1,1,127,93,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4,x)","-\frac{x^{4} \sqrt{-a^{2} x^{2}+1}}{5 a}-\frac{4 x^{2} \sqrt{-a^{2} x^{2}+1}}{15 a^{3}}-\frac{8 \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 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a^{4} \sqrt{a^{2}}}"," ",0,"-1/5*x^4*(-a^2*x^2+1)^(1/2)/a-4/15*x^2*(-a^2*x^2+1)^(1/2)/a^3-8/15*(-a^2*x^2+1)^(1/2)/a^5-1/4*x^3*(-a^2*x^2+1)^(1/2)/a^2-3/8*x*(-a^2*x^2+1)^(1/2)/a^4+3/8/a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
2,1,107,73,0.037000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3,x)","-\frac{x^{3} \sqrt{-a^{2} x^{2}+1}}{4 a}-\frac{3 x \sqrt{-a^{2} x^{2}+1}}{8 a^{3}}+\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\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*x^3*(-a^2*x^2+1)^(1/2)/a-3/8*x*(-a^2*x^2+1)^(1/2)/a^3+3/8/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(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"
3,1,87,62,0.037000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2,x)","-\frac{x^{2} \sqrt{-a^{2} x^{2}+1}}{3 a}-\frac{2 \sqrt{-a^{2} x^{2}+1}}{3 a^{3}}-\frac{x \sqrt{-a^{2} x^{2}+1}}{2 a^{2}}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a^{2} \sqrt{a^{2}}}"," ",0,"-1/3*x^2/a*(-a^2*x^2+1)^(1/2)-2/3*(-a^2*x^2+1)^(1/2)/a^3-1/2*x*(-a^2*x^2+1)^(1/2)/a^2+1/2/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
4,1,67,32,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x,x)","-\frac{x \sqrt{-a^{2} x^{2}+1}}{2 a}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a \sqrt{a^{2}}}-\frac{\sqrt{-a^{2} x^{2}+1}}{a^{2}}"," ",0,"-1/2*x*(-a^2*x^2+1)^(1/2)/a+1/2/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-(-a^2*x^2+1)^(1/2)/a^2","B"
5,1,45,26,0.032000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{a}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}"," ",0,"-(-a^2*x^2+1)^(1/2)/a+1/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
6,1,44,20,0.036000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x,x)","\frac{a \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-arctanh(1/(-a^2*x^2+1)^(1/2))","B"
7,1,35,34,0.035000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2,x)","-a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\sqrt{-a^{2} x^{2}+1}}{x}"," ",0,"-a*arctanh(1/(-a^2*x^2+1)^(1/2))-(-a^2*x^2+1)^(1/2)/x","A"
8,1,55,54,0.039000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3,x)","-\frac{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,"-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"
9,1,77,74,0.037000," ","int((a*x+1)/(-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}+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+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"
10,1,100,94,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^5,x)","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,"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"
11,1,40,40,0.027000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3,x)","-\frac{x^{4}}{4}-\frac{2 x^{3}}{3 a}-\frac{x^{2}}{a^{2}}-\frac{2 x}{a^{3}}-\frac{2 \ln \left(a x -1\right)}{a^{4}}"," ",0,"-1/4*x^4-2/3*x^3/a-x^2/a^2-2*x/a^3-2/a^4*ln(a*x-1)","A"
12,1,32,32,0.027000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2,x)","-\frac{x^{3}}{3}-\frac{x^{2}}{a}-\frac{2 x}{a^{2}}-\frac{2 \ln \left(a x -1\right)}{a^{3}}"," ",0,"-1/3*x^3-x^2/a-2*x/a^2-2/a^3*ln(a*x-1)","A"
13,1,24,24,0.027000," ","int((a*x+1)^2/(-a^2*x^2+1)*x,x)","-\frac{x^{2}}{2}-\frac{2 x}{a}-\frac{2 \ln \left(a x -1\right)}{a^{2}}"," ",0,"-1/2*x^2-2*x/a-2/a^2*ln(a*x-1)","A"
14,1,16,16,0.024000," ","int((a*x+1)^2/(-a^2*x^2+1),x)","-x -\frac{2 \ln \left(a x -1\right)}{a}"," ",0,"-x-2/a*ln(a*x-1)","A"
15,1,12,12,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)/x,x)","\ln \left(x \right)-2 \ln \left(a x -1\right)"," ",0,"ln(x)-2*ln(a*x-1)","A"
16,1,21,21,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^2,x)","-\frac{1}{x}+2 a \ln \left(x \right)-2 a \ln \left(a x -1\right)"," ",0,"-1/x+2*a*ln(x)-2*a*ln(a*x-1)","A"
17,1,31,31,0.034000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^3,x)","-\frac{1}{2 x^{2}}-\frac{2 a}{x}+2 a^{2} \ln \left(x \right)-2 a^{2} \ln \left(a x -1\right)"," ",0,"-1/2/x^2-2*a/x+2*a^2*ln(x)-2*a^2*ln(a*x-1)","A"
18,1,39,39,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^4,x)","-\frac{1}{3 x^{3}}-\frac{a}{x^{2}}-\frac{2 a^{2}}{x}+2 a^{3} \ln \left(x \right)-2 a^{3} \ln \left(a x -1\right)"," ",0,"-1/3/x^3-a/x^2-2*a^2/x+2*a^3*ln(x)-2*a^3*ln(a*x-1)","A"
19,1,122,80,0.051000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2,x)","-\frac{a \,x^{4}}{3 \sqrt{-a^{2} x^{2}+1}}-\frac{13 x^{2}}{3 a \sqrt{-a^{2} x^{2}+1}}+\frac{26}{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 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a^{2} \sqrt{a^{2}}}"," ",0,"-1/3*a*x^4/(-a^2*x^2+1)^(1/2)-13/3/a*x^2/(-a^2*x^2+1)^(1/2)+26/3/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/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
20,1,102,76,0.039000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x,x)","-\frac{a \,x^{3}}{2 \sqrt{-a^{2} x^{2}+1}}+\frac{9 x}{2 a \sqrt{-a^{2} x^{2}+1}}-\frac{9 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\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*a*x^3/(-a^2*x^2+1)^(1/2)+9/2*x/a/(-a^2*x^2+1)^(1/2)-9/2/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-3*x^2/(-a^2*x^2+1)^(1/2)+7/a^2/(-a^2*x^2+1)^(1/2)","A"
21,1,79,51,0.035000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2),x)","-\frac{a \,x^{2}}{\sqrt{-a^{2} x^{2}+1}}+\frac{5}{a \sqrt{-a^{2} x^{2}+1}}+\frac{4 x}{\sqrt{-a^{2} x^{2}+1}}-\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}"," ",0,"-a*x^2/(-a^2*x^2+1)^(1/2)+5/a/(-a^2*x^2+1)^(1/2)+4*x/(-a^2*x^2+1)^(1/2)-3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
22,1,75,44,0.036000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x,x)","\frac{4 a x}{\sqrt{-a^{2} x^{2}+1}}-\frac{a \arctan \left(\frac{\sqrt{a^{2}}\, x}{\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*a*x/(-a^2*x^2+1)^(1/2)-a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+4/(-a^2*x^2+1)^(1/2)-arctanh(1/(-a^2*x^2+1)^(1/2))","A"
23,1,82,57,0.039000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x^2,x)","\frac{a}{\sqrt{-a^{2} x^{2}+1}}+\frac{5 a^{2} x}{\sqrt{-a^{2} x^{2}+1}}+3 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,"a/(-a^2*x^2+1)^(1/2)+5*a^2*x/(-a^2*x^2+1)^(1/2)+3*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"
24,1,108,79,0.042000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x^3,x)","\frac{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 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,"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*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"
25,1,146,99,0.045000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x^4,x)","a^{3} \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}-\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)\right)+\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}-\frac{1}{3 x^{3} \sqrt{-a^{2} x^{2}+1}}+3 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,"a^3*(1/(-a^2*x^2+1)^(1/2)-arctanh(1/(-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))-1/3/x^3/(-a^2*x^2+1)^(1/2)+3*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"
26,1,52,53,0.033000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*x^3,x)","\frac{x^{4}}{4}+\frac{4 x^{3}}{3 a}+\frac{4 x^{2}}{a^{2}}+\frac{12 x}{a^{3}}+\frac{16 \ln \left(a x -1\right)}{a^{4}}-\frac{4}{a^{4} \left(a x -1\right)}"," ",0,"1/4*x^4+4/3*x^3/a+4*x^2/a^2+12*x/a^3+16/a^4*ln(a*x-1)-4/a^4/(a*x-1)","A"
27,1,44,45,0.031000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*x^2,x)","\frac{x^{3}}{3}+\frac{2 x^{2}}{a}+\frac{8 x}{a^{2}}+\frac{12 \ln \left(a x -1\right)}{a^{3}}-\frac{4}{a^{3} \left(a x -1\right)}"," ",0,"1/3*x^3+2*x^2/a+8*x/a^2+12/a^3*ln(a*x-1)-4/a^3/(a*x-1)","A"
28,1,36,37,0.031000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*x,x)","\frac{x^{2}}{2}+\frac{4 x}{a}+\frac{8 \ln \left(a x -1\right)}{a^{2}}-\frac{4}{a^{2} \left(a x -1\right)}"," ",0,"1/2*x^2+4*x/a+8/a^2*ln(a*x-1)-4/a^2/(a*x-1)","A"
29,1,26,27,0.033000," ","int((a*x+1)^4/(-a^2*x^2+1)^2,x)","x +\frac{4 \ln \left(a x -1\right)}{a}-\frac{4}{a \left(a x -1\right)}"," ",0,"x+4/a*ln(a*x-1)-4/a/(a*x-1)","A"
30,1,13,13,0.032000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/x,x)","\ln \left(x \right)-\frac{4}{a x -1}"," ",0,"ln(x)-4/(a*x-1)","A"
31,1,31,32,0.034000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/x^2,x)","-\frac{1}{x}+4 a \ln \left(x \right)-\frac{4 a}{a x -1}-4 a \ln \left(a x -1\right)"," ",0,"-1/x+4*a*ln(x)-4*a/(a*x-1)-4*a*ln(a*x-1)","A"
32,1,43,44,0.036000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/x^3,x)","-\frac{1}{2 x^{2}}-\frac{4 a}{x}+8 a^{2} \ln \left(x \right)-\frac{4 a^{2}}{a x -1}-8 a^{2} \ln \left(a x -1\right)"," ",0,"-1/2/x^2-4*a/x+8*a^2*ln(x)-4*a^2/(a*x-1)-8*a^2*ln(a*x-1)","A"
33,1,51,52,0.034000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/x^4,x)","-\frac{1}{3 x^{3}}-\frac{2 a}{x^{2}}-\frac{8 a^{2}}{x}+12 a^{3} \ln \left(x \right)-\frac{4 a^{3}}{a x -1}-12 a^{3} \ln \left(a x -1\right)"," ",0,"-1/3/x^3-2*a/x^2-8*a^2/x+12*a^3*ln(x)-4*a^3/(a*x-1)-12*a^3*ln(a*x-1)","A"
34,1,154,73,0.043000," ","int(x^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4 a^{3}}+\frac{5 x \sqrt{-a^{2} x^{2}+1}}{8 a^{3}}+\frac{5 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\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{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{a^{4}}-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{a^{3} \sqrt{a^{2}}}"," ",0,"-1/4/a^3*x*(-a^2*x^2+1)^(3/2)+5/8*x*(-a^2*x^2+1)^(1/2)/a^3+5/8/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/3*(-a^2*x^2+1)^(3/2)/a^4-1/a^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-1/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
35,1,134,61,0.039000," ","int(x^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{\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{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a^{2} \sqrt{a^{2}}}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{a^{3}}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{a^{2} \sqrt{a^{2}}}"," ",0,"-1/3*(-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/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/a^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+1/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
36,1,119,33,0.036000," ","int(x/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x \sqrt{-a^{2} x^{2}+1}}{2 a}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a \sqrt{a^{2}}}-\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{a^{2}}-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{a \sqrt{a^{2}}}"," ",0,"1/2*x*(-a^2*x^2+1)^(1/2)/a+1/2/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/a^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-1/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
37,1,66,25,0.030000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{a}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"1/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+1/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
38,1,93,22,0.041000," ","int(1/(a*x+1)*(-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{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}-\frac{a \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"(-a^2*x^2+1)^(1/2)-arctanh(1/(-a^2*x^2+1)^(1/2))-(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
39,1,162,33,0.044000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x)","-a \sqrt{-a^{2} x^{2}+1}+a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{x}-a^{2} x \sqrt{-a^{2} x^{2}+1}-\frac{a^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+a \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}+\frac{a^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-a*(-a^2*x^2+1)^(1/2)+a*arctanh(1/(-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/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
40,1,186,53,0.043000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^3,x)","\frac{a^{2} \sqrt{-a^{2} x^{2}+1}}{2}-\frac{a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{a \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{x}+a^{3} x \sqrt{-a^{2} x^{2}+1}+\frac{a^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{2 x^{2}}-a^{2} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}-\frac{a^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"1/2*a^2*(-a^2*x^2+1)^(1/2)-1/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))+a/x*(-a^2*x^2+1)^(3/2)+a^3*x*(-a^2*x^2+1)^(1/2)+a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/2/x^2*(-a^2*x^2+1)^(3/2)-a^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
41,1,207,74,0.050000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^4,x)","-\frac{a^{3} \sqrt{-a^{2} x^{2}+1}}{2}+\frac{a^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{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} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 x^{3}}+\frac{a \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{2 x^{2}}+a^{3} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}+\frac{a^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-1/2*a^3*(-a^2*x^2+1)^(1/2)+1/2*a^3*arctanh(1/(-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/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/3/x^3*(-a^2*x^2+1)^(3/2)+1/2*a/x^2*(-a^2*x^2+1)^(3/2)+a^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
42,1,226,94,0.053000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^5,x)","\frac{3 a^{4} \sqrt{-a^{2} x^{2}+1}}{8}-\frac{3 a^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8}+\frac{a^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{x}+a^{5} x \sqrt{-a^{2} x^{2}+1}+\frac{a^{5} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{a \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 x^{3}}-\frac{5 a^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{8 x^{2}}-\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4 x^{4}}-a^{4} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}-\frac{a^{5} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"3/8*a^4*(-a^2*x^2+1)^(1/2)-3/8*a^4*arctanh(1/(-a^2*x^2+1)^(1/2))+a^3/x*(-a^2*x^2+1)^(3/2)+a^5*x*(-a^2*x^2+1)^(1/2)+a^5/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/3*a/x^3*(-a^2*x^2+1)^(3/2)-5/8*a^2/x^2*(-a^2*x^2+1)^(3/2)-1/4/x^4*(-a^2*x^2+1)^(3/2)-a^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-a^5/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
43,1,40,39,0.026000," ","int(x^3/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{2 x}{a^{3}}-\frac{x^{2}}{a^{2}}+\frac{2 x^{3}}{3 a}-\frac{x^{4}}{4}-\frac{2 \ln \left(a x +1\right)}{a^{4}}"," ",0,"2*x/a^3-x^2/a^2+2/3*x^3/a-1/4*x^4-2*ln(a*x+1)/a^4","A"
44,1,31,30,0.026000," ","int(x^2/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{2 x}{a^{2}}+\frac{x^{2}}{a}-\frac{x^{3}}{3}+\frac{2 \ln \left(a x +1\right)}{a^{3}}"," ",0,"-2*x/a^2+x^2/a-1/3*x^3+2/a^3*ln(a*x+1)","A"
45,1,24,23,0.025000," ","int(x/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{2 x}{a}-\frac{x^{2}}{2}-\frac{2 \ln \left(a x +1\right)}{a^{2}}"," ",0,"2*x/a-1/2*x^2-2/a^2*ln(a*x+1)","A"
46,1,16,15,0.025000," ","int(1/(a*x+1)^2*(-a^2*x^2+1),x)","-x +\frac{2 \ln \left(a x +1\right)}{a}"," ",0,"-x+2*ln(a*x+1)/a","A"
47,1,12,11,0.030000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/x,x)","\ln \left(x \right)-2 \ln \left(a x +1\right)"," ",0,"ln(x)-2*ln(a*x+1)","A"
48,1,21,20,0.031000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/x^2,x)","-\frac{1}{x}-2 a \ln \left(x \right)+2 a \ln \left(a x +1\right)"," ",0,"-1/x-2*a*ln(x)+2*a*ln(a*x+1)","A"
49,1,31,30,0.032000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/x^3,x)","-\frac{1}{2 x^{2}}+\frac{2 a}{x}+2 a^{2} \ln \left(x \right)-2 a^{2} \ln \left(a x +1\right)"," ",0,"-1/2/x^2+2*a/x+2*a^2*ln(x)-2*a^2*ln(a*x+1)","A"
50,1,38,37,0.033000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/x^4,x)","-\frac{1}{3 x^{3}}+\frac{a}{x^{2}}-\frac{2 a^{2}}{x}-2 a^{3} \ln \left(x \right)+2 a^{3} \ln \left(a x +1\right)"," ",0,"-1/3/x^3+a/x^2-2*a^2/x-2*a^3*ln(x)+2*a^3*ln(a*x+1)","A"
51,1,235,113,0.052000," ","int(x^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4 a^{3}}+\frac{3 x \sqrt{-a^{2} x^{2}+1}}{8 a^{3}}+\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a^{3} \sqrt{a^{2}}}+\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{7} \left(x +\frac{1}{a}\right)^{3}}+\frac{5 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{6} \left(x +\frac{1}{a}\right)^{2}}+\frac{4 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{a^{4}}+\frac{6 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{a^{3}}+\frac{6 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{a^{3} \sqrt{a^{2}}}"," ",0,"1/4/a^3*x*(-a^2*x^2+1)^(3/2)+3/8*x*(-a^2*x^2+1)^(1/2)/a^3+3/8/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/a^7/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+5/a^6/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+4/a^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+6/a^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x+6/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
52,1,170,83,0.046000," ","int(x^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{6} \left(x +\frac{1}{a}\right)^{3}}-\frac{4 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{5} \left(x +\frac{1}{a}\right)^{2}}-\frac{11 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a^{3}}-\frac{11 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{2 a^{2}}-\frac{11 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{2 a^{2} \sqrt{a^{2}}}"," ",0,"-1/a^6/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-4/a^5/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-11/3/a^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-11/2/a^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-11/2/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
53,1,169,74,0.042000," ","int(x/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{5} \left(x +\frac{1}{a}\right)^{3}}+\frac{3 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{4} \left(x +\frac{1}{a}\right)^{2}}+\frac{3 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{a^{2}}+\frac{9 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{2 a}+\frac{9 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{2 a \sqrt{a^{2}}}"," ",0,"1/a^5/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+3/a^4/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+3/a^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+9/2/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x+9/2/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
54,1,164,52,0.036000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{4} \left(x +\frac{1}{a}\right)^{3}}-\frac{2 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{2 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{a}-3 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x -\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-1/a^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-2/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-2/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
55,1,200,41,0.047000," ","int(1/(a*x+1)^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{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x +\frac{1}{a}\right)^{3}}+\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{2} \left(x +\frac{1}{a}\right)^{2}}+\frac{2 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3}+a \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x +\frac{a \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{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))+1/a^3/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+1/a^2/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+2/3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x+a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
56,1,261,56,0.049000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x)","-a \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}-3 a \sqrt{-a^{2} x^{2}+1}+3 a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\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} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{2} \left(x +\frac{1}{a}\right)^{3}}+a \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}+\frac{3 a^{2} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{2}+\frac{3 a^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{2 \sqrt{a^{2}}}"," ",0,"-a*(-a^2*x^2+1)^(3/2)-3*a*(-a^2*x^2+1)^(1/2)+3*a*arctanh(1/(-a^2*x^2+1)^(1/2))-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/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/a^2/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+3/2*a^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x+3/2*a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
57,1,319,78,0.053000," ","int(1/(a*x+1)^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{3 a \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{x}+3 a^{3} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}+\frac{9 a^{3} x \sqrt{-a^{2} x^{2}+1}}{2}+\frac{9 a^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}-\frac{\left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{2 x^{2}}+\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a \left(x +\frac{1}{a}\right)^{3}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{\left(x +\frac{1}{a}\right)^{2}}-3 a^{2} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}-\frac{9 a^{3} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{2}-\frac{9 a^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{2 \sqrt{a^{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))+3*a/x*(-a^2*x^2+1)^(5/2)+3*a^3*x*(-a^2*x^2+1)^(3/2)+9/2*a^3*x*(-a^2*x^2+1)^(1/2)+9/2*a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/2/x^2*(-a^2*x^2+1)^(5/2)+1/a/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-1/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-3*a^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-9/2*a^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-9/2*a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
58,1,338,98,0.062000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x)","-\frac{11 a^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{6}-\frac{11 a^{3} \sqrt{-a^{2} x^{2}+1}}{2}+\frac{11 a^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\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} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{\left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{3 x^{3}}+\frac{3 a \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{2 x^{2}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{\left(x +\frac{1}{a}\right)^{3}}+\frac{2 a \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{\left(x +\frac{1}{a}\right)^{2}}+\frac{16 a^{3} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3}+8 a^{4} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x +\frac{8 a^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-11/6*a^3*(-a^2*x^2+1)^(3/2)-11/2*a^3*(-a^2*x^2+1)^(1/2)+11/2*a^3*arctanh(1/(-a^2*x^2+1)^(1/2))-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/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/3/x^3*(-a^2*x^2+1)^(5/2)+3/2*a/x^2*(-a^2*x^2+1)^(5/2)-1/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+2*a/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+16/3*a^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+8*a^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x+8*a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
59,1,359,117,0.066000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x)","-\frac{\left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{4 x^{4}}+\frac{17 a^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{8}-8 a^{4} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}+\frac{51 a^{4} \sqrt{-a^{2} x^{2}+1}}{8}-\frac{51 a^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8}+\frac{a \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{\left(x +\frac{1}{a}\right)^{3}}-\frac{3 a^{2} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{\left(x +\frac{1}{a}\right)^{2}}-12 a^{5} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x +\frac{8 a^{3} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{x}+8 a^{5} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}+\frac{a \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{3}}-\frac{23 a^{2} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{8 x^{2}}-\frac{12 a^{5} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}+12 a^{5} x \sqrt{-a^{2} x^{2}+1}+\frac{12 a^{5} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}"," ",0,"-1/4/x^4*(-a^2*x^2+1)^(5/2)+17/8*a^4*(-a^2*x^2+1)^(3/2)-8*a^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+51/8*a^4*(-a^2*x^2+1)^(1/2)-51/8*a^4*arctanh(1/(-a^2*x^2+1)^(1/2))+a/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-3*a^2/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-12*a^5*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x+8*a^3/x*(-a^2*x^2+1)^(5/2)+8*a^5*x*(-a^2*x^2+1)^(3/2)+a/x^3*(-a^2*x^2+1)^(5/2)-23/8*a^2/x^2*(-a^2*x^2+1)^(5/2)-12*a^5/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))+12*a^5*x*(-a^2*x^2+1)^(1/2)+12*a^5/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","B"
60,0,0,27,0.039000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^m,x)","\int \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x^{m}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^m,x)","F"
61,0,0,215,0.098000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^2,x)","\int \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x^{2}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^2,x)","F"
62,0,0,194,0.037000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x,x)","\int \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x,x)","F"
63,0,0,174,0.038000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","\int \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","F"
64,0,0,180,0.038000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x,x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{x}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x,x)","F"
65,0,0,61,0.037000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2,x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{x^{2}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2,x)","F"
66,0,0,86,0.038000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^3,x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{x^{3}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^3,x)","F"
67,0,0,109,0.040000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^4,x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{x^{4}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^4,x)","F"
68,0,0,132,0.039000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^5,x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{x^{5}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^5,x)","F"
69,0,0,155,0.038000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^6,x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{x^{6}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^6,x)","F"
70,0,0,27,0.036000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x^m,x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x^{m}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x^m,x)","F"
71,0,0,223,0.043000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x^3,x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x^{3}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x^3,x)","F"
72,0,0,215,0.043000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x^2,x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x^{2}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x^2,x)","F"
73,0,0,194,0.043000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x,x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x,x)","F"
74,0,0,174,0.040000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","F"
75,0,0,180,0.040000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x,x)","F"
76,0,0,61,0.040000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^2,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^2,x)","F"
77,0,0,86,0.043000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^3,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^3,x)","F"
78,0,0,109,0.043000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^4,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^4,x)","F"
79,0,0,132,0.044000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^5,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^5,x)","F"
80,0,0,27,0.038000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x^m,x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{m}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x^m,x)","F"
81,0,0,246,0.056000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x^3,x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{3}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x^3,x)","F"
82,0,0,234,0.053000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x^2,x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{2}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x^2,x)","F"
83,0,0,214,0.047000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x,x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x,x)","F"
84,0,0,194,0.044000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","F"
85,0,0,195,0.052000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}{x}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x,x)","F"
86,0,0,79,0.058000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^2,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^2,x)","F"
87,0,0,106,0.055000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^3,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}{x^{3}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^3,x)","F"
88,0,0,129,0.061000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^4,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}{x^{4}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^4,x)","F"
89,0,0,152,0.060000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^5,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}{x^{5}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^5,x)","F"
90,0,0,27,0.036000," ","int(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","\int \frac{x^{m}}{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}\, dx"," ",0,"int(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","F"
91,0,0,223,0.044000," ","int(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","\int \frac{x^{3}}{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}\, dx"," ",0,"int(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","F"
92,0,0,215,0.044000," ","int(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","\int \frac{x^{2}}{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}\, dx"," ",0,"int(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","F"
93,0,0,194,0.041000," ","int(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","\int \frac{x}{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}\, dx"," ",0,"int(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","F"
94,0,0,173,0.042000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","\int \frac{1}{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x)","F"
95,0,0,178,0.042000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x,x)","\int \frac{1}{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x,x)","F"
96,0,0,60,0.041000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2,x)","\int \frac{1}{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x^{2}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2,x)","F"
97,0,0,86,0.042000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^3,x)","\int \frac{1}{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x^{3}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^3,x)","F"
98,0,0,109,0.043000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^4,x)","\int \frac{1}{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x^{4}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^4,x)","F"
99,0,0,132,0.043000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^5,x)","\int \frac{1}{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x^{5}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^5,x)","F"
100,0,0,27,0.035000," ","int(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","\int \frac{x^{m}}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","F"
101,0,0,223,0.055000," ","int(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","\int \frac{x^{3}}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","F"
102,0,0,215,0.052000," ","int(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","\int \frac{x^{2}}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","F"
103,0,0,194,0.048000," ","int(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","\int \frac{x}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","F"
104,0,0,173,0.046000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x)","F"
105,0,0,178,0.050000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x,x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x,x)","F"
106,0,0,61,0.054000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^2,x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x^{2}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^2,x)","F"
107,0,0,86,0.058000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^3,x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x^{3}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^3,x)","F"
108,0,0,109,0.060000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^4,x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x^{4}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^4,x)","F"
109,0,0,132,0.062000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^5,x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{3}{2}} x^{5}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^5,x)","F"
110,0,0,27,0.039000," ","int(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","\int \frac{x^{m}}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","F"
111,0,0,246,0.044000," ","int(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","\int \frac{x^{3}}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","F"
112,0,0,234,0.044000," ","int(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","\int \frac{x^{2}}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","F"
113,0,0,214,0.044000," ","int(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","\int \frac{x}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"int(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","F"
114,0,0,194,0.037000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x)","F"
115,0,0,197,0.045000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x,x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x,x)","F"
116,0,0,79,0.043000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^2,x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{2}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^2,x)","F"
117,0,0,106,0.044000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^3,x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{3}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^3,x)","F"
118,0,0,129,0.043000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^4,x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{4}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^4,x)","F"
119,0,0,152,0.044000," ","int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^5,x)","\int \frac{1}{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{5}{2}} x^{5}}\, dx"," ",0,"int(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^5,x)","F"
120,0,0,24,0.032000," ","int(((1+x)/(-x^2+1)^(1/2))^(1/3)*x^m,x)","\int \left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{1}{3}} x^{m}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(1/3)*x^m,x)","F"
121,0,0,179,0.076000," ","int(((1+x)/(-x^2+1)^(1/2))^(1/3)*x^2,x)","\int \left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{1}{3}} x^{2}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(1/3)*x^2,x)","F"
122,0,0,164,0.033000," ","int(((1+x)/(-x^2+1)^(1/2))^(1/3)*x,x)","\int \left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{1}{3}} x\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(1/3)*x,x)","F"
123,0,0,150,0.031000," ","int(((1+x)/(-x^2+1)^(1/2))^(1/3),x)","\int \left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{1}{3}}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(1/3),x)","F"
124,0,0,268,0.032000," ","int(((1+x)/(-x^2+1)^(1/2))^(1/3)/x,x)","\int \frac{\left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{1}{3}}}{x}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(1/3)/x,x)","F"
125,0,0,151,0.033000," ","int(((1+x)/(-x^2+1)^(1/2))^(1/3)/x^2,x)","\int \frac{\left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{1}{3}}}{x^{2}}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(1/3)/x^2,x)","F"
126,0,0,168,0.033000," ","int(((1+x)/(-x^2+1)^(1/2))^(1/3)/x^3,x)","\int \frac{\left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{1}{3}}}{x^{3}}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(1/3)/x^3,x)","F"
127,0,0,24,0.033000," ","int(((1+x)/(-x^2+1)^(1/2))^(2/3)*x^m,x)","\int \left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{2}{3}} x^{m}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(2/3)*x^m,x)","F"
128,0,0,97,0.033000," ","int(((1+x)/(-x^2+1)^(1/2))^(2/3)*x^2,x)","\int \left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{2}{3}} x^{2}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(2/3)*x^2,x)","F"
129,0,0,82,0.031000," ","int(((1+x)/(-x^2+1)^(1/2))^(2/3)*x,x)","\int \left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{2}{3}} x\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(2/3)*x,x)","F"
130,0,0,66,0.033000," ","int(((1+x)/(-x^2+1)^(1/2))^(2/3),x)","\int \left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{2}{3}}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(2/3),x)","F"
131,0,0,104,0.032000," ","int(((1+x)/(-x^2+1)^(1/2))^(2/3)/x,x)","\int \frac{\left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{2}{3}}}{x}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(2/3)/x,x)","F"
132,0,0,67,0.034000," ","int(((1+x)/(-x^2+1)^(1/2))^(2/3)/x^2,x)","\int \frac{\left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{2}{3}}}{x^{2}}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(2/3)/x^2,x)","F"
133,0,0,86,0.034000," ","int(((1+x)/(-x^2+1)^(1/2))^(2/3)/x^3,x)","\int \frac{\left(\frac{1+x}{\sqrt{-x^{2}+1}}\right)^{\frac{2}{3}}}{x^{3}}\, dx"," ",0,"int(((1+x)/(-x^2+1)^(1/2))^(2/3)/x^3,x)","F"
134,0,0,27,0.033000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x^m,x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{1}{4}} x^{m}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x^m,x)","F"
135,0,0,484,0.074000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x^2,x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{1}{4}} x^{2}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x^2,x)","F"
136,0,0,463,0.036000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x,x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{1}{4}} x\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x,x)","F"
137,0,0,443,0.035000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4),x)","\int \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{1}{4}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4),x)","F"
138,0,0,576,0.035000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{1}{4}}}{x}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x,x)","F"
139,0,0,207,0.035000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x^2,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{1}{4}}}{x^{2}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x^2,x)","F"
140,0,0,240,0.034000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x^3,x)","\int \frac{\left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)^{\frac{1}{4}}}{x^{3}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x^3,x)","F"
141,1,461,47,0.394000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*x^m,x)","\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}+\frac{2 \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}-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 \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}+\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}} \left(-1-m \right)}{\left(1+m \right) \left(-2 a^{2} x^{2}+2\right)}+\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}"," ",0,"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))+2/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))-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/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))+1/2*(-a^2)^(-1/2-1/2*m)*(-2/(1+m)*x^(1+m)*(-a^2)^(1/2+1/2*m)*(-1-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))","C"
142,1,139,135,0.326000," ","int((a*x+1)^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{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}+\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{3 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}"," ",0,"x^(1+m)*hypergeom([3/2,1/2+1/2*m],[3/2+1/2*m],a^2*x^2)/(1+m)+a^3/(4+m)*x^(4+m)*hypergeom([3/2,2+1/2*m],[3+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)+3*a*x^(2+m)*hypergeom([3/2,1+1/2*m],[2+1/2*m],a^2*x^2)/(2+m)","A"
143,1,184,38,0.352000," ","int((a*x+1)^2/(-a^2*x^2+1)*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{3}{2}+\frac{m}{2}} \left(-3-m \right)}{\left(3+m \right) \left(1+m \right) a^{2}}+\frac{x^{1+m} \left(-a^{2}\right)^{\frac{3}{2}+\frac{m}{2}} \Phi \left(a^{2} x^{2}, 1, \frac{1}{2}+\frac{m}{2}\right)}{a^{2}}\right)}{2}-\frac{\left(-a^{2}\right)^{-\frac{m}{2}} \left(-\frac{2 x^{m} \left(-a^{2}\right)^{\frac{m}{2}} \left(-m -2\right)}{\left(2+m \right) m}-x^{m} \left(-a^{2}\right)^{\frac{m}{2}} \Phi \left(a^{2} x^{2}, 1, \frac{m}{2}\right)\right)}{a}+\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}"," ",0,"-1/2*(-a^2)^(-1/2-1/2*m)*(2/(3+m)*x^(1+m)*(-a^2)^(3/2+1/2*m)*(-3-m)/(1+m)/a^2+x^(1+m)*(-a^2)^(3/2+1/2*m)/a^2*LerchPhi(a^2*x^2,1,1/2+1/2*m))-1/a*(-a^2)^(-1/2*m)*(-2/(2+m)*x^m*(-a^2)^(1/2*m)*(-m-2)/m-x^m*(-a^2)^(1/2*m)*LerchPhi(a^2*x^2,1,1/2*m))+1/(1+m)*x^(1+m)*(1/2+1/2*m)*LerchPhi(a^2*x^2,1,1/2+1/2*m)","C"
144,1,67,66,0.239000," ","int((a*x+1)/(-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{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)+a*x^(2+m)*hypergeom([1/2,1+1/2*m],[2+1/2*m],a^2*x^2)/(2+m)","A"
145,0,0,67,0.312000," ","int(x^m/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int(x^m/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
146,1,126,39,0.271000," ","int(x^m/(a*x+1)^2*(-a^2*x^2+1),x)","-a^{-1-m} \left(\frac{x^{m} a^{m} \left(a^{2} m \,x^{2}-a m x -2 a x -m^{2}-3 m -2\right)}{\left(1+m \right) m \left(a x +1\right)}+x^{m} a^{m} \left(2+m \right) \Phi \left(-a x , 1, m\right)\right)+a^{-1-m} \left(\frac{x^{m} a^{m} \left(-1-m \right)}{\left(1+m \right) \left(a x +1\right)}+x^{m} a^{m} m \Phi \left(-a x , 1, m\right)\right)"," ",0,"-a^(-1-m)*(x^m*a^m*(a^2*m*x^2-a*m*x-2*a*x-m^2-3*m-2)/(1+m)/m/(a*x+1)+x^m*a^m*(2+m)*LerchPhi(-a*x,1,m))+a^(-1-m)*(1/(1+m)*x^m*a^m*(-1-m)/(a*x+1)+x^m*a^m*m*LerchPhi(-a*x,1,m))","C"
147,0,0,134,0.311000," ","int(x^m/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\int \frac{x^{m} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{\left(a x +1\right)^{3}}\, dx"," ",0,"int(x^m/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","F"
148,0,0,31,0.066000," ","int(exp(n*arctanh(a*x))*x^m,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} x^{m}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^m,x)","F"
149,0,0,129,0.054000," ","int(exp(n*arctanh(a*x))*x^3,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} x^{3}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^3,x)","F"
150,0,0,115,0.052000," ","int(exp(n*arctanh(a*x))*x^2,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} x^{2}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^2,x)","F"
151,0,0,81,0.044000," ","int(exp(n*arctanh(a*x))*x,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} x\, dx"," ",0,"int(exp(n*arctanh(a*x))*x,x)","F"
152,0,0,53,0.040000," ","int(exp(n*arctanh(a*x)),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)}\, dx"," ",0,"int(exp(n*arctanh(a*x)),x)","F"
153,0,0,97,0.043000," ","int(exp(n*arctanh(a*x))/x,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x,x)","F"
154,0,0,61,0.046000," ","int(exp(n*arctanh(a*x))/x^2,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x^{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x^2,x)","F"
155,0,0,93,0.052000," ","int(exp(n*arctanh(a*x))/x^3,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x^{3}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x^3,x)","F"
156,0,0,127,0.054000," ","int(exp(n*arctanh(a*x))/x^4,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x^{4}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x^4,x)","F"
157,0,0,53,0.307000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^p,x)","\int \frac{\left(a x +1\right) \left(-a c x +c \right)^{p}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^p,x)","F"
158,1,137,105,0.046000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4,x)","-\frac{c^{4} a^{3} x^{4} \sqrt{-a^{2} x^{2}+1}}{5}-\frac{14 c^{4} a \,x^{2} \sqrt{-a^{2} x^{2}+1}}{15}+\frac{17 c^{4} \sqrt{-a^{2} x^{2}+1}}{15 a}+\frac{3 c^{4} a^{2} x^{3} \sqrt{-a^{2} x^{2}+1}}{4}+\frac{c^{4} x \sqrt{-a^{2} x^{2}+1}}{8}+\frac{7 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}"," ",0,"-1/5*c^4*a^3*x^4*(-a^2*x^2+1)^(1/2)-14/15*c^4*a*x^2*(-a^2*x^2+1)^(1/2)+17/15*c^4*(-a^2*x^2+1)^(1/2)/a+3/4*c^4*a^2*x^3*(-a^2*x^2+1)^(1/2)+1/8*c^4*x*(-a^2*x^2+1)^(1/2)+7/8*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
159,1,114,77,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3,x)","\frac{c^{3} a^{2} x^{3} \sqrt{-a^{2} x^{2}+1}}{4}+\frac{3 c^{3} x \sqrt{-a^{2} x^{2}+1}}{8}+\frac{5 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}-\frac{2 c^{3} a \,x^{2} \sqrt{-a^{2} x^{2}+1}}{3}+\frac{2 c^{3} \sqrt{-a^{2} x^{2}+1}}{3 a}"," ",0,"1/4*c^3*a^2*x^3*(-a^2*x^2+1)^(1/2)+3/8*c^3*x*(-a^2*x^2+1)^(1/2)+5/8*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-2/3*c^3*a*x^2*(-a^2*x^2+1)^(1/2)+2/3*c^3*(-a^2*x^2+1)^(1/2)/a","A"
160,1,91,51,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2,x)","-\frac{c^{2} a \,x^{2} \sqrt{-a^{2} x^{2}+1}}{3}+\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{3 a}+\frac{c^{2} x \sqrt{-a^{2} x^{2}+1}}{2}+\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}"," ",0,"-1/3*c^2*a*x^2*(-a^2*x^2+1)^(1/2)+1/3*c^2*(-a^2*x^2+1)^(1/2)/a+1/2*c^2*x*(-a^2*x^2+1)^(1/2)+1/2*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
161,1,46,27,0.032000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c),x)","\frac{c x \sqrt{-a^{2} x^{2}+1}}{2}+\frac{c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}"," ",0,"1/2*c*x*(-a^2*x^2+1)^(1/2)+1/2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
162,1,76,41,0.035000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c),x)","-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c \sqrt{a^{2}}}-\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{c \,a^{2} \left(x -\frac{1}{a}\right)}"," ",0,"-1/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-2/c/a^2/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
163,1,35,28,0.031000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^2,x)","-\frac{\left(a x +1\right)^{2}}{3 \left(a x -1\right) c^{2} \sqrt{-a^{2} x^{2}+1}\, a}"," ",0,"-1/3*(a*x+1)^2/(a*x-1)/c^2/(-a^2*x^2+1)^(1/2)/a","A"
164,1,40,57,0.028000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^3,x)","-\frac{\left(a x -4\right) \left(a x +1\right)^{2}}{15 \left(a x -1\right)^{2} c^{3} \sqrt{-a^{2} x^{2}+1}\, a}"," ",0,"-1/15*(a*x-4)*(a*x+1)^2/(a*x-1)^2/c^3/(-a^2*x^2+1)^(1/2)/a","A"
165,1,49,85,0.028000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^4,x)","-\frac{\left(2 a^{2} x^{2}-10 a x +23\right) \left(a x +1\right)^{2}}{105 \left(a x -1\right)^{3} c^{4} \sqrt{-a^{2} x^{2}+1}\, a}"," ",0,"-1/105*(2*a^2*x^2-10*a*x+23)*(a*x+1)^2/(a*x-1)^3/c^4/(-a^2*x^2+1)^(1/2)/a","A"
166,1,57,113,0.031000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^5,x)","-\frac{\left(2 x^{3} a^{3}-12 a^{2} x^{2}+33 a x -58\right) \left(a x +1\right)^{2}}{315 \left(a x -1\right)^{4} c^{5} \sqrt{-a^{2} x^{2}+1}\, a}"," ",0,"-1/315*(2*a^3*x^3-12*a^2*x^2+33*a*x-58)*(a*x+1)^2/(a*x-1)^4/c^5/(-a^2*x^2+1)^(1/2)/a","A"
167,1,30,41,0.025000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^p,x)","-\frac{\left(-a c x +c \right)^{p} \left(a p x +p +2\right)}{a p \left(1+p \right)}"," ",0,"-(-a*c*x+c)^p*(a*p*x+p+2)/a/p/(1+p)","A"
168,1,45,33,0.026000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^5,x)","c^{5} \left(\frac{1}{6} x^{6} a^{5}-\frac{3}{5} a^{4} x^{5}+\frac{1}{2} x^{4} a^{3}+\frac{2}{3} x^{3} a^{2}-\frac{3}{2} a \,x^{2}+x \right)"," ",0,"c^5*(1/6*x^6*a^5-3/5*a^4*x^5+1/2*x^4*a^3+2/3*x^3*a^2-3/2*a*x^2+x)","A"
169,1,29,33,0.025000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^4,x)","c^{4} \left(-\frac{1}{5} a^{4} x^{5}+\frac{1}{2} x^{4} a^{3}-a \,x^{2}+x \right)"," ",0,"c^4*(-1/5*a^4*x^5+1/2*x^4*a^3-a*x^2+x)","A"
170,1,29,33,0.023000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^3,x)","c^{3} \left(\frac{1}{4} x^{4} a^{3}-\frac{1}{3} x^{3} a^{2}-\frac{1}{2} a \,x^{2}+x \right)"," ",0,"c^3*(1/4*x^4*a^3-1/3*x^3*a^2-1/2*a*x^2+x)","A"
171,1,15,17,0.024000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^2,x)","c^{2} \left(-\frac{1}{3} x^{3} a^{2}+x \right)"," ",0,"c^2*(-1/3*x^3*a^2+x)","A"
172,1,11,11,0.025000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c),x)","c \left(\frac{1}{2} a \,x^{2}+x \right)"," ",0,"c*(1/2*a*x^2+x)","A"
173,1,30,31,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c),x)","\frac{\ln \left(a x -1\right)}{c a}-\frac{2}{c a \left(a x -1\right)}"," ",0,"1/c/a*ln(a*x-1)-2/c/a/(a*x-1)","A"
174,1,28,13,0.031000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^2,x)","\frac{\frac{1}{a \left(a x -1\right)^{2}}+\frac{1}{a \left(a x -1\right)}}{c^{2}}"," ",0,"1/c^2*(1/a/(a*x-1)^2+1/a/(a*x-1))","B"
175,1,30,33,0.030000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^3,x)","\frac{-\frac{1}{2 a \left(a x -1\right)^{2}}-\frac{2}{3 a \left(a x -1\right)^{3}}}{c^{3}}"," ",0,"1/c^3*(-1/2/a/(a*x-1)^2-2/3/a/(a*x-1)^3)","A"
176,1,30,33,0.031000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^4,x)","\frac{\frac{1}{2 a \left(a x -1\right)^{4}}+\frac{1}{3 a \left(a x -1\right)^{3}}}{c^{4}}"," ",0,"1/c^4*(1/2/a/(a*x-1)^4+1/3/a/(a*x-1)^3)","A"
177,0,0,53,0.391000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^p,x)","\int \frac{\left(a x +1\right)^{3} \left(-a c x +c \right)^{p}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^p,x)","F"
178,1,183,69,0.069000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^4,x)","-\frac{c^{4} a^{5} x^{6}}{5 \sqrt{-a^{2} x^{2}+1}}+\frac{3 c^{4} a^{3} x^{4}}{5 \sqrt{-a^{2} x^{2}+1}}-\frac{3 c^{4} a \,x^{2}}{5 \sqrt{-a^{2} x^{2}+1}}+\frac{c^{4}}{5 a \sqrt{-a^{2} x^{2}+1}}+\frac{c^{4} a^{4} x^{5}}{4 \sqrt{-a^{2} x^{2}+1}}-\frac{7 c^{4} a^{2} x^{3}}{8 \sqrt{-a^{2} x^{2}+1}}+\frac{5 c^{4} x}{8 \sqrt{-a^{2} x^{2}+1}}+\frac{3 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}"," ",0,"-1/5*c^4*a^5*x^6/(-a^2*x^2+1)^(1/2)+3/5*c^4*a^3*x^4/(-a^2*x^2+1)^(1/2)-3/5*c^4*a*x^2/(-a^2*x^2+1)^(1/2)+1/5*c^4/a/(-a^2*x^2+1)^(1/2)+1/4*c^4*a^4*x^5/(-a^2*x^2+1)^(1/2)-7/8*c^4*a^2*x^3/(-a^2*x^2+1)^(1/2)+5/8*c^4*x/(-a^2*x^2+1)^(1/2)+3/8*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","B"
179,1,96,49,0.044000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^3,x)","\frac{c^{3} a^{4} x^{5}}{4 \sqrt{-a^{2} x^{2}+1}}-\frac{7 c^{3} a^{2} x^{3}}{8 \sqrt{-a^{2} x^{2}+1}}+\frac{5 c^{3} x}{8 \sqrt{-a^{2} x^{2}+1}}+\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}"," ",0,"1/4*c^3*a^4*x^5/(-a^2*x^2+1)^(1/2)-7/8*c^3*a^2*x^3/(-a^2*x^2+1)^(1/2)+5/8*c^3*x/(-a^2*x^2+1)^(1/2)+3/8*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
180,1,137,51,0.049000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^2,x)","-\frac{c^{2} a^{3} x^{4}}{3 \sqrt{-a^{2} x^{2}+1}}+\frac{2 c^{2} a \,x^{2}}{3 \sqrt{-a^{2} x^{2}+1}}-\frac{c^{2}}{3 a \sqrt{-a^{2} x^{2}+1}}-\frac{c^{2} a^{2} x^{3}}{2 \sqrt{-a^{2} x^{2}+1}}+\frac{c^{2} x}{2 \sqrt{-a^{2} x^{2}+1}}+\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}"," ",0,"-1/3*c^2*a^3*x^4/(-a^2*x^2+1)^(1/2)+2/3*c^2*a*x^2/(-a^2*x^2+1)^(1/2)-1/3*c^2/a/(-a^2*x^2+1)^(1/2)-1/2*c^2*a^2*x^3/(-a^2*x^2+1)^(1/2)+1/2*c^2*x/(-a^2*x^2+1)^(1/2)+1/2*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","B"
181,1,104,55,0.039000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c),x)","\frac{c \,a^{2} x^{3}}{2 \sqrt{-a^{2} x^{2}+1}}-\frac{c x}{2 \sqrt{-a^{2} x^{2}+1}}+\frac{3 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}+\frac{2 c a \,x^{2}}{\sqrt{-a^{2} x^{2}+1}}-\frac{2 c}{a \sqrt{-a^{2} x^{2}+1}}"," ",0,"1/2*c*a^2*x^3/(-a^2*x^2+1)^(1/2)-1/2*c*x/(-a^2*x^2+1)^(1/2)+3/2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+2*c*a*x^2/(-a^2*x^2+1)^(1/2)-2*c/a/(-a^2*x^2+1)^(1/2)","A"
182,1,146,68,0.036000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c),x)","-\frac{8 x}{c \sqrt{-a^{2} x^{2}+1}}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c \sqrt{a^{2}}}-\frac{4}{c a \sqrt{-a^{2} x^{2}+1}}-\frac{8}{3 c \,a^{2} \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{16 x}{3 c \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}"," ",0,"-8/c*x/(-a^2*x^2+1)^(1/2)+1/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-4/c/a/(-a^2*x^2+1)^(1/2)-8/3/c/a^2/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+16/3/c/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x","B"
183,1,35,28,0.030000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^2,x)","-\frac{\left(a x +1\right)^{4}}{5 \left(a x -1\right) c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a}"," ",0,"-1/5*(a*x+1)^4/(a*x-1)/c^2/(-a^2*x^2+1)^(3/2)/a","A"
184,1,40,57,0.029000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^3,x)","-\frac{\left(a x -6\right) \left(a x +1\right)^{4}}{35 \left(a x -1\right)^{2} c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a}"," ",0,"-1/35*(a*x-6)*(a*x+1)^4/(a*x-1)^2/c^3/(-a^2*x^2+1)^(3/2)/a","A"
185,1,49,85,0.029000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^4,x)","-\frac{\left(2 a^{2} x^{2}-14 a x +47\right) \left(a x +1\right)^{4}}{315 \left(a x -1\right)^{3} c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a}"," ",0,"-1/315*(2*a^2*x^2-14*a*x+47)*(a*x+1)^4/(a*x-1)^3/c^4/(-a^2*x^2+1)^(3/2)/a","A"
186,1,57,113,0.029000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^5,x)","-\frac{\left(2 x^{3} a^{3}-16 a^{2} x^{2}+61 a x -152\right) \left(a x +1\right)^{4}}{1155 \left(a x -1\right)^{4} c^{5} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a}"," ",0,"-1/1155*(2*a^3*x^3-16*a^2*x^2+61*a*x-152)*(a*x+1)^4/(a*x-1)^4/c^5/(-a^2*x^2+1)^(3/2)/a","A"
187,1,74,66,0.031000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^p,x)","\frac{\left(a^{2} p^{2} x^{2}-a^{2} x^{2} p +2 a \,p^{2} x +2 a p x -4 a x +p^{2}+3 p +4\right) \left(-a c x +c \right)^{p}}{\left(a x -1\right) a p \left(p^{2}-1\right)}"," ",0,"(a^2*p^2*x^2-a^2*p*x^2+2*a*p^2*x+2*a*p*x-4*a*x+p^2+3*p+4)*(-a*c*x+c)^p/(a*x-1)/a/p/(p^2-1)","A"
188,1,45,49,0.024000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^5,x)","c^{5} \left(-\frac{1}{6} x^{6} a^{5}+\frac{1}{5} a^{4} x^{5}+\frac{1}{2} x^{4} a^{3}-\frac{2}{3} x^{3} a^{2}-\frac{1}{2} a \,x^{2}+x \right)"," ",0,"c^5*(-1/6*x^6*a^5+1/5*a^4*x^5+1/2*x^4*a^3-2/3*x^3*a^2-1/2*a*x^2+x)","A"
189,1,23,28,0.024000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^4,x)","c^{4} \left(\frac{1}{5} a^{4} x^{5}-\frac{2}{3} x^{3} a^{2}+x \right)"," ",0,"c^4*(1/5*a^4*x^5-2/3*x^3*a^2+x)","A"
190,1,29,31,0.028000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^3,x)","c^{3} \left(-\frac{1}{4} x^{4} a^{3}-\frac{1}{3} x^{3} a^{2}+\frac{1}{2} a \,x^{2}+x \right)"," ",0,"c^3*(-1/4*x^4*a^3-1/3*x^3*a^2+1/2*a*x^2+x)","A"
191,1,16,15,0.023000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^2,x)","\frac{c^{2} \left(a x +1\right)^{3}}{3 a}"," ",0,"1/3*c^2*(a*x+1)^3/a","A"
192,1,25,25,0.027000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c),x)","-\frac{a c \,x^{2}}{2}-3 c x -\frac{4 c \ln \left(a x -1\right)}{a}"," ",0,"-1/2*a*c*x^2-3*c*x-4*c/a*ln(a*x-1)","A"
193,1,46,48,0.031000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(-a*c*x+c),x)","\frac{2}{c a \left(a x -1\right)^{2}}-\frac{\ln \left(a x -1\right)}{c a}+\frac{4}{c a \left(a x -1\right)}"," ",0,"2/c/a/(a*x-1)^2-1/c/a*ln(a*x-1)+4/c/a/(a*x-1)","A"
194,1,42,23,0.033000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(-a*c*x+c)^2,x)","\frac{-\frac{2}{a \left(a x -1\right)^{2}}-\frac{4}{3 a \left(a x -1\right)^{3}}-\frac{1}{a \left(a x -1\right)}}{c^{2}}"," ",0,"1/c^2*(-2/a/(a*x-1)^2-4/3/a/(a*x-1)^3-1/a/(a*x-1))","A"
195,1,41,48,0.031000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(-a*c*x+c)^3,x)","\frac{\frac{1}{2 a \left(a x -1\right)^{2}}+\frac{1}{a \left(a x -1\right)^{4}}+\frac{4}{3 a \left(a x -1\right)^{3}}}{c^{3}}"," ",0,"1/c^3*(1/2/a/(a*x-1)^2+1/a/(a*x-1)^4+4/3/a/(a*x-1)^3)","A"
196,1,42,49,0.030000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(-a*c*x+c)^4,x)","\frac{-\frac{1}{a \left(a x -1\right)^{4}}-\frac{1}{3 a \left(a x -1\right)^{3}}-\frac{4}{5 a \left(a x -1\right)^{5}}}{c^{4}}"," ",0,"1/c^4*(-1/a/(a*x-1)^4-1/3/a/(a*x-1)^3-4/5/a/(a*x-1)^5)","A"
197,0,0,53,0.393000," ","int((-a*c*x+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{\left(-a c x +c \right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int((-a*c*x+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
198,1,160,115,0.041000," ","int((-a*c*x+c)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{c^{3} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4}-\frac{29 c^{3} x \sqrt{-a^{2} x^{2}+1}}{8}-\frac{29 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}-\frac{4 c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 a}+\frac{8 c^{3} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{a}+\frac{8 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"1/4*c^3*x*(-a^2*x^2+1)^(3/2)-29/8*c^3*x*(-a^2*x^2+1)^(1/2)-29/8*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-4/3*c^3*(-a^2*x^2+1)^(3/2)/a+8*c^3/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+8*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","A"
199,1,142,87,0.038000," ","int((-a*c*x+c)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 a}-\frac{3 c^{2} x \sqrt{-a^{2} x^{2}+1}}{2}-\frac{3 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}+\frac{4 c^{2} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{a}+\frac{4 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-1/3*c^2*(-a^2*x^2+1)^(3/2)/a-3/2*c^2*x*(-a^2*x^2+1)^(1/2)-3/2*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+4*c^2/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+4*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","A"
200,1,114,53,0.036000," ","int((-a*c*x+c)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{c x \sqrt{-a^{2} x^{2}+1}}{2}-\frac{c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}+\frac{2 c \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{a}+\frac{2 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-1/2*c*x*(-a^2*x^2+1)^(1/2)-1/2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+2*c/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
201,1,154,11,0.040000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c),x)","-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{2 c a}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{2 c \sqrt{a^{2}}}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{2 c a}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{2 c \sqrt{a^{2}}}"," ",0,"-1/2/c/a*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/2/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+1/2/c/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+1/2/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
202,1,28,27,0.029000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^2,x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{\left(a x -1\right) a \,c^{2}}"," ",0,"-(-a^2*x^2+1)^(1/2)/(a*x-1)/a/c^2","A"
203,1,33,57,0.029000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^3,x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a x -2\right)}{3 \left(a x -1\right)^{2} c^{3} a}"," ",0,"-1/3*(-a^2*x^2+1)^(1/2)*(a*x-2)/(a*x-1)^2/c^3/a","A"
204,1,42,85,0.031000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^4,x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 a^{2} x^{2}-6 a x +7\right)}{15 \left(a x -1\right)^{3} c^{4} a}"," ",0,"-1/15*(-a^2*x^2+1)^(1/2)*(2*a^2*x^2-6*a*x+7)/(a*x-1)^3/c^4/a","A"
205,1,50,113,0.031000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^5,x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}-8 a^{2} x^{2}+13 a x -12\right)}{35 \left(a x -1\right)^{4} c^{5} a}"," ",0,"-1/35*(-a^2*x^2+1)^(1/2)*(2*a^3*x^3-8*a^2*x^2+13*a*x-12)/(a*x-1)^4/c^5/a","A"
206,0,0,40,0.310000," ","int((-a*c*x+c)^p/(a*x+1)^2*(-a^2*x^2+1),x)","\int \frac{\left(-a c x +c \right)^{p} \left(-a^{2} x^{2}+1\right)}{\left(a x +1\right)^{2}}\, dx"," ",0,"int((-a*c*x+c)^p/(a*x+1)^2*(-a^2*x^2+1),x)","F"
207,1,64,85,0.026000," ","int((-a*c*x+c)^4/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{a^{4} c^{4} x^{5}}{5}+\frac{3 c^{4} x^{4} a^{3}}{2}-\frac{16 a^{2} c^{4} x^{3}}{3}+13 c^{4} x^{2} a -31 c^{4} x +\frac{32 c^{4} \ln \left(a x +1\right)}{a}"," ",0,"-1/5*a^4*c^4*x^5+3/2*c^4*x^4*a^3-16/3*a^2*c^4*x^3+13*c^4*x^2*a-31*c^4*x+32*c^4*ln(a*x+1)/a","A"
208,1,53,69,0.025000," ","int((-a*c*x+c)^3/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{c^{3} x^{4} a^{3}}{4}-\frac{5 a^{2} c^{3} x^{3}}{3}+\frac{11 c^{3} x^{2} a}{2}-15 c^{3} x +\frac{16 c^{3} \ln \left(a x +1\right)}{a}"," ",0,"1/4*c^3*x^4*a^3-5/3*a^2*c^3*x^3+11/2*c^3*x^2*a-15*c^3*x+16*c^3*ln(a*x+1)/a","A"
209,1,42,52,0.029000," ","int((-a*c*x+c)^2/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{a^{2} c^{2} x^{3}}{3}+2 c^{2} x^{2} a -7 c^{2} x +\frac{8 c^{2} \ln \left(a x +1\right)}{a}"," ",0,"-1/3*a^2*c^2*x^3+2*c^2*x^2*a-7*c^2*x+8*c^2*ln(a*x+1)/a","A"
210,1,25,24,0.025000," ","int((-a*c*x+c)/(a*x+1)^2*(-a^2*x^2+1),x)","-3 c x +\frac{a c \,x^{2}}{2}+\frac{4 c \ln \left(a x +1\right)}{a}"," ",0,"-3*c*x+1/2*a*c*x^2+4*c*ln(a*x+1)/a","A"
211,1,14,13,0.026000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c),x)","\frac{\ln \left(a x +1\right)}{a c}"," ",0,"ln(a*x+1)/a/c","A"
212,1,30,11,0.032000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^2,x)","-\frac{\ln \left(a x -1\right)}{2 c^{2} a}+\frac{\ln \left(a x +1\right)}{2 a \,c^{2}}"," ",0,"-1/2/c^2/a*ln(a*x-1)+1/2*ln(a*x+1)/a/c^2","B"
213,1,45,29,0.033000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^3,x)","-\frac{1}{2 c^{3} a \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{4 c^{3} a}+\frac{\ln \left(a x +1\right)}{4 a \,c^{3}}"," ",0,"-1/2/c^3/a/(a*x-1)-1/4/c^3/a*ln(a*x-1)+1/4*ln(a*x+1)/a/c^3","A"
214,1,60,45,0.032000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^4,x)","\frac{1}{4 c^{4} a \left(a x -1\right)^{2}}-\frac{1}{4 c^{4} a \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{8 c^{4} a}+\frac{\ln \left(a x +1\right)}{8 a \,c^{4}}"," ",0,"1/4/c^4/a/(a*x-1)^2-1/4/c^4/a/(a*x-1)-1/8/c^4/a*ln(a*x-1)+1/8*ln(a*x+1)/a/c^4","A"
215,1,75,61,0.036000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^5,x)","-\frac{1}{6 c^{5} a \left(a x -1\right)^{3}}+\frac{1}{8 c^{5} a \left(a x -1\right)^{2}}-\frac{1}{8 c^{5} a \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{16 c^{5} a}+\frac{\ln \left(a x +1\right)}{16 c^{5} a}"," ",0,"-1/6/c^5/a/(a*x-1)^3+1/8/c^5/a/(a*x-1)^2-1/8/c^5/a/(a*x-1)-1/16/c^5/a*ln(a*x-1)+1/16/c^5/a*ln(a*x+1)","A"
216,0,0,53,0.401000," ","int((-a*c*x+c)^p/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\int \frac{\left(-a c x +c \right)^{p} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{\left(a x +1\right)^{3}}\, dx"," ",0,"int((-a*c*x+c)^p/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","F"
217,1,245,143,0.048000," ","int((-a*c*x+c)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{c^{3} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4}-\frac{3 c^{3} x \sqrt{-a^{2} x^{2}+1}}{8}-\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}-\frac{28 c^{3} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{26 c^{3} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{a}-39 c^{3} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x -\frac{39 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}-\frac{8 c^{3} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{4} \left(x +\frac{1}{a}\right)^{3}}"," ",0,"-1/4*c^3*x*(-a^2*x^2+1)^(3/2)-3/8*c^3*x*(-a^2*x^2+1)^(1/2)-3/8*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-28*c^3/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-26*c^3/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-39*c^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-39*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-8*c^3/a^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)","A"
218,1,179,115,0.044000," ","int((-a*c*x+c)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{12 c^{2} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{35 c^{2} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a}-\frac{35 c^{2} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{2}-\frac{35 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{2 \sqrt{a^{2}}}-\frac{4 c^{2} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{4} \left(x +\frac{1}{a}\right)^{3}}"," ",0,"-12*c^2/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-35/3*c^2/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-35/2*c^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-35/2*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-4*c^2/a^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)","A"
219,1,169,79,0.043000," ","int((-a*c*x+c)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{5 c \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{5 c \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{a}-\frac{15 c \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{2}-\frac{15 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{2 \sqrt{a^{2}}}-\frac{2 c \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{4} \left(x +\frac{1}{a}\right)^{3}}"," ",0,"-5*c/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-5*c/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-15/2*c*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-15/2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-2*c/a^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)","B"
220,1,292,39,0.048000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c),x)","-\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{24 c a}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}\, x}{16 c}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{16 c \sqrt{a^{2}}}-\frac{3 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{4 c \,a^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{17 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{24 c a}-\frac{17 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{16 c}-\frac{17 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{16 c \sqrt{a^{2}}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{2 c \,a^{4} \left(x +\frac{1}{a}\right)^{3}}"," ",0,"-1/24/c/a*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+1/16/c*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x+1/16/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-3/4/c/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-17/24/c/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-17/16/c*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-17/16/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-1/2/c/a^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)","B"
221,1,34,24,0.031000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^2,x)","\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{\left(a x -1\right) c^{2} a \left(a x +1\right)^{2}}"," ",0,"(-a^2*x^2+1)^(3/2)/(a*x-1)/c^2/a/(a*x+1)^2","A"
222,1,32,17,0.026000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^3,x)","\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} x}{\left(a x -1\right)^{2} c^{3} \left(a x +1\right)^{2}}"," ",0,"(-a^2*x^2+1)^(3/2)*x/(a*x-1)^2/c^3/(a*x+1)^2","A"
223,1,49,47,0.029000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^4,x)","\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \left(2 a^{2} x^{2}-2 a x -1\right)}{3 \left(a x -1\right)^{3} c^{4} a \left(a x +1\right)^{2}}"," ",0,"1/3*(-a^2*x^2+1)^(3/2)*(2*a^2*x^2-2*a*x-1)/(a*x-1)^3/c^4/a/(a*x+1)^2","A"
224,1,56,75,0.029000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^5,x)","\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \left(2 x^{3} a^{3}-4 a^{2} x^{2}+a x +2\right)}{5 \left(a x -1\right)^{4} c^{5} a \left(a x +1\right)^{2}}"," ",0,"1/5*(-a^2*x^2+1)^(3/2)*(2*a^3*x^3-4*a^2*x^2+a*x+2)/(a*x-1)^4/c^5/a/(a*x+1)^2","A"
225,1,65,103,0.032000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^6,x)","\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \left(8 x^{4} a^{4}-24 x^{3} a^{3}+20 a^{2} x^{2}+4 a x -13\right)}{35 \left(a x -1\right)^{5} c^{6} a \left(a x +1\right)^{2}}"," ",0,"1/35*(-a^2*x^2+1)^(3/2)*(8*a^4*x^4-24*a^3*x^3+20*a^2*x^2+4*a*x-13)/(a*x-1)^5/c^6/a/(a*x+1)^2","A"
226,1,71,146,0.031000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(9/2),x)","\frac{2 \left(a x +1\right)^{2} \left(315 x^{4} a^{4}-1820 x^{3} a^{3}+4530 a^{2} x^{2}-6396 a x +5419\right) \left(-a c x +c \right)^{\frac{9}{2}}}{3465 a \left(a x -1\right)^{4} \sqrt{-a^{2} x^{2}+1}}"," ",0,"2/3465*(a*x+1)^2*(315*a^4*x^4-1820*a^3*x^3+4530*a^2*x^2-6396*a*x+5419)*(-a*c*x+c)^(9/2)/a/(a*x-1)^4/(-a^2*x^2+1)^(1/2)","A"
227,1,63,117,0.031000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(7/2),x)","\frac{2 \left(a x +1\right)^{2} \left(35 x^{3} a^{3}-165 a^{2} x^{2}+321 a x -319\right) \left(-a c x +c \right)^{\frac{7}{2}}}{315 a \left(a x -1\right)^{3} \sqrt{-a^{2} x^{2}+1}}"," ",0,"2/315*(a*x+1)^2*(35*a^3*x^3-165*a^2*x^2+321*a*x-319)*(-a*c*x+c)^(7/2)/a/(a*x-1)^3/(-a^2*x^2+1)^(1/2)","A"
228,1,55,88,0.030000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(5/2),x)","\frac{2 \left(a x +1\right)^{2} \left(15 a^{2} x^{2}-54 a x +71\right) \left(-a c x +c \right)^{\frac{5}{2}}}{105 a \left(a x -1\right)^{2} \sqrt{-a^{2} x^{2}+1}}"," ",0,"2/105*(a*x+1)^2*(15*a^2*x^2-54*a*x+71)*(-a*c*x+c)^(5/2)/a/(a*x-1)^2/(-a^2*x^2+1)^(1/2)","A"
229,1,47,59,0.028000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(3/2),x)","\frac{2 \left(a x +1\right)^{2} \left(3 a x -7\right) \left(-a c x +c \right)^{\frac{3}{2}}}{15 a \left(a x -1\right) \sqrt{-a^{2} x^{2}+1}}"," ",0,"2/15*(a*x+1)^2*(3*a*x-7)*(-a*c*x+c)^(3/2)/a/(a*x-1)/(-a^2*x^2+1)^(1/2)","A"
230,1,34,29,0.026000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2),x)","\frac{2 \left(a x +1\right)^{2} \sqrt{-a c x +c}}{3 a \sqrt{-a^{2} x^{2}+1}}"," ",0,"2/3*(a*x+1)^2*(-a*c*x+c)^(1/2)/a/(-a^2*x^2+1)^(1/2)","A"
231,1,84,68,0.057000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(\sqrt{c}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-\sqrt{c \left(a x +1\right)}\right)}{\left(a x -1\right) \sqrt{c \left(a x +1\right)}\, c a}"," ",0,"-2*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(c^(1/2)*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-(c*(a*x+1))^(1/2))/(a*x-1)/(c*(a*x+1))^(1/2)/c/a","A"
232,1,111,67,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(3/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c -\sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +2 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{2 \left(a x -1\right)^{2} \sqrt{c \left(a x +1\right)}\, c^{\frac{5}{2}} a}"," ",0,"1/2*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c-2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c+2*(c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)^2/(c*(a*x+1))^(1/2)/c^(5/2)/a","A"
233,1,156,97,0.051000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(5/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c -2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c -2 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}+\sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -6 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{16 c^{\frac{7}{2}} \left(a x -1\right)^{3} \sqrt{c \left(a x +1\right)}\, a}"," ",0,"1/16*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)/c^(7/2)*(2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c-2*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c-2*x*a*(c*(a*x+1))^(1/2)*c^(1/2)+2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c-6*(c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)^3/(c*(a*x+1))^(1/2)/a","A"
234,1,208,126,0.050000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(7/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{3} a^{3} c -9 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c -6 x^{2} a^{2} \sqrt{c \left(a x +1\right)}\, \sqrt{c}+9 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c +20 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +50 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{192 c^{\frac{9}{2}} \left(a x -1\right)^{4} \sqrt{c \left(a x +1\right)}\, a}"," ",0,"1/192*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)/c^(9/2)*(3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^3*a^3*c-9*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c-6*x^2*a^2*(c*(a*x+1))^(1/2)*c^(1/2)+9*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c+20*x*a*(c*(a*x+1))^(1/2)*c^(1/2)-3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c+50*(c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)^4/(c*(a*x+1))^(1/2)/a","A"
235,1,21,32,0.028000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(7/2),x)","-\frac{2 \left(-a c x +c \right)^{\frac{7}{2}} \left(7 a x +11\right)}{63 a}"," ",0,"-2/63*(-a*c*x+c)^(7/2)*(7*a*x+11)/a","A"
236,1,21,32,0.028000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(5/2),x)","-\frac{2 \left(-a c x +c \right)^{\frac{5}{2}} \left(5 a x +9\right)}{35 a}"," ",0,"-2/35*(-a*c*x+c)^(5/2)*(5*a*x+9)/a","A"
237,1,21,32,0.030000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(3/2),x)","-\frac{2 \left(-a c x +c \right)^{\frac{3}{2}} \left(3 a x +7\right)}{15 a}"," ",0,"-2/15*(-a*c*x+c)^(3/2)*(3*a*x+7)/a","A"
238,1,20,32,0.029000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-a c x +c}\, \left(a x +5\right)}{3 a}"," ",0,"-2/3*(-a*c*x+c)^(1/2)*(a*x+5)/a","A"
239,1,20,32,0.026000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^(1/2),x)","-\frac{2 \left(a x -3\right)}{\sqrt{-a c x +c}\, a}"," ",0,"-2*(a*x-3)/(-a*c*x+c)^(1/2)/a","A"
240,1,21,32,0.028000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^(3/2),x)","\frac{2 a x -\frac{2}{3}}{\left(-a c x +c \right)^{\frac{3}{2}} a}"," ",0,"2/3*(3*a*x-1)/(-a*c*x+c)^(3/2)/a","A"
241,1,21,32,0.028000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^(5/2),x)","\frac{\frac{2 a x}{3}+\frac{2}{15}}{\left(-a c x +c \right)^{\frac{5}{2}} a}"," ",0,"2/15*(5*a*x+1)/(-a*c*x+c)^(5/2)/a","A"
242,1,21,32,0.029000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^(7/2),x)","\frac{\frac{2 a x}{5}+\frac{6}{35}}{\left(-a c x +c \right)^{\frac{7}{2}} a}"," ",0,"2/35*(7*a*x+3)/(-a*c*x+c)^(7/2)/a","A"
243,1,63,117,0.032000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(9/2),x)","\frac{2 \left(a x +1\right)^{4} \left(105 x^{3} a^{3}-455 a^{2} x^{2}+755 a x -533\right) \left(-a c x +c \right)^{\frac{9}{2}}}{1155 a \left(a x -1\right)^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"2/1155*(a*x+1)^4*(105*a^3*x^3-455*a^2*x^2+755*a*x-533)*(-a*c*x+c)^(9/2)/a/(a*x-1)^3/(-a^2*x^2+1)^(3/2)","A"
244,1,55,88,0.029000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(7/2),x)","\frac{2 \left(a x +1\right)^{4} \left(35 a^{2} x^{2}-110 a x +107\right) \left(-a c x +c \right)^{\frac{7}{2}}}{315 a \left(a x -1\right)^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"2/315*(a*x+1)^4*(35*a^2*x^2-110*a*x+107)*(-a*c*x+c)^(7/2)/a/(a*x-1)^2/(-a^2*x^2+1)^(3/2)","A"
245,1,47,59,0.027000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(5/2),x)","\frac{2 \left(a x +1\right)^{4} \left(5 a x -9\right) \left(-a c x +c \right)^{\frac{5}{2}}}{35 a \left(a x -1\right) \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"2/35*(a*x+1)^4*(5*a*x-9)*(-a*c*x+c)^(5/2)/a/(a*x-1)/(-a^2*x^2+1)^(3/2)","A"
246,1,34,29,0.024000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(3/2),x)","\frac{2 \left(a x +1\right)^{4} \left(-a c x +c \right)^{\frac{3}{2}}}{5 a \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"2/5*(a*x+1)^4*(-a*c*x+c)^(3/2)/a/(-a^2*x^2+1)^(3/2)","A"
247,1,95,98,0.042000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(6 \sqrt{c}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-x a \sqrt{c \left(a x +1\right)}-7 \sqrt{c \left(a x +1\right)}\right)}{3 \left(a x -1\right) \sqrt{c \left(a x +1\right)}\, a}"," ",0,"-2/3*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(6*c^(1/2)*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-x*a*(c*(a*x+1))^(1/2)-7*(c*(a*x+1))^(1/2))/(a*x-1)/(c*(a*x+1))^(1/2)/a","A"
248,1,127,96,0.051000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c -2 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +4 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{c^{\frac{3}{2}} \left(a x -1\right)^{2} \sqrt{c \left(a x +1\right)}\, a}"," ",0,"(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c-2*x*a*(c*(a*x+1))^(1/2)*c^(1/2)-3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c+4*(c*(a*x+1))^(1/2)*c^(1/2))/c^(3/2)/(a*x-1)^2/(c*(a*x+1))^(1/2)/a","A"
249,1,158,97,0.049000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c -6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c +10 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -2 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{8 c^{\frac{5}{2}} \left(a x -1\right)^{3} \sqrt{c \left(a x +1\right)}\, a}"," ",0,"-1/8*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)/c^(5/2)*(3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c-6*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c+10*x*a*(c*(a*x+1))^(1/2)*c^(1/2)+3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c-2*(c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)^3/(c*(a*x+1))^(1/2)/a","A"
250,1,208,126,0.052000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{3} a^{3} c -9 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c -6 x^{2} a^{2} \sqrt{c \left(a x +1\right)}\, \sqrt{c}+9 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c -44 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -14 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{96 c^{\frac{7}{2}} \left(a x -1\right)^{4} \sqrt{c \left(a x +1\right)}\, a}"," ",0,"-1/96*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)/c^(7/2)*(3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^3*a^3*c-9*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c-6*x^2*a^2*(c*(a*x+1))^(1/2)*c^(1/2)+9*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c-44*x*a*(c*(a*x+1))^(1/2)*c^(1/2)-3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c-14*(c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)^4/(c*(a*x+1))^(1/2)/a","A"
251,1,258,155,0.055000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(7/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{4} a^{4} c -12 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{3} a^{3} c -6 x^{3} a^{3} \sqrt{c \left(a x +1\right)}\, \sqrt{c}+18 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c +26 x^{2} a^{2} \sqrt{c \left(a x +1\right)}\, \sqrt{c}-12 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c +158 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +78 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{512 c^{\frac{9}{2}} \left(a x -1\right)^{5} \sqrt{c \left(a x +1\right)}\, a}"," ",0,"-1/512*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)/c^(9/2)*(3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^4*a^4*c-12*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^3*a^3*c-6*x^3*a^3*(c*(a*x+1))^(1/2)*c^(1/2)+18*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c+26*x^2*a^2*(c*(a*x+1))^(1/2)*c^(1/2)-12*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c+158*x*a*(c*(a*x+1))^(1/2)*c^(1/2)+3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c+78*(c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)^5/(c*(a*x+1))^(1/2)/a","A"
252,1,72,170,0.031000," ","int((-a*c*x+c)^(9/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{2 \sqrt{-a^{2} x^{2}+1}\, \left(-a c x +c \right)^{\frac{9}{2}} \left(63 x^{5} a^{5}-455 x^{4} a^{4}+1510 x^{3} a^{3}-3198 a^{2} x^{2}+5419 a x -11531\right)}{693 \left(a x -1\right)^{5} a}"," ",0,"2/693*(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(9/2)*(63*a^5*x^5-455*a^4*x^4+1510*a^3*x^3-3198*a^2*x^2+5419*a*x-11531)/(a*x-1)^5/a","A"
253,1,64,141,0.031000," ","int((-a*c*x+c)^(7/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{2 \sqrt{-a^{2} x^{2}+1}\, \left(-a c x +c \right)^{\frac{7}{2}} \left(35 x^{4} a^{4}-220 x^{3} a^{3}+642 a^{2} x^{2}-1276 a x +2867\right)}{315 \left(a x -1\right)^{4} a}"," ",0,"2/315*(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(7/2)*(35*a^4*x^4-220*a^3*x^3+642*a^2*x^2-1276*a*x+2867)/(a*x-1)^4/a","A"
254,1,56,112,0.029000," ","int((-a*c*x+c)^(5/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{2 \sqrt{-a^{2} x^{2}+1}\, \left(-a c x +c \right)^{\frac{5}{2}} \left(5 x^{3} a^{3}-27 a^{2} x^{2}+71 a x -177\right)}{35 \left(a x -1\right)^{3} a}"," ",0,"2/35*(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(5/2)*(5*a^3*x^3-27*a^2*x^2+71*a*x-177)/(a*x-1)^3/a","A"
255,1,48,83,0.030000," ","int((-a*c*x+c)^(3/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{2 \sqrt{-a^{2} x^{2}+1}\, \left(-a c x +c \right)^{\frac{3}{2}} \left(3 a^{2} x^{2}-14 a x +43\right)}{15 \left(a x -1\right)^{2} a}"," ",0,"2/15*(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(3/2)*(3*a^2*x^2-14*a*x+43)/(a*x-1)^2/a","A"
256,1,39,54,0.026000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-a c x +c}\, \left(a x -5\right)}{3 \left(a x -1\right) a}"," ",0,"2/3*(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2)*(a*x-5)/(a*x-1)/a","A"
257,1,27,26,0.026000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(1/2),x)","\frac{2 \sqrt{-a^{2} x^{2}+1}}{a \sqrt{-a c x +c}}"," ",0,"2*(-a^2*x^2+1)^(1/2)/a/(-a*c*x+c)^(1/2)","A"
258,1,68,40,0.041000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(3/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{\left(-a x +1\right) \sqrt{c \left(a x +1\right)}\, c^{\frac{3}{2}} a}"," ",0,"1/(-a*x+1)/(c*(a*x+1))^(1/2)/c^(3/2)/a*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))","A"
259,1,111,71,0.046000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c -\sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -2 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{4 c^{\frac{7}{2}} \left(a x -1\right)^{2} \sqrt{c \left(a x +1\right)}\, a}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)/c^(7/2)*(2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c-2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c-2*(c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)^2/(c*(a*x+1))^(1/2)/a","A"
260,1,158,100,0.049000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(7/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c -6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c -6 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +14 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{32 c^{\frac{9}{2}} \left(a x -1\right)^{3} \sqrt{c \left(a x +1\right)}\, a}"," ",0,"-1/32*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)/c^(9/2)*(3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c-6*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c-6*x*a*(c*(a*x+1))^(1/2)*c^(1/2)+3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c+14*(c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)^3/(c*(a*x+1))^(1/2)/a","A"
261,1,101,110,0.033000," ","int((-a*c*x+c)^(7/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\frac{2 \left(-a c x +c \right)^{\frac{9}{2}}}{9}+\frac{4 \left(-a c x +c \right)^{\frac{7}{2}} c}{7}+\frac{8 \left(-a c x +c \right)^{\frac{5}{2}} c^{2}}{5}+\frac{16 c^{3} \left(-a c x +c \right)^{\frac{3}{2}}}{3}+32 \sqrt{-a c x +c}\, c^{4}-32 c^{\frac{9}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{a c}"," ",0,"2/c/a*(1/9*(-a*c*x+c)^(9/2)+2/7*(-a*c*x+c)^(7/2)*c+4/5*(-a*c*x+c)^(5/2)*c^2+8/3*c^3*(-a*c*x+c)^(3/2)+16*(-a*c*x+c)^(1/2)*c^4-16*c^(9/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
262,1,87,93,0.033000," ","int((-a*c*x+c)^(5/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\frac{2 \left(-a c x +c \right)^{\frac{7}{2}}}{7}+\frac{4 c \left(-a c x +c \right)^{\frac{5}{2}}}{5}+\frac{8 \left(-a c x +c \right)^{\frac{3}{2}} c^{2}}{3}+16 \sqrt{-a c x +c}\, c^{3}-16 c^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{a c}"," ",0,"2/c/a*(1/7*(-a*c*x+c)^(7/2)+2/5*c*(-a*c*x+c)^(5/2)+4/3*(-a*c*x+c)^(3/2)*c^2+8*(-a*c*x+c)^(1/2)*c^3-8*c^(7/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
263,1,73,76,0.032000," ","int((-a*c*x+c)^(3/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\frac{2 \left(-a c x +c \right)^{\frac{5}{2}}}{5}+\frac{4 c \left(-a c x +c \right)^{\frac{3}{2}}}{3}+8 \sqrt{-a c x +c}\, c^{2}-8 c^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{a c}"," ",0,"2/c/a*(1/5*(-a*c*x+c)^(5/2)+2/3*c*(-a*c*x+c)^(3/2)+4*(-a*c*x+c)^(1/2)*c^2-4*c^(5/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
264,1,59,61,0.031000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\frac{2 \left(-a c x +c \right)^{\frac{3}{2}}}{3}+4 c \sqrt{-a c x +c}-4 c^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{a c}"," ",0,"2/c/a*(1/3*(-a*c*x+c)^(3/2)+2*c*(-a*c*x+c)^(1/2)-2*c^(3/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
265,1,45,47,0.031000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^(1/2),x)","\frac{2 \sqrt{-a c x +c}-2 \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, \sqrt{c}}{a c}"," ",0,"2/c/a*((-a*c*x+c)^(1/2)-arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^(1/2))","A"
266,1,30,29,0.030000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^(3/2),x)","-\frac{\arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}}{a \,c^{\frac{3}{2}}}"," ",0,"-arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)/a/c^(3/2)","A"
267,1,50,46,0.035000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^(5/2),x)","\frac{\frac{1}{c \sqrt{-a c x +c}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{2 c^{\frac{3}{2}}}}{a c}"," ",0,"2/c/a*(1/2/c/(-a*c*x+c)^(1/2)-1/4/c^(3/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
268,1,64,64,0.038000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^(7/2),x)","\frac{\frac{1}{2 c^{2} \sqrt{-a c x +c}}+\frac{1}{3 c \left(-a c x +c \right)^{\frac{3}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{4 c^{\frac{5}{2}}}}{a c}"," ",0,"2/c/a*(1/4/c^2/(-a*c*x+c)^(1/2)+1/6/c/(-a*c*x+c)^(3/2)-1/8/c^(5/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
269,1,78,81,0.039000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^(9/2),x)","\frac{\frac{1}{4 c^{3} \sqrt{-a c x +c}}+\frac{1}{6 c^{2} \left(-a c x +c \right)^{\frac{3}{2}}}+\frac{1}{5 c \left(-a c x +c \right)^{\frac{5}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{8 c^{\frac{7}{2}}}}{a c}"," ",0,"2/c/a*(1/8/c^3/(-a*c*x+c)^(1/2)+1/12/c^2/(-a*c*x+c)^(3/2)+1/10/c/(-a*c*x+c)^(5/2)-1/16/c^(7/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
270,1,71,141,0.030000," ","int((-a*c*x+c)^(5/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{2 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \left(-a c x +c \right)^{\frac{5}{2}} \left(5 x^{4} a^{4}-36 x^{3} a^{3}+142 a^{2} x^{2}-708 a x -1451\right)}{35 \left(a x +1\right)^{2} \left(a x -1\right)^{4} a}"," ",0,"2/35*(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(5/2)*(5*a^4*x^4-36*a^3*x^3+142*a^2*x^2-708*a*x-1451)/(a*x+1)^2/(a*x-1)^4/a","A"
271,1,62,112,0.031000," ","int((-a*c*x+c)^(3/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{2 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \left(-a c x +c \right)^{\frac{3}{2}} \left(x^{3} a^{3}-7 a^{2} x^{2}+43 a x +91\right)}{5 \left(a x +1\right)^{2} \left(a x -1\right)^{3} a}"," ",0,"2/5*(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(3/2)*(a^3*x^3-7*a^2*x^2+43*a*x+91)/(a*x+1)^2/(a*x-1)^3/a","A"
272,1,54,85,0.028000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{2 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \sqrt{-a c x +c}\, \left(a^{2} x^{2}-10 a x -23\right)}{3 \left(a x +1\right)^{2} \left(a x -1\right)^{2} a}"," ",0,"2/3*(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)*(a^2*x^2-10*a*x-23)/(a*x+1)^2/(a*x-1)^2/a","A"
273,1,46,59,0.027000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(1/2),x)","\frac{2 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a x +3\right)}{\sqrt{-a c x +c}\, \left(a x +1\right)^{2} \left(a x -1\right) a}"," ",0,"2*(-a^2*x^2+1)^(3/2)*(a*x+3)/(-a*c*x+c)^(1/2)/(a*x+1)^2/(a*x-1)/a","A"
274,1,34,29,0.025000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(3/2),x)","-\frac{2 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{\left(-a c x +c \right)^{\frac{3}{2}} \left(a x +1\right)^{2} a}"," ",0,"-2*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(3/2)/(a*x+1)^2/a","A"
275,1,82,71,0.048000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(\arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, \sqrt{c \left(a x +1\right)}-2 \sqrt{c}\right)}{2 c^{\frac{7}{2}} \left(a x -1\right) \left(a x +1\right) a}"," ",0,"-1/2*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)/c^(7/2)*(arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*(c*(a*x+1))^(1/2)-2*c^(1/2))/(a*x-1)/(a*x+1)/a","A"
276,1,124,100,0.055000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(7/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a \sqrt{c \left(a x +1\right)}-3 \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, \sqrt{c \left(a x +1\right)}-6 x a \sqrt{c}+2 \sqrt{c}\right)}{8 c^{\frac{9}{2}} \left(a x -1\right)^{2} \left(a x +1\right) a}"," ",0,"-1/8*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)/c^(9/2)*(3*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*(c*(a*x+1))^(1/2)-3*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*(c*(a*x+1))^(1/2)-6*x*a*c^(1/2)+2*c^(1/2))/(a*x-1)^2/(a*x+1)/a","A"
277,1,173,129,0.055000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(9/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} \sqrt{c \left(a x +1\right)}-30 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a \sqrt{c \left(a x +1\right)}-30 x^{2} a^{2} \sqrt{c}+15 \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, \sqrt{c \left(a x +1\right)}+40 x a \sqrt{c}+6 \sqrt{c}\right)}{64 c^{\frac{11}{2}} \left(a x -1\right)^{3} \left(a x +1\right) a}"," ",0,"-1/64*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)/c^(11/2)*(15*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*(c*(a*x+1))^(1/2)-30*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*(c*(a*x+1))^(1/2)-30*x^2*a^2*c^(1/2)+15*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*(c*(a*x+1))^(1/2)+40*x*a*c^(1/2)+6*c^(1/2))/(a*x-1)^3/(a*x+1)/a","A"
278,0,0,65,0.214000," ","int(exp(n*arctanh(a*x))*(-a*c*x+c)^(7/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a c x +c \right)^{\frac{7}{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a*c*x+c)^(7/2),x)","F"
279,0,0,65,0.213000," ","int(exp(n*arctanh(a*x))*(-a*c*x+c)^(5/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a c x +c \right)^{\frac{5}{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a*c*x+c)^(5/2),x)","F"
280,0,0,65,0.231000," ","int(exp(n*arctanh(a*x))*(-a*c*x+c)^(3/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a c x +c \right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a*c*x+c)^(3/2),x)","F"
281,0,0,65,0.214000," ","int(exp(n*arctanh(a*x))*(-a*c*x+c)^(1/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \sqrt{-a c x +c}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a*c*x+c)^(1/2),x)","F"
282,0,0,65,0.214000," ","int(exp(n*arctanh(a*x))/(-a*c*x+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\sqrt{-a c x +c}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(-a*c*x+c)^(1/2),x)","F"
283,0,0,62,0.215000," ","int(exp(n*arctanh(a*x))/(-a*c*x+c)^(3/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\left(-a c x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(-a*c*x+c)^(3/2),x)","F"
284,0,0,62,0.216000," ","int(exp(n*arctanh(a*x))/(-a*c*x+c)^(5/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\left(-a c x +c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(-a*c*x+c)^(5/2),x)","F"
285,0,0,62,0.231000," ","int(exp(n*arctanh(a*x))/(-a*c*x+c)^(7/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\left(-a c x +c \right)^{\frac{7}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(-a*c*x+c)^(7/2),x)","F"
286,1,91,69,0.040000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4*(-a*c*x+c),x)","\frac{c \,x^{5} \sqrt{-a^{2} x^{2}+1}}{6}-\frac{c \,x^{3} \sqrt{-a^{2} x^{2}+1}}{24 a^{2}}-\frac{c x \sqrt{-a^{2} x^{2}+1}}{16 a^{4}}+\frac{c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a^{4} \sqrt{a^{2}}}"," ",0,"1/6*c*x^5*(-a^2*x^2+1)^(1/2)-1/24*c*x^3*(-a^2*x^2+1)^(1/2)/a^2-1/16*c*x*(-a^2*x^2+1)^(1/2)/a^4+1/16*c/a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
287,1,43,37,0.028000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c),x)","-\frac{\left(a x -1\right)^{2} \left(a x +1\right)^{2} \left(3 a^{2} x^{2}+2\right) c}{15 a^{4} \sqrt{-a^{2} x^{2}+1}}"," ",0,"-1/15*(a*x-1)^2*(a*x+1)^2*(3*a^2*x^2+2)*c/a^4/(-a^2*x^2+1)^(1/2)","A"
288,1,70,48,0.036000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c),x)","\frac{c \,x^{3} \sqrt{-a^{2} x^{2}+1}}{4}-\frac{c x \sqrt{-a^{2} x^{2}+1}}{8 a^{2}}+\frac{c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a^{2} \sqrt{a^{2}}}"," ",0,"1/4*c*x^3*(-a^2*x^2+1)^(1/2)-1/8*c*x*(-a^2*x^2+1)^(1/2)/a^2+1/8*c/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
289,1,33,18,0.027000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c),x)","-\frac{\left(a x -1\right)^{2} \left(a x +1\right)^{2} c}{3 a^{2} \sqrt{-a^{2} x^{2}+1}}"," ",0,"-1/3*(a*x-1)^2*(a*x+1)^2*c/a^2/(-a^2*x^2+1)^(1/2)","A"
290,1,46,27,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c),x)","\frac{c x \sqrt{-a^{2} x^{2}+1}}{2}+\frac{c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}"," ",0,"1/2*c*x*(-a^2*x^2+1)^(1/2)+1/2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
291,1,32,31,0.030000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x,x)","-c \left(-\sqrt{-a^{2} x^{2}+1}+\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)\right)"," ",0,"-c*(-(-a^2*x^2+1)^(1/2)+arctanh(1/(-a^2*x^2+1)^(1/2)))","A"
292,1,51,27,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x^2,x)","-\frac{c \,a^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{c \sqrt{-a^{2} x^{2}+1}}{x}"," ",0,"-c*a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-c*(-a^2*x^2+1)^(1/2)/x","A"
293,1,40,38,0.036000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x^3,x)","-c \left(-\frac{a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{\sqrt{-a^{2} x^{2}+1}}{2 x^{2}}\right)"," ",0,"-c*(-1/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))+1/2*(-a^2*x^2+1)^(1/2)/x^2)","A"
294,1,33,18,0.026000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x^4,x)","-\frac{\left(a x -1\right)^{2} \left(a x +1\right)^{2} c}{3 x^{3} \sqrt{-a^{2} x^{2}+1}}"," ",0,"-1/3*(a*x-1)^2*(a*x+1)^2*c/x^3/(-a^2*x^2+1)^(1/2)","A"
295,1,163,106,0.048000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c)^2,x)","-\frac{c^{2} a \,x^{5} \sqrt{-a^{2} x^{2}+1}}{6}+\frac{c^{2} x^{3} \sqrt{-a^{2} x^{2}+1}}{24 a}+\frac{c^{2} x \sqrt{-a^{2} x^{2}+1}}{16 a^{3}}-\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a^{3} \sqrt{a^{2}}}+\frac{c^{2} x^{4} \sqrt{-a^{2} x^{2}+1}}{5}-\frac{c^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{15 a^{2}}-\frac{2 c^{2} \sqrt{-a^{2} x^{2}+1}}{15 a^{4}}"," ",0,"-1/6*c^2*a*x^5*(-a^2*x^2+1)^(1/2)+1/24*c^2/a*x^3*(-a^2*x^2+1)^(1/2)+1/16*c^2*x*(-a^2*x^2+1)^(1/2)/a^3-1/16*c^2/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/5*c^2*x^4*(-a^2*x^2+1)^(1/2)-1/15*c^2*x^2/a^2*(-a^2*x^2+1)^(1/2)-2/15*c^2/a^4*(-a^2*x^2+1)^(1/2)","A"
296,1,140,95,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c)^2,x)","-\frac{c^{2} a \,x^{4} \sqrt{-a^{2} x^{2}+1}}{5}+\frac{c^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{15 a}+\frac{2 c^{2} \sqrt{-a^{2} x^{2}+1}}{15 a^{3}}+\frac{c^{2} x^{3} \sqrt{-a^{2} x^{2}+1}}{4}-\frac{c^{2} x \sqrt{-a^{2} x^{2}+1}}{8 a^{2}}+\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a^{2} \sqrt{a^{2}}}"," ",0,"-1/5*c^2*a*x^4*(-a^2*x^2+1)^(1/2)+1/15*c^2/a*x^2*(-a^2*x^2+1)^(1/2)+2/15*c^2/a^3*(-a^2*x^2+1)^(1/2)+1/4*c^2*x^3*(-a^2*x^2+1)^(1/2)-1/8*c^2*x*(-a^2*x^2+1)^(1/2)/a^2+1/8*c^2/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
297,1,117,60,0.037000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^2,x)","-\frac{c^{2} a \,x^{3} \sqrt{-a^{2} x^{2}+1}}{4}+\frac{c^{2} x \sqrt{-a^{2} x^{2}+1}}{8 a}-\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a \sqrt{a^{2}}}+\frac{c^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{3}-\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{3 a^{2}}"," ",0,"-1/4*c^2*a*x^3*(-a^2*x^2+1)^(1/2)+1/8*c^2*x*(-a^2*x^2+1)^(1/2)/a-1/8*c^2/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/3*c^2*x^2*(-a^2*x^2+1)^(1/2)-1/3*c^2/a^2*(-a^2*x^2+1)^(1/2)","A"
298,1,91,51,0.034000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2,x)","-\frac{c^{2} a \,x^{2} \sqrt{-a^{2} x^{2}+1}}{3}+\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{3 a}+\frac{c^{2} x \sqrt{-a^{2} x^{2}+1}}{2}+\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}"," ",0,"-1/3*c^2*a*x^2*(-a^2*x^2+1)^(1/2)+1/3*c^2*(-a^2*x^2+1)^(1/2)/a+1/2*c^2*x*(-a^2*x^2+1)^(1/2)+1/2*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
299,1,86,51,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x,x)","-\frac{c^{2} a x \sqrt{-a^{2} x^{2}+1}}{2}-\frac{c^{2} a \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}+c^{2} \sqrt{-a^{2} x^{2}+1}-c^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*c^2*a*x*(-a^2*x^2+1)^(1/2)-1/2*c^2*a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+c^2*(-a^2*x^2+1)^(1/2)-c^2*arctanh(1/(-a^2*x^2+1)^(1/2))","A"
300,1,91,54,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^2,x)","-c^{2} a \sqrt{-a^{2} x^{2}+1}-\frac{c^{2} a^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+c^{2} a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{x}"," ",0,"-c^2*a*(-a^2*x^2+1)^(1/2)-c^2*a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+c^2*a*arctanh(1/(-a^2*x^2+1)^(1/2))-c^2/x*(-a^2*x^2+1)^(1/2)","A"
301,1,95,59,0.040000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^3,x)","\frac{c^{2} a^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{c^{2} a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{c^{2} a \sqrt{-a^{2} x^{2}+1}}{x}-\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{2 x^{2}}"," ",0,"c^2*a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/2*c^2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))+c^2*a/x*(-a^2*x^2+1)^(1/2)-1/2*c^2/x^2*(-a^2*x^2+1)^(1/2)","A"
302,1,100,63,0.040000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^4,x)","c^{2} \left(-a^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}-\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}-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)\right)"," ",0,"c^2*(-a^3*arctanh(1/(-a^2*x^2+1)^(1/2))+1/3*a^2*(-a^2*x^2+1)^(1/2)/x-1/3*(-a^2*x^2+1)^(1/2)/x^3-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"
303,1,125,86,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^5,x)","c^{2} \left(-\frac{a^{3} \sqrt{-a^{2} x^{2}+1}}{x}-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{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}-\frac{\sqrt{-a^{2} x^{2}+1}}{4 x^{4}}\right)"," ",0,"c^2*(-a^3*(-a^2*x^2+1)^(1/2)/x-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*(-1/2*(-a^2*x^2+1)^(1/2)/x^2-1/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2)))-1/4*(-a^2*x^2+1)^(1/2)/x^4)","A"
304,1,168,109,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^6,x)","c^{2} \left(-\frac{a^{2} \left(-\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}-\frac{2 a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}\right)}{5}+a^{3} \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)-a \left(-\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}\right)-\frac{\sqrt{-a^{2} x^{2}+1}}{5 x^{5}}\right)"," ",0,"c^2*(-1/5*a^2*(-1/3*(-a^2*x^2+1)^(1/2)/x^3-2/3*a^2*(-a^2*x^2+1)^(1/2)/x)+a^3*(-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*(-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))))-1/5/x^5*(-a^2*x^2+1)^(1/2))","A"
305,1,193,132,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^7,x)","c^{2} \left(a^{3} \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{a^{2} \left(-\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}\right)}{6}-\frac{\sqrt{-a^{2} x^{2}+1}}{6 x^{6}}-a \left(-\frac{\sqrt{-a^{2} x^{2}+1}}{5 x^{5}}+\frac{4 a^{2} \left(-\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}-\frac{2 a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}\right)}{5}\right)\right)"," ",0,"c^2*(a^3*(-1/3*(-a^2*x^2+1)^(1/2)/x^3-2/3*a^2*(-a^2*x^2+1)^(1/2)/x)-1/6*a^2*(-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))))-1/6/x^6*(-a^2*x^2+1)^(1/2)-a*(-1/5/x^5*(-a^2*x^2+1)^(1/2)+4/5*a^2*(-1/3*(-a^2*x^2+1)^(1/2)/x^3-2/3*a^2*(-a^2*x^2+1)^(1/2)/x)))","A"
306,1,186,126,0.052000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c)^3,x)","\frac{c^{3} a^{2} x^{6} \sqrt{-a^{2} x^{2}+1}}{7}+\frac{6 c^{3} x^{4} \sqrt{-a^{2} x^{2}+1}}{35}-\frac{11 c^{3} x^{2} \sqrt{-a^{2} x^{2}+1}}{105 a^{2}}-\frac{22 c^{3} \sqrt{-a^{2} x^{2}+1}}{105 a^{4}}-\frac{c^{3} a \,x^{5} \sqrt{-a^{2} x^{2}+1}}{3}+\frac{c^{3} x^{3} \sqrt{-a^{2} x^{2}+1}}{12 a}+\frac{c^{3} x \sqrt{-a^{2} x^{2}+1}}{8 a^{3}}-\frac{c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a^{3} \sqrt{a^{2}}}"," ",0,"1/7*c^3*a^2*x^6*(-a^2*x^2+1)^(1/2)+6/35*c^3*x^4*(-a^2*x^2+1)^(1/2)-11/105*c^3*x^2/a^2*(-a^2*x^2+1)^(1/2)-22/105*c^3/a^4*(-a^2*x^2+1)^(1/2)-1/3*c^3*a*x^5*(-a^2*x^2+1)^(1/2)+1/12*c^3/a*x^3*(-a^2*x^2+1)^(1/2)+1/8*c^3*x*(-a^2*x^2+1)^(1/2)/a^3-1/8*c^3/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
307,1,163,103,0.045000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c)^3,x)","\frac{c^{3} a^{2} x^{5} \sqrt{-a^{2} x^{2}+1}}{6}+\frac{5 c^{3} x^{3} \sqrt{-a^{2} x^{2}+1}}{24}-\frac{3 c^{3} x \sqrt{-a^{2} x^{2}+1}}{16 a^{2}}+\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a^{2} \sqrt{a^{2}}}-\frac{2 c^{3} a \,x^{4} \sqrt{-a^{2} x^{2}+1}}{5}+\frac{2 c^{3} x^{2} \sqrt{-a^{2} x^{2}+1}}{15 a}+\frac{4 c^{3} \sqrt{-a^{2} x^{2}+1}}{15 a^{3}}"," ",0,"1/6*c^3*a^2*x^5*(-a^2*x^2+1)^(1/2)+5/24*c^3*x^3*(-a^2*x^2+1)^(1/2)-3/16*c^3*x*(-a^2*x^2+1)^(1/2)/a^2+3/16*c^3/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-2/5*c^3*a*x^4*(-a^2*x^2+1)^(1/2)+2/15*c^3/a*x^2*(-a^2*x^2+1)^(1/2)+4/15*c^3/a^3*(-a^2*x^2+1)^(1/2)","A"
308,1,140,80,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^3,x)","\frac{c^{3} a^{2} x^{4} \sqrt{-a^{2} x^{2}+1}}{5}+\frac{4 c^{3} x^{2} \sqrt{-a^{2} x^{2}+1}}{15}-\frac{7 c^{3} \sqrt{-a^{2} x^{2}+1}}{15 a^{2}}-\frac{c^{3} a \,x^{3} \sqrt{-a^{2} x^{2}+1}}{2}+\frac{c^{3} x \sqrt{-a^{2} x^{2}+1}}{4 a}-\frac{c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{4 a \sqrt{a^{2}}}"," ",0,"1/5*c^3*a^2*x^4*(-a^2*x^2+1)^(1/2)+4/15*c^3*x^2*(-a^2*x^2+1)^(1/2)-7/15*c^3/a^2*(-a^2*x^2+1)^(1/2)-1/2*c^3*a*x^3*(-a^2*x^2+1)^(1/2)+1/4*c^3*x*(-a^2*x^2+1)^(1/2)/a-1/4*c^3/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
309,1,114,77,0.037000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3,x)","\frac{c^{3} a^{2} x^{3} \sqrt{-a^{2} x^{2}+1}}{4}+\frac{3 c^{3} x \sqrt{-a^{2} x^{2}+1}}{8}+\frac{5 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}-\frac{2 c^{3} a \,x^{2} \sqrt{-a^{2} x^{2}+1}}{3}+\frac{2 c^{3} \sqrt{-a^{2} x^{2}+1}}{3 a}"," ",0,"1/4*c^3*a^2*x^3*(-a^2*x^2+1)^(1/2)+3/8*c^3*x*(-a^2*x^2+1)^(1/2)+5/8*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-2/3*c^3*a*x^2*(-a^2*x^2+1)^(1/2)+2/3*c^3*(-a^2*x^2+1)^(1/2)/a","A"
310,1,110,67,0.039000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x,x)","\frac{c^{3} a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}}{3}+\frac{2 c^{3} \sqrt{-a^{2} x^{2}+1}}{3}-c^{3} a x \sqrt{-a^{2} x^{2}+1}-\frac{c^{3} a \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-c^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"1/3*c^3*a^2*x^2*(-a^2*x^2+1)^(1/2)+2/3*c^3*(-a^2*x^2+1)^(1/2)-c^3*a*x*(-a^2*x^2+1)^(1/2)-c^3*a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-c^3*arctanh(1/(-a^2*x^2+1)^(1/2))","A"
311,1,113,73,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^2,x)","\frac{c^{3} a^{2} x \sqrt{-a^{2} x^{2}+1}}{2}-\frac{c^{3} a^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}-2 c^{3} a \sqrt{-a^{2} x^{2}+1}+2 c^{3} a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{c^{3} \sqrt{-a^{2} x^{2}+1}}{x}"," ",0,"1/2*c^3*a^2*x*(-a^2*x^2+1)^(1/2)-1/2*c^3*a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-2*c^3*a*(-a^2*x^2+1)^(1/2)+2*c^3*a*arctanh(1/(-a^2*x^2+1)^(1/2))-c^3/x*(-a^2*x^2+1)^(1/2)","A"
312,1,116,80,0.040000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^3,x)","c^{3} a^{2} \sqrt{-a^{2} x^{2}+1}+\frac{2 c^{3} a^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{2 c^{3} a \sqrt{-a^{2} x^{2}+1}}{x}-\frac{c^{3} \sqrt{-a^{2} x^{2}+1}}{2 x^{2}}-\frac{c^{3} a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}"," ",0,"c^3*a^2*(-a^2*x^2+1)^(1/2)+2*c^3*a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+2*c^3*a/x*(-a^2*x^2+1)^(1/2)-1/2*c^3/x^2*(-a^2*x^2+1)^(1/2)-1/2*c^3*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))","A"
313,1,119,80,0.041000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^4,x)","-\frac{c^{3} a^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-c^{3} a^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{c^{3} \sqrt{-a^{2} x^{2}+1}}{3 x^{3}}-\frac{2 c^{3} a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}+\frac{c^{3} a \sqrt{-a^{2} x^{2}+1}}{x^{2}}"," ",0,"-c^3*a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-c^3*a^3*arctanh(1/(-a^2*x^2+1)^(1/2))-1/3*c^3/x^3*(-a^2*x^2+1)^(1/2)-2/3*c^3*a^2/x*(-a^2*x^2+1)^(1/2)+c^3*a/x^2*(-a^2*x^2+1)^(1/2)","A"
314,1,144,86,0.042000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^5,x)","-c^{3} \left(-a^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{2 a^{3} \sqrt{-a^{2} x^{2}+1}}{x}+2 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}\right)"," ",0,"-c^3*(-a^4*arctanh(1/(-a^2*x^2+1)^(1/2))+2*a^3*(-a^2*x^2+1)^(1/2)/x+2*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"
315,1,190,109,0.042000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^6,x)","-c^{3} \left(-\frac{a^{4} \sqrt{-a^{2} x^{2}+1}}{x}-2 a^{3} \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)+2 a \left(-\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}\right)+\frac{\sqrt{-a^{2} x^{2}+1}}{5 x^{5}}-\frac{4 a^{2} \left(-\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}-\frac{2 a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}\right)}{5}\right)"," ",0,"-c^3*(-a^4/x*(-a^2*x^2+1)^(1/2)-2*a^3*(-1/2*(-a^2*x^2+1)^(1/2)/x^2-1/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2)))+2*a*(-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))))+1/5/x^5*(-a^2*x^2+1)^(1/2)-4/5*a^2*(-1/3*(-a^2*x^2+1)^(1/2)/x^3-2/3*a^2*(-a^2*x^2+1)^(1/2)/x))","A"
316,1,209,147,0.071000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c)^4,x)","-\frac{c^{4} a^{3} x^{7} \sqrt{-a^{2} x^{2}+1}}{8}-\frac{23 c^{4} a \,x^{5} \sqrt{-a^{2} x^{2}+1}}{48}+\frac{29 c^{4} x^{3} \sqrt{-a^{2} x^{2}+1}}{192 a}+\frac{29 c^{4} x \sqrt{-a^{2} x^{2}+1}}{128 a^{3}}-\frac{29 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{128 a^{3} \sqrt{a^{2}}}+\frac{3 c^{4} a^{2} x^{6} \sqrt{-a^{2} x^{2}+1}}{7}+\frac{4 c^{4} x^{4} \sqrt{-a^{2} x^{2}+1}}{35}-\frac{19 c^{4} x^{2} \sqrt{-a^{2} x^{2}+1}}{105 a^{2}}-\frac{38 c^{4} \sqrt{-a^{2} x^{2}+1}}{105 a^{4}}"," ",0,"-1/8*c^4*a^3*x^7*(-a^2*x^2+1)^(1/2)-23/48*c^4*a*x^5*(-a^2*x^2+1)^(1/2)+29/192*c^4/a*x^3*(-a^2*x^2+1)^(1/2)+29/128*c^4*x*(-a^2*x^2+1)^(1/2)/a^3-29/128*c^4/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+3/7*c^4*a^2*x^6*(-a^2*x^2+1)^(1/2)+4/35*c^4*x^4*(-a^2*x^2+1)^(1/2)-19/105*c^4*x^2/a^2*(-a^2*x^2+1)^(1/2)-38/105*c^4/a^4*(-a^2*x^2+1)^(1/2)","A"
317,1,186,124,0.056000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c)^4,x)","-\frac{c^{4} a^{3} x^{6} \sqrt{-a^{2} x^{2}+1}}{7}-\frac{4 c^{4} a \,x^{4} \sqrt{-a^{2} x^{2}+1}}{7}+\frac{5 c^{4} x^{2} \sqrt{-a^{2} x^{2}+1}}{21 a}+\frac{10 c^{4} \sqrt{-a^{2} x^{2}+1}}{21 a^{3}}+\frac{c^{4} a^{2} x^{5} \sqrt{-a^{2} x^{2}+1}}{2}+\frac{c^{4} x^{3} \sqrt{-a^{2} x^{2}+1}}{8}-\frac{5 c^{4} x \sqrt{-a^{2} x^{2}+1}}{16 a^{2}}+\frac{5 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a^{2} \sqrt{a^{2}}}"," ",0,"-1/7*c^4*a^3*x^6*(-a^2*x^2+1)^(1/2)-4/7*c^4*a*x^4*(-a^2*x^2+1)^(1/2)+5/21*c^4/a*x^2*(-a^2*x^2+1)^(1/2)+10/21*c^4/a^3*(-a^2*x^2+1)^(1/2)+1/2*c^4*a^2*x^5*(-a^2*x^2+1)^(1/2)+1/8*c^4*x^3*(-a^2*x^2+1)^(1/2)-5/16*c^4*x*(-a^2*x^2+1)^(1/2)/a^2+5/16*c^4/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
318,1,163,136,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^4,x)","-\frac{c^{4} a^{3} x^{5} \sqrt{-a^{2} x^{2}+1}}{6}-\frac{17 c^{4} a \,x^{3} \sqrt{-a^{2} x^{2}+1}}{24}+\frac{7 c^{4} x \sqrt{-a^{2} x^{2}+1}}{16 a}-\frac{7 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a \sqrt{a^{2}}}+\frac{3 c^{4} a^{2} x^{4} \sqrt{-a^{2} x^{2}+1}}{5}+\frac{2 c^{4} x^{2} \sqrt{-a^{2} x^{2}+1}}{15}-\frac{11 c^{4} \sqrt{-a^{2} x^{2}+1}}{15 a^{2}}"," ",0,"-1/6*c^4*a^3*x^5*(-a^2*x^2+1)^(1/2)-17/24*c^4*a*x^3*(-a^2*x^2+1)^(1/2)+7/16*c^4*x*(-a^2*x^2+1)^(1/2)/a-7/16*c^4/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+3/5*c^4*a^2*x^4*(-a^2*x^2+1)^(1/2)+2/15*c^4*x^2*(-a^2*x^2+1)^(1/2)-11/15*c^4/a^2*(-a^2*x^2+1)^(1/2)","A"
319,1,137,105,0.042000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4,x)","-\frac{c^{4} a^{3} x^{4} \sqrt{-a^{2} x^{2}+1}}{5}-\frac{14 c^{4} a \,x^{2} \sqrt{-a^{2} x^{2}+1}}{15}+\frac{17 c^{4} \sqrt{-a^{2} x^{2}+1}}{15 a}+\frac{3 c^{4} a^{2} x^{3} \sqrt{-a^{2} x^{2}+1}}{4}+\frac{c^{4} x \sqrt{-a^{2} x^{2}+1}}{8}+\frac{7 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}"," ",0,"-1/5*c^4*a^3*x^4*(-a^2*x^2+1)^(1/2)-14/15*c^4*a*x^2*(-a^2*x^2+1)^(1/2)+17/15*c^4*(-a^2*x^2+1)^(1/2)/a+3/4*c^4*a^2*x^3*(-a^2*x^2+1)^(1/2)+1/8*c^4*x*(-a^2*x^2+1)^(1/2)+7/8*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
320,1,115,87,0.040000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x,x)","-\frac{c^{4} a^{3} x^{3} \sqrt{-a^{2} x^{2}+1}}{4}-\frac{11 c^{4} a x \sqrt{-a^{2} x^{2}+1}}{8}-\frac{13 c^{4} a \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}+c^{4} a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}-c^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/4*c^4*a^3*x^3*(-a^2*x^2+1)^(1/2)-11/8*c^4*a*x*(-a^2*x^2+1)^(1/2)-13/8*c^4*a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+c^4*a^2*x^2*(-a^2*x^2+1)^(1/2)-c^4*arctanh(1/(-a^2*x^2+1)^(1/2))","A"
321,1,136,92,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^2,x)","-\frac{c^{4} a^{3} x^{2} \sqrt{-a^{2} x^{2}+1}}{3}-\frac{8 c^{4} a \sqrt{-a^{2} x^{2}+1}}{3}+\frac{3 c^{4} a^{2} x \sqrt{-a^{2} x^{2}+1}}{2}+\frac{c^{4} a^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}+3 c^{4} a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{c^{4} \sqrt{-a^{2} x^{2}+1}}{x}"," ",0,"-1/3*c^4*a^3*x^2*(-a^2*x^2+1)^(1/2)-8/3*c^4*a*(-a^2*x^2+1)^(1/2)+3/2*c^4*a^2*x*(-a^2*x^2+1)^(1/2)+1/2*c^4*a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+3*c^4*a*arctanh(1/(-a^2*x^2+1)^(1/2))-c^4/x*(-a^2*x^2+1)^(1/2)","A"
322,1,138,100,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^3,x)","-\frac{c^{4} a^{3} x \sqrt{-a^{2} x^{2}+1}}{2}+\frac{5 c^{4} a^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}+3 c^{4} a^{2} \sqrt{-a^{2} x^{2}+1}-\frac{5 c^{4} a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{3 c^{4} a \sqrt{-a^{2} x^{2}+1}}{x}-\frac{c^{4} \sqrt{-a^{2} x^{2}+1}}{2 x^{2}}"," ",0,"-1/2*c^4*a^3*x*(-a^2*x^2+1)^(1/2)+5/2*c^4*a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+3*c^4*a^2*(-a^2*x^2+1)^(1/2)-5/2*c^4*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))+3*c^4*a/x*(-a^2*x^2+1)^(1/2)-1/2*c^4/x^2*(-a^2*x^2+1)^(1/2)","A"
323,1,140,104,0.042000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^4,x)","-c^{4} a^{3} \sqrt{-a^{2} x^{2}+1}-\frac{3 c^{4} a^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{c^{4} a^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{8 c^{4} a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}-\frac{c^{4} \sqrt{-a^{2} x^{2}+1}}{3 x^{3}}+\frac{3 c^{4} a \sqrt{-a^{2} x^{2}+1}}{2 x^{2}}"," ",0,"-c^4*a^3*(-a^2*x^2+1)^(1/2)-3*c^4*a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/2*c^4*a^3*arctanh(1/(-a^2*x^2+1)^(1/2))-8/3*c^4*a^2/x*(-a^2*x^2+1)^(1/2)-1/3*c^4/x^3*(-a^2*x^2+1)^(1/2)+3/2*c^4*a/x^2*(-a^2*x^2+1)^(1/2)","A"
324,1,118,96,0.044000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^5,x)","\frac{c^{4} a^{5} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{13 c^{4} a^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8}+\frac{a \,c^{4} \sqrt{-a^{2} x^{2}+1}}{x^{3}}-\frac{11 a^{2} c^{4} \sqrt{-a^{2} x^{2}+1}}{8 x^{2}}-\frac{c^{4} \sqrt{-a^{2} x^{2}+1}}{4 x^{4}}"," ",0,"c^4*a^5/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+13/8*c^4*a^4*arctanh(1/(-a^2*x^2+1)^(1/2))+a*c^4*(-a^2*x^2+1)^(1/2)/x^3-11/8*a^2*c^4*(-a^2*x^2+1)^(1/2)/x^2-1/4*c^4*(-a^2*x^2+1)^(1/2)/x^4","A"
325,1,207,109,0.045000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^6,x)","c^{4} \left(-a^{5} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{3 a^{4} \sqrt{-a^{2} x^{2}+1}}{x}+\frac{14 a^{2} \left(-\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}-\frac{2 a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}\right)}{5}+2 a^{3} \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)-3 a \left(-\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}\right)-\frac{\sqrt{-a^{2} x^{2}+1}}{5 x^{5}}\right)"," ",0,"c^4*(-a^5*arctanh(1/(-a^2*x^2+1)^(1/2))+3*a^4/x*(-a^2*x^2+1)^(1/2)+14/5*a^2*(-1/3*(-a^2*x^2+1)^(1/2)/x^3-2/3*a^2*(-a^2*x^2+1)^(1/2)/x)+2*a^3*(-1/2*(-a^2*x^2+1)^(1/2)/x^2-1/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2)))-3*a*(-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))))-1/5/x^5*(-a^2*x^2+1)^(1/2))","A"
326,1,255,132,0.048000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^7,x)","c^{4} \left(-\frac{a^{5} \sqrt{-a^{2} x^{2}+1}}{x}+2 a^{3} \left(-\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}-\frac{2 a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}\right)-3 a^{4} \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)+\frac{17 a^{2} \left(-\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}\right)}{6}-3 a \left(-\frac{\sqrt{-a^{2} x^{2}+1}}{5 x^{5}}+\frac{4 a^{2} \left(-\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}-\frac{2 a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}\right)}{5}\right)-\frac{\sqrt{-a^{2} x^{2}+1}}{6 x^{6}}\right)"," ",0,"c^4*(-a^5*(-a^2*x^2+1)^(1/2)/x+2*a^3*(-1/3*(-a^2*x^2+1)^(1/2)/x^3-2/3*a^2*(-a^2*x^2+1)^(1/2)/x)-3*a^4*(-1/2*(-a^2*x^2+1)^(1/2)/x^2-1/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2)))+17/6*a^2*(-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))))-3*a*(-1/5/x^5*(-a^2*x^2+1)^(1/2)+4/5*a^2*(-1/3*(-a^2*x^2+1)^(1/2)/x^3-2/3*a^2*(-a^2*x^2+1)^(1/2)/x))-1/6/x^6*(-a^2*x^2+1)^(1/2))","A"
327,1,166,126,0.048000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c),x)","\frac{x^{3} \sqrt{-a^{2} x^{2}+1}}{4 a^{2} c}+\frac{11 x \sqrt{-a^{2} x^{2}+1}}{8 a^{4} c}-\frac{27 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 c \,a^{4} \sqrt{a^{2}}}+\frac{2 x^{2} \sqrt{-a^{2} x^{2}+1}}{3 a^{3} c}+\frac{10 \sqrt{-a^{2} x^{2}+1}}{3 a^{5} c}-\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{c \,a^{6} \left(x -\frac{1}{a}\right)}"," ",0,"1/4*x^3*(-a^2*x^2+1)^(1/2)/a^2/c+11/8*x*(-a^2*x^2+1)^(1/2)/a^4/c-27/8/c/a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+2/3*x^2*(-a^2*x^2+1)^(1/2)/a^3/c+10/3*(-a^2*x^2+1)^(1/2)/a^5/c-2/c/a^6/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
328,1,142,102,0.040000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c),x)","\frac{x^{2} \sqrt{-a^{2} x^{2}+1}}{3 a^{2} c}+\frac{8 \sqrt{-a^{2} x^{2}+1}}{3 a^{4} c}+\frac{x \sqrt{-a^{2} x^{2}+1}}{a^{3} c}-\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c \,a^{3} \sqrt{a^{2}}}-\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{c \,a^{5} \left(x -\frac{1}{a}\right)}"," ",0,"1/3*x^2*(-a^2*x^2+1)^(1/2)/a^2/c+8/3*(-a^2*x^2+1)^(1/2)/a^4/c+x*(-a^2*x^2+1)^(1/2)/a^3/c-3/c/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-2/c/a^5/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
329,1,120,64,0.040000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c),x)","\frac{x \sqrt{-a^{2} x^{2}+1}}{2 c \,a^{2}}-\frac{5 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 c \,a^{2} \sqrt{a^{2}}}+\frac{2 \sqrt{-a^{2} x^{2}+1}}{a^{3} c}-\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{c \,a^{4} \left(x -\frac{1}{a}\right)}"," ",0,"1/2/c*x/a^2*(-a^2*x^2+1)^(1/2)-5/2/c/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+2*(-a^2*x^2+1)^(1/2)/a^3/c-2/c/a^4/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
330,1,98,60,0.036000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c),x)","\frac{\sqrt{-a^{2} x^{2}+1}}{a^{2} c}-\frac{2 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c a \sqrt{a^{2}}}-\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{c \,a^{3} \left(x -\frac{1}{a}\right)}"," ",0,"(-a^2*x^2+1)^(1/2)/a^2/c-2/c/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-2/c/a^3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
331,1,76,41,0.035000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c),x)","-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c \sqrt{a^{2}}}-\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{c \,a^{2} \left(x -\frac{1}{a}\right)}"," ",0,"-1/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-2/c/a^2/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
332,1,61,41,0.039000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c),x)","-\frac{\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{a \left(x -\frac{1}{a}\right)}}{c}"," ",0,"-1/c*(arctanh(1/(-a^2*x^2+1)^(1/2))+2/a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))","A"
333,1,77,63,0.039000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c),x)","-\frac{2 a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{\sqrt{-a^{2} x^{2}+1}}{x}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}}{c}"," ",0,"-1/c*(2*a*arctanh(1/(-a^2*x^2+1)^(1/2))+(-a^2*x^2+1)^(1/2)/x+2/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))","A"
334,1,99,88,0.042000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c),x)","-\frac{\frac{5 a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{2 a \sqrt{-a^{2} x^{2}+1}}{x}+\frac{2 a \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}+\frac{\sqrt{-a^{2} x^{2}+1}}{2 x^{2}}}{c}"," ",0,"-1/c*(5/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))+2*a*(-a^2*x^2+1)^(1/2)/x+2*a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/2*(-a^2*x^2+1)^(1/2)/x^2)","A"
335,1,142,111,0.045000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a*c*x+c),x)","-\frac{2 a^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{8 a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}+\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}+\frac{2 a^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}-2 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)}{c}"," ",0,"-1/c*(2*a^3*arctanh(1/(-a^2*x^2+1)^(1/2))+8/3*a^2*(-a^2*x^2+1)^(1/2)/x+1/3*(-a^2*x^2+1)^(1/2)/x^3+2*a^2/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2*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"
336,1,187,139,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c)^2,x)","-\frac{x^{2} \sqrt{-a^{2} x^{2}+1}}{3 c^{2} a^{3}}-\frac{17 \sqrt{-a^{2} x^{2}+1}}{3 a^{5} c^{2}}-\frac{3 x \sqrt{-a^{2} x^{2}+1}}{2 c^{2} a^{4}}+\frac{17 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 c^{2} a^{4} \sqrt{a^{2}}}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 c^{2} a^{7} \left(x -\frac{1}{a}\right)^{2}}+\frac{25 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 c^{2} a^{6} \left(x -\frac{1}{a}\right)}"," ",0,"-1/3/c^2/a^3*x^2*(-a^2*x^2+1)^(1/2)-17/3*(-a^2*x^2+1)^(1/2)/a^5/c^2-3/2/c^2/a^4*x*(-a^2*x^2+1)^(1/2)+17/2/c^2/a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+2/3/c^2/a^7/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+25/3/c^2/a^6/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
337,1,164,92,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c)^2,x)","-\frac{x \sqrt{-a^{2} x^{2}+1}}{2 c^{2} a^{3}}+\frac{11 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 c^{2} a^{3} \sqrt{a^{2}}}-\frac{3 \sqrt{-a^{2} x^{2}+1}}{c^{2} a^{4}}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 c^{2} a^{6} \left(x -\frac{1}{a}\right)^{2}}+\frac{19 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 c^{2} a^{5} \left(x -\frac{1}{a}\right)}"," ",0,"-1/2/c^2/a^3*x*(-a^2*x^2+1)^(1/2)+11/2/c^2/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-3/c^2/a^4*(-a^2*x^2+1)^(1/2)+2/3/c^2/a^6/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+19/3/c^2/a^5/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
338,1,143,96,0.045000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c)^2,x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{c^{2} a^{3}}+\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{2} a^{2} \sqrt{a^{2}}}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 c^{2} a^{5} \left(x -\frac{1}{a}\right)^{2}}+\frac{13 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 c^{2} a^{4} \left(x -\frac{1}{a}\right)}"," ",0,"-1/c^2/a^3*(-a^2*x^2+1)^(1/2)+3/c^2/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+2/3/c^2/a^5/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+13/3/c^2/a^4/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
339,1,122,68,0.041000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c)^2,x)","\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{2} a \sqrt{a^{2}}}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 c^{2} a^{4} \left(x -\frac{1}{a}\right)^{2}}+\frac{7 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 c^{2} a^{3} \left(x -\frac{1}{a}\right)}"," ",0,"1/c^2/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+2/3/c^2/a^4/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+7/3/c^2/a^3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
340,1,35,28,0.029000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^2,x)","-\frac{\left(a x +1\right)^{2}}{3 \left(a x -1\right) c^{2} \sqrt{-a^{2} x^{2}+1}\, a}"," ",0,"-1/3*(a*x+1)^2/(a*x-1)/c^2/(-a^2*x^2+1)^(1/2)/a","A"
341,1,147,64,0.039000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c)^2,x)","\frac{-\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}}{a}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{a \left(x -\frac{1}{a}\right)}}{c^{2}}"," ",0,"1/c^2*(-arctanh(1/(-a^2*x^2+1)^(1/2))+2/a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-1/a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))","B"
342,1,118,87,0.044000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c)^2,x)","\frac{-3 a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\sqrt{-a^{2} x^{2}+1}}{x}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{11 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}}{c^{2}}"," ",0,"1/c^2*(-3*a*arctanh(1/(-a^2*x^2+1)^(1/2))-(-a^2*x^2+1)^(1/2)/x+2/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-11/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))","A"
343,1,181,114,0.044000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c)^2,x)","\frac{-\frac{11 a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{3 a \sqrt{-a^{2} x^{2}+1}}{x}+2 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)-\frac{5 a \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}-\frac{\sqrt{-a^{2} x^{2}+1}}{2 x^{2}}}{c^{2}}"," ",0,"1/c^2*(-11/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))-3*a*(-a^2*x^2+1)^(1/2)/x+2*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-5*a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/2*(-a^2*x^2+1)^(1/2)/x^2)","A"
344,1,226,137,0.046000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a*c*x+c)^2,x)","\frac{-7 a^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{17 a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}+2 a^{2} \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)-\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}-\frac{7 a^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}+3 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)}{c^{2}}"," ",0,"1/c^2*(-7*a^3*arctanh(1/(-a^2*x^2+1)^(1/2))-17/3*a^2*(-a^2*x^2+1)^(1/2)/x+2*a^2*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-1/3*(-a^2*x^2+1)^(1/2)/x^3-7*a^2/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+3*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"
345,1,208,119,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c)^3,x)","\frac{x \sqrt{-a^{2} x^{2}+1}}{2 c^{3} a^{4}}-\frac{19 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 c^{3} a^{4} \sqrt{a^{2}}}+\frac{4 \sqrt{-a^{2} x^{2}+1}}{c^{3} a^{5}}-\frac{41 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{15 c^{3} a^{7} \left(x -\frac{1}{a}\right)^{2}}-\frac{199 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{15 c^{3} a^{6} \left(x -\frac{1}{a}\right)}-\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 c^{3} a^{8} \left(x -\frac{1}{a}\right)^{3}}"," ",0,"1/2/c^3/a^4*x*(-a^2*x^2+1)^(1/2)-19/2/c^3/a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+4/c^3/a^5*(-a^2*x^2+1)^(1/2)-41/15/c^3/a^7/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-199/15/c^3/a^6/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5/c^3/a^8/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
346,1,186,125,0.047000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c)^3,x)","\frac{\sqrt{-a^{2} x^{2}+1}}{c^{3} a^{4}}-\frac{4 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{3} a^{3} \sqrt{a^{2}}}-\frac{31 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{15 c^{3} a^{6} \left(x -\frac{1}{a}\right)^{2}}-\frac{104 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{15 c^{3} a^{5} \left(x -\frac{1}{a}\right)}-\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 c^{3} a^{7} \left(x -\frac{1}{a}\right)^{3}}"," ",0,"1/c^3/a^4*(-a^2*x^2+1)^(1/2)-4/c^3/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-31/15/c^3/a^6/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-104/15/c^3/a^5/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5/c^3/a^7/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
347,1,167,97,0.046000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c)^3,x)","-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{3} a^{2} \sqrt{a^{2}}}-\frac{7 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 c^{3} a^{5} \left(x -\frac{1}{a}\right)^{2}}-\frac{13 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 c^{3} a^{4} \left(x -\frac{1}{a}\right)}-\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 c^{3} a^{6} \left(x -\frac{1}{a}\right)^{3}}"," ",0,"-1/c^3/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-7/5/c^3/a^5/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-13/5/c^3/a^4/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5/c^3/a^6/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
348,1,41,57,0.028000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c)^3,x)","\frac{\left(4 a x -1\right) \left(a x +1\right)^{2}}{15 \left(a x -1\right)^{2} c^{3} \sqrt{-a^{2} x^{2}+1}\, a^{2}}"," ",0,"1/15*(4*a*x-1)*(a*x+1)^2/(a*x-1)^2/c^3/(-a^2*x^2+1)^(1/2)/a^2","A"
349,1,40,57,0.028000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^3,x)","-\frac{\left(a x -4\right) \left(a x +1\right)^{2}}{15 \left(a x -1\right)^{2} c^{3} \sqrt{-a^{2} x^{2}+1}\, a}"," ",0,"-1/15*(a*x-4)*(a*x+1)^2/(a*x-1)^2/c^3/(-a^2*x^2+1)^(1/2)/a","A"
350,1,275,83,0.041000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c)^3,x)","-\frac{\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}}{a}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{a \left(x -\frac{1}{a}\right)}+\frac{\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a \left(x -\frac{1}{a}\right)^{3}}-\frac{4 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{5}}{a^{2}}}{c^{3}}"," ",0,"-1/c^3*(arctanh(1/(-a^2*x^2+1)^(1/2))-1/a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+1/a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+2/a^2*(1/5/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))))","B"
351,1,248,111,0.046000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c)^3,x)","-\frac{4 a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{\sqrt{-a^{2} x^{2}+1}}{x}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{a \left(x -\frac{1}{a}\right)^{2}}+\frac{5 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}+\frac{\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a \left(x -\frac{1}{a}\right)^{3}}-\frac{4 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{5}}{a}}{c^{3}}"," ",0,"-1/c^3*(4*a*arctanh(1/(-a^2*x^2+1)^(1/2))+(-a^2*x^2+1)^(1/2)/x-1/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+5/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+2/a*(1/5/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))))","B"
352,1,223,140,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c)^3,x)","-\frac{\frac{19 a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{4 a \sqrt{-a^{2} x^{2}+1}}{x}-\frac{29 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{5}+\frac{9 a \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}+\frac{\sqrt{-a^{2} x^{2}+1}}{2 x^{2}}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a \left(x -\frac{1}{a}\right)^{3}}}{c^{3}}"," ",0,"-1/c^3*(19/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))+4*a*(-a^2*x^2+1)^(1/2)/x-29/5*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+9*a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/2*(-a^2*x^2+1)^(1/2)/x^2+2/5/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))","A"
353,1,355,163,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a*c*x+c)^3,x)","-\frac{16 a^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{29 a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}-7 a^{2} \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)+\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}+\frac{16 a^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}-4 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)+2 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a \left(x -\frac{1}{a}\right)^{3}}-\frac{2 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{5}\right)}{c^{3}}"," ",0,"-1/c^3*(16*a^3*arctanh(1/(-a^2*x^2+1)^(1/2))+29/3*a^2*(-a^2*x^2+1)^(1/2)/x-7*a^2*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+1/3*(-a^2*x^2+1)^(1/2)/x^3+16*a^2/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-4*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)))+2*a*(1/5/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))))","B"
354,1,252,146,0.053000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a*c*x+c)^4,x)","-\frac{x \sqrt{-a^{2} x^{2}+1}}{2 c^{4} a^{5}}+\frac{29 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 c^{4} a^{5} \sqrt{a^{2}}}-\frac{5 \sqrt{-a^{2} x^{2}+1}}{c^{4} a^{6}}+\frac{733 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{105 c^{4} a^{8} \left(x -\frac{1}{a}\right)^{2}}+\frac{2417 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{105 c^{4} a^{7} \left(x -\frac{1}{a}\right)}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{7 c^{4} a^{10} \left(x -\frac{1}{a}\right)^{4}}+\frac{71 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{35 c^{4} a^{9} \left(x -\frac{1}{a}\right)^{3}}"," ",0,"-1/2/c^4/a^5*x*(-a^2*x^2+1)^(1/2)+29/2/c^4/a^5/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-5/c^4/a^6*(-a^2*x^2+1)^(1/2)+733/105/c^4/a^8/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+2417/105/c^4/a^7/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+2/7/c^4/a^10/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+71/35/c^4/a^9/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
355,1,231,152,0.053000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c)^4,x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{c^{4} a^{5}}+\frac{5 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{4} a^{4} \sqrt{a^{2}}}+\frac{446 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{105 c^{4} a^{7} \left(x -\frac{1}{a}\right)^{2}}+\frac{1024 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{105 c^{4} a^{6} \left(x -\frac{1}{a}\right)}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{7 c^{4} a^{9} \left(x -\frac{1}{a}\right)^{4}}+\frac{57 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{35 c^{4} a^{8} \left(x -\frac{1}{a}\right)^{3}}"," ",0,"-1/c^4/a^5*(-a^2*x^2+1)^(1/2)+5/c^4/a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+446/105/c^4/a^7/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1024/105/c^4/a^6/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+2/7/c^4/a^9/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+57/35/c^4/a^8/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
356,1,210,124,0.046000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c)^4,x)","\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{4} a^{3} \sqrt{a^{2}}}+\frac{229 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{105 c^{4} a^{6} \left(x -\frac{1}{a}\right)^{2}}+\frac{296 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{105 c^{4} a^{5} \left(x -\frac{1}{a}\right)}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{7 c^{4} a^{8} \left(x -\frac{1}{a}\right)^{4}}+\frac{43 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{35 c^{4} a^{7} \left(x -\frac{1}{a}\right)^{3}}"," ",0,"1/c^4/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+229/105/c^4/a^6/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+296/105/c^4/a^5/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+2/7/c^4/a^8/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+43/35/c^4/a^7/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
357,1,49,85,0.032000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c)^4,x)","-\frac{\left(23 a^{2} x^{2}-10 a x +2\right) \left(a x +1\right)^{2}}{105 \left(a x -1\right)^{3} c^{4} \sqrt{-a^{2} x^{2}+1}\, a^{3}}"," ",0,"-1/105*(23*a^2*x^2-10*a*x+2)*(a*x+1)^2/(a*x-1)^3/c^4/(-a^2*x^2+1)^(1/2)/a^3","A"
358,1,48,85,0.030000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c)^4,x)","\frac{\left(a^{2} x^{2}-5 a x +1\right) \left(a x +1\right)^{2}}{21 \left(a x -1\right)^{3} c^{4} \sqrt{-a^{2} x^{2}+1}\, a^{2}}"," ",0,"1/21*(a^2*x^2-5*a*x+1)*(a*x+1)^2/(a*x-1)^3/c^4/(-a^2*x^2+1)^(1/2)/a^2","A"
359,1,49,85,0.030000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^4,x)","-\frac{\left(2 a^{2} x^{2}-10 a x +23\right) \left(a x +1\right)^{2}}{105 \left(a x -1\right)^{3} c^{4} \sqrt{-a^{2} x^{2}+1}\, a}"," ",0,"-1/105*(2*a^2*x^2-10*a*x+23)*(a*x+1)^2/(a*x-1)^3/c^4/(-a^2*x^2+1)^(1/2)/a","A"
360,1,451,110,0.047000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c)^4,x)","\frac{-\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}}{a}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{a \left(x -\frac{1}{a}\right)}+\frac{\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{7 a \left(x -\frac{1}{a}\right)^{4}}-\frac{6 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a \left(x -\frac{1}{a}\right)^{3}}-\frac{2 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{5}\right)}{7}}{a^{3}}-\frac{\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a \left(x -\frac{1}{a}\right)^{3}}-\frac{2 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{5}}{a^{2}}}{c^{4}}"," ",0,"1/c^4*(-arctanh(1/(-a^2*x^2+1)^(1/2))+1/a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-1/a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+2/a^3*(1/7/a/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-3/7*a*(1/5/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))))-1/a^2*(1/5/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))))","B"
361,1,423,135,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c)^4,x)","\frac{-5 a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\sqrt{-a^{2} x^{2}+1}}{x}+\frac{4 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{19 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}+\frac{\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{7 a \left(x -\frac{1}{a}\right)^{4}}-\frac{6 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a \left(x -\frac{1}{a}\right)^{3}}-\frac{2 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{5}\right)}{7}}{a^{2}}-\frac{3 \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a \left(x -\frac{1}{a}\right)^{3}}-\frac{2 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{5}\right)}{a}}{c^{4}}"," ",0,"1/c^4*(-5*a*arctanh(1/(-a^2*x^2+1)^(1/2))-(-a^2*x^2+1)^(1/2)/x+4/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-19/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+2/a^2*(1/7/a/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-3/7*a*(1/5/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))))-3/a*(1/5/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))))","B"
362,1,397,166,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c)^4,x)","\frac{-\frac{29 a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{5 a \sqrt{-a^{2} x^{2}+1}}{x}+11 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)-\frac{14 a \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}-\frac{\sqrt{-a^{2} x^{2}+1}}{2 x^{2}}+\frac{\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{7 a \left(x -\frac{1}{a}\right)^{4}}-\frac{6 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a \left(x -\frac{1}{a}\right)^{3}}-\frac{2 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{5}\right)}{7}}{a}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{a \left(x -\frac{1}{a}\right)^{3}}}{c^{4}}"," ",0,"1/c^4*(-29/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))-5*a*(-a^2*x^2+1)^(1/2)/x+11*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-14*a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/2*(-a^2*x^2+1)^(1/2)/x^2+2/a*(1/7/a/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-3/7*a*(1/5/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))))-1/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))","B"
363,1,41,45,0.029000," ","int((1+x)^2/(-x^2+1)^(1/2)*x,x)","-\frac{x^{2} \sqrt{-x^{2}+1}}{3}-\frac{5 \sqrt{-x^{2}+1}}{3}-x \sqrt{-x^{2}+1}+\arcsin \left(x \right)"," ",0,"-1/3*x^2*(-x^2+1)^(1/2)-5/3*(-x^2+1)^(1/2)-x*(-x^2+1)^(1/2)+arcsin(x)","A"
364,1,29,33,0.027000," ","int((1+x)^2/(-x^2+1)^(1/2),x)","-\frac{x \sqrt{-x^{2}+1}}{2}+\frac{3 \arcsin \left(x \right)}{2}-2 \sqrt{-x^{2}+1}"," ",0,"-1/2*x*(-x^2+1)^(1/2)+3/2*arcsin(x)-2*(-x^2+1)^(1/2)","A"
365,1,57,61,0.032000," ","int((1+x)^3/(-x^2+1)^(1/2)*x,x)","-\frac{x^{3} \sqrt{-x^{2}+1}}{4}-\frac{15 x \sqrt{-x^{2}+1}}{8}+\frac{15 \arcsin \left(x \right)}{8}-x^{2} \sqrt{-x^{2}+1}-3 \sqrt{-x^{2}+1}"," ",0,"-1/4*x^3*(-x^2+1)^(1/2)-15/8*x*(-x^2+1)^(1/2)+15/8*arcsin(x)-x^2*(-x^2+1)^(1/2)-3*(-x^2+1)^(1/2)","A"
366,1,43,47,0.031000," ","int((1+x)^3/(-x^2+1)^(1/2),x)","-\frac{x^{2} \sqrt{-x^{2}+1}}{3}-\frac{11 \sqrt{-x^{2}+1}}{3}-\frac{3 x \sqrt{-x^{2}+1}}{2}+\frac{5 \arcsin \left(x \right)}{2}"," ",0,"-1/3*x^2*(-x^2+1)^(1/2)-11/3*(-x^2+1)^(1/2)-3/2*x*(-x^2+1)^(1/2)+5/2*arcsin(x)","A"
367,1,17,14,0.026000," ","int(1/(-x^2+1)^(1/2)*x,x)","\frac{\left(1+x \right) \left(-1+x \right)}{\sqrt{-x^{2}+1}}"," ",0,"(1+x)*(-1+x)/(-x^2+1)^(1/2)","A"
368,1,3,2,0.030000," ","int(1/(-x^2+1)^(1/2),x)","\arcsin \left(x \right)"," ",0,"arcsin(x)","A"
369,1,24,16,0.032000," ","int(1/(1+x)/(-x^2+1)^(1/2)*x,x)","\arcsin \left(x \right)+\frac{\sqrt{-\left(1+x \right)^{2}+2 x +2}}{1+x}"," ",0,"arcsin(x)+1/(1+x)*(-(1+x)^2+2*x+2)^(1/2)","A"
370,1,14,14,0.030000," ","int(1/(1+x)/(-x^2+1)^(1/2),x)","\frac{-1+x}{\sqrt{-x^{2}+1}}"," ",0,"(-1+x)/(-x^2+1)^(1/2)","A"
371,1,35,37,0.026000," ","int((1+x)^(5/2)/(-x^2+1)^(1/2)*x,x)","\frac{2 \left(-1+x \right) \left(3 x^{3}+12 x^{2}+23 x +46\right) \sqrt{1+x}}{21 \sqrt{-x^{2}+1}}"," ",0,"2/21*(-1+x)*(3*x^3+12*x^2+23*x+46)*(1+x)^(1/2)/(-x^2+1)^(1/2)","A"
372,1,30,28,0.028000," ","int((1+x)^(5/2)/(-x^2+1)^(1/2),x)","\frac{2 \left(-1+x \right) \left(3 x^{2}+14 x +43\right) \sqrt{1+x}}{15 \sqrt{-x^{2}+1}}"," ",0,"2/15*(-1+x)*(3*x^2+14*x+43)*(1+x)^(1/2)/(-x^2+1)^(1/2)","A"
373,1,34,22,0.026000," ","int((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2)*x,x)","-\frac{2 \left(1+x \right)^{2} \left(15 x^{2}-33 x +22\right) \sqrt{1-x}}{105 \sqrt{-x^{2}+1}}"," ",0,"-2/105*(1+x)^2*(15*x^2-33*x+22)*(1-x)^(1/2)/(-x^2+1)^(1/2)","A"
374,1,29,15,0.028000," ","int((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2),x)","-\frac{2 \left(1+x \right)^{2} \left(3 x -7\right) \sqrt{1-x}}{15 \sqrt{-x^{2}+1}}"," ",0,"-2/15*(1+x)^2*(3*x-7)*(1-x)^(1/2)/(-x^2+1)^(1/2)","A"
375,1,28,28,0.026000," ","int((1+x)^(3/2)/(-x^2+1)^(1/2)*x,x)","\frac{2 \left(-1+x \right) \left(x^{2}+3 x +6\right) \sqrt{1+x}}{5 \sqrt{-x^{2}+1}}"," ",0,"2/5*(-1+x)*(x^2+3*x+6)*(1+x)^(1/2)/(-x^2+1)^(1/2)","A"
376,1,23,19,0.026000," ","int((1+x)^(3/2)/(-x^2+1)^(1/2),x)","\frac{2 \left(-1+x \right) \left(x +5\right) \sqrt{1+x}}{3 \sqrt{-x^{2}+1}}"," ",0,"2/3*(-1+x)*(x+5)*(1+x)^(1/2)/(-x^2+1)^(1/2)","A"
377,1,29,15,0.027000," ","int((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2)*x,x)","\frac{2 \left(1+x \right)^{2} \left(3 x -2\right) \sqrt{1-x}}{15 \sqrt{-x^{2}+1}}"," ",0,"2/15*(1+x)^2*(3*x-2)*(1-x)^(1/2)/(-x^2+1)^(1/2)","A"
378,1,24,7,0.024000," ","int((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2),x)","\frac{2 \left(1+x \right)^{2} \sqrt{1-x}}{3 \sqrt{-x^{2}+1}}"," ",0,"2/3*(1+x)^2*(1-x)^(1/2)/(-x^2+1)^(1/2)","B"
379,1,23,19,0.028000," ","int((1+x)^(1/2)/(-x^2+1)^(1/2)*x,x)","\frac{2 \left(-1+x \right) \left(x +2\right) \sqrt{1+x}}{3 \sqrt{-x^{2}+1}}"," ",0,"2/3*(-1+x)*(x+2)*(1+x)^(1/2)/(-x^2+1)^(1/2)","A"
380,1,20,9,0.025000," ","int((1+x)^(1/2)/(-x^2+1)^(1/2),x)","\frac{2 \left(-1+x \right) \sqrt{1+x}}{\sqrt{-x^{2}+1}}"," ",0,"2*(-1+x)*(1+x)^(1/2)/(-x^2+1)^(1/2)","B"
381,1,61,31,0.035000," ","int((1+x)/(-x^2+1)^(1/2)*x/(1-x)^(1/2),x)","-\frac{2 \sqrt{-x^{2}+1}\, \sqrt{1-x}\, \left(3 \arctanh \left(\frac{\sqrt{1+x}\, \sqrt{2}}{2}\right) \sqrt{2}-\sqrt{1+x}\, x -4 \sqrt{1+x}\right)}{3 \left(-1+x \right) \sqrt{1+x}}"," ",0,"-2/3*(-x^2+1)^(1/2)*(1-x)^(1/2)*(3*arctanh(1/2*(1+x)^(1/2)*2^(1/2))*2^(1/2)-(1+x)^(1/2)*x-4*(1+x)^(1/2))/(-1+x)/(1+x)^(1/2)","A"
382,1,52,24,0.035000," ","int((1+x)/(-x^2+1)^(1/2)/(1-x)^(1/2),x)","-\frac{2 \sqrt{-x^{2}+1}\, \sqrt{1-x}\, \left(\arctanh \left(\frac{\sqrt{1+x}\, \sqrt{2}}{2}\right) \sqrt{2}-\sqrt{1+x}\right)}{\left(-1+x \right) \sqrt{1+x}}"," ",0,"-2*(-x^2+1)^(1/2)*(1-x)^(1/2)*(arctanh(1/2*(1+x)^(1/2)*2^(1/2))*2^(1/2)-(1+x)^(1/2))/(-1+x)/(1+x)^(1/2)","B"
383,1,50,27,0.034000," ","int(1/(1+x)^(1/2)/(-x^2+1)^(1/2)*x,x)","\frac{\sqrt{-x^{2}+1}\, \left(\arctanh \left(\frac{\sqrt{1-x}\, \sqrt{2}}{2}\right) \sqrt{2}-2 \sqrt{1-x}\right)}{\sqrt{1+x}\, \sqrt{1-x}}"," ",0,"(-x^2+1)^(1/2)*(arctanh(1/2*(1-x)^(1/2)*2^(1/2))*2^(1/2)-2*(1-x)^(1/2))/(1+x)^(1/2)/(1-x)^(1/2)","A"
384,1,40,18,0.033000," ","int(1/(1+x)^(1/2)/(-x^2+1)^(1/2),x)","-\frac{\sqrt{-x^{2}+1}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{1-x}\, \sqrt{2}}{2}\right)}{\sqrt{1+x}\, \sqrt{1-x}}"," ",0,"-1/(1+x)^(1/2)*(-x^2+1)^(1/2)/(1-x)^(1/2)*2^(1/2)*arctanh(1/2*(1-x)^(1/2)*2^(1/2))","B"
385,1,78,38,0.042000," ","int((1+x)/(-x^2+1)^(1/2)*x/(1-x)^(3/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{1-x}\, \left(5 \sqrt{2}\, \arctanh \left(\frac{\sqrt{1+x}\, \sqrt{2}}{2}\right) x -5 \arctanh \left(\frac{\sqrt{1+x}\, \sqrt{2}}{2}\right) \sqrt{2}-4 \sqrt{1+x}\, x +6 \sqrt{1+x}\right)}{2 \left(-1+x \right)^{2} \sqrt{1+x}}"," ",0,"1/2*(-x^2+1)^(1/2)*(1-x)^(1/2)*(5*2^(1/2)*arctanh(1/2*(1+x)^(1/2)*2^(1/2))*x-5*arctanh(1/2*(1+x)^(1/2)*2^(1/2))*2^(1/2)-4*(1+x)^(1/2)*x+6*(1+x)^(1/2))/(-1+x)^2/(1+x)^(1/2)","B"
386,1,69,30,0.044000," ","int((1+x)/(-x^2+1)^(1/2)/(1-x)^(3/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{1-x}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{1+x}\, \sqrt{2}}{2}\right) x -\arctanh \left(\frac{\sqrt{1+x}\, \sqrt{2}}{2}\right) \sqrt{2}+2 \sqrt{1+x}\right)}{2 \left(-1+x \right)^{2} \sqrt{1+x}}"," ",0,"1/2*(-x^2+1)^(1/2)*(1-x)^(1/2)*(2^(1/2)*arctanh(1/2*(1+x)^(1/2)*2^(1/2))*x-arctanh(1/2*(1+x)^(1/2)*2^(1/2))*2^(1/2)+2*(1+x)^(1/2))/(-1+x)^2/(1+x)^(1/2)","B"
387,0,0,56,0.325000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a*c*x+c)^(1/2),x)","\int \frac{\left(a x +1\right) x^{m} \sqrt{-a c x +c}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a*c*x+c)^(1/2),x)","F"
388,1,48,89,0.029000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c)^(1/2),x)","\frac{2 \left(a x +1\right)^{2} \left(15 a^{2} x^{2}-12 a x +8\right) \sqrt{-a c x +c}}{105 a^{3} \sqrt{-a^{2} x^{2}+1}}"," ",0,"2/105*(a*x+1)^2*(15*a^2*x^2-12*a*x+8)*(-a*c*x+c)^(1/2)/a^3/(-a^2*x^2+1)^(1/2)","A"
389,1,40,57,0.026000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^(1/2),x)","\frac{2 \left(a x +1\right)^{2} \left(3 a x -2\right) \sqrt{-a c x +c}}{15 a^{2} \sqrt{-a^{2} x^{2}+1}}"," ",0,"2/15*(a*x+1)^2*(3*a*x-2)*(-a*c*x+c)^(1/2)/a^2/(-a^2*x^2+1)^(1/2)","A"
390,1,34,29,0.027000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2),x)","\frac{2 \left(a x +1\right)^{2} \sqrt{-a c x +c}}{3 a \sqrt{-a^{2} x^{2}+1}}"," ",0,"2/3*(a*x+1)^2*(-a*c*x+c)^(1/2)/a/(-a^2*x^2+1)^(1/2)","A"
391,1,71,56,0.042000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2)/x,x)","\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(\sqrt{c}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right)-\sqrt{c \left(a x +1\right)}\right)}{\left(a x -1\right) \sqrt{c \left(a x +1\right)}}"," ",0,"2*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(c^(1/2)*arctanh((c*(a*x+1))^(1/2)/c^(1/2))-(c*(a*x+1))^(1/2))/(a*x-1)/(c*(a*x+1))^(1/2)","A"
392,1,78,60,0.050000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2)/x^2,x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(\arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x a c +\sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{\left(a x -1\right) \sqrt{c \left(a x +1\right)}\, x \sqrt{c}}"," ",0,"(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x*a*c+(c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)/(c*(a*x+1))^(1/2)/x/c^(1/2)","A"
393,1,45,83,0.031000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-a c x +c}\, \left(35 x^{4} a^{4}+85 x^{3} a^{3}+102 a^{2} x^{2}+136 a x +272\right)}{315 a^{4}}"," ",0,"-2/315*(-a*c*x+c)^(1/2)*(35*a^4*x^4+85*a^3*x^3+102*a^2*x^2+136*a*x+272)/a^4","A"
394,1,37,66,0.031000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-a c x +c}\, \left(15 x^{3} a^{3}+39 a^{2} x^{2}+52 a x +104\right)}{105 a^{3}}"," ",0,"-2/105*(-a*c*x+c)^(1/2)*(15*a^3*x^3+39*a^2*x^2+52*a*x+104)/a^3","A"
395,1,28,49,0.028000," ","int((a*x+1)^2/(-a^2*x^2+1)*x*(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-a c x +c}\, \left(a^{2} x^{2}+3 a x +6\right)}{5 a^{2}}"," ",0,"-2/5*(-a*c*x+c)^(1/2)*(a^2*x^2+3*a*x+6)/a^2","A"
396,1,20,32,0.028000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-a c x +c}\, \left(a x +5\right)}{3 a}"," ",0,"-2/3*(-a*c*x+c)^(1/2)*(a*x+5)/a","A"
397,1,32,31,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2)/x,x)","-2 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right) \sqrt{c}-2 \sqrt{-a c x +c}"," ",0,"-2*arctanh((-a*c*x+c)^(1/2)/c^(1/2))*c^(1/2)-2*(-a*c*x+c)^(1/2)","A"
398,1,45,35,0.042000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2)/x^2,x)","2 a c \left(-\frac{\sqrt{-a c x +c}}{2 x a c}-\frac{3 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{2 \sqrt{c}}\right)"," ",0,"2*a*c*(-1/2*(-a*c*x+c)^(1/2)/x/a/c-3/2/c^(1/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2)))","A"
399,1,65,52,0.038000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2)/x^3,x)","-2 a^{2} c^{2} \left(\frac{-\frac{7 \left(-a c x +c \right)^{\frac{3}{2}}}{8 c}+\frac{9 \sqrt{-a c x +c}}{8}}{x^{2} a^{2} c^{2}}+\frac{7 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{8 c^{\frac{3}{2}}}\right)"," ",0,"-2*a^2*c^2*((-7/8/c*(-a*c*x+c)^(3/2)+9/8*(-a*c*x+c)^(1/2))/x^2/a^2/c^2+7/8/c^(3/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2)))","A"
400,1,80,69,0.042000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2)/x^4,x)","2 a^{3} c^{3} \left(-\frac{\frac{11 \left(-a c x +c \right)^{\frac{5}{2}}}{16 c^{2}}-\frac{11 \left(-a c x +c \right)^{\frac{3}{2}}}{6 c}+\frac{21 \sqrt{-a c x +c}}{16}}{x^{3} a^{3} c^{3}}-\frac{11 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{16 c^{\frac{5}{2}}}\right)"," ",0,"2*a^3*c^3*(-(11/16/c^2*(-a*c*x+c)^(5/2)-11/6/c*(-a*c*x+c)^(3/2)+21/16*(-a*c*x+c)^(1/2))/x^3/a^3/c^3-11/16/c^(5/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2)))","A"
401,1,93,86,0.041000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2)/x^5,x)","-2 a^{4} c^{4} \left(\frac{-\frac{75 \left(-a c x +c \right)^{\frac{7}{2}}}{128 c^{3}}+\frac{275 \left(-a c x +c \right)^{\frac{5}{2}}}{128 c^{2}}-\frac{365 \left(-a c x +c \right)^{\frac{3}{2}}}{128 c}+\frac{181 \sqrt{-a c x +c}}{128}}{x^{4} a^{4} c^{4}}+\frac{75 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{128 c^{\frac{7}{2}}}\right)"," ",0,"-2*a^4*c^4*((-75/128/c^3*(-a*c*x+c)^(7/2)+275/128/c^2*(-a*c*x+c)^(5/2)-365/128/c*(-a*c*x+c)^(3/2)+181/128*(-a*c*x+c)^(1/2))/x^4/a^4/c^4+75/128/c^(7/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2)))","A"
402,1,146,202,0.046000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(-35 x^{4} a^{4} \sqrt{c \left(a x +1\right)}-95 x^{3} a^{3} \sqrt{c \left(a x +1\right)}-138 x^{2} a^{2} \sqrt{c \left(a x +1\right)}+630 \sqrt{c}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-236 x a \sqrt{c \left(a x +1\right)}-788 \sqrt{c \left(a x +1\right)}\right)}{315 \left(a x -1\right) \sqrt{c \left(a x +1\right)}\, a^{4}}"," ",0,"-2/315*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(-35*x^4*a^4*(c*(a*x+1))^(1/2)-95*x^3*a^3*(c*(a*x+1))^(1/2)-138*x^2*a^2*(c*(a*x+1))^(1/2)+630*c^(1/2)*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-236*x*a*(c*(a*x+1))^(1/2)-788*(c*(a*x+1))^(1/2))/(a*x-1)/(c*(a*x+1))^(1/2)/a^4","A"
403,1,129,138,0.045000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(-3 x^{3} a^{3} \sqrt{c \left(a x +1\right)}-9 x^{2} a^{2} \sqrt{c \left(a x +1\right)}+42 \sqrt{c}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-16 x a \sqrt{c \left(a x +1\right)}-52 \sqrt{c \left(a x +1\right)}\right)}{21 \left(a x -1\right) \sqrt{c \left(a x +1\right)}\, a^{3}}"," ",0,"-2/21*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(-3*x^3*a^3*(c*(a*x+1))^(1/2)-9*x^2*a^2*(c*(a*x+1))^(1/2)+42*c^(1/2)*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-16*x*a*(c*(a*x+1))^(1/2)-52*(c*(a*x+1))^(1/2))/(a*x-1)/(c*(a*x+1))^(1/2)/a^3","A"
404,1,112,138,0.043000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(-3 x^{2} a^{2} \sqrt{c \left(a x +1\right)}+30 \sqrt{c}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-11 x a \sqrt{c \left(a x +1\right)}-38 \sqrt{c \left(a x +1\right)}\right)}{15 \left(a x -1\right) \sqrt{c \left(a x +1\right)}\, a^{2}}"," ",0,"-2/15*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(-3*x^2*a^2*(c*(a*x+1))^(1/2)+30*c^(1/2)*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-11*x*a*(c*(a*x+1))^(1/2)-38*(c*(a*x+1))^(1/2))/(a*x-1)/(c*(a*x+1))^(1/2)/a^2","A"
405,1,95,98,0.043000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(6 \sqrt{c}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-x a \sqrt{c \left(a x +1\right)}-7 \sqrt{c \left(a x +1\right)}\right)}{3 \left(a x -1\right) \sqrt{c \left(a x +1\right)}\, a}"," ",0,"-2/3*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(6*c^(1/2)*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-x*a*(c*(a*x+1))^(1/2)-7*(c*(a*x+1))^(1/2))/(a*x-1)/(c*(a*x+1))^(1/2)/a","A"
406,1,98,98,0.050000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x,x)","-\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(2 \sqrt{c}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-\sqrt{c}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right)-\sqrt{c \left(a x +1\right)}\right)}{\left(a x -1\right) \sqrt{c \left(a x +1\right)}}"," ",0,"-2*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(2*c^(1/2)*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-c^(1/2)*arctanh((c*(a*x+1))^(1/2)/c^(1/2))-(c*(a*x+1))^(1/2))/(a*x-1)/(c*(a*x+1))^(1/2)","A"
407,1,105,103,0.051000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^2,x)","\frac{\left(-4 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c +5 \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x a c +\sqrt{c \left(a x +1\right)}\, \sqrt{c}\right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}}{\left(a x -1\right) \sqrt{c \left(a x +1\right)}\, \sqrt{c}\, x}"," ",0,"(-4*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c+5*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x*a*c+(c*(a*x+1))^(1/2)*c^(1/2))*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)/(a*x-1)/(c*(a*x+1))^(1/2)/c^(1/2)/x","A"
408,1,131,140,0.053000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^3,x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(16 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c -23 c \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x^{2} a^{2}-9 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}-2 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{4 \sqrt{c}\, \left(a x -1\right) \sqrt{c \left(a x +1\right)}\, x^{2}}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(16*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c-23*c*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x^2*a^2-9*x*a*(c*(a*x+1))^(1/2)*c^(1/2)-2*(c*(a*x+1))^(1/2)*c^(1/2))/c^(1/2)/(a*x-1)/(c*(a*x+1))^(1/2)/x^2","A"
409,1,151,175,0.056000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^4,x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(96 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{3} a^{3} c -135 c \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x^{3} a^{3}-57 x^{2} a^{2} \sqrt{c \left(a x +1\right)}\, \sqrt{c}-26 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}-8 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{24 \sqrt{c}\, \left(a x -1\right) \sqrt{c \left(a x +1\right)}\, x^{3}}"," ",0,"-1/24*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(96*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^3*a^3*c-135*c*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x^3*a^3-57*x^2*a^2*(c*(a*x+1))^(1/2)*c^(1/2)-26*x*a*(c*(a*x+1))^(1/2)*c^(1/2)-8*(c*(a*x+1))^(1/2)*c^(1/2))/c^(1/2)/(a*x-1)/(c*(a*x+1))^(1/2)/x^3","A"
410,1,171,210,0.054000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^5,x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a x -1\right)}\, \left(768 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{4} a^{4} c -1089 c \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x^{4} a^{4}-447 x^{3} a^{3} \sqrt{c \left(a x +1\right)}\, \sqrt{c}-214 x^{2} a^{2} \sqrt{c \left(a x +1\right)}\, \sqrt{c}-136 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}-48 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{192 \sqrt{c}\, \left(a x -1\right) \sqrt{c \left(a x +1\right)}\, x^{4}}"," ",0,"-1/192*(-a^2*x^2+1)^(1/2)*(-c*(a*x-1))^(1/2)*(768*2^(1/2)*arctanh(1/2*(c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^4*a^4*c-1089*c*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x^4*a^4-447*x^3*a^3*(c*(a*x+1))^(1/2)*c^(1/2)-214*x^2*a^2*(c*(a*x+1))^(1/2)*c^(1/2)-136*x*a*(c*(a*x+1))^(1/2)*c^(1/2)-48*(c*(a*x+1))^(1/2)*c^(1/2))/c^(1/2)/(a*x-1)/(c*(a*x+1))^(1/2)/x^4","A"
411,0,0,104,0.413000," ","int(x^m*(-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \sqrt{-a c x +c}\, \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int(x^m*(-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
412,1,56,111,0.030000," ","int(x^2*(-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-a c x +c}\, \left(15 x^{3} a^{3}-39 a^{2} x^{2}+52 a x -104\right)}{105 \left(a x -1\right) a^{3}}"," ",0,"2/105*(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2)*(15*a^3*x^3-39*a^2*x^2+52*a*x-104)/(a*x-1)/a^3","A"
413,1,47,83,0.029000," ","int(x*(-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-a c x +c}\, \left(a^{2} x^{2}-3 a x +6\right)}{5 \left(a x -1\right) a^{2}}"," ",0,"2/5*(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2)*(a^2*x^2-3*a*x+6)/(a*x-1)/a^2","A"
414,1,39,54,0.027000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{2 \sqrt{-a^{2} x^{2}+1}\, \sqrt{-a c x +c}\, \left(a x -5\right)}{3 \left(a x -1\right) a}"," ",0,"2/3*(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2)*(a*x-5)/(a*x-1)/a","A"
415,1,69,56,0.041000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x)","\frac{2 \sqrt{-c \left(a x -1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(\sqrt{c}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right)+\sqrt{c \left(a x +1\right)}\right)}{\left(a x -1\right) \sqrt{c \left(a x +1\right)}}"," ",0,"2*(-c*(a*x-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(c^(1/2)*arctanh((c*(a*x+1))^(1/2)/c^(1/2))+(c*(a*x+1))^(1/2))/(a*x-1)/(c*(a*x+1))^(1/2)","A"
416,1,79,60,0.049000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x)","\frac{\sqrt{-c \left(a x -1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(-3 \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x a c +\sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{\left(a x -1\right) \sqrt{c \left(a x +1\right)}\, x \sqrt{c}}"," ",0,"(-c*(a*x-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(-3*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x*a*c+(c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)/(c*(a*x+1))^(1/2)/x/c^(1/2)","A"
417,1,101,90,0.050000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^3,x)","\frac{\sqrt{-c \left(a x -1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(7 c \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x^{2} a^{2}-7 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}+2 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{4 \sqrt{c}\, \left(a x -1\right) \sqrt{c \left(a x +1\right)}\, x^{2}}"," ",0,"1/4*(-c*(a*x-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(7*c*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x^2*a^2-7*x*a*(c*(a*x+1))^(1/2)*c^(1/2)+2*(c*(a*x+1))^(1/2)*c^(1/2))/c^(1/2)/(a*x-1)/(c*(a*x+1))^(1/2)/x^2","A"
418,1,121,120,0.053000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^4,x)","-\frac{\sqrt{-c \left(a x -1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(33 c \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x^{3} a^{3}-33 x^{2} a^{2} \sqrt{c \left(a x +1\right)}\, \sqrt{c}+22 x a \sqrt{c \left(a x +1\right)}\, \sqrt{c}-8 \sqrt{c \left(a x +1\right)}\, \sqrt{c}\right)}{24 \sqrt{c}\, \left(a x -1\right) \sqrt{c \left(a x +1\right)}\, x^{3}}"," ",0,"-1/24*(-c*(a*x-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(33*c*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x^3*a^3-33*x^2*a^2*(c*(a*x+1))^(1/2)*c^(1/2)+22*x*a*(c*(a*x+1))^(1/2)*c^(1/2)-8*(c*(a*x+1))^(1/2)*c^(1/2))/c^(1/2)/(a*x-1)/(c*(a*x+1))^(1/2)/x^3","A"
419,1,101,112,0.036000," ","int(x^3*(-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{2 \left(\frac{\left(-a c x +c \right)^{\frac{9}{2}}}{9}-\frac{c \left(-a c x +c \right)^{\frac{7}{2}}}{7}+\frac{\left(-a c x +c \right)^{\frac{5}{2}} c^{2}}{5}+\frac{c^{3} \left(-a c x +c \right)^{\frac{3}{2}}}{3}+2 \sqrt{-a c x +c}\, c^{4}-2 c^{\frac{9}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)\right)}{c^{4} a^{4}}"," ",0,"-2/c^4/a^4*(1/9*(-a*c*x+c)^(9/2)-1/7*c*(-a*c*x+c)^(7/2)+1/5*(-a*c*x+c)^(5/2)*c^2+1/3*c^3*(-a*c*x+c)^(3/2)+2*(-a*c*x+c)^(1/2)*c^4-2*c^(9/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
420,1,75,78,0.036000," ","int(x^2*(-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\frac{2 \left(-a c x +c \right)^{\frac{7}{2}}}{7}+\frac{2 \left(-a c x +c \right)^{\frac{3}{2}} c^{2}}{3}+4 \sqrt{-a c x +c}\, c^{3}-4 c^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{c^{3} a^{3}}"," ",0,"2/c^3/a^3*(1/7*(-a*c*x+c)^(7/2)+1/3*(-a*c*x+c)^(3/2)*c^2+2*(-a*c*x+c)^(1/2)*c^3-2*c^(7/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
421,1,73,78,0.035000," ","int(x*(-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{2 \left(\frac{\left(-a c x +c \right)^{\frac{5}{2}}}{5}+\frac{c \left(-a c x +c \right)^{\frac{3}{2}}}{3}+2 \sqrt{-a c x +c}\, c^{2}-2 c^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)\right)}{c^{2} a^{2}}"," ",0,"-2/c^2/a^2*(1/5*(-a*c*x+c)^(5/2)+1/3*c*(-a*c*x+c)^(3/2)+2*(-a*c*x+c)^(1/2)*c^2-2*c^(5/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
422,1,59,61,0.031000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\frac{2 \left(-a c x +c \right)^{\frac{3}{2}}}{3}+4 c \sqrt{-a c x +c}-4 c^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{a c}"," ",0,"2/c/a*(1/3*(-a*c*x+c)^(3/2)+2*c*(-a*c*x+c)^(1/2)-2*c^(3/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
423,1,58,57,0.038000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x,x)","-2 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right) \sqrt{c}+4 \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, \sqrt{c}-2 \sqrt{-a c x +c}"," ",0,"-2*arctanh((-a*c*x+c)^(1/2)/c^(1/2))*c^(1/2)+4*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^(1/2)-2*(-a*c*x+c)^(1/2)","A"
424,1,71,62,0.042000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^2,x)","2 a c \left(-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{\sqrt{c}}-\frac{\sqrt{-a c x +c}}{2 x a c}+\frac{5 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{2 \sqrt{c}}\right)"," ",0,"2*a*c*(-2*2^(1/2)/c^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))-1/2*(-a*c*x+c)^(1/2)/x/a/c+5/2/c^(1/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2)))","A"
425,1,95,81,0.044000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^3,x)","-2 a^{2} c^{2} \left(-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{c^{\frac{3}{2}}}-\frac{\frac{-\frac{9 \left(-a c x +c \right)^{\frac{3}{2}}}{8}+\frac{7 c \sqrt{-a c x +c}}{8}}{x^{2} a^{2} c^{2}}-\frac{23 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{8 \sqrt{c}}}{c}\right)"," ",0,"-2*a^2*c^2*(-2/c^(3/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))-1/c*((-9/8*(-a*c*x+c)^(3/2)+7/8*c*(-a*c*x+c)^(1/2))/x^2/a^2/c^2-23/8/c^(1/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2))))","A"
426,1,110,98,0.041000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^4,x)","2 a^{3} c^{3} \left(-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{c^{\frac{5}{2}}}-\frac{-\frac{-\frac{19 \left(-a c x +c \right)^{\frac{5}{2}}}{16}+\frac{11 c \left(-a c x +c \right)^{\frac{3}{2}}}{6}-\frac{13 \sqrt{-a c x +c}\, c^{2}}{16}}{x^{3} a^{3} c^{3}}-\frac{45 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{16 \sqrt{c}}}{c^{2}}\right)"," ",0,"2*a^3*c^3*(-2/c^(5/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))-1/c^2*(-(-19/16*(-a*c*x+c)^(5/2)+11/6*c*(-a*c*x+c)^(3/2)-13/16*(-a*c*x+c)^(1/2)*c^2)/x^3/a^3/c^3-45/16/c^(1/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2))))","A"
427,1,123,115,0.044000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^5,x)","-2 a^{4} c^{4} \left(-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{c^{\frac{7}{2}}}-\frac{\frac{-\frac{149 \left(-a c x +c \right)^{\frac{7}{2}}}{128}+\frac{1127 c \left(-a c x +c \right)^{\frac{5}{2}}}{384}-\frac{1049 \left(-a c x +c \right)^{\frac{3}{2}} c^{2}}{384}+\frac{107 \sqrt{-a c x +c}\, c^{3}}{128}}{x^{4} a^{4} c^{4}}-\frac{363 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{128 \sqrt{c}}}{c^{3}}\right)"," ",0,"-2*a^4*c^4*(-2/c^(7/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))-1/c^3*((-149/128*(-a*c*x+c)^(7/2)+1127/384*c*(-a*c*x+c)^(5/2)-1049/384*(-a*c*x+c)^(3/2)*c^2+107/128*(-a*c*x+c)^(1/2)*c^3)/x^4/a^4/c^4-363/128/c^(1/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2))))","A"
428,1,79,193,0.030000," ","int(x^3*(-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{2 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \sqrt{-a c x +c}\, \left(5 x^{5} a^{5}-20 x^{4} a^{4}+41 x^{3} a^{3}-82 a^{2} x^{2}+328 a x +656\right)}{45 \left(a x +1\right)^{2} \left(a x -1\right)^{2} a^{4}}"," ",0,"2/45*(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)*(5*a^5*x^5-20*a^4*x^4+41*a^3*x^3-82*a^2*x^2+328*a*x+656)/(a*x+1)^2/(a*x-1)^2/a^4","A"
429,1,71,161,0.029000," ","int(x^2*(-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{2 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \sqrt{-a c x +c}\, \left(15 x^{4} a^{4}-66 x^{3} a^{3}+167 a^{2} x^{2}-668 a x -1336\right)}{105 \left(a x +1\right)^{2} \left(a x -1\right)^{2} a^{3}}"," ",0,"2/105*(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)*(15*a^4*x^4-66*a^3*x^3+167*a^2*x^2-668*a*x-1336)/(a*x+1)^2/(a*x-1)^2/a^3","A"
430,1,63,129,0.028000," ","int(x*(-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{2 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \sqrt{-a c x +c}\, \left(3 x^{3} a^{3}-16 a^{2} x^{2}+79 a x +158\right)}{15 \left(a x +1\right)^{2} \left(a x -1\right)^{2} a^{2}}"," ",0,"2/15*(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)*(3*a^3*x^3-16*a^2*x^2+79*a*x+158)/(a*x+1)^2/(a*x-1)^2/a^2","A"
431,1,54,85,0.029000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{2 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \sqrt{-a c x +c}\, \left(a^{2} x^{2}-10 a x -23\right)}{3 \left(a x +1\right)^{2} \left(a x -1\right)^{2} a}"," ",0,"2/3*(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)*(a^2*x^2-10*a*x-23)/(a*x+1)^2/(a*x-1)^2/a","A"
432,1,78,89,0.048000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x)","\frac{2 \sqrt{-c \left(a x -1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(\sqrt{c}\, \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) \sqrt{c \left(a x +1\right)}-a c x -5 c \right)}{\left(a x -1\right) c \left(a x +1\right)}"," ",0,"2*(-c*(a*x-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(c^(1/2)*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*(c*(a*x+1))^(1/2)-a*c*x-5*c)/(a*x-1)/c/(a*x+1)","A"
433,1,82,94,0.052000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x)","\frac{\left(-7 \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x a \sqrt{c \left(a x +1\right)}+9 x a \sqrt{c}+\sqrt{c}\right) \sqrt{-c \left(a x -1\right)}\, \sqrt{-a^{2} x^{2}+1}}{\left(a x -1\right) \sqrt{c}\, \left(a x +1\right) x}"," ",0,"(-7*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x*a*(c*(a*x+1))^(1/2)+9*x*a*c^(1/2)+c^(1/2))*(-c*(a*x-1))^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x-1)/c^(1/2)/(a*x+1)/x","A"
434,1,100,131,0.056000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x)","\frac{\sqrt{-c \left(a x -1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(47 \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x^{2} a^{2} \sqrt{c \left(a x +1\right)}-47 x^{2} a^{2} \sqrt{c}-13 x a \sqrt{c}+2 \sqrt{c}\right)}{4 \sqrt{c}\, \left(a x -1\right) \left(a x +1\right) x^{2}}"," ",0,"1/4*(-c*(a*x-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(47*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x^2*a^2*(c*(a*x+1))^(1/2)-47*x^2*a^2*c^(1/2)-13*x*a*c^(1/2)+2*c^(1/2))/c^(1/2)/(a*x-1)/(a*x+1)/x^2","A"
435,1,111,166,0.053000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x)","-\frac{\sqrt{-c \left(a x -1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(357 \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x^{3} a^{3} \sqrt{c \left(a x +1\right)}-357 x^{3} a^{3} \sqrt{c}-119 x^{2} a^{2} \sqrt{c}+38 x a \sqrt{c}-8 \sqrt{c}\right)}{24 \sqrt{c}\, \left(a x -1\right) \left(a x +1\right) x^{3}}"," ",0,"-1/24*(-c*(a*x-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(357*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x^3*a^3*(c*(a*x+1))^(1/2)-357*x^3*a^3*c^(1/2)-119*x^2*a^2*c^(1/2)+38*x*a*c^(1/2)-8*c^(1/2))/c^(1/2)/(a*x-1)/(a*x+1)/x^3","A"
436,1,122,201,0.059000," ","int((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x)","\frac{\sqrt{-c \left(a x -1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(3345 \arctanh \left(\frac{\sqrt{c \left(a x +1\right)}}{\sqrt{c}}\right) x^{4} a^{4} \sqrt{c \left(a x +1\right)}-3345 x^{4} a^{4} \sqrt{c}-1115 x^{3} a^{3} \sqrt{c}+446 x^{2} a^{2} \sqrt{c}-200 x a \sqrt{c}+48 \sqrt{c}\right)}{192 \sqrt{c}\, \left(a x -1\right) \left(a x +1\right) x^{4}}"," ",0,"1/192*(-c*(a*x-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(3345*arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x^4*a^4*(c*(a*x+1))^(1/2)-3345*x^4*a^4*c^(1/2)-1115*x^3*a^3*c^(1/2)+446*x^2*a^2*c^(1/2)-200*x*a*c^(1/2)+48*c^(1/2))/c^(1/2)/(a*x-1)/(a*x+1)/x^4","A"
437,0,0,59,0.250000," ","int((-a*c*x+c)^p/exp(2*p*arctanh(a*x)),x)","\int \left(-a c x +c \right)^{p} {\mathrm e}^{-2 p \arctanh \left(a x \right)}\, dx"," ",0,"int((-a*c*x+c)^p/exp(2*p*arctanh(a*x)),x)","F"
438,1,32,37,0.029000," ","int(exp(2*p*arctanh(a*x))*(-a*c*x+c)^p,x)","\frac{\left(a x +1\right) {\mathrm e}^{2 p \arctanh \left(a x \right)} \left(-a c x +c \right)^{p}}{a \left(1+p \right)}"," ",0,"(a*x+1)/a/(1+p)*exp(2*p*arctanh(a*x))*(-a*c*x+c)^p","A"
439,0,0,72,0.244000," ","int(exp(n*arctanh(a*x))*(-a*c*x+c)^p,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a c x +c \right)^{p}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a*c*x+c)^p,x)","F"
440,0,0,56,0.237000," ","int(exp(n*arctanh(a*x))*(-a*c*x+c)^3,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a c x +c \right)^{3}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a*c*x+c)^3,x)","F"
441,0,0,56,0.230000," ","int(exp(n*arctanh(a*x))*(-a*c*x+c)^2,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a c x +c \right)^{2}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a*c*x+c)^2,x)","F"
442,0,0,54,0.048000," ","int(exp(n*arctanh(a*x))*(-a*c*x+c),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a c x +c \right)\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a*c*x+c),x)","F"
443,0,0,49,0.236000," ","int(exp(n*arctanh(a*x))/(-a*c*x+c),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{-a c x +c}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(-a*c*x+c),x)","F"
444,1,33,35,0.029000," ","int(exp(n*arctanh(a*x))/(-a*c*x+c)^2,x)","-\frac{{\mathrm e}^{n \arctanh \left(a x \right)} \left(a x +1\right)}{\left(a x -1\right) c^{2} \left(2+n \right) a}"," ",0,"-exp(n*arctanh(a*x))*(a*x+1)/(a*x-1)/c^2/(2+n)/a","A"
445,1,46,76,0.029000," ","int(exp(n*arctanh(a*x))/(-a*c*x+c)^3,x)","-\frac{{\mathrm e}^{n \arctanh \left(a x \right)} \left(a x -n -3\right) \left(a x +1\right)}{\left(a x -1\right)^{2} c^{3} \left(n^{2}+6 n +8\right) a}"," ",0,"-exp(n*arctanh(a*x))*(a*x-n-3)*(a*x+1)/(a*x-1)^2/c^3/(n^2+6*n+8)/a","A"
446,1,68,123,0.033000," ","int(exp(n*arctanh(a*x))/(-a*c*x+c)^4,x)","-\frac{\left(a x +1\right) \left(2 a^{2} x^{2}-2 a n x -8 a x +n^{2}+8 n +14\right) {\mathrm e}^{n \arctanh \left(a x \right)}}{\left(a x -1\right)^{3} c^{4} a \left(n^{2}+8 n +12\right) \left(4+n \right)}"," ",0,"-(a*x+1)*(2*a^2*x^2-2*a*n*x-8*a*x+n^2+8*n+14)*exp(n*arctanh(a*x))/(a*x-1)^3/c^4/a/(n^2+8*n+12)/(4+n)","A"
447,0,0,56,0.244000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^p,x)","\int \frac{\left(a x +1\right) \left(c -\frac{c}{a x}\right)^{p}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^p,x)","F"
448,1,142,109,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^4,x)","-\frac{c^{4} \sqrt{-a^{2} x^{2}+1}}{a}-\frac{3 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{c^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}-\frac{8 c^{4} \sqrt{-a^{2} x^{2}+1}}{3 a^{2} x}-\frac{c^{4} \sqrt{-a^{2} x^{2}+1}}{3 a^{4} x^{3}}+\frac{3 c^{4} \sqrt{-a^{2} x^{2}+1}}{2 x^{2} a^{3}}"," ",0,"-c^4*(-a^2*x^2+1)^(1/2)/a-3*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/2*c^4/a*arctanh(1/(-a^2*x^2+1)^(1/2))-8/3*c^4*(-a^2*x^2+1)^(1/2)/a^2/x-1/3*c^4*(-a^2*x^2+1)^(1/2)/a^4/x^3+3/2*c^4*(-a^2*x^2+1)^(1/2)/x^2/a^3","A"
449,1,119,85,0.040000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^3,x)","-\frac{c^{3} \sqrt{-a^{2} x^{2}+1}}{a}-\frac{2 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{2 c^{3} \sqrt{-a^{2} x^{2}+1}}{a^{2} x}+\frac{c^{3} \sqrt{-a^{2} x^{2}+1}}{2 x^{2} a^{3}}+\frac{c^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}"," ",0,"-c^3*(-a^2*x^2+1)^(1/2)/a-2*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-2*c^3*(-a^2*x^2+1)^(1/2)/a^2/x+1/2*c^3*(-a^2*x^2+1)^(1/2)/x^2/a^3+1/2*c^3/a*arctanh(1/(-a^2*x^2+1)^(1/2))","A"
450,1,95,61,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^2,x)","-\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{a}-\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{c^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}-\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{a^{2} x}"," ",0,"-c^2*(-a^2*x^2+1)^(1/2)/a-c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+c^2/a*arctanh(1/(-a^2*x^2+1)^(1/2))-c^2*(-a^2*x^2+1)^(1/2)/a^2/x","A"
451,1,34,37,0.030000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x),x)","\frac{c \left(-\sqrt{-a^{2} x^{2}+1}+\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)\right)}{a}"," ",0,"c/a*(-(-a^2*x^2+1)^(1/2)+arctanh(1/(-a^2*x^2+1)^(1/2)))","A"
452,1,96,61,0.036000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x),x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{a c}+\frac{2 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c \sqrt{a^{2}}}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{a^{2} c \left(x -\frac{1}{a}\right)}"," ",0,"-(-a^2*x^2+1)^(1/2)/a/c+2/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+2/a^2/c/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
453,1,140,96,0.044000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^2,x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{a \,c^{2}}+\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{2} \sqrt{a^{2}}}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a^{3} c^{2} \left(x -\frac{1}{a}\right)^{2}}+\frac{13 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a^{2} c^{2} \left(x -\frac{1}{a}\right)}"," ",0,"-(-a^2*x^2+1)^(1/2)/a/c^2+3/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+2/3/a^3/c^2/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+13/3/a^2/c^2/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
454,1,184,124,0.046000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^3,x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{a \,c^{3}}+\frac{4 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{3} \sqrt{a^{2}}}+\frac{31 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{15 a^{3} c^{3} \left(x -\frac{1}{a}\right)^{2}}+\frac{104 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{15 a^{2} c^{3} \left(x -\frac{1}{a}\right)}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a^{4} c^{3} \left(x -\frac{1}{a}\right)^{3}}"," ",0,"-(-a^2*x^2+1)^(1/2)/a/c^3+4/c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+31/15/a^3/c^3/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+104/15/a^2/c^3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+2/5/a^4/c^3/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
455,1,228,152,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^4,x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{a \,c^{4}}+\frac{5 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{4} \sqrt{a^{2}}}+\frac{446 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{105 a^{3} c^{4} \left(x -\frac{1}{a}\right)^{2}}+\frac{1024 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{105 a^{2} c^{4} \left(x -\frac{1}{a}\right)}+\frac{57 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{35 a^{4} c^{4} \left(x -\frac{1}{a}\right)^{3}}+\frac{2 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{7 a^{5} c^{4} \left(x -\frac{1}{a}\right)^{4}}"," ",0,"-(-a^2*x^2+1)^(1/2)/a/c^4+5/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+446/105/a^3/c^4/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1024/105/a^2/c^4/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+57/35/a^4/c^4/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+2/7/a^5/c^4/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
456,0,0,61,0.327000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^p,x)","\int \frac{\left(a x +1\right)^{2} \left(c -\frac{c}{a x}\right)^{p}}{-a^{2} x^{2}+1}\, dx"," ",0,"int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^p,x)","F"
457,1,61,60,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^5,x)","\frac{c^{5}}{4 a^{5} x^{4}}-\frac{c^{5}}{a^{4} x^{3}}+\frac{c^{5}}{x^{2} a^{3}}+\frac{2 c^{5}}{a^{2} x}-c^{5} x +\frac{3 c^{5} \ln \left(x \right)}{a}"," ",0,"1/4*c^5/a^5/x^4-c^5/a^4/x^3+c^5/x^2/a^3+2*c^5/a^2/x-c^5*x+3*c^5*ln(x)/a","A"
458,1,39,38,0.034000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^4,x)","-\frac{c^{4}}{3 a^{4} x^{3}}+\frac{c^{4}}{x^{2} a^{3}}-c^{4} x +\frac{2 c^{4} \ln \left(x \right)}{a}"," ",0,"-1/3*c^4/a^4/x^3+c^4/x^2/a^3-c^4*x+2*c^4*ln(x)/a","A"
459,1,39,38,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^3,x)","\frac{c^{3}}{2 x^{2} a^{3}}-\frac{c^{3}}{a^{2} x}-c^{3} x +\frac{c^{3} \ln \left(x \right)}{a}"," ",0,"1/2*c^3/x^2/a^3-c^3/a^2/x-c^3*x+c^3*ln(x)/a","A"
460,1,20,18,0.029000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^2,x)","\frac{c^{2} \left(-a^{2} x -\frac{1}{x}\right)}{a^{2}}"," ",0,"c^2/a^2*(-a^2*x-1/x)","A"
461,1,14,13,0.026000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x),x)","-c x -\frac{c \ln \left(x \right)}{a}"," ",0,"-c*x-c*ln(x)/a","A"
462,1,37,38,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x),x)","-\frac{x}{c}+\frac{2}{c a \left(a x -1\right)}-\frac{3 \ln \left(a x -1\right)}{a c}"," ",0,"-x/c+2/c/a/(a*x-1)-3/a/c*ln(a*x-1)","A"
463,1,51,53,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^2,x)","-\frac{x}{c^{2}}+\frac{5}{a \,c^{2} \left(a x -1\right)}-\frac{4 \ln \left(a x -1\right)}{a \,c^{2}}+\frac{1}{a \,c^{2} \left(a x -1\right)^{2}}"," ",0,"-x/c^2+5/a/c^2/(a*x-1)-4/a/c^2*ln(a*x-1)+1/a/c^2/(a*x-1)^2","A"
464,1,67,70,0.038000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^3,x)","-\frac{x}{c^{3}}+\frac{9}{a \,c^{3} \left(a x -1\right)}-\frac{5 \ln \left(a x -1\right)}{c^{3} a}+\frac{7}{2 a \,c^{3} \left(a x -1\right)^{2}}+\frac{2}{3 a \,c^{3} \left(a x -1\right)^{3}}"," ",0,"-x/c^3+9/a/c^3/(a*x-1)-5/c^3/a*ln(a*x-1)+7/2/a/c^3/(a*x-1)^2+2/3/a/c^3/(a*x-1)^3","A"
465,1,82,86,0.035000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^4,x)","-\frac{x}{c^{4}}+\frac{14}{a \,c^{4} \left(a x -1\right)}-\frac{6 \ln \left(a x -1\right)}{a \,c^{4}}+\frac{8}{a \,c^{4} \left(a x -1\right)^{2}}+\frac{1}{2 a \,c^{4} \left(a x -1\right)^{4}}+\frac{3}{a \,c^{4} \left(a x -1\right)^{3}}"," ",0,"-x/c^4+14/a/c^4/(a*x-1)-6/a/c^4*ln(a*x-1)+8/a/c^4/(a*x-1)^2+1/2/a/c^4/(a*x-1)^4+3/a/c^4/(a*x-1)^3","A"
466,1,180,91,0.053000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^4,x)","-\frac{c^{4} a \,x^{2}}{\sqrt{-a^{2} x^{2}+1}}+\frac{c^{4}}{2 a \sqrt{-a^{2} x^{2}+1}}-\frac{4 c^{4} x}{3 \sqrt{-a^{2} x^{2}+1}}+\frac{c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{3 c^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}+\frac{5 c^{4}}{3 a^{2} x \sqrt{-a^{2} x^{2}+1}}-\frac{c^{4}}{3 a^{4} x^{3} \sqrt{-a^{2} x^{2}+1}}+\frac{c^{4}}{2 a^{3} x^{2} \sqrt{-a^{2} x^{2}+1}}"," ",0,"-c^4*a*x^2/(-a^2*x^2+1)^(1/2)+1/2*c^4/a/(-a^2*x^2+1)^(1/2)-4/3*c^4*x/(-a^2*x^2+1)^(1/2)+c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-3/2*c^4/a*arctanh(1/(-a^2*x^2+1)^(1/2))+5/3*c^4/a^2/x/(-a^2*x^2+1)^(1/2)-1/3*c^4/a^4/x^3/(-a^2*x^2+1)^(1/2)+1/2*c^4/a^3/x^2/(-a^2*x^2+1)^(1/2)","A"
467,1,118,65,0.041000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^3,x)","\frac{c^{3} \left(a^{6} \left(-\frac{x^{2}}{a^{2} \sqrt{-a^{2} x^{2}+1}}+\frac{2}{a^{4} \sqrt{-a^{2} x^{2}+1}}\right)-\frac{3 a^{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}+\frac{1}{2 x^{2} \sqrt{-a^{2} x^{2}+1}}\right)}{a^{3}}"," ",0,"c^3/a^3*(a^6*(-1/a^2*x^2/(-a^2*x^2+1)^(1/2)+2/a^4/(-a^2*x^2+1)^(1/2))-3*a^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)))+1/2/x^2/(-a^2*x^2+1)^(1/2))","A"
468,1,133,63,0.046000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^2,x)","-\frac{c^{2} a \,x^{2}}{\sqrt{-a^{2} x^{2}+1}}+\frac{c^{2}}{a \sqrt{-a^{2} x^{2}+1}}+\frac{c^{2} x}{\sqrt{-a^{2} x^{2}+1}}-\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{c^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}-\frac{c^{2}}{a^{2} x \sqrt{-a^{2} x^{2}+1}}"," ",0,"-c^2*a*x^2/(-a^2*x^2+1)^(1/2)+c^2/a/(-a^2*x^2+1)^(1/2)+c^2*x/(-a^2*x^2+1)^(1/2)-c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-c^2/a*arctanh(1/(-a^2*x^2+1)^(1/2))-c^2/a^2/x/(-a^2*x^2+1)^(1/2)","B"
469,1,84,46,0.038000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x),x)","-\frac{c a \,x^{2}}{\sqrt{-a^{2} x^{2}+1}}+\frac{c}{a \sqrt{-a^{2} x^{2}+1}}-\frac{2 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{c \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}"," ",0,"-c*a*x^2/(-a^2*x^2+1)^(1/2)+c/a/(-a^2*x^2+1)^(1/2)-2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+c/a*arctanh(1/(-a^2*x^2+1)^(1/2))","A"
470,1,168,89,0.041000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x),x)","-\frac{a \,x^{2}}{c \sqrt{-a^{2} x^{2}+1}}+\frac{9}{c a \sqrt{-a^{2} x^{2}+1}}+\frac{12 x}{c \sqrt{-a^{2} x^{2}+1}}-\frac{4 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c \sqrt{a^{2}}}+\frac{8}{3 c \,a^{2} \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}-\frac{16 x}{3 c \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}"," ",0,"-a/c*x^2/(-a^2*x^2+1)^(1/2)+9/c/a/(-a^2*x^2+1)^(1/2)+12/c*x/(-a^2*x^2+1)^(1/2)-4/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+8/3/c/a^2/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-16/3/c/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x","A"
471,1,212,114,0.047000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^2,x)","-\frac{a \,x^{2}}{c^{2} \sqrt{-a^{2} x^{2}+1}}+\frac{14}{a \,c^{2} \sqrt{-a^{2} x^{2}+1}}+\frac{25 x}{c^{2} \sqrt{-a^{2} x^{2}+1}}-\frac{5 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{2} \sqrt{a^{2}}}+\frac{8}{5 a^{3} c^{2} \left(x -\frac{1}{a}\right)^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{116}{15 a^{2} c^{2} \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}-\frac{232 x}{15 c^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}"," ",0,"-a/c^2*x^2/(-a^2*x^2+1)^(1/2)+14/a/c^2/(-a^2*x^2+1)^(1/2)+25*x/c^2/(-a^2*x^2+1)^(1/2)-5/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+8/5/a^3/c^2/(x-1/a)^2/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+116/15/a^2/c^2/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-232/15/c^2/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x","A"
472,1,256,141,0.050000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^3,x)","-\frac{a \,x^{2}}{c^{3} \sqrt{-a^{2} x^{2}+1}}+\frac{20}{a \,c^{3} \sqrt{-a^{2} x^{2}+1}}+\frac{44 x}{c^{3} \sqrt{-a^{2} x^{2}+1}}-\frac{6 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{3} \sqrt{a^{2}}}+\frac{44}{7 a^{3} c^{3} \left(x -\frac{1}{a}\right)^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{110}{7 a^{2} c^{3} \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}-\frac{220 x}{7 c^{3} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{8}{7 a^{4} c^{3} \left(x -\frac{1}{a}\right)^{3} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}"," ",0,"-a/c^3*x^2/(-a^2*x^2+1)^(1/2)+20/a/c^3/(-a^2*x^2+1)^(1/2)+44*x/c^3/(-a^2*x^2+1)^(1/2)-6/c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+44/7/a^3/c^3/(x-1/a)^2/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+110/7/a^2/c^3/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-220/7/c^3/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x+8/7/a^4/c^3/(x-1/a)^3/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
473,1,300,168,0.055000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^4,x)","-\frac{a \,x^{2}}{c^{4} \sqrt{-a^{2} x^{2}+1}}+\frac{27}{a \,c^{4} \sqrt{-a^{2} x^{2}+1}}+\frac{70 x}{c^{4} \sqrt{-a^{2} x^{2}+1}}-\frac{7 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{4} \sqrt{a^{2}}}+\frac{5002}{315 a^{3} c^{4} \left(x -\frac{1}{a}\right)^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{8543}{315 a^{2} c^{4} \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}-\frac{17086 x}{315 c^{4} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{356}{63 a^{4} c^{4} \left(x -\frac{1}{a}\right)^{3} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{8}{9 a^{5} c^{4} \left(x -\frac{1}{a}\right)^{4} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}"," ",0,"-a/c^4*x^2/(-a^2*x^2+1)^(1/2)+27/a/c^4/(-a^2*x^2+1)^(1/2)+70*x/c^4/(-a^2*x^2+1)^(1/2)-7/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+5002/315/a^3/c^4/(x-1/a)^2/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+8543/315/a^2/c^4/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-17086/315/c^4/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x+356/63/a^4/c^4/(x-1/a)^3/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+8/9/a^5/c^4/(x-1/a)^4/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
474,0,0,95,0.327000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^p,x)","\int \frac{\left(a x +1\right)^{4} \left(c -\frac{c}{a x}\right)^{p}}{\left(-a^{2} x^{2}+1\right)^{2}}\, dx"," ",0,"int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^p,x)","F"
475,1,61,60,0.031000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^5,x)","\frac{c^{5}}{4 a^{5} x^{4}}-\frac{c^{5}}{3 a^{4} x^{3}}-\frac{c^{5}}{x^{2} a^{3}}+\frac{2 c^{5}}{a^{2} x}+c^{5} x -\frac{c^{5} \ln \left(x \right)}{a}"," ",0,"1/4*c^5/a^5/x^4-1/3*c^5/a^4/x^3-c^5/x^2/a^3+2*c^5/a^2/x+c^5*x-c^5*ln(x)/a","A"
476,1,27,28,0.032000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^4,x)","\frac{c^{4} \left(x \,a^{4}+\frac{2 a^{2}}{x}-\frac{1}{3 x^{3}}\right)}{a^{4}}"," ",0,"c^4/a^4*(x*a^4+2*a^2/x-1/3/x^3)","A"
477,1,37,36,0.032000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^3,x)","\frac{c^{3}}{2 x^{2} a^{3}}+\frac{c^{3}}{a^{2} x}+c^{3} x +\frac{c^{3} \ln \left(x \right)}{a}"," ",0,"1/2*c^3/x^2/a^3+c^3/a^2/x+c^3*x+c^3*ln(x)/a","A"
478,1,28,27,0.033000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^2,x)","-\frac{c^{2}}{a^{2} x}+c^{2} x +\frac{2 c^{2} \ln \left(x \right)}{a}"," ",0,"-c^2/a^2/x+c^2*x+2*c^2*ln(x)/a","A"
479,1,25,25,0.033000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x),x)","c x -\frac{c \ln \left(x \right)}{a}+\frac{4 c \ln \left(a x -1\right)}{a}"," ",0,"c*x-c*ln(x)/a+4*c/a*ln(a*x-1)","A"
480,1,51,53,0.035000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x),x)","\frac{x}{c}-\frac{8}{c a \left(a x -1\right)}+\frac{5 \ln \left(a x -1\right)}{a c}-\frac{2}{a c \left(a x -1\right)^{2}}"," ",0,"x/c-8/c/a/(a*x-1)+5/a/c*ln(a*x-1)-2/a/c/(a*x-1)^2","A"
481,1,66,69,0.034000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x)^2,x)","\frac{x}{c^{2}}-\frac{13}{a \,c^{2} \left(a x -1\right)}+\frac{6 \ln \left(a x -1\right)}{a \,c^{2}}-\frac{6}{a \,c^{2} \left(a x -1\right)^{2}}-\frac{4}{3 a \,c^{2} \left(a x -1\right)^{3}}"," ",0,"x/c^2-13/a/c^2/(a*x-1)+6/a/c^2*ln(a*x-1)-6/a/c^2/(a*x-1)^2-4/3/a/c^2/(a*x-1)^3","A"
482,1,81,85,0.033000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x)^3,x)","\frac{x}{c^{3}}-\frac{19}{a \,c^{3} \left(a x -1\right)}+\frac{7 \ln \left(a x -1\right)}{c^{3} a}-\frac{25}{2 a \,c^{3} \left(a x -1\right)^{2}}-\frac{1}{a \,c^{3} \left(a x -1\right)^{4}}-\frac{16}{3 a \,c^{3} \left(a x -1\right)^{3}}"," ",0,"x/c^3-19/a/c^3/(a*x-1)+7/c^3/a*ln(a*x-1)-25/2/a/c^3/(a*x-1)^2-1/a/c^3/(a*x-1)^4-16/3/a/c^3/(a*x-1)^3","A"
483,1,96,101,0.038000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x)^4,x)","\frac{x}{c^{4}}-\frac{26}{a \,c^{4} \left(a x -1\right)}+\frac{8 \ln \left(a x -1\right)}{a \,c^{4}}-\frac{22}{a \,c^{4} \left(a x -1\right)^{2}}-\frac{4}{5 a \,c^{4} \left(a x -1\right)^{5}}-\frac{5}{a \,c^{4} \left(a x -1\right)^{4}}-\frac{41}{3 a \,c^{4} \left(a x -1\right)^{3}}"," ",0,"x/c^4-26/a/c^4/(a*x-1)+8/a/c^4*ln(a*x-1)-22/a/c^4/(a*x-1)^2-4/5/a/c^4/(a*x-1)^5-5/a/c^4/(a*x-1)^4-41/3/a/c^4/(a*x-1)^3","A"
484,0,0,56,0.325000," ","int((c-c/a/x)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{\left(c -\frac{c}{a x}\right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int((c-c/a/x)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
485,1,232,122,0.050000," ","int((c-c/a/x)^4/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{25 c^{4} \sqrt{-a^{2} x^{2}+1}}{2 a}+\frac{25 c^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}-\frac{11 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{a^{2} x}-11 c^{4} x \sqrt{-a^{2} x^{2}+1}-\frac{11 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 a^{4} x^{3}}+\frac{5 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{2 x^{2} a^{3}}+\frac{16 c^{4} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{a}+\frac{16 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-25/2*c^4*(-a^2*x^2+1)^(1/2)/a+25/2*c^4/a*arctanh(1/(-a^2*x^2+1)^(1/2))-11*c^4/a^2/x*(-a^2*x^2+1)^(3/2)-11*c^4*x*(-a^2*x^2+1)^(1/2)-11*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/3*c^4*(-a^2*x^2+1)^(3/2)/a^4/x^3+5/2*c^4*(-a^2*x^2+1)^(3/2)/x^2/a^3+16*c^4/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+16*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","A"
486,1,209,99,0.045000," ","int((c-c/a/x)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{13 c^{3} \sqrt{-a^{2} x^{2}+1}}{2 a}+\frac{13 c^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}-\frac{4 c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{a^{2} x}-4 c^{3} x \sqrt{-a^{2} x^{2}+1}-\frac{4 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{2 x^{2} a^{3}}+\frac{8 c^{3} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{a}+\frac{8 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-13/2*c^3*(-a^2*x^2+1)^(1/2)/a+13/2*c^3/a*arctanh(1/(-a^2*x^2+1)^(1/2))-4*c^3/a^2/x*(-a^2*x^2+1)^(3/2)-4*c^3*x*(-a^2*x^2+1)^(1/2)-4*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/2*c^3*(-a^2*x^2+1)^(3/2)/x^2/a^3+8*c^3/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+8*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
487,1,186,76,0.041000," ","int((c-c/a/x)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{3 c^{2} \sqrt{-a^{2} x^{2}+1}}{a}+\frac{3 c^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}-\frac{c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{a^{2} x}-c^{2} x \sqrt{-a^{2} x^{2}+1}-\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{4 c^{2} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{a}+\frac{4 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-3*c^2*(-a^2*x^2+1)^(1/2)/a+3*c^2/a*arctanh(1/(-a^2*x^2+1)^(1/2))-c^2/a^2/x*(-a^2*x^2+1)^(3/2)-c^2*x*(-a^2*x^2+1)^(1/2)-c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+4*c^2/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+4*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
488,1,106,46,0.040000," ","int((c-c/a/x)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{c \sqrt{-a^{2} x^{2}+1}}{a}+\frac{c \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}+\frac{2 c \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{a}+\frac{2 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-c*(-a^2*x^2+1)^(1/2)/a+c/a*arctanh(1/(-a^2*x^2+1)^(1/2))+2*c/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
489,1,20,19,0.027000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x),x)","\frac{\sqrt{-a^{2} x^{2}+1}}{a c}"," ",0,"(-a^2*x^2+1)^(1/2)/a/c","A"
490,1,198,59,0.047000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^2,x)","\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{2 a^{3} c^{2} \left(x -\frac{1}{a}\right)^{2}}+\frac{5 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{4 a \,c^{2}}-\frac{5 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{4 c^{2} \sqrt{a^{2}}}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{4 a \,c^{2}}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{4 c^{2} \sqrt{a^{2}}}"," ",0,"1/2/a^3/c^2/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+5/4/a/c^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-5/4/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+1/4/a/c^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+1/4/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
491,1,242,84,0.049000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^3,x)","\frac{5 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{4 a^{3} c^{3} \left(x -\frac{1}{a}\right)^{2}}+\frac{17 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{8 a \,c^{3}}-\frac{17 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{8 c^{3} \sqrt{a^{2}}}+\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{6 a^{4} c^{3} \left(x -\frac{1}{a}\right)^{3}}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{8 a \,c^{3}}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{8 c^{3} \sqrt{a^{2}}}"," ",0,"5/4/a^3/c^3/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+17/8/a/c^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-17/8/c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+1/6/a^4/c^3/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+1/8/a/c^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+1/8/c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
492,1,286,111,0.051000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^4,x)","\frac{17 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{8 a^{3} c^{4} \left(x -\frac{1}{a}\right)^{2}}+\frac{49 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{16 a \,c^{4}}-\frac{49 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{16 c^{4} \sqrt{a^{2}}}+\frac{11 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{20 a^{4} c^{4} \left(x -\frac{1}{a}\right)^{3}}+\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{10 a^{5} c^{4} \left(x -\frac{1}{a}\right)^{4}}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{16 a \,c^{4}}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{16 c^{4} \sqrt{a^{2}}}"," ",0,"17/8/a^3/c^4/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+49/16/a/c^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-49/16/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+11/20/a^4/c^4/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+1/10/a^5/c^4/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+1/16/a/c^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+1/16/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
493,0,0,114,0.244000," ","int((c-c/a/x)^p/(a*x+1)^2*(-a^2*x^2+1),x)","\int \frac{\left(c -\frac{c}{a x}\right)^{p} \left(-a^{2} x^{2}+1\right)}{\left(a x +1\right)^{2}}\, dx"," ",0,"int((c-c/a/x)^p/(a*x+1)^2*(-a^2*x^2+1),x)","F"
494,1,65,64,0.038000," ","int((c-c/a/x)^4/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{c^{4}}{3 a^{4} x^{3}}+\frac{3 c^{4}}{x^{2} a^{3}}-\frac{16 c^{4}}{a^{2} x}-c^{4} x -\frac{26 c^{4} \ln \left(x \right)}{a}+\frac{32 c^{4} \ln \left(a x +1\right)}{a}"," ",0,"-1/3*c^4/a^4/x^3+3*c^4/x^2/a^3-16*c^4/a^2/x-c^4*x-26*c^4*ln(x)/a+32*c^4*ln(a*x+1)/a","A"
495,1,54,53,0.036000," ","int((c-c/a/x)^3/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{c^{3}}{2 x^{2} a^{3}}-\frac{5 c^{3}}{a^{2} x}-c^{3} x -\frac{11 c^{3} \ln \left(x \right)}{a}+\frac{16 c^{3} \ln \left(a x +1\right)}{a}"," ",0,"1/2*c^3/x^2/a^3-5*c^3/a^2/x-c^3*x-11*c^3*ln(x)/a+16*c^3*ln(a*x+1)/a","A"
496,1,43,42,0.034000," ","int((c-c/a/x)^2/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{c^{2}}{a^{2} x}-c^{2} x -\frac{4 c^{2} \ln \left(x \right)}{a}+\frac{8 c^{2} \ln \left(a x +1\right)}{a}"," ",0,"-c^2/a^2/x-c^2*x-4*c^2*ln(x)/a+8*c^2*ln(a*x+1)/a","A"
497,1,26,25,0.030000," ","int((c-c/a/x)/(a*x+1)^2*(-a^2*x^2+1),x)","-c x -\frac{c \ln \left(x \right)}{a}+\frac{4 c \ln \left(a x +1\right)}{a}"," ",0,"-c*x-c*ln(x)/a+4*c*ln(a*x+1)/a","A"
498,1,21,20,0.028000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x),x)","-\frac{x}{c}+\frac{\ln \left(a x +1\right)}{a c}"," ",0,"-x/c+ln(a*x+1)/a/c","A"
499,1,36,18,0.031000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^2,x)","-\frac{x}{c^{2}}-\frac{\ln \left(a x -1\right)}{2 a \,c^{2}}+\frac{\ln \left(a x +1\right)}{2 a \,c^{2}}"," ",0,"-x/c^2-1/2/a/c^2*ln(a*x-1)+1/2*ln(a*x+1)/a/c^2","A"
500,1,51,52,0.034000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^3,x)","-\frac{x}{c^{3}}+\frac{1}{2 a \,c^{3} \left(a x -1\right)}-\frac{5 \ln \left(a x -1\right)}{4 c^{3} a}+\frac{\ln \left(a x +1\right)}{4 a \,c^{3}}"," ",0,"-x/c^3+1/2/a/c^3/(a*x-1)-5/4/c^3/a*ln(a*x-1)+1/4*ln(a*x+1)/a/c^3","A"
501,1,66,68,0.036000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^4,x)","-\frac{x}{c^{4}}+\frac{1}{4 a \,c^{4} \left(a x -1\right)^{2}}+\frac{7}{4 a \,c^{4} \left(a x -1\right)}-\frac{17 \ln \left(a x -1\right)}{8 a \,c^{4}}+\frac{\ln \left(a x +1\right)}{8 a \,c^{4}}"," ",0,"-x/c^4+1/4/a/c^4/(a*x-1)^2+7/4/a/c^4/(a*x-1)-17/8/a/c^4*ln(a*x-1)+1/8*ln(a*x+1)/a/c^4","A"
502,1,352,126,0.056000," ","int((c-c/a/x)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{11 c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{2 a}-\frac{33 c^{3} \sqrt{-a^{2} x^{2}+1}}{2 a}+\frac{33 c^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}-\frac{6 c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{a^{2} x}-6 c^{3} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}-9 c^{3} x \sqrt{-a^{2} x^{2}+1}-\frac{9 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{2 a^{3} x^{2}}-\frac{8 c^{3} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{4} \left(x +\frac{1}{a}\right)^{3}}-\frac{4 c^{3} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x +\frac{1}{a}\right)^{2}}+\frac{2 c^{3} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{a}+3 c^{3} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x +\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-11/2*c^3*(-a^2*x^2+1)^(3/2)/a-33/2*c^3*(-a^2*x^2+1)^(1/2)/a+33/2*c^3/a*arctanh(1/(-a^2*x^2+1)^(1/2))-6*c^3/a^2/x*(-a^2*x^2+1)^(5/2)-6*c^3*x*(-a^2*x^2+1)^(3/2)-9*c^3*x*(-a^2*x^2+1)^(1/2)-9*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/2*c^3/a^3/x^2*(-a^2*x^2+1)^(5/2)-8*c^3/a^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-4*c^3/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+2*c^3/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+3*c^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x+3*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
503,1,329,103,0.052000," ","int((c-c/a/x)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{5 c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 a}-\frac{5 c^{2} \sqrt{-a^{2} x^{2}+1}}{a}+\frac{5 c^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}-\frac{c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{a^{2} x}-c^{2} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}-\frac{3 c^{2} x \sqrt{-a^{2} x^{2}+1}}{2}-\frac{3 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}-\frac{4 c^{2} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{4} \left(x +\frac{1}{a}\right)^{3}}-\frac{4 c^{2} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{7 c^{2} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a}-\frac{7 c^{2} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{2}-\frac{7 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{2 \sqrt{a^{2}}}"," ",0,"-5/3*c^2*(-a^2*x^2+1)^(3/2)/a-5*c^2*(-a^2*x^2+1)^(1/2)/a+5*c^2/a*arctanh(1/(-a^2*x^2+1)^(1/2))-c^2/a^2/x*(-a^2*x^2+1)^(5/2)-c^2*x*(-a^2*x^2+1)^(3/2)-3/2*c^2*x*(-a^2*x^2+1)^(1/2)-3/2*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-4*c^2/a^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-4*c^2/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-7/3*c^2/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-7/2*c^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-7/2*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
504,1,223,71,0.050000," ","int((c-c/a/x)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{c \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 a}-\frac{c \sqrt{-a^{2} x^{2}+1}}{a}+\frac{c \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}-\frac{2 c \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{4} \left(x +\frac{1}{a}\right)^{3}}-\frac{3 c \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{8 c \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a}-4 c \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x -\frac{4 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-1/3*c*(-a^2*x^2+1)^(3/2)/a-c*(-a^2*x^2+1)^(1/2)/a+c/a*arctanh(1/(-a^2*x^2+1)^(1/2))-2*c/a^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-3*c/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-8/3*c/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-4*c*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-4*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
505,1,292,61,0.048000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x),x)","\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{24 a c}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}\, x}{16 c}-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{16 c \sqrt{a^{2}}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{2 a^{4} c \left(x +\frac{1}{a}\right)^{3}}-\frac{5 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{4 c \,a^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{31 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{24 c a}-\frac{31 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{16 c}-\frac{31 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{16 c \sqrt{a^{2}}}"," ",0,"1/24/a/c*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)-1/16/c*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x-1/16/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-1/2/a^4/c/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-5/4/c/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-31/24/c/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-31/16/c*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-31/16/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
506,1,336,57,0.054000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^2,x)","-\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{8 a^{3} c^{2} \left(x -\frac{1}{a}\right)^{2}}-\frac{5 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{48 a \,c^{2}}+\frac{5 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}\, x}{32 c^{2}}+\frac{5 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{32 c^{2} \sqrt{a^{2}}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{4 a^{4} c^{2} \left(x +\frac{1}{a}\right)^{3}}-\frac{3 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{4 a^{3} c^{2} \left(x +\frac{1}{a}\right)^{2}}-\frac{37 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{48 a \,c^{2}}-\frac{37 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{32 c^{2}}-\frac{37 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{32 c^{2} \sqrt{a^{2}}}"," ",0,"-1/8/a^3/c^2/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)-5/48/a/c^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+5/32/c^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x+5/32/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-1/4/a^4/c^2/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-3/4/a^3/c^2/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-37/48/a/c^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-37/32/c^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-37/32/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
507,1,43,41,0.030000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^3,x)","\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a^{2} x^{2}-2\right)}{a \left(a x -1\right)^{2} c^{3} \left(a x +1\right)^{2}}"," ",0,"1/a*(-a^2*x^2+1)^(3/2)*(a^2*x^2-2)/(a*x-1)^2/c^3/(a*x+1)^2","A"
508,1,424,84,0.064000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^4,x)","-\frac{23 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{96 a \,c^{4}}-\frac{29 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{32 a \,c^{4}}+\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{24 a^{5} c^{4} \left(x -\frac{1}{a}\right)^{4}}+\frac{17 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{48 a^{4} c^{4} \left(x -\frac{1}{a}\right)^{3}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{16 a^{4} c^{4} \left(x +\frac{1}{a}\right)^{3}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{4 a^{3} c^{4} \left(x +\frac{1}{a}\right)^{2}}-\frac{23 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{64 c^{4}}-\frac{23 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{64 c^{4} \sqrt{a^{2}}}-\frac{43 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{48 a^{3} c^{4} \left(x -\frac{1}{a}\right)^{2}}+\frac{87 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}\, x}{64 c^{4}}+\frac{87 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{64 c^{4} \sqrt{a^{2}}}"," ",0,"-23/96/a/c^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-29/32/a/c^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+1/24/a^5/c^4/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)+17/48/a^4/c^4/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)-1/16/a^4/c^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-1/4/a^3/c^4/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-23/64/c^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-23/64/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-43/48/a^3/c^4/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)+87/64/c^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x+87/64/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))","B"
509,1,468,111,0.065000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^5,x)","-\frac{49 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{384 a \,c^{5}}+\frac{31 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{48 a^{4} c^{5} \left(x -\frac{1}{a}\right)^{3}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{32 a^{4} c^{5} \left(x +\frac{1}{a}\right)^{3}}-\frac{9 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{64 a^{3} c^{5} \left(x +\frac{1}{a}\right)^{2}}-\frac{49 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{256 c^{5}}-\frac{49 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{256 c^{5} \sqrt{a^{2}}}-\frac{139 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{96 a^{3} c^{5} \left(x -\frac{1}{a}\right)^{2}}+\frac{561 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}\, x}{256 c^{5}}+\frac{561 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{256 c^{5} \sqrt{a^{2}}}+\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{40 a^{6} c^{5} \left(x -\frac{1}{a}\right)^{5}}+\frac{7 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{48 a^{5} c^{5} \left(x -\frac{1}{a}\right)^{4}}-\frac{187 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{128 a \,c^{5}}"," ",0,"-49/384/a/c^5*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+31/48/a^4/c^5/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)-1/32/a^4/c^5/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-9/64/a^3/c^5/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-49/256/c^5*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-49/256/c^5/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-139/96/a^3/c^5/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)+561/256/c^5*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x+561/256/c^5/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+1/40/a^6/c^5/(x-1/a)^5*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)+7/48/a^5/c^5/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)-187/128/a/c^5*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)","B"
510,1,172,181,0.103000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(9/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{4} \sqrt{-a^{2} x^{2}+1}\, \left(210 a^{\frac{9}{2}} \sqrt{-\left(a x +1\right) x}\, x^{4}+735 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{4} a^{4}+584 a^{\frac{7}{2}} x^{3} \sqrt{-\left(a x +1\right) x}-712 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}+324 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}-60 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{210 x^{3} a^{\frac{9}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"-1/210*(c*(a*x-1)/a/x)^(1/2)/x^3*c^4/a^(9/2)*(-a^2*x^2+1)^(1/2)*(210*a^(9/2)*(-(a*x+1)*x)^(1/2)*x^4+735*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^4*a^4+584*a^(7/2)*x^3*(-(a*x+1)*x)^(1/2)-712*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)+324*a^(3/2)*x*(-(a*x+1)*x)^(1/2)-60*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
511,1,154,145,0.060000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(7/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \sqrt{-a^{2} x^{2}+1}\, \left(30 a^{\frac{7}{2}} x^{3} \sqrt{-\left(a x +1\right) x}+75 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{3} a^{3}+112 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}-56 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+12 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{30 x^{2} a^{\frac{7}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"-1/30*(c*(a*x-1)/a/x)^(1/2)/x^2*c^3/a^(7/2)*(-a^2*x^2+1)^(1/2)*(30*a^(7/2)*x^3*(-(a*x+1)*x)^(1/2)+75*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^3*a^3+112*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)-56*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+12*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
512,1,136,139,0.058000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(5/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \sqrt{-a^{2} x^{2}+1}\, \left(6 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}+9 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{2} a^{2}+20 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}-4 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{6 x \,a^{\frac{5}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"-1/6*(c*(a*x-1)/a/x)^(1/2)/x*c^2/a^(5/2)*(-a^2*x^2+1)^(1/2)*(6*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)+9*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^2*a^2+20*a^(3/2)*x*(-(a*x+1)*x)^(1/2)-4*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
513,1,108,106,0.054000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \sqrt{-a^{2} x^{2}+1}\, \left(2 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a +4 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{2 a^{\frac{3}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*c/a^(3/2)*(-a^2*x^2+1)^(1/2)*(2*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a+4*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
514,1,89,68,0.047000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(-2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}+\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right)}{2 \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(-2*a^(1/2)*(-(a*x+1)*x)^(1/2)+arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))/(a*x-1)/(-(a*x+1)*x)^(1/2)/a^(1/2)","A"
515,1,168,121,0.053000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(-2 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}+3 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}-4 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{4 a^{\frac{3}{2}} c \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/4*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)/c*(-a^2*x^2+1)^(1/2)*(-2*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)+3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)-4*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)*2^(1/2)/(-1/a)^(1/2)","A"
516,1,276,156,0.059000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(2 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x -5 a^{2} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x -4 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}+7 a^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x +5 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}-7 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{4 a^{\frac{3}{2}} c^{2} \left(a x -1\right)^{2} \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"-1/4*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)/c^2*(-a^2*x^2+1)^(1/2)*(2*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x-5*a^2*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x-4*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)+7*a^(3/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x+5*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)-7*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/(a*x-1)^2/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
517,1,390,193,0.066000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(5/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(16 a^{\frac{7}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x^{2}-70 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x +79 a^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x^{2}-56 a^{3} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x^{2}+46 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}+112 a^{2} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x -158 a^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x -56 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}+79 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{32 a^{\frac{3}{2}} c^{3} \left(a x -1\right)^{3} \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"-1/32*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(16*a^(7/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x^2-70*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x+79*a^(5/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x^2-56*a^3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x^2+46*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)+112*a^2*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x-158*a^(3/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x-56*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)+79*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/a^(3/2)/c^3/(a*x-1)^3/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","B"
518,1,163,125,0.046000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(9/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{4} \left(-210 a^{\frac{9}{2}} \sqrt{a \,x^{2}-x}\, x^{5}+105 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{5} a^{4}+168 a^{\frac{7}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{3}-16 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2}-24 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x +12 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\right)}{42 x^{4} \sqrt{\left(a x -1\right) x}\, a^{\frac{9}{2}}}"," ",0,"1/42*(c*(a*x-1)/a/x)^(1/2)/x^4*c^4*(-210*a^(9/2)*(a*x^2-x)^(1/2)*x^5+105*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^5*a^4+168*a^(7/2)*(a*x^2-x)^(3/2)*x^3-16*a^(5/2)*(a*x^2-x)^(3/2)*x^2-24*a^(3/2)*(a*x^2-x)^(3/2)*x+12*(a*x^2-x)^(3/2)*a^(1/2))/((a*x-1)*x)^(1/2)/a^(9/2)","A"
519,1,144,104,0.045000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(7/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \left(-30 \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} x^{4}+20 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2}+15 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{4} a^{3}+4 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x -4 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\right)}{10 x^{3} \sqrt{\left(a x -1\right) x}\, a^{\frac{7}{2}}}"," ",0,"1/10*(c*(a*x-1)/a/x)^(1/2)/x^3*c^3*(-30*(a*x^2-x)^(1/2)*a^(7/2)*x^4+20*a^(5/2)*(a*x^2-x)^(3/2)*x^2+15*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^4*a^3+4*a^(3/2)*(a*x^2-x)^(3/2)*x-4*(a*x^2-x)^(3/2)*a^(1/2))/((a*x-1)*x)^(1/2)/a^(7/2)","A"
520,1,108,82,0.043000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(5/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \left(-6 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} x^{3}+3 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{3} a^{2}+4 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\right)}{6 x^{2} \sqrt{\left(a x -1\right) x}\, a^{\frac{5}{2}}}"," ",0,"1/6*(c*(a*x-1)/a/x)^(1/2)/x^2*c^2*(-6*(a*x^2-x)^(1/2)*a^(5/2)*x^3+3*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^3*a^2+4*(a*x^2-x)^(3/2)*a^(1/2))/((a*x-1)*x)^(1/2)/a^(5/2)","A"
521,1,103,61,0.044000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \left(-2 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}} x^{2}+4 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}+\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a \right)}{2 x \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}}}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)/x*c*(-2*(a*x^2-x)^(1/2)*a^(3/2)*x^2+4*(a*x^2-x)^(3/2)*a^(1/2)+ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a)/((a*x-1)*x)^(1/2)/a^(3/2)","A"
522,1,120,43,0.043000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{a \,x^{2}-x}\, \sqrt{a}-4 \sqrt{\left(a x -1\right) x}\, \sqrt{a}-\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)-2 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x*(2*(a*x^2-x)^(1/2)*a^(1/2)-4*((a*x-1)*x)^(1/2)*a^(1/2)-ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))-2*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/a^(1/2)","B"
523,1,194,61,0.045000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(10 a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}+5 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a^{2}-8 a^{\frac{3}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}}-20 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, x -10 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x a +10 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+5 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{2 \sqrt{\left(a x -1\right) x}\, c \left(a x -1\right)^{2} \sqrt{a}}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*x*(10*a^(5/2)*((a*x-1)*x)^(1/2)*x^2+5*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a^2-8*a^(3/2)*((a*x-1)*x)^(3/2)-20*a^(3/2)*((a*x-1)*x)^(1/2)*x-10*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x*a+10*((a*x-1)*x)^(1/2)*a^(1/2)+5*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/c/(a*x-1)^2/a^(1/2)","B"
524,1,260,82,0.046000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(42 a^{\frac{7}{2}} \sqrt{\left(a x -1\right) x}\, x^{3}+21 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{3} a^{3}-36 a^{\frac{5}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x -126 a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}-63 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a^{2}+28 a^{\frac{3}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}}+126 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, x +63 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x a -42 \sqrt{\left(a x -1\right) x}\, \sqrt{a}-21 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{6 \sqrt{\left(a x -1\right) x}\, c^{2} \left(a x -1\right)^{3} \sqrt{a}}"," ",0,"-1/6*(c*(a*x-1)/a/x)^(1/2)*x*(42*a^(7/2)*((a*x-1)*x)^(1/2)*x^3+21*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^3*a^3-36*a^(5/2)*((a*x-1)*x)^(3/2)*x-126*a^(5/2)*((a*x-1)*x)^(1/2)*x^2-63*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a^2+28*a^(3/2)*((a*x-1)*x)^(3/2)+126*a^(3/2)*((a*x-1)*x)^(1/2)*x+63*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x*a-42*((a*x-1)*x)^(1/2)*a^(1/2)-21*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/c^2/(a*x-1)^3/a^(1/2)","B"
525,1,328,103,0.050000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^(5/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(90 a^{\frac{9}{2}} \sqrt{\left(a x -1\right) x}\, x^{4}+45 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{4} a^{4}-80 a^{\frac{7}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x^{2}-360 a^{\frac{7}{2}} \sqrt{\left(a x -1\right) x}\, x^{3}-180 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{3} a^{3}+132 a^{\frac{5}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x +540 a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}+270 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a^{2}-60 a^{\frac{3}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}}-360 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, x -180 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x a +90 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+45 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{10 \sqrt{\left(a x -1\right) x}\, c^{3} \left(a x -1\right)^{4} \sqrt{a}}"," ",0,"-1/10*(c*(a*x-1)/a/x)^(1/2)*x*(90*a^(9/2)*((a*x-1)*x)^(1/2)*x^4+45*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^4*a^4-80*a^(7/2)*((a*x-1)*x)^(3/2)*x^2-360*a^(7/2)*((a*x-1)*x)^(1/2)*x^3-180*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^3*a^3+132*a^(5/2)*((a*x-1)*x)^(3/2)*x+540*a^(5/2)*((a*x-1)*x)^(1/2)*x^2+270*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a^2-60*a^(3/2)*((a*x-1)*x)^(3/2)-360*a^(3/2)*((a*x-1)*x)^(1/2)*x-180*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x*a+90*((a*x-1)*x)^(1/2)*a^(1/2)+45*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/c^3/(a*x-1)^4/a^(1/2)","B"
526,1,396,124,0.053000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^(7/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2310 a^{\frac{11}{2}} \sqrt{\left(a x -1\right) x}\, x^{5}+1155 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{5} a^{5}-2100 a^{\frac{9}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x^{3}-11550 a^{\frac{9}{2}} \sqrt{\left(a x -1\right) x}\, x^{4}-5775 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{4} a^{4}+5368 a^{\frac{7}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x^{2}+23100 a^{\frac{7}{2}} \sqrt{\left(a x -1\right) x}\, x^{3}+11550 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{3} a^{3}-4928 a^{\frac{5}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x -23100 a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}-11550 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a^{2}+1540 a^{\frac{3}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}}+11550 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, x +5775 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x a -2310 \sqrt{\left(a x -1\right) x}\, \sqrt{a}-1155 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{210 \sqrt{\left(a x -1\right) x}\, c^{4} \left(a x -1\right)^{5} \sqrt{a}}"," ",0,"-1/210*(c*(a*x-1)/a/x)^(1/2)*x*(2310*a^(11/2)*((a*x-1)*x)^(1/2)*x^5+1155*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^5*a^5-2100*a^(9/2)*((a*x-1)*x)^(3/2)*x^3-11550*a^(9/2)*((a*x-1)*x)^(1/2)*x^4-5775*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^4*a^4+5368*a^(7/2)*((a*x-1)*x)^(3/2)*x^2+23100*a^(7/2)*((a*x-1)*x)^(1/2)*x^3+11550*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^3*a^3-4928*a^(5/2)*((a*x-1)*x)^(3/2)*x-23100*a^(5/2)*((a*x-1)*x)^(1/2)*x^2-11550*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a^2+1540*a^(3/2)*((a*x-1)*x)^(3/2)+11550*a^(3/2)*((a*x-1)*x)^(1/2)*x+5775*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x*a-2310*((a*x-1)*x)^(1/2)*a^(1/2)-1155*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/c^4/(a*x-1)^5/a^(1/2)","B"
527,1,172,181,0.056000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(9/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{4} \sqrt{-a^{2} x^{2}+1}\, \left(70 a^{\frac{9}{2}} \sqrt{-\left(a x +1\right) x}\, x^{4}+105 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{4} a^{4}+328 a^{\frac{7}{2}} x^{3} \sqrt{-\left(a x +1\right) x}-24 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}-52 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+20 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{70 x^{3} a^{\frac{9}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"1/70*(c*(a*x-1)/a/x)^(1/2)/x^3*c^4/a^(9/2)*(-a^2*x^2+1)^(1/2)*(70*a^(9/2)*(-(a*x+1)*x)^(1/2)*x^4+105*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^4*a^4+328*a^(7/2)*x^3*(-(a*x+1)*x)^(1/2)-24*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)-52*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+20*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
528,1,154,175,0.058000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(7/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \sqrt{-a^{2} x^{2}+1}\, \left(30 a^{\frac{7}{2}} x^{3} \sqrt{-\left(a x +1\right) x}+15 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{3} a^{3}+88 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}+16 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}-12 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{30 x^{2} a^{\frac{7}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"1/30*(c*(a*x-1)/a/x)^(1/2)/x^2*c^3/a^(7/2)*(-a^2*x^2+1)^(1/2)*(30*a^(7/2)*x^3*(-(a*x+1)*x)^(1/2)+15*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^3*a^3+88*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)+16*a^(3/2)*x*(-(a*x+1)*x)^(1/2)-12*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
529,1,136,144,0.052000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(5/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \sqrt{-a^{2} x^{2}+1}\, \left(-6 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}+3 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{2} a^{2}-4 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}-4 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{6 x \,a^{\frac{5}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"-1/6*(c*(a*x-1)/a/x)^(1/2)/x*c^2/a^(5/2)*(-a^2*x^2+1)^(1/2)*(-6*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)+3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^2*a^2-4*a^(3/2)*x*(-(a*x+1)*x)^(1/2)-4*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
530,1,109,103,0.053000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \sqrt{-a^{2} x^{2}+1}\, \left(-2 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+3 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a +4 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{2 a^{\frac{3}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*c/a^(3/2)*(-a^2*x^2+1)^(1/2)*(-2*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a+4*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
531,1,165,119,0.059000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(2 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}-5 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}+8 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{4 \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{-\frac{1}{a}}}"," ",0,"1/4*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(2*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)-5*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)+8*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)/a^(3/2)/(-1/a)^(1/2)","A"
532,1,276,153,0.061000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(2 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x -6 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}-7 a^{2} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x +10 a^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x +7 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}-10 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{4 a^{\frac{3}{2}} c \left(a x -1\right)^{2} \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/4*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(2*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x-6*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)-7*a^2*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x+10*a^(3/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x+7*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)-10*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/a^(3/2)/c/(a*x-1)^2/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
533,1,390,193,0.066000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(3/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(8 a^{\frac{7}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x^{2}-36 a^{3} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x^{2}-46 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x +51 a^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x^{2}+72 a^{2} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x +30 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}-102 a^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x -36 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}+51 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{16 a^{\frac{3}{2}} c^{2} \left(a x -1\right)^{3} \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/16*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)/c^2*(-a^2*x^2+1)^(1/2)*(8*a^(7/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x^2-36*a^3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x^2-46*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x+51*a^(5/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x^2+72*a^2*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x+30*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)-102*a^(3/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x-36*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)+51*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/(a*x-1)^3/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","B"
534,1,504,229,0.071000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(5/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(96 a^{\frac{9}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x^{3}-830 a^{\frac{7}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x^{2}+747 a^{\frac{7}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x^{3}-528 a^{4} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x^{3}+1108 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x +1584 a^{3} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x^{2}-2241 a^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x^{2}-438 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}-1584 a^{2} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x +2241 a^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x +528 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}-747 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{192 a^{\frac{3}{2}} c^{3} \left(a x -1\right)^{4} \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/192*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(96*a^(9/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x^3-830*a^(7/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x^2+747*a^(7/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x^3-528*a^4*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x^3+1108*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x+1584*a^3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x^2-2241*a^(5/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x^2-438*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)-1584*a^2*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x+2241*a^(3/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x+528*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)-747*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/a^(3/2)/c^3/(a*x-1)^4/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","B"
535,1,172,181,0.063000," ","int((c-c/a/x)^(9/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{4} \sqrt{-a^{2} x^{2}+1}\, \left(210 a^{\frac{9}{2}} \sqrt{-\left(a x +1\right) x}\, x^{4}+1155 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{4} a^{4}-8312 a^{\frac{7}{2}} x^{3} \sqrt{-\left(a x +1\right) x}+2056 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}-492 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+60 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{210 x^{3} a^{\frac{9}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"1/210*(c*(a*x-1)/a/x)^(1/2)/x^3*c^4/a^(9/2)*(-a^2*x^2+1)^(1/2)*(210*a^(9/2)*(-(a*x+1)*x)^(1/2)*x^4+1155*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^4*a^4-8312*a^(7/2)*x^3*(-(a*x+1)*x)^(1/2)+2056*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)-492*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+60*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
536,1,154,145,0.064000," ","int((c-c/a/x)^(7/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \sqrt{-a^{2} x^{2}+1}\, \left(10 a^{\frac{7}{2}} x^{3} \sqrt{-\left(a x +1\right) x}+45 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{3} a^{3}-184 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}+32 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}-4 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{10 x^{2} a^{\frac{7}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"1/10*(c*(a*x-1)/a/x)^(1/2)/x^2*c^3/a^(7/2)*(-a^2*x^2+1)^(1/2)*(10*a^(7/2)*x^3*(-(a*x+1)*x)^(1/2)+45*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^3*a^3-184*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)+32*a^(3/2)*x*(-(a*x+1)*x)^(1/2)-4*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
537,1,136,109,0.060000," ","int((c-c/a/x)^(5/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \sqrt{-a^{2} x^{2}+1}\, \left(6 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}+21 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{2} a^{2}-44 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+4 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{6 x \,a^{\frac{5}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"1/6*(c*(a*x-1)/a/x)^(1/2)/x*c^2/a^(5/2)*(-a^2*x^2+1)^(1/2)*(6*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)+21*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^2*a^2-44*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+4*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
538,1,109,102,0.059000," ","int((c-c/a/x)^(3/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \sqrt{-a^{2} x^{2}+1}\, \left(2 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+5 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a -4 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{2 a^{\frac{3}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*c/a^(3/2)*(-a^2*x^2+1)^(1/2)*(2*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+5*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a-4*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
539,1,91,74,0.053000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}+3 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right)}{2 \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(2*a^(1/2)*(-(a*x+1)*x)^(1/2)+3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))/(a*x-1)/(-(a*x+1)*x)^(1/2)/a^(1/2)","A"
540,1,92,70,0.046000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}+\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right)}{2 \sqrt{a}\, c \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x/a^(1/2)/c*(-a^2*x^2+1)^(1/2)*(2*a^(1/2)*(-(a*x+1)*x)^(1/2)+arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
541,1,168,123,0.059000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(3/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(2 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}-\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}+2 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{4 a^{\frac{3}{2}} c^{2} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/4*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(2*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)-arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)+2*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/a^(3/2)/c^2/(a*x-1)/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
542,1,276,160,0.061000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(5/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(4 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x -6 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}-6 a^{2} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x +9 a^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x +6 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}-9 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{8 a^{\frac{3}{2}} c^{3} \left(a x -1\right)^{2} \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/8*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(4*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x-6*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)-6*a^2*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x+9*a^(3/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x+6*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)-9*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/a^(3/2)/c^3/(a*x-1)^2/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
543,1,390,196,0.070000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(7/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(32 a^{\frac{7}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x^{2}-110 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x -80 a^{3} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x^{2}+115 a^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x^{2}+70 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}+160 a^{2} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x -230 a^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x -80 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}+115 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{64 a^{\frac{3}{2}} c^{4} \left(a x -1\right)^{3} \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/64*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(32*a^(7/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x^2-110*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x-80*a^3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x^2+115*a^(5/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x^2+70*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)+160*a^2*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x-230*a^(3/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x-80*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)+115*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/a^(3/2)/c^4/(a*x-1)^3/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
544,1,305,158,0.052000," ","int((c-c/a/x)^(9/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{4} \left(-17430 \sqrt{a \,x^{2}-x}\, \sqrt{\frac{1}{a}}\, a^{\frac{9}{2}} x^{5}+6720 \sqrt{\frac{1}{a}}\, a^{\frac{9}{2}} \sqrt{\left(a x -1\right) x}\, x^{5}+10920 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, a^{\frac{7}{2}} x^{3}+8715 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{5} a^{4}-10080 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{5} a^{4}-6720 \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{2}\, a^{\frac{7}{2}} x^{5}-1936 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2} \sqrt{\frac{1}{a}}+456 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}-60 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{210 x^{4} a^{\frac{9}{2}} \sqrt{\left(a x -1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"-1/210*(c*(a*x-1)/a/x)^(1/2)/x^4*c^4/a^(9/2)*(-17430*(a*x^2-x)^(1/2)*(1/a)^(1/2)*a^(9/2)*x^5+6720*(1/a)^(1/2)*a^(9/2)*((a*x-1)*x)^(1/2)*x^5+10920*(a*x^2-x)^(3/2)*(1/a)^(1/2)*a^(7/2)*x^3+8715*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^5*a^4-10080*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^5*a^4-6720*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*2^(1/2)*a^(7/2)*x^5-1936*a^(5/2)*(a*x^2-x)^(3/2)*x^2*(1/a)^(1/2)+456*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)-60*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/(1/a)^(1/2)","A"
545,1,281,137,0.048000," ","int((c-c/a/x)^(7/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \left(-1110 \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, x^{4}+480 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{4}+660 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2} \sqrt{\frac{1}{a}}+555 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{4} a^{3}-480 a^{\frac{5}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{4}-720 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{4} a^{3}-92 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}+12 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{30 x^{3} a^{\frac{7}{2}} \sqrt{\left(a x -1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"-1/30*(c*(a*x-1)/a/x)^(1/2)/x^3*c^3/a^(7/2)*(-1110*(a*x^2-x)^(1/2)*a^(7/2)*(1/a)^(1/2)*x^4+480*a^(7/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^4+660*a^(5/2)*(a*x^2-x)^(3/2)*x^2*(1/a)^(1/2)+555*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^4*a^3-480*a^(5/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^4-720*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^4*a^3-92*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)+12*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/(1/a)^(1/2)","B"
546,1,257,116,0.046000," ","int((c-c/a/x)^(5/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \left(-90 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, x^{3}+48 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{3}+48 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}+45 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{2}-48 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{3}-72 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{2}-4 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{6 x^{2} a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"-1/6*(c*(a*x-1)/a/x)^(1/2)/x^2*c^2/a^(5/2)*(-90*(a*x^2-x)^(1/2)*a^(5/2)*(1/a)^(1/2)*x^3+48*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^3+48*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)+45*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^2-48*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^3-72*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^2-4*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/(1/a)^(1/2)","B"
547,1,229,94,0.045000," ","int((c-c/a/x)^(3/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \left(-10 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, x^{2}+8 a^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{2}+4 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}+5 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{2} a -8 \sqrt{a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{2}-12 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{2} a \right)}{2 x \,a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)/x*c/a^(3/2)*(-10*(a*x^2-x)^(1/2)*a^(3/2)*(1/a)^(1/2)*x^2+8*a^(3/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^2+4*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2)+5*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^2*a-8*a^(1/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^2-12*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^2*a)/((a*x-1)*x)^(1/2)/(1/a)^(1/2)","B"
548,1,190,76,0.046000," ","int((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-4 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+4 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}-\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+6 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}\right)}{2 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x*(2*(a*x^2-x)^(1/2)*a^(3/2)*(1/a)^(1/2)-4*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+4*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2)-ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)+6*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(3/2)/(1/a)^(1/2)","B"
549,1,136,79,0.036000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-2 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+3 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+2 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}\right)}{2 \sqrt{\left(a x -1\right) x}\, c \,a^{\frac{3}{2}} \sqrt{\frac{1}{a}}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x*(-2*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+3*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)+2*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2))/((a*x-1)*x)^(1/2)/c/a^(3/2)/(1/a)^(1/2)","A"
550,1,134,78,0.042000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^(3/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-2 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+\ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+\sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}\right)}{2 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, c^{2} \sqrt{\frac{1}{a}}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)*(-2*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)+2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2))/((a*x-1)*x)^(1/2)/c^2/(1/a)^(1/2)","A"
551,1,370,100,0.048000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^(5/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(8 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{2}+2 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{2} a^{3}-a^{\frac{5}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{2}-4 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \left(\left(a x -1\right) x \right)^{\frac{3}{2}}-16 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x -4 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x \,a^{2}+2 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x +8 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+2 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}-\sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}\right)}{4 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, c^{3} \left(a x -1\right)^{2} \sqrt{\frac{1}{a}}}"," ",0,"-1/4*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)*(8*a^(7/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^2+2*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^2*a^3-a^(5/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^2-4*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(3/2)-16*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x-4*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x*a^2+2*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x+8*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+2*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)-2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2))/((a*x-1)*x)^(1/2)/c^3/(a*x-1)^2/(1/a)^(1/2)","B"
552,1,497,121,0.048000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^(7/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(84 a^{\frac{9}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{3}+36 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{4}-3 a^{\frac{7}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{3}-60 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x -252 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{2}-108 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{2} a^{3}+9 a^{\frac{5}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{2}+52 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \left(\left(a x -1\right) x \right)^{\frac{3}{2}}+252 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x +108 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x \,a^{2}-9 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x -84 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-36 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+3 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}\right)}{24 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, c^{4} \left(a x -1\right)^{3} \sqrt{\frac{1}{a}}}"," ",0,"-1/24*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)*(84*a^(9/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^3+36*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^4-3*a^(7/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^3-60*a^(7/2)*(1/a)^(1/2)*((a*x-1)*x)^(3/2)*x-252*a^(7/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^2-108*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^2*a^3+9*a^(5/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^2+52*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(3/2)+252*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x+108*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x*a^2-9*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x-84*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-36*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)+3*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2))/((a*x-1)*x)^(1/2)/c^4/(a*x-1)^3/(1/a)^(1/2)","B"
553,1,626,142,0.053000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^(9/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(1260 a^{\frac{11}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{4}+600 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{4} a^{5}-15 a^{\frac{9}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{4}-1020 a^{\frac{9}{2}} \sqrt{\frac{1}{a}}\, \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x^{2}-5040 a^{\frac{9}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{3}-2400 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{4}+60 a^{\frac{7}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{3}+1792 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x +7560 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{2}+3600 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{2} a^{3}-90 a^{\frac{5}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{2}-820 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \left(\left(a x -1\right) x \right)^{\frac{3}{2}}-5040 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x -2400 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x \,a^{2}+60 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x +1260 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+600 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}-15 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}\right)}{240 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, c^{5} \left(a x -1\right)^{4} \sqrt{\frac{1}{a}}}"," ",0,"-1/240*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)*(1260*a^(11/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^4+600*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^4*a^5-15*a^(9/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^4-1020*a^(9/2)*(1/a)^(1/2)*((a*x-1)*x)^(3/2)*x^2-5040*a^(9/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^3-2400*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^4+60*a^(7/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^3+1792*a^(7/2)*(1/a)^(1/2)*((a*x-1)*x)^(3/2)*x+7560*a^(7/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^2+3600*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^2*a^3-90*a^(5/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^2-820*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(3/2)-5040*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x-2400*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x*a^2+60*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x+1260*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+600*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)-15*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2))/((a*x-1)*x)^(1/2)/c^5/(a*x-1)^4/(1/a)^(1/2)","B"
554,1,227,217,0.066000," ","int((c-c/a/x)^(9/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{4} \left(14 \sqrt{-\left(a x +1\right) x}\, a^{\frac{11}{2}} x^{5}+105 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{5} a^{5}+3510 a^{\frac{9}{2}} \sqrt{-\left(a x +1\right) x}\, x^{4}+105 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{4} a^{4}+1440 a^{\frac{7}{2}} x^{3} \sqrt{-\left(a x +1\right) x}-220 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}+40 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}-4 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right) \sqrt{-a^{2} x^{2}+1}}{14 x^{3} a^{\frac{9}{2}} \left(a x +1\right) \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/14*(c*(a*x-1)/a/x)^(1/2)/x^3*c^4/a^(9/2)*(14*(-(a*x+1)*x)^(1/2)*a^(11/2)*x^5+105*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^5*a^5+3510*a^(9/2)*(-(a*x+1)*x)^(1/2)*x^4+105*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^4*a^4+1440*a^(7/2)*x^3*(-(a*x+1)*x)^(1/2)-220*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)+40*a^(3/2)*x*(-(a*x+1)*x)^(1/2)-4*a^(1/2)*(-(a*x+1)*x)^(1/2))*(-a^2*x^2+1)^(1/2)/(a*x+1)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
555,1,209,181,0.065000," ","int((c-c/a/x)^(7/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \left(30 a^{\frac{9}{2}} \sqrt{-\left(a x +1\right) x}\, x^{4}+195 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{4} a^{4}+3182 a^{\frac{7}{2}} x^{3} \sqrt{-\left(a x +1\right) x}+195 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{3} a^{3}+1096 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}-124 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+12 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right) \sqrt{-a^{2} x^{2}+1}}{30 x^{2} a^{\frac{7}{2}} \left(a x +1\right) \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/30*(c*(a*x-1)/a/x)^(1/2)/x^2*c^3/a^(7/2)*(30*a^(9/2)*(-(a*x+1)*x)^(1/2)*x^4+195*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^4*a^4+3182*a^(7/2)*x^3*(-(a*x+1)*x)^(1/2)+195*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^3*a^3+1096*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)-124*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+12*a^(1/2)*(-(a*x+1)*x)^(1/2))*(-a^2*x^2+1)^(1/2)/(a*x+1)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
556,1,191,145,0.066000," ","int((c-c/a/x)^(5/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \left(6 a^{\frac{7}{2}} x^{3} \sqrt{-\left(a x +1\right) x}+33 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{3} a^{3}+266 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}+33 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{2} a^{2}+64 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}-4 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right) \sqrt{-a^{2} x^{2}+1}}{6 x \,a^{\frac{5}{2}} \left(a x +1\right) \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/6*(c*(a*x-1)/a/x)^(1/2)/x*c^2/a^(5/2)*(6*a^(7/2)*x^3*(-(a*x+1)*x)^(1/2)+33*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^3*a^3+266*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)+33*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^2*a^2+64*a^(3/2)*x*(-(a*x+1)*x)^(1/2)-4*a^(1/2)*(-(a*x+1)*x)^(1/2))*(-a^2*x^2+1)^(1/2)/(a*x+1)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
557,1,164,109,0.062000," ","int((c-c/a/x)^(3/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \left(2 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}+9 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{2} a^{2}+38 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+9 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a +4 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right) \sqrt{-a^{2} x^{2}+1}}{2 a^{\frac{3}{2}} \left(a x +1\right) \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*c/a^(3/2)*(2*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)+9*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^2*a^2+38*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+9*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a+4*a^(1/2)*(-(a*x+1)*x)^(1/2))*(-a^2*x^2+1)^(1/2)/(a*x+1)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
558,1,140,99,0.056000," ","int((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+7 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a +18 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}+7 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right) \sqrt{-a^{2} x^{2}+1}}{2 \sqrt{a}\, \left(a x +1\right) \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*x*(2*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+7*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a+18*a^(1/2)*(-(a*x+1)*x)^(1/2)+7*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))*(-a^2*x^2+1)^(1/2)/a^(1/2)/(a*x+1)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
559,1,143,105,0.056000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+5 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a +10 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}+5 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right) \sqrt{-a^{2} x^{2}+1}}{2 \sqrt{a}\, c \left(a x +1\right) \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*x/a^(1/2)/c*(2*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+5*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a+10*a^(1/2)*(-(a*x+1)*x)^(1/2)+5*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))*(-a^2*x^2+1)^(1/2)/(a*x+1)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
560,1,143,107,0.053000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+3 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a +6 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}+3 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right) \sqrt{-a^{2} x^{2}+1}}{2 \sqrt{a}\, c^{2} \left(a x +1\right) \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*x/a^(1/2)/c^2*(2*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a+6*a^(1/2)*(-(a*x+1)*x)^(1/2)+3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))*(-a^2*x^2+1)^(1/2)/(a*x+1)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
561,1,279,158,0.065000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(5/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{2}\, \left(2 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x +a^{2} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x +4 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}+\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}+a^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x +\ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{-a^{2} x^{2}+1}}{4 a^{\frac{3}{2}} c^{3} \left(a x +1\right) \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/4*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)/c^3*2^(1/2)*(2*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x+a^2*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x+4*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)+arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)+a^(3/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x+ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*(-a^2*x^2+1)^(1/2)/(a*x+1)/(-1/a)^(1/2)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
562,1,315,195,0.068000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(7/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{2}\, \left(8 a^{\frac{7}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x^{2}+2 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x -4 a^{3} \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x^{2}+11 a^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x^{2}-14 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}+4 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}-11 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{-a^{2} x^{2}+1}}{16 a^{\frac{3}{2}} c^{4} \left(a x +1\right) \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)^{2}}"," ",0,"-1/16*(c*(a*x-1)/a/x)^(1/2)*x*2^(1/2)*(8*a^(7/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x^2+2*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x-4*a^3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x^2+11*a^(5/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x^2-14*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)+4*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)-11*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*(-a^2*x^2+1)^(1/2)/a^(3/2)/c^4/(a*x+1)/(-1/a)^(1/2)/(-(a*x+1)*x)^(1/2)/(a*x-1)^2","A"
563,1,165,93,0.043000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)/x^3,x)","\frac{a \left(-\frac{a^{2} x}{\sqrt{-a^{2} x^{2}+1}}-4 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}}+8 a \left(\frac{1}{3 a \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{-2 a^{2} \left(x -\frac{1}{a}\right)-2 a}{3 a \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)\right)}{c}"," ",0,"a/c*(-a^2*x/(-a^2*x^2+1)^(1/2)-4*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)+8*a*(1/3/a/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/3/a*(-2*a^2*(x-1/a)-2*a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)))","A"
564,0,0,49,0.248000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(c-c/a/x)^(1/2),x)","\int \frac{\left(a x +1\right) x^{m} \sqrt{c -\frac{c}{a x}}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(c-c/a/x)^(1/2),x)","F"
565,1,125,141,0.044000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(c-c/a/x)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(16 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}+4 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}-6 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}-3 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right)}{48 a^{\frac{5}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"-1/48*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(16*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)+4*a^(3/2)*x*(-(a*x+1)*x)^(1/2)-6*a^(1/2)*(-(a*x+1)*x)^(1/2)-3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))/a^(5/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
566,1,105,105,0.047000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(c-c/a/x)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(4 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}+\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right)}{8 a^{\frac{3}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"-1/8*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)/a^(3/2)*(4*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+2*a^(1/2)*(-(a*x+1)*x)^(1/2)+arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
567,1,91,67,0.042000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}-\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right)}{2 \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(2*a^(1/2)*(-(a*x+1)*x)^(1/2)-arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))/(a*x-1)/(-(a*x+1)*x)^(1/2)/a^(1/2)","A"
568,1,90,68,0.044000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{-a^{2} x^{2}+1}\, \left(\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a +2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right)}{\left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"(c*(a*x-1)/a/x)^(1/2)*(-a^2*x^2+1)^(1/2)*(arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a+2*a^(1/2)*(-(a*x+1)*x)^(1/2))/(a*x-1)/(-(a*x+1)*x)^(1/2)/a^(1/2)","A"
569,1,40,33,0.032000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^2,x)","-\frac{2 \left(a x +1\right)^{2} \sqrt{\frac{c \left(a x -1\right)}{a x}}}{3 x \sqrt{-a^{2} x^{2}+1}}"," ",0,"-2/3*(a*x+1)^2/x/(-a^2*x^2+1)^(1/2)*(c*(a*x-1)/a/x)^(1/2)","A"
570,1,46,68,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^3,x)","\frac{2 \left(a x +1\right)^{2} \left(2 a x -3\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}}{15 x^{2} \sqrt{-a^{2} x^{2}+1}}"," ",0,"2/15*(a*x+1)^2*(2*a*x-3)*(c*(a*x-1)/a/x)^(1/2)/x^2/(-a^2*x^2+1)^(1/2)","A"
571,1,54,104,0.029000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^4,x)","-\frac{2 \left(a x +1\right)^{2} \left(8 a^{2} x^{2}-12 a x +15\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}}{105 x^{3} \sqrt{-a^{2} x^{2}+1}}"," ",0,"-2/105*(a*x+1)^2*(8*a^2*x^2-12*a*x+15)*(c*(a*x-1)/a/x)^(1/2)/x^3/(-a^2*x^2+1)^(1/2)","A"
572,1,62,140,0.032000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^5,x)","\frac{2 \left(a x +1\right)^{2} \left(16 x^{3} a^{3}-24 a^{2} x^{2}+30 a x -35\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}}{315 x^{4} \sqrt{-a^{2} x^{2}+1}}"," ",0,"2/315*(a*x+1)^2*(16*a^3*x^3-24*a^2*x^2+30*a*x-35)*(c*(a*x-1)/a/x)^(1/2)/x^4/(-a^2*x^2+1)^(1/2)","A"
573,1,172,106,0.042000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3*(c-c/a/x)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(32 x \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{7}{2}}+112 \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{5}{2}}+212 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} x -106 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}}+256 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}+128 a \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)-53 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \right)}{128 \sqrt{\left(a x -1\right) x}\, a^{\frac{9}{2}}}"," ",0,"-1/128*(c*(a*x-1)/a/x)^(1/2)*x*(32*x*(a*x^2-x)^(3/2)*a^(7/2)+112*(a*x^2-x)^(3/2)*a^(5/2)+212*(a*x^2-x)^(1/2)*a^(5/2)*x-106*(a*x^2-x)^(1/2)*a^(3/2)+256*a^(3/2)*((a*x-1)*x)^(1/2)+128*a*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))-53*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a)/((a*x-1)*x)^(1/2)/a^(9/2)","A"
574,1,155,85,0.040000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-16 \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{5}{2}}-60 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} x +30 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}}-96 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}-48 a \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)+15 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \right)}{48 \sqrt{\left(a x -1\right) x}\, a^{\frac{7}{2}}}"," ",0,"1/48*(c*(a*x-1)/a/x)^(1/2)*x*(-16*(a*x^2-x)^(3/2)*a^(5/2)-60*(a*x^2-x)^(1/2)*a^(5/2)*x+30*(a*x^2-x)^(1/2)*a^(3/2)-96*a^(3/2)*((a*x-1)*x)^(1/2)-48*a*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))+15*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a)/((a*x-1)*x)^(1/2)/a^(7/2)","A"
575,1,139,64,0.036000," ","int((a*x+1)^2/(-a^2*x^2+1)*x*(c-c/a/x)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(4 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} x -2 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}}+16 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}+8 a \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)-\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \right)}{8 \sqrt{\left(a x -1\right) x}\, a^{\frac{5}{2}}}"," ",0,"-1/8*(c*(a*x-1)/a/x)^(1/2)*x*(4*(a*x^2-x)^(1/2)*a^(5/2)*x-2*(a*x^2-x)^(1/2)*a^(3/2)+16*a^(3/2)*((a*x-1)*x)^(1/2)+8*a*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))-ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a)/((a*x-1)*x)^(1/2)/a^(5/2)","B"
576,1,120,43,0.041000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{a \,x^{2}-x}\, \sqrt{a}-4 \sqrt{\left(a x -1\right) x}\, \sqrt{a}-\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)-2 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x*(2*(a*x^2-x)^(1/2)*a^(1/2)-4*((a*x-1)*x)^(1/2)*a^(1/2)-ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))-2*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/a^(1/2)","B"
577,1,98,39,0.044000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2)/x,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-2 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}+2 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}-\ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a \right)}{x \sqrt{\left(a x -1\right) x}\, \sqrt{a}}"," ",0,"(c*(a*x-1)/a/x)^(1/2)/x*(-2*a^(3/2)*((a*x-1)*x)^(1/2)*x^2+2*(a*x^2-x)^(3/2)*a^(1/2)-ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a)/((a*x-1)*x)^(1/2)/a^(1/2)","B"
578,1,27,36,0.030000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2)/x^2,x)","-\frac{2 \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(5 a x +1\right)}{3 x}"," ",0,"-2/3*(c*(a*x-1)/a/x)^(1/2)*(5*a*x+1)/x","A"
579,1,35,61,0.031000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2)/x^3,x)","-\frac{2 \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(6 a^{2} x^{2}+3 a x +1\right)}{5 x^{2}}"," ",0,"-2/5*(c*(a*x-1)/a/x)^(1/2)*(6*a^2*x^2+3*a*x+1)/x^2","A"
580,1,43,82,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2)/x^4,x)","-\frac{2 \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(104 x^{3} a^{3}+52 a^{2} x^{2}+39 a x +15\right)}{105 x^{3}}"," ",0,"-2/105*(c*(a*x-1)/a/x)^(1/2)*(104*a^3*x^3+52*a^2*x^2+39*a*x+15)/x^3","A"
581,1,51,103,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2)/x^5,x)","-\frac{2 \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(272 x^{4} a^{4}+136 x^{3} a^{3}+102 a^{2} x^{2}+85 a x +35\right)}{315 x^{4}}"," ",0,"-2/315*(c*(a*x-1)/a/x)^(1/2)*(272*a^4*x^4+136*a^3*x^3+102*a^2*x^2+85*a*x+35)/x^4","A"
582,1,247,228,0.059000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(96 a^{\frac{9}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x^{3}+272 a^{\frac{7}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x^{2}+428 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x +894 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}-1089 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}+1536 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{768 a^{\frac{9}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/768*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(96*a^(9/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x^3+272*a^(7/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x^2+428*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x+894*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)-1089*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)+1536*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/a^(9/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
583,1,219,192,0.057000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(16 a^{\frac{7}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x^{2}+52 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x +114 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}-135 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}+192 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{96 a^{\frac{7}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/96*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(16*a^(7/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x^2+52*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x+114*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)-135*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)+192*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/a^(7/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
584,1,191,156,0.050000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(4 a^{\frac{5}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, x +18 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}-23 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}+32 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{16 a^{\frac{5}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/16*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(4*a^(5/2)*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*x+18*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)-23*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)+32*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/a^(5/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
585,1,165,119,0.056000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(2 \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{2}\, \sqrt{-\frac{1}{a}}-5 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) a \sqrt{2}\, \sqrt{-\frac{1}{a}}+8 \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) \sqrt{a}\right) \sqrt{2}}{4 \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{-\frac{1}{a}}}"," ",0,"1/4*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(2*(-(a*x+1)*x)^(1/2)*a^(3/2)*2^(1/2)*(-1/a)^(1/2)-5*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*a*2^(1/2)*(-1/a)^(1/2)+8*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*a^(1/2))*2^(1/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)/a^(3/2)/(-1/a)^(1/2)","A"
586,1,166,118,0.059000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{-a^{2} x^{2}+1}\, \left(-\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x a +2 \sqrt{-\left(a x +1\right) x}\, \sqrt{a}\, \sqrt{2}\, \sqrt{-\frac{1}{a}}+4 \sqrt{a}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x \right) \sqrt{2}}{2 \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{a}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*(-a^2*x^2+1)^(1/2)*(-arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*2^(1/2)*(-1/a)^(1/2)*x*a+2*(-(a*x+1)*x)^(1/2)*a^(1/2)*2^(1/2)*(-1/a)^(1/2)+4*a^(1/2)*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x)*2^(1/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)/a^(1/2)/(-1/a)^(1/2)","A"
587,1,150,115,0.061000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^2,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{-a^{2} x^{2}+1}\, \left(7 a \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x \sqrt{-\left(a x +1\right) x}+6 a \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x^{2}+\sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\right) \sqrt{2}}{3 x \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/3*(c*(a*x-1)/a/x)^(1/2)/x*(-a^2*x^2+1)^(1/2)*(7*a*2^(1/2)*(-1/a)^(1/2)*x*(-(a*x+1)*x)^(1/2)+6*a*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x^2+2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2))*2^(1/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
588,1,181,151,0.064000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^3,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{-a^{2} x^{2}+1}\, \left(38 a^{2} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x^{2} \sqrt{-\left(a x +1\right) x}+30 a^{2} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x^{3}+11 a \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x \sqrt{-\left(a x +1\right) x}+3 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\right) \sqrt{2}}{15 x^{2} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/15*(c*(a*x-1)/a/x)^(1/2)/x^2*(-a^2*x^2+1)^(1/2)*(38*a^2*2^(1/2)*(-1/a)^(1/2)*x^2*(-(a*x+1)*x)^(1/2)+30*a^2*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x^3+11*a*2^(1/2)*(-1/a)^(1/2)*x*(-(a*x+1)*x)^(1/2)+3*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2))*2^(1/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
589,1,209,187,0.064000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^4,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{-a^{2} x^{2}+1}\, \left(52 x^{3} \sqrt{-\left(a x +1\right) x}\, a^{3} \sqrt{2}\, \sqrt{-\frac{1}{a}}+42 a^{3} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x^{4}+16 a^{2} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x^{2} \sqrt{-\left(a x +1\right) x}+9 a \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x \sqrt{-\left(a x +1\right) x}+3 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\right) \sqrt{2}}{21 x^{3} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/21*(c*(a*x-1)/a/x)^(1/2)/x^3*(-a^2*x^2+1)^(1/2)*(52*x^3*(-(a*x+1)*x)^(1/2)*a^3*2^(1/2)*(-1/a)^(1/2)+42*a^3*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x^4+16*a^2*2^(1/2)*(-1/a)^(1/2)*x^2*(-(a*x+1)*x)^(1/2)+9*a*2^(1/2)*(-1/a)^(1/2)*x*(-(a*x+1)*x)^(1/2)+3*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2))*2^(1/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
590,1,237,223,0.064000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^5,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{-a^{2} x^{2}+1}\, \left(788 x^{4} \sqrt{-\left(a x +1\right) x}\, a^{4} \sqrt{2}\, \sqrt{-\frac{1}{a}}+630 a^{4} \ln \left(\frac{2 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\, a -3 a x -1}{a x -1}\right) x^{5}+236 x^{3} \sqrt{-\left(a x +1\right) x}\, a^{3} \sqrt{2}\, \sqrt{-\frac{1}{a}}+138 a^{2} \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x^{2} \sqrt{-\left(a x +1\right) x}+95 a \sqrt{2}\, \sqrt{-\frac{1}{a}}\, x \sqrt{-\left(a x +1\right) x}+35 \sqrt{2}\, \sqrt{-\frac{1}{a}}\, \sqrt{-\left(a x +1\right) x}\right) \sqrt{2}}{315 x^{4} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{-\frac{1}{a}}}"," ",0,"1/315*(c*(a*x-1)/a/x)^(1/2)/x^4*(-a^2*x^2+1)^(1/2)*(788*x^4*(-(a*x+1)*x)^(1/2)*a^4*2^(1/2)*(-1/a)^(1/2)+630*a^4*ln((2*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2)*a-3*a*x-1)/(a*x-1))*x^5+236*x^3*(-(a*x+1)*x)^(1/2)*a^3*2^(1/2)*(-1/a)^(1/2)+138*a^2*2^(1/2)*(-1/a)^(1/2)*x^2*(-(a*x+1)*x)^(1/2)+95*a*2^(1/2)*(-1/a)^(1/2)*x*(-(a*x+1)*x)^(1/2)+35*2^(1/2)*(-1/a)^(1/2)*(-(a*x+1)*x)^(1/2))*2^(1/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)/(-1/a)^(1/2)","A"
591,0,0,104,0.328000," ","int(x^m*(c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \sqrt{c -\frac{c}{a x}}\, \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int(x^m*(c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
592,1,125,146,0.052000," ","int(x^2*(c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(16 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}-44 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+66 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}+33 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right)}{48 a^{\frac{5}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"1/48*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)/a^(5/2)*(16*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)-44*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+66*a^(1/2)*(-(a*x+1)*x)^(1/2)+33*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
593,1,107,110,0.048000," ","int(x*(c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(4 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}-14 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}-7 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right)}{8 a^{\frac{3}{2}} \left(a x -1\right) \sqrt{-\left(a x +1\right) x}}"," ",0,"1/8*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(4*a^(3/2)*x*(-(a*x+1)*x)^(1/2)-14*a^(1/2)*(-(a*x+1)*x)^(1/2)-7*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))/a^(3/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)","A"
594,1,91,74,0.053000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}+3 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right)}{2 \left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(2*a^(1/2)*(-(a*x+1)*x)^(1/2)+3*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))/(a*x-1)/(-(a*x+1)*x)^(1/2)/a^(1/2)","A"
595,1,91,73,0.053000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a +2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right) \sqrt{-a^{2} x^{2}+1}}{\left(a x -1\right) \sqrt{-\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"(c*(a*x-1)/a/x)^(1/2)*(-arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a+2*a^(1/2)*(-(a*x+1)*x)^(1/2))*(-a^2*x^2+1)^(1/2)/(a*x-1)/(-(a*x+1)*x)^(1/2)/a^(1/2)","A"
596,1,46,70,0.031000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x)","-\frac{2 \left(5 a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{-a^{2} x^{2}+1}}{3 \left(a x -1\right) x}"," ",0,"-2/3*(5*a*x-1)*(c*(a*x-1)/a/x)^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x-1)/x","A"
597,1,54,106,0.029000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^3,x)","\frac{2 \left(6 a^{2} x^{2}-3 a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{-a^{2} x^{2}+1}}{5 x^{2} \left(a x -1\right)}"," ",0,"2/5*(6*a^2*x^2-3*a*x+1)*(c*(a*x-1)/a/x)^(1/2)*(-a^2*x^2+1)^(1/2)/x^2/(a*x-1)","A"
598,1,62,142,0.030000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^4,x)","-\frac{2 \left(104 x^{3} a^{3}-52 a^{2} x^{2}+39 a x -15\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{-a^{2} x^{2}+1}}{105 x^{3} \left(a x -1\right)}"," ",0,"-2/105*(104*a^3*x^3-52*a^2*x^2+39*a*x-15)*(c*(a*x-1)/a/x)^(1/2)*(-a^2*x^2+1)^(1/2)/x^3/(a*x-1)","A"
599,1,259,139,0.041000," ","int(x^3*(c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(96 x \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{9}{2}} \sqrt{\frac{1}{a}}-176 \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{7}{2}} \sqrt{\frac{1}{a}}+252 \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, x -126 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} \sqrt{\frac{1}{a}}-768 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}+768 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right)+1152 a^{2} \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}-63 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, a^{2}\right)}{384 \sqrt{\left(a x -1\right) x}\, a^{\frac{11}{2}} \sqrt{\frac{1}{a}}}"," ",0,"-1/384*(c*(a*x-1)/a/x)^(1/2)*x*(96*x*(a*x^2-x)^(3/2)*a^(9/2)*(1/a)^(1/2)-176*(a*x^2-x)^(3/2)*a^(7/2)*(1/a)^(1/2)+252*(a*x^2-x)^(1/2)*a^(7/2)*(1/a)^(1/2)*x-126*(a*x^2-x)^(1/2)*a^(5/2)*(1/a)^(1/2)-768*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)+768*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))+1152*a^2*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)-63*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*a^2)/((a*x-1)*x)^(1/2)/a^(11/2)/(1/a)^(1/2)","A"
600,1,237,118,0.039000," ","int(x^2*(c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(16 \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{7}{2}} \sqrt{\frac{1}{a}}-36 \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, x +18 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} \sqrt{\frac{1}{a}}+96 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}-96 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right)-144 a^{2} \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}+9 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, a^{2}\right)}{48 \sqrt{\left(a x -1\right) x}\, a^{\frac{9}{2}} \sqrt{\frac{1}{a}}}"," ",0,"-1/48*(c*(a*x-1)/a/x)^(1/2)*x*(16*(a*x^2-x)^(3/2)*a^(7/2)*(1/a)^(1/2)-36*(a*x^2-x)^(1/2)*a^(7/2)*(1/a)^(1/2)*x+18*(a*x^2-x)^(1/2)*a^(5/2)*(1/a)^(1/2)+96*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)-96*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))-144*a^2*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)+9*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*a^2)/((a*x-1)*x)^(1/2)/a^(9/2)/(1/a)^(1/2)","A"
601,1,216,97,0.040000," ","int(x*(c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(4 \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, x -2 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} \sqrt{\frac{1}{a}}-16 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}+16 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right)+24 a^{2} \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}-\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, a^{2}\right)}{8 \sqrt{\left(a x -1\right) x}\, a^{\frac{7}{2}} \sqrt{\frac{1}{a}}}"," ",0,"-1/8*(c*(a*x-1)/a/x)^(1/2)*x*(4*(a*x^2-x)^(1/2)*a^(7/2)*(1/a)^(1/2)*x-2*(a*x^2-x)^(1/2)*a^(5/2)*(1/a)^(1/2)-16*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)+16*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))+24*a^2*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)-ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*a^2)/((a*x-1)*x)^(1/2)/a^(7/2)/(1/a)^(1/2)","B"
602,1,190,76,0.043000," ","int((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-4 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+4 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}-\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+6 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}\right)}{2 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x*(2*(a*x^2-x)^(1/2)*a^(3/2)*(1/a)^(1/2)-4*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+4*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2)-ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)+6*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(3/2)/(1/a)^(1/2)","B"
603,1,227,69,0.048000," ","int((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-4 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, x^{2}+2 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} x^{2} \sqrt{\frac{1}{a}}+2 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}+2 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{2} a -2 \sqrt{a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{2}-3 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{2} a \right)}{x \sqrt{\left(a x -1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}}"," ",0,"(c*(a*x-1)/a/x)^(1/2)/x*(-4*(a*x^2-x)^(1/2)*a^(3/2)*(1/a)^(1/2)*x^2+2*((a*x-1)*x)^(1/2)*a^(3/2)*x^2*(1/a)^(1/2)+2*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2)+2*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^2*a-2*a^(1/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^2-3*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^2*a)/((a*x-1)*x)^(1/2)/a^(1/2)/(1/a)^(1/2)","B"
604,1,254,67,0.044000," ","int((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^2,x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-18 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, x^{3}+6 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{3}+12 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}+9 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{2}-6 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{3}-9 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{2}-2 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{3 x^{2} \sqrt{\left(a x -1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}}"," ",0,"-1/3*(c*(a*x-1)/a/x)^(1/2)/x^2*(-18*(a*x^2-x)^(1/2)*a^(5/2)*(1/a)^(1/2)*x^3+6*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^3+12*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)+9*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^2-6*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^3-9*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^2-2*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(1/2)/(1/a)^(1/2)","B"
605,1,278,94,0.047000," ","int((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^3,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-90 \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, x^{4}+30 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{4}+60 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2} \sqrt{\frac{1}{a}}+45 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{4} a^{3}-30 a^{\frac{5}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{4}-45 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{4} a^{3}-16 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}+6 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{15 x^{3} \sqrt{\left(a x -1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}}"," ",0,"1/15*(c*(a*x-1)/a/x)^(1/2)/x^3*(-90*(a*x^2-x)^(1/2)*a^(7/2)*(1/a)^(1/2)*x^4+30*a^(7/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^4+60*a^(5/2)*(a*x^2-x)^(3/2)*x^2*(1/a)^(1/2)+45*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^4*a^3-30*a^(5/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^4-45*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^4*a^3-16*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)+6*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(1/2)/(1/a)^(1/2)","B"
606,1,302,94,0.050000," ","int((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^4,x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-126 \sqrt{a \,x^{2}-x}\, \sqrt{\frac{1}{a}}\, a^{\frac{9}{2}} x^{5}+42 \sqrt{\frac{1}{a}}\, a^{\frac{9}{2}} \sqrt{\left(a x -1\right) x}\, x^{5}+84 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, a^{\frac{7}{2}} x^{3}+63 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{5} a^{4}-42 \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{2}\, a^{\frac{7}{2}} x^{5}-63 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{5} a^{4}-20 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2} \sqrt{\frac{1}{a}}+12 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}-6 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{21 x^{4} \sqrt{\left(a x -1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}}"," ",0,"-1/21*(c*(a*x-1)/a/x)^(1/2)/x^4*(-126*(a*x^2-x)^(1/2)*(1/a)^(1/2)*a^(9/2)*x^5+42*(1/a)^(1/2)*a^(9/2)*((a*x-1)*x)^(1/2)*x^5+84*(a*x^2-x)^(3/2)*(1/a)^(1/2)*a^(7/2)*x^3+63*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^5*a^4-42*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*2^(1/2)*a^(7/2)*x^5-63*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^5*a^4-20*a^(5/2)*(a*x^2-x)^(3/2)*x^2*(1/a)^(1/2)+12*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)-6*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(1/2)/(1/a)^(1/2)","B"
607,1,326,136,0.051000," ","int((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^5,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(630 \sqrt{\left(a x -1\right) x}\, a^{\frac{11}{2}} \sqrt{\frac{1}{a}}\, x^{6}-1890 \sqrt{a \,x^{2}-x}\, a^{\frac{11}{2}} \sqrt{\frac{1}{a}}\, x^{6}+1260 \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{9}{2}} \sqrt{\frac{1}{a}}\, x^{4}+945 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{6} a^{5}-630 a^{\frac{9}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{6}-945 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{6} a^{5}-316 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, a^{\frac{7}{2}} x^{3}+156 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2} \sqrt{\frac{1}{a}}-120 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}+70 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{315 x^{5} \sqrt{\left(a x -1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}}"," ",0,"1/315*(c*(a*x-1)/a/x)^(1/2)/x^5*(630*((a*x-1)*x)^(1/2)*a^(11/2)*(1/a)^(1/2)*x^6-1890*(a*x^2-x)^(1/2)*a^(11/2)*(1/a)^(1/2)*x^6+1260*(a*x^2-x)^(3/2)*a^(9/2)*(1/a)^(1/2)*x^4+945*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^6*a^5-630*a^(9/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^6-945*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^6*a^5-316*(a*x^2-x)^(3/2)*(1/a)^(1/2)*a^(7/2)*x^3+156*a^(5/2)*(a*x^2-x)^(3/2)*x^2*(1/a)^(1/2)-120*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)+70*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(1/2)/(1/a)^(1/2)","B"
608,1,194,210,0.062000," ","int(x^3*(c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(96 a^{\frac{9}{2}} \sqrt{-\left(a x +1\right) x}\, x^{4}-400 a^{\frac{7}{2}} x^{3} \sqrt{-\left(a x +1\right) x}+892 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}-2230 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}-3345 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a -6690 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}-3345 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right) \sqrt{-a^{2} x^{2}+1}}{384 a^{\frac{7}{2}} \left(a x +1\right) \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/384*(c*(a*x-1)/a/x)^(1/2)*x*(96*a^(9/2)*(-(a*x+1)*x)^(1/2)*x^4-400*a^(7/2)*x^3*(-(a*x+1)*x)^(1/2)+892*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)-2230*a^(3/2)*x*(-(a*x+1)*x)^(1/2)-3345*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a-6690*a^(1/2)*(-(a*x+1)*x)^(1/2)-3345*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))*(-a^2*x^2+1)^(1/2)/a^(7/2)/(a*x+1)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
609,1,176,174,0.061000," ","int(x^2*(c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(16 a^{\frac{7}{2}} x^{3} \sqrt{-\left(a x +1\right) x}-76 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}+238 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+357 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a +714 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}+357 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right) \sqrt{-a^{2} x^{2}+1}}{48 a^{\frac{5}{2}} \left(a x +1\right) \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/48*(c*(a*x-1)/a/x)^(1/2)*x*(16*a^(7/2)*x^3*(-(a*x+1)*x)^(1/2)-76*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)+238*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+357*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a+714*a^(1/2)*(-(a*x+1)*x)^(1/2)+357*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))/a^(5/2)*(-a^2*x^2+1)^(1/2)/(a*x+1)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
610,1,158,138,0.058000," ","int(x*(c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(4 a^{\frac{5}{2}} x^{2} \sqrt{-\left(a x +1\right) x}-26 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}-47 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a -94 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}-47 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right) \sqrt{-a^{2} x^{2}+1}}{8 a^{\frac{3}{2}} \left(a x +1\right) \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/8*(c*(a*x-1)/a/x)^(1/2)*x*(4*a^(5/2)*x^2*(-(a*x+1)*x)^(1/2)-26*a^(3/2)*x*(-(a*x+1)*x)^(1/2)-47*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a-94*a^(1/2)*(-(a*x+1)*x)^(1/2)-47*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))*(-a^2*x^2+1)^(1/2)/a^(3/2)/(a*x+1)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
611,1,140,99,0.058000," ","int((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+7 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a +18 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}+7 \arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right)\right) \sqrt{-a^{2} x^{2}+1}}{2 \sqrt{a}\, \left(a x +1\right) \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*x*(2*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+7*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a+18*a^(1/2)*(-(a*x+1)*x)^(1/2)+7*arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2)))*(-a^2*x^2+1)^(1/2)/a^(1/2)/(a*x+1)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
612,1,142,100,0.059000," ","int((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x^{2} a^{2}+10 a^{\frac{3}{2}} x \sqrt{-\left(a x +1\right) x}+\arctan \left(\frac{2 a x +1}{2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}}\right) x a +2 \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\right) \sqrt{-a^{2} x^{2}+1}}{\left(a x +1\right) \sqrt{a}\, \sqrt{-\left(a x +1\right) x}\, \left(a x -1\right)}"," ",0,"(c*(a*x-1)/a/x)^(1/2)*(arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x^2*a^2+10*a^(3/2)*x*(-(a*x+1)*x)^(1/2)+arctan(1/2/a^(1/2)*(2*a*x+1)/(-(a*x+1)*x)^(1/2))*x*a+2*a^(1/2)*(-(a*x+1)*x)^(1/2))*(-a^2*x^2+1)^(1/2)/(a*x+1)/a^(1/2)/(-(a*x+1)*x)^(1/2)/(a*x-1)","A"
613,1,61,99,0.030000," ","int((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x)","\frac{2 \left(23 a^{2} x^{2}+10 a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 \left(a x +1\right)^{2} x \left(a x -1\right)^{2}}"," ",0,"2/3*(23*a^2*x^2+10*a*x-1)*(c*(a*x-1)/a/x)^(1/2)*(-a^2*x^2+1)^(3/2)/(a*x+1)^2/x/(a*x-1)^2","A"
614,1,69,134,0.033000," ","int((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x)","-\frac{2 \left(158 x^{3} a^{3}+79 a^{2} x^{2}-16 a x +3\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{15 \left(a x +1\right)^{2} x^{2} \left(a x -1\right)^{2}}"," ",0,"-2/15*(158*a^3*x^3+79*a^2*x^2-16*a*x+3)*(c*(a*x-1)/a/x)^(1/2)*(-a^2*x^2+1)^(3/2)/(a*x+1)^2/x^2/(a*x-1)^2","A"
615,1,77,173,0.031000," ","int((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x)","\frac{2 \left(1336 x^{4} a^{4}+668 x^{3} a^{3}-167 a^{2} x^{2}+66 a x -15\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{105 \left(a x +1\right)^{2} x^{3} \left(a x -1\right)^{2}}"," ",0,"2/105*(1336*a^4*x^4+668*a^3*x^3-167*a^2*x^2+66*a*x-15)*(c*(a*x-1)/a/x)^(1/2)*(-a^2*x^2+1)^(3/2)/(a*x+1)^2/x^3/(a*x-1)^2","A"
616,1,85,209,0.031000," ","int((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x)","-\frac{2 \left(656 x^{5} a^{5}+328 x^{4} a^{4}-82 x^{3} a^{3}+41 a^{2} x^{2}-20 a x +5\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{45 \left(a x +1\right)^{2} x^{4} \left(a x -1\right)^{2}}"," ",0,"-2/45*(656*a^5*x^5+328*a^4*x^4-82*a^3*x^3+41*a^2*x^2-20*a*x+5)*(c*(a*x-1)/a/x)^(1/2)*(-a^2*x^2+1)^(3/2)/(a*x+1)^2/x^4/(a*x-1)^2","A"
617,0,0,60,0.194000," ","int(exp(n*arctanh(a*x))*(c-c/a/x)^p,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(c -\frac{c}{a x}\right)^{p}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(c-c/a/x)^p,x)","F"
618,0,0,54,0.125000," ","int((c-c/a/x)^p/exp(2*p*arctanh(a*x)),x)","\int \left(c -\frac{c}{a x}\right)^{p} {\mathrm e}^{-2 p \arctanh \left(a x \right)}\, dx"," ",0,"int((c-c/a/x)^p/exp(2*p*arctanh(a*x)),x)","F"
619,0,0,52,0.118000," ","int(exp(2*p*arctanh(a*x))*(c-c/a/x)^p,x)","\int {\mathrm e}^{2 p \arctanh \left(a x \right)} \left(c -\frac{c}{a x}\right)^{p}\, dx"," ",0,"int(exp(2*p*arctanh(a*x))*(c-c/a/x)^p,x)","F"
620,0,0,114,0.049000," ","int(exp(n*arctanh(a*x))*(c-c/a/x)^2,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(c -\frac{c}{a x}\right)^{2}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(c-c/a/x)^2,x)","F"
621,0,0,159,0.044000," ","int(exp(n*arctanh(a*x))*(c-c/a/x),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(c -\frac{c}{a x}\right)\, dx"," ",0,"int(exp(n*arctanh(a*x))*(c-c/a/x),x)","F"
622,0,0,97,0.044000," ","int(exp(n*arctanh(a*x))/(c-c/a/x),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{c -\frac{c}{a x}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(c-c/a/x),x)","F"
623,0,0,121,0.046000," ","int(exp(n*arctanh(a*x))/(c-c/a/x)^2,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\left(c -\frac{c}{a x}\right)^{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(c-c/a/x)^2,x)","F"
624,0,0,42,0.043000," ","int(exp(n*arctanh(a*x))*(c-c/a/x)^(3/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(c -\frac{c}{a x}\right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(c-c/a/x)^(3/2),x)","F"
625,0,0,42,0.043000," ","int(exp(n*arctanh(a*x))*(c-c/a/x)^(1/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \sqrt{c -\frac{c}{a x}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(c-c/a/x)^(1/2),x)","F"
626,0,0,42,0.046000," ","int(exp(n*arctanh(a*x))/(c-c/a/x)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\sqrt{c -\frac{c}{a x}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(c-c/a/x)^(1/2),x)","F"
627,0,0,42,0.045000," ","int(exp(n*arctanh(a*x))/(c-c/a/x)^(3/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\left(c -\frac{c}{a x}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(c-c/a/x)^(3/2),x)","F"
628,1,233,149,0.065000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^4,x)","-\frac{c^{4} \sqrt{-a^{2} x^{2}+1}}{a}+\frac{c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{35 c^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a}+\frac{176 c^{4} \sqrt{-a^{2} x^{2}+1}}{105 a^{2} x}-\frac{122 c^{4} \sqrt{-a^{2} x^{2}+1}}{105 a^{4} x^{3}}-\frac{29 c^{4} \sqrt{-a^{2} x^{2}+1}}{16 x^{2} a^{3}}-\frac{c^{4} \sqrt{-a^{2} x^{2}+1}}{7 a^{8} x^{7}}+\frac{22 c^{4} \sqrt{-a^{2} x^{2}+1}}{35 a^{6} x^{5}}-\frac{c^{4} \sqrt{-a^{2} x^{2}+1}}{6 a^{7} x^{6}}+\frac{19 c^{4} \sqrt{-a^{2} x^{2}+1}}{24 a^{5} x^{4}}"," ",0,"-c^4*(-a^2*x^2+1)^(1/2)/a+c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+35/16*c^4/a*arctanh(1/(-a^2*x^2+1)^(1/2))+176/105*c^4*(-a^2*x^2+1)^(1/2)/a^2/x-122/105*c^4*(-a^2*x^2+1)^(1/2)/a^4/x^3-29/16*c^4*(-a^2*x^2+1)^(1/2)/x^2/a^3-1/7*c^4/a^8/x^7*(-a^2*x^2+1)^(1/2)+22/35*c^4/a^6/x^5*(-a^2*x^2+1)^(1/2)-1/6*c^4/a^7/x^6*(-a^2*x^2+1)^(1/2)+19/24*c^4/a^5/x^4*(-a^2*x^2+1)^(1/2)","A"
629,1,187,120,0.053000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^3,x)","-\frac{c^{3} \sqrt{-a^{2} x^{2}+1}}{a}+\frac{c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{15 c^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}+\frac{23 c^{3} \sqrt{-a^{2} x^{2}+1}}{15 a^{2} x}-\frac{11 c^{3} \sqrt{-a^{2} x^{2}+1}}{15 a^{4} x^{3}}-\frac{9 c^{3} \sqrt{-a^{2} x^{2}+1}}{8 x^{2} a^{3}}+\frac{c^{3} \sqrt{-a^{2} x^{2}+1}}{4 a^{5} x^{4}}+\frac{c^{3} \sqrt{-a^{2} x^{2}+1}}{5 a^{6} x^{5}}"," ",0,"-c^3*(-a^2*x^2+1)^(1/2)/a+c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+15/8*c^3/a*arctanh(1/(-a^2*x^2+1)^(1/2))+23/15*c^3*(-a^2*x^2+1)^(1/2)/a^2/x-11/15*c^3/a^4/x^3*(-a^2*x^2+1)^(1/2)-9/8*c^3*(-a^2*x^2+1)^(1/2)/x^2/a^3+1/4*c^3/a^5/x^4*(-a^2*x^2+1)^(1/2)+1/5*c^3/a^6/x^5*(-a^2*x^2+1)^(1/2)","A"
630,1,141,91,0.045000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^2,x)","-\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{a}+\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{3 c^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}+\frac{4 c^{2} \sqrt{-a^{2} x^{2}+1}}{3 a^{2} x}-\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{3 a^{4} x^{3}}-\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{2 a^{3} x^{2}}"," ",0,"-c^2*(-a^2*x^2+1)^(1/2)/a+c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+3/2*c^2/a*arctanh(1/(-a^2*x^2+1)^(1/2))+4/3*c^2*(-a^2*x^2+1)^(1/2)/a^2/x-1/3*c^2/a^4/x^3*(-a^2*x^2+1)^(1/2)-1/2*c^2/a^3/x^2*(-a^2*x^2+1)^(1/2)","A"
631,1,85,54,0.039000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2),x)","-\frac{c \sqrt{-a^{2} x^{2}+1}}{a}+\frac{c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{c \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}+\frac{c \sqrt{-a^{2} x^{2}+1}}{a^{2} x}"," ",0,"-c*(-a^2*x^2+1)^(1/2)/a+c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+c/a*arctanh(1/(-a^2*x^2+1)^(1/2))+c*(-a^2*x^2+1)^(1/2)/a^2/x","A"
632,1,94,57,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{a c}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c \sqrt{a^{2}}}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{a^{2} c \left(x -\frac{1}{a}\right)}"," ",0,"-(-a^2*x^2+1)^(1/2)/a/c+1/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/a^2/c/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
633,1,177,84,0.047000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^2,x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{a \,c^{2}}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{2} \sqrt{a^{2}}}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{6 a^{3} c^{2} \left(x -\frac{1}{a}\right)^{2}}+\frac{19 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{12 a^{2} c^{2} \left(x -\frac{1}{a}\right)}-\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{4 a^{2} c^{2} \left(x +\frac{1}{a}\right)}"," ",0,"-(-a^2*x^2+1)^(1/2)/a/c^2+1/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/6/a^3/c^2/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+19/12/a^2/c^2/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/4/a^2/c^2/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)","B"
634,1,259,113,0.052000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^3,x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{a \,c^{3}}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{3} \sqrt{a^{2}}}+\frac{23 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{60 a^{3} c^{3} \left(x -\frac{1}{a}\right)^{2}}+\frac{493 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{240 a^{2} c^{3} \left(x -\frac{1}{a}\right)}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{20 a^{4} c^{3} \left(x -\frac{1}{a}\right)^{3}}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{24 a^{3} c^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{25 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{48 a^{2} c^{3} \left(x +\frac{1}{a}\right)}"," ",0,"-(-a^2*x^2+1)^(1/2)/a/c^3+1/c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+23/60/a^3/c^3/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+493/240/a^2/c^3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/20/a^4/c^3/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/24/a^3/c^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-25/48/a^2/c^3/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)","B"
635,1,341,142,0.056000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^4,x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{a \,c^{4}}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{4} \sqrt{a^{2}}}+\frac{211 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{336 a^{3} c^{4} \left(x -\frac{1}{a}\right)^{2}}+\frac{1657 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{672 a^{2} c^{4} \left(x -\frac{1}{a}\right)}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{56 a^{5} c^{4} \left(x -\frac{1}{a}\right)^{4}}+\frac{17 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{112 a^{4} c^{4} \left(x -\frac{1}{a}\right)^{3}}+\frac{7 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{60 a^{3} c^{4} \left(x +\frac{1}{a}\right)^{2}}-\frac{379 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{480 a^{2} c^{4} \left(x +\frac{1}{a}\right)}-\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{80 a^{4} c^{4} \left(x +\frac{1}{a}\right)^{3}}"," ",0,"-(-a^2*x^2+1)^(1/2)/a/c^4+1/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+211/336/a^3/c^4/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1657/672/a^2/c^4/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/56/a^5/c^4/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+17/112/a^4/c^4/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+7/60/a^3/c^4/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-379/480/a^2/c^4/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-1/80/a^4/c^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)","B"
636,1,117,116,0.036000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^5,x)","\frac{c^{5}}{9 a^{10} x^{9}}+\frac{c^{5}}{4 a^{9} x^{8}}-\frac{3 c^{5}}{7 a^{8} x^{7}}-\frac{4 c^{5}}{3 a^{7} x^{6}}+\frac{2 c^{5}}{5 a^{6} x^{5}}+\frac{3 c^{5}}{a^{5} x^{4}}+\frac{2 c^{5}}{3 a^{4} x^{3}}-\frac{4 c^{5}}{x^{2} a^{3}}-\frac{3 c^{5}}{a^{2} x}-c^{5} x -\frac{2 c^{5} \ln \left(x \right)}{a}"," ",0,"1/9*c^5/a^10/x^9+1/4*c^5/a^9/x^8-3/7*c^5/a^8/x^7-4/3*c^5/a^7/x^6+2/5*c^5/a^6/x^5+3*c^5/a^5/x^4+2/3*c^5/a^4/x^3-4*c^5/x^2/a^3-3*c^5/a^2/x-c^5*x-2*c^5*ln(x)/a","A"
637,1,84,83,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^4,x)","-\frac{c^{4}}{7 a^{8} x^{7}}-\frac{c^{4}}{3 a^{7} x^{6}}+\frac{2 c^{4}}{5 a^{6} x^{5}}+\frac{3 c^{4}}{2 a^{5} x^{4}}-\frac{3 c^{4}}{x^{2} a^{3}}-\frac{2 c^{4}}{a^{2} x}-c^{4} x -\frac{2 c^{4} \ln \left(x \right)}{a}"," ",0,"-1/7*c^4/a^8/x^7-1/3*c^4/a^7/x^6+2/5*c^4/a^6/x^5+3/2*c^4/a^5/x^4-3*c^4/x^2/a^3-2*c^4/a^2/x-c^4*x-2*c^4*ln(x)/a","A"
638,1,73,72,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^3,x)","\frac{c^{3}}{5 a^{6} x^{5}}+\frac{c^{3}}{2 a^{5} x^{4}}-\frac{c^{3}}{3 a^{4} x^{3}}-\frac{2 c^{3}}{x^{2} a^{3}}-\frac{c^{3}}{a^{2} x}-c^{3} x -\frac{2 c^{3} \ln \left(x \right)}{a}"," ",0,"1/5*c^3/a^6/x^5+1/2*c^3/a^5/x^4-1/3*c^3/a^4/x^3-2*c^3/x^2/a^3-c^3/a^2/x-c^3*x-2*c^3*ln(x)/a","A"
639,1,40,39,0.031000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^2,x)","-\frac{c^{2}}{3 a^{4} x^{3}}-\frac{c^{2}}{x^{2} a^{3}}-c^{2} x -\frac{2 c^{2} \ln \left(x \right)}{a}"," ",0,"-1/3*c^2/a^4/x^3-c^2/x^2/a^3-c^2*x-2*c^2*ln(x)/a","A"
640,1,22,21,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2),x)","\frac{c}{a^{2} x}-c x -\frac{2 c \ln \left(x \right)}{a}"," ",0,"c/a^2/x-c*x-2*c*ln(x)/a","A"
641,1,36,38,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2),x)","-\frac{x}{c}+\frac{1}{c a \left(a x -1\right)}-\frac{2 \ln \left(a x -1\right)}{a c}"," ",0,"-x/c+1/c/a/(a*x-1)-2/a/c*ln(a*x-1)","A"
642,1,66,68,0.035000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^2,x)","-\frac{x}{c^{2}}+\frac{1}{4 a \,c^{2} \left(a x -1\right)^{2}}+\frac{7}{4 a \,c^{2} \left(a x -1\right)}-\frac{17 \ln \left(a x -1\right)}{8 a \,c^{2}}+\frac{\ln \left(a x +1\right)}{8 a \,c^{2}}"," ",0,"-x/c^2+1/4/a/c^2/(a*x-1)^2+7/4/a/c^2/(a*x-1)-17/8/a/c^2*ln(a*x-1)+1/8*ln(a*x+1)/a/c^2","A"
643,1,96,99,0.037000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^3,x)","-\frac{x}{c^{3}}+\frac{1}{12 a \,c^{3} \left(a x -1\right)^{3}}+\frac{5}{8 a \,c^{3} \left(a x -1\right)^{2}}+\frac{39}{16 a \,c^{3} \left(a x -1\right)}-\frac{9 \ln \left(a x -1\right)}{4 a \,c^{3}}+\frac{1}{16 a \,c^{3} \left(a x +1\right)}+\frac{\ln \left(a x +1\right)}{4 a \,c^{3}}"," ",0,"-x/c^3+1/12/a/c^3/(a*x-1)^3+5/8/a/c^3/(a*x-1)^2+39/16/a/c^3/(a*x-1)-9/4/a/c^3*ln(a*x-1)+1/16/a/c^3/(a*x+1)+1/4*ln(a*x+1)/a/c^3","A"
644,1,126,130,0.038000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^4,x)","-\frac{x}{c^{4}}+\frac{1}{32 a \,c^{4} \left(a x -1\right)^{4}}+\frac{13}{48 a \,c^{4} \left(a x -1\right)^{3}}+\frac{35}{32 a \,c^{4} \left(a x -1\right)^{2}}+\frac{99}{32 a \,c^{4} \left(a x -1\right)}-\frac{303 \ln \left(a x -1\right)}{128 a \,c^{4}}-\frac{1}{64 a \,c^{4} \left(a x +1\right)^{2}}+\frac{11}{64 a \,c^{4} \left(a x +1\right)}+\frac{47 \ln \left(a x +1\right)}{128 a \,c^{4}}"," ",0,"-x/c^4+1/32/a/c^4/(a*x-1)^4+13/48/a/c^4/(a*x-1)^3+35/32/a/c^4/(a*x-1)^2+99/32/a/c^4/(a*x-1)-303/128/a/c^4*ln(a*x-1)-1/64/a/c^4/(a*x+1)^2+11/64/a/c^4/(a*x+1)+47/128*ln(a*x+1)/a/c^4","A"
645,1,273,167,0.088000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^4,x)","-\frac{218 c^{4}}{35 a^{2} x \sqrt{-a^{2} x^{2}+1}}+\frac{15 c^{4}}{8 a^{5} x^{4} \sqrt{-a^{2} x^{2}+1}}-\frac{c^{4}}{7 a^{8} x^{7} \sqrt{-a^{2} x^{2}+1}}-\frac{c^{4}}{35 a^{6} x^{5} \sqrt{-a^{2} x^{2}+1}}+\frac{68 c^{4}}{35 a^{4} x^{3} \sqrt{-a^{2} x^{2}+1}}-\frac{37 c^{4}}{16 a^{3} x^{2} \sqrt{-a^{2} x^{2}+1}}-\frac{c^{4}}{2 a^{7} x^{6} \sqrt{-a^{2} x^{2}+1}}+\frac{156 c^{4} x}{35 \sqrt{-a^{2} x^{2}+1}}-\frac{c^{4} a \,x^{2}}{\sqrt{-a^{2} x^{2}+1}}-\frac{3 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{31 c^{4}}{16 a \sqrt{-a^{2} x^{2}+1}}-\frac{15 c^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a}"," ",0,"-218/35*c^4/a^2/x/(-a^2*x^2+1)^(1/2)+15/8*c^4/a^5/x^4/(-a^2*x^2+1)^(1/2)-1/7*c^4/a^8/x^7/(-a^2*x^2+1)^(1/2)-1/35*c^4/a^6/x^5/(-a^2*x^2+1)^(1/2)+68/35*c^4/a^4/x^3/(-a^2*x^2+1)^(1/2)-37/16*c^4/a^3/x^2/(-a^2*x^2+1)^(1/2)-1/2*c^4/a^7/x^6/(-a^2*x^2+1)^(1/2)+156/35*c^4*x/(-a^2*x^2+1)^(1/2)-c^4*a*x^2/(-a^2*x^2+1)^(1/2)-3*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+31/16*c^4/a/(-a^2*x^2+1)^(1/2)-15/16*c^4/a*arctanh(1/(-a^2*x^2+1)^(1/2))","A"
646,1,227,137,0.060000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^3,x)","-\frac{c^{3} a \,x^{2}}{\sqrt{-a^{2} x^{2}+1}}+\frac{19 c^{3}}{8 a \sqrt{-a^{2} x^{2}+1}}+\frac{19 c^{3} x}{5 \sqrt{-a^{2} x^{2}+1}}-\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{3 c^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}-\frac{22 c^{3}}{5 a^{2} x \sqrt{-a^{2} x^{2}+1}}-\frac{17 c^{3}}{8 a^{3} x^{2} \sqrt{-a^{2} x^{2}+1}}+\frac{3 c^{3}}{4 a^{5} x^{4} \sqrt{-a^{2} x^{2}+1}}+\frac{c^{3}}{5 a^{6} x^{5} \sqrt{-a^{2} x^{2}+1}}+\frac{2 c^{3}}{5 a^{4} x^{3} \sqrt{-a^{2} x^{2}+1}}"," ",0,"-c^3*a*x^2/(-a^2*x^2+1)^(1/2)+19/8*c^3/a/(-a^2*x^2+1)^(1/2)+19/5*c^3*x/(-a^2*x^2+1)^(1/2)-3*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-3/8*c^3/a*arctanh(1/(-a^2*x^2+1)^(1/2))-22/5*c^3/a^2/x/(-a^2*x^2+1)^(1/2)-17/8*c^3/a^3/x^2/(-a^2*x^2+1)^(1/2)+3/4*c^3/a^5/x^4/(-a^2*x^2+1)^(1/2)+1/5*c^3/a^6/x^5/(-a^2*x^2+1)^(1/2)+2/5*c^3/a^4/x^3/(-a^2*x^2+1)^(1/2)","A"
647,1,181,108,0.052000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^2,x)","-\frac{c^{2} a \,x^{2}}{\sqrt{-a^{2} x^{2}+1}}+\frac{5 c^{2}}{2 a \sqrt{-a^{2} x^{2}+1}}+\frac{8 c^{2} x}{3 \sqrt{-a^{2} x^{2}+1}}-\frac{3 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{c^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}-\frac{7 c^{2}}{3 a^{2} x \sqrt{-a^{2} x^{2}+1}}-\frac{c^{2}}{3 a^{4} x^{3} \sqrt{-a^{2} x^{2}+1}}-\frac{3 c^{2}}{2 a^{3} x^{2} \sqrt{-a^{2} x^{2}+1}}"," ",0,"-c^2*a*x^2/(-a^2*x^2+1)^(1/2)+5/2*c^2/a/(-a^2*x^2+1)^(1/2)+8/3*c^2*x/(-a^2*x^2+1)^(1/2)-3*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/2*c^2/a*arctanh(1/(-a^2*x^2+1)^(1/2))-7/3*c^2/a^2/x/(-a^2*x^2+1)^(1/2)-1/3*c^2/a^4/x^3/(-a^2*x^2+1)^(1/2)-3/2*c^2/a^3/x^2/(-a^2*x^2+1)^(1/2)","A"
648,1,121,67,0.046000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2),x)","-\frac{c a \,x^{2}}{\sqrt{-a^{2} x^{2}+1}}+\frac{c}{a \sqrt{-a^{2} x^{2}+1}}-\frac{c x}{\sqrt{-a^{2} x^{2}+1}}-\frac{3 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{3 c \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}+\frac{c}{a^{2} x \sqrt{-a^{2} x^{2}+1}}"," ",0,"-c*a*x^2/(-a^2*x^2+1)^(1/2)+c/a/(-a^2*x^2+1)^(1/2)-c*x/(-a^2*x^2+1)^(1/2)-3*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+3*c/a*arctanh(1/(-a^2*x^2+1)^(1/2))+c/a^2/x/(-a^2*x^2+1)^(1/2)","A"
649,1,168,87,0.042000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2),x)","-\frac{a \,x^{2}}{c \sqrt{-a^{2} x^{2}+1}}+\frac{6}{c a \sqrt{-a^{2} x^{2}+1}}+\frac{7 x}{c \sqrt{-a^{2} x^{2}+1}}-\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c \sqrt{a^{2}}}+\frac{4}{3 c \,a^{2} \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}-\frac{8 x}{3 c \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}"," ",0,"-a/c*x^2/(-a^2*x^2+1)^(1/2)+6/c/a/(-a^2*x^2+1)^(1/2)+7/c*x/(-a^2*x^2+1)^(1/2)-3/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+4/3/c/a^2/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-8/3/c/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x","A"
650,1,212,111,0.048000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^2,x)","-\frac{a \,x^{2}}{c^{2} \sqrt{-a^{2} x^{2}+1}}+\frac{7}{a \,c^{2} \sqrt{-a^{2} x^{2}+1}}+\frac{10 x}{c^{2} \sqrt{-a^{2} x^{2}+1}}-\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{2} \sqrt{a^{2}}}+\frac{2}{5 a^{3} c^{2} \left(x -\frac{1}{a}\right)^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{13}{5 a^{2} c^{2} \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}-\frac{26 x}{5 c^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}"," ",0,"-a/c^2*x^2/(-a^2*x^2+1)^(1/2)+7/a/c^2/(-a^2*x^2+1)^(1/2)+10*x/c^2/(-a^2*x^2+1)^(1/2)-3/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+2/5/a^3/c^2/(x-1/a)^2/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+13/5/a^2/c^2/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-26/5/c^2/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x","A"
651,1,256,137,0.054000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^3,x)","-\frac{a \,x^{2}}{c^{3} \sqrt{-a^{2} x^{2}+1}}+\frac{8}{a \,c^{3} \sqrt{-a^{2} x^{2}+1}}+\frac{13 x}{c^{3} \sqrt{-a^{2} x^{2}+1}}-\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{3} \sqrt{a^{2}}}+\frac{38}{35 a^{3} c^{3} \left(x -\frac{1}{a}\right)^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{137}{35 a^{2} c^{3} \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}-\frac{274 x}{35 c^{3} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{1}{7 a^{4} c^{3} \left(x -\frac{1}{a}\right)^{3} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}"," ",0,"-a/c^3*x^2/(-a^2*x^2+1)^(1/2)+8/a/c^3/(-a^2*x^2+1)^(1/2)+13*x/c^3/(-a^2*x^2+1)^(1/2)-3/c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+38/35/a^3/c^3/(x-1/a)^2/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+137/35/a^2/c^3/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-274/35/c^3/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x+1/7/a^4/c^3/(x-1/a)^3/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
652,1,367,163,0.062000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^4,x)","-\frac{a \,x^{2}}{c^{4} \sqrt{-a^{2} x^{2}+1}}+\frac{9}{a \,c^{4} \sqrt{-a^{2} x^{2}+1}}+\frac{16 x}{c^{4} \sqrt{-a^{2} x^{2}+1}}-\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{4} \sqrt{a^{2}}}+\frac{5111}{2520 a^{3} c^{4} \left(x -\frac{1}{a}\right)^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{26633}{5040 a^{2} c^{4} \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}-\frac{26633 x}{2520 c^{4} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{1}{18 a^{5} c^{4} \left(x -\frac{1}{a}\right)^{4} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{125}{252 a^{4} c^{4} \left(x -\frac{1}{a}\right)^{3} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}-\frac{1}{48 a^{2} c^{4} \left(x +\frac{1}{a}\right) \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}+\frac{x}{24 c^{4} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}"," ",0,"-a/c^4*x^2/(-a^2*x^2+1)^(1/2)+9/a/c^4/(-a^2*x^2+1)^(1/2)+16*x/c^4/(-a^2*x^2+1)^(1/2)-3/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+5111/2520/a^3/c^4/(x-1/a)^2/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+26633/5040/a^2/c^4/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-26633/2520/c^4/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x+1/18/a^5/c^4/(x-1/a)^4/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+125/252/a^4/c^4/(x-1/a)^3/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/48/a^2/c^4/(x+1/a)/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+1/24/c^4/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x","B"
653,1,105,104,0.036000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^5,x)","\frac{c^{5}}{9 a^{10} x^{9}}+\frac{c^{5}}{2 a^{9} x^{8}}+\frac{3 c^{5}}{7 a^{8} x^{7}}-\frac{4 c^{5}}{3 a^{7} x^{6}}-\frac{14 c^{5}}{5 a^{6} x^{5}}+\frac{14 c^{5}}{3 a^{4} x^{3}}+\frac{4 c^{5}}{x^{2} a^{3}}-\frac{3 c^{5}}{a^{2} x}+c^{5} x +\frac{4 c^{5} \ln \left(x \right)}{a}"," ",0,"1/9*c^5/a^10/x^9+1/2*c^5/a^9/x^8+3/7*c^5/a^8/x^7-4/3*c^5/a^7/x^6-14/5*c^5/a^6/x^5+14/3*c^5/a^4/x^3+4*c^5/x^2/a^3-3*c^5/a^2/x+c^5*x+4*c^5*ln(x)/a","A"
654,1,93,92,0.033000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^4,x)","-\frac{c^{4}}{7 a^{8} x^{7}}-\frac{2 c^{4}}{3 a^{7} x^{6}}-\frac{4 c^{4}}{5 a^{6} x^{5}}+\frac{c^{4}}{a^{5} x^{4}}+\frac{10 c^{4}}{3 a^{4} x^{3}}+\frac{2 c^{4}}{x^{2} a^{3}}-\frac{4 c^{4}}{a^{2} x}+c^{4} x +\frac{4 c^{4} \ln \left(x \right)}{a}"," ",0,"-1/7*c^4/a^8/x^7-2/3*c^4/a^7/x^6-4/5*c^4/a^6/x^5+c^4/a^5/x^4+10/3*c^4/a^4/x^3+2*c^4/x^2/a^3-4*c^4/a^2/x+c^4*x+4*c^4*ln(x)/a","A"
655,1,60,59,0.035000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^3,x)","\frac{c^{3}}{5 a^{6} x^{5}}+\frac{c^{3}}{a^{5} x^{4}}+\frac{5 c^{3}}{3 a^{4} x^{3}}-\frac{5 c^{3}}{a^{2} x}+c^{3} x +\frac{4 c^{3} \ln \left(x \right)}{a}"," ",0,"1/5*c^3/a^6/x^5+c^3/a^5/x^4+5/3*c^3/a^4/x^3-5*c^3/a^2/x+c^3*x+4*c^3*ln(x)/a","A"
656,1,50,49,0.032000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^2,x)","-\frac{c^{2}}{3 a^{4} x^{3}}-\frac{2 c^{2}}{x^{2} a^{3}}-\frac{6 c^{2}}{a^{2} x}+c^{2} x +\frac{4 c^{2} \ln \left(x \right)}{a}"," ",0,"-1/3*c^2/a^4/x^3-2*c^2/x^2/a^3-6*c^2/a^2/x+c^2*x+4*c^2*ln(x)/a","A"
657,1,33,33,0.033000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2),x)","c x +\frac{c}{a^{2} x}-\frac{4 c \ln \left(x \right)}{a}+\frac{8 c \ln \left(a x -1\right)}{a}"," ",0,"c*x+c/a^2/x-4*c*ln(x)/a+8*c/a*ln(a*x-1)","A"
658,1,51,53,0.033000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2),x)","\frac{x}{c}-\frac{5}{c a \left(a x -1\right)}+\frac{4 \ln \left(a x -1\right)}{a c}-\frac{1}{a c \left(a x -1\right)^{2}}"," ",0,"x/c-5/c/a/(a*x-1)+4/a/c*ln(a*x-1)-1/a/c/(a*x-1)^2","A"
659,1,66,69,0.033000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2)^2,x)","\frac{x}{c^{2}}-\frac{6}{a \,c^{2} \left(a x -1\right)}-\frac{1}{3 a \,c^{2} \left(a x -1\right)^{3}}+\frac{4 \ln \left(a x -1\right)}{a \,c^{2}}-\frac{2}{a \,c^{2} \left(a x -1\right)^{2}}"," ",0,"x/c^2-6/a/c^2/(a*x-1)-1/3/a/c^2/(a*x-1)^3+4/a/c^2*ln(a*x-1)-2/a/c^2/(a*x-1)^2","A"
660,1,95,99,0.034000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2)^3,x)","\frac{x}{c^{3}}-\frac{1}{8 a \,c^{3} \left(a x -1\right)^{4}}-\frac{11}{12 a \,c^{3} \left(a x -1\right)^{3}}-\frac{49}{16 a \,c^{3} \left(a x -1\right)^{2}}-\frac{111}{16 a \,c^{3} \left(a x -1\right)}+\frac{129 \ln \left(a x -1\right)}{32 a \,c^{3}}-\frac{\ln \left(a x +1\right)}{32 a \,c^{3}}"," ",0,"x/c^3-1/8/a/c^3/(a*x-1)^4-11/12/a/c^3/(a*x-1)^3-49/16/a/c^3/(a*x-1)^2-111/16/a/c^3/(a*x-1)+129/32/a/c^3*ln(a*x-1)-1/32*ln(a*x+1)/a/c^3","A"
661,1,125,130,0.048000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2)^4,x)","\frac{x}{c^{4}}-\frac{1}{20 a \,c^{4} \left(a x -1\right)^{5}}-\frac{7}{16 a \,c^{4} \left(a x -1\right)^{4}}-\frac{83}{48 a \,c^{4} \left(a x -1\right)^{3}}-\frac{67}{16 a \,c^{4} \left(a x -1\right)^{2}}-\frac{501}{64 a \,c^{4} \left(a x -1\right)}+\frac{261 \ln \left(a x -1\right)}{64 a \,c^{4}}-\frac{1}{64 a \,c^{4} \left(a x +1\right)}-\frac{5 \ln \left(a x +1\right)}{64 a \,c^{4}}"," ",0,"x/c^4-1/20/a/c^4/(a*x-1)^5-7/16/a/c^4/(a*x-1)^4-83/48/a/c^4/(a*x-1)^3-67/16/a/c^4/(a*x-1)^2-501/64/a/c^4/(a*x-1)+261/64/a/c^4*ln(a*x-1)-1/64/a/c^4/(a*x+1)-5/64*ln(a*x+1)/a/c^4","A"
662,1,249,149,0.084000," ","int((c-c/a^2/x^2)^4/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{35 c^{4} \sqrt{-a^{2} x^{2}+1}}{16 a}-\frac{35 c^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a}+\frac{c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{a^{2} x}+c^{4} x \sqrt{-a^{2} x^{2}+1}+\frac{c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{6 a^{7} x^{6}}-\frac{5 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{8 a^{5} x^{4}}+\frac{19 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{16 x^{2} a^{3}}-\frac{71 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{105 a^{4} x^{3}}-\frac{c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{7 a^{8} x^{7}}+\frac{17 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{35 a^{6} x^{5}}"," ",0,"35/16*c^4*(-a^2*x^2+1)^(1/2)/a-35/16*c^4/a*arctanh(1/(-a^2*x^2+1)^(1/2))+c^4/a^2/x*(-a^2*x^2+1)^(3/2)+c^4*x*(-a^2*x^2+1)^(1/2)+c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/6*c^4/a^7/x^6*(-a^2*x^2+1)^(3/2)-5/8*c^4/a^5/x^4*(-a^2*x^2+1)^(3/2)+19/16*c^4*(-a^2*x^2+1)^(3/2)/x^2/a^3-71/105*c^4*(-a^2*x^2+1)^(3/2)/a^4/x^3-1/7*c^4/a^8/x^7*(-a^2*x^2+1)^(3/2)+17/35*c^4/a^6/x^5*(-a^2*x^2+1)^(3/2)","A"
663,1,203,120,0.054000," ","int((c-c/a^2/x^2)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{15 c^{3} \sqrt{-a^{2} x^{2}+1}}{8 a}-\frac{15 c^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}+\frac{c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{a^{2} x}+c^{3} x \sqrt{-a^{2} x^{2}+1}+\frac{c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{8 c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{15 a^{4} x^{3}}+\frac{7 c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{8 x^{2} a^{3}}-\frac{c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4 a^{5} x^{4}}+\frac{c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{5 a^{6} x^{5}}"," ",0,"15/8*c^3*(-a^2*x^2+1)^(1/2)/a-15/8*c^3/a*arctanh(1/(-a^2*x^2+1)^(1/2))+c^3/a^2/x*(-a^2*x^2+1)^(3/2)+c^3*x*(-a^2*x^2+1)^(1/2)+c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-8/15*c^3/a^4/x^3*(-a^2*x^2+1)^(3/2)+7/8*c^3*(-a^2*x^2+1)^(3/2)/x^2/a^3-1/4*c^3/a^5/x^4*(-a^2*x^2+1)^(3/2)+1/5*c^3/a^6/x^5*(-a^2*x^2+1)^(3/2)","A"
664,1,157,91,0.043000," ","int((c-c/a^2/x^2)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{3 c^{2} \sqrt{-a^{2} x^{2}+1}}{2 a}-\frac{3 c^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}+\frac{c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{a^{2} x}+c^{2} x \sqrt{-a^{2} x^{2}+1}+\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 a^{4} x^{3}}+\frac{c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{2 x^{2} a^{3}}"," ",0,"3/2*c^2*(-a^2*x^2+1)^(1/2)/a-3/2*c^2/a*arctanh(1/(-a^2*x^2+1)^(1/2))+c^2/a^2/x*(-a^2*x^2+1)^(3/2)+c^2*x*(-a^2*x^2+1)^(1/2)+c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/3*c^2*(-a^2*x^2+1)^(3/2)/a^4/x^3+1/2*c^2*(-a^2*x^2+1)^(3/2)/x^2/a^3","A"
665,1,100,54,0.040000," ","int((c-c/a^2/x^2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{c \sqrt{-a^{2} x^{2}+1}}{a}-\frac{c \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}+\frac{c \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{a^{2} x}+c x \sqrt{-a^{2} x^{2}+1}+\frac{c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}"," ",0,"c*(-a^2*x^2+1)^(1/2)/a-c/a*arctanh(1/(-a^2*x^2+1)^(1/2))+c/a^2/x*(-a^2*x^2+1)^(3/2)+c*x*(-a^2*x^2+1)^(1/2)+c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
666,1,192,56,0.044000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2),x)","\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{4 a c}-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{4 c \sqrt{a^{2}}}+\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{2 a^{3} c \left(x +\frac{1}{a}\right)^{2}}+\frac{5 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{4 a c}+\frac{5 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{4 c \sqrt{a^{2}}}"," ",0,"1/4/a/c*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/4/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+1/2/a^3/c/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+5/4/a/c*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+5/4/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
667,1,274,85,0.051000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^2,x)","\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{8 a^{3} c^{2} \left(x -\frac{1}{a}\right)^{2}}+\frac{7 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{16 a \,c^{2}}-\frac{7 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{16 c^{2} \sqrt{a^{2}}}+\frac{3 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{4 a^{3} c^{2} \left(x +\frac{1}{a}\right)^{2}}+\frac{23 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{16 a \,c^{2}}+\frac{23 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{16 c^{2} \sqrt{a^{2}}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{12 a^{4} c^{2} \left(x +\frac{1}{a}\right)^{3}}"," ",0,"1/8/a^3/c^2/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+7/16/a/c^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-7/16/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+3/4/a^3/c^2/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+23/16/a/c^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+23/16/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-1/12/a^4/c^2/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)","B"
668,1,356,114,0.061000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^3,x)","\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{4 a^{3} c^{3} \left(x -\frac{1}{a}\right)^{2}}+\frac{19 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{32 a \,c^{3}}-\frac{19 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{32 c^{3} \sqrt{a^{2}}}+\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{48 a^{4} c^{3} \left(x -\frac{1}{a}\right)^{3}}+\frac{15 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{16 a^{3} c^{3} \left(x +\frac{1}{a}\right)^{2}}+\frac{51 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{32 a \,c^{3}}+\frac{51 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{32 c^{3} \sqrt{a^{2}}}-\frac{43 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{240 a^{4} c^{3} \left(x +\frac{1}{a}\right)^{3}}+\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{40 a^{5} c^{3} \left(x +\frac{1}{a}\right)^{4}}"," ",0,"1/4/a^3/c^3/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+19/32/a/c^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-19/32/c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+1/48/a^4/c^3/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+15/16/a^3/c^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+51/32/a/c^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+51/32/c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-43/240/a^4/c^3/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+1/40/a^5/c^3/(x+1/a)^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)","B"
669,1,438,143,0.065000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^4,x)","\frac{47 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{128 a^{3} c^{4} \left(x -\frac{1}{a}\right)^{2}}+\frac{187 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{256 a \,c^{4}}-\frac{187 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{256 c^{4} \sqrt{a^{2}}}+\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{160 a^{5} c^{4} \left(x -\frac{1}{a}\right)^{4}}+\frac{53 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{960 a^{4} c^{4} \left(x -\frac{1}{a}\right)^{3}}+\frac{35 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{32 a^{3} c^{4} \left(x +\frac{1}{a}\right)^{2}}+\frac{443 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{256 a \,c^{4}}+\frac{443 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{256 c^{4} \sqrt{a^{2}}}+\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{14 a^{5} c^{4} \left(x +\frac{1}{a}\right)^{4}}-\frac{187 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{672 a^{4} c^{4} \left(x +\frac{1}{a}\right)^{3}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{112 a^{6} c^{4} \left(x +\frac{1}{a}\right)^{5}}"," ",0,"47/128/a^3/c^4/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+187/256/a/c^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-187/256/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+1/160/a^5/c^4/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+53/960/a^4/c^4/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)+35/32/a^3/c^4/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+443/256/a/c^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+443/256/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))+1/14/a^5/c^4/(x+1/a)^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-187/672/a^4/c^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-1/112/a^6/c^4/(x+1/a)^5*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)","B"
670,1,84,83,0.035000," ","int((c-c/a^2/x^2)^4/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{c^{4}}{7 a^{8} x^{7}}+\frac{c^{4}}{3 a^{7} x^{6}}+\frac{2 c^{4}}{5 a^{6} x^{5}}-\frac{3 c^{4}}{2 a^{5} x^{4}}+\frac{3 c^{4}}{x^{2} a^{3}}-\frac{2 c^{4}}{a^{2} x}-c^{4} x +\frac{2 c^{4} \ln \left(x \right)}{a}"," ",0,"-1/7*c^4/a^8/x^7+1/3*c^4/a^7/x^6+2/5*c^4/a^6/x^5-3/2*c^4/a^5/x^4+3*c^4/x^2/a^3-2*c^4/a^2/x-c^4*x+2*c^4*ln(x)/a","A"
671,1,73,72,0.035000," ","int((c-c/a^2/x^2)^3/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{c^{3}}{5 a^{6} x^{5}}-\frac{c^{3}}{2 a^{5} x^{4}}-\frac{c^{3}}{3 a^{4} x^{3}}+\frac{2 c^{3}}{x^{2} a^{3}}-\frac{c^{3}}{a^{2} x}-c^{3} x +\frac{2 c^{3} \ln \left(x \right)}{a}"," ",0,"1/5*c^3/a^6/x^5-1/2*c^3/a^5/x^4-1/3*c^3/a^4/x^3+2*c^3/x^2/a^3-c^3/a^2/x-c^3*x+2*c^3*ln(x)/a","A"
672,1,39,38,0.033000," ","int((c-c/a^2/x^2)^2/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{c^{2}}{3 a^{4} x^{3}}+\frac{c^{2}}{x^{2} a^{3}}-c^{2} x +\frac{2 c^{2} \ln \left(x \right)}{a}"," ",0,"-1/3*c^2/a^4/x^3+c^2/x^2/a^3-c^2*x+2*c^2*ln(x)/a","A"
673,1,22,21,0.032000," ","int((c-c/a^2/x^2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{c}{a^{2} x}-c x +\frac{2 c \ln \left(x \right)}{a}"," ",0,"c/a^2/x-c*x+2*c*ln(x)/a","A"
674,1,36,35,0.032000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2),x)","-\frac{x}{c}+\frac{1}{a c \left(a x +1\right)}+\frac{2 \ln \left(a x +1\right)}{a c}"," ",0,"-x/c+1/a/c/(a*x+1)+2*ln(a*x+1)/a/c","A"
675,1,66,66,0.038000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^2,x)","-\frac{x}{c^{2}}-\frac{\ln \left(a x -1\right)}{8 a \,c^{2}}-\frac{1}{4 a \,c^{2} \left(a x +1\right)^{2}}+\frac{7}{4 a \,c^{2} \left(a x +1\right)}+\frac{17 \ln \left(a x +1\right)}{8 a \,c^{2}}"," ",0,"-x/c^2-1/8/a/c^2*ln(a*x-1)-1/4/a/c^2/(a*x+1)^2+7/4/a/c^2/(a*x+1)+17/8*ln(a*x+1)/a/c^2","A"
676,1,96,97,0.037000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^3,x)","-\frac{x}{c^{3}}+\frac{1}{16 a \,c^{3} \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{4 a \,c^{3}}+\frac{1}{12 a \,c^{3} \left(a x +1\right)^{3}}-\frac{5}{8 a \,c^{3} \left(a x +1\right)^{2}}+\frac{39}{16 a \,c^{3} \left(a x +1\right)}+\frac{9 \ln \left(a x +1\right)}{4 a \,c^{3}}"," ",0,"-x/c^3+1/16/a/c^3/(a*x-1)-1/4/a/c^3*ln(a*x-1)+1/12/a/c^3/(a*x+1)^3-5/8/a/c^3/(a*x+1)^2+39/16/a/c^3/(a*x+1)+9/4*ln(a*x+1)/a/c^3","A"
677,1,126,128,0.040000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^4,x)","-\frac{x}{c^{4}}+\frac{1}{64 a \,c^{4} \left(a x -1\right)^{2}}+\frac{11}{64 a \,c^{4} \left(a x -1\right)}-\frac{47 \ln \left(a x -1\right)}{128 a \,c^{4}}-\frac{1}{32 a \,c^{4} \left(a x +1\right)^{4}}+\frac{13}{48 a \,c^{4} \left(a x +1\right)^{3}}-\frac{35}{32 a \,c^{4} \left(a x +1\right)^{2}}+\frac{99}{32 a \,c^{4} \left(a x +1\right)}+\frac{303 \ln \left(a x +1\right)}{128 a \,c^{4}}"," ",0,"-x/c^4+1/64/a/c^4/(a*x-1)^2+11/64/a/c^4/(a*x-1)-47/128/a/c^4*ln(a*x-1)-1/32/a/c^4/(a*x+1)^4+13/48/a/c^4/(a*x+1)^3-35/32/a/c^4/(a*x+1)^2+99/32/a/c^4/(a*x+1)+303/128*ln(a*x+1)/a/c^4","A"
678,1,289,167,0.099000," ","int((c-c/a^2/x^2)^4/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{2 a^{7} x^{6}}-\frac{3 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{8 a^{5} x^{4}}-\frac{5 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{16 a^{3} x^{2}}-\frac{5 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{16 a}-\frac{15 c^{4} \sqrt{-a^{2} x^{2}+1}}{16 a}+\frac{15 c^{4} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a}+\frac{c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{a^{4} x^{3}}-\frac{2 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{a^{2} x}-2 c^{4} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}-3 c^{4} x \sqrt{-a^{2} x^{2}+1}-\frac{3 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{7 a^{8} x^{7}}-\frac{16 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{35 a^{6} x^{5}}"," ",0,"1/2*c^4/a^7/x^6*(-a^2*x^2+1)^(5/2)-3/8*c^4/a^5/x^4*(-a^2*x^2+1)^(5/2)-5/16*c^4/a^3/x^2*(-a^2*x^2+1)^(5/2)-5/16*c^4*(-a^2*x^2+1)^(3/2)/a-15/16*c^4*(-a^2*x^2+1)^(1/2)/a+15/16*c^4/a*arctanh(1/(-a^2*x^2+1)^(1/2))+c^4/a^4/x^3*(-a^2*x^2+1)^(5/2)-2*c^4/a^2/x*(-a^2*x^2+1)^(5/2)-2*c^4*x*(-a^2*x^2+1)^(3/2)-3*c^4*x*(-a^2*x^2+1)^(1/2)-3*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/7*c^4/a^8/x^7*(-a^2*x^2+1)^(5/2)-16/35*c^4/a^6/x^5*(-a^2*x^2+1)^(5/2)","A"
679,1,243,137,0.059000," ","int((c-c/a^2/x^2)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{a^{4} x^{3}}-\frac{2 c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{a^{2} x}-2 c^{3} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}-3 c^{3} x \sqrt{-a^{2} x^{2}+1}-\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{8 a^{3} x^{2}}-\frac{c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{8 a}-\frac{3 c^{3} \sqrt{-a^{2} x^{2}+1}}{8 a}+\frac{3 c^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}-\frac{3 c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{4 a^{5} x^{4}}+\frac{c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{5 a^{6} x^{5}}"," ",0,"c^3/a^4/x^3*(-a^2*x^2+1)^(5/2)-2*c^3/a^2/x*(-a^2*x^2+1)^(5/2)-2*c^3*x*(-a^2*x^2+1)^(3/2)-3*c^3*x*(-a^2*x^2+1)^(1/2)-3*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/8*c^3/a^3/x^2*(-a^2*x^2+1)^(5/2)-1/8*c^3*(-a^2*x^2+1)^(3/2)/a-3/8*c^3*(-a^2*x^2+1)^(1/2)/a+3/8*c^3/a*arctanh(1/(-a^2*x^2+1)^(1/2))-3/4*c^3*(-a^2*x^2+1)^(5/2)/a^5/x^4+1/5*c^3*(-a^2*x^2+1)^(5/2)/a^6/x^5","A"
680,1,299,109,0.052000," ","int((c-c/a^2/x^2)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{6 a}+\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{2 a}-\frac{c^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}-\frac{10 c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{3 a^{2} x}-\frac{10 c^{2} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3}-5 c^{2} x \sqrt{-a^{2} x^{2}+1}-\frac{5 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\frac{c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{3 a^{4} x^{3}}+\frac{3 c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{2 a^{3} x^{2}}+\frac{4 c^{2} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a}+2 c^{2} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x +\frac{2 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"1/6*c^2*(-a^2*x^2+1)^(3/2)/a+1/2*c^2*(-a^2*x^2+1)^(1/2)/a-1/2*c^2/a*arctanh(1/(-a^2*x^2+1)^(1/2))-10/3*c^2/a^2/x*(-a^2*x^2+1)^(5/2)-10/3*c^2*x*(-a^2*x^2+1)^(3/2)-5*c^2*x*(-a^2*x^2+1)^(1/2)-5*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/3*c^2/a^4/x^3*(-a^2*x^2+1)^(5/2)+3/2*c^2/a^3/x^2*(-a^2*x^2+1)^(5/2)+4/3*c^2/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+2*c^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x+2*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
681,1,266,68,0.048000," ","int((c-c/a^2/x^2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{c \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{a}+\frac{3 c \sqrt{-a^{2} x^{2}+1}}{a}-\frac{3 c \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}+\frac{c \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{a^{2} x}+c x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}+\frac{3 c x \sqrt{-a^{2} x^{2}+1}}{2}+\frac{3 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}-\frac{2 c \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{3 c \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{a}-\frac{9 c \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{2}-\frac{9 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{2 \sqrt{a^{2}}}"," ",0,"c*(-a^2*x^2+1)^(3/2)/a+3*c*(-a^2*x^2+1)^(1/2)/a-3*c/a*arctanh(1/(-a^2*x^2+1)^(1/2))+c/a^2/x*(-a^2*x^2+1)^(5/2)+c*x*(-a^2*x^2+1)^(3/2)+3/2*c*x*(-a^2*x^2+1)^(1/2)+3/2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-2*c/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-3*c/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-9/2*c*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-9/2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
682,1,330,89,0.054000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2),x)","\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{48 a c}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}\, x}{32 c}-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{32 c \sqrt{a^{2}}}-\frac{47 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{24 c \,a^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{95 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{48 a c}-\frac{95 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{32 c}-\frac{95 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{32 c \sqrt{a^{2}}}+\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{6 a^{5} c \left(x +\frac{1}{a}\right)^{4}}-\frac{11 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{12 a^{4} c \left(x +\frac{1}{a}\right)^{3}}"," ",0,"1/48/a/c*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)-1/32/c*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x-1/32/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-47/24/c/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-95/48/a/c*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)-95/32/c*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-95/32/c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))+1/6/a^5/c/(x+1/a)^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-11/12/a^4/c/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)","B"
683,1,412,115,0.064000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^2,x)","-\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{64 a \,c^{2}}-\frac{2 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{3} c^{2} \left(x +\frac{1}{a}\right)^{2}}-\frac{387 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{128 c^{2}}-\frac{387 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{128 c^{2} \sqrt{a^{2}}}-\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{32 a^{3} c^{2} \left(x -\frac{1}{a}\right)^{2}}+\frac{3 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}\, x}{128 c^{2}}+\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{128 c^{2} \sqrt{a^{2}}}-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{20 a^{6} c^{2} \left(x +\frac{1}{a}\right)^{5}}+\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{4 a^{5} c^{2} \left(x +\frac{1}{a}\right)^{4}}-\frac{15 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{16 a^{4} c^{2} \left(x +\frac{1}{a}\right)^{3}}-\frac{129 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{64 a \,c^{2}}"," ",0,"-1/64/a/c^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)-2/a^3/c^2/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-387/128/c^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-387/128/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-1/32/a^3/c^2/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)+3/128/c^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x+3/128/c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-1/20/a^6/c^2/(x+1/a)^5*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+1/4/a^5/c^2/(x+1/a)^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-15/16/a^4/c^2/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-129/64/a/c^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)","B"
684,1,494,141,0.069000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^3,x)","-\frac{529 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{256 a \,c^{3}}+\frac{5 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{16 a^{5} c^{3} \left(x +\frac{1}{a}\right)^{4}}-\frac{31 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{32 a^{4} c^{3} \left(x +\frac{1}{a}\right)^{3}}-\frac{263 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{128 a^{3} c^{3} \left(x +\frac{1}{a}\right)^{2}}-\frac{1587 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{512 c^{3}}-\frac{1587 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{512 c^{3} \sqrt{a^{2}}}+\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{56 a^{7} c^{3} \left(x +\frac{1}{a}\right)^{6}}-\frac{61 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{560 a^{6} c^{3} \left(x +\frac{1}{a}\right)^{5}}-\frac{5 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{64 a^{3} c^{3} \left(x -\frac{1}{a}\right)^{2}}+\frac{51 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}\, x}{512 c^{3}}+\frac{51 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{512 c^{3} \sqrt{a^{2}}}+\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{64 a^{4} c^{3} \left(x -\frac{1}{a}\right)^{3}}-\frac{17 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{256 a \,c^{3}}"," ",0,"-529/256/a/c^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+5/16/a^5/c^3/(x+1/a)^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-31/32/a^4/c^3/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-263/128/a^3/c^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-1587/512/c^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x-1587/512/c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))+1/56/a^7/c^3/(x+1/a)^6*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-61/560/a^6/c^3/(x+1/a)^5*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-5/64/a^3/c^3/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)+51/512/c^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x+51/512/c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+1/64/a^4/c^3/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)-17/256/a/c^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)","B"
685,1,576,167,0.077000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^4,x)","-\frac{\left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{144 a^{8} c^{4} \left(x +\frac{1}{a}\right)^{7}}+\frac{13 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{252 a^{7} c^{4} \left(x +\frac{1}{a}\right)^{6}}-\frac{1629 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{512 c^{4} \sqrt{a^{2}}}-\frac{811 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{384 a^{3} c^{4} \left(x +\frac{1}{a}\right)^{2}}-\frac{1629 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{512 c^{4}}+\frac{\left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{384 a^{5} c^{4} \left(x -\frac{1}{a}\right)^{4}}+\frac{29 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{768 a^{4} c^{4} \left(x -\frac{1}{a}\right)^{3}}-\frac{25 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{192 a^{3} c^{4} \left(x -\frac{1}{a}\right)^{2}}+\frac{93 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}\, x}{512 c^{4}}+\frac{93 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}\right)}{512 c^{4} \sqrt{a^{2}}}-\frac{1723 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{10080 a^{6} c^{4} \left(x +\frac{1}{a}\right)^{5}}+\frac{35 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{96 a^{5} c^{4} \left(x +\frac{1}{a}\right)^{4}}-\frac{769 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{768 a^{4} c^{4} \left(x +\frac{1}{a}\right)^{3}}-\frac{31 \left(-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{256 a \,c^{4}}-\frac{543 \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{256 a \,c^{4}}"," ",0,"-1/144/a^8/c^4/(x+1/a)^7*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+13/252/a^7/c^4/(x+1/a)^6*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-1629/512/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-811/384/a^3/c^4/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-1629/512/c^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x+1/384/a^5/c^4/(x-1/a)^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)+29/768/a^4/c^4/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)-25/192/a^3/c^4/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(5/2)+93/512/c^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x+93/512/c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-1723/10080/a^6/c^4/(x+1/a)^5*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+35/96/a^5/c^4/(x+1/a)^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-769/768/a^4/c^4/(x+1/a)^3*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)-31/256/a/c^4*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(3/2)-543/256/a/c^4*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)","B"
686,1,118,324,0.086000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(9/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{9}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(840 a^{9} x^{9}+840 a^{8} \ln \left(x \right) x^{8}+3360 a^{7} x^{7}+1680 x^{6} a^{6}-1680 x^{5} a^{5}-1260 x^{4} a^{4}+672 x^{3} a^{3}+560 a^{2} x^{2}-120 a x -105\right)}{840 \left(a^{2} x^{2}-1\right)^{5}}"," ",0,"-1/840*(c*(a^2*x^2-1)/a^2/x^2)^(9/2)*x/(a^2*x^2-1)^5*(-a^2*x^2+1)^(1/2)*(840*a^9*x^9+840*a^8*ln(x)*x^8+3360*a^7*x^7+1680*x^6*a^6-1680*x^5*a^5-1260*x^4*a^4+672*x^3*a^3+560*a^2*x^2-120*a*x-105)","A"
687,1,102,259,0.051000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(7/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(60 a^{7} x^{7}+60 a^{6} \ln \left(x \right) x^{6}+180 x^{5} a^{5}+90 x^{4} a^{4}-60 x^{3} a^{3}-45 a^{2} x^{2}+12 a x +10\right)}{60 \left(a^{2} x^{2}-1\right)^{4}}"," ",0,"-1/60*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*x/(a^2*x^2-1)^4*(-a^2*x^2+1)^(1/2)*(60*a^7*x^7+60*a^6*ln(x)*x^6+180*x^5*a^5+90*x^4*a^4-60*x^3*a^3-45*a^2*x^2+12*a*x+10)","A"
688,1,86,191,0.052000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(5/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(12 x^{5} a^{5}+12 a^{4} \ln \left(x \right) x^{4}+24 x^{3} a^{3}+12 a^{2} x^{2}-4 a x -3\right)}{12 \left(a^{2} x^{2}-1\right)^{3}}"," ",0,"-1/12*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*x/(a^2*x^2-1)^3*(-a^2*x^2+1)^(1/2)*(12*x^5*a^5+12*a^4*ln(x)*x^4+24*x^3*a^3+12*a^2*x^2-4*a*x-3)","A"
689,1,70,128,0.048000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(3/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}+2 a^{2} \ln \left(x \right) x^{2}+2 a x +1\right)}{2 \left(a^{2} x^{2}-1\right)^{2}}"," ",0,"-1/2*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*x/(a^2*x^2-1)^2*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3+2*a^2*ln(x)*x^2+2*a*x+1)","A"
690,1,52,60,0.039000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(a x +\ln \left(x \right)\right) \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(a*x+ln(x))*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
691,1,50,71,0.040000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a x +\ln \left(a x -1\right)\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,a^{2}}"," ",0,"-(-a^2*x^2+1)^(1/2)*(a*x+ln(a*x-1))/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/a^2","A"
692,1,93,153,0.052000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(3/2),x)","-\frac{\left(4 a^{2} x^{2}+5 \ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-4 a x -5 \ln \left(a x -1\right)+\ln \left(a x +1\right)-2\right) \left(a x +1\right) \sqrt{-a^{2} x^{2}+1}}{4 a^{4} x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}}}"," ",0,"-1/4*(4*a^2*x^2+5*ln(a*x-1)*x*a-a*x*ln(a*x+1)-4*a*x-5*ln(a*x-1)+ln(a*x+1)-2)*(a*x+1)*(-a^2*x^2+1)^(1/2)/a^4/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)","A"
693,1,167,235,0.056000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a x +1\right) \left(16 x^{4} a^{4}+23 \ln \left(a x -1\right) x^{3} a^{3}-7 a^{3} x^{3} \ln \left(a x +1\right)-16 x^{3} a^{3}-23 \ln \left(a x -1\right) x^{2} a^{2}+7 \ln \left(a x +1\right) x^{2} a^{2}-34 a^{2} x^{2}-23 \ln \left(a x -1\right) x a +7 a x \ln \left(a x +1\right)+18 a x +23 \ln \left(a x -1\right)-7 \ln \left(a x +1\right)+12\right)}{16 a^{6} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}}}"," ",0,"-1/16*(-a^2*x^2+1)^(1/2)*(a*x+1)*(16*x^4*a^4+23*ln(a*x-1)*x^3*a^3-7*a^3*x^3*ln(a*x+1)-16*x^3*a^3-23*ln(a*x-1)*x^2*a^2+7*ln(a*x+1)*x^2*a^2-34*a^2*x^2-23*ln(a*x-1)*x*a+7*a*x*ln(a*x+1)+18*a*x+23*ln(a*x-1)-7*ln(a*x+1)+12)/a^6/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)","A"
694,1,239,315,0.059000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(7/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a x +1\right) \left(96 x^{6} a^{6}+153 \ln \left(a x -1\right) x^{5} a^{5}-57 \ln \left(a x +1\right) x^{5} a^{5}-96 x^{5} a^{5}-153 \ln \left(a x -1\right) x^{4} a^{4}+57 \ln \left(a x +1\right) x^{4} a^{4}-366 x^{4} a^{4}-306 \ln \left(a x -1\right) x^{3} a^{3}+114 a^{3} x^{3} \ln \left(a x +1\right)+222 x^{3} a^{3}+306 \ln \left(a x -1\right) x^{2} a^{2}-114 \ln \left(a x +1\right) x^{2} a^{2}+338 a^{2} x^{2}+153 \ln \left(a x -1\right) x a -57 a x \ln \left(a x +1\right)-122 a x -153 \ln \left(a x -1\right)+57 \ln \left(a x +1\right)-88\right)}{96 a^{8} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}}}"," ",0,"-1/96*(-a^2*x^2+1)^(1/2)*(a*x+1)*(96*x^6*a^6+153*ln(a*x-1)*x^5*a^5-57*ln(a*x+1)*x^5*a^5-96*x^5*a^5-153*ln(a*x-1)*x^4*a^4+57*ln(a*x+1)*x^4*a^4-366*x^4*a^4-306*ln(a*x-1)*x^3*a^3+114*a^3*x^3*ln(a*x+1)+222*x^3*a^3+306*ln(a*x-1)*x^2*a^2-114*ln(a*x+1)*x^2*a^2+338*a^2*x^2+153*ln(a*x-1)*x*a-57*a*x*ln(a*x+1)-122*a*x-153*ln(a*x-1)+57*ln(a*x+1)-88)/a^8/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)","A"
695,1,965,396,0.125000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(9/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{9}{2}} x \left(-5040 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} \sqrt{-\frac{c}{a^{2}}}+77175 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{8} c^{6}+23808 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{7} a^{11}-17535 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{6} a^{10}-13056 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{5} a^{9}-6510 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{4} a^{8}-6912 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{3} a^{7}-10920 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{2} a^{6}-11520 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x \,a^{5}+58590 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{11}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{8} a +22050 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{11}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{8} a -23808 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} x^{9} a^{11} c +8575 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} x^{8} a^{10} c +8960 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{9}{2}} x^{8} a^{10} c +26784 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{9} a^{9} c^{2}+10080 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{9} a^{9} c^{2}-11025 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{8} a^{8} c^{2}-31248 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{9} a^{7} c^{3}-11760 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{9} a^{7} c^{3}+15435 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{8} a^{6} c^{3}+39060 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{9} a^{5} c^{4}+14700 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{9} a^{5} c^{4}-25725 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{8} a^{4} c^{4}-58590 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{9} a^{3} c^{5}-22050 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{9} a^{3} c^{5}+77175 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{8} a^{2} c^{5}\right)}{40320 a^{2} \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} c}"," ",0,"-1/40320*(c*(a^2*x^2-1)/a^2/x^2)^(9/2)*x/a^2*(-5040*a^4*(c*(a^2*x^2-1)/a^2)^(11/2)*(-c/a^2)^(1/2)+77175*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^8*c^6+23808*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^7*a^11-17535*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^6*a^10-13056*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^5*a^9-6510*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^4*a^8-6912*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^3*a^7-10920*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^2*a^6-11520*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x*a^5+58590*(-c/a^2)^(1/2)*c^(11/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^8*a+22050*(-c/a^2)^(1/2)*c^(11/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^8*a-23808*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(9/2)*x^9*a^11*c+8575*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(9/2)*x^8*a^10*c+8960*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(9/2)*x^8*a^10*c+26784*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^9*a^9*c^2+10080*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^9*a^9*c^2-11025*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^8*a^8*c^2-31248*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^9*a^7*c^3-11760*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^9*a^7*c^3+15435*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^8*a^6*c^3+39060*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^9*a^5*c^4+14700*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^9*a^5*c^4-25725*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^8*a^4*c^4-58590*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^9*a^3*c^5-22050*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^9*a^3*c^5+77175*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^8*a^2*c^5)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(9/2)/c","B"
696,1,795,326,0.070000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(7/2),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} x \left(-2016 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{9} c +2016 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{5} a^{9}+375 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{8} c -480 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{6} a^{8} c +105 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{4} a^{8}+2352 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{7} c^{2}-560 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} a^{7} c^{2}+224 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{3} a^{7}-525 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{6} c^{2}-2940 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{5} c^{3}+700 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{7} a^{5} c^{3}+630 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{2} a^{6}+875 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{4} c^{3}+672 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x \,a^{5}+4410 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{3} c^{4}-1050 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{7} a^{3} c^{4}+280 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}-2625 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{2} c^{4}-4410 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{9}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{6} a +1050 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{9}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{6} a -2625 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{6} c^{5}\right)}{1680 a^{2} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"1/1680*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*x/a^2*(-2016*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)*x^7*a^9*c+2016*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^5*a^9+375*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)*x^6*a^8*c-480*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^6*a^8*c+105*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^4*a^8+2352*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)*x^7*a^7*c^2-560*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^7*a^7*c^2+224*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^3*a^7-525*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)*x^6*a^6*c^2-2940*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^7*a^5*c^3+700*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^7*a^5*c^3+630*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^2*a^6+875*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^6*a^4*c^3+672*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x*a^5+4410*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^7*a^3*c^4-1050*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^7*a^3*c^4+280*a^4*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)-2625*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^6*a^2*c^4-4410*(-c/a^2)^(1/2)*c^(9/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^6*a+1050*(-c/a^2)^(1/2)*c^(9/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^6*a-2625*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^6*c^5)/(c*(a^2*x^2-1)/a^2)^(7/2)/(-c/a^2)^(1/2)/c","B"
697,1,625,256,0.053000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(5/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} x \left(-80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{5} a^{7} c +80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{3} a^{7}+48 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{6} c +27 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{6} c +60 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5} c^{2}-75 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{2} a^{6}+100 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5} c^{2}-80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x \,a^{5}-45 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{4} a^{4} c^{2}-90 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{5} a^{3} c^{3}-150 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c^{3}-30 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}+150 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{7}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{4} a +90 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{7}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{4} a +135 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{2} c^{3}+135 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{4} c^{4}\right)}{120 a^{2} \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c}"," ",0,"-1/120*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*x/a^2*(-80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^5*a^7*c+80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^3*a^7+48*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^4*a^6*c+27*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^4*a^6*c+60*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^5*a^5*c^2-75*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^2*a^6+100*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^5*a^5*c^2-80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x*a^5-45*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^4*a^4*c^2-90*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^5*a^3*c^3-150*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c^3-30*a^4*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)+150*(-c/a^2)^(1/2)*c^(7/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^4*a+90*(-c/a^2)^(1/2)*c^(7/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^4*a+135*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^2*c^3+135*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^4*c^4)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(5/2)/c","B"
698,1,455,186,0.049000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(3/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} x \left(12 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{5} c -12 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x \,a^{5}+4 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{4} c -\sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{4} c +6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{3} c^{2}-3 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}-18 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{3} c^{2}+18 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{2} a -6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{5}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{2} a +3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2} c^{2}+3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{2} c^{3}\right)}{6 a^{2} \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} c}"," ",0,"-1/6*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*x/a^2*(12*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^5*c-12*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x*a^5+4*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^2*a^4*c-(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^4*c+6*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^3*c^2-3*a^4*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)-18*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^3*c^2+18*(-c/a^2)^(1/2)*c^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^2*a-6*(-c/a^2)^(1/2)*c^(5/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^2*a+3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2*c^2+3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^2*c^3)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(3/2)/c","B"
699,1,198,100,0.046000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(2 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}+2 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) a \sqrt{-\frac{c}{a^{2}}}-\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-c \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right)\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(2*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)+2*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*a*(-c/a^2)^(1/2)-(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x))/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2/(-c/a^2)^(1/2)","A"
700,1,178,100,0.042000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \left(\sqrt{c}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2}+2 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x a c -2 a \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{c}-\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a \sqrt{c}-2 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) c \right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,c^{\frac{3}{2}} a \left(a x -1\right)}"," ",0,"-(c*(a^2*x^2-1)/a^2)^(1/2)*(c^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2+2*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x*a*c-2*a*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*c^(1/2)-(c*(a^2*x^2-1)/a^2)^(1/2)*a*c^(1/2)-2*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*c)/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/c^(3/2)/a/(a*x-1)","A"
701,1,326,109,0.047000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(3/2),x)","-\frac{\left(3 c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{3}-15 x^{2} a^{2} c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+4 c^{\frac{3}{2}} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2}+6 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c -4 c^{\frac{3}{2}} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x a -6 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a c +12 c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}-2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c^{\frac{3}{2}}\right) \left(a x +1\right)}{3 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} a^{4} c^{\frac{3}{2}}}"," ",0,"-1/3*(3*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^3-15*x^2*a^2*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+4*c^(3/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2+6*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c-4*c^(3/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a-6*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a*c+12*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)-2*(c*(a^2*x^2-1)/a^2)^(1/2)*c^(3/2))*(a*x+1)/((a*x-1)*(a*x+1)*c/a^2)^(1/2)/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)/a^4/c^(3/2)","B"
702,1,462,181,0.050000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(5/2),x)","-\frac{\left(15 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5}-45 x^{4} c^{\frac{5}{2}} a^{4} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}}-16 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{4} a^{4}-60 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+16 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+30 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{4} c +90 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}+24 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-30 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3} c +50 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x a -24 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x a -50 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}}-6 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}}\right) \left(a x +1\right)}{15 \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} a^{6} c^{\frac{5}{2}}}"," ",0,"-1/15*(15*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^5*a^5-45*x^4*c^(5/2)*a^4*((a*x-1)*(a*x+1)*c/a^2)^(3/2)-16*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^4*a^4-60*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^3*a^3+16*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3+30*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^4*c+90*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^2*a^2+24*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2-30*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*a^3*c+50*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x*a-24*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a-50*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)-6*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2))*(a*x+1)/((a*x-1)*(a*x+1)*c/a^2)^(3/2)/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)/a^6/c^(5/2)","B"
703,1,572,253,0.064000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(7/2),x)","-\frac{\left(105 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} a^{7}+96 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{6} a^{6}-553 x^{6} c^{\frac{7}{2}} a^{6} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}}-96 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{5} a^{5}-392 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{5} a^{5}-240 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{4} a^{4}+1540 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{4}+210 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x \,a^{6} c +240 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{3} a^{3}+350 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{3} a^{3}-210 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} a^{5} c +180 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{2} a^{2}-1470 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{2} a^{2}-180 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x a -42 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x a -30 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}}+462 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}}\right) \left(a x +1\right)}{105 \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} a^{8} c^{\frac{7}{2}}}"," ",0,"-1/105*(105*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^7*a^7+96*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^6*a^6-553*x^6*c^(7/2)*a^6*((a*x-1)*(a*x+1)*c/a^2)^(5/2)-96*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^5*a^5-392*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^5*a^5-240*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^4*a^4+1540*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^4*a^4+210*(c*(a^2*x^2-1)/a^2)^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x*a^6*c+240*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^3*a^3+350*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^3*a^3-210*(c*(a^2*x^2-1)/a^2)^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*a^5*c+180*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^2*a^2-1470*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^2*a^2-180*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x*a-42*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x*a-30*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)+462*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2))*(a*x+1)/((a*x-1)*(a*x+1)*c/a^2)^(5/2)/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)/a^8/c^(7/2)","B"
704,1,682,325,0.108000," ","int((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(9/2),x)","\frac{\left(-315 c^{\frac{9}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{9} a^{9}+256 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} c^{\frac{9}{2}} x^{8} a^{8}+1185 x^{8} c^{\frac{9}{2}} a^{8} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}}-256 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} c^{\frac{9}{2}} x^{7} a^{7}+2280 c^{\frac{9}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{7} a^{7}-896 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} c^{\frac{9}{2}} x^{6} a^{6}-4620 c^{\frac{9}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{6} a^{6}+896 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} c^{\frac{9}{2}} x^{5} a^{5}-4620 c^{\frac{9}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{5} a^{5}-630 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x \,a^{8} c +1120 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} c^{\frac{9}{2}} x^{4} a^{4}+7140 c^{\frac{9}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{4} a^{4}+630 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} a^{7} c -1120 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} c^{\frac{9}{2}} x^{3} a^{3}+3948 c^{\frac{9}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{3} a^{3}-560 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} c^{\frac{9}{2}} x^{2} a^{2}-4998 c^{\frac{9}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{2} a^{2}+560 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} c^{\frac{9}{2}} x a -1338 c^{\frac{9}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x a +70 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} c^{\frac{9}{2}}+1338 c^{\frac{9}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}}\right) \left(a x +1\right)}{315 \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{9} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{9}{2}} a^{10} c^{\frac{9}{2}}}"," ",0,"1/315*(-315*c^(9/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^9*a^9+256*(c*(a^2*x^2-1)/a^2)^(7/2)*c^(9/2)*x^8*a^8+1185*x^8*c^(9/2)*a^8*((a*x-1)*(a*x+1)*c/a^2)^(7/2)-256*(c*(a^2*x^2-1)/a^2)^(7/2)*c^(9/2)*x^7*a^7+2280*c^(9/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^7*a^7-896*(c*(a^2*x^2-1)/a^2)^(7/2)*c^(9/2)*x^6*a^6-4620*c^(9/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^6*a^6+896*(c*(a^2*x^2-1)/a^2)^(7/2)*c^(9/2)*x^5*a^5-4620*c^(9/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^5*a^5-630*(c*(a^2*x^2-1)/a^2)^(7/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x*a^8*c+1120*(c*(a^2*x^2-1)/a^2)^(7/2)*c^(9/2)*x^4*a^4+7140*c^(9/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^4*a^4+630*(c*(a^2*x^2-1)/a^2)^(7/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*a^7*c-1120*(c*(a^2*x^2-1)/a^2)^(7/2)*c^(9/2)*x^3*a^3+3948*c^(9/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^3*a^3-560*(c*(a^2*x^2-1)/a^2)^(7/2)*c^(9/2)*x^2*a^2-4998*c^(9/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^2*a^2+560*(c*(a^2*x^2-1)/a^2)^(7/2)*c^(9/2)*x*a-1338*c^(9/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x*a+70*(c*(a^2*x^2-1)/a^2)^(7/2)*c^(9/2)+1338*c^(9/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2))*(a*x+1)/((a*x-1)*(a*x+1)*c/a^2)^(7/2)/x^9/(c*(a^2*x^2-1)/a^2/x^2)^(9/2)/a^10/c^(9/2)","B"
705,1,102,260,0.051000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(9/2),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{9}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(280 a^{9} x^{9}+840 a^{8} \ln \left(x \right) x^{8}+1120 x^{6} a^{6}+560 x^{5} a^{5}-420 x^{4} a^{4}-448 x^{3} a^{3}+120 a x +35\right)}{280 \left(a^{2} x^{2}-1\right)^{5}}"," ",0,"1/280*(c*(a^2*x^2-1)/a^2/x^2)^(9/2)*x/(a^2*x^2-1)^5*(-a^2*x^2+1)^(1/2)*(280*a^9*x^9+840*a^8*ln(x)*x^8+1120*x^6*a^6+560*x^5*a^5-420*x^4*a^4-448*x^3*a^3+120*a*x+35)","A"
706,1,102,259,0.053000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(7/2),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(60 a^{7} x^{7}+180 a^{6} \ln \left(x \right) x^{6}-60 x^{5} a^{5}+150 x^{4} a^{4}+100 x^{3} a^{3}-15 a^{2} x^{2}-36 a x -10\right)}{60 \left(a^{2} x^{2}-1\right)^{4}}"," ",0,"1/60*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*x/(a^2*x^2-1)^4*(-a^2*x^2+1)^(1/2)*(60*a^7*x^7+180*a^6*ln(x)*x^6-60*x^5*a^5+150*x^4*a^4+100*x^3*a^3-15*a^2*x^2-36*a*x-10)","A"
707,1,86,194,0.050000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(5/2),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(4 x^{5} a^{5}+12 a^{4} \ln \left(x \right) x^{4}-8 x^{3} a^{3}+4 a^{2} x^{2}+4 a x +1\right)}{4 \left(a^{2} x^{2}-1\right)^{3}}"," ",0,"1/4*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*x/(a^2*x^2-1)^3*(-a^2*x^2+1)^(1/2)*(4*x^5*a^5+12*a^4*ln(x)*x^4-8*x^3*a^3+4*a^2*x^2+4*a*x+1)","A"
708,1,70,127,0.049000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(3/2),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}+6 a^{2} \ln \left(x \right) x^{2}-6 a x -1\right)}{2 \left(a^{2} x^{2}-1\right)^{2}}"," ",0,"1/2*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*x/(a^2*x^2-1)^2*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3+6*a^2*ln(x)*x^2-6*a*x-1)","A"
709,1,61,96,0.049000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-a x +\ln \left(x \right)-4 \ln \left(a x -1\right)\right) \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-a*x+ln(x)-4*ln(a*x-1))*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
710,1,77,111,0.049000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}+3 \ln \left(a x -1\right) x a -a x -3 \ln \left(a x -1\right)-2\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,a^{2} \left(a x -1\right)}"," ",0,"1/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x*(-a^2*x^2+1)^(1/2)/a^2*(a^2*x^2+3*ln(a*x-1)*x*a-a*x-3*ln(a*x-1)-2)/(a*x-1)","A"
711,1,106,156,0.051000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(3/2),x)","\frac{\left(2 x^{3} a^{3}+6 \ln \left(a x -1\right) x^{2} a^{2}-4 a^{2} x^{2}-12 \ln \left(a x -1\right) x a -4 a x +6 \ln \left(a x -1\right)+5\right) \left(a x +1\right) \sqrt{-a^{2} x^{2}+1}}{2 \left(a x -1\right) a^{4} x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/2*(2*x^3*a^3+6*ln(a*x-1)*x^2*a^2-4*a^2*x^2-12*ln(a*x-1)*x*a-4*a*x+6*ln(a*x-1)+5)*(a*x+1)*(-a^2*x^2+1)^(1/2)/(a*x-1)/a^4/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)","A"
712,1,176,235,0.055000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(5/2),x)","\frac{\left(48 x^{4} a^{4}+147 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)-144 x^{3} a^{3}-441 \ln \left(a x -1\right) x^{2} a^{2}+9 \ln \left(a x +1\right) x^{2} a^{2}-42 a^{2} x^{2}+441 \ln \left(a x -1\right) x a -9 a x \ln \left(a x +1\right)+270 a x -147 \ln \left(a x -1\right)+3 \ln \left(a x +1\right)-140\right) \left(a x +1\right)^{2} \sqrt{-a^{2} x^{2}+1}}{48 \left(a x -1\right) a^{6} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}}}"," ",0,"1/48*(48*x^4*a^4+147*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)-144*x^3*a^3-441*ln(a*x-1)*x^2*a^2+9*ln(a*x+1)*x^2*a^2-42*a^2*x^2+441*ln(a*x-1)*x*a-9*a*x*ln(a*x+1)+270*a*x-147*ln(a*x-1)+3*ln(a*x+1)-140)*(a*x+1)^2*(-a^2*x^2+1)^(1/2)/(a*x-1)/a^6/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)","A"
713,1,248,317,0.057000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(7/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a x +1\right)^{2} \left(64 x^{6} a^{6}+201 \ln \left(a x -1\right) x^{5} a^{5}-9 \ln \left(a x +1\right) x^{5} a^{5}-192 x^{5} a^{5}-603 \ln \left(a x -1\right) x^{4} a^{4}+27 \ln \left(a x +1\right) x^{4} a^{4}-174 x^{4} a^{4}+402 \ln \left(a x -1\right) x^{3} a^{3}-18 a^{3} x^{3} \ln \left(a x +1\right)+618 x^{3} a^{3}+402 \ln \left(a x -1\right) x^{2} a^{2}-18 \ln \left(a x +1\right) x^{2} a^{2}-118 a^{2} x^{2}-603 \ln \left(a x -1\right) x a +27 a x \ln \left(a x +1\right)-414 a x +201 \ln \left(a x -1\right)-9 \ln \left(a x +1\right)+208\right)}{64 \left(a x -1\right) a^{8} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}}}"," ",0,"1/64*(-a^2*x^2+1)^(1/2)*(a*x+1)^2*(64*x^6*a^6+201*ln(a*x-1)*x^5*a^5-9*ln(a*x+1)*x^5*a^5-192*x^5*a^5-603*ln(a*x-1)*x^4*a^4+27*ln(a*x+1)*x^4*a^4-174*x^4*a^4+402*ln(a*x-1)*x^3*a^3-18*a^3*x^3*ln(a*x+1)+618*x^3*a^3+402*ln(a*x-1)*x^2*a^2-18*ln(a*x+1)*x^2*a^2-118*a^2*x^2-603*ln(a*x-1)*x*a+27*a*x*ln(a*x+1)-414*a*x+201*ln(a*x-1)-9*ln(a*x+1)+208)/(a*x-1)/a^8/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)","A"
714,1,118,325,0.053000," ","int((c-c/a^2/x^2)^(9/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{9}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(-840 a^{9} x^{9}+840 a^{8} \ln \left(x \right) x^{8}-3360 a^{7} x^{7}+1680 x^{6} a^{6}+1680 x^{5} a^{5}-1260 x^{4} a^{4}-672 x^{3} a^{3}+560 a^{2} x^{2}+120 a x -105\right)}{840 \left(a^{2} x^{2}-1\right)^{5}}"," ",0,"-1/840*(c*(a^2*x^2-1)/a^2/x^2)^(9/2)*x/(a^2*x^2-1)^5*(-a^2*x^2+1)^(1/2)*(-840*a^9*x^9+840*a^8*ln(x)*x^8-3360*a^7*x^7+1680*x^6*a^6+1680*x^5*a^5-1260*x^4*a^4-672*x^3*a^3+560*a^2*x^2+120*a*x-105)","A"
715,1,102,259,0.049000," ","int((c-c/a^2/x^2)^(7/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(-60 a^{7} x^{7}+60 a^{6} \ln \left(x \right) x^{6}-180 x^{5} a^{5}+90 x^{4} a^{4}+60 x^{3} a^{3}-45 a^{2} x^{2}-12 a x +10\right)}{60 \left(a^{2} x^{2}-1\right)^{4}}"," ",0,"-1/60*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*x/(a^2*x^2-1)^4*(-a^2*x^2+1)^(1/2)*(-60*a^7*x^7+60*a^6*ln(x)*x^6-180*x^5*a^5+90*x^4*a^4+60*x^3*a^3-45*a^2*x^2-12*a*x+10)","A"
716,1,86,192,0.049000," ","int((c-c/a^2/x^2)^(5/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(-12 x^{5} a^{5}+12 a^{4} \ln \left(x \right) x^{4}-24 x^{3} a^{3}+12 a^{2} x^{2}+4 a x -3\right)}{12 \left(a^{2} x^{2}-1\right)^{3}}"," ",0,"-1/12*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*x/(a^2*x^2-1)^3*(-a^2*x^2+1)^(1/2)*(-12*x^5*a^5+12*a^4*ln(x)*x^4-24*x^3*a^3+12*a^2*x^2+4*a*x-3)","A"
717,1,70,126,0.048000," ","int((c-c/a^2/x^2)^(3/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(-2 x^{3} a^{3}+2 a^{2} \ln \left(x \right) x^{2}-2 a x +1\right)}{2 \left(a^{2} x^{2}-1\right)^{2}}"," ",0,"-1/2*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*x/(a^2*x^2-1)^2*(-a^2*x^2+1)^(1/2)*(-2*x^3*a^3+2*a^2*ln(x)*x^2-2*a*x+1)","A"
718,1,53,61,0.041000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-a x +\ln \left(x \right)\right) \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-a*x+ln(x))*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
719,1,51,69,0.042000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(-a x +\ln \left(a x +1\right)\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,a^{2}}"," ",0,"-(-a^2*x^2+1)^(1/2)*(-a*x+ln(a*x+1))/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/a^2","A"
720,1,92,153,0.053000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(3/2),x)","\frac{\left(4 a^{2} x^{2}+\ln \left(a x -1\right) x a -5 a x \ln \left(a x +1\right)+4 a x +\ln \left(a x -1\right)-5 \ln \left(a x +1\right)-2\right) \left(a x -1\right) \sqrt{-a^{2} x^{2}+1}}{4 a^{4} x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/4*(4*a^2*x^2+ln(a*x-1)*x*a-5*a*x*ln(a*x+1)+4*a*x+ln(a*x-1)-5*ln(a*x+1)-2)*(a*x-1)*(-a^2*x^2+1)^(1/2)/a^4/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)","A"
721,1,167,233,0.055000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(5/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a x -1\right) \left(16 x^{4} a^{4}+7 \ln \left(a x -1\right) x^{3} a^{3}-23 a^{3} x^{3} \ln \left(a x +1\right)+16 x^{3} a^{3}+7 \ln \left(a x -1\right) x^{2} a^{2}-23 \ln \left(a x +1\right) x^{2} a^{2}-34 a^{2} x^{2}-7 \ln \left(a x -1\right) x a +23 a x \ln \left(a x +1\right)-18 a x -7 \ln \left(a x -1\right)+23 \ln \left(a x +1\right)+12\right)}{16 a^{6} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}}}"," ",0,"1/16*(-a^2*x^2+1)^(1/2)*(a*x-1)*(16*x^4*a^4+7*ln(a*x-1)*x^3*a^3-23*a^3*x^3*ln(a*x+1)+16*x^3*a^3+7*ln(a*x-1)*x^2*a^2-23*ln(a*x+1)*x^2*a^2-34*a^2*x^2-7*ln(a*x-1)*x*a+23*a*x*ln(a*x+1)-18*a*x-7*ln(a*x-1)+23*ln(a*x+1)+12)/a^6/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)","A"
722,1,239,315,0.056000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(7/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a x -1\right) \left(96 x^{6} a^{6}+57 \ln \left(a x -1\right) x^{5} a^{5}-153 \ln \left(a x +1\right) x^{5} a^{5}+96 x^{5} a^{5}+57 \ln \left(a x -1\right) x^{4} a^{4}-153 \ln \left(a x +1\right) x^{4} a^{4}-366 x^{4} a^{4}-114 \ln \left(a x -1\right) x^{3} a^{3}+306 a^{3} x^{3} \ln \left(a x +1\right)-222 x^{3} a^{3}-114 \ln \left(a x -1\right) x^{2} a^{2}+306 \ln \left(a x +1\right) x^{2} a^{2}+338 a^{2} x^{2}+57 \ln \left(a x -1\right) x a -153 a x \ln \left(a x +1\right)+122 a x +57 \ln \left(a x -1\right)-153 \ln \left(a x +1\right)-88\right)}{96 a^{8} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}}}"," ",0,"1/96*(-a^2*x^2+1)^(1/2)*(a*x-1)*(96*x^6*a^6+57*ln(a*x-1)*x^5*a^5-153*ln(a*x+1)*x^5*a^5+96*x^5*a^5+57*ln(a*x-1)*x^4*a^4-153*ln(a*x+1)*x^4*a^4-366*x^4*a^4-114*ln(a*x-1)*x^3*a^3+306*a^3*x^3*ln(a*x+1)-222*x^3*a^3-114*ln(a*x-1)*x^2*a^2+306*ln(a*x+1)*x^2*a^2+338*a^2*x^2+57*ln(a*x-1)*x*a-153*a*x*ln(a*x+1)+122*a*x+57*ln(a*x-1)-153*ln(a*x+1)-88)/a^8/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)","A"
723,1,965,401,0.120000," ","int((c-c/a^2/x^2)^(9/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{9}{2}} x \left(5040 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} \sqrt{-\frac{c}{a^{2}}}-77175 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{8} c^{6}+23808 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{7} a^{11}+17535 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{6} a^{10}-13056 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{5} a^{9}+6510 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{4} a^{8}-6912 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{3} a^{7}+10920 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x^{2} a^{6}-11520 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{11}{2}} x \,a^{5}+58590 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{11}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{8} a +22050 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{11}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{8} a -23808 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} x^{9} a^{11} c -8575 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} x^{8} a^{10} c -8960 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{9}{2}} x^{8} a^{10} c +26784 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{9} a^{9} c^{2}+10080 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{9} a^{9} c^{2}+11025 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{8} a^{8} c^{2}-31248 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{9} a^{7} c^{3}-11760 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{9} a^{7} c^{3}-15435 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{8} a^{6} c^{3}+39060 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{9} a^{5} c^{4}+14700 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{9} a^{5} c^{4}+25725 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{8} a^{4} c^{4}-58590 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{9} a^{3} c^{5}-22050 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{9} a^{3} c^{5}-77175 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{8} a^{2} c^{5}\right)}{40320 a^{2} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"1/40320*(c*(a^2*x^2-1)/a^2/x^2)^(9/2)*x/a^2*(5040*a^4*(c*(a^2*x^2-1)/a^2)^(11/2)*(-c/a^2)^(1/2)-77175*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^8*c^6+23808*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^7*a^11+17535*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^6*a^10-13056*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^5*a^9+6510*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^4*a^8-6912*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^3*a^7+10920*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x^2*a^6-11520*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(11/2)*x*a^5+58590*(-c/a^2)^(1/2)*c^(11/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^8*a+22050*(-c/a^2)^(1/2)*c^(11/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^8*a-23808*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(9/2)*x^9*a^11*c-8575*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(9/2)*x^8*a^10*c-8960*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(9/2)*x^8*a^10*c+26784*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^9*a^9*c^2+10080*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^9*a^9*c^2+11025*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^8*a^8*c^2-31248*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^9*a^7*c^3-11760*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^9*a^7*c^3-15435*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^8*a^6*c^3+39060*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^9*a^5*c^4+14700*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^9*a^5*c^4+25725*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^8*a^4*c^4-58590*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^9*a^3*c^5-22050*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^9*a^3*c^5-77175*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^8*a^2*c^5)/(c*(a^2*x^2-1)/a^2)^(9/2)/(-c/a^2)^(1/2)/c","B"
724,1,795,329,0.066000," ","int((c-c/a^2/x^2)^(7/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} x \left(-2016 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{9} c +2016 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{5} a^{9}-375 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{8} c +480 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{6} a^{8} c -105 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{4} a^{8}+2352 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{7} c^{2}-560 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} a^{7} c^{2}+224 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{3} a^{7}+525 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{6} c^{2}-2940 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{5} c^{3}+700 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{7} a^{5} c^{3}-630 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{2} a^{6}-875 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{4} c^{3}+672 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x \,a^{5}+4410 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{3} c^{4}-1050 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{7} a^{3} c^{4}-280 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}+2625 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{2} c^{4}-4410 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{9}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{6} a +1050 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{9}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{6} a +2625 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{6} c^{5}\right)}{1680 a^{2} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"-1/1680*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*x/a^2*(-2016*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)*x^7*a^9*c+2016*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^5*a^9-375*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)*x^6*a^8*c+480*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^6*a^8*c-105*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^4*a^8+2352*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)*x^7*a^7*c^2-560*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^7*a^7*c^2+224*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^3*a^7+525*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)*x^6*a^6*c^2-2940*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^7*a^5*c^3+700*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^7*a^5*c^3-630*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^2*a^6-875*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^6*a^4*c^3+672*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x*a^5+4410*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^7*a^3*c^4-1050*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^7*a^3*c^4-280*a^4*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)+2625*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^6*a^2*c^4-4410*(-c/a^2)^(1/2)*c^(9/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^6*a+1050*(-c/a^2)^(1/2)*c^(9/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^6*a+2625*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^6*c^5)/(c*(a^2*x^2-1)/a^2)^(7/2)/(-c/a^2)^(1/2)/c","B"
725,1,625,257,0.054000," ","int((c-c/a^2/x^2)^(5/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} x \left(-80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{5} a^{7} c +80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{3} a^{7}-48 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{6} c -27 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{6} c +60 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5} c^{2}+75 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{2} a^{6}+100 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5} c^{2}-80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x \,a^{5}+45 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{4} a^{4} c^{2}-90 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{5} a^{3} c^{3}-150 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c^{3}+30 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}+150 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{7}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{4} a +90 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{7}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{4} a -135 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{2} c^{3}-135 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{4} c^{4}\right)}{120 a^{2} \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c}"," ",0,"1/120*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*x/a^2*(-80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^5*a^7*c+80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^3*a^7-48*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^4*a^6*c-27*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^4*a^6*c+60*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^5*a^5*c^2+75*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^2*a^6+100*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^5*a^5*c^2-80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x*a^5+45*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^4*a^4*c^2-90*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^5*a^3*c^3-150*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c^3+30*a^4*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)+150*(-c/a^2)^(1/2)*c^(7/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^4*a+90*(-c/a^2)^(1/2)*c^(7/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^4*a-135*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^2*c^3-135*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^4*c^4)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(5/2)/c","B"
726,1,454,184,0.049000," ","int((c-c/a^2/x^2)^(3/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} x \left(12 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{5} c -12 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x \,a^{5}-4 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{4} c +\sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{4} c +6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{3} c^{2}+3 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}-18 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{3} c^{2}+18 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{2} a -6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{5}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{2} a -3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2} c^{2}-3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{2} c^{3}\right)}{6 a^{2} \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} c}"," ",0,"1/6*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*x/a^2*(12*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^5*c-12*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x*a^5-4*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^2*a^4*c+(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^4*c+6*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^3*c^2+3*a^4*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)-18*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^3*c^2+18*(-c/a^2)^(1/2)*c^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^2*a-6*(-c/a^2)^(1/2)*c^(5/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^2*a-3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2*c^2-3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^2*c^3)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(3/2)/c","B"
727,1,198,100,0.045000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(2 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}-2 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) a \sqrt{-\frac{c}{a^{2}}}-\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-c \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right)\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(2*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)-2*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*a*(-c/a^2)^(1/2)-(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x))/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2/(-c/a^2)^(1/2)","A"
728,1,177,101,0.041000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \left(\sqrt{c}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2}-2 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x a c +2 a \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a \sqrt{c}-2 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) c \right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,c^{\frac{3}{2}} a \left(a x +1\right)}"," ",0,"-(c*(a^2*x^2-1)/a^2)^(1/2)*(c^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2-2*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x*a*c+2*a*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2)*a*c^(1/2)-2*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*c)/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/c^(3/2)/a/(a*x+1)","A"
729,1,326,110,0.048000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(3/2),x)","-\frac{\left(3 c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{3}+15 x^{2} a^{2} c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}-4 c^{\frac{3}{2}} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2}-6 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c -4 c^{\frac{3}{2}} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x a -6 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a c -12 c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c^{\frac{3}{2}}\right) \left(a x -1\right)}{3 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} a^{4} c^{\frac{3}{2}}}"," ",0,"-1/3*(3*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^3+15*x^2*a^2*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)-4*c^(3/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2-6*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c-4*c^(3/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a-6*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a*c-12*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+2*(c*(a^2*x^2-1)/a^2)^(1/2)*c^(3/2))*(a*x-1)/((a*x-1)*(a*x+1)*c/a^2)^(1/2)/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)/a^4/c^(3/2)","B"
730,1,462,174,0.051000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(5/2),x)","-\frac{\left(15 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5}+45 x^{4} c^{\frac{5}{2}} a^{4} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}}+16 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{4} a^{4}-60 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+16 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}-30 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{4} c -90 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-24 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-30 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3} c +50 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x a -24 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x a +50 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}}+6 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}}\right) \left(a x -1\right)}{15 \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} a^{6} c^{\frac{5}{2}}}"," ",0,"-1/15*(15*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^5*a^5+45*x^4*c^(5/2)*a^4*((a*x-1)*(a*x+1)*c/a^2)^(3/2)+16*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^4*a^4-60*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^3*a^3+16*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3-30*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^4*c-90*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^2*a^2-24*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2-30*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*a^3*c+50*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x*a-24*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a+50*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)+6*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2))*(a*x-1)/((a*x-1)*(a*x+1)*c/a^2)^(3/2)/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)/a^6/c^(5/2)","B"
731,1,572,240,0.061000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(7/2),x)","\frac{\left(-105 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} a^{7}+96 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{6} a^{6}-553 x^{6} c^{\frac{7}{2}} a^{6} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}}+96 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{5} a^{5}+392 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{5} a^{5}-240 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{4} a^{4}+1540 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{4}+210 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x \,a^{6} c -240 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{3} a^{3}-350 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{3} a^{3}+210 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} a^{5} c +180 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{2} a^{2}-1470 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{2} a^{2}+180 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x a +42 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x a -30 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}}+462 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}}\right) \left(a x -1\right)}{105 \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} a^{8} c^{\frac{7}{2}}}"," ",0,"1/105*(-105*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^7*a^7+96*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^6*a^6-553*x^6*c^(7/2)*a^6*((a*x-1)*(a*x+1)*c/a^2)^(5/2)+96*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^5*a^5+392*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^5*a^5-240*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^4*a^4+1540*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^4*a^4+210*(c*(a^2*x^2-1)/a^2)^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x*a^6*c-240*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^3*a^3-350*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^3*a^3+210*(c*(a^2*x^2-1)/a^2)^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*a^5*c+180*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^2*a^2-1470*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^2*a^2+180*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x*a+42*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x*a-30*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)+462*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2))*(a*x-1)/((a*x-1)*(a*x+1)*c/a^2)^(5/2)/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)/a^8/c^(7/2)","B"
732,1,102,259,0.051000," ","int((c-c/a^2/x^2)^(9/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{9}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(-280 a^{9} x^{9}+840 a^{8} \ln \left(x \right) x^{8}+1120 x^{6} a^{6}-560 x^{5} a^{5}-420 x^{4} a^{4}+448 x^{3} a^{3}-120 a x +35\right)}{280 \left(a^{2} x^{2}-1\right)^{5}}"," ",0,"1/280*(c*(a^2*x^2-1)/a^2/x^2)^(9/2)*x/(a^2*x^2-1)^5*(-a^2*x^2+1)^(1/2)*(-280*a^9*x^9+840*a^8*ln(x)*x^8+1120*x^6*a^6-560*x^5*a^5-420*x^4*a^4+448*x^3*a^3-120*a*x+35)","A"
733,1,102,259,0.047000," ","int((c-c/a^2/x^2)^(7/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(-60 a^{7} x^{7}+180 a^{6} \ln \left(x \right) x^{6}+60 x^{5} a^{5}+150 x^{4} a^{4}-100 x^{3} a^{3}-15 a^{2} x^{2}+36 a x -10\right)}{60 \left(a^{2} x^{2}-1\right)^{4}}"," ",0,"1/60*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*x/(a^2*x^2-1)^4*(-a^2*x^2+1)^(1/2)*(-60*a^7*x^7+180*a^6*ln(x)*x^6+60*x^5*a^5+150*x^4*a^4-100*x^3*a^3-15*a^2*x^2+36*a*x-10)","A"
734,1,86,192,0.049000," ","int((c-c/a^2/x^2)^(5/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(-4 x^{5} a^{5}+12 a^{4} \ln \left(x \right) x^{4}+8 x^{3} a^{3}+4 a^{2} x^{2}-4 a x +1\right)}{4 \left(a^{2} x^{2}-1\right)^{3}}"," ",0,"1/4*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*x/(a^2*x^2-1)^3*(-a^2*x^2+1)^(1/2)*(-4*x^5*a^5+12*a^4*ln(x)*x^4+8*x^3*a^3+4*a^2*x^2-4*a*x+1)","A"
735,1,70,128,0.047000," ","int((c-c/a^2/x^2)^(3/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} x \sqrt{-a^{2} x^{2}+1}\, \left(-2 x^{3} a^{3}+6 a^{2} \ln \left(x \right) x^{2}+6 a x -1\right)}{2 \left(a^{2} x^{2}-1\right)^{2}}"," ",0,"1/2*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*x/(a^2*x^2-1)^2*(-a^2*x^2+1)^(1/2)*(-2*x^3*a^3+6*a^2*ln(x)*x^2+6*a*x-1)","A"
736,1,60,94,0.050000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(a x +\ln \left(x \right)-4 \ln \left(a x +1\right)\right) \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(a*x+ln(x)-4*ln(a*x+1))*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
737,1,78,110,0.049000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \left(-a^{2} x^{2}+3 a x \ln \left(a x +1\right)-a x +3 \ln \left(a x +1\right)+2\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,a^{2} \left(a x +1\right)}"," ",0,"1/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x*(-a^2*x^2+1)^(1/2)/a^2*(-a^2*x^2+3*a*x*ln(a*x+1)-a*x+3*ln(a*x+1)+2)/(a*x+1)","A"
738,1,106,152,0.052000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(3/2),x)","\frac{\left(-2 x^{3} a^{3}+6 \ln \left(a x +1\right) x^{2} a^{2}-4 a^{2} x^{2}+12 a x \ln \left(a x +1\right)+4 a x +6 \ln \left(a x +1\right)+5\right) \left(a x -1\right) \sqrt{-a^{2} x^{2}+1}}{2 \left(a x +1\right) a^{4} x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/2*(-2*x^3*a^3+6*ln(a*x+1)*x^2*a^2-4*a^2*x^2+12*a*x*ln(a*x+1)+4*a*x+6*ln(a*x+1)+5)*(a*x-1)*(-a^2*x^2+1)^(1/2)/(a*x+1)/a^4/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)","A"
739,1,176,233,0.055000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(5/2),x)","-\frac{\left(48 x^{4} a^{4}+3 \ln \left(a x -1\right) x^{3} a^{3}-147 a^{3} x^{3} \ln \left(a x +1\right)+144 x^{3} a^{3}+9 \ln \left(a x -1\right) x^{2} a^{2}-441 \ln \left(a x +1\right) x^{2} a^{2}-42 a^{2} x^{2}+9 \ln \left(a x -1\right) x a -441 a x \ln \left(a x +1\right)-270 a x +3 \ln \left(a x -1\right)-147 \ln \left(a x +1\right)-140\right) \left(a x -1\right)^{2} \sqrt{-a^{2} x^{2}+1}}{48 \left(a x +1\right) a^{6} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}}}"," ",0,"-1/48*(48*x^4*a^4+3*ln(a*x-1)*x^3*a^3-147*a^3*x^3*ln(a*x+1)+144*x^3*a^3+9*ln(a*x-1)*x^2*a^2-441*ln(a*x+1)*x^2*a^2-42*a^2*x^2+9*ln(a*x-1)*x*a-441*a*x*ln(a*x+1)-270*a*x+3*ln(a*x-1)-147*ln(a*x+1)-140)*(a*x-1)^2*(-a^2*x^2+1)^(1/2)/(a*x+1)/a^6/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)","A"
740,1,248,313,0.061000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(7/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a x -1\right)^{2} \left(64 x^{6} a^{6}+9 \ln \left(a x -1\right) x^{5} a^{5}-201 \ln \left(a x +1\right) x^{5} a^{5}+192 x^{5} a^{5}+27 \ln \left(a x -1\right) x^{4} a^{4}-603 \ln \left(a x +1\right) x^{4} a^{4}-174 x^{4} a^{4}+18 \ln \left(a x -1\right) x^{3} a^{3}-402 a^{3} x^{3} \ln \left(a x +1\right)-618 x^{3} a^{3}-18 \ln \left(a x -1\right) x^{2} a^{2}+402 \ln \left(a x +1\right) x^{2} a^{2}-118 a^{2} x^{2}-27 \ln \left(a x -1\right) x a +603 a x \ln \left(a x +1\right)+414 a x -9 \ln \left(a x -1\right)+201 \ln \left(a x +1\right)+208\right)}{64 \left(a x +1\right) a^{8} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}}}"," ",0,"-1/64*(-a^2*x^2+1)^(1/2)*(a*x-1)^2*(64*x^6*a^6+9*ln(a*x-1)*x^5*a^5-201*ln(a*x+1)*x^5*a^5+192*x^5*a^5+27*ln(a*x-1)*x^4*a^4-603*ln(a*x+1)*x^4*a^4-174*x^4*a^4+18*ln(a*x-1)*x^3*a^3-402*a^3*x^3*ln(a*x+1)-618*x^3*a^3-18*ln(a*x-1)*x^2*a^2+402*ln(a*x+1)*x^2*a^2-118*a^2*x^2-27*ln(a*x-1)*x*a+603*a*x*ln(a*x+1)+414*a*x-9*ln(a*x-1)+201*ln(a*x+1)+208)/(a*x+1)/a^8/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)","A"
741,1,53,72,0.028000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(c-c/a^2/x^2)^(1/2),x)","\frac{x^{1+m} \left(a x m +m +1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}}{\left(1+m \right) m \sqrt{-a^{2} x^{2}+1}}"," ",0,"x^(1+m)*(a*m*x+m+1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/(1+m)/m/(-a^2*x^2+1)^(1/2)","A"
742,1,43,62,0.027000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(c-c/a^2/x^2)^(1/2),x)","\frac{x^{3} \left(2 a x +3\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}}{6 \sqrt{-a^{2} x^{2}+1}}"," ",0,"1/6*x^3*(2*a*x+3)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/(-a^2*x^2+1)^(1/2)","A"
743,1,42,61,0.029000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(c-c/a^2/x^2)^(1/2),x)","\frac{x^{2} \left(a x +2\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}}{2 \sqrt{-a^{2} x^{2}+1}}"," ",0,"1/2*x^2*(a*x+2)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/(-a^2*x^2+1)^(1/2)","A"
744,1,52,60,0.039000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(a x +\ln \left(x \right)\right) \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(a*x+ln(x))*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
745,1,52,58,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2)/x,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a \ln \left(x \right) x -1\right) \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*ln(x)*x-1)*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
746,1,43,37,0.030000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2)/x^2,x)","-\frac{\left(2 a x +1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}}{2 x \sqrt{-a^{2} x^{2}+1}}"," ",0,"-1/2*(2*a*x+1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/(-a^2*x^2+1)^(1/2)","A"
747,1,196,136,0.045000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3*(c-c/a^2/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-6 x \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{4}-16 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3}-27 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c +27 c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)-48 c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)-48 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a c \right)}{24 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c \,a^{4}}"," ",0,"1/24*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-6*x*(c*(a^2*x^2-1)/a^2)^(3/2)*a^4-16*(c*(a^2*x^2-1)/a^2)^(3/2)*a^3-27*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c+27*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))-48*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))-48*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a*c)/(c*(a^2*x^2-1)/a^2)^(1/2)/c/a^4","A"
748,1,174,107,0.040000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2*(c-c/a^2/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3}-3 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c +3 c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)-6 c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)-6 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a c \right)}{3 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{3} c}"," ",0,"1/3*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-(c*(a^2*x^2-1)/a^2)^(3/2)*a^3-3*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c+3*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))-6*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))-6*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a*c)/(c*(a^2*x^2-1)/a^2)^(1/2)/a^3/c","A"
749,1,147,82,0.038000," ","int((a*x+1)^2/(-a^2*x^2+1)*x*(c-c/a^2/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}+\sqrt{c}\, \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)-4 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)-4 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a \right)}{2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}}"," ",0,"1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-x*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2+c^(1/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))-4*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))-4*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a)/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2","A"
750,1,198,100,0.043000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(2 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) a \sqrt{-\frac{c}{a^{2}}}+2 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}-\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-c \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right)\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(2*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*a*(-c/a^2)^(1/2)+2*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)-(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x))/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2/(-c/a^2)^(1/2)","A"
751,1,305,100,0.049000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2)/x,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(-\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{3} c +a^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}+\sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x a -2 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x a -2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x \,a^{2} c +2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}\, c x +2 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x \,c^{2}\right)}{a \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/a*(-(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^3*c+a^3*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)+(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x*a-2*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x*a-2*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x*a^2*c+2*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)*c*x+2*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x*c^2)/(c*(a^2*x^2-1)/a^2)^(1/2)/(-c/a^2)^(1/2)/c","B"
752,1,347,91,0.050000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2)/x^2,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(-4 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{3} c +4 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{3}+4 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{2} a -4 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{2} a -4 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{2} a^{2} c +3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2} c +a^{2} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}+3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{2} c^{2}\right)}{2 x \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x*(-4*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^3*c+4*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^3+4*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^2*a-4*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^2*a-4*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^2*a^2*c+3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2*c+a^2*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)+3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^2*c^2)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
753,1,378,119,0.051000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2)/x^3,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a \left(-6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{3} c +6 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{3}+6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{3} a -6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{3} a -6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{2} c +3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{2} c +3 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{2}+3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{3} c^{2}+a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{3 x^{2} \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"1/3*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^2*a*(-6*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^3*c+6*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^3+6*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^3*a-6*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^3*a-6*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^2*c+3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^2*c+3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^2+3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^3*c^2+a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
754,1,410,128,0.052000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2)/x^4,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a^{2} \left(-48 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c +48 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+48 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{4} a -48 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{4} a -48 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{4} a^{2} c +21 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{2} c +27 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}+21 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{4} c^{2}+16 a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x +6 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{24 x^{3} \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"1/24*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^3*a^2*(-48*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c+48*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3+48*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^4*a-48*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^4*a-48*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^4*a^2*c+21*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^2*c+27*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2+21*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^4*c^2+16*a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x+6*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
755,1,447,149,0.057000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2)/x^5,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a^{2} \left(-40 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{4} c +40 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{4} a^{4}+15 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c +40 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{5} a^{2}-40 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{5} a^{2}-40 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{5} a^{3} c +25 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+15 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{5} a \,c^{2}+16 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}+10 a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x +4 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{20 x^{4} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"1/20*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^4*a^2*(-40*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^6*a^4*c+40*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^4*a^4+15*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c+40*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^5*a^2-40*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^5*a^2-40*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^5*a^3*c+25*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3+15*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^5*a*c^2+16*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2+10*a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x+4*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(c*(a^2*x^2-1)/a^2)^(1/2)/(-c/a^2)^(1/2)/c","B"
756,1,85,166,0.046000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(c-c/a^2/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(x^{4} a^{4}+4 x^{3} a^{3}+8 a^{2} x^{2}+16 a x +16 \ln \left(a x -1\right)\right)}{4 \left(a^{2} x^{2}-1\right) a^{3}}"," ",0,"1/4*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(x^4*a^4+4*x^3*a^3+8*a^2*x^2+16*a*x+16*ln(a*x-1))/(a^2*x^2-1)/a^3","A"
757,1,78,133,0.045000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(c-c/a^2/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(2 x^{3} a^{3}+9 a^{2} x^{2}+24 a x +24 \ln \left(a x -1\right)\right)}{6 \left(a^{2} x^{2}-1\right) a^{2}}"," ",0,"1/6*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(2*x^3*a^3+9*a^2*x^2+24*a*x+24*ln(a*x-1))/(a^2*x^2-1)/a^2","A"
758,1,69,100,0.042000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(c-c/a^2/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}+6 a x +8 \ln \left(a x -1\right)\right)}{2 \left(a^{2} x^{2}-1\right) a}"," ",0,"1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(a^2*x^2+6*a*x+8*ln(a*x-1))/(a^2*x^2-1)/a","A"
759,1,61,96,0.044000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-a x +\ln \left(x \right)-4 \ln \left(a x -1\right)\right) \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-a*x+ln(x)-4*ln(a*x-1))*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
760,1,63,95,0.052000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(3 a \ln \left(x \right) x -4 \ln \left(a x -1\right) x a -1\right) \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(3*a*ln(x)*x-4*ln(a*x-1)*x*a-1)*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
761,1,78,130,0.052000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^2,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}\, \left(8 a^{2} \ln \left(x \right) x^{2}-8 \ln \left(a x -1\right) x^{2} a^{2}-6 a x -1\right)}{2 x \left(a^{2} x^{2}-1\right)}"," ",0,"-1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x*(-a^2*x^2+1)^(1/2)*(8*a^2*ln(x)*x^2-8*ln(a*x-1)*x^2*a^2-6*a*x-1)/(a^2*x^2-1)","A"
762,1,86,163,0.054000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^3,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}\, \left(24 a^{3} \ln \left(x \right) x^{3}-24 \ln \left(a x -1\right) x^{3} a^{3}-24 a^{2} x^{2}-9 a x -2\right)}{6 x^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/6*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^2*(-a^2*x^2+1)^(1/2)*(24*a^3*ln(x)*x^3-24*ln(a*x-1)*x^3*a^3-24*a^2*x^2-9*a*x-2)/(a^2*x^2-1)","A"
763,1,94,196,0.052000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^4,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}\, \left(16 a^{4} \ln \left(x \right) x^{4}-16 \ln \left(a x -1\right) x^{4} a^{4}-16 x^{3} a^{3}-8 a^{2} x^{2}-4 a x -1\right)}{4 x^{3} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/4*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^3*(-a^2*x^2+1)^(1/2)*(16*a^4*ln(x)*x^4-16*ln(a*x-1)*x^4*a^4-16*x^3*a^3-8*a^2*x^2-4*a*x-1)/(a^2*x^2-1)","A"
764,1,102,229,0.051000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^5,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}\, \left(240 a^{5} \ln \left(x \right) x^{5}-240 \ln \left(a x -1\right) x^{5} a^{5}-240 x^{4} a^{4}-120 x^{3} a^{3}-80 a^{2} x^{2}-45 a x -12\right)}{60 x^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/60*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^4*(-a^2*x^2+1)^(1/2)*(240*a^5*ln(x)*x^5-240*ln(a*x-1)*x^5*a^5-240*x^4*a^4-120*x^3*a^3-80*a^2*x^2-45*a*x-12)/(a^2*x^2-1)","A"
765,1,69,73,0.029000," ","int(x^m*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x^{1+m} \left(a x m -m -1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}}{\left(1+m \right) m \left(a x -1\right) \left(a x +1\right)}"," ",0,"x^(1+m)*(a*m*x-m-1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(-a^2*x^2+1)^(1/2)/(1+m)/m/(a*x-1)/(a*x+1)","A"
766,1,57,62,0.028000," ","int(x^2*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x^{3} \left(2 a x -3\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}}{6 \left(a x -1\right) \left(a x +1\right)}"," ",0,"1/6*x^3*(2*a*x-3)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x-1)/(a*x+1)","A"
767,1,56,61,0.028000," ","int(x*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x^{2} \left(a x -2\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}}{2 \left(a x -1\right) \left(a x +1\right)}"," ",0,"1/2*x^2*(a*x-2)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x-1)/(a*x+1)","A"
768,1,53,61,0.035000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-a x +\ln \left(x \right)\right) \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-a*x+ln(x))*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
769,1,51,59,0.046000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}\, \left(a \ln \left(x \right) x +1\right)}{a^{2} x^{2}-1}"," ",0,"(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(-a^2*x^2+1)^(1/2)*(a*ln(x)*x+1)/(a^2*x^2-1)","A"
770,1,57,38,0.030000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x)","-\frac{\left(2 a x -1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}}{2 \left(a x -1\right) \left(a x +1\right) x}"," ",0,"-1/2*(2*a*x-1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x-1)/(a*x+1)/x","A"
771,1,196,139,0.043000," ","int(x^3*(c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-6 x \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{4}+16 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3}-27 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c +27 c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)-48 c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)+48 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a c \right)}{24 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c \,a^{4}}"," ",0,"1/24*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-6*x*(c*(a^2*x^2-1)/a^2)^(3/2)*a^4+16*(c*(a^2*x^2-1)/a^2)^(3/2)*a^3-27*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c+27*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))-48*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))+48*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a*c)/(c*(a^2*x^2-1)/a^2)^(1/2)/c/a^4","A"
772,1,173,110,0.040000," ","int(x^2*(c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3}-3 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c +3 c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)-6 c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)+6 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a c \right)}{3 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{3} c}"," ",0,"-1/3*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*((c*(a^2*x^2-1)/a^2)^(3/2)*a^3-3*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c+3*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))-6*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))+6*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a*c)/(c*(a^2*x^2-1)/a^2)^(1/2)/a^3/c","A"
773,1,147,83,0.038000," ","int(x*(c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}+\sqrt{c}\, \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)-4 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)+4 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a \right)}{2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}}"," ",0,"1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-x*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2+c^(1/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))-4*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))+4*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a)/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2","A"
774,1,198,100,0.042000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(2 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}-2 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) a \sqrt{-\frac{c}{a^{2}}}-\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-c \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right)\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(2*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)-2*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*a*(-c/a^2)^(1/2)-(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x))/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2/(-c/a^2)^(1/2)","A"
775,1,307,100,0.044000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{3} c -a^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}+2 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x a -\sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x a -2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x \,a^{2} c +2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}\, c x +2 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x \,c^{2}\right)}{a \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/a*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^3*c-a^3*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)+2*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x*a-(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x*a-2*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x*a^2*c+2*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)*c*x+2*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x*c^2)/(c*(a^2*x^2-1)/a^2)^(1/2)/(-c/a^2)^(1/2)/c","B"
776,1,348,92,0.047000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^2,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(-4 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{3} c +4 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{3}+4 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{2} a -4 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{2} a +4 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{2} a^{2} c -3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2} c -a^{2} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}-3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{2} c^{2}\right)}{2 x \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"-1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x*(-4*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^3*c+4*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^3+4*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^2*a-4*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^2*a+4*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^2*a^2*c-3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2*c-a^2*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)-3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^2*c^2)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
777,1,378,120,0.047000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^3,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a \left(-6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{3} c +6 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{3}+6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{3} a -6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{3} a +6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{2} c -3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{2} c -3 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{2}-3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{3} c^{2}+a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{3 x^{2} \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"1/3*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^2*a*(-6*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^3*c+6*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^3+6*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^3*a-6*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^3*a+6*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^2*c-3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^2*c-3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^2-3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^3*c^2+a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
778,1,410,128,0.051000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^4,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a^{2} \left(-48 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c +48 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+48 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{4} a -48 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{4} a +48 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{4} a^{2} c -21 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{2} c -27 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-21 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{4} c^{2}+16 a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x -6 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{24 x^{3} \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"-1/24*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^3*a^2*(-48*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c+48*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3+48*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^4*a-48*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^4*a+48*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^4*a^2*c-21*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^2*c-27*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2-21*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^4*c^2+16*a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x-6*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
779,1,447,149,0.055000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^5,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a^{2} \left(-40 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{4} c +40 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{4} a^{4}-15 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c +40 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{5} a^{2}-40 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{5} a^{2}+40 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{5} a^{3} c -25 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}-15 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{5} a \,c^{2}+16 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-10 a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x +4 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{20 x^{4} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"1/20*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^4*a^2*(-40*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^6*a^4*c+40*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^4*a^4-15*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c+40*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^5*a^2-40*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^5*a^2+40*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^5*a^3*c-25*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3-15*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^5*a*c^2+16*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2-10*a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x+4*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(c*(a^2*x^2-1)/a^2)^(1/2)/(-c/a^2)^(1/2)/c","B"
780,1,85,165,0.044000," ","int(x^3*(c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(x^{4} a^{4}-4 x^{3} a^{3}+8 a^{2} x^{2}-16 a x +16 \ln \left(a x +1\right)\right)}{4 \left(a^{2} x^{2}-1\right) a^{3}}"," ",0,"-1/4*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(x^4*a^4-4*x^3*a^3+8*a^2*x^2-16*a*x+16*ln(a*x+1))/(a^2*x^2-1)/a^3","A"
781,1,78,132,0.046000," ","int(x^2*(c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(-2 x^{3} a^{3}+9 a^{2} x^{2}-24 a x +24 \ln \left(a x +1\right)\right)}{6 \left(a^{2} x^{2}-1\right) a^{2}}"," ",0,"1/6*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(-2*x^3*a^3+9*a^2*x^2-24*a*x+24*ln(a*x+1))/(a^2*x^2-1)/a^2","A"
782,1,69,99,0.043000," ","int(x*(c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}-6 a x +8 \ln \left(a x +1\right)\right)}{2 \left(a^{2} x^{2}-1\right) a}"," ",0,"-1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-a^2*x^2+1)^(1/2)*(a^2*x^2-6*a*x+8*ln(a*x+1))/(a^2*x^2-1)/a","A"
783,1,60,94,0.043000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(a x +\ln \left(x \right)-4 \ln \left(a x +1\right)\right) \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(a*x+ln(x)-4*ln(a*x+1))*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
784,1,62,94,0.047000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}\, \left(3 a \ln \left(x \right) x -4 a x \ln \left(a x +1\right)+1\right)}{a^{2} x^{2}-1}"," ",0,"(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(-a^2*x^2+1)^(1/2)*(3*a*ln(x)*x-4*a*x*ln(a*x+1)+1)/(a^2*x^2-1)","A"
785,1,78,129,0.048000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}\, \left(8 a^{2} \ln \left(x \right) x^{2}-8 \ln \left(a x +1\right) x^{2} a^{2}+6 a x -1\right)}{2 x \left(a^{2} x^{2}-1\right)}"," ",0,"-1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x*(-a^2*x^2+1)^(1/2)*(8*a^2*ln(x)*x^2-8*ln(a*x+1)*x^2*a^2+6*a*x-1)/(a^2*x^2-1)","A"
786,1,86,162,0.049000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}\, \left(24 a^{3} \ln \left(x \right) x^{3}-24 a^{3} x^{3} \ln \left(a x +1\right)+24 a^{2} x^{2}-9 a x +2\right)}{6 x^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"1/6*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^2*(-a^2*x^2+1)^(1/2)*(24*a^3*ln(x)*x^3-24*a^3*x^3*ln(a*x+1)+24*a^2*x^2-9*a*x+2)/(a^2*x^2-1)","A"
787,1,94,194,0.055000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}\, \left(16 a^{4} \ln \left(x \right) x^{4}-16 \ln \left(a x +1\right) x^{4} a^{4}+16 x^{3} a^{3}-8 a^{2} x^{2}+4 a x -1\right)}{4 x^{3} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/4*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^3*(-a^2*x^2+1)^(1/2)*(16*a^4*ln(x)*x^4-16*ln(a*x+1)*x^4*a^4+16*x^3*a^3-8*a^2*x^2+4*a*x-1)/(a^2*x^2-1)","A"
788,1,102,228,0.050000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{-a^{2} x^{2}+1}\, \left(240 a^{5} \ln \left(x \right) x^{5}-240 \ln \left(a x +1\right) x^{5} a^{5}+240 x^{4} a^{4}-120 x^{3} a^{3}+80 a^{2} x^{2}-45 a x +12\right)}{60 x^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"1/60*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^4*(-a^2*x^2+1)^(1/2)*(240*a^5*ln(x)*x^5-240*ln(a*x+1)*x^5*a^5+240*x^4*a^4-120*x^3*a^3+80*a^2*x^2-45*a*x+12)/(a^2*x^2-1)","A"
789,0,0,55,0.212000," ","int((c-c/a^2/x^2)^p/exp(2*p*arctanh(a*x)),x)","\int \left(c -\frac{c}{a^{2} x^{2}}\right)^{p} {\mathrm e}^{-2 p \arctanh \left(a x \right)}\, dx"," ",0,"int((c-c/a^2/x^2)^p/exp(2*p*arctanh(a*x)),x)","F"
790,0,0,56,0.131000," ","int(exp(2*p*arctanh(a*x))*(c-c/a^2/x^2)^p,x)","\int {\mathrm e}^{2 p \arctanh \left(a x \right)} \left(c -\frac{c}{a^{2} x^{2}}\right)^{p}\, dx"," ",0,"int(exp(2*p*arctanh(a*x))*(c-c/a^2/x^2)^p,x)","F"
791,0,0,287,0.060000," ","int(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^2,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(c -\frac{c}{a^{2} x^{2}}\right)^{2}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^2,x)","F"
792,0,0,119,0.051000," ","int(exp(n*arctanh(a*x))*(c-c/a^2/x^2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(c -\frac{c}{a^{2} x^{2}}\right)\, dx"," ",0,"int(exp(n*arctanh(a*x))*(c-c/a^2/x^2),x)","F"
793,0,0,111,0.044000," ","int(exp(n*arctanh(a*x))/(c-c/a^2/x^2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{c -\frac{c}{a^{2} x^{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(c-c/a^2/x^2),x)","F"
794,0,0,335,0.059000," ","int(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^2,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\left(c -\frac{c}{a^{2} x^{2}}\right)^{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^2,x)","F"
795,0,0,360,0.056000," ","int(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^(3/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(c -\frac{c}{a^{2} x^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^(3/2),x)","F"
796,0,0,226,0.043000," ","int(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^(1/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \sqrt{c -\frac{c}{a^{2} x^{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^(1/2),x)","F"
797,0,0,148,0.048000," ","int(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\sqrt{c -\frac{c}{a^{2} x^{2}}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^(1/2),x)","F"
798,0,0,223,0.046000," ","int(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^(3/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\left(c -\frac{c}{a^{2} x^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^(3/2),x)","F"
799,0,0,895,0.046000," ","int(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^(5/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\left(c -\frac{c}{a^{2} x^{2}}\right)^{\frac{5}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^(5/2),x)","F"
800,0,0,68,0.151000," ","int(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^p,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(c -\frac{c}{a^{2} x^{2}}\right)^{p}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^p,x)","F"
801,0,0,323,0.335000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^p,x)","\int \frac{\left(a x +1\right)^{4} \left(c -\frac{c}{a^{2} x^{2}}\right)^{p}}{\left(-a^{2} x^{2}+1\right)^{2}}\, dx"," ",0,"int((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^p,x)","F"
802,0,0,203,0.337000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^p,x)","\int \frac{\left(a x +1\right)^{3} \left(c -\frac{c}{a^{2} x^{2}}\right)^{p}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^p,x)","F"
803,0,0,207,0.344000," ","int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^p,x)","\int \frac{\left(a x +1\right)^{2} \left(c -\frac{c}{a^{2} x^{2}}\right)^{p}}{-a^{2} x^{2}+1}\, dx"," ",0,"int((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^p,x)","F"
804,0,0,127,0.258000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^p,x)","\int \frac{\left(a x +1\right) \left(c -\frac{c}{a^{2} x^{2}}\right)^{p}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^p,x)","F"
805,0,0,127,0.342000," ","int((c-c/a^2/x^2)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{\left(c -\frac{c}{a^{2} x^{2}}\right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int((c-c/a^2/x^2)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
806,0,0,208,0.255000," ","int((c-c/a^2/x^2)^p/(a*x+1)^2*(-a^2*x^2+1),x)","\int \frac{\left(c -\frac{c}{a^{2} x^{2}}\right)^{p} \left(-a^{2} x^{2}+1\right)}{\left(a x +1\right)^{2}}\, dx"," ",0,"int((c-c/a^2/x^2)^p/(a*x+1)^2*(-a^2*x^2+1),x)","F"
807,0,0,202,0.348000," ","int((c-c/a^2/x^2)^p/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\int \frac{\left(c -\frac{c}{a^{2} x^{2}}\right)^{p} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{\left(a x +1\right)^{3}}\, dx"," ",0,"int((c-c/a^2/x^2)^p/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","F"
808,0,0,134,0.362000," ","int((1+x)^(3/2)/(-x^2+1)^(1/2)*x*sin(x),x)","\int \frac{\left(1+x \right)^{\frac{3}{2}} x \sin \left(x \right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((1+x)^(3/2)/(-x^2+1)^(1/2)*x*sin(x),x)","F"
809,0,0,111,0.355000," ","int((1+x)^(3/2)/(-x^2+1)^(1/2)*sin(x),x)","\int \frac{\left(1+x \right)^{\frac{3}{2}} \sin \left(x \right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((1+x)^(3/2)/(-x^2+1)^(1/2)*sin(x),x)","F"
810,0,0,119,0.367000," ","int((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2)*x*sin(x),x)","\int \frac{\left(1+x \right) \sqrt{1-x}\, x \sin \left(x \right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2)*x*sin(x),x)","F"
811,0,0,56,0.375000," ","int((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2)*sin(x),x)","\int \frac{\left(1+x \right) \sqrt{1-x}\, \sin \left(x \right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2)*sin(x),x)","F"
812,0,0,155,0.361000," ","int((1+x)^(5/2)/(-x^2+1)^(1/2)*x*sin(x),x)","\int \frac{\left(1+x \right)^{\frac{5}{2}} x \sin \left(x \right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((1+x)^(5/2)/(-x^2+1)^(1/2)*x*sin(x),x)","F"
813,0,0,134,0.356000," ","int((1+x)^(5/2)/(-x^2+1)^(1/2)*sin(x),x)","\int \frac{\left(1+x \right)^{\frac{5}{2}} \sin \left(x \right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((1+x)^(5/2)/(-x^2+1)^(1/2)*sin(x),x)","F"
814,0,0,137,0.375000," ","int((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2)*x*sin(x),x)","\int \frac{\left(1+x \right) \left(1-x \right)^{\frac{3}{2}} x \sin \left(x \right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2)*x*sin(x),x)","F"
815,0,0,117,0.375000," ","int((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2)*sin(x),x)","\int \frac{\left(1+x \right) \left(1-x \right)^{\frac{3}{2}} \sin \left(x \right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2)*sin(x),x)","F"
816,0,0,110,0.370000," ","int((1+x)^(1/2)/(-x^2+1)^(1/2)*x*sin(x),x)","\int \frac{\sqrt{1+x}\, x \sin \left(x \right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((1+x)^(1/2)/(-x^2+1)^(1/2)*x*sin(x),x)","F"
817,0,0,50,0.364000," ","int((1+x)^(1/2)/(-x^2+1)^(1/2)*sin(x),x)","\int \frac{\sqrt{1+x}\, \sin \left(x \right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((1+x)^(1/2)/(-x^2+1)^(1/2)*sin(x),x)","F"
818,1,487,136,0.042000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x^3,x)","-\frac{x^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{4 b}+\frac{a \,x^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{4 b^{2}}-\frac{a^{2} x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{4 b^{3}}+\frac{a^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{4 b^{4}}+\frac{3 a^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 b^{3} \sqrt{b^{2}}}+\frac{13 a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{8 b^{4}}-\frac{3 x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{8 b^{3}}+\frac{3 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{8 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} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b^{3} \sqrt{b^{2}}}-\frac{3 a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\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,"-1/4*x^3/b*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/4*a/b^2*x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/4*a^2/b^3*x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/4*a^3/b^4*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3/2*a^2/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+13/8*a/b^4*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3/8/b^3*x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3/8/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(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/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-3/2*a/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-2/3/b^4*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)","B"
819,1,315,110,0.039000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x^2,x)","-\frac{x^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{3 b}+\frac{a x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{3 b^{2}}-\frac{a^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{3 b^{3}}-\frac{a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b^{2} \sqrt{b^{2}}}-\frac{2 \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} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b^{2} \sqrt{b^{2}}}+\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 b^{2} \sqrt{b^{2}}}"," ",0,"-1/3*x^2/b*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/3*a/b^2*x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/3*a^2/b^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-a/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-2/3/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/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/2/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))","B"
820,1,178,70,0.036000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x,x)","-\frac{x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 b}+\frac{a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 b^{2}}+\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\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 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b \sqrt{b^{2}}}"," ",0,"-1/2*x/b*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/2*a/b^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/2/b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/b^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-a/b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))","B"
821,1,71,35,0.035000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2),x)","-\frac{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{b}+\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\sqrt{b^{2}}}"," ",0,"-1/b*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))","A"
822,1,168,54,0.035000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x,x)","\frac{b \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\sqrt{b^{2}}}-\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}}-\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) a}{\sqrt{-a^{2}+1}}"," ",0,"b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-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)-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)*a","B"
823,1,265,84,0.041000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^2,x)","-\frac{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{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(-a^{2}+1\right) x}-\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}}}-\frac{a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(-a^{2}+1\right) x}-\frac{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}}}"," ",0,"-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)-1/(-a^2+1)/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-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)-a/(-a^2+1)/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-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)","B"
824,1,453,140,0.041000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^3,x)","-\frac{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(-a^{2}+1\right) x}-\frac{3 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{3}{2}}}-\frac{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(-a^{2}+1\right) x^{2}}-\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 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}}}-\frac{a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(-a^{2}+1\right) x^{2}}-\frac{3 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^{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}}}"," ",0,"-b/(-a^2+1)/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3/2*a*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)-1/2/(-a^2+1)/x^2*(-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*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)-1/2*a/(-a^2+1)/x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3/2*a^2*b/(-a^2+1)^2/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3/2*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)","B"
825,1,683,185,0.044000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^4,x)","-\frac{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{3 \left(-a^{2}+1\right) x^{3}}-\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 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{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{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{2 b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{3 \left(-a^{2}+1\right)^{2} x}-\frac{a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{3 \left(-a^{2}+1\right) x^{3}}-\frac{5 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^{3} b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(-a^{2}+1\right)^{3} x}-\frac{5 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{3 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{13 a \,b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{6 \left(-a^{2}+1\right)^{2} x}-\frac{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(-a^{2}+1\right) x^{2}}-\frac{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}}}"," ",0,"-1/3/(-a^2+1)/x^3*(-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*a^2*b^2/(-a^2+1)^3/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-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)-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)-2/3*b^2/(-a^2+1)^2/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/3*a/(-a^2+1)/x^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-5/6*a^2*b/(-a^2+1)^2/x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-5/2*a^3*b^2/(-a^2+1)^3/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-5/2*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)-3*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)-13/6*a*b^2/(-a^2+1)^2/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/2*b/(-a^2+1)/x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/2*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)","B"
826,1,161,77,0.028000," ","int((b*x+a+1)^2/(1-(b*x+a)^2)*x^4,x)","-\frac{x^{5}}{5}-\frac{x^{4}}{2 b}+\frac{2 x^{3} a}{3 b^{2}}-\frac{2 x^{3}}{3 b^{2}}-\frac{x^{2} a^{2}}{b^{3}}+\frac{2 x^{2} a}{b^{3}}+\frac{2 x \,a^{3}}{b^{4}}-\frac{x^{2}}{b^{3}}-\frac{6 a^{2} x}{b^{4}}+\frac{6 a x}{b^{4}}-\frac{2 x}{b^{4}}-\frac{2 \ln \left(b x +a -1\right) a^{4}}{b^{5}}+\frac{8 \ln \left(b x +a -1\right) a^{3}}{b^{5}}-\frac{12 \ln \left(b x +a -1\right) a^{2}}{b^{5}}+\frac{8 \ln \left(b x +a -1\right) a}{b^{5}}-\frac{2 \ln \left(b x +a -1\right)}{b^{5}}"," ",0,"-1/5*x^5-1/2*x^4/b+2/3/b^2*x^3*a-2/3/b^2*x^3-1/b^3*x^2*a^2+2/b^3*x^2*a+2/b^4*x*a^3-1/b^3*x^2-6/b^4*a^2*x+6/b^4*a*x-2/b^4*x-2/b^5*ln(b*x+a-1)*a^4+8/b^5*ln(b*x+a-1)*a^3-12/b^5*ln(b*x+a-1)*a^2+8/b^5*ln(b*x+a-1)*a-2/b^5*ln(b*x+a-1)","B"
827,1,108,62,0.030000," ","int((b*x+a+1)^2/(1-(b*x+a)^2)*x^3,x)","-\frac{x^{4}}{4}-\frac{2 x^{3}}{3 b}+\frac{x^{2} a}{b^{2}}-\frac{x^{2}}{b^{2}}-\frac{2 a^{2} x}{b^{3}}+\frac{4 a x}{b^{3}}-\frac{2 x}{b^{3}}+\frac{2 \ln \left(b x +a -1\right) a^{3}}{b^{4}}-\frac{6 \ln \left(b x +a -1\right) a^{2}}{b^{4}}+\frac{6 \ln \left(b x +a -1\right) a}{b^{4}}-\frac{2 \ln \left(b x +a -1\right)}{b^{4}}"," ",0,"-1/4*x^4-2/3*x^3/b+1/b^2*x^2*a-1/b^2*x^2-2/b^3*a^2*x+4*a*x/b^3-2/b^3*x+2/b^4*ln(b*x+a-1)*a^3-6/b^4*ln(b*x+a-1)*a^2+6/b^4*ln(b*x+a-1)*a-2/b^4*ln(b*x+a-1)","A"
828,1,68,47,0.028000," ","int((b*x+a+1)^2/(1-(b*x+a)^2)*x^2,x)","-\frac{x^{3}}{3}-\frac{x^{2}}{b}+\frac{2 a x}{b^{2}}-\frac{2 x}{b^{2}}-\frac{2 \ln \left(b x +a -1\right) a^{2}}{b^{3}}+\frac{4 \ln \left(b x +a -1\right) a}{b^{3}}-\frac{2 \ln \left(b x +a -1\right)}{b^{3}}"," ",0,"-1/3*x^3-x^2/b+2/b^2*a*x-2*x/b^2-2/b^3*ln(b*x+a-1)*a^2+4/b^3*ln(b*x+a-1)*a-2/b^3*ln(b*x+a-1)","A"
829,1,38,32,0.029000," ","int((b*x+a+1)^2/(1-(b*x+a)^2)*x,x)","-\frac{x^{2}}{2}-\frac{2 x}{b}+\frac{2 \ln \left(b x +a -1\right) a}{b^{2}}-\frac{2 \ln \left(b x +a -1\right)}{b^{2}}"," ",0,"-1/2*x^2-2*x/b+2/b^2*ln(b*x+a-1)*a-2/b^2*ln(b*x+a-1)","A"
830,1,17,19,0.025000," ","int((b*x+a+1)^2/(1-(b*x+a)^2),x)","-x -\frac{2 \ln \left(b x +a -1\right)}{b}"," ",0,"-x-2/b*ln(b*x+a-1)","A"
831,1,35,33,0.034000," ","int((b*x+a+1)^2/(1-(b*x+a)^2)/x,x)","-\frac{\ln \left(x \right)}{a -1}-\frac{\ln \left(x \right) a}{a -1}+\frac{2 \ln \left(b x +a -1\right)}{a -1}"," ",0,"-1/(a-1)*ln(x)-1/(a-1)*ln(x)*a+2/(a-1)*ln(b*x+a-1)","A"
832,1,46,49,0.034000," ","int((b*x+a+1)^2/(1-(b*x+a)^2)/x^2,x)","\frac{1}{\left(a -1\right) x}+\frac{a}{\left(a -1\right) x}+\frac{2 b \ln \left(x \right)}{\left(a -1\right)^{2}}-\frac{2 b \ln \left(b x +a -1\right)}{\left(a -1\right)^{2}}"," ",0,"1/(a-1)/x+1/(a-1)/x*a+2*b/(a-1)^2*ln(x)-2*b/(a-1)^2*ln(b*x+a-1)","A"
833,1,63,67,0.033000," ","int((b*x+a+1)^2/(1-(b*x+a)^2)/x^3,x)","\frac{1}{2 \left(a -1\right) x^{2}}+\frac{a}{2 \left(a -1\right) x^{2}}-\frac{2 b}{\left(a -1\right)^{2} x}-\frac{2 b^{2} \ln \left(x \right)}{\left(a -1\right)^{3}}+\frac{2 b^{2} \ln \left(b x +a -1\right)}{\left(a -1\right)^{3}}"," ",0,"1/2/(a-1)/x^2+1/2/(a-1)/x^2*a-2*b/(a-1)^2/x-2/(a-1)^3*b^2*ln(x)+2/(a-1)^3*b^2*ln(b*x+a-1)","A"
834,1,76,82,0.035000," ","int((b*x+a+1)^2/(1-(b*x+a)^2)/x^4,x)","\frac{1}{3 \left(a -1\right) x^{3}}+\frac{a}{3 \left(a -1\right) x^{3}}-\frac{b}{\left(a -1\right)^{2} x^{2}}+\frac{2 b^{3} \ln \left(x \right)}{\left(a -1\right)^{4}}+\frac{2 b^{2}}{\left(a -1\right)^{3} x}-\frac{2 b^{3} \ln \left(b x +a -1\right)}{\left(a -1\right)^{4}}"," ",0,"1/3/(a-1)/x^3+1/3/(a-1)/x^3*a-b/(a-1)^2/x^2+2/(a-1)^4*b^3*ln(x)+2/(a-1)^3*b^2/x-2/(a-1)^4*b^3*ln(b*x+a-1)","A"
835,1,756,163,0.066000," ","int((b*x+a+1)^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{27 a^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 b^{3} \sqrt{b^{2}}}+\frac{265 a^{2} x}{8 b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{53 a \,x^{2}}{8 b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{a^{4} x}{4 b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{3 a^{3} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b^{3} \sqrt{b^{2}}}+\frac{33 a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 b^{3} \sqrt{b^{2}}}-\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{x^{4}}{\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}}-\frac{a \,x^{4}}{4 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{17 x^{3}}{8 b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{51 x}{8 b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{155 a^{3}}{8 b^{4} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{157 a}{8 b^{4} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{b \,x^{5}}{4 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{a^{5}}{4 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{51 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{8 b^{3} \sqrt{b^{2}}}+\frac{10}{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)-27/2*a^2/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+265/8/b^3*a^2*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+53/8/b^2*a*x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/4/b^3*a^4*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3*a^3/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+33/2*a/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-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-x^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-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)-1/4*a*x^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-17/8/b*x^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+51/8/b^3*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+155/8/b^4*a^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-157/8/b^4*a/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/4*b*x^5/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/4/b^4*a^5/(-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)-51/8/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-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)","B"
836,1,552,144,0.053000," ","int((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)*x^2,x)","-\frac{3 a^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b^{2} \sqrt{b^{2}}}+\frac{23 a^{2} x}{2 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{3 a \,x^{2}}{2 b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a^{3} x}{3 b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{53 a x}{3 b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{25 a^{2}}{3 b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{13 x^{2}}{3 b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{9 a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b^{2} \sqrt{b^{2}}}-\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{b \,x^{4}}{3 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a \,x^{3}}{3 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a^{4}}{3 b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{11 x}{2 b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{11 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 b^{2} \sqrt{b^{2}}}+\frac{26}{3 b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}"," ",0,"-3*a^2/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-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-3/2*x^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)-1/3/b^2*a^3*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-53/3/b^2*a*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-25/3/b^3*a^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-13/3/b*x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+9*a/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-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)-1/3*b*x^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/3*a*x^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/3/b^3*a^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+11/2*x/b^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-11/2/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+26/3/b^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)","B"
837,1,381,103,0.046000," ","int((b*x+a+1)^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{3 a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b \sqrt{b^{2}}}+\frac{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{7}{b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{9 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 b \sqrt{b^{2}}}-\frac{7 a^{2}}{b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a}{2 b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{9 x}{2 b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{b \,x^{3}}{2 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a \,x^{2}}{2 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{a^{3}}{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+3*a/b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/2/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)+7/b^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-9/2/b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-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)-1/2/b^2*a/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+9/2/b*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/2*b*x^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/2*a*x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/2/b^2*a^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)","B"
838,1,388,60,0.037000," ","int((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2),x)","\frac{2 \left(1+a \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 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\sqrt{b^{2}}}+\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{4 a^{2}}{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a^{3} x}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a^{4}}{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{b \,x^{2}}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{5 a x}{\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}}+\frac{5}{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}"," ",0,"2*(1+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/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/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)-4/b*a^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-a^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-1/b*a^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-b*x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-5*a*x/(-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)+5/b/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)","B"
839,1,1019,93,0.041000," ","int((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x,x)","-\frac{3 b a x}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{2 b \,a^{2} x}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{6 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{3}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{1}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{2 a}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{2 a^{3}}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{3 a^{2}}{\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{a b x}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{a^{4} b x}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{6 a^{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{12 a 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{3 a^{3} b x}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{3 a^{2} b x}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{b \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\sqrt{b^{2}}}+\frac{b x}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{4 a^{3}}{\left(-a^{2}+1\right) \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}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{a^{5}}{\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{\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{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}}}-\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}{\left(-a^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-3*b*a/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-2*b*a^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+6*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)+3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+2*a/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-2*a^3/(-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)-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)+a*b/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+a^4*b/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+6*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)+12*a*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)+3*a^3*b/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+3*a^2*b/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+b*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+4/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a^3+4*a^2/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+a^5/(-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)-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)*a^3-3/(-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^2-3/(-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","B"
840,1,1520,116,0.046000," ","int((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^2,x)","\frac{9 a^{2} b}{\left(-a^{2}+1\right)^{2} \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{5 b \,a^{4}}{\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{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) a^{2}}{\left(-a^{2}+1\right)^{\frac{3}{2}}}+\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^{2}}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{b^{2} a x}{\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{12 a^{4} b}{\left(-a^{2}+1\right)^{2} \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{3 a}{\left(-a^{2}+1\right) x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a^{3}}{\left(-a^{2}+1\right) x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\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^{6} b}{\left(-a^{2}+1\right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{3 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{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{9 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{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{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{9 a^{5} b}{\left(-a^{2}+1\right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{b}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{6 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{3 a^{5} b^{2} x}{\left(-a^{2}+1\right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{1}{\left(-a^{2}+1\right) x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{b \,a^{2}}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{3 b}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{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{3}{2}}}+\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{9 a^{3} 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{5 a^{3} b^{2} x}{\left(-a^{2}+1\right) \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 a \,b^{2} x}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}"," ",0,"9*a^2*b/(-a^2+1)^2/(-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)+5*b*a^4/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+12*b*a^3/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3*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^2+8*b/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+12*b*a^2/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-b^2*a/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-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)+12*a^4*b/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3/(-a^2+1)/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a^2-3/(-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)*a^3+2/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b^2+3*a^6*b/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3*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)-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)-9*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)+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)-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)+9*a^5*b/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+b/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+6*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)+3*a^5*b^2/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-1/(-a^2+1)/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-b*a^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3*b/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3*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)+9*a^4*b^2/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+9*a^3*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+5*a^3*b^2/(-a^2+1)/(-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+9*a*b^2/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x","B"
841,1,2194,176,0.046000," ","int((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^3,x)","-\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{45 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{a^{3}}{2 \left(-a^{2}+1\right) x^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\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{3 a}{2 \left(-a^{2}+1\right) x^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{30 a^{5} b^{2}}{\left(-a^{2}+1\right)^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{45 a^{3} b^{2}}{2 \left(-a^{2}+1\right)^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{2 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{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{27 a \,b^{2}}{2 \left(-a^{2}+1\right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{3 b}{\left(-a^{2}+1\right) x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{39 a^{3} b^{2}}{\left(-a^{2}+1\right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{9 b^{2} a}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{9 b^{2} a^{3}}{\left(-a^{2}+1\right) \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{15 a^{7} b^{2}}{2 \left(-a^{2}+1\right)^{3} \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{15 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{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{27 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{6 x \,b^{3}}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{31 a^{5} b^{2}}{2 \left(-a^{2}+1\right)^{2} \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{29 a^{2} b^{2}}{\left(-a^{2}+1\right)^{2} \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{21 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 \,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 \,a^{2}}{\left(-a^{2}+1\right) x \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{15 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 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{45 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{5 a^{4} 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}{2 \left(-a^{2}+1\right)^{2} x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{15 a^{2} b}{2 \left(-a^{2}+1\right)^{2} x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{57 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{15 b^{3} a x}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{9 b^{3} a^{2} 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)}{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}}+\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{31 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{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{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{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}}}"," ",0,"-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)-45/2*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/(-a^2+1)/x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a^3-3/2/(-a^2+1)/x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a^2-3/2/(-a^2+1)/x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+30*a^5*b^2/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+45/2*a^3*b^2/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+2*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)-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)+27/2*a*b^2/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3*b/(-a^2+1)/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+39*a^3*b^2/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+9*b^2*a/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+9*b^2*a^3/(-a^2+1)/(-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)+15/2*a^7*b^2/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+45/2*a^6*b^2/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-15/2*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)+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)-27/2*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)+6/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b^3+31/2*a^5*b^2/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+75/2*a^4*b^2/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+29*a^2*b^2/(-a^2+1)^2/(-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)-21/2*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*a*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*b/(-a^2+1)/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a^2-6*b/(-a^2+1)/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+15/2*a^6*b^3/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+45/2*a^5*b^3/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+45/2*a^4*b^3/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-5/2*a^4*b/(-a^2+1)^2/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-15/2*a^3*b/(-a^2+1)^2/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-15/2*a^2*b/(-a^2+1)^2/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+57/2*a^2*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+9*b^3*a^2/(-a^2+1)/(-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)+13/2*a*b^3/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+31/2*a^4*b^3/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+75/2*a^3*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-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)","B"
842,1,2947,226,0.049000," ","int((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^4,x)","\text{output too large to display}"," ",0,"8/3*b^4/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+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)-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)-105/2*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)-1/(-a^2+1)/x^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a^2-1/(-a^2+1)/x^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+70*a^6*b^3/(-a^2+1)^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+105/2*a^4*b^3/(-a^2+1)^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+35/2*a^8*b^3/(-a^2+1)^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-45*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)-4/3*b^2/(-a^2+1)^2/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+62/3*b^3*a/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+56*b^3*a^3/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+7*b^3*a^2/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3/2*b/(-a^2+1)/x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-30*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*a^6*b^3/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+205/2*a^5*b^3/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+110*a^4*b^3/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+45*a^2*b^3/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/3/(-a^2+1)/x^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a^3+105/2*a^7*b^3/(-a^2+1)^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-35/2*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*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)+41*b^3*a^2/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+187/6*b^3*a^4/(-a^2+1)^2/(-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)-27/2*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)-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)+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-23/2*b^2/(-a^2+1)^2/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+55/2*b^4/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*a-3/2*b/(-a^2+1)/x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a^2-53/6*b^2/(-a^2+1)^2/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a^3-19*b^2/(-a^2+1)^2/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a^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)-35/2*a^3*b^2/(-a^2+1)^3/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+35/2*a^7*b^4/(-a^2+1)^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+105/2*a^6*b^4/(-a^2+1)^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+105/2*a^5*b^4/(-a^2+1)^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+125/3*a^5*b^4/(-a^2+1)^3/(-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+80*a^3*b^4/(-a^2+1)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+7*b^4*a/(-a^2+1)/(-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)+56*b^4*a^2/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-3*b^2*a/(-a^2+1)/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+187/6*b^4*a^3/(-a^2+1)^2/(-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-7/6*a^4*b/(-a^2+1)^2/x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-7/2*a^3*b/(-a^2+1)^2/x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-7/2*a^2*b/(-a^2+1)^2/x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-35/6*a^5*b^2/(-a^2+1)^3/x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+9/2*b^3/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-9/2*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)+b^3/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-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)-1/3/(-a^2+1)/x^3/(-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+35/2*a^4*b^4/(-a^2+1)^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x","B"
843,1,809,136,0.046000," ","int(x^3/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x)","\frac{3 a^{2} x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 b^{3}}+\frac{3 a^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 b^{3} \sqrt{b^{2}}}+\frac{3 a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 b^{3} \sqrt{b^{2}}}-\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right) a^{3}}{b^{3} \sqrt{b^{2}}}-\frac{3 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right) a^{2}}{b^{3} \sqrt{b^{2}}}-\frac{3 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right) a}{b^{3} \sqrt{b^{2}}}+\frac{3 a x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 b^{3}}-\frac{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}{b^{4}}+\frac{\left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{3 b^{4}}+\frac{3 a^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 b^{4}}-\frac{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a^{3}}{b^{4}}-\frac{3 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a^{2}}{b^{4}}-\frac{3 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a}{b^{4}}-\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{b^{3} \sqrt{b^{2}}}+\frac{5 a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{8 b^{4}}-\frac{x \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{4 b^{3}}+\frac{3 a \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{4 b^{4}}+\frac{3 a^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 b^{4}}+\frac{5 x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{8 b^{3}}+\frac{5 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{8 b^{3} \sqrt{b^{2}}}"," ",0,"3/2*a^2/b^3*x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3/2*a^2/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+3/2*a/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))*a^3-3/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))*a^2-3/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))*a+3/2*a/b^3*x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)+1/3/b^4*(-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)-1/b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a^3-3/b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a^2-3/b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a-1/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))+5/8*a/b^4*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/4/b^3*x*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+3/4/b^4*a*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+3/2*a^3/b^4*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+5/8/b^3*x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+5/8/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))","B"
844,1,535,110,0.043000," ","int(x^2/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x)","-\frac{\left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{3 b^{3}}-\frac{a x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{b^{2}}-\frac{a^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{b^{3}}-\frac{a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\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{a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 b^{3}}-\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 b^{2} \sqrt{b^{2}}}+\frac{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a^{2}}{b^{3}}+\frac{2 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a}{b^{3}}+\frac{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}{b^{3}}+\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right) a^{2}}{b^{2} \sqrt{b^{2}}}+\frac{2 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right) a}{b^{2} \sqrt{b^{2}}}+\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{b^{2} \sqrt{b^{2}}}"," ",0,"-1/3/b^3*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-a/b^2*x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-a^2/b^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-a/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-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)-1/2*a/b^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/2/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a^2+2/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a+1/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)+1/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))*a^2+2/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))*a+1/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))","B"
845,1,302,70,0.036000," ","int(x/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x)","\frac{x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 b}+\frac{a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 b^{2}}+\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 b \sqrt{b^{2}}}-\frac{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}{b^{2}}-\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{b \sqrt{b^{2}}}-\frac{a \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}{b^{2}}-\frac{a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{b \sqrt{b^{2}}}"," ",0,"1/2*x/b*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/2*a/b^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/2/b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)-1/b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))-1/b^2*a*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)-1/b*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))","B"
846,1,95,34,0.032000," ","int(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x)","\frac{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}{b}+\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{\sqrt{b^{2}}}"," ",0,"1/b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)+1/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))","B"
847,1,249,58,0.043000," ","int(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x,x)","\frac{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{1+a}-\frac{a b \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right) \sqrt{b^{2}}}-\frac{\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)}{1+a}-\frac{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}{1+a}-\frac{b \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{\left(1+a \right) \sqrt{b^{2}}}"," ",0,"1/(1+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/(1+a)*a*b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/(1+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/(1+a)*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)-1/(1+a)*b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))","B"
848,1,565,80,0.047000," ","int(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x^2,x)","-\frac{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(1+a \right)^{2}}+\frac{b^{2} a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right)^{2} \sqrt{b^{2}}}+\frac{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(1+a \right)^{2}}-\frac{\left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{\left(1+a \right) \left(-a^{2}+1\right) x}-\frac{2 a b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(1+a \right) \left(-a^{2}+1\right)}+\frac{a^{2} b^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right) \left(-a^{2}+1\right) \sqrt{b^{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(1+a \right) \sqrt{-a^{2}+1}}-\frac{b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x}{\left(1+a \right) \left(-a^{2}+1\right)}-\frac{b^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right) \left(-a^{2}+1\right) \sqrt{b^{2}}}+\frac{b \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}{\left(1+a \right)^{2}}+\frac{b^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{\left(1+a \right)^{2} \sqrt{b^{2}}}"," ",0,"-1/(1+a)^2*b*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/(1+a)^2*b^2*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/(1+a)^2*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)-1/(1+a)/(-a^2+1)/x*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-2/(1+a)*a*b/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/(1+a)*a^2*b^2/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/(1+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)-1/(1+a)*b^2/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-1/(1+a)*b^2/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/(1+a)^2*b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)+1/(1+a)^2*b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))","B"
849,1,1116,140,0.050000," ","int(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x^3,x)","\frac{b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(1+a \right)^{3}}-\frac{b^{3} a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right)^{3} \sqrt{b^{2}}}-\frac{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(1+a \right)^{3}}+\frac{b \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{\left(1+a \right)^{2} \left(-a^{2}+1\right) x}+\frac{2 b^{2} a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(1+a \right)^{2} \left(-a^{2}+1\right)}-\frac{b^{3} a^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right)^{2} \left(-a^{2}+1\right) \sqrt{b^{2}}}-\frac{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(1+a \right)^{2} \sqrt{-a^{2}+1}}+\frac{b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x}{\left(1+a \right)^{2} \left(-a^{2}+1\right)}+\frac{b^{3} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right)^{2} \left(-a^{2}+1\right) \sqrt{b^{2}}}-\frac{b^{2} \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}{\left(1+a \right)^{3}}-\frac{b^{3} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{\left(1+a \right)^{3} \sqrt{b^{2}}}-\frac{\left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{2 \left(1+a \right) \left(-a^{2}+1\right) x^{2}}-\frac{a b \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{2 \left(1+a \right) \left(-a^{2}+1\right)^{2} x}-\frac{a^{2} b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(1+a \right) \left(-a^{2}+1\right)^{2}}+\frac{a^{3} b^{3} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right) \left(-a^{2}+1\right)^{2} \sqrt{b^{2}}}+\frac{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(1+a \right) \left(-a^{2}+1\right)^{\frac{3}{2}}}-\frac{a \,b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x}{2 \left(1+a \right) \left(-a^{2}+1\right)^{2}}-\frac{a \,b^{3} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right) \left(-a^{2}+1\right)^{2} \sqrt{b^{2}}}-\frac{b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(1+a \right) \left(-a^{2}+1\right)}+\frac{b^{3} a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right) \left(-a^{2}+1\right) \sqrt{b^{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(1+a \right) \sqrt{-a^{2}+1}}"," ",0,"1/(1+a)^3*b^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/(1+a)^3*b^3*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/(1+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)+1/(1+a)^2*b/(-a^2+1)/x*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+2/(1+a)^2*b^2*a/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/(1+a)^2*b^3*a^2/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/(1+a)^2*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)+1/(1+a)^2*b^3/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+1/(1+a)^2*b^3/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/(1+a)^3*b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)-1/(1+a)^3*b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))-1/2/(1+a)/(-a^2+1)/x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-1/2/(1+a)*a*b/(-a^2+1)^2/x*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-1/(1+a)*a^2*b^2/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/2/(1+a)*a^3*b^3/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/2/(1+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)-1/2/(1+a)*a*b^3/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-1/2/(1+a)*a*b^3/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/2/(1+a)*b^2/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/2/(1+a)*b^3/(-a^2+1)*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/2/(1+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"
850,1,1711,182,0.053000," ","int(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x^4,x)","\frac{b^{4} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{\left(1+a \right)^{4} \sqrt{b^{2}}}+\frac{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(1+a \right)^{4}}+\frac{b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(1+a \right)^{2} \left(-a^{2}+1\right)}-\frac{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(1+a \right)^{2} \sqrt{-a^{2}+1}}-\frac{\left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{3 \left(1+a \right) \left(-a^{2}+1\right) x^{3}}+\frac{b^{4} a^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right)^{3} \left(-a^{2}+1\right) \sqrt{b^{2}}}-\frac{a b \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{2 \left(1+a \right) \left(-a^{2}+1\right)^{2} x^{2}}-\frac{a^{2} b^{2} \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{2 \left(1+a \right) \left(-a^{2}+1\right)^{3} x}+\frac{a^{4} b^{4} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right) \left(-a^{2}+1\right)^{3} \sqrt{b^{2}}}-\frac{a^{2} b^{4} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x}{2 \left(1+a \right) \left(-a^{2}+1\right)^{3}}-\frac{a^{2} b^{4} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right) \left(-a^{2}+1\right)^{3} \sqrt{b^{2}}}-\frac{b^{4} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right)^{3} \left(-a^{2}+1\right) \sqrt{b^{2}}}-\frac{b^{2} \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{\left(1+a \right)^{3} \left(-a^{2}+1\right) x}-\frac{2 b^{3} a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(1+a \right)^{3} \left(-a^{2}+1\right)}+\frac{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(1+a \right)^{3} \sqrt{-a^{2}+1}}-\frac{b^{4} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x}{\left(1+a \right)^{3} \left(-a^{2}+1\right)}+\frac{a^{2} b^{4} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right) \left(-a^{2}+1\right)^{2} \sqrt{b^{2}}}+\frac{b^{2} a \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{2 \left(1+a \right)^{2} \left(-a^{2}+1\right)^{2} x}-\frac{b^{4} a^{3} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right)^{2} \left(-a^{2}+1\right)^{2} \sqrt{b^{2}}}+\frac{b^{4} a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x}{2 \left(1+a \right)^{2} \left(-a^{2}+1\right)^{2}}+\frac{b^{4} a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right)^{2} \left(-a^{2}+1\right)^{2} \sqrt{b^{2}}}-\frac{b^{4} a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right)^{2} \left(-a^{2}+1\right) \sqrt{b^{2}}}+\frac{b^{3} \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}{\left(1+a \right)^{4}}-\frac{b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(1+a \right)^{4}}+\frac{b^{4} a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right)^{4} \sqrt{b^{2}}}+\frac{b \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{2 \left(1+a \right)^{2} \left(-a^{2}+1\right) x^{2}}+\frac{b^{3} a^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(1+a \right)^{2} \left(-a^{2}+1\right)^{2}}-\frac{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(1+a \right)^{2} \left(-a^{2}+1\right)^{\frac{3}{2}}}-\frac{a^{3} b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(1+a \right) \left(-a^{2}+1\right)^{3}}+\frac{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(1+a \right) \left(-a^{2}+1\right)^{\frac{5}{2}}}-\frac{a \,b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(1+a \right) \left(-a^{2}+1\right)^{2}}+\frac{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(1+a \right) \left(-a^{2}+1\right)^{\frac{3}{2}}}"," ",0,"1/(1+a)^4*b^4/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))+1/(1+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)+1/2/(1+a)^2*b^3/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/2/(1+a)^2*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/(1+a)/(-a^2+1)/x^3*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+1/(1+a)^3*b^4*a^2/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/2/(1+a)*a*b/(-a^2+1)^2/x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-1/2/(1+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/(1+a)*a^4*b^4/(-a^2+1)^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/2/(1+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/(1+a)*a^2*b^4/(-a^2+1)^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/(1+a)^3*b^4/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/(1+a)^3*b^2/(-a^2+1)/x*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-2/(1+a)^3*b^3*a/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/(1+a)^3*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)-1/(1+a)^3*b^4/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+1/2/(1+a)*a^2*b^4/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/2/(1+a)^2*b^2*a/(-a^2+1)^2/x*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-1/2/(1+a)^2*b^4*a^3/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/2/(1+a)^2*b^4*a/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+1/2/(1+a)^2*b^4*a/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/2/(1+a)^2*b^4/(-a^2+1)*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/(1+a)^4*b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)-1/(1+a)^4*b^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/(1+a)^4*b^4*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/2/(1+a)^2*b/(-a^2+1)/x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+1/(1+a)^2*b^3*a^2/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/2/(1+a)^2*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)-1/(1+a)*a^3*b^3/(-a^2+1)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/2/(1+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/(1+a)*a*b^3/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/2/(1+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)","B"
851,1,159,65,0.027000," ","int(x^4/(b*x+a+1)^2*(1-(b*x+a)^2),x)","-\frac{x^{5}}{5}+\frac{x^{4}}{2 b}-\frac{2 x^{3} a}{3 b^{2}}-\frac{2 x^{3}}{3 b^{2}}+\frac{x^{2} a^{2}}{b^{3}}+\frac{2 x^{2} a}{b^{3}}-\frac{2 x \,a^{3}}{b^{4}}+\frac{x^{2}}{b^{3}}-\frac{6 a^{2} x}{b^{4}}-\frac{6 a x}{b^{4}}-\frac{2 x}{b^{4}}+\frac{2 \ln \left(b x +a +1\right) a^{4}}{b^{5}}+\frac{8 \ln \left(b x +a +1\right) a^{3}}{b^{5}}+\frac{12 \ln \left(b x +a +1\right) a^{2}}{b^{5}}+\frac{8 \ln \left(b x +a +1\right) a}{b^{5}}+\frac{2 \ln \left(b x +a +1\right)}{b^{5}}"," ",0,"-1/5*x^5+1/2*x^4/b-2/3/b^2*x^3*a-2/3/b^2*x^3+1/b^3*x^2*a^2+2/b^3*x^2*a-2/b^4*x*a^3+1/b^3*x^2-6/b^4*a^2*x-6/b^4*a*x-2/b^4*x+2/b^5*ln(b*x+a+1)*a^4+8/b^5*ln(b*x+a+1)*a^3+12/b^5*ln(b*x+a+1)*a^2+8/b^5*ln(b*x+a+1)*a+2/b^5*ln(b*x+a+1)","B"
852,1,109,53,0.027000," ","int(x^3/(b*x+a+1)^2*(1-(b*x+a)^2),x)","-\frac{x^{4}}{4}+\frac{2 x^{3}}{3 b}-\frac{x^{2} a}{b^{2}}-\frac{x^{2}}{b^{2}}+\frac{2 a^{2} x}{b^{3}}+\frac{4 a x}{b^{3}}+\frac{2 x}{b^{3}}-\frac{2 \ln \left(b x +a +1\right) a^{3}}{b^{4}}-\frac{6 \ln \left(b x +a +1\right) a^{2}}{b^{4}}-\frac{6 \ln \left(b x +a +1\right) a}{b^{4}}-\frac{2 \ln \left(b x +a +1\right)}{b^{4}}"," ",0,"-1/4*x^4+2/3*x^3/b-1/b^2*x^2*a-1/b^2*x^2+2/b^3*a^2*x+4*a*x/b^3+2/b^3*x-2/b^4*ln(b*x+a+1)*a^3-6/b^4*ln(b*x+a+1)*a^2-6/b^4*ln(b*x+a+1)*a-2/b^4*ln(b*x+a+1)","B"
853,1,67,39,0.026000," ","int(x^2/(b*x+a+1)^2*(1-(b*x+a)^2),x)","-\frac{x^{3}}{3}+\frac{x^{2}}{b}-\frac{2 a x}{b^{2}}-\frac{2 x}{b^{2}}+\frac{2 \ln \left(b x +a +1\right) a^{2}}{b^{3}}+\frac{4 \ln \left(b x +a +1\right) a}{b^{3}}+\frac{2 \ln \left(b x +a +1\right)}{b^{3}}"," ",0,"-1/3*x^3+x^2/b-2/b^2*a*x-2*x/b^2+2/b^3*ln(b*x+a+1)*a^2+4/b^3*ln(b*x+a+1)*a+2/b^3*ln(b*x+a+1)","A"
854,1,38,27,0.026000," ","int(x/(b*x+a+1)^2*(1-(b*x+a)^2),x)","-\frac{x^{2}}{2}+\frac{2 x}{b}-\frac{2 \ln \left(b x +a +1\right) a}{b^{2}}-\frac{2 \ln \left(b x +a +1\right)}{b^{2}}"," ",0,"-1/2*x^2+2*x/b-2/b^2*ln(b*x+a+1)*a-2/b^2*ln(b*x+a+1)","A"
855,1,17,16,0.025000," ","int(1/(b*x+a+1)^2*(1-(b*x+a)^2),x)","-x +\frac{2 \ln \left(b x +a +1\right)}{b}"," ",0,"-x+2*ln(b*x+a+1)/b","A"
856,1,34,28,0.031000," ","int(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x,x)","\frac{\ln \left(x \right)}{1+a}-\frac{\ln \left(x \right) a}{1+a}-\frac{2 \ln \left(b x +a +1\right)}{1+a}"," ",0,"1/(1+a)*ln(x)-1/(1+a)*ln(x)*a-2*ln(b*x+a+1)/(1+a)","A"
857,1,47,38,0.034000," ","int(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x^2,x)","-\frac{1}{\left(1+a \right) x}+\frac{a}{\left(1+a \right) x}-\frac{2 b \ln \left(x \right)}{\left(1+a \right)^{2}}+\frac{2 b \ln \left(b x +a +1\right)}{\left(1+a \right)^{2}}"," ",0,"-1/(1+a)/x+1/(1+a)/x*a-2*b*ln(x)/(1+a)^2+2*b*ln(b*x+a+1)/(1+a)^2","A"
858,1,63,54,0.036000," ","int(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x^3,x)","-\frac{1}{2 \left(1+a \right) x^{2}}+\frac{a}{2 \left(1+a \right) x^{2}}+\frac{2 b}{\left(1+a \right)^{2} x}+\frac{2 b^{2} \ln \left(x \right)}{\left(1+a \right)^{3}}-\frac{2 b^{2} \ln \left(b x +a +1\right)}{\left(1+a \right)^{3}}"," ",0,"-1/2/(1+a)/x^2+1/2/(1+a)/x^2*a+2*b/(1+a)^2/x+2*b^2*ln(x)/(1+a)^3-2*b^2*ln(b*x+a+1)/(1+a)^3","A"
859,1,75,66,0.033000," ","int(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x^4,x)","-\frac{1}{3 \left(1+a \right) x^{3}}+\frac{a}{3 \left(1+a \right) x^{3}}+\frac{b}{\left(1+a \right)^{2} x^{2}}-\frac{2 b^{3} \ln \left(x \right)}{\left(1+a \right)^{4}}-\frac{2 b^{2}}{\left(1+a \right)^{3} x}+\frac{2 b^{3} \ln \left(b x +a +1\right)}{\left(1+a \right)^{4}}"," ",0,"-1/3/(1+a)/x^3+1/3/(1+a)/x^3*a+b/(1+a)^2/x^2-2*b^3*ln(x)/(1+a)^4-2*b^2/(1+a)^3/x+2*b^3*ln(b*x+a+1)/(1+a)^4","A"
860,1,1271,163,0.054000," ","int(x^3/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x)","\frac{27 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x \,a^{2}}{2 b^{3}}+\frac{33 a \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x}{2 b^{3}}+\frac{3 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}} a^{2}}{b^{7} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}+\frac{3 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}} a}{b^{7} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}+\frac{2 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}} a^{3}}{b^{6} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}+\frac{9 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}} a^{2}}{b^{6} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}+\frac{12 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}} a}{b^{6} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}+\frac{3 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x \,a^{3}}{b^{3}}+\frac{\left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}} a^{3}}{b^{7} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}+\frac{33 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right) a}{2 b^{3} \sqrt{b^{2}}}+\frac{27 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right) a^{2}}{2 b^{3} \sqrt{b^{2}}}+\frac{3 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right) a^{3}}{b^{3} \sqrt{b^{2}}}+\frac{\left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{b^{7} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}+\frac{5 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{b^{6} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}+\frac{2 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}} a^{3}}{b^{4}}+\frac{9 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}} a^{2}}{b^{4}}+\frac{3 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a^{4}}{b^{4}}+\frac{6 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x}{b^{3}}+\frac{11 a \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{b^{4}}+\frac{27 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a^{3}}{2 b^{4}}+\frac{33 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a^{2}}{2 b^{4}}+\frac{6 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a}{b^{4}}+\frac{6 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{b^{3} \sqrt{b^{2}}}+\frac{x \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{4 b^{3}}+\frac{a \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{4 b^{4}}+\frac{3 a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{8 b^{4}}+\frac{3 x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{8 b^{3}}+\frac{3 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{8 b^{3} \sqrt{b^{2}}}+\frac{4 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{b^{4}}"," ",0,"27/2/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x*a^2+33/2/b^3*a*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x+3/b^7/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)*a^2+3/b^7/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)*a+2/b^6/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)*a^3+9/b^6/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)*a^2+12/b^6/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)*a+3/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x*a^3+1/b^7/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)*a^3+33/2/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))*a+27/2/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))*a^2+3/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))*a^3+1/b^7/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)+5/b^6/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)+2/b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)*a^3+9/b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)*a^2+3/b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a^4+6/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x+11/b^4*a*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)+27/2/b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a^3+33/2/b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a^2+6/b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a+6/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))+1/4/b^3*x*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+1/4/b^4*a*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+3/8*a/b^4*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3/8/b^3*x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3/8/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+4/b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)","B"
861,1,830,143,0.050000," ","int(x^2/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x)","-\frac{3 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right) a^{2}}{b^{2} \sqrt{b^{2}}}-\frac{9 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right) a}{b^{2} \sqrt{b^{2}}}-\frac{3 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x \,a^{2}}{b^{2}}-\frac{9 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x a}{b^{2}}-\frac{\left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}} a^{2}}{b^{6} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}-\frac{2 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}} a}{b^{6} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}-\frac{2 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}} a^{2}}{b^{5} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}-\frac{6 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}} a}{b^{5} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}-\frac{11 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{3 b^{3}}-\frac{11 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x}{2 b^{2}}-\frac{\left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{b^{6} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}-\frac{4 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{b^{5} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}-\frac{2 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}} a^{2}}{b^{3}}-\frac{6 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}} a}{b^{3}}-\frac{3 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a^{3}}{b^{3}}-\frac{9 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a^{2}}{b^{3}}-\frac{11 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a}{2 b^{3}}-\frac{11 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{2 b^{2} \sqrt{b^{2}}}"," ",0,"-3/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))*a^2-9/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))*a-3/b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x*a^2-9/b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x*a-1/b^6/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)*a^2-2/b^6/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)*a-2/b^5/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)*a^2-6/b^5/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)*a-11/3/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)-11/2/b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x-1/b^6/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)-4/b^5/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)-2/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)*a^2-6/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)*a-3/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a^3-9/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a^2-11/2/b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a-11/2/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))","B"
862,1,543,101,0.043000," ","int(x/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x)","\frac{\left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{b^{5} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}+\frac{3 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{b^{4} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}+\frac{3 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{b^{2}}+\frac{9 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x}{2 b}+\frac{9 a \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}{2 b^{2}}+\frac{9 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{2 b \sqrt{b^{2}}}+\frac{a \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{b^{5} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}+\frac{2 a \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{b^{4} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}+\frac{2 a \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{b^{2}}+\frac{3 a \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x}{b}+\frac{3 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a^{2}}{b^{2}}+\frac{3 a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{b \sqrt{b^{2}}}"," ",0,"1/b^5/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)+3/b^4/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)+3/b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)+9/2/b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x+9/2/b^2*a*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)+9/2/b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))+1/b^5*a/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)+2/b^4*a/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)+2/b^2*a*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)+3/b*a*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x+3/b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a^2+3/b*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))","B"
863,1,264,60,0.036000," ","int(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x)","-\frac{\left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{b^{4} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}-\frac{2 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{b^{3} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}-\frac{2 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{b}-3 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x -\frac{3 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a}{b}-\frac{3 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{\sqrt{b^{2}}}"," ",0,"-1/b^4/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)-2/b^3/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)-2/b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)-3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x-3/b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a-3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))","B"
864,1,1062,89,0.051000," ","int(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x,x)","\frac{\left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{3 \left(1+a \right)^{3}}-\frac{a b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x}{2 \left(1+a \right)^{3}}-\frac{3 a^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(1+a \right)^{3}}-\frac{3 a b \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right)^{3} \sqrt{b^{2}}}+\frac{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(1+a \right)^{3}}+\frac{a^{3} b \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right)^{3} \sqrt{b^{2}}}+\frac{\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(1+a \right)^{3}}-\frac{\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(1+a \right)^{3}}-\frac{\left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{3 \left(1+a \right)^{3}}-\frac{b \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x}{2 \left(1+a \right)^{3}}-\frac{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a}{2 \left(1+a \right)^{3}}-\frac{b \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{2 \left(1+a \right)^{3} \sqrt{b^{2}}}+\frac{\left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{\left(1+a \right) b^{3} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}+\frac{2 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{\left(1+a \right) b^{2} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}+\frac{2 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{1+a}+\frac{3 b \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x}{1+a}+\frac{3 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a}{1+a}+\frac{3 b \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{\left(1+a \right) \sqrt{b^{2}}}-\frac{\left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{\left(1+a \right)^{2} b^{2} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}-\frac{\left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{\left(1+a \right)^{2}}-\frac{3 b \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x}{2 \left(1+a \right)^{2}}-\frac{3 \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a}{2 \left(1+a \right)^{2}}-\frac{3 b \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{2 \left(1+a \right)^{2} \sqrt{b^{2}}}"," ",0,"1/3/(1+a)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-1/2/(1+a)^3*a*b*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-3/2/(1+a)^3*a^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3/2/(1+a)^3*a*b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/(1+a)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/(1+a)^3*a^3*b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/(1+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^2-1/(1+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)-1/3/(1+a)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)-1/2/(1+a)^3*b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x-1/2/(1+a)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a-1/2/(1+a)^3*b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))+1/(1+a)/b^3/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)+2/(1+a)/b^2/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)+2/(1+a)*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)+3/(1+a)*b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x+3/(1+a)*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a+3/(1+a)*b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))-1/(1+a)^2/b^2/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)-1/(1+a)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)-3/2/(1+a)^2*b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x-3/2/(1+a)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a-3/2/(1+a)^2*b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))","B"
865,1,1710,112,0.056000," ","int(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x^2,x)","-\frac{3 a^{4} b^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right)^{3} \left(-a^{2}+1\right) \sqrt{b^{2}}}+\frac{9 a^{2} b^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right)^{3} \left(-a^{2}+1\right) \sqrt{b^{2}}}+\frac{3 a^{2} b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x}{2 \left(1+a \right)^{3} \left(-a^{2}+1\right)}-\frac{3 b^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{\left(1+a \right)^{2} \sqrt{b^{2}}}+\frac{2 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{\left(1+a \right)^{3} b \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}+\frac{3 b^{2} \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x}{\left(1+a \right)^{3}}+\frac{3 b \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a}{\left(1+a \right)^{3}}-\frac{\left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{\left(1+a \right)^{2} b^{2} \left(x +\frac{1}{b}+\frac{a}{b}\right)^{3}}-\frac{2 \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{5}{2}}}{\left(1+a \right)^{2} b \left(x +\frac{1}{b}+\frac{a}{b}\right)^{2}}-\frac{3 b^{2} \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x}{\left(1+a \right)^{2}}-\frac{3 b \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a}{\left(1+a \right)^{2}}+\frac{3 b^{2} \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, x}{2 \left(1+a \right)^{4}}+\frac{3 b \sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}\, a}{2 \left(1+a \right)^{4}}+\frac{3 b^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{2 \left(1+a \right)^{4} \sqrt{b^{2}}}-\frac{\left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{5}{2}}}{\left(1+a \right)^{3} \left(-a^{2}+1\right) x}+\frac{9 b \,a^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(1+a \right)^{4}}+\frac{3 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(1+a \right)^{4}}+\frac{3 b^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1+a}{b}-\frac{1}{b}\right)}{\sqrt{-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)}}\right)}{\left(1+a \right)^{3} \sqrt{b^{2}}}+\frac{b \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{\left(1+a \right)^{4}}-\frac{b \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{\left(1+a \right)^{4}}-\frac{3 b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{\left(1+a \right)^{4}}-\frac{2 b \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{\left(1+a \right)^{2}}+\frac{2 b \left(-\left(x +\frac{1+a}{b}\right)^{2} b^{2}+2 b \left(x +\frac{1+a}{b}\right)\right)^{\frac{3}{2}}}{\left(1+a \right)^{3}}+\frac{3 b^{2} a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x}{2 \left(1+a \right)^{4}}+\frac{9 b^{2} a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right)^{4} \sqrt{b^{2}}}-\frac{3 b^{2} a^{3} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{\left(1+a \right)^{4} \sqrt{b^{2}}}-\frac{3 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(1+a \right)^{4}}-\frac{2 a b \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}{\left(1+a \right)^{3} \left(-a^{2}+1\right)}+\frac{9 a^{3} b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(1+a \right)^{3} \left(-a^{2}+1\right)}-\frac{9 a b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(1+a \right)^{3} \left(-a^{2}+1\right)}-\frac{3 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(1+a \right)^{3} \sqrt{-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(1+a \right)^{3} \sqrt{-a^{2}+1}}-\frac{b^{2} \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}} x}{\left(1+a \right)^{3} \left(-a^{2}+1\right)}-\frac{3 b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x}{2 \left(1+a \right)^{3} \left(-a^{2}+1\right)}-\frac{3 b^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 \left(1+a \right)^{3} \left(-a^{2}+1\right) \sqrt{b^{2}}}"," ",0,"-3/(1+a)^3*a^4*b^2/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+9/2/(1+a)^3*a^2*b^2/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+3/2/(1+a)^3*a^2*b^2/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-3/(1+a)^2*b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))+2/(1+a)^3/b/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)+3/(1+a)^3*b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x+3/(1+a)^3*b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a-1/(1+a)^2/b^2/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)-2/(1+a)^2/b/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)-3/(1+a)^2*b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x-3/(1+a)^2*b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a+3/2/(1+a)^4*b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x+3/2/(1+a)^4*b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a+3/2/(1+a)^4*b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))-1/(1+a)^3/(-a^2+1)/x*(-b^2*x^2-2*a*b*x-a^2+1)^(5/2)+9/2/(1+a)^4*b*a^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3/(1+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)+3/(1+a)^3*b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))+1/(1+a)^4*b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)-1/(1+a)^4*b*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-3/(1+a)^4*b*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-2/(1+a)^2*b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)+2/(1+a)^3*b*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)+3/2/(1+a)^4*b^2*a*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+9/2/(1+a)^4*b^2*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-3/(1+a)^4*b^2*a^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-3/(1+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/(1+a)^3*a*b/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+9/2/(1+a)^3*a^3*b/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-9/2/(1+a)^3*a*b/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3/(1+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)+3/(1+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)-1/(1+a)^3*b^2/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*x-3/2/(1+a)^3*b^2/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-3/2/(1+a)^3*b^2/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))","B"
866,1,2848,174,0.064000," ","int(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x^3,x)","\text{output too large to display}"," ",0,"3/(1+a)^3*b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))-9/4/(1+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/(1+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/(1+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/(1+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)+9/4/(1+a)^3*b^2/(-a^2+1)*a^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3/2/(1+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+27/2/(1+a)^4*b^2*a/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+9/(1+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/(1+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/(1+a)^4*b^3/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*x+9/2/(1+a)^4*b^3/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+9/2/(1+a)^4*b^3/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+6/(1+a)^5*b^3*a^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+6/(1+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+3/2/(1+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)+1/(1+a)^3/b/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)+3/(1+a)^3*b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x+3/(1+a)^3*b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a-9/2/(1+a)^4*b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))-1/2/(1+a)^3/(-a^2+1)/x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(5/2)-1/2/(1+a)^3*b^2/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-3/2/(1+a)^3*b^2/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-9/2/(1+a)^4*b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a-6/(1+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)-3/(1+a)^5*b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x-3/(1+a)^5*b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a-3/(1+a)^5*b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))-9/2/(1+a)^4*b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x-9/(1+a)^5*b^2*a^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-9/2/(1+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/(1+a)^4*b^3*a^2/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+9/(1+a)^4*b^3*a^4/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/2/(1+a)^3*a*b/(-a^2+1)^2/x*(-b^2*x^2-2*a*b*x-a^2+1)^(5/2)-3/4/(1+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/(1+a)^3*a^3*b^3/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+3/2/(1+a)^3*a^5*b^3/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/2/(1+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/(1+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/(1+a)^3*a*b^3/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+3/4/(1+a)^3*b^3/(-a^2+1)*a*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+9/4/(1+a)^3*b^3/(-a^2+1)*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-3/2/(1+a)^3*b^3/(-a^2+1)*a^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-2/(1+a)^5*b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)+2/(1+a)^5*b^2*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+6/(1+a)^5*b^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+2/(1+a)^3/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)+2/(1+a)^3*b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)-3/(1+a)^4/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)-3/(1+a)^4*b^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)-3/(1+a)^5*b^3*a*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-9/(1+a)^5*b^3*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+3/(1+a)^4*b/(-a^2+1)/x*(-b^2*x^2-2*a*b*x-a^2+1)^(5/2)+6/(1+a)^4*b^2*a/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-27/2/(1+a)^4*b^2*a^3/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+1/(1+a)^3*a^2*b^2/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)","B"
867,1,4212,223,0.069000," ","int(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x^4,x)","\text{output too large to display}"," ",0,"-3/(1+a)^4*b^4/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))+1/(1+a)^3*b^4/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+1/(1+a)^3*b^4/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+5/(1+a)^6*b^4*a*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+15/(1+a)^6*b^4*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-10/(1+a)^6*b^4*a^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-10/(1+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+1/2/(1+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)-1/2/(1+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/(1+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)-3/2/(1+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)+2/3/(1+a)^3*b^4/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*x+3/2/(1+a)^4*b/(-a^2+1)/x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(5/2)-3/(1+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/(1+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/(1+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/(1+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)-6/(1+a)^5*b^2/(-a^2+1)/x*(-b^2*x^2-2*a*b*x-a^2+1)^(5/2)-12/(1+a)^5*b^3*a/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+27/(1+a)^5*b^3*a^3/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-27/(1+a)^5*b^3*a/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-18/(1+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/(1+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)-6/(1+a)^5*b^4/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*x-9/(1+a)^5*b^4/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-9/(1+a)^5*b^4/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+2/3/(1+a)^3*b^2/(-a^2+1)^2/x*(-b^2*x^2-2*a*b*x-a^2+1)^(5/2)+1/3/(1+a)^3*a^3*b^3/(-a^2+1)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-3/4/(1+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/(1+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/(1+a)^3*a*b^3/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)-9/4/(1+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/(1+a)^3*a*b^3/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-27/4/(1+a)^4*b^3/(-a^2+1)*a^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+9/2/(1+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+9/2/(1+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)+9/(1+a)^5*b^4*a^2/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+27/(1+a)^5*b^4*a^2/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-18/(1+a)^5*b^4*a^4/(-a^2+1)/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-1/6/(1+a)^3*a*b/(-a^2+1)^2/x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(5/2)+1/6/(1+a)^3*a^2*b^2/(-a^2+1)^3/x*(-b^2*x^2-2*a*b*x-a^2+1)^(5/2)-1/4/(1+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/(1+a)^3*a^4*b^4/(-a^2+1)^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/2/(1+a)^3*a^6*b^4/(-a^2+1)^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/6/(1+a)^3*a^2*b^4/(-a^2+1)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*x+1/4/(1+a)^3*a^2*b^4/(-a^2+1)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-9/4/(1+a)^4*b^4/(-a^2+1)*a*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-27/4/(1+a)^4*b^4/(-a^2+1)*a/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+9/2/(1+a)^4*b^4/(-a^2+1)*a^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+27/4/(1+a)^4*b^4*a^3/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-9/2/(1+a)^4*b^4*a^5/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-3/2/(1+a)^4*b^4*a/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*x-9/4/(1+a)^4*b^4*a/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-9/4/(1+a)^4*b^4*a/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+5/(1+a)^6*b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x+5/(1+a)^6*b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a+5/(1+a)^6*b^4/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))+10/(1+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)+15/(1+a)^6*b^3*a^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-2/(1+a)^4*b/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)-3/(1+a)^4*b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x-3/(1+a)^4*b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a-1/3/(1+a)^3/(-a^2+1)/x^3*(-b^2*x^2-2*a*b*x-a^2+1)^(5/2)+4/(1+a)^5*b/(x+1/b+a/b)^2*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)-2/(1+a)^4*b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)-1/(1+a)^4/(x+1/b+a/b)^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(5/2)-10/(1+a)^6*b^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-10/3/(1+a)^6*b^3*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+10/3/(1+a)^6*b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)+4/(1+a)^5*b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(3/2)+1/4/(1+a)^3*a^2*b^4/(-a^2+1)^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-3/4/(1+a)^3*a^2*b^4/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-9/4/(1+a)^3*a^2*b^4/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+3/2/(1+a)^3*a^4*b^4/(-a^2+1)^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-3/2/(1+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/(1+a)^4*b^4*a^3/(-a^2+1)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+6/(1+a)^5*b^4*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*x+6/(1+a)^5*b^3*(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2)*a+6/(1+a)^5*b^4/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+(1+a)/b-1/b)/(-(x+(1+a)/b)^2*b^2+2*b*(x+(1+a)/b))^(1/2))+3/2/(1+a)^4*b^3/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)+9/2/(1+a)^4*b^3/(-a^2+1)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-9/2/(1+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)","B"
868,1,34,10,0.028000," ","int(1/(-(b*x+1)^2+1)^(1/2),x)","\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{1}{b}\right)}{\sqrt{-b^{2} x^{2}-2 b x}}\right)}{\sqrt{b^{2}}}"," ",0,"1/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+1/b)/(-b^2*x^2-2*b*x)^(1/2))","B"
869,1,499,97,0.044000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x^3/(-b^2*x^2-2*a*b*x-a^2+1),x)","-\frac{x^{3}}{2 b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{3 a \,x^{2}}{2 b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{15 a^{2} x}{2 b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{9 a^{3}}{2 b^{4} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{3 a^{2} \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b^{3} \sqrt{b^{2}}}-\frac{9 a}{2 b^{4} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{3 x}{2 b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{3 \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{2 b^{3} \sqrt{b^{2}}}-\frac{x^{2}}{b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{5 a x}{b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a^{2}}{b^{4} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a^{3} x}{b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a^{4}}{b^{4} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{3 a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b^{3} \sqrt{b^{2}}}+\frac{2}{b^{4} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}"," ",0,"-1/2/b*x^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3/2/b^2*a*x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+15/2/b^3*a^2*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+9/2/b^4*a^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3*a^2/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-9/2/b^4*a/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3/2/b^3*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3/2/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))-x^2/b^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-5*a/b^3*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-a^2/b^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-a^3/b^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-a^4/b^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3*a/b^3/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+2/b^4/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)","B"
870,1,325,70,0.042000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x^2/(-b^2*x^2-2*a*b*x-a^2+1),x)","-\frac{x^{2}}{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{4 a x}{b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{2 a^{2}}{b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{2 a \arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b^{2} \sqrt{b^{2}}}+\frac{2}{b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{x}{b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a}{b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{a^{2} x}{b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{a^{3}}{b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b^{2} \sqrt{b^{2}}}"," ",0,"-1/b*x^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-4/b^2*a*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-2/b^3*a^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+2*a/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+2/b^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+x/b^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-a/b^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+a^2/b^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+a^3/b^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/b^2/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))","B"
871,1,160,40,0.039000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x/(-b^2*x^2-2*a*b*x-a^2+1),x)","\frac{x}{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{\arctan \left(\frac{\sqrt{b^{2}}\, \left(x +\frac{a}{b}\right)}{\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}\right)}{b \sqrt{b^{2}}}+\frac{1}{b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a x}{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a^{2}}{b^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}"," ",0,"1/b*x/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/b/(b^2)^(1/2)*arctan((b^2)^(1/2)*(x+a/b)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))+1/b^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-a/b/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x-a^2/b^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)","B"
872,1,42,23,0.029000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/(-b^2*x^2-2*a*b*x-a^2+1),x)","-\frac{\left(b x +a -1\right) \left(b x +a +1\right)^{2}}{b \left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-(b*x+a-1)*(b*x+a+1)^2/b/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)","A"
873,1,391,79,0.037000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x/(-b^2*x^2-2*a*b*x-a^2+1),x)","\frac{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{1}{\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{a^{2}}{\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{a}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{a^{2} b x}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{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) a}{\left(-a^{2}+1\right)^{\frac{3}{2}}}"," ",0,"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)+1/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+a*b/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+a^2/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-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)+1/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+a^2*b/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+1/(-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)*a","B"
874,1,671,132,0.043000," ","int((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^2/(-b^2*x^2-2*a*b*x-a^2+1),x)","\frac{b}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{3 a \,b^{2} x}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{3 b \,a^{2}}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{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{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{3 a^{3} b}{\left(-a^{2}+1\right)^{2} \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{2 b a}{\left(-a^{2}+1\right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{a}{\left(-a^{2}+1\right) x \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{3 a^{2} b}{\left(-a^{2}+1\right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{3 a^{3} b^{2} x}{\left(-a^{2}+1\right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}+\frac{3 a^{4} b}{\left(-a^{2}+1\right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}-\frac{3 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}}}"," ",0,"b/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3*a*b^2/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+3*b*a^2/(-a^2+1)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-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)-1/(-a^2+1)/x/(-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)+3*a^2*b^2/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+3*a^3*b/(-a^2+1)^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+2*b/(-a^2+1)/(-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)*a+3*a^2*b/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)+3*a^3*b^2/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x+3*a^4*b/(-a^2+1)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-3*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)","B"
875,0,0,101,0.072000," ","int(exp(n*arctanh(b*x+a))*x^m,x)","\int {\mathrm e}^{n \arctanh \left(b x +a \right)} x^{m}\, dx"," ",0,"int(exp(n*arctanh(b*x+a))*x^m,x)","F"
876,0,0,180,0.056000," ","int(exp(n*arctanh(b*x+a))*x^3,x)","\int {\mathrm e}^{n \arctanh \left(b x +a \right)} x^{3}\, dx"," ",0,"int(exp(n*arctanh(b*x+a))*x^3,x)","F"
877,0,0,144,0.052000," ","int(exp(n*arctanh(b*x+a))*x^2,x)","\int {\mathrm e}^{n \arctanh \left(b x +a \right)} x^{2}\, dx"," ",0,"int(exp(n*arctanh(b*x+a))*x^2,x)","F"
878,0,0,96,0.046000," ","int(exp(n*arctanh(b*x+a))*x,x)","\int {\mathrm e}^{n \arctanh \left(b x +a \right)} x\, dx"," ",0,"int(exp(n*arctanh(b*x+a))*x,x)","F"
879,0,0,59,0.040000," ","int(exp(n*arctanh(b*x+a)),x)","\int {\mathrm e}^{n \arctanh \left(b x +a \right)}\, dx"," ",0,"int(exp(n*arctanh(b*x+a)),x)","F"
880,0,0,121,0.047000," ","int(exp(n*arctanh(b*x+a))/x,x)","\int \frac{{\mathrm e}^{n \arctanh \left(b x +a \right)}}{x}\, dx"," ",0,"int(exp(n*arctanh(b*x+a))/x,x)","F"
881,0,0,86,0.049000," ","int(exp(n*arctanh(b*x+a))/x^2,x)","\int \frac{{\mathrm e}^{n \arctanh \left(b x +a \right)}}{x^{2}}\, dx"," ",0,"int(exp(n*arctanh(b*x+a))/x^2,x)","F"
882,0,0,140,0.057000," ","int(exp(n*arctanh(b*x+a))/x^3,x)","\int \frac{{\mathrm e}^{n \arctanh \left(b x +a \right)}}{x^{3}}\, dx"," ",0,"int(exp(n*arctanh(b*x+a))/x^3,x)","F"
883,1,229,105,0.092000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^4,x)","\frac{93 c^{4} x \sqrt{-a^{2} x^{2}+1}}{128}-\frac{c^{4} \sqrt{-a^{2} x^{2}+1}}{9 a}-\frac{c^{4} a^{7} x^{8} \sqrt{-a^{2} x^{2}+1}}{9}+\frac{4 c^{4} a^{5} x^{6} \sqrt{-a^{2} x^{2}+1}}{9}-\frac{2 c^{4} a^{3} x^{4} \sqrt{-a^{2} x^{2}+1}}{3}+\frac{4 c^{4} a \,x^{2} \sqrt{-a^{2} x^{2}+1}}{9}-\frac{c^{4} a^{6} x^{7} \sqrt{-a^{2} x^{2}+1}}{8}+\frac{25 c^{4} a^{4} x^{5} \sqrt{-a^{2} x^{2}+1}}{48}-\frac{163 c^{4} a^{2} x^{3} \sqrt{-a^{2} x^{2}+1}}{192}+\frac{35 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{128 \sqrt{a^{2}}}"," ",0,"93/128*c^4*x*(-a^2*x^2+1)^(1/2)-1/9*c^4*(-a^2*x^2+1)^(1/2)/a-1/9*c^4*a^7*x^8*(-a^2*x^2+1)^(1/2)+4/9*c^4*a^5*x^6*(-a^2*x^2+1)^(1/2)-2/3*c^4*a^3*x^4*(-a^2*x^2+1)^(1/2)+4/9*c^4*a*x^2*(-a^2*x^2+1)^(1/2)-1/8*c^4*a^6*x^7*(-a^2*x^2+1)^(1/2)+25/48*c^4*a^4*x^5*(-a^2*x^2+1)^(1/2)-163/192*c^4*a^2*x^3*(-a^2*x^2+1)^(1/2)+35/128*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","B"
884,1,183,87,0.059000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^3,x)","\frac{c^{3} a^{5} x^{6} \sqrt{-a^{2} x^{2}+1}}{7}-\frac{3 c^{3} a^{3} x^{4} \sqrt{-a^{2} x^{2}+1}}{7}+\frac{3 c^{3} a \,x^{2} \sqrt{-a^{2} x^{2}+1}}{7}-\frac{c^{3} \sqrt{-a^{2} x^{2}+1}}{7 a}+\frac{c^{3} a^{4} x^{5} \sqrt{-a^{2} x^{2}+1}}{6}-\frac{13 c^{3} a^{2} x^{3} \sqrt{-a^{2} x^{2}+1}}{24}+\frac{11 c^{3} x \sqrt{-a^{2} x^{2}+1}}{16}+\frac{5 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 \sqrt{a^{2}}}"," ",0,"1/7*c^3*a^5*x^6*(-a^2*x^2+1)^(1/2)-3/7*c^3*a^3*x^4*(-a^2*x^2+1)^(1/2)+3/7*c^3*a*x^2*(-a^2*x^2+1)^(1/2)-1/7*c^3*(-a^2*x^2+1)^(1/2)/a+1/6*c^3*a^4*x^5*(-a^2*x^2+1)^(1/2)-13/24*c^3*a^2*x^3*(-a^2*x^2+1)^(1/2)+11/16*c^3*x*(-a^2*x^2+1)^(1/2)+5/16*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","B"
885,1,137,69,0.044000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^2,x)","-\frac{c^{2} a^{3} x^{4} \sqrt{-a^{2} x^{2}+1}}{5}+\frac{2 c^{2} a \,x^{2} \sqrt{-a^{2} x^{2}+1}}{5}-\frac{c^{2} \sqrt{-a^{2} x^{2}+1}}{5 a}-\frac{c^{2} a^{2} x^{3} \sqrt{-a^{2} x^{2}+1}}{4}+\frac{5 c^{2} x \sqrt{-a^{2} x^{2}+1}}{8}+\frac{3 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}"," ",0,"-1/5*c^2*a^3*x^4*(-a^2*x^2+1)^(1/2)+2/5*c^2*a*x^2*(-a^2*x^2+1)^(1/2)-1/5*c^2*(-a^2*x^2+1)^(1/2)/a-1/4*c^2*a^2*x^3*(-a^2*x^2+1)^(1/2)+5/8*c^2*x*(-a^2*x^2+1)^(1/2)+3/8*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
886,1,83,45,0.035000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c),x)","\frac{c a \,x^{2} \sqrt{-a^{2} x^{2}+1}}{3}-\frac{c \sqrt{-a^{2} x^{2}+1}}{3 a}+\frac{c x \sqrt{-a^{2} x^{2}+1}}{2}+\frac{c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}"," ",0,"1/3*c*a*x^2*(-a^2*x^2+1)^(1/2)-1/3*c*(-a^2*x^2+1)^(1/2)/a+1/2*c*x*(-a^2*x^2+1)^(1/2)+1/2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
887,1,143,89,0.045000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c),x)","\frac{x^{2} \sqrt{-a^{2} x^{2}+1}}{3 a^{3} c}+\frac{5 \sqrt{-a^{2} x^{2}+1}}{3 a^{5} c}+\frac{x \sqrt{-a^{2} x^{2}+1}}{2 a^{4} c}-\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 c \,a^{4} \sqrt{a^{2}}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{c \,a^{6} \left(x -\frac{1}{a}\right)}"," ",0,"1/3*x^2*(-a^2*x^2+1)^(1/2)/a^3/c+5/3*(-a^2*x^2+1)^(1/2)/a^5/c+1/2*x*(-a^2*x^2+1)^(1/2)/a^4/c-3/2/c/a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/c/a^6/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
888,1,119,66,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c),x)","\frac{x \sqrt{-a^{2} x^{2}+1}}{2 a^{3} c}-\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 c \,a^{3} \sqrt{a^{2}}}+\frac{\sqrt{-a^{2} x^{2}+1}}{a^{4} c}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{c \,a^{5} \left(x -\frac{1}{a}\right)}"," ",0,"1/2*x*(-a^2*x^2+1)^(1/2)/a^3/c-3/2/c/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+(-a^2*x^2+1)^(1/2)/a^4/c-1/c/a^5/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
889,1,98,56,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c),x)","\frac{\sqrt{-a^{2} x^{2}+1}}{a^{3} c}-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c \,a^{2} \sqrt{a^{2}}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{c \,a^{4} \left(x -\frac{1}{a}\right)}"," ",0,"(-a^2*x^2+1)^(1/2)/a^3/c-1/c/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/c/a^4/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","A"
890,1,79,37,0.041000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c),x)","-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c a \sqrt{a^{2}}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{c \,a^{3} \left(x -\frac{1}{a}\right)}"," ",0,"-1/c/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/c/a^3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)","B"
891,1,25,24,0.029000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c),x)","\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}\, a c}"," ",0,"(a*x+1)/(-a^2*x^2+1)^(1/2)/a/c","A"
892,1,60,40,0.040000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c),x)","-\frac{\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{a \left(x -\frac{1}{a}\right)}}{c}"," ",0,"-1/c*(arctanh(1/(-a^2*x^2+1)^(1/2))+1/a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))","A"
893,1,75,64,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c),x)","-\frac{a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{\sqrt{-a^{2} x^{2}+1}}{x}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}}{c}"," ",0,"-1/c*(a*arctanh(1/(-a^2*x^2+1)^(1/2))+(-a^2*x^2+1)^(1/2)/x+1/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))","A"
894,1,97,87,0.045000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c),x)","-\frac{\frac{3 a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{a \sqrt{-a^{2} x^{2}+1}}{x}+\frac{a \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}+\frac{\sqrt{-a^{2} x^{2}+1}}{2 x^{2}}}{c}"," ",0,"-1/c*(3/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))+a*(-a^2*x^2+1)^(1/2)/x+a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/2*(-a^2*x^2+1)^(1/2)/x^2)","A"
895,1,140,110,0.046000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c),x)","-\frac{a^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{5 a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}+\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}+\frac{a^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{x -\frac{1}{a}}-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)}{c}"," ",0,"-1/c*(a^3*arctanh(1/(-a^2*x^2+1)^(1/2))+5/3*a^2*(-a^2*x^2+1)^(1/2)/x+1/3*(-a^2*x^2+1)^(1/2)/x^3+a^2/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-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"
896,1,225,119,0.054000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^6/(-a^2*c*x^2+c)^2,x)","-\frac{x^{2} \sqrt{-a^{2} x^{2}+1}}{3 a^{5} c^{2}}-\frac{8 \sqrt{-a^{2} x^{2}+1}}{3 c^{2} a^{7}}-\frac{x \sqrt{-a^{2} x^{2}+1}}{2 c^{2} a^{6}}+\frac{5 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 c^{2} a^{6} \sqrt{a^{2}}}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{6 c^{2} a^{9} \left(x -\frac{1}{a}\right)^{2}}+\frac{31 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{12 c^{2} a^{8} \left(x -\frac{1}{a}\right)}-\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{4 c^{2} a^{8} \left(x +\frac{1}{a}\right)}"," ",0,"-1/3*x^2*(-a^2*x^2+1)^(1/2)/a^5/c^2-8/3/c^2/a^7*(-a^2*x^2+1)^(1/2)-1/2/c^2/a^6*x*(-a^2*x^2+1)^(1/2)+5/2/c^2/a^6/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/6/c^2/a^9/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+31/12/c^2/a^8/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/4/c^2/a^8/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)","A"
897,1,202,96,0.050000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^2,x)","-\frac{x \sqrt{-a^{2} x^{2}+1}}{2 c^{2} a^{5}}+\frac{5 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 c^{2} a^{5} \sqrt{a^{2}}}-\frac{\sqrt{-a^{2} x^{2}+1}}{c^{2} a^{6}}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{6 c^{2} a^{8} \left(x -\frac{1}{a}\right)^{2}}+\frac{25 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{12 c^{2} a^{7} \left(x -\frac{1}{a}\right)}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{4 c^{2} a^{7} \left(x +\frac{1}{a}\right)}"," ",0,"-1/2/c^2/a^5*x*(-a^2*x^2+1)^(1/2)+5/2/c^2/a^5/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-1/c^2/a^6*(-a^2*x^2+1)^(1/2)+1/6/c^2/a^8/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+25/12/c^2/a^7/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/4/c^2/a^7/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)","B"
898,1,180,87,0.046000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^2,x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{a^{5} c^{2}}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{2} a^{4} \sqrt{a^{2}}}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{6 c^{2} a^{7} \left(x -\frac{1}{a}\right)^{2}}+\frac{19 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{12 c^{2} a^{6} \left(x -\frac{1}{a}\right)}-\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{4 c^{2} a^{6} \left(x +\frac{1}{a}\right)}"," ",0,"-(-a^2*x^2+1)^(1/2)/a^5/c^2+1/c^2/a^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/6/c^2/a^7/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+19/12/c^2/a^6/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/4/c^2/a^6/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)","B"
899,1,160,66,0.045000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^2,x)","\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{2} a^{3} \sqrt{a^{2}}}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{6 c^{2} a^{6} \left(x -\frac{1}{a}\right)^{2}}+\frac{13 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{12 c^{2} a^{5} \left(x -\frac{1}{a}\right)}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{4 c^{2} a^{5} \left(x +\frac{1}{a}\right)}"," ",0,"1/c^2/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/6/c^2/a^6/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+13/12/c^2/a^5/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/4/c^2/a^5/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)","B"
900,1,41,49,0.031000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^2,x)","-\frac{a^{2} x^{2}+2 a x -2}{3 \left(a x -1\right) c^{2} \sqrt{-a^{2} x^{2}+1}\, a^{3}}"," ",0,"-1/3*(a^2*x^2+2*a*x-2)/(a*x-1)/c^2/(-a^2*x^2+1)^(1/2)/a^3","A"
901,1,41,47,0.030000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^2,x)","-\frac{a^{2} x^{2}-a x +1}{3 \left(a x -1\right) c^{2} \sqrt{-a^{2} x^{2}+1}\, a^{2}}"," ",0,"-1/3*(a^2*x^2-a*x+1)/(a*x-1)/c^2/(-a^2*x^2+1)^(1/2)/a^2","A"
902,1,42,44,0.030000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^2,x)","\frac{2 a^{2} x^{2}-2 a x -1}{3 \left(a x -1\right) c^{2} \sqrt{-a^{2} x^{2}+1}\, a}"," ",0,"1/3*(2*a^2*x^2-2*a*x-1)/(a*x-1)/c^2/(-a^2*x^2+1)^(1/2)/a","A"
903,1,182,64,0.045000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^2,x)","\frac{-\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}}{2 a}-\frac{3 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{4 a \left(x -\frac{1}{a}\right)}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{4 a \left(x +\frac{1}{a}\right)}}{c^{2}}"," ",0,"1/c^2*(-arctanh(1/(-a^2*x^2+1)^(1/2))+1/2/a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-3/4/a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/4/a/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
904,1,150,91,0.048000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^2,x)","\frac{-a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\sqrt{-a^{2} x^{2}+1}}{x}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{6 a \left(x -\frac{1}{a}\right)^{2}}-\frac{17 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{12 \left(x -\frac{1}{a}\right)}-\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{4 \left(x +\frac{1}{a}\right)}}{c^{2}}"," ",0,"1/c^2*(-a*arctanh(1/(-a^2*x^2+1)^(1/2))-(-a^2*x^2+1)^(1/2)/x+1/6/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-17/12/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/4/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","A"
905,1,214,114,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^2,x)","\frac{-\frac{5 a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{a \sqrt{-a^{2} x^{2}+1}}{x}+\frac{a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{2}-\frac{7 a \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{4 \left(x -\frac{1}{a}\right)}-\frac{\sqrt{-a^{2} x^{2}+1}}{2 x^{2}}+\frac{a \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{4 x +\frac{4}{a}}}{c^{2}}"," ",0,"1/c^2*(-5/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))-a*(-a^2*x^2+1)^(1/2)/x+1/2*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-7/4*a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/2*(-a^2*x^2+1)^(1/2)/x^2+1/4*a/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","A"
906,1,260,137,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c)^2,x)","\frac{-2 a^{3} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{8 a^{2} \sqrt{-a^{2} x^{2}+1}}{3 x}+\frac{a^{2} \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{2}-\frac{\sqrt{-a^{2} x^{2}+1}}{3 x^{3}}-\frac{9 a^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{4 \left(x -\frac{1}{a}\right)}+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)-\frac{a^{2} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{4 \left(x +\frac{1}{a}\right)}}{c^{2}}"," ",0,"1/c^2*(-2*a^3*arctanh(1/(-a^2*x^2+1)^(1/2))-8/3*a^2*(-a^2*x^2+1)^(1/2)/x+1/2*a^2*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))-1/3*(-a^2*x^2+1)^(1/2)/x^3-9/4*a^2/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+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)))-1/4*a^2/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","A"
907,1,283,125,0.054000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^7/(-a^2*c*x^2+c)^3,x)","\frac{x \sqrt{-a^{2} x^{2}+1}}{2 c^{3} a^{7}}-\frac{7 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 c^{3} a^{7} \sqrt{a^{2}}}+\frac{\sqrt{-a^{2} x^{2}+1}}{c^{3} a^{8}}-\frac{7 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{15 c^{3} a^{10} \left(x -\frac{1}{a}\right)^{2}}-\frac{773 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{240 c^{3} a^{9} \left(x -\frac{1}{a}\right)}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{20 c^{3} a^{11} \left(x -\frac{1}{a}\right)^{3}}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{24 c^{3} a^{10} \left(x +\frac{1}{a}\right)^{2}}-\frac{31 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{48 c^{3} a^{9} \left(x +\frac{1}{a}\right)}"," ",0,"1/2/c^3/a^7*x*(-a^2*x^2+1)^(1/2)-7/2/c^3/a^7/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/c^3/a^8*(-a^2*x^2+1)^(1/2)-7/15/c^3/a^10/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-773/240/c^3/a^9/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/20/c^3/a^11/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/24/c^3/a^10/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-31/48/c^3/a^9/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)","B"
908,1,262,117,0.052000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^6/(-a^2*c*x^2+c)^3,x)","\frac{\sqrt{-a^{2} x^{2}+1}}{a^{7} c^{3}}-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{3} a^{6} \sqrt{a^{2}}}-\frac{23 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{60 c^{3} a^{9} \left(x -\frac{1}{a}\right)^{2}}-\frac{493 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{240 c^{3} a^{8} \left(x -\frac{1}{a}\right)}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{20 c^{3} a^{10} \left(x -\frac{1}{a}\right)^{3}}-\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{24 c^{3} a^{9} \left(x +\frac{1}{a}\right)^{2}}+\frac{25 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{48 c^{3} a^{8} \left(x +\frac{1}{a}\right)}"," ",0,"(-a^2*x^2+1)^(1/2)/a^7/c^3-1/c^3/a^6/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-23/60/c^3/a^9/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-493/240/c^3/a^8/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/20/c^3/a^10/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/24/c^3/a^9/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+25/48/c^3/a^8/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)","B"
909,1,243,96,0.050000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^3,x)","-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c^{3} a^{5} \sqrt{a^{2}}}-\frac{3 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{10 c^{3} a^{8} \left(x -\frac{1}{a}\right)^{2}}-\frac{91 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{80 c^{3} a^{7} \left(x -\frac{1}{a}\right)}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{20 c^{3} a^{9} \left(x -\frac{1}{a}\right)^{3}}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{24 c^{3} a^{8} \left(x +\frac{1}{a}\right)^{2}}-\frac{19 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{48 c^{3} a^{7} \left(x +\frac{1}{a}\right)}"," ",0,"-1/c^3/a^5/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-3/10/c^3/a^8/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-91/80/c^3/a^7/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/20/c^3/a^9/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/24/c^3/a^8/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-19/48/c^3/a^7/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)","B"
910,1,58,69,0.032000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^3,x)","-\frac{3 x^{4} a^{4}+12 x^{3} a^{3}-12 a^{2} x^{2}-8 a x +8}{15 \left(a x -1\right) c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a^{5}}"," ",0,"-1/15*(3*a^4*x^4+12*a^3*x^3-12*a^2*x^2-8*a*x+8)/(a*x-1)/c^3/(-a^2*x^2+1)^(3/2)/a^5","A"
911,1,58,62,0.032000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^3,x)","-\frac{3 x^{4} a^{4}-3 x^{3} a^{3}+3 a^{2} x^{2}+2 a x -2}{15 \left(a x -1\right) c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a^{4}}"," ",0,"-1/15*(3*a^4*x^4-3*a^3*x^3+3*a^2*x^2+2*a*x-2)/(a*x-1)/c^3/(-a^2*x^2+1)^(3/2)/a^4","A"
912,1,58,76,0.032000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^3,x)","\frac{2 x^{4} a^{4}-2 x^{3} a^{3}-3 a^{2} x^{2}-2 a x +2}{15 \left(a x -1\right) c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a^{3}}"," ",0,"1/15*(2*a^4*x^4-2*a^3*x^3-3*a^2*x^2-2*a*x+2)/(a*x-1)/c^3/(-a^2*x^2+1)^(3/2)/a^3","A"
913,1,58,68,0.031000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^3,x)","\frac{2 x^{4} a^{4}-2 x^{3} a^{3}-3 a^{2} x^{2}+3 a x -3}{15 \left(a x -1\right) c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a^{2}}"," ",0,"1/15*(2*a^4*x^4-2*a^3*x^3-3*a^2*x^2+3*a*x-3)/(a*x-1)/c^3/(-a^2*x^2+1)^(3/2)/a^2","A"
914,1,58,62,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^3,x)","-\frac{8 x^{4} a^{4}-8 x^{3} a^{3}-12 a^{2} x^{2}+12 a x +3}{15 \left(a x -1\right) c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a}"," ",0,"-1/15*(8*a^4*x^4-8*a^3*x^3-12*a^2*x^2+12*a*x+3)/(a*x-1)/c^3/(-a^2*x^2+1)^(3/2)/a","A"
915,1,384,87,0.051000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^3,x)","-\frac{\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}}{2 a}+\frac{11 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{16 a \left(x -\frac{1}{a}\right)}+\frac{\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a \left(x -\frac{1}{a}\right)^{3}}-\frac{2 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{5}}{4 a^{2}}+\frac{-\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{3 a \left(x +\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{3 \left(x +\frac{1}{a}\right)}}{8 a}-\frac{5 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{16 a \left(x +\frac{1}{a}\right)}}{c^{3}}"," ",0,"-1/c^3*(arctanh(1/(-a^2*x^2+1)^(1/2))-1/2/a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+11/16/a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/4/a^2*(1/5/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)))+1/8/a*(-1/3/a/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-1/3/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-5/16/a/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
916,1,314,117,0.051000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^3,x)","-\frac{a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{\sqrt{-a^{2} x^{2}+1}}{x}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{4 a \left(x -\frac{1}{a}\right)^{2}}+\frac{27 \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{16 \left(x -\frac{1}{a}\right)}+\frac{\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{5 a \left(x -\frac{1}{a}\right)^{3}}-\frac{2 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{5}}{4 a}+\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{24 a \left(x +\frac{1}{a}\right)^{2}}+\frac{23 \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{48 \left(x +\frac{1}{a}\right)}}{c^{3}}"," ",0,"-1/c^3*(a*arctanh(1/(-a^2*x^2+1)^(1/2))+(-a^2*x^2+1)^(1/2)/x-1/4/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+27/16/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/4/a*(1/5/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-2/5*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)))+1/24/a/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)+23/48/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
917,1,326,140,0.055000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^3,x)","-\frac{\frac{7 a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{a \sqrt{-a^{2} x^{2}+1}}{x}-\frac{11 a \left(\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 a \left(x -\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{3 \left(x -\frac{1}{a}\right)}\right)}{10}+\frac{39 a \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{16 \left(x -\frac{1}{a}\right)}+\frac{\sqrt{-a^{2} x^{2}+1}}{2 x^{2}}+\frac{\sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}{20 a \left(x -\frac{1}{a}\right)^{3}}+\frac{a \left(-\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{3 a \left(x +\frac{1}{a}\right)^{2}}-\frac{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{3 \left(x +\frac{1}{a}\right)}\right)}{8}-\frac{9 a \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}{16 \left(x +\frac{1}{a}\right)}}{c^{3}}"," ",0,"-1/c^3*(7/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))+a*(-a^2*x^2+1)^(1/2)/x-11/10*a*(1/3/a/(x-1/a)^2*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)-1/3/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2))+39/16*a/(x-1/a)*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/2*(-a^2*x^2+1)^(1/2)/x^2+1/20/a/(x-1/a)^3*(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+1/8*a*(-1/3/a/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)-1/3/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))-9/16*a/(x+1/a)*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","B"
918,1,74,80,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^4,x)","\frac{16 x^{6} a^{6}-16 x^{5} a^{5}-40 x^{4} a^{4}+40 x^{3} a^{3}+30 a^{2} x^{2}-30 a x -5}{35 \left(a x -1\right) c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}} a}"," ",0,"1/35*(16*a^6*x^6-16*a^5*x^5-40*a^4*x^4+40*a^3*x^3+30*a^2*x^2-30*a*x-5)/(a*x-1)/c^4/(-a^2*x^2+1)^(5/2)/a","A"
919,1,90,98,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^5,x)","-\frac{128 x^{8} a^{8}-128 a^{7} x^{7}-448 x^{6} a^{6}+448 x^{5} a^{5}+560 x^{4} a^{4}-560 x^{3} a^{3}-280 a^{2} x^{2}+280 a x +35}{315 \left(a x -1\right) c^{5} \left(-a^{2} x^{2}+1\right)^{\frac{7}{2}} a}"," ",0,"-1/315*(128*a^8*x^8-128*a^7*x^7-448*a^6*x^6+448*a^5*x^5+560*a^4*x^4-560*a^3*x^3-280*a^2*x^2+280*a*x+35)/(a*x-1)/c^5/(-a^2*x^2+1)^(7/2)/a","A"
920,1,43,43,0.026000," ","int((a*x+1)/(-a^2*x^2+1)*x^4,x)","-\frac{x^{4}}{4 a}-\frac{x^{3}}{3 a^{2}}-\frac{x^{2}}{2 a^{3}}-\frac{x}{a^{4}}-\frac{\ln \left(a x -1\right)}{a^{5}}"," ",0,"-1/4*x^4/a-1/3*x^3/a^2-1/2*x^2/a^3-x/a^4-1/a^5*ln(a*x-1)","A"
921,1,35,35,0.029000," ","int((a*x+1)/(-a^2*x^2+1)*x^3,x)","-\frac{x^{3}}{3 a}-\frac{x^{2}}{2 a^{2}}-\frac{x}{a^{3}}-\frac{\ln \left(a x -1\right)}{a^{4}}"," ",0,"-1/3*x^3/a-1/2*x^2/a^2-x/a^3-1/a^4*ln(a*x-1)","A"
922,1,27,27,0.026000," ","int((a*x+1)/(-a^2*x^2+1)*x^2,x)","-\frac{x^{2}}{2 a}-\frac{x}{a^{2}}-\frac{\ln \left(a x -1\right)}{a^{3}}"," ",0,"-1/2*x^2/a-x/a^2-1/a^3*ln(a*x-1)","A"
923,1,19,19,0.029000," ","int((a*x+1)/(-a^2*x^2+1)*x,x)","-\frac{x}{a}-\frac{\ln \left(a x -1\right)}{a^{2}}"," ",0,"-x/a-1/a^2*ln(a*x-1)","A"
924,1,12,12,0.026000," ","int((a*x+1)/(-a^2*x^2+1),x)","-\frac{\ln \left(a x -1\right)}{a}"," ",0,"-1/a*ln(a*x-1)","A"
925,1,12,12,0.032000," ","int((a*x+1)/(-a^2*x^2+1)/x,x)","\ln \left(x \right)-\ln \left(a x -1\right)"," ",0,"ln(x)-ln(a*x-1)","A"
926,1,20,20,0.031000," ","int((a*x+1)/(-a^2*x^2+1)/x^2,x)","-\frac{1}{x}+a \ln \left(x \right)-a \ln \left(a x -1\right)"," ",0,"-1/x+a*ln(x)-a*ln(a*x-1)","A"
927,1,30,30,0.033000," ","int((a*x+1)/(-a^2*x^2+1)/x^3,x)","-\frac{1}{2 x^{2}}-\frac{a}{x}+a^{2} \ln \left(x \right)-a^{2} \ln \left(a x -1\right)"," ",0,"-1/2/x^2-a/x+a^2*ln(x)-a^2*ln(a*x-1)","A"
928,1,38,38,0.032000," ","int((a*x+1)/(-a^2*x^2+1)/x^4,x)","-\frac{1}{3 x^{3}}-\frac{a}{2 x^{2}}-\frac{a^{2}}{x}+a^{3} \ln \left(x \right)-a^{3} \ln \left(a x -1\right)"," ",0,"-1/3/x^3-1/2*a/x^2-a^2/x+a^3*ln(x)-a^3*ln(a*x-1)","A"
929,1,49,50,0.034000," ","int((a*x+1)/(-a^2*x^2+1)^2*x^4,x)","\frac{x^{2}}{2 a^{3}}+\frac{x}{a^{4}}-\frac{1}{2 a^{5} \left(a x -1\right)}+\frac{7 \ln \left(a x -1\right)}{4 a^{5}}+\frac{\ln \left(a x +1\right)}{4 a^{5}}"," ",0,"1/2*x^2/a^3+x/a^4-1/2/a^5/(a*x-1)+7/4/a^5*ln(a*x-1)+1/4*ln(a*x+1)/a^5","A"
930,1,41,42,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^2*x^3,x)","\frac{x}{a^{3}}-\frac{1}{2 a^{4} \left(a x -1\right)}+\frac{5 \ln \left(a x -1\right)}{4 a^{4}}-\frac{\ln \left(a x +1\right)}{4 a^{4}}"," ",0,"x/a^3-1/2/a^4/(a*x-1)+5/4/a^4*ln(a*x-1)-1/4*ln(a*x+1)/a^4","A"
931,1,36,37,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^2*x^2,x)","-\frac{1}{2 a^{3} \left(a x -1\right)}+\frac{3 \ln \left(a x -1\right)}{4 a^{3}}+\frac{\ln \left(a x +1\right)}{4 a^{3}}"," ",0,"-1/2/a^3/(a*x-1)+3/4/a^3*ln(a*x-1)+1/4/a^3*ln(a*x+1)","A"
932,1,36,23,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^2*x,x)","-\frac{1}{2 a^{2} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{4 a^{2}}-\frac{\ln \left(a x +1\right)}{4 a^{2}}"," ",0,"-1/2/a^2/(a*x-1)+1/4/a^2*ln(a*x-1)-1/4/a^2*ln(a*x+1)","A"
933,1,36,23,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^2,x)","-\frac{1}{2 a \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{4 a}+\frac{\ln \left(a x +1\right)}{4 a}"," ",0,"-1/2/a/(a*x-1)-1/4/a*ln(a*x-1)+1/4*ln(a*x+1)/a","A"
934,1,29,30,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^2/x,x)","\ln \left(x \right)-\frac{1}{2 \left(a x -1\right)}-\frac{3 \ln \left(a x -1\right)}{4}-\frac{\ln \left(a x +1\right)}{4}"," ",0,"ln(x)-1/2/(a*x-1)-3/4*ln(a*x-1)-1/4*ln(a*x+1)","A"
935,1,39,40,0.034000," ","int((a*x+1)/(-a^2*x^2+1)^2/x^2,x)","-\frac{1}{x}+a \ln \left(x \right)-\frac{a}{2 \left(a x -1\right)}-\frac{5 a \ln \left(a x -1\right)}{4}+\frac{a \ln \left(a x +1\right)}{4}"," ",0,"-1/x+a*ln(x)-1/2*a/(a*x-1)-5/4*a*ln(a*x-1)+1/4*a*ln(a*x+1)","A"
936,1,54,55,0.037000," ","int((a*x+1)/(-a^2*x^2+1)^2/x^3,x)","-\frac{1}{2 x^{2}}-\frac{a}{x}+2 a^{2} \ln \left(x \right)-\frac{a^{2}}{2 \left(a x -1\right)}-\frac{7 a^{2} \ln \left(a x -1\right)}{4}-\frac{a^{2} \ln \left(a x +1\right)}{4}"," ",0,"-1/2/x^2-a/x+2*a^2*ln(x)-1/2*a^2/(a*x-1)-7/4*a^2*ln(a*x-1)-1/4*a^2*ln(a*x+1)","A"
937,1,62,63,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^2/x^4,x)","-\frac{1}{3 x^{3}}-\frac{a}{2 x^{2}}-\frac{2 a^{2}}{x}+2 a^{3} \ln \left(x \right)-\frac{a^{3}}{2 \left(a x -1\right)}-\frac{9 a^{3} \ln \left(a x -1\right)}{4}+\frac{a^{3} \ln \left(a x +1\right)}{4}"," ",0,"-1/3/x^3-1/2*a/x^2-2*a^2/x+2*a^3*ln(x)-1/2*a^3/(a*x-1)-9/4*a^3*ln(a*x-1)+1/4*a^3*ln(a*x+1)","A"
938,1,74,76,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^3*x^6,x)","-\frac{x^{2}}{2 a^{5}}-\frac{x}{a^{6}}+\frac{1}{8 a^{7} \left(a x -1\right)^{2}}+\frac{5}{4 a^{7} \left(a x -1\right)}-\frac{39 \ln \left(a x -1\right)}{16 a^{7}}-\frac{1}{8 a^{7} \left(a x +1\right)}-\frac{9 \ln \left(a x +1\right)}{16 a^{7}}"," ",0,"-1/2*x^2/a^5-x/a^6+1/8/a^7/(a*x-1)^2+5/4/a^7/(a*x-1)-39/16/a^7*ln(a*x-1)-1/8/a^7/(a*x+1)-9/16*ln(a*x+1)/a^7","A"
939,1,65,68,0.037000," ","int((a*x+1)/(-a^2*x^2+1)^3*x^5,x)","-\frac{x}{a^{5}}-\frac{23 \ln \left(a x -1\right)}{16 a^{6}}+\frac{1}{8 a^{6} \left(a x -1\right)^{2}}+\frac{1}{a^{6} \left(a x -1\right)}+\frac{1}{8 a^{6} \left(a x +1\right)}+\frac{7 \ln \left(a x +1\right)}{16 a^{6}}"," ",0,"-x/a^5-23/16/a^6*ln(a*x-1)+1/8/a^6/(a*x-1)^2+1/a^6/(a*x-1)+1/8/a^6/(a*x+1)+7/16*ln(a*x+1)/a^6","A"
940,1,60,62,0.037000," ","int((a*x+1)/(-a^2*x^2+1)^3*x^4,x)","\frac{1}{8 a^{5} \left(a x -1\right)^{2}}+\frac{3}{4 a^{5} \left(a x -1\right)}-\frac{11 \ln \left(a x -1\right)}{16 a^{5}}-\frac{1}{8 a^{5} \left(a x +1\right)}-\frac{5 \ln \left(a x +1\right)}{16 a^{5}}"," ",0,"1/8/a^5/(a*x-1)^2+3/4/a^5/(a*x-1)-11/16/a^5*ln(a*x-1)-1/8/a^5/(a*x+1)-5/16*ln(a*x+1)/a^5","A"
941,1,60,48,0.035000," ","int((a*x+1)/(-a^2*x^2+1)^3*x^3,x)","\frac{1}{8 a^{4} \left(a x -1\right)^{2}}+\frac{1}{2 a^{4} \left(a x -1\right)}-\frac{3 \ln \left(a x -1\right)}{16 a^{4}}+\frac{1}{8 a^{4} \left(a x +1\right)}+\frac{3 \ln \left(a x +1\right)}{16 a^{4}}"," ",0,"1/8/a^4/(a*x-1)^2+1/2/a^4/(a*x-1)-3/16/a^4*ln(a*x-1)+1/8/a^4/(a*x+1)+3/16*ln(a*x+1)/a^4","A"
942,1,60,48,0.036000," ","int((a*x+1)/(-a^2*x^2+1)^3*x^2,x)","\frac{1}{8 a^{3} \left(a x -1\right)^{2}}+\frac{1}{4 a^{3} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{16 a^{3}}-\frac{1}{8 a^{3} \left(a x +1\right)}-\frac{\ln \left(a x +1\right)}{16 a^{3}}"," ",0,"1/8/a^3/(a*x-1)^2+1/4/a^3/(a*x-1)+1/16/a^3*ln(a*x-1)-1/8/a^3/(a*x+1)-1/16/a^3*ln(a*x+1)","A"
943,1,48,35,0.036000," ","int((a*x+1)/(-a^2*x^2+1)^3*x,x)","\frac{1}{8 a^{2} \left(a x -1\right)^{2}}+\frac{\ln \left(a x -1\right)}{16 a^{2}}+\frac{1}{8 a^{2} \left(a x +1\right)}-\frac{\ln \left(a x +1\right)}{16 a^{2}}"," ",0,"1/8/a^2/(a*x-1)^2+1/16/a^2*ln(a*x-1)+1/8/a^2/(a*x+1)-1/16/a^2*ln(a*x+1)","A"
944,1,60,48,0.034000," ","int((a*x+1)/(-a^2*x^2+1)^3,x)","\frac{1}{8 a \left(a x -1\right)^{2}}-\frac{1}{4 a \left(a x -1\right)}-\frac{3 \ln \left(a x -1\right)}{16 a}-\frac{1}{8 a \left(a x +1\right)}+\frac{3 \ln \left(a x +1\right)}{16 a}"," ",0,"1/8/a/(a*x-1)^2-1/4/a/(a*x-1)-3/16/a*ln(a*x-1)-1/8/a/(a*x+1)+3/16*ln(a*x+1)/a","A"
945,1,47,49,0.036000," ","int((a*x+1)/(-a^2*x^2+1)^3/x,x)","\ln \left(x \right)+\frac{1}{8 \left(a x -1\right)^{2}}-\frac{1}{2 \left(a x -1\right)}-\frac{11 \ln \left(a x -1\right)}{16}+\frac{1}{8 a x +8}-\frac{5 \ln \left(a x +1\right)}{16}"," ",0,"ln(x)+1/8/(a*x-1)^2-1/2/(a*x-1)-11/16*ln(a*x-1)+1/8/(a*x+1)-5/16*ln(a*x+1)","A"
946,1,59,61,0.037000," ","int((a*x+1)/(-a^2*x^2+1)^3/x^2,x)","-\frac{1}{x}+a \ln \left(x \right)+\frac{a}{8 \left(a x -1\right)^{2}}-\frac{3 a}{4 \left(a x -1\right)}-\frac{23 a \ln \left(a x -1\right)}{16}-\frac{a}{8 \left(a x +1\right)}+\frac{7 a \ln \left(a x +1\right)}{16}"," ",0,"-1/x+a*ln(x)+1/8*a/(a*x-1)^2-3/4*a/(a*x-1)-23/16*a*ln(a*x-1)-1/8*a/(a*x+1)+7/16*a*ln(a*x+1)","A"
947,1,78,79,0.039000," ","int((a*x+1)/(-a^2*x^2+1)^3/x^3,x)","-\frac{1}{2 x^{2}}-\frac{a}{x}+3 a^{2} \ln \left(x \right)-\frac{a^{2}}{a x -1}+\frac{a^{2}}{8 \left(a x -1\right)^{2}}-\frac{39 a^{2} \ln \left(a x -1\right)}{16}+\frac{a^{2}}{8 a x +8}-\frac{9 a^{2} \ln \left(a x +1\right)}{16}"," ",0,"-1/2/x^2-a/x+3*a^2*ln(x)-a^2/(a*x-1)+1/8*a^2/(a*x-1)^2-39/16*a^2*ln(a*x-1)+1/8*a^2/(a*x+1)-9/16*a^2*ln(a*x+1)","A"
948,1,86,88,0.040000," ","int((a*x+1)/(-a^2*x^2+1)^3/x^4,x)","-\frac{1}{3 x^{3}}-\frac{a}{2 x^{2}}-\frac{3 a^{2}}{x}+3 a^{3} \ln \left(x \right)+\frac{a^{3}}{8 \left(a x -1\right)^{2}}-\frac{5 a^{3}}{4 \left(a x -1\right)}-\frac{59 a^{3} \ln \left(a x -1\right)}{16}-\frac{a^{3}}{8 \left(a x +1\right)}+\frac{11 a^{3} \ln \left(a x +1\right)}{16}"," ",0,"-1/3/x^3-1/2*a/x^2-3*a^2/x+3*a^3*ln(x)+1/8*a^3/(a*x-1)^2-5/4*a^3/(a*x-1)-59/16*a^3*ln(a*x-1)-1/8*a^3/(a*x+1)+11/16*a^3*ln(a*x+1)","A"
949,1,37,62,0.026000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*c*x^2+c)^(1/2),x)","\frac{x^{3} \left(3 a x +4\right) \sqrt{-a^{2} c \,x^{2}+c}}{12 \sqrt{-a^{2} x^{2}+1}}"," ",0,"1/12*x^3*(3*a*x+4)*(-a^2*c*x^2+c)^(1/2)/(-a^2*x^2+1)^(1/2)","A"
950,1,37,62,0.027000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*c*x^2+c)^(1/2),x)","\frac{x^{2} \left(2 a x +3\right) \sqrt{-a^{2} c \,x^{2}+c}}{6 \sqrt{-a^{2} x^{2}+1}}"," ",0,"1/6*x^2*(2*a*x+3)*(-a^2*c*x^2+c)^(1/2)/(-a^2*x^2+1)^(1/2)","A"
951,1,34,59,0.026000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(1/2),x)","\frac{x \left(a x +2\right) \sqrt{-a^{2} c \,x^{2}+c}}{2 \sqrt{-a^{2} x^{2}+1}}"," ",0,"1/2*x*(a*x+2)*(-a^2*c*x^2+c)^(1/2)/(-a^2*x^2+1)^(1/2)","A"
952,1,48,57,0.047000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(1/2)/x,x)","\frac{\left(-a x -\ln \left(x \right)\right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}}{a^{2} x^{2}-1}"," ",0,"(-a*x-ln(x))*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/(a^2*x^2-1)","A"
953,1,50,60,0.039000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x)","\frac{\left(-a \ln \left(x \right) x +1\right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}}{\left(a^{2} x^{2}-1\right) x}"," ",0,"(-a*ln(x)*x+1)*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/(a^2*x^2-1)/x","A"
954,1,65,77,0.028000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(3/2),x)","\frac{x \left(3 x^{3} a^{3}+4 a^{2} x^{2}-6 a x -12\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{12 \left(a x -1\right) \left(a x +1\right) \sqrt{-a^{2} x^{2}+1}}"," ",0,"1/12*x*(3*a^3*x^3+4*a^2*x^2-6*a*x-12)*(-a^2*c*x^2+c)^(3/2)/(a*x-1)/(a*x+1)/(-a^2*x^2+1)^(1/2)","A"
955,1,81,120,0.032000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(5/2),x)","\frac{x \left(5 x^{5} a^{5}+6 x^{4} a^{4}-15 x^{3} a^{3}-20 a^{2} x^{2}+15 a x +30\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{30 \left(a x -1\right)^{2} \left(a x +1\right)^{2} \sqrt{-a^{2} x^{2}+1}}"," ",0,"1/30*x*(5*a^5*x^5+6*a^4*x^4-15*a^3*x^3-20*a^2*x^2+15*a*x+30)*(-a^2*c*x^2+c)^(5/2)/(a*x-1)^2/(a*x+1)^2/(-a^2*x^2+1)^(1/2)","A"
956,1,97,161,0.030000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(7/2),x)","\frac{x \left(35 a^{7} x^{7}+40 x^{6} a^{6}-140 x^{5} a^{5}-168 x^{4} a^{4}+210 x^{3} a^{3}+280 a^{2} x^{2}-140 a x -280\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{280 \left(a x -1\right)^{3} \left(a x +1\right)^{3} \sqrt{-a^{2} x^{2}+1}}"," ",0,"1/280*x*(35*a^7*x^7+40*a^6*x^6-140*a^5*x^5-168*a^4*x^4+210*a^3*x^3+280*a^2*x^2-140*a*x-280)*(-a^2*c*x^2+c)^(7/2)/(a*x-1)^3/(a*x+1)^3/(-a^2*x^2+1)^(1/2)","A"
957,1,83,168,0.039000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 x^{4} a^{4}+4 x^{3} a^{3}+6 a^{2} x^{2}+12 a x +12 \ln \left(a x -1\right)\right)}{12 \left(a^{2} x^{2}-1\right) c \,a^{5}}"," ",0,"1/12*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(3*x^4*a^4+4*x^3*a^3+6*a^2*x^2+12*a*x+12*ln(a*x-1))/(a^2*x^2-1)/c/a^5","A"
958,1,75,135,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 x^{3} a^{3}+3 a^{2} x^{2}+6 a x +6 \ln \left(a x -1\right)\right)}{6 \left(a^{2} x^{2}-1\right) c \,a^{4}}"," ",0,"1/6*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(2*x^3*a^3+3*a^2*x^2+6*a*x+6*ln(a*x-1))/(a^2*x^2-1)/c/a^4","A"
959,1,66,102,0.038000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a^{2} x^{2}+2 a x +2 \ln \left(a x -1\right)\right)}{2 \left(a^{2} x^{2}-1\right) c \,a^{3}}"," ",0,"1/2*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(a^2*x^2+2*a*x+2*ln(a*x-1))/(a^2*x^2-1)/c/a^3","A"
960,1,55,69,0.035000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x +\ln \left(a x -1\right)\right)}{\left(a^{2} x^{2}-1\right) c \,a^{2}}"," ",0,"(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(a*x+ln(a*x-1))/(a^2*x^2-1)/c/a^2","A"
961,1,51,37,0.033000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \ln \left(a x -1\right)}{\left(a^{2} x^{2}-1\right) c a}"," ",0,"(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/(a^2*x^2-1)/c/a*ln(a*x-1)","A"
962,1,53,63,0.041000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^(1/2),x)","\frac{\left(-\ln \left(x \right)+\ln \left(a x -1\right)\right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}}{c \left(a^{2} x^{2}-1\right)}"," ",0,"(-ln(x)+ln(a*x-1))*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/c/(a^2*x^2-1)","A"
963,1,62,95,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^(1/2),x)","\frac{\left(-a \ln \left(x \right) x +\ln \left(a x -1\right) x a +1\right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}}{\left(a^{2} x^{2}-1\right) c x}"," ",0,"(-a*ln(x)*x+ln(a*x-1)*x*a+1)*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/(a^2*x^2-1)/c/x","A"
964,1,76,130,0.043000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 a^{2} \ln \left(x \right) x^{2}-2 \ln \left(a x -1\right) x^{2} a^{2}-2 a x -1\right)}{2 \left(a^{2} x^{2}-1\right) c \,x^{2}}"," ",0,"-1/2*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(2*a^2*ln(x)*x^2-2*ln(a*x-1)*x^2*a^2-2*a*x-1)/(a^2*x^2-1)/c/x^2","A"
965,1,84,163,0.044000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(6 a^{3} \ln \left(x \right) x^{3}-6 \ln \left(a x -1\right) x^{3} a^{3}-6 a^{2} x^{2}-3 a x -2\right)}{6 \left(a^{2} x^{2}-1\right) c \,x^{3}}"," ",0,"-1/6*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(6*a^3*ln(x)*x^3-6*ln(a*x-1)*x^3*a^3-6*a^2*x^2-3*a*x-2)/(a^2*x^2-1)/c/x^3","A"
966,1,119,227,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(4 x^{4} a^{4}+2 x^{3} a^{3}+18 a^{2} x^{2}+27 \ln \left(a x -1\right) x a -3 a x \ln \left(a x +1\right)-24 a x -27 \ln \left(a x -1\right)+3 \ln \left(a x +1\right)-6\right)}{12 \left(a^{2} x^{2}-1\right) c^{2} a^{6} \left(a x -1\right)}"," ",0,"-1/12*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(4*x^4*a^4+2*x^3*a^3+18*a^2*x^2+27*ln(a*x-1)*x*a-3*a*x*ln(a*x+1)-24*a*x-27*ln(a*x-1)+3*ln(a*x+1)-6)/(a^2*x^2-1)/c^2/a^6/(a*x-1)","A"
967,1,110,190,0.050000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 x^{3} a^{3}+2 a^{2} x^{2}+7 \ln \left(a x -1\right) x a +a x \ln \left(a x +1\right)-4 a x -7 \ln \left(a x -1\right)-\ln \left(a x +1\right)-2\right)}{4 \left(a^{2} x^{2}-1\right) c^{2} a^{5} \left(a x -1\right)}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(2*x^3*a^3+2*a^2*x^2+7*ln(a*x-1)*x*a+a*x*ln(a*x+1)-4*a*x-7*ln(a*x-1)-ln(a*x+1)-2)/(a^2*x^2-1)/c^2/a^5/(a*x-1)","A"
968,1,101,154,0.048000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(4 a^{2} x^{2}+5 \ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-4 a x -5 \ln \left(a x -1\right)+\ln \left(a x +1\right)-2\right)}{4 \left(a^{2} x^{2}-1\right) c^{2} a^{4} \left(a x -1\right)}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(4*a^2*x^2+5*ln(a*x-1)*x*a-a*x*ln(a*x+1)-4*a*x-5*ln(a*x-1)+ln(a*x+1)-2)/(a^2*x^2-1)/c^2/a^4/(a*x-1)","A"
969,1,90,121,0.046000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x a +a x \ln \left(a x +1\right)-3 \ln \left(a x -1\right)-\ln \left(a x +1\right)-2\right)}{4 \left(a^{2} x^{2}-1\right) c^{2} a^{3} \left(a x -1\right)}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x*a+a*x*ln(a*x+1)-3*ln(a*x-1)-ln(a*x+1)-2)/(a^2*x^2-1)/c^2/a^3/(a*x-1)","A"
970,1,88,79,0.051000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-\ln \left(a x -1\right)+\ln \left(a x +1\right)-2\right)}{4 \left(a^{2} x^{2}-1\right) c^{2} a^{2} \left(a x -1\right)}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x*a-a*x*ln(a*x+1)-ln(a*x-1)+ln(a*x+1)-2)/(a^2*x^2-1)/c^2/a^2/(a*x-1)","A"
971,1,88,79,0.046000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-\ln \left(a x -1\right)+\ln \left(a x +1\right)+2\right)}{4 \left(a^{2} x^{2}-1\right) c^{2} a \left(a x -1\right)}"," ",0,"1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x*a-a*x*ln(a*x+1)-ln(a*x-1)+ln(a*x+1)+2)/(a^2*x^2-1)/c^2/a/(a*x-1)","A"
972,1,96,143,0.048000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(4 a \ln \left(x \right) x -3 \ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-4 \ln \left(x \right)+3 \ln \left(a x -1\right)+\ln \left(a x +1\right)-2\right)}{4 c^{2} \left(a x -1\right) \left(a^{2} x^{2}-1\right)}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(4*a*ln(x)*x-3*ln(a*x-1)*x*a-a*x*ln(a*x+1)-4*ln(x)+3*ln(a*x-1)+ln(a*x+1)-2)/c^2/(a*x-1)/(a^2*x^2-1)","A"
973,1,122,180,0.048000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(4 a^{2} \ln \left(x \right) x^{2}-5 \ln \left(a x -1\right) x^{2} a^{2}+\ln \left(a x +1\right) x^{2} a^{2}-4 a \ln \left(x \right) x +5 \ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-6 a x +4\right)}{4 \left(a^{2} x^{2}-1\right) c^{2} \left(a x -1\right) x}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(4*a^2*ln(x)*x^2-5*ln(a*x-1)*x^2*a^2+ln(a*x+1)*x^2*a^2-4*a*ln(x)*x+5*ln(a*x-1)*x*a-a*x*ln(a*x+1)-6*a*x+4)/(a^2*x^2-1)/c^2/(a*x-1)/x","A"
974,1,142,223,0.050000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 a^{3} \ln \left(x \right) x^{3}-7 \ln \left(a x -1\right) x^{3} a^{3}-a^{3} x^{3} \ln \left(a x +1\right)-8 a^{2} \ln \left(x \right) x^{2}+7 \ln \left(a x -1\right) x^{2} a^{2}+\ln \left(a x +1\right) x^{2} a^{2}-6 a^{2} x^{2}+2 a x +2\right)}{4 \left(a^{2} x^{2}-1\right) c^{2} \left(a x -1\right) x^{2}}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(8*a^3*ln(x)*x^3-7*ln(a*x-1)*x^3*a^3-a^3*x^3*ln(a*x+1)-8*a^2*ln(x)*x^2+7*ln(a*x-1)*x^2*a^2+ln(a*x+1)*x^2*a^2-6*a^2*x^2+2*a*x+2)/(a^2*x^2-1)/c^2/(a*x-1)/x^2","A"
975,1,151,259,0.051000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(24 a^{4} \ln \left(x \right) x^{4}-27 \ln \left(a x -1\right) x^{4} a^{4}+3 \ln \left(a x +1\right) x^{4} a^{4}-24 a^{3} \ln \left(x \right) x^{3}+27 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)-30 x^{3} a^{3}+18 a^{2} x^{2}+2 a x +4\right)}{12 \left(a^{2} x^{2}-1\right) c^{2} x^{3} \left(a x -1\right)}"," ",0,"-1/12*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(24*a^4*ln(x)*x^4-27*ln(a*x-1)*x^4*a^4+3*ln(a*x+1)*x^4*a^4-24*a^3*ln(x)*x^3+27*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)-30*x^3*a^3+18*a^2*x^2+2*a*x+4)/(a^2*x^2-1)/c^2/x^3/(a*x-1)","A"
976,1,190,272,0.052000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^6/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 x^{5} a^{5}+8 x^{4} a^{4}+39 \ln \left(a x -1\right) x^{3} a^{3}+9 a^{3} x^{3} \ln \left(a x +1\right)-24 x^{3} a^{3}-39 \ln \left(a x -1\right) x^{2} a^{2}-9 \ln \left(a x +1\right) x^{2} a^{2}-26 a^{2} x^{2}-39 \ln \left(a x -1\right) x a -9 a x \ln \left(a x +1\right)+10 a x +39 \ln \left(a x -1\right)+9 \ln \left(a x +1\right)+20\right)}{16 \left(a^{2} x^{2}-1\right) c^{3} a^{7} \left(a x -1\right)^{2} \left(a x +1\right)}"," ",0,"1/16*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(8*x^5*a^5+8*x^4*a^4+39*ln(a*x-1)*x^3*a^3+9*a^3*x^3*ln(a*x+1)-24*x^3*a^3-39*ln(a*x-1)*x^2*a^2-9*ln(a*x+1)*x^2*a^2-26*a^2*x^2-39*ln(a*x-1)*x*a-9*a*x*ln(a*x+1)+10*a*x+39*ln(a*x-1)+9*ln(a*x+1)+20)/(a^2*x^2-1)/c^3/a^7/(a*x-1)^2/(a*x+1)","A"
977,1,182,236,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(16 x^{4} a^{4}+23 \ln \left(a x -1\right) x^{3} a^{3}-7 a^{3} x^{3} \ln \left(a x +1\right)-16 x^{3} a^{3}-23 \ln \left(a x -1\right) x^{2} a^{2}+7 \ln \left(a x +1\right) x^{2} a^{2}-34 a^{2} x^{2}-23 \ln \left(a x -1\right) x a +7 a x \ln \left(a x +1\right)+18 a x +23 \ln \left(a x -1\right)-7 \ln \left(a x +1\right)+12\right)}{16 \left(a^{2} x^{2}-1\right) c^{3} a^{6} \left(a x -1\right)^{2} \left(a x +1\right)}"," ",0,"1/16*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(16*x^4*a^4+23*ln(a*x-1)*x^3*a^3-7*a^3*x^3*ln(a*x+1)-16*x^3*a^3-23*ln(a*x-1)*x^2*a^2+7*ln(a*x+1)*x^2*a^2-34*a^2*x^2-23*ln(a*x-1)*x*a+7*a*x*ln(a*x+1)+18*a*x+23*ln(a*x-1)-7*ln(a*x+1)+12)/(a^2*x^2-1)/c^3/a^6/(a*x-1)^2/(a*x+1)","A"
978,1,166,202,0.050000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(11 \ln \left(a x -1\right) x^{3} a^{3}+5 a^{3} x^{3} \ln \left(a x +1\right)-11 \ln \left(a x -1\right) x^{2} a^{2}-5 \ln \left(a x +1\right) x^{2} a^{2}-10 a^{2} x^{2}-11 \ln \left(a x -1\right) x a -5 a x \ln \left(a x +1\right)-6 a x +11 \ln \left(a x -1\right)+5 \ln \left(a x +1\right)+12\right)}{16 \left(a^{2} x^{2}-1\right) c^{3} a^{5} \left(a x -1\right)^{2} \left(a x +1\right)}"," ",0,"1/16*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(11*ln(a*x-1)*x^3*a^3+5*a^3*x^3*ln(a*x+1)-11*ln(a*x-1)*x^2*a^2-5*ln(a*x+1)*x^2*a^2-10*a^2*x^2-11*ln(a*x-1)*x*a-5*a*x*ln(a*x+1)-6*a*x+11*ln(a*x-1)+5*ln(a*x+1)+12)/(a^2*x^2-1)/c^3/a^5/(a*x-1)^2/(a*x+1)","A"
979,1,166,160,0.052000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)-3 \ln \left(a x -1\right) x^{2} a^{2}+3 \ln \left(a x +1\right) x^{2} a^{2}-10 a^{2} x^{2}-3 \ln \left(a x -1\right) x a +3 a x \ln \left(a x +1\right)+2 a x +3 \ln \left(a x -1\right)-3 \ln \left(a x +1\right)+4\right)}{16 \left(a^{2} x^{2}-1\right) c^{3} a^{4} \left(a x -1\right)^{2} \left(a x +1\right)}"," ",0,"1/16*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)-3*ln(a*x-1)*x^2*a^2+3*ln(a*x+1)*x^2*a^2-10*a^2*x^2-3*ln(a*x-1)*x*a+3*a*x*ln(a*x+1)+2*a*x+3*ln(a*x-1)-3*ln(a*x+1)+4)/(a^2*x^2-1)/c^3/a^4/(a*x-1)^2/(a*x+1)","A"
980,1,161,160,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x^{3} a^{3}-a^{3} x^{3} \ln \left(a x +1\right)-\ln \left(a x -1\right) x^{2} a^{2}+\ln \left(a x +1\right) x^{2} a^{2}+2 a^{2} x^{2}-\ln \left(a x -1\right) x a +a x \ln \left(a x +1\right)+6 a x +\ln \left(a x -1\right)-\ln \left(a x +1\right)-4\right)}{16 \left(a^{2} x^{2}-1\right) c^{3} a^{3} \left(a x -1\right)^{2} \left(a x +1\right)}"," ",0,"-1/16*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x^3*a^3-a^3*x^3*ln(a*x+1)-ln(a*x-1)*x^2*a^2+ln(a*x+1)*x^2*a^2+2*a^2*x^2-ln(a*x-1)*x*a+a*x*ln(a*x+1)+6*a*x+ln(a*x-1)-ln(a*x+1)-4)/(a^2*x^2-1)/c^3/a^3/(a*x-1)^2/(a*x+1)","A"
981,1,161,119,0.051000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x^{3} a^{3}-a^{3} x^{3} \ln \left(a x +1\right)-\ln \left(a x -1\right) x^{2} a^{2}+\ln \left(a x +1\right) x^{2} a^{2}+2 a^{2} x^{2}-\ln \left(a x -1\right) x a +a x \ln \left(a x +1\right)-2 a x +\ln \left(a x -1\right)-\ln \left(a x +1\right)+4\right)}{16 \left(a^{2} x^{2}-1\right) c^{3} a^{2} \left(a x -1\right)^{2} \left(a x +1\right)}"," ",0,"-1/16*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x^3*a^3-a^3*x^3*ln(a*x+1)-ln(a*x-1)*x^2*a^2+ln(a*x+1)*x^2*a^2+2*a^2*x^2-ln(a*x-1)*x*a+a*x*ln(a*x+1)-2*a*x+ln(a*x-1)-ln(a*x+1)+4)/(a^2*x^2-1)/c^3/a^2/(a*x-1)^2/(a*x+1)","A"
982,1,166,160,0.049000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)-3 \ln \left(a x -1\right) x^{2} a^{2}+3 \ln \left(a x +1\right) x^{2} a^{2}+6 a^{2} x^{2}-3 \ln \left(a x -1\right) x a +3 a x \ln \left(a x +1\right)-6 a x +3 \ln \left(a x -1\right)-3 \ln \left(a x +1\right)-4\right)}{16 \left(a^{2} x^{2}-1\right) c^{3} a \left(a x -1\right)^{2} \left(a x +1\right)}"," ",0,"1/16*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)-3*ln(a*x-1)*x^2*a^2+3*ln(a*x+1)*x^2*a^2+6*a^2*x^2-3*ln(a*x-1)*x*a+3*a*x*ln(a*x+1)-6*a*x+3*ln(a*x-1)-3*ln(a*x+1)-4)/(a^2*x^2-1)/c^3/a/(a*x-1)^2/(a*x+1)","A"
983,1,193,218,0.050000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(16 a^{3} \ln \left(x \right) x^{3}-11 \ln \left(a x -1\right) x^{3} a^{3}-5 a^{3} x^{3} \ln \left(a x +1\right)-16 a^{2} \ln \left(x \right) x^{2}+11 \ln \left(a x -1\right) x^{2} a^{2}+5 \ln \left(a x +1\right) x^{2} a^{2}-6 a^{2} x^{2}-16 a \ln \left(x \right) x +11 \ln \left(a x -1\right) x a +5 a x \ln \left(a x +1\right)-2 a x +16 \ln \left(x \right)-11 \ln \left(a x -1\right)-5 \ln \left(a x +1\right)+12\right)}{16 \left(a^{2} x^{2}-1\right) c^{3} \left(a x -1\right)^{2} \left(a x +1\right)}"," ",0,"-1/16*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(16*a^3*ln(x)*x^3-11*ln(a*x-1)*x^3*a^3-5*a^3*x^3*ln(a*x+1)-16*a^2*ln(x)*x^2+11*ln(a*x-1)*x^2*a^2+5*ln(a*x+1)*x^2*a^2-6*a^2*x^2-16*a*ln(x)*x+11*ln(a*x-1)*x*a+5*a*x*ln(a*x+1)-2*a*x+16*ln(x)-11*ln(a*x-1)-5*ln(a*x+1)+12)/(a^2*x^2-1)/c^3/(a*x-1)^2/(a*x+1)","A"
984,1,222,257,0.051000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(16 a^{4} \ln \left(x \right) x^{4}-23 \ln \left(a x -1\right) x^{4} a^{4}+7 \ln \left(a x +1\right) x^{4} a^{4}-16 a^{3} \ln \left(x \right) x^{3}+23 \ln \left(a x -1\right) x^{3} a^{3}-7 a^{3} x^{3} \ln \left(a x +1\right)-30 x^{3} a^{3}-16 a^{2} \ln \left(x \right) x^{2}+23 \ln \left(a x -1\right) x^{2} a^{2}-7 \ln \left(a x +1\right) x^{2} a^{2}+22 a^{2} x^{2}+16 a \ln \left(x \right) x -23 \ln \left(a x -1\right) x a +7 a x \ln \left(a x +1\right)+28 a x -16\right)}{16 \left(a^{2} x^{2}-1\right) c^{3} \left(a x -1\right)^{2} \left(a x +1\right) x}"," ",0,"-1/16*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(16*a^4*ln(x)*x^4-23*ln(a*x-1)*x^4*a^4+7*ln(a*x+1)*x^4*a^4-16*a^3*ln(x)*x^3+23*ln(a*x-1)*x^3*a^3-7*a^3*x^3*ln(a*x+1)-30*x^3*a^3-16*a^2*ln(x)*x^2+23*ln(a*x-1)*x^2*a^2-7*ln(a*x+1)*x^2*a^2+22*a^2*x^2+16*a*ln(x)*x-23*ln(a*x-1)*x*a+7*a*x*ln(a*x+1)+28*a*x-16)/(a^2*x^2-1)/c^3/(a*x-1)^2/(a*x+1)/x","A"
985,1,242,303,0.053000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(48 a^{5} \ln \left(x \right) x^{5}-39 \ln \left(a x -1\right) x^{5} a^{5}-9 \ln \left(a x +1\right) x^{5} a^{5}-48 a^{4} \ln \left(x \right) x^{4}+39 \ln \left(a x -1\right) x^{4} a^{4}+9 \ln \left(a x +1\right) x^{4} a^{4}-30 x^{4} a^{4}-48 a^{3} \ln \left(x \right) x^{3}+39 \ln \left(a x -1\right) x^{3} a^{3}+9 a^{3} x^{3} \ln \left(a x +1\right)+6 x^{3} a^{3}+48 a^{2} \ln \left(x \right) x^{2}-39 \ln \left(a x -1\right) x^{2} a^{2}-9 \ln \left(a x +1\right) x^{2} a^{2}+44 a^{2} x^{2}-8 a x -8\right)}{16 \left(a^{2} x^{2}-1\right) c^{3} \left(a x -1\right)^{2} \left(a x +1\right) x^{2}}"," ",0,"-1/16*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(48*a^5*ln(x)*x^5-39*ln(a*x-1)*x^5*a^5-9*ln(a*x+1)*x^5*a^5-48*a^4*ln(x)*x^4+39*ln(a*x-1)*x^4*a^4+9*ln(a*x+1)*x^4*a^4-30*x^4*a^4-48*a^3*ln(x)*x^3+39*ln(a*x-1)*x^3*a^3+9*a^3*x^3*ln(a*x+1)+6*x^3*a^3+48*a^2*ln(x)*x^2-39*ln(a*x-1)*x^2*a^2-9*ln(a*x+1)*x^2*a^2+44*a^2*x^2-8*a*x-8)/(a^2*x^2-1)/c^3/(a*x-1)^2/(a*x+1)/x^2","A"
986,1,238,241,0.052000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(7/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(15 \ln \left(a x -1\right) x^{5} a^{5}-15 \ln \left(a x +1\right) x^{5} a^{5}-15 \ln \left(a x -1\right) x^{4} a^{4}+15 \ln \left(a x +1\right) x^{4} a^{4}+30 x^{4} a^{4}-30 \ln \left(a x -1\right) x^{3} a^{3}+30 a^{3} x^{3} \ln \left(a x +1\right)-30 x^{3} a^{3}+30 \ln \left(a x -1\right) x^{2} a^{2}-30 \ln \left(a x +1\right) x^{2} a^{2}-50 a^{2} x^{2}+15 \ln \left(a x -1\right) x a -15 a x \ln \left(a x +1\right)+50 a x -15 \ln \left(a x -1\right)+15 \ln \left(a x +1\right)+16\right)}{96 \left(a^{2} x^{2}-1\right) c^{4} a \left(a x -1\right)^{3} \left(a x +1\right)^{2}}"," ",0,"1/96*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(15*ln(a*x-1)*x^5*a^5-15*ln(a*x+1)*x^5*a^5-15*ln(a*x-1)*x^4*a^4+15*ln(a*x+1)*x^4*a^4+30*x^4*a^4-30*ln(a*x-1)*x^3*a^3+30*a^3*x^3*ln(a*x+1)-30*x^3*a^3+30*ln(a*x-1)*x^2*a^2-30*ln(a*x+1)*x^2*a^2-50*a^2*x^2+15*ln(a*x-1)*x*a-15*a*x*ln(a*x+1)+50*a*x-15*ln(a*x-1)+15*ln(a*x+1)+16)/(a^2*x^2-1)/c^4/a/(a*x-1)^3/(a*x+1)^2","A"
987,1,227,72,0.369000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^2,x)","\frac{a^{5} c^{2} x^{6+m} \hypergeom \left(\left[\frac{1}{2}, 3+\frac{m}{2}\right], \left[4+\frac{m}{2}\right], a^{2} x^{2}\right)}{6+m}-\frac{2 a^{3} c^{2} x^{4+m} \hypergeom \left(\left[\frac{1}{2}, 2+\frac{m}{2}\right], \left[3+\frac{m}{2}\right], a^{2} x^{2}\right)}{4+m}+\frac{a \,c^{2} 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}+\frac{c^{2} a^{4} x^{5+m} \hypergeom \left(\left[\frac{1}{2}, \frac{5}{2}+\frac{m}{2}\right], \left[\frac{7}{2}+\frac{m}{2}\right], a^{2} x^{2}\right)}{5+m}-\frac{2 c^{2} a^{2} x^{3+m} \hypergeom \left(\left[\frac{1}{2}, \frac{3}{2}+\frac{m}{2}\right], \left[\frac{5}{2}+\frac{m}{2}\right], a^{2} x^{2}\right)}{3+m}+\frac{c^{2} 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}"," ",0,"a^5*c^2/(6+m)*x^(6+m)*hypergeom([1/2,3+1/2*m],[4+1/2*m],a^2*x^2)-2*a^3*c^2/(4+m)*x^(4+m)*hypergeom([1/2,2+1/2*m],[3+1/2*m],a^2*x^2)+a*c^2/(2+m)*x^(2+m)*hypergeom([1/2,1+1/2*m],[2+1/2*m],a^2*x^2)+c^2*a^4/(5+m)*x^(5+m)*hypergeom([1/2,5/2+1/2*m],[7/2+1/2*m],a^2*x^2)-2*c^2*a^2/(3+m)*x^(3+m)*hypergeom([1/2,3/2+1/2*m],[5/2+1/2*m],a^2*x^2)+c^2/(1+m)*x^(1+m)*hypergeom([1/2,1/2+1/2*m],[3/2+1/2*m],a^2*x^2)","B"
988,1,143,68,0.260000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c),x)","-\frac{a^{3} c \,x^{4+m} \hypergeom \left(\left[\frac{1}{2}, 2+\frac{m}{2}\right], \left[3+\frac{m}{2}\right], a^{2} x^{2}\right)}{4+m}+\frac{a c \,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}-\frac{c \,a^{2} x^{3+m} \hypergeom \left(\left[\frac{1}{2}, \frac{3}{2}+\frac{m}{2}\right], \left[\frac{5}{2}+\frac{m}{2}\right], a^{2} x^{2}\right)}{3+m}+\frac{c \,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}"," ",0,"-a^3*c/(4+m)*x^(4+m)*hypergeom([1/2,2+1/2*m],[3+1/2*m],a^2*x^2)+a*c/(2+m)*x^(2+m)*hypergeom([1/2,1+1/2*m],[2+1/2*m],a^2*x^2)-c*a^2/(3+m)*x^(3+m)*hypergeom([1/2,3/2+1/2*m],[5/2+1/2*m],a^2*x^2)+c/(1+m)*x^(1+m)*hypergeom([1/2,1/2+1/2*m],[3/2+1/2*m],a^2*x^2)","B"
989,0,0,72,0.327000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c),x)","\int \frac{\left(a x +1\right) x^{m}}{\sqrt{-a^{2} x^{2}+1}\, \left(-a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c),x)","F"
990,0,0,72,0.325000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^2,x)","\int \frac{\left(a x +1\right) x^{m}}{\sqrt{-a^{2} x^{2}+1}\, \left(-a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^2,x)","F"
991,0,0,72,0.327000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^3,x)","\int \frac{\left(a x +1\right) x^{m}}{\sqrt{-a^{2} x^{2}+1}\, \left(-a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^3,x)","F"
992,1,338,82,0.032000," ","int((a*x+1)*(-a^2*x^2+1)^2*x^m,x)","\frac{x^{1+m} \left(a^{5} m^{5} x^{5}+15 a^{5} m^{4} x^{5}+85 a^{5} m^{3} x^{5}+a^{4} m^{5} x^{4}+225 a^{5} m^{2} x^{5}+16 a^{4} m^{4} x^{4}+274 a^{5} m \,x^{5}+95 a^{4} m^{3} x^{4}-2 a^{3} m^{5} x^{3}+120 x^{5} a^{5}+260 a^{4} m^{2} x^{4}-34 a^{3} m^{4} x^{3}+324 a^{4} m \,x^{4}-214 a^{3} m^{3} x^{3}-2 a^{2} m^{5} x^{2}+144 x^{4} a^{4}-614 a^{3} m^{2} x^{3}-36 a^{2} m^{4} x^{2}-792 a^{3} m \,x^{3}-242 a^{2} m^{3} x^{2}+a \,m^{5} x -360 x^{3} a^{3}-744 a^{2} m^{2} x^{2}+19 a \,m^{4} x -1016 a^{2} m \,x^{2}+137 a \,m^{3} x +m^{5}-480 a^{2} x^{2}+461 a \,m^{2} x +20 m^{4}+702 a m x +155 m^{3}+360 a x +580 m^{2}+1044 m +720\right)}{\left(6+m \right) \left(5+m \right) \left(4+m \right) \left(3+m \right) \left(2+m \right) \left(1+m \right)}"," ",0,"x^(1+m)*(a^5*m^5*x^5+15*a^5*m^4*x^5+85*a^5*m^3*x^5+a^4*m^5*x^4+225*a^5*m^2*x^5+16*a^4*m^4*x^4+274*a^5*m*x^5+95*a^4*m^3*x^4-2*a^3*m^5*x^3+120*a^5*x^5+260*a^4*m^2*x^4-34*a^3*m^4*x^3+324*a^4*m*x^4-214*a^3*m^3*x^3-2*a^2*m^5*x^2+144*a^4*x^4-614*a^3*m^2*x^3-36*a^2*m^4*x^2-792*a^3*m*x^3-242*a^2*m^3*x^2+a*m^5*x-360*a^3*x^3-744*a^2*m^2*x^2+19*a*m^4*x-1016*a^2*m*x^2+137*a*m^3*x+m^5-480*a^2*x^2+461*a*m^2*x+20*m^4+702*a*m*x+155*m^3+360*a*x+580*m^2+1044*m+720)/(6+m)/(5+m)/(4+m)/(3+m)/(2+m)/(1+m)","B"
993,1,142,54,0.030000," ","int((a*x+1)*(-a^2*x^2+1)*x^m,x)","-\frac{x^{1+m} \left(a^{3} m^{3} x^{3}+6 a^{3} m^{2} x^{3}+11 a^{3} m \,x^{3}+a^{2} m^{3} x^{2}+6 x^{3} a^{3}+7 a^{2} m^{2} x^{2}+14 a^{2} m \,x^{2}-a \,m^{3} x +8 a^{2} x^{2}-8 a \,m^{2} x -19 a m x -m^{3}-12 a x -9 m^{2}-26 m -24\right)}{\left(4+m \right) \left(3+m \right) \left(2+m \right) \left(1+m \right)}"," ",0,"-x^(1+m)*(a^3*m^3*x^3+6*a^3*m^2*x^3+11*a^3*m*x^3+a^2*m^3*x^2+6*a^3*x^3+7*a^2*m^2*x^2+14*a^2*m*x^2-a*m^3*x+8*a^2*x^2-8*a*m^2*x-19*a*m*x-m^3-12*a*x-9*m^2-26*m-24)/(4+m)/(3+m)/(2+m)/(1+m)","B"
994,1,27,24,0.025000," ","int((a*x+1)*x^m,x)","\frac{x^{1+m} \left(a m x +a x +m +2\right)}{\left(2+m \right) \left(1+m \right)}"," ",0,"x^(1+m)*(a*m*x+a*x+m+2)/(2+m)/(1+m)","A"
995,1,100,24,0.260000," ","int((a*x+1)/(-a^2*x^2+1)*x^m,x)","-\frac{\left(-a^{2}\right)^{-\frac{m}{2}} \left(-\frac{2 x^{m} \left(-a^{2}\right)^{\frac{m}{2}} \left(-m -2\right)}{\left(2+m \right) m}-x^{m} \left(-a^{2}\right)^{\frac{m}{2}} \Phi \left(a^{2} x^{2}, 1, \frac{m}{2}\right)\right)}{2 a}+\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}"," ",0,"-1/2/a*(-a^2)^(-1/2*m)*(-2/(2+m)*x^m*(-a^2)^(1/2*m)*(-m-2)/m-x^m*(-a^2)^(1/2*m)*LerchPhi(a^2*x^2,1,1/2*m))+1/(1+m)*x^(1+m)*(1/2+1/2*m)*LerchPhi(a^2*x^2,1,1/2+1/2*m)","C"
996,1,177,66,0.256000," ","int((a*x+1)/(-a^2*x^2+1)^2*x^m,x)","-\frac{\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)}{2 a}+\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}} \left(-1-m \right)}{\left(1+m \right) \left(-2 a^{2} x^{2}+2\right)}+\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}"," ",0,"-1/2/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))+1/2*(-a^2)^(-1/2-1/2*m)*(-2/(1+m)*x^(1+m)*(-a^2)^(1/2+1/2*m)*(-1-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))","C"
997,1,224,66,0.285000," ","int((a*x+1)/(-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{\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)}{4 a}"," ",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))-1/4/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))","C"
998,1,377,250,0.031000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^(5/2),x)","\frac{x^{1+m} \left(a^{5} m^{5} x^{5}+15 a^{5} m^{4} x^{5}+85 a^{5} m^{3} x^{5}+a^{4} m^{5} x^{4}+225 a^{5} m^{2} x^{5}+16 a^{4} m^{4} x^{4}+274 a^{5} m \,x^{5}+95 a^{4} m^{3} x^{4}-2 a^{3} m^{5} x^{3}+120 x^{5} a^{5}+260 a^{4} m^{2} x^{4}-34 a^{3} m^{4} x^{3}+324 a^{4} m \,x^{4}-214 a^{3} m^{3} x^{3}-2 a^{2} m^{5} x^{2}+144 x^{4} a^{4}-614 a^{3} m^{2} x^{3}-36 a^{2} m^{4} x^{2}-792 a^{3} m \,x^{3}-242 a^{2} m^{3} x^{2}+a \,m^{5} x -360 x^{3} a^{3}-744 a^{2} m^{2} x^{2}+19 a \,m^{4} x -1016 a^{2} m \,x^{2}+137 a \,m^{3} x +m^{5}-480 a^{2} x^{2}+461 a \,m^{2} x +20 m^{4}+702 a m x +155 m^{3}+360 a x +580 m^{2}+1044 m +720\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\left(6+m \right) \left(5+m \right) \left(4+m \right) \left(3+m \right) \left(2+m \right) \left(1+m \right) \left(a x -1\right)^{2} \left(a x +1\right)^{2} \sqrt{-a^{2} x^{2}+1}}"," ",0,"x^(1+m)*(a^5*m^5*x^5+15*a^5*m^4*x^5+85*a^5*m^3*x^5+a^4*m^5*x^4+225*a^5*m^2*x^5+16*a^4*m^4*x^4+274*a^5*m*x^5+95*a^4*m^3*x^4-2*a^3*m^5*x^3+120*a^5*x^5+260*a^4*m^2*x^4-34*a^3*m^4*x^3+324*a^4*m*x^4-214*a^3*m^3*x^3-2*a^2*m^5*x^2+144*a^4*x^4-614*a^3*m^2*x^3-36*a^2*m^4*x^2-792*a^3*m*x^3-242*a^2*m^3*x^2+a*m^5*x-360*a^3*x^3-744*a^2*m^2*x^2+19*a*m^4*x-1016*a^2*m*x^2+137*a*m^3*x+m^5-480*a^2*x^2+461*a*m^2*x+20*m^4+702*a*m*x+155*m^3+360*a*x+580*m^2+1044*m+720)*(-a^2*c*x^2+c)^(5/2)/(6+m)/(5+m)/(4+m)/(3+m)/(2+m)/(1+m)/(a*x-1)^2/(a*x+1)^2/(-a^2*x^2+1)^(1/2)","A"
999,1,180,158,0.030000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^(3/2),x)","\frac{x^{1+m} \left(a^{3} m^{3} x^{3}+6 a^{3} m^{2} x^{3}+11 a^{3} m \,x^{3}+a^{2} m^{3} x^{2}+6 x^{3} a^{3}+7 a^{2} m^{2} x^{2}+14 a^{2} m \,x^{2}-a \,m^{3} x +8 a^{2} x^{2}-8 a \,m^{2} x -19 a m x -m^{3}-12 a x -9 m^{2}-26 m -24\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\left(4+m \right) \left(3+m \right) \left(2+m \right) \left(1+m \right) \left(a x -1\right) \left(a x +1\right) \sqrt{-a^{2} x^{2}+1}}"," ",0,"x^(1+m)*(a^3*m^3*x^3+6*a^3*m^2*x^3+11*a^3*m*x^3+a^2*m^3*x^2+6*a^3*x^3+7*a^2*m^2*x^2+14*a^2*m*x^2-a*m^3*x+8*a^2*x^2-8*a*m^2*x-19*a*m*x-m^3-12*a*x-9*m^2-26*m-24)*(-a^2*c*x^2+c)^(3/2)/(4+m)/(3+m)/(2+m)/(1+m)/(a*x-1)/(a*x+1)/(-a^2*x^2+1)^(1/2)","A"
1000,1,52,74,0.026000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^(1/2),x)","\frac{x^{1+m} \left(a m x +a x +m +2\right) \sqrt{-a^{2} c \,x^{2}+c}}{\left(2+m \right) \left(1+m \right) \sqrt{-a^{2} x^{2}+1}}"," ",0,"x^(1+m)*(a*m*x+a*x+m+2)*(-a^2*c*x^2+c)^(1/2)/(2+m)/(1+m)/(-a^2*x^2+1)^(1/2)","A"
1001,0,0,49,0.336000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(1/2),x)","\int \frac{\left(a x +1\right) x^{m}}{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-a^{2} c \,x^{2}+c}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(1/2),x)","F"
1002,0,0,122,0.328000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{\left(a x +1\right) x^{m}}{\sqrt{-a^{2} x^{2}+1}\, \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(3/2),x)","F"
1003,0,0,122,0.327000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(5/2),x)","\int \frac{\left(a x +1\right) x^{m}}{\sqrt{-a^{2} x^{2}+1}\, \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(5/2),x)","F"
1004,0,0,128,0.339000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right) x^{m} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^p,x)","F"
1005,1,47,75,0.354000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a^2*x^2+1)^p,x)","\frac{a \,x^{5} \hypergeom \left(\left[\frac{5}{2}, \frac{1}{2}-p \right], \left[\frac{7}{2}\right], a^{2} x^{2}\right)}{5}+\frac{x^{4} \hypergeom \left(\left[2, \frac{1}{2}-p \right], \left[3\right], a^{2} x^{2}\right)}{4}"," ",0,"1/5*a*x^5*hypergeom([5/2,1/2-p],[7/2],a^2*x^2)+1/4*x^4*hypergeom([2,1/2-p],[3],a^2*x^2)","A"
1006,1,47,74,0.340000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*x^2+1)^p,x)","\frac{a \,x^{4} \hypergeom \left(\left[2, \frac{1}{2}-p \right], \left[3\right], a^{2} x^{2}\right)}{4}+\frac{x^{3} \hypergeom \left(\left[\frac{3}{2}, \frac{1}{2}-p \right], \left[\frac{5}{2}\right], a^{2} x^{2}\right)}{3}"," ",0,"1/4*a*x^4*hypergeom([2,1/2-p],[3],a^2*x^2)+1/3*x^3*hypergeom([3/2,1/2-p],[5/2],a^2*x^2)","A"
1007,1,47,50,0.339000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*x^2+1)^p,x)","\frac{a \,x^{3} \hypergeom \left(\left[\frac{3}{2}, \frac{1}{2}-p \right], \left[\frac{5}{2}\right], a^{2} x^{2}\right)}{3}+\frac{x^{2} \hypergeom \left(\left[1, \frac{1}{2}-p \right], \left[2\right], a^{2} x^{2}\right)}{2}"," ",0,"1/3*a*x^3*hypergeom([3/2,1/2-p],[5/2],a^2*x^2)+1/2*x^2*hypergeom([1,1/2-p],[2],a^2*x^2)","A"
1008,1,44,47,0.344000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p,x)","\frac{a \,x^{2} \hypergeom \left(\left[1, \frac{1}{2}-p \right], \left[2\right], a^{2} x^{2}\right)}{2}+x \hypergeom \left(\left[\frac{1}{2}, \frac{1}{2}-p \right], \left[\frac{3}{2}\right], a^{2} x^{2}\right)"," ",0,"1/2*a*x^2*hypergeom([1,1/2-p],[2],a^2*x^2)+x*hypergeom([1/2,1/2-p],[3/2],a^2*x^2)","A"
1009,1,90,64,0.377000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p/x,x)","a x \hypergeom \left(\left[\frac{1}{2}, \frac{1}{2}-p \right], \left[\frac{3}{2}\right], a^{2} x^{2}\right)+\frac{\Gamma \left(\frac{3}{2}-p \right) a^{2} x^{2} \hypergeom \left(\left[1, 1, \frac{3}{2}-p \right], \left[2, 2\right], a^{2} x^{2}\right)+\left(\Psi \left(\frac{1}{2}-p \right)+\gamma +2 \ln \left(x \right)+\ln \left(-a^{2}\right)\right) \Gamma \left(\frac{1}{2}-p \right)}{2 \Gamma \left(\frac{1}{2}-p \right)}"," ",0,"a*x*hypergeom([1/2,1/2-p],[3/2],a^2*x^2)+1/2*(GAMMA(3/2-p)*a^2*x^2*hypergeom([1,1,3/2-p],[2,2],a^2*x^2)+(Psi(1/2-p)+gamma+2*ln(x)+ln(-a^2))*GAMMA(1/2-p))/GAMMA(1/2-p)","A"
1010,1,93,67,0.362000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p/x^2,x)","\frac{a \left(\Gamma \left(\frac{3}{2}-p \right) a^{2} x^{2} \hypergeom \left(\left[1, 1, \frac{3}{2}-p \right], \left[2, 2\right], a^{2} x^{2}\right)+\left(\Psi \left(\frac{1}{2}-p \right)+\gamma +2 \ln \left(x \right)+\ln \left(-a^{2}\right)\right) \Gamma \left(\frac{1}{2}-p \right)\right)}{2 \Gamma \left(\frac{1}{2}-p \right)}-\frac{\hypergeom \left(\left[-\frac{1}{2}, \frac{1}{2}-p \right], \left[\frac{1}{2}\right], a^{2} x^{2}\right)}{x}"," ",0,"1/2*a*(GAMMA(3/2-p)*a^2*x^2*hypergeom([1,1,3/2-p],[2,2],a^2*x^2)+(Psi(1/2-p)+gamma+2*ln(x)+ln(-a^2))*GAMMA(1/2-p))/GAMMA(1/2-p)-hypergeom([-1/2,1/2-p],[1/2],a^2*x^2)/x","A"
1011,1,112,70,0.402000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p/x^3,x)","-\frac{a \hypergeom \left(\left[-\frac{1}{2}, \frac{1}{2}-p \right], \left[\frac{1}{2}\right], a^{2} x^{2}\right)}{x}-\frac{a^{2} \left(-\frac{\Gamma \left(\frac{5}{2}-p \right) a^{2} x^{2} \hypergeom \left(\left[1, 1, \frac{5}{2}-p \right], \left[2, 3\right], a^{2} x^{2}\right)}{2}-\left(\Psi \left(\frac{3}{2}-p \right)+\gamma -1+2 \ln \left(x \right)+\ln \left(-a^{2}\right)\right) \Gamma \left(\frac{3}{2}-p \right)+\frac{\Gamma \left(\frac{1}{2}-p \right)}{x^{2} a^{2}}\right)}{2 \Gamma \left(\frac{1}{2}-p \right)}"," ",0,"-a*hypergeom([-1/2,1/2-p],[1/2],a^2*x^2)/x-1/2*a^2*(-1/2*GAMMA(5/2-p)*a^2*x^2*hypergeom([1,1,5/2-p],[2,3],a^2*x^2)-(Psi(3/2-p)+gamma-1+2*ln(x)+ln(-a^2))*GAMMA(3/2-p)+GAMMA(1/2-p)/x^2/a^2)/GAMMA(1/2-p)","A"
1012,0,0,124,0.333000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right) x^{3} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a^2*c*x^2+c)^p,x)","F"
1013,0,0,123,0.334000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right) x^{2} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*c*x^2+c)^p,x)","F"
1014,0,0,88,0.329000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right) x \left(-a^{2} c \,x^{2}+c \right)^{p}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*c*x^2+c)^p,x)","F"
1015,0,0,74,0.327000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right) \left(-a^{2} c \,x^{2}+c \right)^{p}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p,x)","F"
1016,0,0,102,0.326000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x,x)","\int \frac{\left(a x +1\right) \left(-a^{2} c \,x^{2}+c \right)^{p}}{\sqrt{-a^{2} x^{2}+1}\, x}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x,x)","F"
1017,0,0,105,0.329000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x^2,x)","\int \frac{\left(a x +1\right) \left(-a^{2} c \,x^{2}+c \right)^{p}}{\sqrt{-a^{2} x^{2}+1}\, x^{2}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x^2,x)","F"
1018,0,0,108,0.330000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x^3,x)","\int \frac{\left(a x +1\right) \left(-a^{2} c \,x^{2}+c \right)^{p}}{\sqrt{-a^{2} x^{2}+1}\, x^{3}}\, dx"," ",0,"int((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x^3,x)","F"
1019,1,23,23,0.024000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^4*(-a^2*c*x^2+c),x)","c \left(\frac{1}{7} a^{2} x^{7}+\frac{1}{3} x^{6} a +\frac{1}{5} x^{5}\right)"," ",0,"c*(1/7*a^2*x^7+1/3*x^6*a+1/5*x^5)","A"
1020,1,23,23,0.025000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c),x)","c \left(\frac{1}{6} a^{2} x^{6}+\frac{2}{5} a \,x^{5}+\frac{1}{4} x^{4}\right)"," ",0,"c*(1/6*a^2*x^6+2/5*a*x^5+1/4*x^4)","A"
1021,1,23,23,0.026000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c),x)","c \left(\frac{1}{5} x^{5} a^{2}+\frac{1}{2} x^{4} a +\frac{1}{3} x^{3}\right)"," ",0,"c*(1/5*x^5*a^2+1/2*x^4*a+1/3*x^3)","A"
1022,1,23,23,0.025000," ","int((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c),x)","c \left(\frac{1}{4} a^{2} x^{4}+\frac{2}{3} x^{3} a +\frac{1}{2} x^{2}\right)"," ",0,"c*(1/4*a^2*x^4+2/3*x^3*a+1/2*x^2)","A"
1023,1,14,13,0.023000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c),x)","\frac{c \left(a x +1\right)^{3}}{3 a}"," ",0,"1/3*c*(a*x+1)^3/a","A"
1024,1,20,19,0.027000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x,x)","2 a c x +\frac{a^{2} c \,x^{2}}{2}+c \ln \left(x \right)"," ",0,"2*a*c*x+1/2*a^2*c*x^2+c*ln(x)","A"
1025,1,20,19,0.030000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x^2,x)","-\frac{c}{x}+a^{2} c x +2 a c \ln \left(x \right)"," ",0,"-c/x+a^2*c*x+2*a*c*ln(x)","A"
1026,1,22,21,0.030000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x^3,x)","-\frac{c}{2 x^{2}}-\frac{2 a c}{x}+a^{2} c \ln \left(x \right)"," ",0,"-1/2*c/x^2-2*a*c/x+a^2*c*ln(x)","A"
1027,1,23,13,0.030000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x^4,x)","c \left(-\frac{a^{2}}{x}-\frac{1}{3 x^{3}}-\frac{a}{x^{2}}\right)"," ",0,"c*(-a^2/x-1/3/x^3-a/x^2)","A"
1028,1,33,40,0.025000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^4*(-a^2*c*x^2+c)^2,x)","c^{2} \left(-\frac{1}{9} a^{4} x^{9}-\frac{1}{4} a^{3} x^{8}+\frac{1}{3} x^{6} a +\frac{1}{5} x^{5}\right)"," ",0,"c^2*(-1/9*a^4*x^9-1/4*a^3*x^8+1/3*x^6*a+1/5*x^5)","A"
1029,1,33,40,0.023000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^2,x)","c^{2} \left(-\frac{1}{8} a^{4} x^{8}-\frac{2}{7} a^{3} x^{7}+\frac{2}{5} a \,x^{5}+\frac{1}{4} x^{4}\right)"," ",0,"c^2*(-1/8*a^4*x^8-2/7*a^3*x^7+2/5*a*x^5+1/4*x^4)","A"
1030,1,33,40,0.030000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^2,x)","c^{2} \left(-\frac{1}{7} x^{7} a^{4}-\frac{1}{3} x^{6} a^{3}+\frac{1}{2} x^{4} a +\frac{1}{3} x^{3}\right)"," ",0,"c^2*(-1/7*x^7*a^4-1/3*x^6*a^3+1/2*x^4*a+1/3*x^3)","A"
1031,1,33,40,0.024000," ","int((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^2,x)","c^{2} \left(-\frac{1}{6} x^{6} a^{4}-\frac{2}{5} a^{3} x^{5}+\frac{2}{3} x^{3} a +\frac{1}{2} x^{2}\right)"," ",0,"c^2*(-1/6*x^6*a^4-2/5*a^3*x^5+2/3*x^3*a+1/2*x^2)","A"
1032,1,28,31,0.025000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2,x)","c^{2} \left(-\frac{1}{5} a^{4} x^{5}-\frac{1}{2} x^{4} a^{3}+a \,x^{2}+x \right)"," ",0,"c^2*(-1/5*a^4*x^5-1/2*x^4*a^3+a*x^2+x)","A"
1033,1,37,36,0.026000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x,x)","2 a \,c^{2} x -\frac{2 a^{3} c^{2} x^{3}}{3}-\frac{a^{4} c^{2} x^{4}}{4}+c^{2} \ln \left(x \right)"," ",0,"2*a*c^2*x-2/3*a^3*c^2*x^3-1/4*a^4*c^2*x^4+c^2*ln(x)","A"
1034,1,40,39,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^2,x)","-\frac{c^{2}}{x}-a^{3} c^{2} x^{2}-\frac{a^{4} c^{2} x^{3}}{3}+2 a \,c^{2} \ln \left(x \right)"," ",0,"-c^2/x-a^3*c^2*x^2-1/3*a^4*c^2*x^3+2*a*c^2*ln(x)","A"
1035,1,31,15,0.029000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^3,x)","c^{2} \left(-\frac{x^{2} a^{4}}{2}-2 a^{3} x -\frac{2 a}{x}-\frac{1}{2 x^{2}}\right)"," ",0,"c^2*(-1/2*x^2*a^4-2*a^3*x-2*a/x-1/2/x^2)","A"
1036,1,38,37,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^4,x)","-\frac{c^{2}}{3 x^{3}}-\frac{a \,c^{2}}{x^{2}}-a^{4} c^{2} x -2 a^{3} c^{2} \ln \left(x \right)"," ",0,"-1/3*c^2/x^3-a*c^2/x^2-a^4*c^2*x-2*a^3*c^2*ln(x)","A"
1037,1,40,39,0.031000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^5,x)","-\frac{c^{2}}{4 x^{4}}-\frac{2 a \,c^{2}}{3 x^{3}}+\frac{2 a^{3} c^{2}}{x}-a^{4} c^{2} \ln \left(x \right)"," ",0,"-1/4*c^2/x^4-2/3*a*c^2/x^3+2*a^3*c^2/x-a^4*c^2*ln(x)","A"
1038,1,31,38,0.030000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^6,x)","c^{2} \left(\frac{a^{4}}{x}+\frac{a^{3}}{x^{2}}-\frac{a}{2 x^{4}}-\frac{1}{5 x^{5}}\right)"," ",0,"c^2*(a^4/x+a^3/x^2-1/2*a/x^4-1/5/x^5)","A"
1039,1,57,73,0.023000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^4*(-a^2*c*x^2+c)^3,x)","c^{3} \left(\frac{1}{11} a^{6} x^{11}+\frac{1}{5} a^{5} x^{10}-\frac{1}{9} a^{4} x^{9}-\frac{1}{2} a^{3} x^{8}-\frac{1}{7} a^{2} x^{7}+\frac{1}{3} x^{6} a +\frac{1}{5} x^{5}\right)"," ",0,"c^3*(1/11*a^6*x^11+1/5*a^5*x^10-1/9*a^4*x^9-1/2*a^3*x^8-1/7*a^2*x^7+1/3*x^6*a+1/5*x^5)","A"
1040,1,57,73,0.024000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^3,x)","c^{3} \left(\frac{1}{10} a^{6} x^{10}+\frac{2}{9} a^{5} x^{9}-\frac{1}{8} a^{4} x^{8}-\frac{4}{7} a^{3} x^{7}-\frac{1}{6} a^{2} x^{6}+\frac{2}{5} a \,x^{5}+\frac{1}{4} x^{4}\right)"," ",0,"c^3*(1/10*a^6*x^10+2/9*a^5*x^9-1/8*a^4*x^8-4/7*a^3*x^7-1/6*a^2*x^6+2/5*a*x^5+1/4*x^4)","A"
1041,1,57,76,0.025000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^3,x)","c^{3} \left(\frac{1}{9} x^{9} a^{6}+\frac{1}{4} a^{5} x^{8}-\frac{1}{7} x^{7} a^{4}-\frac{2}{3} x^{6} a^{3}-\frac{1}{5} x^{5} a^{2}+\frac{1}{2} x^{4} a +\frac{1}{3} x^{3}\right)"," ",0,"c^3*(1/9*x^9*a^6+1/4*a^5*x^8-1/7*x^7*a^4-2/3*x^6*a^3-1/5*x^5*a^2+1/2*x^4*a+1/3*x^3)","A"
1042,1,57,61,0.026000," ","int((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^3,x)","c^{3} \left(\frac{1}{8} x^{8} a^{6}+\frac{2}{7} a^{5} x^{7}-\frac{1}{6} x^{6} a^{4}-\frac{4}{5} a^{3} x^{5}-\frac{1}{4} a^{2} x^{4}+\frac{2}{3} x^{3} a +\frac{1}{2} x^{2}\right)"," ",0,"c^3*(1/8*x^8*a^6+2/7*a^5*x^7-1/6*x^6*a^4-4/5*a^3*x^5-1/4*a^2*x^4+2/3*x^3*a+1/2*x^2)","A"
1043,1,52,46,0.026000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3,x)","c^{3} \left(\frac{1}{7} x^{7} a^{6}+\frac{1}{3} x^{6} a^{5}-\frac{1}{5} a^{4} x^{5}-x^{4} a^{3}-\frac{1}{3} x^{3} a^{2}+a \,x^{2}+x \right)"," ",0,"c^3*(1/7*x^7*a^6+1/3*x^6*a^5-1/5*a^4*x^5-x^4*a^3-1/3*x^3*a^2+a*x^2+x)","A"
1044,1,70,69,0.026000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x,x)","2 a \,c^{3} x -\frac{a^{2} c^{3} x^{2}}{2}-\frac{4 a^{3} c^{3} x^{3}}{3}-\frac{a^{4} c^{3} x^{4}}{4}+\frac{2 a^{5} c^{3} x^{5}}{5}+\frac{a^{6} c^{3} x^{6}}{6}+c^{3} \ln \left(x \right)"," ",0,"2*a*c^3*x-1/2*a^2*c^3*x^2-4/3*a^3*c^3*x^3-1/4*a^4*c^3*x^4+2/5*a^5*c^3*x^5+1/6*a^6*c^3*x^6+c^3*ln(x)","A"
1045,1,71,70,0.030000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x^2,x)","-\frac{c^{3}}{x}-a^{2} c^{3} x -2 a^{3} c^{3} x^{2}-\frac{a^{4} c^{3} x^{3}}{3}+\frac{a^{5} c^{3} x^{4}}{2}+\frac{a^{6} c^{3} x^{5}}{5}+2 a \,c^{3} \ln \left(x \right)"," ",0,"-c^3/x-a^2*c^3*x-2*a^3*c^3*x^2-1/3*a^4*c^3*x^3+1/2*a^5*c^3*x^4+1/5*a^6*c^3*x^5+2*a*c^3*ln(x)","A"
1046,1,71,70,0.034000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x^3,x)","-\frac{c^{3}}{2 x^{2}}-\frac{2 a \,c^{3}}{x}-4 a^{3} c^{3} x -\frac{a^{4} c^{3} x^{2}}{2}+\frac{2 a^{5} c^{3} x^{3}}{3}+\frac{a^{6} c^{3} x^{4}}{4}-a^{2} c^{3} \ln \left(x \right)"," ",0,"-1/2*c^3/x^2-2*a*c^3/x-4*a^3*c^3*x-1/2*a^4*c^3*x^2+2/3*a^5*c^3*x^3+1/4*a^6*c^3*x^4-a^2*c^3*ln(x)","A"
1047,1,69,68,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x^4,x)","-\frac{c^{3}}{3 x^{3}}-\frac{a \,c^{3}}{x^{2}}+\frac{a^{2} c^{3}}{x}-a^{4} c^{3} x +a^{5} c^{3} x^{2}+\frac{a^{6} c^{3} x^{3}}{3}-4 a^{3} c^{3} \ln \left(x \right)"," ",0,"-1/3*c^3/x^3-a*c^3/x^2+a^2*c^3/x-a^4*c^3*x+a^5*c^3*x^2+1/3*a^6*c^3*x^3-4*a^3*c^3*ln(x)","A"
1048,1,59,61,0.024000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^4,x)","c^{4} \left(-\frac{1}{9} x^{9} a^{8}-\frac{1}{4} a^{7} x^{8}+\frac{2}{7} x^{7} a^{6}+x^{6} a^{5}-\frac{3}{2} x^{4} a^{3}-\frac{2}{3} x^{3} a^{2}+a \,x^{2}+x \right)"," ",0,"c^4*(-1/9*x^9*a^8-1/4*a^7*x^8+2/7*x^7*a^6+x^6*a^5-3/2*x^4*a^3-2/3*x^3*a^2+a*x^2+x)","A"
1049,1,61,61,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^4/(-a^2*c*x^2+c),x)","\frac{x^{3}}{3 a^{2} c}+\frac{x^{2}}{a^{3} c}+\frac{3 x}{a^{4} c}-\frac{1}{c \,a^{5} \left(a x -1\right)}+\frac{4 \ln \left(a x -1\right)}{c \,a^{5}}"," ",0,"1/3*x^3/a^2/c+x^2/a^3/c+3*x/a^4/c-1/c/a^5/(a*x-1)+4/c/a^5*ln(a*x-1)","A"
1050,1,51,51,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c),x)","\frac{x^{2}}{2 a^{2} c}+\frac{2 x}{a^{3} c}-\frac{1}{c \,a^{4} \left(a x -1\right)}+\frac{3 \ln \left(a x -1\right)}{c \,a^{4}}"," ",0,"1/2*x^2/a^2/c+2*x/a^3/c-1/c/a^4/(a*x-1)+3/c/a^4*ln(a*x-1)","A"
1051,1,39,39,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c),x)","\frac{x}{a^{2} c}-\frac{1}{c \,a^{3} \left(a x -1\right)}+\frac{2 \ln \left(a x -1\right)}{c \,a^{3}}"," ",0,"x/a^2/c-1/c/a^3/(a*x-1)+2/c/a^3*ln(a*x-1)","A"
1052,1,30,30,0.031000," ","int((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c),x)","-\frac{1}{c \,a^{2} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{c \,a^{2}}"," ",0,"-1/c/a^2/(a*x-1)+1/c/a^2*ln(a*x-1)","A"
1053,1,16,15,0.025000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c),x)","-\frac{1}{c a \left(a x -1\right)}"," ",0,"-1/c/a/(a*x-1)","A"
1054,1,31,31,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c),x)","\frac{\ln \left(x \right)}{c}-\frac{1}{c \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{c}"," ",0,"ln(x)/c-1/c/(a*x-1)-1/c*ln(a*x-1)","A"
1055,1,43,43,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c),x)","-\frac{1}{c x}+\frac{2 a \ln \left(x \right)}{c}-\frac{a}{c \left(a x -1\right)}-\frac{2 a \ln \left(a x -1\right)}{c}"," ",0,"-1/c/x+2*a*ln(x)/c-1/c*a/(a*x-1)-2/c*a*ln(a*x-1)","A"
1056,1,58,58,0.035000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c),x)","-\frac{1}{2 c \,x^{2}}-\frac{2 a}{c x}+\frac{3 a^{2} \ln \left(x \right)}{c}-\frac{a^{2}}{c \left(a x -1\right)}-\frac{3 a^{2} \ln \left(a x -1\right)}{c}"," ",0,"-1/2/c/x^2-2*a/c/x+3*a^2*ln(x)/c-1/c*a^2/(a*x-1)-3/c*a^2*ln(a*x-1)","A"
1057,1,69,69,0.036000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^4/(-a^2*c*x^2+c),x)","-\frac{1}{3 c \,x^{3}}-\frac{a}{c \,x^{2}}-\frac{3 a^{2}}{c x}+\frac{4 a^{3} \ln \left(x \right)}{c}-\frac{a^{3}}{c \left(a x -1\right)}-\frac{4 a^{3} \ln \left(a x -1\right)}{c}"," ",0,"-1/3/c/x^3-a/c/x^2-3*a^2/c/x+4*a^3*ln(x)/c-1/c*a^3/(a*x-1)-4/c*a^3*ln(a*x-1)","A"
1058,1,69,71,0.035000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^4/(-a^2*c*x^2+c)^2,x)","-\frac{x}{a^{4} c^{2}}+\frac{7}{4 c^{2} a^{5} \left(a x -1\right)}-\frac{17 \ln \left(a x -1\right)}{8 c^{2} a^{5}}+\frac{1}{4 c^{2} a^{5} \left(a x -1\right)^{2}}+\frac{\ln \left(a x +1\right)}{8 a^{5} c^{2}}"," ",0,"-x/a^4/c^2+7/4/c^2/a^5/(a*x-1)-17/8/c^2/a^5*ln(a*x-1)+1/4/c^2/a^5/(a*x-1)^2+1/8*ln(a*x+1)/a^5/c^2","A"
1059,1,60,62,0.035000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^2,x)","\frac{1}{4 c^{2} a^{4} \left(a x -1\right)^{2}}+\frac{5}{4 c^{2} a^{4} \left(a x -1\right)}-\frac{7 \ln \left(a x -1\right)}{8 c^{2} a^{4}}-\frac{\ln \left(a x +1\right)}{8 a^{4} c^{2}}"," ",0,"1/4/c^2/a^4/(a*x-1)^2+5/4/c^2/a^4/(a*x-1)-7/8/c^2/a^4*ln(a*x-1)-1/8*ln(a*x+1)/a^4/c^2","A"
1060,1,60,45,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^2,x)","\frac{1}{4 c^{2} a^{3} \left(a x -1\right)^{2}}+\frac{3}{4 c^{2} a^{3} \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{8 c^{2} a^{3}}+\frac{\ln \left(a x +1\right)}{8 c^{2} a^{3}}"," ",0,"1/4/c^2/a^3/(a*x-1)^2+3/4/c^2/a^3/(a*x-1)-1/8/c^2/a^3*ln(a*x-1)+1/8/c^2/a^3*ln(a*x+1)","A"
1061,1,60,45,0.035000," ","int((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c)^2,x)","\frac{1}{4 c^{2} a^{2} \left(a x -1\right)^{2}}+\frac{1}{4 c^{2} a^{2} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{8 c^{2} a^{2}}-\frac{\ln \left(a x +1\right)}{8 c^{2} a^{2}}"," ",0,"1/4/c^2/a^2/(a*x-1)^2+1/4/c^2/a^2/(a*x-1)+1/8/c^2/a^2*ln(a*x-1)-1/8/c^2/a^2*ln(a*x+1)","A"
1062,1,60,45,0.036000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^2,x)","\frac{1}{4 c^{2} a \left(a x -1\right)^{2}}-\frac{1}{4 c^{2} a \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{8 c^{2} a}+\frac{\ln \left(a x +1\right)}{8 a \,c^{2}}"," ",0,"1/4/c^2/a/(a*x-1)^2-1/4/c^2/a/(a*x-1)-1/8/c^2/a*ln(a*x-1)+1/8*ln(a*x+1)/a/c^2","A"
1063,1,54,56,0.036000," ","int((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^2,x)","\frac{\ln \left(x \right)}{c^{2}}+\frac{1}{4 c^{2} \left(a x -1\right)^{2}}-\frac{3}{4 c^{2} \left(a x -1\right)}-\frac{7 \ln \left(a x -1\right)}{8 c^{2}}-\frac{\ln \left(a x +1\right)}{8 c^{2}}"," ",0,"ln(x)/c^2+1/4/c^2/(a*x-1)^2-3/4/c^2/(a*x-1)-7/8/c^2*ln(a*x-1)-1/8*ln(a*x+1)/c^2","A"
1064,1,68,70,0.036000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^2,x)","-\frac{1}{c^{2} x}+\frac{2 a \ln \left(x \right)}{c^{2}}+\frac{a}{4 c^{2} \left(a x -1\right)^{2}}-\frac{5 a}{4 c^{2} \left(a x -1\right)}-\frac{17 a \ln \left(a x -1\right)}{8 c^{2}}+\frac{a \ln \left(a x +1\right)}{8 c^{2}}"," ",0,"-1/c^2/x+2*a*ln(x)/c^2+1/4/c^2*a/(a*x-1)^2-5/4/c^2*a/(a*x-1)-17/8/c^2*a*ln(a*x-1)+1/8*a*ln(a*x+1)/c^2","A"
1065,1,87,89,0.036000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^2,x)","-\frac{1}{2 c^{2} x^{2}}-\frac{2 a}{c^{2} x}+\frac{4 a^{2} \ln \left(x \right)}{c^{2}}+\frac{a^{2}}{4 c^{2} \left(a x -1\right)^{2}}-\frac{7 a^{2}}{4 c^{2} \left(a x -1\right)}-\frac{31 a^{2} \ln \left(a x -1\right)}{8 c^{2}}-\frac{a^{2} \ln \left(a x +1\right)}{8 c^{2}}"," ",0,"-1/2/c^2/x^2-2*a/c^2/x+4*a^2*ln(x)/c^2+1/4/c^2*a^2/(a*x-1)^2-7/4/c^2*a^2/(a*x-1)-31/8/c^2*a^2*ln(a*x-1)-1/8*a^2*ln(a*x+1)/c^2","A"
1066,1,98,100,0.036000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^4/(-a^2*c*x^2+c)^2,x)","-\frac{1}{3 c^{2} x^{3}}-\frac{a}{c^{2} x^{2}}-\frac{4 a^{2}}{c^{2} x}+\frac{6 a^{3} \ln \left(x \right)}{c^{2}}+\frac{a^{3}}{4 c^{2} \left(a x -1\right)^{2}}-\frac{9 a^{3}}{4 c^{2} \left(a x -1\right)}-\frac{49 a^{3} \ln \left(a x -1\right)}{8 c^{2}}+\frac{a^{3} \ln \left(a x +1\right)}{8 c^{2}}"," ",0,"-1/3/c^2/x^3-a/c^2/x^2-4*a^2/c^2/x+6*a^3*ln(x)/c^2+1/4/c^2*a^3/(a*x-1)^2-9/4/c^2*a^3/(a*x-1)-49/8/c^2*a^3*ln(a*x-1)+1/8*a^3*ln(a*x+1)/c^2","A"
1067,1,90,93,0.037000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^5/(-a^2*c*x^2+c)^3,x)","-\frac{1}{2 c^{3} a^{6} \left(a x -1\right)^{2}}-\frac{1}{12 c^{3} a^{6} \left(a x -1\right)^{3}}-\frac{23}{16 c^{3} a^{6} \left(a x -1\right)}+\frac{13 \ln \left(a x -1\right)}{16 c^{3} a^{6}}+\frac{1}{16 a^{6} c^{3} \left(a x +1\right)}+\frac{3 \ln \left(a x +1\right)}{16 a^{6} c^{3}}"," ",0,"-1/2/c^3/a^6/(a*x-1)^2-1/12/c^3/a^6/(a*x-1)^3-23/16/c^3/a^6/(a*x-1)+13/16/c^3/a^6*ln(a*x-1)+1/16/a^6/c^3/(a*x+1)+3/16*ln(a*x+1)/a^6/c^3","A"
1068,1,90,76,0.035000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^4/(-a^2*c*x^2+c)^3,x)","-\frac{1}{12 c^{3} a^{5} \left(a x -1\right)^{3}}-\frac{3}{8 c^{3} a^{5} \left(a x -1\right)^{2}}-\frac{11}{16 c^{3} a^{5} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{8 c^{3} a^{5}}-\frac{1}{16 a^{5} c^{3} \left(a x +1\right)}-\frac{\ln \left(a x +1\right)}{8 c^{3} a^{5}}"," ",0,"-1/12/c^3/a^5/(a*x-1)^3-3/8/c^3/a^5/(a*x-1)^2-11/16/c^3/a^5/(a*x-1)+1/8/c^3/a^5*ln(a*x-1)-1/16/a^5/c^3/(a*x+1)-1/8/c^3/a^5*ln(a*x+1)","A"
1069,1,90,76,0.036000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^3,x)","-\frac{1}{12 c^{3} a^{4} \left(a x -1\right)^{3}}-\frac{1}{4 c^{3} a^{4} \left(a x -1\right)^{2}}-\frac{3}{16 c^{3} a^{4} \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{16 c^{3} a^{4}}+\frac{1}{16 a^{4} c^{3} \left(a x +1\right)}+\frac{\ln \left(a x +1\right)}{16 c^{3} a^{4}}"," ",0,"-1/12/c^3/a^4/(a*x-1)^3-1/4/c^3/a^4/(a*x-1)^2-3/16/c^3/a^4/(a*x-1)-1/16/c^3/a^4*ln(a*x-1)+1/16/a^4/c^3/(a*x+1)+1/16/c^3/a^4*ln(a*x+1)","A"
1070,1,54,29,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^3,x)","\frac{-\frac{1}{12 a^{3} \left(a x -1\right)^{3}}-\frac{1}{8 a^{3} \left(a x -1\right)^{2}}+\frac{1}{16 a^{3} \left(a x -1\right)}-\frac{1}{16 a^{3} \left(a x +1\right)}}{c^{3}}"," ",0,"1/c^3*(-1/12/a^3/(a*x-1)^3-1/8/a^3/(a*x-1)^2+1/16/a^3/(a*x-1)-1/16/a^3/(a*x+1))","A"
1071,1,75,60,0.037000," ","int((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c)^3,x)","-\frac{1}{12 c^{3} a^{2} \left(a x -1\right)^{3}}+\frac{1}{16 c^{3} a^{2} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{16 c^{3} a^{2}}+\frac{1}{16 a^{2} c^{3} \left(a x +1\right)}-\frac{\ln \left(a x +1\right)}{16 c^{3} a^{2}}"," ",0,"-1/12/c^3/a^2/(a*x-1)^3+1/16/c^3/a^2/(a*x-1)+1/16/c^3/a^2*ln(a*x-1)+1/16/a^2/c^3/(a*x+1)-1/16/c^3/a^2*ln(a*x+1)","A"
1072,1,90,76,0.038000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^3,x)","-\frac{1}{12 c^{3} a \left(a x -1\right)^{3}}+\frac{1}{8 c^{3} a \left(a x -1\right)^{2}}-\frac{3}{16 c^{3} a \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{8 a \,c^{3}}-\frac{1}{16 a \,c^{3} \left(a x +1\right)}+\frac{\ln \left(a x +1\right)}{8 a \,c^{3}}"," ",0,"-1/12/c^3/a/(a*x-1)^3+1/8/c^3/a/(a*x-1)^2-3/16/c^3/a/(a*x-1)-1/8/a/c^3*ln(a*x-1)-1/16/a/c^3/(a*x+1)+1/8*ln(a*x+1)/a/c^3","A"
1073,1,78,81,0.038000," ","int((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^3,x)","\frac{\ln \left(x \right)}{c^{3}}-\frac{1}{12 c^{3} \left(a x -1\right)^{3}}+\frac{1}{4 c^{3} \left(a x -1\right)^{2}}-\frac{11}{16 c^{3} \left(a x -1\right)}-\frac{13 \ln \left(a x -1\right)}{16 c^{3}}+\frac{1}{16 c^{3} \left(a x +1\right)}-\frac{3 \ln \left(a x +1\right)}{16 c^{3}}"," ",0,"ln(x)/c^3-1/12/c^3/(a*x-1)^3+1/4/c^3/(a*x-1)^2-11/16/c^3/(a*x-1)-13/16/c^3*ln(a*x-1)+1/16/c^3/(a*x+1)-3/16*ln(a*x+1)/c^3","A"
1074,1,94,97,0.039000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^3,x)","-\frac{1}{c^{3} x}+\frac{2 a \ln \left(x \right)}{c^{3}}-\frac{a}{12 c^{3} \left(a x -1\right)^{3}}+\frac{3 a}{8 c^{3} \left(a x -1\right)^{2}}-\frac{23 a}{16 c^{3} \left(a x -1\right)}-\frac{9 a \ln \left(a x -1\right)}{4 c^{3}}-\frac{a}{16 c^{3} \left(a x +1\right)}+\frac{a \ln \left(a x +1\right)}{4 c^{3}}"," ",0,"-1/c^3/x+2*a*ln(x)/c^3-1/12/c^3*a/(a*x-1)^3+3/8/c^3*a/(a*x-1)^2-23/16/c^3*a/(a*x-1)-9/4/c^3*a*ln(a*x-1)-1/16*a/c^3/(a*x+1)+1/4*a*ln(a*x+1)/c^3","A"
1075,1,117,120,0.040000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^3,x)","-\frac{1}{2 c^{3} x^{2}}-\frac{2 a}{c^{3} x}+\frac{5 a^{2} \ln \left(x \right)}{c^{3}}-\frac{a^{2}}{12 c^{3} \left(a x -1\right)^{3}}+\frac{a^{2}}{2 c^{3} \left(a x -1\right)^{2}}-\frac{39 a^{2}}{16 c^{3} \left(a x -1\right)}-\frac{75 a^{2} \ln \left(a x -1\right)}{16 c^{3}}+\frac{a^{2}}{16 c^{3} \left(a x +1\right)}-\frac{5 a^{2} \ln \left(a x +1\right)}{16 c^{3}}"," ",0,"-1/2/c^3/x^2-2*a/c^3/x+5*a^2*ln(x)/c^3-1/12/c^3*a^2/(a*x-1)^3+1/2/c^3*a^2/(a*x-1)^2-39/16/c^3*a^2/(a*x-1)-75/16/c^3*a^2*ln(a*x-1)+1/16*a^2/c^3/(a*x+1)-5/16*a^2*ln(a*x+1)/c^3","A"
1076,1,120,107,0.037000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^4,x)","\frac{1}{32 c^{4} a \left(a x -1\right)^{4}}-\frac{1}{16 c^{4} a \left(a x -1\right)^{3}}+\frac{3}{32 c^{4} a \left(a x -1\right)^{2}}-\frac{5}{32 c^{4} a \left(a x -1\right)}-\frac{15 \ln \left(a x -1\right)}{128 c^{4} a}-\frac{1}{64 a \,c^{4} \left(a x +1\right)^{2}}-\frac{5}{64 a \,c^{4} \left(a x +1\right)}+\frac{15 \ln \left(a x +1\right)}{128 a \,c^{4}}"," ",0,"1/32/c^4/a/(a*x-1)^4-1/16/c^4/a/(a*x-1)^3+3/32/c^4/a/(a*x-1)^2-5/32/c^4/a/(a*x-1)-15/128/c^4/a*ln(a*x-1)-1/64/a/c^4/(a*x+1)^2-5/64/a/c^4/(a*x+1)+15/128*ln(a*x+1)/a/c^4","A"
1077,1,210,113,0.045000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^(1/2),x)","\frac{x^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{5 a^{2} c}+\frac{4 \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{5 c \,a^{4}}+\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{2 a^{3} c}-\frac{5 x \sqrt{-a^{2} c \,x^{2}+c}}{4 a^{3}}-\frac{5 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{4 a^{3} \sqrt{a^{2} c}}-\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a^{4}}+\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{a^{3} \sqrt{a^{2} c}}"," ",0,"1/5*x^2*(-a^2*c*x^2+c)^(3/2)/a^2/c+4/5/c/a^4*(-a^2*c*x^2+c)^(3/2)+1/2/a^3*x*(-a^2*c*x^2+c)^(3/2)/c-5/4/a^3*x*(-a^2*c*x^2+c)^(1/2)-5/4/a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a^4*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+2/a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","A"
1078,1,186,92,0.040000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^(1/2),x)","\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4 a^{2} c}-\frac{9 x \sqrt{-a^{2} c \,x^{2}+c}}{8 a^{2}}-\frac{9 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{8 a^{2} \sqrt{a^{2} c}}+\frac{2 \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 a^{3} c}-\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a^{3}}+\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{a^{2} \sqrt{a^{2} c}}"," ",0,"1/4*x*(-a^2*c*x^2+c)^(3/2)/a^2/c-9/8/a^2*x*(-a^2*c*x^2+c)^(1/2)-9/8/a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/3/a^3*(-a^2*c*x^2+c)^(3/2)/c-2/a^3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+2/a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1079,1,164,70,0.040000," ","int((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^(1/2),x)","\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 a^{2} c}-\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{a}-\frac{c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{a \sqrt{a^{2} c}}-\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a^{2}}+\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{a \sqrt{a^{2} c}}"," ",0,"1/3*(-a^2*c*x^2+c)^(3/2)/a^2/c-x/a*(-a^2*c*x^2+c)^(1/2)-1/a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+2/a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1080,1,134,70,0.037000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2),x)","-\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{2}-\frac{c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{2 \sqrt{a^{2} c}}-\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a}+\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"-1/2*x*(-a^2*c*x^2+c)^(1/2)-1/2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","A"
1081,1,128,64,0.041000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2)/x,x)","\sqrt{-a^{2} c \,x^{2}+c}-\sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)-2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}+\frac{2 a c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"(-a^2*c*x^2+c)^(1/2)-c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+2*a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","A"
1082,1,211,68,0.046000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2)/x^2,x)","-2 \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a +2 \sqrt{-a^{2} c \,x^{2}+c}\, a -\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}-a^{2} x \sqrt{-a^{2} c \,x^{2}+c}-\frac{a^{2} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-2 a \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}+\frac{2 a^{2} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"-2*c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a+2*(-a^2*c*x^2+c)^(1/2)*a-1/c/x*(-a^2*c*x^2+c)^(3/2)-a^2*x*(-a^2*c*x^2+c)^(1/2)-a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2*a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+2*a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1083,1,239,64,0.045000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2)/x^3,x)","-\frac{3 \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a^{2}}{2}+\frac{3 \sqrt{-a^{2} c \,x^{2}+c}\, a^{2}}{2}-\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}-2 a^{3} x \sqrt{-a^{2} c \,x^{2}+c}-\frac{2 a^{3} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-2 a^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}+\frac{2 a^{3} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{2 c \,x^{2}}"," ",0,"-3/2*c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a^2+3/2*(-a^2*c*x^2+c)^(1/2)*a^2-2*a/c/x*(-a^2*c*x^2+c)^(3/2)-2*a^3*x*(-a^2*c*x^2+c)^(1/2)-2*a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2*a^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+2*a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-1/2/c/x^2*(-a^2*c*x^2+c)^(3/2)","B"
1084,1,262,85,0.050000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2)/x^4,x)","-\sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a^{3}+\sqrt{-a^{2} c \,x^{2}+c}\, a^{3}-\frac{2 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}-2 a^{4} x \sqrt{-a^{2} c \,x^{2}+c}-\frac{2 a^{4} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 c \,x^{3}}-2 a^{3} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}+\frac{2 a^{4} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}-\frac{a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c \,x^{2}}"," ",0,"-c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a^3+(-a^2*c*x^2+c)^(1/2)*a^3-2*a^2/c/x*(-a^2*c*x^2+c)^(3/2)-2*a^4*x*(-a^2*c*x^2+c)^(1/2)-2*a^4*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-1/3/c/x^3*(-a^2*c*x^2+c)^(3/2)-2*a^3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+2*a^4*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-a/c/x^2*(-a^2*c*x^2+c)^(3/2)","B"
1085,1,287,106,0.053000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2)/x^5,x)","-\frac{7 \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a^{4}}{8}+\frac{7 \sqrt{-a^{2} c \,x^{2}+c}\, a^{4}}{8}-\frac{2 a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}-2 a^{5} x \sqrt{-a^{2} c \,x^{2}+c}-\frac{2 a^{5} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 c \,x^{3}}-2 a^{4} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}+\frac{2 a^{5} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}-\frac{9 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{8 c \,x^{2}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4 c \,x^{4}}"," ",0,"-7/8*c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a^4+7/8*(-a^2*c*x^2+c)^(1/2)*a^4-2*a^3/c/x*(-a^2*c*x^2+c)^(3/2)-2*a^5*x*(-a^2*c*x^2+c)^(1/2)-2*a^5*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3*a/c/x^3*(-a^2*c*x^2+c)^(3/2)-2*a^4*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+2*a^5*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-9/8*a^2/c/x^2*(-a^2*c*x^2+c)^(3/2)-1/4/c/x^4*(-a^2*c*x^2+c)^(3/2)","B"
1086,1,268,133,0.046000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^(3/2),x)","\frac{x^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{7 a^{2} c}+\frac{16 \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{35 c \,a^{4}}+\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 a^{3} c}-\frac{7 x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{12 a^{3}}-\frac{7 c x \sqrt{-a^{2} c \,x^{2}+c}}{8 a^{3}}-\frac{7 c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{8 a^{3} \sqrt{a^{2} c}}-\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a^{4}}+\frac{c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{a^{3}}+\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{a^{3} \sqrt{a^{2} c}}"," ",0,"1/7*x^2*(-a^2*c*x^2+c)^(5/2)/a^2/c+16/35/c/a^4*(-a^2*c*x^2+c)^(5/2)+1/3/a^3*x*(-a^2*c*x^2+c)^(5/2)/c-7/12/a^3*x*(-a^2*c*x^2+c)^(3/2)-7/8*c*x*(-a^2*c*x^2+c)^(1/2)/a^3-7/8/a^3*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3/a^4*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)+1/a^3*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+1/a^3*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1087,1,244,112,0.041000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^(3/2),x)","\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{6 a^{2} c}-\frac{13 x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{24 a^{2}}-\frac{13 c x \sqrt{-a^{2} c \,x^{2}+c}}{16 a^{2}}-\frac{13 c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{16 a^{2} \sqrt{a^{2} c}}+\frac{2 \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{5 a^{3} c}-\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a^{3}}+\frac{c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{a^{2}}+\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{a^{2} \sqrt{a^{2} c}}"," ",0,"1/6*x*(-a^2*c*x^2+c)^(5/2)/a^2/c-13/24/a^2*x*(-a^2*c*x^2+c)^(3/2)-13/16*c*x*(-a^2*c*x^2+c)^(1/2)/a^2-13/16/a^2*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/5/a^3*(-a^2*c*x^2+c)^(5/2)/c-2/3/a^3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)+1/a^2*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+1/a^2*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1088,1,222,91,0.037000," ","int((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^(3/2),x)","\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{5 a^{2} c}-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{2 a}-\frac{3 c x \sqrt{-a^{2} c \,x^{2}+c}}{4 a}-\frac{3 c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{4 a \sqrt{a^{2} c}}-\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a^{2}}+\frac{c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{a}+\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{a \sqrt{a^{2} c}}"," ",0,"1/5*(-a^2*c*x^2+c)^(5/2)/a^2/c-1/2*x/a*(-a^2*c*x^2+c)^(3/2)-3/4*c*x*(-a^2*c*x^2+c)^(1/2)/a-3/4/a*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3/a^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)+1/a*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+1/a*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1089,1,186,87,0.036000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2),x)","-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4}-\frac{3 c x \sqrt{-a^{2} c \,x^{2}+c}}{8}-\frac{3 c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{8 \sqrt{a^{2} c}}-\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a}+c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x +\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"-1/4*x*(-a^2*c*x^2+c)^(3/2)-3/8*c*x*(-a^2*c*x^2+c)^(1/2)-3/8*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3/a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)+c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1090,1,179,83,0.043000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x,x)","\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3}-c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)+\sqrt{-a^{2} c \,x^{2}+c}\, c -\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3}+a c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x +\frac{a \,c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"1/3*(-a^2*c*x^2+c)^(3/2)-c^(3/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)+(-a^2*c*x^2+c)^(1/2)*c-2/3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)+a*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+a*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1091,1,286,92,0.045000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^2,x)","\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3}-2 a \,c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)+2 a \sqrt{-a^{2} c \,x^{2}+c}\, c -\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{c x}-a^{2} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}-\frac{3 a^{2} c x \sqrt{-a^{2} c \,x^{2}+c}}{2}-\frac{3 a^{2} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{2 \sqrt{a^{2} c}}-\frac{2 a \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3}+a^{2} c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x +\frac{a^{2} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"2/3*a*(-a^2*c*x^2+c)^(3/2)-2*a*c^(3/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)+2*a*(-a^2*c*x^2+c)^(1/2)*c-1/c/x*(-a^2*c*x^2+c)^(5/2)-a^2*x*(-a^2*c*x^2+c)^(3/2)-3/2*a^2*c*x*(-a^2*c*x^2+c)^(1/2)-3/2*a^2*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3*a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)+a^2*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+a^2*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1092,1,316,99,0.046000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^3,x)","\frac{a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{6}-\frac{a^{2} c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{2}+\frac{a^{2} \sqrt{-a^{2} c \,x^{2}+c}\, c}{2}-\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{c x}-2 a^{3} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}-3 a^{3} c x \sqrt{-a^{2} c \,x^{2}+c}-\frac{3 a^{3} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{2 a^{2} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3}+a^{3} c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x +\frac{a^{3} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{2 c \,x^{2}}"," ",0,"1/6*a^2*(-a^2*c*x^2+c)^(3/2)-1/2*a^2*c^(3/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)+1/2*a^2*(-a^2*c*x^2+c)^(1/2)*c-2*a/c/x*(-a^2*c*x^2+c)^(5/2)-2*a^3*x*(-a^2*c*x^2+c)^(3/2)-3*a^3*c*x*(-a^2*c*x^2+c)^(1/2)-3*a^3*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3*a^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)+a^3*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+a^3*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-1/2/c/x^2*(-a^2*c*x^2+c)^(5/2)","B"
1093,1,339,97,0.051000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^4,x)","-\frac{a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3}+a^{3} c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)-a^{3} \sqrt{-a^{2} c \,x^{2}+c}\, c -\frac{4 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 c x}-\frac{4 a^{4} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3}-2 a^{4} c x \sqrt{-a^{2} c \,x^{2}+c}-\frac{2 a^{4} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 c \,x^{3}}-\frac{2 a^{3} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3}+a^{4} c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x +\frac{a^{4} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}-\frac{a \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{c \,x^{2}}"," ",0,"-1/3*a^3*(-a^2*c*x^2+c)^(3/2)+a^3*c^(3/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-a^3*(-a^2*c*x^2+c)^(1/2)*c-4/3*a^2/c/x*(-a^2*c*x^2+c)^(5/2)-4/3*a^4*x*(-a^2*c*x^2+c)^(3/2)-2*a^4*c*x*(-a^2*c*x^2+c)^(1/2)-2*a^4*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-1/3/c/x^3*(-a^2*c*x^2+c)^(5/2)-2/3*a^3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)+a^4*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+a^4*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-a/c/x^2*(-a^2*c*x^2+c)^(5/2)","B"
1094,1,364,86,0.059000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^5,x)","-\frac{5 a^{4} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{24}+\frac{5 a^{4} c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{8}-\frac{5 a^{4} \sqrt{-a^{2} c \,x^{2}+c}\, c}{8}-\frac{2 a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 c x}-\frac{2 a^{5} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3}-a^{5} c x \sqrt{-a^{2} c \,x^{2}+c}-\frac{a^{5} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 c \,x^{3}}-\frac{2 a^{4} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3}+a^{5} c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x +\frac{a^{5} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}-\frac{7 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{8 c \,x^{2}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{4 c \,x^{4}}"," ",0,"-5/24*a^4*(-a^2*c*x^2+c)^(3/2)+5/8*a^4*c^(3/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-5/8*a^4*(-a^2*c*x^2+c)^(1/2)*c-2/3*a^3/c/x*(-a^2*c*x^2+c)^(5/2)-2/3*a^5*x*(-a^2*c*x^2+c)^(3/2)-a^5*c*x*(-a^2*c*x^2+c)^(1/2)-a^5*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3*a/c/x^3*(-a^2*c*x^2+c)^(5/2)-2/3*a^4*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)+a^5*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+a^5*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-7/8*a^2/c/x^2*(-a^2*c*x^2+c)^(5/2)-1/4/c/x^4*(-a^2*c*x^2+c)^(5/2)","B"
1095,1,388,107,0.067000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^6,x)","-\frac{2 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 c \,x^{3}}-\frac{2 a^{4} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 c x}-a^{6} c x \sqrt{-a^{2} c \,x^{2}+c}-\frac{a^{6} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}+a^{6} c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x +\frac{a^{6} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}-\frac{3 a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{4 c \,x^{2}}-\frac{2 a^{5} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3}-\frac{a^{5} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{12}-\frac{a \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{2 c \,x^{4}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{5 c \,x^{5}}+\frac{a^{5} c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{4}-\frac{a^{5} \sqrt{-a^{2} c \,x^{2}+c}\, c}{4}-\frac{2 a^{6} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3}"," ",0,"-2/3*a^2/c/x^3*(-a^2*c*x^2+c)^(5/2)-2/3*a^4/c/x*(-a^2*c*x^2+c)^(5/2)-a^6*c*x*(-a^2*c*x^2+c)^(1/2)-a^6*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+a^6*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+a^6*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-3/4*a^3/c/x^2*(-a^2*c*x^2+c)^(5/2)-2/3*a^5*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)-1/12*a^5*(-a^2*c*x^2+c)^(3/2)-1/2*a/c/x^4*(-a^2*c*x^2+c)^(5/2)-1/5/c/x^5*(-a^2*c*x^2+c)^(5/2)+1/4*a^5*c^(3/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-1/4*a^5*(-a^2*c*x^2+c)^(1/2)*c-2/3*a^6*x*(-a^2*c*x^2+c)^(3/2)","B"
1096,1,412,128,0.079000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^7,x)","-\frac{a^{6} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{16}+a^{7} c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x +\frac{a^{7} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}-\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{5 c \,x^{5}}-\frac{2 a^{5} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 c x}-a^{7} c x \sqrt{-a^{2} c \,x^{2}+c}-\frac{a^{7} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{13 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{24 c \,x^{4}}-\frac{35 a^{4} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{48 c \,x^{2}}-\frac{2 a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 c \,x^{3}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{6 c \,x^{6}}+\frac{3 a^{6} c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{16}-\frac{3 a^{6} \sqrt{-a^{2} c \,x^{2}+c}\, c}{16}-\frac{2 a^{7} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3}-\frac{2 a^{6} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3}"," ",0,"-1/16*a^6*(-a^2*c*x^2+c)^(3/2)+a^7*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+a^7*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-2/5*a/c/x^5*(-a^2*c*x^2+c)^(5/2)-2/3*a^5/c/x*(-a^2*c*x^2+c)^(5/2)-a^7*c*x*(-a^2*c*x^2+c)^(1/2)-a^7*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-13/24*a^2/c/x^4*(-a^2*c*x^2+c)^(5/2)-35/48*a^4/c/x^2*(-a^2*c*x^2+c)^(5/2)-2/3*a^3/c/x^3*(-a^2*c*x^2+c)^(5/2)-1/6/c/x^6*(-a^2*c*x^2+c)^(5/2)+3/16*a^6*c^(3/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-3/16*a^6*(-a^2*c*x^2+c)^(1/2)*c-2/3*a^7*x*(-a^2*c*x^2+c)^(3/2)-2/3*a^6*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)","B"
1097,1,436,149,0.099000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^8,x)","-\frac{a \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 c \,x^{6}}-\frac{7 a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{12 c \,x^{4}}-\frac{17 a^{5} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{24 c \,x^{2}}-\frac{2 a^{8} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3}-a^{8} c x \sqrt{-a^{2} c \,x^{2}+c}-\frac{a^{8} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{2 a^{4} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 c \,x^{3}}-\frac{16 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{35 c \,x^{5}}+\frac{a^{7} c^{\frac{3}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{8}-\frac{a^{7} \sqrt{-a^{2} c \,x^{2}+c}\, c}{8}+a^{8} c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x +\frac{a^{8} c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{7 c \,x^{7}}-\frac{2 a^{6} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 c x}-\frac{2 a^{7} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3}-\frac{a^{7} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{24}"," ",0,"-1/3*a/c/x^6*(-a^2*c*x^2+c)^(5/2)-7/12*a^3/c/x^4*(-a^2*c*x^2+c)^(5/2)-17/24*a^5/c/x^2*(-a^2*c*x^2+c)^(5/2)-2/3*a^8*x*(-a^2*c*x^2+c)^(3/2)-a^8*c*x*(-a^2*c*x^2+c)^(1/2)-a^8*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3*a^4/c/x^3*(-a^2*c*x^2+c)^(5/2)-16/35*a^2/c/x^5*(-a^2*c*x^2+c)^(5/2)+1/8*a^7*c^(3/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-1/8*a^7*(-a^2*c*x^2+c)^(1/2)*c+a^8*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+a^8*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-1/7/c/x^7*(-a^2*c*x^2+c)^(5/2)-2/3*a^6/c/x*(-a^2*c*x^2+c)^(5/2)-2/3*a^7*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)-1/24*a^7*(-a^2*c*x^2+c)^(3/2)","B"
1098,1,330,155,0.048000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^(5/2),x)","\frac{x^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{9 a^{2} c}+\frac{20 \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{63 c \,a^{4}}+\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{4 a^{3} c}-\frac{3 x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{8 a^{3}}-\frac{15 c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{32 a^{3}}-\frac{45 c^{2} x \sqrt{-a^{2} c \,x^{2}+c}}{64 a^{3}}-\frac{45 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{64 a^{3} \sqrt{a^{2} c}}-\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{5 a^{4}}+\frac{c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{2 a^{3}}+\frac{3 c^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{4 a^{3}}+\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{4 a^{3} \sqrt{a^{2} c}}"," ",0,"1/9*x^2*(-a^2*c*x^2+c)^(7/2)/a^2/c+20/63/c/a^4*(-a^2*c*x^2+c)^(7/2)+1/4/a^3*x*(-a^2*c*x^2+c)^(7/2)/c-3/8/a^3*x*(-a^2*c*x^2+c)^(5/2)-15/32*c*x*(-a^2*c*x^2+c)^(3/2)/a^3-45/64*c^2*x*(-a^2*c*x^2+c)^(1/2)/a^3-45/64/a^3*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/5/a^4*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)+1/2/a^3*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x+3/4/a^3*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+3/4/a^3*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1099,1,306,134,0.042000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^(5/2),x)","\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{8 a^{2} c}-\frac{17 x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{48 a^{2}}-\frac{85 c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{192 a^{2}}-\frac{85 c^{2} x \sqrt{-a^{2} c \,x^{2}+c}}{128 a^{2}}-\frac{85 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{128 a^{2} \sqrt{a^{2} c}}+\frac{2 \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{7 a^{3} c}-\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{5 a^{3}}+\frac{c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{2 a^{2}}+\frac{3 c^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{4 a^{2}}+\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{4 a^{2} \sqrt{a^{2} c}}"," ",0,"1/8*x*(-a^2*c*x^2+c)^(7/2)/a^2/c-17/48/a^2*x*(-a^2*c*x^2+c)^(5/2)-85/192*c*x*(-a^2*c*x^2+c)^(3/2)/a^2-85/128*c^2*x*(-a^2*c*x^2+c)^(1/2)/a^2-85/128/a^2*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/7/a^3*(-a^2*c*x^2+c)^(7/2)/c-2/5/a^3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)+1/2/a^2*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x+3/4/a^2*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+3/4/a^2*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1100,1,284,113,0.040000," ","int((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^(5/2),x)","\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{7 a^{2} c}-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3 a}-\frac{5 c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{12 a}-\frac{5 c^{2} x \sqrt{-a^{2} c \,x^{2}+c}}{8 a}-\frac{5 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{8 a \sqrt{a^{2} c}}-\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{5 a^{2}}+\frac{c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{2 a}+\frac{3 c^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{4 a}+\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{4 a \sqrt{a^{2} c}}"," ",0,"1/7*(-a^2*c*x^2+c)^(7/2)/a^2/c-1/3*x/a*(-a^2*c*x^2+c)^(5/2)-5/12*c*x*(-a^2*c*x^2+c)^(3/2)/a-5/8*c^2*x*(-a^2*c*x^2+c)^(1/2)/a-5/8/a*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/5/a^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)+1/2/a*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x+3/4/a*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+3/4/a*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1101,1,242,106,0.037000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2),x)","-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{6}-\frac{5 c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{24}-\frac{5 c^{2} x \sqrt{-a^{2} c \,x^{2}+c}}{16}-\frac{5 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{16 \sqrt{a^{2} c}}-\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{5 a}+\frac{c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{2}+\frac{3 c^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{4}+\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{4 \sqrt{a^{2} c}}"," ",0,"-1/6*x*(-a^2*c*x^2+c)^(5/2)-5/24*c*x*(-a^2*c*x^2+c)^(3/2)-5/16*c^2*x*(-a^2*c*x^2+c)^(1/2)-5/16*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/5/a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)+1/2*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x+3/4*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+3/4*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1102,1,235,110,0.043000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x,x)","\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{5}+\frac{c \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3}-c^{\frac{5}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)+\sqrt{-a^{2} c \,x^{2}+c}\, c^{2}-\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{5}+\frac{a c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{2}+\frac{3 a \,c^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{4}+\frac{3 a \,c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{4 \sqrt{a^{2} c}}"," ",0,"1/5*(-a^2*c*x^2+c)^(5/2)+1/3*c*(-a^2*c*x^2+c)^(3/2)-c^(5/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)+(-a^2*c*x^2+c)^(1/2)*c^2-2/5*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)+1/2*a*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x+3/4*a*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+3/4*a*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1103,1,367,117,0.045000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^2,x)","\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{5}+\frac{2 a c \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3}-2 a \,c^{\frac{5}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)+2 a \sqrt{-a^{2} c \,x^{2}+c}\, c^{2}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{c x}-a^{2} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}-\frac{5 a^{2} c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4}-\frac{15 a^{2} c^{2} x \sqrt{-a^{2} c \,x^{2}+c}}{8}-\frac{15 a^{2} c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{8 \sqrt{a^{2} c}}-\frac{2 a \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{5}+\frac{a^{2} c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{2}+\frac{3 a^{2} c^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{4}+\frac{3 a^{2} c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{4 \sqrt{a^{2} c}}"," ",0,"2/5*a*(-a^2*c*x^2+c)^(5/2)+2/3*a*c*(-a^2*c*x^2+c)^(3/2)-2*a*c^(5/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)+2*a*(-a^2*c*x^2+c)^(1/2)*c^2-1/c/x*(-a^2*c*x^2+c)^(7/2)-a^2*x*(-a^2*c*x^2+c)^(5/2)-5/4*a^2*c*x*(-a^2*c*x^2+c)^(3/2)-15/8*a^2*c^2*x*(-a^2*c*x^2+c)^(1/2)-15/8*a^2*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/5*a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)+1/2*a^2*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x+3/4*a^2*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+3/4*a^2*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1104,1,399,125,0.049000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^3,x)","-\frac{a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{10}-\frac{a^{2} c \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{6}+\frac{a^{2} c^{\frac{5}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{2}-\frac{a^{2} \sqrt{-a^{2} c \,x^{2}+c}\, c^{2}}{2}-\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{c x}-2 a^{3} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}-\frac{5 a^{3} c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{2}-\frac{15 a^{3} c^{2} x \sqrt{-a^{2} c \,x^{2}+c}}{4}-\frac{15 a^{3} c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{4 \sqrt{a^{2} c}}-\frac{2 a^{2} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{5}+\frac{a^{3} c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{2}+\frac{3 a^{3} c^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{4}+\frac{3 a^{3} c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{4 \sqrt{a^{2} c}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{2 c \,x^{2}}"," ",0,"-1/10*a^2*(-a^2*c*x^2+c)^(5/2)-1/6*a^2*c*(-a^2*c*x^2+c)^(3/2)+1/2*a^2*c^(5/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-1/2*a^2*(-a^2*c*x^2+c)^(1/2)*c^2-2*a/c/x*(-a^2*c*x^2+c)^(7/2)-2*a^3*x*(-a^2*c*x^2+c)^(5/2)-5/2*a^3*c*x*(-a^2*c*x^2+c)^(3/2)-15/4*a^3*c^2*x*(-a^2*c*x^2+c)^(1/2)-15/4*a^3*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/5*a^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)+1/2*a^3*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x+3/4*a^3*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+3/4*a^3*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-1/2/c/x^2*(-a^2*c*x^2+c)^(7/2)","B"
1105,1,423,129,0.054000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^4,x)","-\frac{3 a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{5}-a^{3} c \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}+3 a^{3} c^{\frac{5}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)-3 a^{3} \sqrt{-a^{2} c \,x^{2}+c}\, c^{2}-\frac{2 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{3 c x}-\frac{2 a^{4} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3}-\frac{5 a^{4} c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{6}-\frac{5 a^{4} c^{2} x \sqrt{-a^{2} c \,x^{2}+c}}{4}-\frac{5 a^{4} c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{4 \sqrt{a^{2} c}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{3 c \,x^{3}}-\frac{2 a^{3} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{5}+\frac{a^{4} c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{2}+\frac{3 a^{4} c^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{4}+\frac{3 a^{4} c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{4 \sqrt{a^{2} c}}-\frac{a \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{c \,x^{2}}"," ",0,"-3/5*a^3*(-a^2*c*x^2+c)^(5/2)-a^3*c*(-a^2*c*x^2+c)^(3/2)+3*a^3*c^(5/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-3*a^3*(-a^2*c*x^2+c)^(1/2)*c^2-2/3*a^2/c/x*(-a^2*c*x^2+c)^(7/2)-2/3*a^4*x*(-a^2*c*x^2+c)^(5/2)-5/6*a^4*c*x*(-a^2*c*x^2+c)^(3/2)-5/4*a^4*c^2*x*(-a^2*c*x^2+c)^(1/2)-5/4*a^4*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-1/3/c/x^3*(-a^2*c*x^2+c)^(7/2)-2/5*a^3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)+1/2*a^4*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x+3/4*a^4*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+3/4*a^4*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-a/c/x^2*(-a^2*c*x^2+c)^(7/2)","B"
1106,1,447,129,0.060000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^5,x)","\frac{2 a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{3 c x}+\frac{5 a^{5} c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{6}+\frac{5 a^{5} c^{2} x \sqrt{-a^{2} c \,x^{2}+c}}{4}+\frac{5 a^{5} c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{4 \sqrt{a^{2} c}}-\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{3 c \,x^{3}}-\frac{2 a^{4} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{5}+\frac{2 a^{5} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{3}-\frac{5 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{8 c \,x^{2}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{4 c \,x^{4}}-\frac{3 a^{4} c \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{8}+\frac{9 a^{4} c^{\frac{5}{2}} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{8}-\frac{9 a^{4} \sqrt{-a^{2} c \,x^{2}+c}\, c^{2}}{8}+\frac{a^{5} c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{2}+\frac{3 a^{5} c^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{4}+\frac{3 a^{5} c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{4 \sqrt{a^{2} c}}-\frac{9 a^{4} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{40}"," ",0,"2/3*a^3/c/x*(-a^2*c*x^2+c)^(7/2)+5/6*a^5*c*x*(-a^2*c*x^2+c)^(3/2)+5/4*a^5*c^2*x*(-a^2*c*x^2+c)^(1/2)+5/4*a^5*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3*a/c/x^3*(-a^2*c*x^2+c)^(7/2)-2/5*a^4*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)+2/3*a^5*x*(-a^2*c*x^2+c)^(5/2)-5/8*a^2/c/x^2*(-a^2*c*x^2+c)^(7/2)-1/4/c/x^4*(-a^2*c*x^2+c)^(7/2)-3/8*a^4*c*(-a^2*c*x^2+c)^(3/2)+9/8*a^4*c^(5/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-9/8*a^4*(-a^2*c*x^2+c)^(1/2)*c^2+1/2*a^5*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x+3/4*a^5*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+3/4*a^5*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))-9/40*a^4*(-a^2*c*x^2+c)^(5/2)","B"
1107,1,296,125,0.039000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(7/2),x)","-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{8}-\frac{7 c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{48}-\frac{35 c^{2} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{192}-\frac{35 c^{3} x \sqrt{-a^{2} c \,x^{2}+c}}{128}-\frac{35 c^{4} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{128 \sqrt{a^{2} c}}-\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{7}{2}}}{7 a}+\frac{c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}} x}{3}+\frac{5 c^{2} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{12}+\frac{5 c^{3} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{8}+\frac{5 c^{4} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{8 \sqrt{a^{2} c}}"," ",0,"-1/8*x*(-a^2*c*x^2+c)^(7/2)-7/48*c*x*(-a^2*c*x^2+c)^(5/2)-35/192*c^2*x*(-a^2*c*x^2+c)^(3/2)-35/128*c^3*x*(-a^2*c*x^2+c)^(1/2)-35/128*c^4/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/7/a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(7/2)+1/3*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)*x+5/12*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x+5/8*c^3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x+5/8*c^4/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
1108,1,149,119,0.044000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^(1/2),x)","\frac{x^{2} \sqrt{-a^{2} c \,x^{2}+c}}{3 a^{2} c}+\frac{8 \sqrt{-a^{2} c \,x^{2}+c}}{3 a^{4} c}+\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{a^{3} c}-\frac{3 \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{a^{3} \sqrt{a^{2} c}}-\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a^{5} c \left(x -\frac{1}{a}\right)}"," ",0,"1/3*x^2*(-a^2*c*x^2+c)^(1/2)/a^2/c+8/3*(-a^2*c*x^2+c)^(1/2)/a^4/c+x*(-a^2*c*x^2+c)^(1/2)/a^3/c-3/a^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a^5/c/(x-1/a)*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)","A"
1109,1,126,79,0.041000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^(1/2),x)","\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{2 a^{2} c}-\frac{5 \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{2 a^{2} \sqrt{a^{2} c}}+\frac{2 \sqrt{-a^{2} c \,x^{2}+c}}{a^{3} c}-\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a^{4} c \left(x -\frac{1}{a}\right)}"," ",0,"1/2*x/a^2/c*(-a^2*c*x^2+c)^(1/2)-5/2/a^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/a^3/c*(-a^2*c*x^2+c)^(1/2)-2/a^4/c/(x-1/a)*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)","A"
1110,1,103,74,0.037000," ","int((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{-a^{2} c \,x^{2}+c}}{a^{2} c}-\frac{2 \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{a \sqrt{a^{2} c}}-\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a^{3} c \left(x -\frac{1}{a}\right)}"," ",0,"(-a^2*c*x^2+c)^(1/2)/a^2/c-2/a/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a^3/c/(x-1/a)*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)","A"
1111,1,80,52,0.036000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a^{2} c \left(x -\frac{1}{a}\right)}"," ",0,"-1/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a^2/c/(x-1/a)*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)","A"
1112,1,80,44,0.038000," ","int((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{\sqrt{c}}-\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a c \left(x -\frac{1}{a}\right)}"," ",0,"-1/c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-2/a/c/(x-1/a)*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)","A"
1113,1,99,67,0.043000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^(1/2),x)","-\frac{2 a \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{\sqrt{c}}-\frac{\sqrt{-a^{2} c \,x^{2}+c}}{c x}-\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{c \left(x -\frac{1}{a}\right)}"," ",0,"-2*a/c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-(-a^2*c*x^2+c)^(1/2)/c/x-2/c/(x-1/a)*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)","A"
1114,1,124,93,0.045000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^(1/2),x)","-\frac{5 a^{2} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{2 \sqrt{c}}-\frac{2 a \sqrt{-a^{2} c \,x^{2}+c}}{c x}-\frac{2 a \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{c \left(x -\frac{1}{a}\right)}-\frac{\sqrt{-a^{2} c \,x^{2}+c}}{2 c \,x^{2}}"," ",0,"-5/2*a^2/c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-2*a*(-a^2*c*x^2+c)^(1/2)/c/x-2*a/c/(x-1/a)*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-1/2*(-a^2*c*x^2+c)^(1/2)/c/x^2","A"
1115,1,150,117,0.047000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^4/(-a^2*c*x^2+c)^(1/2),x)","-\frac{3 a^{3} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{\sqrt{c}}-\frac{8 a^{2} \sqrt{-a^{2} c \,x^{2}+c}}{3 c x}-\frac{\sqrt{-a^{2} c \,x^{2}+c}}{3 c \,x^{3}}-\frac{2 a^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{c \left(x -\frac{1}{a}\right)}-\frac{a \sqrt{-a^{2} c \,x^{2}+c}}{c \,x^{2}}"," ",0,"-3*a^3/c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-8/3*a^2*(-a^2*c*x^2+c)^(1/2)/c/x-1/3*(-a^2*c*x^2+c)^(1/2)/c/x^3-2*a^2/c/(x-1/a)*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-a*(-a^2*c*x^2+c)^(1/2)/c/x^2","A"
1116,1,190,101,0.042000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^(3/2),x)","\frac{x^{2}}{a^{2} c \sqrt{-a^{2} c \,x^{2}+c}}-\frac{4}{c \,a^{4} \sqrt{-a^{2} c \,x^{2}+c}}-\frac{4 x}{a^{3} c \sqrt{-a^{2} c \,x^{2}+c}}+\frac{2 \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{a^{3} c \sqrt{a^{2} c}}-\frac{2}{3 a^{5} c \left(x -\frac{1}{a}\right) \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}+\frac{4 x}{3 a^{3} c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}"," ",0,"x^2/a^2/c/(-a^2*c*x^2+c)^(1/2)-4/c/a^4/(-a^2*c*x^2+c)^(1/2)-4/a^3*x/c/(-a^2*c*x^2+c)^(1/2)+2/a^3/c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3/a^5/c/(x-1/a)/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+4/3/a^3/c/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x","A"
1117,1,166,79,0.043000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^(3/2),x)","-\frac{3 x}{a^{2} c \sqrt{-a^{2} c \,x^{2}+c}}+\frac{\arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{a^{2} c \sqrt{a^{2} c}}-\frac{2}{a^{3} c \sqrt{-a^{2} c \,x^{2}+c}}-\frac{2}{3 a^{4} c \left(x -\frac{1}{a}\right) \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}+\frac{4 x}{3 a^{2} c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}"," ",0,"-3*x/a^2/c/(-a^2*c*x^2+c)^(1/2)+1/a^2/c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a^3/c/(-a^2*c*x^2+c)^(1/2)-2/3/a^4/c/(x-1/a)/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+4/3/a^2/c/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x","B"
1118,1,32,52,0.032000," ","int((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c)^(3/2),x)","\frac{\left(2 a x -1\right) \left(a x +1\right)^{2}}{3 \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} a^{2}}"," ",0,"1/3*(2*a*x-1)*(a*x+1)^2/(-a^2*c*x^2+c)^(3/2)/a^2","A"
1119,1,31,43,0.029000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\left(a x -2\right) \left(a x +1\right)^{2}}{3 \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} a}"," ",0,"-1/3*(a*x-2)*(a*x+1)^2/(-a^2*c*x^2+c)^(3/2)/a","A"
1120,1,152,68,0.040000," ","int((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^(3/2),x)","\frac{1}{c \sqrt{-a^{2} c \,x^{2}+c}}-\frac{\ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{c^{\frac{3}{2}}}-\frac{2}{3 a c \left(x -\frac{1}{a}\right) \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}-\frac{2 \left(-2 \left(x -\frac{1}{a}\right) a^{2} c -2 a c \right)}{3 a \,c^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}"," ",0,"1/c/(-a^2*c*x^2+c)^(1/2)-1/c^(3/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-2/3/a/c/(x-1/a)/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-2/3/a/c^2*(-2*(x-1/a)*a^2*c-2*a*c)/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)","B"
1121,1,178,92,0.043000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^(3/2),x)","\frac{2 a}{c \sqrt{-a^{2} c \,x^{2}+c}}-\frac{2 a \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{c^{\frac{3}{2}}}-\frac{1}{c x \sqrt{-a^{2} c \,x^{2}+c}}+\frac{2 a^{2} x}{c \sqrt{-a^{2} c \,x^{2}+c}}-\frac{2}{3 c \left(x -\frac{1}{a}\right) \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}+\frac{4 a^{2} x}{3 c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}"," ",0,"2*a/c/(-a^2*c*x^2+c)^(1/2)-2*a/c^(3/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-1/c/x/(-a^2*c*x^2+c)^(1/2)+2*a^2/c*x/(-a^2*c*x^2+c)^(1/2)-2/3/c/(x-1/a)/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+4/3*a^2/c/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x","A"
1122,1,205,120,0.048000," ","int((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^(3/2),x)","\frac{7 a^{2}}{2 c \sqrt{-a^{2} c \,x^{2}+c}}-\frac{7 a^{2} \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)}{2 c^{\frac{3}{2}}}-\frac{2 a}{c x \sqrt{-a^{2} c \,x^{2}+c}}+\frac{4 a^{3} x}{c \sqrt{-a^{2} c \,x^{2}+c}}-\frac{2 a}{3 c \left(x -\frac{1}{a}\right) \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}+\frac{4 a^{3} x}{3 c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}-\frac{1}{2 c \,x^{2} \sqrt{-a^{2} c \,x^{2}+c}}"," ",0,"7/2*a^2/c/(-a^2*c*x^2+c)^(1/2)-7/2*a^2/c^(3/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-2*a/c/x/(-a^2*c*x^2+c)^(1/2)+4*a^3/c*x/(-a^2*c*x^2+c)^(1/2)-2/3*a/c/(x-1/a)/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)+4/3*a^3/c/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x-1/2/c/x^2/(-a^2*c*x^2+c)^(1/2)","A"
1123,1,47,62,0.030000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^(5/2),x)","\frac{\left(2 x^{3} a^{3}-4 a^{2} x^{2}+a x +2\right) \left(a x +1\right)^{2}}{5 \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} a}"," ",0,"1/5*(2*a^3*x^3-4*a^2*x^2+a*x+2)*(a*x+1)^2/(-a^2*c*x^2+c)^(5/2)/a","A"
1124,1,64,81,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^(7/2),x)","-\frac{\left(8 x^{5} a^{5}-16 x^{4} a^{4}-4 x^{3} a^{3}+24 a^{2} x^{2}-9 a x -6\right) \left(a x +1\right)^{2}}{21 \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}} a}"," ",0,"-1/21*(8*a^5*x^5-16*a^4*x^4-4*a^3*x^3+24*a^2*x^2-9*a*x-6)*(a*x+1)^2/(-a^2*c*x^2+c)^(7/2)/a","A"
1125,1,476,120,0.031000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^3,x)","\frac{c^{3} x^{1+m} \left(a^{6} m^{6} x^{6}+21 a^{6} m^{5} x^{6}+175 a^{6} m^{4} x^{6}+2 a^{5} m^{6} x^{5}+735 a^{6} m^{3} x^{6}+44 a^{5} m^{5} x^{5}+1624 a^{6} m^{2} x^{6}+380 a^{5} m^{4} x^{5}-a^{4} m^{6} x^{4}+1764 a^{6} m \,x^{6}+1640 a^{5} m^{3} x^{5}-23 a^{4} m^{5} x^{4}+720 x^{6} a^{6}+3698 a^{5} m^{2} x^{5}-207 a^{4} m^{4} x^{4}-4 a^{3} m^{6} x^{3}+4076 a^{5} m \,x^{5}-925 a^{4} m^{3} x^{4}-96 a^{3} m^{5} x^{3}+1680 x^{5} a^{5}-2144 a^{4} m^{2} x^{4}-904 a^{3} m^{4} x^{3}-a^{2} m^{6} x^{2}-2412 a^{4} m \,x^{4}-4224 a^{3} m^{3} x^{3}-25 a^{2} m^{5} x^{2}-1008 x^{4} a^{4}-10180 a^{3} m^{2} x^{3}-247 a^{2} m^{4} x^{2}+2 a \,m^{6} x -11808 a^{3} m \,x^{3}-1219 a^{2} m^{3} x^{2}+52 a \,m^{5} x -5040 x^{3} a^{3}-3112 a^{2} m^{2} x^{2}+540 a \,m^{4} x +m^{6}-3796 a^{2} m \,x^{2}+2840 a \,m^{3} x +27 m^{5}-1680 a^{2} x^{2}+7858 a \,m^{2} x +295 m^{4}+10548 a m x +1665 m^{3}+5040 a x +5104 m^{2}+8028 m +5040\right)}{\left(7+m \right) \left(6+m \right) \left(5+m \right) \left(4+m \right) \left(3+m \right) \left(2+m \right) \left(1+m \right)}"," ",0,"c^3*x^(1+m)*(a^6*m^6*x^6+21*a^6*m^5*x^6+175*a^6*m^4*x^6+2*a^5*m^6*x^5+735*a^6*m^3*x^6+44*a^5*m^5*x^5+1624*a^6*m^2*x^6+380*a^5*m^4*x^5-a^4*m^6*x^4+1764*a^6*m*x^6+1640*a^5*m^3*x^5-23*a^4*m^5*x^4+720*a^6*x^6+3698*a^5*m^2*x^5-207*a^4*m^4*x^4-4*a^3*m^6*x^3+4076*a^5*m*x^5-925*a^4*m^3*x^4-96*a^3*m^5*x^3+1680*a^5*x^5-2144*a^4*m^2*x^4-904*a^3*m^4*x^3-a^2*m^6*x^2-2412*a^4*m*x^4-4224*a^3*m^3*x^3-25*a^2*m^5*x^2-1008*a^4*x^4-10180*a^3*m^2*x^3-247*a^2*m^4*x^2+2*a*m^6*x-11808*a^3*m*x^3-1219*a^2*m^3*x^2+52*a*m^5*x-5040*a^3*x^3-3112*a^2*m^2*x^2+540*a*m^4*x+m^6-3796*a^2*m*x^2+2840*a*m^3*x+27*m^5-1680*a^2*x^2+7858*a*m^2*x+295*m^4+10548*a*m*x+1665*m^3+5040*a*x+5104*m^2+8028*m+5040)/(7+m)/(6+m)/(5+m)/(4+m)/(3+m)/(2+m)/(1+m)","B"
1126,1,146,67,0.029000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^2,x)","-\frac{c^{2} x^{1+m} \left(a^{4} m^{3} x^{4}+7 a^{4} m^{2} x^{4}+14 a^{4} m \,x^{4}+2 a^{3} m^{3} x^{3}+8 x^{4} a^{4}+16 a^{3} m^{2} x^{3}+34 a^{3} m \,x^{3}+20 x^{3} a^{3}-2 a \,m^{3} x -20 a \,m^{2} x -58 a m x -m^{3}-40 a x -11 m^{2}-38 m -40\right)}{\left(5+m \right) \left(4+m \right) \left(2+m \right) \left(1+m \right)}"," ",0,"-c^2*x^(1+m)*(a^4*m^3*x^4+7*a^4*m^2*x^4+14*a^4*m*x^4+2*a^3*m^3*x^3+8*a^4*x^4+16*a^3*m^2*x^3+34*a^3*m*x^3+20*a^3*x^3-2*a*m^3*x-20*a*m^2*x-58*a*m*x-m^3-40*a*x-11*m^2-38*m-40)/(5+m)/(4+m)/(2+m)/(1+m)","B"
1127,1,74,42,0.028000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c),x)","\frac{c \,x^{1+m} \left(a^{2} m^{2} x^{2}+3 a^{2} m \,x^{2}+2 a^{2} x^{2}+2 a \,m^{2} x +8 a m x +6 a x +m^{2}+5 m +6\right)}{\left(3+m \right) \left(2+m \right) \left(1+m \right)}"," ",0,"c*x^(1+m)*(a^2*m^2*x^2+3*a^2*m*x^2+2*a^2*x^2+2*a*m^2*x+8*a*m*x+6*a*x+m^2+5*m+6)/(3+m)/(2+m)/(1+m)","A"
1128,0,0,27,0.416000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c),x)","\int \frac{\left(a x +1\right)^{2} x^{m}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c),x)","F"
1129,0,0,109,0.416000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^2,x)","\int \frac{\left(a x +1\right)^{2} x^{m}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^2,x)","F"
1130,0,0,195,0.415000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^3,x)","\int \frac{\left(a x +1\right)^{2} x^{m}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c \,x^{2}+c \right)^{3}}\, dx"," ",0,"int((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^3,x)","F"
1131,0,0,158,0.414000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(5/2),x)","\int \frac{\left(a x +1\right)^{2} x^{m} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{-a^{2} x^{2}+1}\, dx"," ",0,"int((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(5/2),x)","F"
1132,0,0,154,0.418000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(3/2),x)","\int \frac{\left(a x +1\right)^{2} x^{m} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{-a^{2} x^{2}+1}\, dx"," ",0,"int((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(3/2),x)","F"
1133,0,0,154,0.411000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(1/2),x)","\int \frac{\left(a x +1\right)^{2} x^{m} \sqrt{-a^{2} c \,x^{2}+c}}{-a^{2} x^{2}+1}\, dx"," ",0,"int((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(1/2),x)","F"
1134,0,0,151,0.411000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^(1/2),x)","\int \frac{\left(a x +1\right)^{2} x^{m}}{\left(-a^{2} x^{2}+1\right) \sqrt{-a^{2} c \,x^{2}+c}}\, dx"," ",0,"int((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^(1/2),x)","F"
1135,0,0,159,0.416000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{\left(a x +1\right)^{2} x^{m}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^(3/2),x)","F"
1136,0,0,53,0.469000," ","int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right)^{2} \left(-a^{2} c \,x^{2}+c \right)^{p}}{-a^{2} x^{2}+1}\, dx"," ",0,"int((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^p,x)","F"
1137,1,191,114,0.089000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c),x)","\frac{c \,a^{3} x^{7}}{6 \sqrt{-a^{2} x^{2}+1}}+\frac{19 c a \,x^{5}}{24 \sqrt{-a^{2} x^{2}+1}}+\frac{23 c \,x^{3}}{48 a \sqrt{-a^{2} x^{2}+1}}-\frac{23 c x}{16 a^{3} \sqrt{-a^{2} x^{2}+1}}+\frac{23 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a^{3} \sqrt{a^{2}}}+\frac{3 c \,a^{2} x^{6}}{5 \sqrt{-a^{2} x^{2}+1}}+\frac{8 c \,x^{4}}{15 \sqrt{-a^{2} x^{2}+1}}+\frac{17 c \,x^{2}}{15 a^{2} \sqrt{-a^{2} x^{2}+1}}-\frac{34 c}{15 a^{4} \sqrt{-a^{2} x^{2}+1}}"," ",0,"1/6*c*a^3*x^7/(-a^2*x^2+1)^(1/2)+19/24*c*a*x^5/(-a^2*x^2+1)^(1/2)+23/48*c/a*x^3/(-a^2*x^2+1)^(1/2)-23/16*c/a^3*x/(-a^2*x^2+1)^(1/2)+23/16*c/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+3/5*c*a^2*x^6/(-a^2*x^2+1)^(1/2)+8/15*c*x^4/(-a^2*x^2+1)^(1/2)+17/15*c/a^2*x^2/(-a^2*x^2+1)^(1/2)-34/15*c/a^4/(-a^2*x^2+1)^(1/2)","A"
1138,1,170,93,0.069000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c),x)","\frac{c \,a^{3} x^{6}}{5 \sqrt{-a^{2} x^{2}+1}}+\frac{16 c a \,x^{4}}{15 \sqrt{-a^{2} x^{2}+1}}+\frac{19 c \,x^{2}}{15 a \sqrt{-a^{2} x^{2}+1}}-\frac{38 c}{15 a^{3} \sqrt{-a^{2} x^{2}+1}}+\frac{3 c \,a^{2} x^{5}}{4 \sqrt{-a^{2} x^{2}+1}}+\frac{7 c \,x^{3}}{8 \sqrt{-a^{2} x^{2}+1}}-\frac{13 c x}{8 a^{2} \sqrt{-a^{2} x^{2}+1}}+\frac{13 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a^{2} \sqrt{a^{2}}}"," ",0,"1/5*c*a^3*x^6/(-a^2*x^2+1)^(1/2)+16/15*c*a*x^4/(-a^2*x^2+1)^(1/2)+19/15*c/a*x^2/(-a^2*x^2+1)^(1/2)-38/15*c/a^3/(-a^2*x^2+1)^(1/2)+3/4*c*a^2*x^5/(-a^2*x^2+1)^(1/2)+7/8*c*x^3/(-a^2*x^2+1)^(1/2)-13/8*c*x/a^2/(-a^2*x^2+1)^(1/2)+13/8*c/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
1139,1,148,102,0.054000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c),x)","\frac{c \,a^{3} x^{5}}{4 \sqrt{-a^{2} x^{2}+1}}+\frac{13 c a \,x^{3}}{8 \sqrt{-a^{2} x^{2}+1}}-\frac{15 c x}{8 a \sqrt{-a^{2} x^{2}+1}}+\frac{15 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a \sqrt{a^{2}}}+\frac{c \,a^{2} x^{4}}{\sqrt{-a^{2} x^{2}+1}}+\frac{2 c \,x^{2}}{\sqrt{-a^{2} x^{2}+1}}-\frac{3 c}{a^{2} \sqrt{-a^{2} x^{2}+1}}"," ",0,"1/4*c*a^3*x^5/(-a^2*x^2+1)^(1/2)+13/8*c*a*x^3/(-a^2*x^2+1)^(1/2)-15/8*c/a*x/(-a^2*x^2+1)^(1/2)+15/8*c/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+c*a^2*x^4/(-a^2*x^2+1)^(1/2)+2*c*x^2/(-a^2*x^2+1)^(1/2)-3*c/a^2/(-a^2*x^2+1)^(1/2)","A"
1140,1,125,77,0.048000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c),x)","\frac{c \,a^{3} x^{4}}{3 \sqrt{-a^{2} x^{2}+1}}+\frac{10 c a \,x^{2}}{3 \sqrt{-a^{2} x^{2}+1}}-\frac{11 c}{3 a \sqrt{-a^{2} x^{2}+1}}+\frac{3 c \,a^{2} x^{3}}{2 \sqrt{-a^{2} x^{2}+1}}-\frac{3 c x}{2 \sqrt{-a^{2} x^{2}+1}}+\frac{5 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}"," ",0,"1/3*c*a^3*x^4/(-a^2*x^2+1)^(1/2)+10/3*c*a*x^2/(-a^2*x^2+1)^(1/2)-11/3*c/a/(-a^2*x^2+1)^(1/2)+3/2*c*a^2*x^3/(-a^2*x^2+1)^(1/2)-3/2*c*x/(-a^2*x^2+1)^(1/2)+5/2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
1141,1,121,56,0.045000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x,x)","\frac{c \,a^{3} x^{3}}{2 \sqrt{-a^{2} x^{2}+1}}-\frac{c a x}{2 \sqrt{-a^{2} x^{2}+1}}+\frac{7 c a \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}+\frac{3 c \,a^{2} x^{2}}{\sqrt{-a^{2} x^{2}+1}}-\frac{3 c}{\sqrt{-a^{2} x^{2}+1}}-c \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"1/2*c*a^3*x^3/(-a^2*x^2+1)^(1/2)-1/2*c*a*x/(-a^2*x^2+1)^(1/2)+7/2*c*a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+3*c*a^2*x^2/(-a^2*x^2+1)^(1/2)-3*c/(-a^2*x^2+1)^(1/2)-c*arctanh(1/(-a^2*x^2+1)^(1/2))","B"
1142,1,122,60,0.046000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^2,x)","\frac{c \,a^{3} x^{2}}{\sqrt{-a^{2} x^{2}+1}}-\frac{c a}{\sqrt{-a^{2} x^{2}+1}}+\frac{c \,a^{2} x}{\sqrt{-a^{2} x^{2}+1}}+\frac{3 c \,a^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-3 c a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{c}{x \sqrt{-a^{2} x^{2}+1}}"," ",0,"c*a^3*x^2/(-a^2*x^2+1)^(1/2)-c*a/(-a^2*x^2+1)^(1/2)+c*a^2*x/(-a^2*x^2+1)^(1/2)+3*c*a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-3*c*a*arctanh(1/(-a^2*x^2+1)^(1/2))-c/x/(-a^2*x^2+1)^(1/2)","B"
1143,1,125,66,0.047000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^3,x)","\frac{3 c \,a^{3} x}{\sqrt{-a^{2} x^{2}+1}}+\frac{c \,a^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}+\frac{c \,a^{2}}{2 \sqrt{-a^{2} x^{2}+1}}-\frac{7 c \,a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{3 c a}{x \sqrt{-a^{2} x^{2}+1}}-\frac{c}{2 x^{2} \sqrt{-a^{2} x^{2}+1}}"," ",0,"3*c*a^3*x/(-a^2*x^2+1)^(1/2)+c*a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+1/2*c*a^2/(-a^2*x^2+1)^(1/2)-7/2*c*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))-3*c*a/x/(-a^2*x^2+1)^(1/2)-1/2*c/x^2/(-a^2*x^2+1)^(1/2)","A"
1144,1,184,78,0.043000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^4,x)","-c \left(\frac{a^{3}}{\sqrt{-a^{2} x^{2}+1}}+\frac{3 x \,a^{4}}{\sqrt{-a^{2} x^{2}+1}}+2 a^{3} \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}-\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)\right)-\frac{10 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}+\frac{1}{3 x^{3} \sqrt{-a^{2} x^{2}+1}}-3 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)\right)"," ",0,"-c*(a^3/(-a^2*x^2+1)^(1/2)+3*x*a^4/(-a^2*x^2+1)^(1/2)+2*a^3*(1/(-a^2*x^2+1)^(1/2)-arctanh(1/(-a^2*x^2+1)^(1/2)))-10/3*a^2*(-1/x/(-a^2*x^2+1)^(1/2)+2*a^2*x/(-a^2*x^2+1)^(1/2))+1/3/x^3/(-a^2*x^2+1)^(1/2)-3*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)))))","B"
1145,1,231,99,0.049000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^5,x)","-c \left(\frac{x \,a^{5}}{\sqrt{-a^{2} x^{2}+1}}+3 a^{4} \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}-\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)\right)+2 a^{3} \left(-\frac{1}{x \sqrt{-a^{2} x^{2}+1}}+\frac{2 a^{2} x}{\sqrt{-a^{2} x^{2}+1}}\right)-3 a \left(-\frac{1}{3 x^{3} \sqrt{-a^{2} x^{2}+1}}+\frac{4 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}\right)-\frac{13 a^{2} \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)}{4}+\frac{1}{4 x^{4} \sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-c*(x*a^5/(-a^2*x^2+1)^(1/2)+3*a^4*(1/(-a^2*x^2+1)^(1/2)-arctanh(1/(-a^2*x^2+1)^(1/2)))+2*a^3*(-1/x/(-a^2*x^2+1)^(1/2)+2*a^2*x/(-a^2*x^2+1)^(1/2))-3*a*(-1/3/x^3/(-a^2*x^2+1)^(1/2)+4/3*a^2*(-1/x/(-a^2*x^2+1)^(1/2)+2*a^2*x/(-a^2*x^2+1)^(1/2)))-13/4*a^2*(-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))))+1/4/x^4/(-a^2*x^2+1)^(1/2))","B"
1146,1,292,120,0.052000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^6,x)","-c \left(a^{5} \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}-\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)\right)+3 a^{4} \left(-\frac{1}{x \sqrt{-a^{2} x^{2}+1}}+\frac{2 a^{2} x}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{16 a^{2} \left(-\frac{1}{3 x^{3} \sqrt{-a^{2} x^{2}+1}}+\frac{4 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}\right)}{5}+2 a^{3} \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)-3 a \left(-\frac{1}{4 x^{4} \sqrt{-a^{2} x^{2}+1}}+\frac{5 a^{2} \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)}{4}\right)+\frac{1}{5 x^{5} \sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-c*(a^5*(1/(-a^2*x^2+1)^(1/2)-arctanh(1/(-a^2*x^2+1)^(1/2)))+3*a^4*(-1/x/(-a^2*x^2+1)^(1/2)+2*a^2*x/(-a^2*x^2+1)^(1/2))-16/5*a^2*(-1/3/x^3/(-a^2*x^2+1)^(1/2)+4/3*a^2*(-1/x/(-a^2*x^2+1)^(1/2)+2*a^2*x/(-a^2*x^2+1)^(1/2)))+2*a^3*(-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))))-3*a*(-1/4/x^4/(-a^2*x^2+1)^(1/2)+5/4*a^2*(-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)))))+1/5/x^5/(-a^2*x^2+1)^(1/2))","B"
1147,1,183,103,0.069000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^2,x)","-\frac{c^{2} a^{5} x^{6}}{5 \sqrt{-a^{2} x^{2}+1}}-\frac{11 c^{2} a^{3} x^{4}}{15 \sqrt{-a^{2} x^{2}+1}}+\frac{31 c^{2} a \,x^{2}}{15 \sqrt{-a^{2} x^{2}+1}}-\frac{17 c^{2}}{15 a \sqrt{-a^{2} x^{2}+1}}-\frac{3 c^{2} a^{4} x^{5}}{4 \sqrt{-a^{2} x^{2}+1}}+\frac{5 c^{2} a^{2} x^{3}}{8 \sqrt{-a^{2} x^{2}+1}}+\frac{c^{2} x}{8 \sqrt{-a^{2} x^{2}+1}}+\frac{7 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}"," ",0,"-1/5*c^2*a^5*x^6/(-a^2*x^2+1)^(1/2)-11/15*c^2*a^3*x^4/(-a^2*x^2+1)^(1/2)+31/15*c^2*a*x^2/(-a^2*x^2+1)^(1/2)-17/15*c^2/a/(-a^2*x^2+1)^(1/2)-3/4*c^2*a^4*x^5/(-a^2*x^2+1)^(1/2)+5/8*c^2*a^2*x^3/(-a^2*x^2+1)^(1/2)+1/8*c^2*x/(-a^2*x^2+1)^(1/2)+7/8*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
1148,1,229,121,0.112000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^3,x)","\frac{c^{3} a^{7} x^{8}}{7 \sqrt{-a^{2} x^{2}+1}}+\frac{8 c^{3} a^{5} x^{6}}{35 \sqrt{-a^{2} x^{2}+1}}-\frac{54 c^{3} a^{3} x^{4}}{35 \sqrt{-a^{2} x^{2}+1}}+\frac{64 c^{3} a \,x^{2}}{35 \sqrt{-a^{2} x^{2}+1}}-\frac{23 c^{3}}{35 a \sqrt{-a^{2} x^{2}+1}}+\frac{c^{3} a^{6} x^{7}}{2 \sqrt{-a^{2} x^{2}+1}}-\frac{9 c^{3} a^{4} x^{5}}{8 \sqrt{-a^{2} x^{2}+1}}+\frac{3 c^{3} a^{2} x^{3}}{16 \sqrt{-a^{2} x^{2}+1}}+\frac{7 c^{3} x}{16 \sqrt{-a^{2} x^{2}+1}}+\frac{9 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 \sqrt{a^{2}}}"," ",0,"1/7*c^3*a^7*x^8/(-a^2*x^2+1)^(1/2)+8/35*c^3*a^5*x^6/(-a^2*x^2+1)^(1/2)-54/35*c^3*a^3*x^4/(-a^2*x^2+1)^(1/2)+64/35*c^3*a*x^2/(-a^2*x^2+1)^(1/2)-23/35*c^3/a/(-a^2*x^2+1)^(1/2)+1/2*c^3*a^6*x^7/(-a^2*x^2+1)^(1/2)-9/8*c^3*a^4*x^5/(-a^2*x^2+1)^(1/2)+3/16*c^3*a^2*x^3/(-a^2*x^2+1)^(1/2)+7/16*c^3*x/(-a^2*x^2+1)^(1/2)+9/16*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
1149,1,275,139,0.252000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^4,x)","-\frac{c^{4} a^{9} x^{10}}{9 \sqrt{-a^{2} x^{2}+1}}-\frac{c^{4} a^{7} x^{8}}{63 \sqrt{-a^{2} x^{2}+1}}+\frac{74 c^{4} a^{5} x^{6}}{63 \sqrt{-a^{2} x^{2}+1}}-\frac{146 c^{4} a^{3} x^{4}}{63 \sqrt{-a^{2} x^{2}+1}}+\frac{109 c^{4} a \,x^{2}}{63 \sqrt{-a^{2} x^{2}+1}}-\frac{3 c^{4} a^{8} x^{9}}{8 \sqrt{-a^{2} x^{2}+1}}+\frac{61 c^{4} a^{6} x^{7}}{48 \sqrt{-a^{2} x^{2}+1}}-\frac{245 c^{4} a^{4} x^{5}}{192 \sqrt{-a^{2} x^{2}+1}}-\frac{73 c^{4} a^{2} x^{3}}{384 \sqrt{-a^{2} x^{2}+1}}+\frac{55 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{128 \sqrt{a^{2}}}+\frac{73 c^{4} x}{128 \sqrt{-a^{2} x^{2}+1}}-\frac{29 c^{4}}{63 a \sqrt{-a^{2} x^{2}+1}}"," ",0,"-1/9*c^4*a^9*x^10/(-a^2*x^2+1)^(1/2)-1/63*c^4*a^7*x^8/(-a^2*x^2+1)^(1/2)+74/63*c^4*a^5*x^6/(-a^2*x^2+1)^(1/2)-146/63*c^4*a^3*x^4/(-a^2*x^2+1)^(1/2)+109/63*c^4*a*x^2/(-a^2*x^2+1)^(1/2)-3/8*c^4*a^8*x^9/(-a^2*x^2+1)^(1/2)+61/48*c^4*a^6*x^7/(-a^2*x^2+1)^(1/2)-245/192*c^4*a^4*x^5/(-a^2*x^2+1)^(1/2)-73/384*c^4*a^2*x^3/(-a^2*x^2+1)^(1/2)+55/128*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+73/128*c^4*x/(-a^2*x^2+1)^(1/2)-29/63*c^4/a/(-a^2*x^2+1)^(1/2)","A"
1150,1,178,87,0.040000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2/(-a^2*c*x^2+c),x)","\frac{x^{2}}{c a \sqrt{-a^{2} x^{2}+1}}-\frac{6}{c \,a^{3} \sqrt{-a^{2} x^{2}+1}}-\frac{7 x}{c \,a^{2} \sqrt{-a^{2} x^{2}+1}}+\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c \,a^{2} \sqrt{a^{2}}}-\frac{4}{3 c \,a^{4} \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{8 x}{3 c \,a^{2} \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}"," ",0,"1/c/a*x^2/(-a^2*x^2+1)^(1/2)-6/c/a^3/(-a^2*x^2+1)^(1/2)-7/c*x/a^2/(-a^2*x^2+1)^(1/2)+3/c/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-4/3/c/a^4/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+8/3/c/a^2/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x","B"
1151,1,155,64,0.038000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x/(-a^2*c*x^2+c),x)","-\frac{5 x}{c a \sqrt{-a^{2} x^{2}+1}}+\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{c a \sqrt{a^{2}}}-\frac{3}{c \,a^{2} \sqrt{-a^{2} x^{2}+1}}-\frac{4}{3 c \,a^{3} \left(x -\frac{1}{a}\right) \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}+\frac{8 x}{3 c a \sqrt{-a^{2} \left(x -\frac{1}{a}\right)^{2}-2 a \left(x -\frac{1}{a}\right)}}"," ",0,"-5/c*x/a/(-a^2*x^2+1)^(1/2)+1/c/a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))-3/c/a^2/(-a^2*x^2+1)^(1/2)-4/3/c/a^3/(x-1/a)/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)+8/3/c/a/(-a^2*(x-1/a)^2-2*a*(x-1/a))^(1/2)*x","B"
1152,1,28,27,0.029000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c),x)","\frac{\left(a x +1\right)^{3}}{3 a c \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"1/3*(a*x+1)^3/a/c/(-a^2*x^2+1)^(3/2)","A"
1153,1,49,85,0.029000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^2,x)","-\frac{\left(2 a^{2} x^{2}-6 a x +7\right) \left(a x +1\right)^{2}}{15 \left(a x -1\right) c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a}"," ",0,"-1/15*(2*a^2*x^2-6*a*x+7)*(a*x+1)^2/(a*x-1)/c^2/(-a^2*x^2+1)^(3/2)/a","A"
1154,1,63,103,0.032000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^3,x)","-\frac{\left(8 x^{4} a^{4}-24 x^{3} a^{3}+20 a^{2} x^{2}+4 a x -13\right) \left(a x +1\right)}{35 \left(a x -1\right)^{2} c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a}"," ",0,"-1/35*(8*a^4*x^4-24*a^3*x^3+20*a^2*x^2+4*a*x-13)*(a*x+1)/(a*x-1)^2/c^3/(-a^2*x^2+1)^(3/2)/a","A"
1155,1,74,121,0.032000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^4,x)","-\frac{16 x^{6} a^{6}-48 x^{5} a^{5}+24 x^{4} a^{4}+56 x^{3} a^{3}-66 a^{2} x^{2}+6 a x +19}{63 \left(a x -1\right)^{3} c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a}"," ",0,"-1/63*(16*a^6*x^6-48*a^5*x^5+24*a^4*x^4+56*a^3*x^3-66*a^2*x^2+6*a*x+19)/(a*x-1)^3/c^4/(-a^2*x^2+1)^(3/2)/a","A"
1156,1,88,196,0.040000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(12 x^{5} a^{5}+45 x^{4} a^{4}+80 x^{3} a^{3}+120 a^{2} x^{2}+240 a x +240 \ln \left(a x -1\right)\right)}{60 \left(a^{2} x^{2}-1\right) a^{4}}"," ",0,"1/60*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(12*x^5*a^5+45*x^4*a^4+80*x^3*a^3+120*a^2*x^2+240*a*x+240*ln(a*x-1))/(a^2*x^2-1)/a^4","A"
1157,1,79,163,0.040000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(x^{4} a^{4}+4 x^{3} a^{3}+8 a^{2} x^{2}+16 a x +16 \ln \left(a x -1\right)\right)}{4 \left(a^{2} x^{2}-1\right) a^{3}}"," ",0,"1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(x^4*a^4+4*x^3*a^3+8*a^2*x^2+16*a*x+16*ln(a*x-1))/(a^2*x^2-1)/a^3","A"
1158,1,72,130,0.040000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 x^{3} a^{3}+9 a^{2} x^{2}+24 a x +24 \ln \left(a x -1\right)\right)}{6 \left(a^{2} x^{2}-1\right) a^{2}}"," ",0,"1/6*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(2*x^3*a^3+9*a^2*x^2+24*a*x+24*ln(a*x-1))/(a^2*x^2-1)/a^2","A"
1159,1,63,97,0.038000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a^{2} x^{2}+6 a x +8 \ln \left(a x -1\right)\right)}{2 \left(a^{2} x^{2}-1\right) a}"," ",0,"1/2*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(a^2*x^2+6*a*x+8*ln(a*x-1))/(a^2*x^2-1)/a","A"
1160,1,55,92,0.042000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x,x)","\frac{\left(a x -\ln \left(x \right)+4 \ln \left(a x -1\right)\right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}}{a^{2} x^{2}-1}"," ",0,"(a*x-ln(x)+4*ln(a*x-1))*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/(a^2*x^2-1)","A"
1161,1,60,96,0.047000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x)","\frac{\left(-3 a \ln \left(x \right) x +4 \ln \left(a x -1\right) x a +1\right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}}{\left(a^{2} x^{2}-1\right) x}"," ",0,"(-3*a*ln(x)*x+4*ln(a*x-1)*x*a+1)*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/(a^2*x^2-1)/x","A"
1162,1,73,131,0.045000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^3,x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 a^{2} \ln \left(x \right) x^{2}-8 \ln \left(a x -1\right) x^{2} a^{2}-6 a x -1\right)}{2 \left(a^{2} x^{2}-1\right) x^{2}}"," ",0,"-1/2*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(8*a^2*ln(x)*x^2-8*ln(a*x-1)*x^2*a^2-6*a*x-1)/(a^2*x^2-1)/x^2","A"
1163,1,81,164,0.047000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^4,x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(24 a^{3} \ln \left(x \right) x^{3}-24 \ln \left(a x -1\right) x^{3} a^{3}-24 a^{2} x^{2}-9 a x -2\right)}{6 \left(a^{2} x^{2}-1\right) x^{3}}"," ",0,"-1/6*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(24*a^3*ln(x)*x^3-24*ln(a*x-1)*x^3*a^3-24*a^2*x^2-9*a*x-2)/(a^2*x^2-1)/x^3","A"
1164,1,89,197,0.046000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^5,x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(16 a^{4} \ln \left(x \right) x^{4}-16 \ln \left(a x -1\right) x^{4} a^{4}-16 x^{3} a^{3}-8 a^{2} x^{2}-4 a x -1\right)}{4 \left(a^{2} x^{2}-1\right) x^{4}}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(16*a^4*ln(x)*x^4-16*ln(a*x-1)*x^4*a^4-16*x^3*a^3-8*a^2*x^2-4*a*x-1)/(a^2*x^2-1)/x^4","A"
1165,1,50,38,0.030000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(3/2),x)","\frac{x \left(x^{3} a^{3}+4 a^{2} x^{2}+6 a x +4\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"1/4*x*(a^3*x^3+4*a^2*x^2+6*a*x+4)*(-a^2*c*x^2+c)^(3/2)/(-a^2*x^2+1)^(3/2)","A"
1166,1,81,81,0.029000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(5/2),x)","\frac{x \left(5 x^{5} a^{5}+18 x^{4} a^{4}+15 x^{3} a^{3}-20 a^{2} x^{2}-45 a x -30\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{30 \left(a x -1\right) \left(a x +1\right) \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"1/30*x*(5*a^5*x^5+18*a^4*x^4+15*a^3*x^3-20*a^2*x^2-45*a*x-30)*(-a^2*c*x^2+c)^(5/2)/(a*x-1)/(a*x+1)/(-a^2*x^2+1)^(3/2)","A"
1167,1,97,121,0.030000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(7/2),x)","\frac{x \left(21 a^{7} x^{7}+72 x^{6} a^{6}+28 x^{5} a^{5}-168 x^{4} a^{4}-210 x^{3} a^{3}+56 a^{2} x^{2}+252 a x +168\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{168 \left(a x -1\right)^{2} \left(a x +1\right)^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"1/168*x*(21*a^7*x^7+72*a^6*x^6+28*a^5*x^5-168*a^4*x^4-210*a^3*x^3+56*a^2*x^2+252*a*x+168)*(-a^2*c*x^2+c)^(7/2)/(a*x-1)^2/(a*x+1)^2/(-a^2*x^2+1)^(3/2)","A"
1168,1,97,161,0.032000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(9/2),x)","\frac{x \left(21 a^{9} x^{9}+70 x^{8} a^{8}-240 x^{6} a^{6}-210 x^{5} a^{5}+252 x^{4} a^{4}+420 x^{3} a^{3}-315 a x -210\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}}}{210 \left(a x -1\right)^{3} \left(a x +1\right)^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"1/210*x*(21*a^9*x^9+70*a^8*x^8-240*a^6*x^6-210*a^5*x^5+252*a^4*x^4+420*a^3*x^3-315*a*x-210)*(-a^2*c*x^2+c)^(9/2)/(a*x-1)^3/(a*x+1)^3/(-a^2*x^2+1)^(3/2)","A"
1169,1,70,75,0.041000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(1/2),x)","\frac{\left(-\ln \left(a x -1\right) x a +\ln \left(a x -1\right)+2\right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}}{\left(a^{2} x^{2}-1\right) c a \left(a x -1\right)}"," ",0,"(-ln(a*x-1)*x*a+ln(a*x-1)+2)*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/(a^2*x^2-1)/c/a/(a*x-1)","A"
1170,1,43,41,0.027000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\left(a x -1\right) \left(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*(a*x-1)/a*(a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(3/2)","A"
1171,1,159,161,0.046000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)-9 \ln \left(a x -1\right) x^{2} a^{2}+9 \ln \left(a x +1\right) x^{2} a^{2}+6 a^{2} x^{2}+9 \ln \left(a x -1\right) x a -9 a x \ln \left(a x +1\right)-18 a x -3 \ln \left(a x -1\right)+3 \ln \left(a x +1\right)+20\right)}{48 \left(a^{2} x^{2}-1\right) c^{3} a \left(a x -1\right)^{3}}"," ",0,"1/48*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)-9*ln(a*x-1)*x^2*a^2+9*ln(a*x+1)*x^2*a^2+6*a^2*x^2+9*ln(a*x-1)*x*a-9*a*x*ln(a*x+1)-18*a*x-3*ln(a*x-1)+3*ln(a*x+1)+20)/(a^2*x^2-1)/c^3/a/(a*x-1)^3","A"
1172,1,238,242,0.051000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(7/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(15 \ln \left(a x -1\right) x^{5} a^{5}-15 \ln \left(a x +1\right) x^{5} a^{5}-45 \ln \left(a x -1\right) x^{4} a^{4}+45 \ln \left(a x +1\right) x^{4} a^{4}+30 x^{4} a^{4}+30 \ln \left(a x -1\right) x^{3} a^{3}-30 a^{3} x^{3} \ln \left(a x +1\right)-90 x^{3} a^{3}+30 \ln \left(a x -1\right) x^{2} a^{2}-30 \ln \left(a x +1\right) x^{2} a^{2}+70 a^{2} x^{2}-45 \ln \left(a x -1\right) x a +45 a x \ln \left(a x +1\right)+30 a x +15 \ln \left(a x -1\right)-15 \ln \left(a x +1\right)-64\right)}{192 \left(a^{2} x^{2}-1\right) c^{4} a \left(a x -1\right)^{4} \left(a x +1\right)}"," ",0,"1/192*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(15*ln(a*x-1)*x^5*a^5-15*ln(a*x+1)*x^5*a^5-45*ln(a*x-1)*x^4*a^4+45*ln(a*x+1)*x^4*a^4+30*x^4*a^4+30*ln(a*x-1)*x^3*a^3-30*a^3*x^3*ln(a*x+1)-90*x^3*a^3+30*ln(a*x-1)*x^2*a^2-30*ln(a*x+1)*x^2*a^2+70*a^2*x^2-45*ln(a*x-1)*x*a+45*a*x*ln(a*x+1)+30*a*x+15*ln(a*x-1)-15*ln(a*x+1)-64)/(a^2*x^2-1)/c^4/a/(a*x-1)^4/(a*x+1)","A"
1173,0,0,126,0.417000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^m*(-a^2*c*x^2+c)^(1/2),x)","\int \frac{\left(a x +1\right)^{3} x^{m} \sqrt{-a^{2} c \,x^{2}+c}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^m*(-a^2*c*x^2+c)^(1/2),x)","F"
1174,0,0,239,0.413000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^m*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right)^{3} x^{m} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^m*(-a^2*c*x^2+c)^p,x)","F"
1175,0,0,208,0.415000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right)^{3} x^{3} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c)^p,x)","F"
1176,0,0,206,0.413000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right)^{3} x^{2} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c)^p,x)","F"
1177,0,0,122,0.416000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right)^{3} x \left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c)^p,x)","F"
1178,0,0,73,0.414000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right)^{3} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p,x)","F"
1179,0,0,177,0.483000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x,x)","\int \frac{\left(a x +1\right)^{3} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} x}\, dx"," ",0,"int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x,x)","F"
1180,0,0,175,0.423000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x^2,x)","\int \frac{\left(a x +1\right)^{3} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} x^{2}}\, dx"," ",0,"int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x^2,x)","F"
1181,0,0,178,0.414000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x^3,x)","\int \frac{\left(a x +1\right)^{3} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} x^{3}}\, dx"," ",0,"int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x^3,x)","F"
1182,1,75,60,0.023000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^5,x)","c^{5} \left(-\frac{1}{11} a^{10} x^{11}-\frac{2}{5} a^{9} x^{10}-\frac{1}{3} x^{9} a^{8}+a^{7} x^{8}+2 x^{7} a^{6}-\frac{14}{5} a^{4} x^{5}-2 x^{4} a^{3}+x^{3} a^{2}+2 a \,x^{2}+x \right)"," ",0,"c^5*(-1/11*a^10*x^11-2/5*a^9*x^10-1/3*x^9*a^8+a^7*x^8+2*x^7*a^6-14/5*a^4*x^5-2*x^4*a^3+x^3*a^2+2*a*x^2+x)","A"
1183,1,69,46,0.025000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^4,x)","c^{4} \left(\frac{1}{9} x^{9} a^{8}+\frac{1}{2} a^{7} x^{8}+\frac{4}{7} x^{7} a^{6}-\frac{2}{3} x^{6} a^{5}-2 a^{4} x^{5}-x^{4} a^{3}+\frac{4}{3} x^{3} a^{2}+2 a \,x^{2}+x \right)"," ",0,"c^4*(1/9*x^9*a^8+1/2*a^7*x^8+4/7*x^7*a^6-2/3*x^6*a^5-2*a^4*x^5-x^4*a^3+4/3*x^3*a^2+2*a*x^2+x)","A"
1184,1,45,31,0.023000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^3,x)","c^{3} \left(-\frac{1}{7} x^{7} a^{6}-\frac{2}{3} x^{6} a^{5}-a^{4} x^{5}+\frac{5}{3} x^{3} a^{2}+2 a \,x^{2}+x \right)"," ",0,"c^3*(-1/7*x^7*a^6-2/3*x^6*a^5-a^4*x^5+5/3*x^3*a^2+2*a*x^2+x)","A"
1185,1,16,15,0.024000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^2,x)","\frac{c^{2} \left(a x +1\right)^{5}}{5 a}"," ",0,"1/5*c^2*(a*x+1)^5/a","A"
1186,1,34,34,0.027000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c),x)","-\frac{a^{2} c \,x^{3}}{3}-2 a c \,x^{2}-7 c x -\frac{8 c \ln \left(a x -1\right)}{a}"," ",0,"-1/3*a^2*c*x^3-2*a*c*x^2-7*c*x-8*c/a*ln(a*x-1)","A"
1187,1,28,13,0.030000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(-a^2*c*x^2+c),x)","\frac{\frac{1}{a \left(a x -1\right)}+\frac{1}{a \left(a x -1\right)^{2}}}{c}"," ",0,"1/c*(1/a/(a*x-1)+1/a/(a*x-1)^2)","B"
1188,1,16,16,0.023000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(-a^2*c*x^2+c)^2,x)","-\frac{1}{3 c^{2} a \left(a x -1\right)^{3}}"," ",0,"-1/3/c^2/a/(a*x-1)^3","A"
1189,1,90,77,0.034000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(-a^2*c*x^2+c)^3,x)","\frac{1}{8 c^{3} a \left(a x -1\right)^{4}}-\frac{1}{12 c^{3} a \left(a x -1\right)^{3}}+\frac{1}{16 c^{3} a \left(a x -1\right)^{2}}-\frac{1}{16 c^{3} a \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{32 a \,c^{3}}+\frac{\ln \left(a x +1\right)}{32 a \,c^{3}}"," ",0,"1/8/c^3/a/(a*x-1)^4-1/12/c^3/a/(a*x-1)^3+1/16/c^3/a/(a*x-1)^2-1/16/c^3/a/(a*x-1)-1/32/a/c^3*ln(a*x-1)+1/32*ln(a*x+1)/a/c^3","A"
1190,1,120,108,0.036000," ","int((a*x+1)^4/(-a^2*x^2+1)^2/(-a^2*c*x^2+c)^4,x)","-\frac{1}{20 c^{4} a \left(a x -1\right)^{5}}+\frac{1}{16 c^{4} a \left(a x -1\right)^{4}}-\frac{1}{16 c^{4} a \left(a x -1\right)^{3}}+\frac{1}{16 c^{4} a \left(a x -1\right)^{2}}-\frac{5}{64 c^{4} a \left(a x -1\right)}-\frac{3 \ln \left(a x -1\right)}{64 c^{4} a}-\frac{1}{64 a \,c^{4} \left(a x +1\right)}+\frac{3 \ln \left(a x +1\right)}{64 a \,c^{4}}"," ",0,"-1/20/c^4/a/(a*x-1)^5+1/16/c^4/a/(a*x-1)^4-1/16/c^4/a/(a*x-1)^3+1/16/c^4/a/(a*x-1)^2-5/64/c^4/a/(a*x-1)-3/64/c^4/a*ln(a*x-1)-1/64/a/c^4/(a*x+1)+3/64*ln(a*x+1)/a/c^4","A"
1191,0,0,61,0.426000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right)^{4} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(-a^{2} x^{2}+1\right)^{2}}\, dx"," ",0,"int((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^p,x)","F"
1192,1,201,105,0.073000," ","int((-a^2*c*x^2+c)^4/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{c^{4} a^{5} x^{6} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{9}+\frac{c^{4} a^{3} x^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3}-\frac{c^{4} a \,x^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3}+\frac{c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{9 a}+\frac{c^{4} a^{4} x^{5} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{8}-\frac{19 c^{4} a^{2} x^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{48}+\frac{29 c^{4} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{64}+\frac{35 c^{4} x \sqrt{-a^{2} x^{2}+1}}{128}+\frac{35 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{128 \sqrt{a^{2}}}"," ",0,"-1/9*c^4*a^5*x^6*(-a^2*x^2+1)^(3/2)+1/3*c^4*a^3*x^4*(-a^2*x^2+1)^(3/2)-1/3*c^4*a*x^2*(-a^2*x^2+1)^(3/2)+1/9*c^4*(-a^2*x^2+1)^(3/2)/a+1/8*c^4*a^4*x^5*(-a^2*x^2+1)^(3/2)-19/48*c^4*a^2*x^3*(-a^2*x^2+1)^(3/2)+29/64*c^4*x*(-a^2*x^2+1)^(3/2)+35/128*c^4*x*(-a^2*x^2+1)^(1/2)+35/128*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
1193,1,155,87,0.047000," ","int((-a^2*c*x^2+c)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{c^{3} a^{3} x^{4} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{7}-\frac{2 c^{3} a \,x^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{7}+\frac{c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{7 a}-\frac{c^{3} a^{2} x^{3} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{6}+\frac{3 c^{3} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{8}+\frac{5 c^{3} x \sqrt{-a^{2} x^{2}+1}}{16}+\frac{5 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 \sqrt{a^{2}}}"," ",0,"1/7*c^3*a^3*x^4*(-a^2*x^2+1)^(3/2)-2/7*c^3*a*x^2*(-a^2*x^2+1)^(3/2)+1/7*c^3*(-a^2*x^2+1)^(3/2)/a-1/6*c^3*a^2*x^3*(-a^2*x^2+1)^(3/2)+3/8*c^3*x*(-a^2*x^2+1)^(3/2)+5/16*c^3*x*(-a^2*x^2+1)^(1/2)+5/16*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
1194,1,109,69,0.039000," ","int((-a^2*c*x^2+c)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","-\frac{c^{2} a \,x^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{5}+\frac{c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{5 a}+\frac{c^{2} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4}+\frac{3 c^{2} x \sqrt{-a^{2} x^{2}+1}}{8}+\frac{3 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}"," ",0,"-1/5*c^2*a*x^2*(-a^2*x^2+1)^(3/2)+1/5*c^2*(-a^2*x^2+1)^(3/2)/a+1/4*c^2*x*(-a^2*x^2+1)^(3/2)+3/8*c^2*x*(-a^2*x^2+1)^(1/2)+3/8*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
1195,1,64,45,0.031000," ","int((-a^2*c*x^2+c)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{c \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 a}+\frac{c x \sqrt{-a^{2} x^{2}+1}}{2}+\frac{c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}"," ",0,"1/3*c*(-a^2*x^2+1)^(3/2)/a+1/2*c*x*(-a^2*x^2+1)^(1/2)+1/2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
1196,1,28,27,0.029000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c),x)","-\frac{\sqrt{-a^{2} x^{2}+1}}{a c \left(a x +1\right)}"," ",0,"-1/a/c/(a*x+1)*(-a^2*x^2+1)^(1/2)","A"
1197,1,42,44,0.029000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^2,x)","\frac{2 a^{2} x^{2}+2 a x -1}{3 \sqrt{-a^{2} x^{2}+1}\, \left(a x +1\right) a \,c^{2}}"," ",0,"1/3/(-a^2*x^2+1)^(1/2)*(2*a^2*x^2+2*a*x-1)/(a*x+1)/a/c^2","A"
1198,1,58,62,0.031000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^3,x)","-\frac{8 x^{4} a^{4}+8 x^{3} a^{3}-12 a^{2} x^{2}-12 a x +3}{15 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a x +1\right) c^{3} a}"," ",0,"-1/15/(-a^2*x^2+1)^(3/2)*(8*a^4*x^4+8*a^3*x^3-12*a^2*x^2-12*a*x+3)/(a*x+1)/c^3/a","A"
1199,1,74,80,0.031000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^4,x)","\frac{16 x^{6} a^{6}+16 x^{5} a^{5}-40 x^{4} a^{4}-40 x^{3} a^{3}+30 a^{2} x^{2}+30 a x -5}{35 \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a x +1\right) c^{4} a}"," ",0,"1/35/(-a^2*x^2+1)^(5/2)*(16*a^6*x^6+16*a^5*x^5-40*a^4*x^4-40*a^3*x^3+30*a^2*x^2+30*a*x-5)/(a*x+1)/c^4/a","A"
1200,1,90,98,0.033000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^5,x)","-\frac{128 x^{8} a^{8}+128 a^{7} x^{7}-448 x^{6} a^{6}-448 x^{5} a^{5}+560 x^{4} a^{4}+560 x^{3} a^{3}-280 a^{2} x^{2}-280 a x +35}{315 \left(-a^{2} x^{2}+1\right)^{\frac{7}{2}} \left(a x +1\right) c^{5} a}"," ",0,"-1/315/(-a^2*x^2+1)^(7/2)*(128*a^8*x^8+128*a^7*x^7-448*a^6*x^6-448*a^5*x^5+560*a^4*x^4+560*a^3*x^3-280*a^2*x^2-280*a*x+35)/(a*x+1)/c^5/a","A"
1201,1,68,75,0.028000," ","int(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x^{1+m} \left(a m x +a x -m -2\right) \sqrt{-a^{2} c \,x^{2}+c}\, \sqrt{-a^{2} x^{2}+1}}{\left(2+m \right) \left(1+m \right) \left(a x -1\right) \left(a x +1\right)}"," ",0,"x^(1+m)*(a*m*x+a*x-m-2)*(-a^2*c*x^2+c)^(1/2)*(-a^2*x^2+1)^(1/2)/(2+m)/(1+m)/(a*x-1)/(a*x+1)","A"
1202,1,51,62,0.028000," ","int(x^2*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x^{3} \left(3 a x -4\right) \sqrt{-a^{2} c \,x^{2}+c}\, \sqrt{-a^{2} x^{2}+1}}{12 \left(a x -1\right) \left(a x +1\right)}"," ",0,"1/12*x^3*(3*a*x-4)*(-a^2*c*x^2+c)^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x-1)/(a*x+1)","A"
1203,1,51,62,0.027000," ","int(x*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x^{2} \left(2 a x -3\right) \sqrt{-a^{2} c \,x^{2}+c}\, \sqrt{-a^{2} x^{2}+1}}{6 \left(a x -1\right) \left(a x +1\right)}"," ",0,"1/6*x^2*(2*a*x-3)*(-a^2*c*x^2+c)^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x-1)/(a*x+1)","A"
1204,1,48,59,0.024000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x \left(a x -2\right) \sqrt{-a^{2} c \,x^{2}+c}\, \sqrt{-a^{2} x^{2}+1}}{2 \left(a x -1\right) \left(a x +1\right)}"," ",0,"1/2*x*(a*x-2)*(-a^2*c*x^2+c)^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x-1)/(a*x+1)","A"
1205,1,47,58,0.033000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x)","\frac{\left(a x -\ln \left(x \right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"(a*x-ln(x))*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
1206,1,49,61,0.039000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(a \ln \left(x \right) x +1\right)}{\left(a^{2} x^{2}-1\right) x}"," ",0,"(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(a*ln(x)*x+1)/(a^2*x^2-1)/x","A"
1207,1,65,79,0.028000," ","int((-a^2*c*x^2+c)^(3/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x \left(3 x^{3} a^{3}-4 a^{2} x^{2}-6 a x +12\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{-a^{2} x^{2}+1}}{12 \left(a x +1\right)^{2} \left(a x -1\right)^{2}}"," ",0,"1/12*x*(3*a^3*x^3-4*a^2*x^2-6*a*x+12)*(-a^2*c*x^2+c)^(3/2)*(-a^2*x^2+1)^(1/2)/(a*x+1)^2/(a*x-1)^2","A"
1208,1,81,124,0.034000," ","int((-a^2*c*x^2+c)^(5/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x \left(5 x^{5} a^{5}-6 x^{4} a^{4}-15 x^{3} a^{3}+20 a^{2} x^{2}+15 a x -30\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{-a^{2} x^{2}+1}}{30 \left(a x +1\right)^{3} \left(a x -1\right)^{3}}"," ",0,"1/30*x*(5*a^5*x^5-6*a^4*x^4-15*a^3*x^3+20*a^2*x^2+15*a*x-30)*(-a^2*c*x^2+c)^(5/2)*(-a^2*x^2+1)^(1/2)/(a*x+1)^3/(a*x-1)^3","A"
1209,1,97,165,0.030000," ","int((-a^2*c*x^2+c)^(7/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x \left(35 a^{7} x^{7}-40 x^{6} a^{6}-140 x^{5} a^{5}+168 x^{4} a^{4}+210 x^{3} a^{3}-280 a^{2} x^{2}-140 a x +280\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}} \sqrt{-a^{2} x^{2}+1}}{280 \left(a x +1\right)^{4} \left(a x -1\right)^{4}}"," ",0,"1/280*x*(35*a^7*x^7-40*a^6*x^6-140*a^5*x^5+168*a^4*x^4+210*a^3*x^3-280*a^2*x^2-140*a*x+280)*(-a^2*c*x^2+c)^(7/2)*(-a^2*x^2+1)^(1/2)/(a*x+1)^4/(a*x-1)^4","A"
1210,1,113,206,0.031000," ","int((-a^2*c*x^2+c)^(9/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\frac{x \left(63 a^{9} x^{9}-70 x^{8} a^{8}-315 a^{7} x^{7}+360 x^{6} a^{6}+630 x^{5} a^{5}-756 x^{4} a^{4}-630 x^{3} a^{3}+840 a^{2} x^{2}+315 a x -630\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}} \sqrt{-a^{2} x^{2}+1}}{630 \left(a x +1\right)^{5} \left(a x -1\right)^{5}}"," ",0,"1/630*x*(63*a^9*x^9-70*a^8*x^8-315*a^7*x^7+360*a^6*x^6+630*a^5*x^5-756*a^4*x^4-630*a^3*x^3+840*a^2*x^2+315*a*x-630)*(-a^2*c*x^2+c)^(9/2)*(-a^2*x^2+1)^(1/2)/(a*x+1)^5/(a*x-1)^5","A"
1211,1,40,35,0.033000," ","int(1/(a*x+1)*(-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)}\, \ln \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}\, c a}"," ",0,"1/(-a^2*x^2+1)^(1/2)/c/a*(-c*(a^2*x^2-1))^(1/2)*ln(a*x+1)","A"
1212,1,88,78,0.046000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)+\ln \left(a x -1\right)-\ln \left(a x +1\right)+2\right)}{4 \left(a^{2} x^{2}-1\right) c^{2} a \left(a x +1\right)}"," ",0,"1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x*a-a*x*ln(a*x+1)+ln(a*x-1)-ln(a*x+1)+2)/(a^2*x^2-1)/c^2/a/(a*x+1)","A"
1213,1,166,159,0.050000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)+3 \ln \left(a x -1\right) x^{2} a^{2}-3 \ln \left(a x +1\right) x^{2} a^{2}+6 a^{2} x^{2}-3 \ln \left(a x -1\right) x a +3 a x \ln \left(a x +1\right)+6 a x -3 \ln \left(a x -1\right)+3 \ln \left(a x +1\right)-4\right)}{16 \left(a^{2} x^{2}-1\right) c^{3} a \left(a x -1\right) \left(a x +1\right)^{2}}"," ",0,"1/16*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)+3*ln(a*x-1)*x^2*a^2-3*ln(a*x+1)*x^2*a^2+6*a^2*x^2-3*ln(a*x-1)*x*a+3*a*x*ln(a*x+1)+6*a*x-3*ln(a*x-1)+3*ln(a*x+1)-4)/(a^2*x^2-1)/c^3/a/(a*x-1)/(a*x+1)^2","A"
1214,1,238,240,0.050000," ","int(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(7/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(15 \ln \left(a x -1\right) x^{5} a^{5}-15 \ln \left(a x +1\right) x^{5} a^{5}+15 \ln \left(a x -1\right) x^{4} a^{4}-15 \ln \left(a x +1\right) x^{4} a^{4}+30 x^{4} a^{4}-30 \ln \left(a x -1\right) x^{3} a^{3}+30 a^{3} x^{3} \ln \left(a x +1\right)+30 x^{3} a^{3}-30 \ln \left(a x -1\right) x^{2} a^{2}+30 \ln \left(a x +1\right) x^{2} a^{2}-50 a^{2} x^{2}+15 \ln \left(a x -1\right) x a -15 a x \ln \left(a x +1\right)-50 a x +15 \ln \left(a x -1\right)-15 \ln \left(a x +1\right)+16\right)}{96 \left(a^{2} x^{2}-1\right) c^{4} a \left(a x -1\right)^{2} \left(a x +1\right)^{3}}"," ",0,"1/96*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(15*ln(a*x-1)*x^5*a^5-15*ln(a*x+1)*x^5*a^5+15*ln(a*x-1)*x^4*a^4-15*ln(a*x+1)*x^4*a^4+30*x^4*a^4-30*ln(a*x-1)*x^3*a^3+30*a^3*x^3*ln(a*x+1)+30*x^3*a^3-30*ln(a*x-1)*x^2*a^2+30*ln(a*x+1)*x^2*a^2-50*a^2*x^2+15*ln(a*x-1)*x*a-15*a*x*ln(a*x+1)-50*a*x+15*ln(a*x-1)-15*ln(a*x+1)+16)/(a^2*x^2-1)/c^4/a/(a*x-1)^2/(a*x+1)^3","A"
1215,0,0,129,0.413000," ","int(x^m*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \left(-a^{2} c \,x^{2}+c \right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int(x^m*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
1216,0,0,75,0.423000," ","int(x^3*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{3} \left(-a^{2} x^{2}+1\right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int(x^3*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
1217,0,0,74,0.426000," ","int(x^2*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{2} \left(-a^{2} x^{2}+1\right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int(x^2*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
1218,0,0,50,0.422000," ","int(x*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{x \left(-a^{2} x^{2}+1\right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int(x*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
1219,0,0,47,0.420000," ","int((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{\left(-a^{2} x^{2}+1\right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
1220,0,0,65,0.426000," ","int((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x)","\int \frac{\left(-a^{2} x^{2}+1\right)^{p} \sqrt{-a^{2} x^{2}+1}}{\left(a x +1\right) x}\, dx"," ",0,"int((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x)","F"
1221,0,0,66,0.421000," ","int((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x)","\int \frac{\left(-a^{2} x^{2}+1\right)^{p} \sqrt{-a^{2} x^{2}+1}}{\left(a x +1\right) x^{2}}\, dx"," ",0,"int((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x)","F"
1222,0,0,124,0.415000," ","int(x^3*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{3} \left(-a^{2} c \,x^{2}+c \right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int(x^3*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
1223,0,0,123,0.418000," ","int(x^2*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{2} \left(-a^{2} c \,x^{2}+c \right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int(x^2*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
1224,0,0,88,0.419000," ","int(x*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{x \left(-a^{2} c \,x^{2}+c \right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int(x*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
1225,0,0,74,0.418000," ","int((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{p} \sqrt{-a^{2} x^{2}+1}}{a x +1}\, dx"," ",0,"int((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x)","F"
1226,0,0,103,0.420000," ","int((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{p} \sqrt{-a^{2} x^{2}+1}}{\left(a x +1\right) x}\, dx"," ",0,"int((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x)","F"
1227,0,0,104,0.417000," ","int((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{p} \sqrt{-a^{2} x^{2}+1}}{\left(a x +1\right) x^{2}}\, dx"," ",0,"int((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x)","F"
1228,1,61,65,0.026000," ","int((-a^2*c*x^2+c)^4/(a*x+1)^2*(-a^2*x^2+1),x)","c^{4} \left(-\frac{1}{9} x^{9} a^{8}+\frac{1}{4} a^{7} x^{8}+\frac{2}{7} x^{7} a^{6}-x^{6} a^{5}+\frac{3}{2} x^{4} a^{3}-\frac{2}{3} x^{3} a^{2}-a \,x^{2}+x \right)"," ",0,"c^4*(-1/9*x^9*a^8+1/4*a^7*x^8+2/7*x^7*a^6-x^6*a^5+3/2*x^4*a^3-2/3*x^3*a^2-a*x^2+x)","A"
1229,1,52,49,0.026000," ","int((-a^2*c*x^2+c)^3/(a*x+1)^2*(-a^2*x^2+1),x)","c^{3} \left(\frac{1}{7} x^{7} a^{6}-\frac{1}{3} x^{6} a^{5}-\frac{1}{5} a^{4} x^{5}+x^{4} a^{3}-\frac{1}{3} x^{3} a^{2}-a \,x^{2}+x \right)"," ",0,"c^3*(1/7*x^7*a^6-1/3*x^6*a^5-1/5*a^4*x^5+x^4*a^3-1/3*x^3*a^2-a*x^2+x)","A"
1230,1,29,33,0.025000," ","int((-a^2*c*x^2+c)^2/(a*x+1)^2*(-a^2*x^2+1),x)","c^{2} \left(-\frac{1}{5} a^{4} x^{5}+\frac{1}{2} x^{4} a^{3}-a \,x^{2}+x \right)"," ",0,"c^2*(-1/5*a^4*x^5+1/2*x^4*a^3-a*x^2+x)","A"
1231,1,14,14,0.024000," ","int((-a^2*c*x^2+c)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{c \left(a x -1\right)^{3}}{3 a}"," ",0,"1/3*c*(a*x-1)^3/a","A"
1232,1,16,15,0.025000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c),x)","-\frac{1}{a c \left(a x +1\right)}"," ",0,"-1/a/c/(a*x+1)","A"
1233,1,60,43,0.034000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^2,x)","-\frac{\ln \left(a x -1\right)}{8 c^{2} a}-\frac{1}{4 a \,c^{2} \left(a x +1\right)^{2}}-\frac{1}{4 a \,c^{2} \left(a x +1\right)}+\frac{\ln \left(a x +1\right)}{8 a \,c^{2}}"," ",0,"-1/8/c^2/a*ln(a*x-1)-1/4/a/c^2/(a*x+1)^2-1/4/a/c^2/(a*x+1)+1/8*ln(a*x+1)/a/c^2","A"
1234,1,90,74,0.037000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^3,x)","-\frac{1}{16 c^{3} a \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{8 a \,c^{3}}-\frac{1}{12 a \,c^{3} \left(a x +1\right)^{3}}-\frac{1}{8 a \,c^{3} \left(a x +1\right)^{2}}-\frac{3}{16 a \,c^{3} \left(a x +1\right)}+\frac{\ln \left(a x +1\right)}{8 a \,c^{3}}"," ",0,"-1/16/c^3/a/(a*x-1)-1/8/a/c^3*ln(a*x-1)-1/12/a/c^3/(a*x+1)^3-1/8/a/c^3/(a*x+1)^2-3/16/a/c^3/(a*x+1)+1/8*ln(a*x+1)/a/c^3","A"
1235,1,120,105,0.037000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^4,x)","\frac{1}{64 c^{4} a \left(a x -1\right)^{2}}-\frac{5}{64 c^{4} a \left(a x -1\right)}-\frac{15 \ln \left(a x -1\right)}{128 c^{4} a}-\frac{1}{32 a \,c^{4} \left(a x +1\right)^{4}}-\frac{1}{16 a \,c^{4} \left(a x +1\right)^{3}}-\frac{3}{32 a \,c^{4} \left(a x +1\right)^{2}}-\frac{5}{32 a \,c^{4} \left(a x +1\right)}+\frac{15 \ln \left(a x +1\right)}{128 a \,c^{4}}"," ",0,"1/64/c^4/a/(a*x-1)^2-5/64/c^4/a/(a*x-1)-15/128/c^4/a*ln(a*x-1)-1/32/a/c^4/(a*x+1)^4-1/16/a/c^4/(a*x+1)^3-3/32/a/c^4/(a*x+1)^2-5/32/a/c^4/(a*x+1)+15/128*ln(a*x+1)/a/c^4","A"
1236,1,202,113,0.049000," ","int(x^3*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{x^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{5 a^{2} c}+\frac{4 \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{5 c \,a^{4}}-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{2 a^{3} c}+\frac{5 x \sqrt{-a^{2} c \,x^{2}+c}}{4 a^{3}}+\frac{5 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{4 a^{3} \sqrt{a^{2} c}}-\frac{2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}{a^{4}}-\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{a^{3} \sqrt{a^{2} c}}"," ",0,"1/5*x^2*(-a^2*c*x^2+c)^(3/2)/a^2/c+4/5/c/a^4*(-a^2*c*x^2+c)^(3/2)-1/2/a^3*x*(-a^2*c*x^2+c)^(3/2)/c+5/4/a^3*x*(-a^2*c*x^2+c)^(1/2)+5/4/a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a^4*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)-2/a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","A"
1237,1,178,92,0.043000," ","int(x^2*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4 a^{2} c}-\frac{9 x \sqrt{-a^{2} c \,x^{2}+c}}{8 a^{2}}-\frac{9 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{8 a^{2} \sqrt{a^{2} c}}-\frac{2 \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 a^{3} c}+\frac{2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}{a^{3}}+\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{a^{2} \sqrt{a^{2} c}}"," ",0,"1/4*x*(-a^2*c*x^2+c)^(3/2)/a^2/c-9/8/a^2*x*(-a^2*c*x^2+c)^(1/2)-9/8/a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3/a^3*(-a^2*c*x^2+c)^(3/2)/c+2/a^3*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)+2/a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","A"
1238,1,154,71,0.039000," ","int(x*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 a^{2} c}+\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{a}+\frac{c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{a \sqrt{a^{2} c}}-\frac{2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}{a^{2}}-\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{a \sqrt{a^{2} c}}"," ",0,"1/3*(-a^2*c*x^2+c)^(3/2)/a^2/c+x/a*(-a^2*c*x^2+c)^(1/2)+1/a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a^2*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)-2/a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","B"
1239,1,126,71,0.036000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{2}-\frac{c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{2 \sqrt{a^{2} c}}+\frac{2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}{a}+\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"-1/2*x*(-a^2*c*x^2+c)^(1/2)-1/2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/a*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)+2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","A"
1240,1,120,64,0.041000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x,x)","\sqrt{-a^{2} c \,x^{2}+c}-\sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)-2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}-\frac{2 a c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"(-a^2*c*x^2+c)^(1/2)-c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)-2*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)-2*a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","A"
1241,1,203,68,0.043000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^2,x)","2 \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a -2 \sqrt{-a^{2} c \,x^{2}+c}\, a -\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}-a^{2} x \sqrt{-a^{2} c \,x^{2}+c}-\frac{a^{2} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}+2 a \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}+\frac{2 a^{2} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"2*c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a-2*(-a^2*c*x^2+c)^(1/2)*a-1/c/x*(-a^2*c*x^2+c)^(3/2)-a^2*x*(-a^2*c*x^2+c)^(1/2)-a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2*a*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)+2*a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","B"
1242,1,231,64,0.047000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^3,x)","-\frac{3 \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a^{2}}{2}+\frac{3 \sqrt{-a^{2} c \,x^{2}+c}\, a^{2}}{2}+\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}+2 a^{3} x \sqrt{-a^{2} c \,x^{2}+c}+\frac{2 a^{3} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{2 c \,x^{2}}-2 a^{2} \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}-\frac{2 a^{3} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"-3/2*c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a^2+3/2*(-a^2*c*x^2+c)^(1/2)*a^2+2*a/c/x*(-a^2*c*x^2+c)^(3/2)+2*a^3*x*(-a^2*c*x^2+c)^(1/2)+2*a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-1/2/c/x^2*(-a^2*c*x^2+c)^(3/2)-2*a^2*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)-2*a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","B"
1243,1,253,83,0.052000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^4,x)","\sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a^{3}-\sqrt{-a^{2} c \,x^{2}+c}\, a^{3}-\frac{2 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}-2 a^{4} x \sqrt{-a^{2} c \,x^{2}+c}-\frac{2 a^{4} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 c \,x^{3}}+\frac{a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c \,x^{2}}+2 a^{3} \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}+\frac{2 a^{4} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a^3-(-a^2*c*x^2+c)^(1/2)*a^3-2*a^2/c/x*(-a^2*c*x^2+c)^(3/2)-2*a^4*x*(-a^2*c*x^2+c)^(1/2)-2*a^4*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-1/3/c/x^3*(-a^2*c*x^2+c)^(3/2)+a/c/x^2*(-a^2*c*x^2+c)^(3/2)+2*a^3*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)+2*a^4*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","B"
1244,1,279,106,0.054000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^5,x)","-\frac{7 \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a^{4}}{8}+\frac{7 \sqrt{-a^{2} c \,x^{2}+c}\, a^{4}}{8}+\frac{2 a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}+2 a^{5} x \sqrt{-a^{2} c \,x^{2}+c}+\frac{2 a^{5} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}+\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 c \,x^{3}}-\frac{9 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{8 c \,x^{2}}-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4 c \,x^{4}}-2 a^{4} \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}-\frac{2 a^{5} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"-7/8*c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a^4+7/8*(-a^2*c*x^2+c)^(1/2)*a^4+2*a^3/c/x*(-a^2*c*x^2+c)^(3/2)+2*a^5*x*(-a^2*c*x^2+c)^(1/2)+2*a^5*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/3*a/c/x^3*(-a^2*c*x^2+c)^(3/2)-9/8*a^2/c/x^2*(-a^2*c*x^2+c)^(3/2)-1/4/c/x^4*(-a^2*c*x^2+c)^(3/2)-2*a^4*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)-2*a^5*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","B"
1245,1,174,88,0.036000," ","int((-a^2*c*x^2+c)^(3/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4}-\frac{3 c x \sqrt{-a^{2} c \,x^{2}+c}}{8}-\frac{3 c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{8 \sqrt{a^{2} c}}+\frac{2 \left(-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a}+c \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}\, x +\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"-1/4*x*(-a^2*c*x^2+c)^(3/2)-3/8*c*x*(-a^2*c*x^2+c)^(1/2)-3/8*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/3/a*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(3/2)+c*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)*x+c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","A"
1246,1,226,107,0.037000," ","int((-a^2*c*x^2+c)^(5/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{6}-\frac{5 c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{24}-\frac{5 c^{2} x \sqrt{-a^{2} c \,x^{2}+c}}{16}-\frac{5 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{16 \sqrt{a^{2} c}}+\frac{2 \left(-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{5 a}+\frac{c \left(-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{2}+\frac{3 c^{2} \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}\, x}{4}+\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{4 \sqrt{a^{2} c}}"," ",0,"-1/6*x*(-a^2*c*x^2+c)^(5/2)-5/24*c*x*(-a^2*c*x^2+c)^(3/2)-5/16*c^2*x*(-a^2*c*x^2+c)^(1/2)-5/16*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/5/a*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(5/2)+1/2*c*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(3/2)*x+3/4*c^2*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)*x+3/4*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","B"
1247,1,276,126,0.037000," ","int((-a^2*c*x^2+c)^(7/2)/(a*x+1)^2*(-a^2*x^2+1),x)","-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{8}-\frac{7 c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{48}-\frac{35 c^{2} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{192}-\frac{35 c^{3} x \sqrt{-a^{2} c \,x^{2}+c}}{128}-\frac{35 c^{4} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{128 \sqrt{a^{2} c}}+\frac{2 \left(-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)\right)^{\frac{7}{2}}}{7 a}+\frac{c \left(-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}} x}{3}+\frac{5 c^{2} \left(-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{12}+\frac{5 c^{3} \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}\, x}{8}+\frac{5 c^{4} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}\right)}{8 \sqrt{a^{2} c}}"," ",0,"-1/8*x*(-a^2*c*x^2+c)^(7/2)-7/48*c*x*(-a^2*c*x^2+c)^(5/2)-35/192*c^2*x*(-a^2*c*x^2+c)^(3/2)-35/128*c^3*x*(-a^2*c*x^2+c)^(1/2)-35/128*c^4/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/7/a*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(7/2)+1/3*c*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(5/2)*x+5/12*c^2*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(3/2)*x+5/8*c^3*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)*x+5/8*c^4/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2))","B"
1248,1,74,53,0.036000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 a c \left(x +\frac{1}{a}\right)}}{a^{2} c \left(x +\frac{1}{a}\right)}"," ",0,"-1/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a^2/c/(x+1/a)*(-(x+1/a)^2*a^2*c+2*a*c*(x+1/a))^(1/2)","A"
1249,1,31,44,0.027000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\left(a x -1\right)^{2} \left(a x +2\right)}{3 \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} a}"," ",0,"-1/3*(a*x-1)^2*(a*x+2)/(-a^2*c*x^2+c)^(3/2)/a","A"
1250,1,47,63,0.031000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(5/2),x)","\frac{\left(a x -1\right)^{2} \left(2 x^{3} a^{3}+4 a^{2} x^{2}+a x -2\right)}{5 \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} a}"," ",0,"1/5*(a*x-1)^2*(2*a^3*x^3+4*a^2*x^2+a*x-2)/(-a^2*c*x^2+c)^(5/2)/a","A"
1251,1,64,82,0.032000," ","int(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(7/2),x)","-\frac{\left(a x -1\right)^{2} \left(8 x^{5} a^{5}+16 x^{4} a^{4}-4 x^{3} a^{3}-24 a^{2} x^{2}-9 a x +6\right)}{21 \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}} a}"," ",0,"-1/21*(a*x-1)^2*(8*a^5*x^5+16*a^4*x^4-4*a^3*x^3-24*a^2*x^2-9*a*x+6)/(-a^2*c*x^2+c)^(7/2)/a","A"
1252,0,0,154,0.337000," ","int(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","\int \frac{x^{m} \sqrt{-a^{2} c \,x^{2}+c}\, \left(-a^{2} x^{2}+1\right)}{\left(a x +1\right)^{2}}\, dx"," ",0,"int(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x)","F"
1253,0,0,53,0.382000," ","int((-a^2*c*x^2+c)^p/(a*x+1)^2*(-a^2*x^2+1),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{p} \left(-a^{2} x^{2}+1\right)}{\left(a x +1\right)^{2}}\, dx"," ",0,"int((-a^2*c*x^2+c)^p/(a*x+1)^2*(-a^2*x^2+1),x)","F"
1254,1,173,141,0.054000," ","int((-a^2*c*x^2+c)^4/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{c^{4} a^{3} x^{4} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{9}-\frac{22 c^{4} a \,x^{2} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{63}+\frac{29 c^{4} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{63 a}+\frac{3 c^{4} a^{2} x^{3} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{8}-\frac{7 c^{4} x \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{48}+\frac{55 c^{4} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{192}+\frac{55 c^{4} x \sqrt{-a^{2} x^{2}+1}}{128}+\frac{55 c^{4} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{128 \sqrt{a^{2}}}"," ",0,"-1/9*c^4*a^3*x^4*(-a^2*x^2+1)^(5/2)-22/63*c^4*a*x^2*(-a^2*x^2+1)^(5/2)+29/63*c^4*(-a^2*x^2+1)^(5/2)/a+3/8*c^4*a^2*x^3*(-a^2*x^2+1)^(5/2)-7/48*c^4*x*(-a^2*x^2+1)^(5/2)+55/192*c^4*x*(-a^2*x^2+1)^(3/2)+55/128*c^4*x*(-a^2*x^2+1)^(1/2)+55/128*c^4/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
1255,1,127,123,0.039000," ","int((-a^2*c*x^2+c)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{c^{3} a \,x^{2} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{7}+\frac{23 c^{3} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{35 a}-\frac{c^{3} x \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{2}+\frac{3 c^{3} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{8}+\frac{9 c^{3} x \sqrt{-a^{2} x^{2}+1}}{16}+\frac{9 c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 \sqrt{a^{2}}}"," ",0,"1/7*c^3*a*x^2*(-a^2*x^2+1)^(5/2)+23/35*c^3*(-a^2*x^2+1)^(5/2)/a-1/2*c^3*x*(-a^2*x^2+1)^(5/2)+3/8*c^3*x*(-a^2*x^2+1)^(3/2)+9/16*c^3*x*(-a^2*x^2+1)^(1/2)+9/16*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
1256,1,189,105,0.036000," ","int((-a^2*c*x^2+c)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{c^{2} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{5 a}-\frac{3 c^{2} x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4}-\frac{9 c^{2} x \sqrt{-a^{2} x^{2}+1}}{8}-\frac{9 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 \sqrt{a^{2}}}+\frac{4 c^{2} \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a}+2 c^{2} \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x +\frac{2 c^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{\sqrt{a^{2}}}"," ",0,"-1/5*c^2*(-a^2*x^2+1)^(5/2)/a-3/4*c^2*x*(-a^2*x^2+1)^(3/2)-9/8*c^2*x*(-a^2*x^2+1)^(1/2)-9/8*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+4/3*c^2/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+2*c^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x+2*c^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","A"
1257,1,133,79,0.040000," ","int((-a^2*c*x^2+c)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{2 c \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{5}{2}}}{a^{3} \left(x +\frac{1}{a}\right)^{2}}+\frac{5 c \left(-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a}+\frac{5 c \sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}\, x}{2}+\frac{5 c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} \left(x +\frac{1}{a}\right)^{2}+2 a \left(x +\frac{1}{a}\right)}}\right)}{2 \sqrt{a^{2}}}"," ",0,"2*c/a^3/(x+1/a)^2*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(5/2)+5/3*c/a*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(3/2)+5/2*c*(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2)*x+5/2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*(x+1/a)^2+2*a*(x+1/a))^(1/2))","A"
1258,1,28,27,0.030000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c),x)","-\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{3 a c \left(a x +1\right)^{3}}"," ",0,"-1/3/a/c/(a*x+1)^3*(-a^2*x^2+1)^(3/2)","A"
1259,1,42,82,0.029000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^2,x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(2 a^{2} x^{2}+6 a x +7\right)}{15 \left(a x +1\right)^{3} c^{2} a}"," ",0,"-1/15*(-a^2*x^2+1)^(1/2)*(2*a^2*x^2+6*a*x+7)/(a*x+1)^3/c^2/a","A"
1260,1,58,100,0.031000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^3,x)","\frac{8 x^{4} a^{4}+24 x^{3} a^{3}+20 a^{2} x^{2}-4 a x -13}{35 \sqrt{-a^{2} x^{2}+1}\, \left(a x +1\right)^{3} c^{3} a}"," ",0,"1/35/(-a^2*x^2+1)^(1/2)*(8*a^4*x^4+24*a^3*x^3+20*a^2*x^2-4*a*x-13)/(a*x+1)^3/c^3/a","A"
1261,1,74,118,0.031000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^4,x)","-\frac{16 x^{6} a^{6}+48 x^{5} a^{5}+24 x^{4} a^{4}-56 x^{3} a^{3}-66 a^{2} x^{2}-6 a x +19}{63 \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a x +1\right)^{3} c^{4} a}"," ",0,"-1/63/(-a^2*x^2+1)^(3/2)*(16*a^6*x^6+48*a^5*x^5+24*a^4*x^4-56*a^3*x^3-66*a^2*x^2-6*a*x+19)/(a*x+1)^3/c^4/a","A"
1262,1,88,195,0.040000," ","int(x^3*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(-12 x^{5} a^{5}+45 x^{4} a^{4}-80 x^{3} a^{3}+120 a^{2} x^{2}-240 a x +240 \ln \left(a x +1\right)\right)}{60 \left(a^{2} x^{2}-1\right) a^{4}}"," ",0,"1/60*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(-12*x^5*a^5+45*x^4*a^4-80*x^3*a^3+120*a^2*x^2-240*a*x+240*ln(a*x+1))/(a^2*x^2-1)/a^4","A"
1263,1,79,162,0.038000," ","int(x^2*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(x^{4} a^{4}-4 x^{3} a^{3}+8 a^{2} x^{2}-16 a x +16 \ln \left(a x +1\right)\right)}{4 \left(a^{2} x^{2}-1\right) a^{3}}"," ",0,"-1/4*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(x^4*a^4-4*x^3*a^3+8*a^2*x^2-16*a*x+16*ln(a*x+1))/(a^2*x^2-1)/a^3","A"
1264,1,72,129,0.037000," ","int(x*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(-2 x^{3} a^{3}+9 a^{2} x^{2}-24 a x +24 \ln \left(a x +1\right)\right)}{6 \left(a^{2} x^{2}-1\right) a^{2}}"," ",0,"1/6*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(-2*x^3*a^3+9*a^2*x^2-24*a*x+24*ln(a*x+1))/(a^2*x^2-1)/a^2","A"
1265,1,63,96,0.038000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2}-6 a x +8 \ln \left(a x +1\right)\right)}{2 \left(a^{2} x^{2}-1\right) a}"," ",0,"-1/2*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(a^2*x^2-6*a*x+8*ln(a*x+1))/(a^2*x^2-1)/a","A"
1266,1,56,90,0.044000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x)","\frac{\left(-a x -\ln \left(x \right)+4 \ln \left(a x +1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}}{a^{2} x^{2}-1}"," ",0,"(-a*x-ln(x)+4*ln(a*x+1))*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
1267,1,60,95,0.044000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(3 a \ln \left(x \right) x -4 a x \ln \left(a x +1\right)+1\right)}{\left(a^{2} x^{2}-1\right) x}"," ",0,"(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(3*a*ln(x)*x-4*a*x*ln(a*x+1)+1)/(a^2*x^2-1)/x","A"
1268,1,73,130,0.045000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(8 a^{2} \ln \left(x \right) x^{2}-8 \ln \left(a x +1\right) x^{2} a^{2}+6 a x -1\right)}{2 \left(a^{2} x^{2}-1\right) x^{2}}"," ",0,"-1/2*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(8*a^2*ln(x)*x^2-8*ln(a*x+1)*x^2*a^2+6*a*x-1)/(a^2*x^2-1)/x^2","A"
1269,1,81,163,0.046000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(24 a^{3} \ln \left(x \right) x^{3}-24 a^{3} x^{3} \ln \left(a x +1\right)+24 a^{2} x^{2}-9 a x +2\right)}{6 \left(a^{2} x^{2}-1\right) x^{3}}"," ",0,"1/6*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(24*a^3*ln(x)*x^3-24*a^3*x^3*ln(a*x+1)+24*a^2*x^2-9*a*x+2)/(a^2*x^2-1)/x^3","A"
1270,1,89,195,0.046000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(16 a^{4} \ln \left(x \right) x^{4}-16 \ln \left(a x +1\right) x^{4} a^{4}+16 x^{3} a^{3}-8 a^{2} x^{2}+4 a x -1\right)}{4 \left(a^{2} x^{2}-1\right) x^{4}}"," ",0,"-1/4*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(16*a^4*ln(x)*x^4-16*ln(a*x+1)*x^4*a^4+16*x^3*a^3-8*a^2*x^2+4*a*x-1)/(a^2*x^2-1)/x^4","A"
1271,1,97,165,0.030000," ","int((-a^2*c*x^2+c)^(9/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{x \left(21 a^{9} x^{9}-70 x^{8} a^{8}+240 x^{6} a^{6}-210 x^{5} a^{5}-252 x^{4} a^{4}+420 x^{3} a^{3}-315 a x +210\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{210 \left(a x +1\right)^{6} \left(a x -1\right)^{6}}"," ",0,"1/210*x*(21*a^9*x^9-70*a^8*x^8+240*a^6*x^6-210*a^5*x^5-252*a^4*x^4+420*a^3*x^3-315*a*x+210)*(-a^2*c*x^2+c)^(9/2)*(-a^2*x^2+1)^(3/2)/(a*x+1)^6/(a*x-1)^6","A"
1272,1,97,124,0.030000," ","int((-a^2*c*x^2+c)^(7/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{x \left(21 a^{7} x^{7}-72 x^{6} a^{6}+28 x^{5} a^{5}+168 x^{4} a^{4}-210 x^{3} a^{3}-56 a^{2} x^{2}+252 a x -168\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{168 \left(a x +1\right)^{5} \left(a x -1\right)^{5}}"," ",0,"1/168*x*(21*a^7*x^7-72*a^6*x^6+28*a^5*x^5+168*a^4*x^4-210*a^3*x^3-56*a^2*x^2+252*a*x-168)*(-a^2*c*x^2+c)^(7/2)*(-a^2*x^2+1)^(3/2)/(a*x+1)^5/(a*x-1)^5","A"
1273,1,81,83,0.030000," ","int((-a^2*c*x^2+c)^(5/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{x \left(5 x^{5} a^{5}-18 x^{4} a^{4}+15 x^{3} a^{3}+20 a^{2} x^{2}-45 a x +30\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{30 \left(a x +1\right)^{4} \left(a x -1\right)^{4}}"," ",0,"1/30*x*(5*a^5*x^5-18*a^4*x^4+15*a^3*x^3+20*a^2*x^2-45*a*x+30)*(-a^2*c*x^2+c)^(5/2)*(-a^2*x^2+1)^(3/2)/(a*x+1)^4/(a*x-1)^4","A"
1274,1,64,39,0.031000," ","int((-a^2*c*x^2+c)^(3/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\frac{x \left(x^{3} a^{3}-4 a^{2} x^{2}+6 a x -4\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{4 \left(a x -1\right)^{3} \left(a x +1\right)^{3}}"," ",0,"1/4*x*(a^3*x^3-4*a^2*x^2+6*a*x-4)*(-a^2*c*x^2+c)^(3/2)*(-a^2*x^2+1)^(3/2)/(a*x-1)^3/(a*x+1)^3","A"
1275,1,69,74,0.043000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x \ln \left(a x +1\right)+\ln \left(a x +1\right)+2\right)}{\left(a^{2} x^{2}-1\right) c \left(a x +1\right) a}"," ",0,"(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(a*x*ln(a*x+1)+ln(a*x+1)+2)/(a^2*x^2-1)/c/(a*x+1)/a","A"
1276,1,38,40,0.027000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{2 \left(a x +1\right)^{2} a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"-1/2/(a*x+1)^2/a*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(3/2)","A"
1277,1,159,158,0.047000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)+9 \ln \left(a x -1\right) x^{2} a^{2}-9 \ln \left(a x +1\right) x^{2} a^{2}+6 a^{2} x^{2}+9 \ln \left(a x -1\right) x a -9 a x \ln \left(a x +1\right)+18 a x +3 \ln \left(a x -1\right)-3 \ln \left(a x +1\right)+20\right)}{48 \left(a^{2} x^{2}-1\right) c^{3} a \left(a x +1\right)^{3}}"," ",0,"1/48*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)+9*ln(a*x-1)*x^2*a^2-9*ln(a*x+1)*x^2*a^2+6*a^2*x^2+9*ln(a*x-1)*x*a-9*a*x*ln(a*x+1)+18*a*x+3*ln(a*x-1)-3*ln(a*x+1)+20)/(a^2*x^2-1)/c^3/a/(a*x+1)^3","A"
1278,1,238,239,0.054000," ","int(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(7/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(15 \ln \left(a x -1\right) x^{5} a^{5}-15 \ln \left(a x +1\right) x^{5} a^{5}+45 \ln \left(a x -1\right) x^{4} a^{4}-45 \ln \left(a x +1\right) x^{4} a^{4}+30 x^{4} a^{4}+30 \ln \left(a x -1\right) x^{3} a^{3}-30 a^{3} x^{3} \ln \left(a x +1\right)+90 x^{3} a^{3}-30 \ln \left(a x -1\right) x^{2} a^{2}+30 \ln \left(a x +1\right) x^{2} a^{2}+70 a^{2} x^{2}-45 \ln \left(a x -1\right) x a +45 a x \ln \left(a x +1\right)-30 a x -15 \ln \left(a x -1\right)+15 \ln \left(a x +1\right)-64\right)}{192 \left(a^{2} x^{2}-1\right) c^{4} a \left(a x -1\right) \left(a x +1\right)^{4}}"," ",0,"1/192*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(15*ln(a*x-1)*x^5*a^5-15*ln(a*x+1)*x^5*a^5+45*ln(a*x-1)*x^4*a^4-45*ln(a*x+1)*x^4*a^4+30*x^4*a^4+30*ln(a*x-1)*x^3*a^3-30*a^3*x^3*ln(a*x+1)+90*x^3*a^3-30*ln(a*x-1)*x^2*a^2+30*ln(a*x+1)*x^2*a^2+70*a^2*x^2-45*ln(a*x-1)*x*a+45*a*x*ln(a*x+1)-30*a*x-15*ln(a*x-1)+15*ln(a*x+1)-64)/(a^2*x^2-1)/c^4/a/(a*x-1)/(a*x+1)^4","A"
1279,0,0,126,0.443000," ","int(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\int \frac{x^{m} \sqrt{-a^{2} c \,x^{2}+c}\, \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{\left(a x +1\right)^{3}}\, dx"," ",0,"int(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","F"
1280,0,0,74,0.446000," ","int((-a^2*c*x^2+c)^p/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{p} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{\left(a x +1\right)^{3}}\, dx"," ",0,"int((-a^2*c*x^2+c)^p/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x)","F"
1281,0,0,274,0.269000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(5/2),x)","\int \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(5/2),x)","F"
1282,0,0,234,0.269000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(3/2),x)","\int \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(3/2),x)","F"
1283,0,0,194,0.266000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(1/2),x)","\int \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, \sqrt{-a^{2} x^{2}+1}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(1/2),x)","F"
1284,0,0,154,0.276000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(1/2),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(1/2),x)","F"
1285,1,54,43,0.030000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(3/2),x)","-\frac{2 \left(a x -1\right) \left(a x +1\right) \left(2 a x -1\right) \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{3 a \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-2/3*(a*x-1)*(a*x+1)*(2*a*x-1)*((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/a/(-a^2*x^2+1)^(3/2)","A"
1286,1,70,87,0.032000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(5/2),x)","\frac{2 \left(a x -1\right) \left(a x +1\right) \left(16 x^{3} a^{3}-8 a^{2} x^{2}-22 a x +9\right) \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{35 a \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}"," ",0,"2/35*(a*x-1)*(a*x+1)*(16*a^3*x^3-8*a^2*x^2-22*a*x+9)*((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/a/(-a^2*x^2+1)^(5/2)","A"
1287,1,86,130,0.033000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(7/2),x)","-\frac{2 \left(a x -1\right) \left(a x +1\right) \left(256 x^{5} a^{5}-128 x^{4} a^{4}-608 x^{3} a^{3}+272 a^{2} x^{2}+422 a x -151\right) \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{693 a \left(-a^{2} x^{2}+1\right)^{\frac{7}{2}}}"," ",0,"-2/693*(a*x-1)*(a*x+1)*(256*a^5*x^5-128*a^4*x^4-608*a^3*x^3+272*a^2*x^2+422*a*x-151)*((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/a/(-a^2*x^2+1)^(7/2)","A"
1288,1,102,173,0.032000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(9/2),x)","\frac{2 \left(a x -1\right) \left(a x +1\right) \left(2048 a^{7} x^{7}-1024 x^{6} a^{6}-6912 x^{5} a^{5}+3200 x^{4} a^{4}+8240 x^{3} a^{3}-3384 a^{2} x^{2}-3838 a x +1241\right) \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{6435 a \left(-a^{2} x^{2}+1\right)^{\frac{9}{2}}}"," ",0,"2/6435*(a*x-1)*(a*x+1)*(2048*a^7*x^7-1024*a^6*x^6-6912*a^5*x^5+3200*a^4*x^4+8240*a^3*x^3-3384*a^2*x^2-3838*a*x+1241)*((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/a/(-a^2*x^2+1)^(9/2)","A"
1289,0,0,554,0.276000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(5/2),x)","\int \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(5/2),x)","F"
1290,0,0,442,0.268000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(3/2),x)","\int \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(3/2),x)","F"
1291,0,0,344,0.279000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(1/2),x)","\int \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, \sqrt{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(1/2),x)","F"
1292,0,0,254,0.281000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(1/2),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{\sqrt{-a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(1/2),x)","F"
1293,1,55,47,0.029000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(3/2),x)","-\frac{2 \left(a x -1\right) \left(a x +1\right) \left(2 a x -1\right) \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{3 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"-2/3*(a*x-1)*(a*x+1)*(2*a*x-1)*((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/a/(-a^2*c*x^2+c)^(3/2)","A"
1294,1,71,95,0.031000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(5/2),x)","\frac{2 \left(a x -1\right) \left(a x +1\right) \left(16 x^{3} a^{3}-8 a^{2} x^{2}-22 a x +9\right) \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{35 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"2/35*(a*x-1)*(a*x+1)*(16*a^3*x^3-8*a^2*x^2-22*a*x+9)*((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/a/(-a^2*c*x^2+c)^(5/2)","A"
1295,1,87,142,0.031000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(7/2),x)","-\frac{2 \left(a x -1\right) \left(a x +1\right) \left(256 x^{5} a^{5}-128 x^{4} a^{4}-608 x^{3} a^{3}+272 a^{2} x^{2}+422 a x -151\right) \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{693 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}"," ",0,"-2/693*(a*x-1)*(a*x+1)*(256*a^5*x^5-128*a^4*x^4-608*a^3*x^3+272*a^2*x^2+422*a*x-151)*((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/a/(-a^2*c*x^2+c)^(7/2)","A"
1296,1,103,189,0.033000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(9/2),x)","\frac{2 \left(a x -1\right) \left(a x +1\right) \left(2048 a^{7} x^{7}-1024 x^{6} a^{6}-6912 x^{5} a^{5}+3200 x^{4} a^{4}+8240 x^{3} a^{3}-3384 a^{2} x^{2}-3838 a x +1241\right) \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{6435 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}}}"," ",0,"2/6435*(a*x-1)*(a*x+1)*(2048*a^7*x^7-1024*a^6*x^6-6912*a^5*x^5+3200*a^4*x^4+8240*a^3*x^3-3384*a^2*x^2-3838*a*x+1241)*((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/a/(-a^2*c*x^2+c)^(9/2)","A"
1297,0,0,173,0.274000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^3/(-a^2*c*x^2+c)^(5/4),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x^{3}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{4}}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^3/(-a^2*c*x^2+c)^(5/4),x)","F"
1298,0,0,132,0.271000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^2/(-a^2*c*x^2+c)^(5/4),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x^{2}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{4}}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^2/(-a^2*c*x^2+c)^(5/4),x)","F"
1299,0,0,91,0.281000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x/(-a^2*c*x^2+c)^(5/4),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{4}}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x/(-a^2*c*x^2+c)^(5/4),x)","F"
1300,0,0,91,0.274000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(5/4),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{4}}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(5/4),x)","F"
1301,0,0,124,0.275000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x/(-a^2*c*x^2+c)^(5/4),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{4}}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x/(-a^2*c*x^2+c)^(5/4),x)","F"
1302,0,0,169,0.277000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2/(-a^2*c*x^2+c)^(5/4),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{x^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{4}}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2/(-a^2*c*x^2+c)^(5/4),x)","F"
1303,0,0,162,0.275000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^3/(-a^2*c*x^2+c)^(9/8),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x^{3}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{8}}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^3/(-a^2*c*x^2+c)^(9/8),x)","F"
1304,1,54,47,0.031000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^2/(-a^2*c*x^2+c)^(9/8),x)","\frac{4 \left(a x -1\right) \left(a x +1\right) \left(a x -2\right) \sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{3 a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{8}}}"," ",0,"4/3*(a*x-1)*(a*x+1)*(a*x-2)*((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/a^3/(-a^2*c*x^2+c)^(9/8)","A"
1305,0,0,105,0.278000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x/(-a^2*c*x^2+c)^(9/8),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}\, x}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{8}}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x/(-a^2*c*x^2+c)^(9/8),x)","F"
1306,0,0,56,0.280000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(9/8),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{8}}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(9/8),x)","F"
1307,0,0,56,0.293000," ","int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x/(-a^2*c*x^2+c)^(9/8),x)","\int \frac{\sqrt{\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}}}{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{8}}}\, dx"," ",0,"int(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x/(-a^2*c*x^2+c)^(9/8),x)","F"
1308,0,0,56,0.049000," ","int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c),x)","F"
1309,0,0,58,0.272000," ","int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^2,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)^{2}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^2,x)","F"
1310,0,0,58,0.269000," ","int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^3,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)^{3}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^3,x)","F"
1311,0,0,183,0.281000," ","int(exp(n*arctanh(a*x))*x^4/(-a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x^{4}}{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^4/(-a^2*c*x^2+c),x)","F"
1312,0,0,140,0.268000," ","int(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x^{3}}{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c),x)","F"
1313,0,0,73,0.273000," ","int(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x^{2}}{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c),x)","F"
1314,0,0,82,0.273000," ","int(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x}{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c),x)","F"
1315,1,18,17,0.029000," ","int(exp(n*arctanh(a*x))/(-a^2*c*x^2+c),x)","\frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{a c n}"," ",0,"exp(n*arctanh(a*x))/a/c/n","A"
1316,0,0,84,0.264000," ","int(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x \left(-a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c),x)","F"
1317,0,0,115,0.272000," ","int(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x^{2} \left(-a^{2} c \,x^{2}+c \right)}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c),x)","F"
1318,0,0,338,0.273000," ","int(exp(n*arctanh(a*x))*x^4/(-a^2*c*x^2+c)^2,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x^{4}}{\left(-a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^4/(-a^2*c*x^2+c)^2,x)","F"
1319,0,0,279,0.270000," ","int(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^2,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x^{3}}{\left(-a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^2,x)","F"
1320,1,62,77,0.031000," ","int(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^2,x)","-\frac{{\mathrm e}^{n \arctanh \left(a x \right)} \left(a^{2} n^{2} x^{2}-2 a^{2} x^{2}-2 n a x +2\right)}{\left(a^{2} x^{2}-1\right) c^{2} a^{3} n \left(n^{2}-4\right)}"," ",0,"-exp(n*arctanh(a*x))*(a^2*n^2*x^2-2*a^2*x^2-2*a*n*x+2)/(a^2*x^2-1)/c^2/a^3/n/(n^2-4)","A"
1321,1,47,67,0.033000," ","int(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c)^2,x)","\frac{{\mathrm e}^{n \arctanh \left(a x \right)} \left(a^{2} x^{2}-n a x +1\right)}{\left(a^{2} x^{2}-1\right) c^{2} a^{2} \left(n^{2}-4\right)}"," ",0,"exp(n*arctanh(a*x))*(a^2*x^2-a*n*x+1)/(a^2*x^2-1)/c^2/a^2/(n^2-4)","A"
1322,1,55,70,0.030000," ","int(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^2,x)","-\frac{{\mathrm e}^{n \arctanh \left(a x \right)} \left(2 a^{2} x^{2}-2 n a x +n^{2}-2\right)}{\left(a^{2} x^{2}-1\right) c^{2} a n \left(n^{2}-4\right)}"," ",0,"-exp(n*arctanh(a*x))*(2*a^2*x^2-2*a*n*x+n^2-2)/(a^2*x^2-1)/c^2/a/n/(n^2-4)","A"
1323,0,0,176,0.276000," ","int(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^2,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x \left(-a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^2,x)","F"
1324,0,0,221,0.269000," ","int(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^2,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x^{2} \left(-a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^2,x)","F"
1325,1,101,118,0.032000," ","int(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^3,x)","\frac{\left(24 x^{4} a^{4}-24 x^{3} a^{3} n +12 a^{2} n^{2} x^{2}-4 a \,n^{3} x -48 a^{2} x^{2}+n^{4}+40 n a x -16 n^{2}+24\right) {\mathrm e}^{n \arctanh \left(a x \right)}}{\left(a^{2} x^{2}-1\right)^{2} c^{3} a \left(n^{2}-16\right) \left(n^{2}-4\right) n}"," ",0,"(24*a^4*x^4-24*a^3*n*x^3+12*a^2*n^2*x^2-4*a*n^3*x-48*a^2*x^2+n^4+40*a*n*x-16*n^2+24)*exp(n*arctanh(a*x))/(a^2*x^2-1)^2/c^3/a/(n^2-16)/(n^2-4)/n","A"
1326,1,167,181,0.034000," ","int(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^4,x)","-\frac{\left(720 x^{6} a^{6}-720 a^{5} x^{5} n +360 a^{4} n^{2} x^{4}-120 a^{3} n^{3} x^{3}-2160 x^{4} a^{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 \arctanh \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*arctanh(a*x))/(a^2*x^2-1)^3/c^4/a/n/(n^6-56*n^4+784*n^2-2304)","A"
1327,0,0,206,0.264000," ","int(exp(n*arctanh(a*x))*x^3*(-a^2*c*x^2+c)^(1/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} x^{3} \sqrt{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^3*(-a^2*c*x^2+c)^(1/2),x)","F"
1328,0,0,194,0.272000," ","int(exp(n*arctanh(a*x))*x^2*(-a^2*c*x^2+c)^(1/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} x^{2} \sqrt{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^2*(-a^2*c*x^2+c)^(1/2),x)","F"
1329,0,0,135,0.270000," ","int(exp(n*arctanh(a*x))*x*(-a^2*c*x^2+c)^(1/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} x \sqrt{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x*(-a^2*c*x^2+c)^(1/2),x)","F"
1330,0,0,80,0.270000," ","int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(1/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \sqrt{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(1/2),x)","F"
1331,0,0,223,0.273000," ","int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(1/2)/x,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} \sqrt{-a^{2} c \,x^{2}+c}}{x}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(1/2)/x,x)","F"
1332,0,0,218,0.273000," ","int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(1/2)/x^2,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} \sqrt{-a^{2} c \,x^{2}+c}}{x^{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(1/2)/x^2,x)","F"
1333,0,0,81,0.276000," ","int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(3/2),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(3/2),x)","F"
1334,0,0,221,0.271000," ","int(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x^{3}}{\sqrt{-a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^(1/2),x)","F"
1335,0,0,205,0.276000," ","int(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x^{2}}{\sqrt{-a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^(1/2),x)","F"
1336,0,0,142,0.278000," ","int(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x}{\sqrt{-a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c)^(1/2),x)","F"
1337,0,0,80,0.267000," ","int(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{\sqrt{-a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^(1/2),x)","F"
1338,0,0,85,0.278000," ","int(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x \sqrt{-a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^(1/2),x)","F"
1339,0,0,141,0.271000," ","int(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x^{2} \sqrt{-a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^(1/2),x)","F"
1340,0,0,202,0.273000," ","int(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x^{3} \sqrt{-a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(1/2),x)","F"
1341,0,0,226,0.291000," ","int(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x^{3}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^(3/2),x)","F"
1342,0,0,126,0.276000," ","int(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x^{2}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^(3/2),x)","F"
1343,1,49,43,0.032000," ","int(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\left(a x -1\right) \left(a x +1\right) \left(n a x -1\right) {\mathrm e}^{n \arctanh \left(a x \right)}}{a^{2} \left(n^{2}-1\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"-(a*x-1)*(a*x+1)*(a*n*x-1)*exp(n*arctanh(a*x))/a^2/(n^2-1)/(-a^2*c*x^2+c)^(3/2)","A"
1344,1,49,43,0.030000," ","int(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^(3/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(a x -n \right) {\mathrm e}^{n \arctanh \left(a x \right)}}{\left(n^{2}-1\right) a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"(a*x-1)*(a*x+1)*(a*x-n)*exp(n*arctanh(a*x))/(n^2-1)/a/(-a^2*c*x^2+c)^(3/2)","A"
1345,0,0,211,0.266000," ","int(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^(3/2),x)","F"
1346,0,0,279,0.269000," ","int(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^(3/2),x)","F"
1347,0,0,357,0.273000," ","int(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(3/2),x)","F"
1348,1,93,357,0.033000," ","int(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\left(a x -1\right) \left(a x +1\right) \left(a^{3} n^{3} x^{3}-7 x^{3} a^{3} n -3 a^{2} n^{2} x^{2}+9 a^{2} x^{2}+6 n a x -6\right) {\mathrm e}^{n \arctanh \left(a x \right)}}{a^{4} \left(n^{4}-10 n^{2}+9\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"-(a*x-1)*(a*x+1)*(a^3*n^3*x^3-7*a^3*n*x^3-3*a^2*n^2*x^2+9*a^2*x^2+6*a*n*x-6)*exp(n*arctanh(a*x))/a^4/(n^4-10*n^2+9)/(-a^2*c*x^2+c)^(5/2)","A"
1349,1,96,96,0.031000," ","int(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^(5/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(a^{3} n^{2} x^{3}-a^{2} n^{3} x^{2}-3 x^{3} a^{3}+3 n \,x^{2} a^{2}+2 n^{2} x a -2 n \right) {\mathrm e}^{n \arctanh \left(a x \right)}}{\left(n^{4}-10 n^{2}+9\right) a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"(a*x-1)*(a*x+1)*(a^3*n^2*x^3-a^2*n^3*x^2-3*a^3*x^3+3*a^2*n*x^2+2*a*n^2*x-2*n)*exp(n*arctanh(a*x))/(n^4-10*n^2+9)/a^3/(-a^2*c*x^2+c)^(5/2)","A"
1350,1,86,120,0.032000," ","int(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\left(a x -1\right) \left(a x +1\right) \left(2 x^{3} a^{3} n -2 a^{2} n^{2} x^{2}+a \,n^{3} x -3 n a x -n^{2}+3\right) {\mathrm e}^{n \arctanh \left(a x \right)}}{a^{2} \left(n^{4}-10 n^{2}+9\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"-(a*x-1)*(a*x+1)*(2*a^3*n*x^3-2*a^2*n^2*x^2+a*n^3*x-3*a*n*x-n^2+3)*exp(n*arctanh(a*x))/a^2/(n^4-10*n^2+9)/(-a^2*c*x^2+c)^(5/2)","A"
1351,1,84,90,0.032000," ","int(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^(5/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(6 x^{3} a^{3}-6 n \,x^{2} a^{2}+3 n^{2} x a -n^{3}-9 a x +7 n \right) {\mathrm e}^{n \arctanh \left(a x \right)}}{a \left(n^{4}-10 n^{2}+9\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"(a*x-1)*(a*x+1)*(6*a^3*x^3-6*a^2*n*x^2+3*a*n^2*x-n^3-9*a*x+7*n)*exp(n*arctanh(a*x))/a/(n^4-10*n^2+9)/(-a^2*c*x^2+c)^(5/2)","A"
1352,0,0,366,0.273000," ","int(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^(5/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^(5/2),x)","F"
1353,0,0,446,0.274000," ","int(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^(5/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^(5/2),x)","F"
1354,0,0,540,0.325000," ","int(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(5/2),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)}}{x^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(5/2),x)","F"
1355,1,140,145,0.040000," ","int(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^(7/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(120 x^{5} a^{5}-120 n \,a^{4} x^{4}+60 a^{3} n^{2} x^{3}-20 a^{2} n^{3} x^{2}-300 x^{3} a^{3}+5 a \,n^{4} x +260 n \,x^{2} a^{2}-n^{5}-110 n^{2} x a +30 n^{3}+225 a x -149 n \right) {\mathrm e}^{n \arctanh \left(a x \right)}}{a \left(n^{6}-35 n^{4}+259 n^{2}-225\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}"," ",0,"(a*x-1)*(a*x+1)*(120*a^5*x^5-120*a^4*n*x^4+60*a^3*n^2*x^3-20*a^2*n^3*x^2-300*a^3*x^3+5*a*n^4*x+260*a^2*n*x^2-n^5-110*a*n^2*x+30*n^3+225*a*x-149*n)*exp(n*arctanh(a*x))/a/(n^6-35*n^4+259*n^2-225)/(-a^2*c*x^2+c)^(7/2)","A"
1356,0,0,38,0.313000," ","int(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c)^2,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} x^{m} \left(-a^{2} c \,x^{2}+c \right)^{2}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c)^2,x)","F"
1357,0,0,36,0.082000," ","int(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c),x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} x^{m} \left(-a^{2} c \,x^{2}+c \right)\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c),x)","F"
1358,0,0,38,0.297000," ","int(exp(n*arctanh(a*x))*x^m/(-a^2*c*x^2+c),x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x^{m}}{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^m/(-a^2*c*x^2+c),x)","F"
1359,0,0,38,0.273000," ","int(exp(n*arctanh(a*x))*x^m/(-a^2*c*x^2+c)^2,x)","\int \frac{{\mathrm e}^{n \arctanh \left(a x \right)} x^{m}}{\left(-a^{2} c \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^m/(-a^2*c*x^2+c)^2,x)","F"
1360,0,0,66,0.277000," ","int(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c)^p,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} x^{m} \left(-a^{2} c \,x^{2}+c \right)^{p}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c)^p,x)","F"
1361,0,0,159,0.272000," ","int(exp(n*arctanh(a*x))*x*(-a^2*c*x^2+c)^p,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} x \left(-a^{2} c \,x^{2}+c \right)^{p}\, dx"," ",0,"int(exp(n*arctanh(a*x))*x*(-a^2*c*x^2+c)^p,x)","F"
1362,0,0,91,0.304000," ","int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^p,x)","\int {\mathrm e}^{n \arctanh \left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)^{p}\, dx"," ",0,"int(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^p,x)","F"
1363,1,59,43,0.029000," ","int(exp(2*(1+p)*arctanh(a*x))/((-a^2*x^2+1)^p),x)","-\frac{\left(a x -1\right) \left(a p x +p -1\right) {\mathrm e}^{2 \left(1+p \right) \arctanh \left(a x \right)} \left(-a^{2} x^{2}+1\right)^{-p}}{a p \left(2 p -1\right) \left(a x +1\right)}"," ",0,"-(a*x-1)*(a*p*x+p-1)*exp(2*(1+p)*arctanh(a*x))/a/p/(2*p-1)/(a*x+1)/((-a^2*x^2+1)^p)","A"
1364,1,60,97,0.028000," ","int(exp(2*(1+p)*arctanh(a*x))/((-a^2*c*x^2+c)^p),x)","-\frac{\left(a x -1\right) \left(a p x +p -1\right) {\mathrm e}^{2 \left(1+p \right) \arctanh \left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)^{-p}}{a p \left(2 p -1\right) \left(a x +1\right)}"," ",0,"-(a*x-1)*(a*p*x+p-1)*exp(2*(1+p)*arctanh(a*x))/a/p/(2*p-1)/(a*x+1)/((-a^2*c*x^2+c)^p)","A"
1365,1,38,49,0.026000," ","int(exp(2*p*arctanh(a*x))*(-a^2*c*x^2+c)^p,x)","\frac{\left(a x +1\right) {\mathrm e}^{2 p \arctanh \left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(1+2 p \right) a}"," ",0,"(a*x+1)/(1+2*p)/a*exp(2*p*arctanh(a*x))*(-a^2*c*x^2+c)^p","A"
1366,1,40,51,0.028000," ","int((-a^2*c*x^2+c)^p/exp(2*p*arctanh(a*x)),x)","\frac{\left(a x -1\right) \left(-a^{2} c \,x^{2}+c \right)^{p} {\mathrm e}^{-2 p \arctanh \left(a x \right)}}{\left(1+2 p \right) a}"," ",0,"(a*x-1)/(1+2*p)/a*(-a^2*c*x^2+c)^p/exp(2*p*arctanh(a*x))","A"
1367,1,58,52,0.030000," ","int(exp(n*arctanh(a*x))*x^2*(-a^2*c*x^2+c)^(-1-1/2*n^2),x)","-\frac{\left(a x -1\right) \left(a x +1\right) \left(n a x -1\right) {\mathrm e}^{n \arctanh \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-1)*(a*x+1)*(a*n*x-1)*exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(-1-1/2*n^2)/a^3/n/(n^2-1)","A"
1368,1,426,29,0.061000," ","int((a*x+1)^6/(-a^2*x^2+1)^3*x^2/(-a^2*c*x^2+c)^19,x)","\frac{-\frac{3991995}{8589934592 a^{3} \left(a x -1\right)^{4}}+\frac{1964315}{4294967296 a^{3} \left(a x -1\right)^{3}}-\frac{930465}{2147483648 a^{3} \left(a x -1\right)^{2}}-\frac{1}{65536 a^{3} \left(a x -1\right)^{19}}-\frac{858429}{4294967296 a^{3} \left(a x +1\right)^{5}}-\frac{2211105}{8589934592 a^{3} \left(a x +1\right)^{4}}-\frac{1344005}{4294967296 a^{3} \left(a x +1\right)^{3}}-\frac{1550775}{4294967296 a^{3} \left(a x +1\right)^{2}}-\frac{13}{16777216 a^{3} \left(a x +1\right)^{13}}-\frac{1}{62914560 a^{3} \left(a x +1\right)^{15}}-\frac{9}{58720256 a^{3} \left(a x +1\right)^{14}}-\frac{275}{100663296 a^{3} \left(a x +1\right)^{12}}-\frac{253}{33554432 a^{3} \left(a x +1\right)^{11}}-\frac{5819}{335544320 a^{3} \left(a x +1\right)^{10}}-\frac{13915}{402653184 a^{3} \left(a x +1\right)^{9}}-\frac{16445}{268435456 a^{3} \left(a x +1\right)^{8}}-\frac{740025}{7516192768 a^{3} \left(a x +1\right)^{7}}-\frac{312455}{2147483648 a^{3} \left(a x +1\right)^{6}}-\frac{1}{1376256 a^{3} \left(a x -1\right)^{21}}+\frac{3}{655360 a^{3} \left(a x -1\right)^{20}}+\frac{7}{196608 a^{3} \left(a x -1\right)^{18}}-\frac{17}{262144 a^{3} \left(a x -1\right)^{17}}+\frac{51}{524288 a^{3} \left(a x -1\right)^{16}}-\frac{323}{2621440 a^{3} \left(a x -1\right)^{15}}+\frac{969}{7340032 a^{3} \left(a x -1\right)^{14}}-\frac{969}{8388608 a^{3} \left(a x -1\right)^{13}}+\frac{3553}{50331648 a^{3} \left(a x -1\right)^{12}}-\frac{7429}{83886080 a^{3} \left(a x -1\right)^{10}}+\frac{37145}{201326592 a^{3} \left(a x -1\right)^{9}}-\frac{37145}{134217728 a^{3} \left(a x -1\right)^{8}}+\frac{334305}{939524096 a^{3} \left(a x -1\right)^{7}}-\frac{111435}{268435456 a^{3} \left(a x -1\right)^{6}}+\frac{1938969}{4294967296 a^{3} \left(a x -1\right)^{5}}+\frac{3411705}{8589934592 a^{3} \left(a x -1\right)}-\frac{3411705}{8589934592 a^{3} \left(a x +1\right)}}{c^{19}}"," ",0,"1/c^19*(-3991995/8589934592/a^3/(a*x-1)^4+1964315/4294967296/a^3/(a*x-1)^3-930465/2147483648/a^3/(a*x-1)^2-1/65536/a^3/(a*x-1)^19-858429/4294967296/a^3/(a*x+1)^5-2211105/8589934592/a^3/(a*x+1)^4-1344005/4294967296/a^3/(a*x+1)^3-1550775/4294967296/a^3/(a*x+1)^2-13/16777216/a^3/(a*x+1)^13-1/62914560/a^3/(a*x+1)^15-9/58720256/a^3/(a*x+1)^14-275/100663296/a^3/(a*x+1)^12-253/33554432/a^3/(a*x+1)^11-5819/335544320/a^3/(a*x+1)^10-13915/402653184/a^3/(a*x+1)^9-16445/268435456/a^3/(a*x+1)^8-740025/7516192768/a^3/(a*x+1)^7-312455/2147483648/a^3/(a*x+1)^6-1/1376256/a^3/(a*x-1)^21+3/655360/a^3/(a*x-1)^20+7/196608/a^3/(a*x-1)^18-17/262144/a^3/(a*x-1)^17+51/524288/a^3/(a*x-1)^16-323/2621440/a^3/(a*x-1)^15+969/7340032/a^3/(a*x-1)^14-969/8388608/a^3/(a*x-1)^13+3553/50331648/a^3/(a*x-1)^12-7429/83886080/a^3/(a*x-1)^10+37145/201326592/a^3/(a*x-1)^9-37145/134217728/a^3/(a*x-1)^8+334305/939524096/a^3/(a*x-1)^7-111435/268435456/a^3/(a*x-1)^6+1938969/4294967296/a^3/(a*x-1)^5+3411705/8589934592/a^3/(a*x-1)-3411705/8589934592/a^3/(a*x+1))","B"
1369,1,186,29,0.039000," ","int((a*x+1)^4/(-a^2*x^2+1)^2*x^2/(-a^2*c*x^2+c)^9,x)","\frac{\frac{1}{1280 a^{3} \left(a x -1\right)^{10}}-\frac{1}{768 a^{3} \left(a x -1\right)^{9}}-\frac{7}{6144 a^{3} \left(a x -1\right)^{6}}+\frac{21}{10240 a^{3} \left(a x -1\right)^{5}}-\frac{21}{8192 a^{3} \left(a x -1\right)^{4}}+\frac{11}{4096 a^{3} \left(a x -1\right)^{3}}-\frac{165}{65536 a^{3} \left(a x -1\right)^{2}}+\frac{143}{65536 a^{3} \left(a x -1\right)}+\frac{1}{1024 a^{3} \left(a x -1\right)^{8}}-\frac{1}{12288 a^{3} \left(a x +1\right)^{6}}-\frac{7}{20480 a^{3} \left(a x +1\right)^{5}}-\frac{11}{8192 a^{3} \left(a x +1\right)^{3}}-\frac{121}{65536 a^{3} \left(a x +1\right)^{2}}-\frac{143}{65536 a^{3} \left(a x +1\right)}-\frac{13}{16384 a^{3} \left(a x +1\right)^{4}}}{c^{9}}"," ",0,"1/c^9*(1/1280/a^3/(a*x-1)^10-1/768/a^3/(a*x-1)^9-7/6144/a^3/(a*x-1)^6+21/10240/a^3/(a*x-1)^5-21/8192/a^3/(a*x-1)^4+11/4096/a^3/(a*x-1)^3-165/65536/a^3/(a*x-1)^2+143/65536/a^3/(a*x-1)+1/1024/a^3/(a*x-1)^8-1/12288/a^3/(a*x+1)^6-7/20480/a^3/(a*x+1)^5-11/8192/a^3/(a*x+1)^3-121/65536/a^3/(a*x+1)^2-143/65536/a^3/(a*x+1)-13/16384/a^3/(a*x+1)^4)","B"
1370,1,54,29,0.033000," ","int((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^3,x)","\frac{-\frac{1}{12 a^{3} \left(a x -1\right)^{3}}-\frac{1}{8 a^{3} \left(a x -1\right)^{2}}+\frac{1}{16 a^{3} \left(a x -1\right)}-\frac{1}{16 a^{3} \left(a x +1\right)}}{c^{3}}"," ",0,"1/c^3*(-1/12/a^3/(a*x-1)^3-1/8/a^3/(a*x-1)^2+1/16/a^3/(a*x-1)-1/16/a^3/(a*x+1))","A"
1371,1,54,29,0.036000," ","int(x^2/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^3,x)","\frac{-\frac{1}{16 a^{3} \left(a x -1\right)}-\frac{1}{12 a^{3} \left(a x +1\right)^{3}}+\frac{1}{8 a^{3} \left(a x +1\right)^{2}}+\frac{1}{16 a^{3} \left(a x +1\right)}}{c^{3}}"," ",0,"1/c^3*(-1/16/a^3/(a*x-1)-1/12/a^3/(a*x+1)^3+1/8/a^3/(a*x+1)^2+1/16/a^3/(a*x+1))","A"
1372,1,186,29,0.042000," ","int(x^2/(a*x+1)^4*(-a^2*x^2+1)^2/(-a^2*c*x^2+c)^9,x)","\frac{\frac{1}{12288 a^{3} \left(a x -1\right)^{6}}-\frac{7}{20480 a^{3} \left(a x -1\right)^{5}}-\frac{11}{8192 a^{3} \left(a x -1\right)^{3}}+\frac{121}{65536 a^{3} \left(a x -1\right)^{2}}-\frac{143}{65536 a^{3} \left(a x -1\right)}+\frac{13}{16384 a^{3} \left(a x -1\right)^{4}}-\frac{1}{1280 a^{3} \left(a x +1\right)^{10}}-\frac{1}{768 a^{3} \left(a x +1\right)^{9}}+\frac{7}{6144 a^{3} \left(a x +1\right)^{6}}+\frac{21}{10240 a^{3} \left(a x +1\right)^{5}}+\frac{21}{8192 a^{3} \left(a x +1\right)^{4}}+\frac{11}{4096 a^{3} \left(a x +1\right)^{3}}+\frac{165}{65536 a^{3} \left(a x +1\right)^{2}}+\frac{143}{65536 a^{3} \left(a x +1\right)}-\frac{1}{1024 a^{3} \left(a x +1\right)^{8}}}{c^{9}}"," ",0,"1/c^9*(1/12288/a^3/(a*x-1)^6-7/20480/a^3/(a*x-1)^5-11/8192/a^3/(a*x-1)^3+121/65536/a^3/(a*x-1)^2-143/65536/a^3/(a*x-1)+13/16384/a^3/(a*x-1)^4-1/1280/a^3/(a*x+1)^10-1/768/a^3/(a*x+1)^9+7/6144/a^3/(a*x+1)^6+21/10240/a^3/(a*x+1)^5+21/8192/a^3/(a*x+1)^4+11/4096/a^3/(a*x+1)^3+165/65536/a^3/(a*x+1)^2+143/65536/a^3/(a*x+1)-1/1024/a^3/(a*x+1)^8)","B"
1373,1,49,54,0.045000," ","int((a*x+1)^5/(-a^2*x^2+1)^(5/2)*x^2/(-a^2*c*x^2+c)^(27/2),x)","-\frac{\left(a x -1\right) \left(a x +1\right)^{6} \left(5 a x -1\right)}{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-1)*(a*x+1)^6*(5*a*x-1)/a^3/(-a^2*x^2+1)^(5/2)/(-a^2*c*x^2+c)^(27/2)","A"
1374,1,49,54,0.034000," ","int((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2/(-a^2*c*x^2+c)^(11/2),x)","-\frac{\left(a x -1\right) \left(a x +1\right)^{4} \left(3 a x -1\right)}{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-1)*(a*x+1)^4*(3*a*x-1)/a^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(11/2)","A"
1375,1,90,121,0.048000," ","int((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x a +a x \ln \left(a x +1\right)-3 \ln \left(a x -1\right)-\ln \left(a x +1\right)-2\right)}{4 \left(a^{2} x^{2}-1\right) c^{2} a^{3} \left(a x -1\right)}"," ",0,"-1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x*a+a*x*ln(a*x+1)-3*ln(a*x-1)-ln(a*x+1)-2)/(a^2*x^2-1)/c^2/a^3/(a*x-1)","A"
1376,1,88,120,0.049000," ","int(x^2/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x a +3 a x \ln \left(a x +1\right)+\ln \left(a x -1\right)+3 \ln \left(a x +1\right)+2\right)}{4 \left(a^{2} x^{2}-1\right) c^{2} a^{3} \left(a x +1\right)}"," ",0,"1/4*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x*a+3*a*x*ln(a*x+1)+ln(a*x-1)+3*ln(a*x+1)+2)/(a^2*x^2-1)/c^2/a^3/(a*x+1)","A"
1377,1,49,54,0.034000," ","int(x^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(11/2),x)","-\frac{\left(a x -1\right) \left(3 a x +1\right) \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}{24 \left(a x +1\right)^{2} a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{11}{2}}}"," ",0,"-1/24*(a*x-1)*(3*a*x+1)*(-a^2*x^2+1)^(3/2)/(a*x+1)^2/a^3/(-a^2*c*x^2+c)^(11/2)","A"
1378,1,49,54,0.044000," ","int(x^2/(a*x+1)^5*(-a^2*x^2+1)^(5/2)/(-a^2*c*x^2+c)^(27/2),x)","-\frac{\left(a x -1\right) \left(5 a x +1\right) \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{120 \left(a x +1\right)^{4} a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{27}{2}}}"," ",0,"-1/120*(a*x-1)*(5*a*x+1)*(-a^2*x^2+1)^(5/2)/(a*x+1)^4/a^3/(-a^2*c*x^2+c)^(27/2)","A"