1,1,92,0,0.529550," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^3,x, algorithm=""fricas"")","\frac{{\left(6 \, a^{4} x^{4} + 14 \, a^{3} x^{3} + 17 \, a^{2} x^{2} + 25 \, a x + 16\right)} \sqrt{\frac{a x - 1}{a x + 1}} + 9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{24 \, a^{4}}"," ",0,"1/24*((6*a^4*x^4 + 14*a^3*x^3 + 17*a^2*x^2 + 25*a*x + 16)*sqrt((a*x - 1)/(a*x + 1)) + 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 9*log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^4","A",0
2,1,84,0,0.712488," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} + 5 \, a^{2} x^{2} + 7 \, a x + 4\right)} \sqrt{\frac{a x - 1}{a x + 1}} + 3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{6 \, a^{3}}"," ",0,"1/6*((2*a^3*x^3 + 5*a^2*x^2 + 7*a*x + 4)*sqrt((a*x - 1)/(a*x + 1)) + 3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^3","A",0
3,1,73,0,0.513784," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x,x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} + 3 \, a x + 2\right)} \sqrt{\frac{a x - 1}{a x + 1}} + \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{2 \, a^{2}}"," ",0,"1/2*((a^2*x^2 + 3*a*x + 2)*sqrt((a*x - 1)/(a*x + 1)) + log(sqrt((a*x - 1)/(a*x + 1)) + 1) - log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2","A",0
4,1,64,0,0.659604," ","integrate(1/((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} + \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a}"," ",0,"((a*x + 1)*sqrt((a*x - 1)/(a*x + 1)) + log(sqrt((a*x - 1)/(a*x + 1)) + 1) - log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a","A",0
5,1,57,0,0.667914," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""fricas"")","2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)"," ",0,"2*arctan(sqrt((a*x - 1)/(a*x + 1))) + log(sqrt((a*x - 1)/(a*x + 1)) + 1) - log(sqrt((a*x - 1)/(a*x + 1)) - 1)","B",0
6,1,46,0,0.562799," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""fricas"")","\frac{2 \, a x \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{x}"," ",0,"(2*a*x*arctan(sqrt((a*x - 1)/(a*x + 1))) + (a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/x","B",0
7,1,60,0,0.627717," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, a^{2} x^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + {\left(2 \, a^{2} x^{2} + 3 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, x^{2}}"," ",0,"1/2*(2*a^2*x^2*arctan(sqrt((a*x - 1)/(a*x + 1))) + (2*a^2*x^2 + 3*a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/x^2","A",0
8,1,68,0,0.512642," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^4,x, algorithm=""fricas"")","\frac{6 \, a^{3} x^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + {\left(4 \, a^{3} x^{3} + 7 \, a^{2} x^{2} + 5 \, a x + 2\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, x^{3}}"," ",0,"1/6*(6*a^3*x^3*arctan(sqrt((a*x - 1)/(a*x + 1))) + (4*a^3*x^3 + 7*a^2*x^2 + 5*a*x + 2)*sqrt((a*x - 1)/(a*x + 1)))/x^3","A",0
9,1,76,0,0.548457," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^5,x, algorithm=""fricas"")","\frac{18 \, a^{4} x^{4} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + {\left(16 \, a^{4} x^{4} + 25 \, a^{3} x^{3} + 17 \, a^{2} x^{2} + 14 \, a x + 6\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{24 \, x^{4}}"," ",0,"1/24*(18*a^4*x^4*arctan(sqrt((a*x - 1)/(a*x + 1))) + (16*a^4*x^4 + 25*a^3*x^3 + 17*a^2*x^2 + 14*a*x + 6)*sqrt((a*x - 1)/(a*x + 1)))/x^4","A",0
10,1,42,0,0.572169," ","integrate(1/(a*x-1)*(a*x+1)*x^3,x, algorithm=""fricas"")","\frac{3 \, a^{4} x^{4} + 8 \, a^{3} x^{3} + 12 \, a^{2} x^{2} + 24 \, a x + 24 \, \log\left(a x - 1\right)}{12 \, a^{4}}"," ",0,"1/12*(3*a^4*x^4 + 8*a^3*x^3 + 12*a^2*x^2 + 24*a*x + 24*log(a*x - 1))/a^4","A",0
11,1,33,0,0.572468," ","integrate(1/(a*x-1)*(a*x+1)*x^2,x, algorithm=""fricas"")","\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 6 \, a x + 6 \, \log\left(a x - 1\right)}{3 \, a^{3}}"," ",0,"1/3*(a^3*x^3 + 3*a^2*x^2 + 6*a*x + 6*log(a*x - 1))/a^3","A",0
12,1,25,0,0.495292," ","integrate(1/(a*x-1)*(a*x+1)*x,x, algorithm=""fricas"")","\frac{a^{2} x^{2} + 4 \, a x + 4 \, \log\left(a x - 1\right)}{2 \, a^{2}}"," ",0,"1/2*(a^2*x^2 + 4*a*x + 4*log(a*x - 1))/a^2","A",0
13,1,16,0,0.449088," ","integrate(1/(a*x-1)*(a*x+1),x, algorithm=""fricas"")","\frac{a x + 2 \, \log\left(a x - 1\right)}{a}"," ",0,"(a*x + 2*log(a*x - 1))/a","A",0
14,1,13,0,0.447903," ","integrate(1/(a*x-1)*(a*x+1)/x,x, algorithm=""fricas"")","2 \, \log\left(a x - 1\right) - \log\left(x\right)"," ",0,"2*log(a*x - 1) - log(x)","A",0
15,1,22,0,0.807435," ","integrate(1/(a*x-1)*(a*x+1)/x^2,x, algorithm=""fricas"")","\frac{2 \, a x \log\left(a x - 1\right) - 2 \, a x \log\left(x\right) + 1}{x}"," ",0,"(2*a*x*log(a*x - 1) - 2*a*x*log(x) + 1)/x","A",0
16,1,35,0,0.524835," ","integrate(1/(a*x-1)*(a*x+1)/x^3,x, algorithm=""fricas"")","\frac{4 \, a^{2} x^{2} \log\left(a x - 1\right) - 4 \, a^{2} x^{2} \log\left(x\right) + 4 \, a x + 1}{2 \, x^{2}}"," ",0,"1/2*(4*a^2*x^2*log(a*x - 1) - 4*a^2*x^2*log(x) + 4*a*x + 1)/x^2","A",0
17,1,43,0,0.593393," ","integrate(1/(a*x-1)*(a*x+1)/x^4,x, algorithm=""fricas"")","\frac{6 \, a^{3} x^{3} \log\left(a x - 1\right) - 6 \, a^{3} x^{3} \log\left(x\right) + 6 \, a^{2} x^{2} + 3 \, a x + 1}{3 \, x^{3}}"," ",0,"1/3*(6*a^3*x^3*log(a*x - 1) - 6*a^3*x^3*log(x) + 6*a^2*x^2 + 3*a*x + 1)/x^3","A",0
18,1,112,0,0.512381," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2,x, algorithm=""fricas"")","\frac{33 \, {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 33 \, {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(2 \, a^{4} x^{4} + 9 \, a^{3} x^{3} + 26 \, a^{2} x^{2} - 33 \, a x - 52\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, {\left(a^{4} x - a^{3}\right)}}"," ",0,"1/6*(33*(a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 33*(a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (2*a^4*x^4 + 9*a^3*x^3 + 26*a^2*x^2 - 33*a*x - 52)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*x - a^3)","A",0
19,1,103,0,0.492546," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x,x, algorithm=""fricas"")","\frac{9 \, {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 9 \, {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a^{3} x^{3} + 6 \, a^{2} x^{2} - 9 \, a x - 14\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, {\left(a^{3} x - a^{2}\right)}}"," ",0,"1/2*(9*(a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 9*(a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a^3*x^3 + 6*a^2*x^2 - 9*a*x - 14)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*x - a^2)","A",0
20,1,92,0,0.516264," ","integrate(1/((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{3 \, {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a^{2} x^{2} - 4 \, a x - 5\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x - a}"," ",0,"(3*(a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*(a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a^2*x^2 - 4*a*x - 5)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x - a)","A",0
21,1,104,0,0.588181," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""fricas"")","-\frac{2 \, {\left(a x - 1\right)} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + 4 \, {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x - 1}"," ",0,"-(2*(a*x - 1)*arctan(sqrt((a*x - 1)/(a*x + 1))) - (a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + (a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + 4*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x - 1)","B",0
22,1,74,0,0.510692," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""fricas"")","-\frac{6 \, {\left(a^{2} x^{2} - a x\right)} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + {\left(5 \, a^{2} x^{2} + 4 \, a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x^{2} - x}"," ",0,"-(6*(a^2*x^2 - a*x)*arctan(sqrt((a*x - 1)/(a*x + 1))) + (5*a^2*x^2 + 4*a*x - 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^2 - x)","A",0
23,1,88,0,0.384383," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""fricas"")","-\frac{18 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + {\left(14 \, a^{3} x^{3} + 9 \, a^{2} x^{2} - 6 \, a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, {\left(a x^{3} - x^{2}\right)}}"," ",0,"-1/2*(18*(a^3*x^3 - a^2*x^2)*arctan(sqrt((a*x - 1)/(a*x + 1))) + (14*a^3*x^3 + 9*a^2*x^2 - 6*a*x - 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^3 - x^2)","A",0
24,1,96,0,0.557078," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""fricas"")","-\frac{66 \, {\left(a^{4} x^{4} - a^{3} x^{3}\right)} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + {\left(52 \, a^{4} x^{4} + 33 \, a^{3} x^{3} - 26 \, a^{2} x^{2} - 9 \, a x - 2\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, {\left(a x^{4} - x^{3}\right)}}"," ",0,"-1/6*(66*(a^4*x^4 - a^3*x^3)*arctan(sqrt((a*x - 1)/(a*x + 1))) + (52*a^4*x^4 + 33*a^3*x^3 - 26*a^2*x^2 - 9*a*x - 2)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^4 - x^3)","A",0
25,1,66,0,0.635163," ","integrate(1/(a*x-1)^2*(a*x+1)^2*x^3,x, algorithm=""fricas"")","\frac{3 \, a^{5} x^{5} + 13 \, a^{4} x^{4} + 32 \, a^{3} x^{3} + 96 \, a^{2} x^{2} - 144 \, a x + 192 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 48}{12 \, {\left(a^{5} x - a^{4}\right)}}"," ",0,"1/12*(3*a^5*x^5 + 13*a^4*x^4 + 32*a^3*x^3 + 96*a^2*x^2 - 144*a*x + 192*(a*x - 1)*log(a*x - 1) - 48)/(a^5*x - a^4)","A",0
26,1,57,0,0.551698," ","integrate(1/(a*x-1)^2*(a*x+1)^2*x^2,x, algorithm=""fricas"")","\frac{a^{4} x^{4} + 5 \, a^{3} x^{3} + 18 \, a^{2} x^{2} - 24 \, a x + 36 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 12}{3 \, {\left(a^{4} x - a^{3}\right)}}"," ",0,"1/3*(a^4*x^4 + 5*a^3*x^3 + 18*a^2*x^2 - 24*a*x + 36*(a*x - 1)*log(a*x - 1) - 12)/(a^4*x - a^3)","A",0
27,1,49,0,0.564488," ","integrate(1/(a*x-1)^2*(a*x+1)^2*x,x, algorithm=""fricas"")","\frac{a^{3} x^{3} + 7 \, a^{2} x^{2} - 8 \, a x + 16 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 8}{2 \, {\left(a^{3} x - a^{2}\right)}}"," ",0,"1/2*(a^3*x^3 + 7*a^2*x^2 - 8*a*x + 16*(a*x - 1)*log(a*x - 1) - 8)/(a^3*x - a^2)","A",0
28,1,38,0,0.686306," ","integrate(1/(a*x-1)^2*(a*x+1)^2,x, algorithm=""fricas"")","\frac{a^{2} x^{2} - a x + 4 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 4}{a^{2} x - a}"," ",0,"(a^2*x^2 - a*x + 4*(a*x - 1)*log(a*x - 1) - 4)/(a^2*x - a)","A",0
29,1,18,0,0.548219," ","integrate(1/(a*x-1)^2*(a*x+1)^2/x,x, algorithm=""fricas"")","\frac{{\left(a x - 1\right)} \log\left(x\right) - 4}{a x - 1}"," ",0,"((a*x - 1)*log(x) - 4)/(a*x - 1)","A",0
30,1,55,0,0.455804," ","integrate(1/(a*x-1)^2*(a*x+1)^2/x^2,x, algorithm=""fricas"")","-\frac{5 \, a x + 4 \, {\left(a^{2} x^{2} - a x\right)} \log\left(a x - 1\right) - 4 \, {\left(a^{2} x^{2} - a x\right)} \log\left(x\right) - 1}{a x^{2} - x}"," ",0,"-(5*a*x + 4*(a^2*x^2 - a*x)*log(a*x - 1) - 4*(a^2*x^2 - a*x)*log(x) - 1)/(a*x^2 - x)","A",0
31,1,73,0,0.585707," ","integrate(1/(a*x-1)^2*(a*x+1)^2/x^3,x, algorithm=""fricas"")","-\frac{16 \, a^{2} x^{2} - 7 \, a x + 16 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \log\left(a x - 1\right) - 16 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \log\left(x\right) - 1}{2 \, {\left(a x^{3} - x^{2}\right)}}"," ",0,"-1/2*(16*a^2*x^2 - 7*a*x + 16*(a^3*x^3 - a^2*x^2)*log(a*x - 1) - 16*(a^3*x^3 - a^2*x^2)*log(x) - 1)/(a*x^3 - x^2)","A",0
32,1,81,0,0.609971," ","integrate(1/(a*x-1)^2*(a*x+1)^2/x^4,x, algorithm=""fricas"")","-\frac{36 \, a^{3} x^{3} - 18 \, a^{2} x^{2} - 5 \, a x + 36 \, {\left(a^{4} x^{4} - a^{3} x^{3}\right)} \log\left(a x - 1\right) - 36 \, {\left(a^{4} x^{4} - a^{3} x^{3}\right)} \log\left(x\right) - 1}{3 \, {\left(a x^{4} - x^{3}\right)}}"," ",0,"-1/3*(36*a^3*x^3 - 18*a^2*x^2 - 5*a*x + 36*(a^4*x^4 - a^3*x^3)*log(a*x - 1) - 36*(a^4*x^4 - a^3*x^3)*log(x) - 1)/(a*x^4 - x^3)","A",0
33,1,91,0,0.473593," ","integrate(x^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(6 \, a^{4} x^{4} - 2 \, a^{3} x^{3} + a^{2} x^{2} - 7 \, a x - 16\right)} \sqrt{\frac{a x - 1}{a x + 1}} + 9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{24 \, a^{4}}"," ",0,"1/24*((6*a^4*x^4 - 2*a^3*x^3 + a^2*x^2 - 7*a*x - 16)*sqrt((a*x - 1)/(a*x + 1)) + 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 9*log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^4","A",0
34,1,83,0,0.616683," ","integrate(x^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} - a^{2} x^{2} + a x + 4\right)} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{6 \, a^{3}}"," ",0,"1/6*((2*a^3*x^3 - a^2*x^2 + a*x + 4)*sqrt((a*x - 1)/(a*x + 1)) - 3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 3*log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^3","A",0
35,1,73,0,0.761544," ","integrate(x*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} - a x - 2\right)} \sqrt{\frac{a x - 1}{a x + 1}} + \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{2 \, a^{2}}"," ",0,"1/2*((a^2*x^2 - a*x - 2)*sqrt((a*x - 1)/(a*x + 1)) + log(sqrt((a*x - 1)/(a*x + 1)) + 1) - log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2","A",0
36,1,64,0,0.651873," ","integrate(((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} - \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a}"," ",0,"((a*x + 1)*sqrt((a*x - 1)/(a*x + 1)) - log(sqrt((a*x - 1)/(a*x + 1)) + 1) + log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a","A",0
37,1,57,0,0.571416," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""fricas"")","-2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)"," ",0,"-2*arctan(sqrt((a*x - 1)/(a*x + 1))) + log(sqrt((a*x - 1)/(a*x + 1)) + 1) - log(sqrt((a*x - 1)/(a*x + 1)) - 1)","B",0
38,1,47,0,0.570581," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""fricas"")","\frac{2 \, a x \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{x}"," ",0,"(2*a*x*arctan(sqrt((a*x - 1)/(a*x + 1))) - (a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/x","B",0
39,1,60,0,0.656168," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a^{2} x^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - {\left(2 \, a^{2} x^{2} + a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, x^{2}}"," ",0,"-1/2*(2*a^2*x^2*arctan(sqrt((a*x - 1)/(a*x + 1))) - (2*a^2*x^2 + a*x - 1)*sqrt((a*x - 1)/(a*x + 1)))/x^2","A",0
40,1,68,0,0.520114," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^4,x, algorithm=""fricas"")","\frac{6 \, a^{3} x^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - {\left(4 \, a^{3} x^{3} + a^{2} x^{2} - a x + 2\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, x^{3}}"," ",0,"1/6*(6*a^3*x^3*arctan(sqrt((a*x - 1)/(a*x + 1))) - (4*a^3*x^3 + a^2*x^2 - a*x + 2)*sqrt((a*x - 1)/(a*x + 1)))/x^3","A",0
41,1,77,0,1.335124," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{18 \, a^{4} x^{4} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - {\left(16 \, a^{4} x^{4} + 7 \, a^{3} x^{3} - a^{2} x^{2} + 2 \, a x - 6\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{24 \, x^{4}}"," ",0,"-1/24*(18*a^4*x^4*arctan(sqrt((a*x - 1)/(a*x + 1))) - (16*a^4*x^4 + 7*a^3*x^3 - a^2*x^2 + 2*a*x - 6)*sqrt((a*x - 1)/(a*x + 1)))/x^4","A",0
42,1,42,0,0.436777," ","integrate(x^3*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{3 \, a^{4} x^{4} - 8 \, a^{3} x^{3} + 12 \, a^{2} x^{2} - 24 \, a x + 24 \, \log\left(a x + 1\right)}{12 \, a^{4}}"," ",0,"1/12*(3*a^4*x^4 - 8*a^3*x^3 + 12*a^2*x^2 - 24*a*x + 24*log(a*x + 1))/a^4","A",0
43,1,33,0,0.443514," ","integrate(x^2*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 6 \, a x - 6 \, \log\left(a x + 1\right)}{3 \, a^{3}}"," ",0,"1/3*(a^3*x^3 - 3*a^2*x^2 + 6*a*x - 6*log(a*x + 1))/a^3","A",0
44,1,25,0,0.450691," ","integrate(x*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{a^{2} x^{2} - 4 \, a x + 4 \, \log\left(a x + 1\right)}{2 \, a^{2}}"," ",0,"1/2*(a^2*x^2 - 4*a*x + 4*log(a*x + 1))/a^2","A",0
45,1,16,0,0.472054," ","integrate((a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{a x - 2 \, \log\left(a x + 1\right)}{a}"," ",0,"(a*x - 2*log(a*x + 1))/a","A",0
46,1,13,0,0.497879," ","integrate((a*x-1)/(a*x+1)/x,x, algorithm=""fricas"")","2 \, \log\left(a x + 1\right) - \log\left(x\right)"," ",0,"2*log(a*x + 1) - log(x)","A",0
47,1,23,0,0.522713," ","integrate((a*x-1)/(a*x+1)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a x \log\left(a x + 1\right) - 2 \, a x \log\left(x\right) - 1}{x}"," ",0,"-(2*a*x*log(a*x + 1) - 2*a*x*log(x) - 1)/x","A",0
48,1,35,0,0.498108," ","integrate((a*x-1)/(a*x+1)/x^3,x, algorithm=""fricas"")","\frac{4 \, a^{2} x^{2} \log\left(a x + 1\right) - 4 \, a^{2} x^{2} \log\left(x\right) - 4 \, a x + 1}{2 \, x^{2}}"," ",0,"1/2*(4*a^2*x^2*log(a*x + 1) - 4*a^2*x^2*log(x) - 4*a*x + 1)/x^2","A",0
49,1,43,0,0.671878," ","integrate((a*x-1)/(a*x+1)/x^4,x, algorithm=""fricas"")","-\frac{6 \, a^{3} x^{3} \log\left(a x + 1\right) - 6 \, a^{3} x^{3} \log\left(x\right) - 6 \, a^{2} x^{2} + 3 \, a x - 1}{3 \, x^{3}}"," ",0,"-1/3*(6*a^3*x^3*log(a*x + 1) - 6*a^3*x^3*log(x) - 6*a^2*x^2 + 3*a*x - 1)/x^3","A",0
50,1,92,0,0.673543," ","integrate(x^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{4} x^{4} - 6 \, a^{3} x^{3} + 11 \, a^{2} x^{2} - 29 \, a x - 80\right)} \sqrt{\frac{a x - 1}{a x + 1}} + 51 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 51 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{8 \, a^{4}}"," ",0,"1/8*((2*a^4*x^4 - 6*a^3*x^3 + 11*a^2*x^2 - 29*a*x - 80)*sqrt((a*x - 1)/(a*x + 1)) + 51*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 51*log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^4","A",0
51,1,84,0,0.401421," ","integrate(x^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} - 7 \, a^{2} x^{2} + 19 \, a x + 52\right)} \sqrt{\frac{a x - 1}{a x + 1}} - 33 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 33 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{6 \, a^{3}}"," ",0,"1/6*((2*a^3*x^3 - 7*a^2*x^2 + 19*a*x + 52)*sqrt((a*x - 1)/(a*x + 1)) - 33*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 33*log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^3","A",0
52,1,75,0,0.437357," ","integrate(x*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} - 5 \, a x - 14\right)} \sqrt{\frac{a x - 1}{a x + 1}} + 9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{2 \, a^{2}}"," ",0,"1/2*((a^2*x^2 - 5*a*x - 14)*sqrt((a*x - 1)/(a*x + 1)) + 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 9*log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2","A",0
53,1,66,0,0.460653," ","integrate(((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a x + 5\right)} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a}"," ",0,"((a*x + 5)*sqrt((a*x - 1)/(a*x + 1)) - 3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 3*log(sqrt((a*x - 1)/(a*x + 1)) - 1))/a","A",0
54,1,74,0,0.805855," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""fricas"")","-4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)"," ",0,"-4*sqrt((a*x - 1)/(a*x + 1)) + 2*arctan(sqrt((a*x - 1)/(a*x + 1))) + log(sqrt((a*x - 1)/(a*x + 1)) + 1) - log(sqrt((a*x - 1)/(a*x + 1)) - 1)","A",0
55,1,49,0,0.626305," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""fricas"")","-\frac{6 \, a x \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - {\left(5 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{x}"," ",0,"-(6*a*x*arctan(sqrt((a*x - 1)/(a*x + 1))) - (5*a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/x","A",0
56,1,61,0,0.481296," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""fricas"")","\frac{18 \, a^{2} x^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - {\left(14 \, a^{2} x^{2} + 5 \, a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, x^{2}}"," ",0,"1/2*(18*a^2*x^2*arctan(sqrt((a*x - 1)/(a*x + 1))) - (14*a^2*x^2 + 5*a*x - 1)*sqrt((a*x - 1)/(a*x + 1)))/x^2","A",0
57,1,69,0,0.499983," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""fricas"")","-\frac{66 \, a^{3} x^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - {\left(52 \, a^{3} x^{3} + 19 \, a^{2} x^{2} - 7 \, a x + 2\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, x^{3}}"," ",0,"-1/6*(66*a^3*x^3*arctan(sqrt((a*x - 1)/(a*x + 1))) - (52*a^3*x^3 + 19*a^2*x^2 - 7*a*x + 2)*sqrt((a*x - 1)/(a*x + 1)))/x^3","A",0
58,1,77,0,0.670869," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""fricas"")","\frac{102 \, a^{4} x^{4} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - {\left(80 \, a^{4} x^{4} + 29 \, a^{3} x^{3} - 11 \, a^{2} x^{2} + 6 \, a x - 2\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{8 \, x^{4}}"," ",0,"1/8*(102*a^4*x^4*arctan(sqrt((a*x - 1)/(a*x + 1))) - (80*a^4*x^4 + 29*a^3*x^3 - 11*a^2*x^2 + 6*a*x - 2)*sqrt((a*x - 1)/(a*x + 1)))/x^4","A",0
59,1,119,0,0.528586," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^4,x, algorithm=""fricas"")","\frac{2 \, {\left(384 \, a^{5} x^{5} + 816 \, a^{4} x^{4} + 872 \, a^{3} x^{3} + 978 \, a^{2} x^{2} + 1149 \, a x + 611\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}} - 930 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 465 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 465 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{3840 \, a^{5}}"," ",0,"1/3840*(2*(384*a^5*x^5 + 816*a^4*x^4 + 872*a^3*x^3 + 978*a^2*x^2 + 1149*a*x + 611)*((a*x - 1)/(a*x + 1))^(3/4) - 930*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 465*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 465*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^5","A",0
60,1,111,0,0.622715," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^3,x, algorithm=""fricas"")","\frac{2 \, {\left(48 \, a^{4} x^{4} + 104 \, a^{3} x^{3} + 114 \, a^{2} x^{2} + 141 \, a x + 83\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}} - 66 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 33 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 33 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{384 \, a^{4}}"," ",0,"1/384*(2*(48*a^4*x^4 + 104*a^3*x^3 + 114*a^2*x^2 + 141*a*x + 83)*((a*x - 1)/(a*x + 1))^(3/4) - 66*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 33*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 33*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^4","A",0
61,1,103,0,0.424361," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^2,x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a^{3} x^{3} + 18 \, a^{2} x^{2} + 21 \, a x + 11\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}} - 18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{48 \, a^{3}}"," ",0,"1/48*(2*(8*a^3*x^3 + 18*a^2*x^2 + 21*a*x + 11)*((a*x - 1)/(a*x + 1))^(3/4) - 18*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 9*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^3","A",0
62,1,93,0,0.553604," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} x^{2} + 5 \, a x + 3\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}} - 2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{8 \, a^{2}}"," ",0,"1/8*(2*(2*a^2*x^2 + 5*a*x + 3)*((a*x - 1)/(a*x + 1))^(3/4) - 2*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^2","A",0
63,1,84,0,0.575594," ","integrate(1/((a*x-1)/(a*x+1))^(1/4),x, algorithm=""fricas"")","\frac{2 \, {\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}} - 2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{2 \, a}"," ",0,"1/2*(2*(a*x + 1)*((a*x - 1)/(a*x + 1))^(3/4) - 2*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a","A",0
64,1,291,0,0.697492," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x,x, algorithm=""fricas"")","-2 \, \sqrt{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) - 2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - \frac{1}{2} \, \sqrt{2} \log\left(4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) + \frac{1}{2} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) - 2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)"," ",0,"-2*sqrt(2)*arctan(sqrt(2)*sqrt(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) - 1) - 2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 1) - 1/2*sqrt(2)*log(4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) + 1/2*sqrt(2)*log(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - 2*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - log(((a*x - 1)/(a*x + 1))^(1/4) - 1)","A",0
65,1,396,0,0.466263," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x^2,x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \arctan\left(-\frac{a^{4} + \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{4}} a^{4} + \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{4}\right)}^{\frac{1}{4}}}{a^{4}}\right) + 4 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \arctan\left(\frac{a^{4} - \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{4}} a^{4} - \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{4}\right)}^{\frac{1}{4}}}{a^{4}}\right) + \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \log\left(a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{4}} a^{4} + \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \log\left(a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{4}} a^{4} - \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 4 \, {\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{4 \, x}"," ",0,"-1/4*(4*sqrt(2)*(a^4)^(1/4)*x*arctan(-(a^4 + sqrt(2)*(a^4)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^4)*a^4 + sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4))*(a^4)^(1/4))/a^4) + 4*sqrt(2)*(a^4)^(1/4)*x*arctan((a^4 - sqrt(2)*(a^4)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^4)*a^4 - sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4))*(a^4)^(1/4))/a^4) + sqrt(2)*(a^4)^(1/4)*x*log(a^6*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^4)*a^4 + sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4)) - sqrt(2)*(a^4)^(1/4)*x*log(a^6*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^4)*a^4 - sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4)) - 4*(a*x + 1)*((a*x - 1)/(a*x + 1))^(3/4))/x","A",0
66,1,413,0,0.644931," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x^3,x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \arctan\left(-\frac{a^{8} + \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} \sqrt{a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{8}} a^{8} + \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{8}\right)}^{\frac{1}{4}}}{a^{8}}\right) + 4 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \arctan\left(\frac{a^{8} - \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} \sqrt{a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{8}} a^{8} - \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{8}\right)}^{\frac{1}{4}}}{a^{8}}\right) + \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \log\left(a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{8}} a^{8} + \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \log\left(a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{8}} a^{8} - \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 4 \, {\left(3 \, a^{2} x^{2} + 5 \, a x + 2\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{16 \, x^{2}}"," ",0,"-1/16*(4*sqrt(2)*(a^8)^(1/4)*x^2*arctan(-(a^8 + sqrt(2)*(a^8)^(1/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*sqrt(a^12*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^8)*a^8 + sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4))*(a^8)^(1/4))/a^8) + 4*sqrt(2)*(a^8)^(1/4)*x^2*arctan((a^8 - sqrt(2)*(a^8)^(1/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*sqrt(a^12*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^8)*a^8 - sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4))*(a^8)^(1/4))/a^8) + sqrt(2)*(a^8)^(1/4)*x^2*log(a^12*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^8)*a^8 + sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4)) - sqrt(2)*(a^8)^(1/4)*x^2*log(a^12*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^8)*a^8 - sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4)) - 4*(3*a^2*x^2 + 5*a*x + 2)*((a*x - 1)/(a*x + 1))^(3/4))/x^2","A",0
67,1,427,0,0.418464," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x^4,x, algorithm=""fricas"")","-\frac{36 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \arctan\left(-\frac{a^{12} + \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} \sqrt{a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{12}} a^{12} + \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{12}\right)}^{\frac{1}{4}}}{a^{12}}\right) + 36 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \arctan\left(\frac{a^{12} - \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} \sqrt{a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{12}} a^{12} - \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{12}\right)}^{\frac{1}{4}}}{a^{12}}\right) + 9 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \log\left(729 \, a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + 729 \, \sqrt{a^{12}} a^{12} + 729 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 9 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \log\left(729 \, a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + 729 \, \sqrt{a^{12}} a^{12} - 729 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 4 \, {\left(11 \, a^{3} x^{3} + 21 \, a^{2} x^{2} + 18 \, a x + 8\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{96 \, x^{3}}"," ",0,"-1/96*(36*sqrt(2)*(a^12)^(1/4)*x^3*arctan(-(a^12 + sqrt(2)*(a^12)^(1/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*sqrt(a^18*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^12)*a^12 + sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4))*(a^12)^(1/4))/a^12) + 36*sqrt(2)*(a^12)^(1/4)*x^3*arctan((a^12 - sqrt(2)*(a^12)^(1/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*sqrt(a^18*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^12)*a^12 - sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4))*(a^12)^(1/4))/a^12) + 9*sqrt(2)*(a^12)^(1/4)*x^3*log(729*a^18*sqrt((a*x - 1)/(a*x + 1)) + 729*sqrt(a^12)*a^12 + 729*sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4)) - 9*sqrt(2)*(a^12)^(1/4)*x^3*log(729*a^18*sqrt((a*x - 1)/(a*x + 1)) + 729*sqrt(a^12)*a^12 - 729*sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4)) - 4*(11*a^3*x^3 + 21*a^2*x^2 + 18*a*x + 8)*((a*x - 1)/(a*x + 1))^(3/4))/x^3","A",0
68,1,119,0,0.637822," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^4,x, algorithm=""fricas"")","\frac{2 \, {\left(128 \, a^{5} x^{5} + 304 \, a^{4} x^{4} + 376 \, a^{3} x^{3} + 514 \, a^{2} x^{2} + 871 \, a x + 557\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 2370 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 1185 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 1185 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{1280 \, a^{5}}"," ",0,"1/1280*(2*(128*a^5*x^5 + 304*a^4*x^4 + 376*a^3*x^3 + 514*a^2*x^2 + 871*a*x + 557)*((a*x - 1)/(a*x + 1))^(1/4) + 2370*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 1185*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 1185*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^5","A",0
69,1,111,0,0.647180," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^3,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, a^{4} x^{4} + 40 \, a^{3} x^{3} + 54 \, a^{2} x^{2} + 93 \, a x + 63\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 246 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 123 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 123 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{128 \, a^{4}}"," ",0,"1/128*(2*(16*a^4*x^4 + 40*a^3*x^3 + 54*a^2*x^2 + 93*a*x + 63)*((a*x - 1)/(a*x + 1))^(1/4) + 246*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 123*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 123*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^4","A",0
70,1,103,0,0.564237," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^2,x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a^{3} x^{3} + 22 \, a^{2} x^{2} + 37 \, a x + 23\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 102 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 51 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 51 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{48 \, a^{3}}"," ",0,"1/48*(2*(8*a^3*x^3 + 22*a^2*x^2 + 37*a*x + 23)*((a*x - 1)/(a*x + 1))^(1/4) + 102*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 51*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 51*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^3","A",0
71,1,95,0,0.551198," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} x^{2} + 7 \, a x + 5\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{8 \, a^{2}}"," ",0,"1/8*(2*(2*a^2*x^2 + 7*a*x + 5)*((a*x - 1)/(a*x + 1))^(1/4) + 18*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 9*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^2","A",0
72,1,86,0,0.639740," ","integrate(1/((a*x-1)/(a*x+1))^(3/4),x, algorithm=""fricas"")","\frac{2 \, {\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 6 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 3 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 3 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{2 \, a}"," ",0,"1/2*(2*(a*x + 1)*((a*x - 1)/(a*x + 1))^(1/4) + 6*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 3*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 3*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a","A",0
73,1,291,0,0.564912," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x,x, algorithm=""fricas"")","-2 \, \sqrt{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) - 2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + \frac{1}{2} \, \sqrt{2} \log\left(4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) - \frac{1}{2} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) + 2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)"," ",0,"-2*sqrt(2)*arctan(sqrt(2)*sqrt(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) - 1) - 2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 1) + 1/2*sqrt(2)*log(4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - 1/2*sqrt(2)*log(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) + 2*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - log(((a*x - 1)/(a*x + 1))^(1/4) - 1)","A",0
74,1,376,0,0.457783," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x^2,x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \arctan\left(-\frac{a^{4} + \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} \sqrt{a^{2} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{4}}}}{a^{4}}\right) + 12 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \arctan\left(\frac{a^{4} - \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} \sqrt{a^{2} \sqrt{\frac{a x - 1}{a x + 1}} - \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{4}}}}{a^{4}}\right) - 3 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \log\left(9 \, a^{2} \sqrt{\frac{a x - 1}{a x + 1}} + 9 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 9 \, \sqrt{a^{4}}\right) + 3 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \log\left(9 \, a^{2} \sqrt{\frac{a x - 1}{a x + 1}} - 9 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 9 \, \sqrt{a^{4}}\right) - 4 \, {\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{4 \, x}"," ",0,"-1/4*(12*sqrt(2)*(a^4)^(1/4)*x*arctan(-(a^4 + sqrt(2)*(a^4)^(3/4)*a*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*(a^4)^(3/4)*sqrt(a^2*sqrt((a*x - 1)/(a*x + 1)) + sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^4)))/a^4) + 12*sqrt(2)*(a^4)^(1/4)*x*arctan((a^4 - sqrt(2)*(a^4)^(3/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*(a^4)^(3/4)*sqrt(a^2*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^4)))/a^4) - 3*sqrt(2)*(a^4)^(1/4)*x*log(9*a^2*sqrt((a*x - 1)/(a*x + 1)) + 9*sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + 9*sqrt(a^4)) + 3*sqrt(2)*(a^4)^(1/4)*x*log(9*a^2*sqrt((a*x - 1)/(a*x + 1)) - 9*sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + 9*sqrt(a^4)) - 4*(a*x + 1)*((a*x - 1)/(a*x + 1))^(1/4))/x","A",0
75,1,405,0,0.498862," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x^3,x, algorithm=""fricas"")","-\frac{36 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \arctan\left(-\frac{a^{8} + \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} \sqrt{a^{4} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{8}}}}{a^{8}}\right) + 36 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \arctan\left(\frac{a^{8} - \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} \sqrt{a^{4} \sqrt{\frac{a x - 1}{a x + 1}} - \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{8}}}}{a^{8}}\right) - 9 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \log\left(81 \, a^{4} \sqrt{\frac{a x - 1}{a x + 1}} + 81 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 81 \, \sqrt{a^{8}}\right) + 9 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \log\left(81 \, a^{4} \sqrt{\frac{a x - 1}{a x + 1}} - 81 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 81 \, \sqrt{a^{8}}\right) - 4 \, {\left(5 \, a^{2} x^{2} + 7 \, a x + 2\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{16 \, x^{2}}"," ",0,"-1/16*(36*sqrt(2)*(a^8)^(1/4)*x^2*arctan(-(a^8 + sqrt(2)*(a^8)^(3/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*(a^8)^(3/4)*sqrt(a^4*sqrt((a*x - 1)/(a*x + 1)) + sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^8)))/a^8) + 36*sqrt(2)*(a^8)^(1/4)*x^2*arctan((a^8 - sqrt(2)*(a^8)^(3/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*(a^8)^(3/4)*sqrt(a^4*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^8)))/a^8) - 9*sqrt(2)*(a^8)^(1/4)*x^2*log(81*a^4*sqrt((a*x - 1)/(a*x + 1)) + 81*sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + 81*sqrt(a^8)) + 9*sqrt(2)*(a^8)^(1/4)*x^2*log(81*a^4*sqrt((a*x - 1)/(a*x + 1)) - 81*sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + 81*sqrt(a^8)) - 4*(5*a^2*x^2 + 7*a*x + 2)*((a*x - 1)/(a*x + 1))^(1/4))/x^2","A",0
76,1,413,0,0.557973," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x^4,x, algorithm=""fricas"")","-\frac{204 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \arctan\left(-\frac{a^{12} + \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{12}}}}{a^{12}}\right) + 204 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \arctan\left(\frac{a^{12} - \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} - \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{12}}}}{a^{12}}\right) - 51 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \log\left(289 \, a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + 289 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 289 \, \sqrt{a^{12}}\right) + 51 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \log\left(289 \, a^{6} \sqrt{\frac{a x - 1}{a x + 1}} - 289 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 289 \, \sqrt{a^{12}}\right) - 4 \, {\left(23 \, a^{3} x^{3} + 37 \, a^{2} x^{2} + 22 \, a x + 8\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{96 \, x^{3}}"," ",0,"-1/96*(204*sqrt(2)*(a^12)^(1/4)*x^3*arctan(-(a^12 + sqrt(2)*(a^12)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*(a^12)^(3/4)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) + sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^12)))/a^12) + 204*sqrt(2)*(a^12)^(1/4)*x^3*arctan((a^12 - sqrt(2)*(a^12)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*(a^12)^(3/4)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^12)))/a^12) - 51*sqrt(2)*(a^12)^(1/4)*x^3*log(289*a^6*sqrt((a*x - 1)/(a*x + 1)) + 289*sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + 289*sqrt(a^12)) + 51*sqrt(2)*(a^12)^(1/4)*x^3*log(289*a^6*sqrt((a*x - 1)/(a*x + 1)) - 289*sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + 289*sqrt(a^12)) - 4*(23*a^3*x^3 + 37*a^2*x^2 + 22*a*x + 8)*((a*x - 1)/(a*x + 1))^(1/4))/x^3","A",0
77,1,152,0,0.550903," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^4,x, algorithm=""fricas"")","-\frac{30090 \, {\left(a x - 1\right)} \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 15045 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 15045 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) - 2 \, {\left(384 \, a^{6} x^{6} + 1392 \, a^{5} x^{5} + 2456 \, a^{4} x^{4} + 3826 \, a^{3} x^{3} + 7911 \, a^{2} x^{2} - 20578 \, a x - 26111\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{3840 \, {\left(a^{6} x - a^{5}\right)}}"," ",0,"-1/3840*(30090*(a*x - 1)*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 15045*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 15045*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) - 1) - 2*(384*a^6*x^6 + 1392*a^5*x^5 + 2456*a^4*x^4 + 3826*a^3*x^3 + 7911*a^2*x^2 - 20578*a*x - 26111)*((a*x - 1)/(a*x + 1))^(3/4))/(a^6*x - a^5)","A",0
78,1,144,0,0.560138," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^3,x, algorithm=""fricas"")","-\frac{2850 \, {\left(a x - 1\right)} \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 1425 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 1425 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) - 2 \, {\left(48 \, a^{5} x^{5} + 184 \, a^{4} x^{4} + 362 \, a^{3} x^{3} + 747 \, a^{2} x^{2} - 1946 \, a x - 2467\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{384 \, {\left(a^{5} x - a^{4}\right)}}"," ",0,"-1/384*(2850*(a*x - 1)*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 1425*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 1425*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) - 1) - 2*(48*a^5*x^5 + 184*a^4*x^4 + 362*a^3*x^3 + 747*a^2*x^2 - 1946*a*x - 2467)*((a*x - 1)/(a*x + 1))^(3/4))/(a^5*x - a^4)","A",0
79,1,136,0,0.580346," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^2,x, algorithm=""fricas"")","-\frac{330 \, {\left(a x - 1\right)} \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 165 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 165 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) - 2 \, {\left(8 \, a^{4} x^{4} + 34 \, a^{3} x^{3} + 87 \, a^{2} x^{2} - 226 \, a x - 287\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{48 \, {\left(a^{4} x - a^{3}\right)}}"," ",0,"-1/48*(330*(a*x - 1)*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 165*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 165*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) - 1) - 2*(8*a^4*x^4 + 34*a^3*x^3 + 87*a^2*x^2 - 226*a*x - 287)*((a*x - 1)/(a*x + 1))^(3/4))/(a^4*x - a^3)","A",0
80,1,128,0,0.625290," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x,x, algorithm=""fricas"")","-\frac{50 \, {\left(a x - 1\right)} \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 25 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 25 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) - 2 \, {\left(2 \, a^{3} x^{3} + 11 \, a^{2} x^{2} - 34 \, a x - 43\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{8 \, {\left(a^{3} x - a^{2}\right)}}"," ",0,"-1/8*(50*(a*x - 1)*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 25*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 25*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) - 1) - 2*(2*a^3*x^3 + 11*a^2*x^2 - 34*a*x - 43)*((a*x - 1)/(a*x + 1))^(3/4))/(a^3*x - a^2)","A",0
81,1,117,0,0.711409," ","integrate(1/((a*x-1)/(a*x+1))^(5/4),x, algorithm=""fricas"")","-\frac{10 \, {\left(a x - 1\right)} \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 5 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 5 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) - 2 \, {\left(a^{2} x^{2} - 8 \, a x - 9\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{2 \, {\left(a^{2} x - a\right)}}"," ",0,"-1/2*(10*(a*x - 1)*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 5*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 5*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) - 1) - 2*(a^2*x^2 - 8*a*x - 9)*((a*x - 1)/(a*x + 1))^(3/4))/(a^2*x - a)","A",0
82,1,358,0,0.554961," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x,x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(a x - 1\right)} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) + 4 \, \sqrt{2} {\left(a x - 1\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + \sqrt{2} {\left(a x - 1\right)} \log\left(4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) - \sqrt{2} {\left(a x - 1\right)} \log\left(-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) - 4 \, {\left(a x - 1\right)} \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 2 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 2 \, {\left(a x - 1\right)} \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) - 16 \, {\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{2 \, {\left(a x - 1\right)}}"," ",0,"1/2*(4*sqrt(2)*(a*x - 1)*arctan(sqrt(2)*sqrt(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) - 1) + 4*sqrt(2)*(a*x - 1)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 1) + sqrt(2)*(a*x - 1)*log(4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - sqrt(2)*(a*x - 1)*log(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - 4*(a*x - 1)*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 2*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 2*(a*x - 1)*log(((a*x - 1)/(a*x + 1))^(1/4) - 1) - 16*(a*x + 1)*((a*x - 1)/(a*x + 1))^(3/4))/(a*x - 1)","A",0
83,1,451,0,0.667015," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x^2,x, algorithm=""fricas"")","\frac{20 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} {\left(a x^{2} - x\right)} \arctan\left(-\frac{a^{4} + \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{4}} a^{4} + \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{4}\right)}^{\frac{1}{4}}}{a^{4}}\right) + 20 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} {\left(a x^{2} - x\right)} \arctan\left(\frac{a^{4} - \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{4}} a^{4} - \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{4}\right)}^{\frac{1}{4}}}{a^{4}}\right) + 5 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} {\left(a x^{2} - x\right)} \log\left(15625 \, a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + 15625 \, \sqrt{a^{4}} a^{4} + 15625 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 5 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} {\left(a x^{2} - x\right)} \log\left(15625 \, a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + 15625 \, \sqrt{a^{4}} a^{4} - 15625 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 4 \, {\left(9 \, a^{2} x^{2} + 8 \, a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{4 \, {\left(a x^{2} - x\right)}}"," ",0,"1/4*(20*sqrt(2)*(a^4)^(1/4)*(a*x^2 - x)*arctan(-(a^4 + sqrt(2)*(a^4)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^4)*a^4 + sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4))*(a^4)^(1/4))/a^4) + 20*sqrt(2)*(a^4)^(1/4)*(a*x^2 - x)*arctan((a^4 - sqrt(2)*(a^4)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^4)*a^4 - sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4))*(a^4)^(1/4))/a^4) + 5*sqrt(2)*(a^4)^(1/4)*(a*x^2 - x)*log(15625*a^6*sqrt((a*x - 1)/(a*x + 1)) + 15625*sqrt(a^4)*a^4 + 15625*sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4)) - 5*sqrt(2)*(a^4)^(1/4)*(a*x^2 - x)*log(15625*a^6*sqrt((a*x - 1)/(a*x + 1)) + 15625*sqrt(a^4)*a^4 - 15625*sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4)) - 4*(9*a^2*x^2 + 8*a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4))/(a*x^2 - x)","A",0
84,1,469,0,0.481797," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x^3,x, algorithm=""fricas"")","\frac{100 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} {\left(a x^{3} - x^{2}\right)} \arctan\left(-\frac{a^{8} + \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} \sqrt{a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{8}} a^{8} + \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{8}\right)}^{\frac{1}{4}}}{a^{8}}\right) + 100 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} {\left(a x^{3} - x^{2}\right)} \arctan\left(\frac{a^{8} - \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} \sqrt{a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{8}} a^{8} - \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{8}\right)}^{\frac{1}{4}}}{a^{8}}\right) + 25 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} {\left(a x^{3} - x^{2}\right)} \log\left(244140625 \, a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + 244140625 \, \sqrt{a^{8}} a^{8} + 244140625 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 25 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} {\left(a x^{3} - x^{2}\right)} \log\left(244140625 \, a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + 244140625 \, \sqrt{a^{8}} a^{8} - 244140625 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 4 \, {\left(43 \, a^{3} x^{3} + 34 \, a^{2} x^{2} - 11 \, a x - 2\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{16 \, {\left(a x^{3} - x^{2}\right)}}"," ",0,"1/16*(100*sqrt(2)*(a^8)^(1/4)*(a*x^3 - x^2)*arctan(-(a^8 + sqrt(2)*(a^8)^(1/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*sqrt(a^12*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^8)*a^8 + sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4))*(a^8)^(1/4))/a^8) + 100*sqrt(2)*(a^8)^(1/4)*(a*x^3 - x^2)*arctan((a^8 - sqrt(2)*(a^8)^(1/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*sqrt(a^12*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^8)*a^8 - sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4))*(a^8)^(1/4))/a^8) + 25*sqrt(2)*(a^8)^(1/4)*(a*x^3 - x^2)*log(244140625*a^12*sqrt((a*x - 1)/(a*x + 1)) + 244140625*sqrt(a^8)*a^8 + 244140625*sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4)) - 25*sqrt(2)*(a^8)^(1/4)*(a*x^3 - x^2)*log(244140625*a^12*sqrt((a*x - 1)/(a*x + 1)) + 244140625*sqrt(a^8)*a^8 - 244140625*sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4)) - 4*(43*a^3*x^3 + 34*a^2*x^2 - 11*a*x - 2)*((a*x - 1)/(a*x + 1))^(3/4))/(a*x^3 - x^2)","A",0
85,1,477,0,0.596948," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x^4,x, algorithm=""fricas"")","\frac{660 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} {\left(a x^{4} - x^{3}\right)} \arctan\left(-\frac{a^{12} + \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} \sqrt{a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{12}} a^{12} + \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{12}\right)}^{\frac{1}{4}}}{a^{12}}\right) + 660 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} {\left(a x^{4} - x^{3}\right)} \arctan\left(\frac{a^{12} - \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} \sqrt{a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{12}} a^{12} - \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{12}\right)}^{\frac{1}{4}}}{a^{12}}\right) + 165 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} {\left(a x^{4} - x^{3}\right)} \log\left(27680640625 \, a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + 27680640625 \, \sqrt{a^{12}} a^{12} + 27680640625 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 165 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} {\left(a x^{4} - x^{3}\right)} \log\left(27680640625 \, a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + 27680640625 \, \sqrt{a^{12}} a^{12} - 27680640625 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 4 \, {\left(287 \, a^{4} x^{4} + 226 \, a^{3} x^{3} - 87 \, a^{2} x^{2} - 34 \, a x - 8\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{96 \, {\left(a x^{4} - x^{3}\right)}}"," ",0,"1/96*(660*sqrt(2)*(a^12)^(1/4)*(a*x^4 - x^3)*arctan(-(a^12 + sqrt(2)*(a^12)^(1/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*sqrt(a^18*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^12)*a^12 + sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4))*(a^12)^(1/4))/a^12) + 660*sqrt(2)*(a^12)^(1/4)*(a*x^4 - x^3)*arctan((a^12 - sqrt(2)*(a^12)^(1/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*sqrt(a^18*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^12)*a^12 - sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4))*(a^12)^(1/4))/a^12) + 165*sqrt(2)*(a^12)^(1/4)*(a*x^4 - x^3)*log(27680640625*a^18*sqrt((a*x - 1)/(a*x + 1)) + 27680640625*sqrt(a^12)*a^12 + 27680640625*sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4)) - 165*sqrt(2)*(a^12)^(1/4)*(a*x^4 - x^3)*log(27680640625*a^18*sqrt((a*x - 1)/(a*x + 1)) + 27680640625*sqrt(a^12)*a^12 - 27680640625*sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4)) - 4*(287*a^4*x^4 + 226*a^3*x^3 - 87*a^2*x^2 - 34*a*x - 8)*((a*x - 1)/(a*x + 1))^(3/4))/(a*x^4 - x^3)","A",0
86,1,119,0,0.697582," ","integrate(x^4*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""fricas"")","\frac{2 \, {\left(384 \, a^{5} x^{5} - 48 \, a^{4} x^{4} + 8 \, a^{3} x^{3} - 98 \, a^{2} x^{2} + 73 \, a x + 611\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 930 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 465 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 465 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{3840 \, a^{5}}"," ",0,"1/3840*(2*(384*a^5*x^5 - 48*a^4*x^4 + 8*a^3*x^3 - 98*a^2*x^2 + 73*a*x + 611)*((a*x - 1)/(a*x + 1))^(1/4) - 930*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 465*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 465*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^5","A",0
87,1,111,0,0.606699," ","integrate(x^3*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""fricas"")","\frac{2 \, {\left(48 \, a^{4} x^{4} - 8 \, a^{3} x^{3} + 2 \, a^{2} x^{2} - 25 \, a x - 83\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 66 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 33 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 33 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{384 \, a^{4}}"," ",0,"1/384*(2*(48*a^4*x^4 - 8*a^3*x^3 + 2*a^2*x^2 - 25*a*x - 83)*((a*x - 1)/(a*x + 1))^(1/4) + 66*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 33*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 33*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^4","A",0
88,1,102,0,0.585113," ","integrate(x^2*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a^{3} x^{3} - 2 \, a^{2} x^{2} + a x + 11\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{48 \, a^{3}}"," ",0,"1/48*(2*(8*a^3*x^3 - 2*a^2*x^2 + a*x + 11)*((a*x - 1)/(a*x + 1))^(1/4) - 18*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 9*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^3","A",0
89,1,93,0,1.582380," ","integrate(x*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} x^{2} - a x - 3\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{8 \, a^{2}}"," ",0,"1/8*(2*(2*a^2*x^2 - a*x - 3)*((a*x - 1)/(a*x + 1))^(1/4) + 2*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^2","A",0
90,1,84,0,0.592113," ","integrate(((a*x-1)/(a*x+1))^(1/4),x, algorithm=""fricas"")","\frac{2 \, {\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{2 \, a}"," ",0,"1/2*(2*(a*x + 1)*((a*x - 1)/(a*x + 1))^(1/4) - 2*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a","A",0
91,1,291,0,0.912996," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x,x, algorithm=""fricas"")","2 \, \sqrt{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) + 2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - \frac{1}{2} \, \sqrt{2} \log\left(4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) + \frac{1}{2} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) + 2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)"," ",0,"2*sqrt(2)*arctan(sqrt(2)*sqrt(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) - 1) + 2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 1) - 1/2*sqrt(2)*log(4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) + 1/2*sqrt(2)*log(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) + 2*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - log(((a*x - 1)/(a*x + 1))^(1/4) - 1)","A",0
92,1,368,0,0.574719," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x^2,x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \arctan\left(-\frac{a^{4} + \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} \sqrt{a^{2} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{4}}}}{a^{4}}\right) + 4 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \arctan\left(\frac{a^{4} - \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} \sqrt{a^{2} \sqrt{\frac{a x - 1}{a x + 1}} - \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{4}}}}{a^{4}}\right) - \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \log\left(a^{2} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{4}}\right) + \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \log\left(a^{2} \sqrt{\frac{a x - 1}{a x + 1}} - \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{4}}\right) + 4 \, {\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{4 \, x}"," ",0,"-1/4*(4*sqrt(2)*(a^4)^(1/4)*x*arctan(-(a^4 + sqrt(2)*(a^4)^(3/4)*a*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*(a^4)^(3/4)*sqrt(a^2*sqrt((a*x - 1)/(a*x + 1)) + sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^4)))/a^4) + 4*sqrt(2)*(a^4)^(1/4)*x*arctan((a^4 - sqrt(2)*(a^4)^(3/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*(a^4)^(3/4)*sqrt(a^2*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^4)))/a^4) - sqrt(2)*(a^4)^(1/4)*x*log(a^2*sqrt((a*x - 1)/(a*x + 1)) + sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^4)) + sqrt(2)*(a^4)^(1/4)*x*log(a^2*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^4)) + 4*(a*x + 1)*((a*x - 1)/(a*x + 1))^(1/4))/x","A",0
93,1,396,0,0.565361," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x^3,x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \arctan\left(-\frac{a^{8} + \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} \sqrt{a^{4} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{8}}}}{a^{8}}\right) + 4 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \arctan\left(\frac{a^{8} - \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} \sqrt{a^{4} \sqrt{\frac{a x - 1}{a x + 1}} - \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{8}}}}{a^{8}}\right) - \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \log\left(a^{4} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{8}}\right) + \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \log\left(a^{4} \sqrt{\frac{a x - 1}{a x + 1}} - \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{8}}\right) + 4 \, {\left(3 \, a^{2} x^{2} + a x - 2\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{16 \, x^{2}}"," ",0,"1/16*(4*sqrt(2)*(a^8)^(1/4)*x^2*arctan(-(a^8 + sqrt(2)*(a^8)^(3/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*(a^8)^(3/4)*sqrt(a^4*sqrt((a*x - 1)/(a*x + 1)) + sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^8)))/a^8) + 4*sqrt(2)*(a^8)^(1/4)*x^2*arctan((a^8 - sqrt(2)*(a^8)^(3/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*(a^8)^(3/4)*sqrt(a^4*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^8)))/a^8) - sqrt(2)*(a^8)^(1/4)*x^2*log(a^4*sqrt((a*x - 1)/(a*x + 1)) + sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^8)) + sqrt(2)*(a^8)^(1/4)*x^2*log(a^4*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^8)) + 4*(3*a^2*x^2 + a*x - 2)*((a*x - 1)/(a*x + 1))^(1/4))/x^2","A",0
94,1,412,0,0.522291," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x^4,x, algorithm=""fricas"")","-\frac{36 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \arctan\left(-\frac{a^{12} + \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{12}}}}{a^{12}}\right) + 36 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \arctan\left(\frac{a^{12} - \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} - \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{12}}}}{a^{12}}\right) - 9 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \log\left(9 \, a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + 9 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 9 \, \sqrt{a^{12}}\right) + 9 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \log\left(9 \, a^{6} \sqrt{\frac{a x - 1}{a x + 1}} - 9 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 9 \, \sqrt{a^{12}}\right) + 4 \, {\left(11 \, a^{3} x^{3} + a^{2} x^{2} - 2 \, a x + 8\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{96 \, x^{3}}"," ",0,"-1/96*(36*sqrt(2)*(a^12)^(1/4)*x^3*arctan(-(a^12 + sqrt(2)*(a^12)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*(a^12)^(3/4)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) + sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^12)))/a^12) + 36*sqrt(2)*(a^12)^(1/4)*x^3*arctan((a^12 - sqrt(2)*(a^12)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*(a^12)^(3/4)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^12)))/a^12) - 9*sqrt(2)*(a^12)^(1/4)*x^3*log(9*a^6*sqrt((a*x - 1)/(a*x + 1)) + 9*sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + 9*sqrt(a^12)) + 9*sqrt(2)*(a^12)^(1/4)*x^3*log(9*a^6*sqrt((a*x - 1)/(a*x + 1)) - 9*sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + 9*sqrt(a^12)) + 4*(11*a^3*x^3 + a^2*x^2 - 2*a*x + 8)*((a*x - 1)/(a*x + 1))^(1/4))/x^3","A",0
95,1,119,0,0.555279," ","integrate(x^4*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""fricas"")","\frac{2 \, {\left(128 \, a^{5} x^{5} - 48 \, a^{4} x^{4} + 24 \, a^{3} x^{3} - 114 \, a^{2} x^{2} + 243 \, a x + 557\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}} + 2370 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 1185 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 1185 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{1280 \, a^{5}}"," ",0,"1/1280*(2*(128*a^5*x^5 - 48*a^4*x^4 + 24*a^3*x^3 - 114*a^2*x^2 + 243*a*x + 557)*((a*x - 1)/(a*x + 1))^(3/4) + 2370*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 1185*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 1185*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^5","A",0
96,1,111,0,0.574573," ","integrate(x^3*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, a^{4} x^{4} - 8 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 33 \, a x - 63\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}} - 246 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 123 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 123 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{128 \, a^{4}}"," ",0,"1/128*(2*(16*a^4*x^4 - 8*a^3*x^3 + 6*a^2*x^2 - 33*a*x - 63)*((a*x - 1)/(a*x + 1))^(3/4) - 246*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 123*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 123*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^4","A",0
97,1,103,0,0.501332," ","integrate(x^2*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 9 \, a x + 23\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}} + 102 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 51 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 51 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{48 \, a^{3}}"," ",0,"1/48*(2*(8*a^3*x^3 - 6*a^2*x^2 + 9*a*x + 23)*((a*x - 1)/(a*x + 1))^(3/4) + 102*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 51*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 51*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^3","A",0
98,1,95,0,0.528538," ","integrate(x*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} x^{2} - 3 \, a x - 5\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}} - 18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{8 \, a^{2}}"," ",0,"1/8*(2*(2*a^2*x^2 - 3*a*x - 5)*((a*x - 1)/(a*x + 1))^(3/4) - 18*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 9*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^2","A",0
99,1,86,0,0.476154," ","integrate(((a*x-1)/(a*x+1))^(3/4),x, algorithm=""fricas"")","\frac{2 \, {\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}} + 6 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 3 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 3 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{2 \, a}"," ",0,"1/2*(2*(a*x + 1)*((a*x - 1)/(a*x + 1))^(3/4) + 6*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 3*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 3*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a","A",0
100,1,291,0,0.531185," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x,x, algorithm=""fricas"")","2 \, \sqrt{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) + 2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + \frac{1}{2} \, \sqrt{2} \log\left(4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) - \frac{1}{2} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) - 2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)"," ",0,"2*sqrt(2)*arctan(sqrt(2)*sqrt(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) - 1) + 2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 1) + 1/2*sqrt(2)*log(4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - 1/2*sqrt(2)*log(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - 2*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - log(((a*x - 1)/(a*x + 1))^(1/4) - 1)","A",0
101,1,402,0,0.565874," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x^2,x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \arctan\left(-\frac{a^{4} + \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{4}} a^{4} + \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{4}\right)}^{\frac{1}{4}}}{a^{4}}\right) + 12 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \arctan\left(\frac{a^{4} - \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{4}} a^{4} - \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{4}\right)}^{\frac{1}{4}}}{a^{4}}\right) + 3 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \log\left(729 \, a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + 729 \, \sqrt{a^{4}} a^{4} + 729 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 3 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \log\left(729 \, a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + 729 \, \sqrt{a^{4}} a^{4} - 729 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 4 \, {\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{4 \, x}"," ",0,"-1/4*(12*sqrt(2)*(a^4)^(1/4)*x*arctan(-(a^4 + sqrt(2)*(a^4)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^4)*a^4 + sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4))*(a^4)^(1/4))/a^4) + 12*sqrt(2)*(a^4)^(1/4)*x*arctan((a^4 - sqrt(2)*(a^4)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^4)*a^4 - sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4))*(a^4)^(1/4))/a^4) + 3*sqrt(2)*(a^4)^(1/4)*x*log(729*a^6*sqrt((a*x - 1)/(a*x + 1)) + 729*sqrt(a^4)*a^4 + 729*sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4)) - 3*sqrt(2)*(a^4)^(1/4)*x*log(729*a^6*sqrt((a*x - 1)/(a*x + 1)) + 729*sqrt(a^4)*a^4 - 729*sqrt(2)*(a^4)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4)) + 4*(a*x + 1)*((a*x - 1)/(a*x + 1))^(3/4))/x","A",0
102,1,419,0,0.530843," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x^3,x, algorithm=""fricas"")","\frac{36 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \arctan\left(-\frac{a^{8} + \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} \sqrt{a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{8}} a^{8} + \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{8}\right)}^{\frac{1}{4}}}{a^{8}}\right) + 36 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \arctan\left(\frac{a^{8} - \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} \sqrt{a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{8}} a^{8} - \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{8}\right)}^{\frac{1}{4}}}{a^{8}}\right) + 9 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \log\left(531441 \, a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + 531441 \, \sqrt{a^{8}} a^{8} + 531441 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 9 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \log\left(531441 \, a^{12} \sqrt{\frac{a x - 1}{a x + 1}} + 531441 \, \sqrt{a^{8}} a^{8} - 531441 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 4 \, {\left(5 \, a^{2} x^{2} + 3 \, a x - 2\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{16 \, x^{2}}"," ",0,"1/16*(36*sqrt(2)*(a^8)^(1/4)*x^2*arctan(-(a^8 + sqrt(2)*(a^8)^(1/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*sqrt(a^12*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^8)*a^8 + sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4))*(a^8)^(1/4))/a^8) + 36*sqrt(2)*(a^8)^(1/4)*x^2*arctan((a^8 - sqrt(2)*(a^8)^(1/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*sqrt(a^12*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^8)*a^8 - sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4))*(a^8)^(1/4))/a^8) + 9*sqrt(2)*(a^8)^(1/4)*x^2*log(531441*a^12*sqrt((a*x - 1)/(a*x + 1)) + 531441*sqrt(a^8)*a^8 + 531441*sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4)) - 9*sqrt(2)*(a^8)^(1/4)*x^2*log(531441*a^12*sqrt((a*x - 1)/(a*x + 1)) + 531441*sqrt(a^8)*a^8 - 531441*sqrt(2)*(a^8)^(3/4)*a^6*((a*x - 1)/(a*x + 1))^(1/4)) + 4*(5*a^2*x^2 + 3*a*x - 2)*((a*x - 1)/(a*x + 1))^(3/4))/x^2","A",0
103,1,427,0,0.617667," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x^4,x, algorithm=""fricas"")","-\frac{204 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \arctan\left(-\frac{a^{12} + \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} \sqrt{a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{12}} a^{12} + \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{12}\right)}^{\frac{1}{4}}}{a^{12}}\right) + 204 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \arctan\left(\frac{a^{12} - \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} \sqrt{a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{a^{12}} a^{12} - \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} {\left(a^{12}\right)}^{\frac{1}{4}}}{a^{12}}\right) + 51 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \log\left(24137569 \, a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + 24137569 \, \sqrt{a^{12}} a^{12} + 24137569 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 51 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \log\left(24137569 \, a^{18} \sqrt{\frac{a x - 1}{a x + 1}} + 24137569 \, \sqrt{a^{12}} a^{12} - 24137569 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 4 \, {\left(23 \, a^{3} x^{3} + 9 \, a^{2} x^{2} - 6 \, a x + 8\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{96 \, x^{3}}"," ",0,"-1/96*(204*sqrt(2)*(a^12)^(1/4)*x^3*arctan(-(a^12 + sqrt(2)*(a^12)^(1/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*sqrt(a^18*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^12)*a^12 + sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4))*(a^12)^(1/4))/a^12) + 204*sqrt(2)*(a^12)^(1/4)*x^3*arctan((a^12 - sqrt(2)*(a^12)^(1/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*sqrt(a^18*sqrt((a*x - 1)/(a*x + 1)) + sqrt(a^12)*a^12 - sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4))*(a^12)^(1/4))/a^12) + 51*sqrt(2)*(a^12)^(1/4)*x^3*log(24137569*a^18*sqrt((a*x - 1)/(a*x + 1)) + 24137569*sqrt(a^12)*a^12 + 24137569*sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4)) - 51*sqrt(2)*(a^12)^(1/4)*x^3*log(24137569*a^18*sqrt((a*x - 1)/(a*x + 1)) + 24137569*sqrt(a^12)*a^12 - 24137569*sqrt(2)*(a^12)^(3/4)*a^9*((a*x - 1)/(a*x + 1))^(1/4)) + 4*(23*a^3*x^3 + 9*a^2*x^2 - 6*a*x + 8)*((a*x - 1)/(a*x + 1))^(3/4))/x^3","A",0
104,1,119,0,1.169813," ","integrate(x^4*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""fricas"")","\frac{2 \, {\left(384 \, a^{5} x^{5} - 1008 \, a^{4} x^{4} + 1448 \, a^{3} x^{3} - 2378 \, a^{2} x^{2} + 5533 \, a x + 26111\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 30090 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 15045 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 15045 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{3840 \, a^{5}}"," ",0,"1/3840*(2*(384*a^5*x^5 - 1008*a^4*x^4 + 1448*a^3*x^3 - 2378*a^2*x^2 + 5533*a*x + 26111)*((a*x - 1)/(a*x + 1))^(1/4) - 30090*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 15045*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 15045*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^5","A",0
105,1,111,0,0.652469," ","integrate(x^3*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""fricas"")","\frac{2 \, {\left(48 \, a^{4} x^{4} - 136 \, a^{3} x^{3} + 226 \, a^{2} x^{2} - 521 \, a x - 2467\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 2850 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 1425 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 1425 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{384 \, a^{4}}"," ",0,"1/384*(2*(48*a^4*x^4 - 136*a^3*x^3 + 226*a^2*x^2 - 521*a*x - 2467)*((a*x - 1)/(a*x + 1))^(1/4) + 2850*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 1425*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 1425*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^4","A",0
106,1,103,0,0.813363," ","integrate(x^2*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a^{3} x^{3} - 26 \, a^{2} x^{2} + 61 \, a x + 287\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 330 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 165 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 165 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{48 \, a^{3}}"," ",0,"1/48*(2*(8*a^3*x^3 - 26*a^2*x^2 + 61*a*x + 287)*((a*x - 1)/(a*x + 1))^(1/4) - 330*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 165*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 165*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^3","A",0
107,1,95,0,0.901461," ","integrate(x*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} x^{2} - 9 \, a x - 43\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 50 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 25 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - 25 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{8 \, a^{2}}"," ",0,"1/8*(2*(2*a^2*x^2 - 9*a*x - 43)*((a*x - 1)/(a*x + 1))^(1/4) + 50*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + 25*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - 25*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^2","A",0
108,1,86,0,0.473922," ","integrate(((a*x-1)/(a*x+1))^(5/4),x, algorithm=""fricas"")","\frac{2 \, {\left(a x + 9\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 10 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 5 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + 5 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)}{2 \, a}"," ",0,"1/2*(2*(a*x + 9)*((a*x - 1)/(a*x + 1))^(1/4) - 10*arctan(((a*x - 1)/(a*x + 1))^(1/4)) - 5*log(((a*x - 1)/(a*x + 1))^(1/4) + 1) + 5*log(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a","A",0
109,1,308,0,0.675376," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x,x, algorithm=""fricas"")","-2 \, \sqrt{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right) - 2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) + \frac{1}{2} \, \sqrt{2} \log\left(4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) - \frac{1}{2} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} + 4\right) - 8 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right) - \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1\right)"," ",0,"-2*sqrt(2)*arctan(sqrt(2)*sqrt(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) - 1) - 2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 1) + 1/2*sqrt(2)*log(4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - 1/2*sqrt(2)*log(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + 4*sqrt((a*x - 1)/(a*x + 1)) + 4) - 8*((a*x - 1)/(a*x + 1))^(1/4) + 2*arctan(((a*x - 1)/(a*x + 1))^(1/4)) + log(((a*x - 1)/(a*x + 1))^(1/4) + 1) - log(((a*x - 1)/(a*x + 1))^(1/4) - 1)","A",0
110,1,377,0,0.544687," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x^2,x, algorithm=""fricas"")","\frac{20 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \arctan\left(-\frac{a^{4} + \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} \sqrt{a^{2} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{4}}}}{a^{4}}\right) + 20 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \arctan\left(\frac{a^{4} - \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} {\left(a^{4}\right)}^{\frac{3}{4}} \sqrt{a^{2} \sqrt{\frac{a x - 1}{a x + 1}} - \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{4}}}}{a^{4}}\right) - 5 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \log\left(25 \, a^{2} \sqrt{\frac{a x - 1}{a x + 1}} + 25 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 25 \, \sqrt{a^{4}}\right) + 5 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} x \log\left(25 \, a^{2} \sqrt{\frac{a x - 1}{a x + 1}} - 25 \, \sqrt{2} {\left(a^{4}\right)}^{\frac{1}{4}} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 25 \, \sqrt{a^{4}}\right) + 4 \, {\left(9 \, a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{4 \, x}"," ",0,"1/4*(20*sqrt(2)*(a^4)^(1/4)*x*arctan(-(a^4 + sqrt(2)*(a^4)^(3/4)*a*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*(a^4)^(3/4)*sqrt(a^2*sqrt((a*x - 1)/(a*x + 1)) + sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^4)))/a^4) + 20*sqrt(2)*(a^4)^(1/4)*x*arctan((a^4 - sqrt(2)*(a^4)^(3/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*(a^4)^(3/4)*sqrt(a^2*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^4)))/a^4) - 5*sqrt(2)*(a^4)^(1/4)*x*log(25*a^2*sqrt((a*x - 1)/(a*x + 1)) + 25*sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + 25*sqrt(a^4)) + 5*sqrt(2)*(a^4)^(1/4)*x*log(25*a^2*sqrt((a*x - 1)/(a*x + 1)) - 25*sqrt(2)*(a^4)^(1/4)*a*((a*x - 1)/(a*x + 1))^(1/4) + 25*sqrt(a^4)) + 4*(9*a*x + 1)*((a*x - 1)/(a*x + 1))^(1/4))/x","A",0
111,1,405,0,0.508263," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x^3,x, algorithm=""fricas"")","-\frac{100 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \arctan\left(-\frac{a^{8} + \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} \sqrt{a^{4} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{8}}}}{a^{8}}\right) + 100 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \arctan\left(\frac{a^{8} - \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} {\left(a^{8}\right)}^{\frac{3}{4}} \sqrt{a^{4} \sqrt{\frac{a x - 1}{a x + 1}} - \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{8}}}}{a^{8}}\right) - 25 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \log\left(625 \, a^{4} \sqrt{\frac{a x - 1}{a x + 1}} + 625 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 625 \, \sqrt{a^{8}}\right) + 25 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} x^{2} \log\left(625 \, a^{4} \sqrt{\frac{a x - 1}{a x + 1}} - 625 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{4}} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 625 \, \sqrt{a^{8}}\right) + 4 \, {\left(43 \, a^{2} x^{2} + 9 \, a x - 2\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{16 \, x^{2}}"," ",0,"-1/16*(100*sqrt(2)*(a^8)^(1/4)*x^2*arctan(-(a^8 + sqrt(2)*(a^8)^(3/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*(a^8)^(3/4)*sqrt(a^4*sqrt((a*x - 1)/(a*x + 1)) + sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^8)))/a^8) + 100*sqrt(2)*(a^8)^(1/4)*x^2*arctan((a^8 - sqrt(2)*(a^8)^(3/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*(a^8)^(3/4)*sqrt(a^4*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^8)))/a^8) - 25*sqrt(2)*(a^8)^(1/4)*x^2*log(625*a^4*sqrt((a*x - 1)/(a*x + 1)) + 625*sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + 625*sqrt(a^8)) + 25*sqrt(2)*(a^8)^(1/4)*x^2*log(625*a^4*sqrt((a*x - 1)/(a*x + 1)) - 625*sqrt(2)*(a^8)^(1/4)*a^2*((a*x - 1)/(a*x + 1))^(1/4) + 625*sqrt(a^8)) + 4*(43*a^2*x^2 + 9*a*x - 2)*((a*x - 1)/(a*x + 1))^(1/4))/x^2","A",0
112,1,413,0,0.579388," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x^4,x, algorithm=""fricas"")","\frac{660 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \arctan\left(-\frac{a^{12} + \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{12}}}}{a^{12}}\right) + 660 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \arctan\left(\frac{a^{12} - \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{2} {\left(a^{12}\right)}^{\frac{3}{4}} \sqrt{a^{6} \sqrt{\frac{a x - 1}{a x + 1}} - \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{a^{12}}}}{a^{12}}\right) - 165 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \log\left(3025 \, a^{6} \sqrt{\frac{a x - 1}{a x + 1}} + 3025 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 3025 \, \sqrt{a^{12}}\right) + 165 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} x^{3} \log\left(3025 \, a^{6} \sqrt{\frac{a x - 1}{a x + 1}} - 3025 \, \sqrt{2} {\left(a^{12}\right)}^{\frac{1}{4}} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 3025 \, \sqrt{a^{12}}\right) + 4 \, {\left(287 \, a^{3} x^{3} + 61 \, a^{2} x^{2} - 26 \, a x + 8\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{96 \, x^{3}}"," ",0,"1/96*(660*sqrt(2)*(a^12)^(1/4)*x^3*arctan(-(a^12 + sqrt(2)*(a^12)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) - sqrt(2)*(a^12)^(3/4)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) + sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^12)))/a^12) + 660*sqrt(2)*(a^12)^(1/4)*x^3*arctan((a^12 - sqrt(2)*(a^12)^(3/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(2)*(a^12)^(3/4)*sqrt(a^6*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + sqrt(a^12)))/a^12) - 165*sqrt(2)*(a^12)^(1/4)*x^3*log(3025*a^6*sqrt((a*x - 1)/(a*x + 1)) + 3025*sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + 3025*sqrt(a^12)) + 165*sqrt(2)*(a^12)^(1/4)*x^3*log(3025*a^6*sqrt((a*x - 1)/(a*x + 1)) - 3025*sqrt(2)*(a^12)^(1/4)*a^3*((a*x - 1)/(a*x + 1))^(1/4) + 3025*sqrt(a^12)) + 4*(287*a^3*x^3 + 61*a^2*x^2 - 26*a*x + 8)*((a*x - 1)/(a*x + 1))^(1/4))/x^3","A",0
113,1,173,0,0.476666," ","integrate(1/((-1+x)/(1+x))^(1/6)*x^2,x, algorithm=""fricas"")","\frac{1}{54} \, {\left(18 \, x^{3} + 39 \, x^{2} + 43 \, x + 22\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}} - \frac{19}{162} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \frac{1}{3} \, \sqrt{3}\right) - \frac{19}{162} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - \frac{1}{3} \, \sqrt{3}\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,"1/54*(18*x^3 + 39*x^2 + 43*x + 22)*((x - 1)/(x + 1))^(5/6) - 19/162*sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 1/3*sqrt(3)) - 19/162*sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/6) - 1/3*sqrt(3)) + 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
114,1,168,0,0.665867," ","integrate(1/((-1+x)/(1+x))^(1/6)*x,x, algorithm=""fricas"")","\frac{1}{6} \, {\left(3 \, x^{2} + 7 \, x + 4\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}} - \frac{1}{18} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \frac{1}{3} \, \sqrt{3}\right) - \frac{1}{18} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - \frac{1}{3} \, \sqrt{3}\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,"1/6*(3*x^2 + 7*x + 4)*((x - 1)/(x + 1))^(5/6) - 1/18*sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 1/3*sqrt(3)) - 1/18*sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/6) - 1/3*sqrt(3)) + 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
115,1,160,0,0.609405," ","integrate(1/((-1+x)/(1+x))^(1/6),x, algorithm=""fricas"")","{\left(x + 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}} - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \frac{1}{3} \, \sqrt{3}\right) - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - \frac{1}{3} \, \sqrt{3}\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}{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,"(x + 1)*((x - 1)/(x + 1))^(5/6) - 1/3*sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 1/3*sqrt(3)) - 1/3*sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/6) - 1/3*sqrt(3)) + 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
116,1,340,0,0.556078," ","integrate(1/((-1+x)/(1+x))^(1/6)/x,x, algorithm=""fricas"")","-\sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \frac{1}{3} \, \sqrt{3}\right) - \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - \frac{1}{3} \, \sqrt{3}\right) - \frac{1}{2} \, \sqrt{3} \log\left(16 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 16 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 16\right) + \frac{1}{2} \, \sqrt{3} \log\left(-16 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 16 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 16\right) - 2 \, \arctan\left(\sqrt{3} + \frac{1}{2} \, \sqrt{-16 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 16 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 16} - 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) - 2 \, \arctan\left(-\sqrt{3} + 2 \, \sqrt{\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1} - 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + 2 \, \arctan\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{1}{2} \, \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}{2} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) + \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) - \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1\right)"," ",0,"-sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 1/3*sqrt(3)) - sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/6) - 1/3*sqrt(3)) - 1/2*sqrt(3)*log(16*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 16*((x - 1)/(x + 1))^(1/3) + 16) + 1/2*sqrt(3)*log(-16*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 16*((x - 1)/(x + 1))^(1/3) + 16) - 2*arctan(sqrt(3) + 1/2*sqrt(-16*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 16*((x - 1)/(x + 1))^(1/3) + 16) - 2*((x - 1)/(x + 1))^(1/6)) - 2*arctan(-sqrt(3) + 2*sqrt(sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) - 2*((x - 1)/(x + 1))^(1/6)) + 2*arctan(((x - 1)/(x + 1))^(1/6)) + 1/2*log(((x - 1)/(x + 1))^(1/3) + ((x - 1)/(x + 1))^(1/6) + 1) - 1/2*log(((x - 1)/(x + 1))^(1/3) - ((x - 1)/(x + 1))^(1/6) + 1) + log(((x - 1)/(x + 1))^(1/6) + 1) - log(((x - 1)/(x + 1))^(1/6) - 1)","A",0
117,1,223,0,0.607244," ","integrate(1/((-1+x)/(1+x))^(1/6)/x^2,x, algorithm=""fricas"")","-\frac{\sqrt{3} x \log\left(16 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 16 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 16\right) - \sqrt{3} x \log\left(-16 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 16 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 16\right) + 4 \, x \arctan\left(\sqrt{3} + \frac{1}{2} \, \sqrt{-16 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 16 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 16} - 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + 4 \, x \arctan\left(-\sqrt{3} + 2 \, \sqrt{\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1} - 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) - 4 \, x \arctan\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) - 6 \, {\left(x + 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{6 \, x}"," ",0,"-1/6*(sqrt(3)*x*log(16*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 16*((x - 1)/(x + 1))^(1/3) + 16) - sqrt(3)*x*log(-16*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 16*((x - 1)/(x + 1))^(1/3) + 16) + 4*x*arctan(sqrt(3) + 1/2*sqrt(-16*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 16*((x - 1)/(x + 1))^(1/3) + 16) - 2*((x - 1)/(x + 1))^(1/6)) + 4*x*arctan(-sqrt(3) + 2*sqrt(sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) - 2*((x - 1)/(x + 1))^(1/6)) - 4*x*arctan(((x - 1)/(x + 1))^(1/6)) - 6*(x + 1)*((x - 1)/(x + 1))^(5/6))/x","A",0
118,1,240,0,0.516787," ","integrate(1/((-1+x)/(1+x))^(1/6)/x^3,x, algorithm=""fricas"")","-\frac{\sqrt{3} x^{2} \log\left(16 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 16 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 16\right) - \sqrt{3} x^{2} \log\left(-16 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 16 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 16\right) + 4 \, x^{2} \arctan\left(\sqrt{3} + \frac{1}{2} \, \sqrt{-16 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 16 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 16} - 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + 4 \, x^{2} \arctan\left(-\sqrt{3} + 2 \, \sqrt{\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1} - 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) - 4 \, x^{2} \arctan\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) - 6 \, {\left(4 \, x^{2} + 7 \, x + 3\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{36 \, x^{2}}"," ",0,"-1/36*(sqrt(3)*x^2*log(16*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 16*((x - 1)/(x + 1))^(1/3) + 16) - sqrt(3)*x^2*log(-16*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 16*((x - 1)/(x + 1))^(1/3) + 16) + 4*x^2*arctan(sqrt(3) + 1/2*sqrt(-16*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 16*((x - 1)/(x + 1))^(1/3) + 16) - 2*((x - 1)/(x + 1))^(1/6)) + 4*x^2*arctan(-sqrt(3) + 2*sqrt(sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) - 2*((x - 1)/(x + 1))^(1/6)) - 4*x^2*arctan(((x - 1)/(x + 1))^(1/6)) - 6*(4*x^2 + 7*x + 3)*((x - 1)/(x + 1))^(5/6))/x^2","A",0
119,1,246,0,0.415773," ","integrate(1/((-1+x)/(1+x))^(1/6)/x^4,x, algorithm=""fricas"")","-\frac{19 \, \sqrt{3} x^{3} \log\left(5776 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 5776 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 5776\right) - 19 \, \sqrt{3} x^{3} \log\left(-5776 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 5776 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 5776\right) + 76 \, x^{3} \arctan\left(\sqrt{3} + \frac{1}{38} \, \sqrt{-5776 \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 5776 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 5776} - 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + 76 \, x^{3} \arctan\left(-\sqrt{3} + 2 \, \sqrt{\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1} - 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) - 76 \, x^{3} \arctan\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) - 6 \, {\left(22 \, x^{3} + 43 \, x^{2} + 39 \, x + 18\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{324 \, x^{3}}"," ",0,"-1/324*(19*sqrt(3)*x^3*log(5776*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 5776*((x - 1)/(x + 1))^(1/3) + 5776) - 19*sqrt(3)*x^3*log(-5776*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 5776*((x - 1)/(x + 1))^(1/3) + 5776) + 76*x^3*arctan(sqrt(3) + 1/38*sqrt(-5776*sqrt(3)*((x - 1)/(x + 1))^(1/6) + 5776*((x - 1)/(x + 1))^(1/3) + 5776) - 2*((x - 1)/(x + 1))^(1/6)) + 76*x^3*arctan(-sqrt(3) + 2*sqrt(sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) - 2*((x - 1)/(x + 1))^(1/6)) - 76*x^3*arctan(((x - 1)/(x + 1))^(1/6)) - 6*(22*x^3 + 43*x^2 + 39*x + 18)*((x - 1)/(x + 1))^(5/6))/x^3","A",0
120,1,100,0,0.397588," ","integrate(1/((-1+x)/(1+x))^(1/3)*x^2,x, algorithm=""fricas"")","\frac{1}{27} \, {\left(9 \, x^{3} + 21 \, x^{2} + 26 \, x + 14\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} - \frac{22}{81} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\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,"1/27*(9*x^3 + 21*x^2 + 26*x + 14)*((x - 1)/(x + 1))^(2/3) - 22/81*sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/3) + 1/3*sqrt(3)) + 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
121,1,95,0,0.583806," ","integrate(1/((-1+x)/(1+x))^(1/3)*x,x, algorithm=""fricas"")","\frac{1}{6} \, {\left(3 \, x^{2} + 8 \, x + 5\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} - \frac{2}{9} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\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,"1/6*(3*x^2 + 8*x + 5)*((x - 1)/(x + 1))^(2/3) - 2/9*sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/3) + 1/3*sqrt(3)) + 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
122,1,87,0,0.542274," ","integrate(1/((-1+x)/(1+x))^(1/3),x, algorithm=""fricas"")","{\left(x + 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} - \frac{2}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + \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,"(x + 1)*((x - 1)/(x + 1))^(2/3) - 2/3*sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/3) + 1/3*sqrt(3)) + 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
123,1,86,0,0.648170," ","integrate(1/((-1+x)/(1+x))^(1/3)/x,x, algorithm=""fricas"")","\sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} + \frac{1}{3} \, \sqrt{3}\right) - \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} - 1\right) + \frac{1}{2} \, \log\left(\frac{{\left(x + 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} + {\left(x - 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + x + 1}{x + 1}\right)"," ",0,"sqrt(3)*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(2/3) + 1/3*sqrt(3)) - log(((x - 1)/(x + 1))^(2/3) - 1) + 1/2*log(((x + 1)*((x - 1)/(x + 1))^(2/3) + (x - 1)*((x - 1)/(x + 1))^(1/3) + x + 1)/(x + 1))","A",0
124,1,97,0,0.676689," ","integrate(1/((-1+x)/(1+x))^(1/3)/x^2,x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} x \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + x \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} - \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) - 2 \, x \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + 3 \, {\left(x + 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}}{3 \, x}"," ",0,"1/3*(2*sqrt(3)*x*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/3) - 1/3*sqrt(3)) + x*log(((x - 1)/(x + 1))^(2/3) - ((x - 1)/(x + 1))^(1/3) + 1) - 2*x*log(((x - 1)/(x + 1))^(1/3) + 1) + 3*(x + 1)*((x - 1)/(x + 1))^(2/3))/x","A",0
125,1,111,0,0.575484," ","integrate(1/((-1+x)/(1+x))^(1/3)/x^3,x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} x^{2} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 2 \, x^{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) - 4 \, x^{2} \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + 3 \, {\left(5 \, x^{2} + 8 \, x + 3\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}}{18 \, x^{2}}"," ",0,"1/18*(4*sqrt(3)*x^2*arctan(2/3*sqrt(3)*((x - 1)/(x + 1))^(1/3) - 1/3*sqrt(3)) + 2*x^2*log(((x - 1)/(x + 1))^(2/3) - ((x - 1)/(x + 1))^(1/3) + 1) - 4*x^2*log(((x - 1)/(x + 1))^(1/3) + 1) + 3*(5*x^2 + 8*x + 3)*((x - 1)/(x + 1))^(2/3))/x^2","A",0
126,1,457,0,0.489088," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)*x^2,x, algorithm=""fricas"")","\frac{132 \, \sqrt{2} a^{3} \frac{1}{a^{12}}^{\frac{1}{4}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{12}}^{\frac{3}{4}} + a^{6} \sqrt{\frac{1}{a^{12}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} a^{3} \frac{1}{a^{12}}^{\frac{1}{4}} - \sqrt{2} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{12}}^{\frac{1}{4}} - 1\right) + 132 \, \sqrt{2} a^{3} \frac{1}{a^{12}}^{\frac{1}{4}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{12}}^{\frac{3}{4}} + a^{6} \sqrt{\frac{1}{a^{12}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} a^{3} \frac{1}{a^{12}}^{\frac{1}{4}} - \sqrt{2} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{12}}^{\frac{1}{4}} + 1\right) + 33 \, \sqrt{2} a^{3} \frac{1}{a^{12}}^{\frac{1}{4}} \log\left(\sqrt{2} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{12}}^{\frac{3}{4}} + a^{6} \sqrt{\frac{1}{a^{12}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - 33 \, \sqrt{2} a^{3} \frac{1}{a^{12}}^{\frac{1}{4}} \log\left(-\sqrt{2} a^{9} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{12}}^{\frac{3}{4}} + a^{6} \sqrt{\frac{1}{a^{12}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 8 \, {\left(32 \, a^{3} x^{3} + 68 \, a^{2} x^{2} + 73 \, a x + 37\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}} - 132 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) + 66 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right) - 66 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1\right)}{768 \, a^{3}}"," ",0,"1/768*(132*sqrt(2)*a^3*(a^(-12))^(1/4)*arctan(sqrt(2)*sqrt(sqrt(2)*a^9*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-12))^(3/4) + a^6*sqrt(a^(-12)) + ((a*x - 1)/(a*x + 1))^(1/4))*a^3*(a^(-12))^(1/4) - sqrt(2)*a^3*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-12))^(1/4) - 1) + 132*sqrt(2)*a^3*(a^(-12))^(1/4)*arctan(sqrt(2)*sqrt(-sqrt(2)*a^9*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-12))^(3/4) + a^6*sqrt(a^(-12)) + ((a*x - 1)/(a*x + 1))^(1/4))*a^3*(a^(-12))^(1/4) - sqrt(2)*a^3*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-12))^(1/4) + 1) + 33*sqrt(2)*a^3*(a^(-12))^(1/4)*log(sqrt(2)*a^9*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-12))^(3/4) + a^6*sqrt(a^(-12)) + ((a*x - 1)/(a*x + 1))^(1/4)) - 33*sqrt(2)*a^3*(a^(-12))^(1/4)*log(-sqrt(2)*a^9*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-12))^(3/4) + a^6*sqrt(a^(-12)) + ((a*x - 1)/(a*x + 1))^(1/4)) + 8*(32*a^3*x^3 + 68*a^2*x^2 + 73*a*x + 37)*((a*x - 1)/(a*x + 1))^(7/8) - 132*arctan(((a*x - 1)/(a*x + 1))^(1/8)) + 66*log(((a*x - 1)/(a*x + 1))^(1/8) + 1) - 66*log(((a*x - 1)/(a*x + 1))^(1/8) - 1))/a^3","A",0
127,1,448,0,0.499678," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)*x,x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} a^{2} \frac{1}{a^{8}}^{\frac{1}{4}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{8}}^{\frac{3}{4}} + a^{4} \sqrt{\frac{1}{a^{8}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} a^{2} \frac{1}{a^{8}}^{\frac{1}{4}} - \sqrt{2} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{8}}^{\frac{1}{4}} - 1\right) + 4 \, \sqrt{2} a^{2} \frac{1}{a^{8}}^{\frac{1}{4}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{8}}^{\frac{3}{4}} + a^{4} \sqrt{\frac{1}{a^{8}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} a^{2} \frac{1}{a^{8}}^{\frac{1}{4}} - \sqrt{2} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{8}}^{\frac{1}{4}} + 1\right) + \sqrt{2} a^{2} \frac{1}{a^{8}}^{\frac{1}{4}} \log\left(\sqrt{2} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{8}}^{\frac{3}{4}} + a^{4} \sqrt{\frac{1}{a^{8}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - \sqrt{2} a^{2} \frac{1}{a^{8}}^{\frac{1}{4}} \log\left(-\sqrt{2} a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{8}}^{\frac{3}{4}} + a^{4} \sqrt{\frac{1}{a^{8}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 8 \, {\left(4 \, a^{2} x^{2} + 9 \, a x + 5\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}} - 4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) + 2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right) - 2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1\right)}{64 \, a^{2}}"," ",0,"1/64*(4*sqrt(2)*a^2*(a^(-8))^(1/4)*arctan(sqrt(2)*sqrt(sqrt(2)*a^6*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-8))^(3/4) + a^4*sqrt(a^(-8)) + ((a*x - 1)/(a*x + 1))^(1/4))*a^2*(a^(-8))^(1/4) - sqrt(2)*a^2*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-8))^(1/4) - 1) + 4*sqrt(2)*a^2*(a^(-8))^(1/4)*arctan(sqrt(2)*sqrt(-sqrt(2)*a^6*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-8))^(3/4) + a^4*sqrt(a^(-8)) + ((a*x - 1)/(a*x + 1))^(1/4))*a^2*(a^(-8))^(1/4) - sqrt(2)*a^2*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-8))^(1/4) + 1) + sqrt(2)*a^2*(a^(-8))^(1/4)*log(sqrt(2)*a^6*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-8))^(3/4) + a^4*sqrt(a^(-8)) + ((a*x - 1)/(a*x + 1))^(1/4)) - sqrt(2)*a^2*(a^(-8))^(1/4)*log(-sqrt(2)*a^6*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-8))^(3/4) + a^4*sqrt(a^(-8)) + ((a*x - 1)/(a*x + 1))^(1/4)) + 8*(4*a^2*x^2 + 9*a*x + 5)*((a*x - 1)/(a*x + 1))^(7/8) - 4*arctan(((a*x - 1)/(a*x + 1))^(1/8)) + 2*log(((a*x - 1)/(a*x + 1))^(1/8) + 1) - 2*log(((a*x - 1)/(a*x + 1))^(1/8) - 1))/a^2","A",0
128,1,423,0,0.517616," ","integrate(1/((a*x-1)/(a*x+1))^(1/8),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} a \frac{1}{a^{4}}^{\frac{1}{4}} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{4}}^{\frac{3}{4}} + a^{2} \sqrt{\frac{1}{a^{4}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} a \frac{1}{a^{4}}^{\frac{1}{4}} - \sqrt{2} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{4}}^{\frac{1}{4}} - 1\right) + 4 \, \sqrt{2} a \frac{1}{a^{4}}^{\frac{1}{4}} \arctan\left(\sqrt{2} \sqrt{-\sqrt{2} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{4}}^{\frac{3}{4}} + a^{2} \sqrt{\frac{1}{a^{4}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} a \frac{1}{a^{4}}^{\frac{1}{4}} - \sqrt{2} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{4}}^{\frac{1}{4}} + 1\right) + \sqrt{2} a \frac{1}{a^{4}}^{\frac{1}{4}} \log\left(\sqrt{2} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{4}}^{\frac{3}{4}} + a^{2} \sqrt{\frac{1}{a^{4}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) - \sqrt{2} a \frac{1}{a^{4}}^{\frac{1}{4}} \log\left(-\sqrt{2} a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} \frac{1}{a^{4}}^{\frac{3}{4}} + a^{2} \sqrt{\frac{1}{a^{4}}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right) + 8 \, {\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}} - 4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) + 2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right) - 2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1\right)}{8 \, a}"," ",0,"1/8*(4*sqrt(2)*a*(a^(-4))^(1/4)*arctan(sqrt(2)*sqrt(sqrt(2)*a^3*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-4))^(3/4) + a^2*sqrt(a^(-4)) + ((a*x - 1)/(a*x + 1))^(1/4))*a*(a^(-4))^(1/4) - sqrt(2)*a*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-4))^(1/4) - 1) + 4*sqrt(2)*a*(a^(-4))^(1/4)*arctan(sqrt(2)*sqrt(-sqrt(2)*a^3*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-4))^(3/4) + a^2*sqrt(a^(-4)) + ((a*x - 1)/(a*x + 1))^(1/4))*a*(a^(-4))^(1/4) - sqrt(2)*a*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-4))^(1/4) + 1) + sqrt(2)*a*(a^(-4))^(1/4)*log(sqrt(2)*a^3*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-4))^(3/4) + a^2*sqrt(a^(-4)) + ((a*x - 1)/(a*x + 1))^(1/4)) - sqrt(2)*a*(a^(-4))^(1/4)*log(-sqrt(2)*a^3*((a*x - 1)/(a*x + 1))^(1/8)*(a^(-4))^(3/4) + a^2*sqrt(a^(-4)) + ((a*x - 1)/(a*x + 1))^(1/4)) + 8*(a*x + 1)*((a*x - 1)/(a*x + 1))^(7/8) - 4*arctan(((a*x - 1)/(a*x + 1))^(1/8)) + 2*log(((a*x - 1)/(a*x + 1))^(1/8) + 1) - 2*log(((a*x - 1)/(a*x + 1))^(1/8) - 1))/a","A",0
129,1,2289,0,0.767123," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)/x,x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - {\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} - \sqrt{2} \sqrt{2 \, {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)} - \sqrt{2}\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{2} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4} + 2 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 3 \, \sqrt{\sqrt{2} + 2}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{\sqrt{2} + 2}}\right) - \frac{1}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - {\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} + \sqrt{2} \sqrt{-2 \, {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)} - \sqrt{2}\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{2} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4} - 2 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 3 \, \sqrt{\sqrt{2} + 2}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{\sqrt{2} + 2}}\right) - \frac{1}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} - \sqrt{2} \sqrt{2 \, {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)} - \sqrt{2}\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{2} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4} + 2 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 3 \, \sqrt{\sqrt{2} + 2}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - {\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{\sqrt{2} + 2}}\right) - \frac{1}{2} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} + \sqrt{2} \sqrt{-2 \, {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)} - \sqrt{2}\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{2} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4} - 2 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 3 \, \sqrt{\sqrt{2} + 2}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - {\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(2 \, {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)} - \sqrt{2}\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{2} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4\right) + \frac{1}{8} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(-2 \, {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)} - \sqrt{2}\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{2} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4\right) + \frac{1}{8} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(2 \, {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)} - \sqrt{2}\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{2} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4\right) - \frac{1}{8} \, {\left(\sqrt{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(-2 \, {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - {\left(\sqrt{2} {\left(\sqrt{2} + 2\right)} - \sqrt{2}\right)} \sqrt{-\sqrt{2} + 2} - 3 \, \sqrt{2} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4\right) + 2 \, \sqrt{2} \arctan\left(\sqrt{2} \sqrt{\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} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1\right) + 2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4} - \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right) - \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{{\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} - 2 \, \sqrt{{\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 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} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2}}\right) - \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{{\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2} + 2 \, \sqrt{-{\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 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} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2}}\right) - \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 2 \, \sqrt{{\left({\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2}\right)} \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} - 3 \, \sqrt{\sqrt{2} + 2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{{\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2}}\right) - \sqrt{\sqrt{2} + 2} \arctan\left(\frac{{\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} + 2 \, \sqrt{-{\left({\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2}\right)} \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} - 3 \, \sqrt{\sqrt{2} + 2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{{\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{4} \, \sqrt{\sqrt{2} + 2} \log\left({\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 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) + \frac{1}{4} \, \sqrt{\sqrt{2} + 2} \log\left(-{\left(\sqrt{2} + 1\right)} \sqrt{-\sqrt{2} + 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) - \frac{1}{4} \, \sqrt{-\sqrt{2} + 2} \log\left({\left({\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2}\right)} \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) + \frac{1}{4} \, \sqrt{-\sqrt{2} + 2} \log\left(-{\left({\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{2} + 2}\right)} \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) + \frac{1}{2} \, \sqrt{2} \log\left(4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4\right) - \frac{1}{2} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4\right) - 2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) + \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right) - \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1\right)"," ",0,"-1/2*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-((sqrt(2) + 2)^(3/2) - (sqrt(2) + 1)*sqrt(-sqrt(2) + 2) - sqrt(2)*sqrt(2*(sqrt(2)*(sqrt(2) + 2)^(3/2) - (sqrt(2)*(sqrt(2) + 2) - sqrt(2))*sqrt(-sqrt(2) + 2) - 3*sqrt(2)*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + 4*((a*x - 1)/(a*x + 1))^(1/4) + 4) + 2*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) - 3*sqrt(sqrt(2) + 2))/((sqrt(2) + 2)^(3/2) + (sqrt(2) + 1)*sqrt(-sqrt(2) + 2) - 3*sqrt(sqrt(2) + 2))) - 1/2*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(((sqrt(2) + 2)^(3/2) - (sqrt(2) + 1)*sqrt(-sqrt(2) + 2) + sqrt(2)*sqrt(-2*(sqrt(2)*(sqrt(2) + 2)^(3/2) - (sqrt(2)*(sqrt(2) + 2) - sqrt(2))*sqrt(-sqrt(2) + 2) - 3*sqrt(2)*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + 4*((a*x - 1)/(a*x + 1))^(1/4) + 4) - 2*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) - 3*sqrt(sqrt(2) + 2))/((sqrt(2) + 2)^(3/2) + (sqrt(2) + 1)*sqrt(-sqrt(2) + 2) - 3*sqrt(sqrt(2) + 2))) - 1/2*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(((sqrt(2) + 2)^(3/2) + (sqrt(2) + 1)*sqrt(-sqrt(2) + 2) - sqrt(2)*sqrt(2*(sqrt(2)*(sqrt(2) + 2)^(3/2) + (sqrt(2)*(sqrt(2) + 2) - sqrt(2))*sqrt(-sqrt(2) + 2) - 3*sqrt(2)*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + 4*((a*x - 1)/(a*x + 1))^(1/4) + 4) + 2*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) - 3*sqrt(sqrt(2) + 2))/((sqrt(2) + 2)^(3/2) - (sqrt(2) + 1)*sqrt(-sqrt(2) + 2) - 3*sqrt(sqrt(2) + 2))) - 1/2*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*arctan(-((sqrt(2) + 2)^(3/2) + (sqrt(2) + 1)*sqrt(-sqrt(2) + 2) + sqrt(2)*sqrt(-2*(sqrt(2)*(sqrt(2) + 2)^(3/2) + (sqrt(2)*(sqrt(2) + 2) - sqrt(2))*sqrt(-sqrt(2) + 2) - 3*sqrt(2)*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + 4*((a*x - 1)/(a*x + 1))^(1/4) + 4) - 2*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) - 3*sqrt(sqrt(2) + 2))/((sqrt(2) + 2)^(3/2) - (sqrt(2) + 1)*sqrt(-sqrt(2) + 2) - 3*sqrt(sqrt(2) + 2))) - 1/8*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(2*(sqrt(2)*(sqrt(2) + 2)^(3/2) + (sqrt(2)*(sqrt(2) + 2) - sqrt(2))*sqrt(-sqrt(2) + 2) - 3*sqrt(2)*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + 4*((a*x - 1)/(a*x + 1))^(1/4) + 4) + 1/8*(sqrt(2)*sqrt(sqrt(2) + 2) + sqrt(2)*sqrt(-sqrt(2) + 2))*log(-2*(sqrt(2)*(sqrt(2) + 2)^(3/2) + (sqrt(2)*(sqrt(2) + 2) - sqrt(2))*sqrt(-sqrt(2) + 2) - 3*sqrt(2)*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + 4*((a*x - 1)/(a*x + 1))^(1/4) + 4) + 1/8*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(2*(sqrt(2)*(sqrt(2) + 2)^(3/2) - (sqrt(2)*(sqrt(2) + 2) - sqrt(2))*sqrt(-sqrt(2) + 2) - 3*sqrt(2)*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + 4*((a*x - 1)/(a*x + 1))^(1/4) + 4) - 1/8*(sqrt(2)*sqrt(sqrt(2) + 2) - sqrt(2)*sqrt(-sqrt(2) + 2))*log(-2*(sqrt(2)*(sqrt(2) + 2)^(3/2) - (sqrt(2)*(sqrt(2) + 2) - sqrt(2))*sqrt(-sqrt(2) + 2) - 3*sqrt(2)*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + 4*((a*x - 1)/(a*x + 1))^(1/4) + 4) + 2*sqrt(2)*arctan(sqrt(2)*sqrt(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) - 1) + 2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + 4*((a*x - 1)/(a*x + 1))^(1/4) + 4) - sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + 1) - sqrt(-sqrt(2) + 2)*arctan(-((sqrt(2) + 1)*sqrt(-sqrt(2) + 2) - 2*sqrt((sqrt(2) + 1)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + 2*((a*x - 1)/(a*x + 1))^(1/8))/((sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2))) - sqrt(-sqrt(2) + 2)*arctan(((sqrt(2) + 1)*sqrt(-sqrt(2) + 2) + 2*sqrt(-(sqrt(2) + 1)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) - 2*((a*x - 1)/(a*x + 1))^(1/8))/((sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2))) - sqrt(sqrt(2) + 2)*arctan(-((sqrt(2) + 2)^(3/2) - 2*sqrt(((sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) - 3*sqrt(sqrt(2) + 2) + 2*((a*x - 1)/(a*x + 1))^(1/8))/((sqrt(2) + 1)*sqrt(-sqrt(2) + 2))) - sqrt(sqrt(2) + 2)*arctan(((sqrt(2) + 2)^(3/2) + 2*sqrt(-((sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) - 3*sqrt(sqrt(2) + 2) - 2*((a*x - 1)/(a*x + 1))^(1/8))/((sqrt(2) + 1)*sqrt(-sqrt(2) + 2))) - 1/4*sqrt(sqrt(2) + 2)*log((sqrt(2) + 1)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + 1/4*sqrt(sqrt(2) + 2)*log(-(sqrt(2) + 1)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) - 1/4*sqrt(-sqrt(2) + 2)*log(((sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + 1/4*sqrt(-sqrt(2) + 2)*log(-((sqrt(2) + 2)^(3/2) - 3*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + 1/2*sqrt(2)*log(4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + 4*((a*x - 1)/(a*x + 1))^(1/4) + 4) - 1/2*sqrt(2)*log(-4*sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + 4*((a*x - 1)/(a*x + 1))^(1/4) + 4) - 2*arctan(((a*x - 1)/(a*x + 1))^(1/8)) + log(((a*x - 1)/(a*x + 1))^(1/8) + 1) - log(((a*x - 1)/(a*x + 1))^(1/8) - 1)","B",0
130,1,2874,0,0.783682," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)/x^2,x, algorithm=""fricas"")","-\frac{8 \, {\left(a^{8}\right)}^{\frac{1}{8}} x \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, {\left(a^{8}\right)}^{\frac{1}{8}} a^{7} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + {\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2} - 2 \, \sqrt{a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} + {\left(a^{8}\right)}^{\frac{7}{8}} {\left(a^{7} {\left(\sqrt{2} + 2\right)} - a^{7}\right)} \sqrt{-\sqrt{2} + 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{8}\right)}^{\frac{1}{8}}}{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2}}\right) + 8 \, {\left(a^{8}\right)}^{\frac{1}{8}} x \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, {\left(a^{8}\right)}^{\frac{1}{8}} a^{7} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - {\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2} - 2 \, \sqrt{a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} - {\left(a^{8}\right)}^{\frac{7}{8}} {\left(a^{7} {\left(\sqrt{2} + 2\right)} - a^{7}\right)} \sqrt{-\sqrt{2} + 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{8}\right)}^{\frac{1}{8}}}{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2}}\right) + 8 \, {\left(a^{8}\right)}^{\frac{1}{8}} x \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2} + 2 \, {\left(a^{8}\right)}^{\frac{1}{8}} a^{7} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 2 \, \sqrt{a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} + {\left(a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{7} \sqrt{\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{8}\right)}^{\frac{1}{8}}}{{\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2}}\right) + 8 \, {\left(a^{8}\right)}^{\frac{1}{8}} x \sqrt{\sqrt{2} + 2} \arctan\left(\frac{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2} - 2 \, {\left(a^{8}\right)}^{\frac{1}{8}} a^{7} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 2 \, \sqrt{a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} - {\left(a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{7} \sqrt{\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{8}\right)}^{\frac{1}{8}}}{{\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2}}\right) + 2 \, {\left(a^{8}\right)}^{\frac{1}{8}} x \sqrt{\sqrt{2} + 2} \log\left(a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} + {\left(a^{8}\right)}^{\frac{7}{8}} {\left(a^{7} {\left(\sqrt{2} + 2\right)} - a^{7}\right)} \sqrt{-\sqrt{2} + 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) - 2 \, {\left(a^{8}\right)}^{\frac{1}{8}} x \sqrt{\sqrt{2} + 2} \log\left(a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} - {\left(a^{8}\right)}^{\frac{7}{8}} {\left(a^{7} {\left(\sqrt{2} + 2\right)} - a^{7}\right)} \sqrt{-\sqrt{2} + 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) + 2 \, {\left(a^{8}\right)}^{\frac{1}{8}} x \sqrt{-\sqrt{2} + 2} \log\left(a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} + {\left(a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{7} \sqrt{\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) - 2 \, {\left(a^{8}\right)}^{\frac{1}{8}} x \sqrt{-\sqrt{2} + 2} \log\left(a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} - {\left(a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{7} \sqrt{\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) + 4 \, {\left(a^{8}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} + \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{8}} a^{7} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - {\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2} - \sqrt{2} \sqrt{4 \, a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} + 2 \, {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{7} \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{7}\right)} \sqrt{-\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{8}\right)}^{\frac{1}{8}}}{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2} + {\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2}}\right) + 4 \, {\left(a^{8}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} + \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{8}} a^{7} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - {\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2} + \sqrt{2} \sqrt{4 \, a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} - 2 \, {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{7} \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{7}\right)} \sqrt{-\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{8}\right)}^{\frac{1}{8}}}{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2} + {\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2}}\right) + 4 \, {\left(a^{8}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} - \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{8}} a^{7} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + {\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2} - \sqrt{2} \sqrt{4 \, a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} + 2 \, {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{7} \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{7}\right)} \sqrt{-\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{8}\right)}^{\frac{1}{8}}}{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2} - {\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2}}\right) + 4 \, {\left(a^{8}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} - \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{2} {\left(a^{8}\right)}^{\frac{1}{8}} a^{7} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + {\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2} + \sqrt{2} \sqrt{4 \, a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} - 2 \, {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{7} \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{7}\right)} \sqrt{-\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{8}\right)}^{\frac{1}{8}}}{a^{8} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{8} \sqrt{\sqrt{2} + 2} - {\left(a^{8} {\left(\sqrt{2} + 2\right)} - a^{8}\right)} \sqrt{-\sqrt{2} + 2}}\right) + {\left(a^{8}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} + \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \log\left(4 \, a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} + 2 \, {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{7} \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{7}\right)} \sqrt{-\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) - {\left(a^{8}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} + \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \log\left(4 \, a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} - 2 \, {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{7} \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{7}\right)} \sqrt{-\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) - {\left(a^{8}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} - \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \log\left(4 \, a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} + 2 \, {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{7} \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{7}\right)} \sqrt{-\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) + {\left(a^{8}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x \sqrt{\sqrt{2} + 2} - \sqrt{2} x \sqrt{-\sqrt{2} + 2}\right)} \log\left(4 \, a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{8}\right)}^{\frac{3}{4}} a^{8} - 2 \, {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{7} \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} a^{7} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{7}\right)} \sqrt{-\sqrt{2} + 2}\right)} {\left(a^{8}\right)}^{\frac{7}{8}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) - 32 \, {\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}}{32 \, x}"," ",0,"-1/32*(8*(a^8)^(1/8)*x*sqrt(-sqrt(2) + 2)*arctan(-(2*(a^8)^(1/8)*a^7*((a*x - 1)/(a*x + 1))^(1/8) + (a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2) - 2*sqrt(a^14*((a*x - 1)/(a*x + 1))^(1/4) + (a^8)^(3/4)*a^8 + (a^8)^(7/8)*(a^7*(sqrt(2) + 2) - a^7)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8))*(a^8)^(1/8))/(a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2))) + 8*(a^8)^(1/8)*x*sqrt(-sqrt(2) + 2)*arctan(-(2*(a^8)^(1/8)*a^7*((a*x - 1)/(a*x + 1))^(1/8) - (a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2) - 2*sqrt(a^14*((a*x - 1)/(a*x + 1))^(1/4) + (a^8)^(3/4)*a^8 - (a^8)^(7/8)*(a^7*(sqrt(2) + 2) - a^7)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8))*(a^8)^(1/8))/(a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2))) + 8*(a^8)^(1/8)*x*sqrt(sqrt(2) + 2)*arctan(-(a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2) + 2*(a^8)^(1/8)*a^7*((a*x - 1)/(a*x + 1))^(1/8) - 2*sqrt(a^14*((a*x - 1)/(a*x + 1))^(1/4) + (a^8)^(3/4)*a^8 + (a^7*(sqrt(2) + 2)^(3/2) - 3*a^7*sqrt(sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8))*(a^8)^(1/8))/((a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2))) + 8*(a^8)^(1/8)*x*sqrt(sqrt(2) + 2)*arctan((a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2) - 2*(a^8)^(1/8)*a^7*((a*x - 1)/(a*x + 1))^(1/8) + 2*sqrt(a^14*((a*x - 1)/(a*x + 1))^(1/4) + (a^8)^(3/4)*a^8 - (a^7*(sqrt(2) + 2)^(3/2) - 3*a^7*sqrt(sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8))*(a^8)^(1/8))/((a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2))) + 2*(a^8)^(1/8)*x*sqrt(sqrt(2) + 2)*log(a^14*((a*x - 1)/(a*x + 1))^(1/4) + (a^8)^(3/4)*a^8 + (a^8)^(7/8)*(a^7*(sqrt(2) + 2) - a^7)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8)) - 2*(a^8)^(1/8)*x*sqrt(sqrt(2) + 2)*log(a^14*((a*x - 1)/(a*x + 1))^(1/4) + (a^8)^(3/4)*a^8 - (a^8)^(7/8)*(a^7*(sqrt(2) + 2) - a^7)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8)) + 2*(a^8)^(1/8)*x*sqrt(-sqrt(2) + 2)*log(a^14*((a*x - 1)/(a*x + 1))^(1/4) + (a^8)^(3/4)*a^8 + (a^7*(sqrt(2) + 2)^(3/2) - 3*a^7*sqrt(sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8)) - 2*(a^8)^(1/8)*x*sqrt(-sqrt(2) + 2)*log(a^14*((a*x - 1)/(a*x + 1))^(1/4) + (a^8)^(3/4)*a^8 - (a^7*(sqrt(2) + 2)^(3/2) - 3*a^7*sqrt(sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8)) + 4*(a^8)^(1/8)*(sqrt(2)*x*sqrt(sqrt(2) + 2) + sqrt(2)*x*sqrt(-sqrt(2) + 2))*arctan(-(a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2) + 2*sqrt(2)*(a^8)^(1/8)*a^7*((a*x - 1)/(a*x + 1))^(1/8) - (a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2) - sqrt(2)*sqrt(4*a^14*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^8)^(3/4)*a^8 + 2*(sqrt(2)*a^7*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^7*sqrt(sqrt(2) + 2) - (sqrt(2)*a^7*(sqrt(2) + 2) - sqrt(2)*a^7)*sqrt(-sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8))*(a^8)^(1/8))/(a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2) + (a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2))) + 4*(a^8)^(1/8)*(sqrt(2)*x*sqrt(sqrt(2) + 2) + sqrt(2)*x*sqrt(-sqrt(2) + 2))*arctan((a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2) - 2*sqrt(2)*(a^8)^(1/8)*a^7*((a*x - 1)/(a*x + 1))^(1/8) - (a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2) + sqrt(2)*sqrt(4*a^14*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^8)^(3/4)*a^8 - 2*(sqrt(2)*a^7*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^7*sqrt(sqrt(2) + 2) - (sqrt(2)*a^7*(sqrt(2) + 2) - sqrt(2)*a^7)*sqrt(-sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8))*(a^8)^(1/8))/(a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2) + (a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2))) + 4*(a^8)^(1/8)*(sqrt(2)*x*sqrt(sqrt(2) + 2) - sqrt(2)*x*sqrt(-sqrt(2) + 2))*arctan((a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2) + 2*sqrt(2)*(a^8)^(1/8)*a^7*((a*x - 1)/(a*x + 1))^(1/8) + (a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2) - sqrt(2)*sqrt(4*a^14*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^8)^(3/4)*a^8 + 2*(sqrt(2)*a^7*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^7*sqrt(sqrt(2) + 2) + (sqrt(2)*a^7*(sqrt(2) + 2) - sqrt(2)*a^7)*sqrt(-sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8))*(a^8)^(1/8))/(a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2) - (a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2))) + 4*(a^8)^(1/8)*(sqrt(2)*x*sqrt(sqrt(2) + 2) - sqrt(2)*x*sqrt(-sqrt(2) + 2))*arctan(-(a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2) - 2*sqrt(2)*(a^8)^(1/8)*a^7*((a*x - 1)/(a*x + 1))^(1/8) + (a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2) + sqrt(2)*sqrt(4*a^14*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^8)^(3/4)*a^8 - 2*(sqrt(2)*a^7*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^7*sqrt(sqrt(2) + 2) + (sqrt(2)*a^7*(sqrt(2) + 2) - sqrt(2)*a^7)*sqrt(-sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8))*(a^8)^(1/8))/(a^8*(sqrt(2) + 2)^(3/2) - 3*a^8*sqrt(sqrt(2) + 2) - (a^8*(sqrt(2) + 2) - a^8)*sqrt(-sqrt(2) + 2))) + (a^8)^(1/8)*(sqrt(2)*x*sqrt(sqrt(2) + 2) + sqrt(2)*x*sqrt(-sqrt(2) + 2))*log(4*a^14*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^8)^(3/4)*a^8 + 2*(sqrt(2)*a^7*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^7*sqrt(sqrt(2) + 2) + (sqrt(2)*a^7*(sqrt(2) + 2) - sqrt(2)*a^7)*sqrt(-sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8)) - (a^8)^(1/8)*(sqrt(2)*x*sqrt(sqrt(2) + 2) + sqrt(2)*x*sqrt(-sqrt(2) + 2))*log(4*a^14*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^8)^(3/4)*a^8 - 2*(sqrt(2)*a^7*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^7*sqrt(sqrt(2) + 2) + (sqrt(2)*a^7*(sqrt(2) + 2) - sqrt(2)*a^7)*sqrt(-sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8)) - (a^8)^(1/8)*(sqrt(2)*x*sqrt(sqrt(2) + 2) - sqrt(2)*x*sqrt(-sqrt(2) + 2))*log(4*a^14*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^8)^(3/4)*a^8 + 2*(sqrt(2)*a^7*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^7*sqrt(sqrt(2) + 2) - (sqrt(2)*a^7*(sqrt(2) + 2) - sqrt(2)*a^7)*sqrt(-sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8)) + (a^8)^(1/8)*(sqrt(2)*x*sqrt(sqrt(2) + 2) - sqrt(2)*x*sqrt(-sqrt(2) + 2))*log(4*a^14*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^8)^(3/4)*a^8 - 2*(sqrt(2)*a^7*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^7*sqrt(sqrt(2) + 2) - (sqrt(2)*a^7*(sqrt(2) + 2) - sqrt(2)*a^7)*sqrt(-sqrt(2) + 2))*(a^8)^(7/8)*((a*x - 1)/(a*x + 1))^(1/8)) - 32*(a*x + 1)*((a*x - 1)/(a*x + 1))^(7/8))/x","B",0
131,1,2931,0,0.936035," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)/x^3,x, algorithm=""fricas"")","-\frac{8 \, {\left(a^{16}\right)}^{\frac{1}{8}} x^{2} \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, {\left(a^{16}\right)}^{\frac{1}{8}} a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + {\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2} - 2 \, \sqrt{a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} + {\left(a^{16}\right)}^{\frac{7}{8}} {\left(a^{14} {\left(\sqrt{2} + 2\right)} - a^{14}\right)} \sqrt{-\sqrt{2} + 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{16}\right)}^{\frac{1}{8}}}{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2}}\right) + 8 \, {\left(a^{16}\right)}^{\frac{1}{8}} x^{2} \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, {\left(a^{16}\right)}^{\frac{1}{8}} a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - {\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2} - 2 \, \sqrt{a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} - {\left(a^{16}\right)}^{\frac{7}{8}} {\left(a^{14} {\left(\sqrt{2} + 2\right)} - a^{14}\right)} \sqrt{-\sqrt{2} + 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{16}\right)}^{\frac{1}{8}}}{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2}}\right) + 8 \, {\left(a^{16}\right)}^{\frac{1}{8}} x^{2} \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2} + 2 \, {\left(a^{16}\right)}^{\frac{1}{8}} a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 2 \, \sqrt{a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} + {\left(a^{16}\right)}^{\frac{7}{8}} {\left(a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{14} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{16}\right)}^{\frac{1}{8}}}{{\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2}}\right) + 8 \, {\left(a^{16}\right)}^{\frac{1}{8}} x^{2} \sqrt{\sqrt{2} + 2} \arctan\left(\frac{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2} - 2 \, {\left(a^{16}\right)}^{\frac{1}{8}} a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 2 \, \sqrt{a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} - {\left(a^{16}\right)}^{\frac{7}{8}} {\left(a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{14} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{16}\right)}^{\frac{1}{8}}}{{\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2}}\right) + 2 \, {\left(a^{16}\right)}^{\frac{1}{8}} x^{2} \sqrt{\sqrt{2} + 2} \log\left(a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} + {\left(a^{16}\right)}^{\frac{7}{8}} {\left(a^{14} {\left(\sqrt{2} + 2\right)} - a^{14}\right)} \sqrt{-\sqrt{2} + 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) - 2 \, {\left(a^{16}\right)}^{\frac{1}{8}} x^{2} \sqrt{\sqrt{2} + 2} \log\left(a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} - {\left(a^{16}\right)}^{\frac{7}{8}} {\left(a^{14} {\left(\sqrt{2} + 2\right)} - a^{14}\right)} \sqrt{-\sqrt{2} + 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) + 2 \, {\left(a^{16}\right)}^{\frac{1}{8}} x^{2} \sqrt{-\sqrt{2} + 2} \log\left(a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} + {\left(a^{16}\right)}^{\frac{7}{8}} {\left(a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{14} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) - 2 \, {\left(a^{16}\right)}^{\frac{1}{8}} x^{2} \sqrt{-\sqrt{2} + 2} \log\left(a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} - {\left(a^{16}\right)}^{\frac{7}{8}} {\left(a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{14} \sqrt{\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) + 4 \, {\left(a^{16}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x^{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{2} {\left(a^{16}\right)}^{\frac{1}{8}} a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - {\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2} - \sqrt{2} \sqrt{4 \, a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} + 2 \, {\left(a^{16}\right)}^{\frac{7}{8}} {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{14} \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{14}\right)} \sqrt{-\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{16}\right)}^{\frac{1}{8}}}{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2} + {\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2}}\right) + 4 \, {\left(a^{16}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x^{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{2} {\left(a^{16}\right)}^{\frac{1}{8}} a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - {\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2} + \sqrt{2} \sqrt{4 \, a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} - 2 \, {\left(a^{16}\right)}^{\frac{7}{8}} {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{14} \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{14}\right)} \sqrt{-\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{16}\right)}^{\frac{1}{8}}}{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2} + {\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2}}\right) + 4 \, {\left(a^{16}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x^{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(\frac{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{2} {\left(a^{16}\right)}^{\frac{1}{8}} a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + {\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2} - \sqrt{2} \sqrt{4 \, a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} + 2 \, {\left(a^{16}\right)}^{\frac{7}{8}} {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{14} \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{14}\right)} \sqrt{-\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{16}\right)}^{\frac{1}{8}}}{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2} - {\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2}}\right) + 4 \, {\left(a^{16}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x^{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{2} \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{2} {\left(a^{16}\right)}^{\frac{1}{8}} a^{14} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + {\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2} + \sqrt{2} \sqrt{4 \, a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} - 2 \, {\left(a^{16}\right)}^{\frac{7}{8}} {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{14} \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{14}\right)} \sqrt{-\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}} {\left(a^{16}\right)}^{\frac{1}{8}}}{a^{16} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, a^{16} \sqrt{\sqrt{2} + 2} - {\left(a^{16} {\left(\sqrt{2} + 2\right)} - a^{16}\right)} \sqrt{-\sqrt{2} + 2}}\right) + {\left(a^{16}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x^{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(4 \, a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} + 2 \, {\left(a^{16}\right)}^{\frac{7}{8}} {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{14} \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{14}\right)} \sqrt{-\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) - {\left(a^{16}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x^{2} \sqrt{\sqrt{2} + 2} + \sqrt{2} x^{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(4 \, a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} - 2 \, {\left(a^{16}\right)}^{\frac{7}{8}} {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{14} \sqrt{\sqrt{2} + 2} + {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{14}\right)} \sqrt{-\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) - {\left(a^{16}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x^{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(4 \, a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} + 2 \, {\left(a^{16}\right)}^{\frac{7}{8}} {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{14} \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{14}\right)} \sqrt{-\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) + {\left(a^{16}\right)}^{\frac{1}{8}} {\left(\sqrt{2} x^{2} \sqrt{\sqrt{2} + 2} - \sqrt{2} x^{2} \sqrt{-\sqrt{2} + 2}\right)} \log\left(4 \, a^{28} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 4 \, {\left(a^{16}\right)}^{\frac{3}{4}} a^{16} - 2 \, {\left(a^{16}\right)}^{\frac{7}{8}} {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)}^{\frac{3}{2}} - 3 \, \sqrt{2} a^{14} \sqrt{\sqrt{2} + 2} - {\left(\sqrt{2} a^{14} {\left(\sqrt{2} + 2\right)} - \sqrt{2} a^{14}\right)} \sqrt{-\sqrt{2} + 2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right) - 32 \, {\left(5 \, a^{2} x^{2} + 9 \, a x + 4\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}}{256 \, x^{2}}"," ",0,"-1/256*(8*(a^16)^(1/8)*x^2*sqrt(-sqrt(2) + 2)*arctan(-(2*(a^16)^(1/8)*a^14*((a*x - 1)/(a*x + 1))^(1/8) + (a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2) - 2*sqrt(a^28*((a*x - 1)/(a*x + 1))^(1/4) + (a^16)^(3/4)*a^16 + (a^16)^(7/8)*(a^14*(sqrt(2) + 2) - a^14)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8))*(a^16)^(1/8))/(a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2))) + 8*(a^16)^(1/8)*x^2*sqrt(-sqrt(2) + 2)*arctan(-(2*(a^16)^(1/8)*a^14*((a*x - 1)/(a*x + 1))^(1/8) - (a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2) - 2*sqrt(a^28*((a*x - 1)/(a*x + 1))^(1/4) + (a^16)^(3/4)*a^16 - (a^16)^(7/8)*(a^14*(sqrt(2) + 2) - a^14)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8))*(a^16)^(1/8))/(a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2))) + 8*(a^16)^(1/8)*x^2*sqrt(sqrt(2) + 2)*arctan(-(a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2) + 2*(a^16)^(1/8)*a^14*((a*x - 1)/(a*x + 1))^(1/8) - 2*sqrt(a^28*((a*x - 1)/(a*x + 1))^(1/4) + (a^16)^(3/4)*a^16 + (a^16)^(7/8)*(a^14*(sqrt(2) + 2)^(3/2) - 3*a^14*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8))*(a^16)^(1/8))/((a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2))) + 8*(a^16)^(1/8)*x^2*sqrt(sqrt(2) + 2)*arctan((a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2) - 2*(a^16)^(1/8)*a^14*((a*x - 1)/(a*x + 1))^(1/8) + 2*sqrt(a^28*((a*x - 1)/(a*x + 1))^(1/4) + (a^16)^(3/4)*a^16 - (a^16)^(7/8)*(a^14*(sqrt(2) + 2)^(3/2) - 3*a^14*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8))*(a^16)^(1/8))/((a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2))) + 2*(a^16)^(1/8)*x^2*sqrt(sqrt(2) + 2)*log(a^28*((a*x - 1)/(a*x + 1))^(1/4) + (a^16)^(3/4)*a^16 + (a^16)^(7/8)*(a^14*(sqrt(2) + 2) - a^14)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8)) - 2*(a^16)^(1/8)*x^2*sqrt(sqrt(2) + 2)*log(a^28*((a*x - 1)/(a*x + 1))^(1/4) + (a^16)^(3/4)*a^16 - (a^16)^(7/8)*(a^14*(sqrt(2) + 2) - a^14)*sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8)) + 2*(a^16)^(1/8)*x^2*sqrt(-sqrt(2) + 2)*log(a^28*((a*x - 1)/(a*x + 1))^(1/4) + (a^16)^(3/4)*a^16 + (a^16)^(7/8)*(a^14*(sqrt(2) + 2)^(3/2) - 3*a^14*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8)) - 2*(a^16)^(1/8)*x^2*sqrt(-sqrt(2) + 2)*log(a^28*((a*x - 1)/(a*x + 1))^(1/4) + (a^16)^(3/4)*a^16 - (a^16)^(7/8)*(a^14*(sqrt(2) + 2)^(3/2) - 3*a^14*sqrt(sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8)) + 4*(a^16)^(1/8)*(sqrt(2)*x^2*sqrt(sqrt(2) + 2) + sqrt(2)*x^2*sqrt(-sqrt(2) + 2))*arctan(-(a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2) + 2*sqrt(2)*(a^16)^(1/8)*a^14*((a*x - 1)/(a*x + 1))^(1/8) - (a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2) - sqrt(2)*sqrt(4*a^28*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^16)^(3/4)*a^16 + 2*(a^16)^(7/8)*(sqrt(2)*a^14*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^14*sqrt(sqrt(2) + 2) - (sqrt(2)*a^14*(sqrt(2) + 2) - sqrt(2)*a^14)*sqrt(-sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8))*(a^16)^(1/8))/(a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2) + (a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2))) + 4*(a^16)^(1/8)*(sqrt(2)*x^2*sqrt(sqrt(2) + 2) + sqrt(2)*x^2*sqrt(-sqrt(2) + 2))*arctan((a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2) - 2*sqrt(2)*(a^16)^(1/8)*a^14*((a*x - 1)/(a*x + 1))^(1/8) - (a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2) + sqrt(2)*sqrt(4*a^28*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^16)^(3/4)*a^16 - 2*(a^16)^(7/8)*(sqrt(2)*a^14*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^14*sqrt(sqrt(2) + 2) - (sqrt(2)*a^14*(sqrt(2) + 2) - sqrt(2)*a^14)*sqrt(-sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8))*(a^16)^(1/8))/(a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2) + (a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2))) + 4*(a^16)^(1/8)*(sqrt(2)*x^2*sqrt(sqrt(2) + 2) - sqrt(2)*x^2*sqrt(-sqrt(2) + 2))*arctan((a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2) + 2*sqrt(2)*(a^16)^(1/8)*a^14*((a*x - 1)/(a*x + 1))^(1/8) + (a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2) - sqrt(2)*sqrt(4*a^28*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^16)^(3/4)*a^16 + 2*(a^16)^(7/8)*(sqrt(2)*a^14*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^14*sqrt(sqrt(2) + 2) + (sqrt(2)*a^14*(sqrt(2) + 2) - sqrt(2)*a^14)*sqrt(-sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8))*(a^16)^(1/8))/(a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2) - (a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2))) + 4*(a^16)^(1/8)*(sqrt(2)*x^2*sqrt(sqrt(2) + 2) - sqrt(2)*x^2*sqrt(-sqrt(2) + 2))*arctan(-(a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2) - 2*sqrt(2)*(a^16)^(1/8)*a^14*((a*x - 1)/(a*x + 1))^(1/8) + (a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2) + sqrt(2)*sqrt(4*a^28*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^16)^(3/4)*a^16 - 2*(a^16)^(7/8)*(sqrt(2)*a^14*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^14*sqrt(sqrt(2) + 2) + (sqrt(2)*a^14*(sqrt(2) + 2) - sqrt(2)*a^14)*sqrt(-sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8))*(a^16)^(1/8))/(a^16*(sqrt(2) + 2)^(3/2) - 3*a^16*sqrt(sqrt(2) + 2) - (a^16*(sqrt(2) + 2) - a^16)*sqrt(-sqrt(2) + 2))) + (a^16)^(1/8)*(sqrt(2)*x^2*sqrt(sqrt(2) + 2) + sqrt(2)*x^2*sqrt(-sqrt(2) + 2))*log(4*a^28*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^16)^(3/4)*a^16 + 2*(a^16)^(7/8)*(sqrt(2)*a^14*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^14*sqrt(sqrt(2) + 2) + (sqrt(2)*a^14*(sqrt(2) + 2) - sqrt(2)*a^14)*sqrt(-sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8)) - (a^16)^(1/8)*(sqrt(2)*x^2*sqrt(sqrt(2) + 2) + sqrt(2)*x^2*sqrt(-sqrt(2) + 2))*log(4*a^28*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^16)^(3/4)*a^16 - 2*(a^16)^(7/8)*(sqrt(2)*a^14*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^14*sqrt(sqrt(2) + 2) + (sqrt(2)*a^14*(sqrt(2) + 2) - sqrt(2)*a^14)*sqrt(-sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8)) - (a^16)^(1/8)*(sqrt(2)*x^2*sqrt(sqrt(2) + 2) - sqrt(2)*x^2*sqrt(-sqrt(2) + 2))*log(4*a^28*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^16)^(3/4)*a^16 + 2*(a^16)^(7/8)*(sqrt(2)*a^14*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^14*sqrt(sqrt(2) + 2) - (sqrt(2)*a^14*(sqrt(2) + 2) - sqrt(2)*a^14)*sqrt(-sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8)) + (a^16)^(1/8)*(sqrt(2)*x^2*sqrt(sqrt(2) + 2) - sqrt(2)*x^2*sqrt(-sqrt(2) + 2))*log(4*a^28*((a*x - 1)/(a*x + 1))^(1/4) + 4*(a^16)^(3/4)*a^16 - 2*(a^16)^(7/8)*(sqrt(2)*a^14*(sqrt(2) + 2)^(3/2) - 3*sqrt(2)*a^14*sqrt(sqrt(2) + 2) - (sqrt(2)*a^14*(sqrt(2) + 2) - sqrt(2)*a^14)*sqrt(-sqrt(2) + 2))*((a*x - 1)/(a*x + 1))^(1/8)) - 32*(5*a^2*x^2 + 9*a*x + 4)*((a*x - 1)/(a*x + 1))^(7/8))/x^2","B",0
132,0,0,0,0.566088," ","integrate(1/(a*x-1)^2*(a*x+1)^2*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{2} + 2 \, a x + 1\right)} x^{m}}{a^{2} x^{2} - 2 \, a x + 1}, x\right)"," ",0,"integral((a^2*x^2 + 2*a*x + 1)*x^m/(a^2*x^2 - 2*a*x + 1), x)","F",0
133,0,0,0,0.546525," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{2} + 2 \, a x + 1\right)} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x^{2} - 2 \, a x + 1}, x\right)"," ",0,"integral((a^2*x^2 + 2*a*x + 1)*x^m*sqrt((a*x - 1)/(a*x + 1))/(a^2*x^2 - 2*a*x + 1), x)","F",0
134,0,0,0,0.476943," ","integrate(1/(a*x-1)*(a*x+1)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)} x^{m}}{a x - 1}, x\right)"," ",0,"integral((a*x + 1)*x^m/(a*x - 1), x)","F",0
135,0,0,0,0.592680," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}}{a x - 1}, x\right)"," ",0,"integral((a*x + 1)*x^m*sqrt((a*x - 1)/(a*x + 1))/(a*x - 1), x)","F",0
136,0,0,0,0.607502," ","integrate(x^m*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \sqrt{\frac{a x - 1}{a x + 1}}, x\right)"," ",0,"integral(x^m*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
137,0,0,0,0.561124," ","integrate(x^m*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x - 1\right)} x^{m}}{a x + 1}, x\right)"," ",0,"integral((a*x - 1)*x^m/(a*x + 1), x)","F",0
138,0,0,0,0.888765," ","integrate(x^m*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x - 1\right)} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1}, x\right)"," ",0,"integral((a*x - 1)*x^m*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1), x)","F",0
139,0,0,0,0.564163," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{2} + 2 \, a x + 1\right)} x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a^{2} x^{2} - 2 \, a x + 1}, x\right)"," ",0,"integral((a^2*x^2 + 2*a*x + 1)*x^m*((a*x - 1)/(a*x + 1))^(3/4)/(a^2*x^2 - 2*a*x + 1), x)","F",0
140,0,0,0,0.454186," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)} x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x - 1}, x\right)"," ",0,"integral((a*x + 1)*x^m*((a*x - 1)/(a*x + 1))^(1/4)/(a*x - 1), x)","F",0
141,0,0,0,0.634032," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)} x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x - 1}, x\right)"," ",0,"integral((a*x + 1)*x^m*((a*x - 1)/(a*x + 1))^(3/4)/(a*x - 1), x)","F",0
142,0,0,0,0.583474," ","integrate(x^m*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}, x\right)"," ",0,"integral(x^m*((a*x - 1)/(a*x + 1))^(1/4), x)","F",0
143,0,0,0,0.618678," ","integrate(x^m*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}, x\right)"," ",0,"integral(x^m*((a*x - 1)/(a*x + 1))^(3/4), x)","F",0
144,0,0,0,0.549612," ","integrate(x^m*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x - 1\right)} x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1}, x\right)"," ",0,"integral((a*x - 1)*x^m*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1), x)","F",0
145,0,0,0,0.454255," ","integrate(1/((-1+x)/(1+x))^(1/3)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x + 1\right)} x^{m} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}}{x - 1}, x\right)"," ",0,"integral((x + 1)*x^m*((x - 1)/(x + 1))^(2/3)/(x - 1), x)","F",0
146,0,0,0,0.772049," ","integrate(1/((-1+x)/(1+x))^(1/6)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x + 1\right)} x^{m} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{x - 1}, x\right)"," ",0,"integral((x + 1)*x^m*((x - 1)/(x + 1))^(5/6)/(x - 1), x)","F",0
147,0,0,0,0.624312," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)} x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}}{a x - 1}, x\right)"," ",0,"integral((a*x + 1)*x^m*((a*x - 1)/(a*x + 1))^(7/8)/(a*x - 1), x)","F",0
148,0,0,0,0.691793," ","integrate(exp(n*arccoth(a*x))*x^m,x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(x^m*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
149,0,0,0,0.594368," ","integrate(exp(n*arccoth(a*x))*x^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(x^2*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
150,0,0,0,0.541842," ","integrate(exp(n*arccoth(a*x))*x,x, algorithm=""fricas"")","{\rm integral}\left(x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(x*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
151,0,0,0,0.523922," ","integrate(exp(n*arccoth(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
152,0,0,0,0.910935," ","integrate(exp(n*arccoth(a*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{x}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^(1/2*n)/x, x)","F",0
153,0,0,0,0.676515," ","integrate(exp(n*arccoth(a*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{x^{2}}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^(1/2*n)/x^2, x)","F",0
154,0,0,0,0.645323," ","integrate(exp(n*arccoth(a*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{x^{3}}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^(1/2*n)/x^3, x)","F",0
155,0,0,0,0.595803," ","integrate(exp(n*arccoth(a*x))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{x^{4}}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^(1/2*n)/x^4, x)","F",0
156,0,0,0,0.551610," ","integrate(exp(n*arccoth(a*x))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{x^{5}}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^(1/2*n)/x^5, x)","F",0
157,0,0,0,0.662069," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^p,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)} {\left(-a c x + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}}{a x - 1}, x\right)"," ",0,"integral((a*x + 1)*(-a*c*x + c)^p*sqrt((a*x - 1)/(a*x + 1))/(a*x - 1), x)","F",0
158,1,125,0,0.475101," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^4,x, algorithm=""fricas"")","\frac{105 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 105 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(24 \, a^{5} c^{4} x^{5} - 66 \, a^{4} c^{4} x^{4} + 22 \, a^{3} c^{4} x^{3} + 97 \, a^{2} c^{4} x^{2} - 151 \, a c^{4} x - 136 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{120 \, a}"," ",0,"1/120*(105*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 105*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (24*a^5*c^4*x^5 - 66*a^4*c^4*x^4 + 22*a^3*c^4*x^3 + 97*a^2*c^4*x^2 - 151*a*c^4*x - 136*c^4)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
159,1,115,0,0.499210," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^3,x, algorithm=""fricas"")","\frac{15 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(6 \, a^{4} c^{3} x^{4} - 10 \, a^{3} c^{3} x^{3} - 7 \, a^{2} c^{3} x^{2} + 25 \, a c^{3} x + 16 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{24 \, a}"," ",0,"1/24*(15*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (6*a^4*c^3*x^4 - 10*a^3*c^3*x^3 - 7*a^2*c^3*x^2 + 25*a*c^3*x + 16*c^3)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
160,1,103,0,0.513815," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(2 \, a^{3} c^{2} x^{3} - a^{2} c^{2} x^{2} - 5 \, a c^{2} x - 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a}"," ",0,"1/6*(3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (2*a^3*c^2*x^3 - a^2*c^2*x^2 - 5*a*c^2*x - 2*c^2)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
161,1,77,0,0.542015," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c),x, algorithm=""fricas"")","\frac{c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(a^{2} c x^{2} + a c x\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, a}"," ",0,"1/2*(c*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - c*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (a^2*c*x^2 + a*c*x)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
162,1,87,0,0.467991," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c),x, algorithm=""fricas"")","-\frac{{\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - 2 \, {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c x - a c}"," ",0,"-((a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - (a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - 2*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c*x - a*c)","A",0
163,1,57,0,0.461764," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} x^{2} + 2 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"-1/3*(a^2*x^2 + 2*a*x + 1)*sqrt((a*x - 1)/(a*x + 1))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)","A",0
164,1,77,0,0.484367," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{3} x^{3} - 2 \, a^{2} x^{2} - 7 \, a x - 4\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\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,"-1/15*(a^3*x^3 - 2*a^2*x^2 - 7*a*x - 4)*sqrt((a*x - 1)/(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
165,1,96,0,0.677026," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^4,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{4} x^{4} - 6 \, a^{3} x^{3} + 5 \, a^{2} x^{2} + 36 \, a x + 23\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{105 \, {\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,"-1/105*(2*a^4*x^4 - 6*a^3*x^3 + 5*a^2*x^2 + 36*a*x + 23)*sqrt((a*x - 1)/(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
166,1,116,0,0.419389," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^5,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{5} x^{5} - 8 \, a^{4} x^{4} + 11 \, a^{3} x^{3} - 4 \, a^{2} x^{2} - 83 \, a x - 58\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{315 \, {\left(a^{6} c^{5} x^{5} - 5 \, a^{5} c^{5} x^{4} + 10 \, a^{4} c^{5} x^{3} - 10 \, a^{3} c^{5} x^{2} + 5 \, a^{2} c^{5} x - a c^{5}\right)}}"," ",0,"-1/315*(2*a^5*x^5 - 8*a^4*x^4 + 11*a^3*x^3 - 4*a^2*x^2 - 83*a*x - 58)*sqrt((a*x - 1)/(a*x + 1))/(a^6*c^5*x^5 - 5*a^5*c^5*x^4 + 10*a^4*c^5*x^3 - 10*a^3*c^5*x^2 + 5*a^2*c^5*x - a*c^5)","A",0
167,1,28,0,0.529536," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^p,x, algorithm=""fricas"")","\frac{{\left(a p x + p + 2\right)} {\left(-a c x + c\right)}^{p}}{a p^{2} + a p}"," ",0,"(a*p*x + p + 2)*(-a*c*x + c)^p/(a*p^2 + a*p)","A",0
168,1,60,0,0.514076," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^5,x, algorithm=""fricas"")","-\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
169,1,37,0,0.634242," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^4,x, algorithm=""fricas"")","\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
170,1,38,0,0.924992," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^3,x, algorithm=""fricas"")","-\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
171,1,18,0,0.542809," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^2,x, algorithm=""fricas"")","\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
172,1,12,0,0.543304," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c),x, algorithm=""fricas"")","-\frac{1}{2} \, a c x^{2} - c x"," ",0,"-1/2*a*c*x^2 - c*x","A",0
173,1,29,0,0.468061," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c),x, algorithm=""fricas"")","-\frac{{\left(a x - 1\right)} \log\left(a x - 1\right) - 2}{a^{2} c x - a c}"," ",0,"-((a*x - 1)*log(a*x - 1) - 2)/(a^2*c*x - a*c)","A",0
174,1,26,0,0.649785," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^2,x, algorithm=""fricas"")","-\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
175,1,47,0,0.448243," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^3,x, algorithm=""fricas"")","\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
176,1,57,0,0.457562," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^4,x, algorithm=""fricas"")","-\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
177,0,0,0,0.484147," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^p,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{2} + 2 \, a x + 1\right)} {\left(-a c x + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x^{2} - 2 \, a x + 1}, x\right)"," ",0,"integral((a^2*x^2 + 2*a*x + 1)*(-a*c*x + c)^p*sqrt((a*x - 1)/(a*x + 1))/(a^2*x^2 - 2*a*x + 1), x)","F",0
178,1,126,0,0.522878," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^4,x, algorithm=""fricas"")","-\frac{15 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(8 \, a^{5} c^{4} x^{5} - 2 \, a^{4} c^{4} x^{4} - 26 \, a^{3} c^{4} x^{3} + 9 \, a^{2} c^{4} x^{2} + 33 \, a c^{4} x + 8 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{40 \, a}"," ",0,"-1/40*(15*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (8*a^5*c^4*x^5 - 2*a^4*c^4*x^4 - 26*a^3*c^4*x^3 + 9*a^2*c^4*x^2 + 33*a*c^4*x + 8*c^4)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
179,1,109,0,0.549362," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^3,x, algorithm=""fricas"")","-\frac{3 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(2 \, a^{4} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{3} - 5 \, a^{2} c^{3} x^{2} - 5 \, a c^{3} x\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{8 \, a}"," ",0,"-1/8*(3*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (2*a^4*c^3*x^4 + 2*a^3*c^3*x^3 - 5*a^2*c^3*x^2 - 5*a*c^3*x)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
180,1,103,0,0.398470," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^2,x, algorithm=""fricas"")","-\frac{3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(2 \, a^{3} c^{2} x^{3} + 5 \, a^{2} c^{2} x^{2} + a c^{2} x - 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a}"," ",0,"-1/6*(3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (2*a^3*c^2*x^3 + 5*a^2*c^2*x^2 + a*c^2*x - 2*c^2)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
181,1,81,0,0.508965," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c),x, algorithm=""fricas"")","-\frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a^{2} c x^{2} + 5 \, a c x + 4 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, a}"," ",0,"-1/2*(3*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a^2*c*x^2 + 5*a*c*x + 4*c)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
182,1,120,0,0.471838," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c),x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - 4 \, {\left(2 \, a^{2} x^{2} + a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c x^{2} - 2 \, a^{2} c x + a c\right)}}"," ",0,"-1/3*(3*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - 4*(2*a^2*x^2 + a*x - 1)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c*x^2 - 2*a^2*c*x + a*c)","A",0
183,1,77,0,0.518797," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{5 \, {\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,"-1/5*(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)*sqrt((a*x - 1)/(a*x + 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
184,1,95,0,0.685844," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{4} x^{4} - 3 \, a^{3} x^{3} - 15 \, a^{2} x^{2} - 17 \, a x - 6\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\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,"-1/35*(a^4*x^4 - 3*a^3*x^3 - 15*a^2*x^2 - 17*a*x - 6)*sqrt((a*x - 1)/(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
185,1,116,0,0.700808," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^4,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{5} x^{5} - 8 \, a^{4} x^{4} + 11 \, a^{3} x^{3} + 101 \, a^{2} x^{2} + 127 \, a x + 47\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{315 \, {\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,"-1/315*(2*a^5*x^5 - 8*a^4*x^4 + 11*a^3*x^3 + 101*a^2*x^2 + 127*a*x + 47)*sqrt((a*x - 1)/(a*x + 1))/(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
186,1,134,0,0.894429," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^5,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{6} x^{6} - 10 \, a^{5} x^{5} + 19 \, a^{4} x^{4} - 15 \, a^{3} x^{3} - 289 \, a^{2} x^{2} - 395 \, a x - 152\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{1155 \, {\left(a^{7} c^{5} x^{6} - 6 \, a^{6} c^{5} x^{5} + 15 \, a^{5} c^{5} x^{4} - 20 \, a^{4} c^{5} x^{3} + 15 \, a^{3} c^{5} x^{2} - 6 \, a^{2} c^{5} x + a c^{5}\right)}}"," ",0,"-1/1155*(2*a^6*x^6 - 10*a^5*x^5 + 19*a^4*x^4 - 15*a^3*x^3 - 289*a^2*x^2 - 395*a*x - 152)*sqrt((a*x - 1)/(a*x + 1))/(a^7*c^5*x^6 - 6*a^6*c^5*x^5 + 15*a^5*c^5*x^4 - 20*a^4*c^5*x^3 + 15*a^3*c^5*x^2 - 6*a^2*c^5*x + a*c^5)","A",0
187,1,81,0,0.656325," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^p,x, algorithm=""fricas"")","-\frac{{\left({\left(a^{2} p^{2} - a^{2} p\right)} x^{2} + p^{2} + 2 \, {\left(a p^{2} + a p - 2 \, a\right)} x + 3 \, p + 4\right)} {\left(-a c x + c\right)}^{p}}{a p^{3} - a p - {\left(a^{2} p^{3} - a^{2} p\right)} x}"," ",0,"-((a^2*p^2 - a^2*p)*x^2 + p^2 + 2*(a*p^2 + a*p - 2*a)*x + 3*p + 4)*(-a*c*x + c)^p/(a*p^3 - a*p - (a^2*p^3 - a^2*p)*x)","A",0
188,1,59,0,0.424137," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^5,x, algorithm=""fricas"")","-\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
189,1,28,0,0.483986," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^4,x, algorithm=""fricas"")","\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
190,1,37,0,0.471023," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^3,x, algorithm=""fricas"")","-\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
191,1,25,0,0.591566," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^2,x, algorithm=""fricas"")","\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
192,1,28,0,0.572924," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c),x, algorithm=""fricas"")","-\frac{a^{2} c x^{2} + 6 \, a c x + 8 \, c \log\left(a x - 1\right)}{2 \, a}"," ",0,"-1/2*(a^2*c*x^2 + 6*a*c*x + 8*c*log(a*x - 1))/a","A",0
193,1,49,0,0.431802," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c),x, algorithm=""fricas"")","\frac{4 \, a x - {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x - 1\right) - 2}{a^{3} c x^{2} - 2 \, a^{2} c x + a c}"," ",0,"(4*a*x - (a^2*x^2 - 2*a*x + 1)*log(a*x - 1) - 2)/(a^3*c*x^2 - 2*a^2*c*x + a*c)","A",0
194,1,51,0,0.548788," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c)^2,x, algorithm=""fricas"")","-\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
195,1,65,0,0.626499," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c)^3,x, algorithm=""fricas"")","\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
196,1,77,0,0.694578," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c)^4,x, algorithm=""fricas"")","-\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
197,0,0,0,2.264802," ","integrate((-a*c*x+c)^p*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(-a c x + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}, x\right)"," ",0,"integral((-a*c*x + c)^p*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
198,1,114,0,1.838425," ","integrate((-a*c*x+c)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(6 \, a^{4} c^{3} x^{4} - 26 \, a^{3} c^{3} x^{3} + 49 \, a^{2} c^{3} x^{2} - 79 \, a c^{3} x - 160 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{24 \, a}"," ",0,"-1/24*(105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (6*a^4*c^3*x^4 - 26*a^3*c^3*x^3 + 49*a^2*c^3*x^2 - 79*a*c^3*x - 160*c^3)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
199,1,104,0,0.486480," ","integrate((-a*c*x+c)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(2 \, a^{3} c^{2} x^{3} - 7 \, a^{2} c^{2} x^{2} + 13 \, a c^{2} x + 22 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a}"," ",0,"-1/6*(15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (2*a^3*c^2*x^3 - 7*a^2*c^2*x^2 + 13*a*c^2*x + 22*c^2)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
200,1,81,0,0.604213," ","integrate((-a*c*x+c)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a^{2} c x^{2} - 3 \, a c x - 4 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, a}"," ",0,"-1/2*(3*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a^2*c*x^2 - 3*a*c*x - 4*c)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
201,1,47,0,0.491352," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c),x, algorithm=""fricas"")","-\frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a c}"," ",0,"-(log(sqrt((a*x - 1)/(a*x + 1)) + 1) - log(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a*c)","B",0
202,1,39,0,0.565695," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^2,x, algorithm=""fricas"")","-\frac{{\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2} x - a c^{2}}"," ",0,"-(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^2*x - a*c^2)","A",0
203,1,57,0,0.595045," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} x^{2} - a x - 2\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c^{3} x^{2} - 2 \, a^{2} c^{3} x + a c^{3}\right)}}"," ",0,"-1/3*(a^2*x^2 - a*x - 2)*sqrt((a*x - 1)/(a*x + 1))/(a^3*c^3*x^2 - 2*a^2*c^3*x + a*c^3)","A",0
204,1,77,0,0.580790," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^4,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{3} x^{3} - 4 \, a^{2} x^{2} + a x + 7\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\left(a^{4} c^{4} x^{3} - 3 \, a^{3} c^{4} x^{2} + 3 \, a^{2} c^{4} x - a c^{4}\right)}}"," ",0,"-1/15*(2*a^3*x^3 - 4*a^2*x^2 + a*x + 7)*sqrt((a*x - 1)/(a*x + 1))/(a^4*c^4*x^3 - 3*a^3*c^4*x^2 + 3*a^2*c^4*x - a*c^4)","A",0
205,1,95,0,0.644971," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^5,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{4} x^{4} - 6 \, a^{3} x^{3} + 5 \, a^{2} x^{2} + a x - 12\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\left(a^{5} c^{5} x^{4} - 4 \, a^{4} c^{5} x^{3} + 6 \, a^{3} c^{5} x^{2} - 4 \, a^{2} c^{5} x + a c^{5}\right)}}"," ",0,"-1/35*(2*a^4*x^4 - 6*a^3*x^3 + 5*a^2*x^2 + a*x - 12)*sqrt((a*x - 1)/(a*x + 1))/(a^5*c^5*x^4 - 4*a^4*c^5*x^3 + 6*a^3*c^5*x^2 - 4*a^2*c^5*x + a*c^5)","A",0
206,0,0,0,0.553126," ","integrate((-a*c*x+c)^p*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x - 1\right)} {\left(-a c x + c\right)}^{p}}{a x + 1}, x\right)"," ",0,"integral((a*x - 1)*(-a*c*x + c)^p/(a*x + 1), x)","F",0
207,1,68,0,0.812578," ","integrate((-a*c*x+c)^4*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{6 \, a^{5} c^{4} x^{5} - 45 \, a^{4} c^{4} x^{4} + 160 \, a^{3} c^{4} x^{3} - 390 \, a^{2} c^{4} x^{2} + 930 \, a c^{4} x - 960 \, c^{4} \log\left(a x + 1\right)}{30 \, a}"," ",0,"1/30*(6*a^5*c^4*x^5 - 45*a^4*c^4*x^4 + 160*a^3*c^4*x^3 - 390*a^2*c^4*x^2 + 930*a*c^4*x - 960*c^4*log(a*x + 1))/a","A",0
208,1,57,0,0.547080," ","integrate((-a*c*x+c)^3*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","-\frac{3 \, a^{4} c^{3} x^{4} - 20 \, a^{3} c^{3} x^{3} + 66 \, a^{2} c^{3} x^{2} - 180 \, a c^{3} x + 192 \, c^{3} \log\left(a x + 1\right)}{12 \, a}"," ",0,"-1/12*(3*a^4*c^3*x^4 - 20*a^3*c^3*x^3 + 66*a^2*c^3*x^2 - 180*a*c^3*x + 192*c^3*log(a*x + 1))/a","A",0
209,1,45,0,0.637133," ","integrate((-a*c*x+c)^2*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{a^{3} c^{2} x^{3} - 6 \, a^{2} c^{2} x^{2} + 21 \, a c^{2} x - 24 \, c^{2} \log\left(a x + 1\right)}{3 \, a}"," ",0,"1/3*(a^3*c^2*x^3 - 6*a^2*c^2*x^2 + 21*a*c^2*x - 24*c^2*log(a*x + 1))/a","A",0
210,1,28,0,0.465197," ","integrate((-a*c*x+c)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","-\frac{a^{2} c x^{2} - 6 \, a c x + 8 \, c \log\left(a x + 1\right)}{2 \, a}"," ",0,"-1/2*(a^2*c*x^2 - 6*a*c*x + 8*c*log(a*x + 1))/a","A",0
211,1,14,0,0.461447," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c),x, algorithm=""fricas"")","-\frac{\log\left(a x + 1\right)}{a c}"," ",0,"-log(a*x + 1)/(a*c)","A",0
212,1,23,0,0.702897," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^2,x, algorithm=""fricas"")","-\frac{\log\left(a x + 1\right) - \log\left(a x - 1\right)}{2 \, a c^{2}}"," ",0,"-1/2*(log(a*x + 1) - log(a*x - 1))/(a*c^2)","A",0
213,1,46,0,0.730854," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^3,x, algorithm=""fricas"")","-\frac{{\left(a x - 1\right)} \log\left(a x + 1\right) - {\left(a x - 1\right)} \log\left(a x - 1\right) - 2}{4 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"-1/4*((a*x - 1)*log(a*x + 1) - (a*x - 1)*log(a*x - 1) - 2)/(a^2*c^3*x - a*c^3)","A",0
214,1,76,0,0.509838," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^4,x, algorithm=""fricas"")","\frac{2 \, a x - {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x + 1\right) + {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x - 1\right) - 4}{8 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}"," ",0,"1/8*(2*a*x - (a^2*x^2 - 2*a*x + 1)*log(a*x + 1) + (a^2*x^2 - 2*a*x + 1)*log(a*x - 1) - 4)/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4)","A",0
215,1,113,0,0.457721," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^5,x, algorithm=""fricas"")","\frac{6 \, a^{2} x^{2} - 18 \, a x - 3 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(a x - 1\right) + 20}{48 \, {\left(a^{4} c^{5} x^{3} - 3 \, a^{3} c^{5} x^{2} + 3 \, a^{2} c^{5} x - a c^{5}\right)}}"," ",0,"1/48*(6*a^2*x^2 - 18*a*x - 3*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(a*x + 1) + 3*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(a*x - 1) + 20)/(a^4*c^5*x^3 - 3*a^3*c^5*x^2 + 3*a^2*c^5*x - a*c^5)","A",0
216,0,0,0,0.533133," ","integrate((-a*c*x+c)^p*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x - 1\right)} {\left(-a c x + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1}, x\right)"," ",0,"integral((a*x - 1)*(-a*c*x + c)^p*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1), x)","F",0
217,1,114,0,0.492981," ","integrate((-a*c*x+c)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(2 \, a^{4} c^{3} x^{4} - 14 \, a^{3} c^{3} x^{3} + 51 \, a^{2} c^{3} x^{2} - 173 \, a c^{3} x - 496 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{8 \, a}"," ",0,"-1/8*(315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (2*a^4*c^3*x^4 - 14*a^3*c^3*x^3 + 51*a^2*c^3*x^2 - 173*a*c^3*x - 496*c^3)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
218,1,104,0,0.570402," ","integrate((-a*c*x+c)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(2 \, a^{3} c^{2} x^{3} - 13 \, a^{2} c^{2} x^{2} + 55 \, a c^{2} x + 166 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a}"," ",0,"-1/6*(105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (2*a^3*c^2*x^3 - 13*a^2*c^2*x^2 + 55*a*c^2*x + 166*c^2)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
219,1,81,0,0.530327," ","integrate((-a*c*x+c)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a^{2} c x^{2} - 7 \, a c x - 24 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, a}"," ",0,"-1/2*(15*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a^2*c*x^2 - 7*a*c*x - 24*c)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
220,1,63,0,0.670080," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{a x - 1}{a x + 1}} - \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a c}"," ",0,"(2*sqrt((a*x - 1)/(a*x + 1)) - log(sqrt((a*x - 1)/(a*x + 1)) + 1) + log(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a*c)","A",0
221,1,22,0,0.610082," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^2,x, algorithm=""fricas"")","\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
222,1,31,0,0.450322," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^3,x, algorithm=""fricas"")","\frac{x \sqrt{\frac{a x - 1}{a x + 1}}}{a c^{3} x - c^{3}}"," ",0,"x*sqrt((a*x - 1)/(a*x + 1))/(a*c^3*x - c^3)","A",0
223,1,58,0,0.408485," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^4,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} x^{2} - 2 \, a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}"," ",0,"1/3*(2*a^2*x^2 - 2*a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4)","A",0
224,1,77,0,0.497627," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^5,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} - 4 \, a^{2} x^{2} + a x + 2\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{5 \, {\left(a^{4} c^{5} x^{3} - 3 \, a^{3} c^{5} x^{2} + 3 \, a^{2} c^{5} x - a c^{5}\right)}}"," ",0,"1/5*(2*a^3*x^3 - 4*a^2*x^2 + a*x + 2)*sqrt((a*x - 1)/(a*x + 1))/(a^4*c^5*x^3 - 3*a^3*c^5*x^2 + 3*a^2*c^5*x - a*c^5)","A",0
225,1,96,0,0.616154," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^6,x, algorithm=""fricas"")","\frac{{\left(8 \, a^{4} x^{4} - 24 \, a^{3} x^{3} + 20 \, a^{2} x^{2} + 4 \, a x - 13\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\left(a^{5} c^{6} x^{4} - 4 \, a^{4} c^{6} x^{3} + 6 \, a^{3} c^{6} x^{2} - 4 \, a^{2} c^{6} x + a c^{6}\right)}}"," ",0,"1/35*(8*a^4*x^4 - 24*a^3*x^3 + 20*a^2*x^2 + 4*a*x - 13)*sqrt((a*x - 1)/(a*x + 1))/(a^5*c^6*x^4 - 4*a^4*c^6*x^3 + 6*a^3*c^6*x^2 - 4*a^2*c^6*x + a*c^6)","A",0
226,1,105,0,0.581711," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, a^{6} c^{4} x^{6} - 1190 \, a^{5} c^{4} x^{5} + 1205 \, a^{4} c^{4} x^{4} + 844 \, a^{3} c^{4} x^{3} - 2843 \, a^{2} c^{4} x^{2} + 4442 \, a c^{4} x + 5419 \, c^{4}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{3465 \, {\left(a^{2} x - a\right)}}"," ",0,"2/3465*(315*a^6*c^4*x^6 - 1190*a^5*c^4*x^5 + 1205*a^4*c^4*x^4 + 844*a^3*c^4*x^3 - 2843*a^2*c^4*x^2 + 4442*a*c^4*x + 5419*c^4)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
227,1,94,0,0.390303," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, a^{5} c^{3} x^{5} - 95 \, a^{4} c^{3} x^{4} + 26 \, a^{3} c^{3} x^{3} + 158 \, a^{2} c^{3} x^{2} - 317 \, a c^{3} x - 319 \, c^{3}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{315 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/315*(35*a^5*c^3*x^5 - 95*a^4*c^3*x^4 + 26*a^3*c^3*x^3 + 158*a^2*c^3*x^2 - 317*a*c^3*x - 319*c^3)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
228,1,83,0,0.459249," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, a^{4} c^{2} x^{4} - 24 \, a^{3} c^{2} x^{3} - 22 \, a^{2} c^{2} x^{2} + 88 \, a c^{2} x + 71 \, c^{2}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{105 \, {\left(a^{2} x - a\right)}}"," ",0,"2/105*(15*a^4*c^2*x^4 - 24*a^3*c^2*x^3 - 22*a^2*c^2*x^2 + 88*a*c^2*x + 71*c^2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
229,1,64,0,0.526011," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a^{3} c x^{3} - a^{2} c x^{2} - 11 \, a c x - 7 \, c\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/15*(3*a^3*c*x^3 - a^2*c*x^2 - 11*a*c*x - 7*c)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
230,1,50,0,0.625011," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{2} x - a\right)}}"," ",0,"2/3*(a^2*x^2 + 2*a*x + 1)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
231,1,239,0,0.515444," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(a c x - c\right)} \sqrt{-\frac{1}{c}} \log\left(-\frac{a^{2} x^{2} - 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{-\frac{1}{c}} + 2 \, a x - 3}{a^{2} x^{2} - 2 \, a x + 1}\right) - 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c x - a c}, -\frac{2 \, {\left(\sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} - \frac{\sqrt{2} {\left(a c x - c\right)} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x - 1\right)} \sqrt{c}}\right)}{\sqrt{c}}\right)}}{a^{2} c x - a c}\right]"," ",0,"[(sqrt(2)*(a*c*x - c)*sqrt(-1/c)*log(-(a^2*x^2 - 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt(-1/c) + 2*a*x - 3)/(a^2*x^2 - 2*a*x + 1)) - 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c*x - a*c), -2*(sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)) - sqrt(2)*(a*c*x - c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*sqrt(c)))/sqrt(c))/(a^2*c*x - a*c)]","A",0
232,1,281,0,0.465085," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + 4 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{4 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}, -\frac{\sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}\right]"," ",0,"[-1/4*(sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + 4*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2), -1/2*(sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)]","A",0
233,1,337,0,0.547609," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) - 4 \, {\left(a^{2} x^{2} + 4 \, a x + 3\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{32 \, {\left(a^{4} c^{3} x^{3} - 3 \, a^{3} c^{3} x^{2} + 3 \, a^{2} c^{3} x - a c^{3}\right)}}, -\frac{\sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 2 \, {\left(a^{2} x^{2} + 4 \, a x + 3\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{16 \, {\left(a^{4} c^{3} x^{3} - 3 \, a^{3} c^{3} x^{2} + 3 \, a^{2} c^{3} x - a c^{3}\right)}}\right]"," ",0,"[-1/32*(sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) - 4*(a^2*x^2 + 4*a*x + 3)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(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), -1/16*(sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 2*(a^2*x^2 + 4*a*x + 3)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(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
234,1,393,0,1.149413," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(7/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) - 4 \, {\left(3 \, a^{3} x^{3} - 7 \, a^{2} x^{2} - 35 \, a x - 25\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{384 \, {\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{3 \, \sqrt{2} {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 2 \, {\left(3 \, a^{3} x^{3} - 7 \, a^{2} x^{2} - 35 \, a x - 25\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{192 \, {\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)}}\right]"," ",0,"[-1/384*(3*sqrt(2)*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) - 4*(3*a^3*x^3 - 7*a^2*x^2 - 35*a*x - 25)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(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), -1/192*(3*sqrt(2)*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 2*(3*a^3*x^3 - 7*a^2*x^2 - 35*a*x - 25)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(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
235,1,60,0,0.455550," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(7 \, a^{4} c^{3} x^{4} - 10 \, a^{3} c^{3} x^{3} - 12 \, a^{2} c^{3} x^{2} + 26 \, a c^{3} x - 11 \, c^{3}\right)} \sqrt{-a c x + c}}{63 \, a}"," ",0,"-2/63*(7*a^4*c^3*x^4 - 10*a^3*c^3*x^3 - 12*a^2*c^3*x^2 + 26*a*c^3*x - 11*c^3)*sqrt(-a*c*x + c)/a","A",0
236,1,49,0,0.693700," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a^{3} c^{2} x^{3} - a^{2} c^{2} x^{2} - 13 \, a c^{2} x + 9 \, c^{2}\right)} \sqrt{-a c x + c}}{35 \, a}"," ",0,"2/35*(5*a^3*c^2*x^3 - a^2*c^2*x^2 - 13*a*c^2*x + 9*c^2)*sqrt(-a*c*x + c)/a","A",0
237,1,32,0,0.502390," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a^{2} c x^{2} + 4 \, a c x - 7 \, c\right)} \sqrt{-a c x + c}}{15 \, a}"," ",0,"-2/15*(3*a^2*c*x^2 + 4*a*c*x - 7*c)*sqrt(-a*c*x + c)/a","A",0
238,1,19,0,0.580282," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-a c x + c} {\left(a x + 5\right)}}{3 \, a}"," ",0,"2/3*sqrt(-a*c*x + c)*(a*x + 5)/a","A",0
239,1,29,0,0.622284," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-a c x + c} {\left(a x - 3\right)}}{a^{2} c x - a c}"," ",0,"-2*sqrt(-a*c*x + c)*(a*x - 3)/(a^2*c*x - a*c)","A",0
240,1,44,0,0.519665," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-a c x + c} {\left(3 \, a x - 1\right)}}{3 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"-2/3*sqrt(-a*c*x + c)*(3*a*x - 1)/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)","A",0
241,1,56,0,0.512714," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-a c x + c} {\left(5 \, a x + 1\right)}}{15 \, {\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,"2/15*sqrt(-a*c*x + c)*(5*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
242,1,66,0,0.677391," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-a c x + c} {\left(7 \, a x + 3\right)}}{35 \, {\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,"-2/35*sqrt(-a*c*x + c)*(7*a*x + 3)/(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)","B",0
243,1,105,0,0.502890," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, a^{6} c^{4} x^{6} - 140 \, a^{5} c^{4} x^{5} - 295 \, a^{4} c^{4} x^{4} + 472 \, a^{3} c^{4} x^{3} + 211 \, a^{2} c^{4} x^{2} - 844 \, a c^{4} x - 533 \, c^{4}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{1155 \, {\left(a^{2} x - a\right)}}"," ",0,"2/1155*(105*a^6*c^4*x^6 - 140*a^5*c^4*x^5 - 295*a^4*c^4*x^4 + 472*a^3*c^4*x^3 + 211*a^2*c^4*x^2 - 844*a*c^4*x - 533*c^4)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
244,1,94,0,0.595419," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, a^{5} c^{3} x^{5} - 5 \, a^{4} c^{3} x^{4} - 118 \, a^{3} c^{3} x^{3} + 26 \, a^{2} c^{3} x^{2} + 211 \, a c^{3} x + 107 \, c^{3}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{315 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/315*(35*a^5*c^3*x^5 - 5*a^4*c^3*x^4 - 118*a^3*c^3*x^3 + 26*a^2*c^3*x^2 + 211*a*c^3*x + 107*c^3)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
245,1,83,0,0.522713," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a^{4} c^{2} x^{4} + 6 \, a^{3} c^{2} x^{3} - 12 \, a^{2} c^{2} x^{2} - 22 \, a c^{2} x - 9 \, c^{2}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\left(a^{2} x - a\right)}}"," ",0,"2/35*(5*a^4*c^2*x^4 + 6*a^3*c^2*x^3 - 12*a^2*c^2*x^2 - 22*a*c^2*x - 9*c^2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
246,1,61,0,0.584233," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} c x^{3} + 3 \, a^{2} c x^{2} + 3 \, a c x + c\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{5 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/5*(a^3*c*x^3 + 3*a^2*c*x^2 + 3*a*c*x + c)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
247,1,250,0,0.854532," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + {\left(a^{2} x^{2} + 8 \, a x + 7\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{3 \, {\left(a^{2} x - a\right)}}, -\frac{2 \, {\left(6 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(a^{2} x^{2} + 8 \, a x + 7\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{3 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[2/3*(3*sqrt(2)*(a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + (a^2*x^2 + 8*a*x + 7)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x - a), -2/3*(6*sqrt(2)*(a*x - 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (a^2*x^2 + 8*a*x + 7)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x - a)]","A",0
248,1,288,0,0.504605," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left(a^{2} c x^{2} - 2 \, a c x + c\right)} \sqrt{-\frac{1}{c}} \log\left(-\frac{a^{2} x^{2} - 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{-\frac{1}{c}} + 2 \, a x - 3}{a^{2} x^{2} - 2 \, a x + 1}\right) - 4 \, {\left(a^{2} x^{2} - a x - 2\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, {\left(a^{3} c x^{2} - 2 \, a^{2} c x + a c\right)}}, -\frac{2 \, {\left(a^{2} x^{2} - a x - 2\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}} - \frac{3 \, \sqrt{2} {\left(a^{2} c x^{2} - 2 \, a c x + c\right)} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x - 1\right)} \sqrt{c}}\right)}{\sqrt{c}}}{a^{3} c x^{2} - 2 \, a^{2} c x + a c}\right]"," ",0,"[1/2*(3*sqrt(2)*(a^2*c*x^2 - 2*a*c*x + c)*sqrt(-1/c)*log(-(a^2*x^2 - 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt(-1/c) + 2*a*x - 3)/(a^2*x^2 - 2*a*x + 1)) - 4*(a^2*x^2 - a*x - 2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c*x^2 - 2*a^2*c*x + a*c), -(2*(a^2*x^2 - a*x - 2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)) - 3*sqrt(2)*(a^2*c*x^2 - 2*a*c*x + c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*sqrt(c)))/sqrt(c))/(a^3*c*x^2 - 2*a^2*c*x + a*c)]","A",0
249,1,341,0,0.666341," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + 4 \, {\left(5 \, a^{2} x^{2} + 4 \, a x - 1\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{16 \, {\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{3 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) + 2 \, {\left(5 \, a^{2} x^{2} + 4 \, a x - 1\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{8 \, {\left(a^{4} c^{2} x^{3} - 3 \, a^{3} c^{2} x^{2} + 3 \, a^{2} c^{2} x - a c^{2}\right)}}\right]"," ",0,"[-1/16*(3*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + 4*(5*a^2*x^2 + 4*a*x - 1)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2), -1/8*(3*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) + 2*(5*a^2*x^2 + 4*a*x - 1)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2)]","A",0
250,1,393,0,0.612458," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) - 4 \, {\left(3 \, a^{3} x^{3} + 25 \, a^{2} x^{2} + 29 \, a x + 7\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{192 \, {\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{3 \, \sqrt{2} {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 2 \, {\left(3 \, a^{3} x^{3} + 25 \, a^{2} x^{2} + 29 \, a x + 7\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{96 \, {\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)}}\right]"," ",0,"[-1/192*(3*sqrt(2)*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) - 4*(3*a^3*x^3 + 25*a^2*x^2 + 29*a*x + 7)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(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), -1/96*(3*sqrt(2)*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 2*(3*a^3*x^3 + 25*a^2*x^2 + 29*a*x + 7)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(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
251,1,449,0,0.501840," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(7/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left(a^{5} x^{5} - 5 \, a^{4} x^{4} + 10 \, a^{3} x^{3} - 10 \, a^{2} x^{2} + 5 \, a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) - 4 \, {\left(3 \, a^{4} x^{4} - 10 \, a^{3} x^{3} - 92 \, a^{2} x^{2} - 118 \, a x - 39\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{1024 \, {\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{3 \, \sqrt{2} {\left(a^{5} x^{5} - 5 \, a^{4} x^{4} + 10 \, a^{3} x^{3} - 10 \, a^{2} x^{2} + 5 \, a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 2 \, {\left(3 \, a^{4} x^{4} - 10 \, a^{3} x^{3} - 92 \, a^{2} x^{2} - 118 \, a x - 39\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{512 \, {\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)}}\right]"," ",0,"[-1/1024*(3*sqrt(2)*(a^5*x^5 - 5*a^4*x^4 + 10*a^3*x^3 - 10*a^2*x^2 + 5*a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) - 4*(3*a^4*x^4 - 10*a^3*x^3 - 92*a^2*x^2 - 118*a*x - 39)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(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), -1/512*(3*sqrt(2)*(a^5*x^5 - 5*a^4*x^4 + 10*a^3*x^3 - 10*a^2*x^2 + 5*a*x - 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 2*(3*a^4*x^4 - 10*a^3*x^3 - 92*a^2*x^2 - 118*a*x - 39)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(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
252,1,105,0,0.526893," ","integrate((-a*c*x+c)^(9/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, a^{6} c^{4} x^{6} - 392 \, a^{5} c^{4} x^{5} + 1055 \, a^{4} c^{4} x^{4} - 1688 \, a^{3} c^{4} x^{3} + 2221 \, a^{2} c^{4} x^{2} - 6112 \, a c^{4} x - 11531 \, c^{4}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{693 \, {\left(a^{2} x - a\right)}}"," ",0,"2/693*(63*a^6*c^4*x^6 - 392*a^5*c^4*x^5 + 1055*a^4*c^4*x^4 - 1688*a^3*c^4*x^3 + 2221*a^2*c^4*x^2 - 6112*a*c^4*x - 11531*c^4)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
253,1,94,0,0.589664," ","integrate((-a*c*x+c)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, a^{5} c^{3} x^{5} - 185 \, a^{4} c^{3} x^{4} + 422 \, a^{3} c^{3} x^{3} - 634 \, a^{2} c^{3} x^{2} + 1591 \, a c^{3} x + 2867 \, c^{3}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{315 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/315*(35*a^5*c^3*x^5 - 185*a^4*c^3*x^4 + 422*a^3*c^3*x^3 - 634*a^2*c^3*x^2 + 1591*a*c^3*x + 2867*c^3)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
254,1,83,0,0.562663," ","integrate((-a*c*x+c)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a^{4} c^{2} x^{4} - 22 \, a^{3} c^{2} x^{3} + 44 \, a^{2} c^{2} x^{2} - 106 \, a c^{2} x - 177 \, c^{2}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\left(a^{2} x - a\right)}}"," ",0,"2/35*(5*a^4*c^2*x^4 - 22*a^3*c^2*x^3 + 44*a^2*c^2*x^2 - 106*a*c^2*x - 177*c^2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
255,1,64,0,0.597295," ","integrate((-a*c*x+c)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a^{3} c x^{3} - 11 \, a^{2} c x^{2} + 29 \, a c x + 43 \, c\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/15*(3*a^3*c*x^3 - 11*a^2*c*x^2 + 29*a*c*x + 43*c)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
256,1,50,0,0.575543," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} x^{2} - 4 \, a x - 5\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{2} x - a\right)}}"," ",0,"2/3*(a^2*x^2 - 4*a*x - 5)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
257,1,44,0,0.720481," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c x - a c}"," ",0,"-2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))/(a^2*c*x - a*c)","A",0
258,1,141,0,0.592112," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-\frac{1}{c}} \log\left(-\frac{a^{2} x^{2} + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{-\frac{1}{c}} + 2 \, a x - 3}{a^{2} x^{2} - 2 \, a x + 1}\right)}{2 \, a c}, -\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x - 1\right)} \sqrt{c}}\right)}{a c^{\frac{3}{2}}}\right]"," ",0,"[1/2*sqrt(2)*sqrt(-1/c)*log(-(a^2*x^2 + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt(-1/c) + 2*a*x - 3)/(a^2*x^2 - 2*a*x + 1))/(a*c), -sqrt(2)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)*sqrt(c)))/(a*c^(3/2))]","A",0
259,1,281,0,0.484642," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) - 4 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{8 \, {\left(a^{3} c^{3} x^{2} - 2 \, a^{2} c^{3} x + a c^{3}\right)}}, -\frac{\sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{4 \, {\left(a^{3} c^{3} x^{2} - 2 \, a^{2} c^{3} x + a c^{3}\right)}}\right]"," ",0,"[-1/8*(sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) - 4*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^3*x^2 - 2*a^2*c^3*x + a*c^3), -1/4*(sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^3*x^2 - 2*a^2*c^3*x + a*c^3)]","A",0
260,1,341,0,0.532047," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(7/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) - 4 \, {\left(3 \, a^{2} x^{2} - 4 \, a x - 7\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{64 \, {\left(a^{4} c^{4} x^{3} - 3 \, a^{3} c^{4} x^{2} + 3 \, a^{2} c^{4} x - a c^{4}\right)}}, -\frac{3 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 2 \, {\left(3 \, a^{2} x^{2} - 4 \, a x - 7\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{32 \, {\left(a^{4} c^{4} x^{3} - 3 \, a^{3} c^{4} x^{2} + 3 \, a^{2} c^{4} x - a c^{4}\right)}}\right]"," ",0,"[-1/64*(3*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) - 4*(3*a^2*x^2 - 4*a*x - 7)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*c^4*x^3 - 3*a^3*c^4*x^2 + 3*a^2*c^4*x - a*c^4), -1/32*(3*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 2*(3*a^2*x^2 - 4*a*x - 7)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*c^4*x^3 - 3*a^3*c^4*x^2 + 3*a^2*c^4*x - a*c^4)]","A",0
261,1,204,0,0.508906," ","integrate((-a*c*x+c)^(7/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(2520 \, \sqrt{2} c^{\frac{7}{2}} \log\left(\frac{a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) - {\left(35 \, a^{4} c^{3} x^{4} - 230 \, a^{3} c^{3} x^{3} + 732 \, a^{2} c^{3} x^{2} - 1754 \, a c^{3} x + 6257 \, c^{3}\right)} \sqrt{-a c x + c}\right)}}{315 \, a}, -\frac{2 \, {\left(5040 \, \sqrt{2} \sqrt{-c} c^{3} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) + {\left(35 \, a^{4} c^{3} x^{4} - 230 \, a^{3} c^{3} x^{3} + 732 \, a^{2} c^{3} x^{2} - 1754 \, a c^{3} x + 6257 \, c^{3}\right)} \sqrt{-a c x + c}\right)}}{315 \, a}\right]"," ",0,"[2/315*(2520*sqrt(2)*c^(7/2)*log((a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) - (35*a^4*c^3*x^4 - 230*a^3*c^3*x^3 + 732*a^2*c^3*x^2 - 1754*a*c^3*x + 6257*c^3)*sqrt(-a*c*x + c))/a, -2/315*(5040*sqrt(2)*sqrt(-c)*c^3*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) + (35*a^4*c^3*x^4 - 230*a^3*c^3*x^3 + 732*a^2*c^3*x^2 - 1754*a*c^3*x + 6257*c^3)*sqrt(-a*c*x + c))/a]","A",0
262,1,182,0,0.521012," ","integrate((-a*c*x+c)^(5/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(420 \, \sqrt{2} c^{\frac{5}{2}} \log\left(\frac{a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + {\left(15 \, a^{3} c^{2} x^{3} - 87 \, a^{2} c^{2} x^{2} + 269 \, a c^{2} x - 1037 \, c^{2}\right)} \sqrt{-a c x + c}\right)}}{105 \, a}, -\frac{2 \, {\left(840 \, \sqrt{2} \sqrt{-c} c^{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - {\left(15 \, a^{3} c^{2} x^{3} - 87 \, a^{2} c^{2} x^{2} + 269 \, a c^{2} x - 1037 \, c^{2}\right)} \sqrt{-a c x + c}\right)}}{105 \, a}\right]"," ",0,"[2/105*(420*sqrt(2)*c^(5/2)*log((a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + (15*a^3*c^2*x^3 - 87*a^2*c^2*x^2 + 269*a*c^2*x - 1037*c^2)*sqrt(-a*c*x + c))/a, -2/105*(840*sqrt(2)*sqrt(-c)*c^2*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - (15*a^3*c^2*x^3 - 87*a^2*c^2*x^2 + 269*a*c^2*x - 1037*c^2)*sqrt(-a*c*x + c))/a]","A",0
263,1,146,0,0.595726," ","integrate((-a*c*x+c)^(3/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(30 \, \sqrt{2} c^{\frac{3}{2}} \log\left(\frac{a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) - {\left(3 \, a^{2} c x^{2} - 16 \, a c x + 73 \, c\right)} \sqrt{-a c x + c}\right)}}{15 \, a}, -\frac{2 \, {\left(60 \, \sqrt{2} \sqrt{-c} c \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) + {\left(3 \, a^{2} c x^{2} - 16 \, a c x + 73 \, c\right)} \sqrt{-a c x + c}\right)}}{15 \, a}\right]"," ",0,"[2/15*(30*sqrt(2)*c^(3/2)*log((a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) - (3*a^2*c*x^2 - 16*a*c*x + 73*c)*sqrt(-a*c*x + c))/a, -2/15*(60*sqrt(2)*sqrt(-c)*c*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) + (3*a^2*c*x^2 - 16*a*c*x + 73*c)*sqrt(-a*c*x + c))/a]","A",0
264,1,119,0,0.854223," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, \sqrt{2} \sqrt{c} \log\left(\frac{a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + \sqrt{-a c x + c} {\left(a x - 7\right)}\right)}}{3 \, a}, -\frac{2 \, {\left(6 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - \sqrt{-a c x + c} {\left(a x - 7\right)}\right)}}{3 \, a}\right]"," ",0,"[2/3*(3*sqrt(2)*sqrt(c)*log((a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + sqrt(-a*c*x + c)*(a*x - 7))/a, -2/3*(6*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - sqrt(-a*c*x + c)*(a*x - 7))/a]","A",0
265,1,118,0,0.563816," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{c} \log\left(\frac{a x - \frac{2 \, \sqrt{2} \sqrt{-a c x + c}}{\sqrt{c}} - 3}{a x + 1}\right) - 2 \, \sqrt{-a c x + c}}{a c}, \frac{2 \, {\left(\sqrt{2} c \sqrt{-\frac{1}{c}} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-\frac{1}{c}}}{a x - 1}\right) - \sqrt{-a c x + c}\right)}}{a c}\right]"," ",0,"[(sqrt(2)*sqrt(c)*log((a*x - 2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(c) - 3)/(a*x + 1)) - 2*sqrt(-a*c*x + c))/(a*c), 2*(sqrt(2)*c*sqrt(-1/c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(-1/c)/(a*x - 1)) - sqrt(-a*c*x + c))/(a*c)]","A",0
266,1,88,0,0.880109," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(\frac{a x - \frac{2 \, \sqrt{2} \sqrt{-a c x + c}}{\sqrt{c}} - 3}{a x + 1}\right)}{2 \, a c^{\frac{3}{2}}}, \frac{\sqrt{2} \sqrt{-\frac{1}{c}} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-\frac{1}{c}}}{a x - 1}\right)}{a c}\right]"," ",0,"[1/2*sqrt(2)*log((a*x - 2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(c) - 3)/(a*x + 1))/(a*c^(3/2)), sqrt(2)*sqrt(-1/c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(-1/c)/(a*x - 1))/(a*c)]","A",0
267,1,146,0,0.706870," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(a x - 1\right)} \sqrt{c} \log\left(\frac{a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + 4 \, \sqrt{-a c x + c}}{4 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}, -\frac{\sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - 2 \, \sqrt{-a c x + c}}{2 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}\right]"," ",0,"[1/4*(sqrt(2)*(a*x - 1)*sqrt(c)*log((a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + 4*sqrt(-a*c*x + c))/(a^2*c^3*x - a*c^3), -1/2*(sqrt(2)*(a*x - 1)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - 2*sqrt(-a*c*x + c))/(a^2*c^3*x - a*c^3)]","A",0
268,1,196,0,0.644973," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(\frac{a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + 4 \, \sqrt{-a c x + c} {\left(3 \, a x - 5\right)}}{24 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}, -\frac{3 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - 2 \, \sqrt{-a c x + c} {\left(3 \, a x - 5\right)}}{12 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}\right]"," ",0,"[1/24*(3*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log((a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + 4*sqrt(-a*c*x + c)*(3*a*x - 5))/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4), -1/12*(3*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - 2*sqrt(-a*c*x + c)*(3*a*x - 5))/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4)]","A",0
269,1,252,0,0.481637," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^(9/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \log\left(\frac{a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + 4 \, {\left(15 \, a^{2} x^{2} - 40 \, a x + 37\right)} \sqrt{-a c x + c}}{240 \, {\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{15 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - 2 \, {\left(15 \, a^{2} x^{2} - 40 \, a x + 37\right)} \sqrt{-a c x + c}}{120 \, {\left(a^{4} c^{5} x^{3} - 3 \, a^{3} c^{5} x^{2} + 3 \, a^{2} c^{5} x - a c^{5}\right)}}\right]"," ",0,"[1/240*(15*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*log((a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + 4*(15*a^2*x^2 - 40*a*x + 37)*sqrt(-a*c*x + c))/(a^4*c^5*x^3 - 3*a^3*c^5*x^2 + 3*a^2*c^5*x - a*c^5), -1/120*(15*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - 2*(15*a^2*x^2 - 40*a*x + 37)*sqrt(-a*c*x + c))/(a^4*c^5*x^3 - 3*a^3*c^5*x^2 + 3*a^2*c^5*x - a*c^5)]","A",0
270,1,105,0,0.484697," ","integrate((-a*c*x+c)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(21 \, a^{6} c^{4} x^{6} - 182 \, a^{5} c^{4} x^{5} + 755 \, a^{4} c^{4} x^{4} - 2132 \, a^{3} c^{4} x^{3} + 5419 \, a^{2} c^{4} x^{2} - 23062 \, a c^{4} x - 46355 \, c^{4}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{231 \, {\left(a^{2} x - a\right)}}"," ",0,"2/231*(21*a^6*c^4*x^6 - 182*a^5*c^4*x^5 + 755*a^4*c^4*x^4 - 2132*a^3*c^4*x^3 + 5419*a^2*c^4*x^2 - 23062*a*c^4*x - 46355*c^4)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
271,1,94,0,0.707640," ","integrate((-a*c*x+c)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(7 \, a^{5} c^{3} x^{5} - 55 \, a^{4} c^{3} x^{4} + 214 \, a^{3} c^{3} x^{3} - 638 \, a^{2} c^{3} x^{2} + 2867 \, a c^{3} x + 5797 \, c^{3}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{63 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/63*(7*a^5*c^3*x^5 - 55*a^4*c^3*x^4 + 214*a^3*c^3*x^3 - 638*a^2*c^3*x^2 + 2867*a*c^3*x + 5797*c^3)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
272,1,83,0,0.688364," ","integrate((-a*c*x+c)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a^{4} c^{2} x^{4} - 36 \, a^{3} c^{2} x^{3} + 142 \, a^{2} c^{2} x^{2} - 708 \, a c^{2} x - 1451 \, c^{2}\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\left(a^{2} x - a\right)}}"," ",0,"2/35*(5*a^4*c^2*x^4 - 36*a^3*c^2*x^3 + 142*a^2*c^2*x^2 - 708*a*c^2*x - 1451*c^2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
273,1,63,0,0.715008," ","integrate((-a*c*x+c)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} c x^{3} - 7 \, a^{2} c x^{2} + 43 \, a c x + 91 \, c\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{5 \, {\left(a^{2} x - a\right)}}"," ",0,"-2/5*(a^3*c*x^3 - 7*a^2*c*x^2 + 43*a*c*x + 91*c)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
274,1,50,0,0.766496," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} x^{2} - 10 \, a x - 23\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{2} x - a\right)}}"," ",0,"2/3*(a^2*x^2 - 10*a*x - 23)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
275,1,44,0,0.612229," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-a c x + c} {\left(a x + 3\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c x - a c}"," ",0,"-2*sqrt(-a*c*x + c)*(a*x + 3)*sqrt((a*x - 1)/(a*x + 1))/(a^2*c*x - a*c)","A",0
276,1,43,0,0.493680," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2} x - a c^{2}}"," ",0,"-2*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^2*x - a*c^2)","A",0
277,1,235,0,0.580307," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + 4 \, \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{4 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}, \frac{\sqrt{2} {\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 2 \, \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}\right]"," ",0,"[-1/4*(sqrt(2)*(a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + 4*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^3*x - a*c^3), 1/2*(sqrt(2)*(a*x - 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 2*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^3*x - a*c^3)]","A",0
278,1,285,0,0.635831," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(7/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + 4 \, \sqrt{-a c x + c} {\left(3 \, a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{16 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}, \frac{3 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 2 \, \sqrt{-a c x + c} {\left(3 \, a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{8 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}\right]"," ",0,"[-1/16*(3*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + 4*sqrt(-a*c*x + c)*(3*a*x - 1)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4), 1/8*(3*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 2*sqrt(-a*c*x + c)*(3*a*x - 1)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4)]","A",0
279,1,57,0,0.803288," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(x^{3} + 4 \, x^{2} + 8 \, x + 5\right)} \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,"1/3*(x^3 + 4*x^2 + 8*x + 5)*sqrt((x - 1)/(x + 1)) + log(sqrt((x - 1)/(x + 1)) + 1) - log(sqrt((x - 1)/(x + 1)) - 1)","A",0
280,1,54,0,0.521236," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x^{2} + 5 \, x + 4\right)} \sqrt{\frac{x - 1}{x + 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,"1/2*(x^2 + 5*x + 4)*sqrt((x - 1)/(x + 1)) + 3/2*log(sqrt((x - 1)/(x + 1)) + 1) - 3/2*log(sqrt((x - 1)/(x + 1)) - 1)","A",0
281,1,24,0,0.549694," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)*x,x, algorithm=""fricas"")","-\frac{1}{3} \, {\left(x^{3} + x^{2} - x - 1\right)} \sqrt{\frac{x - 1}{x + 1}}"," ",0,"-1/3*(x^3 + x^2 - x - 1)*sqrt((x - 1)/(x + 1))","A",0
282,1,51,0,0.445376," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(x^{2} + x\right)} \sqrt{\frac{x - 1}{x + 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,"-1/2*(x^2 + x)*sqrt((x - 1)/(x + 1)) + 1/2*log(sqrt((x - 1)/(x + 1)) + 1) - 1/2*log(sqrt((x - 1)/(x + 1)) - 1)","A",0
283,1,66,0,0.457859," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^2,x, algorithm=""fricas"")","\frac{1}{8} \, {\left(2 \, x^{4} + 10 \, x^{3} + 23 \, x^{2} + 39 \, x + 24\right)} \sqrt{\frac{x - 1}{x + 1}} + \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,"1/8*(2*x^4 + 10*x^3 + 23*x^2 + 39*x + 24)*sqrt((x - 1)/(x + 1)) + 15/8*log(sqrt((x - 1)/(x + 1)) + 1) - 15/8*log(sqrt((x - 1)/(x + 1)) - 1)","A",0
284,1,61,0,0.449868," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x)^2,x, algorithm=""fricas"")","\frac{1}{6} \, {\left(2 \, x^{3} + 11 \, x^{2} + 31 \, x + 22\right)} \sqrt{\frac{x - 1}{x + 1}} + \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,"1/6*(2*x^3 + 11*x^2 + 31*x + 22)*sqrt((x - 1)/(x + 1)) + 5/2*log(sqrt((x - 1)/(x + 1)) + 1) - 5/2*log(sqrt((x - 1)/(x + 1)) - 1)","A",0
285,1,66,0,0.475705," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^2*x,x, algorithm=""fricas"")","\frac{1}{24} \, {\left(6 \, x^{4} - 2 \, x^{3} - 11 \, x^{2} + 5 \, x + 8\right)} \sqrt{\frac{x - 1}{x + 1}} - \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,"1/24*(6*x^4 - 2*x^3 - 11*x^2 + 5*x + 8)*sqrt((x - 1)/(x + 1)) - 1/8*log(sqrt((x - 1)/(x + 1)) + 1) + 1/8*log(sqrt((x - 1)/(x + 1)) - 1)","A",0
286,1,61,0,0.550461," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^2,x, algorithm=""fricas"")","\frac{1}{6} \, {\left(2 \, x^{3} - x^{2} - 5 \, x - 2\right)} \sqrt{\frac{x - 1}{x + 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,"1/6*(2*x^3 - x^2 - 5*x - 2)*sqrt((x - 1)/(x + 1)) + 1/2*log(sqrt((x - 1)/(x + 1)) + 1) - 1/2*log(sqrt((x - 1)/(x + 1)) - 1)","A",0
287,1,15,0,0.440067," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x),x, algorithm=""fricas"")","{\left(x + 1\right)} \sqrt{\frac{x - 1}{x + 1}}"," ",0,"(x + 1)*sqrt((x - 1)/(x + 1))","A",0
288,1,31,0,0.610843," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x),x, algorithm=""fricas"")","\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
289,1,66,0,0.579116," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x),x, algorithm=""fricas"")","-\frac{2 \, {\left(x - 1\right)} \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - 2 \, {\left(x - 1\right)} \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right) + {\left(x^{2} - 2 \, x - 3\right)} \sqrt{\frac{x - 1}{x + 1}}}{x - 1}"," ",0,"-(2*(x - 1)*log(sqrt((x - 1)/(x + 1)) + 1) - 2*(x - 1)*log(sqrt((x - 1)/(x + 1)) - 1) + (x^2 - 2*x - 3)*sqrt((x - 1)/(x + 1)))/(x - 1)","A",0
290,1,61,0,0.543339," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x),x, algorithm=""fricas"")","-\frac{{\left(x - 1\right)} \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - {\left(x - 1\right)} \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right) - 2 \, {\left(x + 1\right)} \sqrt{\frac{x - 1}{x + 1}}}{x - 1}"," ",0,"-((x - 1)*log(sqrt((x - 1)/(x + 1)) + 1) - (x - 1)*log(sqrt((x - 1)/(x + 1)) - 1) - 2*(x + 1)*sqrt((x - 1)/(x + 1)))/(x - 1)","B",0
291,1,44,0,0.427487," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^2,x, algorithm=""fricas"")","-\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
292,1,11,0,0.635197," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x)^2,x, algorithm=""fricas"")","\sqrt{\frac{x - 1}{x + 1}}"," ",0,"sqrt((x - 1)/(x + 1))","A",0
293,1,84,0,0.605917," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(x^{2} - 2 \, x + 1\right)} \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - 3 \, {\left(x^{2} - 2 \, x + 1\right)} \log\left(\sqrt{\frac{x - 1}{x + 1}} - 1\right) - {\left(7 \, x^{2} + 2 \, x - 5\right)} \sqrt{\frac{x - 1}{x + 1}}}{3 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"1/3*(3*(x^2 - 2*x + 1)*log(sqrt((x - 1)/(x + 1)) + 1) - 3*(x^2 - 2*x + 1)*log(sqrt((x - 1)/(x + 1)) - 1) - (7*x^2 + 2*x - 5)*sqrt((x - 1)/(x + 1)))/(x^2 - 2*x + 1)","A",0
294,1,31,0,0.513916," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x)^2,x, algorithm=""fricas"")","-\frac{{\left(x^{2} + 2 \, x + 1\right)} \sqrt{\frac{x - 1}{x + 1}}}{3 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"-1/3*(x^2 + 2*x + 1)*sqrt((x - 1)/(x + 1))/(x^2 - 2*x + 1)","A",0
295,0,0,0,0.662337," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a c x + c} {\left(a x + 1\right)} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}}{a x - 1}, x\right)"," ",0,"integral(sqrt(-a*c*x + c)*(a*x + 1)*x^m*sqrt((a*x - 1)/(a*x + 1))/(a*x - 1), x)","F",0
296,1,69,0,0.505947," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, a^{4} x^{4} + 18 \, a^{3} x^{3} - a^{2} x^{2} + 4 \, a x + 8\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{105 \, {\left(a^{4} x - a^{3}\right)}}"," ",0,"2/105*(15*a^4*x^4 + 18*a^3*x^3 - a^2*x^2 + 4*a*x + 8)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^4*x - a^3)","A",0
297,1,61,0,0.742782," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} - a x - 2\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\left(a^{3} x - a^{2}\right)}}"," ",0,"2/15*(3*a^3*x^3 + 4*a^2*x^2 - a*x - 2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^3*x - a^2)","A",0
298,1,50,0,1.173811," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{2} x - a\right)}}"," ",0,"2/3*(a^2*x^2 + 2*a*x + 1)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
299,1,207,0,0.532276," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x - 1}, -\frac{2 \, {\left({\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a x - 1}\right]"," ",0,"[((a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x - 1), -2*((a*x - 1)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x - 1)]","A",0
300,1,229,0,0.441119," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} x^{2} - a x\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) - 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, {\left(a x^{2} - x\right)}}, -\frac{{\left(a^{2} x^{2} - a x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) + \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x^{2} - x}\right]"," ",0,"[1/2*((a^2*x^2 - a*x)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) - 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^2 - x), -((a^2*x^2 - a*x)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) + sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^2 - x)]","A",0
301,1,44,0,0.446632," ","integrate(1/(a*x-1)*(a*x+1)*x^3*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, a^{4} x^{4} + 85 \, a^{3} x^{3} + 102 \, a^{2} x^{2} + 136 \, a x + 272\right)} \sqrt{-a c x + c}}{315 \, a^{4}}"," ",0,"2/315*(35*a^4*x^4 + 85*a^3*x^3 + 102*a^2*x^2 + 136*a*x + 272)*sqrt(-a*c*x + c)/a^4","A",0
302,1,36,0,0.493197," ","integrate(1/(a*x-1)*(a*x+1)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, a^{3} x^{3} + 39 \, a^{2} x^{2} + 52 \, a x + 104\right)} \sqrt{-a c x + c}}{105 \, a^{3}}"," ",0,"2/105*(15*a^3*x^3 + 39*a^2*x^2 + 52*a*x + 104)*sqrt(-a*c*x + c)/a^3","A",0
303,1,27,0,0.496250," ","integrate(1/(a*x-1)*(a*x+1)*x*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} x^{2} + 3 \, a x + 6\right)} \sqrt{-a c x + c}}{5 \, a^{2}}"," ",0,"2/5*(a^2*x^2 + 3*a*x + 6)*sqrt(-a*c*x + c)/a^2","A",0
304,1,19,0,0.461970," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-a c x + c} {\left(a x + 5\right)}}{3 \, a}"," ",0,"2/3*sqrt(-a*c*x + c)*(a*x + 5)/a","A",0
305,1,82,0,0.462930," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\sqrt{c} \log\left(\frac{a c x - 2 \, \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{x}\right) + 2 \, \sqrt{-a c x + c}, -2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{-c}}{c}\right) + 2 \, \sqrt{-a c x + c}\right]"," ",0,"[sqrt(c)*log((a*c*x - 2*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/x) + 2*sqrt(-a*c*x + c), -2*sqrt(-c)*arctan(sqrt(-a*c*x + c)*sqrt(-c)/c) + 2*sqrt(-a*c*x + c)]","A",0
306,1,97,0,0.581386," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{c} x \log\left(\frac{a c x - 2 \, \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{x}\right) + 2 \, \sqrt{-a c x + c}}{2 \, x}, -\frac{3 \, a \sqrt{-c} x \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{-c}}{c}\right) - \sqrt{-a c x + c}}{x}\right]"," ",0,"[1/2*(3*a*sqrt(c)*x*log((a*c*x - 2*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/x) + 2*sqrt(-a*c*x + c))/x, -(3*a*sqrt(-c)*x*arctan(sqrt(-a*c*x + c)*sqrt(-c)/c) - sqrt(-a*c*x + c))/x]","A",0
307,1,117,0,0.564339," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{7 \, a^{2} \sqrt{c} x^{2} \log\left(\frac{a c x - 2 \, \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{x}\right) + 2 \, \sqrt{-a c x + c} {\left(7 \, a x + 2\right)}}{8 \, x^{2}}, -\frac{7 \, a^{2} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{-c}}{c}\right) - \sqrt{-a c x + c} {\left(7 \, a x + 2\right)}}{4 \, x^{2}}\right]"," ",0,"[1/8*(7*a^2*sqrt(c)*x^2*log((a*c*x - 2*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/x) + 2*sqrt(-a*c*x + c)*(7*a*x + 2))/x^2, -1/4*(7*a^2*sqrt(-c)*x^2*arctan(sqrt(-a*c*x + c)*sqrt(-c)/c) - sqrt(-a*c*x + c)*(7*a*x + 2))/x^2]","A",0
308,1,133,0,0.635377," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{33 \, a^{3} \sqrt{c} x^{3} \log\left(\frac{a c x - 2 \, \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{x}\right) + 2 \, {\left(33 \, a^{2} x^{2} + 22 \, a x + 8\right)} \sqrt{-a c x + c}}{48 \, x^{3}}, -\frac{33 \, a^{3} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{-c}}{c}\right) - {\left(33 \, a^{2} x^{2} + 22 \, a x + 8\right)} \sqrt{-a c x + c}}{24 \, x^{3}}\right]"," ",0,"[1/48*(33*a^3*sqrt(c)*x^3*log((a*c*x - 2*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/x) + 2*(33*a^2*x^2 + 22*a*x + 8)*sqrt(-a*c*x + c))/x^3, -1/24*(33*a^3*sqrt(-c)*x^3*arctan(sqrt(-a*c*x + c)*sqrt(-c)/c) - (33*a^2*x^2 + 22*a*x + 8)*sqrt(-a*c*x + c))/x^3]","A",0
309,1,149,0,0.527082," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{75 \, a^{4} \sqrt{c} x^{4} \log\left(\frac{a c x - 2 \, \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{x}\right) + 2 \, {\left(75 \, a^{3} x^{3} + 50 \, a^{2} x^{2} + 40 \, a x + 16\right)} \sqrt{-a c x + c}}{128 \, x^{4}}, -\frac{75 \, a^{4} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{-c}}{c}\right) - {\left(75 \, a^{3} x^{3} + 50 \, a^{2} x^{2} + 40 \, a x + 16\right)} \sqrt{-a c x + c}}{64 \, x^{4}}\right]"," ",0,"[1/128*(75*a^4*sqrt(c)*x^4*log((a*c*x - 2*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/x) + 2*(75*a^3*x^3 + 50*a^2*x^2 + 40*a*x + 16)*sqrt(-a*c*x + c))/x^4, -1/64*(75*a^4*sqrt(-c)*x^4*arctan(sqrt(-a*c*x + c)*sqrt(-c)/c) - (75*a^3*x^3 + 50*a^2*x^2 + 40*a*x + 16)*sqrt(-a*c*x + c))/x^4]","A",0
310,1,304,0,0.718341," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(315 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + {\left(35 \, a^{5} x^{5} + 130 \, a^{4} x^{4} + 233 \, a^{3} x^{3} + 374 \, a^{2} x^{2} + 1024 \, a x + 788\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{315 \, {\left(a^{5} x - a^{4}\right)}}, -\frac{2 \, {\left(630 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(35 \, a^{5} x^{5} + 130 \, a^{4} x^{4} + 233 \, a^{3} x^{3} + 374 \, a^{2} x^{2} + 1024 \, a x + 788\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{315 \, {\left(a^{5} x - a^{4}\right)}}\right]"," ",0,"[2/315*(315*sqrt(2)*(a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + (35*a^5*x^5 + 130*a^4*x^4 + 233*a^3*x^3 + 374*a^2*x^2 + 1024*a*x + 788)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^5*x - a^4), -2/315*(630*sqrt(2)*(a*x - 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (35*a^5*x^5 + 130*a^4*x^4 + 233*a^3*x^3 + 374*a^2*x^2 + 1024*a*x + 788)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^5*x - a^4)]","A",0
311,1,288,0,0.565897," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(21 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + {\left(3 \, a^{4} x^{4} + 12 \, a^{3} x^{3} + 25 \, a^{2} x^{2} + 68 \, a x + 52\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{21 \, {\left(a^{4} x - a^{3}\right)}}, -\frac{2 \, {\left(42 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(3 \, a^{4} x^{4} + 12 \, a^{3} x^{3} + 25 \, a^{2} x^{2} + 68 \, a x + 52\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{21 \, {\left(a^{4} x - a^{3}\right)}}\right]"," ",0,"[2/21*(21*sqrt(2)*(a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + (3*a^4*x^4 + 12*a^3*x^3 + 25*a^2*x^2 + 68*a*x + 52)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*x - a^3), -2/21*(42*sqrt(2)*(a*x - 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (3*a^4*x^4 + 12*a^3*x^3 + 25*a^2*x^2 + 68*a*x + 52)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*x - a^3)]","A",0
312,1,272,0,0.532613," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(15 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + {\left(3 \, a^{3} x^{3} + 14 \, a^{2} x^{2} + 49 \, a x + 38\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{15 \, {\left(a^{3} x - a^{2}\right)}}, -\frac{2 \, {\left(30 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(3 \, a^{3} x^{3} + 14 \, a^{2} x^{2} + 49 \, a x + 38\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{15 \, {\left(a^{3} x - a^{2}\right)}}\right]"," ",0,"[2/15*(15*sqrt(2)*(a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + (3*a^3*x^3 + 14*a^2*x^2 + 49*a*x + 38)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*x - a^2), -2/15*(30*sqrt(2)*(a*x - 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (3*a^3*x^3 + 14*a^2*x^2 + 49*a*x + 38)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*x - a^2)]","A",0
313,1,250,0,0.574492," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + {\left(a^{2} x^{2} + 8 \, a x + 7\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{3 \, {\left(a^{2} x - a\right)}}, -\frac{2 \, {\left(6 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(a^{2} x^{2} + 8 \, a x + 7\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{3 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[2/3*(3*sqrt(2)*(a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + (a^2*x^2 + 8*a*x + 7)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x - a), -2/3*(6*sqrt(2)*(a*x - 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (a^2*x^2 + 8*a*x + 7)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x - a)]","A",0
314,1,352,0,1.226813," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + {\left(a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x - 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x - 1}, -\frac{2 \, {\left(2 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a x - 1}\right]"," ",0,"[(2*sqrt(2)*(a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + (a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x - 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x - 1), -2*(2*sqrt(2)*(a*x - 1)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (a*x - 1)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x - 1)]","A",0
315,1,390,0,0.582930," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(a^{2} x^{2} - a x\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + 5 \, {\left(a^{2} x^{2} - a x\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x - 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, {\left(a x^{2} - x\right)}}, -\frac{4 \, \sqrt{2} {\left(a^{2} x^{2} - a x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 5 \, {\left(a^{2} x^{2} - a x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x^{2} - x}\right]"," ",0,"[1/2*(4*sqrt(2)*(a^2*x^2 - a*x)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + 5*(a^2*x^2 - a*x)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x - 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^2 - x), -(4*sqrt(2)*(a^2*x^2 - a*x)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 5*(a^2*x^2 - a*x)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^2 - x)]","A",0
316,1,428,0,0.484444," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{16 \, \sqrt{2} {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + 23 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x - 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) + 2 \, {\left(9 \, a^{2} x^{2} + 11 \, a x + 2\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{8 \, {\left(a x^{3} - x^{2}\right)}}, -\frac{16 \, \sqrt{2} {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 23 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(9 \, a^{2} x^{2} + 11 \, a x + 2\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{4 \, {\left(a x^{3} - x^{2}\right)}}\right]"," ",0,"[1/8*(16*sqrt(2)*(a^3*x^3 - a^2*x^2)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + 23*(a^3*x^3 - a^2*x^2)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x - 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) + 2*(9*a^2*x^2 + 11*a*x + 2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^3 - x^2), -1/4*(16*sqrt(2)*(a^3*x^3 - a^2*x^2)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 23*(a^3*x^3 - a^2*x^2)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (9*a^2*x^2 + 11*a*x + 2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^3 - x^2)]","A",0
317,1,444,0,0.721811," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{96 \, \sqrt{2} {\left(a^{4} x^{4} - a^{3} x^{3}\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + 135 \, {\left(a^{4} x^{4} - a^{3} x^{3}\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x - 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) + 2 \, {\left(57 \, a^{3} x^{3} + 83 \, a^{2} x^{2} + 34 \, a x + 8\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{48 \, {\left(a x^{4} - x^{3}\right)}}, -\frac{96 \, \sqrt{2} {\left(a^{4} x^{4} - a^{3} x^{3}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 135 \, {\left(a^{4} x^{4} - a^{3} x^{3}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(57 \, a^{3} x^{3} + 83 \, a^{2} x^{2} + 34 \, a x + 8\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{24 \, {\left(a x^{4} - x^{3}\right)}}\right]"," ",0,"[1/48*(96*sqrt(2)*(a^4*x^4 - a^3*x^3)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + 135*(a^4*x^4 - a^3*x^3)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x - 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) + 2*(57*a^3*x^3 + 83*a^2*x^2 + 34*a*x + 8)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^4 - x^3), -1/24*(96*sqrt(2)*(a^4*x^4 - a^3*x^3)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 135*(a^4*x^4 - a^3*x^3)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (57*a^3*x^3 + 83*a^2*x^2 + 34*a*x + 8)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^4 - x^3)]","A",0
318,1,460,0,0.657278," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{768 \, \sqrt{2} {\left(a^{5} x^{5} - a^{4} x^{4}\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 3 \, c}{a^{2} x^{2} - 2 \, a x + 1}\right) + 1089 \, {\left(a^{5} x^{5} - a^{4} x^{4}\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x - 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) + 2 \, {\left(447 \, a^{4} x^{4} + 661 \, a^{3} x^{3} + 350 \, a^{2} x^{2} + 184 \, a x + 48\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{384 \, {\left(a x^{5} - x^{4}\right)}}, -\frac{768 \, \sqrt{2} {\left(a^{5} x^{5} - a^{4} x^{4}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - 1089 \, {\left(a^{5} x^{5} - a^{4} x^{4}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(447 \, a^{4} x^{4} + 661 \, a^{3} x^{3} + 350 \, a^{2} x^{2} + 184 \, a x + 48\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{192 \, {\left(a x^{5} - x^{4}\right)}}\right]"," ",0,"[1/384*(768*sqrt(2)*(a^5*x^5 - a^4*x^4)*sqrt(-c)*log(-(a^2*c*x^2 + 2*a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 3*c)/(a^2*x^2 - 2*a*x + 1)) + 1089*(a^5*x^5 - a^4*x^4)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x - 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) + 2*(447*a^4*x^4 + 661*a^3*x^3 + 350*a^2*x^2 + 184*a*x + 48)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^5 - x^4), -1/192*(768*sqrt(2)*(a^5*x^5 - a^4*x^4)*sqrt(c)*arctan(sqrt(2)*sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - 1089*(a^5*x^5 - a^4*x^4)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (447*a^4*x^4 + 661*a^3*x^3 + 350*a^2*x^2 + 184*a*x + 48)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^5 - x^4)]","A",0
319,1,33,0,0.633870," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^(3/2),x, algorithm=""fricas"")","\frac{2}{21} \, {\left(3 \, x^{3} + 12 \, x^{2} + 23 \, x + 46\right)} \sqrt{x + 1} \sqrt{\frac{x - 1}{x + 1}}"," ",0,"2/21*(3*x^3 + 12*x^2 + 23*x + 46)*sqrt(x + 1)*sqrt((x - 1)/(x + 1))","A",0
320,1,28,0,0.540310," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x)^(3/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(3 \, x^{2} + 14 \, x + 43\right)} \sqrt{x + 1} \sqrt{\frac{x - 1}{x + 1}}"," ",0,"2/15*(3*x^2 + 14*x + 43)*sqrt(x + 1)*sqrt((x - 1)/(x + 1))","A",0
321,1,45,0,0.496217," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^(3/2)*x,x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, x^{4} - 3 \, x^{3} - 29 \, x^{2} + 11 \, x + 22\right)} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}{105 \, {\left(x - 1\right)}}"," ",0,"-2/105*(15*x^4 - 3*x^3 - 29*x^2 + 11*x + 22)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1))/(x - 1)","A",0
322,1,40,0,0.411656," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, x^{3} - x^{2} - 11 \, x - 7\right)} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}{15 \, {\left(x - 1\right)}}"," ",0,"-2/15*(3*x^3 - x^2 - 11*x - 7)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1))/(x - 1)","A",0
323,1,26,0,0.406690," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^(1/2),x, algorithm=""fricas"")","\frac{2}{5} \, {\left(x^{2} + 3 \, x + 6\right)} \sqrt{x + 1} \sqrt{\frac{x - 1}{x + 1}}"," ",0,"2/5*(x^2 + 3*x + 6)*sqrt(x + 1)*sqrt((x - 1)/(x + 1))","A",0
324,1,21,0,0.523904," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(x + 5\right)} \sqrt{x + 1} \sqrt{\frac{x - 1}{x + 1}}"," ",0,"2/3*(x + 5)*sqrt(x + 1)*sqrt((x - 1)/(x + 1))","A",0
325,1,40,0,0.630107," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1-x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, x^{3} + 4 \, x^{2} - x - 2\right)} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}{15 \, {\left(x - 1\right)}}"," ",0,"2/15*(3*x^3 + 4*x^2 - x - 2)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1))/(x - 1)","A",0
326,1,33,0,0.597383," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(x^{2} + 2 \, x + 1\right)} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}{3 \, {\left(x - 1\right)}}"," ",0,"2/3*(x^2 + 2*x + 1)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1))/(x - 1)","A",0
327,1,21,0,0.626515," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(x + 2\right)} \sqrt{x + 1} \sqrt{\frac{x - 1}{x + 1}}"," ",0,"2/3*(x + 2)*sqrt(x + 1)*sqrt((x - 1)/(x + 1))","A",0
328,1,18,0,0.588676," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{x + 1} \sqrt{\frac{x - 1}{x + 1}}"," ",0,"2*sqrt(x + 1)*sqrt((x - 1)/(x + 1))","A",0
329,1,72,0,0.521567," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, \sqrt{2} {\left(x - 1\right)} \arctan\left(\frac{\sqrt{2} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}{x - 1}\right) - {\left(x^{2} + 5 \, x + 4\right)} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}\right)}}{3 \, {\left(x - 1\right)}}"," ",0,"2/3*(3*sqrt(2)*(x - 1)*arctan(sqrt(2)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1))/(x - 1)) - (x^2 + 5*x + 4)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1)))/(x - 1)","A",0
330,1,66,0,0.476755," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{2} {\left(x - 1\right)} \arctan\left(\frac{\sqrt{2} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}{x - 1}\right) - {\left(x + 1\right)} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}\right)}}{x - 1}"," ",0,"2*(sqrt(2)*(x - 1)*arctan(sqrt(2)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1))/(x - 1)) - (x + 1)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1)))/(x - 1)","A",0
331,1,46,0,0.873859," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^(3/2),x, algorithm=""fricas"")","-\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{x + 1} \sqrt{\frac{x - 1}{x + 1}}\right) + 2 \, \sqrt{x + 1} \sqrt{\frac{x - 1}{x + 1}}"," ",0,"-sqrt(2)*arctan(1/2*sqrt(2)*sqrt(x + 1)*sqrt((x - 1)/(x + 1))) + 2*sqrt(x + 1)*sqrt((x - 1)/(x + 1))","A",0
332,1,26,0,0.638042," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x)^(3/2),x, algorithm=""fricas"")","\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{x + 1} \sqrt{\frac{x - 1}{x + 1}}\right)"," ",0,"sqrt(2)*arctan(1/2*sqrt(2)*sqrt(x + 1)*sqrt((x - 1)/(x + 1)))","A",0
333,1,84,0,0.514103," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^(3/2),x, algorithm=""fricas"")","-\frac{5 \, \sqrt{2} {\left(x^{2} - 2 \, x + 1\right)} \arctan\left(\frac{\sqrt{2} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}{x - 1}\right) - 2 \, {\left(2 \, x^{2} - x - 3\right)} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}{2 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"-1/2*(5*sqrt(2)*(x^2 - 2*x + 1)*arctan(sqrt(2)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1))/(x - 1)) - 2*(2*x^2 - x - 3)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1)))/(x^2 - 2*x + 1)","A",0
334,1,76,0,0.512626," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(x^{2} - 2 \, x + 1\right)} \arctan\left(\frac{\sqrt{2} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}{x - 1}\right) + 2 \, {\left(x + 1\right)} \sqrt{-x + 1} \sqrt{\frac{x - 1}{x + 1}}}{2 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"-1/2*(sqrt(2)*(x^2 - 2*x + 1)*arctan(sqrt(2)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1))/(x - 1)) + 2*(x + 1)*sqrt(-x + 1)*sqrt((x - 1)/(x + 1)))/(x^2 - 2*x + 1)","A",0
335,0,0,0,0.555247," ","integrate(x^m*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a c x + c} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}, x\right)"," ",0,"integral(sqrt(-a*c*x + c)*x^m*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
336,1,69,0,0.575392," ","integrate(x^2*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, a^{4} x^{4} - 24 \, a^{3} x^{3} + 13 \, a^{2} x^{2} - 52 \, a x - 104\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{105 \, {\left(a^{4} x - a^{3}\right)}}"," ",0,"2/105*(15*a^4*x^4 - 24*a^3*x^3 + 13*a^2*x^2 - 52*a*x - 104)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^4*x - a^3)","A",0
337,1,60,0,0.657655," ","integrate(x*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} x^{3} - 2 \, a^{2} x^{2} + 3 \, a x + 6\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{5 \, {\left(a^{3} x - a^{2}\right)}}"," ",0,"2/5*(a^3*x^3 - 2*a^2*x^2 + 3*a*x + 6)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^3*x - a^2)","A",0
338,1,50,0,0.526381," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} x^{2} - 4 \, a x - 5\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{2} x - a\right)}}"," ",0,"2/3*(a^2*x^2 - 4*a*x - 5)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
339,1,206,0,0.453134," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x - 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x - 1}, \frac{2 \, {\left({\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) + \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a x - 1}\right]"," ",0,"[((a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x - 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x - 1), 2*((a*x - 1)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) + sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x - 1)]","A",0
340,1,232,0,0.696433," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} x^{2} - a x\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, {\left(a x^{2} - x\right)}}, -\frac{3 \, {\left(a^{2} x^{2} - a x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x^{2} - x}\right]"," ",0,"[1/2*(3*(a^2*x^2 - a*x)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^2 - x), -(3*(a^2*x^2 - a*x)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - sqrt(-a*c*x + c)*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^2 - x)]","A",0
341,1,168,0,0.479107," ","integrate(x^3*(-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(315 \, \sqrt{2} \sqrt{c} \log\left(\frac{a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + {\left(35 \, a^{4} x^{4} - 95 \, a^{3} x^{3} + 138 \, a^{2} x^{2} - 236 \, a x + 788\right)} \sqrt{-a c x + c}\right)}}{315 \, a^{4}}, \frac{2 \, {\left(630 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) + {\left(35 \, a^{4} x^{4} - 95 \, a^{3} x^{3} + 138 \, a^{2} x^{2} - 236 \, a x + 788\right)} \sqrt{-a c x + c}\right)}}{315 \, a^{4}}\right]"," ",0,"[2/315*(315*sqrt(2)*sqrt(c)*log((a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + (35*a^4*x^4 - 95*a^3*x^3 + 138*a^2*x^2 - 236*a*x + 788)*sqrt(-a*c*x + c))/a^4, 2/315*(630*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) + (35*a^4*x^4 - 95*a^3*x^3 + 138*a^2*x^2 - 236*a*x + 788)*sqrt(-a*c*x + c))/a^4]","A",0
342,1,153,0,0.555322," ","integrate(x^2*(-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(21 \, \sqrt{2} \sqrt{c} \log\left(\frac{a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + {\left(3 \, a^{3} x^{3} - 9 \, a^{2} x^{2} + 16 \, a x - 52\right)} \sqrt{-a c x + c}\right)}}{21 \, a^{3}}, -\frac{2 \, {\left(42 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - {\left(3 \, a^{3} x^{3} - 9 \, a^{2} x^{2} + 16 \, a x - 52\right)} \sqrt{-a c x + c}\right)}}{21 \, a^{3}}\right]"," ",0,"[2/21*(21*sqrt(2)*sqrt(c)*log((a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + (3*a^3*x^3 - 9*a^2*x^2 + 16*a*x - 52)*sqrt(-a*c*x + c))/a^3, -2/21*(42*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - (3*a^3*x^3 - 9*a^2*x^2 + 16*a*x - 52)*sqrt(-a*c*x + c))/a^3]","A",0
343,1,136,0,0.628182," ","integrate(x*(-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(15 \, \sqrt{2} \sqrt{c} \log\left(\frac{a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + {\left(3 \, a^{2} x^{2} - 11 \, a x + 38\right)} \sqrt{-a c x + c}\right)}}{15 \, a^{2}}, \frac{2 \, {\left(30 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) + {\left(3 \, a^{2} x^{2} - 11 \, a x + 38\right)} \sqrt{-a c x + c}\right)}}{15 \, a^{2}}\right]"," ",0,"[2/15*(15*sqrt(2)*sqrt(c)*log((a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + (3*a^2*x^2 - 11*a*x + 38)*sqrt(-a*c*x + c))/a^2, 2/15*(30*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) + (3*a^2*x^2 - 11*a*x + 38)*sqrt(-a*c*x + c))/a^2]","A",0
344,1,119,0,0.504086," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, \sqrt{2} \sqrt{c} \log\left(\frac{a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + \sqrt{-a c x + c} {\left(a x - 7\right)}\right)}}{3 \, a}, -\frac{2 \, {\left(6 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - \sqrt{-a c x + c} {\left(a x - 7\right)}\right)}}{3 \, a}\right]"," ",0,"[2/3*(3*sqrt(2)*sqrt(c)*log((a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + sqrt(-a*c*x + c)*(a*x - 7))/a, -2/3*(6*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - sqrt(-a*c*x + c)*(a*x - 7))/a]","A",0
345,1,157,0,0.507139," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1)/x,x, algorithm=""fricas"")","\left[2 \, \sqrt{2} \sqrt{c} \log\left(\frac{a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + \sqrt{c} \log\left(\frac{a c x - 2 \, \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{x}\right) + 2 \, \sqrt{-a c x + c}, 4 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - 2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{-c}}{c}\right) + 2 \, \sqrt{-a c x + c}\right]"," ",0,"[2*sqrt(2)*sqrt(c)*log((a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + sqrt(c)*log((a*c*x - 2*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/x) + 2*sqrt(-a*c*x + c), 4*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - 2*sqrt(-c)*arctan(sqrt(-a*c*x + c)*sqrt(-c)/c) + 2*sqrt(-a*c*x + c)]","A",0
346,1,176,0,0.601454," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1)/x^2,x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} a \sqrt{c} x \log\left(\frac{a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + 5 \, a \sqrt{c} x \log\left(\frac{a c x + 2 \, \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{x}\right) + 2 \, \sqrt{-a c x + c}}{2 \, x}, -\frac{4 \, \sqrt{2} a \sqrt{-c} x \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - 5 \, a \sqrt{-c} x \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{-c}}{c}\right) - \sqrt{-a c x + c}}{x}\right]"," ",0,"[1/2*(4*sqrt(2)*a*sqrt(c)*x*log((a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + 5*a*sqrt(c)*x*log((a*c*x + 2*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/x) + 2*sqrt(-a*c*x + c))/x, -(4*sqrt(2)*a*sqrt(-c)*x*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - 5*a*sqrt(-c)*x*arctan(sqrt(-a*c*x + c)*sqrt(-c)/c) - sqrt(-a*c*x + c))/x]","A",0
347,1,204,0,0.591779," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1)/x^3,x, algorithm=""fricas"")","\left[\frac{16 \, \sqrt{2} a^{2} \sqrt{c} x^{2} \log\left(\frac{a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + 23 \, a^{2} \sqrt{c} x^{2} \log\left(\frac{a c x - 2 \, \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{x}\right) - 2 \, \sqrt{-a c x + c} {\left(9 \, a x - 2\right)}}{8 \, x^{2}}, \frac{16 \, \sqrt{2} a^{2} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - 23 \, a^{2} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{-c}}{c}\right) - \sqrt{-a c x + c} {\left(9 \, a x - 2\right)}}{4 \, x^{2}}\right]"," ",0,"[1/8*(16*sqrt(2)*a^2*sqrt(c)*x^2*log((a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + 23*a^2*sqrt(c)*x^2*log((a*c*x - 2*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/x) - 2*sqrt(-a*c*x + c)*(9*a*x - 2))/x^2, 1/4*(16*sqrt(2)*a^2*sqrt(-c)*x^2*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - 23*a^2*sqrt(-c)*x^2*arctan(sqrt(-a*c*x + c)*sqrt(-c)/c) - sqrt(-a*c*x + c)*(9*a*x - 2))/x^2]","A",0
348,1,220,0,0.571978," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1)/x^4,x, algorithm=""fricas"")","\left[\frac{96 \, \sqrt{2} a^{3} \sqrt{c} x^{3} \log\left(\frac{a c x - 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + 135 \, a^{3} \sqrt{c} x^{3} \log\left(\frac{a c x + 2 \, \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{x}\right) + 2 \, {\left(57 \, a^{2} x^{2} - 26 \, a x + 8\right)} \sqrt{-a c x + c}}{48 \, x^{3}}, -\frac{96 \, \sqrt{2} a^{3} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - 135 \, a^{3} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{-c}}{c}\right) - {\left(57 \, a^{2} x^{2} - 26 \, a x + 8\right)} \sqrt{-a c x + c}}{24 \, x^{3}}\right]"," ",0,"[1/48*(96*sqrt(2)*a^3*sqrt(c)*x^3*log((a*c*x - 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + 135*a^3*sqrt(c)*x^3*log((a*c*x + 2*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/x) + 2*(57*a^2*x^2 - 26*a*x + 8)*sqrt(-a*c*x + c))/x^3, -1/24*(96*sqrt(2)*a^3*sqrt(-c)*x^3*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - 135*a^3*sqrt(-c)*x^3*arctan(sqrt(-a*c*x + c)*sqrt(-c)/c) - (57*a^2*x^2 - 26*a*x + 8)*sqrt(-a*c*x + c))/x^3]","A",0
349,1,236,0,0.407474," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1)/x^5,x, algorithm=""fricas"")","\left[\frac{768 \, \sqrt{2} a^{4} \sqrt{c} x^{4} \log\left(\frac{a c x + 2 \, \sqrt{2} \sqrt{-a c x + c} \sqrt{c} - 3 \, c}{a x + 1}\right) + 1089 \, a^{4} \sqrt{c} x^{4} \log\left(\frac{a c x - 2 \, \sqrt{-a c x + c} \sqrt{c} - 2 \, c}{x}\right) - 2 \, {\left(447 \, a^{3} x^{3} - 214 \, a^{2} x^{2} + 136 \, a x - 48\right)} \sqrt{-a c x + c}}{384 \, x^{4}}, \frac{768 \, \sqrt{2} a^{4} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c} \sqrt{-c}}{2 \, c}\right) - 1089 \, a^{4} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{-c}}{c}\right) - {\left(447 \, a^{3} x^{3} - 214 \, a^{2} x^{2} + 136 \, a x - 48\right)} \sqrt{-a c x + c}}{192 \, x^{4}}\right]"," ",0,"[1/384*(768*sqrt(2)*a^4*sqrt(c)*x^4*log((a*c*x + 2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(c) - 3*c)/(a*x + 1)) + 1089*a^4*sqrt(c)*x^4*log((a*c*x - 2*sqrt(-a*c*x + c)*sqrt(c) - 2*c)/x) - 2*(447*a^3*x^3 - 214*a^2*x^2 + 136*a*x - 48)*sqrt(-a*c*x + c))/x^4, 1/192*(768*sqrt(2)*a^4*sqrt(-c)*x^4*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)*sqrt(-c)/c) - 1089*a^4*sqrt(-c)*x^4*arctan(sqrt(-a*c*x + c)*sqrt(-c)/c) - (447*a^3*x^3 - 214*a^2*x^2 + 136*a*x - 48)*sqrt(-a*c*x + c))/x^4]","A",0
350,1,77,0,0.516568," ","integrate(x^3*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a^{5} x^{5} - 20 \, a^{4} x^{4} + 41 \, a^{3} x^{3} - 82 \, a^{2} x^{2} + 328 \, a x + 656\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{45 \, {\left(a^{5} x - a^{4}\right)}}"," ",0,"2/45*(5*a^5*x^5 - 20*a^4*x^4 + 41*a^3*x^3 - 82*a^2*x^2 + 328*a*x + 656)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^5*x - a^4)","A",0
351,1,69,0,0.649764," ","integrate(x^2*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, a^{4} x^{4} - 66 \, a^{3} x^{3} + 167 \, a^{2} x^{2} - 668 \, a x - 1336\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{105 \, {\left(a^{4} x - a^{3}\right)}}"," ",0,"2/105*(15*a^4*x^4 - 66*a^3*x^3 + 167*a^2*x^2 - 668*a*x - 1336)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^4*x - a^3)","A",0
352,1,61,0,0.719200," ","integrate(x*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{3} x^{3} - 16 \, a^{2} x^{2} + 79 \, a x + 158\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\left(a^{3} x - a^{2}\right)}}"," ",0,"2/15*(3*a^3*x^3 - 16*a^2*x^2 + 79*a*x + 158)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^3*x - a^2)","A",0
353,1,50,0,0.530022," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} x^{2} - 10 \, a x - 23\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{2} x - a\right)}}"," ",0,"2/3*(a^2*x^2 - 10*a*x - 23)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1))/(a^2*x - a)","A",0
354,1,207,0,0.640733," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) + 2 \, \sqrt{-a c x + c} {\left(a x + 5\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x - 1}, -\frac{2 \, {\left({\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - \sqrt{-a c x + c} {\left(a x + 5\right)} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a x - 1}\right]"," ",0,"[((a*x - 1)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) + 2*sqrt(-a*c*x + c)*(a*x + 5)*sqrt((a*x - 1)/(a*x + 1)))/(a*x - 1), -2*((a*x - 1)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - sqrt(-a*c*x + c)*(a*x + 5)*sqrt((a*x - 1)/(a*x + 1)))/(a*x - 1)]","A",0
355,1,233,0,0.426456," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""fricas"")","\left[\frac{7 \, {\left(a^{2} x^{2} - a x\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x - 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) - 2 \, \sqrt{-a c x + c} {\left(9 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, {\left(a x^{2} - x\right)}}, \frac{7 \, {\left(a^{2} x^{2} - a x\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - \sqrt{-a c x + c} {\left(9 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x^{2} - x}\right]"," ",0,"[1/2*(7*(a^2*x^2 - a*x)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x - 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) - 2*sqrt(-a*c*x + c)*(9*a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^2 - x), (7*(a^2*x^2 - a*x)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - sqrt(-a*c*x + c)*(9*a*x + 1)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^2 - x)]","A",0
356,1,262,0,0.625621," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{47 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) + 2 \, {\left(47 \, a^{2} x^{2} + 13 \, a x - 2\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{8 \, {\left(a x^{3} - x^{2}\right)}}, -\frac{47 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(47 \, a^{2} x^{2} + 13 \, a x - 2\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{4 \, {\left(a x^{3} - x^{2}\right)}}\right]"," ",0,"[1/8*(47*(a^3*x^3 - a^2*x^2)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) + 2*(47*a^2*x^2 + 13*a*x - 2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^3 - x^2), -1/4*(47*(a^3*x^3 - a^2*x^2)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (47*a^2*x^2 + 13*a*x - 2)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^3 - x^2)]","A",0
357,1,278,0,0.537050," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{357 \, {\left(a^{4} x^{4} - a^{3} x^{3}\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x - 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) - 2 \, {\left(357 \, a^{3} x^{3} + 119 \, a^{2} x^{2} - 38 \, a x + 8\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{48 \, {\left(a x^{4} - x^{3}\right)}}, \frac{357 \, {\left(a^{4} x^{4} - a^{3} x^{3}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(357 \, a^{3} x^{3} + 119 \, a^{2} x^{2} - 38 \, a x + 8\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{24 \, {\left(a x^{4} - x^{3}\right)}}\right]"," ",0,"[1/48*(357*(a^4*x^4 - a^3*x^3)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x - 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) - 2*(357*a^3*x^3 + 119*a^2*x^2 - 38*a*x + 8)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^4 - x^3), 1/24*(357*(a^4*x^4 - a^3*x^3)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (357*a^3*x^3 + 119*a^2*x^2 - 38*a*x + 8)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^4 - x^3)]","A",0
358,1,294,0,0.598889," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{3345 \, {\left(a^{5} x^{5} - a^{4} x^{4}\right)} \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + a c x + 2 \, \sqrt{-a c x + c} {\left(a x + 1\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, c}{a x^{2} - x}\right) + 2 \, {\left(3345 \, a^{4} x^{4} + 1115 \, a^{3} x^{3} - 446 \, a^{2} x^{2} + 200 \, a x - 48\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{384 \, {\left(a x^{5} - x^{4}\right)}}, -\frac{3345 \, {\left(a^{5} x^{5} - a^{4} x^{4}\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x + c} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}}}{a c x - c}\right) - {\left(3345 \, a^{4} x^{4} + 1115 \, a^{3} x^{3} - 446 \, a^{2} x^{2} + 200 \, a x - 48\right)} \sqrt{-a c x + c} \sqrt{\frac{a x - 1}{a x + 1}}}{192 \, {\left(a x^{5} - x^{4}\right)}}\right]"," ",0,"[1/384*(3345*(a^5*x^5 - a^4*x^4)*sqrt(-c)*log(-(a^2*c*x^2 + a*c*x + 2*sqrt(-a*c*x + c)*(a*x + 1)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1)) - 2*c)/(a*x^2 - x)) + 2*(3345*a^4*x^4 + 1115*a^3*x^3 - 446*a^2*x^2 + 200*a*x - 48)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^5 - x^4), -1/192*(3345*(a^5*x^5 - a^4*x^4)*sqrt(c)*arctan(sqrt(-a*c*x + c)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))/(a*c*x - c)) - (3345*a^4*x^4 + 1115*a^3*x^3 - 446*a^2*x^2 + 200*a*x - 48)*sqrt(-a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a*x^5 - x^4)]","A",0
359,0,0,0,0.547678," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(2+1/2*n),x, algorithm=""fricas"")","{\rm integral}\left({\left(-a c x + c\right)}^{\frac{1}{2} \, n + 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral((-a*c*x + c)^(1/2*n + 2)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
360,0,0,0,0.543677," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(1+1/2*n),x, algorithm=""fricas"")","{\rm integral}\left({\left(-a c x + c\right)}^{\frac{1}{2} \, n + 1} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral((-a*c*x + c)^(1/2*n + 1)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
361,0,0,0,0.498966," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(1/2*n),x, algorithm=""fricas"")","{\rm integral}\left({\left(-a c x + c\right)}^{\frac{1}{2} \, n} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral((-a*c*x + c)^(1/2*n)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
362,0,0,0,0.492923," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(-1+1/2*n),x, algorithm=""fricas"")","{\rm integral}\left({\left(-a c x + c\right)}^{\frac{1}{2} \, n - 1} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral((-a*c*x + c)^(1/2*n - 1)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
363,0,0,0,0.516318," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(-2+1/2*n),x, algorithm=""fricas"")","{\rm integral}\left({\left(-a c x + c\right)}^{\frac{1}{2} \, n - 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral((-a*c*x + c)^(1/2*n - 2)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
364,0,0,0,0.596991," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(-a c x + c\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral((-a*c*x + c)^p*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
365,0,0,0,0.584724," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{3} c^{3} x^{3} - 3 \, a^{2} c^{3} x^{2} + 3 \, a c^{3} x - c^{3}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(-(a^3*c^3*x^3 - 3*a^2*c^3*x^2 + 3*a*c^3*x - c^3)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
366,0,0,0,0.560557," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c^{2} x^{2} - 2 \, a c^{2} x + c^{2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral((a^2*c^2*x^2 - 2*a*c^2*x + c^2)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
367,0,0,0,0.525768," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c x - c\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(-(a*c*x - c)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
368,0,0,0,0.557866," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c x - c}, x\right)"," ",0,"integral(-((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c*x - c), x)","F",0
369,1,59,0,0.441257," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^2,x, algorithm=""fricas"")","-\frac{{\left(a x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{2} n - 2 \, a c^{2} - {\left(a^{2} c^{2} n - 2 \, a^{2} c^{2}\right)} x}"," ",0,"-(a*x + 1)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^2*n - 2*a*c^2 - (a^2*c^2*n - 2*a^2*c^2)*x)","A",0
370,1,125,0,0.535356," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} x^{2} + {\left(a n - 2 \, a\right)} x + n - 3\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{3} n^{2} - 6 \, a c^{3} n + 8 \, a c^{3} + {\left(a^{3} c^{3} n^{2} - 6 \, a^{3} c^{3} n + 8 \, a^{3} c^{3}\right)} x^{2} - 2 \, {\left(a^{2} c^{3} n^{2} - 6 \, a^{2} c^{3} n + 8 \, a^{2} c^{3}\right)} x}"," ",0,"-(a^2*x^2 + (a*n - 2*a)*x + n - 3)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^3*n^2 - 6*a*c^3*n + 8*a*c^3 + (a^3*c^3*n^2 - 6*a^3*c^3*n + 8*a^3*c^3)*x^2 - 2*(a^2*c^3*n^2 - 6*a^2*c^3*n + 8*a^2*c^3)*x)","A",0
371,1,229,0,0.909283," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^4,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{3} x^{3} + 2 \, {\left(a^{2} n - 3 \, a^{2}\right)} x^{2} + n^{2} + {\left(a n^{2} - 6 \, a n + 6 \, a\right)} x - 8 \, n + 14\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{4} n^{3} - 12 \, a c^{4} n^{2} + 44 \, a c^{4} n - 48 \, a c^{4} - {\left(a^{4} c^{4} n^{3} - 12 \, a^{4} c^{4} n^{2} + 44 \, a^{4} c^{4} n - 48 \, a^{4} c^{4}\right)} x^{3} + 3 \, {\left(a^{3} c^{4} n^{3} - 12 \, a^{3} c^{4} n^{2} + 44 \, a^{3} c^{4} n - 48 \, a^{3} c^{4}\right)} x^{2} - 3 \, {\left(a^{2} c^{4} n^{3} - 12 \, a^{2} c^{4} n^{2} + 44 \, a^{2} c^{4} n - 48 \, a^{2} c^{4}\right)} x}"," ",0,"-(2*a^3*x^3 + 2*(a^2*n - 3*a^2)*x^2 + n^2 + (a*n^2 - 6*a*n + 6*a)*x - 8*n + 14)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^4*n^3 - 12*a*c^4*n^2 + 44*a*c^4*n - 48*a*c^4 - (a^4*c^4*n^3 - 12*a^4*c^4*n^2 + 44*a^4*c^4*n - 48*a^4*c^4)*x^3 + 3*(a^3*c^4*n^3 - 12*a^3*c^4*n^2 + 44*a^3*c^4*n - 48*a^3*c^4)*x^2 - 3*(a^2*c^4*n^3 - 12*a^2*c^4*n^2 + 44*a^2*c^4*n - 48*a^2*c^4)*x)","A",0
372,0,0,0,0.528478," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c^{2} x^{2} - 2 \, a c^{2} x + c^{2}\right)} \sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral((a^2*c^2*x^2 - 2*a*c^2*x + c^2)*sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
373,0,0,0,0.609084," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c x - c\right)} \sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(-(a*c*x - c)*sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
374,0,0,0,0.514167," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
375,0,0,0,0.694984," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c x - c}, x\right)"," ",0,"integral(-sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c*x - c), x)","F",0
376,0,0,0,0.625445," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{2} c^{2} x^{2} - 2 \, a c^{2} x + c^{2}}, x\right)"," ",0,"integral(sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^2*c^2*x^2 - 2*a*c^2*x + c^2), x)","F",0
377,0,0,0,0.615102," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{3} c^{3} x^{3} - 3 \, a^{2} c^{3} x^{2} + 3 \, a c^{3} x - c^{3}}, x\right)"," ",0,"integral(-sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^3*c^3*x^3 - 3*a^2*c^3*x^2 + 3*a*c^3*x - c^3), x)","F",0
378,0,0,0,0.573406," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{4} c^{4} x^{4} - 4 \, a^{3} c^{4} x^{3} + 6 \, a^{2} c^{4} x^{2} - 4 \, a c^{4} x + c^{4}}, x\right)"," ",0,"integral(sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^4*c^4*x^4 - 4*a^3*c^4*x^3 + 6*a^2*c^4*x^2 - 4*a*c^4*x + c^4), x)","F",0
379,1,156,0,0.436155," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^4,x, algorithm=""fricas"")","\frac{6 \, a^{3} c^{4} x^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 18 \, a^{3} c^{4} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 18 \, a^{3} c^{4} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(6 \, a^{4} c^{4} x^{4} + 22 \, a^{3} c^{4} x^{3} + 7 \, a^{2} c^{4} x^{2} - 7 \, a c^{4} x + 2 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a^{4} x^{3}}"," ",0,"1/6*(6*a^3*c^4*x^3*arctan(sqrt((a*x - 1)/(a*x + 1))) - 18*a^3*c^4*x^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 18*a^3*c^4*x^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (6*a^4*c^4*x^4 + 22*a^3*c^4*x^3 + 7*a^2*c^4*x^2 - 7*a*c^4*x + 2*c^4)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*x^3)","A",0
380,1,146,0,0.472198," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^3,x, algorithm=""fricas"")","-\frac{2 \, a^{2} c^{3} x^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 4 \, a^{2} c^{3} x^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 4 \, a^{2} c^{3} x^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(2 \, a^{3} c^{3} x^{3} + 6 \, a^{2} c^{3} x^{2} + 3 \, a c^{3} x - c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, a^{3} x^{2}}"," ",0,"-1/2*(2*a^2*c^3*x^2*arctan(sqrt((a*x - 1)/(a*x + 1))) + 4*a^2*c^3*x^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 4*a^2*c^3*x^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (2*a^3*c^3*x^3 + 6*a^2*c^3*x^2 + 3*a*c^3*x - c^3)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*x^2)","A",0
381,1,119,0,0.416629," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^2,x, algorithm=""fricas"")","-\frac{2 \, a c^{2} x \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + a c^{2} x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - a c^{2} x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(a^{2} c^{2} x^{2} + 2 \, a c^{2} x + c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x}"," ",0,"-(2*a*c^2*x*arctan(sqrt((a*x - 1)/(a*x + 1))) + a*c^2*x*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - a*c^2*x*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (a^2*c^2*x^2 + 2*a*c^2*x + c^2)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x)","B",0
382,1,48,0,0.558675," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x),x, algorithm=""fricas"")","-\frac{2 \, c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - {\left(a c x + c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a}"," ",0,"-(2*c*arctan(sqrt((a*x - 1)/(a*x + 1))) - (a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
383,1,94,0,0.538976," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x),x, algorithm=""fricas"")","\frac{2 \, {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 2 \, {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a^{2} x^{2} - 2 \, a x - 3\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c x - a c}"," ",0,"(2*(a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 2*(a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a^2*x^2 - 2*a*x - 3)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c*x - a*c)","A",0
384,1,134,0,0.732701," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^2,x, algorithm=""fricas"")","\frac{9 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 9 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(3 \, a^{3} x^{3} - 16 \, a^{2} x^{2} - 5 \, a x + 14\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"1/3*(9*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 9*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (3*a^3*x^3 - 16*a^2*x^2 - 5*a*x + 14)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)","A",0
385,1,170,0,0.579575," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^3,x, algorithm=""fricas"")","\frac{60 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 60 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(15 \, a^{4} x^{4} - 134 \, a^{3} x^{3} + 73 \, a^{2} x^{2} + 128 \, a x - 94\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\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,"1/15*(60*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 60*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (15*a^4*x^4 - 134*a^3*x^3 + 73*a^2*x^2 + 128*a*x - 94)*sqrt((a*x - 1)/(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
386,1,204,0,0.569518," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^4,x, algorithm=""fricas"")","\frac{525 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 525 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(105 \, a^{5} x^{5} - 1339 \, a^{4} x^{4} + 1812 \, a^{3} x^{3} + 485 \, a^{2} x^{2} - 1947 \, a x + 824\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{105 \, {\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,"1/105*(525*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 525*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (105*a^5*x^5 - 1339*a^4*x^4 + 1812*a^3*x^3 + 485*a^2*x^2 - 1947*a*x + 824)*sqrt((a*x - 1)/(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
387,1,67,0,0.532549," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^5,x, algorithm=""fricas"")","\frac{4 \, a^{5} c^{5} x^{5} - 12 \, a^{4} c^{5} x^{4} \log\left(x\right) - 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,"1/4*(4*a^5*c^5*x^5 - 12*a^4*c^5*x^4*log(x) - 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
388,1,43,0,0.623102," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^4,x, algorithm=""fricas"")","\frac{3 \, a^{4} c^{4} x^{4} - 6 \, a^{3} c^{4} x^{3} \log\left(x\right) - 3 \, a c^{4} x + c^{4}}{3 \, a^{4} x^{3}}"," ",0,"1/3*(3*a^4*c^4*x^4 - 6*a^3*c^4*x^3*log(x) - 3*a*c^4*x + c^4)/(a^4*x^3)","A",0
389,1,45,0,0.734740," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} c^{3} x^{3} - 2 \, a^{2} c^{3} x^{2} \log\left(x\right) + 2 \, a c^{3} x - c^{3}}{2 \, a^{3} x^{2}}"," ",0,"1/2*(2*a^3*c^3*x^3 - 2*a^2*c^3*x^2*log(x) + 2*a*c^3*x - c^3)/(a^3*x^2)","A",0
390,1,21,0,0.489697," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^2,x, algorithm=""fricas"")","\frac{a^{2} c^{2} x^{2} + c^{2}}{a^{2} x}"," ",0,"(a^2*c^2*x^2 + c^2)/(a^2*x)","A",0
391,1,13,0,0.658834," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x),x, algorithm=""fricas"")","\frac{a c x + c \log\left(x\right)}{a}"," ",0,"(a*c*x + c*log(x))/a","A",0
392,1,40,0,0.562028," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x),x, algorithm=""fricas"")","\frac{a^{2} x^{2} - a x + 3 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 2}{a^{2} c x - a c}"," ",0,"(a^2*x^2 - a*x + 3*(a*x - 1)*log(a*x - 1) - 2)/(a^2*c*x - a*c)","A",0
393,1,70,0,0.561728," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^2,x, algorithm=""fricas"")","\frac{a^{3} x^{3} - 2 \, a^{2} x^{2} - 4 \, a x + 4 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x - 1\right) + 4}{a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}}"," ",0,"(a^3*x^3 - 2*a^2*x^2 - 4*a*x + 4*(a^2*x^2 - 2*a*x + 1)*log(a*x - 1) + 4)/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)","A",0
394,1,100,0,0.493449," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^3,x, algorithm=""fricas"")","\frac{6 \, a^{4} x^{4} - 18 \, a^{3} x^{3} - 36 \, a^{2} x^{2} + 81 \, a x + 30 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(a x - 1\right) - 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)}}"," ",0,"1/6*(6*a^4*x^4 - 18*a^3*x^3 - 36*a^2*x^2 + 81*a*x + 30*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(a*x - 1) - 37)/(a^4*c^3*x^3 - 3*a^3*c^3*x^2 + 3*a^2*c^3*x - a*c^3)","A",0
395,1,126,0,1.503222," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^4,x, algorithm=""fricas"")","\frac{2 \, a^{5} x^{5} - 8 \, a^{4} x^{4} - 16 \, a^{3} x^{3} + 60 \, a^{2} x^{2} - 56 \, a x + 12 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(a x - 1\right) + 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)}}"," ",0,"1/2*(2*a^5*x^5 - 8*a^4*x^4 - 16*a^3*x^3 + 60*a^2*x^2 - 56*a*x + 12*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(a*x - 1) + 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)","A",0
396,1,156,0,0.745952," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^4,x, algorithm=""fricas"")","-\frac{18 \, a^{3} c^{4} x^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 6 \, a^{3} c^{4} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 6 \, a^{3} c^{4} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(6 \, a^{4} c^{4} x^{4} + 14 \, a^{3} c^{4} x^{3} + 11 \, a^{2} c^{4} x^{2} + a c^{4} x - 2 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a^{4} x^{3}}"," ",0,"-1/6*(18*a^3*c^4*x^3*arctan(sqrt((a*x - 1)/(a*x + 1))) + 6*a^3*c^4*x^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 6*a^3*c^4*x^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (6*a^4*c^4*x^4 + 14*a^3*c^4*x^3 + 11*a^2*c^4*x^2 + a*c^4*x - 2*c^4)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*x^3)","A",0
397,1,85,0,0.491700," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^3,x, algorithm=""fricas"")","-\frac{6 \, a^{2} c^{3} x^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - {\left(2 \, a^{3} c^{3} x^{3} + 2 \, a^{2} c^{3} x^{2} + a c^{3} x + c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, a^{3} x^{2}}"," ",0,"-1/2*(6*a^2*c^3*x^2*arctan(sqrt((a*x - 1)/(a*x + 1))) - (2*a^3*c^3*x^3 + 2*a^2*c^3*x^2 + a*c^3*x + c^3)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*x^2)","A",0
398,1,114,0,0.528653," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^2,x, algorithm=""fricas"")","-\frac{2 \, a c^{2} x \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - a c^{2} x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + a c^{2} x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(a^{2} c^{2} x^{2} - c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x}"," ",0,"-(2*a*c^2*x*arctan(sqrt((a*x - 1)/(a*x + 1))) - a*c^2*x*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + a*c^2*x*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (a^2*c^2*x^2 - c^2)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x)","A",0
399,1,88,0,0.598713," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x),x, algorithm=""fricas"")","\frac{2 \, c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 2 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 2 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a c x + c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a}"," ",0,"(2*c*arctan(sqrt((a*x - 1)/(a*x + 1))) + 2*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 2*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
400,1,128,0,0.576465," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x),x, algorithm=""fricas"")","\frac{12 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 12 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(3 \, a^{3} x^{3} - 23 \, a^{2} x^{2} - 7 \, a x + 19\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c x^{2} - 2 \, a^{2} c x + a c\right)}}"," ",0,"1/3*(12*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 12*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (3*a^3*x^3 - 23*a^2*x^2 - 7*a*x + 19)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c*x^2 - 2*a^2*c*x + a*c)","A",0
401,1,170,0,0.474236," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^2,x, algorithm=""fricas"")","\frac{75 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 75 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(15 \, a^{4} x^{4} - 173 \, a^{3} x^{3} + 91 \, a^{2} x^{2} + 161 \, a x - 118\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\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,"1/15*(75*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 75*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (15*a^4*x^4 - 173*a^3*x^3 + 91*a^2*x^2 + 161*a*x - 118)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2)","A",0
402,1,204,0,0.602440," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^3,x, algorithm=""fricas"")","\frac{42 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 42 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(7 \, a^{5} x^{5} - 109 \, a^{4} x^{4} + 145 \, a^{3} x^{3} + 39 \, a^{2} x^{2} - 156 \, a x + 66\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{7 \, {\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,"1/7*(42*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 42*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (7*a^5*x^5 - 109*a^4*x^4 + 145*a^3*x^3 + 39*a^2*x^2 - 156*a*x + 66)*sqrt((a*x - 1)/(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
403,1,240,0,0.583408," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^4,x, algorithm=""fricas"")","\frac{2205 \, {\left(a^{5} x^{5} - 5 \, a^{4} x^{4} + 10 \, a^{3} x^{3} - 10 \, a^{2} x^{2} + 5 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 2205 \, {\left(a^{5} x^{5} - 5 \, a^{4} x^{4} + 10 \, a^{3} x^{3} - 10 \, a^{2} x^{2} + 5 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(315 \, a^{6} x^{6} - 6224 \, a^{5} x^{5} + 13241 \, a^{4} x^{4} - 5567 \, a^{3} x^{3} - 10232 \, a^{2} x^{2} + 11651 \, a x - 3464\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{315 \, {\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,"1/315*(2205*(a^5*x^5 - 5*a^4*x^4 + 10*a^3*x^3 - 10*a^2*x^2 + 5*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 2205*(a^5*x^5 - 5*a^4*x^4 + 10*a^3*x^3 - 10*a^2*x^2 + 5*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (315*a^6*x^6 - 6224*a^5*x^5 + 13241*a^4*x^4 - 5567*a^3*x^3 - 10232*a^2*x^2 + 11651*a*x - 3464)*sqrt((a*x - 1)/(a*x + 1)))/(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
404,1,67,0,0.464164," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^5,x, algorithm=""fricas"")","\frac{12 \, a^{5} c^{5} x^{5} - 12 \, a^{4} c^{5} x^{4} \log\left(x\right) + 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,"1/12*(12*a^5*c^5*x^5 - 12*a^4*c^5*x^4*log(x) + 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
405,1,36,0,0.449002," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^4,x, algorithm=""fricas"")","\frac{3 \, a^{4} c^{4} x^{4} + 6 \, a^{2} c^{4} x^{2} - c^{4}}{3 \, a^{4} x^{3}}"," ",0,"1/3*(3*a^4*c^4*x^4 + 6*a^2*c^4*x^2 - c^4)/(a^4*x^3)","A",0
406,1,43,0,0.474091," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} c^{3} x^{3} + 2 \, a^{2} c^{3} x^{2} \log\left(x\right) + 2 \, a c^{3} x + c^{3}}{2 \, a^{3} x^{2}}"," ",0,"1/2*(2*a^3*c^3*x^3 + 2*a^2*c^3*x^2*log(x) + 2*a*c^3*x + c^3)/(a^3*x^2)","A",0
407,1,32,0,0.541867," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^2,x, algorithm=""fricas"")","\frac{a^{2} c^{2} x^{2} + 2 \, a c^{2} x \log\left(x\right) - c^{2}}{a^{2} x}"," ",0,"(a^2*c^2*x^2 + 2*a*c^2*x*log(x) - c^2)/(a^2*x)","A",0
408,1,23,0,0.655115," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x),x, algorithm=""fricas"")","\frac{a c x + 4 \, c \log\left(a x - 1\right) - c \log\left(x\right)}{a}"," ",0,"(a*c*x + 4*c*log(a*x - 1) - c*log(x))/a","A",0
409,1,64,0,0.539558," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x),x, algorithm=""fricas"")","\frac{a^{3} x^{3} - 2 \, a^{2} x^{2} - 7 \, a x + 5 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x - 1\right) + 6}{a^{3} c x^{2} - 2 \, a^{2} c x + a c}"," ",0,"(a^3*x^3 - 2*a^2*x^2 - 7*a*x + 5*(a^2*x^2 - 2*a*x + 1)*log(a*x - 1) + 6)/(a^3*c*x^2 - 2*a^2*c*x + a*c)","A",0
410,1,100,0,0.516345," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x)^2,x, algorithm=""fricas"")","\frac{3 \, a^{4} x^{4} - 9 \, a^{3} x^{3} - 30 \, a^{2} x^{2} + 57 \, a x + 18 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(a x - 1\right) - 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)}}"," ",0,"1/3*(3*a^4*x^4 - 9*a^3*x^3 - 30*a^2*x^2 + 57*a*x + 18*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(a*x - 1) - 25)/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2)","A",0
411,1,126,0,0.459858," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x)^3,x, algorithm=""fricas"")","\frac{6 \, a^{5} x^{5} - 24 \, a^{4} x^{4} - 78 \, a^{3} x^{3} + 243 \, a^{2} x^{2} - 218 \, a x + 42 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(a x - 1\right) + 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)}}"," ",0,"1/6*(6*a^5*x^5 - 24*a^4*x^4 - 78*a^3*x^3 + 243*a^2*x^2 - 218*a*x + 42*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(a*x - 1) + 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)","A",0
412,1,154,0,0.505146," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x)^4,x, algorithm=""fricas"")","\frac{15 \, a^{6} x^{6} - 75 \, a^{5} x^{5} - 240 \, a^{4} x^{4} + 1080 \, a^{3} x^{3} - 1480 \, a^{2} x^{2} + 890 \, a x + 120 \, {\left(a^{5} x^{5} - 5 \, a^{4} x^{4} + 10 \, a^{3} x^{3} - 10 \, a^{2} x^{2} + 5 \, a x - 1\right)} \log\left(a x - 1\right) - 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)}}"," ",0,"1/15*(15*a^6*x^6 - 75*a^5*x^5 - 240*a^4*x^4 + 1080*a^3*x^3 - 1480*a^2*x^2 + 890*a*x + 120*(a^5*x^5 - 5*a^4*x^4 + 10*a^3*x^3 - 10*a^2*x^2 + 5*a*x - 1)*log(a*x - 1) - 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)","A",0
413,1,156,0,0.580975," ","integrate((c-c/a/x)^4*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{150 \, a^{3} c^{4} x^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 30 \, a^{3} c^{4} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 30 \, a^{3} c^{4} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(6 \, a^{4} c^{4} x^{4} - 58 \, a^{3} c^{4} x^{3} - 49 \, a^{2} c^{4} x^{2} + 13 \, a c^{4} x - 2 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a^{4} x^{3}}"," ",0,"1/6*(150*a^3*c^4*x^3*arctan(sqrt((a*x - 1)/(a*x + 1))) - 30*a^3*c^4*x^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 30*a^3*c^4*x^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (6*a^4*c^4*x^4 - 58*a^3*c^4*x^3 - 49*a^2*c^4*x^2 + 13*a*c^4*x - 2*c^4)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*x^3)","A",0
414,1,143,0,0.545233," ","integrate((c-c/a/x)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{26 \, a^{2} c^{3} x^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 8 \, a^{2} c^{3} x^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 8 \, a^{2} c^{3} x^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(2 \, a^{3} c^{3} x^{3} - 6 \, a^{2} c^{3} x^{2} - 7 \, a c^{3} x + c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, a^{3} x^{2}}"," ",0,"1/2*(26*a^2*c^3*x^2*arctan(sqrt((a*x - 1)/(a*x + 1))) - 8*a^2*c^3*x^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*a^2*c^3*x^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (2*a^3*c^3*x^3 - 6*a^2*c^3*x^2 - 7*a*c^3*x + c^3)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*x^2)","A",0
415,1,113,0,0.539377," ","integrate((c-c/a/x)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{6 \, a c^{2} x \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 3 \, a c^{2} x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 3 \, a c^{2} x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a^{2} c^{2} x^{2} - c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x}"," ",0,"(6*a*c^2*x*arctan(sqrt((a*x - 1)/(a*x + 1))) - 3*a*c^2*x*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 3*a*c^2*x*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a^2*c^2*x^2 - c^2)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x)","A",0
416,1,88,0,0.517896," ","integrate((c-c/a/x)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{2 \, c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 2 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 2 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a c x + c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a}"," ",0,"(2*c*arctan(sqrt((a*x - 1)/(a*x + 1))) - 2*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 2*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
417,1,27,0,1.499554," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x),x, algorithm=""fricas"")","\frac{{\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a c}"," ",0,"(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))/(a*c)","A",0
418,1,97,0,0.799445," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^2,x, algorithm=""fricas"")","\frac{{\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a^{2} x^{2} - a x - 2\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2} x - a c^{2}}"," ",0,"((a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - (a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a^2*x^2 - a*x - 2)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c^2*x - a*c^2)","A",0
419,1,134,0,0.556189," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^3,x, algorithm=""fricas"")","\frac{6 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 6 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(3 \, a^{3} x^{3} - 11 \, a^{2} x^{2} - 4 \, a x + 10\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c^{3} x^{2} - 2 \, a^{2} c^{3} x + a c^{3}\right)}}"," ",0,"1/3*(6*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 6*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (3*a^3*x^3 - 11*a^2*x^2 - 4*a*x + 10)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^3*x^2 - 2*a^2*c^3*x + a*c^3)","A",0
420,1,170,0,0.603962," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^4,x, algorithm=""fricas"")","\frac{15 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(5 \, a^{4} x^{4} - 34 \, a^{3} x^{3} + 18 \, a^{2} x^{2} + 33 \, a x - 24\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{5 \, {\left(a^{4} c^{4} x^{3} - 3 \, a^{3} c^{4} x^{2} + 3 \, a^{2} c^{4} x - a c^{4}\right)}}"," ",0,"1/5*(15*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (5*a^4*x^4 - 34*a^3*x^3 + 18*a^2*x^2 + 33*a*x - 24)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*c^4*x^3 - 3*a^3*c^4*x^2 + 3*a^2*c^4*x - a*c^4)","A",0
421,1,71,0,0.469302," ","integrate((c-c/a/x)^4*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{3 \, a^{4} c^{4} x^{4} - 96 \, a^{3} c^{4} x^{3} \log\left(a x + 1\right) + 78 \, a^{3} c^{4} x^{3} \log\left(x\right) + 48 \, a^{2} c^{4} x^{2} - 9 \, a c^{4} x + c^{4}}{3 \, a^{4} x^{3}}"," ",0,"1/3*(3*a^4*c^4*x^4 - 96*a^3*c^4*x^3*log(a*x + 1) + 78*a^3*c^4*x^3*log(x) + 48*a^2*c^4*x^2 - 9*a*c^4*x + c^4)/(a^4*x^3)","A",0
422,1,62,0,0.491606," ","integrate((c-c/a/x)^3*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{2 \, a^{3} c^{3} x^{3} - 32 \, a^{2} c^{3} x^{2} \log\left(a x + 1\right) + 22 \, a^{2} c^{3} x^{2} \log\left(x\right) + 10 \, a c^{3} x - c^{3}}{2 \, a^{3} x^{2}}"," ",0,"1/2*(2*a^3*c^3*x^3 - 32*a^2*c^3*x^2*log(a*x + 1) + 22*a^2*c^3*x^2*log(x) + 10*a*c^3*x - c^3)/(a^3*x^2)","A",0
423,1,43,0,0.658564," ","integrate((c-c/a/x)^2*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{a^{2} c^{2} x^{2} - 8 \, a c^{2} x \log\left(a x + 1\right) + 4 \, a c^{2} x \log\left(x\right) + c^{2}}{a^{2} x}"," ",0,"(a^2*c^2*x^2 - 8*a*c^2*x*log(a*x + 1) + 4*a*c^2*x*log(x) + c^2)/(a^2*x)","A",0
424,1,22,0,0.498248," ","integrate((c-c/a/x)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{a c x - 4 \, c \log\left(a x + 1\right) + c \log\left(x\right)}{a}"," ",0,"(a*c*x - 4*c*log(a*x + 1) + c*log(x))/a","A",0
425,1,19,0,0.934204," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x),x, algorithm=""fricas"")","\frac{a x - \log\left(a x + 1\right)}{a c}"," ",0,"(a*x - log(a*x + 1))/(a*c)","A",0
426,1,27,0,0.570597," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^2,x, algorithm=""fricas"")","\frac{2 \, a x - \log\left(a x + 1\right) + \log\left(a x - 1\right)}{2 \, a c^{2}}"," ",0,"1/2*(2*a*x - log(a*x + 1) + log(a*x - 1))/(a*c^2)","A",0
427,1,59,0,0.749213," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^3,x, algorithm=""fricas"")","\frac{4 \, a^{2} x^{2} - 4 \, a x - {\left(a x - 1\right)} \log\left(a x + 1\right) + 5 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 2}{4 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"1/4*(4*a^2*x^2 - 4*a*x - (a*x - 1)*log(a*x + 1) + 5*(a*x - 1)*log(a*x - 1) - 2)/(a^2*c^3*x - a*c^3)","A",0
428,1,93,0,0.546155," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^4,x, algorithm=""fricas"")","\frac{8 \, a^{3} x^{3} - 16 \, a^{2} x^{2} - 6 \, a x - {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x + 1\right) + 17 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x - 1\right) + 12}{8 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}"," ",0,"1/8*(8*a^3*x^3 - 16*a^2*x^2 - 6*a*x - (a^2*x^2 - 2*a*x + 1)*log(a*x + 1) + 17*(a^2*x^2 - 2*a*x + 1)*log(a*x - 1) + 12)/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4)","A",0
429,1,157,0,0.576863," ","integrate((c-c/a/x)^4*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{546 \, a^{3} c^{4} x^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 42 \, a^{3} c^{4} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 42 \, a^{3} c^{4} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(6 \, a^{4} c^{4} x^{4} + 526 \, a^{3} c^{4} x^{3} + 115 \, a^{2} c^{4} x^{2} - 19 \, a c^{4} x + 2 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a^{4} x^{3}}"," ",0,"-1/6*(546*a^3*c^4*x^3*arctan(sqrt((a*x - 1)/(a*x + 1))) + 42*a^3*c^4*x^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 42*a^3*c^4*x^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (6*a^4*c^4*x^4 + 526*a^3*c^4*x^3 + 115*a^2*c^4*x^2 - 19*a*c^4*x + 2*c^4)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*x^3)","A",0
430,1,146,0,0.809259," ","integrate((c-c/a/x)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{66 \, a^{2} c^{3} x^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 12 \, a^{2} c^{3} x^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 12 \, a^{2} c^{3} x^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(2 \, a^{3} c^{3} x^{3} + 78 \, a^{2} c^{3} x^{2} + 11 \, a c^{3} x - c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{2 \, a^{3} x^{2}}"," ",0,"-1/2*(66*a^2*c^3*x^2*arctan(sqrt((a*x - 1)/(a*x + 1))) + 12*a^2*c^3*x^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 12*a^2*c^3*x^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (2*a^3*c^3*x^3 + 78*a^2*c^3*x^2 + 11*a*c^3*x - c^3)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*x^2)","A",0
431,1,120,0,0.634315," ","integrate((c-c/a/x)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{10 \, a c^{2} x \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 5 \, a c^{2} x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 5 \, a c^{2} x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(a^{2} c^{2} x^{2} + 18 \, a c^{2} x + c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x}"," ",0,"-(10*a*c^2*x*arctan(sqrt((a*x - 1)/(a*x + 1))) + 5*a*c^2*x*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 5*a*c^2*x*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (a^2*c^2*x^2 + 18*a*c^2*x + c^2)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x)","A",0
432,1,92,0,0.645730," ","integrate((c-c/a/x)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, c \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 4 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 4 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(a c x + 9 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a}"," ",0,"-(2*c*arctan(sqrt((a*x - 1)/(a*x + 1))) + 4*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 4*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (a*c*x + 9*c)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
433,1,69,0,0.582862," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x),x, algorithm=""fricas"")","\frac{{\left(a x + 3\right)} \sqrt{\frac{a x - 1}{a x + 1}} - 2 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 2 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a c}"," ",0,"((a*x + 3)*sqrt((a*x - 1)/(a*x + 1)) - 2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 2*log(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a*c)","A",0
434,1,67,0,0.602757," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^2,x, algorithm=""fricas"")","\frac{{\left(a x + 2\right)} \sqrt{\frac{a x - 1}{a x + 1}} - \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a c^{2}}"," ",0,"((a*x + 2)*sqrt((a*x - 1)/(a*x + 1)) - log(sqrt((a*x - 1)/(a*x + 1)) + 1) + log(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a*c^2)","A",0
435,1,42,0,0.532289," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^3,x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} - 2\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3} x - a c^{3}}"," ",0,"(a^2*x^2 - 2)*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^3*x - a*c^3)","A",0
436,1,134,0,0.513849," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(3 \, a^{3} x^{3} - 7 \, a^{2} x^{2} - 5 \, a x + 8\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}"," ",0,"1/3*(3*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (3*a^3*x^3 - 7*a^2*x^2 - 5*a*x + 8)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4)","A",0
437,1,170,0,0.605939," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^5,x, algorithm=""fricas"")","\frac{30 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 30 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(15 \, a^{4} x^{4} - 76 \, a^{3} x^{3} + 32 \, a^{2} x^{2} + 82 \, a x - 56\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\left(a^{4} c^{5} x^{3} - 3 \, a^{3} c^{5} x^{2} + 3 \, a^{2} c^{5} x - a c^{5}\right)}}"," ",0,"1/15*(30*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 30*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (15*a^4*x^4 - 76*a^3*x^3 + 32*a^2*x^2 + 82*a*x - 56)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*c^5*x^3 - 3*a^3*c^5*x^2 + 3*a^2*c^5*x - a*c^5)","A",0
438,1,437,0,0.559475," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(9/2),x, algorithm=""fricas"")","\left[\frac{735 \, {\left(a^{4} c^{4} x^{4} - a^{3} c^{4} x^{3}\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(105 \, a^{5} c^{4} x^{5} + 397 \, a^{4} c^{4} x^{4} - 64 \, a^{3} c^{4} x^{3} - 194 \, a^{2} c^{4} x^{2} + 132 \, a c^{4} x - 30 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{420 \, {\left(a^{5} x^{4} - a^{4} x^{3}\right)}}, \frac{735 \, {\left(a^{4} c^{4} x^{4} - a^{3} c^{4} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(105 \, a^{5} c^{4} x^{5} + 397 \, a^{4} c^{4} x^{4} - 64 \, a^{3} c^{4} x^{3} - 194 \, a^{2} c^{4} x^{2} + 132 \, a c^{4} x - 30 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{210 \, {\left(a^{5} x^{4} - a^{4} x^{3}\right)}}\right]"," ",0,"[1/420*(735*(a^4*c^4*x^4 - a^3*c^4*x^3)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(105*a^5*c^4*x^5 + 397*a^4*c^4*x^4 - 64*a^3*c^4*x^3 - 194*a^2*c^4*x^2 + 132*a*c^4*x - 30*c^4)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^5*x^4 - a^4*x^3), 1/210*(735*(a^4*c^4*x^4 - a^3*c^4*x^3)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(105*a^5*c^4*x^5 + 397*a^4*c^4*x^4 - 64*a^3*c^4*x^3 - 194*a^2*c^4*x^2 + 132*a*c^4*x - 30*c^4)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^5*x^4 - a^4*x^3)]","A",0
439,1,415,0,0.714910," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(7/2),x, algorithm=""fricas"")","\left[\frac{75 \, {\left(a^{3} c^{3} x^{3} - a^{2} c^{3} x^{2}\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(15 \, a^{4} c^{3} x^{4} + 71 \, a^{3} c^{3} x^{3} + 28 \, a^{2} c^{3} x^{2} - 22 \, a c^{3} x + 6 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{60 \, {\left(a^{4} x^{3} - a^{3} x^{2}\right)}}, \frac{75 \, {\left(a^{3} c^{3} x^{3} - a^{2} c^{3} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(15 \, a^{4} c^{3} x^{4} + 71 \, a^{3} c^{3} x^{3} + 28 \, a^{2} c^{3} x^{2} - 22 \, a c^{3} x + 6 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{30 \, {\left(a^{4} x^{3} - a^{3} x^{2}\right)}}\right]"," ",0,"[1/60*(75*(a^3*c^3*x^3 - a^2*c^3*x^2)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(15*a^4*c^3*x^4 + 71*a^3*c^3*x^3 + 28*a^2*c^3*x^2 - 22*a*c^3*x + 6*c^3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x^3 - a^3*x^2), 1/30*(75*(a^3*c^3*x^3 - a^2*c^3*x^2)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(15*a^4*c^3*x^4 + 71*a^3*c^3*x^3 + 28*a^2*c^3*x^2 - 22*a*c^3*x + 6*c^3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x^3 - a^3*x^2)]","A",0
440,1,381,0,0.728716," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{9 \, {\left(a^{2} c^{2} x^{2} - a c^{2} x\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(3 \, a^{3} c^{2} x^{3} + 13 \, a^{2} c^{2} x^{2} + 8 \, a c^{2} x - 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{12 \, {\left(a^{3} x^{2} - a^{2} x\right)}}, \frac{9 \, {\left(a^{2} c^{2} x^{2} - a c^{2} x\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(3 \, a^{3} c^{2} x^{3} + 13 \, a^{2} c^{2} x^{2} + 8 \, a c^{2} x - 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{6 \, {\left(a^{3} x^{2} - a^{2} x\right)}}\right]"," ",0,"[1/12*(9*(a^2*c^2*x^2 - a*c^2*x)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(3*a^3*c^2*x^3 + 13*a^2*c^2*x^2 + 8*a*c^2*x - 2*c^2)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2 - a^2*x), 1/6*(9*(a^2*c^2*x^2 - a*c^2*x)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(3*a^3*c^2*x^3 + 13*a^2*c^2*x^2 + 8*a*c^2*x - 2*c^2)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2 - a^2*x)]","A",0
441,1,313,0,0.605293," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a c x - c\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} c x^{2} + 3 \, a c x + 2 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, \frac{{\left(a c x - c\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} c x^{2} + 3 \, a c x + 2 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*((a*c*x - c)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*c*x^2 + 3*a*c*x + 2*c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), 1/2*((a*c*x - c)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*c*x^2 + 3*a*c*x + 2*c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","A",0
442,1,295,0,0.666798," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, -\frac{{\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) - 2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*((a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), -1/2*((a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) - 2*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","B",0
443,1,517,0,0.760029," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} + \frac{2 \, \sqrt{2} {\left(a c x - c\right)} \log\left(-\frac{17 \, a^{3} x^{3} - 3 \, a^{2} x^{2} - 13 \, a x - \frac{4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{\sqrt{c}} - 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right)}{\sqrt{c}}}{4 \, {\left(a^{2} c x - a c\right)}}, \frac{2 \, \sqrt{2} {\left(a c x - c\right)} \sqrt{-\frac{1}{c}} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{-\frac{1}{c}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} x^{2} - 2 \, a x - 1}\right) - 3 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} c x - a c\right)}}\right]"," ",0,"[1/4*(3*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) + 2*sqrt(2)*(a*c*x - c)*log(-(17*a^3*x^3 - 3*a^2*x^2 - 13*a*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/sqrt(c) - 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1))/sqrt(c))/(a^2*c*x - a*c), 1/2*(2*sqrt(2)*(a*c*x - c)*sqrt(-1/c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt(-1/c)*sqrt((a*c*x - c)/(a*x))/(3*a^2*x^2 - 2*a*x - 1)) - 3*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*c*x - a*c)]","A",0
444,1,594,0,1.636441," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{7 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 10 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 8 \, {\left(a^{3} x^{3} - a^{2} x^{2} - 2 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{8 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}, \frac{7 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 10 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 4 \, {\left(a^{3} x^{3} - a^{2} x^{2} - 2 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}\right]"," ",0,"[1/8*(7*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 10*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 8*(a^3*x^3 - a^2*x^2 - 2*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2), 1/4*(7*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 10*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 4*(a^3*x^3 - a^2*x^2 - 2*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)]","A",0
445,1,668,0,0.737828," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{79 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 112 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 8 \, {\left(8 \, a^{4} x^{4} - 27 \, a^{3} x^{3} - 12 \, a^{2} x^{2} + 23 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{64 \, {\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{79 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 112 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 4 \, {\left(8 \, a^{4} x^{4} - 27 \, a^{3} x^{3} - 12 \, a^{2} x^{2} + 23 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{32 \, {\left(a^{4} c^{3} x^{3} - 3 \, a^{3} c^{3} x^{2} + 3 \, a^{2} c^{3} x - a c^{3}\right)}}\right]"," ",0,"[1/64*(79*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 112*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 8*(8*a^4*x^4 - 27*a^3*x^3 - 12*a^2*x^2 + 23*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*c^3*x^3 - 3*a^3*c^3*x^2 + 3*a^2*c^3*x - a*c^3), 1/32*(79*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 112*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 4*(8*a^4*x^4 - 27*a^3*x^3 - 12*a^2*x^2 + 23*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*c^3*x^3 - 3*a^3*c^3*x^2 + 3*a^2*c^3*x - a*c^3)]","A",0
446,1,234,0,0.700525," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, a^{3} c^{\frac{9}{2}} x^{3} \log\left(-2 \, a c x + 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, {\left(21 \, a^{4} c^{4} x^{4} + 92 \, a^{3} c^{4} x^{3} + 4 \, a^{2} c^{4} x^{2} - 18 \, a c^{4} x + 6 \, c^{4}\right)} \sqrt{\frac{a c x - c}{a x}}}{42 \, a^{4} x^{3}}, \frac{105 \, a^{3} \sqrt{-c} c^{4} x^{3} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) + {\left(21 \, a^{4} c^{4} x^{4} + 92 \, a^{3} c^{4} x^{3} + 4 \, a^{2} c^{4} x^{2} - 18 \, a c^{4} x + 6 \, c^{4}\right)} \sqrt{\frac{a c x - c}{a x}}}{21 \, a^{4} x^{3}}\right]"," ",0,"[1/42*(105*a^3*c^(9/2)*x^3*log(-2*a*c*x + 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*(21*a^4*c^4*x^4 + 92*a^3*c^4*x^3 + 4*a^2*c^4*x^2 - 18*a*c^4*x + 6*c^4)*sqrt((a*c*x - c)/(a*x)))/(a^4*x^3), 1/21*(105*a^3*sqrt(-c)*c^4*x^3*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + (21*a^4*c^4*x^4 + 92*a^3*c^4*x^3 + 4*a^2*c^4*x^2 - 18*a*c^4*x + 6*c^4)*sqrt((a*c*x - c)/(a*x)))/(a^4*x^3)]","A",0
447,1,212,0,0.465961," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(7/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} c^{\frac{7}{2}} x^{2} \log\left(-2 \, a c x + 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, {\left(5 \, a^{3} c^{3} x^{3} + 8 \, a^{2} c^{3} x^{2} + 4 \, a c^{3} x - 2 \, c^{3}\right)} \sqrt{\frac{a c x - c}{a x}}}{10 \, a^{3} x^{2}}, \frac{15 \, a^{2} \sqrt{-c} c^{3} x^{2} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) + {\left(5 \, a^{3} c^{3} x^{3} + 8 \, a^{2} c^{3} x^{2} + 4 \, a c^{3} x - 2 \, c^{3}\right)} \sqrt{\frac{a c x - c}{a x}}}{5 \, a^{3} x^{2}}\right]"," ",0,"[1/10*(15*a^2*c^(7/2)*x^2*log(-2*a*c*x + 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*(5*a^3*c^3*x^3 + 8*a^2*c^3*x^2 + 4*a*c^3*x - 2*c^3)*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2), 1/5*(15*a^2*sqrt(-c)*c^3*x^2*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + (5*a^3*c^3*x^3 + 8*a^2*c^3*x^2 + 4*a*c^3*x - 2*c^3)*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2)]","A",0
448,1,182,0,0.600363," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, a c^{\frac{5}{2}} x \log\left(-2 \, a c x + 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, {\left(3 \, a^{2} c^{2} x^{2} - 2 \, a c^{2} x + 2 \, c^{2}\right)} \sqrt{\frac{a c x - c}{a x}}}{6 \, a^{2} x}, \frac{3 \, a \sqrt{-c} c^{2} x \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) + {\left(3 \, a^{2} c^{2} x^{2} - 2 \, a c^{2} x + 2 \, c^{2}\right)} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} x}\right]"," ",0,"[1/6*(3*a*c^(5/2)*x*log(-2*a*c*x + 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*(3*a^2*c^2*x^2 - 2*a*c^2*x + 2*c^2)*sqrt((a*c*x - c)/(a*x)))/(a^2*x), 1/3*(3*a*sqrt(-c)*c^2*x*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + (3*a^2*c^2*x^2 - 2*a*c^2*x + 2*c^2)*sqrt((a*c*x - c)/(a*x)))/(a^2*x)]","A",0
449,1,137,0,0.676180," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{c^{\frac{3}{2}} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, {\left(a c x - 2 \, c\right)} \sqrt{\frac{a c x - c}{a x}}}{2 \, a}, -\frac{\sqrt{-c} c \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) - {\left(a c x - 2 \, c\right)} \sqrt{\frac{a c x - c}{a x}}}{a}\right]"," ",0,"[1/2*(c^(3/2)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*(a*c*x - 2*c)*sqrt((a*c*x - c)/(a*x)))/a, -(sqrt(-c)*c*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - (a*c*x - 2*c)*sqrt((a*c*x - c)/(a*x)))/a]","A",0
450,1,124,0,0.399243," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a c x - c}{a x}} + 3 \, \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{2 \, a}, \frac{a x \sqrt{\frac{a c x - c}{a x}} - 3 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{a}\right]"," ",0,"[1/2*(2*a*x*sqrt((a*c*x - c)/(a*x)) + 3*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/a, (a*x*sqrt((a*c*x - c)/(a*x)) - 3*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/a]","A",0
451,1,176,0,0.516905," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{5 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, {\left(a^{2} x^{2} - 5 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} c x - a c\right)}}, -\frac{5 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) - {\left(a^{2} x^{2} - 5 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{a^{2} c x - a c}\right]"," ",0,"[1/2*(5*(a*x - 1)*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*(a^2*x^2 - 5*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^2*c*x - a*c), -(5*(a*x - 1)*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - (a^2*x^2 - 5*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^2*c*x - a*c)]","A",0
452,1,238,0,0.543503," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{21 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, {\left(3 \, a^{3} x^{3} - 28 \, a^{2} x^{2} + 21 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{6 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}, -\frac{21 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) - {\left(3 \, a^{3} x^{3} - 28 \, a^{2} x^{2} + 21 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{3 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}\right]"," ",0,"[1/6*(21*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*(3*a^3*x^3 - 28*a^2*x^2 + 21*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2), -1/3*(21*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - (3*a^3*x^3 - 28*a^2*x^2 + 21*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)]","A",0
453,1,294,0,0.483103," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{45 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, {\left(5 \, a^{4} x^{4} - 69 \, a^{3} x^{3} + 105 \, a^{2} x^{2} - 45 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{10 \, {\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{45 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) - {\left(5 \, a^{4} x^{4} - 69 \, a^{3} x^{3} + 105 \, a^{2} x^{2} - 45 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{5 \, {\left(a^{4} c^{3} x^{3} - 3 \, a^{3} c^{3} x^{2} + 3 \, a^{2} c^{3} x - a c^{3}\right)}}\right]"," ",0,"[1/10*(45*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*(5*a^4*x^4 - 69*a^3*x^3 + 105*a^2*x^2 - 45*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^4*c^3*x^3 - 3*a^3*c^3*x^2 + 3*a^2*c^3*x - a*c^3), -1/5*(45*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - (5*a^4*x^4 - 69*a^3*x^3 + 105*a^2*x^2 - 45*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^4*c^3*x^3 - 3*a^3*c^3*x^2 + 3*a^2*c^3*x - a*c^3)]","A",0
454,1,346,0,0.600719," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(7/2),x, algorithm=""fricas"")","\left[\frac{1155 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, {\left(105 \, a^{5} x^{5} - 1936 \, a^{4} x^{4} + 4466 \, a^{3} x^{3} - 3850 \, a^{2} x^{2} + 1155 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{210 \, {\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{1155 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) - {\left(105 \, a^{5} x^{5} - 1936 \, a^{4} x^{4} + 4466 \, a^{3} x^{3} - 3850 \, a^{2} x^{2} + 1155 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{105 \, {\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)}}\right]"," ",0,"[1/210*(1155*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*(105*a^5*x^5 - 1936*a^4*x^4 + 4466*a^3*x^3 - 3850*a^2*x^2 + 1155*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^5*c^4*x^4 - 4*a^4*c^4*x^3 + 6*a^3*c^4*x^2 - 4*a^2*c^4*x + a*c^4), -1/105*(1155*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - (105*a^5*x^5 - 1936*a^4*x^4 + 4466*a^3*x^3 - 3850*a^2*x^2 + 1155*a*x)*sqrt((a*c*x - c)/(a*x)))/(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
455,1,437,0,0.818931," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{4} c^{4} x^{4} - a^{3} c^{4} x^{3}\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(35 \, a^{5} c^{4} x^{5} + 199 \, a^{4} c^{4} x^{4} + 152 \, a^{3} c^{4} x^{3} - 38 \, a^{2} c^{4} x^{2} - 16 \, a c^{4} x + 10 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{140 \, {\left(a^{5} x^{4} - a^{4} x^{3}\right)}}, \frac{105 \, {\left(a^{4} c^{4} x^{4} - a^{3} c^{4} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(35 \, a^{5} c^{4} x^{5} + 199 \, a^{4} c^{4} x^{4} + 152 \, a^{3} c^{4} x^{3} - 38 \, a^{2} c^{4} x^{2} - 16 \, a c^{4} x + 10 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{70 \, {\left(a^{5} x^{4} - a^{4} x^{3}\right)}}\right]"," ",0,"[1/140*(105*(a^4*c^4*x^4 - a^3*c^4*x^3)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(35*a^5*c^4*x^5 + 199*a^4*c^4*x^4 + 152*a^3*c^4*x^3 - 38*a^2*c^4*x^2 - 16*a*c^4*x + 10*c^4)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^5*x^4 - a^4*x^3), 1/70*(105*(a^4*c^4*x^4 - a^3*c^4*x^3)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(35*a^5*c^4*x^5 + 199*a^4*c^4*x^4 + 152*a^3*c^4*x^3 - 38*a^2*c^4*x^2 - 16*a*c^4*x + 10*c^4)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^5*x^4 - a^4*x^3)]","A",0
456,1,415,0,0.637971," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(7/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{3} c^{3} x^{3} - a^{2} c^{3} x^{2}\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(15 \, a^{4} c^{3} x^{4} + 59 \, a^{3} c^{3} x^{3} + 52 \, a^{2} c^{3} x^{2} + 2 \, a c^{3} x - 6 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{60 \, {\left(a^{4} x^{3} - a^{3} x^{2}\right)}}, \frac{15 \, {\left(a^{3} c^{3} x^{3} - a^{2} c^{3} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(15 \, a^{4} c^{3} x^{4} + 59 \, a^{3} c^{3} x^{3} + 52 \, a^{2} c^{3} x^{2} + 2 \, a c^{3} x - 6 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{30 \, {\left(a^{4} x^{3} - a^{3} x^{2}\right)}}\right]"," ",0,"[1/60*(15*(a^3*c^3*x^3 - a^2*c^3*x^2)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(15*a^4*c^3*x^4 + 59*a^3*c^3*x^3 + 52*a^2*c^3*x^2 + 2*a*c^3*x - 6*c^3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x^3 - a^3*x^2), 1/30*(15*(a^3*c^3*x^3 - a^2*c^3*x^2)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(15*a^4*c^3*x^4 + 59*a^3*c^3*x^3 + 52*a^2*c^3*x^2 + 2*a*c^3*x - 6*c^3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x^3 - a^3*x^2)]","A",0
457,1,381,0,0.527845," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} c^{2} x^{2} - a c^{2} x\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(3 \, a^{3} c^{2} x^{3} + 5 \, a^{2} c^{2} x^{2} + 4 \, a c^{2} x + 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{12 \, {\left(a^{3} x^{2} - a^{2} x\right)}}, -\frac{3 \, {\left(a^{2} c^{2} x^{2} - a c^{2} x\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) - 2 \, {\left(3 \, a^{3} c^{2} x^{3} + 5 \, a^{2} c^{2} x^{2} + 4 \, a c^{2} x + 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{6 \, {\left(a^{3} x^{2} - a^{2} x\right)}}\right]"," ",0,"[1/12*(3*(a^2*c^2*x^2 - a*c^2*x)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(3*a^3*c^2*x^3 + 5*a^2*c^2*x^2 + 4*a*c^2*x + 2*c^2)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2 - a^2*x), -1/6*(3*(a^2*c^2*x^2 - a*c^2*x)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) - 2*(3*a^3*c^2*x^3 + 5*a^2*c^2*x^2 + 4*a*c^2*x + 2*c^2)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2 - a^2*x)]","A",0
458,1,315,0,0.893962," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a c x - c\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} c x^{2} - a c x - 2 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, -\frac{3 \, {\left(a c x - c\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) - 2 \, {\left(a^{2} c x^{2} - a c x - 2 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*(3*(a*c*x - c)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*c*x^2 - a*c*x - 2*c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), -1/2*(3*(a*c*x - c)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) - 2*(a^2*c*x^2 - a*c*x - 2*c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","A",0
459,1,512,0,0.729201," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 5 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, \frac{4 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 5 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*(4*sqrt(2)*(a*x - 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 5*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), 1/2*(4*sqrt(2)*(a*x - 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 5*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","A",0
460,1,581,0,0.719961," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{7 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{3} x^{3} - 2 \, a^{2} x^{2} - 3 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} + \frac{5 \, \sqrt{2} {\left(a^{2} c x^{2} - 2 \, a c x + c\right)} \log\left(-\frac{17 \, a^{3} x^{3} - 3 \, a^{2} x^{2} - 13 \, a x - \frac{4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{\sqrt{c}} - 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right)}{\sqrt{c}}}{4 \, {\left(a^{3} c x^{2} - 2 \, a^{2} c x + a c\right)}}, \frac{5 \, \sqrt{2} {\left(a^{2} c x^{2} - 2 \, a c x + c\right)} \sqrt{-\frac{1}{c}} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{-\frac{1}{c}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} x^{2} - 2 \, a x - 1}\right) - 7 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{3} x^{3} - 2 \, a^{2} x^{2} - 3 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{3} c x^{2} - 2 \, a^{2} c x + a c\right)}}\right]"," ",0,"[1/4*(7*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^3*x^3 - 2*a^2*x^2 - 3*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) + 5*sqrt(2)*(a^2*c*x^2 - 2*a*c*x + c)*log(-(17*a^3*x^3 - 3*a^2*x^2 - 13*a*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/sqrt(c) - 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1))/sqrt(c))/(a^3*c*x^2 - 2*a^2*c*x + a*c), 1/2*(5*sqrt(2)*(a^2*c*x^2 - 2*a*c*x + c)*sqrt(-1/c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt(-1/c)*sqrt((a*c*x - c)/(a*x))/(3*a^2*x^2 - 2*a*x - 1)) - 7*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^3*x^3 - 2*a^2*x^2 - 3*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*c*x^2 - 2*a^2*c*x + a*c)]","A",0
461,1,668,0,0.820556," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{51 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 72 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 8 \, {\left(4 \, a^{4} x^{4} - 19 \, a^{3} x^{3} - 8 \, a^{2} x^{2} + 15 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{32 \, {\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{51 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 72 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 4 \, {\left(4 \, a^{4} x^{4} - 19 \, a^{3} x^{3} - 8 \, a^{2} x^{2} + 15 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{16 \, {\left(a^{4} c^{2} x^{3} - 3 \, a^{3} c^{2} x^{2} + 3 \, a^{2} c^{2} x - a c^{2}\right)}}\right]"," ",0,"[1/32*(51*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 72*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 8*(4*a^4*x^4 - 19*a^3*x^3 - 8*a^2*x^2 + 15*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2), 1/16*(51*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 72*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 4*(4*a^4*x^4 - 19*a^3*x^3 - 8*a^2*x^2 + 15*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2)]","A",0
462,1,736,0,1.633997," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{747 \, \sqrt{2} {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 1056 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 8 \, {\left(48 \, a^{5} x^{5} - 367 \, a^{4} x^{4} + 139 \, a^{3} x^{3} + 335 \, a^{2} x^{2} - 219 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{384 \, {\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{747 \, \sqrt{2} {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 1056 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 4 \, {\left(48 \, a^{5} x^{5} - 367 \, a^{4} x^{4} + 139 \, a^{3} x^{3} + 335 \, a^{2} x^{2} - 219 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{192 \, {\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)}}\right]"," ",0,"[1/384*(747*sqrt(2)*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 1056*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 8*(48*a^5*x^5 - 367*a^4*x^4 + 139*a^3*x^3 + 335*a^2*x^2 - 219*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(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), 1/192*(747*sqrt(2)*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 1056*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 4*(48*a^5*x^5 - 367*a^4*x^4 + 139*a^3*x^3 + 335*a^2*x^2 - 219*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(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
463,1,415,0,0.588218," ","integrate((c-c/a/x)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\left[\frac{45 \, {\left(a^{3} c^{3} x^{3} - a^{2} c^{3} x^{2}\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(5 \, a^{4} c^{3} x^{4} - 87 \, a^{3} c^{3} x^{3} - 76 \, a^{2} c^{3} x^{2} + 14 \, a c^{3} x - 2 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{20 \, {\left(a^{4} x^{3} - a^{3} x^{2}\right)}}, \frac{45 \, {\left(a^{3} c^{3} x^{3} - a^{2} c^{3} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(5 \, a^{4} c^{3} x^{4} - 87 \, a^{3} c^{3} x^{3} - 76 \, a^{2} c^{3} x^{2} + 14 \, a c^{3} x - 2 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{10 \, {\left(a^{4} x^{3} - a^{3} x^{2}\right)}}\right]"," ",0,"[1/20*(45*(a^3*c^3*x^3 - a^2*c^3*x^2)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(5*a^4*c^3*x^4 - 87*a^3*c^3*x^3 - 76*a^2*c^3*x^2 + 14*a*c^3*x - 2*c^3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x^3 - a^3*x^2), 1/10*(45*(a^3*c^3*x^3 - a^2*c^3*x^2)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(5*a^4*c^3*x^4 - 87*a^3*c^3*x^3 - 76*a^2*c^3*x^2 + 14*a*c^3*x - 2*c^3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x^3 - a^3*x^2)]","A",0
464,1,381,0,0.658522," ","integrate((c-c/a/x)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\left[\frac{21 \, {\left(a^{2} c^{2} x^{2} - a c^{2} x\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(3 \, a^{3} c^{2} x^{3} - 19 \, a^{2} c^{2} x^{2} - 20 \, a c^{2} x + 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{12 \, {\left(a^{3} x^{2} - a^{2} x\right)}}, \frac{21 \, {\left(a^{2} c^{2} x^{2} - a c^{2} x\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(3 \, a^{3} c^{2} x^{3} - 19 \, a^{2} c^{2} x^{2} - 20 \, a c^{2} x + 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{6 \, {\left(a^{3} x^{2} - a^{2} x\right)}}\right]"," ",0,"[1/12*(21*(a^2*c^2*x^2 - a*c^2*x)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(3*a^3*c^2*x^3 - 19*a^2*c^2*x^2 - 20*a*c^2*x + 2*c^2)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2 - a^2*x), 1/6*(21*(a^2*c^2*x^2 - a*c^2*x)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(3*a^3*c^2*x^3 - 19*a^2*c^2*x^2 - 20*a*c^2*x + 2*c^2)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2 - a^2*x)]","A",0
465,1,315,0,0.467370," ","integrate((c-c/a/x)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\left[\frac{5 \, {\left(a c x - c\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} c x^{2} - a c x - 2 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, \frac{5 \, {\left(a c x - c\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} c x^{2} - a c x - 2 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*(5*(a*c*x - c)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*c*x^2 - a*c*x - 2*c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), 1/2*(5*(a*c*x - c)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*c*x^2 - a*c*x - 2*c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","A",0
466,1,297,0,0.495563," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, \frac{3 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*(3*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), 1/2*(3*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","B",0
467,1,299,0,0.745393," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} c x - a c\right)}}, \frac{{\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} c x - a c\right)}}\right]"," ",0,"[1/4*((a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*c*x - a*c), 1/2*((a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*c*x - a*c)]","B",0
468,1,522,0,0.941531," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} + \frac{\sqrt{2} {\left(a c x - c\right)} \log\left(-\frac{17 \, a^{3} x^{3} - 3 \, a^{2} x^{2} - 13 \, a x - \frac{4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{\sqrt{c}} - 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right)}{\sqrt{c}}}{4 \, {\left(a^{2} c^{2} x - a c^{2}\right)}}, \frac{\sqrt{2} {\left(a c x - c\right)} \sqrt{-\frac{1}{c}} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{-\frac{1}{c}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} x^{2} - 2 \, a x - 1}\right) - {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} c^{2} x - a c^{2}\right)}}\right]"," ",0,"[1/4*((a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) + sqrt(2)*(a*c*x - c)*log(-(17*a^3*x^3 - 3*a^2*x^2 - 13*a*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/sqrt(c) - 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1))/sqrt(c))/(a^2*c^2*x - a*c^2), 1/2*(sqrt(2)*(a*c*x - c)*sqrt(-1/c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt(-1/c)*sqrt((a*c*x - c)/(a*x))/(3*a^2*x^2 - 2*a*x - 1)) - (a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*c^2*x - a*c^2)]","A",0
469,1,596,0,0.794524," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{9 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 12 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 8 \, {\left(2 \, a^{3} x^{3} - a^{2} x^{2} - 3 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{16 \, {\left(a^{3} c^{3} x^{2} - 2 \, a^{2} c^{3} x + a c^{3}\right)}}, \frac{9 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 12 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 4 \, {\left(2 \, a^{3} x^{3} - a^{2} x^{2} - 3 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{8 \, {\left(a^{3} c^{3} x^{2} - 2 \, a^{2} c^{3} x + a c^{3}\right)}}\right]"," ",0,"[1/16*(9*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 12*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 8*(2*a^3*x^3 - a^2*x^2 - 3*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*c^3*x^2 - 2*a^2*c^3*x + a*c^3), 1/8*(9*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 12*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 4*(2*a^3*x^3 - a^2*x^2 - 3*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*c^3*x^2 - 2*a^2*c^3*x + a*c^3)]","A",0
470,1,668,0,0.698518," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(7/2),x, algorithm=""fricas"")","\left[\frac{115 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 160 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 8 \, {\left(16 \, a^{4} x^{4} - 39 \, a^{3} x^{3} - 20 \, a^{2} x^{2} + 35 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{128 \, {\left(a^{4} c^{4} x^{3} - 3 \, a^{3} c^{4} x^{2} + 3 \, a^{2} c^{4} x - a c^{4}\right)}}, \frac{115 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 160 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 4 \, {\left(16 \, a^{4} x^{4} - 39 \, a^{3} x^{3} - 20 \, a^{2} x^{2} + 35 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{64 \, {\left(a^{4} c^{4} x^{3} - 3 \, a^{3} c^{4} x^{2} + 3 \, a^{2} c^{4} x - a c^{4}\right)}}\right]"," ",0,"[1/128*(115*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 160*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 8*(16*a^4*x^4 - 39*a^3*x^3 - 20*a^2*x^2 + 35*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*c^4*x^3 - 3*a^3*c^4*x^2 + 3*a^2*c^4*x - a*c^4), 1/64*(115*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 160*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 4*(16*a^4*x^4 - 39*a^3*x^3 - 20*a^2*x^2 + 35*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*c^4*x^3 - 3*a^3*c^4*x^2 + 3*a^2*c^4*x - a*c^4)]","A",0
471,1,323,0,0.585127," ","integrate((c-c/a/x)^(7/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{480 \, \sqrt{2} a^{2} c^{\frac{7}{2}} x^{2} \log\left(-\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + 3 \, a c x - c}{a x + 1}\right) + 165 \, a^{2} c^{\frac{7}{2}} x^{2} \log\left(-2 \, a c x + 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, {\left(15 \, a^{3} c^{3} x^{3} - 376 \, a^{2} c^{3} x^{2} + 52 \, a c^{3} x - 6 \, c^{3}\right)} \sqrt{\frac{a c x - c}{a x}}}{30 \, a^{3} x^{2}}, -\frac{480 \, \sqrt{2} a^{2} \sqrt{-c} c^{3} x^{2} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) - 165 \, a^{2} \sqrt{-c} c^{3} x^{2} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) - {\left(15 \, a^{3} c^{3} x^{3} - 376 \, a^{2} c^{3} x^{2} + 52 \, a c^{3} x - 6 \, c^{3}\right)} \sqrt{\frac{a c x - c}{a x}}}{15 \, a^{3} x^{2}}\right]"," ",0,"[1/30*(480*sqrt(2)*a^2*c^(7/2)*x^2*log(-(2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + 3*a*c*x - c)/(a*x + 1)) + 165*a^2*c^(7/2)*x^2*log(-2*a*c*x + 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*(15*a^3*c^3*x^3 - 376*a^2*c^3*x^2 + 52*a*c^3*x - 6*c^3)*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2), -1/15*(480*sqrt(2)*a^2*sqrt(-c)*c^3*x^2*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - 165*a^2*sqrt(-c)*c^3*x^2*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - (15*a^3*c^3*x^3 - 376*a^2*c^3*x^2 + 52*a*c^3*x - 6*c^3)*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2)]","A",0
472,1,285,0,0.725659," ","integrate((c-c/a/x)^(5/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{48 \, \sqrt{2} a c^{\frac{5}{2}} x \log\left(-\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + 3 \, a c x - c}{a x + 1}\right) + 27 \, a c^{\frac{5}{2}} x \log\left(-2 \, a c x + 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, {\left(3 \, a^{2} c^{2} x^{2} - 26 \, a c^{2} x + 2 \, c^{2}\right)} \sqrt{\frac{a c x - c}{a x}}}{6 \, a^{2} x}, -\frac{48 \, \sqrt{2} a \sqrt{-c} c^{2} x \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) - 27 \, a \sqrt{-c} c^{2} x \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) - {\left(3 \, a^{2} c^{2} x^{2} - 26 \, a c^{2} x + 2 \, c^{2}\right)} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} x}\right]"," ",0,"[1/6*(48*sqrt(2)*a*c^(5/2)*x*log(-(2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + 3*a*c*x - c)/(a*x + 1)) + 27*a*c^(5/2)*x*log(-2*a*c*x + 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*(3*a^2*c^2*x^2 - 26*a*c^2*x + 2*c^2)*sqrt((a*c*x - c)/(a*x)))/(a^2*x), -1/3*(48*sqrt(2)*a*sqrt(-c)*c^2*x*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - 27*a*sqrt(-c)*c^2*x*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - (3*a^2*c^2*x^2 - 26*a*c^2*x + 2*c^2)*sqrt((a*c*x - c)/(a*x)))/(a^2*x)]","A",0
473,1,235,0,0.432780," ","integrate((c-c/a/x)^(3/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{2} c^{\frac{3}{2}} \log\left(-\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + 3 \, a c x - c}{a x + 1}\right) + 7 \, c^{\frac{3}{2}} \log\left(-2 \, a c x + 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, {\left(a c x - 2 \, c\right)} \sqrt{\frac{a c x - c}{a x}}}{2 \, a}, -\frac{8 \, \sqrt{2} \sqrt{-c} c \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) - 7 \, \sqrt{-c} c \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) - {\left(a c x - 2 \, c\right)} \sqrt{\frac{a c x - c}{a x}}}{a}\right]"," ",0,"[1/2*(8*sqrt(2)*c^(3/2)*log(-(2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + 3*a*c*x - c)/(a*x + 1)) + 7*c^(3/2)*log(-2*a*c*x + 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*(a*c*x - 2*c)*sqrt((a*c*x - c)/(a*x)))/a, -(8*sqrt(2)*sqrt(-c)*c*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - 7*sqrt(-c)*c*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - (a*c*x - 2*c)*sqrt((a*c*x - c)/(a*x)))/a]","A",0
474,1,219,0,0.869744," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a c x - c}{a x}} + 4 \, \sqrt{2} \sqrt{c} \log\left(-\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + 3 \, a c x - c}{a x + 1}\right) + 5 \, \sqrt{c} \log\left(-2 \, a c x + 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{2 \, a}, \frac{a x \sqrt{\frac{a c x - c}{a x}} - 4 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) + 5 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{a}\right]"," ",0,"[1/2*(2*a*x*sqrt((a*c*x - c)/(a*x)) + 4*sqrt(2)*sqrt(c)*log(-(2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + 3*a*c*x - c)/(a*x + 1)) + 5*sqrt(c)*log(-2*a*c*x + 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/a, (a*x*sqrt((a*c*x - c)/(a*x)) - 4*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + 5*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/a]","A",0
475,1,234,0,0.607589," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a c x - c}{a x}} + 2 \, \sqrt{2} \sqrt{c} \log\left(-\frac{\frac{2 \, \sqrt{2} a x \sqrt{\frac{a c x - c}{a x}}}{\sqrt{c}} + 3 \, a x - 1}{a x + 1}\right) + 3 \, \sqrt{c} \log\left(-2 \, a c x + 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{2 \, a c}, -\frac{2 \, \sqrt{2} c \sqrt{-\frac{1}{c}} \arctan\left(\frac{\sqrt{2} a x \sqrt{-\frac{1}{c}} \sqrt{\frac{a c x - c}{a x}}}{a x - 1}\right) - a x \sqrt{\frac{a c x - c}{a x}} - 3 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{a c}\right]"," ",0,"[1/2*(2*a*x*sqrt((a*c*x - c)/(a*x)) + 2*sqrt(2)*sqrt(c)*log(-(2*sqrt(2)*a*x*sqrt((a*c*x - c)/(a*x))/sqrt(c) + 3*a*x - 1)/(a*x + 1)) + 3*sqrt(c)*log(-2*a*c*x + 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/(a*c), -(2*sqrt(2)*c*sqrt(-1/c)*arctan(sqrt(2)*a*x*sqrt(-1/c)*sqrt((a*c*x - c)/(a*x))/(a*x - 1)) - a*x*sqrt((a*c*x - c)/(a*x)) - 3*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/(a*c)]","A",0
476,1,231,0,0.578744," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a c x - c}{a x}} + \sqrt{2} \sqrt{c} \log\left(-\frac{\frac{2 \, \sqrt{2} a x \sqrt{\frac{a c x - c}{a x}}}{\sqrt{c}} + 3 \, a x - 1}{a x + 1}\right) + \sqrt{c} \log\left(-2 \, a c x + 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{2 \, a c^{2}}, -\frac{\sqrt{2} c \sqrt{-\frac{1}{c}} \arctan\left(\frac{\sqrt{2} a x \sqrt{-\frac{1}{c}} \sqrt{\frac{a c x - c}{a x}}}{a x - 1}\right) - a x \sqrt{\frac{a c x - c}{a x}} - \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{a c^{2}}\right]"," ",0,"[1/2*(2*a*x*sqrt((a*c*x - c)/(a*x)) + sqrt(2)*sqrt(c)*log(-(2*sqrt(2)*a*x*sqrt((a*c*x - c)/(a*x))/sqrt(c) + 3*a*x - 1)/(a*x + 1)) + sqrt(c)*log(-2*a*c*x + 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/(a*c^2), -(sqrt(2)*c*sqrt(-1/c)*arctan(sqrt(2)*a*x*sqrt(-1/c)*sqrt((a*c*x - c)/(a*x))/(a*x - 1)) - a*x*sqrt((a*c*x - c)/(a*x)) - sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/(a*c^2)]","A",0
477,1,287,0,0.603854," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + 3 \, a c x - c}{a x + 1}\right) + 2 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 4 \, {\left(a^{2} x^{2} - 2 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}, -\frac{\sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) + 2 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) - 2 \, {\left(a^{2} x^{2} - 2 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}\right]"," ",0,"[1/4*(sqrt(2)*(a*x - 1)*sqrt(c)*log(-(2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + 3*a*c*x - c)/(a*x + 1)) + 2*(a*x - 1)*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 4*(a^2*x^2 - 2*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^2*c^3*x - a*c^3), -1/2*(sqrt(2)*(a*x - 1)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + 2*(a*x - 1)*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - 2*(a^2*x^2 - 2*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^2*c^3*x - a*c^3)]","A",0
478,1,359,0,0.525933," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(-\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + 3 \, a c x - c}{a x + 1}\right) + 36 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 4 \, {\left(6 \, a^{3} x^{3} - 29 \, a^{2} x^{2} + 21 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{24 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}, -\frac{3 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) + 36 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) - 2 \, {\left(6 \, a^{3} x^{3} - 29 \, a^{2} x^{2} + 21 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{12 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}\right]"," ",0,"[1/24*(3*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(-(2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + 3*a*c*x - c)/(a*x + 1)) + 36*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 4*(6*a^3*x^3 - 29*a^2*x^2 + 21*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4), -1/12*(3*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + 36*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - 2*(6*a^3*x^3 - 29*a^2*x^2 + 21*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4)]","A",0
479,1,431,0,0.670136," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(9/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \log\left(-\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + 3 \, a c x - c}{a x + 1}\right) + 600 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 4 \, {\left(60 \, a^{4} x^{4} - 497 \, a^{3} x^{3} + 740 \, a^{2} x^{2} - 315 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{240 \, {\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{15 \, \sqrt{2} {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) + 600 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) - 2 \, {\left(60 \, a^{4} x^{4} - 497 \, a^{3} x^{3} + 740 \, a^{2} x^{2} - 315 \, a x\right)} \sqrt{\frac{a c x - c}{a x}}}{120 \, {\left(a^{4} c^{5} x^{3} - 3 \, a^{3} c^{5} x^{2} + 3 \, a^{2} c^{5} x - a c^{5}\right)}}\right]"," ",0,"[1/240*(15*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*log(-(2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + 3*a*c*x - c)/(a*x + 1)) + 600*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 4*(60*a^4*x^4 - 497*a^3*x^3 + 740*a^2*x^2 - 315*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^4*c^5*x^3 - 3*a^3*c^5*x^2 + 3*a^2*c^5*x - a*c^5), -1/120*(15*sqrt(2)*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + 600*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - 2*(60*a^4*x^4 - 497*a^3*x^3 + 740*a^2*x^2 - 315*a*x)*sqrt((a*c*x - c)/(a*x)))/(a^4*c^5*x^3 - 3*a^3*c^5*x^2 + 3*a^2*c^5*x - a*c^5)]","A",0
480,1,437,0,0.688206," ","integrate((c-c/a/x)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{4} c^{4} x^{4} - a^{3} c^{4} x^{3}\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(7 \, a^{5} c^{4} x^{5} + 1755 \, a^{4} c^{4} x^{4} + 720 \, a^{3} c^{4} x^{3} - 110 \, a^{2} c^{4} x^{2} + 20 \, a c^{4} x - 2 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{28 \, {\left(a^{5} x^{4} - a^{4} x^{3}\right)}}, \frac{105 \, {\left(a^{4} c^{4} x^{4} - a^{3} c^{4} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(7 \, a^{5} c^{4} x^{5} + 1755 \, a^{4} c^{4} x^{4} + 720 \, a^{3} c^{4} x^{3} - 110 \, a^{2} c^{4} x^{2} + 20 \, a c^{4} x - 2 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{14 \, {\left(a^{5} x^{4} - a^{4} x^{3}\right)}}\right]"," ",0,"[1/28*(105*(a^4*c^4*x^4 - a^3*c^4*x^3)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(7*a^5*c^4*x^5 + 1755*a^4*c^4*x^4 + 720*a^3*c^4*x^3 - 110*a^2*c^4*x^2 + 20*a*c^4*x - 2*c^4)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^5*x^4 - a^4*x^3), 1/14*(105*(a^4*c^4*x^4 - a^3*c^4*x^3)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(7*a^5*c^4*x^5 + 1755*a^4*c^4*x^4 + 720*a^3*c^4*x^3 - 110*a^2*c^4*x^2 + 20*a*c^4*x - 2*c^4)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^5*x^4 - a^4*x^3)]","A",0
481,1,415,0,0.511746," ","integrate((c-c/a/x)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\left[\frac{195 \, {\left(a^{3} c^{3} x^{3} - a^{2} c^{3} x^{2}\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(15 \, a^{4} c^{3} x^{4} + 1591 \, a^{3} c^{3} x^{3} + 548 \, a^{2} c^{3} x^{2} - 62 \, a c^{3} x + 6 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{60 \, {\left(a^{4} x^{3} - a^{3} x^{2}\right)}}, \frac{195 \, {\left(a^{3} c^{3} x^{3} - a^{2} c^{3} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(15 \, a^{4} c^{3} x^{4} + 1591 \, a^{3} c^{3} x^{3} + 548 \, a^{2} c^{3} x^{2} - 62 \, a c^{3} x + 6 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{30 \, {\left(a^{4} x^{3} - a^{3} x^{2}\right)}}\right]"," ",0,"[1/60*(195*(a^3*c^3*x^3 - a^2*c^3*x^2)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(15*a^4*c^3*x^4 + 1591*a^3*c^3*x^3 + 548*a^2*c^3*x^2 - 62*a*c^3*x + 6*c^3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x^3 - a^3*x^2), 1/30*(195*(a^3*c^3*x^3 - a^2*c^3*x^2)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(15*a^4*c^3*x^4 + 1591*a^3*c^3*x^3 + 548*a^2*c^3*x^2 - 62*a*c^3*x + 6*c^3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x^3 - a^3*x^2)]","A",0
482,1,381,0,0.777601," ","integrate((c-c/a/x)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\left[\frac{33 \, {\left(a^{2} c^{2} x^{2} - a c^{2} x\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(3 \, a^{3} c^{2} x^{3} + 133 \, a^{2} c^{2} x^{2} + 32 \, a c^{2} x - 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{12 \, {\left(a^{3} x^{2} - a^{2} x\right)}}, \frac{33 \, {\left(a^{2} c^{2} x^{2} - a c^{2} x\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(3 \, a^{3} c^{2} x^{3} + 133 \, a^{2} c^{2} x^{2} + 32 \, a c^{2} x - 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{6 \, {\left(a^{3} x^{2} - a^{2} x\right)}}\right]"," ",0,"[1/12*(33*(a^2*c^2*x^2 - a*c^2*x)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(3*a^3*c^2*x^3 + 133*a^2*c^2*x^2 + 32*a*c^2*x - 2*c^2)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2 - a^2*x), 1/6*(33*(a^2*c^2*x^2 - a*c^2*x)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(3*a^3*c^2*x^3 + 133*a^2*c^2*x^2 + 32*a*c^2*x - 2*c^2)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x^2 - a^2*x)]","A",0
483,1,315,0,0.804026," ","integrate((c-c/a/x)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\left[\frac{9 \, {\left(a c x - c\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} c x^{2} + 19 \, a c x + 2 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, \frac{9 \, {\left(a c x - c\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} c x^{2} + 19 \, a c x + 2 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*(9*(a*c*x - c)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*c*x^2 + 19*a*c*x + 2*c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), 1/2*(9*(a*c*x - c)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*c*x^2 + 19*a*c*x + 2*c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","A",0
484,1,299,0,0.665152," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\left[\frac{7 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + 9 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, \frac{7 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} x^{2} + 9 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*(7*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + 9*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), 1/2*(7*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*x^2 + 9*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","A",0
485,1,303,0,1.158268," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{5 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + 5 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} c x - a c\right)}}, \frac{5 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} x^{2} + 5 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} c x - a c\right)}}\right]"," ",0,"[1/4*(5*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + 5*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*c*x - a*c), 1/2*(5*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*x^2 + 5*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*c*x - a*c)]","A",0
486,1,311,0,0.670354," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + 3 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} c^{2} x - a c^{2}\right)}}, \frac{3 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} x^{2} + 3 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} c^{2} x - a c^{2}\right)}}\right]"," ",0,"[1/4*(3*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + 3*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*c^2*x - a*c^2), 1/2*(3*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*x^2 + 3*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*c^2*x - a*c^2)]","A",0
487,1,524,0,0.687432," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 2 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 8 \, {\left(a^{2} x^{2} + 2 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{8 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}, \frac{\sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) + 2 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 4 \, {\left(a^{2} x^{2} + 2 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} c^{3} x - a c^{3}\right)}}\right]"," ",0,"[1/8*(sqrt(2)*(a*x - 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 2*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 8*(a^2*x^2 + 2*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*c^3*x - a*c^3), 1/4*(sqrt(2)*(a*x - 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) + 2*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 4*(a^2*x^2 + 2*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*c^3*x - a*c^3)]","A",0
488,1,594,0,0.765775," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(7/2),x, algorithm=""fricas"")","\left[\frac{11 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 8 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 8 \, {\left(4 \, a^{3} x^{3} + a^{2} x^{2} - 7 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{32 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}, \frac{11 \, \sqrt{2} {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 8 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 4 \, {\left(4 \, a^{3} x^{3} + a^{2} x^{2} - 7 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{16 \, {\left(a^{3} c^{4} x^{2} - 2 \, a^{2} c^{4} x + a c^{4}\right)}}\right]"," ",0,"[1/32*(11*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 8*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 8*(4*a^3*x^3 + a^2*x^2 - 7*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4), 1/16*(11*sqrt(2)*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 8*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 4*(4*a^3*x^3 + a^2*x^2 - 7*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*c^4*x^2 - 2*a^2*c^4*x + a*c^4)]","A",0
489,0,0,0,0.517470," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)} x^{m} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{a x - 1}, x\right)"," ",0,"integral((a*x + 1)*x^m*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x - 1), x)","F",0
490,1,337,0,0.646177," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(8 \, a^{4} x^{4} + 10 \, a^{3} x^{3} - a^{2} x^{2} - 3 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{96 \, {\left(a^{4} x - a^{3}\right)}}, -\frac{3 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) - 2 \, {\left(8 \, a^{4} x^{4} + 10 \, a^{3} x^{3} - a^{2} x^{2} - 3 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{48 \, {\left(a^{4} x - a^{3}\right)}}\right]"," ",0,"[1/96*(3*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(8*a^4*x^4 + 10*a^3*x^3 - a^2*x^2 - 3*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x - a^3), -1/48*(3*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) - 2*(8*a^4*x^4 + 10*a^3*x^3 - a^2*x^2 - 3*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x - a^3)]","A",0
491,1,317,0,0.667953," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{16 \, {\left(a^{3} x - a^{2}\right)}}, \frac{{\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{8 \, {\left(a^{3} x - a^{2}\right)}}\right]"," ",0,"[1/16*((a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x - a^2), 1/8*((a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x - a^2)]","A",0
492,1,295,0,0.733542," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, -\frac{{\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) - 2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*((a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), -1/2*((a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) - 2*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","B",0
493,1,275,0,0.653247," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) - 4 \, {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a x - 1\right)}}, -\frac{{\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{a x - 1}\right]"," ",0,"[1/2*((a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) - 4*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x - 1), -((a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x - 1)]","B",0
494,1,58,0,0.679184," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, {\left(a x^{2} - x\right)}}"," ",0,"-2/3*(a^2*x^2 + 2*a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x^2 - x)","A",0
495,1,68,0,0.512439," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{3} x^{3} + a^{2} x^{2} - 4 \, a x - 3\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{15 \, {\left(a x^{3} - x^{2}\right)}}"," ",0,"2/15*(2*a^3*x^3 + a^2*x^2 - 4*a*x - 3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x^3 - x^2)","A",0
496,1,77,0,0.528348," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a^{4} x^{4} + 4 \, a^{3} x^{3} - a^{2} x^{2} + 18 \, a x + 15\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{105 \, {\left(a x^{4} - x^{3}\right)}}"," ",0,"-2/105*(8*a^4*x^4 + 4*a^3*x^3 - a^2*x^2 + 18*a*x + 15)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x^4 - x^3)","A",0
497,1,84,0,0.479248," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, a^{5} x^{5} + 8 \, a^{4} x^{4} - 2 \, a^{3} x^{3} + a^{2} x^{2} - 40 \, a x - 35\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{315 \, {\left(a x^{5} - x^{4}\right)}}"," ",0,"2/315*(16*a^5*x^5 + 8*a^4*x^4 - 2*a^3*x^3 + a^2*x^2 - 40*a*x - 35)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x^5 - x^4)","A",0
498,1,179,0,0.510532," ","integrate(1/(a*x-1)*(a*x+1)*x^3*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(16 \, a^{4} x^{4} + 40 \, a^{3} x^{3} + 50 \, a^{2} x^{2} + 75 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} + 75 \, \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{128 \, a^{4}}, \frac{{\left(16 \, a^{4} x^{4} + 40 \, a^{3} x^{3} + 50 \, a^{2} x^{2} + 75 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} - 75 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{64 \, a^{4}}\right]"," ",0,"[1/128*(2*(16*a^4*x^4 + 40*a^3*x^3 + 50*a^2*x^2 + 75*a*x)*sqrt((a*c*x - c)/(a*x)) + 75*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/a^4, 1/64*((16*a^4*x^4 + 40*a^3*x^3 + 50*a^2*x^2 + 75*a*x)*sqrt((a*c*x - c)/(a*x)) - 75*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/a^4]","A",0
499,1,163,0,0.436389," ","integrate(1/(a*x-1)*(a*x+1)*x^2*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(8 \, a^{3} x^{3} + 22 \, a^{2} x^{2} + 33 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} + 33 \, \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{48 \, a^{3}}, \frac{{\left(8 \, a^{3} x^{3} + 22 \, a^{2} x^{2} + 33 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} - 33 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{24 \, a^{3}}\right]"," ",0,"[1/48*(2*(8*a^3*x^3 + 22*a^2*x^2 + 33*a*x)*sqrt((a*c*x - c)/(a*x)) + 33*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/a^3, 1/24*((8*a^3*x^3 + 22*a^2*x^2 + 33*a*x)*sqrt((a*c*x - c)/(a*x)) - 33*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/a^3]","A",0
500,1,147,0,0.624247," ","integrate(1/(a*x-1)*(a*x+1)*x*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(2 \, a^{2} x^{2} + 7 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} + 7 \, \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{8 \, a^{2}}, \frac{{\left(2 \, a^{2} x^{2} + 7 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} - 7 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{4 \, a^{2}}\right]"," ",0,"[1/8*(2*(2*a^2*x^2 + 7*a*x)*sqrt((a*c*x - c)/(a*x)) + 7*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/a^2, 1/4*((2*a^2*x^2 + 7*a*x)*sqrt((a*c*x - c)/(a*x)) - 7*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/a^2]","A",0
501,1,124,0,0.641725," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a c x - c}{a x}} + 3 \, \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{2 \, a}, \frac{a x \sqrt{\frac{a c x - c}{a x}} - 3 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{a}\right]"," ",0,"[1/2*(2*a*x*sqrt((a*c*x - c)/(a*x)) + 3*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/a, (a*x*sqrt((a*c*x - c)/(a*x)) - 3*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/a]","A",0
502,1,111,0,0.632406," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x,x, algorithm=""fricas"")","\left[\sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, \sqrt{\frac{a c x - c}{a x}}, -2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) + 2 \, \sqrt{\frac{a c x - c}{a x}}\right]"," ",0,"[sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*sqrt((a*c*x - c)/(a*x)), -2*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + 2*sqrt((a*c*x - c)/(a*x))]","A",0
503,1,28,0,0.440814," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a x + 1\right)} \sqrt{\frac{a c x - c}{a x}}}{3 \, x}"," ",0,"2/3*(5*a*x + 1)*sqrt((a*c*x - c)/(a*x))/x","A",0
504,1,36,0,0.422288," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, {\left(6 \, a^{2} x^{2} + 3 \, a x + 1\right)} \sqrt{\frac{a c x - c}{a x}}}{5 \, x^{2}}"," ",0,"2/5*(6*a^2*x^2 + 3*a*x + 1)*sqrt((a*c*x - c)/(a*x))/x^2","A",0
505,1,44,0,0.661694," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""fricas"")","\frac{2 \, {\left(104 \, a^{3} x^{3} + 52 \, a^{2} x^{2} + 39 \, a x + 15\right)} \sqrt{\frac{a c x - c}{a x}}}{105 \, x^{3}}"," ",0,"2/105*(104*a^3*x^3 + 52*a^2*x^2 + 39*a*x + 15)*sqrt((a*c*x - c)/(a*x))/x^3","A",0
506,1,52,0,0.543293," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""fricas"")","\frac{2 \, {\left(272 \, a^{4} x^{4} + 136 \, a^{3} x^{3} + 102 \, a^{2} x^{2} + 85 \, a x + 35\right)} \sqrt{\frac{a c x - c}{a x}}}{315 \, x^{4}}"," ",0,"2/315*(272*a^4*x^4 + 136*a^3*x^3 + 102*a^2*x^2 + 85*a*x + 35)*sqrt((a*c*x - c)/(a*x))/x^4","A",0
507,1,568,0,0.883073," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{768 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 1089 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(48 \, a^{5} x^{5} + 184 \, a^{4} x^{4} + 350 \, a^{3} x^{3} + 661 \, a^{2} x^{2} + 447 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{768 \, {\left(a^{5} x - a^{4}\right)}}, \frac{768 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 1089 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(48 \, a^{5} x^{5} + 184 \, a^{4} x^{4} + 350 \, a^{3} x^{3} + 661 \, a^{2} x^{2} + 447 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{384 \, {\left(a^{5} x - a^{4}\right)}}\right]"," ",0,"[1/768*(768*sqrt(2)*(a*x - 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 1089*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(48*a^5*x^5 + 184*a^4*x^4 + 350*a^3*x^3 + 661*a^2*x^2 + 447*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^5*x - a^4), 1/384*(768*sqrt(2)*(a*x - 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 1089*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(48*a^5*x^5 + 184*a^4*x^4 + 350*a^3*x^3 + 661*a^2*x^2 + 447*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^5*x - a^4)]","A",0
508,1,552,0,0.850640," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{96 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 135 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(8 \, a^{4} x^{4} + 34 \, a^{3} x^{3} + 83 \, a^{2} x^{2} + 57 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{96 \, {\left(a^{4} x - a^{3}\right)}}, \frac{96 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 135 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(8 \, a^{4} x^{4} + 34 \, a^{3} x^{3} + 83 \, a^{2} x^{2} + 57 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{48 \, {\left(a^{4} x - a^{3}\right)}}\right]"," ",0,"[1/96*(96*sqrt(2)*(a*x - 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 135*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(8*a^4*x^4 + 34*a^3*x^3 + 83*a^2*x^2 + 57*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x - a^3), 1/48*(96*sqrt(2)*(a*x - 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 135*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(8*a^4*x^4 + 34*a^3*x^3 + 83*a^2*x^2 + 57*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x - a^3)]","A",0
509,1,536,0,0.888740," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{16 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 23 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(2 \, a^{3} x^{3} + 11 \, a^{2} x^{2} + 9 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{16 \, {\left(a^{3} x - a^{2}\right)}}, \frac{16 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 23 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(2 \, a^{3} x^{3} + 11 \, a^{2} x^{2} + 9 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{8 \, {\left(a^{3} x - a^{2}\right)}}\right]"," ",0,"[1/16*(16*sqrt(2)*(a*x - 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 23*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(2*a^3*x^3 + 11*a^2*x^2 + 9*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x - a^2), 1/8*(16*sqrt(2)*(a*x - 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 23*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(2*a^3*x^3 + 11*a^2*x^2 + 9*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x - a^2)]","A",0
510,1,512,0,0.750699," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 5 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, \frac{4 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - 5 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*(4*sqrt(2)*(a*x - 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 5*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), 1/2*(4*sqrt(2)*(a*x - 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - 5*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","A",0
511,1,490,0,1.518881," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a x - 1\right)}}, \frac{2 \, \sqrt{2} {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) - {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{a x - 1}\right]"," ",0,"[1/2*(2*sqrt(2)*(a*x - 1)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + (a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x - 1), (2*sqrt(2)*(a*x - 1)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) - (a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x - 1)]","A",0
512,1,353,0,0.593040," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left(a^{2} x^{2} - a x\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 2 \, {\left(7 \, a^{2} x^{2} + 8 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, {\left(a x^{2} - x\right)}}, \frac{2 \, {\left(3 \, \sqrt{2} {\left(a^{2} x^{2} - a x\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) + {\left(7 \, a^{2} x^{2} + 8 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}\right)}}{3 \, {\left(a x^{2} - x\right)}}\right]"," ",0,"[1/3*(3*sqrt(2)*(a^2*x^2 - a*x)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 2*(7*a^2*x^2 + 8*a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x^2 - x), 2/3*(3*sqrt(2)*(a^2*x^2 - a*x)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) + (7*a^2*x^2 + 8*a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x^2 - x)]","A",0
513,1,381,0,0.528996," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 2 \, {\left(38 \, a^{3} x^{3} + 49 \, a^{2} x^{2} + 14 \, a x + 3\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{15 \, {\left(a x^{3} - x^{2}\right)}}, \frac{2 \, {\left(15 \, \sqrt{2} {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) + {\left(38 \, a^{3} x^{3} + 49 \, a^{2} x^{2} + 14 \, a x + 3\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}\right)}}{15 \, {\left(a x^{3} - x^{2}\right)}}\right]"," ",0,"[1/15*(15*sqrt(2)*(a^3*x^3 - a^2*x^2)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 2*(38*a^3*x^3 + 49*a^2*x^2 + 14*a*x + 3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x^3 - x^2), 2/15*(15*sqrt(2)*(a^3*x^3 - a^2*x^2)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) + (38*a^3*x^3 + 49*a^2*x^2 + 14*a*x + 3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x^3 - x^2)]","A",0
514,1,397,0,0.945126," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{21 \, \sqrt{2} {\left(a^{4} x^{4} - a^{3} x^{3}\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 2 \, {\left(52 \, a^{4} x^{4} + 68 \, a^{3} x^{3} + 25 \, a^{2} x^{2} + 12 \, a x + 3\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{21 \, {\left(a x^{4} - x^{3}\right)}}, \frac{2 \, {\left(21 \, \sqrt{2} {\left(a^{4} x^{4} - a^{3} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) + {\left(52 \, a^{4} x^{4} + 68 \, a^{3} x^{3} + 25 \, a^{2} x^{2} + 12 \, a x + 3\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}\right)}}{21 \, {\left(a x^{4} - x^{3}\right)}}\right]"," ",0,"[1/21*(21*sqrt(2)*(a^4*x^4 - a^3*x^3)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 2*(52*a^4*x^4 + 68*a^3*x^3 + 25*a^2*x^2 + 12*a*x + 3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x^4 - x^3), 2/21*(21*sqrt(2)*(a^4*x^4 - a^3*x^3)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) + (52*a^4*x^4 + 68*a^3*x^3 + 25*a^2*x^2 + 12*a*x + 3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x^4 - x^3)]","A",0
515,1,413,0,0.746925," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{315 \, \sqrt{2} {\left(a^{5} x^{5} - a^{4} x^{4}\right)} \sqrt{c} \log\left(-\frac{17 \, a^{3} c x^{3} - 3 \, a^{2} c x^{2} - 13 \, a c x - 4 \, \sqrt{2} {\left(3 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 2 \, {\left(788 \, a^{5} x^{5} + 1024 \, a^{4} x^{4} + 374 \, a^{3} x^{3} + 233 \, a^{2} x^{2} + 130 \, a x + 35\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{315 \, {\left(a x^{5} - x^{4}\right)}}, \frac{2 \, {\left(315 \, \sqrt{2} {\left(a^{5} x^{5} - a^{4} x^{4}\right)} \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{2} {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, a^{2} c x^{2} - 2 \, a c x - c}\right) + {\left(788 \, a^{5} x^{5} + 1024 \, a^{4} x^{4} + 374 \, a^{3} x^{3} + 233 \, a^{2} x^{2} + 130 \, a x + 35\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}\right)}}{315 \, {\left(a x^{5} - x^{4}\right)}}\right]"," ",0,"[1/315*(315*sqrt(2)*(a^5*x^5 - a^4*x^4)*sqrt(c)*log(-(17*a^3*c*x^3 - 3*a^2*c*x^2 - 13*a*c*x - 4*sqrt(2)*(3*a^3*x^3 + 4*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 2*(788*a^5*x^5 + 1024*a^4*x^4 + 374*a^3*x^3 + 233*a^2*x^2 + 130*a*x + 35)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x^5 - x^4), 2/315*(315*sqrt(2)*(a^5*x^5 - a^4*x^4)*sqrt(-c)*arctan(2*sqrt(2)*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(3*a^2*c*x^2 - 2*a*c*x - c)) + (788*a^5*x^5 + 1024*a^4*x^4 + 374*a^3*x^3 + 233*a^2*x^2 + 130*a*x + 35)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x^5 - x^4)]","A",0
516,0,0,0,0.533289," ","integrate(x^m*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}, x\right)"," ",0,"integral(x^m*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)), x)","F",0
517,1,337,0,0.720300," ","integrate(x^2*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\left[\frac{33 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(8 \, a^{4} x^{4} - 14 \, a^{3} x^{3} + 11 \, a^{2} x^{2} + 33 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{96 \, {\left(a^{4} x - a^{3}\right)}}, \frac{33 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(8 \, a^{4} x^{4} - 14 \, a^{3} x^{3} + 11 \, a^{2} x^{2} + 33 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{48 \, {\left(a^{4} x - a^{3}\right)}}\right]"," ",0,"[1/96*(33*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(8*a^4*x^4 - 14*a^3*x^3 + 11*a^2*x^2 + 33*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x - a^3), 1/48*(33*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(8*a^4*x^4 - 14*a^3*x^3 + 11*a^2*x^2 + 33*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x - a^3)]","A",0
518,1,321,0,0.873001," ","integrate(x*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\left[\frac{7 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(2 \, a^{3} x^{3} - 5 \, a^{2} x^{2} - 7 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{16 \, {\left(a^{3} x - a^{2}\right)}}, -\frac{7 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) - 2 \, {\left(2 \, a^{3} x^{3} - 5 \, a^{2} x^{2} - 7 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{8 \, {\left(a^{3} x - a^{2}\right)}}\right]"," ",0,"[1/16*(7*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(2*a^3*x^3 - 5*a^2*x^2 - 7*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x - a^2), -1/8*(7*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) - 2*(2*a^3*x^3 - 5*a^2*x^2 - 7*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x - a^2)]","A",0
519,1,297,0,0.635080," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, \frac{3 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*(3*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), 1/2*(3*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*x^2 + a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","B",0
520,1,275,0,0.448042," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a x - 1\right)}}, -\frac{{\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) - 2 \, {\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{a x - 1}\right]"," ",0,"[1/2*((a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x - 1), -((a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) - 2*(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x - 1)]","B",0
521,1,59,0,0.553923," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, a^{2} x^{2} + 4 \, a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, {\left(a x^{2} - x\right)}}"," ",0,"-2/3*(5*a^2*x^2 + 4*a*x - 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x^2 - x)","A",0
522,1,69,0,0.506562," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, {\left(6 \, a^{3} x^{3} + 3 \, a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{5 \, {\left(a x^{3} - x^{2}\right)}}"," ",0,"2/5*(6*a^3*x^3 + 3*a^2*x^2 - 2*a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x^3 - x^2)","A",0
523,1,77,0,0.510497," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(104 \, a^{4} x^{4} + 52 \, a^{3} x^{3} - 13 \, a^{2} x^{2} + 24 \, a x - 15\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{105 \, {\left(a x^{4} - x^{3}\right)}}"," ",0,"-2/105*(104*a^4*x^4 + 52*a^3*x^3 - 13*a^2*x^2 + 24*a*x - 15)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x^4 - x^3)","A",0
524,1,271,0,0.894991," ","integrate(x^3*(c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{768 \, \sqrt{2} \sqrt{c} \log\left(\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} - 3 \, a c x + c}{a x + 1}\right) + 2 \, {\left(48 \, a^{4} x^{4} - 136 \, a^{3} x^{3} + 214 \, a^{2} x^{2} - 447 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} + 1089 \, \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{384 \, a^{4}}, \frac{768 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) + {\left(48 \, a^{4} x^{4} - 136 \, a^{3} x^{3} + 214 \, a^{2} x^{2} - 447 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} - 1089 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{192 \, a^{4}}\right]"," ",0,"[1/384*(768*sqrt(2)*sqrt(c)*log((2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) - 3*a*c*x + c)/(a*x + 1)) + 2*(48*a^4*x^4 - 136*a^3*x^3 + 214*a^2*x^2 - 447*a*x)*sqrt((a*c*x - c)/(a*x)) + 1089*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/a^4, 1/192*(768*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + (48*a^4*x^4 - 136*a^3*x^3 + 214*a^2*x^2 - 447*a*x)*sqrt((a*c*x - c)/(a*x)) - 1089*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/a^4]","A",0
525,1,259,0,0.529710," ","integrate(x^2*(c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{96 \, \sqrt{2} \sqrt{c} \log\left(-\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + 3 \, a c x - c}{a x + 1}\right) + 2 \, {\left(8 \, a^{3} x^{3} - 26 \, a^{2} x^{2} + 57 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} + 135 \, \sqrt{c} \log\left(-2 \, a c x + 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{48 \, a^{3}}, -\frac{96 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) - {\left(8 \, a^{3} x^{3} - 26 \, a^{2} x^{2} + 57 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} - 135 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{24 \, a^{3}}\right]"," ",0,"[1/48*(96*sqrt(2)*sqrt(c)*log(-(2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + 3*a*c*x - c)/(a*x + 1)) + 2*(8*a^3*x^3 - 26*a^2*x^2 + 57*a*x)*sqrt((a*c*x - c)/(a*x)) + 135*sqrt(c)*log(-2*a*c*x + 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/a^3, -1/24*(96*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - (8*a^3*x^3 - 26*a^2*x^2 + 57*a*x)*sqrt((a*c*x - c)/(a*x)) - 135*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/a^3]","A",0
526,1,239,0,0.469731," ","integrate(x*(c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{16 \, \sqrt{2} \sqrt{c} \log\left(\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} - 3 \, a c x + c}{a x + 1}\right) + 2 \, {\left(2 \, a^{2} x^{2} - 9 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} + 23 \, \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{8 \, a^{2}}, \frac{16 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) + {\left(2 \, a^{2} x^{2} - 9 \, a x\right)} \sqrt{\frac{a c x - c}{a x}} - 23 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{4 \, a^{2}}\right]"," ",0,"[1/8*(16*sqrt(2)*sqrt(c)*log((2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) - 3*a*c*x + c)/(a*x + 1)) + 2*(2*a^2*x^2 - 9*a*x)*sqrt((a*c*x - c)/(a*x)) + 23*sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/a^2, 1/4*(16*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + (2*a^2*x^2 - 9*a*x)*sqrt((a*c*x - c)/(a*x)) - 23*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/a^2]","A",0
527,1,219,0,0.423569," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a c x - c}{a x}} + 4 \, \sqrt{2} \sqrt{c} \log\left(-\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + 3 \, a c x - c}{a x + 1}\right) + 5 \, \sqrt{c} \log\left(-2 \, a c x + 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right)}{2 \, a}, \frac{a x \sqrt{\frac{a c x - c}{a x}} - 4 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) + 5 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right)}{a}\right]"," ",0,"[1/2*(2*a*x*sqrt((a*c*x - c)/(a*x)) + 4*sqrt(2)*sqrt(c)*log(-(2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + 3*a*c*x - c)/(a*x + 1)) + 5*sqrt(c)*log(-2*a*c*x + 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c))/a, (a*x*sqrt((a*c*x - c)/(a*x)) - 4*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + 5*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c))/a]","A",0
528,1,203,0,0.525194," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x,x, algorithm=""fricas"")","\left[2 \, \sqrt{2} \sqrt{c} \log\left(\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} - 3 \, a c x + c}{a x + 1}\right) + \sqrt{c} \log\left(-2 \, a c x - 2 \, a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + c\right) + 2 \, \sqrt{\frac{a c x - c}{a x}}, 4 \, \sqrt{2} \sqrt{-c} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) - 2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{c}\right) + 2 \, \sqrt{\frac{a c x - c}{a x}}\right]"," ",0,"[2*sqrt(2)*sqrt(c)*log((2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) - 3*a*c*x + c)/(a*x + 1)) + sqrt(c)*log(-2*a*c*x - 2*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + c) + 2*sqrt((a*c*x - c)/(a*x)), 4*sqrt(2)*sqrt(-c)*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) - 2*sqrt(-c)*arctan(sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + 2*sqrt((a*c*x - c)/(a*x))]","A",0
529,1,161,0,0.576009," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, \sqrt{2} a \sqrt{c} x \log\left(-\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + 3 \, a c x - c}{a x + 1}\right) - {\left(7 \, a x - 1\right)} \sqrt{\frac{a c x - c}{a x}}\right)}}{3 \, x}, -\frac{2 \, {\left(6 \, \sqrt{2} a \sqrt{-c} x \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) + {\left(7 \, a x - 1\right)} \sqrt{\frac{a c x - c}{a x}}\right)}}{3 \, x}\right]"," ",0,"[2/3*(3*sqrt(2)*a*sqrt(c)*x*log(-(2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + 3*a*c*x - c)/(a*x + 1)) - (7*a*x - 1)*sqrt((a*c*x - c)/(a*x)))/x, -2/3*(6*sqrt(2)*a*sqrt(-c)*x*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + (7*a*x - 1)*sqrt((a*c*x - c)/(a*x)))/x]","A",0
530,1,181,0,0.439512," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(15 \, \sqrt{2} a^{2} \sqrt{c} x^{2} \log\left(\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} - 3 \, a c x + c}{a x + 1}\right) + {\left(38 \, a^{2} x^{2} - 11 \, a x + 3\right)} \sqrt{\frac{a c x - c}{a x}}\right)}}{15 \, x^{2}}, \frac{2 \, {\left(30 \, \sqrt{2} a^{2} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) + {\left(38 \, a^{2} x^{2} - 11 \, a x + 3\right)} \sqrt{\frac{a c x - c}{a x}}\right)}}{15 \, x^{2}}\right]"," ",0,"[2/15*(15*sqrt(2)*a^2*sqrt(c)*x^2*log((2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) - 3*a*c*x + c)/(a*x + 1)) + (38*a^2*x^2 - 11*a*x + 3)*sqrt((a*c*x - c)/(a*x)))/x^2, 2/15*(30*sqrt(2)*a^2*sqrt(-c)*x^2*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + (38*a^2*x^2 - 11*a*x + 3)*sqrt((a*c*x - c)/(a*x)))/x^2]","A",0
531,1,201,0,0.603766," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^4,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(21 \, \sqrt{2} a^{3} \sqrt{c} x^{3} \log\left(-\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} + 3 \, a c x - c}{a x + 1}\right) - {\left(52 \, a^{3} x^{3} - 16 \, a^{2} x^{2} + 9 \, a x - 3\right)} \sqrt{\frac{a c x - c}{a x}}\right)}}{21 \, x^{3}}, -\frac{2 \, {\left(42 \, \sqrt{2} a^{3} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) + {\left(52 \, a^{3} x^{3} - 16 \, a^{2} x^{2} + 9 \, a x - 3\right)} \sqrt{\frac{a c x - c}{a x}}\right)}}{21 \, x^{3}}\right]"," ",0,"[2/21*(21*sqrt(2)*a^3*sqrt(c)*x^3*log(-(2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) + 3*a*c*x - c)/(a*x + 1)) - (52*a^3*x^3 - 16*a^2*x^2 + 9*a*x - 3)*sqrt((a*c*x - c)/(a*x)))/x^3, -2/21*(42*sqrt(2)*a^3*sqrt(-c)*x^3*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + (52*a^3*x^3 - 16*a^2*x^2 + 9*a*x - 3)*sqrt((a*c*x - c)/(a*x)))/x^3]","A",0
532,1,213,0,0.470477," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^5,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(315 \, \sqrt{2} a^{4} \sqrt{c} x^{4} \log\left(\frac{2 \, \sqrt{2} a \sqrt{c} x \sqrt{\frac{a c x - c}{a x}} - 3 \, a c x + c}{a x + 1}\right) + {\left(788 \, a^{4} x^{4} - 236 \, a^{3} x^{3} + 138 \, a^{2} x^{2} - 95 \, a x + 35\right)} \sqrt{\frac{a c x - c}{a x}}\right)}}{315 \, x^{4}}, \frac{2 \, {\left(630 \, \sqrt{2} a^{4} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{2} \sqrt{-c} \sqrt{\frac{a c x - c}{a x}}}{2 \, c}\right) + {\left(788 \, a^{4} x^{4} - 236 \, a^{3} x^{3} + 138 \, a^{2} x^{2} - 95 \, a x + 35\right)} \sqrt{\frac{a c x - c}{a x}}\right)}}{315 \, x^{4}}\right]"," ",0,"[2/315*(315*sqrt(2)*a^4*sqrt(c)*x^4*log((2*sqrt(2)*a*sqrt(c)*x*sqrt((a*c*x - c)/(a*x)) - 3*a*c*x + c)/(a*x + 1)) + (788*a^4*x^4 - 236*a^3*x^3 + 138*a^2*x^2 - 95*a*x + 35)*sqrt((a*c*x - c)/(a*x)))/x^4, 2/315*(630*sqrt(2)*a^4*sqrt(-c)*x^4*arctan(1/2*sqrt(2)*sqrt(-c)*sqrt((a*c*x - c)/(a*x))/c) + (788*a^4*x^4 - 236*a^3*x^3 + 138*a^2*x^2 - 95*a*x + 35)*sqrt((a*c*x - c)/(a*x)))/x^4]","A",0
533,1,353,0,0.728485," ","integrate(x^3*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\left[\frac{3345 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(48 \, a^{5} x^{5} - 200 \, a^{4} x^{4} + 446 \, a^{3} x^{3} - 1115 \, a^{2} x^{2} - 3345 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{768 \, {\left(a^{5} x - a^{4}\right)}}, -\frac{3345 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) - 2 \, {\left(48 \, a^{5} x^{5} - 200 \, a^{4} x^{4} + 446 \, a^{3} x^{3} - 1115 \, a^{2} x^{2} - 3345 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{384 \, {\left(a^{5} x - a^{4}\right)}}\right]"," ",0,"[1/768*(3345*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(48*a^5*x^5 - 200*a^4*x^4 + 446*a^3*x^3 - 1115*a^2*x^2 - 3345*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^5*x - a^4), -1/384*(3345*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) - 2*(48*a^5*x^5 - 200*a^4*x^4 + 446*a^3*x^3 - 1115*a^2*x^2 - 3345*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^5*x - a^4)]","A",0
534,1,337,0,0.598543," ","integrate(x^2*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\left[\frac{357 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(8 \, a^{4} x^{4} - 38 \, a^{3} x^{3} + 119 \, a^{2} x^{2} + 357 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{96 \, {\left(a^{4} x - a^{3}\right)}}, \frac{357 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(8 \, a^{4} x^{4} - 38 \, a^{3} x^{3} + 119 \, a^{2} x^{2} + 357 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{48 \, {\left(a^{4} x - a^{3}\right)}}\right]"," ",0,"[1/96*(357*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(8*a^4*x^4 - 38*a^3*x^3 + 119*a^2*x^2 + 357*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x - a^3), 1/48*(357*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(8*a^4*x^4 - 38*a^3*x^3 + 119*a^2*x^2 + 357*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^4*x - a^3)]","A",0
535,1,321,0,0.531451," ","integrate(x*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\left[\frac{47 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(2 \, a^{3} x^{3} - 13 \, a^{2} x^{2} - 47 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{16 \, {\left(a^{3} x - a^{2}\right)}}, -\frac{47 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) - 2 \, {\left(2 \, a^{3} x^{3} - 13 \, a^{2} x^{2} - 47 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{8 \, {\left(a^{3} x - a^{2}\right)}}\right]"," ",0,"[1/16*(47*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(2*a^3*x^3 - 13*a^2*x^2 - 47*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x - a^2), -1/8*(47*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) - 2*(2*a^3*x^3 - 13*a^2*x^2 - 47*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^3*x - a^2)]","A",0
536,1,299,0,0.836419," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\left[\frac{7 \, {\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x - 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + 9 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{4 \, {\left(a^{2} x - a\right)}}, \frac{7 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(a^{2} x^{2} + 9 \, a x\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a^{2} x - a\right)}}\right]"," ",0,"[1/4*(7*(a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x - 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) + 4*(a^2*x^2 + 9*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a), 1/2*(7*(a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(a^2*x^2 + 9*a*x)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a^2*x - a)]","A",0
537,1,277,0,0.645435," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{c} \log\left(-\frac{8 \, a^{3} c x^{3} - 7 \, a c x + 4 \, {\left(2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + a x\right)} \sqrt{c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}} - c}{a x - 1}\right) - 4 \, {\left(5 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, {\left(a x - 1\right)}}, -\frac{{\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{2 \, {\left(a^{2} x^{2} + a x\right)} \sqrt{-c} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{2 \, a^{2} c x^{2} - a c x - c}\right) + 2 \, {\left(5 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{a x - 1}\right]"," ",0,"[1/2*((a*x - 1)*sqrt(c)*log(-(8*a^3*c*x^3 - 7*a*c*x + 4*(2*a^3*x^3 + 3*a^2*x^2 + a*x)*sqrt(c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)) - c)/(a*x - 1)) - 4*(5*a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x - 1), -((a*x - 1)*sqrt(-c)*arctan(2*(a^2*x^2 + a*x)*sqrt(-c)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(2*a^2*c*x^2 - a*c*x - c)) + 2*(5*a*x + 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x)))/(a*x - 1)]","A",0
538,1,59,0,0.497902," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""fricas"")","\frac{2 \, {\left(23 \, a^{2} x^{2} + 10 \, a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{3 \, {\left(a x^{2} - x\right)}}"," ",0,"2/3*(23*a^2*x^2 + 10*a*x - 1)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x^2 - x)","A",0
539,1,69,0,0.495649," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(158 \, a^{3} x^{3} + 79 \, a^{2} x^{2} - 16 \, a x + 3\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{15 \, {\left(a x^{3} - x^{2}\right)}}"," ",0,"-2/15*(158*a^3*x^3 + 79*a^2*x^2 - 16*a*x + 3)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x^3 - x^2)","A",0
540,1,77,0,0.817952," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""fricas"")","\frac{2 \, {\left(1336 \, a^{4} x^{4} + 668 \, a^{3} x^{3} - 167 \, a^{2} x^{2} + 66 \, a x - 15\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{105 \, {\left(a x^{4} - x^{3}\right)}}"," ",0,"2/105*(1336*a^4*x^4 + 668*a^3*x^3 - 167*a^2*x^2 + 66*a*x - 15)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x^4 - x^3)","A",0
541,1,85,0,0.547969," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(656 \, a^{5} x^{5} + 328 \, a^{4} x^{4} - 82 \, a^{3} x^{3} + 41 \, a^{2} x^{2} - 20 \, a x + 5\right)} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a c x - c}{a x}}}{45 \, {\left(a x^{5} - x^{4}\right)}}"," ",0,"-2/45*(656*a^5*x^5 + 328*a^4*x^4 - 82*a^3*x^3 + 41*a^2*x^2 - 20*a*x + 5)*sqrt((a*x - 1)/(a*x + 1))*sqrt((a*c*x - c)/(a*x))/(a*x^5 - x^4)","A",0
542,0,0,0,0.694344," ","integrate(exp(n*arccoth(a*x))*(c-c/a/x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c x - c\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a x}, x\right)"," ",0,"integral((a*c*x - c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*x), x)","F",0
543,0,0,0,0.655074," ","integrate(exp(n*arccoth(a*x))/(c-c/a/x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c x - c}, x\right)"," ",0,"integral(a*x*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c*x - c), x)","F",0
544,0,0,0,0.472641," ","integrate(exp(n*arccoth(a*x))/(c-c/a/x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{2} c^{2} x^{2} - 2 \, a c^{2} x + c^{2}}, x\right)"," ",0,"integral(a^2*x^2*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^2*c^2*x^2 - 2*a*c^2*x + c^2), x)","F",0
545,0,0,0,0.585791," ","integrate(exp(n*arccoth(a*x))*(c-c/a/x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c x - c\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n} \sqrt{\frac{a c x - c}{a x}}}{a x}, x\right)"," ",0,"integral((a*c*x - c)*((a*x - 1)/(a*x + 1))^(1/2*n)*sqrt((a*c*x - c)/(a*x))/(a*x), x)","F",0
546,0,0,0,0.566573," ","integrate(exp(n*arccoth(a*x))*(c-c/a/x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n} \sqrt{\frac{a c x - c}{a x}}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^(1/2*n)*sqrt((a*c*x - c)/(a*x)), x)","F",0
547,0,0,0,0.535283," ","integrate(exp(n*arccoth(a*x))/(c-c/a/x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n} \sqrt{\frac{a c x - c}{a x}}}{a c x - c}, x\right)"," ",0,"integral(a*x*((a*x - 1)/(a*x + 1))^(1/2*n)*sqrt((a*c*x - c)/(a*x))/(a*c*x - c), x)","F",0
548,0,0,0,0.608182," ","integrate(exp(n*arccoth(a*x))/(c-c/a/x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n} \sqrt{\frac{a c x - c}{a x}}}{a^{2} c^{2} x^{2} - 2 \, a c^{2} x + c^{2}}, x\right)"," ",0,"integral(a^2*x^2*((a*x - 1)/(a*x + 1))^(1/2*n)*sqrt((a*c*x - c)/(a*x))/(a^2*c^2*x^2 - 2*a*c^2*x + c^2), x)","F",0
549,0,0,0,0.753969," ","integrate(exp(n*arccoth(a*x))*(c-c/a/x)^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n} \left(\frac{a c x - c}{a x}\right)^{p}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^(1/2*n)*((a*c*x - c)/(a*x))^p, x)","F",0
550,0,0,0,0.411889," ","integrate(exp(2*p*arccoth(a*x))*(c-c/a/x)^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x - 1}{a x + 1}\right)^{p} \left(\frac{a c x - c}{a x}\right)^{p}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^p*((a*c*x - c)/(a*x))^p, x)","F",0
551,0,0,0,0.493130," ","integrate((c-c/a/x)^p/exp(2*p*arccoth(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a c x - c}{a x}\right)^{p}}{\left(\frac{a x - 1}{a x + 1}\right)^{p}}, x\right)"," ",0,"integral(((a*c*x - c)/(a*x))^p/((a*x - 1)/(a*x + 1))^p, x)","F",0
552,0,0,0,0.570302," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^p,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)} \left(\frac{a c x - c}{a x}\right)^{p}}{a x - 1}, x\right)"," ",0,"integral((a*x + 1)*((a*c*x - c)/(a*x))^p/(a*x - 1), x)","F",0
553,0,0,0,0.467907," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^p,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)} \left(\frac{a c x - c}{a x}\right)^{p} \sqrt{\frac{a x - 1}{a x + 1}}}{a x - 1}, x\right)"," ",0,"integral((a*x + 1)*((a*c*x - c)/(a*x))^p*sqrt((a*x - 1)/(a*x + 1))/(a*x - 1), x)","F",0
554,0,0,0,0.509504," ","integrate((c-c/a/x)^p*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a c x - c}{a x}\right)^{p} \sqrt{\frac{a x - 1}{a x + 1}}, x\right)"," ",0,"integral(((a*c*x - c)/(a*x))^p*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
555,0,0,0,0.519303," ","integrate((c-c/a/x)^p*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x - 1\right)} \left(\frac{a c x - c}{a x}\right)^{p}}{a x + 1}, x\right)"," ",0,"integral((a*x - 1)*((a*c*x - c)/(a*x))^p/(a*x + 1), x)","F",0
556,1,169,0,0.550249," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","\frac{315 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 315 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(128 \, a^{9} c^{4} x^{9} + 272 \, a^{8} c^{4} x^{8} - 368 \, a^{7} c^{4} x^{7} - 1112 \, a^{6} c^{4} x^{6} + 168 \, a^{5} c^{4} x^{5} + 1746 \, a^{4} c^{4} x^{4} + 466 \, a^{3} c^{4} x^{3} - 1349 \, a^{2} c^{4} x^{2} - 709 \, a c^{4} x + 128 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{1152 \, a}"," ",0,"1/1152*(315*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 315*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (128*a^9*c^4*x^9 + 272*a^8*c^4*x^8 - 368*a^7*c^4*x^7 - 1112*a^6*c^4*x^6 + 168*a^5*c^4*x^5 + 1746*a^4*c^4*x^4 + 466*a^3*c^4*x^3 - 1349*a^2*c^4*x^2 - 709*a*c^4*x + 128*c^4)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
557,1,148,0,0.567384," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(48 \, a^{7} c^{3} x^{7} + 104 \, a^{6} c^{3} x^{6} - 88 \, a^{5} c^{3} x^{5} - 326 \, a^{4} c^{3} x^{4} - 38 \, a^{3} c^{3} x^{3} + 375 \, a^{2} c^{3} x^{2} + 183 \, a c^{3} x - 48 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{336 \, a}"," ",0,"1/336*(105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (48*a^7*c^3*x^7 + 104*a^6*c^3*x^6 - 88*a^5*c^3*x^5 - 326*a^4*c^3*x^4 - 38*a^3*c^3*x^3 + 375*a^2*c^3*x^2 + 183*a*c^3*x - 48*c^3)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
558,1,125,0,0.574197," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(8 \, a^{5} c^{2} x^{5} + 18 \, a^{4} c^{2} x^{4} - 6 \, a^{3} c^{2} x^{3} - 41 \, a^{2} c^{2} x^{2} - 17 \, a c^{2} x + 8 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{40 \, a}"," ",0,"1/40*(15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (8*a^5*c^2*x^5 + 18*a^4*c^2*x^4 - 6*a^3*c^2*x^3 - 41*a^2*c^2*x^2 - 17*a*c^2*x + 8*c^2)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
559,1,91,0,0.563872," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(2 \, a^{3} c x^{3} + 5 \, a^{2} c x^{2} + a c x - 2 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a}"," ",0,"1/6*(3*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (2*a^3*c*x^3 + 5*a^2*c*x^2 + a*c*x - 2*c)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
560,1,34,0,0.787604," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{{\left(a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c x - a c}"," ",0,"(a*x + 1)*sqrt((a*x - 1)/(a*x + 1))/(a^2*c*x - a*c)","A",0
561,1,58,0,0.484254," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} x^{2} - 2 \, a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"1/3*(2*a^2*x^2 - 2*a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)","A",0
562,1,86,0,0.524209," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{{\left(8 \, a^{4} x^{4} - 8 \, a^{3} x^{3} - 12 \, a^{2} x^{2} + 12 \, a x + 3\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{4} c^{3} x^{3} + 2 \, a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"1/15*(8*a^4*x^4 - 8*a^3*x^3 - 12*a^2*x^2 + 12*a*x + 3)*sqrt((a*x - 1)/(a*x + 1))/(a^5*c^3*x^4 - 2*a^4*c^3*x^3 + 2*a^2*c^3*x - a*c^3)","A",0
563,1,134,0,0.554894," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","\frac{{\left(16 \, a^{6} x^{6} - 16 \, a^{5} x^{5} - 40 \, a^{4} x^{4} + 40 \, a^{3} x^{3} + 30 \, a^{2} x^{2} - 30 \, a x - 5\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\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)}}"," ",0,"1/35*(16*a^6*x^6 - 16*a^5*x^5 - 40*a^4*x^4 + 40*a^3*x^3 + 30*a^2*x^2 - 30*a*x - 5)*sqrt((a*x - 1)/(a*x + 1))/(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)","A",0
564,1,113,0,0.447334," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^5,x, algorithm=""fricas"")","-\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
565,1,82,0,0.532365," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","\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
566,1,70,0,0.501052," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\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
567,1,38,0,0.523919," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\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
568,1,21,0,0.523614," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c),x, algorithm=""fricas"")","-\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
569,1,13,0,0.493806," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{1}{a^{2} c x - a c}"," ",0,"1/(a^2*c*x - a*c)","A",0
570,1,76,0,0.427861," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{2 \, a x - {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x + 1\right) + {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x - 1\right) - 4}{8 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"1/8*(2*a*x - (a^2*x^2 - 2*a*x + 1)*log(a*x + 1) + (a^2*x^2 - 2*a*x + 1)*log(a*x - 1) - 4)/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)","A",0
571,1,121,0,0.432160," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{6 \, a^{3} x^{3} - 12 \, a^{2} x^{2} + 2 \, a x - 3 \, {\left(a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a x - 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a x - 1\right)} \log\left(a x - 1\right) + 8}{24 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{4} c^{3} x^{3} + 2 \, a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"1/24*(6*a^3*x^3 - 12*a^2*x^2 + 2*a*x - 3*(a^4*x^4 - 2*a^3*x^3 + 2*a*x - 1)*log(a*x + 1) + 3*(a^4*x^4 - 2*a^3*x^3 + 2*a*x - 1)*log(a*x - 1) + 8)/(a^5*c^3*x^4 - 2*a^4*c^3*x^3 + 2*a^2*c^3*x - a*c^3)","A",0
572,1,217,0,0.604913," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","\frac{30 \, a^{5} x^{5} - 60 \, a^{4} x^{4} - 20 \, a^{3} x^{3} + 100 \, a^{2} x^{2} - 34 \, a x - 15 \, {\left(a^{6} x^{6} - 2 \, a^{5} x^{5} - a^{4} x^{4} + 4 \, a^{3} x^{3} - a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x + 1\right) + 15 \, {\left(a^{6} x^{6} - 2 \, a^{5} x^{5} - a^{4} x^{4} + 4 \, a^{3} x^{3} - a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x - 1\right) - 32}{128 \, {\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)}}"," ",0,"1/128*(30*a^5*x^5 - 60*a^4*x^4 - 20*a^3*x^3 + 100*a^2*x^2 - 34*a*x - 15*(a^6*x^6 - 2*a^5*x^5 - a^4*x^4 + 4*a^3*x^3 - a^2*x^2 - 2*a*x + 1)*log(a*x + 1) + 15*(a^6*x^6 - 2*a^5*x^5 - a^4*x^4 + 4*a^3*x^3 - a^2*x^2 - 2*a*x + 1)*log(a*x - 1) - 32)/(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)","B",0
573,1,170,0,0.714659," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","-\frac{3465 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3465 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(896 \, a^{9} c^{4} x^{9} + 3920 \, a^{8} c^{4} x^{8} + 4048 \, a^{7} c^{4} x^{7} - 6200 \, a^{6} c^{4} x^{6} - 15672 \, a^{5} c^{4} x^{5} - 5382 \, a^{4} c^{4} x^{4} + 13306 \, a^{3} c^{4} x^{3} + 14839 \, a^{2} c^{4} x^{2} + 887 \, a c^{4} x - 3712 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{8064 \, a}"," ",0,"-1/8064*(3465*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3465*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (896*a^9*c^4*x^9 + 3920*a^8*c^4*x^8 + 4048*a^7*c^4*x^7 - 6200*a^6*c^4*x^6 - 15672*a^5*c^4*x^5 - 5382*a^4*c^4*x^4 + 13306*a^3*c^4*x^3 + 14839*a^2*c^4*x^2 + 887*a*c^4*x - 3712*c^4)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
574,1,147,0,0.676219," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(80 \, a^{7} c^{3} x^{7} + 360 \, a^{6} c^{3} x^{6} + 488 \, a^{5} c^{3} x^{5} - 142 \, a^{4} c^{3} x^{4} - 1006 \, a^{3} c^{3} x^{3} - 901 \, a^{2} c^{3} x^{2} + 123 \, a c^{3} x + 368 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{560 \, a}"," ",0,"-1/560*(315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (80*a^7*c^3*x^7 + 360*a^6*c^3*x^6 + 488*a^5*c^3*x^5 - 142*a^4*c^3*x^4 - 1006*a^3*c^3*x^3 - 901*a^2*c^3*x^2 + 123*a*c^3*x + 368*c^3)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
575,1,126,0,0.472380," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\frac{105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(24 \, a^{5} c^{2} x^{5} + 114 \, a^{4} c^{2} x^{4} + 202 \, a^{3} c^{2} x^{3} + 127 \, a^{2} c^{2} x^{2} - 121 \, a c^{2} x - 136 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{120 \, a}"," ",0,"-1/120*(105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (24*a^5*c^2*x^5 + 114*a^4*c^2*x^4 + 202*a^3*c^2*x^3 + 127*a^2*c^2*x^2 - 121*a*c^2*x - 136*c^2)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
576,1,91,0,0.602751," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c),x, algorithm=""fricas"")","-\frac{15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(2 \, a^{3} c x^{3} + 11 \, a^{2} c x^{2} + 31 \, a c x + 22 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a}"," ",0,"-1/6*(15*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (2*a^3*c*x^3 + 11*a^2*c*x^2 + 31*a*c*x + 22*c)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
577,1,51,0,0.593604," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} + 2 \, a x + 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c x^{2} - 2 \, a^{2} c x + a c\right)}}"," ",0,"1/3*(a^2*x^2 + 2*a*x + 1)*sqrt((a*x - 1)/(a*x + 1))/(a^3*c*x^2 - 2*a^2*c*x + a*c)","B",0
578,1,77,0,0.594311," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{3} x^{3} - 4 \, a^{2} x^{2} + a x + 7\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\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,"-1/15*(2*a^3*x^3 - 4*a^2*x^2 + a*x + 7)*sqrt((a*x - 1)/(a*x + 1))/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2)","A",0
579,1,96,0,0.470888," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{{\left(8 \, a^{4} x^{4} - 24 \, a^{3} x^{3} + 20 \, a^{2} x^{2} + 4 \, a x - 13\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\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,"-1/35*(8*a^4*x^4 - 24*a^3*x^3 + 20*a^2*x^2 + 4*a*x - 13)*sqrt((a*x - 1)/(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
580,1,124,0,0.625324," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","-\frac{{\left(16 \, a^{6} x^{6} - 48 \, a^{5} x^{5} + 24 \, a^{4} x^{4} + 56 \, a^{3} x^{3} - 66 \, a^{2} x^{2} + 6 \, a x + 19\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{63 \, {\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)}}"," ",0,"-1/63*(16*a^6*x^6 - 48*a^5*x^5 + 24*a^4*x^4 + 56*a^3*x^3 - 66*a^2*x^2 + 6*a*x + 19)*sqrt((a*x - 1)/(a*x + 1))/(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)","A",0
581,1,101,0,0.546489," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^5,x, algorithm=""fricas"")","-\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
582,1,92,0,0.535092," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","\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
583,1,59,0,0.419369," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\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
584,1,47,0,0.440785," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\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
585,1,37,0,0.635257," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c),x, algorithm=""fricas"")","-\frac{a^{3} c x^{3} + 6 \, a^{2} c x^{2} + 21 \, a c x + 24 \, c \log\left(a x - 1\right)}{3 \, a}"," ",0,"-1/3*(a^3*c*x^3 + 6*a^2*c*x^2 + 21*a*c*x + 24*c*log(a*x - 1))/a","A",0
586,1,19,0,1.013448," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c),x, algorithm=""fricas"")","\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
587,1,41,0,0.687996," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\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
588,1,147,0,0.561757," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{6 \, a^{3} x^{3} - 24 \, a^{2} x^{2} + 38 \, a x - 3 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(a x - 1\right) - 32}{96 \, {\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,"-1/96*(6*a^3*x^3 - 24*a^2*x^2 + 38*a*x - 3*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(a*x + 1) + 3*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(a*x - 1) - 32)/(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)","B",0
589,1,191,0,0.582379," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","-\frac{30 \, a^{5} x^{5} - 120 \, a^{4} x^{4} + 160 \, a^{3} x^{3} - 40 \, a^{2} x^{2} - 94 \, a x - 15 \, {\left(a^{6} x^{6} - 4 \, a^{5} x^{5} + 5 \, a^{4} x^{4} - 5 \, a^{2} x^{2} + 4 \, a x - 1\right)} \log\left(a x + 1\right) + 15 \, {\left(a^{6} x^{6} - 4 \, a^{5} x^{5} + 5 \, a^{4} x^{4} - 5 \, a^{2} x^{2} + 4 \, a x - 1\right)} \log\left(a x - 1\right) + 96}{320 \, {\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)}}"," ",0,"-1/320*(30*a^5*x^5 - 120*a^4*x^4 + 160*a^3*x^3 - 40*a^2*x^2 - 94*a*x - 15*(a^6*x^6 - 4*a^5*x^5 + 5*a^4*x^4 - 5*a^2*x^2 + 4*a*x - 1)*log(a*x + 1) + 15*(a^6*x^6 - 4*a^5*x^5 + 5*a^4*x^4 - 5*a^2*x^2 + 4*a*x - 1)*log(a*x - 1) + 96)/(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)","A",0
590,1,170,0,0.571447," ","integrate((-a^2*c*x^2+c)^4*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{315 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 315 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(128 \, a^{9} c^{4} x^{9} - 16 \, a^{8} c^{4} x^{8} - 656 \, a^{7} c^{4} x^{7} + 88 \, a^{6} c^{4} x^{6} + 1368 \, a^{5} c^{4} x^{5} - 210 \, a^{4} c^{4} x^{4} - 1490 \, a^{3} c^{4} x^{3} + 325 \, a^{2} c^{4} x^{2} + 965 \, a c^{4} x + 128 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{1152 \, a}"," ",0,"-1/1152*(315*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 315*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (128*a^9*c^4*x^9 - 16*a^8*c^4*x^8 - 656*a^7*c^4*x^7 + 88*a^6*c^4*x^6 + 1368*a^5*c^4*x^5 - 210*a^4*c^4*x^4 - 1490*a^3*c^4*x^3 + 325*a^2*c^4*x^2 + 965*a*c^4*x + 128*c^4)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
591,1,147,0,0.581552," ","integrate((-a^2*c*x^2+c)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 105 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(48 \, a^{7} c^{3} x^{7} - 8 \, a^{6} c^{3} x^{6} - 200 \, a^{5} c^{3} x^{5} + 38 \, a^{4} c^{3} x^{4} + 326 \, a^{3} c^{3} x^{3} - 87 \, a^{2} c^{3} x^{2} - 279 \, a c^{3} x - 48 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{336 \, a}"," ",0,"-1/336*(105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 105*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (48*a^7*c^3*x^7 - 8*a^6*c^3*x^6 - 200*a^5*c^3*x^5 + 38*a^4*c^3*x^4 + 326*a^3*c^3*x^3 - 87*a^2*c^3*x^2 - 279*a*c^3*x - 48*c^3)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
592,1,126,0,1.243748," ","integrate((-a^2*c*x^2+c)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(8 \, a^{5} c^{2} x^{5} - 2 \, a^{4} c^{2} x^{4} - 26 \, a^{3} c^{2} x^{3} + 9 \, a^{2} c^{2} x^{2} + 33 \, a c^{2} x + 8 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{40 \, a}"," ",0,"-1/40*(15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (8*a^5*c^2*x^5 - 2*a^4*c^2*x^4 - 26*a^3*c^2*x^3 + 9*a^2*c^2*x^2 + 33*a*c^2*x + 8*c^2)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
593,1,91,0,0.460428," ","integrate((-a^2*c*x^2+c)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(2 \, a^{3} c x^{3} - a^{2} c x^{2} - 5 \, a c x - 2 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a}"," ",0,"-1/6*(3*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (2*a^3*c*x^3 - a^2*c*x^2 - 5*a*c*x - 2*c)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
594,1,23,0,0.900044," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{a x - 1}{a x + 1}}}{a c}"," ",0,"-sqrt((a*x - 1)/(a*x + 1))/(a*c)","A",0
595,1,50,0,0.641161," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} x^{2} + 2 \, a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c^{2} x^{2} - a c^{2}\right)}}"," ",0,"-1/3*(2*a^2*x^2 + 2*a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a^3*c^2*x^2 - a*c^2)","A",0
596,1,76,0,0.508882," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{{\left(8 \, a^{4} x^{4} + 8 \, a^{3} x^{3} - 12 \, a^{2} x^{2} - 12 \, a x + 3\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"-1/15*(8*a^4*x^4 + 8*a^3*x^3 - 12*a^2*x^2 - 12*a*x + 3)*sqrt((a*x - 1)/(a*x + 1))/(a^5*c^3*x^4 - 2*a^3*c^3*x^2 + a*c^3)","A",0
597,1,104,0,0.633879," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","-\frac{{\left(16 \, a^{6} x^{6} + 16 \, a^{5} x^{5} - 40 \, a^{4} x^{4} - 40 \, a^{3} x^{3} + 30 \, a^{2} x^{2} + 30 \, a x - 5\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\left(a^{7} c^{4} x^{6} - 3 \, a^{5} c^{4} x^{4} + 3 \, a^{3} c^{4} x^{2} - a c^{4}\right)}}"," ",0,"-1/35*(16*a^6*x^6 + 16*a^5*x^5 - 40*a^4*x^4 - 40*a^3*x^3 + 30*a^2*x^2 + 30*a*x - 5)*sqrt((a*x - 1)/(a*x + 1))/(a^7*c^4*x^6 - 3*a^5*c^4*x^4 + 3*a^3*c^4*x^2 - a*c^4)","A",0
598,1,80,0,0.720448," ","integrate((-a^2*c*x^2+c)^4*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\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
599,1,70,0,0.519581," ","integrate((-a^2*c*x^2+c)^3*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","-\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
600,1,37,0,0.587862," ","integrate((-a^2*c*x^2+c)^2*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\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
601,1,20,0,0.472775," ","integrate((-a^2*c*x^2+c)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","-\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
602,1,12,0,0.454833," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{1}{a^{2} c x + a c}"," ",0,"1/(a^2*c*x + a*c)","A",0
603,1,76,0,0.594505," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{2 \, a x - {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(a x + 1\right) + {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(a x - 1\right) + 4}{8 \, {\left(a^{3} c^{2} x^{2} + 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"1/8*(2*a*x - (a^2*x^2 + 2*a*x + 1)*log(a*x + 1) + (a^2*x^2 + 2*a*x + 1)*log(a*x - 1) + 4)/(a^3*c^2*x^2 + 2*a^2*c^2*x + a*c^2)","A",0
604,1,121,0,0.544519," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{6 \, a^{3} x^{3} + 12 \, a^{2} x^{2} + 2 \, a x - 3 \, {\left(a^{4} x^{4} + 2 \, a^{3} x^{3} - 2 \, a x - 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{4} x^{4} + 2 \, a^{3} x^{3} - 2 \, a x - 1\right)} \log\left(a x - 1\right) - 8}{24 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{3} - 2 \, a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"1/24*(6*a^3*x^3 + 12*a^2*x^2 + 2*a*x - 3*(a^4*x^4 + 2*a^3*x^3 - 2*a*x - 1)*log(a*x + 1) + 3*(a^4*x^4 + 2*a^3*x^3 - 2*a*x - 1)*log(a*x - 1) - 8)/(a^5*c^3*x^4 + 2*a^4*c^3*x^3 - 2*a^2*c^3*x - a*c^3)","A",0
605,1,217,0,0.579006," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","\frac{30 \, a^{5} x^{5} + 60 \, a^{4} x^{4} - 20 \, a^{3} x^{3} - 100 \, a^{2} x^{2} - 34 \, a x - 15 \, {\left(a^{6} x^{6} + 2 \, a^{5} x^{5} - a^{4} x^{4} - 4 \, a^{3} x^{3} - a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(a x + 1\right) + 15 \, {\left(a^{6} x^{6} + 2 \, a^{5} x^{5} - a^{4} x^{4} - 4 \, a^{3} x^{3} - a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(a x - 1\right) + 32}{128 \, {\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)}}"," ",0,"1/128*(30*a^5*x^5 + 60*a^4*x^4 - 20*a^3*x^3 - 100*a^2*x^2 - 34*a*x - 15*(a^6*x^6 + 2*a^5*x^5 - a^4*x^4 - 4*a^3*x^3 - a^2*x^2 + 2*a*x + 1)*log(a*x + 1) + 15*(a^6*x^6 + 2*a^5*x^5 - a^4*x^4 - 4*a^3*x^3 - a^2*x^2 + 2*a*x + 1)*log(a*x - 1) + 32)/(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)","B",0
606,1,169,0,0.935503," ","integrate((-a^2*c*x^2+c)^4*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{3465 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3465 \, c^{4} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(896 \, a^{9} c^{4} x^{9} - 2128 \, a^{8} c^{4} x^{8} - 2000 \, a^{7} c^{4} x^{7} + 8248 \, a^{6} c^{4} x^{6} - 1224 \, a^{5} c^{4} x^{5} - 11514 \, a^{4} c^{4} x^{4} + 7174 \, a^{3} c^{4} x^{3} + 5641 \, a^{2} c^{4} x^{2} - 8311 \, a c^{4} x - 3712 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{8064 \, a}"," ",0,"1/8064*(3465*c^4*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3465*c^4*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (896*a^9*c^4*x^9 - 2128*a^8*c^4*x^8 - 2000*a^7*c^4*x^7 + 8248*a^6*c^4*x^6 - 1224*a^5*c^4*x^5 - 11514*a^4*c^4*x^4 + 7174*a^3*c^4*x^3 + 5641*a^2*c^4*x^2 - 8311*a*c^4*x - 3712*c^4)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
607,1,148,0,0.533050," ","integrate((-a^2*c*x^2+c)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 315 \, c^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(80 \, a^{7} c^{3} x^{7} - 200 \, a^{6} c^{3} x^{6} - 72 \, a^{5} c^{3} x^{5} + 558 \, a^{4} c^{3} x^{4} - 306 \, a^{3} c^{3} x^{3} - 411 \, a^{2} c^{3} x^{2} + 613 \, a c^{3} x + 368 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{560 \, a}"," ",0,"1/560*(315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 315*c^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (80*a^7*c^3*x^7 - 200*a^6*c^3*x^6 - 72*a^5*c^3*x^5 + 558*a^4*c^3*x^4 - 306*a^3*c^3*x^3 - 411*a^2*c^3*x^2 + 613*a*c^3*x + 368*c^3)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
608,1,125,0,0.522744," ","integrate((-a^2*c*x^2+c)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 105 \, c^{2} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(24 \, a^{5} c^{2} x^{5} - 66 \, a^{4} c^{2} x^{4} + 22 \, a^{3} c^{2} x^{3} + 97 \, a^{2} c^{2} x^{2} - 151 \, a c^{2} x - 136 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{120 \, a}"," ",0,"1/120*(105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 105*c^2*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (24*a^5*c^2*x^5 - 66*a^4*c^2*x^4 + 22*a^3*c^2*x^3 + 97*a^2*c^2*x^2 - 151*a*c^2*x - 136*c^2)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
609,1,92,0,0.559653," ","integrate((-a^2*c*x^2+c)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, c \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(2 \, a^{3} c x^{3} - 7 \, a^{2} c x^{2} + 13 \, a c x + 22 \, c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a}"," ",0,"1/6*(15*c*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*c*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (2*a^3*c*x^3 - 7*a^2*c*x^2 + 13*a*c*x + 22*c)*sqrt((a*x - 1)/(a*x + 1)))/a","A",0
610,1,34,0,0.406607," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c),x, algorithm=""fricas"")","-\frac{{\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{2} c x + a c\right)}}"," ",0,"-1/3*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a^2*c*x + a*c)","A",0
611,1,58,0,0.654211," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} x^{2} + 6 \, a x + 7\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\left(a^{3} c^{2} x^{2} + 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"1/15*(2*a^2*x^2 + 6*a*x + 7)*sqrt((a*x - 1)/(a*x + 1))/(a^3*c^2*x^2 + 2*a^2*c^2*x + a*c^2)","A",0
612,1,86,0,0.543774," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{{\left(8 \, a^{4} x^{4} + 24 \, a^{3} x^{3} + 20 \, a^{2} x^{2} - 4 \, a x - 13\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{3} - 2 \, a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"1/35*(8*a^4*x^4 + 24*a^3*x^3 + 20*a^2*x^2 - 4*a*x - 13)*sqrt((a*x - 1)/(a*x + 1))/(a^5*c^3*x^4 + 2*a^4*c^3*x^3 - 2*a^2*c^3*x - a*c^3)","A",0
613,1,134,0,0.476002," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","\frac{{\left(16 \, a^{6} x^{6} + 48 \, a^{5} x^{5} + 24 \, a^{4} x^{4} - 56 \, a^{3} x^{3} - 66 \, a^{2} x^{2} - 6 \, a x + 19\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{63 \, {\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)}}"," ",0,"1/63*(16*a^6*x^6 + 48*a^5*x^5 + 24*a^4*x^4 - 56*a^3*x^3 - 66*a^2*x^2 - 6*a*x + 19)*sqrt((a*x - 1)/(a*x + 1))/(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)","A",0
614,1,117,0,0.485844," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(9/2),x, algorithm=""fricas"")","\frac{{\left(63 \, a^{9} c^{4} x^{10} + 70 \, a^{8} c^{4} x^{9} - 315 \, a^{7} c^{4} x^{8} - 360 \, a^{6} c^{4} x^{7} + 630 \, a^{5} c^{4} x^{6} + 756 \, a^{4} c^{4} x^{5} - 630 \, a^{3} c^{4} x^{4} - 840 \, a^{2} c^{4} x^{3} + 315 \, a c^{4} x^{2} + 630 \, c^{4} x\right)} \sqrt{-a^{2} c}}{630 \, a}"," ",0,"1/630*(63*a^9*c^4*x^10 + 70*a^8*c^4*x^9 - 315*a^7*c^4*x^8 - 360*a^6*c^4*x^7 + 630*a^5*c^4*x^6 + 756*a^4*c^4*x^5 - 630*a^3*c^4*x^4 - 840*a^2*c^4*x^3 + 315*a*c^4*x^2 + 630*c^4*x)*sqrt(-a^2*c)/a","A",0
615,1,95,0,0.538379," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","-\frac{{\left(35 \, a^{7} c^{3} x^{8} + 40 \, a^{6} c^{3} x^{7} - 140 \, a^{5} c^{3} x^{6} - 168 \, a^{4} c^{3} x^{5} + 210 \, a^{3} c^{3} x^{4} + 280 \, a^{2} c^{3} x^{3} - 140 \, a c^{3} x^{2} - 280 \, c^{3} x\right)} \sqrt{-a^{2} c}}{280 \, a}"," ",0,"-1/280*(35*a^7*c^3*x^8 + 40*a^6*c^3*x^7 - 140*a^5*c^3*x^6 - 168*a^4*c^3*x^5 + 210*a^3*c^3*x^4 + 280*a^2*c^3*x^3 - 140*a*c^3*x^2 - 280*c^3*x)*sqrt(-a^2*c)/a","A",0
616,1,73,0,0.627521," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(5 \, a^{5} c^{2} x^{6} + 6 \, a^{4} c^{2} x^{5} - 15 \, a^{3} c^{2} x^{4} - 20 \, a^{2} c^{2} x^{3} + 15 \, a c^{2} x^{2} + 30 \, c^{2} x\right)} \sqrt{-a^{2} c}}{30 \, a}"," ",0,"1/30*(5*a^5*c^2*x^6 + 6*a^4*c^2*x^5 - 15*a^3*c^2*x^4 - 20*a^2*c^2*x^3 + 15*a*c^2*x^2 + 30*c^2*x)*sqrt(-a^2*c)/a","A",0
617,1,43,0,0.569041," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{3} c x^{4} + 4 \, a^{2} c x^{3} - 6 \, a c x^{2} - 12 \, c x\right)} \sqrt{-a^{2} c}}{12 \, a}"," ",0,"-1/12*(3*a^3*c*x^4 + 4*a^2*c*x^3 - 6*a*c*x^2 - 12*c*x)*sqrt(-a^2*c)/a","A",0
618,1,22,0,0.457474," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(a x^{2} + 2 \, x\right)}}{2 \, a}"," ",0,"1/2*sqrt(-a^2*c)*(a*x^2 + 2*x)/a","A",0
619,1,22,0,0.630403," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c} \log\left(a x - 1\right)}{a^{2} c}"," ",0,"-sqrt(-a^2*c)*log(a*x - 1)/(a^2*c)","A",0
620,1,86,0,1.056528," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(a^{2} x - a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) + 2 \, \sqrt{-a^{2} c}}{4 \, {\left(a^{3} c^{2} x - a^{2} c^{2}\right)}}"," ",0,"-1/4*((a^2*x - a)*sqrt(-c)*log((a^2*c*x^2 + 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) + 2*sqrt(-a^2*c))/(a^3*c^2*x - a^2*c^2)","A",0
621,1,136,0,0.499659," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{4} x^{3} - a^{3} x^{2} - a^{2} x + a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) + 2 \, {\left(3 \, a^{2} x^{2} - 3 \, a x - 2\right)} \sqrt{-a^{2} c}}{16 \, {\left(a^{5} c^{3} x^{3} - a^{4} c^{3} x^{2} - a^{3} c^{3} x + a^{2} c^{3}\right)}}"," ",0,"-1/16*(3*(a^4*x^3 - a^3*x^2 - a^2*x + a)*sqrt(-c)*log((a^2*c*x^2 + 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) + 2*(3*a^2*x^2 - 3*a*x - 2)*sqrt(-a^2*c))/(a^5*c^3*x^3 - a^4*c^3*x^2 - a^3*c^3*x + a^2*c^3)","A",0
622,1,191,0,0.591204," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","-\frac{15 \, {\left(a^{6} x^{5} - a^{5} x^{4} - 2 \, a^{4} x^{3} + 2 \, a^{3} x^{2} + a^{2} x - a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) + 2 \, {\left(15 \, a^{4} x^{4} - 15 \, a^{3} x^{3} - 25 \, a^{2} x^{2} + 25 \, a x + 8\right)} \sqrt{-a^{2} c}}{96 \, {\left(a^{7} c^{4} x^{5} - a^{6} c^{4} x^{4} - 2 \, a^{5} c^{4} x^{3} + 2 \, a^{4} c^{4} x^{2} + a^{3} c^{4} x - a^{2} c^{4}\right)}}"," ",0,"-1/96*(15*(a^6*x^5 - a^5*x^4 - 2*a^4*x^3 + 2*a^3*x^2 + a^2*x - a)*sqrt(-c)*log((a^2*c*x^2 + 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) + 2*(15*a^4*x^4 - 15*a^3*x^3 - 25*a^2*x^2 + 25*a*x + 8)*sqrt(-a^2*c))/(a^7*c^4*x^5 - a^6*c^4*x^4 - 2*a^5*c^4*x^3 + 2*a^4*c^4*x^2 + a^3*c^4*x - a^2*c^4)","A",0
623,1,329,0,0.701339," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(9/2),x, algorithm=""fricas"")","\left[\frac{3465 \, \sqrt{-c} c^{4} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) + 2 \, {\left(1152 \, a^{9} c^{4} x^{9} + 2560 \, a^{8} c^{4} x^{8} - 3024 \, a^{7} c^{4} x^{7} - 10240 \, a^{6} c^{4} x^{6} + 312 \, a^{5} c^{4} x^{5} + 15360 \, a^{4} c^{4} x^{4} + 6150 \, a^{3} c^{4} x^{3} - 10240 \, a^{2} c^{4} x^{2} - 8055 \, a c^{4} x + 2560 \, c^{4}\right)} \sqrt{-a^{2} c x^{2} + c}}{23040 \, a}, \frac{3465 \, c^{\frac{9}{2}} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) + {\left(1152 \, a^{9} c^{4} x^{9} + 2560 \, a^{8} c^{4} x^{8} - 3024 \, a^{7} c^{4} x^{7} - 10240 \, a^{6} c^{4} x^{6} + 312 \, a^{5} c^{4} x^{5} + 15360 \, a^{4} c^{4} x^{4} + 6150 \, a^{3} c^{4} x^{3} - 10240 \, a^{2} c^{4} x^{2} - 8055 \, a c^{4} x + 2560 \, c^{4}\right)} \sqrt{-a^{2} c x^{2} + c}}{11520 \, a}\right]"," ",0,"[1/23040*(3465*sqrt(-c)*c^4*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) + 2*(1152*a^9*c^4*x^9 + 2560*a^8*c^4*x^8 - 3024*a^7*c^4*x^7 - 10240*a^6*c^4*x^6 + 312*a^5*c^4*x^5 + 15360*a^4*c^4*x^4 + 6150*a^3*c^4*x^3 - 10240*a^2*c^4*x^2 - 8055*a*c^4*x + 2560*c^4)*sqrt(-a^2*c*x^2 + c))/a, 1/11520*(3465*c^(9/2)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) + (1152*a^9*c^4*x^9 + 2560*a^8*c^4*x^8 - 3024*a^7*c^4*x^7 - 10240*a^6*c^4*x^6 + 312*a^5*c^4*x^5 + 15360*a^4*c^4*x^4 + 6150*a^3*c^4*x^3 - 10240*a^2*c^4*x^2 - 8055*a*c^4*x + 2560*c^4)*sqrt(-a^2*c*x^2 + c))/a]","A",0
624,1,286,0,0.590798," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","\left[\frac{315 \, \sqrt{-c} c^{3} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) - 2 \, {\left(112 \, a^{7} c^{3} x^{7} + 256 \, a^{6} c^{3} x^{6} - 168 \, a^{5} c^{3} x^{5} - 768 \, a^{4} c^{3} x^{4} - 210 \, a^{3} c^{3} x^{3} + 768 \, a^{2} c^{3} x^{2} + 581 \, a c^{3} x - 256 \, c^{3}\right)} \sqrt{-a^{2} c x^{2} + c}}{1792 \, a}, \frac{315 \, c^{\frac{7}{2}} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) - {\left(112 \, a^{7} c^{3} x^{7} + 256 \, a^{6} c^{3} x^{6} - 168 \, a^{5} c^{3} x^{5} - 768 \, a^{4} c^{3} x^{4} - 210 \, a^{3} c^{3} x^{3} + 768 \, a^{2} c^{3} x^{2} + 581 \, a c^{3} x - 256 \, c^{3}\right)} \sqrt{-a^{2} c x^{2} + c}}{896 \, a}\right]"," ",0,"[1/1792*(315*sqrt(-c)*c^3*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) - 2*(112*a^7*c^3*x^7 + 256*a^6*c^3*x^6 - 168*a^5*c^3*x^5 - 768*a^4*c^3*x^4 - 210*a^3*c^3*x^3 + 768*a^2*c^3*x^2 + 581*a*c^3*x - 256*c^3)*sqrt(-a^2*c*x^2 + c))/a, 1/896*(315*c^(7/2)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) - (112*a^7*c^3*x^7 + 256*a^6*c^3*x^6 - 168*a^5*c^3*x^5 - 768*a^4*c^3*x^4 - 210*a^3*c^3*x^3 + 768*a^2*c^3*x^2 + 581*a*c^3*x - 256*c^3)*sqrt(-a^2*c*x^2 + c))/a]","A",0
625,1,241,0,0.638882," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{-c} c^{2} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) + 2 \, {\left(40 \, a^{5} c^{2} x^{5} + 96 \, a^{4} c^{2} x^{4} - 10 \, a^{3} c^{2} x^{3} - 192 \, a^{2} c^{2} x^{2} - 135 \, a c^{2} x + 96 \, c^{2}\right)} \sqrt{-a^{2} c x^{2} + c}}{480 \, a}, \frac{105 \, c^{\frac{5}{2}} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) + {\left(40 \, a^{5} c^{2} x^{5} + 96 \, a^{4} c^{2} x^{4} - 10 \, a^{3} c^{2} x^{3} - 192 \, a^{2} c^{2} x^{2} - 135 \, a c^{2} x + 96 \, c^{2}\right)} \sqrt{-a^{2} c x^{2} + c}}{240 \, a}\right]"," ",0,"[1/480*(105*sqrt(-c)*c^2*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) + 2*(40*a^5*c^2*x^5 + 96*a^4*c^2*x^4 - 10*a^3*c^2*x^3 - 192*a^2*c^2*x^2 - 135*a*c^2*x + 96*c^2)*sqrt(-a^2*c*x^2 + c))/a, 1/240*(105*c^(5/2)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) + (40*a^5*c^2*x^5 + 96*a^4*c^2*x^4 - 10*a^3*c^2*x^3 - 192*a^2*c^2*x^2 - 135*a*c^2*x + 96*c^2)*sqrt(-a^2*c*x^2 + c))/a]","A",0
626,1,180,0,0.602803," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{-c} c \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) - 2 \, {\left(6 \, a^{3} c x^{3} + 16 \, a^{2} c x^{2} + 9 \, a c x - 16 \, c\right)} \sqrt{-a^{2} c x^{2} + c}}{48 \, a}, \frac{15 \, c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) - {\left(6 \, a^{3} c x^{3} + 16 \, a^{2} c x^{2} + 9 \, a c x - 16 \, c\right)} \sqrt{-a^{2} c x^{2} + c}}{24 \, a}\right]"," ",0,"[1/48*(15*sqrt(-c)*c*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) - 2*(6*a^3*c*x^3 + 16*a^2*c*x^2 + 9*a*c*x - 16*c)*sqrt(-a^2*c*x^2 + c))/a, 1/24*(15*c^(3/2)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) - (6*a^3*c*x^3 + 16*a^2*c*x^2 + 9*a*c*x - 16*c)*sqrt(-a^2*c*x^2 + c))/a]","A",0
627,1,134,0,0.422662," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-a^{2} c x^{2} + c} {\left(a x + 4\right)} + 3 \, \sqrt{-c} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right)}{4 \, a}, \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 4\right)} + 3 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right)}{2 \, a}\right]"," ",0,"[1/4*(2*sqrt(-a^2*c*x^2 + c)*(a*x + 4) + 3*sqrt(-c)*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c))/a, 1/2*(sqrt(-a^2*c*x^2 + c)*(a*x + 4) + 3*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)))/a]","A",0
628,1,153,0,0.456342," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(a x - 1\right)} \sqrt{-c} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) - 4 \, \sqrt{-a^{2} c x^{2} + c}}{2 \, {\left(a^{2} c x - a c\right)}}, -\frac{{\left(a x - 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) - 2 \, \sqrt{-a^{2} c x^{2} + c}}{a^{2} c x - a c}\right]"," ",0,"[-1/2*((a*x - 1)*sqrt(-c)*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) - 4*sqrt(-a^2*c*x^2 + c))/(a^2*c*x - a*c), -((a*x - 1)*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) - 2*sqrt(-a^2*c*x^2 + c))/(a^2*c*x - a*c)]","A",0
629,1,47,0,0.878941," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x - 2\right)}}{3 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"1/3*sqrt(-a^2*c*x^2 + c)*(a*x - 2)/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)","A",0
630,1,75,0,0.737293," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} - 4 \, a^{2} x^{2} + a x + 2\right)} \sqrt{-a^{2} c x^{2} + c}}{5 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{4} c^{3} x^{3} + 2 \, a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"1/5*(2*a^3*x^3 - 4*a^2*x^2 + a*x + 2)*sqrt(-a^2*c*x^2 + c)/(a^5*c^3*x^4 - 2*a^4*c^3*x^3 + 2*a^2*c^3*x - a*c^3)","A",0
631,1,124,0,0.818507," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","\frac{{\left(8 \, a^{5} x^{5} - 16 \, a^{4} x^{4} - 4 \, a^{3} x^{3} + 24 \, a^{2} x^{2} - 9 \, a x - 6\right)} \sqrt{-a^{2} c x^{2} + c}}{21 \, {\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)}}"," ",0,"1/21*(8*a^5*x^5 - 16*a^4*x^4 - 4*a^3*x^3 + 24*a^2*x^2 - 9*a*x - 6)*sqrt(-a^2*c*x^2 + c)/(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)","A",0
632,1,152,0,1.841713," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^(9/2),x, algorithm=""fricas"")","\frac{{\left(16 \, a^{7} x^{7} - 32 \, a^{6} x^{6} - 24 \, a^{5} x^{5} + 80 \, a^{4} x^{4} - 10 \, a^{3} x^{3} - 60 \, a^{2} x^{2} + 25 \, a x + 10\right)} \sqrt{-a^{2} c x^{2} + c}}{45 \, {\left(a^{9} c^{5} x^{8} - 2 \, a^{8} c^{5} x^{7} - 2 \, a^{7} c^{5} x^{6} + 6 \, a^{6} c^{5} x^{5} - 6 \, a^{4} c^{5} x^{3} + 2 \, a^{3} c^{5} x^{2} + 2 \, a^{2} c^{5} x - a c^{5}\right)}}"," ",0,"1/45*(16*a^7*x^7 - 32*a^6*x^6 - 24*a^5*x^5 + 80*a^4*x^4 - 10*a^3*x^3 - 60*a^2*x^2 + 25*a*x + 10)*sqrt(-a^2*c*x^2 + c)/(a^9*c^5*x^8 - 2*a^8*c^5*x^7 - 2*a^7*c^5*x^6 + 6*a^6*c^5*x^5 - 6*a^4*c^5*x^3 + 2*a^3*c^5*x^2 + 2*a^2*c^5*x - a*c^5)","A",0
633,1,95,0,0.670789," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(9/2),x, algorithm=""fricas"")","\frac{{\left(21 \, a^{9} c^{4} x^{10} + 70 \, a^{8} c^{4} x^{9} - 240 \, a^{6} c^{4} x^{7} - 210 \, a^{5} c^{4} x^{6} + 252 \, a^{4} c^{4} x^{5} + 420 \, a^{3} c^{4} x^{4} - 315 \, a c^{4} x^{2} - 210 \, c^{4} x\right)} \sqrt{-a^{2} c}}{210 \, a}"," ",0,"1/210*(21*a^9*c^4*x^10 + 70*a^8*c^4*x^9 - 240*a^6*c^4*x^7 - 210*a^5*c^4*x^6 + 252*a^4*c^4*x^5 + 420*a^3*c^4*x^4 - 315*a*c^4*x^2 - 210*c^4*x)*sqrt(-a^2*c)/a","A",0
634,1,95,0,0.399299," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","-\frac{{\left(21 \, a^{7} c^{3} x^{8} + 72 \, a^{6} c^{3} x^{7} + 28 \, a^{5} c^{3} x^{6} - 168 \, a^{4} c^{3} x^{5} - 210 \, a^{3} c^{3} x^{4} + 56 \, a^{2} c^{3} x^{3} + 252 \, a c^{3} x^{2} + 168 \, c^{3} x\right)} \sqrt{-a^{2} c}}{168 \, a}"," ",0,"-1/168*(21*a^7*c^3*x^8 + 72*a^6*c^3*x^7 + 28*a^5*c^3*x^6 - 168*a^4*c^3*x^5 - 210*a^3*c^3*x^4 + 56*a^2*c^3*x^3 + 252*a*c^3*x^2 + 168*c^3*x)*sqrt(-a^2*c)/a","A",0
635,1,73,0,0.551442," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(5 \, a^{5} c^{2} x^{6} + 18 \, a^{4} c^{2} x^{5} + 15 \, a^{3} c^{2} x^{4} - 20 \, a^{2} c^{2} x^{3} - 45 \, a c^{2} x^{2} - 30 \, c^{2} x\right)} \sqrt{-a^{2} c}}{30 \, a}"," ",0,"1/30*(5*a^5*c^2*x^6 + 18*a^4*c^2*x^5 + 15*a^3*c^2*x^4 - 20*a^2*c^2*x^3 - 45*a*c^2*x^2 - 30*c^2*x)*sqrt(-a^2*c)/a","A",0
636,1,42,0,0.906631," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(a^{3} c x^{4} + 4 \, a^{2} c x^{3} + 6 \, a c x^{2} + 4 \, c x\right)} \sqrt{-a^{2} c}}{4 \, a}"," ",0,"-1/4*(a^3*c*x^4 + 4*a^2*c*x^3 + 6*a*c*x^2 + 4*c*x)*sqrt(-a^2*c)/a","A",0
637,1,33,0,0.655596," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} + 6 \, a x + 8 \, \log\left(a x - 1\right)\right)} \sqrt{-a^{2} c}}{2 \, a^{2}}"," ",0,"1/2*(a^2*x^2 + 6*a*x + 8*log(a*x - 1))*sqrt(-a^2*c)/a^2","A",0
638,1,39,0,0.556879," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c} {\left({\left(a x - 1\right)} \log\left(a x - 1\right) - 2\right)}}{a^{3} c x - a^{2} c}"," ",0,"-sqrt(-a^2*c)*((a*x - 1)*log(a*x - 1) - 2)/(a^3*c*x - a^2*c)","A",0
639,1,39,0,0.463603," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c}}{2 \, {\left(a^{4} c^{2} x^{2} - 2 \, a^{3} c^{2} x + a^{2} c^{2}\right)}}"," ",0,"-1/2*sqrt(-a^2*c)/(a^4*c^2*x^2 - 2*a^3*c^2*x + a^2*c^2)","A",0
640,1,139,0,0.501410," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{4} x^{3} - 3 \, a^{3} x^{2} + 3 \, a^{2} x - a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) - 2 \, {\left(3 \, a^{2} x^{2} - 9 \, a x + 10\right)} \sqrt{-a^{2} c}}{48 \, {\left(a^{5} c^{3} x^{3} - 3 \, a^{4} c^{3} x^{2} + 3 \, a^{3} c^{3} x - a^{2} c^{3}\right)}}"," ",0,"-1/48*(3*(a^4*x^3 - 3*a^3*x^2 + 3*a^2*x - a)*sqrt(-c)*log((a^2*c*x^2 - 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) - 2*(3*a^2*x^2 - 9*a*x + 10)*sqrt(-a^2*c))/(a^5*c^3*x^3 - 3*a^4*c^3*x^2 + 3*a^3*c^3*x - a^2*c^3)","A",0
641,1,190,0,0.610604," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","-\frac{15 \, {\left(a^{6} x^{5} - 3 \, a^{5} x^{4} + 2 \, a^{4} x^{3} + 2 \, a^{3} x^{2} - 3 \, a^{2} x + a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) - 2 \, {\left(15 \, a^{4} x^{4} - 45 \, a^{3} x^{3} + 35 \, a^{2} x^{2} + 15 \, a x - 32\right)} \sqrt{-a^{2} c}}{192 \, {\left(a^{7} c^{4} x^{5} - 3 \, a^{6} c^{4} x^{4} + 2 \, a^{5} c^{4} x^{3} + 2 \, a^{4} c^{4} x^{2} - 3 \, a^{3} c^{4} x + a^{2} c^{4}\right)}}"," ",0,"-1/192*(15*(a^6*x^5 - 3*a^5*x^4 + 2*a^4*x^3 + 2*a^3*x^2 - 3*a^2*x + a)*sqrt(-c)*log((a^2*c*x^2 - 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) - 2*(15*a^4*x^4 - 45*a^3*x^3 + 35*a^2*x^2 + 15*a*x - 32)*sqrt(-a^2*c))/(a^7*c^4*x^5 - 3*a^6*c^4*x^4 + 2*a^5*c^4*x^3 + 2*a^4*c^4*x^2 - 3*a^3*c^4*x + a^2*c^4)","A",0
642,1,117,0,0.648916," ","integrate((-a^2*c*x^2+c)^(9/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(63 \, a^{9} c^{4} x^{10} - 70 \, a^{8} c^{4} x^{9} - 315 \, a^{7} c^{4} x^{8} + 360 \, a^{6} c^{4} x^{7} + 630 \, a^{5} c^{4} x^{6} - 756 \, a^{4} c^{4} x^{5} - 630 \, a^{3} c^{4} x^{4} + 840 \, a^{2} c^{4} x^{3} + 315 \, a c^{4} x^{2} - 630 \, c^{4} x\right)} \sqrt{-a^{2} c}}{630 \, a}"," ",0,"1/630*(63*a^9*c^4*x^10 - 70*a^8*c^4*x^9 - 315*a^7*c^4*x^8 + 360*a^6*c^4*x^7 + 630*a^5*c^4*x^6 - 756*a^4*c^4*x^5 - 630*a^3*c^4*x^4 + 840*a^2*c^4*x^3 + 315*a*c^4*x^2 - 630*c^4*x)*sqrt(-a^2*c)/a","A",0
643,1,95,0,0.614649," ","integrate((-a^2*c*x^2+c)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(35 \, a^{7} c^{3} x^{8} - 40 \, a^{6} c^{3} x^{7} - 140 \, a^{5} c^{3} x^{6} + 168 \, a^{4} c^{3} x^{5} + 210 \, a^{3} c^{3} x^{4} - 280 \, a^{2} c^{3} x^{3} - 140 \, a c^{3} x^{2} + 280 \, c^{3} x\right)} \sqrt{-a^{2} c}}{280 \, a}"," ",0,"-1/280*(35*a^7*c^3*x^8 - 40*a^6*c^3*x^7 - 140*a^5*c^3*x^6 + 168*a^4*c^3*x^5 + 210*a^3*c^3*x^4 - 280*a^2*c^3*x^3 - 140*a*c^3*x^2 + 280*c^3*x)*sqrt(-a^2*c)/a","A",0
644,1,73,0,0.428260," ","integrate((-a^2*c*x^2+c)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(5 \, a^{5} c^{2} x^{6} - 6 \, a^{4} c^{2} x^{5} - 15 \, a^{3} c^{2} x^{4} + 20 \, a^{2} c^{2} x^{3} + 15 \, a c^{2} x^{2} - 30 \, c^{2} x\right)} \sqrt{-a^{2} c}}{30 \, a}"," ",0,"1/30*(5*a^5*c^2*x^6 - 6*a^4*c^2*x^5 - 15*a^3*c^2*x^4 + 20*a^2*c^2*x^3 + 15*a*c^2*x^2 - 30*c^2*x)*sqrt(-a^2*c)/a","A",0
645,1,43,0,0.767949," ","integrate((-a^2*c*x^2+c)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{3} c x^{4} - 4 \, a^{2} c x^{3} - 6 \, a c x^{2} + 12 \, c x\right)} \sqrt{-a^{2} c}}{12 \, a}"," ",0,"-1/12*(3*a^3*c*x^4 - 4*a^2*c*x^3 - 6*a*c*x^2 + 12*c*x)*sqrt(-a^2*c)/a","A",0
646,1,22,0,1.170974," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(a x^{2} - 2 \, x\right)}}{2 \, a}"," ",0,"1/2*sqrt(-a^2*c)*(a*x^2 - 2*x)/a","A",0
647,1,22,0,0.489020," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c} \log\left(a x + 1\right)}{a^{2} c}"," ",0,"-sqrt(-a^2*c)*log(a*x + 1)/(a^2*c)","A",0
648,1,83,0,0.594405," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(a^{2} x + a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) - 2 \, \sqrt{-a^{2} c}}{4 \, {\left(a^{3} c^{2} x + a^{2} c^{2}\right)}}"," ",0,"-1/4*((a^2*x + a)*sqrt(-c)*log((a^2*c*x^2 - 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) - 2*sqrt(-a^2*c))/(a^3*c^2*x + a^2*c^2)","A",0
649,1,137,0,0.521191," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{4} x^{3} + a^{3} x^{2} - a^{2} x - a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) - 2 \, {\left(3 \, a^{2} x^{2} + 3 \, a x - 2\right)} \sqrt{-a^{2} c}}{16 \, {\left(a^{5} c^{3} x^{3} + a^{4} c^{3} x^{2} - a^{3} c^{3} x - a^{2} c^{3}\right)}}"," ",0,"-1/16*(3*(a^4*x^3 + a^3*x^2 - a^2*x - a)*sqrt(-c)*log((a^2*c*x^2 - 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) - 2*(3*a^2*x^2 + 3*a*x - 2)*sqrt(-a^2*c))/(a^5*c^3*x^3 + a^4*c^3*x^2 - a^3*c^3*x - a^2*c^3)","A",0
650,1,186,0,0.431721," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","-\frac{15 \, {\left(a^{6} x^{5} + a^{5} x^{4} - 2 \, a^{4} x^{3} - 2 \, a^{3} x^{2} + a^{2} x + a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) - 2 \, {\left(15 \, a^{4} x^{4} + 15 \, a^{3} x^{3} - 25 \, a^{2} x^{2} - 25 \, a x + 8\right)} \sqrt{-a^{2} c}}{96 \, {\left(a^{7} c^{4} x^{5} + a^{6} c^{4} x^{4} - 2 \, a^{5} c^{4} x^{3} - 2 \, a^{4} c^{4} x^{2} + a^{3} c^{4} x + a^{2} c^{4}\right)}}"," ",0,"-1/96*(15*(a^6*x^5 + a^5*x^4 - 2*a^4*x^3 - 2*a^3*x^2 + a^2*x + a)*sqrt(-c)*log((a^2*c*x^2 - 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) - 2*(15*a^4*x^4 + 15*a^3*x^3 - 25*a^2*x^2 - 25*a*x + 8)*sqrt(-a^2*c))/(a^7*c^4*x^5 + a^6*c^4*x^4 - 2*a^5*c^4*x^3 - 2*a^4*c^4*x^2 + a^3*c^4*x + a^2*c^4)","A",0
651,1,241,0,0.756480," ","integrate((-a^2*c*x^2+c)^(5/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{-c} c^{2} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) + 2 \, {\left(40 \, a^{5} c^{2} x^{5} - 96 \, a^{4} c^{2} x^{4} - 10 \, a^{3} c^{2} x^{3} + 192 \, a^{2} c^{2} x^{2} - 135 \, a c^{2} x - 96 \, c^{2}\right)} \sqrt{-a^{2} c x^{2} + c}}{480 \, a}, \frac{105 \, c^{\frac{5}{2}} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) + {\left(40 \, a^{5} c^{2} x^{5} - 96 \, a^{4} c^{2} x^{4} - 10 \, a^{3} c^{2} x^{3} + 192 \, a^{2} c^{2} x^{2} - 135 \, a c^{2} x - 96 \, c^{2}\right)} \sqrt{-a^{2} c x^{2} + c}}{240 \, a}\right]"," ",0,"[1/480*(105*sqrt(-c)*c^2*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) + 2*(40*a^5*c^2*x^5 - 96*a^4*c^2*x^4 - 10*a^3*c^2*x^3 + 192*a^2*c^2*x^2 - 135*a*c^2*x - 96*c^2)*sqrt(-a^2*c*x^2 + c))/a, 1/240*(105*c^(5/2)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) + (40*a^5*c^2*x^5 - 96*a^4*c^2*x^4 - 10*a^3*c^2*x^3 + 192*a^2*c^2*x^2 - 135*a*c^2*x - 96*c^2)*sqrt(-a^2*c*x^2 + c))/a]","A",0
652,1,180,0,0.629779," ","integrate((-a^2*c*x^2+c)^(3/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{-c} c \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) - 2 \, {\left(6 \, a^{3} c x^{3} - 16 \, a^{2} c x^{2} + 9 \, a c x + 16 \, c\right)} \sqrt{-a^{2} c x^{2} + c}}{48 \, a}, \frac{15 \, c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) - {\left(6 \, a^{3} c x^{3} - 16 \, a^{2} c x^{2} + 9 \, a c x + 16 \, c\right)} \sqrt{-a^{2} c x^{2} + c}}{24 \, a}\right]"," ",0,"[1/48*(15*sqrt(-c)*c*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) - 2*(6*a^3*c*x^3 - 16*a^2*c*x^2 + 9*a*c*x + 16*c)*sqrt(-a^2*c*x^2 + c))/a, 1/24*(15*c^(3/2)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) - (6*a^3*c*x^3 - 16*a^2*c*x^2 + 9*a*c*x + 16*c)*sqrt(-a^2*c*x^2 + c))/a]","A",0
653,1,134,0,0.480625," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-a^{2} c x^{2} + c} {\left(a x - 4\right)} + 3 \, \sqrt{-c} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right)}{4 \, a}, \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x - 4\right)} + 3 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right)}{2 \, a}\right]"," ",0,"[1/4*(2*sqrt(-a^2*c*x^2 + c)*(a*x - 4) + 3*sqrt(-c)*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c))/a, 1/2*(sqrt(-a^2*c*x^2 + c)*(a*x - 4) + 3*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)))/a]","A",0
654,1,151,0,0.571830," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(a x + 1\right)} \sqrt{-c} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) - 4 \, \sqrt{-a^{2} c x^{2} + c}}{2 \, {\left(a^{2} c x + a c\right)}}, -\frac{{\left(a x + 1\right)} \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) - 2 \, \sqrt{-a^{2} c x^{2} + c}}{a^{2} c x + a c}\right]"," ",0,"[-1/2*((a*x + 1)*sqrt(-c)*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) - 4*sqrt(-a^2*c*x^2 + c))/(a^2*c*x + a*c), -((a*x + 1)*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) - 2*sqrt(-a^2*c*x^2 + c))/(a^2*c*x + a*c)]","A",0
655,1,47,0,0.576856," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 2\right)}}{3 \, {\left(a^{3} c^{2} x^{2} + 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"1/3*sqrt(-a^2*c*x^2 + c)*(a*x + 2)/(a^3*c^2*x^2 + 2*a^2*c^2*x + a*c^2)","A",0
656,1,75,0,0.565472," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} + 4 \, a^{2} x^{2} + a x - 2\right)} \sqrt{-a^{2} c x^{2} + c}}{5 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{3} - 2 \, a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"1/5*(2*a^3*x^3 + 4*a^2*x^2 + a*x - 2)*sqrt(-a^2*c*x^2 + c)/(a^5*c^3*x^4 + 2*a^4*c^3*x^3 - 2*a^2*c^3*x - a*c^3)","A",0
657,1,124,0,1.198572," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","\frac{{\left(8 \, a^{5} x^{5} + 16 \, a^{4} x^{4} - 4 \, a^{3} x^{3} - 24 \, a^{2} x^{2} - 9 \, a x + 6\right)} \sqrt{-a^{2} c x^{2} + c}}{21 \, {\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)}}"," ",0,"1/21*(8*a^5*x^5 + 16*a^4*x^4 - 4*a^3*x^3 - 24*a^2*x^2 - 9*a*x + 6)*sqrt(-a^2*c*x^2 + c)/(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)","A",0
658,1,152,0,1.319478," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^(9/2),x, algorithm=""fricas"")","\frac{{\left(16 \, a^{7} x^{7} + 32 \, a^{6} x^{6} - 24 \, a^{5} x^{5} - 80 \, a^{4} x^{4} - 10 \, a^{3} x^{3} + 60 \, a^{2} x^{2} + 25 \, a x - 10\right)} \sqrt{-a^{2} c x^{2} + c}}{45 \, {\left(a^{9} c^{5} x^{8} + 2 \, a^{8} c^{5} x^{7} - 2 \, a^{7} c^{5} x^{6} - 6 \, a^{6} c^{5} x^{5} + 6 \, a^{4} c^{5} x^{3} + 2 \, a^{3} c^{5} x^{2} - 2 \, a^{2} c^{5} x - a c^{5}\right)}}"," ",0,"1/45*(16*a^7*x^7 + 32*a^6*x^6 - 24*a^5*x^5 - 80*a^4*x^4 - 10*a^3*x^3 + 60*a^2*x^2 + 25*a*x - 10)*sqrt(-a^2*c*x^2 + c)/(a^9*c^5*x^8 + 2*a^8*c^5*x^7 - 2*a^7*c^5*x^6 - 6*a^6*c^5*x^5 + 6*a^4*c^5*x^3 + 2*a^3*c^5*x^2 - 2*a^2*c^5*x - a*c^5)","A",0
659,1,95,0,0.979083," ","integrate((-a^2*c*x^2+c)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(21 \, a^{9} c^{4} x^{10} - 70 \, a^{8} c^{4} x^{9} + 240 \, a^{6} c^{4} x^{7} - 210 \, a^{5} c^{4} x^{6} - 252 \, a^{4} c^{4} x^{5} + 420 \, a^{3} c^{4} x^{4} - 315 \, a c^{4} x^{2} + 210 \, c^{4} x\right)} \sqrt{-a^{2} c}}{210 \, a}"," ",0,"1/210*(21*a^9*c^4*x^10 - 70*a^8*c^4*x^9 + 240*a^6*c^4*x^7 - 210*a^5*c^4*x^6 - 252*a^4*c^4*x^5 + 420*a^3*c^4*x^4 - 315*a*c^4*x^2 + 210*c^4*x)*sqrt(-a^2*c)/a","A",0
660,1,95,0,0.623726," ","integrate((-a^2*c*x^2+c)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(21 \, a^{7} c^{3} x^{8} - 72 \, a^{6} c^{3} x^{7} + 28 \, a^{5} c^{3} x^{6} + 168 \, a^{4} c^{3} x^{5} - 210 \, a^{3} c^{3} x^{4} - 56 \, a^{2} c^{3} x^{3} + 252 \, a c^{3} x^{2} - 168 \, c^{3} x\right)} \sqrt{-a^{2} c}}{168 \, a}"," ",0,"-1/168*(21*a^7*c^3*x^8 - 72*a^6*c^3*x^7 + 28*a^5*c^3*x^6 + 168*a^4*c^3*x^5 - 210*a^3*c^3*x^4 - 56*a^2*c^3*x^3 + 252*a*c^3*x^2 - 168*c^3*x)*sqrt(-a^2*c)/a","A",0
661,1,73,0,0.543438," ","integrate((-a^2*c*x^2+c)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(5 \, a^{5} c^{2} x^{6} - 18 \, a^{4} c^{2} x^{5} + 15 \, a^{3} c^{2} x^{4} + 20 \, a^{2} c^{2} x^{3} - 45 \, a c^{2} x^{2} + 30 \, c^{2} x\right)} \sqrt{-a^{2} c}}{30 \, a}"," ",0,"1/30*(5*a^5*c^2*x^6 - 18*a^4*c^2*x^5 + 15*a^3*c^2*x^4 + 20*a^2*c^2*x^3 - 45*a*c^2*x^2 + 30*c^2*x)*sqrt(-a^2*c)/a","A",0
662,1,42,0,0.491559," ","integrate((-a^2*c*x^2+c)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(a^{3} c x^{4} - 4 \, a^{2} c x^{3} + 6 \, a c x^{2} - 4 \, c x\right)} \sqrt{-a^{2} c}}{4 \, a}"," ",0,"-1/4*(a^3*c*x^4 - 4*a^2*c*x^3 + 6*a*c*x^2 - 4*c*x)*sqrt(-a^2*c)/a","A",0
663,1,33,0,0.586931," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} - 6 \, a x + 8 \, \log\left(a x + 1\right)\right)} \sqrt{-a^{2} c}}{2 \, a^{2}}"," ",0,"1/2*(a^2*x^2 - 6*a*x + 8*log(a*x + 1))*sqrt(-a^2*c)/a^2","A",0
664,1,38,0,0.622594," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c} {\left({\left(a x + 1\right)} \log\left(a x + 1\right) + 2\right)}}{a^{3} c x + a^{2} c}"," ",0,"-sqrt(-a^2*c)*((a*x + 1)*log(a*x + 1) + 2)/(a^3*c*x + a^2*c)","A",0
665,1,39,0,0.526271," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c}}{2 \, {\left(a^{4} c^{2} x^{2} + 2 \, a^{3} c^{2} x + a^{2} c^{2}\right)}}"," ",0,"-1/2*sqrt(-a^2*c)/(a^4*c^2*x^2 + 2*a^3*c^2*x + a^2*c^2)","A",0
666,1,136,0,0.558531," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{4} x^{3} + 3 \, a^{3} x^{2} + 3 \, a^{2} x + a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) + 2 \, {\left(3 \, a^{2} x^{2} + 9 \, a x + 10\right)} \sqrt{-a^{2} c}}{48 \, {\left(a^{5} c^{3} x^{3} + 3 \, a^{4} c^{3} x^{2} + 3 \, a^{3} c^{3} x + a^{2} c^{3}\right)}}"," ",0,"-1/48*(3*(a^4*x^3 + 3*a^3*x^2 + 3*a^2*x + a)*sqrt(-c)*log((a^2*c*x^2 + 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) + 2*(3*a^2*x^2 + 9*a*x + 10)*sqrt(-a^2*c))/(a^5*c^3*x^3 + 3*a^4*c^3*x^2 + 3*a^3*c^3*x + a^2*c^3)","A",0
667,1,193,0,1.295912," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","-\frac{15 \, {\left(a^{6} x^{5} + 3 \, a^{5} x^{4} + 2 \, a^{4} x^{3} - 2 \, a^{3} x^{2} - 3 \, a^{2} x - a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) + 2 \, {\left(15 \, a^{4} x^{4} + 45 \, a^{3} x^{3} + 35 \, a^{2} x^{2} - 15 \, a x - 32\right)} \sqrt{-a^{2} c}}{192 \, {\left(a^{7} c^{4} x^{5} + 3 \, a^{6} c^{4} x^{4} + 2 \, a^{5} c^{4} x^{3} - 2 \, a^{4} c^{4} x^{2} - 3 \, a^{3} c^{4} x - a^{2} c^{4}\right)}}"," ",0,"-1/192*(15*(a^6*x^5 + 3*a^5*x^4 + 2*a^4*x^3 - 2*a^3*x^2 - 3*a^2*x - a)*sqrt(-c)*log((a^2*c*x^2 + 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) + 2*(15*a^4*x^4 + 45*a^3*x^3 + 35*a^2*x^2 - 15*a*x - 32)*sqrt(-a^2*c))/(a^7*c^4*x^5 + 3*a^6*c^4*x^4 + 2*a^5*c^4*x^3 - 2*a^4*c^4*x^2 - 3*a^3*c^4*x - a^2*c^4)","A",0
668,1,25,0,0.682220," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a x^{4} + 4 \, x^{3}\right)} \sqrt{-a^{2} c}}{12 \, a}"," ",0,"1/12*(3*a*x^4 + 4*x^3)*sqrt(-a^2*c)/a","A",0
669,1,25,0,0.463711," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a x^{3} + 3 \, x^{2}\right)} \sqrt{-a^{2} c}}{6 \, a}"," ",0,"1/6*(2*a*x^3 + 3*x^2)*sqrt(-a^2*c)/a","A",0
670,1,22,0,0.541921," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(a x^{2} + 2 \, x\right)}}{2 \, a}"," ",0,"1/2*sqrt(-a^2*c)*(a*x^2 + 2*x)/a","A",0
671,1,18,0,0.522305," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(a x + \log\left(x\right)\right)}}{a}"," ",0,"sqrt(-a^2*c)*(a*x + log(x))/a","A",0
672,1,22,0,0.593615," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(a x \log\left(x\right) - 1\right)}}{a x}"," ",0,"sqrt(-a^2*c)*(a*x*log(x) - 1)/(a*x)","A",0
673,1,184,0,0.720254," ","integrate(1/(a*x-1)*(a*x+1)*x^3*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(4 \, a^{4} x^{4} + 10 \, a^{3} x^{3} + 12 \, a^{2} x^{2} + 15 \, a x + 24\right)} \sqrt{-a^{2} c x^{2} + c} + 15 \, \sqrt{-c} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right)}{40 \, a^{4}}, \frac{{\left(4 \, a^{4} x^{4} + 10 \, a^{3} x^{3} + 12 \, a^{2} x^{2} + 15 \, a x + 24\right)} \sqrt{-a^{2} c x^{2} + c} + 15 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right)}{20 \, a^{4}}\right]"," ",0,"[1/40*(2*(4*a^4*x^4 + 10*a^3*x^3 + 12*a^2*x^2 + 15*a*x + 24)*sqrt(-a^2*c*x^2 + c) + 15*sqrt(-c)*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c))/a^4, 1/20*((4*a^4*x^4 + 10*a^3*x^3 + 12*a^2*x^2 + 15*a*x + 24)*sqrt(-a^2*c*x^2 + c) + 15*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)))/a^4]","A",0
674,1,168,0,0.570832," ","integrate(1/(a*x-1)*(a*x+1)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(6 \, a^{3} x^{3} + 16 \, a^{2} x^{2} + 21 \, a x + 32\right)} \sqrt{-a^{2} c x^{2} + c} + 21 \, \sqrt{-c} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right)}{48 \, a^{3}}, \frac{{\left(6 \, a^{3} x^{3} + 16 \, a^{2} x^{2} + 21 \, a x + 32\right)} \sqrt{-a^{2} c x^{2} + c} + 21 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right)}{24 \, a^{3}}\right]"," ",0,"[1/48*(2*(6*a^3*x^3 + 16*a^2*x^2 + 21*a*x + 32)*sqrt(-a^2*c*x^2 + c) + 21*sqrt(-c)*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c))/a^3, 1/24*((6*a^3*x^3 + 16*a^2*x^2 + 21*a*x + 32)*sqrt(-a^2*c*x^2 + c) + 21*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)))/a^3]","A",0
675,1,150,0,0.693789," ","integrate(1/(a*x-1)*(a*x+1)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} + 3 \, a x + 5\right)} + 3 \, \sqrt{-c} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right)}{6 \, a^{2}}, \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} + 3 \, a x + 5\right)} + 3 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right)}{3 \, a^{2}}\right]"," ",0,"[1/6*(2*sqrt(-a^2*c*x^2 + c)*(a^2*x^2 + 3*a*x + 5) + 3*sqrt(-c)*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c))/a^2, 1/3*(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 + 3*a*x + 5) + 3*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)))/a^2]","A",0
676,1,134,0,0.575890," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-a^{2} c x^{2} + c} {\left(a x + 4\right)} + 3 \, \sqrt{-c} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right)}{4 \, a}, \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 4\right)} + 3 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right)}{2 \, a}\right]"," ",0,"[1/4*(2*sqrt(-a^2*c*x^2 + c)*(a*x + 4) + 3*sqrt(-c)*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c))/a, 1/2*(sqrt(-a^2*c*x^2 + c)*(a*x + 4) + 3*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)))/a]","A",0
677,1,191,0,0.705731," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""fricas"")","\left[2 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) + \frac{1}{2} \, \sqrt{c} \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c} - 2 \, c}{x^{2}}\right) + \sqrt{-a^{2} c x^{2} + c}, \sqrt{-c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right) + \sqrt{-c} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) + \sqrt{-a^{2} c x^{2} + c}\right]"," ",0,"[2*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) + 1/2*sqrt(c)*log(-(a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*sqrt(c) - 2*c)/x^2) + sqrt(-a^2*c*x^2 + c), sqrt(-c)*arctan(sqrt(-a^2*c*x^2 + c)*sqrt(-c)/(a^2*c*x^2 - c)) + sqrt(-c)*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) + sqrt(-a^2*c*x^2 + c)]","A",0
678,1,209,0,0.539586," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{a \sqrt{c} x \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) + a \sqrt{c} x \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c} - 2 \, c}{x^{2}}\right) + \sqrt{-a^{2} c x^{2} + c}}{x}, \frac{4 \, a \sqrt{-c} x \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right) + a \sqrt{-c} x \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) + 2 \, \sqrt{-a^{2} c x^{2} + c}}{2 \, x}\right]"," ",0,"[(a*sqrt(c)*x*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) + a*sqrt(c)*x*log(-(a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*sqrt(c) - 2*c)/x^2) + sqrt(-a^2*c*x^2 + c))/x, 1/2*(4*a*sqrt(-c)*x*arctan(sqrt(-a^2*c*x^2 + c)*sqrt(-c)/(a^2*c*x^2 - c)) + a*sqrt(-c)*x*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) + 2*sqrt(-a^2*c*x^2 + c))/x]","A",0
679,1,148,0,0.690410," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{c} x^{2} \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c} - 2 \, c}{x^{2}}\right) + 2 \, \sqrt{-a^{2} c x^{2} + c} {\left(4 \, a x + 1\right)}}{4 \, x^{2}}, \frac{3 \, a^{2} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right) + \sqrt{-a^{2} c x^{2} + c} {\left(4 \, a x + 1\right)}}{2 \, x^{2}}\right]"," ",0,"[1/4*(3*a^2*sqrt(c)*x^2*log(-(a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*sqrt(c) - 2*c)/x^2) + 2*sqrt(-a^2*c*x^2 + c)*(4*a*x + 1))/x^2, 1/2*(3*a^2*sqrt(-c)*x^2*arctan(sqrt(-a^2*c*x^2 + c)*sqrt(-c)/(a^2*c*x^2 - c)) + sqrt(-a^2*c*x^2 + c)*(4*a*x + 1))/x^2]","A",0
680,1,164,0,0.490836," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, a^{3} \sqrt{c} x^{3} \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c} - 2 \, c}{x^{2}}\right) + 2 \, \sqrt{-a^{2} c x^{2} + c} {\left(5 \, a^{2} x^{2} + 3 \, a x + 1\right)}}{6 \, x^{3}}, \frac{3 \, a^{3} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right) + \sqrt{-a^{2} c x^{2} + c} {\left(5 \, a^{2} x^{2} + 3 \, a x + 1\right)}}{3 \, x^{3}}\right]"," ",0,"[1/6*(3*a^3*sqrt(c)*x^3*log(-(a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*sqrt(c) - 2*c)/x^2) + 2*sqrt(-a^2*c*x^2 + c)*(5*a^2*x^2 + 3*a*x + 1))/x^3, 1/3*(3*a^3*sqrt(-c)*x^3*arctan(sqrt(-a^2*c*x^2 + c)*sqrt(-c)/(a^2*c*x^2 - c)) + sqrt(-a^2*c*x^2 + c)*(5*a^2*x^2 + 3*a*x + 1))/x^3]","A",0
681,1,180,0,0.663465," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{21 \, a^{4} \sqrt{c} x^{4} \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c} - 2 \, c}{x^{2}}\right) + 2 \, {\left(32 \, a^{3} x^{3} + 21 \, a^{2} x^{2} + 16 \, a x + 6\right)} \sqrt{-a^{2} c x^{2} + c}}{48 \, x^{4}}, \frac{21 \, a^{4} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right) + {\left(32 \, a^{3} x^{3} + 21 \, a^{2} x^{2} + 16 \, a x + 6\right)} \sqrt{-a^{2} c x^{2} + c}}{24 \, x^{4}}\right]"," ",0,"[1/48*(21*a^4*sqrt(c)*x^4*log(-(a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*sqrt(c) - 2*c)/x^2) + 2*(32*a^3*x^3 + 21*a^2*x^2 + 16*a*x + 6)*sqrt(-a^2*c*x^2 + c))/x^4, 1/24*(21*a^4*sqrt(-c)*x^4*arctan(sqrt(-a^2*c*x^2 + c)*sqrt(-c)/(a^2*c*x^2 - c)) + (32*a^3*x^3 + 21*a^2*x^2 + 16*a*x + 6)*sqrt(-a^2*c*x^2 + c))/x^4]","A",0
682,1,58,0,0.536202," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(12 \, a^{5} x^{5} + 45 \, a^{4} x^{4} + 80 \, a^{3} x^{3} + 120 \, a^{2} x^{2} + 240 \, a x + 240 \, \log\left(a x - 1\right)\right)} \sqrt{-a^{2} c}}{60 \, a^{5}}"," ",0,"1/60*(12*a^5*x^5 + 45*a^4*x^4 + 80*a^3*x^3 + 120*a^2*x^2 + 240*a*x + 240*log(a*x - 1))*sqrt(-a^2*c)/a^5","A",0
683,1,49,0,0.561315," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{4} x^{4} + 4 \, a^{3} x^{3} + 8 \, a^{2} x^{2} + 16 \, a x + 16 \, \log\left(a x - 1\right)\right)} \sqrt{-a^{2} c}}{4 \, a^{4}}"," ",0,"1/4*(a^4*x^4 + 4*a^3*x^3 + 8*a^2*x^2 + 16*a*x + 16*log(a*x - 1))*sqrt(-a^2*c)/a^4","A",0
684,1,42,0,0.545173," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} + 9 \, a^{2} x^{2} + 24 \, a x + 24 \, \log\left(a x - 1\right)\right)} \sqrt{-a^{2} c}}{6 \, a^{3}}"," ",0,"1/6*(2*a^3*x^3 + 9*a^2*x^2 + 24*a*x + 24*log(a*x - 1))*sqrt(-a^2*c)/a^3","A",0
685,1,33,0,0.626947," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} + 6 \, a x + 8 \, \log\left(a x - 1\right)\right)} \sqrt{-a^{2} c}}{2 \, a^{2}}"," ",0,"1/2*(a^2*x^2 + 6*a*x + 8*log(a*x - 1))*sqrt(-a^2*c)/a^2","A",0
686,1,28,0,0.680043," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(a x + 4 \, \log\left(a x - 1\right) - \log\left(x\right)\right)}}{a}"," ",0,"sqrt(-a^2*c)*(a*x + 4*log(a*x - 1) - log(x))/a","A",0
687,1,33,0,0.546471," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(4 \, a x \log\left(a x - 1\right) - 3 \, a x \log\left(x\right) + 1\right)}}{a x}"," ",0,"sqrt(-a^2*c)*(4*a*x*log(a*x - 1) - 3*a*x*log(x) + 1)/(a*x)","A",0
688,1,90,0,0.582511," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{8 \, a^{3} \sqrt{-c} x^{2} \log\left(\frac{2 \, a^{3} c x^{2} - 2 \, a^{2} c x + \sqrt{-a^{2} c} {\left(2 \, a x - 1\right)} \sqrt{-c} + a c}{a x^{2} - x}\right) + \sqrt{-a^{2} c} {\left(6 \, a x + 1\right)}}{2 \, a x^{2}}"," ",0,"1/2*(8*a^3*sqrt(-c)*x^2*log((2*a^3*c*x^2 - 2*a^2*c*x + sqrt(-a^2*c)*(2*a*x - 1)*sqrt(-c) + a*c)/(a*x^2 - x)) + sqrt(-a^2*c)*(6*a*x + 1))/(a*x^2)","A",0
689,1,98,0,0.640539," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""fricas"")","\frac{24 \, a^{4} \sqrt{-c} x^{3} \log\left(\frac{2 \, a^{3} c x^{2} - 2 \, a^{2} c x + \sqrt{-a^{2} c} {\left(2 \, a x - 1\right)} \sqrt{-c} + a c}{a x^{2} - x}\right) + {\left(24 \, a^{2} x^{2} + 9 \, a x + 2\right)} \sqrt{-a^{2} c}}{6 \, a x^{3}}"," ",0,"1/6*(24*a^4*sqrt(-c)*x^3*log((2*a^3*c*x^2 - 2*a^2*c*x + sqrt(-a^2*c)*(2*a*x - 1)*sqrt(-c) + a*c)/(a*x^2 - x)) + (24*a^2*x^2 + 9*a*x + 2)*sqrt(-a^2*c))/(a*x^3)","A",0
690,1,106,0,0.553592," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^5,x, algorithm=""fricas"")","\frac{16 \, a^{5} \sqrt{-c} x^{4} \log\left(\frac{2 \, a^{3} c x^{2} - 2 \, a^{2} c x + \sqrt{-a^{2} c} {\left(2 \, a x - 1\right)} \sqrt{-c} + a c}{a x^{2} - x}\right) + {\left(16 \, a^{3} x^{3} + 8 \, a^{2} x^{2} + 4 \, a x + 1\right)} \sqrt{-a^{2} c}}{4 \, a x^{4}}"," ",0,"1/4*(16*a^5*sqrt(-c)*x^4*log((2*a^3*c*x^2 - 2*a^2*c*x + sqrt(-a^2*c)*(2*a*x - 1)*sqrt(-c) + a*c)/(a*x^2 - x)) + (16*a^3*x^3 + 8*a^2*x^2 + 4*a*x + 1)*sqrt(-a^2*c))/(a*x^4)","A",0
691,1,76,0,0.609609," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^4/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} - 4 \, a x + {\left(a x - 1\right)} \log\left(a x + 1\right) + 7 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 2\right)} \sqrt{-a^{2} c}}{4 \, {\left(a^{7} c^{2} x - a^{6} c^{2}\right)}}"," ",0,"1/4*(2*a^3*x^3 + 2*a^2*x^2 - 4*a*x + (a*x - 1)*log(a*x + 1) + 7*(a*x - 1)*log(a*x - 1) - 2)*sqrt(-a^2*c)/(a^7*c^2*x - a^6*c^2)","A",0
692,1,69,0,0.588838," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(4 \, a^{2} x^{2} - 4 \, a x - {\left(a x - 1\right)} \log\left(a x + 1\right) + 5 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 2\right)} \sqrt{-a^{2} c}}{4 \, {\left(a^{6} c^{2} x - a^{5} c^{2}\right)}}"," ",0,"1/4*(4*a^2*x^2 - 4*a*x - (a*x - 1)*log(a*x + 1) + 5*(a*x - 1)*log(a*x - 1) - 2)*sqrt(-a^2*c)/(a^6*c^2*x - a^5*c^2)","A",0
693,1,56,0,0.569241," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left({\left(a x - 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 2\right)}}{4 \, {\left(a^{5} c^{2} x - a^{4} c^{2}\right)}}"," ",0,"1/4*sqrt(-a^2*c)*((a*x - 1)*log(a*x + 1) + 3*(a*x - 1)*log(a*x - 1) - 2)/(a^5*c^2*x - a^4*c^2)","A",0
694,1,86,0,0.571110," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(a^{2} x - a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) + 2 \, \sqrt{-a^{2} c}}{4 \, {\left(a^{4} c^{2} x - a^{3} c^{2}\right)}}"," ",0,"-1/4*((a^2*x - a)*sqrt(-c)*log((a^2*c*x^2 - 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) + 2*sqrt(-a^2*c))/(a^4*c^2*x - a^3*c^2)","A",0
695,1,86,0,0.583881," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(a^{2} x - a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) + 2 \, \sqrt{-a^{2} c}}{4 \, {\left(a^{3} c^{2} x - a^{2} c^{2}\right)}}"," ",0,"-1/4*((a^2*x - a)*sqrt(-c)*log((a^2*c*x^2 + 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) + 2*sqrt(-a^2*c))/(a^3*c^2*x - a^2*c^2)","A",0
696,1,63,0,0.495109," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c} {\left({\left(a x - 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 4 \, {\left(a x - 1\right)} \log\left(x\right) + 2\right)}}{4 \, {\left(a^{2} c^{2} x - a c^{2}\right)}}"," ",0,"-1/4*sqrt(-a^2*c)*((a*x - 1)*log(a*x + 1) + 3*(a*x - 1)*log(a*x - 1) - 4*(a*x - 1)*log(x) + 2)/(a^2*c^2*x - a*c^2)","A",0
697,1,92,0,0.625482," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c} {\left(6 \, a x - {\left(a^{2} x^{2} - a x\right)} \log\left(a x + 1\right) + 5 \, {\left(a^{2} x^{2} - a x\right)} \log\left(a x - 1\right) - 4 \, {\left(a^{2} x^{2} - a x\right)} \log\left(x\right) - 4\right)}}{4 \, {\left(a^{2} c^{2} x^{2} - a c^{2} x\right)}}"," ",0,"-1/4*sqrt(-a^2*c)*(6*a*x - (a^2*x^2 - a*x)*log(a*x + 1) + 5*(a^2*x^2 - a*x)*log(a*x - 1) - 4*(a^2*x^2 - a*x)*log(x) - 4)/(a^2*c^2*x^2 - a*c^2*x)","A",0
698,1,113,0,0.543939," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(6 \, a^{2} x^{2} - 2 \, a x + {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \log\left(a x + 1\right) + 7 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \log\left(a x - 1\right) - 8 \, {\left(a^{3} x^{3} - a^{2} x^{2}\right)} \log\left(x\right) - 2\right)} \sqrt{-a^{2} c}}{4 \, {\left(a^{2} c^{2} x^{3} - a c^{2} x^{2}\right)}}"," ",0,"-1/4*(6*a^2*x^2 - 2*a*x + (a^3*x^3 - a^2*x^2)*log(a*x + 1) + 7*(a^3*x^3 - a^2*x^2)*log(a*x - 1) - 8*(a^3*x^3 - a^2*x^2)*log(x) - 2)*sqrt(-a^2*c)/(a^2*c^2*x^3 - a*c^2*x^2)","A",0
699,1,138,0,0.508302," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^5/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(16 \, a^{4} x^{4} - 16 \, a^{3} x^{3} - 34 \, a^{2} x^{2} + 18 \, a x - 7 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right) + 23 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x - 1\right) + 12\right)} \sqrt{-a^{2} c}}{16 \, {\left(a^{10} c^{3} x^{3} - a^{9} c^{3} x^{2} - a^{8} c^{3} x + a^{7} c^{3}\right)}}"," ",0,"-1/16*(16*a^4*x^4 - 16*a^3*x^3 - 34*a^2*x^2 + 18*a*x - 7*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x + 1) + 23*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x - 1) + 12)*sqrt(-a^2*c)/(a^10*c^3*x^3 - a^9*c^3*x^2 - a^8*c^3*x + a^7*c^3)","A",0
700,1,122,0,0.465388," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^4/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(10 \, a^{2} x^{2} + 6 \, a x - 5 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right) - 11 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x - 1\right) - 12\right)} \sqrt{-a^{2} c}}{16 \, {\left(a^{9} c^{3} x^{3} - a^{8} c^{3} x^{2} - a^{7} c^{3} x + a^{6} c^{3}\right)}}"," ",0,"1/16*(10*a^2*x^2 + 6*a*x - 5*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x + 1) - 11*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x - 1) - 12)*sqrt(-a^2*c)/(a^9*c^3*x^3 - a^8*c^3*x^2 - a^7*c^3*x + a^6*c^3)","A",0
701,1,136,0,0.615049," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{4} x^{3} - a^{3} x^{2} - a^{2} x + a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) - 2 \, {\left(5 \, a^{2} x^{2} - a x - 2\right)} \sqrt{-a^{2} c}}{16 \, {\left(a^{8} c^{3} x^{3} - a^{7} c^{3} x^{2} - a^{6} c^{3} x + a^{5} c^{3}\right)}}"," ",0,"-1/16*(3*(a^4*x^3 - a^3*x^2 - a^2*x + a)*sqrt(-c)*log((a^2*c*x^2 + 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) - 2*(5*a^2*x^2 - a*x - 2)*sqrt(-a^2*c))/(a^8*c^3*x^3 - a^7*c^3*x^2 - a^6*c^3*x + a^5*c^3)","A",0
702,1,134,0,0.575826," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(a^{4} x^{3} - a^{3} x^{2} - a^{2} x + a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) - 2 \, {\left(a^{2} x^{2} + 3 \, a x - 2\right)} \sqrt{-a^{2} c}}{16 \, {\left(a^{7} c^{3} x^{3} - a^{6} c^{3} x^{2} - a^{5} c^{3} x + a^{4} c^{3}\right)}}"," ",0,"-1/16*((a^4*x^3 - a^3*x^2 - a^2*x + a)*sqrt(-c)*log((a^2*c*x^2 - 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) - 2*(a^2*x^2 + 3*a*x - 2)*sqrt(-a^2*c))/(a^7*c^3*x^3 - a^6*c^3*x^2 - a^5*c^3*x + a^4*c^3)","A",0
703,1,134,0,0.669143," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(a^{4} x^{3} - a^{3} x^{2} - a^{2} x + a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) - 2 \, {\left(a^{2} x^{2} - a x + 2\right)} \sqrt{-a^{2} c}}{16 \, {\left(a^{6} c^{3} x^{3} - a^{5} c^{3} x^{2} - a^{4} c^{3} x + a^{3} c^{3}\right)}}"," ",0,"-1/16*((a^4*x^3 - a^3*x^2 - a^2*x + a)*sqrt(-c)*log((a^2*c*x^2 - 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) - 2*(a^2*x^2 - a*x + 2)*sqrt(-a^2*c))/(a^6*c^3*x^3 - a^5*c^3*x^2 - a^4*c^3*x + a^3*c^3)","A",0
704,1,136,0,0.714133," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{4} x^{3} - a^{3} x^{2} - a^{2} x + a\right)} \sqrt{-c} \log\left(\frac{a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c} \sqrt{-c} x + c}{a^{2} x^{2} - 1}\right) + 2 \, {\left(3 \, a^{2} x^{2} - 3 \, a x - 2\right)} \sqrt{-a^{2} c}}{16 \, {\left(a^{5} c^{3} x^{3} - a^{4} c^{3} x^{2} - a^{3} c^{3} x + a^{2} c^{3}\right)}}"," ",0,"-1/16*(3*(a^4*x^3 - a^3*x^2 - a^2*x + a)*sqrt(-c)*log((a^2*c*x^2 + 2*sqrt(-a^2*c)*sqrt(-c)*x + c)/(a^2*x^2 - 1)) + 2*(3*a^2*x^2 - 3*a*x - 2)*sqrt(-a^2*c))/(a^5*c^3*x^3 - a^4*c^3*x^2 - a^3*c^3*x + a^2*c^3)","A",0
705,1,145,0,0.502076," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(6 \, a^{2} x^{2} + 2 \, a x + 5 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right) + 11 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x - 1\right) - 16 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(x\right) - 12\right)} \sqrt{-a^{2} c}}{16 \, {\left(a^{4} c^{3} x^{3} - a^{3} c^{3} x^{2} - a^{2} c^{3} x + a c^{3}\right)}}"," ",0,"-1/16*(6*a^2*x^2 + 2*a*x + 5*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x + 1) + 11*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x - 1) - 16*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(x) - 12)*sqrt(-a^2*c)/(a^4*c^3*x^3 - a^3*c^3*x^2 - a^2*c^3*x + a*c^3)","A",0
706,1,174,0,0.692353," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(30 \, a^{3} x^{3} - 22 \, a^{2} x^{2} - 28 \, a x - 7 \, {\left(a^{4} x^{4} - a^{3} x^{3} - a^{2} x^{2} + a x\right)} \log\left(a x + 1\right) + 23 \, {\left(a^{4} x^{4} - a^{3} x^{3} - a^{2} x^{2} + a x\right)} \log\left(a x - 1\right) - 16 \, {\left(a^{4} x^{4} - a^{3} x^{3} - a^{2} x^{2} + a x\right)} \log\left(x\right) + 16\right)} \sqrt{-a^{2} c}}{16 \, {\left(a^{4} c^{3} x^{4} - a^{3} c^{3} x^{3} - a^{2} c^{3} x^{2} + a c^{3} x\right)}}"," ",0,"-1/16*(30*a^3*x^3 - 22*a^2*x^2 - 28*a*x - 7*(a^4*x^4 - a^3*x^3 - a^2*x^2 + a*x)*log(a*x + 1) + 23*(a^4*x^4 - a^3*x^3 - a^2*x^2 + a*x)*log(a*x - 1) - 16*(a^4*x^4 - a^3*x^3 - a^2*x^2 + a*x)*log(x) + 16)*sqrt(-a^2*c)/(a^4*c^3*x^4 - a^3*c^3*x^3 - a^2*c^3*x^2 + a*c^3*x)","A",0
707,1,25,0,0.691939," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a x^{4} - 4 \, x^{3}\right)} \sqrt{-a^{2} c}}{12 \, a}"," ",0,"1/12*(3*a*x^4 - 4*x^3)*sqrt(-a^2*c)/a","A",0
708,1,25,0,1.419352," ","integrate(x*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a x^{3} - 3 \, x^{2}\right)} \sqrt{-a^{2} c}}{6 \, a}"," ",0,"1/6*(2*a*x^3 - 3*x^2)*sqrt(-a^2*c)/a","A",0
709,1,22,0,0.660369," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(a x^{2} - 2 \, x\right)}}{2 \, a}"," ",0,"1/2*sqrt(-a^2*c)*(a*x^2 - 2*x)/a","A",0
710,1,20,0,0.575402," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(a x - \log\left(x\right)\right)}}{a}"," ",0,"sqrt(-a^2*c)*(a*x - log(x))/a","A",0
711,1,22,0,0.706364," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(a x \log\left(x\right) + 1\right)}}{a x}"," ",0,"sqrt(-a^2*c)*(a*x*log(x) + 1)/(a*x)","A",0
712,1,184,0,0.534469," ","integrate(x^3*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(4 \, a^{4} x^{4} - 10 \, a^{3} x^{3} + 12 \, a^{2} x^{2} - 15 \, a x + 24\right)} \sqrt{-a^{2} c x^{2} + c} + 15 \, \sqrt{-c} \log\left(2 \, a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right)}{40 \, a^{4}}, \frac{{\left(4 \, a^{4} x^{4} - 10 \, a^{3} x^{3} + 12 \, a^{2} x^{2} - 15 \, a x + 24\right)} \sqrt{-a^{2} c x^{2} + c} - 15 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right)}{20 \, a^{4}}\right]"," ",0,"[1/40*(2*(4*a^4*x^4 - 10*a^3*x^3 + 12*a^2*x^2 - 15*a*x + 24)*sqrt(-a^2*c*x^2 + c) + 15*sqrt(-c)*log(2*a^2*c*x^2 + 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c))/a^4, 1/20*((4*a^4*x^4 - 10*a^3*x^3 + 12*a^2*x^2 - 15*a*x + 24)*sqrt(-a^2*c*x^2 + c) - 15*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)))/a^4]","A",0
713,1,168,0,1.293820," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(6 \, a^{3} x^{3} - 16 \, a^{2} x^{2} + 21 \, a x - 32\right)} \sqrt{-a^{2} c x^{2} + c} + 21 \, \sqrt{-c} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right)}{48 \, a^{3}}, \frac{{\left(6 \, a^{3} x^{3} - 16 \, a^{2} x^{2} + 21 \, a x - 32\right)} \sqrt{-a^{2} c x^{2} + c} + 21 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right)}{24 \, a^{3}}\right]"," ",0,"[1/48*(2*(6*a^3*x^3 - 16*a^2*x^2 + 21*a*x - 32)*sqrt(-a^2*c*x^2 + c) + 21*sqrt(-c)*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c))/a^3, 1/24*((6*a^3*x^3 - 16*a^2*x^2 + 21*a*x - 32)*sqrt(-a^2*c*x^2 + c) + 21*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)))/a^3]","A",0
714,1,150,0,0.601234," ","integrate(x*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 3 \, a x + 5\right)} + 3 \, \sqrt{-c} \log\left(2 \, a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right)}{6 \, a^{2}}, \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 3 \, a x + 5\right)} - 3 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right)}{3 \, a^{2}}\right]"," ",0,"[1/6*(2*sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 3*a*x + 5) + 3*sqrt(-c)*log(2*a^2*c*x^2 + 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c))/a^2, 1/3*(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 3*a*x + 5) - 3*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)))/a^2]","A",0
715,1,134,0,0.530902," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-a^{2} c x^{2} + c} {\left(a x - 4\right)} + 3 \, \sqrt{-c} \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right)}{4 \, a}, \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x - 4\right)} + 3 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right)}{2 \, a}\right]"," ",0,"[1/4*(2*sqrt(-a^2*c*x^2 + c)*(a*x - 4) + 3*sqrt(-c)*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c))/a, 1/2*(sqrt(-a^2*c*x^2 + c)*(a*x - 4) + 3*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)))/a]","A",0
716,1,191,0,0.894706," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x,x, algorithm=""fricas"")","\left[-2 \, \sqrt{c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) + \frac{1}{2} \, \sqrt{c} \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c} - 2 \, c}{x^{2}}\right) + \sqrt{-a^{2} c x^{2} + c}, \sqrt{-c} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right) + \sqrt{-c} \log\left(2 \, a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) + \sqrt{-a^{2} c x^{2} + c}\right]"," ",0,"[-2*sqrt(c)*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) + 1/2*sqrt(c)*log(-(a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*sqrt(c) - 2*c)/x^2) + sqrt(-a^2*c*x^2 + c), sqrt(-c)*arctan(sqrt(-a^2*c*x^2 + c)*sqrt(-c)/(a^2*c*x^2 - c)) + sqrt(-c)*log(2*a^2*c*x^2 + 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) + sqrt(-a^2*c*x^2 + c)]","A",0
717,1,210,0,0.749512," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^2,x, algorithm=""fricas"")","\left[\frac{a \sqrt{c} x \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} a \sqrt{c} x}{a^{2} c x^{2} - c}\right) + a \sqrt{c} x \log\left(-\frac{a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c} - 2 \, c}{x^{2}}\right) + \sqrt{-a^{2} c x^{2} + c}}{x}, -\frac{4 \, a \sqrt{-c} x \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right) - a \sqrt{-c} x \log\left(2 \, a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} a \sqrt{-c} x - c\right) - 2 \, \sqrt{-a^{2} c x^{2} + c}}{2 \, x}\right]"," ",0,"[(a*sqrt(c)*x*arctan(sqrt(-a^2*c*x^2 + c)*a*sqrt(c)*x/(a^2*c*x^2 - c)) + a*sqrt(c)*x*log(-(a^2*c*x^2 + 2*sqrt(-a^2*c*x^2 + c)*sqrt(c) - 2*c)/x^2) + sqrt(-a^2*c*x^2 + c))/x, -1/2*(4*a*sqrt(-c)*x*arctan(sqrt(-a^2*c*x^2 + c)*sqrt(-c)/(a^2*c*x^2 - c)) - a*sqrt(-c)*x*log(2*a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*a*sqrt(-c)*x - c) - 2*sqrt(-a^2*c*x^2 + c))/x]","A",0
718,1,149,0,0.587899," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{c} x^{2} \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c} - 2 \, c}{x^{2}}\right) - 2 \, \sqrt{-a^{2} c x^{2} + c} {\left(4 \, a x - 1\right)}}{4 \, x^{2}}, \frac{3 \, a^{2} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right) - \sqrt{-a^{2} c x^{2} + c} {\left(4 \, a x - 1\right)}}{2 \, x^{2}}\right]"," ",0,"[1/4*(3*a^2*sqrt(c)*x^2*log(-(a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*sqrt(c) - 2*c)/x^2) - 2*sqrt(-a^2*c*x^2 + c)*(4*a*x - 1))/x^2, 1/2*(3*a^2*sqrt(-c)*x^2*arctan(sqrt(-a^2*c*x^2 + c)*sqrt(-c)/(a^2*c*x^2 - c)) - sqrt(-a^2*c*x^2 + c)*(4*a*x - 1))/x^2]","A",0
719,1,165,0,0.716317," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, a^{3} \sqrt{c} x^{3} \log\left(-\frac{a^{2} c x^{2} + 2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c} - 2 \, c}{x^{2}}\right) + 2 \, \sqrt{-a^{2} c x^{2} + c} {\left(5 \, a^{2} x^{2} - 3 \, a x + 1\right)}}{6 \, x^{3}}, -\frac{3 \, a^{3} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right) - \sqrt{-a^{2} c x^{2} + c} {\left(5 \, a^{2} x^{2} - 3 \, a x + 1\right)}}{3 \, x^{3}}\right]"," ",0,"[1/6*(3*a^3*sqrt(c)*x^3*log(-(a^2*c*x^2 + 2*sqrt(-a^2*c*x^2 + c)*sqrt(c) - 2*c)/x^2) + 2*sqrt(-a^2*c*x^2 + c)*(5*a^2*x^2 - 3*a*x + 1))/x^3, -1/3*(3*a^3*sqrt(-c)*x^3*arctan(sqrt(-a^2*c*x^2 + c)*sqrt(-c)/(a^2*c*x^2 - c)) - sqrt(-a^2*c*x^2 + c)*(5*a^2*x^2 - 3*a*x + 1))/x^3]","A",0
720,1,181,0,0.543074," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^5,x, algorithm=""fricas"")","\left[\frac{21 \, a^{4} \sqrt{c} x^{4} \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{c} - 2 \, c}{x^{2}}\right) - 2 \, {\left(32 \, a^{3} x^{3} - 21 \, a^{2} x^{2} + 16 \, a x - 6\right)} \sqrt{-a^{2} c x^{2} + c}}{48 \, x^{4}}, \frac{21 \, a^{4} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-c}}{a^{2} c x^{2} - c}\right) - {\left(32 \, a^{3} x^{3} - 21 \, a^{2} x^{2} + 16 \, a x - 6\right)} \sqrt{-a^{2} c x^{2} + c}}{24 \, x^{4}}\right]"," ",0,"[1/48*(21*a^4*sqrt(c)*x^4*log(-(a^2*c*x^2 - 2*sqrt(-a^2*c*x^2 + c)*sqrt(c) - 2*c)/x^2) - 2*(32*a^3*x^3 - 21*a^2*x^2 + 16*a*x - 6)*sqrt(-a^2*c*x^2 + c))/x^4, 1/24*(21*a^4*sqrt(-c)*x^4*arctan(sqrt(-a^2*c*x^2 + c)*sqrt(-c)/(a^2*c*x^2 - c)) - (32*a^3*x^3 - 21*a^2*x^2 + 16*a*x - 6)*sqrt(-a^2*c*x^2 + c))/x^4]","A",0
721,1,58,0,0.690999," ","integrate(x^3*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(12 \, a^{5} x^{5} - 45 \, a^{4} x^{4} + 80 \, a^{3} x^{3} - 120 \, a^{2} x^{2} + 240 \, a x - 240 \, \log\left(a x + 1\right)\right)} \sqrt{-a^{2} c}}{60 \, a^{5}}"," ",0,"1/60*(12*a^5*x^5 - 45*a^4*x^4 + 80*a^3*x^3 - 120*a^2*x^2 + 240*a*x - 240*log(a*x + 1))*sqrt(-a^2*c)/a^5","A",0
722,1,49,0,0.472325," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 8 \, a^{2} x^{2} - 16 \, a x + 16 \, \log\left(a x + 1\right)\right)} \sqrt{-a^{2} c}}{4 \, a^{4}}"," ",0,"1/4*(a^4*x^4 - 4*a^3*x^3 + 8*a^2*x^2 - 16*a*x + 16*log(a*x + 1))*sqrt(-a^2*c)/a^4","A",0
723,1,42,0,0.582879," ","integrate(x*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} - 9 \, a^{2} x^{2} + 24 \, a x - 24 \, \log\left(a x + 1\right)\right)} \sqrt{-a^{2} c}}{6 \, a^{3}}"," ",0,"1/6*(2*a^3*x^3 - 9*a^2*x^2 + 24*a*x - 24*log(a*x + 1))*sqrt(-a^2*c)/a^3","A",0
724,1,33,0,0.572885," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} - 6 \, a x + 8 \, \log\left(a x + 1\right)\right)} \sqrt{-a^{2} c}}{2 \, a^{2}}"," ",0,"1/2*(a^2*x^2 - 6*a*x + 8*log(a*x + 1))*sqrt(-a^2*c)/a^2","A",0
725,1,26,0,0.643432," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(a x - 4 \, \log\left(a x + 1\right) + \log\left(x\right)\right)}}{a}"," ",0,"sqrt(-a^2*c)*(a*x - 4*log(a*x + 1) + log(x))/a","A",0
726,1,33,0,0.623219," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c} {\left(4 \, a x \log\left(a x + 1\right) - 3 \, a x \log\left(x\right) - 1\right)}}{a x}"," ",0,"sqrt(-a^2*c)*(4*a*x*log(a*x + 1) - 3*a*x*log(x) - 1)/(a*x)","A",0
727,1,88,0,0.767047," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""fricas"")","\frac{8 \, a^{3} \sqrt{-c} x^{2} \log\left(\frac{2 \, a^{3} c x^{2} + 2 \, a^{2} c x + \sqrt{-a^{2} c} {\left(2 \, a x + 1\right)} \sqrt{-c} + a c}{a x^{2} + x}\right) + \sqrt{-a^{2} c} {\left(6 \, a x - 1\right)}}{2 \, a x^{2}}"," ",0,"1/2*(8*a^3*sqrt(-c)*x^2*log((2*a^3*c*x^2 + 2*a^2*c*x + sqrt(-a^2*c)*(2*a*x + 1)*sqrt(-c) + a*c)/(a*x^2 + x)) + sqrt(-a^2*c)*(6*a*x - 1))/(a*x^2)","A",0
728,1,98,0,0.576710," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""fricas"")","\frac{24 \, a^{4} \sqrt{-c} x^{3} \log\left(\frac{2 \, a^{3} c x^{2} + 2 \, a^{2} c x - \sqrt{-a^{2} c} {\left(2 \, a x + 1\right)} \sqrt{-c} + a c}{a x^{2} + x}\right) - {\left(24 \, a^{2} x^{2} - 9 \, a x + 2\right)} \sqrt{-a^{2} c}}{6 \, a x^{3}}"," ",0,"1/6*(24*a^4*sqrt(-c)*x^3*log((2*a^3*c*x^2 + 2*a^2*c*x - sqrt(-a^2*c)*(2*a*x + 1)*sqrt(-c) + a*c)/(a*x^2 + x)) - (24*a^2*x^2 - 9*a*x + 2)*sqrt(-a^2*c))/(a*x^3)","A",0
729,1,104,0,0.422665," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""fricas"")","\frac{16 \, a^{5} \sqrt{-c} x^{4} \log\left(\frac{2 \, a^{3} c x^{2} + 2 \, a^{2} c x + \sqrt{-a^{2} c} {\left(2 \, a x + 1\right)} \sqrt{-c} + a c}{a x^{2} + x}\right) + {\left(16 \, a^{3} x^{3} - 8 \, a^{2} x^{2} + 4 \, a x - 1\right)} \sqrt{-a^{2} c}}{4 \, a x^{4}}"," ",0,"1/4*(16*a^5*sqrt(-c)*x^4*log((2*a^3*c*x^2 + 2*a^2*c*x + sqrt(-a^2*c)*(2*a*x + 1)*sqrt(-c) + a*c)/(a*x^2 + x)) + (16*a^3*x^3 - 8*a^2*x^2 + 4*a*x - 1)*sqrt(-a^2*c))/(a*x^4)","A",0
730,0,0,0,0.627852," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} + 2 \, a x + 1\right)} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x^{2} - 2 \, a x + 1}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 + 2*a*x + 1)*x^m*sqrt((a*x - 1)/(a*x + 1))/(a^2*x^2 - 2*a*x + 1), x)","F",0
731,0,0,0,0.621830," ","integrate(1/(a*x-1)*(a*x+1)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)} x^{m}}{a x - 1}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*(a*x + 1)*x^m/(a*x - 1), x)","F",0
732,1,74,0,0.600268," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c x^{2} + c} {\left({\left(a m + a\right)} x^{2} + {\left(m + 2\right)} x\right)} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}}{m^{2} - {\left(a m^{2} + 3 \, a m + 2 \, a\right)} x + 3 \, m + 2}"," ",0,"-sqrt(-a^2*c*x^2 + c)*((a*m + a)*x^2 + (m + 2)*x)*x^m*sqrt((a*x - 1)/(a*x + 1))/(m^2 - (a*m^2 + 3*a*m + 2*a)*x + 3*m + 2)","A",0
733,1,75,0,0.528779," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c x^{2} + c} {\left({\left(a m + a\right)} x^{2} - {\left(m + 2\right)} x\right)} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}}{m^{2} - {\left(a m^{2} + 3 \, a m + 2 \, a\right)} x + 3 \, m + 2}"," ",0,"-sqrt(-a^2*c*x^2 + c)*((a*m + a)*x^2 - (m + 2)*x)*x^m*sqrt((a*x - 1)/(a*x + 1))/(m^2 - (a*m^2 + 3*a*m + 2*a)*x + 3*m + 2)","A",0
734,0,0,0,0.558154," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x - 1\right)} x^{m}}{a x + 1}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*(a*x - 1)*x^m/(a*x + 1), x)","F",0
735,0,0,0,0.592114," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x - 1\right)} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*(a*x - 1)*x^m*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1), x)","F",0
736,0,0,0,0.537659," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(-(a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
737,0,0,0,0.682150," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral((a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
738,0,0,0,0.629246," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c x^{2} - c\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(-(a^2*c*x^2 - c)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
739,0,0,0,0.475470," ","integrate(exp(n*arccoth(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
740,1,28,0,0.818681," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c),x, algorithm=""fricas"")","-\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c n}"," ",0,"-((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c*n)","A",0
741,1,80,0,0.574052," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} x^{2} + 2 \, a n x + n^{2} - 2\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{2} n^{3} - 4 \, a c^{2} n - {\left(a^{3} c^{2} n^{3} - 4 \, a^{3} c^{2} n\right)} x^{2}}"," ",0,"-(2*a^2*x^2 + 2*a*n*x + n^2 - 2)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^2*n^3 - 4*a*c^2*n - (a^3*c^2*n^3 - 4*a^3*c^2*n)*x^2)","A",0
742,1,175,0,0.599516," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{{\left(24 \, a^{4} x^{4} + 24 \, a^{3} n x^{3} + n^{4} + 12 \, {\left(a^{2} n^{2} - 4 \, a^{2}\right)} x^{2} - 16 \, n^{2} + 4 \, {\left(a n^{3} - 10 \, a n\right)} x + 24\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{3} n^{5} - 20 \, a c^{3} n^{3} + 64 \, a c^{3} n + {\left(a^{5} c^{3} n^{5} - 20 \, a^{5} c^{3} n^{3} + 64 \, a^{5} c^{3} n\right)} x^{4} - 2 \, {\left(a^{3} c^{3} n^{5} - 20 \, a^{3} c^{3} n^{3} + 64 \, a^{3} c^{3} n\right)} x^{2}}"," ",0,"-(24*a^4*x^4 + 24*a^3*n*x^3 + n^4 + 12*(a^2*n^2 - 4*a^2)*x^2 - 16*n^2 + 4*(a*n^3 - 10*a*n)*x + 24)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^3*n^5 - 20*a*c^3*n^3 + 64*a*c^3*n + (a^5*c^3*n^5 - 20*a^5*c^3*n^3 + 64*a^5*c^3*n)*x^4 - 2*(a^3*c^3*n^5 - 20*a^3*c^3*n^3 + 64*a^3*c^3*n)*x^2)","A",0
743,1,310,0,0.625263," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^4,x, algorithm=""fricas"")","-\frac{{\left(720 \, a^{6} x^{6} + 720 \, a^{5} n x^{5} + n^{6} + 360 \, {\left(a^{4} n^{2} - 6 \, a^{4}\right)} x^{4} - 50 \, n^{4} + 120 \, {\left(a^{3} n^{3} - 16 \, a^{3} n\right)} x^{3} + 30 \, {\left(a^{2} n^{4} - 28 \, a^{2} n^{2} + 72 \, a^{2}\right)} x^{2} + 544 \, n^{2} + 6 \, {\left(a n^{5} - 40 \, a n^{3} + 264 \, a n\right)} x - 720\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{4} n^{7} - 56 \, a c^{4} n^{5} + 784 \, a c^{4} n^{3} - {\left(a^{7} c^{4} n^{7} - 56 \, a^{7} c^{4} n^{5} + 784 \, a^{7} c^{4} n^{3} - 2304 \, a^{7} c^{4} n\right)} x^{6} - 2304 \, a c^{4} n + 3 \, {\left(a^{5} c^{4} n^{7} - 56 \, a^{5} c^{4} n^{5} + 784 \, a^{5} c^{4} n^{3} - 2304 \, a^{5} c^{4} n\right)} x^{4} - 3 \, {\left(a^{3} c^{4} n^{7} - 56 \, a^{3} c^{4} n^{5} + 784 \, a^{3} c^{4} n^{3} - 2304 \, a^{3} c^{4} n\right)} x^{2}}"," ",0,"-(720*a^6*x^6 + 720*a^5*n*x^5 + n^6 + 360*(a^4*n^2 - 6*a^4)*x^4 - 50*n^4 + 120*(a^3*n^3 - 16*a^3*n)*x^3 + 30*(a^2*n^4 - 28*a^2*n^2 + 72*a^2)*x^2 + 544*n^2 + 6*(a*n^5 - 40*a*n^3 + 264*a*n)*x - 720)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^4*n^7 - 56*a*c^4*n^5 + 784*a*c^4*n^3 - (a^7*c^4*n^7 - 56*a^7*c^4*n^5 + 784*a^7*c^4*n^3 - 2304*a^7*c^4*n)*x^6 - 2304*a*c^4*n + 3*(a^5*c^4*n^7 - 56*a^5*c^4*n^5 + 784*a^5*c^4*n^3 - 2304*a^5*c^4*n)*x^4 - 3*(a^3*c^4*n^7 - 56*a^3*c^4*n^5 + 784*a^3*c^4*n^3 - 2304*a^3*c^4*n)*x^2)","A",0
744,0,0,0,0.509199," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c x^{2} - c\right)} \sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(-(a^2*c*x^2 - c)*sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
745,0,0,0,0.658541," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
746,0,0,0,0.764038," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}, x\right)"," ",0,"integral(-sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
747,1,78,0,0.493158," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + n\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{2} n^{2} - a c^{2} - {\left(a^{3} c^{2} n^{2} - a^{3} c^{2}\right)} x^{2}}"," ",0,"-sqrt(-a^2*c*x^2 + c)*(a*x + n)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^2*n^2 - a*c^2 - (a^3*c^2*n^2 - a^3*c^2)*x^2)","A",0
748,1,163,0,0.774611," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(6 \, a^{3} x^{3} + 6 \, a^{2} n x^{2} + n^{3} + 3 \, {\left(a n^{2} - 3 \, a\right)} x - 7 \, n\right)} \sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{3} n^{4} - 10 \, a c^{3} n^{2} + {\left(a^{5} c^{3} n^{4} - 10 \, a^{5} c^{3} n^{2} + 9 \, a^{5} c^{3}\right)} x^{4} + 9 \, a c^{3} - 2 \, {\left(a^{3} c^{3} n^{4} - 10 \, a^{3} c^{3} n^{2} + 9 \, a^{3} c^{3}\right)} x^{2}}"," ",0,"-(6*a^3*x^3 + 6*a^2*n*x^2 + n^3 + 3*(a*n^2 - 3*a)*x - 7*n)*sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^3*n^4 - 10*a*c^3*n^2 + (a^5*c^3*n^4 - 10*a^5*c^3*n^2 + 9*a^5*c^3)*x^4 + 9*a*c^3 - 2*(a^3*c^3*n^4 - 10*a^3*c^3*n^2 + 9*a^3*c^3)*x^2)","A",0
749,1,289,0,0.854175," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","-\frac{{\left(120 \, a^{5} x^{5} + 120 \, a^{4} n x^{4} + n^{5} + 60 \, {\left(a^{3} n^{2} - 5 \, a^{3}\right)} x^{3} - 30 \, n^{3} + 20 \, {\left(a^{2} n^{3} - 13 \, a^{2} n\right)} x^{2} + 5 \, {\left(a n^{4} - 22 \, a n^{2} + 45 \, a\right)} x + 149 \, n\right)} \sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{4} n^{6} - 35 \, a c^{4} n^{4} + 259 \, a c^{4} n^{2} - {\left(a^{7} c^{4} n^{6} - 35 \, a^{7} c^{4} n^{4} + 259 \, a^{7} c^{4} n^{2} - 225 \, a^{7} c^{4}\right)} x^{6} - 225 \, a c^{4} + 3 \, {\left(a^{5} c^{4} n^{6} - 35 \, a^{5} c^{4} n^{4} + 259 \, a^{5} c^{4} n^{2} - 225 \, a^{5} c^{4}\right)} x^{4} - 3 \, {\left(a^{3} c^{4} n^{6} - 35 \, a^{3} c^{4} n^{4} + 259 \, a^{3} c^{4} n^{2} - 225 \, a^{3} c^{4}\right)} x^{2}}"," ",0,"-(120*a^5*x^5 + 120*a^4*n*x^4 + n^5 + 60*(a^3*n^2 - 5*a^3)*x^3 - 30*n^3 + 20*(a^2*n^3 - 13*a^2*n)*x^2 + 5*(a*n^4 - 22*a*n^2 + 45*a)*x + 149*n)*sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^4*n^6 - 35*a*c^4*n^4 + 259*a*c^4*n^2 - (a^7*c^4*n^6 - 35*a^7*c^4*n^4 + 259*a^7*c^4*n^2 - 225*a^7*c^4)*x^6 - 225*a*c^4 + 3*(a^5*c^4*n^6 - 35*a^5*c^4*n^4 + 259*a^5*c^4*n^2 - 225*a^5*c^4)*x^4 - 3*(a^3*c^4*n^6 - 35*a^3*c^4*n^4 + 259*a^3*c^4*n^2 - 225*a^3*c^4)*x^2)","A",0
750,1,451,0,0.582029," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(9/2),x, algorithm=""fricas"")","-\frac{{\left(5040 \, a^{7} x^{7} + 5040 \, a^{6} n x^{6} + n^{7} + 2520 \, {\left(a^{5} n^{2} - 7 \, a^{5}\right)} x^{5} - 77 \, n^{5} + 840 \, {\left(a^{4} n^{3} - 19 \, a^{4} n\right)} x^{4} + 210 \, {\left(a^{3} n^{4} - 34 \, a^{3} n^{2} + 105 \, a^{3}\right)} x^{3} + 1519 \, n^{3} + 42 \, {\left(a^{2} n^{5} - 50 \, a^{2} n^{3} + 409 \, a^{2} n\right)} x^{2} + 7 \, {\left(a n^{6} - 65 \, a n^{4} + 919 \, a n^{2} - 1575 \, a\right)} x - 6483 \, n\right)} \sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{5} n^{8} - 84 \, a c^{5} n^{6} + 1974 \, a c^{5} n^{4} + {\left(a^{9} c^{5} n^{8} - 84 \, a^{9} c^{5} n^{6} + 1974 \, a^{9} c^{5} n^{4} - 12916 \, a^{9} c^{5} n^{2} + 11025 \, a^{9} c^{5}\right)} x^{8} - 12916 \, a c^{5} n^{2} - 4 \, {\left(a^{7} c^{5} n^{8} - 84 \, a^{7} c^{5} n^{6} + 1974 \, a^{7} c^{5} n^{4} - 12916 \, a^{7} c^{5} n^{2} + 11025 \, a^{7} c^{5}\right)} x^{6} + 11025 \, a c^{5} + 6 \, {\left(a^{5} c^{5} n^{8} - 84 \, a^{5} c^{5} n^{6} + 1974 \, a^{5} c^{5} n^{4} - 12916 \, a^{5} c^{5} n^{2} + 11025 \, a^{5} c^{5}\right)} x^{4} - 4 \, {\left(a^{3} c^{5} n^{8} - 84 \, a^{3} c^{5} n^{6} + 1974 \, a^{3} c^{5} n^{4} - 12916 \, a^{3} c^{5} n^{2} + 11025 \, a^{3} c^{5}\right)} x^{2}}"," ",0,"-(5040*a^7*x^7 + 5040*a^6*n*x^6 + n^7 + 2520*(a^5*n^2 - 7*a^5)*x^5 - 77*n^5 + 840*(a^4*n^3 - 19*a^4*n)*x^4 + 210*(a^3*n^4 - 34*a^3*n^2 + 105*a^3)*x^3 + 1519*n^3 + 42*(a^2*n^5 - 50*a^2*n^3 + 409*a^2*n)*x^2 + 7*(a*n^6 - 65*a*n^4 + 919*a*n^2 - 1575*a)*x - 6483*n)*sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^5*n^8 - 84*a*c^5*n^6 + 1974*a*c^5*n^4 + (a^9*c^5*n^8 - 84*a^9*c^5*n^6 + 1974*a^9*c^5*n^4 - 12916*a^9*c^5*n^2 + 11025*a^9*c^5)*x^8 - 12916*a*c^5*n^2 - 4*(a^7*c^5*n^8 - 84*a^7*c^5*n^6 + 1974*a^7*c^5*n^4 - 12916*a^7*c^5*n^2 + 11025*a^7*c^5)*x^6 + 11025*a*c^5 + 6*(a^5*c^5*n^8 - 84*a^5*c^5*n^6 + 1974*a^5*c^5*n^4 - 12916*a^5*c^5*n^2 + 11025*a^5*c^5)*x^4 - 4*(a^3*c^5*n^8 - 84*a^3*c^5*n^6 + 1974*a^3*c^5*n^4 - 12916*a^3*c^5*n^2 + 11025*a^3*c^5)*x^2)","A",0
751,0,0,0,0.411356," ","integrate(exp(n*arccoth(a*x))*x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*x^3*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2), x)","F",0
752,0,0,0,0.607562," ","integrate(exp(n*arccoth(a*x))*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*x^2*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2), x)","F",0
753,1,83,0,1.202727," ","integrate(exp(n*arccoth(a*x))*x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c x^{2} + c} {\left(a n x + 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{2} c^{2} n^{2} - a^{2} c^{2} - {\left(a^{4} c^{2} n^{2} - a^{4} c^{2}\right)} x^{2}}"," ",0,"-sqrt(-a^2*c*x^2 + c)*(a*n*x + 1)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^2*c^2*n^2 - a^2*c^2 - (a^4*c^2*n^2 - a^4*c^2)*x^2)","A",0
754,1,78,0,0.548759," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + n\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{2} n^{2} - a c^{2} - {\left(a^{3} c^{2} n^{2} - a^{3} c^{2}\right)} x^{2}}"," ",0,"-sqrt(-a^2*c*x^2 + c)*(a*x + n)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^2*n^2 - a*c^2 - (a^3*c^2*n^2 - a^3*c^2)*x^2)","A",0
755,0,0,0,0.662209," ","integrate(exp(n*arccoth(a*x))/x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{4} c^{2} x^{5} - 2 \, a^{2} c^{2} x^{3} + c^{2} x}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^4*c^2*x^5 - 2*a^2*c^2*x^3 + c^2*x), x)","F",0
756,0,0,0,0.629406," ","integrate(exp(n*arccoth(a*x))*x^4/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} c x^{2} + c} x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*c*x^2 + c)*x^4*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3), x)","F",0
757,1,176,0,0.535408," ","integrate(exp(n*arccoth(a*x))*x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c x^{2} + c} {\left({\left(a^{3} n^{3} - 7 \, a^{3} n\right)} x^{3} + 6 \, a n x + 3 \, {\left(a^{2} n^{2} - 3 \, a^{2}\right)} x^{2} + 6\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{4} c^{3} n^{4} - 10 \, a^{4} c^{3} n^{2} + 9 \, a^{4} c^{3} + {\left(a^{8} c^{3} n^{4} - 10 \, a^{8} c^{3} n^{2} + 9 \, a^{8} c^{3}\right)} x^{4} - 2 \, {\left(a^{6} c^{3} n^{4} - 10 \, a^{6} c^{3} n^{2} + 9 \, a^{6} c^{3}\right)} x^{2}}"," ",0,"-sqrt(-a^2*c*x^2 + c)*((a^3*n^3 - 7*a^3*n)*x^3 + 6*a*n*x + 3*(a^2*n^2 - 3*a^2)*x^2 + 6)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^4*c^3*n^4 - 10*a^4*c^3*n^2 + 9*a^4*c^3 + (a^8*c^3*n^4 - 10*a^8*c^3*n^2 + 9*a^8*c^3)*x^4 - 2*(a^6*c^3*n^4 - 10*a^6*c^3*n^2 + 9*a^6*c^3)*x^2)","A",0
758,1,179,0,0.565198," ","integrate(exp(n*arccoth(a*x))*x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c x^{2} + c} {\left(2 \, a n^{2} x + {\left(a^{3} n^{2} - 3 \, a^{3}\right)} x^{3} + {\left(a^{2} n^{3} - 3 \, a^{2} n\right)} x^{2} + 2 \, n\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{3} c^{3} n^{4} - 10 \, a^{3} c^{3} n^{2} + 9 \, a^{3} c^{3} + {\left(a^{7} c^{3} n^{4} - 10 \, a^{7} c^{3} n^{2} + 9 \, a^{7} c^{3}\right)} x^{4} - 2 \, {\left(a^{5} c^{3} n^{4} - 10 \, a^{5} c^{3} n^{2} + 9 \, a^{5} c^{3}\right)} x^{2}}"," ",0,"-sqrt(-a^2*c*x^2 + c)*(2*a*n^2*x + (a^3*n^2 - 3*a^3)*x^3 + (a^2*n^3 - 3*a^2*n)*x^2 + 2*n)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^3*c^3*n^4 - 10*a^3*c^3*n^2 + 9*a^3*c^3 + (a^7*c^3*n^4 - 10*a^7*c^3*n^2 + 9*a^7*c^3)*x^4 - 2*(a^5*c^3*n^4 - 10*a^5*c^3*n^2 + 9*a^5*c^3)*x^2)","A",0
759,1,170,0,0.531150," ","integrate(exp(n*arccoth(a*x))*x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{3} n x^{3} + 2 \, a^{2} n^{2} x^{2} + n^{2} + {\left(a n^{3} - 3 \, a n\right)} x - 3\right)} \sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{2} c^{3} n^{4} - 10 \, a^{2} c^{3} n^{2} + 9 \, a^{2} c^{3} + {\left(a^{6} c^{3} n^{4} - 10 \, a^{6} c^{3} n^{2} + 9 \, a^{6} c^{3}\right)} x^{4} - 2 \, {\left(a^{4} c^{3} n^{4} - 10 \, a^{4} c^{3} n^{2} + 9 \, a^{4} c^{3}\right)} x^{2}}"," ",0,"-(2*a^3*n*x^3 + 2*a^2*n^2*x^2 + n^2 + (a*n^3 - 3*a*n)*x - 3)*sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^2*c^3*n^4 - 10*a^2*c^3*n^2 + 9*a^2*c^3 + (a^6*c^3*n^4 - 10*a^6*c^3*n^2 + 9*a^6*c^3)*x^4 - 2*(a^4*c^3*n^4 - 10*a^4*c^3*n^2 + 9*a^4*c^3)*x^2)","A",0
760,1,163,0,0.503689," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(6 \, a^{3} x^{3} + 6 \, a^{2} n x^{2} + n^{3} + 3 \, {\left(a n^{2} - 3 \, a\right)} x - 7 \, n\right)} \sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c^{3} n^{4} - 10 \, a c^{3} n^{2} + {\left(a^{5} c^{3} n^{4} - 10 \, a^{5} c^{3} n^{2} + 9 \, a^{5} c^{3}\right)} x^{4} + 9 \, a c^{3} - 2 \, {\left(a^{3} c^{3} n^{4} - 10 \, a^{3} c^{3} n^{2} + 9 \, a^{3} c^{3}\right)} x^{2}}"," ",0,"-(6*a^3*x^3 + 6*a^2*n*x^2 + n^3 + 3*(a*n^2 - 3*a)*x - 7*n)*sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c^3*n^4 - 10*a*c^3*n^2 + (a^5*c^3*n^4 - 10*a^5*c^3*n^2 + 9*a^5*c^3)*x^4 + 9*a*c^3 - 2*(a^3*c^3*n^4 - 10*a^3*c^3*n^2 + 9*a^3*c^3)*x^2)","A",0
761,0,0,0,0.519777," ","integrate(exp(n*arccoth(a*x))/x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{6} c^{3} x^{7} - 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} - c^{3} x}, x\right)"," ",0,"integral(-sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^6*c^3*x^7 - 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 - c^3*x), x)","F",0
762,0,0,0,0.541620," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(-a^{2} c x^{2} + c\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}, x\right)"," ",0,"integral((-a^2*c*x^2 + c)^p*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
763,1,42,0,0.745273," ","integrate(exp(2*p*arccoth(a*x))*(-a^2*c*x^2+c)^p,x, algorithm=""fricas"")","\frac{{\left(a x - 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{p}}{2 \, a p + a}"," ",0,"(a*x - 1)*(-a^2*c*x^2 + c)^p*((a*x - 1)/(a*x + 1))^p/(2*a*p + a)","A",0
764,1,44,0,0.836548," ","integrate((-a^2*c*x^2+c)^p/exp(2*p*arccoth(a*x)),x, algorithm=""fricas"")","\frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(2 \, a p + a\right)} \left(\frac{a x - 1}{a x + 1}\right)^{p}}"," ",0,"(a*x + 1)*(-a^2*c*x^2 + c)^p/((2*a*p + a)*((a*x - 1)/(a*x + 1))^p)","A",0
765,0,0,0,0.558598," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^p,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{2} + 2 \, a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{a^{2} x^{2} - 2 \, a x + 1}, x\right)"," ",0,"integral((a^2*x^2 + 2*a*x + 1)*(-a^2*c*x^2 + c)^p/(a^2*x^2 - 2*a*x + 1), x)","F",0
766,0,0,0,0.763059," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^p,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} x^{2} + 2 \, a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x^{2} - 2 \, a x + 1}, x\right)"," ",0,"integral((a^2*x^2 + 2*a*x + 1)*(-a^2*c*x^2 + c)^p*sqrt((a*x - 1)/(a*x + 1))/(a^2*x^2 - 2*a*x + 1), x)","F",0
767,0,0,0,0.652671," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^p,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{a x - 1}, x\right)"," ",0,"integral((a*x + 1)*(-a^2*c*x^2 + c)^p/(a*x - 1), x)","F",0
768,0,0,0,0.731687," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^p,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}}{a x - 1}, x\right)"," ",0,"integral((a*x + 1)*(-a^2*c*x^2 + c)^p*sqrt((a*x - 1)/(a*x + 1))/(a*x - 1), x)","F",0
769,0,0,0,0.650552," ","integrate((-a^2*c*x^2+c)^p*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(-a^{2} c x^{2} + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}, x\right)"," ",0,"integral((-a^2*c*x^2 + c)^p*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
770,0,0,0,0.484603," ","integrate((-a^2*c*x^2+c)^p*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x - 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{a x + 1}, x\right)"," ",0,"integral((a*x - 1)*(-a^2*c*x^2 + c)^p/(a*x + 1), x)","F",0
771,0,0,0,0.665895," ","integrate((-a^2*c*x^2+c)^p*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x - 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1}, x\right)"," ",0,"integral((a*x - 1)*(-a^2*c*x^2 + c)^p*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1), x)","F",0
772,1,201,0,0.626610," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^4,x, algorithm=""fricas"")","-\frac{7350 \, a^{7} c^{4} x^{7} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 1680 \, a^{7} c^{4} x^{7} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 1680 \, a^{7} c^{4} x^{7} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(1680 \, a^{8} c^{4} x^{8} - 1136 \, a^{7} c^{4} x^{7} + 229 \, a^{6} c^{4} x^{6} + 4997 \, a^{5} c^{4} x^{5} + 622 \, a^{4} c^{4} x^{4} - 2386 \, a^{3} c^{4} x^{3} - 776 \, a^{2} c^{4} x^{2} + 520 \, a c^{4} x + 240 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{1680 \, a^{8} x^{7}}"," ",0,"-1/1680*(7350*a^7*c^4*x^7*arctan(sqrt((a*x - 1)/(a*x + 1))) - 1680*a^7*c^4*x^7*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 1680*a^7*c^4*x^7*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (1680*a^8*c^4*x^8 - 1136*a^7*c^4*x^7 + 229*a^6*c^4*x^6 + 4997*a^5*c^4*x^5 + 622*a^4*c^4*x^4 - 2386*a^3*c^4*x^3 - 776*a^2*c^4*x^2 + 520*a*c^4*x + 240*c^4)*sqrt((a*x - 1)/(a*x + 1)))/(a^8*x^7)","A",0
773,1,179,0,0.515140," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^3,x, algorithm=""fricas"")","-\frac{450 \, a^{5} c^{3} x^{5} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 120 \, a^{5} c^{3} x^{5} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 120 \, a^{5} c^{3} x^{5} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(120 \, a^{6} c^{3} x^{6} - 64 \, a^{5} c^{3} x^{5} - 49 \, a^{4} c^{3} x^{4} + 223 \, a^{3} c^{3} x^{3} + 58 \, a^{2} c^{3} x^{2} - 54 \, a c^{3} x - 24 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{120 \, a^{6} x^{5}}"," ",0,"-1/120*(450*a^5*c^3*x^5*arctan(sqrt((a*x - 1)/(a*x + 1))) - 120*a^5*c^3*x^5*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 120*a^5*c^3*x^5*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (120*a^6*c^3*x^6 - 64*a^5*c^3*x^5 - 49*a^4*c^3*x^4 + 223*a^3*c^3*x^3 + 58*a^2*c^3*x^2 - 54*a*c^3*x - 24*c^3)*sqrt((a*x - 1)/(a*x + 1)))/(a^6*x^5)","A",0
774,1,157,0,0.516295," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","-\frac{18 \, a^{3} c^{2} x^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 6 \, a^{3} c^{2} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 6 \, a^{3} c^{2} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(6 \, a^{4} c^{2} x^{4} - 2 \, a^{3} c^{2} x^{3} - 5 \, a^{2} c^{2} x^{2} + 5 \, a c^{2} x + 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a^{4} x^{3}}"," ",0,"-1/6*(18*a^3*c^2*x^3*arctan(sqrt((a*x - 1)/(a*x + 1))) - 6*a^3*c^2*x^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 6*a^3*c^2*x^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (6*a^4*c^2*x^4 - 2*a^3*c^2*x^3 - 5*a^2*c^2*x^2 + 5*a*c^2*x + 2*c^2)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*x^3)","A",0
775,1,104,0,0.716112," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2),x, algorithm=""fricas"")","-\frac{2 \, a c x \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - a c x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + a c x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(a^{2} c x^{2} - c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x}"," ",0,"-(2*a*c*x*arctan(sqrt((a*x - 1)/(a*x + 1))) - a*c*x*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + a*c*x*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (a^2*c*x^2 - c)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x)","A",0
776,1,93,0,0.495180," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2),x, algorithm=""fricas"")","\frac{{\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - {\left(a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a^{2} x^{2} - a x - 2\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c x - a c}"," ",0,"((a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - (a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a^2*x^2 - a*x - 2)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c*x - a*c)","A",0
777,1,134,0,0.521680," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(3 \, a^{3} x^{3} - 7 \, a^{2} x^{2} - 5 \, a x + 8\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"1/3*(3*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (3*a^3*x^3 - 7*a^2*x^2 - 5*a*x + 8)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)","A",0
778,1,178,0,0.580232," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^3,x, algorithm=""fricas"")","\frac{15 \, {\left(a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, {\left(a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(15 \, a^{5} x^{5} - 38 \, a^{4} x^{4} - 52 \, a^{3} x^{3} + 87 \, a^{2} x^{2} + 33 \, a x - 48\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{4} c^{3} x^{3} + 2 \, a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"1/15*(15*(a^4*x^4 - 2*a^3*x^3 + 2*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*(a^4*x^4 - 2*a^3*x^3 + 2*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (15*a^5*x^5 - 38*a^4*x^4 - 52*a^3*x^3 + 87*a^2*x^2 + 33*a*x - 48)*sqrt((a*x - 1)/(a*x + 1)))/(a^5*c^3*x^4 - 2*a^4*c^3*x^3 + 2*a^2*c^3*x - a*c^3)","A",0
779,1,274,0,0.683747," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^4,x, algorithm=""fricas"")","\frac{105 \, {\left(a^{6} x^{6} - 2 \, a^{5} x^{5} - a^{4} x^{4} + 4 \, a^{3} x^{3} - a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 105 \, {\left(a^{6} x^{6} - 2 \, a^{5} x^{5} - a^{4} x^{4} + 4 \, a^{3} x^{3} - a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(105 \, a^{7} x^{7} - 281 \, a^{6} x^{6} - 559 \, a^{5} x^{5} + 965 \, a^{4} x^{4} + 715 \, a^{3} x^{3} - 1065 \, a^{2} x^{2} - 279 \, a x + 384\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{105 \, {\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)}}"," ",0,"1/105*(105*(a^6*x^6 - 2*a^5*x^5 - a^4*x^4 + 4*a^3*x^3 - a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 105*(a^6*x^6 - 2*a^5*x^5 - a^4*x^4 + 4*a^3*x^3 - a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (105*a^7*x^7 - 281*a^6*x^6 - 559*a^5*x^5 + 965*a^4*x^4 + 715*a^3*x^3 - 1065*a^2*x^2 - 279*a*x + 384)*sqrt((a*x - 1)/(a*x + 1)))/(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)","A",0
780,1,122,0,1.515633," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^5,x, algorithm=""fricas"")","\frac{1260 \, a^{10} c^{5} x^{10} + 2520 \, a^{9} c^{5} x^{9} \log\left(x\right) + 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,"1/1260*(1260*a^10*c^5*x^10 + 2520*a^9*c^5*x^9*log(x) + 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
781,1,89,0,0.413888," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^4,x, algorithm=""fricas"")","\frac{210 \, a^{8} c^{4} x^{8} + 420 \, a^{7} c^{4} x^{7} \log\left(x\right) + 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,"1/210*(210*a^8*c^4*x^8 + 420*a^7*c^4*x^7*log(x) + 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
782,1,78,0,0.774356," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^3,x, algorithm=""fricas"")","\frac{30 \, a^{6} c^{3} x^{6} + 60 \, a^{5} c^{3} x^{5} \log\left(x\right) + 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,"1/30*(30*a^6*c^3*x^6 + 60*a^5*c^3*x^5*log(x) + 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
783,1,43,0,0.450805," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","\frac{3 \, a^{4} c^{2} x^{4} + 6 \, a^{3} c^{2} x^{3} \log\left(x\right) + 3 \, a c^{2} x + c^{2}}{3 \, a^{4} x^{3}}"," ",0,"1/3*(3*a^4*c^2*x^4 + 6*a^3*c^2*x^3*log(x) + 3*a*c^2*x + c^2)/(a^4*x^3)","A",0
784,1,26,0,0.497919," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2),x, algorithm=""fricas"")","\frac{a^{2} c x^{2} + 2 \, a c x \log\left(x\right) - c}{a^{2} x}"," ",0,"(a^2*c*x^2 + 2*a*c*x*log(x) - c)/(a^2*x)","A",0
785,1,40,0,0.605952," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2),x, algorithm=""fricas"")","\frac{a^{2} x^{2} - a x + 2 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 1}{a^{2} c x - a c}"," ",0,"(a^2*x^2 - a*x + 2*(a*x - 1)*log(a*x - 1) - 1)/(a^2*c*x - a*c)","A",0
786,1,93,0,0.543724," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","\frac{8 \, a^{3} x^{3} - 16 \, a^{2} x^{2} - 6 \, a x - {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x + 1\right) + 17 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x - 1\right) + 12}{8 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"1/8*(8*a^3*x^3 - 16*a^2*x^2 - 6*a*x - (a^2*x^2 - 2*a*x + 1)*log(a*x + 1) + 17*(a^2*x^2 - 2*a*x + 1)*log(a*x - 1) + 12)/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)","A",0
787,1,137,0,0.458626," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^3,x, algorithm=""fricas"")","\frac{12 \, a^{5} x^{5} - 24 \, a^{4} x^{4} - 30 \, a^{3} x^{3} + 48 \, a^{2} x^{2} + 14 \, a x - 3 \, {\left(a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a x - 1\right)} \log\left(a x + 1\right) + 27 \, {\left(a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a x - 1\right)} \log\left(a x - 1\right) - 22}{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)}}"," ",0,"1/12*(12*a^5*x^5 - 24*a^4*x^4 - 30*a^3*x^3 + 48*a^2*x^2 + 14*a*x - 3*(a^4*x^4 - 2*a^3*x^3 + 2*a*x - 1)*log(a*x + 1) + 27*(a^4*x^4 - 2*a^3*x^3 + 2*a*x - 1)*log(a*x - 1) - 22)/(a^5*c^3*x^4 - 2*a^4*c^3*x^3 + 2*a^2*c^3*x - a*c^3)","A",0
788,1,233,0,0.856190," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^4,x, algorithm=""fricas"")","\frac{384 \, a^{7} x^{7} - 768 \, a^{6} x^{6} - 1638 \, a^{5} x^{5} + 2508 \, a^{4} x^{4} + 1732 \, a^{3} x^{3} - 2516 \, a^{2} x^{2} - 550 \, a x - 141 \, {\left(a^{6} x^{6} - 2 \, a^{5} x^{5} - a^{4} x^{4} + 4 \, a^{3} x^{3} - a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x + 1\right) + 909 \, {\left(a^{6} x^{6} - 2 \, a^{5} x^{5} - a^{4} x^{4} + 4 \, a^{3} x^{3} - a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x - 1\right) + 800}{384 \, {\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)}}"," ",0,"1/384*(384*a^7*x^7 - 768*a^6*x^6 - 1638*a^5*x^5 + 2508*a^4*x^4 + 1732*a^3*x^3 - 2516*a^2*x^2 - 550*a*x - 141*(a^6*x^6 - 2*a^5*x^5 - a^4*x^4 + 4*a^3*x^3 - a^2*x^2 - 2*a*x + 1)*log(a*x + 1) + 909*(a^6*x^6 - 2*a^5*x^5 - a^4*x^4 + 4*a^3*x^3 - a^2*x^2 - 2*a*x + 1)*log(a*x - 1) + 800)/(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)","A",0
789,1,201,0,0.490519," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^4,x, algorithm=""fricas"")","-\frac{1050 \, a^{7} c^{4} x^{7} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 1680 \, a^{7} c^{4} x^{7} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 1680 \, a^{7} c^{4} x^{7} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(560 \, a^{8} c^{4} x^{8} - 1936 \, a^{7} c^{4} x^{7} - 3021 \, a^{6} c^{4} x^{6} + 467 \, a^{5} c^{4} x^{5} + 1762 \, a^{4} c^{4} x^{4} + 674 \, a^{3} c^{4} x^{3} - 376 \, a^{2} c^{4} x^{2} - 360 \, a c^{4} x - 80 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{560 \, a^{8} x^{7}}"," ",0,"-1/560*(1050*a^7*c^4*x^7*arctan(sqrt((a*x - 1)/(a*x + 1))) - 1680*a^7*c^4*x^7*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 1680*a^7*c^4*x^7*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (560*a^8*c^4*x^8 - 1936*a^7*c^4*x^7 - 3021*a^6*c^4*x^6 + 467*a^5*c^4*x^5 + 1762*a^4*c^4*x^4 + 674*a^3*c^4*x^3 - 376*a^2*c^4*x^2 - 360*a*c^4*x - 80*c^4)*sqrt((a*x - 1)/(a*x + 1)))/(a^8*x^7)","A",0
790,1,179,0,0.614265," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^3,x, algorithm=""fricas"")","-\frac{30 \, a^{5} c^{3} x^{5} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 120 \, a^{5} c^{3} x^{5} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 120 \, a^{5} c^{3} x^{5} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(40 \, a^{6} c^{3} x^{6} - 112 \, a^{5} c^{3} x^{5} - 207 \, a^{4} c^{3} x^{4} - 31 \, a^{3} c^{3} x^{3} + 54 \, a^{2} c^{3} x^{2} + 38 \, a c^{3} x + 8 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{40 \, a^{6} x^{5}}"," ",0,"-1/40*(30*a^5*c^3*x^5*arctan(sqrt((a*x - 1)/(a*x + 1))) - 120*a^5*c^3*x^5*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 120*a^5*c^3*x^5*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (40*a^6*c^3*x^6 - 112*a^5*c^3*x^5 - 207*a^4*c^3*x^4 - 31*a^3*c^3*x^3 + 54*a^2*c^3*x^2 + 38*a*c^3*x + 8*c^3)*sqrt((a*x - 1)/(a*x + 1)))/(a^6*x^5)","A",0
791,1,156,0,0.594353," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","\frac{6 \, a^{3} c^{2} x^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 18 \, a^{3} c^{2} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 18 \, a^{3} c^{2} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(6 \, a^{4} c^{2} x^{4} - 10 \, a^{3} c^{2} x^{3} - 25 \, a^{2} c^{2} x^{2} - 11 \, a c^{2} x - 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a^{4} x^{3}}"," ",0,"1/6*(6*a^3*c^2*x^3*arctan(sqrt((a*x - 1)/(a*x + 1))) + 18*a^3*c^2*x^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 18*a^3*c^2*x^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (6*a^4*c^2*x^4 - 10*a^3*c^2*x^3 - 25*a^2*c^2*x^2 - 11*a*c^2*x - 2*c^2)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*x^3)","A",0
792,1,106,0,0.482865," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2),x, algorithm=""fricas"")","\frac{6 \, a c x \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 3 \, a c x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, a c x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a^{2} c x^{2} + 2 \, a c x + c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x}"," ",0,"(6*a*c*x*arctan(sqrt((a*x - 1)/(a*x + 1))) + 3*a*c*x*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*a*c*x*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a^2*c*x^2 + 2*a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x)","A",0
793,1,128,0,0.546323," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2),x, algorithm=""fricas"")","\frac{9 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 9 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(3 \, a^{3} x^{3} - 16 \, a^{2} x^{2} - 5 \, a x + 14\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c x^{2} - 2 \, a^{2} c x + a c\right)}}"," ",0,"1/3*(9*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 9*(a^2*x^2 - 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (3*a^3*x^3 - 16*a^2*x^2 - 5*a*x + 14)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c*x^2 - 2*a^2*c*x + a*c)","A",0
794,1,170,0,0.705112," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","\frac{15 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(5 \, a^{4} x^{4} - 34 \, a^{3} x^{3} + 18 \, a^{2} x^{2} + 33 \, a x - 24\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{5 \, {\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,"1/5*(15*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (5*a^4*x^4 - 34*a^3*x^3 + 18*a^2*x^2 + 33*a*x - 24)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2)","A",0
795,1,204,0,0.549756," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^3,x, algorithm=""fricas"")","\frac{105 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 105 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(35 \, a^{5} x^{5} - 286 \, a^{4} x^{4} + 368 \, a^{3} x^{3} + 125 \, a^{2} x^{2} - 423 \, a x + 176\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\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,"1/35*(105*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 105*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (35*a^5*x^5 - 286*a^4*x^4 + 368*a^3*x^3 + 125*a^2*x^2 - 423*a*x + 176)*sqrt((a*x - 1)/(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
796,1,248,0,0.544564," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^4,x, algorithm=""fricas"")","\frac{945 \, {\left(a^{6} x^{6} - 4 \, a^{5} x^{5} + 5 \, a^{4} x^{4} - 5 \, a^{2} x^{2} + 4 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 945 \, {\left(a^{6} x^{6} - 4 \, a^{5} x^{5} + 5 \, a^{4} x^{4} - 5 \, a^{2} x^{2} + 4 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(315 \, a^{7} x^{7} - 2669 \, a^{6} x^{6} + 2967 \, a^{5} x^{5} + 4029 \, a^{4} x^{4} - 7399 \, a^{3} x^{3} + 339 \, a^{2} x^{2} + 4047 \, a x - 1664\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{315 \, {\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)}}"," ",0,"1/315*(945*(a^6*x^6 - 4*a^5*x^5 + 5*a^4*x^4 - 5*a^2*x^2 + 4*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 945*(a^6*x^6 - 4*a^5*x^5 + 5*a^4*x^4 - 5*a^2*x^2 + 4*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (315*a^7*x^7 - 2669*a^6*x^6 + 2967*a^5*x^5 + 4029*a^4*x^4 - 7399*a^3*x^3 + 339*a^2*x^2 + 4047*a*x - 1664)*sqrt((a*x - 1)/(a*x + 1)))/(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)","A",0
797,1,111,0,0.442115," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^5,x, algorithm=""fricas"")","\frac{630 \, a^{10} c^{5} x^{10} + 2520 \, a^{9} c^{5} x^{9} \log\left(x\right) - 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,"1/630*(630*a^10*c^5*x^10 + 2520*a^9*c^5*x^9*log(x) - 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
798,1,100,0,0.549144," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^4,x, algorithm=""fricas"")","\frac{105 \, a^{8} c^{4} x^{8} + 420 \, a^{7} c^{4} x^{7} \log\left(x\right) - 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,"1/105*(105*a^8*c^4*x^8 + 420*a^7*c^4*x^7*log(x) - 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
799,1,67,0,0.474539," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^3,x, algorithm=""fricas"")","\frac{15 \, a^{6} c^{3} x^{6} + 60 \, a^{5} c^{3} x^{5} \log\left(x\right) - 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,"1/15*(15*a^6*c^3*x^6 + 60*a^5*c^3*x^5*log(x) - 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
800,1,56,0,0.406148," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","\frac{3 \, a^{4} c^{2} x^{4} + 12 \, a^{3} c^{2} x^{3} \log\left(x\right) - 18 \, a^{2} c^{2} x^{2} - 6 \, a c^{2} x - c^{2}}{3 \, a^{4} x^{3}}"," ",0,"1/3*(3*a^4*c^2*x^4 + 12*a^3*c^2*x^3*log(x) - 18*a^2*c^2*x^2 - 6*a*c^2*x - c^2)/(a^4*x^3)","A",0
801,1,35,0,0.592892," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2),x, algorithm=""fricas"")","\frac{a^{2} c x^{2} + 8 \, a c x \log\left(a x - 1\right) - 4 \, a c x \log\left(x\right) + c}{a^{2} x}"," ",0,"(a^2*c*x^2 + 8*a*c*x*log(a*x - 1) - 4*a*c*x*log(x) + c)/(a^2*x)","A",0
802,1,64,0,0.454649," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2),x, algorithm=""fricas"")","\frac{a^{3} x^{3} - 2 \, a^{2} x^{2} - 4 \, a x + 4 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x - 1\right) + 4}{a^{3} c x^{2} - 2 \, a^{2} c x + a c}"," ",0,"(a^3*x^3 - 2*a^2*x^2 - 4*a*x + 4*(a^2*x^2 - 2*a*x + 1)*log(a*x - 1) + 4)/(a^3*c*x^2 - 2*a^2*c*x + a*c)","A",0
803,1,100,0,0.644425," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","\frac{3 \, a^{4} x^{4} - 9 \, a^{3} x^{3} - 9 \, a^{2} x^{2} + 27 \, a x + 12 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(a x - 1\right) - 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)}}"," ",0,"1/3*(3*a^4*x^4 - 9*a^3*x^3 - 9*a^2*x^2 + 27*a*x + 12*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(a*x - 1) - 13)/(a^4*c^2*x^3 - 3*a^3*c^2*x^2 + 3*a^2*c^2*x - a*c^2)","A",0
804,1,163,0,0.533051," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2)^3,x, algorithm=""fricas"")","\frac{96 \, a^{5} x^{5} - 384 \, a^{4} x^{4} - 90 \, a^{3} x^{3} + 1320 \, a^{2} x^{2} - 1402 \, a x - 3 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(a x + 1\right) + 387 \, {\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 4 \, a x + 1\right)} \log\left(a x - 1\right) + 448}{96 \, {\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,"1/96*(96*a^5*x^5 - 384*a^4*x^4 - 90*a^3*x^3 + 1320*a^2*x^2 - 1402*a*x - 3*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(a*x + 1) + 387*(a^4*x^4 - 4*a^3*x^3 + 6*a^2*x^2 - 4*a*x + 1)*log(a*x - 1) + 448)/(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
805,1,207,0,0.419231," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2)^4,x, algorithm=""fricas"")","\frac{960 \, a^{7} x^{7} - 3840 \, a^{6} x^{6} - 2730 \, a^{5} x^{5} + 18600 \, a^{4} x^{4} - 13600 \, a^{3} x^{3} - 9800 \, a^{2} x^{2} + 15082 \, a x - 75 \, {\left(a^{6} x^{6} - 4 \, a^{5} x^{5} + 5 \, a^{4} x^{4} - 5 \, a^{2} x^{2} + 4 \, a x - 1\right)} \log\left(a x + 1\right) + 3915 \, {\left(a^{6} x^{6} - 4 \, a^{5} x^{5} + 5 \, a^{4} x^{4} - 5 \, a^{2} x^{2} + 4 \, a x - 1\right)} \log\left(a x - 1\right) - 4768}{960 \, {\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)}}"," ",0,"1/960*(960*a^7*x^7 - 3840*a^6*x^6 - 2730*a^5*x^5 + 18600*a^4*x^4 - 13600*a^3*x^3 - 9800*a^2*x^2 + 15082*a*x - 75*(a^6*x^6 - 4*a^5*x^5 + 5*a^4*x^4 - 5*a^2*x^2 + 4*a*x - 1)*log(a*x + 1) + 3915*(a^6*x^6 - 4*a^5*x^5 + 5*a^4*x^4 - 5*a^2*x^2 + 4*a*x - 1)*log(a*x - 1) - 4768)/(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)","A",0
806,1,201,0,0.613983," ","integrate((c-c/a^2/x^2)^4*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{7350 \, a^{7} c^{4} x^{7} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 1680 \, a^{7} c^{4} x^{7} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 1680 \, a^{7} c^{4} x^{7} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(1680 \, a^{8} c^{4} x^{8} + 4496 \, a^{7} c^{4} x^{7} + 5861 \, a^{6} c^{4} x^{6} + 1093 \, a^{5} c^{4} x^{5} - 3282 \, a^{4} c^{4} x^{4} - 274 \, a^{3} c^{4} x^{3} + 1336 \, a^{2} c^{4} x^{2} + 40 \, a c^{4} x - 240 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{1680 \, a^{8} x^{7}}"," ",0,"-1/1680*(7350*a^7*c^4*x^7*arctan(sqrt((a*x - 1)/(a*x + 1))) + 1680*a^7*c^4*x^7*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 1680*a^7*c^4*x^7*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (1680*a^8*c^4*x^8 + 4496*a^7*c^4*x^7 + 5861*a^6*c^4*x^6 + 1093*a^5*c^4*x^5 - 3282*a^4*c^4*x^4 - 274*a^3*c^4*x^3 + 1336*a^2*c^4*x^2 + 40*a*c^4*x - 240*c^4)*sqrt((a*x - 1)/(a*x + 1)))/(a^8*x^7)","A",0
807,1,179,0,0.513790," ","integrate((c-c/a^2/x^2)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{450 \, a^{5} c^{3} x^{5} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 120 \, a^{5} c^{3} x^{5} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 120 \, a^{5} c^{3} x^{5} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(120 \, a^{6} c^{3} x^{6} + 304 \, a^{5} c^{3} x^{5} + 319 \, a^{4} c^{3} x^{4} + 47 \, a^{3} c^{3} x^{3} - 118 \, a^{2} c^{3} x^{2} - 6 \, a c^{3} x + 24 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{120 \, a^{6} x^{5}}"," ",0,"-1/120*(450*a^5*c^3*x^5*arctan(sqrt((a*x - 1)/(a*x + 1))) + 120*a^5*c^3*x^5*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 120*a^5*c^3*x^5*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (120*a^6*c^3*x^6 + 304*a^5*c^3*x^5 + 319*a^4*c^3*x^4 + 47*a^3*c^3*x^3 - 118*a^2*c^3*x^2 - 6*a*c^3*x + 24*c^3)*sqrt((a*x - 1)/(a*x + 1)))/(a^6*x^5)","A",0
808,1,156,0,0.635671," ","integrate((c-c/a^2/x^2)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{18 \, a^{3} c^{2} x^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 6 \, a^{3} c^{2} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 6 \, a^{3} c^{2} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(6 \, a^{4} c^{2} x^{4} + 14 \, a^{3} c^{2} x^{3} + 11 \, a^{2} c^{2} x^{2} + a c^{2} x - 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a^{4} x^{3}}"," ",0,"-1/6*(18*a^3*c^2*x^3*arctan(sqrt((a*x - 1)/(a*x + 1))) + 6*a^3*c^2*x^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 6*a^3*c^2*x^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (6*a^4*c^2*x^4 + 14*a^3*c^2*x^3 + 11*a^2*c^2*x^2 + a*c^2*x - 2*c^2)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*x^3)","A",0
809,1,107,0,0.588224," ","integrate((c-c/a^2/x^2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, a c x \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + a c x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - a c x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(a^{2} c x^{2} + 2 \, a c x + c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x}"," ",0,"-(2*a*c*x*arctan(sqrt((a*x - 1)/(a*x + 1))) + a*c*x*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - a*c*x*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (a^2*c*x^2 + 2*a*c*x + c)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x)","A",0
810,1,67,0,0.527641," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2),x, algorithm=""fricas"")","\frac{{\left(a x + 2\right)} \sqrt{\frac{a x - 1}{a x + 1}} - \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right)}{a c}"," ",0,"((a*x + 2)*sqrt((a*x - 1)/(a*x + 1)) - log(sqrt((a*x - 1)/(a*x + 1)) + 1) + log(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a*c)","A",0
811,1,119,0,0.435599," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, {\left(a^{2} x^{2} - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(3 \, a^{3} x^{3} + 7 \, a^{2} x^{2} - 5 \, a x - 8\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{3} c^{2} x^{2} - a c^{2}\right)}}"," ",0,"-1/3*(3*(a^2*x^2 - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*(a^2*x^2 - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (3*a^3*x^3 + 7*a^2*x^2 - 5*a*x - 8)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^2*x^2 - a*c^2)","A",0
812,1,161,0,0.787659," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(15 \, a^{5} x^{5} + 38 \, a^{4} x^{4} - 52 \, a^{3} x^{3} - 87 \, a^{2} x^{2} + 33 \, a x + 48\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{15 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"-1/15*(15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*(a^4*x^4 - 2*a^2*x^2 + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (15*a^5*x^5 + 38*a^4*x^4 - 52*a^3*x^3 - 87*a^2*x^2 + 33*a*x + 48)*sqrt((a*x - 1)/(a*x + 1)))/(a^5*c^3*x^4 - 2*a^3*c^3*x^2 + a*c^3)","A",0
813,1,205,0,0.582971," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^4,x, algorithm=""fricas"")","-\frac{105 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 105 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(105 \, a^{7} x^{7} + 281 \, a^{6} x^{6} - 559 \, a^{5} x^{5} - 965 \, a^{4} x^{4} + 715 \, a^{3} x^{3} + 1065 \, a^{2} x^{2} - 279 \, a x - 384\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{105 \, {\left(a^{7} c^{4} x^{6} - 3 \, a^{5} c^{4} x^{4} + 3 \, a^{3} c^{4} x^{2} - a c^{4}\right)}}"," ",0,"-1/105*(105*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 105*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (105*a^7*x^7 + 281*a^6*x^6 - 559*a^5*x^5 - 965*a^4*x^4 + 715*a^3*x^3 + 1065*a^2*x^2 - 279*a*x - 384)*sqrt((a*x - 1)/(a*x + 1)))/(a^7*c^4*x^6 - 3*a^5*c^4*x^4 + 3*a^3*c^4*x^2 - a*c^4)","A",0
814,1,89,0,1.165631," ","integrate((c-c/a^2/x^2)^4*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{210 \, a^{8} c^{4} x^{8} - 420 \, a^{7} c^{4} x^{7} \log\left(x\right) + 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,"1/210*(210*a^8*c^4*x^8 - 420*a^7*c^4*x^7*log(x) + 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
815,1,78,0,0.466372," ","integrate((c-c/a^2/x^2)^3*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{30 \, a^{6} c^{3} x^{6} - 60 \, a^{5} c^{3} x^{5} \log\left(x\right) + 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,"1/30*(30*a^6*c^3*x^6 - 60*a^5*c^3*x^5*log(x) + 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
816,1,43,0,0.433358," ","integrate((c-c/a^2/x^2)^2*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{3 \, a^{4} c^{2} x^{4} - 6 \, a^{3} c^{2} x^{3} \log\left(x\right) - 3 \, a c^{2} x + c^{2}}{3 \, a^{4} x^{3}}"," ",0,"1/3*(3*a^4*c^2*x^4 - 6*a^3*c^2*x^3*log(x) - 3*a*c^2*x + c^2)/(a^4*x^3)","A",0
817,1,26,0,0.505703," ","integrate((c-c/a^2/x^2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\frac{a^{2} c x^{2} - 2 \, a c x \log\left(x\right) - c}{a^{2} x}"," ",0,"(a^2*c*x^2 - 2*a*c*x*log(x) - c)/(a^2*x)","A",0
818,1,38,0,0.558217," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2),x, algorithm=""fricas"")","\frac{a^{2} x^{2} + a x - 2 \, {\left(a x + 1\right)} \log\left(a x + 1\right) - 1}{a^{2} c x + a c}"," ",0,"(a^2*x^2 + a*x - 2*(a*x + 1)*log(a*x + 1) - 1)/(a^2*c*x + a*c)","A",0
819,1,92,0,0.538304," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","\frac{8 \, a^{3} x^{3} + 16 \, a^{2} x^{2} - 6 \, a x - 17 \, {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(a x + 1\right) + {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(a x - 1\right) - 12}{8 \, {\left(a^{3} c^{2} x^{2} + 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"1/8*(8*a^3*x^3 + 16*a^2*x^2 - 6*a*x - 17*(a^2*x^2 + 2*a*x + 1)*log(a*x + 1) + (a^2*x^2 + 2*a*x + 1)*log(a*x - 1) - 12)/(a^3*c^2*x^2 + 2*a^2*c^2*x + a*c^2)","A",0
820,1,137,0,0.570518," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^3,x, algorithm=""fricas"")","\frac{12 \, a^{5} x^{5} + 24 \, a^{4} x^{4} - 30 \, a^{3} x^{3} - 48 \, a^{2} x^{2} + 14 \, a x - 27 \, {\left(a^{4} x^{4} + 2 \, a^{3} x^{3} - 2 \, a x - 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{4} x^{4} + 2 \, a^{3} x^{3} - 2 \, a x - 1\right)} \log\left(a x - 1\right) + 22}{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)}}"," ",0,"1/12*(12*a^5*x^5 + 24*a^4*x^4 - 30*a^3*x^3 - 48*a^2*x^2 + 14*a*x - 27*(a^4*x^4 + 2*a^3*x^3 - 2*a*x - 1)*log(a*x + 1) + 3*(a^4*x^4 + 2*a^3*x^3 - 2*a*x - 1)*log(a*x - 1) + 22)/(a^5*c^3*x^4 + 2*a^4*c^3*x^3 - 2*a^2*c^3*x - a*c^3)","A",0
821,1,233,0,0.591952," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^4,x, algorithm=""fricas"")","\frac{384 \, a^{7} x^{7} + 768 \, a^{6} x^{6} - 1638 \, a^{5} x^{5} - 2508 \, a^{4} x^{4} + 1732 \, a^{3} x^{3} + 2516 \, a^{2} x^{2} - 550 \, a x - 909 \, {\left(a^{6} x^{6} + 2 \, a^{5} x^{5} - a^{4} x^{4} - 4 \, a^{3} x^{3} - a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(a x + 1\right) + 141 \, {\left(a^{6} x^{6} + 2 \, a^{5} x^{5} - a^{4} x^{4} - 4 \, a^{3} x^{3} - a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(a x - 1\right) - 800}{384 \, {\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)}}"," ",0,"1/384*(384*a^7*x^7 + 768*a^6*x^6 - 1638*a^5*x^5 - 2508*a^4*x^4 + 1732*a^3*x^3 + 2516*a^2*x^2 - 550*a*x - 909*(a^6*x^6 + 2*a^5*x^5 - a^4*x^4 - 4*a^3*x^3 - a^2*x^2 + 2*a*x + 1)*log(a*x + 1) + 141*(a^6*x^6 + 2*a^5*x^5 - a^4*x^4 - 4*a^3*x^3 - a^2*x^2 + 2*a*x + 1)*log(a*x - 1) - 800)/(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)","A",0
822,1,201,0,0.487434," ","integrate((c-c/a^2/x^2)^4*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{1050 \, a^{7} c^{4} x^{7} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 1680 \, a^{7} c^{4} x^{7} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 1680 \, a^{7} c^{4} x^{7} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(560 \, a^{8} c^{4} x^{8} + 3056 \, a^{7} c^{4} x^{7} + 1971 \, a^{6} c^{4} x^{6} - 1517 \, a^{5} c^{4} x^{5} - 222 \, a^{4} c^{4} x^{4} + 866 \, a^{3} c^{4} x^{3} - 184 \, a^{2} c^{4} x^{2} - 200 \, a c^{4} x + 80 \, c^{4}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{560 \, a^{8} x^{7}}"," ",0,"-1/560*(1050*a^7*c^4*x^7*arctan(sqrt((a*x - 1)/(a*x + 1))) + 1680*a^7*c^4*x^7*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 1680*a^7*c^4*x^7*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (560*a^8*c^4*x^8 + 3056*a^7*c^4*x^7 + 1971*a^6*c^4*x^6 - 1517*a^5*c^4*x^5 - 222*a^4*c^4*x^4 + 866*a^3*c^4*x^3 - 184*a^2*c^4*x^2 - 200*a*c^4*x + 80*c^4)*sqrt((a*x - 1)/(a*x + 1)))/(a^8*x^7)","A",0
823,1,179,0,0.444640," ","integrate((c-c/a^2/x^2)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","-\frac{30 \, a^{5} c^{3} x^{5} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + 120 \, a^{5} c^{3} x^{5} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 120 \, a^{5} c^{3} x^{5} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(40 \, a^{6} c^{3} x^{6} + 192 \, a^{5} c^{3} x^{5} + 97 \, a^{4} c^{3} x^{4} - 79 \, a^{3} c^{3} x^{3} + 6 \, a^{2} c^{3} x^{2} + 22 \, a c^{3} x - 8 \, c^{3}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{40 \, a^{6} x^{5}}"," ",0,"-1/40*(30*a^5*c^3*x^5*arctan(sqrt((a*x - 1)/(a*x + 1))) + 120*a^5*c^3*x^5*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 120*a^5*c^3*x^5*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (40*a^6*c^3*x^6 + 192*a^5*c^3*x^5 + 97*a^4*c^3*x^4 - 79*a^3*c^3*x^3 + 6*a^2*c^3*x^2 + 22*a*c^3*x - 8*c^3)*sqrt((a*x - 1)/(a*x + 1)))/(a^6*x^5)","A",0
824,1,156,0,0.516622," ","integrate((c-c/a^2/x^2)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{6 \, a^{3} c^{2} x^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 18 \, a^{3} c^{2} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 18 \, a^{3} c^{2} x^{3} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(6 \, a^{4} c^{2} x^{4} + 22 \, a^{3} c^{2} x^{3} + 7 \, a^{2} c^{2} x^{2} - 7 \, a c^{2} x + 2 \, c^{2}\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{6 \, a^{4} x^{3}}"," ",0,"1/6*(6*a^3*c^2*x^3*arctan(sqrt((a*x - 1)/(a*x + 1))) - 18*a^3*c^2*x^3*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 18*a^3*c^2*x^3*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (6*a^4*c^2*x^4 + 22*a^3*c^2*x^3 + 7*a^2*c^2*x^2 - 7*a*c^2*x + 2*c^2)*sqrt((a*x - 1)/(a*x + 1)))/(a^4*x^3)","A",0
825,1,103,0,1.014518," ","integrate((c-c/a^2/x^2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{6 \, a c x \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) - 3 \, a c x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 3 \, a c x \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) + {\left(a^{2} c x^{2} - c\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} x}"," ",0,"(6*a*c*x*arctan(sqrt((a*x - 1)/(a*x + 1))) - 3*a*c*x*log(sqrt((a*x - 1)/(a*x + 1)) + 1) + 3*a*c*x*log(sqrt((a*x - 1)/(a*x + 1)) - 1) + (a^2*c*x^2 - c)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*x)","A",0
826,1,96,0,0.594726," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2),x, algorithm=""fricas"")","-\frac{9 \, {\left(a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 9 \, {\left(a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(3 \, a^{2} x^{2} + 19 \, a x + 14\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{3 \, {\left(a^{2} c x + a c\right)}}"," ",0,"-1/3*(9*(a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 9*(a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (3*a^2*x^2 + 19*a*x + 14)*sqrt((a*x - 1)/(a*x + 1)))/(a^2*c*x + a*c)","A",0
827,1,135,0,0.502774," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","-\frac{15 \, {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 15 \, {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(5 \, a^{3} x^{3} + 39 \, a^{2} x^{2} + 57 \, a x + 24\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{5 \, {\left(a^{3} c^{2} x^{2} + 2 \, a^{2} c^{2} x + a c^{2}\right)}}"," ",0,"-1/5*(15*(a^2*x^2 + 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 15*(a^2*x^2 + 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (5*a^3*x^3 + 39*a^2*x^2 + 57*a*x + 24)*sqrt((a*x - 1)/(a*x + 1)))/(a^3*c^2*x^2 + 2*a^2*c^2*x + a*c^2)","A",0
828,1,179,0,0.459607," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^3,x, algorithm=""fricas"")","-\frac{105 \, {\left(a^{4} x^{4} + 2 \, a^{3} x^{3} - 2 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 105 \, {\left(a^{4} x^{4} + 2 \, a^{3} x^{3} - 2 \, a x - 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(35 \, a^{5} x^{5} + 286 \, a^{4} x^{4} + 368 \, a^{3} x^{3} - 125 \, a^{2} x^{2} - 423 \, a x - 176\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{35 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{3} - 2 \, a^{2} c^{3} x - a c^{3}\right)}}"," ",0,"-1/35*(105*(a^4*x^4 + 2*a^3*x^3 - 2*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 105*(a^4*x^4 + 2*a^3*x^3 - 2*a*x - 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (35*a^5*x^5 + 286*a^4*x^4 + 368*a^3*x^3 - 125*a^2*x^2 - 423*a*x - 176)*sqrt((a*x - 1)/(a*x + 1)))/(a^5*c^3*x^4 + 2*a^4*c^3*x^3 - 2*a^2*c^3*x - a*c^3)","A",0
829,1,275,0,0.605973," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^4,x, algorithm=""fricas"")","-\frac{945 \, {\left(a^{6} x^{6} + 2 \, a^{5} x^{5} - a^{4} x^{4} - 4 \, a^{3} x^{3} - a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 945 \, {\left(a^{6} x^{6} + 2 \, a^{5} x^{5} - a^{4} x^{4} - 4 \, a^{3} x^{3} - a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(\sqrt{\frac{a x - 1}{a x + 1}} - 1\right) - {\left(315 \, a^{7} x^{7} + 2669 \, a^{6} x^{6} + 2967 \, a^{5} x^{5} - 4029 \, a^{4} x^{4} - 7399 \, a^{3} x^{3} - 339 \, a^{2} x^{2} + 4047 \, a x + 1664\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{315 \, {\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)}}"," ",0,"-1/315*(945*(a^6*x^6 + 2*a^5*x^5 - a^4*x^4 - 4*a^3*x^3 - a^2*x^2 + 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) + 1) - 945*(a^6*x^6 + 2*a^5*x^5 - a^4*x^4 - 4*a^3*x^3 - a^2*x^2 + 2*a*x + 1)*log(sqrt((a*x - 1)/(a*x + 1)) - 1) - (315*a^7*x^7 + 2669*a^6*x^6 + 2967*a^5*x^5 - 4029*a^4*x^4 - 7399*a^3*x^3 - 339*a^2*x^2 + 4047*a*x + 1664)*sqrt((a*x - 1)/(a*x + 1)))/(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)","A",0
830,1,96,0,0.694415," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(7/2),x, algorithm=""fricas"")","\frac{{\left(60 \, a^{7} c^{3} x^{7} + 60 \, a^{6} c^{3} x^{6} \log\left(x\right) + 180 \, a^{5} c^{3} x^{5} + 90 \, a^{4} c^{3} x^{4} - 60 \, a^{3} c^{3} x^{3} - 45 \, a^{2} c^{3} x^{2} + 12 \, a c^{3} x + 10 \, c^{3}\right)} \sqrt{a^{2} c}}{60 \, a^{8} x^{6}}"," ",0,"1/60*(60*a^7*c^3*x^7 + 60*a^6*c^3*x^6*log(x) + 180*a^5*c^3*x^5 + 90*a^4*c^3*x^4 - 60*a^3*c^3*x^3 - 45*a^2*c^3*x^2 + 12*a*c^3*x + 10*c^3)*sqrt(a^2*c)/(a^8*x^6)","A",0
831,1,74,0,0.554068," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(12 \, a^{5} c^{2} x^{5} + 12 \, a^{4} c^{2} x^{4} \log\left(x\right) + 24 \, a^{3} c^{2} x^{3} + 12 \, a^{2} c^{2} x^{2} - 4 \, a c^{2} x - 3 \, c^{2}\right)} \sqrt{a^{2} c}}{12 \, a^{6} x^{4}}"," ",0,"1/12*(12*a^5*c^2*x^5 + 12*a^4*c^2*x^4*log(x) + 24*a^3*c^2*x^3 + 12*a^2*c^2*x^2 - 4*a*c^2*x - 3*c^2)*sqrt(a^2*c)/(a^6*x^4)","A",0
832,1,42,0,0.649131," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} c x^{3} + 2 \, a^{2} c x^{2} \log\left(x\right) + 2 \, a c x + c\right)} \sqrt{a^{2} c}}{2 \, a^{4} x^{2}}"," ",0,"1/2*(2*a^3*c*x^3 + 2*a^2*c*x^2*log(x) + 2*a*c*x + c)*sqrt(a^2*c)/(a^4*x^2)","A",0
833,1,17,0,0.483709," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x + \log\left(x\right)\right)}}{a^{2}}"," ",0,"sqrt(a^2*c)*(a*x + log(x))/a^2","A",0
834,1,24,0,0.641819," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x + \log\left(a x - 1\right)\right)}}{a^{2} c}"," ",0,"sqrt(a^2*c)*(a*x + log(a*x - 1))/(a^2*c)","A",0
835,1,68,0,0.567002," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(4 \, a^{2} x^{2} - 4 \, a x - {\left(a x - 1\right)} \log\left(a x + 1\right) + 5 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 2\right)} \sqrt{a^{2} c}}{4 \, {\left(a^{3} c^{2} x - a^{2} c^{2}\right)}}"," ",0,"1/4*(4*a^2*x^2 - 4*a*x - (a*x - 1)*log(a*x + 1) + 5*(a*x - 1)*log(a*x - 1) - 2)*sqrt(a^2*c)/(a^3*c^2*x - a^2*c^2)","A",0
836,1,137,0,0.658567," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(16 \, a^{4} x^{4} - 16 \, a^{3} x^{3} - 34 \, a^{2} x^{2} + 18 \, a x - 7 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x + 1\right) + 23 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)} \log\left(a x - 1\right) + 12\right)} \sqrt{a^{2} c}}{16 \, {\left(a^{5} c^{3} x^{3} - a^{4} c^{3} x^{2} - a^{3} c^{3} x + a^{2} c^{3}\right)}}"," ",0,"1/16*(16*a^4*x^4 - 16*a^3*x^3 - 34*a^2*x^2 + 18*a*x - 7*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x + 1) + 23*(a^3*x^3 - a^2*x^2 - a*x + 1)*log(a*x - 1) + 12)*sqrt(a^2*c)/(a^5*c^3*x^3 - a^4*c^3*x^2 - a^3*c^3*x + a^2*c^3)","A",0
837,1,205,0,0.598305," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""fricas"")","\frac{{\left(96 \, a^{6} x^{6} - 96 \, a^{5} x^{5} - 366 \, a^{4} x^{4} + 222 \, a^{3} x^{3} + 338 \, a^{2} x^{2} - 122 \, a x - 57 \, {\left(a^{5} x^{5} - a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} + a x - 1\right)} \log\left(a x + 1\right) + 153 \, {\left(a^{5} x^{5} - a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} + a x - 1\right)} \log\left(a x - 1\right) - 88\right)} \sqrt{a^{2} c}}{96 \, {\left(a^{7} c^{4} x^{5} - a^{6} c^{4} x^{4} - 2 \, a^{5} c^{4} x^{3} + 2 \, a^{4} c^{4} x^{2} + a^{3} c^{4} x - a^{2} c^{4}\right)}}"," ",0,"1/96*(96*a^6*x^6 - 96*a^5*x^5 - 366*a^4*x^4 + 222*a^3*x^3 + 338*a^2*x^2 - 122*a*x - 57*(a^5*x^5 - a^4*x^4 - 2*a^3*x^3 + 2*a^2*x^2 + a*x - 1)*log(a*x + 1) + 153*(a^5*x^5 - a^4*x^4 - 2*a^3*x^3 + 2*a^2*x^2 + a*x - 1)*log(a*x - 1) - 88)*sqrt(a^2*c)/(a^7*c^4*x^5 - a^6*c^4*x^4 - 2*a^5*c^4*x^3 + 2*a^4*c^4*x^2 + a^3*c^4*x - a^2*c^4)","A",0
838,1,438,0,0.760733," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(7/2),x, algorithm=""fricas"")","\left[-\frac{960 \, a^{5} \sqrt{-c} c^{3} x^{5} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) - 375 \, a^{5} \sqrt{-c} c^{3} x^{5} \log\left(-\frac{a^{2} c x^{2} - 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) - 2 \, {\left(240 \, a^{6} c^{3} x^{6} - 736 \, a^{5} c^{3} x^{5} + 105 \, a^{4} c^{3} x^{4} + 352 \, a^{3} c^{3} x^{3} + 70 \, a^{2} c^{3} x^{2} - 96 \, a c^{3} x - 40 \, c^{3}\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{480 \, a^{6} x^{5}}, \frac{375 \, a^{5} c^{\frac{7}{2}} x^{5} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + 240 \, a^{5} c^{\frac{7}{2}} x^{5} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(240 \, a^{6} c^{3} x^{6} - 736 \, a^{5} c^{3} x^{5} + 105 \, a^{4} c^{3} x^{4} + 352 \, a^{3} c^{3} x^{3} + 70 \, a^{2} c^{3} x^{2} - 96 \, a c^{3} x - 40 \, c^{3}\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{240 \, a^{6} x^{5}}\right]"," ",0,"[-1/480*(960*a^5*sqrt(-c)*c^3*x^5*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) - 375*a^5*sqrt(-c)*c^3*x^5*log(-(a^2*c*x^2 - 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) - 2*(240*a^6*c^3*x^6 - 736*a^5*c^3*x^5 + 105*a^4*c^3*x^4 + 352*a^3*c^3*x^3 + 70*a^2*c^3*x^2 - 96*a*c^3*x - 40*c^3)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^6*x^5), 1/240*(375*a^5*c^(7/2)*x^5*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + 240*a^5*c^(7/2)*x^5*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (240*a^6*c^3*x^6 - 736*a^5*c^3*x^5 + 105*a^4*c^3*x^4 + 352*a^3*c^3*x^3 + 70*a^2*c^3*x^2 - 96*a*c^3*x - 40*c^3)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^6*x^5)]","A",0
839,1,394,0,0.630260," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{96 \, a^{3} \sqrt{-c} c^{2} x^{3} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) - 27 \, a^{3} \sqrt{-c} c^{2} x^{3} \log\left(-\frac{a^{2} c x^{2} - 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) - 2 \, {\left(24 \, a^{4} c^{2} x^{4} - 64 \, a^{3} c^{2} x^{3} - 3 \, a^{2} c^{2} x^{2} + 16 \, a c^{2} x + 6 \, c^{2}\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{48 \, a^{4} x^{3}}, \frac{27 \, a^{3} c^{\frac{5}{2}} x^{3} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + 24 \, a^{3} c^{\frac{5}{2}} x^{3} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(24 \, a^{4} c^{2} x^{4} - 64 \, a^{3} c^{2} x^{3} - 3 \, a^{2} c^{2} x^{2} + 16 \, a c^{2} x + 6 \, c^{2}\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{24 \, a^{4} x^{3}}\right]"," ",0,"[-1/48*(96*a^3*sqrt(-c)*c^2*x^3*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) - 27*a^3*sqrt(-c)*c^2*x^3*log(-(a^2*c*x^2 - 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) - 2*(24*a^4*c^2*x^4 - 64*a^3*c^2*x^3 - 3*a^2*c^2*x^2 + 16*a*c^2*x + 6*c^2)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^4*x^3), 1/24*(27*a^3*c^(5/2)*x^3*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + 24*a^3*c^(5/2)*x^3*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (24*a^4*c^2*x^4 - 64*a^3*c^2*x^3 - 3*a^2*c^2*x^2 + 16*a*c^2*x + 6*c^2)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^4*x^3)]","A",0
840,1,317,0,0.810076," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{8 \, a \sqrt{-c} c x \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) - a \sqrt{-c} c x \log\left(-\frac{a^{2} c x^{2} - 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) - 2 \, {\left(2 \, a^{2} c x^{2} - 4 \, a c x - c\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{4 \, a^{2} x}, \frac{a c^{\frac{3}{2}} x \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + 2 \, a c^{\frac{3}{2}} x \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(2 \, a^{2} c x^{2} - 4 \, a c x - c\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{2 \, a^{2} x}\right]"," ",0,"[-1/4*(8*a*sqrt(-c)*c*x*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) - a*sqrt(-c)*c*x*log(-(a^2*c*x^2 - 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) - 2*(2*a^2*c*x^2 - 4*a*c*x - c)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^2*x), 1/2*(a*c^(3/2)*x*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + 2*a*c^(3/2)*x*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (2*a^2*c*x^2 - 4*a*c*x - c)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^2*x)]","A",0
841,1,267,0,0.599068," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 4 \, \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right)}{2 \, a}, \frac{a x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - \sqrt{c} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right)}{a}\right]"," ",0,"[1/2*(2*a*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 4*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + sqrt(-c)*log(-(a^2*c*x^2 + 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2))/a, (a*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - sqrt(c)*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c))/a]","A",0
842,1,216,0,0.526793," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a x - 1\right)} \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(a^{2} x^{2} - 3 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x - a c}, -\frac{2 \, {\left(a x - 1\right)} \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) - {\left(a^{2} x^{2} - 3 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x - a c}\right]"," ",0,"[((a*x - 1)*sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (a^2*x^2 - 3*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^2*c*x - a*c), -(2*(a*x - 1)*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) - (a^2*x^2 - 3*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^2*c*x - a*c)]","A",0
843,1,280,0,0.634530," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(3 \, a^{3} x^{3} - 14 \, a^{2} x^{2} + 10 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{3 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}, -\frac{6 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) - {\left(3 \, a^{3} x^{3} - 14 \, a^{2} x^{2} + 10 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{3 \, {\left(a^{3} c^{2} x^{2} - 2 \, a^{2} c^{2} x + a c^{2}\right)}}\right]"," ",0,"[1/3*(3*(a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (3*a^3*x^3 - 14*a^2*x^2 + 10*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2), -1/3*(6*(a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) - (3*a^3*x^3 - 14*a^2*x^2 + 10*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^3*c^2*x^2 - 2*a^2*c^2*x + a*c^2)]","A",0
844,1,352,0,0.669163," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a x - 1\right)} \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(15 \, a^{5} x^{5} - 76 \, a^{4} x^{4} + 32 \, a^{3} x^{3} + 82 \, a^{2} x^{2} - 56 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{15 \, {\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{30 \, {\left(a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) - {\left(15 \, a^{5} x^{5} - 76 \, a^{4} x^{4} + 32 \, a^{3} x^{3} + 82 \, a^{2} x^{2} - 56 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{15 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{4} c^{3} x^{3} + 2 \, a^{2} c^{3} x - a c^{3}\right)}}\right]"," ",0,"[1/15*(15*(a^4*x^4 - 2*a^3*x^3 + 2*a*x - 1)*sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (15*a^5*x^5 - 76*a^4*x^4 + 32*a^3*x^3 + 82*a^2*x^2 - 56*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^5*c^3*x^4 - 2*a^4*c^3*x^3 + 2*a^2*c^3*x - a*c^3), -1/15*(30*(a^4*x^4 - 2*a^3*x^3 + 2*a*x - 1)*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) - (15*a^5*x^5 - 76*a^4*x^4 + 32*a^3*x^3 + 82*a^2*x^2 - 56*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^5*c^3*x^4 - 2*a^4*c^3*x^3 + 2*a^2*c^3*x - a*c^3)]","A",0
845,1,496,0,0.590671," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(7/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{6} x^{6} - 2 \, a^{5} x^{5} - a^{4} x^{4} + 4 \, a^{3} x^{3} - a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(105 \, a^{7} x^{7} - 562 \, a^{6} x^{6} + 74 \, a^{5} x^{5} + 1226 \, a^{4} x^{4} - 636 \, a^{3} x^{3} - 654 \, a^{2} x^{2} + 432 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{105 \, {\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{210 \, {\left(a^{6} x^{6} - 2 \, a^{5} x^{5} - a^{4} x^{4} + 4 \, a^{3} x^{3} - a^{2} x^{2} - 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) - {\left(105 \, a^{7} x^{7} - 562 \, a^{6} x^{6} + 74 \, a^{5} x^{5} + 1226 \, a^{4} x^{4} - 636 \, a^{3} x^{3} - 654 \, a^{2} x^{2} + 432 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{105 \, {\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)}}\right]"," ",0,"[1/105*(105*(a^6*x^6 - 2*a^5*x^5 - a^4*x^4 + 4*a^3*x^3 - a^2*x^2 - 2*a*x + 1)*sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (105*a^7*x^7 - 562*a^6*x^6 + 74*a^5*x^5 + 1226*a^4*x^4 - 636*a^3*x^3 - 654*a^2*x^2 + 432*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(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), -1/105*(210*(a^6*x^6 - 2*a^5*x^5 - a^4*x^4 + 4*a^3*x^3 - a^2*x^2 - 2*a*x + 1)*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) - (105*a^7*x^7 - 562*a^6*x^6 + 74*a^5*x^5 + 1226*a^4*x^4 - 636*a^3*x^3 - 654*a^2*x^2 + 432*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(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)]","A",0
846,1,96,0,0.831263," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(9/2),x, algorithm=""fricas"")","\frac{{\left(280 \, a^{9} c^{4} x^{9} + 840 \, a^{8} c^{4} x^{8} \log\left(x\right) + 1120 \, a^{6} c^{4} x^{6} + 560 \, a^{5} c^{4} x^{5} - 420 \, a^{4} c^{4} x^{4} - 448 \, a^{3} c^{4} x^{3} + 120 \, a c^{4} x + 35 \, c^{4}\right)} \sqrt{a^{2} c}}{280 \, a^{10} x^{8}}"," ",0,"1/280*(280*a^9*c^4*x^9 + 840*a^8*c^4*x^8*log(x) + 1120*a^6*c^4*x^6 + 560*a^5*c^4*x^5 - 420*a^4*c^4*x^4 - 448*a^3*c^4*x^3 + 120*a*c^4*x + 35*c^4)*sqrt(a^2*c)/(a^10*x^8)","A",0
847,1,96,0,0.759570," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(7/2),x, algorithm=""fricas"")","\frac{{\left(60 \, a^{7} c^{3} x^{7} + 180 \, a^{6} c^{3} x^{6} \log\left(x\right) - 60 \, a^{5} c^{3} x^{5} + 150 \, a^{4} c^{3} x^{4} + 100 \, a^{3} c^{3} x^{3} - 15 \, a^{2} c^{3} x^{2} - 36 \, a c^{3} x - 10 \, c^{3}\right)} \sqrt{a^{2} c}}{60 \, a^{8} x^{6}}"," ",0,"1/60*(60*a^7*c^3*x^7 + 180*a^6*c^3*x^6*log(x) - 60*a^5*c^3*x^5 + 150*a^4*c^3*x^4 + 100*a^3*c^3*x^3 - 15*a^2*c^3*x^2 - 36*a*c^3*x - 10*c^3)*sqrt(a^2*c)/(a^8*x^6)","A",0
848,1,72,0,0.595423," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(4 \, a^{5} c^{2} x^{5} + 12 \, a^{4} c^{2} x^{4} \log\left(x\right) - 8 \, a^{3} c^{2} x^{3} + 4 \, a^{2} c^{2} x^{2} + 4 \, a c^{2} x + c^{2}\right)} \sqrt{a^{2} c}}{4 \, a^{6} x^{4}}"," ",0,"1/4*(4*a^5*c^2*x^5 + 12*a^4*c^2*x^4*log(x) - 8*a^3*c^2*x^3 + 4*a^2*c^2*x^2 + 4*a*c^2*x + c^2)*sqrt(a^2*c)/(a^6*x^4)","A",0
849,1,44,0,0.473082," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} c x^{3} + 6 \, a^{2} c x^{2} \log\left(x\right) - 6 \, a c x - c\right)} \sqrt{a^{2} c}}{2 \, a^{4} x^{2}}"," ",0,"1/2*(2*a^3*c*x^3 + 6*a^2*c*x^2*log(x) - 6*a*c*x - c)*sqrt(a^2*c)/(a^4*x^2)","A",0
850,1,27,0,0.730542," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x + 4 \, \log\left(a x - 1\right) - \log\left(x\right)\right)}}{a^{2}}"," ",0,"sqrt(a^2*c)*(a*x + 4*log(a*x - 1) - log(x))/a^2","A",0
851,1,49,0,0.497384," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} - a x + 3 \, {\left(a x - 1\right)} \log\left(a x - 1\right) - 2\right)} \sqrt{a^{2} c}}{a^{3} c x - a^{2} c}"," ",0,"(a^2*x^2 - a*x + 3*(a*x - 1)*log(a*x - 1) - 2)*sqrt(a^2*c)/(a^3*c*x - a^2*c)","A",0
852,1,81,0,0.498153," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} - 4 \, a^{2} x^{2} - 4 \, a x + 6 \, {\left(a^{2} x^{2} - 2 \, a x + 1\right)} \log\left(a x - 1\right) + 5\right)} \sqrt{a^{2} c}}{2 \, {\left(a^{4} c^{2} x^{2} - 2 \, a^{3} c^{2} x + a^{2} c^{2}\right)}}"," ",0,"1/2*(2*a^3*x^3 - 4*a^2*x^2 - 4*a*x + 6*(a^2*x^2 - 2*a*x + 1)*log(a*x - 1) + 5)*sqrt(a^2*c)/(a^4*c^2*x^2 - 2*a^3*c^2*x + a^2*c^2)","A",0
853,1,138,0,0.629161," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(48 \, a^{4} x^{4} - 144 \, a^{3} x^{3} - 42 \, a^{2} x^{2} + 270 \, a x - 3 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(a x + 1\right) + 147 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1\right)} \log\left(a x - 1\right) - 140\right)} \sqrt{a^{2} c}}{48 \, {\left(a^{5} c^{3} x^{3} - 3 \, a^{4} c^{3} x^{2} + 3 \, a^{3} c^{3} x - a^{2} c^{3}\right)}}"," ",0,"1/48*(48*a^4*x^4 - 144*a^3*x^3 - 42*a^2*x^2 + 270*a*x - 3*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(a*x + 1) + 147*(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)*log(a*x - 1) - 140)*sqrt(a^2*c)/(a^5*c^3*x^3 - 3*a^4*c^3*x^2 + 3*a^3*c^3*x - a^2*c^3)","A",0
854,1,207,0,0.520455," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""fricas"")","\frac{{\left(64 \, a^{6} x^{6} - 192 \, a^{5} x^{5} - 174 \, a^{4} x^{4} + 618 \, a^{3} x^{3} - 118 \, a^{2} x^{2} - 414 \, a x - 9 \, {\left(a^{5} x^{5} - 3 \, a^{4} x^{4} + 2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} - 3 \, a x + 1\right)} \log\left(a x + 1\right) + 201 \, {\left(a^{5} x^{5} - 3 \, a^{4} x^{4} + 2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} - 3 \, a x + 1\right)} \log\left(a x - 1\right) + 208\right)} \sqrt{a^{2} c}}{64 \, {\left(a^{7} c^{4} x^{5} - 3 \, a^{6} c^{4} x^{4} + 2 \, a^{5} c^{4} x^{3} + 2 \, a^{4} c^{4} x^{2} - 3 \, a^{3} c^{4} x + a^{2} c^{4}\right)}}"," ",0,"1/64*(64*a^6*x^6 - 192*a^5*x^5 - 174*a^4*x^4 + 618*a^3*x^3 - 118*a^2*x^2 - 414*a*x - 9*(a^5*x^5 - 3*a^4*x^4 + 2*a^3*x^3 + 2*a^2*x^2 - 3*a*x + 1)*log(a*x + 1) + 201*(a^5*x^5 - 3*a^4*x^4 + 2*a^3*x^3 + 2*a^2*x^2 - 3*a*x + 1)*log(a*x - 1) + 208)*sqrt(a^2*c)/(a^7*c^4*x^5 - 3*a^6*c^4*x^4 + 2*a^5*c^4*x^3 + 2*a^4*c^4*x^2 - 3*a^3*c^4*x + a^2*c^4)","A",0
855,1,96,0,0.524518," ","integrate((c-c/a^2/x^2)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(60 \, a^{7} c^{3} x^{7} - 60 \, a^{6} c^{3} x^{6} \log\left(x\right) + 180 \, a^{5} c^{3} x^{5} - 90 \, a^{4} c^{3} x^{4} - 60 \, a^{3} c^{3} x^{3} + 45 \, a^{2} c^{3} x^{2} + 12 \, a c^{3} x - 10 \, c^{3}\right)} \sqrt{a^{2} c}}{60 \, a^{8} x^{6}}"," ",0,"1/60*(60*a^7*c^3*x^7 - 60*a^6*c^3*x^6*log(x) + 180*a^5*c^3*x^5 - 90*a^4*c^3*x^4 - 60*a^3*c^3*x^3 + 45*a^2*c^3*x^2 + 12*a*c^3*x - 10*c^3)*sqrt(a^2*c)/(a^8*x^6)","A",0
856,1,74,0,1.622423," ","integrate((c-c/a^2/x^2)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(12 \, a^{5} c^{2} x^{5} - 12 \, a^{4} c^{2} x^{4} \log\left(x\right) + 24 \, a^{3} c^{2} x^{3} - 12 \, a^{2} c^{2} x^{2} - 4 \, a c^{2} x + 3 \, c^{2}\right)} \sqrt{a^{2} c}}{12 \, a^{6} x^{4}}"," ",0,"1/12*(12*a^5*c^2*x^5 - 12*a^4*c^2*x^4*log(x) + 24*a^3*c^2*x^3 - 12*a^2*c^2*x^2 - 4*a*c^2*x + 3*c^2)*sqrt(a^2*c)/(a^6*x^4)","A",0
857,1,44,0,0.821363," ","integrate((c-c/a^2/x^2)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} c x^{3} - 2 \, a^{2} c x^{2} \log\left(x\right) + 2 \, a c x - c\right)} \sqrt{a^{2} c}}{2 \, a^{4} x^{2}}"," ",0,"1/2*(2*a^3*c*x^3 - 2*a^2*c*x^2*log(x) + 2*a*c*x - c)*sqrt(a^2*c)/(a^4*x^2)","A",0
858,1,19,0,0.453774," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x - \log\left(x\right)\right)}}{a^{2}}"," ",0,"sqrt(a^2*c)*(a*x - log(x))/a^2","A",0
859,1,26,0,0.495109," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x - \log\left(a x + 1\right)\right)}}{a^{2} c}"," ",0,"sqrt(a^2*c)*(a*x - log(a*x + 1))/(a^2*c)","A",0
860,1,66,0,0.824690," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(4 \, a^{2} x^{2} + 4 \, a x - 5 \, {\left(a x + 1\right)} \log\left(a x + 1\right) + {\left(a x + 1\right)} \log\left(a x - 1\right) - 2\right)} \sqrt{a^{2} c}}{4 \, {\left(a^{3} c^{2} x + a^{2} c^{2}\right)}}"," ",0,"1/4*(4*a^2*x^2 + 4*a*x - 5*(a*x + 1)*log(a*x + 1) + (a*x + 1)*log(a*x - 1) - 2)*sqrt(a^2*c)/(a^3*c^2*x + a^2*c^2)","A",0
861,1,135,0,0.545571," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(16 \, a^{4} x^{4} + 16 \, a^{3} x^{3} - 34 \, a^{2} x^{2} - 18 \, a x - 23 \, {\left(a^{3} x^{3} + a^{2} x^{2} - a x - 1\right)} \log\left(a x + 1\right) + 7 \, {\left(a^{3} x^{3} + a^{2} x^{2} - a x - 1\right)} \log\left(a x - 1\right) + 12\right)} \sqrt{a^{2} c}}{16 \, {\left(a^{5} c^{3} x^{3} + a^{4} c^{3} x^{2} - a^{3} c^{3} x - a^{2} c^{3}\right)}}"," ",0,"1/16*(16*a^4*x^4 + 16*a^3*x^3 - 34*a^2*x^2 - 18*a*x - 23*(a^3*x^3 + a^2*x^2 - a*x - 1)*log(a*x + 1) + 7*(a^3*x^3 + a^2*x^2 - a*x - 1)*log(a*x - 1) + 12)*sqrt(a^2*c)/(a^5*c^3*x^3 + a^4*c^3*x^2 - a^3*c^3*x - a^2*c^3)","A",0
862,1,201,0,0.800984," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""fricas"")","\frac{{\left(96 \, a^{6} x^{6} + 96 \, a^{5} x^{5} - 366 \, a^{4} x^{4} - 222 \, a^{3} x^{3} + 338 \, a^{2} x^{2} + 122 \, a x - 153 \, {\left(a^{5} x^{5} + a^{4} x^{4} - 2 \, a^{3} x^{3} - 2 \, a^{2} x^{2} + a x + 1\right)} \log\left(a x + 1\right) + 57 \, {\left(a^{5} x^{5} + a^{4} x^{4} - 2 \, a^{3} x^{3} - 2 \, a^{2} x^{2} + a x + 1\right)} \log\left(a x - 1\right) - 88\right)} \sqrt{a^{2} c}}{96 \, {\left(a^{7} c^{4} x^{5} + a^{6} c^{4} x^{4} - 2 \, a^{5} c^{4} x^{3} - 2 \, a^{4} c^{4} x^{2} + a^{3} c^{4} x + a^{2} c^{4}\right)}}"," ",0,"1/96*(96*a^6*x^6 + 96*a^5*x^5 - 366*a^4*x^4 - 222*a^3*x^3 + 338*a^2*x^2 + 122*a*x - 153*(a^5*x^5 + a^4*x^4 - 2*a^3*x^3 - 2*a^2*x^2 + a*x + 1)*log(a*x + 1) + 57*(a^5*x^5 + a^4*x^4 - 2*a^3*x^3 - 2*a^2*x^2 + a*x + 1)*log(a*x - 1) - 88)*sqrt(a^2*c)/(a^7*c^4*x^5 + a^6*c^4*x^4 - 2*a^5*c^4*x^3 - 2*a^4*c^4*x^2 + a^3*c^4*x + a^2*c^4)","A",0
863,1,438,0,0.639339," ","integrate((c-c/a^2/x^2)^(7/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{960 \, a^{5} \sqrt{-c} c^{3} x^{5} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + 375 \, a^{5} \sqrt{-c} c^{3} x^{5} \log\left(-\frac{a^{2} c x^{2} - 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) + 2 \, {\left(240 \, a^{6} c^{3} x^{6} + 736 \, a^{5} c^{3} x^{5} + 105 \, a^{4} c^{3} x^{4} - 352 \, a^{3} c^{3} x^{3} + 70 \, a^{2} c^{3} x^{2} + 96 \, a c^{3} x - 40 \, c^{3}\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{480 \, a^{6} x^{5}}, \frac{375 \, a^{5} c^{\frac{7}{2}} x^{5} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + 240 \, a^{5} c^{\frac{7}{2}} x^{5} \log\left(2 \, a^{2} c x^{2} - 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(240 \, a^{6} c^{3} x^{6} + 736 \, a^{5} c^{3} x^{5} + 105 \, a^{4} c^{3} x^{4} - 352 \, a^{3} c^{3} x^{3} + 70 \, a^{2} c^{3} x^{2} + 96 \, a c^{3} x - 40 \, c^{3}\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{240 \, a^{6} x^{5}}\right]"," ",0,"[1/480*(960*a^5*sqrt(-c)*c^3*x^5*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + 375*a^5*sqrt(-c)*c^3*x^5*log(-(a^2*c*x^2 - 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) + 2*(240*a^6*c^3*x^6 + 736*a^5*c^3*x^5 + 105*a^4*c^3*x^4 - 352*a^3*c^3*x^3 + 70*a^2*c^3*x^2 + 96*a*c^3*x - 40*c^3)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^6*x^5), 1/240*(375*a^5*c^(7/2)*x^5*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + 240*a^5*c^(7/2)*x^5*log(2*a^2*c*x^2 - 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (240*a^6*c^3*x^6 + 736*a^5*c^3*x^5 + 105*a^4*c^3*x^4 - 352*a^3*c^3*x^3 + 70*a^2*c^3*x^2 + 96*a*c^3*x - 40*c^3)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^6*x^5)]","A",0
864,1,394,0,0.524145," ","integrate((c-c/a^2/x^2)^(5/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{96 \, a^{3} \sqrt{-c} c^{2} x^{3} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + 27 \, a^{3} \sqrt{-c} c^{2} x^{3} \log\left(-\frac{a^{2} c x^{2} - 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) + 2 \, {\left(24 \, a^{4} c^{2} x^{4} + 64 \, a^{3} c^{2} x^{3} - 3 \, a^{2} c^{2} x^{2} - 16 \, a c^{2} x + 6 \, c^{2}\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{48 \, a^{4} x^{3}}, \frac{27 \, a^{3} c^{\frac{5}{2}} x^{3} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + 24 \, a^{3} c^{\frac{5}{2}} x^{3} \log\left(2 \, a^{2} c x^{2} - 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(24 \, a^{4} c^{2} x^{4} + 64 \, a^{3} c^{2} x^{3} - 3 \, a^{2} c^{2} x^{2} - 16 \, a c^{2} x + 6 \, c^{2}\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{24 \, a^{4} x^{3}}\right]"," ",0,"[1/48*(96*a^3*sqrt(-c)*c^2*x^3*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + 27*a^3*sqrt(-c)*c^2*x^3*log(-(a^2*c*x^2 - 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) + 2*(24*a^4*c^2*x^4 + 64*a^3*c^2*x^3 - 3*a^2*c^2*x^2 - 16*a*c^2*x + 6*c^2)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^4*x^3), 1/24*(27*a^3*c^(5/2)*x^3*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + 24*a^3*c^(5/2)*x^3*log(2*a^2*c*x^2 - 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (24*a^4*c^2*x^4 + 64*a^3*c^2*x^3 - 3*a^2*c^2*x^2 - 16*a*c^2*x + 6*c^2)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^4*x^3)]","A",0
865,1,316,0,0.505965," ","integrate((c-c/a^2/x^2)^(3/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{8 \, a \sqrt{-c} c x \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + a \sqrt{-c} c x \log\left(-\frac{a^{2} c x^{2} - 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) + 2 \, {\left(2 \, a^{2} c x^{2} + 4 \, a c x - c\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{4 \, a^{2} x}, \frac{a c^{\frac{3}{2}} x \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + 2 \, a c^{\frac{3}{2}} x \log\left(2 \, a^{2} c x^{2} - 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(2 \, a^{2} c x^{2} + 4 \, a c x - c\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{2 \, a^{2} x}\right]"," ",0,"[1/4*(8*a*sqrt(-c)*c*x*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + a*sqrt(-c)*c*x*log(-(a^2*c*x^2 - 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) + 2*(2*a^2*c*x^2 + 4*a*c*x - c)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^2*x), 1/2*(a*c^(3/2)*x*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + 2*a*c^(3/2)*x*log(2*a^2*c*x^2 - 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (2*a^2*c*x^2 + 4*a*c*x - c)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^2*x)]","A",0
866,1,267,0,0.788897," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} + 4 \, \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right)}{2 \, a}, \frac{a x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - \sqrt{c} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \sqrt{c} \log\left(2 \, a^{2} c x^{2} - 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right)}{a}\right]"," ",0,"[1/2*(2*a*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) + 4*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + sqrt(-c)*log(-(a^2*c*x^2 + 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2))/a, (a*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - sqrt(c)*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + sqrt(c)*log(2*a^2*c*x^2 - 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c))/a]","A",0
867,1,212,0,0.579760," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a x + 1\right)} \sqrt{c} \log\left(2 \, a^{2} c x^{2} - 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(a^{2} x^{2} + 3 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x + a c}, \frac{2 \, {\left(a x + 1\right)} \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + {\left(a^{2} x^{2} + 3 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x + a c}\right]"," ",0,"[((a*x + 1)*sqrt(c)*log(2*a^2*c*x^2 - 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (a^2*x^2 + 3*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^2*c*x + a*c), (2*(a*x + 1)*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + (a^2*x^2 + 3*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^2*c*x + a*c)]","A",0
868,1,279,0,0.590228," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \sqrt{c} \log\left(2 \, a^{2} c x^{2} - 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(3 \, a^{3} x^{3} + 14 \, a^{2} x^{2} + 10 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{3 \, {\left(a^{3} c^{2} x^{2} + 2 \, a^{2} c^{2} x + a c^{2}\right)}}, \frac{6 \, {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + {\left(3 \, a^{3} x^{3} + 14 \, a^{2} x^{2} + 10 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{3 \, {\left(a^{3} c^{2} x^{2} + 2 \, a^{2} c^{2} x + a c^{2}\right)}}\right]"," ",0,"[1/3*(3*(a^2*x^2 + 2*a*x + 1)*sqrt(c)*log(2*a^2*c*x^2 - 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (3*a^3*x^3 + 14*a^2*x^2 + 10*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^3*c^2*x^2 + 2*a^2*c^2*x + a*c^2), 1/3*(6*(a^2*x^2 + 2*a*x + 1)*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + (3*a^3*x^3 + 14*a^2*x^2 + 10*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^3*c^2*x^2 + 2*a^2*c^2*x + a*c^2)]","A",0
869,1,351,0,1.095084," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{4} x^{4} + 2 \, a^{3} x^{3} - 2 \, a x - 1\right)} \sqrt{c} \log\left(2 \, a^{2} c x^{2} - 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(15 \, a^{5} x^{5} + 76 \, a^{4} x^{4} + 32 \, a^{3} x^{3} - 82 \, a^{2} x^{2} - 56 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{15 \, {\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{30 \, {\left(a^{4} x^{4} + 2 \, a^{3} x^{3} - 2 \, a x - 1\right)} \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + {\left(15 \, a^{5} x^{5} + 76 \, a^{4} x^{4} + 32 \, a^{3} x^{3} - 82 \, a^{2} x^{2} - 56 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{15 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{3} - 2 \, a^{2} c^{3} x - a c^{3}\right)}}\right]"," ",0,"[1/15*(15*(a^4*x^4 + 2*a^3*x^3 - 2*a*x - 1)*sqrt(c)*log(2*a^2*c*x^2 - 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (15*a^5*x^5 + 76*a^4*x^4 + 32*a^3*x^3 - 82*a^2*x^2 - 56*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^5*c^3*x^4 + 2*a^4*c^3*x^3 - 2*a^2*c^3*x - a*c^3), 1/15*(30*(a^4*x^4 + 2*a^3*x^3 - 2*a*x - 1)*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + (15*a^5*x^5 + 76*a^4*x^4 + 32*a^3*x^3 - 82*a^2*x^2 - 56*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(a^5*c^3*x^4 + 2*a^4*c^3*x^3 - 2*a^2*c^3*x - a*c^3)]","A",0
870,1,495,0,0.740668," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(7/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{6} x^{6} + 2 \, a^{5} x^{5} - a^{4} x^{4} - 4 \, a^{3} x^{3} - a^{2} x^{2} + 2 \, a x + 1\right)} \sqrt{c} \log\left(2 \, a^{2} c x^{2} - 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + {\left(105 \, a^{7} x^{7} + 562 \, a^{6} x^{6} + 74 \, a^{5} x^{5} - 1226 \, a^{4} x^{4} - 636 \, a^{3} x^{3} + 654 \, a^{2} x^{2} + 432 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{105 \, {\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{210 \, {\left(a^{6} x^{6} + 2 \, a^{5} x^{5} - a^{4} x^{4} - 4 \, a^{3} x^{3} - a^{2} x^{2} + 2 \, a x + 1\right)} \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + {\left(105 \, a^{7} x^{7} + 562 \, a^{6} x^{6} + 74 \, a^{5} x^{5} - 1226 \, a^{4} x^{4} - 636 \, a^{3} x^{3} + 654 \, a^{2} x^{2} + 432 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{105 \, {\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)}}\right]"," ",0,"[1/105*(105*(a^6*x^6 + 2*a^5*x^5 - a^4*x^4 - 4*a^3*x^3 - a^2*x^2 + 2*a*x + 1)*sqrt(c)*log(2*a^2*c*x^2 - 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + (105*a^7*x^7 + 562*a^6*x^6 + 74*a^5*x^5 - 1226*a^4*x^4 - 636*a^3*x^3 + 654*a^2*x^2 + 432*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(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), 1/105*(210*(a^6*x^6 + 2*a^5*x^5 - a^4*x^4 - 4*a^3*x^3 - a^2*x^2 + 2*a*x + 1)*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + (105*a^7*x^7 + 562*a^6*x^6 + 74*a^5*x^5 - 1226*a^4*x^4 - 636*a^3*x^3 + 654*a^2*x^2 + 432*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/(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)]","A",0
871,1,96,0,0.612505," ","integrate((c-c/a^2/x^2)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(280 \, a^{9} c^{4} x^{9} - 840 \, a^{8} c^{4} x^{8} \log\left(x\right) - 1120 \, a^{6} c^{4} x^{6} + 560 \, a^{5} c^{4} x^{5} + 420 \, a^{4} c^{4} x^{4} - 448 \, a^{3} c^{4} x^{3} + 120 \, a c^{4} x - 35 \, c^{4}\right)} \sqrt{a^{2} c}}{280 \, a^{10} x^{8}}"," ",0,"1/280*(280*a^9*c^4*x^9 - 840*a^8*c^4*x^8*log(x) - 1120*a^6*c^4*x^6 + 560*a^5*c^4*x^5 + 420*a^4*c^4*x^4 - 448*a^3*c^4*x^3 + 120*a*c^4*x - 35*c^4)*sqrt(a^2*c)/(a^10*x^8)","A",0
872,1,96,0,0.466289," ","integrate((c-c/a^2/x^2)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(60 \, a^{7} c^{3} x^{7} - 180 \, a^{6} c^{3} x^{6} \log\left(x\right) - 60 \, a^{5} c^{3} x^{5} - 150 \, a^{4} c^{3} x^{4} + 100 \, a^{3} c^{3} x^{3} + 15 \, a^{2} c^{3} x^{2} - 36 \, a c^{3} x + 10 \, c^{3}\right)} \sqrt{a^{2} c}}{60 \, a^{8} x^{6}}"," ",0,"1/60*(60*a^7*c^3*x^7 - 180*a^6*c^3*x^6*log(x) - 60*a^5*c^3*x^5 - 150*a^4*c^3*x^4 + 100*a^3*c^3*x^3 + 15*a^2*c^3*x^2 - 36*a*c^3*x + 10*c^3)*sqrt(a^2*c)/(a^8*x^6)","A",0
873,1,74,0,0.428722," ","integrate((c-c/a^2/x^2)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(4 \, a^{5} c^{2} x^{5} - 12 \, a^{4} c^{2} x^{4} \log\left(x\right) - 8 \, a^{3} c^{2} x^{3} - 4 \, a^{2} c^{2} x^{2} + 4 \, a c^{2} x - c^{2}\right)} \sqrt{a^{2} c}}{4 \, a^{6} x^{4}}"," ",0,"1/4*(4*a^5*c^2*x^5 - 12*a^4*c^2*x^4*log(x) - 8*a^3*c^2*x^3 - 4*a^2*c^2*x^2 + 4*a*c^2*x - c^2)*sqrt(a^2*c)/(a^6*x^4)","A",0
874,1,42,0,0.625907," ","integrate((c-c/a^2/x^2)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} c x^{3} - 6 \, a^{2} c x^{2} \log\left(x\right) - 6 \, a c x + c\right)} \sqrt{a^{2} c}}{2 \, a^{4} x^{2}}"," ",0,"1/2*(2*a^3*c*x^3 - 6*a^2*c*x^2*log(x) - 6*a*c*x + c)*sqrt(a^2*c)/(a^4*x^2)","A",0
875,1,25,0,0.637535," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x - 4 \, \log\left(a x + 1\right) + \log\left(x\right)\right)}}{a^{2}}"," ",0,"sqrt(a^2*c)*(a*x - 4*log(a*x + 1) + log(x))/a^2","A",0
876,1,47,0,0.586976," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} + a x - 3 \, {\left(a x + 1\right)} \log\left(a x + 1\right) - 2\right)} \sqrt{a^{2} c}}{a^{3} c x + a^{2} c}"," ",0,"(a^2*x^2 + a*x - 3*(a*x + 1)*log(a*x + 1) - 2)*sqrt(a^2*c)/(a^3*c*x + a^2*c)","A",0
877,1,81,0,0.469493," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} + 4 \, a^{2} x^{2} - 4 \, a x - 6 \, {\left(a^{2} x^{2} + 2 \, a x + 1\right)} \log\left(a x + 1\right) - 5\right)} \sqrt{a^{2} c}}{2 \, {\left(a^{4} c^{2} x^{2} + 2 \, a^{3} c^{2} x + a^{2} c^{2}\right)}}"," ",0,"1/2*(2*a^3*x^3 + 4*a^2*x^2 - 4*a*x - 6*(a^2*x^2 + 2*a*x + 1)*log(a*x + 1) - 5)*sqrt(a^2*c)/(a^4*c^2*x^2 + 2*a^3*c^2*x + a^2*c^2)","A",0
878,1,137,0,0.617591," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(48 \, a^{4} x^{4} + 144 \, a^{3} x^{3} - 42 \, a^{2} x^{2} - 270 \, a x - 147 \, {\left(a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1\right)} \log\left(a x - 1\right) - 140\right)} \sqrt{a^{2} c}}{48 \, {\left(a^{5} c^{3} x^{3} + 3 \, a^{4} c^{3} x^{2} + 3 \, a^{3} c^{3} x + a^{2} c^{3}\right)}}"," ",0,"1/48*(48*a^4*x^4 + 144*a^3*x^3 - 42*a^2*x^2 - 270*a*x - 147*(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)*log(a*x + 1) + 3*(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)*log(a*x - 1) - 140)*sqrt(a^2*c)/(a^5*c^3*x^3 + 3*a^4*c^3*x^2 + 3*a^3*c^3*x + a^2*c^3)","A",0
879,1,208,0,0.634711," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""fricas"")","\frac{{\left(64 \, a^{6} x^{6} + 192 \, a^{5} x^{5} - 174 \, a^{4} x^{4} - 618 \, a^{3} x^{3} - 118 \, a^{2} x^{2} + 414 \, a x - 201 \, {\left(a^{5} x^{5} + 3 \, a^{4} x^{4} + 2 \, a^{3} x^{3} - 2 \, a^{2} x^{2} - 3 \, a x - 1\right)} \log\left(a x + 1\right) + 9 \, {\left(a^{5} x^{5} + 3 \, a^{4} x^{4} + 2 \, a^{3} x^{3} - 2 \, a^{2} x^{2} - 3 \, a x - 1\right)} \log\left(a x - 1\right) + 208\right)} \sqrt{a^{2} c}}{64 \, {\left(a^{7} c^{4} x^{5} + 3 \, a^{6} c^{4} x^{4} + 2 \, a^{5} c^{4} x^{3} - 2 \, a^{4} c^{4} x^{2} - 3 \, a^{3} c^{4} x - a^{2} c^{4}\right)}}"," ",0,"1/64*(64*a^6*x^6 + 192*a^5*x^5 - 174*a^4*x^4 - 618*a^3*x^3 - 118*a^2*x^2 + 414*a*x - 201*(a^5*x^5 + 3*a^4*x^4 + 2*a^3*x^3 - 2*a^2*x^2 - 3*a*x - 1)*log(a*x + 1) + 9*(a^5*x^5 + 3*a^4*x^4 + 2*a^3*x^3 - 2*a^2*x^2 - 3*a*x - 1)*log(a*x - 1) + 208)*sqrt(a^2*c)/(a^7*c^4*x^5 + 3*a^6*c^4*x^4 + 2*a^5*c^4*x^3 - 2*a^4*c^4*x^2 - 3*a^3*c^4*x - a^2*c^4)","A",0
880,1,72,0,0.420857," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a m x^{2} + {\left(m + 1\right)} x\right)} x^{m} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{m^{2} - {\left(a m^{2} + a m\right)} x + m}"," ",0,"-(a*m*x^2 + (m + 1)*x)*x^m*sqrt((a*x - 1)/(a*x + 1))*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(m^2 - (a*m^2 + a*m)*x + m)","A",0
881,1,24,0,0.393981," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a x^{3} + 3 \, x^{2}\right)} \sqrt{a^{2} c}}{6 \, a^{2}}"," ",0,"1/6*(2*a*x^3 + 3*x^2)*sqrt(a^2*c)/a^2","A",0
882,1,21,0,0.664484," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x^{2} + 2 \, x\right)}}{2 \, a^{2}}"," ",0,"1/2*sqrt(a^2*c)*(a*x^2 + 2*x)/a^2","A",0
883,1,17,0,0.537837," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x + \log\left(x\right)\right)}}{a^{2}}"," ",0,"sqrt(a^2*c)*(a*x + log(x))/a^2","A",0
884,1,21,0,0.789261," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x \log\left(x\right) - 1\right)}}{a^{2} x}"," ",0,"sqrt(a^2*c)*(a*x*log(x) - 1)/(a^2*x)","A",0
885,1,21,0,0.480350," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{\sqrt{a^{2} c} {\left(2 \, a x + 1\right)}}{2 \, a^{2} x^{2}}"," ",0,"-1/2*sqrt(a^2*c)*(2*a*x + 1)/(a^2*x^2)","A",0
886,1,222,0,0.567320," ","integrate(1/(a*x-1)*(a*x+1)*x^3*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(6 \, a^{4} x^{4} + 16 \, a^{3} x^{3} + 21 \, a^{2} x^{2} + 32 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} + 21 \, \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right)}{48 \, a^{4}}, \frac{{\left(6 \, a^{4} x^{4} + 16 \, a^{3} x^{3} + 21 \, a^{2} x^{2} + 32 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 21 \, \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right)}{24 \, a^{4}}\right]"," ",0,"[1/48*(2*(6*a^4*x^4 + 16*a^3*x^3 + 21*a^2*x^2 + 32*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) + 21*sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c))/a^4, 1/24*((6*a^4*x^4 + 16*a^3*x^3 + 21*a^2*x^2 + 32*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 21*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)))/a^4]","A",0
887,1,204,0,0.568411," ","integrate(1/(a*x-1)*(a*x+1)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{3} x^{3} + 3 \, a^{2} x^{2} + 5 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} + 3 \, \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right)}{6 \, a^{3}}, \frac{{\left(a^{3} x^{3} + 3 \, a^{2} x^{2} + 5 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 3 \, \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right)}{3 \, a^{3}}\right]"," ",0,"[1/6*(2*(a^3*x^3 + 3*a^2*x^2 + 5*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) + 3*sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c))/a^3, 1/3*((a^3*x^3 + 3*a^2*x^2 + 5*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 3*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)))/a^3]","A",0
888,1,188,0,0.756700," ","integrate(1/(a*x-1)*(a*x+1)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} x^{2} + 4 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} + 3 \, \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right)}{4 \, a^{2}}, \frac{{\left(a^{2} x^{2} + 4 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 3 \, \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right)}{2 \, a^{2}}\right]"," ",0,"[1/4*(2*(a^2*x^2 + 4*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) + 3*sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c))/a^2, 1/2*((a^2*x^2 + 4*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 3*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)))/a^2]","A",0
889,1,267,0,0.811659," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 4 \, \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right)}{2 \, a}, \frac{a x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - \sqrt{c} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right)}{a}\right]"," ",0,"[1/2*(2*a*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 4*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + sqrt(-c)*log(-(a^2*c*x^2 + 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2))/a, (a*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - sqrt(c)*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c))/a]","A",0
890,1,252,0,0.498546," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""fricas"")","\left[-\sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) + \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}, -2 \, \sqrt{c} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \frac{1}{2} \, \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}\right]"," ",0,"[-sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + sqrt(-c)*log(-(a^2*c*x^2 + 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) + sqrt((a^2*c*x^2 - c)/(a^2*x^2)), -2*sqrt(c)*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + 1/2*sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + sqrt((a^2*c*x^2 - c)/(a^2*x^2))]","A",0
891,1,177,0,0.729836," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{-c} x \log\left(-\frac{a^{2} c x^{2} + 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) + 2 \, {\left(4 \, a x + 1\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{4 \, x}, -\frac{3 \, a \sqrt{c} x \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) - {\left(4 \, a x + 1\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{2 \, x}\right]"," ",0,"[1/4*(3*a*sqrt(-c)*x*log(-(a^2*c*x^2 + 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) + 2*(4*a*x + 1)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x, -1/2*(3*a*sqrt(c)*x*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) - (4*a*x + 1)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x]","A",0
892,1,201,0,0.672101," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{-c} x^{2} \log\left(-\frac{a^{2} c x^{2} + 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) + 2 \, {\left(5 \, a^{2} x^{2} + 3 \, a x + 1\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{6 \, x^{2}}, -\frac{3 \, a^{2} \sqrt{c} x^{2} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) - {\left(5 \, a^{2} x^{2} + 3 \, a x + 1\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{3 \, x^{2}}\right]"," ",0,"[1/6*(3*a^2*sqrt(-c)*x^2*log(-(a^2*c*x^2 + 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) + 2*(5*a^2*x^2 + 3*a*x + 1)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^2, -1/3*(3*a^2*sqrt(c)*x^2*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) - (5*a^2*x^2 + 3*a*x + 1)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^2]","A",0
893,1,217,0,0.604205," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{21 \, a^{3} \sqrt{-c} x^{3} \log\left(-\frac{a^{2} c x^{2} + 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) + 2 \, {\left(32 \, a^{3} x^{3} + 21 \, a^{2} x^{2} + 16 \, a x + 6\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{48 \, x^{3}}, -\frac{21 \, a^{3} \sqrt{c} x^{3} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) - {\left(32 \, a^{3} x^{3} + 21 \, a^{2} x^{2} + 16 \, a x + 6\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{24 \, x^{3}}\right]"," ",0,"[1/48*(21*a^3*sqrt(-c)*x^3*log(-(a^2*c*x^2 + 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) + 2*(32*a^3*x^3 + 21*a^2*x^2 + 16*a*x + 6)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^3, -1/24*(21*a^3*sqrt(c)*x^3*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) - (32*a^3*x^3 + 21*a^2*x^2 + 16*a*x + 6)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^3]","A",0
894,1,233,0,0.553530," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{15 \, a^{4} \sqrt{-c} x^{4} \log\left(-\frac{a^{2} c x^{2} + 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) + 2 \, {\left(24 \, a^{4} x^{4} + 15 \, a^{3} x^{3} + 12 \, a^{2} x^{2} + 10 \, a x + 4\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{40 \, x^{4}}, -\frac{15 \, a^{4} \sqrt{c} x^{4} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) - {\left(24 \, a^{4} x^{4} + 15 \, a^{3} x^{3} + 12 \, a^{2} x^{2} + 10 \, a x + 4\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{20 \, x^{4}}\right]"," ",0,"[1/40*(15*a^4*sqrt(-c)*x^4*log(-(a^2*c*x^2 + 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) + 2*(24*a^4*x^4 + 15*a^3*x^3 + 12*a^2*x^2 + 10*a*x + 4)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^4, -1/20*(15*a^4*sqrt(c)*x^4*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) - (24*a^4*x^4 + 15*a^3*x^3 + 12*a^2*x^2 + 10*a*x + 4)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^4]","A",0
895,1,48,0,0.427928," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{4} x^{4} + 4 \, a^{3} x^{3} + 8 \, a^{2} x^{2} + 16 \, a x + 16 \, \log\left(a x - 1\right)\right)} \sqrt{a^{2} c}}{4 \, a^{5}}"," ",0,"1/4*(a^4*x^4 + 4*a^3*x^3 + 8*a^2*x^2 + 16*a*x + 16*log(a*x - 1))*sqrt(a^2*c)/a^5","A",0
896,1,41,0,0.481116," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} + 9 \, a^{2} x^{2} + 24 \, a x + 24 \, \log\left(a x - 1\right)\right)} \sqrt{a^{2} c}}{6 \, a^{4}}"," ",0,"1/6*(2*a^3*x^3 + 9*a^2*x^2 + 24*a*x + 24*log(a*x - 1))*sqrt(a^2*c)/a^4","A",0
897,1,32,0,0.685848," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} + 6 \, a x + 8 \, \log\left(a x - 1\right)\right)} \sqrt{a^{2} c}}{2 \, a^{3}}"," ",0,"1/2*(a^2*x^2 + 6*a*x + 8*log(a*x - 1))*sqrt(a^2*c)/a^3","A",0
898,1,27,0,0.710502," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x + 4 \, \log\left(a x - 1\right) - \log\left(x\right)\right)}}{a^{2}}"," ",0,"sqrt(a^2*c)*(a*x + 4*log(a*x - 1) - log(x))/a^2","A",0
899,1,32,0,0.582385," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(4 \, a x \log\left(a x - 1\right) - 3 \, a x \log\left(x\right) + 1\right)}}{a^{2} x}"," ",0,"sqrt(a^2*c)*(4*a*x*log(a*x - 1) - 3*a*x*log(x) + 1)/(a^2*x)","A",0
900,1,85,0,0.503514," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{8 \, a^{3} \sqrt{c} x^{2} \log\left(\frac{2 \, a^{3} c x^{2} - 2 \, a^{2} c x - \sqrt{a^{2} c} {\left(2 \, a x - 1\right)} \sqrt{c} + a c}{a x^{2} - x}\right) + \sqrt{a^{2} c} {\left(6 \, a x + 1\right)}}{2 \, a^{2} x^{2}}"," ",0,"1/2*(8*a^3*sqrt(c)*x^2*log((2*a^3*c*x^2 - 2*a^2*c*x - sqrt(a^2*c)*(2*a*x - 1)*sqrt(c) + a*c)/(a*x^2 - x)) + sqrt(a^2*c)*(6*a*x + 1))/(a^2*x^2)","A",0
901,1,93,0,0.920237," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{24 \, a^{4} \sqrt{c} x^{3} \log\left(\frac{2 \, a^{3} c x^{2} - 2 \, a^{2} c x - \sqrt{a^{2} c} {\left(2 \, a x - 1\right)} \sqrt{c} + a c}{a x^{2} - x}\right) + {\left(24 \, a^{2} x^{2} + 9 \, a x + 2\right)} \sqrt{a^{2} c}}{6 \, a^{2} x^{3}}"," ",0,"1/6*(24*a^4*sqrt(c)*x^3*log((2*a^3*c*x^2 - 2*a^2*c*x - sqrt(a^2*c)*(2*a*x - 1)*sqrt(c) + a*c)/(a*x^2 - x)) + (24*a^2*x^2 + 9*a*x + 2)*sqrt(a^2*c))/(a^2*x^3)","A",0
902,1,101,0,0.418344," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^4,x, algorithm=""fricas"")","\frac{16 \, a^{5} \sqrt{c} x^{4} \log\left(\frac{2 \, a^{3} c x^{2} - 2 \, a^{2} c x - \sqrt{a^{2} c} {\left(2 \, a x - 1\right)} \sqrt{c} + a c}{a x^{2} - x}\right) + {\left(16 \, a^{3} x^{3} + 8 \, a^{2} x^{2} + 4 \, a x + 1\right)} \sqrt{a^{2} c}}{4 \, a^{2} x^{4}}"," ",0,"1/4*(16*a^5*sqrt(c)*x^4*log((2*a^3*c*x^2 - 2*a^2*c*x - sqrt(a^2*c)*(2*a*x - 1)*sqrt(c) + a*c)/(a*x^2 - x)) + (16*a^3*x^3 + 8*a^2*x^2 + 4*a*x + 1)*sqrt(a^2*c))/(a^2*x^4)","A",0
903,1,109,0,0.432705," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^5,x, algorithm=""fricas"")","\frac{240 \, a^{6} \sqrt{c} x^{5} \log\left(\frac{2 \, a^{3} c x^{2} - 2 \, a^{2} c x - \sqrt{a^{2} c} {\left(2 \, a x - 1\right)} \sqrt{c} + a c}{a x^{2} - x}\right) + {\left(240 \, a^{4} x^{4} + 120 \, a^{3} x^{3} + 80 \, a^{2} x^{2} + 45 \, a x + 12\right)} \sqrt{a^{2} c}}{60 \, a^{2} x^{5}}"," ",0,"1/60*(240*a^6*sqrt(c)*x^5*log((2*a^3*c*x^2 - 2*a^2*c*x - sqrt(a^2*c)*(2*a*x - 1)*sqrt(c) + a*c)/(a*x^2 - x)) + (240*a^4*x^4 + 120*a^3*x^3 + 80*a^2*x^2 + 45*a*x + 12)*sqrt(a^2*c))/(a^2*x^5)","A",0
904,1,73,0,0.446522," ","integrate(x^m*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(a m x^{2} - {\left(m + 1\right)} x\right)} x^{m} \sqrt{\frac{a x - 1}{a x + 1}} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{m^{2} - {\left(a m^{2} + a m\right)} x + m}"," ",0,"-(a*m*x^2 - (m + 1)*x)*x^m*sqrt((a*x - 1)/(a*x + 1))*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(m^2 - (a*m^2 + a*m)*x + m)","A",0
905,1,24,0,0.401774," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a x^{3} - 3 \, x^{2}\right)} \sqrt{a^{2} c}}{6 \, a^{2}}"," ",0,"1/6*(2*a*x^3 - 3*x^2)*sqrt(a^2*c)/a^2","A",0
906,1,21,0,0.408972," ","integrate(x*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x^{2} - 2 \, x\right)}}{2 \, a^{2}}"," ",0,"1/2*sqrt(a^2*c)*(a*x^2 - 2*x)/a^2","A",0
907,1,19,0,0.395035," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x - \log\left(x\right)\right)}}{a^{2}}"," ",0,"sqrt(a^2*c)*(a*x - log(x))/a^2","A",0
908,1,21,0,0.448728," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x \log\left(x\right) + 1\right)}}{a^{2} x}"," ",0,"sqrt(a^2*c)*(a*x*log(x) + 1)/(a^2*x)","A",0
909,1,21,0,0.436307," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{\sqrt{a^{2} c} {\left(2 \, a x - 1\right)}}{2 \, a^{2} x^{2}}"," ",0,"-1/2*sqrt(a^2*c)*(2*a*x - 1)/(a^2*x^2)","A",0
910,1,222,0,0.465404," ","integrate(x^3*(c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(6 \, a^{4} x^{4} - 16 \, a^{3} x^{3} + 21 \, a^{2} x^{2} - 32 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} + 21 \, \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right)}{48 \, a^{4}}, \frac{{\left(6 \, a^{4} x^{4} - 16 \, a^{3} x^{3} + 21 \, a^{2} x^{2} - 32 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 21 \, \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right)}{24 \, a^{4}}\right]"," ",0,"[1/48*(2*(6*a^4*x^4 - 16*a^3*x^3 + 21*a^2*x^2 - 32*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) + 21*sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c))/a^4, 1/24*((6*a^4*x^4 - 16*a^3*x^3 + 21*a^2*x^2 - 32*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 21*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)))/a^4]","A",0
911,1,204,0,0.410930," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 5 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} + 3 \, \sqrt{c} \log\left(2 \, a^{2} c x^{2} - 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right)}{6 \, a^{3}}, \frac{{\left(a^{3} x^{3} - 3 \, a^{2} x^{2} + 5 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} + 3 \, \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right)}{3 \, a^{3}}\right]"," ",0,"[1/6*(2*(a^3*x^3 - 3*a^2*x^2 + 5*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) + 3*sqrt(c)*log(2*a^2*c*x^2 - 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c))/a^3, 1/3*((a^3*x^3 - 3*a^2*x^2 + 5*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) + 3*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)))/a^3]","A",0
912,1,188,0,0.477854," ","integrate(x*(c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} x^{2} - 4 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} + 3 \, \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right)}{4 \, a^{2}}, \frac{{\left(a^{2} x^{2} - 4 \, a x\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 3 \, \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right)}{2 \, a^{2}}\right]"," ",0,"[1/4*(2*(a^2*x^2 - 4*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) + 3*sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c))/a^2, 1/2*((a^2*x^2 - 4*a*x)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 3*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)))/a^2]","A",0
913,1,267,0,0.441545," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""fricas"")","\left[\frac{2 \, a x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} + 4 \, \sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} + 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right)}{2 \, a}, \frac{a x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - \sqrt{c} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \sqrt{c} \log\left(2 \, a^{2} c x^{2} - 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right)}{a}\right]"," ",0,"[1/2*(2*a*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) + 4*sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + sqrt(-c)*log(-(a^2*c*x^2 + 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2))/a, (a*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - sqrt(c)*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + sqrt(c)*log(2*a^2*c*x^2 - 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c))/a]","A",0
914,1,252,0,0.455423," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x,x, algorithm=""fricas"")","\left[-\sqrt{-c} \arctan\left(\frac{a^{2} \sqrt{-c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \sqrt{-c} \log\left(-\frac{a^{2} c x^{2} - 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) + \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}, 2 \, \sqrt{c} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + \frac{1}{2} \, \sqrt{c} \log\left(2 \, a^{2} c x^{2} + 2 \, a^{2} \sqrt{c} x^{2} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - c\right) + \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}\right]"," ",0,"[-sqrt(-c)*arctan(a^2*sqrt(-c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + sqrt(-c)*log(-(a^2*c*x^2 - 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) + sqrt((a^2*c*x^2 - c)/(a^2*x^2)), 2*sqrt(c)*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + 1/2*sqrt(c)*log(2*a^2*c*x^2 + 2*a^2*sqrt(c)*x^2*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - c) + sqrt((a^2*c*x^2 - c)/(a^2*x^2))]","A",0
915,1,176,0,0.476836," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{-c} x \log\left(-\frac{a^{2} c x^{2} + 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) - 2 \, {\left(4 \, a x - 1\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{4 \, x}, -\frac{3 \, a \sqrt{c} x \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + {\left(4 \, a x - 1\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{2 \, x}\right]"," ",0,"[1/4*(3*a*sqrt(-c)*x*log(-(a^2*c*x^2 + 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) - 2*(4*a*x - 1)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x, -1/2*(3*a*sqrt(c)*x*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + (4*a*x - 1)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x]","A",0
916,1,200,0,0.442976," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{-c} x^{2} \log\left(-\frac{a^{2} c x^{2} - 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) + 2 \, {\left(5 \, a^{2} x^{2} - 3 \, a x + 1\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{6 \, x^{2}}, \frac{3 \, a^{2} \sqrt{c} x^{2} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + {\left(5 \, a^{2} x^{2} - 3 \, a x + 1\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{3 \, x^{2}}\right]"," ",0,"[1/6*(3*a^2*sqrt(-c)*x^2*log(-(a^2*c*x^2 - 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) + 2*(5*a^2*x^2 - 3*a*x + 1)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^2, 1/3*(3*a^2*sqrt(c)*x^2*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + (5*a^2*x^2 - 3*a*x + 1)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^2]","A",0
917,1,216,0,0.440914," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^4,x, algorithm=""fricas"")","\left[\frac{21 \, a^{3} \sqrt{-c} x^{3} \log\left(-\frac{a^{2} c x^{2} + 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) - 2 \, {\left(32 \, a^{3} x^{3} - 21 \, a^{2} x^{2} + 16 \, a x - 6\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{48 \, x^{3}}, -\frac{21 \, a^{3} \sqrt{c} x^{3} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + {\left(32 \, a^{3} x^{3} - 21 \, a^{2} x^{2} + 16 \, a x - 6\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{24 \, x^{3}}\right]"," ",0,"[1/48*(21*a^3*sqrt(-c)*x^3*log(-(a^2*c*x^2 + 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) - 2*(32*a^3*x^3 - 21*a^2*x^2 + 16*a*x - 6)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^3, -1/24*(21*a^3*sqrt(c)*x^3*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + (32*a^3*x^3 - 21*a^2*x^2 + 16*a*x - 6)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^3]","A",0
918,1,232,0,0.448075," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^5,x, algorithm=""fricas"")","\left[\frac{15 \, a^{4} \sqrt{-c} x^{4} \log\left(-\frac{a^{2} c x^{2} - 2 \, a \sqrt{-c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}} - 2 \, c}{x^{2}}\right) + 2 \, {\left(24 \, a^{4} x^{4} - 15 \, a^{3} x^{3} + 12 \, a^{2} x^{2} - 10 \, a x + 4\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{40 \, x^{4}}, \frac{15 \, a^{4} \sqrt{c} x^{4} \arctan\left(\frac{a \sqrt{c} x \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}\right) + {\left(24 \, a^{4} x^{4} - 15 \, a^{3} x^{3} + 12 \, a^{2} x^{2} - 10 \, a x + 4\right)} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{20 \, x^{4}}\right]"," ",0,"[1/40*(15*a^4*sqrt(-c)*x^4*log(-(a^2*c*x^2 - 2*a*sqrt(-c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2)) - 2*c)/x^2) + 2*(24*a^4*x^4 - 15*a^3*x^3 + 12*a^2*x^2 - 10*a*x + 4)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^4, 1/20*(15*a^4*sqrt(c)*x^4*arctan(a*sqrt(c)*x*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c)) + (24*a^4*x^4 - 15*a^3*x^3 + 12*a^2*x^2 - 10*a*x + 4)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)))/x^4]","A",0
919,1,48,0,0.427309," ","integrate(x^3*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{4} x^{4} - 4 \, a^{3} x^{3} + 8 \, a^{2} x^{2} - 16 \, a x + 16 \, \log\left(a x + 1\right)\right)} \sqrt{a^{2} c}}{4 \, a^{5}}"," ",0,"1/4*(a^4*x^4 - 4*a^3*x^3 + 8*a^2*x^2 - 16*a*x + 16*log(a*x + 1))*sqrt(a^2*c)/a^5","A",0
920,1,41,0,0.455886," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} - 9 \, a^{2} x^{2} + 24 \, a x - 24 \, \log\left(a x + 1\right)\right)} \sqrt{a^{2} c}}{6 \, a^{4}}"," ",0,"1/6*(2*a^3*x^3 - 9*a^2*x^2 + 24*a*x - 24*log(a*x + 1))*sqrt(a^2*c)/a^4","A",0
921,1,32,0,0.411626," ","integrate(x*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} - 6 \, a x + 8 \, \log\left(a x + 1\right)\right)} \sqrt{a^{2} c}}{2 \, a^{3}}"," ",0,"1/2*(a^2*x^2 - 6*a*x + 8*log(a*x + 1))*sqrt(a^2*c)/a^3","A",0
922,1,25,0,0.413884," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(a x - 4 \, \log\left(a x + 1\right) + \log\left(x\right)\right)}}{a^{2}}"," ",0,"sqrt(a^2*c)*(a*x - 4*log(a*x + 1) + log(x))/a^2","A",0
923,1,32,0,0.450435," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c} {\left(4 \, a x \log\left(a x + 1\right) - 3 \, a x \log\left(x\right) - 1\right)}}{a^{2} x}"," ",0,"sqrt(a^2*c)*(4*a*x*log(a*x + 1) - 3*a*x*log(x) - 1)/(a^2*x)","A",0
924,1,83,0,0.409449," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""fricas"")","\frac{8 \, a^{3} \sqrt{c} x^{2} \log\left(\frac{2 \, a^{3} c x^{2} + 2 \, a^{2} c x - \sqrt{a^{2} c} {\left(2 \, a x + 1\right)} \sqrt{c} + a c}{a x^{2} + x}\right) + \sqrt{a^{2} c} {\left(6 \, a x - 1\right)}}{2 \, a^{2} x^{2}}"," ",0,"1/2*(8*a^3*sqrt(c)*x^2*log((2*a^3*c*x^2 + 2*a^2*c*x - sqrt(a^2*c)*(2*a*x + 1)*sqrt(c) + a*c)/(a*x^2 + x)) + sqrt(a^2*c)*(6*a*x - 1))/(a^2*x^2)","A",0
925,1,91,0,0.526574," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""fricas"")","\frac{24 \, a^{4} \sqrt{c} x^{3} \log\left(\frac{2 \, a^{3} c x^{2} + 2 \, a^{2} c x + \sqrt{a^{2} c} {\left(2 \, a x + 1\right)} \sqrt{c} + a c}{a x^{2} + x}\right) - {\left(24 \, a^{2} x^{2} - 9 \, a x + 2\right)} \sqrt{a^{2} c}}{6 \, a^{2} x^{3}}"," ",0,"1/6*(24*a^4*sqrt(c)*x^3*log((2*a^3*c*x^2 + 2*a^2*c*x + sqrt(a^2*c)*(2*a*x + 1)*sqrt(c) + a*c)/(a*x^2 + x)) - (24*a^2*x^2 - 9*a*x + 2)*sqrt(a^2*c))/(a^2*x^3)","A",0
926,1,99,0,0.543184," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""fricas"")","\frac{16 \, a^{5} \sqrt{c} x^{4} \log\left(\frac{2 \, a^{3} c x^{2} + 2 \, a^{2} c x - \sqrt{a^{2} c} {\left(2 \, a x + 1\right)} \sqrt{c} + a c}{a x^{2} + x}\right) + {\left(16 \, a^{3} x^{3} - 8 \, a^{2} x^{2} + 4 \, a x - 1\right)} \sqrt{a^{2} c}}{4 \, a^{2} x^{4}}"," ",0,"1/4*(16*a^5*sqrt(c)*x^4*log((2*a^3*c*x^2 + 2*a^2*c*x - sqrt(a^2*c)*(2*a*x + 1)*sqrt(c) + a*c)/(a*x^2 + x)) + (16*a^3*x^3 - 8*a^2*x^2 + 4*a*x - 1)*sqrt(a^2*c))/(a^2*x^4)","A",0
927,1,107,0,0.573514," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""fricas"")","\frac{240 \, a^{6} \sqrt{c} x^{5} \log\left(\frac{2 \, a^{3} c x^{2} + 2 \, a^{2} c x + \sqrt{a^{2} c} {\left(2 \, a x + 1\right)} \sqrt{c} + a c}{a x^{2} + x}\right) - {\left(240 \, a^{4} x^{4} - 120 \, a^{3} x^{3} + 80 \, a^{2} x^{2} - 45 \, a x + 12\right)} \sqrt{a^{2} c}}{60 \, a^{2} x^{5}}"," ",0,"1/60*(240*a^6*sqrt(c)*x^5*log((2*a^3*c*x^2 + 2*a^2*c*x + sqrt(a^2*c)*(2*a*x + 1)*sqrt(c) + a*c)/(a*x^2 + x)) - (240*a^4*x^4 - 120*a^3*x^3 + 80*a^2*x^2 - 45*a*x + 12)*sqrt(a^2*c))/(a^2*x^5)","A",0
928,0,0,0,0.628687," ","integrate(exp(n*arccoth(a*x))*(c-c/a^2/x^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} - c\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{2} x^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 - c)*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^2*x^2), x)","F",0
929,0,0,0,0.559534," ","integrate(exp(n*arccoth(a*x))/(c-c/a^2/x^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}, x\right)"," ",0,"integral(a^2*x^2*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
930,0,0,0,0.694851," ","integrate(exp(n*arccoth(a*x))/(c-c/a^2/x^2)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(a^4*x^4*((a*x - 1)/(a*x + 1))^(1/2*n)/(a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2), x)","F",0
931,0,0,0,0.756568," ","integrate(exp(n*arccoth(a*x))*(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^(1/2*n)*sqrt((a^2*c*x^2 - c)/(a^2*x^2)), x)","F",0
932,0,0,0,0.644377," ","integrate(exp(n*arccoth(a*x))/(c-c/a^2/x^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n} \sqrt{\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}}}{a^{2} c x^{2} - c}, x\right)"," ",0,"integral(a^2*x^2*((a*x - 1)/(a*x + 1))^(1/2*n)*sqrt((a^2*c*x^2 - c)/(a^2*x^2))/(a^2*c*x^2 - c), x)","F",0
933,0,0,0,0.657762," ","integrate(exp(n*arccoth(a*x))*(c-c/a^2/x^2)^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n} \left(\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}\right)^{p}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^(1/2*n)*((a^2*c*x^2 - c)/(a^2*x^2))^p, x)","F",0
934,0,0,0,0.672231," ","integrate((c-c/a^2/x^2)^p/exp(2*p*arccoth(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}\right)^{p}}{\left(\frac{a x - 1}{a x + 1}\right)^{p}}, x\right)"," ",0,"integral(((a^2*c*x^2 - c)/(a^2*x^2))^p/((a*x - 1)/(a*x + 1))^p, x)","F",0
935,0,0,0,0.710136," ","integrate(exp(2*p*arccoth(a*x))*(c-c/a^2/x^2)^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x - 1}{a x + 1}\right)^{p} \left(\frac{a^{2} c x^{2} - c}{a^{2} x^{2}}\right)^{p}, x\right)"," ",0,"integral(((a*x - 1)/(a*x + 1))^p*((a^2*c*x^2 - c)/(a^2*x^2))^p, x)","F",0
