}} - \frac{-3 i \, a^{2} b - 6 \, a b + 3 i \, b}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}}"," ",0,"-6*I*a^3*b^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + 5*I*(a^2 + 1)*a*b^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - I*(a^2 + 1)*a^2*b/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 2*(-3*I*a*b^2 - 3*b^2)*a^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-3*I*a^2*b - 6*a*b + 3*I*b)*a*b*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 1/4*(-4*I*a^3 - 12*a^2 + 12*I*a + 4)*b^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - I*b*x^2/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + (-3*I*a^2*b - 6*a*b + 3*I*b)*a^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - (-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + 3*I*a*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b - (-3*I*a*b^2 - 3*b^2)*(a^2 + 1)*a/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + (-2*I*a^2 - 2*I)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b) + (-3*I*a*b^2 - 3*b^2)*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))/b^3 - (-3*I*a^2*b - 6*a*b + 3*I*b)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2)","B",0
185,1,738,0,0.344541," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x,x, algorithm=""maxima"")","\frac{2 i \, a^{2} b^{3} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{{\left(4 i \, a^{2} + 4 i\right)} b^{3} x}{4 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{{\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b^{3} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{i \, {\left(a^{2} + 1\right)} a b^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{{\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{2} b^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a b x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} b^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a b}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{{\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{3}{2}}} + \frac{-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} - \frac{-3 i \, a b^{2} - 3 \, b^{2}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} b^{2}} - i \, \operatorname{arsinh}\left(\frac{2 \, {\left(b^{2} x + a b\right)}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}}}\right)"," ",0,"2*I*a^2*b^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 1/4*(4*I*a^2 + 4*I)*b^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + I*(a^2 + 1)*a*b^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-I*a^3 - 3*a^2 + 3*I*a + 1)*a^2*b^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + (-3*I*a*b^2 - 3*b^2)*a*b*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - (-3*I*a^2*b - 6*a*b + 3*I*b)*b^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + (-3*I*a*b^2 - 3*b^2)*a^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - (-3*I*a^2*b - 6*a*b + 3*I*b)*a*b/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - (-I*a^3 - 3*a^2 + 3*I*a + 1)*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) + (-I*a^3 - 3*a^2 + 3*I*a + 1)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) - (-3*I*a*b^2 - 3*b^2)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*b^2) - I*arcsinh(2*(b^2*x + a*b)/sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2))","B",0
186,1,993,0,0.352191," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x^2,x, algorithm=""maxima"")","-\frac{i \, a b^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{3 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{2} b^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{i \, a^{2} b^{3}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{3 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{3} b^{3}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} + \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a b^{3} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{2 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} b^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{2} b^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{2 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b^{3}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} - \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} b^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a b}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} + \frac{3 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{5}{2}}} + \frac{i \, b}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{3 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{{\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{3}{2}}} + \frac{-3 i \, a^{2} b - 6 \, a b + 3 i \, b}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} - \frac{-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} x}"," ",0,"-I*a*b^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 3*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^2*b^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - I*a^2*b^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 3*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^3*b^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) + (-3*I*a^2*b - 6*a*b + 3*I*b)*a*b^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + 2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*b^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + (-3*I*a^2*b - 6*a*b + 3*I*b)*a^2*b^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + 2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) - (-3*I*a*b^2 - 3*b^2)*b^2*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - (-3*I*a*b^2 - 3*b^2)*a*b/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) + 3*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) + I*b/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 3*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - (-3*I*a^2*b - 6*a*b + 3*I*b)*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) + (-3*I*a^2*b - 6*a*b + 3*I*b)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) - (-I*a^3 - 3*a^2 + 3*I*a + 1)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*x)","B",0
187,1,1541,0,0.366910," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x^3,x, algorithm=""maxima"")","\frac{15 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{3} b^{5} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{3}} + \frac{15 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{4} b^{4}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{3}} - \frac{3 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{2} b^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} + \frac{i \, b^{5} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{13 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b^{5} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{3 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{3} b^{3}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} + \frac{i \, a b^{4}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}} - \frac{13 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{2} b^{4}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} + \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a b^{3} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{2 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} b^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{2} b^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{2 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a b^{3}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} - \frac{15 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{2} b^{2} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{7}{2}}} + \frac{15 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{2} b^{2}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{3}} + \frac{3 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a b \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{5}{2}}} + \frac{3 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} b^{2} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{5}{2}}} - \frac{3 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a b}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{3 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} b^{2}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{{\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{3}{2}}} + \frac{-3 i \, a b^{2} - 3 \, b^{2}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{5 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2} x} - \frac{-3 i \, a^{2} b - 6 \, a b + 3 i \, b}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} x} - \frac{-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} x^{2}}"," ",0,"15/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^3*b^5*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^3) + 15/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^4*b^4/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^3) - 3*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^2*b^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) + I*b^5*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 13/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b^5*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - 3*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^3*b^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) + I*a*b^4/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)) - 13/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^2*b^4/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) + (-3*I*a*b^2 - 3*b^2)*a*b^3*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + 2*(-3*I*a^2*b - 6*a*b + 3*I*b)*b^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + (-3*I*a*b^2 - 3*b^2)*a^2*b^2/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + 2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a*b^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) - 15/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^2*b^2*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(7/2) + 15/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^2*b^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^3) + 3*(-3*I*a^2*b - 6*a*b + 3*I*b)*a*b*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) + 3/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*b^2*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) - 3*(-3*I*a^2*b - 6*a*b + 3*I*b)*a*b/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - 3/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*b^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - (-3*I*a*b^2 - 3*b^2)*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) + (-3*I*a*b^2 - 3*b^2)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + 5/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2*x) - (-3*I*a^2*b - 6*a*b + 3*I*b)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*x) - 1/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*x^2)","B",0
188,1,2327,0,0.377419," ","integrate((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x^4,x, algorithm=""maxima"")","-\frac{35 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{4} b^{6} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{4}} - \frac{35 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{5} b^{5}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{4}} + \frac{15 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{3} b^{5} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{3}} - \frac{i \, a b^{6} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{115 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{2} b^{6} x}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{3}} + \frac{15 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{4} b^{4}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{3}} - \frac{i \, a^{2} b^{5}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{115 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{3} b^{5}}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{3}} - \frac{3 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{2} b^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{13 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a b^{5} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{8 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} b^{6} x}{3 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{3 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a^{3} b^{3}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{13 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{2} b^{4}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{8 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b^{5}}{3 \, {\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} + \frac{2 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} b^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{35 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{3} b^{3} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{9}{2}}} + \frac{2 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a b^{3}}{{\left(a^{2} b^{2} - {\left(a^{2} + 1\right)} b^{2}\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} - \frac{35 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{3} b^{3}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{4}} - \frac{15 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{2} b^{2} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{7}{2}}} + \frac{i \, b^{3} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{3}{2}}} - \frac{15 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b^{3} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{7}{2}}} + \frac{15 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a^{2} b^{2}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{3}} - \frac{i \, b^{3}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}} + \frac{15 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b^{3}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{3}} + \frac{3 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a b \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{{\left(a^{2} + 1\right)}^{\frac{5}{2}}} + \frac{3 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} b^{2} \operatorname{arsinh}\left(\frac{2 \, a b x}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2 \, a^{2}}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}} + \frac{2}{\sqrt{-4 \, a^{2} b^{2} + 4 \, {\left(a^{2} + 1\right)} b^{2}} {\left| x \right|}}\right)}{2 \, {\left(a^{2} + 1\right)}^{\frac{5}{2}}} - \frac{3 \, {\left(-3 i \, a b^{2} - 3 \, b^{2}\right)} a b}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{3 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} b^{2}}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2}} - \frac{35 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a^{2} b^{2}}{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{3} x} + \frac{5 \, {\left(-3 i \, a^{2} b - 6 \, a b + 3 i \, b\right)} a b}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2} x} + \frac{4 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} b^{2}}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2} x} + \frac{7 \, {\left(-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1\right)} a b}{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)}^{2} x^{2}} - \frac{-3 i \, a b^{2} - 3 \, b^{2}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} x} - \frac{-3 i \, a^{2} b - 6 \, a b + 3 i \, b}{2 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} x^{2}} - \frac{-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1}{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} {\left(a^{2} + 1\right)} x^{3}}"," ",0,"-35/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^4*b^6*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^4) - 35/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^5*b^5/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^4) + 15/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^3*b^5*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^3) - I*a*b^6*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + 115/6*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^2*b^6*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^3) + 15/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^4*b^4/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^3) - I*a^2*b^5/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + 115/6*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^3*b^5/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^3) - 3*(-3*I*a*b^2 - 3*b^2)*a^2*b^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - 13/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a*b^5*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - 8/3*(-I*a^3 - 3*a^2 + 3*I*a + 1)*b^6*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - 3*(-3*I*a*b^2 - 3*b^2)*a^3*b^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - 13/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^2*b^4/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - 8/3*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b^5/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) + 2*(-3*I*a*b^2 - 3*b^2)*b^4*x/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + 35/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^3*b^3*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(9/2) + 2*(-3*I*a*b^2 - 3*b^2)*a*b^3/((a^2*b^2 - (a^2 + 1)*b^2)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) - 35/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^3*b^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^4) - 15/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^2*b^2*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(7/2) + I*b^3*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(3/2) - 15/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b^3*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(7/2) + 15/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a^2*b^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^3) - I*b^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)) + 15/2*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b^3/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^3) + 3*(-3*I*a*b^2 - 3*b^2)*a*b*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) + 3/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*b^2*arcsinh(2*a*b*x/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2*a^2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)) + 2/(sqrt(-4*a^2*b^2 + 4*(a^2 + 1)*b^2)*abs(x)))/(a^2 + 1)^(5/2) - 3*(-3*I*a*b^2 - 3*b^2)*a*b/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - 3/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*b^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2) - 35/6*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a^2*b^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^3*x) + 5/2*(-3*I*a^2*b - 6*a*b + 3*I*b)*a*b/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2*x) + 4/3*(-I*a^3 - 3*a^2 + 3*I*a + 1)*b^2/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2*x) + 7/6*(-I*a^3 - 3*a^2 + 3*I*a + 1)*a*b/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)^2*x^2) - (-3*I*a*b^2 - 3*b^2)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*x) - 1/2*(-3*I*a^2*b - 6*a*b + 3*I*b)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*x^2) - 1/3*(-I*a^3 - 3*a^2 + 3*I*a + 1)/(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*(a^2 + 1)*x^3)","B",0
189,1,456,0,0.467327," ","integrate(x^4/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{2 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{3} x}{b^{4}} - \frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{5 \, b^{3}} + \frac{a^{4} \operatorname{arsinh}\left(b x + a\right)}{b^{5}} + \frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{4}}{b^{5}} + \frac{3 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a x}{5 \, b^{4}} + \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2} x}{b^{4}} - \frac{2 i \, a^{3} \operatorname{arsinh}\left(b x + a\right)}{b^{5}} - \frac{6 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{5 \, b^{5}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{3}}{b^{5}} + \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, b^{4}} - \frac{5 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a x}{2 \, b^{4}} - \frac{3 \, a^{2} \operatorname{arsinh}\left(b x + a\right)}{b^{5}} - \frac{13 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{12 \, b^{5}} + \frac{7 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2}}{2 \, b^{5}} - \frac{5 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x}{8 \, b^{4}} + \frac{3 i \, a \operatorname{arsinh}\left(b x + a\right)}{2 \, b^{5}} + \frac{7 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{15 \, b^{5}} + \frac{27 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{8 \, b^{5}} + \frac{3 \, \operatorname{arsinh}\left(b x + a\right)}{8 \, b^{5}} - \frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b^{5}}"," ",0,"2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^3*x/b^4 - 1/5*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*x^2/b^3 + a^4*arcsinh(b*x + a)/b^5 + I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^4/b^5 + 3/5*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a*x/b^4 + 3*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2*x/b^4 - 2*I*a^3*arcsinh(b*x + a)/b^5 - 6/5*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^2/b^5 - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^3/b^5 + 1/4*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*x/b^4 - 5/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*x/b^4 - 3*a^2*arcsinh(b*x + a)/b^5 - 13/12*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/b^5 + 7/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2/b^5 - 5/8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x/b^4 + 3/2*I*a*arcsinh(b*x + a)/b^5 + 7/15*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/b^5 + 27/8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b^5 + 3/8*arcsinh(b*x + a)/b^5 - I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^5","B",0
190,1,308,0,0.440197," ","integrate(x^3/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","-\frac{3 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2} x}{2 \, b^{3}} - \frac{a^{3} \operatorname{arsinh}\left(b x + a\right)}{b^{4}} - \frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{3}}{2 \, b^{4}} - \frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, b^{3}} - \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a x}{2 \, b^{3}} + \frac{3 i \, a^{2} \operatorname{arsinh}\left(b x + a\right)}{2 \, b^{4}} + \frac{3 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{4 \, b^{4}} + \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2}}{2 \, b^{4}} + \frac{5 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x}{8 \, b^{3}} + \frac{3 \, a \operatorname{arsinh}\left(b x + a\right)}{2 \, b^{4}} + \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{3 \, b^{4}} - \frac{19 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{8 \, b^{4}} - \frac{3 i \, \operatorname{arsinh}\left(b x + a\right)}{8 \, b^{4}} - \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b^{4}}"," ",0,"-3/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2*x/b^3 - a^3*arcsinh(b*x + a)/b^4 - 1/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^3/b^4 - 1/4*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*x/b^3 - 3/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*x/b^3 + 3/2*I*a^2*arcsinh(b*x + a)/b^4 + 3/4*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/b^4 + 3/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2/b^4 + 5/8*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x/b^3 + 3/2*a*arcsinh(b*x + a)/b^4 + 1/3*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/b^4 - 19/8*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b^4 - 3/8*I*arcsinh(b*x + a)/b^4 - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^4","B",0
191,1,161,0,0.439111," ","integrate(x^2/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a x}{b^{2}} + \frac{a^{2} \operatorname{arsinh}\left(b x + a\right)}{b^{3}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x}{2 \, b^{2}} - \frac{i \, a \operatorname{arsinh}\left(b x + a\right)}{b^{3}} - \frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{3 \, b^{3}} - \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{2 \, b^{3}} - \frac{\operatorname{arsinh}\left(b x + a\right)}{2 \, b^{3}} + \frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b^{3}}"," ",0,"I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*x/b^2 + a^2*arcsinh(b*x + a)/b^3 + 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x/b^2 - I*a*arcsinh(b*x + a)/b^3 - 1/3*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/b^3 - 3/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b^3 - 1/2*arcsinh(b*x + a)/b^3 + I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^3","A",0
192,1,97,0,0.430345," ","integrate(x/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","-\frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x}{2 \, b} - \frac{a \operatorname{arsinh}\left(b x + a\right)}{b^{2}} + \frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{2 \, b^{2}} + \frac{i \, \operatorname{arsinh}\left(b x + a\right)}{2 \, b^{2}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b^{2}}"," ",0,"-1/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x/b - a*arcsinh(b*x + a)/b^2 + 1/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b^2 + 1/2*I*arcsinh(b*x + a)/b^2 + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^2","A",0
193,1,35,0,0.425028," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(b x + a\right)}{b} - \frac{i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b}"," ",0,"arcsinh(b*x + a)/b - I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/b","A",0
194,-2,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
195,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{{\left(b x + a\right)}^{2} + 1}}{{\left(i \, b x + i \, a + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt((b*x + a)^2 + 1)/((I*b*x + I*a + 1)*x^2), x)","F",0
196,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{{\left(b x + a\right)}^{2} + 1}}{{\left(i \, b x + i \, a + 1\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt((b*x + a)^2 + 1)/((I*b*x + I*a + 1)*x^3), x)","F",0
197,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{{\left(b x + a\right)}^{2} + 1}}{{\left(i \, b x + i \, a + 1\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt((b*x + a)^2 + 1)/((I*b*x + I*a + 1)*x^4), x)","F",0
198,1,102,0,0.317997," ","integrate(x^4/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x, algorithm=""maxima"")","-\frac{6 \, b^{4} x^{5} + 15 i \, b^{3} x^{4} - 20 \, {\left(i \, a + 1\right)} b^{2} x^{3} + {\left(30 i \, a^{2} + 60 \, a - 30 i\right)} b x^{2} + {\left(-60 i \, a^{3} - 180 \, a^{2} + 180 i \, a + 60\right)} x}{30 \, b^{4}} + \frac{{\left(-2 i \, a^{4} - 8 \, a^{3} + 12 i \, a^{2} + 8 \, a - 2 i\right)} \log\left(i \, b x + i \, a + 1\right)}{b^{5}}"," ",0,"-1/30*(6*b^4*x^5 + 15*I*b^3*x^4 - 20*(I*a + 1)*b^2*x^3 + (30*I*a^2 + 60*a - 30*I)*b*x^2 + (-60*I*a^3 - 180*a^2 + 180*I*a + 60)*x)/b^4 + (-2*I*a^4 - 8*a^3 + 12*I*a^2 + 8*a - 2*I)*log(I*b*x + I*a + 1)/b^5","A",0
199,1,74,0,0.317589," ","integrate(x^3/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x, algorithm=""maxima"")","-\frac{i \, {\left(-3 i \, b^{3} x^{4} + 8 \, b^{2} x^{3} - {\left(12 \, a - 12 i\right)} b x^{2} + 24 \, {\left(a^{2} - 2 i \, a - 1\right)} x\right)}}{12 \, b^{3}} + \frac{{\left(2 i \, a^{3} + 6 \, a^{2} - 6 i \, a - 2\right)} \log\left(i \, b x + i \, a + 1\right)}{b^{4}}"," ",0,"-1/12*I*(-3*I*b^3*x^4 + 8*b^2*x^3 - (12*a - 12*I)*b*x^2 + 24*(a^2 - 2*I*a - 1)*x)/b^3 + (2*I*a^3 + 6*a^2 - 6*I*a - 2)*log(I*b*x + I*a + 1)/b^4","A",0
200,1,52,0,0.320497," ","integrate(x^2/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x, algorithm=""maxima"")","-\frac{b^{2} x^{3} + 3 i \, b x^{2} + 6 \, {\left(-i \, a - 1\right)} x}{3 \, b^{2}} + \frac{{\left(-2 i \, a^{2} - 4 \, a + 2 i\right)} \log\left(i \, b x + i \, a + 1\right)}{b^{3}}"," ",0,"-1/3*(b^2*x^3 + 3*I*b*x^2 + 6*(-I*a - 1)*x)/b^2 + (-2*I*a^2 - 4*a + 2*I)*log(I*b*x + I*a + 1)/b^3","A",0
201,1,36,0,0.315587," ","integrate(x/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x, algorithm=""maxima"")","\frac{i \, {\left(i \, b x^{2} - 4 \, x\right)}}{2 \, b} - \frac{2 \, {\left(-i \, a - 1\right)} \log\left(i \, b x + i \, a + 1\right)}{b^{2}}"," ",0,"1/2*I*(I*b*x^2 - 4*x)/b - 2*(-I*a - 1)*log(I*b*x + I*a + 1)/b^2","A",0
202,1,19,0,0.317770," ","integrate(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x, algorithm=""maxima"")","-x - \frac{2 i \, \log\left(i \, b x + i \, a + 1\right)}{b}"," ",0,"-x - 2*I*log(I*b*x + I*a + 1)/b","A",0
203,1,47,0,0.330375," ","integrate(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x,x, algorithm=""maxima"")","-\frac{2 \, {\left(-i \, a - 1\right)} \log\left(i \, b x + i \, a + 1\right)}{a^{2} - 2 i \, a - 1} - \frac{{\left(a^{2} + 1\right)} \log\left(x\right)}{a^{2} - 2 i \, a - 1}"," ",0,"-2*(-I*a - 1)*log(I*b*x + I*a + 1)/(a^2 - 2*I*a - 1) - (a^2 + 1)*log(x)/(a^2 - 2*I*a - 1)","A",0
204,1,113,0,0.324958," ","integrate(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, a - 2 i\right)} b \log\left(i \, b x + i \, a + 1\right)}{-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1} + \frac{{\left(2 \, a - 2 i\right)} b \log\left(x\right)}{-i \, a^{3} - 3 \, a^{2} + 3 i \, a + 1} + \frac{a^{3} + {\left(a^{2} + 1\right)} b x - i \, a^{2} + a - i}{{\left(a^{2} - 2 i \, a - 1\right)} b x^{2} + {\left(a^{3} - 3 i \, a^{2} - 3 \, a + i\right)} x}"," ",0,"-(2*a - 2*I)*b*log(I*b*x + I*a + 1)/(-I*a^3 - 3*a^2 + 3*I*a + 1) + (2*a - 2*I)*b*log(x)/(-I*a^3 - 3*a^2 + 3*I*a + 1) + (a^3 + (a^2 + 1)*b*x - I*a^2 + a - I)/((a^2 - 2*I*a - 1)*b*x^2 + (a^3 - 3*I*a^2 - 3*a + I)*x)","B",0
205,1,163,0,0.339878," ","integrate(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(-i \, a - 1\right)} b^{2} \log\left(i \, b x + i \, a + 1\right)}{a^{4} - 4 i \, a^{3} - 6 \, a^{2} + 4 i \, a + 1} - \frac{2 \, {\left(i \, a + 1\right)} b^{2} \log\left(x\right)}{a^{4} - 4 i \, a^{3} - 6 \, a^{2} + 4 i \, a + 1} + \frac{4 \, {\left(-i \, a - 1\right)} b^{2} x^{2} + a^{4} - 2 i \, a^{3} + {\left(a^{3} - 5 i \, a^{2} - 7 \, a + 3 i\right)} b x - 2 i \, a - 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,"-2*(-I*a - 1)*b^2*log(I*b*x + I*a + 1)/(a^4 - 4*I*a^3 - 6*a^2 + 4*I*a + 1) - 2*(I*a + 1)*b^2*log(x)/(a^4 - 4*I*a^3 - 6*a^2 + 4*I*a + 1) + (4*(-I*a - 1)*b^2*x^2 + a^4 - 2*I*a^3 + (a^3 - 5*I*a^2 - 7*a + 3*I)*b*x - 2*I*a - 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
206,1,222,0,0.340539," ","integrate(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x^4,x, algorithm=""maxima"")","\frac{{\left(2 \, a - 2 i\right)} b^{3} \log\left(i \, b x + i \, a + 1\right)}{i \, a^{5} + 5 \, a^{4} - 10 i \, a^{3} - 10 \, a^{2} + 5 i \, a + 1} - \frac{{\left(2 \, a - 2 i\right)} b^{3} \log\left(x\right)}{i \, a^{5} + 5 \, a^{4} - 10 i \, a^{3} - 10 \, a^{2} + 5 i \, a + 1} - \frac{{\left(6 \, a - 6 i\right)} b^{3} x^{3} - i \, a^{5} + 3 \, {\left(a^{2} - 2 i \, a - 1\right)} b^{2} x^{2} - 3 \, a^{4} + 2 i \, a^{3} - {\left(i \, a^{4} + 5 \, a^{3} - 9 i \, a^{2} - 7 \, a + 2 i\right)} b x - 2 \, a^{2} + 3 i \, a + 1}{{\left(3 i \, a^{4} + 12 \, a^{3} - 18 i \, a^{2} - 12 \, a + 3 i\right)} b x^{4} + {\left(3 i \, a^{5} + 15 \, a^{4} - 30 i \, a^{3} - 30 \, a^{2} + 15 i \, a + 3\right)} x^{3}}"," ",0,"(2*a - 2*I)*b^3*log(I*b*x + I*a + 1)/(I*a^5 + 5*a^4 - 10*I*a^3 - 10*a^2 + 5*I*a + 1) - (2*a - 2*I)*b^3*log(x)/(I*a^5 + 5*a^4 - 10*I*a^3 - 10*a^2 + 5*I*a + 1) - ((6*a - 6*I)*b^3*x^3 - I*a^5 + 3*(a^2 - 2*I*a - 1)*b^2*x^2 - 3*a^4 + 2*I*a^3 - (I*a^4 + 5*a^3 - 9*I*a^2 - 7*a + 2*I)*b*x - 2*a^2 + 3*I*a + 1)/((3*I*a^4 + 12*a^3 - 18*I*a^2 - 12*a + 3*I)*b*x^4 + (3*I*a^5 + 15*a^4 - 30*I*a^3 - 30*a^2 + 15*I*a + 3)*x^3)","B",0
207,1,1368,0,0.477924," ","integrate(x^4/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{4}}{b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5} - 2 i \, b^{6} x - 2 i \, a b^{5} - b^{5}} + \frac{4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{3}}{b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5} - 2 i \, b^{6} x - 2 i \, a b^{5} - b^{5}} + \frac{4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{3}}{2 i \, b^{6} x + 2 i \, a b^{5} + 2 \, b^{5}} + \frac{6 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{4}}{i \, b^{6} x + i \, a b^{5} + b^{5}} - \frac{6 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5} - 2 i \, b^{6} x - 2 i \, a b^{5} - b^{5}} - \frac{12 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{2 i \, b^{6} x + 2 i \, a b^{5} + 2 \, b^{5}} + \frac{24 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{3}}{i \, b^{6} x + i \, a b^{5} + b^{5}} - \frac{4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5} - 2 i \, b^{6} x - 2 i \, a b^{5} - b^{5}} - \frac{12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{2 i \, b^{6} x + 2 i \, a b^{5} + 2 \, b^{5}} - \frac{36 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2}}{i \, b^{6} x + i \, a b^{5} + b^{5}} + \frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5} - 2 i \, b^{6} x - 2 i \, a b^{5} - b^{5}} + \frac{4 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{2 i \, b^{6} x + 2 i \, a b^{5} + 2 \, b^{5}} - \frac{24 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{i \, b^{6} x + i \, a b^{5} + b^{5}} - \frac{3 \, a^{4} \operatorname{arsinh}\left(b x + a\right)}{b^{5}} + \frac{6 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{i \, b^{6} x + i \, a b^{5} + b^{5}} - \frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a x}{b^{4}} - \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} a^{2} x}{b^{4}} + \frac{18 i \, a^{3} \operatorname{arsinh}\left(b x + a\right)}{b^{5}} + \frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{b^{5}} + \frac{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{3}}{b^{5}} - \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} a^{3}}{b^{5}} - \frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, b^{4}} - \frac{3 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a x}{2 \, b^{4}} + \frac{6 i \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} a x}{b^{4}} + \frac{3 \, a^{2} \arcsin\left(i \, b x + i \, a + 2\right)}{b^{5}} + \frac{36 \, a^{2} \operatorname{arsinh}\left(b x + a\right)}{b^{5}} + \frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{5}{2}}}{5 \, b^{5}} + \frac{13 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{4 \, b^{5}} - \frac{39 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2}}{2 \, b^{5}} + \frac{12 i \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} a^{2}}{b^{5}} - \frac{9 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x}{8 \, b^{4}} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} x}{b^{4}} - \frac{6 i \, a \arcsin\left(i \, b x + i \, a + 2\right)}{b^{5}} - \frac{63 i \, a \operatorname{arsinh}\left(b x + a\right)}{2 \, b^{5}} - \frac{2 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{b^{5}} - \frac{153 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{8 \, b^{5}} + \frac{15 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} a}{b^{5}} - \frac{3 \, \arcsin\left(i \, b x + i \, a + 2\right)}{b^{5}} - \frac{81 \, \operatorname{arsinh}\left(b x + a\right)}{8 \, b^{5}} + \frac{6 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b^{5}} - \frac{6 i \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3}}{b^{5}}"," ",0,"I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^4/(b^7*x^2 + 2*a*b^6*x + a^2*b^5 - 2*I*b^6*x - 2*I*a*b^5 - b^5) + 4*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^3/(b^7*x^2 + 2*a*b^6*x + a^2*b^5 - 2*I*b^6*x - 2*I*a*b^5 - b^5) + 4*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^3/(2*I*b^6*x + 2*I*a*b^5 + 2*b^5) + 6*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^4/(I*b^6*x + I*a*b^5 + b^5) - 6*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^2/(b^7*x^2 + 2*a*b^6*x + a^2*b^5 - 2*I*b^6*x - 2*I*a*b^5 - b^5) - 12*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^2/(2*I*b^6*x + 2*I*a*b^5 + 2*b^5) + 24*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^3/(I*b^6*x + I*a*b^5 + b^5) - 4*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/(b^7*x^2 + 2*a*b^6*x + a^2*b^5 - 2*I*b^6*x - 2*I*a*b^5 - b^5) - 12*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/(2*I*b^6*x + 2*I*a*b^5 + 2*b^5) - 36*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2/(I*b^6*x + I*a*b^5 + b^5) + I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/(b^7*x^2 + 2*a*b^6*x + a^2*b^5 - 2*I*b^6*x - 2*I*a*b^5 - b^5) + 4*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/(2*I*b^6*x + 2*I*a*b^5 + 2*b^5) - 24*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/(I*b^6*x + I*a*b^5 + b^5) - 3*a^4*arcsinh(b*x + a)/b^5 + 6*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(I*b^6*x + I*a*b^5 + b^5) - I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a*x/b^4 - 3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*a^2*x/b^4 + 18*I*a^3*arcsinh(b*x + a)/b^5 + I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^2/b^5 + 6*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^3/b^5 - 3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*a^3/b^5 - 3/4*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*x/b^4 - 3/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a*x/b^4 + 6*I*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*a*x/b^4 + 3*a^2*arcsin(I*b*x + I*a + 2)/b^5 + 36*a^2*arcsinh(b*x + a)/b^5 + 1/5*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(5/2)/b^5 + 13/4*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/b^5 - 39/2*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2/b^5 + 12*I*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*a^2/b^5 - 9/8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x/b^4 + 3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*x/b^4 - 6*I*a*arcsin(I*b*x + I*a + 2)/b^5 - 63/2*I*a*arcsinh(b*x + a)/b^5 - 2*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/b^5 - 153/8*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b^5 + 15*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*a/b^5 - 3*arcsin(I*b*x + I*a + 2)/b^5 - 81/8*arcsinh(b*x + a)/b^5 + 6*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^5 - 6*I*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)/b^5","B",0
208,1,979,0,0.465271," ","integrate(x^3/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x, algorithm=""maxima"")","-\frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{3}}{b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4} - 2 i \, b^{5} x - 2 i \, a b^{4} - b^{4}} - \frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4} - 2 i \, b^{5} x - 2 i \, a b^{4} - b^{4}} - \frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{2 i \, b^{5} x + 2 i \, a b^{4} + 2 \, b^{4}} - \frac{6 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{3}}{i \, b^{5} x + i \, a b^{4} + b^{4}} + \frac{3 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4} - 2 i \, b^{5} x - 2 i \, a b^{4} - b^{4}} + \frac{6 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{2 i \, b^{5} x + 2 i \, a b^{4} + 2 \, b^{4}} - \frac{18 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2}}{i \, b^{5} x + i \, a b^{4} + b^{4}} + \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4} - 2 i \, b^{5} x - 2 i \, a b^{4} - b^{4}} + \frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{2 i \, b^{5} x + 2 i \, a b^{4} + 2 \, b^{4}} + \frac{18 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{i \, b^{5} x + i \, a b^{4} + b^{4}} + \frac{3 \, a^{3} \operatorname{arsinh}\left(b x + a\right)}{b^{4}} + \frac{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{i \, b^{5} x + i \, a b^{4} + b^{4}} + \frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, b^{3}} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} a x}{2 \, b^{3}} - \frac{27 i \, a^{2} \operatorname{arsinh}\left(b x + a\right)}{2 \, b^{4}} - \frac{3 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{4 \, b^{4}} - \frac{9 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2}}{2 \, b^{4}} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} a^{2}}{2 \, b^{4}} + \frac{3 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} x}{8 \, b^{3}} - \frac{3 i \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} x}{2 \, b^{3}} - \frac{3 \, a \arcsin\left(i \, b x + i \, a + 2\right)}{2 \, b^{4}} - \frac{18 \, a \operatorname{arsinh}\left(b x + a\right)}{b^{4}} - \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{b^{4}} + \frac{75 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{8 \, b^{4}} - \frac{9 i \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} a}{2 \, b^{4}} + \frac{3 i \, \arcsin\left(i \, b x + i \, a + 2\right)}{2 \, b^{4}} + \frac{63 i \, \operatorname{arsinh}\left(b x + a\right)}{8 \, b^{4}} + \frac{9 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{2 \, b^{4}} - \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3}}{b^{4}}"," ",0,"-I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^3/(b^6*x^2 + 2*a*b^5*x + a^2*b^4 - 2*I*b^5*x - 2*I*a*b^4 - b^4) - 3*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^2/(b^6*x^2 + 2*a*b^5*x + a^2*b^4 - 2*I*b^5*x - 2*I*a*b^4 - b^4) - 3*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^2/(2*I*b^5*x + 2*I*a*b^4 + 2*b^4) - 6*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^3/(I*b^5*x + I*a*b^4 + b^4) + 3*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/(b^6*x^2 + 2*a*b^5*x + a^2*b^4 - 2*I*b^5*x - 2*I*a*b^4 - b^4) + 6*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/(2*I*b^5*x + 2*I*a*b^4 + 2*b^4) - 18*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2/(I*b^5*x + I*a*b^4 + b^4) + (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/(b^6*x^2 + 2*a*b^5*x + a^2*b^4 - 2*I*b^5*x - 2*I*a*b^4 - b^4) + 3*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/(2*I*b^5*x + 2*I*a*b^4 + 2*b^4) + 18*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/(I*b^5*x + I*a*b^4 + b^4) + 3*a^3*arcsinh(b*x + a)/b^4 + 6*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(I*b^5*x + I*a*b^4 + b^4) + 1/4*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*x/b^3 + 3/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*a*x/b^3 - 27/2*I*a^2*arcsinh(b*x + a)/b^4 - 3/4*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/b^4 - 9/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2/b^4 + 3/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*a^2/b^4 + 3/8*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*x/b^3 - 3/2*I*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*x/b^3 - 3/2*a*arcsin(I*b*x + I*a + 2)/b^4 - 18*a*arcsinh(b*x + a)/b^4 - (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/b^4 + 75/8*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b^4 - 9/2*I*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*a/b^4 + 3/2*I*arcsin(I*b*x + I*a + 2)/b^4 + 63/8*I*arcsinh(b*x + a)/b^4 + 9/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^4 - 3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)/b^4","B",0
209,1,624,0,0.442452," ","integrate(x^2/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3} - 2 i \, b^{4} x - 2 i \, a b^{3} - b^{3}} + \frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3} - 2 i \, b^{4} x - 2 i \, a b^{3} - b^{3}} + \frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{2 i \, b^{4} x + 2 i \, a b^{3} + 2 \, b^{3}} + \frac{6 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a^{2}}{i \, b^{4} x + i \, a b^{3} + b^{3}} - \frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3} - 2 i \, b^{4} x - 2 i \, a b^{3} - b^{3}} - \frac{2 i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{2 i \, b^{4} x + 2 i \, a b^{3} + 2 \, b^{3}} + \frac{12 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{i \, b^{4} x + i \, a b^{3} + b^{3}} - \frac{3 \, a^{2} \operatorname{arsinh}\left(b x + a\right)}{b^{3}} - \frac{6 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{i \, b^{4} x + i \, a b^{3} + b^{3}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} x}{2 \, b^{2}} + \frac{9 i \, a \operatorname{arsinh}\left(b x + a\right)}{b^{3}} + \frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{3 \, b^{3}} + \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{b^{3}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3} a}{2 \, b^{3}} + \frac{\arcsin\left(i \, b x + i \, a + 2\right)}{2 \, b^{3}} + \frac{6 \, \operatorname{arsinh}\left(b x + a\right)}{b^{3}} - \frac{3 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{b^{3}} + \frac{i \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 4 i \, b x + 4 i \, a + 3}}{b^{3}}"," ",0,"I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a^2/(b^5*x^2 + 2*a*b^4*x + a^2*b^3 - 2*I*b^4*x - 2*I*a*b^3 - b^3) + 2*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/(b^5*x^2 + 2*a*b^4*x + a^2*b^3 - 2*I*b^4*x - 2*I*a*b^3 - b^3) + 2*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/(2*I*b^4*x + 2*I*a*b^3 + 2*b^3) + 6*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a^2/(I*b^4*x + I*a*b^3 + b^3) - I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/(b^5*x^2 + 2*a*b^4*x + a^2*b^3 - 2*I*b^4*x - 2*I*a*b^3 - b^3) - 2*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/(2*I*b^4*x + 2*I*a*b^3 + 2*b^3) + 12*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/(I*b^4*x + I*a*b^3 + b^3) - 3*a^2*arcsinh(b*x + a)/b^3 - 6*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(I*b^4*x + I*a*b^3 + b^3) - 1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*x/b^2 + 9*I*a*arcsinh(b*x + a)/b^3 + 1/3*I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/b^3 + 3*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/b^3 - 1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)*a/b^3 + 1/2*arcsin(I*b*x + I*a + 2)/b^3 + 6*arcsinh(b*x + a)/b^3 - 3*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^3 + I*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 4*I*b*x + 4*I*a + 3)/b^3","B",0
210,1,293,0,0.437748," ","integrate(x/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x, algorithm=""maxima"")","-\frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}} a}{b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2} - 2 i \, b^{3} x - 2 i \, a b^{2} - b^{2}} - \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2} - 2 i \, b^{3} x - 2 i \, a b^{2} - b^{2}} - \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{2 i \, b^{3} x + 2 i \, a b^{2} + 2 \, b^{2}} - \frac{6 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} a}{i \, b^{3} x + i \, a b^{2} + b^{2}} + \frac{3 \, a \operatorname{arsinh}\left(b x + a\right)}{b^{2}} - \frac{6 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{i \, b^{3} x + i \, a b^{2} + b^{2}} - \frac{9 i \, \operatorname{arsinh}\left(b x + a\right)}{2 \, b^{2}} - \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{2 \, b^{2}}"," ",0,"-I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)*a/(b^4*x^2 + 2*a*b^3*x + a^2*b^2 - 2*I*b^3*x - 2*I*a*b^2 - b^2) - (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2 - 2*I*b^3*x - 2*I*a*b^2 - b^2) - (b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/(2*I*b^3*x + 2*I*a*b^2 + 2*b^2) - 6*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)*a/(I*b^3*x + I*a*b^2 + b^2) + 3*a*arcsinh(b*x + a)/b^2 - 6*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(I*b^3*x + I*a*b^2 + b^2) - 9/2*I*arcsinh(b*x + a)/b^2 - 3/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^2","B",0
211,1,103,0,0.435817," ","integrate(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{3}{2}}}{b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b - 2 i \, b^{2} x - 2 i \, a b - b} - \frac{3 \, \operatorname{arsinh}\left(b x + a\right)}{b} + \frac{6 i \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}{i \, b^{2} x + i \, a b + b}"," ",0,"I*(b^2*x^2 + 2*a*b*x + a^2 + 1)^(3/2)/(b^3*x^2 + 2*a*b^2*x + a^2*b - 2*I*b^2*x - 2*I*a*b - b) - 3*arcsinh(b*x + a)/b + 6*I*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)/(I*b^2*x + I*a*b + b)","A",0
212,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x,x, algorithm=""maxima"")","\int \frac{{\left({\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{{\left(i \, b x + i \, a + 1\right)}^{3} x}\,{d x}"," ",0,"integrate(((b*x + a)^2 + 1)^(3/2)/((I*b*x + I*a + 1)^3*x), x)","F",0
213,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left({\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{{\left(i \, b x + i \, a + 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate(((b*x + a)^2 + 1)^(3/2)/((I*b*x + I*a + 1)^3*x^2), x)","F",0
214,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left({\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{{\left(i \, b x + i \, a + 1\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate(((b*x + a)^2 + 1)^(3/2)/((I*b*x + I*a + 1)^3*x^3), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left({\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{{\left(i \, b x + i \, a + 1\right)}^{3} x^{4}}\,{d x}"," ",0,"integrate(((b*x + a)^2 + 1)^(3/2)/((I*b*x + I*a + 1)^3*x^4), x)","F",0
216,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)*x^2,x, algorithm=""maxima"")","\int x^{2} \sqrt{\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}}\,{d x}"," ",0,"integrate(x^2*sqrt((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1)), x)","F",0
217,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)*x,x, algorithm=""maxima"")","\int x \sqrt{\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}}\,{d x}"," ",0,"integrate(x*sqrt((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1)), x)","F",0
218,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \sqrt{\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}}\,{d x}"," ",0,"integrate(sqrt((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1)), x)","F",0
219,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}}}{x}\,{d x}"," ",0,"integrate(sqrt((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))/x, x)","F",0
220,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))/x^2, x)","F",0
221,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^2*((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))^(3/2), x)","F",0
222,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)*x,x, algorithm=""maxima"")","\int x \left(\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x*((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))^(3/2), x)","F",0
223,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \left(\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))^(3/2), x)","F",0
224,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))^(3/2)/x, x)","F",0
225,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))^(3/2)/x^2, x)","F",0
226,0,0,0,0.000000," ","integrate(x^2/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}}}\,{d x}"," ",0,"integrate(x^2/sqrt((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1)), x)","F",0
227,0,0,0,0.000000," ","integrate(x/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}}}\,{d x}"," ",0,"integrate(x/sqrt((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1)), x)","F",0
228,0,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/sqrt((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1)), x)","F",0
229,0,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{1}{x \sqrt{\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x*sqrt((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))), x)","F",0
230,0,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{1}{x^{2} \sqrt{\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^2*sqrt((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))), x)","F",0
231,0,0,0,0.000000," ","integrate(x^2/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\left(\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))^(3/2), x)","F",0
232,0,0,0,0.000000," ","integrate(x/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{x}{\left(\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))^(3/2), x)","F",0
233,0,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))^(-3/2), x)","F",0
234,0,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x,x, algorithm=""maxima"")","\int \frac{1}{x \left(\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x*((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))^(3/2)), x)","F",0
235,0,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{1}{x^{2} \left(\frac{i \, b x + i \, a + 1}{\sqrt{{\left(b x + a\right)}^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x^2*((I*b*x + I*a + 1)/sqrt((b*x + a)^2 + 1))^(3/2)), x)","F",0
236,0,0,0,0.000000," ","integrate(exp(n*arctan(b*x+a))*x^m,x, algorithm=""maxima"")","\int x^{m} e^{\left(n \arctan\left(b x + a\right)\right)}\,{d x}"," ",0,"integrate(x^m*e^(n*arctan(b*x + a)), x)","F",0
237,0,0,0,0.000000," ","integrate(exp(n*arctan(b*x+a))*x^3,x, algorithm=""maxima"")","\int x^{3} e^{\left(n \arctan\left(b x + a\right)\right)}\,{d x}"," ",0,"integrate(x^3*e^(n*arctan(b*x + a)), x)","F",0
238,0,0,0,0.000000," ","integrate(exp(n*arctan(b*x+a))*x^2,x, algorithm=""maxima"")","\int x^{2} e^{\left(n \arctan\left(b x + a\right)\right)}\,{d x}"," ",0,"integrate(x^2*e^(n*arctan(b*x + a)), x)","F",0
239,0,0,0,0.000000," ","integrate(exp(n*arctan(b*x+a))*x,x, algorithm=""maxima"")","\int x e^{\left(n \arctan\left(b x + a\right)\right)}\,{d x}"," ",0,"integrate(x*e^(n*arctan(b*x + a)), x)","F",0
240,0,0,0,0.000000," ","integrate(exp(n*arctan(b*x+a)),x, algorithm=""maxima"")","\int e^{\left(n \arctan\left(b x + a\right)\right)}\,{d x}"," ",0,"integrate(e^(n*arctan(b*x + a)), x)","F",0
241,0,0,0,0.000000," ","integrate(exp(n*arctan(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(b x + a\right)\right)}}{x}\,{d x}"," ",0,"integrate(e^(n*arctan(b*x + a))/x, x)","F",0
242,0,0,0,0.000000," ","integrate(exp(n*arctan(b*x+a))/x^2,x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(b x + a\right)\right)}}{x^{2}}\,{d x}"," ",0,"integrate(e^(n*arctan(b*x + a))/x^2, x)","F",0
243,0,0,0,0.000000," ","integrate(exp(n*arctan(b*x+a))/x^3,x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(b x + a\right)\right)}}{x^{3}}\,{d x}"," ",0,"integrate(e^(n*arctan(b*x + a))/x^3, x)","F",0
244,0,0,0,0.000000," ","integrate(exp(arctan(a*x))*(a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{p} e^{\left(\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^p*e^(arctan(a*x)), x)","F",0
245,0,0,0,0.000000," ","integrate(exp(arctan(a*x))*(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{2} e^{\left(\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^2*e^(arctan(a*x)), x)","F",0
246,0,0,0,0.000000," ","integrate(exp(arctan(a*x))*(a^2*c*x^2+c),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)} e^{\left(\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)*e^(arctan(a*x)), x)","F",0
247,0,0,0,0.000000," ","integrate(exp(arctan(a*x)),x, algorithm=""maxima"")","\int e^{\left(\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(e^(arctan(a*x)), x)","F",0
248,1,12,0,0.435322," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{e^{\left(\arctan\left(a x\right)\right)}}{a c}"," ",0,"e^(arctan(a*x))/(a*c)","A",0
249,0,0,0,0.000000," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{e^{\left(\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(e^(arctan(a*x))/(a^2*c*x^2 + c)^2, x)","F",0
250,0,0,0,0.000000," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{e^{\left(\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(e^(arctan(a*x))/(a^2*c*x^2 + c)^3, x)","F",0
251,0,0,0,0.000000," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{e^{\left(\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{4}}\,{d x}"," ",0,"integrate(e^(arctan(a*x))/(a^2*c*x^2 + c)^4, x)","F",0
252,0,0,0,0.000000," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^5,x, algorithm=""maxima"")","\int \frac{e^{\left(\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{5}}\,{d x}"," ",0,"integrate(e^(arctan(a*x))/(a^2*c*x^2 + c)^5, x)","F",0
253,0,0,0,0.000000," ","integrate(exp(arctan(a*x))*(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} e^{\left(\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*e^(arctan(a*x)), x)","F",0
254,0,0,0,0.000000," ","integrate(exp(arctan(a*x))*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} e^{\left(\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*e^(arctan(a*x)), x)","F",0
255,0,0,0,0.000000," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{e^{\left(\arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(e^(arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
256,0,0,0,0.000000," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{e^{\left(\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(e^(arctan(a*x))/(a^2*c*x^2 + c)^(3/2), x)","F",0
257,0,0,0,0.000000," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{e^{\left(\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(e^(arctan(a*x))/(a^2*c*x^2 + c)^(5/2), x)","F",0
258,0,0,0,0.000000," ","integrate(exp(arctan(a*x))/(a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{e^{\left(\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(e^(arctan(a*x))/(a^2*c*x^2 + c)^(7/2), x)","F",0
259,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))*(a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{p} e^{\left(2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^p*e^(2*arctan(a*x)), x)","F",0
260,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))*(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{2} e^{\left(2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^2*e^(2*arctan(a*x)), x)","F",0
261,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))*(a^2*c*x^2+c),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)} e^{\left(2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)*e^(2*arctan(a*x)), x)","F",0
262,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x)),x, algorithm=""maxima"")","\int e^{\left(2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(e^(2*arctan(a*x)), x)","F",0
263,1,15,0,0.430808," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c),x, algorithm=""maxima"")","\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
264,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{e^{\left(2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(e^(2*arctan(a*x))/(a^2*c*x^2 + c)^2, x)","F",0
265,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{e^{\left(2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(e^(2*arctan(a*x))/(a^2*c*x^2 + c)^3, x)","F",0
266,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{e^{\left(2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{4}}\,{d x}"," ",0,"integrate(e^(2*arctan(a*x))/(a^2*c*x^2 + c)^4, x)","F",0
267,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))*(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} e^{\left(2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*e^(2*arctan(a*x)), x)","F",0
268,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} e^{\left(2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*e^(2*arctan(a*x)), x)","F",0
269,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{e^{\left(2 \, \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(e^(2*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
270,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{e^{\left(2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(e^(2*arctan(a*x))/(a^2*c*x^2 + c)^(3/2), x)","F",0
271,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{e^{\left(2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(e^(2*arctan(a*x))/(a^2*c*x^2 + c)^(5/2), x)","F",0
272,0,0,0,0.000000," ","integrate(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{e^{\left(2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(e^(2*arctan(a*x))/(a^2*c*x^2 + c)^(7/2), x)","F",0
273,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^p/exp(arctan(a*x)),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{p} e^{\left(-\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^p*e^(-arctan(a*x)), x)","F",0
274,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/exp(arctan(a*x)),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{2} e^{\left(-\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^2*e^(-arctan(a*x)), x)","F",0
275,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)/exp(arctan(a*x)),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)} e^{\left(-\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)*e^(-arctan(a*x)), x)","F",0
276,0,0,0,0.000000," ","integrate(exp(-arctan(a*x)),x, algorithm=""maxima"")","\int e^{\left(-\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(e^(-arctan(a*x)), x)","F",0
277,1,23,0,0.352948," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{2 \, e^{\left(-\arctan\left(a x\right)\right)}}{a^{3} c x^{2} + a c}"," ",0,"-2*e^(-arctan(a*x))/(a^3*c*x^2 + a*c)","A",0
278,0,0,0,0.000000," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{e^{\left(-\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(e^(-arctan(a*x))/(a^2*c*x^2 + c)^2, x)","F",0
279,0,0,0,0.000000," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{e^{\left(-\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(e^(-arctan(a*x))/(a^2*c*x^2 + c)^3, x)","F",0
280,0,0,0,0.000000," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{e^{\left(-\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{4}}\,{d x}"," ",0,"integrate(e^(-arctan(a*x))/(a^2*c*x^2 + c)^4, x)","F",0
281,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/exp(arctan(a*x)),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} e^{\left(-\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*e^(-arctan(a*x)), x)","F",0
282,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/exp(arctan(a*x)),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} e^{\left(-\arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*e^(-arctan(a*x)), x)","F",0
283,0,0,0,0.000000," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{e^{\left(-\arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(e^(-arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
284,0,0,0,0.000000," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{e^{\left(-\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(e^(-arctan(a*x))/(a^2*c*x^2 + c)^(3/2), x)","F",0
285,0,0,0,0.000000," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{e^{\left(-\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(e^(-arctan(a*x))/(a^2*c*x^2 + c)^(5/2), x)","F",0
286,0,0,0,0.000000," ","integrate(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{e^{\left(-\arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(e^(-arctan(a*x))/(a^2*c*x^2 + c)^(7/2), x)","F",0
287,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^p/exp(2*arctan(a*x)),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{p} e^{\left(-2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^p*e^(-2*arctan(a*x)), x)","F",0
288,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/exp(2*arctan(a*x)),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{2} e^{\left(-2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^2*e^(-2*arctan(a*x)), x)","F",0
289,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)/exp(2*arctan(a*x)),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)} e^{\left(-2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)*e^(-2*arctan(a*x)), x)","F",0
290,0,0,0,0.000000," ","integrate(exp(-2*arctan(a*x)),x, algorithm=""maxima"")","\int e^{\left(-2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(e^(-2*arctan(a*x)), x)","F",0
291,1,23,0,0.340709," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{e^{\left(-2 \, \arctan\left(a x\right)\right)}}{a^{3} c x^{2} + a c}"," ",0,"-e^(-2*arctan(a*x))/(a^3*c*x^2 + a*c)","A",0
292,0,0,0,0.000000," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{e^{\left(-2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(e^(-2*arctan(a*x))/(a^2*c*x^2 + c)^2, x)","F",0
293,0,0,0,0.000000," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{e^{\left(-2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(e^(-2*arctan(a*x))/(a^2*c*x^2 + c)^3, x)","F",0
294,0,0,0,0.000000," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{e^{\left(-2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{4}}\,{d x}"," ",0,"integrate(e^(-2*arctan(a*x))/(a^2*c*x^2 + c)^4, x)","F",0
295,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/exp(2*arctan(a*x)),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} e^{\left(-2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*e^(-2*arctan(a*x)), x)","F",0
296,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/exp(2*arctan(a*x)),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} e^{\left(-2 \, \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*e^(-2*arctan(a*x)), x)","F",0
297,0,0,0,0.000000," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{e^{\left(-2 \, \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(e^(-2*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
298,0,0,0,0.000000," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{e^{\left(-2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(e^(-2*arctan(a*x))/(a^2*c*x^2 + c)^(3/2), x)","F",0
299,0,0,0,0.000000," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{e^{\left(-2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(e^(-2*arctan(a*x))/(a^2*c*x^2 + c)^(5/2), x)","F",0
300,0,0,0,0.000000," ","integrate(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{e^{\left(-2 \, \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(e^(-2*arctan(a*x))/(a^2*c*x^2 + c)^(7/2), x)","F",0
301,1,63,0,0.428463," ","integrate((1+I*a*x)^5/(a^2*x^2+1)^3,x, algorithm=""maxima"")","-\frac{32 \, a^{3} x^{3} - 48 i \, a^{2} x^{2} - 16 i}{8 \, {\left(a^{5} x^{4} + 2 \, a^{3} x^{2} + a\right)}} + \frac{\arctan\left(a x\right)}{a} + \frac{i \, \log\left(a^{2} x^{2} + 1\right)}{2 \, a}"," ",0,"-1/8*(32*a^3*x^3 - 48*I*a^2*x^2 - 16*I)/(a^5*x^4 + 2*a^3*x^2 + a) + arctan(a*x)/a + 1/2*I*log(a^2*x^2 + 1)/a","A",0
302,1,112,0,0.324405," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{4} x {\left(\frac{3 \, x^{2}}{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}} + \frac{2}{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{4}}\right)} + \frac{4 i \, a x^{2}}{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} - \frac{5 \, x}{3 \, \sqrt{a^{2} x^{2} + 1}} + \frac{\operatorname{arsinh}\left(a x\right)}{a} + \frac{7 \, x}{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} + \frac{4 i}{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a}"," ",0,"-1/3*a^4*x*(3*x^2/((a^2*x^2 + 1)^(3/2)*a^2) + 2/((a^2*x^2 + 1)^(3/2)*a^4)) + 4*I*a*x^2/(a^2*x^2 + 1)^(3/2) - 5/3*x/sqrt(a^2*x^2 + 1) + arcsinh(a*x)/a + 7/3*x/(a^2*x^2 + 1)^(3/2) + 4/3*I/((a^2*x^2 + 1)^(3/2)*a)","B",0
303,1,44,0,0.425629," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{4 \, a x - 4 i}{2 \, {\left(a^{3} x^{2} + a\right)}} - \frac{\arctan\left(a x\right)}{a} - \frac{i \, \log\left(a^{2} x^{2} + 1\right)}{2 \, a}"," ",0,"1/2*(4*a*x - 4*I)/(a^3*x^2 + a) - arctan(a*x)/a - 1/2*I*log(a^2*x^2 + 1)/a","A",0
304,1,40,0,0.325386," ","integrate((1+I*a*x)^2/(a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{2 \, x}{\sqrt{a^{2} x^{2} + 1}} - \frac{\operatorname{arsinh}\left(a x\right)}{a} - \frac{2 i}{\sqrt{a^{2} x^{2} + 1} a}"," ",0,"2*x/sqrt(a^2*x^2 + 1) - arcsinh(a*x)/a - 2*I/(sqrt(a^2*x^2 + 1)*a)","A",0
305,1,24,0,0.427943," ","integrate((1+I*a*x)/(a^2*x^2+1),x, algorithm=""maxima"")","\frac{\arctan\left(a x\right)}{a} + \frac{i \, \log\left(a^{2} x^{2} + 1\right)}{2 \, a}"," ",0,"arctan(a*x)/a + 1/2*I*log(a^2*x^2 + 1)/a","B",0
306,1,12,0,0.319068," ","integrate(1/(1+I*a*x),x, algorithm=""maxima"")","-\frac{i \, \log\left(i \, a x + 1\right)}{a}"," ",0,"-I*log(I*a*x + 1)/a","A",0
307,1,33,0,0.433549," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\operatorname{arsinh}\left(a x\right)}{a} + \frac{2 i \, \sqrt{a^{2} x^{2} + 1}}{i \, a^{2} x + a}"," ",0,"-arcsinh(a*x)/a + 2*I*sqrt(a^2*x^2 + 1)/(I*a^2*x + a)","A",0
308,1,41,0,0.315772," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1),x, algorithm=""maxima"")","-\frac{4 \, {\left(-i \, a x - 1\right)}}{2 i \, a^{3} x^{2} + 4 \, a^{2} x - 2 i \, a} + \frac{i \, \log\left(i \, a x + 1\right)}{a}"," ",0,"-4*(-I*a*x - 1)/(2*I*a^3*x^2 + 4*a^2*x - 2*I*a) + I*log(I*a*x + 1)/a","A",0
309,1,108,0,0.422612," ","integrate(1/(1+I*a*x)^4*(a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{-3 i \, a^{4} x^{3} - 9 \, a^{3} x^{2} + 9 i \, a^{2} x + 3 \, a} + \frac{\operatorname{arsinh}\left(a x\right)}{a} - \frac{2 i \, \sqrt{a^{2} x^{2} + 1}}{3 \, a^{3} x^{2} - 6 i \, a^{2} x - 3 \, a} - \frac{7 i \, \sqrt{a^{2} x^{2} + 1}}{3 i \, a^{2} x + 3 \, a}"," ",0,"I*(a^2*x^2 + 1)^(3/2)/(-3*I*a^4*x^3 - 9*a^3*x^2 + 9*I*a^2*x + 3*a) + arcsinh(a*x)/a - 2*I*sqrt(a^2*x^2 + 1)/(3*a^3*x^2 - 6*I*a^2*x - 3*a) - 7*I*sqrt(a^2*x^2 + 1)/(3*I*a^2*x + 3*a)","B",0
310,0,0,0,0.000000," ","integrate((1+I*a*x)^5/(a^2*x^2+1)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)}^{5}}{\sqrt{a^{2} c x^{2} + c} {\left(a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*x + 1)^5/(sqrt(a^2*c*x^2 + c)*(a^2*x^2 + 1)^(5/2)), x)","F",0
311,0,0,0,0.000000," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)}^{4}}{\sqrt{a^{2} c x^{2} + c} {\left(a^{2} x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((I*a*x + 1)^4/(sqrt(a^2*c*x^2 + c)*(a^2*x^2 + 1)^2), x)","F",0
312,0,0,0,0.000000," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)}^{3}}{\sqrt{a^{2} c x^{2} + c} {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*x + 1)^3/(sqrt(a^2*c*x^2 + c)*(a^2*x^2 + 1)^(3/2)), x)","F",0
313,0,0,0,0.000000," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)}^{2}}{\sqrt{a^{2} c x^{2} + c} {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((I*a*x + 1)^2/(sqrt(a^2*c*x^2 + c)*(a^2*x^2 + 1)), x)","F",0
314,-2,0,0,0.000000," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
315,1,15,0,0.335526," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{i \, \log\left(i \, a x + 1\right)}{a \sqrt{c}}"," ",0,"-I*log(I*a*x + 1)/(a*sqrt(c))","A",0
316,1,40,0,0.421817," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{2 i \, \sqrt{a^{2} c x^{2} + c}}{i \, a^{2} c x + a c} - \frac{\operatorname{arsinh}\left(a x\right)}{a \sqrt{c}}"," ",0,"2*I*sqrt(a^2*c*x^2 + c)/(I*a^2*c*x + a*c) - arcsinh(a*x)/(a*sqrt(c))","A",0
317,1,35,0,0.335991," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{i \, \log\left(i \, a x + 1\right)}{a \sqrt{c}} + \frac{2}{a^{2} \sqrt{c} x - i \, a \sqrt{c}}"," ",0,"I*log(I*a*x + 1)/(a*sqrt(c)) + 2/(a^2*sqrt(c)*x - I*a*sqrt(c))","A",0
318,1,76,0,0.421681," ","integrate(1/(1+I*a*x)^4*(a^2*x^2+1)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{4 i \, \sqrt{a^{2} c x^{2} + c}}{3 \, {\left(a^{3} c x^{2} - 2 i \, a^{2} c x - a c\right)}} - \frac{8 i \, \sqrt{a^{2} c x^{2} + c}}{3 i \, a^{2} c x + 3 \, a c} + \frac{\operatorname{arsinh}\left(a x\right)}{a \sqrt{c}}"," ",0,"-4/3*I*sqrt(a^2*c*x^2 + c)/(a^3*c*x^2 - 2*I*a^2*c*x - a*c) - 8*I*sqrt(a^2*c*x^2 + c)/(3*I*a^2*c*x + 3*a*c) + arcsinh(a*x)/(a*sqrt(c))","A",0
319,1,59,0,0.428112," ","integrate((1+I*a*x)^5/(a^2*x^2+1)^4,x, algorithm=""maxima"")","\frac{-24 i \, a^{4} x^{4} - 80 \, a^{3} x^{3} + 96 i \, a^{2} x^{2} + 48 \, a x - 8 i}{48 \, {\left(a^{7} x^{6} + 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} + a\right)}}"," ",0,"1/48*(-24*I*a^4*x^4 - 80*a^3*x^3 + 96*I*a^2*x^2 + 48*a*x - 8*I)/(a^7*x^6 + 3*a^5*x^4 + 3*a^3*x^2 + a)","B",0
320,1,95,0,0.332936," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^(7/2),x, algorithm=""maxima"")","-\frac{a^{2} x^{3}}{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{5}{2}}} - \frac{x}{15 \, \sqrt{a^{2} x^{2} + 1}} + \frac{4 i \, a x^{2}}{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{5}{2}}} - \frac{x}{30 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} + \frac{11 \, x}{10 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{5}{2}}} - \frac{4 i}{15 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a}"," ",0,"-1/2*a^2*x^3/(a^2*x^2 + 1)^(5/2) - 1/15*x/sqrt(a^2*x^2 + 1) + 4/3*I*a*x^2/(a^2*x^2 + 1)^(5/2) - 1/30*x/(a^2*x^2 + 1)^(3/2) + 11/10*x/(a^2*x^2 + 1)^(5/2) - 4/15*I/((a^2*x^2 + 1)^(5/2)*a)","B",0
321,1,35,0,0.425078," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^3,x, algorithm=""maxima"")","\frac{4 i \, a^{2} x^{2} + 8 \, a x - 4 i}{8 \, {\left(a^{5} x^{4} + 2 \, a^{3} x^{2} + a\right)}}"," ",0,"1/8*(4*I*a^2*x^2 + 8*a*x - 4*I)/(a^5*x^4 + 2*a^3*x^2 + a)","B",0
322,1,45,0,0.322311," ","integrate((1+I*a*x)^2/(a^2*x^2+1)^(5/2),x, algorithm=""maxima"")","\frac{x}{3 \, \sqrt{a^{2} x^{2} + 1}} + \frac{2 \, x}{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}} - \frac{2 i}{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a}"," ",0,"1/3*x/sqrt(a^2*x^2 + 1) + 2/3*x/(a^2*x^2 + 1)^(3/2) - 2/3*I/((a^2*x^2 + 1)^(3/2)*a)","A",0
323,1,28,0,0.425511," ","integrate((1+I*a*x)/(a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{a x - i}{2 \, {\left(a^{3} x^{2} + a\right)}} + \frac{\arctan\left(a x\right)}{2 \, a}"," ",0,"1/2*(a*x - I)/(a^3*x^2 + a) + 1/2*arctan(a*x)/a","A",0
324,-2,0,0,0.000000," ","integrate(1/(1+I*a*x)/(a^2*x^2+1),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
325,1,59,0,0.414988," ","integrate(1/(1+I*a*x)^2/(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{i \, \sqrt{a^{2} x^{2} + 1}}{3 \, a^{3} x^{2} - 6 i \, a^{2} x - 3 \, a} + \frac{i \, \sqrt{a^{2} x^{2} + 1}}{3 i \, a^{2} x + 3 \, a}"," ",0,"-I*sqrt(a^2*x^2 + 1)/(3*a^3*x^2 - 6*I*a^2*x - 3*a) + I*sqrt(a^2*x^2 + 1)/(3*I*a^2*x + 3*a)","A",0
326,1,13,0,0.318812," ","integrate(1/(1+I*a*x)^3,x, algorithm=""maxima"")","\frac{i}{2 \, {\left(i \, a x + 1\right)}^{2} a}"," ",0,"1/2*I/((I*a*x + 1)^2*a)","A",0
327,1,100,0,0.320119," ","integrate(1/(1+I*a*x)^4*(a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{2 i \, \sqrt{a^{2} x^{2} + 1}}{-5 i \, a^{4} x^{3} - 15 \, a^{3} x^{2} + 15 i \, a^{2} x + 5 \, a} + \frac{i \, \sqrt{a^{2} x^{2} + 1}}{15 \, a^{3} x^{2} - 30 i \, a^{2} x - 15 \, a} - \frac{i \, \sqrt{a^{2} x^{2} + 1}}{15 i \, a^{2} x + 15 \, a}"," ",0,"2*I*sqrt(a^2*x^2 + 1)/(-5*I*a^4*x^3 - 15*a^3*x^2 + 15*I*a^2*x + 5*a) + I*sqrt(a^2*x^2 + 1)/(15*a^3*x^2 - 30*I*a^2*x - 15*a) - I*sqrt(a^2*x^2 + 1)/(15*I*a^2*x + 15*a)","B",0
328,0,0,0,0.000000," ","integrate((1+I*a*x)^5/(a^2*x^2+1)^(5/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)}^{5}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*x + 1)^5/((a^2*c*x^2 + c)^(3/2)*(a^2*x^2 + 1)^(5/2)), x)","F",0
329,0,0,0,0.000000," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)}^{4}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a^{2} x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate((I*a*x + 1)^4/((a^2*c*x^2 + c)^(3/2)*(a^2*x^2 + 1)^2), x)","F",0
330,-2,0,0,0.000000," ","integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
331,0,0,0,0.000000," ","integrate((1+I*a*x)^2/(a^2*x^2+1)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a x + 1\right)}^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((I*a*x + 1)^2/((a^2*c*x^2 + c)^(3/2)*(a^2*x^2 + 1)), x)","F",0
332,-2,0,0,0.000000," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
333,1,52,0,0.332336," ","integrate(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{c}}{2 \, a^{2} c^{2} x - 2 i \, a c^{2}} - \frac{i \, \log\left(a x - i\right)}{4 \, a c^{\frac{3}{2}}} + \frac{i \, \log\left(i \, a x - 1\right)}{4 \, a c^{\frac{3}{2}}}"," ",0,"sqrt(c)/(2*a^2*c^2*x - 2*I*a*c^2) - 1/4*I*log(a*x - I)/(a*c^(3/2)) + 1/4*I*log(I*a*x - 1)/(a*c^(3/2))","A",0
334,1,59,0,0.327417," ","integrate(1/(1+I*a*x)^2*(a^2*x^2+1)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{x}{3 \, \sqrt{a^{2} c x^{2} + c} c} + \frac{2 i}{3 i \, \sqrt{a^{2} c x^{2} + c} a^{2} c x + 3 \, \sqrt{a^{2} c x^{2} + c} a c}"," ",0,"1/3*x/(sqrt(a^2*c*x^2 + c)*c) + 2*I/(3*I*sqrt(a^2*c*x^2 + c)*a^2*c*x + 3*sqrt(a^2*c*x^2 + c)*a*c)","A",0
335,1,29,0,0.335068," ","integrate(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{1}{2 i \, a^{3} c^{\frac{3}{2}} x^{2} + 4 \, a^{2} c^{\frac{3}{2}} x - 2 i \, a c^{\frac{3}{2}}}"," ",0,"1/(2*I*a^3*c^(3/2)*x^2 + 4*a^2*c^(3/2)*x - 2*I*a*c^(3/2))","A",0
336,1,120,0,0.331837," ","integrate(1/(1+I*a*x)^4*(a^2*x^2+1)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{x}{15 \, \sqrt{a^{2} c x^{2} + c} c} - \frac{4 i}{5 \, \sqrt{a^{2} c x^{2} + c} a^{3} c x^{2} - 10 i \, \sqrt{a^{2} c x^{2} + c} a^{2} c x - 5 \, \sqrt{a^{2} c x^{2} + c} a c} - \frac{8 i}{15 i \, \sqrt{a^{2} c x^{2} + c} a^{2} c x + 15 \, \sqrt{a^{2} c x^{2} + c} a c}"," ",0,"-1/15*x/(sqrt(a^2*c*x^2 + c)*c) - 4*I/(5*sqrt(a^2*c*x^2 + c)*a^3*c*x^2 - 10*I*sqrt(a^2*c*x^2 + c)*a^2*c*x - 5*sqrt(a^2*c*x^2 + c)*a*c) - 8*I/(15*I*sqrt(a^2*c*x^2 + c)*a^2*c*x + 15*sqrt(a^2*c*x^2 + c)*a*c)","B",0
337,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{2} e^{\left(n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^2*e^(n*arctan(a*x)), x)","F",0
338,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)} e^{\left(n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)*e^(n*arctan(a*x)), x)","F",0
339,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x)),x, algorithm=""maxima"")","\int e^{\left(n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x)), x)","F",0
340,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x^{3} e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x^3*e^(n*arctan(a*x))/(a^2*c*x^2 + c), x)","F",0
341,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^2/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x^{2} e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x^2*e^(n*arctan(a*x))/(a^2*c*x^2 + c), x)","F",0
342,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x*e^(n*arctan(a*x))/(a^2*c*x^2 + c), x)","F",0
343,1,17,0,0.425722," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{e^{\left(n \arctan\left(a x\right)\right)}}{a c n}"," ",0,"e^(n*arctan(a*x))/(a*c*n)","A",0
344,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/x/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)} x}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/((a^2*c*x^2 + c)*x), x)","F",0
345,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/x^2/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)} x^{2}}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/((a^2*c*x^2 + c)*x^2), x)","F",0
346,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/x^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)} x^{3}}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/((a^2*c*x^2 + c)*x^3), x)","F",0
347,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{4}}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/(a^2*c*x^2 + c)^4, x)","F",0
348,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} e^{\left(n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*e^(n*arctan(a*x)), x)","F",0
349,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} e^{\left(n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*e^(n*arctan(a*x)), x)","F",0
350,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
351,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^2*(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2} e^{\left(n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^2*e^(n*arctan(a*x)), x)","F",0
352,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^2*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} x^{2} e^{\left(n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^2*e^(n*arctan(a*x)), x)","F",0
353,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3} e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^3*e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
354,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^2*e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
355,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x*e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
356,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
357,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/x/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c} x}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/(sqrt(a^2*c*x^2 + c)*x), x)","F",0
358,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c} x^{2}}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/(sqrt(a^2*c*x^2 + c)*x^2), x)","F",0
359,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c} x^{3}}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/(sqrt(a^2*c*x^2 + c)*x^3), x)","F",0
360,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(1/3),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{1}{3}} e^{\left(n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(1/3)*e^(n*arctan(a*x)), x)","F",0
361,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/3),x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/(a^2*c*x^2 + c)^(1/3), x)","F",0
362,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(2/3),x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/(a^2*c*x^2 + c)^(2/3), x)","F",0
363,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(4/3),x, algorithm=""maxima"")","\int \frac{e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(e^(n*arctan(a*x))/(a^2*c*x^2 + c)^(4/3), x)","F",0
364,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^m*(a^2*c*x^2+c),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)} x^{m} e^{\left(n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)*x^m*e^(n*arctan(a*x)), x)","F",0
365,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x^m*e^(n*arctan(a*x))/(a^2*c*x^2 + c), x)","F",0
366,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(x^m*e^(n*arctan(a*x))/(a^2*c*x^2 + c)^2, x)","F",0
367,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(x^m*e^(n*arctan(a*x))/(a^2*c*x^2 + c)^3, x)","F",0
368,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^m*e^(n*arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
369,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m*e^(n*arctan(a*x))/(a^2*c*x^2 + c)^(3/2), x)","F",0
370,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{m} e^{\left(n \arctan\left(a x\right)\right)}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^m*e^(n*arctan(a*x))/(a^2*c*x^2 + c)^(5/2), x)","F",0
371,0,0,0,0.000000," ","integrate(exp(n*arctan(a*x))*(a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{p} e^{\left(n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^p*e^(n*arctan(a*x)), x)","F",0
372,1,76,0,0.360679," ","integrate((a^2*c*x^2+c)^p/exp(2*I*p*arctan(a*x)),x, algorithm=""maxima"")","\frac{{\left(a c^{p} x + i \, c^{p}\right)} {\left(a^{2} x^{2} + 1\right)}^{p} \cos\left(2 \, p \arctan\left(a x\right)\right) - {\left(i \, a c^{p} x - c^{p}\right)} {\left(a^{2} x^{2} + 1\right)}^{p} \sin\left(2 \, p \arctan\left(a x\right)\right)}{2 \, a p + a}"," ",0,"((a*c^p*x + I*c^p)*(a^2*x^2 + 1)^p*cos(2*p*arctan(a*x)) - (I*a*c^p*x - c^p)*(a^2*x^2 + 1)^p*sin(2*p*arctan(a*x)))/(2*a*p + a)","A",0
373,0,0,0,0.000000," ","integrate(exp(2*I*p*arctan(a*x))*(a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{p} e^{\left(2 i \, p \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^p*e^(2*I*p*arctan(a*x)), x)","F",0
374,0,0,0,0.000000," ","integrate(exp(I*n*arctan(a*x))*x^2*(a^2*c*x^2+c)^(-1-1/2*n^2),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{-\frac{1}{2} \, n^{2} - 1} x^{2} e^{\left(i \, n \arctan\left(a x\right)\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(-1/2*n^2 - 1)*x^2*e^(I*n*arctan(a*x)), x)","F",0
375,1,292,0,0.539466," ","integrate((1+I*a*x)^6/(a^2*x^2+1)^3*x^2/(a^2*c*x^2+c)^19,x, algorithm=""maxima"")","\frac{20775821962641408 \, a^{7} x^{7} - 121192294782074880 i \, a^{6} x^{6} - 290861507476979712 \, a^{5} x^{5} + 363576884346224640 i \, a^{4} x^{4} + 242384589564149760 \, a^{3} x^{3} - 72715376869244928 i \, a^{2} x^{2} - 3462636993773568 i}{727153768692449280 \, {\left(a^{45} c^{19} x^{42} + 21 \, a^{43} c^{19} x^{40} + 210 \, a^{41} c^{19} x^{38} + 1330 \, a^{39} c^{19} x^{36} + 5985 \, a^{37} c^{19} x^{34} + 20349 \, a^{35} c^{19} x^{32} + 54264 \, a^{33} c^{19} x^{30} + 116280 \, a^{31} c^{19} x^{28} + 203490 \, a^{29} c^{19} x^{26} + 293930 \, a^{27} c^{19} x^{24} + 352716 \, a^{25} c^{19} x^{22} + 352716 \, a^{23} c^{19} x^{20} + 293930 \, a^{21} c^{19} x^{18} + 203490 \, a^{19} c^{19} x^{16} + 116280 \, a^{17} c^{19} x^{14} + 54264 \, a^{15} c^{19} x^{12} + 20349 \, a^{13} c^{19} x^{10} + 5985 \, a^{11} c^{19} x^{8} + 1330 \, a^{9} c^{19} x^{6} + 210 \, a^{7} c^{19} x^{4} + 21 \, a^{5} c^{19} x^{2} + a^{3} c^{19}\right)}}"," ",0,"1/727153768692449280*(20775821962641408*a^7*x^7 - 121192294782074880*I*a^6*x^6 - 290861507476979712*a^5*x^5 + 363576884346224640*I*a^4*x^4 + 242384589564149760*a^3*x^3 - 72715376869244928*I*a^2*x^2 - 3462636993773568*I)/(a^45*c^19*x^42 + 21*a^43*c^19*x^40 + 210*a^41*c^19*x^38 + 1330*a^39*c^19*x^36 + 5985*a^37*c^19*x^34 + 20349*a^35*c^19*x^32 + 54264*a^33*c^19*x^30 + 116280*a^31*c^19*x^28 + 203490*a^29*c^19*x^26 + 293930*a^27*c^19*x^24 + 352716*a^25*c^19*x^22 + 352716*a^23*c^19*x^20 + 293930*a^21*c^19*x^18 + 203490*a^19*c^19*x^16 + 116280*a^17*c^19*x^14 + 54264*a^15*c^19*x^12 + 20349*a^13*c^19*x^10 + 5985*a^11*c^19*x^8 + 1330*a^9*c^19*x^6 + 210*a^7*c^19*x^4 + 21*a^5*c^19*x^2 + a^3*c^19)","B",0
376,1,155,0,0.433366," ","integrate((1+I*a*x)^4/(a^2*x^2+1)^2*x^2/(a^2*c*x^2+c)^9,x, algorithm=""maxima"")","-\frac{5505024 \, a^{5} x^{5} - 20643840 i \, a^{4} x^{4} - 27525120 \, a^{3} x^{3} + 13762560 i \, a^{2} x^{2} + 1376256 i}{82575360 \, {\left(a^{23} c^{9} x^{20} + 10 \, a^{21} c^{9} x^{18} + 45 \, a^{19} c^{9} x^{16} + 120 \, a^{17} c^{9} x^{14} + 210 \, a^{15} c^{9} x^{12} + 252 \, a^{13} c^{9} x^{10} + 210 \, a^{11} c^{9} x^{8} + 120 \, a^{9} c^{9} x^{6} + 45 \, a^{7} c^{9} x^{4} + 10 \, a^{5} c^{9} x^{2} + a^{3} c^{9}\right)}}"," ",0,"-1/82575360*(5505024*a^5*x^5 - 20643840*I*a^4*x^4 - 27525120*a^3*x^3 + 13762560*I*a^2*x^2 + 1376256*I)/(a^23*c^9*x^20 + 10*a^21*c^9*x^18 + 45*a^19*c^9*x^16 + 120*a^17*c^9*x^14 + 210*a^15*c^9*x^12 + 252*a^13*c^9*x^10 + 210*a^11*c^9*x^8 + 120*a^9*c^9*x^6 + 45*a^7*c^9*x^4 + 10*a^5*c^9*x^2 + a^3*c^9)","B",0
377,1,62,0,0.416537," ","integrate((1+I*a*x)^2/(a^2*x^2+1)*x^2/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{16 \, a^{3} x^{3} - 24 i \, a^{2} x^{2} - 8 i}{48 \, {\left(a^{9} c^{3} x^{6} + 3 \, a^{7} c^{3} x^{4} + 3 \, a^{5} c^{3} x^{2} + a^{3} c^{3}\right)}}"," ",0,"1/48*(16*a^3*x^3 - 24*I*a^2*x^2 - 8*I)/(a^9*c^3*x^6 + 3*a^7*c^3*x^4 + 3*a^5*c^3*x^2 + a^3*c^3)","B",0
378,-2,0,0,0.000000," ","integrate(x^2/(1+I*a*x)^2*(a^2*x^2+1)/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
379,-2,0,0,0.000000," ","integrate(x^2/(1+I*a*x)^4*(a^2*x^2+1)^2/(a^2*c*x^2+c)^9,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
380,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
381,-2,0,0,0.000000," ","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
382,-2,0,0,0.000000," ","integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
383,1,55,0,0.337188," ","integrate(x^2/(1+I*a*x)*(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{c}}{2 \, a^{4} c^{2} x - 2 i \, a^{3} c^{2}} - \frac{3 i \, \log\left(a x - i\right)}{4 \, a^{3} c^{\frac{3}{2}}} - \frac{i \, \log\left(i \, a x - 1\right)}{4 \, a^{3} c^{\frac{3}{2}}}"," ",0,"-sqrt(c)/(2*a^4*c^2*x - 2*I*a^3*c^2) - 3/4*I*log(a*x - I)/(a^3*c^(3/2)) - 1/4*I*log(I*a*x - 1)/(a^3*c^(3/2))","A",0
384,1,93,0,0.356158," ","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=""maxima"")","\frac{3 \, a x - i}{24 i \, a^{12} c^{\frac{11}{2}} x^{9} + 72 \, a^{11} c^{\frac{11}{2}} x^{8} + 192 \, a^{9} c^{\frac{11}{2}} x^{6} - 144 i \, a^{8} c^{\frac{11}{2}} x^{5} + 144 \, a^{7} c^{\frac{11}{2}} x^{4} - 192 i \, a^{6} c^{\frac{11}{2}} x^{3} - 72 i \, a^{4} c^{\frac{11}{2}} x - 24 \, a^{3} c^{\frac{11}{2}}}"," ",0,"(3*a*x - I)/(24*I*a^12*c^(11/2)*x^9 + 72*a^11*c^(11/2)*x^8 + 192*a^9*c^(11/2)*x^6 - 144*I*a^8*c^(11/2)*x^5 + 144*a^7*c^(11/2)*x^4 - 192*I*a^6*c^(11/2)*x^3 - 72*I*a^4*c^(11/2)*x - 24*a^3*c^(11/2))","A",0
385,1,274,0,0.449604," ","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=""maxima"")","\frac{5 i \, a \sqrt{c} x + \sqrt{c}}{120 \, a^{28} c^{14} x^{25} - 600 i \, a^{27} c^{14} x^{24} - 4800 i \, a^{25} c^{14} x^{22} - 6000 \, a^{24} c^{14} x^{21} - 15120 i \, a^{23} c^{14} x^{20} - 33600 \, a^{22} c^{14} x^{19} - 19200 i \, a^{21} c^{14} x^{18} - 91800 \, a^{20} c^{14} x^{17} + 12600 i \, a^{19} c^{14} x^{16} - 149760 \, a^{18} c^{14} x^{15} + 86400 i \, a^{17} c^{14} x^{14} - 151200 \, a^{16} c^{14} x^{13} + 151200 i \, a^{15} c^{14} x^{12} - 86400 \, a^{14} c^{14} x^{11} + 149760 i \, a^{13} c^{14} x^{10} - 12600 \, a^{12} c^{14} x^{9} + 91800 i \, a^{11} c^{14} x^{8} + 19200 \, a^{10} c^{14} x^{7} + 33600 i \, a^{9} c^{14} x^{6} + 15120 \, a^{8} c^{14} x^{5} + 6000 i \, a^{7} c^{14} x^{4} + 4800 \, a^{6} c^{14} x^{3} + 600 \, a^{4} c^{14} x - 120 i \, a^{3} c^{14}}"," ",0,"(5*I*a*sqrt(c)*x + sqrt(c))/(120*a^28*c^14*x^25 - 600*I*a^27*c^14*x^24 - 4800*I*a^25*c^14*x^22 - 6000*a^24*c^14*x^21 - 15120*I*a^23*c^14*x^20 - 33600*a^22*c^14*x^19 - 19200*I*a^21*c^14*x^18 - 91800*a^20*c^14*x^17 + 12600*I*a^19*c^14*x^16 - 149760*a^18*c^14*x^15 + 86400*I*a^17*c^14*x^14 - 151200*a^16*c^14*x^13 + 151200*I*a^15*c^14*x^12 - 86400*a^14*c^14*x^11 + 149760*I*a^13*c^14*x^10 - 12600*a^12*c^14*x^9 + 91800*I*a^11*c^14*x^8 + 19200*a^10*c^14*x^7 + 33600*I*a^9*c^14*x^6 + 15120*a^8*c^14*x^5 + 6000*I*a^7*c^14*x^4 + 4800*a^6*c^14*x^3 + 600*a^4*c^14*x - 120*I*a^3*c^14)","B",0
