1,1,128,92,0.164000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^4,x)","\frac{i x^{4} \sqrt{a^{2} x^{2}+1}}{5 a}-\frac{4 i x^{2} \sqrt{a^{2} x^{2}+1}}{15 a^{3}}+\frac{8 i \sqrt{a^{2} x^{2}+1}}{15 a^{5}}+\frac{x^{3} \sqrt{a^{2} x^{2}+1}}{4 a^{2}}-\frac{3 x \sqrt{a^{2} x^{2}+1}}{8 a^{4}}+\frac{3 \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{8 a^{4} \sqrt{a^{2}}}"," ",0,"1/5*I*x^4*(a^2*x^2+1)^(1/2)/a-4/15*I*x^2*(a^2*x^2+1)^(1/2)/a^3+8/15*I/a^5*(a^2*x^2+1)^(1/2)+1/4*x^3*(a^2*x^2+1)^(1/2)/a^2-3/8/a^4*x*(a^2*x^2+1)^(1/2)+3/8/a^4*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)","A"
2,1,109,73,0.176000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^3,x)","\frac{i x^{3} \sqrt{a^{2} x^{2}+1}}{4 a}-\frac{3 i x \sqrt{a^{2} x^{2}+1}}{8 a^{3}}+\frac{3 i \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{8 a^{3} \sqrt{a^{2}}}+\frac{x^{2} \sqrt{a^{2} x^{2}+1}}{3 a^{2}}-\frac{2 \sqrt{a^{2} x^{2}+1}}{3 a^{4}}"," ",0,"1/4*I*x^3*(a^2*x^2+1)^(1/2)/a-3/8*I/a^3*x*(a^2*x^2+1)^(1/2)+3/8*I/a^3*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+1/3*x^2*(a^2*x^2+1)^(1/2)/a^2-2/3*(a^2*x^2+1)^(1/2)/a^4","A"
3,1,89,61,0.182000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^2,x)","\frac{i x^{2} \sqrt{a^{2} x^{2}+1}}{3 a}-\frac{2 i \sqrt{a^{2} x^{2}+1}}{3 a^{3}}+\frac{x \sqrt{a^{2} x^{2}+1}}{2 a^{2}}-\frac{\ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{2 a^{2} \sqrt{a^{2}}}"," ",0,"1/3*I/a*x^2*(a^2*x^2+1)^(1/2)-2/3*I/a^3*(a^2*x^2+1)^(1/2)+1/2*x*(a^2*x^2+1)^(1/2)/a^2-1/2/a^2*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)","A"
4,1,69,34,0.168000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)*x,x)","\frac{i x \sqrt{a^{2} x^{2}+1}}{2 a}-\frac{i \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{2 a \sqrt{a^{2}}}+\frac{\sqrt{a^{2} x^{2}+1}}{a^{2}}"," ",0,"1/2*I/a*x*(a^2*x^2+1)^(1/2)-1/2*I/a*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+(a^2*x^2+1)^(1/2)/a^2","A"
5,1,48,26,0.104000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2),x)","\frac{\ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}+\frac{i \sqrt{a^{2} x^{2}+1}}{a}"," ",0,"ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+I*(a^2*x^2+1)^(1/2)/a","A"
6,1,48,22,0.157000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)/x,x)","\frac{i a \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}-\arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)"," ",0,"I*a*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)-arctanh(1/(a^2*x^2+1)^(1/2))","B"
7,1,34,33,0.164000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^2,x)","-i a \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{\sqrt{a^{2} x^{2}+1}}{x}"," ",0,"-I*a*arctanh(1/(a^2*x^2+1)^(1/2))-(a^2*x^2+1)^(1/2)/x","A"
8,1,53,52,0.161000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^3,x)","-\frac{i a \sqrt{a^{2} x^{2}+1}}{x}-\frac{\sqrt{a^{2} x^{2}+1}}{2 x^{2}}+\frac{a^{2} \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)}{2}"," ",0,"-I*a*(a^2*x^2+1)^(1/2)/x-1/2*(a^2*x^2+1)^(1/2)/x^2+1/2*a^2*arctanh(1/(a^2*x^2+1)^(1/2))","A"
9,1,75,72,0.157000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^4,x)","-\frac{\sqrt{a^{2} x^{2}+1}}{3 x^{3}}+\frac{2 a^{2} \sqrt{a^{2} x^{2}+1}}{3 x}+i a \left(-\frac{\sqrt{a^{2} x^{2}+1}}{2 x^{2}}+\frac{a^{2} \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)}{2}\right)"," ",0,"-1/3*(a^2*x^2+1)^(1/2)/x^3+2/3*a^2*(a^2*x^2+1)^(1/2)/x+I*a*(-1/2*(a^2*x^2+1)^(1/2)/x^2+1/2*a^2*arctanh(1/(a^2*x^2+1)^(1/2)))","A"
10,1,97,91,0.162000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)/x^5,x)","i a \left(-\frac{\sqrt{a^{2} x^{2}+1}}{3 x^{3}}+\frac{2 a^{2} \sqrt{a^{2} x^{2}+1}}{3 x}\right)-\frac{\sqrt{a^{2} x^{2}+1}}{4 x^{4}}-\frac{3 a^{2} \left(-\frac{\sqrt{a^{2} x^{2}+1}}{2 x^{2}}+\frac{a^{2} \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)}{2}\right)}{4}"," ",0,"I*a*(-1/3*(a^2*x^2+1)^(1/2)/x^3+2/3*a^2*(a^2*x^2+1)^(1/2)/x)-1/4*(a^2*x^2+1)^(1/2)/x^4-3/4*a^2*(-1/2*(a^2*x^2+1)^(1/2)/x^2+1/2*a^2*arctanh(1/(a^2*x^2+1)^(1/2)))","A"
11,1,55,41,0.042000," ","int((1+I*a*x)^2/(a^2*x^2+1)*x^3,x)","-\frac{x^{4}}{4}+\frac{2 i x^{3}}{3 a}+\frac{x^{2}}{a^{2}}-\frac{2 i x}{a^{3}}-\frac{\ln \left(a^{2} x^{2}+1\right)}{a^{4}}+\frac{2 i \arctan \left(a x \right)}{a^{4}}"," ",0,"-1/4*x^4+2/3*I*x^3/a+x^2/a^2-2*I*x/a^3-1/a^4*ln(a^2*x^2+1)+2*I/a^4*arctan(a*x)","A"
12,1,47,34,0.045000," ","int((1+I*a*x)^2/(a^2*x^2+1)*x^2,x)","-\frac{x^{3}}{3}+\frac{i x^{2}}{a}+\frac{2 x}{a^{2}}-\frac{i \ln \left(a^{2} x^{2}+1\right)}{a^{3}}-\frac{2 \arctan \left(a x \right)}{a^{3}}"," ",0,"-1/3*x^3+I*x^2/a+2*x/a^2-I/a^3*ln(a^2*x^2+1)-2/a^3*arctan(a*x)","A"
13,1,38,25,0.043000," ","int((1+I*a*x)^2/(a^2*x^2+1)*x,x)","-\frac{x^{2}}{2}+\frac{2 i x}{a}+\frac{\ln \left(a^{2} x^{2}+1\right)}{a^{2}}-\frac{2 i \arctan \left(a x \right)}{a^{2}}"," ",0,"-1/2*x^2+2*I*x/a+1/a^2*ln(a^2*x^2+1)-2*I/a^2*arctan(a*x)","A"
14,1,30,17,0.040000," ","int((1+I*a*x)^2/(a^2*x^2+1),x)","-x +\frac{i \ln \left(a^{2} x^{2}+1\right)}{a}+\frac{2 \arctan \left(a x \right)}{a}"," ",0,"-x+I/a*ln(a^2*x^2+1)+2*arctan(a*x)/a","A"
15,1,23,12,0.045000," ","int((1+I*a*x)^2/(a^2*x^2+1)/x,x)","\ln \left(x \right)+2 i \arctan \left(a x \right)-\ln \left(a^{2} x^{2}+1\right)"," ",0,"ln(x)+2*I*arctan(a*x)-ln(a^2*x^2+1)","A"
16,1,34,23,0.047000," ","int((1+I*a*x)^2/(a^2*x^2+1)/x^2,x)","-\frac{1}{x}+2 i a \ln \left(x \right)-i a \ln \left(a^{2} x^{2}+1\right)-2 a \arctan \left(a x \right)"," ",0,"-1/x+2*I*a*ln(x)-I*a*ln(a^2*x^2+1)-2*a*arctan(a*x)","A"
17,1,45,32,0.046000," ","int((1+I*a*x)^2/(a^2*x^2+1)/x^3,x)","-\frac{1}{2 x^{2}}-\frac{2 i a}{x}-2 a^{2} \ln \left(x \right)-2 i a^{2} \arctan \left(a x \right)+a^{2} \ln \left(a^{2} x^{2}+1\right)"," ",0,"-1/2/x^2-2*I*a/x-2*a^2*ln(x)-2*I*a^2*arctan(a*x)+a^2*ln(a^2*x^2+1)","A"
18,1,55,42,0.050000," ","int((1+I*a*x)^2/(a^2*x^2+1)/x^4,x)","-\frac{1}{3 x^{3}}-2 i a^{3} \ln \left(x \right)-\frac{i a}{x^{2}}+\frac{2 a^{2}}{x}+i a^{3} \ln \left(a^{2} x^{2}+1\right)+2 a^{3} \arctan \left(a x \right)"," ",0,"-1/3/x^3-2*I*a^3*ln(x)-I*a/x^2+2*a^2/x+I*a^3*ln(a^2*x^2+1)+2*a^3*arctan(a*x)","A"
19,1,143,114,0.163000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^3,x)","-\frac{i a \,x^{5}}{4 \sqrt{a^{2} x^{2}+1}}+\frac{17 i x^{3}}{8 a \sqrt{a^{2} x^{2}+1}}+\frac{51 i x}{8 a^{3} \sqrt{a^{2} x^{2}+1}}-\frac{51 i \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{8 a^{3} \sqrt{a^{2}}}-\frac{x^{4}}{\sqrt{a^{2} x^{2}+1}}+\frac{5 x^{2}}{a^{2} \sqrt{a^{2} x^{2}+1}}+\frac{10}{a^{4} \sqrt{a^{2} x^{2}+1}}"," ",0,"-1/4*I*a*x^5/(a^2*x^2+1)^(1/2)+17/8*I/a*x^3/(a^2*x^2+1)^(1/2)+51/8*I/a^3*x/(a^2*x^2+1)^(1/2)-51/8*I/a^3*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)-x^4/(a^2*x^2+1)^(1/2)+5*x^2/a^2/(a^2*x^2+1)^(1/2)+10/a^4/(a^2*x^2+1)^(1/2)","A"
20,1,123,85,0.159000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^2,x)","-\frac{i a \,x^{4}}{3 \sqrt{a^{2} x^{2}+1}}+\frac{13 i x^{2}}{3 a \sqrt{a^{2} x^{2}+1}}+\frac{26 i}{3 a^{3} \sqrt{a^{2} x^{2}+1}}-\frac{3 x^{3}}{2 \sqrt{a^{2} x^{2}+1}}-\frac{11 x}{2 a^{2} \sqrt{a^{2} x^{2}+1}}+\frac{11 \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{2 a^{2} \sqrt{a^{2}}}"," ",0,"-1/3*I*a*x^4/(a^2*x^2+1)^(1/2)+13/3*I/a*x^2/(a^2*x^2+1)^(1/2)+26/3*I/a^3/(a^2*x^2+1)^(1/2)-3/2*x^3/(a^2*x^2+1)^(1/2)-11/2*x/a^2/(a^2*x^2+1)^(1/2)+11/2/a^2*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)","A"
21,1,104,77,0.156000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x,x)","-\frac{i a \,x^{3}}{2 \sqrt{a^{2} x^{2}+1}}-\frac{9 i x}{2 a \sqrt{a^{2} x^{2}+1}}+\frac{9 i \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{2 a \sqrt{a^{2}}}-\frac{3 x^{2}}{\sqrt{a^{2} x^{2}+1}}-\frac{7}{a^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"-1/2*I*a*x^3/(a^2*x^2+1)^(1/2)-9/2*I/a*x/(a^2*x^2+1)^(1/2)+9/2*I/a*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)-3*x^2/(a^2*x^2+1)^(1/2)-7/a^2/(a^2*x^2+1)^(1/2)","A"
22,1,81,53,0.114000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2),x)","\frac{4 x}{\sqrt{a^{2} x^{2}+1}}-\frac{i a \,x^{2}}{\sqrt{a^{2} x^{2}+1}}-\frac{5 i}{a \sqrt{a^{2} x^{2}+1}}-\frac{3 \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}"," ",0,"4*x/(a^2*x^2+1)^(1/2)-I*a*x^2/(a^2*x^2+1)^(1/2)-5*I/a/(a^2*x^2+1)^(1/2)-3*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)","A"
23,1,77,44,0.143000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x,x)","\frac{4 i a x}{\sqrt{a^{2} x^{2}+1}}-\frac{i a \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}+\frac{4}{\sqrt{a^{2} x^{2}+1}}-\arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)"," ",0,"4*I*a*x/(a^2*x^2+1)^(1/2)-I*a*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+4/(a^2*x^2+1)^(1/2)-arctanh(1/(a^2*x^2+1)^(1/2))","A"
24,1,80,55,0.148000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x^2,x)","\frac{i a}{\sqrt{a^{2} x^{2}+1}}-\frac{5 a^{2} x}{\sqrt{a^{2} x^{2}+1}}+3 i a \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}-\arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)\right)-\frac{1}{x \sqrt{a^{2} x^{2}+1}}"," ",0,"I*a/(a^2*x^2+1)^(1/2)-5*a^2*x/(a^2*x^2+1)^(1/2)+3*I*a*(1/(a^2*x^2+1)^(1/2)-arctanh(1/(a^2*x^2+1)^(1/2)))-1/x/(a^2*x^2+1)^(1/2)","A"
25,1,105,77,0.153000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x^3,x)","-\frac{i a^{3} x}{\sqrt{a^{2} x^{2}+1}}-\frac{9 a^{2} \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}-\arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2}+3 i a \left(-\frac{1}{x \sqrt{a^{2} x^{2}+1}}-\frac{2 a^{2} x}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{1}{2 x^{2} \sqrt{a^{2} x^{2}+1}}"," ",0,"-I*a^3*x/(a^2*x^2+1)^(1/2)-9/2*a^2*(1/(a^2*x^2+1)^(1/2)-arctanh(1/(a^2*x^2+1)^(1/2)))+3*I*a*(-1/x/(a^2*x^2+1)^(1/2)-2*a^2*x/(a^2*x^2+1)^(1/2))-1/2/x^2/(a^2*x^2+1)^(1/2)","A"
26,1,141,96,0.150000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/x^4,x)","-\frac{1}{3 x^{3} \sqrt{a^{2} x^{2}+1}}-\frac{13 a^{2} \left(-\frac{1}{x \sqrt{a^{2} x^{2}+1}}-\frac{2 a^{2} x}{\sqrt{a^{2} x^{2}+1}}\right)}{3}-i a^{3} \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}-\arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)\right)+3 i a \left(-\frac{1}{2 x^{2} \sqrt{a^{2} x^{2}+1}}-\frac{3 a^{2} \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}-\arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)\right)}{2}\right)"," ",0,"-1/3/x^3/(a^2*x^2+1)^(1/2)-13/3*a^2*(-1/x/(a^2*x^2+1)^(1/2)-2*a^2*x/(a^2*x^2+1)^(1/2))-I*a^3*(1/(a^2*x^2+1)^(1/2)-arctanh(1/(a^2*x^2+1)^(1/2)))+3*I*a*(-1/2/x^2/(a^2*x^2+1)^(1/2)-3/2*a^2*(1/(a^2*x^2+1)^(1/2)-arctanh(1/(a^2*x^2+1)^(1/2))))","A"
27,1,70,56,0.060000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2*x^3,x)","\frac{x^{4}}{4}-\frac{4 i x^{3}}{3 a}-\frac{4 x^{2}}{a^{2}}+\frac{12 i x}{a^{3}}+\frac{4 i}{a^{4} \left(a x +i\right)}+\frac{8 \ln \left(a^{2} x^{2}+1\right)}{a^{4}}-\frac{16 i \arctan \left(a x \right)}{a^{4}}"," ",0,"1/4*x^4-4/3*I*x^3/a-4*x^2/a^2+12*I*x/a^3+4*I/a^4/(I+a*x)+8/a^4*ln(a^2*x^2+1)-16*I/a^4*arctan(a*x)","A"
28,1,60,47,0.056000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2*x^2,x)","\frac{x^{3}}{3}-\frac{2 i x^{2}}{a}-\frac{8 x}{a^{2}}-\frac{4}{a^{3} \left(a x +i\right)}+\frac{6 i \ln \left(a^{2} x^{2}+1\right)}{a^{3}}+\frac{12 \arctan \left(a x \right)}{a^{3}}"," ",0,"1/3*x^3-2*I*x^2/a-8*x/a^2-4/a^3/(I+a*x)+6*I/a^3*ln(a^2*x^2+1)+12/a^3*arctan(a*x)","A"
29,1,53,39,0.056000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2*x,x)","\frac{x^{2}}{2}-\frac{4 i x}{a}-\frac{4 i}{a^{2} \left(a x +i\right)}-\frac{4 \ln \left(a^{2} x^{2}+1\right)}{a^{2}}+\frac{8 i \arctan \left(a x \right)}{a^{2}}"," ",0,"1/2*x^2-4*I*x/a-4*I/a^2/(I+a*x)-4/a^2*ln(a^2*x^2+1)+8*I/a^2*arctan(a*x)","A"
30,1,41,28,0.052000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2,x)","x +\frac{4}{a \left(a x +i\right)}-\frac{2 i \ln \left(a^{2} x^{2}+1\right)}{a}-\frac{4 \arctan \left(a x \right)}{a}"," ",0,"x+4/a/(I+a*x)-2*I/a*ln(a^2*x^2+1)-4*arctan(a*x)/a","A"
31,1,15,14,0.054000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2/x,x)","\frac{4 i}{a x +i}+\ln \left(x \right)"," ",0,"4*I/(I+a*x)+ln(x)","A"
32,1,45,34,0.059000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2/x^2,x)","-\frac{1}{x}+4 i a \ln \left(x \right)-\frac{4 a}{a x +i}-2 i a \ln \left(a^{2} x^{2}+1\right)-4 a \arctan \left(a x \right)"," ",0,"-1/x+4*I*a*ln(x)-4*a/(I+a*x)-2*I*a*ln(a^2*x^2+1)-4*a*arctan(a*x)","A"
33,1,60,46,0.056000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2/x^3,x)","-\frac{1}{2 x^{2}}-\frac{4 i a}{x}-8 a^{2} \ln \left(x \right)-\frac{4 i a^{2}}{a x +i}+4 a^{2} \ln \left(a^{2} x^{2}+1\right)-8 i a^{2} \arctan \left(a x \right)"," ",0,"-1/2/x^2-4*I*a/x-8*a^2*ln(x)-4*I*a^2/(I+a*x)+4*a^2*ln(a^2*x^2+1)-8*I*a^2*arctan(a*x)","A"
34,1,68,55,0.058000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2/x^4,x)","-\frac{1}{3 x^{3}}-12 i a^{3} \ln \left(x \right)-\frac{2 i a}{x^{2}}+\frac{8 a^{2}}{x}+\frac{4 a^{3}}{a x +i}+6 i a^{3} \ln \left(a^{2} x^{2}+1\right)+12 a^{3} \arctan \left(a x \right)"," ",0,"-1/3/x^3-12*I*a^3*ln(x)-2*I*a/x^2+8*a^2/x+4*a^3/(I+a*x)+6*I*a^3*ln(a^2*x^2+1)+12*a^3*arctan(a*x)","A"
35,1,187,73,0.190000," ","int(x^3/(1+I*a*x)*(a^2*x^2+1)^(1/2),x)","-\frac{i x \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4 a^{3}}+\frac{5 i x \sqrt{a^{2} x^{2}+1}}{8 a^{3}}+\frac{5 i \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{8 a^{3} \sqrt{a^{2}}}+\frac{\left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 a^{4}}-\frac{\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}}{a^{4}}-\frac{i \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{a^{3} \sqrt{a^{2}}}"," ",0,"-1/4*I/a^3*x*(a^2*x^2+1)^(3/2)+5/8*I/a^3*x*(a^2*x^2+1)^(1/2)+5/8*I/a^3*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+1/3/a^4*(a^2*x^2+1)^(3/2)-1/a^4*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)-I/a^3*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)","B"
36,1,168,61,0.165000," ","int(x^2/(1+I*a*x)*(a^2*x^2+1)^(1/2),x)","-\frac{i \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 a^{3}}+\frac{x \sqrt{a^{2} x^{2}+1}}{2 a^{2}}+\frac{\ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{2 a^{2} \sqrt{a^{2}}}+\frac{i \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}}{a^{3}}-\frac{\ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{a^{2} \sqrt{a^{2}}}"," ",0,"-1/3*I*(a^2*x^2+1)^(3/2)/a^3+1/2*x*(a^2*x^2+1)^(1/2)/a^2+1/2/a^2*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+I/a^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)-1/a^2*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)","B"
37,1,152,34,0.155000," ","int(x/(1+I*a*x)*(a^2*x^2+1)^(1/2),x)","-\frac{i x \sqrt{a^{2} x^{2}+1}}{2 a}-\frac{i \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{2 a \sqrt{a^{2}}}+\frac{\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}}{a^{2}}+\frac{i \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{a \sqrt{a^{2}}}"," ",0,"-1/2*I/a*x*(a^2*x^2+1)^(1/2)-1/2*I/a*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+1/a^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)+I/a*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)","B"
38,1,97,26,0.102000," ","int(1/(1+I*a*x)*(a^2*x^2+1)^(1/2),x)","-\frac{i \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}}{a}+\frac{\ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}"," ",0,"-I/a*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)+ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)","B"
39,1,121,22,0.162000," ","int(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x,x)","\sqrt{a^{2} x^{2}+1}-\arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)-\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}-\frac{i a \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}"," ",0,"(a^2*x^2+1)^(1/2)-arctanh(1/(a^2*x^2+1)^(1/2))-((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)-I*a*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)","B"
40,1,194,33,0.168000," ","int(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^2,x)","i a \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)-i a \sqrt{a^{2} x^{2}+1}-\frac{\left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{x}+a^{2} x \sqrt{a^{2} x^{2}+1}+\frac{a^{2} \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}+i a \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}-\frac{a^{2} \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}"," ",0,"I*a*arctanh(1/(a^2*x^2+1)^(1/2))-I*a*(a^2*x^2+1)^(1/2)-1/x*(a^2*x^2+1)^(3/2)+a^2*x*(a^2*x^2+1)^(1/2)+a^2*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+I*a*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)-a^2*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)","B"
41,1,219,52,0.167000," ","int(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^3,x)","\frac{a^{2} \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)}{2}-\frac{a^{2} \sqrt{a^{2} x^{2}+1}}{2}+\frac{i a \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{x}-i a^{3} x \sqrt{a^{2} x^{2}+1}-\frac{i a^{3} \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}+a^{2} \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}+\frac{i a^{3} \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}-\frac{\left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{2 x^{2}}"," ",0,"1/2*a^2*arctanh(1/(a^2*x^2+1)^(1/2))-1/2*a^2*(a^2*x^2+1)^(1/2)+I*a/x*(a^2*x^2+1)^(3/2)-I*a^3*x*(a^2*x^2+1)^(1/2)-I*a^3*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+a^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)+I*a^3*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)-1/2/x^2*(a^2*x^2+1)^(3/2)","B"
42,1,237,72,0.170000," ","int(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^4,x)","-\frac{\left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 x^{3}}-\frac{i a^{3} \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)}{2}+\frac{i a^{3} \sqrt{a^{2} x^{2}+1}}{2}+\frac{a^{2} \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{x}-a^{4} x \sqrt{a^{2} x^{2}+1}-\frac{a^{4} \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}-i a^{3} \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}+\frac{a^{4} \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}+\frac{i a \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{2 x^{2}}"," ",0,"-1/3/x^3*(a^2*x^2+1)^(3/2)-1/2*I*a^3*arctanh(1/(a^2*x^2+1)^(1/2))+1/2*I*a^3*(a^2*x^2+1)^(1/2)+a^2/x*(a^2*x^2+1)^(3/2)-a^4*x*(a^2*x^2+1)^(1/2)-a^4*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)-I*a^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)+a^4*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)+1/2*I*a/x^2*(a^2*x^2+1)^(3/2)","B"
43,1,259,91,0.179000," ","int(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/x^5,x)","\frac{i a \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 x^{3}}-\frac{3 a^{4} \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)}{8}+\frac{3 a^{4} \sqrt{a^{2} x^{2}+1}}{8}-\frac{i a^{3} \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{x}+i a^{5} x \sqrt{a^{2} x^{2}+1}+\frac{i a^{5} \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}-a^{4} \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}-\frac{i a^{5} \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}-\frac{\left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4 x^{4}}+\frac{5 a^{2} \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{8 x^{2}}"," ",0,"1/3*I*a/x^3*(a^2*x^2+1)^(3/2)-3/8*a^4*arctanh(1/(a^2*x^2+1)^(1/2))+3/8*a^4*(a^2*x^2+1)^(1/2)-I*a^3/x*(a^2*x^2+1)^(3/2)+I*a^5*x*(a^2*x^2+1)^(1/2)+I*a^5*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)-a^4*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)-I*a^5*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)-1/4/x^4*(a^2*x^2+1)^(3/2)+5/8*a^2/x^2*(a^2*x^2+1)^(3/2)","B"
44,1,55,42,0.053000," ","int(x^3/(1+I*a*x)^2*(a^2*x^2+1),x)","-\frac{x^{4}}{4}-\frac{2 i x^{3}}{3 a}+\frac{x^{2}}{a^{2}}+\frac{2 i x}{a^{3}}-\frac{\ln \left(a^{2} x^{2}+1\right)}{a^{4}}-\frac{2 i \arctan \left(a x \right)}{a^{4}}"," ",0,"-1/4*x^4-2/3*I*x^3/a+x^2/a^2+2*I*x/a^3-1/a^4*ln(a^2*x^2+1)-2*I/a^4*arctan(a*x)","A"
45,1,47,35,0.053000," ","int(x^2/(1+I*a*x)^2*(a^2*x^2+1),x)","-\frac{x^{3}}{3}-\frac{i x^{2}}{a}+\frac{2 x}{a^{2}}+\frac{i \ln \left(a^{2} x^{2}+1\right)}{a^{3}}-\frac{2 \arctan \left(a x \right)}{a^{3}}"," ",0,"-1/3*x^3-I*x^2/a+2*x/a^2+I/a^3*ln(a^2*x^2+1)-2/a^3*arctan(a*x)","A"
46,1,38,26,0.052000," ","int(x/(1+I*a*x)^2*(a^2*x^2+1),x)","-\frac{x^{2}}{2}-\frac{2 i x}{a}+\frac{\ln \left(a^{2} x^{2}+1\right)}{a^{2}}+\frac{2 i \arctan \left(a x \right)}{a^{2}}"," ",0,"-1/2*x^2-2*I*x/a+1/a^2*ln(a^2*x^2+1)+2*I/a^2*arctan(a*x)","A"
47,1,30,18,0.050000," ","int(1/(1+I*a*x)^2*(a^2*x^2+1),x)","-x -\frac{i \ln \left(a^{2} x^{2}+1\right)}{a}+\frac{2 \arctan \left(a x \right)}{a}"," ",0,"-x-I/a*ln(a^2*x^2+1)+2*arctan(a*x)/a","A"
48,1,23,13,0.055000," ","int(1/(1+I*a*x)^2*(a^2*x^2+1)/x,x)","\ln \left(x \right)-\ln \left(a^{2} x^{2}+1\right)-2 i \arctan \left(a x \right)"," ",0,"ln(x)-ln(a^2*x^2+1)-2*I*arctan(a*x)","A"
49,1,34,24,0.066000," ","int(1/(1+I*a*x)^2*(a^2*x^2+1)/x^2,x)","-\frac{1}{x}-2 i a \ln \left(x \right)-2 a \arctan \left(a x \right)+i a \ln \left(a^{2} x^{2}+1\right)"," ",0,"-1/x-2*I*a*ln(x)-2*a*arctan(a*x)+I*a*ln(a^2*x^2+1)","A"
50,1,45,33,0.059000," ","int(1/(1+I*a*x)^2*(a^2*x^2+1)/x^3,x)","-\frac{1}{2 x^{2}}+\frac{2 i a}{x}-2 a^{2} \ln \left(x \right)+2 i a^{2} \arctan \left(a x \right)+a^{2} \ln \left(a^{2} x^{2}+1\right)"," ",0,"-1/2/x^2+2*I*a/x-2*a^2*ln(x)+2*I*a^2*arctan(a*x)+a^2*ln(a^2*x^2+1)","A"
51,1,55,43,0.059000," ","int(1/(1+I*a*x)^2*(a^2*x^2+1)/x^4,x)","-\frac{1}{3 x^{3}}+\frac{i a}{x^{2}}+2 i a^{3} \ln \left(x \right)+\frac{2 a^{2}}{x}+2 a^{3} \arctan \left(a x \right)-i a^{3} \ln \left(a^{2} x^{2}+1\right)"," ",0,"-1/3/x^3+I*a/x^2+2*I*a^3*ln(x)+2*a^2/x+2*a^3*arctan(a*x)-I*a^3*ln(a^2*x^2+1)","A"
52,1,296,114,0.179000," ","int(x^3/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x)","\frac{i x \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4 a^{3}}+\frac{3 i x \sqrt{a^{2} x^{2}+1}}{8 a^{3}}+\frac{3 i \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{8 a^{3} \sqrt{a^{2}}}+\frac{i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a^{7} \left(x -\frac{i}{a}\right)^{3}}-\frac{5 \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a^{6} \left(x -\frac{i}{a}\right)^{2}}+\frac{4 \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}}{a^{4}}+\frac{6 i \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\, x}{a^{3}}+\frac{6 i \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{a^{3} \sqrt{a^{2}}}"," ",0,"1/4*I/a^3*x*(a^2*x^2+1)^(3/2)+3/8*I/a^3*x*(a^2*x^2+1)^(1/2)+3/8*I/a^3*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+I/a^7/(x-I/a)^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)-5/a^6/(x-I/a)^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)+4/a^4*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)+6*I/a^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)*x+6*I/a^3*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)","B"
53,1,224,85,0.172000," ","int(x^2/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x)","\frac{4 i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a^{5} \left(x -\frac{i}{a}\right)^{2}}-\frac{11 i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}}{3 a^{3}}+\frac{11 \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\, x}{2 a^{2}}+\frac{11 \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{2 a^{2} \sqrt{a^{2}}}+\frac{\left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a^{6} \left(x -\frac{i}{a}\right)^{3}}"," ",0,"4*I/a^5/(x-I/a)^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)-11/3*I/a^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)+11/2/a^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)*x+11/2/a^2*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)+1/a^6/(x-I/a)^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)","B"
54,1,226,77,0.169000," ","int(x/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x)","\frac{3 \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a^{4} \left(x -\frac{i}{a}\right)^{2}}-\frac{3 \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}}{a^{2}}-\frac{9 i \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\, x}{2 a}-\frac{9 i \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{2 a \sqrt{a^{2}}}-\frac{i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a^{5} \left(x -\frac{i}{a}\right)^{3}}"," ",0,"3/a^4/(x-I/a)^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)-3/a^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)-9/2*I/a*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)*x-9/2*I/a*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)-I/a^5/(x-I/a)^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)","B"
55,1,219,53,0.111000," ","int(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x)","-\frac{\left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a^{4} \left(x -\frac{i}{a}\right)^{3}}-\frac{2 i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x -\frac{i}{a}\right)^{2}}+\frac{2 i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}}{a}-3 \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\, x -\frac{3 \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}"," ",0,"-1/a^4/(x-I/a)^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)-2*I/a^3/(x-I/a)^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)+2*I/a*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)-3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)*x-3*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)","B"
56,1,257,45,0.171000," ","int(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x,x)","\frac{\left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3}+\sqrt{a^{2} x^{2}+1}-\arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x -\frac{i}{a}\right)^{3}}-\frac{\left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a^{2} \left(x -\frac{i}{a}\right)^{2}}+\frac{2 \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}}{3}+i a \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\, x +\frac{i a \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}"," ",0,"1/3*(a^2*x^2+1)^(3/2)+(a^2*x^2+1)^(1/2)-arctanh(1/(a^2*x^2+1)^(1/2))+I/a^3/(x-I/a)^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)-1/a^2/(x-I/a)^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)+2/3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)+I*a*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)*x+I*a*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)","B"
57,1,305,56,0.168000," ","int(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^2,x)","i a \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}+3 i a \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)-i a \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}-\frac{\left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}{x}+a^{2} x \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}+\frac{3 a^{2} x \sqrt{a^{2} x^{2}+1}}{2}+\frac{3 a^{2} \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{2 \sqrt{a^{2}}}-3 i a \sqrt{a^{2} x^{2}+1}-\frac{3 a^{2} \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\, x}{2}-\frac{3 a^{2} \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{2 \sqrt{a^{2}}}+\frac{\left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a^{2} \left(x -\frac{i}{a}\right)^{3}}"," ",0,"I*a*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)+3*I*a*arctanh(1/(a^2*x^2+1)^(1/2))-I*a*(a^2*x^2+1)^(3/2)-1/x*(a^2*x^2+1)^(5/2)+a^2*x*(a^2*x^2+1)^(3/2)+3/2*a^2*x*(a^2*x^2+1)^(1/2)+3/2*a^2*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)-3*I*a*(a^2*x^2+1)^(1/2)-3/2*a^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)*x-3/2*a^2*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)+1/a^2/(x-I/a)^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)","B"
58,1,376,78,0.175000," ","int(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^3,x)","-\frac{3 a^{2} \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{2}-\frac{9 a^{2} \sqrt{a^{2} x^{2}+1}}{2}+\frac{9 a^{2} \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)}{2}-\frac{i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{a \left(x -\frac{i}{a}\right)^{3}}-\frac{9 i a^{3} x \sqrt{a^{2} x^{2}+1}}{2}-\frac{9 i a^{3} \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{2 \sqrt{a^{2}}}-3 i a^{3} x \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}+3 a^{2} \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}+\frac{3 i a \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}{x}+\frac{9 i a^{3} \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\, x}{2}-\frac{\left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{\left(x -\frac{i}{a}\right)^{2}}+\frac{9 i a^{3} \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{2 \sqrt{a^{2}}}-\frac{\left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}{2 x^{2}}"," ",0,"-3/2*a^2*(a^2*x^2+1)^(3/2)-9/2*a^2*(a^2*x^2+1)^(1/2)+9/2*a^2*arctanh(1/(a^2*x^2+1)^(1/2))-I/a/(x-I/a)^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)-9/2*I*a^3*x*(a^2*x^2+1)^(1/2)-9/2*I*a^3*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)-3*I*a^3*x*(a^2*x^2+1)^(3/2)+3*a^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)+3*I*a/x*(a^2*x^2+1)^(5/2)+9/2*I*a^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)*x-1/(x-I/a)^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)+9/2*I*a^3*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)-1/2/x^2*(a^2*x^2+1)^(5/2)","B"
59,1,392,97,0.176000," ","int(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^4,x)","-\frac{\left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}{3 x^{3}}+\frac{16 a^{2} \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}{3 x}-\frac{16 a^{4} x \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3}-8 a^{4} x \sqrt{a^{2} x^{2}+1}-\frac{8 a^{4} \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}+\frac{2 i a \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{\left(x -\frac{i}{a}\right)^{2}}-\frac{11 i a^{3} \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)}{2}+8 a^{4} \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\, x +\frac{8 a^{4} \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}+\frac{11 i a^{3} \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{6}+\frac{3 i a \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}{2 x^{2}}+\frac{11 i a^{3} \sqrt{a^{2} x^{2}+1}}{2}-\frac{\left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{\left(x -\frac{i}{a}\right)^{3}}-\frac{16 i a^{3} \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}}{3}"," ",0,"-1/3/x^3*(a^2*x^2+1)^(5/2)+16/3*a^2/x*(a^2*x^2+1)^(5/2)-16/3*a^4*x*(a^2*x^2+1)^(3/2)-8*a^4*x*(a^2*x^2+1)^(1/2)-8*a^4*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+2*I*a/(x-I/a)^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)-11/2*I*a^3*arctanh(1/(a^2*x^2+1)^(1/2))+8*a^4*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)*x+8*a^4*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)+11/6*I*a^3*(a^2*x^2+1)^(3/2)+3/2*I*a/x^2*(a^2*x^2+1)^(5/2)+11/2*I*a^3*(a^2*x^2+1)^(1/2)-1/(x-I/a)^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)-16/3*I*a^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)","B"
60,1,416,117,0.193000," ","int(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/x^5,x)","\frac{3 a^{2} \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{\left(x -\frac{i}{a}\right)^{2}}+\frac{51 a^{4} \sqrt{a^{2} x^{2}+1}}{8}-8 a^{4} \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}+\frac{12 i a^{5} \ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}+12 i a^{5} x \sqrt{a^{2} x^{2}+1}+8 i a^{5} x \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}-\frac{8 i a^{3} \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}{x}+\frac{17 a^{4} \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{8}+\frac{i a \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{\left(x -\frac{i}{a}\right)^{3}}-\frac{12 i a^{5} \ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}+\frac{i a \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{3}}-\frac{51 a^{4} \arctanh \left(\frac{1}{\sqrt{a^{2} x^{2}+1}}\right)}{8}-\frac{\left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}{4 x^{4}}-12 i a^{5} \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\, x +\frac{23 a^{2} \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}{8 x^{2}}"," ",0,"3*a^2/(x-I/a)^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)+51/8*a^4*(a^2*x^2+1)^(1/2)-8*a^4*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)+12*I*a^5*ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+12*I*a^5*x*(a^2*x^2+1)^(1/2)+8*I*a^5*x*(a^2*x^2+1)^(3/2)-8*I*a^3/x*(a^2*x^2+1)^(5/2)+17/8*a^4*(a^2*x^2+1)^(3/2)+I*a/(x-I/a)^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)-12*I*a^5*ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)+I*a/x^3*(a^2*x^2+1)^(5/2)-51/8*a^4*arctanh(1/(a^2*x^2+1)^(1/2))-1/4/x^4*(a^2*x^2+1)^(5/2)-12*I*a^5*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)*x+23/8*a^2/x^2*(a^2*x^2+1)^(5/2)","B"
61,0,0,249,0.248000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x^2,x)","\int \sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}\, x^{2}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x^2,x)","F"
62,0,0,219,0.168000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x,x)","\int \sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}\, x\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x,x)","F"
63,0,0,201,0.112000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","\int \sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","F"
64,0,0,204,0.161000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x,x)","\int \frac{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}}{x}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x,x)","F"
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66,0,0,99,0.164000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^3,x)","\int \frac{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}}{x^{3}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^3,x)","F"
67,0,0,127,0.167000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^4,x)","\int \frac{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}}{x^{4}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^4,x)","F"
68,0,0,152,0.162000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^5,x)","\int \frac{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}}{x^{5}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^5,x)","F"
69,0,0,180,0.165000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^6,x)","\int \frac{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}}{x^{6}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^6,x)","F"
70,0,0,252,0.178000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^3,x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x^{3}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^3,x)","F"
71,0,0,249,0.173000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^2,x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x^{2}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^2,x)","F"
72,0,0,219,0.179000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x,x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x,x)","F"
73,0,0,201,0.116000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x)","F"
74,0,0,204,0.181000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x,x)","F"
75,0,0,72,0.170000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^2,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^2,x)","F"
76,0,0,99,0.172000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^3,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^3,x)","F"
77,0,0,127,0.173000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^4,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^4,x)","F"
78,0,0,152,0.168000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^5,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^5,x)","F"
79,0,0,280,0.187000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^3,x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{3}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^3,x)","F"
80,0,0,273,0.197000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^2,x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{2}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^2,x)","F"
81,0,0,242,0.181000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x,x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x,x)","F"
82,0,0,225,0.121000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x)","F"
83,0,0,224,0.179000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}{x}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x,x)","F"
84,0,0,94,0.179000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^2,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^2,x)","F"
85,0,0,122,0.184000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^3,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}{x^{3}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^3,x)","F"
86,0,0,151,0.185000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^4,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}{x^{4}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^4,x)","F"
87,0,0,175,0.187000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^5,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}{x^{5}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^5,x)","F"
88,0,0,252,0.188000," ","int(x^3/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","\int \frac{x^{3}}{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}}\, dx"," ",0,"int(x^3/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","F"
89,0,0,249,0.178000," ","int(x^2/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","\int \frac{x^{2}}{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}}\, dx"," ",0,"int(x^2/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","F"
90,0,0,219,0.179000," ","int(x/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","\int \frac{x}{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}}\, dx"," ",0,"int(x/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","F"
91,0,0,201,0.119000," ","int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","\int \frac{1}{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}}\, dx"," ",0,"int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","F"
92,0,0,204,0.177000," ","int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x,x)","\int \frac{1}{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}\, x}\, dx"," ",0,"int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x,x)","F"
93,0,0,72,0.167000," ","int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^2,x)","\int \frac{1}{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}\, x^{2}}\, dx"," ",0,"int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^2,x)","F"
94,0,0,99,0.215000," ","int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^3,x)","\int \frac{1}{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}\, x^{3}}\, dx"," ",0,"int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^3,x)","F"
95,0,0,127,0.171000," ","int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^4,x)","\int \frac{1}{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}\, x^{4}}\, dx"," ",0,"int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^4,x)","F"
96,0,0,152,0.171000," ","int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^5,x)","\int \frac{1}{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}\, x^{5}}\, dx"," ",0,"int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)/x^5,x)","F"
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100,0,0,201,0.126000," ","int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x)","\int \frac{1}{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x)","F"
101,0,0,204,0.178000," ","int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x,x)","\int \frac{1}{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x}\, dx"," ",0,"int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x,x)","F"
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104,0,0,127,0.188000," ","int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^4,x)","\int \frac{1}{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x^{4}}\, dx"," ",0,"int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)/x^4,x)","F"
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113,0,0,151,0.170000," ","int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^4,x)","\int \frac{1}{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{4}}\, dx"," ",0,"int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^4,x)","F"
114,0,0,175,0.167000," ","int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^5,x)","\int \frac{1}{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{5}}\, dx"," ",0,"int(1/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)/x^5,x)","F"
115,0,0,226,0.166000," ","int(((1+I*x)/(x^2+1)^(1/2))^(1/3)*x^2,x)","\int \left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{1}{3}} x^{2}\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(1/3)*x^2,x)","F"
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117,0,0,188,0.085000," ","int(((1+I*x)/(x^2+1)^(1/2))^(1/3),x)","\int \left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{1}{3}}\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(1/3),x)","F"
118,0,0,324,0.103000," ","int(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x,x)","\int \frac{\left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{1}{3}}}{x}\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x,x)","F"
119,0,0,188,0.101000," ","int(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^2,x)","\int \frac{\left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{1}{3}}}{x^{2}}\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^2,x)","F"
120,0,0,205,0.104000," ","int(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^3,x)","\int \frac{\left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{1}{3}}}{x^{3}}\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^3,x)","F"
121,0,0,231,0.101000," ","int(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^4,x)","\int \frac{\left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{1}{3}}}{x^{4}}\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(1/3)/x^4,x)","F"
122,0,0,125,0.063000," ","int(((1+I*x)/(x^2+1)^(1/2))^(2/3)*x^2,x)","\int \left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{2}{3}} x^{2}\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(2/3)*x^2,x)","F"
123,0,0,101,0.130000," ","int(((1+I*x)/(x^2+1)^(1/2))^(2/3)*x,x)","\int \left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{2}{3}} x\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(2/3)*x,x)","F"
124,0,0,87,0.106000," ","int(((1+I*x)/(x^2+1)^(1/2))^(2/3),x)","\int \left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{2}{3}}\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(2/3),x)","F"
125,0,0,122,0.092000," ","int(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x,x)","\int \frac{\left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{2}{3}}}{x}\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x,x)","F"
126,0,0,84,0.065000," ","int(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x^2,x)","\int \frac{\left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{2}{3}}}{x^{2}}\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x^2,x)","F"
127,0,0,103,0.099000," ","int(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x^3,x)","\int \frac{\left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)^{\frac{2}{3}}}{x^{3}}\, dx"," ",0,"int(((1+I*x)/(x^2+1)^(1/2))^(2/3)/x^3,x)","F"
128,0,0,539,0.206000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x^2,x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{1}{4}} x^{2}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x^2,x)","F"
129,0,0,505,0.161000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x,x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{1}{4}} x\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x,x)","F"
130,0,0,491,0.105000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4),x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{1}{4}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4),x)","F"
131,0,0,636,0.162000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{1}{4}}}{x}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x,x)","F"
132,0,0,240,0.151000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x^2,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{1}{4}}}{x^{2}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x^2,x)","F"
133,0,0,271,0.158000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x^3,x)","\int \frac{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{1}{4}}}{x^{3}}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)/x^3,x)","F"
134,1,748,110,0.752000," ","int((1+I*a*x)^6/(a^2*x^2+1)^3*x^m,x)","\frac{\left(a^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} \left(\frac{x^{1+m} \left(a^{2}\right)^{\frac{1}{2}+\frac{m}{2}} \left(-a^{2} m^{2} x^{2}+2 a^{2} m \,x^{2}+3 a^{2} x^{2}-m^{2}+4 m +5\right)}{2 \left(1+m \right) \left(a^{2} x^{2}+1\right)^{2}}+\frac{4 x^{1+m} \left(a^{2}\right)^{\frac{1}{2}+\frac{m}{2}} \left(\frac{1}{16} m^{3}-\frac{3}{16} m^{2}-\frac{1}{16} m +\frac{3}{16}\right) \Phi \left(-a^{2} x^{2}, 1, \frac{1}{2}+\frac{m}{2}\right)}{1+m}\right)}{4}+\frac{3 i \left(a^{2}\right)^{-\frac{m}{2}} \left(\frac{x^{m} \left(a^{2}\right)^{\frac{m}{2}} \left(a^{2} m \,x^{2}+m -2\right)}{2 \left(a^{2} x^{2}+1\right)^{2}}-\frac{x^{m} \left(a^{2}\right)^{\frac{m}{2}} \left(-2+m \right) m \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{4}\right)}{2 a}-\frac{15 \left(a^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} \left(\frac{x^{1+m} \left(a^{2}\right)^{\frac{3}{2}+\frac{m}{2}} \left(a^{2} m \,x^{2}+a^{2} x^{2}+m -1\right)}{2 \left(a^{2} x^{2}+1\right)^{2} a^{2}}-\frac{x^{1+m} \left(a^{2}\right)^{\frac{3}{2}+\frac{m}{2}} \left(1+m \right) \left(-1+m \right) \Phi \left(-a^{2} x^{2}, 1, \frac{1}{2}+\frac{m}{2}\right)}{4 a^{2}}\right)}{4}-\frac{5 i \left(a^{2}\right)^{-\frac{m}{2}} \left(-\frac{x^{m} \left(a^{2}\right)^{\frac{m}{2}} \left(a^{2} m \,x^{2}+4 a^{2} x^{2}+m +2\right)}{2 \left(a^{2} x^{2}+1\right)^{2}}+\frac{x^{m} \left(a^{2}\right)^{\frac{m}{2}} \left(2+m \right) m \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{4}\right)}{a}+\frac{15 \left(a^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} \left(-\frac{x^{1+m} \left(a^{2}\right)^{\frac{5}{2}+\frac{m}{2}} \left(a^{2} m \,x^{2}+5 a^{2} x^{2}+m +3\right)}{2 a^{4} \left(a^{2} x^{2}+1\right)^{2}}+\frac{x^{1+m} \left(a^{2}\right)^{\frac{5}{2}+\frac{m}{2}} \left(m^{2}+4 m +3\right) \Phi \left(-a^{2} x^{2}, 1, \frac{1}{2}+\frac{m}{2}\right)}{4 a^{4}}\right)}{4}+\frac{3 i \left(a^{2}\right)^{-\frac{m}{2}} \left(\frac{x^{m} \left(a^{2}\right)^{\frac{m}{2}} \left(8 a^{4} x^{4}+a^{2} m^{2} x^{2}+8 a^{2} m \,x^{2}+16 a^{2} x^{2}+m^{2}+6 m +8\right)}{2 \left(a^{2} x^{2}+1\right)^{2} m}-\frac{x^{m} \left(a^{2}\right)^{\frac{m}{2}} \left(m^{2}+6 m +8\right) \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{4}\right)}{2 a}-\frac{\left(a^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} \left(\frac{x^{1+m} \left(a^{2}\right)^{\frac{7}{2}+\frac{m}{2}} \left(8 a^{4} x^{4}+a^{2} m^{2} x^{2}+10 a^{2} m \,x^{2}+25 a^{2} x^{2}+m^{2}+8 m +15\right)}{2 \left(a^{2} x^{2}+1\right)^{2} \left(1+m \right) a^{6}}-\frac{x^{1+m} \left(a^{2}\right)^{\frac{7}{2}+\frac{m}{2}} \left(m^{2}+8 m +15\right) \Phi \left(-a^{2} x^{2}, 1, \frac{1}{2}+\frac{m}{2}\right)}{4 a^{6}}\right)}{4}"," ",0,"1/4*(a^2)^(-1/2-1/2*m)*(1/2/(1+m)*x^(1+m)*(a^2)^(1/2+1/2*m)*(-a^2*m^2*x^2+2*a^2*m*x^2+3*a^2*x^2-m^2+4*m+5)/(a^2*x^2+1)^2+4/(1+m)*x^(1+m)*(a^2)^(1/2+1/2*m)*(1/16*m^3-3/16*m^2-1/16*m+3/16)*LerchPhi(-a^2*x^2,1,1/2+1/2*m))+3/2*I/a*(a^2)^(-1/2*m)*(1/2*x^m*(a^2)^(1/2*m)*(a^2*m*x^2+m-2)/(a^2*x^2+1)^2-1/4*x^m*(a^2)^(1/2*m)*(-2+m)*m*LerchPhi(-a^2*x^2,1,1/2*m))-15/4*(a^2)^(-1/2-1/2*m)*(1/2*x^(1+m)*(a^2)^(3/2+1/2*m)*(a^2*m*x^2+a^2*x^2+m-1)/(a^2*x^2+1)^2/a^2-1/4*x^(1+m)*(a^2)^(3/2+1/2*m)*(1+m)*(-1+m)/a^2*LerchPhi(-a^2*x^2,1,1/2+1/2*m))-5*I/a*(a^2)^(-1/2*m)*(-1/2*x^m*(a^2)^(1/2*m)*(a^2*m*x^2+4*a^2*x^2+m+2)/(a^2*x^2+1)^2+1/4*x^m*(a^2)^(1/2*m)*(2+m)*m*LerchPhi(-a^2*x^2,1,1/2*m))+15/4*(a^2)^(-1/2-1/2*m)*(-1/2*x^(1+m)*(a^2)^(5/2+1/2*m)*(a^2*m*x^2+5*a^2*x^2+m+3)/a^4/(a^2*x^2+1)^2+1/4*x^(1+m)*(a^2)^(5/2+1/2*m)*(m^2+4*m+3)/a^4*LerchPhi(-a^2*x^2,1,1/2+1/2*m))+3/2*I/a*(a^2)^(-1/2*m)*(1/2*x^m*(a^2)^(1/2*m)*(8*a^4*x^4+a^2*m^2*x^2+8*a^2*m*x^2+16*a^2*x^2+m^2+6*m+8)/(a^2*x^2+1)^2/m-1/4*x^m*(a^2)^(1/2*m)*(m^2+6*m+8)*LerchPhi(-a^2*x^2,1,1/2*m))-1/4*(a^2)^(-1/2-1/2*m)*(1/2*x^(1+m)*(a^2)^(7/2+1/2*m)*(8*a^4*x^4+a^2*m^2*x^2+10*a^2*m*x^2+25*a^2*x^2+m^2+8*m+15)/(a^2*x^2+1)^2/(1+m)/a^6-1/4*x^(1+m)*(a^2)^(7/2+1/2*m)*(m^2+8*m+15)/a^6*LerchPhi(-a^2*x^2,1,1/2+1/2*m))","C"
135,1,417,50,0.574000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2*x^m,x)","\frac{\left(a^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} \left(\frac{2 x^{1+m} \left(a^{2}\right)^{\frac{1}{2}+\frac{m}{2}}}{2 a^{2} x^{2}+2}+\frac{2 x^{1+m} \left(a^{2}\right)^{\frac{1}{2}+\frac{m}{2}} \left(-\frac{m^{2}}{4}+\frac{1}{4}\right) \Phi \left(-a^{2} x^{2}, 1, \frac{1}{2}+\frac{m}{2}\right)}{1+m}\right)}{2}+\frac{2 i \left(a^{2}\right)^{-\frac{m}{2}} \left(\frac{x^{m} \left(a^{2}\right)^{\frac{m}{2}} \left(-m -2\right)}{\left(2+m \right) \left(a^{2} x^{2}+1\right)}+\frac{x^{m} \left(a^{2}\right)^{\frac{m}{2}} m \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{2}\right)}{a}-3 \left(a^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} \left(\frac{x^{1+m} \left(a^{2}\right)^{\frac{3}{2}+\frac{m}{2}} \left(-3-m \right)}{\left(3+m \right) a^{2} \left(a^{2} x^{2}+1\right)}+\frac{x^{1+m} \left(a^{2}\right)^{\frac{3}{2}+\frac{m}{2}} \left(1+m \right) \Phi \left(-a^{2} x^{2}, 1, \frac{1}{2}+\frac{m}{2}\right)}{2 a^{2}}\right)-\frac{2 i \left(a^{2}\right)^{-\frac{m}{2}} \left(\frac{x^{m} \left(a^{2}\right)^{\frac{m}{2}} \left(2 a^{2} x^{2}+m +2\right)}{\left(a^{2} x^{2}+1\right) m}-\frac{x^{m} \left(a^{2}\right)^{\frac{m}{2}} \left(2+m \right) \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{2}\right)}{a}+\frac{\left(a^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} \left(\frac{x^{1+m} \left(a^{2}\right)^{\frac{5}{2}+\frac{m}{2}} \left(2 a^{2} x^{2}+m +3\right)}{\left(a^{2} x^{2}+1\right) a^{4} \left(1+m \right)}-\frac{x^{1+m} \left(a^{2}\right)^{\frac{5}{2}+\frac{m}{2}} \left(3+m \right) \Phi \left(-a^{2} x^{2}, 1, \frac{1}{2}+\frac{m}{2}\right)}{2 a^{4}}\right)}{2}"," ",0,"1/2*(a^2)^(-1/2-1/2*m)*(2*x^(1+m)*(a^2)^(1/2+1/2*m)/(2*a^2*x^2+2)+2/(1+m)*x^(1+m)*(a^2)^(1/2+1/2*m)*(-1/4*m^2+1/4)*LerchPhi(-a^2*x^2,1,1/2+1/2*m))+2*I/a*(a^2)^(-1/2*m)*(1/(2+m)*x^m*(a^2)^(1/2*m)*(-m-2)/(a^2*x^2+1)+1/2*x^m*(a^2)^(1/2*m)*m*LerchPhi(-a^2*x^2,1,1/2*m))-3*(a^2)^(-1/2-1/2*m)*(1/(3+m)*x^(1+m)*(a^2)^(3/2+1/2*m)*(-3-m)/a^2/(a^2*x^2+1)+1/2*x^(1+m)*(a^2)^(3/2+1/2*m)*(1+m)/a^2*LerchPhi(-a^2*x^2,1,1/2+1/2*m))-2*I/a*(a^2)^(-1/2*m)*(x^m*(a^2)^(1/2*m)*(2*a^2*x^2+m+2)/(a^2*x^2+1)/m-1/2*x^m*(a^2)^(1/2*m)*(2+m)*LerchPhi(-a^2*x^2,1,1/2*m))+1/2*(a^2)^(-1/2-1/2*m)*(x^(1+m)*(a^2)^(5/2+1/2*m)*(2*a^2*x^2+m+3)/(a^2*x^2+1)/a^4/(1+m)-1/2*x^(1+m)*(a^2)^(5/2+1/2*m)*(3+m)/a^4*LerchPhi(-a^2*x^2,1,1/2+1/2*m))","C"
136,1,175,40,0.513000," ","int((1+I*a*x)^2/(a^2*x^2+1)*x^m,x)","\frac{x^{1+m} \left(\frac{1}{2}+\frac{m}{2}\right) \Phi \left(-a^{2} x^{2}, 1, \frac{1}{2}+\frac{m}{2}\right)}{1+m}+\frac{i \left(a^{2}\right)^{-\frac{m}{2}} \left(\frac{2 x^{m} \left(a^{2}\right)^{\frac{m}{2}}}{m}+\frac{x^{m} \left(a^{2}\right)^{\frac{m}{2}} \left(-m -2\right) \Phi \left(-a^{2} x^{2}, 1, \frac{m}{2}\right)}{2+m}\right)}{a}-\frac{\left(a^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} \left(\frac{2 x^{1+m} \left(a^{2}\right)^{\frac{3}{2}+\frac{m}{2}}}{\left(1+m \right) a^{2}}+\frac{x^{1+m} \left(a^{2}\right)^{\frac{3}{2}+\frac{m}{2}} \left(-3-m \right) \Phi \left(-a^{2} x^{2}, 1, \frac{1}{2}+\frac{m}{2}\right)}{\left(3+m \right) a^{2}}\right)}{2}"," ",0,"1/(1+m)*x^(1+m)*(1/2+1/2*m)*LerchPhi(-a^2*x^2,1,1/2+1/2*m)+I/a*(a^2)^(-1/2*m)*(2*x^m*(a^2)^(1/2*m)/m+1/(2+m)*x^m*(a^2)^(1/2*m)*(-m-2)*LerchPhi(-a^2*x^2,1,1/2*m))-1/2*(a^2)^(-1/2-1/2*m)*(2*x^(1+m)*(a^2)^(3/2+1/2*m)/(1+m)/a^2+1/(3+m)*x^(1+m)*(a^2)^(3/2+1/2*m)*(-3-m)/a^2*LerchPhi(-a^2*x^2,1,1/2+1/2*m))","C"
137,1,158,40,0.420000," ","int(x^m/(1+I*a*x)^2*(a^2*x^2+1),x)","\frac{i \left(i a \right)^{-m} \left(\frac{x^{m} \left(i a \right)^{m} \left(-a^{2} m \,x^{2}-i a m x -2 i a x -m^{2}-3 m -2\right)}{\left(1+m \right) m \left(i a x +1\right)}+x^{m} \left(i a \right)^{m} \left(2+m \right) \Phi \left(-i a x , 1, m\right)\right)}{a}-\frac{i \left(i a \right)^{-m} \left(\frac{x^{m} \left(i a \right)^{m} \left(-1-m \right)}{\left(1+m \right) \left(i a x +1\right)}+x^{m} \left(i a \right)^{m} m \Phi \left(-i a x , 1, m\right)\right)}{a}"," ",0,"I*(I*a)^(-m)/a*(x^m*(I*a)^m*(-a^2*m*x^2-I*a*m*x-m^2-2*I*a*x-3*m-2)/(1+m)/m/(1+I*a*x)+x^m*(I*a)^m*(2+m)*LerchPhi(-I*a*x,1,m))-I*(I*a)^(-m)/a*(1/(1+m)*x^m*(I*a)^m*(-1-m)/(1+I*a*x)+x^m*(I*a)^m*m*LerchPhi(-I*a*x,1,m))","C"
138,1,428,50,0.565000," ","int(x^m/(1+I*a*x)^4*(a^2*x^2+1)^2,x)","-\frac{i \left(i a \right)^{-m} \left(\frac{x^{m} \left(i a \right)^{m} \left(6 a^{4} x^{4} m +6 i a^{3} x^{3} m +a^{2} x^{2} m^{4}+24 i a^{3} x^{3}+11 a^{2} x^{2} m^{3}-2 i a x \,m^{4}+46 a^{2} m^{2} x^{2}-21 i a x \,m^{3}+90 a^{2} m \,x^{2}-79 i a x \,m^{2}+72 a^{2} x^{2}-126 i a m x -m^{4}-72 i a x -10 m^{3}-35 m^{2}-50 m -24\right)}{\left(1+m \right) m \left(i a x +1\right)^{3}}+x^{m} \left(i a \right)^{m} \left(m^{3}+9 m^{2}+26 m +24\right) \Phi \left(-i a x , 1, m\right)\right)}{6 a}+\frac{i \left(i a \right)^{-m} \left(-\frac{x^{m} \left(i a \right)^{m} \left(-a^{2} m^{2} x^{2}-4 a^{2} m \,x^{2}+2 i a x \,m^{2}-6 a^{2} x^{2}+7 i a m x +6 i a x +m^{2}+3 m +2\right)}{\left(i a x +1\right)^{3}}+x^{m} \left(i a \right)^{m} m \left(m^{2}+3 m +2\right) \Phi \left(-i a x , 1, m\right)\right)}{3 a}-\frac{i \left(i a \right)^{-m} \left(-\frac{x^{m} \left(i a \right)^{m} \left(-a^{2} m^{2} x^{2}+2 a^{2} m \,x^{2}+2 i a x \,m^{2}-5 i a m x +m^{2}-3 m +2\right)}{\left(i a x +1\right)^{3}}+x^{m} \left(i a \right)^{m} \left(m^{2}-3 m +2\right) m \Phi \left(-i a x , 1, m\right)\right)}{6 a}"," ",0,"-1/6*I*(I*a)^(-m)/a*(x^m*(I*a)^m*(a^2*x^2*m^4+6*a^4*x^4*m+11*a^2*x^2*m^3-72*I*a*x-21*I*a*x*m^3+46*a^2*m^2*x^2+24*I*a^3*x^3-m^4-2*I*a*x*m^4+90*a^2*m*x^2+6*I*a^3*x^3*m-10*m^3+72*a^2*x^2-126*I*a*m*x-35*m^2-79*I*a*x*m^2-50*m-24)/(1+m)/m/(1+I*a*x)^3+x^m*(I*a)^m*(m^3+9*m^2+26*m+24)*LerchPhi(-I*a*x,1,m))+1/3*I*(I*a)^(-m)/a*(-x^m*(I*a)^m*(-a^2*m^2*x^2-4*a^2*m*x^2+2*I*a*x*m^2-6*a^2*x^2+7*I*a*m*x+m^2+6*I*a*x+3*m+2)/(1+I*a*x)^3+x^m*(I*a)^m*m*(m^2+3*m+2)*LerchPhi(-I*a*x,1,m))-1/6*I*(I*a)^(-m)/a*(-x^m*(I*a)^m*(-a^2*m^2*x^2+2*a^2*m*x^2+2*I*a*x*m^2-5*I*a*m*x+m^2-3*m+2)/(1+I*a*x)^3+x^m*(I*a)^m*(m^2-3*m+2)*m*LerchPhi(-I*a*x,1,m))","C"
139,1,1196,111,0.744000," ","int(x^m/(1+I*a*x)^6*(a^2*x^2+1)^3,x)","\frac{i \left(i a \right)^{-m} \left(\frac{x^{m} \left(i a \right)^{m} \left(-a^{4} x^{4} m^{6}-120 a^{6} x^{6} m -22 a^{4} x^{4} m^{5}+4 i a^{3} x^{3} m^{6}-120 i a^{5} x^{5} m -197 a^{4} x^{4} m^{4}+87 i a^{3} x^{3} m^{5}-720 i a^{5} x^{5}-932 a^{4} x^{4} m^{3}+764 i a^{3} x^{3} m^{4}-2556 a^{4} x^{4} m^{2}+3483 i a^{3} x^{3} m^{3}+6 a^{2} x^{2} m^{6}-4200 a^{4} x^{4} m +8802 i a^{3} x^{3} m^{2}+129 a^{2} x^{2} m^{5}-4 i a x \,m^{6}-3600 a^{4} x^{4}+12000 i a^{3} x^{3} m +1112 a^{2} x^{2} m^{4}-85 i a x \,m^{5}+7200 i a^{3} x^{3}+4911 a^{2} x^{2} m^{3}-720 i a x \,m^{4}+11722 a^{2} m^{2} x^{2}-3095 i a x \,m^{3}-m^{6}+14400 a^{2} m \,x^{2}-7076 i a x \,m^{2}-21 m^{5}+7200 a^{2} x^{2}-8100 i a m x -175 m^{4}-3600 i a x -735 m^{3}-1624 m^{2}-1764 m -720\right)}{\left(1+m \right) m \left(i a x +1\right)^{5}}+x^{m} \left(i a \right)^{m} \left(m^{5}+20 m^{4}+155 m^{3}+580 m^{2}+1044 m +720\right) \Phi \left(-i a x , 1, m\right)\right)}{120 a}-\frac{i \left(i a \right)^{-m} \left(-\frac{x^{m} \left(i a \right)^{m} \left(a^{4} x^{4} m^{4}+11 a^{4} x^{4} m^{3}-4 i a^{3} x^{3} m^{4}+46 a^{4} x^{4} m^{2}-43 i a^{3} x^{3} m^{3}+96 a^{4} x^{4} m -171 i a^{3} x^{3} m^{2}+120 a^{4} x^{4}-312 i a^{3} x^{3} m -6 a^{2} x^{2} m^{4}-240 i a^{3} x^{3}-63 a^{2} x^{2} m^{3}+4 i a x \,m^{4}-239 a^{2} m^{2} x^{2}+41 i a x \,m^{3}-392 a^{2} m \,x^{2}+149 i a x \,m^{2}-240 a^{2} x^{2}+226 i a m x +m^{4}+120 i a x +10 m^{3}+35 m^{2}+50 m +24\right)}{\left(i a x +1\right)^{5}}+x^{m} \left(i a \right)^{m} m \left(m^{4}+10 m^{3}+35 m^{2}+50 m +24\right) \Phi \left(-i a x , 1, m\right)\right)}{40 a}+\frac{i \left(i a \right)^{-m} \left(-\frac{x^{m} \left(i a \right)^{m} \left(a^{4} x^{4} m^{4}+a^{4} x^{4} m^{3}-4 i a^{3} x^{3} m^{4}-4 a^{4} x^{4} m^{2}-3 i a^{3} x^{3} m^{3}-4 a^{4} x^{4} m +19 i a^{3} x^{3} m^{2}+18 i a^{3} x^{3} m -6 a^{2} x^{2} m^{4}-3 a^{2} x^{2} m^{3}+4 i a x \,m^{4}+31 a^{2} m^{2} x^{2}+i a x \,m^{3}+18 a^{2} m \,x^{2}-21 i a x \,m^{2}-40 a^{2} x^{2}-4 i a m x +m^{4}+20 i a x -5 m^{2}+4\right)}{\left(i a x +1\right)^{5}}+x^{m} \left(i a \right)^{m} \left(m^{2}-3 m +2\right) m \left(m^{2}+3 m +2\right) \Phi \left(-i a x , 1, m\right)\right)}{40 a}-\frac{i \left(i a \right)^{-m} \left(-\frac{x^{m} \left(i a \right)^{m} \left(a^{4} x^{4} m^{4}-9 a^{4} x^{4} m^{3}-4 i a^{3} x^{3} m^{4}+26 a^{4} x^{4} m^{2}+37 i a^{3} x^{3} m^{3}-24 a^{4} x^{4} m -111 i a^{3} x^{3} m^{2}+108 i a^{3} x^{3} m -6 a^{2} x^{2} m^{4}+57 a^{2} x^{2} m^{3}+4 i a x \,m^{4}-179 a^{2} m^{2} x^{2}-39 i a x \,m^{3}+188 a^{2} m \,x^{2}+129 i a x \,m^{2}-154 i a m x +m^{4}-10 m^{3}+35 m^{2}-50 m +24\right)}{\left(i a x +1\right)^{5}}+x^{m} \left(i a \right)^{m} \left(m^{4}-10 m^{3}+35 m^{2}-50 m +24\right) m \Phi \left(-i a x , 1, m\right)\right)}{120 a}"," ",0,"1/120*I*(I*a)^(-m)/a*(x^m*(I*a)^m*(-720+764*I*a^3*x^3*m^4+12000*I*a^3*x^3*m-3095*I*a*x*m^3+11722*a^2*m^2*x^2+6*a^2*x^2*m^6-120*a^6*x^6*m+129*a^2*x^2*m^5-720*I*a^5*x^5+7200*I*a^3*x^3-3600*I*a*x-197*a^4*x^4*m^4-m^6-175*m^4-4*I*a*x*m^6-120*I*a^5*x^5*m-932*a^4*x^4*m^3-22*a^4*x^4*m^5+4*I*a^3*x^3*m^6+87*I*a^3*x^3*m^5+8802*I*a^3*x^3*m^2-720*I*a*x*m^4-8100*I*a*m*x-1764*m+7200*a^2*x^2+14400*a^2*m*x^2-85*I*a*x*m^5-21*m^5-7076*I*a*x*m^2-2556*a^4*x^4*m^2-4200*a^4*x^4*m-735*m^3+1112*a^2*x^2*m^4+4911*a^2*x^2*m^3+3483*I*a^3*x^3*m^3-a^4*x^4*m^6-1624*m^2-3600*a^4*x^4)/(1+m)/m/(1+I*a*x)^5+x^m*(I*a)^m*(m^5+20*m^4+155*m^3+580*m^2+1044*m+720)*LerchPhi(-I*a*x,1,m))-1/40*I*(I*a)^(-m)/a*(-x^m*(I*a)^m*(24-312*I*a^3*x^3*m+41*I*a*x*m^3+149*I*a*x*m^2+226*I*a*m*x-239*a^2*m^2*x^2+a^4*x^4*m^4-240*I*a^3*x^3+120*I*a*x+m^4+11*a^4*x^4*m^3-4*I*a^3*x^3*m^4-171*I*a^3*x^3*m^2+4*I*a*x*m^4-43*I*a^3*x^3*m^3+50*m-240*a^2*x^2-392*a^2*m*x^2+46*a^4*x^4*m^2+96*a^4*x^4*m+10*m^3-6*a^2*x^2*m^4-63*a^2*x^2*m^3+35*m^2+120*a^4*x^4)/(1+I*a*x)^5+x^m*(I*a)^m*m*(m^4+10*m^3+35*m^2+50*m+24)*LerchPhi(-I*a*x,1,m))+1/40*I*(I*a)^(-m)/a*(-x^m*(I*a)^m*(a^4*x^4*m^4+a^4*x^4*m^3+20*I*a*x-4*a^4*x^4*m^2+18*I*a^3*x^3*m-6*a^2*x^2*m^4-4*a^4*x^4*m+4*I*a*x*m^4-3*a^2*x^2*m^3+19*I*a^3*x^3*m^2-4*I*a*m*x+31*a^2*m^2*x^2-3*I*a^3*x^3*m^3+m^4+18*a^2*m*x^2-21*I*a*x*m^2-40*a^2*x^2+I*a*x*m^3-5*m^2-4*I*a^3*x^3*m^4+4)/(1+I*a*x)^5+x^m*(I*a)^m*(m^2-3*m+2)*m*(m^2+3*m+2)*LerchPhi(-I*a*x,1,m))-1/120*I*(I*a)^(-m)/a*(-x^m*(I*a)^m*(a^4*x^4*m^4-9*a^4*x^4*m^3+108*I*a^3*x^3*m+26*a^4*x^4*m^2+4*I*a*x*m^4-6*a^2*x^2*m^4-24*a^4*x^4*m-111*I*a^3*x^3*m^2+57*a^2*x^2*m^3-154*I*a*m*x+37*I*a^3*x^3*m^3-179*a^2*m^2*x^2+129*I*a*x*m^2+m^4+188*a^2*m*x^2-39*I*a*x*m^3-10*m^3-4*I*a^3*x^3*m^4+35*m^2-50*m+24)/(1+I*a*x)^5+x^m*(I*a)^m*(m^4-10*m^3+35*m^2-50*m+24)*m*LerchPhi(-I*a*x,1,m))","C"
140,1,146,141,0.428000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^m,x)","\frac{x^{1+m} \hypergeom \left(\left[\frac{3}{2}, \frac{1}{2}+\frac{m}{2}\right], \left[\frac{3}{2}+\frac{m}{2}\right], -a^{2} x^{2}\right)}{1+m}+\frac{3 i a \,x^{2+m} \hypergeom \left(\left[\frac{3}{2}, 1+\frac{m}{2}\right], \left[2+\frac{m}{2}\right], -a^{2} x^{2}\right)}{2+m}-\frac{3 a^{2} x^{3+m} \hypergeom \left(\left[\frac{3}{2}, \frac{3}{2}+\frac{m}{2}\right], \left[\frac{5}{2}+\frac{m}{2}\right], -a^{2} x^{2}\right)}{3+m}-\frac{i a^{3} x^{4+m} \hypergeom \left(\left[\frac{3}{2}, 2+\frac{m}{2}\right], \left[3+\frac{m}{2}\right], -a^{2} x^{2}\right)}{4+m}"," ",0,"x^(1+m)*hypergeom([3/2,1/2+1/2*m],[3/2+1/2*m],-a^2*x^2)/(1+m)+3*I*a/(2+m)*x^(2+m)*hypergeom([3/2,1+1/2*m],[2+1/2*m],-a^2*x^2)-3*a^2/(3+m)*x^(3+m)*hypergeom([3/2,3/2+1/2*m],[5/2+1/2*m],-a^2*x^2)-I*a^3/(4+m)*x^(4+m)*hypergeom([3/2,2+1/2*m],[3+1/2*m],-a^2*x^2)","A"
141,1,71,70,0.313000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^m,x)","\frac{x^{1+m} \hypergeom \left(\left[\frac{1}{2}, \frac{1}{2}+\frac{m}{2}\right], \left[\frac{3}{2}+\frac{m}{2}\right], -a^{2} x^{2}\right)}{1+m}+\frac{i a \,x^{2+m} \hypergeom \left(\left[\frac{1}{2}, 1+\frac{m}{2}\right], \left[2+\frac{m}{2}\right], -a^{2} x^{2}\right)}{2+m}"," ",0,"x^(1+m)*hypergeom([1/2,1/2+1/2*m],[3/2+1/2*m],-a^2*x^2)/(1+m)+I*a*x^(2+m)*hypergeom([1/2,1+1/2*m],[2+1/2*m],-a^2*x^2)/(2+m)","A"
142,0,0,70,0.449000," ","int(x^m/(1+I*a*x)*(a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \sqrt{a^{2} x^{2}+1}}{i a x +1}\, dx"," ",0,"int(x^m/(1+I*a*x)*(a^2*x^2+1)^(1/2),x)","F"
143,0,0,141,0.476000," ","int(x^m/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x)","\int \frac{x^{m} \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{\left(i a x +1\right)^{3}}\, dx"," ",0,"int(x^m/(1+I*a*x)^3*(a^2*x^2+1)^(3/2),x)","F"
144,0,0,30,0.125000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^m,x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{m}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2)*x^m,x)","F"
145,0,0,30,0.120000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^m,x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x^{m}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2)*x^m,x)","F"
146,0,0,30,0.123000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x^m,x)","\int \sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}\, x^{m}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2)*x^m,x)","F"
147,0,0,30,0.114000," ","int(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","\int \frac{x^{m}}{\sqrt{\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}}}\, dx"," ",0,"int(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/2),x)","F"
148,0,0,30,0.114000," ","int(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x)","\int \frac{x^{m}}{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(3/2),x)","F"
149,0,0,30,0.115000," ","int(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x)","\int \frac{x^{m}}{\left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m/((1+I*a*x)/(a^2*x^2+1)^(1/2))^(5/2),x)","F"
150,0,0,30,0.214000," ","int(exp(2/3*arctan(x))*x^m,x)","\int {\mathrm e}^{\frac{2 \arctan \left(x \right)}{3}} x^{m}\, dx"," ",0,"int(exp(2/3*arctan(x))*x^m,x)","F"
151,0,0,30,0.193000," ","int(exp(1/3*arctan(x))*x^m,x)","\int {\mathrm e}^{\frac{\arctan \left(x \right)}{3}} x^{m}\, dx"," ",0,"int(exp(1/3*arctan(x))*x^m,x)","F"
152,0,0,30,0.114000," ","int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x^m,x)","\int \left(\frac{i a x +1}{\sqrt{a^{2} x^{2}+1}}\right)^{\frac{1}{4}} x^{m}\, dx"," ",0,"int(((1+I*a*x)/(a^2*x^2+1)^(1/2))^(1/4)*x^m,x)","F"
153,0,0,34,0.171000," ","int(exp(I*n*arctan(a*x))*x^m,x)","\int {\mathrm e}^{i n \arctan \left(a x \right)} x^{m}\, dx"," ",0,"int(exp(I*n*arctan(a*x))*x^m,x)","F"
154,0,0,138,0.135000," ","int(exp(I*n*arctan(a*x))*x^3,x)","\int {\mathrm e}^{i n \arctan \left(a x \right)} x^{3}\, dx"," ",0,"int(exp(I*n*arctan(a*x))*x^3,x)","F"
155,0,0,125,0.133000," ","int(exp(I*n*arctan(a*x))*x^2,x)","\int {\mathrm e}^{i n \arctan \left(a x \right)} x^{2}\, dx"," ",0,"int(exp(I*n*arctan(a*x))*x^2,x)","F"
156,0,0,85,0.132000," ","int(exp(I*n*arctan(a*x))*x,x)","\int {\mathrm e}^{i n \arctan \left(a x \right)} x\, dx"," ",0,"int(exp(I*n*arctan(a*x))*x,x)","F"
157,0,0,56,0.119000," ","int(exp(I*n*arctan(a*x)),x)","\int {\mathrm e}^{i n \arctan \left(a x \right)}\, dx"," ",0,"int(exp(I*n*arctan(a*x)),x)","F"
158,0,0,105,0.132000," ","int(exp(I*n*arctan(a*x))/x,x)","\int \frac{{\mathrm e}^{i n \arctan \left(a x \right)}}{x}\, dx"," ",0,"int(exp(I*n*arctan(a*x))/x,x)","F"
159,0,0,68,0.132000," ","int(exp(I*n*arctan(a*x))/x^2,x)","\int \frac{{\mathrm e}^{i n \arctan \left(a x \right)}}{x^{2}}\, dx"," ",0,"int(exp(I*n*arctan(a*x))/x^2,x)","F"
160,0,0,102,0.157000," ","int(exp(I*n*arctan(a*x))/x^3,x)","\int \frac{{\mathrm e}^{i n \arctan \left(a x \right)}}{x^{3}}\, dx"," ",0,"int(exp(I*n*arctan(a*x))/x^3,x)","F"
161,0,0,141,0.161000," ","int(exp(I*n*arctan(a*x))/x^4,x)","\int \frac{{\mathrm e}^{i n \arctan \left(a x \right)}}{x^{4}}\, dx"," ",0,"int(exp(I*n*arctan(a*x))/x^4,x)","F"
162,1,656,225,0.200000," ","int((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x^4,x)","-\frac{7 a \,x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{12 b^{3}}+\frac{13 a^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{12 b^{4}}+\frac{a^{4} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{4} \sqrt{b^{2}}}-\frac{3 a^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{4} \sqrt{b^{2}}}-\frac{83 i a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{30 b^{5}}+\frac{29 i a x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{30 b^{4}}-\frac{3 i a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{4} \sqrt{b^{2}}}-\frac{i a \,x^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{5 b^{2}}+\frac{i a^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{5 b^{5}}+\frac{i a^{2} x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{5 b^{3}}-\frac{4 i x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{15 b^{3}}+\frac{8 i \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{15 b^{5}}-\frac{i a^{3} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{5 b^{4}}+\frac{2 i a^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{4} \sqrt{b^{2}}}+\frac{x^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{4 b^{2}}-\frac{25 a^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{12 b^{5}}+\frac{55 a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{24 b^{5}}+\frac{i x^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{5 b}-\frac{3 x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 b^{4}}+\frac{3 \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 b^{4} \sqrt{b^{2}}}"," ",0,"-7/12*a/b^3*x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+13/12*a^2/b^4*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+a^4/b^4*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3*a^2/b^4*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-83/30*I/b^5*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+29/30*I/b^4*a*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/2*I/b^4*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/5*I/b^2*a*x^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/5*I/b^5*a^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/5*I/b^3*a^2*x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-4/15*I/b^3*x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+8/15*I/b^5*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/5*I/b^4*a^3*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+2*I/b^4*a^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/4*x^3/b^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-25/12*a^3/b^5*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+55/24*a/b^5*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/5*I/b*x^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/8/b^4*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/8/b^4*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)","B"
163,1,465,163,0.186000," ","int((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x^3,x)","\frac{3 i \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 b^{3} \sqrt{b^{2}}}-\frac{3 i x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 b^{3}}+\frac{13 i a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 b^{4}}-\frac{i a^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{4 b^{4}}+\frac{i x^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{4 b}-\frac{i a \,x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{4 b^{2}}+\frac{i a^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{4 b^{3}}-\frac{3 i a^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{3} \sqrt{b^{2}}}+\frac{x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{3 b^{2}}-\frac{5 a x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{6 b^{3}}+\frac{11 a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{6 b^{4}}-\frac{a^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{3} \sqrt{b^{2}}}+\frac{3 a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{3} \sqrt{b^{2}}}-\frac{2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{3 b^{4}}"," ",0,"3/8*I/b^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3/8*I/b^3*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+13/8*I/b^4*a*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/4*I/b^4*a^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/4*I/b*x^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/4*I/b^2*a*x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/4*I/b^3*a^2*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/2*I/b^3*a^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/3*x^2/b^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-5/6*a/b^3*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+11/6*a^2/b^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-a^3/b^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+3/2*a/b^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-2/3/b^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)","B"
164,1,302,135,0.177000," ","int((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x^2,x)","\frac{i x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{3 b}-\frac{i a x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{3 b^{2}}+\frac{i a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{3 b^{3}}+\frac{i a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{2} \sqrt{b^{2}}}-\frac{2 i \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{3 b^{3}}+\frac{x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{2}}-\frac{3 a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{3}}+\frac{a^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{2} \sqrt{b^{2}}}-\frac{\ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{2} \sqrt{b^{2}}}"," ",0,"1/3*I/b*x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/3*I/b^2*a*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/3*I/b^3*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I/b^2*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-2/3*I/b^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*x/b^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/2*a/b^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+a^2/b^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/2/b^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)","B"
165,1,171,86,0.170000," ","int((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)*x,x)","\frac{i x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b}-\frac{i a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{2}}-\frac{i \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b \sqrt{b^{2}}}+\frac{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b^{2}}-\frac{a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b \sqrt{b^{2}}}"," ",0,"1/2*I/b*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*I/b^2*a*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*I/b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/b^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-a/b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)","A"
166,1,69,43,0.109000," ","int((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2),x)","\frac{i \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b}+\frac{\ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\sqrt{b^{2}}}"," ",0,"I/b*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)","A"
167,1,157,68,0.165000," ","int((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x,x)","\frac{i b \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\sqrt{b^{2}}}-\frac{i \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right) a}{\sqrt{a^{2}+1}}-\frac{\ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\sqrt{a^{2}+1}}"," ",0,"I*b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-I/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)*a-1/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)","B"
168,1,236,100,0.171000," ","int((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x^2,x)","-\frac{i b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\sqrt{a^{2}+1}}-\frac{i \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a}{\left(a^{2}+1\right) x}-\frac{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(a^{2}+1\right) x}+\frac{i a^{2} b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}}}+\frac{a b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-I*b/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-I/(a^2+1)/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-1/(a^2+1)/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I*a^2*b/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+a*b/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)","B"
169,1,405,157,0.175000," ","int((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x^3,x)","-\frac{i b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(a^{2}+1\right) x}+\frac{3 i b^{2} a \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{i \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a}{2 \left(a^{2}+1\right) x^{2}}-\frac{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(a^{2}+1\right) x^{2}}+\frac{3 i a^{2} b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(a^{2}+1\right)^{2} x}+\frac{3 a b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(a^{2}+1\right)^{2} x}-\frac{3 i a^{3} b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{3 a^{2} b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-I*b/(a^2+1)/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/2*I*b^2*a/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-1/2*I/(a^2+1)/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-1/2/(a^2+1)/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/2*I*a^2*b/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/2*a*b/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/2*I*a^3*b^2/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-3/2*a^2*b^2/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+1/2*b^2/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)","B"
170,1,611,227,0.181000," ","int((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2)/x^4,x)","-\frac{i \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a}{3 \left(a^{2}+1\right) x^{3}}-\frac{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{3 \left(a^{2}+1\right) x^{3}}+\frac{5 i a^{2} b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{6 \left(a^{2}+1\right)^{2} x^{2}}+\frac{5 a b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{6 \left(a^{2}+1\right)^{2} x^{2}}+\frac{5 i a^{4} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{7}{2}}}-\frac{5 a^{2} b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(a^{2}+1\right)^{3} x}+\frac{i b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{3}{2}}}+\frac{5 a^{3} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{7}{2}}}-\frac{5 i a^{3} b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(a^{2}+1\right)^{3} x}-\frac{3 a \,b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{13 i b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a}{6 \left(a^{2}+1\right)^{2} x}+\frac{2 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{3 \left(a^{2}+1\right)^{2} x}-\frac{3 i a^{2} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{i b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(a^{2}+1\right) x^{2}}"," ",0,"-1/3*I/(a^2+1)/x^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-1/3/(a^2+1)/x^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+5/6*I*a^2*b/(a^2+1)^2/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+5/6*a*b/(a^2+1)^2/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+5/2*I*a^4*b^3/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-5/2*a^2*b^2/(a^2+1)^3/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*I*b^3/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+5/2*a^3*b^3/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-5/2*I*a^3*b^2/(a^2+1)^3/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/2*a*b^3/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+13/6*I*b^2/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+2/3*b^2/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*I*a^2*b^3/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-1/2*I*b/(a^2+1)/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)","B"
171,1,347,78,0.044000," ","int((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x^4,x)","-\frac{x^{5}}{5}+\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{b^{5}}-\frac{2 i x^{3} a}{3 b^{2}}+\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{4}}{b^{5}}+\frac{i x^{4}}{2 b}+\frac{2 x^{3}}{3 b^{2}}-\frac{i x^{2}}{b^{3}}-\frac{2 a \,x^{2}}{b^{3}}-\frac{6 i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{2}}{b^{5}}+\frac{6 x \,a^{2}}{b^{4}}-\frac{2 x}{b^{4}}-\frac{8 i \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a}{b^{5}}+\frac{8 i \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{3}}{b^{5}}-\frac{4 \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{3}}{b^{5}}-\frac{2 i a^{3} x}{b^{4}}+\frac{4 \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{b^{5}}+\frac{i x^{2} a^{2}}{b^{3}}+\frac{2 \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{4}}{b^{5}}+\frac{6 i a x}{b^{4}}-\frac{12 \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{2}}{b^{5}}+\frac{2 \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right)}{b^{5}}"," ",0,"-1/5*x^5+I/b^5*ln(b^2*x^2+2*a*b*x+a^2+1)-2/3*I/b^2*x^3*a+I/b^5*ln(b^2*x^2+2*a*b*x+a^2+1)*a^4+1/2*I*x^4/b+2/3/b^2*x^3-I/b^3*x^2-2/b^3*a*x^2-6*I/b^5*ln(b^2*x^2+2*a*b*x+a^2+1)*a^2+6/b^4*x*a^2-2/b^4*x-8*I/b^5*arctan(1/2*(2*b^2*x+2*a*b)/b)*a+8*I/b^5*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^3-4/b^5*ln(b^2*x^2+2*a*b*x+a^2+1)*a^3-2*I/b^4*a^3*x+4/b^5*ln(b^2*x^2+2*a*b*x+a^2+1)*a+I/b^3*x^2*a^2+2/b^5*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^4+6*I/b^4*a*x-12/b^5*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^2+2/b^5*arctan(1/2*(2*b^2*x+2*a*b)/b)","B"
172,1,255,62,0.044000," ","int((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x^3,x)","-\frac{x^{4}}{4}+\frac{2 i x^{3}}{3 b}-\frac{i x^{2} a}{b^{2}}+\frac{2 i a^{2} x}{b^{3}}+\frac{x^{2}}{b^{2}}-\frac{2 i x}{b^{3}}-\frac{4 a x}{b^{3}}-\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{3}}{b^{4}}+\frac{3 i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{b^{4}}+\frac{3 \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{2}}{b^{4}}-\frac{\ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{b^{4}}-\frac{6 i \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{2}}{b^{4}}-\frac{2 \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{3}}{b^{4}}+\frac{2 i \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right)}{b^{4}}+\frac{6 \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a}{b^{4}}"," ",0,"-1/4*x^4+2/3*I*x^3/b-I/b^2*x^2*a+2*I/b^3*a^2*x+1/b^2*x^2-2*I/b^3*x-4*a*x/b^3-I/b^4*ln(b^2*x^2+2*a*b*x+a^2+1)*a^3+3*I/b^4*ln(b^2*x^2+2*a*b*x+a^2+1)*a+3/b^4*ln(b^2*x^2+2*a*b*x+a^2+1)*a^2-1/b^4*ln(b^2*x^2+2*a*b*x+a^2+1)-6*I/b^4*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^2-2/b^4*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^3+2*I/b^4*arctan(1/2*(2*b^2*x+2*a*b)/b)+6/b^4*arctan(1/2*(2*b^2*x+2*a*b)/b)*a","B"
173,1,176,47,0.042000," ","int((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x^2,x)","-\frac{x^{3}}{3}+\frac{i x^{2}}{b}-\frac{2 i a x}{b^{2}}+\frac{2 x}{b^{2}}+\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{2}}{b^{3}}-\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{b^{3}}-\frac{2 \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{b^{3}}+\frac{4 i \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a}{b^{3}}+\frac{2 \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{2}}{b^{3}}-\frac{2 \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right)}{b^{3}}"," ",0,"-1/3*x^3+I*x^2/b-2*I/b^2*a*x+2*x/b^2+I/b^3*ln(b^2*x^2+2*a*b*x+a^2+1)*a^2-I/b^3*ln(b^2*x^2+2*a*b*x+a^2+1)-2/b^3*ln(b^2*x^2+2*a*b*x+a^2+1)*a+4*I/b^3*arctan(1/2*(2*b^2*x+2*a*b)/b)*a+2/b^3*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^2-2/b^3*arctan(1/2*(2*b^2*x+2*a*b)/b)","B"
174,1,107,32,0.041000," ","int((1+I*(b*x+a))^2/(1+(b*x+a)^2)*x,x)","-\frac{x^{2}}{2}+\frac{2 i x}{b}-\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{b^{2}}+\frac{\ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{b^{2}}-\frac{2 i \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right)}{b^{2}}-\frac{2 \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a}{b^{2}}"," ",0,"-1/2*x^2+2*I*x/b-I/b^2*ln(b^2*x^2+2*a*b*x+a^2+1)*a+1/b^2*ln(b^2*x^2+2*a*b*x+a^2+1)-2*I/b^2*arctan(1/2*(2*b^2*x+2*a*b)/b)-2/b^2*arctan(1/2*(2*b^2*x+2*a*b)/b)*a","B"
175,1,51,18,0.040000," ","int((1+I*(b*x+a))^2/(1+(b*x+a)^2),x)","-x +\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{b}+\frac{2 \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right)}{b}"," ",0,"-x+I/b*ln(b^2*x^2+2*a*b*x+a^2+1)+2/b*arctan(1/2*(2*b^2*x+2*a*b)/b)","B"
176,1,149,34,0.046000," ","int((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x,x)","\frac{2 i \ln \left(x \right) a}{a^{2}+1}-\frac{\ln \left(x \right) a^{2}}{a^{2}+1}+\frac{\ln \left(x \right)}{a^{2}+1}-\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{a^{2}+1}-\frac{\ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{a^{2}+1}+\frac{2 i \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right)}{a^{2}+1}-\frac{2 \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a}{a^{2}+1}"," ",0,"2*I/(a^2+1)*ln(x)*a-1/(a^2+1)*ln(x)*a^2+1/(a^2+1)*ln(x)-I/(a^2+1)*ln(b^2*x^2+2*a*b*x+a^2+1)*a-1/(a^2+1)*ln(b^2*x^2+2*a*b*x+a^2+1)+2*I/(a^2+1)*arctan(1/2*(2*b^2*x+2*a*b)/b)-2/(a^2+1)*arctan(1/2*(2*b^2*x+2*a*b)/b)*a","B"
177,1,260,45,0.051000," ","int((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x^2,x)","-\frac{2 i a}{\left(a^{2}+1\right) x}+\frac{a^{2}}{\left(a^{2}+1\right) x}-\frac{1}{\left(a^{2}+1\right) x}-\frac{2 i b \ln \left(x \right) a^{2}}{\left(a^{2}+1\right)^{2}}+\frac{2 i b \ln \left(x \right)}{\left(a^{2}+1\right)^{2}}-\frac{4 b \ln \left(x \right) a}{\left(a^{2}+1\right)^{2}}+\frac{i b \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{2}}{\left(a^{2}+1\right)^{2}}-\frac{i b \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{\left(a^{2}+1\right)^{2}}+\frac{2 b \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{\left(a^{2}+1\right)^{2}}-\frac{4 i b \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a}{\left(a^{2}+1\right)^{2}}+\frac{2 b \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{2}}{\left(a^{2}+1\right)^{2}}-\frac{2 b \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right)}{\left(a^{2}+1\right)^{2}}"," ",0,"-2*I/(a^2+1)/x*a+1/(a^2+1)/x*a^2-1/(a^2+1)/x-2*I*b/(a^2+1)^2*ln(x)*a^2+2*I*b/(a^2+1)^2*ln(x)-4*b/(a^2+1)^2*ln(x)*a+I*b/(a^2+1)^2*ln(b^2*x^2+2*a*b*x+a^2+1)*a^2-I*b/(a^2+1)^2*ln(b^2*x^2+2*a*b*x+a^2+1)+2*b/(a^2+1)^2*ln(b^2*x^2+2*a*b*x+a^2+1)*a-4*I*b/(a^2+1)^2*arctan(1/2*(2*b^2*x+2*a*b)/b)*a+2*b/(a^2+1)^2*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^2-2*b/(a^2+1)^2*arctan(1/2*(2*b^2*x+2*a*b)/b)","B"
178,1,406,65,0.052000," ","int((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x^3,x)","\frac{6 i b^{2} \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{2}}{\left(a^{2}+1\right)^{3}}+\frac{a^{2}}{2 \left(a^{2}+1\right) x^{2}}-\frac{1}{2 \left(a^{2}+1\right) x^{2}}-\frac{i b^{2} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{3}}{\left(a^{2}+1\right)^{3}}+\frac{2 i b \,a^{2}}{\left(a^{2}+1\right)^{2} x}+\frac{4 b a}{\left(a^{2}+1\right)^{2} x}+\frac{2 i b^{2} \ln \left(x \right) a^{3}}{\left(a^{2}+1\right)^{3}}-\frac{2 i b}{\left(a^{2}+1\right)^{2} x}+\frac{6 b^{2} \ln \left(x \right) a^{2}}{\left(a^{2}+1\right)^{3}}-\frac{2 b^{2} \ln \left(x \right)}{\left(a^{2}+1\right)^{3}}+\frac{3 i b^{2} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{\left(a^{2}+1\right)^{3}}-\frac{i a}{\left(a^{2}+1\right) x^{2}}-\frac{3 b^{2} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{2}}{\left(a^{2}+1\right)^{3}}+\frac{b^{2} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{\left(a^{2}+1\right)^{3}}-\frac{2 i b^{2} \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right)}{\left(a^{2}+1\right)^{3}}-\frac{2 b^{2} \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{3}}{\left(a^{2}+1\right)^{3}}-\frac{6 i b^{2} \ln \left(x \right) a}{\left(a^{2}+1\right)^{3}}+\frac{6 b^{2} \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a}{\left(a^{2}+1\right)^{3}}"," ",0,"6*I*b^2/(a^2+1)^3*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^2+1/2/(a^2+1)/x^2*a^2-1/2/(a^2+1)/x^2-I*b^2/(a^2+1)^3*ln(b^2*x^2+2*a*b*x+a^2+1)*a^3+2*I*b/(a^2+1)^2/x*a^2+4*b/(a^2+1)^2/x*a+2*I*b^2/(a^2+1)^3*ln(x)*a^3-2*I*b/(a^2+1)^2/x+6*b^2/(a^2+1)^3*ln(x)*a^2-2*b^2/(a^2+1)^3*ln(x)+3*I*b^2/(a^2+1)^3*ln(b^2*x^2+2*a*b*x+a^2+1)*a-I/(a^2+1)/x^2*a-3*b^2/(a^2+1)^3*ln(b^2*x^2+2*a*b*x+a^2+1)*a^2+b^2/(a^2+1)^3*ln(b^2*x^2+2*a*b*x+a^2+1)-2*I*b^2/(a^2+1)^3*arctan(1/2*(2*b^2*x+2*a*b)/b)-2*b^2/(a^2+1)^3*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^3-6*I*b^2/(a^2+1)^3*ln(x)*a+6*b^2/(a^2+1)^3*arctan(1/2*(2*b^2*x+2*a*b)/b)*a","B"
179,1,560,79,0.062000," ","int((1+I*(b*x+a))^2/(1+(b*x+a)^2)/x^4,x)","\frac{2 b^{3} \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right)}{\left(a^{2}+1\right)^{4}}+\frac{a^{2}}{3 \left(a^{2}+1\right) x^{3}}+\frac{2 b^{2}}{\left(a^{2}+1\right)^{3} x}-\frac{8 b^{3} \ln \left(x \right) a^{3}}{\left(a^{2}+1\right)^{4}}+\frac{2 b a}{\left(a^{2}+1\right)^{2} x^{2}}-\frac{6 b^{2} a^{2}}{\left(a^{2}+1\right)^{3} x}-\frac{4 b^{3} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{\left(a^{2}+1\right)^{4}}+\frac{2 b^{3} \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{4}}{\left(a^{2}+1\right)^{4}}-\frac{12 b^{3} \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{2}}{\left(a^{2}+1\right)^{4}}+\frac{4 b^{3} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{3}}{\left(a^{2}+1\right)^{4}}+\frac{8 b^{3} \ln \left(x \right) a}{\left(a^{2}+1\right)^{4}}-\frac{1}{3 \left(a^{2}+1\right) x^{3}}-\frac{2 i b^{3} \ln \left(x \right) a^{4}}{\left(a^{2}+1\right)^{4}}+\frac{12 i b^{3} \ln \left(x \right) a^{2}}{\left(a^{2}+1\right)^{4}}+\frac{i b \,a^{2}}{\left(a^{2}+1\right)^{2} x^{2}}-\frac{2 i b^{2} a^{3}}{\left(a^{2}+1\right)^{3} x}-\frac{6 i b^{3} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{2}}{\left(a^{2}+1\right)^{4}}-\frac{8 i b^{3} \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a^{3}}{\left(a^{2}+1\right)^{4}}+\frac{8 i b^{3} \arctan \left(\frac{2 b^{2} x +2 a b}{2 b}\right) a}{\left(a^{2}+1\right)^{4}}+\frac{i b^{3} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{4}}{\left(a^{2}+1\right)^{4}}+\frac{6 i b^{2} a}{\left(a^{2}+1\right)^{3} x}-\frac{2 i b^{3} \ln \left(x \right)}{\left(a^{2}+1\right)^{4}}-\frac{2 i a}{3 \left(a^{2}+1\right) x^{3}}-\frac{i b}{\left(a^{2}+1\right)^{2} x^{2}}+\frac{i b^{3} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{\left(a^{2}+1\right)^{4}}"," ",0,"2*b^3/(a^2+1)^4*arctan(1/2*(2*b^2*x+2*a*b)/b)+1/3/(a^2+1)/x^3*a^2+2*b^2/(a^2+1)^3/x-2*I*b^3/(a^2+1)^4*ln(x)-8*b^3/(a^2+1)^4*ln(x)*a^3-2/3*I/(a^2+1)/x^3*a+2*b/(a^2+1)^2/x^2*a-I*b/(a^2+1)^2/x^2-6*b^2/(a^2+1)^3/x*a^2-4*b^3/(a^2+1)^4*ln(b^2*x^2+2*a*b*x+a^2+1)*a+2*b^3/(a^2+1)^4*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^4-12*b^3/(a^2+1)^4*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^2+4*b^3/(a^2+1)^4*ln(b^2*x^2+2*a*b*x+a^2+1)*a^3+I*b^3/(a^2+1)^4*ln(b^2*x^2+2*a*b*x+a^2+1)+8*b^3/(a^2+1)^4*ln(x)*a-1/3/(a^2+1)/x^3+8*I*b^3/(a^2+1)^4*arctan(1/2*(2*b^2*x+2*a*b)/b)*a+I*b^3/(a^2+1)^4*ln(b^2*x^2+2*a*b*x+a^2+1)*a^4+6*I*b^2/(a^2+1)^3/x*a-2*I*b^3/(a^2+1)^4*ln(x)*a^4+12*I*b^3/(a^2+1)^4*ln(x)*a^2+I*b/(a^2+1)^2/x^2*a^2-2*I*b^2/(a^2+1)^3/x*a^3-6*I*b^3/(a^2+1)^4*ln(b^2*x^2+2*a*b*x+a^2+1)*a^2-8*I*b^3/(a^2+1)^4*arctan(1/2*(2*b^2*x+2*a*b)/b)*a^3","B"
180,1,933,262,0.196000," ","int((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x^4,x)","\frac{33 a^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{4} \sqrt{b^{2}}}+\frac{89 i a^{2} x^{2}}{10 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{501 i a^{3} x}{10 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{7 i x^{4}}{5 b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{28 i x^{2}}{5 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{i b \,x^{6}}{5 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{319 i a^{4}}{10 b^{5} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{i a^{6}}{5 b^{5} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{209 i a^{2}}{10 b^{5} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{i a \,x^{5}}{5 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{x^{3} a^{2}}{2 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a^{3} x^{2}}{2 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 a^{4} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{4} \sqrt{b^{2}}}+\frac{a \,x^{4}}{4 b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{29 i a \,x^{3}}{10 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{367 i a x}{10 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{i a^{5} x}{5 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 x^{5}}{4 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{18 i a^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{4} \sqrt{b^{2}}}-\frac{103 a \,x^{2}}{8 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{527 a^{2} x}{8 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{53 a^{4} x}{4 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{51 i a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{4} \sqrt{b^{2}}}-\frac{56 i}{5 b^{5} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{57 x}{8 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{57 \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 b^{4} \sqrt{b^{2}}}-\frac{181 a^{3}}{8 b^{5} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{41 a^{5}}{4 b^{5} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{263 a}{8 b^{5} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{19 x^{3}}{8 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}"," ",0,"33*a^2/b^4*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+89/10*I/b^3*a^2*x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+501/10*I/b^4*a^3*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-29/10*I/b^2*a*x^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-367/10*I/b^4*a*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-28/5*I/b^3*x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*x^3/b^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^2+3/2*a^3/b^3*x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*a^4/b^4*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/4/b*a*x^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/4*x^5/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-103/8*a/b^3*x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/5*I*b*x^6/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-527/8*a^2/b^4*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+53/4*a^4/b^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+319/10*I/b^5*a^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/5*I/b^5*a^6/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+209/10*I/b^5*a^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/5*I*a*x^5/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+7/5*I/b*x^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-56/5*I/b^5/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+57/8/b^4*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-57/8/b^4*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-181/8*a^3/b^5/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+41/4*a^5/b^5/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-263/8*a/b^5/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+19/8*x^3/b^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/5*I/b^4*a^5*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-18*I/b^4*a^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+51/2*I/b^4*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)","B"
181,1,711,200,0.186000," ","int((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x^3,x)","-\frac{3 x^{2} a^{2}}{2 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{a \,x^{3}}{2 b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{3} \sqrt{b^{2}}}-\frac{33 a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{3} \sqrt{b^{2}}}-\frac{265 i a^{2} x}{8 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{53 i a \,x^{2}}{8 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{51 i \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 b^{3} \sqrt{b^{2}}}-\frac{155 i a^{3}}{8 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{17 i x^{3}}{8 b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{10}{b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{27 i a^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{3} \sqrt{b^{2}}}-\frac{i b \,x^{5}}{4 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{i a^{4} x}{4 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{i a \,x^{4}}{4 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{i a^{5}}{4 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{51 i x}{8 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{157 i a}{8 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{5 x^{2}}{b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{x^{4}}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{53 a x}{2 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{25 a^{3} x}{2 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{a^{2}}{2 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{19 a^{4}}{2 b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}"," ",0,"-3/2*x^2/b^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^2+1/2/b*a*x^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*a^3/b^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-33/2*a/b^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-265/8*I/b^3*a^2*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-53/8*I/b^2*a*x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-51/8*I/b^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-155/8*I/b^4*a^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+17/8*I/b*x^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+10/b^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+27/2*I/b^3*a^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/4*I*b*x^5/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/4*I/b^3*a^4*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/4*I*a*x^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/4*I/b^4*a^5/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+51/8*I/b^3*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-157/8*I/b^4*a/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+5*x^2/b^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-x^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+53/2*a/b^3*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-25/2*a^3/b^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+1/2*a^2/b^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-19/2*a^4/b^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)","B"
182,1,519,179,0.182000," ","int((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x^2,x)","-\frac{i b \,x^{4}}{3 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{i a \,x^{3}}{3 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{26 i}{3 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a \,x^{2}}{2 b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right) a^{2}}{b^{2} \sqrt{b^{2}}}-\frac{i a^{3} x}{3 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{13 i x^{2}}{3 b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{i a^{4}}{3 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{11 \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{2} \sqrt{b^{2}}}-\frac{11 x}{2 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{53 i a x}{3 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 x^{3}}{2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{9 i a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{2} \sqrt{b^{2}}}+\frac{25 i a^{2}}{3 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{17 a}{2 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{17 a^{3}}{2 b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{23 a^{2} x}{2 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}"," ",0,"-1/3*I*b*x^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/3*I*a*x^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+26/3*I/b^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/2/b*a*x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/b^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)*a^2-1/3*I/b^2*a^3*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+13/3*I/b*x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/3*I/b^3*a^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+11/2/b^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-11/2*x/b^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+53/3*I/b^2*a*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/2*x^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-9*I/b^2*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+25/3*I/b^3*a^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+17/2*a/b^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+17/2*a^3/b^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+23/2*a^2/b^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x","B"
183,1,358,129,0.175000," ","int((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)*x,x)","-\frac{10 a x}{b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{9 i \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b \sqrt{b^{2}}}+\frac{i a^{3}}{2 b^{2} \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{7}{b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b \sqrt{b^{2}}}+\frac{i a^{2} x}{2 b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 x^{2}}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{i a \,x^{2}}{2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{i a}{2 b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{9 i x}{2 b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{7 a^{2}}{b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}"," ",0,"-10*a/b/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+9/2*I/b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*I/b^2*a^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*I*b*x^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-7/b^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*a/b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*I/b*a^2*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*I*a*x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*I/b^2*a/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-9/2*I/b*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-7*a^2/b^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)","B"
184,1,362,76,0.111000," ","int((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2),x)","-\frac{5 i}{b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a}{b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a^{2} x}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a^{3}}{b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\sqrt{b^{2}}}-\frac{4 i a^{2}}{b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{i a^{3} x}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{i a^{4}}{b \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{5 i a x}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{2 \left(i a +1\right)^{3} \left(2 b^{2} x +2 a b \right)}{\left(4 b^{2} \left(a^{2}+1\right)-4 a^{2} b^{2}\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 x}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}"," ",0,"-5*I/b/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/b*a/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*a^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+3/b*a^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-4*I/b*a^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I*a^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+I/b*a^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-I*b*x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-5*I*a*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+2*(1+I*a)^3*(2*b^2*x+2*a*b)/(4*b^2*(a^2+1)-4*a^2*b^2)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)","B"
185,1,818,104,0.171000," ","int((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x,x)","\frac{1}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{i a^{5}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{i a^{4} b x}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{6 i \left(i a +1\right)^{2} b \left(2 b^{2} x +2 a b \right)}{\left(4 b^{2} \left(a^{2}+1\right)-4 a^{2} b^{2}\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{2 i a}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 b a x}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{4 i a^{3}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{\ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}}}+\frac{3 a^{2}}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a^{3} b x}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{a b x}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 i a^{2} b x}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{i \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right) a^{3}}{\left(a^{2}+1\right)^{\frac{3}{2}}}+\frac{2 i a^{3}}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{i b \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\sqrt{b^{2}}}+\frac{i b x}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 i \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right) a}{\left(a^{2}+1\right)^{\frac{3}{2}}}+\frac{3 i a}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{2 i b \,a^{2} x}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{4 a^{2}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a^{4}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right) a^{2}}{\left(a^{2}+1\right)^{\frac{3}{2}}}"," ",0,"1/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I*a^5/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I*a^4*b/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+6*I*(1+I*a)^2*b*(2*b^2*x+2*a*b)/(4*b^2*(a^2+1)-4*a^2*b^2)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+2*I*a/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*b*a/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-4*I/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^3-1/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+3*a^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*a^3*b/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-a*b/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-3*I*a^2*b/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+I/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)*a^3+2*I*a^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-I*b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+I*b*x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*I/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)*a+3*I/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+2*I*b*a^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-4*a^2/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*a^4/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)*a^2","B"
186,1,1358,136,0.174000," ","int((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x^2,x)","-\frac{3 i a}{\left(a^{2}+1\right) x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{12 i a^{4} b}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{9 i a^{2} b}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 i a^{6} b}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 i a^{4} b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{5 i b \,a^{4}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{i b^{2} a x}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{12 i b \,a^{2}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{9 i a^{3} b^{2} x}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{9 i a^{2} b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{i a^{3}}{\left(a^{2}+1\right) x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{9 a^{4} b^{2} x}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a^{2} b^{2} x}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{12 a^{2} b^{2} x}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{9 i a \,b^{2} x}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{6 i a \,b^{2} \left(2 b^{2} x +2 a b \right)}{\left(4 b^{2} \left(a^{2}+1\right)-4 a^{2} b^{2}\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{5 i a^{3} b^{2} x}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{6 a b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{3 i a^{5} b^{2} x}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 i a^{2} b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{1}{\left(a^{2}+1\right) x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 a b}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{12 a^{3} b}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{8 b a}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{12 b \,a^{3}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{6 b^{2} \left(2 b^{2} x +2 a b \right)}{\left(4 b^{2} \left(a^{2}+1\right)-4 a^{2} b^{2}\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{2 x \,b^{2}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 a^{2}}{\left(a^{2}+1\right) x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{9 a^{5} b}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{9 a^{3} b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{3 i b}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 i b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}}}+\frac{i b}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{i b \,a^{2}}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}"," ",0,"9*I*a^2*b/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+I/(a^2+1)/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^3-9*a^4*b^2/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+3*a^2*b^2/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+3*I*a^2*b/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+I*b^2*a/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+12*a^2*b^2/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-12*I*b/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^2-3*I/(a^2+1)/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+12*I*a^4*b/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-9*I*a^2*b/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*I*a^6*b/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*I*a^4*b/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+6*a*b/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+5*I*b*a^4/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*I*a^5*b^2/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+9*I*a^3*b^2/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+5*I*a^3*b^2/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-9*I*a*b^2/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-6*I*a*b^2*(2*b^2*x+2*a*b)/(4*b^2*(a^2+1)-4*a^2*b^2)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/(a^2+1)/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I*b/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*a*b/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+12*a^3*b/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*I*b/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*I*b/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-8*b/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+12*b*a^3/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I*b*a^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-6*b^2*(2*b^2*x+2*a*b)/(4*b^2*(a^2+1)-4*a^2*b^2)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*a*b/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-2/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*b^2+3/(a^2+1)/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^2-9*a^5*b/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-9*a^3*b/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)","B"
187,1,1955,209,0.178000," ","int((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x^3,x)","\frac{15 i a^{6} b^{3} x}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{45 i a^{4} b^{3} x}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 i b \,a^{2}}{\left(a^{2}+1\right) x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{75 a^{4} b^{2}}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{15 a^{2} b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{7}{2}}}+\frac{29 a^{2} b^{2}}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{15 b^{2} a^{2}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{45 a^{2} b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{3 a^{2}}{2 \left(a^{2}+1\right) x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{45 a^{6} b^{2}}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{45 a^{4} b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{7}{2}}}+\frac{15 a^{2} b^{2}}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{30 a^{4} b^{2}}{\left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{9 i b^{3} a^{2} x}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{31 i a^{4} b^{3} x}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{57 i a^{2} b^{3} x}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{5 i a^{4} b}{2 \left(a^{2}+1\right)^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{9 i b^{2} a^{3}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{39 i a^{3} b^{2}}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{6 i x \,b^{3}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 i b}{\left(a^{2}+1\right) x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{45 i a^{3} b^{2}}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{15 i a^{7} b^{2}}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{15 i a^{5} b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{7}{2}}}+\frac{3 i b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right) a}{\left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{9 i b^{2} a}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{27 i a \,b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{45 i a^{3} b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{7}{2}}}+\frac{i a^{3}}{2 \left(a^{2}+1\right) x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 i a}{2 \left(a^{2}+1\right) x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{15 i a^{2} b}{2 \left(a^{2}+1\right)^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{21 i a^{3} b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{2 i b^{3} \left(2 b^{2} x +2 a b \right)}{\left(4 b^{2} \left(a^{2}+1\right)-4 a^{2} b^{2}\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{30 i a^{5} b^{2}}{\left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{27 i a \,b^{2}}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{31 i a^{5} b^{2}}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{45 a^{5} b^{3} x}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{15 a^{3} b}{2 \left(a^{2}+1\right)^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{13 a \,b^{3} x}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{5 a b}{2 \left(a^{2}+1\right)^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{15 a^{3} b^{3} x}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{6 b a}{\left(a^{2}+1\right) x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{75 a^{3} b^{3} x}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{15 b^{3} a x}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}}}+\frac{3 b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{3 b^{2}}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{3 b^{2}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{1}{2 \left(a^{2}+1\right) x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}"," ",0,"-75/2*a^4*b^2/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-15/2*a^2*b^2/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+29*a^2*b^2/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+15*b^2*a^2/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-45/2*a^2*b^2/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+3/2/(a^2+1)/x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^2+45/2*a^6*b^2/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+45/2*a^4*b^2/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+15/2*a^2*b^2/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-30*a^4*b^2/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+15/2*I*a^2*b/(a^2+1)^2/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+9*I*b^3*a^2/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-31/2*I*a^4*b^3/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+57/2*I*a^2*b^3/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-5/2*I*a^4*b/(a^2+1)^2/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+15/2*I*a^6*b^3/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-45/2*I*a^4*b^3/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+3*I*b/(a^2+1)/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^2-2*I*b^3*(2*b^2*x+2*a*b)/(4*b^2*(a^2+1)-4*a^2*b^2)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-30*I*a^5*b^2/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-27/2*I*a*b^2/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-31/2*I*a^5*b^2/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+27/2*I*a*b^2/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-45/2*I*a^3*b^2/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+1/2*I/(a^2+1)/x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^3-3/2*I/(a^2+1)/x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+9*I*b^2*a^3/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-21/2*I*a^3*b^2/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+39*I*a^3*b^2/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+45/2*a^5*b^3/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-15/2*a^3*b/(a^2+1)^2/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+13/2*a*b^3/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+5/2*a*b/(a^2+1)^2/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-15/2*a^3*b^3/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-6*I/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*b^3-3*I*b/(a^2+1)/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+45/2*I*a^3*b^2/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+15/2*I*a^7*b^2/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+15/2*I*a^5*b^2/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+6*b/(a^2+1)/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-75/2*a^3*b^3/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+15*b^3*a/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+3*I*b^2/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)*a-9*I*b^2/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+3*b^2/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+3/2*b^2/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-3/2*b^2/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*b^2/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2/(a^2+1)/x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)","B"
188,1,2624,266,0.181000," ","int((1+I*(b*x+a))^3/(1+(b*x+a)^2)^(3/2)/x^4,x)","\frac{105 i a^{5} b^{4} x}{2 \left(a^{2}+1\right)^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 i b \,a^{2}}{2 \left(a^{2}+1\right) x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{7 i b^{4} a x}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{55 i b^{4} x a}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{23 i b^{2} a}{2 \left(a^{2}+1\right)^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{35 i a^{7} b^{4} x}{2 \left(a^{2}+1\right)^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{7 i a^{4} b}{6 \left(a^{2}+1\right)^{2} x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{7 i a^{2} b}{2 \left(a^{2}+1\right)^{2} x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{35 i a^{3} b^{2}}{2 \left(a^{2}+1\right)^{3} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 i b^{2} a}{\left(a^{2}+1\right) x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{35 i a^{5} b^{2}}{6 \left(a^{2}+1\right)^{3} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{i b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{i b^{3}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{9 i b^{3}}{2 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{9 i b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{35 a^{3} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{9}{2}}}-\frac{15 a \,b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{7}{2}}}+\frac{105 i a^{4} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{9}{2}}}-\frac{3 i b}{2 \left(a^{2}+1\right) x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{35 i a^{8} b^{3}}{2 \left(a^{2}+1\right)^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{35 i a^{6} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{9}{2}}}-\frac{110 i a^{4} b^{3}}{\left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{27 i b^{3} a^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{i a^{3}}{3 \left(a^{2}+1\right) x^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{i a}{\left(a^{2}+1\right) x^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{70 i a^{6} b^{3}}{\left(a^{2}+1\right)^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{105 i a^{4} b^{3}}{2 \left(a^{2}+1\right)^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{7 i b^{3} a^{2}}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{45 i a^{2} b^{3}}{\left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{135 a^{3} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{7}{2}}}-\frac{18 a \,b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{45 i a^{2} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{7}{2}}}-\frac{187 i b^{3} a^{4}}{6 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{41 i b^{3} a^{2}}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{30 i a^{4} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(a^{2}+1\right)^{\frac{7}{2}}}+\frac{125 i a^{6} b^{3}}{3 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{80 i a^{3} b^{4} x}{\left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{53 i b^{2} a^{3}}{6 \left(a^{2}+1\right)^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{187 i b^{4} x \,a^{3}}{6 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{125 i a^{5} b^{4} x}{3 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 b^{2}}{\left(a^{2}+1\right) x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{6 b^{4} x}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{6 b^{3} a}{\left(a^{2}+1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{35 a^{3} b^{3}}{2 \left(a^{2}+1\right)^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{70 a^{5} b^{3}}{\left(a^{2}+1\right)^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{260 a^{3} b^{3}}{3 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{15 a \,b^{3}}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{a^{2}}{\left(a^{2}+1\right) x^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{105 a^{7} b^{3}}{2 \left(a^{2}+1\right)^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{105 a^{5} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(a^{2}+1\right)^{\frac{9}{2}}}+\frac{205 a^{5} b^{3}}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{56 b^{3} a^{3}}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{4 b^{2}}{3 \left(a^{2}+1\right)^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{8 b^{4} x}{3 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{62 b^{3} a}{3 \left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{7 a b}{6 \left(a^{2}+1\right)^{2} x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{35 a^{2} b^{2}}{6 \left(a^{2}+1\right)^{3} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{35 a^{4} b^{4} x}{2 \left(a^{2}+1\right)^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{3 b a}{\left(a^{2}+1\right) x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{19 b^{2} a^{2}}{\left(a^{2}+1\right)^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{56 b^{4} x \,a^{2}}{\left(a^{2}+1\right)^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{7 a^{3} b}{2 \left(a^{2}+1\right)^{2} x^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{35 a^{4} b^{2}}{2 \left(a^{2}+1\right)^{3} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{105 a^{6} b^{4} x}{2 \left(a^{2}+1\right)^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}+\frac{205 a^{4} b^{4} x}{2 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{115 a^{2} b^{4} x}{6 \left(a^{2}+1\right)^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}-\frac{1}{3 \left(a^{2}+1\right) x^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}"," ",0,"35/2*a^3*b^3/(a^2+1)^(9/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-15/2*a*b^3/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+135/2*a^3*b^3/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-18*a*b^3/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+7*I*b^3*a^2/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+45*I*a^2*b^3/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-45*I*a^2*b^3/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-187/6*I*b^3/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^4+41*I*b^3/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^2+30*I*a^4*b^3/(a^2+1)^(7/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+125/3*I*a^6*b^3/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-110*I*a^4*b^3/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-27/2*I*b^3*a^2/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+1/3*I/(a^2+1)/x^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^3-I/(a^2+1)/x^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+70*I*a^6*b^3/(a^2+1)^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-105/2*I*a^4*b^3/(a^2+1)^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-35/2*I*a^8*b^3/(a^2+1)^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*b^2/(a^2+1)/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+6*b^4/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+6*b^3/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-35/2*a^3*b^3/(a^2+1)^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+70*a^5*b^3/(a^2+1)^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-260/3*a^3*b^3/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+15/2*a*b^3/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I*b^3/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-I*b^3/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-9/2*I*b^3/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+9/2*I*b^3/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+1/(a^2+1)/x^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^2-105/2*a^7*b^3/(a^2+1)^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-105/2*a^5*b^3/(a^2+1)^(9/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+205/2*a^5*b^3/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-56*b^3/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^3+4/3*b^2/(a^2+1)^2/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+8/3*b^4/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+62/3*b^3/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-35/2*I*a^6*b^3/(a^2+1)^(9/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+105/2*I*a^4*b^3/(a^2+1)^(9/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+7/6*a*b/(a^2+1)^2/x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-35/6*a^2*b^2/(a^2+1)^3/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+35/2*a^4*b^4/(a^2+1)^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-3/2*I*b/(a^2+1)/x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*b/(a^2+1)/x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-19*b^2/(a^2+1)^2/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^2-56*b^4/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*a^2-7/2*a^3*b/(a^2+1)^2/x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+35/2*a^4*b^2/(a^2+1)^3/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-105/2*a^6*b^4/(a^2+1)^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+205/2*a^4*b^4/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-115/6*a^2*b^4/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-1/3/(a^2+1)/x^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*I*b^2/(a^2+1)/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+35/6*I*a^5*b^2/(a^2+1)^3/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-7/6*I*a^4*b/(a^2+1)^2/x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+7/2*I*a^2*b/(a^2+1)^2/x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-35/2*I*a^3*b^2/(a^2+1)^3/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-35/2*I*a^7*b^4/(a^2+1)^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+105/2*I*a^5*b^4/(a^2+1)^4/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+3/2*I*b/(a^2+1)/x^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^2+7*I*b^4*a/(a^2+1)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+55/2*I*b^4/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*a+23/2*I*b^2/(a^2+1)^2/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-187/6*I*b^4/(a^2+1)^2/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x*a^3+125/3*I*a^5*b^4/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-80*I*a^3*b^4/(a^2+1)^3/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-53/6*I*b^2/(a^2+1)^2/x/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a^3","B"
189,1,1208,225,0.225000," ","int(x^4/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x)","\frac{3 a^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{4} \sqrt{b^{2}}}+\frac{3 a^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b^{4}}-\frac{i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{4}}{b^{5}}+\frac{6 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{2}}{b^{5}}+\frac{2 i a^{3} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b^{4}}-\frac{5 i a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{4} \sqrt{b^{2}}}-\frac{5 i a x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{4}}-\frac{4 i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{3}}{b^{4} \sqrt{b^{2}}}+\frac{4 i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a}{b^{4} \sqrt{b^{2}}}+\frac{3 i a x \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{5 b^{4}}-\frac{5 i a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{5}}-\frac{6 i a^{2} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{5 b^{5}}-\frac{i x^{2} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{5 b^{3}}+\frac{\ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{4}}{b^{4} \sqrt{b^{2}}}-\frac{6 \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{2}}{b^{4} \sqrt{b^{2}}}+\frac{2 i a^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b^{5}}+\frac{2 i a^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{4} \sqrt{b^{2}}}-\frac{4 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{3}}{b^{5}}+\frac{4 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{b^{5}}+\frac{\ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{b^{4} \sqrt{b^{2}}}-\frac{i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}}{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{x \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{4 b^{4}}-\frac{13 a \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{12 b^{5}}+\frac{3 a^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b^{5}}-\frac{5 x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 b^{4}}-\frac{5 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a}{8 b^{5}}-\frac{5 \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 b^{4} \sqrt{b^{2}}}"," ",0,"3*a^2/b^4*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+3*a^2/b^4*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+2*I/b^4*a^3*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-5/2*I/b^4*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+2*I/b^4*a^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-4*I/b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^3+4*I/b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a+3/5*I/b^4*a*x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-5/2*I/b^5*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+2*I/b^5*a^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-6/5*I/b^5*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-1/5*I/b^3*x^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+1/b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^4-6/b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^2-I/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^4+6*I/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^2-5/2*I/b^4*a*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-4/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^3+4/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+1/b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-I/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)+7/15*I/b^5*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+1/4/b^4*x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-13/12/b^5*a*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+3/b^5*a^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-5/8/b^4*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-5/8/b^5*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-5/8/b^4*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)","B"
190,1,894,163,0.190000," ","int(x^3/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x)","\frac{i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{3}}{b^{4}}+\frac{5 i a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 b^{4}}-\frac{3 i a^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{4}}-\frac{3 a x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{3}}-\frac{3 a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{3} \sqrt{b^{2}}}-\frac{3 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{b^{4}}+\frac{5 i \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 b^{3} \sqrt{b^{2}}}-\frac{i x \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{4 b^{3}}+\frac{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{3 b^{4}}-\frac{3 i a^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{3} \sqrt{b^{2}}}-\frac{\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}}{b^{4}}+\frac{3 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{2}}{b^{4}}+\frac{3 i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{2}}{b^{3} \sqrt{b^{2}}}-\frac{\ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{3}}{b^{3} \sqrt{b^{2}}}+\frac{3 \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a}{b^{3} \sqrt{b^{2}}}-\frac{i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{b^{3} \sqrt{b^{2}}}-\frac{3 i a^{2} x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{3}}+\frac{5 i x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 b^{3}}+\frac{3 i a \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{4 b^{4}}-\frac{3 a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{4}}"," ",0,"I/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^3+5/8*I/b^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-3/2*I/b^4*a^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/2*a/b^3*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/2*a/b^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3*I/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+5/8*I/b^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/4*I/b^3*x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+1/3/b^4*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-3/2*I/b^3*a^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)+3/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^2+3*I/b^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^2-1/b^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^3+3/b^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a-I/b^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-3/2*I/b^3*a^2*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+5/8*I/b^3*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/4*I/b^4*a*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-3/2*a^2/b^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)","B"
191,1,605,135,0.183000," ","int(x^2/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x)","-\frac{i \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{3 b^{3}}+\frac{i a x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b^{2}}+\frac{i a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{b^{3}}+\frac{i a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{b^{2} \sqrt{b^{2}}}+\frac{x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{2}}+\frac{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a}{2 b^{3}}+\frac{\ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{2} \sqrt{b^{2}}}-\frac{i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{2}}{b^{3}}+\frac{i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}}{b^{3}}-\frac{2 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{b^{3}}+\frac{\ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{2}}{b^{2} \sqrt{b^{2}}}-\frac{\ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{b^{2} \sqrt{b^{2}}}-\frac{2 i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a}{b^{2} \sqrt{b^{2}}}"," ",0,"-1/3*I/b^3*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+I/b^2*a*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I/b^3*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I/b^2*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*x/b^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2/b^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a+1/2/b^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-I/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^2+I/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)-2/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+1/b^2*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^2-1/b^2*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-2*I/b^2*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a","B"
192,1,350,86,0.175000," ","int(x/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x)","-\frac{i x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b}-\frac{i a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{2}}-\frac{i \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b \sqrt{b^{2}}}+\frac{i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{b^{2}}+\frac{\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}}{b^{2}}-\frac{\ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a}{b \sqrt{b^{2}}}+\frac{i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{b \sqrt{b^{2}}}"," ",0,"-1/2*I/b*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*I/b^2*a*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*I/b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+I/b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+1/b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)-1/b*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a+I/b*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)","B"
193,1,122,43,0.110000," ","int(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2),x)","-\frac{i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}}{b}+\frac{\ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{\sqrt{b^{2}}}"," ",0,"-I/b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)+ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)","B"
194,1,283,68,0.177000," ","int(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x,x)","\frac{i \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{i-a}+\frac{i a b \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right) \sqrt{b^{2}}}-\frac{i \sqrt{a^{2}+1}\, \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{i-a}-\frac{i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}}{i-a}+\frac{b \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{\left(i-a \right) \sqrt{b^{2}}}"," ",0,"I/(I-a)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I/(I-a)*a*b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-I/(I-a)*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-I/(I-a)*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)+1/(I-a)*b*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)","B"
195,1,602,100,0.184000," ","int(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x^2,x)","\frac{i b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(i-a \right)^{2}}+\frac{i b^{2} a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right)^{2} \sqrt{b^{2}}}-\frac{i b \sqrt{a^{2}+1}\, \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(i-a \right)^{2}}-\frac{i \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{\left(i-a \right) \left(a^{2}+1\right) x}+\frac{2 i a b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(i-a \right) \left(a^{2}+1\right)}+\frac{i a^{2} b^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right) \left(a^{2}+1\right) \sqrt{b^{2}}}-\frac{i a b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(i-a \right) \sqrt{a^{2}+1}}+\frac{i b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{\left(i-a \right) \left(a^{2}+1\right)}+\frac{i b^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right) \left(a^{2}+1\right) \sqrt{b^{2}}}-\frac{i b \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}}{\left(i-a \right)^{2}}+\frac{b^{2} \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{\left(i-a \right)^{2} \sqrt{b^{2}}}"," ",0,"I*b/(I-a)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I*b^2/(I-a)^2*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-I*b/(I-a)^2*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-I/(I-a)/(a^2+1)/x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+2*I/(I-a)*a*b/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I/(I-a)*a^2*b^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-I/(I-a)*a*b/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+I/(I-a)*b^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+I/(I-a)*b^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-I*b/(I-a)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)+b^2/(I-a)^2*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)","B"
196,1,1146,157,0.181000," ","int(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x^3,x)","-\frac{i b^{2} a \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(i-a \right)^{2} \sqrt{a^{2}+1}}+\frac{i b^{3} a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right) \left(a^{2}+1\right) \sqrt{b^{2}}}-\frac{i a^{2} b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(i-a \right) \left(a^{2}+1\right)^{2}}+\frac{i a^{2} b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(i-a \right) \left(a^{2}+1\right)^{\frac{3}{2}}}+\frac{i b^{3} a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right)^{3} \sqrt{b^{2}}}-\frac{i b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{\left(i-a \right)^{2} \left(a^{2}+1\right) x}-\frac{i b^{2} \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}}{\left(i-a \right)^{3}}+\frac{i b^{3} a^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right)^{2} \left(a^{2}+1\right) \sqrt{b^{2}}}+\frac{2 i b^{2} a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(i-a \right)^{2} \left(a^{2}+1\right)}-\frac{i b^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(i-a \right) \sqrt{a^{2}+1}}+\frac{b^{3} \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{\left(i-a \right)^{3} \sqrt{b^{2}}}-\frac{i b^{2} \sqrt{a^{2}+1}\, \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(i-a \right)^{3}}+\frac{i b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{\left(i-a \right)^{2} \left(a^{2}+1\right)}-\frac{i \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{2 \left(i-a \right) \left(a^{2}+1\right) x^{2}}-\frac{i a \,b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{2 \left(i-a \right) \left(a^{2}+1\right)^{2}}-\frac{i a \,b^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right) \left(a^{2}+1\right)^{2} \sqrt{b^{2}}}+\frac{i b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(i-a \right) \left(a^{2}+1\right)}+\frac{i a b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{2 \left(i-a \right) \left(a^{2}+1\right)^{2} x}+\frac{i b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(i-a \right)^{3}}+\frac{i b^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right)^{2} \left(a^{2}+1\right) \sqrt{b^{2}}}-\frac{i a^{3} b^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right) \left(a^{2}+1\right)^{2} \sqrt{b^{2}}}"," ",0,"-I*b^2/(I-a)^2*a/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+1/2*I/(I-a)*b^3/(a^2+1)*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-I/(I-a)*a^2*b^2/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*I/(I-a)*a^2*b^2/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+I*b^3/(I-a)^3*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-I*b/(I-a)^2/(a^2+1)/x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-I*b^2/(I-a)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)+I*b^3/(I-a)^2*a^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+2*I*b^2/(I-a)^2*a/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*I/(I-a)*b^2/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+b^3/(I-a)^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-I*b^2/(I-a)^3*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+I*b^3/(I-a)^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-1/2*I/(I-a)/(a^2+1)/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-1/2*I/(I-a)*a*b^3/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-1/2*I/(I-a)*a*b^3/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*I/(I-a)*b^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*I/(I-a)*a*b/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+I*b^2/(I-a)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+I*b^3/(I-a)^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/2*I/(I-a)*a^3*b^3/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)","B"
197,1,1738,226,0.201000," ","int(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x^4,x)","-\frac{i b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{2 \left(i-a \right)^{2} \left(a^{2}+1\right) x^{2}}+\frac{i b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{\left(i-a \right)^{3} \left(a^{2}+1\right)}+\frac{i b^{4} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right)^{3} \left(a^{2}+1\right) \sqrt{b^{2}}}+\frac{i b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(i-a \right)^{4}}+\frac{b^{4} \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{\left(i-a \right)^{4} \sqrt{b^{2}}}-\frac{i b^{3} \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}}{\left(i-a \right)^{4}}-\frac{i \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{3 \left(i-a \right) \left(a^{2}+1\right) x^{3}}+\frac{i b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(i-a \right)^{2} \left(a^{2}+1\right)}-\frac{i b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(i-a \right)^{2} \sqrt{a^{2}+1}}-\frac{i b^{3} \sqrt{a^{2}+1}\, \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(i-a \right)^{4}}+\frac{i b^{4} a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right)^{2} \left(a^{2}+1\right) \sqrt{b^{2}}}+\frac{i b^{4} a^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right)^{3} \left(a^{2}+1\right) \sqrt{b^{2}}}+\frac{i a b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{2 \left(i-a \right) \left(a^{2}+1\right)^{2} x^{2}}-\frac{i a^{2} b^{2} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{2 \left(i-a \right) \left(a^{2}+1\right)^{3} x}+\frac{i a^{4} b^{4} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right) \left(a^{2}+1\right)^{3} \sqrt{b^{2}}}+\frac{i a^{2} b^{4} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{2 \left(i-a \right) \left(a^{2}+1\right)^{3}}+\frac{i a^{2} b^{4} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right) \left(a^{2}+1\right)^{3} \sqrt{b^{2}}}+\frac{i a^{3} b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(i-a \right) \left(a^{2}+1\right)^{3}}-\frac{i a^{3} b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(i-a \right) \left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{i a \,b^{3} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(i-a \right) \left(a^{2}+1\right)^{2}}+\frac{i a \,b^{3} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(i-a \right) \left(a^{2}+1\right)^{\frac{3}{2}}}+\frac{i b^{4} a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right)^{4} \sqrt{b^{2}}}-\frac{i b^{2} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{\left(i-a \right)^{3} \left(a^{2}+1\right) x}+\frac{2 i b^{3} a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(i-a \right)^{3} \left(a^{2}+1\right)}-\frac{i b^{3} a \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(i-a \right)^{3} \sqrt{a^{2}+1}}-\frac{i b^{3} a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(i-a \right)^{2} \left(a^{2}+1\right)^{2}}+\frac{i b^{3} a^{2} \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{2 \left(i-a \right)^{2} \left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{i a^{2} b^{4} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right) \left(a^{2}+1\right)^{2} \sqrt{b^{2}}}+\frac{i b^{2} a \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{2 \left(i-a \right)^{2} \left(a^{2}+1\right)^{2} x}-\frac{i b^{4} a^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right)^{2} \left(a^{2}+1\right)^{2} \sqrt{b^{2}}}-\frac{i b^{4} a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{2 \left(i-a \right)^{2} \left(a^{2}+1\right)^{2}}-\frac{i b^{4} a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right)^{2} \left(a^{2}+1\right)^{2} \sqrt{b^{2}}}"," ",0,"-1/2*I*b/(I-a)^2/(a^2+1)/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+I*b^4/(I-a)^3/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+I*b^4/(I-a)^3/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-I*b^2/(I-a)^3/(a^2+1)/x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+2*I*b^3/(I-a)^3*a/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-I*b^3/(I-a)^3*a/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-I*b^3/(I-a)^2*a^2/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*I*b^3/(I-a)^2*a^2/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+I/(I-a)*a^3*b^3/(a^2+1)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/2*I/(I-a)*a^3*b^3/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-1/2*I/(I-a)*a*b^3/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*I/(I-a)*a*b^3/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+I*b^4/(I-a)^4*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/2*I*b^3/(I-a)^2/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-I*b^3/(I-a)^4*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-1/3*I/(I-a)/(a^2+1)/x^3*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+I*b^3/(I-a)^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+b^4/(I-a)^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-I*b^3/(I-a)^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)+1/2*I*b^3/(I-a)^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+1/2*I*b^4/(I-a)^2/(a^2+1)*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+I*b^4/(I-a)^3*a^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*I/(I-a)*a*b/(a^2+1)^2/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-1/2*I/(I-a)*a^2*b^2/(a^2+1)^3/x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)+1/2*I/(I-a)*a^4*b^4/(a^2+1)^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*I/(I-a)*a^2*b^4/(a^2+1)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+1/2*I/(I-a)*a^2*b^4/(a^2+1)^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/2*I/(I-a)*a^2*b^4/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*I*b^2/(I-a)^2*a/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-1/2*I*b^4/(I-a)^2*a^3/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/2*I*b^4/(I-a)^2*a/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-1/2*I*b^4/(I-a)^2*a/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)","B"
198,1,292,85,0.056000," ","int(x^4/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x)","-\frac{x^{5}}{5}+\frac{8 i \arctan \left(b x +a \right) a}{b^{5}}-\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{4}}{b^{5}}-\frac{i x^{2} a^{2}}{b^{3}}-\frac{6 i a x}{b^{4}}+\frac{2 x^{3}}{3 b^{2}}+\frac{2 i x^{3} a}{3 b^{2}}-\frac{2 a \,x^{2}}{b^{3}}+\frac{6 i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{2}}{b^{5}}+\frac{6 x \,a^{2}}{b^{4}}-\frac{2 x}{b^{4}}+\frac{2 \arctan \left(b x +a \right) a^{4}}{b^{5}}-\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{b^{5}}-\frac{12 \arctan \left(b x +a \right) a^{2}}{b^{5}}+\frac{i x^{2}}{b^{3}}+\frac{2 i a^{3} x}{b^{4}}-\frac{4 \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{3}}{b^{5}}+\frac{2 \arctan \left(b x +a \right)}{b^{5}}-\frac{i x^{4}}{2 b}-\frac{8 i \arctan \left(b x +a \right) a^{3}}{b^{5}}+\frac{4 \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{b^{5}}"," ",0,"-1/5*x^5+8*I/b^5*arctan(b*x+a)*a-I/b^5*ln(b^2*x^2+2*a*b*x+a^2+1)*a^4-I/b^3*x^2*a^2-6*I/b^4*a*x+2/3/b^2*x^3+2/3*I/b^2*x^3*a-2/b^3*a*x^2+6*I/b^5*ln(b^2*x^2+2*a*b*x+a^2+1)*a^2+6/b^4*x*a^2-2/b^4*x+2/b^5*arctan(b*x+a)*a^4-I/b^5*ln(b^2*x^2+2*a*b*x+a^2+1)-12/b^5*arctan(b*x+a)*a^2+I/b^3*x^2+2*I/b^4*a^3*x-4/b^5*ln(b^2*x^2+2*a*b*x+a^2+1)*a^3+2/b^5*arctan(b*x+a)-1/2*I*x^4/b-8*I/b^5*arctan(b*x+a)*a^3+4/b^5*ln(b^2*x^2+2*a*b*x+a^2+1)*a","B"
199,1,211,67,0.056000," ","int(x^3/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x)","-\frac{x^{4}}{4}-\frac{2 i x^{3}}{3 b}+\frac{i x^{2} a}{b^{2}}-\frac{2 i a^{2} x}{b^{3}}+\frac{x^{2}}{b^{2}}+\frac{2 i x}{b^{3}}-\frac{4 a x}{b^{3}}-\frac{2 \arctan \left(b x +a \right) a^{3}}{b^{4}}+\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{3}}{b^{4}}+\frac{6 \arctan \left(b x +a \right) a}{b^{4}}+\frac{6 i \arctan \left(b x +a \right) a^{2}}{b^{4}}-\frac{3 i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{b^{4}}+\frac{3 \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{2}}{b^{4}}-\frac{2 i \arctan \left(b x +a \right)}{b^{4}}-\frac{\ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{b^{4}}"," ",0,"-1/4*x^4-2/3*I*x^3/b+I/b^2*x^2*a-2*I/b^3*a^2*x+1/b^2*x^2+2*I/b^3*x-4*a*x/b^3-2/b^4*arctan(b*x+a)*a^3+I/b^4*ln(b^2*x^2+2*a*b*x+a^2+1)*a^3+6/b^4*arctan(b*x+a)*a+6*I/b^4*arctan(b*x+a)*a^2-3*I/b^4*ln(b^2*x^2+2*a*b*x+a^2+1)*a+3/b^4*ln(b^2*x^2+2*a*b*x+a^2+1)*a^2-2*I/b^4*arctan(b*x+a)-1/b^4*ln(b^2*x^2+2*a*b*x+a^2+1)","B"
200,1,143,52,0.056000," ","int(x^2/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x)","-\frac{x^{3}}{3}-\frac{i x^{2}}{b}+\frac{2 i a x}{b^{2}}+\frac{2 x}{b^{2}}+\frac{2 \arctan \left(b x +a \right) a^{2}}{b^{3}}-\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a^{2}}{b^{3}}-\frac{2 \arctan \left(b x +a \right)}{b^{3}}-\frac{4 i \arctan \left(b x +a \right) a}{b^{3}}+\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{b^{3}}-\frac{2 \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{b^{3}}"," ",0,"-1/3*x^3-I*x^2/b+2*I/b^2*a*x+2*x/b^2+2/b^3*arctan(b*x+a)*a^2-I/b^3*ln(b^2*x^2+2*a*b*x+a^2+1)*a^2-2/b^3*arctan(b*x+a)-4*I/b^3*arctan(b*x+a)*a+I/b^3*ln(b^2*x^2+2*a*b*x+a^2+1)-2/b^3*ln(b^2*x^2+2*a*b*x+a^2+1)*a","B"
201,1,85,35,0.056000," ","int(x/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x)","-\frac{x^{2}}{2}-\frac{2 i x}{b}-\frac{2 \arctan \left(b x +a \right) a}{b^{2}}+\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{b^{2}}+\frac{2 i \arctan \left(b x +a \right)}{b^{2}}+\frac{\ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{b^{2}}"," ",0,"-1/2*x^2-2*I*x/b-2/b^2*arctan(b*x+a)*a+I/b^2*ln(b^2*x^2+2*a*b*x+a^2+1)*a+2*I/b^2*arctan(b*x+a)+1/b^2*ln(b^2*x^2+2*a*b*x+a^2+1)","B"
202,1,40,21,0.054000," ","int(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2),x)","-x -\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{b}+\frac{2 \arctan \left(b x +a \right)}{b}"," ",0,"-x-I/b*ln(b^2*x^2+2*a*b*x+a^2+1)+2/b*arctan(b*x+a)","A"
203,1,74,37,0.056000," ","int(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x,x)","-\frac{\ln \left(x \right) a^{2}}{\left(i-a \right)^{2}}-\frac{\ln \left(x \right)}{\left(i-a \right)^{2}}-\frac{i \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{i-a}+\frac{2 \arctan \left(b x +a \right)}{i-a}"," ",0,"-1/(I-a)^2*ln(x)*a^2-1/(I-a)^2*ln(x)-I/(I-a)*ln(b^2*x^2+2*a*b*x+a^2+1)+2/(I-a)*arctan(b*x+a)","A"
204,1,152,56,0.062000," ","int(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x^2,x)","\frac{a^{2}}{x \left(i-a \right)^{2}}+\frac{1}{x \left(i-a \right)^{2}}-\frac{2 i b \ln \left(x \right) a}{\left(i-a \right)^{3}}-\frac{2 b \ln \left(x \right)}{\left(i-a \right)^{3}}+\frac{i b \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{\left(i-a \right)^{3}}+\frac{b \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{\left(i-a \right)^{3}}-\frac{2 b \arctan \left(b x +a \right) a}{\left(i-a \right)^{3}}+\frac{2 i b \arctan \left(b x +a \right)}{\left(i-a \right)^{3}}"," ",0,"1/x/(I-a)^2*a^2+1/x/(I-a)^2-2*I*b/(I-a)^3*ln(x)*a-2*b/(I-a)^3*ln(x)+I*b/(I-a)^3*ln(b^2*x^2+2*a*b*x+a^2+1)*a+b/(I-a)^3*ln(b^2*x^2+2*a*b*x+a^2+1)-2*b/(I-a)^3*arctan(b*x+a)*a+2*I*b/(I-a)^3*arctan(b*x+a)","B"
205,1,246,74,0.065000," ","int(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x^3,x)","-\frac{2 i b^{2} \ln \left(x \right) a}{\left(i-a \right)^{4}}-\frac{2 b^{2} \ln \left(x \right)}{\left(i-a \right)^{4}}-\frac{2 i b \,a^{2}}{\left(i-a \right)^{4} x}+\frac{2 i b}{\left(i-a \right)^{4} x}-\frac{4 b a}{\left(i-a \right)^{4} x}-\frac{i a^{3}}{\left(i-a \right)^{4} x^{2}}+\frac{a^{4}}{2 \left(i-a \right)^{4} x^{2}}-\frac{i a}{\left(i-a \right)^{4} x^{2}}-\frac{1}{2 \left(i-a \right)^{4} x^{2}}+\frac{i b^{2} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{\left(i-a \right)^{4}}+\frac{b^{2} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{\left(i-a \right)^{4}}-\frac{2 b^{2} \arctan \left(b x +a \right) a}{\left(i-a \right)^{4}}+\frac{2 i b^{2} \arctan \left(b x +a \right)}{\left(i-a \right)^{4}}"," ",0,"-2*I*b^2/(I-a)^4*ln(x)*a-2*b^2/(I-a)^4*ln(x)-2*I*b/(I-a)^4/x*a^2+2*I*b/(I-a)^4/x-4*b/(I-a)^4/x*a-I/(I-a)^4/x^2*a^3+1/2/(I-a)^4/x^2*a^4-I/(I-a)^4/x^2*a-1/2/(I-a)^4/x^2+I*b^2/(I-a)^4*ln(b^2*x^2+2*a*b*x+a^2+1)*a+b^2/(I-a)^4*ln(b^2*x^2+2*a*b*x+a^2+1)-2*b^2/(I-a)^4*arctan(b*x+a)*a+2*I*b^2/(I-a)^4*arctan(b*x+a)","B"
206,1,349,92,0.062000," ","int(1/(1+I*(b*x+a))^2*(1+(b*x+a)^2)/x^4,x)","\frac{i a^{4}}{\left(i-a \right)^{5} x^{3}}-\frac{a^{5}}{3 \left(i-a \right)^{5} x^{3}}+\frac{2 i b^{3} \arctan \left(b x +a \right)}{\left(i-a \right)^{5}}+\frac{2 a^{3}}{3 \left(i-a \right)^{5} x^{3}}+\frac{i b^{3} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right) a}{\left(i-a \right)^{5}}+\frac{a}{\left(i-a \right)^{5} x^{3}}-\frac{i}{3 \left(i-a \right)^{5} x^{3}}-\frac{2 b^{3} \ln \left(x \right)}{\left(i-a \right)^{5}}+\frac{i b \,a^{3}}{\left(i-a \right)^{5} x^{2}}+\frac{2 i b^{2}}{\left(i-a \right)^{5} x}-\frac{4 b^{2} a}{\left(i-a \right)^{5} x}-\frac{2 i b^{2} a^{2}}{\left(i-a \right)^{5} x}-\frac{3 i b a}{\left(i-a \right)^{5} x^{2}}+\frac{3 b \,a^{2}}{\left(i-a \right)^{5} x^{2}}-\frac{b}{\left(i-a \right)^{5} x^{2}}+\frac{2 i a^{2}}{3 \left(i-a \right)^{5} x^{3}}+\frac{b^{3} \ln \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)}{\left(i-a \right)^{5}}-\frac{2 b^{3} \arctan \left(b x +a \right) a}{\left(i-a \right)^{5}}-\frac{2 i b^{3} \ln \left(x \right) a}{\left(i-a \right)^{5}}"," ",0,"I/(I-a)^5/x^3*a^4-1/3/(I-a)^5/x^3*a^5+2*I*b^3/(I-a)^5*arctan(b*x+a)+2/3/(I-a)^5/x^3*a^3+I*b^3/(I-a)^5*ln(b^2*x^2+2*a*b*x+a^2+1)*a+1/(I-a)^5/x^3*a-1/3*I/(I-a)^5/x^3-2*b^3/(I-a)^5*ln(x)+I*b/(I-a)^5/x^2*a^3+2*I*b^2/(I-a)^5/x-4*b^2/(I-a)^5/x*a-2*I*b^2/(I-a)^5/x*a^2-3*I*b/(I-a)^5/x^2*a+3*b/(I-a)^5/x^2*a^2-b/(I-a)^5/x^2+2/3*I/(I-a)^5/x^3*a^2+b^3/(I-a)^5*ln(b^2*x^2+2*a*b*x+a^2+1)-2*b^3/(I-a)^5*arctan(b*x+a)*a-2*I*b^3/(I-a)^5*ln(x)*a","B"
207,1,2058,262,0.199000," ","int(x^4/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x)","-\frac{22 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}} a^{2}}{b^{5}}-\frac{3 i a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{5}}-\frac{3 \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{4}}{b^{4} \sqrt{b^{2}}}-\frac{\left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{4}}{b^{8} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}+\frac{6 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{2}}{b^{8} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{3 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x \,a^{4}}{b^{4}}+\frac{33 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x \,a^{2}}{b^{4}}-\frac{12 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{3}}{b^{7} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}+\frac{20 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a}{b^{7} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}+\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}} a^{4}}{b^{5}}+\frac{18 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{4}}{b^{5}}-\frac{24 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{2}}{b^{5}}-\frac{6 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{7} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}-\frac{3 i a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 b^{4} \sqrt{b^{2}}}-\frac{i a x \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{b^{4}}+\frac{18 i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{3}}{b^{4} \sqrt{b^{2}}}+\frac{18 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x \,a^{3}}{b^{4}}+\frac{24 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{2}}{b^{7} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}-\frac{24 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x a}{b^{4}}-\frac{24 i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a}{b^{4} \sqrt{b^{2}}}-\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{4}}{b^{7} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}+\frac{4 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{3}}{b^{8} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{4 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a}{b^{8} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{3 i a x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b^{4}}-\frac{i a^{2} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{b^{5}}+\frac{33 \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{2}}{b^{4} \sqrt{b^{2}}}+\frac{4 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{b^{5}}-\frac{16 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}} a}{b^{5}}+\frac{12 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}} a^{3}}{b^{5}}-\frac{\left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{8} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{6 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x}{b^{4}}-\frac{3 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{5}}{b^{5}}+\frac{i \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{5}{2}}}{5 b^{5}}-\frac{6 \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{b^{4} \sqrt{b^{2}}}-\frac{9 x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 b^{4}}-\frac{9 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a}{8 b^{5}}-\frac{9 \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 b^{4} \sqrt{b^{2}}}-\frac{3 x \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{4 b^{4}}-\frac{3 a \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{4 b^{5}}+\frac{33 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{3}}{b^{5}}-\frac{6 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{b^{5}}"," ",0,"2*I/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)*a^4+18*I/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^4-24*I/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^2-6*I/b^7/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-22*I/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)*a^2-I/b^5*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-3/2*I/b^5*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^4+33/b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^2-1/b^8/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^4+6/b^8/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^2-3/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x*a^4+33/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x*a^2-12/b^7/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^3+20/b^7/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a-I/b^4*a*x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-3/2*I/b^4*a*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-3/2*I/b^4*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+18*I/b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^3+18*I/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x*a^3+24*I/b^7/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^2-24*I/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x*a-24*I/b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a-2*I/b^7/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^4+4*I/b^8/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^3-4*I/b^8/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a-9/8/b^4*x*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-9/8/b^5*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-9/8/b^4*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+4*I/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-16/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)*a+12/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)*a^3-1/b^8/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-6/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-3/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^5+1/5*I/b^5*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)+33/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^3-6/b^5*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a-6/b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-3/4/b^4*x*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-3/4/b^5*a*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)","B"
208,1,1529,200,0.188000," ","int(x^3/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x)","\frac{3 i \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{8 b^{3} \sqrt{b^{2}}}+\frac{3 i x \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{8 b^{3}}+\frac{4 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{b^{4}}+\frac{6 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{b^{4}}+\frac{6 i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{b^{3} \sqrt{b^{2}}}+\frac{3 \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{3}}{b^{3} \sqrt{b^{2}}}-\frac{33 \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a}{2 b^{3} \sqrt{b^{2}}}-\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}} a^{3}}{b^{4}}+\frac{\left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{3}}{b^{7} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{3 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a}{b^{7} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}+\frac{i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{7} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}+\frac{9 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{2}}{b^{6} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}+\frac{3 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x \,a^{3}}{b^{3}}-\frac{33 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x a}{2 b^{3}}+\frac{i \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}} x}{4 b^{3}}+\frac{i \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}} a}{4 b^{4}}+\frac{3 i \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, a}{8 b^{4}}-\frac{27 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{3}}{2 b^{4}}+\frac{11 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}} a}{b^{4}}+\frac{6 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x}{b^{3}}-\frac{5 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{6} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}-\frac{9 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}} a^{2}}{b^{4}}+\frac{3 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{4}}{b^{4}}-\frac{27 i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{2}}{2 b^{3} \sqrt{b^{2}}}-\frac{3 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{2}}{b^{7} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}+\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{3}}{b^{6} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}-\frac{12 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a}{b^{6} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}-\frac{27 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x \,a^{2}}{2 b^{3}}-\frac{33 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{2}}{2 b^{4}}"," ",0,"-27/2*I/b^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^2-3*I/b^7/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^2+2*I/b^6/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^3-12*I/b^6/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a-27/2*I/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x*a^2+4/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-2*I/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)*a^3+1/b^7/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^3-3/b^7/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a+I/b^7/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)+9/b^6/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^2+3/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x*a^3-33/2/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x*a+1/4*I/b^3*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)*x+1/4*I/b^4*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)*a+3/8*I/b^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+3/8*I/b^4*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*a-27/2*I/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^3+11*I/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)*a+6*I/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x+6*I/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+6*I/b^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)+3/b^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^3-33/2/b^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a-5/b^6/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-9/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)*a^2+3/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^4-33/2/b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^2+3/8*I/b^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)","B"
209,1,1026,181,0.184000," ","int(x^2/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x)","\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}} a^{2}}{b^{3}}-\frac{11 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{3 b^{3}}-\frac{3 \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a^{2}}{b^{2} \sqrt{b^{2}}}+\frac{9 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{2}}{b^{3}}+\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a}{b^{6} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{2}}{b^{5} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}-\frac{6 a \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{5} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}+\frac{9 i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a}{b^{2} \sqrt{b^{2}}}+\frac{\left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{6} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{\left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}} a^{2}}{b^{6} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{3 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x \,a^{2}}{b^{2}}+\frac{9 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x a}{b^{2}}+\frac{4 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{5} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}-\frac{3 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{3}}{b^{3}}+\frac{11 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x}{2 b^{2}}+\frac{11 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{2 b^{3}}+\frac{11 \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{2 b^{2} \sqrt{b^{2}}}+\frac{6 a \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{b^{3}}"," ",0,"2*I/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)*a^2-11/3*I/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-3/b^2*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a^2+9*I/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^2+2*I/b^6/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a-2*I/b^5/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^2-6/b^5*a/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)+9*I/b^2*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a+1/b^6/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-1/b^6/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)*a^2-3/b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x*a^2+9*I/b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x*a+4*I/b^5/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-3/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^3+11/2/b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x+11/2/b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+11/2/b^2*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)+6/b^3*a*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)","B"
210,1,676,129,0.183000," ","int(x/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x)","\frac{2 i a \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{4} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}+\frac{3 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{4} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}-\frac{3 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{b^{2}}-\frac{2 i a \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{b^{2}}-\frac{9 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{2 b^{2}}-\frac{9 i \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{2 b \sqrt{b^{2}}}+\frac{a \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{5} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{5} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{9 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x}{2 b}+\frac{3 a \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x}{b}+\frac{3 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a^{2}}{b^{2}}+\frac{3 \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right) a}{b \sqrt{b^{2}}}"," ",0,"2*I/b^4*a/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)+3/b^4/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-3/b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-2*I/b^2*a*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-9/2*I/b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a-9/2*I/b*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)+1/b^5*a/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-I/b^5/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-9/2*I/b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x+3/b*a*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x+3/b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a^2+3/b*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)*a","B"
211,1,329,76,0.115000," ","int(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2),x)","-\frac{\left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{4} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{b^{3} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}+\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{b}-3 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x -\frac{3 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{b}-\frac{3 \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{\sqrt{b^{2}}}"," ",0,"-1/b^4/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-2*I/b^3/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)+2*I/b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-3/b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a-3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)","B"
212,1,1278,104,0.145000," ","int(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x,x)","-\frac{\left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{\left(i-a \right)^{2} b^{2} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}+\frac{\left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{\left(i-a \right)^{2}}-\frac{3 i a b \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right)^{3} \sqrt{b^{2}}}-\frac{i \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(i-a \right)^{3}}-\frac{i \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{3 \left(i-a \right)^{3}}-\frac{i a b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{2 \left(i-a \right)^{3}}+\frac{i \sqrt{a^{2}+1}\, \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(i-a \right)^{3}}+\frac{3 i \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{2 \left(i-a \right)^{2}}-\frac{i a^{3} b \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right)^{3} \sqrt{b^{2}}}+\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{i-a}+\frac{i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{3 \left(i-a \right)^{3}}-\frac{3 i a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(i-a \right)^{3}}+\frac{3 i b \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x}{2 \left(i-a \right)^{2}}-\frac{\left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{\left(i-a \right) b^{3} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{\left(i-a \right) b^{2} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}+\frac{i \sqrt{a^{2}+1}\, \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right) a^{2}}{\left(i-a \right)^{3}}-\frac{3 b \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x}{i-a}-\frac{3 \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{i-a}-\frac{3 b \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{\left(i-a \right) \sqrt{b^{2}}}+\frac{3 i b \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{2 \left(i-a \right)^{2} \sqrt{b^{2}}}-\frac{b \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x}{2 \left(i-a \right)^{3}}-\frac{\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{2 \left(i-a \right)^{3}}-\frac{b \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{2 \left(i-a \right)^{3} \sqrt{b^{2}}}"," ",0,"-1/(I-a)^2/b^2/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)+1/(I-a)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-3/2*I/(I-a)^3*a*b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-I/(I-a)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/3*I/(I-a)^3*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-1/2*I/(I-a)^3*a*b*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+I/(I-a)^3*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+3/2*I/(I-a)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a-I/(I-a)^3*a^3*b*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+2*I/(I-a)*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)+1/3*I/(I-a)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-3/2*I/(I-a)^3*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/2*I/(I-a)^2*b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-1/(I-a)/b^3/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-2*I/(I-a)/b^2/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)+I/(I-a)^3*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)*a^2-3/(I-a)*b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-3/(I-a)*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a-3/(I-a)*b*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)+3/2*I/(I-a)^2*b*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-1/2/(I-a)^3*b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-1/2/(I-a)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a-1/2/(I-a)^3*b*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)","B"
213,1,1917,138,0.188000," ","int(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x^2,x)","-\frac{9 i b \,a^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(i-a \right)^{4}}-\frac{3 i b^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right)^{3} \left(a^{2}+1\right) \sqrt{b^{2}}}-\frac{9 i a^{3} b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(i-a \right)^{3} \left(a^{2}+1\right)}-\frac{3 i b^{2} a^{3} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right)^{4} \sqrt{b^{2}}}+\frac{3 i a b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(i-a \right)^{3} \sqrt{a^{2}+1}}-\frac{i b^{2} \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}} x}{\left(i-a \right)^{3} \left(a^{2}+1\right)}-\frac{3 i b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{2 \left(i-a \right)^{3} \left(a^{2}+1\right)}-\frac{3 b \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{\left(i-a \right)^{2}}+\frac{2 i b \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{\left(i-a \right)^{2}}-\frac{i b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{\left(i-a \right)^{4}}-\frac{3 i b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{\left(i-a \right)^{4}}-\frac{2 \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{\left(i-a \right)^{3} b \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}-\frac{3 b^{2} \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{\left(i-a \right)^{2} \sqrt{b^{2}}}+\frac{i b \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{\left(i-a \right)^{4}}-\frac{3 b^{2} \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x}{2 \left(i-a \right)^{4}}-\frac{3 b \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{2 \left(i-a \right)^{4}}-\frac{3 b^{2} \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{2 \left(i-a \right)^{4} \sqrt{b^{2}}}-\frac{\left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{\left(i-a \right)^{2} b^{2} \left(x -\frac{i}{b}+\frac{a}{b}\right)^{3}}-\frac{3 b^{2} \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x}{\left(i-a \right)^{2}}+\frac{3 i b \sqrt{a^{2}+1}\, \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(i-a \right)^{4}}+\frac{3 i b \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, a}{\left(i-a \right)^{3}}+\frac{3 i b^{2} \ln \left(\frac{i b +\left(x -\frac{i-a}{b}\right) b^{2}}{\sqrt{b^{2}}}+\sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\right)}{\left(i-a \right)^{3} \sqrt{b^{2}}}-\frac{2 i \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{5}{2}}}{\left(i-a \right)^{2} b \left(x -\frac{i}{b}+\frac{a}{b}\right)^{2}}+\frac{i \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{5}{2}}}{\left(i-a \right)^{3} \left(a^{2}+1\right) x}+\frac{3 i b^{2} \sqrt{\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)}\, x}{\left(i-a \right)^{3}}+\frac{2 b \left(\left(x -\frac{i-a}{b}\right)^{2} b^{2}+2 i b \left(x -\frac{i-a}{b}\right)\right)^{\frac{3}{2}}}{\left(i-a \right)^{3}}-\frac{3 i a^{2} b^{2} \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{2 \left(i-a \right)^{3} \left(a^{2}+1\right)}-\frac{9 i a^{2} b^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right)^{3} \left(a^{2}+1\right) \sqrt{b^{2}}}-\frac{3 i a^{4} b^{2} \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{\left(i-a \right)^{3} \left(a^{2}+1\right) \sqrt{b^{2}}}+\frac{3 i b \sqrt{a^{2}+1}\, \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right) a^{2}}{\left(i-a \right)^{4}}-\frac{2 i a b \left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{3}{2}}}{\left(i-a \right)^{3} \left(a^{2}+1\right)}-\frac{3 i b^{2} a \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, x}{2 \left(i-a \right)^{4}}-\frac{9 i b^{2} a \ln \left(\frac{b^{2} x +a b}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\right)}{2 \left(i-a \right)^{4} \sqrt{b^{2}}}-\frac{9 i a b \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 \left(i-a \right)^{3} \left(a^{2}+1\right)}+\frac{3 i a^{3} b \ln \left(\frac{2 a^{2}+2+2 a b x +2 \sqrt{a^{2}+1}\, \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{x}\right)}{\left(i-a \right)^{3} \sqrt{a^{2}+1}}"," ",0,"3*I/(I-a)^3*a*b/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-I/(I-a)^3*b^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)*x-3/2*I/(I-a)^3*b^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-3/2*I/(I-a)^3*b^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-9/2*I/(I-a)^3*a^3*b/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3*I/(I-a)^4*b^2*a^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+3*I/(I-a)^4*b*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)*a^2-2*I/(I-a)^3*a*b/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-3/2*I/(I-a)^4*b^2*a*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-9/2*I/(I-a)^4*b^2*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-9/2*I/(I-a)^4*b*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*I/(I-a)^4*b*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-9/2*I/(I-a)^3*a*b/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3*I/(I-a)^3*a^3*b/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+I/(I-a)^4*b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-3/2/(I-a)^4*b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-3/2/(I-a)^4*b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a-3/2/(I-a)^4*b^2*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-1/(I-a)^2/b^2/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-3/(I-a)^2*b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-3/(I-a)^2*b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+2*I/(I-a)^2*b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-I/(I-a)^4*b*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-3*I/(I-a)^4*b*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-2/(I-a)^3/b/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)+3*I/(I-a)^3*b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+3*I/(I-a)^3*b^2*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-2*I/(I-a)^2/b/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)+I/(I-a)^3/(a^2+1)/x*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)+3*I/(I-a)^3*b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-3/2*I/(I-a)^3*a^2*b^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-9/2*I/(I-a)^3*a^2*b^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3*I/(I-a)^3*a^4*b^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3*b^2/(I-a)^2*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)+2/(I-a)^3*b*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)","B"
214,1,3042,209,0.198000," ","int(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x^3,x)","\text{output too large to display}"," ",0,"-9/4*I/(I-a)^3*b^2/(a^2+1)*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/2*I/(I-a)^3*b^2/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)*a^2-9/2*I/(I-a)^4*b^3/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-9/2*I/(I-a)^4*b^3/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+3*I/(I-a)^4*b/(a^2+1)/x*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)-6*I/(I-a)^4*b^2*a/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-27/2*I/(I-a)^4*b^2*a^3/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-1/(I-a)^3/b/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-3/(I-a)^3*b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-3/(I-a)^3*b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+9/2*I/(I-a)^4*b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+9/2*I/(I-a)^4*b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-9/2*I/(I-a)^4*b^3*a^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-27/2*I/(I-a)^4*b^3*a^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-9*I/(I-a)^4*b^3*a^4/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3/4*I/(I-a)^3*b^3/(a^2+1)*a*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-9/4*I/(I-a)^3*b^3/(a^2+1)*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3/2*I/(I-a)^3*b^3/(a^2+1)*a^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/2*I/(I-a)^3*a*b/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)-3/4*I/(I-a)^3*a^3*b^3/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-9/4*I/(I-a)^3*a^3*b^3/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3/2*I/(I-a)^3*a^5*b^3/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/2*I/(I-a)^3*a*b^3/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)*x-3/4*I/(I-a)^3*a*b^3/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-3/4*I/(I-a)^3*a*b^3/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-27/2*I/(I-a)^4*b^2*a/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+9*I/(I-a)^4*b^2*a^3/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+9*I/(I-a)^4*b^2*a/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-3*I/(I-a)^4*b^3/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)*x-3*I/(I-a)^5*b^3*a*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-9*I/(I-a)^5*b^3*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-6*I/(I-a)^5*b^3*a^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+6*I/(I-a)^5*b^2*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)*a^2-I/(I-a)^3*a^2*b^2/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-9/4*I/(I-a)^3*a^4*b^2/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-9/4*I/(I-a)^3*a^2*b^2/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/2*I/(I-a)^3*a^4*b^2/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+3/2*I/(I-a)^3*a^2*b^2/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+9/2*I/(I-a)^4*b^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-9*I/(I-a)^5*b^2*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+6*I/(I-a)^5*b^2*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+1/2*I/(I-a)^3/(a^2+1)/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)-1/2*I/(I-a)^3*b^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-3/2*I/(I-a)^3*b^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/2*I/(I-a)^3*b^2/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-3/(I-a)^4/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)+3/(I-a)^4*b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-3/(I-a)^3*b^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-2*I/(I-a)^3/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)+2*I/(I-a)^3*b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-2*I/(I-a)^5*b^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-6*I/(I-a)^5*b^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-3/(I-a)^5*b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-3/(I-a)^5*b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a-3/(I-a)^5*b^3*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)+2*I/(I-a)^5*b^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)","B"
215,1,4390,267,0.200000," ","int(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x^4,x)","\text{output too large to display}"," ",0,"-3/2*I/(I-a)^3*a^4*b^4/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-9/2*I/(I-a)^4*b^4*a^5/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3/2*I/(I-a)^4*b^4*a/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)*x-9/2*I/(I-a)^4*b^4/(a^2+1)*a^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3*b^4/(I-a)^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-3/2*I/(I-a)^4*b^3/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-9*I/(I-a)^5*b^4*a^2/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-27*I/(I-a)^5*b^4*a^2/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-9/4*I/(I-a)^3*a^2*b^4/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-9*I/(I-a)^5*b^4/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-9*I/(I-a)^5*b^4/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+18*I/(I-a)^5*b^3*a^3/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+18*I/(I-a)^5*b^3*a/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+2/3*I/(I-a)^3*b^2/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)+6*I/(I-a)^5*b^2/(a^2+1)/x*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)-12*I/(I-a)^5*b^3*a/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-6*I/(I-a)^5*b^4/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)*x+3/4*I/(I-a)^3*a^5*b^3/(a^2+1)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+3/4*I/(I-a)^3*a^3*b^3/(a^2+1)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-7/6*I/(I-a)^3*a*b^3/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-9/4*I/(I-a)^3*a^3*b^3/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-5/2*I/(I-a)^3*a*b^3/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-2/3*I/(I-a)^3*b^4/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)*x-I/(I-a)^3*b^4/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-27*I/(I-a)^5*b^3*a^3/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-27*I/(I-a)^5*b^3*a/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+10*I/(I-a)^6*b^3*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)*a^2-I/(I-a)^3*b^4/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+3/2*I/(I-a)^3*a*b^3/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-5*I/(I-a)^6*b^4*a*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-15*I/(I-a)^6*b^4*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-10*I/(I-a)^6*b^4*a^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/2*I/(I-a)^3*a^3*b^3/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+3/2*I/(I-a)^3*a^3*b^3/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-1/2*I/(I-a)^3*a^5*b^3/(a^2+1)^(5/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+1/3*I/(I-a)^3*a^3*b^3/(a^2+1)^3*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-3*I/(I-a)^4*b^3*a^2/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-27/4*I/(I-a)^4*b^3*a^4/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-27/4*I/(I-a)^4*b^3*a^2/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+9/2*I/(I-a)^4*b^3*a^4/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+9/2*I/(I-a)^4*b^3*a^2/(a^2+1)^(3/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)-27/4*I/(I-a)^4*b^3/(a^2+1)*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+9/2*I/(I-a)^4*b^3/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)*a^2+3/2*I/(I-a)^4*b/(a^2+1)/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)-10/3*I/(I-a)^6*b^3*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)-10*I/(I-a)^6*b^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)-5/(I-a)^6*b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-5/(I-a)^6*b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a-5/(I-a)^6*b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)+10/3*I/(I-a)^6*b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-3/(I-a)^4*b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x-3/(I-a)^4*b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+2*I/(I-a)^4*b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-4/(I-a)^5*b/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)-9/4*I/(I-a)^4*b^4*a^3/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-1/6*I/(I-a)^3*a^2*b^2/(a^2+1)^3/x*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)+3/2*I/(I-a)^4*b^2*a/(a^2+1)^2/x*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)-9/4*I/(I-a)^4*b^4*a/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+1/2*I/(I-a)^3*a^6*b^4/(a^2+1)^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-18*I/(I-a)^5*b^4*a^4/(a^2+1)*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/6*I/(I-a)^3*a^2*b^4/(a^2+1)^3*(b^2*x^2+2*a*b*x+a^2+1)^(3/2)*x-9/4*I/(I-a)^4*b^4/(a^2+1)*a*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-27/4*I/(I-a)^4*b^4/(a^2+1)*a*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-1/6*I/(I-a)^3*a*b/(a^2+1)^2/x^2*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)-27/4*I/(I-a)^4*b^4*a^3/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-9/4*I/(I-a)^4*b^4*a/(a^2+1)^2*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/4*I/(I-a)^3*a^2*b^4/(a^2+1)^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)+1/4*I/(I-a)^3*a^2*b^4/(a^2+1)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+1/4*I/(I-a)^3*a^4*b^4/(a^2+1)^3*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x+3/4*I/(I-a)^3*a^4*b^4/(a^2+1)^3*ln((b^2*x+a*b)/(b^2)^(1/2)+(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/(b^2)^(1/2)-3/4*I/(I-a)^3*a^2*b^4/(a^2+1)^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)*x-1/(I-a)^4/(x-I/b+a/b)^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)+4/(I-a)^5*b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(3/2)-9/2*I/(I-a)^4*b^3/(a^2+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+9/2*I/(I-a)^4*b^3/(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+1/3*I/(I-a)^3/(a^2+1)/x^3*(b^2*x^2+2*a*b*x+a^2+1)^(5/2)-15*I/(I-a)^6*b^3*a^2*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)+10*I/(I-a)^6*b^3*(a^2+1)^(1/2)*ln((2*a^2+2+2*a*b*x+2*(a^2+1)^(1/2)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2))/x)+6*I/(I-a)^5*b^4*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*x+6*I/(I-a)^5*b^3*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2)*a+6*I/(I-a)^5*b^4*ln((I*b+(x-(I-a)/b)*b^2)/(b^2)^(1/2)+((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(1/2))/(b^2)^(1/2)-2*I/(I-a)^4*b/(x-I/b+a/b)^2*((x-(I-a)/b)^2*b^2+2*I*b*(x-(I-a)/b))^(5/2)","B"
216,0,0,381,0.345000," ","int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)*x^2,x)","\int \sqrt{\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}\, x^{2}\, dx"," ",0,"int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)*x^2,x)","F"
217,0,0,313,0.190000," ","int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)*x,x)","\int \sqrt{\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}\, x\, dx"," ",0,"int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)*x,x)","F"
218,0,0,257,0.115000," ","int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x)","\int \sqrt{\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}\, dx"," ",0,"int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x)","F"
219,0,0,308,0.171000," ","int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x,x)","\int \frac{\sqrt{\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}}{x}\, dx"," ",0,"int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x,x)","F"
220,0,0,159,0.168000," ","int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x^2,x)","\int \frac{\sqrt{\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}}{x^{2}}\, dx"," ",0,"int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x^2,x)","F"
221,0,0,381,0.194000," ","int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)*x^2,x)","\int \left(\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)^{\frac{3}{2}} x^{2}\, dx"," ",0,"int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)*x^2,x)","F"
222,0,0,313,0.190000," ","int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)*x,x)","\int \left(\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)^{\frac{3}{2}} x\, dx"," ",0,"int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)*x,x)","F"
223,0,0,257,0.125000," ","int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x)","\int \left(\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)^{\frac{3}{2}}\, dx"," ",0,"int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x)","F"
224,0,0,324,0.181000," ","int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x,x)","\int \frac{\left(\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x,x)","F"
225,0,0,160,0.181000," ","int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x^2,x)","\int \frac{\left(\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"int(((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x^2,x)","F"
226,0,0,381,0.186000," ","int(x^2/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x)","\int \frac{x^{2}}{\sqrt{\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}}\, dx"," ",0,"int(x^2/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x)","F"
227,0,0,313,0.185000," ","int(x/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x)","\int \frac{x}{\sqrt{\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}}\, dx"," ",0,"int(x/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x)","F"
228,0,0,257,0.123000," ","int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x)","\int \frac{1}{\sqrt{\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}}\, dx"," ",0,"int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2),x)","F"
229,0,0,308,0.184000," ","int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x,x)","\int \frac{1}{\sqrt{\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}\, x}\, dx"," ",0,"int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x,x)","F"
230,0,0,164,0.172000," ","int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x^2,x)","\int \frac{1}{\sqrt{\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}}\, x^{2}}\, dx"," ",0,"int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(1/2)/x^2,x)","F"
231,0,0,381,0.198000," ","int(x^2/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x)","\int \frac{x^{2}}{\left(\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x)","F"
232,0,0,313,0.190000," ","int(x/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x)","\int \frac{x}{\left(\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x)","F"
233,0,0,257,0.128000," ","int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x)","\int \frac{1}{\left(\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2),x)","F"
234,0,0,324,0.194000," ","int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x,x)","\int \frac{1}{\left(\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)^{\frac{3}{2}} x}\, dx"," ",0,"int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x,x)","F"
235,0,0,160,0.198000," ","int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x^2,x)","\int \frac{1}{\left(\frac{1+i \left(b x +a \right)}{\sqrt{1+\left(b x +a \right)^{2}}}\right)^{\frac{3}{2}} x^{2}}\, dx"," ",0,"int(1/((1+I*(b*x+a))/(1+(b*x+a)^2)^(1/2))^(3/2)/x^2,x)","F"
236,0,0,118,0.208000," ","int(exp(n*arctan(b*x+a))*x^m,x)","\int {\mathrm e}^{n \arctan \left(b x +a \right)} x^{m}\, dx"," ",0,"int(exp(n*arctan(b*x+a))*x^m,x)","F"
237,0,0,212,0.118000," ","int(exp(n*arctan(b*x+a))*x^3,x)","\int {\mathrm e}^{n \arctan \left(b x +a \right)} x^{3}\, dx"," ",0,"int(exp(n*arctan(b*x+a))*x^3,x)","F"
238,0,0,174,0.074000," ","int(exp(n*arctan(b*x+a))*x^2,x)","\int {\mathrm e}^{n \arctan \left(b x +a \right)} x^{2}\, dx"," ",0,"int(exp(n*arctan(b*x+a))*x^2,x)","F"
239,0,0,115,0.070000," ","int(exp(n*arctan(b*x+a))*x,x)","\int {\mathrm e}^{n \arctan \left(b x +a \right)} x\, dx"," ",0,"int(exp(n*arctan(b*x+a))*x,x)","F"
240,0,0,69,0.066000," ","int(exp(n*arctan(b*x+a)),x)","\int {\mathrm e}^{n \arctan \left(b x +a \right)}\, dx"," ",0,"int(exp(n*arctan(b*x+a)),x)","F"
241,0,0,150,0.110000," ","int(exp(n*arctan(b*x+a))/x,x)","\int \frac{{\mathrm e}^{n \arctan \left(b x +a \right)}}{x}\, dx"," ",0,"int(exp(n*arctan(b*x+a))/x,x)","F"
242,0,0,106,0.105000," ","int(exp(n*arctan(b*x+a))/x^2,x)","\int \frac{{\mathrm e}^{n \arctan \left(b x +a \right)}}{x^{2}}\, dx"," ",0,"int(exp(n*arctan(b*x+a))/x^2,x)","F"
243,0,0,172,0.124000," ","int(exp(n*arctan(b*x+a))/x^3,x)","\int \frac{{\mathrm e}^{n \arctan \left(b x +a \right)}}{x^{3}}\, dx"," ",0,"int(exp(n*arctan(b*x+a))/x^3,x)","F"
244,0,0,86,0.306000," ","int(exp(arctan(a*x))*(a^2*c*x^2+c)^p,x)","\int {\mathrm e}^{\arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{p}\, dx"," ",0,"int(exp(arctan(a*x))*(a^2*c*x^2+c)^p,x)","F"
245,0,0,45,0.273000," ","int(exp(arctan(a*x))*(a^2*c*x^2+c)^2,x)","\int {\mathrm e}^{\arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{2}\, dx"," ",0,"int(exp(arctan(a*x))*(a^2*c*x^2+c)^2,x)","F"
246,0,0,43,0.066000," ","int(exp(arctan(a*x))*(a^2*c*x^2+c),x)","\int {\mathrm e}^{\arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)\, dx"," ",0,"int(exp(arctan(a*x))*(a^2*c*x^2+c),x)","F"
247,0,0,41,0.063000," ","int(exp(arctan(a*x)),x)","\int {\mathrm e}^{\arctan \left(a x \right)}\, dx"," ",0,"int(exp(arctan(a*x)),x)","F"
248,1,13,12,0.038000," ","int(exp(arctan(a*x))/(a^2*c*x^2+c),x)","\frac{{\mathrm e}^{\arctan \left(a x \right)}}{a c}"," ",0,"exp(arctan(a*x))/a/c","A"
249,1,39,44,0.041000," ","int(exp(arctan(a*x))/(a^2*c*x^2+c)^2,x)","\frac{{\mathrm e}^{\arctan \left(a x \right)} \left(2 a^{2} x^{2}+2 a x +3\right)}{5 \left(a^{2} x^{2}+1\right) a \,c^{2}}"," ",0,"1/5*exp(arctan(a*x))*(2*a^2*x^2+2*a*x+3)/(a^2*x^2+1)/a/c^2","A"
250,1,55,74,0.041000," ","int(exp(arctan(a*x))/(a^2*c*x^2+c)^3,x)","\frac{{\mathrm e}^{\arctan \left(a x \right)} \left(24 a^{4} x^{4}+24 a^{3} x^{3}+60 a^{2} x^{2}+44 a x +41\right)}{85 \left(a^{2} x^{2}+1\right)^{2} a \,c^{3}}"," ",0,"1/85*exp(arctan(a*x))*(24*a^4*x^4+24*a^3*x^3+60*a^2*x^2+44*a*x+41)/(a^2*x^2+1)^2/a/c^3","A"
251,1,71,104,0.040000," ","int(exp(arctan(a*x))/(a^2*c*x^2+c)^4,x)","\frac{{\mathrm e}^{\arctan \left(a x \right)} \left(144 a^{6} x^{6}+144 a^{5} x^{5}+504 a^{4} x^{4}+408 a^{3} x^{3}+606 a^{2} x^{2}+366 a x +263\right)}{629 \left(a^{2} x^{2}+1\right)^{3} a \,c^{4}}"," ",0,"1/629*exp(arctan(a*x))*(144*a^6*x^6+144*a^5*x^5+504*a^4*x^4+408*a^3*x^3+606*a^2*x^2+366*a*x+263)/(a^2*x^2+1)^3/a/c^4","A"
252,1,87,134,0.042000," ","int(exp(arctan(a*x))/(a^2*c*x^2+c)^5,x)","\frac{{\mathrm e}^{\arctan \left(a x \right)} \left(8064 a^{8} x^{8}+8064 a^{7} x^{7}+36288 a^{6} x^{6}+30912 a^{5} x^{5}+62160 a^{4} x^{4}+43344 a^{3} x^{3}+48664 a^{2} x^{2}+25528 a x +15357\right)}{40885 \left(a^{2} x^{2}+1\right)^{4} c^{5} a}"," ",0,"1/40885*exp(arctan(a*x))*(8064*a^8*x^8+8064*a^7*x^7+36288*a^6*x^6+30912*a^5*x^5+62160*a^4*x^4+43344*a^3*x^3+48664*a^2*x^2+25528*a*x+15357)/(a^2*x^2+1)^4/c^5/a","A"
253,0,0,66,0.295000," ","int(exp(arctan(a*x))*(a^2*c*x^2+c)^(3/2),x)","\int {\mathrm e}^{\arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(arctan(a*x))*(a^2*c*x^2+c)^(3/2),x)","F"
254,0,0,65,0.291000," ","int(exp(arctan(a*x))*(a^2*c*x^2+c)^(1/2),x)","\int {\mathrm e}^{\arctan \left(a x \right)} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(arctan(a*x))*(a^2*c*x^2+c)^(1/2),x)","F"
255,0,0,65,0.290000," ","int(exp(arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{\arctan \left(a x \right)}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","F"
256,1,37,30,0.040000," ","int(exp(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(a x +1\right) {\mathrm e}^{\arctan \left(a x \right)}}{2 a \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"1/2*(a^2*x^2+1)*(a*x+1)*exp(arctan(a*x))/a/(a^2*c*x^2+c)^(3/2)","A"
257,1,54,62,0.037000," ","int(exp(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(3 a^{3} x^{3}+3 a^{2} x^{2}+6 a x +4\right) {\mathrm e}^{\arctan \left(a x \right)}}{10 a \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"1/10*(a^2*x^2+1)*(3*a^3*x^3+3*a^2*x^2+6*a*x+4)*exp(arctan(a*x))/a/(a^2*c*x^2+c)^(5/2)","A"
258,1,70,93,0.037000," ","int(exp(arctan(a*x))/(a^2*c*x^2+c)^(7/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(6 a^{5} x^{5}+6 a^{4} x^{4}+18 a^{3} x^{3}+14 a^{2} x^{2}+17 a x +9\right) {\mathrm e}^{\arctan \left(a x \right)}}{26 a \left(a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}"," ",0,"1/26*(a^2*x^2+1)*(6*a^5*x^5+6*a^4*x^4+18*a^3*x^3+14*a^2*x^2+17*a*x+9)*exp(arctan(a*x))/a/(a^2*c*x^2+c)^(7/2)","A"
259,0,0,83,0.319000," ","int(exp(2*arctan(a*x))*(a^2*c*x^2+c)^p,x)","\int {\mathrm e}^{2 \arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{p}\, dx"," ",0,"int(exp(2*arctan(a*x))*(a^2*c*x^2+c)^p,x)","F"
260,0,0,45,0.265000," ","int(exp(2*arctan(a*x))*(a^2*c*x^2+c)^2,x)","\int {\mathrm e}^{2 \arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{2}\, dx"," ",0,"int(exp(2*arctan(a*x))*(a^2*c*x^2+c)^2,x)","F"
261,0,0,43,0.065000," ","int(exp(2*arctan(a*x))*(a^2*c*x^2+c),x)","\int {\mathrm e}^{2 \arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)\, dx"," ",0,"int(exp(2*arctan(a*x))*(a^2*c*x^2+c),x)","F"
262,0,0,41,0.062000," ","int(exp(2*arctan(a*x)),x)","\int {\mathrm e}^{2 \arctan \left(a x \right)}\, dx"," ",0,"int(exp(2*arctan(a*x)),x)","F"
263,1,16,15,0.036000," ","int(exp(2*arctan(a*x))/(a^2*c*x^2+c),x)","\frac{{\mathrm e}^{2 \arctan \left(a x \right)}}{2 a c}"," ",0,"1/2*exp(2*arctan(a*x))/a/c","A"
264,1,40,47,0.037000," ","int(exp(2*arctan(a*x))/(a^2*c*x^2+c)^2,x)","\frac{{\mathrm e}^{2 \arctan \left(a x \right)} \left(a^{2} x^{2}+2 a x +3\right)}{8 \left(a^{2} x^{2}+1\right) a \,c^{2}}"," ",0,"1/8*exp(2*arctan(a*x))*(a^2*x^2+2*a*x+3)/(a^2*x^2+1)/a/c^2","A"
265,1,57,79,0.041000," ","int(exp(2*arctan(a*x))/(a^2*c*x^2+c)^3,x)","\frac{{\mathrm e}^{2 \arctan \left(a x \right)} \left(3 a^{4} x^{4}+6 a^{3} x^{3}+12 a^{2} x^{2}+14 a x +13\right)}{40 \left(a^{2} x^{2}+1\right)^{2} a \,c^{3}}"," ",0,"1/40*exp(2*arctan(a*x))*(3*a^4*x^4+6*a^3*x^3+12*a^2*x^2+14*a*x+13)/(a^2*x^2+1)^2/a/c^3","A"
266,1,73,111,0.042000," ","int(exp(2*arctan(a*x))/(a^2*c*x^2+c)^4,x)","\frac{{\mathrm e}^{2 \arctan \left(a x \right)} \left(9 a^{6} x^{6}+18 a^{5} x^{5}+45 a^{4} x^{4}+60 a^{3} x^{3}+75 a^{2} x^{2}+66 a x +47\right)}{160 \left(a^{2} x^{2}+1\right)^{3} a \,c^{4}}"," ",0,"1/160*exp(2*arctan(a*x))*(9*a^6*x^6+18*a^5*x^5+45*a^4*x^4+60*a^3*x^3+75*a^2*x^2+66*a*x+47)/(a^2*x^2+1)^3/a/c^4","A"
267,0,0,66,0.325000," ","int(exp(2*arctan(a*x))*(a^2*c*x^2+c)^(3/2),x)","\int {\mathrm e}^{2 \arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(2*arctan(a*x))*(a^2*c*x^2+c)^(3/2),x)","F"
268,0,0,65,0.290000," ","int(exp(2*arctan(a*x))*(a^2*c*x^2+c)^(1/2),x)","\int {\mathrm e}^{2 \arctan \left(a x \right)} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(2*arctan(a*x))*(a^2*c*x^2+c)^(1/2),x)","F"
269,0,0,65,0.288000," ","int(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{2 \arctan \left(a x \right)}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","F"
270,1,39,32,0.039000," ","int(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(a x +2\right) {\mathrm e}^{2 \arctan \left(a x \right)}}{5 a \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"1/5*(a^2*x^2+1)*(a*x+2)*exp(2*arctan(a*x))/a/(a^2*c*x^2+c)^(3/2)","A"
271,1,56,66,0.037000," ","int(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(6 a^{3} x^{3}+12 a^{2} x^{2}+21 a x +22\right) {\mathrm e}^{2 \arctan \left(a x \right)}}{65 a \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"1/65*(a^2*x^2+1)*(6*a^3*x^3+12*a^2*x^2+21*a*x+22)*exp(2*arctan(a*x))/a/(a^2*c*x^2+c)^(5/2)","A"
272,1,72,99,0.040000," ","int(exp(2*arctan(a*x))/(a^2*c*x^2+c)^(7/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(24 a^{5} x^{5}+48 a^{4} x^{4}+108 a^{3} x^{3}+136 a^{2} x^{2}+149 a x +114\right) {\mathrm e}^{2 \arctan \left(a x \right)}}{377 a \left(a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}"," ",0,"1/377*(a^2*x^2+1)*(24*a^5*x^5+48*a^4*x^4+108*a^3*x^3+136*a^2*x^2+149*a*x+114)*exp(2*arctan(a*x))/a/(a^2*c*x^2+c)^(7/2)","A"
273,0,0,85,0.312000," ","int((a^2*c*x^2+c)^p/exp(arctan(a*x)),x)","\int \left(a^{2} c \,x^{2}+c \right)^{p} {\mathrm e}^{-\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^p/exp(arctan(a*x)),x)","F"
274,0,0,45,0.267000," ","int((a^2*c*x^2+c)^2/exp(arctan(a*x)),x)","\int \left(a^{2} c \,x^{2}+c \right)^{2} {\mathrm e}^{-\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^2/exp(arctan(a*x)),x)","F"
275,0,0,43,0.070000," ","int((a^2*c*x^2+c)/exp(arctan(a*x)),x)","\int \left(a^{2} c \,x^{2}+c \right) {\mathrm e}^{-\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)/exp(arctan(a*x)),x)","F"
276,0,0,41,0.060000," ","int(exp(-arctan(a*x)),x)","\int {\mathrm e}^{-\arctan \left(a x \right)}\, dx"," ",0,"int(exp(-arctan(a*x)),x)","F"
277,1,16,15,0.039000," ","int(1/exp(arctan(a*x))/(a^2*c*x^2+c),x)","-\frac{{\mathrm e}^{-\arctan \left(a x \right)}}{a c}"," ",0,"-1/a/c/exp(arctan(a*x))","A"
278,1,41,48,0.040000," ","int(1/exp(arctan(a*x))/(a^2*c*x^2+c)^2,x)","-\frac{\left(2 a^{2} x^{2}-2 a x +3\right) {\mathrm e}^{-\arctan \left(a x \right)}}{5 \left(a^{2} x^{2}+1\right) c^{2} a}"," ",0,"-1/5*(2*a^2*x^2-2*a*x+3)/(a^2*x^2+1)/c^2/exp(arctan(a*x))/a","A"
279,1,57,80,0.039000," ","int(1/exp(arctan(a*x))/(a^2*c*x^2+c)^3,x)","-\frac{\left(24 a^{4} x^{4}-24 a^{3} x^{3}+60 a^{2} x^{2}-44 a x +41\right) {\mathrm e}^{-\arctan \left(a x \right)}}{85 \left(a^{2} x^{2}+1\right)^{2} c^{3} a}"," ",0,"-1/85*(24*a^4*x^4-24*a^3*x^3+60*a^2*x^2-44*a*x+41)/(a^2*x^2+1)^2/c^3/exp(arctan(a*x))/a","A"
280,1,73,112,0.040000," ","int(1/exp(arctan(a*x))/(a^2*c*x^2+c)^4,x)","-\frac{\left(144 a^{6} x^{6}-144 a^{5} x^{5}+504 a^{4} x^{4}-408 a^{3} x^{3}+606 a^{2} x^{2}-366 a x +263\right) {\mathrm e}^{-\arctan \left(a x \right)}}{629 \left(a^{2} x^{2}+1\right)^{3} c^{4} a}"," ",0,"-1/629*(144*a^6*x^6-144*a^5*x^5+504*a^4*x^4-408*a^3*x^3+606*a^2*x^2-366*a*x+263)/(a^2*x^2+1)^3/c^4/exp(arctan(a*x))/a","A"
281,0,0,66,0.291000," ","int((a^2*c*x^2+c)^(3/2)/exp(arctan(a*x)),x)","\int \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} {\mathrm e}^{-\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/exp(arctan(a*x)),x)","F"
282,0,0,65,0.290000," ","int((a^2*c*x^2+c)^(1/2)/exp(arctan(a*x)),x)","\int \sqrt{a^{2} c \,x^{2}+c}\, {\mathrm e}^{-\arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/exp(arctan(a*x)),x)","F"
283,0,0,65,0.283000," ","int(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{-\arctan \left(a x \right)}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","F"
284,1,39,32,0.039000," ","int(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(a x -1\right) {\mathrm e}^{-\arctan \left(a x \right)}}{2 a \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"1/2*(a^2*x^2+1)*(a*x-1)/a/exp(arctan(a*x))/(a^2*c*x^2+c)^(3/2)","A"
285,1,56,67,0.038000," ","int(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(3 a^{3} x^{3}-3 a^{2} x^{2}+6 a x -4\right) {\mathrm e}^{-\arctan \left(a x \right)}}{10 a \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"1/10*(a^2*x^2+1)*(3*a^3*x^3-3*a^2*x^2+6*a*x-4)/a/exp(arctan(a*x))/(a^2*c*x^2+c)^(5/2)","A"
286,1,72,100,0.038000," ","int(1/exp(arctan(a*x))/(a^2*c*x^2+c)^(7/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(6 a^{5} x^{5}-6 a^{4} x^{4}+18 a^{3} x^{3}-14 a^{2} x^{2}+17 a x -9\right) {\mathrm e}^{-\arctan \left(a x \right)}}{26 a \left(a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}"," ",0,"1/26*(a^2*x^2+1)*(6*a^5*x^5-6*a^4*x^4+18*a^3*x^3-14*a^2*x^2+17*a*x-9)/a/exp(arctan(a*x))/(a^2*c*x^2+c)^(7/2)","A"
287,0,0,83,0.312000," ","int((a^2*c*x^2+c)^p/exp(2*arctan(a*x)),x)","\int \left(a^{2} c \,x^{2}+c \right)^{p} {\mathrm e}^{-2 \arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^p/exp(2*arctan(a*x)),x)","F"
288,0,0,45,0.272000," ","int((a^2*c*x^2+c)^2/exp(2*arctan(a*x)),x)","\int \left(a^{2} c \,x^{2}+c \right)^{2} {\mathrm e}^{-2 \arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^2/exp(2*arctan(a*x)),x)","F"
289,0,0,43,0.066000," ","int((a^2*c*x^2+c)/exp(2*arctan(a*x)),x)","\int \left(a^{2} c \,x^{2}+c \right) {\mathrm e}^{-2 \arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)/exp(2*arctan(a*x)),x)","F"
290,0,0,41,0.064000," ","int(exp(-2*arctan(a*x)),x)","\int {\mathrm e}^{-2 \arctan \left(a x \right)}\, dx"," ",0,"int(exp(-2*arctan(a*x)),x)","F"
291,1,18,17,0.037000," ","int(1/exp(2*arctan(a*x))/(a^2*c*x^2+c),x)","-\frac{{\mathrm e}^{-2 \arctan \left(a x \right)}}{2 a c}"," ",0,"-1/2/a/c/exp(2*arctan(a*x))","A"
292,1,42,51,0.039000," ","int(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^2,x)","-\frac{\left(a^{2} x^{2}-2 a x +3\right) {\mathrm e}^{-2 \arctan \left(a x \right)}}{8 \left(a^{2} x^{2}+1\right) c^{2} a}"," ",0,"-1/8*(a^2*x^2-2*a*x+3)/(a^2*x^2+1)/c^2/exp(2*arctan(a*x))/a","A"
293,1,59,86,0.039000," ","int(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^3,x)","-\frac{\left(3 a^{4} x^{4}-6 a^{3} x^{3}+12 a^{2} x^{2}-14 a x +13\right) {\mathrm e}^{-2 \arctan \left(a x \right)}}{40 \left(a^{2} x^{2}+1\right)^{2} c^{3} a}"," ",0,"-1/40*(3*a^4*x^4-6*a^3*x^3+12*a^2*x^2-14*a*x+13)/(a^2*x^2+1)^2/c^3/exp(2*arctan(a*x))/a","A"
294,1,75,120,0.039000," ","int(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^4,x)","-\frac{\left(9 a^{6} x^{6}-18 a^{5} x^{5}+45 a^{4} x^{4}-60 a^{3} x^{3}+75 a^{2} x^{2}-66 a x +47\right) {\mathrm e}^{-2 \arctan \left(a x \right)}}{160 \left(a^{2} x^{2}+1\right)^{3} c^{4} a}"," ",0,"-1/160*(9*a^6*x^6-18*a^5*x^5+45*a^4*x^4-60*a^3*x^3+75*a^2*x^2-66*a*x+47)/(a^2*x^2+1)^3/c^4/exp(2*arctan(a*x))/a","A"
295,0,0,66,0.313000," ","int((a^2*c*x^2+c)^(3/2)/exp(2*arctan(a*x)),x)","\int \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} {\mathrm e}^{-2 \arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(3/2)/exp(2*arctan(a*x)),x)","F"
296,0,0,65,0.291000," ","int((a^2*c*x^2+c)^(1/2)/exp(2*arctan(a*x)),x)","\int \sqrt{a^{2} c \,x^{2}+c}\, {\mathrm e}^{-2 \arctan \left(a x \right)}\, dx"," ",0,"int((a^2*c*x^2+c)^(1/2)/exp(2*arctan(a*x)),x)","F"
297,0,0,65,0.297000," ","int(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{-2 \arctan \left(a x \right)}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","F"
298,1,41,34,0.037000," ","int(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(a x -2\right) {\mathrm e}^{-2 \arctan \left(a x \right)}}{5 a \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"1/5*(a^2*x^2+1)*(a*x-2)/a/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(3/2)","A"
299,1,58,71,0.036000," ","int(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(5/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(6 a^{3} x^{3}-12 a^{2} x^{2}+21 a x -22\right) {\mathrm e}^{-2 \arctan \left(a x \right)}}{65 a \left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"1/65*(a^2*x^2+1)*(6*a^3*x^3-12*a^2*x^2+21*a*x-22)/a/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(5/2)","A"
300,1,74,106,0.039000," ","int(1/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(7/2),x)","\frac{\left(a^{2} x^{2}+1\right) \left(24 a^{5} x^{5}-48 a^{4} x^{4}+108 a^{3} x^{3}-136 a^{2} x^{2}+149 a x -114\right) {\mathrm e}^{-2 \arctan \left(a x \right)}}{377 a \left(a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}"," ",0,"1/377*(a^2*x^2+1)*(24*a^5*x^5-48*a^4*x^4+108*a^3*x^3-136*a^2*x^2+149*a*x-114)/a/exp(2*arctan(a*x))/(a^2*c*x^2+c)^(7/2)","A"
301,1,45,44,0.060000," ","int((1+I*a*x)^5/(a^2*x^2+1)^3,x)","\frac{-4 x -\frac{2 i}{a}}{\left(a x +i\right)^{2}}+\frac{i \ln \left(a^{2} x^{2}+1\right)}{2 a}+\frac{\arctan \left(a x \right)}{a}"," ",0,"(-4*x-2*I/a)/(I+a*x)^2+1/2*I/a*ln(a^2*x^2+1)+arctan(a*x)/a","A"
302,1,113,57,0.181000," ","int((1+I*a*x)^4/(a^2*x^2+1)^(5/2),x)","\frac{7 x}{3 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}-\frac{7 x}{3 \sqrt{a^{2} x^{2}+1}}-\frac{a^{2} x^{3}}{3 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{\ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}+\frac{4 i a \,x^{2}}{\left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{4 i}{3 a \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"7/3*x/(a^2*x^2+1)^(3/2)-7/3*x/(a^2*x^2+1)^(1/2)-1/3*a^2*x^3/(a^2*x^2+1)^(3/2)+ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)+4*I*a*x^2/(a^2*x^2+1)^(3/2)+4/3*I/a/(a^2*x^2+1)^(3/2)","A"
303,1,40,27,0.056000," ","int((1+I*a*x)^3/(a^2*x^2+1)^2,x)","\frac{2}{a \left(a x +i\right)}-\frac{i \ln \left(a^{2} x^{2}+1\right)}{2 a}-\frac{\arctan \left(a x \right)}{a}"," ",0,"2/a/(I+a*x)-1/2*I/a*ln(a^2*x^2+1)-arctan(a*x)/a","A"
304,1,63,34,0.170000," ","int((1+I*a*x)^2/(a^2*x^2+1)^(3/2),x)","\frac{2 x}{\sqrt{a^{2} x^{2}+1}}-\frac{\ln \left(\frac{x \,a^{2}}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}+1}\right)}{\sqrt{a^{2}}}-\frac{2 i}{a \sqrt{a^{2} x^{2}+1}}"," ",0,"2*x/(a^2*x^2+1)^(1/2)-ln(x*a^2/(a^2)^(1/2)+(a^2*x^2+1)^(1/2))/(a^2)^(1/2)-2*I/a/(a^2*x^2+1)^(1/2)","A"
305,1,26,13,0.036000," ","int((1+I*a*x)/(a^2*x^2+1),x)","\frac{i \ln \left(a^{2} x^{2}+1\right)}{2 a}+\frac{\arctan \left(a x \right)}{a}"," ",0,"1/2*I/a*ln(a^2*x^2+1)+arctan(a*x)/a","A"
306,1,26,14,0.033000," ","int(1/(1+I*a*x),x)","-\frac{i \ln \left(a^{2} x^{2}+1\right)}{2 a}+\frac{\arctan \left(a x \right)}{a}"," ",0,"-1/2*I/a*ln(a^2*x^2+1)+arctan(a*x)/a","A"
307,1,143,34,0.184000," ","int(1/(1+I*a*x)^2*(a^2*x^2+1)^(1/2),x)","-\frac{i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}}{a^{3} \left(x -\frac{i}{a}\right)^{2}}+\frac{i \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}}{a}-\frac{\ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}"," ",0,"-I/a^3/(x-I/a)^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)+I/a*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)-ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)","B"
308,1,41,29,0.052000," ","int(1/(1+I*a*x)^3*(a^2*x^2+1),x)","-\frac{2}{a \left(-a x +i\right)}+\frac{i \ln \left(a^{2} x^{2}+1\right)}{2 a}-\frac{\arctan \left(a x \right)}{a}"," ",0,"-2/a/(-a*x+I)+1/2*I/a*ln(a^2*x^2+1)-arctan(a*x)/a","A"
309,1,262,57,0.186000," ","int(1/(1+I*a*x)^4*(a^2*x^2+1)^(3/2),x)","\frac{i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{3 a^{5} \left(x -\frac{i}{a}\right)^{4}}+\frac{\left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{3 a^{4} \left(x -\frac{i}{a}\right)^{3}}+\frac{2 i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{5}{2}}}{3 a^{3} \left(x -\frac{i}{a}\right)^{2}}-\frac{2 i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}}{3 a}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\, x +\frac{\ln \left(\frac{i a +\left(x -\frac{i}{a}\right) a^{2}}{\sqrt{a^{2}}}+\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}\right)}{\sqrt{a^{2}}}"," ",0,"1/3*I/a^5/(x-I/a)^4*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)+1/3/a^4/(x-I/a)^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)+2/3*I/a^3/(x-I/a)^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(5/2)-2/3*I/a*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)*x+ln((I*a+(x-I/a)*a^2)/(a^2)^(1/2)+((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))/(a^2)^(1/2)","B"
310,1,84,113,0.197000," ","int((1+I*a*x)^5/(a^2*x^2+1)^(5/2)/(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(i \ln \left(a x +i\right) x^{2} a^{2}-2 \ln \left(a x +i\right) x a -i \ln \left(a x +i\right)-4 a x -2 i\right)}{\sqrt{a^{2} x^{2}+1}\, c a \left(a x +i\right)^{2}}"," ",0,"1/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)*(I*ln(I+a*x)*x^2*a^2-2*ln(I+a*x)*x*a-I*ln(I+a*x)-4*a*x-2*I)/c/a/(I+a*x)^2","A"
311,1,800,80,0.242000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2/(a^2*c*x^2+c)^(1/2),x)","\frac{\ln \left(\frac{x \,a^{2} c}{\sqrt{a^{2} c}}+\sqrt{a^{2} c \,x^{2}+c}\right)}{\sqrt{a^{2} c}}-\frac{2 \left(i \sqrt{-a^{2}}+a \right) \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}{a^{3} c \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}+\frac{2 i \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}{3 a^{3} c \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2}}-\frac{2 \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}{3 a^{2} c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2}}-\frac{2 i \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}\, \sqrt{-a^{2}}}{3 a^{3} c \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}+\frac{2 \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}{3 a^{2} c \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}+\frac{2 i \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}{3 a^{3} c \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2}}+\frac{2 \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}{3 a^{2} c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2}}+\frac{2 i \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}\, \sqrt{-a^{2}}}{3 a^{3} c \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}+\frac{2 \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}{3 a^{2} c \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}+\frac{2 \left(i \sqrt{-a^{2}}-a \right) \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}{a^{3} c \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}"," ",0,"ln(x*a^2*c/(a^2*c)^(1/2)+(a^2*c*x^2+c)^(1/2))/(a^2*c)^(1/2)-2/a^3*(I*(-a^2)^(1/2)+a)/c/(x-(-a^2)^(1/2)/a^2)*((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2)+2/3*I/a^3/c/(x+(-a^2)^(1/2)/a^2)^2*((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2)-2/3/a^2/c/(-a^2)^(1/2)/(x+(-a^2)^(1/2)/a^2)^2*((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2)-2/3*I/a^3/c/(x+(-a^2)^(1/2)/a^2)*((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2)*(-a^2)^(1/2)+2/3/a^2/c/(x+(-a^2)^(1/2)/a^2)*((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2)+2/3*I/a^3/c/(x-(-a^2)^(1/2)/a^2)^2*((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2)+2/3/a^2/c/(-a^2)^(1/2)/(x-(-a^2)^(1/2)/a^2)^2*((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2)+2/3*I/a^3/c/(x-(-a^2)^(1/2)/a^2)*((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2)*(-a^2)^(1/2)+2/3/a^2/c/(x-(-a^2)^(1/2)/a^2)*((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2)+2/a^3*(I*(-a^2)^(1/2)-a)/c/(x+(-a^2)^(1/2)/a^2)*((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2)","B"
312,1,61,73,0.159000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(-i \ln \left(a x +i\right) x a +\ln \left(a x +i\right)+2\right) \sqrt{c \left(a^{2} x^{2}+1\right)}}{\sqrt{a^{2} x^{2}+1}\, c a \left(a x +i\right)}"," ",0,"(-I*ln(I+a*x)*x*a+ln(I+a*x)+2)/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)/c/a/(I+a*x)","A"
313,1,204,53,0.181000," ","int((1+I*a*x)^2/(a^2*x^2+1)/(a^2*c*x^2+c)^(1/2),x)","-\frac{\ln \left(\frac{x \,a^{2} c}{\sqrt{a^{2} c}}+\sqrt{a^{2} c \,x^{2}+c}\right)}{\sqrt{a^{2} c}}+\frac{\left(i \sqrt{-a^{2}}+a \right) \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}{a^{3} c \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}-\frac{\left(i \sqrt{-a^{2}}-a \right) \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}{a^{3} c \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}"," ",0,"-ln(x*a^2*c/(a^2*c)^(1/2)+(a^2*c*x^2+c)^(1/2))/(a^2*c)^(1/2)+1/a^3*(I*(-a^2)^(1/2)+a)/c/(x-(-a^2)^(1/2)/a^2)*((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2)-1/a^3*(I*(-a^2)^(1/2)-a)/c/(x+(-a^2)^(1/2)/a^2)*((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2)","B"
314,1,53,36,0.099000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(i \ln \left(a^{2} x^{2}+1\right)+2 \arctan \left(a x \right)\right)}{2 \sqrt{a^{2} x^{2}+1}\, c a}"," ",0,"1/2/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)*(I*ln(a^2*x^2+1)+2*arctan(a*x))/c/a","A"
315,1,42,37,0.047000," ","int(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(1/2),x)","-\frac{i \sqrt{c \left(a^{2} x^{2}+1\right)}\, \ln \left(i a x +1\right)}{\sqrt{a^{2} x^{2}+1}\, c a}"," ",0,"-I/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)/c*ln(1+I*a*x)/a","A"
316,1,87,53,0.218000," ","int(1/(1+I*a*x)^2*(a^2*x^2+1)/(a^2*c*x^2+c)^(1/2),x)","-\frac{\ln \left(\frac{x \,a^{2} c}{\sqrt{a^{2} c}}+\sqrt{a^{2} c \,x^{2}+c}\right)}{\sqrt{a^{2} c}}+\frac{2 \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2} c +2 i a c \left(x -\frac{i}{a}\right)}}{a^{2} c \left(x -\frac{i}{a}\right)}"," ",0,"-ln(x*a^2*c/(a^2*c)^(1/2)+(a^2*c*x^2+c)^(1/2))/(a^2*c)^(1/2)+2/a^2/c/(x-I/a)*((x-I/a)^2*a^2*c+2*I*a*c*(x-I/a))^(1/2)","A"
317,1,66,75,0.155000," ","int(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(1/2),x)","\frac{\left(-i \ln \left(-a x +i\right) x a -\ln \left(-a x +i\right)-2\right) \sqrt{c \left(a^{2} x^{2}+1\right)}}{\sqrt{a^{2} x^{2}+1}\, c a \left(-a x +i\right)}"," ",0,"(-I*ln(-a*x+I)*x*a-ln(-a*x+I)-2)/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)/c/a/(-a*x+I)","A"
318,1,136,80,0.192000," ","int(1/(1+I*a*x)^4*(a^2*x^2+1)^2/(a^2*c*x^2+c)^(1/2),x)","\frac{\ln \left(\frac{x \,a^{2} c}{\sqrt{a^{2} c}}+\sqrt{a^{2} c \,x^{2}+c}\right)}{\sqrt{a^{2} c}}-\frac{8 \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2} c +2 i a c \left(x -\frac{i}{a}\right)}}{3 a^{2} c \left(x -\frac{i}{a}\right)}-\frac{4 i \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2} c +2 i a c \left(x -\frac{i}{a}\right)}}{3 a^{3} c \left(x -\frac{i}{a}\right)^{2}}"," ",0,"ln(x*a^2*c/(a^2*c)^(1/2)+(a^2*c*x^2+c)^(1/2))/(a^2*c)^(1/2)-8/3/a^2/c/(x-I/a)*((x-I/a)^2*a^2*c+2*I*a*c*(x-I/a))^(1/2)-4/3*I/a^3/c/(x-I/a)^2*((x-I/a)^2*a^2*c+2*I*a*c*(x-I/a))^(1/2)","A"
319,1,20,28,0.057000," ","int((1+I*a*x)^5/(a^2*x^2+1)^4,x)","\frac{-\frac{i x}{2}-\frac{1}{6 a}}{\left(a x +i\right)^{3}}"," ",0,"(-1/2*I*x-1/6/a)/(I+a*x)^3","A"
320,1,269,49,0.178000," ","int((1+I*a*x)^4/(a^2*x^2+1)^(7/2),x)","\frac{x}{5 \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}+\frac{4 x}{15 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{8 x}{15 \sqrt{a^{2} x^{2}+1}}+a^{4} \left(-\frac{x^{3}}{2 a^{2} \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}+\frac{-\frac{3 x}{8 a^{2} \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}+\frac{3 \left(\frac{x}{5 \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}+\frac{4 x}{15 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{8 x}{15 \sqrt{a^{2} x^{2}+1}}\right)}{8 a^{2}}}{a^{2}}\right)-4 i a^{3} \left(-\frac{x^{2}}{3 a^{2} \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}-\frac{2}{15 a^{4} \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}\right)-6 a^{2} \left(-\frac{x}{4 a^{2} \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}+\frac{\frac{x}{5 \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}+\frac{4 x}{15 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{8 x}{15 \sqrt{a^{2} x^{2}+1}}}{4 a^{2}}\right)-\frac{4 i}{5 a \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}"," ",0,"1/5*x/(a^2*x^2+1)^(5/2)+4/15*x/(a^2*x^2+1)^(3/2)+8/15*x/(a^2*x^2+1)^(1/2)+a^4*(-1/2*x^3/a^2/(a^2*x^2+1)^(5/2)+3/2/a^2*(-1/4*x/a^2/(a^2*x^2+1)^(5/2)+1/4/a^2*(1/5*x/(a^2*x^2+1)^(5/2)+4/15*x/(a^2*x^2+1)^(3/2)+8/15*x/(a^2*x^2+1)^(1/2))))-4*I*a^3*(-1/3*x^2/a^2/(a^2*x^2+1)^(5/2)-2/15/a^4/(a^2*x^2+1)^(5/2))-6*a^2*(-1/4*x/a^2/(a^2*x^2+1)^(5/2)+1/4/a^2*(1/5*x/(a^2*x^2+1)^(5/2)+4/15*x/(a^2*x^2+1)^(3/2)+8/15*x/(a^2*x^2+1)^(1/2)))-4/5*I/a/(a^2*x^2+1)^(5/2)","B"
321,1,15,15,0.056000," ","int((1+I*a*x)^3/(a^2*x^2+1)^3,x)","\frac{i}{2 a \left(a x +i\right)^{2}}"," ",0,"1/2*I/a/(I+a*x)^2","A"
322,1,104,49,0.178000," ","int((1+I*a*x)^2/(a^2*x^2+1)^(5/2),x)","-a^{2} \left(-\frac{x}{2 a^{2} \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{\frac{x}{3 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{2 x}{3 \sqrt{a^{2} x^{2}+1}}}{2 a^{2}}\right)-\frac{2 i}{3 a \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{x}{3 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}+\frac{2 x}{3 \sqrt{a^{2} x^{2}+1}}"," ",0,"-a^2*(-1/2*x/a^2/(a^2*x^2+1)^(3/2)+1/2/a^2*(1/3*x/(a^2*x^2+1)^(3/2)+2/3*x/(a^2*x^2+1)^(1/2)))-2/3*I/a/(a^2*x^2+1)^(3/2)+1/3*x/(a^2*x^2+1)^(3/2)+2/3*x/(a^2*x^2+1)^(1/2)","B"
323,1,38,23,0.040000," ","int((1+I*a*x)/(a^2*x^2+1)^2,x)","\frac{2 a^{2} x -2 i a}{4 a^{2} \left(a^{2} x^{2}+1\right)}+\frac{\arctan \left(a x \right)}{2 a}"," ",0,"1/4*(2*a^2*x-2*I*a)/a^2/(a^2*x^2+1)+1/2*arctan(a*x)/a","A"
324,1,25,24,0.097000," ","int(1/(1+I*a*x)/(a^2*x^2+1),x)","-\frac{1}{2 a \left(-a x +i\right)}+\frac{\arctan \left(a x \right)}{2 a}"," ",0,"-1/2/a/(-a*x+I)+1/2*arctan(a*x)/a","A"
325,1,93,49,0.175000," ","int(1/(1+I*a*x)^2/(a^2*x^2+1)^(1/2),x)","-\frac{\frac{i \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}}{3 a \left(x -\frac{i}{a}\right)^{2}}-\frac{\sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)}}{3 \left(x -\frac{i}{a}\right)}}{a^{2}}"," ",0,"-1/a^2*(1/3*I/a/(x-I/a)^2*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2)-1/3/(x-I/a)*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(1/2))","A"
326,1,16,15,0.034000," ","int(1/(1+I*a*x)^3,x)","\frac{i}{2 a \left(i a x +1\right)^{2}}"," ",0,"1/2*I/a/(1+I*a*x)^2","A"
327,1,92,49,0.175000," ","int(1/(1+I*a*x)^4*(a^2*x^2+1)^(1/2),x)","\frac{\frac{i \left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}}{5 a \left(x -\frac{i}{a}\right)^{4}}-\frac{\left(\left(x -\frac{i}{a}\right)^{2} a^{2}+2 i a \left(x -\frac{i}{a}\right)\right)^{\frac{3}{2}}}{15 \left(x -\frac{i}{a}\right)^{3}}}{a^{4}}"," ",0,"1/a^4*(1/5*I/a/(x-I/a)^4*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2)-1/15/(x-I/a)^3*((x-I/a)^2*a^2+2*I*a*(x-I/a))^(3/2))","A"
328,1,48,80,0.165000," ","int((1+I*a*x)^5/(a^2*x^2+1)^(5/2)/(a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(3 i a x +1\right)}{6 \sqrt{a^{2} x^{2}+1}\, c^{2} a \left(a x +i\right)^{3}}"," ",0,"-1/6/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)*(3*I*a*x+1)/c^2/a/(I+a*x)^3","A"
329,1,940,57,0.193000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2/(a^2*c*x^2+c)^(3/2),x)","\frac{x}{c \sqrt{a^{2} c \,x^{2}+c}}-\frac{2 \left(i \sqrt{-a^{2}}+a \right) \left(-\frac{1}{5 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}-\frac{3 a^{2} \left(-\frac{1}{3 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right) \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}-\frac{2 \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right) a^{2} c +2 c \sqrt{-a^{2}}}{3 c^{2} \sqrt{-a^{2}}\, \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}\right)}{5 \sqrt{-a^{2}}}\right)}{a^{3}}-\frac{2 \left(i \sqrt{-a^{2}}+a \right) \left(-\frac{1}{3 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right) \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}-\frac{2 \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right) a^{2} c +2 c \sqrt{-a^{2}}}{3 c^{2} \sqrt{-a^{2}}\, \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}\right)}{a \sqrt{-a^{2}}}+\frac{2 \left(i \sqrt{-a^{2}}-a \right) \left(\frac{1}{5 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}+\frac{3 a^{2} \left(\frac{1}{3 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right) \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}+\frac{2 \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right) a^{2} c -2 c \sqrt{-a^{2}}}{3 c^{2} \sqrt{-a^{2}}\, \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}\right)}{5 \sqrt{-a^{2}}}\right)}{a^{3}}-\frac{2 \left(i \sqrt{-a^{2}}-a \right) \left(\frac{1}{3 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right) \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}+\frac{2 \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right) a^{2} c -2 c \sqrt{-a^{2}}}{3 c^{2} \sqrt{-a^{2}}\, \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}\right)}{a \sqrt{-a^{2}}}"," ",0,"x/c/(a^2*c*x^2+c)^(1/2)-2/a^3*(I*(-a^2)^(1/2)+a)*(-1/5/c/(-a^2)^(1/2)/(x-(-a^2)^(1/2)/a^2)^2/((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2)-3/5*a^2/(-a^2)^(1/2)*(-1/3/c/(-a^2)^(1/2)/(x-(-a^2)^(1/2)/a^2)/((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2)-1/3/c^2/(-a^2)^(1/2)*(2*(x-(-a^2)^(1/2)/a^2)*a^2*c+2*c*(-a^2)^(1/2))/((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2)))-2/a*(I*(-a^2)^(1/2)+a)/(-a^2)^(1/2)*(-1/3/c/(-a^2)^(1/2)/(x-(-a^2)^(1/2)/a^2)/((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2)-1/3/c^2/(-a^2)^(1/2)*(2*(x-(-a^2)^(1/2)/a^2)*a^2*c+2*c*(-a^2)^(1/2))/((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2))+2/a^3*(I*(-a^2)^(1/2)-a)*(1/5/c/(-a^2)^(1/2)/(x+(-a^2)^(1/2)/a^2)^2/((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2)+3/5*a^2/(-a^2)^(1/2)*(1/3/c/(-a^2)^(1/2)/(x+(-a^2)^(1/2)/a^2)/((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2)+1/3/c^2/(-a^2)^(1/2)*(2*(x+(-a^2)^(1/2)/a^2)*a^2*c-2*c*(-a^2)^(1/2))/((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2)))-2/a*(I*(-a^2)^(1/2)-a)/(-a^2)^(1/2)*(1/3/c/(-a^2)^(1/2)/(x+(-a^2)^(1/2)/a^2)/((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2)+1/3/c^2/(-a^2)^(1/2)*(2*(x+(-a^2)^(1/2)/a^2)*a^2*c-2*c*(-a^2)^(1/2))/((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2))","B"
330,1,44,41,0.096000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","-\frac{\left(a x +i\right) \left(i a x +1\right)^{3}}{2 a \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"-1/2*(I+a*x)/a*(1+I*a*x)^3/(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(3/2)","A"
331,1,398,44,0.182000," ","int((1+I*a*x)^2/(a^2*x^2+1)/(a^2*c*x^2+c)^(3/2),x)","-\frac{x}{c \sqrt{a^{2} c \,x^{2}+c}}+\frac{\left(i \sqrt{-a^{2}}+a \right) \left(-\frac{1}{3 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right) \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}-\frac{2 \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right) a^{2} c +2 c \sqrt{-a^{2}}}{3 c^{2} \sqrt{-a^{2}}\, \sqrt{\left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c +2 c \sqrt{-a^{2}}\, \left(x -\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}\right)}{a \sqrt{-a^{2}}}+\frac{\left(i \sqrt{-a^{2}}-a \right) \left(\frac{1}{3 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right) \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}+\frac{2 \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right) a^{2} c -2 c \sqrt{-a^{2}}}{3 c^{2} \sqrt{-a^{2}}\, \sqrt{\left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)^{2} a^{2} c -2 c \sqrt{-a^{2}}\, \left(x +\frac{\sqrt{-a^{2}}}{a^{2}}\right)}}\right)}{a \sqrt{-a^{2}}}"," ",0,"-x/c/(a^2*c*x^2+c)^(1/2)+1/a*(I*(-a^2)^(1/2)+a)/(-a^2)^(1/2)*(-1/3/c/(-a^2)^(1/2)/(x-(-a^2)^(1/2)/a^2)/((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2)-1/3/c^2/(-a^2)^(1/2)*(2*(x-(-a^2)^(1/2)/a^2)*a^2*c+2*c*(-a^2)^(1/2))/((x-(-a^2)^(1/2)/a^2)^2*a^2*c+2*c*(-a^2)^(1/2)*(x-(-a^2)^(1/2)/a^2))^(1/2))+1/a*(I*(-a^2)^(1/2)-a)/(-a^2)^(1/2)*(1/3/c/(-a^2)^(1/2)/(x+(-a^2)^(1/2)/a^2)/((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2)+1/3/c^2/(-a^2)^(1/2)*(2*(x+(-a^2)^(1/2)/a^2)*a^2*c-2*c*(-a^2)^(1/2))/((x+(-a^2)^(1/2)/a^2)^2*a^2*c-2*c*(-a^2)^(1/2)*(x+(-a^2)^(1/2)/a^2))^(1/2))","B"
332,1,54,75,0.182000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(\arctan \left(a x \right) x^{2} a^{2}+a x +\arctan \left(a x \right)-i\right)}{2 \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} a \,c^{2}}"," ",0,"1/2/(a^2*x^2+1)^(3/2)*(c*(a^2*x^2+1))^(1/2)/a*(arctan(a*x)*x^2*a^2+a*x+arctan(a*x)-I)/c^2","A"
333,1,86,76,0.197000," ","int(1/(1+I*a*x)*(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(i \ln \left(a x +i\right) x a -i \ln \left(-a x +i\right) x a +\ln \left(a x +i\right)-\ln \left(-a x +i\right)+2\right)}{4 \sqrt{a^{2} x^{2}+1}\, c^{2} a \left(-a x +i\right)}"," ",0,"-1/4/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)*(I*ln(I+a*x)*x*a-I*ln(-a*x+I)*x*a+ln(I+a*x)-ln(-a*x+I)+2)/c^2/a/(-a*x+I)","A"
334,1,137,44,0.181000," ","int(1/(1+I*a*x)^2*(a^2*x^2+1)/(a^2*c*x^2+c)^(3/2),x)","-\frac{x}{c \sqrt{a^{2} c \,x^{2}+c}}-\frac{2 i \left(\frac{i}{3 a c \left(x -\frac{i}{a}\right) \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2} c +2 i a c \left(x -\frac{i}{a}\right)}}+\frac{i \left(2 \left(x -\frac{i}{a}\right) a^{2} c +2 i a c \right)}{3 a \,c^{2} \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2} c +2 i a c \left(x -\frac{i}{a}\right)}}\right)}{a}"," ",0,"-x/c/(a^2*c*x^2+c)^(1/2)-2*I/a*(1/3*I/a/c/(x-I/a)/((x-I/a)^2*a^2*c+2*I*a*c*(x-I/a))^(1/2)+1/3*I/a/c^2*(2*(x-I/a)*a^2*c+2*I*a*c)/((x-I/a)^2*a^2*c+2*I*a*c*(x-I/a))^(1/2))","B"
335,1,45,41,0.041000," ","int(1/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(3/2),x)","\frac{\left(-a x +i\right) \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{2 a \left(i a x +1\right)^{3} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"1/2*(-a*x+I)/a/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(3/2)","A"
336,1,307,57,0.185000," ","int(1/(1+I*a*x)^4*(a^2*x^2+1)^2/(a^2*c*x^2+c)^(3/2),x)","\frac{x}{c \sqrt{a^{2} c \,x^{2}+c}}-\frac{4 \left(\frac{i}{5 a c \left(x -\frac{i}{a}\right)^{2} \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2} c +2 i a c \left(x -\frac{i}{a}\right)}}+\frac{3 i a \left(\frac{i}{3 a c \left(x -\frac{i}{a}\right) \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2} c +2 i a c \left(x -\frac{i}{a}\right)}}+\frac{i \left(2 \left(x -\frac{i}{a}\right) a^{2} c +2 i a c \right)}{3 a \,c^{2} \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2} c +2 i a c \left(x -\frac{i}{a}\right)}}\right)}{5}\right)}{a^{2}}+\frac{4 i \left(\frac{i}{3 a c \left(x -\frac{i}{a}\right) \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2} c +2 i a c \left(x -\frac{i}{a}\right)}}+\frac{i \left(2 \left(x -\frac{i}{a}\right) a^{2} c +2 i a c \right)}{3 a \,c^{2} \sqrt{\left(x -\frac{i}{a}\right)^{2} a^{2} c +2 i a c \left(x -\frac{i}{a}\right)}}\right)}{a}"," ",0,"x/c/(a^2*c*x^2+c)^(1/2)-4/a^2*(1/5*I/a/c/(x-I/a)^2/((x-I/a)^2*a^2*c+2*I*a*c*(x-I/a))^(1/2)+3/5*I*a*(1/3*I/a/c/(x-I/a)/((x-I/a)^2*a^2*c+2*I*a*c*(x-I/a))^(1/2)+1/3*I/a/c^2*(2*(x-I/a)*a^2*c+2*I*a*c)/((x-I/a)^2*a^2*c+2*I*a*c*(x-I/a))^(1/2)))+4*I/a*(1/3*I/a/c/(x-I/a)/((x-I/a)^2*a^2*c+2*I*a*c*(x-I/a))^(1/2)+1/3*I/a/c^2*(2*(x-I/a)*a^2*c+2*I*a*c)/((x-I/a)^2*a^2*c+2*I*a*c*(x-I/a))^(1/2))","B"
337,0,0,66,0.270000," ","int(exp(n*arctan(a*x))*(a^2*c*x^2+c)^2,x)","\int {\mathrm e}^{n \arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{2}\, dx"," ",0,"int(exp(n*arctan(a*x))*(a^2*c*x^2+c)^2,x)","F"
338,0,0,64,0.067000," ","int(exp(n*arctan(a*x))*(a^2*c*x^2+c),x)","\int {\mathrm e}^{n \arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)\, dx"," ",0,"int(exp(n*arctan(a*x))*(a^2*c*x^2+c),x)","F"
339,0,0,61,0.066000," ","int(exp(n*arctan(a*x)),x)","\int {\mathrm e}^{n \arctan \left(a x \right)}\, dx"," ",0,"int(exp(n*arctan(a*x)),x)","F"
340,0,0,124,0.306000," ","int(exp(n*arctan(a*x))*x^3/(a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x^{3}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^3/(a^2*c*x^2+c),x)","F"
341,0,0,131,0.286000," ","int(exp(n*arctan(a*x))*x^2/(a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x^{2}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^2/(a^2*c*x^2+c),x)","F"
342,0,0,95,0.315000," ","int(exp(n*arctan(a*x))*x/(a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctan(a*x))*x/(a^2*c*x^2+c),x)","F"
343,1,18,17,0.036000," ","int(exp(n*arctan(a*x))/(a^2*c*x^2+c),x)","\frac{{\mathrm e}^{n \arctan \left(a x \right)}}{a c n}"," ",0,"exp(n*arctan(a*x))/a/c/n","A"
344,0,0,68,0.295000," ","int(exp(n*arctan(a*x))/x/(a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)}}{x \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(exp(n*arctan(a*x))/x/(a^2*c*x^2+c),x)","F"
345,0,0,78,0.298000," ","int(exp(n*arctan(a*x))/x^2/(a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)}}{x^{2} \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(exp(n*arctan(a*x))/x^2/(a^2*c*x^2+c),x)","F"
346,0,0,120,0.293000," ","int(exp(n*arctan(a*x))/x^3/(a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)}}{x^{3} \left(a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(exp(n*arctan(a*x))/x^3/(a^2*c*x^2+c),x)","F"
347,1,166,173,0.041000," ","int(exp(n*arctan(a*x))/(a^2*c*x^2+c)^4,x)","\frac{\left(720 a^{6} x^{6}+720 a^{5} x^{5} n +360 a^{4} n^{2} x^{4}+120 a^{3} n^{3} x^{3}+2160 a^{4} x^{4}+30 a^{2} n^{4} x^{2}+1920 x^{3} a^{3} n +6 a \,n^{5} x +840 a^{2} n^{2} x^{2}+n^{6}+240 a \,n^{3} x +2160 a^{2} x^{2}+50 n^{4}+1584 n a x +544 n^{2}+720\right) {\mathrm e}^{n \arctan \left(a x \right)}}{\left(a^{2} x^{2}+1\right)^{3} c^{4} a n \left(n^{6}+56 n^{4}+784 n^{2}+2304\right)}"," ",0,"(720*a^6*x^6+720*a^5*n*x^5+360*a^4*n^2*x^4+120*a^3*n^3*x^3+2160*a^4*x^4+30*a^2*n^4*x^2+1920*a^3*n*x^3+6*a*n^5*x+840*a^2*n^2*x^2+n^6+240*a*n^3*x+2160*a^2*x^2+50*n^4+1584*a*n*x+544*n^2+720)*exp(n*arctan(a*x))/(a^2*x^2+1)^3/c^4/a/n/(n^6+56*n^4+784*n^2+2304)","A"
348,0,0,87,0.300000," ","int(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(3/2),x)","\int {\mathrm e}^{n \arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(3/2),x)","F"
349,0,0,86,0.287000," ","int(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(1/2),x)","\int {\mathrm e}^{n \arctan \left(a x \right)} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(1/2),x)","F"
350,0,0,86,0.291000," ","int(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","F"
351,0,0,211,0.287000," ","int(exp(n*arctan(a*x))*x^2*(a^2*c*x^2+c)^(3/2),x)","\int {\mathrm e}^{n \arctan \left(a x \right)} x^{2} \left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^2*(a^2*c*x^2+c)^(3/2),x)","F"
352,0,0,208,0.295000," ","int(exp(n*arctan(a*x))*x^2*(a^2*c*x^2+c)^(1/2),x)","\int {\mathrm e}^{n \arctan \left(a x \right)} x^{2} \sqrt{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^2*(a^2*c*x^2+c)^(1/2),x)","F"
353,0,0,247,0.296000," ","int(exp(n*arctan(a*x))*x^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x^{3}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^3/(a^2*c*x^2+c)^(1/2),x)","F"
354,0,0,219,0.289000," ","int(exp(n*arctan(a*x))*x^2/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x^{2}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^2/(a^2*c*x^2+c)^(1/2),x)","F"
355,0,0,151,0.286000," ","int(exp(n*arctan(a*x))*x/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctan(a*x))*x/(a^2*c*x^2+c)^(1/2),x)","F"
356,0,0,86,0.034000," ","int(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/2),x)","F"
357,0,0,94,0.291000," ","int(exp(n*arctan(a*x))/x/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)}}{x \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctan(a*x))/x/(a^2*c*x^2+c)^(1/2),x)","F"
358,0,0,153,0.289000," ","int(exp(n*arctan(a*x))/x^2/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)}}{x^{2} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctan(a*x))/x^2/(a^2*c*x^2+c)^(1/2),x)","F"
359,0,0,218,0.295000," ","int(exp(n*arctan(a*x))/x^3/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)}}{x^{3} \sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctan(a*x))/x^3/(a^2*c*x^2+c)^(1/2),x)","F"
360,0,0,86,0.289000," ","int(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(1/3),x)","\int {\mathrm e}^{n \arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{\frac{1}{3}}\, dx"," ",0,"int(exp(n*arctan(a*x))*(a^2*c*x^2+c)^(1/3),x)","F"
361,0,0,86,0.293000," ","int(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/3),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{1}{3}}}\, dx"," ",0,"int(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(1/3),x)","F"
362,0,0,86,0.292000," ","int(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(2/3),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{2}{3}}}\, dx"," ",0,"int(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(2/3),x)","F"
363,0,0,89,0.288000," ","int(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(4/3),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{4}{3}}}\, dx"," ",0,"int(exp(n*arctan(a*x))/(a^2*c*x^2+c)^(4/3),x)","F"
364,0,0,41,0.189000," ","int(exp(n*arctan(a*x))*x^m*(a^2*c*x^2+c),x)","\int {\mathrm e}^{n \arctan \left(a x \right)} x^{m} \left(a^{2} c \,x^{2}+c \right)\, dx"," ",0,"int(exp(n*arctan(a*x))*x^m*(a^2*c*x^2+c),x)","F"
365,0,0,43,0.346000," ","int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x^{m}}{a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c),x)","F"
366,0,0,43,0.344000," ","int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^2,x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^2,x)","F"
367,0,0,43,0.357000," ","int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^3,x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^3,x)","F"
368,0,0,63,0.315000," ","int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x^{m}}{\sqrt{a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(1/2),x)","F"
369,0,0,66,0.312000," ","int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(3/2),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(3/2),x)","F"
370,0,0,66,0.312000," ","int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(5/2),x)","\int \frac{{\mathrm e}^{n \arctan \left(a x \right)} x^{m}}{\left(a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(exp(n*arctan(a*x))*x^m/(a^2*c*x^2+c)^(5/2),x)","F"
371,0,0,95,0.294000," ","int(exp(n*arctan(a*x))*(a^2*c*x^2+c)^p,x)","\int {\mathrm e}^{n \arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{p}\, dx"," ",0,"int(exp(n*arctan(a*x))*(a^2*c*x^2+c)^p,x)","F"
372,1,41,51,0.095000," ","int((a^2*c*x^2+c)^p/exp(2*I*p*arctan(a*x)),x)","\frac{\left(a x +i\right) \left(a^{2} c \,x^{2}+c \right)^{p} {\mathrm e}^{-2 i p \arctan \left(a x \right)}}{a \left(1+2 p \right)}"," ",0,"(I+a*x)/a/(1+2*p)*(a^2*c*x^2+c)^p/exp(2*I*p*arctan(a*x))","A"
373,1,41,51,0.086000," ","int(exp(2*I*p*arctan(a*x))*(a^2*c*x^2+c)^p,x)","-\frac{\left(-a x +i\right) {\mathrm e}^{2 i p \arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{p}}{a \left(1+2 p \right)}"," ",0,"-(-a*x+I)/a/(1+2*p)*exp(2*I*p*arctan(a*x))*(a^2*c*x^2+c)^p","A"
374,1,62,56,0.142000," ","int(exp(I*n*arctan(a*x))*x^2*(a^2*c*x^2+c)^(-1-1/2*n^2),x)","\frac{\left(-a x +i\right) \left(a x +i\right) \left(n a x +i\right) {\mathrm e}^{i n \arctan \left(a x \right)} \left(a^{2} c \,x^{2}+c \right)^{-1-\frac{n^{2}}{2}}}{a^{3} n \left(n^{2}-1\right)}"," ",0,"(-a*x+I)*(I+a*x)*(n*a*x+I)*exp(I*n*arctan(a*x))*(a^2*c*x^2+c)^(-1-1/2*n^2)/a^3/n/(n^2-1)","A"
375,1,34,33,0.370000," ","int((1+I*a*x)^6/(a^2*x^2+1)^3*x^2/(a^2*c*x^2+c)^19,x)","\frac{\frac{x}{35 a^{2}}+\frac{i}{210 a^{3}}}{c^{19} \left(a x +i\right)^{21} \left(a x -i\right)^{15}}"," ",0,"1/c^19*(1/35*x/a^2+1/210*I/a^3)/(I+a*x)^21/(a*x-I)^15","A"
376,1,35,33,0.129000," ","int((1+I*a*x)^4/(a^2*x^2+1)^2*x^2/(a^2*c*x^2+c)^9,x)","-\frac{\frac{i}{60 a^{3}}+\frac{x}{15 a^{2}}}{c^{9} \left(a x +i\right)^{10} \left(a x -i\right)^{6}}"," ",0,"-1/c^9*(1/60*I/a^3+1/15*x/a^2)/(I+a*x)^10/(a*x-I)^6","A"
377,1,34,33,0.062000," ","int((1+I*a*x)^2/(a^2*x^2+1)*x^2/(a^2*c*x^2+c)^3,x)","\frac{\frac{x}{3 a^{2}}+\frac{i}{6 a^{3}}}{c^{3} \left(a x +i\right)^{3} \left(a x -i\right)}"," ",0,"1/c^3*(1/3*x/a^2+1/6*I/a^3)/(I+a*x)^3/(a*x-I)","A"
378,1,62,33,0.101000," ","int(x^2/(1+I*a*x)^2*(a^2*x^2+1)/(a^2*c*x^2+c)^3,x)","\frac{-\frac{1}{16 a^{3} \left(a x +i\right)}-\frac{i}{8 a^{3} \left(-a x +i\right)^{2}}-\frac{1}{12 a^{3} \left(-a x +i\right)^{3}}-\frac{1}{16 a^{3} \left(-a x +i\right)}}{c^{3}}"," ",0,"1/c^3*(-1/16/a^3/(I+a*x)-1/8*I/a^3/(-a*x+I)^2-1/12/a^3/(-a*x+I)^3-1/16/a^3/(-a*x+I))","A"
379,1,218,33,0.112000," ","int(x^2/(1+I*a*x)^4*(a^2*x^2+1)^2/(a^2*c*x^2+c)^9,x)","\frac{\frac{13 i}{16384 a^{3} \left(a x +i\right)^{4}}-\frac{i}{12288 a^{3} \left(a x +i\right)^{6}}-\frac{121 i}{65536 a^{3} \left(a x +i\right)^{2}}-\frac{7}{20480 a^{3} \left(a x +i\right)^{5}}+\frac{11}{8192 a^{3} \left(a x +i\right)^{3}}-\frac{143}{65536 a^{3} \left(a x +i\right)}+\frac{21 i}{8192 a^{3} \left(-a x +i\right)^{4}}+\frac{i}{1280 a^{3} \left(-a x +i\right)^{10}}-\frac{i}{1024 a^{3} \left(-a x +i\right)^{8}}-\frac{7 i}{6144 a^{3} \left(-a x +i\right)^{6}}-\frac{165 i}{65536 a^{3} \left(-a x +i\right)^{2}}+\frac{1}{768 a^{3} \left(-a x +i\right)^{9}}-\frac{21}{10240 a^{3} \left(-a x +i\right)^{5}}+\frac{11}{4096 a^{3} \left(-a x +i\right)^{3}}-\frac{143}{65536 a^{3} \left(-a x +i\right)}}{c^{9}}"," ",0,"1/c^9*(13/16384*I/a^3/(I+a*x)^4-1/12288*I/a^3/(I+a*x)^6-121/65536*I/a^3/(I+a*x)^2-7/20480/a^3/(I+a*x)^5+11/8192/a^3/(I+a*x)^3-143/65536/a^3/(I+a*x)+21/8192*I/a^3/(-a*x+I)^4+1/1280*I/a^3/(-a*x+I)^10-1/1024*I/a^3/(-a*x+I)^8-7/6144*I/a^3/(-a*x+I)^6-165/65536*I/a^3/(-a*x+I)^2+1/768/a^3/(-a*x+I)^9-21/10240/a^3/(-a*x+I)^5+11/4096/a^3/(-a*x+I)^3-143/65536/a^3/(-a*x+I))","B"
380,1,58,56,0.175000," ","int((1+I*a*x)^5/(a^2*x^2+1)^(5/2)*x^2/(a^2*c*x^2+c)^(27/2),x)","\frac{\left(-a x +i\right) \left(a x +i\right) \left(5 a x +i\right) \left(i a x +1\right)^{5}}{120 a^{3} \left(a^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a^{2} c \,x^{2}+c \right)^{\frac{27}{2}}}"," ",0,"1/120*(-a*x+I)*(I+a*x)*(I+5*a*x)*(1+I*a*x)^5/a^3/(a^2*x^2+1)^(5/2)/(a^2*c*x^2+c)^(27/2)","A"
381,1,58,56,0.151000," ","int((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^2/(a^2*c*x^2+c)^(11/2),x)","\frac{\left(-a x +i\right) \left(a x +i\right) \left(3 a x +i\right) \left(i a x +1\right)^{3}}{24 a^{3} \left(a^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a^{2} c \,x^{2}+c \right)^{\frac{11}{2}}}"," ",0,"1/24*(-a*x+I)*(I+a*x)*(I+3*a*x)*(1+I*a*x)^3/a^3/(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(11/2)","A"
382,1,87,119,0.174000," ","int((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^2/(a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(3 i \ln \left(a x +i\right) x a +i \ln \left(-a x +i\right) x a -3 \ln \left(a x +i\right)-\ln \left(-a x +i\right)-2\right)}{4 \sqrt{a^{2} x^{2}+1}\, c^{2} a^{3} \left(a x +i\right)}"," ",0,"1/4/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)*(3*I*ln(I+a*x)*x*a+I*ln(-a*x+I)*x*a-3*ln(I+a*x)-ln(-a*x+I)-2)/c^2/a^3/(I+a*x)","A"
383,1,86,120,0.176000," ","int(x^2/(1+I*a*x)*(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{c \left(a^{2} x^{2}+1\right)}\, \left(i \ln \left(a x +i\right) x a +3 i \ln \left(-a x +i\right) x a +\ln \left(a x +i\right)+3 \ln \left(-a x +i\right)+2\right)}{4 \sqrt{a^{2} x^{2}+1}\, c^{2} a^{3} \left(-a x +i\right)}"," ",0,"1/4/(a^2*x^2+1)^(1/2)*(c*(a^2*x^2+1))^(1/2)*(I*ln(I+a*x)*x*a+3*I*ln(-a*x+I)*x*a+ln(I+a*x)+3*ln(-a*x+I)+2)/c^2/a^3/(-a*x+I)","A"
384,1,58,56,0.154000," ","int(x^2/(1+I*a*x)^3*(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(11/2),x)","-\frac{\left(-a x +i\right) \left(a x +i\right) \left(-3 a x +i\right) \left(a^{2} x^{2}+1\right)^{\frac{3}{2}}}{24 a^{3} \left(i a x +1\right)^{3} \left(a^{2} c \,x^{2}+c \right)^{\frac{11}{2}}}"," ",0,"-1/24*(-a*x+I)*(I+a*x)*(I-3*a*x)*(a^2*x^2+1)^(3/2)/a^3/(1+I*a*x)^3/(a^2*c*x^2+c)^(11/2)","A"
385,1,58,56,0.164000," ","int(x^2/(1+I*a*x)^5*(a^2*x^2+1)^(5/2)/(a^2*c*x^2+c)^(27/2),x)","-\frac{\left(-a x +i\right) \left(a x +i\right) \left(-5 a x +i\right) \left(a^{2} x^{2}+1\right)^{\frac{5}{2}}}{120 a^{3} \left(i a x +1\right)^{5} \left(a^{2} c \,x^{2}+c \right)^{\frac{27}{2}}}"," ",0,"-1/120*(-a*x+I)*(I+a*x)*(I-5*a*x)*(a^2*x^2+1)^(5/2)/a^3/(1+I*a*x)^5/(a^2*c*x^2+c)^(27/2)","A"