1,1,105,0,0.420452," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4,x, algorithm=""maxima"")","-\frac{\sqrt{-a^{2} x^{2} + 1} x^{4}}{5 \, a} - \frac{\sqrt{-a^{2} x^{2} + 1} x^{3}}{4 \, a^{2}} - \frac{4 \, \sqrt{-a^{2} x^{2} + 1} x^{2}}{15 \, a^{3}} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1} x}{8 \, a^{4}} + \frac{3 \, \arcsin\left(a x\right)}{8 \, a^{5}} - \frac{8 \, \sqrt{-a^{2} x^{2} + 1}}{15 \, a^{5}}"," ",0,"-1/5*sqrt(-a^2*x^2 + 1)*x^4/a - 1/4*sqrt(-a^2*x^2 + 1)*x^3/a^2 - 4/15*sqrt(-a^2*x^2 + 1)*x^2/a^3 - 3/8*sqrt(-a^2*x^2 + 1)*x/a^4 + 3/8*arcsin(a*x)/a^5 - 8/15*sqrt(-a^2*x^2 + 1)/a^5","A",0
2,1,85,0,0.416595," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3,x, algorithm=""maxima"")","-\frac{\sqrt{-a^{2} x^{2} + 1} x^{3}}{4 \, a} - \frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{3 \, a^{2}} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1} x}{8 \, a^{3}} + \frac{3 \, \arcsin\left(a x\right)}{8 \, a^{4}} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, a^{4}}"," ",0,"-1/4*sqrt(-a^2*x^2 + 1)*x^3/a - 1/3*sqrt(-a^2*x^2 + 1)*x^2/a^2 - 3/8*sqrt(-a^2*x^2 + 1)*x/a^3 + 3/8*arcsin(a*x)/a^4 - 2/3*sqrt(-a^2*x^2 + 1)/a^4","A",0
3,1,65,0,0.411948," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2,x, algorithm=""maxima"")","-\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{3 \, a} - \frac{\sqrt{-a^{2} x^{2} + 1} x}{2 \, a^{2}} + \frac{\arcsin\left(a x\right)}{2 \, a^{3}} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, a^{3}}"," ",0,"-1/3*sqrt(-a^2*x^2 + 1)*x^2/a - 1/2*sqrt(-a^2*x^2 + 1)*x/a^2 + 1/2*arcsin(a*x)/a^3 - 2/3*sqrt(-a^2*x^2 + 1)/a^3","A",0
4,1,45,0,0.422222," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x,x, algorithm=""maxima"")","-\frac{\sqrt{-a^{2} x^{2} + 1} x}{2 \, a} + \frac{\arcsin\left(a x\right)}{2 \, a^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{2}}"," ",0,"-1/2*sqrt(-a^2*x^2 + 1)*x/a + 1/2*arcsin(a*x)/a^2 - sqrt(-a^2*x^2 + 1)/a^2","A",0
5,1,26,0,0.411776," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\arcsin\left(a x\right)}{a} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a}"," ",0,"arcsin(a*x)/a - sqrt(-a^2*x^2 + 1)/a","A",0
6,1,33,0,0.405092," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","\arcsin\left(a x\right) - \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)"," ",0,"arcsin(a*x) - log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))","A",0
7,1,47,0,0.408904," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","-a \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{\sqrt{-a^{2} x^{2} + 1}}{x}"," ",0,"-a*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - sqrt(-a^2*x^2 + 1)/x","A",0
8,1,67,0,0.409480," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{\sqrt{-a^{2} x^{2} + 1} a}{x} - \frac{\sqrt{-a^{2} x^{2} + 1}}{2 \, x^{2}}"," ",0,"-1/2*a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - sqrt(-a^2*x^2 + 1)*a/x - 1/2*sqrt(-a^2*x^2 + 1)/x^2","A",0
9,1,87,0,0.401520," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{3} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{3 \, x} - \frac{\sqrt{-a^{2} x^{2} + 1} a}{2 \, x^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{3 \, x^{3}}"," ",0,"-1/2*a^3*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 2/3*sqrt(-a^2*x^2 + 1)*a^2/x - 1/2*sqrt(-a^2*x^2 + 1)*a/x^2 - 1/3*sqrt(-a^2*x^2 + 1)/x^3","A",0
10,1,107,0,0.412614," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^5,x, algorithm=""maxima"")","-\frac{3}{8} \, a^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{3}}{3 \, x} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{8 \, x^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1} a}{3 \, x^{3}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{4 \, x^{4}}"," ",0,"-3/8*a^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 2/3*sqrt(-a^2*x^2 + 1)*a^3/x - 3/8*sqrt(-a^2*x^2 + 1)*a^2/x^2 - 1/3*sqrt(-a^2*x^2 + 1)*a/x^3 - 1/4*sqrt(-a^2*x^2 + 1)/x^4","A",0
11,1,43,0,0.308734," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3,x, algorithm=""maxima"")","-\frac{3 \, a^{3} x^{4} + 8 \, a^{2} x^{3} + 12 \, a x^{2} + 24 \, x}{12 \, a^{3}} - \frac{2 \, \log\left(a x - 1\right)}{a^{4}}"," ",0,"-1/12*(3*a^3*x^4 + 8*a^2*x^3 + 12*a*x^2 + 24*x)/a^3 - 2*log(a*x - 1)/a^4","A",0
12,1,34,0,0.312432," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2,x, algorithm=""maxima"")","-\frac{a^{2} x^{3} + 3 \, a x^{2} + 6 \, x}{3 \, a^{2}} - \frac{2 \, \log\left(a x - 1\right)}{a^{3}}"," ",0,"-1/3*(a^2*x^3 + 3*a*x^2 + 6*x)/a^2 - 2*log(a*x - 1)/a^3","A",0
13,1,26,0,0.307254," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x,x, algorithm=""maxima"")","-\frac{a x^{2} + 4 \, x}{2 \, a} - \frac{2 \, \log\left(a x - 1\right)}{a^{2}}"," ",0,"-1/2*(a*x^2 + 4*x)/a - 2*log(a*x - 1)/a^2","A",0
14,1,15,0,0.308975," ","integrate((a*x+1)^2/(-a^2*x^2+1),x, algorithm=""maxima"")","-x - \frac{2 \, \log\left(a x - 1\right)}{a}"," ",0,"-x - 2*log(a*x - 1)/a","A",0
15,1,11,0,0.314948," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x,x, algorithm=""maxima"")","-2 \, \log\left(a x - 1\right) + \log\left(x\right)"," ",0,"-2*log(a*x - 1) + log(x)","A",0
16,1,20,0,0.310283," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^2,x, algorithm=""maxima"")","-2 \, a \log\left(a x - 1\right) + 2 \, a \log\left(x\right) - \frac{1}{x}"," ",0,"-2*a*log(a*x - 1) + 2*a*log(x) - 1/x","A",0
17,1,30,0,0.308586," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^3,x, algorithm=""maxima"")","-2 \, a^{2} \log\left(a x - 1\right) + 2 \, a^{2} \log\left(x\right) - \frac{4 \, a x + 1}{2 \, x^{2}}"," ",0,"-2*a^2*log(a*x - 1) + 2*a^2*log(x) - 1/2*(4*a*x + 1)/x^2","A",0
18,1,38,0,0.308892," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^4,x, algorithm=""maxima"")","-2 \, a^{3} \log\left(a x - 1\right) + 2 \, a^{3} \log\left(x\right) - \frac{6 \, a^{2} x^{2} + 3 \, a x + 1}{3 \, x^{3}}"," ",0,"-2*a^3*log(a*x - 1) + 2*a^3*log(x) - 1/3*(6*a^2*x^2 + 3*a*x + 1)/x^3","A",0
19,1,100,0,0.408650," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2,x, algorithm=""maxima"")","-\frac{a x^{4}}{3 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{3 \, x^{3}}{2 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{13 \, x^{2}}{3 \, \sqrt{-a^{2} x^{2} + 1} a} + \frac{11 \, x}{2 \, \sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{11 \, \arcsin\left(a x\right)}{2 \, a^{3}} + \frac{26}{3 \, \sqrt{-a^{2} x^{2} + 1} a^{3}}"," ",0,"-1/3*a*x^4/sqrt(-a^2*x^2 + 1) - 3/2*x^3/sqrt(-a^2*x^2 + 1) - 13/3*x^2/(sqrt(-a^2*x^2 + 1)*a) + 11/2*x/(sqrt(-a^2*x^2 + 1)*a^2) - 11/2*arcsin(a*x)/a^3 + 26/3/(sqrt(-a^2*x^2 + 1)*a^3)","A",0
20,1,80,0,0.409953," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x,x, algorithm=""maxima"")","-\frac{a x^{3}}{2 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{3 \, x^{2}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{9 \, x}{2 \, \sqrt{-a^{2} x^{2} + 1} a} - \frac{9 \, \arcsin\left(a x\right)}{2 \, a^{2}} + \frac{7}{\sqrt{-a^{2} x^{2} + 1} a^{2}}"," ",0,"-1/2*a*x^3/sqrt(-a^2*x^2 + 1) - 3*x^2/sqrt(-a^2*x^2 + 1) + 9/2*x/(sqrt(-a^2*x^2 + 1)*a) - 9/2*arcsin(a*x)/a^2 + 7/(sqrt(-a^2*x^2 + 1)*a^2)","A",0
21,1,60,0,0.413938," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{a x^{2}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{4 \, x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{3 \, \arcsin\left(a x\right)}{a} + \frac{5}{\sqrt{-a^{2} x^{2} + 1} a}"," ",0,"-a*x^2/sqrt(-a^2*x^2 + 1) + 4*x/sqrt(-a^2*x^2 + 1) - 3*arcsin(a*x)/a + 5/(sqrt(-a^2*x^2 + 1)*a)","A",0
22,1,65,0,0.411072," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x,x, algorithm=""maxima"")","\frac{4 \, a x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{4}{\sqrt{-a^{2} x^{2} + 1}} - \arcsin\left(a x\right) - \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)"," ",0,"4*a*x/sqrt(-a^2*x^2 + 1) + 4/sqrt(-a^2*x^2 + 1) - arcsin(a*x) - log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))","A",0
23,1,80,0,0.310703," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""maxima"")","\frac{5 \, a^{2} x}{\sqrt{-a^{2} x^{2} + 1}} - 3 \, a \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{4 \, a}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x}"," ",0,"5*a^2*x/sqrt(-a^2*x^2 + 1) - 3*a*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 4*a/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*x)","A",0
24,1,102,0,0.314633," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""maxima"")","\frac{7 \, a^{3} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{9}{2} \, a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{9 \, a^{2}}{2 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{3 \, a}{\sqrt{-a^{2} x^{2} + 1} x} - \frac{1}{2 \, \sqrt{-a^{2} x^{2} + 1} x^{2}}"," ",0,"7*a^3*x/sqrt(-a^2*x^2 + 1) - 9/2*a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 9/2*a^2/sqrt(-a^2*x^2 + 1) - 3*a/(sqrt(-a^2*x^2 + 1)*x) - 1/2/(sqrt(-a^2*x^2 + 1)*x^2)","A",0
25,1,122,0,0.318148," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""maxima"")","\frac{26 \, a^{4} x}{3 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{11}{2} \, a^{3} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{11 \, a^{3}}{2 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{13 \, a^{2}}{3 \, \sqrt{-a^{2} x^{2} + 1} x} - \frac{3 \, a}{2 \, \sqrt{-a^{2} x^{2} + 1} x^{2}} - \frac{1}{3 \, \sqrt{-a^{2} x^{2} + 1} x^{3}}"," ",0,"26/3*a^4*x/sqrt(-a^2*x^2 + 1) - 11/2*a^3*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 11/2*a^3/sqrt(-a^2*x^2 + 1) - 13/3*a^2/(sqrt(-a^2*x^2 + 1)*x) - 3/2*a/(sqrt(-a^2*x^2 + 1)*x^2) - 1/3/(sqrt(-a^2*x^2 + 1)*x^3)","A",0
26,1,58,0,0.305043," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*x^3,x, algorithm=""maxima"")","-\frac{4}{a^{5} x - a^{4}} + \frac{3 \, a^{3} x^{4} + 16 \, a^{2} x^{3} + 48 \, a x^{2} + 144 \, x}{12 \, a^{3}} + \frac{16 \, \log\left(a x - 1\right)}{a^{4}}"," ",0,"-4/(a^5*x - a^4) + 1/12*(3*a^3*x^4 + 16*a^2*x^3 + 48*a*x^2 + 144*x)/a^3 + 16*log(a*x - 1)/a^4","A",0
27,1,49,0,0.315859," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*x^2,x, algorithm=""maxima"")","-\frac{4}{a^{4} x - a^{3}} + \frac{a^{2} x^{3} + 6 \, a x^{2} + 24 \, x}{3 \, a^{2}} + \frac{12 \, \log\left(a x - 1\right)}{a^{3}}"," ",0,"-4/(a^4*x - a^3) + 1/3*(a^2*x^3 + 6*a*x^2 + 24*x)/a^2 + 12*log(a*x - 1)/a^3","A",0
28,1,41,0,0.312879," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*x,x, algorithm=""maxima"")","\frac{a x^{2} + 8 \, x}{2 \, a} - \frac{4}{a^{3} x - a^{2}} + \frac{8 \, \log\left(a x - 1\right)}{a^{2}}"," ",0,"1/2*(a*x^2 + 8*x)/a - 4/(a^3*x - a^2) + 8*log(a*x - 1)/a^2","A",0
29,1,26,0,0.309073," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","x + \frac{4 \, \log\left(a x - 1\right)}{a} - \frac{4}{a^{2} x - a}"," ",0,"x + 4*log(a*x - 1)/a - 4/(a^2*x - a)","A",0
30,1,12,0,0.314276," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/x,x, algorithm=""maxima"")","-\frac{4}{a x - 1} + \log\left(x\right)"," ",0,"-4/(a*x - 1) + log(x)","A",0
31,1,34,0,0.317116," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/x^2,x, algorithm=""maxima"")","-4 \, a \log\left(a x - 1\right) + 4 \, a \log\left(x\right) - \frac{5 \, a x - 1}{a x^{2} - x}"," ",0,"-4*a*log(a*x - 1) + 4*a*log(x) - (5*a*x - 1)/(a*x^2 - x)","A",0
32,1,48,0,0.302975," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/x^3,x, algorithm=""maxima"")","-8 \, a^{2} \log\left(a x - 1\right) + 8 \, a^{2} \log\left(x\right) - \frac{16 \, a^{2} x^{2} - 7 \, a x - 1}{2 \, {\left(a x^{3} - x^{2}\right)}}"," ",0,"-8*a^2*log(a*x - 1) + 8*a^2*log(x) - 1/2*(16*a^2*x^2 - 7*a*x - 1)/(a*x^3 - x^2)","A",0
33,1,56,0,0.308457," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/x^4,x, algorithm=""maxima"")","-12 \, a^{3} \log\left(a x - 1\right) + 12 \, a^{3} \log\left(x\right) - \frac{36 \, a^{3} x^{3} - 18 \, a^{2} x^{2} - 5 \, a x - 1}{3 \, {\left(a x^{4} - x^{3}\right)}}"," ",0,"-12*a^3*log(a*x - 1) + 12*a^3*log(x) - 1/3*(36*a^3*x^3 - 18*a^2*x^2 - 5*a*x - 1)/(a*x^4 - x^3)","A",0
34,1,80,0,0.405107," ","integrate(x^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, a^{3}} + \frac{5 \, \sqrt{-a^{2} x^{2} + 1} x}{8 \, a^{3}} + \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{3 \, a^{4}} - \frac{3 \, \arcsin\left(a x\right)}{8 \, a^{4}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{4}}"," ",0,"-1/4*(-a^2*x^2 + 1)^(3/2)*x/a^3 + 5/8*sqrt(-a^2*x^2 + 1)*x/a^3 + 1/3*(-a^2*x^2 + 1)^(3/2)/a^4 - 3/8*arcsin(a*x)/a^4 - sqrt(-a^2*x^2 + 1)/a^4","A",0
35,1,61,0,0.414942," ","integrate(x^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-a^{2} x^{2} + 1} x}{2 \, a^{2}} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{3 \, a^{3}} + \frac{\arcsin\left(a x\right)}{2 \, a^{3}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{3}}"," ",0,"-1/2*sqrt(-a^2*x^2 + 1)*x/a^2 - 1/3*(-a^2*x^2 + 1)^(3/2)/a^3 + 1/2*arcsin(a*x)/a^3 + sqrt(-a^2*x^2 + 1)/a^3","A",0
36,1,45,0,0.407169," ","integrate(x/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{-a^{2} x^{2} + 1} x}{2 \, a} - \frac{\arcsin\left(a x\right)}{2 \, a^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{2}}"," ",0,"1/2*sqrt(-a^2*x^2 + 1)*x/a - 1/2*arcsin(a*x)/a^2 - sqrt(-a^2*x^2 + 1)/a^2","A",0
37,1,25,0,0.416061," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\arcsin\left(a x\right)}{a} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a}"," ",0,"arcsin(a*x)/a + sqrt(-a^2*x^2 + 1)/a","A",0
38,1,42,0,0.415142," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","-a {\left(\frac{\arcsin\left(a x\right)}{a} + \frac{\log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a}\right)}"," ",0,"-a*(arcsin(a*x)/a + log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a)","A",0
39,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*x^2), x)","F",0
40,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*x^3), x)","F",0
41,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*x^4), x)","F",0
42,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} x^{5}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*x^5), x)","F",0
43,1,43,0,0.312537," ","integrate(x^3/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{3 \, a^{3} x^{4} - 8 \, a^{2} x^{3} + 12 \, a x^{2} - 24 \, x}{12 \, a^{3}} - \frac{2 \, \log\left(a x + 1\right)}{a^{4}}"," ",0,"-1/12*(3*a^3*x^4 - 8*a^2*x^3 + 12*a*x^2 - 24*x)/a^3 - 2*log(a*x + 1)/a^4","A",0
44,1,34,0,0.318009," ","integrate(x^2/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{a^{2} x^{3} - 3 \, a x^{2} + 6 \, x}{3 \, a^{2}} + \frac{2 \, \log\left(a x + 1\right)}{a^{3}}"," ",0,"-1/3*(a^2*x^3 - 3*a*x^2 + 6*x)/a^2 + 2*log(a*x + 1)/a^3","A",0
45,1,26,0,0.313271," ","integrate(x/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{a x^{2} - 4 \, x}{2 \, a} - \frac{2 \, \log\left(a x + 1\right)}{a^{2}}"," ",0,"-1/2*(a*x^2 - 4*x)/a - 2*log(a*x + 1)/a^2","A",0
46,1,15,0,0.310445," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-x + \frac{2 \, \log\left(a x + 1\right)}{a}"," ",0,"-x + 2*log(a*x + 1)/a","A",0
47,1,11,0,0.310039," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/x,x, algorithm=""maxima"")","-2 \, \log\left(a x + 1\right) + \log\left(x\right)"," ",0,"-2*log(a*x + 1) + log(x)","A",0
48,1,20,0,0.313682," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/x^2,x, algorithm=""maxima"")","2 \, a \log\left(a x + 1\right) - 2 \, a \log\left(x\right) - \frac{1}{x}"," ",0,"2*a*log(a*x + 1) - 2*a*log(x) - 1/x","A",0
49,1,30,0,0.310962," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/x^3,x, algorithm=""maxima"")","-2 \, a^{2} \log\left(a x + 1\right) + 2 \, a^{2} \log\left(x\right) + \frac{4 \, a x - 1}{2 \, x^{2}}"," ",0,"-2*a^2*log(a*x + 1) + 2*a^2*log(x) + 1/2*(4*a*x - 1)/x^2","A",0
50,1,38,0,0.312943," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/x^4,x, algorithm=""maxima"")","2 \, a^{3} \log\left(a x + 1\right) - 2 \, a^{3} \log\left(x\right) - \frac{6 \, a^{2} x^{2} - 3 \, a x + 1}{3 \, x^{3}}"," ",0,"2*a^3*log(a*x + 1) - 2*a^3*log(x) - 1/3*(6*a^2*x^2 - 3*a*x + 1)/x^3","A",0
51,1,215,0,0.430485," ","integrate(x^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{6} x^{2} + 2 \, a^{5} x + a^{4}} + \frac{3 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{2 \, {\left(a^{5} x + a^{4}\right)}} + \frac{6 \, \sqrt{-a^{2} x^{2} + 1}}{a^{5} x + a^{4}} + \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, a^{3}} - \frac{3 \, \sqrt{a^{2} x^{2} + 4 \, a x + 3} x}{2 \, a^{3}} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1} x}{8 \, a^{3}} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{4}} + \frac{3 i \, \arcsin\left(a x + 2\right)}{2 \, a^{4}} + \frac{63 \, \arcsin\left(a x\right)}{8 \, a^{4}} - \frac{3 \, \sqrt{a^{2} x^{2} + 4 \, a x + 3}}{a^{4}} + \frac{9 \, \sqrt{-a^{2} x^{2} + 1}}{2 \, a^{4}}"," ",0,"-(-a^2*x^2 + 1)^(3/2)/(a^6*x^2 + 2*a^5*x + a^4) + 3/2*(-a^2*x^2 + 1)^(3/2)/(a^5*x + a^4) + 6*sqrt(-a^2*x^2 + 1)/(a^5*x + a^4) + 1/4*(-a^2*x^2 + 1)^(3/2)*x/a^3 - 3/2*sqrt(a^2*x^2 + 4*a*x + 3)*x/a^3 + 3/8*sqrt(-a^2*x^2 + 1)*x/a^3 - (-a^2*x^2 + 1)^(3/2)/a^4 + 3/2*I*arcsin(a*x + 2)/a^4 + 63/8*arcsin(a*x)/a^4 - 3*sqrt(a^2*x^2 + 4*a*x + 3)/a^4 + 9/2*sqrt(-a^2*x^2 + 1)/a^4","C",0
52,1,177,0,0.425553," ","integrate(x^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{5} x^{2} + 2 \, a^{4} x + a^{3}} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{4} x + a^{3}} - \frac{6 \, \sqrt{-a^{2} x^{2} + 1}}{a^{4} x + a^{3}} + \frac{\sqrt{a^{2} x^{2} + 4 \, a x + 3} x}{2 \, a^{2}} + \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{3 \, a^{3}} - \frac{i \, \arcsin\left(a x + 2\right)}{2 \, a^{3}} - \frac{6 \, \arcsin\left(a x\right)}{a^{3}} + \frac{\sqrt{a^{2} x^{2} + 4 \, a x + 3}}{a^{3}} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1}}{a^{3}}"," ",0,"(-a^2*x^2 + 1)^(3/2)/(a^5*x^2 + 2*a^4*x + a^3) - (-a^2*x^2 + 1)^(3/2)/(a^4*x + a^3) - 6*sqrt(-a^2*x^2 + 1)/(a^4*x + a^3) + 1/2*sqrt(a^2*x^2 + 4*a*x + 3)*x/a^2 + 1/3*(-a^2*x^2 + 1)^(3/2)/a^3 - 1/2*I*arcsin(a*x + 2)/a^3 - 6*arcsin(a*x)/a^3 + sqrt(a^2*x^2 + 4*a*x + 3)/a^3 - 3*sqrt(-a^2*x^2 + 1)/a^3","C",0
53,1,110,0,0.440610," ","integrate(x/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{4} x^{2} + 2 \, a^{3} x + a^{2}} + \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{2 \, {\left(a^{3} x + a^{2}\right)}} + \frac{6 \, \sqrt{-a^{2} x^{2} + 1}}{a^{3} x + a^{2}} + \frac{9 \, \arcsin\left(a x\right)}{2 \, a^{2}} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1}}{2 \, a^{2}}"," ",0,"-(-a^2*x^2 + 1)^(3/2)/(a^4*x^2 + 2*a^3*x + a^2) + 1/2*(-a^2*x^2 + 1)^(3/2)/(a^3*x + a^2) + 6*sqrt(-a^2*x^2 + 1)/(a^3*x + a^2) + 9/2*arcsin(a*x)/a^2 + 3/2*sqrt(-a^2*x^2 + 1)/a^2","A",0
54,1,63,0,0.429292," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{3} x^{2} + 2 \, a^{2} x + a} - \frac{3 \, \arcsin\left(a x\right)}{a} - \frac{6 \, \sqrt{-a^{2} x^{2} + 1}}{a^{2} x + a}"," ",0,"(-a^2*x^2 + 1)^(3/2)/(a^3*x^2 + 2*a^2*x + a) - 3*arcsin(a*x)/a - 6*sqrt(-a^2*x^2 + 1)/(a^2*x + a)","A",0
55,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^2), x)","F",0
57,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^3), x)","F",0
58,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{4}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^4), x)","F",0
59,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{5}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^5), x)","F",0
60,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^m,x, algorithm=""maxima"")","\int x^{m} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(x^m*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
61,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^2,x, algorithm=""maxima"")","\int x^{2} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(x^2*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
62,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x,x, algorithm=""maxima"")","\int x \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(x*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
63,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
64,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x, x)","F",0
65,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x^2, x)","F",0
66,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x^3, x)","F",0
67,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x^4, x)","F",0
68,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x^5, x)","F",0
69,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^6,x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x^6, x)","F",0
70,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x^m,x, algorithm=""maxima"")","\int x^{m} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^m*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
71,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x^3,x, algorithm=""maxima"")","\int x^{3} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^3*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
72,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^2*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
73,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x,x, algorithm=""maxima"")","\int x \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
74,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
75,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)/x, x)","F",0
76,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)/x^2, x)","F",0
77,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)/x^3, x)","F",0
78,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)/x^4, x)","F",0
79,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{5}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)/x^5, x)","F",0
80,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x^m,x, algorithm=""maxima"")","\int x^{m} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x^m*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2), x)","F",0
81,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x^3,x, algorithm=""maxima"")","\int x^{3} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x^3*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2), x)","F",0
82,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x^2*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2), x)","F",0
83,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x,x, algorithm=""maxima"")","\int x \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2), x)","F",0
84,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2), x)","F",0
85,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}{x}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)/x, x)","F",0
86,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)/x^2, x)","F",0
87,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)/x^3, x)","F",0
88,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^4,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}{x^{4}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)/x^4, x)","F",0
89,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^5,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}{x^{5}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)/x^5, x)","F",0
90,0,0,0,0.000000," ","integrate(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(x^m/sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
91,0,0,0,0.000000," ","integrate(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(x^3/sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
92,0,0,0,0.000000," ","integrate(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(x^2/sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
93,0,0,0,0.000000," ","integrate(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(x/sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
94,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
95,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{1}{x \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))), x)","F",0
96,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{1}{x^{2} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^2*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))), x)","F",0
97,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{1}{x^{3} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^3*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))), x)","F",0
98,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{1}{x^{4} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^4*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))), x)","F",0
99,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{1}{x^{5} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^5*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))), x)","F",0
100,0,0,0,0.000000," ","integrate(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m/((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
101,0,0,0,0.000000," ","integrate(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3/((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
102,0,0,0,0.000000," ","integrate(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
103,0,0,0,0.000000," ","integrate(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{x}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
104,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(-3/2), x)","F",0
105,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x,x, algorithm=""maxima"")","\int \frac{1}{x \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)), x)","F",0
106,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{1}{x^{2} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x^2*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)), x)","F",0
107,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{1}{x^{3} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x^3*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)), x)","F",0
108,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{1}{x^{4} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x^4*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)), x)","F",0
109,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{1}{x^{5} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x^5*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)), x)","F",0
110,0,0,0,0.000000," ","integrate(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^m/((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2), x)","F",0
111,0,0,0,0.000000," ","integrate(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^3/((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2), x)","F",0
112,0,0,0,0.000000," ","integrate(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^2/((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2), x)","F",0
113,0,0,0,0.000000," ","integrate(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \frac{x}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x/((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2), x)","F",0
114,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(-5/2), x)","F",0
115,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x,x, algorithm=""maxima"")","\int \frac{1}{x \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)), x)","F",0
116,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^2,x, algorithm=""maxima"")","\int \frac{1}{x^{2} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x^2*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)), x)","F",0
117,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^3,x, algorithm=""maxima"")","\int \frac{1}{x^{3} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x^3*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)), x)","F",0
118,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^4,x, algorithm=""maxima"")","\int \frac{1}{x^{4} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x^4*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)), x)","F",0
119,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^5,x, algorithm=""maxima"")","\int \frac{1}{x^{5} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x^5*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)), x)","F",0
120,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)*x^m,x, algorithm=""maxima"")","\int x^{m} \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(x^m*((x + 1)/sqrt(-x^2 + 1))^(1/3), x)","F",0
121,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(x^2*((x + 1)/sqrt(-x^2 + 1))^(1/3), x)","F",0
122,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)*x,x, algorithm=""maxima"")","\int x \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(x*((x + 1)/sqrt(-x^2 + 1))^(1/3), x)","F",0
123,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3),x, algorithm=""maxima"")","\int \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(1/3), x)","F",0
124,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}}{x}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(1/3)/x, x)","F",0
125,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}}{x^{2}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(1/3)/x^2, x)","F",0
126,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}}{x^{3}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(1/3)/x^3, x)","F",0
127,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)*x^m,x, algorithm=""maxima"")","\int x^{m} \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(x^m*((x + 1)/sqrt(-x^2 + 1))^(2/3), x)","F",0
128,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(x^2*((x + 1)/sqrt(-x^2 + 1))^(2/3), x)","F",0
129,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)*x,x, algorithm=""maxima"")","\int x \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(x*((x + 1)/sqrt(-x^2 + 1))^(2/3), x)","F",0
130,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3),x, algorithm=""maxima"")","\int \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(2/3), x)","F",0
131,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}}{x}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(2/3)/x, x)","F",0
132,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}}{x^{2}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(2/3)/x^2, x)","F",0
133,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}}{x^{3}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(2/3)/x^3, x)","F",0
134,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x^m,x, algorithm=""maxima"")","\int x^{m} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}\,{d x}"," ",0,"integrate(x^m*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(1/4), x)","F",0
135,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}\,{d x}"," ",0,"integrate(x^2*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(1/4), x)","F",0
136,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x,x, algorithm=""maxima"")","\int x \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}\,{d x}"," ",0,"integrate(x*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(1/4), x)","F",0
137,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4),x, algorithm=""maxima"")","\int \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(1/4), x)","F",0
138,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}}{x}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(1/4)/x, x)","F",0
139,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}}{x^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(1/4)/x^2, x)","F",0
140,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{1}{4}}}{x^{3}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(1/4)/x^3, x)","F",0
141,0,0,0,0.000000," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*x^m,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{4} x^{m}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^4*x^m/(a^2*x^2 - 1)^2, x)","F",0
142,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^m,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} x^{m}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*x^m/(-a^2*x^2 + 1)^(3/2), x)","F",0
143,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} x^{m}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*x^m/(a^2*x^2 - 1), x)","F",0
144,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
145,0,0,0,0.000000," ","integrate(x^m/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*x^m/(a*x + 1), x)","F",0
146,0,0,0,0.000000," ","integrate(x^m/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} x^{m}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*x^m/(a*x + 1)^2, x)","F",0
147,0,0,0,0.000000," ","integrate(x^m/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{m}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*x^m/(a*x + 1)^3, x)","F",0
148,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^m,x, algorithm=""maxima"")","\int x^{m} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^m*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
149,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^3,x, algorithm=""maxima"")","\int x^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^3*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
150,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^2*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
151,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x,x, algorithm=""maxima"")","\int x \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
152,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x)),x, algorithm=""maxima"")","\int \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
153,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{x}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/x, x)","F",0
154,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{x^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/x^2, x)","F",0
155,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{x^{3}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/x^3, x)","F",0
156,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^4,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{x^{4}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/x^4, x)","F",0
157,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^p,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(-a c x + c\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a*c*x + c)^p/sqrt(-a^2*x^2 + 1), x)","F",0
158,1,118,0,0.449950," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4,x, algorithm=""maxima"")","-\frac{1}{5} \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x^{4} + \frac{3}{4} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x^{3} - \frac{14}{15} \, \sqrt{-a^{2} x^{2} + 1} a c^{4} x^{2} + \frac{1}{8} \, \sqrt{-a^{2} x^{2} + 1} c^{4} x + \frac{7 \, c^{4} \arcsin\left(a x\right)}{8 \, a} + \frac{17 \, \sqrt{-a^{2} x^{2} + 1} c^{4}}{15 \, a}"," ",0,"-1/5*sqrt(-a^2*x^2 + 1)*a^3*c^4*x^4 + 3/4*sqrt(-a^2*x^2 + 1)*a^2*c^4*x^3 - 14/15*sqrt(-a^2*x^2 + 1)*a*c^4*x^2 + 1/8*sqrt(-a^2*x^2 + 1)*c^4*x + 7/8*c^4*arcsin(a*x)/a + 17/15*sqrt(-a^2*x^2 + 1)*c^4/a","A",0
159,1,95,0,0.422746," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3,x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x^{3} - \frac{2}{3} \, \sqrt{-a^{2} x^{2} + 1} a c^{3} x^{2} + \frac{3}{8} \, \sqrt{-a^{2} x^{2} + 1} c^{3} x + \frac{5 \, c^{3} \arcsin\left(a x\right)}{8 \, a} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{3 \, a}"," ",0,"1/4*sqrt(-a^2*x^2 + 1)*a^2*c^3*x^3 - 2/3*sqrt(-a^2*x^2 + 1)*a*c^3*x^2 + 3/8*sqrt(-a^2*x^2 + 1)*c^3*x + 5/8*c^3*arcsin(a*x)/a + 2/3*sqrt(-a^2*x^2 + 1)*c^3/a","A",0
160,1,72,0,0.423998," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{1}{3} \, \sqrt{-a^{2} x^{2} + 1} a c^{2} x^{2} + \frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} c^{2} x + \frac{c^{2} \arcsin\left(a x\right)}{2 \, a} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{3 \, a}"," ",0,"-1/3*sqrt(-a^2*x^2 + 1)*a*c^2*x^2 + 1/2*sqrt(-a^2*x^2 + 1)*c^2*x + 1/2*c^2*arcsin(a*x)/a + 1/3*sqrt(-a^2*x^2 + 1)*c^2/a","A",0
161,1,27,0,0.416553," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} c x + \frac{c \arcsin\left(a x\right)}{2 \, a}"," ",0,"1/2*sqrt(-a^2*x^2 + 1)*c*x + 1/2*c*arcsin(a*x)/a","A",0
162,1,40,0,0.436115," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{2} c x - a c} - \frac{\arcsin\left(a x\right)}{a c}"," ",0,"-2*sqrt(-a^2*x^2 + 1)/(a^2*c*x - a*c) - arcsin(a*x)/(a*c)","A",0
163,1,73,0,0.425178," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{2} c^{2} x - a c^{2}\right)}}"," ",0,"2/3*sqrt(-a^2*x^2 + 1)/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2) + 1/3*sqrt(-a^2*x^2 + 1)/(a^2*c^2*x - a*c^2)","B",0
164,1,126,0,0.435652," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{5 \, {\left(a^{4} c^{3} x^{3} - 3 \, a^{3} c^{3} x^{2} + 3 \, a^{2} c^{3} x - a c^{3}\right)}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{15 \, {\left(a^{3} c^{3} x^{2} - 2 \, a^{2} c^{3} x + a c^{3}\right)}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{15 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"-2/5*sqrt(-a^2*x^2 + 1)/(a^4*c^3*x^3 - 3*a^3*c^3*x^2 + 3*a^2*c^3*x - a*c^3) - 1/15*sqrt(-a^2*x^2 + 1)/(a^3*c^3*x^2 - 2*a^2*c^3*x + a*c^3) + 1/15*sqrt(-a^2*x^2 + 1)/(a^2*c^3*x - a*c^3)","B",0
165,1,189,0,0.497847," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{7 \, {\left(a^{5} c^{4} x^{4} - 4 \, a^{4} c^{4} x^{3} + 6 \, a^{3} c^{4} x^{2} - 4 \, a^{2} c^{4} x + a c^{4}\right)}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{35 \, {\left(a^{4} c^{4} x^{3} - 3 \, a^{3} c^{4} x^{2} + 3 \, a^{2} c^{4} x - a c^{4}\right)}} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{2} c^{4} x - a c^{4}\right)}}"," ",0,"2/7*sqrt(-a^2*x^2 + 1)/(a^5*c^4*x^4 - 4*a^4*c^4*x^3 + 6*a^3*c^4*x^2 - 4*a^2*c^4*x + a*c^4) + 1/35*sqrt(-a^2*x^2 + 1)/(a^4*c^4*x^3 - 3*a^3*c^4*x^2 + 3*a^2*c^4*x - a*c^4) - 2/105*sqrt(-a^2*x^2 + 1)/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4) + 2/105*sqrt(-a^2*x^2 + 1)/(a^2*c^4*x - a*c^4)","B",0
166,1,264,0,0.434229," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^5,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{9 \, {\left(a^{6} c^{5} x^{5} - 5 \, a^{5} c^{5} x^{4} + 10 \, a^{4} c^{5} x^{3} - 10 \, a^{3} c^{5} x^{2} + 5 \, a^{2} c^{5} x - a c^{5}\right)}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{63 \, {\left(a^{5} c^{5} x^{4} - 4 \, a^{4} c^{5} x^{3} + 6 \, a^{3} c^{5} x^{2} - 4 \, a^{2} c^{5} x + a c^{5}\right)}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{4} c^{5} x^{3} - 3 \, a^{3} c^{5} x^{2} + 3 \, a^{2} c^{5} x - a c^{5}\right)}} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{315 \, {\left(a^{3} c^{5} x^{2} - 2 \, a^{2} c^{5} x + a c^{5}\right)}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{315 \, {\left(a^{2} c^{5} x - a c^{5}\right)}}"," ",0,"-2/9*sqrt(-a^2*x^2 + 1)/(a^6*c^5*x^5 - 5*a^5*c^5*x^4 + 10*a^4*c^5*x^3 - 10*a^3*c^5*x^2 + 5*a^2*c^5*x - a*c^5) - 1/63*sqrt(-a^2*x^2 + 1)/(a^5*c^5*x^4 - 4*a^4*c^5*x^3 + 6*a^3*c^5*x^2 - 4*a^2*c^5*x + a*c^5) + 1/105*sqrt(-a^2*x^2 + 1)/(a^4*c^5*x^3 - 3*a^3*c^5*x^2 + 3*a^2*c^5*x - a*c^5) - 2/315*sqrt(-a^2*x^2 + 1)/(a^3*c^5*x^2 - 2*a^2*c^5*x + a*c^5) + 2/315*sqrt(-a^2*x^2 + 1)/(a^2*c^5*x - a*c^5)","B",0
167,1,35,0,0.377356," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^p,x, algorithm=""maxima"")","-\frac{{\left(a c^{p} p x + c^{p} {\left(p + 2\right)}\right)} {\left(-a x + 1\right)}^{p}}{{\left(p^{2} + p\right)} a}"," ",0,"-(a*c^p*p*x + c^p*(p + 2))*(-a*x + 1)^p/((p^2 + p)*a)","A",0
168,1,59,0,0.345178," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^5,x, algorithm=""maxima"")","\frac{1}{6} \, a^{5} c^{5} x^{6} - \frac{3}{5} \, a^{4} c^{5} x^{5} + \frac{1}{2} \, a^{3} c^{5} x^{4} + \frac{2}{3} \, a^{2} c^{5} x^{3} - \frac{3}{2} \, a c^{5} x^{2} + c^{5} x"," ",0,"1/6*a^5*c^5*x^6 - 3/5*a^4*c^5*x^5 + 1/2*a^3*c^5*x^4 + 2/3*a^2*c^5*x^3 - 3/2*a*c^5*x^2 + c^5*x","A",0
169,1,37,0,0.338266," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^4,x, algorithm=""maxima"")","-\frac{1}{5} \, a^{4} c^{4} x^{5} + \frac{1}{2} \, a^{3} c^{4} x^{4} - a c^{4} x^{2} + c^{4} x"," ",0,"-1/5*a^4*c^4*x^5 + 1/2*a^3*c^4*x^4 - a*c^4*x^2 + c^4*x","A",0
170,1,37,0,0.315083," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a^{3} c^{3} x^{4} - \frac{1}{3} \, a^{2} c^{3} x^{3} - \frac{1}{2} \, a c^{3} x^{2} + c^{3} x"," ",0,"1/4*a^3*c^3*x^4 - 1/3*a^2*c^3*x^3 - 1/2*a*c^3*x^2 + c^3*x","A",0
171,1,17,0,0.306095," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} c^{2} x^{3} + c^{2} x"," ",0,"-1/3*a^2*c^2*x^3 + c^2*x","A",0
172,1,11,0,0.316582," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c),x, algorithm=""maxima"")","\frac{1}{2} \, a c x^{2} + c x"," ",0,"1/2*a*c*x^2 + c*x","A",0
173,1,29,0,0.338594," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{2}{a^{2} c x - a c} + \frac{\log\left(a x - 1\right)}{a c}"," ",0,"-2/(a^2*c*x - a*c) + log(a*x - 1)/(a*c)","A",0
174,1,25,0,0.342184," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{x}{a^{2} c^{2} x^{2} - 2 \, a c^{2} x + c^{2}}"," ",0,"x/(a^2*c^2*x^2 - 2*a*c^2*x + c^2)","B",0
175,1,47,0,0.337420," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{3 \, a x + 1}{6 \, {\left(a^{4} c^{3} x^{3} - 3 \, a^{3} c^{3} x^{2} + 3 \, a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"-1/6*(3*a*x + 1)/(a^4*c^3*x^3 - 3*a^3*c^3*x^2 + 3*a^2*c^3*x - a*c^3)","A",0
176,1,57,0,0.328101," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, a x + 1}{6 \, {\left(a^{5} c^{4} x^{4} - 4 \, a^{4} c^{4} x^{3} + 6 \, a^{3} c^{4} x^{2} - 4 \, a^{2} c^{4} x + a c^{4}\right)}}"," ",0,"1/6*(2*a*x + 1)/(a^5*c^4*x^4 - 4*a^4*c^4*x^3 + 6*a^3*c^4*x^2 - 4*a^2*c^4*x + a*c^4)","A",0
177,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^p,x, algorithm=""maxima"")","\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}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a*c*x + c)^p/(-a^2*x^2 + 1)^(3/2), x)","F",0
178,1,164,0,0.417267," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^4,x, algorithm=""maxima"")","-\frac{a^{5} c^{4} x^{6}}{5 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{a^{4} c^{4} x^{5}}{4 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{3 \, a^{3} c^{4} x^{4}}{5 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{7 \, a^{2} c^{4} x^{3}}{8 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{3 \, a c^{4} x^{2}}{5 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{5 \, c^{4} x}{8 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{3 \, c^{4} \arcsin\left(a x\right)}{8 \, a} + \frac{c^{4}}{5 \, \sqrt{-a^{2} x^{2} + 1} a}"," ",0,"-1/5*a^5*c^4*x^6/sqrt(-a^2*x^2 + 1) + 1/4*a^4*c^4*x^5/sqrt(-a^2*x^2 + 1) + 3/5*a^3*c^4*x^4/sqrt(-a^2*x^2 + 1) - 7/8*a^2*c^4*x^3/sqrt(-a^2*x^2 + 1) - 3/5*a*c^4*x^2/sqrt(-a^2*x^2 + 1) + 5/8*c^4*x/sqrt(-a^2*x^2 + 1) + 3/8*c^4*arcsin(a*x)/a + 1/5*c^4/(sqrt(-a^2*x^2 + 1)*a)","B",0
179,1,77,0,0.414919," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^3,x, algorithm=""maxima"")","\frac{a^{4} c^{3} x^{5}}{4 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{7 \, a^{2} c^{3} 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} \arcsin\left(a x\right)}{8 \, a}"," ",0,"1/4*a^4*c^3*x^5/sqrt(-a^2*x^2 + 1) - 7/8*a^2*c^3*x^3/sqrt(-a^2*x^2 + 1) + 5/8*c^3*x/sqrt(-a^2*x^2 + 1) + 3/8*c^3*arcsin(a*x)/a","A",0
180,1,118,0,0.418239," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{a^{3} c^{2} x^{4}}{3 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{a^{2} c^{2} x^{3}}{2 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{2 \, a c^{2} x^{2}}{3 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{c^{2} x}{2 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{c^{2} \arcsin\left(a x\right)}{2 \, a} - \frac{c^{2}}{3 \, \sqrt{-a^{2} x^{2} + 1} a}"," ",0,"-1/3*a^3*c^2*x^4/sqrt(-a^2*x^2 + 1) - 1/2*a^2*c^2*x^3/sqrt(-a^2*x^2 + 1) + 2/3*a*c^2*x^2/sqrt(-a^2*x^2 + 1) + 1/2*c^2*x/sqrt(-a^2*x^2 + 1) + 1/2*c^2*arcsin(a*x)/a - 1/3*c^2/(sqrt(-a^2*x^2 + 1)*a)","B",0
181,1,85,0,0.417935," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c),x, algorithm=""maxima"")","\frac{a^{2} c x^{3}}{2 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{2 \, a c x^{2}}{\sqrt{-a^{2} x^{2} + 1}} - \frac{c x}{2 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{3 \, c \arcsin\left(a x\right)}{2 \, a} - \frac{2 \, c}{\sqrt{-a^{2} x^{2} + 1} a}"," ",0,"1/2*a^2*c*x^3/sqrt(-a^2*x^2 + 1) + 2*a*c*x^2/sqrt(-a^2*x^2 + 1) - 1/2*c*x/sqrt(-a^2*x^2 + 1) + 3/2*c*arcsin(a*x)/a - 2*c/(sqrt(-a^2*x^2 + 1)*a)","A",0
182,1,89,0,0.426765," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{8 \, x}{3 \, \sqrt{-a^{2} x^{2} + 1} c} - \frac{8}{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{2} c x - \sqrt{-a^{2} x^{2} + 1} a c\right)}} + \frac{\arcsin\left(a x\right)}{a c} - \frac{4}{\sqrt{-a^{2} x^{2} + 1} a c}"," ",0,"-8/3*x/(sqrt(-a^2*x^2 + 1)*c) - 8/3/(sqrt(-a^2*x^2 + 1)*a^2*c*x - sqrt(-a^2*x^2 + 1)*a*c) + arcsin(a*x)/(a*c) - 4/(sqrt(-a^2*x^2 + 1)*a*c)","A",0
183,1,146,0,0.336929," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{8}{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{3} c^{2} x^{2} - 2 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{2} x + \sqrt{-a^{2} x^{2} + 1} a c^{2}\right)}} + \frac{12}{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{2} c^{2} x - \sqrt{-a^{2} x^{2} + 1} a c^{2}\right)}} + \frac{x}{5 \, \sqrt{-a^{2} x^{2} + 1} c^{2}} + \frac{1}{\sqrt{-a^{2} x^{2} + 1} a c^{2}}"," ",0,"8/5/(sqrt(-a^2*x^2 + 1)*a^3*c^2*x^2 - 2*sqrt(-a^2*x^2 + 1)*a^2*c^2*x + sqrt(-a^2*x^2 + 1)*a*c^2) + 12/5/(sqrt(-a^2*x^2 + 1)*a^2*c^2*x - sqrt(-a^2*x^2 + 1)*a*c^2) + 1/5*x/(sqrt(-a^2*x^2 + 1)*c^2) + 1/(sqrt(-a^2*x^2 + 1)*a*c^2)","B",0
184,1,216,0,0.356349," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{8}{7 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{4} c^{3} x^{3} - 3 \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{3} x^{2} + 3 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x - \sqrt{-a^{2} x^{2} + 1} a c^{3}\right)}} - \frac{52}{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{3} c^{3} x^{2} - 2 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x + \sqrt{-a^{2} x^{2} + 1} a c^{3}\right)}} - \frac{18}{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x - \sqrt{-a^{2} x^{2} + 1} a c^{3}\right)}} + \frac{x}{35 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}"," ",0,"-8/7/(sqrt(-a^2*x^2 + 1)*a^4*c^3*x^3 - 3*sqrt(-a^2*x^2 + 1)*a^3*c^3*x^2 + 3*sqrt(-a^2*x^2 + 1)*a^2*c^3*x - sqrt(-a^2*x^2 + 1)*a*c^3) - 52/35/(sqrt(-a^2*x^2 + 1)*a^3*c^3*x^2 - 2*sqrt(-a^2*x^2 + 1)*a^2*c^3*x + sqrt(-a^2*x^2 + 1)*a*c^3) - 18/35/(sqrt(-a^2*x^2 + 1)*a^2*c^3*x - sqrt(-a^2*x^2 + 1)*a*c^3) + 1/35*x/(sqrt(-a^2*x^2 + 1)*c^3)","B",0
185,1,327,0,0.352290," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{8}{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{5} c^{4} x^{4} - 4 \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{4} x^{3} + 6 \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x^{2} - 4 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x + \sqrt{-a^{2} x^{2} + 1} a c^{4}\right)}} + \frac{68}{63 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{4} c^{4} x^{3} - 3 \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x^{2} + 3 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x - \sqrt{-a^{2} x^{2} + 1} a c^{4}\right)}} + \frac{106}{315 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x^{2} - 2 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x + \sqrt{-a^{2} x^{2} + 1} a c^{4}\right)}} - \frac{1}{315 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x - \sqrt{-a^{2} x^{2} + 1} a c^{4}\right)}} + \frac{2 \, x}{315 \, \sqrt{-a^{2} x^{2} + 1} c^{4}}"," ",0,"8/9/(sqrt(-a^2*x^2 + 1)*a^5*c^4*x^4 - 4*sqrt(-a^2*x^2 + 1)*a^4*c^4*x^3 + 6*sqrt(-a^2*x^2 + 1)*a^3*c^4*x^2 - 4*sqrt(-a^2*x^2 + 1)*a^2*c^4*x + sqrt(-a^2*x^2 + 1)*a*c^4) + 68/63/(sqrt(-a^2*x^2 + 1)*a^4*c^4*x^3 - 3*sqrt(-a^2*x^2 + 1)*a^3*c^4*x^2 + 3*sqrt(-a^2*x^2 + 1)*a^2*c^4*x - sqrt(-a^2*x^2 + 1)*a*c^4) + 106/315/(sqrt(-a^2*x^2 + 1)*a^3*c^4*x^2 - 2*sqrt(-a^2*x^2 + 1)*a^2*c^4*x + sqrt(-a^2*x^2 + 1)*a*c^4) - 1/315/(sqrt(-a^2*x^2 + 1)*a^2*c^4*x - sqrt(-a^2*x^2 + 1)*a*c^4) + 2/315*x/(sqrt(-a^2*x^2 + 1)*c^4)","B",0
186,1,462,0,0.355630," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^5,x, algorithm=""maxima"")","-\frac{8}{11 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{6} c^{5} x^{5} - 5 \, \sqrt{-a^{2} x^{2} + 1} a^{5} c^{5} x^{4} + 10 \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{5} x^{3} - 10 \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{5} x^{2} + 5 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{5} x - \sqrt{-a^{2} x^{2} + 1} a c^{5}\right)}} - \frac{28}{33 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{5} c^{5} x^{4} - 4 \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{5} x^{3} + 6 \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{5} x^{2} - 4 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{5} x + \sqrt{-a^{2} x^{2} + 1} a c^{5}\right)}} - \frac{58}{231 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{4} c^{5} x^{3} - 3 \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{5} x^{2} + 3 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{5} x - \sqrt{-a^{2} x^{2} + 1} a c^{5}\right)}} + \frac{1}{1155 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{3} c^{5} x^{2} - 2 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{5} x + \sqrt{-a^{2} x^{2} + 1} a c^{5}\right)}} - \frac{1}{1155 \, {\left(\sqrt{-a^{2} x^{2} + 1} a^{2} c^{5} x - \sqrt{-a^{2} x^{2} + 1} a c^{5}\right)}} + \frac{2 \, x}{1155 \, \sqrt{-a^{2} x^{2} + 1} c^{5}}"," ",0,"-8/11/(sqrt(-a^2*x^2 + 1)*a^6*c^5*x^5 - 5*sqrt(-a^2*x^2 + 1)*a^5*c^5*x^4 + 10*sqrt(-a^2*x^2 + 1)*a^4*c^5*x^3 - 10*sqrt(-a^2*x^2 + 1)*a^3*c^5*x^2 + 5*sqrt(-a^2*x^2 + 1)*a^2*c^5*x - sqrt(-a^2*x^2 + 1)*a*c^5) - 28/33/(sqrt(-a^2*x^2 + 1)*a^5*c^5*x^4 - 4*sqrt(-a^2*x^2 + 1)*a^4*c^5*x^3 + 6*sqrt(-a^2*x^2 + 1)*a^3*c^5*x^2 - 4*sqrt(-a^2*x^2 + 1)*a^2*c^5*x + sqrt(-a^2*x^2 + 1)*a*c^5) - 58/231/(sqrt(-a^2*x^2 + 1)*a^4*c^5*x^3 - 3*sqrt(-a^2*x^2 + 1)*a^3*c^5*x^2 + 3*sqrt(-a^2*x^2 + 1)*a^2*c^5*x - sqrt(-a^2*x^2 + 1)*a*c^5) + 1/1155/(sqrt(-a^2*x^2 + 1)*a^3*c^5*x^2 - 2*sqrt(-a^2*x^2 + 1)*a^2*c^5*x + sqrt(-a^2*x^2 + 1)*a*c^5) - 1/1155/(sqrt(-a^2*x^2 + 1)*a^2*c^5*x - sqrt(-a^2*x^2 + 1)*a*c^5) + 2/1155*x/(sqrt(-a^2*x^2 + 1)*c^5)","B",0
187,1,77,0,0.401758," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^p,x, algorithm=""maxima"")","\frac{{\left({\left(p^{2} - p\right)} a^{2} c^{p} x^{2} + 2 \, {\left(p^{2} + p - 2\right)} a c^{p} x + {\left(p^{2} + 3 \, p + 4\right)} c^{p}\right)} {\left(-a x + 1\right)}^{p}}{{\left(p^{3} - p\right)} a^{2} x - {\left(p^{3} - p\right)} a}"," ",0,"((p^2 - p)*a^2*c^p*x^2 + 2*(p^2 + p - 2)*a*c^p*x + (p^2 + 3*p + 4)*c^p)*(-a*x + 1)^p/((p^3 - p)*a^2*x - (p^3 - p)*a)","A",0
188,1,59,0,0.327770," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^5,x, algorithm=""maxima"")","-\frac{1}{6} \, a^{5} c^{5} x^{6} + \frac{1}{5} \, a^{4} c^{5} x^{5} + \frac{1}{2} \, a^{3} c^{5} x^{4} - \frac{2}{3} \, a^{2} c^{5} x^{3} - \frac{1}{2} \, a c^{5} x^{2} + c^{5} x"," ",0,"-1/6*a^5*c^5*x^6 + 1/5*a^4*c^5*x^5 + 1/2*a^3*c^5*x^4 - 2/3*a^2*c^5*x^3 - 1/2*a*c^5*x^2 + c^5*x","A",0
189,1,28,0,0.332319," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{1}{5} \, a^{4} c^{4} x^{5} - \frac{2}{3} \, a^{2} c^{4} x^{3} + c^{4} x"," ",0,"1/5*a^4*c^4*x^5 - 2/3*a^2*c^4*x^3 + c^4*x","A",0
190,1,37,0,0.331401," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{3} c^{3} x^{4} - \frac{1}{3} \, a^{2} c^{3} x^{3} + \frac{1}{2} \, a c^{3} x^{2} + c^{3} x"," ",0,"-1/4*a^3*c^3*x^4 - 1/3*a^2*c^3*x^3 + 1/2*a*c^3*x^2 + c^3*x","A",0
191,1,25,0,0.316820," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} c^{2} x^{3} + a c^{2} x^{2} + c^{2} x"," ",0,"1/3*a^2*c^2*x^3 + a*c^2*x^2 + c^2*x","A",0
192,1,24,0,0.324523," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c),x, algorithm=""maxima"")","-\frac{1}{2} \, a c x^{2} - 3 \, c x - \frac{4 \, c \log\left(a x - 1\right)}{a}"," ",0,"-1/2*a*c*x^2 - 3*c*x - 4*c*log(a*x - 1)/a","A",0
193,1,44,0,0.318773," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a*c*x+c),x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, a x - 1\right)}}{a^{3} c x^{2} - 2 \, a^{2} c x + a c} - \frac{\log\left(a x - 1\right)}{a c}"," ",0,"2*(2*a*x - 1)/(a^3*c*x^2 - 2*a^2*c*x + a*c) - log(a*x - 1)/(a*c)","A",0
194,1,51,0,0.331495," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{3 \, a^{2} x^{2} + 1}{3 \, {\left(a^{4} c^{2} x^{3} - 3 \, a^{3} c^{2} x^{2} + 3 \, a^{2} c^{2} x - a c^{2}\right)}}"," ",0,"-1/3*(3*a^2*x^2 + 1)/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2)","B",0
195,1,65,0,0.328336," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a*c*x+c)^3,x, algorithm=""maxima"")","\frac{3 \, a^{2} x^{2} + 2 \, a x + 1}{6 \, {\left(a^{5} c^{3} x^{4} - 4 \, a^{4} c^{3} x^{3} + 6 \, a^{3} c^{3} x^{2} - 4 \, a^{2} c^{3} x + a c^{3}\right)}}"," ",0,"1/6*(3*a^2*x^2 + 2*a*x + 1)/(a^5*c^3*x^4 - 4*a^4*c^3*x^3 + 6*a^3*c^3*x^2 - 4*a^2*c^3*x + a*c^3)","A",0
196,1,77,0,0.332604," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a*c*x+c)^4,x, algorithm=""maxima"")","-\frac{5 \, a^{2} x^{2} + 5 \, a x + 2}{15 \, {\left(a^{6} c^{4} x^{5} - 5 \, a^{5} c^{4} x^{4} + 10 \, a^{4} c^{4} x^{3} - 10 \, a^{3} c^{4} x^{2} + 5 \, a^{2} c^{4} x - a c^{4}\right)}}"," ",0,"-1/15*(5*a^2*x^2 + 5*a*x + 2)/(a^6*c^4*x^5 - 5*a^5*c^4*x^4 + 10*a^4*c^4*x^3 - 10*a^3*c^4*x^2 + 5*a^2*c^4*x - a*c^4)","A",0
197,0,0,0,0.000000," ","integrate((-a*c*x+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a c x + c\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a*c*x + c)^p/(a*x + 1), x)","F",0
198,1,89,0,0.431638," ","integrate((-a*c*x+c)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{3} x - \frac{29}{8} \, \sqrt{-a^{2} x^{2} + 1} c^{3} x - \frac{4 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{3}}{3 \, a} + \frac{35 \, c^{3} \arcsin\left(a x\right)}{8 \, a} + \frac{8 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{a}"," ",0,"1/4*(-a^2*x^2 + 1)^(3/2)*c^3*x - 29/8*sqrt(-a^2*x^2 + 1)*c^3*x - 4/3*(-a^2*x^2 + 1)^(3/2)*c^3/a + 35/8*c^3*arcsin(a*x)/a + 8*sqrt(-a^2*x^2 + 1)*c^3/a","A",0
199,1,71,0,0.433624," ","integrate((-a*c*x+c)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{3}{2} \, \sqrt{-a^{2} x^{2} + 1} c^{2} x - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2}}{3 \, a} + \frac{5 \, c^{2} \arcsin\left(a x\right)}{2 \, a} + \frac{4 \, \sqrt{-a^{2} x^{2} + 1} c^{2}}{a}"," ",0,"-3/2*sqrt(-a^2*x^2 + 1)*c^2*x - 1/3*(-a^2*x^2 + 1)^(3/2)*c^2/a + 5/2*c^2*arcsin(a*x)/a + 4*sqrt(-a^2*x^2 + 1)*c^2/a","A",0
200,1,45,0,0.463383," ","integrate((-a*c*x+c)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} c x + \frac{3 \, c \arcsin\left(a x\right)}{2 \, a} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c}{a}"," ",0,"-1/2*sqrt(-a^2*x^2 + 1)*c*x + 3/2*c*arcsin(a*x)/a + 2*sqrt(-a^2*x^2 + 1)*c/a","A",0
201,1,11,0,0.432022," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c),x, algorithm=""maxima"")","\frac{\arcsin\left(a x\right)}{a c}"," ",0,"arcsin(a*x)/(a*c)","A",0
202,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a c x - c\right)}^{2} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*c*x - c)^2*(a*x + 1)), x)","F",0
203,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a c x - c\right)}^{3} {\left(a x + 1\right)}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*x^2 + 1)/((a*c*x - c)^3*(a*x + 1)), x)","F",0
204,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a c x - c\right)}^{4} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*c*x - c)^4*(a*x + 1)), x)","F",0
205,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^5,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a c x - c\right)}^{5} {\left(a x + 1\right)}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*x^2 + 1)/((a*c*x - c)^5*(a*x + 1)), x)","F",0
206,0,0,0,0.000000," ","integrate((-a*c*x+c)^p/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(-a c x + c\right)}^{p}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(-a*c*x + c)^p/(a*x + 1)^2, x)","F",0
207,1,63,0,0.326656," ","integrate((-a*c*x+c)^4/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{5} \, a^{4} c^{4} x^{5} + \frac{3}{2} \, a^{3} c^{4} x^{4} - \frac{16}{3} \, a^{2} c^{4} x^{3} + 13 \, a c^{4} x^{2} - 31 \, c^{4} x + \frac{32 \, c^{4} \log\left(a x + 1\right)}{a}"," ",0,"-1/5*a^4*c^4*x^5 + 3/2*a^3*c^4*x^4 - 16/3*a^2*c^4*x^3 + 13*a*c^4*x^2 - 31*c^4*x + 32*c^4*log(a*x + 1)/a","A",0
208,1,52,0,0.333954," ","integrate((-a*c*x+c)^3/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{4} \, a^{3} c^{3} x^{4} - \frac{5}{3} \, a^{2} c^{3} x^{3} + \frac{11}{2} \, a c^{3} x^{2} - 15 \, c^{3} x + \frac{16 \, c^{3} \log\left(a x + 1\right)}{a}"," ",0,"1/4*a^3*c^3*x^4 - 5/3*a^2*c^3*x^3 + 11/2*a*c^3*x^2 - 15*c^3*x + 16*c^3*log(a*x + 1)/a","A",0
209,1,41,0,0.348677," ","integrate((-a*c*x+c)^2/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} c^{2} x^{3} + 2 \, a c^{2} x^{2} - 7 \, c^{2} x + \frac{8 \, c^{2} \log\left(a x + 1\right)}{a}"," ",0,"-1/3*a^2*c^2*x^3 + 2*a*c^2*x^2 - 7*c^2*x + 8*c^2*log(a*x + 1)/a","A",0
210,1,24,0,0.313833," ","integrate((-a*c*x+c)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a c x^{2} - 3 \, c x + \frac{4 \, c \log\left(a x + 1\right)}{a}"," ",0,"1/2*a*c*x^2 - 3*c*x + 4*c*log(a*x + 1)/a","A",0
211,1,13,0,0.309220," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c),x, algorithm=""maxima"")","\frac{\log\left(a x + 1\right)}{a c}"," ",0,"log(a*x + 1)/(a*c)","A",0
212,1,29,0,0.310799," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{\log\left(a x + 1\right)}{2 \, a c^{2}} - \frac{\log\left(a x - 1\right)}{2 \, a c^{2}}"," ",0,"1/2*log(a*x + 1)/(a*c^2) - 1/2*log(a*x - 1)/(a*c^2)","B",0
213,1,48,0,0.343440," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(a^{2} c^{3} x - a c^{3}\right)}} + \frac{\log\left(a x + 1\right)}{4 \, a c^{3}} - \frac{\log\left(a x - 1\right)}{4 \, a c^{3}}"," ",0,"-1/2/(a^2*c^3*x - a*c^3) + 1/4*log(a*x + 1)/(a*c^3) - 1/4*log(a*x - 1)/(a*c^3)","A",0
214,1,63,0,0.325815," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^4,x, algorithm=""maxima"")","-\frac{a x - 2}{4 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}} + \frac{\log\left(a x + 1\right)}{8 \, a c^{4}} - \frac{\log\left(a x - 1\right)}{8 \, a c^{4}}"," ",0,"-1/4*(a*x - 2)/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4) + 1/8*log(a*x + 1)/(a*c^4) - 1/8*log(a*x - 1)/(a*c^4)","A",0
215,1,84,0,0.347216," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^5,x, algorithm=""maxima"")","-\frac{3 \, a^{2} x^{2} - 9 \, a x + 10}{24 \, {\left(a^{4} c^{5} x^{3} - 3 \, a^{3} c^{5} x^{2} + 3 \, a^{2} c^{5} x - a c^{5}\right)}} + \frac{\log\left(a x + 1\right)}{16 \, a c^{5}} - \frac{\log\left(a x - 1\right)}{16 \, a c^{5}}"," ",0,"-1/24*(3*a^2*x^2 - 9*a*x + 10)/(a^4*c^5*x^3 - 3*a^3*c^5*x^2 + 3*a^2*c^5*x - a*c^5) + 1/16*log(a*x + 1)/(a*c^5) - 1/16*log(a*x - 1)/(a*c^5)","A",0
216,0,0,0,0.000000," ","integrate((-a*c*x+c)^p/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(-a c x + c\right)}^{p}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(-a*c*x + c)^p/(a*x + 1)^3, x)","F",0
217,1,233,0,0.451588," ","integrate((-a*c*x+c)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{3} x + 3 \, \sqrt{a^{2} x^{2} + 4 \, a x + 3} c^{3} x - \frac{3}{8} \, \sqrt{-a^{2} x^{2} + 1} c^{3} x + \frac{8 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{3}}{a^{3} x^{2} + 2 \, a^{2} x + a} - \frac{6 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{3}}{a^{2} x + a} + \frac{2 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{3}}{a} - \frac{3 i \, c^{3} \arcsin\left(a x + 2\right)}{a} - \frac{339 \, c^{3} \arcsin\left(a x\right)}{8 \, a} - \frac{48 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{a^{2} x + a} + \frac{6 \, \sqrt{a^{2} x^{2} + 4 \, a x + 3} c^{3}}{a} - \frac{18 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{a}"," ",0,"-1/4*(-a^2*x^2 + 1)^(3/2)*c^3*x + 3*sqrt(a^2*x^2 + 4*a*x + 3)*c^3*x - 3/8*sqrt(-a^2*x^2 + 1)*c^3*x + 8*(-a^2*x^2 + 1)^(3/2)*c^3/(a^3*x^2 + 2*a^2*x + a) - 6*(-a^2*x^2 + 1)^(3/2)*c^3/(a^2*x + a) + 2*(-a^2*x^2 + 1)^(3/2)*c^3/a - 3*I*c^3*arcsin(a*x + 2)/a - 339/8*c^3*arcsin(a*x)/a - 48*sqrt(-a^2*x^2 + 1)*c^3/(a^2*x + a) + 6*sqrt(a^2*x^2 + 4*a*x + 3)*c^3/a - 18*sqrt(-a^2*x^2 + 1)*c^3/a","C",0
218,1,196,0,0.436337," ","integrate((-a*c*x+c)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{a^{2} x^{2} + 4 \, a x + 3} c^{2} x + \frac{4 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2}}{a^{3} x^{2} + 2 \, a^{2} x + a} - \frac{2 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2}}{a^{2} x + a} + \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2}}{3 \, a} - \frac{i \, c^{2} \arcsin\left(a x + 2\right)}{2 \, a} - \frac{18 \, c^{2} \arcsin\left(a x\right)}{a} - \frac{24 \, \sqrt{-a^{2} x^{2} + 1} c^{2}}{a^{2} x + a} + \frac{\sqrt{a^{2} x^{2} + 4 \, a x + 3} c^{2}}{a} - \frac{6 \, \sqrt{-a^{2} x^{2} + 1} c^{2}}{a}"," ",0,"1/2*sqrt(a^2*x^2 + 4*a*x + 3)*c^2*x + 4*(-a^2*x^2 + 1)^(3/2)*c^2/(a^3*x^2 + 2*a^2*x + a) - 2*(-a^2*x^2 + 1)^(3/2)*c^2/(a^2*x + a) + 1/3*(-a^2*x^2 + 1)^(3/2)*c^2/a - 1/2*I*c^2*arcsin(a*x + 2)/a - 18*c^2*arcsin(a*x)/a - 24*sqrt(-a^2*x^2 + 1)*c^2/(a^2*x + a) + sqrt(a^2*x^2 + 4*a*x + 3)*c^2/a - 6*sqrt(-a^2*x^2 + 1)*c^2/a","C",0
219,1,109,0,0.448968," ","integrate((-a*c*x+c)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c}{a^{3} x^{2} + 2 \, a^{2} x + a} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c}{2 \, {\left(a^{2} x + a\right)}} - \frac{15 \, c \arcsin\left(a x\right)}{2 \, a} - \frac{12 \, \sqrt{-a^{2} x^{2} + 1} c}{a^{2} x + a} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1} c}{2 \, a}"," ",0,"2*(-a^2*x^2 + 1)^(3/2)*c/(a^3*x^2 + 2*a^2*x + a) - 1/2*(-a^2*x^2 + 1)^(3/2)*c/(a^2*x + a) - 15/2*c*arcsin(a*x)/a - 12*sqrt(-a^2*x^2 + 1)*c/(a^2*x + a) - 3/2*sqrt(-a^2*x^2 + 1)*c/a","A",0
220,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c),x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a c x - c\right)} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"-integrate((-a^2*x^2 + 1)^(3/2)/((a*c*x - c)*(a*x + 1)^3), x)","F",0
221,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a c x - c\right)}^{2} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*c*x - c)^2*(a*x + 1)^3), x)","F",0
222,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a c x - c\right)}^{3} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"-integrate((-a^2*x^2 + 1)^(3/2)/((a*c*x - c)^3*(a*x + 1)^3), x)","F",0
223,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^4,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a c x - c\right)}^{4} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*c*x - c)^4*(a*x + 1)^3), x)","F",0
224,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^5,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a c x - c\right)}^{5} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"-integrate((-a^2*x^2 + 1)^(3/2)/((a*c*x - c)^5*(a*x + 1)^3), x)","F",0
225,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^6,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a c x - c\right)}^{6} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*c*x - c)^6*(a*x + 1)^3), x)","F",0
226,1,150,0,0.358594," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(9/2),x, algorithm=""maxima"")","\frac{2 \, {\left(35 \, a^{6} c^{\frac{9}{2}} x^{6} - 175 \, a^{5} c^{\frac{9}{2}} x^{5} + 360 \, a^{4} c^{\frac{9}{2}} x^{4} - 422 \, a^{3} c^{\frac{9}{2}} x^{3} + 459 \, a^{2} c^{\frac{9}{2}} x^{2} - 1451 \, a c^{\frac{9}{2}} x - 2902 \, c^{\frac{9}{2}}\right)}}{385 \, \sqrt{a x + 1} a} + \frac{2 \, {\left(35 \, a^{5} c^{\frac{9}{2}} x^{5} - 185 \, a^{4} c^{\frac{9}{2}} x^{4} + 422 \, a^{3} c^{\frac{9}{2}} x^{3} - 634 \, a^{2} c^{\frac{9}{2}} x^{2} + 1591 \, a c^{\frac{9}{2}} x + 2867 \, c^{\frac{9}{2}}\right)}}{315 \, \sqrt{a x + 1} a}"," ",0,"2/385*(35*a^6*c^(9/2)*x^6 - 175*a^5*c^(9/2)*x^5 + 360*a^4*c^(9/2)*x^4 - 422*a^3*c^(9/2)*x^3 + 459*a^2*c^(9/2)*x^2 - 1451*a*c^(9/2)*x - 2902*c^(9/2))/(sqrt(a*x + 1)*a) + 2/315*(35*a^5*c^(9/2)*x^5 - 185*a^4*c^(9/2)*x^4 + 422*a^3*c^(9/2)*x^3 - 634*a^2*c^(9/2)*x^2 + 1591*a*c^(9/2)*x + 2867*c^(9/2))/(sqrt(a*x + 1)*a)","A",0
227,1,128,0,0.390401," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(5 \, a^{5} c^{\frac{7}{2}} x^{5} - 20 \, a^{4} c^{\frac{7}{2}} x^{4} + 32 \, a^{3} c^{\frac{7}{2}} x^{3} - 34 \, a^{2} c^{\frac{7}{2}} x^{2} + 91 \, a c^{\frac{7}{2}} x + 182 \, c^{\frac{7}{2}}\right)}}{45 \, \sqrt{a x + 1} a} - \frac{2 \, {\left(5 \, a^{4} c^{\frac{7}{2}} x^{4} - 22 \, a^{3} c^{\frac{7}{2}} x^{3} + 44 \, a^{2} c^{\frac{7}{2}} x^{2} - 106 \, a c^{\frac{7}{2}} x - 177 \, c^{\frac{7}{2}}\right)}}{35 \, \sqrt{a x + 1} a}"," ",0,"-2/45*(5*a^5*c^(7/2)*x^5 - 20*a^4*c^(7/2)*x^4 + 32*a^3*c^(7/2)*x^3 - 34*a^2*c^(7/2)*x^2 + 91*a*c^(7/2)*x + 182*c^(7/2))/(sqrt(a*x + 1)*a) - 2/35*(5*a^4*c^(7/2)*x^4 - 22*a^3*c^(7/2)*x^3 + 44*a^2*c^(7/2)*x^2 - 106*a*c^(7/2)*x - 177*c^(7/2))/(sqrt(a*x + 1)*a)","A",0
228,1,106,0,0.350856," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, a^{4} c^{\frac{5}{2}} x^{4} - 9 \, a^{3} c^{\frac{5}{2}} x^{3} + 11 \, a^{2} c^{\frac{5}{2}} x^{2} - 23 \, a c^{\frac{5}{2}} x - 46 \, c^{\frac{5}{2}}\right)}}{21 \, \sqrt{a x + 1} a} + \frac{2 \, {\left(3 \, a^{3} c^{\frac{5}{2}} x^{3} - 11 \, a^{2} c^{\frac{5}{2}} x^{2} + 29 \, a c^{\frac{5}{2}} x + 43 \, c^{\frac{5}{2}}\right)}}{15 \, \sqrt{a x + 1} a}"," ",0,"2/21*(3*a^4*c^(5/2)*x^4 - 9*a^3*c^(5/2)*x^3 + 11*a^2*c^(5/2)*x^2 - 23*a*c^(5/2)*x - 46*c^(5/2))/(sqrt(a*x + 1)*a) + 2/15*(3*a^3*c^(5/2)*x^3 - 11*a^2*c^(5/2)*x^2 + 29*a*c^(5/2)*x + 43*c^(5/2))/(sqrt(a*x + 1)*a)","A",0
229,1,82,0,0.346870," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{3} c^{\frac{3}{2}} x^{3} - 2 \, a^{2} c^{\frac{3}{2}} x^{2} + 3 \, a c^{\frac{3}{2}} x + 6 \, c^{\frac{3}{2}}\right)}}{5 \, \sqrt{a x + 1} a} - \frac{2 \, {\left(a^{2} c^{\frac{3}{2}} x^{2} - 4 \, a c^{\frac{3}{2}} x - 5 \, c^{\frac{3}{2}}\right)}}{3 \, \sqrt{a x + 1} a}"," ",0,"-2/5*(a^3*c^(3/2)*x^3 - 2*a^2*c^(3/2)*x^2 + 3*a*c^(3/2)*x + 6*c^(3/2))/(sqrt(a*x + 1)*a) - 2/3*(a^2*c^(3/2)*x^2 - 4*a*c^(3/2)*x - 5*c^(3/2))/(sqrt(a*x + 1)*a)","A",0
230,1,58,0,0.347147," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{2} \sqrt{c} x^{2} - a \sqrt{c} x - 2 \, \sqrt{c}\right)}}{3 \, \sqrt{a x + 1} a} + \frac{2 \, {\left(a \sqrt{c} x + \sqrt{c}\right)}}{\sqrt{a x + 1} a}"," ",0,"2/3*(a^2*sqrt(c)*x^2 - a*sqrt(c)*x - 2*sqrt(c))/(sqrt(a*x + 1)*a) + 2*(a*sqrt(c)*x + sqrt(c))/(sqrt(a*x + 1)*a)","A",0
231,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)), x)","F",0
232,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(-a c x + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(-a*c*x + c)^(3/2)), x)","F",0
233,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(-a c x + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(-a*c*x + c)^(5/2)), x)","F",0
234,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(-a c x + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(-a*c*x + c)^(7/2)), x)","F",0
235,1,32,0,0.328831," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(7 \, {\left(-a c x + c\right)}^{\frac{9}{2}} - 18 \, {\left(-a c x + c\right)}^{\frac{7}{2}} c\right)}}{63 \, a c}"," ",0,"2/63*(7*(-a*c*x + c)^(9/2) - 18*(-a*c*x + c)^(7/2)*c)/(a*c)","A",0
236,1,32,0,0.313569," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, {\left(-a c x + c\right)}^{\frac{7}{2}} - 14 \, {\left(-a c x + c\right)}^{\frac{5}{2}} c\right)}}{35 \, a c}"," ",0,"2/35*(5*(-a*c*x + c)^(7/2) - 14*(-a*c*x + c)^(5/2)*c)/(a*c)","A",0
237,1,32,0,0.326166," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, {\left(-a c x + c\right)}^{\frac{5}{2}} - 10 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c\right)}}{15 \, a c}"," ",0,"2/15*(3*(-a*c*x + c)^(5/2) - 10*(-a*c*x + c)^(3/2)*c)/(a*c)","A",0
238,1,30,0,0.318394," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left({\left(-a c x + c\right)}^{\frac{3}{2}} - 6 \, \sqrt{-a c x + c} c\right)}}{3 \, a c}"," ",0,"2/3*((-a*c*x + c)^(3/2) - 6*sqrt(-a*c*x + c)*c)/(a*c)","A",0
239,1,30,0,0.309184," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\sqrt{-a c x + c} + \frac{2 \, c}{\sqrt{-a c x + c}}\right)}}{a c}"," ",0,"2*(sqrt(-a*c*x + c) + 2*c/sqrt(-a*c*x + c))/(a*c)","A",0
240,1,26,0,0.319917," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, a c x - c\right)}}{3 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a c}"," ",0,"2/3*(3*a*c*x - c)/((-a*c*x + c)^(3/2)*a*c)","A",0
241,1,24,0,0.311717," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a c x + c\right)}}{15 \, {\left(-a c x + c\right)}^{\frac{5}{2}} a c}"," ",0,"2/15*(5*a*c*x + c)/((-a*c*x + c)^(5/2)*a*c)","A",0
242,1,26,0,0.311858," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(7 \, a c x + 3 \, c\right)}}{35 \, {\left(-a c x + c\right)}^{\frac{7}{2}} a c}"," ",0,"2/35*(7*a*c*x + 3*c)/((-a*c*x + c)^(7/2)*a*c)","A",0
243,1,254,0,0.411889," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(9/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(35 \, a^{6} c^{\frac{9}{2}} x^{6} - 175 \, a^{5} c^{\frac{9}{2}} x^{5} + 415 \, a^{4} c^{\frac{9}{2}} x^{4} - 741 \, a^{3} c^{\frac{9}{2}} x^{3} + 1482 \, a^{2} c^{\frac{9}{2}} x^{2} - 5928 \, a c^{\frac{9}{2}} x - 11856 \, c^{\frac{9}{2}}\right)}}{385 \, \sqrt{a x + 1} a} - \frac{2 \, {\left(7 \, a^{5} c^{\frac{9}{2}} x^{5} - 37 \, a^{4} c^{\frac{9}{2}} x^{4} + 97 \, a^{3} c^{\frac{9}{2}} x^{3} - 215 \, a^{2} c^{\frac{9}{2}} x^{2} + 860 \, a c^{\frac{9}{2}} x + 1720 \, c^{\frac{9}{2}}\right)}}{21 \, \sqrt{a x + 1} a} - \frac{6 \, {\left(5 \, a^{4} c^{\frac{9}{2}} x^{4} - 29 \, a^{3} c^{\frac{9}{2}} x^{3} + 93 \, a^{2} c^{\frac{9}{2}} x^{2} - 407 \, a c^{\frac{9}{2}} x - 814 \, c^{\frac{9}{2}}\right)}}{35 \, \sqrt{a x + 1} a} - \frac{2 \, {\left(a^{3} c^{\frac{9}{2}} x^{3} - 7 \, a^{2} c^{\frac{9}{2}} x^{2} + 43 \, a c^{\frac{9}{2}} x + 91 \, c^{\frac{9}{2}}\right)}}{5 \, \sqrt{a x + 1} a}"," ",0,"-2/385*(35*a^6*c^(9/2)*x^6 - 175*a^5*c^(9/2)*x^5 + 415*a^4*c^(9/2)*x^4 - 741*a^3*c^(9/2)*x^3 + 1482*a^2*c^(9/2)*x^2 - 5928*a*c^(9/2)*x - 11856*c^(9/2))/(sqrt(a*x + 1)*a) - 2/21*(7*a^5*c^(9/2)*x^5 - 37*a^4*c^(9/2)*x^4 + 97*a^3*c^(9/2)*x^3 - 215*a^2*c^(9/2)*x^2 + 860*a*c^(9/2)*x + 1720*c^(9/2))/(sqrt(a*x + 1)*a) - 6/35*(5*a^4*c^(9/2)*x^4 - 29*a^3*c^(9/2)*x^3 + 93*a^2*c^(9/2)*x^2 - 407*a*c^(9/2)*x - 814*c^(9/2))/(sqrt(a*x + 1)*a) - 2/5*(a^3*c^(9/2)*x^3 - 7*a^2*c^(9/2)*x^2 + 43*a*c^(9/2)*x + 91*c^(9/2))/(sqrt(a*x + 1)*a)","B",0
244,1,210,0,0.383941," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a^{5} c^{\frac{7}{2}} x^{5} - 20 \, a^{4} c^{\frac{7}{2}} x^{4} + 41 \, a^{3} c^{\frac{7}{2}} x^{3} - 82 \, a^{2} c^{\frac{7}{2}} x^{2} + 328 \, a c^{\frac{7}{2}} x + 656 \, c^{\frac{7}{2}}\right)}}{45 \, \sqrt{a x + 1} a} + \frac{2 \, {\left(15 \, a^{4} c^{\frac{7}{2}} x^{4} - 66 \, a^{3} c^{\frac{7}{2}} x^{3} + 167 \, a^{2} c^{\frac{7}{2}} x^{2} - 668 \, a c^{\frac{7}{2}} x - 1336 \, c^{\frac{7}{2}}\right)}}{35 \, \sqrt{a x + 1} a} + \frac{2 \, {\left(3 \, a^{3} c^{\frac{7}{2}} x^{3} - 16 \, a^{2} c^{\frac{7}{2}} x^{2} + 79 \, a c^{\frac{7}{2}} x + 158 \, c^{\frac{7}{2}}\right)}}{5 \, \sqrt{a x + 1} a} + \frac{2 \, {\left(a^{2} c^{\frac{7}{2}} x^{2} - 10 \, a c^{\frac{7}{2}} x - 23 \, c^{\frac{7}{2}}\right)}}{3 \, \sqrt{a x + 1} a}"," ",0,"2/45*(5*a^5*c^(7/2)*x^5 - 20*a^4*c^(7/2)*x^4 + 41*a^3*c^(7/2)*x^3 - 82*a^2*c^(7/2)*x^2 + 328*a*c^(7/2)*x + 656*c^(7/2))/(sqrt(a*x + 1)*a) + 2/35*(15*a^4*c^(7/2)*x^4 - 66*a^3*c^(7/2)*x^3 + 167*a^2*c^(7/2)*x^2 - 668*a*c^(7/2)*x - 1336*c^(7/2))/(sqrt(a*x + 1)*a) + 2/5*(3*a^3*c^(7/2)*x^3 - 16*a^2*c^(7/2)*x^2 + 79*a*c^(7/2)*x + 158*c^(7/2))/(sqrt(a*x + 1)*a) + 2/3*(a^2*c^(7/2)*x^2 - 10*a*c^(7/2)*x - 23*c^(7/2))/(sqrt(a*x + 1)*a)","B",0
245,1,164,0,0.401731," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{4} c^{\frac{5}{2}} x^{4} - 3 \, a^{3} c^{\frac{5}{2}} x^{3} + 6 \, a^{2} c^{\frac{5}{2}} x^{2} - 24 \, a c^{\frac{5}{2}} x - 48 \, c^{\frac{5}{2}}\right)}}{7 \, \sqrt{a x + 1} a} - \frac{2 \, {\left(3 \, a^{3} c^{\frac{5}{2}} x^{3} - 11 \, a^{2} c^{\frac{5}{2}} x^{2} + 44 \, a c^{\frac{5}{2}} x + 88 \, c^{\frac{5}{2}}\right)}}{5 \, \sqrt{a x + 1} a} - \frac{2 \, {\left(a^{2} c^{\frac{5}{2}} x^{2} - 7 \, a c^{\frac{5}{2}} x - 14 \, c^{\frac{5}{2}}\right)}}{\sqrt{a x + 1} a} - \frac{2 \, {\left(a c^{\frac{5}{2}} x + 3 \, c^{\frac{5}{2}}\right)}}{\sqrt{a x + 1} a}"," ",0,"-2/7*(a^4*c^(5/2)*x^4 - 3*a^3*c^(5/2)*x^3 + 6*a^2*c^(5/2)*x^2 - 24*a*c^(5/2)*x - 48*c^(5/2))/(sqrt(a*x + 1)*a) - 2/5*(3*a^3*c^(5/2)*x^3 - 11*a^2*c^(5/2)*x^2 + 44*a*c^(5/2)*x + 88*c^(5/2))/(sqrt(a*x + 1)*a) - 2*(a^2*c^(5/2)*x^2 - 7*a*c^(5/2)*x - 14*c^(5/2))/(sqrt(a*x + 1)*a) - 2*(a*c^(5/2)*x + 3*c^(5/2))/(sqrt(a*x + 1)*a)","B",0
246,1,121,0,0.423328," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, c^{\frac{3}{2}}}{\sqrt{a x + 1} a} + \frac{2 \, {\left(a^{3} c^{\frac{3}{2}} x^{3} - 2 \, a^{2} c^{\frac{3}{2}} x^{2} + 8 \, a c^{\frac{3}{2}} x + 16 \, c^{\frac{3}{2}}\right)}}{5 \, \sqrt{a x + 1} a} + \frac{2 \, {\left(a^{2} c^{\frac{3}{2}} x^{2} - 4 \, a c^{\frac{3}{2}} x - 8 \, c^{\frac{3}{2}}\right)}}{\sqrt{a x + 1} a} + \frac{6 \, {\left(a c^{\frac{3}{2}} x + 2 \, c^{\frac{3}{2}}\right)}}{\sqrt{a x + 1} a}"," ",0,"-2*c^(3/2)/(sqrt(a*x + 1)*a) + 2/5*(a^3*c^(3/2)*x^3 - 2*a^2*c^(3/2)*x^2 + 8*a*c^(3/2)*x + 16*c^(3/2))/(sqrt(a*x + 1)*a) + 2*(a^2*c^(3/2)*x^2 - 4*a*c^(3/2)*x - 8*c^(3/2))/(sqrt(a*x + 1)*a) + 6*(a*c^(3/2)*x + 2*c^(3/2))/(sqrt(a*x + 1)*a)","B",0
247,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
248,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{-a c x + c}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*sqrt(-a*c*x + c)), x)","F",0
249,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(-a c x + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(-a*c*x + c)^(3/2)), x)","F",0
250,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(-a c x + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(-a*c*x + c)^(5/2)), x)","F",0
251,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(-a c x + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(-a*c*x + c)^(7/2)), x)","F",0
252,1,82,0,0.375161," ","integrate((-a*c*x+c)^(9/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(63 \, a^{5} c^{\frac{9}{2}} x^{5} - 455 \, a^{4} c^{\frac{9}{2}} x^{4} + 1510 \, a^{3} c^{\frac{9}{2}} x^{3} - 3198 \, a^{2} c^{\frac{9}{2}} x^{2} + 5419 \, a c^{\frac{9}{2}} x - 11531 \, c^{\frac{9}{2}}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{693 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/693*(63*a^5*c^(9/2)*x^5 - 455*a^4*c^(9/2)*x^4 + 1510*a^3*c^(9/2)*x^3 - 3198*a^2*c^(9/2)*x^2 + 5419*a*c^(9/2)*x - 11531*c^(9/2))*sqrt(a*x + 1)*(a*x - 1)/(a^2*x - a)","A",0
253,1,71,0,0.365893," ","integrate((-a*c*x+c)^(7/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(35 \, a^{4} c^{\frac{7}{2}} x^{4} - 220 \, a^{3} c^{\frac{7}{2}} x^{3} + 642 \, a^{2} c^{\frac{7}{2}} x^{2} - 1276 \, a c^{\frac{7}{2}} x + 2867 \, c^{\frac{7}{2}}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{315 \, {\left(a^{2} x - a\right)}}"," ",0,"2/315*(35*a^4*c^(7/2)*x^4 - 220*a^3*c^(7/2)*x^3 + 642*a^2*c^(7/2)*x^2 - 1276*a*c^(7/2)*x + 2867*c^(7/2))*sqrt(a*x + 1)*(a*x - 1)/(a^2*x - a)","A",0
254,1,60,0,0.389032," ","integrate((-a*c*x+c)^(5/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(5 \, a^{3} c^{\frac{5}{2}} x^{3} - 27 \, a^{2} c^{\frac{5}{2}} x^{2} + 71 \, a c^{\frac{5}{2}} x - 177 \, c^{\frac{5}{2}}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{35 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/35*(5*a^3*c^(5/2)*x^3 - 27*a^2*c^(5/2)*x^2 + 71*a*c^(5/2)*x - 177*c^(5/2))*sqrt(a*x + 1)*(a*x - 1)/(a^2*x - a)","A",0
255,1,49,0,0.349554," ","integrate((-a*c*x+c)^(3/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, a^{2} c^{\frac{3}{2}} x^{2} - 14 \, a c^{\frac{3}{2}} x + 43 \, c^{\frac{3}{2}}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{15 \, {\left(a^{2} x - a\right)}}"," ",0,"2/15*(3*a^2*c^(3/2)*x^2 - 14*a*c^(3/2)*x + 43*c^(3/2))*sqrt(a*x + 1)*(a*x - 1)/(a^2*x - a)","A",0
256,1,37,0,0.366873," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a \sqrt{c} x - 5 \, \sqrt{c}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{3 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/3*(a*sqrt(c)*x - 5*sqrt(c))*sqrt(a*x + 1)*(a*x - 1)/(a^2*x - a)","A",0
257,1,15,0,0.365581," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{a x + 1}}{a \sqrt{c}}"," ",0,"2*sqrt(a*x + 1)/(a*sqrt(c))","A",0
258,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(-a c x + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((-a*c*x + c)^(3/2)*(a*x + 1)), x)","F",0
259,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(-a c x + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((-a*c*x + c)^(5/2)*(a*x + 1)), x)","F",0
260,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(-a c x + c\right)}^{\frac{7}{2}} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((-a*c*x + c)^(7/2)*(a*x + 1)), x)","F",0
261,1,123,0,0.464611," ","integrate((-a*c*x+c)^(7/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{2 \, {\left(2520 \, \sqrt{2} c^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right) + 35 \, {\left(-a c x + c\right)}^{\frac{9}{2}} + 90 \, {\left(-a c x + c\right)}^{\frac{7}{2}} c + 252 \, {\left(-a c x + c\right)}^{\frac{5}{2}} c^{2} + 840 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{3} + 5040 \, \sqrt{-a c x + c} c^{4}\right)}}{315 \, a c}"," ",0,"2/315*(2520*sqrt(2)*c^(9/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c))) + 35*(-a*c*x + c)^(9/2) + 90*(-a*c*x + c)^(7/2)*c + 252*(-a*c*x + c)^(5/2)*c^2 + 840*(-a*c*x + c)^(3/2)*c^3 + 5040*sqrt(-a*c*x + c)*c^4)/(a*c)","A",0
262,1,109,0,0.419992," ","integrate((-a*c*x+c)^(5/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{2 \, {\left(420 \, \sqrt{2} c^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right) + 15 \, {\left(-a c x + c\right)}^{\frac{7}{2}} + 42 \, {\left(-a c x + c\right)}^{\frac{5}{2}} c + 140 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{2} + 840 \, \sqrt{-a c x + c} c^{3}\right)}}{105 \, a c}"," ",0,"2/105*(420*sqrt(2)*c^(7/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c))) + 15*(-a*c*x + c)^(7/2) + 42*(-a*c*x + c)^(5/2)*c + 140*(-a*c*x + c)^(3/2)*c^2 + 840*sqrt(-a*c*x + c)*c^3)/(a*c)","A",0
263,1,95,0,0.472472," ","integrate((-a*c*x+c)^(3/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{2 \, {\left(30 \, \sqrt{2} c^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right) + 3 \, {\left(-a c x + c\right)}^{\frac{5}{2}} + 10 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c + 60 \, \sqrt{-a c x + c} c^{2}\right)}}{15 \, a c}"," ",0,"2/15*(30*sqrt(2)*c^(5/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c))) + 3*(-a*c*x + c)^(5/2) + 10*(-a*c*x + c)^(3/2)*c + 60*sqrt(-a*c*x + c)*c^2)/(a*c)","A",0
264,1,79,0,0.435929," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, \sqrt{2} c^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right) + {\left(-a c x + c\right)}^{\frac{3}{2}} + 6 \, \sqrt{-a c x + c} c\right)}}{3 \, a c}"," ",0,"2/3*(3*sqrt(2)*c^(3/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c))) + (-a*c*x + c)^(3/2) + 6*sqrt(-a*c*x + c)*c)/(a*c)","A",0
265,1,67,0,0.487384," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} \sqrt{c} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right) + 2 \, \sqrt{-a c x + c}}{a c}"," ",0,"(sqrt(2)*sqrt(c)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c))) + 2*sqrt(-a*c*x + c))/(a*c)","A",0
266,1,52,0,0.449199," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right)}{2 \, a c^{\frac{3}{2}}}"," ",0,"1/2*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c)))/(a*c^(3/2))","A",0
267,1,71,0,0.415099," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\frac{\frac{\sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right)}{c^{\frac{3}{2}}} + \frac{4}{\sqrt{-a c x + c} c}}{4 \, a c}"," ",0,"1/4*(sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c)))/c^(3/2) + 4/(sqrt(-a*c*x + c)*c))/(a*c)","A",0
268,1,81,0,0.497823," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\frac{3 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right)}{c^{\frac{5}{2}}} - \frac{4 \, {\left(3 \, a c x - 5 \, c\right)}}{{\left(-a c x + c\right)}^{\frac{3}{2}} c^{2}}}{24 \, a c}"," ",0,"1/24*(3*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c)))/c^(5/2) - 4*(3*a*c*x - 5*c)/((-a*c*x + c)^(3/2)*c^2))/(a*c)","A",0
269,1,101,0,0.419868," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\frac{15 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right)}{c^{\frac{7}{2}}} + \frac{4 \, {\left(15 \, {\left(a c x - c\right)}^{2} - 10 \, {\left(a c x - c\right)} c + 12 \, c^{2}\right)}}{{\left(-a c x + c\right)}^{\frac{5}{2}} c^{3}}}{240 \, a c}"," ",0,"1/240*(15*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c)))/c^(7/2) + 4*(15*(a*c*x - c)^2 - 10*(a*c*x - c)*c + 12*c^2)/((-a*c*x + c)^(5/2)*c^3))/(a*c)","A",0
270,1,73,0,0.344549," ","integrate((-a*c*x+c)^(5/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a^{4} c^{\frac{5}{2}} x^{4} - 36 \, a^{3} c^{\frac{5}{2}} x^{3} + 142 \, a^{2} c^{\frac{5}{2}} x^{2} - 708 \, a c^{\frac{5}{2}} x - 1451 \, c^{\frac{5}{2}}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{35 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"2/35*(5*a^4*c^(5/2)*x^4 - 36*a^3*c^(5/2)*x^3 + 142*a^2*c^(5/2)*x^2 - 708*a*c^(5/2)*x - 1451*c^(5/2))*sqrt(a*x + 1)*(a*x - 1)/(a^3*x^2 - a)","A",0
271,1,61,0,0.391510," ","integrate((-a*c*x+c)^(3/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{3} c^{\frac{3}{2}} x^{3} - 7 \, a^{2} c^{\frac{3}{2}} x^{2} + 43 \, a c^{\frac{3}{2}} x + 91 \, c^{\frac{3}{2}}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{5 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"-2/5*(a^3*c^(3/2)*x^3 - 7*a^2*c^(3/2)*x^2 + 43*a*c^(3/2)*x + 91*c^(3/2))*sqrt(a*x + 1)*(a*x - 1)/(a^3*x^2 - a)","A",0
272,1,50,0,0.345761," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{2} \sqrt{c} x^{2} - 10 \, a \sqrt{c} x - 23 \, \sqrt{c}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{3 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"2/3*(a^2*sqrt(c)*x^2 - 10*a*sqrt(c)*x - 23*sqrt(c))*sqrt(a*x + 1)*(a*x - 1)/(a^3*x^2 - a)","A",0
273,1,30,0,0.353532," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a x + 3\right)} \sqrt{a x + 1}}{a^{2} \sqrt{c} x + a \sqrt{c}}"," ",0,"-2*(a*x + 3)*sqrt(a*x + 1)/(a^2*sqrt(c)*x + a*sqrt(c))","A",0
274,1,28,0,0.333558," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{a x + 1} \sqrt{c}}{a^{2} c^{2} x + a c^{2}}"," ",0,"-2*sqrt(a*x + 1)*sqrt(c)/(a^2*c^2*x + a*c^2)","A",0
275,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(-a c x + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((-a*c*x + c)^(5/2)*(a*x + 1)^3), x)","F",0
276,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(-a c x + c\right)}^{\frac{7}{2}} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((-a*c*x + c)^(7/2)*(a*x + 1)^3), x)","F",0
277,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(-a c x + c\right)}^{\frac{9}{2}} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((-a*c*x + c)^(9/2)*(a*x + 1)^3), x)","F",0
278,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(-a c x + c\right)}^{\frac{7}{2}} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(7/2)*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
279,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(-a c x + c\right)}^{\frac{5}{2}} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(5/2)*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
280,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(-a c x + c\right)}^{\frac{3}{2}} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(3/2)*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
281,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a c x + c} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
282,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a c x + c}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/sqrt(-a*c*x + c), x)","F",0
283,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a c x + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(-a*c*x + c)^(3/2), x)","F",0
284,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a c x + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(-a*c*x + c)^(5/2), x)","F",0
285,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a c x + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(-a*c*x + c)^(7/2), x)","F",0
286,1,69,0,0.400917," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4*(-a*c*x+c),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} c x^{5} - \frac{\sqrt{-a^{2} x^{2} + 1} c x^{3}}{24 \, a^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1} c x}{16 \, a^{4}} + \frac{c \arcsin\left(a x\right)}{16 \, a^{5}}"," ",0,"1/6*sqrt(-a^2*x^2 + 1)*c*x^5 - 1/24*sqrt(-a^2*x^2 + 1)*c*x^3/a^2 - 1/16*sqrt(-a^2*x^2 + 1)*c*x/a^4 + 1/16*c*arcsin(a*x)/a^5","A",0
287,1,58,0,0.403238," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c),x, algorithm=""maxima"")","\frac{1}{5} \, \sqrt{-a^{2} x^{2} + 1} c x^{4} - \frac{\sqrt{-a^{2} x^{2} + 1} c x^{2}}{15 \, a^{2}} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c}{15 \, a^{4}}"," ",0,"1/5*sqrt(-a^2*x^2 + 1)*c*x^4 - 1/15*sqrt(-a^2*x^2 + 1)*c*x^2/a^2 - 2/15*sqrt(-a^2*x^2 + 1)*c/a^4","A",0
288,1,48,0,0.460452," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{-a^{2} x^{2} + 1} c x^{3} - \frac{\sqrt{-a^{2} x^{2} + 1} c x}{8 \, a^{2}} + \frac{c \arcsin\left(a x\right)}{8 \, a^{3}}"," ",0,"1/4*sqrt(-a^2*x^2 + 1)*c*x^3 - 1/8*sqrt(-a^2*x^2 + 1)*c*x/a^2 + 1/8*c*arcsin(a*x)/a^3","A",0
289,1,37,0,0.467048," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{-a^{2} x^{2} + 1} c x^{2} - \frac{\sqrt{-a^{2} x^{2} + 1} c}{3 \, a^{2}}"," ",0,"1/3*sqrt(-a^2*x^2 + 1)*c*x^2 - 1/3*sqrt(-a^2*x^2 + 1)*c/a^2","B",0
290,1,27,0,0.400558," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} c x + \frac{c \arcsin\left(a x\right)}{2 \, a}"," ",0,"1/2*sqrt(-a^2*x^2 + 1)*c*x + 1/2*c*arcsin(a*x)/a","A",0
291,1,44,0,0.403622," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x,x, algorithm=""maxima"")","-c \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \sqrt{-a^{2} x^{2} + 1} c"," ",0,"-c*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-a^2*x^2 + 1)*c","A",0
292,1,27,0,0.465742," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x^2,x, algorithm=""maxima"")","-a c \arcsin\left(a x\right) - \frac{\sqrt{-a^{2} x^{2} + 1} c}{x}"," ",0,"-a*c*arcsin(a*x) - sqrt(-a^2*x^2 + 1)*c/x","A",0
293,1,51,0,0.397618," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} c \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{\sqrt{-a^{2} x^{2} + 1} c}{2 \, x^{2}}"," ",0,"1/2*a^2*c*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 1/2*sqrt(-a^2*x^2 + 1)*c/x^2","A",0
294,1,40,0,0.444130," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x^4,x, algorithm=""maxima"")","\frac{\sqrt{-a^{2} x^{2} + 1} a^{2} c}{3 \, x} - \frac{\sqrt{-a^{2} x^{2} + 1} c}{3 \, x^{3}}"," ",0,"1/3*sqrt(-a^2*x^2 + 1)*a^2*c/x - 1/3*sqrt(-a^2*x^2 + 1)*c/x^3","B",0
295,1,141,0,0.406029," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} a c^{2} x^{5} + \frac{1}{5} \, \sqrt{-a^{2} x^{2} + 1} c^{2} x^{4} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{2} x^{3}}{24 \, a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2} x^{2}}{15 \, a^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{2} x}{16 \, a^{3}} - \frac{c^{2} \arcsin\left(a x\right)}{16 \, a^{4}} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c^{2}}{15 \, a^{4}}"," ",0,"-1/6*sqrt(-a^2*x^2 + 1)*a*c^2*x^5 + 1/5*sqrt(-a^2*x^2 + 1)*c^2*x^4 + 1/24*sqrt(-a^2*x^2 + 1)*c^2*x^3/a - 1/15*sqrt(-a^2*x^2 + 1)*c^2*x^2/a^2 + 1/16*sqrt(-a^2*x^2 + 1)*c^2*x/a^3 - 1/16*c^2*arcsin(a*x)/a^4 - 2/15*sqrt(-a^2*x^2 + 1)*c^2/a^4","A",0
296,1,118,0,0.524993," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{1}{5} \, \sqrt{-a^{2} x^{2} + 1} a c^{2} x^{4} + \frac{1}{4} \, \sqrt{-a^{2} x^{2} + 1} c^{2} x^{3} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{2} x^{2}}{15 \, a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2} x}{8 \, a^{2}} + \frac{c^{2} \arcsin\left(a x\right)}{8 \, a^{3}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c^{2}}{15 \, a^{3}}"," ",0,"-1/5*sqrt(-a^2*x^2 + 1)*a*c^2*x^4 + 1/4*sqrt(-a^2*x^2 + 1)*c^2*x^3 + 1/15*sqrt(-a^2*x^2 + 1)*c^2*x^2/a - 1/8*sqrt(-a^2*x^2 + 1)*c^2*x/a^2 + 1/8*c^2*arcsin(a*x)/a^3 + 2/15*sqrt(-a^2*x^2 + 1)*c^2/a^3","A",0
297,1,95,0,0.500800," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, \sqrt{-a^{2} x^{2} + 1} a c^{2} x^{3} + \frac{1}{3} \, \sqrt{-a^{2} x^{2} + 1} c^{2} x^{2} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{2} x}{8 \, a} - \frac{c^{2} \arcsin\left(a x\right)}{8 \, a^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{3 \, a^{2}}"," ",0,"-1/4*sqrt(-a^2*x^2 + 1)*a*c^2*x^3 + 1/3*sqrt(-a^2*x^2 + 1)*c^2*x^2 + 1/8*sqrt(-a^2*x^2 + 1)*c^2*x/a - 1/8*c^2*arcsin(a*x)/a^2 - 1/3*sqrt(-a^2*x^2 + 1)*c^2/a^2","A",0
298,1,72,0,0.427685," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{1}{3} \, \sqrt{-a^{2} x^{2} + 1} a c^{2} x^{2} + \frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} c^{2} x + \frac{c^{2} \arcsin\left(a x\right)}{2 \, a} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{3 \, a}"," ",0,"-1/3*sqrt(-a^2*x^2 + 1)*a*c^2*x^2 + 1/2*sqrt(-a^2*x^2 + 1)*c^2*x + 1/2*c^2*arcsin(a*x)/a + 1/3*sqrt(-a^2*x^2 + 1)*c^2/a","A",0
299,1,76,0,0.407620," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x,x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} a c^{2} x - \frac{1}{2} \, c^{2} \arcsin\left(a x\right) - c^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \sqrt{-a^{2} x^{2} + 1} c^{2}"," ",0,"-1/2*sqrt(-a^2*x^2 + 1)*a*c^2*x - 1/2*c^2*arcsin(a*x) - c^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-a^2*x^2 + 1)*c^2","A",0
300,1,80,0,0.404070," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^2,x, algorithm=""maxima"")","-a c^{2} \arcsin\left(a x\right) + a c^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \sqrt{-a^{2} x^{2} + 1} a c^{2} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{x}"," ",0,"-a*c^2*arcsin(a*x) + a*c^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - sqrt(-a^2*x^2 + 1)*a*c^2 - sqrt(-a^2*x^2 + 1)*c^2/x","A",0
301,1,86,0,0.410136," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^3,x, algorithm=""maxima"")","a^{2} c^{2} \arcsin\left(a x\right) + \frac{1}{2} \, a^{2} c^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-a^{2} x^{2} + 1} a c^{2}}{x} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{2 \, x^{2}}"," ",0,"a^2*c^2*arcsin(a*x) + 1/2*a^2*c^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-a^2*x^2 + 1)*a*c^2/x - 1/2*sqrt(-a^2*x^2 + 1)*c^2/x^2","A",0
302,1,99,0,0.399318," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^4,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{3} c^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-a^{2} x^{2} + 1} a^{2} c^{2}}{3 \, x} + \frac{\sqrt{-a^{2} x^{2} + 1} a c^{2}}{2 \, x^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{3 \, x^{3}}"," ",0,"-1/2*a^3*c^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 1/3*sqrt(-a^2*x^2 + 1)*a^2*c^2/x + 1/2*sqrt(-a^2*x^2 + 1)*a*c^2/x^2 - 1/3*sqrt(-a^2*x^2 + 1)*c^2/x^3","A",0
303,1,122,0,0.407539," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^5,x, algorithm=""maxima"")","\frac{1}{8} \, a^{4} c^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{\sqrt{-a^{2} x^{2} + 1} a^{3} c^{2}}{3 \, x} + \frac{\sqrt{-a^{2} x^{2} + 1} a^{2} c^{2}}{8 \, x^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} a c^{2}}{3 \, x^{3}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{4 \, x^{4}}"," ",0,"1/8*a^4*c^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 1/3*sqrt(-a^2*x^2 + 1)*a^3*c^2/x + 1/8*sqrt(-a^2*x^2 + 1)*a^2*c^2/x^2 + 1/3*sqrt(-a^2*x^2 + 1)*a*c^2/x^3 - 1/4*sqrt(-a^2*x^2 + 1)*c^2/x^4","A",0
304,1,145,0,0.407062," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^6,x, algorithm=""maxima"")","-\frac{1}{8} \, a^{5} c^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{2}}{15 \, x} - \frac{\sqrt{-a^{2} x^{2} + 1} a^{3} c^{2}}{8 \, x^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} a^{2} c^{2}}{15 \, x^{3}} + \frac{\sqrt{-a^{2} x^{2} + 1} a c^{2}}{4 \, x^{4}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{5 \, x^{5}}"," ",0,"-1/8*a^5*c^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 2/15*sqrt(-a^2*x^2 + 1)*a^4*c^2/x - 1/8*sqrt(-a^2*x^2 + 1)*a^3*c^2/x^2 + 1/15*sqrt(-a^2*x^2 + 1)*a^2*c^2/x^3 + 1/4*sqrt(-a^2*x^2 + 1)*a*c^2/x^4 - 1/5*sqrt(-a^2*x^2 + 1)*c^2/x^5","A",0
305,1,168,0,0.403978," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^7,x, algorithm=""maxima"")","\frac{1}{16} \, a^{6} c^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{5} c^{2}}{15 \, x} + \frac{\sqrt{-a^{2} x^{2} + 1} a^{4} c^{2}}{16 \, x^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1} a^{3} c^{2}}{15 \, x^{3}} + \frac{\sqrt{-a^{2} x^{2} + 1} a^{2} c^{2}}{24 \, x^{4}} + \frac{\sqrt{-a^{2} x^{2} + 1} a c^{2}}{5 \, x^{5}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{6 \, x^{6}}"," ",0,"1/16*a^6*c^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 2/15*sqrt(-a^2*x^2 + 1)*a^5*c^2/x + 1/16*sqrt(-a^2*x^2 + 1)*a^4*c^2/x^2 - 1/15*sqrt(-a^2*x^2 + 1)*a^3*c^2/x^3 + 1/24*sqrt(-a^2*x^2 + 1)*a^2*c^2/x^4 + 1/5*sqrt(-a^2*x^2 + 1)*a*c^2/x^5 - 1/6*sqrt(-a^2*x^2 + 1)*c^2/x^6","A",0
306,1,164,0,0.402933," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c)^3,x, algorithm=""maxima"")","\frac{1}{7} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x^{6} - \frac{1}{3} \, \sqrt{-a^{2} x^{2} + 1} a c^{3} x^{5} + \frac{6}{35} \, \sqrt{-a^{2} x^{2} + 1} c^{3} x^{4} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{3} x^{3}}{12 \, a} - \frac{11 \, \sqrt{-a^{2} x^{2} + 1} c^{3} x^{2}}{105 \, a^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{3} x}{8 \, a^{3}} - \frac{c^{3} \arcsin\left(a x\right)}{8 \, a^{4}} - \frac{22 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{105 \, a^{4}}"," ",0,"1/7*sqrt(-a^2*x^2 + 1)*a^2*c^3*x^6 - 1/3*sqrt(-a^2*x^2 + 1)*a*c^3*x^5 + 6/35*sqrt(-a^2*x^2 + 1)*c^3*x^4 + 1/12*sqrt(-a^2*x^2 + 1)*c^3*x^3/a - 11/105*sqrt(-a^2*x^2 + 1)*c^3*x^2/a^2 + 1/8*sqrt(-a^2*x^2 + 1)*c^3*x/a^3 - 1/8*c^3*arcsin(a*x)/a^4 - 22/105*sqrt(-a^2*x^2 + 1)*c^3/a^4","A",0
307,1,141,0,0.465587," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c)^3,x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x^{5} - \frac{2}{5} \, \sqrt{-a^{2} x^{2} + 1} a c^{3} x^{4} + \frac{5}{24} \, \sqrt{-a^{2} x^{2} + 1} c^{3} x^{3} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c^{3} x^{2}}{15 \, a} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1} c^{3} x}{16 \, a^{2}} + \frac{3 \, c^{3} \arcsin\left(a x\right)}{16 \, a^{3}} + \frac{4 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{15 \, a^{3}}"," ",0,"1/6*sqrt(-a^2*x^2 + 1)*a^2*c^3*x^5 - 2/5*sqrt(-a^2*x^2 + 1)*a*c^3*x^4 + 5/24*sqrt(-a^2*x^2 + 1)*c^3*x^3 + 2/15*sqrt(-a^2*x^2 + 1)*c^3*x^2/a - 3/16*sqrt(-a^2*x^2 + 1)*c^3*x/a^2 + 3/16*c^3*arcsin(a*x)/a^3 + 4/15*sqrt(-a^2*x^2 + 1)*c^3/a^3","A",0
308,1,118,0,0.410513," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^3,x, algorithm=""maxima"")","\frac{1}{5} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x^{4} - \frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} a c^{3} x^{3} + \frac{4}{15} \, \sqrt{-a^{2} x^{2} + 1} c^{3} x^{2} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{3} x}{4 \, a} - \frac{c^{3} \arcsin\left(a x\right)}{4 \, a^{2}} - \frac{7 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{15 \, a^{2}}"," ",0,"1/5*sqrt(-a^2*x^2 + 1)*a^2*c^3*x^4 - 1/2*sqrt(-a^2*x^2 + 1)*a*c^3*x^3 + 4/15*sqrt(-a^2*x^2 + 1)*c^3*x^2 + 1/4*sqrt(-a^2*x^2 + 1)*c^3*x/a - 1/4*c^3*arcsin(a*x)/a^2 - 7/15*sqrt(-a^2*x^2 + 1)*c^3/a^2","A",0
309,1,95,0,0.405973," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3,x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x^{3} - \frac{2}{3} \, \sqrt{-a^{2} x^{2} + 1} a c^{3} x^{2} + \frac{3}{8} \, \sqrt{-a^{2} x^{2} + 1} c^{3} x + \frac{5 \, c^{3} \arcsin\left(a x\right)}{8 \, a} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{3 \, a}"," ",0,"1/4*sqrt(-a^2*x^2 + 1)*a^2*c^3*x^3 - 2/3*sqrt(-a^2*x^2 + 1)*a*c^3*x^2 + 3/8*sqrt(-a^2*x^2 + 1)*c^3*x + 5/8*c^3*arcsin(a*x)/a + 2/3*sqrt(-a^2*x^2 + 1)*c^3/a","A",0
310,1,100,0,0.486420," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x,x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x^{2} - \sqrt{-a^{2} x^{2} + 1} a c^{3} x - c^{3} \arcsin\left(a x\right) - c^{3} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{2}{3} \, \sqrt{-a^{2} x^{2} + 1} c^{3}"," ",0,"1/3*sqrt(-a^2*x^2 + 1)*a^2*c^3*x^2 - sqrt(-a^2*x^2 + 1)*a*c^3*x - c^3*arcsin(a*x) - c^3*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 2/3*sqrt(-a^2*x^2 + 1)*c^3","A",0
311,1,102,0,0.408456," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x - \frac{1}{2} \, a c^{3} \arcsin\left(a x\right) + 2 \, a c^{3} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - 2 \, \sqrt{-a^{2} x^{2} + 1} a c^{3} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{x}"," ",0,"1/2*sqrt(-a^2*x^2 + 1)*a^2*c^3*x - 1/2*a*c^3*arcsin(a*x) + 2*a*c^3*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 2*sqrt(-a^2*x^2 + 1)*a*c^3 - sqrt(-a^2*x^2 + 1)*c^3/x","A",0
312,1,107,0,0.407716," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^3,x, algorithm=""maxima"")","2 \, a^{2} c^{3} \arcsin\left(a x\right) - \frac{1}{2} \, a^{2} c^{3} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a c^{3}}{x} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{2 \, x^{2}}"," ",0,"2*a^2*c^3*arcsin(a*x) - 1/2*a^2*c^3*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-a^2*x^2 + 1)*a^2*c^3 + 2*sqrt(-a^2*x^2 + 1)*a*c^3/x - 1/2*sqrt(-a^2*x^2 + 1)*c^3/x^2","A",0
313,1,110,0,0.441955," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^4,x, algorithm=""maxima"")","-a^{3} c^{3} \arcsin\left(a x\right) - a^{3} c^{3} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3}}{3 \, x} + \frac{\sqrt{-a^{2} x^{2} + 1} a c^{3}}{x^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{3 \, x^{3}}"," ",0,"-a^3*c^3*arcsin(a*x) - a^3*c^3*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 2/3*sqrt(-a^2*x^2 + 1)*a^2*c^3/x + sqrt(-a^2*x^2 + 1)*a*c^3/x^2 - 1/3*sqrt(-a^2*x^2 + 1)*c^3/x^3","A",0
314,1,122,0,0.433880," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^5,x, algorithm=""maxima"")","\frac{5}{8} \, a^{4} c^{3} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{3}}{3 \, x} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3}}{8 \, x^{2}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a c^{3}}{3 \, x^{3}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{4 \, x^{4}}"," ",0,"5/8*a^4*c^3*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 2/3*sqrt(-a^2*x^2 + 1)*a^3*c^3/x - 3/8*sqrt(-a^2*x^2 + 1)*a^2*c^3/x^2 + 2/3*sqrt(-a^2*x^2 + 1)*a*c^3/x^3 - 1/4*sqrt(-a^2*x^2 + 1)*c^3/x^4","A",0
315,1,145,0,0.399357," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^6,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{5} c^{3} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{7 \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{3}}{15 \, x} - \frac{\sqrt{-a^{2} x^{2} + 1} a^{3} c^{3}}{4 \, x^{2}} - \frac{4 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3}}{15 \, x^{3}} + \frac{\sqrt{-a^{2} x^{2} + 1} a c^{3}}{2 \, x^{4}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{5 \, x^{5}}"," ",0,"-1/4*a^5*c^3*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 7/15*sqrt(-a^2*x^2 + 1)*a^4*c^3/x - 1/4*sqrt(-a^2*x^2 + 1)*a^3*c^3/x^2 - 4/15*sqrt(-a^2*x^2 + 1)*a^2*c^3/x^3 + 1/2*sqrt(-a^2*x^2 + 1)*a*c^3/x^4 - 1/5*sqrt(-a^2*x^2 + 1)*c^3/x^5","A",0
316,1,187,0,0.409524," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c)^4,x, algorithm=""maxima"")","-\frac{1}{8} \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x^{7} + \frac{3}{7} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x^{6} - \frac{23}{48} \, \sqrt{-a^{2} x^{2} + 1} a c^{4} x^{5} + \frac{4}{35} \, \sqrt{-a^{2} x^{2} + 1} c^{4} x^{4} + \frac{29 \, \sqrt{-a^{2} x^{2} + 1} c^{4} x^{3}}{192 \, a} - \frac{19 \, \sqrt{-a^{2} x^{2} + 1} c^{4} x^{2}}{105 \, a^{2}} + \frac{29 \, \sqrt{-a^{2} x^{2} + 1} c^{4} x}{128 \, a^{3}} - \frac{29 \, c^{4} \arcsin\left(a x\right)}{128 \, a^{4}} - \frac{38 \, \sqrt{-a^{2} x^{2} + 1} c^{4}}{105 \, a^{4}}"," ",0,"-1/8*sqrt(-a^2*x^2 + 1)*a^3*c^4*x^7 + 3/7*sqrt(-a^2*x^2 + 1)*a^2*c^4*x^6 - 23/48*sqrt(-a^2*x^2 + 1)*a*c^4*x^5 + 4/35*sqrt(-a^2*x^2 + 1)*c^4*x^4 + 29/192*sqrt(-a^2*x^2 + 1)*c^4*x^3/a - 19/105*sqrt(-a^2*x^2 + 1)*c^4*x^2/a^2 + 29/128*sqrt(-a^2*x^2 + 1)*c^4*x/a^3 - 29/128*c^4*arcsin(a*x)/a^4 - 38/105*sqrt(-a^2*x^2 + 1)*c^4/a^4","A",0
317,1,164,0,0.411364," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c)^4,x, algorithm=""maxima"")","-\frac{1}{7} \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x^{6} + \frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x^{5} - \frac{4}{7} \, \sqrt{-a^{2} x^{2} + 1} a c^{4} x^{4} + \frac{1}{8} \, \sqrt{-a^{2} x^{2} + 1} c^{4} x^{3} + \frac{5 \, \sqrt{-a^{2} x^{2} + 1} c^{4} x^{2}}{21 \, a} - \frac{5 \, \sqrt{-a^{2} x^{2} + 1} c^{4} x}{16 \, a^{2}} + \frac{5 \, c^{4} \arcsin\left(a x\right)}{16 \, a^{3}} + \frac{10 \, \sqrt{-a^{2} x^{2} + 1} c^{4}}{21 \, a^{3}}"," ",0,"-1/7*sqrt(-a^2*x^2 + 1)*a^3*c^4*x^6 + 1/2*sqrt(-a^2*x^2 + 1)*a^2*c^4*x^5 - 4/7*sqrt(-a^2*x^2 + 1)*a*c^4*x^4 + 1/8*sqrt(-a^2*x^2 + 1)*c^4*x^3 + 5/21*sqrt(-a^2*x^2 + 1)*c^4*x^2/a - 5/16*sqrt(-a^2*x^2 + 1)*c^4*x/a^2 + 5/16*c^4*arcsin(a*x)/a^3 + 10/21*sqrt(-a^2*x^2 + 1)*c^4/a^3","A",0
318,1,141,0,0.424121," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^4,x, algorithm=""maxima"")","-\frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x^{5} + \frac{3}{5} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x^{4} - \frac{17}{24} \, \sqrt{-a^{2} x^{2} + 1} a c^{4} x^{3} + \frac{2}{15} \, \sqrt{-a^{2} x^{2} + 1} c^{4} x^{2} + \frac{7 \, \sqrt{-a^{2} x^{2} + 1} c^{4} x}{16 \, a} - \frac{7 \, c^{4} \arcsin\left(a x\right)}{16 \, a^{2}} - \frac{11 \, \sqrt{-a^{2} x^{2} + 1} c^{4}}{15 \, a^{2}}"," ",0,"-1/6*sqrt(-a^2*x^2 + 1)*a^3*c^4*x^5 + 3/5*sqrt(-a^2*x^2 + 1)*a^2*c^4*x^4 - 17/24*sqrt(-a^2*x^2 + 1)*a*c^4*x^3 + 2/15*sqrt(-a^2*x^2 + 1)*c^4*x^2 + 7/16*sqrt(-a^2*x^2 + 1)*c^4*x/a - 7/16*c^4*arcsin(a*x)/a^2 - 11/15*sqrt(-a^2*x^2 + 1)*c^4/a^2","A",0
319,1,118,0,0.455118," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4,x, algorithm=""maxima"")","-\frac{1}{5} \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x^{4} + \frac{3}{4} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x^{3} - \frac{14}{15} \, \sqrt{-a^{2} x^{2} + 1} a c^{4} x^{2} + \frac{1}{8} \, \sqrt{-a^{2} x^{2} + 1} c^{4} x + \frac{7 \, c^{4} \arcsin\left(a x\right)}{8 \, a} + \frac{17 \, \sqrt{-a^{2} x^{2} + 1} c^{4}}{15 \, a}"," ",0,"-1/5*sqrt(-a^2*x^2 + 1)*a^3*c^4*x^4 + 3/4*sqrt(-a^2*x^2 + 1)*a^2*c^4*x^3 - 14/15*sqrt(-a^2*x^2 + 1)*a*c^4*x^2 + 1/8*sqrt(-a^2*x^2 + 1)*c^4*x + 7/8*c^4*arcsin(a*x)/a + 17/15*sqrt(-a^2*x^2 + 1)*c^4/a","A",0
320,1,105,0,0.404830," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x,x, algorithm=""maxima"")","-\frac{1}{4} \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x^{3} + \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x^{2} - \frac{11}{8} \, \sqrt{-a^{2} x^{2} + 1} a c^{4} x - \frac{13}{8} \, c^{4} \arcsin\left(a x\right) - c^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)"," ",0,"-1/4*sqrt(-a^2*x^2 + 1)*a^3*c^4*x^3 + sqrt(-a^2*x^2 + 1)*a^2*c^4*x^2 - 11/8*sqrt(-a^2*x^2 + 1)*a*c^4*x - 13/8*c^4*arcsin(a*x) - c^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))","A",0
321,1,125,0,0.457393," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^2,x, algorithm=""maxima"")","-\frac{1}{3} \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x^{2} + \frac{3}{2} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x + \frac{1}{2} \, a c^{4} \arcsin\left(a x\right) + 3 \, a c^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{8}{3} \, \sqrt{-a^{2} x^{2} + 1} a c^{4} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{x}"," ",0,"-1/3*sqrt(-a^2*x^2 + 1)*a^3*c^4*x^2 + 3/2*sqrt(-a^2*x^2 + 1)*a^2*c^4*x + 1/2*a*c^4*arcsin(a*x) + 3*a*c^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 8/3*sqrt(-a^2*x^2 + 1)*a*c^4 - sqrt(-a^2*x^2 + 1)*c^4/x","A",0
322,1,129,0,0.524410," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x + \frac{5}{2} \, a^{2} c^{4} \arcsin\left(a x\right) - \frac{5}{2} \, a^{2} c^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + 3 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1} a c^{4}}{x} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{2 \, x^{2}}"," ",0,"-1/2*sqrt(-a^2*x^2 + 1)*a^3*c^4*x + 5/2*a^2*c^4*arcsin(a*x) - 5/2*a^2*c^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 3*sqrt(-a^2*x^2 + 1)*a^2*c^4 + 3*sqrt(-a^2*x^2 + 1)*a*c^4/x - 1/2*sqrt(-a^2*x^2 + 1)*c^4/x^2","A",0
323,1,131,0,0.539243," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^4,x, algorithm=""maxima"")","-3 \, a^{3} c^{4} \arcsin\left(a x\right) - \frac{1}{2} \, a^{3} c^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} - \frac{8 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4}}{3 \, x} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1} a c^{4}}{2 \, x^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{3 \, x^{3}}"," ",0,"-3*a^3*c^4*arcsin(a*x) - 1/2*a^3*c^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - sqrt(-a^2*x^2 + 1)*a^3*c^4 - 8/3*sqrt(-a^2*x^2 + 1)*a^2*c^4/x + 3/2*sqrt(-a^2*x^2 + 1)*a*c^4/x^2 - 1/3*sqrt(-a^2*x^2 + 1)*c^4/x^3","A",0
324,1,109,0,0.408278," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^5,x, algorithm=""maxima"")","a^{4} c^{4} \arcsin\left(a x\right) + \frac{13}{8} \, a^{4} c^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{11 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4}}{8 \, x^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} a c^{4}}{x^{3}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{4 \, x^{4}}"," ",0,"a^4*c^4*arcsin(a*x) + 13/8*a^4*c^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 11/8*sqrt(-a^2*x^2 + 1)*a^2*c^4/x^2 + sqrt(-a^2*x^2 + 1)*a*c^4/x^3 - 1/4*sqrt(-a^2*x^2 + 1)*c^4/x^4","A",0
325,1,145,0,0.535062," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^6,x, algorithm=""maxima"")","-\frac{7}{8} \, a^{5} c^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{17 \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{4}}{15 \, x} + \frac{\sqrt{-a^{2} x^{2} + 1} a^{3} c^{4}}{8 \, x^{2}} - \frac{14 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4}}{15 \, x^{3}} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1} a c^{4}}{4 \, x^{4}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{5 \, x^{5}}"," ",0,"-7/8*a^5*c^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 17/15*sqrt(-a^2*x^2 + 1)*a^4*c^4/x + 1/8*sqrt(-a^2*x^2 + 1)*a^3*c^4/x^2 - 14/15*sqrt(-a^2*x^2 + 1)*a^2*c^4/x^3 + 3/4*sqrt(-a^2*x^2 + 1)*a*c^4/x^4 - 1/5*sqrt(-a^2*x^2 + 1)*c^4/x^5","A",0
326,1,168,0,0.396002," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^7,x, algorithm=""maxima"")","\frac{7}{16} \, a^{6} c^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{11 \, \sqrt{-a^{2} x^{2} + 1} a^{5} c^{4}}{15 \, x} + \frac{7 \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{4}}{16 \, x^{2}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4}}{15 \, x^{3}} - \frac{17 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4}}{24 \, x^{4}} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1} a c^{4}}{5 \, x^{5}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{6 \, x^{6}}"," ",0,"7/16*a^6*c^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 11/15*sqrt(-a^2*x^2 + 1)*a^5*c^4/x + 7/16*sqrt(-a^2*x^2 + 1)*a^4*c^4/x^2 + 2/15*sqrt(-a^2*x^2 + 1)*a^3*c^4/x^3 - 17/24*sqrt(-a^2*x^2 + 1)*a^2*c^4/x^4 + 3/5*sqrt(-a^2*x^2 + 1)*a*c^4/x^5 - 1/6*sqrt(-a^2*x^2 + 1)*c^4/x^6","A",0
327,1,129,0,0.452668," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c),x, algorithm=""maxima"")","\frac{\sqrt{-a^{2} x^{2} + 1} x^{3}}{4 \, a^{2} c} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{6} c x - a^{5} c} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1} x^{2}}{3 \, a^{3} c} + \frac{11 \, \sqrt{-a^{2} x^{2} + 1} x}{8 \, a^{4} c} - \frac{27 \, \arcsin\left(a x\right)}{8 \, a^{5} c} + \frac{10 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, a^{5} c}"," ",0,"1/4*sqrt(-a^2*x^2 + 1)*x^3/(a^2*c) - 2*sqrt(-a^2*x^2 + 1)/(a^6*c*x - a^5*c) + 2/3*sqrt(-a^2*x^2 + 1)*x^2/(a^3*c) + 11/8*sqrt(-a^2*x^2 + 1)*x/(a^4*c) - 27/8*arcsin(a*x)/(a^5*c) + 10/3*sqrt(-a^2*x^2 + 1)/(a^5*c)","A",0
328,1,105,0,0.476974," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{5} c x - a^{4} c} + \frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{3 \, a^{2} c} + \frac{\sqrt{-a^{2} x^{2} + 1} x}{a^{3} c} - \frac{3 \, \arcsin\left(a x\right)}{a^{4} c} + \frac{8 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, a^{4} c}"," ",0,"-2*sqrt(-a^2*x^2 + 1)/(a^5*c*x - a^4*c) + 1/3*sqrt(-a^2*x^2 + 1)*x^2/(a^2*c) + sqrt(-a^2*x^2 + 1)*x/(a^3*c) - 3*arcsin(a*x)/(a^4*c) + 8/3*sqrt(-a^2*x^2 + 1)/(a^4*c)","A",0
329,1,83,0,0.410411," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{4} c x - a^{3} c} + \frac{\sqrt{-a^{2} x^{2} + 1} x}{2 \, a^{2} c} - \frac{5 \, \arcsin\left(a x\right)}{2 \, a^{3} c} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{3} c}"," ",0,"-2*sqrt(-a^2*x^2 + 1)/(a^4*c*x - a^3*c) + 1/2*sqrt(-a^2*x^2 + 1)*x/(a^2*c) - 5/2*arcsin(a*x)/(a^3*c) + 2*sqrt(-a^2*x^2 + 1)/(a^3*c)","A",0
330,1,61,0,0.453502," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{3} c x - a^{2} c} - \frac{2 \, \arcsin\left(a x\right)}{a^{2} c} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{2} c}"," ",0,"-2*sqrt(-a^2*x^2 + 1)/(a^3*c*x - a^2*c) - 2*arcsin(a*x)/(a^2*c) + sqrt(-a^2*x^2 + 1)/(a^2*c)","A",0
331,1,40,0,0.505404," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{2} c x - a c} - \frac{\arcsin\left(a x\right)}{a c}"," ",0,"-2*sqrt(-a^2*x^2 + 1)/(a^2*c*x - a*c) - arcsin(a*x)/(a*c)","A",0
332,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c),x, algorithm=""maxima"")","-\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)} x}\,{d x}"," ",0,"-integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)*x), x)","F",0
333,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c),x, algorithm=""maxima"")","-\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)} x^{2}}\,{d x}"," ",0,"-integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)*x^2), x)","F",0
334,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c),x, algorithm=""maxima"")","-\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)} x^{3}}\,{d x}"," ",0,"-integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)*x^3), x)","F",0
335,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a*c*x+c),x, algorithm=""maxima"")","-\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)} x^{4}}\,{d x}"," ",0,"-integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)*x^4), x)","F",0
336,1,153,0,0.440728," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{7} c^{2} x^{2} - 2 \, a^{6} c^{2} x + a^{5} c^{2}\right)}} + \frac{25 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{6} c^{2} x - a^{5} c^{2}\right)}} - \frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{3 \, a^{3} c^{2}} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1} x}{2 \, a^{4} c^{2}} + \frac{17 \, \arcsin\left(a x\right)}{2 \, a^{5} c^{2}} - \frac{17 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, a^{5} c^{2}}"," ",0,"2/3*sqrt(-a^2*x^2 + 1)/(a^7*c^2*x^2 - 2*a^6*c^2*x + a^5*c^2) + 25/3*sqrt(-a^2*x^2 + 1)/(a^6*c^2*x - a^5*c^2) - 1/3*sqrt(-a^2*x^2 + 1)*x^2/(a^3*c^2) - 3/2*sqrt(-a^2*x^2 + 1)*x/(a^4*c^2) + 17/2*arcsin(a*x)/(a^5*c^2) - 17/3*sqrt(-a^2*x^2 + 1)/(a^5*c^2)","A",0
337,1,130,0,0.478004," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{6} c^{2} x^{2} - 2 \, a^{5} c^{2} x + a^{4} c^{2}\right)}} + \frac{19 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{5} c^{2} x - a^{4} c^{2}\right)}} - \frac{\sqrt{-a^{2} x^{2} + 1} x}{2 \, a^{3} c^{2}} + \frac{11 \, \arcsin\left(a x\right)}{2 \, a^{4} c^{2}} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1}}{a^{4} c^{2}}"," ",0,"2/3*sqrt(-a^2*x^2 + 1)/(a^6*c^2*x^2 - 2*a^5*c^2*x + a^4*c^2) + 19/3*sqrt(-a^2*x^2 + 1)/(a^5*c^2*x - a^4*c^2) - 1/2*sqrt(-a^2*x^2 + 1)*x/(a^3*c^2) + 11/2*arcsin(a*x)/(a^4*c^2) - 3*sqrt(-a^2*x^2 + 1)/(a^4*c^2)","A",0
338,1,109,0,0.434650," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{5} c^{2} x^{2} - 2 \, a^{4} c^{2} x + a^{3} c^{2}\right)}} + \frac{13 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{4} c^{2} x - a^{3} c^{2}\right)}} + \frac{3 \, \arcsin\left(a x\right)}{a^{3} c^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{3} c^{2}}"," ",0,"2/3*sqrt(-a^2*x^2 + 1)/(a^5*c^2*x^2 - 2*a^4*c^2*x + a^3*c^2) + 13/3*sqrt(-a^2*x^2 + 1)/(a^4*c^2*x - a^3*c^2) + 3*arcsin(a*x)/(a^3*c^2) - sqrt(-a^2*x^2 + 1)/(a^3*c^2)","A",0
339,1,88,0,0.443102," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{4} c^{2} x^{2} - 2 \, a^{3} c^{2} x + a^{2} c^{2}\right)}} + \frac{7 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{3} c^{2} x - a^{2} c^{2}\right)}} + \frac{\arcsin\left(a x\right)}{a^{2} c^{2}}"," ",0,"2/3*sqrt(-a^2*x^2 + 1)/(a^4*c^2*x^2 - 2*a^3*c^2*x + a^2*c^2) + 7/3*sqrt(-a^2*x^2 + 1)/(a^3*c^2*x - a^2*c^2) + arcsin(a*x)/(a^2*c^2)","A",0
340,1,73,0,0.399484," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{2} c^{2} x - a c^{2}\right)}}"," ",0,"2/3*sqrt(-a^2*x^2 + 1)/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2) + 1/3*sqrt(-a^2*x^2 + 1)/(a^2*c^2*x - a*c^2)","B",0
341,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c)^2,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)}^{2} x}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)^2*x), x)","F",0
342,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c)^2,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)^2*x^2), x)","F",0
343,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c)^2,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)^2*x^3), x)","F",0
344,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a*c*x+c)^2,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)}^{2} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)^2*x^4), x)","F",0
345,1,185,0,0.406883," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{5 \, {\left(a^{8} c^{3} x^{3} - 3 \, a^{7} c^{3} x^{2} + 3 \, a^{6} c^{3} x - a^{5} c^{3}\right)}} - \frac{41 \, \sqrt{-a^{2} x^{2} + 1}}{15 \, {\left(a^{7} c^{3} x^{2} - 2 \, a^{6} c^{3} x + a^{5} c^{3}\right)}} - \frac{199 \, \sqrt{-a^{2} x^{2} + 1}}{15 \, {\left(a^{6} c^{3} x - a^{5} c^{3}\right)}} + \frac{\sqrt{-a^{2} x^{2} + 1} x}{2 \, a^{4} c^{3}} - \frac{19 \, \arcsin\left(a x\right)}{2 \, a^{5} c^{3}} + \frac{4 \, \sqrt{-a^{2} x^{2} + 1}}{a^{5} c^{3}}"," ",0,"-2/5*sqrt(-a^2*x^2 + 1)/(a^8*c^3*x^3 - 3*a^7*c^3*x^2 + 3*a^6*c^3*x - a^5*c^3) - 41/15*sqrt(-a^2*x^2 + 1)/(a^7*c^3*x^2 - 2*a^6*c^3*x + a^5*c^3) - 199/15*sqrt(-a^2*x^2 + 1)/(a^6*c^3*x - a^5*c^3) + 1/2*sqrt(-a^2*x^2 + 1)*x/(a^4*c^3) - 19/2*arcsin(a*x)/(a^5*c^3) + 4*sqrt(-a^2*x^2 + 1)/(a^5*c^3)","A",0
346,1,163,0,0.463133," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{5 \, {\left(a^{7} c^{3} x^{3} - 3 \, a^{6} c^{3} x^{2} + 3 \, a^{5} c^{3} x - a^{4} c^{3}\right)}} - \frac{31 \, \sqrt{-a^{2} x^{2} + 1}}{15 \, {\left(a^{6} c^{3} x^{2} - 2 \, a^{5} c^{3} x + a^{4} c^{3}\right)}} - \frac{104 \, \sqrt{-a^{2} x^{2} + 1}}{15 \, {\left(a^{5} c^{3} x - a^{4} c^{3}\right)}} - \frac{4 \, \arcsin\left(a x\right)}{a^{4} c^{3}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{4} c^{3}}"," ",0,"-2/5*sqrt(-a^2*x^2 + 1)/(a^7*c^3*x^3 - 3*a^6*c^3*x^2 + 3*a^5*c^3*x - a^4*c^3) - 31/15*sqrt(-a^2*x^2 + 1)/(a^6*c^3*x^2 - 2*a^5*c^3*x + a^4*c^3) - 104/15*sqrt(-a^2*x^2 + 1)/(a^5*c^3*x - a^4*c^3) - 4*arcsin(a*x)/(a^4*c^3) + sqrt(-a^2*x^2 + 1)/(a^4*c^3)","A",0
347,1,144,0,0.410402," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{5 \, {\left(a^{6} c^{3} x^{3} - 3 \, a^{5} c^{3} x^{2} + 3 \, a^{4} c^{3} x - a^{3} c^{3}\right)}} - \frac{7 \, \sqrt{-a^{2} x^{2} + 1}}{5 \, {\left(a^{5} c^{3} x^{2} - 2 \, a^{4} c^{3} x + a^{3} c^{3}\right)}} - \frac{13 \, \sqrt{-a^{2} x^{2} + 1}}{5 \, {\left(a^{4} c^{3} x - a^{3} c^{3}\right)}} - \frac{\arcsin\left(a x\right)}{a^{3} c^{3}}"," ",0,"-2/5*sqrt(-a^2*x^2 + 1)/(a^6*c^3*x^3 - 3*a^5*c^3*x^2 + 3*a^4*c^3*x - a^3*c^3) - 7/5*sqrt(-a^2*x^2 + 1)/(a^5*c^3*x^2 - 2*a^4*c^3*x + a^3*c^3) - 13/5*sqrt(-a^2*x^2 + 1)/(a^4*c^3*x - a^3*c^3) - arcsin(a*x)/(a^3*c^3)","A",0
348,1,132,0,0.404291," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{5 \, {\left(a^{5} c^{3} x^{3} - 3 \, a^{4} c^{3} x^{2} + 3 \, a^{3} c^{3} x - a^{2} c^{3}\right)}} - \frac{11 \, \sqrt{-a^{2} x^{2} + 1}}{15 \, {\left(a^{4} c^{3} x^{2} - 2 \, a^{3} c^{3} x + a^{2} c^{3}\right)}} - \frac{4 \, \sqrt{-a^{2} x^{2} + 1}}{15 \, {\left(a^{3} c^{3} x - a^{2} c^{3}\right)}}"," ",0,"-2/5*sqrt(-a^2*x^2 + 1)/(a^5*c^3*x^3 - 3*a^4*c^3*x^2 + 3*a^3*c^3*x - a^2*c^3) - 11/15*sqrt(-a^2*x^2 + 1)/(a^4*c^3*x^2 - 2*a^3*c^3*x + a^2*c^3) - 4/15*sqrt(-a^2*x^2 + 1)/(a^3*c^3*x - a^2*c^3)","B",0
349,1,126,0,0.493053," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{5 \, {\left(a^{4} c^{3} x^{3} - 3 \, a^{3} c^{3} x^{2} + 3 \, a^{2} c^{3} x - a c^{3}\right)}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{15 \, {\left(a^{3} c^{3} x^{2} - 2 \, a^{2} c^{3} x + a c^{3}\right)}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{15 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"-2/5*sqrt(-a^2*x^2 + 1)/(a^4*c^3*x^3 - 3*a^3*c^3*x^2 + 3*a^2*c^3*x - a*c^3) - 1/15*sqrt(-a^2*x^2 + 1)/(a^3*c^3*x^2 - 2*a^2*c^3*x + a*c^3) + 1/15*sqrt(-a^2*x^2 + 1)/(a^2*c^3*x - a*c^3)","B",0
350,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)}^{3} x}\,{d x}"," ",0,"-integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)^3*x), x)","F",0
351,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)}^{3} x^{2}}\,{d x}"," ",0,"-integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)^3*x^2), x)","F",0
352,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)}^{3} x^{3}}\,{d x}"," ",0,"-integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)^3*x^3), x)","F",0
353,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)}^{3} x^{4}}\,{d x}"," ",0,"-integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)^3*x^4), x)","F",0
354,1,250,0,0.410672," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{7 \, {\left(a^{10} c^{4} x^{4} - 4 \, a^{9} c^{4} x^{3} + 6 \, a^{8} c^{4} x^{2} - 4 \, a^{7} c^{4} x + a^{6} c^{4}\right)}} + \frac{71 \, \sqrt{-a^{2} x^{2} + 1}}{35 \, {\left(a^{9} c^{4} x^{3} - 3 \, a^{8} c^{4} x^{2} + 3 \, a^{7} c^{4} x - a^{6} c^{4}\right)}} + \frac{733 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{8} c^{4} x^{2} - 2 \, a^{7} c^{4} x + a^{6} c^{4}\right)}} + \frac{2417 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{7} c^{4} x - a^{6} c^{4}\right)}} - \frac{\sqrt{-a^{2} x^{2} + 1} x}{2 \, a^{5} c^{4}} + \frac{29 \, \arcsin\left(a x\right)}{2 \, a^{6} c^{4}} - \frac{5 \, \sqrt{-a^{2} x^{2} + 1}}{a^{6} c^{4}}"," ",0,"2/7*sqrt(-a^2*x^2 + 1)/(a^10*c^4*x^4 - 4*a^9*c^4*x^3 + 6*a^8*c^4*x^2 - 4*a^7*c^4*x + a^6*c^4) + 71/35*sqrt(-a^2*x^2 + 1)/(a^9*c^4*x^3 - 3*a^8*c^4*x^2 + 3*a^7*c^4*x - a^6*c^4) + 733/105*sqrt(-a^2*x^2 + 1)/(a^8*c^4*x^2 - 2*a^7*c^4*x + a^6*c^4) + 2417/105*sqrt(-a^2*x^2 + 1)/(a^7*c^4*x - a^6*c^4) - 1/2*sqrt(-a^2*x^2 + 1)*x/(a^5*c^4) + 29/2*arcsin(a*x)/(a^6*c^4) - 5*sqrt(-a^2*x^2 + 1)/(a^6*c^4)","A",0
355,1,229,0,0.467411," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{7 \, {\left(a^{9} c^{4} x^{4} - 4 \, a^{8} c^{4} x^{3} + 6 \, a^{7} c^{4} x^{2} - 4 \, a^{6} c^{4} x + a^{5} c^{4}\right)}} + \frac{57 \, \sqrt{-a^{2} x^{2} + 1}}{35 \, {\left(a^{8} c^{4} x^{3} - 3 \, a^{7} c^{4} x^{2} + 3 \, a^{6} c^{4} x - a^{5} c^{4}\right)}} + \frac{446 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{7} c^{4} x^{2} - 2 \, a^{6} c^{4} x + a^{5} c^{4}\right)}} + \frac{1024 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{6} c^{4} x - a^{5} c^{4}\right)}} + \frac{5 \, \arcsin\left(a x\right)}{a^{5} c^{4}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{5} c^{4}}"," ",0,"2/7*sqrt(-a^2*x^2 + 1)/(a^9*c^4*x^4 - 4*a^8*c^4*x^3 + 6*a^7*c^4*x^2 - 4*a^6*c^4*x + a^5*c^4) + 57/35*sqrt(-a^2*x^2 + 1)/(a^8*c^4*x^3 - 3*a^7*c^4*x^2 + 3*a^6*c^4*x - a^5*c^4) + 446/105*sqrt(-a^2*x^2 + 1)/(a^7*c^4*x^2 - 2*a^6*c^4*x + a^5*c^4) + 1024/105*sqrt(-a^2*x^2 + 1)/(a^6*c^4*x - a^5*c^4) + 5*arcsin(a*x)/(a^5*c^4) - sqrt(-a^2*x^2 + 1)/(a^5*c^4)","A",0
356,1,208,0,0.644804," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{7 \, {\left(a^{8} c^{4} x^{4} - 4 \, a^{7} c^{4} x^{3} + 6 \, a^{6} c^{4} x^{2} - 4 \, a^{5} c^{4} x + a^{4} c^{4}\right)}} + \frac{43 \, \sqrt{-a^{2} x^{2} + 1}}{35 \, {\left(a^{7} c^{4} x^{3} - 3 \, a^{6} c^{4} x^{2} + 3 \, a^{5} c^{4} x - a^{4} c^{4}\right)}} + \frac{229 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{6} c^{4} x^{2} - 2 \, a^{5} c^{4} x + a^{4} c^{4}\right)}} + \frac{296 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{5} c^{4} x - a^{4} c^{4}\right)}} + \frac{\arcsin\left(a x\right)}{a^{4} c^{4}}"," ",0,"2/7*sqrt(-a^2*x^2 + 1)/(a^8*c^4*x^4 - 4*a^7*c^4*x^3 + 6*a^6*c^4*x^2 - 4*a^5*c^4*x + a^4*c^4) + 43/35*sqrt(-a^2*x^2 + 1)/(a^7*c^4*x^3 - 3*a^6*c^4*x^2 + 3*a^5*c^4*x - a^4*c^4) + 229/105*sqrt(-a^2*x^2 + 1)/(a^6*c^4*x^2 - 2*a^5*c^4*x + a^4*c^4) + 296/105*sqrt(-a^2*x^2 + 1)/(a^5*c^4*x - a^4*c^4) + arcsin(a*x)/(a^4*c^4)","A",0
357,1,197,0,0.407580," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{7 \, {\left(a^{7} c^{4} x^{4} - 4 \, a^{6} c^{4} x^{3} + 6 \, a^{5} c^{4} x^{2} - 4 \, a^{4} c^{4} x + a^{3} c^{4}\right)}} + \frac{29 \, \sqrt{-a^{2} x^{2} + 1}}{35 \, {\left(a^{6} c^{4} x^{3} - 3 \, a^{5} c^{4} x^{2} + 3 \, a^{4} c^{4} x - a^{3} c^{4}\right)}} + \frac{82 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{5} c^{4} x^{2} - 2 \, a^{4} c^{4} x + a^{3} c^{4}\right)}} + \frac{23 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{4} c^{4} x - a^{3} c^{4}\right)}}"," ",0,"2/7*sqrt(-a^2*x^2 + 1)/(a^7*c^4*x^4 - 4*a^6*c^4*x^3 + 6*a^5*c^4*x^2 - 4*a^4*c^4*x + a^3*c^4) + 29/35*sqrt(-a^2*x^2 + 1)/(a^6*c^4*x^3 - 3*a^5*c^4*x^2 + 3*a^4*c^4*x - a^3*c^4) + 82/105*sqrt(-a^2*x^2 + 1)/(a^5*c^4*x^2 - 2*a^4*c^4*x + a^3*c^4) + 23/105*sqrt(-a^2*x^2 + 1)/(a^4*c^4*x - a^3*c^4)","B",0
358,1,197,0,0.431032," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{7 \, {\left(a^{6} c^{4} x^{4} - 4 \, a^{5} c^{4} x^{3} + 6 \, a^{4} c^{4} x^{2} - 4 \, a^{3} c^{4} x + a^{2} c^{4}\right)}} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1}}{7 \, {\left(a^{5} c^{4} x^{3} - 3 \, a^{4} c^{4} x^{2} + 3 \, a^{3} c^{4} x - a^{2} c^{4}\right)}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{21 \, {\left(a^{4} c^{4} x^{2} - 2 \, a^{3} c^{4} x + a^{2} c^{4}\right)}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{21 \, {\left(a^{3} c^{4} x - a^{2} c^{4}\right)}}"," ",0,"2/7*sqrt(-a^2*x^2 + 1)/(a^6*c^4*x^4 - 4*a^5*c^4*x^3 + 6*a^4*c^4*x^2 - 4*a^3*c^4*x + a^2*c^4) + 3/7*sqrt(-a^2*x^2 + 1)/(a^5*c^4*x^3 - 3*a^4*c^4*x^2 + 3*a^3*c^4*x - a^2*c^4) + 1/21*sqrt(-a^2*x^2 + 1)/(a^4*c^4*x^2 - 2*a^3*c^4*x + a^2*c^4) - 1/21*sqrt(-a^2*x^2 + 1)/(a^3*c^4*x - a^2*c^4)","B",0
359,1,189,0,0.405084," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{7 \, {\left(a^{5} c^{4} x^{4} - 4 \, a^{4} c^{4} x^{3} + 6 \, a^{3} c^{4} x^{2} - 4 \, a^{2} c^{4} x + a c^{4}\right)}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{35 \, {\left(a^{4} c^{4} x^{3} - 3 \, a^{3} c^{4} x^{2} + 3 \, a^{2} c^{4} x - a c^{4}\right)}} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{105 \, {\left(a^{2} c^{4} x - a c^{4}\right)}}"," ",0,"2/7*sqrt(-a^2*x^2 + 1)/(a^5*c^4*x^4 - 4*a^4*c^4*x^3 + 6*a^3*c^4*x^2 - 4*a^2*c^4*x + a*c^4) + 1/35*sqrt(-a^2*x^2 + 1)/(a^4*c^4*x^3 - 3*a^3*c^4*x^2 + 3*a^2*c^4*x - a*c^4) - 2/105*sqrt(-a^2*x^2 + 1)/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4) + 2/105*sqrt(-a^2*x^2 + 1)/(a^2*c^4*x - a*c^4)","B",0
360,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c)^4,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)}^{4} x}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)^4*x), x)","F",0
361,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c)^4,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)}^{4} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)^4*x^2), x)","F",0
362,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c)^4,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(a c x - c\right)}^{4} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(a*c*x - c)^4*x^3), x)","F",0
363,1,40,0,0.439977," ","integrate((1+x)^2/(-x^2+1)^(1/2)*x,x, algorithm=""maxima"")","-\frac{1}{3} \, \sqrt{-x^{2} + 1} x^{2} - \sqrt{-x^{2} + 1} x - \frac{5}{3} \, \sqrt{-x^{2} + 1} + \arcsin\left(x\right)"," ",0,"-1/3*sqrt(-x^2 + 1)*x^2 - sqrt(-x^2 + 1)*x - 5/3*sqrt(-x^2 + 1) + arcsin(x)","A",0
364,1,28,0,0.472803," ","integrate((1+x)^2/(-x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{-x^{2} + 1} x - 2 \, \sqrt{-x^{2} + 1} + \frac{3}{2} \, \arcsin\left(x\right)"," ",0,"-1/2*sqrt(-x^2 + 1)*x - 2*sqrt(-x^2 + 1) + 3/2*arcsin(x)","A",0
365,1,56,0,0.395318," ","integrate((1+x)^3/(-x^2+1)^(1/2)*x,x, algorithm=""maxima"")","-\frac{1}{4} \, \sqrt{-x^{2} + 1} x^{3} - \sqrt{-x^{2} + 1} x^{2} - \frac{15}{8} \, \sqrt{-x^{2} + 1} x - 3 \, \sqrt{-x^{2} + 1} + \frac{15}{8} \, \arcsin\left(x\right)"," ",0,"-1/4*sqrt(-x^2 + 1)*x^3 - sqrt(-x^2 + 1)*x^2 - 15/8*sqrt(-x^2 + 1)*x - 3*sqrt(-x^2 + 1) + 15/8*arcsin(x)","A",0
366,1,42,0,0.491324," ","integrate((1+x)^3/(-x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, \sqrt{-x^{2} + 1} x^{2} - \frac{3}{2} \, \sqrt{-x^{2} + 1} x - \frac{11}{3} \, \sqrt{-x^{2} + 1} + \frac{5}{2} \, \arcsin\left(x\right)"," ",0,"-1/3*sqrt(-x^2 + 1)*x^2 - 3/2*sqrt(-x^2 + 1)*x - 11/3*sqrt(-x^2 + 1) + 5/2*arcsin(x)","A",0
367,1,11,0,0.391301," ","integrate(x/(-x^2+1)^(1/2),x, algorithm=""maxima"")","-\sqrt{-x^{2} + 1}"," ",0,"-sqrt(-x^2 + 1)","C",0
368,1,2,0,0.399042," ","integrate(1/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\arcsin\left(x\right)"," ",0,"arcsin(x)","A",0
369,1,18,0,0.540711," ","integrate(1/(1+x)/(-x^2+1)^(1/2)*x,x, algorithm=""maxima"")","\frac{\sqrt{-x^{2} + 1}}{x + 1} + \arcsin\left(x\right)"," ",0,"sqrt(-x^2 + 1)/(x + 1) + arcsin(x)","A",0
370,1,16,0,0.406594," ","integrate(1/(1+x)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-x^{2} + 1}}{x + 1}"," ",0,"-sqrt(-x^2 + 1)/(x + 1)","A",0
371,1,29,0,0.344462," ","integrate((1+x)^(5/2)/(-x^2+1)^(1/2)*x,x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, x^{4} + 9 \, x^{3} + 11 \, x^{2} + 23 \, x - 46\right)}}{21 \, \sqrt{-x + 1}}"," ",0,"2/21*(3*x^4 + 9*x^3 + 11*x^2 + 23*x - 46)/sqrt(-x + 1)","A",0
372,1,24,0,0.309964," ","integrate((1+x)^(5/2)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, x^{3} + 11 \, x^{2} + 29 \, x - 43\right)}}{15 \, \sqrt{-x + 1}}"," ",0,"2/15*(3*x^3 + 11*x^2 + 29*x - 43)/sqrt(-x + 1)","A",0
373,1,48,0,0.380729," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2)*x,x, algorithm=""maxima"")","-\frac{2 \, {\left(15 \, x^{4} - 24 \, x^{3} + 13 \, x^{2} - 52 \, x - 104\right)}}{105 \, \sqrt{x + 1}} - \frac{2 \, {\left(x^{3} - 2 \, x^{2} + 3 \, x + 6\right)}}{5 \, \sqrt{x + 1}}"," ",0,"-2/105*(15*x^4 - 24*x^3 + 13*x^2 - 52*x - 104)/sqrt(x + 1) - 2/5*(x^3 - 2*x^2 + 3*x + 6)/sqrt(x + 1)","B",0
374,1,36,0,0.329638," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(x^{3} - 2 \, x^{2} + 3 \, x + 6\right)}}{5 \, \sqrt{x + 1}} - \frac{2 \, {\left(x^{2} - 4 \, x - 5\right)}}{3 \, \sqrt{x + 1}}"," ",0,"-2/5*(x^3 - 2*x^2 + 3*x + 6)/sqrt(x + 1) - 2/3*(x^2 - 4*x - 5)/sqrt(x + 1)","B",0
375,1,22,0,0.305610," ","integrate((1+x)^(3/2)/(-x^2+1)^(1/2)*x,x, algorithm=""maxima"")","\frac{2 \, {\left(x^{3} + 2 \, x^{2} + 3 \, x - 6\right)}}{5 \, \sqrt{-x + 1}}"," ",0,"2/5*(x^3 + 2*x^2 + 3*x - 6)/sqrt(-x + 1)","A",0
376,1,17,0,0.300212," ","integrate((1+x)^(3/2)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(x^{2} + 4 \, x - 5\right)}}{3 \, \sqrt{-x + 1}}"," ",0,"2/3*(x^2 + 4*x - 5)/sqrt(-x + 1)","A",0
377,1,38,0,0.321868," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2)*x,x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, x^{3} - x^{2} + 4 \, x + 8\right)}}{15 \, \sqrt{x + 1}} + \frac{2 \, {\left(x^{2} - x - 2\right)}}{3 \, \sqrt{x + 1}}"," ",0,"2/15*(3*x^3 - x^2 + 4*x + 8)/sqrt(x + 1) + 2/3*(x^2 - x - 2)/sqrt(x + 1)","B",0
378,1,23,0,0.375021," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(x^{2} - x - 2\right)}}{3 \, \sqrt{x + 1}} + 2 \, \sqrt{x + 1}"," ",0,"2/3*(x^2 - x - 2)/sqrt(x + 1) + 2*sqrt(x + 1)","B",0
379,1,15,0,0.303410," ","integrate((1+x)^(1/2)/(-x^2+1)^(1/2)*x,x, algorithm=""maxima"")","\frac{2 \, {\left(x^{2} + x - 2\right)}}{3 \, \sqrt{-x + 1}}"," ",0,"2/3*(x^2 + x - 2)/sqrt(-x + 1)","A",0
380,1,12,0,0.370782," ","integrate((1+x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(x - 1\right)}}{\sqrt{-x + 1}}"," ",0,"2*(x - 1)/sqrt(-x + 1)","C",0
381,0,0,0,0.000000," ","integrate((1+x)/(-x^2+1)^(1/2)*x/(1-x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(x + 1\right)} x}{\sqrt{-x^{2} + 1} \sqrt{-x + 1}}\,{d x}"," ",0,"integrate((x + 1)*x/(sqrt(-x^2 + 1)*sqrt(-x + 1)), x)","F",0
382,0,0,0,0.000000," ","integrate((1+x)/(-x^2+1)^(1/2)/(1-x)^(1/2),x, algorithm=""maxima"")","\int \frac{x + 1}{\sqrt{-x^{2} + 1} \sqrt{-x + 1}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(-x^2 + 1)*sqrt(-x + 1)), x)","F",0
383,0,0,0,0.000000," ","integrate(1/(1+x)^(1/2)/(-x^2+1)^(1/2)*x,x, algorithm=""maxima"")","\int \frac{x}{\sqrt{-x^{2} + 1} \sqrt{x + 1}}\,{d x}"," ",0,"integrate(x/(sqrt(-x^2 + 1)*sqrt(x + 1)), x)","F",0
384,0,0,0,0.000000," ","integrate(1/(1+x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-x^{2} + 1} \sqrt{x + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 + 1)*sqrt(x + 1)), x)","F",0
385,0,0,0,0.000000," ","integrate((1+x)/(-x^2+1)^(1/2)*x/(1-x)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(x + 1\right)} x}{\sqrt{-x^{2} + 1} {\left(-x + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x + 1)*x/(sqrt(-x^2 + 1)*(-x + 1)^(3/2)), x)","F",0
386,0,0,0,0.000000," ","integrate((1+x)/(-x^2+1)^(1/2)/(1-x)^(3/2),x, algorithm=""maxima"")","\int \frac{x + 1}{\sqrt{-x^{2} + 1} {\left(-x + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(-x^2 + 1)*(-x + 1)^(3/2)), x)","F",0
387,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
388,1,106,0,0.332379," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a^{4} \sqrt{c} x^{4} - a^{3} \sqrt{c} x^{3} + 2 \, a^{2} \sqrt{c} x^{2} - 8 \, a \sqrt{c} x - 16 \, \sqrt{c}\right)}}{35 \, \sqrt{a x + 1} a^{3}} + \frac{2 \, {\left(3 \, a^{3} \sqrt{c} x^{3} - a^{2} \sqrt{c} x^{2} + 4 \, a \sqrt{c} x + 8 \, \sqrt{c}\right)}}{15 \, \sqrt{a x + 1} a^{3}}"," ",0,"2/35*(5*a^4*sqrt(c)*x^4 - a^3*sqrt(c)*x^3 + 2*a^2*sqrt(c)*x^2 - 8*a*sqrt(c)*x - 16*sqrt(c))/(sqrt(a*x + 1)*a^3) + 2/15*(3*a^3*sqrt(c)*x^3 - a^2*sqrt(c)*x^2 + 4*a*sqrt(c)*x + 8*sqrt(c))/(sqrt(a*x + 1)*a^3)","A",0
389,1,83,0,0.327045," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, a^{3} \sqrt{c} x^{3} - a^{2} \sqrt{c} x^{2} + 4 \, a \sqrt{c} x + 8 \, \sqrt{c}\right)}}{15 \, \sqrt{a x + 1} a^{2}} + \frac{2 \, {\left(a^{2} \sqrt{c} x^{2} - a \sqrt{c} x - 2 \, \sqrt{c}\right)}}{3 \, \sqrt{a x + 1} a^{2}}"," ",0,"2/15*(3*a^3*sqrt(c)*x^3 - a^2*sqrt(c)*x^2 + 4*a*sqrt(c)*x + 8*sqrt(c))/(sqrt(a*x + 1)*a^2) + 2/3*(a^2*sqrt(c)*x^2 - a*sqrt(c)*x - 2*sqrt(c))/(sqrt(a*x + 1)*a^2)","A",0
390,1,58,0,0.330320," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{2} \sqrt{c} x^{2} - a \sqrt{c} x - 2 \, \sqrt{c}\right)}}{3 \, \sqrt{a x + 1} a} + \frac{2 \, {\left(a \sqrt{c} x + \sqrt{c}\right)}}{\sqrt{a x + 1} a}"," ",0,"2/3*(a^2*sqrt(c)*x^2 - a*sqrt(c)*x - 2*sqrt(c))/(sqrt(a*x + 1)*a) + 2*(a*sqrt(c)*x + sqrt(c))/(sqrt(a*x + 1)*a)","A",0
391,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2)/x,x, algorithm=""maxima"")","\sqrt{c} \int \frac{1}{\sqrt{a x + 1} x}\,{d x} + \frac{2 \, {\left(a \sqrt{c} x + \sqrt{c}\right)}}{\sqrt{a x + 1}}"," ",0,"sqrt(c)*integrate(1/(sqrt(a*x + 1)*x), x) + 2*(a*sqrt(c)*x + sqrt(c))/sqrt(a*x + 1)","F",0
392,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)}}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)/(sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
393,1,74,0,0.305859," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(35 \, {\left(-a c x + c\right)}^{\frac{9}{2}} - 225 \, {\left(-a c x + c\right)}^{\frac{7}{2}} c + 567 \, {\left(-a c x + c\right)}^{\frac{5}{2}} c^{2} - 735 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{3} + 630 \, \sqrt{-a c x + c} c^{4}\right)}}{315 \, a^{4} c^{4}}"," ",0,"-2/315*(35*(-a*c*x + c)^(9/2) - 225*(-a*c*x + c)^(7/2)*c + 567*(-a*c*x + c)^(5/2)*c^2 - 735*(-a*c*x + c)^(3/2)*c^3 + 630*sqrt(-a*c*x + c)*c^4)/(a^4*c^4)","A",0
394,1,60,0,0.308622," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15 \, {\left(-a c x + c\right)}^{\frac{7}{2}} - 84 \, {\left(-a c x + c\right)}^{\frac{5}{2}} c + 175 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{2} - 210 \, \sqrt{-a c x + c} c^{3}\right)}}{105 \, a^{3} c^{3}}"," ",0,"2/105*(15*(-a*c*x + c)^(7/2) - 84*(-a*c*x + c)^(5/2)*c + 175*(-a*c*x + c)^(3/2)*c^2 - 210*sqrt(-a*c*x + c)*c^3)/(a^3*c^3)","A",0
395,1,44,0,0.300093," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(-a c x + c\right)}^{\frac{5}{2}} - 5 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c + 10 \, \sqrt{-a c x + c} c^{2}\right)}}{5 \, a^{2} c^{2}}"," ",0,"-2/5*((-a*c*x + c)^(5/2) - 5*(-a*c*x + c)^(3/2)*c + 10*sqrt(-a*c*x + c)*c^2)/(a^2*c^2)","A",0
396,1,30,0,0.305946," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left({\left(-a c x + c\right)}^{\frac{3}{2}} - 6 \, \sqrt{-a c x + c} c\right)}}{3 \, a c}"," ",0,"2/3*((-a*c*x + c)^(3/2) - 6*sqrt(-a*c*x + c)*c)/(a*c)","A",0
397,1,48,0,0.446868," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2)/x,x, algorithm=""maxima"")","\sqrt{c} \log\left(\frac{\sqrt{-a c x + c} - \sqrt{c}}{\sqrt{-a c x + c} + \sqrt{c}}\right) - 2 \, \sqrt{-a c x + c}"," ",0,"sqrt(c)*log((sqrt(-a*c*x + c) - sqrt(c))/(sqrt(-a*c*x + c) + sqrt(c))) - 2*sqrt(-a*c*x + c)","A",0
398,1,62,0,0.404184," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, a c {\left(\frac{3 \, \log\left(\frac{\sqrt{-a c x + c} - \sqrt{c}}{\sqrt{-a c x + c} + \sqrt{c}}\right)}{\sqrt{c}} - \frac{2 \, \sqrt{-a c x + c}}{a c x}\right)}"," ",0,"1/2*a*c*(3*log((sqrt(-a*c*x + c) - sqrt(c))/(sqrt(-a*c*x + c) + sqrt(c)))/sqrt(c) - 2*sqrt(-a*c*x + c)/(a*c*x))","A",0
399,1,103,0,0.400747," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2)/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, a^{2} c^{2} {\left(\frac{2 \, {\left(7 \, {\left(-a c x + c\right)}^{\frac{3}{2}} - 9 \, \sqrt{-a c x + c} c\right)}}{{\left(a c x - c\right)}^{2} c + 2 \, {\left(a c x - c\right)} c^{2} + c^{3}} + \frac{7 \, \log\left(\frac{\sqrt{-a c x + c} - \sqrt{c}}{\sqrt{-a c x + c} + \sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)}"," ",0,"1/8*a^2*c^2*(2*(7*(-a*c*x + c)^(3/2) - 9*sqrt(-a*c*x + c)*c)/((a*c*x - c)^2*c + 2*(a*c*x - c)*c^2 + c^3) + 7*log((sqrt(-a*c*x + c) - sqrt(c))/(sqrt(-a*c*x + c) + sqrt(c)))/c^(3/2))","A",0
400,1,134,0,0.469188," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2)/x^4,x, algorithm=""maxima"")","-\frac{1}{48} \, a^{3} c^{3} {\left(\frac{2 \, {\left(33 \, {\left(-a c x + c\right)}^{\frac{5}{2}} - 88 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c + 63 \, \sqrt{-a c x + c} c^{2}\right)}}{{\left(a c x - c\right)}^{3} c^{2} + 3 \, {\left(a c x - c\right)}^{2} c^{3} + 3 \, {\left(a c x - c\right)} c^{4} + c^{5}} - \frac{33 \, \log\left(\frac{\sqrt{-a c x + c} - \sqrt{c}}{\sqrt{-a c x + c} + \sqrt{c}}\right)}{c^{\frac{5}{2}}}\right)}"," ",0,"-1/48*a^3*c^3*(2*(33*(-a*c*x + c)^(5/2) - 88*(-a*c*x + c)^(3/2)*c + 63*sqrt(-a*c*x + c)*c^2)/((a*c*x - c)^3*c^2 + 3*(a*c*x - c)^2*c^3 + 3*(a*c*x - c)*c^4 + c^5) - 33*log((sqrt(-a*c*x + c) - sqrt(c))/(sqrt(-a*c*x + c) + sqrt(c)))/c^(5/2))","A",0
401,1,163,0,0.458425," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^(1/2)/x^5,x, algorithm=""maxima"")","\frac{1}{128} \, a^{4} c^{4} {\left(\frac{2 \, {\left(75 \, {\left(-a c x + c\right)}^{\frac{7}{2}} - 275 \, {\left(-a c x + c\right)}^{\frac{5}{2}} c + 365 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{2} - 181 \, \sqrt{-a c x + c} c^{3}\right)}}{{\left(a c x - c\right)}^{4} c^{3} + 4 \, {\left(a c x - c\right)}^{3} c^{4} + 6 \, {\left(a c x - c\right)}^{2} c^{5} + 4 \, {\left(a c x - c\right)} c^{6} + c^{7}} + \frac{75 \, \log\left(\frac{\sqrt{-a c x + c} - \sqrt{c}}{\sqrt{-a c x + c} + \sqrt{c}}\right)}{c^{\frac{7}{2}}}\right)}"," ",0,"1/128*a^4*c^4*(2*(75*(-a*c*x + c)^(7/2) - 275*(-a*c*x + c)^(5/2)*c + 365*(-a*c*x + c)^(3/2)*c^2 - 181*sqrt(-a*c*x + c)*c^3)/((a*c*x - c)^4*c^3 + 4*(a*c*x - c)^3*c^4 + 6*(a*c*x - c)^2*c^5 + 4*(a*c*x - c)*c^6 + c^7) + 75*log((sqrt(-a*c*x + c) - sqrt(c))/(sqrt(-a*c*x + c) + sqrt(c)))/c^(7/2))","A",0
402,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)}^{3} x^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)^3*x^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
403,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)}^{3} x^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)^3*x^2/(-a^2*x^2 + 1)^(3/2), x)","F",0
404,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)}^{3} x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)^3*x/(-a^2*x^2 + 1)^(3/2), x)","F",0
405,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
406,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*x), x)","F",0
407,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*x^2), x)","F",0
408,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*x^3), x)","F",0
409,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*x^4), x)","F",0
410,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{5}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*x^5), x)","F",0
411,0,0,0,0.000000," ","integrate(x^m*(-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)*x^m/(a*x + 1), x)","F",0
412,1,62,0,0.325596," ","integrate(x^2*(-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(15 \, a^{3} \sqrt{c} x^{3} - 39 \, a^{2} \sqrt{c} x^{2} + 52 \, a \sqrt{c} x - 104 \, \sqrt{c}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{105 \, {\left(a^{4} x - a^{3}\right)}}"," ",0,"-2/105*(15*a^3*sqrt(c)*x^3 - 39*a^2*sqrt(c)*x^2 + 52*a*sqrt(c)*x - 104*sqrt(c))*sqrt(a*x + 1)*(a*x - 1)/(a^4*x - a^3)","A",0
413,1,50,0,0.371489," ","integrate(x*(-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{2} \sqrt{c} x^{2} - 3 \, a \sqrt{c} x + 6 \, \sqrt{c}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{5 \, {\left(a^{3} x - a^{2}\right)}}"," ",0,"-2/5*(a^2*sqrt(c)*x^2 - 3*a*sqrt(c)*x + 6*sqrt(c))*sqrt(a*x + 1)*(a*x - 1)/(a^3*x - a^2)","A",0
414,1,37,0,0.382971," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a \sqrt{c} x - 5 \, \sqrt{c}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{3 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/3*(a*sqrt(c)*x - 5*sqrt(c))*sqrt(a*x + 1)*(a*x - 1)/(a^2*x - a)","A",0
415,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)/((a*x + 1)*x), x)","F",0
416,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)/((a*x + 1)*x^2), x)","F",0
417,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c}}{{\left(a x + 1\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)/((a*x + 1)*x^3), x)","F",0
418,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c}}{{\left(a x + 1\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)/((a*x + 1)*x^4), x)","F",0
419,1,123,0,0.461621," ","integrate(x^3*(-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{2 \, {\left(315 \, \sqrt{2} c^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right) + 35 \, {\left(-a c x + c\right)}^{\frac{9}{2}} - 45 \, {\left(-a c x + c\right)}^{\frac{7}{2}} c + 63 \, {\left(-a c x + c\right)}^{\frac{5}{2}} c^{2} + 105 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{3} + 630 \, \sqrt{-a c x + c} c^{4}\right)}}{315 \, a^{4} c^{4}}"," ",0,"-2/315*(315*sqrt(2)*c^(9/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c))) + 35*(-a*c*x + c)^(9/2) - 45*(-a*c*x + c)^(7/2)*c + 63*(-a*c*x + c)^(5/2)*c^2 + 105*(-a*c*x + c)^(3/2)*c^3 + 630*sqrt(-a*c*x + c)*c^4)/(a^4*c^4)","A",0
420,1,97,0,0.423991," ","integrate(x^2*(-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{2 \, {\left(21 \, \sqrt{2} c^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right) + 3 \, {\left(-a c x + c\right)}^{\frac{7}{2}} + 7 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{2} + 42 \, \sqrt{-a c x + c} c^{3}\right)}}{21 \, a^{3} c^{3}}"," ",0,"2/21*(21*sqrt(2)*c^(7/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c))) + 3*(-a*c*x + c)^(7/2) + 7*(-a*c*x + c)^(3/2)*c^2 + 42*sqrt(-a*c*x + c)*c^3)/(a^3*c^3)","A",0
421,1,95,0,0.401965," ","integrate(x*(-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{2 \, {\left(15 \, \sqrt{2} c^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right) + 3 \, {\left(-a c x + c\right)}^{\frac{5}{2}} + 5 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c + 30 \, \sqrt{-a c x + c} c^{2}\right)}}{15 \, a^{2} c^{2}}"," ",0,"-2/15*(15*sqrt(2)*c^(5/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c))) + 3*(-a*c*x + c)^(5/2) + 5*(-a*c*x + c)^(3/2)*c + 30*sqrt(-a*c*x + c)*c^2)/(a^2*c^2)","A",0
422,1,79,0,0.403977," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, \sqrt{2} c^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right) + {\left(-a c x + c\right)}^{\frac{3}{2}} + 6 \, \sqrt{-a c x + c} c\right)}}{3 \, a c}"," ",0,"2/3*(3*sqrt(2)*c^(3/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c))) + (-a*c*x + c)^(3/2) + 6*sqrt(-a*c*x + c)*c)/(a*c)","A",0
423,1,97,0,0.405676," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x,x, algorithm=""maxima"")","-2 \, \sqrt{2} \sqrt{c} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right) + \sqrt{c} \log\left(\frac{\sqrt{-a c x + c} - \sqrt{c}}{\sqrt{-a c x + c} + \sqrt{c}}\right) - 2 \, \sqrt{-a c x + c}"," ",0,"-2*sqrt(2)*sqrt(c)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c))) + sqrt(c)*log((sqrt(-a*c*x + c) - sqrt(c))/(sqrt(-a*c*x + c) + sqrt(c))) - 2*sqrt(-a*c*x + c)","A",0
424,1,111,0,0.437043," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, a c {\left(\frac{4 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right)}{\sqrt{c}} - \frac{5 \, \log\left(\frac{\sqrt{-a c x + c} - \sqrt{c}}{\sqrt{-a c x + c} + \sqrt{c}}\right)}{\sqrt{c}} - \frac{2 \, \sqrt{-a c x + c}}{a c x}\right)}"," ",0,"1/2*a*c*(4*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c)))/sqrt(c) - 5*log((sqrt(-a*c*x + c) - sqrt(c))/(sqrt(-a*c*x + c) + sqrt(c)))/sqrt(c) - 2*sqrt(-a*c*x + c)/(a*c*x))","A",0
425,1,152,0,0.400810," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^3,x, algorithm=""maxima"")","-\frac{1}{8} \, a^{2} c^{2} {\left(\frac{2 \, {\left(9 \, {\left(-a c x + c\right)}^{\frac{3}{2}} - 7 \, \sqrt{-a c x + c} c\right)}}{{\left(a c x - c\right)}^{2} c + 2 \, {\left(a c x - c\right)} c^{2} + c^{3}} + \frac{16 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right)}{c^{\frac{3}{2}}} - \frac{23 \, \log\left(\frac{\sqrt{-a c x + c} - \sqrt{c}}{\sqrt{-a c x + c} + \sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)}"," ",0,"-1/8*a^2*c^2*(2*(9*(-a*c*x + c)^(3/2) - 7*sqrt(-a*c*x + c)*c)/((a*c*x - c)^2*c + 2*(a*c*x - c)*c^2 + c^3) + 16*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c)))/c^(3/2) - 23*log((sqrt(-a*c*x + c) - sqrt(c))/(sqrt(-a*c*x + c) + sqrt(c)))/c^(3/2))","A",0
426,1,183,0,0.412991," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^4,x, algorithm=""maxima"")","-\frac{1}{48} \, a^{3} c^{3} {\left(\frac{2 \, {\left(57 \, {\left(-a c x + c\right)}^{\frac{5}{2}} - 88 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c + 39 \, \sqrt{-a c x + c} c^{2}\right)}}{{\left(a c x - c\right)}^{3} c^{2} + 3 \, {\left(a c x - c\right)}^{2} c^{3} + 3 \, {\left(a c x - c\right)} c^{4} + c^{5}} - \frac{96 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right)}{c^{\frac{5}{2}}} + \frac{135 \, \log\left(\frac{\sqrt{-a c x + c} - \sqrt{c}}{\sqrt{-a c x + c} + \sqrt{c}}\right)}{c^{\frac{5}{2}}}\right)}"," ",0,"-1/48*a^3*c^3*(2*(57*(-a*c*x + c)^(5/2) - 88*(-a*c*x + c)^(3/2)*c + 39*sqrt(-a*c*x + c)*c^2)/((a*c*x - c)^3*c^2 + 3*(a*c*x - c)^2*c^3 + 3*(a*c*x - c)*c^4 + c^5) - 96*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c)))/c^(5/2) + 135*log((sqrt(-a*c*x + c) - sqrt(c))/(sqrt(-a*c*x + c) + sqrt(c)))/c^(5/2))","A",0
427,1,212,0,0.602511," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^5,x, algorithm=""maxima"")","-\frac{1}{384} \, a^{4} c^{4} {\left(\frac{2 \, {\left(447 \, {\left(-a c x + c\right)}^{\frac{7}{2}} - 1127 \, {\left(-a c x + c\right)}^{\frac{5}{2}} c + 1049 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{2} - 321 \, \sqrt{-a c x + c} c^{3}\right)}}{{\left(a c x - c\right)}^{4} c^{3} + 4 \, {\left(a c x - c\right)}^{3} c^{4} + 6 \, {\left(a c x - c\right)}^{2} c^{5} + 4 \, {\left(a c x - c\right)} c^{6} + c^{7}} + \frac{768 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-a c x + c}}{\sqrt{2} \sqrt{c} + \sqrt{-a c x + c}}\right)}{c^{\frac{7}{2}}} - \frac{1089 \, \log\left(\frac{\sqrt{-a c x + c} - \sqrt{c}}{\sqrt{-a c x + c} + \sqrt{c}}\right)}{c^{\frac{7}{2}}}\right)}"," ",0,"-1/384*a^4*c^4*(2*(447*(-a*c*x + c)^(7/2) - 1127*(-a*c*x + c)^(5/2)*c + 1049*(-a*c*x + c)^(3/2)*c^2 - 321*sqrt(-a*c*x + c)*c^3)/((a*c*x - c)^4*c^3 + 4*(a*c*x - c)^3*c^4 + 6*(a*c*x - c)^2*c^5 + 4*(a*c*x - c)*c^6 + c^7) + 768*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-a*c*x + c))/(sqrt(2)*sqrt(c) + sqrt(-a*c*x + c)))/c^(7/2) - 1089*log((sqrt(-a*c*x + c) - sqrt(c))/(sqrt(-a*c*x + c) + sqrt(c)))/c^(7/2))","A",0
428,1,86,0,0.337645," ","integrate(x^3*(-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a^{5} \sqrt{c} x^{5} - 20 \, a^{4} \sqrt{c} x^{4} + 41 \, a^{3} \sqrt{c} x^{3} - 82 \, a^{2} \sqrt{c} x^{2} + 328 \, a \sqrt{c} x + 656 \, \sqrt{c}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{45 \, {\left(a^{6} x^{2} - a^{4}\right)}}"," ",0,"2/45*(5*a^5*sqrt(c)*x^5 - 20*a^4*sqrt(c)*x^4 + 41*a^3*sqrt(c)*x^3 - 82*a^2*sqrt(c)*x^2 + 328*a*sqrt(c)*x + 656*sqrt(c))*sqrt(a*x + 1)*(a*x - 1)/(a^6*x^2 - a^4)","A",0
429,1,75,0,0.366395," ","integrate(x^2*(-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15 \, a^{4} \sqrt{c} x^{4} - 66 \, a^{3} \sqrt{c} x^{3} + 167 \, a^{2} \sqrt{c} x^{2} - 668 \, a \sqrt{c} x - 1336 \, \sqrt{c}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{105 \, {\left(a^{5} x^{2} - a^{3}\right)}}"," ",0,"2/105*(15*a^4*sqrt(c)*x^4 - 66*a^3*sqrt(c)*x^3 + 167*a^2*sqrt(c)*x^2 - 668*a*sqrt(c)*x - 1336*sqrt(c))*sqrt(a*x + 1)*(a*x - 1)/(a^5*x^2 - a^3)","A",0
430,1,64,0,0.404900," ","integrate(x*(-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, a^{3} \sqrt{c} x^{3} - 16 \, a^{2} \sqrt{c} x^{2} + 79 \, a \sqrt{c} x + 158 \, \sqrt{c}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{15 \, {\left(a^{4} x^{2} - a^{2}\right)}}"," ",0,"2/15*(3*a^3*sqrt(c)*x^3 - 16*a^2*sqrt(c)*x^2 + 79*a*sqrt(c)*x + 158*sqrt(c))*sqrt(a*x + 1)*(a*x - 1)/(a^4*x^2 - a^2)","A",0
431,1,50,0,0.423099," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{2} \sqrt{c} x^{2} - 10 \, a \sqrt{c} x - 23 \, \sqrt{c}\right)} \sqrt{a x + 1} {\left(a x - 1\right)}}{3 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"2/3*(a^2*sqrt(c)*x^2 - 10*a*sqrt(c)*x - 23*sqrt(c))*sqrt(a*x + 1)*(a*x - 1)/(a^3*x^2 - a)","A",0
432,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{-a c x + c}}{{\left(a x + 1\right)}^{3} x}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(-a*c*x + c)/((a*x + 1)^3*x), x)","F",0
433,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{-a c x + c}}{{\left(a x + 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(-a*c*x + c)/((a*x + 1)^3*x^2), x)","F",0
434,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{-a c x + c}}{{\left(a x + 1\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(-a*c*x + c)/((a*x + 1)^3*x^3), x)","F",0
435,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{-a c x + c}}{{\left(a x + 1\right)}^{3} x^{4}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(-a*c*x + c)/((a*x + 1)^3*x^4), x)","F",0
436,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{-a c x + c}}{{\left(a x + 1\right)}^{3} x^{5}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(-a*c*x + c)/((a*x + 1)^3*x^5), x)","F",0
437,0,0,0,0.000000," ","integrate((-a*c*x+c)^p/exp(2*p*arctanh(a*x)),x, algorithm=""maxima"")","\int \frac{{\left(-a c x + c\right)}^{p}}{\left(\frac{a x + 1}{a x - 1}\right)^{p}}\,{d x}"," ",0,"integrate((-a*c*x + c)^p/((a*x + 1)/(a*x - 1))^p, x)","F",0
438,1,30,0,0.398550," ","integrate(exp(2*p*arctanh(a*x))*(-a*c*x+c)^p,x, algorithm=""maxima"")","\frac{{\left(a \left(-c\right)^{p} x + \left(-c\right)^{p}\right)} {\left(a x + 1\right)}^{p}}{a {\left(p + 1\right)}}"," ",0,"(a*(-c)^p*x + (-c)^p)*(a*x + 1)^p/(a*(p + 1))","A",0
439,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a*c*x+c)^p,x, algorithm=""maxima"")","\int {\left(-a c x + c\right)}^{p} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^p*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
440,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a*c*x+c)^3,x, algorithm=""maxima"")","-\int {\left(a c x - c\right)}^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"-integrate((a*c*x - c)^3*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
441,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a*c*x+c)^2,x, algorithm=""maxima"")","\int {\left(a c x - c\right)}^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((a*c*x - c)^2*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
442,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a*c*x+c),x, algorithm=""maxima"")","-\int {\left(a c x - c\right)} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"-integrate((a*c*x - c)*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
443,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a*c*x+c),x, algorithm=""maxima"")","-\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{a c x - c}\,{d x}"," ",0,"-integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(a*c*x - c), x)","F",0
444,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a*c*x+c)^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a c x - c\right)}^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(a*c*x - c)^2, x)","F",0
445,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a c x - c\right)}^{3}}\,{d x}"," ",0,"-integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(a*c*x - c)^3, x)","F",0
446,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a*c*x+c)^4,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a c x - c\right)}^{4}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(a*c*x - c)^4, x)","F",0
447,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^p,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^p/sqrt(-a^2*x^2 + 1), x)","F",0
448,1,190,0,0.506411," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^4,x, algorithm=""maxima"")","-\frac{3 \, c^{4} \arcsin\left(a x\right)}{a} - \frac{2 \, c^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{a} + \frac{3 \, {\left(a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-a^{2} x^{2} + 1}}{x^{2}}\right)} c^{4}}{2 \, a^{3}} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c^{4}}{a^{2} x} - \frac{{\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{x} + \frac{\sqrt{-a^{2} x^{2} + 1}}{x^{3}}\right)} c^{4}}{3 \, a^{4}}"," ",0,"-3*c^4*arcsin(a*x)/a - 2*c^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a - sqrt(-a^2*x^2 + 1)*c^4/a + 3/2*(a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-a^2*x^2 + 1)/x^2)*c^4/a^3 - 2*sqrt(-a^2*x^2 + 1)*c^4/(a^2*x) - 1/3*(2*sqrt(-a^2*x^2 + 1)*a^2/x + sqrt(-a^2*x^2 + 1)/x^3)*c^4/a^4","A",0
449,1,111,0,0.572200," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^3,x, algorithm=""maxima"")","-\frac{2 \, c^{3} \arcsin\left(a x\right)}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{a} + \frac{{\left(a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-a^{2} x^{2} + 1}}{x^{2}}\right)} c^{3}}{2 \, a^{3}} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{a^{2} x}"," ",0,"-2*c^3*arcsin(a*x)/a - sqrt(-a^2*x^2 + 1)*c^3/a + 1/2*(a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-a^2*x^2 + 1)/x^2)*c^3/a^3 - 2*sqrt(-a^2*x^2 + 1)*c^3/(a^2*x)","A",0
450,1,89,0,0.535804," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^2,x, algorithm=""maxima"")","-\frac{c^{2} \arcsin\left(a x\right)}{a} + \frac{c^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a^{2} x}"," ",0,"-c^2*arcsin(a*x)/a + c^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a - sqrt(-a^2*x^2 + 1)*c^2/a - sqrt(-a^2*x^2 + 1)*c^2/(a^2*x)","A",0
451,1,50,0,0.446177," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x),x, algorithm=""maxima"")","\frac{c \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} c}{a}"," ",0,"c*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a - sqrt(-a^2*x^2 + 1)*c/a","A",0
452,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))), x)","F",0
453,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^2,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^2), x)","F",0
454,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^3,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^3), x)","F",0
455,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^4,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{4}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^4), x)","F",0
456,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^p,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a x}\right)}^{p}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*(c - c/(a*x))^p/(a^2*x^2 - 1), x)","F",0
457,1,58,0,0.474886," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^5,x, algorithm=""maxima"")","-c^{5} x + \frac{3 \, c^{5} \log\left(x\right)}{a} + \frac{8 \, a^{3} c^{5} x^{3} + 4 \, a^{2} c^{5} x^{2} - 4 \, a c^{5} x + c^{5}}{4 \, a^{5} x^{4}}"," ",0,"-c^5*x + 3*c^5*log(x)/a + 1/4*(8*a^3*c^5*x^3 + 4*a^2*c^5*x^2 - 4*a*c^5*x + c^5)/(a^5*x^4)","A",0
458,1,38,0,0.301434," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^4,x, algorithm=""maxima"")","-c^{4} x + \frac{2 \, c^{4} \log\left(x\right)}{a} + \frac{3 \, a c^{4} x - c^{4}}{3 \, a^{4} x^{3}}"," ",0,"-c^4*x + 2*c^4*log(x)/a + 1/3*(3*a*c^4*x - c^4)/(a^4*x^3)","A",0
459,-1,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,1,18,0,0.353058," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^2,x, algorithm=""maxima"")","-c^{2} x - \frac{c^{2}}{a^{2} x}"," ",0,"-c^2*x - c^2/(a^2*x)","A",0
461,1,13,0,0.408226," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x),x, algorithm=""maxima"")","-c x - \frac{c \log\left(x\right)}{a}"," ",0,"-c*x - c*log(x)/a","A",0
462,1,36,0,0.350691," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x),x, algorithm=""maxima"")","-\frac{x}{c} + \frac{2}{a^{2} c x - a c} - \frac{3 \, \log\left(a x - 1\right)}{a c}"," ",0,"-x/c + 2/(a^2*c*x - a*c) - 3*log(a*x - 1)/(a*c)","A",0
463,1,55,0,0.307437," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^2,x, algorithm=""maxima"")","\frac{5 \, a x - 4}{a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}} - \frac{x}{c^{2}} - \frac{4 \, \log\left(a x - 1\right)}{a c^{2}}"," ",0,"(5*a*x - 4)/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2) - x/c^2 - 4*log(a*x - 1)/(a*c^2)","A",0
464,1,76,0,0.364361," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^3,x, algorithm=""maxima"")","\frac{54 \, a^{2} x^{2} - 87 \, a x + 37}{6 \, {\left(a^{4} c^{3} x^{3} - 3 \, a^{3} c^{3} x^{2} + 3 \, a^{2} c^{3} x - a c^{3}\right)}} - \frac{x}{c^{3}} - \frac{5 \, \log\left(a x - 1\right)}{a c^{3}}"," ",0,"1/6*(54*a^2*x^2 - 87*a*x + 37)/(a^4*c^3*x^3 - 3*a^3*c^3*x^2 + 3*a^2*c^3*x - a*c^3) - x/c^3 - 5*log(a*x - 1)/(a*c^3)","A",0
465,1,94,0,0.356855," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^4,x, algorithm=""maxima"")","\frac{28 \, a^{3} x^{3} - 68 \, a^{2} x^{2} + 58 \, a x - 17}{2 \, {\left(a^{5} c^{4} x^{4} - 4 \, a^{4} c^{4} x^{3} + 6 \, a^{3} c^{4} x^{2} - 4 \, a^{2} c^{4} x + a c^{4}\right)}} - \frac{x}{c^{4}} - \frac{6 \, \log\left(a x - 1\right)}{a c^{4}}"," ",0,"1/2*(28*a^3*x^3 - 68*a^2*x^2 + 58*a*x - 17)/(a^5*c^4*x^4 - 4*a^4*c^4*x^3 + 6*a^3*c^4*x^2 - 4*a^2*c^4*x + a*c^4) - x/c^4 - 6*log(a*x - 1)/(a*c^4)","A",0
466,1,349,0,0.500064," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^4,x, algorithm=""maxima"")","-a^{3} c^{4} {\left(\frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{2}{\sqrt{-a^{2} x^{2} + 1} a^{4}}\right)} - a^{2} c^{4} {\left(\frac{x}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}\right)} + \frac{3 \, c^{4} x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{3 \, c^{4} {\left(\frac{1}{\sqrt{-a^{2} x^{2} + 1}} - \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)\right)}}{a} - \frac{3 \, {\left(\frac{2 \, a^{2} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x}\right)} c^{4}}{a^{2}} - \frac{3 \, c^{4}}{\sqrt{-a^{2} x^{2} + 1} a} + \frac{{\left(3 \, a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{3 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\right)} c^{4}}{2 \, a^{3}} + \frac{{\left(\frac{8 \, a^{4} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{4 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1} x} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\right)} c^{4}}{3 \, a^{4}}"," ",0,"-a^3*c^4*(x^2/(sqrt(-a^2*x^2 + 1)*a^2) - 2/(sqrt(-a^2*x^2 + 1)*a^4)) - a^2*c^4*(x/(sqrt(-a^2*x^2 + 1)*a^2) - arcsin(a*x)/a^3) + 3*c^4*x/sqrt(-a^2*x^2 + 1) + 3*c^4*(1/sqrt(-a^2*x^2 + 1) - log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)))/a - 3*(2*a^2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*x))*c^4/a^2 - 3*c^4/(sqrt(-a^2*x^2 + 1)*a) + 1/2*(3*a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 3*a^2/sqrt(-a^2*x^2 + 1) + 1/(sqrt(-a^2*x^2 + 1)*x^2))*c^4/a^3 + 1/3*(8*a^4*x/sqrt(-a^2*x^2 + 1) - 4*a^2/(sqrt(-a^2*x^2 + 1)*x) - 1/(sqrt(-a^2*x^2 + 1)*x^3))*c^4/a^4","B",0
467,1,188,0,0.412372," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^3,x, algorithm=""maxima"")","-a^{3} c^{3} {\left(\frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{2}{\sqrt{-a^{2} x^{2} + 1} a^{4}}\right)} + \frac{3 \, c^{3} {\left(\frac{1}{\sqrt{-a^{2} x^{2} + 1}} - \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)\right)}}{a} - \frac{3 \, c^{3}}{\sqrt{-a^{2} x^{2} + 1} a} + \frac{{\left(3 \, a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{3 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\right)} c^{3}}{2 \, a^{3}}"," ",0,"-a^3*c^3*(x^2/(sqrt(-a^2*x^2 + 1)*a^2) - 2/(sqrt(-a^2*x^2 + 1)*a^4)) + 3*c^3*(1/sqrt(-a^2*x^2 + 1) - log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)))/a - 3*c^3/(sqrt(-a^2*x^2 + 1)*a) + 1/2*(3*a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 3*a^2/sqrt(-a^2*x^2 + 1) + 1/(sqrt(-a^2*x^2 + 1)*x^2))*c^3/a^3","B",0
468,1,209,0,0.429284," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^2,x, algorithm=""maxima"")","-a^{3} c^{2} {\left(\frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{2}{\sqrt{-a^{2} x^{2} + 1} a^{4}}\right)} + a^{2} c^{2} {\left(\frac{x}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}\right)} - \frac{2 \, c^{2} x}{\sqrt{-a^{2} x^{2} + 1}} + \frac{c^{2} {\left(\frac{1}{\sqrt{-a^{2} x^{2} + 1}} - \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)\right)}}{a} + \frac{{\left(\frac{2 \, a^{2} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x}\right)} c^{2}}{a^{2}} - \frac{2 \, c^{2}}{\sqrt{-a^{2} x^{2} + 1} a}"," ",0,"-a^3*c^2*(x^2/(sqrt(-a^2*x^2 + 1)*a^2) - 2/(sqrt(-a^2*x^2 + 1)*a^4)) + a^2*c^2*(x/(sqrt(-a^2*x^2 + 1)*a^2) - arcsin(a*x)/a^3) - 2*c^2*x/sqrt(-a^2*x^2 + 1) + c^2*(1/sqrt(-a^2*x^2 + 1) - log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)))/a + (2*a^2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*x))*c^2/a^2 - 2*c^2/(sqrt(-a^2*x^2 + 1)*a)","B",0
469,1,140,0,0.473925," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x),x, algorithm=""maxima"")","-a^{3} c {\left(\frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{2}{\sqrt{-a^{2} x^{2} + 1} a^{4}}\right)} + 2 \, a^{2} c {\left(\frac{x}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}\right)} - \frac{2 \, c x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{c {\left(\frac{1}{\sqrt{-a^{2} x^{2} + 1}} - \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)\right)}}{a}"," ",0,"-a^3*c*(x^2/(sqrt(-a^2*x^2 + 1)*a^2) - 2/(sqrt(-a^2*x^2 + 1)*a^4)) + 2*a^2*c*(x/(sqrt(-a^2*x^2 + 1)*a^2) - arcsin(a*x)/a^3) - 2*c*x/sqrt(-a^2*x^2 + 1) - c*(1/sqrt(-a^2*x^2 + 1) - log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)))/a","B",0
470,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))), x)","F",0
471,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^2), x)","F",0
472,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^3,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{3}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^3), x)","F",0
473,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^4,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{4}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^4), x)","F",0
474,0,0,0,0.000000," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^p,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{4} {\left(c - \frac{c}{a x}\right)}^{p}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^4*(c - c/(a*x))^p/(a^2*x^2 - 1)^2, x)","F",0
475,1,59,0,0.352479," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^5,x, algorithm=""maxima"")","c^{5} x - \frac{c^{5} \log\left(x\right)}{a} + \frac{24 \, a^{3} c^{5} x^{3} - 12 \, a^{2} c^{5} x^{2} - 4 \, a c^{5} x + 3 \, c^{5}}{12 \, a^{5} x^{4}}"," ",0,"c^5*x - c^5*log(x)/a + 1/12*(24*a^3*c^5*x^3 - 12*a^2*c^5*x^2 - 4*a*c^5*x + 3*c^5)/(a^5*x^4)","A",0
476,1,31,0,0.374792," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^4,x, algorithm=""maxima"")","c^{4} x + \frac{6 \, a^{2} c^{4} x^{2} - c^{4}}{3 \, a^{4} x^{3}}"," ",0,"c^4*x + 1/3*(6*a^2*c^4*x^2 - c^4)/(a^4*x^3)","A",0
477,1,34,0,0.379107," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^3,x, algorithm=""maxima"")","c^{3} x + \frac{c^{3} \log\left(x\right)}{a} + \frac{2 \, a c^{3} x + c^{3}}{2 \, a^{3} x^{2}}"," ",0,"c^3*x + c^3*log(x)/a + 1/2*(2*a*c^3*x + c^3)/(a^3*x^2)","A",0
478,1,27,0,0.352454," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^2,x, algorithm=""maxima"")","c^{2} x + \frac{2 \, c^{2} \log\left(x\right)}{a} - \frac{c^{2}}{a^{2} x}"," ",0,"c^2*x + 2*c^2*log(x)/a - c^2/(a^2*x)","A",0
479,1,24,0,0.327155," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x),x, algorithm=""maxima"")","c x + \frac{4 \, c \log\left(a x - 1\right)}{a} - \frac{c \log\left(x\right)}{a}"," ",0,"c*x + 4*c*log(a*x - 1)/a - c*log(x)/a","A",0
480,1,49,0,0.335308," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x),x, algorithm=""maxima"")","-\frac{2 \, {\left(4 \, a x - 3\right)}}{a^{3} c x^{2} - 2 \, a^{2} c x + a c} + \frac{x}{c} + \frac{5 \, \log\left(a x - 1\right)}{a c}"," ",0,"-2*(4*a*x - 3)/(a^3*c*x^2 - 2*a^2*c*x + a*c) + x/c + 5*log(a*x - 1)/(a*c)","A",0
481,1,75,0,0.306419," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x)^2,x, algorithm=""maxima"")","-\frac{39 \, a^{2} x^{2} - 60 \, a x + 25}{3 \, {\left(a^{4} c^{2} x^{3} - 3 \, a^{3} c^{2} x^{2} + 3 \, a^{2} c^{2} x - a c^{2}\right)}} + \frac{x}{c^{2}} + \frac{6 \, \log\left(a x - 1\right)}{a c^{2}}"," ",0,"-1/3*(39*a^2*x^2 - 60*a*x + 25)/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2) + x/c^2 + 6*log(a*x - 1)/(a*c^2)","A",0
482,1,93,0,0.342386," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x)^3,x, algorithm=""maxima"")","-\frac{114 \, a^{3} x^{3} - 267 \, a^{2} x^{2} + 224 \, a x - 65}{6 \, {\left(a^{5} c^{3} x^{4} - 4 \, a^{4} c^{3} x^{3} + 6 \, a^{3} c^{3} x^{2} - 4 \, a^{2} c^{3} x + a c^{3}\right)}} + \frac{x}{c^{3}} + \frac{7 \, \log\left(a x - 1\right)}{a c^{3}}"," ",0,"-1/6*(114*a^3*x^3 - 267*a^2*x^2 + 224*a*x - 65)/(a^5*c^3*x^4 - 4*a^4*c^3*x^3 + 6*a^3*c^3*x^2 - 4*a^2*c^3*x + a*c^3) + x/c^3 + 7*log(a*x - 1)/(a*c^3)","A",0
483,1,113,0,0.325224," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x)^4,x, algorithm=""maxima"")","-\frac{390 \, a^{4} x^{4} - 1230 \, a^{3} x^{3} + 1555 \, a^{2} x^{2} - 905 \, a x + 202}{15 \, {\left(a^{6} c^{4} x^{5} - 5 \, a^{5} c^{4} x^{4} + 10 \, a^{4} c^{4} x^{3} - 10 \, a^{3} c^{4} x^{2} + 5 \, a^{2} c^{4} x - a c^{4}\right)}} + \frac{x}{c^{4}} + \frac{8 \, \log\left(a x - 1\right)}{a c^{4}}"," ",0,"-1/15*(390*a^4*x^4 - 1230*a^3*x^3 + 1555*a^2*x^2 - 905*a*x + 202)/(a^6*c^4*x^5 - 5*a^5*c^4*x^4 + 10*a^4*c^4*x^3 - 10*a^3*c^4*x^2 + 5*a^2*c^4*x - a*c^4) + x/c^4 + 8*log(a*x - 1)/(a*c^4)","A",0
484,0,0,0,0.000000," ","integrate((c-c/a/x)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^p/(a*x + 1), x)","F",0
485,0,0,0,0.000000," ","integrate((c-c/a/x)^4/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","4 \, a c^{4} {\left(\frac{\arcsin\left(a x\right)}{a^{2}} + \frac{\log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a^{2}}\right)} + c^{4} {\left(\frac{\arcsin\left(a x\right)}{a} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a}\right)} + \int \frac{{\left(6 \, a^{2} c^{4} x^{2} - 4 \, a c^{4} x + c^{4}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{a^{5} x^{5} + a^{4} x^{4}}\,{d x}"," ",0,"4*a*c^4*(arcsin(a*x)/a^2 + log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a^2) + c^4*(arcsin(a*x)/a + sqrt(-a^2*x^2 + 1)/a) + integrate((6*a^2*c^4*x^2 - 4*a*c^4*x + c^4)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^5*x^5 + a^4*x^4), x)","F",0
486,0,0,0,0.000000," ","integrate((c-c/a/x)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","3 \, a c^{3} {\left(\frac{\arcsin\left(a x\right)}{a^{2}} + \frac{\log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a^{2}}\right)} + c^{3} {\left(\frac{\arcsin\left(a x\right)}{a} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a}\right)} + \int \frac{{\left(3 \, a c^{3} x - c^{3}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{a^{4} x^{4} + a^{3} x^{3}}\,{d x}"," ",0,"3*a*c^3*(arcsin(a*x)/a^2 + log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a^2) + c^3*(arcsin(a*x)/a + sqrt(-a^2*x^2 + 1)/a) + integrate((3*a*c^3*x - c^3)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^4*x^4 + a^3*x^3), x)","F",0
487,0,0,0,0.000000," ","integrate((c-c/a/x)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","2 \, a c^{2} {\left(\frac{\arcsin\left(a x\right)}{a^{2}} + \frac{\log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a^{2}}\right)} + c^{2} {\left(\frac{\arcsin\left(a x\right)}{a} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a}\right)} + c^{2} \int \frac{\sqrt{a x + 1} \sqrt{-a x + 1}}{a^{3} x^{3} + a^{2} x^{2}}\,{d x}"," ",0,"2*a*c^2*(arcsin(a*x)/a^2 + log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a^2) + c^2*(arcsin(a*x)/a + sqrt(-a^2*x^2 + 1)/a) + c^2*integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^3*x^3 + a^2*x^2), x)","F",0
488,1,70,0,0.463911," ","integrate((c-c/a/x)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","a c {\left(\frac{\arcsin\left(a x\right)}{a^{2}} + \frac{\log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a^{2}}\right)} + c {\left(\frac{\arcsin\left(a x\right)}{a} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a}\right)}"," ",0,"a*c*(arcsin(a*x)/a^2 + log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a^2) + c*(arcsin(a*x)/a + sqrt(-a^2*x^2 + 1)/a)","A",0
489,1,22,0,0.329921," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x),x, algorithm=""maxima"")","\frac{\sqrt{a x + 1} \sqrt{-a x + 1}}{a c}"," ",0,"sqrt(a*x + 1)*sqrt(-a*x + 1)/(a*c)","A",0
490,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a*x))^2), x)","F",0
491,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a*x))^3), x)","F",0
492,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a*x))^4), x)","F",0
493,0,0,0,0.000000," ","integrate((c-c/a/x)^p/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a x}\right)}^{p}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(c - c/(a*x))^p/(a*x + 1)^2, x)","F",0
494,1,61,0,0.309532," ","integrate((c-c/a/x)^4/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-c^{4} x + \frac{32 \, c^{4} \log\left(a x + 1\right)}{a} - \frac{26 \, c^{4} \log\left(x\right)}{a} - \frac{48 \, a^{2} c^{4} x^{2} - 9 \, a c^{4} x + c^{4}}{3 \, a^{4} x^{3}}"," ",0,"-c^4*x + 32*c^4*log(a*x + 1)/a - 26*c^4*log(x)/a - 1/3*(48*a^2*c^4*x^2 - 9*a*c^4*x + c^4)/(a^4*x^3)","A",0
495,1,52,0,0.307092," ","integrate((c-c/a/x)^3/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-c^{3} x + \frac{16 \, c^{3} \log\left(a x + 1\right)}{a} - \frac{11 \, c^{3} \log\left(x\right)}{a} - \frac{10 \, a c^{3} x - c^{3}}{2 \, a^{3} x^{2}}"," ",0,"-c^3*x + 16*c^3*log(a*x + 1)/a - 11*c^3*log(x)/a - 1/2*(10*a*c^3*x - c^3)/(a^3*x^2)","A",0
496,1,42,0,0.312817," ","integrate((c-c/a/x)^2/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-c^{2} x + \frac{8 \, c^{2} \log\left(a x + 1\right)}{a} - \frac{4 \, c^{2} \log\left(x\right)}{a} - \frac{c^{2}}{a^{2} x}"," ",0,"-c^2*x + 8*c^2*log(a*x + 1)/a - 4*c^2*log(x)/a - c^2/(a^2*x)","A",0
497,1,25,0,0.314659," ","integrate((c-c/a/x)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-c x + \frac{4 \, c \log\left(a x + 1\right)}{a} - \frac{c \log\left(x\right)}{a}"," ",0,"-c*x + 4*c*log(a*x + 1)/a - c*log(x)/a","A",0
498,1,20,0,0.345586," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x),x, algorithm=""maxima"")","-\frac{x}{c} + \frac{\log\left(a x + 1\right)}{a c}"," ",0,"-x/c + log(a*x + 1)/(a*c)","A",0
499,1,35,0,0.375153," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^2,x, algorithm=""maxima"")","-\frac{x}{c^{2}} + \frac{\log\left(a x + 1\right)}{2 \, a c^{2}} - \frac{\log\left(a x - 1\right)}{2 \, a c^{2}}"," ",0,"-x/c^2 + 1/2*log(a*x + 1)/(a*c^2) - 1/2*log(a*x - 1)/(a*c^2)","A",0
500,1,54,0,0.340168," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^3,x, algorithm=""maxima"")","\frac{1}{2 \, {\left(a^{2} c^{3} x - a c^{3}\right)}} - \frac{x}{c^{3}} + \frac{\log\left(a x + 1\right)}{4 \, a c^{3}} - \frac{5 \, \log\left(a x - 1\right)}{4 \, a c^{3}}"," ",0,"1/2/(a^2*c^3*x - a*c^3) - x/c^3 + 1/4*log(a*x + 1)/(a*c^3) - 5/4*log(a*x - 1)/(a*c^3)","A",0
501,1,70,0,0.315381," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^4,x, algorithm=""maxima"")","\frac{7 \, a x - 6}{4 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}} - \frac{x}{c^{4}} + \frac{\log\left(a x + 1\right)}{8 \, a c^{4}} - \frac{17 \, \log\left(a x - 1\right)}{8 \, a c^{4}}"," ",0,"1/4*(7*a*x - 6)/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4) - x/c^4 + 1/8*log(a*x + 1)/(a*c^4) - 17/8*log(a*x - 1)/(a*c^4)","A",0
502,0,0,0,0.000000," ","integrate((c-c/a/x)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{3}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^3/(a*x + 1)^3, x)","F",0
503,0,0,0,0.000000," ","integrate((c-c/a/x)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{2}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^2/(a*x + 1)^3, x)","F",0
504,0,0,0,0.000000," ","integrate((c-c/a/x)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))/(a*x + 1)^3, x)","F",0
505,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a*x))), x)","F",0
506,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^2,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{2}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a*x))^2), x)","F",0
507,1,45,0,0.325667," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^3,x, algorithm=""maxima"")","-\frac{{\left(a^{2} x^{2} - 2\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{a^{3} c^{3} x^{2} - a c^{3}}"," ",0,"-(a^2*x^2 - 2)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^3*c^3*x^2 - a*c^3)","A",0
508,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^4,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{4}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a*x))^4), x)","F",0
509,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^5,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{5}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a*x))^5), x)","F",0
510,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^(9/2)/sqrt(-a^2*x^2 + 1), x)","F",0
511,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^(7/2)/sqrt(-a^2*x^2 + 1), x)","F",0
512,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^(5/2)/sqrt(-a^2*x^2 + 1), x)","F",0
513,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^(3/2)/sqrt(-a^2*x^2 + 1), x)","F",0
514,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/sqrt(-a^2*x^2 + 1), x)","F",0
515,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))), x)","F",0
516,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^(3/2)), x)","F",0
517,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^(5/2)), x)","F",0
518,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(9/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*(c - c/(a*x))^(9/2)/(a^2*x^2 - 1), x)","F",0
519,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(7/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*(c - c/(a*x))^(7/2)/(a^2*x^2 - 1), x)","F",0
520,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(5/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*(c - c/(a*x))^(5/2)/(a^2*x^2 - 1), x)","F",0
521,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*(c - c/(a*x))^(3/2)/(a^2*x^2 - 1), x)","F",0
522,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a x}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a*x))/(a^2*x^2 - 1), x)","F",0
523,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((a^2*x^2 - 1)*sqrt(c - c/(a*x))), x)","F",0
524,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((a^2*x^2 - 1)*(c - c/(a*x))^(3/2)), x)","F",0
525,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((a^2*x^2 - 1)*(c - c/(a*x))^(5/2)), x)","F",0
526,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a/x)^(7/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((a^2*x^2 - 1)*(c - c/(a*x))^(7/2)), x)","F",0
527,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a*x))^(9/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
528,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a*x))^(7/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
529,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a*x))^(5/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
530,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a*x))^(3/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
531,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a*x))/(-a^2*x^2 + 1)^(3/2), x)","F",0
532,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a*x))), x)","F",0
533,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^(3/2)), x)","F",0
534,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^(5/2)), x)","F",0
535,0,0,0,0.000000," ","integrate((c-c/a/x)^(9/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^(9/2)/(a*x + 1), x)","F",0
536,0,0,0,0.000000," ","integrate((c-c/a/x)^(7/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^(7/2)/(a*x + 1), x)","F",0
537,0,0,0,0.000000," ","integrate((c-c/a/x)^(5/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^(5/2)/(a*x + 1), x)","F",0
538,0,0,0,0.000000," ","integrate((c-c/a/x)^(3/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^(3/2)/(a*x + 1), x)","F",0
539,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/(a*x + 1), x)","F",0
540,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*sqrt(c - c/(a*x))), x)","F",0
541,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a*x))^(3/2)), x)","F",0
542,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a*x))^(5/2)), x)","F",0
543,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a*x))^(7/2)), x)","F",0
544,0,0,0,0.000000," ","integrate((c-c/a/x)^(9/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(c - c/(a*x))^(9/2)/(a*x + 1)^2, x)","F",0
545,0,0,0,0.000000," ","integrate((c-c/a/x)^(7/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(c - c/(a*x))^(7/2)/(a*x + 1)^2, x)","F",0
546,0,0,0,0.000000," ","integrate((c-c/a/x)^(5/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(c - c/(a*x))^(5/2)/(a*x + 1)^2, x)","F",0
547,0,0,0,0.000000," ","integrate((c-c/a/x)^(3/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(c - c/(a*x))^(3/2)/(a*x + 1)^2, x)","F",0
548,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a*x))/(a*x + 1)^2, x)","F",0
549,0,0,0,0.000000," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","-\int \frac{a^{2} x^{2} - 1}{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)/((a*x + 1)^2*sqrt(c - c/(a*x))), x)","F",0
550,0,0,0,0.000000," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","-\int \frac{a^{2} x^{2} - 1}{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)/((a*x + 1)^2*(c - c/(a*x))^(3/2)), x)","F",0
551,0,0,0,0.000000," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","-\int \frac{a^{2} x^{2} - 1}{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)/((a*x + 1)^2*(c - c/(a*x))^(5/2)), x)","F",0
552,0,0,0,0.000000," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^(7/2),x, algorithm=""maxima"")","-\int \frac{a^{2} x^{2} - 1}{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)/((a*x + 1)^2*(c - c/(a*x))^(7/2)), x)","F",0
553,0,0,0,0.000000," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^(9/2),x, algorithm=""maxima"")","-\int \frac{a^{2} x^{2} - 1}{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)/((a*x + 1)^2*(c - c/(a*x))^(9/2)), x)","F",0
554,0,0,0,0.000000," ","integrate((c-c/a/x)^(9/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^(9/2)/(a*x + 1)^3, x)","F",0
555,0,0,0,0.000000," ","integrate((c-c/a/x)^(7/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^(7/2)/(a*x + 1)^3, x)","F",0
556,0,0,0,0.000000," ","integrate((c-c/a/x)^(5/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^(5/2)/(a*x + 1)^3, x)","F",0
557,0,0,0,0.000000," ","integrate((c-c/a/x)^(3/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^(3/2)/(a*x + 1)^3, x)","F",0
558,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a*x))/(a*x + 1)^3, x)","F",0
559,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*sqrt(c - c/(a*x))), x)","F",0
560,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a*x))^(3/2)), x)","F",0
561,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a*x))^(5/2)), x)","F",0
562,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a*x))^(7/2)), x)","F",0
563,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))*x^3), x)","F",0
564,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
565,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}} x^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))*x^2/sqrt(-a^2*x^2 + 1), x)","F",0
566,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}} x}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))*x/sqrt(-a^2*x^2 + 1), x)","F",0
567,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/sqrt(-a^2*x^2 + 1), x)","F",0
568,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
569,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
570,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
571,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(sqrt(-a^2*x^2 + 1)*x^4), x)","F",0
572,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1} x^{5}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(sqrt(-a^2*x^2 + 1)*x^5), x)","F",0
573,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a x}} x^{3}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a*x))*x^3/(a^2*x^2 - 1), x)","F",0
574,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a x}} x^{2}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a*x))*x^2/(a^2*x^2 - 1), x)","F",0
575,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a x}} x}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a*x))*x/(a^2*x^2 - 1), x)","F",0
576,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a x}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a*x))/(a^2*x^2 - 1), x)","F",0
577,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2)/x,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a x}}}{{\left(a^{2} x^{2} - 1\right)} x}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a*x))/((a^2*x^2 - 1)*x), x)","F",0
578,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a x}}}{{\left(a^{2} x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a*x))/((a^2*x^2 - 1)*x^2), x)","F",0
579,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a x}}}{{\left(a^{2} x^{2} - 1\right)} x^{3}}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a*x))/((a^2*x^2 - 1)*x^3), x)","F",0
580,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a x}}}{{\left(a^{2} x^{2} - 1\right)} x^{4}}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a*x))/((a^2*x^2 - 1)*x^4), x)","F",0
581,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a x}}}{{\left(a^{2} x^{2} - 1\right)} x^{5}}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a*x))/((a^2*x^2 - 1)*x^5), x)","F",0
582,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}} x^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a*x))*x^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
583,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}} x^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a*x))*x^2/(-a^2*x^2 + 1)^(3/2), x)","F",0
584,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}} x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a*x))*x/(-a^2*x^2 + 1)^(3/2), x)","F",0
585,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a*x))/(-a^2*x^2 + 1)^(3/2), x)","F",0
586,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a*x))/((-a^2*x^2 + 1)^(3/2)*x), x)","F",0
587,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a*x))/((-a^2*x^2 + 1)^(3/2)*x^2), x)","F",0
588,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a*x))/((-a^2*x^2 + 1)^(3/2)*x^3), x)","F",0
589,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a*x))/((-a^2*x^2 + 1)^(3/2)*x^4), x)","F",0
590,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{5}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a*x))/((-a^2*x^2 + 1)^(3/2)*x^5), x)","F",0
591,0,0,0,0.000000," ","integrate(x^m*(c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))*x^m/(a*x + 1), x)","F",0
592,0,0,0,0.000000," ","integrate(x^2*(c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}} x^{2}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))*x^2/(a*x + 1), x)","F",0
593,0,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}} x}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))*x/(a*x + 1), x)","F",0
594,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/(a*x + 1), x)","F",0
595,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/((a*x + 1)*x), x)","F",0
596,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/((a*x + 1)*x^2), x)","F",0
597,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/((a*x + 1)*x^3), x)","F",0
598,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/((a*x + 1)*x^4), x)","F",0
599,0,0,0,0.000000," ","integrate(x^3*(c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a x}} x^{3}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a*x))*x^3/(a*x + 1)^2, x)","F",0
600,0,0,0,0.000000," ","integrate(x^2*(c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a x}} x^{2}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a*x))*x^2/(a*x + 1)^2, x)","F",0
601,0,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a x}} x}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a*x))*x/(a*x + 1)^2, x)","F",0
602,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a*x))/(a*x + 1)^2, x)","F",0
603,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x,x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{2} x}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a*x))/((a*x + 1)^2*x), x)","F",0
604,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^2,x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{2} x^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a*x))/((a*x + 1)^2*x^2), x)","F",0
605,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^3,x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{2} x^{3}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a*x))/((a*x + 1)^2*x^3), x)","F",0
606,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^4,x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{2} x^{4}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a*x))/((a*x + 1)^2*x^4), x)","F",0
607,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^5,x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{2} x^{5}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a*x))/((a*x + 1)^2*x^5), x)","F",0
608,0,0,0,0.000000," ","integrate(x^3*(c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a x}} x^{3}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a*x))*x^3/(a*x + 1)^3, x)","F",0
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610,0,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a x}} x}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a*x))*x/(a*x + 1)^3, x)","F",0
611,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a*x))/(a*x + 1)^3, x)","F",0
612,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{3} x}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a*x))/((a*x + 1)^3*x), x)","F",0
613,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a*x))/((a*x + 1)^3*x^2), x)","F",0
614,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a*x))/((a*x + 1)^3*x^3), x)","F",0
615,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{3} x^{4}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a*x))/((a*x + 1)^3*x^4), x)","F",0
616,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)}^{3} x^{5}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a*x))/((a*x + 1)^3*x^5), x)","F",0
617,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a/x)^p,x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)}^{p} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a*x))^p*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
618,0,0,0,0.000000," ","integrate((c-c/a/x)^p/exp(2*p*arctanh(a*x)),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{p}}{\left(\frac{a x + 1}{a x - 1}\right)^{p}}\,{d x}"," ",0,"integrate((c - c/(a*x))^p/((a*x + 1)/(a*x - 1))^p, x)","F",0
619,0,0,0,0.000000," ","integrate(exp(2*p*arctanh(a*x))*(c-c/a/x)^p,x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)}^{p} \left(\frac{a x + 1}{a x - 1}\right)^{p}\,{d x}"," ",0,"integrate((c - c/(a*x))^p*((a*x + 1)/(a*x - 1))^p, x)","F",0
620,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a/x)^2,x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)}^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a*x))^2*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
621,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a/x),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a*x))*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
622,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(c-c/a/x),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{c - \frac{c}{a x}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(c - c/(a*x)), x)","F",0
623,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(c-c/a/x)^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(c - \frac{c}{a x}\right)}^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(c - c/(a*x))^2, x)","F",0
624,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a*x))^(3/2)*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
625,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a x}} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
626,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/sqrt(c - c/(a*x)), x)","F",0
627,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(c - c/(a*x))^(3/2), x)","F",0
628,1,515,0,0.420382," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","\frac{c^{4} \arcsin\left(a x\right)}{a} + \frac{4 \, c^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{a} - \frac{3 \, {\left(a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-a^{2} x^{2} + 1}}{x^{2}}\right)} c^{4}}{a^{3}} + \frac{4 \, \sqrt{-a^{2} x^{2} + 1} c^{4}}{a^{2} x} - \frac{2 \, {\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{x} + \frac{\sqrt{-a^{2} x^{2} + 1}}{x^{3}}\right)} c^{4}}{a^{4}} + \frac{{\left(3 \, a^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{3 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{x^{2}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{x^{4}}\right)} c^{4}}{2 \, a^{5}} + \frac{4 \, {\left(\frac{8 \, \sqrt{-a^{2} x^{2} + 1} a^{4}}{x} + \frac{4 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{x^{3}} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1}}{x^{5}}\right)} c^{4}}{15 \, a^{6}} - \frac{{\left(15 \, a^{6} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{15 \, \sqrt{-a^{2} x^{2} + 1} a^{4}}{x^{2}} + \frac{10 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{x^{4}} + \frac{8 \, \sqrt{-a^{2} x^{2} + 1}}{x^{6}}\right)} c^{4}}{48 \, a^{7}} - \frac{{\left(\frac{16 \, \sqrt{-a^{2} x^{2} + 1} a^{6}}{x} + \frac{8 \, \sqrt{-a^{2} x^{2} + 1} a^{4}}{x^{3}} + \frac{6 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{x^{5}} + \frac{5 \, \sqrt{-a^{2} x^{2} + 1}}{x^{7}}\right)} c^{4}}{35 \, a^{8}}"," ",0,"c^4*arcsin(a*x)/a + 4*c^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a - sqrt(-a^2*x^2 + 1)*c^4/a - 3*(a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-a^2*x^2 + 1)/x^2)*c^4/a^3 + 4*sqrt(-a^2*x^2 + 1)*c^4/(a^2*x) - 2*(2*sqrt(-a^2*x^2 + 1)*a^2/x + sqrt(-a^2*x^2 + 1)/x^3)*c^4/a^4 + 1/2*(3*a^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 3*sqrt(-a^2*x^2 + 1)*a^2/x^2 + 2*sqrt(-a^2*x^2 + 1)/x^4)*c^4/a^5 + 4/15*(8*sqrt(-a^2*x^2 + 1)*a^4/x + 4*sqrt(-a^2*x^2 + 1)*a^2/x^3 + 3*sqrt(-a^2*x^2 + 1)/x^5)*c^4/a^6 - 1/48*(15*a^6*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 15*sqrt(-a^2*x^2 + 1)*a^4/x^2 + 10*sqrt(-a^2*x^2 + 1)*a^2/x^4 + 8*sqrt(-a^2*x^2 + 1)/x^6)*c^4/a^7 - 1/35*(16*sqrt(-a^2*x^2 + 1)*a^6/x + 8*sqrt(-a^2*x^2 + 1)*a^4/x^3 + 6*sqrt(-a^2*x^2 + 1)*a^2/x^5 + 5*sqrt(-a^2*x^2 + 1)/x^7)*c^4/a^8","B",0
629,1,332,0,0.416216," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","\frac{c^{3} \arcsin\left(a x\right)}{a} + \frac{3 \, c^{3} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{a} - \frac{3 \, {\left(a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-a^{2} x^{2} + 1}}{x^{2}}\right)} c^{3}}{2 \, a^{3}} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{a^{2} x} - \frac{{\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{x} + \frac{\sqrt{-a^{2} x^{2} + 1}}{x^{3}}\right)} c^{3}}{a^{4}} + \frac{{\left(3 \, a^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{3 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{x^{2}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{x^{4}}\right)} c^{3}}{8 \, a^{5}} + \frac{{\left(\frac{8 \, \sqrt{-a^{2} x^{2} + 1} a^{4}}{x} + \frac{4 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{x^{3}} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1}}{x^{5}}\right)} c^{3}}{15 \, a^{6}}"," ",0,"c^3*arcsin(a*x)/a + 3*c^3*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a - sqrt(-a^2*x^2 + 1)*c^3/a - 3/2*(a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-a^2*x^2 + 1)/x^2)*c^3/a^3 + 3*sqrt(-a^2*x^2 + 1)*c^3/(a^2*x) - (2*sqrt(-a^2*x^2 + 1)*a^2/x + sqrt(-a^2*x^2 + 1)/x^3)*c^3/a^4 + 1/8*(3*a^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 3*sqrt(-a^2*x^2 + 1)*a^2/x^2 + 2*sqrt(-a^2*x^2 + 1)/x^4)*c^3/a^5 + 1/15*(8*sqrt(-a^2*x^2 + 1)*a^4/x + 4*sqrt(-a^2*x^2 + 1)*a^2/x^3 + 3*sqrt(-a^2*x^2 + 1)/x^5)*c^3/a^6","B",0
630,1,189,0,0.410253," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\frac{c^{2} \arcsin\left(a x\right)}{a} + \frac{2 \, c^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a} - \frac{{\left(a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-a^{2} x^{2} + 1}}{x^{2}}\right)} c^{2}}{2 \, a^{3}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c^{2}}{a^{2} x} - \frac{{\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{2}}{x} + \frac{\sqrt{-a^{2} x^{2} + 1}}{x^{3}}\right)} c^{2}}{3 \, a^{4}}"," ",0,"c^2*arcsin(a*x)/a + 2*c^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a - sqrt(-a^2*x^2 + 1)*c^2/a - 1/2*(a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-a^2*x^2 + 1)/x^2)*c^2/a^3 + 2*sqrt(-a^2*x^2 + 1)*c^2/(a^2*x) - 1/3*(2*sqrt(-a^2*x^2 + 1)*a^2/x + sqrt(-a^2*x^2 + 1)/x^3)*c^2/a^4","B",0
631,1,79,0,0.402952," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2),x, algorithm=""maxima"")","\frac{c \arcsin\left(a x\right)}{a} + \frac{c \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} c}{a} + \frac{\sqrt{-a^{2} x^{2} + 1} c}{a^{2} x}"," ",0,"c*arcsin(a*x)/a + c*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x))/a - sqrt(-a^2*x^2 + 1)*c/a + sqrt(-a^2*x^2 + 1)*c/(a^2*x)","A",0
632,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))), x)","F",0
633,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^2), x)","F",0
634,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^3), x)","F",0
635,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{4}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^4), x)","F",0
636,1,115,0,0.306833," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^5,x, algorithm=""maxima"")","-c^{5} x - \frac{2 \, c^{5} \log\left(x\right)}{a} - \frac{3780 \, a^{8} c^{5} x^{8} + 5040 \, a^{7} c^{5} x^{7} - 840 \, a^{6} c^{5} x^{6} - 3780 \, a^{5} c^{5} x^{5} - 504 \, a^{4} c^{5} x^{4} + 1680 \, a^{3} c^{5} x^{3} + 540 \, a^{2} c^{5} x^{2} - 315 \, a c^{5} x - 140 \, c^{5}}{1260 \, a^{10} x^{9}}"," ",0,"-c^5*x - 2*c^5*log(x)/a - 1/1260*(3780*a^8*c^5*x^8 + 5040*a^7*c^5*x^7 - 840*a^6*c^5*x^6 - 3780*a^5*c^5*x^5 - 504*a^4*c^5*x^4 + 1680*a^3*c^5*x^3 + 540*a^2*c^5*x^2 - 315*a*c^5*x - 140*c^5)/(a^10*x^9)","A",0
637,1,82,0,0.314230," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","-c^{4} x - \frac{2 \, c^{4} \log\left(x\right)}{a} - \frac{420 \, a^{6} c^{4} x^{6} + 630 \, a^{5} c^{4} x^{5} - 315 \, a^{3} c^{4} x^{3} - 84 \, a^{2} c^{4} x^{2} + 70 \, a c^{4} x + 30 \, c^{4}}{210 \, a^{8} x^{7}}"," ",0,"-c^4*x - 2*c^4*log(x)/a - 1/210*(420*a^6*c^4*x^6 + 630*a^5*c^4*x^5 - 315*a^3*c^4*x^3 - 84*a^2*c^4*x^2 + 70*a*c^4*x + 30*c^4)/(a^8*x^7)","A",0
638,1,71,0,0.308903," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","-c^{3} x - \frac{2 \, c^{3} \log\left(x\right)}{a} - \frac{30 \, a^{4} c^{3} x^{4} + 60 \, a^{3} c^{3} x^{3} + 10 \, a^{2} c^{3} x^{2} - 15 \, a c^{3} x - 6 \, c^{3}}{30 \, a^{6} x^{5}}"," ",0,"-c^3*x - 2*c^3*log(x)/a - 1/30*(30*a^4*c^3*x^4 + 60*a^3*c^3*x^3 + 10*a^2*c^3*x^2 - 15*a*c^3*x - 6*c^3)/(a^6*x^5)","A",0
639,1,36,0,0.311973," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","-c^{2} x - \frac{2 \, c^{2} \log\left(x\right)}{a} - \frac{3 \, a c^{2} x + c^{2}}{3 \, a^{4} x^{3}}"," ",0,"-c^2*x - 2*c^2*log(x)/a - 1/3*(3*a*c^2*x + c^2)/(a^4*x^3)","A",0
640,1,21,0,0.307018," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2),x, algorithm=""maxima"")","-c x - \frac{2 \, c \log\left(x\right)}{a} + \frac{c}{a^{2} x}"," ",0,"-c*x - 2*c*log(x)/a + c/(a^2*x)","A",0
641,1,34,0,0.304414," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2),x, algorithm=""maxima"")","-\frac{x}{c} + \frac{1}{a^{2} c x - a c} - \frac{2 \, \log\left(a x - 1\right)}{a c}"," ",0,"-x/c + 1/(a^2*c*x - a*c) - 2*log(a*x - 1)/(a*c)","A",0
642,1,70,0,0.306153," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\frac{7 \, a x - 6}{4 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}} - \frac{x}{c^{2}} + \frac{\log\left(a x + 1\right)}{8 \, a c^{2}} - \frac{17 \, \log\left(a x - 1\right)}{8 \, a c^{2}}"," ",0,"1/4*(7*a*x - 6)/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2) - x/c^2 + 1/8*log(a*x + 1)/(a*c^2) - 17/8*log(a*x - 1)/(a*c^2)","A",0
643,1,98,0,0.306603," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","\frac{15 \, a^{3} x^{3} - 12 \, a^{2} x^{2} - 13 \, a x + 11}{6 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{4} c^{3} x^{3} + 2 \, a^{2} c^{3} x - a c^{3}\right)}} - \frac{x}{c^{3}} + \frac{\log\left(a x + 1\right)}{4 \, a c^{3}} - \frac{9 \, \log\left(a x - 1\right)}{4 \, a c^{3}}"," ",0,"1/6*(15*a^3*x^3 - 12*a^2*x^2 - 13*a*x + 11)/(a^5*c^3*x^4 - 2*a^4*c^3*x^3 + 2*a^2*c^3*x - a*c^3) - x/c^3 + 1/4*log(a*x + 1)/(a*c^3) - 9/4*log(a*x - 1)/(a*c^3)","A",0
644,1,146,0,0.307825," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","\frac{627 \, a^{5} x^{5} - 486 \, a^{4} x^{4} - 1058 \, a^{3} x^{3} + 874 \, a^{2} x^{2} + 467 \, a x - 400}{192 \, {\left(a^{7} c^{4} x^{6} - 2 \, a^{6} c^{4} x^{5} - a^{5} c^{4} x^{4} + 4 \, a^{4} c^{4} x^{3} - a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}} - \frac{x}{c^{4}} + \frac{47 \, \log\left(a x + 1\right)}{128 \, a c^{4}} - \frac{303 \, \log\left(a x - 1\right)}{128 \, a c^{4}}"," ",0,"1/192*(627*a^5*x^5 - 486*a^4*x^4 - 1058*a^3*x^3 + 874*a^2*x^2 + 467*a*x - 400)/(a^7*c^4*x^6 - 2*a^6*c^4*x^5 - a^5*c^4*x^4 + 4*a^4*c^4*x^3 - a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4) - x/c^4 + 47/128*log(a*x + 1)/(a*c^4) - 303/128*log(a*x - 1)/(a*c^4)","A",0
645,1,745,0,0.420670," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","-a^{3} c^{4} {\left(\frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{2}{\sqrt{-a^{2} x^{2} + 1} a^{4}}\right)} + 3 \, a^{2} c^{4} {\left(\frac{x}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}\right)} - \frac{11 \, c^{4} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{6 \, c^{4} {\left(\frac{1}{\sqrt{-a^{2} x^{2} + 1}} - \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)\right)}}{a} + \frac{14 \, {\left(\frac{2 \, a^{2} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x}\right)} c^{4}}{a^{2}} - \frac{c^{4}}{\sqrt{-a^{2} x^{2} + 1} a} - \frac{7 \, {\left(3 \, a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{3 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\right)} c^{4}}{a^{3}} - \frac{2 \, {\left(\frac{8 \, a^{4} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{4 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1} x} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\right)} c^{4}}{a^{4}} + \frac{11 \, {\left(15 \, a^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{15 \, a^{4}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{5 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1} x^{2}} + \frac{2}{\sqrt{-a^{2} x^{2} + 1} x^{4}}\right)} c^{4}}{8 \, a^{5}} - \frac{{\left(\frac{16 \, a^{6} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{8 \, a^{4}}{\sqrt{-a^{2} x^{2} + 1} x} - \frac{2 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1} x^{3}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{5}}\right)} c^{4}}{5 \, a^{6}} - \frac{{\left(105 \, a^{6} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{105 \, a^{6}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{35 \, a^{4}}{\sqrt{-a^{2} x^{2} + 1} x^{2}} + \frac{14 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1} x^{4}} + \frac{8}{\sqrt{-a^{2} x^{2} + 1} x^{6}}\right)} c^{4}}{16 \, a^{7}} + \frac{{\left(\frac{128 \, a^{8} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{64 \, a^{6}}{\sqrt{-a^{2} x^{2} + 1} x} - \frac{16 \, a^{4}}{\sqrt{-a^{2} x^{2} + 1} x^{3}} - \frac{8 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1} x^{5}} - \frac{5}{\sqrt{-a^{2} x^{2} + 1} x^{7}}\right)} c^{4}}{35 \, a^{8}}"," ",0,"-a^3*c^4*(x^2/(sqrt(-a^2*x^2 + 1)*a^2) - 2/(sqrt(-a^2*x^2 + 1)*a^4)) + 3*a^2*c^4*(x/(sqrt(-a^2*x^2 + 1)*a^2) - arcsin(a*x)/a^3) - 11*c^4*x/sqrt(-a^2*x^2 + 1) - 6*c^4*(1/sqrt(-a^2*x^2 + 1) - log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)))/a + 14*(2*a^2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*x))*c^4/a^2 - c^4/(sqrt(-a^2*x^2 + 1)*a) - 7*(3*a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 3*a^2/sqrt(-a^2*x^2 + 1) + 1/(sqrt(-a^2*x^2 + 1)*x^2))*c^4/a^3 - 2*(8*a^4*x/sqrt(-a^2*x^2 + 1) - 4*a^2/(sqrt(-a^2*x^2 + 1)*x) - 1/(sqrt(-a^2*x^2 + 1)*x^3))*c^4/a^4 + 11/8*(15*a^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 15*a^4/sqrt(-a^2*x^2 + 1) + 5*a^2/(sqrt(-a^2*x^2 + 1)*x^2) + 2/(sqrt(-a^2*x^2 + 1)*x^4))*c^4/a^5 - 1/5*(16*a^6*x/sqrt(-a^2*x^2 + 1) - 8*a^4/(sqrt(-a^2*x^2 + 1)*x) - 2*a^2/(sqrt(-a^2*x^2 + 1)*x^3) - 1/(sqrt(-a^2*x^2 + 1)*x^5))*c^4/a^6 - 1/16*(105*a^6*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 105*a^6/sqrt(-a^2*x^2 + 1) + 35*a^4/(sqrt(-a^2*x^2 + 1)*x^2) + 14*a^2/(sqrt(-a^2*x^2 + 1)*x^4) + 8/(sqrt(-a^2*x^2 + 1)*x^6))*c^4/a^7 + 1/35*(128*a^8*x/sqrt(-a^2*x^2 + 1) - 64*a^6/(sqrt(-a^2*x^2 + 1)*x) - 16*a^4/(sqrt(-a^2*x^2 + 1)*x^3) - 8*a^2/(sqrt(-a^2*x^2 + 1)*x^5) - 5/(sqrt(-a^2*x^2 + 1)*x^7))*c^4/a^8","B",0
646,1,443,0,0.421094," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","-a^{3} c^{3} {\left(\frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{2}{\sqrt{-a^{2} x^{2} + 1} a^{4}}\right)} + 3 \, a^{2} c^{3} {\left(\frac{x}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}\right)} - \frac{8 \, c^{3} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{6 \, c^{3} {\left(\frac{1}{\sqrt{-a^{2} x^{2} + 1}} - \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)\right)}}{a} + \frac{6 \, {\left(\frac{2 \, a^{2} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x}\right)} c^{3}}{a^{2}} - \frac{4 \, {\left(3 \, a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{3 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\right)} c^{3}}{a^{3}} + \frac{3 \, {\left(15 \, a^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{15 \, a^{4}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{5 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1} x^{2}} + \frac{2}{\sqrt{-a^{2} x^{2} + 1} x^{4}}\right)} c^{3}}{8 \, a^{5}} - \frac{{\left(\frac{16 \, a^{6} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{8 \, a^{4}}{\sqrt{-a^{2} x^{2} + 1} x} - \frac{2 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1} x^{3}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{5}}\right)} c^{3}}{5 \, a^{6}}"," ",0,"-a^3*c^3*(x^2/(sqrt(-a^2*x^2 + 1)*a^2) - 2/(sqrt(-a^2*x^2 + 1)*a^4)) + 3*a^2*c^3*(x/(sqrt(-a^2*x^2 + 1)*a^2) - arcsin(a*x)/a^3) - 8*c^3*x/sqrt(-a^2*x^2 + 1) - 6*c^3*(1/sqrt(-a^2*x^2 + 1) - log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)))/a + 6*(2*a^2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*x))*c^3/a^2 - 4*(3*a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 3*a^2/sqrt(-a^2*x^2 + 1) + 1/(sqrt(-a^2*x^2 + 1)*x^2))*c^3/a^3 + 3/8*(15*a^4*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 15*a^4/sqrt(-a^2*x^2 + 1) + 5*a^2/(sqrt(-a^2*x^2 + 1)*x^2) + 2/(sqrt(-a^2*x^2 + 1)*x^4))*c^3/a^5 - 1/5*(16*a^6*x/sqrt(-a^2*x^2 + 1) - 8*a^4/(sqrt(-a^2*x^2 + 1)*x) - 2*a^2/(sqrt(-a^2*x^2 + 1)*x^3) - 1/(sqrt(-a^2*x^2 + 1)*x^5))*c^3/a^6","B",0
647,1,347,0,0.416377," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","-a^{3} c^{2} {\left(\frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{2}{\sqrt{-a^{2} x^{2} + 1} a^{4}}\right)} + 3 \, a^{2} c^{2} {\left(\frac{x}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}\right)} - \frac{5 \, c^{2} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{5 \, c^{2} {\left(\frac{1}{\sqrt{-a^{2} x^{2} + 1}} - \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)\right)}}{a} + \frac{{\left(\frac{2 \, a^{2} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x}\right)} c^{2}}{a^{2}} + \frac{c^{2}}{\sqrt{-a^{2} x^{2} + 1} a} - \frac{3 \, {\left(3 \, a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{3 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\right)} c^{2}}{2 \, a^{3}} + \frac{{\left(\frac{8 \, a^{4} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{4 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1} x} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\right)} c^{2}}{3 \, a^{4}}"," ",0,"-a^3*c^2*(x^2/(sqrt(-a^2*x^2 + 1)*a^2) - 2/(sqrt(-a^2*x^2 + 1)*a^4)) + 3*a^2*c^2*(x/(sqrt(-a^2*x^2 + 1)*a^2) - arcsin(a*x)/a^3) - 5*c^2*x/sqrt(-a^2*x^2 + 1) - 5*c^2*(1/sqrt(-a^2*x^2 + 1) - log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)))/a + (2*a^2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*x))*c^2/a^2 + c^2/(sqrt(-a^2*x^2 + 1)*a) - 3/2*(3*a^2*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 3*a^2/sqrt(-a^2*x^2 + 1) + 1/(sqrt(-a^2*x^2 + 1)*x^2))*c^2/a^3 + 1/3*(8*a^4*x/sqrt(-a^2*x^2 + 1) - 4*a^2/(sqrt(-a^2*x^2 + 1)*x) - 1/(sqrt(-a^2*x^2 + 1)*x^3))*c^2/a^4","B",0
648,1,200,0,0.424889," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2),x, algorithm=""maxima"")","-a^{3} c {\left(\frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{2}{\sqrt{-a^{2} x^{2} + 1} a^{4}}\right)} + 3 \, a^{2} c {\left(\frac{x}{\sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}\right)} - \frac{2 \, c x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{3 \, c {\left(\frac{1}{\sqrt{-a^{2} x^{2} + 1}} - \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)\right)}}{a} - \frac{{\left(\frac{2 \, a^{2} x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{1}{\sqrt{-a^{2} x^{2} + 1} x}\right)} c}{a^{2}} + \frac{2 \, c}{\sqrt{-a^{2} x^{2} + 1} a}"," ",0,"-a^3*c*(x^2/(sqrt(-a^2*x^2 + 1)*a^2) - 2/(sqrt(-a^2*x^2 + 1)*a^4)) + 3*a^2*c*(x/(sqrt(-a^2*x^2 + 1)*a^2) - arcsin(a*x)/a^3) - 2*c*x/sqrt(-a^2*x^2 + 1) - 3*c*(1/sqrt(-a^2*x^2 + 1) - log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)))/a - (2*a^2*x/sqrt(-a^2*x^2 + 1) - 1/(sqrt(-a^2*x^2 + 1)*x))*c/a^2 + 2*c/(sqrt(-a^2*x^2 + 1)*a)","B",0
649,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))), x)","F",0
650,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^2), x)","F",0
651,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{3}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^3), x)","F",0
652,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{4}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^4), x)","F",0
653,1,103,0,0.311570," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^5,x, algorithm=""maxima"")","c^{5} x + \frac{4 \, c^{5} \log\left(x\right)}{a} - \frac{1890 \, a^{8} c^{5} x^{8} - 2520 \, a^{7} c^{5} x^{7} - 2940 \, a^{6} c^{5} x^{6} + 1764 \, a^{4} c^{5} x^{4} + 840 \, a^{3} c^{5} x^{3} - 270 \, a^{2} c^{5} x^{2} - 315 \, a c^{5} x - 70 \, c^{5}}{630 \, a^{10} x^{9}}"," ",0,"c^5*x + 4*c^5*log(x)/a - 1/630*(1890*a^8*c^5*x^8 - 2520*a^7*c^5*x^7 - 2940*a^6*c^5*x^6 + 1764*a^4*c^5*x^4 + 840*a^3*c^5*x^3 - 270*a^2*c^5*x^2 - 315*a*c^5*x - 70*c^5)/(a^10*x^9)","A",0
654,1,92,0,0.303438," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","c^{4} x + \frac{4 \, c^{4} \log\left(x\right)}{a} - \frac{420 \, a^{6} c^{4} x^{6} - 210 \, a^{5} c^{4} x^{5} - 350 \, a^{4} c^{4} x^{4} - 105 \, a^{3} c^{4} x^{3} + 84 \, a^{2} c^{4} x^{2} + 70 \, a c^{4} x + 15 \, c^{4}}{105 \, a^{8} x^{7}}"," ",0,"c^4*x + 4*c^4*log(x)/a - 1/105*(420*a^6*c^4*x^6 - 210*a^5*c^4*x^5 - 350*a^4*c^4*x^4 - 105*a^3*c^4*x^3 + 84*a^2*c^4*x^2 + 70*a*c^4*x + 15*c^4)/(a^8*x^7)","A",0
655,1,59,0,0.308337," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","c^{3} x + \frac{4 \, c^{3} \log\left(x\right)}{a} - \frac{75 \, a^{4} c^{3} x^{4} - 25 \, a^{2} c^{3} x^{2} - 15 \, a c^{3} x - 3 \, c^{3}}{15 \, a^{6} x^{5}}"," ",0,"c^3*x + 4*c^3*log(x)/a - 1/15*(75*a^4*c^3*x^4 - 25*a^2*c^3*x^2 - 15*a*c^3*x - 3*c^3)/(a^6*x^5)","A",0
656,1,46,0,0.302490," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","c^{2} x + \frac{4 \, c^{2} \log\left(x\right)}{a} - \frac{18 \, a^{2} c^{2} x^{2} + 6 \, a c^{2} x + c^{2}}{3 \, a^{4} x^{3}}"," ",0,"c^2*x + 4*c^2*log(x)/a - 1/3*(18*a^2*c^2*x^2 + 6*a*c^2*x + c^2)/(a^4*x^3)","A",0
657,1,32,0,0.304061," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2),x, algorithm=""maxima"")","c x + \frac{8 \, c \log\left(a x - 1\right)}{a} - \frac{4 \, c \log\left(x\right)}{a} + \frac{c}{a^{2} x}"," ",0,"c*x + 8*c*log(a*x - 1)/a - 4*c*log(x)/a + c/(a^2*x)","A",0
658,1,49,0,0.308397," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2),x, algorithm=""maxima"")","-\frac{5 \, a x - 4}{a^{3} c x^{2} - 2 \, a^{2} c x + a c} + \frac{x}{c} + \frac{4 \, \log\left(a x - 1\right)}{a c}"," ",0,"-(5*a*x - 4)/(a^3*c*x^2 - 2*a^2*c*x + a*c) + x/c + 4*log(a*x - 1)/(a*c)","A",0
659,1,75,0,0.311499," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","-\frac{18 \, a^{2} x^{2} - 30 \, a x + 13}{3 \, {\left(a^{4} c^{2} x^{3} - 3 \, a^{3} c^{2} x^{2} + 3 \, a^{2} c^{2} x - a c^{2}\right)}} + \frac{x}{c^{2}} + \frac{4 \, \log\left(a x - 1\right)}{a c^{2}}"," ",0,"-1/3*(18*a^2*x^2 - 30*a*x + 13)/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2) + x/c^2 + 4*log(a*x - 1)/(a*c^2)","A",0
660,1,107,0,0.312910," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","-\frac{333 \, a^{3} x^{3} - 852 \, a^{2} x^{2} + 749 \, a x - 224}{48 \, {\left(a^{5} c^{3} x^{4} - 4 \, a^{4} c^{3} x^{3} + 6 \, a^{3} c^{3} x^{2} - 4 \, a^{2} c^{3} x + a c^{3}\right)}} + \frac{x}{c^{3}} - \frac{\log\left(a x + 1\right)}{32 \, a c^{3}} + \frac{129 \, \log\left(a x - 1\right)}{32 \, a c^{3}}"," ",0,"-1/48*(333*a^3*x^3 - 852*a^2*x^2 + 749*a*x - 224)/(a^5*c^3*x^4 - 4*a^4*c^3*x^3 + 6*a^3*c^3*x^2 - 4*a^2*c^3*x + a*c^3) + x/c^3 - 1/32*log(a*x + 1)/(a*c^3) + 129/32*log(a*x - 1)/(a*c^3)","A",0
661,1,135,0,0.318180," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","-\frac{3765 \, a^{5} x^{5} - 9300 \, a^{4} x^{4} + 4400 \, a^{3} x^{3} + 6820 \, a^{2} x^{2} - 8021 \, a x + 2384}{480 \, {\left(a^{7} c^{4} x^{6} - 4 \, a^{6} c^{4} x^{5} + 5 \, a^{5} c^{4} x^{4} - 5 \, a^{3} c^{4} x^{2} + 4 \, a^{2} c^{4} x - a c^{4}\right)}} + \frac{x}{c^{4}} - \frac{5 \, \log\left(a x + 1\right)}{64 \, a c^{4}} + \frac{261 \, \log\left(a x - 1\right)}{64 \, a c^{4}}"," ",0,"-1/480*(3765*a^5*x^5 - 9300*a^4*x^4 + 4400*a^3*x^3 + 6820*a^2*x^2 - 8021*a*x + 2384)/(a^7*c^4*x^6 - 4*a^6*c^4*x^5 + 5*a^5*c^4*x^4 - 5*a^3*c^4*x^2 + 4*a^2*c^4*x - a*c^4) + x/c^4 - 5/64*log(a*x + 1)/(a*c^4) + 261/64*log(a*x - 1)/(a*c^4)","A",0
662,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^4/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","c^{4} {\left(\frac{\arcsin\left(a x\right)}{a} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a}\right)} - \int \frac{{\left(4 \, a^{6} c^{4} x^{6} - 6 \, a^{4} c^{4} x^{4} + 4 \, a^{2} c^{4} x^{2} - c^{4}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{a^{9} x^{9} + a^{8} x^{8}}\,{d x}"," ",0,"c^4*(arcsin(a*x)/a + sqrt(-a^2*x^2 + 1)/a) - integrate((4*a^6*c^4*x^6 - 6*a^4*c^4*x^4 + 4*a^2*c^4*x^2 - c^4)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^9*x^9 + a^8*x^8), x)","F",0
663,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","c^{3} {\left(\frac{\arcsin\left(a x\right)}{a} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a}\right)} - \int \frac{{\left(3 \, a^{4} c^{3} x^{4} - 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{a^{7} x^{7} + a^{6} x^{6}}\,{d x}"," ",0,"c^3*(arcsin(a*x)/a + sqrt(-a^2*x^2 + 1)/a) - integrate((3*a^4*c^3*x^4 - 3*a^2*c^3*x^2 + c^3)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^7*x^7 + a^6*x^6), x)","F",0
664,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","c^{2} {\left(\frac{\arcsin\left(a x\right)}{a} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a}\right)} - \int \frac{{\left(2 \, a^{2} c^{2} x^{2} - c^{2}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{a^{5} x^{5} + a^{4} x^{4}}\,{d x}"," ",0,"c^2*(arcsin(a*x)/a + sqrt(-a^2*x^2 + 1)/a) - integrate((2*a^2*c^2*x^2 - c^2)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^5*x^5 + a^4*x^4), x)","F",0
665,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","c {\left(\frac{\arcsin\left(a x\right)}{a} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a}\right)} - c \int \frac{\sqrt{a x + 1} \sqrt{-a x + 1}}{a^{3} x^{3} + a^{2} x^{2}}\,{d x}"," ",0,"c*(arcsin(a*x)/a + sqrt(-a^2*x^2 + 1)/a) - c*integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^3*x^3 + a^2*x^2), x)","F",0
666,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))), x)","F",0
667,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^2), x)","F",0
668,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^3), x)","F",0
669,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^4), x)","F",0
670,1,82,0,0.305959," ","integrate((c-c/a^2/x^2)^4/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-c^{4} x + \frac{2 \, c^{4} \log\left(x\right)}{a} - \frac{420 \, a^{6} c^{4} x^{6} - 630 \, a^{5} c^{4} x^{5} + 315 \, a^{3} c^{4} x^{3} - 84 \, a^{2} c^{4} x^{2} - 70 \, a c^{4} x + 30 \, c^{4}}{210 \, a^{8} x^{7}}"," ",0,"-c^4*x + 2*c^4*log(x)/a - 1/210*(420*a^6*c^4*x^6 - 630*a^5*c^4*x^5 + 315*a^3*c^4*x^3 - 84*a^2*c^4*x^2 - 70*a*c^4*x + 30*c^4)/(a^8*x^7)","A",0
671,1,71,0,0.491164," ","integrate((c-c/a^2/x^2)^3/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-c^{3} x + \frac{2 \, c^{3} \log\left(x\right)}{a} - \frac{30 \, a^{4} c^{3} x^{4} - 60 \, a^{3} c^{3} x^{3} + 10 \, a^{2} c^{3} x^{2} + 15 \, a c^{3} x - 6 \, c^{3}}{30 \, a^{6} x^{5}}"," ",0,"-c^3*x + 2*c^3*log(x)/a - 1/30*(30*a^4*c^3*x^4 - 60*a^3*c^3*x^3 + 10*a^2*c^3*x^2 + 15*a*c^3*x - 6*c^3)/(a^6*x^5)","A",0
672,1,38,0,0.305568," ","integrate((c-c/a^2/x^2)^2/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-c^{2} x + \frac{2 \, c^{2} \log\left(x\right)}{a} + \frac{3 \, a c^{2} x - c^{2}}{3 \, a^{4} x^{3}}"," ",0,"-c^2*x + 2*c^2*log(x)/a + 1/3*(3*a*c^2*x - c^2)/(a^4*x^3)","A",0
673,1,21,0,0.301754," ","integrate((c-c/a^2/x^2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-c x + \frac{2 \, c \log\left(x\right)}{a} + \frac{c}{a^{2} x}"," ",0,"-c*x + 2*c*log(x)/a + c/(a^2*x)","A",0
674,1,33,0,0.304039," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2),x, algorithm=""maxima"")","-\frac{x}{c} + \frac{1}{a^{2} c x + a c} + \frac{2 \, \log\left(a x + 1\right)}{a c}"," ",0,"-x/c + 1/(a^2*c*x + a*c) + 2*log(a*x + 1)/(a*c)","A",0
675,1,70,0,0.306212," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\frac{7 \, a x + 6}{4 \, {\left(a^{3} c^{2} x^{2} + 2 \, a^{2} c^{2} x + a c^{2}\right)}} - \frac{x}{c^{2}} + \frac{17 \, \log\left(a x + 1\right)}{8 \, a c^{2}} - \frac{\log\left(a x - 1\right)}{8 \, a c^{2}}"," ",0,"1/4*(7*a*x + 6)/(a^3*c^2*x^2 + 2*a^2*c^2*x + a*c^2) - x/c^2 + 17/8*log(a*x + 1)/(a*c^2) - 1/8*log(a*x - 1)/(a*c^2)","A",0
676,1,98,0,0.309874," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","\frac{15 \, a^{3} x^{3} + 12 \, a^{2} x^{2} - 13 \, a x - 11}{6 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{3} - 2 \, a^{2} c^{3} x - a c^{3}\right)}} - \frac{x}{c^{3}} + \frac{9 \, \log\left(a x + 1\right)}{4 \, a c^{3}} - \frac{\log\left(a x - 1\right)}{4 \, a c^{3}}"," ",0,"1/6*(15*a^3*x^3 + 12*a^2*x^2 - 13*a*x - 11)/(a^5*c^3*x^4 + 2*a^4*c^3*x^3 - 2*a^2*c^3*x - a*c^3) - x/c^3 + 9/4*log(a*x + 1)/(a*c^3) - 1/4*log(a*x - 1)/(a*c^3)","A",0
677,1,146,0,0.312266," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","\frac{627 \, a^{5} x^{5} + 486 \, a^{4} x^{4} - 1058 \, a^{3} x^{3} - 874 \, a^{2} x^{2} + 467 \, a x + 400}{192 \, {\left(a^{7} c^{4} x^{6} + 2 \, a^{6} c^{4} x^{5} - a^{5} c^{4} x^{4} - 4 \, a^{4} c^{4} x^{3} - a^{3} c^{4} x^{2} + 2 \, a^{2} c^{4} x + a c^{4}\right)}} - \frac{x}{c^{4}} + \frac{303 \, \log\left(a x + 1\right)}{128 \, a c^{4}} - \frac{47 \, \log\left(a x - 1\right)}{128 \, a c^{4}}"," ",0,"1/192*(627*a^5*x^5 + 486*a^4*x^4 - 1058*a^3*x^3 - 874*a^2*x^2 + 467*a*x + 400)/(a^7*c^4*x^6 + 2*a^6*c^4*x^5 - a^5*c^4*x^4 - 4*a^4*c^4*x^3 - a^3*c^4*x^2 + 2*a^2*c^4*x + a*c^4) - x/c^4 + 303/128*log(a*x + 1)/(a*c^4) - 47/128*log(a*x - 1)/(a*c^4)","A",0
678,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^4/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{4}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^4/(a*x + 1)^3, x)","F",0
679,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{3}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^3/(a*x + 1)^3, x)","F",0
680,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^2/(a*x + 1)^3, x)","F",0
681,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))/(a*x + 1)^3, x)","F",0
682,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a^2*x^2))), x)","F",0
683,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a^2*x^2))^2), x)","F",0
684,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a^2*x^2))^3), x)","F",0
685,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{4}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a^2*x^2))^4), x)","F",0
686,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^(9/2)/sqrt(-a^2*x^2 + 1), x)","F",0
687,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^(7/2)/sqrt(-a^2*x^2 + 1), x)","F",0
688,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^(5/2)/sqrt(-a^2*x^2 + 1), x)","F",0
689,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^(3/2)/sqrt(-a^2*x^2 + 1), x)","F",0
690,1,17,0,0.389729," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-i \, \sqrt{c} x - \frac{i \, \sqrt{c} \log\left(x\right)}{a}"," ",0,"-I*sqrt(c)*x - I*sqrt(c)*log(x)/a","C",0
691,1,21,0,0.433204," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\frac{i \, x}{\sqrt{c}} - \frac{i \, \log\left(a x - 1\right)}{a \sqrt{c}}"," ",0,"-I*x/sqrt(c) - I*log(a*x - 1)/(a*sqrt(c))","C",0
692,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(3/2)), x)","F",0
693,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
694,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
695,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(9/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*(c - c/(a^2*x^2))^(9/2)/(a^2*x^2 - 1), x)","F",0
696,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*(c - c/(a^2*x^2))^(7/2)/(a^2*x^2 - 1), x)","F",0
697,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*(c - c/(a^2*x^2))^(5/2)/(a^2*x^2 - 1), x)","F",0
698,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*(c - c/(a^2*x^2))^(3/2)/(a^2*x^2 - 1), x)","F",0
699,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a^2*x^2))/(a^2*x^2 - 1), x)","F",0
700,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))), x)","F",0
701,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(3/2)), x)","F",0
702,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
703,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
704,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(9/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(9/2)), x)","F",0
705,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a^2*x^2))^(9/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
706,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a^2*x^2))^(7/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
707,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a^2*x^2))^(5/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
708,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a^2*x^2))^(3/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
709,1,148,0,0.449406," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{3} {\left(-\frac{2 i \, \sqrt{c} x}{a^{3}} + \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{4}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{4}}\right)} - \frac{3}{2} \, a^{2} {\left(-\frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{3}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{3}}\right)} - \frac{3}{2} \, a {\left(\frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{2}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{2}}\right)} + \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{2 \, a} + \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{2 \, a} - \frac{i \, \sqrt{c} \log\left(x\right)}{a}"," ",0,"-1/2*a^3*(-2*I*sqrt(c)*x/a^3 + I*sqrt(c)*log(a*x + 1)/a^4 - I*sqrt(c)*log(a*x - 1)/a^4) - 3/2*a^2*(-I*sqrt(c)*log(a*x + 1)/a^3 - I*sqrt(c)*log(a*x - 1)/a^3) - 3/2*a*(I*sqrt(c)*log(a*x + 1)/a^2 - I*sqrt(c)*log(a*x - 1)/a^2) + 1/2*I*sqrt(c)*log(a*x + 1)/a + 1/2*I*sqrt(c)*log(a*x - 1)/a - I*sqrt(c)*log(x)/a","C",0
710,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\frac{i}{2 \, {\left(a x + 1\right)} {\left(a x - 1\right)} a \sqrt{c}} - \int \frac{a^{4} x^{4} + 3 \, a^{3} x^{3} + 3 \, a^{2} x^{2}}{{\left(i \, a^{2} \sqrt{c} x^{2} - i \, \sqrt{c}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}\,{d x}"," ",0,"-1/2*I/((a*x + 1)*(a*x - 1)*a*sqrt(c)) - integrate((a^4*x^4 + 3*a^3*x^3 + 3*a^2*x^2)/((I*a^2*sqrt(c)*x^2 - I*sqrt(c))*(a*x + 1)*(a*x - 1)), x)","F",0
711,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(3/2)), x)","F",0
712,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
713,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
714,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(9/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(9/2)/(a*x + 1), x)","F",0
715,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(7/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(7/2)/(a*x + 1), x)","F",0
716,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(5/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(5/2)/(a*x + 1), x)","F",0
717,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(3/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(3/2)/(a*x + 1), x)","F",0
718,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a^2*x^2))/(a*x + 1), x)","F",0
719,1,21,0,0.376184," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\frac{i \, x}{\sqrt{c}} - \frac{i \, \log\left(a x + 1\right)}{a \sqrt{c}}"," ",0,"I*x/sqrt(c) - I*log(a*x + 1)/(a*sqrt(c))","C",0
720,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^(3/2)), x)","F",0
721,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
722,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
723,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(9/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(9/2)/(a*x + 1)^2, x)","F",0
724,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(7/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(7/2)/(a*x + 1)^2, x)","F",0
725,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(5/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(5/2)/(a*x + 1)^2, x)","F",0
726,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(3/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(3/2)/(a*x + 1)^2, x)","F",0
727,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))/(a*x + 1)^2, x)","F",0
728,0,0,0,0.000000," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\int \frac{a^{2} x^{2} - 1}{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)/((a*x + 1)^2*sqrt(c - c/(a^2*x^2))), x)","F",0
729,0,0,0,0.000000," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","-\int \frac{a^{2} x^{2} - 1}{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)/((a*x + 1)^2*(c - c/(a^2*x^2))^(3/2)), x)","F",0
730,0,0,0,0.000000," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","-\int \frac{a^{2} x^{2} - 1}{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)/((a*x + 1)^2*(c - c/(a^2*x^2))^(5/2)), x)","F",0
731,0,0,0,0.000000," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","-\int \frac{a^{2} x^{2} - 1}{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)/((a*x + 1)^2*(c - c/(a^2*x^2))^(7/2)), x)","F",0
732,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(9/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(9/2)/(a*x + 1)^3, x)","F",0
733,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(7/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(7/2)/(a*x + 1)^3, x)","F",0
734,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(5/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(5/2)/(a*x + 1)^3, x)","F",0
735,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(3/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(3/2)/(a*x + 1)^3, x)","F",0
736,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/(a*x + 1)^3, x)","F",0
737,1,53,0,0.343688," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\frac{i \, a^{2} \sqrt{c} x^{2} + i \, a \sqrt{c} x - 2 i \, \sqrt{c}}{a^{2} c x + a c} + \frac{3 i \, \log\left(a x + 1\right)}{a \sqrt{c}}"," ",0,"-(I*a^2*sqrt(c)*x^2 + I*a*sqrt(c)*x - 2*I*sqrt(c))/(a^2*c*x + a*c) + 3*I*log(a*x + 1)/(a*sqrt(c))","C",0
738,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a^2*x^2))^(3/2)), x)","F",0
739,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a^2*x^2))^(5/2)), x)","F",0
740,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a^2*x^2))^(7/2)), x)","F",0
741,1,30,0,0.385472," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c} x x^{m}}{i \, m + i} - \frac{i \, \sqrt{c} x^{m}}{a m}"," ",0,"sqrt(c)*x*x^m/(I*m + I) - I*sqrt(c)*x^m/(a*m)","C",0
742,1,20,0,0.392317," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} i \, \sqrt{c} x^{3} - \frac{i \, \sqrt{c} x^{2}}{2 \, a}"," ",0,"-1/3*I*sqrt(c)*x^3 - 1/2*I*sqrt(c)*x^2/a","C",0
743,1,18,0,0.387835," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} i \, \sqrt{c} x^{2} - \frac{i \, \sqrt{c} x}{a}"," ",0,"-1/2*I*sqrt(c)*x^2 - I*sqrt(c)*x/a","C",0
744,1,17,0,0.386116," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-i \, \sqrt{c} x - \frac{i \, \sqrt{c} \log\left(x\right)}{a}"," ",0,"-I*sqrt(c)*x - I*sqrt(c)*log(x)/a","C",0
745,1,19,0,0.381175," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""maxima"")","-i \, \sqrt{c} \log\left(x\right) + \frac{i \, \sqrt{c}}{a x}"," ",0,"-I*sqrt(c)*log(x) + I*sqrt(c)/(a*x)","C",0
746,1,20,0,0.383911," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""maxima"")","\frac{i \, \sqrt{c}}{x} + \frac{i \, \sqrt{c}}{2 \, a x^{2}}"," ",0,"I*sqrt(c)/x + 1/2*I*sqrt(c)/(a*x^2)","C",0
747,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{3}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a^2*x^2))*x^3/(a^2*x^2 - 1), x)","F",0
748,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a^2*x^2))*x^2/(a^2*x^2 - 1), x)","F",0
749,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a^{2} x^{2}}} x}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a^2*x^2))*x/(a^2*x^2 - 1), x)","F",0
750,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a^2*x^2))/(a^2*x^2 - 1), x)","F",0
751,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""maxima"")","-\frac{\sqrt{a x + 1} \sqrt{a x - 1} \sqrt{c}}{a x} - \int \frac{{\left(a \sqrt{c} x + 2 \, \sqrt{c}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{a^{2} x^{3} - x}\,{d x}"," ",0,"-sqrt(a*x + 1)*sqrt(a*x - 1)*sqrt(c)/(a*x) - integrate((a*sqrt(c)*x + 2*sqrt(c))*sqrt(a*x + 1)*sqrt(a*x - 1)/(a^2*x^3 - x), x)","F",0
752,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a^{2} x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a^2*x^2))/((a^2*x^2 - 1)*x^2), x)","F",0
753,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2)/x^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, a^{2} \sqrt{c} x^{2} + \sqrt{c}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{3 \, a x^{3}} - \int \frac{{\left(a \sqrt{c} x + 2 \, \sqrt{c}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{a^{2} x^{5} - x^{3}}\,{d x}"," ",0,"-1/3*(2*a^2*sqrt(c)*x^2 + sqrt(c))*sqrt(a*x + 1)*sqrt(a*x - 1)/(a*x^3) - integrate((a*sqrt(c)*x + 2*sqrt(c))*sqrt(a*x + 1)*sqrt(a*x - 1)/(a^2*x^5 - x^3), x)","F",0
754,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2)/x^4,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a^{2} x^{2} - 1\right)} x^{4}}\,{d x}"," ",0,"-integrate((a*x + 1)^2*sqrt(c - c/(a^2*x^2))/((a^2*x^2 - 1)*x^4), x)","F",0
755,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(1/2)/x^5,x, algorithm=""maxima"")","-\frac{{\left(8 \, a^{4} \sqrt{c} x^{4} + 4 \, a^{2} \sqrt{c} x^{2} + 3 \, \sqrt{c}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{15 \, a x^{5}} - \int \frac{{\left(a \sqrt{c} x + 2 \, \sqrt{c}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{a^{2} x^{7} - x^{5}}\,{d x}"," ",0,"-1/15*(8*a^4*sqrt(c)*x^4 + 4*a^2*sqrt(c)*x^2 + 3*sqrt(c))*sqrt(a*x + 1)*sqrt(a*x - 1)/(a*x^5) - integrate((a*sqrt(c)*x + 2*sqrt(c))*sqrt(a*x + 1)*sqrt(a*x - 1)/(a^2*x^7 - x^5), x)","F",0
756,1,196,0,0.463745," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, a^{3} {\left(\frac{i \, a^{2} \sqrt{c} x^{4} + 2 i \, \sqrt{c} x^{2}}{a^{5}} + \frac{2 i \, \sqrt{c} \log\left(a x + 1\right)}{a^{7}} + \frac{2 i \, \sqrt{c} \log\left(a x - 1\right)}{a^{7}}\right)} + \frac{1}{2} \, a^{2} {\left(\frac{2 \, {\left(i \, a^{2} \sqrt{c} x^{3} + 3 i \, \sqrt{c} x\right)}}{a^{5}} - \frac{3 i \, \sqrt{c} \log\left(a x + 1\right)}{a^{6}} + \frac{3 i \, \sqrt{c} \log\left(a x - 1\right)}{a^{6}}\right)} - \frac{3}{2} \, a {\left(-\frac{i \, \sqrt{c} x^{2}}{a^{3}} - \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{5}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{5}}\right)} + \frac{i \, \sqrt{c} x}{a^{3}} - \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{2 \, a^{4}} + \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{2 \, a^{4}}"," ",0,"1/4*a^3*((I*a^2*sqrt(c)*x^4 + 2*I*sqrt(c)*x^2)/a^5 + 2*I*sqrt(c)*log(a*x + 1)/a^7 + 2*I*sqrt(c)*log(a*x - 1)/a^7) + 1/2*a^2*(2*(I*a^2*sqrt(c)*x^3 + 3*I*sqrt(c)*x)/a^5 - 3*I*sqrt(c)*log(a*x + 1)/a^6 + 3*I*sqrt(c)*log(a*x - 1)/a^6) - 3/2*a*(-I*sqrt(c)*x^2/a^3 - I*sqrt(c)*log(a*x + 1)/a^5 - I*sqrt(c)*log(a*x - 1)/a^5) + I*sqrt(c)*x/a^3 - 1/2*I*sqrt(c)*log(a*x + 1)/a^4 + 1/2*I*sqrt(c)*log(a*x - 1)/a^4","C",0
757,1,172,0,0.461338," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{6} \, a^{3} {\left(\frac{2 \, {\left(i \, a^{2} \sqrt{c} x^{3} + 3 i \, \sqrt{c} x\right)}}{a^{5}} - \frac{3 i \, \sqrt{c} \log\left(a x + 1\right)}{a^{6}} + \frac{3 i \, \sqrt{c} \log\left(a x - 1\right)}{a^{6}}\right)} - \frac{3}{2} \, a^{2} {\left(-\frac{i \, \sqrt{c} x^{2}}{a^{3}} - \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{5}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{5}}\right)} - \frac{3}{2} \, a {\left(-\frac{2 i \, \sqrt{c} x}{a^{3}} + \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{4}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{4}}\right)} + \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{2 \, a^{3}} + \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{2 \, a^{3}}"," ",0,"1/6*a^3*(2*(I*a^2*sqrt(c)*x^3 + 3*I*sqrt(c)*x)/a^5 - 3*I*sqrt(c)*log(a*x + 1)/a^6 + 3*I*sqrt(c)*log(a*x - 1)/a^6) - 3/2*a^2*(-I*sqrt(c)*x^2/a^3 - I*sqrt(c)*log(a*x + 1)/a^5 - I*sqrt(c)*log(a*x - 1)/a^5) - 3/2*a*(-2*I*sqrt(c)*x/a^3 + I*sqrt(c)*log(a*x + 1)/a^4 - I*sqrt(c)*log(a*x - 1)/a^4) + 1/2*I*sqrt(c)*log(a*x + 1)/a^3 + 1/2*I*sqrt(c)*log(a*x - 1)/a^3","C",0
758,1,149,0,0.466840," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{3} {\left(-\frac{i \, \sqrt{c} x^{2}}{a^{3}} - \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{5}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{5}}\right)} - \frac{3}{2} \, a^{2} {\left(-\frac{2 i \, \sqrt{c} x}{a^{3}} + \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{4}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{4}}\right)} - \frac{3}{2} \, a {\left(-\frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{3}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{3}}\right)} - \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{2 \, a^{2}} + \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{2 \, a^{2}}"," ",0,"-1/2*a^3*(-I*sqrt(c)*x^2/a^3 - I*sqrt(c)*log(a*x + 1)/a^5 - I*sqrt(c)*log(a*x - 1)/a^5) - 3/2*a^2*(-2*I*sqrt(c)*x/a^3 + I*sqrt(c)*log(a*x + 1)/a^4 - I*sqrt(c)*log(a*x - 1)/a^4) - 3/2*a*(-I*sqrt(c)*log(a*x + 1)/a^3 - I*sqrt(c)*log(a*x - 1)/a^3) - 1/2*I*sqrt(c)*log(a*x + 1)/a^2 + 1/2*I*sqrt(c)*log(a*x - 1)/a^2","C",0
759,1,148,0,0.474259," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{3} {\left(-\frac{2 i \, \sqrt{c} x}{a^{3}} + \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{4}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{4}}\right)} - \frac{3}{2} \, a^{2} {\left(-\frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{3}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{3}}\right)} - \frac{3}{2} \, a {\left(\frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{2}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{2}}\right)} + \frac{i \, \sqrt{c} \log\left(a x + 1\right)}{2 \, a} + \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{2 \, a} - \frac{i \, \sqrt{c} \log\left(x\right)}{a}"," ",0,"-1/2*a^3*(-2*I*sqrt(c)*x/a^3 + I*sqrt(c)*log(a*x + 1)/a^4 - I*sqrt(c)*log(a*x - 1)/a^4) - 3/2*a^2*(-I*sqrt(c)*log(a*x + 1)/a^3 - I*sqrt(c)*log(a*x - 1)/a^3) - 3/2*a*(I*sqrt(c)*log(a*x + 1)/a^2 - I*sqrt(c)*log(a*x - 1)/a^2) + 1/2*I*sqrt(c)*log(a*x + 1)/a + 1/2*I*sqrt(c)*log(a*x - 1)/a - I*sqrt(c)*log(x)/a","C",0
760,1,144,0,0.515311," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{3} {\left(-\frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{3}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{3}}\right)} - \frac{3}{2} \, a^{2} {\left(\frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{2}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{2}}\right)} - \frac{3}{2} \, a {\left(-\frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a} + \frac{2 i \, \sqrt{c} \log\left(x\right)}{a}\right)} - \frac{1}{2} i \, \sqrt{c} \log\left(a x + 1\right) + \frac{1}{2} i \, \sqrt{c} \log\left(a x - 1\right) + \frac{i \, \sqrt{c}}{a x}"," ",0,"-1/2*a^3*(-I*sqrt(c)*log(a*x + 1)/a^3 - I*sqrt(c)*log(a*x - 1)/a^3) - 3/2*a^2*(I*sqrt(c)*log(a*x + 1)/a^2 - I*sqrt(c)*log(a*x - 1)/a^2) - 3/2*a*(-I*sqrt(c)*log(a*x + 1)/a - I*sqrt(c)*log(a*x - 1)/a + 2*I*sqrt(c)*log(x)/a) - 1/2*I*sqrt(c)*log(a*x + 1) + 1/2*I*sqrt(c)*log(a*x - 1) + I*sqrt(c)/(a*x)","C",0
761,1,159,0,0.452635," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{3} {\left(\frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a^{2}} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a^{2}}\right)} - \frac{3}{2} \, a^{2} {\left(-\frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a} + \frac{2 i \, \sqrt{c} \log\left(x\right)}{a}\right)} + \frac{1}{2} i \, a \sqrt{c} \log\left(a x + 1\right) + \frac{1}{2} i \, a \sqrt{c} \log\left(a x - 1\right) - i \, a \sqrt{c} \log\left(x\right) - \frac{3}{2} \, {\left(i \, \sqrt{c} \log\left(a x + 1\right) - i \, \sqrt{c} \log\left(a x - 1\right) - \frac{2 i \, \sqrt{c}}{a x}\right)} a + \frac{i \, \sqrt{c}}{2 \, a x^{2}}"," ",0,"-1/2*a^3*(I*sqrt(c)*log(a*x + 1)/a^2 - I*sqrt(c)*log(a*x - 1)/a^2) - 3/2*a^2*(-I*sqrt(c)*log(a*x + 1)/a - I*sqrt(c)*log(a*x - 1)/a + 2*I*sqrt(c)*log(x)/a) + 1/2*I*a*sqrt(c)*log(a*x + 1) + 1/2*I*a*sqrt(c)*log(a*x - 1) - I*a*sqrt(c)*log(x) - 3/2*(I*sqrt(c)*log(a*x + 1) - I*sqrt(c)*log(a*x - 1) - 2*I*sqrt(c)/(a*x))*a + 1/2*I*sqrt(c)/(a*x^2)","C",0
762,1,184,0,0.457911," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{3} {\left(-\frac{i \, \sqrt{c} \log\left(a x + 1\right)}{a} - \frac{i \, \sqrt{c} \log\left(a x - 1\right)}{a} + \frac{2 i \, \sqrt{c} \log\left(x\right)}{a}\right)} - \frac{1}{2} i \, a^{2} \sqrt{c} \log\left(a x + 1\right) + \frac{1}{2} i \, a^{2} \sqrt{c} \log\left(a x - 1\right) - \frac{3}{2} \, {\left(i \, \sqrt{c} \log\left(a x + 1\right) - i \, \sqrt{c} \log\left(a x - 1\right) - \frac{2 i \, \sqrt{c}}{a x}\right)} a^{2} - \frac{3}{2} \, {\left(-i \, a \sqrt{c} \log\left(a x + 1\right) - i \, a \sqrt{c} \log\left(a x - 1\right) + 2 i \, a \sqrt{c} \log\left(x\right) - \frac{i \, \sqrt{c}}{a x^{2}}\right)} a + \frac{3 i \, a^{2} \sqrt{c} x^{2} + i \, \sqrt{c}}{3 \, a x^{3}}"," ",0,"-1/2*a^3*(-I*sqrt(c)*log(a*x + 1)/a - I*sqrt(c)*log(a*x - 1)/a + 2*I*sqrt(c)*log(x)/a) - 1/2*I*a^2*sqrt(c)*log(a*x + 1) + 1/2*I*a^2*sqrt(c)*log(a*x - 1) - 3/2*(I*sqrt(c)*log(a*x + 1) - I*sqrt(c)*log(a*x - 1) - 2*I*sqrt(c)/(a*x))*a^2 - 3/2*(-I*a*sqrt(c)*log(a*x + 1) - I*a*sqrt(c)*log(a*x - 1) + 2*I*a*sqrt(c)*log(x) - I*sqrt(c)/(a*x^2))*a + 1/3*(3*I*a^2*sqrt(c)*x^2 + I*sqrt(c))/(a*x^3)","C",0
763,1,209,0,0.456654," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^4,x, algorithm=""maxima"")","\frac{1}{2} i \, a^{3} \sqrt{c} \log\left(a x + 1\right) + \frac{1}{2} i \, a^{3} \sqrt{c} \log\left(a x - 1\right) - i \, a^{3} \sqrt{c} \log\left(x\right) - \frac{1}{2} \, {\left(i \, \sqrt{c} \log\left(a x + 1\right) - i \, \sqrt{c} \log\left(a x - 1\right) - \frac{2 i \, \sqrt{c}}{a x}\right)} a^{3} - \frac{3}{2} \, {\left(-i \, a \sqrt{c} \log\left(a x + 1\right) - i \, a \sqrt{c} \log\left(a x - 1\right) + 2 i \, a \sqrt{c} \log\left(x\right) - \frac{i \, \sqrt{c}}{a x^{2}}\right)} a^{2} - \frac{1}{2} \, {\left(3 i \, a^{2} \sqrt{c} \log\left(a x + 1\right) - 3 i \, a^{2} \sqrt{c} \log\left(a x - 1\right) - \frac{2 \, {\left(3 i \, a^{2} \sqrt{c} x^{2} + i \, \sqrt{c}\right)}}{a x^{3}}\right)} a + \frac{2 i \, a^{2} \sqrt{c} x^{2} + i \, \sqrt{c}}{4 \, a x^{4}}"," ",0,"1/2*I*a^3*sqrt(c)*log(a*x + 1) + 1/2*I*a^3*sqrt(c)*log(a*x - 1) - I*a^3*sqrt(c)*log(x) - 1/2*(I*sqrt(c)*log(a*x + 1) - I*sqrt(c)*log(a*x - 1) - 2*I*sqrt(c)/(a*x))*a^3 - 3/2*(-I*a*sqrt(c)*log(a*x + 1) - I*a*sqrt(c)*log(a*x - 1) + 2*I*a*sqrt(c)*log(x) - I*sqrt(c)/(a*x^2))*a^2 - 1/2*(3*I*a^2*sqrt(c)*log(a*x + 1) - 3*I*a^2*sqrt(c)*log(a*x - 1) - 2*(3*I*a^2*sqrt(c)*x^2 + I*sqrt(c))/(a*x^3))*a + 1/4*(2*I*a^2*sqrt(c)*x^2 + I*sqrt(c))/(a*x^4)","C",0
764,1,240,0,0.461533," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^5,x, algorithm=""maxima"")","-\frac{1}{2} i \, a^{4} \sqrt{c} \log\left(a x + 1\right) + \frac{1}{2} i \, a^{4} \sqrt{c} \log\left(a x - 1\right) - \frac{1}{2} \, {\left(-i \, a \sqrt{c} \log\left(a x + 1\right) - i \, a \sqrt{c} \log\left(a x - 1\right) + 2 i \, a \sqrt{c} \log\left(x\right) - \frac{i \, \sqrt{c}}{a x^{2}}\right)} a^{3} - \frac{1}{2} \, {\left(3 i \, a^{2} \sqrt{c} \log\left(a x + 1\right) - 3 i \, a^{2} \sqrt{c} \log\left(a x - 1\right) - \frac{2 \, {\left(3 i \, a^{2} \sqrt{c} x^{2} + i \, \sqrt{c}\right)}}{a x^{3}}\right)} a^{2} - \frac{3}{4} \, {\left(-2 i \, a^{3} \sqrt{c} \log\left(a x + 1\right) - 2 i \, a^{3} \sqrt{c} \log\left(a x - 1\right) + 4 i \, a^{3} \sqrt{c} \log\left(x\right) - \frac{2 i \, a^{2} \sqrt{c} x^{2} + i \, \sqrt{c}}{a x^{4}}\right)} a + \frac{i \, {\left(15 \, a^{4} \sqrt{c} x^{4} + 5 \, a^{2} \sqrt{c} x^{2} + 3 \, \sqrt{c}\right)}}{15 \, a x^{5}}"," ",0,"-1/2*I*a^4*sqrt(c)*log(a*x + 1) + 1/2*I*a^4*sqrt(c)*log(a*x - 1) - 1/2*(-I*a*sqrt(c)*log(a*x + 1) - I*a*sqrt(c)*log(a*x - 1) + 2*I*a*sqrt(c)*log(x) - I*sqrt(c)/(a*x^2))*a^3 - 1/2*(3*I*a^2*sqrt(c)*log(a*x + 1) - 3*I*a^2*sqrt(c)*log(a*x - 1) - 2*(3*I*a^2*sqrt(c)*x^2 + I*sqrt(c))/(a*x^3))*a^2 - 3/4*(-2*I*a^3*sqrt(c)*log(a*x + 1) - 2*I*a^3*sqrt(c)*log(a*x - 1) + 4*I*a^3*sqrt(c)*log(x) - (2*I*a^2*sqrt(c)*x^2 + I*sqrt(c))/(a*x^4))*a + 1/15*I*(15*a^4*sqrt(c)*x^4 + 5*a^2*sqrt(c)*x^2 + 3*sqrt(c))/(a*x^5)","C",0
765,1,55,0,0.389831," ","integrate(x^m*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{{\left(i \, a \sqrt{c} m x + \sqrt{c} {\left(-i \, m - i\right)}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} x^{m}}{{\left(m^{2} + m\right)} a^{3} x^{2} - {\left(m^{2} + m\right)} a}"," ",0,"(I*a*sqrt(c)*m*x + sqrt(c)*(-I*m - I))*(a*x + 1)*(a*x - 1)*x^m/((m^2 + m)*a^3*x^2 - (m^2 + m)*a)","C",0
766,1,43,0,0.381784," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{{\left(2 i \, a \sqrt{c} x^{3} - 3 i \, \sqrt{c} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}{6 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"1/6*(2*I*a*sqrt(c)*x^3 - 3*I*sqrt(c)*x^2)*(a*x + 1)*(a*x - 1)/(a^3*x^2 - a)","C",0
767,1,51,0,0.386654," ","integrate(x*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{{\left(i \, a^{2} \sqrt{c} x^{2} - 2 i \, a \sqrt{c} x + 2 i \, \sqrt{c}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}{2 \, {\left(a^{4} x^{2} - a^{2}\right)}}"," ",0,"1/2*(I*a^2*sqrt(c)*x^2 - 2*I*a*sqrt(c)*x + 2*I*sqrt(c))*(a*x + 1)*(a*x - 1)/(a^4*x^2 - a^2)","C",0
768,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a^2*x^2))/(a*x + 1), x)","F",0
769,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)*x), x)","F",0
770,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)*x^2), x)","F",0
771,0,0,0,0.000000," ","integrate(x^3*(c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{3}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))*x^3/(a*x + 1)^2, x)","F",0
772,0,0,0,0.000000," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))*x^2/(a*x + 1)^2, x)","F",0
773,0,0,0,0.000000," ","integrate(x*(c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))*x/(a*x + 1)^2, x)","F",0
774,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))/(a*x + 1)^2, x)","F",0
775,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x,x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{2} x}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^2*x), x)","F",0
776,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^2,x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{2} x^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^2*x^2), x)","F",0
777,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^3,x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{2} x^{3}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^2*x^3), x)","F",0
778,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^4,x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{2} x^{4}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^2*x^4), x)","F",0
779,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^5,x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{2} x^{5}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^2*x^5), x)","F",0
780,0,0,0,0.000000," ","integrate(x^3*(c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{3}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))*x^3/(a*x + 1)^3, x)","F",0
781,0,0,0,0.000000," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))*x^2/(a*x + 1)^3, x)","F",0
782,0,0,0,0.000000," ","integrate(x*(c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}} x}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))*x/(a*x + 1)^3, x)","F",0
783,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/(a*x + 1)^3, x)","F",0
784,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3} x}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^3*x), x)","F",0
785,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^3*x^2), x)","F",0
786,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^3*x^3), x)","F",0
787,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3} x^{4}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^3*x^4), x)","F",0
788,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3} x^{5}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^3*x^5), x)","F",0
789,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^p/exp(2*p*arctanh(a*x)),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{\left(\frac{a x + 1}{a x - 1}\right)^{p}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^p/((a*x + 1)/(a*x - 1))^p, x)","F",0
790,0,0,0,0.000000," ","integrate(exp(2*p*arctanh(a*x))*(c-c/a^2/x^2)^p,x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p} \left(\frac{a x + 1}{a x - 1}\right)^{p}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^p*((a*x + 1)/(a*x - 1))^p, x)","F",0
791,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^2*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
792,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a^2/x^2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
793,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(c-c/a^2/x^2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{c - \frac{c}{a^{2} x^{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(c - c/(a^2*x^2)), x)","F",0
794,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(c - c/(a^2*x^2))^2, x)","F",0
795,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(3/2)*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
796,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
797,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/sqrt(c - c/(a^2*x^2)), x)","F",0
798,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(c - c/(a^2*x^2))^(3/2), x)","F",0
799,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(c - c/(a^2*x^2))^(5/2), x)","F",0
800,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^p,x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^p*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
801,0,0,0,0.000000," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^p,x, algorithm=""maxima"")","\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}}\,{d x}"," ",0,"integrate((a*x + 1)^4*(c - c/(a^2*x^2))^p/(a^2*x^2 - 1)^2, x)","F",0
802,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^p,x, algorithm=""maxima"")","\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}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a^2*x^2))^p/(-a^2*x^2 + 1)^(3/2), x)","F",0
803,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^p,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*(c - c/(a^2*x^2))^p/(a^2*x^2 - 1), x)","F",0
804,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^p,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^p/sqrt(-a^2*x^2 + 1), x)","F",0
805,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^p/(a*x + 1), x)","F",0
806,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^p/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(c - c/(a^2*x^2))^p/(a*x + 1)^2, x)","F",0
807,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^p/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^p/(a*x + 1)^3, x)","F",0
808,1,639,0,0.438393," ","integrate((1+x)^(3/2)/(-x^2+1)^(1/2)*x*sin(x),x, algorithm=""maxima"")","-\frac{{\left({\left({\left({\left(2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} - 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + 2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left(2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(-2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left(x - 1\right)}^{2} + {\left({\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} x^{2} - {\left({\left(3 \, {\left({\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left({\left(3 \, \cos\left(1\right) - 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(3 \, \cos\left(1\right) + 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left| x - 1 \right|} + 2 \, {\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(2 \, \cos\left(1\right) - 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(2 \, \cos\left(1\right) + 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} x - {\left(3 \, {\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(3 \, \cos\left(1\right) - 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(3 \, \cos\left(1\right) + 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left| x - 1 \right|} + {\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} \sqrt{-x + 1}}{2 \, {\left(x - 1\right)}^{2} \sqrt{{\left| x - 1 \right|}}}"," ",0,"-1/2*((((2*I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) - 2*I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + 2*(sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*cos(1/2*arctan2(x - 1, 0)) + (2*(sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + (-2*I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + 2*I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*sin(1/2*arctan2(x - 1, 0)))*(x - 1)^2 + (((-I*cos(1) - sin(1))*gamma(5/2, I*x - I) + (I*cos(1) - sin(1))*gamma(5/2, -I*x + I))*cos(5/2*arctan2(x - 1, 0)) - ((cos(1) - I*sin(1))*gamma(5/2, I*x - I) + (cos(1) + I*sin(1))*gamma(5/2, -I*x + I))*sin(5/2*arctan2(x - 1, 0)))*x^2 - ((3*((I*cos(1) + sin(1))*gamma(3/2, I*x - I) + (-I*cos(1) + sin(1))*gamma(3/2, -I*x + I))*cos(3/2*arctan2(x - 1, 0)) + ((3*cos(1) - 3*I*sin(1))*gamma(3/2, I*x - I) + (3*cos(1) + 3*I*sin(1))*gamma(3/2, -I*x + I))*sin(3/2*arctan2(x - 1, 0)))*abs(x - 1) + 2*((-I*cos(1) - sin(1))*gamma(5/2, I*x - I) + (I*cos(1) - sin(1))*gamma(5/2, -I*x + I))*cos(5/2*arctan2(x - 1, 0)) - ((2*cos(1) - 2*I*sin(1))*gamma(5/2, I*x - I) + (2*cos(1) + 2*I*sin(1))*gamma(5/2, -I*x + I))*sin(5/2*arctan2(x - 1, 0)))*x - (3*((-I*cos(1) - sin(1))*gamma(3/2, I*x - I) + (I*cos(1) - sin(1))*gamma(3/2, -I*x + I))*cos(3/2*arctan2(x - 1, 0)) - ((3*cos(1) - 3*I*sin(1))*gamma(3/2, I*x - I) + (3*cos(1) + 3*I*sin(1))*gamma(3/2, -I*x + I))*sin(3/2*arctan2(x - 1, 0)))*abs(x - 1) + ((-I*cos(1) - sin(1))*gamma(5/2, I*x - I) + (I*cos(1) - sin(1))*gamma(5/2, -I*x + I))*cos(5/2*arctan2(x - 1, 0)) - ((cos(1) - I*sin(1))*gamma(5/2, I*x - I) + (cos(1) + I*sin(1))*gamma(5/2, -I*x + I))*sin(5/2*arctan2(x - 1, 0)))*sqrt(-x + 1)/((x - 1)^2*sqrt(abs(x - 1)))","C",0
809,1,349,0,0.405192," ","integrate((1+x)^(3/2)/(-x^2+1)^(1/2)*sin(x),x, algorithm=""maxima"")","-\frac{{\left({\left({\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} x + {\left({\left({\left(2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} - 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + 2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left(2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(-2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left| x - 1 \right|} + {\left({\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left({\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} \sqrt{-x + 1} \sqrt{{\left| x - 1 \right|}}}{2 \, {\left(x - 1\right)}^{2}}"," ",0,"-1/2*((((-I*cos(1) - sin(1))*gamma(3/2, I*x - I) + (I*cos(1) - sin(1))*gamma(3/2, -I*x + I))*cos(3/2*arctan2(x - 1, 0)) - ((cos(1) - I*sin(1))*gamma(3/2, I*x - I) + (cos(1) + I*sin(1))*gamma(3/2, -I*x + I))*sin(3/2*arctan2(x - 1, 0)))*x + (((2*I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) - 2*I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + 2*(sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*cos(1/2*arctan2(x - 1, 0)) + (2*(sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + (-2*I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + 2*I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*sin(1/2*arctan2(x - 1, 0)))*abs(x - 1) + ((I*cos(1) + sin(1))*gamma(3/2, I*x - I) + (-I*cos(1) + sin(1))*gamma(3/2, -I*x + I))*cos(3/2*arctan2(x - 1, 0)) + ((cos(1) - I*sin(1))*gamma(3/2, I*x - I) + (cos(1) + I*sin(1))*gamma(3/2, -I*x + I))*sin(3/2*arctan2(x - 1, 0)))*sqrt(-x + 1)*sqrt(abs(x - 1))/(x - 1)^2","C",0
810,1,909,0,0.495864," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2)*x*sin(x),x, algorithm=""maxima"")","-\frac{{\left({\left({\left(i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} - i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) - {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left| x + 1 \right|} \cos\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} - i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left| x + 1 \right|} \sin\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right)\right)} \sqrt{{\left| x + 1 \right|}}}{2 \, {\left(x + 1\right)}^{\frac{3}{2}}} - \frac{{\left({\left(-i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left(x + 1\right)}^{2} \cos\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) - {\left({\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) - {\left(-i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left(x + 1\right)}^{2} \sin\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) - 2 \, {\left({\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} {\left| x + 1 \right|} \cos\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right) - {\left({\left({\left(2 \, \cos\left(1\right) + 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(2 \, \cos\left(1\right) - 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(2 \, \cos\left(1\right) + 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(2 \, \cos\left(1\right) - 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} {\left| x + 1 \right|} \sin\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x^{2} - 2 \, {\left({\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x^{2} + {\left({\left(2 \, \cos\left(1\right) + 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(2 \, \cos\left(1\right) - 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x + 1, 0\right)\right)}{2 \, {\left(x + 1\right)}^{\frac{3}{2}} \sqrt{{\left| x + 1 \right|}}}"," ",0,"-1/2*(((I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) - I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) - (sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*abs(x + 1)*cos(1/2*arctan2(x + 1, 0)) + ((sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) + (I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) - I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*abs(x + 1)*sin(1/2*arctan2(x + 1, 0)) + (((I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*x + (I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*cos(3/2*arctan2(x + 1, 0)) + (((cos(1) + I*sin(1))*gamma(3/2, I*x + I) + (cos(1) - I*sin(1))*gamma(3/2, -I*x - I))*x + (cos(1) + I*sin(1))*gamma(3/2, I*x + I) + (cos(1) - I*sin(1))*gamma(3/2, -I*x - I))*sin(3/2*arctan2(x + 1, 0)))*sqrt(abs(x + 1))/(x + 1)^(3/2) - 1/2*(((-I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) + (sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*(x + 1)^2*cos(1/2*arctan2(x + 1, 0)) - ((sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) - (-I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*(x + 1)^2*sin(1/2*arctan2(x + 1, 0)) - 2*(((I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*x + (I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*abs(x + 1)*cos(3/2*arctan2(x + 1, 0)) - (((2*cos(1) + 2*I*sin(1))*gamma(3/2, I*x + I) + (2*cos(1) - 2*I*sin(1))*gamma(3/2, -I*x - I))*x + (2*cos(1) + 2*I*sin(1))*gamma(3/2, I*x + I) + (2*cos(1) - 2*I*sin(1))*gamma(3/2, -I*x - I))*abs(x + 1)*sin(3/2*arctan2(x + 1, 0)) + (((I*cos(1) - sin(1))*gamma(5/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(5/2, -I*x - I))*x^2 - 2*((-I*cos(1) + sin(1))*gamma(5/2, I*x + I) + (I*cos(1) + sin(1))*gamma(5/2, -I*x - I))*x + (I*cos(1) - sin(1))*gamma(5/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(5/2, -I*x - I))*cos(5/2*arctan2(x + 1, 0)) + (((cos(1) + I*sin(1))*gamma(5/2, I*x + I) + (cos(1) - I*sin(1))*gamma(5/2, -I*x - I))*x^2 + ((2*cos(1) + 2*I*sin(1))*gamma(5/2, I*x + I) + (2*cos(1) - 2*I*sin(1))*gamma(5/2, -I*x - I))*x + (cos(1) + I*sin(1))*gamma(5/2, I*x + I) + (cos(1) - I*sin(1))*gamma(5/2, -I*x - I))*sin(5/2*arctan2(x + 1, 0)))/((x + 1)^(3/2)*sqrt(abs(x + 1)))","C",0
811,1,498,0,0.439579," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2)*sin(x),x, algorithm=""maxima"")","-\frac{{\left({\left({\left(-i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) - {\left({\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) - {\left(-i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right)\right)} \sqrt{x + 1}}{2 \, \sqrt{{\left| x + 1 \right|}}} - \frac{{\left({\left({\left(i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} - i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) - {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left| x + 1 \right|} \cos\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} - i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left| x + 1 \right|} \sin\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right)\right)} \sqrt{{\left| x + 1 \right|}}}{2 \, {\left(x + 1\right)}^{\frac{3}{2}}}"," ",0,"-1/2*(((-I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) + (sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*cos(1/2*arctan2(x + 1, 0)) - ((sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) - (-I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*sin(1/2*arctan2(x + 1, 0)))*sqrt(x + 1)/sqrt(abs(x + 1)) - 1/2*(((I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) - I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) - (sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*abs(x + 1)*cos(1/2*arctan2(x + 1, 0)) + ((sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) + (I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) - I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*abs(x + 1)*sin(1/2*arctan2(x + 1, 0)) + (((I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*x + (I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*cos(3/2*arctan2(x + 1, 0)) + (((cos(1) + I*sin(1))*gamma(3/2, I*x + I) + (cos(1) - I*sin(1))*gamma(3/2, -I*x - I))*x + (cos(1) + I*sin(1))*gamma(3/2, I*x + I) + (cos(1) - I*sin(1))*gamma(3/2, -I*x - I))*sin(3/2*arctan2(x + 1, 0)))*sqrt(abs(x + 1))/(x + 1)^(3/2)","C",0
812,1,1010,0,0.469899," ","integrate((1+x)^(5/2)/(-x^2+1)^(1/2)*x*sin(x),x, algorithm=""maxima"")","-\frac{{\left({\left({\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x + i\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x - i\right) + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x + i\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} x^{3} + {\left({\left({\left(4 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} - 4 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + 4 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left(4 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(-4 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + 4 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left(x - 1\right)}^{2} {\left| x - 1 \right|} - {\left(8 \, {\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(8 \, \cos\left(1\right) - 8 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(8 \, \cos\left(1\right) + 8 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left(x - 1\right)}^{2} - {\left({\left(5 \, {\left({\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left({\left(5 \, \cos\left(1\right) - 5 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(5 \, \cos\left(1\right) + 5 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left| x - 1 \right|} + 3 \, {\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x + i\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(3 \, \cos\left(1\right) - 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x - i\right) + {\left(3 \, \cos\left(1\right) + 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x + i\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} x^{2} - {\left({\left(8 \, {\left({\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left({\left(8 \, \cos\left(1\right) - 8 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(8 \, \cos\left(1\right) + 8 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left(x - 1\right)}^{2} + {\left(10 \, {\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(10 \, \cos\left(1\right) - 10 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(10 \, \cos\left(1\right) + 10 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left| x - 1 \right|} + 3 \, {\left({\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x - i\right) + {\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x + i\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left({\left(3 \, \cos\left(1\right) - 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x - i\right) + {\left(3 \, \cos\left(1\right) + 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x + i\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} x - {\left(5 \, {\left({\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left({\left(5 \, \cos\left(1\right) - 5 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(5 \, \cos\left(1\right) + 5 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left| x - 1 \right|} + {\left({\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x - i\right) + {\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x + i\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left({\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x - i\right) + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x + i\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} \sqrt{-x + 1} \sqrt{{\left| x - 1 \right|}}}{2 \, {\left(x - 1\right)}^{4}}"," ",0,"-1/2*((((-I*cos(1) - sin(1))*gamma(7/2, I*x - I) + (I*cos(1) - sin(1))*gamma(7/2, -I*x + I))*cos(7/2*arctan2(x - 1, 0)) - ((cos(1) - I*sin(1))*gamma(7/2, I*x - I) + (cos(1) + I*sin(1))*gamma(7/2, -I*x + I))*sin(7/2*arctan2(x - 1, 0)))*x^3 + (((4*I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) - 4*I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + 4*(sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*cos(1/2*arctan2(x - 1, 0)) + (4*(sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + (-4*I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + 4*I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*sin(1/2*arctan2(x - 1, 0)))*(x - 1)^2*abs(x - 1) - (8*((-I*cos(1) - sin(1))*gamma(3/2, I*x - I) + (I*cos(1) - sin(1))*gamma(3/2, -I*x + I))*cos(3/2*arctan2(x - 1, 0)) - ((8*cos(1) - 8*I*sin(1))*gamma(3/2, I*x - I) + (8*cos(1) + 8*I*sin(1))*gamma(3/2, -I*x + I))*sin(3/2*arctan2(x - 1, 0)))*(x - 1)^2 - ((5*((I*cos(1) + sin(1))*gamma(5/2, I*x - I) + (-I*cos(1) + sin(1))*gamma(5/2, -I*x + I))*cos(5/2*arctan2(x - 1, 0)) + ((5*cos(1) - 5*I*sin(1))*gamma(5/2, I*x - I) + (5*cos(1) + 5*I*sin(1))*gamma(5/2, -I*x + I))*sin(5/2*arctan2(x - 1, 0)))*abs(x - 1) + 3*((-I*cos(1) - sin(1))*gamma(7/2, I*x - I) + (I*cos(1) - sin(1))*gamma(7/2, -I*x + I))*cos(7/2*arctan2(x - 1, 0)) - ((3*cos(1) - 3*I*sin(1))*gamma(7/2, I*x - I) + (3*cos(1) + 3*I*sin(1))*gamma(7/2, -I*x + I))*sin(7/2*arctan2(x - 1, 0)))*x^2 - ((8*((I*cos(1) + sin(1))*gamma(3/2, I*x - I) + (-I*cos(1) + sin(1))*gamma(3/2, -I*x + I))*cos(3/2*arctan2(x - 1, 0)) + ((8*cos(1) - 8*I*sin(1))*gamma(3/2, I*x - I) + (8*cos(1) + 8*I*sin(1))*gamma(3/2, -I*x + I))*sin(3/2*arctan2(x - 1, 0)))*(x - 1)^2 + (10*((-I*cos(1) - sin(1))*gamma(5/2, I*x - I) + (I*cos(1) - sin(1))*gamma(5/2, -I*x + I))*cos(5/2*arctan2(x - 1, 0)) - ((10*cos(1) - 10*I*sin(1))*gamma(5/2, I*x - I) + (10*cos(1) + 10*I*sin(1))*gamma(5/2, -I*x + I))*sin(5/2*arctan2(x - 1, 0)))*abs(x - 1) + 3*((I*cos(1) + sin(1))*gamma(7/2, I*x - I) + (-I*cos(1) + sin(1))*gamma(7/2, -I*x + I))*cos(7/2*arctan2(x - 1, 0)) + ((3*cos(1) - 3*I*sin(1))*gamma(7/2, I*x - I) + (3*cos(1) + 3*I*sin(1))*gamma(7/2, -I*x + I))*sin(7/2*arctan2(x - 1, 0)))*x - (5*((I*cos(1) + sin(1))*gamma(5/2, I*x - I) + (-I*cos(1) + sin(1))*gamma(5/2, -I*x + I))*cos(5/2*arctan2(x - 1, 0)) + ((5*cos(1) - 5*I*sin(1))*gamma(5/2, I*x - I) + (5*cos(1) + 5*I*sin(1))*gamma(5/2, -I*x + I))*sin(5/2*arctan2(x - 1, 0)))*abs(x - 1) + ((I*cos(1) + sin(1))*gamma(7/2, I*x - I) + (-I*cos(1) + sin(1))*gamma(7/2, -I*x + I))*cos(7/2*arctan2(x - 1, 0)) + ((cos(1) - I*sin(1))*gamma(7/2, I*x - I) + (cos(1) + I*sin(1))*gamma(7/2, -I*x + I))*sin(7/2*arctan2(x - 1, 0)))*sqrt(-x + 1)*sqrt(abs(x - 1))/(x - 1)^4","C",0
813,1,639,0,0.440654," ","integrate((1+x)^(5/2)/(-x^2+1)^(1/2)*sin(x),x, algorithm=""maxima"")","-\frac{{\left({\left({\left({\left(4 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} - 4 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + 4 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left(4 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(-4 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + 4 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left(x - 1\right)}^{2} + {\left({\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} x^{2} - {\left({\left(4 \, {\left({\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left({\left(4 \, \cos\left(1\right) - 4 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(4 \, \cos\left(1\right) + 4 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left| x - 1 \right|} + 2 \, {\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(2 \, \cos\left(1\right) - 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(2 \, \cos\left(1\right) + 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} x - {\left(4 \, {\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(4 \, \cos\left(1\right) - 4 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(4 \, \cos\left(1\right) + 4 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left| x - 1 \right|} + {\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x - i\right) + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x + i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} \sqrt{-x + 1}}{2 \, {\left(x - 1\right)}^{2} \sqrt{{\left| x - 1 \right|}}}"," ",0,"-1/2*((((4*I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) - 4*I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + 4*(sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*cos(1/2*arctan2(x - 1, 0)) + (4*(sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + (-4*I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + 4*I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*sin(1/2*arctan2(x - 1, 0)))*(x - 1)^2 + (((-I*cos(1) - sin(1))*gamma(5/2, I*x - I) + (I*cos(1) - sin(1))*gamma(5/2, -I*x + I))*cos(5/2*arctan2(x - 1, 0)) - ((cos(1) - I*sin(1))*gamma(5/2, I*x - I) + (cos(1) + I*sin(1))*gamma(5/2, -I*x + I))*sin(5/2*arctan2(x - 1, 0)))*x^2 - ((4*((I*cos(1) + sin(1))*gamma(3/2, I*x - I) + (-I*cos(1) + sin(1))*gamma(3/2, -I*x + I))*cos(3/2*arctan2(x - 1, 0)) + ((4*cos(1) - 4*I*sin(1))*gamma(3/2, I*x - I) + (4*cos(1) + 4*I*sin(1))*gamma(3/2, -I*x + I))*sin(3/2*arctan2(x - 1, 0)))*abs(x - 1) + 2*((-I*cos(1) - sin(1))*gamma(5/2, I*x - I) + (I*cos(1) - sin(1))*gamma(5/2, -I*x + I))*cos(5/2*arctan2(x - 1, 0)) - ((2*cos(1) - 2*I*sin(1))*gamma(5/2, I*x - I) + (2*cos(1) + 2*I*sin(1))*gamma(5/2, -I*x + I))*sin(5/2*arctan2(x - 1, 0)))*x - (4*((-I*cos(1) - sin(1))*gamma(3/2, I*x - I) + (I*cos(1) - sin(1))*gamma(3/2, -I*x + I))*cos(3/2*arctan2(x - 1, 0)) - ((4*cos(1) - 4*I*sin(1))*gamma(3/2, I*x - I) + (4*cos(1) + 4*I*sin(1))*gamma(3/2, -I*x + I))*sin(3/2*arctan2(x - 1, 0)))*abs(x - 1) + ((-I*cos(1) - sin(1))*gamma(5/2, I*x - I) + (I*cos(1) - sin(1))*gamma(5/2, -I*x + I))*cos(5/2*arctan2(x - 1, 0)) - ((cos(1) - I*sin(1))*gamma(5/2, I*x - I) + (cos(1) + I*sin(1))*gamma(5/2, -I*x + I))*sin(5/2*arctan2(x - 1, 0)))*sqrt(-x + 1)/((x - 1)^2*sqrt(abs(x - 1)))","C",0
814,1,1488,0,0.573451," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2)*x*sin(x),x, algorithm=""maxima"")","\frac{{\left({\left(-2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) + 2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left(x + 1\right)}^{2} \cos\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) - {\left(2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) - {\left(-2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left(x + 1\right)}^{2} \sin\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) - 3 \, {\left({\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} {\left| x + 1 \right|} \cos\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right) - {\left({\left({\left(3 \, \cos\left(1\right) + 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(3 \, \cos\left(1\right) - 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(3 \, \cos\left(1\right) + 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(3 \, \cos\left(1\right) - 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} {\left| x + 1 \right|} \sin\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x^{2} - 2 \, {\left({\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x^{2} + {\left({\left(2 \, \cos\left(1\right) + 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(2 \, \cos\left(1\right) - 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x + 1, 0\right)\right)}{2 \, {\left(x + 1\right)}^{\frac{3}{2}} \sqrt{{\left| x + 1 \right|}}} + \frac{{\left({\left({\left(2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} - 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) - 2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left(x + 1\right)}^{2} {\left| x + 1 \right|} \cos\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left(2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} - 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left(x + 1\right)}^{2} {\left| x + 1 \right|} \sin\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) - 5 \, {\left({\left({\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} {\left(x + 1\right)}^{2} \cos\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(5 \, \cos\left(1\right) + 5 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(5 \, \cos\left(1\right) - 5 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(5 \, \cos\left(1\right) + 5 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(5 \, \cos\left(1\right) - 5 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} {\left(x + 1\right)}^{2} \sin\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right) - 4 \, {\left({\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x^{2} + 2 \, {\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} {\left| x + 1 \right|} \cos\left(\frac{5}{2} \, \arctan\left(x + 1, 0\right)\right) - {\left({\left({\left(4 \, \cos\left(1\right) + 4 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(4 \, \cos\left(1\right) - 4 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x^{2} + {\left({\left(8 \, \cos\left(1\right) + 8 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(8 \, \cos\left(1\right) - 8 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x + {\left(4 \, \cos\left(1\right) + 4 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(4 \, \cos\left(1\right) - 4 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} {\left| x + 1 \right|} \sin\left(\frac{5}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x - i\right)\right)} x^{3} - 3 \, {\left({\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x + i\right) + {\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x - i\right)\right)} x^{2} - 3 \, {\left({\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x + i\right) + {\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x - i\right)\right)} x + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x - i\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x - i\right)\right)} x^{3} + {\left({\left(3 \, \cos\left(1\right) + 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x + i\right) + {\left(3 \, \cos\left(1\right) - 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x - i\right)\right)} x^{2} + {\left({\left(3 \, \cos\left(1\right) + 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x + i\right) + {\left(3 \, \cos\left(1\right) - 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x - i\right)\right)} x + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{7}{2}, -i \, x - i\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(x + 1, 0\right)\right)\right)} \sqrt{{\left| x + 1 \right|}}}{2 \, {\left(x + 1\right)}^{\frac{7}{2}}}"," ",0,"1/2*(((-2*I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + 2*I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) + 2*(sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*(x + 1)^2*cos(1/2*arctan2(x + 1, 0)) - (2*(sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) - (-2*I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + 2*I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*(x + 1)^2*sin(1/2*arctan2(x + 1, 0)) - 3*(((I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*x + (I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*abs(x + 1)*cos(3/2*arctan2(x + 1, 0)) - (((3*cos(1) + 3*I*sin(1))*gamma(3/2, I*x + I) + (3*cos(1) - 3*I*sin(1))*gamma(3/2, -I*x - I))*x + (3*cos(1) + 3*I*sin(1))*gamma(3/2, I*x + I) + (3*cos(1) - 3*I*sin(1))*gamma(3/2, -I*x - I))*abs(x + 1)*sin(3/2*arctan2(x + 1, 0)) + (((I*cos(1) - sin(1))*gamma(5/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(5/2, -I*x - I))*x^2 - 2*((-I*cos(1) + sin(1))*gamma(5/2, I*x + I) + (I*cos(1) + sin(1))*gamma(5/2, -I*x - I))*x + (I*cos(1) - sin(1))*gamma(5/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(5/2, -I*x - I))*cos(5/2*arctan2(x + 1, 0)) + (((cos(1) + I*sin(1))*gamma(5/2, I*x + I) + (cos(1) - I*sin(1))*gamma(5/2, -I*x - I))*x^2 + ((2*cos(1) + 2*I*sin(1))*gamma(5/2, I*x + I) + (2*cos(1) - 2*I*sin(1))*gamma(5/2, -I*x - I))*x + (cos(1) + I*sin(1))*gamma(5/2, I*x + I) + (cos(1) - I*sin(1))*gamma(5/2, -I*x - I))*sin(5/2*arctan2(x + 1, 0)))/((x + 1)^(3/2)*sqrt(abs(x + 1))) + 1/2*(((2*I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) - 2*I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) - 2*(sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*(x + 1)^2*abs(x + 1)*cos(1/2*arctan2(x + 1, 0)) + (2*(sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) + (2*I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) - 2*I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*(x + 1)^2*abs(x + 1)*sin(1/2*arctan2(x + 1, 0)) - 5*(((-I*cos(1) + sin(1))*gamma(3/2, I*x + I) + (I*cos(1) + sin(1))*gamma(3/2, -I*x - I))*x + (-I*cos(1) + sin(1))*gamma(3/2, I*x + I) + (I*cos(1) + sin(1))*gamma(3/2, -I*x - I))*(x + 1)^2*cos(3/2*arctan2(x + 1, 0)) + (((5*cos(1) + 5*I*sin(1))*gamma(3/2, I*x + I) + (5*cos(1) - 5*I*sin(1))*gamma(3/2, -I*x - I))*x + (5*cos(1) + 5*I*sin(1))*gamma(3/2, I*x + I) + (5*cos(1) - 5*I*sin(1))*gamma(3/2, -I*x - I))*(x + 1)^2*sin(3/2*arctan2(x + 1, 0)) - 4*(((I*cos(1) - sin(1))*gamma(5/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(5/2, -I*x - I))*x^2 + 2*((I*cos(1) - sin(1))*gamma(5/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(5/2, -I*x - I))*x + (I*cos(1) - sin(1))*gamma(5/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(5/2, -I*x - I))*abs(x + 1)*cos(5/2*arctan2(x + 1, 0)) - (((4*cos(1) + 4*I*sin(1))*gamma(5/2, I*x + I) + (4*cos(1) - 4*I*sin(1))*gamma(5/2, -I*x - I))*x^2 + ((8*cos(1) + 8*I*sin(1))*gamma(5/2, I*x + I) + (8*cos(1) - 8*I*sin(1))*gamma(5/2, -I*x - I))*x + (4*cos(1) + 4*I*sin(1))*gamma(5/2, I*x + I) + (4*cos(1) - 4*I*sin(1))*gamma(5/2, -I*x - I))*abs(x + 1)*sin(5/2*arctan2(x + 1, 0)) + (((I*cos(1) - sin(1))*gamma(7/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(7/2, -I*x - I))*x^3 - 3*((-I*cos(1) + sin(1))*gamma(7/2, I*x + I) + (I*cos(1) + sin(1))*gamma(7/2, -I*x - I))*x^2 - 3*((-I*cos(1) + sin(1))*gamma(7/2, I*x + I) + (I*cos(1) + sin(1))*gamma(7/2, -I*x - I))*x + (I*cos(1) - sin(1))*gamma(7/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(7/2, -I*x - I))*cos(7/2*arctan2(x + 1, 0)) + (((cos(1) + I*sin(1))*gamma(7/2, I*x + I) + (cos(1) - I*sin(1))*gamma(7/2, -I*x - I))*x^3 + ((3*cos(1) + 3*I*sin(1))*gamma(7/2, I*x + I) + (3*cos(1) - 3*I*sin(1))*gamma(7/2, -I*x - I))*x^2 + ((3*cos(1) + 3*I*sin(1))*gamma(7/2, I*x + I) + (3*cos(1) - 3*I*sin(1))*gamma(7/2, -I*x - I))*x + (cos(1) + I*sin(1))*gamma(7/2, I*x + I) + (cos(1) - I*sin(1))*gamma(7/2, -I*x - I))*sin(7/2*arctan2(x + 1, 0)))*sqrt(abs(x + 1))/(x + 1)^(7/2)","C",0
815,1,912,0,0.500683," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2)*sin(x),x, algorithm=""maxima"")","\frac{{\left({\left({\left(2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} - 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) - 2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left| x + 1 \right|} \cos\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left(2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} - 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left| x + 1 \right|} \sin\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right)\right)} \sqrt{{\left| x + 1 \right|}}}{2 \, {\left(x + 1\right)}^{\frac{3}{2}}} + \frac{{\left({\left(-2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) + 2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left(x + 1\right)}^{2} \cos\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) - {\left(2 \, {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \cos\left(1\right) - {\left(-2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x + i}\right) - 1\right)} + 2 i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x - i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} {\left(x + 1\right)}^{2} \sin\left(\frac{1}{2} \, \arctan\left(x + 1, 0\right)\right) - 3 \, {\left({\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} {\left| x + 1 \right|} \cos\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right) - {\left({\left({\left(3 \, \cos\left(1\right) + 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(3 \, \cos\left(1\right) - 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} x + {\left(3 \, \cos\left(1\right) + 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x + i\right) + {\left(3 \, \cos\left(1\right) - 3 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x - i\right)\right)} {\left| x + 1 \right|} \sin\left(\frac{3}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x^{2} - 2 \, {\left({\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(x + 1, 0\right)\right) + {\left({\left({\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x^{2} + {\left({\left(2 \, \cos\left(1\right) + 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(2 \, \cos\left(1\right) - 2 i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} x + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, i \, x + i\right) + {\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{5}{2}, -i \, x - i\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(x + 1, 0\right)\right)}{2 \, {\left(x + 1\right)}^{\frac{3}{2}} \sqrt{{\left| x + 1 \right|}}}"," ",0,"1/2*(((2*I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) - 2*I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) - 2*(sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*abs(x + 1)*cos(1/2*arctan2(x + 1, 0)) + (2*(sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) + (2*I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) - 2*I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*abs(x + 1)*sin(1/2*arctan2(x + 1, 0)) + (((I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*x + (I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*cos(3/2*arctan2(x + 1, 0)) + (((cos(1) + I*sin(1))*gamma(3/2, I*x + I) + (cos(1) - I*sin(1))*gamma(3/2, -I*x - I))*x + (cos(1) + I*sin(1))*gamma(3/2, I*x + I) + (cos(1) - I*sin(1))*gamma(3/2, -I*x - I))*sin(3/2*arctan2(x + 1, 0)))*sqrt(abs(x + 1))/(x + 1)^(3/2) + 1/2*(((-2*I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + 2*I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) + 2*(sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*(x + 1)^2*cos(1/2*arctan2(x + 1, 0)) - (2*(sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*cos(1) - (-2*I*sqrt(pi)*(erf(sqrt(I*x + I)) - 1) + 2*I*sqrt(pi)*(erf(sqrt(-I*x - I)) - 1))*sin(1))*(x + 1)^2*sin(1/2*arctan2(x + 1, 0)) - 3*(((I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*x + (I*cos(1) - sin(1))*gamma(3/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(3/2, -I*x - I))*abs(x + 1)*cos(3/2*arctan2(x + 1, 0)) - (((3*cos(1) + 3*I*sin(1))*gamma(3/2, I*x + I) + (3*cos(1) - 3*I*sin(1))*gamma(3/2, -I*x - I))*x + (3*cos(1) + 3*I*sin(1))*gamma(3/2, I*x + I) + (3*cos(1) - 3*I*sin(1))*gamma(3/2, -I*x - I))*abs(x + 1)*sin(3/2*arctan2(x + 1, 0)) + (((I*cos(1) - sin(1))*gamma(5/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(5/2, -I*x - I))*x^2 - 2*((-I*cos(1) + sin(1))*gamma(5/2, I*x + I) + (I*cos(1) + sin(1))*gamma(5/2, -I*x - I))*x + (I*cos(1) - sin(1))*gamma(5/2, I*x + I) + (-I*cos(1) - sin(1))*gamma(5/2, -I*x - I))*cos(5/2*arctan2(x + 1, 0)) + (((cos(1) + I*sin(1))*gamma(5/2, I*x + I) + (cos(1) - I*sin(1))*gamma(5/2, -I*x - I))*x^2 + ((2*cos(1) + 2*I*sin(1))*gamma(5/2, I*x + I) + (2*cos(1) - 2*I*sin(1))*gamma(5/2, -I*x - I))*x + (cos(1) + I*sin(1))*gamma(5/2, I*x + I) + (cos(1) - I*sin(1))*gamma(5/2, -I*x - I))*sin(5/2*arctan2(x + 1, 0)))/((x + 1)^(3/2)*sqrt(abs(x + 1)))","C",0
816,1,347,0,0.408603," ","integrate((1+x)^(1/2)/(-x^2+1)^(1/2)*x*sin(x),x, algorithm=""maxima"")","-\frac{{\left({\left({\left({\left(-i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(i \, \cos\left(1\right) - \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right) - {\left({\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} x + {\left({\left({\left(i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} - i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left({\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(-i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} {\left| x - 1 \right|} + {\left({\left(i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(-i \, \cos\left(1\right) + \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left({\left(\cos\left(1\right) - i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, i \, x - i\right) + {\left(\cos\left(1\right) + i \, \sin\left(1\right)\right)} \Gamma\left(\frac{3}{2}, -i \, x + i\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} \sqrt{-x + 1} \sqrt{{\left| x - 1 \right|}}}{2 \, {\left(x - 1\right)}^{2}}"," ",0,"-1/2*((((-I*cos(1) - sin(1))*gamma(3/2, I*x - I) + (I*cos(1) - sin(1))*gamma(3/2, -I*x + I))*cos(3/2*arctan2(x - 1, 0)) - ((cos(1) - I*sin(1))*gamma(3/2, I*x - I) + (cos(1) + I*sin(1))*gamma(3/2, -I*x + I))*sin(3/2*arctan2(x - 1, 0)))*x + (((I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) - I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + (sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*cos(1/2*arctan2(x - 1, 0)) + ((sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + (-I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*sin(1/2*arctan2(x - 1, 0)))*abs(x - 1) + ((I*cos(1) + sin(1))*gamma(3/2, I*x - I) + (-I*cos(1) + sin(1))*gamma(3/2, -I*x + I))*cos(3/2*arctan2(x - 1, 0)) + ((cos(1) - I*sin(1))*gamma(3/2, I*x - I) + (cos(1) + I*sin(1))*gamma(3/2, -I*x + I))*sin(3/2*arctan2(x - 1, 0)))*sqrt(-x + 1)*sqrt(abs(x - 1))/(x - 1)^2","C",0
817,1,168,0,0.375526," ","integrate((1+x)^(1/2)/(-x^2+1)^(1/2)*sin(x),x, algorithm=""maxima"")","-\frac{{\left({\left({\left(i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} - i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right) + {\left({\left(\sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \cos\left(1\right) + {\left(-i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{i \, x - i}\right) - 1\right)} + i \, \sqrt{\pi} {\left(\operatorname{erf}\left(\sqrt{-i \, x + i}\right) - 1\right)}\right)} \sin\left(1\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(x - 1, 0\right)\right)\right)} \sqrt{-x + 1}}{2 \, \sqrt{{\left| x - 1 \right|}}}"," ",0,"-1/2*(((I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) - I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + (sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*cos(1/2*arctan2(x - 1, 0)) + ((sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*cos(1) + (-I*sqrt(pi)*(erf(sqrt(I*x - I)) - 1) + I*sqrt(pi)*(erf(sqrt(-I*x + I)) - 1))*sin(1))*sin(1/2*arctan2(x - 1, 0)))*sqrt(-x + 1)/sqrt(abs(x - 1))","C",0
818,1,540,0,0.425592," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x^3,x, algorithm=""maxima"")","-\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} x^{3}}{4 \, b} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a + 1\right)} x^{2}}{3 \, b^{2}} + \frac{7 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a x^{2}}{12 \, b^{2}} + \frac{5 \, {\left(a + 1\right)} a^{3} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{4}} - \frac{35 \, a^{4} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{8 \, b^{4}} + \frac{5 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a + 1\right)} a x}{6 \, b^{3}} - \frac{35 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2} x}{24 \, b^{3}} - \frac{3 \, {\left(a^{2} - 1\right)} {\left(a + 1\right)} a \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{4}} + \frac{15 \, {\left(a^{2} - 1\right)} a^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{4 \, b^{4}} - \frac{5 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a + 1\right)} a^{2}}{2 \, b^{4}} + \frac{35 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{3}}{8 \, b^{4}} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a^{2} - 1\right)} x}{8 \, b^{3}} - \frac{3 \, {\left(a^{2} - 1\right)}^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{8 \, b^{4}} + \frac{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a^{2} - 1\right)} {\left(a + 1\right)}}{3 \, b^{4}} - \frac{55 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a^{2} - 1\right)} a}{24 \, b^{4}}"," ",0,"-1/4*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*x^3/b - 1/3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a + 1)*x^2/b^2 + 7/12*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a*x^2/b^2 + 5/2*(a + 1)*a^3*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 - 35/8*a^4*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 + 5/6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a + 1)*a*x/b^3 - 35/24*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2*x/b^3 - 3/2*(a^2 - 1)*(a + 1)*a*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 + 15/4*(a^2 - 1)*a^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 - 5/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a + 1)*a^2/b^4 + 35/8*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^3/b^4 + 3/8*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a^2 - 1)*x/b^3 - 3/8*(a^2 - 1)^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 + 2/3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a^2 - 1)*(a + 1)/b^4 - 55/24*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a^2 - 1)*a/b^4","B",0
819,1,355,0,0.424980," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x^2,x, algorithm=""maxima"")","-\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} x^{2}}{3 \, b} - \frac{3 \, {\left(a + 1\right)} a^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{3}} + \frac{5 \, a^{3} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{3}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a + 1\right)} x}{2 \, b^{2}} + \frac{5 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a x}{6 \, b^{2}} + \frac{{\left(a^{2} - 1\right)} {\left(a + 1\right)} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{3}} - \frac{3 \, {\left(a^{2} - 1\right)} a \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{3}} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a + 1\right)} a}{2 \, b^{3}} - \frac{5 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2}}{2 \, b^{3}} + \frac{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a^{2} - 1\right)}}{3 \, b^{3}}"," ",0,"-1/3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*x^2/b - 3/2*(a + 1)*a^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 + 5/2*a^3*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 - 1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a + 1)*x/b^2 + 5/6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a*x/b^2 + 1/2*(a^2 - 1)*(a + 1)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 - 3/2*(a^2 - 1)*a*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 + 3/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a + 1)*a/b^3 - 5/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2/b^3 + 2/3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a^2 - 1)/b^3","B",0
820,1,209,0,0.406301," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x,x, algorithm=""maxima"")","\frac{{\left(a + 1\right)} a \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{2}} - \frac{3 \, a^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{2}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} x}{2 \, b} + \frac{{\left(a^{2} - 1\right)} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{2}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(a + 1\right)}}{b^{2}} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{2 \, b^{2}}"," ",0,"(a + 1)*a*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^2 - 3/2*a^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^2 - 1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*x/b + 1/2*(a^2 - 1)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^2 - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(a + 1)/b^2 + 3/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/b^2","B",0
821,1,65,0,0.408123," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b}"," ",0,"-arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b","A",0
822,-2,0,0,0.000000," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
823,-2,0,0,0.000000," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
824,-2,0,0,0.000000," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
825,-2,0,0,0.000000," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
826,1,94,0,0.305285," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)*x^4,x, algorithm=""maxima"")","-\frac{6 \, b^{4} x^{5} + 15 \, b^{3} x^{4} - 20 \, {\left(a - 1\right)} b^{2} x^{3} + 30 \, {\left(a^{2} - 2 \, a + 1\right)} b x^{2} - 60 \, {\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)} x}{30 \, b^{4}} - \frac{2 \, {\left(a^{4} - 4 \, a^{3} + 6 \, a^{2} - 4 \, a + 1\right)} \log\left(b x + a - 1\right)}{b^{5}}"," ",0,"-1/30*(6*b^4*x^5 + 15*b^3*x^4 - 20*(a - 1)*b^2*x^3 + 30*(a^2 - 2*a + 1)*b*x^2 - 60*(a^3 - 3*a^2 + 3*a - 1)*x)/b^4 - 2*(a^4 - 4*a^3 + 6*a^2 - 4*a + 1)*log(b*x + a - 1)/b^5","A",0
827,1,68,0,0.304983," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)*x^3,x, algorithm=""maxima"")","-\frac{3 \, b^{3} x^{4} + 8 \, b^{2} x^{3} - 12 \, {\left(a - 1\right)} b x^{2} + 24 \, {\left(a^{2} - 2 \, a + 1\right)} x}{12 \, b^{3}} + \frac{2 \, {\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)} \log\left(b x + a - 1\right)}{b^{4}}"," ",0,"-1/12*(3*b^3*x^4 + 8*b^2*x^3 - 12*(a - 1)*b*x^2 + 24*(a^2 - 2*a + 1)*x)/b^3 + 2*(a^3 - 3*a^2 + 3*a - 1)*log(b*x + a - 1)/b^4","A",0
828,1,46,0,0.306626," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)*x^2,x, algorithm=""maxima"")","-\frac{b^{2} x^{3} + 3 \, b x^{2} - 6 \, {\left(a - 1\right)} x}{3 \, b^{2}} - \frac{2 \, {\left(a^{2} - 2 \, a + 1\right)} \log\left(b x + a - 1\right)}{b^{3}}"," ",0,"-1/3*(b^2*x^3 + 3*b*x^2 - 6*(a - 1)*x)/b^2 - 2*(a^2 - 2*a + 1)*log(b*x + a - 1)/b^3","A",0
829,1,30,0,0.300251," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)*x,x, algorithm=""maxima"")","-\frac{b x^{2} + 4 \, x}{2 \, b} + \frac{2 \, {\left(a - 1\right)} \log\left(b x + a - 1\right)}{b^{2}}"," ",0,"-1/2*(b*x^2 + 4*x)/b + 2*(a - 1)*log(b*x + a - 1)/b^2","A",0
830,1,16,0,0.316028," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2),x, algorithm=""maxima"")","-x - \frac{2 \, \log\left(b x + a - 1\right)}{b}"," ",0,"-x - 2*log(b*x + a - 1)/b","A",0
831,1,27,0,0.309899," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)/x,x, algorithm=""maxima"")","-\frac{{\left(a + 1\right)} \log\left(x\right)}{a - 1} + \frac{2 \, \log\left(b x + a - 1\right)}{a - 1}"," ",0,"-(a + 1)*log(x)/(a - 1) + 2*log(b*x + a - 1)/(a - 1)","A",0
832,1,48,0,0.312898," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)/x^2,x, algorithm=""maxima"")","-\frac{2 \, b \log\left(b x + a - 1\right)}{a^{2} - 2 \, a + 1} + \frac{2 \, b \log\left(x\right)}{a^{2} - 2 \, a + 1} + \frac{a + 1}{{\left(a - 1\right)} x}"," ",0,"-2*b*log(b*x + a - 1)/(a^2 - 2*a + 1) + 2*b*log(x)/(a^2 - 2*a + 1) + (a + 1)/((a - 1)*x)","A",0
833,1,74,0,0.309065," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)/x^3,x, algorithm=""maxima"")","\frac{2 \, b^{2} \log\left(b x + a - 1\right)}{a^{3} - 3 \, a^{2} + 3 \, a - 1} - \frac{2 \, b^{2} \log\left(x\right)}{a^{3} - 3 \, a^{2} + 3 \, a - 1} + \frac{a^{2} - 4 \, b x - 1}{2 \, {\left(a^{2} - 2 \, a + 1\right)} x^{2}}"," ",0,"2*b^2*log(b*x + a - 1)/(a^3 - 3*a^2 + 3*a - 1) - 2*b^2*log(x)/(a^3 - 3*a^2 + 3*a - 1) + 1/2*(a^2 - 4*b*x - 1)/((a^2 - 2*a + 1)*x^2)","A",0
834,1,108,0,0.317868," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)/x^4,x, algorithm=""maxima"")","-\frac{2 \, b^{3} \log\left(b x + a - 1\right)}{a^{4} - 4 \, a^{3} + 6 \, a^{2} - 4 \, a + 1} + \frac{2 \, b^{3} \log\left(x\right)}{a^{4} - 4 \, a^{3} + 6 \, a^{2} - 4 \, a + 1} + \frac{6 \, b^{2} x^{2} + a^{3} - 3 \, {\left(a - 1\right)} b x - a^{2} - a + 1}{3 \, {\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)} x^{3}}"," ",0,"-2*b^3*log(b*x + a - 1)/(a^4 - 4*a^3 + 6*a^2 - 4*a + 1) + 2*b^3*log(x)/(a^4 - 4*a^3 + 6*a^2 - 4*a + 1) + 1/3*(6*b^2*x^2 + a^3 - 3*(a - 1)*b*x - a^2 - a + 1)/((a^3 - 3*a^2 + 3*a - 1)*x^3)","A",0
835,1,2349,0,0.451289," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)*x^3,x, algorithm=""maxima"")","-\frac{b x^{5}}{4 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{315 \, a^{6} x}{4 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} + \frac{3 \, a x^{4}}{4 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{945 \, {\left(a^{2} - 1\right)} a^{4} x}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} - \frac{21 \, a^{2} x^{3}}{8 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} + \frac{105 \, {\left(a^{2} - 1\right)} a^{5}}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{105 \, {\left(a b^{2} + b^{2}\right)} a^{5} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} + \frac{45 \, {\left(a^{2} b + 2 \, a b + b\right)} a^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} + \frac{169 \, {\left(a^{2} - 1\right)}^{2} a^{2} x}{4 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} - \frac{6 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} a^{3} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} + \frac{105 \, a^{3} x^{2}}{8 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} + \frac{5 \, {\left(a^{2} - 1\right)} x^{3}}{8 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} - \frac{{\left(a b^{2} + b^{2}\right)} x^{4}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{14 \, {\left(a^{2} - 1\right)}^{2} a^{3}}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} + \frac{265 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} a^{3} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} - \frac{93 \, {\left(a^{2} b + 2 \, a b + b\right)} {\left(a^{2} - 1\right)} a^{2} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{15 \, {\left(a^{2} - 1\right)}^{3} x}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} + \frac{5 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} {\left(a^{2} - 1\right)} a x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} - \frac{49 \, {\left(a^{2} - 1\right)} a x^{2}}{8 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} + \frac{7 \, {\left(a b^{2} + b^{2}\right)} a x^{3}}{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} - \frac{3 \, {\left(a^{2} b + 2 \, a b + b\right)} x^{3}}{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} + \frac{315 \, a^{4} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{8 \, b^{4}} - \frac{35 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} a^{4}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{4}} + \frac{15 \, {\left(a^{2} b + 2 \, a b + b\right)} {\left(a^{2} - 1\right)} a^{3}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} + \frac{15 \, {\left(a^{2} - 1\right)}^{3} a}{8 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} {\left(a^{2} - 1\right)} a^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{61 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)}^{2} a x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} + \frac{9 \, {\left(a^{2} b + 2 \, a b + b\right)} {\left(a^{2} - 1\right)}^{2} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{35 \, {\left(a b^{2} + b^{2}\right)} a^{2} x^{2}}{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{4}} + \frac{15 \, {\left(a^{2} b + 2 \, a b + b\right)} a x^{2}}{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} - \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} x^{2}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{105 \, {\left(a^{2} - 1\right)} a^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{4 \, b^{4}} + \frac{29 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)}^{2} a^{2}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{4}} + \frac{105 \, {\left(a^{2} - 1\right)} a^{3}}{4 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{4}} - \frac{9 \, {\left(a^{2} b + 2 \, a b + b\right)} {\left(a^{2} - 1\right)}^{2} a}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} + \frac{4 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} x^{2}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{4}} - \frac{105 \, {\left(a b^{2} + b^{2}\right)} a^{3} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{6}} + \frac{45 \, {\left(a^{2} b + 2 \, a b + b\right)} a^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{5}} + \frac{15 \, {\left(a^{2} - 1\right)}^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{8 \, b^{4}} - \frac{3 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} a \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{4}} - \frac{49 \, {\left(a^{2} - 1\right)}^{2} a}{4 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{4}} + \frac{45 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} a \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{6}} - \frac{9 \, {\left(a^{2} b + 2 \, a b + b\right)} {\left(a^{2} - 1\right)} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{5}} - \frac{35 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} a^{2}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{6}} + \frac{15 \, {\left(a^{2} b + 2 \, a b + b\right)} {\left(a^{2} - 1\right)} a}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{5}} - \frac{2 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} {\left(a^{2} - 1\right)}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{4}} + \frac{8 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)}^{2}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{6}}"," ",0,"-1/4*b*x^5/sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1) + 315/4*a^6*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) + 3/4*a*x^4/sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1) - 945/8*(a^2 - 1)*a^4*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) - 21/8*a^2*x^3/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) + 105/8*(a^2 - 1)*a^5/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - 105*(a*b^2 + b^2)*a^5*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) + 45*(a^2*b + 2*a*b + b)*a^4*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) + 169/4*(a^2 - 1)^2*a^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) - 6*(a^3 + 3*a^2 + 3*a + 1)*a^3*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) + 105/8*a^3*x^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) + 5/8*(a^2 - 1)*x^3/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) - (a*b^2 + b^2)*x^4/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - 14*(a^2 - 1)^2*a^3/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) + 265/2*(a*b^2 + b^2)*(a^2 - 1)*a^3*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) - 93/2*(a^2*b + 2*a*b + b)*(a^2 - 1)*a^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - 15/8*(a^2 - 1)^3*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) + 5*(a^3 + 3*a^2 + 3*a + 1)*(a^2 - 1)*a*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) - 49/8*(a^2 - 1)*a*x^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) + 7/2*(a*b^2 + b^2)*a*x^3/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) - 3/2*(a^2*b + 2*a*b + b)*x^3/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) + 315/8*a^4*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 - 35/2*(a*b^2 + b^2)*(a^2 - 1)*a^4/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^4) + 15/2*(a^2*b + 2*a*b + b)*(a^2 - 1)*a^3/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) + 15/8*(a^2 - 1)^3*a/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - (a^3 + 3*a^2 + 3*a + 1)*(a^2 - 1)*a^2/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - 61/2*(a*b^2 + b^2)*(a^2 - 1)^2*a*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) + 9/2*(a^2*b + 2*a*b + b)*(a^2 - 1)^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - 35/2*(a*b^2 + b^2)*a^2*x^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^4) + 15/2*(a^2*b + 2*a*b + b)*a*x^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) - (a^3 + 3*a^2 + 3*a + 1)*x^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - 105/4*(a^2 - 1)*a^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 + 29/2*(a*b^2 + b^2)*(a^2 - 1)^2*a^2/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^4) + 105/4*(a^2 - 1)*a^3/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^4) - 9/2*(a^2*b + 2*a*b + b)*(a^2 - 1)^2*a/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) + 4*(a*b^2 + b^2)*(a^2 - 1)*x^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^4) - 105/2*(a*b^2 + b^2)*a^3*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^6 + 45/2*(a^2*b + 2*a*b + b)*a^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^5 + 15/8*(a^2 - 1)^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 - 3*(a^3 + 3*a^2 + 3*a + 1)*a*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 - 49/4*(a^2 - 1)^2*a/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^4) + 45/2*(a*b^2 + b^2)*(a^2 - 1)*a*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^6 - 9/2*(a^2*b + 2*a*b + b)*(a^2 - 1)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^5 - 35*(a*b^2 + b^2)*(a^2 - 1)*a^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^6) + 15*(a^2*b + 2*a*b + b)*(a^2 - 1)*a/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^5) - 2*(a^3 + 3*a^2 + 3*a + 1)*(a^2 - 1)/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^4) + 8*(a*b^2 + b^2)*(a^2 - 1)^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^6)","B",0
836,1,1645,0,0.432600," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)*x^2,x, algorithm=""maxima"")","-\frac{35 \, a^{5} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{b x^{4}}{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{265 \, {\left(a^{2} - 1\right)} a^{3} x}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{7 \, a x^{3}}{6 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{35 \, {\left(a^{2} - 1\right)} a^{4}}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} - \frac{61 \, {\left(a^{2} - 1\right)}^{2} a x}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{2 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} a^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{45 \, {\left(a b^{2} + b^{2}\right)} a^{4} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{18 \, {\left(a^{2} b + 2 \, a b + b\right)} a^{3} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} - \frac{35 \, a^{2} x^{2}}{6 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} + \frac{29 \, {\left(a^{2} - 1\right)}^{2} a^{2}}{6 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} - \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} {\left(a^{2} - 1\right)} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{93 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} a^{2} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} + \frac{15 \, {\left(a^{2} b + 2 \, a b + b\right)} {\left(a^{2} - 1\right)} a x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} + \frac{4 \, {\left(a^{2} - 1\right)} x^{2}}{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} - \frac{3 \, {\left(a b^{2} + b^{2}\right)} x^{3}}{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{35 \, a^{3} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{3}} + \frac{15 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} a^{3}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} - \frac{3 \, {\left(a^{2} b + 2 \, a b + b\right)} {\left(a^{2} - 1\right)} a^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} + \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} {\left(a^{2} - 1\right)} a}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} + \frac{9 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)}^{2} x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} + \frac{15 \, {\left(a b^{2} + b^{2}\right)} a x^{2}}{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} - \frac{3 \, {\left(a^{2} b + 2 \, a b + b\right)} x^{2}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} + \frac{15 \, {\left(a^{2} - 1\right)} a \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{3}} - \frac{9 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)}^{2} a}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} - \frac{35 \, {\left(a^{2} - 1\right)} a^{2}}{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} + \frac{45 \, {\left(a b^{2} + b^{2}\right)} a^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{5}} - \frac{9 \, {\left(a^{2} b + 2 \, a b + b\right)} a \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{4}} + \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{3}} + \frac{8 \, {\left(a^{2} - 1\right)}^{2}}{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{3}} - \frac{9 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{5}} + \frac{15 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} a}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{5}} - \frac{6 \, {\left(a^{2} b + 2 \, a b + b\right)} {\left(a^{2} - 1\right)}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{4}}"," ",0,"-35*a^5*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - 1/3*b*x^4/sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1) + 265/6*(a^2 - 1)*a^3*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + 7/6*a*x^3/sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1) - 35/6*(a^2 - 1)*a^4/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) - 61/6*(a^2 - 1)^2*a*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + 2*(a^3 + 3*a^2 + 3*a + 1)*a^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + 45*(a*b^2 + b^2)*a^4*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - 18*(a^2*b + 2*a*b + b)*a^3*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) - 35/6*a^2*x^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) + 29/6*(a^2 - 1)^2*a^2/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) - (a^3 + 3*a^2 + 3*a + 1)*(a^2 - 1)*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - 93/2*(a*b^2 + b^2)*(a^2 - 1)*a^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) + 15*(a^2*b + 2*a*b + b)*(a^2 - 1)*a*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) + 4/3*(a^2 - 1)*x^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) - 3/2*(a*b^2 + b^2)*x^3/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - 35/2*a^3*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 + 15/2*(a*b^2 + b^2)*(a^2 - 1)*a^3/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) - 3*(a^2*b + 2*a*b + b)*(a^2 - 1)*a^2/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) + (a^3 + 3*a^2 + 3*a + 1)*(a^2 - 1)*a/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) + 9/2*(a*b^2 + b^2)*(a^2 - 1)^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) + 15/2*(a*b^2 + b^2)*a*x^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) - 3*(a^2*b + 2*a*b + b)*x^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) + 15/2*(a^2 - 1)*a*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 - 9/2*(a*b^2 + b^2)*(a^2 - 1)^2*a/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) - 35/3*(a^2 - 1)*a^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) + 45/2*(a*b^2 + b^2)*a^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^5 - 9*(a^2*b + 2*a*b + b)*a*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 + (a^3 + 3*a^2 + 3*a + 1)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 + 8/3*(a^2 - 1)^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^3) - 9/2*(a*b^2 + b^2)*(a^2 - 1)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^5 + 15*(a*b^2 + b^2)*(a^2 - 1)*a/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^5) - 6*(a^2*b + 2*a*b + b)*(a^2 - 1)/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^4)","B",0
837,1,1137,0,0.425242," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)*x,x, algorithm=""maxima"")","\frac{15 \, a^{4} b x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{31 \, {\left(a^{2} - 1\right)} a^{2} b x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{b x^{3}}{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{5 \, {\left(a^{2} - 1\right)} a^{3}}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{6 \, {\left(a^{2} b + 2 \, a b + b\right)} a^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{18 \, {\left(a b^{2} + b^{2}\right)} a^{3} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} + \frac{3 \, {\left(a^{2} - 1\right)}^{2} b x}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} a b x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{5 \, a x^{2}}{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{3 \, {\left(a^{2} - 1\right)}^{2} a}{2 \, {\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} a^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{3 \, {\left(a^{2} b + 2 \, a b + b\right)} {\left(a^{2} - 1\right)} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{15 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} a x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} + \frac{15 \, a^{2} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{2}} - \frac{3 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} a^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} + \frac{3 \, {\left(a^{2} b + 2 \, a b + b\right)} {\left(a^{2} - 1\right)} a}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} - \frac{3 \, {\left(a b^{2} + b^{2}\right)} x^{2}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{3 \, {\left(a^{2} - 1\right)} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{2 \, b^{2}} + \frac{5 \, {\left(a^{2} - 1\right)} a}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{9 \, {\left(a b^{2} + b^{2}\right)} a \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{4}} + \frac{3 \, {\left(a^{2} b + 2 \, a b + b\right)} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{3}} + \frac{a^{3} + 3 \, a^{2} + 3 \, a + 1}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}} - \frac{6 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{4}}"," ",0,"15*a^4*b*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - 31/2*(a^2 - 1)*a^2*b*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - 1/2*b*x^3/sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1) + 5/2*(a^2 - 1)*a^3/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + 6*(a^2*b + 2*a*b + b)*a^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - 18*(a*b^2 + b^2)*a^3*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) + 3/2*(a^2 - 1)^2*b*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - (a^3 + 3*a^2 + 3*a + 1)*a*b*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + 5/2*a*x^2/sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1) - 3/2*(a^2 - 1)^2*a/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - (a^3 + 3*a^2 + 3*a + 1)*a^2/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - 3*(a^2*b + 2*a*b + b)*(a^2 - 1)*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + 15*(a*b^2 + b^2)*(a^2 - 1)*a*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) + 15/2*a^2*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^2 - 3*(a*b^2 + b^2)*(a^2 - 1)*a^2/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) + 3*(a^2*b + 2*a*b + b)*(a^2 - 1)*a/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) - 3*(a*b^2 + b^2)*x^2/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - 3/2*(a^2 - 1)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^2 + 5*(a^2 - 1)*a/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - 9*(a*b^2 + b^2)*a*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^4 + 3*(a^2*b + 2*a*b + b)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 + (a^3 + 3*a^2 + 3*a + 1)/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2) - 6*(a*b^2 + b^2)*(a^2 - 1)/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^4)","B",0
838,1,753,0,0.416008," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2),x, algorithm=""maxima"")","-\frac{6 \, a^{3} b^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{5 \, {\left(a^{2} - 1\right)} a b^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{{\left(a^{2} - 1\right)} a^{2} b}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{6 \, {\left(a b^{2} + b^{2}\right)} a^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{3 \, {\left(a^{2} b + 2 \, a b + b\right)} a b x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} b^{2} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{b x^{2}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{3 \, {\left(a^{2} b + 2 \, a b + b\right)} a^{2}}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} + \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} a b}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{3 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} x}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}} - \frac{3 \, a \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b} + \frac{3 \, {\left(a b^{2} + b^{2}\right)} {\left(a^{2} - 1\right)} a}{{\left(a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}\right)} \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} - \frac{2 \, {\left(a^{2} - 1\right)}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b} + \frac{3 \, {\left(a b^{2} + b^{2}\right)} \arcsin\left(-\frac{b^{2} x + a b}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}\right)}{b^{3}} + \frac{3 \, {\left(a^{2} b + 2 \, a b + b\right)}}{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}}"," ",0,"-6*a^3*b^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + 5*(a^2 - 1)*a*b^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - (a^2 - 1)*a^2*b/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + 6*(a*b^2 + b^2)*a^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - 3*(a^2*b + 2*a*b + b)*a*b*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + (a^3 + 3*a^2 + 3*a + 1)*b^2*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - b*x^2/sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1) - 3*(a^2*b + 2*a*b + b)*a^2/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) + (a^3 + 3*a^2 + 3*a + 1)*a*b/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - 3*(a*b^2 + b^2)*(a^2 - 1)*x/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)) - 3*a*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b + 3*(a*b^2 + b^2)*(a^2 - 1)*a/((a^2*b^2 - (a^2 - 1)*b^2)*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) - 2*(a^2 - 1)/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b) + 3*(a*b^2 + b^2)*arcsin(-(b^2*x + a*b)/sqrt(a^2*b^2 - (a^2 - 1)*b^2))/b^3 + 3*(a^2*b + 2*a*b + b)/(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2)","B",0
839,-2,0,0,0.000000," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
840,-2,0,0,0.000000," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
841,-2,0,0,0.000000," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
842,-2,0,0,0.000000," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 positive, negative or zero?","F(-2)",0
843,1,338,0,0.421961," ","integrate(x^3/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2} x}{2 \, b^{3}} - \frac{a^{3} \arcsin\left(b x + a\right)}{b^{4}} + \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{3}}{2 \, b^{4}} - \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, b^{3}} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a x}{2 \, b^{3}} - \frac{3 \, a^{2} \arcsin\left(b x + a\right)}{2 \, b^{4}} + \frac{3 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a}{4 \, b^{4}} - \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2}}{2 \, b^{4}} + \frac{5 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} x}{8 \, b^{3}} - \frac{3 \, a \arcsin\left(b x + a\right)}{2 \, b^{4}} + \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{3 \, b^{4}} - \frac{19 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{8 \, b^{4}} - \frac{3 \, \arcsin\left(b x + a\right)}{8 \, b^{4}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{4}}"," ",0,"3/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2*x/b^3 - a^3*arcsin(b*x + a)/b^4 + 1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^3/b^4 - 1/4*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*x/b^3 + 3/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a*x/b^3 - 3/2*a^2*arcsin(b*x + a)/b^4 + 3/4*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a/b^4 - 3/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2/b^4 + 5/8*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*x/b^3 - 3/2*a*arcsin(b*x + a)/b^4 + 1/3*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/b^4 - 19/8*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/b^4 - 3/8*arcsin(b*x + a)/b^4 - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b^4","B",0
844,1,174,0,0.425636," ","integrate(x^2/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a x}{b^{2}} + \frac{a^{2} \arcsin\left(b x + a\right)}{b^{3}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} x}{2 \, b^{2}} + \frac{a \arcsin\left(b x + a\right)}{b^{3}} - \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{3 \, b^{3}} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{2 \, b^{3}} + \frac{\arcsin\left(b x + a\right)}{2 \, b^{3}} + \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{3}}"," ",0,"-sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a*x/b^2 + a^2*arcsin(b*x + a)/b^3 - 1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*x/b^2 + a*arcsin(b*x + a)/b^3 - 1/3*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/b^3 + 3/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/b^3 + 1/2*arcsin(b*x + a)/b^3 + sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b^3","A",0
845,1,107,0,0.414324," ","integrate(x/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} x}{2 \, b} - \frac{a \arcsin\left(b x + a\right)}{b^{2}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{2 \, b^{2}} - \frac{\arcsin\left(b x + a\right)}{2 \, b^{2}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{2}}"," ",0,"1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*x/b - a*arcsin(b*x + a)/b^2 - 1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/b^2 - 1/2*arcsin(b*x + a)/b^2 - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b^2","A",0
846,1,37,0,0.443944," ","integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x, algorithm=""maxima"")","\frac{\arcsin\left(b x + a\right)}{b} + \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b}"," ",0,"arcsin(b*x + a)/b + sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b","A",0
847,-2,0,0,0.000000," ","integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more details)Is a-1 zero or nonzero?","F(-2)",0
848,0,0,0,0.000000," ","integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1}}{{\left(b x + a + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-(b*x + a)^2 + 1)/((b*x + a + 1)*x^2), x)","F",0
849,0,0,0,0.000000," ","integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1}}{{\left(b x + a + 1\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-(b*x + a)^2 + 1)/((b*x + a + 1)*x^3), x)","F",0
850,0,0,0,0.000000," ","integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1}}{{\left(b x + a + 1\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-(b*x + a)^2 + 1)/((b*x + a + 1)*x^4), x)","F",0
851,1,94,0,0.351338," ","integrate(x^4/(b*x+a+1)^2*(1-(b*x+a)^2),x, algorithm=""maxima"")","-\frac{6 \, b^{4} x^{5} - 15 \, b^{3} x^{4} + 20 \, {\left(a + 1\right)} b^{2} x^{3} - 30 \, {\left(a^{2} + 2 \, a + 1\right)} b x^{2} + 60 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} x}{30 \, b^{4}} + \frac{2 \, {\left(a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{5}}"," ",0,"-1/30*(6*b^4*x^5 - 15*b^3*x^4 + 20*(a + 1)*b^2*x^3 - 30*(a^2 + 2*a + 1)*b*x^2 + 60*(a^3 + 3*a^2 + 3*a + 1)*x)/b^4 + 2*(a^4 + 4*a^3 + 6*a^2 + 4*a + 1)*log(b*x + a + 1)/b^5","A",0
852,1,68,0,0.306072," ","integrate(x^3/(b*x+a+1)^2*(1-(b*x+a)^2),x, algorithm=""maxima"")","-\frac{3 \, b^{3} x^{4} - 8 \, b^{2} x^{3} + 12 \, {\left(a + 1\right)} b x^{2} - 24 \, {\left(a^{2} + 2 \, a + 1\right)} x}{12 \, b^{3}} - \frac{2 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{4}}"," ",0,"-1/12*(3*b^3*x^4 - 8*b^2*x^3 + 12*(a + 1)*b*x^2 - 24*(a^2 + 2*a + 1)*x)/b^3 - 2*(a^3 + 3*a^2 + 3*a + 1)*log(b*x + a + 1)/b^4","A",0
853,1,46,0,0.320730," ","integrate(x^2/(b*x+a+1)^2*(1-(b*x+a)^2),x, algorithm=""maxima"")","-\frac{b^{2} x^{3} - 3 \, b x^{2} + 6 \, {\left(a + 1\right)} x}{3 \, b^{2}} + \frac{2 \, {\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{3}}"," ",0,"-1/3*(b^2*x^3 - 3*b*x^2 + 6*(a + 1)*x)/b^2 + 2*(a^2 + 2*a + 1)*log(b*x + a + 1)/b^3","A",0
854,1,30,0,0.317753," ","integrate(x/(b*x+a+1)^2*(1-(b*x+a)^2),x, algorithm=""maxima"")","-\frac{b x^{2} - 4 \, x}{2 \, b} - \frac{2 \, {\left(a + 1\right)} \log\left(b x + a + 1\right)}{b^{2}}"," ",0,"-1/2*(b*x^2 - 4*x)/b - 2*(a + 1)*log(b*x + a + 1)/b^2","A",0
855,1,16,0,0.311897," ","integrate(1/(b*x+a+1)^2*(1-(b*x+a)^2),x, algorithm=""maxima"")","-x + \frac{2 \, \log\left(b x + a + 1\right)}{b}"," ",0,"-x + 2*log(b*x + a + 1)/b","A",0
856,1,27,0,0.305732," ","integrate(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x,x, algorithm=""maxima"")","-\frac{{\left(a - 1\right)} \log\left(x\right)}{a + 1} - \frac{2 \, \log\left(b x + a + 1\right)}{a + 1}"," ",0,"-(a - 1)*log(x)/(a + 1) - 2*log(b*x + a + 1)/(a + 1)","A",0
857,1,48,0,0.306131," ","integrate(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x^2,x, algorithm=""maxima"")","\frac{2 \, b \log\left(b x + a + 1\right)}{a^{2} + 2 \, a + 1} - \frac{2 \, b \log\left(x\right)}{a^{2} + 2 \, a + 1} + \frac{a - 1}{{\left(a + 1\right)} x}"," ",0,"2*b*log(b*x + a + 1)/(a^2 + 2*a + 1) - 2*b*log(x)/(a^2 + 2*a + 1) + (a - 1)/((a + 1)*x)","A",0
858,1,74,0,0.307813," ","integrate(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x^3,x, algorithm=""maxima"")","-\frac{2 \, b^{2} \log\left(b x + a + 1\right)}{a^{3} + 3 \, a^{2} + 3 \, a + 1} + \frac{2 \, b^{2} \log\left(x\right)}{a^{3} + 3 \, a^{2} + 3 \, a + 1} + \frac{a^{2} + 4 \, b x - 1}{2 \, {\left(a^{2} + 2 \, a + 1\right)} x^{2}}"," ",0,"-2*b^2*log(b*x + a + 1)/(a^3 + 3*a^2 + 3*a + 1) + 2*b^2*log(x)/(a^3 + 3*a^2 + 3*a + 1) + 1/2*(a^2 + 4*b*x - 1)/((a^2 + 2*a + 1)*x^2)","A",0
859,1,108,0,0.306991," ","integrate(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x^4,x, algorithm=""maxima"")","\frac{2 \, b^{3} \log\left(b x + a + 1\right)}{a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1} - \frac{2 \, b^{3} \log\left(x\right)}{a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1} - \frac{6 \, b^{2} x^{2} - a^{3} - 3 \, {\left(a + 1\right)} b x - a^{2} + a + 1}{3 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} x^{3}}"," ",0,"2*b^3*log(b*x + a + 1)/(a^4 + 4*a^3 + 6*a^2 + 4*a + 1) - 2*b^3*log(x)/(a^4 + 4*a^3 + 6*a^2 + 4*a + 1) - 1/3*(6*b^2*x^2 - a^3 - 3*(a + 1)*b*x - a^2 + a + 1)/((a^3 + 3*a^2 + 3*a + 1)*x^3)","A",0
860,1,985,0,0.433812," ","integrate(x^3/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a^{3}}{b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4} + 2 \, b^{5} x + 2 \, a b^{4} + b^{4}} - \frac{3 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4} + 2 \, b^{5} x + 2 \, a b^{4} + b^{4}} + \frac{3 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{2 \, {\left(b^{5} x + a b^{4} + b^{4}\right)}} + \frac{6 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{3}}{b^{5} x + a b^{4} + b^{4}} - \frac{3 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a}{b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4} + 2 \, b^{5} x + 2 \, a b^{4} + b^{4}} + \frac{3 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a}{b^{5} x + a b^{4} + b^{4}} + \frac{18 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2}}{b^{5} x + a b^{4} + b^{4}} - \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4} + 2 \, b^{5} x + 2 \, a b^{4} + b^{4}} + \frac{3 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{2 \, {\left(b^{5} x + a b^{4} + b^{4}\right)}} + \frac{18 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b^{5} x + a b^{4} + b^{4}} + \frac{3 \, a^{3} \arcsin\left(b x + a\right)}{b^{4}} + \frac{6 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{5} x + a b^{4} + b^{4}} + \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, b^{3}} - \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 4 \, b x + 4 \, a + 3} a x}{2 \, b^{3}} + \frac{27 \, a^{2} \arcsin\left(b x + a\right)}{2 \, b^{4}} - \frac{3 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a}{4 \, b^{4}} - \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 4 \, b x + 4 \, a + 3} a^{2}}{2 \, b^{4}} + \frac{9 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2}}{2 \, b^{4}} - \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 4 \, b x + 4 \, a + 3} x}{2 \, b^{3}} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} x}{8 \, b^{3}} + \frac{3 i \, a \arcsin\left(b x + a + 2\right)}{2 \, b^{4}} + \frac{18 \, a \arcsin\left(b x + a\right)}{b^{4}} - \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{b^{4}} - \frac{9 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 4 \, b x + 4 \, a + 3} a}{2 \, b^{4}} + \frac{75 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{8 \, b^{4}} + \frac{3 i \, \arcsin\left(b x + a + 2\right)}{2 \, b^{4}} + \frac{63 \, \arcsin\left(b x + a\right)}{8 \, b^{4}} - \frac{3 \, \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 4 \, b x + 4 \, a + 3}}{b^{4}} + \frac{9 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{2 \, b^{4}}"," ",0,"-(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a^3/(b^6*x^2 + 2*a*b^5*x + a^2*b^4 + 2*b^5*x + 2*a*b^4 + b^4) - 3*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a^2/(b^6*x^2 + 2*a*b^5*x + a^2*b^4 + 2*b^5*x + 2*a*b^4 + b^4) + 3/2*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a^2/(b^5*x + a*b^4 + b^4) + 6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^3/(b^5*x + a*b^4 + b^4) - 3*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a/(b^6*x^2 + 2*a*b^5*x + a^2*b^4 + 2*b^5*x + 2*a*b^4 + b^4) + 3*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a/(b^5*x + a*b^4 + b^4) + 18*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2/(b^5*x + a*b^4 + b^4) - (-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/(b^6*x^2 + 2*a*b^5*x + a^2*b^4 + 2*b^5*x + 2*a*b^4 + b^4) + 3/2*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/(b^5*x + a*b^4 + b^4) + 18*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/(b^5*x + a*b^4 + b^4) + 3*a^3*arcsin(b*x + a)/b^4 + 6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/(b^5*x + a*b^4 + b^4) + 1/4*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*x/b^3 - 3/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 4*b*x + 4*a + 3)*a*x/b^3 + 27/2*a^2*arcsin(b*x + a)/b^4 - 3/4*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a/b^4 - 3/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 4*b*x + 4*a + 3)*a^2/b^4 + 9/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2/b^4 - 3/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 4*b*x + 4*a + 3)*x/b^3 + 3/8*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*x/b^3 + 3/2*I*a*arcsin(b*x + a + 2)/b^4 + 18*a*arcsin(b*x + a)/b^4 - (-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/b^4 - 9/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 4*b*x + 4*a + 3)*a/b^4 + 75/8*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/b^4 + 3/2*I*arcsin(b*x + a + 2)/b^4 + 63/8*arcsin(b*x + a)/b^4 - 3*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 4*b*x + 4*a + 3)/b^4 + 9/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b^4","C",0
861,1,622,0,0.420767," ","integrate(x^2/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3} + 2 \, b^{4} x + 2 \, a b^{3} + b^{3}} + \frac{2 \, {\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a}{b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3} + 2 \, b^{4} x + 2 \, a b^{3} + b^{3}} - \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a}{b^{4} x + a b^{3} + b^{3}} - \frac{6 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2}}{b^{4} x + a b^{3} + b^{3}} + \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3} + 2 \, b^{4} x + 2 \, a b^{3} + b^{3}} - \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{b^{4} x + a b^{3} + b^{3}} - \frac{12 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b^{4} x + a b^{3} + b^{3}} - \frac{3 \, a^{2} \arcsin\left(b x + a\right)}{b^{3}} - \frac{6 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{4} x + a b^{3} + b^{3}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 4 \, b x + 4 \, a + 3} x}{2 \, b^{2}} - \frac{9 \, a \arcsin\left(b x + a\right)}{b^{3}} + \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{3 \, b^{3}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 4 \, b x + 4 \, a + 3} a}{2 \, b^{3}} - \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b^{3}} - \frac{i \, \arcsin\left(b x + a + 2\right)}{2 \, b^{3}} - \frac{6 \, \arcsin\left(b x + a\right)}{b^{3}} + \frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 4 \, b x + 4 \, a + 3}}{b^{3}} - \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{3}}"," ",0,"(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a^2/(b^5*x^2 + 2*a*b^4*x + a^2*b^3 + 2*b^4*x + 2*a*b^3 + b^3) + 2*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a/(b^5*x^2 + 2*a*b^4*x + a^2*b^3 + 2*b^4*x + 2*a*b^3 + b^3) - (-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a/(b^4*x + a*b^3 + b^3) - 6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2/(b^4*x + a*b^3 + b^3) + (-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/(b^5*x^2 + 2*a*b^4*x + a^2*b^3 + 2*b^4*x + 2*a*b^3 + b^3) - (-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/(b^4*x + a*b^3 + b^3) - 12*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/(b^4*x + a*b^3 + b^3) - 3*a^2*arcsin(b*x + a)/b^3 - 6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/(b^4*x + a*b^3 + b^3) + 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 4*b*x + 4*a + 3)*x/b^2 - 9*a*arcsin(b*x + a)/b^3 + 1/3*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/b^3 + 1/2*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 4*b*x + 4*a + 3)*a/b^3 - 3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/b^3 - 1/2*I*arcsin(b*x + a + 2)/b^3 - 6*arcsin(b*x + a)/b^3 + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 4*b*x + 4*a + 3)/b^3 - 3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b^3","C",0
862,1,299,0,0.412059," ","integrate(x/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}} a}{b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2} + 2 \, b^{3} x + 2 \, a b^{2} + b^{2}} - \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2} + 2 \, b^{3} x + 2 \, a b^{2} + b^{2}} + \frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{2 \, {\left(b^{3} x + a b^{2} + b^{2}\right)}} + \frac{6 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b^{3} x + a b^{2} + b^{2}} + \frac{3 \, a \arcsin\left(b x + a\right)}{b^{2}} + \frac{6 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{3} x + a b^{2} + b^{2}} + \frac{9 \, \arcsin\left(b x + a\right)}{2 \, b^{2}} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{2 \, b^{2}}"," ",0,"-(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)*a/(b^4*x^2 + 2*a*b^3*x + a^2*b^2 + 2*b^3*x + 2*a*b^2 + b^2) - (-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2 + 2*b^3*x + 2*a*b^2 + b^2) + 1/2*(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/(b^3*x + a*b^2 + b^2) + 6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/(b^3*x + a*b^2 + b^2) + 3*a*arcsin(b*x + a)/b^2 + 6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/(b^3*x + a*b^2 + b^2) + 9/2*arcsin(b*x + a)/b^2 + 3/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b^2","B",0
863,1,104,0,0.413572," ","integrate(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(-b^{2} x^{2} - 2 \, a b x - a^{2} + 1\right)}^{\frac{3}{2}}}{b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b + 2 \, b^{2} x + 2 \, a b + b} - \frac{3 \, \arcsin\left(b x + a\right)}{b} - \frac{6 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{2} x + a b + b}"," ",0,"(-b^2*x^2 - 2*a*b*x - a^2 + 1)^(3/2)/(b^3*x^2 + 2*a*b^2*x + a^2*b + 2*b^2*x + 2*a*b + b) - 3*arcsin(b*x + a)/b - 6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/(b^2*x + a*b + b)","A",0
864,0,0,0,0.000000," ","integrate(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b x + a + 1\right)}^{3} x}\,{d x}"," ",0,"integrate((-(b*x + a)^2 + 1)^(3/2)/((b*x + a + 1)^3*x), x)","F",0
865,0,0,0,0.000000," ","integrate(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b x + a + 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate((-(b*x + a)^2 + 1)^(3/2)/((b*x + a + 1)^3*x^2), x)","F",0
866,0,0,0,0.000000," ","integrate(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b x + a + 1\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate((-(b*x + a)^2 + 1)^(3/2)/((b*x + a + 1)^3*x^3), x)","F",0
867,0,0,0,0.000000," ","integrate(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(-{\left(b x + a\right)}^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b x + a + 1\right)}^{3} x^{4}}\,{d x}"," ",0,"integrate((-(b*x + a)^2 + 1)^(3/2)/((b*x + a + 1)^3*x^4), x)","F",0
868,1,18,0,0.395375," ","integrate(1/(1-(b*x+1)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\arcsin\left(-\frac{b^{2} x + b}{b}\right)}{b}"," ",0,"-arcsin(-(b^2*x + b)/b)/b","A",0
869,1,576,0,0.603154," ","integrate((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, algorithm=""maxima"")","\frac{{\left(\frac{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{3}}{b^{6} x + a b^{5} - b^{5}} - \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2} b}{b^{7} x + a b^{6} + b^{6}} - \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2} b}{b^{7} x + a b^{6} - b^{6}} + \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2}}{b^{6} x + a b^{5} + b^{5}} - \frac{3 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2}}{b^{6} x + a b^{5} - b^{5}} + \frac{6 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b^{6} x + a b^{5} - b^{5}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b}{b^{7} x + a b^{6} + b^{6}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b}{b^{7} x + a b^{6} - b^{6}} + \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{6} x + a b^{5} + b^{5}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{6} x + a b^{5} - b^{5}} - \frac{6 \, a^{2} \arcsin\left(b x + a\right)}{b^{5}} + \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} x}{b^{4}} + \frac{6 \, a \arcsin\left(b x + a\right)}{b^{5}} - \frac{5 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b^{5}} - \frac{3 \, \arcsin\left(b x + a\right)}{b^{5}} + \frac{2 \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{5}}\right)} b^{2}}{2 \, \sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}"," ",0,"1/2*(2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^3/(b^6*x + a*b^5 - b^5) - 3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2*b/(b^7*x + a*b^6 + b^6) - 3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2*b/(b^7*x + a*b^6 - b^6) + 3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2/(b^6*x + a*b^5 + b^5) - 3*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2/(b^6*x + a*b^5 - b^5) + 6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/(b^6*x + a*b^5 - b^5) - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b/(b^7*x + a*b^6 + b^6) - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b/(b^7*x + a*b^6 - b^6) + sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/(b^6*x + a*b^5 + b^5) - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/(b^6*x + a*b^5 - b^5) - 6*a^2*arcsin(b*x + a)/b^5 + sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*x/b^4 + 6*a*arcsin(b*x + a)/b^5 - 5*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/b^5 - 3*arcsin(b*x + a)/b^5 + 2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b^5)*b^2/sqrt(a^2*b^2 - (a^2 - 1)*b^2)","B",0
870,1,329,0,0.521840," ","integrate((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, algorithm=""maxima"")","-\frac{{\left(\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a^{2}}{b^{5} x + a b^{4} - b^{4}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a b}{b^{6} x + a b^{5} + b^{5}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a b}{b^{6} x + a b^{5} - b^{5}} + \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b^{5} x + a b^{4} + b^{4}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b^{5} x + a b^{4} - b^{4}} + \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{5} x + a b^{4} - b^{4}} - \frac{2 \, a \arcsin\left(b x + a\right)}{b^{4}} + \frac{\arcsin\left(b x + a\right)}{b^{4}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{4}}\right)} b^{2}}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}"," ",0,"-(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a^2/(b^5*x + a*b^4 - b^4) - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a*b/(b^6*x + a*b^5 + b^5) - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a*b/(b^6*x + a*b^5 - b^5) + sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/(b^5*x + a*b^4 + b^4) - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/(b^5*x + a*b^4 - b^4) + sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/(b^5*x + a*b^4 - b^4) - 2*a*arcsin(b*x + a)/b^4 + arcsin(b*x + a)/b^4 - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b^4)*b^2/sqrt(a^2*b^2 - (a^2 - 1)*b^2)","B",0
871,1,120,0,0.460080," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x/(-b^2*x^2-2*a*b*x-a^2+1),x, algorithm=""maxima"")","\frac{b^{2} {\left(\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} a}{b^{4} x + a b^{3} - b^{3}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b^{4} x + a b^{3} - b^{3}} - \frac{\arcsin\left(b x + a\right)}{b^{3}}\right)}}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}}}"," ",0,"b^2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*a/(b^4*x + a*b^3 - b^3) - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/(b^4*x + a*b^3 - b^3) - arcsin(b*x + a)/b^3)/sqrt(a^2*b^2 - (a^2 - 1)*b^2)","B",0
872,1,65,0,0.425555," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/(-b^2*x^2-2*a*b*x-a^2+1),x, algorithm=""maxima"")","-\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} b^{2}}{\sqrt{a^{2} b^{2} - {\left(a^{2} - 1\right)} b^{2}} {\left(b^{3} x + a b^{2} - b^{2}\right)}}"," ",0,"-sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*b^2/(sqrt(a^2*b^2 - (a^2 - 1)*b^2)*(b^3*x + a*b^2 - b^2))","B",0
873,0,0,0,0.000000," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x/(-b^2*x^2-2*a*b*x-a^2+1),x, algorithm=""maxima"")","-\int \frac{b x + a + 1}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} \sqrt{-{\left(b x + a\right)}^{2} + 1} x}\,{d x}"," ",0,"-integrate((b*x + a + 1)/((b^2*x^2 + 2*a*b*x + a^2 - 1)*sqrt(-(b*x + a)^2 + 1)*x), x)","F",0
874,0,0,0,0.000000," ","integrate((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, algorithm=""maxima"")","-\int \frac{b x + a + 1}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} \sqrt{-{\left(b x + a\right)}^{2} + 1} x^{2}}\,{d x}"," ",0,"-integrate((b*x + a + 1)/((b^2*x^2 + 2*a*b*x + a^2 - 1)*sqrt(-(b*x + a)^2 + 1)*x^2), x)","F",0
875,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))*x^m,x, algorithm=""maxima"")","\int x^{m} \left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^m*((b*x + a + 1)/(b*x + a - 1))^(1/2*n), x)","F",0
876,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))*x^3,x, algorithm=""maxima"")","\int x^{3} \left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^3*((b*x + a + 1)/(b*x + a - 1))^(1/2*n), x)","F",0
877,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))*x^2,x, algorithm=""maxima"")","\int x^{2} \left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^2*((b*x + a + 1)/(b*x + a - 1))^(1/2*n), x)","F",0
878,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))*x,x, algorithm=""maxima"")","\int x \left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x*((b*x + a + 1)/(b*x + a - 1))^(1/2*n), x)","F",0
879,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a)),x, algorithm=""maxima"")","\int \left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(((b*x + a + 1)/(b*x + a - 1))^(1/2*n), x)","F",0
880,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{\left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}}{x}\,{d x}"," ",0,"integrate(((b*x + a + 1)/(b*x + a - 1))^(1/2*n)/x, x)","F",0
881,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))/x^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}}{x^{2}}\,{d x}"," ",0,"integrate(((b*x + a + 1)/(b*x + a - 1))^(1/2*n)/x^2, x)","F",0
882,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))/x^3,x, algorithm=""maxima"")","\int \frac{\left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}}{x^{3}}\,{d x}"," ",0,"integrate(((b*x + a + 1)/(b*x + a - 1))^(1/2*n)/x^3, x)","F",0
883,1,210,0,0.414122," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","-\frac{1}{9} \, \sqrt{-a^{2} x^{2} + 1} a^{7} c^{4} x^{8} - \frac{1}{8} \, \sqrt{-a^{2} x^{2} + 1} a^{6} c^{4} x^{7} + \frac{4}{9} \, \sqrt{-a^{2} x^{2} + 1} a^{5} c^{4} x^{6} + \frac{25}{48} \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{4} x^{5} - \frac{2}{3} \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} x^{4} - \frac{163}{192} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{4} x^{3} + \frac{4}{9} \, \sqrt{-a^{2} x^{2} + 1} a c^{4} x^{2} + \frac{93}{128} \, \sqrt{-a^{2} x^{2} + 1} c^{4} x + \frac{35 \, c^{4} \arcsin\left(a x\right)}{128 \, a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{9 \, a}"," ",0,"-1/9*sqrt(-a^2*x^2 + 1)*a^7*c^4*x^8 - 1/8*sqrt(-a^2*x^2 + 1)*a^6*c^4*x^7 + 4/9*sqrt(-a^2*x^2 + 1)*a^5*c^4*x^6 + 25/48*sqrt(-a^2*x^2 + 1)*a^4*c^4*x^5 - 2/3*sqrt(-a^2*x^2 + 1)*a^3*c^4*x^4 - 163/192*sqrt(-a^2*x^2 + 1)*a^2*c^4*x^3 + 4/9*sqrt(-a^2*x^2 + 1)*a*c^4*x^2 + 93/128*sqrt(-a^2*x^2 + 1)*c^4*x + 35/128*c^4*arcsin(a*x)/a - 1/9*sqrt(-a^2*x^2 + 1)*c^4/a","A",0
884,1,164,0,0.411230," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{7} \, \sqrt{-a^{2} x^{2} + 1} a^{5} c^{3} x^{6} + \frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{3} x^{5} - \frac{3}{7} \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{3} x^{4} - \frac{13}{24} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x^{3} + \frac{3}{7} \, \sqrt{-a^{2} x^{2} + 1} a c^{3} x^{2} + \frac{11}{16} \, \sqrt{-a^{2} x^{2} + 1} c^{3} x + \frac{5 \, c^{3} \arcsin\left(a x\right)}{16 \, a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{7 \, a}"," ",0,"1/7*sqrt(-a^2*x^2 + 1)*a^5*c^3*x^6 + 1/6*sqrt(-a^2*x^2 + 1)*a^4*c^3*x^5 - 3/7*sqrt(-a^2*x^2 + 1)*a^3*c^3*x^4 - 13/24*sqrt(-a^2*x^2 + 1)*a^2*c^3*x^3 + 3/7*sqrt(-a^2*x^2 + 1)*a*c^3*x^2 + 11/16*sqrt(-a^2*x^2 + 1)*c^3*x + 5/16*c^3*arcsin(a*x)/a - 1/7*sqrt(-a^2*x^2 + 1)*c^3/a","A",0
885,1,118,0,0.408456," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{5} \, \sqrt{-a^{2} x^{2} + 1} a^{3} c^{2} x^{4} - \frac{1}{4} \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{2} x^{3} + \frac{2}{5} \, \sqrt{-a^{2} x^{2} + 1} a c^{2} x^{2} + \frac{5}{8} \, \sqrt{-a^{2} x^{2} + 1} c^{2} x + \frac{3 \, c^{2} \arcsin\left(a x\right)}{8 \, a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{5 \, a}"," ",0,"-1/5*sqrt(-a^2*x^2 + 1)*a^3*c^2*x^4 - 1/4*sqrt(-a^2*x^2 + 1)*a^2*c^2*x^3 + 2/5*sqrt(-a^2*x^2 + 1)*a*c^2*x^2 + 5/8*sqrt(-a^2*x^2 + 1)*c^2*x + 3/8*c^2*arcsin(a*x)/a - 1/5*sqrt(-a^2*x^2 + 1)*c^2/a","A",0
886,1,64,0,0.402563," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{-a^{2} x^{2} + 1} a c x^{2} + \frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} c x + \frac{c \arcsin\left(a x\right)}{2 \, a} - \frac{\sqrt{-a^{2} x^{2} + 1} c}{3 \, a}"," ",0,"1/3*sqrt(-a^2*x^2 + 1)*a*c*x^2 + 1/2*sqrt(-a^2*x^2 + 1)*c*x + 1/2*c*arcsin(a*x)/a - 1/3*sqrt(-a^2*x^2 + 1)*c/a","A",0
887,1,204,0,0.541340," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{3 \, \sqrt{-a^{2} x^{2} + 1} c}{a^{7} c^{2} x + a^{6} c^{2}} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1} c}{a^{7} c^{2} x - a^{6} c^{2}} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1}}{a^{7} c x + a^{6} c} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1}}{a^{7} c x - a^{6} c} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} x^{2}}{a^{4} c} - \frac{3 \, \sqrt{-a^{2} x^{2} + 1} x}{a^{5} c} + \frac{9 \, \arcsin\left(a x\right)}{a^{6} c} - \frac{10 \, \sqrt{-a^{2} x^{2} + 1}}{a^{6} c}\right)}"," ",0,"-1/6*a*(3*sqrt(-a^2*x^2 + 1)*c/(a^7*c^2*x + a^6*c^2) + 3*sqrt(-a^2*x^2 + 1)*c/(a^7*c^2*x - a^6*c^2) - 3*sqrt(-a^2*x^2 + 1)/(a^7*c*x + a^6*c) + 3*sqrt(-a^2*x^2 + 1)/(a^7*c*x - a^6*c) - 2*sqrt(-a^2*x^2 + 1)*x^2/(a^4*c) - 3*sqrt(-a^2*x^2 + 1)*x/(a^5*c) + 9*arcsin(a*x)/(a^6*c) - 10*sqrt(-a^2*x^2 + 1)/(a^6*c))","B",0
888,1,178,0,0.490219," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\sqrt{-a^{2} x^{2} + 1} c}{a^{6} c^{2} x + a^{5} c^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} c}{a^{6} c^{2} x - a^{5} c^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{6} c x + a^{5} c} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{6} c x - a^{5} c} - \frac{\sqrt{-a^{2} x^{2} + 1} x}{a^{4} c} + \frac{3 \, \arcsin\left(a x\right)}{a^{5} c} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{5} c}\right)}"," ",0,"-1/2*a*(sqrt(-a^2*x^2 + 1)*c/(a^6*c^2*x + a^5*c^2) + sqrt(-a^2*x^2 + 1)*c/(a^6*c^2*x - a^5*c^2) - sqrt(-a^2*x^2 + 1)/(a^6*c*x + a^5*c) + sqrt(-a^2*x^2 + 1)/(a^6*c*x - a^5*c) - sqrt(-a^2*x^2 + 1)*x/(a^4*c) + 3*arcsin(a*x)/(a^5*c) - 2*sqrt(-a^2*x^2 + 1)/(a^5*c))","B",0
889,1,157,0,0.458177," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\sqrt{-a^{2} x^{2} + 1} c}{a^{5} c^{2} x + a^{4} c^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} c}{a^{5} c^{2} x - a^{4} c^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{5} c x + a^{4} c} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{5} c x - a^{4} c} + \frac{2 \, \arcsin\left(a x\right)}{a^{4} c} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{4} c}\right)}"," ",0,"-1/2*a*(sqrt(-a^2*x^2 + 1)*c/(a^5*c^2*x + a^4*c^2) + sqrt(-a^2*x^2 + 1)*c/(a^5*c^2*x - a^4*c^2) - sqrt(-a^2*x^2 + 1)/(a^5*c*x + a^4*c) + sqrt(-a^2*x^2 + 1)/(a^5*c*x - a^4*c) + 2*arcsin(a*x)/(a^4*c) - 2*sqrt(-a^2*x^2 + 1)/(a^4*c))","B",0
890,1,137,0,0.443171," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\sqrt{-a^{2} x^{2} + 1} c}{a^{4} c^{2} x + a^{3} c^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} c}{a^{4} c^{2} x - a^{3} c^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{4} c x + a^{3} c} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{4} c x - a^{3} c} + \frac{2 \, \arcsin\left(a x\right)}{a^{3} c}\right)}"," ",0,"-1/2*a*(sqrt(-a^2*x^2 + 1)*c/(a^4*c^2*x + a^3*c^2) + sqrt(-a^2*x^2 + 1)*c/(a^4*c^2*x - a^3*c^2) - sqrt(-a^2*x^2 + 1)/(a^4*c*x + a^3*c) + sqrt(-a^2*x^2 + 1)/(a^4*c*x - a^3*c) + 2*arcsin(a*x)/(a^3*c))","B",0
891,1,125,0,0.417223," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\sqrt{-a^{2} x^{2} + 1} c}{a^{3} c^{2} x + a^{2} c^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} c}{a^{3} c^{2} x - a^{2} c^{2}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{3} c x + a^{2} c} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{3} c x - a^{2} c}\right)}"," ",0,"-1/2*a*(sqrt(-a^2*x^2 + 1)*c/(a^3*c^2*x + a^2*c^2) + sqrt(-a^2*x^2 + 1)*c/(a^3*c^2*x - a^2*c^2) - sqrt(-a^2*x^2 + 1)/(a^3*c*x + a^2*c) + sqrt(-a^2*x^2 + 1)/(a^3*c*x - a^2*c))","B",0
892,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)} \sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"-integrate((a*x + 1)/((a^2*c*x^2 - c)*sqrt(-a^2*x^2 + 1)*x), x)","F",0
893,1,104,0,0.323626," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{\frac{a^{2} \log\left(\sqrt{-a^{2} x^{2} + 1} + 1\right)}{c} - \frac{a^{2} \log\left(\sqrt{-a^{2} x^{2} + 1} - 1\right)}{c} - \frac{2 \, a^{2}}{\sqrt{-a^{2} x^{2} + 1} c}}{2 \, a} + \frac{2 \, a^{2} x^{2} - 1}{\sqrt{a x + 1} \sqrt{-a x + 1} c x}"," ",0,"-1/2*(a^2*log(sqrt(-a^2*x^2 + 1) + 1)/c - a^2*log(sqrt(-a^2*x^2 + 1) - 1)/c - 2*a^2/(sqrt(-a^2*x^2 + 1)*c))/a + (2*a^2*x^2 - 1)/(sqrt(a*x + 1)*sqrt(-a*x + 1)*c*x)","A",0
894,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)} \sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"-integrate((a*x + 1)/((a^2*c*x^2 - c)*sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
895,1,148,0,0.327294," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{\frac{3 \, a^{4} \log\left(\sqrt{-a^{2} x^{2} + 1} + 1\right)}{c} - \frac{3 \, a^{4} \log\left(\sqrt{-a^{2} x^{2} + 1} - 1\right)}{c} + \frac{2 \, {\left(3 \, {\left(a^{2} x^{2} - 1\right)} a^{4} + 2 \, a^{4}\right)}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c - \sqrt{-a^{2} x^{2} + 1} c}}{4 \, a} + \frac{8 \, a^{4} x^{4} - 4 \, a^{2} x^{2} - 1}{3 \, \sqrt{a x + 1} \sqrt{-a x + 1} c x^{3}}"," ",0,"-1/4*(3*a^4*log(sqrt(-a^2*x^2 + 1) + 1)/c - 3*a^4*log(sqrt(-a^2*x^2 + 1) - 1)/c + 2*(3*(a^2*x^2 - 1)*a^4 + 2*a^4)/((-a^2*x^2 + 1)^(3/2)*c - sqrt(-a^2*x^2 + 1)*c))/a + 1/3*(8*a^4*x^4 - 4*a^2*x^2 - 1)/(sqrt(a*x + 1)*sqrt(-a*x + 1)*c*x^3)","A",0
896,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^6/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{6}}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^6/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)), x)","F",0
897,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","a \int \frac{x^{6}}{{\left(a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x} - \frac{\frac{3 \, \sqrt{-a^{2} x^{2} + 1}}{c^{2}} - \frac{6 \, a^{2} x^{2} - 5}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2}}}{3 \, a^{6}}"," ",0,"a*integrate(x^6/((a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)*sqrt(a*x + 1)*sqrt(-a*x + 1)), x) - 1/3*(3*sqrt(-a^2*x^2 + 1)/c^2 - (6*a^2*x^2 - 5)/((-a^2*x^2 + 1)^(3/2)*c^2))/a^6","F",0
898,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{4}}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^4/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)), x)","F",0
899,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","a \int \frac{x^{4}}{{\left(a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x} + \frac{3 \, a^{2} x^{2} - 2}{3 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{4} c^{2}}"," ",0,"a*integrate(x^4/((a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)*sqrt(a*x + 1)*sqrt(-a*x + 1)), x) + 1/3*(3*a^2*x^2 - 2)/((-a^2*x^2 + 1)^(3/2)*a^4*c^2)","F",0
900,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{2}}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^2/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)), x)","F",0
901,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","a \int \frac{x^{2}}{{\left(a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x} + \frac{1}{3 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2} c^{2}}"," ",0,"a*integrate(x^2/((a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)*sqrt(a*x + 1)*sqrt(-a*x + 1)), x) + 1/3/((-a^2*x^2 + 1)^(3/2)*a^2*c^2)","F",0
902,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)), x)","F",0
903,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)*x), x)","F",0
904,1,144,0,0.340403," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, a^{2} \log\left(\sqrt{-a^{2} x^{2} + 1} + 1\right)}{c^{2}} - \frac{3 \, a^{2} \log\left(\sqrt{-a^{2} x^{2} + 1} - 1\right)}{c^{2}} + \frac{2 \, {\left(3 \, {\left(a^{2} x^{2} - 1\right)} a^{2} - a^{2}\right)}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2}}}{6 \, a} + \frac{8 \, a^{4} x^{4} - 12 \, a^{2} x^{2} + 3}{3 \, {\left(a^{2} c^{2} x^{3} - c^{2} x\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}"," ",0,"-1/6*(3*a^2*log(sqrt(-a^2*x^2 + 1) + 1)/c^2 - 3*a^2*log(sqrt(-a^2*x^2 + 1) - 1)/c^2 + 2*(3*(a^2*x^2 - 1)*a^2 - a^2)/((-a^2*x^2 + 1)^(3/2)*c^2))/a + 1/3*(8*a^4*x^4 - 12*a^2*x^2 + 3)/((a^2*c^2*x^3 - c^2*x)*sqrt(a*x + 1)*sqrt(-a*x + 1))","A",0
905,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
906,1,191,0,0.339134," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{\frac{15 \, a^{4} \log\left(\sqrt{-a^{2} x^{2} + 1} + 1\right)}{c^{2}} - \frac{15 \, a^{4} \log\left(\sqrt{-a^{2} x^{2} + 1} - 1\right)}{c^{2}} - \frac{2 \, {\left(15 \, {\left(a^{2} x^{2} - 1\right)}^{2} a^{4} + 10 \, {\left(a^{2} x^{2} - 1\right)} a^{4} - 2 \, a^{4}\right)}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} c^{2} - {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2}}}{12 \, a} + \frac{16 \, a^{6} x^{6} - 24 \, a^{4} x^{4} + 6 \, a^{2} x^{2} + 1}{3 \, {\left(a^{2} c^{2} x^{5} - c^{2} x^{3}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}"," ",0,"-1/12*(15*a^4*log(sqrt(-a^2*x^2 + 1) + 1)/c^2 - 15*a^4*log(sqrt(-a^2*x^2 + 1) - 1)/c^2 - 2*(15*(a^2*x^2 - 1)^2*a^4 + 10*(a^2*x^2 - 1)*a^4 - 2*a^4)/((-a^2*x^2 + 1)^(5/2)*c^2 - (-a^2*x^2 + 1)^(3/2)*c^2))/a + 1/3*(16*a^6*x^6 - 24*a^4*x^4 + 6*a^2*x^2 + 1)/((a^2*c^2*x^5 - c^2*x^3)*sqrt(a*x + 1)*sqrt(-a*x + 1))","A",0
907,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^7/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-a \int \frac{x^{8}}{{\left(a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x} + \frac{\frac{5 \, \sqrt{-a^{2} x^{2} + 1}}{c^{3}} + \frac{5 \, a^{2} x^{2} + 15 \, {\left(a^{2} x^{2} - 1\right)}^{2} - 4}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} c^{3}}}{5 \, a^{8}}"," ",0,"-a*integrate(x^8/((a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)*sqrt(a*x + 1)*sqrt(-a*x + 1)), x) + 1/5*(5*sqrt(-a^2*x^2 + 1)/c^3 + (5*a^2*x^2 + 15*(a^2*x^2 - 1)^2 - 4)/((-a^2*x^2 + 1)^(5/2)*c^3))/a^8","F",0
908,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^6/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)} x^{6}}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"-integrate((a*x + 1)*x^6/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)), x)","F",0
909,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-a \int \frac{x^{6}}{{\left(a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x} + \frac{10 \, a^{2} x^{2} + 15 \, {\left(a^{2} x^{2} - 1\right)}^{2} - 7}{15 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{6} c^{3}}"," ",0,"-a*integrate(x^6/((a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)*sqrt(a*x + 1)*sqrt(-a*x + 1)), x) + 1/15*(10*a^2*x^2 + 15*(a^2*x^2 - 1)^2 - 7)/((-a^2*x^2 + 1)^(5/2)*a^6*c^3)","F",0
910,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)} x^{4}}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"-integrate((a*x + 1)*x^4/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)), x)","F",0
911,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-a \int \frac{x^{4}}{{\left(a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x} + \frac{5 \, a^{2} x^{2} - 2}{15 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{4} c^{3}}"," ",0,"-a*integrate(x^4/((a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)*sqrt(a*x + 1)*sqrt(-a*x + 1)), x) + 1/15*(5*a^2*x^2 - 2)/((-a^2*x^2 + 1)^(5/2)*a^4*c^3)","F",0
912,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)} x^{2}}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"-integrate((a*x + 1)*x^2/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)), x)","F",0
913,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-a \int \frac{x^{2}}{{\left(a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x} + \frac{1}{5 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{2} c^{3}}"," ",0,"-a*integrate(x^2/((a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)*sqrt(a*x + 1)*sqrt(-a*x + 1)), x) + 1/5/((-a^2*x^2 + 1)^(5/2)*a^2*c^3)","F",0
914,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"-integrate((a*x + 1)/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)), x)","F",0
915,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"-integrate((a*x + 1)/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)*x), x)","F",0
916,1,178,0,0.360987," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{\frac{15 \, a^{2} \log\left(\sqrt{-a^{2} x^{2} + 1} + 1\right)}{c^{3}} - \frac{15 \, a^{2} \log\left(\sqrt{-a^{2} x^{2} + 1} - 1\right)}{c^{3}} - \frac{2 \, {\left(15 \, {\left(a^{2} x^{2} - 1\right)}^{2} a^{2} - 5 \, {\left(a^{2} x^{2} - 1\right)} a^{2} + 3 \, a^{2}\right)}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} c^{3}}}{30 \, a} + \frac{16 \, a^{6} x^{6} - 40 \, a^{4} x^{4} + 30 \, a^{2} x^{2} - 5}{5 \, {\left(a^{4} c^{3} x^{5} - 2 \, a^{2} c^{3} x^{3} + c^{3} x\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}"," ",0,"-1/30*(15*a^2*log(sqrt(-a^2*x^2 + 1) + 1)/c^3 - 15*a^2*log(sqrt(-a^2*x^2 + 1) - 1)/c^3 - 2*(15*(a^2*x^2 - 1)^2*a^2 - 5*(a^2*x^2 - 1)*a^2 + 3*a^2)/((-a^2*x^2 + 1)^(5/2)*c^3))/a + 1/5*(16*a^6*x^6 - 40*a^4*x^4 + 30*a^2*x^2 - 5)/((a^4*c^3*x^5 - 2*a^2*c^3*x^3 + c^3*x)*sqrt(a*x + 1)*sqrt(-a*x + 1))","A",0
917,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"-integrate((a*x + 1)/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
918,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{4} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/((a^2*c*x^2 - c)^4*sqrt(-a^2*x^2 + 1)), x)","F",0
919,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^5,x, algorithm=""maxima"")","-\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{5} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"-integrate((a*x + 1)/((a^2*c*x^2 - c)^5*sqrt(-a^2*x^2 + 1)), x)","F",0
920,1,43,0,0.314449," ","integrate((a*x+1)/(-a^2*x^2+1)*x^4,x, algorithm=""maxima"")","-\frac{3 \, a^{3} x^{4} + 4 \, a^{2} x^{3} + 6 \, a x^{2} + 12 \, x}{12 \, a^{4}} - \frac{\log\left(a x - 1\right)}{a^{5}}"," ",0,"-1/12*(3*a^3*x^4 + 4*a^2*x^3 + 6*a*x^2 + 12*x)/a^4 - log(a*x - 1)/a^5","A",0
921,1,35,0,0.317932," ","integrate((a*x+1)/(-a^2*x^2+1)*x^3,x, algorithm=""maxima"")","-\frac{2 \, a^{2} x^{3} + 3 \, a x^{2} + 6 \, x}{6 \, a^{3}} - \frac{\log\left(a x - 1\right)}{a^{4}}"," ",0,"-1/6*(2*a^2*x^3 + 3*a*x^2 + 6*x)/a^3 - log(a*x - 1)/a^4","A",0
922,1,26,0,0.321402," ","integrate((a*x+1)/(-a^2*x^2+1)*x^2,x, algorithm=""maxima"")","-\frac{a x^{2} + 2 \, x}{2 \, a^{2}} - \frac{\log\left(a x - 1\right)}{a^{3}}"," ",0,"-1/2*(a*x^2 + 2*x)/a^2 - log(a*x - 1)/a^3","A",0
923,1,18,0,0.361881," ","integrate((a*x+1)/(-a^2*x^2+1)*x,x, algorithm=""maxima"")","-\frac{x}{a} - \frac{\log\left(a x - 1\right)}{a^{2}}"," ",0,"-x/a - log(a*x - 1)/a^2","A",0
924,1,11,0,0.310802," ","integrate((a*x+1)/(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{\log\left(a x - 1\right)}{a}"," ",0,"-log(a*x - 1)/a","A",0
925,1,11,0,0.314374," ","integrate((a*x+1)/(-a^2*x^2+1)/x,x, algorithm=""maxima"")","-\log\left(a x - 1\right) + \log\left(x\right)"," ",0,"-log(a*x - 1) + log(x)","A",0
926,1,19,0,0.305958," ","integrate((a*x+1)/(-a^2*x^2+1)/x^2,x, algorithm=""maxima"")","-a \log\left(a x - 1\right) + a \log\left(x\right) - \frac{1}{x}"," ",0,"-a*log(a*x - 1) + a*log(x) - 1/x","A",0
927,1,29,0,0.305846," ","integrate((a*x+1)/(-a^2*x^2+1)/x^3,x, algorithm=""maxima"")","-a^{2} \log\left(a x - 1\right) + a^{2} \log\left(x\right) - \frac{2 \, a x + 1}{2 \, x^{2}}"," ",0,"-a^2*log(a*x - 1) + a^2*log(x) - 1/2*(2*a*x + 1)/x^2","A",0
928,1,37,0,0.309850," ","integrate((a*x+1)/(-a^2*x^2+1)/x^4,x, algorithm=""maxima"")","-a^{3} \log\left(a x - 1\right) + a^{3} \log\left(x\right) - \frac{6 \, a^{2} x^{2} + 3 \, a x + 2}{6 \, x^{3}}"," ",0,"-a^3*log(a*x - 1) + a^3*log(x) - 1/6*(6*a^2*x^2 + 3*a*x + 2)/x^3","A",0
929,1,52,0,0.314158," ","integrate((a*x+1)/(-a^2*x^2+1)^2*x^4,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(a^{6} x - a^{5}\right)}} + \frac{a x^{2} + 2 \, x}{2 \, a^{4}} + \frac{\log\left(a x + 1\right)}{4 \, a^{5}} + \frac{7 \, \log\left(a x - 1\right)}{4 \, a^{5}}"," ",0,"-1/2/(a^6*x - a^5) + 1/2*(a*x^2 + 2*x)/a^4 + 1/4*log(a*x + 1)/a^5 + 7/4*log(a*x - 1)/a^5","A",0
930,1,43,0,0.305033," ","integrate((a*x+1)/(-a^2*x^2+1)^2*x^3,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(a^{5} x - a^{4}\right)}} + \frac{x}{a^{3}} - \frac{\log\left(a x + 1\right)}{4 \, a^{4}} + \frac{5 \, \log\left(a x - 1\right)}{4 \, a^{4}}"," ",0,"-1/2/(a^5*x - a^4) + x/a^3 - 1/4*log(a*x + 1)/a^4 + 5/4*log(a*x - 1)/a^4","A",0
931,1,38,0,0.305709," ","integrate((a*x+1)/(-a^2*x^2+1)^2*x^2,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(a^{4} x - a^{3}\right)}} + \frac{\log\left(a x + 1\right)}{4 \, a^{3}} + \frac{3 \, \log\left(a x - 1\right)}{4 \, a^{3}}"," ",0,"-1/2/(a^4*x - a^3) + 1/4*log(a*x + 1)/a^3 + 3/4*log(a*x - 1)/a^3","A",0
932,1,38,0,0.339098," ","integrate((a*x+1)/(-a^2*x^2+1)^2*x,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(a^{3} x - a^{2}\right)}} - \frac{\log\left(a x + 1\right)}{4 \, a^{2}} + \frac{\log\left(a x - 1\right)}{4 \, a^{2}}"," ",0,"-1/2/(a^3*x - a^2) - 1/4*log(a*x + 1)/a^2 + 1/4*log(a*x - 1)/a^2","A",0
933,1,36,0,0.321079," ","integrate((a*x+1)/(-a^2*x^2+1)^2,x, algorithm=""maxima"")","\frac{\log\left(a x + 1\right)}{4 \, a} - \frac{\log\left(a x - 1\right)}{4 \, a} - \frac{1}{2 \, {\left(a^{2} x - a\right)}}"," ",0,"1/4*log(a*x + 1)/a - 1/4*log(a*x - 1)/a - 1/2/(a^2*x - a)","A",0
934,1,28,0,0.335278," ","integrate((a*x+1)/(-a^2*x^2+1)^2/x,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(a x - 1\right)}} - \frac{1}{4} \, \log\left(a x + 1\right) - \frac{3}{4} \, \log\left(a x - 1\right) + \log\left(x\right)"," ",0,"-1/2/(a*x - 1) - 1/4*log(a*x + 1) - 3/4*log(a*x - 1) + log(x)","A",0
935,1,42,0,0.319672," ","integrate((a*x+1)/(-a^2*x^2+1)^2/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, a \log\left(a x + 1\right) - \frac{5}{4} \, a \log\left(a x - 1\right) + a \log\left(x\right) - \frac{3 \, a x - 2}{2 \, {\left(a x^{2} - x\right)}}"," ",0,"1/4*a*log(a*x + 1) - 5/4*a*log(a*x - 1) + a*log(x) - 1/2*(3*a*x - 2)/(a*x^2 - x)","A",0
936,1,59,0,0.313791," ","integrate((a*x+1)/(-a^2*x^2+1)^2/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} \log\left(a x + 1\right) - \frac{7}{4} \, a^{2} \log\left(a x - 1\right) + 2 \, a^{2} \log\left(x\right) - \frac{3 \, a^{2} x^{2} - a x - 1}{2 \, {\left(a x^{3} - x^{2}\right)}}"," ",0,"-1/4*a^2*log(a*x + 1) - 7/4*a^2*log(a*x - 1) + 2*a^2*log(x) - 1/2*(3*a^2*x^2 - a*x - 1)/(a*x^3 - x^2)","A",0
937,1,67,0,0.318665," ","integrate((a*x+1)/(-a^2*x^2+1)^2/x^4,x, algorithm=""maxima"")","\frac{1}{4} \, a^{3} \log\left(a x + 1\right) - \frac{9}{4} \, a^{3} \log\left(a x - 1\right) + 2 \, a^{3} \log\left(x\right) - \frac{15 \, a^{3} x^{3} - 9 \, a^{2} x^{2} - a x - 2}{6 \, {\left(a x^{4} - x^{3}\right)}}"," ",0,"1/4*a^3*log(a*x + 1) - 9/4*a^3*log(a*x - 1) + 2*a^3*log(x) - 1/6*(15*a^3*x^3 - 9*a^2*x^2 - a*x - 2)/(a*x^4 - x^3)","A",0
938,1,80,0,0.320353," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^6,x, algorithm=""maxima"")","\frac{9 \, a^{2} x^{2} + 3 \, a x - 10}{8 \, {\left(a^{10} x^{3} - a^{9} x^{2} - a^{8} x + a^{7}\right)}} - \frac{a x^{2} + 2 \, x}{2 \, a^{6}} - \frac{9 \, \log\left(a x + 1\right)}{16 \, a^{7}} - \frac{39 \, \log\left(a x - 1\right)}{16 \, a^{7}}"," ",0,"1/8*(9*a^2*x^2 + 3*a*x - 10)/(a^10*x^3 - a^9*x^2 - a^8*x + a^7) - 1/2*(a*x^2 + 2*x)/a^6 - 9/16*log(a*x + 1)/a^7 - 39/16*log(a*x - 1)/a^7","A",0
939,1,72,0,0.325920," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^5,x, algorithm=""maxima"")","\frac{9 \, a^{2} x^{2} - a x - 6}{8 \, {\left(a^{9} x^{3} - a^{8} x^{2} - a^{7} x + a^{6}\right)}} - \frac{x}{a^{5}} + \frac{7 \, \log\left(a x + 1\right)}{16 \, a^{6}} - \frac{23 \, \log\left(a x - 1\right)}{16 \, a^{6}}"," ",0,"1/8*(9*a^2*x^2 - a*x - 6)/(a^9*x^3 - a^8*x^2 - a^7*x + a^6) - x/a^5 + 7/16*log(a*x + 1)/a^6 - 23/16*log(a*x - 1)/a^6","A",0
940,1,66,0,0.318977," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^4,x, algorithm=""maxima"")","\frac{5 \, a^{2} x^{2} + 3 \, a x - 6}{8 \, {\left(a^{8} x^{3} - a^{7} x^{2} - a^{6} x + a^{5}\right)}} - \frac{5 \, \log\left(a x + 1\right)}{16 \, a^{5}} - \frac{11 \, \log\left(a x - 1\right)}{16 \, a^{5}}"," ",0,"1/8*(5*a^2*x^2 + 3*a*x - 6)/(a^8*x^3 - a^7*x^2 - a^6*x + a^5) - 5/16*log(a*x + 1)/a^5 - 11/16*log(a*x - 1)/a^5","A",0
941,1,66,0,0.314342," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^3,x, algorithm=""maxima"")","\frac{5 \, a^{2} x^{2} - a x - 2}{8 \, {\left(a^{7} x^{3} - a^{6} x^{2} - a^{5} x + a^{4}\right)}} + \frac{3 \, \log\left(a x + 1\right)}{16 \, a^{4}} - \frac{3 \, \log\left(a x - 1\right)}{16 \, a^{4}}"," ",0,"1/8*(5*a^2*x^2 - a*x - 2)/(a^7*x^3 - a^6*x^2 - a^5*x + a^4) + 3/16*log(a*x + 1)/a^4 - 3/16*log(a*x - 1)/a^4","A",0
942,1,65,0,0.320668," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^2,x, algorithm=""maxima"")","\frac{a^{2} x^{2} + 3 \, a x - 2}{8 \, {\left(a^{6} x^{3} - a^{5} x^{2} - a^{4} x + a^{3}\right)}} - \frac{\log\left(a x + 1\right)}{16 \, a^{3}} + \frac{\log\left(a x - 1\right)}{16 \, a^{3}}"," ",0,"1/8*(a^2*x^2 + 3*a*x - 2)/(a^6*x^3 - a^5*x^2 - a^4*x + a^3) - 1/16*log(a*x + 1)/a^3 + 1/16*log(a*x - 1)/a^3","A",0
943,1,65,0,0.316735," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x,x, algorithm=""maxima"")","\frac{a^{2} x^{2} - a x + 2}{8 \, {\left(a^{5} x^{3} - a^{4} x^{2} - a^{3} x + a^{2}\right)}} - \frac{\log\left(a x + 1\right)}{16 \, a^{2}} + \frac{\log\left(a x - 1\right)}{16 \, a^{2}}"," ",0,"1/8*(a^2*x^2 - a*x + 2)/(a^5*x^3 - a^4*x^2 - a^3*x + a^2) - 1/16*log(a*x + 1)/a^2 + 1/16*log(a*x - 1)/a^2","A",0
944,1,64,0,0.312666," ","integrate((a*x+1)/(-a^2*x^2+1)^3,x, algorithm=""maxima"")","-\frac{3 \, a^{2} x^{2} - 3 \, a x - 2}{8 \, {\left(a^{4} x^{3} - a^{3} x^{2} - a^{2} x + a\right)}} + \frac{3 \, \log\left(a x + 1\right)}{16 \, a} - \frac{3 \, \log\left(a x - 1\right)}{16 \, a}"," ",0,"-1/8*(3*a^2*x^2 - 3*a*x - 2)/(a^4*x^3 - a^3*x^2 - a^2*x + a) + 3/16*log(a*x + 1)/a - 3/16*log(a*x - 1)/a","A",0
945,1,57,0,0.311118," ","integrate((a*x+1)/(-a^2*x^2+1)^3/x,x, algorithm=""maxima"")","-\frac{3 \, a^{2} x^{2} + a x - 6}{8 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)}} - \frac{5}{16} \, \log\left(a x + 1\right) - \frac{11}{16} \, \log\left(a x - 1\right) + \log\left(x\right)"," ",0,"-1/8*(3*a^2*x^2 + a*x - 6)/(a^3*x^3 - a^2*x^2 - a*x + 1) - 5/16*log(a*x + 1) - 11/16*log(a*x - 1) + log(x)","A",0
946,1,72,0,0.310017," ","integrate((a*x+1)/(-a^2*x^2+1)^3/x^2,x, algorithm=""maxima"")","\frac{7}{16} \, a \log\left(a x + 1\right) - \frac{23}{16} \, a \log\left(a x - 1\right) + a \log\left(x\right) - \frac{15 \, a^{3} x^{3} - 11 \, a^{2} x^{2} - 14 \, a x + 8}{8 \, {\left(a^{3} x^{4} - a^{2} x^{3} - a x^{2} + x\right)}}"," ",0,"7/16*a*log(a*x + 1) - 23/16*a*log(a*x - 1) + a*log(x) - 1/8*(15*a^3*x^3 - 11*a^2*x^2 - 14*a*x + 8)/(a^3*x^4 - a^2*x^3 - a*x^2 + x)","A",0
947,1,89,0,0.328569," ","integrate((a*x+1)/(-a^2*x^2+1)^3/x^3,x, algorithm=""maxima"")","-\frac{9}{16} \, a^{2} \log\left(a x + 1\right) - \frac{39}{16} \, a^{2} \log\left(a x - 1\right) + 3 \, a^{2} \log\left(x\right) - \frac{15 \, a^{4} x^{4} - 3 \, a^{3} x^{3} - 22 \, a^{2} x^{2} + 4 \, a x + 4}{8 \, {\left(a^{3} x^{5} - a^{2} x^{4} - a x^{3} + x^{2}\right)}}"," ",0,"-9/16*a^2*log(a*x + 1) - 39/16*a^2*log(a*x - 1) + 3*a^2*log(x) - 1/8*(15*a^4*x^4 - 3*a^3*x^3 - 22*a^2*x^2 + 4*a*x + 4)/(a^3*x^5 - a^2*x^4 - a*x^3 + x^2)","A",0
948,1,97,0,0.306847," ","integrate((a*x+1)/(-a^2*x^2+1)^3/x^4,x, algorithm=""maxima"")","\frac{11}{16} \, a^{3} \log\left(a x + 1\right) - \frac{59}{16} \, a^{3} \log\left(a x - 1\right) + 3 \, a^{3} \log\left(x\right) - \frac{105 \, a^{5} x^{5} - 69 \, a^{4} x^{4} - 106 \, a^{3} x^{3} + 52 \, a^{2} x^{2} + 4 \, a x + 8}{24 \, {\left(a^{3} x^{6} - a^{2} x^{5} - a x^{4} + x^{3}\right)}}"," ",0,"11/16*a^3*log(a*x + 1) - 59/16*a^3*log(a*x - 1) + 3*a^3*log(x) - 1/24*(105*a^5*x^5 - 69*a^4*x^4 - 106*a^3*x^3 + 52*a^2*x^2 + 4*a*x + 8)/(a^3*x^6 - a^2*x^5 - a*x^4 + x^3)","A",0
949,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
950,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
951,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
952,1,56,0,0.338360," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""maxima"")","a \sqrt{c} x - \frac{1}{2} \, \left(-1\right)^{-2 \, a^{2} c x^{2} + 2 \, c} \sqrt{c} \log\left(-2 \, a^{2} c + \frac{2 \, c}{x^{2}}\right) - \frac{1}{2} \, \sqrt{c} \log\left(x^{2} - \frac{1}{a^{2}}\right)"," ",0,"a*sqrt(c)*x - 1/2*(-1)^(-2*a^2*c*x^2 + 2*c)*sqrt(c)*log(-2*a^2*c + 2*c/x^2) - 1/2*sqrt(c)*log(x^2 - 1/a^2)","A",0
953,1,60,0,0.347624," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\left(-1\right)^{-2 \, a^{2} c x^{2} + 2 \, c} \sqrt{c} \log\left(-2 \, a^{2} c + \frac{2 \, c}{x^{2}}\right) + \sqrt{c} \log\left(x^{2} - \frac{1}{a^{2}}\right)\right)} a - \frac{\sqrt{c}}{x}"," ",0,"-1/2*((-1)^(-2*a^2*c*x^2 + 2*c)*sqrt(c)*log(-2*a^2*c + 2*c/x^2) + sqrt(c)*log(x^2 - 1/a^2))*a - sqrt(c)/x","A",0
954,1,66,0,0.330589," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} c^{\frac{3}{2}} x^{3} + c^{\frac{3}{2}} x + \frac{1}{4} \, {\left(a^{2} c^{\frac{3}{2}} x^{4} + 2 \, c^{\frac{3}{2}} x^{2} - \frac{4 \, \sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} c}{a^{2}}\right)} a"," ",0,"-1/3*a^2*c^(3/2)*x^3 + c^(3/2)*x + 1/4*(a^2*c^(3/2)*x^4 + 2*c^(3/2)*x^2 - 4*sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*c/a^2)*a","A",0
955,1,111,0,0.338220," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{1}{5} \, a^{4} c^{\frac{5}{2}} x^{5} - \frac{2}{3} \, a^{2} c^{\frac{5}{2}} x^{3} + c^{\frac{5}{2}} x - \frac{1}{6} \, {\left(\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} a^{2} c^{2} x^{4} - 2 \, a^{2} c^{\frac{5}{2}} x^{4} - 4 \, c^{\frac{5}{2}} x^{2} + \frac{7 \, \sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} c^{2}}{a^{2}}\right)} a"," ",0,"1/5*a^4*c^(5/2)*x^5 - 2/3*a^2*c^(5/2)*x^3 + c^(5/2)*x - 1/6*(sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*a^2*c^2*x^4 - 2*a^2*c^(5/2)*x^4 - 4*c^(5/2)*x^2 + 7*sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*c^2/a^2)*a","A",0
956,1,154,0,0.406516," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","-\frac{1}{7} \, a^{6} c^{\frac{7}{2}} x^{7} + \frac{3}{5} \, a^{4} c^{\frac{7}{2}} x^{5} - a^{2} c^{\frac{7}{2}} x^{3} + c^{\frac{7}{2}} x + \frac{1}{8} \, {\left(\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} a^{4} c^{3} x^{6} - 3 \, \sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} a^{2} c^{3} x^{4} + 3 \, a^{2} c^{\frac{7}{2}} x^{4} + 6 \, c^{\frac{7}{2}} x^{2} - \frac{10 \, \sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} c^{3}}{a^{2}}\right)} a"," ",0,"-1/7*a^6*c^(7/2)*x^7 + 3/5*a^4*c^(7/2)*x^5 - a^2*c^(7/2)*x^3 + c^(7/2)*x + 1/8*(sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*a^4*c^3*x^6 - 3*sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*a^2*c^3*x^4 + 3*a^2*c^(7/2)*x^4 + 6*c^(7/2)*x^2 - 10*sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*c^3/a^2)*a","A",0
957,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{4}}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^4/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)), x)","F",0
958,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{-\frac{1}{6} \, a {\left(\frac{2 \, {\left(a^{2} x^{3} + 3 \, x\right)}}{a^{4}} - \frac{3 \, \log\left(a x + 1\right)}{a^{5}} + \frac{3 \, \log\left(a x - 1\right)}{a^{5}}\right)}}{\sqrt{c}} + \frac{\log\left(x^{2} - \frac{1}{a^{2}}\right)}{2 \, a^{4} \sqrt{c}} + \frac{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}}{2 \, a^{4} c}"," ",0,"a*integrate(-x^4/((a*x + 1)*(a*x - 1)), x)/sqrt(c) + 1/2*log(x^2 - 1/a^2)/(a^4*sqrt(c)) + 1/2*sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)/(a^4*c)","F",0
959,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{2}}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^2/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)), x)","F",0
960,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{-\frac{1}{2} \, a {\left(\frac{2 \, x}{a^{2}} - \frac{\log\left(a x + 1\right)}{a^{3}} + \frac{\log\left(a x - 1\right)}{a^{3}}\right)}}{\sqrt{c}} + \frac{\log\left(x^{2} - \frac{1}{a^{2}}\right)}{2 \, a^{2} \sqrt{c}}"," ",0,"a*integrate(-x^2/((a*x + 1)*(a*x - 1)), x)/sqrt(c) + 1/2*log(x^2 - 1/a^2)/(a^2*sqrt(c))","F",0
961,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)), x)","F",0
962,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)*x), x)","F",0
963,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
964,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{\left(-1\right)^{-2 \, a^{2} c x^{2} + 2 \, c} a^{2} \log\left(-2 \, a^{2} c + \frac{2 \, c}{x^{2}}\right)}{2 \, \sqrt{c}} + \frac{\frac{1}{2} \, {\left(a \log\left(a x + 1\right) - a \log\left(a x - 1\right) - \frac{2}{x}\right)} a}{\sqrt{c}} - \frac{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}}{2 \, c x^{2}}"," ",0,"-1/2*(-1)^(-2*a^2*c*x^2 + 2*c)*a^2*log(-2*a^2*c + 2*c/x^2)/sqrt(c) + a*integrate(-1/((a*x + 1)*(a*x - 1)*x^2), x)/sqrt(c) - 1/2*sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)/(c*x^2)","F",0
965,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)*x^4), x)","F",0
966,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-a \int -\frac{x^{6}}{{\left(a^{2} c^{\frac{3}{2}} x^{2} - c^{\frac{3}{2}}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}\,{d x} - \frac{1}{2 \, {\left(a^{8} c^{\frac{3}{2}} x^{2} - a^{6} c^{\frac{3}{2}}\right)}} + \frac{\log\left(-a^{2} c x^{2} + c\right)}{a^{6} c^{\frac{3}{2}}} - \frac{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}}{2 \, a^{6} c^{2}}"," ",0,"-a*integrate(-x^6/((a^2*c^(3/2)*x^2 - c^(3/2))*(a*x + 1)*(a*x - 1)), x) - 1/2/(a^8*c^(3/2)*x^2 - a^6*c^(3/2)) + log(-a^2*c*x^2 + c)/(a^6*c^(3/2)) - 1/2*sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)/(a^6*c^2)","F",0
967,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{4}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^4/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
968,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-a \int -\frac{x^{4}}{{\left(a^{2} c^{\frac{3}{2}} x^{2} - c^{\frac{3}{2}}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}\,{d x} - \frac{1}{2 \, {\left(a^{6} c^{\frac{3}{2}} x^{2} - a^{4} c^{\frac{3}{2}}\right)}} + \frac{\log\left(-a^{2} c x^{2} + c\right)}{2 \, a^{4} c^{\frac{3}{2}}}"," ",0,"-a*integrate(-x^4/((a^2*c^(3/2)*x^2 - c^(3/2))*(a*x + 1)*(a*x - 1)), x) - 1/2/(a^6*c^(3/2)*x^2 - a^4*c^(3/2)) + 1/2*log(-a^2*c*x^2 + c)/(a^4*c^(3/2))","F",0
969,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^2/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
970,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-a \int -\frac{x^{2}}{{\left(a^{2} c^{\frac{3}{2}} x^{2} - c^{\frac{3}{2}}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}\,{d x} - \frac{1}{2 \, {\left(a^{4} c^{\frac{3}{2}} x^{2} - a^{2} c^{\frac{3}{2}}\right)}}"," ",0,"-a*integrate(-x^2/((a^2*c^(3/2)*x^2 - c^(3/2))*(a*x + 1)*(a*x - 1)), x) - 1/2/(a^4*c^(3/2)*x^2 - a^2*c^(3/2))","F",0
971,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
972,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)*x), x)","F",0
973,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
974,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
975,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)*x^4), x)","F",0
976,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^6/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{6}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^6/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
977,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","a \int -\frac{x^{6}}{{\left(a^{4} c^{\frac{5}{2}} x^{4} - 2 \, a^{2} c^{\frac{5}{2}} x^{2} + c^{\frac{5}{2}}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}\,{d x} + \frac{1}{4 \, {\left(a^{10} c^{\frac{5}{2}} x^{4} - 2 \, a^{8} c^{\frac{5}{2}} x^{2} + a^{6} c^{\frac{5}{2}}\right)}} + \frac{1}{a^{8} c^{\frac{5}{2}} x^{2} - a^{6} c^{\frac{5}{2}}} - \frac{\log\left(-a^{2} c x^{2} + c\right)}{2 \, a^{6} c^{\frac{5}{2}}}"," ",0,"a*integrate(-x^6/((a^4*c^(5/2)*x^4 - 2*a^2*c^(5/2)*x^2 + c^(5/2))*(a*x + 1)*(a*x - 1)), x) + 1/4/(a^10*c^(5/2)*x^4 - 2*a^8*c^(5/2)*x^2 + a^6*c^(5/2)) + 1/(a^8*c^(5/2)*x^2 - a^6*c^(5/2)) - 1/2*log(-a^2*c*x^2 + c)/(a^6*c^(5/2))","F",0
978,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{4}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^4/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
979,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","a \int -\frac{x^{4}}{{\left(a^{4} c^{\frac{5}{2}} x^{4} - 2 \, a^{2} c^{\frac{5}{2}} x^{2} + c^{\frac{5}{2}}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}\,{d x} + \frac{1}{4 \, {\left(a^{8} c^{\frac{5}{2}} x^{4} - 2 \, a^{6} c^{\frac{5}{2}} x^{2} + a^{4} c^{\frac{5}{2}}\right)}} + \frac{1}{2 \, {\left(a^{6} c^{\frac{5}{2}} x^{2} - a^{4} c^{\frac{5}{2}}\right)}}"," ",0,"a*integrate(-x^4/((a^4*c^(5/2)*x^4 - 2*a^2*c^(5/2)*x^2 + c^(5/2))*(a*x + 1)*(a*x - 1)), x) + 1/4/(a^8*c^(5/2)*x^4 - 2*a^6*c^(5/2)*x^2 + a^4*c^(5/2)) + 1/2/(a^6*c^(5/2)*x^2 - a^4*c^(5/2))","F",0
980,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^2/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
981,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","a \int -\frac{x^{2}}{{\left(a^{4} c^{\frac{5}{2}} x^{4} - 2 \, a^{2} c^{\frac{5}{2}} x^{2} + c^{\frac{5}{2}}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}\,{d x} + \frac{1}{4 \, {\left(a^{6} c^{\frac{5}{2}} x^{4} - 2 \, a^{4} c^{\frac{5}{2}} x^{2} + a^{2} c^{\frac{5}{2}}\right)}}"," ",0,"a*integrate(-x^2/((a^4*c^(5/2)*x^4 - 2*a^2*c^(5/2)*x^2 + c^(5/2))*(a*x + 1)*(a*x - 1)), x) + 1/4/(a^6*c^(5/2)*x^4 - 2*a^4*c^(5/2)*x^2 + a^2*c^(5/2))","F",0
982,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
983,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)*x), x)","F",0
984,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
985,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
986,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(7/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
987,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} - c\right)}^{2} {\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a^2*c*x^2 - c)^2*(a*x + 1)*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
988,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} c x^{2} - c\right)} {\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"-integrate((a^2*c*x^2 - c)*(a*x + 1)*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
989,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(a^{2} c x^{2} - c\right)} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"-integrate((a*x + 1)*x^m/((a^2*c*x^2 - c)*sqrt(-a^2*x^2 + 1)), x)","F",0
990,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)), x)","F",0
991,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"-integrate((a*x + 1)*x^m/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)), x)","F",0
992,1,82,0,0.317256," ","integrate((a*x+1)*(-a^2*x^2+1)^2*x^m,x, algorithm=""maxima"")","\frac{a^{5} x^{m + 6}}{m + 6} + \frac{a^{4} x^{m + 5}}{m + 5} - \frac{2 \, a^{3} x^{m + 4}}{m + 4} - \frac{2 \, a^{2} x^{m + 3}}{m + 3} + \frac{a x^{m + 2}}{m + 2} + \frac{x^{m + 1}}{m + 1}"," ",0,"a^5*x^(m + 6)/(m + 6) + a^4*x^(m + 5)/(m + 5) - 2*a^3*x^(m + 4)/(m + 4) - 2*a^2*x^(m + 3)/(m + 3) + a*x^(m + 2)/(m + 2) + x^(m + 1)/(m + 1)","A",0
993,1,54,0,0.349024," ","integrate((a*x+1)*(-a^2*x^2+1)*x^m,x, algorithm=""maxima"")","-\frac{a^{3} x^{m + 4}}{m + 4} - \frac{a^{2} x^{m + 3}}{m + 3} + \frac{a x^{m + 2}}{m + 2} + \frac{x^{m + 1}}{m + 1}"," ",0,"-a^3*x^(m + 4)/(m + 4) - a^2*x^(m + 3)/(m + 3) + a*x^(m + 2)/(m + 2) + x^(m + 1)/(m + 1)","A",0
994,1,24,0,0.304142," ","integrate((a*x+1)*x^m,x, algorithm=""maxima"")","\frac{a x^{m + 2}}{m + 2} + \frac{x^{m + 1}}{m + 1}"," ",0,"a*x^(m + 2)/(m + 2) + x^(m + 1)/(m + 1)","A",0
995,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)*x^m,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)} x^{m}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)*x^m/(a^2*x^2 - 1), x)","F",0
996,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^2*x^m,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/(a^2*x^2 - 1)^2, x)","F",0
997,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^m,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(a^{2} x^{2} - 1\right)}^{3}}\,{d x}"," ",0,"-integrate((a*x + 1)*x^m/(a^2*x^2 - 1)^3, x)","F",0
998,1,144,0,0.346544," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{{\left({\left(m^{2} + 6 \, m + 8\right)} a^{4} c^{\frac{5}{2}} x^{6} - 2 \, {\left(m^{2} + 8 \, m + 12\right)} a^{2} c^{\frac{5}{2}} x^{4} + {\left(m^{2} + 10 \, m + 24\right)} c^{\frac{5}{2}} x^{2}\right)} a x^{m}}{m^{3} + 12 \, m^{2} + 44 \, m + 48} + \frac{{\left({\left(m^{2} + 4 \, m + 3\right)} a^{4} c^{\frac{5}{2}} x^{5} - 2 \, {\left(m^{2} + 6 \, m + 5\right)} a^{2} c^{\frac{5}{2}} x^{3} + {\left(m^{2} + 8 \, m + 15\right)} c^{\frac{5}{2}} x\right)} x^{m}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"((m^2 + 6*m + 8)*a^4*c^(5/2)*x^6 - 2*(m^2 + 8*m + 12)*a^2*c^(5/2)*x^4 + (m^2 + 10*m + 24)*c^(5/2)*x^2)*a*x^m/(m^3 + 12*m^2 + 44*m + 48) + ((m^2 + 4*m + 3)*a^4*c^(5/2)*x^5 - 2*(m^2 + 6*m + 5)*a^2*c^(5/2)*x^3 + (m^2 + 8*m + 15)*c^(5/2)*x)*x^m/(m^3 + 9*m^2 + 23*m + 15)","A",0
999,1,80,0,0.369886," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(a^{2} c^{\frac{3}{2}} {\left(m + 2\right)} x^{4} - c^{\frac{3}{2}} {\left(m + 4\right)} x^{2}\right)} a x^{m}}{m^{2} + 6 \, m + 8} - \frac{{\left(a^{2} c^{\frac{3}{2}} {\left(m + 1\right)} x^{3} - c^{\frac{3}{2}} {\left(m + 3\right)} x\right)} x^{m}}{m^{2} + 4 \, m + 3}"," ",0,"-(a^2*c^(3/2)*(m + 2)*x^4 - c^(3/2)*(m + 4)*x^2)*a*x^m/(m^2 + 6*m + 8) - (a^2*c^(3/2)*(m + 1)*x^3 - c^(3/2)*(m + 3)*x)*x^m/(m^2 + 4*m + 3)","A",0
1000,1,30,0,0.343225," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{a \sqrt{c} x^{2} x^{m}}{m + 2} + \frac{\sqrt{c} x x^{m}}{m + 1}"," ",0,"a*sqrt(c)*x^2*x^m/(m + 2) + sqrt(c)*x*x^m/(m + 1)","A",0
1001,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)), x)","F",0
1002,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
1003,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
1004,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
1005,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a^2*x^2+1)^p,x, algorithm=""maxima"")","a \int \frac{x^{4} e^{\left(p \log\left(a x + 1\right) + p \log\left(-a x + 1\right)\right)}}{\sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x} + \frac{{\left(a^{4} {\left(2 \, p + 1\right)} x^{4} - a^{2} {\left(2 \, p - 1\right)} x^{2} - 2\right)} {\left(-a^{2} x^{2} + 1\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} {\left(4 \, p^{2} + 8 \, p + 3\right)} a^{4}}"," ",0,"a*integrate(x^4*e^(p*log(a*x + 1) + p*log(-a*x + 1))/(sqrt(a*x + 1)*sqrt(-a*x + 1)), x) + (a^4*(2*p + 1)*x^4 - a^2*(2*p - 1)*x^2 - 2)*(-a^2*x^2 + 1)^p/(sqrt(-a^2*x^2 + 1)*(4*p^2 + 8*p + 3)*a^4)","F",0
1006,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*x^2+1)^p,x, algorithm=""maxima"")","\int {\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p - \frac{1}{2}} x^{2}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^(p - 1/2)*x^2, x)","F",0
1007,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*x^2+1)^p,x, algorithm=""maxima"")","a \int \frac{x^{2} e^{\left(p \log\left(a x + 1\right) + p \log\left(-a x + 1\right)\right)}}{\sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{p + \frac{1}{2}}}{a^{2} {\left(2 \, p + 1\right)}}"," ",0,"a*integrate(x^2*e^(p*log(a*x + 1) + p*log(-a*x + 1))/(sqrt(a*x + 1)*sqrt(-a*x + 1)), x) - (-a^2*x^2 + 1)^(p + 1/2)/(a^2*(2*p + 1))","F",0
1008,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p,x, algorithm=""maxima"")","\int {\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p - \frac{1}{2}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^(p - 1/2), x)","F",0
1009,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p/x,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p - \frac{1}{2}}}{x}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^(p - 1/2)/x, x)","F",0
1010,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p - \frac{1}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^(p - 1/2)/x^2, x)","F",0
1011,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p - \frac{1}{2}}}{x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^(p - 1/2)/x^3, x)","F",0
1012,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","a c^{p} \int \frac{x^{4} e^{\left(p \log\left(a x + 1\right) + p \log\left(-a x + 1\right)\right)}}{\sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x} + \frac{{\left(a^{4} c^{p} {\left(2 \, p + 1\right)} x^{4} - a^{2} c^{p} {\left(2 \, p - 1\right)} x^{2} - 2 \, c^{p}\right)} {\left(-a^{2} x^{2} + 1\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} {\left(4 \, p^{2} + 8 \, p + 3\right)} a^{4}}"," ",0,"a*c^p*integrate(x^4*e^(p*log(a*x + 1) + p*log(-a*x + 1))/(sqrt(a*x + 1)*sqrt(-a*x + 1)), x) + (a^4*c^p*(2*p + 1)*x^4 - a^2*c^p*(2*p - 1)*x^2 - 2*c^p)*(-a^2*x^2 + 1)^p/(sqrt(-a^2*x^2 + 1)*(4*p^2 + 8*p + 3)*a^4)","F",0
1013,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p*x^2/sqrt(-a^2*x^2 + 1), x)","F",0
1014,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","a c^{p} \int \frac{x^{2} e^{\left(p \log\left(a x + 1\right) + p \log\left(-a x + 1\right)\right)}}{\sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x} + \frac{{\left(a^{2} c^{p} x^{2} - c^{p}\right)} {\left(-a^{2} x^{2} + 1\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} a^{2} {\left(2 \, p + 1\right)}}"," ",0,"a*c^p*integrate(x^2*e^(p*log(a*x + 1) + p*log(-a*x + 1))/(sqrt(a*x + 1)*sqrt(-a*x + 1)), x) + (a^2*c^p*x^2 - c^p)*(-a^2*x^2 + 1)^p/(sqrt(-a^2*x^2 + 1)*a^2*(2*p + 1))","F",0
1015,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p/sqrt(-a^2*x^2 + 1), x)","F",0
1016,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
1017,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p/(sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
1018,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
1019,1,23,0,0.368185," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{7} \, a^{2} c x^{7} + \frac{1}{3} \, a c x^{6} + \frac{1}{5} \, c x^{5}"," ",0,"1/7*a^2*c*x^7 + 1/3*a*c*x^6 + 1/5*c*x^5","A",0
1020,1,23,0,0.333871," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} c x^{6} + \frac{2}{5} \, a c x^{5} + \frac{1}{4} \, c x^{4}"," ",0,"1/6*a^2*c*x^6 + 2/5*a*c*x^5 + 1/4*c*x^4","A",0
1021,1,23,0,0.332210," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} c x^{5} + \frac{1}{2} \, a c x^{4} + \frac{1}{3} \, c x^{3}"," ",0,"1/5*a^2*c*x^5 + 1/2*a*c*x^4 + 1/3*c*x^3","A",0
1022,1,23,0,0.331501," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} c x^{4} + \frac{2}{3} \, a c x^{3} + \frac{1}{2} \, c x^{2}"," ",0,"1/4*a^2*c*x^4 + 2/3*a*c*x^3 + 1/2*c*x^2","A",0
1023,1,19,0,0.302377," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} c x^{3} + a c x^{2} + c x"," ",0,"1/3*a^2*c*x^3 + a*c*x^2 + c*x","A",0
1024,1,19,0,0.320133," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} c x^{2} + 2 \, a c x + c \log\left(x\right)"," ",0,"1/2*a^2*c*x^2 + 2*a*c*x + c*log(x)","A",0
1025,1,19,0,0.337607," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x^2,x, algorithm=""maxima"")","a^{2} c x + 2 \, a c \log\left(x\right) - \frac{c}{x}"," ",0,"a^2*c*x + 2*a*c*log(x) - c/x","A",0
1026,1,20,0,0.329323," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x^3,x, algorithm=""maxima"")","a^{2} c \log\left(x\right) - \frac{4 \, a c x + c}{2 \, x^{2}}"," ",0,"a^2*c*log(x) - 1/2*(4*a*c*x + c)/x^2","A",0
1027,1,21,0,0.312936," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x^4,x, algorithm=""maxima"")","-\frac{3 \, a^{2} c x^{2} + 3 \, a c x + c}{3 \, x^{3}}"," ",0,"-1/3*(3*a^2*c*x^2 + 3*a*c*x + c)/x^3","A",0
1028,1,40,0,0.351139," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{9} \, a^{4} c^{2} x^{9} - \frac{1}{4} \, a^{3} c^{2} x^{8} + \frac{1}{3} \, a c^{2} x^{6} + \frac{1}{5} \, c^{2} x^{5}"," ",0,"-1/9*a^4*c^2*x^9 - 1/4*a^3*c^2*x^8 + 1/3*a*c^2*x^6 + 1/5*c^2*x^5","A",0
1029,1,40,0,0.304558," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{8} \, a^{4} c^{2} x^{8} - \frac{2}{7} \, a^{3} c^{2} x^{7} + \frac{2}{5} \, a c^{2} x^{5} + \frac{1}{4} \, c^{2} x^{4}"," ",0,"-1/8*a^4*c^2*x^8 - 2/7*a^3*c^2*x^7 + 2/5*a*c^2*x^5 + 1/4*c^2*x^4","A",0
1030,1,40,0,0.320103," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{7} \, a^{4} c^{2} x^{7} - \frac{1}{3} \, a^{3} c^{2} x^{6} + \frac{1}{2} \, a c^{2} x^{4} + \frac{1}{3} \, c^{2} x^{3}"," ",0,"-1/7*a^4*c^2*x^7 - 1/3*a^3*c^2*x^6 + 1/2*a*c^2*x^4 + 1/3*c^2*x^3","A",0
1031,1,40,0,0.339258," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{6} \, a^{4} c^{2} x^{6} - \frac{2}{5} \, a^{3} c^{2} x^{5} + \frac{2}{3} \, a c^{2} x^{3} + \frac{1}{2} \, c^{2} x^{2}"," ",0,"-1/6*a^4*c^2*x^6 - 2/5*a^3*c^2*x^5 + 2/3*a*c^2*x^3 + 1/2*c^2*x^2","A",0
1032,1,36,0,0.318089," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{5} \, a^{4} c^{2} x^{5} - \frac{1}{2} \, a^{3} c^{2} x^{4} + a c^{2} x^{2} + c^{2} x"," ",0,"-1/5*a^4*c^2*x^5 - 1/2*a^3*c^2*x^4 + a*c^2*x^2 + c^2*x","A",0
1033,1,36,0,0.333764," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{4} c^{2} x^{4} - \frac{2}{3} \, a^{3} c^{2} x^{3} + 2 \, a c^{2} x + c^{2} \log\left(x\right)"," ",0,"-1/4*a^4*c^2*x^4 - 2/3*a^3*c^2*x^3 + 2*a*c^2*x + c^2*log(x)","A",0
1034,1,39,0,0.344730," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^2,x, algorithm=""maxima"")","-\frac{1}{3} \, a^{4} c^{2} x^{3} - a^{3} c^{2} x^{2} + 2 \, a c^{2} \log\left(x\right) - \frac{c^{2}}{x}"," ",0,"-1/3*a^4*c^2*x^3 - a^3*c^2*x^2 + 2*a*c^2*log(x) - c^2/x","A",0
1035,1,37,0,0.302416," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{4} c^{2} x^{2} - 2 \, a^{3} c^{2} x - \frac{4 \, a c^{2} x + c^{2}}{2 \, x^{2}}"," ",0,"-1/2*a^4*c^2*x^2 - 2*a^3*c^2*x - 1/2*(4*a*c^2*x + c^2)/x^2","B",0
1036,1,36,0,0.310358," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^4,x, algorithm=""maxima"")","-a^{4} c^{2} x - 2 \, a^{3} c^{2} \log\left(x\right) - \frac{3 \, a c^{2} x + c^{2}}{3 \, x^{3}}"," ",0,"-a^4*c^2*x - 2*a^3*c^2*log(x) - 1/3*(3*a*c^2*x + c^2)/x^3","A",0
1037,1,40,0,0.312214," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^5,x, algorithm=""maxima"")","-a^{4} c^{2} \log\left(x\right) + \frac{24 \, a^{3} c^{2} x^{3} - 8 \, a c^{2} x - 3 \, c^{2}}{12 \, x^{4}}"," ",0,"-a^4*c^2*log(x) + 1/12*(24*a^3*c^2*x^3 - 8*a*c^2*x - 3*c^2)/x^4","A",0
1038,1,40,0,0.298097," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^6,x, algorithm=""maxima"")","\frac{10 \, a^{4} c^{2} x^{4} + 10 \, a^{3} c^{2} x^{3} - 5 \, a c^{2} x - 2 \, c^{2}}{10 \, x^{5}}"," ",0,"1/10*(10*a^4*c^2*x^4 + 10*a^3*c^2*x^3 - 5*a*c^2*x - 2*c^2)/x^5","A",0
1039,1,73,0,0.342838," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{11} \, a^{6} c^{3} x^{11} + \frac{1}{5} \, a^{5} c^{3} x^{10} - \frac{1}{9} \, a^{4} c^{3} x^{9} - \frac{1}{2} \, a^{3} c^{3} x^{8} - \frac{1}{7} \, a^{2} c^{3} x^{7} + \frac{1}{3} \, a c^{3} x^{6} + \frac{1}{5} \, c^{3} x^{5}"," ",0,"1/11*a^6*c^3*x^11 + 1/5*a^5*c^3*x^10 - 1/9*a^4*c^3*x^9 - 1/2*a^3*c^3*x^8 - 1/7*a^2*c^3*x^7 + 1/3*a*c^3*x^6 + 1/5*c^3*x^5","A",0
1040,1,73,0,0.359554," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{10} \, a^{6} c^{3} x^{10} + \frac{2}{9} \, a^{5} c^{3} x^{9} - \frac{1}{8} \, a^{4} c^{3} x^{8} - \frac{4}{7} \, a^{3} c^{3} x^{7} - \frac{1}{6} \, a^{2} c^{3} x^{6} + \frac{2}{5} \, a c^{3} x^{5} + \frac{1}{4} \, c^{3} x^{4}"," ",0,"1/10*a^6*c^3*x^10 + 2/9*a^5*c^3*x^9 - 1/8*a^4*c^3*x^8 - 4/7*a^3*c^3*x^7 - 1/6*a^2*c^3*x^6 + 2/5*a*c^3*x^5 + 1/4*c^3*x^4","A",0
1041,1,73,0,0.306235," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{9} \, a^{6} c^{3} x^{9} + \frac{1}{4} \, a^{5} c^{3} x^{8} - \frac{1}{7} \, a^{4} c^{3} x^{7} - \frac{2}{3} \, a^{3} c^{3} x^{6} - \frac{1}{5} \, a^{2} c^{3} x^{5} + \frac{1}{2} \, a c^{3} x^{4} + \frac{1}{3} \, c^{3} x^{3}"," ",0,"1/9*a^6*c^3*x^9 + 1/4*a^5*c^3*x^8 - 1/7*a^4*c^3*x^7 - 2/3*a^3*c^3*x^6 - 1/5*a^2*c^3*x^5 + 1/2*a*c^3*x^4 + 1/3*c^3*x^3","A",0
1042,1,73,0,0.314574," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a^{6} c^{3} x^{8} + \frac{2}{7} \, a^{5} c^{3} x^{7} - \frac{1}{6} \, a^{4} c^{3} x^{6} - \frac{4}{5} \, a^{3} c^{3} x^{5} - \frac{1}{4} \, a^{2} c^{3} x^{4} + \frac{2}{3} \, a c^{3} x^{3} + \frac{1}{2} \, c^{3} x^{2}"," ",0,"1/8*a^6*c^3*x^8 + 2/7*a^5*c^3*x^7 - 1/6*a^4*c^3*x^6 - 4/5*a^3*c^3*x^5 - 1/4*a^2*c^3*x^4 + 2/3*a*c^3*x^3 + 1/2*c^3*x^2","A",0
1043,1,69,0,0.331312," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{7} \, a^{6} c^{3} x^{7} + \frac{1}{3} \, a^{5} c^{3} x^{6} - \frac{1}{5} \, a^{4} c^{3} x^{5} - a^{3} c^{3} x^{4} - \frac{1}{3} \, a^{2} c^{3} x^{3} + a c^{3} x^{2} + c^{3} x"," ",0,"1/7*a^6*c^3*x^7 + 1/3*a^5*c^3*x^6 - 1/5*a^4*c^3*x^5 - a^3*c^3*x^4 - 1/3*a^2*c^3*x^3 + a*c^3*x^2 + c^3*x","A",0
1044,1,69,0,0.303739," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x,x, algorithm=""maxima"")","\frac{1}{6} \, a^{6} c^{3} x^{6} + \frac{2}{5} \, a^{5} c^{3} x^{5} - \frac{1}{4} \, a^{4} c^{3} x^{4} - \frac{4}{3} \, a^{3} c^{3} x^{3} - \frac{1}{2} \, a^{2} c^{3} x^{2} + 2 \, a c^{3} x + c^{3} \log\left(x\right)"," ",0,"1/6*a^6*c^3*x^6 + 2/5*a^5*c^3*x^5 - 1/4*a^4*c^3*x^4 - 4/3*a^3*c^3*x^3 - 1/2*a^2*c^3*x^2 + 2*a*c^3*x + c^3*log(x)","A",0
1045,1,70,0,0.300628," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{6} c^{3} x^{5} + \frac{1}{2} \, a^{5} c^{3} x^{4} - \frac{1}{3} \, a^{4} c^{3} x^{3} - 2 \, a^{3} c^{3} x^{2} - a^{2} c^{3} x + 2 \, a c^{3} \log\left(x\right) - \frac{c^{3}}{x}"," ",0,"1/5*a^6*c^3*x^5 + 1/2*a^5*c^3*x^4 - 1/3*a^4*c^3*x^3 - 2*a^3*c^3*x^2 - a^2*c^3*x + 2*a*c^3*log(x) - c^3/x","A",0
1046,1,69,0,0.308223," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, a^{6} c^{3} x^{4} + \frac{2}{3} \, a^{5} c^{3} x^{3} - \frac{1}{2} \, a^{4} c^{3} x^{2} - 4 \, a^{3} c^{3} x - a^{2} c^{3} \log\left(x\right) - \frac{4 \, a c^{3} x + c^{3}}{2 \, x^{2}}"," ",0,"1/4*a^6*c^3*x^4 + 2/3*a^5*c^3*x^3 - 1/2*a^4*c^3*x^2 - 4*a^3*c^3*x - a^2*c^3*log(x) - 1/2*(4*a*c^3*x + c^3)/x^2","A",0
1047,1,70,0,0.306122," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, a^{6} c^{3} x^{3} + a^{5} c^{3} x^{2} - a^{4} c^{3} x - 4 \, a^{3} c^{3} \log\left(x\right) + \frac{3 \, a^{2} c^{3} x^{2} - 3 \, a c^{3} x - c^{3}}{3 \, x^{3}}"," ",0,"1/3*a^6*c^3*x^3 + a^5*c^3*x^2 - a^4*c^3*x - 4*a^3*c^3*log(x) + 1/3*(3*a^2*c^3*x^2 - 3*a*c^3*x - c^3)/x^3","A",0
1048,1,79,0,0.325767," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","-\frac{1}{9} \, a^{8} c^{4} x^{9} - \frac{1}{4} \, a^{7} c^{4} x^{8} + \frac{2}{7} \, a^{6} c^{4} x^{7} + a^{5} c^{4} x^{6} - \frac{3}{2} \, a^{3} c^{4} x^{4} - \frac{2}{3} \, a^{2} c^{4} x^{3} + a c^{4} x^{2} + c^{4} x"," ",0,"-1/9*a^8*c^4*x^9 - 1/4*a^7*c^4*x^8 + 2/7*a^6*c^4*x^7 + a^5*c^4*x^6 - 3/2*a^3*c^4*x^4 - 2/3*a^2*c^4*x^3 + a*c^4*x^2 + c^4*x","A",0
1049,1,57,0,0.303680," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{a^{6} c x - a^{5} c} + \frac{a^{2} x^{3} + 3 \, a x^{2} + 9 \, x}{3 \, a^{4} c} + \frac{4 \, \log\left(a x - 1\right)}{a^{5} c}"," ",0,"-1/(a^6*c*x - a^5*c) + 1/3*(a^2*x^3 + 3*a*x^2 + 9*x)/(a^4*c) + 4*log(a*x - 1)/(a^5*c)","A",0
1050,1,49,0,0.309165," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{a^{5} c x - a^{4} c} + \frac{a x^{2} + 4 \, x}{2 \, a^{3} c} + \frac{3 \, \log\left(a x - 1\right)}{a^{4} c}"," ",0,"-1/(a^5*c*x - a^4*c) + 1/2*(a*x^2 + 4*x)/(a^3*c) + 3*log(a*x - 1)/(a^4*c)","A",0
1051,1,40,0,0.317609," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{a^{4} c x - a^{3} c} + \frac{x}{a^{2} c} + \frac{2 \, \log\left(a x - 1\right)}{a^{3} c}"," ",0,"-1/(a^4*c*x - a^3*c) + x/(a^2*c) + 2*log(a*x - 1)/(a^3*c)","A",0
1052,1,31,0,0.317466," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{a^{3} c x - a^{2} c} + \frac{\log\left(a x - 1\right)}{a^{2} c}"," ",0,"-1/(a^3*c*x - a^2*c) + log(a*x - 1)/(a^2*c)","A",0
1053,1,15,0,0.341422," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{a^{2} c x - a c}"," ",0,"-1/(a^2*c*x - a*c)","A",0
1054,1,30,0,0.312783," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{\log\left(a x - 1\right)}{c} + \frac{\log\left(x\right)}{c} - \frac{1}{a c x - c}"," ",0,"-log(a*x - 1)/c + log(x)/c - 1/(a*c*x - c)","A",0
1055,1,42,0,0.310441," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{2 \, a \log\left(a x - 1\right)}{c} + \frac{2 \, a \log\left(x\right)}{c} - \frac{2 \, a x - 1}{a c x^{2} - c x}"," ",0,"-2*a*log(a*x - 1)/c + 2*a*log(x)/c - (2*a*x - 1)/(a*c*x^2 - c*x)","A",0
1056,1,56,0,0.312841," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{3 \, a^{2} \log\left(a x - 1\right)}{c} + \frac{3 \, a^{2} \log\left(x\right)}{c} - \frac{6 \, a^{2} x^{2} - 3 \, a x - 1}{2 \, {\left(a c x^{3} - c x^{2}\right)}}"," ",0,"-3*a^2*log(a*x - 1)/c + 3*a^2*log(x)/c - 1/2*(6*a^2*x^2 - 3*a*x - 1)/(a*c*x^3 - c*x^2)","A",0
1057,1,64,0,0.311316," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^4/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{4 \, a^{3} \log\left(a x - 1\right)}{c} + \frac{4 \, a^{3} \log\left(x\right)}{c} - \frac{12 \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 2 \, a x - 1}{3 \, {\left(a c x^{4} - c x^{3}\right)}}"," ",0,"-4*a^3*log(a*x - 1)/c + 4*a^3*log(x)/c - 1/3*(12*a^3*x^3 - 6*a^2*x^2 - 2*a*x - 1)/(a*c*x^4 - c*x^3)","A",0
1058,1,75,0,0.343772," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{7 \, a x - 6}{4 \, {\left(a^{7} c^{2} x^{2} - 2 \, a^{6} c^{2} x + a^{5} c^{2}\right)}} - \frac{x}{a^{4} c^{2}} + \frac{\log\left(a x + 1\right)}{8 \, a^{5} c^{2}} - \frac{17 \, \log\left(a x - 1\right)}{8 \, a^{5} c^{2}}"," ",0,"1/4*(7*a*x - 6)/(a^7*c^2*x^2 - 2*a^6*c^2*x + a^5*c^2) - x/(a^4*c^2) + 1/8*log(a*x + 1)/(a^5*c^2) - 17/8*log(a*x - 1)/(a^5*c^2)","A",0
1059,1,66,0,0.318869," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{5 \, a x - 4}{4 \, {\left(a^{6} c^{2} x^{2} - 2 \, a^{5} c^{2} x + a^{4} c^{2}\right)}} - \frac{\log\left(a x + 1\right)}{8 \, a^{4} c^{2}} - \frac{7 \, \log\left(a x - 1\right)}{8 \, a^{4} c^{2}}"," ",0,"1/4*(5*a*x - 4)/(a^6*c^2*x^2 - 2*a^5*c^2*x + a^4*c^2) - 1/8*log(a*x + 1)/(a^4*c^2) - 7/8*log(a*x - 1)/(a^4*c^2)","A",0
1060,1,66,0,0.315969," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{3 \, a x - 2}{4 \, {\left(a^{5} c^{2} x^{2} - 2 \, a^{4} c^{2} x + a^{3} c^{2}\right)}} + \frac{\log\left(a x + 1\right)}{8 \, a^{3} c^{2}} - \frac{\log\left(a x - 1\right)}{8 \, a^{3} c^{2}}"," ",0,"1/4*(3*a*x - 2)/(a^5*c^2*x^2 - 2*a^4*c^2*x + a^3*c^2) + 1/8*log(a*x + 1)/(a^3*c^2) - 1/8*log(a*x - 1)/(a^3*c^2)","A",0
1061,1,59,0,0.343892," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{x}{4 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}} - \frac{\log\left(a x + 1\right)}{8 \, a^{2} c^{2}} + \frac{\log\left(a x - 1\right)}{8 \, a^{2} c^{2}}"," ",0,"1/4*x/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2) - 1/8*log(a*x + 1)/(a^2*c^2) + 1/8*log(a*x - 1)/(a^2*c^2)","A",0
1062,1,63,0,0.346367," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{a x - 2}{4 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}} + \frac{\log\left(a x + 1\right)}{8 \, a c^{2}} - \frac{\log\left(a x - 1\right)}{8 \, a c^{2}}"," ",0,"-1/4*(a*x - 2)/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2) + 1/8*log(a*x + 1)/(a*c^2) - 1/8*log(a*x - 1)/(a*c^2)","A",0
1063,1,60,0,0.346961," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{3 \, a x - 4}{4 \, {\left(a^{2} c^{2} x^{2} - 2 \, a c^{2} x + c^{2}\right)}} - \frac{\log\left(a x + 1\right)}{8 \, c^{2}} - \frac{7 \, \log\left(a x - 1\right)}{8 \, c^{2}} + \frac{\log\left(x\right)}{c^{2}}"," ",0,"-1/4*(3*a*x - 4)/(a^2*c^2*x^2 - 2*a*c^2*x + c^2) - 1/8*log(a*x + 1)/c^2 - 7/8*log(a*x - 1)/c^2 + log(x)/c^2","A",0
1064,1,76,0,0.309479," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{9 \, a^{2} x^{2} - 14 \, a x + 4}{4 \, {\left(a^{2} c^{2} x^{3} - 2 \, a c^{2} x^{2} + c^{2} x\right)}} + \frac{a \log\left(a x + 1\right)}{8 \, c^{2}} - \frac{17 \, a \log\left(a x - 1\right)}{8 \, c^{2}} + \frac{2 \, a \log\left(x\right)}{c^{2}}"," ",0,"-1/4*(9*a^2*x^2 - 14*a*x + 4)/(a^2*c^2*x^3 - 2*a*c^2*x^2 + c^2*x) + 1/8*a*log(a*x + 1)/c^2 - 17/8*a*log(a*x - 1)/c^2 + 2*a*log(x)/c^2","A",0
1065,1,92,0,0.313699," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{a^{2} \log\left(a x + 1\right)}{8 \, c^{2}} - \frac{31 \, a^{2} \log\left(a x - 1\right)}{8 \, c^{2}} + \frac{4 \, a^{2} \log\left(x\right)}{c^{2}} - \frac{15 \, a^{3} x^{3} - 22 \, a^{2} x^{2} + 4 \, a x + 2}{4 \, {\left(a^{2} c^{2} x^{4} - 2 \, a c^{2} x^{3} + c^{2} x^{2}\right)}}"," ",0,"-1/8*a^2*log(a*x + 1)/c^2 - 31/8*a^2*log(a*x - 1)/c^2 + 4*a^2*log(x)/c^2 - 1/4*(15*a^3*x^3 - 22*a^2*x^2 + 4*a*x + 2)/(a^2*c^2*x^4 - 2*a*c^2*x^3 + c^2*x^2)","A",0
1066,1,100,0,0.312187," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^4/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{a^{3} \log\left(a x + 1\right)}{8 \, c^{2}} - \frac{49 \, a^{3} \log\left(a x - 1\right)}{8 \, c^{2}} + \frac{6 \, a^{3} \log\left(x\right)}{c^{2}} - \frac{75 \, a^{4} x^{4} - 114 \, a^{3} x^{3} + 28 \, a^{2} x^{2} + 4 \, a x + 4}{12 \, {\left(a^{2} c^{2} x^{5} - 2 \, a c^{2} x^{4} + c^{2} x^{3}\right)}}"," ",0,"1/8*a^3*log(a*x + 1)/c^2 - 49/8*a^3*log(a*x - 1)/c^2 + 6*a^3*log(x)/c^2 - 1/12*(75*a^4*x^4 - 114*a^3*x^3 + 28*a^2*x^2 + 4*a*x + 4)/(a^2*c^2*x^5 - 2*a*c^2*x^4 + c^2*x^3)","A",0
1067,1,94,0,0.319256," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^5/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{33 \, a^{3} x^{3} - 18 \, a^{2} x^{2} - 37 \, a x + 26}{24 \, {\left(a^{10} c^{3} x^{4} - 2 \, a^{9} c^{3} x^{3} + 2 \, a^{7} c^{3} x - a^{6} c^{3}\right)}} + \frac{3 \, \log\left(a x + 1\right)}{16 \, a^{6} c^{3}} + \frac{13 \, \log\left(a x - 1\right)}{16 \, a^{6} c^{3}}"," ",0,"-1/24*(33*a^3*x^3 - 18*a^2*x^2 - 37*a*x + 26)/(a^10*c^3*x^4 - 2*a^9*c^3*x^3 + 2*a^7*c^3*x - a^6*c^3) + 3/16*log(a*x + 1)/(a^6*c^3) + 13/16*log(a*x - 1)/(a^6*c^3)","A",0
1068,1,94,0,0.329576," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{9 \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 5 \, a x + 4}{12 \, {\left(a^{9} c^{3} x^{4} - 2 \, a^{8} c^{3} x^{3} + 2 \, a^{6} c^{3} x - a^{5} c^{3}\right)}} - \frac{\log\left(a x + 1\right)}{8 \, a^{5} c^{3}} + \frac{\log\left(a x - 1\right)}{8 \, a^{5} c^{3}}"," ",0,"-1/12*(9*a^3*x^3 - 6*a^2*x^2 - 5*a*x + 4)/(a^9*c^3*x^4 - 2*a^8*c^3*x^3 + 2*a^6*c^3*x - a^5*c^3) - 1/8*log(a*x + 1)/(a^5*c^3) + 1/8*log(a*x - 1)/(a^5*c^3)","A",0
1069,1,94,0,0.343934," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{3 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 7 \, a x + 2}{24 \, {\left(a^{8} c^{3} x^{4} - 2 \, a^{7} c^{3} x^{3} + 2 \, a^{5} c^{3} x - a^{4} c^{3}\right)}} + \frac{\log\left(a x + 1\right)}{16 \, a^{4} c^{3}} - \frac{\log\left(a x - 1\right)}{16 \, a^{4} c^{3}}"," ",0,"-1/24*(3*a^3*x^3 + 6*a^2*x^2 - 7*a*x + 2)/(a^8*c^3*x^4 - 2*a^7*c^3*x^3 + 2*a^5*c^3*x - a^4*c^3) + 1/16*log(a*x + 1)/(a^4*c^3) - 1/16*log(a*x - 1)/(a^4*c^3)","A",0
1070,1,49,0,0.318906," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{2 \, a x - 1}{6 \, {\left(a^{7} c^{3} x^{4} - 2 \, a^{6} c^{3} x^{3} + 2 \, a^{4} c^{3} x - a^{3} c^{3}\right)}}"," ",0,"-1/6*(2*a*x - 1)/(a^7*c^3*x^4 - 2*a^6*c^3*x^3 + 2*a^4*c^3*x - a^3*c^3)","A",0
1071,1,93,0,0.334883," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{3 \, a^{3} x^{3} - 6 \, a^{2} x^{2} + a x - 2}{24 \, {\left(a^{6} c^{3} x^{4} - 2 \, a^{5} c^{3} x^{3} + 2 \, a^{3} c^{3} x - a^{2} c^{3}\right)}} - \frac{\log\left(a x + 1\right)}{16 \, a^{2} c^{3}} + \frac{\log\left(a x - 1\right)}{16 \, a^{2} c^{3}}"," ",0,"1/24*(3*a^3*x^3 - 6*a^2*x^2 + a*x - 2)/(a^6*c^3*x^4 - 2*a^5*c^3*x^3 + 2*a^3*c^3*x - a^2*c^3) - 1/16*log(a*x + 1)/(a^2*c^3) + 1/16*log(a*x - 1)/(a^2*c^3)","A",0
1072,1,91,0,0.324224," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{3 \, a^{3} x^{3} - 6 \, a^{2} x^{2} + a x + 4}{12 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{4} c^{3} x^{3} + 2 \, a^{2} c^{3} x - a c^{3}\right)}} + \frac{\log\left(a x + 1\right)}{8 \, a c^{3}} - \frac{\log\left(a x - 1\right)}{8 \, a c^{3}}"," ",0,"-1/12*(3*a^3*x^3 - 6*a^2*x^2 + a*x + 4)/(a^5*c^3*x^4 - 2*a^4*c^3*x^3 + 2*a^2*c^3*x - a*c^3) + 1/8*log(a*x + 1)/(a*c^3) - 1/8*log(a*x - 1)/(a*c^3)","A",0
1073,1,89,0,0.315526," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{15 \, a^{3} x^{3} - 18 \, a^{2} x^{2} - 19 \, a x + 26}{24 \, {\left(a^{4} c^{3} x^{4} - 2 \, a^{3} c^{3} x^{3} + 2 \, a c^{3} x - c^{3}\right)}} - \frac{3 \, \log\left(a x + 1\right)}{16 \, c^{3}} - \frac{13 \, \log\left(a x - 1\right)}{16 \, c^{3}} + \frac{\log\left(x\right)}{c^{3}}"," ",0,"-1/24*(15*a^3*x^3 - 18*a^2*x^2 - 19*a*x + 26)/(a^4*c^3*x^4 - 2*a^3*c^3*x^3 + 2*a*c^3*x - c^3) - 3/16*log(a*x + 1)/c^3 - 13/16*log(a*x - 1)/c^3 + log(x)/c^3","A",0
1074,1,104,0,0.312217," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{15 \, a^{4} x^{4} - 24 \, a^{3} x^{3} - 7 \, a^{2} x^{2} + 23 \, a x - 6}{6 \, {\left(a^{4} c^{3} x^{5} - 2 \, a^{3} c^{3} x^{4} + 2 \, a c^{3} x^{2} - c^{3} x\right)}} + \frac{a \log\left(a x + 1\right)}{4 \, c^{3}} - \frac{9 \, a \log\left(a x - 1\right)}{4 \, c^{3}} + \frac{2 \, a \log\left(x\right)}{c^{3}}"," ",0,"-1/6*(15*a^4*x^4 - 24*a^3*x^3 - 7*a^2*x^2 + 23*a*x - 6)/(a^4*c^3*x^5 - 2*a^3*c^3*x^4 + 2*a*c^3*x^2 - c^3*x) + 1/4*a*log(a*x + 1)/c^3 - 9/4*a*log(a*x - 1)/c^3 + 2*a*log(x)/c^3","A",0
1075,1,120,0,0.332297," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{105 \, a^{5} x^{5} - 150 \, a^{4} x^{4} - 85 \, a^{3} x^{3} + 170 \, a^{2} x^{2} - 24 \, a x - 12}{24 \, {\left(a^{4} c^{3} x^{6} - 2 \, a^{3} c^{3} x^{5} + 2 \, a c^{3} x^{3} - c^{3} x^{2}\right)}} - \frac{5 \, a^{2} \log\left(a x + 1\right)}{16 \, c^{3}} - \frac{75 \, a^{2} \log\left(a x - 1\right)}{16 \, c^{3}} + \frac{5 \, a^{2} \log\left(x\right)}{c^{3}}"," ",0,"-1/24*(105*a^5*x^5 - 150*a^4*x^4 - 85*a^3*x^3 + 170*a^2*x^2 - 24*a*x - 12)/(a^4*c^3*x^6 - 2*a^3*c^3*x^5 + 2*a*c^3*x^3 - c^3*x^2) - 5/16*a^2*log(a*x + 1)/c^3 - 75/16*a^2*log(a*x - 1)/c^3 + 5*a^2*log(x)/c^3","A",0
1076,1,140,0,0.338688," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","-\frac{15 \, a^{5} x^{5} - 30 \, a^{4} x^{4} - 10 \, a^{3} x^{3} + 50 \, a^{2} x^{2} - 17 \, a x - 16}{64 \, {\left(a^{7} c^{4} x^{6} - 2 \, a^{6} c^{4} x^{5} - a^{5} c^{4} x^{4} + 4 \, a^{4} c^{4} x^{3} - a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}} + \frac{15 \, \log\left(a x + 1\right)}{128 \, a c^{4}} - \frac{15 \, \log\left(a x - 1\right)}{128 \, a c^{4}}"," ",0,"-1/64*(15*a^5*x^5 - 30*a^4*x^4 - 10*a^3*x^3 + 50*a^2*x^2 - 17*a*x - 16)/(a^7*c^4*x^6 - 2*a^6*c^4*x^5 - a^5*c^4*x^4 + 4*a^4*c^4*x^3 - a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4) + 15/128*log(a*x + 1)/(a*c^4) - 15/128*log(a*x - 1)/(a*c^4)","A",0
1077,1,120,0,0.599724," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{1}{20} \, a {\left(\frac{4 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2}}{a^{3} c} - \frac{25 \, \sqrt{-a^{2} c x^{2} + c} x}{a^{4}} + \frac{10 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}{a^{4} c} + \frac{15 \, \sqrt{c} \arcsin\left(a x\right)}{a^{5}} - \frac{40 \, \sqrt{-a^{2} c x^{2} + c}}{a^{5}} + \frac{16 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{a^{5} c}\right)}"," ",0,"1/20*a*(4*(-a^2*c*x^2 + c)^(3/2)*x^2/(a^3*c) - 25*sqrt(-a^2*c*x^2 + c)*x/a^4 + 10*(-a^2*c*x^2 + c)^(3/2)*x/(a^4*c) + 15*sqrt(c)*arcsin(a*x)/a^5 - 40*sqrt(-a^2*c*x^2 + c)/a^5 + 16*(-a^2*c*x^2 + c)^(3/2)/(a^5*c))","A",0
1078,1,96,0,0.644633," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{1}{24} \, a {\left(\frac{27 \, \sqrt{-a^{2} c x^{2} + c} x}{a^{3}} - \frac{6 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}{a^{3} c} - \frac{21 \, \sqrt{c} \arcsin\left(a x\right)}{a^{4}} + \frac{48 \, \sqrt{-a^{2} c x^{2} + c}}{a^{4}} - \frac{16 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{a^{4} c}\right)}"," ",0,"-1/24*a*(27*sqrt(-a^2*c*x^2 + c)*x/a^3 - 6*(-a^2*c*x^2 + c)^(3/2)*x/(a^3*c) - 21*sqrt(c)*arcsin(a*x)/a^4 + 48*sqrt(-a^2*c*x^2 + c)/a^4 - 16*(-a^2*c*x^2 + c)^(3/2)/(a^4*c))","A",0
1079,1,74,0,0.516545," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, \sqrt{-a^{2} c x^{2} + c} x}{a^{2}} - \frac{3 \, \sqrt{c} \arcsin\left(a x\right)}{a^{3}} + \frac{6 \, \sqrt{-a^{2} c x^{2} + c}}{a^{3}} - \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{a^{3} c}\right)}"," ",0,"-1/3*a*(3*sqrt(-a^2*c*x^2 + c)*x/a^2 - 3*sqrt(c)*arcsin(a*x)/a^3 + 6*sqrt(-a^2*c*x^2 + c)/a^3 - (-a^2*c*x^2 + c)^(3/2)/(a^3*c))","A",0
1080,1,52,0,0.456571," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\sqrt{-a^{2} c x^{2} + c} x}{a} - \frac{3 \, \sqrt{c} \arcsin\left(a x\right)}{a^{2}} + \frac{4 \, \sqrt{-a^{2} c x^{2} + c}}{a^{2}}\right)}"," ",0,"-1/2*a*(sqrt(-a^2*c*x^2 + c)*x/a - 3*sqrt(c)*arcsin(a*x)/a^2 + 4*sqrt(-a^2*c*x^2 + c)/a^2)","A",0
1081,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x}\,{d x}"," ",0,"-integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^2/((a^2*x^2 - 1)*x), x)","F",0
1082,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""maxima"")","-a^{2} \sqrt{c} \int \frac{\sqrt{a x + 1} \sqrt{-a x + 1}}{a^{2} x^{2} - 1}\,{d x} + a \sqrt{c} \log\left(\frac{\sqrt{-a^{2} c x^{2} + c} - \sqrt{c}}{\sqrt{-a^{2} c x^{2} + c} + \sqrt{c}}\right) - \frac{\sqrt{a x + 1} \sqrt{-a x + 1} \sqrt{c}}{x}"," ",0,"-a^2*sqrt(c)*integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^2*x^2 - 1), x) + a*sqrt(c)*log((sqrt(-a^2*c*x^2 + c) - sqrt(c))/(sqrt(-a^2*c*x^2 + c) + sqrt(c))) - sqrt(a*x + 1)*sqrt(-a*x + 1)*sqrt(c)/x","F",0
1083,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{3}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^2/((a^2*x^2 - 1)*x^3), x)","F",0
1084,1,140,0,0.470079," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""maxima"")","-\frac{\sqrt{a x + 1} \sqrt{-a x + 1} a^{2} \sqrt{c}}{x} + \frac{a^{4} c^{\frac{3}{2}} \log\left(\frac{\sqrt{-a^{2} c x^{2} + c} - \sqrt{c}}{\sqrt{-a^{2} c x^{2} + c} + \sqrt{c}}\right) - \frac{2 \, \sqrt{-a^{2} c x^{2} + c} a^{2} c}{x^{2}}}{2 \, a c} - \frac{{\left(2 \, a^{2} \sqrt{c} x^{2} + \sqrt{c}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{3 \, x^{3}}"," ",0,"-sqrt(a*x + 1)*sqrt(-a*x + 1)*a^2*sqrt(c)/x + 1/2*(a^4*c^(3/2)*log((sqrt(-a^2*c*x^2 + c) - sqrt(c))/(sqrt(-a^2*c*x^2 + c) + sqrt(c))) - 2*sqrt(-a^2*c*x^2 + c)*a^2*c/x^2)/(a*c) - 1/3*(2*a^2*sqrt(c)*x^2 + sqrt(c))*sqrt(a*x + 1)*sqrt(-a*x + 1)/x^3","A",0
1085,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(1/2)/x^5,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{5}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^2/((a^2*x^2 - 1)*x^5), x)","F",0
1086,1,213,0,0.753347," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{1}{840} \, a {\left(\frac{120 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2}}{a^{3} c} - \frac{490 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}{a^{4}} + \frac{280 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}{a^{4} c} + \frac{840 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c x}{a^{4}} - \frac{735 \, \sqrt{-a^{2} c x^{2} + c} c x}{a^{4}} - \frac{735 \, c^{\frac{3}{2}} \arcsin\left(a x\right)}{a^{5}} - \frac{560 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{a^{5}} + \frac{384 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{a^{5} c} - \frac{1680 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c}{a^{5}} + \frac{840 \, c^{3} \arcsin\left(a x - 2\right)}{a^{8} \left(-\frac{c}{a^{2}}\right)^{\frac{3}{2}}}\right)}"," ",0,"1/840*a*(120*(-a^2*c*x^2 + c)^(5/2)*x^2/(a^3*c) - 490*(-a^2*c*x^2 + c)^(3/2)*x/a^4 + 280*(-a^2*c*x^2 + c)^(5/2)*x/(a^4*c) + 840*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c*x/a^4 - 735*sqrt(-a^2*c*x^2 + c)*c*x/a^4 - 735*c^(3/2)*arcsin(a*x)/a^5 - 560*(-a^2*c*x^2 + c)^(3/2)/a^5 + 384*(-a^2*c*x^2 + c)^(5/2)/(a^5*c) - 1680*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c/a^5 + 840*c^3*arcsin(a*x - 2)/(a^8*(-c/a^2)^(3/2)))","A",0
1087,1,189,0,0.645910," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{1}{240} \, a {\left(\frac{130 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}{a^{3}} - \frac{40 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}{a^{3} c} - \frac{240 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c x}{a^{3}} + \frac{195 \, \sqrt{-a^{2} c x^{2} + c} c x}{a^{3}} + \frac{195 \, c^{\frac{3}{2}} \arcsin\left(a x\right)}{a^{4}} + \frac{160 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{a^{4}} - \frac{96 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{a^{4} c} + \frac{480 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c}{a^{4}} - \frac{240 \, c^{3} \arcsin\left(a x - 2\right)}{a^{7} \left(-\frac{c}{a^{2}}\right)^{\frac{3}{2}}}\right)}"," ",0,"-1/240*a*(130*(-a^2*c*x^2 + c)^(3/2)*x/a^3 - 40*(-a^2*c*x^2 + c)^(5/2)*x/(a^3*c) - 240*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c*x/a^3 + 195*sqrt(-a^2*c*x^2 + c)*c*x/a^3 + 195*c^(3/2)*arcsin(a*x)/a^4 + 160*(-a^2*c*x^2 + c)^(3/2)/a^4 - 96*(-a^2*c*x^2 + c)^(5/2)/(a^4*c) + 480*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c/a^4 - 240*c^3*arcsin(a*x - 2)/(a^7*(-c/a^2)^(3/2)))","A",0
1088,1,167,0,0.529911," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{1}{60} \, a {\left(\frac{30 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}{a^{2}} - \frac{60 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c x}{a^{2}} + \frac{45 \, \sqrt{-a^{2} c x^{2} + c} c x}{a^{2}} + \frac{45 \, c^{\frac{3}{2}} \arcsin\left(a x\right)}{a^{3}} + \frac{40 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{a^{3}} - \frac{12 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{a^{3} c} + \frac{120 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c}{a^{3}} - \frac{60 \, c^{3} \arcsin\left(a x - 2\right)}{a^{6} \left(-\frac{c}{a^{2}}\right)^{\frac{3}{2}}}\right)}"," ",0,"-1/60*a*(30*(-a^2*c*x^2 + c)^(3/2)*x/a^2 - 60*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c*x/a^2 + 45*sqrt(-a^2*c*x^2 + c)*c*x/a^2 + 45*c^(3/2)*arcsin(a*x)/a^3 + 40*(-a^2*c*x^2 + c)^(3/2)/a^3 - 12*(-a^2*c*x^2 + c)^(5/2)/(a^3*c) + 120*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c/a^3 - 60*c^3*arcsin(a*x - 2)/(a^6*(-c/a^2)^(3/2)))","A",0
1089,1,146,0,0.523328," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{1}{24} \, {\left(\frac{6 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}{a} - \frac{24 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c x}{a} + \frac{9 \, \sqrt{-a^{2} c x^{2} + c} c x}{a} + \frac{9 \, c^{\frac{3}{2}} \arcsin\left(a x\right)}{a^{2}} + \frac{16 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{a^{2}} + \frac{48 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c}{a^{2}} - \frac{24 \, c^{3} \arcsin\left(a x - 2\right)}{a^{5} \left(-\frac{c}{a^{2}}\right)^{\frac{3}{2}}}\right)} a"," ",0,"-1/24*(6*(-a^2*c*x^2 + c)^(3/2)*x/a - 24*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c*x/a + 9*sqrt(-a^2*c*x^2 + c)*c*x/a + 9*c^(3/2)*arcsin(a*x)/a^2 + 16*(-a^2*c*x^2 + c)^(3/2)/a^2 + 48*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c/a^2 - 24*c^3*arcsin(a*x - 2)/(a^5*(-c/a^2)^(3/2)))*a","A",0
1090,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)^2/((a^2*x^2 - 1)*x), x)","F",0
1091,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^2,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)^2/((a^2*x^2 - 1)*x^2), x)","F",0
1092,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^3,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{3}}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)^2/((a^2*x^2 - 1)*x^3), x)","F",0
1093,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^4,x, algorithm=""maxima"")","a^{2} c^{\frac{3}{2}} \int \frac{\sqrt{a x + 1} \sqrt{-a x + 1}}{x^{2}}\,{d x} - \frac{a^{4} c^{\frac{5}{2}} \log\left(\frac{\sqrt{-a^{2} c x^{2} + c} - \sqrt{c}}{\sqrt{-a^{2} c x^{2} + c} + \sqrt{c}}\right) + \frac{2 \, \sqrt{-a^{2} c x^{2} + c} a^{2} c^{2}}{x^{2}}}{2 \, a c} + \frac{{\left(a^{2} c^{\frac{3}{2}} x^{2} - c^{\frac{3}{2}}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{3 \, x^{3}}"," ",0,"a^2*c^(3/2)*integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/x^2, x) - 1/2*(a^4*c^(5/2)*log((sqrt(-a^2*c*x^2 + c) - sqrt(c))/(sqrt(-a^2*c*x^2 + c) + sqrt(c))) + 2*sqrt(-a^2*c*x^2 + c)*a^2*c^2/x^2)/(a*c) + 1/3*(a^2*c^(3/2)*x^2 - c^(3/2))*sqrt(a*x + 1)*sqrt(-a*x + 1)/x^3","F",0
1094,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^5,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{5}}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)^2/((a^2*x^2 - 1)*x^5), x)","F",0
1095,1,221,0,0.457153," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^6,x, algorithm=""maxima"")","\frac{{\left(a^{2} c^{\frac{3}{2}} x^{2} - c^{\frac{3}{2}}\right)} \sqrt{a x + 1} \sqrt{-a x + 1} a^{2}}{3 \, x^{3}} - \frac{a^{6} c^{\frac{5}{2}} \log\left(\frac{\sqrt{-a^{2} c x^{2} + c} - \sqrt{c}}{\sqrt{-a^{2} c x^{2} + c} + \sqrt{c}}\right) + \frac{2 \, {\left({\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{6} c^{3} + \sqrt{-a^{2} c x^{2} + c} a^{6} c^{4}\right)}}{{\left(a^{2} c x^{2} - c\right)}^{2} + 2 \, {\left(a^{2} c x^{2} - c\right)} c + c^{2}}}{8 \, a c} + \frac{{\left(2 \, a^{4} c^{\frac{3}{2}} x^{4} + a^{2} c^{\frac{3}{2}} x^{2} - 3 \, c^{\frac{3}{2}}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{15 \, x^{5}}"," ",0,"1/3*(a^2*c^(3/2)*x^2 - c^(3/2))*sqrt(a*x + 1)*sqrt(-a*x + 1)*a^2/x^3 - 1/8*(a^6*c^(5/2)*log((sqrt(-a^2*c*x^2 + c) - sqrt(c))/(sqrt(-a^2*c*x^2 + c) + sqrt(c))) + 2*((-a^2*c*x^2 + c)^(3/2)*a^6*c^3 + sqrt(-a^2*c*x^2 + c)*a^6*c^4)/((a^2*c*x^2 - c)^2 + 2*(a^2*c*x^2 - c)*c + c^2))/(a*c) + 1/15*(2*a^4*c^(3/2)*x^4 + a^2*c^(3/2)*x^2 - 3*c^(3/2))*sqrt(a*x + 1)*sqrt(-a*x + 1)/x^5","B",0
1096,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^7,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{7}}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)^2/((a^2*x^2 - 1)*x^7), x)","F",0
1097,1,287,0,0.451381," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^8,x, algorithm=""maxima"")","-\frac{3 \, a^{8} c^{\frac{5}{2}} \log\left(\frac{\sqrt{-a^{2} c x^{2} + c} - \sqrt{c}}{\sqrt{-a^{2} c x^{2} + c} + \sqrt{c}}\right) - \frac{2 \, {\left(3 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a^{8} c^{3} - 8 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{8} c^{4} - 3 \, \sqrt{-a^{2} c x^{2} + c} a^{8} c^{5}\right)}}{{\left(a^{2} c x^{2} - c\right)}^{3} + 3 \, {\left(a^{2} c x^{2} - c\right)}^{2} c + 3 \, {\left(a^{2} c x^{2} - c\right)} c^{2} + c^{3}}}{48 \, a c} + \frac{{\left(2 \, a^{4} c^{\frac{3}{2}} x^{4} + a^{2} c^{\frac{3}{2}} x^{2} - 3 \, c^{\frac{3}{2}}\right)} \sqrt{a x + 1} \sqrt{-a x + 1} a^{2}}{15 \, x^{5}} + \frac{{\left(8 \, a^{6} c^{\frac{3}{2}} x^{6} + 4 \, a^{4} c^{\frac{3}{2}} x^{4} + 3 \, a^{2} c^{\frac{3}{2}} x^{2} - 15 \, c^{\frac{3}{2}}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{105 \, x^{7}}"," ",0,"-1/48*(3*a^8*c^(5/2)*log((sqrt(-a^2*c*x^2 + c) - sqrt(c))/(sqrt(-a^2*c*x^2 + c) + sqrt(c))) - 2*(3*(-a^2*c*x^2 + c)^(5/2)*a^8*c^3 - 8*(-a^2*c*x^2 + c)^(3/2)*a^8*c^4 - 3*sqrt(-a^2*c*x^2 + c)*a^8*c^5)/((a^2*c*x^2 - c)^3 + 3*(a^2*c*x^2 - c)^2*c + 3*(a^2*c*x^2 - c)*c^2 + c^3))/(a*c) + 1/15*(2*a^4*c^(3/2)*x^4 + a^2*c^(3/2)*x^2 - 3*c^(3/2))*sqrt(a*x + 1)*sqrt(-a*x + 1)*a^2/x^5 + 1/105*(8*a^6*c^(3/2)*x^6 + 4*a^4*c^(3/2)*x^4 + 3*a^2*c^(3/2)*x^2 - 15*c^(3/2))*sqrt(a*x + 1)*sqrt(-a*x + 1)/x^7","A",0
1098,1,239,0,0.791360," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{1}{20160} \, {\left(\frac{2240 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} x^{2}}{a^{3} c} - \frac{7560 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}{a^{4}} + \frac{5040 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} x}{a^{4} c} + \frac{630 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c x}{a^{4}} + \frac{15120 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{2} x}{a^{4}} - \frac{14175 \, \sqrt{-a^{2} c x^{2} + c} c^{2} x}{a^{4}} - \frac{14175 \, c^{\frac{5}{2}} \arcsin\left(a x\right)}{a^{5}} - \frac{8064 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{a^{5}} + \frac{6400 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}{a^{5} c} - \frac{30240 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{2}}{a^{5}} + \frac{15120 \, c^{4} \arcsin\left(a x - 2\right)}{a^{8} \left(-\frac{c}{a^{2}}\right)^{\frac{3}{2}}}\right)} a"," ",0,"1/20160*(2240*(-a^2*c*x^2 + c)^(7/2)*x^2/(a^3*c) - 7560*(-a^2*c*x^2 + c)^(5/2)*x/a^4 + 5040*(-a^2*c*x^2 + c)^(7/2)*x/(a^4*c) + 630*(-a^2*c*x^2 + c)^(3/2)*c*x/a^4 + 15120*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^2*x/a^4 - 14175*sqrt(-a^2*c*x^2 + c)*c^2*x/a^4 - 14175*c^(5/2)*arcsin(a*x)/a^5 - 8064*(-a^2*c*x^2 + c)^(5/2)/a^5 + 6400*(-a^2*c*x^2 + c)^(7/2)/(a^5*c) - 30240*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^2/a^5 + 15120*c^4*arcsin(a*x - 2)/(a^8*(-c/a^2)^(3/2)))*a","A",0
1099,1,215,0,0.671590," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{1}{13440} \, a {\left(\frac{4760 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}{a^{3}} - \frac{1680 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} x}{a^{3} c} - \frac{770 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c x}{a^{3}} - \frac{10080 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{2} x}{a^{3}} + \frac{8925 \, \sqrt{-a^{2} c x^{2} + c} c^{2} x}{a^{3}} + \frac{8925 \, c^{\frac{5}{2}} \arcsin\left(a x\right)}{a^{4}} + \frac{5376 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{a^{4}} - \frac{3840 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}{a^{4} c} + \frac{20160 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{2}}{a^{4}} - \frac{10080 \, c^{4} \arcsin\left(a x - 2\right)}{a^{7} \left(-\frac{c}{a^{2}}\right)^{\frac{3}{2}}}\right)}"," ",0,"-1/13440*a*(4760*(-a^2*c*x^2 + c)^(5/2)*x/a^3 - 1680*(-a^2*c*x^2 + c)^(7/2)*x/(a^3*c) - 770*(-a^2*c*x^2 + c)^(3/2)*c*x/a^3 - 10080*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^2*x/a^3 + 8925*sqrt(-a^2*c*x^2 + c)*c^2*x/a^3 + 8925*c^(5/2)*arcsin(a*x)/a^4 + 5376*(-a^2*c*x^2 + c)^(5/2)/a^4 - 3840*(-a^2*c*x^2 + c)^(7/2)/(a^4*c) + 20160*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^2/a^4 - 10080*c^4*arcsin(a*x - 2)/(a^7*(-c/a^2)^(3/2)))","A",0
1100,1,193,0,0.648804," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{1}{840} \, {\left(\frac{280 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}{a^{2}} - \frac{70 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c x}{a^{2}} - \frac{630 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{2} x}{a^{2}} + \frac{525 \, \sqrt{-a^{2} c x^{2} + c} c^{2} x}{a^{2}} + \frac{525 \, c^{\frac{5}{2}} \arcsin\left(a x\right)}{a^{3}} + \frac{336 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{a^{3}} - \frac{120 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}{a^{3} c} + \frac{1260 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{2}}{a^{3}} - \frac{630 \, c^{4} \arcsin\left(a x - 2\right)}{a^{6} \left(-\frac{c}{a^{2}}\right)^{\frac{3}{2}}}\right)} a"," ",0,"-1/840*(280*(-a^2*c*x^2 + c)^(5/2)*x/a^2 - 70*(-a^2*c*x^2 + c)^(3/2)*c*x/a^2 - 630*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^2*x/a^2 + 525*sqrt(-a^2*c*x^2 + c)*c^2*x/a^2 + 525*c^(5/2)*arcsin(a*x)/a^3 + 336*(-a^2*c*x^2 + c)^(5/2)/a^3 - 120*(-a^2*c*x^2 + c)^(7/2)/(a^3*c) + 1260*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^2/a^3 - 630*c^4*arcsin(a*x - 2)/(a^6*(-c/a^2)^(3/2)))*a","A",0
1101,1,172,0,0.546923," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{1}{240} \, {\left(\frac{40 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}{a} - \frac{70 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c x}{a} - \frac{180 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{2} x}{a} + \frac{75 \, \sqrt{-a^{2} c x^{2} + c} c^{2} x}{a} + \frac{75 \, c^{\frac{5}{2}} \arcsin\left(a x\right)}{a^{2}} + \frac{96 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{a^{2}} + \frac{360 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{2}}{a^{2}} - \frac{180 \, c^{4} \arcsin\left(a x - 2\right)}{a^{5} \left(-\frac{c}{a^{2}}\right)^{\frac{3}{2}}}\right)} a"," ",0,"-1/240*(40*(-a^2*c*x^2 + c)^(5/2)*x/a - 70*(-a^2*c*x^2 + c)^(3/2)*c*x/a - 180*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^2*x/a + 75*sqrt(-a^2*c*x^2 + c)*c^2*x/a + 75*c^(5/2)*arcsin(a*x)/a^2 + 96*(-a^2*c*x^2 + c)^(5/2)/a^2 + 360*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^2/a^2 - 180*c^4*arcsin(a*x - 2)/(a^5*(-c/a^2)^(3/2)))*a","A",0
1102,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)^2/((a^2*x^2 - 1)*x), x)","F",0
1103,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^2,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)^2/((a^2*x^2 - 1)*x^2), x)","F",0
1104,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^3,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{3}}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)^2/((a^2*x^2 - 1)*x^3), x)","F",0
1105,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^4,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{4}}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)^2/((a^2*x^2 - 1)*x^4), x)","F",0
1106,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^5,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} x^{5}}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)^2/((a^2*x^2 - 1)*x^5), x)","F",0
1107,1,194,0,0.566114," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","-\frac{1}{896} \, {\left(\frac{112 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} x}{a} - \frac{168 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} c x}{a} - \frac{210 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c^{2} x}{a} - \frac{560 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{3} x}{a} + \frac{245 \, \sqrt{-a^{2} c x^{2} + c} c^{3} x}{a} + \frac{245 \, c^{\frac{7}{2}} \arcsin\left(a x\right)}{a^{2}} + \frac{256 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}{a^{2}} + \frac{1120 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{3}}{a^{2}} - \frac{560 \, c^{5} \arcsin\left(a x - 2\right)}{a^{5} \left(-\frac{c}{a^{2}}\right)^{\frac{3}{2}}}\right)} a"," ",0,"-1/896*(112*(-a^2*c*x^2 + c)^(7/2)*x/a - 168*(-a^2*c*x^2 + c)^(5/2)*c*x/a - 210*(-a^2*c*x^2 + c)^(3/2)*c^2*x/a - 560*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^3*x/a + 245*sqrt(-a^2*c*x^2 + c)*c^3*x/a + 245*c^(7/2)*arcsin(a*x)/a^2 + 256*(-a^2*c*x^2 + c)^(7/2)/a^2 + 1120*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^3/a^2 - 560*c^5*arcsin(a*x - 2)/(a^5*(-c/a^2)^(3/2)))*a","A",0
1108,1,113,0,0.545115," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{6 \, \sqrt{-a^{2} c x^{2} + c}}{a^{6} c x - a^{5} c} - \frac{\sqrt{-a^{2} c x^{2} + c} x^{2}}{a^{3} c} - \frac{3 \, \sqrt{-a^{2} c x^{2} + c} x}{a^{4} c} + \frac{9 \, \arcsin\left(a x\right)}{a^{5} \sqrt{c}} - \frac{8 \, \sqrt{-a^{2} c x^{2} + c}}{a^{5} c}\right)}"," ",0,"-1/3*a*(6*sqrt(-a^2*c*x^2 + c)/(a^6*c*x - a^5*c) - sqrt(-a^2*c*x^2 + c)*x^2/(a^3*c) - 3*sqrt(-a^2*c*x^2 + c)*x/(a^4*c) + 9*arcsin(a*x)/(a^5*sqrt(c)) - 8*sqrt(-a^2*c*x^2 + c)/(a^5*c))","A",0
1109,1,89,0,0.502116," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{4 \, \sqrt{-a^{2} c x^{2} + c}}{a^{5} c x - a^{4} c} - \frac{\sqrt{-a^{2} c x^{2} + c} x}{a^{3} c} + \frac{5 \, \arcsin\left(a x\right)}{a^{4} \sqrt{c}} - \frac{4 \, \sqrt{-a^{2} c x^{2} + c}}{a^{4} c}\right)}"," ",0,"-1/2*a*(4*sqrt(-a^2*c*x^2 + c)/(a^5*c*x - a^4*c) - sqrt(-a^2*c*x^2 + c)*x/(a^3*c) + 5*arcsin(a*x)/(a^4*sqrt(c)) - 4*sqrt(-a^2*c*x^2 + c)/(a^4*c))","A",0
1110,1,67,0,0.457457," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, \sqrt{-a^{2} c x^{2} + c}}{a^{4} c x - a^{3} c} + \frac{2 \, \arcsin\left(a x\right)}{a^{3} \sqrt{c}} - \frac{\sqrt{-a^{2} c x^{2} + c}}{a^{3} c}\right)}"," ",0,"-a*(2*sqrt(-a^2*c*x^2 + c)/(a^4*c*x - a^3*c) + 2*arcsin(a*x)/(a^3*sqrt(c)) - sqrt(-a^2*c*x^2 + c)/(a^3*c))","A",0
1111,1,45,0,0.449945," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, \sqrt{-a^{2} c x^{2} + c}}{a^{3} c x - a^{2} c} + \frac{\arcsin\left(a x\right)}{a^{2} \sqrt{c}}\right)}"," ",0,"-a*(2*sqrt(-a^2*c*x^2 + c)/(a^3*c*x - a^2*c) + arcsin(a*x)/(a^2*sqrt(c)))","A",0
1112,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)} x}\,{d x}"," ",0,"-integrate((a*x + 1)^2/(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)*x), x)","F",0
1113,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)*x^2), x)","F",0
1114,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)} x^{3}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)*x^3), x)","F",0
1115,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^4/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)} x^{4}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)*x^4), x)","F",0
1116,1,260,0,0.549595," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{a^{3}}{\sqrt{-a^{2} c x^{2} + c} a^{9} c x + \sqrt{-a^{2} c x^{2} + c} a^{8} c} - \frac{a^{3}}{\sqrt{-a^{2} c x^{2} + c} a^{9} c x - \sqrt{-a^{2} c x^{2} + c} a^{8} c} - \frac{a}{\sqrt{-a^{2} c x^{2} + c} a^{7} c x + \sqrt{-a^{2} c x^{2} + c} a^{6} c} - \frac{a}{\sqrt{-a^{2} c x^{2} + c} a^{7} c x - \sqrt{-a^{2} c x^{2} + c} a^{6} c} + \frac{3 \, x^{2}}{\sqrt{-a^{2} c x^{2} + c} a^{3} c} - \frac{8 \, x}{\sqrt{-a^{2} c x^{2} + c} a^{4} c} + \frac{6 \, \arcsin\left(a x\right)}{a^{5} c^{\frac{3}{2}}} - \frac{12}{\sqrt{-a^{2} c x^{2} + c} a^{5} c}\right)} a"," ",0,"1/3*(a^3/(sqrt(-a^2*c*x^2 + c)*a^9*c*x + sqrt(-a^2*c*x^2 + c)*a^8*c) - a^3/(sqrt(-a^2*c*x^2 + c)*a^9*c*x - sqrt(-a^2*c*x^2 + c)*a^8*c) - a/(sqrt(-a^2*c*x^2 + c)*a^7*c*x + sqrt(-a^2*c*x^2 + c)*a^6*c) - a/(sqrt(-a^2*c*x^2 + c)*a^7*c*x - sqrt(-a^2*c*x^2 + c)*a^6*c) + 3*x^2/(sqrt(-a^2*c*x^2 + c)*a^3*c) - 8*x/(sqrt(-a^2*c*x^2 + c)*a^4*c) + 6*arcsin(a*x)/(a^5*c^(3/2)) - 12/(sqrt(-a^2*c*x^2 + c)*a^5*c))*a","B",0
1117,1,230,0,0.511412," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{a}{\sqrt{-a^{2} c x^{2} + c} a^{6} c x + \sqrt{-a^{2} c x^{2} + c} a^{5} c} - \frac{a}{\sqrt{-a^{2} c x^{2} + c} a^{6} c x - \sqrt{-a^{2} c x^{2} + c} a^{5} c} - \frac{1}{\sqrt{-a^{2} c x^{2} + c} a^{5} c x + \sqrt{-a^{2} c x^{2} + c} a^{4} c} - \frac{1}{\sqrt{-a^{2} c x^{2} + c} a^{5} c x - \sqrt{-a^{2} c x^{2} + c} a^{4} c} - \frac{5 \, x}{\sqrt{-a^{2} c x^{2} + c} a^{3} c} + \frac{3 \, \arcsin\left(a x\right)}{a^{4} c^{\frac{3}{2}}} - \frac{6}{\sqrt{-a^{2} c x^{2} + c} a^{4} c}\right)}"," ",0,"1/3*a*(a/(sqrt(-a^2*c*x^2 + c)*a^6*c*x + sqrt(-a^2*c*x^2 + c)*a^5*c) - a/(sqrt(-a^2*c*x^2 + c)*a^6*c*x - sqrt(-a^2*c*x^2 + c)*a^5*c) - 1/(sqrt(-a^2*c*x^2 + c)*a^5*c*x + sqrt(-a^2*c*x^2 + c)*a^4*c) - 1/(sqrt(-a^2*c*x^2 + c)*a^5*c*x - sqrt(-a^2*c*x^2 + c)*a^4*c) - 5*x/(sqrt(-a^2*c*x^2 + c)*a^3*c) + 3*arcsin(a*x)/(a^4*c^(3/2)) - 6/(sqrt(-a^2*c*x^2 + c)*a^4*c))","B",0
1118,1,218,0,0.479141," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{a}{\sqrt{-a^{2} c x^{2} + c} a^{5} c x + \sqrt{-a^{2} c x^{2} + c} a^{4} c} - \frac{a}{\sqrt{-a^{2} c x^{2} + c} a^{5} c x - \sqrt{-a^{2} c x^{2} + c} a^{4} c} - \frac{1}{\sqrt{-a^{2} c x^{2} + c} a^{4} c x + \sqrt{-a^{2} c x^{2} + c} a^{3} c} - \frac{1}{\sqrt{-a^{2} c x^{2} + c} a^{4} c x - \sqrt{-a^{2} c x^{2} + c} a^{3} c} - \frac{2 \, x}{\sqrt{-a^{2} c x^{2} + c} a^{2} c} - \frac{3}{\sqrt{-a^{2} c x^{2} + c} a^{3} c}\right)}"," ",0,"1/3*a*(a/(sqrt(-a^2*c*x^2 + c)*a^5*c*x + sqrt(-a^2*c*x^2 + c)*a^4*c) - a/(sqrt(-a^2*c*x^2 + c)*a^5*c*x - sqrt(-a^2*c*x^2 + c)*a^4*c) - 1/(sqrt(-a^2*c*x^2 + c)*a^4*c*x + sqrt(-a^2*c*x^2 + c)*a^3*c) - 1/(sqrt(-a^2*c*x^2 + c)*a^4*c*x - sqrt(-a^2*c*x^2 + c)*a^3*c) - 2*x/(sqrt(-a^2*c*x^2 + c)*a^2*c) - 3/(sqrt(-a^2*c*x^2 + c)*a^3*c))","B",0
1119,1,196,0,0.380023," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{a}{\sqrt{-a^{2} c x^{2} + c} a^{4} c x + \sqrt{-a^{2} c x^{2} + c} a^{3} c} - \frac{a}{\sqrt{-a^{2} c x^{2} + c} a^{4} c x - \sqrt{-a^{2} c x^{2} + c} a^{3} c} - \frac{1}{\sqrt{-a^{2} c x^{2} + c} a^{3} c x + \sqrt{-a^{2} c x^{2} + c} a^{2} c} - \frac{1}{\sqrt{-a^{2} c x^{2} + c} a^{3} c x - \sqrt{-a^{2} c x^{2} + c} a^{2} c} + \frac{x}{\sqrt{-a^{2} c x^{2} + c} a c}\right)}"," ",0,"1/3*a*(a/(sqrt(-a^2*c*x^2 + c)*a^4*c*x + sqrt(-a^2*c*x^2 + c)*a^3*c) - a/(sqrt(-a^2*c*x^2 + c)*a^4*c*x - sqrt(-a^2*c*x^2 + c)*a^3*c) - 1/(sqrt(-a^2*c*x^2 + c)*a^3*c*x + sqrt(-a^2*c*x^2 + c)*a^2*c) - 1/(sqrt(-a^2*c*x^2 + c)*a^3*c*x - sqrt(-a^2*c*x^2 + c)*a^2*c) + x/(sqrt(-a^2*c*x^2 + c)*a*c))","B",0
1120,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a^{2} x^{2} - 1\right)} x}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((-a^2*c*x^2 + c)^(3/2)*(a^2*x^2 - 1)*x), x)","F",0
1121,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a^{2} x^{2} - 1\right)} x^{2}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((-a^2*c*x^2 + c)^(3/2)*(a^2*x^2 - 1)*x^2), x)","F",0
1122,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a^{2} x^{2} - 1\right)} x^{3}}\,{d x}"," ",0,"-integrate((a*x + 1)^2/((-a^2*c*x^2 + c)^(3/2)*(a^2*x^2 - 1)*x^3), x)","F",0
1123,1,218,0,0.398967," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{1}{5} \, a {\left(\frac{a}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{4} c x + {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{3} c} - \frac{a}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{4} c x - {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{3} c} - \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{3} c x + {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{2} c} - \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{3} c x - {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{2} c} + \frac{2 \, x}{\sqrt{-a^{2} c x^{2} + c} a c^{2}} + \frac{x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a c}\right)}"," ",0,"1/5*a*(a/((-a^2*c*x^2 + c)^(3/2)*a^4*c*x + (-a^2*c*x^2 + c)^(3/2)*a^3*c) - a/((-a^2*c*x^2 + c)^(3/2)*a^4*c*x - (-a^2*c*x^2 + c)^(3/2)*a^3*c) - 1/((-a^2*c*x^2 + c)^(3/2)*a^3*c*x + (-a^2*c*x^2 + c)^(3/2)*a^2*c) - 1/((-a^2*c*x^2 + c)^(3/2)*a^3*c*x - (-a^2*c*x^2 + c)^(3/2)*a^2*c) + 2*x/(sqrt(-a^2*c*x^2 + c)*a*c^2) + x/((-a^2*c*x^2 + c)^(3/2)*a*c))","B",0
1124,1,242,0,0.447937," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\frac{1}{21} \, a {\left(\frac{3 \, a}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a^{4} c x + {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a^{3} c} - \frac{3 \, a}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a^{4} c x - {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a^{3} c} - \frac{3}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a^{3} c x + {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a^{2} c} - \frac{3}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a^{3} c x - {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a^{2} c} + \frac{8 \, x}{\sqrt{-a^{2} c x^{2} + c} a c^{3}} + \frac{4 \, x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a c^{2}} + \frac{3 \, x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a c}\right)}"," ",0,"1/21*a*(3*a/((-a^2*c*x^2 + c)^(5/2)*a^4*c*x + (-a^2*c*x^2 + c)^(5/2)*a^3*c) - 3*a/((-a^2*c*x^2 + c)^(5/2)*a^4*c*x - (-a^2*c*x^2 + c)^(5/2)*a^3*c) - 3/((-a^2*c*x^2 + c)^(5/2)*a^3*c*x + (-a^2*c*x^2 + c)^(5/2)*a^2*c) - 3/((-a^2*c*x^2 + c)^(5/2)*a^3*c*x - (-a^2*c*x^2 + c)^(5/2)*a^2*c) + 8*x/(sqrt(-a^2*c*x^2 + c)*a*c^3) + 4*x/((-a^2*c*x^2 + c)^(3/2)*a*c^2) + 3*x/((-a^2*c*x^2 + c)^(5/2)*a*c))","B",0
1125,1,304,0,0.385635," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left({\left(m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right)} a^{6} c^{3} x^{7} + 2 \, {\left(m^{6} + 22 \, m^{5} + 190 \, m^{4} + 820 \, m^{3} + 1849 \, m^{2} + 2038 \, m + 840\right)} a^{5} c^{3} x^{6} - {\left(m^{6} + 23 \, m^{5} + 207 \, m^{4} + 925 \, m^{3} + 2144 \, m^{2} + 2412 \, m + 1008\right)} a^{4} c^{3} x^{5} - 4 \, {\left(m^{6} + 24 \, m^{5} + 226 \, m^{4} + 1056 \, m^{3} + 2545 \, m^{2} + 2952 \, m + 1260\right)} a^{3} c^{3} x^{4} - {\left(m^{6} + 25 \, m^{5} + 247 \, m^{4} + 1219 \, m^{3} + 3112 \, m^{2} + 3796 \, m + 1680\right)} a^{2} c^{3} x^{3} + 2 \, {\left(m^{6} + 26 \, m^{5} + 270 \, m^{4} + 1420 \, m^{3} + 3929 \, m^{2} + 5274 \, m + 2520\right)} a c^{3} x^{2} + {\left(m^{6} + 27 \, m^{5} + 295 \, m^{4} + 1665 \, m^{3} + 5104 \, m^{2} + 8028 \, m + 5040\right)} c^{3} x\right)} x^{m}}{m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040}"," ",0,"((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*a^6*c^3*x^7 + 2*(m^6 + 22*m^5 + 190*m^4 + 820*m^3 + 1849*m^2 + 2038*m + 840)*a^5*c^3*x^6 - (m^6 + 23*m^5 + 207*m^4 + 925*m^3 + 2144*m^2 + 2412*m + 1008)*a^4*c^3*x^5 - 4*(m^6 + 24*m^5 + 226*m^4 + 1056*m^3 + 2545*m^2 + 2952*m + 1260)*a^3*c^3*x^4 - (m^6 + 25*m^5 + 247*m^4 + 1219*m^3 + 3112*m^2 + 3796*m + 1680)*a^2*c^3*x^3 + 2*(m^6 + 26*m^5 + 270*m^4 + 1420*m^3 + 3929*m^2 + 5274*m + 2520)*a*c^3*x^2 + (m^6 + 27*m^5 + 295*m^4 + 1665*m^3 + 5104*m^2 + 8028*m + 5040)*c^3*x)*x^m/(m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)","B",0
1126,1,114,0,0.373031," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left({\left(m^{3} + 7 \, m^{2} + 14 \, m + 8\right)} a^{4} c^{2} x^{5} + 2 \, {\left(m^{3} + 8 \, m^{2} + 17 \, m + 10\right)} a^{3} c^{2} x^{4} - 2 \, {\left(m^{3} + 10 \, m^{2} + 29 \, m + 20\right)} a c^{2} x^{2} - {\left(m^{3} + 11 \, m^{2} + 38 \, m + 40\right)} c^{2} x\right)} x^{m}}{m^{4} + 12 \, m^{3} + 49 \, m^{2} + 78 \, m + 40}"," ",0,"-((m^3 + 7*m^2 + 14*m + 8)*a^4*c^2*x^5 + 2*(m^3 + 8*m^2 + 17*m + 10)*a^3*c^2*x^4 - 2*(m^3 + 10*m^2 + 29*m + 20)*a*c^2*x^2 - (m^3 + 11*m^2 + 38*m + 40)*c^2*x)*x^m/(m^4 + 12*m^3 + 49*m^2 + 78*m + 40)","A",0
1127,1,62,0,0.378023," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{{\left({\left(m^{2} + 3 \, m + 2\right)} a^{2} c x^{3} + 2 \, {\left(m^{2} + 4 \, m + 3\right)} a c x^{2} + {\left(m^{2} + 5 \, m + 6\right)} c x\right)} x^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6}"," ",0,"((m^2 + 3*m + 2)*a^2*c*x^3 + 2*(m^2 + 4*m + 3)*a*c*x^2 + (m^2 + 5*m + 6)*c*x)*x^m/(m^3 + 6*m^2 + 11*m + 6)","A",0
1128,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{2} x^{m}}{{\left(a^{2} c x^{2} - c\right)} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((a*x + 1)^2*x^m/((a^2*c*x^2 - c)*(a^2*x^2 - 1)), x)","F",0
1129,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} x^{m}}{{\left(a^{2} c x^{2} - c\right)}^{2} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"-integrate((a*x + 1)^2*x^m/((a^2*c*x^2 - c)^2*(a^2*x^2 - 1)), x)","F",0
1130,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{2} x^{m}}{{\left(a^{2} c x^{2} - c\right)}^{3} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((a*x + 1)^2*x^m/((a^2*c*x^2 - c)^3*(a^2*x^2 - 1)), x)","F",0
1131,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}^{2} x^{m}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)^2*x^m/(a^2*x^2 - 1), x)","F",0
1132,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}^{2} x^{m}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)^2*x^m/(a^2*x^2 - 1), x)","F",0
1133,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{2} x^{m}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^2*x^m/(a^2*x^2 - 1), x)","F",0
1134,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} x^{m}}{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"-integrate((a*x + 1)^2*x^m/(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)), x)","F",0
1135,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} x^{m}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"-integrate((a*x + 1)^2*x^m/((-a^2*c*x^2 + c)^(3/2)*(a^2*x^2 - 1)), x)","F",0
1136,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{2} {\left(-a^{2} c x^{2} + c\right)}^{p}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x + 1)^2*(-a^2*c*x^2 + c)^p/(a^2*x^2 - 1), x)","F",0
1137,1,169,0,0.425690," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{a^{3} c x^{7}}{6 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{3 \, a^{2} c x^{6}}{5 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{19 \, a c x^{5}}{24 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{8 \, c x^{4}}{15 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{23 \, c x^{3}}{48 \, \sqrt{-a^{2} x^{2} + 1} a} + \frac{17 \, c x^{2}}{15 \, \sqrt{-a^{2} x^{2} + 1} a^{2}} - \frac{23 \, c x}{16 \, \sqrt{-a^{2} x^{2} + 1} a^{3}} + \frac{23 \, c \arcsin\left(a x\right)}{16 \, a^{4}} - \frac{34 \, c}{15 \, \sqrt{-a^{2} x^{2} + 1} a^{4}}"," ",0,"1/6*a^3*c*x^7/sqrt(-a^2*x^2 + 1) + 3/5*a^2*c*x^6/sqrt(-a^2*x^2 + 1) + 19/24*a*c*x^5/sqrt(-a^2*x^2 + 1) + 8/15*c*x^4/sqrt(-a^2*x^2 + 1) + 23/48*c*x^3/(sqrt(-a^2*x^2 + 1)*a) + 17/15*c*x^2/(sqrt(-a^2*x^2 + 1)*a^2) - 23/16*c*x/(sqrt(-a^2*x^2 + 1)*a^3) + 23/16*c*arcsin(a*x)/a^4 - 34/15*c/(sqrt(-a^2*x^2 + 1)*a^4)","A",0
1138,1,148,0,0.422233," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{a^{3} c x^{6}}{5 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{3 \, a^{2} c x^{5}}{4 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{16 \, a c x^{4}}{15 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{7 \, c x^{3}}{8 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{19 \, c x^{2}}{15 \, \sqrt{-a^{2} x^{2} + 1} a} - \frac{13 \, c x}{8 \, \sqrt{-a^{2} x^{2} + 1} a^{2}} + \frac{13 \, c \arcsin\left(a x\right)}{8 \, a^{3}} - \frac{38 \, c}{15 \, \sqrt{-a^{2} x^{2} + 1} a^{3}}"," ",0,"1/5*a^3*c*x^6/sqrt(-a^2*x^2 + 1) + 3/4*a^2*c*x^5/sqrt(-a^2*x^2 + 1) + 16/15*a*c*x^4/sqrt(-a^2*x^2 + 1) + 7/8*c*x^3/sqrt(-a^2*x^2 + 1) + 19/15*c*x^2/(sqrt(-a^2*x^2 + 1)*a) - 13/8*c*x/(sqrt(-a^2*x^2 + 1)*a^2) + 13/8*c*arcsin(a*x)/a^3 - 38/15*c/(sqrt(-a^2*x^2 + 1)*a^3)","A",0
1139,1,126,0,0.428343," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{a^{3} c x^{5}}{4 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{a^{2} c x^{4}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{13 \, a c x^{3}}{8 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{2 \, c x^{2}}{\sqrt{-a^{2} x^{2} + 1}} - \frac{15 \, c x}{8 \, \sqrt{-a^{2} x^{2} + 1} a} + \frac{15 \, c \arcsin\left(a x\right)}{8 \, a^{2}} - \frac{3 \, c}{\sqrt{-a^{2} x^{2} + 1} a^{2}}"," ",0,"1/4*a^3*c*x^5/sqrt(-a^2*x^2 + 1) + a^2*c*x^4/sqrt(-a^2*x^2 + 1) + 13/8*a*c*x^3/sqrt(-a^2*x^2 + 1) + 2*c*x^2/sqrt(-a^2*x^2 + 1) - 15/8*c*x/(sqrt(-a^2*x^2 + 1)*a) + 15/8*c*arcsin(a*x)/a^2 - 3*c/(sqrt(-a^2*x^2 + 1)*a^2)","A",0
1140,1,106,0,0.426985," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{a^{3} c x^{4}}{3 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{3 \, a^{2} c x^{3}}{2 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{10 \, a c x^{2}}{3 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{3 \, c x}{2 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{5 \, c \arcsin\left(a x\right)}{2 \, a} - \frac{11 \, c}{3 \, \sqrt{-a^{2} x^{2} + 1} a}"," ",0,"1/3*a^3*c*x^4/sqrt(-a^2*x^2 + 1) + 3/2*a^2*c*x^3/sqrt(-a^2*x^2 + 1) + 10/3*a*c*x^2/sqrt(-a^2*x^2 + 1) - 3/2*c*x/sqrt(-a^2*x^2 + 1) + 5/2*c*arcsin(a*x)/a - 11/3*c/(sqrt(-a^2*x^2 + 1)*a)","A",0
1141,1,111,0,0.428149," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x,x, algorithm=""maxima"")","\frac{a^{3} c x^{3}}{2 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{3 \, a^{2} c x^{2}}{\sqrt{-a^{2} x^{2} + 1}} - \frac{a c x}{2 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{7}{2} \, c \arcsin\left(a x\right) - c \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{3 \, c}{\sqrt{-a^{2} x^{2} + 1}}"," ",0,"1/2*a^3*c*x^3/sqrt(-a^2*x^2 + 1) + 3*a^2*c*x^2/sqrt(-a^2*x^2 + 1) - 1/2*a*c*x/sqrt(-a^2*x^2 + 1) + 7/2*c*arcsin(a*x) - c*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - 3*c/sqrt(-a^2*x^2 + 1)","A",0
1142,1,111,0,0.425185," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^2,x, algorithm=""maxima"")","\frac{a^{3} c x^{2}}{\sqrt{-a^{2} x^{2} + 1}} + \frac{a^{2} c x}{\sqrt{-a^{2} x^{2} + 1}} + 3 \, a c \arcsin\left(a x\right) - 3 \, a c \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{a c}{\sqrt{-a^{2} x^{2} + 1}} - \frac{c}{\sqrt{-a^{2} x^{2} + 1} x}"," ",0,"a^3*c*x^2/sqrt(-a^2*x^2 + 1) + a^2*c*x/sqrt(-a^2*x^2 + 1) + 3*a*c*arcsin(a*x) - 3*a*c*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) - a*c/sqrt(-a^2*x^2 + 1) - c/(sqrt(-a^2*x^2 + 1)*x)","A",0
1143,1,116,0,0.429280," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^3,x, algorithm=""maxima"")","\frac{3 \, a^{3} c x}{\sqrt{-a^{2} x^{2} + 1}} + a^{2} c \arcsin\left(a x\right) - \frac{7}{2} \, a^{2} c \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{a^{2} c}{2 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{3 \, a c}{\sqrt{-a^{2} x^{2} + 1} x} - \frac{c}{2 \, \sqrt{-a^{2} x^{2} + 1} x^{2}}"," ",0,"3*a^3*c*x/sqrt(-a^2*x^2 + 1) + a^2*c*arcsin(a*x) - 7/2*a^2*c*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 1/2*a^2*c/sqrt(-a^2*x^2 + 1) - 3*a*c/(sqrt(-a^2*x^2 + 1)*x) - 1/2*c/(sqrt(-a^2*x^2 + 1)*x^2)","A",0
1144,1,128,0,0.330667," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^4,x, algorithm=""maxima"")","\frac{11 \, a^{4} c x}{3 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{5}{2} \, a^{3} c \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{3 \, a^{3} c}{2 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{10 \, a^{2} c}{3 \, \sqrt{-a^{2} x^{2} + 1} x} - \frac{3 \, a c}{2 \, \sqrt{-a^{2} x^{2} + 1} x^{2}} - \frac{c}{3 \, \sqrt{-a^{2} x^{2} + 1} x^{3}}"," ",0,"11/3*a^4*c*x/sqrt(-a^2*x^2 + 1) - 5/2*a^3*c*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 3/2*a^3*c/sqrt(-a^2*x^2 + 1) - 10/3*a^2*c/(sqrt(-a^2*x^2 + 1)*x) - 3/2*a*c/(sqrt(-a^2*x^2 + 1)*x^2) - 1/3*c/(sqrt(-a^2*x^2 + 1)*x^3)","A",0
1145,1,149,0,0.326740," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^5,x, algorithm=""maxima"")","\frac{3 \, a^{5} c x}{\sqrt{-a^{2} x^{2} + 1}} - \frac{15}{8} \, a^{4} c \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{15 \, a^{4} c}{8 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{2 \, a^{3} c}{\sqrt{-a^{2} x^{2} + 1} x} - \frac{13 \, a^{2} c}{8 \, \sqrt{-a^{2} x^{2} + 1} x^{2}} - \frac{a c}{\sqrt{-a^{2} x^{2} + 1} x^{3}} - \frac{c}{4 \, \sqrt{-a^{2} x^{2} + 1} x^{4}}"," ",0,"3*a^5*c*x/sqrt(-a^2*x^2 + 1) - 15/8*a^4*c*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 15/8*a^4*c/sqrt(-a^2*x^2 + 1) - 2*a^3*c/(sqrt(-a^2*x^2 + 1)*x) - 13/8*a^2*c/(sqrt(-a^2*x^2 + 1)*x^2) - a*c/(sqrt(-a^2*x^2 + 1)*x^3) - 1/4*c/(sqrt(-a^2*x^2 + 1)*x^4)","A",0
1146,1,170,0,0.330422," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^6,x, algorithm=""maxima"")","\frac{38 \, a^{6} c x}{15 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{13}{8} \, a^{5} c \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{13 \, a^{5} c}{8 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{19 \, a^{4} c}{15 \, \sqrt{-a^{2} x^{2} + 1} x} - \frac{7 \, a^{3} c}{8 \, \sqrt{-a^{2} x^{2} + 1} x^{2}} - \frac{16 \, a^{2} c}{15 \, \sqrt{-a^{2} x^{2} + 1} x^{3}} - \frac{3 \, a c}{4 \, \sqrt{-a^{2} x^{2} + 1} x^{4}} - \frac{c}{5 \, \sqrt{-a^{2} x^{2} + 1} x^{5}}"," ",0,"38/15*a^6*c*x/sqrt(-a^2*x^2 + 1) - 13/8*a^5*c*log(2*sqrt(-a^2*x^2 + 1)/abs(x) + 2/abs(x)) + 13/8*a^5*c/sqrt(-a^2*x^2 + 1) - 19/15*a^4*c/(sqrt(-a^2*x^2 + 1)*x) - 7/8*a^3*c/(sqrt(-a^2*x^2 + 1)*x^2) - 16/15*a^2*c/(sqrt(-a^2*x^2 + 1)*x^3) - 3/4*a*c/(sqrt(-a^2*x^2 + 1)*x^4) - 1/5*c/(sqrt(-a^2*x^2 + 1)*x^5)","A",0
1147,1,164,0,0.425172," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{a^{5} c^{2} x^{6}}{5 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{3 \, a^{4} c^{2} x^{5}}{4 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{11 \, a^{3} c^{2} x^{4}}{15 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{5 \, a^{2} c^{2} x^{3}}{8 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{31 \, a c^{2} x^{2}}{15 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{c^{2} x}{8 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{7 \, c^{2} \arcsin\left(a x\right)}{8 \, a} - \frac{17 \, c^{2}}{15 \, \sqrt{-a^{2} x^{2} + 1} a}"," ",0,"-1/5*a^5*c^2*x^6/sqrt(-a^2*x^2 + 1) - 3/4*a^4*c^2*x^5/sqrt(-a^2*x^2 + 1) - 11/15*a^3*c^2*x^4/sqrt(-a^2*x^2 + 1) + 5/8*a^2*c^2*x^3/sqrt(-a^2*x^2 + 1) + 31/15*a*c^2*x^2/sqrt(-a^2*x^2 + 1) + 1/8*c^2*x/sqrt(-a^2*x^2 + 1) + 7/8*c^2*arcsin(a*x)/a - 17/15*c^2/(sqrt(-a^2*x^2 + 1)*a)","A",0
1148,1,210,0,0.435603," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{a^{7} c^{3} x^{8}}{7 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{a^{6} c^{3} x^{7}}{2 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{8 \, a^{5} c^{3} x^{6}}{35 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{9 \, a^{4} c^{3} x^{5}}{8 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{54 \, a^{3} c^{3} x^{4}}{35 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{3 \, a^{2} c^{3} x^{3}}{16 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{64 \, a c^{3} x^{2}}{35 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{7 \, c^{3} x}{16 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{9 \, c^{3} \arcsin\left(a x\right)}{16 \, a} - \frac{23 \, c^{3}}{35 \, \sqrt{-a^{2} x^{2} + 1} a}"," ",0,"1/7*a^7*c^3*x^8/sqrt(-a^2*x^2 + 1) + 1/2*a^6*c^3*x^7/sqrt(-a^2*x^2 + 1) + 8/35*a^5*c^3*x^6/sqrt(-a^2*x^2 + 1) - 9/8*a^4*c^3*x^5/sqrt(-a^2*x^2 + 1) - 54/35*a^3*c^3*x^4/sqrt(-a^2*x^2 + 1) + 3/16*a^2*c^3*x^3/sqrt(-a^2*x^2 + 1) + 64/35*a*c^3*x^2/sqrt(-a^2*x^2 + 1) + 7/16*c^3*x/sqrt(-a^2*x^2 + 1) + 9/16*c^3*arcsin(a*x)/a - 23/35*c^3/(sqrt(-a^2*x^2 + 1)*a)","A",0
1149,1,256,0,0.422018," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","-\frac{a^{9} c^{4} x^{10}}{9 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{3 \, a^{8} c^{4} x^{9}}{8 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{a^{7} c^{4} x^{8}}{63 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{61 \, a^{6} c^{4} x^{7}}{48 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{74 \, a^{5} c^{4} x^{6}}{63 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{245 \, a^{4} c^{4} x^{5}}{192 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{146 \, a^{3} c^{4} x^{4}}{63 \, \sqrt{-a^{2} x^{2} + 1}} - \frac{73 \, a^{2} c^{4} x^{3}}{384 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{109 \, a c^{4} x^{2}}{63 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{73 \, c^{4} x}{128 \, \sqrt{-a^{2} x^{2} + 1}} + \frac{55 \, c^{4} \arcsin\left(a x\right)}{128 \, a} - \frac{29 \, c^{4}}{63 \, \sqrt{-a^{2} x^{2} + 1} a}"," ",0,"-1/9*a^9*c^4*x^10/sqrt(-a^2*x^2 + 1) - 3/8*a^8*c^4*x^9/sqrt(-a^2*x^2 + 1) - 1/63*a^7*c^4*x^8/sqrt(-a^2*x^2 + 1) + 61/48*a^6*c^4*x^7/sqrt(-a^2*x^2 + 1) + 74/63*a^5*c^4*x^6/sqrt(-a^2*x^2 + 1) - 245/192*a^4*c^4*x^5/sqrt(-a^2*x^2 + 1) - 146/63*a^3*c^4*x^4/sqrt(-a^2*x^2 + 1) - 73/384*a^2*c^4*x^3/sqrt(-a^2*x^2 + 1) + 109/63*a*c^4*x^2/sqrt(-a^2*x^2 + 1) + 73/128*c^4*x/sqrt(-a^2*x^2 + 1) + 55/128*c^4*arcsin(a*x)/a - 29/63*c^4/(sqrt(-a^2*x^2 + 1)*a)","A",0
1150,1,364,0,0.569041," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{a^{3} c^{3}}{\sqrt{-a^{2} x^{2} + 1} a^{8} c^{4} x + \sqrt{-a^{2} x^{2} + 1} a^{7} c^{4}} - \frac{a^{3} c^{3}}{\sqrt{-a^{2} x^{2} + 1} a^{8} c^{4} x - \sqrt{-a^{2} x^{2} + 1} a^{7} c^{4}} + \frac{3 \, a c}{\sqrt{-a^{2} x^{2} + 1} a^{6} c^{2} x + \sqrt{-a^{2} x^{2} + 1} a^{5} c^{2}} - \frac{3 \, a c}{\sqrt{-a^{2} x^{2} + 1} a^{6} c^{2} x - \sqrt{-a^{2} x^{2} + 1} a^{5} c^{2}} - \frac{4 \, c}{\sqrt{-a^{2} x^{2} + 1} a^{5} c^{2} x + \sqrt{-a^{2} x^{2} + 1} a^{4} c^{2}} - \frac{4 \, c}{\sqrt{-a^{2} x^{2} + 1} a^{5} c^{2} x - \sqrt{-a^{2} x^{2} + 1} a^{4} c^{2}} + \frac{6 \, x^{2}}{\sqrt{-a^{2} x^{2} + 1} a^{2} c} - \frac{26 \, x}{\sqrt{-a^{2} x^{2} + 1} a^{3} c} + \frac{18 \, \arcsin\left(a x\right)}{a^{4} c} - \frac{36}{\sqrt{-a^{2} x^{2} + 1} a^{4} c}\right)} a"," ",0,"1/6*(a^3*c^3/(sqrt(-a^2*x^2 + 1)*a^8*c^4*x + sqrt(-a^2*x^2 + 1)*a^7*c^4) - a^3*c^3/(sqrt(-a^2*x^2 + 1)*a^8*c^4*x - sqrt(-a^2*x^2 + 1)*a^7*c^4) + 3*a*c/(sqrt(-a^2*x^2 + 1)*a^6*c^2*x + sqrt(-a^2*x^2 + 1)*a^5*c^2) - 3*a*c/(sqrt(-a^2*x^2 + 1)*a^6*c^2*x - sqrt(-a^2*x^2 + 1)*a^5*c^2) - 4*c/(sqrt(-a^2*x^2 + 1)*a^5*c^2*x + sqrt(-a^2*x^2 + 1)*a^4*c^2) - 4*c/(sqrt(-a^2*x^2 + 1)*a^5*c^2*x - sqrt(-a^2*x^2 + 1)*a^4*c^2) + 6*x^2/(sqrt(-a^2*x^2 + 1)*a^2*c) - 26*x/(sqrt(-a^2*x^2 + 1)*a^3*c) + 18*arcsin(a*x)/(a^4*c) - 36/(sqrt(-a^2*x^2 + 1)*a^4*c))*a","B",0
1151,1,241,0,0.520641," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{2 \, a c}{\sqrt{-a^{2} x^{2} + 1} a^{5} c^{2} x + \sqrt{-a^{2} x^{2} + 1} a^{4} c^{2}} - \frac{2 \, a c}{\sqrt{-a^{2} x^{2} + 1} a^{5} c^{2} x - \sqrt{-a^{2} x^{2} + 1} a^{4} c^{2}} - \frac{2 \, c}{\sqrt{-a^{2} x^{2} + 1} a^{4} c^{2} x + \sqrt{-a^{2} x^{2} + 1} a^{3} c^{2}} - \frac{2 \, c}{\sqrt{-a^{2} x^{2} + 1} a^{4} c^{2} x - \sqrt{-a^{2} x^{2} + 1} a^{3} c^{2}} - \frac{7 \, x}{\sqrt{-a^{2} x^{2} + 1} a^{2} c} + \frac{3 \, \arcsin\left(a x\right)}{a^{3} c} - \frac{9}{\sqrt{-a^{2} x^{2} + 1} a^{3} c}\right)}"," ",0,"1/3*a*(2*a*c/(sqrt(-a^2*x^2 + 1)*a^5*c^2*x + sqrt(-a^2*x^2 + 1)*a^4*c^2) - 2*a*c/(sqrt(-a^2*x^2 + 1)*a^5*c^2*x - sqrt(-a^2*x^2 + 1)*a^4*c^2) - 2*c/(sqrt(-a^2*x^2 + 1)*a^4*c^2*x + sqrt(-a^2*x^2 + 1)*a^3*c^2) - 2*c/(sqrt(-a^2*x^2 + 1)*a^4*c^2*x - sqrt(-a^2*x^2 + 1)*a^3*c^2) - 7*x/(sqrt(-a^2*x^2 + 1)*a^2*c) + 3*arcsin(a*x)/(a^3*c) - 9/(sqrt(-a^2*x^2 + 1)*a^3*c))","B",0
1152,1,329,0,0.488446," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{a^{3} c^{3}}{\sqrt{-a^{2} x^{2} + 1} a^{6} c^{4} x + \sqrt{-a^{2} x^{2} + 1} a^{5} c^{4}} - \frac{a^{3} c^{3}}{\sqrt{-a^{2} x^{2} + 1} a^{6} c^{4} x - \sqrt{-a^{2} x^{2} + 1} a^{5} c^{4}} + \frac{3 \, a c}{\sqrt{-a^{2} x^{2} + 1} a^{4} c^{2} x + \sqrt{-a^{2} x^{2} + 1} a^{3} c^{2}} - \frac{3 \, a c}{\sqrt{-a^{2} x^{2} + 1} a^{4} c^{2} x - \sqrt{-a^{2} x^{2} + 1} a^{3} c^{2}} - \frac{4 \, c}{\sqrt{-a^{2} x^{2} + 1} a^{3} c^{2} x + \sqrt{-a^{2} x^{2} + 1} a^{2} c^{2}} - \frac{4 \, c}{\sqrt{-a^{2} x^{2} + 1} a^{3} c^{2} x - \sqrt{-a^{2} x^{2} + 1} a^{2} c^{2}} - \frac{2 \, x}{\sqrt{-a^{2} x^{2} + 1} a c} - \frac{6}{\sqrt{-a^{2} x^{2} + 1} a^{2} c}\right)} a"," ",0,"1/6*(a^3*c^3/(sqrt(-a^2*x^2 + 1)*a^6*c^4*x + sqrt(-a^2*x^2 + 1)*a^5*c^4) - a^3*c^3/(sqrt(-a^2*x^2 + 1)*a^6*c^4*x - sqrt(-a^2*x^2 + 1)*a^5*c^4) + 3*a*c/(sqrt(-a^2*x^2 + 1)*a^4*c^2*x + sqrt(-a^2*x^2 + 1)*a^3*c^2) - 3*a*c/(sqrt(-a^2*x^2 + 1)*a^4*c^2*x - sqrt(-a^2*x^2 + 1)*a^3*c^2) - 4*c/(sqrt(-a^2*x^2 + 1)*a^3*c^2*x + sqrt(-a^2*x^2 + 1)*a^2*c^2) - 4*c/(sqrt(-a^2*x^2 + 1)*a^3*c^2*x - sqrt(-a^2*x^2 + 1)*a^2*c^2) - 2*x/(sqrt(-a^2*x^2 + 1)*a*c) - 6/(sqrt(-a^2*x^2 + 1)*a^2*c))*a","B",0
1153,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(a^{2} c x^{2} - c\right)}^{2} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((a^2*c*x^2 - c)^2*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1154,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int \frac{{\left(a x + 1\right)}^{3}}{{\left(a^{2} c x^{2} - c\right)}^{3} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((a*x + 1)^3/((a^2*c*x^2 - c)^3*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1155,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(a^{2} c x^{2} - c\right)}^{4} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((a^2*c*x^2 - c)^4*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1156,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1157,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1158,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1159,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1160,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1161,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1162,1,160,0,0.376083," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""maxima"")","-2 \, \left(-1\right)^{-2 \, a^{2} c x^{2} + 2 \, c} a^{2} \sqrt{c} \log\left(-2 \, a^{2} c + \frac{2 \, c}{x^{2}}\right) + \frac{1}{2} \, a^{3} {\left(\frac{\sqrt{c} \log\left(a x + 1\right)}{a} - \frac{\sqrt{c} \log\left(a x - 1\right)}{a}\right)} + \frac{a^{2} c}{2 \, \sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{3}{2} \, {\left(a \sqrt{c} \log\left(a x + 1\right) - a \sqrt{c} \log\left(a x - 1\right) - \frac{2 \, \sqrt{c}}{x}\right)} a - \frac{c}{2 \, \sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} x^{2}}"," ",0,"-2*(-1)^(-2*a^2*c*x^2 + 2*c)*a^2*sqrt(c)*log(-2*a^2*c + 2*c/x^2) + 1/2*a^3*(sqrt(c)*log(a*x + 1)/a - sqrt(c)*log(a*x - 1)/a) + 1/2*a^2*c/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + 3/2*(a*sqrt(c)*log(a*x + 1) - a*sqrt(c)*log(a*x - 1) - 2*sqrt(c)/x)*a - 1/2*c/(sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*x^2)","A",0
1163,1,216,0,0.378109," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""maxima"")","-\frac{1}{2} \, \left(-1\right)^{-2 \, a^{2} c x^{2} + 2 \, c} a^{3} \sqrt{c} \log\left(-2 \, a^{2} c + \frac{2 \, c}{x^{2}}\right) + \frac{1}{2} \, a^{3} \sqrt{c} \log\left(a x + 1\right) - \frac{1}{2} \, a^{3} \sqrt{c} \log\left(a x - 1\right) + \frac{3}{2} \, {\left(a \sqrt{c} \log\left(a x + 1\right) - a \sqrt{c} \log\left(a x - 1\right) - \frac{2 \, \sqrt{c}}{x}\right)} a^{2} - \frac{3}{2} \, {\left(\left(-1\right)^{-2 \, a^{2} c x^{2} + 2 \, c} a^{2} \sqrt{c} \log\left(-2 \, a^{2} c + \frac{2 \, c}{x^{2}}\right) - \frac{a^{2} c}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{c}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} x^{2}}\right)} a - \frac{3 \, a^{2} \sqrt{c} x^{2} + \sqrt{c}}{3 \, x^{3}}"," ",0,"-1/2*(-1)^(-2*a^2*c*x^2 + 2*c)*a^3*sqrt(c)*log(-2*a^2*c + 2*c/x^2) + 1/2*a^3*sqrt(c)*log(a*x + 1) - 1/2*a^3*sqrt(c)*log(a*x - 1) + 3/2*(a*sqrt(c)*log(a*x + 1) - a*sqrt(c)*log(a*x - 1) - 2*sqrt(c)/x)*a^2 - 3/2*((-1)^(-2*a^2*c*x^2 + 2*c)*a^2*sqrt(c)*log(-2*a^2*c + 2*c/x^2) - a^2*c/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + c/(sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*x^2))*a - 1/3*(3*a^2*sqrt(c)*x^2 + sqrt(c))/x^3","A",0
1164,1,306,0,0.386880," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^5,x, algorithm=""maxima"")","-\frac{1}{2} \, \left(-1\right)^{-2 \, a^{2} c x^{2} + 2 \, c} a^{4} \sqrt{c} \log\left(-2 \, a^{2} c + \frac{2 \, c}{x^{2}}\right) + \frac{a^{4} c}{2 \, \sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{1}{2} \, {\left(a \sqrt{c} \log\left(a x + 1\right) - a \sqrt{c} \log\left(a x - 1\right) - \frac{2 \, \sqrt{c}}{x}\right)} a^{3} - \frac{3}{2} \, {\left(\left(-1\right)^{-2 \, a^{2} c x^{2} + 2 \, c} a^{2} \sqrt{c} \log\left(-2 \, a^{2} c + \frac{2 \, c}{x^{2}}\right) - \frac{a^{2} c}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{c}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} x^{2}}\right)} a^{2} + \frac{1}{2} \, {\left(3 \, a^{3} \sqrt{c} \log\left(a x + 1\right) - 3 \, a^{3} \sqrt{c} \log\left(a x - 1\right) - \frac{2 \, {\left(3 \, a^{2} \sqrt{c} x^{2} + \sqrt{c}\right)}}{x^{3}}\right)} a - \frac{a^{2} c}{4 \, \sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} x^{2}} - \frac{c}{4 \, \sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} x^{4}}"," ",0,"-1/2*(-1)^(-2*a^2*c*x^2 + 2*c)*a^4*sqrt(c)*log(-2*a^2*c + 2*c/x^2) + 1/2*a^4*c/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + 1/2*(a*sqrt(c)*log(a*x + 1) - a*sqrt(c)*log(a*x - 1) - 2*sqrt(c)/x)*a^3 - 3/2*((-1)^(-2*a^2*c*x^2 + 2*c)*a^2*sqrt(c)*log(-2*a^2*c + 2*c/x^2) - a^2*c/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + c/(sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*x^2))*a^2 + 1/2*(3*a^3*sqrt(c)*log(a*x + 1) - 3*a^3*sqrt(c)*log(a*x - 1) - 2*(3*a^2*sqrt(c)*x^2 + sqrt(c))/x^3)*a - 1/4*a^2*c/(sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*x^2) - 1/4*c/(sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*x^4)","A",0
1165,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1166,1,237,0,0.388084," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} c^{\frac{5}{2}} x^{3} + \frac{1}{12} \, {\left(\frac{2 \, a^{4} c^{3} x^{8}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} - \frac{5 \, a^{2} c^{3} x^{6}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{3 \, c^{3} x^{4}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}}\right)} a^{3} + c^{\frac{5}{2}} x - \frac{1}{5} \, {\left(3 \, a^{2} c^{\frac{5}{2}} x^{5} - 5 \, c^{\frac{5}{2}} x^{3}\right)} a^{2} + \frac{3}{4} \, {\left(\frac{a^{4} c^{3} x^{6}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} - \frac{3 \, a^{2} c^{3} x^{4}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{2 \, c^{3}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} a^{2}}\right)} a"," ",0,"-1/3*a^2*c^(5/2)*x^3 + 1/12*(2*a^4*c^3*x^8/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) - 5*a^2*c^3*x^6/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + 3*c^3*x^4/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c))*a^3 + c^(5/2)*x - 1/5*(3*a^2*c^(5/2)*x^5 - 5*c^(5/2)*x^3)*a^2 + 3/4*(a^4*c^3*x^6/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) - 3*a^2*c^3*x^4/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + 2*c^3/(sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*a^2))*a","B",0
1167,1,323,0,0.431254," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\frac{1}{5} \, a^{4} c^{\frac{7}{2}} x^{5} - \frac{2}{3} \, a^{2} c^{\frac{7}{2}} x^{3} + c^{\frac{7}{2}} x - \frac{1}{24} \, {\left(\frac{3 \, a^{6} c^{4} x^{10}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} - \frac{11 \, a^{4} c^{4} x^{8}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{14 \, a^{2} c^{4} x^{6}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} - \frac{6 \, c^{4} x^{4}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}}\right)} a^{3} + \frac{1}{35} \, {\left(15 \, a^{4} c^{\frac{7}{2}} x^{7} - 42 \, a^{2} c^{\frac{7}{2}} x^{5} + 35 \, c^{\frac{7}{2}} x^{3}\right)} a^{2} - \frac{1}{2} \, {\left(\frac{a^{6} c^{4} x^{8}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} - \frac{4 \, a^{4} c^{4} x^{6}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{6 \, a^{2} c^{4} x^{4}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} - \frac{3 \, c^{4}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} a^{2}}\right)} a"," ",0,"1/5*a^4*c^(7/2)*x^5 - 2/3*a^2*c^(7/2)*x^3 + c^(7/2)*x - 1/24*(3*a^6*c^4*x^10/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) - 11*a^4*c^4*x^8/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + 14*a^2*c^4*x^6/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) - 6*c^4*x^4/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c))*a^3 + 1/35*(15*a^4*c^(7/2)*x^7 - 42*a^2*c^(7/2)*x^5 + 35*c^(7/2)*x^3)*a^2 - 1/2*(a^6*c^4*x^8/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) - 4*a^4*c^4*x^6/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + 6*a^2*c^4*x^4/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) - 3*c^4/(sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*a^2))*a","B",0
1168,1,409,0,0.495948," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(9/2),x, algorithm=""maxima"")","-\frac{1}{7} \, a^{6} c^{\frac{9}{2}} x^{7} + \frac{3}{5} \, a^{4} c^{\frac{9}{2}} x^{5} - a^{2} c^{\frac{9}{2}} x^{3} + c^{\frac{9}{2}} x + \frac{1}{40} \, {\left(\frac{4 \, a^{8} c^{5} x^{12}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} - \frac{19 \, a^{6} c^{5} x^{10}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{35 \, a^{4} c^{5} x^{8}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} - \frac{30 \, a^{2} c^{5} x^{6}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{10 \, c^{5} x^{4}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}}\right)} a^{3} - \frac{1}{105} \, {\left(35 \, a^{6} c^{\frac{9}{2}} x^{9} - 135 \, a^{4} c^{\frac{9}{2}} x^{7} + 189 \, a^{2} c^{\frac{9}{2}} x^{5} - 105 \, c^{\frac{9}{2}} x^{3}\right)} a^{2} + \frac{3}{8} \, {\left(\frac{a^{8} c^{5} x^{10}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} - \frac{5 \, a^{6} c^{5} x^{8}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{10 \, a^{4} c^{5} x^{6}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} - \frac{10 \, a^{2} c^{5} x^{4}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c}} + \frac{4 \, c^{5}}{\sqrt{a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c} a^{2}}\right)} a"," ",0,"-1/7*a^6*c^(9/2)*x^7 + 3/5*a^4*c^(9/2)*x^5 - a^2*c^(9/2)*x^3 + c^(9/2)*x + 1/40*(4*a^8*c^5*x^12/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) - 19*a^6*c^5*x^10/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + 35*a^4*c^5*x^8/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) - 30*a^2*c^5*x^6/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + 10*c^5*x^4/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c))*a^3 - 1/105*(35*a^6*c^(9/2)*x^9 - 135*a^4*c^(9/2)*x^7 + 189*a^2*c^(9/2)*x^5 - 105*c^(9/2)*x^3)*a^2 + 3/8*(a^8*c^5*x^10/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) - 5*a^6*c^5*x^8/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + 10*a^4*c^5*x^6/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) - 10*a^2*c^5*x^4/sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c) + 4*c^5/(sqrt(a^4*c*x^4 - 2*a^2*c*x^2 + c)*a^2))*a","B",0
1169,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1170,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*c*x^2 + c)^(3/2)*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1171,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*c*x^2 + c)^(5/2)*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1172,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*c*x^2 + c)^(7/2)*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1173,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{3} x^{m}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^3*x^m/(-a^2*x^2 + 1)^(3/2), x)","F",0
1174,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^m*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{m}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p*x^m/(-a^2*x^2 + 1)^(3/2), x)","F",0
1175,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","-\frac{{\left(a^{2} c^{p} {\left(2 \, p - 1\right)} x^{2} + 2 \, c^{p}\right)} {\left(-a^{2} x^{2} + 1\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} {\left(4 \, p^{2} - 1\right)} a^{4}} - \int \frac{{\left(a^{3} c^{p} x^{6} + 3 \, a^{2} c^{p} x^{5} + 3 \, a c^{p} x^{4}\right)} e^{\left(p \log\left(a x + 1\right) + p \log\left(-a x + 1\right)\right)}}{{\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x}"," ",0,"-(a^2*c^p*(2*p - 1)*x^2 + 2*c^p)*(-a^2*x^2 + 1)^p/(sqrt(-a^2*x^2 + 1)*(4*p^2 - 1)*a^4) - integrate((a^3*c^p*x^6 + 3*a^2*c^p*x^5 + 3*a*c^p*x^4)*e^(p*log(a*x + 1) + p*log(-a*x + 1))/((a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(-a*x + 1)), x)","F",0
1176,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p*x^2/(-a^2*x^2 + 1)^(3/2), x)","F",0
1177,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","-\frac{{\left(-a^{2} x^{2} + 1\right)}^{p} c^{p}}{\sqrt{-a^{2} x^{2} + 1} a^{2} {\left(2 \, p - 1\right)}} - \int \frac{{\left(a^{3} c^{p} x^{4} + 3 \, a^{2} c^{p} x^{3} + 3 \, a c^{p} x^{2}\right)} e^{\left(p \log\left(a x + 1\right) + p \log\left(-a x + 1\right)\right)}}{{\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}\,{d x}"," ",0,"-(-a^2*x^2 + 1)^p*c^p/(sqrt(-a^2*x^2 + 1)*a^2*(2*p - 1)) - integrate((a^3*c^p*x^4 + 3*a^2*c^p*x^3 + 3*a*c^p*x^2)*e^(p*log(a*x + 1) + p*log(-a*x + 1))/((a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(-a*x + 1)), x)","F",0
1178,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\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}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p/(-a^2*x^2 + 1)^(3/2), x)","F",0
1179,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x,x, algorithm=""maxima"")","\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}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p/((-a^2*x^2 + 1)^(3/2)*x), x)","F",0
1180,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x^2,x, algorithm=""maxima"")","\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}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p/((-a^2*x^2 + 1)^(3/2)*x^2), x)","F",0
1181,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x^3,x, algorithm=""maxima"")","\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}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p/((-a^2*x^2 + 1)^(3/2)*x^3), x)","F",0
1182,1,101,0,0.354767," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^5,x, algorithm=""maxima"")","-\frac{1}{11} \, a^{10} c^{5} x^{11} - \frac{2}{5} \, a^{9} c^{5} x^{10} - \frac{1}{3} \, a^{8} c^{5} x^{9} + a^{7} c^{5} x^{8} + 2 \, a^{6} c^{5} x^{7} - \frac{14}{5} \, a^{4} c^{5} x^{5} - 2 \, a^{3} c^{5} x^{4} + a^{2} c^{5} x^{3} + 2 \, a c^{5} x^{2} + c^{5} x"," ",0,"-1/11*a^10*c^5*x^11 - 2/5*a^9*c^5*x^10 - 1/3*a^8*c^5*x^9 + a^7*c^5*x^8 + 2*a^6*c^5*x^7 - 14/5*a^4*c^5*x^5 - 2*a^3*c^5*x^4 + a^2*c^5*x^3 + 2*a*c^5*x^2 + c^5*x","A",0
1183,1,92,0,0.317719," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\frac{1}{9} \, a^{8} c^{4} x^{9} + \frac{1}{2} \, a^{7} c^{4} x^{8} + \frac{4}{7} \, a^{6} c^{4} x^{7} - \frac{2}{3} \, a^{5} c^{4} x^{6} - 2 \, a^{4} c^{4} x^{5} - a^{3} c^{4} x^{4} + \frac{4}{3} \, a^{2} c^{4} x^{3} + 2 \, a c^{4} x^{2} + c^{4} x"," ",0,"1/9*a^8*c^4*x^9 + 1/2*a^7*c^4*x^8 + 4/7*a^6*c^4*x^7 - 2/3*a^5*c^4*x^6 - 2*a^4*c^4*x^5 - a^3*c^4*x^4 + 4/3*a^2*c^4*x^3 + 2*a*c^4*x^2 + c^4*x","A",0
1184,1,59,0,0.333605," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{1}{7} \, a^{6} c^{3} x^{7} - \frac{2}{3} \, a^{5} c^{3} x^{6} - a^{4} c^{3} x^{5} + \frac{5}{3} \, a^{2} c^{3} x^{3} + 2 \, a c^{3} x^{2} + c^{3} x"," ",0,"-1/7*a^6*c^3*x^7 - 2/3*a^5*c^3*x^6 - a^4*c^3*x^5 + 5/3*a^2*c^3*x^3 + 2*a*c^3*x^2 + c^3*x","A",0
1185,1,47,0,0.319179," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{4} c^{2} x^{5} + a^{3} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{3} + 2 \, a c^{2} x^{2} + c^{2} x"," ",0,"1/5*a^4*c^2*x^5 + a^3*c^2*x^4 + 2*a^2*c^2*x^3 + 2*a*c^2*x^2 + c^2*x","B",0
1186,1,33,0,0.315725," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} c x^{3} - 2 \, a c x^{2} - 7 \, c x - \frac{8 \, c \log\left(a x - 1\right)}{a}"," ",0,"-1/3*a^2*c*x^3 - 2*a*c*x^2 - 7*c*x - 8*c*log(a*x - 1)/a","A",0
1187,1,19,0,0.316375," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{x}{a^{2} c x^{2} - 2 \, a c x + c}"," ",0,"x/(a^2*c*x^2 - 2*a*c*x + c)","A",0
1188,1,41,0,0.322413," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{3 \, {\left(a^{4} c^{2} x^{3} - 3 \, a^{3} c^{2} x^{2} + 3 \, a^{2} c^{2} x - a c^{2}\right)}}"," ",0,"-1/3/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2)","B",0
1189,1,102,0,0.317856," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{3 \, a^{3} x^{3} - 12 \, a^{2} x^{2} + 19 \, a x - 16}{48 \, {\left(a^{5} c^{3} x^{4} - 4 \, a^{4} c^{3} x^{3} + 6 \, a^{3} c^{3} x^{2} - 4 \, a^{2} c^{3} x + a c^{3}\right)}} + \frac{\log\left(a x + 1\right)}{32 \, a c^{3}} - \frac{\log\left(a x - 1\right)}{32 \, a c^{3}}"," ",0,"-1/48*(3*a^3*x^3 - 12*a^2*x^2 + 19*a*x - 16)/(a^5*c^3*x^4 - 4*a^4*c^3*x^3 + 6*a^3*c^3*x^2 - 4*a^2*c^3*x + a*c^3) + 1/32*log(a*x + 1)/(a*c^3) - 1/32*log(a*x - 1)/(a*c^3)","A",0
1190,1,130,0,0.333703," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","-\frac{15 \, a^{5} x^{5} - 60 \, a^{4} x^{4} + 80 \, a^{3} x^{3} - 20 \, a^{2} x^{2} - 47 \, a x + 48}{160 \, {\left(a^{7} c^{4} x^{6} - 4 \, a^{6} c^{4} x^{5} + 5 \, a^{5} c^{4} x^{4} - 5 \, a^{3} c^{4} x^{2} + 4 \, a^{2} c^{4} x - a c^{4}\right)}} + \frac{3 \, \log\left(a x + 1\right)}{64 \, a c^{4}} - \frac{3 \, \log\left(a x - 1\right)}{64 \, a c^{4}}"," ",0,"-1/160*(15*a^5*x^5 - 60*a^4*x^4 + 80*a^3*x^3 - 20*a^2*x^2 - 47*a*x + 48)/(a^7*c^4*x^6 - 4*a^6*c^4*x^5 + 5*a^5*c^4*x^4 - 5*a^3*c^4*x^2 + 4*a^2*c^4*x - a*c^4) + 3/64*log(a*x + 1)/(a*c^4) - 3/64*log(a*x - 1)/(a*c^4)","A",0
1191,0,0,0,0.000000," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\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}}\,{d x}"," ",0,"integrate((a*x + 1)^4*(-a^2*c*x^2 + c)^p/(a^2*x^2 - 1)^2, x)","F",0
1192,1,182,0,0.430261," ","integrate((-a^2*c*x^2+c)^4/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{9} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{5} c^{4} x^{6} + \frac{1}{8} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{4} c^{4} x^{5} + \frac{1}{3} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{3} c^{4} x^{4} - \frac{19}{48} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2} c^{4} x^{3} - \frac{1}{3} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a c^{4} x^{2} + \frac{29}{64} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{4} x + \frac{35}{128} \, \sqrt{-a^{2} x^{2} + 1} c^{4} x + \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{4}}{9 \, a} + \frac{35 \, c^{4} \arcsin\left(a x\right)}{128 \, a}"," ",0,"-1/9*(-a^2*x^2 + 1)^(3/2)*a^5*c^4*x^6 + 1/8*(-a^2*x^2 + 1)^(3/2)*a^4*c^4*x^5 + 1/3*(-a^2*x^2 + 1)^(3/2)*a^3*c^4*x^4 - 19/48*(-a^2*x^2 + 1)^(3/2)*a^2*c^4*x^3 - 1/3*(-a^2*x^2 + 1)^(3/2)*a*c^4*x^2 + 29/64*(-a^2*x^2 + 1)^(3/2)*c^4*x + 35/128*sqrt(-a^2*x^2 + 1)*c^4*x + 1/9*(-a^2*x^2 + 1)^(3/2)*c^4/a + 35/128*c^4*arcsin(a*x)/a","A",0
1193,1,136,0,0.416858," ","integrate((-a^2*c*x^2+c)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{7} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{3} c^{3} x^{4} - \frac{1}{6} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2} c^{3} x^{3} - \frac{2}{7} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a c^{3} x^{2} + \frac{3}{8} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{3} x + \frac{5}{16} \, \sqrt{-a^{2} x^{2} + 1} c^{3} x + \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{3}}{7 \, a} + \frac{5 \, c^{3} \arcsin\left(a x\right)}{16 \, a}"," ",0,"1/7*(-a^2*x^2 + 1)^(3/2)*a^3*c^3*x^4 - 1/6*(-a^2*x^2 + 1)^(3/2)*a^2*c^3*x^3 - 2/7*(-a^2*x^2 + 1)^(3/2)*a*c^3*x^2 + 3/8*(-a^2*x^2 + 1)^(3/2)*c^3*x + 5/16*sqrt(-a^2*x^2 + 1)*c^3*x + 1/7*(-a^2*x^2 + 1)^(3/2)*c^3/a + 5/16*c^3*arcsin(a*x)/a","A",0
1194,1,90,0,0.445630," ","integrate((-a^2*c*x^2+c)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{5} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a c^{2} x^{2} + \frac{1}{4} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2} x + \frac{3}{8} \, \sqrt{-a^{2} x^{2} + 1} c^{2} x + \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2}}{5 \, a} + \frac{3 \, c^{2} \arcsin\left(a x\right)}{8 \, a}"," ",0,"-1/5*(-a^2*x^2 + 1)^(3/2)*a*c^2*x^2 + 1/4*(-a^2*x^2 + 1)^(3/2)*c^2*x + 3/8*sqrt(-a^2*x^2 + 1)*c^2*x + 1/5*(-a^2*x^2 + 1)^(3/2)*c^2/a + 3/8*c^2*arcsin(a*x)/a","A",0
1195,1,45,0,0.414271," ","integrate((-a^2*c*x^2+c)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} c x + \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c}{3 \, a} + \frac{c \arcsin\left(a x\right)}{2 \, a}"," ",0,"1/2*sqrt(-a^2*x^2 + 1)*c*x + 1/3*(-a^2*x^2 + 1)^(3/2)*c/a + 1/2*c*arcsin(a*x)/a","A",0
1196,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} c x^{2} - c\right)} {\left(a x + 1\right)}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*x^2 + 1)/((a^2*c*x^2 - c)*(a*x + 1)), x)","F",0
1197,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} c x^{2} - c\right)}^{2} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a^2*c*x^2 - c)^2*(a*x + 1)), x)","F",0
1198,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} c x^{2} - c\right)}^{3} {\left(a x + 1\right)}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*x^2 + 1)/((a^2*c*x^2 - c)^3*(a*x + 1)), x)","F",0
1199,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} c x^{2} - c\right)}^{4} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a^2*c*x^2 - c)^4*(a*x + 1)), x)","F",0
1200,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^5,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} c x^{2} - c\right)}^{5} {\left(a x + 1\right)}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*x^2 + 1)/((a^2*c*x^2 - c)^5*(a*x + 1)), x)","F",0
1201,1,63,0,0.366376," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(a \sqrt{c} {\left(m + 1\right)} x^{2} - \sqrt{c} {\left(m + 2\right)} x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} x^{m}}{{\left(m^{2} + 3 \, m + 2\right)} a^{2} x^{2} - m^{2} - 3 \, m - 2}"," ",0,"-(a*sqrt(c)*(m + 1)*x^2 - sqrt(c)*(m + 2)*x)*(a*x + 1)*(a*x - 1)*x^m/((m^2 + 3*m + 2)*a^2*x^2 - m^2 - 3*m - 2)","A",0
1202,1,41,0,0.348292," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(3 \, a \sqrt{c} x^{4} - 4 \, \sqrt{c} x^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}{12 \, {\left(a^{2} x^{2} - 1\right)}}"," ",0,"-1/12*(3*a*sqrt(c)*x^4 - 4*sqrt(c)*x^3)*(a*x + 1)*(a*x - 1)/(a^2*x^2 - 1)","A",0
1203,1,41,0,0.339654," ","integrate(x*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(2 \, a \sqrt{c} x^{3} - 3 \, \sqrt{c} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}{6 \, {\left(a^{2} x^{2} - 1\right)}}"," ",0,"-1/6*(2*a*sqrt(c)*x^3 - 3*sqrt(c)*x^2)*(a*x + 1)*(a*x - 1)/(a^2*x^2 - 1)","A",0
1204,1,48,0,0.342534," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(a^{2} \sqrt{c} x^{2} - 2 \, a \sqrt{c} x + 2 \, \sqrt{c}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}{2 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"-1/2*(a^2*sqrt(c)*x^2 - 2*a*sqrt(c)*x + 2*sqrt(c))*(a*x + 1)*(a*x - 1)/(a^3*x^2 - a)","A",0
1205,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)/((a*x + 1)*x), x)","F",0
1206,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)/((a*x + 1)*x^2), x)","F",0
1207,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)/(a*x + 1), x)","F",0
1208,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)/(a*x + 1), x)","F",0
1209,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(7/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} \sqrt{-a^{2} x^{2} + 1}}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)*sqrt(-a^2*x^2 + 1)/(a*x + 1), x)","F",0
1210,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(9/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}} \sqrt{-a^{2} x^{2} + 1}}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(9/2)*sqrt(-a^2*x^2 + 1)/(a*x + 1), x)","F",0
1211,1,13,0,0.334917," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(a x + 1\right)}{a \sqrt{c}}"," ",0,"log(a*x + 1)/(a*sqrt(c))","A",0
1212,1,50,0,0.337255," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{c}}{2 \, {\left(a^{2} c^{2} x + a c^{2}\right)}} + \frac{\log\left(a x + 1\right)}{4 \, a c^{\frac{3}{2}}} - \frac{\log\left(a x - 1\right)}{4 \, a c^{\frac{3}{2}}}"," ",0,"-1/2*sqrt(c)/(a^2*c^2*x + a*c^2) + 1/4*log(a*x + 1)/(a*c^(3/2)) - 1/4*log(a*x - 1)/(a*c^(3/2))","A",0
1213,1,83,0,0.337133," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{3 \, a^{2} x^{2} + 3 \, a x - 2}{8 \, {\left(a^{4} c^{\frac{5}{2}} x^{3} + a^{3} c^{\frac{5}{2}} x^{2} - a^{2} c^{\frac{5}{2}} x - a c^{\frac{5}{2}}\right)}} + \frac{3 \, \log\left(a x + 1\right)}{16 \, a c^{\frac{5}{2}}} - \frac{3 \, \log\left(a x - 1\right)}{16 \, a c^{\frac{5}{2}}}"," ",0,"-1/8*(3*a^2*x^2 + 3*a*x - 2)/(a^4*c^(5/2)*x^3 + a^3*c^(5/2)*x^2 - a^2*c^(5/2)*x - a*c^(5/2)) + 3/16*log(a*x + 1)/(a*c^(5/2)) - 3/16*log(a*x - 1)/(a*c^(5/2))","A",0
1214,1,135,0,0.346835," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","-\frac{15 \, a^{4} \sqrt{c} x^{4} + 15 \, a^{3} \sqrt{c} x^{3} - 25 \, a^{2} \sqrt{c} x^{2} - 25 \, a \sqrt{c} x + 8 \, \sqrt{c}}{48 \, {\left(a^{6} c^{4} x^{5} + a^{5} c^{4} x^{4} - 2 \, a^{4} c^{4} x^{3} - 2 \, a^{3} c^{4} x^{2} + a^{2} c^{4} x + a c^{4}\right)}} + \frac{5 \, \log\left(a x + 1\right)}{32 \, a c^{\frac{7}{2}}} - \frac{5 \, \log\left(a x - 1\right)}{32 \, a c^{\frac{7}{2}}}"," ",0,"-1/48*(15*a^4*sqrt(c)*x^4 + 15*a^3*sqrt(c)*x^3 - 25*a^2*sqrt(c)*x^2 - 25*a*sqrt(c)*x + 8*sqrt(c))/(a^6*c^4*x^5 + a^5*c^4*x^4 - 2*a^4*c^4*x^3 - 2*a^3*c^4*x^2 + a^2*c^4*x + a*c^4) + 5/32*log(a*x + 1)/(a*c^(7/2)) - 5/32*log(a*x - 1)/(a*c^(7/2))","A",0
1215,0,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p*x^m/(a*x + 1), x)","F",0
1216,0,0,0,0.000000," ","integrate(x^3*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{p + \frac{1}{2}} x^{3}}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(p + 1/2)*x^3/(a*x + 1), x)","F",0
1217,0,0,0,0.000000," ","integrate(x^2*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{p + \frac{1}{2}} x^{2}}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(p + 1/2)*x^2/(a*x + 1), x)","F",0
1218,0,0,0,0.000000," ","integrate(x*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{p + \frac{1}{2}} x}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(p + 1/2)*x/(a*x + 1), x)","F",0
1219,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{p + \frac{1}{2}}}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(p + 1/2)/(a*x + 1), x)","F",0
1220,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{p + \frac{1}{2}}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(p + 1/2)/((a*x + 1)*x), x)","F",0
1221,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{p + \frac{1}{2}}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(p + 1/2)/((a*x + 1)*x^2), x)","F",0
1222,0,0,0,0.000000," ","integrate(x^3*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{3}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p*x^3/(a*x + 1), x)","F",0
1223,0,0,0,0.000000," ","integrate(x^2*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{2}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p*x^2/(a*x + 1), x)","F",0
1224,0,0,0,0.000000," ","integrate(x*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p} x}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p*x/(a*x + 1), x)","F",0
1225,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p/(a*x + 1), x)","F",0
1226,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p/((a*x + 1)*x), x)","F",0
1227,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p/((a*x + 1)*x^2), x)","F",0
1228,1,81,0,0.340144," ","integrate((-a^2*c*x^2+c)^4/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{9} \, a^{8} c^{4} x^{9} + \frac{1}{4} \, a^{7} c^{4} x^{8} + \frac{2}{7} \, a^{6} c^{4} x^{7} - a^{5} c^{4} x^{6} + \frac{3}{2} \, a^{3} c^{4} x^{4} - \frac{2}{3} \, a^{2} c^{4} x^{3} - a c^{4} x^{2} + c^{4} x"," ",0,"-1/9*a^8*c^4*x^9 + 1/4*a^7*c^4*x^8 + 2/7*a^6*c^4*x^7 - a^5*c^4*x^6 + 3/2*a^3*c^4*x^4 - 2/3*a^2*c^4*x^3 - a*c^4*x^2 + c^4*x","A",0
1229,1,69,0,0.337138," ","integrate((-a^2*c*x^2+c)^3/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{7} \, a^{6} c^{3} x^{7} - \frac{1}{3} \, a^{5} c^{3} x^{6} - \frac{1}{5} \, a^{4} c^{3} x^{5} + a^{3} c^{3} x^{4} - \frac{1}{3} \, a^{2} c^{3} x^{3} - a c^{3} x^{2} + c^{3} x"," ",0,"1/7*a^6*c^3*x^7 - 1/3*a^5*c^3*x^6 - 1/5*a^4*c^3*x^5 + a^3*c^3*x^4 - 1/3*a^2*c^3*x^3 - a*c^3*x^2 + c^3*x","A",0
1230,1,37,0,0.335231," ","integrate((-a^2*c*x^2+c)^2/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{5} \, a^{4} c^{2} x^{5} + \frac{1}{2} \, a^{3} c^{2} x^{4} - a c^{2} x^{2} + c^{2} x"," ",0,"-1/5*a^4*c^2*x^5 + 1/2*a^3*c^2*x^4 - a*c^2*x^2 + c^2*x","A",0
1231,1,20,0,0.375070," ","integrate((-a^2*c*x^2+c)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} c x^{3} - a c x^{2} + c x"," ",0,"1/3*a^2*c*x^3 - a*c*x^2 + c*x","A",0
1232,1,14,0,0.357585," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{a^{2} c x + a c}"," ",0,"-1/(a^2*c*x + a*c)","A",0
1233,1,63,0,0.360106," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{a x + 2}{4 \, {\left(a^{3} c^{2} x^{2} + 2 \, a^{2} c^{2} x + a c^{2}\right)}} + \frac{\log\left(a x + 1\right)}{8 \, a c^{2}} - \frac{\log\left(a x - 1\right)}{8 \, a c^{2}}"," ",0,"-1/4*(a*x + 2)/(a^3*c^2*x^2 + 2*a^2*c^2*x + a*c^2) + 1/8*log(a*x + 1)/(a*c^2) - 1/8*log(a*x - 1)/(a*c^2)","A",0
1234,1,91,0,0.357043," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{3 \, a^{3} x^{3} + 6 \, a^{2} x^{2} + a x - 4}{12 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{3} - 2 \, a^{2} c^{3} x - a c^{3}\right)}} + \frac{\log\left(a x + 1\right)}{8 \, a c^{3}} - \frac{\log\left(a x - 1\right)}{8 \, a c^{3}}"," ",0,"-1/12*(3*a^3*x^3 + 6*a^2*x^2 + a*x - 4)/(a^5*c^3*x^4 + 2*a^4*c^3*x^3 - 2*a^2*c^3*x - a*c^3) + 1/8*log(a*x + 1)/(a*c^3) - 1/8*log(a*x - 1)/(a*c^3)","A",0
1235,1,140,0,0.339634," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","-\frac{15 \, a^{5} x^{5} + 30 \, a^{4} x^{4} - 10 \, a^{3} x^{3} - 50 \, a^{2} x^{2} - 17 \, a x + 16}{64 \, {\left(a^{7} c^{4} x^{6} + 2 \, a^{6} c^{4} x^{5} - a^{5} c^{4} x^{4} - 4 \, a^{4} c^{4} x^{3} - a^{3} c^{4} x^{2} + 2 \, a^{2} c^{4} x + a c^{4}\right)}} + \frac{15 \, \log\left(a x + 1\right)}{128 \, a c^{4}} - \frac{15 \, \log\left(a x - 1\right)}{128 \, a c^{4}}"," ",0,"-1/64*(15*a^5*x^5 + 30*a^4*x^4 - 10*a^3*x^3 - 50*a^2*x^2 - 17*a*x + 16)/(a^7*c^4*x^6 + 2*a^6*c^4*x^5 - a^5*c^4*x^4 - 4*a^4*c^4*x^3 - a^3*c^4*x^2 + 2*a^2*c^4*x + a*c^4) + 15/128*log(a*x + 1)/(a*c^4) - 15/128*log(a*x - 1)/(a*c^4)","A",0
1236,1,117,0,0.443526," ","integrate(x^3*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2}}{5 \, a^{2} c} + \frac{5 \, \sqrt{-a^{2} c x^{2} + c} x}{4 \, a^{3}} - \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}{2 \, a^{3} c} - \frac{3 \, \sqrt{c} \arcsin\left(a x\right)}{4 \, a^{4}} - \frac{2 \, \sqrt{-a^{2} c x^{2} + c}}{a^{4}} + \frac{4 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{5 \, a^{4} c}"," ",0,"1/5*(-a^2*c*x^2 + c)^(3/2)*x^2/(a^2*c) + 5/4*sqrt(-a^2*c*x^2 + c)*x/a^3 - 1/2*(-a^2*c*x^2 + c)^(3/2)*x/(a^3*c) - 3/4*sqrt(c)*arcsin(a*x)/a^4 - 2*sqrt(-a^2*c*x^2 + c)/a^4 + 4/5*(-a^2*c*x^2 + c)^(3/2)/(a^4*c)","A",0
1237,1,93,0,0.431128," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{9 \, \sqrt{-a^{2} c x^{2} + c} x}{8 \, a^{2}} + \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}{4 \, a^{2} c} + \frac{7 \, \sqrt{c} \arcsin\left(a x\right)}{8 \, a^{3}} + \frac{2 \, \sqrt{-a^{2} c x^{2} + c}}{a^{3}} - \frac{2 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{3 \, a^{3} c}"," ",0,"-9/8*sqrt(-a^2*c*x^2 + c)*x/a^2 + 1/4*(-a^2*c*x^2 + c)^(3/2)*x/(a^2*c) + 7/8*sqrt(c)*arcsin(a*x)/a^3 + 2*sqrt(-a^2*c*x^2 + c)/a^3 - 2/3*(-a^2*c*x^2 + c)^(3/2)/(a^3*c)","A",0
1238,1,70,0,0.430713," ","integrate(x*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{\sqrt{-a^{2} c x^{2} + c} x}{a} - \frac{\sqrt{c} \arcsin\left(a x\right)}{a^{2}} - \frac{2 \, \sqrt{-a^{2} c x^{2} + c}}{a^{2}} + \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{3 \, a^{2} c}"," ",0,"sqrt(-a^2*c*x^2 + c)*x/a - sqrt(c)*arcsin(a*x)/a^2 - 2*sqrt(-a^2*c*x^2 + c)/a^2 + 1/3*(-a^2*c*x^2 + c)^(3/2)/(a^2*c)","A",0
1239,1,47,0,0.441024," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{-a^{2} c x^{2} + c} x + \frac{3 \, \sqrt{c} \arcsin\left(a x\right)}{2 \, a} + \frac{2 \, \sqrt{-a^{2} c x^{2} + c}}{a}"," ",0,"-1/2*sqrt(-a^2*c*x^2 + c)*x + 3/2*sqrt(c)*arcsin(a*x)/a + 2*sqrt(-a^2*c*x^2 + c)/a","A",0
1240,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)}}{{\left(a x + 1\right)}^{2} x}\,{d x}"," ",0,"-integrate(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)/((a*x + 1)^2*x), x)","F",0
1241,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^2,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)}}{{\left(a x + 1\right)}^{2} x^{2}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)/((a*x + 1)^2*x^2), x)","F",0
1242,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^3,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)}}{{\left(a x + 1\right)}^{2} x^{3}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)/((a*x + 1)^2*x^3), x)","F",0
1243,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^4,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)}}{{\left(a x + 1\right)}^{2} x^{4}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)/((a*x + 1)^2*x^4), x)","F",0
1244,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^5,x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)}}{{\left(a x + 1\right)}^{2} x^{5}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)/((a*x + 1)^2*x^5), x)","F",0
1245,1,130,0,0.466185," ","integrate((-a^2*c*x^2+c)^(3/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x + \sqrt{a^{2} c x^{2} + 4 \, a c x + 3 \, c} c x - \frac{3}{8} \, \sqrt{-a^{2} c x^{2} + c} c x - \frac{c^{3} \arcsin\left(a x + 2\right)}{a \left(-c\right)^{\frac{3}{2}}} - \frac{3 \, c^{\frac{3}{2}} \arcsin\left(a x\right)}{8 \, a} + \frac{2 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{3 \, a} + \frac{2 \, \sqrt{a^{2} c x^{2} + 4 \, a c x + 3 \, c} c}{a}"," ",0,"-1/4*(-a^2*c*x^2 + c)^(3/2)*x + sqrt(a^2*c*x^2 + 4*a*c*x + 3*c)*c*x - 3/8*sqrt(-a^2*c*x^2 + c)*c*x - c^3*arcsin(a*x + 2)/(a*(-c)^(3/2)) - 3/8*c^(3/2)*arcsin(a*x)/a + 2/3*(-a^2*c*x^2 + c)^(3/2)/a + 2*sqrt(a^2*c*x^2 + 4*a*c*x + 3*c)*c/a","A",0
1246,1,154,0,0.423046," ","integrate((-a^2*c*x^2+c)^(5/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x + \frac{7}{24} \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c x + \frac{3}{4} \, \sqrt{a^{2} c x^{2} + 4 \, a c x + 3 \, c} c^{2} x - \frac{5}{16} \, \sqrt{-a^{2} c x^{2} + c} c^{2} x - \frac{3 \, c^{4} \arcsin\left(a x + 2\right)}{4 \, a \left(-c\right)^{\frac{3}{2}}} - \frac{5 \, c^{\frac{5}{2}} \arcsin\left(a x\right)}{16 \, a} + \frac{2 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{5 \, a} + \frac{3 \, \sqrt{a^{2} c x^{2} + 4 \, a c x + 3 \, c} c^{2}}{2 \, a}"," ",0,"-1/6*(-a^2*c*x^2 + c)^(5/2)*x + 7/24*(-a^2*c*x^2 + c)^(3/2)*c*x + 3/4*sqrt(a^2*c*x^2 + 4*a*c*x + 3*c)*c^2*x - 5/16*sqrt(-a^2*c*x^2 + c)*c^2*x - 3/4*c^4*arcsin(a*x + 2)/(a*(-c)^(3/2)) - 5/16*c^(5/2)*arcsin(a*x)/a + 2/5*(-a^2*c*x^2 + c)^(5/2)/a + 3/2*sqrt(a^2*c*x^2 + 4*a*c*x + 3*c)*c^2/a","A",0
1247,1,173,0,0.421061," ","integrate((-a^2*c*x^2+c)^(7/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} x + \frac{3}{16} \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} c x + \frac{15}{64} \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c^{2} x + \frac{5}{8} \, \sqrt{a^{2} c x^{2} + 4 \, a c x + 3 \, c} c^{3} x - \frac{35}{128} \, \sqrt{-a^{2} c x^{2} + c} c^{3} x - \frac{5 \, c^{5} \arcsin\left(a x + 2\right)}{8 \, a \left(-c\right)^{\frac{3}{2}}} - \frac{35 \, c^{\frac{7}{2}} \arcsin\left(a x\right)}{128 \, a} + \frac{2 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}{7 \, a} + \frac{5 \, \sqrt{a^{2} c x^{2} + 4 \, a c x + 3 \, c} c^{3}}{4 \, a}"," ",0,"-1/8*(-a^2*c*x^2 + c)^(7/2)*x + 3/16*(-a^2*c*x^2 + c)^(5/2)*c*x + 15/64*(-a^2*c*x^2 + c)^(3/2)*c^2*x + 5/8*sqrt(a^2*c*x^2 + 4*a*c*x + 3*c)*c^3*x - 35/128*sqrt(-a^2*c*x^2 + c)*c^3*x - 5/8*c^5*arcsin(a*x + 2)/(a*(-c)^(3/2)) - 35/128*c^(7/2)*arcsin(a*x)/a + 2/7*(-a^2*c*x^2 + c)^(7/2)/a + 5/4*sqrt(a^2*c*x^2 + 4*a*c*x + 3*c)*c^3/a","A",0
1248,1,40,0,0.452367," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-a^{2} c x^{2} + c}}{a^{2} c x + a c} - \frac{\arcsin\left(a x\right)}{a \sqrt{c}}"," ",0,"-2*sqrt(-a^2*c*x^2 + c)/(a^2*c*x + a*c) - arcsin(a*x)/(a*sqrt(c))","A",0
1249,1,60,0,0.319499," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{x}{3 \, \sqrt{-a^{2} c x^{2} + c} c} - \frac{2}{3 \, {\left(\sqrt{-a^{2} c x^{2} + c} a^{2} c x + \sqrt{-a^{2} c x^{2} + c} a c\right)}}"," ",0,"1/3*x/(sqrt(-a^2*c*x^2 + c)*c) - 2/3/(sqrt(-a^2*c*x^2 + c)*a^2*c*x + sqrt(-a^2*c*x^2 + c)*a*c)","A",0
1250,1,79,0,0.325018," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{2}{5 \, {\left({\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{2} c x + {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a c\right)}} + \frac{2 \, x}{5 \, \sqrt{-a^{2} c x^{2} + c} c^{2}} + \frac{x}{5 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c}"," ",0,"-2/5/((-a^2*c*x^2 + c)^(3/2)*a^2*c*x + (-a^2*c*x^2 + c)^(3/2)*a*c) + 2/5*x/(sqrt(-a^2*c*x^2 + c)*c^2) + 1/5*x/((-a^2*c*x^2 + c)^(3/2)*c)","A",0
1251,1,98,0,0.328917," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","-\frac{2}{7 \, {\left({\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a^{2} c x + {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} a c\right)}} + \frac{8 \, x}{21 \, \sqrt{-a^{2} c x^{2} + c} c^{3}} + \frac{4 \, x}{21 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{x}{7 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} c}"," ",0,"-2/7/((-a^2*c*x^2 + c)^(5/2)*a^2*c*x + (-a^2*c*x^2 + c)^(5/2)*a*c) + 8/21*x/(sqrt(-a^2*c*x^2 + c)*c^3) + 4/21*x/((-a^2*c*x^2 + c)^(3/2)*c^2) + 1/7*x/((-a^2*c*x^2 + c)^(5/2)*c)","A",0
1252,0,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)} x^{m}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)*x^m/(a*x + 1)^2, x)","F",0
1253,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} x^{2} - 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"-integrate((a^2*x^2 - 1)*(-a^2*c*x^2 + c)^p/(a*x + 1)^2, x)","F",0
1254,1,154,0,0.444824," ","integrate((-a^2*c*x^2+c)^4/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{1}{9} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{3} c^{4} x^{4} + \frac{3}{8} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a^{2} c^{4} x^{3} - \frac{22}{63} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a c^{4} x^{2} - \frac{7}{48} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} c^{4} x + \frac{55}{192} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{4} x + \frac{29 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} c^{4}}{63 \, a} + \frac{55}{128} \, \sqrt{-a^{2} x^{2} + 1} c^{4} x + \frac{55 \, c^{4} \arcsin\left(a x\right)}{128 \, a}"," ",0,"-1/9*(-a^2*x^2 + 1)^(5/2)*a^3*c^4*x^4 + 3/8*(-a^2*x^2 + 1)^(5/2)*a^2*c^4*x^3 - 22/63*(-a^2*x^2 + 1)^(5/2)*a*c^4*x^2 - 7/48*(-a^2*x^2 + 1)^(5/2)*c^4*x + 55/192*(-a^2*x^2 + 1)^(3/2)*c^4*x + 29/63*(-a^2*x^2 + 1)^(5/2)*c^4/a + 55/128*sqrt(-a^2*x^2 + 1)*c^4*x + 55/128*c^4*arcsin(a*x)/a","A",0
1255,1,108,0,0.451804," ","integrate((-a^2*c*x^2+c)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{1}{7} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} a c^{3} x^{2} - \frac{1}{2} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} c^{3} x + \frac{3}{8} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{3} x + \frac{23 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} c^{3}}{35 \, a} + \frac{9}{16} \, \sqrt{-a^{2} x^{2} + 1} c^{3} x + \frac{9 \, c^{3} \arcsin\left(a x\right)}{16 \, a}"," ",0,"1/7*(-a^2*x^2 + 1)^(5/2)*a*c^3*x^2 - 1/2*(-a^2*x^2 + 1)^(5/2)*c^3*x + 3/8*(-a^2*x^2 + 1)^(3/2)*c^3*x + 23/35*(-a^2*x^2 + 1)^(5/2)*c^3/a + 9/16*sqrt(-a^2*x^2 + 1)*c^3*x + 9/16*c^3*arcsin(a*x)/a","A",0
1256,1,147,0,0.458805," ","integrate((-a^2*c*x^2+c)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{3}{4} \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2} x - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} c^{2}}{5 \, a} + 2 \, \sqrt{a^{2} x^{2} + 4 \, a x + 3} c^{2} x - \frac{9}{8} \, \sqrt{-a^{2} x^{2} + 1} c^{2} x + \frac{4 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2}}{3 \, a} - \frac{2 i \, c^{2} \arcsin\left(a x + 2\right)}{a} - \frac{9 \, c^{2} \arcsin\left(a x\right)}{8 \, a} + \frac{4 \, \sqrt{a^{2} x^{2} + 4 \, a x + 3} c^{2}}{a}"," ",0,"-3/4*(-a^2*x^2 + 1)^(3/2)*c^2*x - 1/5*(-a^2*x^2 + 1)^(5/2)*c^2/a + 2*sqrt(a^2*x^2 + 4*a*x + 3)*c^2*x - 9/8*sqrt(-a^2*x^2 + 1)*c^2*x + 4/3*(-a^2*x^2 + 1)^(3/2)*c^2/a - 2*I*c^2*arcsin(a*x + 2)/a - 9/8*c^2*arcsin(a*x)/a + 4*sqrt(a^2*x^2 + 4*a*x + 3)*c^2/a","C",0
1257,1,122,0,0.498863," ","integrate((-a^2*c*x^2+c)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{a^{2} x^{2} + 4 \, a x + 3} c x + \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c}{a^{2} x + a} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c}{3 \, a} + \frac{i \, c \arcsin\left(a x + 2\right)}{2 \, a} + \frac{3 \, c \arcsin\left(a x\right)}{a} - \frac{\sqrt{a^{2} x^{2} + 4 \, a x + 3} c}{a} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1} c}{a}"," ",0,"-1/2*sqrt(a^2*x^2 + 4*a*x + 3)*c*x + (-a^2*x^2 + 1)^(3/2)*c/(a^2*x + a) - 1/3*(-a^2*x^2 + 1)^(3/2)*c/a + 1/2*I*c*arcsin(a*x + 2)/a + 3*c*arcsin(a*x)/a - sqrt(a^2*x^2 + 4*a*x + 3)*c/a + 3*sqrt(-a^2*x^2 + 1)*c/a","C",0
1258,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a^{2} c x^{2} - c\right)} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"-integrate((-a^2*x^2 + 1)^(3/2)/((a^2*c*x^2 - c)*(a*x + 1)^3), x)","F",0
1259,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a^{2} c x^{2} - c\right)}^{2} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a^2*c*x^2 - c)^2*(a*x + 1)^3), x)","F",0
1260,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a^{2} c x^{2} - c\right)}^{3} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"-integrate((-a^2*x^2 + 1)^(3/2)/((a^2*c*x^2 - c)^3*(a*x + 1)^3), x)","F",0
1261,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a^{2} c x^{2} - c\right)}^{4} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a^2*c*x^2 - c)^4*(a*x + 1)^3), x)","F",0
1262,0,0,0,0.000000," ","integrate(x^3*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)*x^3/(a*x + 1)^3, x)","F",0
1263,0,0,0,0.000000," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)*x^2/(a*x + 1)^3, x)","F",0
1264,0,0,0,0.000000," ","integrate(x*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)*x/(a*x + 1)^3, x)","F",0
1265,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/(a*x + 1)^3, x)","F",0
1266,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x), x)","F",0
1267,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^2), x)","F",0
1268,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^3), x)","F",0
1269,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^4), x)","F",0
1270,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{5}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^5), x)","F",0
1271,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(9/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(9/2)*(-a^2*x^2 + 1)^(3/2)/(a*x + 1)^3, x)","F",0
1272,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(7/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)*(-a^2*x^2 + 1)^(3/2)/(a*x + 1)^3, x)","F",0
1273,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*(-a^2*x^2 + 1)^(3/2)/(a*x + 1)^3, x)","F",0
1274,1,70,0,0.350259," ","integrate((-a^2*c*x^2+c)^(3/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(a^{4} c^{\frac{3}{2}} x^{4} - 4 \, a^{3} c^{\frac{3}{2}} x^{3} + 6 \, a^{2} c^{\frac{3}{2}} x^{2} - 4 \, a c^{\frac{3}{2}} x + 4 \, c^{\frac{3}{2}}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)}}{4 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"-1/4*(a^4*c^(3/2)*x^4 - 4*a^3*c^(3/2)*x^3 + 6*a^2*c^(3/2)*x^2 - 4*a*c^(3/2)*x + 4*c^(3/2))*(a*x + 1)*(a*x - 1)/(a^3*x^2 - a)","A",0
1275,1,33,0,0.343821," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{\log\left(a x + 1\right)}{a \sqrt{c}} - \frac{2}{a^{2} \sqrt{c} x + a \sqrt{c}}"," ",0,"-log(a*x + 1)/(a*sqrt(c)) - 2/(a^2*sqrt(c)*x + a*sqrt(c))","A",0
1276,1,29,0,0.432225," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(a^{3} c^{\frac{3}{2}} x^{2} + 2 \, a^{2} c^{\frac{3}{2}} x + a c^{\frac{3}{2}}\right)}}"," ",0,"-1/2/(a^3*c^(3/2)*x^2 + 2*a^2*c^(3/2)*x + a*c^(3/2))","A",0
1277,1,93,0,0.353393," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{3 \, a^{2} \sqrt{c} x^{2} + 9 \, a \sqrt{c} x + 10 \, \sqrt{c}}{24 \, {\left(a^{4} c^{3} x^{3} + 3 \, a^{3} c^{3} x^{2} + 3 \, a^{2} c^{3} x + a c^{3}\right)}} + \frac{\log\left(a x + 1\right)}{16 \, a c^{\frac{5}{2}}} - \frac{\log\left(a x - 1\right)}{16 \, a c^{\frac{5}{2}}}"," ",0,"-1/24*(3*a^2*sqrt(c)*x^2 + 9*a*sqrt(c)*x + 10*sqrt(c))/(a^4*c^3*x^3 + 3*a^3*c^3*x^2 + 3*a^2*c^3*x + a*c^3) + 1/16*log(a*x + 1)/(a*c^(5/2)) - 1/16*log(a*x - 1)/(a*c^(5/2))","A",0
1278,1,122,0,0.342556," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","-\frac{15 \, a^{4} x^{4} + 45 \, a^{3} x^{3} + 35 \, a^{2} x^{2} - 15 \, a x - 32}{96 \, {\left(a^{6} c^{\frac{7}{2}} x^{5} + 3 \, a^{5} c^{\frac{7}{2}} x^{4} + 2 \, a^{4} c^{\frac{7}{2}} x^{3} - 2 \, a^{3} c^{\frac{7}{2}} x^{2} - 3 \, a^{2} c^{\frac{7}{2}} x - a c^{\frac{7}{2}}\right)}} + \frac{5 \, \log\left(a x + 1\right)}{64 \, a c^{\frac{7}{2}}} - \frac{5 \, \log\left(a x - 1\right)}{64 \, a c^{\frac{7}{2}}}"," ",0,"-1/96*(15*a^4*x^4 + 45*a^3*x^3 + 35*a^2*x^2 - 15*a*x - 32)/(a^6*c^(7/2)*x^5 + 3*a^5*c^(7/2)*x^4 + 2*a^4*c^(7/2)*x^3 - 2*a^3*c^(7/2)*x^2 - 3*a^2*c^(7/2)*x - a*c^(7/2)) + 5/64*log(a*x + 1)/(a*c^(7/2)) - 5/64*log(a*x - 1)/(a*c^(7/2))","A",0
1279,0,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{m}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)*x^m/(a*x + 1)^3, x)","F",0
1280,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(-a^2*c*x^2 + c)^p/(a*x + 1)^3, x)","F",0
1281,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(5/2),x, algorithm=""maxima"")","\int {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(5/2)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1282,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1283,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} x^{2} + 1} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1284,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/sqrt(-a^2*x^2 + 1), x)","F",0
1285,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*x^2 + 1)^(3/2), x)","F",0
1286,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*x^2 + 1)^(5/2), x)","F",0
1287,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*x^2 + 1)^(7/2), x)","F",0
1288,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(9/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*x^2 + 1)^(9/2), x)","F",0
1289,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1290,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1291,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1292,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/sqrt(-a^2*c*x^2 + c), x)","F",0
1293,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1294,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1295,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1296,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(9/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1297,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^3/(-a^2*c*x^2+c)^(5/4),x, algorithm=""maxima"")","\int \frac{x^{3} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^3*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(5/4), x)","F",0
1298,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^2/(-a^2*c*x^2+c)^(5/4),x, algorithm=""maxima"")","\int \frac{x^{2} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^2*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(5/4), x)","F",0
1299,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x/(-a^2*c*x^2+c)^(5/4),x, algorithm=""maxima"")","\int \frac{x \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(5/4), x)","F",0
1300,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(5/4),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(5/4), x)","F",0
1301,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x/(-a^2*c*x^2+c)^(5/4),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{4}} x}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/((-a^2*c*x^2 + c)^(5/4)*x), x)","F",0
1302,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2/(-a^2*c*x^2+c)^(5/4),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{4}} x^{2}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/((-a^2*c*x^2 + c)^(5/4)*x^2), x)","F",0
1303,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^3/(-a^2*c*x^2+c)^(9/8),x, algorithm=""maxima"")","\int \frac{x^{3} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{8}}}\,{d x}"," ",0,"integrate(x^3*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(9/8), x)","F",0
1304,1,28,0,1.060350," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^2/(-a^2*c*x^2+c)^(9/8),x, algorithm=""maxima"")","-\frac{4 \, {\left(a x + 1\right)}^{\frac{1}{8}} {\left(a x - 2\right)}}{3 \, {\left(-a x + 1\right)}^{\frac{3}{8}} a^{3} c^{\frac{9}{8}}}"," ",0,"-4/3*(a*x + 1)^(1/8)*(a*x - 2)/((-a*x + 1)^(3/8)*a^3*c^(9/8))","A",0
1305,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x/(-a^2*c*x^2+c)^(9/8),x, algorithm=""maxima"")","\int \frac{x \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{8}}}\,{d x}"," ",0,"integrate(x*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(9/8), x)","F",0
1306,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(9/8),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{8}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(9/8), x)","F",0
1307,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x/(-a^2*c*x^2+c)^(9/8),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{8}} x}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/((-a^2*c*x^2 + c)^(9/8)*x), x)","F",0
1308,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int {\left(a^{2} c x^{2} - c\right)} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"-integrate((a^2*c*x^2 - c)*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1309,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} - c\right)}^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((a^2*c*x^2 - c)^2*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1310,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int {\left(a^{2} c x^{2} - c\right)}^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"-integrate((a^2*c*x^2 - c)^3*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1311,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^4/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{x^{4} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}\,{d x}"," ",0,"-integrate(x^4*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
1312,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{x^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}\,{d x}"," ",0,"-integrate(x^3*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
1313,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{x^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}\,{d x}"," ",0,"-integrate(x^2*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
1314,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{x \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}\,{d x}"," ",0,"-integrate(x*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
1315,1,30,0,0.330989," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{e^{\left(\frac{1}{2} \, n \log\left(a x + 1\right) - \frac{1}{2} \, n \log\left(a x - 1\right)\right)}}{a c n}"," ",0,"e^(1/2*n*log(a*x + 1) - 1/2*n*log(a*x - 1))/(a*c*n)","A",0
1316,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)} x}\,{d x}"," ",0,"-integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((a^2*c*x^2 - c)*x), x)","F",0
1317,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)} x^{2}}\,{d x}"," ",0,"-integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((a^2*c*x^2 - c)*x^2), x)","F",0
1318,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^4/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{4} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{2}}\,{d x}"," ",0,"integrate(x^4*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
1319,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
1320,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{2}}\,{d x}"," ",0,"integrate(x^2*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
1321,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{2}}\,{d x}"," ",0,"integrate(x*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
1322,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
1323,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{2} x}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((a^2*c*x^2 - c)^2*x), x)","F",0
1324,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((a^2*c*x^2 - c)^2*x^2), x)","F",0
1325,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{3}}\,{d x}"," ",0,"-integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^3, x)","F",0
1326,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{4}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^4, x)","F",0
1327,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^3*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} x^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^3*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1328,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} x^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^2*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1329,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} x \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1330,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1331,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{x}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x + 1)/(a*x - 1))^(1/2*n)/x, x)","F",0
1332,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x + 1)/(a*x - 1))^(1/2*n)/x^2, x)","F",0
1333,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1334,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^3*((a*x + 1)/(a*x - 1))^(1/2*n)/sqrt(-a^2*c*x^2 + c), x)","F",0
1335,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^2*((a*x + 1)/(a*x - 1))^(1/2*n)/sqrt(-a^2*c*x^2 + c), x)","F",0
1336,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x*((a*x + 1)/(a*x - 1))^(1/2*n)/sqrt(-a^2*c*x^2 + c), x)","F",0
1337,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/sqrt(-a^2*c*x^2 + c), x)","F",0
1338,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c} x}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(sqrt(-a^2*c*x^2 + c)*x), x)","F",0
1339,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c} x^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(sqrt(-a^2*c*x^2 + c)*x^2), x)","F",0
1340,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c} x^{3}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(sqrt(-a^2*c*x^2 + c)*x^3), x)","F",0
1341,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3*((a*x + 1)/(a*x - 1))^(1/2*n)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
1342,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2*((a*x + 1)/(a*x - 1))^(1/2*n)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
1343,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*((a*x + 1)/(a*x - 1))^(1/2*n)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
1344,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
1345,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((-a^2*c*x^2 + c)^(3/2)*x), x)","F",0
1346,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((-a^2*c*x^2 + c)^(3/2)*x^2), x)","F",0
1347,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((-a^2*c*x^2 + c)^(3/2)*x^3), x)","F",0
1348,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^3*((a*x + 1)/(a*x - 1))^(1/2*n)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
1349,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^2*((a*x + 1)/(a*x - 1))^(1/2*n)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
1350,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x*((a*x + 1)/(a*x - 1))^(1/2*n)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
1351,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
1352,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((-a^2*c*x^2 + c)^(5/2)*x), x)","F",0
1353,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((-a^2*c*x^2 + c)^(5/2)*x^2), x)","F",0
1354,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((-a^2*c*x^2 + c)^(5/2)*x^3), x)","F",0
1355,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(-a^2*c*x^2 + c)^(7/2), x)","F",0
1356,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} - c\right)}^{2} x^{m} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((a^2*c*x^2 - c)^2*x^m*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1357,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int {\left(a^{2} c x^{2} - c\right)} x^{m} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"-integrate((a^2*c*x^2 - c)*x^m*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1358,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^m/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\int \frac{x^{m} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}\,{d x}"," ",0,"-integrate(x^m*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
1359,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^m/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{m} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{2}}\,{d x}"," ",0,"integrate(x^m*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
1360,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{p} x^{m} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p*x^m*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1361,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{p} x \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p*x*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1362,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{p} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1363,1,40,0,0.340349," ","integrate(exp(2*(1+p)*arctanh(a*x))/((-a^2*x^2+1)^p),x, algorithm=""maxima"")","-\frac{a p x + p - 1}{{\left(2 \, \left(-1\right)^{p} p^{2} - \left(-1\right)^{p} p\right)} {\left(a x - 1\right)}^{2 \, p} a}"," ",0,"-(a*p*x + p - 1)/((2*(-1)^p*p^2 - (-1)^p*p)*(a*x - 1)^(2*p)*a)","A",0
1364,1,41,0,0.356442," ","integrate(exp(2*(1+p)*arctanh(a*x))/((-a^2*c*x^2+c)^p),x, algorithm=""maxima"")","-\frac{a p x + p - 1}{{\left(2 \, p^{2} - p\right)} {\left(a x - 1\right)}^{2 \, p} a \left(-c\right)^{p}}"," ",0,"-(a*p*x + p - 1)/((2*p^2 - p)*(a*x - 1)^(2*p)*a*(-c)^p)","A",0
1365,1,34,0,0.340592," ","integrate(exp(2*p*arctanh(a*x))*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\frac{{\left(a \left(-c\right)^{p} x + \left(-c\right)^{p}\right)} {\left(a x + 1\right)}^{2 \, p}}{a {\left(2 \, p + 1\right)}}"," ",0,"(a*(-c)^p*x + (-c)^p)*(a*x + 1)^(2*p)/(a*(2*p + 1))","A",0
1366,1,36,0,0.349572," ","integrate((-a^2*c*x^2+c)^p/exp(2*p*arctanh(a*x)),x, algorithm=""maxima"")","\frac{{\left(a \left(-c\right)^{p} x - \left(-c\right)^{p}\right)} {\left(a x - 1\right)}^{2 \, p}}{a {\left(2 \, p + 1\right)}}"," ",0,"(a*(-c)^p*x - (-c)^p)*(a*x - 1)^(2*p)/(a*(2*p + 1))","A",0
1367,1,75,0,0.364023," ","integrate(exp(n*arctanh(a*x))*x^2*(-a^2*c*x^2+c)^(-1-1/2*n^2),x, algorithm=""maxima"")","\frac{{\left(a n x - 1\right)} e^{\left(-\frac{1}{2} \, n^{2} \log\left(a x + 1\right) - \frac{1}{2} \, n^{2} \log\left(a x - 1\right) + \frac{1}{2} \, n \log\left(a x + 1\right) - \frac{1}{2} \, n \log\left(a x - 1\right)\right)}}{{\left(n^{3} - n\right)} a^{3} \left(-c\right)^{\frac{1}{2} \, n^{2}} c}"," ",0,"(a*n*x - 1)*e^(-1/2*n^2*log(a*x + 1) - 1/2*n^2*log(a*x - 1) + 1/2*n*log(a*x + 1) - 1/2*n*log(a*x - 1))/((n^3 - n)*a^3*(-c)^(1/2*n^2)*c)","A",0
1368,1,379,0,0.567745," ","integrate((a*x+1)^6/(-a^2*x^2+1)^3*x^2/(-a^2*c*x^2+c)^19,x, algorithm=""maxima"")","-\frac{6 \, a x - 1}{210 \, {\left(a^{39} c^{19} x^{36} - 6 \, a^{38} c^{19} x^{35} + 70 \, a^{36} c^{19} x^{33} - 105 \, a^{35} c^{19} x^{32} - 336 \, a^{34} c^{19} x^{31} + 896 \, a^{33} c^{19} x^{30} + 720 \, a^{32} c^{19} x^{29} - 3900 \, a^{31} c^{19} x^{28} + 280 \, a^{30} c^{19} x^{27} + 10752 \, a^{29} c^{19} x^{26} - 6552 \, a^{28} c^{19} x^{25} - 20020 \, a^{27} c^{19} x^{24} + 21840 \, a^{26} c^{19} x^{23} + 24960 \, a^{25} c^{19} x^{22} - 43472 \, a^{24} c^{19} x^{21} - 18018 \, a^{23} c^{19} x^{20} + 60060 \, a^{22} c^{19} x^{19} - 60060 \, a^{20} c^{19} x^{17} + 18018 \, a^{19} c^{19} x^{16} + 43472 \, a^{18} c^{19} x^{15} - 24960 \, a^{17} c^{19} x^{14} - 21840 \, a^{16} c^{19} x^{13} + 20020 \, a^{15} c^{19} x^{12} + 6552 \, a^{14} c^{19} x^{11} - 10752 \, a^{13} c^{19} x^{10} - 280 \, a^{12} c^{19} x^{9} + 3900 \, a^{11} c^{19} x^{8} - 720 \, a^{10} c^{19} x^{7} - 896 \, a^{9} c^{19} x^{6} + 336 \, a^{8} c^{19} x^{5} + 105 \, a^{7} c^{19} x^{4} - 70 \, a^{6} c^{19} x^{3} + 6 \, a^{4} c^{19} x - a^{3} c^{19}\right)}}"," ",0,"-1/210*(6*a*x - 1)/(a^39*c^19*x^36 - 6*a^38*c^19*x^35 + 70*a^36*c^19*x^33 - 105*a^35*c^19*x^32 - 336*a^34*c^19*x^31 + 896*a^33*c^19*x^30 + 720*a^32*c^19*x^29 - 3900*a^31*c^19*x^28 + 280*a^30*c^19*x^27 + 10752*a^29*c^19*x^26 - 6552*a^28*c^19*x^25 - 20020*a^27*c^19*x^24 + 21840*a^26*c^19*x^23 + 24960*a^25*c^19*x^22 - 43472*a^24*c^19*x^21 - 18018*a^23*c^19*x^20 + 60060*a^22*c^19*x^19 - 60060*a^20*c^19*x^17 + 18018*a^19*c^19*x^16 + 43472*a^18*c^19*x^15 - 24960*a^17*c^19*x^14 - 21840*a^16*c^19*x^13 + 20020*a^15*c^19*x^12 + 6552*a^14*c^19*x^11 - 10752*a^13*c^19*x^10 - 280*a^12*c^19*x^9 + 3900*a^11*c^19*x^8 - 720*a^10*c^19*x^7 - 896*a^9*c^19*x^6 + 336*a^8*c^19*x^5 + 105*a^7*c^19*x^4 - 70*a^6*c^19*x^3 + 6*a^4*c^19*x - a^3*c^19)","B",0
1369,1,169,0,0.356204," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*x^2/(-a^2*c*x^2+c)^9,x, algorithm=""maxima"")","\frac{4 \, a x - 1}{60 \, {\left(a^{19} c^{9} x^{16} - 4 \, a^{18} c^{9} x^{15} + 20 \, a^{16} c^{9} x^{13} - 20 \, a^{15} c^{9} x^{12} - 36 \, a^{14} c^{9} x^{11} + 64 \, a^{13} c^{9} x^{10} + 20 \, a^{12} c^{9} x^{9} - 90 \, a^{11} c^{9} x^{8} + 20 \, a^{10} c^{9} x^{7} + 64 \, a^{9} c^{9} x^{6} - 36 \, a^{8} c^{9} x^{5} - 20 \, a^{7} c^{9} x^{4} + 20 \, a^{6} c^{9} x^{3} - 4 \, a^{4} c^{9} x + a^{3} c^{9}\right)}}"," ",0,"1/60*(4*a*x - 1)/(a^19*c^9*x^16 - 4*a^18*c^9*x^15 + 20*a^16*c^9*x^13 - 20*a^15*c^9*x^12 - 36*a^14*c^9*x^11 + 64*a^13*c^9*x^10 + 20*a^12*c^9*x^9 - 90*a^11*c^9*x^8 + 20*a^10*c^9*x^7 + 64*a^9*c^9*x^6 - 36*a^8*c^9*x^5 - 20*a^7*c^9*x^4 + 20*a^6*c^9*x^3 - 4*a^4*c^9*x + a^3*c^9)","B",0
1370,1,49,0,0.317321," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{2 \, a x - 1}{6 \, {\left(a^{7} c^{3} x^{4} - 2 \, a^{6} c^{3} x^{3} + 2 \, a^{4} c^{3} x - a^{3} c^{3}\right)}}"," ",0,"-1/6*(2*a*x - 1)/(a^7*c^3*x^4 - 2*a^6*c^3*x^3 + 2*a^4*c^3*x - a^3*c^3)","A",0
1371,1,49,0,0.328562," ","integrate(x^2/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{2 \, a x + 1}{6 \, {\left(a^{7} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{3} - 2 \, a^{4} c^{3} x - a^{3} c^{3}\right)}}"," ",0,"-1/6*(2*a*x + 1)/(a^7*c^3*x^4 + 2*a^6*c^3*x^3 - 2*a^4*c^3*x - a^3*c^3)","A",0
1372,1,169,0,0.358267," ","integrate(x^2/(a*x+1)^4*(-a^2*x^2+1)^2/(-a^2*c*x^2+c)^9,x, algorithm=""maxima"")","\frac{4 \, a x + 1}{60 \, {\left(a^{19} c^{9} x^{16} + 4 \, a^{18} c^{9} x^{15} - 20 \, a^{16} c^{9} x^{13} - 20 \, a^{15} c^{9} x^{12} + 36 \, a^{14} c^{9} x^{11} + 64 \, a^{13} c^{9} x^{10} - 20 \, a^{12} c^{9} x^{9} - 90 \, a^{11} c^{9} x^{8} - 20 \, a^{10} c^{9} x^{7} + 64 \, a^{9} c^{9} x^{6} + 36 \, a^{8} c^{9} x^{5} - 20 \, a^{7} c^{9} x^{4} - 20 \, a^{6} c^{9} x^{3} + 4 \, a^{4} c^{9} x + a^{3} c^{9}\right)}}"," ",0,"1/60*(4*a*x + 1)/(a^19*c^9*x^16 + 4*a^18*c^9*x^15 - 20*a^16*c^9*x^13 - 20*a^15*c^9*x^12 + 36*a^14*c^9*x^11 + 64*a^13*c^9*x^10 - 20*a^12*c^9*x^9 - 90*a^11*c^9*x^8 - 20*a^10*c^9*x^7 + 64*a^9*c^9*x^6 + 36*a^8*c^9*x^5 - 20*a^7*c^9*x^4 - 20*a^6*c^9*x^3 + 4*a^4*c^9*x + a^3*c^9)","B",0
1373,0,0,0,0.000000," ","integrate((a*x+1)^5/(-a^2*x^2+1)^(5/2)*x^2/(-a^2*c*x^2+c)^(27/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{5} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{27}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^5*x^2/((-a^2*c*x^2 + c)^(27/2)*(-a^2*x^2 + 1)^(5/2)), x)","F",0
1374,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2/(-a^2*c*x^2+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{3} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{11}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*x^2/((-a^2*c*x^2 + c)^(11/2)*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1375,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^2/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
1376,1,52,0,0.345307," ","integrate(x^2/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{c}}{2 \, {\left(a^{4} c^{2} x + a^{3} c^{2}\right)}} - \frac{3 \, \log\left(a x + 1\right)}{4 \, a^{3} c^{\frac{3}{2}}} - \frac{\log\left(a x - 1\right)}{4 \, a^{3} c^{\frac{3}{2}}}"," ",0,"-1/2*sqrt(c)/(a^4*c^2*x + a^3*c^2) - 3/4*log(a*x + 1)/(a^3*c^(3/2)) - 1/4*log(a*x - 1)/(a^3*c^(3/2))","A",0
1377,1,93,0,0.363195," ","integrate(x^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(11/2),x, algorithm=""maxima"")","-\frac{3 \, a x + 1}{24 \, {\left(a^{12} c^{\frac{11}{2}} x^{9} + 3 \, a^{11} c^{\frac{11}{2}} x^{8} - 8 \, a^{9} c^{\frac{11}{2}} x^{6} - 6 \, a^{8} c^{\frac{11}{2}} x^{5} + 6 \, a^{7} c^{\frac{11}{2}} x^{4} + 8 \, a^{6} c^{\frac{11}{2}} x^{3} - 3 \, a^{4} c^{\frac{11}{2}} x - a^{3} c^{\frac{11}{2}}\right)}}"," ",0,"-1/24*(3*a*x + 1)/(a^12*c^(11/2)*x^9 + 3*a^11*c^(11/2)*x^8 - 8*a^9*c^(11/2)*x^6 - 6*a^8*c^(11/2)*x^5 + 6*a^7*c^(11/2)*x^4 + 8*a^6*c^(11/2)*x^3 - 3*a^4*c^(11/2)*x - a^3*c^(11/2))","A",0
1378,1,273,0,0.962325," ","integrate(x^2/(a*x+1)^5*(-a^2*x^2+1)^(5/2)/(-a^2*c*x^2+c)^(27/2),x, algorithm=""maxima"")","\frac{5 \, a \sqrt{c} x + \sqrt{c}}{120 \, {\left(a^{28} c^{14} x^{25} + 5 \, a^{27} c^{14} x^{24} - 40 \, a^{25} c^{14} x^{22} - 50 \, a^{24} c^{14} x^{21} + 126 \, a^{23} c^{14} x^{20} + 280 \, a^{22} c^{14} x^{19} - 160 \, a^{21} c^{14} x^{18} - 765 \, a^{20} c^{14} x^{17} - 105 \, a^{19} c^{14} x^{16} + 1248 \, a^{18} c^{14} x^{15} + 720 \, a^{17} c^{14} x^{14} - 1260 \, a^{16} c^{14} x^{13} - 1260 \, a^{15} c^{14} x^{12} + 720 \, a^{14} c^{14} x^{11} + 1248 \, a^{13} c^{14} x^{10} - 105 \, a^{12} c^{14} x^{9} - 765 \, a^{11} c^{14} x^{8} - 160 \, a^{10} c^{14} x^{7} + 280 \, a^{9} c^{14} x^{6} + 126 \, a^{8} c^{14} x^{5} - 50 \, a^{7} c^{14} x^{4} - 40 \, a^{6} c^{14} x^{3} + 5 \, a^{4} c^{14} x + a^{3} c^{14}\right)}}"," ",0,"1/120*(5*a*sqrt(c)*x + sqrt(c))/(a^28*c^14*x^25 + 5*a^27*c^14*x^24 - 40*a^25*c^14*x^22 - 50*a^24*c^14*x^21 + 126*a^23*c^14*x^20 + 280*a^22*c^14*x^19 - 160*a^21*c^14*x^18 - 765*a^20*c^14*x^17 - 105*a^19*c^14*x^16 + 1248*a^18*c^14*x^15 + 720*a^17*c^14*x^14 - 1260*a^16*c^14*x^13 - 1260*a^15*c^14*x^12 + 720*a^14*c^14*x^11 + 1248*a^13*c^14*x^10 - 105*a^12*c^14*x^9 - 765*a^11*c^14*x^8 - 160*a^10*c^14*x^7 + 280*a^9*c^14*x^6 + 126*a^8*c^14*x^5 - 50*a^7*c^14*x^4 - 40*a^6*c^14*x^3 + 5*a^4*c^14*x + a^3*c^14)","B",0
