1,1,203,0,0.315013," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^3,x, algorithm=""maxima"")","\frac{1}{24} \, a {\left(\frac{2 \, {\left(9 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 49 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 31 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 39 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{5}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{5}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{5}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{5}}{{\left(a x + 1\right)}^{4}} - a^{5}} + \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{5}} - \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{5}}\right)}"," ",0,"1/24*a*(2*(9*((a*x - 1)/(a*x + 1))^(7/2) - 49*((a*x - 1)/(a*x + 1))^(5/2) + 31*((a*x - 1)/(a*x + 1))^(3/2) - 39*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)*a^5/(a*x + 1) - 6*(a*x - 1)^2*a^5/(a*x + 1)^2 + 4*(a*x - 1)^3*a^5/(a*x + 1)^3 - (a*x - 1)^4*a^5/(a*x + 1)^4 - a^5) + 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^5 - 9*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^5)","B",0
2,1,166,0,0.320265," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2,x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{2 \, {\left(3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 9 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{4}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{4}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{4}}{{\left(a x + 1\right)}^{3}} - a^{4}} - \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{4}} + \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{4}}\right)}"," ",0,"-1/6*a*(2*(3*((a*x - 1)/(a*x + 1))^(5/2) - 4*((a*x - 1)/(a*x + 1))^(3/2) + 9*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)*a^4/(a*x + 1) - 3*(a*x - 1)^2*a^4/(a*x + 1)^2 + (a*x - 1)^3*a^4/(a*x + 1)^3 - a^4) - 3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^4 + 3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^4)","B",0
3,1,128,0,0.313573," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, {\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 3 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{3}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{3}}{{\left(a x + 1\right)}^{2}} - a^{3}} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{3}} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{3}}\right)}"," ",0,"1/2*a*(2*(((a*x - 1)/(a*x + 1))^(3/2) - 3*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^3/(a*x + 1) - (a*x - 1)^2*a^3/(a*x + 1)^2 - a^3) + log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^3 - log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^3)","B",0
4,1,90,0,0.312675," ","integrate(1/((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"-a*(2*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2/(a*x + 1) - a^2) - log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","B",0
5,1,69,0,0.415404," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""maxima"")","a {\left(\frac{2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a}\right)}"," ",0,"a*(2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a + log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a - log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a)","B",0
6,1,53,0,0.413253," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""maxima"")","2 \, a {\left(\frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\frac{a x - 1}{a x + 1} + 1} + \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)\right)}"," ",0,"2*a*(sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)/(a*x + 1) + 1) + arctan(sqrt((a*x - 1)/(a*x + 1))))","B",0
7,1,91,0,0.413087," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^3,x, algorithm=""maxima"")","{\left(a \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \frac{a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 3 \, a \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{2 \, {\left(a x - 1\right)}}{a x + 1} + \frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}\right)} a"," ",0,"(a*arctan(sqrt((a*x - 1)/(a*x + 1))) + (a*((a*x - 1)/(a*x + 1))^(3/2) + 3*a*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)/(a*x + 1) + (a*x - 1)^2/(a*x + 1)^2 + 1))*a","B",0
8,1,136,0,0.415708," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(3 \, a^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \frac{3 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 4 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 9 \, a^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 1}\right)} a"," ",0,"1/3*(3*a^2*arctan(sqrt((a*x - 1)/(a*x + 1))) + (3*a^2*((a*x - 1)/(a*x + 1))^(5/2) + 4*a^2*((a*x - 1)/(a*x + 1))^(3/2) + 9*a^2*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)/(a*x + 1) + 3*(a*x - 1)^2/(a*x + 1)^2 + (a*x - 1)^3/(a*x + 1)^3 + 1))*a","B",0
9,1,172,0,0.415622," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^5,x, algorithm=""maxima"")","\frac{1}{12} \, {\left(9 \, a^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \frac{9 \, a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 49 \, a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 31 \, a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 39 \, a^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{4 \, {\left(a x - 1\right)}}{a x + 1} + \frac{6 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + \frac{{\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} + 1}\right)} a"," ",0,"1/12*(9*a^3*arctan(sqrt((a*x - 1)/(a*x + 1))) + (9*a^3*((a*x - 1)/(a*x + 1))^(7/2) + 49*a^3*((a*x - 1)/(a*x + 1))^(5/2) + 31*a^3*((a*x - 1)/(a*x + 1))^(3/2) + 39*a^3*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)/(a*x + 1) + 6*(a*x - 1)^2/(a*x + 1)^2 + 4*(a*x - 1)^3/(a*x + 1)^3 + (a*x - 1)^4/(a*x + 1)^4 + 1))*a","B",0
10,1,43,0,0.313171," ","integrate(1/(a*x-1)*(a*x+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
11,1,34,0,0.316479," ","integrate(1/(a*x-1)*(a*x+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
12,1,26,0,0.300658," ","integrate(1/(a*x-1)*(a*x+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
13,1,13,0,0.305707," ","integrate(1/(a*x-1)*(a*x+1),x, algorithm=""maxima"")","x + \frac{2 \, \log\left(a x - 1\right)}{a}"," ",0,"x + 2*log(a*x - 1)/a","A",0
14,1,13,0,0.307047," ","integrate(1/(a*x-1)*(a*x+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
15,1,18,0,0.309706," ","integrate(1/(a*x-1)*(a*x+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
16,1,30,0,0.313282," ","integrate(1/(a*x-1)*(a*x+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
17,1,38,0,0.308281," ","integrate(1/(a*x-1)*(a*x+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
18,1,182,0,0.309579," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2,x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{2 \, {\left(\frac{75 \, {\left(a x - 1\right)}}{a x + 1} - \frac{88 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{33 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 12\right)}}{a^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 3 \, a^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 3 \, a^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - a^{4} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{33 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{4}} + \frac{33 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{4}}\right)}"," ",0,"-1/6*a*(2*(75*(a*x - 1)/(a*x + 1) - 88*(a*x - 1)^2/(a*x + 1)^2 + 33*(a*x - 1)^3/(a*x + 1)^3 - 12)/(a^4*((a*x - 1)/(a*x + 1))^(7/2) - 3*a^4*((a*x - 1)/(a*x + 1))^(5/2) + 3*a^4*((a*x - 1)/(a*x + 1))^(3/2) - a^4*sqrt((a*x - 1)/(a*x + 1))) - 33*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^4 + 33*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^4)","A",0
19,1,145,0,0.308615," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, {\left(\frac{15 \, {\left(a x - 1\right)}}{a x + 1} - \frac{9 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 4\right)}}{a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 2 \, a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + a^{3} \sqrt{\frac{a x - 1}{a x + 1}}} + \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{3}} - \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{3}}\right)}"," ",0,"1/2*a*(2*(15*(a*x - 1)/(a*x + 1) - 9*(a*x - 1)^2/(a*x + 1)^2 - 4)/(a^3*((a*x - 1)/(a*x + 1))^(5/2) - 2*a^3*((a*x - 1)/(a*x + 1))^(3/2) + a^3*sqrt((a*x - 1)/(a*x + 1))) + 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^3 - 9*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^3)","A",0
20,1,110,0,0.303097," ","integrate(1/((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, {\left(\frac{3 \, {\left(a x - 1\right)}}{a x + 1} - 2\right)}}{a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - a^{2} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"-a*(2*(3*(a*x - 1)/(a*x + 1) - 2)/(a^2*((a*x - 1)/(a*x + 1))^(3/2) - a^2*sqrt((a*x - 1)/(a*x + 1))) - 3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","A",0
21,1,90,0,0.410568," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""maxima"")","-a {\left(\frac{2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a} + \frac{4}{a \sqrt{\frac{a x - 1}{a x + 1}}}\right)}"," ",0,"-a*(2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a - log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a + log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a + 4/(a*sqrt((a*x - 1)/(a*x + 1))))","B",0
22,1,72,0,0.409059," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""maxima"")","-2 \, a {\left(\frac{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + 2}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + \sqrt{\frac{a x - 1}{a x + 1}}} + 3 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)\right)}"," ",0,"-2*a*((3*(a*x - 1)/(a*x + 1) + 2)/(((a*x - 1)/(a*x + 1))^(3/2) + sqrt((a*x - 1)/(a*x + 1))) + 3*arctan(sqrt((a*x - 1)/(a*x + 1))))","A",0
23,1,110,0,0.408698," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""maxima"")","-{\left(9 \, a \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \frac{\frac{15 \, {\left(a x - 1\right)} a}{a x + 1} + \frac{9 \, {\left(a x - 1\right)}^{2} a}{{\left(a x + 1\right)}^{2}} + 4 \, a}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + \sqrt{\frac{a x - 1}{a x + 1}}}\right)} a"," ",0,"-(9*a*arctan(sqrt((a*x - 1)/(a*x + 1))) + (15*(a*x - 1)*a/(a*x + 1) + 9*(a*x - 1)^2*a/(a*x + 1)^2 + 4*a)/(((a*x - 1)/(a*x + 1))^(5/2) + 2*((a*x - 1)/(a*x + 1))^(3/2) + sqrt((a*x - 1)/(a*x + 1))))*a","A",0
24,1,154,0,0.415191," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(33 \, a^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \frac{\frac{75 \, {\left(a x - 1\right)} a^{2}}{a x + 1} + \frac{88 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{33 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} + 12 \, a^{2}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + \sqrt{\frac{a x - 1}{a x + 1}}}\right)} a"," ",0,"-1/3*(33*a^2*arctan(sqrt((a*x - 1)/(a*x + 1))) + (75*(a*x - 1)*a^2/(a*x + 1) + 88*(a*x - 1)^2*a^2/(a*x + 1)^2 + 33*(a*x - 1)^3*a^2/(a*x + 1)^3 + 12*a^2)/(((a*x - 1)/(a*x + 1))^(7/2) + 3*((a*x - 1)/(a*x + 1))^(5/2) + 3*((a*x - 1)/(a*x + 1))^(3/2) + sqrt((a*x - 1)/(a*x + 1))))*a","A",0
25,1,58,0,0.311697," ","integrate(1/(a*x-1)^2*(a*x+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
26,1,49,0,0.311975," ","integrate(1/(a*x-1)^2*(a*x+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
27,1,41,0,0.305045," ","integrate(1/(a*x-1)^2*(a*x+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
28,1,26,0,0.304735," ","integrate(1/(a*x-1)^2*(a*x+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
29,1,12,0,0.306505," ","integrate(1/(a*x-1)^2*(a*x+1)^2/x,x, algorithm=""maxima"")","-\frac{4}{a x - 1} + \log\left(x\right)"," ",0,"-4/(a*x - 1) + log(x)","A",0
30,1,34,0,0.313720," ","integrate(1/(a*x-1)^2*(a*x+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
31,1,48,0,0.302521," ","integrate(1/(a*x-1)^2*(a*x+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
32,1,56,0,0.303188," ","integrate(1/(a*x-1)^2*(a*x+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
33,1,203,0,0.307466," ","integrate(x^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{1}{24} \, a {\left(\frac{2 \, {\left(39 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 31 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 49 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 9 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{5}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{5}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{5}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{5}}{{\left(a x + 1\right)}^{4}} - a^{5}} - \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{5}} + \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{5}}\right)}"," ",0,"-1/24*a*(2*(39*((a*x - 1)/(a*x + 1))^(7/2) - 31*((a*x - 1)/(a*x + 1))^(5/2) + 49*((a*x - 1)/(a*x + 1))^(3/2) - 9*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)*a^5/(a*x + 1) - 6*(a*x - 1)^2*a^5/(a*x + 1)^2 + 4*(a*x - 1)^3*a^5/(a*x + 1)^3 - (a*x - 1)^4*a^5/(a*x + 1)^4 - a^5) - 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^5 + 9*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^5)","B",0
34,1,166,0,0.305054," ","integrate(x^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{2 \, {\left(9 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 3 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{4}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{4}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{4}}{{\left(a x + 1\right)}^{3}} - a^{4}} + \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{4}} - \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{4}}\right)}"," ",0,"-1/6*a*(2*(9*((a*x - 1)/(a*x + 1))^(5/2) - 4*((a*x - 1)/(a*x + 1))^(3/2) + 3*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)*a^4/(a*x + 1) - 3*(a*x - 1)^2*a^4/(a*x + 1)^2 + (a*x - 1)^3*a^4/(a*x + 1)^3 - a^4) + 3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^4 - 3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^4)","B",0
35,1,130,0,0.308398," ","integrate(x*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, {\left(3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{3}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{3}}{{\left(a x + 1\right)}^{2}} - a^{3}} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{3}} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{3}}\right)}"," ",0,"-1/2*a*(2*(3*((a*x - 1)/(a*x + 1))^(3/2) - sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^3/(a*x + 1) - (a*x - 1)^2*a^3/(a*x + 1)^2 - a^3) - log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^3 + log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^3)","B",0
36,1,90,0,0.304661," ","integrate(((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"-a*(2*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2/(a*x + 1) - a^2) + log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","B",0
37,1,70,0,0.401863," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""maxima"")","-a {\left(\frac{2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a}\right)}"," ",0,"-a*(2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a - log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a + log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a)","B",0
38,1,55,0,0.404822," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""maxima"")","-2 \, a {\left(\frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\frac{a x - 1}{a x + 1} + 1} - \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)\right)}"," ",0,"-2*a*(sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)/(a*x + 1) + 1) - arctan(sqrt((a*x - 1)/(a*x + 1))))","B",0
39,1,93,0,0.410907," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^3,x, algorithm=""maxima"")","-{\left(a \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - \frac{3 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + a \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{2 \, {\left(a x - 1\right)}}{a x + 1} + \frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}\right)} a"," ",0,"-(a*arctan(sqrt((a*x - 1)/(a*x + 1))) - (3*a*((a*x - 1)/(a*x + 1))^(3/2) + a*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)/(a*x + 1) + (a*x - 1)^2/(a*x + 1)^2 + 1))*a","B",0
40,1,137,0,0.407104," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(3 \, a^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - \frac{9 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 4 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 3 \, a^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 1}\right)} a"," ",0,"1/3*(3*a^2*arctan(sqrt((a*x - 1)/(a*x + 1))) - (9*a^2*((a*x - 1)/(a*x + 1))^(5/2) + 4*a^2*((a*x - 1)/(a*x + 1))^(3/2) + 3*a^2*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)/(a*x + 1) + 3*(a*x - 1)^2/(a*x + 1)^2 + (a*x - 1)^3/(a*x + 1)^3 + 1))*a","B",0
41,1,173,0,0.409165," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^5,x, algorithm=""maxima"")","-\frac{1}{12} \, {\left(9 \, a^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - \frac{39 \, a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 31 \, a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 49 \, a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 9 \, a^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{4 \, {\left(a x - 1\right)}}{a x + 1} + \frac{6 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + \frac{{\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} + 1}\right)} a"," ",0,"-1/12*(9*a^3*arctan(sqrt((a*x - 1)/(a*x + 1))) - (39*a^3*((a*x - 1)/(a*x + 1))^(7/2) + 31*a^3*((a*x - 1)/(a*x + 1))^(5/2) + 49*a^3*((a*x - 1)/(a*x + 1))^(3/2) + 9*a^3*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)/(a*x + 1) + 6*(a*x - 1)^2/(a*x + 1)^2 + 4*(a*x - 1)^3/(a*x + 1)^3 + (a*x - 1)^4/(a*x + 1)^4 + 1))*a","B",0
42,1,43,0,0.310641," ","integrate(x^3*(a*x-1)/(a*x+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
43,1,34,0,0.309081," ","integrate(x^2*(a*x-1)/(a*x+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
44,1,26,0,0.304294," ","integrate(x*(a*x-1)/(a*x+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
45,1,13,0,0.310237," ","integrate((a*x-1)/(a*x+1),x, algorithm=""maxima"")","x - \frac{2 \, \log\left(a x + 1\right)}{a}"," ",0,"x - 2*log(a*x + 1)/a","A",0
46,1,13,0,0.311049," ","integrate((a*x-1)/(a*x+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
47,1,18,0,0.309480," ","integrate((a*x-1)/(a*x+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
48,1,30,0,0.310826," ","integrate((a*x-1)/(a*x+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
49,1,38,0,0.303829," ","integrate((a*x-1)/(a*x+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
50,1,223,0,0.318190," ","integrate(x^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{2 \, {\left(77 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 149 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 123 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 35 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{5}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{5}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{5}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{5}}{{\left(a x + 1\right)}^{4}} - a^{5}} - \frac{51 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{5}} + \frac{51 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{5}} + \frac{32 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{5}}\right)}"," ",0,"-1/8*a*(2*(77*((a*x - 1)/(a*x + 1))^(7/2) - 149*((a*x - 1)/(a*x + 1))^(5/2) + 123*((a*x - 1)/(a*x + 1))^(3/2) - 35*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)*a^5/(a*x + 1) - 6*(a*x - 1)^2*a^5/(a*x + 1)^2 + 4*(a*x - 1)^3*a^5/(a*x + 1)^3 - (a*x - 1)^4*a^5/(a*x + 1)^4 - a^5) - 51*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^5 + 51*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^5 + 32*sqrt((a*x - 1)/(a*x + 1))/a^5)","A",0
51,1,186,0,0.318920," ","integrate(x^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{2 \, {\left(39 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 52 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 21 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{4}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{4}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{4}}{{\left(a x + 1\right)}^{3}} - a^{4}} + \frac{33 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{4}} - \frac{33 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{4}} - \frac{24 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{4}}\right)}"," ",0,"-1/6*a*(2*(39*((a*x - 1)/(a*x + 1))^(5/2) - 52*((a*x - 1)/(a*x + 1))^(3/2) + 21*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)*a^4/(a*x + 1) - 3*(a*x - 1)^2*a^4/(a*x + 1)^2 + (a*x - 1)^3*a^4/(a*x + 1)^3 - a^4) + 33*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^4 - 33*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^4 - 24*sqrt((a*x - 1)/(a*x + 1))/a^4)","A",0
52,1,151,0,0.314559," ","integrate(x*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, {\left(7 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 5 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{3}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{3}}{{\left(a x + 1\right)}^{2}} - a^{3}} - \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{3}} + \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{3}} + \frac{8 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{3}}\right)}"," ",0,"-1/2*a*(2*(7*((a*x - 1)/(a*x + 1))^(3/2) - 5*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^3/(a*x + 1) - (a*x - 1)^2*a^3/(a*x + 1)^2 - a^3) - 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^3 + 9*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^3 + 8*sqrt((a*x - 1)/(a*x + 1))/a^3)","A",0
53,1,111,0,0.318846," ","integrate(((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} + \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{4 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2}}\right)}"," ",0,"-a*(2*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2/(a*x + 1) - a^2) + 3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 4*sqrt((a*x - 1)/(a*x + 1))/a^2)","B",0
54,1,89,0,0.415152," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""maxima"")","a {\left(\frac{2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a} - \frac{4 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a}\right)}"," ",0,"a*(2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a + log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a - log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a - 4*sqrt((a*x - 1)/(a*x + 1))/a)","B",0
55,1,72,0,0.423888," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""maxima"")","2 \, a {\left(2 \, \sqrt{\frac{a x - 1}{a x + 1}} + \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\frac{a x - 1}{a x + 1} + 1} - 3 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)\right)}"," ",0,"2*a*(2*sqrt((a*x - 1)/(a*x + 1)) + sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)/(a*x + 1) + 1) - 3*arctan(sqrt((a*x - 1)/(a*x + 1))))","A",0
56,1,112,0,0.411589," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""maxima"")","{\left(9 \, a \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 4 \, a \sqrt{\frac{a x - 1}{a x + 1}} - \frac{7 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 5 \, a \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{2 \, {\left(a x - 1\right)}}{a x + 1} + \frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}\right)} a"," ",0,"(9*a*arctan(sqrt((a*x - 1)/(a*x + 1))) - 4*a*sqrt((a*x - 1)/(a*x + 1)) - (7*a*((a*x - 1)/(a*x + 1))^(3/2) + 5*a*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)/(a*x + 1) + (a*x - 1)^2/(a*x + 1)^2 + 1))*a","A",0
57,1,157,0,0.417708," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(33 \, a^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 12 \, a^{2} \sqrt{\frac{a x - 1}{a x + 1}} - \frac{39 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 52 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 21 \, a^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 1}\right)} a"," ",0,"-1/3*(33*a^2*arctan(sqrt((a*x - 1)/(a*x + 1))) - 12*a^2*sqrt((a*x - 1)/(a*x + 1)) - (39*a^2*((a*x - 1)/(a*x + 1))^(5/2) + 52*a^2*((a*x - 1)/(a*x + 1))^(3/2) + 21*a^2*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)/(a*x + 1) + 3*(a*x - 1)^2/(a*x + 1)^2 + (a*x - 1)^3/(a*x + 1)^3 + 1))*a","A",0
58,1,193,0,0.415122," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(51 \, a^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 16 \, a^{3} \sqrt{\frac{a x - 1}{a x + 1}} - \frac{77 \, a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 149 \, a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 123 \, a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 35 \, a^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{4 \, {\left(a x - 1\right)}}{a x + 1} + \frac{6 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + \frac{{\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} + 1}\right)} a"," ",0,"1/4*(51*a^3*arctan(sqrt((a*x - 1)/(a*x + 1))) - 16*a^3*sqrt((a*x - 1)/(a*x + 1)) - (77*a^3*((a*x - 1)/(a*x + 1))^(7/2) + 149*a^3*((a*x - 1)/(a*x + 1))^(5/2) + 123*a^3*((a*x - 1)/(a*x + 1))^(3/2) + 35*a^3*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)/(a*x + 1) + 6*(a*x - 1)^2/(a*x + 1)^2 + 4*(a*x - 1)^3/(a*x + 1)^3 + (a*x - 1)^4/(a*x + 1)^4 + 1))*a","A",0
59,1,259,0,0.416091," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^4,x, algorithm=""maxima"")","-\frac{1}{3840} \, a {\left(\frac{4 \, {\left(465 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{19}{4}} - 696 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{4}} + 5090 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{4}} - 1120 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} + 2405 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{5 \, {\left(a x - 1\right)} a^{6}}{a x + 1} - \frac{10 \, {\left(a x - 1\right)}^{2} a^{6}}{{\left(a x + 1\right)}^{2}} + \frac{10 \, {\left(a x - 1\right)}^{3} a^{6}}{{\left(a x + 1\right)}^{3}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{6}}{{\left(a x + 1\right)}^{4}} + \frac{{\left(a x - 1\right)}^{5} a^{6}}{{\left(a x + 1\right)}^{5}} - a^{6}} + \frac{930 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} - \frac{465 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} + \frac{465 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{6}}\right)}"," ",0,"-1/3840*a*(4*(465*((a*x - 1)/(a*x + 1))^(19/4) - 696*((a*x - 1)/(a*x + 1))^(15/4) + 5090*((a*x - 1)/(a*x + 1))^(11/4) - 1120*((a*x - 1)/(a*x + 1))^(7/4) + 2405*((a*x - 1)/(a*x + 1))^(3/4))/(5*(a*x - 1)*a^6/(a*x + 1) - 10*(a*x - 1)^2*a^6/(a*x + 1)^2 + 10*(a*x - 1)^3*a^6/(a*x + 1)^3 - 5*(a*x - 1)^4*a^6/(a*x + 1)^4 + (a*x - 1)^5*a^6/(a*x + 1)^5 - a^6) + 930*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 - 465*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 + 465*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^6)","A",0
60,1,224,0,0.415671," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^3,x, algorithm=""maxima"")","\frac{1}{384} \, a {\left(\frac{4 \, {\left(33 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{4}} - 279 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{4}} + 107 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} - 245 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{5}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{5}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{5}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{5}}{{\left(a x + 1\right)}^{4}} - a^{5}} - \frac{66 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} + \frac{33 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} - \frac{33 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{5}}\right)}"," ",0,"1/384*a*(4*(33*((a*x - 1)/(a*x + 1))^(15/4) - 279*((a*x - 1)/(a*x + 1))^(11/4) + 107*((a*x - 1)/(a*x + 1))^(7/4) - 245*((a*x - 1)/(a*x + 1))^(3/4))/(4*(a*x - 1)*a^5/(a*x + 1) - 6*(a*x - 1)^2*a^5/(a*x + 1)^2 + 4*(a*x - 1)^3*a^5/(a*x + 1)^3 - (a*x - 1)^4*a^5/(a*x + 1)^4 - a^5) - 66*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 + 33*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 - 33*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^5)","A",0
61,1,187,0,0.418287," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^2,x, algorithm=""maxima"")","-\frac{1}{48} \, a {\left(\frac{4 \, {\left(9 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{4}} - 6 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} + 29 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{4}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{4}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{4}}{{\left(a x + 1\right)}^{3}} - a^{4}} + \frac{18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} - \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} + \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{4}}\right)}"," ",0,"-1/48*a*(4*(9*((a*x - 1)/(a*x + 1))^(11/4) - 6*((a*x - 1)/(a*x + 1))^(7/4) + 29*((a*x - 1)/(a*x + 1))^(3/4))/(3*(a*x - 1)*a^4/(a*x + 1) - 3*(a*x - 1)^2*a^4/(a*x + 1)^2 + (a*x - 1)^3*a^4/(a*x + 1)^3 - a^4) + 18*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 - 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 + 9*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^4)","A",0
62,1,149,0,0.410221," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{4 \, {\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} - 5 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{3}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{3}}{{\left(a x + 1\right)}^{2}} - a^{3}} - \frac{2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} + \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} - \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{3}}\right)}"," ",0,"1/8*a*(4*(((a*x - 1)/(a*x + 1))^(7/4) - 5*((a*x - 1)/(a*x + 1))^(3/4))/(2*(a*x - 1)*a^3/(a*x + 1) - (a*x - 1)^2*a^3/(a*x + 1)^2 - a^3) - 2*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 + log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 - log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^3)","A",0
63,1,111,0,0.410197," ","integrate(1/((a*x-1)/(a*x+1))^(1/4),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} + \frac{2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} - \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} + \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{2}}\right)}"," ",0,"-1/2*a*(4*((a*x - 1)/(a*x + 1))^(3/4)/((a*x - 1)*a^2/(a*x + 1) - a^2) + 2*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 - log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 + log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^2)","A",0
64,1,224,0,0.419832," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} - \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} + \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a}\right)}"," ",0,"1/2*a*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))/a - 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a + 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a - 2*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a)","A",0
65,1,186,0,0.413181," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{\frac{a x - 1}{a x + 1} + 1}\right)} a"," ",0,"1/4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*((a*x - 1)/(a*x + 1))^(3/4)/((a*x - 1)/(a*x + 1) + 1))*a","A",0
66,1,226,0,0.410980," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x^3,x, algorithm=""maxima"")","\frac{1}{16} \, {\left({\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)\right)} a + \frac{8 \, {\left(a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} + 5 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{2 \, {\left(a x - 1\right)}}{a x + 1} + \frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}\right)} a"," ",0,"1/16*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))*a + 8*(a*((a*x - 1)/(a*x + 1))^(7/4) + 5*a*((a*x - 1)/(a*x + 1))^(3/4))/(2*(a*x - 1)/(a*x + 1) + (a*x - 1)^2/(a*x + 1)^2 + 1))*a","A",0
67,1,270,0,0.412879," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x^4,x, algorithm=""maxima"")","\frac{1}{96} \, {\left(9 \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)\right)} a^{2} + \frac{8 \, {\left(9 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{4}} + 6 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} + 29 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 1}\right)} a"," ",0,"1/96*(9*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))*a^2 + 8*(9*a^2*((a*x - 1)/(a*x + 1))^(11/4) + 6*a^2*((a*x - 1)/(a*x + 1))^(7/4) + 29*a^2*((a*x - 1)/(a*x + 1))^(3/4))/(3*(a*x - 1)/(a*x + 1) + 3*(a*x - 1)^2/(a*x + 1)^2 + (a*x - 1)^3/(a*x + 1)^3 + 1))*a","A",0
68,1,259,0,0.404258," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^4,x, algorithm=""maxima"")","-\frac{1}{1280} \, a {\left(\frac{4 \, {\left(395 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{17}{4}} - 1440 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{4}} + 3710 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} - 1992 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + 1375 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{5 \, {\left(a x - 1\right)} a^{6}}{a x + 1} - \frac{10 \, {\left(a x - 1\right)}^{2} a^{6}}{{\left(a x + 1\right)}^{2}} + \frac{10 \, {\left(a x - 1\right)}^{3} a^{6}}{{\left(a x + 1\right)}^{3}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{6}}{{\left(a x + 1\right)}^{4}} + \frac{{\left(a x - 1\right)}^{5} a^{6}}{{\left(a x + 1\right)}^{5}} - a^{6}} - \frac{2370 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} - \frac{1185 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} + \frac{1185 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{6}}\right)}"," ",0,"-1/1280*a*(4*(395*((a*x - 1)/(a*x + 1))^(17/4) - 1440*((a*x - 1)/(a*x + 1))^(13/4) + 3710*((a*x - 1)/(a*x + 1))^(9/4) - 1992*((a*x - 1)/(a*x + 1))^(5/4) + 1375*((a*x - 1)/(a*x + 1))^(1/4))/(5*(a*x - 1)*a^6/(a*x + 1) - 10*(a*x - 1)^2*a^6/(a*x + 1)^2 + 10*(a*x - 1)^3*a^6/(a*x + 1)^3 - 5*(a*x - 1)^4*a^6/(a*x + 1)^4 + (a*x - 1)^5*a^6/(a*x + 1)^5 - a^6) - 2370*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 - 1185*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 + 1185*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^6)","A",0
69,1,224,0,0.413378," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^3,x, algorithm=""maxima"")","\frac{1}{128} \, a {\left(\frac{4 \, {\left(41 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{4}} - 183 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} + 147 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} - 133 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{5}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{5}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{5}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{5}}{{\left(a x + 1\right)}^{4}} - a^{5}} + \frac{246 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} + \frac{123 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} - \frac{123 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{5}}\right)}"," ",0,"1/128*a*(4*(41*((a*x - 1)/(a*x + 1))^(13/4) - 183*((a*x - 1)/(a*x + 1))^(9/4) + 147*((a*x - 1)/(a*x + 1))^(5/4) - 133*((a*x - 1)/(a*x + 1))^(1/4))/(4*(a*x - 1)*a^5/(a*x + 1) - 6*(a*x - 1)^2*a^5/(a*x + 1)^2 + 4*(a*x - 1)^3*a^5/(a*x + 1)^3 - (a*x - 1)^4*a^5/(a*x + 1)^4 - a^5) + 246*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 + 123*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 - 123*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^5)","A",0
70,1,187,0,0.406763," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^2,x, algorithm=""maxima"")","-\frac{1}{48} \, a {\left(\frac{4 \, {\left(17 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} - 30 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + 45 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{4}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{4}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{4}}{{\left(a x + 1\right)}^{3}} - a^{4}} - \frac{102 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} - \frac{51 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} + \frac{51 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{4}}\right)}"," ",0,"-1/48*a*(4*(17*((a*x - 1)/(a*x + 1))^(9/4) - 30*((a*x - 1)/(a*x + 1))^(5/4) + 45*((a*x - 1)/(a*x + 1))^(1/4))/(3*(a*x - 1)*a^4/(a*x + 1) - 3*(a*x - 1)^2*a^4/(a*x + 1)^2 + (a*x - 1)^3*a^4/(a*x + 1)^3 - a^4) - 102*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 - 51*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 + 51*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^4)","A",0
71,1,152,0,0.403666," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{4 \, {\left(3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} - 7 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{3}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{3}}{{\left(a x + 1\right)}^{2}} - a^{3}} + \frac{18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} + \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} - \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{3}}\right)}"," ",0,"1/8*a*(4*(3*((a*x - 1)/(a*x + 1))^(5/4) - 7*((a*x - 1)/(a*x + 1))^(1/4))/(2*(a*x - 1)*a^3/(a*x + 1) - (a*x - 1)^2*a^3/(a*x + 1)^2 - a^3) + 18*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 + 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 - 9*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^3)","A",0
72,1,112,0,0.402138," ","integrate(1/((a*x-1)/(a*x+1))^(3/4),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} - \frac{6 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} - \frac{3 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} + \frac{3 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{2}}\right)}"," ",0,"-1/2*a*(4*((a*x - 1)/(a*x + 1))^(1/4)/((a*x - 1)*a^2/(a*x + 1) - a^2) - 6*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 - 3*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 + 3*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^2)","A",0
73,1,224,0,0.403878," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} + \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a}\right)}"," ",0,"1/2*a*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))/a + 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a + 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a - 2*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a)","A",0
74,1,187,0,0.404643," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(6 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 6 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 3 \, \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{\frac{a x - 1}{a x + 1} + 1}\right)} a"," ",0,"1/4*(6*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 6*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 3*sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*((a*x - 1)/(a*x + 1))^(1/4)/((a*x - 1)/(a*x + 1) + 1))*a","A",0
75,1,229,0,0.410425," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x^3,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(18 \, \sqrt{2} a \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 18 \, \sqrt{2} a \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 9 \, \sqrt{2} a \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 9 \, \sqrt{2} a \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, {\left(3 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + 7 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{2 \, {\left(a x - 1\right)}}{a x + 1} + \frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}\right)} a"," ",0,"1/16*(18*sqrt(2)*a*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 18*sqrt(2)*a*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 9*sqrt(2)*a*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 9*sqrt(2)*a*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*(3*a*((a*x - 1)/(a*x + 1))^(5/4) + 7*a*((a*x - 1)/(a*x + 1))^(1/4))/(2*(a*x - 1)/(a*x + 1) + (a*x - 1)^2/(a*x + 1)^2 + 1))*a","A",0
76,1,277,0,0.411793," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x^4,x, algorithm=""maxima"")","\frac{1}{96} \, {\left(102 \, \sqrt{2} a^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 102 \, \sqrt{2} a^{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 51 \, \sqrt{2} a^{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 51 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, {\left(17 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} + 30 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + 45 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 1}\right)} a"," ",0,"1/96*(102*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 102*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 51*sqrt(2)*a^2*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 51*sqrt(2)*a^2*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*(17*a^2*((a*x - 1)/(a*x + 1))^(9/4) + 30*a^2*((a*x - 1)/(a*x + 1))^(5/4) + 45*a^2*((a*x - 1)/(a*x + 1))^(1/4))/(3*(a*x - 1)/(a*x + 1) + 3*(a*x - 1)^2/(a*x + 1)^2 + (a*x - 1)^3/(a*x + 1)^3 + 1))*a","A",0
77,1,275,0,0.418894," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^4,x, algorithm=""maxima"")","-\frac{1}{3840} \, a {\left(\frac{4 \, {\left(\frac{58985 \, {\left(a x - 1\right)}}{a x + 1} - \frac{125920 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{137930 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - \frac{72216 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} + \frac{15045 \, {\left(a x - 1\right)}^{5}}{{\left(a x + 1\right)}^{5}} - 7680\right)}}{a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{21}{4}} - 5 \, a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{17}{4}} + 10 \, a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{4}} - 10 \, a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} + 5 \, a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} - a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} + \frac{30090 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} - \frac{15045 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} + \frac{15045 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{6}}\right)}"," ",0,"-1/3840*a*(4*(58985*(a*x - 1)/(a*x + 1) - 125920*(a*x - 1)^2/(a*x + 1)^2 + 137930*(a*x - 1)^3/(a*x + 1)^3 - 72216*(a*x - 1)^4/(a*x + 1)^4 + 15045*(a*x - 1)^5/(a*x + 1)^5 - 7680)/(a^6*((a*x - 1)/(a*x + 1))^(21/4) - 5*a^6*((a*x - 1)/(a*x + 1))^(17/4) + 10*a^6*((a*x - 1)/(a*x + 1))^(13/4) - 10*a^6*((a*x - 1)/(a*x + 1))^(9/4) + 5*a^6*((a*x - 1)/(a*x + 1))^(5/4) - a^6*((a*x - 1)/(a*x + 1))^(1/4)) + 30090*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 - 15045*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 + 15045*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^6)","A",0
78,1,238,0,0.417347," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^3,x, algorithm=""maxima"")","\frac{1}{384} \, a {\left(\frac{4 \, {\left(\frac{4645 \, {\left(a x - 1\right)}}{a x + 1} - \frac{7483 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{5415 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - \frac{1425 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} - 768\right)}}{a^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{17}{4}} - 4 \, a^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{4}} + 6 \, a^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} - 4 \, a^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + a^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} - \frac{2850 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} + \frac{1425 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} - \frac{1425 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{5}}\right)}"," ",0,"1/384*a*(4*(4645*(a*x - 1)/(a*x + 1) - 7483*(a*x - 1)^2/(a*x + 1)^2 + 5415*(a*x - 1)^3/(a*x + 1)^3 - 1425*(a*x - 1)^4/(a*x + 1)^4 - 768)/(a^5*((a*x - 1)/(a*x + 1))^(17/4) - 4*a^5*((a*x - 1)/(a*x + 1))^(13/4) + 6*a^5*((a*x - 1)/(a*x + 1))^(9/4) - 4*a^5*((a*x - 1)/(a*x + 1))^(5/4) + a^5*((a*x - 1)/(a*x + 1))^(1/4)) - 2850*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 + 1425*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 - 1425*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^5)","A",0
79,1,203,0,0.410045," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^2,x, algorithm=""maxima"")","-\frac{1}{48} \, a {\left(\frac{4 \, {\left(\frac{425 \, {\left(a x - 1\right)}}{a x + 1} - \frac{462 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{165 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 96\right)}}{a^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{4}} - 3 \, a^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} + 3 \, a^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} - a^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} + \frac{330 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} - \frac{165 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} + \frac{165 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{4}}\right)}"," ",0,"-1/48*a*(4*(425*(a*x - 1)/(a*x + 1) - 462*(a*x - 1)^2/(a*x + 1)^2 + 165*(a*x - 1)^3/(a*x + 1)^3 - 96)/(a^4*((a*x - 1)/(a*x + 1))^(13/4) - 3*a^4*((a*x - 1)/(a*x + 1))^(9/4) + 3*a^4*((a*x - 1)/(a*x + 1))^(5/4) - a^4*((a*x - 1)/(a*x + 1))^(1/4)) + 330*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 - 165*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 + 165*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^4)","A",0
80,1,166,0,0.406330," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{4 \, {\left(\frac{45 \, {\left(a x - 1\right)}}{a x + 1} - \frac{25 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 16\right)}}{a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} - 2 \, a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} - \frac{50 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} + \frac{25 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} - \frac{25 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{3}}\right)}"," ",0,"1/8*a*(4*(45*(a*x - 1)/(a*x + 1) - 25*(a*x - 1)^2/(a*x + 1)^2 - 16)/(a^3*((a*x - 1)/(a*x + 1))^(9/4) - 2*a^3*((a*x - 1)/(a*x + 1))^(5/4) + a^3*((a*x - 1)/(a*x + 1))^(1/4)) - 50*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 + 25*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 - 25*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^3)","A",0
81,1,131,0,0.403610," ","integrate(1/((a*x-1)/(a*x+1))^(5/4),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{4 \, {\left(\frac{5 \, {\left(a x - 1\right)}}{a x + 1} - 4\right)}}{a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} - a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} + \frac{10 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} - \frac{5 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} + \frac{5 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{2}}\right)}"," ",0,"-1/2*a*(4*(5*(a*x - 1)/(a*x + 1) - 4)/(a^2*((a*x - 1)/(a*x + 1))^(5/4) - a^2*((a*x - 1)/(a*x + 1))^(1/4)) + 10*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 - 5*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 + 5*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^2)","A",0
82,1,244,0,0.406492," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} + \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a} + \frac{16}{a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}\right)}"," ",0,"-1/2*a*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))/a + 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a - 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a + 2*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a + 16/(a*((a*x - 1)/(a*x + 1))^(1/4)))","A",0
83,1,204,0,0.402978," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(10 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 10 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - 5 \, \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 5 \, \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, {\left(\frac{5 \, {\left(a x - 1\right)}}{a x + 1} + 4\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}\right)} a"," ",0,"-1/4*(10*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 10*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - 5*sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 5*sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*(5*(a*x - 1)/(a*x + 1) + 4)/(((a*x - 1)/(a*x + 1))^(5/4) + ((a*x - 1)/(a*x + 1))^(1/4)))*a","A",0
84,1,244,0,0.407053," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(25 \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)\right)} a + \frac{8 \, {\left(\frac{45 \, {\left(a x - 1\right)} a}{a x + 1} + \frac{25 \, {\left(a x - 1\right)}^{2} a}{{\left(a x + 1\right)}^{2}} + 16 \, a\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}\right)} a"," ",0,"-1/16*(25*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))*a + 8*(45*(a*x - 1)*a/(a*x + 1) + 25*(a*x - 1)^2*a/(a*x + 1)^2 + 16*a)/(((a*x - 1)/(a*x + 1))^(9/4) + 2*((a*x - 1)/(a*x + 1))^(5/4) + ((a*x - 1)/(a*x + 1))^(1/4)))*a","A",0
85,1,288,0,0.414318," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x^4,x, algorithm=""maxima"")","-\frac{1}{96} \, {\left(165 \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)\right)} a^{2} + \frac{8 \, {\left(\frac{425 \, {\left(a x - 1\right)} a^{2}}{a x + 1} + \frac{462 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{165 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} + 96 \, a^{2}\right)}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{4}} + 3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} + 3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}\right)} a"," ",0,"-1/96*(165*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))*a^2 + 8*(425*(a*x - 1)*a^2/(a*x + 1) + 462*(a*x - 1)^2*a^2/(a*x + 1)^2 + 165*(a*x - 1)^3*a^2/(a*x + 1)^3 + 96*a^2)/(((a*x - 1)/(a*x + 1))^(13/4) + 3*((a*x - 1)/(a*x + 1))^(9/4) + 3*((a*x - 1)/(a*x + 1))^(5/4) + ((a*x - 1)/(a*x + 1))^(1/4)))*a","A",0
86,1,259,0,0.407421," ","integrate(x^4*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""maxima"")","-\frac{1}{3840} \, a {\left(\frac{4 \, {\left(2405 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{17}{4}} - 1120 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{4}} + 5090 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} - 696 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + 465 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{5 \, {\left(a x - 1\right)} a^{6}}{a x + 1} - \frac{10 \, {\left(a x - 1\right)}^{2} a^{6}}{{\left(a x + 1\right)}^{2}} + \frac{10 \, {\left(a x - 1\right)}^{3} a^{6}}{{\left(a x + 1\right)}^{3}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{6}}{{\left(a x + 1\right)}^{4}} + \frac{{\left(a x - 1\right)}^{5} a^{6}}{{\left(a x + 1\right)}^{5}} - a^{6}} + \frac{930 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} + \frac{465 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} - \frac{465 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{6}}\right)}"," ",0,"-1/3840*a*(4*(2405*((a*x - 1)/(a*x + 1))^(17/4) - 1120*((a*x - 1)/(a*x + 1))^(13/4) + 5090*((a*x - 1)/(a*x + 1))^(9/4) - 696*((a*x - 1)/(a*x + 1))^(5/4) + 465*((a*x - 1)/(a*x + 1))^(1/4))/(5*(a*x - 1)*a^6/(a*x + 1) - 10*(a*x - 1)^2*a^6/(a*x + 1)^2 + 10*(a*x - 1)^3*a^6/(a*x + 1)^3 - 5*(a*x - 1)^4*a^6/(a*x + 1)^4 + (a*x - 1)^5*a^6/(a*x + 1)^5 - a^6) + 930*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 + 465*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 - 465*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^6)","A",0
87,1,224,0,0.406997," ","integrate(x^3*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""maxima"")","-\frac{1}{384} \, a {\left(\frac{4 \, {\left(245 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{4}} - 107 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} + 279 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} - 33 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{5}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{5}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{5}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{5}}{{\left(a x + 1\right)}^{4}} - a^{5}} - \frac{66 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} - \frac{33 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} + \frac{33 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{5}}\right)}"," ",0,"-1/384*a*(4*(245*((a*x - 1)/(a*x + 1))^(13/4) - 107*((a*x - 1)/(a*x + 1))^(9/4) + 279*((a*x - 1)/(a*x + 1))^(5/4) - 33*((a*x - 1)/(a*x + 1))^(1/4))/(4*(a*x - 1)*a^5/(a*x + 1) - 6*(a*x - 1)^2*a^5/(a*x + 1)^2 + 4*(a*x - 1)^3*a^5/(a*x + 1)^3 - (a*x - 1)^4*a^5/(a*x + 1)^4 - a^5) - 66*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 - 33*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 + 33*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^5)","A",0
88,1,187,0,0.413201," ","integrate(x^2*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""maxima"")","-\frac{1}{48} \, a {\left(\frac{4 \, {\left(29 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} - 6 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + 9 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{4}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{4}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{4}}{{\left(a x + 1\right)}^{3}} - a^{4}} + \frac{18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} + \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} - \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{4}}\right)}"," ",0,"-1/48*a*(4*(29*((a*x - 1)/(a*x + 1))^(9/4) - 6*((a*x - 1)/(a*x + 1))^(5/4) + 9*((a*x - 1)/(a*x + 1))^(1/4))/(3*(a*x - 1)*a^4/(a*x + 1) - 3*(a*x - 1)^2*a^4/(a*x + 1)^2 + (a*x - 1)^3*a^4/(a*x + 1)^3 - a^4) + 18*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 + 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 - 9*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^4)","A",0
89,1,151,0,0.413054," ","integrate(x*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{4 \, {\left(5 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} - \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{3}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{3}}{{\left(a x + 1\right)}^{2}} - a^{3}} - \frac{2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} - \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} + \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{3}}\right)}"," ",0,"-1/8*a*(4*(5*((a*x - 1)/(a*x + 1))^(5/4) - ((a*x - 1)/(a*x + 1))^(1/4))/(2*(a*x - 1)*a^3/(a*x + 1) - (a*x - 1)^2*a^3/(a*x + 1)^2 - a^3) - 2*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 - log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 + log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^3)","A",0
90,1,111,0,0.409673," ","integrate(((a*x-1)/(a*x+1))^(1/4),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} + \frac{2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} + \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} - \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{2}}\right)}"," ",0,"-1/2*a*(4*((a*x - 1)/(a*x + 1))^(1/4)/((a*x - 1)*a^2/(a*x + 1) - a^2) + 2*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 + log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 - log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^2)","A",0
91,1,224,0,0.410781," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} - \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} + \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a}\right)}"," ",0,"-1/2*a*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))/a - 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a - 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a + 2*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a)","A",0
92,1,186,0,0.405180," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \frac{8 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{\frac{a x - 1}{a x + 1} + 1}\right)} a"," ",0,"1/4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 8*((a*x - 1)/(a*x + 1))^(1/4)/((a*x - 1)/(a*x + 1) + 1))*a","A",0
93,1,227,0,0.405435," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(2 \, \sqrt{2} a \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} a \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + \sqrt{2} a \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \sqrt{2} a \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \frac{8 \, {\left(5 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{2 \, {\left(a x - 1\right)}}{a x + 1} + \frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}\right)} a"," ",0,"-1/16*(2*sqrt(2)*a*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*a*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + sqrt(2)*a*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*a*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 8*(5*a*((a*x - 1)/(a*x + 1))^(5/4) + a*((a*x - 1)/(a*x + 1))^(1/4))/(2*(a*x - 1)/(a*x + 1) + (a*x - 1)^2/(a*x + 1)^2 + 1))*a","A",0
94,1,277,0,0.404519," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x^4,x, algorithm=""maxima"")","\frac{1}{96} \, {\left(18 \, \sqrt{2} a^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 18 \, \sqrt{2} a^{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 9 \, \sqrt{2} a^{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 9 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \frac{8 \, {\left(29 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} + 6 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + 9 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 1}\right)} a"," ",0,"1/96*(18*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 18*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 9*sqrt(2)*a^2*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 9*sqrt(2)*a^2*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 8*(29*a^2*((a*x - 1)/(a*x + 1))^(9/4) + 6*a^2*((a*x - 1)/(a*x + 1))^(5/4) + 9*a^2*((a*x - 1)/(a*x + 1))^(1/4))/(3*(a*x - 1)/(a*x + 1) + 3*(a*x - 1)^2/(a*x + 1)^2 + (a*x - 1)^3/(a*x + 1)^3 + 1))*a","A",0
95,1,259,0,0.411517," ","integrate(x^4*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""maxima"")","-\frac{1}{1280} \, a {\left(\frac{4 \, {\left(1375 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{19}{4}} - 1992 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{4}} + 3710 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{4}} - 1440 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} + 395 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{5 \, {\left(a x - 1\right)} a^{6}}{a x + 1} - \frac{10 \, {\left(a x - 1\right)}^{2} a^{6}}{{\left(a x + 1\right)}^{2}} + \frac{10 \, {\left(a x - 1\right)}^{3} a^{6}}{{\left(a x + 1\right)}^{3}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{6}}{{\left(a x + 1\right)}^{4}} + \frac{{\left(a x - 1\right)}^{5} a^{6}}{{\left(a x + 1\right)}^{5}} - a^{6}} - \frac{2370 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} + \frac{1185 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} - \frac{1185 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{6}}\right)}"," ",0,"-1/1280*a*(4*(1375*((a*x - 1)/(a*x + 1))^(19/4) - 1992*((a*x - 1)/(a*x + 1))^(15/4) + 3710*((a*x - 1)/(a*x + 1))^(11/4) - 1440*((a*x - 1)/(a*x + 1))^(7/4) + 395*((a*x - 1)/(a*x + 1))^(3/4))/(5*(a*x - 1)*a^6/(a*x + 1) - 10*(a*x - 1)^2*a^6/(a*x + 1)^2 + 10*(a*x - 1)^3*a^6/(a*x + 1)^3 - 5*(a*x - 1)^4*a^6/(a*x + 1)^4 + (a*x - 1)^5*a^6/(a*x + 1)^5 - a^6) - 2370*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 + 1185*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 - 1185*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^6)","A",0
96,1,224,0,0.403763," ","integrate(x^3*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""maxima"")","-\frac{1}{128} \, a {\left(\frac{4 \, {\left(133 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{4}} - 147 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{4}} + 183 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} - 41 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{5}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{5}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{5}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{5}}{{\left(a x + 1\right)}^{4}} - a^{5}} + \frac{246 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} - \frac{123 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} + \frac{123 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{5}}\right)}"," ",0,"-1/128*a*(4*(133*((a*x - 1)/(a*x + 1))^(15/4) - 147*((a*x - 1)/(a*x + 1))^(11/4) + 183*((a*x - 1)/(a*x + 1))^(7/4) - 41*((a*x - 1)/(a*x + 1))^(3/4))/(4*(a*x - 1)*a^5/(a*x + 1) - 6*(a*x - 1)^2*a^5/(a*x + 1)^2 + 4*(a*x - 1)^3*a^5/(a*x + 1)^3 - (a*x - 1)^4*a^5/(a*x + 1)^4 - a^5) + 246*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 - 123*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 + 123*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^5)","A",0
97,1,187,0,0.409299," ","integrate(x^2*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""maxima"")","-\frac{1}{48} \, a {\left(\frac{4 \, {\left(45 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{4}} - 30 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} + 17 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{4}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{4}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{4}}{{\left(a x + 1\right)}^{3}} - a^{4}} - \frac{102 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} + \frac{51 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} - \frac{51 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{4}}\right)}"," ",0,"-1/48*a*(4*(45*((a*x - 1)/(a*x + 1))^(11/4) - 30*((a*x - 1)/(a*x + 1))^(7/4) + 17*((a*x - 1)/(a*x + 1))^(3/4))/(3*(a*x - 1)*a^4/(a*x + 1) - 3*(a*x - 1)^2*a^4/(a*x + 1)^2 + (a*x - 1)^3*a^4/(a*x + 1)^3 - a^4) - 102*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 + 51*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 - 51*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^4)","A",0
98,1,152,0,0.408421," ","integrate(x*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{4 \, {\left(7 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} - 3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{3}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{3}}{{\left(a x + 1\right)}^{2}} - a^{3}} + \frac{18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} - \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} + \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{3}}\right)}"," ",0,"-1/8*a*(4*(7*((a*x - 1)/(a*x + 1))^(7/4) - 3*((a*x - 1)/(a*x + 1))^(3/4))/(2*(a*x - 1)*a^3/(a*x + 1) - (a*x - 1)^2*a^3/(a*x + 1)^2 - a^3) + 18*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 - 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 + 9*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^3)","A",0
99,1,112,0,0.408754," ","integrate(((a*x-1)/(a*x+1))^(3/4),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} - \frac{6 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} + \frac{3 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} - \frac{3 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{2}}\right)}"," ",0,"-1/2*a*(4*((a*x - 1)/(a*x + 1))^(3/4)/((a*x - 1)*a^2/(a*x + 1) - a^2) - 6*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 + 3*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 - 3*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^2)","A",0
100,1,224,0,0.415966," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} + \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a}\right)}"," ",0,"-1/2*a*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))/a + 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a - 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a + 2*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a)","A",0
101,1,187,0,0.457379," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(6 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 6 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - 3 \, \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 3 \, \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \frac{8 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{\frac{a x - 1}{a x + 1} + 1}\right)} a"," ",0,"1/4*(6*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 6*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - 3*sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 3*sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 8*((a*x - 1)/(a*x + 1))^(3/4)/((a*x - 1)/(a*x + 1) + 1))*a","A",0
102,1,228,0,0.415758," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(9 \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)\right)} a - \frac{8 \, {\left(7 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} + 3 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{2 \, {\left(a x - 1\right)}}{a x + 1} + \frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}\right)} a"," ",0,"-1/16*(9*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))*a - 8*(7*a*((a*x - 1)/(a*x + 1))^(7/4) + 3*a*((a*x - 1)/(a*x + 1))^(3/4))/(2*(a*x - 1)/(a*x + 1) + (a*x - 1)^2/(a*x + 1)^2 + 1))*a","A",0
103,1,270,0,0.411346," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x^4,x, algorithm=""maxima"")","\frac{1}{96} \, {\left(51 \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)\right)} a^{2} - \frac{8 \, {\left(45 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{4}} + 30 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{4}} + 17 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 1}\right)} a"," ",0,"1/96*(51*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))*a^2 - 8*(45*a^2*((a*x - 1)/(a*x + 1))^(11/4) + 30*a^2*((a*x - 1)/(a*x + 1))^(7/4) + 17*a^2*((a*x - 1)/(a*x + 1))^(3/4))/(3*(a*x - 1)/(a*x + 1) + 3*(a*x - 1)^2/(a*x + 1)^2 + (a*x - 1)^3/(a*x + 1)^3 + 1))*a","A",0
104,1,279,0,0.405757," ","integrate(x^4*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""maxima"")","-\frac{1}{3840} \, a {\left(\frac{4 \, {\left(20585 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{17}{4}} - 49120 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{4}} + 61130 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} - 33816 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + 7365 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{5 \, {\left(a x - 1\right)} a^{6}}{a x + 1} - \frac{10 \, {\left(a x - 1\right)}^{2} a^{6}}{{\left(a x + 1\right)}^{2}} + \frac{10 \, {\left(a x - 1\right)}^{3} a^{6}}{{\left(a x + 1\right)}^{3}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{6}}{{\left(a x + 1\right)}^{4}} + \frac{{\left(a x - 1\right)}^{5} a^{6}}{{\left(a x + 1\right)}^{5}} - a^{6}} + \frac{30090 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} + \frac{15045 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} - \frac{15045 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{6}} - \frac{30720 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{6}}\right)}"," ",0,"-1/3840*a*(4*(20585*((a*x - 1)/(a*x + 1))^(17/4) - 49120*((a*x - 1)/(a*x + 1))^(13/4) + 61130*((a*x - 1)/(a*x + 1))^(9/4) - 33816*((a*x - 1)/(a*x + 1))^(5/4) + 7365*((a*x - 1)/(a*x + 1))^(1/4))/(5*(a*x - 1)*a^6/(a*x + 1) - 10*(a*x - 1)^2*a^6/(a*x + 1)^2 + 10*(a*x - 1)^3*a^6/(a*x + 1)^3 - 5*(a*x - 1)^4*a^6/(a*x + 1)^4 + (a*x - 1)^5*a^6/(a*x + 1)^5 - a^6) + 30090*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 + 15045*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 - 15045*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^6 - 30720*((a*x - 1)/(a*x + 1))^(1/4)/a^6)","A",0
105,1,244,0,0.407294," ","integrate(x^3*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""maxima"")","-\frac{1}{384} \, a {\left(\frac{4 \, {\left(1573 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{4}} - 2875 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} + 2343 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} - 657 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{5}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{5}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{5}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{5}}{{\left(a x + 1\right)}^{4}} - a^{5}} - \frac{2850 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} - \frac{1425 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} + \frac{1425 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{5}} + \frac{3072 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{5}}\right)}"," ",0,"-1/384*a*(4*(1573*((a*x - 1)/(a*x + 1))^(13/4) - 2875*((a*x - 1)/(a*x + 1))^(9/4) + 2343*((a*x - 1)/(a*x + 1))^(5/4) - 657*((a*x - 1)/(a*x + 1))^(1/4))/(4*(a*x - 1)*a^5/(a*x + 1) - 6*(a*x - 1)^2*a^5/(a*x + 1)^2 + 4*(a*x - 1)^3*a^5/(a*x + 1)^3 - (a*x - 1)^4*a^5/(a*x + 1)^4 - a^5) - 2850*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 - 1425*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 + 1425*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^5 + 3072*((a*x - 1)/(a*x + 1))^(1/4)/a^5)","A",0
106,1,207,0,0.405434," ","integrate(x^2*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""maxima"")","-\frac{1}{48} \, a {\left(\frac{4 \, {\left(137 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} - 174 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + 69 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{4}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{4}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{4}}{{\left(a x + 1\right)}^{3}} - a^{4}} + \frac{330 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} + \frac{165 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} - \frac{165 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{4}} - \frac{384 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{4}}\right)}"," ",0,"-1/48*a*(4*(137*((a*x - 1)/(a*x + 1))^(9/4) - 174*((a*x - 1)/(a*x + 1))^(5/4) + 69*((a*x - 1)/(a*x + 1))^(1/4))/(3*(a*x - 1)*a^4/(a*x + 1) - 3*(a*x - 1)^2*a^4/(a*x + 1)^2 + (a*x - 1)^3*a^4/(a*x + 1)^3 - a^4) + 330*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 + 165*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 - 165*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^4 - 384*((a*x - 1)/(a*x + 1))^(1/4)/a^4)","A",0
107,1,172,0,0.414428," ","integrate(x*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{4 \, {\left(13 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} - 9 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{3}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{3}}{{\left(a x + 1\right)}^{2}} - a^{3}} - \frac{50 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} - \frac{25 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} + \frac{25 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{3}} + \frac{64 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{3}}\right)}"," ",0,"-1/8*a*(4*(13*((a*x - 1)/(a*x + 1))^(5/4) - 9*((a*x - 1)/(a*x + 1))^(1/4))/(2*(a*x - 1)*a^3/(a*x + 1) - (a*x - 1)^2*a^3/(a*x + 1)^2 - a^3) - 50*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 - 25*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 + 25*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^3 + 64*((a*x - 1)/(a*x + 1))^(1/4)/a^3)","A",0
108,1,132,0,0.412704," ","integrate(((a*x-1)/(a*x+1))^(5/4),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} + \frac{10 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} + \frac{5 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} - \frac{5 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a^{2}} - \frac{16 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{2}}\right)}"," ",0,"-1/2*a*(4*((a*x - 1)/(a*x + 1))^(1/4)/((a*x - 1)*a^2/(a*x + 1) - a^2) + 10*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 + 5*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 - 5*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a^2 - 16*((a*x - 1)/(a*x + 1))^(1/4)/a^2)","A",0
109,1,244,0,0.420619," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} + \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{a} - \frac{16 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a}\right)}"," ",0,"1/2*a*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1))/a + 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a + 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a - 2*log(((a*x - 1)/(a*x + 1))^(1/4) - 1)/a - 16*((a*x - 1)/(a*x + 1))^(1/4)/a)","A",0
110,1,204,0,0.420530," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(10 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 10 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 5 \, \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 5 \, \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 32 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \frac{8 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{\frac{a x - 1}{a x + 1} + 1}\right)} a"," ",0,"-1/4*(10*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 10*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 5*sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 5*sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 32*((a*x - 1)/(a*x + 1))^(1/4) - 8*((a*x - 1)/(a*x + 1))^(1/4)/((a*x - 1)/(a*x + 1) + 1))*a","A",0
111,1,247,0,0.418986," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x^3,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(50 \, \sqrt{2} a \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 50 \, \sqrt{2} a \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 25 \, \sqrt{2} a \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 25 \, \sqrt{2} a \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 128 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \frac{8 \, {\left(13 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + 9 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{2 \, {\left(a x - 1\right)}}{a x + 1} + \frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}\right)} a"," ",0,"1/16*(50*sqrt(2)*a*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 50*sqrt(2)*a*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 25*sqrt(2)*a*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 25*sqrt(2)*a*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 128*a*((a*x - 1)/(a*x + 1))^(1/4) - 8*(13*a*((a*x - 1)/(a*x + 1))^(5/4) + 9*a*((a*x - 1)/(a*x + 1))^(1/4))/(2*(a*x - 1)/(a*x + 1) + (a*x - 1)^2/(a*x + 1)^2 + 1))*a","A",0
112,1,297,0,0.420408," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x^4,x, algorithm=""maxima"")","-\frac{1}{96} \, {\left(330 \, \sqrt{2} a^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 330 \, \sqrt{2} a^{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 165 \, \sqrt{2} a^{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 165 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 768 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \frac{8 \, {\left(137 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{4}} + 174 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}} + 69 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 1}\right)} a"," ",0,"-1/96*(330*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 330*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 165*sqrt(2)*a^2*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 165*sqrt(2)*a^2*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 768*a^2*((a*x - 1)/(a*x + 1))^(1/4) - 8*(137*a^2*((a*x - 1)/(a*x + 1))^(9/4) + 174*a^2*((a*x - 1)/(a*x + 1))^(5/4) + 69*a^2*((a*x - 1)/(a*x + 1))^(1/4))/(3*(a*x - 1)/(a*x + 1) + 3*(a*x - 1)^2/(a*x + 1)^2 + (a*x - 1)^3/(a*x + 1)^3 + 1))*a","A",0
113,1,220,0,0.424953," ","integrate(1/((-1+x)/(1+x))^(1/6)*x^2,x, algorithm=""maxima"")","-\frac{19}{162} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right)}\right) - \frac{19}{162} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1\right)}\right) - \frac{19 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{17}{6}} - 8 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{11}{6}} + 61 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{27 \, {\left(\frac{3 \, {\left(x - 1\right)}}{x + 1} - \frac{3 \, {\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{{\left(x - 1\right)}^{3}}{{\left(x + 1\right)}^{3}} - 1\right)}} + \frac{19}{324} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) - \frac{19}{324} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) + \frac{19}{162} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) - \frac{19}{162} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1\right)"," ",0,"-19/162*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) + 1)) - 19/162*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) - 1)) - 1/27*(19*((x - 1)/(x + 1))^(17/6) - 8*((x - 1)/(x + 1))^(11/6) + 61*((x - 1)/(x + 1))^(5/6))/(3*(x - 1)/(x + 1) - 3*(x - 1)^2/(x + 1)^2 + (x - 1)^3/(x + 1)^3 - 1) + 19/324*log(((x - 1)/(x + 1))^(1/3) + ((x - 1)/(x + 1))^(1/6) + 1) - 19/324*log(((x - 1)/(x + 1))^(1/3) - ((x - 1)/(x + 1))^(1/6) + 1) + 19/162*log(((x - 1)/(x + 1))^(1/6) + 1) - 19/162*log(((x - 1)/(x + 1))^(1/6) - 1)","A",0
114,1,194,0,0.396600," ","integrate(1/((-1+x)/(1+x))^(1/6)*x,x, algorithm=""maxima"")","-\frac{1}{18} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right)}\right) - \frac{1}{18} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1\right)}\right) + \frac{\left(\frac{x - 1}{x + 1}\right)^{\frac{11}{6}} - 7 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{3 \, {\left(\frac{2 \, {\left(x - 1\right)}}{x + 1} - \frac{{\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} - 1\right)}} + \frac{1}{36} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) - \frac{1}{36} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) + \frac{1}{18} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) - \frac{1}{18} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1\right)"," ",0,"-1/18*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) + 1)) - 1/18*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) - 1)) + 1/3*(((x - 1)/(x + 1))^(11/6) - 7*((x - 1)/(x + 1))^(5/6))/(2*(x - 1)/(x + 1) - (x - 1)^2/(x + 1)^2 - 1) + 1/36*log(((x - 1)/(x + 1))^(1/3) + ((x - 1)/(x + 1))^(1/6) + 1) - 1/36*log(((x - 1)/(x + 1))^(1/3) - ((x - 1)/(x + 1))^(1/6) + 1) + 1/18*log(((x - 1)/(x + 1))^(1/6) + 1) - 1/18*log(((x - 1)/(x + 1))^(1/6) - 1)","A",0
115,1,167,0,0.430845," ","integrate(1/((-1+x)/(1+x))^(1/6),x, algorithm=""maxima"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right)}\right) - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1\right)}\right) - \frac{2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{\frac{x - 1}{x + 1} - 1} + \frac{1}{6} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) - \frac{1}{6} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) + \frac{1}{3} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) - \frac{1}{3} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) + 1)) - 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) - 1)) - 2*((x - 1)/(x + 1))^(5/6)/((x - 1)/(x + 1) - 1) + 1/6*log(((x - 1)/(x + 1))^(1/3) + ((x - 1)/(x + 1))^(1/6) + 1) - 1/6*log(((x - 1)/(x + 1))^(1/3) - ((x - 1)/(x + 1))^(1/6) + 1) + 1/3*log(((x - 1)/(x + 1))^(1/6) + 1) - 1/3*log(((x - 1)/(x + 1))^(1/6) - 1)","A",0
116,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/6)/x,x, algorithm=""maxima"")","\int \frac{1}{x \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}}\,{d x}"," ",0,"integrate(1/(x*((x - 1)/(x + 1))^(1/6)), x)","F",0
117,1,152,0,0.409313," ","integrate(1/((-1+x)/(1+x))^(1/6)/x^2,x, algorithm=""maxima"")","-\frac{1}{6} \, \sqrt{3} \log\left(\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{1}{6} \, \sqrt{3} \log\left(-\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{\frac{x - 1}{x + 1} + 1} + \frac{1}{3} \, \arctan\left(\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{1}{3} \, \arctan\left(-\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{2}{3} \, \arctan\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right)"," ",0,"-1/6*sqrt(3)*log(sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 1/6*sqrt(3)*log(-sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 2*((x - 1)/(x + 1))^(5/6)/((x - 1)/(x + 1) + 1) + 1/3*arctan(sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 1/3*arctan(-sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 2/3*arctan(((x - 1)/(x + 1))^(1/6))","A",0
118,1,178,0,0.422978," ","integrate(1/((-1+x)/(1+x))^(1/6)/x^3,x, algorithm=""maxima"")","-\frac{1}{36} \, \sqrt{3} \log\left(\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{1}{36} \, \sqrt{3} \log\left(-\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{\left(\frac{x - 1}{x + 1}\right)^{\frac{11}{6}} + 7 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{3 \, {\left(\frac{2 \, {\left(x - 1\right)}}{x + 1} + \frac{{\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} + 1\right)}} + \frac{1}{18} \, \arctan\left(\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{1}{18} \, \arctan\left(-\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{1}{9} \, \arctan\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right)"," ",0,"-1/36*sqrt(3)*log(sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 1/36*sqrt(3)*log(-sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 1/3*(((x - 1)/(x + 1))^(11/6) + 7*((x - 1)/(x + 1))^(5/6))/(2*(x - 1)/(x + 1) + (x - 1)^2/(x + 1)^2 + 1) + 1/18*arctan(sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 1/18*arctan(-sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 1/9*arctan(((x - 1)/(x + 1))^(1/6))","A",0
119,1,205,0,0.414722," ","integrate(1/((-1+x)/(1+x))^(1/6)/x^4,x, algorithm=""maxima"")","-\frac{19}{324} \, \sqrt{3} \log\left(\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{19}{324} \, \sqrt{3} \log\left(-\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{19 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{17}{6}} + 8 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{11}{6}} + 61 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{27 \, {\left(\frac{3 \, {\left(x - 1\right)}}{x + 1} + \frac{3 \, {\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{{\left(x - 1\right)}^{3}}{{\left(x + 1\right)}^{3}} + 1\right)}} + \frac{19}{162} \, \arctan\left(\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{19}{162} \, \arctan\left(-\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{19}{81} \, \arctan\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right)"," ",0,"-19/324*sqrt(3)*log(sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 19/324*sqrt(3)*log(-sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 1/27*(19*((x - 1)/(x + 1))^(17/6) + 8*((x - 1)/(x + 1))^(11/6) + 61*((x - 1)/(x + 1))^(5/6))/(3*(x - 1)/(x + 1) + 3*(x - 1)^2/(x + 1)^2 + (x - 1)^3/(x + 1)^3 + 1) + 19/162*arctan(sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 19/162*arctan(-sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 19/81*arctan(((x - 1)/(x + 1))^(1/6))","A",0
120,1,149,0,0.416940," ","integrate(1/((-1+x)/(1+x))^(1/3)*x^2,x, algorithm=""maxima"")","-\frac{22}{81} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right)}\right) - \frac{2 \, {\left(11 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{8}{3}} - 10 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{3}} + 35 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}\right)}}{27 \, {\left(\frac{3 \, {\left(x - 1\right)}}{x + 1} - \frac{3 \, {\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{{\left(x - 1\right)}^{3}}{{\left(x + 1\right)}^{3}} - 1\right)}} + \frac{11}{81} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) - \frac{22}{81} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1\right)"," ",0,"-22/81*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) + 1)) - 2/27*(11*((x - 1)/(x + 1))^(8/3) - 10*((x - 1)/(x + 1))^(5/3) + 35*((x - 1)/(x + 1))^(2/3))/(3*(x - 1)/(x + 1) - 3*(x - 1)^2/(x + 1)^2 + (x - 1)^3/(x + 1)^3 - 1) + 11/81*log(((x - 1)/(x + 1))^(2/3) + ((x - 1)/(x + 1))^(1/3) + 1) - 22/81*log(((x - 1)/(x + 1))^(1/3) - 1)","A",0
121,1,123,0,0.402267," ","integrate(1/((-1+x)/(1+x))^(1/3)*x,x, algorithm=""maxima"")","-\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right)}\right) + \frac{2 \, {\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{5}{3}} - 4 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}\right)}}{3 \, {\left(\frac{2 \, {\left(x - 1\right)}}{x + 1} - \frac{{\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} - 1\right)}} + \frac{1}{9} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) - \frac{2}{9} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1\right)"," ",0,"-2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) + 1)) + 2/3*(((x - 1)/(x + 1))^(5/3) - 4*((x - 1)/(x + 1))^(2/3))/(2*(x - 1)/(x + 1) - (x - 1)^2/(x + 1)^2 - 1) + 1/9*log(((x - 1)/(x + 1))^(2/3) + ((x - 1)/(x + 1))^(1/3) + 1) - 2/9*log(((x - 1)/(x + 1))^(1/3) - 1)","A",0
122,1,96,0,0.403618," ","integrate(1/((-1+x)/(1+x))^(1/3),x, algorithm=""maxima"")","-\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right)}\right) - \frac{2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}}{\frac{x - 1}{x + 1} - 1} + \frac{1}{3} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) - \frac{2}{3} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1\right)"," ",0,"-2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) + 1)) - 2*((x - 1)/(x + 1))^(2/3)/((x - 1)/(x + 1) - 1) + 1/3*log(((x - 1)/(x + 1))^(2/3) + ((x - 1)/(x + 1))^(1/3) + 1) - 2/3*log(((x - 1)/(x + 1))^(1/3) - 1)","A",0
123,1,140,0,0.417791," ","integrate(1/((-1+x)/(1+x))^(1/3)/x,x, algorithm=""maxima"")","-\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right)}\right) + \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1\right)}\right) + \frac{1}{2} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{1}{2} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} - \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) - \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) - \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1\right)"," ",0,"-sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) + 1)) + sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) - 1)) + 1/2*log(((x - 1)/(x + 1))^(2/3) + ((x - 1)/(x + 1))^(1/3) + 1) + 1/2*log(((x - 1)/(x + 1))^(2/3) - ((x - 1)/(x + 1))^(1/3) + 1) - log(((x - 1)/(x + 1))^(1/3) + 1) - log(((x - 1)/(x + 1))^(1/3) - 1)","A",0
124,1,98,0,0.411488," ","integrate(1/((-1+x)/(1+x))^(1/3)/x^2,x, algorithm=""maxima"")","\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1\right)}\right) + \frac{2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}}{\frac{x - 1}{x + 1} + 1} + \frac{1}{3} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} - \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) - \frac{2}{3} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right)"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) - 1)) + 2*((x - 1)/(x + 1))^(2/3)/((x - 1)/(x + 1) + 1) + 1/3*log(((x - 1)/(x + 1))^(2/3) - ((x - 1)/(x + 1))^(1/3) + 1) - 2/3*log(((x - 1)/(x + 1))^(1/3) + 1)","A",0
125,1,124,0,0.406585," ","integrate(1/((-1+x)/(1+x))^(1/3)/x^3,x, algorithm=""maxima"")","\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1\right)}\right) + \frac{2 \, {\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{5}{3}} + 4 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}\right)}}{3 \, {\left(\frac{2 \, {\left(x - 1\right)}}{x + 1} + \frac{{\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} + 1\right)}} + \frac{1}{9} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} - \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) - \frac{2}{9} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right)"," ",0,"2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) - 1)) + 2/3*(((x - 1)/(x + 1))^(5/3) + 4*((x - 1)/(x + 1))^(2/3))/(2*(x - 1)/(x + 1) + (x - 1)^2/(x + 1)^2 + 1) + 1/9*log(((x - 1)/(x + 1))^(2/3) - ((x - 1)/(x + 1))^(1/3) + 1) - 2/9*log(((x - 1)/(x + 1))^(1/3) + 1)","A",0
126,1,341,0,0.410771," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)*x^2,x, algorithm=""maxima"")","-\frac{1}{768} \, a {\left(\frac{16 \, {\left(33 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{23}{8}} - 10 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{8}} + 105 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{4}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{4}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{4}}{{\left(a x + 1\right)}^{3}} - a^{4}} + \frac{33 \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)\right)}}{a^{4}} + \frac{132 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}{a^{4}} - \frac{66 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right)}{a^{4}} + \frac{66 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1\right)}{a^{4}}\right)}"," ",0,"-1/768*a*(16*(33*((a*x - 1)/(a*x + 1))^(23/8) - 10*((a*x - 1)/(a*x + 1))^(15/8) + 105*((a*x - 1)/(a*x + 1))^(7/8))/(3*(a*x - 1)*a^4/(a*x + 1) - 3*(a*x - 1)^2*a^4/(a*x + 1)^2 + (a*x - 1)^3*a^4/(a*x + 1)^3 - a^4) + 33*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/8))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/8))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1))/a^4 + 132*arctan(((a*x - 1)/(a*x + 1))^(1/8))/a^4 - 66*log(((a*x - 1)/(a*x + 1))^(1/8) + 1)/a^4 + 66*log(((a*x - 1)/(a*x + 1))^(1/8) - 1)/a^4)","A",0
127,1,304,0,0.418181," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)*x,x, algorithm=""maxima"")","\frac{1}{64} \, a {\left(\frac{16 \, {\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{8}} - 9 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{3}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{3}}{{\left(a x + 1\right)}^{2}} - a^{3}} - \frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} - \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}{a^{3}} + \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right)}{a^{3}} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1\right)}{a^{3}}\right)}"," ",0,"1/64*a*(16*(((a*x - 1)/(a*x + 1))^(15/8) - 9*((a*x - 1)/(a*x + 1))^(7/8))/(2*(a*x - 1)*a^3/(a*x + 1) - (a*x - 1)^2*a^3/(a*x + 1)^2 - a^3) - (2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/8))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/8))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1))/a^3 - 4*arctan(((a*x - 1)/(a*x + 1))^(1/8))/a^3 + 2*log(((a*x - 1)/(a*x + 1))^(1/8) + 1)/a^3 - 2*log(((a*x - 1)/(a*x + 1))^(1/8) - 1)/a^3)","A",0
128,1,265,0,0.420716," ","integrate(1/((a*x-1)/(a*x+1))^(1/8),x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{16 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}{a^{2}} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right)}{a^{2}} + \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1\right)}{a^{2}}\right)}"," ",0,"-1/8*a*(16*((a*x - 1)/(a*x + 1))^(7/8)/((a*x - 1)*a^2/(a*x + 1) - a^2) + (2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/8))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/8))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1))/a^2 + 4*arctan(((a*x - 1)/(a*x + 1))^(1/8))/a^2 - 2*log(((a*x - 1)/(a*x + 1))^(1/8) + 1)/a^2 + 2*log(((a*x - 1)/(a*x + 1))^(1/8) - 1)/a^2)","A",0
129,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)/x,x, algorithm=""maxima"")","\int \frac{1}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}\,{d x}"," ",0,"integrate(1/(x*((a*x - 1)/(a*x + 1))^(1/8)), x)","F",0
130,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)/x^2,x, algorithm=""maxima"")","\int \frac{1}{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}\,{d x}"," ",0,"integrate(1/(x^2*((a*x - 1)/(a*x + 1))^(1/8)), x)","F",0
131,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)/x^3,x, algorithm=""maxima"")","\int \frac{1}{x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}\,{d x}"," ",0,"integrate(1/(x^3*((a*x - 1)/(a*x + 1))^(1/8)), x)","F",0
132,0,0,0,0.000000," ","integrate(1/(a*x-1)^2*(a*x+1)^2*x^m,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)}^{2} x^{m}}{{\left(a x - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^2*x^m/(a*x - 1)^2, x)","F",0
133,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^m,x, algorithm=""maxima"")","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
134,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x^m,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} x^{m}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/(a*x - 1), x)","F",0
135,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m,x, algorithm=""maxima"")","\int \frac{x^{m}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^m/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
136,0,0,0,0.000000," ","integrate(x^m*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int x^{m} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(x^m*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
137,0,0,0,0.000000," ","integrate(x^m*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*x^m/(a*x + 1), x)","F",0
138,0,0,0,0.000000," ","integrate(x^m*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^m*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
139,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^m,x, algorithm=""maxima"")","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^m/((a*x - 1)/(a*x + 1))^(5/4), x)","F",0
140,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^m,x, algorithm=""maxima"")","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^m/((a*x - 1)/(a*x + 1))^(3/4), x)","F",0
141,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^m,x, algorithm=""maxima"")","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^m/((a*x - 1)/(a*x + 1))^(1/4), x)","F",0
142,0,0,0,0.000000," ","integrate(x^m*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""maxima"")","\int x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\,{d x}"," ",0,"integrate(x^m*((a*x - 1)/(a*x + 1))^(1/4), x)","F",0
143,0,0,0,0.000000," ","integrate(x^m*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""maxima"")","\int x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\,{d x}"," ",0,"integrate(x^m*((a*x - 1)/(a*x + 1))^(3/4), x)","F",0
144,0,0,0,0.000000," ","integrate(x^m*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""maxima"")","\int x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}\,{d x}"," ",0,"integrate(x^m*((a*x - 1)/(a*x + 1))^(5/4), x)","F",0
145,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/3)*x^m,x, algorithm=""maxima"")","\int \frac{x^{m}}{\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^m/((x - 1)/(x + 1))^(1/3), x)","F",0
146,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/6)*x^m,x, algorithm=""maxima"")","\int \frac{x^{m}}{\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}}\,{d x}"," ",0,"integrate(x^m/((x - 1)/(x + 1))^(1/6), x)","F",0
147,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)*x^m,x, algorithm=""maxima"")","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}\,{d x}"," ",0,"integrate(x^m/((a*x - 1)/(a*x + 1))^(1/8), x)","F",0
148,0,0,0,0.000000," ","integrate(exp(n*arccoth(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*arccoth(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
150,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
151,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
152,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
153,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
154,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
155,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
156,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/x^5,x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{x^{5}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/x^5, x)","F",0
157,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^p,x, algorithm=""maxima"")","\int \frac{{\left(-a c x + c\right)}^{p}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a*c*x + c)^p/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
158,1,259,0,0.326366," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{1}{120} \, {\left(\frac{105 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{105 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(105 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 790 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 896 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 490 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 105 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{5 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{10 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{10 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{{\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - a^{2}}\right)} a"," ",0,"1/120*(105*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 105*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(105*c^4*((a*x - 1)/(a*x + 1))^(9/2) + 790*c^4*((a*x - 1)/(a*x + 1))^(7/2) - 896*c^4*((a*x - 1)/(a*x + 1))^(5/2) + 490*c^4*((a*x - 1)/(a*x + 1))^(3/2) - 105*c^4*sqrt((a*x - 1)/(a*x + 1)))/(5*(a*x - 1)*a^2/(a*x + 1) - 10*(a*x - 1)^2*a^2/(a*x + 1)^2 + 10*(a*x - 1)^3*a^2/(a*x + 1)^3 - 5*(a*x - 1)^4*a^2/(a*x + 1)^4 + (a*x - 1)^5*a^2/(a*x + 1)^5 - a^2))*a","B",0
159,1,221,0,0.308832," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^3,x, algorithm=""maxima"")","\frac{1}{24} \, {\left(\frac{15 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{15 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} + \frac{2 \, {\left(15 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 73 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 55 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 15 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} - a^{2}}\right)} a"," ",0,"1/24*(15*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 15*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 + 2*(15*c^3*((a*x - 1)/(a*x + 1))^(7/2) + 73*c^3*((a*x - 1)/(a*x + 1))^(5/2) - 55*c^3*((a*x - 1)/(a*x + 1))^(3/2) + 15*c^3*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)*a^2/(a*x + 1) - 6*(a*x - 1)^2*a^2/(a*x + 1)^2 + 4*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 - a^2))*a","B",0
160,1,181,0,0.310477," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(3 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 8 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 3 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - a^{2}}\right)}"," ",0,"1/6*a*(3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(3*c^2*((a*x - 1)/(a*x + 1))^(5/2) + 8*c^2*((a*x - 1)/(a*x + 1))^(3/2) - 3*c^2*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)*a^2/(a*x + 1) - 3*(a*x - 1)^2*a^2/(a*x + 1)^2 + (a*x - 1)^3*a^2/(a*x + 1)^3 - a^2))","B",0
161,1,132,0,0.307625," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, {\left(c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + c \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} + \frac{c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"1/2*a*(2*(c*((a*x - 1)/(a*x + 1))^(3/2) + c*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - (a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) + c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","B",0
162,1,78,0,0.304111," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c),x, algorithm=""maxima"")","-a {\left(\frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c} - \frac{2}{a^{2} c \sqrt{\frac{a x - 1}{a x + 1}}}\right)}"," ",0,"-a*(log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c) - 2/(a^2*c*sqrt((a*x - 1)/(a*x + 1))))","A",0
163,1,23,0,0.312476," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{1}{3 \, a c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}"," ",0,"-1/3/(a*c^2*((a*x - 1)/(a*x + 1))^(3/2))","A",0
164,1,39,0,0.307700," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{\frac{5 \, {\left(a x - 1\right)}}{a x + 1} - 3}{30 \, a c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}}"," ",0,"-1/30*(5*(a*x - 1)/(a*x + 1) - 3)/(a*c^3*((a*x - 1)/(a*x + 1))^(5/2))","A",0
165,1,55,0,0.302854," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{\frac{42 \, {\left(a x - 1\right)}}{a x + 1} - \frac{35 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 15}{420 \, a c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}}}"," ",0,"1/420*(42*(a*x - 1)/(a*x + 1) - 35*(a*x - 1)^2/(a*x + 1)^2 - 15)/(a*c^4*((a*x - 1)/(a*x + 1))^(7/2))","A",0
166,1,71,0,0.304238," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^5,x, algorithm=""maxima"")","-\frac{\frac{135 \, {\left(a x - 1\right)}}{a x + 1} - \frac{189 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{105 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 35}{2520 \, a c^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}}}"," ",0,"-1/2520*(135*(a*x - 1)/(a*x + 1) - 189*(a*x - 1)^2/(a*x + 1)^2 + 105*(a*x - 1)^3/(a*x + 1)^3 - 35)/(a*c^5*((a*x - 1)/(a*x + 1))^(9/2))","A",0
167,1,49,0,0.319881," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^p,x, algorithm=""maxima"")","\frac{{\left(a c^{p} p x + c^{p}\right)} {\left(-a x + 1\right)}^{p}}{{\left(p^{2} + p\right)} a} + \frac{{\left(-a x + 1\right)}^{p} c^{p}}{a p}"," ",0,"(a*c^p*p*x + c^p)*(-a*x + 1)^p/((p^2 + p)*a) + (-a*x + 1)^p*c^p/(a*p)","A",0
168,1,60,0,0.306742," ","integrate(1/(a*x-1)*(a*x+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
169,1,37,0,0.303827," ","integrate(1/(a*x-1)*(a*x+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
170,1,38,0,0.304449," ","integrate(1/(a*x-1)*(a*x+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
171,1,18,0,0.307203," ","integrate(1/(a*x-1)*(a*x+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
172,1,12,0,0.321253," ","integrate(1/(a*x-1)*(a*x+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
173,1,30,0,0.311889," ","integrate(1/(a*x-1)*(a*x+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
174,1,26,0,0.309336," ","integrate(1/(a*x-1)*(a*x+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)","A",0
175,1,47,0,0.299377," ","integrate(1/(a*x-1)*(a*x+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
176,1,57,0,0.318490," ","integrate(1/(a*x-1)*(a*x+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(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^p,x, algorithm=""maxima"")","\int \frac{{\left(-a c x + c\right)}^{p}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a*c*x + c)^p/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
178,1,259,0,0.333834," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^4,x, algorithm=""maxima"")","-\frac{1}{40} \, {\left(\frac{15 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{15 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(15 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - 70 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 128 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 70 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 15 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{5 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{10 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{10 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{{\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - a^{2}}\right)} a"," ",0,"-1/40*(15*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 15*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(15*c^4*((a*x - 1)/(a*x + 1))^(9/2) - 70*c^4*((a*x - 1)/(a*x + 1))^(7/2) - 128*c^4*((a*x - 1)/(a*x + 1))^(5/2) + 70*c^4*((a*x - 1)/(a*x + 1))^(3/2) - 15*c^4*sqrt((a*x - 1)/(a*x + 1)))/(5*(a*x - 1)*a^2/(a*x + 1) - 10*(a*x - 1)^2*a^2/(a*x + 1)^2 + 10*(a*x - 1)^3*a^2/(a*x + 1)^3 - 5*(a*x - 1)^4*a^2/(a*x + 1)^4 + (a*x - 1)^5*a^2/(a*x + 1)^5 - a^2))*a","B",0
179,1,221,0,0.318171," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(\frac{3 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} + \frac{2 \, {\left(3 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 11 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 11 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 3 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} - a^{2}}\right)} a"," ",0,"-1/8*(3*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 + 2*(3*c^3*((a*x - 1)/(a*x + 1))^(7/2) - 11*c^3*((a*x - 1)/(a*x + 1))^(5/2) - 11*c^3*((a*x - 1)/(a*x + 1))^(3/2) + 3*c^3*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)*a^2/(a*x + 1) - 6*(a*x - 1)^2*a^2/(a*x + 1)^2 + 4*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 - a^2))*a","B",0
180,1,181,0,0.316070," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(3 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 8 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 3 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - a^{2}}\right)}"," ",0,"-1/6*a*(3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(3*c^2*((a*x - 1)/(a*x + 1))^(5/2) - 8*c^2*((a*x - 1)/(a*x + 1))^(3/2) - 3*c^2*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)*a^2/(a*x + 1) - 3*(a*x - 1)^2*a^2/(a*x + 1)^2 + (a*x - 1)^3*a^2/(a*x + 1)^3 - a^2))","B",0
181,1,135,0,0.308856," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, {\left(3 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 5 \, c \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} + \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"-1/2*a*(2*(3*c*((a*x - 1)/(a*x + 1))^(3/2) - 5*c*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - (a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) + 3*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","B",0
182,1,95,0,0.312646," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c} - \frac{2 \, {\left(\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + 1\right)}}{a^{2} c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\right)}"," ",0,"-1/3*a*(3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - 3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c) - 2*(3*(a*x - 1)/(a*x + 1) + 1)/(a^2*c*((a*x - 1)/(a*x + 1))^(3/2)))","A",0
183,1,23,0,0.314261," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{1}{5 \, a c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}}"," ",0,"-1/5/(a*c^2*((a*x - 1)/(a*x + 1))^(5/2))","A",0
184,1,39,0,0.316060," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{\frac{7 \, {\left(a x - 1\right)}}{a x + 1} - 5}{70 \, a c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}}}"," ",0,"-1/70*(7*(a*x - 1)/(a*x + 1) - 5)/(a*c^3*((a*x - 1)/(a*x + 1))^(7/2))","A",0
185,1,55,0,0.304111," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{\frac{90 \, {\left(a x - 1\right)}}{a x + 1} - \frac{63 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 35}{1260 \, a c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}}}"," ",0,"1/1260*(90*(a*x - 1)/(a*x + 1) - 63*(a*x - 1)^2/(a*x + 1)^2 - 35)/(a*c^4*((a*x - 1)/(a*x + 1))^(9/2))","A",0
186,1,71,0,0.306703," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^5,x, algorithm=""maxima"")","-\frac{\frac{385 \, {\left(a x - 1\right)}}{a x + 1} - \frac{495 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{231 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 105}{9240 \, a c^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}}}"," ",0,"-1/9240*(385*(a*x - 1)/(a*x + 1) - 495*(a*x - 1)^2/(a*x + 1)^2 + 231*(a*x - 1)^3/(a*x + 1)^3 - 105)/(a*c^5*((a*x - 1)/(a*x + 1))^(11/2))","A",0
187,1,153,0,0.331700," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^p,x, algorithm=""maxima"")","\frac{{\left({\left(p^{2} - p\right)} a^{2} c^{p} x^{2} + 2 \, a c^{p} {\left(p - 1\right)} x + 2 \, c^{p}\right)} {\left(-a x + 1\right)}^{p} a^{2}}{{\left(p^{3} - p\right)} a^{4} x - {\left(p^{3} - p\right)} a^{3}} + \frac{2 \, {\left(a c^{p} {\left(p - 1\right)} x + c^{p}\right)} {\left(-a x + 1\right)}^{p} a}{{\left(p^{2} - p\right)} a^{3} x - {\left(p^{2} - p\right)} a^{2}} + \frac{{\left(-a x + 1\right)}^{p} c^{p}}{a^{2} {\left(p - 1\right)} x - a {\left(p - 1\right)}}"," ",0,"((p^2 - p)*a^2*c^p*x^2 + 2*a*c^p*(p - 1)*x + 2*c^p)*(-a*x + 1)^p*a^2/((p^3 - p)*a^4*x - (p^3 - p)*a^3) + 2*(a*c^p*(p - 1)*x + c^p)*(-a*x + 1)^p*a/((p^2 - p)*a^3*x - (p^2 - p)*a^2) + (-a*x + 1)^p*c^p/(a^2*(p - 1)*x - a*(p - 1))","B",0
188,1,59,0,0.298637," ","integrate(1/(a*x-1)^2*(a*x+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
189,1,28,0,0.304282," ","integrate(1/(a*x-1)^2*(a*x+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
190,1,37,0,0.303945," ","integrate(1/(a*x-1)^2*(a*x+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
191,1,25,0,0.305245," ","integrate(1/(a*x-1)^2*(a*x+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
192,1,24,0,0.306522," ","integrate(1/(a*x-1)^2*(a*x+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
193,1,44,0,0.305314," ","integrate(1/(a*x-1)^2*(a*x+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
194,1,51,0,0.309384," ","integrate(1/(a*x-1)^2*(a*x+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
195,1,65,0,0.304828," ","integrate(1/(a*x-1)^2*(a*x+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
196,1,77,0,0.305967," ","integrate(1/(a*x-1)^2*(a*x+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*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(-a c x + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a*c*x + c)^p*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
198,1,221,0,0.322178," ","integrate((-a*c*x+c)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{1}{24} \, {\left(\frac{105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(279 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 511 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 385 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 105 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} - a^{2}}\right)} a"," ",0,"-1/24*(105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(279*c^3*((a*x - 1)/(a*x + 1))^(7/2) - 511*c^3*((a*x - 1)/(a*x + 1))^(5/2) + 385*c^3*((a*x - 1)/(a*x + 1))^(3/2) - 105*c^3*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)*a^2/(a*x + 1) - 6*(a*x - 1)^2*a^2/(a*x + 1)^2 + 4*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 - a^2))*a","B",0
199,1,181,0,0.308198," ","integrate((-a*c*x+c)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} + \frac{2 \, {\left(33 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 40 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 15 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - a^{2}}\right)}"," ",0,"-1/6*a*(15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 + 2*(33*c^2*((a*x - 1)/(a*x + 1))^(5/2) - 40*c^2*((a*x - 1)/(a*x + 1))^(3/2) + 15*c^2*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)*a^2/(a*x + 1) - 3*(a*x - 1)^2*a^2/(a*x + 1)^2 + (a*x - 1)^3*a^2/(a*x + 1)^3 - a^2))","B",0
200,1,135,0,0.308361," ","integrate((-a*c*x+c)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, {\left(5 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 3 \, c \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} - \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"1/2*a*(2*(5*c*((a*x - 1)/(a*x + 1))^(3/2) - 3*c*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - (a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) - 3*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 3*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","B",0
201,1,55,0,0.309243," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c),x, algorithm=""maxima"")","-a {\left(\frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c}\right)}"," ",0,"-a*(log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c))","B",0
202,1,23,0,0.304348," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^2,x, algorithm=""maxima"")","-\frac{1}{a c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"-1/(a*c^2*sqrt((a*x - 1)/(a*x + 1)))","A",0
203,1,39,0,0.306257," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} - 1}{6 \, a c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}"," ",0,"-1/6*(3*(a*x - 1)/(a*x + 1) - 1)/(a*c^3*((a*x - 1)/(a*x + 1))^(3/2))","A",0
204,1,55,0,0.311995," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{\frac{10 \, {\left(a x - 1\right)}}{a x + 1} - \frac{15 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 3}{60 \, a c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}}"," ",0,"1/60*(10*(a*x - 1)/(a*x + 1) - 15*(a*x - 1)^2/(a*x + 1)^2 - 3)/(a*c^4*((a*x - 1)/(a*x + 1))^(5/2))","A",0
205,1,71,0,0.312434," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^5,x, algorithm=""maxima"")","-\frac{\frac{21 \, {\left(a x - 1\right)}}{a x + 1} - \frac{35 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{35 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 5}{280 \, a c^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}}}"," ",0,"-1/280*(21*(a*x - 1)/(a*x + 1) - 35*(a*x - 1)^2/(a*x + 1)^2 + 35*(a*x - 1)^3/(a*x + 1)^3 - 5)/(a*c^5*((a*x - 1)/(a*x + 1))^(7/2))","A",0
206,0,0,0,0.000000," ","integrate((-a*c*x+c)^p*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} {\left(-a c x + c\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(-a*c*x + c)^p/(a*x + 1), x)","F",0
207,1,63,0,0.306980," ","integrate((-a*c*x+c)^4*(a*x-1)/(a*x+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
208,1,52,0,0.302135," ","integrate((-a*c*x+c)^3*(a*x-1)/(a*x+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
209,1,41,0,0.304060," ","integrate((-a*c*x+c)^2*(a*x-1)/(a*x+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
210,1,24,0,0.301448," ","integrate((-a*c*x+c)*(a*x-1)/(a*x+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
211,1,14,0,0.303512," ","integrate((a*x-1)/(a*x+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
212,1,29,0,0.306376," ","integrate((a*x-1)/(a*x+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
213,1,48,0,0.302564," ","integrate((a*x-1)/(a*x+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
214,1,63,0,0.305921," ","integrate((a*x-1)/(a*x+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
215,1,84,0,0.307100," ","integrate((a*x-1)/(a*x+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)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int {\left(-a c x + c\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-a*c*x + c)^p*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
217,1,244,0,0.319242," ","integrate((-a*c*x+c)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(\frac{315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{256 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2}} - \frac{2 \, {\left(325 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 765 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 643 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 187 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{4 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{6 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} - a^{2}}\right)} a"," ",0,"-1/8*(315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 256*c^3*sqrt((a*x - 1)/(a*x + 1))/a^2 - 2*(325*c^3*((a*x - 1)/(a*x + 1))^(7/2) - 765*c^3*((a*x - 1)/(a*x + 1))^(5/2) + 643*c^3*((a*x - 1)/(a*x + 1))^(3/2) - 187*c^3*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)*a^2/(a*x + 1) - 6*(a*x - 1)^2*a^2/(a*x + 1)^2 + 4*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 - a^2))*a","A",0
218,1,204,0,0.306756," ","integrate((-a*c*x+c)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{96 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2}} + \frac{2 \, {\left(87 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 136 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 57 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - a^{2}}\right)}"," ",0,"-1/6*a*(105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 96*c^2*sqrt((a*x - 1)/(a*x + 1))/a^2 + 2*(87*c^2*((a*x - 1)/(a*x + 1))^(5/2) - 136*c^2*((a*x - 1)/(a*x + 1))^(3/2) + 57*c^2*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)*a^2/(a*x + 1) - 3*(a*x - 1)^2*a^2/(a*x + 1)^2 + (a*x - 1)^3*a^2/(a*x + 1)^3 - a^2))","A",0
219,1,156,0,0.307834," ","integrate((-a*c*x+c)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, {\left(9 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 7 \, c \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} - \frac{15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} + \frac{16 \, c \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2}}\right)}"," ",0,"1/2*a*(2*(9*c*((a*x - 1)/(a*x + 1))^(3/2) - 7*c*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - (a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) - 15*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 15*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 + 16*c*sqrt((a*x - 1)/(a*x + 1))/a^2)","A",0
220,1,78,0,0.304610," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c),x, algorithm=""maxima"")","-a {\left(\frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c} - \frac{2 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c}\right)}"," ",0,"-a*(log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c) - 2*sqrt((a*x - 1)/(a*x + 1))/(a^2*c))","A",0
221,1,22,0,0.305914," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^2,x, algorithm=""maxima"")","\frac{\sqrt{\frac{a x - 1}{a x + 1}}}{a c^{2}}"," ",0,"sqrt((a*x - 1)/(a*x + 1))/(a*c^2)","A",0
222,1,48,0,0.307317," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^3,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{\sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3}} + \frac{1}{a^{2} c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}\right)}"," ",0,"1/2*a*(sqrt((a*x - 1)/(a*x + 1))/(a^2*c^3) + 1/(a^2*c^3*sqrt((a*x - 1)/(a*x + 1))))","B",0
223,1,65,0,0.307669," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^4,x, algorithm=""maxima"")","\frac{1}{12} \, a {\left(\frac{3 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{4}} + \frac{\frac{6 \, {\left(a x - 1\right)}}{a x + 1} - 1}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\right)}"," ",0,"1/12*a*(3*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^4) + (6*(a*x - 1)/(a*x + 1) - 1)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(3/2)))","A",0
224,1,82,0,0.307401," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^5,x, algorithm=""maxima"")","\frac{1}{40} \, a {\left(\frac{5 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{5}} - \frac{\frac{5 \, {\left(a x - 1\right)}}{a x + 1} - \frac{15 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 1}{a^{2} c^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}}\right)}"," ",0,"1/40*a*(5*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^5) - (5*(a*x - 1)/(a*x + 1) - 15*(a*x - 1)^2/(a*x + 1)^2 - 1)/(a^2*c^5*((a*x - 1)/(a*x + 1))^(5/2)))","A",0
225,1,97,0,0.311662," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^6,x, algorithm=""maxima"")","\frac{1}{560} \, a {\left(\frac{35 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{6}} + \frac{\frac{28 \, {\left(a x - 1\right)}}{a x + 1} - \frac{70 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{140 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 5}{a^{2} c^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}}}\right)}"," ",0,"1/560*a*(35*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^6) + (28*(a*x - 1)/(a*x + 1) - 70*(a*x - 1)^2/(a*x + 1)^2 + 140*(a*x - 1)^3/(a*x + 1)^3 - 5)/(a^2*c^6*((a*x - 1)/(a*x + 1))^(7/2)))","A",0
226,1,99,0,0.329603," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(9/2),x, algorithm=""maxima"")","\frac{2 \, {\left(315 \, a^{5} \sqrt{-c} c^{4} x^{5} - 1505 \, a^{4} \sqrt{-c} c^{4} x^{4} + 2710 \, a^{3} \sqrt{-c} c^{4} x^{3} - 1866 \, a^{2} \sqrt{-c} c^{4} x^{2} - 977 \, a \sqrt{-c} c^{4} x + 5419 \, \sqrt{-c} c^{4}\right)} \sqrt{a x + 1}}{3465 \, a}"," ",0,"2/3465*(315*a^5*sqrt(-c)*c^4*x^5 - 1505*a^4*sqrt(-c)*c^4*x^4 + 2710*a^3*sqrt(-c)*c^4*x^3 - 1866*a^2*sqrt(-c)*c^4*x^2 - 977*a*sqrt(-c)*c^4*x + 5419*sqrt(-c)*c^4)*sqrt(a*x + 1)/a","A",0
227,1,83,0,0.333355," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(35 \, a^{4} \sqrt{-c} c^{3} x^{4} - 130 \, a^{3} \sqrt{-c} c^{3} x^{3} + 156 \, a^{2} \sqrt{-c} c^{3} x^{2} + 2 \, a \sqrt{-c} c^{3} x - 319 \, \sqrt{-c} c^{3}\right)} \sqrt{a x + 1}}{315 \, a}"," ",0,"-2/315*(35*a^4*sqrt(-c)*c^3*x^4 - 130*a^3*sqrt(-c)*c^3*x^3 + 156*a^2*sqrt(-c)*c^3*x^2 + 2*a*sqrt(-c)*c^3*x - 319*sqrt(-c)*c^3)*sqrt(a*x + 1)/a","A",0
228,1,67,0,0.326273," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15 \, a^{3} \sqrt{-c} c^{2} x^{3} - 39 \, a^{2} \sqrt{-c} c^{2} x^{2} + 17 \, a \sqrt{-c} c^{2} x + 71 \, \sqrt{-c} c^{2}\right)} \sqrt{a x + 1}}{105 \, a}"," ",0,"2/105*(15*a^3*sqrt(-c)*c^2*x^3 - 39*a^2*sqrt(-c)*c^2*x^2 + 17*a*sqrt(-c)*c^2*x + 71*sqrt(-c)*c^2)*sqrt(a*x + 1)/a","A",0
229,1,45,0,0.327494," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, a^{2} \sqrt{-c} c x^{2} - 4 \, a \sqrt{-c} c x - 7 \, \sqrt{-c} c\right)} \sqrt{a x + 1}}{15 \, a}"," ",0,"-2/15*(3*a^2*sqrt(-c)*c*x^2 - 4*a*sqrt(-c)*c*x - 7*sqrt(-c)*c)*sqrt(a*x + 1)/a","A",0
230,1,26,0,0.330452," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a \sqrt{-c} x + \sqrt{-c}\right)} \sqrt{a x + 1}}{3 \, a}"," ",0,"2/3*(a*sqrt(-c)*x + sqrt(-c))*sqrt(a*x + 1)/a","A",0
231,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/(sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
232,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a c x + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a*c*x + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
233,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a c x + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a*c*x + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
234,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a c x + c\right)}^{\frac{7}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a*c*x + c)^(7/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
235,1,32,0,0.309613," ","integrate(1/(a*x-1)*(a*x+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
236,1,32,0,0.306833," ","integrate(1/(a*x-1)*(a*x+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
237,1,32,0,0.303450," ","integrate(1/(a*x-1)*(a*x+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
238,1,30,0,0.314472," ","integrate(1/(a*x-1)*(a*x+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
239,1,30,0,0.306230," ","integrate(1/(a*x-1)*(a*x+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
240,1,26,0,0.303561," ","integrate(1/(a*x-1)*(a*x+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
241,1,24,0,0.304918," ","integrate(1/(a*x-1)*(a*x+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
242,1,26,0,0.319177," ","integrate(1/(a*x-1)*(a*x+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
243,1,106,0,0.350094," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(9/2),x, algorithm=""maxima"")","\frac{2 \, {\left(105 \, a^{5} \sqrt{-c} c^{4} x^{5} - 455 \, a^{4} \sqrt{-c} c^{4} x^{4} + 650 \, a^{3} \sqrt{-c} c^{4} x^{3} - 78 \, a^{2} \sqrt{-c} c^{4} x^{2} - 755 \, a \sqrt{-c} c^{4} x + 533 \, \sqrt{-c} c^{4}\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}{1155 \, {\left(a x - 1\right)} a}"," ",0,"2/1155*(105*a^5*sqrt(-c)*c^4*x^5 - 455*a^4*sqrt(-c)*c^4*x^4 + 650*a^3*sqrt(-c)*c^4*x^3 - 78*a^2*sqrt(-c)*c^4*x^2 - 755*a*sqrt(-c)*c^4*x + 533*sqrt(-c)*c^4)*(a*x + 1)^(3/2)/((a*x - 1)*a)","A",0
244,1,90,0,0.337262," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(35 \, a^{4} \sqrt{-c} c^{3} x^{4} - 110 \, a^{3} \sqrt{-c} c^{3} x^{3} + 72 \, a^{2} \sqrt{-c} c^{3} x^{2} + 110 \, a \sqrt{-c} c^{3} x - 107 \, \sqrt{-c} c^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}{315 \, {\left(a x - 1\right)} a}"," ",0,"-2/315*(35*a^4*sqrt(-c)*c^3*x^4 - 110*a^3*sqrt(-c)*c^3*x^3 + 72*a^2*sqrt(-c)*c^3*x^2 + 110*a*sqrt(-c)*c^3*x - 107*sqrt(-c)*c^3)*(a*x + 1)^(3/2)/((a*x - 1)*a)","A",0
245,1,74,0,0.341925," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a^{3} \sqrt{-c} c^{2} x^{3} - 9 \, a^{2} \sqrt{-c} c^{2} x^{2} - 5 \, a \sqrt{-c} c^{2} x + 9 \, \sqrt{-c} c^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}{35 \, {\left(a x - 1\right)} a}"," ",0,"2/35*(5*a^3*sqrt(-c)*c^2*x^3 - 9*a^2*sqrt(-c)*c^2*x^2 - 5*a*sqrt(-c)*c^2*x + 9*sqrt(-c)*c^2)*(a*x + 1)^(3/2)/((a*x - 1)*a)","A",0
246,1,41,0,0.343213," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{2} \sqrt{-c} c x^{2} - \sqrt{-c} c\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}{5 \, {\left(a x - 1\right)} a}"," ",0,"-2/5*(a^2*sqrt(-c)*c*x^2 - sqrt(-c)*c)*(a*x + 1)^(3/2)/((a*x - 1)*a)","A",0
247,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
248,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
249,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a c x + c\right)}^{\frac{3}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((-a*c*x + c)^(3/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
250,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a c x + c\right)}^{\frac{5}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((-a*c*x + c)^(5/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
251,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a c x + c\right)}^{\frac{7}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((-a*c*x + c)^(7/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
252,1,128,0,0.332626," ","integrate((-a*c*x+c)^(9/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(63 \, a^{6} \sqrt{-c} c^{4} x^{6} - 392 \, a^{5} \sqrt{-c} c^{4} x^{5} + 1055 \, a^{4} \sqrt{-c} c^{4} x^{4} - 1688 \, a^{3} \sqrt{-c} c^{4} x^{3} + 2221 \, a^{2} \sqrt{-c} c^{4} x^{2} - 6112 \, a \sqrt{-c} c^{4} x - 11531 \, \sqrt{-c} c^{4}\right)} {\left(a x - 1\right)}}{693 \, {\left(a^{2} x - a\right)} \sqrt{a x + 1}}"," ",0,"2/693*(63*a^6*sqrt(-c)*c^4*x^6 - 392*a^5*sqrt(-c)*c^4*x^5 + 1055*a^4*sqrt(-c)*c^4*x^4 - 1688*a^3*sqrt(-c)*c^4*x^3 + 2221*a^2*sqrt(-c)*c^4*x^2 - 6112*a*sqrt(-c)*c^4*x - 11531*sqrt(-c)*c^4)*(a*x - 1)/((a^2*x - a)*sqrt(a*x + 1))","A",0
253,1,112,0,0.337222," ","integrate((-a*c*x+c)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(35 \, a^{5} \sqrt{-c} c^{3} x^{5} - 185 \, a^{4} \sqrt{-c} c^{3} x^{4} + 422 \, a^{3} \sqrt{-c} c^{3} x^{3} - 634 \, a^{2} \sqrt{-c} c^{3} x^{2} + 1591 \, a \sqrt{-c} c^{3} x + 2867 \, \sqrt{-c} c^{3}\right)} {\left(a x - 1\right)}}{315 \, {\left(a^{2} x - a\right)} \sqrt{a x + 1}}"," ",0,"-2/315*(35*a^5*sqrt(-c)*c^3*x^5 - 185*a^4*sqrt(-c)*c^3*x^4 + 422*a^3*sqrt(-c)*c^3*x^3 - 634*a^2*sqrt(-c)*c^3*x^2 + 1591*a*sqrt(-c)*c^3*x + 2867*sqrt(-c)*c^3)*(a*x - 1)/((a^2*x - a)*sqrt(a*x + 1))","A",0
254,1,96,0,0.335703," ","integrate((-a*c*x+c)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a^{4} \sqrt{-c} c^{2} x^{4} - 22 \, a^{3} \sqrt{-c} c^{2} x^{3} + 44 \, a^{2} \sqrt{-c} c^{2} x^{2} - 106 \, a \sqrt{-c} c^{2} x - 177 \, \sqrt{-c} c^{2}\right)} {\left(a x - 1\right)}}{35 \, {\left(a^{2} x - a\right)} \sqrt{a x + 1}}"," ",0,"2/35*(5*a^4*sqrt(-c)*c^2*x^4 - 22*a^3*sqrt(-c)*c^2*x^3 + 44*a^2*sqrt(-c)*c^2*x^2 - 106*a*sqrt(-c)*c^2*x - 177*sqrt(-c)*c^2)*(a*x - 1)/((a^2*x - a)*sqrt(a*x + 1))","A",0
255,1,72,0,0.332911," ","integrate((-a*c*x+c)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, a^{3} \sqrt{-c} c x^{3} - 11 \, a^{2} \sqrt{-c} c x^{2} + 29 \, a \sqrt{-c} c x + 43 \, \sqrt{-c} c\right)} {\left(a x - 1\right)}}{15 \, {\left(a^{2} x - a\right)} \sqrt{a x + 1}}"," ",0,"-2/15*(3*a^3*sqrt(-c)*c*x^3 - 11*a^2*sqrt(-c)*c*x^2 + 29*a*sqrt(-c)*c*x + 43*sqrt(-c)*c)*(a*x - 1)/((a^2*x - a)*sqrt(a*x + 1))","A",0
256,1,54,0,0.329710," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{2} \sqrt{-c} x^{2} - 4 \, a \sqrt{-c} x - 5 \, \sqrt{-c}\right)} {\left(a x - 1\right)}}{3 \, {\left(a^{2} x - a\right)} \sqrt{a x + 1}}"," ",0,"2/3*(a^2*sqrt(-c)*x^2 - 4*a*sqrt(-c)*x - 5*sqrt(-c))*(a*x - 1)/((a^2*x - a)*sqrt(a*x + 1))","A",0
257,1,29,0,0.328106," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a \sqrt{-c} x + \sqrt{-c}\right)}}{\sqrt{a x + 1} a c}"," ",0,"-2*(a*sqrt(-c)*x + sqrt(-c))/(sqrt(a*x + 1)*a*c)","A",0
258,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(-a c x + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(-a*c*x + c)^(3/2), x)","F",0
259,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(-a c x + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(-a*c*x + c)^(5/2), x)","F",0
260,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(-a c x + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(-a*c*x + c)^(7/2), x)","F",0
261,1,123,0,0.404653," ","integrate((-a*c*x+c)^(7/2)*(a*x-1)/(a*x+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
262,1,109,0,0.405822," ","integrate((-a*c*x+c)^(5/2)*(a*x-1)/(a*x+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
263,1,95,0,0.405042," ","integrate((-a*c*x+c)^(3/2)*(a*x-1)/(a*x+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
264,1,79,0,0.405524," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+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
265,1,68,0,0.409615," ","integrate((a*x-1)/(a*x+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
266,1,52,0,0.405294," ","integrate((a*x-1)/(a*x+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
267,1,71,0,0.415801," ","integrate((a*x-1)/(a*x+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
268,1,81,0,0.406034," ","integrate((a*x-1)/(a*x+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
269,1,101,0,0.413765," ","integrate((a*x-1)/(a*x+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
270,1,152,0,0.341837," ","integrate((-a*c*x+c)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(21 \, a^{7} \sqrt{-c} c^{4} x^{7} - 161 \, a^{6} \sqrt{-c} c^{4} x^{6} + 573 \, a^{5} \sqrt{-c} c^{4} x^{5} - 1377 \, a^{4} \sqrt{-c} c^{4} x^{4} + 3287 \, a^{3} \sqrt{-c} c^{4} x^{3} - 17643 \, a^{2} \sqrt{-c} c^{4} x^{2} - 69417 \, a \sqrt{-c} c^{4} x - 46355 \, \sqrt{-c} c^{4}\right)} {\left(a x - 1\right)}^{2}}{231 \, {\left(a^{3} x^{2} - 2 \, a^{2} x + a\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}"," ",0,"2/231*(21*a^7*sqrt(-c)*c^4*x^7 - 161*a^6*sqrt(-c)*c^4*x^6 + 573*a^5*sqrt(-c)*c^4*x^5 - 1377*a^4*sqrt(-c)*c^4*x^4 + 3287*a^3*sqrt(-c)*c^4*x^3 - 17643*a^2*sqrt(-c)*c^4*x^2 - 69417*a*sqrt(-c)*c^4*x - 46355*sqrt(-c)*c^4)*(a*x - 1)^2/((a^3*x^2 - 2*a^2*x + a)*(a*x + 1)^(3/2))","A",0
271,1,136,0,0.339839," ","integrate((-a*c*x+c)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(7 \, a^{6} \sqrt{-c} c^{3} x^{6} - 48 \, a^{5} \sqrt{-c} c^{3} x^{5} + 159 \, a^{4} \sqrt{-c} c^{3} x^{4} - 424 \, a^{3} \sqrt{-c} c^{3} x^{3} + 2229 \, a^{2} \sqrt{-c} c^{3} x^{2} + 8664 \, a \sqrt{-c} c^{3} x + 5797 \, \sqrt{-c} c^{3}\right)} {\left(a x - 1\right)}^{2}}{63 \, {\left(a^{3} x^{2} - 2 \, a^{2} x + a\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}"," ",0,"-2/63*(7*a^6*sqrt(-c)*c^3*x^6 - 48*a^5*sqrt(-c)*c^3*x^5 + 159*a^4*sqrt(-c)*c^3*x^4 - 424*a^3*sqrt(-c)*c^3*x^3 + 2229*a^2*sqrt(-c)*c^3*x^2 + 8664*a*sqrt(-c)*c^3*x + 5797*sqrt(-c)*c^3)*(a*x - 1)^2/((a^3*x^2 - 2*a^2*x + a)*(a*x + 1)^(3/2))","A",0
272,1,120,0,0.347411," ","integrate((-a*c*x+c)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a^{5} \sqrt{-c} c^{2} x^{5} - 31 \, a^{4} \sqrt{-c} c^{2} x^{4} + 106 \, a^{3} \sqrt{-c} c^{2} x^{3} - 566 \, a^{2} \sqrt{-c} c^{2} x^{2} - 2159 \, a \sqrt{-c} c^{2} x - 1451 \, \sqrt{-c} c^{2}\right)} {\left(a x - 1\right)}^{2}}{35 \, {\left(a^{3} x^{2} - 2 \, a^{2} x + a\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}"," ",0,"2/35*(5*a^5*sqrt(-c)*c^2*x^5 - 31*a^4*sqrt(-c)*c^2*x^4 + 106*a^3*sqrt(-c)*c^2*x^3 - 566*a^2*sqrt(-c)*c^2*x^2 - 2159*a*sqrt(-c)*c^2*x - 1451*sqrt(-c)*c^2)*(a*x - 1)^2/((a^3*x^2 - 2*a^2*x + a)*(a*x + 1)^(3/2))","A",0
273,1,93,0,0.339937," ","integrate((-a*c*x+c)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{4} \sqrt{-c} c x^{4} - 6 \, a^{3} \sqrt{-c} c x^{3} + 36 \, a^{2} \sqrt{-c} c x^{2} + 134 \, a \sqrt{-c} c x + 91 \, \sqrt{-c} c\right)} {\left(a x - 1\right)}^{2}}{5 \, {\left(a^{3} x^{2} - 2 \, a^{2} x + a\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}"," ",0,"-2/5*(a^4*sqrt(-c)*c*x^4 - 6*a^3*sqrt(-c)*c*x^3 + 36*a^2*sqrt(-c)*c*x^2 + 134*a*sqrt(-c)*c*x + 91*sqrt(-c)*c)*(a*x - 1)^2/((a^3*x^2 - 2*a^2*x + a)*(a*x + 1)^(3/2))","A",0
274,1,75,0,0.331612," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{3} \sqrt{-c} x^{3} - 9 \, a^{2} \sqrt{-c} x^{2} - 33 \, a \sqrt{-c} x - 23 \, \sqrt{-c}\right)} {\left(a x - 1\right)}^{2}}{3 \, {\left(a^{3} x^{2} - 2 \, a^{2} x + a\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}"," ",0,"2/3*(a^3*sqrt(-c)*x^3 - 9*a^2*sqrt(-c)*x^2 - 33*a*sqrt(-c)*x - 23*sqrt(-c))*(a*x - 1)^2/((a^3*x^2 - 2*a^2*x + a)*(a*x + 1)^(3/2))","A",0
275,1,48,0,0.337914," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{2} x^{2} + 4 \, a x + 3\right)} {\left(a x - 1\right)}}{{\left(a^{2} \sqrt{-c} x - a \sqrt{-c}\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}"," ",0,"2*(a^2*x^2 + 4*a*x + 3)*(a*x - 1)/((a^2*sqrt(-c)*x - a*sqrt(-c))*(a*x + 1)^(3/2))","A",0
276,1,45,0,0.340324," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a \sqrt{-c} x + \sqrt{-c}\right)} {\left(a x - 1\right)}}{{\left(a^{2} c^{2} x - a c^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}"," ",0,"-2*(a*sqrt(-c)*x + sqrt(-c))*(a*x - 1)/((a^2*c^2*x - a*c^2)*(a*x + 1)^(3/2))","A",0
277,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(-a c x + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(-a*c*x + c)^(5/2), x)","F",0
278,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(-a c x + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(-a*c*x + c)^(7/2), x)","F",0
279,1,110,0,0.314304," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x),x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{2}} - 8 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{3}{2}} + 9 \, \sqrt{\frac{x - 1}{x + 1}}\right)}}{3 \, {\left(\frac{3 \, {\left(x - 1\right)}}{x + 1} - \frac{3 \, {\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{{\left(x - 1\right)}^{3}}{{\left(x + 1\right)}^{3}} - 1\right)}} + \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"-2/3*(3*((x - 1)/(x + 1))^(5/2) - 8*((x - 1)/(x + 1))^(3/2) + 9*sqrt((x - 1)/(x + 1)))/(3*(x - 1)/(x + 1) - 3*(x - 1)^2/(x + 1)^2 + (x - 1)^3/(x + 1)^3 - 1) + log(sqrt((x - 1)/(x + 1)) + 1) - log(sqrt((x - 1)/(x + 1)) - 1)","A",0
280,1,87,0,0.311595," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x),x, algorithm=""maxima"")","\frac{3 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{3}{2}} - 5 \, \sqrt{\frac{x - 1}{x + 1}}}{\frac{2 \, {\left(x - 1\right)}}{x + 1} - \frac{{\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} - 1} + \frac{3}{2} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \frac{3}{2} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"(3*((x - 1)/(x + 1))^(3/2) - 5*sqrt((x - 1)/(x + 1)))/(2*(x - 1)/(x + 1) - (x - 1)^2/(x + 1)^2 - 1) + 3/2*log(sqrt((x - 1)/(x + 1)) + 1) - 3/2*log(sqrt((x - 1)/(x + 1)) - 1)","A",0
281,1,50,0,0.310986," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)*x,x, algorithm=""maxima"")","\frac{8 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{3}{2}}}{3 \, {\left(\frac{3 \, {\left(x - 1\right)}}{x + 1} - \frac{3 \, {\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{{\left(x - 1\right)}^{3}}{{\left(x + 1\right)}^{3}} - 1\right)}}"," ",0,"8/3*((x - 1)/(x + 1))^(3/2)/(3*(x - 1)/(x + 1) - 3*(x - 1)^2/(x + 1)^2 + (x - 1)^3/(x + 1)^3 - 1)","B",0
282,1,83,0,0.319248," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x),x, algorithm=""maxima"")","\frac{\left(\frac{x - 1}{x + 1}\right)^{\frac{3}{2}} + \sqrt{\frac{x - 1}{x + 1}}}{\frac{2 \, {\left(x - 1\right)}}{x + 1} - \frac{{\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} - 1} + \frac{1}{2} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"(((x - 1)/(x + 1))^(3/2) + sqrt((x - 1)/(x + 1)))/(2*(x - 1)/(x + 1) - (x - 1)^2/(x + 1)^2 - 1) + 1/2*log(sqrt((x - 1)/(x + 1)) + 1) - 1/2*log(sqrt((x - 1)/(x + 1)) - 1)","B",0
283,1,138,0,0.311313," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^2,x, algorithm=""maxima"")","\frac{15 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{7}{2}} - 55 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{2}} + 73 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{3}{2}} - 49 \, \sqrt{\frac{x - 1}{x + 1}}}{4 \, {\left(\frac{4 \, {\left(x - 1\right)}}{x + 1} - \frac{6 \, {\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{4 \, {\left(x - 1\right)}^{3}}{{\left(x + 1\right)}^{3}} - \frac{{\left(x - 1\right)}^{4}}{{\left(x + 1\right)}^{4}} - 1\right)}} + \frac{15}{8} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \frac{15}{8} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"1/4*(15*((x - 1)/(x + 1))^(7/2) - 55*((x - 1)/(x + 1))^(5/2) + 73*((x - 1)/(x + 1))^(3/2) - 49*sqrt((x - 1)/(x + 1)))/(4*(x - 1)/(x + 1) - 6*(x - 1)^2/(x + 1)^2 + 4*(x - 1)^3/(x + 1)^3 - (x - 1)^4/(x + 1)^4 - 1) + 15/8*log(sqrt((x - 1)/(x + 1)) + 1) - 15/8*log(sqrt((x - 1)/(x + 1)) - 1)","A",0
284,1,112,0,0.316655," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x)^2,x, algorithm=""maxima"")","-\frac{15 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{2}} - 40 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{3}{2}} + 33 \, \sqrt{\frac{x - 1}{x + 1}}}{3 \, {\left(\frac{3 \, {\left(x - 1\right)}}{x + 1} - \frac{3 \, {\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{{\left(x - 1\right)}^{3}}{{\left(x + 1\right)}^{3}} - 1\right)}} + \frac{5}{2} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \frac{5}{2} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"-1/3*(15*((x - 1)/(x + 1))^(5/2) - 40*((x - 1)/(x + 1))^(3/2) + 33*sqrt((x - 1)/(x + 1)))/(3*(x - 1)/(x + 1) - 3*(x - 1)^2/(x + 1)^2 + (x - 1)^3/(x + 1)^3 - 1) + 5/2*log(sqrt((x - 1)/(x + 1)) + 1) - 5/2*log(sqrt((x - 1)/(x + 1)) - 1)","A",0
285,1,138,0,0.318457," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^2*x,x, algorithm=""maxima"")","-\frac{3 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{7}{2}} + 53 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{2}} - 11 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{3}{2}} + 3 \, \sqrt{\frac{x - 1}{x + 1}}}{12 \, {\left(\frac{4 \, {\left(x - 1\right)}}{x + 1} - \frac{6 \, {\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{4 \, {\left(x - 1\right)}^{3}}{{\left(x + 1\right)}^{3}} - \frac{{\left(x - 1\right)}^{4}}{{\left(x + 1\right)}^{4}} - 1\right)}} - \frac{1}{8} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) + \frac{1}{8} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"-1/12*(3*((x - 1)/(x + 1))^(7/2) + 53*((x - 1)/(x + 1))^(5/2) - 11*((x - 1)/(x + 1))^(3/2) + 3*sqrt((x - 1)/(x + 1)))/(4*(x - 1)/(x + 1) - 6*(x - 1)^2/(x + 1)^2 + 4*(x - 1)^3/(x + 1)^3 - (x - 1)^4/(x + 1)^4 - 1) - 1/8*log(sqrt((x - 1)/(x + 1)) + 1) + 1/8*log(sqrt((x - 1)/(x + 1)) - 1)","B",0
286,1,112,0,0.305791," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^2,x, algorithm=""maxima"")","-\frac{3 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{2}} + 8 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{3}{2}} - 3 \, \sqrt{\frac{x - 1}{x + 1}}}{3 \, {\left(\frac{3 \, {\left(x - 1\right)}}{x + 1} - \frac{3 \, {\left(x - 1\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{{\left(x - 1\right)}^{3}}{{\left(x + 1\right)}^{3}} - 1\right)}} + \frac{1}{2} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"-1/3*(3*((x - 1)/(x + 1))^(5/2) + 8*((x - 1)/(x + 1))^(3/2) - 3*sqrt((x - 1)/(x + 1)))/(3*(x - 1)/(x + 1) - 3*(x - 1)^2/(x + 1)^2 + (x - 1)^3/(x + 1)^3 - 1) + 1/2*log(sqrt((x - 1)/(x + 1)) + 1) - 1/2*log(sqrt((x - 1)/(x + 1)) - 1)","B",0
287,1,26,0,0.310643," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{\frac{x - 1}{x + 1}}}{\frac{x - 1}{x + 1} - 1}"," ",0,"-2*sqrt((x - 1)/(x + 1))/((x - 1)/(x + 1) - 1)","A",0
288,1,31,0,0.321183," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x),x, algorithm=""maxima"")","\log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"log(sqrt((x - 1)/(x + 1)) + 1) - log(sqrt((x - 1)/(x + 1)) - 1)","A",0
289,1,74,0,0.307991," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{2 \, {\left(x - 1\right)}}{x + 1} - 1\right)}}{\left(\frac{x - 1}{x + 1}\right)^{\frac{3}{2}} - \sqrt{\frac{x - 1}{x + 1}}} - 2 \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) + 2 \, \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"2*(2*(x - 1)/(x + 1) - 1)/(((x - 1)/(x + 1))^(3/2) - sqrt((x - 1)/(x + 1))) - 2*log(sqrt((x - 1)/(x + 1)) + 1) + 2*log(sqrt((x - 1)/(x + 1)) - 1)","A",0
290,1,44,0,0.308283," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x),x, algorithm=""maxima"")","\frac{2}{\sqrt{\frac{x - 1}{x + 1}}} - \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) + \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"2/sqrt((x - 1)/(x + 1)) - log(sqrt((x - 1)/(x + 1)) + 1) + log(sqrt((x - 1)/(x + 1)) - 1)","A",0
291,1,44,0,0.311584," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^2,x, algorithm=""maxima"")","-\sqrt{\frac{x - 1}{x + 1}} + \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"-sqrt((x - 1)/(x + 1)) + log(sqrt((x - 1)/(x + 1)) + 1) - log(sqrt((x - 1)/(x + 1)) - 1)","A",0
292,1,11,0,0.307575," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x)^2,x, algorithm=""maxima"")","\sqrt{\frac{x - 1}{x + 1}}"," ",0,"sqrt((x - 1)/(x + 1))","A",0
293,1,56,0,0.318724," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^2,x, algorithm=""maxima"")","-\frac{\frac{6 \, {\left(x - 1\right)}}{x + 1} + 1}{3 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{3}{2}}} + \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right)"," ",0,"-1/3*(6*(x - 1)/(x + 1) + 1)/((x - 1)/(x + 1))^(3/2) + log(sqrt((x - 1)/(x + 1)) + 1) - log(sqrt((x - 1)/(x + 1)) - 1)","A",0
294,1,13,0,0.309390," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x)^2,x, algorithm=""maxima"")","-\frac{1}{3 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{3}{2}}}"," ",0,"-1/3/((x - 1)/(x + 1))^(3/2)","A",0
295,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} x^{m}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*x^m/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
296,1,55,0,0.322739," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15 \, a^{3} \sqrt{-c} x^{3} + 3 \, a^{2} \sqrt{-c} x^{2} - 4 \, a \sqrt{-c} x + 8 \, \sqrt{-c}\right)} \sqrt{a x + 1}}{105 \, a^{3}}"," ",0,"2/105*(15*a^3*sqrt(-c)*x^3 + 3*a^2*sqrt(-c)*x^2 - 4*a*sqrt(-c)*x + 8*sqrt(-c))*sqrt(a*x + 1)/a^3","A",0
297,1,41,0,0.337492," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, a^{2} \sqrt{-c} x^{2} + a \sqrt{-c} x - 2 \, \sqrt{-c}\right)} \sqrt{a x + 1}}{15 \, a^{2}}"," ",0,"2/15*(3*a^2*sqrt(-c)*x^2 + a*sqrt(-c)*x - 2*sqrt(-c))*sqrt(a*x + 1)/a^2","A",0
298,1,26,0,0.341118," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a \sqrt{-c} x + \sqrt{-c}\right)} \sqrt{a x + 1}}{3 \, a}"," ",0,"2/3*(a*sqrt(-c)*x + sqrt(-c))*sqrt(a*x + 1)/a","A",0
299,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c}}{x \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)/(x*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
300,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c}}{x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)/(x^2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
301,1,74,0,0.325415," ","integrate(1/(a*x-1)*(a*x+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
302,1,60,0,0.313607," ","integrate(1/(a*x-1)*(a*x+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
303,1,44,0,0.314415," ","integrate(1/(a*x-1)*(a*x+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
304,1,30,0,0.315747," ","integrate(1/(a*x-1)*(a*x+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
305,1,49,0,0.399288," ","integrate(1/(a*x-1)*(a*x+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
306,1,62,0,0.418779," ","integrate(1/(a*x-1)*(a*x+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
307,1,103,0,0.618306," ","integrate(1/(a*x-1)*(a*x+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
308,1,134,0,1.079427," ","integrate(1/(a*x-1)*(a*x+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
309,1,163,0,0.451305," ","integrate(1/(a*x-1)*(a*x+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
310,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} x^{3}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*x^3/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
311,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} x^{2}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*x^2/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
312,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} x}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*x/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
313,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
314,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c}}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)/(x*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
315,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c}}{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)/(x^2*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
316,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c}}{x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)/(x^3*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
317,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c}}{x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)/(x^4*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
318,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c}}{x^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)/(x^5*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
319,1,27,0,0.317998," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^(3/2),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
320,1,22,0,1.028044," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x)^(3/2),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
321,1,22,0,0.990433," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^(3/2)*x,x, algorithm=""maxima"")","-\frac{1}{105} \, {\left(30 i \, x^{3} - 36 i \, x^{2} - 22 i \, x + 44 i\right)} \sqrt{x + 1}"," ",0,"-1/105*(30*I*x^3 - 36*I*x^2 - 22*I*x + 44*I)*sqrt(x + 1)","C",0
322,1,17,0,0.461398," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^(3/2),x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(6 i \, x^{2} - 8 i \, x - 14 i\right)} \sqrt{x + 1}"," ",0,"-1/15*(6*I*x^2 - 8*I*x - 14*I)*sqrt(x + 1)","C",0
323,1,20,0,0.456281," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^(1/2),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
324,1,15,0,0.889141," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x)^(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
325,1,17,0,1.276380," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1-x)^(1/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(6 i \, x^{2} + 2 i \, x - 4 i\right)} \sqrt{x + 1}"," ",0,"1/15*(6*I*x^2 + 2*I*x - 4*I)*sqrt(x + 1)","C",0
326,1,12,0,0.500391," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{x + 1} {\left(2 i \, x + 2 i\right)}"," ",0,"1/3*sqrt(x + 1)*(2*I*x + 2*I)","C",0
327,1,13,0,0.997077," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^(1/2),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
328,1,7,0,0.373900," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x)^(1/2),x, algorithm=""maxima"")","2 \, \sqrt{x - 1}"," ",0,"2*sqrt(x - 1)","A",0
329,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}\,{d x}"," ",0,"integrate(x/(sqrt(-x + 1)*sqrt((x - 1)/(x + 1))), x)","F",0
330,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}\,{d x}"," ",0,"integrate(1/(sqrt(-x + 1)*sqrt((x - 1)/(x + 1))), x)","F",0
331,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^(3/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(x + 1\right)}^{\frac{3}{2}} \sqrt{\frac{x - 1}{x + 1}}}\,{d x}"," ",0,"integrate(x/((x + 1)^(3/2)*sqrt((x - 1)/(x + 1))), x)","F",0
332,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(x + 1\right)}^{\frac{3}{2}} \sqrt{\frac{x - 1}{x + 1}}}\,{d x}"," ",0,"integrate(1/((x + 1)^(3/2)*sqrt((x - 1)/(x + 1))), x)","F",0
333,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^(3/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(-x + 1\right)}^{\frac{3}{2}} \sqrt{\frac{x - 1}{x + 1}}}\,{d x}"," ",0,"integrate(x/((-x + 1)^(3/2)*sqrt((x - 1)/(x + 1))), x)","F",0
334,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-x + 1\right)}^{\frac{3}{2}} \sqrt{\frac{x - 1}{x + 1}}}\,{d x}"," ",0,"integrate(1/((-x + 1)^(3/2)*sqrt((x - 1)/(x + 1))), x)","F",0
335,0,0,0,0.000000," ","integrate(x^m*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a c x + c} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*x^m*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
336,1,83,0,0.408506," ","integrate(x^2*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15 \, a^{4} \sqrt{-c} x^{4} - 24 \, a^{3} \sqrt{-c} x^{3} + 13 \, a^{2} \sqrt{-c} x^{2} - 52 \, a \sqrt{-c} x - 104 \, \sqrt{-c}\right)} {\left(a x - 1\right)}}{105 \, {\left(a^{4} x - a^{3}\right)} \sqrt{a x + 1}}"," ",0,"2/105*(15*a^4*sqrt(-c)*x^4 - 24*a^3*sqrt(-c)*x^3 + 13*a^2*sqrt(-c)*x^2 - 52*a*sqrt(-c)*x - 104*sqrt(-c))*(a*x - 1)/((a^4*x - a^3)*sqrt(a*x + 1))","A",0
337,1,69,0,0.338469," ","integrate(x*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{3} \sqrt{-c} x^{3} - 2 \, a^{2} \sqrt{-c} x^{2} + 3 \, a \sqrt{-c} x + 6 \, \sqrt{-c}\right)} {\left(a x - 1\right)}}{5 \, {\left(a^{3} x - a^{2}\right)} \sqrt{a x + 1}}"," ",0,"2/5*(a^3*sqrt(-c)*x^3 - 2*a^2*sqrt(-c)*x^2 + 3*a*sqrt(-c)*x + 6*sqrt(-c))*(a*x - 1)/((a^3*x - a^2)*sqrt(a*x + 1))","A",0
338,1,54,0,0.337961," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{2} \sqrt{-c} x^{2} - 4 \, a \sqrt{-c} x - 5 \, \sqrt{-c}\right)} {\left(a x - 1\right)}}{3 \, {\left(a^{2} x - a\right)} \sqrt{a x + 1}}"," ",0,"2/3*(a^2*sqrt(-c)*x^2 - 4*a*sqrt(-c)*x - 5*sqrt(-c))*(a*x - 1)/((a^2*x - a)*sqrt(a*x + 1))","A",0
339,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{x}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/x, x)","F",0
340,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/x^2, x)","F",0
341,1,123,0,0.406491," ","integrate(x^3*(-a*c*x+c)^(1/2)*(a*x-1)/(a*x+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
342,1,97,0,0.414664," ","integrate(x^2*(-a*c*x+c)^(1/2)*(a*x-1)/(a*x+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
343,1,95,0,0.419917," ","integrate(x*(-a*c*x+c)^(1/2)*(a*x-1)/(a*x+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
344,1,79,0,0.416970," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+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
345,1,98,0,0.413669," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+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
346,1,111,0,0.418734," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+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
347,1,152,0,0.421629," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+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
348,1,183,0,0.427243," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+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
349,1,212,0,0.418137," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+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
350,1,117,0,0.345442," ","integrate(x^3*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a^{6} \sqrt{-c} x^{6} - 15 \, a^{5} \sqrt{-c} x^{5} + 21 \, a^{4} \sqrt{-c} x^{4} - 41 \, a^{3} \sqrt{-c} x^{3} + 246 \, a^{2} \sqrt{-c} x^{2} + 984 \, a \sqrt{-c} x + 656 \, \sqrt{-c}\right)} {\left(a x - 1\right)}^{2}}{45 \, {\left(a^{6} x^{2} - 2 \, a^{5} x + a^{4}\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}"," ",0,"2/45*(5*a^6*sqrt(-c)*x^6 - 15*a^5*sqrt(-c)*x^5 + 21*a^4*sqrt(-c)*x^4 - 41*a^3*sqrt(-c)*x^3 + 246*a^2*sqrt(-c)*x^2 + 984*a*sqrt(-c)*x + 656*sqrt(-c))*(a*x - 1)^2/((a^6*x^2 - 2*a^5*x + a^4)*(a*x + 1)^(3/2))","A",0
351,1,104,0,0.345780," ","integrate(x^2*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15 \, a^{5} \sqrt{-c} x^{5} - 51 \, a^{4} \sqrt{-c} x^{4} + 101 \, a^{3} \sqrt{-c} x^{3} - 501 \, a^{2} \sqrt{-c} x^{2} - 2004 \, a \sqrt{-c} x - 1336 \, \sqrt{-c}\right)} {\left(a x - 1\right)}^{2}}{105 \, {\left(a^{5} x^{2} - 2 \, a^{4} x + a^{3}\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}"," ",0,"2/105*(15*a^5*sqrt(-c)*x^5 - 51*a^4*sqrt(-c)*x^4 + 101*a^3*sqrt(-c)*x^3 - 501*a^2*sqrt(-c)*x^2 - 2004*a*sqrt(-c)*x - 1336*sqrt(-c))*(a*x - 1)^2/((a^5*x^2 - 2*a^4*x + a^3)*(a*x + 1)^(3/2))","A",0
352,1,91,0,0.343573," ","integrate(x*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, a^{4} \sqrt{-c} x^{4} - 13 \, a^{3} \sqrt{-c} x^{3} + 63 \, a^{2} \sqrt{-c} x^{2} + 237 \, a \sqrt{-c} x + 158 \, \sqrt{-c}\right)} {\left(a x - 1\right)}^{2}}{15 \, {\left(a^{4} x^{2} - 2 \, a^{3} x + a^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}"," ",0,"2/15*(3*a^4*sqrt(-c)*x^4 - 13*a^3*sqrt(-c)*x^3 + 63*a^2*sqrt(-c)*x^2 + 237*a*sqrt(-c)*x + 158*sqrt(-c))*(a*x - 1)^2/((a^4*x^2 - 2*a^3*x + a^2)*(a*x + 1)^(3/2))","A",0
353,1,75,0,0.344087," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{3} \sqrt{-c} x^{3} - 9 \, a^{2} \sqrt{-c} x^{2} - 33 \, a \sqrt{-c} x - 23 \, \sqrt{-c}\right)} {\left(a x - 1\right)}^{2}}{3 \, {\left(a^{3} x^{2} - 2 \, a^{2} x + a\right)} {\left(a x + 1\right)}^{\frac{3}{2}}}"," ",0,"2/3*(a^3*sqrt(-c)*x^3 - 9*a^2*sqrt(-c)*x^2 - 33*a*sqrt(-c)*x - 23*sqrt(-c))*(a*x - 1)^2/((a^3*x^2 - 2*a^2*x + a)*(a*x + 1)^(3/2))","A",0
354,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(3/2)/x, x)","F",0
355,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^2, x)","F",0
356,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^3, x)","F",0
357,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^4, x)","F",0
358,0,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^5, x)","F",0
359,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(2+1/2*n),x, algorithm=""maxima"")","\int {\left(-a c x + c\right)}^{\frac{1}{2} \, n + 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(1/2*n + 2)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
360,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(1+1/2*n),x, algorithm=""maxima"")","\int {\left(-a c x + c\right)}^{\frac{1}{2} \, n + 1} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(1/2*n + 1)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
361,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(1/2*n),x, algorithm=""maxima"")","\int {\left(-a c x + c\right)}^{\frac{1}{2} \, n} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(1/2*n)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
362,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(-1+1/2*n),x, algorithm=""maxima"")","\int {\left(-a c x + c\right)}^{\frac{1}{2} \, n - 1} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(1/2*n - 1)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
363,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(-2+1/2*n),x, algorithm=""maxima"")","\int {\left(-a c x + c\right)}^{\frac{1}{2} \, n - 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(1/2*n - 2)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
364,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
365,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
366,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
367,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
368,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
369,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
370,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
371,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
372,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
373,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
374,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
375,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
376,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
377,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
378,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
379,1,224,0,0.405978," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{3 \, c^{4} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{9 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{9 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{21 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 17 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 37 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 15 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{2 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + a^{2}}\right)} a"," ",0,"1/3*(3*c^4*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 9*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 9*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - (21*c^4*((a*x - 1)/(a*x + 1))^(7/2) - 17*c^4*((a*x - 1)/(a*x + 1))^(5/2) - 37*c^4*((a*x - 1)/(a*x + 1))^(3/2) - 15*c^4*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - 2*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 + a^2))*a","B",0
380,1,201,0,0.415679," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^3,x, algorithm=""maxima"")","-{\left(\frac{c^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{2 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{2 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} + \frac{3 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 6 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 5 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} + a^{2}}\right)} a"," ",0,"-(c^3*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 2*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 2*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 + (3*c^3*((a*x - 1)/(a*x + 1))^(5/2) - 6*c^3*((a*x - 1)/(a*x + 1))^(3/2) - 5*c^3*sqrt((a*x - 1)/(a*x + 1)))/((a*x - 1)*a^2/(a*x + 1) - (a*x - 1)^2*a^2/(a*x + 1)^2 - (a*x - 1)^3*a^2/(a*x + 1)^3 + a^2))*a","B",0
381,1,125,0,0.404652," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^2,x, algorithm=""maxima"")","-{\left(\frac{4 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} + \frac{2 \, c^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)} a"," ",0,"-(4*c^2*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) + 2*c^2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)*a","B",0
382,1,66,0,0.401477," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x),x, algorithm=""maxima"")","-2 \, a {\left(\frac{c \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} + \frac{c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}}\right)}"," ",0,"-2*a*(c*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2/(a*x + 1) - a^2) + c*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2)","B",0
383,1,116,0,0.303671," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x),x, algorithm=""maxima"")","-2 \, a {\left(\frac{\frac{2 \, {\left(a x - 1\right)}}{a x + 1} - 1}{a^{2} c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - a^{2} c \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c}\right)}"," ",0,"-2*a*((2*(a*x - 1)/(a*x + 1) - 1)/(a^2*c*((a*x - 1)/(a*x + 1))^(3/2) - a^2*c*sqrt((a*x - 1)/(a*x + 1))) - log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) + log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c))","A",0
384,1,137,0,0.306133," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^2,x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{\frac{11 \, {\left(a x - 1\right)}}{a x + 1} - \frac{18 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}{a^{2} c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - a^{2} c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}} + \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} - \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{2}}\right)}"," ",0,"1/3*a*((11*(a*x - 1)/(a*x + 1) - 18*(a*x - 1)^2/(a*x + 1)^2 + 1)/(a^2*c^2*((a*x - 1)/(a*x + 1))^(5/2) - a^2*c^2*((a*x - 1)/(a*x + 1))^(3/2)) + 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) - 9*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^2))","A",0
385,1,153,0,0.307018," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^3,x, algorithm=""maxima"")","\frac{1}{30} \, a {\left(\frac{\frac{22 \, {\left(a x - 1\right)}}{a x + 1} + \frac{155 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - \frac{240 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 3}{a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}} + \frac{120 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{3}} - \frac{120 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{3}}\right)}"," ",0,"1/30*a*((22*(a*x - 1)/(a*x + 1) + 155*(a*x - 1)^2/(a*x + 1)^2 - 240*(a*x - 1)^3/(a*x + 1)^3 + 3)/(a^2*c^3*((a*x - 1)/(a*x + 1))^(7/2) - a^2*c^3*((a*x - 1)/(a*x + 1))^(5/2)) + 120*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^3) - 120*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^3))","A",0
386,1,169,0,0.302327," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^4,x, algorithm=""maxima"")","\frac{1}{420} \, a {\left(\frac{\frac{111 \, {\left(a x - 1\right)}}{a x + 1} + \frac{469 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{2765 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - \frac{4200 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} + 15}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}}} + \frac{2100 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} - \frac{2100 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{4}}\right)}"," ",0,"1/420*a*((111*(a*x - 1)/(a*x + 1) + 469*(a*x - 1)^2/(a*x + 1)^2 + 2765*(a*x - 1)^3/(a*x + 1)^3 - 4200*(a*x - 1)^4/(a*x + 1)^4 + 15)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(9/2) - a^2*c^4*((a*x - 1)/(a*x + 1))^(7/2)) + 2100*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) - 2100*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^4))","A",0
387,1,57,0,0.303282," ","integrate(1/(a*x-1)*(a*x+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
388,1,37,0,0.306788," ","integrate(1/(a*x-1)*(a*x+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
389,1,37,0,0.301755," ","integrate(1/(a*x-1)*(a*x+1)*(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
390,1,16,0,0.302283," ","integrate(1/(a*x-1)*(a*x+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
391,1,11,0,0.297468," ","integrate(1/(a*x-1)*(a*x+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
392,1,35,0,0.301399," ","integrate(1/(a*x-1)*(a*x+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
393,1,55,0,0.304242," ","integrate(1/(a*x-1)*(a*x+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
394,1,75,0,0.306446," ","integrate(1/(a*x-1)*(a*x+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
395,1,93,0,0.304930," ","integrate(1/(a*x-1)*(a*x+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
396,1,223,0,0.407801," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^4,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{9 \, c^{4} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{3 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{3 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 29 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 15 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{2 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + a^{2}}\right)} a"," ",0,"-1/3*(9*c^4*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 3*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - (3*c^4*((a*x - 1)/(a*x + 1))^(7/2) + c^4*((a*x - 1)/(a*x + 1))^(5/2) + 29*c^4*((a*x - 1)/(a*x + 1))^(3/2) + 15*c^4*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - 2*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 + a^2))*a","B",0
397,1,151,0,0.411079," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^3,x, algorithm=""maxima"")","-{\left(\frac{3 \, c^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{3 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 2 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 3 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} + a^{2}}\right)} a"," ",0,"-(3*c^3*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - (3*c^3*((a*x - 1)/(a*x + 1))^(5/2) + 2*c^3*((a*x - 1)/(a*x + 1))^(3/2) + 3*c^3*sqrt((a*x - 1)/(a*x + 1)))/((a*x - 1)*a^2/(a*x + 1) - (a*x - 1)^2*a^2/(a*x + 1)^2 - (a*x - 1)^3*a^2/(a*x + 1)^3 + a^2))*a","B",0
398,1,125,0,0.410320," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^2,x, algorithm=""maxima"")","-{\left(\frac{4 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{\frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} + \frac{2 \, c^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)} a"," ",0,"-(4*c^2*((a*x - 1)/(a*x + 1))^(3/2)/((a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) + 2*c^2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)*a","B",0
399,1,114,0,0.408216," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x),x, algorithm=""maxima"")","-2 \, a {\left(\frac{c \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} - \frac{c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"-2*a*(c*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2/(a*x + 1) - a^2) - c*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","B",0
400,1,133,0,0.318249," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x),x, algorithm=""maxima"")","\frac{2}{3} \, a {\left(\frac{\frac{8 \, {\left(a x - 1\right)}}{a x + 1} - \frac{12 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}{a^{2} c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - a^{2} c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}} + \frac{6 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{6 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c}\right)}"," ",0,"2/3*a*((8*(a*x - 1)/(a*x + 1) - 12*(a*x - 1)^2/(a*x + 1)^2 + 1)/(a^2*c*((a*x - 1)/(a*x + 1))^(5/2) - a^2*c*((a*x - 1)/(a*x + 1))^(3/2)) + 6*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - 6*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c))","A",0
401,1,153,0,0.318425," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^2,x, algorithm=""maxima"")","\frac{1}{15} \, a {\left(\frac{\frac{17 \, {\left(a x - 1\right)}}{a x + 1} + \frac{100 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - \frac{150 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 3}{a^{2} c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - a^{2} c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}} + \frac{75 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} - \frac{75 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{2}}\right)}"," ",0,"1/15*a*((17*(a*x - 1)/(a*x + 1) + 100*(a*x - 1)^2/(a*x + 1)^2 - 150*(a*x - 1)^3/(a*x + 1)^3 + 3)/(a^2*c^2*((a*x - 1)/(a*x + 1))^(7/2) - a^2*c^2*((a*x - 1)/(a*x + 1))^(5/2)) + 75*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) - 75*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^2))","A",0
402,1,169,0,0.311132," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^3,x, algorithm=""maxima"")","\frac{1}{14} \, a {\left(\frac{\frac{6 \, {\left(a x - 1\right)}}{a x + 1} + \frac{21 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{112 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - \frac{168 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} + 1}{a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}}} + \frac{84 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{3}} - \frac{84 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{3}}\right)}"," ",0,"1/14*a*((6*(a*x - 1)/(a*x + 1) + 21*(a*x - 1)^2/(a*x + 1)^2 + 112*(a*x - 1)^3/(a*x + 1)^3 - 168*(a*x - 1)^4/(a*x + 1)^4 + 1)/(a^2*c^3*((a*x - 1)/(a*x + 1))^(9/2) - a^2*c^3*((a*x - 1)/(a*x + 1))^(7/2)) + 84*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^3) - 84*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^3))","A",0
403,1,185,0,0.314593," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^4,x, algorithm=""maxima"")","\frac{1}{1260} \, a {\left(\frac{\frac{235 \, {\left(a x - 1\right)}}{a x + 1} + \frac{801 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{2289 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + \frac{11760 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} - \frac{17640 \, {\left(a x - 1\right)}^{5}}{{\left(a x + 1\right)}^{5}} + 35}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} - a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}}} + \frac{8820 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} - \frac{8820 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{4}}\right)}"," ",0,"1/1260*a*((235*(a*x - 1)/(a*x + 1) + 801*(a*x - 1)^2/(a*x + 1)^2 + 2289*(a*x - 1)^3/(a*x + 1)^3 + 11760*(a*x - 1)^4/(a*x + 1)^4 - 17640*(a*x - 1)^5/(a*x + 1)^5 + 35)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(11/2) - a^2*c^4*((a*x - 1)/(a*x + 1))^(9/2)) + 8820*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) - 8820*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^4))","A",0
404,1,59,0,0.308290," ","integrate(1/(a*x-1)^2*(a*x+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
405,1,31,0,0.305685," ","integrate(1/(a*x-1)^2*(a*x+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
406,1,34,0,0.309289," ","integrate(1/(a*x-1)^2*(a*x+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
407,1,27,0,0.313249," ","integrate(1/(a*x-1)^2*(a*x+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
408,1,24,0,0.305877," ","integrate(1/(a*x-1)^2*(a*x+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
409,1,49,0,0.304584," ","integrate(1/(a*x-1)^2*(a*x+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
410,1,75,0,0.310797," ","integrate(1/(a*x-1)^2*(a*x+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
411,1,93,0,0.311109," ","integrate(1/(a*x-1)^2*(a*x+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
412,1,113,0,0.306377," ","integrate(1/(a*x-1)^2*(a*x+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
413,1,223,0,0.412910," ","integrate((c-c/a/x)^4*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{75 \, c^{4} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{15 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{15 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} + \frac{87 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 61 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 55 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 45 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{2 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + a^{2}}\right)} a"," ",0,"1/3*(75*c^4*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 15*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 15*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 + (87*c^4*((a*x - 1)/(a*x + 1))^(7/2) + 61*c^4*((a*x - 1)/(a*x + 1))^(5/2) - 55*c^4*((a*x - 1)/(a*x + 1))^(3/2) - 45*c^4*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - 2*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 + a^2))*a","A",0
414,1,201,0,0.413871," ","integrate((c-c/a/x)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","{\left(\frac{13 \, c^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{4 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{4 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} + \frac{11 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 2 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 5 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} + a^{2}}\right)} a"," ",0,"(13*c^3*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 4*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 4*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 + (11*c^3*((a*x - 1)/(a*x + 1))^(5/2) + 2*c^3*((a*x - 1)/(a*x + 1))^(3/2) - 5*c^3*sqrt((a*x - 1)/(a*x + 1)))/((a*x - 1)*a^2/(a*x + 1) - (a*x - 1)^2*a^2/(a*x + 1)^2 - (a*x - 1)^3*a^2/(a*x + 1)^3 + a^2))*a","B",0
415,1,126,0,0.418417," ","integrate((c-c/a/x)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-{\left(\frac{4 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{\frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} - \frac{6 \, c^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)} a"," ",0,"-(4*c^2*((a*x - 1)/(a*x + 1))^(3/2)/((a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) - 6*c^2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)*a","A",0
416,1,114,0,0.410552," ","integrate((c-c/a/x)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-2 \, a {\left(\frac{c \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} - \frac{c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"-2*a*(c*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2/(a*x + 1) - a^2) - c*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","B",0
417,1,44,0,0.314667," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x),x, algorithm=""maxima"")","-\frac{2 \, a \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2} c}{a x + 1} - a^{2} c}"," ",0,"-2*a*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2*c/(a*x + 1) - a^2*c)","B",0
418,1,120,0,0.319050," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^2,x, algorithm=""maxima"")","-a {\left(\frac{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} - 1}{a^{2} c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - a^{2} c^{2} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{2}}\right)}"," ",0,"-a*((3*(a*x - 1)/(a*x + 1) - 1)/(a^2*c^2*((a*x - 1)/(a*x + 1))^(3/2) - a^2*c^2*sqrt((a*x - 1)/(a*x + 1))) - log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) + log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^2))","A",0
419,1,137,0,0.312358," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^3,x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{\frac{14 \, {\left(a x - 1\right)}}{a x + 1} - \frac{27 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}{a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}} + \frac{12 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{3}} - \frac{12 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{3}}\right)}"," ",0,"1/6*a*((14*(a*x - 1)/(a*x + 1) - 27*(a*x - 1)^2/(a*x + 1)^2 + 1)/(a^2*c^3*((a*x - 1)/(a*x + 1))^(5/2) - a^2*c^3*((a*x - 1)/(a*x + 1))^(3/2)) + 12*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^3) - 12*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^3))","A",0
420,1,153,0,0.308292," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^4,x, algorithm=""maxima"")","\frac{1}{20} \, a {\left(\frac{\frac{9 \, {\left(a x - 1\right)}}{a x + 1} + \frac{75 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - \frac{125 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 1}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}} + \frac{60 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} - \frac{60 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{4}}\right)}"," ",0,"1/20*a*((9*(a*x - 1)/(a*x + 1) + 75*(a*x - 1)^2/(a*x + 1)^2 - 125*(a*x - 1)^3/(a*x + 1)^3 + 1)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(7/2) - a^2*c^4*((a*x - 1)/(a*x + 1))^(5/2)) + 60*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) - 60*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^4))","A",0
421,1,60,0,0.303881," ","integrate((c-c/a/x)^4*(a*x-1)/(a*x+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
422,1,51,0,0.310692," ","integrate((c-c/a/x)^3*(a*x-1)/(a*x+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
423,1,40,0,0.309568," ","integrate((c-c/a/x)^2*(a*x-1)/(a*x+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
424,1,23,0,0.305815," ","integrate((c-c/a/x)*(a*x-1)/(a*x+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
425,1,20,0,0.308651," ","integrate((a*x-1)/(a*x+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
426,1,34,0,0.310158," ","integrate((a*x-1)/(a*x+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
427,1,53,0,0.303392," ","integrate((a*x-1)/(a*x+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
428,1,69,0,0.308701," ","integrate((a*x-1)/(a*x+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
429,1,246,0,0.431180," ","integrate((c-c/a/x)^4*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{273 \, c^{4} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{21 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{21 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{192 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2}} + \frac{153 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 91 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 169 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 123 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{2 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + a^{2}}\right)} a"," ",0,"-1/3*(273*c^4*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 21*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 21*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 192*c^4*sqrt((a*x - 1)/(a*x + 1))/a^2 + (153*c^4*((a*x - 1)/(a*x + 1))^(7/2) + 91*c^4*((a*x - 1)/(a*x + 1))^(5/2) - 169*c^4*((a*x - 1)/(a*x + 1))^(3/2) - 123*c^4*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - 2*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 + a^2))*a","A",0
430,1,225,0,0.407906," ","integrate((c-c/a/x)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-{\left(\frac{33 \, c^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{6 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{6 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{32 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2}} + \frac{11 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 6 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 13 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} + a^{2}}\right)} a"," ",0,"-(33*c^3*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 6*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 6*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 32*c^3*sqrt((a*x - 1)/(a*x + 1))/a^2 + (11*c^3*((a*x - 1)/(a*x + 1))^(5/2) - 6*c^3*((a*x - 1)/(a*x + 1))^(3/2) - 13*c^3*sqrt((a*x - 1)/(a*x + 1)))/((a*x - 1)*a^2/(a*x + 1) - (a*x - 1)^2*a^2/(a*x + 1)^2 - (a*x - 1)^3*a^2/(a*x + 1)^3 + a^2))*a","A",0
431,1,149,0,0.418074," ","integrate((c-c/a/x)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-{\left(\frac{4 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} + \frac{10 \, c^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{5 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{5 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{16 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2}}\right)} a"," ",0,"-(4*c^2*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) + 10*c^2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 5*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 5*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 16*c^2*sqrt((a*x - 1)/(a*x + 1))/a^2)*a","A",0
432,1,135,0,0.420625," ","integrate((c-c/a/x)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-2 \, a {\left(\frac{c \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2}}{a x + 1} - a^{2}} + \frac{c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{2 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{2 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{4 \, c \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2}}\right)}"," ",0,"-2*a*(c*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2/(a*x + 1) - a^2) + c*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 2*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 2*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 4*c*sqrt((a*x - 1)/(a*x + 1))/a^2)","A",0
433,1,120,0,0.305321," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x),x, algorithm=""maxima"")","-2 \, a {\left(\frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2} c}{a x + 1} - a^{2} c} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c} - \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c}\right)}"," ",0,"-2*a*(sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2*c/(a*x + 1) - a^2*c) + log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c) - sqrt((a*x - 1)/(a*x + 1))/(a^2*c))","A",0
434,1,125,0,0.304390," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^2,x, algorithm=""maxima"")","-a {\left(\frac{2 \, \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2} c^{2}}{a x + 1} - a^{2} c^{2}} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{2}} - \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2}}\right)}"," ",0,"-a*(2*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2*c^2/(a*x + 1) - a^2*c^2) + log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) - log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^2) - sqrt((a*x - 1)/(a*x + 1))/(a^2*c^2))","A",0
435,1,92,0,0.303909," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\frac{5 \, {\left(a x - 1\right)}}{a x + 1} - 1}{a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - a^{2} c^{3} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3}}\right)}"," ",0,"-1/2*a*((5*(a*x - 1)/(a*x + 1) - 1)/(a^2*c^3*((a*x - 1)/(a*x + 1))^(3/2) - a^2*c^3*sqrt((a*x - 1)/(a*x + 1))) - sqrt((a*x - 1)/(a*x + 1))/(a^2*c^3))","B",0
436,1,160,0,0.311309," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^4,x, algorithm=""maxima"")","\frac{1}{12} \, a {\left(\frac{\frac{17 \, {\left(a x - 1\right)}}{a x + 1} - \frac{42 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}} + \frac{12 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} - \frac{12 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{4}} + \frac{3 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{4}}\right)}"," ",0,"1/12*a*((17*(a*x - 1)/(a*x + 1) - 42*(a*x - 1)^2/(a*x + 1)^2 + 1)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(5/2) - a^2*c^4*((a*x - 1)/(a*x + 1))^(3/2)) + 12*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) - 12*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^4) + 3*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^4))","A",0
437,1,176,0,0.318638," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^5,x, algorithm=""maxima"")","\frac{1}{120} \, a {\left(\frac{\frac{32 \, {\left(a x - 1\right)}}{a x + 1} + \frac{310 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - \frac{585 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 3}{a^{2} c^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - a^{2} c^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}} + \frac{240 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{5}} - \frac{240 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{5}} + \frac{15 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{5}}\right)}"," ",0,"1/120*a*((32*(a*x - 1)/(a*x + 1) + 310*(a*x - 1)^2/(a*x + 1)^2 - 585*(a*x - 1)^3/(a*x + 1)^3 + 3)/(a^2*c^5*((a*x - 1)/(a*x + 1))^(7/2) - a^2*c^5*((a*x - 1)/(a*x + 1))^(5/2)) + 240*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^5) - 240*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^5) + 15*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^5))","A",0
438,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(9/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
439,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(7/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
440,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(5/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
441,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(3/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
442,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
443,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
444,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((c - c/(a*x))^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
445,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((c - c/(a*x))^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
446,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(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}}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^(9/2)/(a*x - 1), x)","F",0
447,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(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}}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^(7/2)/(a*x - 1), x)","F",0
448,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(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}}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^(5/2)/(a*x - 1), x)","F",0
449,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(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}}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^(3/2)/(a*x - 1), x)","F",0
450,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(a*x - 1), x)","F",0
451,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*sqrt(c - c/(a*x))), x)","F",0
452,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a x - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*(c - c/(a*x))^(3/2)), x)","F",0
453,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a x - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*(c - c/(a*x))^(5/2)), x)","F",0
454,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(7/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a x - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*(c - c/(a*x))^(7/2)), x)","F",0
455,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(9/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
456,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(7/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
457,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(5/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
458,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(3/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
459,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
460,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c - \frac{c}{a x}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c - c/(a*x))*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
461,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c - c/(a*x))^(3/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
462,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c - c/(a*x))^(5/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
463,0,0,0,0.000000," ","integrate((c-c/a/x)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(7/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
464,0,0,0,0.000000," ","integrate((c-c/a/x)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(5/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
465,0,0,0,0.000000," ","integrate((c-c/a/x)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(3/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
466,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
467,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/sqrt(c - c/(a*x)), x)","F",0
468,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(c - c/(a*x))^(3/2), x)","F",0
469,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(c - c/(a*x))^(5/2), x)","F",0
470,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(c - c/(a*x))^(7/2), x)","F",0
471,0,0,0,0.000000," ","integrate((c-c/a/x)^(7/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(c - c/(a*x))^(7/2)/(a*x + 1), x)","F",0
472,0,0,0,0.000000," ","integrate((c-c/a/x)^(5/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(c - c/(a*x))^(5/2)/(a*x + 1), x)","F",0
473,0,0,0,0.000000," ","integrate((c-c/a/x)^(3/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(c - c/(a*x))^(3/2)/(a*x + 1), x)","F",0
474,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a x}}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a*x))/(a*x + 1), x)","F",0
475,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{a x - 1}{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*sqrt(c - c/(a*x))), x)","F",0
476,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{a x - 1}{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*(c - c/(a*x))^(3/2)), x)","F",0
477,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{a x - 1}{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*(c - c/(a*x))^(5/2)), x)","F",0
478,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(7/2),x, algorithm=""maxima"")","\int \frac{a x - 1}{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*(c - c/(a*x))^(7/2)), x)","F",0
479,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(9/2),x, algorithm=""maxima"")","\int \frac{a x - 1}{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*(c - c/(a*x))^(9/2)), x)","F",0
480,0,0,0,0.000000," ","integrate((c-c/a/x)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(9/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
481,0,0,0,0.000000," ","integrate((c-c/a/x)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(7/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
482,0,0,0,0.000000," ","integrate((c-c/a/x)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(5/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
483,0,0,0,0.000000," ","integrate((c-c/a/x)^(3/2)*((a*x-1)/(a*x+1))^(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{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(3/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
484,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a x}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
485,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{\sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/sqrt(c - c/(a*x)), x)","F",0
486,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(c - c/(a*x))^(3/2), x)","F",0
487,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(c - c/(a*x))^(5/2), x)","F",0
488,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(7/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(c - \frac{c}{a x}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(c - c/(a*x))^(7/2), x)","F",0
489,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} x^{m}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^m/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
490,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} x^{2}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^2/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
491,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} x}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
492,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
493,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{x \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/(x*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
494,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/(x^2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
495,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{x^{3} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/(x^3*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
496,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{x^{4} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/(x^4*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
497,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{x^{5} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/(x^5*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
498,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x^3*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}} x^{3}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))*x^3/(a*x - 1), x)","F",0
499,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*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}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))*x^2/(a*x - 1), x)","F",0
500,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}} x}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))*x/(a*x - 1), x)","F",0
501,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(a*x - 1), x)","F",0
502,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x - 1\right)} x}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/((a*x - 1)*x), x)","F",0
503,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/((a*x - 1)*x^2), x)","F",0
504,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/((a*x - 1)*x^3), x)","F",0
505,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x - 1\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/((a*x - 1)*x^4), x)","F",0
506,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x - 1\right)} x^{5}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/((a*x - 1)*x^5), x)","F",0
507,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} x^{3}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^3/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
508,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} x^{2}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^2/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
509,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} x}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
510,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
511,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/(x*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
512,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/(x^2*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
513,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/(x^3*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
514,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/(x^4*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
515,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{x^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/(x^5*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
516,0,0,0,0.000000," ","integrate(x^m*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a x}} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^m*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
517,0,0,0,0.000000," ","integrate(x^2*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a x}} x^{2} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^2*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
518,0,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a x}} x \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
519,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
520,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}}{x}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1))/x, x)","F",0
521,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1))/x^2, x)","F",0
522,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1))/x^3, x)","F",0
523,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1))/x^4, x)","F",0
524,0,0,0,0.000000," ","integrate(x^3*(c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a x}} x^{3}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a*x))*x^3/(a*x + 1), x)","F",0
525,0,0,0,0.000000," ","integrate(x^2*(c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a x}} x^{2}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a*x))*x^2/(a*x + 1), x)","F",0
526,0,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a x}} x}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a*x))*x/(a*x + 1), x)","F",0
527,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a x}}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a*x))/(a*x + 1), x)","F",0
528,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x,x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a*x))/((a*x + 1)*x), x)","F",0
529,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a*x))/((a*x + 1)*x^2), x)","F",0
530,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x^{3}}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a*x))/((a*x + 1)*x^3), x)","F",0
531,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a*x))/((a*x + 1)*x^4), x)","F",0
532,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x^{5}}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a*x))/((a*x + 1)*x^5), x)","F",0
533,0,0,0,0.000000," ","integrate(x^3*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a x}} x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^3*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
534,0,0,0,0.000000," ","integrate(x^2*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a x}} x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^2*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
535,0,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a x}} x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
536,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a x}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
537,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*((a*x - 1)/(a*x + 1))^(3/2)/x, x)","F",0
538,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*((a*x - 1)/(a*x + 1))^(3/2)/x^2, x)","F",0
539,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*((a*x - 1)/(a*x + 1))^(3/2)/x^3, x)","F",0
540,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*((a*x - 1)/(a*x + 1))^(3/2)/x^4, x)","F",0
541,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a x}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*((a*x - 1)/(a*x + 1))^(3/2)/x^5, x)","F",0
542,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
543,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
544,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
545,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
546,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
547,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
548,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
549,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
550,0,0,0,0.000000," ","integrate(exp(2*p*arccoth(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
551,0,0,0,0.000000," ","integrate((c-c/a/x)^p/exp(2*p*arccoth(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
552,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^p,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{p}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^p/(a*x - 1), x)","F",0
553,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^p,x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{p}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^p/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
554,0,0,0,0.000000," ","integrate((c-c/a/x)^p*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a x}\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((c - c/(a*x))^p*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
555,0,0,0,0.000000," ","integrate((c-c/a/x)^p*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} {\left(c - \frac{c}{a x}\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(c - c/(a*x))^p/(a*x + 1), x)","F",0
556,1,415,0,0.319538," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\frac{1}{1152} \, {\left(\frac{315 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{315 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(315 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{17}{2}} - 2730 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{2}} + 10458 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} - 23202 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 32768 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 23202 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 10458 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 2730 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 315 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{9 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{36 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{84 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{126 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{126 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{84 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + \frac{36 \, {\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - \frac{9 \, {\left(a x - 1\right)}^{8} a^{2}}{{\left(a x + 1\right)}^{8}} + \frac{{\left(a x - 1\right)}^{9} a^{2}}{{\left(a x + 1\right)}^{9}} - a^{2}}\right)} a"," ",0,"1/1152*(315*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 315*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(315*c^4*((a*x - 1)/(a*x + 1))^(17/2) - 2730*c^4*((a*x - 1)/(a*x + 1))^(15/2) + 10458*c^4*((a*x - 1)/(a*x + 1))^(13/2) - 23202*c^4*((a*x - 1)/(a*x + 1))^(11/2) + 32768*c^4*((a*x - 1)/(a*x + 1))^(9/2) + 23202*c^4*((a*x - 1)/(a*x + 1))^(7/2) - 10458*c^4*((a*x - 1)/(a*x + 1))^(5/2) + 2730*c^4*((a*x - 1)/(a*x + 1))^(3/2) - 315*c^4*sqrt((a*x - 1)/(a*x + 1)))/(9*(a*x - 1)*a^2/(a*x + 1) - 36*(a*x - 1)^2*a^2/(a*x + 1)^2 + 84*(a*x - 1)^3*a^2/(a*x + 1)^3 - 126*(a*x - 1)^4*a^2/(a*x + 1)^4 + 126*(a*x - 1)^5*a^2/(a*x + 1)^5 - 84*(a*x - 1)^6*a^2/(a*x + 1)^6 + 36*(a*x - 1)^7*a^2/(a*x + 1)^7 - 9*(a*x - 1)^8*a^2/(a*x + 1)^8 + (a*x - 1)^9*a^2/(a*x + 1)^9 - a^2))*a","A",0
557,1,337,0,0.315484," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{336} \, {\left(\frac{105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(105 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} - 700 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 1981 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - 3072 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 1981 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 700 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 105 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{7 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{21 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{35 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{35 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{21 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{7 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + \frac{{\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - a^{2}}\right)} a"," ",0,"1/336*(105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(105*c^3*((a*x - 1)/(a*x + 1))^(13/2) - 700*c^3*((a*x - 1)/(a*x + 1))^(11/2) + 1981*c^3*((a*x - 1)/(a*x + 1))^(9/2) - 3072*c^3*((a*x - 1)/(a*x + 1))^(7/2) - 1981*c^3*((a*x - 1)/(a*x + 1))^(5/2) + 700*c^3*((a*x - 1)/(a*x + 1))^(3/2) - 105*c^3*sqrt((a*x - 1)/(a*x + 1)))/(7*(a*x - 1)*a^2/(a*x + 1) - 21*(a*x - 1)^2*a^2/(a*x + 1)^2 + 35*(a*x - 1)^3*a^2/(a*x + 1)^3 - 35*(a*x - 1)^4*a^2/(a*x + 1)^4 + 21*(a*x - 1)^5*a^2/(a*x + 1)^5 - 7*(a*x - 1)^6*a^2/(a*x + 1)^6 + (a*x - 1)^7*a^2/(a*x + 1)^7 - a^2))*a","A",0
558,1,259,0,0.312492," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{40} \, a {\left(\frac{15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(15 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - 70 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 128 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 70 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 15 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{5 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{10 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{10 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{{\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - a^{2}}\right)}"," ",0,"1/40*a*(15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(15*c^2*((a*x - 1)/(a*x + 1))^(9/2) - 70*c^2*((a*x - 1)/(a*x + 1))^(7/2) + 128*c^2*((a*x - 1)/(a*x + 1))^(5/2) + 70*c^2*((a*x - 1)/(a*x + 1))^(3/2) - 15*c^2*sqrt((a*x - 1)/(a*x + 1)))/(5*(a*x - 1)*a^2/(a*x + 1) - 10*(a*x - 1)^2*a^2/(a*x + 1)^2 + 10*(a*x - 1)^3*a^2/(a*x + 1)^3 - 5*(a*x - 1)^4*a^2/(a*x + 1)^4 + (a*x - 1)^5*a^2/(a*x + 1)^5 - a^2))","A",0
559,1,171,0,0.300845," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{2 \, {\left(3 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 8 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 3 \, c \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - a^{2}} - \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"-1/6*a*(2*(3*c*((a*x - 1)/(a*x + 1))^(5/2) - 8*c*((a*x - 1)/(a*x + 1))^(3/2) - 3*c*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)*a^2/(a*x + 1) - 3*(a*x - 1)^2*a^2/(a*x + 1)^2 + (a*x - 1)^3*a^2/(a*x + 1)^3 - a^2) - 3*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 3*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","A",0
560,1,22,0,0.299999," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{a c \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"1/(a*c*sqrt((a*x - 1)/(a*x + 1)))","A",0
561,1,65,0,0.304626," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{12} \, a {\left(\frac{3 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2}} + \frac{\frac{6 \, {\left(a x - 1\right)}}{a x + 1} - 1}{a^{2} c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\right)}"," ",0,"1/12*a*(3*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^2) + (6*(a*x - 1)/(a*x + 1) - 1)/(a^2*c^2*((a*x - 1)/(a*x + 1))^(3/2)))","A",0
562,1,99,0,0.313054," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{1}{240} \, a {\left(\frac{5 \, {\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 12 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} c^{3}} + \frac{\frac{20 \, {\left(a x - 1\right)}}{a x + 1} - \frac{90 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 3}{a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}}\right)}"," ",0,"-1/240*a*(5*(((a*x - 1)/(a*x + 1))^(3/2) - 12*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^3) + (20*(a*x - 1)/(a*x + 1) - 90*(a*x - 1)^2/(a*x + 1)^2 - 3)/(a^2*c^3*((a*x - 1)/(a*x + 1))^(5/2)))","A",0
563,1,132,0,0.307854," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\frac{1}{2240} \, a {\left(\frac{7 \, {\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 10 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 75 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} c^{4}} + \frac{\frac{42 \, {\left(a x - 1\right)}}{a x + 1} - \frac{175 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{700 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 5}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}}}\right)}"," ",0,"1/2240*a*(7*(((a*x - 1)/(a*x + 1))^(5/2) - 10*((a*x - 1)/(a*x + 1))^(3/2) + 75*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^4) + (42*(a*x - 1)/(a*x + 1) - 175*(a*x - 1)^2/(a*x + 1)^2 + 700*(a*x - 1)^3/(a*x + 1)^3 - 5)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(7/2)))","A",0
564,1,113,0,0.310656," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^5,x, algorithm=""maxima"")","-\frac{1}{11} \, a^{10} c^{5} x^{11} - \frac{1}{5} \, a^{9} c^{5} x^{10} + \frac{1}{3} \, a^{8} c^{5} x^{9} + a^{7} c^{5} x^{8} - \frac{2}{7} \, a^{6} c^{5} x^{7} - 2 \, a^{5} c^{5} x^{6} - \frac{2}{5} \, a^{4} c^{5} x^{5} + 2 \, a^{3} c^{5} x^{4} + a^{2} c^{5} x^{3} - a c^{5} x^{2} - c^{5} x"," ",0,"-1/11*a^10*c^5*x^11 - 1/5*a^9*c^5*x^10 + 1/3*a^8*c^5*x^9 + a^7*c^5*x^8 - 2/7*a^6*c^5*x^7 - 2*a^5*c^5*x^6 - 2/5*a^4*c^5*x^5 + 2*a^3*c^5*x^4 + a^2*c^5*x^3 - a*c^5*x^2 - c^5*x","A",0
565,1,82,0,0.306468," ","integrate(1/(a*x-1)*(a*x+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
566,1,70,0,0.302728," ","integrate(1/(a*x-1)*(a*x+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
567,1,38,0,0.303811," ","integrate(1/(a*x-1)*(a*x+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
568,1,21,0,0.310130," ","integrate(1/(a*x-1)*(a*x+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
569,1,13,0,0.296384," ","integrate(1/(a*x-1)*(a*x+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
570,1,63,0,0.307075," ","integrate(1/(a*x-1)*(a*x+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
571,1,91,0,0.306443," ","integrate(1/(a*x-1)*(a*x+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
572,1,140,0,0.304294," ","integrate(1/(a*x-1)*(a*x+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
573,1,415,0,0.318676," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","-\frac{1}{8064} \, {\left(\frac{3465 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3465 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(3465 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{17}{2}} - 30030 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{2}} + 115038 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} - 255222 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 360448 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - 334602 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 115038 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 30030 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 3465 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{9 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{36 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{84 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{126 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{126 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{84 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + \frac{36 \, {\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - \frac{9 \, {\left(a x - 1\right)}^{8} a^{2}}{{\left(a x + 1\right)}^{8}} + \frac{{\left(a x - 1\right)}^{9} a^{2}}{{\left(a x + 1\right)}^{9}} - a^{2}}\right)} a"," ",0,"-1/8064*(3465*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3465*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(3465*c^4*((a*x - 1)/(a*x + 1))^(17/2) - 30030*c^4*((a*x - 1)/(a*x + 1))^(15/2) + 115038*c^4*((a*x - 1)/(a*x + 1))^(13/2) - 255222*c^4*((a*x - 1)/(a*x + 1))^(11/2) + 360448*c^4*((a*x - 1)/(a*x + 1))^(9/2) - 334602*c^4*((a*x - 1)/(a*x + 1))^(7/2) - 115038*c^4*((a*x - 1)/(a*x + 1))^(5/2) + 30030*c^4*((a*x - 1)/(a*x + 1))^(3/2) - 3465*c^4*sqrt((a*x - 1)/(a*x + 1)))/(9*(a*x - 1)*a^2/(a*x + 1) - 36*(a*x - 1)^2*a^2/(a*x + 1)^2 + 84*(a*x - 1)^3*a^2/(a*x + 1)^3 - 126*(a*x - 1)^4*a^2/(a*x + 1)^4 + 126*(a*x - 1)^5*a^2/(a*x + 1)^5 - 84*(a*x - 1)^6*a^2/(a*x + 1)^6 + 36*(a*x - 1)^7*a^2/(a*x + 1)^7 - 9*(a*x - 1)^8*a^2/(a*x + 1)^8 + (a*x - 1)^9*a^2/(a*x + 1)^9 - a^2))*a","A",0
574,1,337,0,0.318642," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{1}{560} \, {\left(\frac{315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(315 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} - 2100 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 5943 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - 9216 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 8393 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 2100 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 315 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{7 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{21 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{35 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{35 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{21 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{7 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + \frac{{\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - a^{2}}\right)} a"," ",0,"-1/560*(315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(315*c^3*((a*x - 1)/(a*x + 1))^(13/2) - 2100*c^3*((a*x - 1)/(a*x + 1))^(11/2) + 5943*c^3*((a*x - 1)/(a*x + 1))^(9/2) - 9216*c^3*((a*x - 1)/(a*x + 1))^(7/2) + 8393*c^3*((a*x - 1)/(a*x + 1))^(5/2) + 2100*c^3*((a*x - 1)/(a*x + 1))^(3/2) - 315*c^3*sqrt((a*x - 1)/(a*x + 1)))/(7*(a*x - 1)*a^2/(a*x + 1) - 21*(a*x - 1)^2*a^2/(a*x + 1)^2 + 35*(a*x - 1)^3*a^2/(a*x + 1)^3 - 35*(a*x - 1)^4*a^2/(a*x + 1)^4 + 21*(a*x - 1)^5*a^2/(a*x + 1)^5 - 7*(a*x - 1)^6*a^2/(a*x + 1)^6 + (a*x - 1)^7*a^2/(a*x + 1)^7 - a^2))*a","A",0
575,1,259,0,0.314562," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{120} \, a {\left(\frac{105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(105 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - 490 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 896 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 790 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 105 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{5 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{10 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{10 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{{\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - a^{2}}\right)}"," ",0,"-1/120*a*(105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(105*c^2*((a*x - 1)/(a*x + 1))^(9/2) - 490*c^2*((a*x - 1)/(a*x + 1))^(7/2) + 896*c^2*((a*x - 1)/(a*x + 1))^(5/2) - 790*c^2*((a*x - 1)/(a*x + 1))^(3/2) - 105*c^2*sqrt((a*x - 1)/(a*x + 1)))/(5*(a*x - 1)*a^2/(a*x + 1) - 10*(a*x - 1)^2*a^2/(a*x + 1)^2 + 10*(a*x - 1)^3*a^2/(a*x + 1)^3 - 5*(a*x - 1)^4*a^2/(a*x + 1)^4 + (a*x - 1)^5*a^2/(a*x + 1)^5 - a^2))","A",0
576,1,171,0,0.301415," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{2 \, {\left(15 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 40 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 33 \, c \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - a^{2}} - \frac{15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"1/6*a*(2*(15*c*((a*x - 1)/(a*x + 1))^(5/2) - 40*c*((a*x - 1)/(a*x + 1))^(3/2) + 33*c*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)*a^2/(a*x + 1) - 3*(a*x - 1)^2*a^2/(a*x + 1)^2 + (a*x - 1)^3*a^2/(a*x + 1)^3 - a^2) - 15*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 15*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","A",0
577,1,23,0,0.302144," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{3 \, a c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}"," ",0,"1/3/(a*c*((a*x - 1)/(a*x + 1))^(3/2))","A",0
578,1,55,0,0.299230," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{\frac{10 \, {\left(a x - 1\right)}}{a x + 1} - \frac{15 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 3}{60 \, a c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}}"," ",0,"1/60*(10*(a*x - 1)/(a*x + 1) - 15*(a*x - 1)^2/(a*x + 1)^2 - 3)/(a*c^2*((a*x - 1)/(a*x + 1))^(5/2))","A",0
579,1,97,0,0.300884," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{1}{560} \, a {\left(\frac{35 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3}} + \frac{\frac{28 \, {\left(a x - 1\right)}}{a x + 1} - \frac{70 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{140 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 5}{a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}}}\right)}"," ",0,"-1/560*a*(35*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^3) + (28*(a*x - 1)/(a*x + 1) - 70*(a*x - 1)^2/(a*x + 1)^2 + 140*(a*x - 1)^3/(a*x + 1)^3 - 5)/(a^2*c^3*((a*x - 1)/(a*x + 1))^(7/2)))","A",0
580,1,131,0,0.306509," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\frac{1}{4032} \, a {\left(\frac{21 \, {\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 18 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} c^{4}} + \frac{\frac{54 \, {\left(a x - 1\right)}}{a x + 1} - \frac{189 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{420 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - \frac{945 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} - 7}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}}}\right)}"," ",0,"1/4032*a*(21*(((a*x - 1)/(a*x + 1))^(3/2) - 18*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^4) + (54*(a*x - 1)/(a*x + 1) - 189*(a*x - 1)^2/(a*x + 1)^2 + 420*(a*x - 1)^3/(a*x + 1)^3 - 945*(a*x - 1)^4/(a*x + 1)^4 - 7)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(9/2)))","A",0
581,1,101,0,0.301176," ","integrate(1/(a*x-1)^2*(a*x+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
582,1,92,0,0.301429," ","integrate(1/(a*x-1)^2*(a*x+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
583,1,59,0,0.304278," ","integrate(1/(a*x-1)^2*(a*x+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
584,1,47,0,0.297104," ","integrate(1/(a*x-1)^2*(a*x+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
585,1,33,0,0.298076," ","integrate(1/(a*x-1)^2*(a*x+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
586,1,19,0,0.305723," ","integrate(1/(a*x-1)^2*(a*x+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
587,1,41,0,0.300955," ","integrate(1/(a*x-1)^2*(a*x+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
588,1,102,0,0.303166," ","integrate(1/(a*x-1)^2*(a*x+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
589,1,130,0,0.321782," ","integrate(1/(a*x-1)^2*(a*x+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
590,1,415,0,0.331760," ","integrate((-a^2*c*x^2+c)^4*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{1}{1152} \, {\left(\frac{315 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{315 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(315 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{17}{2}} - 2730 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{2}} + 10458 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} - 23202 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} - 32768 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 23202 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 10458 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 2730 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 315 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{9 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{36 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{84 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{126 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{126 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{84 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + \frac{36 \, {\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - \frac{9 \, {\left(a x - 1\right)}^{8} a^{2}}{{\left(a x + 1\right)}^{8}} + \frac{{\left(a x - 1\right)}^{9} a^{2}}{{\left(a x + 1\right)}^{9}} - a^{2}}\right)} a"," ",0,"-1/1152*(315*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 315*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(315*c^4*((a*x - 1)/(a*x + 1))^(17/2) - 2730*c^4*((a*x - 1)/(a*x + 1))^(15/2) + 10458*c^4*((a*x - 1)/(a*x + 1))^(13/2) - 23202*c^4*((a*x - 1)/(a*x + 1))^(11/2) - 32768*c^4*((a*x - 1)/(a*x + 1))^(9/2) + 23202*c^4*((a*x - 1)/(a*x + 1))^(7/2) - 10458*c^4*((a*x - 1)/(a*x + 1))^(5/2) + 2730*c^4*((a*x - 1)/(a*x + 1))^(3/2) - 315*c^4*sqrt((a*x - 1)/(a*x + 1)))/(9*(a*x - 1)*a^2/(a*x + 1) - 36*(a*x - 1)^2*a^2/(a*x + 1)^2 + 84*(a*x - 1)^3*a^2/(a*x + 1)^3 - 126*(a*x - 1)^4*a^2/(a*x + 1)^4 + 126*(a*x - 1)^5*a^2/(a*x + 1)^5 - 84*(a*x - 1)^6*a^2/(a*x + 1)^6 + 36*(a*x - 1)^7*a^2/(a*x + 1)^7 - 9*(a*x - 1)^8*a^2/(a*x + 1)^8 + (a*x - 1)^9*a^2/(a*x + 1)^9 - a^2))*a","A",0
591,1,337,0,0.325498," ","integrate((-a^2*c*x^2+c)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{1}{336} \, {\left(\frac{105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(105 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} - 700 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 1981 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 3072 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 1981 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 700 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 105 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{7 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{21 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{35 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{35 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{21 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{7 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + \frac{{\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - a^{2}}\right)} a"," ",0,"-1/336*(105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(105*c^3*((a*x - 1)/(a*x + 1))^(13/2) - 700*c^3*((a*x - 1)/(a*x + 1))^(11/2) + 1981*c^3*((a*x - 1)/(a*x + 1))^(9/2) + 3072*c^3*((a*x - 1)/(a*x + 1))^(7/2) - 1981*c^3*((a*x - 1)/(a*x + 1))^(5/2) + 700*c^3*((a*x - 1)/(a*x + 1))^(3/2) - 105*c^3*sqrt((a*x - 1)/(a*x + 1)))/(7*(a*x - 1)*a^2/(a*x + 1) - 21*(a*x - 1)^2*a^2/(a*x + 1)^2 + 35*(a*x - 1)^3*a^2/(a*x + 1)^3 - 35*(a*x - 1)^4*a^2/(a*x + 1)^4 + 21*(a*x - 1)^5*a^2/(a*x + 1)^5 - 7*(a*x - 1)^6*a^2/(a*x + 1)^6 + (a*x - 1)^7*a^2/(a*x + 1)^7 - a^2))*a","A",0
592,1,259,0,0.335330," ","integrate((-a^2*c*x^2+c)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{1}{40} \, a {\left(\frac{15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(15 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - 70 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 128 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 70 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 15 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{5 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{10 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{10 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{{\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - a^{2}}\right)}"," ",0,"-1/40*a*(15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(15*c^2*((a*x - 1)/(a*x + 1))^(9/2) - 70*c^2*((a*x - 1)/(a*x + 1))^(7/2) - 128*c^2*((a*x - 1)/(a*x + 1))^(5/2) + 70*c^2*((a*x - 1)/(a*x + 1))^(3/2) - 15*c^2*sqrt((a*x - 1)/(a*x + 1)))/(5*(a*x - 1)*a^2/(a*x + 1) - 10*(a*x - 1)^2*a^2/(a*x + 1)^2 + 10*(a*x - 1)^3*a^2/(a*x + 1)^3 - 5*(a*x - 1)^4*a^2/(a*x + 1)^4 + (a*x - 1)^5*a^2/(a*x + 1)^5 - a^2))","A",0
593,1,171,0,0.307825," ","integrate((-a^2*c*x^2+c)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{2 \, {\left(3 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 8 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 3 \, c \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - a^{2}} - \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"1/6*a*(2*(3*c*((a*x - 1)/(a*x + 1))^(5/2) + 8*c*((a*x - 1)/(a*x + 1))^(3/2) - 3*c*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)*a^2/(a*x + 1) - 3*(a*x - 1)^2*a^2/(a*x + 1)^2 + (a*x - 1)^3*a^2/(a*x + 1)^3 - a^2) - 3*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 3*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","A",0
594,1,23,0,0.308855," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{\sqrt{\frac{a x - 1}{a x + 1}}}{a c}"," ",0,"-sqrt((a*x - 1)/(a*x + 1))/(a*c)","A",0
595,1,67,0,0.320246," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{12} \, a {\left(\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 6 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2}} - \frac{3}{a^{2} c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\right)}"," ",0,"1/12*a*((((a*x - 1)/(a*x + 1))^(3/2) - 6*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^2) - 3/(a^2*c^2*sqrt((a*x - 1)/(a*x + 1))))","A",0
596,1,102,0,0.310380," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{1}{240} \, a {\left(\frac{3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 20 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 90 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3}} + \frac{5 \, {\left(\frac{12 \, {\left(a x - 1\right)}}{a x + 1} - 1\right)}}{a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\right)}"," ",0,"-1/240*a*((3*((a*x - 1)/(a*x + 1))^(5/2) - 20*((a*x - 1)/(a*x + 1))^(3/2) + 90*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^3) + 5*(12*(a*x - 1)/(a*x + 1) - 1)/(a^2*c^3*((a*x - 1)/(a*x + 1))^(3/2)))","A",0
597,1,135,0,0.311671," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\frac{1}{2240} \, a {\left(\frac{5 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 42 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 175 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 700 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{4}} + \frac{7 \, {\left(\frac{10 \, {\left(a x - 1\right)}}{a x + 1} - \frac{75 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 1\right)}}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}}\right)}"," ",0,"1/2240*a*((5*((a*x - 1)/(a*x + 1))^(7/2) - 42*((a*x - 1)/(a*x + 1))^(5/2) + 175*((a*x - 1)/(a*x + 1))^(3/2) - 700*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^4) + 7*(10*(a*x - 1)/(a*x + 1) - 75*(a*x - 1)^2/(a*x + 1)^2 - 1)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(5/2)))","A",0
598,1,80,0,0.301903," ","integrate((-a^2*c*x^2+c)^4*(a*x-1)/(a*x+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
599,1,70,0,0.310357," ","integrate((-a^2*c*x^2+c)^3*(a*x-1)/(a*x+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
600,1,37,0,0.306821," ","integrate((-a^2*c*x^2+c)^2*(a*x-1)/(a*x+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
601,1,20,0,0.299088," ","integrate((-a^2*c*x^2+c)*(a*x-1)/(a*x+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
602,1,12,0,0.303249," ","integrate((a*x-1)/(a*x+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
603,1,63,0,0.301533," ","integrate((a*x-1)/(a*x+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
604,1,91,0,0.300136," ","integrate((a*x-1)/(a*x+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
605,1,140,0,0.314267," ","integrate((a*x-1)/(a*x+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
606,1,415,0,1.387918," ","integrate((-a^2*c*x^2+c)^4*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{1}{8064} \, {\left(\frac{3465 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3465 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(3465 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{17}{2}} - 30030 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{2}} + 115038 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} + 334602 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} - 360448 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 255222 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 115038 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 30030 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 3465 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{9 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{36 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{84 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{126 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{126 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{84 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + \frac{36 \, {\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - \frac{9 \, {\left(a x - 1\right)}^{8} a^{2}}{{\left(a x + 1\right)}^{8}} + \frac{{\left(a x - 1\right)}^{9} a^{2}}{{\left(a x + 1\right)}^{9}} - a^{2}}\right)} a"," ",0,"1/8064*(3465*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3465*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(3465*c^4*((a*x - 1)/(a*x + 1))^(17/2) - 30030*c^4*((a*x - 1)/(a*x + 1))^(15/2) + 115038*c^4*((a*x - 1)/(a*x + 1))^(13/2) + 334602*c^4*((a*x - 1)/(a*x + 1))^(11/2) - 360448*c^4*((a*x - 1)/(a*x + 1))^(9/2) + 255222*c^4*((a*x - 1)/(a*x + 1))^(7/2) - 115038*c^4*((a*x - 1)/(a*x + 1))^(5/2) + 30030*c^4*((a*x - 1)/(a*x + 1))^(3/2) - 3465*c^4*sqrt((a*x - 1)/(a*x + 1)))/(9*(a*x - 1)*a^2/(a*x + 1) - 36*(a*x - 1)^2*a^2/(a*x + 1)^2 + 84*(a*x - 1)^3*a^2/(a*x + 1)^3 - 126*(a*x - 1)^4*a^2/(a*x + 1)^4 + 126*(a*x - 1)^5*a^2/(a*x + 1)^5 - 84*(a*x - 1)^6*a^2/(a*x + 1)^6 + 36*(a*x - 1)^7*a^2/(a*x + 1)^7 - 9*(a*x - 1)^8*a^2/(a*x + 1)^8 + (a*x - 1)^9*a^2/(a*x + 1)^9 - a^2))*a","A",0
607,1,337,0,0.971234," ","integrate((-a^2*c*x^2+c)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{1}{560} \, {\left(\frac{315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(315 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} - 2100 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} - 8393 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 9216 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 5943 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 2100 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 315 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{7 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{21 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{35 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{35 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{21 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{7 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + \frac{{\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - a^{2}}\right)} a"," ",0,"1/560*(315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(315*c^3*((a*x - 1)/(a*x + 1))^(13/2) - 2100*c^3*((a*x - 1)/(a*x + 1))^(11/2) - 8393*c^3*((a*x - 1)/(a*x + 1))^(9/2) + 9216*c^3*((a*x - 1)/(a*x + 1))^(7/2) - 5943*c^3*((a*x - 1)/(a*x + 1))^(5/2) + 2100*c^3*((a*x - 1)/(a*x + 1))^(3/2) - 315*c^3*sqrt((a*x - 1)/(a*x + 1)))/(7*(a*x - 1)*a^2/(a*x + 1) - 21*(a*x - 1)^2*a^2/(a*x + 1)^2 + 35*(a*x - 1)^3*a^2/(a*x + 1)^3 - 35*(a*x - 1)^4*a^2/(a*x + 1)^4 + 21*(a*x - 1)^5*a^2/(a*x + 1)^5 - 7*(a*x - 1)^6*a^2/(a*x + 1)^6 + (a*x - 1)^7*a^2/(a*x + 1)^7 - a^2))*a","A",0
608,1,259,0,0.869415," ","integrate((-a^2*c*x^2+c)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{1}{120} \, a {\left(\frac{105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2 \, {\left(105 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 790 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 896 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 490 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 105 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{5 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{10 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{10 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + \frac{{\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - a^{2}}\right)}"," ",0,"1/120*a*(105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - 2*(105*c^2*((a*x - 1)/(a*x + 1))^(9/2) + 790*c^2*((a*x - 1)/(a*x + 1))^(7/2) - 896*c^2*((a*x - 1)/(a*x + 1))^(5/2) + 490*c^2*((a*x - 1)/(a*x + 1))^(3/2) - 105*c^2*sqrt((a*x - 1)/(a*x + 1)))/(5*(a*x - 1)*a^2/(a*x + 1) - 10*(a*x - 1)^2*a^2/(a*x + 1)^2 + 10*(a*x - 1)^3*a^2/(a*x + 1)^3 - 5*(a*x - 1)^4*a^2/(a*x + 1)^4 + (a*x - 1)^5*a^2/(a*x + 1)^5 - a^2))","A",0
609,1,171,0,0.307961," ","integrate((-a^2*c*x^2+c)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{2 \, {\left(33 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 40 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 15 \, c \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{\frac{3 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{{\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - a^{2}} + \frac{15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"1/6*a*(2*(33*c*((a*x - 1)/(a*x + 1))^(5/2) - 40*c*((a*x - 1)/(a*x + 1))^(3/2) + 15*c*sqrt((a*x - 1)/(a*x + 1)))/(3*(a*x - 1)*a^2/(a*x + 1) - 3*(a*x - 1)^2*a^2/(a*x + 1)^2 + (a*x - 1)^3*a^2/(a*x + 1)^3 - a^2) + 15*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 15*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","A",0
610,1,23,0,0.444186," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c),x, algorithm=""maxima"")","-\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{3 \, a c}"," ",0,"-1/3*((a*x - 1)/(a*x + 1))^(3/2)/(a*c)","A",0
611,1,60,0,0.303923," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 10 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 15 \, \sqrt{\frac{a x - 1}{a x + 1}}}{60 \, a c^{2}}"," ",0,"1/60*(3*((a*x - 1)/(a*x + 1))^(5/2) - 10*((a*x - 1)/(a*x + 1))^(3/2) + 15*sqrt((a*x - 1)/(a*x + 1)))/(a*c^2)","A",0
612,1,103,0,0.302035," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{1}{560} \, a {\left(\frac{5 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 28 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 70 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 140 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3}} - \frac{35}{a^{2} c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}\right)}"," ",0,"-1/560*a*((5*((a*x - 1)/(a*x + 1))^(7/2) - 28*((a*x - 1)/(a*x + 1))^(5/2) + 70*((a*x - 1)/(a*x + 1))^(3/2) - 140*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^3) - 35/(a^2*c^3*sqrt((a*x - 1)/(a*x + 1))))","A",0
613,1,136,0,0.475102," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^4,x, algorithm=""maxima"")","\frac{1}{4032} \, a {\left(\frac{7 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - 54 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 189 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 420 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 945 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{4}} + \frac{21 \, {\left(\frac{18 \, {\left(a x - 1\right)}}{a x + 1} - 1\right)}}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\right)}"," ",0,"1/4032*a*((7*((a*x - 1)/(a*x + 1))^(9/2) - 54*((a*x - 1)/(a*x + 1))^(7/2) + 189*((a*x - 1)/(a*x + 1))^(5/2) - 420*((a*x - 1)/(a*x + 1))^(3/2) + 945*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^4) + 21*(18*(a*x - 1)/(a*x + 1) - 1)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(3/2)))","A",0
614,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(9/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
615,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
616,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
617,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
618,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
619,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*c*x^2 + c)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
620,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
621,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
622,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(7/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
623,1,192,0,0.414205," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(9/2),x, algorithm=""maxima"")","\frac{1}{10} \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}} x - \frac{11}{80} \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} c x - \frac{77}{480} \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} c^{2} x - \frac{77}{384} \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c^{3} x - \frac{35}{64} \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{4} x + \frac{63}{256} \, \sqrt{-a^{2} c x^{2} + c} c^{4} x - \frac{35 \, c^{6} \arcsin\left(a x - 2\right)}{64 \, a \left(-c\right)^{\frac{3}{2}}} + \frac{63 \, c^{\frac{9}{2}} \arcsin\left(a x\right)}{256 \, a} + \frac{2 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}}}{9 \, a} + \frac{35 \, \sqrt{a^{2} c x^{2} - 4 \, a c x + 3 \, c} c^{4}}{32 \, a}"," ",0,"1/10*(-a^2*c*x^2 + c)^(9/2)*x - 11/80*(-a^2*c*x^2 + c)^(7/2)*c*x - 77/480*(-a^2*c*x^2 + c)^(5/2)*c^2*x - 77/384*(-a^2*c*x^2 + c)^(3/2)*c^3*x - 35/64*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^4*x + 63/256*sqrt(-a^2*c*x^2 + c)*c^4*x - 35/64*c^6*arcsin(a*x - 2)/(a*(-c)^(3/2)) + 63/256*c^(9/2)*arcsin(a*x)/a + 2/9*(-a^2*c*x^2 + c)^(9/2)/a + 35/32*sqrt(a^2*c*x^2 - 4*a*c*x + 3*c)*c^4/a","A",0
624,1,173,0,0.422215," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(7/2),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
625,1,154,0,0.422344," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(5/2),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
626,1,131,0,0.421589," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(3/2),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
627,1,47,0,0.418357," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2),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
628,1,40,0,0.404215," ","integrate(1/(a*x-1)*(a*x+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
629,1,61,0,0.304059," ","integrate(1/(a*x-1)*(a*x+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
630,1,80,0,0.319613," ","integrate(1/(a*x-1)*(a*x+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
631,1,99,0,0.317176," ","integrate(1/(a*x-1)*(a*x+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
632,1,118,0,0.324713," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^(9/2),x, algorithm=""maxima"")","\frac{2}{9 \, {\left({\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} a^{2} c x - {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} a c\right)}} - \frac{16 \, x}{45 \, \sqrt{-a^{2} c x^{2} + c} c^{4}} - \frac{8 \, x}{45 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c^{3}} - \frac{2 \, x}{15 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} c^{2}} - \frac{x}{9 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} c}"," ",0,"2/9/((-a^2*c*x^2 + c)^(7/2)*a^2*c*x - (-a^2*c*x^2 + c)^(7/2)*a*c) - 16/45*x/(sqrt(-a^2*c*x^2 + c)*c^4) - 8/45*x/((-a^2*c*x^2 + c)^(3/2)*c^3) - 2/15*x/((-a^2*c*x^2 + c)^(5/2)*c^2) - 1/9*x/((-a^2*c*x^2 + c)^(7/2)*c)","A",0
633,1,204,0,0.361735," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(9/2),x, algorithm=""maxima"")","\frac{{\left(21 \, a^{11} \sqrt{-c} c^{4} x^{11} + 49 \, a^{10} \sqrt{-c} c^{4} x^{10} - 70 \, a^{9} \sqrt{-c} c^{4} x^{9} - 240 \, a^{8} \sqrt{-c} c^{4} x^{8} + 30 \, a^{7} \sqrt{-c} c^{4} x^{7} + 462 \, a^{6} \sqrt{-c} c^{4} x^{6} + 168 \, a^{5} \sqrt{-c} c^{4} x^{5} - 420 \, a^{4} \sqrt{-c} c^{4} x^{4} - 315 \, a^{3} \sqrt{-c} c^{4} x^{3} + 105 \, a^{2} \sqrt{-c} c^{4} x^{2} + 210 \, \sqrt{-c} c^{4}\right)} {\left(a x + 1\right)}^{2}}{210 \, {\left(a^{3} x^{2} + 2 \, a^{2} x + a\right)} {\left(a x - 1\right)}}"," ",0,"1/210*(21*a^11*sqrt(-c)*c^4*x^11 + 49*a^10*sqrt(-c)*c^4*x^10 - 70*a^9*sqrt(-c)*c^4*x^9 - 240*a^8*sqrt(-c)*c^4*x^8 + 30*a^7*sqrt(-c)*c^4*x^7 + 462*a^6*sqrt(-c)*c^4*x^6 + 168*a^5*sqrt(-c)*c^4*x^5 - 420*a^4*sqrt(-c)*c^4*x^4 - 315*a^3*sqrt(-c)*c^4*x^3 + 105*a^2*sqrt(-c)*c^4*x^2 + 210*sqrt(-c)*c^4)*(a*x + 1)^2/((a^3*x^2 + 2*a^2*x + a)*(a*x - 1))","A",0
634,1,172,0,0.341230," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","-\frac{{\left(21 \, a^{9} \sqrt{-c} c^{3} x^{9} + 51 \, a^{8} \sqrt{-c} c^{3} x^{8} - 44 \, a^{7} \sqrt{-c} c^{3} x^{7} - 196 \, a^{6} \sqrt{-c} c^{3} x^{6} - 42 \, a^{5} \sqrt{-c} c^{3} x^{5} + 266 \, a^{4} \sqrt{-c} c^{3} x^{4} + 196 \, a^{3} \sqrt{-c} c^{3} x^{3} - 84 \, a^{2} \sqrt{-c} c^{3} x^{2} - 168 \, \sqrt{-c} c^{3}\right)} {\left(a x + 1\right)}^{2}}{168 \, {\left(a^{3} x^{2} + 2 \, a^{2} x + a\right)} {\left(a x - 1\right)}}"," ",0,"-1/168*(21*a^9*sqrt(-c)*c^3*x^9 + 51*a^8*sqrt(-c)*c^3*x^8 - 44*a^7*sqrt(-c)*c^3*x^7 - 196*a^6*sqrt(-c)*c^3*x^6 - 42*a^5*sqrt(-c)*c^3*x^5 + 266*a^4*sqrt(-c)*c^3*x^4 + 196*a^3*sqrt(-c)*c^3*x^3 - 84*a^2*sqrt(-c)*c^3*x^2 - 168*sqrt(-c)*c^3)*(a*x + 1)^2/((a^3*x^2 + 2*a^2*x + a)*(a*x - 1))","A",0
635,1,140,0,0.344255," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{{\left(5 \, a^{7} \sqrt{-c} c^{2} x^{7} + 13 \, a^{6} \sqrt{-c} c^{2} x^{6} - 3 \, a^{5} \sqrt{-c} c^{2} x^{5} - 35 \, a^{4} \sqrt{-c} c^{2} x^{4} - 25 \, a^{3} \sqrt{-c} c^{2} x^{3} + 15 \, a^{2} \sqrt{-c} c^{2} x^{2} + 30 \, \sqrt{-c} c^{2}\right)} {\left(a x + 1\right)}^{2}}{30 \, {\left(a^{3} x^{2} + 2 \, a^{2} x + a\right)} {\left(a x - 1\right)}}"," ",0,"1/30*(5*a^7*sqrt(-c)*c^2*x^7 + 13*a^6*sqrt(-c)*c^2*x^6 - 3*a^5*sqrt(-c)*c^2*x^5 - 35*a^4*sqrt(-c)*c^2*x^4 - 25*a^3*sqrt(-c)*c^2*x^3 + 15*a^2*sqrt(-c)*c^2*x^2 + 30*sqrt(-c)*c^2)*(a*x + 1)^2/((a^3*x^2 + 2*a^2*x + a)*(a*x - 1))","A",0
636,1,97,0,0.336496," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(a^{5} \sqrt{-c} c x^{5} + 3 \, a^{4} \sqrt{-c} c x^{4} + 2 \, a^{3} \sqrt{-c} c x^{3} - 2 \, a^{2} \sqrt{-c} c x^{2} - 4 \, \sqrt{-c} c\right)} {\left(a x + 1\right)}^{2}}{4 \, {\left(a^{3} x^{2} + 2 \, a^{2} x + a\right)} {\left(a x - 1\right)}}"," ",0,"-1/4*(a^5*sqrt(-c)*c*x^5 + 3*a^4*sqrt(-c)*c*x^4 + 2*a^3*sqrt(-c)*c*x^3 - 2*a^2*sqrt(-c)*c*x^2 - 4*sqrt(-c)*c)*(a*x + 1)^2/((a^3*x^2 + 2*a^2*x + a)*(a*x - 1))","B",0
637,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
638,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
639,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
640,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
641,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(7/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
642,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(9/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(9/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
643,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
644,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
645,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
646,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
647,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/sqrt(-a^2*c*x^2 + c), x)","F",0
648,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(-a^2*c*x^2 + c)^(3/2), x)","F",0
649,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(-a^2*c*x^2 + c)^(5/2), x)","F",0
650,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(-a^2*c*x^2 + c)^(7/2), x)","F",0
651,1,154,0,0.414526," ","integrate((-a^2*c*x^2+c)^(5/2)*(a*x-1)/(a*x+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
652,1,130,0,0.405381," ","integrate((-a^2*c*x^2+c)^(3/2)*(a*x-1)/(a*x+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
653,1,47,0,0.407680," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+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
654,1,39,0,0.402755," ","integrate((a*x-1)/(a*x+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
655,1,60,0,0.312665," ","integrate((a*x-1)/(a*x+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
656,1,79,0,0.319144," ","integrate((a*x-1)/(a*x+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
657,1,98,0,0.320089," ","integrate((a*x-1)/(a*x+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
658,1,117,0,0.327626," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^(9/2),x, algorithm=""maxima"")","\frac{2}{9 \, {\left({\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} a^{2} c x + {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} a c\right)}} - \frac{16 \, x}{45 \, \sqrt{-a^{2} c x^{2} + c} c^{4}} - \frac{8 \, x}{45 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c^{3}} - \frac{2 \, x}{15 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} c^{2}} - \frac{x}{9 \, {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} c}"," ",0,"2/9/((-a^2*c*x^2 + c)^(7/2)*a^2*c*x + (-a^2*c*x^2 + c)^(7/2)*a*c) - 16/45*x/(sqrt(-a^2*c*x^2 + c)*c^4) - 8/45*x/((-a^2*c*x^2 + c)^(3/2)*c^3) - 2/15*x/((-a^2*c*x^2 + c)^(5/2)*c^2) - 1/9*x/((-a^2*c*x^2 + c)^(7/2)*c)","A",0
659,1,204,0,0.335620," ","integrate((-a^2*c*x^2+c)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{{\left(21 \, a^{11} \sqrt{-c} c^{4} x^{11} - 49 \, a^{10} \sqrt{-c} c^{4} x^{10} - 70 \, a^{9} \sqrt{-c} c^{4} x^{9} + 240 \, a^{8} \sqrt{-c} c^{4} x^{8} + 30 \, a^{7} \sqrt{-c} c^{4} x^{7} - 462 \, a^{6} \sqrt{-c} c^{4} x^{6} + 168 \, a^{5} \sqrt{-c} c^{4} x^{5} + 420 \, a^{4} \sqrt{-c} c^{4} x^{4} - 315 \, a^{3} \sqrt{-c} c^{4} x^{3} - 105 \, a^{2} \sqrt{-c} c^{4} x^{2} - 210 \, \sqrt{-c} c^{4}\right)} {\left(a x - 1\right)}^{2}}{210 \, {\left(a^{3} x^{2} - 2 \, a^{2} x + a\right)} {\left(a x + 1\right)}}"," ",0,"1/210*(21*a^11*sqrt(-c)*c^4*x^11 - 49*a^10*sqrt(-c)*c^4*x^10 - 70*a^9*sqrt(-c)*c^4*x^9 + 240*a^8*sqrt(-c)*c^4*x^8 + 30*a^7*sqrt(-c)*c^4*x^7 - 462*a^6*sqrt(-c)*c^4*x^6 + 168*a^5*sqrt(-c)*c^4*x^5 + 420*a^4*sqrt(-c)*c^4*x^4 - 315*a^3*sqrt(-c)*c^4*x^3 - 105*a^2*sqrt(-c)*c^4*x^2 - 210*sqrt(-c)*c^4)*(a*x - 1)^2/((a^3*x^2 - 2*a^2*x + a)*(a*x + 1))","A",0
660,1,172,0,0.337911," ","integrate((-a^2*c*x^2+c)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(21 \, a^{9} \sqrt{-c} c^{3} x^{9} - 51 \, a^{8} \sqrt{-c} c^{3} x^{8} - 44 \, a^{7} \sqrt{-c} c^{3} x^{7} + 196 \, a^{6} \sqrt{-c} c^{3} x^{6} - 42 \, a^{5} \sqrt{-c} c^{3} x^{5} - 266 \, a^{4} \sqrt{-c} c^{3} x^{4} + 196 \, a^{3} \sqrt{-c} c^{3} x^{3} + 84 \, a^{2} \sqrt{-c} c^{3} x^{2} + 168 \, \sqrt{-c} c^{3}\right)} {\left(a x - 1\right)}^{2}}{168 \, {\left(a^{3} x^{2} - 2 \, a^{2} x + a\right)} {\left(a x + 1\right)}}"," ",0,"-1/168*(21*a^9*sqrt(-c)*c^3*x^9 - 51*a^8*sqrt(-c)*c^3*x^8 - 44*a^7*sqrt(-c)*c^3*x^7 + 196*a^6*sqrt(-c)*c^3*x^6 - 42*a^5*sqrt(-c)*c^3*x^5 - 266*a^4*sqrt(-c)*c^3*x^4 + 196*a^3*sqrt(-c)*c^3*x^3 + 84*a^2*sqrt(-c)*c^3*x^2 + 168*sqrt(-c)*c^3)*(a*x - 1)^2/((a^3*x^2 - 2*a^2*x + a)*(a*x + 1))","A",0
661,1,140,0,0.340461," ","integrate((-a^2*c*x^2+c)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{{\left(5 \, a^{7} \sqrt{-c} c^{2} x^{7} - 13 \, a^{6} \sqrt{-c} c^{2} x^{6} - 3 \, a^{5} \sqrt{-c} c^{2} x^{5} + 35 \, a^{4} \sqrt{-c} c^{2} x^{4} - 25 \, a^{3} \sqrt{-c} c^{2} x^{3} - 15 \, a^{2} \sqrt{-c} c^{2} x^{2} - 30 \, \sqrt{-c} c^{2}\right)} {\left(a x - 1\right)}^{2}}{30 \, {\left(a^{3} x^{2} - 2 \, a^{2} x + a\right)} {\left(a x + 1\right)}}"," ",0,"1/30*(5*a^7*sqrt(-c)*c^2*x^7 - 13*a^6*sqrt(-c)*c^2*x^6 - 3*a^5*sqrt(-c)*c^2*x^5 + 35*a^4*sqrt(-c)*c^2*x^4 - 25*a^3*sqrt(-c)*c^2*x^3 - 15*a^2*sqrt(-c)*c^2*x^2 - 30*sqrt(-c)*c^2)*(a*x - 1)^2/((a^3*x^2 - 2*a^2*x + a)*(a*x + 1))","A",0
662,1,97,0,0.333337," ","integrate((-a^2*c*x^2+c)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(a^{5} \sqrt{-c} c x^{5} - 3 \, a^{4} \sqrt{-c} c x^{4} + 2 \, a^{3} \sqrt{-c} c x^{3} + 2 \, a^{2} \sqrt{-c} c x^{2} + 4 \, \sqrt{-c} c\right)} {\left(a x - 1\right)}^{2}}{4 \, {\left(a^{3} x^{2} - 2 \, a^{2} x + a\right)} {\left(a x + 1\right)}}"," ",0,"-1/4*(a^5*sqrt(-c)*c*x^5 - 3*a^4*sqrt(-c)*c*x^4 + 2*a^3*sqrt(-c)*c*x^3 + 2*a^2*sqrt(-c)*c*x^2 + 4*sqrt(-c)*c)*(a*x - 1)^2/((a^3*x^2 - 2*a^2*x + a)*(a*x + 1))","B",0
663,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
664,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/sqrt(-a^2*c*x^2 + c), x)","F",0
665,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
666,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
667,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(-a^2*c*x^2 + c)^(7/2), x)","F",0
668,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} x^{2}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^2/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
669,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} x}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
670,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
671,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
672,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x^2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
673,1,117,0,0.422459," ","integrate(1/(a*x-1)*(a*x+1)*x^3*(-a^2*c*x^2+c)^(1/2),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
674,1,93,0,0.422686," ","integrate(1/(a*x-1)*(a*x+1)*x^2*(-a^2*c*x^2+c)^(1/2),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
675,1,70,0,0.423604," ","integrate(1/(a*x-1)*(a*x+1)*x*(-a^2*c*x^2+c)^(1/2),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
676,1,47,0,0.420777," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2),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
677,1,90,0,0.436833," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""maxima"")","-a^{2} {\left(\frac{\sqrt{c} \arcsin\left(a x\right)}{a^{2}} - \frac{\sqrt{-a^{2} c x^{2} + c}}{a^{2}}\right)} - a {\left(\frac{\sqrt{c} \arcsin\left(a x\right)}{a} - \frac{\sqrt{c} \log\left(\frac{2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c}}{{\left| x \right|}} + \frac{2 \, c}{{\left| x \right|}}\right)}{a}\right)}"," ",0,"-a^2*(sqrt(c)*arcsin(a*x)/a^2 - sqrt(-a^2*c*x^2 + c)/a^2) - a*(sqrt(c)*arcsin(a*x)/a - sqrt(c)*log(2*sqrt(-a^2*c*x^2 + c)*sqrt(c)/abs(x) + 2*c/abs(x))/a)","A",0
678,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}}{{\left(a x - 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)/((a*x - 1)*x^2), x)","F",0
679,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+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)}}{{\left(a x - 1\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)/((a*x - 1)*x^3), x)","F",0
680,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}}{{\left(a x - 1\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)/((a*x - 1)*x^4), x)","F",0
681,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+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)}}{{\left(a x - 1\right)} x^{5}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)/((a*x - 1)*x^5), x)","F",0
682,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} x^{3}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^3/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
683,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} x^{2}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^2/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
684,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} x}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
685,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
686,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
687,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x^2*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
688,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x^3*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
689,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x^4*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
690,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x^5*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
691,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^4/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^4/((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
692,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^3/((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
693,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^2/((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
694,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x/((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
695,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
696,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*x*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
697,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*x^2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
698,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{3} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*x^3*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
699,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^5/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{5}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^5/((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
700,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^4/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^4/((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
701,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^3/((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
702,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^2/((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
703,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x/((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
704,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
705,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*x*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
706,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*x^2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
707,0,0,0,0.000000," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} x^{2} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^2*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
708,0,0,0,0.000000," ","integrate(x*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} x \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
709,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
710,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{\frac{a x - 1}{a x + 1}}}{x}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt((a*x - 1)/(a*x + 1))/x, x)","F",0
711,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{\frac{a x - 1}{a x + 1}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt((a*x - 1)/(a*x + 1))/x^2, x)","F",0
712,1,117,0,0.410644," ","integrate(x^3*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+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
713,1,93,0,0.413576," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+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
714,1,70,0,0.418006," ","integrate(x*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+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
715,1,47,0,0.409061," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+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
716,1,86,0,0.427541," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x,x, algorithm=""maxima"")","a^{2} {\left(\frac{\sqrt{c} \arcsin\left(a x\right)}{a^{2}} + \frac{\sqrt{-a^{2} c x^{2} + c}}{a^{2}}\right)} + a {\left(\frac{\sqrt{c} \arcsin\left(a x\right)}{a} + \frac{\sqrt{c} \log\left(\frac{2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c}}{{\left| x \right|}} + \frac{2 \, c}{{\left| x \right|}}\right)}{a}\right)}"," ",0,"a^2*(sqrt(c)*arcsin(a*x)/a^2 + sqrt(-a^2*c*x^2 + c)/a^2) + a*(sqrt(c)*arcsin(a*x)/a + sqrt(c)*log(2*sqrt(-a^2*c*x^2 + c)*sqrt(c)/abs(x) + 2*c/abs(x))/a)","A",0
717,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x - 1\right)}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x - 1)/((a*x + 1)*x^2), x)","F",0
718,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x - 1\right)}}{{\left(a x + 1\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x - 1)/((a*x + 1)*x^3), x)","F",0
719,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x - 1\right)}}{{\left(a x + 1\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x - 1)/((a*x + 1)*x^4), x)","F",0
720,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x - 1\right)}}{{\left(a x + 1\right)} x^{5}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x - 1)/((a*x + 1)*x^5), x)","F",0
721,0,0,0,0.000000," ","integrate(x^3*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^3*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
722,0,0,0,0.000000," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^2*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
723,0,0,0,0.000000," ","integrate(x*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
724,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
725,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)/x, x)","F",0
726,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^2, x)","F",0
727,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^3, x)","F",0
728,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^4, x)","F",0
729,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^5, x)","F",0
730,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+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} x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^m/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
731,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+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)} x^{m}}{a x - 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)*x^m/(a*x - 1), x)","F",0
732,1,54,0,0.339283," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(-a^2*c*x^2+c)^(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)} x^{m}}{{\left(m^{2} + 3 \, m + 2\right)} a x + m^{2} + 3 \, m + 2}"," ",0,"(a*sqrt(-c)*(m + 1)*x^2 + sqrt(-c)*(m + 2)*x)*(a*x + 1)*x^m/((m^2 + 3*m + 2)*a*x + m^2 + 3*m + 2)","A",0
733,1,57,0,0.330030," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+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)} x^{m}}{{\left(m^{2} + 3 \, m + 2\right)} a x - m^{2} - 3 \, m - 2}"," ",0,"(a*sqrt(-c)*(m + 1)*x^2 - sqrt(-c)*(m + 2)*x)*(a*x - 1)*x^m/((m^2 + 3*m + 2)*a*x - m^2 - 3*m - 2)","A",0
734,0,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x - 1\right)} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x - 1)*x^m/(a*x + 1), x)","F",0
735,0,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^m*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
736,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
737,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
738,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
739,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
740,1,31,0,0.322037," ","integrate(exp(n*arccoth(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
741,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
742,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
743,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
744,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
745,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
746,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
747,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
748,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
749,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
750,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(9/2),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{9}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(9/2), x)","F",0
751,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
752,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
753,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
754,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
755,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
756,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*x^4/(-a^2*c*x^2+c)^(5/2),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)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^4*((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
757,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
758,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
759,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
760,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
761,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
762,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
763,1,36,0,0.334034," ","integrate(exp(2*p*arccoth(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
764,1,34,0,0.336360," ","integrate((-a^2*c*x^2+c)^p/exp(2*p*arccoth(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
765,0,0,0,0.000000," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-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}}{{\left(a x - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^2*(-a^2*c*x^2 + c)^p/(a*x - 1)^2, x)","F",0
766,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{p}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
767,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-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}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p/(a*x - 1), x)","F",0
768,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^p,x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{p}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
769,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
770,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(-a^2*c*x^2 + c)^p/(a*x + 1), x)","F",0
771,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
772,1,380,0,0.422649," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","-\frac{1}{840} \, {\left(\frac{3675 \, c^{4} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{840 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{840 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{5355 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{2}} + 31465 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} + 72051 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 71801 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 4569 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 17619 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 10185 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 1995 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{6 \, {\left(a x - 1\right)} a^{2}}{a x + 1} + \frac{14 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{14 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{14 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{14 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} - \frac{6 \, {\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - \frac{{\left(a x - 1\right)}^{8} a^{2}}{{\left(a x + 1\right)}^{8}} + a^{2}}\right)} a"," ",0,"-1/840*(3675*c^4*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 840*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 840*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - (5355*c^4*((a*x - 1)/(a*x + 1))^(15/2) + 31465*c^4*((a*x - 1)/(a*x + 1))^(13/2) + 72051*c^4*((a*x - 1)/(a*x + 1))^(11/2) + 71801*c^4*((a*x - 1)/(a*x + 1))^(9/2) + 4569*c^4*((a*x - 1)/(a*x + 1))^(7/2) + 17619*c^4*((a*x - 1)/(a*x + 1))^(5/2) + 10185*c^4*((a*x - 1)/(a*x + 1))^(3/2) + 1995*c^4*sqrt((a*x - 1)/(a*x + 1)))/(6*(a*x - 1)*a^2/(a*x + 1) + 14*(a*x - 1)^2*a^2/(a*x + 1)^2 + 14*(a*x - 1)^3*a^2/(a*x + 1)^3 - 14*(a*x - 1)^5*a^2/(a*x + 1)^5 - 14*(a*x - 1)^6*a^2/(a*x + 1)^6 - 6*(a*x - 1)^7*a^2/(a*x + 1)^7 - (a*x - 1)^8*a^2/(a*x + 1)^8 + a^2))*a","A",0
773,1,302,0,0.413039," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","-\frac{1}{60} \, {\left(\frac{225 \, c^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{60 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{60 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{345 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 1345 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 1654 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 86 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 305 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 105 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{4 \, {\left(a x - 1\right)} a^{2}}{a x + 1} + \frac{5 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} - \frac{4 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{{\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + a^{2}}\right)} a"," ",0,"-1/60*(225*c^3*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 60*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 60*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - (345*c^3*((a*x - 1)/(a*x + 1))^(11/2) + 1345*c^3*((a*x - 1)/(a*x + 1))^(9/2) + 1654*c^3*((a*x - 1)/(a*x + 1))^(7/2) + 86*c^3*((a*x - 1)/(a*x + 1))^(5/2) + 305*c^3*((a*x - 1)/(a*x + 1))^(3/2) + 105*c^3*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)*a^2/(a*x + 1) + 5*(a*x - 1)^2*a^2/(a*x + 1)^2 - 5*(a*x - 1)^4*a^2/(a*x + 1)^4 - 4*(a*x - 1)^5*a^2/(a*x + 1)^5 - (a*x - 1)^6*a^2/(a*x + 1)^6 + a^2))*a","A",0
774,1,223,0,0.412423," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{9 \, c^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{15 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 29 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 3 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{2 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + a^{2}}\right)}"," ",0,"-1/3*a*(9*c^2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - (15*c^2*((a*x - 1)/(a*x + 1))^(7/2) + 29*c^2*((a*x - 1)/(a*x + 1))^(5/2) + c^2*((a*x - 1)/(a*x + 1))^(3/2) + 3*c^2*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - 2*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 + a^2))","A",0
775,1,117,0,0.415961," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2),x, algorithm=""maxima"")","-{\left(\frac{4 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{\frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} + \frac{2 \, c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)} a"," ",0,"-(4*c*((a*x - 1)/(a*x + 1))^(3/2)/((a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) + 2*c*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)*a","A",0
776,1,116,0,0.316993," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2),x, algorithm=""maxima"")","-a {\left(\frac{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} - 1}{a^{2} c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - a^{2} c \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c}\right)}"," ",0,"-a*((3*(a*x - 1)/(a*x + 1) - 1)/(a^2*c*((a*x - 1)/(a*x + 1))^(3/2) - a^2*c*sqrt((a*x - 1)/(a*x + 1))) - log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) + log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c))","A",0
777,1,160,0,0.313754," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\frac{1}{12} \, a {\left(\frac{\frac{17 \, {\left(a x - 1\right)}}{a x + 1} - \frac{42 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}{a^{2} c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - a^{2} c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}} + \frac{12 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} - \frac{12 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{2}} + \frac{3 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2}}\right)}"," ",0,"1/12*a*((17*(a*x - 1)/(a*x + 1) - 42*(a*x - 1)^2/(a*x + 1)^2 + 1)/(a^2*c^2*((a*x - 1)/(a*x + 1))^(5/2) - a^2*c^2*((a*x - 1)/(a*x + 1))^(3/2)) + 12*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) - 12*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^2) + 3*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^2))","A",0
778,1,194,0,0.320264," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","\frac{1}{240} \, a {\left(\frac{\frac{37 \, {\left(a x - 1\right)}}{a x + 1} + \frac{410 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - \frac{930 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 3}{a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}} + \frac{5 \, {\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 24 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} c^{3}} + \frac{240 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{3}} - \frac{240 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{3}}\right)}"," ",0,"1/240*a*((37*(a*x - 1)/(a*x + 1) + 410*(a*x - 1)^2/(a*x + 1)^2 - 930*(a*x - 1)^3/(a*x + 1)^3 + 3)/(a^2*c^3*((a*x - 1)/(a*x + 1))^(7/2) - a^2*c^3*((a*x - 1)/(a*x + 1))^(5/2)) + 5*(((a*x - 1)/(a*x + 1))^(3/2) + 24*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^3) + 240*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^3) - 240*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^3))","A",0
779,1,230,0,0.326576," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","\frac{1}{6720} \, a {\left(\frac{5 \, {\left(\frac{39 \, {\left(a x - 1\right)}}{a x + 1} + \frac{287 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{2611 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - \frac{5628 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} + 3\right)}}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}}} + \frac{7 \, {\left(3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 50 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 705 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} c^{4}} + \frac{6720 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} - \frac{6720 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{4}}\right)}"," ",0,"1/6720*a*(5*(39*(a*x - 1)/(a*x + 1) + 287*(a*x - 1)^2/(a*x + 1)^2 + 2611*(a*x - 1)^3/(a*x + 1)^3 - 5628*(a*x - 1)^4/(a*x + 1)^4 + 3)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(9/2) - a^2*c^4*((a*x - 1)/(a*x + 1))^(7/2)) + 7*(3*((a*x - 1)/(a*x + 1))^(5/2) + 50*((a*x - 1)/(a*x + 1))^(3/2) + 705*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^4) + 6720*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) - 6720*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^4))","A",0
780,1,114,0,0.311286," ","integrate(1/(a*x-1)*(a*x+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
781,1,81,0,0.315538," ","integrate(1/(a*x-1)*(a*x+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
782,1,70,0,0.313811," ","integrate(1/(a*x-1)*(a*x+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
783,1,35,0,0.307383," ","integrate(1/(a*x-1)*(a*x+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
784,1,21,0,0.309072," ","integrate(1/(a*x-1)*(a*x+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
785,1,35,0,0.303971," ","integrate(1/(a*x-1)*(a*x+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
786,1,69,0,0.309623," ","integrate(1/(a*x-1)*(a*x+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
787,1,97,0,0.308489," ","integrate(1/(a*x-1)*(a*x+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
788,1,145,0,0.312748," ","integrate(1/(a*x-1)*(a*x+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
789,1,380,0,0.431264," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","-\frac{1}{280} \, {\left(\frac{525 \, c^{4} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{840 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{840 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{2205 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{2}} + 13615 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} + 33621 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 39071 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 12799 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 20811 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 7665 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 1155 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{6 \, {\left(a x - 1\right)} a^{2}}{a x + 1} + \frac{14 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{14 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{14 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{14 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} - \frac{6 \, {\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - \frac{{\left(a x - 1\right)}^{8} a^{2}}{{\left(a x + 1\right)}^{8}} + a^{2}}\right)} a"," ",0,"-1/280*(525*c^4*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 840*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 840*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - (2205*c^4*((a*x - 1)/(a*x + 1))^(15/2) + 13615*c^4*((a*x - 1)/(a*x + 1))^(13/2) + 33621*c^4*((a*x - 1)/(a*x + 1))^(11/2) + 39071*c^4*((a*x - 1)/(a*x + 1))^(9/2) + 12799*c^4*((a*x - 1)/(a*x + 1))^(7/2) - 20811*c^4*((a*x - 1)/(a*x + 1))^(5/2) - 7665*c^4*((a*x - 1)/(a*x + 1))^(3/2) - 1155*c^4*sqrt((a*x - 1)/(a*x + 1)))/(6*(a*x - 1)*a^2/(a*x + 1) + 14*(a*x - 1)^2*a^2/(a*x + 1)^2 + 14*(a*x - 1)^3*a^2/(a*x + 1)^3 - 14*(a*x - 1)^5*a^2/(a*x + 1)^5 - 14*(a*x - 1)^6*a^2/(a*x + 1)^6 - 6*(a*x - 1)^7*a^2/(a*x + 1)^7 - (a*x - 1)^8*a^2/(a*x + 1)^8 + a^2))*a","A",0
790,1,302,0,0.420977," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","-\frac{1}{20} \, {\left(\frac{15 \, c^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{60 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{60 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{135 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 575 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 842 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 298 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 465 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 105 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{4 \, {\left(a x - 1\right)} a^{2}}{a x + 1} + \frac{5 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} - \frac{4 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{{\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + a^{2}}\right)} a"," ",0,"-1/20*(15*c^3*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 60*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 60*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - (135*c^3*((a*x - 1)/(a*x + 1))^(11/2) + 575*c^3*((a*x - 1)/(a*x + 1))^(9/2) + 842*c^3*((a*x - 1)/(a*x + 1))^(7/2) + 298*c^3*((a*x - 1)/(a*x + 1))^(5/2) - 465*c^3*((a*x - 1)/(a*x + 1))^(3/2) - 105*c^3*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)*a^2/(a*x + 1) + 5*(a*x - 1)^2*a^2/(a*x + 1)^2 - 5*(a*x - 1)^4*a^2/(a*x + 1)^4 - 4*(a*x - 1)^5*a^2/(a*x + 1)^5 - (a*x - 1)^6*a^2/(a*x + 1)^6 + a^2))*a","A",0
791,1,223,0,0.418714," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{3 \, c^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{9 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{9 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} + \frac{15 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 37 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 17 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 21 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{2 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + a^{2}}\right)}"," ",0,"1/3*a*(3*c^2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 9*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 9*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 + (15*c^2*((a*x - 1)/(a*x + 1))^(7/2) + 37*c^2*((a*x - 1)/(a*x + 1))^(5/2) + 17*c^2*((a*x - 1)/(a*x + 1))^(3/2) - 21*c^2*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - 2*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 + a^2))","A",0
792,1,118,0,0.416378," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2),x, algorithm=""maxima"")","-a {\left(\frac{4 \, c \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} - \frac{6 \, c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"-a*(4*c*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) - 6*c*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 3*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 3*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","A",0
793,1,133,0,0.318941," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{\frac{11 \, {\left(a x - 1\right)}}{a x + 1} - \frac{18 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1}{a^{2} c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - a^{2} c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}} + \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c}\right)}"," ",0,"1/3*a*((11*(a*x - 1)/(a*x + 1) - 18*(a*x - 1)^2/(a*x + 1)^2 + 1)/(a^2*c*((a*x - 1)/(a*x + 1))^(5/2) - a^2*c*((a*x - 1)/(a*x + 1))^(3/2)) + 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - 9*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c))","A",0
794,1,153,0,0.318759," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","\frac{1}{20} \, a {\left(\frac{\frac{9 \, {\left(a x - 1\right)}}{a x + 1} + \frac{75 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - \frac{125 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 1}{a^{2} c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - a^{2} c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}} + \frac{60 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} - \frac{60 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{2}}\right)}"," ",0,"1/20*a*((9*(a*x - 1)/(a*x + 1) + 75*(a*x - 1)^2/(a*x + 1)^2 - 125*(a*x - 1)^3/(a*x + 1)^3 + 1)/(a^2*c^2*((a*x - 1)/(a*x + 1))^(7/2) - a^2*c^2*((a*x - 1)/(a*x + 1))^(5/2)) + 60*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) - 60*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^2))","A",0
795,1,192,0,0.328682," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","\frac{1}{560} \, a {\left(\frac{\frac{51 \, {\left(a x - 1\right)}}{a x + 1} + \frac{294 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{2170 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - \frac{3640 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} + 5}{a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}}} + \frac{1680 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{3}} - \frac{1680 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{3}} + \frac{35 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3}}\right)}"," ",0,"1/560*a*((51*(a*x - 1)/(a*x + 1) + 294*(a*x - 1)^2/(a*x + 1)^2 + 2170*(a*x - 1)^3/(a*x + 1)^3 - 3640*(a*x - 1)^4/(a*x + 1)^4 + 5)/(a^2*c^3*((a*x - 1)/(a*x + 1))^(9/2) - a^2*c^3*((a*x - 1)/(a*x + 1))^(7/2)) + 1680*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^3) - 1680*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^3) + 35*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^3))","A",0
796,1,226,0,0.322697," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","\frac{1}{20160} \, a {\left(\frac{\frac{415 \, {\left(a x - 1\right)}}{a x + 1} + \frac{2511 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{11739 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + \frac{80745 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} - \frac{135765 \, {\left(a x - 1\right)}^{5}}{{\left(a x + 1\right)}^{5}} + 35}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} - a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}}} + \frac{105 \, {\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 30 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} c^{4}} + \frac{60480 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} - \frac{60480 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{4}}\right)}"," ",0,"1/20160*a*((415*(a*x - 1)/(a*x + 1) + 2511*(a*x - 1)^2/(a*x + 1)^2 + 11739*(a*x - 1)^3/(a*x + 1)^3 + 80745*(a*x - 1)^4/(a*x + 1)^4 - 135765*(a*x - 1)^5/(a*x + 1)^5 + 35)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(11/2) - a^2*c^4*((a*x - 1)/(a*x + 1))^(9/2)) + 105*(((a*x - 1)/(a*x + 1))^(3/2) + 30*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^4) + 60480*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) - 60480*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^4))","A",0
797,1,103,0,0.304315," ","integrate(1/(a*x-1)^2*(a*x+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
798,1,92,0,0.315356," ","integrate(1/(a*x-1)^2*(a*x+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
799,1,59,0,0.313228," ","integrate(1/(a*x-1)^2*(a*x+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
800,1,46,0,0.309978," ","integrate(1/(a*x-1)^2*(a*x+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
801,1,32,0,0.301598," ","integrate(1/(a*x-1)^2*(a*x+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
802,1,49,0,0.302098," ","integrate(1/(a*x-1)^2*(a*x+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
803,1,75,0,0.315548," ","integrate(1/(a*x-1)^2*(a*x+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
804,1,107,0,0.305271," ","integrate(1/(a*x-1)^2*(a*x+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
805,1,135,0,0.321109," ","integrate(1/(a*x-1)^2*(a*x+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
806,1,380,0,0.420210," ","integrate((c-c/a^2/x^2)^4*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{1}{840} \, {\left(\frac{3675 \, c^{4} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{840 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{840 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{1995 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{2}} + 10185 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} + 17619 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 4569 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 71801 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 72051 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 31465 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 5355 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{6 \, {\left(a x - 1\right)} a^{2}}{a x + 1} + \frac{14 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{14 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{14 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{14 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} - \frac{6 \, {\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - \frac{{\left(a x - 1\right)}^{8} a^{2}}{{\left(a x + 1\right)}^{8}} + a^{2}}\right)} a"," ",0,"-1/840*(3675*c^4*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 840*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 840*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - (1995*c^4*((a*x - 1)/(a*x + 1))^(15/2) + 10185*c^4*((a*x - 1)/(a*x + 1))^(13/2) + 17619*c^4*((a*x - 1)/(a*x + 1))^(11/2) + 4569*c^4*((a*x - 1)/(a*x + 1))^(9/2) + 71801*c^4*((a*x - 1)/(a*x + 1))^(7/2) + 72051*c^4*((a*x - 1)/(a*x + 1))^(5/2) + 31465*c^4*((a*x - 1)/(a*x + 1))^(3/2) + 5355*c^4*sqrt((a*x - 1)/(a*x + 1)))/(6*(a*x - 1)*a^2/(a*x + 1) + 14*(a*x - 1)^2*a^2/(a*x + 1)^2 + 14*(a*x - 1)^3*a^2/(a*x + 1)^3 - 14*(a*x - 1)^5*a^2/(a*x + 1)^5 - 14*(a*x - 1)^6*a^2/(a*x + 1)^6 - 6*(a*x - 1)^7*a^2/(a*x + 1)^7 - (a*x - 1)^8*a^2/(a*x + 1)^8 + a^2))*a","A",0
807,1,302,0,0.413373," ","integrate((c-c/a^2/x^2)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{1}{60} \, {\left(\frac{225 \, c^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{60 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{60 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{105 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 305 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 86 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 1654 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 1345 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 345 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{4 \, {\left(a x - 1\right)} a^{2}}{a x + 1} + \frac{5 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} - \frac{4 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{{\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + a^{2}}\right)} a"," ",0,"-1/60*(225*c^3*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 60*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 60*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - (105*c^3*((a*x - 1)/(a*x + 1))^(11/2) + 305*c^3*((a*x - 1)/(a*x + 1))^(9/2) + 86*c^3*((a*x - 1)/(a*x + 1))^(7/2) + 1654*c^3*((a*x - 1)/(a*x + 1))^(5/2) + 1345*c^3*((a*x - 1)/(a*x + 1))^(3/2) + 345*c^3*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)*a^2/(a*x + 1) + 5*(a*x - 1)^2*a^2/(a*x + 1)^2 - 5*(a*x - 1)^4*a^2/(a*x + 1)^4 - 4*(a*x - 1)^5*a^2/(a*x + 1)^5 - (a*x - 1)^6*a^2/(a*x + 1)^6 + a^2))*a","A",0
808,1,223,0,0.418474," ","integrate((c-c/a^2/x^2)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{9 \, c^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{3 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 29 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 15 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{2 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + a^{2}}\right)}"," ",0,"-1/3*a*(9*c^2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - (3*c^2*((a*x - 1)/(a*x + 1))^(7/2) + c^2*((a*x - 1)/(a*x + 1))^(5/2) + 29*c^2*((a*x - 1)/(a*x + 1))^(3/2) + 15*c^2*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - 2*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 + a^2))","A",0
809,1,117,0,0.408274," ","integrate((c-c/a^2/x^2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","-a {\left(\frac{4 \, c \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} + \frac{2 \, c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)}"," ",0,"-a*(4*c*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) + 2*c*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)","A",0
810,1,121,0,0.315019," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2} c}{a x + 1} - a^{2} c} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c} - \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c}\right)}"," ",0,"-a*(2*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2*c/(a*x + 1) - a^2*c) + log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c) - sqrt((a*x - 1)/(a*x + 1))/(a^2*c))","A",0
811,1,163,0,0.304830," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","-\frac{1}{12} \, a {\left(\frac{3 \, {\left(\frac{9 \, {\left(a x - 1\right)}}{a x + 1} - 1\right)}}{a^{2} c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - a^{2} c^{2} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 18 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2}} + \frac{12 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} - \frac{12 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{2}}\right)}"," ",0,"-1/12*a*(3*(9*(a*x - 1)/(a*x + 1) - 1)/(a^2*c^2*((a*x - 1)/(a*x + 1))^(3/2) - a^2*c^2*sqrt((a*x - 1)/(a*x + 1))) - (((a*x - 1)/(a*x + 1))^(3/2) + 18*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^2) + 12*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) - 12*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^2))","A",0
812,1,197,0,0.318004," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","\frac{1}{240} \, a {\left(\frac{5 \, {\left(\frac{23 \, {\left(a x - 1\right)}}{a x + 1} - \frac{120 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1\right)}}{a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}} + \frac{3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 40 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 450 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3}} - \frac{240 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{3}} + \frac{240 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{3}}\right)}"," ",0,"1/240*a*(5*(23*(a*x - 1)/(a*x + 1) - 120*(a*x - 1)^2/(a*x + 1)^2 + 1)/(a^2*c^3*((a*x - 1)/(a*x + 1))^(5/2) - a^2*c^3*((a*x - 1)/(a*x + 1))^(3/2)) + (3*((a*x - 1)/(a*x + 1))^(5/2) + 40*((a*x - 1)/(a*x + 1))^(3/2) + 450*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^3) - 240*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^3) + 240*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^3))","A",0
813,1,231,0,0.329274," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","\frac{1}{6720} \, a {\left(\frac{7 \, {\left(\frac{47 \, {\left(a x - 1\right)}}{a x + 1} + \frac{655 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - \frac{2625 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 3\right)}}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}}} + \frac{5 \, {\left(3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 42 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 329 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 2940 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} c^{4}} - \frac{6720 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} + \frac{6720 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{4}}\right)}"," ",0,"1/6720*a*(7*(47*(a*x - 1)/(a*x + 1) + 655*(a*x - 1)^2/(a*x + 1)^2 - 2625*(a*x - 1)^3/(a*x + 1)^3 + 3)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(7/2) - a^2*c^4*((a*x - 1)/(a*x + 1))^(5/2)) + 5*(3*((a*x - 1)/(a*x + 1))^(7/2) + 42*((a*x - 1)/(a*x + 1))^(5/2) + 329*((a*x - 1)/(a*x + 1))^(3/2) + 2940*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^4) - 6720*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) + 6720*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^4))","A",0
814,1,81,0,0.302327," ","integrate((c-c/a^2/x^2)^4*(a*x-1)/(a*x+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
815,1,70,0,0.300916," ","integrate((c-c/a^2/x^2)^3*(a*x-1)/(a*x+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
816,1,37,0,0.313026," ","integrate((c-c/a^2/x^2)^2*(a*x-1)/(a*x+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
817,1,21,0,0.310165," ","integrate((c-c/a^2/x^2)*(a*x-1)/(a*x+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
818,1,34,0,0.306338," ","integrate((a*x-1)/(a*x+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
819,1,69,0,0.311404," ","integrate((a*x-1)/(a*x+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
820,1,97,0,0.308523," ","integrate((a*x-1)/(a*x+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
821,1,145,0,0.316743," ","integrate((a*x-1)/(a*x+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
822,1,379,0,0.426257," ","integrate((c-c/a^2/x^2)^4*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{1}{280} \, {\left(\frac{525 \, c^{4} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{840 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{840 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} + \frac{1155 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{15}{2}} + 7665 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{13}{2}} + 20811 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} - 12799 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - 39071 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 33621 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 13615 \, c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 2205 \, c^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{6 \, {\left(a x - 1\right)} a^{2}}{a x + 1} + \frac{14 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} + \frac{14 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{14 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{14 \, {\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} - \frac{6 \, {\left(a x - 1\right)}^{7} a^{2}}{{\left(a x + 1\right)}^{7}} - \frac{{\left(a x - 1\right)}^{8} a^{2}}{{\left(a x + 1\right)}^{8}} + a^{2}}\right)} a"," ",0,"-1/280*(525*c^4*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 840*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 840*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 + (1155*c^4*((a*x - 1)/(a*x + 1))^(15/2) + 7665*c^4*((a*x - 1)/(a*x + 1))^(13/2) + 20811*c^4*((a*x - 1)/(a*x + 1))^(11/2) - 12799*c^4*((a*x - 1)/(a*x + 1))^(9/2) - 39071*c^4*((a*x - 1)/(a*x + 1))^(7/2) - 33621*c^4*((a*x - 1)/(a*x + 1))^(5/2) - 13615*c^4*((a*x - 1)/(a*x + 1))^(3/2) - 2205*c^4*sqrt((a*x - 1)/(a*x + 1)))/(6*(a*x - 1)*a^2/(a*x + 1) + 14*(a*x - 1)^2*a^2/(a*x + 1)^2 + 14*(a*x - 1)^3*a^2/(a*x + 1)^3 - 14*(a*x - 1)^5*a^2/(a*x + 1)^5 - 14*(a*x - 1)^6*a^2/(a*x + 1)^6 - 6*(a*x - 1)^7*a^2/(a*x + 1)^7 - (a*x - 1)^8*a^2/(a*x + 1)^8 + a^2))*a","A",0
823,1,301,0,0.418979," ","integrate((c-c/a^2/x^2)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-\frac{1}{20} \, {\left(\frac{15 \, c^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{60 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{60 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} + \frac{105 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{11}{2}} + 465 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} - 298 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 842 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 575 \, c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 135 \, c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{4 \, {\left(a x - 1\right)} a^{2}}{a x + 1} + \frac{5 \, {\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - \frac{5 \, {\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} - \frac{4 \, {\left(a x - 1\right)}^{5} a^{2}}{{\left(a x + 1\right)}^{5}} - \frac{{\left(a x - 1\right)}^{6} a^{2}}{{\left(a x + 1\right)}^{6}} + a^{2}}\right)} a"," ",0,"-1/20*(15*c^3*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 60*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 60*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 + (105*c^3*((a*x - 1)/(a*x + 1))^(11/2) + 465*c^3*((a*x - 1)/(a*x + 1))^(9/2) - 298*c^3*((a*x - 1)/(a*x + 1))^(7/2) - 842*c^3*((a*x - 1)/(a*x + 1))^(5/2) - 575*c^3*((a*x - 1)/(a*x + 1))^(3/2) - 135*c^3*sqrt((a*x - 1)/(a*x + 1)))/(4*(a*x - 1)*a^2/(a*x + 1) + 5*(a*x - 1)^2*a^2/(a*x + 1)^2 - 5*(a*x - 1)^4*a^2/(a*x + 1)^4 - 4*(a*x - 1)^5*a^2/(a*x + 1)^5 - (a*x - 1)^6*a^2/(a*x + 1)^6 + a^2))*a","A",0
824,1,224,0,0.422298," ","integrate((c-c/a^2/x^2)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{3 \, c^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{9 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{9 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}} - \frac{21 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} - 17 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - 37 \, c^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - 15 \, c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{2 \, {\left(a x - 1\right)} a^{2}}{a x + 1} - \frac{2 \, {\left(a x - 1\right)}^{3} a^{2}}{{\left(a x + 1\right)}^{3}} - \frac{{\left(a x - 1\right)}^{4} a^{2}}{{\left(a x + 1\right)}^{4}} + a^{2}}\right)}"," ",0,"1/3*a*(3*c^2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 9*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 9*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2 - (21*c^2*((a*x - 1)/(a*x + 1))^(7/2) - 17*c^2*((a*x - 1)/(a*x + 1))^(5/2) - 37*c^2*((a*x - 1)/(a*x + 1))^(3/2) - 15*c^2*sqrt((a*x - 1)/(a*x + 1)))/(2*(a*x - 1)*a^2/(a*x + 1) - 2*(a*x - 1)^3*a^2/(a*x + 1)^3 - (a*x - 1)^4*a^2/(a*x + 1)^4 + a^2))","A",0
825,1,118,0,0.421247," ","integrate((c-c/a^2/x^2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","-{\left(\frac{4 \, c \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{\frac{{\left(a x - 1\right)}^{2} a^{2}}{{\left(a x + 1\right)}^{2}} - a^{2}} - \frac{6 \, c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2}}\right)} a"," ",0,"-(4*c*((a*x - 1)/(a*x + 1))^(3/2)/((a*x - 1)^2*a^2/(a*x + 1)^2 - a^2) - 6*c*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 3*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/a^2)*a","A",0
826,1,140,0,0.311159," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{6 \, \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2} c}{a x + 1} - a^{2} c} - \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 12 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c} + \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c}\right)}"," ",0,"-1/3*a*(6*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2*c/(a*x + 1) - a^2*c) - (((a*x - 1)/(a*x + 1))^(3/2) + 12*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c) + 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - 9*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c))","A",0
827,1,161,0,0.313934," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^2,x, algorithm=""maxima"")","-\frac{1}{20} \, a {\left(\frac{40 \, \sqrt{\frac{a x - 1}{a x + 1}}}{\frac{{\left(a x - 1\right)} a^{2} c^{2}}{a x + 1} - a^{2} c^{2}} - \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 10 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 85 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2}} + \frac{60 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} - \frac{60 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{2}}\right)}"," ",0,"-1/20*a*(40*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*a^2*c^2/(a*x + 1) - a^2*c^2) - (((a*x - 1)/(a*x + 1))^(5/2) + 10*((a*x - 1)/(a*x + 1))^(3/2) + 85*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^2) + 60*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) - 60*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^2))","A",0
828,1,199,0,0.307741," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^3,x, algorithm=""maxima"")","-\frac{1}{560} \, a {\left(\frac{35 \, {\left(\frac{33 \, {\left(a x - 1\right)}}{a x + 1} - 1\right)}}{a^{2} c^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} - a^{2} c^{3} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{5 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 56 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 350 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 2520 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3}} + \frac{1680 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{3}} - \frac{1680 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{3}}\right)}"," ",0,"-1/560*a*(35*(33*(a*x - 1)/(a*x + 1) - 1)/(a^2*c^3*((a*x - 1)/(a*x + 1))^(3/2) - a^2*c^3*sqrt((a*x - 1)/(a*x + 1))) - (5*((a*x - 1)/(a*x + 1))^(7/2) + 56*((a*x - 1)/(a*x + 1))^(5/2) + 350*((a*x - 1)/(a*x + 1))^(3/2) + 2520*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^3) + 1680*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^3) - 1680*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^3))","A",0
829,1,231,0,0.328133," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^4,x, algorithm=""maxima"")","\frac{1}{20160} \, a {\left(\frac{105 \, {\left(\frac{29 \, {\left(a x - 1\right)}}{a x + 1} - \frac{414 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1\right)}}{a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} - a^{2} c^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}} + \frac{35 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{9}{2}} + 450 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{2}} + 2961 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{2}} + 14700 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}} + 95445 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{4}} - \frac{60480 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} + \frac{60480 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a^{2} c^{4}}\right)}"," ",0,"1/20160*a*(105*(29*(a*x - 1)/(a*x + 1) - 414*(a*x - 1)^2/(a*x + 1)^2 + 1)/(a^2*c^4*((a*x - 1)/(a*x + 1))^(5/2) - a^2*c^4*((a*x - 1)/(a*x + 1))^(3/2)) + (35*((a*x - 1)/(a*x + 1))^(9/2) + 450*((a*x - 1)/(a*x + 1))^(7/2) + 2961*((a*x - 1)/(a*x + 1))^(5/2) + 14700*((a*x - 1)/(a*x + 1))^(3/2) + 95445*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^4) - 60480*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) + 60480*log(sqrt((a*x - 1)/(a*x + 1)) - 1)/(a^2*c^4))","A",0
830,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(7/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
831,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(5/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
832,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(3/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
833,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
834,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c - \frac{c}{a^{2} x^{2}}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/(sqrt(c - c/(a^2*x^2))*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
835,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
836,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
837,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(7/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
838,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(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}}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^(7/2)/(a*x - 1), x)","F",0
839,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(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}}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^(5/2)/(a*x - 1), x)","F",0
840,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(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}}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^(3/2)/(a*x - 1), x)","F",0
841,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))/(a*x - 1), x)","F",0
842,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*sqrt(c - c/(a^2*x^2))), x)","F",0
843,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a x - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*(c - c/(a^2*x^2))^(3/2)), x)","F",0
844,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a x - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
845,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{a x + 1}{{\left(a x - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
846,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(9/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
847,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(7/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
848,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(5/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
849,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(3/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
850,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
851,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
852,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(3/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
853,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(5/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
854,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(7/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
855,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(7/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
856,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(5/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
857,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(3/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
858,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
859,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/sqrt(c - c/(a^2*x^2)), x)","F",0
860,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(c - c/(a^2*x^2))^(3/2), x)","F",0
861,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(c - c/(a^2*x^2))^(5/2), x)","F",0
862,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(c - c/(a^2*x^2))^(7/2), x)","F",0
863,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(7/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(c - c/(a^2*x^2))^(7/2)/(a*x + 1), x)","F",0
864,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(5/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(c - c/(a^2*x^2))^(5/2)/(a*x + 1), x)","F",0
865,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(3/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(c - c/(a^2*x^2))^(3/2)/(a*x + 1), x)","F",0
866,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a^2*x^2))/(a*x + 1), x)","F",0
867,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{a x - 1}{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*sqrt(c - c/(a^2*x^2))), x)","F",0
868,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{a x - 1}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*(c - c/(a^2*x^2))^(3/2)), x)","F",0
869,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{a x - 1}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
870,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{a x - 1}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
871,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(9/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
872,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(7/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
873,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(5/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
874,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(3/2)*((a*x-1)/(a*x+1))^(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{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(3/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
875,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
876,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{\sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/sqrt(c - c/(a^2*x^2)), x)","F",0
877,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(c - c/(a^2*x^2))^(3/2), x)","F",0
878,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(c - c/(a^2*x^2))^(5/2), x)","F",0
879,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(c - c/(a^2*x^2))^(7/2), x)","F",0
880,1,44,0,0.379753," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\frac{{\left(a \sqrt{c} m x + \sqrt{c} {\left(m + 1\right)}\right)} {\left(a x + 1\right)} x^{m}}{{\left(m^{2} + m\right)} a^{2} x + {\left(m^{2} + m\right)} a}"," ",0,"(a*sqrt(c)*m*x + sqrt(c)*(m + 1))*(a*x + 1)*x^m/((m^2 + m)*a^2*x + (m^2 + m)*a)","A",0
881,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^2/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
882,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} x}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
883,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
884,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
885,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x^2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
886,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x^3*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{3}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))*x^3/(a*x - 1), x)","F",0
887,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))*x^2/(a*x - 1), x)","F",0
888,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))*x/(a*x - 1), x)","F",0
889,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))/(a*x - 1), x)","F",0
890,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x - 1\right)} x}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))/((a*x - 1)*x), x)","F",0
891,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x - 1\right)} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))/((a*x - 1)*x^2), x)","F",0
892,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x - 1\right)} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))/((a*x - 1)*x^3), x)","F",0
893,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x - 1\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))/((a*x - 1)*x^4), x)","F",0
894,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x - 1\right)} x^{5}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))/((a*x - 1)*x^5), x)","F",0
895,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} x^{3}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^3/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
896,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^2/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
897,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} x}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
898,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
899,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
900,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x^2*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
901,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x^3*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
902,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x^4*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
903,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x^5*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
904,1,46,0,0.388370," ","integrate(x^m*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\frac{{\left(a \sqrt{c} m x - \sqrt{c} {\left(m + 1\right)}\right)} {\left(a x - 1\right)} x^{m}}{{\left(m^{2} + m\right)} a^{2} x - {\left(m^{2} + m\right)} a}"," ",0,"(a*sqrt(c)*m*x - sqrt(c)*(m + 1))*(a*x - 1)*x^m/((m^2 + m)*a^2*x - (m^2 + m)*a)","A",0
905,0,0,0,0.000000," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^2*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
906,0,0,0,0.000000," ","integrate(x*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} x \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
907,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
908,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \sqrt{\frac{a x - 1}{a x + 1}}}{x}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*sqrt((a*x - 1)/(a*x + 1))/x, x)","F",0
909,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \sqrt{\frac{a x - 1}{a x + 1}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*sqrt((a*x - 1)/(a*x + 1))/x^2, x)","F",0
910,0,0,0,0.000000," ","integrate(x^3*(c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{3}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a^2*x^2))*x^3/(a*x + 1), x)","F",0
911,0,0,0,0.000000," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a^2*x^2))*x^2/(a*x + 1), x)","F",0
912,0,0,0,0.000000," ","integrate(x*(c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a^2*x^2))*x/(a*x + 1), x)","F",0
913,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a^2*x^2))/(a*x + 1), x)","F",0
914,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x,x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)*x), x)","F",0
915,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)*x^2), x)","F",0
916,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)} x^{3}}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)*x^3), x)","F",0
917,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)} x^{4}}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)*x^4), x)","F",0
918,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^5,x, algorithm=""maxima"")","\int \frac{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)} x^{5}}\,{d x}"," ",0,"integrate((a*x - 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)*x^5), x)","F",0
919,0,0,0,0.000000," ","integrate(x^3*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^3*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
920,0,0,0,0.000000," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^2*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
921,0,0,0,0.000000," ","integrate(x*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
922,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""maxima"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
923,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)/x, x)","F",0
924,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)/x^2, x)","F",0
925,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)/x^3, x)","F",0
926,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)/x^4, x)","F",0
927,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""maxima"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)/x^5, x)","F",0
928,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
929,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
930,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
931,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
932,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
933,0,0,0,0.000000," ","integrate(exp(n*arccoth(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
934,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^p/exp(2*p*arccoth(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
935,0,0,0,0.000000," ","integrate(exp(2*p*arccoth(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
