1,1,182,0,0.153724," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^3,x, algorithm=""giac"")","\frac{1}{24} \, a {\left(\frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{5}} - \frac{9 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{5}} - \frac{2 \, {\left(\frac{31 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{49 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + \frac{9 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} - 39 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{5} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{4}}\right)}"," ",0,"1/24*a*(9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^5 - 9*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^5 - 2*(31*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 49*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 9*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 - 39*sqrt((a*x - 1)/(a*x + 1)))/(a^5*((a*x - 1)/(a*x + 1) - 1)^4))","A",0
2,1,151,0,0.156813," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2,x, algorithm=""giac"")","\frac{1}{6} \, a {\left(\frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{4}} - \frac{3 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{4}} + \frac{2 \, {\left(\frac{4 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} - 9 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"1/6*a*(3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^4 - 3*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^4 + 2*(4*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 3*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 - 9*sqrt((a*x - 1)/(a*x + 1)))/(a^4*((a*x - 1)/(a*x + 1) - 1)^3))","B",0
3,1,118,0,0.141813," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x,x, algorithm=""giac"")","\frac{1}{2} \, a {\left(\frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{3}} - \frac{\log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{3}} - \frac{2 \, {\left(\frac{{\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - 3 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{2}}\right)}"," ",0,"1/2*a*(log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^3 - log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^3 - 2*((a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 3*sqrt((a*x - 1)/(a*x + 1)))/(a^3*((a*x - 1)/(a*x + 1) - 1)^2))","B",0
4,1,57,0,0.170279," ","integrate(1/((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right)}{{\left| a \right|} \mathrm{sgn}\left(a x + 1\right)} + \frac{\sqrt{a^{2} x^{2} - 1}}{a \mathrm{sgn}\left(a x + 1\right)}"," ",0,"-log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))/(abs(a)*sgn(a*x + 1)) + sqrt(a^2*x^2 - 1)/(a*sgn(a*x + 1))","A",0
5,1,70,0,0.160810," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""giac"")","a {\left(\frac{2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} - \frac{\log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a}\right)}"," ",0,"a*(2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a + log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a - log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a)","B",0
6,1,53,0,0.142276," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""giac"")","2 \, a {\left(\frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\frac{a x - 1}{a x + 1} + 1} + \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)\right)}"," ",0,"2*a*(sqrt((a*x - 1)/(a*x + 1))/((a*x - 1)/(a*x + 1) + 1) + arctan(sqrt((a*x - 1)/(a*x + 1))))","B",0
7,1,87,0,0.143594," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^3,x, algorithm=""giac"")","{\left(a \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \frac{\frac{{\left(a x - 1\right)} a \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + 3 \, a \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{2}}\right)} a"," ",0,"(a*arctan(sqrt((a*x - 1)/(a*x + 1))) + ((a*x - 1)*a*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 3*a*sqrt((a*x - 1)/(a*x + 1)))/((a*x - 1)/(a*x + 1) + 1)^2)*a","B",0
8,1,130,0,0.146317," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^4,x, algorithm=""giac"")","\frac{1}{3} \, {\left(3 \, a^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \frac{\frac{4 \, {\left(a x - 1\right)} a^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2} a^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + 9 \, a^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)} a"," ",0,"1/3*(3*a^2*arctan(sqrt((a*x - 1)/(a*x + 1))) + (4*(a*x - 1)*a^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 3*(a*x - 1)^2*a^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 9*a^2*sqrt((a*x - 1)/(a*x + 1)))/((a*x - 1)/(a*x + 1) + 1)^3)*a","B",0
9,1,164,0,0.152880," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^5,x, algorithm=""giac"")","\frac{1}{12} \, {\left(9 \, a^{3} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \frac{\frac{31 \, {\left(a x - 1\right)} a^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{49 \, {\left(a x - 1\right)}^{2} a^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + \frac{9 \, {\left(a x - 1\right)}^{3} a^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + 39 \, a^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{4}}\right)} a"," ",0,"1/12*(9*a^3*arctan(sqrt((a*x - 1)/(a*x + 1))) + (31*(a*x - 1)*a^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 49*(a*x - 1)^2*a^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 9*(a*x - 1)^3*a^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 39*a^3*sqrt((a*x - 1)/(a*x + 1)))/((a*x - 1)/(a*x + 1) + 1)^4)*a","B",0
10,1,47,0,0.135124," ","integrate(1/(a*x-1)*(a*x+1)*x^3,x, algorithm=""giac"")","\frac{3 \, a^{4} x^{4} + 8 \, a^{3} x^{3} + 12 \, a^{2} x^{2} + 24 \, a x}{12 \, a^{4}} + \frac{2 \, \log\left({\left| a x - 1 \right|}\right)}{a^{4}}"," ",0,"1/12*(3*a^4*x^4 + 8*a^3*x^3 + 12*a^2*x^2 + 24*a*x)/a^4 + 2*log(abs(a*x - 1))/a^4","A",0
11,1,38,0,0.126292," ","integrate(1/(a*x-1)*(a*x+1)*x^2,x, algorithm=""giac"")","\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 6 \, a x}{3 \, a^{3}} + \frac{2 \, \log\left({\left| a x - 1 \right|}\right)}{a^{3}}"," ",0,"1/3*(a^3*x^3 + 3*a^2*x^2 + 6*a*x)/a^3 + 2*log(abs(a*x - 1))/a^3","A",0
12,1,30,0,0.115534," ","integrate(1/(a*x-1)*(a*x+1)*x,x, algorithm=""giac"")","\frac{a^{2} x^{2} + 4 \, a x}{2 \, a^{2}} + \frac{2 \, \log\left({\left| a x - 1 \right|}\right)}{a^{2}}"," ",0,"1/2*(a^2*x^2 + 4*a*x)/a^2 + 2*log(abs(a*x - 1))/a^2","A",0
13,1,14,0,0.114337," ","integrate(1/(a*x-1)*(a*x+1),x, algorithm=""giac"")","x + \frac{2 \, \log\left({\left| a x - 1 \right|}\right)}{a}"," ",0,"x + 2*log(abs(a*x - 1))/a","A",0
14,1,15,0,0.117612," ","integrate(1/(a*x-1)*(a*x+1)/x,x, algorithm=""giac"")","2 \, \log\left({\left| a x - 1 \right|}\right) - \log\left({\left| x \right|}\right)"," ",0,"2*log(abs(a*x - 1)) - log(abs(x))","A",0
15,1,20,0,0.117650," ","integrate(1/(a*x-1)*(a*x+1)/x^2,x, algorithm=""giac"")","2 \, a \log\left({\left| a x - 1 \right|}\right) - 2 \, a \log\left({\left| x \right|}\right) + \frac{1}{x}"," ",0,"2*a*log(abs(a*x - 1)) - 2*a*log(abs(x)) + 1/x","A",0
16,1,32,0,0.140266," ","integrate(1/(a*x-1)*(a*x+1)/x^3,x, algorithm=""giac"")","2 \, a^{2} \log\left({\left| a x - 1 \right|}\right) - 2 \, a^{2} \log\left({\left| x \right|}\right) + \frac{4 \, a x + 1}{2 \, x^{2}}"," ",0,"2*a^2*log(abs(a*x - 1)) - 2*a^2*log(abs(x)) + 1/2*(4*a*x + 1)/x^2","A",0
17,1,40,0,0.134233," ","integrate(1/(a*x-1)*(a*x+1)/x^4,x, algorithm=""giac"")","2 \, a^{3} \log\left({\left| a x - 1 \right|}\right) - 2 \, a^{3} \log\left({\left| x \right|}\right) + \frac{6 \, a^{2} x^{2} + 3 \, a x + 1}{3 \, x^{3}}"," ",0,"2*a^3*log(abs(a*x - 1)) - 2*a^3*log(abs(x)) + 1/3*(6*a^2*x^2 + 3*a*x + 1)/x^3","A",0
18,1,171,0,0.150799," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2,x, algorithm=""giac"")","\frac{1}{6} \, a {\left(\frac{33 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{4}} - \frac{33 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{4}} - \frac{24}{a^{4} \sqrt{\frac{a x - 1}{a x + 1}}} + \frac{2 \, {\left(\frac{52 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{21 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} - 39 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"1/6*a*(33*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^4 - 33*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^4 - 24/(a^4*sqrt((a*x - 1)/(a*x + 1))) + 2*(52*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 21*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 - 39*sqrt((a*x - 1)/(a*x + 1)))/(a^4*((a*x - 1)/(a*x + 1) - 1)^3))","A",0
19,1,140,0,0.171905," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x,x, algorithm=""giac"")","\frac{1}{2} \, a {\left(\frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{3}} - \frac{9 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{3}} - \frac{8}{a^{3} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{2 \, {\left(\frac{5 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - 7 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{2}}\right)}"," ",0,"1/2*a*(9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^3 - 9*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^3 - 8/(a^3*sqrt((a*x - 1)/(a*x + 1))) - 2*(5*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 7*sqrt((a*x - 1)/(a*x + 1)))/(a^3*((a*x - 1)/(a*x + 1) - 1)^2))","A",0
20,1,119,0,0.164912," ","integrate(1/((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","a {\left(\frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(\frac{3 \, {\left(a x - 1\right)}}{a x + 1} - 2\right)}}{a^{2} {\left(\frac{{\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \sqrt{\frac{a x - 1}{a x + 1}}\right)}}\right)}"," ",0,"a*(3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 2*(3*(a*x - 1)/(a*x + 1) - 2)/(a^2*((a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - sqrt((a*x - 1)/(a*x + 1)))))","B",0
21,1,91,0,0.156189," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""giac"")","-a {\left(\frac{2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{\log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a} + \frac{4}{a \sqrt{\frac{a x - 1}{a x + 1}}}\right)}"," ",0,"-a*(2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a - log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a + log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a + 4/(a*sqrt((a*x - 1)/(a*x + 1))))","B",0
22,1,85,0,0.162130," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""giac"")","-2 \, a {\left(\frac{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + 2}{\frac{{\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \sqrt{\frac{a x - 1}{a x + 1}}} + 3 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)\right)}"," ",0,"-2*a*((3*(a*x - 1)/(a*x + 1) + 2)/((a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + sqrt((a*x - 1)/(a*x + 1))) + 3*arctan(sqrt((a*x - 1)/(a*x + 1))))","A",0
23,1,108,0,0.136314," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""giac"")","-{\left(9 \, a \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \frac{4 \, a}{\sqrt{\frac{a x - 1}{a x + 1}}} + \frac{\frac{5 \, {\left(a x - 1\right)} a \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + 7 \, a \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{2}}\right)} a"," ",0,"-(9*a*arctan(sqrt((a*x - 1)/(a*x + 1))) + 4*a/sqrt((a*x - 1)/(a*x + 1)) + (5*(a*x - 1)*a*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 7*a*sqrt((a*x - 1)/(a*x + 1)))/((a*x - 1)/(a*x + 1) + 1)^2)*a","A",0
24,1,150,0,0.133903," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""giac"")","-\frac{1}{3} \, {\left(33 \, a^{2} \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right) + \frac{12 \, a^{2}}{\sqrt{\frac{a x - 1}{a x + 1}}} + \frac{\frac{52 \, {\left(a x - 1\right)} a^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{21 \, {\left(a x - 1\right)}^{2} a^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + 39 \, a^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)} a"," ",0,"-1/3*(33*a^2*arctan(sqrt((a*x - 1)/(a*x + 1))) + 12*a^2/sqrt((a*x - 1)/(a*x + 1)) + (52*(a*x - 1)*a^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 21*(a*x - 1)^2*a^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 39*a^2*sqrt((a*x - 1)/(a*x + 1)))/((a*x - 1)/(a*x + 1) + 1)^3)*a","A",0
25,1,78,0,0.140863," ","integrate(1/(a*x-1)^2*(a*x+1)^2*x^3,x, algorithm=""giac"")","\frac{{\left(a x - 1\right)}^{4} {\left(\frac{28}{a x - 1} + \frac{114}{{\left(a x - 1\right)}^{2}} + \frac{300}{{\left(a x - 1\right)}^{3}} + 3\right)}}{12 \, a^{4}} - \frac{16 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a^{4}} - \frac{4}{{\left(a x - 1\right)} a^{4}}"," ",0,"1/12*(a*x - 1)^4*(28/(a*x - 1) + 114/(a*x - 1)^2 + 300/(a*x - 1)^3 + 3)/a^4 - 16*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a^4 - 4/((a*x - 1)*a^4)","A",0
26,1,69,0,0.144079," ","integrate(1/(a*x-1)^2*(a*x+1)^2*x^2,x, algorithm=""giac"")","\frac{{\left(a x - 1\right)}^{3} {\left(\frac{9}{a x - 1} + \frac{39}{{\left(a x - 1\right)}^{2}} + 1\right)}}{3 \, a^{3}} - \frac{12 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a^{3}} - \frac{4}{{\left(a x - 1\right)} a^{3}}"," ",0,"1/3*(a*x - 1)^3*(9/(a*x - 1) + 39/(a*x - 1)^2 + 1)/a^3 - 12*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a^3 - 4/((a*x - 1)*a^3)","A",0
27,1,64,0,0.138201," ","integrate(1/(a*x-1)^2*(a*x+1)^2*x,x, algorithm=""giac"")","\frac{\frac{{\left(a x - 1\right)}^{2} {\left(\frac{10}{a x - 1} + 1\right)}}{a} - \frac{16 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} - \frac{8}{{\left(a x - 1\right)} a}}{2 \, a}"," ",0,"1/2*((a*x - 1)^2*(10/(a*x - 1) + 1)/a - 16*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a - 8/((a*x - 1)*a))/a","A",0
28,1,46,0,0.141199," ","integrate(1/(a*x-1)^2*(a*x+1)^2,x, algorithm=""giac"")","\frac{a x - 1}{a} - \frac{4 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} - \frac{4}{{\left(a x - 1\right)} a}"," ",0,"(a*x - 1)/a - 4*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a - 4/((a*x - 1)*a)","A",0
29,1,57,0,0.145271," ","integrate(1/(a*x-1)^2*(a*x+1)^2/x,x, algorithm=""giac"")","-a {\left(\frac{\log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} - \frac{\log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right)}{a} + \frac{4}{{\left(a x - 1\right)} a}\right)}"," ",0,"-a*(log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a - log(abs(-1/(a*x - 1) - 1))/a + 4/((a*x - 1)*a))","B",0
30,1,40,0,0.142856," ","integrate(1/(a*x-1)^2*(a*x+1)^2/x^2,x, algorithm=""giac"")","4 \, a \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right) - \frac{4 \, a}{a x - 1} + \frac{a}{\frac{1}{a x - 1} + 1}"," ",0,"4*a*log(abs(-1/(a*x - 1) - 1)) - 4*a/(a*x - 1) + a/(1/(a*x - 1) + 1)","A",0
31,1,62,0,0.141348," ","integrate(1/(a*x-1)^2*(a*x+1)^2/x^3,x, algorithm=""giac"")","8 \, a^{2} \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right) - \frac{4 \, a^{2}}{a x - 1} + \frac{9 \, a^{2} + \frac{10 \, a^{2}}{a x - 1}}{2 \, {\left(\frac{1}{a x - 1} + 1\right)}^{2}}"," ",0,"8*a^2*log(abs(-1/(a*x - 1) - 1)) - 4*a^2/(a*x - 1) + 1/2*(9*a^2 + 10*a^2/(a*x - 1))/(1/(a*x - 1) + 1)^2","A",0
32,1,74,0,0.119269," ","integrate(1/(a*x-1)^2*(a*x+1)^2/x^4,x, algorithm=""giac"")","12 \, a^{3} \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right) - \frac{4 \, a^{3}}{a x - 1} + \frac{31 \, a^{3} + \frac{69 \, a^{3}}{a x - 1} + \frac{39 \, a^{3}}{{\left(a x - 1\right)}^{2}}}{3 \, {\left(\frac{1}{a x - 1} + 1\right)}^{3}}"," ",0,"12*a^3*log(abs(-1/(a*x - 1) - 1)) - 4*a^3/(a*x - 1) + 1/3*(31*a^3 + 69*a^3/(a*x - 1) + 39*a^3/(a*x - 1)^2)/(1/(a*x - 1) + 1)^3","A",0
33,-2,0,0,0.000000," ","integrate(x^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
34,1,86,0,0.140942," ","integrate(x^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{a^{2} x^{2} - 1} {\left(x {\left(\frac{2 \, x \mathrm{sgn}\left(a x + 1\right)}{a} - \frac{3 \, \mathrm{sgn}\left(a x + 1\right)}{a^{2}}\right)} + \frac{4 \, \mathrm{sgn}\left(a x + 1\right)}{a^{3}}\right)} + \frac{\log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{2 \, a^{2} {\left| a \right|}}"," ",0,"1/6*sqrt(a^2*x^2 - 1)*(x*(2*x*sgn(a*x + 1)/a - 3*sgn(a*x + 1)/a^2) + 4*sgn(a*x + 1)/a^3) + 1/2*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/(a^2*abs(a))","A",0
35,1,71,0,0.149250," ","integrate(x*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{a^{2} x^{2} - 1} {\left(\frac{x \mathrm{sgn}\left(a x + 1\right)}{a} - \frac{2 \, \mathrm{sgn}\left(a x + 1\right)}{a^{2}}\right)} - \frac{\log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{2 \, a {\left| a \right|}}"," ",0,"1/2*sqrt(a^2*x^2 - 1)*(x*sgn(a*x + 1)/a - 2*sgn(a*x + 1)/a^2) - 1/2*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/(a*abs(a))","A",0
36,1,52,0,0.141019," ","integrate(((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} \mathrm{sgn}\left(a x + 1\right)}{a}"," ",0,"log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*sgn(a*x + 1)/a","A",0
37,1,59,0,0.160256," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""giac"")","-2 \, \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right) - \frac{a \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}}"," ",0,"-2*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1) - a*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a)","B",0
38,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
39,1,157,0,0.137512," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^3,x, algorithm=""giac"")","-a^{2} \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right) + \frac{{\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{3} a^{2} \mathrm{sgn}\left(a x + 1\right) + 2 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} a {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)} a^{2} \mathrm{sgn}\left(a x + 1\right) + 2 \, a {\left| a \right|} \mathrm{sgn}\left(a x + 1\right)}{{\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)}^{2}}"," ",0,"-a^2*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1) + ((x*abs(a) - sqrt(a^2*x^2 - 1))^3*a^2*sgn(a*x + 1) + 2*(x*abs(a) - sqrt(a^2*x^2 - 1))^2*a*abs(a)*sgn(a*x + 1) - (x*abs(a) - sqrt(a^2*x^2 - 1))*a^2*sgn(a*x + 1) + 2*a*abs(a)*sgn(a*x + 1))/((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)^2","B",0
40,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
41,1,258,0,0.162961," ","integrate(((a*x-1)/(a*x+1))^(1/2)/x^5,x, algorithm=""giac"")","-\frac{3}{4} \, a^{4} \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right) + \frac{9 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{7} a^{4} \mathrm{sgn}\left(a x + 1\right) + 33 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{5} a^{4} \mathrm{sgn}\left(a x + 1\right) + 48 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{4} a^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 33 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{3} a^{4} \mathrm{sgn}\left(a x + 1\right) + 64 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} a^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 9 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)} a^{4} \mathrm{sgn}\left(a x + 1\right) + 16 \, a^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right)}{12 \, {\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)}^{4}}"," ",0,"-3/4*a^4*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1) + 1/12*(9*(x*abs(a) - sqrt(a^2*x^2 - 1))^7*a^4*sgn(a*x + 1) + 33*(x*abs(a) - sqrt(a^2*x^2 - 1))^5*a^4*sgn(a*x + 1) + 48*(x*abs(a) - sqrt(a^2*x^2 - 1))^4*a^3*abs(a)*sgn(a*x + 1) - 33*(x*abs(a) - sqrt(a^2*x^2 - 1))^3*a^4*sgn(a*x + 1) + 64*(x*abs(a) - sqrt(a^2*x^2 - 1))^2*a^3*abs(a)*sgn(a*x + 1) - 9*(x*abs(a) - sqrt(a^2*x^2 - 1))*a^4*sgn(a*x + 1) + 16*a^3*abs(a)*sgn(a*x + 1))/((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)^4","B",0
42,1,47,0,0.142547," ","integrate(x^3*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{3 \, a^{4} x^{4} - 8 \, a^{3} x^{3} + 12 \, a^{2} x^{2} - 24 \, a x}{12 \, a^{4}} + \frac{2 \, \log\left({\left| a x + 1 \right|}\right)}{a^{4}}"," ",0,"1/12*(3*a^4*x^4 - 8*a^3*x^3 + 12*a^2*x^2 - 24*a*x)/a^4 + 2*log(abs(a*x + 1))/a^4","A",0
43,1,38,0,0.120682," ","integrate(x^2*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 6 \, a x}{3 \, a^{3}} - \frac{2 \, \log\left({\left| a x + 1 \right|}\right)}{a^{3}}"," ",0,"1/3*(a^3*x^3 - 3*a^2*x^2 + 6*a*x)/a^3 - 2*log(abs(a*x + 1))/a^3","A",0
44,1,30,0,0.133408," ","integrate(x*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{a^{2} x^{2} - 4 \, a x}{2 \, a^{2}} + \frac{2 \, \log\left({\left| a x + 1 \right|}\right)}{a^{2}}"," ",0,"1/2*(a^2*x^2 - 4*a*x)/a^2 + 2*log(abs(a*x + 1))/a^2","A",0
45,1,14,0,0.125377," ","integrate((a*x-1)/(a*x+1),x, algorithm=""giac"")","x - \frac{2 \, \log\left({\left| a x + 1 \right|}\right)}{a}"," ",0,"x - 2*log(abs(a*x + 1))/a","A",0
46,1,15,0,0.118023," ","integrate((a*x-1)/(a*x+1)/x,x, algorithm=""giac"")","2 \, \log\left({\left| a x + 1 \right|}\right) - \log\left({\left| x \right|}\right)"," ",0,"2*log(abs(a*x + 1)) - log(abs(x))","A",0
47,1,20,0,0.113342," ","integrate((a*x-1)/(a*x+1)/x^2,x, algorithm=""giac"")","-2 \, a \log\left({\left| a x + 1 \right|}\right) + 2 \, a \log\left({\left| x \right|}\right) + \frac{1}{x}"," ",0,"-2*a*log(abs(a*x + 1)) + 2*a*log(abs(x)) + 1/x","A",0
48,1,32,0,0.146185," ","integrate((a*x-1)/(a*x+1)/x^3,x, algorithm=""giac"")","2 \, a^{2} \log\left({\left| a x + 1 \right|}\right) - 2 \, a^{2} \log\left({\left| x \right|}\right) - \frac{4 \, a x - 1}{2 \, x^{2}}"," ",0,"2*a^2*log(abs(a*x + 1)) - 2*a^2*log(abs(x)) - 1/2*(4*a*x - 1)/x^2","A",0
49,1,40,0,0.145373," ","integrate((a*x-1)/(a*x+1)/x^4,x, algorithm=""giac"")","-2 \, a^{3} \log\left({\left| a x + 1 \right|}\right) + 2 \, a^{3} \log\left({\left| x \right|}\right) + \frac{6 \, a^{2} x^{2} - 3 \, a x + 1}{3 \, x^{3}}"," ",0,"-2*a^3*log(abs(a*x + 1)) + 2*a^3*log(abs(x)) + 1/3*(6*a^2*x^2 - 3*a*x + 1)/x^3","A",0
50,0,0,0,0.000000," ","integrate(x^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
51,0,0,0,0.000000," ","integrate(x^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
52,0,0,0,0.000000," ","integrate(x*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
53,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
54,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
55,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
56,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
57,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
58,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
59,1,234,0,0.268816," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^4,x, algorithm=""giac"")","-\frac{1}{3840} \, a {\left(\frac{930 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} - \frac{465 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} + \frac{465 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{6}} - \frac{4 \, {\left(\frac{1120 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - \frac{5090 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{696 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{3}} - \frac{465 \, {\left(a x - 1\right)}^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{4}} - 2405 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{6} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{5}}\right)}"," ",0,"-1/3840*a*(930*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 - 465*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 + 465*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^6 - 4*(1120*(a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 5090*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 + 696*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^3 - 465*(a*x - 1)^4*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^4 - 2405*((a*x - 1)/(a*x + 1))^(3/4))/(a^6*((a*x - 1)/(a*x + 1) - 1)^5))","A",0
60,1,203,0,0.271405," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^3,x, algorithm=""giac"")","-\frac{1}{384} \, a {\left(\frac{66 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} - \frac{33 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} + \frac{33 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{5}} + \frac{4 \, {\left(\frac{107 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - \frac{279 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{33 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{3}} - 245 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{5} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{4}}\right)}"," ",0,"-1/384*a*(66*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 - 33*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 + 33*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^5 + 4*(107*(a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 279*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 + 33*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^3 - 245*((a*x - 1)/(a*x + 1))^(3/4))/(a^5*((a*x - 1)/(a*x + 1) - 1)^4))","A",0
61,1,172,0,0.235021," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^2,x, algorithm=""giac"")","-\frac{1}{48} \, a {\left(\frac{18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} - \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} + \frac{9 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{4}} - \frac{4 \, {\left(\frac{6 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - \frac{9 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} - 29 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"-1/48*a*(18*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 - 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 + 9*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^4 - 4*(6*(a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 9*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 - 29*((a*x - 1)/(a*x + 1))^(3/4))/(a^4*((a*x - 1)/(a*x + 1) - 1)^3))","A",0
62,1,139,0,0.241114," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x,x, algorithm=""giac"")","-\frac{1}{8} \, a {\left(\frac{2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} - \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} + \frac{\log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{3}} + \frac{4 \, {\left(\frac{{\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - 5 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{2}}\right)}"," ",0,"-1/8*a*(2*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 - log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 + log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^3 + 4*((a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 5*((a*x - 1)/(a*x + 1))^(3/4))/(a^3*((a*x - 1)/(a*x + 1) - 1)^2))","A",0
63,1,108,0,0.213386," ","integrate(1/((a*x-1)/(a*x+1))^(1/4),x, algorithm=""giac"")","-\frac{1}{2} \, a {\left(\frac{2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} - \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} + \frac{\log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{2}} + \frac{4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"-1/2*a*(2*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 - log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 + log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^2 + 4*((a*x - 1)/(a*x + 1))^(3/4)/(a^2*((a*x - 1)/(a*x + 1) - 1)))","A",0
64,1,232,0,0.211653," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x,x, algorithm=""giac"")","\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} - \frac{\sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{\sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} - \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} + \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} - \frac{2 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a}\right)}"," ",0,"1/2*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4)))/a + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4)))/a - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a - 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a + 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a - 2*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a)","A",0
65,1,186,0,0.190630," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x^2,x, algorithm=""giac"")","\frac{1}{4} \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{\frac{a x - 1}{a x + 1} + 1}\right)} a"," ",0,"1/4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*((a*x - 1)/(a*x + 1))^(3/4)/((a*x - 1)/(a*x + 1) + 1))*a","A",0
66,1,223,0,0.186452," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x^3,x, algorithm=""giac"")","\frac{1}{16} \, {\left(2 \, \sqrt{2} a \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} a \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - \sqrt{2} a \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \sqrt{2} a \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, {\left(\frac{{\left(a x - 1\right)} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} + 5 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{2}}\right)} a"," ",0,"1/16*(2*sqrt(2)*a*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*a*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - sqrt(2)*a*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + sqrt(2)*a*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*((a*x - 1)*a*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) + 5*a*((a*x - 1)/(a*x + 1))^(3/4))/((a*x - 1)/(a*x + 1) + 1)^2)*a","A",0
67,1,271,0,0.216749," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)/x^4,x, algorithm=""giac"")","\frac{1}{96} \, {\left(18 \, \sqrt{2} a^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 18 \, \sqrt{2} a^{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - 9 \, \sqrt{2} a^{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 9 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, {\left(\frac{6 \, {\left(a x - 1\right)} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} + \frac{9 \, {\left(a x - 1\right)}^{2} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} + 29 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)} a"," ",0,"1/96*(18*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 18*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - 9*sqrt(2)*a^2*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 9*sqrt(2)*a^2*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*(6*(a*x - 1)*a^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) + 9*(a*x - 1)^2*a^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 + 29*a^2*((a*x - 1)/(a*x + 1))^(3/4))/((a*x - 1)/(a*x + 1) + 1)^3)*a","A",0
68,1,234,0,0.403000," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^4,x, algorithm=""giac"")","\frac{1}{1280} \, a {\left(\frac{2370 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} + \frac{1185 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} - \frac{1185 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{6}} + \frac{4 \, {\left(\frac{1992 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - \frac{3710 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{1440 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{3}} - \frac{395 \, {\left(a x - 1\right)}^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{4}} - 1375 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{6} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{5}}\right)}"," ",0,"1/1280*a*(2370*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 + 1185*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 - 1185*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^6 + 4*(1992*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - 3710*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 + 1440*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^3 - 395*(a*x - 1)^4*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^4 - 1375*((a*x - 1)/(a*x + 1))^(1/4))/(a^6*((a*x - 1)/(a*x + 1) - 1)^5))","A",0
69,1,203,0,0.390364," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^3,x, algorithm=""giac"")","\frac{1}{128} \, a {\left(\frac{246 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} + \frac{123 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} - \frac{123 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{5}} - \frac{4 \, {\left(\frac{147 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - \frac{183 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{41 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{3}} - 133 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{5} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{4}}\right)}"," ",0,"1/128*a*(246*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 + 123*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 - 123*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^5 - 4*(147*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - 183*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 + 41*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^3 - 133*((a*x - 1)/(a*x + 1))^(1/4))/(a^5*((a*x - 1)/(a*x + 1) - 1)^4))","A",0
70,1,172,0,0.330379," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^2,x, algorithm=""giac"")","\frac{1}{48} \, a {\left(\frac{102 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} + \frac{51 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} - \frac{51 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{4}} + \frac{4 \, {\left(\frac{30 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - \frac{17 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} - 45 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"1/48*a*(102*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 + 51*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 - 51*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^4 + 4*(30*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - 17*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 - 45*((a*x - 1)/(a*x + 1))^(1/4))/(a^4*((a*x - 1)/(a*x + 1) - 1)^3))","A",0
71,1,141,0,0.292359," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x,x, algorithm=""giac"")","\frac{1}{8} \, a {\left(\frac{18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} + \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} - \frac{9 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{3}} - \frac{4 \, {\left(\frac{3 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - 7 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{2}}\right)}"," ",0,"1/8*a*(18*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 + 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 - 9*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^3 - 4*(3*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - 7*((a*x - 1)/(a*x + 1))^(1/4))/(a^3*((a*x - 1)/(a*x + 1) - 1)^2))","A",0
72,1,109,0,0.237171," ","integrate(1/((a*x-1)/(a*x+1))^(3/4),x, algorithm=""giac"")","\frac{1}{2} \, a {\left(\frac{6 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} + \frac{3 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} - \frac{3 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{2}} - \frac{4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/2*a*(6*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 + 3*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 - 3*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^2 - 4*((a*x - 1)/(a*x + 1))^(1/4)/(a^2*((a*x - 1)/(a*x + 1) - 1)))","A",0
73,1,232,0,0.254869," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x,x, algorithm=""giac"")","\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} + \frac{\sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} - \frac{\sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} + \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} - \frac{2 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a}\right)}"," ",0,"1/2*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4)))/a + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4)))/a + sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a - sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a + 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a + 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a - 2*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a)","A",0
74,1,187,0,0.221391," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x^2,x, algorithm=""giac"")","\frac{1}{4} \, {\left(6 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 6 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 3 \, \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 3 \, \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{\frac{a x - 1}{a x + 1} + 1}\right)} a"," ",0,"1/4*(6*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 6*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 3*sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 3*sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*((a*x - 1)/(a*x + 1))^(1/4)/((a*x - 1)/(a*x + 1) + 1))*a","A",0
75,1,225,0,0.245141," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x^3,x, algorithm=""giac"")","\frac{1}{16} \, {\left(18 \, \sqrt{2} a \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 18 \, \sqrt{2} a \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 9 \, \sqrt{2} a \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 9 \, \sqrt{2} a \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, {\left(\frac{3 \, {\left(a x - 1\right)} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} + 7 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{2}}\right)} a"," ",0,"1/16*(18*sqrt(2)*a*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 18*sqrt(2)*a*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 9*sqrt(2)*a*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 9*sqrt(2)*a*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*(3*(a*x - 1)*a*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) + 7*a*((a*x - 1)/(a*x + 1))^(1/4))/((a*x - 1)/(a*x + 1) + 1)^2)*a","A",0
76,1,271,0,0.279955," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)/x^4,x, algorithm=""giac"")","\frac{1}{96} \, {\left(102 \, \sqrt{2} a^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 102 \, \sqrt{2} a^{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 51 \, \sqrt{2} a^{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 51 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, {\left(\frac{30 \, {\left(a x - 1\right)} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} + \frac{17 \, {\left(a x - 1\right)}^{2} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} + 45 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)} a"," ",0,"1/96*(102*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 102*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 51*sqrt(2)*a^2*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 51*sqrt(2)*a^2*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*(30*(a*x - 1)*a^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) + 17*(a*x - 1)^2*a^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 + 45*a^2*((a*x - 1)/(a*x + 1))^(1/4))/((a*x - 1)/(a*x + 1) + 1)^3)*a","A",0
77,1,254,0,0.281321," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^4,x, algorithm=""giac"")","-\frac{1}{3840} \, a {\left(\frac{30090 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} - \frac{15045 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} + \frac{15045 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{6}} + \frac{30720}{a^{6} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} - \frac{4 \, {\left(\frac{49120 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - \frac{61130 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{33816 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{3}} - \frac{7365 \, {\left(a x - 1\right)}^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{4}} - 20585 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{6} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{5}}\right)}"," ",0,"-1/3840*a*(30090*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 - 15045*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 + 15045*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^6 + 30720/(a^6*((a*x - 1)/(a*x + 1))^(1/4)) - 4*(49120*(a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 61130*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 + 33816*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^3 - 7365*(a*x - 1)^4*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^4 - 20585*((a*x - 1)/(a*x + 1))^(3/4))/(a^6*((a*x - 1)/(a*x + 1) - 1)^5))","A",0
78,1,223,0,0.272080," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^3,x, algorithm=""giac"")","-\frac{1}{384} \, a {\left(\frac{2850 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} - \frac{1425 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} + \frac{1425 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{5}} + \frac{3072}{a^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} + \frac{4 \, {\left(\frac{2875 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - \frac{2343 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{657 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{3}} - 1573 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{5} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{4}}\right)}"," ",0,"-1/384*a*(2850*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 - 1425*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 + 1425*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^5 + 3072/(a^5*((a*x - 1)/(a*x + 1))^(1/4)) + 4*(2875*(a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 2343*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 + 657*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^3 - 1573*((a*x - 1)/(a*x + 1))^(3/4))/(a^5*((a*x - 1)/(a*x + 1) - 1)^4))","A",0
79,1,192,0,0.252692," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^2,x, algorithm=""giac"")","-\frac{1}{48} \, a {\left(\frac{330 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} - \frac{165 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} + \frac{165 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{4}} + \frac{384}{a^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} - \frac{4 \, {\left(\frac{174 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - \frac{69 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} - 137 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"-1/48*a*(330*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 - 165*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 + 165*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^4 + 384/(a^4*((a*x - 1)/(a*x + 1))^(1/4)) - 4*(174*(a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 69*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 - 137*((a*x - 1)/(a*x + 1))^(3/4))/(a^4*((a*x - 1)/(a*x + 1) - 1)^3))","A",0
80,1,161,0,0.246095," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x,x, algorithm=""giac"")","-\frac{1}{8} \, a {\left(\frac{50 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} - \frac{25 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} + \frac{25 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{3}} + \frac{64}{a^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} + \frac{4 \, {\left(\frac{9 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - 13 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{2}}\right)}"," ",0,"-1/8*a*(50*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 - 25*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 + 25*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^3 + 64/(a^3*((a*x - 1)/(a*x + 1))^(1/4)) + 4*(9*(a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 13*((a*x - 1)/(a*x + 1))^(3/4))/(a^3*((a*x - 1)/(a*x + 1) - 1)^2))","A",0
81,1,141,0,0.203048," ","integrate(1/((a*x-1)/(a*x+1))^(5/4),x, algorithm=""giac"")","-\frac{1}{2} \, a {\left(\frac{10 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} - \frac{5 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} + \frac{5 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{2}} + \frac{4 \, {\left(\frac{5 \, {\left(a x - 1\right)}}{a x + 1} - 4\right)}}{a^{2} {\left(\frac{{\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}\right)}"," ",0,"-1/2*a*(10*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 - 5*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 + 5*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^2 + 4*(5*(a*x - 1)/(a*x + 1) - 4)/(a^2*((a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - ((a*x - 1)/(a*x + 1))^(1/4))))","A",0
82,1,252,0,0.215289," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x,x, algorithm=""giac"")","-\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} - \frac{\sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{\sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} + \frac{2 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a} + \frac{16}{a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}\right)}"," ",0,"-1/2*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4)))/a + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4)))/a - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a + 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a - 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a + 2*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a + 16/(a*((a*x - 1)/(a*x + 1))^(1/4)))","A",0
83,1,217,0,0.185139," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x^2,x, algorithm=""giac"")","-\frac{1}{4} \, {\left(10 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 10 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - 5 \, \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 5 \, \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{8 \, {\left(\frac{5 \, {\left(a x - 1\right)}}{a x + 1} + 4\right)}}{\frac{{\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}\right)} a"," ",0,"-1/4*(10*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 10*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - 5*sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 5*sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 8*(5*(a*x - 1)/(a*x + 1) + 4)/((a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) + ((a*x - 1)/(a*x + 1))^(1/4)))*a","A",0
84,1,243,0,0.193564," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x^3,x, algorithm=""giac"")","-\frac{1}{16} \, {\left(50 \, \sqrt{2} a \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 50 \, \sqrt{2} a \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - 25 \, \sqrt{2} a \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 25 \, \sqrt{2} a \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{128 \, a}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} + \frac{8 \, {\left(\frac{9 \, {\left(a x - 1\right)} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} + 13 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{2}}\right)} a"," ",0,"-1/16*(50*sqrt(2)*a*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 50*sqrt(2)*a*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - 25*sqrt(2)*a*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 25*sqrt(2)*a*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 128*a/((a*x - 1)/(a*x + 1))^(1/4) + 8*(9*(a*x - 1)*a*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) + 13*a*((a*x - 1)/(a*x + 1))^(3/4))/((a*x - 1)/(a*x + 1) + 1)^2)*a","A",0
85,1,291,0,0.248420," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)/x^4,x, algorithm=""giac"")","-\frac{1}{96} \, {\left(330 \, \sqrt{2} a^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 330 \, \sqrt{2} a^{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - 165 \, \sqrt{2} a^{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 165 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + \frac{768 \, a^{2}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}} + \frac{8 \, {\left(\frac{174 \, {\left(a x - 1\right)} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} + \frac{69 \, {\left(a x - 1\right)}^{2} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} + 137 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)} a"," ",0,"-1/96*(330*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 330*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - 165*sqrt(2)*a^2*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 165*sqrt(2)*a^2*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 768*a^2/((a*x - 1)/(a*x + 1))^(1/4) + 8*(174*(a*x - 1)*a^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) + 69*(a*x - 1)^2*a^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 + 137*a^2*((a*x - 1)/(a*x + 1))^(3/4))/((a*x - 1)/(a*x + 1) + 1)^3)*a","A",0
86,1,234,0,0.242738," ","integrate(x^4*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""giac"")","-\frac{1}{3840} \, a {\left(\frac{930 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} + \frac{465 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} - \frac{465 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{6}} - \frac{4 \, {\left(\frac{696 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - \frac{5090 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{1120 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{3}} - \frac{2405 \, {\left(a x - 1\right)}^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{4}} - 465 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{6} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{5}}\right)}"," ",0,"-1/3840*a*(930*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 + 465*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 - 465*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^6 - 4*(696*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - 5090*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 + 1120*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^3 - 2405*(a*x - 1)^4*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^4 - 465*((a*x - 1)/(a*x + 1))^(1/4))/(a^6*((a*x - 1)/(a*x + 1) - 1)^5))","A",0
87,1,203,0,0.221962," ","integrate(x^3*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""giac"")","\frac{1}{384} \, a {\left(\frac{66 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} + \frac{33 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} - \frac{33 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{5}} + \frac{4 \, {\left(\frac{279 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - \frac{107 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{245 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{3}} - 33 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{5} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{4}}\right)}"," ",0,"1/384*a*(66*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 + 33*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 - 33*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^5 + 4*(279*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - 107*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 + 245*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^3 - 33*((a*x - 1)/(a*x + 1))^(1/4))/(a^5*((a*x - 1)/(a*x + 1) - 1)^4))","A",0
88,1,172,0,0.199624," ","integrate(x^2*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""giac"")","-\frac{1}{48} \, a {\left(\frac{18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} + \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} - \frac{9 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{4}} - \frac{4 \, {\left(\frac{6 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - \frac{29 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} - 9 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"-1/48*a*(18*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 + 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 - 9*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^4 - 4*(6*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - 29*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 - 9*((a*x - 1)/(a*x + 1))^(1/4))/(a^4*((a*x - 1)/(a*x + 1) - 1)^3))","A",0
89,1,140,0,0.217621," ","integrate(x*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""giac"")","\frac{1}{8} \, a {\left(\frac{2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} + \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} - \frac{\log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{3}} + \frac{4 \, {\left(\frac{5 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{2}}\right)}"," ",0,"1/8*a*(2*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 + log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 - log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^3 + 4*(5*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - ((a*x - 1)/(a*x + 1))^(1/4))/(a^3*((a*x - 1)/(a*x + 1) - 1)^2))","A",0
90,1,108,0,0.197288," ","integrate(((a*x-1)/(a*x+1))^(1/4),x, algorithm=""giac"")","-\frac{1}{2} \, a {\left(\frac{2 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} + \frac{\log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} - \frac{\log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{2}} + \frac{4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"-1/2*a*(2*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 + log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 - log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^2 + 4*((a*x - 1)/(a*x + 1))^(1/4)/(a^2*((a*x - 1)/(a*x + 1) - 1)))","A",0
91,1,232,0,0.192527," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x,x, algorithm=""giac"")","-\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} + \frac{\sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} - \frac{\sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} - \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} + \frac{2 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a}\right)}"," ",0,"-1/2*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4)))/a + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4)))/a + sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a - sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a - 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a - 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a + 2*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a)","A",0
92,1,186,0,0.156127," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x^2,x, algorithm=""giac"")","\frac{1}{4} \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \frac{8 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{\frac{a x - 1}{a x + 1} + 1}\right)} a"," ",0,"1/4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 8*((a*x - 1)/(a*x + 1))^(1/4)/((a*x - 1)/(a*x + 1) + 1))*a","A",0
93,1,223,0,0.198105," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x^3,x, algorithm=""giac"")","-\frac{1}{16} \, {\left(2 \, \sqrt{2} a \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} a \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + \sqrt{2} a \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \sqrt{2} a \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \frac{8 \, {\left(\frac{5 \, {\left(a x - 1\right)} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} + a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{2}}\right)} a"," ",0,"-1/16*(2*sqrt(2)*a*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 2*sqrt(2)*a*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + sqrt(2)*a*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - sqrt(2)*a*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 8*(5*(a*x - 1)*a*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) + a*((a*x - 1)/(a*x + 1))^(1/4))/((a*x - 1)/(a*x + 1) + 1)^2)*a","A",0
94,1,271,0,0.212708," ","integrate(((a*x-1)/(a*x+1))^(1/4)/x^4,x, algorithm=""giac"")","\frac{1}{96} \, {\left(18 \, \sqrt{2} a^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 18 \, \sqrt{2} a^{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 9 \, \sqrt{2} a^{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 9 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \frac{8 \, {\left(\frac{6 \, {\left(a x - 1\right)} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} + \frac{29 \, {\left(a x - 1\right)}^{2} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} + 9 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)} a"," ",0,"1/96*(18*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 18*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 9*sqrt(2)*a^2*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 9*sqrt(2)*a^2*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 8*(6*(a*x - 1)*a^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) + 29*(a*x - 1)^2*a^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 + 9*a^2*((a*x - 1)/(a*x + 1))^(1/4))/((a*x - 1)/(a*x + 1) + 1)^3)*a","A",0
95,1,234,0,0.273232," ","integrate(x^4*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""giac"")","\frac{1}{1280} \, a {\left(\frac{2370 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} - \frac{1185 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} + \frac{1185 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{6}} + \frac{4 \, {\left(\frac{1440 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - \frac{3710 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{1992 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{3}} - \frac{1375 \, {\left(a x - 1\right)}^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{4}} - 395 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{6} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{5}}\right)}"," ",0,"1/1280*a*(2370*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 - 1185*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 + 1185*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^6 + 4*(1440*(a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 3710*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 + 1992*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^3 - 1375*(a*x - 1)^4*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^4 - 395*((a*x - 1)/(a*x + 1))^(3/4))/(a^6*((a*x - 1)/(a*x + 1) - 1)^5))","A",0
96,1,203,0,0.290506," ","integrate(x^3*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""giac"")","-\frac{1}{128} \, a {\left(\frac{246 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} - \frac{123 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} + \frac{123 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{5}} - \frac{4 \, {\left(\frac{183 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - \frac{147 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{133 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{3}} - 41 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{5} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{4}}\right)}"," ",0,"-1/128*a*(246*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 - 123*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 + 123*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^5 - 4*(183*(a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 147*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 + 133*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^3 - 41*((a*x - 1)/(a*x + 1))^(3/4))/(a^5*((a*x - 1)/(a*x + 1) - 1)^4))","A",0
97,1,172,0,0.224599," ","integrate(x^2*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""giac"")","\frac{1}{48} \, a {\left(\frac{102 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} - \frac{51 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} + \frac{51 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{4}} + \frac{4 \, {\left(\frac{30 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - \frac{45 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} - 17 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"1/48*a*(102*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 - 51*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 + 51*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^4 + 4*(30*(a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 45*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 - 17*((a*x - 1)/(a*x + 1))^(3/4))/(a^4*((a*x - 1)/(a*x + 1) - 1)^3))","A",0
98,1,141,0,0.245324," ","integrate(x*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""giac"")","-\frac{1}{8} \, a {\left(\frac{18 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} - \frac{9 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} + \frac{9 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{3}} - \frac{4 \, {\left(\frac{7 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} - 3 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{a^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{2}}\right)}"," ",0,"-1/8*a*(18*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 - 9*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 + 9*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^3 - 4*(7*(a*x - 1)*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) - 3*((a*x - 1)/(a*x + 1))^(3/4))/(a^3*((a*x - 1)/(a*x + 1) - 1)^2))","A",0
99,1,109,0,0.166675," ","integrate(((a*x-1)/(a*x+1))^(3/4),x, algorithm=""giac"")","\frac{1}{2} \, a {\left(\frac{6 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} - \frac{3 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} + \frac{3 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{2}} - \frac{4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/2*a*(6*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 - 3*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 + 3*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^2 - 4*((a*x - 1)/(a*x + 1))^(3/4)/(a^2*((a*x - 1)/(a*x + 1) - 1)))","A",0
100,1,232,0,0.174561," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} - \frac{\sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{\sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} + \frac{2 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a}\right)}"," ",0,"-1/2*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4)))/a + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4)))/a - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a + 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a - 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a + 2*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a)","A",0
101,1,187,0,0.158513," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x^2,x, algorithm=""giac"")","\frac{1}{4} \, {\left(6 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 6 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - 3 \, \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 3 \, \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \frac{8 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{\frac{a x - 1}{a x + 1} + 1}\right)} a"," ",0,"1/4*(6*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 6*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - 3*sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 3*sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 8*((a*x - 1)/(a*x + 1))^(3/4)/((a*x - 1)/(a*x + 1) + 1))*a","A",0
102,1,225,0,0.226084," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x^3,x, algorithm=""giac"")","-\frac{1}{16} \, {\left(18 \, \sqrt{2} a \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 18 \, \sqrt{2} a \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - 9 \, \sqrt{2} a \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 9 \, \sqrt{2} a \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \frac{8 \, {\left(\frac{7 \, {\left(a x - 1\right)} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} + 3 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{2}}\right)} a"," ",0,"-1/16*(18*sqrt(2)*a*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 18*sqrt(2)*a*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - 9*sqrt(2)*a*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 9*sqrt(2)*a*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 8*(7*(a*x - 1)*a*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) + 3*a*((a*x - 1)/(a*x + 1))^(3/4))/((a*x - 1)/(a*x + 1) + 1)^2)*a","A",0
103,1,271,0,0.252473," ","integrate(((a*x-1)/(a*x+1))^(3/4)/x^4,x, algorithm=""giac"")","\frac{1}{96} \, {\left(102 \, \sqrt{2} a^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 102 \, \sqrt{2} a^{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) - 51 \, \sqrt{2} a^{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) + 51 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - \frac{8 \, {\left(\frac{30 \, {\left(a x - 1\right)} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{a x + 1} + \frac{45 \, {\left(a x - 1\right)}^{2} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}{{\left(a x + 1\right)}^{2}} + 17 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)} a"," ",0,"1/96*(102*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 102*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) - 51*sqrt(2)*a^2*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) + 51*sqrt(2)*a^2*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 8*(30*(a*x - 1)*a^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1) + 45*(a*x - 1)^2*a^2*((a*x - 1)/(a*x + 1))^(3/4)/(a*x + 1)^2 + 17*a^2*((a*x - 1)/(a*x + 1))^(3/4))/((a*x - 1)/(a*x + 1) + 1)^3)*a","A",0
104,1,254,0,0.212955," ","integrate(x^4*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""giac"")","-\frac{1}{3840} \, a {\left(\frac{30090 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{6}} + \frac{15045 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{6}} - \frac{15045 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{6}} - \frac{30720 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{6}} - \frac{4 \, {\left(\frac{33816 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - \frac{61130 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{49120 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{3}} - \frac{20585 \, {\left(a x - 1\right)}^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{4}} - 7365 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{6} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{5}}\right)}"," ",0,"-1/3840*a*(30090*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^6 + 15045*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^6 - 15045*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^6 - 30720*((a*x - 1)/(a*x + 1))^(1/4)/a^6 - 4*(33816*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - 61130*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 + 49120*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^3 - 20585*(a*x - 1)^4*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^4 - 7365*((a*x - 1)/(a*x + 1))^(1/4))/(a^6*((a*x - 1)/(a*x + 1) - 1)^5))","A",0
105,1,223,0,0.229337," ","integrate(x^3*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""giac"")","\frac{1}{384} \, a {\left(\frac{2850 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{5}} + \frac{1425 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{5}} - \frac{1425 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{5}} - \frac{3072 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{5}} + \frac{4 \, {\left(\frac{2343 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - \frac{2875 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} + \frac{1573 \, {\left(a x - 1\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{3}} - 657 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{5} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{4}}\right)}"," ",0,"1/384*a*(2850*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^5 + 1425*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^5 - 1425*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^5 - 3072*((a*x - 1)/(a*x + 1))^(1/4)/a^5 + 4*(2343*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - 2875*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 + 1573*(a*x - 1)^3*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^3 - 657*((a*x - 1)/(a*x + 1))^(1/4))/(a^5*((a*x - 1)/(a*x + 1) - 1)^4))","A",0
106,1,192,0,0.210932," ","integrate(x^2*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""giac"")","-\frac{1}{48} \, a {\left(\frac{330 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{4}} + \frac{165 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} - \frac{165 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{4}} - \frac{384 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{4}} - \frac{4 \, {\left(\frac{174 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - \frac{137 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} - 69 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"-1/48*a*(330*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^4 + 165*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 - 165*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^4 - 384*((a*x - 1)/(a*x + 1))^(1/4)/a^4 - 4*(174*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - 137*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 - 69*((a*x - 1)/(a*x + 1))^(1/4))/(a^4*((a*x - 1)/(a*x + 1) - 1)^3))","A",0
107,1,161,0,0.194377," ","integrate(x*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""giac"")","\frac{1}{8} \, a {\left(\frac{50 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{3}} + \frac{25 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} - \frac{25 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{3}} - \frac{64 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{3}} + \frac{4 \, {\left(\frac{13 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} - 9 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{a^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{2}}\right)}"," ",0,"1/8*a*(50*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^3 + 25*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 - 25*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^3 - 64*((a*x - 1)/(a*x + 1))^(1/4)/a^3 + 4*(13*(a*x - 1)*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) - 9*((a*x - 1)/(a*x + 1))^(1/4))/(a^3*((a*x - 1)/(a*x + 1) - 1)^2))","A",0
108,1,129,0,0.162281," ","integrate(((a*x-1)/(a*x+1))^(5/4),x, algorithm=""giac"")","-\frac{1}{2} \, a {\left(\frac{10 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a^{2}} + \frac{5 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} - \frac{5 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a^{2}} - \frac{16 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{2}} + \frac{4 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"-1/2*a*(10*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a^2 + 5*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 - 5*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a^2 - 16*((a*x - 1)/(a*x + 1))^(1/4)/a^2 + 4*((a*x - 1)/(a*x + 1))^(1/4)/(a^2*((a*x - 1)/(a*x + 1) - 1)))","A",0
109,1,252,0,0.172650," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x,x, algorithm=""giac"")","\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right)}{a} + \frac{\sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} - \frac{\sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}{a} + \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} - \frac{2 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - 1 \right|}\right)}{a} - \frac{16 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a}\right)}"," ",0,"1/2*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4)))/a + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4)))/a + sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a - sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1)/a + 4*arctan(((a*x - 1)/(a*x + 1))^(1/4))/a + 2*log(((a*x - 1)/(a*x + 1))^(1/4) + 1)/a - 2*log(abs(((a*x - 1)/(a*x + 1))^(1/4) - 1))/a - 16*((a*x - 1)/(a*x + 1))^(1/4)/a)","A",0
110,1,204,0,0.176343," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x^2,x, algorithm=""giac"")","-\frac{1}{4} \, {\left(10 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 10 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 5 \, \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 5 \, \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 32 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \frac{8 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{\frac{a x - 1}{a x + 1} + 1}\right)} a"," ",0,"-1/4*(10*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 10*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 5*sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 5*sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 32*((a*x - 1)/(a*x + 1))^(1/4) - 8*((a*x - 1)/(a*x + 1))^(1/4)/((a*x - 1)/(a*x + 1) + 1))*a","A",0
111,1,243,0,0.179433," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x^3,x, algorithm=""giac"")","\frac{1}{16} \, {\left(50 \, \sqrt{2} a \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 50 \, \sqrt{2} a \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 25 \, \sqrt{2} a \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 25 \, \sqrt{2} a \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 128 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \frac{8 \, {\left(\frac{13 \, {\left(a x - 1\right)} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} + 9 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{2}}\right)} a"," ",0,"1/16*(50*sqrt(2)*a*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 50*sqrt(2)*a*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 25*sqrt(2)*a*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 25*sqrt(2)*a*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 128*a*((a*x - 1)/(a*x + 1))^(1/4) - 8*(13*(a*x - 1)*a*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) + 9*a*((a*x - 1)/(a*x + 1))^(1/4))/((a*x - 1)/(a*x + 1) + 1)^2)*a","A",0
112,1,291,0,0.188639," ","integrate(((a*x-1)/(a*x+1))^(5/4)/x^4,x, algorithm=""giac"")","-\frac{1}{96} \, {\left(330 \, \sqrt{2} a^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 330 \, \sqrt{2} a^{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}\right) + 165 \, \sqrt{2} a^{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 165 \, \sqrt{2} a^{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a x - 1}{a x + 1}} + 1\right) - 768 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} - \frac{8 \, {\left(\frac{174 \, {\left(a x - 1\right)} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{a x + 1} + \frac{137 \, {\left(a x - 1\right)}^{2} a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}{{\left(a x + 1\right)}^{2}} + 69 \, a^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)} a"," ",0,"-1/96*(330*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/4))) + 330*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/4))) + 165*sqrt(2)*a^2*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 165*sqrt(2)*a^2*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/4) + sqrt((a*x - 1)/(a*x + 1)) + 1) - 768*a^2*((a*x - 1)/(a*x + 1))^(1/4) - 8*(174*(a*x - 1)*a^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1) + 137*(a*x - 1)^2*a^2*((a*x - 1)/(a*x + 1))^(1/4)/(a*x + 1)^2 + 69*a^2*((a*x - 1)/(a*x + 1))^(1/4))/((a*x - 1)/(a*x + 1) + 1)^3)*a","A",0
113,1,215,0,0.186123," ","integrate(1/((-1+x)/(1+x))^(1/6)*x^2,x, algorithm=""giac"")","-\frac{19}{162} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right)}\right) - \frac{19}{162} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1\right)}\right) + \frac{\frac{8 \, {\left(x - 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{x + 1} - \frac{19 \, {\left(x - 1\right)}^{2} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{{\left(x + 1\right)}^{2}} - 61 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{27 \, {\left(\frac{x - 1}{x + 1} - 1\right)}^{3}} + \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| \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1 \right|}\right)"," ",0,"-19/162*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) + 1)) - 19/162*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) - 1)) + 1/27*(8*(x - 1)*((x - 1)/(x + 1))^(5/6)/(x + 1) - 19*(x - 1)^2*((x - 1)/(x + 1))^(5/6)/(x + 1)^2 - 61*((x - 1)/(x + 1))^(5/6))/((x - 1)/(x + 1) - 1)^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(abs(((x - 1)/(x + 1))^(1/6) - 1))","A",0
114,1,191,0,0.161209," ","integrate(1/((-1+x)/(1+x))^(1/6)*x,x, algorithm=""giac"")","-\frac{1}{18} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right)}\right) - \frac{1}{18} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1\right)}\right) - \frac{\frac{{\left(x - 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{x + 1} - 7 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{3 \, {\left(\frac{x - 1}{x + 1} - 1\right)}^{2}} + \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| \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1 \right|}\right)"," ",0,"-1/18*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) + 1)) - 1/18*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) - 1)) - 1/3*((x - 1)*((x - 1)/(x + 1))^(5/6)/(x + 1) - 7*((x - 1)/(x + 1))^(5/6))/((x - 1)/(x + 1) - 1)^2 + 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(abs(((x - 1)/(x + 1))^(1/6) - 1))","A",0
115,1,168,0,0.155190," ","integrate(1/((-1+x)/(1+x))^(1/6),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right)}\right) - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1\right)}\right) - \frac{2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{\frac{x - 1}{x + 1} - 1} + \frac{1}{6} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) - \frac{1}{6} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) + \frac{1}{3} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right) - \frac{1}{3} \, \log\left({\left| \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1 \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) + 1)) - 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) - 1)) - 2*((x - 1)/(x + 1))^(5/6)/((x - 1)/(x + 1) - 1) + 1/6*log(((x - 1)/(x + 1))^(1/3) + ((x - 1)/(x + 1))^(1/6) + 1) - 1/6*log(((x - 1)/(x + 1))^(1/3) - ((x - 1)/(x + 1))^(1/6) + 1) + 1/3*log(((x - 1)/(x + 1))^(1/6) + 1) - 1/3*log(abs(((x - 1)/(x + 1))^(1/6) - 1))","A",0
116,1,261,0,0.164807," ","integrate(1/((-1+x)/(1+x))^(1/6)/x,x, algorithm=""giac"")","-\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + 1\right)}\right) - \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1\right)}\right) - \frac{1}{2} \, \sqrt{3} \log\left(\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{1}{2} \, \sqrt{3} \log\left(-\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \arctan\left(\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \arctan\left(-\sqrt{3} + 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| \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} - 1 \right|}\right)"," ",0,"-sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) + 1)) - sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/6) - 1)) - 1/2*sqrt(3)*log(sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 1/2*sqrt(3)*log(-sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + arctan(sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + arctan(-sqrt(3) + 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(abs(((x - 1)/(x + 1))^(1/6) - 1))","A",0
117,1,152,0,0.154685," ","integrate(1/((-1+x)/(1+x))^(1/6)/x^2,x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \log\left(\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{1}{6} \, \sqrt{3} \log\left(-\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{\frac{x - 1}{x + 1} + 1} + \frac{1}{3} \, \arctan\left(\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{1}{3} \, \arctan\left(-\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{2}{3} \, \arctan\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right)"," ",0,"-1/6*sqrt(3)*log(sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 1/6*sqrt(3)*log(-sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 2*((x - 1)/(x + 1))^(5/6)/((x - 1)/(x + 1) + 1) + 1/3*arctan(sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 1/3*arctan(-sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 2/3*arctan(((x - 1)/(x + 1))^(1/6))","A",0
118,1,175,0,0.156431," ","integrate(1/((-1+x)/(1+x))^(1/6)/x^3,x, algorithm=""giac"")","-\frac{1}{36} \, \sqrt{3} \log\left(\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{1}{36} \, \sqrt{3} \log\left(-\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{\frac{{\left(x - 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{x + 1} + 7 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{3 \, {\left(\frac{x - 1}{x + 1} + 1\right)}^{2}} + \frac{1}{18} \, \arctan\left(\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{1}{18} \, \arctan\left(-\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{1}{9} \, \arctan\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right)"," ",0,"-1/36*sqrt(3)*log(sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 1/36*sqrt(3)*log(-sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 1/3*((x - 1)*((x - 1)/(x + 1))^(5/6)/(x + 1) + 7*((x - 1)/(x + 1))^(5/6))/((x - 1)/(x + 1) + 1)^2 + 1/18*arctan(sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 1/18*arctan(-sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 1/9*arctan(((x - 1)/(x + 1))^(1/6))","A",0
119,1,199,0,0.184736," ","integrate(1/((-1+x)/(1+x))^(1/6)/x^4,x, algorithm=""giac"")","-\frac{19}{324} \, \sqrt{3} \log\left(\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{19}{324} \, \sqrt{3} \log\left(-\sqrt{3} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) + \frac{\frac{8 \, {\left(x - 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{x + 1} + \frac{19 \, {\left(x - 1\right)}^{2} \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{{\left(x + 1\right)}^{2}} + 61 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{5}{6}}}{27 \, {\left(\frac{x - 1}{x + 1} + 1\right)}^{3}} + \frac{19}{162} \, \arctan\left(\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{19}{162} \, \arctan\left(-\sqrt{3} + 2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right) + \frac{19}{81} \, \arctan\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}\right)"," ",0,"-19/324*sqrt(3)*log(sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 19/324*sqrt(3)*log(-sqrt(3)*((x - 1)/(x + 1))^(1/6) + ((x - 1)/(x + 1))^(1/3) + 1) + 1/27*(8*(x - 1)*((x - 1)/(x + 1))^(5/6)/(x + 1) + 19*(x - 1)^2*((x - 1)/(x + 1))^(5/6)/(x + 1)^2 + 61*((x - 1)/(x + 1))^(5/6))/((x - 1)/(x + 1) + 1)^3 + 19/162*arctan(sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 19/162*arctan(-sqrt(3) + 2*((x - 1)/(x + 1))^(1/6)) + 19/81*arctan(((x - 1)/(x + 1))^(1/6))","A",0
120,1,144,0,0.178144," ","integrate(1/((-1+x)/(1+x))^(1/3)*x^2,x, algorithm=""giac"")","-\frac{22}{81} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right)}\right) + \frac{2 \, {\left(\frac{10 \, {\left(x - 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}}{x + 1} - \frac{11 \, {\left(x - 1\right)}^{2} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}}{{\left(x + 1\right)}^{2}} - 35 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}\right)}}{27 \, {\left(\frac{x - 1}{x + 1} - 1\right)}^{3}} + \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| \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-22/81*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) + 1)) + 2/27*(10*(x - 1)*((x - 1)/(x + 1))^(2/3)/(x + 1) - 11*(x - 1)^2*((x - 1)/(x + 1))^(2/3)/(x + 1)^2 - 35*((x - 1)/(x + 1))^(2/3))/((x - 1)/(x + 1) - 1)^3 + 11/81*log(((x - 1)/(x + 1))^(2/3) + ((x - 1)/(x + 1))^(1/3) + 1) - 22/81*log(abs(((x - 1)/(x + 1))^(1/3) - 1))","A",0
121,1,120,0,0.172193," ","integrate(1/((-1+x)/(1+x))^(1/3)*x,x, algorithm=""giac"")","-\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right)}\right) - \frac{2 \, {\left(\frac{{\left(x - 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}}{x + 1} - 4 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}\right)}}{3 \, {\left(\frac{x - 1}{x + 1} - 1\right)}^{2}} + \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| \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) + 1)) - 2/3*((x - 1)*((x - 1)/(x + 1))^(2/3)/(x + 1) - 4*((x - 1)/(x + 1))^(2/3))/((x - 1)/(x + 1) - 1)^2 + 1/9*log(((x - 1)/(x + 1))^(2/3) + ((x - 1)/(x + 1))^(1/3) + 1) - 2/9*log(abs(((x - 1)/(x + 1))^(1/3) - 1))","A",0
122,1,97,0,0.139387," ","integrate(1/((-1+x)/(1+x))^(1/3),x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right)}\right) - \frac{2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}}{\frac{x - 1}{x + 1} - 1} + \frac{1}{3} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} + \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) - \frac{2}{3} \, \log\left({\left| \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) + 1)) - 2*((x - 1)/(x + 1))^(2/3)/((x - 1)/(x + 1) - 1) + 1/3*log(((x - 1)/(x + 1))^(2/3) + ((x - 1)/(x + 1))^(1/3) + 1) - 2/3*log(abs(((x - 1)/(x + 1))^(1/3) - 1))","A",0
123,1,79,0,0.175495," ","integrate(1/((-1+x)/(1+x))^(1/3)/x,x, algorithm=""giac"")","\sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} + 1\right)}\right) + \frac{1}{2} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} + \frac{{\left(x - 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}}}{x + 1} + 1\right) - \log\left({\left| \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} - 1 \right|}\right)"," ",0,"sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(2/3) + 1)) + 1/2*log(((x - 1)/(x + 1))^(2/3) + (x - 1)*((x - 1)/(x + 1))^(1/3)/(x + 1) + 1) - log(abs(((x - 1)/(x + 1))^(2/3) - 1))","A",0
124,1,99,0,0.142858," ","integrate(1/((-1+x)/(1+x))^(1/3)/x^2,x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1\right)}\right) + \frac{2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}}{\frac{x - 1}{x + 1} + 1} + \frac{1}{3} \, \log\left(\left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}} - \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1\right) - \frac{2}{3} \, \log\left({\left| \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) - 1)) + 2*((x - 1)/(x + 1))^(2/3)/((x - 1)/(x + 1) + 1) + 1/3*log(((x - 1)/(x + 1))^(2/3) - ((x - 1)/(x + 1))^(1/3) + 1) - 2/3*log(abs(((x - 1)/(x + 1))^(1/3) + 1))","A",0
125,1,122,0,0.140150," ","integrate(1/((-1+x)/(1+x))^(1/3)/x^3,x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} - 1\right)}\right) + \frac{2 \, {\left(\frac{{\left(x - 1\right)} \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}}{x + 1} + 4 \, \left(\frac{x - 1}{x + 1}\right)^{\frac{2}{3}}\right)}}{3 \, {\left(\frac{x - 1}{x + 1} + 1\right)}^{2}} + \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| \left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*((x - 1)/(x + 1))^(1/3) - 1)) + 2/3*((x - 1)*((x - 1)/(x + 1))^(2/3)/(x + 1) + 4*((x - 1)/(x + 1))^(2/3))/((x - 1)/(x + 1) + 1)^2 + 1/9*log(((x - 1)/(x + 1))^(2/3) - ((x - 1)/(x + 1))^(1/3) + 1) - 2/9*log(abs(((x - 1)/(x + 1))^(1/3) + 1))","A",0
126,1,333,0,0.245011," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)*x^2,x, algorithm=""giac"")","-\frac{1}{768} \, a {\left(\frac{66 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right)}{a^{4}} + \frac{66 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right)}{a^{4}} - \frac{33 \, \sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} + \frac{33 \, \sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{4}} + \frac{132 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}{a^{4}} - \frac{66 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right)}{a^{4}} + \frac{66 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1 \right|}\right)}{a^{4}} - \frac{16 \, {\left(\frac{10 \, {\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}}{a x + 1} - \frac{33 \, {\left(a x - 1\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}}{{\left(a x + 1\right)}^{2}} - 105 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}\right)}}{a^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"-1/768*a*(66*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/8)))/a^4 + 66*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/8)))/a^4 - 33*sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 + 33*sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^4 + 132*arctan(((a*x - 1)/(a*x + 1))^(1/8))/a^4 - 66*log(((a*x - 1)/(a*x + 1))^(1/8) + 1)/a^4 + 66*log(abs(((a*x - 1)/(a*x + 1))^(1/8) - 1))/a^4 - 16*(10*(a*x - 1)*((a*x - 1)/(a*x + 1))^(7/8)/(a*x + 1) - 33*(a*x - 1)^2*((a*x - 1)/(a*x + 1))^(7/8)/(a*x + 1)^2 - 105*((a*x - 1)/(a*x + 1))^(7/8))/(a^4*((a*x - 1)/(a*x + 1) - 1)^3))","A",0
127,1,300,0,0.229789," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)*x,x, algorithm=""giac"")","-\frac{1}{64} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right)}{a^{3}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right)}{a^{3}} - \frac{\sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{3}} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}{a^{3}} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right)}{a^{3}} + \frac{2 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1 \right|}\right)}{a^{3}} + \frac{16 \, {\left(\frac{{\left(a x - 1\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}}{a x + 1} - 9 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}\right)}}{a^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{2}}\right)}"," ",0,"-1/64*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/8)))/a^3 + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/8)))/a^3 - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^3 + 4*arctan(((a*x - 1)/(a*x + 1))^(1/8))/a^3 - 2*log(((a*x - 1)/(a*x + 1))^(1/8) + 1)/a^3 + 2*log(abs(((a*x - 1)/(a*x + 1))^(1/8) - 1))/a^3 + 16*((a*x - 1)*((a*x - 1)/(a*x + 1))^(7/8)/(a*x + 1) - 9*((a*x - 1)/(a*x + 1))^(7/8))/(a^3*((a*x - 1)/(a*x + 1) - 1)^2))","A",0
128,1,269,0,0.206602," ","integrate(1/((a*x-1)/(a*x+1))^(1/8),x, algorithm=""giac"")","-\frac{1}{8} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right)}{a^{2}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right)}{a^{2}} - \frac{\sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a^{2}} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}{a^{2}} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right)}{a^{2}} + \frac{2 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1 \right|}\right)}{a^{2}} + \frac{16 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"-1/8*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/8)))/a^2 + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/8)))/a^2 - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/a^2 + 4*arctan(((a*x - 1)/(a*x + 1))^(1/8))/a^2 - 2*log(((a*x - 1)/(a*x + 1))^(1/8) + 1)/a^2 + 2*log(abs(((a*x - 1)/(a*x + 1))^(1/8) - 1))/a^2 + 16*((a*x - 1)/(a*x + 1))^(7/8)/(a^2*((a*x - 1)/(a*x + 1) - 1)))","A",0
129,1,660,0,1.849252," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)/x,x, algorithm=""giac"")","-\frac{1}{2} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right)}{a} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}\right)}{a} - \frac{\sqrt{2} \log\left(\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} + \frac{\sqrt{2} \log\left(-\sqrt{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}} + 1\right)}{a} + \frac{4 \, \arctan\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}\right)}{a} - \frac{2 \, \log\left(\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} + 1\right)}{a} + \frac{2 \, \log\left({\left| \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}} - 1 \right|}\right)}{a} - \frac{4 \, \arctan\left(\frac{\sqrt{\sqrt{2} + 2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2}}\right)}{a \sqrt{2 \, \sqrt{2} + 4}} - \frac{4 \, \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2}}\right)}{a \sqrt{2 \, \sqrt{2} + 4}} - \frac{4 \, \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2}}\right)}{a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{4 \, \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2}}\right)}{a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{2 \, \log\left(\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)}{a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{2 \, \log\left(-\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)}{a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{2 \, \log\left(\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)}{a \sqrt{2 \, \sqrt{2} + 4}} - \frac{2 \, \log\left(-\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)}{a \sqrt{2 \, \sqrt{2} + 4}}\right)}"," ",0,"-1/2*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*((a*x - 1)/(a*x + 1))^(1/8)))/a + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*((a*x - 1)/(a*x + 1))^(1/8)))/a - sqrt(2)*log(sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/a + sqrt(2)*log(-sqrt(2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/a + 4*arctan(((a*x - 1)/(a*x + 1))^(1/8))/a - 2*log(((a*x - 1)/(a*x + 1))^(1/8) + 1)/a + 2*log(abs(((a*x - 1)/(a*x + 1))^(1/8) - 1))/a - 4*arctan((sqrt(sqrt(2) + 2) + 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(-sqrt(2) + 2))/(a*sqrt(2*sqrt(2) + 4)) - 4*arctan(-(sqrt(sqrt(2) + 2) - 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(-sqrt(2) + 2))/(a*sqrt(2*sqrt(2) + 4)) - 4*arctan((sqrt(-sqrt(2) + 2) + 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(sqrt(2) + 2))/(a*sqrt(-2*sqrt(2) + 4)) - 4*arctan(-(sqrt(-sqrt(2) + 2) - 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(sqrt(2) + 2))/(a*sqrt(-2*sqrt(2) + 4)) + 2*log(sqrt(sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/(a*sqrt(-2*sqrt(2) + 4)) - 2*log(-sqrt(sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/(a*sqrt(-2*sqrt(2) + 4)) + 2*log(sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/(a*sqrt(2*sqrt(2) + 4)) - 2*log(-sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1)/(a*sqrt(2*sqrt(2) + 4)))","A",0
130,1,432,0,0.398717," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)/x^2,x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2}}\right) + 2 \, \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2}}\right) + 2 \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2}}\right) + 2 \, \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2}}\right) - \sqrt{\sqrt{2} + 2} \log\left(\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) + \sqrt{\sqrt{2} + 2} \log\left(-\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) - \sqrt{-\sqrt{2} + 2} \log\left(\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) + \sqrt{-\sqrt{2} + 2} \log\left(-\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{16 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}}{\frac{a x - 1}{a x + 1} + 1}\right)} a"," ",0,"1/8*(2*sqrt(-sqrt(2) + 2)*arctan((sqrt(sqrt(2) + 2) + 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(-sqrt(2) + 2)) + 2*sqrt(-sqrt(2) + 2)*arctan(-(sqrt(sqrt(2) + 2) - 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(-sqrt(2) + 2)) + 2*sqrt(sqrt(2) + 2)*arctan((sqrt(-sqrt(2) + 2) + 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(sqrt(2) + 2)) + 2*sqrt(sqrt(2) + 2)*arctan(-(sqrt(-sqrt(2) + 2) - 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(sqrt(2) + 2)) - sqrt(sqrt(2) + 2)*log(sqrt(sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + sqrt(sqrt(2) + 2)*log(-sqrt(sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) - sqrt(-sqrt(2) + 2)*log(sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + sqrt(-sqrt(2) + 2)*log(-sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + 16*((a*x - 1)/(a*x + 1))^(7/8)/((a*x - 1)/(a*x + 1) + 1))*a","A",0
131,1,473,0,0.465476," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)/x^3,x, algorithm=""giac"")","\frac{1}{64} \, {\left(2 \, a \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2}}\right) + 2 \, a \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2}}\right) + 2 \, a \sqrt{\sqrt{2} + 2} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} + 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2}}\right) + 2 \, a \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} - 2 \, \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2}}\right) - a \sqrt{\sqrt{2} + 2} \log\left(\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) + a \sqrt{\sqrt{2} + 2} \log\left(-\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) - a \sqrt{-\sqrt{2} + 2} \log\left(\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) + a \sqrt{-\sqrt{2} + 2} \log\left(-\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{16 \, {\left(\frac{{\left(a x - 1\right)} a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}}{a x + 1} + 9 \, a \left(\frac{a x - 1}{a x + 1}\right)^{\frac{7}{8}}\right)}}{{\left(\frac{a x - 1}{a x + 1} + 1\right)}^{2}}\right)} a"," ",0,"1/64*(2*a*sqrt(-sqrt(2) + 2)*arctan((sqrt(sqrt(2) + 2) + 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(-sqrt(2) + 2)) + 2*a*sqrt(-sqrt(2) + 2)*arctan(-(sqrt(sqrt(2) + 2) - 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(-sqrt(2) + 2)) + 2*a*sqrt(sqrt(2) + 2)*arctan((sqrt(-sqrt(2) + 2) + 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(sqrt(2) + 2)) + 2*a*sqrt(sqrt(2) + 2)*arctan(-(sqrt(-sqrt(2) + 2) - 2*((a*x - 1)/(a*x + 1))^(1/8))/sqrt(sqrt(2) + 2)) - a*sqrt(sqrt(2) + 2)*log(sqrt(sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + a*sqrt(sqrt(2) + 2)*log(-sqrt(sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) - a*sqrt(-sqrt(2) + 2)*log(sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + a*sqrt(-sqrt(2) + 2)*log(-sqrt(-sqrt(2) + 2)*((a*x - 1)/(a*x + 1))^(1/8) + ((a*x - 1)/(a*x + 1))^(1/4) + 1) + 16*((a*x - 1)*a*((a*x - 1)/(a*x + 1))^(7/8)/(a*x + 1) + 9*a*((a*x - 1)/(a*x + 1))^(7/8))/((a*x - 1)/(a*x + 1) + 1)^2)*a","A",0
132,0,0,0,0.000000," ","integrate(1/(a*x-1)^2*(a*x+1)^2*x^m,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{2} x^{m}}{{\left(a x - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^2*x^m/(a*x - 1)^2, x)","F",0
133,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^m,x, algorithm=""giac"")","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
134,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x^m,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{m}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/(a*x - 1), x)","F",0
135,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m,x, algorithm=""giac"")","\int \frac{x^{m}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^m/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
136,0,0,0,0.000000," ","integrate(x^m*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int x^{m} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(x^m*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
137,0,0,0,0.000000," ","integrate(x^m*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\int \frac{{\left(a x - 1\right)} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*x^m/(a*x + 1), x)","F",0
138,-2,0,0,0.000000," ","integrate(x^m*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
139,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(5/4)*x^m,x, algorithm=""giac"")","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^m/((a*x - 1)/(a*x + 1))^(5/4), x)","F",0
140,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/4)*x^m,x, algorithm=""giac"")","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^m/((a*x - 1)/(a*x + 1))^(3/4), x)","F",0
141,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/4)*x^m,x, algorithm=""giac"")","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^m/((a*x - 1)/(a*x + 1))^(1/4), x)","F",0
142,0,0,0,0.000000," ","integrate(x^m*((a*x-1)/(a*x+1))^(1/4),x, algorithm=""giac"")","\int x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{4}}\,{d x}"," ",0,"integrate(x^m*((a*x - 1)/(a*x + 1))^(1/4), x)","F",0
143,0,0,0,0.000000," ","integrate(x^m*((a*x-1)/(a*x+1))^(3/4),x, algorithm=""giac"")","\int x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{4}}\,{d x}"," ",0,"integrate(x^m*((a*x - 1)/(a*x + 1))^(3/4), x)","F",0
144,0,0,0,0.000000," ","integrate(x^m*((a*x-1)/(a*x+1))^(5/4),x, algorithm=""giac"")","\int x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{5}{4}}\,{d x}"," ",0,"integrate(x^m*((a*x - 1)/(a*x + 1))^(5/4), x)","F",0
145,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/3)*x^m,x, algorithm=""giac"")","\int \frac{x^{m}}{\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^m/((x - 1)/(x + 1))^(1/3), x)","F",0
146,0,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/6)*x^m,x, algorithm=""giac"")","\int \frac{x^{m}}{\left(\frac{x - 1}{x + 1}\right)^{\frac{1}{6}}}\,{d x}"," ",0,"integrate(x^m/((x - 1)/(x + 1))^(1/6), x)","F",0
147,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/8)*x^m,x, algorithm=""giac"")","\int \frac{x^{m}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{8}}}\,{d x}"," ",0,"integrate(x^m/((a*x - 1)/(a*x + 1))^(1/8), x)","F",0
148,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*x^m,x, algorithm=""giac"")","\int x^{m} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^m*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
149,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*x^2,x, algorithm=""giac"")","\int x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^2*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
150,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*x,x, algorithm=""giac"")","\int x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
151,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x)),x, algorithm=""giac"")","\int \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
152,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/x,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{x}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/x, x)","F",0
153,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/x^2,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{x^{2}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/x^2, x)","F",0
154,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/x^3,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{x^{3}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/x^3, x)","F",0
155,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/x^4,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{x^{4}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/x^4, x)","F",0
156,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/x^5,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{x^{5}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/x^5, x)","F",0
157,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^p,x, algorithm=""giac"")","\int \frac{{\left(-a c x + c\right)}^{p}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a*c*x + c)^p/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
158,1,216,0,0.177851," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^4,x, algorithm=""giac"")","\frac{1}{120} \, a c^{4} {\left(\frac{105 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{105 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(\frac{490 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{896 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + \frac{790 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + \frac{105 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} - 105 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{5}}\right)}"," ",0,"1/120*a*c^4*(105*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 105*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 2*(490*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 896*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 790*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 105*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 - 105*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^5))","A",0
159,1,185,0,0.174894," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{1}{24} \, a c^{3} {\left(\frac{15 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{15 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(\frac{55 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{73 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} - \frac{15 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} - 15 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{4}}\right)}"," ",0,"1/24*a*c^3*(15*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 15*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 2*(55*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 73*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 - 15*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 - 15*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^4))","B",0
160,1,154,0,0.148145," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^2,x, algorithm=""giac"")","\frac{1}{6} \, a c^{2} {\left(\frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(\frac{8 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} - 3 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"1/6*a*c^2*(3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 2*(8*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 3*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 - 3*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^3))","B",0
161,1,154,0,0.195567," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c),x, algorithm=""giac"")","\frac{1}{4} \, a c {\left(\frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}} + 2\right)}{a^{2}} - \frac{\log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} + \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}} - 2 \right|}\right)}{a^{2}} - \frac{4 \, {\left(\sqrt{\frac{a x - 1}{a x + 1}} + \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}}\right)}}{{\left({\left(\sqrt{\frac{a x - 1}{a x + 1}} + \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}}\right)}^{2} - 4\right)} a^{2}}\right)}"," ",0,"1/4*a*c*(log(sqrt((a*x - 1)/(a*x + 1)) + 1/sqrt((a*x - 1)/(a*x + 1)) + 2)/a^2 - log(abs(sqrt((a*x - 1)/(a*x + 1)) + 1/sqrt((a*x - 1)/(a*x + 1)) - 2))/a^2 - 4*(sqrt((a*x - 1)/(a*x + 1)) + 1/sqrt((a*x - 1)/(a*x + 1)))/(((sqrt((a*x - 1)/(a*x + 1)) + 1/sqrt((a*x - 1)/(a*x + 1)))^2 - 4)*a^2))","B",0
162,1,79,0,0.178110," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c),x, algorithm=""giac"")","-a {\left(\frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{\log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c} - \frac{2}{a^{2} c \sqrt{\frac{a x - 1}{a x + 1}}}\right)}"," ",0,"-a*(log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c) - 2/(a^2*c*sqrt((a*x - 1)/(a*x + 1))))","A",0
163,1,35,0,0.127350," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{a x + 1}{3 \, {\left(a x - 1\right)} a c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"-1/3*(a*x + 1)/((a*x - 1)*a*c^2*sqrt((a*x - 1)/(a*x + 1)))","A",0
164,1,53,0,0.132113," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{{\left(a x + 1\right)}^{2} {\left(\frac{5 \, {\left(a x - 1\right)}}{a x + 1} - 3\right)}}{30 \, {\left(a x - 1\right)}^{2} a c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"-1/30*(a*x + 1)^2*(5*(a*x - 1)/(a*x + 1) - 3)/((a*x - 1)^2*a*c^3*sqrt((a*x - 1)/(a*x + 1)))","A",0
165,1,69,0,0.137743," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^4,x, algorithm=""giac"")","\frac{{\left(a x + 1\right)}^{3} {\left(\frac{42 \, {\left(a x - 1\right)}}{a x + 1} - \frac{35 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 15\right)}}{420 \, {\left(a x - 1\right)}^{3} a c^{4} \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"1/420*(a*x + 1)^3*(42*(a*x - 1)/(a*x + 1) - 35*(a*x - 1)^2/(a*x + 1)^2 - 15)/((a*x - 1)^3*a*c^4*sqrt((a*x - 1)/(a*x + 1)))","A",0
166,1,85,0,0.158597," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^5,x, algorithm=""giac"")","-\frac{{\left(a x + 1\right)}^{4} {\left(\frac{135 \, {\left(a x - 1\right)}}{a x + 1} - \frac{189 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{105 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 35\right)}}{2520 \, {\left(a x - 1\right)}^{4} a c^{5} \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"-1/2520*(a*x + 1)^4*(135*(a*x - 1)/(a*x + 1) - 189*(a*x - 1)^2/(a*x + 1)^2 + 105*(a*x - 1)^3/(a*x + 1)^3 - 35)/((a*x - 1)^4*a*c^5*sqrt((a*x - 1)/(a*x + 1)))","A",0
167,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a c x + c\right)}^{p}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(-a*c*x + c)^p/(a*x - 1), x)","F",0
168,1,60,0,0.120908," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^5,x, algorithm=""giac"")","-\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
169,1,37,0,0.137007," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^4,x, algorithm=""giac"")","\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
170,1,38,0,0.140806," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^3,x, algorithm=""giac"")","-\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
171,1,18,0,0.134199," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^2,x, algorithm=""giac"")","\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
172,1,12,0,0.120158," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c),x, algorithm=""giac"")","-\frac{1}{2} \, a c x^{2} - c x"," ",0,"-1/2*a*c*x^2 - c*x","A",0
173,1,31,0,0.126912," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c),x, algorithm=""giac"")","-\frac{\log\left({\left| a x - 1 \right|}\right)}{a c} + \frac{2}{{\left(a x - 1\right)} a c}"," ",0,"-log(abs(a*x - 1))/(a*c) + 2/((a*x - 1)*a*c)","A",0
174,1,34,0,0.136567," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{1}{{\left(a c x - c\right)}^{2} a} - \frac{1}{{\left(a c x - c\right)} a c}"," ",0,"-1/((a*c*x - c)^2*a) - 1/((a*c*x - c)*a*c)","B",0
175,1,21,0,0.136285," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{3 \, a x + 1}{6 \, {\left(a x - 1\right)}^{3} a c^{3}}"," ",0,"1/6*(3*a*x + 1)/((a*x - 1)^3*a*c^3)","A",0
176,1,21,0,0.138691," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{2 \, a x + 1}{6 \, {\left(a x - 1\right)}^{4} a c^{4}}"," ",0,"-1/6*(2*a*x + 1)/((a*x - 1)^4*a*c^4)","A",0
177,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^p,x, algorithm=""giac"")","\int \frac{{\left(-a c x + c\right)}^{p}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a*c*x + c)^p/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
178,1,216,0,0.184952," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{1}{40} \, a c^{4} {\left(\frac{15 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{15 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(\frac{70 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{128 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} - \frac{70 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + \frac{15 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} - 15 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{5}}\right)}"," ",0,"-1/40*a*c^4*(15*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 15*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 2*(70*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 128*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 - 70*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 15*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 - 15*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^5))","B",0
179,1,196,0,0.180019," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{1}{16} \, a c^{3} {\left(\frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}} + 2\right)}{a^{2}} - \frac{3 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} + \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}} - 2 \right|}\right)}{a^{2}} - \frac{4 \, {\left(3 \, {\left(\sqrt{\frac{a x - 1}{a x + 1}} + \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}}\right)}^{3} - 20 \, \sqrt{\frac{a x - 1}{a x + 1}} - \frac{20}{\sqrt{\frac{a x - 1}{a x + 1}}}\right)}}{{\left({\left(\sqrt{\frac{a x - 1}{a x + 1}} + \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}}\right)}^{2} - 4\right)}^{2} a^{2}}\right)}"," ",0,"-1/16*a*c^3*(3*log(sqrt((a*x - 1)/(a*x + 1)) + 1/sqrt((a*x - 1)/(a*x + 1)) + 2)/a^2 - 3*log(abs(sqrt((a*x - 1)/(a*x + 1)) + 1/sqrt((a*x - 1)/(a*x + 1)) - 2))/a^2 - 4*(3*(sqrt((a*x - 1)/(a*x + 1)) + 1/sqrt((a*x - 1)/(a*x + 1)))^3 - 20*sqrt((a*x - 1)/(a*x + 1)) - 20/sqrt((a*x - 1)/(a*x + 1)))/(((sqrt((a*x - 1)/(a*x + 1)) + 1/sqrt((a*x - 1)/(a*x + 1)))^2 - 4)^2*a^2))","B",0
180,1,154,0,0.182277," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{1}{6} \, a c^{2} {\left(\frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(\frac{8 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + 3 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"-1/6*a*c^2*(3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 2*(8*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 3*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 3*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^3))","B",0
181,1,121,0,0.171640," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c),x, algorithm=""giac"")","-\frac{1}{2} \, a c {\left(\frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(\frac{3 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - 5 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{2}}\right)}"," ",0,"-1/2*a*c*(3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 2*(3*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 5*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^2))","B",0
182,1,108,0,0.149728," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c),x, algorithm=""giac"")","-\frac{1}{3} \, a {\left(\frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{3 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c} - \frac{2 \, {\left(a x + 1\right)} {\left(\frac{3 \, {\left(a x - 1\right)}}{a x + 1} + 1\right)}}{{\left(a x - 1\right)} a^{2} c \sqrt{\frac{a x - 1}{a x + 1}}}\right)}"," ",0,"-1/3*a*(3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - 3*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c) - 2*(a*x + 1)*(3*(a*x - 1)/(a*x + 1) + 1)/((a*x - 1)*a^2*c*sqrt((a*x - 1)/(a*x + 1))))","A",0
183,1,37,0,0.164939," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{{\left(a x + 1\right)}^{2}}{5 \, {\left(a x - 1\right)}^{2} a c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"-1/5*(a*x + 1)^2/((a*x - 1)^2*a*c^2*sqrt((a*x - 1)/(a*x + 1)))","A",0
184,1,53,0,0.159463," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{{\left(a x + 1\right)}^{3} {\left(\frac{7 \, {\left(a x - 1\right)}}{a x + 1} - 5\right)}}{70 \, {\left(a x - 1\right)}^{3} a c^{3} \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"-1/70*(a*x + 1)^3*(7*(a*x - 1)/(a*x + 1) - 5)/((a*x - 1)^3*a*c^3*sqrt((a*x - 1)/(a*x + 1)))","A",0
185,1,69,0,0.144502," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^4,x, algorithm=""giac"")","\frac{{\left(a x + 1\right)}^{4} {\left(\frac{90 \, {\left(a x - 1\right)}}{a x + 1} - \frac{63 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 35\right)}}{1260 \, {\left(a x - 1\right)}^{4} a c^{4} \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"1/1260*(a*x + 1)^4*(90*(a*x - 1)/(a*x + 1) - 63*(a*x - 1)^2/(a*x + 1)^2 - 35)/((a*x - 1)^4*a*c^4*sqrt((a*x - 1)/(a*x + 1)))","A",0
186,1,85,0,0.163765," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^5,x, algorithm=""giac"")","-\frac{{\left(a x + 1\right)}^{5} {\left(\frac{385 \, {\left(a x - 1\right)}}{a x + 1} - \frac{495 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{231 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 105\right)}}{9240 \, {\left(a x - 1\right)}^{5} a c^{5} \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"-1/9240*(a*x + 1)^5*(385*(a*x - 1)/(a*x + 1) - 495*(a*x - 1)^2/(a*x + 1)^2 + 231*(a*x - 1)^3/(a*x + 1)^3 - 105)/((a*x - 1)^5*a*c^5*sqrt((a*x - 1)/(a*x + 1)))","A",0
187,0,0,0,0.000000," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{2} {\left(-a c x + c\right)}^{p}}{{\left(a x - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^2*(-a*c*x + c)^p/(a*x - 1)^2, x)","F",0
188,1,42,0,0.126576," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^5,x, algorithm=""giac"")","-\frac{{\left(5 \, c^{5} + \frac{24 \, c^{5}}{a x - 1} + \frac{30 \, c^{5}}{{\left(a x - 1\right)}^{2}}\right)} {\left(a x - 1\right)}^{6}}{30 \, a}"," ",0,"-1/30*(5*c^5 + 24*c^5/(a*x - 1) + 30*c^5/(a*x - 1)^2)*(a*x - 1)^6/a","A",0
189,1,42,0,0.126888," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^4,x, algorithm=""giac"")","\frac{{\left(3 \, c^{4} + \frac{15 \, c^{4}}{a x - 1} + \frac{20 \, c^{4}}{{\left(a x - 1\right)}^{2}}\right)} {\left(a x - 1\right)}^{5}}{15 \, a}"," ",0,"1/15*(3*c^4 + 15*c^4/(a*x - 1) + 20*c^4/(a*x - 1)^2)*(a*x - 1)^5/a","A",0
190,1,42,0,0.138744," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{{\left(3 \, c^{3} + \frac{16 \, c^{3}}{a x - 1} + \frac{24 \, c^{3}}{{\left(a x - 1\right)}^{2}}\right)} {\left(a x - 1\right)}^{4}}{12 \, a}"," ",0,"-1/12*(3*c^3 + 16*c^3/(a*x - 1) + 24*c^3/(a*x - 1)^2)*(a*x - 1)^4/a","A",0
191,1,40,0,0.137373," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^2,x, algorithm=""giac"")","\frac{{\left(c^{2} + \frac{6 \, c^{2}}{a x - 1} + \frac{12 \, c^{2}}{{\left(a x - 1\right)}^{2}}\right)} {\left(a x - 1\right)}^{3}}{3 \, a}"," ",0,"1/3*(c^2 + 6*c^2/(a*x - 1) + 12*c^2/(a*x - 1)^2)*(a*x - 1)^3/a","B",0
192,1,50,0,0.144596," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c),x, algorithm=""giac"")","-\frac{{\left(a x - 1\right)}^{2} {\left(c + \frac{8 \, c}{a x - 1}\right)}}{2 \, a} + \frac{4 \, c \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a}"," ",0,"-1/2*(a*x - 1)^2*(c + 8*c/(a*x - 1))/a + 4*c*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a","A",0
193,1,57,0,0.136360," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c),x, algorithm=""giac"")","\frac{\log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a c} + \frac{2 \, {\left(\frac{2 \, a c}{a x - 1} + \frac{a c}{{\left(a x - 1\right)}^{2}}\right)}}{a^{2} c^{2}}"," ",0,"log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/(a*c) + 2*(2*a*c/(a*x - 1) + a*c/(a*x - 1)^2)/(a^2*c^2)","A",0
194,1,50,0,0.137653," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{2}{{\left(a c x - c\right)}^{2} a} - \frac{1}{{\left(a c x - c\right)} a c} - \frac{4 \, c}{3 \, {\left(a c x - c\right)}^{3} a}"," ",0,"-2/((a*c*x - c)^2*a) - 1/((a*c*x - c)*a*c) - 4/3*c/((a*c*x - c)^3*a)","B",0
195,1,42,0,0.143149," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{\frac{3}{{\left(a x - 1\right)}^{2} a} + \frac{8}{{\left(a x - 1\right)}^{3} a} + \frac{6}{{\left(a x - 1\right)}^{4} a}}{6 \, c^{3}}"," ",0,"1/6*(3/((a*x - 1)^2*a) + 8/((a*x - 1)^3*a) + 6/((a*x - 1)^4*a))/c^3","A",0
196,1,42,0,0.139533," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{\frac{5}{{\left(a x - 1\right)}^{3} a} + \frac{15}{{\left(a x - 1\right)}^{4} a} + \frac{12}{{\left(a x - 1\right)}^{5} a}}{15 \, c^{4}}"," ",0,"-1/15*(5/((a*x - 1)^3*a) + 15/((a*x - 1)^4*a) + 12/((a*x - 1)^5*a))/c^4","A",0
197,0,0,0,0.000000," ","integrate((-a*c*x+c)^p*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int {\left(-a c x + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a*c*x + c)^p*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
198,1,109,0,0.162876," ","integrate((-a*c*x+c)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{35 \, c^{3} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{8 \, {\left| a \right|}} + \frac{1}{24} \, \sqrt{a^{2} x^{2} - 1} {\left(\frac{160 \, c^{3} \mathrm{sgn}\left(a x + 1\right)}{a} - {\left(81 \, c^{3} \mathrm{sgn}\left(a x + 1\right) + 2 \, {\left(3 \, a^{2} c^{3} x \mathrm{sgn}\left(a x + 1\right) - 16 \, a c^{3} \mathrm{sgn}\left(a x + 1\right)\right)} x\right)} x\right)}"," ",0,"35/8*c^3*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + 1/24*sqrt(a^2*x^2 - 1)*(160*c^3*sgn(a*x + 1)/a - (81*c^3*sgn(a*x + 1) + 2*(3*a^2*c^3*x*sgn(a*x + 1) - 16*a*c^3*sgn(a*x + 1))*x)*x)","A",0
199,1,90,0,0.175475," ","integrate((-a*c*x+c)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{5 \, c^{2} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{2 \, {\left| a \right|}} + \frac{1}{6} \, \sqrt{a^{2} x^{2} - 1} {\left({\left(2 \, a c^{2} x \mathrm{sgn}\left(a x + 1\right) - 9 \, c^{2} \mathrm{sgn}\left(a x + 1\right)\right)} x + \frac{22 \, c^{2} \mathrm{sgn}\left(a x + 1\right)}{a}\right)}"," ",0,"5/2*c^2*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + 1/6*sqrt(a^2*x^2 - 1)*((2*a*c^2*x*sgn(a*x + 1) - 9*c^2*sgn(a*x + 1))*x + 22*c^2*sgn(a*x + 1)/a)","A",0
200,1,68,0,0.145719," ","integrate((-a*c*x+c)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{3 \, c \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{2 \, {\left| a \right|}} - \frac{1}{2} \, \sqrt{a^{2} x^{2} - 1} {\left(c x \mathrm{sgn}\left(a x + 1\right) - \frac{4 \, c \mathrm{sgn}\left(a x + 1\right)}{a}\right)}"," ",0,"3/2*c*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) - 1/2*sqrt(a^2*x^2 - 1)*(c*x*sgn(a*x + 1) - 4*c*sgn(a*x + 1)/a)","A",0
201,1,33,0,0.134836," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c),x, algorithm=""giac"")","\frac{\log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{c {\left| a \right|}}"," ",0,"log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/(c*abs(a))","A",0
202,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^2,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
203,1,45,0,0.197835," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)} x - 1\right)}}{3 \, {\left({\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)} x - 1\right)}^{3} a c^{3}}"," ",0,"2/3*(3*(a + sqrt(a^2 - 1/x^2))*x - 1)/(((a + sqrt(a^2 - 1/x^2))*x - 1)^3*a*c^3)","A",0
204,1,65,0,0.206131," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{4 \, {\left(10 \, {\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)}^{2} x^{2} - 5 \, {\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)} x + 1\right)}}{15 \, {\left({\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)} x - 1\right)}^{5} a c^{4}}"," ",0,"-4/15*(10*(a + sqrt(a^2 - 1/x^2))^2*x^2 - 5*(a + sqrt(a^2 - 1/x^2))*x + 1)/(((a + sqrt(a^2 - 1/x^2))*x - 1)^5*a*c^4)","A",0
205,1,85,0,0.302733," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^5,x, algorithm=""giac"")","\frac{4 \, {\left(35 \, {\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)}^{3} x^{3} - 21 \, {\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)}^{2} x^{2} + 7 \, {\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)} x - 1\right)}}{35 \, {\left({\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)} x - 1\right)}^{7} a c^{5}}"," ",0,"4/35*(35*(a + sqrt(a^2 - 1/x^2))^3*x^3 - 21*(a + sqrt(a^2 - 1/x^2))^2*x^2 + 7*(a + sqrt(a^2 - 1/x^2))*x - 1)/(((a + sqrt(a^2 - 1/x^2))*x - 1)^7*a*c^5)","A",0
206,0,0,0,0.000000," ","integrate((-a*c*x+c)^p*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\int \frac{{\left(a x - 1\right)} {\left(-a c x + c\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(-a*c*x + c)^p/(a*x + 1), x)","F",0
207,1,75,0,0.143501," ","integrate((-a*c*x+c)^4*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{32 \, c^{4} \log\left({\left| a x + 1 \right|}\right)}{a} + \frac{6 \, a^{9} c^{4} x^{5} - 45 \, a^{8} c^{4} x^{4} + 160 \, a^{7} c^{4} x^{3} - 390 \, a^{6} c^{4} x^{2} + 930 \, a^{5} c^{4} x}{30 \, a^{5}}"," ",0,"-32*c^4*log(abs(a*x + 1))/a + 1/30*(6*a^9*c^4*x^5 - 45*a^8*c^4*x^4 + 160*a^7*c^4*x^3 - 390*a^6*c^4*x^2 + 930*a^5*c^4*x)/a^5","A",0
208,1,64,0,0.137196," ","integrate((-a*c*x+c)^3*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{16 \, c^{3} \log\left({\left| a x + 1 \right|}\right)}{a} - \frac{3 \, a^{7} c^{3} x^{4} - 20 \, a^{6} c^{3} x^{3} + 66 \, a^{5} c^{3} x^{2} - 180 \, a^{4} c^{3} x}{12 \, a^{4}}"," ",0,"-16*c^3*log(abs(a*x + 1))/a - 1/12*(3*a^7*c^3*x^4 - 20*a^6*c^3*x^3 + 66*a^5*c^3*x^2 - 180*a^4*c^3*x)/a^4","A",0
209,1,52,0,0.127700," ","integrate((-a*c*x+c)^2*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{8 \, c^{2} \log\left({\left| a x + 1 \right|}\right)}{a} + \frac{a^{5} c^{2} x^{3} - 6 \, a^{4} c^{2} x^{2} + 21 \, a^{3} c^{2} x}{3 \, a^{3}}"," ",0,"-8*c^2*log(abs(a*x + 1))/a + 1/3*(a^5*c^2*x^3 - 6*a^4*c^2*x^2 + 21*a^3*c^2*x)/a^3","A",0
210,1,35,0,0.132731," ","integrate((-a*c*x+c)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{4 \, c \log\left({\left| a x + 1 \right|}\right)}{a} - \frac{a^{3} c x^{2} - 6 \, a^{2} c x}{2 \, a^{2}}"," ",0,"-4*c*log(abs(a*x + 1))/a - 1/2*(a^3*c*x^2 - 6*a^2*c*x)/a^2","A",0
211,1,15,0,0.123335," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c),x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{a c}"," ",0,"-log(abs(a*x + 1))/(a*c)","A",0
212,1,25,0,0.142750," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| -\frac{2 \, c}{a c x - c} - 1 \right|}\right)}{2 \, a c^{2}}"," ",0,"-1/2*log(abs(-2*c/(a*c*x - c) - 1))/(a*c^2)","B",0
213,1,46,0,0.146114," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{4 \, a c^{3}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{4 \, a c^{3}} + \frac{1}{2 \, {\left(a x - 1\right)} a c^{3}}"," ",0,"-1/4*log(abs(a*x + 1))/(a*c^3) + 1/4*log(abs(a*x - 1))/(a*c^3) + 1/2/((a*x - 1)*a*c^3)","A",0
214,1,51,0,0.138154," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a c^{4}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{8 \, a c^{4}} + \frac{a x - 2}{4 \, {\left(a x - 1\right)}^{2} a c^{4}}"," ",0,"-1/8*log(abs(a*x + 1))/(a*c^4) + 1/8*log(abs(a*x - 1))/(a*c^4) + 1/4*(a*x - 2)/((a*x - 1)^2*a*c^4)","A",0
215,1,89,0,0.136473," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^5,x, algorithm=""giac"")","-\frac{\log\left({\left| -\frac{2 \, c}{a c x - c} - 1 \right|}\right)}{16 \, a c^{5}} + \frac{\frac{3 \, a^{2} c^{2}}{a c x - c} - \frac{3 \, a^{2} c^{3}}{{\left(a c x - c\right)}^{2}} + \frac{4 \, a^{2} c^{4}}{{\left(a c x - c\right)}^{3}}}{24 \, a^{3} c^{6}}"," ",0,"-1/16*log(abs(-2*c/(a*c*x - c) - 1))/(a*c^5) + 1/24*(3*a^2*c^2/(a*c*x - c) - 3*a^2*c^3/(a*c*x - c)^2 + 4*a^2*c^4/(a*c*x - c)^3)/(a^3*c^6)","A",0
216,-2,0,0,0.000000," ","integrate((-a*c*x+c)^p*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
217,0,0,0,0.000000," ","integrate((-a*c*x+c)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
218,0,0,0,0.000000," ","integrate((-a*c*x+c)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
219,0,0,0,0.000000," ","integrate((-a*c*x+c)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
220,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
221,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^2,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
222,1,22,0,0.144509," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{x \mathrm{sgn}\left(a x + 1\right)}{\sqrt{a^{2} x^{2} - 1} c^{3}}"," ",0,"x*sgn(a*x + 1)/(sqrt(a^2*x^2 - 1)*c^3)","A",0
223,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^4,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(a c x - c\right)}^{4}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(a*c*x - c)^4, x)","F",0
224,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^5,x, algorithm=""giac"")","\int -\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(a c x - c\right)}^{5}}\,{d x}"," ",0,"integrate(-((a*x - 1)/(a*x + 1))^(3/2)/(a*c*x - c)^5, x)","F",0
225,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^6,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(a c x - c\right)}^{6}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(a*c*x - c)^6, x)","F",0
226,1,147,0,0.206864," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(9/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{4096 \, \sqrt{2} \sqrt{-c} c^{4}}{\mathrm{sgn}\left(c\right)} + \frac{315 \, {\left(a c x + c\right)}^{5} \sqrt{-a c x - c} - 3080 \, {\left(a c x + c\right)}^{4} \sqrt{-a c x - c} c + 11880 \, {\left(a c x + c\right)}^{3} \sqrt{-a c x - c} c^{2} - 22176 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} c^{3} - 18480 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c^{4}}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}}{3465 \, a}"," ",0,"2/3465*(4096*sqrt(2)*sqrt(-c)*c^4/sgn(c) + (315*(a*c*x + c)^5*sqrt(-a*c*x - c) - 3080*(a*c*x + c)^4*sqrt(-a*c*x - c)*c + 11880*(a*c*x + c)^3*sqrt(-a*c*x - c)*c^2 - 22176*(a*c*x + c)^2*sqrt(-a*c*x - c)*c^3 - 18480*(-a*c*x - c)^(3/2)*c^4)/(c*sgn(-a*c*x - c)))/a","A",0
227,1,124,0,0.169423," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(7/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{256 \, \sqrt{2} \sqrt{-c} c^{3}}{\mathrm{sgn}\left(c\right)} - \frac{35 \, {\left(a c x + c\right)}^{4} \sqrt{-a c x - c} - 270 \, {\left(a c x + c\right)}^{3} \sqrt{-a c x - c} c + 756 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} c^{2} + 840 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c^{3}}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}}{315 \, a}"," ",0,"2/315*(256*sqrt(2)*sqrt(-c)*c^3/sgn(c) - (35*(a*c*x + c)^4*sqrt(-a*c*x - c) - 270*(a*c*x + c)^3*sqrt(-a*c*x - c)*c + 756*(a*c*x + c)^2*sqrt(-a*c*x - c)*c^2 + 840*(-a*c*x - c)^(3/2)*c^3)/(c*sgn(-a*c*x - c)))/a","A",0
228,1,99,0,0.158154," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{64 \, \sqrt{2} \sqrt{-c} c^{2}}{\mathrm{sgn}\left(c\right)} + \frac{15 \, {\left(a c x + c\right)}^{3} \sqrt{-a c x - c} - 84 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} c - 140 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c^{2}}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}}{105 \, a}"," ",0,"2/105*(64*sqrt(2)*sqrt(-c)*c^2/sgn(c) + (15*(a*c*x + c)^3*sqrt(-a*c*x - c) - 84*(a*c*x + c)^2*sqrt(-a*c*x - c)*c - 140*(-a*c*x - c)^(3/2)*c^2)/(c*sgn(-a*c*x - c)))/a","A",0
229,1,74,0,0.143535," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{8 \, \sqrt{2} \sqrt{-c} c}{\mathrm{sgn}\left(c\right)} - \frac{3 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} + 10 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}}{15 \, a}"," ",0,"2/15*(8*sqrt(2)*sqrt(-c)*c/sgn(c) - (3*(a*c*x + c)^2*sqrt(-a*c*x - c) + 10*(-a*c*x - c)^(3/2)*c)/(c*sgn(-a*c*x - c)))/a","A",0
230,1,48,0,0.159100," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2 \, \sqrt{2} \sqrt{-c}}{\mathrm{sgn}\left(c\right)} - \frac{{\left(-a c x - c\right)}^{\frac{3}{2}}}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}}{3 \, a}"," ",0,"2/3*(2*sqrt(2)*sqrt(-c)/sgn(c) - (-a*c*x - c)^(3/2)/(c*sgn(-a*c*x - c)))/a","A",0
231,1,91,0,0.149124," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{\sqrt{2} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right) - \sqrt{-a c x - c}}{\mathrm{sgn}\left(-a c x - c\right)} - \frac{-i \, \sqrt{2} \sqrt{-c} \arctan\left(-i\right) + \sqrt{2} \sqrt{-c}}{\mathrm{sgn}\left(c\right)}\right)}}{a c}"," ",0,"2*((sqrt(2)*sqrt(c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c)) - sqrt(-a*c*x - c))/sgn(-a*c*x - c) - (-I*sqrt(2)*sqrt(-c)*arctan(-I) + sqrt(2)*sqrt(-c))/sgn(c))/(a*c)","C",0
232,1,71,0,0.182863," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(3/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{2 \, \sqrt{-a c x - c}}{a c x - c}}{2 \, a c \mathrm{sgn}\left(-a c x - c\right)}"," ",0,"-1/2*(sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/sqrt(c) + 2*sqrt(-a*c*x - c)/(a*c*x - c))/(a*c*sgn(-a*c*x - c))","A",0
233,1,89,0,0.178015," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(5/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, {\left({\left(-a c x - c\right)}^{\frac{3}{2}} - 2 \, \sqrt{-a c x - c} c\right)}}{{\left(a c x - c\right)}^{2} c}}{16 \, a c \mathrm{sgn}\left(-a c x - c\right)}"," ",0,"-1/16*(sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/c^(3/2) + 2*((-a*c*x - c)^(3/2) - 2*sqrt(-a*c*x - c)*c)/((a*c*x - c)^2*c))/(a*c*sgn(-a*c*x - c))","A",0
234,1,116,0,0.202910," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(7/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{c^{\frac{5}{2}}} - \frac{2 \, {\left(3 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} + 16 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c - 12 \, \sqrt{-a c x - c} c^{2}\right)}}{{\left(a c x - c\right)}^{3} c^{2}}}{192 \, a c \mathrm{sgn}\left(-a c x - c\right)}"," ",0,"-1/192*(3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/c^(5/2) - 2*(3*(a*c*x + c)^2*sqrt(-a*c*x - c) + 16*(-a*c*x - c)^(3/2)*c - 12*sqrt(-a*c*x - c)*c^2)/((a*c*x - c)^3*c^2))/(a*c*sgn(-a*c*x - c))","A",0
235,1,205,0,0.157052," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(7/2),x, algorithm=""giac"")","\frac{2 \, {\left(90 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} + 378 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} c - 630 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{2} + 945 \, \sqrt{-a c x + c} c^{3} + 210 \, {\left({\left(-a c x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{-a c x + c} c\right)} c^{2} - \frac{35 \, {\left(a c x - c\right)}^{4} \sqrt{-a c x + c} + 180 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} c + 378 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} c^{2} - 420 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{3} + 315 \, \sqrt{-a c x + c} c^{4}}{c}\right)}}{315 \, a}"," ",0,"2/315*(90*(a*c*x - c)^3*sqrt(-a*c*x + c) + 378*(a*c*x - c)^2*sqrt(-a*c*x + c)*c - 630*(-a*c*x + c)^(3/2)*c^2 + 945*sqrt(-a*c*x + c)*c^3 + 210*((-a*c*x + c)^(3/2) - 3*sqrt(-a*c*x + c)*c)*c^2 - (35*(a*c*x - c)^4*sqrt(-a*c*x + c) + 180*(a*c*x - c)^3*sqrt(-a*c*x + c)*c + 378*(a*c*x - c)^2*sqrt(-a*c*x + c)*c^2 - 420*(-a*c*x + c)^(3/2)*c^3 + 315*sqrt(-a*c*x + c)*c^4)/c)/a","B",0
236,1,141,0,0.149671," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(21 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} - 70 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c - 35 \, {\left({\left(-a c x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{-a c x + c} c\right)} c - \frac{3 \, {\left(5 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} + 21 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} c - 35 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{2} + 35 \, \sqrt{-a c x + c} c^{3}\right)}}{c}\right)}}{105 \, a}"," ",0,"-2/105*(21*(a*c*x - c)^2*sqrt(-a*c*x + c) - 70*(-a*c*x + c)^(3/2)*c - 35*((-a*c*x + c)^(3/2) - 3*sqrt(-a*c*x + c)*c)*c - 3*(5*(a*c*x - c)^3*sqrt(-a*c*x + c) + 21*(a*c*x - c)^2*sqrt(-a*c*x + c)*c - 35*(-a*c*x + c)^(3/2)*c^2 + 35*sqrt(-a*c*x + c)*c^3)/c)/a","B",0
237,1,71,0,0.134949," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \sqrt{-a c x + c} c - \frac{3 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} - 10 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{-a c x + c} c^{2}}{c}\right)}}{15 \, a}"," ",0,"2/15*(15*sqrt(-a*c*x + c)*c - (3*(a*c*x - c)^2*sqrt(-a*c*x + c) - 10*(-a*c*x + c)^(3/2)*c + 15*sqrt(-a*c*x + c)*c^2)/c)/a","B",0
238,1,44,0,0.152233," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, \sqrt{-a c x + c} - \frac{{\left(-a c x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{-a c x + c} c}{c}\right)}}{3 \, a}"," ",0,"2/3*(3*sqrt(-a*c*x + c) - ((-a*c*x + c)^(3/2) - 3*sqrt(-a*c*x + c)*c)/c)/a","A",0
239,1,32,0,0.172686," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{4}{\sqrt{-a c x + c} a} - \frac{2 \, \sqrt{-a c x + c}}{a c}"," ",0,"-4/(sqrt(-a*c*x + c)*a) - 2*sqrt(-a*c*x + c)/(a*c)","A",0
240,1,36,0,0.130332," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, a c x - c\right)}}{3 \, {\left(a c x - c\right)} \sqrt{-a c x + c} a c}"," ",0,"2/3*(3*a*c*x - c)/((a*c*x - c)*sqrt(-a*c*x + c)*a*c)","A",0
241,1,34,0,0.136714," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(5 \, a c x + c\right)}}{15 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} a c}"," ",0,"-2/15*(5*a*c*x + c)/((a*c*x - c)^2*sqrt(-a*c*x + c)*a*c)","A",0
242,1,36,0,0.132799," ","integrate(1/(a*x-1)*(a*x+1)/(-a*c*x+c)^(7/2),x, algorithm=""giac"")","\frac{2 \, {\left(7 \, a c x + 3 \, c\right)}}{35 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} a c}"," ",0,"2/35*(7*a*c*x + 3*c)/((a*c*x - c)^3*sqrt(-a*c*x + c)*a*c)","A",0
243,1,132,0,0.199455," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(9/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{512 \, \sqrt{2} \sqrt{-c} c^{4}}{\mathrm{sgn}\left(c\right)} - \frac{105 \, {\left(a c x + c\right)}^{5} \sqrt{-a c x - c} - 770 \, {\left(a c x + c\right)}^{4} \sqrt{-a c x - c} c + 1980 \, {\left(a c x + c\right)}^{3} \sqrt{-a c x - c} c^{2} - 1848 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} c^{3}}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}}{1155 \, a}"," ",0,"-2/1155*(512*sqrt(2)*sqrt(-c)*c^4/sgn(c) - (105*(a*c*x + c)^5*sqrt(-a*c*x - c) - 770*(a*c*x + c)^4*sqrt(-a*c*x - c)*c + 1980*(a*c*x + c)^3*sqrt(-a*c*x - c)*c^2 - 1848*(a*c*x + c)^2*sqrt(-a*c*x - c)*c^3)/(c*sgn(-a*c*x - c)))/a","A",0
244,1,107,0,0.205562," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{128 \, \sqrt{2} \sqrt{-c} c^{3}}{\mathrm{sgn}\left(c\right)} + \frac{35 \, {\left(a c x + c\right)}^{4} \sqrt{-a c x - c} - 180 \, {\left(a c x + c\right)}^{3} \sqrt{-a c x - c} c + 252 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} c^{2}}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}}{315 \, a}"," ",0,"-2/315*(128*sqrt(2)*sqrt(-c)*c^3/sgn(c) + (35*(a*c*x + c)^4*sqrt(-a*c*x - c) - 180*(a*c*x + c)^3*sqrt(-a*c*x - c)*c + 252*(a*c*x + c)^2*sqrt(-a*c*x - c)*c^2)/(c*sgn(-a*c*x - c)))/a","A",0
245,1,84,0,0.187692," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{16 \, \sqrt{2} \sqrt{-c} c^{2}}{\mathrm{sgn}\left(c\right)} - \frac{5 \, {\left(a c x + c\right)}^{3} \sqrt{-a c x - c} - 14 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} c}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}}{35 \, a}"," ",0,"-2/35*(16*sqrt(2)*sqrt(-c)*c^2/sgn(c) - (5*(a*c*x + c)^3*sqrt(-a*c*x - c) - 14*(a*c*x + c)^2*sqrt(-a*c*x - c)*c)/(c*sgn(-a*c*x - c)))/a","A",0
246,1,56,0,0.152030," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{4 \, \sqrt{2} \sqrt{-c} c}{\mathrm{sgn}\left(c\right)} + \frac{{\left(a c x + c\right)}^{2} \sqrt{-a c x - c}}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}}{5 \, a}"," ",0,"-2/5*(4*sqrt(2)*sqrt(-c)*c/sgn(c) + (a*c*x + c)^2*sqrt(-a*c*x - c)/(c*sgn(-a*c*x - c)))/a","A",0
247,1,105,0,0.170700," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{12 i \, \sqrt{2} \sqrt{-c} \arctan\left(-i\right) - 16 \, \sqrt{2} \sqrt{-c}}{\mathrm{sgn}\left(c\right)} + \frac{2 \, {\left(6 \, \sqrt{2} c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right) + {\left(-a c x - c\right)}^{\frac{3}{2}} - 6 \, \sqrt{-a c x - c} c\right)}}{c \mathrm{sgn}\left(-a c x - c\right)}}{3 \, a}"," ",0,"-1/3*((12*I*sqrt(2)*sqrt(-c)*arctan(-I) - 16*sqrt(2)*sqrt(-c))/sgn(c) + 2*(6*sqrt(2)*c^(3/2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c)) + (-a*c*x - c)^(3/2) - 6*sqrt(-a*c*x - c)*c)/(c*sgn(-a*c*x - c)))/a","C",0
248,1,85,0,0.166541," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{3 \, \sqrt{2} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right) - 2 \, \sqrt{-a c x - c} + \frac{2 \, \sqrt{-a c x - c} c}{a c x - c}}{a c \mathrm{sgn}\left(-a c x - c\right)}"," ",0,"(3*sqrt(2)*sqrt(c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c)) - 2*sqrt(-a*c*x - c) + 2*sqrt(-a*c*x - c)*c/(a*c*x - c))/(a*c*sgn(-a*c*x - c))","A",0
249,1,89,0,0.171528," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(3/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} - \frac{2 \, {\left(5 \, {\left(-a c x - c\right)}^{\frac{3}{2}} + 6 \, \sqrt{-a c x - c} c\right)}}{{\left(a c x - c\right)}^{2}}}{8 \, a c \mathrm{sgn}\left(-a c x - c\right)}"," ",0,"-1/8*(3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/sqrt(c) - 2*(5*(-a*c*x - c)^(3/2) + 6*sqrt(-a*c*x - c)*c)/(a*c*x - c)^2)/(a*c*sgn(-a*c*x - c))","A",0
250,1,116,0,0.218023," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(5/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} - \frac{2 \, {\left(3 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} - 16 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c - 12 \, \sqrt{-a c x - c} c^{2}\right)}}{{\left(a c x - c\right)}^{3} c}}{96 \, a c \mathrm{sgn}\left(-a c x - c\right)}"," ",0,"-1/96*(3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/c^(3/2) - 2*(3*(a*c*x + c)^2*sqrt(-a*c*x - c) - 16*(-a*c*x - c)^(3/2)*c - 12*sqrt(-a*c*x - c)*c^2)/((a*c*x - c)^3*c))/(a*c*sgn(-a*c*x - c))","A",0
251,1,140,0,0.215304," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(7/2),x, algorithm=""giac"")","-\frac{\frac{3 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{c^{\frac{5}{2}}} - \frac{2 \, {\left(3 \, {\left(a c x + c\right)}^{3} \sqrt{-a c x - c} - 22 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} c + 44 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c^{2} + 24 \, \sqrt{-a c x - c} c^{3}\right)}}{{\left(a c x - c\right)}^{4} c^{2}}}{512 \, a c \mathrm{sgn}\left(-a c x - c\right)}"," ",0,"-1/512*(3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/c^(5/2) - 2*(3*(a*c*x + c)^3*sqrt(-a*c*x - c) - 22*(a*c*x + c)^2*sqrt(-a*c*x - c)*c + 44*(-a*c*x - c)^(3/2)*c^2 + 24*sqrt(-a*c*x - c)*c^3)/((a*c*x - c)^4*c^2))/(a*c*sgn(-a*c*x - c))","A",0
252,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(9/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
253,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
254,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
255,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
256,1,43,0,0.144711," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(-a c x - c\right)}^{\frac{3}{2}} {\left| c \right|}}{3 \, a c^{2}} + \frac{4 \, \sqrt{-a c x - c} {\left| c \right|}}{a c}"," ",0,"2/3*(-a*c*x - c)^(3/2)*abs(c)/(a*c^2) + 4*sqrt(-a*c*x - c)*abs(c)/(a*c)","A",0
257,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
258,1,64,0,0.143894," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{a \sqrt{c}} - \frac{\sqrt{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{c}}\right)}{a \sqrt{c}}\right)} {\left| c \right|} \mathrm{sgn}\left(a x + 1\right)}{c^{2}}"," ",0,"(sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/(a*sqrt(c)) - sqrt(2)*arctan(sqrt(-c)/sqrt(c))/(a*sqrt(c)))*abs(c)*sgn(a*x + 1)/c^2","A",0
259,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
260,1,88,0,0.234086," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(7/2),x, algorithm=""giac"")","\frac{{\left(\frac{3 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{c^{\frac{5}{2}}} + \frac{2 \, {\left(3 \, {\left(-a c x - c\right)}^{\frac{3}{2}} + 10 \, \sqrt{-a c x - c} c\right)}}{{\left(a c x - c\right)}^{2} c^{2}}\right)} {\left| c \right|} \mathrm{sgn}\left(a x + 1\right)}{32 \, a c^{2}}"," ",0,"1/32*(3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/c^(5/2) + 2*(3*(-a*c*x - c)^(3/2) + 10*sqrt(-a*c*x - c)*c)/((a*c*x - c)^2*c^2))*abs(c)*sgn(a*x + 1)/(a*c^2)","A",0
261,1,161,0,0.164580," ","integrate((-a*c*x+c)^(7/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{32 \, \sqrt{2} c^{4} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{a \sqrt{-c}} - \frac{2 \, {\left(35 \, {\left(a c x - c\right)}^{4} \sqrt{-a c x + c} a^{8} c^{8} - 90 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} a^{8} c^{9} + 252 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} a^{8} c^{10} + 840 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{8} c^{11} + 5040 \, \sqrt{-a c x + c} a^{8} c^{12}\right)}}{315 \, a^{9} c^{9}}"," ",0,"-32*sqrt(2)*c^4*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a*sqrt(-c)) - 2/315*(35*(a*c*x - c)^4*sqrt(-a*c*x + c)*a^8*c^8 - 90*(a*c*x - c)^3*sqrt(-a*c*x + c)*a^8*c^9 + 252*(a*c*x - c)^2*sqrt(-a*c*x + c)*a^8*c^10 + 840*(-a*c*x + c)^(3/2)*a^8*c^11 + 5040*sqrt(-a*c*x + c)*a^8*c^12)/(a^9*c^9)","A",0
262,1,134,0,0.163588," ","integrate((-a*c*x+c)^(5/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{16 \, \sqrt{2} c^{3} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{a \sqrt{-c}} + \frac{2 \, {\left(15 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} a^{6} c^{6} - 42 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} a^{6} c^{7} - 140 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{6} c^{8} - 840 \, \sqrt{-a c x + c} a^{6} c^{9}\right)}}{105 \, a^{7} c^{7}}"," ",0,"-16*sqrt(2)*c^3*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a*sqrt(-c)) + 2/105*(15*(a*c*x - c)^3*sqrt(-a*c*x + c)*a^6*c^6 - 42*(a*c*x - c)^2*sqrt(-a*c*x + c)*a^6*c^7 - 140*(-a*c*x + c)^(3/2)*a^6*c^8 - 840*sqrt(-a*c*x + c)*a^6*c^9)/(a^7*c^7)","A",0
263,1,107,0,0.140611," ","integrate((-a*c*x+c)^(3/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{8 \, \sqrt{2} c^{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{a \sqrt{-c}} - \frac{2 \, {\left(3 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} a^{4} c^{4} + 10 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{4} c^{5} + 60 \, \sqrt{-a c x + c} a^{4} c^{6}\right)}}{15 \, a^{5} c^{5}}"," ",0,"-8*sqrt(2)*c^2*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a*sqrt(-c)) - 2/15*(3*(a*c*x - c)^2*sqrt(-a*c*x + c)*a^4*c^4 + 10*(-a*c*x + c)^(3/2)*a^4*c^5 + 60*sqrt(-a*c*x + c)*a^4*c^6)/(a^5*c^5)","A",0
264,1,77,0,0.154167," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{4 \, \sqrt{2} c \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{a \sqrt{-c}} - \frac{2 \, {\left({\left(-a c x + c\right)}^{\frac{3}{2}} a^{2} c^{2} + 6 \, \sqrt{-a c x + c} a^{2} c^{3}\right)}}{3 \, a^{3} c^{3}}"," ",0,"-4*sqrt(2)*c*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a*sqrt(-c)) - 2/3*((-a*c*x + c)^(3/2)*a^2*c^2 + 6*sqrt(-a*c*x + c)*a^2*c^3)/(a^3*c^3)","A",0
265,1,51,0,0.157579," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{a \sqrt{-c}} - \frac{2 \, \sqrt{-a c x + c}}{a c}"," ",0,"-2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a*sqrt(-c)) - 2*sqrt(-a*c*x + c)/(a*c)","A",0
266,1,36,0,0.158676," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{a \sqrt{-c} c}"," ",0,"-sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a*sqrt(-c)*c)","A",0
267,1,54,0,0.137025," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{2 \, a \sqrt{-c} c^{2}} - \frac{1}{\sqrt{-a c x + c} a c^{2}}"," ",0,"-1/2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a*sqrt(-c)*c^2) - 1/(sqrt(-a*c*x + c)*a*c^2)","A",0
268,1,73,0,0.154598," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{4 \, a \sqrt{-c} c^{3}} - \frac{3 \, a c x - 5 \, c}{6 \, {\left(a c x - c\right)} \sqrt{-a c x + c} a c^{3}}"," ",0,"-1/4*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a*sqrt(-c)*c^3) - 1/6*(3*a*c*x - 5*c)/((a*c*x - c)*sqrt(-a*c*x + c)*a*c^3)","A",0
269,1,93,0,0.134384," ","integrate((a*x-1)/(a*x+1)/(-a*c*x+c)^(9/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{8 \, a \sqrt{-c} c^{4}} - \frac{15 \, {\left(a c x - c\right)}^{2} - 10 \, {\left(a c x - c\right)} c + 12 \, c^{2}}{60 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} a c^{4}}"," ",0,"-1/8*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a*sqrt(-c)*c^4) - 1/60*(15*(a*c*x - c)^2 - 10*(a*c*x - c)*c + 12*c^2)/((a*c*x - c)^2*sqrt(-a*c*x + c)*a*c^4)","A",0
270,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
271,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
272,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
273,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
274,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
275,1,42,0,0.157229," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(1/2),x, algorithm=""giac"")","2 \, {\left(\frac{\sqrt{-a c x - c}}{a c^{2}} - \frac{2}{\sqrt{-a c x - c} a c}\right)} {\left| c \right|}"," ",0,"2*(sqrt(-a*c*x - c)/(a*c^2) - 2/(sqrt(-a*c*x - c)*a*c))*abs(c)","A",0
276,1,41,0,0.160021," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{\sqrt{2}}{a \sqrt{-c}} - \frac{2}{\sqrt{-a c x - c} a}\right)} {\left| c \right|} \mathrm{sgn}\left(a x + 1\right)}{c^{2}}"," ",0,"(sqrt(2)/(a*sqrt(-c)) - 2/(sqrt(-a*c*x - c)*a))*abs(c)*sgn(a*x + 1)/c^2","A",0
277,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
278,1,90,0,0.215754," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(7/2),x, algorithm=""giac"")","-\frac{{\left(\frac{3 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{a c^{\frac{5}{2}}} - \frac{2 \, {\left(3 \, a c x - c\right)}}{{\left({\left(-a c x - c\right)}^{\frac{3}{2}} + 2 \, \sqrt{-a c x - c} c\right)} a c^{2}}\right)} {\left| c \right|} \mathrm{sgn}\left(a x + 1\right)}{8 \, c^{2}}"," ",0,"-1/8*(3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/(a*c^(5/2)) - 2*(3*a*c*x - c)/(((-a*c*x - c)^(3/2) + 2*sqrt(-a*c*x - c)*c)*a*c^2))*abs(c)*sgn(a*x + 1)/c^2","A",0
279,1,105,0,0.156880," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{8 \, {\left(x - 1\right)} \sqrt{\frac{x - 1}{x + 1}}}{x + 1} - \frac{3 \, {\left(x - 1\right)}^{2} \sqrt{\frac{x - 1}{x + 1}}}{{\left(x + 1\right)}^{2}} - 9 \, \sqrt{\frac{x - 1}{x + 1}}\right)}}{3 \, {\left(\frac{x - 1}{x + 1} - 1\right)}^{3}} + \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} - 1 \right|}\right)"," ",0,"2/3*(8*(x - 1)*sqrt((x - 1)/(x + 1))/(x + 1) - 3*(x - 1)^2*sqrt((x - 1)/(x + 1))/(x + 1)^2 - 9*sqrt((x - 1)/(x + 1)))/((x - 1)/(x + 1) - 1)^3 + log(sqrt((x - 1)/(x + 1)) + 1) - log(abs(sqrt((x - 1)/(x + 1)) - 1))","A",0
280,1,84,0,0.147710," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(x - 1\right)} \sqrt{\frac{x - 1}{x + 1}}}{x + 1} - 5 \, \sqrt{\frac{x - 1}{x + 1}}}{{\left(\frac{x - 1}{x + 1} - 1\right)}^{2}} + \frac{3}{2} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \frac{3}{2} \, \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} - 1 \right|}\right)"," ",0,"-(3*(x - 1)*sqrt((x - 1)/(x + 1))/(x + 1) - 5*sqrt((x - 1)/(x + 1)))/((x - 1)/(x + 1) - 1)^2 + 3/2*log(sqrt((x - 1)/(x + 1)) + 1) - 3/2*log(abs(sqrt((x - 1)/(x + 1)) - 1))","A",0
281,1,29,0,0.151366," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)*x,x, algorithm=""giac"")","\frac{8}{3 \, {\left(\sqrt{\frac{x - 1}{x + 1}} - \frac{1}{\sqrt{\frac{x - 1}{x + 1}}}\right)}^{3}}"," ",0,"8/3/(sqrt((x - 1)/(x + 1)) - 1/sqrt((x - 1)/(x + 1)))^3","B",0
282,1,110,0,0.135590," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x),x, algorithm=""giac"")","-\frac{\sqrt{\frac{x - 1}{x + 1}} + \frac{1}{\sqrt{\frac{x - 1}{x + 1}}}}{{\left(\sqrt{\frac{x - 1}{x + 1}} + \frac{1}{\sqrt{\frac{x - 1}{x + 1}}}\right)}^{2} - 4} + \frac{1}{4} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + \frac{1}{\sqrt{\frac{x - 1}{x + 1}}} + 2\right) - \frac{1}{4} \, \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} + \frac{1}{\sqrt{\frac{x - 1}{x + 1}}} - 2 \right|}\right)"," ",0,"-(sqrt((x - 1)/(x + 1)) + 1/sqrt((x - 1)/(x + 1)))/((sqrt((x - 1)/(x + 1)) + 1/sqrt((x - 1)/(x + 1)))^2 - 4) + 1/4*log(sqrt((x - 1)/(x + 1)) + 1/sqrt((x - 1)/(x + 1)) + 2) - 1/4*log(abs(sqrt((x - 1)/(x + 1)) + 1/sqrt((x - 1)/(x + 1)) - 2))","B",0
283,1,130,0,0.139955," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^2,x, algorithm=""giac"")","-\frac{\frac{73 \, {\left(x - 1\right)} \sqrt{\frac{x - 1}{x + 1}}}{x + 1} - \frac{55 \, {\left(x - 1\right)}^{2} \sqrt{\frac{x - 1}{x + 1}}}{{\left(x + 1\right)}^{2}} + \frac{15 \, {\left(x - 1\right)}^{3} \sqrt{\frac{x - 1}{x + 1}}}{{\left(x + 1\right)}^{3}} - 49 \, \sqrt{\frac{x - 1}{x + 1}}}{4 \, {\left(\frac{x - 1}{x + 1} - 1\right)}^{4}} + \frac{15}{8} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \frac{15}{8} \, \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} - 1 \right|}\right)"," ",0,"-1/4*(73*(x - 1)*sqrt((x - 1)/(x + 1))/(x + 1) - 55*(x - 1)^2*sqrt((x - 1)/(x + 1))/(x + 1)^2 + 15*(x - 1)^3*sqrt((x - 1)/(x + 1))/(x + 1)^3 - 49*sqrt((x - 1)/(x + 1)))/((x - 1)/(x + 1) - 1)^4 + 15/8*log(sqrt((x - 1)/(x + 1)) + 1) - 15/8*log(abs(sqrt((x - 1)/(x + 1)) - 1))","A",0
284,1,107,0,0.134971," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x)^2,x, algorithm=""giac"")","\frac{\frac{40 \, {\left(x - 1\right)} \sqrt{\frac{x - 1}{x + 1}}}{x + 1} - \frac{15 \, {\left(x - 1\right)}^{2} \sqrt{\frac{x - 1}{x + 1}}}{{\left(x + 1\right)}^{2}} - 33 \, \sqrt{\frac{x - 1}{x + 1}}}{3 \, {\left(\frac{x - 1}{x + 1} - 1\right)}^{3}} + \frac{5}{2} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \frac{5}{2} \, \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} - 1 \right|}\right)"," ",0,"1/3*(40*(x - 1)*sqrt((x - 1)/(x + 1))/(x + 1) - 15*(x - 1)^2*sqrt((x - 1)/(x + 1))/(x + 1)^2 - 33*sqrt((x - 1)/(x + 1)))/((x - 1)/(x + 1) - 1)^3 + 5/2*log(sqrt((x - 1)/(x + 1)) + 1) - 5/2*log(abs(sqrt((x - 1)/(x + 1)) - 1))","A",0
285,1,130,0,0.132286," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^2*x,x, algorithm=""giac"")","-\frac{\frac{11 \, {\left(x - 1\right)} \sqrt{\frac{x - 1}{x + 1}}}{x + 1} - \frac{53 \, {\left(x - 1\right)}^{2} \sqrt{\frac{x - 1}{x + 1}}}{{\left(x + 1\right)}^{2}} - \frac{3 \, {\left(x - 1\right)}^{3} \sqrt{\frac{x - 1}{x + 1}}}{{\left(x + 1\right)}^{3}} - 3 \, \sqrt{\frac{x - 1}{x + 1}}}{12 \, {\left(\frac{x - 1}{x + 1} - 1\right)}^{4}} - \frac{1}{8} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) + \frac{1}{8} \, \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} - 1 \right|}\right)"," ",0,"-1/12*(11*(x - 1)*sqrt((x - 1)/(x + 1))/(x + 1) - 53*(x - 1)^2*sqrt((x - 1)/(x + 1))/(x + 1)^2 - 3*(x - 1)^3*sqrt((x - 1)/(x + 1))/(x + 1)^3 - 3*sqrt((x - 1)/(x + 1)))/((x - 1)/(x + 1) - 1)^4 - 1/8*log(sqrt((x - 1)/(x + 1)) + 1) + 1/8*log(abs(sqrt((x - 1)/(x + 1)) - 1))","B",0
286,1,107,0,0.154649," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^2,x, algorithm=""giac"")","-\frac{\frac{8 \, {\left(x - 1\right)} \sqrt{\frac{x - 1}{x + 1}}}{x + 1} + \frac{3 \, {\left(x - 1\right)}^{2} \sqrt{\frac{x - 1}{x + 1}}}{{\left(x + 1\right)}^{2}} - 3 \, \sqrt{\frac{x - 1}{x + 1}}}{3 \, {\left(\frac{x - 1}{x + 1} - 1\right)}^{3}} + \frac{1}{2} \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \frac{1}{2} \, \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} - 1 \right|}\right)"," ",0,"-1/3*(8*(x - 1)*sqrt((x - 1)/(x + 1))/(x + 1) + 3*(x - 1)^2*sqrt((x - 1)/(x + 1))/(x + 1)^2 - 3*sqrt((x - 1)/(x + 1)))/((x - 1)/(x + 1) - 1)^3 + 1/2*log(sqrt((x - 1)/(x + 1)) + 1) - 1/2*log(abs(sqrt((x - 1)/(x + 1)) - 1))","B",0
287,1,29,0,0.140987," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x),x, algorithm=""giac"")","-\frac{2}{\sqrt{\frac{x - 1}{x + 1}} - \frac{1}{\sqrt{\frac{x - 1}{x + 1}}}}"," ",0,"-2/(sqrt((x - 1)/(x + 1)) - 1/sqrt((x - 1)/(x + 1)))","A",0
288,1,32,0,0.125699," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x),x, algorithm=""giac"")","\log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} - 1 \right|}\right)"," ",0,"log(sqrt((x - 1)/(x + 1)) + 1) - log(abs(sqrt((x - 1)/(x + 1)) - 1))","A",0
289,1,84,0,0.131458," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2 \, {\left(x - 1\right)}}{x + 1} - 1\right)}}{\frac{{\left(x - 1\right)} \sqrt{\frac{x - 1}{x + 1}}}{x + 1} - \sqrt{\frac{x - 1}{x + 1}}} - 2 \, \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) + 2 \, \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} - 1 \right|}\right)"," ",0,"2*(2*(x - 1)/(x + 1) - 1)/((x - 1)*sqrt((x - 1)/(x + 1))/(x + 1) - sqrt((x - 1)/(x + 1))) - 2*log(sqrt((x - 1)/(x + 1)) + 1) + 2*log(abs(sqrt((x - 1)/(x + 1)) - 1))","B",0
290,1,45,0,0.136980," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x),x, algorithm=""giac"")","\frac{2}{\sqrt{\frac{x - 1}{x + 1}}} - \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) + \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} - 1 \right|}\right)"," ",0,"2/sqrt((x - 1)/(x + 1)) - log(sqrt((x - 1)/(x + 1)) + 1) + log(abs(sqrt((x - 1)/(x + 1)) - 1))","A",0
291,1,45,0,0.126097," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^2,x, algorithm=""giac"")","-\sqrt{\frac{x - 1}{x + 1}} + \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} - 1 \right|}\right)"," ",0,"-sqrt((x - 1)/(x + 1)) + log(sqrt((x - 1)/(x + 1)) + 1) - log(abs(sqrt((x - 1)/(x + 1)) - 1))","A",0
292,1,11,0,0.127331," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x)^2,x, algorithm=""giac"")","\sqrt{\frac{x - 1}{x + 1}}"," ",0,"sqrt((x - 1)/(x + 1))","A",0
293,1,65,0,0.151443," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^2,x, algorithm=""giac"")","-\frac{{\left(x + 1\right)} {\left(\frac{6 \, {\left(x - 1\right)}}{x + 1} + 1\right)}}{3 \, {\left(x - 1\right)} \sqrt{\frac{x - 1}{x + 1}}} + \log\left(\sqrt{\frac{x - 1}{x + 1}} + 1\right) - \log\left({\left| \sqrt{\frac{x - 1}{x + 1}} - 1 \right|}\right)"," ",0,"-1/3*(x + 1)*(6*(x - 1)/(x + 1) + 1)/((x - 1)*sqrt((x - 1)/(x + 1))) + log(sqrt((x - 1)/(x + 1)) + 1) - log(abs(sqrt((x - 1)/(x + 1)) - 1))","A",0
294,1,21,0,0.137594," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x)^2,x, algorithm=""giac"")","-\frac{x + 1}{3 \, {\left(x - 1\right)} \sqrt{\frac{x - 1}{x + 1}}}"," ",0,"-1/3*(x + 1)/((x - 1)*sqrt((x - 1)/(x + 1)))","A",0
295,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a c x + c} x^{m}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*x^m/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
296,1,102,0,0.173430," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{22 \, \sqrt{2} \sqrt{-c}}{a^{2} \mathrm{sgn}\left(c\right)} + \frac{15 \, {\left(a c x + c\right)}^{3} \sqrt{-a c x - c} - 42 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} c - 35 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c^{2}}{a^{2} c^{3} \mathrm{sgn}\left(-a c x - c\right)}\right)}}{105 \, a}"," ",0,"2/105*(22*sqrt(2)*sqrt(-c)/(a^2*sgn(c)) + (15*(a*c*x + c)^3*sqrt(-a*c*x - c) - 42*(a*c*x + c)^2*sqrt(-a*c*x - c)*c - 35*(-a*c*x - c)^(3/2)*c^2)/(a^2*c^3*sgn(-a*c*x - c)))/a","A",0
297,1,78,0,0.149857," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2 \, \sqrt{2} \sqrt{-c}}{a \mathrm{sgn}\left(c\right)} + \frac{3 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} + 5 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c}{a c^{2} \mathrm{sgn}\left(-a c x - c\right)}\right)}}{15 \, a}"," ",0,"2/15*(2*sqrt(2)*sqrt(-c)/(a*sgn(c)) + (3*(a*c*x + c)^2*sqrt(-a*c*x - c) + 5*(-a*c*x - c)^(3/2)*c)/(a*c^2*sgn(-a*c*x - c)))/a","A",0
298,1,48,0,0.163846," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2 \, \sqrt{2} \sqrt{-c}}{\mathrm{sgn}\left(c\right)} - \frac{{\left(-a c x - c\right)}^{\frac{3}{2}}}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}}{3 \, a}"," ",0,"2/3*(2*sqrt(2)*sqrt(-c)/sgn(c) - (-a*c*x - c)^(3/2)/(c*sgn(-a*c*x - c)))/a","A",0
299,1,86,0,0.186177," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2)/x,x, algorithm=""giac"")","-2 \, c {\left(\frac{\arctan\left(\frac{\sqrt{-a c x - c}}{\sqrt{c}}\right)}{\sqrt{c} \mathrm{sgn}\left(-a c x - c\right)} + \frac{\sqrt{2} - i \, \arctan\left(-i \, \sqrt{2}\right)}{\sqrt{-c} \mathrm{sgn}\left(c\right)} - \frac{\sqrt{-a c x - c}}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}"," ",0,"-2*c*(arctan(sqrt(-a*c*x - c)/sqrt(c))/(sqrt(c)*sgn(-a*c*x - c)) + (sqrt(2) - I*arctan(-I*sqrt(2)))/(sqrt(-c)*sgn(c)) - sqrt(-a*c*x - c)/(c*sgn(-a*c*x - c)))","C",0
300,1,100,0,0.202158," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""giac"")","-\frac{\frac{a^{2} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x - c}}{\sqrt{c}}\right)}{\mathrm{sgn}\left(-a c x - c\right)} + \frac{a^{2} \sqrt{c} \arctan\left(-i \, \sqrt{2}\right) + \sqrt{2} a^{2} \sqrt{-c}}{\mathrm{sgn}\left(c\right)} + \frac{\sqrt{-a c x - c} a}{x \mathrm{sgn}\left(-a c x - c\right)}}{a}"," ",0,"-(a^2*sqrt(c)*arctan(sqrt(-a*c*x - c)/sqrt(c))/sgn(-a*c*x - c) + (a^2*sqrt(c)*arctan(-I*sqrt(2)) + sqrt(2)*a^2*sqrt(-c))/sgn(c) + sqrt(-a*c*x - c)*a/(x*sgn(-a*c*x - c)))/a","C",0
301,1,189,0,0.144675," ","integrate(1/(a*x-1)*(a*x+1)*x^3*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{9 \, {\left(5 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} + 21 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} c - 35 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{2} + 35 \, \sqrt{-a c x + c} c^{3}\right)}}{a^{3} c^{3}} + \frac{35 \, {\left(a c x - c\right)}^{4} \sqrt{-a c x + c} + 180 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} c + 378 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} c^{2} - 420 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{3} + 315 \, \sqrt{-a c x + c} c^{4}}{a^{3} c^{4}}\right)}}{315 \, a}"," ",0,"2/315*(9*(5*(a*c*x - c)^3*sqrt(-a*c*x + c) + 21*(a*c*x - c)^2*sqrt(-a*c*x + c)*c - 35*(-a*c*x + c)^(3/2)*c^2 + 35*sqrt(-a*c*x + c)*c^3)/(a^3*c^3) + (35*(a*c*x - c)^4*sqrt(-a*c*x + c) + 180*(a*c*x - c)^3*sqrt(-a*c*x + c)*c + 378*(a*c*x - c)^2*sqrt(-a*c*x + c)*c^2 - 420*(-a*c*x + c)^(3/2)*c^3 + 315*sqrt(-a*c*x + c)*c^4)/(a^3*c^4))/a","B",0
302,1,142,0,0.142218," ","integrate(1/(a*x-1)*(a*x+1)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{7 \, {\left(3 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} - 10 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{-a c x + c} c^{2}\right)}}{a^{2} c^{2}} + \frac{3 \, {\left(5 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} + 21 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} c - 35 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c^{2} + 35 \, \sqrt{-a c x + c} c^{3}\right)}}{a^{2} c^{3}}\right)}}{105 \, a}"," ",0,"2/105*(7*(3*(a*c*x - c)^2*sqrt(-a*c*x + c) - 10*(-a*c*x + c)^(3/2)*c + 15*sqrt(-a*c*x + c)*c^2)/(a^2*c^2) + 3*(5*(a*c*x - c)^3*sqrt(-a*c*x + c) + 21*(a*c*x - c)^2*sqrt(-a*c*x + c)*c - 35*(-a*c*x + c)^(3/2)*c^2 + 35*sqrt(-a*c*x + c)*c^3)/(a^2*c^3))/a","B",0
303,1,92,0,0.132559," ","integrate(1/(a*x-1)*(a*x+1)*x*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{5 \, {\left({\left(-a c x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{-a c x + c} c\right)}}{a c} - \frac{3 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} - 10 \, {\left(-a c x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{-a c x + c} c^{2}}{a c^{2}}\right)}}{15 \, a}"," ",0,"-2/15*(5*((-a*c*x + c)^(3/2) - 3*sqrt(-a*c*x + c)*c)/(a*c) - (3*(a*c*x - c)^2*sqrt(-a*c*x + c) - 10*(-a*c*x + c)^(3/2)*c + 15*sqrt(-a*c*x + c)*c^2)/(a*c^2))/a","A",0
304,1,44,0,0.135520," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, \sqrt{-a c x + c} - \frac{{\left(-a c x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{-a c x + c} c}{c}\right)}}{3 \, a}"," ",0,"2/3*(3*sqrt(-a*c*x + c) - ((-a*c*x + c)^(3/2) - 3*sqrt(-a*c*x + c)*c)/c)/a","A",0
305,1,40,0,0.140262," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2)/x,x, algorithm=""giac"")","-2 \, c {\left(\frac{\arctan\left(\frac{\sqrt{-a c x + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{\sqrt{-a c x + c}}{c}\right)}"," ",0,"-2*c*(arctan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) - sqrt(-a*c*x + c)/c)","A",0
306,1,48,0,0.135938," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""giac"")","-\frac{\frac{3 \, a^{2} c \arctan\left(\frac{\sqrt{-a c x + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{\sqrt{-a c x + c} a}{x}}{a}"," ",0,"-(3*a^2*c*arctan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) - sqrt(-a*c*x + c)*a/x)/a","A",0
307,1,76,0,0.139308," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2)/x^3,x, algorithm=""giac"")","-\frac{\frac{7 \, a^{3} c \arctan\left(\frac{\sqrt{-a c x + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{7 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{3} c - 9 \, \sqrt{-a c x + c} a^{3} c^{2}}{a^{2} c^{2} x^{2}}}{4 \, a}"," ",0,"-1/4*(7*a^3*c*arctan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + (7*(-a*c*x + c)^(3/2)*a^3*c - 9*sqrt(-a*c*x + c)*a^3*c^2)/(a^2*c^2*x^2))/a","A",0
308,1,104,0,0.146909," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{\frac{33 \, a^{4} c \arctan\left(\frac{\sqrt{-a c x + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{33 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} a^{4} c - 88 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{4} c^{2} + 63 \, \sqrt{-a c x + c} a^{4} c^{3}}{a^{3} c^{3} x^{3}}}{24 \, a}"," ",0,"-1/24*(33*a^4*c*arctan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) - (33*(a*c*x - c)^2*sqrt(-a*c*x + c)*a^4*c - 88*(-a*c*x + c)^(3/2)*a^4*c^2 + 63*sqrt(-a*c*x + c)*a^4*c^3)/(a^3*c^3*x^3))/a","A",0
309,1,131,0,0.127462," ","integrate(1/(a*x-1)*(a*x+1)*(-a*c*x+c)^(1/2)/x^5,x, algorithm=""giac"")","-\frac{\frac{75 \, a^{5} c \arctan\left(\frac{\sqrt{-a c x + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{75 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} a^{5} c + 275 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} a^{5} c^{2} - 365 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{5} c^{3} + 181 \, \sqrt{-a c x + c} a^{5} c^{4}}{a^{4} c^{4} x^{4}}}{64 \, a}"," ",0,"-1/64*(75*a^5*c*arctan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) - (75*(a*c*x - c)^3*sqrt(-a*c*x + c)*a^5*c + 275*(a*c*x - c)^2*sqrt(-a*c*x + c)*a^5*c^2 - 365*(-a*c*x + c)^(3/2)*a^5*c^3 + 181*sqrt(-a*c*x + c)*a^5*c^4)/(a^4*c^4*x^4))/a","A",0
310,1,185,0,0.198873," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{1260 i \, \sqrt{2} \sqrt{-c} \arctan\left(-i\right) - 2584 \, \sqrt{2} \sqrt{-c}}{a^{3} \mathrm{sgn}\left(c\right)} + \frac{2 \, {\left(630 \, \sqrt{2} c^{\frac{9}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right) - 35 \, {\left(a c x + c\right)}^{4} \sqrt{-a c x - c} + 45 \, {\left(a c x + c\right)}^{3} \sqrt{-a c x - c} c - 63 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} c^{2} + 105 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c^{3} - 630 \, \sqrt{-a c x - c} c^{4}\right)}}{a^{3} c^{4} \mathrm{sgn}\left(-a c x - c\right)}}{315 \, a}"," ",0,"-1/315*((1260*I*sqrt(2)*sqrt(-c)*arctan(-I) - 2584*sqrt(2)*sqrt(-c))/(a^3*sgn(c)) + 2*(630*sqrt(2)*c^(9/2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c)) - 35*(a*c*x + c)^4*sqrt(-a*c*x - c) + 45*(a*c*x + c)^3*sqrt(-a*c*x - c)*c - 63*(a*c*x + c)^2*sqrt(-a*c*x - c)*c^2 + 105*(-a*c*x - c)^(3/2)*c^3 - 630*sqrt(-a*c*x - c)*c^4)/(a^3*c^4*sgn(-a*c*x - c)))/a","C",0
311,1,139,0,0.195830," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{84 i \, \sqrt{2} \sqrt{-c} \arctan\left(-i\right) - 160 \, \sqrt{2} \sqrt{-c}}{a^{2} \mathrm{sgn}\left(c\right)} + \frac{2 \, {\left(42 \, \sqrt{2} c^{\frac{7}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right) - 3 \, {\left(a c x + c\right)}^{3} \sqrt{-a c x - c} + 7 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c^{2} - 42 \, \sqrt{-a c x - c} c^{3}\right)}}{a^{2} c^{3} \mathrm{sgn}\left(-a c x - c\right)}}{21 \, a}"," ",0,"-1/21*((84*I*sqrt(2)*sqrt(-c)*arctan(-I) - 160*sqrt(2)*sqrt(-c))/(a^2*sgn(c)) + 2*(42*sqrt(2)*c^(7/2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c)) - 3*(a*c*x + c)^3*sqrt(-a*c*x - c) + 7*(-a*c*x - c)^(3/2)*c^2 - 42*sqrt(-a*c*x - c)*c^3)/(a^2*c^3*sgn(-a*c*x - c)))/a","C",0
312,1,137,0,0.178665," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{60 i \, \sqrt{2} \sqrt{-c} \arctan\left(-i\right) - 104 \, \sqrt{2} \sqrt{-c}}{a \mathrm{sgn}\left(c\right)} + \frac{2 \, {\left(30 \, \sqrt{2} c^{\frac{5}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right) - 3 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} + 5 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c - 30 \, \sqrt{-a c x - c} c^{2}\right)}}{a c^{2} \mathrm{sgn}\left(-a c x - c\right)}}{15 \, a}"," ",0,"-1/15*((60*I*sqrt(2)*sqrt(-c)*arctan(-I) - 104*sqrt(2)*sqrt(-c))/(a*sgn(c)) + 2*(30*sqrt(2)*c^(5/2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c)) - 3*(a*c*x + c)^2*sqrt(-a*c*x - c) + 5*(-a*c*x - c)^(3/2)*c - 30*sqrt(-a*c*x - c)*c^2)/(a*c^2*sgn(-a*c*x - c)))/a","C",0
313,1,105,0,0.179329," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{12 i \, \sqrt{2} \sqrt{-c} \arctan\left(-i\right) - 16 \, \sqrt{2} \sqrt{-c}}{\mathrm{sgn}\left(c\right)} + \frac{2 \, {\left(6 \, \sqrt{2} c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right) + {\left(-a c x - c\right)}^{\frac{3}{2}} - 6 \, \sqrt{-a c x - c} c\right)}}{c \mathrm{sgn}\left(-a c x - c\right)}}{3 \, a}"," ",0,"-1/3*((12*I*sqrt(2)*sqrt(-c)*arctan(-I) - 16*sqrt(2)*sqrt(-c))/sgn(c) + 2*(6*sqrt(2)*c^(3/2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c)) + (-a*c*x - c)^(3/2) - 6*sqrt(-a*c*x - c)*c)/(c*sgn(-a*c*x - c)))/a","C",0
314,1,136,0,0.206529," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x,x, algorithm=""giac"")","-c {\left(\frac{4 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{\sqrt{c} \mathrm{sgn}\left(-a c x - c\right)} - \frac{2 \, \arctan\left(\frac{\sqrt{-a c x - c}}{\sqrt{c}}\right)}{\sqrt{c} \mathrm{sgn}\left(-a c x - c\right)} + \frac{-4 i \, \sqrt{2} \arctan\left(-i\right) + 2 \, \sqrt{2} + 2 i \, \arctan\left(-i \, \sqrt{2}\right)}{\sqrt{-c} \mathrm{sgn}\left(c\right)} - \frac{2 \, \sqrt{-a c x - c}}{c \mathrm{sgn}\left(-a c x - c\right)}\right)}"," ",0,"-c*(4*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/(sqrt(c)*sgn(-a*c*x - c)) - 2*arctan(sqrt(-a*c*x - c)/sqrt(c))/(sqrt(c)*sgn(-a*c*x - c)) + (-4*I*sqrt(2)*arctan(-I) + 2*sqrt(2) + 2*I*arctan(-I*sqrt(2)))/(sqrt(-c)*sgn(c)) - 2*sqrt(-a*c*x - c)/(c*sgn(-a*c*x - c)))","C",0
315,1,164,0,0.226678," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""giac"")","-\frac{\frac{4 \, \sqrt{2} a^{2} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{\mathrm{sgn}\left(-a c x - c\right)} - \frac{5 \, a^{2} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x - c}}{\sqrt{c}}\right)}{\mathrm{sgn}\left(-a c x - c\right)} - \frac{-4 i \, \sqrt{2} a^{2} \sqrt{-c} \arctan\left(-i\right) + 5 i \, a^{2} \sqrt{-c} \arctan\left(-i \, \sqrt{2}\right) + \sqrt{2} a^{2} \sqrt{-c}}{\mathrm{sgn}\left(c\right)} - \frac{\sqrt{-a c x - c} a}{x \mathrm{sgn}\left(-a c x - c\right)}}{a}"," ",0,"-(4*sqrt(2)*a^2*sqrt(c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/sgn(-a*c*x - c) - 5*a^2*sqrt(c)*arctan(sqrt(-a*c*x - c)/sqrt(c))/sgn(-a*c*x - c) - (-4*I*sqrt(2)*a^2*sqrt(-c)*arctan(-I) + 5*I*a^2*sqrt(-c)*arctan(-I*sqrt(2)) + sqrt(2)*a^2*sqrt(-c))/sgn(c) - sqrt(-a*c*x - c)*a/(x*sgn(-a*c*x - c)))/a","C",0
316,1,194,0,0.209105," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^3,x, algorithm=""giac"")","-\frac{\frac{16 \, \sqrt{2} a^{3} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{\mathrm{sgn}\left(-a c x - c\right)} - \frac{23 \, a^{3} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x - c}}{\sqrt{c}}\right)}{\mathrm{sgn}\left(-a c x - c\right)} + \frac{16 i \, \sqrt{2} a^{3} \sqrt{-c} \arctan\left(-i\right) - 23 i \, a^{3} \sqrt{-c} \arctan\left(-i \, \sqrt{2}\right) - 11 \, \sqrt{2} a^{3} \sqrt{-c}}{\mathrm{sgn}\left(c\right)} + \frac{9 \, {\left(-a c x - c\right)}^{\frac{3}{2}} a^{3} c + 7 \, \sqrt{-a c x - c} a^{3} c^{2}}{a^{2} c^{2} x^{2} \mathrm{sgn}\left(-a c x - c\right)}}{4 \, a}"," ",0,"-1/4*(16*sqrt(2)*a^3*sqrt(c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/sgn(-a*c*x - c) - 23*a^3*sqrt(c)*arctan(sqrt(-a*c*x - c)/sqrt(c))/sgn(-a*c*x - c) + (16*I*sqrt(2)*a^3*sqrt(-c)*arctan(-I) - 23*I*a^3*sqrt(-c)*arctan(-I*sqrt(2)) - 11*sqrt(2)*a^3*sqrt(-c))/sgn(c) + (9*(-a*c*x - c)^(3/2)*a^3*c + 7*sqrt(-a*c*x - c)*a^3*c^2)/(a^2*c^2*x^2*sgn(-a*c*x - c)))/a","C",0
317,1,222,0,0.217795," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{\frac{96 \, \sqrt{2} a^{4} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{\mathrm{sgn}\left(-a c x - c\right)} - \frac{135 \, a^{4} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x - c}}{\sqrt{c}}\right)}{\mathrm{sgn}\left(-a c x - c\right)} + \frac{96 i \, \sqrt{2} a^{4} \sqrt{-c} \arctan\left(-i\right) - 135 i \, a^{4} \sqrt{-c} \arctan\left(-i \, \sqrt{2}\right) - 91 \, \sqrt{2} a^{4} \sqrt{-c}}{\mathrm{sgn}\left(c\right)} - \frac{57 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} a^{4} c + 88 \, {\left(-a c x - c\right)}^{\frac{3}{2}} a^{4} c^{2} + 39 \, \sqrt{-a c x - c} a^{4} c^{3}}{a^{3} c^{3} x^{3} \mathrm{sgn}\left(-a c x - c\right)}}{24 \, a}"," ",0,"-1/24*(96*sqrt(2)*a^4*sqrt(c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/sgn(-a*c*x - c) - 135*a^4*sqrt(c)*arctan(sqrt(-a*c*x - c)/sqrt(c))/sgn(-a*c*x - c) + (96*I*sqrt(2)*a^4*sqrt(-c)*arctan(-I) - 135*I*a^4*sqrt(-c)*arctan(-I*sqrt(2)) - 91*sqrt(2)*a^4*sqrt(-c))/sgn(c) - (57*(a*c*x + c)^2*sqrt(-a*c*x - c)*a^4*c + 88*(-a*c*x - c)^(3/2)*a^4*c^2 + 39*sqrt(-a*c*x - c)*a^4*c^3)/(a^3*c^3*x^3*sgn(-a*c*x - c)))/a","C",0
318,1,249,0,0.222462," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^5,x, algorithm=""giac"")","-\frac{\frac{768 \, \sqrt{2} a^{5} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{-a c x - c}}{2 \, \sqrt{c}}\right)}{\mathrm{sgn}\left(-a c x - c\right)} - \frac{1089 \, a^{5} \sqrt{c} \arctan\left(\frac{\sqrt{-a c x - c}}{\sqrt{c}}\right)}{\mathrm{sgn}\left(-a c x - c\right)} + \frac{768 i \, \sqrt{2} a^{5} \sqrt{-c} \arctan\left(-i\right) - 1089 i \, a^{5} \sqrt{-c} \arctan\left(-i \, \sqrt{2}\right) - 845 \, \sqrt{2} a^{5} \sqrt{-c}}{\mathrm{sgn}\left(c\right)} - \frac{447 \, {\left(a c x + c\right)}^{3} \sqrt{-a c x - c} a^{5} c - 1127 \, {\left(a c x + c\right)}^{2} \sqrt{-a c x - c} a^{5} c^{2} - 1049 \, {\left(-a c x - c\right)}^{\frac{3}{2}} a^{5} c^{3} - 321 \, \sqrt{-a c x - c} a^{5} c^{4}}{a^{4} c^{4} x^{4} \mathrm{sgn}\left(-a c x - c\right)}}{192 \, a}"," ",0,"-1/192*(768*sqrt(2)*a^5*sqrt(c)*arctan(1/2*sqrt(2)*sqrt(-a*c*x - c)/sqrt(c))/sgn(-a*c*x - c) - 1089*a^5*sqrt(c)*arctan(sqrt(-a*c*x - c)/sqrt(c))/sgn(-a*c*x - c) + (768*I*sqrt(2)*a^5*sqrt(-c)*arctan(-I) - 1089*I*a^5*sqrt(-c)*arctan(-I*sqrt(2)) - 845*sqrt(2)*a^5*sqrt(-c))/sgn(c) - (447*(a*c*x + c)^3*sqrt(-a*c*x - c)*a^5*c - 1127*(a*c*x + c)^2*sqrt(-a*c*x - c)*a^5*c^2 - 1049*(-a*c*x - c)^(3/2)*a^5*c^3 - 321*sqrt(-a*c*x - c)*a^5*c^4)/(a^4*c^4*x^4*sgn(-a*c*x - c)))/a","C",0
319,-2,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
320,-2,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
321,1,58,0,0.172134," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^(3/2)*x,x, algorithm=""giac"")","\frac{1}{105} \, {\left(16 i \, \sqrt{2} + \frac{2 \, {\left(15 \, {\left(x + 1\right)}^{3} \sqrt{-x - 1} - 63 \, {\left(x + 1\right)}^{2} \sqrt{-x - 1} - 70 \, {\left(-x - 1\right)}^{\frac{3}{2}}\right)}}{\mathrm{sgn}\left(-x - 1\right)}\right)} \mathrm{sgn}\left(x\right)"," ",0,"1/105*(16*I*sqrt(2) + 2*(15*(x + 1)^3*sqrt(-x - 1) - 63*(x + 1)^2*sqrt(-x - 1) - 70*(-x - 1)^(3/2))/sgn(-x - 1))*sgn(x)","C",0
322,1,44,0,0.158223," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^(3/2),x, algorithm=""giac"")","\frac{1}{15} \, {\left(-16 i \, \sqrt{2} + \frac{2 \, {\left(3 \, {\left(x + 1\right)}^{2} \sqrt{-x - 1} + 10 \, {\left(-x - 1\right)}^{\frac{3}{2}}\right)}}{\mathrm{sgn}\left(-x - 1\right)}\right)} \mathrm{sgn}\left(x\right)"," ",0,"1/15*(-16*I*sqrt(2) + 2*(3*(x + 1)^2*sqrt(-x - 1) + 10*(-x - 1)^(3/2))/sgn(-x - 1))*sgn(x)","C",0
323,-2,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
324,-2,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1+x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
325,1,44,0,0.179146," ","integrate(1/((-1+x)/(1+x))^(1/2)*x*(1-x)^(1/2),x, algorithm=""giac"")","\frac{1}{15} \, {\left(-4 i \, \sqrt{2} - \frac{2 \, {\left(3 \, {\left(x + 1\right)}^{2} \sqrt{-x - 1} + 5 \, {\left(-x - 1\right)}^{\frac{3}{2}}\right)}}{\mathrm{sgn}\left(-x - 1\right)}\right)} \mathrm{sgn}\left(x\right)"," ",0,"1/15*(-4*I*sqrt(2) - 2*(3*(x + 1)^2*sqrt(-x - 1) + 5*(-x - 1)^(3/2))/sgn(-x - 1))*sgn(x)","C",0
326,1,27,0,0.151520," ","integrate(1/((-1+x)/(1+x))^(1/2)*(1-x)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(-4 i \, \sqrt{2} + \frac{2 \, {\left(-x - 1\right)}^{\frac{3}{2}}}{\mathrm{sgn}\left(-x - 1\right)}\right)} \mathrm{sgn}\left(x\right)"," ",0,"1/3*(-4*I*sqrt(2) + 2*(-x - 1)^(3/2)/sgn(-x - 1))*sgn(x)","C",0
327,-2,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
328,1,13,0,0.142443," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","-2 i \, \sqrt{2} + 2 \, \sqrt{x - 1}"," ",0,"-2*I*sqrt(2) + 2*sqrt(x - 1)","C",0
329,-2,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*sign(x)*((-3*sqrt(2)*atan(i)-(-5*i)*sqrt(2))/3+(-sqrt(2)*atan(sqrt(-x-1)/sqrt(2))-1/3*sqrt(-x-1)*(-x-1)+sqrt(-x-1))/sign(-x-1))","F(-2)",0
330,-2,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*sign(x)*(-sqrt(2)*atan(i)-(-i)*sqrt(2)+(sqrt(-x-1)-sqrt(2)*atan(sqrt(-x-1)/sqrt(2)))/sign(-x-1))","F(-2)",0
331,-2,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*(sqrt(x-1)-atan(sqrt(x-1)/sqrt(2))/sqrt(2)+(atan(i)-2*i)/sqrt(2))","F(-2)",0
332,-2,0,0,0.000000," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1+x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*(-sqrt(2)*atan(i)/2+1/2*sqrt(2)*atan(sqrt(x-1)/sqrt(2)))","F(-2)",0
333,1,54,0,0.134181," ","integrate(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^(3/2),x, algorithm=""giac"")","\frac{{\left(5 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-x - 1}\right) - 4 \, \sqrt{-x - 1} + \frac{2 \, \sqrt{-x - 1}}{x - 1}\right)} \mathrm{sgn}\left(x\right)}{2 \, \mathrm{sgn}\left(-x - 1\right)}"," ",0,"1/2*(5*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-x - 1)) - 4*sqrt(-x - 1) + 2*sqrt(-x - 1)/(x - 1))*sgn(x)/sgn(-x - 1)","A",0
334,1,44,0,0.139032," ","integrate(1/((-1+x)/(1+x))^(1/2)/(1-x)^(3/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-x - 1}\right) + \frac{2 \, \sqrt{-x - 1}}{x - 1}\right)} \mathrm{sgn}\left(x\right)}{2 \, \mathrm{sgn}\left(-x - 1\right)}"," ",0,"1/2*(sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-x - 1)) + 2*sqrt(-x - 1)/(x - 1))*sgn(x)/sgn(-x - 1)","A",0
335,0,0,0,0.000000," ","integrate(x^m*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{-a c x + c} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*x^m*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
336,-2,0,0,0.000000," ","integrate(x^2*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
337,1,69,0,0.138618," ","integrate(x*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","-\frac{4 \, \sqrt{-a c x - c} {\left| c \right|}}{a^{2} c} - \frac{2 \, {\left({\left(a c x + c\right)}^{2} \sqrt{-a c x - c} {\left| c \right|} + 5 \, {\left(-a c x - c\right)}^{\frac{3}{2}} c {\left| c \right|}\right)}}{5 \, a^{2} c^{3}}"," ",0,"-4*sqrt(-a*c*x - c)*abs(c)/(a^2*c) - 2/5*((a*c*x + c)^2*sqrt(-a*c*x - c)*abs(c) + 5*(-a*c*x - c)^(3/2)*c*abs(c))/(a^2*c^3)","A",0
338,1,43,0,0.130785," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(-a c x - c\right)}^{\frac{3}{2}} {\left| c \right|}}{3 \, a c^{2}} + \frac{4 \, \sqrt{-a c x - c} {\left| c \right|}}{a c}"," ",0,"2/3*(-a*c*x - c)^(3/2)*abs(c)/(a*c^2) + 4*sqrt(-a*c*x - c)*abs(c)/(a*c)","A",0
339,1,40,0,0.135752," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""giac"")","-2 \, {\left(\frac{\arctan\left(\frac{\sqrt{-a c x - c}}{\sqrt{c}}\right)}{\sqrt{c}} + \frac{\sqrt{-a c x - c}}{c}\right)} {\left| c \right|}"," ",0,"-2*(arctan(sqrt(-a*c*x - c)/sqrt(c))/sqrt(c) + sqrt(-a*c*x - c)/c)*abs(c)","A",0
340,1,48,0,0.161214," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""giac"")","a {\left(\frac{3 \, \arctan\left(\frac{\sqrt{-a c x - c}}{\sqrt{c}}\right)}{\sqrt{c}} - \frac{\sqrt{-a c x - c}}{a c x}\right)} {\left| c \right|}"," ",0,"a*(3*arctan(sqrt(-a*c*x - c)/sqrt(c))/sqrt(c) - sqrt(-a*c*x - c)/(a*c*x))*abs(c)","A",0
341,1,159,0,0.146389," ","integrate(x^3*(-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{4 \, \sqrt{2} c \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{a^{4} \sqrt{-c}} + \frac{2 \, {\left(35 \, {\left(a c x - c\right)}^{4} \sqrt{-a c x + c} a^{32} c^{32} + 45 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} a^{32} c^{33} + 63 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} a^{32} c^{34} + 105 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{32} c^{35} + 630 \, \sqrt{-a c x + c} a^{32} c^{36}\right)}}{315 \, a^{36} c^{36}}"," ",0,"4*sqrt(2)*c*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a^4*sqrt(-c)) + 2/315*(35*(a*c*x - c)^4*sqrt(-a*c*x + c)*a^32*c^32 + 45*(a*c*x - c)^3*sqrt(-a*c*x + c)*a^32*c^33 + 63*(a*c*x - c)^2*sqrt(-a*c*x + c)*a^32*c^34 + 105*(-a*c*x + c)^(3/2)*a^32*c^35 + 630*sqrt(-a*c*x + c)*a^32*c^36)/(a^36*c^36)","A",0
342,1,105,0,0.139723," ","integrate(x^2*(-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{4 \, \sqrt{2} c \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{a^{3} \sqrt{-c}} + \frac{2 \, {\left(3 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} a^{18} c^{18} - 7 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{18} c^{20} - 42 \, \sqrt{-a c x + c} a^{18} c^{21}\right)}}{21 \, a^{21} c^{21}}"," ",0,"-4*sqrt(2)*c*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a^3*sqrt(-c)) + 2/21*(3*(a*c*x - c)^3*sqrt(-a*c*x + c)*a^18*c^18 - 7*(-a*c*x + c)^(3/2)*a^18*c^20 - 42*sqrt(-a*c*x + c)*a^18*c^21)/(a^21*c^21)","A",0
343,1,105,0,0.122828," ","integrate(x*(-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{4 \, \sqrt{2} c \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{a^{2} \sqrt{-c}} + \frac{2 \, {\left(3 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} a^{8} c^{8} + 5 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{8} c^{9} + 30 \, \sqrt{-a c x + c} a^{8} c^{10}\right)}}{15 \, a^{10} c^{10}}"," ",0,"4*sqrt(2)*c*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a^2*sqrt(-c)) + 2/15*(3*(a*c*x - c)^2*sqrt(-a*c*x + c)*a^8*c^8 + 5*(-a*c*x + c)^(3/2)*a^8*c^9 + 30*sqrt(-a*c*x + c)*a^8*c^10)/(a^10*c^10)","A",0
344,1,77,0,0.143975," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{4 \, \sqrt{2} c \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{a \sqrt{-c}} - \frac{2 \, {\left({\left(-a c x + c\right)}^{\frac{3}{2}} a^{2} c^{2} + 6 \, \sqrt{-a c x + c} a^{2} c^{3}\right)}}{3 \, a^{3} c^{3}}"," ",0,"-4*sqrt(2)*c*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/(a*sqrt(-c)) - 2/3*((-a*c*x + c)^(3/2)*a^2*c^2 + 6*sqrt(-a*c*x + c)*a^2*c^3)/(a^3*c^3)","A",0
345,1,67,0,0.128824," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1)/x,x, algorithm=""giac"")","\frac{4 \, \sqrt{2} c \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{\sqrt{-c}} - \frac{2 \, c \arctan\left(\frac{\sqrt{-a c x + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + 2 \, \sqrt{-a c x + c}"," ",0,"4*sqrt(2)*c*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) - 2*c*arctan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + 2*sqrt(-a*c*x + c)","A",0
346,1,71,0,0.136878," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1)/x^2,x, algorithm=""giac"")","-\frac{4 \, \sqrt{2} a c \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{\sqrt{-c}} + \frac{5 \, a c \arctan\left(\frac{\sqrt{-a c x + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{\sqrt{-a c x + c}}{x}"," ",0,"-4*sqrt(2)*a*c*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + 5*a*c*arctan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + sqrt(-a*c*x + c)/x","A",0
347,1,106,0,0.157280," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1)/x^3,x, algorithm=""giac"")","\frac{4 \, \sqrt{2} a^{2} c \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{\sqrt{-c}} - \frac{23 \, a^{2} c \arctan\left(\frac{\sqrt{-a c x + c}}{\sqrt{-c}}\right)}{4 \, \sqrt{-c}} + \frac{9 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{2} c - 7 \, \sqrt{-a c x + c} a^{2} c^{2}}{4 \, a^{2} c^{2} x^{2}}"," ",0,"4*sqrt(2)*a^2*c*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) - 23/4*a^2*c*arctan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + 1/4*(9*(-a*c*x + c)^(3/2)*a^2*c - 7*sqrt(-a*c*x + c)*a^2*c^2)/(a^2*c^2*x^2)","A",0
348,1,133,0,0.132306," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1)/x^4,x, algorithm=""giac"")","-\frac{4 \, \sqrt{2} a^{3} c \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{\sqrt{-c}} + \frac{45 \, a^{3} c \arctan\left(\frac{\sqrt{-a c x + c}}{\sqrt{-c}}\right)}{8 \, \sqrt{-c}} + \frac{57 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} a^{3} c - 88 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{3} c^{2} + 39 \, \sqrt{-a c x + c} a^{3} c^{3}}{24 \, a^{3} c^{3} x^{3}}"," ",0,"-4*sqrt(2)*a^3*c*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + 45/8*a^3*c*arctan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) + 1/24*(57*(a*c*x - c)^2*sqrt(-a*c*x + c)*a^3*c - 88*(-a*c*x + c)^(3/2)*a^3*c^2 + 39*sqrt(-a*c*x + c)*a^3*c^3)/(a^3*c^3*x^3)","A",0
349,1,160,0,0.153191," ","integrate((-a*c*x+c)^(1/2)*(a*x-1)/(a*x+1)/x^5,x, algorithm=""giac"")","\frac{4 \, \sqrt{2} a^{4} c \arctan\left(\frac{\sqrt{2} \sqrt{-a c x + c}}{2 \, \sqrt{-c}}\right)}{\sqrt{-c}} - \frac{363 \, a^{4} c \arctan\left(\frac{\sqrt{-a c x + c}}{\sqrt{-c}}\right)}{64 \, \sqrt{-c}} - \frac{447 \, {\left(a c x - c\right)}^{3} \sqrt{-a c x + c} a^{4} c + 1127 \, {\left(a c x - c\right)}^{2} \sqrt{-a c x + c} a^{4} c^{2} - 1049 \, {\left(-a c x + c\right)}^{\frac{3}{2}} a^{4} c^{3} + 321 \, \sqrt{-a c x + c} a^{4} c^{4}}{192 \, a^{4} c^{4} x^{4}}"," ",0,"4*sqrt(2)*a^4*c*arctan(1/2*sqrt(2)*sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) - 363/64*a^4*c*arctan(sqrt(-a*c*x + c)/sqrt(-c))/sqrt(-c) - 1/192*(447*(a*c*x - c)^3*sqrt(-a*c*x + c)*a^4*c + 1127*(a*c*x - c)^2*sqrt(-a*c*x + c)*a^4*c^2 - 1049*(-a*c*x + c)^(3/2)*a^4*c^3 + 321*sqrt(-a*c*x + c)*a^4*c^4)/(a^4*c^4*x^4)","A",0
350,-2,0,0,0.000000," ","integrate(x^3*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
351,-2,0,0,0.000000," ","integrate(x^2*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
352,-2,0,0,0.000000," ","integrate(x*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
353,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
354,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
355,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
356,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
357,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
358,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
359,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(2+1/2*n),x, algorithm=""giac"")","\int {\left(-a c x + c\right)}^{\frac{1}{2} \, n + 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(1/2*n + 2)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
360,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(1+1/2*n),x, algorithm=""giac"")","\int {\left(-a c x + c\right)}^{\frac{1}{2} \, n + 1} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(1/2*n + 1)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
361,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(1/2*n),x, algorithm=""giac"")","\int {\left(-a c x + c\right)}^{\frac{1}{2} \, n} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(1/2*n)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
362,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(-1+1/2*n),x, algorithm=""giac"")","\int {\left(-a c x + c\right)}^{\frac{1}{2} \, n - 1} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(1/2*n - 1)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
363,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(-2+1/2*n),x, algorithm=""giac"")","\int {\left(-a c x + c\right)}^{\frac{1}{2} \, n - 2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^(1/2*n - 2)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
364,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^p,x, algorithm=""giac"")","\int {\left(-a c x + c\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a*c*x + c)^p*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
365,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^3,x, algorithm=""giac"")","\int -{\left(a c x - c\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(-(a*c*x - c)^3*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
366,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^2,x, algorithm=""giac"")","\int {\left(a c x - c\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((a*c*x - c)^2*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
367,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c),x, algorithm=""giac"")","\int -{\left(a c x - c\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(-(a*c*x - c)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
368,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c),x, algorithm=""giac"")","\int -\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a c x - c}\,{d x}"," ",0,"integrate(-((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c*x - c), x)","F",0
369,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^2,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(a c x - c\right)}^{2}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c*x - c)^2, x)","F",0
370,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^3,x, algorithm=""giac"")","\int -\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(a c x - c\right)}^{3}}\,{d x}"," ",0,"integrate(-((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c*x - c)^3, x)","F",0
371,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^4,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(a c x - c\right)}^{4}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(a*c*x - c)^4, x)","F",0
372,-2,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{-1,[0,6,1,0,0]%%%}+%%%{3,[0,4,1,1,0]%%%}+%%%{-3,[0,2,1,2,0]%%%}+%%%{1,[0,0,1,3,0]%%%} / %%%{1,[0,0,0,3,3]%%%} Error: Bad Argument Value","F(-2)",0
373,-2,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[0,4,1,0,0]%%%}+%%%{-2,[0,2,1,1,0]%%%}+%%%{1,[0,0,1,2,0]%%%} / %%%{1,[0,0,0,2,2]%%%} Error: Bad Argument Value","F(-2)",0
374,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\int \sqrt{-a c x + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
375,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a c x + c}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/sqrt(-a*c*x + c), x)","F",0
376,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a c x + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(-a*c*x + c)^(3/2), x)","F",0
377,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a c x + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(-a*c*x + c)^(5/2), x)","F",0
378,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a*c*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a c x + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(-a*c*x + c)^(7/2), x)","F",0
379,1,211,0,0.181185," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^4,x, algorithm=""giac"")","\frac{1}{3} \, a c^{4} {\left(\frac{3 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{9 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{6 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} + \frac{\frac{28 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{27 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + 9 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)}"," ",0,"1/3*a*c^4*(3*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 9*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 6*sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)/(a*x + 1) - 1)) + (28*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 27*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 9*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) + 1)^3))","B",0
380,1,180,0,0.159736," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^3,x, algorithm=""giac"")","-a c^{3} {\left(\frac{\arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{2 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{2 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{2 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} - \frac{\frac{5 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + 3 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} + 1\right)}^{2}}\right)}"," ",0,"-a*c^3*(arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 2*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 2*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 2*sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)/(a*x + 1) - 1)) - (5*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 3*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) + 1)^2))","B",0
381,1,113,0,0.162405," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^2,x, algorithm=""giac"")","-a c^{2} {\left(\frac{2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{\log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{4 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 1\right)}}\right)}"," ",0,"-a*c^2*(2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 4*sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)^2/(a*x + 1)^2 - 1)))","A",0
382,1,86,0,0.132276," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x),x, algorithm=""giac"")","-\frac{1}{2} \, a c {\left(\frac{\pi + 2 \, \arctan\left(\frac{\frac{a x - 1}{a x + 1} - 1}{2 \, \sqrt{\frac{a x - 1}{a x + 1}}}\right)}{a^{2}} + \frac{4}{a^{2} {\left(\sqrt{\frac{a x - 1}{a x + 1}} - \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}}\right)}}\right)}"," ",0,"-1/2*a*c*((pi + 2*arctan(1/2*((a*x - 1)/(a*x + 1) - 1)/sqrt((a*x - 1)/(a*x + 1))))/a^2 + 4/(a^2*(sqrt((a*x - 1)/(a*x + 1)) - 1/sqrt((a*x - 1)/(a*x + 1)))))","B",0
383,1,128,0,0.151995," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x),x, algorithm=""giac"")","2 \, a {\left(\frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{\log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c} - \frac{\frac{2 \, {\left(a x - 1\right)}}{a x + 1} - 1}{a^{2} c {\left(\frac{{\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \sqrt{\frac{a x - 1}{a x + 1}}\right)}}\right)}"," ",0,"2*a*(log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c) - (2*(a*x - 1)/(a*x + 1) - 1)/(a^2*c*((a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - sqrt((a*x - 1)/(a*x + 1)))))","A",0
384,1,148,0,0.173849," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^2,x, algorithm=""giac"")","\frac{1}{3} \, a {\left(\frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} - \frac{9 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{2}} - \frac{{\left(a x + 1\right)} {\left(\frac{12 \, {\left(a x - 1\right)}}{a x + 1} + 1\right)}}{{\left(a x - 1\right)} a^{2} c^{2} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{6 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/3*a*(9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) - 9*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^2) - (a*x + 1)*(12*(a*x - 1)/(a*x + 1) + 1)/((a*x - 1)*a^2*c^2*sqrt((a*x - 1)/(a*x + 1))) - 6*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^2*((a*x - 1)/(a*x + 1) - 1)))","A",0
385,1,166,0,0.176842," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^3,x, algorithm=""giac"")","\frac{1}{30} \, a {\left(\frac{120 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{3}} - \frac{120 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{3}} - \frac{{\left(a x + 1\right)}^{2} {\left(\frac{25 \, {\left(a x - 1\right)}}{a x + 1} + \frac{180 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 3\right)}}{{\left(a x - 1\right)}^{2} a^{2} c^{3} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{60 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/30*a*(120*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^3) - 120*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^3) - (a*x + 1)^2*(25*(a*x - 1)/(a*x + 1) + 180*(a*x - 1)^2/(a*x + 1)^2 + 3)/((a*x - 1)^2*a^2*c^3*sqrt((a*x - 1)/(a*x + 1))) - 60*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^3*((a*x - 1)/(a*x + 1) - 1)))","A",0
386,1,182,0,0.177554," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^4,x, algorithm=""giac"")","\frac{1}{420} \, a {\left(\frac{2100 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} - \frac{2100 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{4}} - \frac{{\left(a x + 1\right)}^{3} {\left(\frac{126 \, {\left(a x - 1\right)}}{a x + 1} + \frac{595 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{3360 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 15\right)}}{{\left(a x - 1\right)}^{3} a^{2} c^{4} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{840 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/420*a*(2100*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) - 2100*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^4) - (a*x + 1)^3*(126*(a*x - 1)/(a*x + 1) + 595*(a*x - 1)^2/(a*x + 1)^2 + 3360*(a*x - 1)^3/(a*x + 1)^3 + 15)/((a*x - 1)^3*a^2*c^4*sqrt((a*x - 1)/(a*x + 1))) - 840*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^4*((a*x - 1)/(a*x + 1) - 1)))","A",0
387,1,58,0,0.118707," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^5,x, algorithm=""giac"")","c^{5} x - \frac{3 \, c^{5} \log\left({\left| x \right|}\right)}{a} - \frac{8 \, a^{3} c^{5} x^{3} + 4 \, a^{2} c^{5} x^{2} - 4 \, a c^{5} x + c^{5}}{4 \, a^{5} x^{4}}"," ",0,"c^5*x - 3*c^5*log(abs(x))/a - 1/4*(8*a^3*c^5*x^3 + 4*a^2*c^5*x^2 - 4*a*c^5*x + c^5)/(a^5*x^4)","A",0
388,1,38,0,0.145040," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^4,x, algorithm=""giac"")","c^{4} x - \frac{2 \, c^{4} \log\left({\left| x \right|}\right)}{a} - \frac{3 \, a c^{4} x - c^{4}}{3 \, a^{4} x^{3}}"," ",0,"c^4*x - 2*c^4*log(abs(x))/a - 1/3*(3*a*c^4*x - c^4)/(a^4*x^3)","A",0
389,1,38,0,0.121365," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^3,x, algorithm=""giac"")","c^{3} x - \frac{c^{3} \log\left({\left| x \right|}\right)}{a} + \frac{2 \, a c^{3} x - c^{3}}{2 \, a^{3} x^{2}}"," ",0,"c^3*x - c^3*log(abs(x))/a + 1/2*(2*a*c^3*x - c^3)/(a^3*x^2)","A",0
390,1,16,0,0.134123," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^2,x, algorithm=""giac"")","c^{2} x + \frac{c^{2}}{a^{2} x}"," ",0,"c^2*x + c^2/(a^2*x)","A",0
391,1,12,0,0.123953," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x),x, algorithm=""giac"")","c x + \frac{c \log\left({\left| x \right|}\right)}{a}"," ",0,"c*x + c*log(abs(x))/a","A",0
392,1,36,0,0.137896," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x),x, algorithm=""giac"")","\frac{x}{c} + \frac{3 \, \log\left({\left| a x - 1 \right|}\right)}{a c} - \frac{2}{{\left(a x - 1\right)} a c}"," ",0,"x/c + 3*log(abs(a*x - 1))/(a*c) - 2/((a*x - 1)*a*c)","A",0
393,1,42,0,0.124546," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^2,x, algorithm=""giac"")","\frac{x}{c^{2}} + \frac{4 \, \log\left({\left| a x - 1 \right|}\right)}{a c^{2}} - \frac{5 \, a x - 4}{{\left(a x - 1\right)}^{2} a c^{2}}"," ",0,"x/c^2 + 4*log(abs(a*x - 1))/(a*c^2) - (5*a*x - 4)/((a*x - 1)^2*a*c^2)","A",0
394,1,50,0,0.138070," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^3,x, algorithm=""giac"")","\frac{x}{c^{3}} + \frac{5 \, \log\left({\left| a x - 1 \right|}\right)}{a c^{3}} - \frac{54 \, a^{2} x^{2} - 87 \, a x + 37}{6 \, {\left(a x - 1\right)}^{3} a c^{3}}"," ",0,"x/c^3 + 5*log(abs(a*x - 1))/(a*c^3) - 1/6*(54*a^2*x^2 - 87*a*x + 37)/((a*x - 1)^3*a*c^3)","A",0
395,1,58,0,0.139170," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^4,x, algorithm=""giac"")","\frac{x}{c^{4}} + \frac{6 \, \log\left({\left| a x - 1 \right|}\right)}{a c^{4}} - \frac{28 \, a^{3} x^{3} - 68 \, a^{2} x^{2} + 58 \, a x - 17}{2 \, {\left(a x - 1\right)}^{4} a c^{4}}"," ",0,"x/c^4 + 6*log(abs(a*x - 1))/(a*c^4) - 1/2*(28*a^3*x^3 - 68*a^2*x^2 + 58*a*x - 17)/((a*x - 1)^4*a*c^4)","A",0
396,1,212,0,0.180475," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^4,x, algorithm=""giac"")","-\frac{1}{3} \, a c^{4} {\left(\frac{9 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{6 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} - \frac{\frac{20 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + 9 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)}"," ",0,"-1/3*a*c^4*(9*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 6*sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)/(a*x + 1) - 1)) - (20*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 3*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 9*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) + 1)^3))","B",0
397,1,165,0,0.163349," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^3,x, algorithm=""giac"")","-\frac{1}{4} \, a c^{3} {\left(\frac{3 \, {\left(\pi + 2 \, \arctan\left(\frac{\frac{a x - 1}{a x + 1} - 1}{2 \, \sqrt{\frac{a x - 1}{a x + 1}}}\right)\right)}}{a^{2}} + \frac{4 \, {\left(3 \, {\left(\sqrt{\frac{a x - 1}{a x + 1}} - \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}}\right)}^{2} + 8\right)}}{{\left({\left(\sqrt{\frac{a x - 1}{a x + 1}} - \frac{1}{\sqrt{\frac{a x - 1}{a x + 1}}}\right)}^{3} + 4 \, \sqrt{\frac{a x - 1}{a x + 1}} - \frac{4}{\sqrt{\frac{a x - 1}{a x + 1}}}\right)} a^{2}}\right)}"," ",0,"-1/4*a*c^3*(3*(pi + 2*arctan(1/2*((a*x - 1)/(a*x + 1) - 1)/sqrt((a*x - 1)/(a*x + 1))))/a^2 + 4*(3*(sqrt((a*x - 1)/(a*x + 1)) - 1/sqrt((a*x - 1)/(a*x + 1)))^2 + 8)/(((sqrt((a*x - 1)/(a*x + 1)) - 1/sqrt((a*x - 1)/(a*x + 1)))^3 + 4*sqrt((a*x - 1)/(a*x + 1)) - 4/sqrt((a*x - 1)/(a*x + 1)))*a^2))","B",0
398,1,125,0,0.172524," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^2,x, algorithm=""giac"")","-a c^{2} {\left(\frac{2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{\log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{4 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)} a^{2} {\left(\frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 1\right)}}\right)}"," ",0,"-a*c^2*(2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 4*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/((a*x + 1)*a^2*((a*x - 1)^2/(a*x + 1)^2 - 1)))","B",0
399,1,108,0,0.163972," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x),x, algorithm=""giac"")","2 \, a c {\left(\frac{\arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{\log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"2*a*c*(arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)/(a*x + 1) - 1)))","B",0
400,1,148,0,0.176690," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x),x, algorithm=""giac"")","\frac{2}{3} \, a {\left(\frac{6 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{6 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c} - \frac{{\left(a x + 1\right)} {\left(\frac{9 \, {\left(a x - 1\right)}}{a x + 1} + 1\right)}}{{\left(a x - 1\right)} a^{2} c \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{3 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"2/3*a*(6*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - 6*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c) - (a*x + 1)*(9*(a*x - 1)/(a*x + 1) + 1)/((a*x - 1)*a^2*c*sqrt((a*x - 1)/(a*x + 1))) - 3*sqrt((a*x - 1)/(a*x + 1))/(a^2*c*((a*x - 1)/(a*x + 1) - 1)))","A",0
401,1,166,0,0.165493," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^2,x, algorithm=""giac"")","\frac{1}{15} \, a {\left(\frac{75 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} - \frac{75 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{2}} - \frac{{\left(a x + 1\right)}^{2} {\left(\frac{20 \, {\left(a x - 1\right)}}{a x + 1} + \frac{120 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 3\right)}}{{\left(a x - 1\right)}^{2} a^{2} c^{2} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{30 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/15*a*(75*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) - 75*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^2) - (a*x + 1)^2*(20*(a*x - 1)/(a*x + 1) + 120*(a*x - 1)^2/(a*x + 1)^2 + 3)/((a*x - 1)^2*a^2*c^2*sqrt((a*x - 1)/(a*x + 1))) - 30*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^2*((a*x - 1)/(a*x + 1) - 1)))","A",0
402,1,182,0,0.180637," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^3,x, algorithm=""giac"")","\frac{1}{14} \, a {\left(\frac{84 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{3}} - \frac{84 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{3}} - \frac{{\left(a x + 1\right)}^{3} {\left(\frac{7 \, {\left(a x - 1\right)}}{a x + 1} + \frac{28 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{140 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 1\right)}}{{\left(a x - 1\right)}^{3} a^{2} c^{3} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{28 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/14*a*(84*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^3) - 84*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^3) - (a*x + 1)^3*(7*(a*x - 1)/(a*x + 1) + 28*(a*x - 1)^2/(a*x + 1)^2 + 140*(a*x - 1)^3/(a*x + 1)^3 + 1)/((a*x - 1)^3*a^2*c^3*sqrt((a*x - 1)/(a*x + 1))) - 28*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^3*((a*x - 1)/(a*x + 1) - 1)))","A",0
403,1,198,0,0.184372," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^4,x, algorithm=""giac"")","\frac{1}{1260} \, a {\left(\frac{8820 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} - \frac{8820 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{4}} - \frac{{\left(a x + 1\right)}^{4} {\left(\frac{270 \, {\left(a x - 1\right)}}{a x + 1} + \frac{1071 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{3360 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + \frac{15120 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} + 35\right)}}{{\left(a x - 1\right)}^{4} a^{2} c^{4} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{2520 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/1260*a*(8820*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) - 8820*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^4) - (a*x + 1)^4*(270*(a*x - 1)/(a*x + 1) + 1071*(a*x - 1)^2/(a*x + 1)^2 + 3360*(a*x - 1)^3/(a*x + 1)^3 + 15120*(a*x - 1)^4/(a*x + 1)^4 + 35)/((a*x - 1)^4*a^2*c^4*sqrt((a*x - 1)/(a*x + 1))) - 2520*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^4*((a*x - 1)/(a*x + 1) - 1)))","A",0
404,1,123,0,0.121188," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^5,x, algorithm=""giac"")","\frac{c^{5} \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} - \frac{c^{5} \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right)}{a} + \frac{{\left(12 \, c^{5} + \frac{37 \, c^{5}}{a x - 1} + \frac{52 \, c^{5}}{{\left(a x - 1\right)}^{2}} + \frac{42 \, c^{5}}{{\left(a x - 1\right)}^{3}} + \frac{12 \, c^{5}}{{\left(a x - 1\right)}^{4}}\right)} {\left(a x - 1\right)}}{12 \, a {\left(\frac{1}{a x - 1} + 1\right)}^{4}}"," ",0,"c^5*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a - c^5*log(abs(-1/(a*x - 1) - 1))/a + 1/12*(12*c^5 + 37*c^5/(a*x - 1) + 52*c^5/(a*x - 1)^2 + 42*c^5/(a*x - 1)^3 + 12*c^5/(a*x - 1)^4)*(a*x - 1)/(a*(1/(a*x - 1) + 1)^4)","B",0
405,1,59,0,0.124217," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^4,x, algorithm=""giac"")","\frac{{\left(a x - 1\right)} c^{4}}{a} - \frac{5 \, c^{4} + \frac{9 \, c^{4}}{a x - 1} + \frac{3 \, c^{4}}{{\left(a x - 1\right)}^{2}}}{3 \, a {\left(\frac{1}{a x - 1} + 1\right)}^{3}}"," ",0,"(a*x - 1)*c^4/a - 1/3*(5*c^4 + 9*c^4/(a*x - 1) + 3*c^4/(a*x - 1)^2)/(a*(1/(a*x - 1) + 1)^3)","B",0
406,1,98,0,0.149906," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^3,x, algorithm=""giac"")","-\frac{c^{3} \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} + \frac{c^{3} \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right)}{a} + \frac{{\left(2 \, c^{3} + \frac{c^{3}}{a x - 1} - \frac{2 \, c^{3}}{{\left(a x - 1\right)}^{2}}\right)} {\left(a x - 1\right)}}{2 \, a {\left(\frac{1}{a x - 1} + 1\right)}^{2}}"," ",0,"-c^3*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a + c^3*log(abs(-1/(a*x - 1) - 1))/a + 1/2*(2*c^3 + c^3/(a*x - 1) - 2*c^3/(a*x - 1)^2)*(a*x - 1)/(a*(1/(a*x - 1) + 1)^2)","B",0
407,1,94,0,0.120124," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^2,x, algorithm=""giac"")","-\frac{2 \, c^{2} \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} + \frac{2 \, c^{2} \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right)}{a} + \frac{c^{2} + \frac{2 \, c^{2}}{a x - 1}}{a^{2} {\left(\frac{1}{{\left(a x - 1\right)} a} + \frac{1}{{\left(a x - 1\right)}^{2} a}\right)}}"," ",0,"-2*c^2*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a + 2*c^2*log(abs(-1/(a*x - 1) - 1))/a + (c^2 + 2*c^2/(a*x - 1))/(a^2*(1/((a*x - 1)*a) + 1/((a*x - 1)^2*a)))","B",0
408,1,55,0,0.118454," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x),x, algorithm=""giac"")","\frac{{\left(a x - 1\right)} c}{a} - \frac{3 \, c \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} - \frac{c \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right)}{a}"," ",0,"(a*x - 1)*c/a - 3*c*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a - c*log(abs(-1/(a*x - 1) - 1))/a","B",0
409,1,74,0,0.125700," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x),x, algorithm=""giac"")","\frac{a x - 1}{a c} - \frac{5 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a c} - \frac{2 \, {\left(\frac{4 \, a^{3} c}{a x - 1} + \frac{a^{3} c}{{\left(a x - 1\right)}^{2}}\right)}}{a^{4} c^{2}}"," ",0,"(a*x - 1)/(a*c) - 5*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/(a*c) - 2*(4*a^3*c/(a*x - 1) + a^3*c/(a*x - 1)^2)/(a^4*c^2)","A",0
410,1,94,0,0.139720," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x)^2,x, algorithm=""giac"")","\frac{a x - 1}{a c^{2}} - \frac{6 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a c^{2}} - \frac{\frac{39 \, a^{5} c^{4}}{a x - 1} + \frac{18 \, a^{5} c^{4}}{{\left(a x - 1\right)}^{2}} + \frac{4 \, a^{5} c^{4}}{{\left(a x - 1\right)}^{3}}}{3 \, a^{6} c^{6}}"," ",0,"(a*x - 1)/(a*c^2) - 6*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/(a*c^2) - 1/3*(39*a^5*c^4/(a*x - 1) + 18*a^5*c^4/(a*x - 1)^2 + 4*a^5*c^4/(a*x - 1)^3)/(a^6*c^6)","A",0
411,1,109,0,0.123488," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x)^3,x, algorithm=""giac"")","\frac{a x - 1}{a c^{3}} - \frac{7 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a c^{3}} - \frac{\frac{114 \, a^{7} c^{9}}{a x - 1} + \frac{75 \, a^{7} c^{9}}{{\left(a x - 1\right)}^{2}} + \frac{32 \, a^{7} c^{9}}{{\left(a x - 1\right)}^{3}} + \frac{6 \, a^{7} c^{9}}{{\left(a x - 1\right)}^{4}}}{6 \, a^{8} c^{12}}"," ",0,"(a*x - 1)/(a*c^3) - 7*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/(a*c^3) - 1/6*(114*a^7*c^9/(a*x - 1) + 75*a^7*c^9/(a*x - 1)^2 + 32*a^7*c^9/(a*x - 1)^3 + 6*a^7*c^9/(a*x - 1)^4)/(a^8*c^12)","A",0
412,1,124,0,0.137509," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x)^4,x, algorithm=""giac"")","\frac{a x - 1}{a c^{4}} - \frac{8 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a c^{4}} - \frac{\frac{390 \, a^{9} c^{16}}{a x - 1} + \frac{330 \, a^{9} c^{16}}{{\left(a x - 1\right)}^{2}} + \frac{205 \, a^{9} c^{16}}{{\left(a x - 1\right)}^{3}} + \frac{75 \, a^{9} c^{16}}{{\left(a x - 1\right)}^{4}} + \frac{12 \, a^{9} c^{16}}{{\left(a x - 1\right)}^{5}}}{15 \, a^{10} c^{20}}"," ",0,"(a*x - 1)/(a*c^4) - 8*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/(a*c^4) - 1/15*(390*a^9*c^16/(a*x - 1) + 330*a^9*c^16/(a*x - 1)^2 + 205*a^9*c^16/(a*x - 1)^3 + 75*a^9*c^16/(a*x - 1)^4 + 12*a^9*c^16/(a*x - 1)^5)/(a^10*c^20)","A",0
413,1,265,0,0.174653," ","integrate((c-c/a/x)^4*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{25 \, c^{4} \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{5 \, c^{4} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c^{4} \mathrm{sgn}\left(a x + 1\right)}{a} - \frac{15 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{5} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 60 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{4} a c^{4} \mathrm{sgn}\left(a x + 1\right) + 132 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} a c^{4} \mathrm{sgn}\left(a x + 1\right) - 15 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 64 \, a c^{4} \mathrm{sgn}\left(a x + 1\right)}{3 \, {\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)}^{3} a {\left| a \right|}}"," ",0,"25*c^4*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + 5*c^4*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c^4*sgn(a*x + 1)/a - 1/3*(15*(x*abs(a) - sqrt(a^2*x^2 - 1))^5*c^4*abs(a)*sgn(a*x + 1) + 60*(x*abs(a) - sqrt(a^2*x^2 - 1))^4*a*c^4*sgn(a*x + 1) + 132*(x*abs(a) - sqrt(a^2*x^2 - 1))^2*a*c^4*sgn(a*x + 1) - 15*(x*abs(a) - sqrt(a^2*x^2 - 1))*c^4*abs(a)*sgn(a*x + 1) + 64*a*c^4*sgn(a*x + 1))/(((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)^3*a*abs(a))","B",0
414,1,232,0,0.180570," ","integrate((c-c/a/x)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{13 \, c^{3} \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{4 \, c^{3} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c^{3} \mathrm{sgn}\left(a x + 1\right)}{a} - \frac{{\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{3} c^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 8 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} a c^{3} \mathrm{sgn}\left(a x + 1\right) - {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)} c^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 8 \, a c^{3} \mathrm{sgn}\left(a x + 1\right)}{{\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)}^{2} a {\left| a \right|}}"," ",0,"13*c^3*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + 4*c^3*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c^3*sgn(a*x + 1)/a - ((x*abs(a) - sqrt(a^2*x^2 - 1))^3*c^3*abs(a)*sgn(a*x + 1) + 8*(x*abs(a) - sqrt(a^2*x^2 - 1))^2*a*c^3*sgn(a*x + 1) - (x*abs(a) - sqrt(a^2*x^2 - 1))*c^3*abs(a)*sgn(a*x + 1) + 8*a*c^3*sgn(a*x + 1))/(((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)^2*a*abs(a))","B",0
415,1,130,0,0.169797," ","integrate((c-c/a/x)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{6 \, c^{2} \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{3 \, c^{2} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c^{2} \mathrm{sgn}\left(a x + 1\right)}{a} - \frac{2 \, c^{2} \mathrm{sgn}\left(a x + 1\right)}{{\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)} {\left| a \right|}}"," ",0,"6*c^2*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + 3*c^2*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c^2*sgn(a*x + 1)/a - 2*c^2*sgn(a*x + 1)/(((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)*abs(a))","A",0
416,1,85,0,0.148408," ","integrate((c-c/a/x)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{2 \, c \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{2 \, c \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c \mathrm{sgn}\left(a x + 1\right)}{a}"," ",0,"2*c*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + 2*c*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c*sgn(a*x + 1)/a","A",0
417,1,24,0,0.137909," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x),x, algorithm=""giac"")","\frac{\sqrt{a^{2} x^{2} - 1} \mathrm{sgn}\left(a x + 1\right)}{a c}"," ",0,"sqrt(a^2*x^2 - 1)*sgn(a*x + 1)/(a*c)","A",0
418,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^2,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
419,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
420,1,59,0,0.186452," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^4,x, algorithm=""giac"")","-\frac{3 \, \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{c^{4} {\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} \mathrm{sgn}\left(a x + 1\right)}{a c^{4}}"," ",0,"-3*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/(c^4*abs(a)) + sqrt(a^2*x^2 - 1)*sgn(a*x + 1)/(a*c^4)","A",0
421,1,62,0,0.142960," ","integrate((c-c/a/x)^4*(a*x-1)/(a*x+1),x, algorithm=""giac"")","c^{4} x - \frac{32 \, c^{4} \log\left({\left| a x + 1 \right|}\right)}{a} + \frac{26 \, c^{4} \log\left({\left| x \right|}\right)}{a} + \frac{48 \, a^{2} c^{4} x^{2} - 9 \, a c^{4} x + c^{4}}{3 \, a^{4} x^{3}}"," ",0,"c^4*x - 32*c^4*log(abs(a*x + 1))/a + 26*c^4*log(abs(x))/a + 1/3*(48*a^2*c^4*x^2 - 9*a*c^4*x + c^4)/(a^4*x^3)","A",0
422,1,53,0,0.138267," ","integrate((c-c/a/x)^3*(a*x-1)/(a*x+1),x, algorithm=""giac"")","c^{3} x - \frac{16 \, c^{3} \log\left({\left| a x + 1 \right|}\right)}{a} + \frac{11 \, c^{3} \log\left({\left| x \right|}\right)}{a} + \frac{10 \, a c^{3} x - c^{3}}{2 \, a^{3} x^{2}}"," ",0,"c^3*x - 16*c^3*log(abs(a*x + 1))/a + 11*c^3*log(abs(x))/a + 1/2*(10*a*c^3*x - c^3)/(a^3*x^2)","A",0
423,1,42,0,0.141420," ","integrate((c-c/a/x)^2*(a*x-1)/(a*x+1),x, algorithm=""giac"")","c^{2} x - \frac{8 \, c^{2} \log\left({\left| a x + 1 \right|}\right)}{a} + \frac{4 \, c^{2} \log\left({\left| x \right|}\right)}{a} + \frac{c^{2}}{a^{2} x}"," ",0,"c^2*x - 8*c^2*log(abs(a*x + 1))/a + 4*c^2*log(abs(x))/a + c^2/(a^2*x)","A",0
424,1,25,0,0.137976," ","integrate((c-c/a/x)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","c x - \frac{4 \, c \log\left({\left| a x + 1 \right|}\right)}{a} + \frac{c \log\left({\left| x \right|}\right)}{a}"," ",0,"c*x - 4*c*log(abs(a*x + 1))/a + c*log(abs(x))/a","A",0
425,1,21,0,0.134480," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x),x, algorithm=""giac"")","\frac{x}{c} - \frac{\log\left({\left| a x + 1 \right|}\right)}{a c}"," ",0,"x/c - log(abs(a*x + 1))/(a*c)","A",0
426,1,36,0,0.119162," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^2,x, algorithm=""giac"")","\frac{x}{c^{2}} - \frac{\log\left({\left| a x + 1 \right|}\right)}{2 \, a c^{2}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{2 \, a c^{2}}"," ",0,"x/c^2 - 1/2*log(abs(a*x + 1))/(a*c^2) + 1/2*log(abs(a*x - 1))/(a*c^2)","A",0
427,1,51,0,0.127031," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^3,x, algorithm=""giac"")","\frac{x}{c^{3}} - \frac{\log\left({\left| a x + 1 \right|}\right)}{4 \, a c^{3}} + \frac{5 \, \log\left({\left| a x - 1 \right|}\right)}{4 \, a c^{3}} - \frac{1}{2 \, {\left(a x - 1\right)} a c^{3}}"," ",0,"x/c^3 - 1/4*log(abs(a*x + 1))/(a*c^3) + 5/4*log(abs(a*x - 1))/(a*c^3) - 1/2/((a*x - 1)*a*c^3)","A",0
428,1,57,0,0.142713," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^4,x, algorithm=""giac"")","\frac{x}{c^{4}} - \frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a c^{4}} + \frac{17 \, \log\left({\left| a x - 1 \right|}\right)}{8 \, a c^{4}} - \frac{7 \, a x - 6}{4 \, {\left(a x - 1\right)}^{2} a c^{4}}"," ",0,"x/c^4 - 1/8*log(abs(a*x + 1))/(a*c^4) + 17/8*log(abs(a*x - 1))/(a*c^4) - 1/4*(7*a*x - 6)/((a*x - 1)^2*a*c^4)","A",0
429,0,0,0,0.000000," ","integrate((c-c/a/x)^4*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
430,0,0,0,0.000000," ","integrate((c-c/a/x)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
431,0,0,0,0.000000," ","integrate((c-c/a/x)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
432,0,0,0,0.000000," ","integrate((c-c/a/x)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
433,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
434,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^2,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
435,1,42,0,0.130176," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^3,x, algorithm=""giac"")","\frac{{\left(\frac{\sqrt{a^{2} x^{2} - 1}}{c^{3}} - \frac{1}{\sqrt{a^{2} x^{2} - 1} c^{3}}\right)} \mathrm{sgn}\left(a x + 1\right)}{a}"," ",0,"(sqrt(a^2*x^2 - 1)/c^3 - 1/(sqrt(a^2*x^2 - 1)*c^3))*sgn(a*x + 1)/a","A",0
436,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^4,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(c - \frac{c}{a x}\right)}^{4}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(c - c/(a*x))^4, x)","F",0
437,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^5,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
438,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(9/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
439,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(7/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
440,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(5/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
441,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
442,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
443,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
444,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((c - c/(a*x))^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
445,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((c - c/(a*x))^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
446,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(9/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-97,36.6646323889,7]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-89,7.79369851155,-49]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-64,-30,70]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [22,42,56]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-9,-13,46]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [24,49,-6]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-49,-33,-70]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [8,63,-64]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [2,62,-37]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-80,-23,65]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-85,28,-44]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-22,93,91]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [31,-21,88]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [76,-66,66]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [5,-23,79]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{2,[1,0,1]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{4,[3,1,3]%%%}+%%%{-2,[3,0,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{-2,[2,1,2]%%%}+%%%{1,[2,0,2]%%%}] at parameters values [-88,9,6]Warning, choosing root of [1,0,%%%{-2,[2,1,0]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,0]%%%}+%%%{-2,[3,2,1]%%%}+%%%{1,[2,2,2]%%%}+%%%{-2,[2,2,0]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-69,-8,31]Warning, choosing root of [1,0,%%%{-2,[2,1,0]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,0]%%%}+%%%{-2,[3,2,1]%%%}+%%%{1,[2,2,2]%%%}+%%%{-2,[2,2,0]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [89,2,97]Warning, choosing root of [1,0,%%%{-2,[2,1,0]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,0]%%%}+%%%{-2,[3,2,1]%%%}+%%%{1,[2,2,2]%%%}+%%%{-2,[2,2,0]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-92,80,-24]Warning, choosing root of [1,0,%%%{-2,[2,1,0]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,0]%%%}+%%%{-2,[3,2,1]%%%}+%%%{1,[2,2,2]%%%}+%%%{-2,[2,2,0]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-17,41,64]Warning, choosing root of [1,0,%%%{2,[1,1,1]%%%}+%%%{-2,[0,2,1]%%%}+%%%{-2,[0,0,1]%%%},0,%%%{1,[2,2,2]%%%}+%%%{-2,[1,3,2]%%%}+%%%{2,[1,1,2]%%%}+%%%{1,[0,4,2]%%%}+%%%{-2,[0,2,2]%%%}+%%%{1,[0,0,2]%%%}] at parameters values [18,-51,-42]Warning, choosing root of [1,0,%%%{2,[1,1,1]%%%}+%%%{-2,[0,2,1]%%%}+%%%{-2,[0,0,1]%%%},0,%%%{1,[2,2,2]%%%}+%%%{-2,[1,3,2]%%%}+%%%{2,[1,1,2]%%%}+%%%{1,[0,4,2]%%%}+%%%{-2,[0,2,2]%%%}+%%%{1,[0,0,2]%%%}] at parameters values [-65,22,-94]Sign error (%%%{sqrt(c)*a,0%%%}+%%%{2*sqrt(-a*c)*abs(a),1/2%%%}+%%%{-2*sqrt(c)*a^2,1%%%}+%%%{-a*sqrt(-a*c)*abs(a),3/2%%%}+%%%{-a^2*sqrt(-a*c)*abs(a)/4,5/2%%%}+%%%{undef,7/2%%%})Evaluation time: 3.43Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
447,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-97,36.6646323889,7]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-89,7.79369851155,-49]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-64,-30,70]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [22,42,56]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-9,-13,46]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [24,49,-6]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-49,-33,-70]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [8,63,-64]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [2,62,-37]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-80,-23,65]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-85,28,-44]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-22,93,91]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [31,-21,88]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{2,[1,0,1]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{4,[3,1,3]%%%}+%%%{-2,[3,0,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{-2,[2,1,2]%%%}+%%%{1,[2,0,2]%%%}] at parameters values [76,-66,66]Warning, choosing root of [1,0,%%%{-2,[2,1,0]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,0]%%%}+%%%{-2,[3,2,1]%%%}+%%%{1,[2,2,2]%%%}+%%%{-2,[2,2,0]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [5,-23,79]Warning, choosing root of [1,0,%%%{-2,[2,1,0]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,0]%%%}+%%%{-2,[3,2,1]%%%}+%%%{1,[2,2,2]%%%}+%%%{-2,[2,2,0]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-88,9,6]Warning, choosing root of [1,0,%%%{-2,[2,1,0]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,0]%%%}+%%%{-2,[3,2,1]%%%}+%%%{1,[2,2,2]%%%}+%%%{-2,[2,2,0]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-69,-8,31]Warning, choosing root of [1,0,%%%{-2,[2,1,0]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,0]%%%}+%%%{-2,[3,2,1]%%%}+%%%{1,[2,2,2]%%%}+%%%{-2,[2,2,0]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [89,2,97]Warning, choosing root of [1,0,%%%{2,[1,1,1]%%%}+%%%{-2,[0,2,1]%%%}+%%%{-2,[0,0,1]%%%},0,%%%{1,[2,2,2]%%%}+%%%{-2,[1,3,2]%%%}+%%%{2,[1,1,2]%%%}+%%%{1,[0,4,2]%%%}+%%%{-2,[0,2,2]%%%}+%%%{1,[0,0,2]%%%}] at parameters values [-92,80,-24]Warning, choosing root of [1,0,%%%{2,[1,1,1]%%%}+%%%{-2,[0,2,1]%%%}+%%%{-2,[0,0,1]%%%},0,%%%{1,[2,2,2]%%%}+%%%{-2,[1,3,2]%%%}+%%%{2,[1,1,2]%%%}+%%%{1,[0,4,2]%%%}+%%%{-2,[0,2,2]%%%}+%%%{1,[0,0,2]%%%}] at parameters values [-17,41,64]Sign error (%%%{sqrt(c)*a,0%%%}+%%%{2*sqrt(-a*c)*abs(a),1/2%%%}+%%%{-2*sqrt(c)*a^2,1%%%}+%%%{-a*sqrt(-a*c)*abs(a),3/2%%%}+%%%{-a^2*sqrt(-a*c)*abs(a)/4,5/2%%%}+%%%{undef,7/2%%%})Evaluation time: 0.55Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
448,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-89,63,-49]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-86,-64,-30]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [70,22,42]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [56,-9,-13]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [46,24,49]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [18,-49,-33]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-70,8,63]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{2,[1,0,1]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{4,[3,1,3]%%%}+%%%{-2,[3,0,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{-2,[2,1,2]%%%}+%%%{1,[2,0,2]%%%}] at parameters values [-64,2,62]Sign error (%%%{sqrt(c)*a,0%%%}+%%%{2*sqrt(-a*c)*abs(a),1/2%%%}+%%%{-2*sqrt(c)*a^2,1%%%}+%%%{-a*sqrt(-a*c)*abs(a),3/2%%%}+%%%{-a^2*sqrt(-a*c)*abs(a)/4,5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
449,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-89,63,-49]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-86,-64,-30]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [70,22,42]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [56,-9,-13]Sign error (%%%{sqrt(c)*a,0%%%}+%%%{2*sqrt(-a*c)*abs(a),1/2%%%}+%%%{-2*sqrt(c)*a^2,1%%%}+%%%{-a*sqrt(-a*c)*abs(a),3/2%%%}+%%%{-a^2*sqrt(-a*c)*abs(a)/4,5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
450,1,96,0,0.193371," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\frac{3 \, \sqrt{c} \log\left({\left| a \right|} {\left| c \right|}\right) \mathrm{sgn}\left(x\right)}{2 \, a} - \frac{3 \, \sqrt{c} \log\left({\left| -2 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)} \sqrt{c} {\left| a \right|} + a c \right|}\right)}{2 \, a \mathrm{sgn}\left(x\right)} + \frac{\sqrt{a^{2} c x^{2} - a c x} {\left| a \right|}}{a^{2} \mathrm{sgn}\left(x\right)}"," ",0,"3/2*sqrt(c)*log(abs(a)*abs(c))*sgn(x)/a - 3/2*sqrt(c)*log(abs(-2*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))*sqrt(c)*abs(a) + a*c))/(a*sgn(x)) + sqrt(a^2*c*x^2 - a*c*x)*abs(a)/(a^2*sgn(x))","B",0
451,1,124,0,0.158331," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(1/2),x, algorithm=""giac"")","-\frac{a {\left(\frac{5 \, c \arctan\left(\frac{\sqrt{\frac{a c x - c}{a x}}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c}} + \frac{4 \, c^{2} - \frac{5 \, {\left(a c x - c\right)} c}{a x}}{{\left(c \sqrt{\frac{a c x - c}{a x}} - \frac{{\left(a c x - c\right)} \sqrt{\frac{a c x - c}{a x}}}{a x}\right)} a^{2}}\right)}}{c}"," ",0,"-a*(5*c*arctan(sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)) + (4*c^2 - 5*(a*c*x - c)*c/(a*x))/((c*sqrt((a*c*x - c)/(a*x)) - (a*c*x - c)*sqrt((a*c*x - c)/(a*x))/(a*x))*a^2))/c","B",0
452,1,136,0,0.169970," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(3/2),x, algorithm=""giac"")","-\frac{a {\left(\frac{2 \, {\left(2 \, c + \frac{9 \, {\left(a c x - c\right)}}{a x}\right)} x}{{\left(a c x - c\right)} a \sqrt{\frac{a c x - c}{a x}}} + \frac{21 \, \arctan\left(\frac{\sqrt{\frac{a c x - c}{a x}}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c}} - \frac{3 \, \sqrt{\frac{a c x - c}{a x}}}{a^{2} {\left(c - \frac{a c x - c}{a x}\right)}}\right)}}{3 \, c}"," ",0,"-1/3*a*(2*(2*c + 9*(a*c*x - c)/(a*x))*x/((a*c*x - c)*a*sqrt((a*c*x - c)/(a*x))) + 21*arctan(sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)) - 3*sqrt((a*c*x - c)/(a*x))/(a^2*(c - (a*c*x - c)/(a*x))))/c","A",0
453,1,165,0,0.142903," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(5/2),x, algorithm=""giac"")","-\frac{a {\left(\frac{2 \, {\left(2 \, c^{2} + \frac{5 \, {\left(a c x - c\right)} c}{a x} + \frac{20 \, {\left(a c x - c\right)}^{2}}{a^{2} x^{2}}\right)} x^{2}}{{\left(a c x - c\right)}^{2} c \sqrt{\frac{a c x - c}{a x}}} + \frac{45 \, \arctan\left(\frac{\sqrt{\frac{a c x - c}{a x}}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c} c} - \frac{5 \, \sqrt{\frac{a c x - c}{a x}}}{a^{2} {\left(c - \frac{a c x - c}{a x}\right)} c}\right)}}{5 \, c}"," ",0,"-1/5*a*(2*(2*c^2 + 5*(a*c*x - c)*c/(a*x) + 20*(a*c*x - c)^2/(a^2*x^2))*x^2/((a*c*x - c)^2*c*sqrt((a*c*x - c)/(a*x))) + 45*arctan(sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c) - 5*sqrt((a*c*x - c)/(a*x))/(a^2*(c - (a*c*x - c)/(a*x))*c))/c","A",0
454,1,187,0,0.144849," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a/x)^(7/2),x, algorithm=""giac"")","-\frac{a {\left(\frac{2 \, {\left(30 \, c^{3} + \frac{63 \, {\left(a c x - c\right)} c^{2}}{a x} + \frac{140 \, {\left(a c x - c\right)}^{2} c}{a^{2} x^{2}} + \frac{525 \, {\left(a c x - c\right)}^{3}}{a^{3} x^{3}}\right)} a x^{3}}{{\left(a c x - c\right)}^{3} c^{2} \sqrt{\frac{a c x - c}{a x}}} + \frac{1155 \, \arctan\left(\frac{\sqrt{\frac{a c x - c}{a x}}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c} c^{2}} - \frac{105 \, \sqrt{\frac{a c x - c}{a x}}}{a^{2} {\left(c - \frac{a c x - c}{a x}\right)} c^{2}}\right)}}{105 \, c}"," ",0,"-1/105*a*(2*(30*c^3 + 63*(a*c*x - c)*c^2/(a*x) + 140*(a*c*x - c)^2*c/(a^2*x^2) + 525*(a*c*x - c)^3/(a^3*x^3))*a*x^3/((a*c*x - c)^3*c^2*sqrt((a*c*x - c)/(a*x))) + 1155*arctan(sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c^2) - 105*sqrt((a*c*x - c)/(a*x))/(a^2*(c - (a*c*x - c)/(a*x))*c^2))/c","A",0
455,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(9/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
456,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(7/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
457,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^(5/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
458,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
459,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
460,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c - \frac{c}{a x}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c - c/(a*x))*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
461,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c - c/(a*x))^(3/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
462,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c - c/(a*x))^(5/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
463,-2,0,0,0.000000," ","integrate((c-c/a/x)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
464,-2,0,0,0.000000," ","integrate((c-c/a/x)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
465,-2,0,0,0.000000," ","integrate((c-c/a/x)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
466,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
467,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
468,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
469,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(5/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),sign(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
470,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
471,-2,0,0,0.000000," ","integrate((c-c/a/x)^(7/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
472,-2,0,0,0.000000," ","integrate((c-c/a/x)^(5/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
473,-2,0,0,0.000000," ","integrate((c-c/a/x)^(3/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
474,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Error: Bad Argument Type","F(-2)",0
475,1,131,0,0.163815," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(1/2),x, algorithm=""giac"")","-a c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a c x - c}{a x}}}{2 \, \sqrt{-c}}\right)}{a^{2} \sqrt{-c} c} - \frac{3 \, \arctan\left(\frac{\sqrt{\frac{a c x - c}{a x}}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c} c} - \frac{\sqrt{\frac{a c x - c}{a x}}}{a^{2} {\left(c - \frac{a c x - c}{a x}\right)} c}\right)}"," ",0,"-a*c*(2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c) - 3*arctan(sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c) - sqrt((a*c*x - c)/(a*x))/(a^2*(c - (a*c*x - c)/(a*x))*c))","A",0
476,1,130,0,0.148502," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(3/2),x, algorithm=""giac"")","-a c {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a c x - c}{a x}}}{2 \, \sqrt{-c}}\right)}{a^{2} \sqrt{-c} c^{2}} - \frac{\arctan\left(\frac{\sqrt{\frac{a c x - c}{a x}}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c} c^{2}} - \frac{\sqrt{\frac{a c x - c}{a x}}}{a^{2} {\left(c - \frac{a c x - c}{a x}\right)} c^{2}}\right)}"," ",0,"-a*c*(sqrt(2)*arctan(1/2*sqrt(2)*sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c^2) - arctan(sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c^2) - sqrt((a*c*x - c)/(a*x))/(a^2*(c - (a*c*x - c)/(a*x))*c^2))","A",0
477,1,166,0,0.137980," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(5/2),x, algorithm=""giac"")","-\frac{1}{2} \, a c {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a c x - c}{a x}}}{2 \, \sqrt{-c}}\right)}{a^{2} \sqrt{-c} c^{3}} + \frac{2 \, \arctan\left(\frac{\sqrt{\frac{a c x - c}{a x}}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c} c^{3}} + \frac{2 \, {\left(c - \frac{2 \, {\left(a c x - c\right)}}{a x}\right)}}{{\left(c \sqrt{\frac{a c x - c}{a x}} - \frac{{\left(a c x - c\right)} \sqrt{\frac{a c x - c}{a x}}}{a x}\right)} a^{2} c^{3}}\right)}"," ",0,"-1/2*a*c*(sqrt(2)*arctan(1/2*sqrt(2)*sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c^3) + 2*arctan(sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c^3) + 2*(c - 2*(a*c*x - c)/(a*x))/((c*sqrt((a*c*x - c)/(a*x)) - (a*c*x - c)*sqrt((a*c*x - c)/(a*x))/(a*x))*a^2*c^3))","A",0
478,1,187,0,0.143476," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(7/2),x, algorithm=""giac"")","-\frac{1}{12} \, a c {\left(\frac{2 \, {\left(2 \, c + \frac{15 \, {\left(a c x - c\right)}}{a x}\right)} x}{{\left(a c x - c\right)} a c^{4} \sqrt{\frac{a c x - c}{a x}}} + \frac{3 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a c x - c}{a x}}}{2 \, \sqrt{-c}}\right)}{a^{2} \sqrt{-c} c^{4}} + \frac{36 \, \arctan\left(\frac{\sqrt{\frac{a c x - c}{a x}}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c} c^{4}} - \frac{12 \, \sqrt{\frac{a c x - c}{a x}}}{a^{2} {\left(c - \frac{a c x - c}{a x}\right)} c^{4}}\right)}"," ",0,"-1/12*a*c*(2*(2*c + 15*(a*c*x - c)/(a*x))*x/((a*c*x - c)*a*c^4*sqrt((a*c*x - c)/(a*x))) + 3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c^4) + 36*arctan(sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c^4) - 12*sqrt((a*c*x - c)/(a*x))/(a^2*(c - (a*c*x - c)/(a*x))*c^4))","A",0
479,1,207,0,0.135546," ","integrate((a*x-1)/(a*x+1)/(c-c/a/x)^(9/2),x, algorithm=""giac"")","-\frac{1}{120} \, a c {\left(\frac{2 \, {\left(12 \, c^{2} + \frac{50 \, {\left(a c x - c\right)} c}{a x} + \frac{255 \, {\left(a c x - c\right)}^{2}}{a^{2} x^{2}}\right)} x^{2}}{{\left(a c x - c\right)}^{2} c^{5} \sqrt{\frac{a c x - c}{a x}}} + \frac{15 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a c x - c}{a x}}}{2 \, \sqrt{-c}}\right)}{a^{2} \sqrt{-c} c^{5}} + \frac{600 \, \arctan\left(\frac{\sqrt{\frac{a c x - c}{a x}}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c} c^{5}} - \frac{120 \, \sqrt{\frac{a c x - c}{a x}}}{a^{2} {\left(c - \frac{a c x - c}{a x}\right)} c^{5}}\right)}"," ",0,"-1/120*a*c*(2*(12*c^2 + 50*(a*c*x - c)*c/(a*x) + 255*(a*c*x - c)^2/(a^2*x^2))*x^2/((a*c*x - c)^2*c^5*sqrt((a*c*x - c)/(a*x))) + 15*sqrt(2)*arctan(1/2*sqrt(2)*sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c^5) + 600*arctan(sqrt((a*c*x - c)/(a*x))/sqrt(-c))/(a^2*sqrt(-c)*c^5) - 120*sqrt((a*c*x - c)/(a*x))/(a^2*(c - (a*c*x - c)/(a*x))*c^5))","A",0
480,-2,0,0,0.000000," ","integrate((c-c/a/x)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
481,-2,0,0,0.000000," ","integrate((c-c/a/x)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
482,-2,0,0,0.000000," ","integrate((c-c/a/x)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
483,-2,0,0,0.000000," ","integrate((c-c/a/x)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
484,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
485,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{3,[2,2,2]%%%}+%%%{-2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{2,[1,1]%%%}+%%%{2,[0,1]%%%},0,%%%{1,[2,2]%%%}+%%%{-2,[1,2]%%%}+%%%{1,[0,2]%%%}] at parameters values [-27,-94.616423693]Warning, choosing root of [1,0,%%%{2,[1,1]%%%}+%%%{2,[0,1]%%%},0,%%%{1,[2,2]%%%}+%%%{-2,[1,2]%%%}+%%%{1,[0,2]%%%}] at parameters values [-49,-82.3579015951]Warning, choosing root of [1,0,%%%{2,[1,1]%%%}+%%%{2,[0,1]%%%},0,%%%{1,[2,2]%%%}+%%%{-2,[1,2]%%%}+%%%{1,[0,2]%%%}] at parameters values [70,-29.292030761]Undef/Unsigned Inf encountered in limitLimit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
486,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
487,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{3,[2,2,2]%%%}+%%%{-2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{3,[2,2,2]%%%}+%%%{-2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-89,63,-49]Warning, choosing root of [1,0,%%%{2,[1,1]%%%}+%%%{2,[0,1]%%%},0,%%%{1,[2,2]%%%}+%%%{-2,[1,2]%%%}+%%%{1,[0,2]%%%}] at parameters values [-64,-15.6438432182]Warning, choosing root of [1,0,%%%{2,[1,1]%%%}+%%%{2,[0,1]%%%},0,%%%{1,[2,2]%%%}+%%%{-2,[1,2]%%%}+%%%{1,[0,2]%%%}] at parameters values [42,-55.0901457258]Warning, choosing root of [1,0,%%%{2,[1,1]%%%}+%%%{2,[0,1]%%%},0,%%%{1,[2,2]%%%}+%%%{-2,[1,2]%%%}+%%%{1,[0,2]%%%}] at parameters values [46,-26.2290649475]Undef/Unsigned Inf encountered in limitEvaluation time: 0.42Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
488,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
489,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a x}} x^{m}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^m/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
490,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a x}} x^{2}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^2/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
491,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a x}} x}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
492,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a x}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
493,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{2,[3,1,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [-89,63,-49]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{-2,[1,1,1]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{2,[3,2,3]%%%}+%%%{-2,[3,1,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [-86,-64,-30]Evaluation time: 0.47sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
494,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{2,[3,1,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{-2,[1,1,1]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{2,[3,2,3]%%%}+%%%{-2,[3,1,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [7,-27,26]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*t_nostep+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
495,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{2,[3,1,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [-89,63,-49]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{-2,[1,1,1]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{2,[3,2,3]%%%}+%%%{-2,[3,1,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [-86,-64,-30]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
496,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{2,[3,1,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{-2,[1,1,1]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{2,[3,2,3]%%%}+%%%{-2,[3,1,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [7,-27,26]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*t_nostep+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
497,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{2,[3,1,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [-89,63,-49]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{-2,[1,1,1]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{2,[3,2,3]%%%}+%%%{-2,[3,1,3]%%%}+%%%{1,[2,2,2]%%%}+%%%{2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [-86,-64,-30]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
498,1,142,0,0.174167," ","integrate(1/(a*x-1)*(a*x+1)*x^3*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\frac{1}{64} \, \sqrt{a^{2} c x^{2} - a c x} {\left(2 \, {\left(4 \, x {\left(\frac{2 \, x {\left| a \right|}}{a^{2} \mathrm{sgn}\left(x\right)} + \frac{5 \, {\left| a \right|}}{a^{3} \mathrm{sgn}\left(x\right)}\right)} + \frac{25 \, {\left| a \right|}}{a^{4} \mathrm{sgn}\left(x\right)}\right)} x + \frac{75 \, {\left| a \right|}}{a^{5} \mathrm{sgn}\left(x\right)}\right)} + \frac{75 \, \sqrt{c} \log\left({\left| a \right|} {\left| c \right|}\right) \mathrm{sgn}\left(x\right)}{128 \, a^{4}} - \frac{75 \, \sqrt{c} \log\left({\left| -2 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)} \sqrt{c} {\left| a \right|} + a c \right|}\right)}{128 \, a^{4} \mathrm{sgn}\left(x\right)}"," ",0,"1/64*sqrt(a^2*c*x^2 - a*c*x)*(2*(4*x*(2*x*abs(a)/(a^2*sgn(x)) + 5*abs(a)/(a^3*sgn(x))) + 25*abs(a)/(a^4*sgn(x)))*x + 75*abs(a)/(a^5*sgn(x))) + 75/128*sqrt(c)*log(abs(a)*abs(c))*sgn(x)/a^4 - 75/128*sqrt(c)*log(abs(-2*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))*sqrt(c)*abs(a) + a*c))/(a^4*sgn(x))","A",0
499,1,127,0,0.436933," ","integrate(1/(a*x-1)*(a*x+1)*x^2*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{a^{2} c x^{2} - a c x} {\left(2 \, x {\left(\frac{4 \, x {\left| a \right|}}{a^{2} \mathrm{sgn}\left(x\right)} + \frac{11 \, {\left| a \right|}}{a^{3} \mathrm{sgn}\left(x\right)}\right)} + \frac{33 \, {\left| a \right|}}{a^{4} \mathrm{sgn}\left(x\right)}\right)} + \frac{11 \, \sqrt{c} \log\left({\left| a \right|} {\left| c \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, a^{3}} - \frac{11 \, \sqrt{c} \log\left({\left| -2 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)} \sqrt{c} {\left| a \right|} + a c \right|}\right)}{16 \, a^{3} \mathrm{sgn}\left(x\right)}"," ",0,"1/24*sqrt(a^2*c*x^2 - a*c*x)*(2*x*(4*x*abs(a)/(a^2*sgn(x)) + 11*abs(a)/(a^3*sgn(x))) + 33*abs(a)/(a^4*sgn(x))) + 11/16*sqrt(c)*log(abs(a)*abs(c))*sgn(x)/a^3 - 11/16*sqrt(c)*log(abs(-2*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))*sqrt(c)*abs(a) + a*c))/(a^3*sgn(x))","A",0
500,1,112,0,0.176795," ","integrate(1/(a*x-1)*(a*x+1)*x*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{a^{2} c x^{2} - a c x} {\left(\frac{2 \, x {\left| a \right|}}{a^{2} \mathrm{sgn}\left(x\right)} + \frac{7 \, {\left| a \right|}}{a^{3} \mathrm{sgn}\left(x\right)}\right)} + \frac{7 \, \sqrt{c} \log\left({\left| a \right|} {\left| c \right|}\right) \mathrm{sgn}\left(x\right)}{8 \, a^{2}} - \frac{7 \, \sqrt{c} \log\left({\left| -2 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)} \sqrt{c} {\left| a \right|} + a c \right|}\right)}{8 \, a^{2} \mathrm{sgn}\left(x\right)}"," ",0,"1/4*sqrt(a^2*c*x^2 - a*c*x)*(2*x*abs(a)/(a^2*sgn(x)) + 7*abs(a)/(a^3*sgn(x))) + 7/8*sqrt(c)*log(abs(a)*abs(c))*sgn(x)/a^2 - 7/8*sqrt(c)*log(abs(-2*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))*sqrt(c)*abs(a) + a*c))/(a^2*sgn(x))","A",0
501,1,96,0,0.191710," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\frac{3 \, \sqrt{c} \log\left({\left| a \right|} {\left| c \right|}\right) \mathrm{sgn}\left(x\right)}{2 \, a} - \frac{3 \, \sqrt{c} \log\left({\left| -2 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)} \sqrt{c} {\left| a \right|} + a c \right|}\right)}{2 \, a \mathrm{sgn}\left(x\right)} + \frac{\sqrt{a^{2} c x^{2} - a c x} {\left| a \right|}}{a^{2} \mathrm{sgn}\left(x\right)}"," ",0,"3/2*sqrt(c)*log(abs(a)*abs(c))*sgn(x)/a - 3/2*sqrt(c)*log(abs(-2*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))*sqrt(c)*abs(a) + a*c))/(a*sgn(x)) + sqrt(a^2*c*x^2 - a*c*x)*abs(a)/(a^2*sgn(x))","B",0
502,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-89,63,-49]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-86,-64,-30]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [70,22,42]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [56,-9,-13]Sign error (%%%{sqrt(c)*a,0%%%}+%%%{2*sqrt(-a*c)*abs(a),1/2%%%}+%%%{-2*sqrt(c)*a^2,1%%%}+%%%{-a*sqrt(-a*c)*abs(a),3/2%%%}+%%%{-a^2*sqrt(-a*c)*abs(a)/4,5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
503,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Unable to divide, perhaps due to rounding error%%%{%%%{6,[2,1,5]%%%}+%%%{-6,[1,1,4]%%%}+%%%{-6,[0,1,3]%%%},[4]%%%}+%%%{%%{[%%%{-9,[2,0,4]%%%}+%%%{9,[1,0,3]%%%}+%%%{9,[0,0,2]%%%},0,%%%{9,[4,1,6]%%%}+%%%{-18,[3,1,5]%%%}+%%%{9,[2,1,4]%%%}+%%%{-9,[0,1,2]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[3]%%%}+%%%{%%%{18,[4,1,5]%%%}+%%%{-36,[3,1,4]%%%}+%%%{18,[1,1,2]%%%},[2]%%%}+%%%{%%{[%%%{-3,[4,0,4]%%%}+%%%{6,[3,0,3]%%%}+%%%{-3,[1,0,1]%%%},0,%%%{3,[6,1,6]%%%}+%%%{-9,[5,1,5]%%%}+%%%{9,[4,1,4]%%%}+%%%{-3,[3,1,3]%%%}+%%%{-3,[2,1,2]%%%}+%%%{3,[1,1,1]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[1]%%%} / %%%{%%%{256,[8,8,8]%%%}+%%%{-1024,[7,8,7]%%%}+%%%{1536,[6,8,6]%%%}+%%%{-1024,[5,8,5]%%%}+%%%{256,[4,8,4]%%%},[4]%%%}+%%%{%%{[%%%{-384,[8,7,7]%%%}+%%%{1536,[7,7,6]%%%}+%%%{-2304,[6,7,5]%%%}+%%%{1536,[5,7,4]%%%}+%%%{-384,[4,7,3]%%%},0,%%%{384,[10,8,9]%%%}+%%%{-1920,[9,8,8]%%%}+%%%{4224,[8,8,7]%%%}+%%%{-5376,[7,8,6]%%%}+%%%{4224,[6,8,5]%%%}+%%%{-1920,[5,8,4]%%%}+%%%{384,[4,8,3]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[3]%%%}+%%%{%%%{768,[10,8,8]%%%}+%%%{-3840,[9,8,7]%%%}+%%%{7680,[8,8,6]%%%}+%%%{-7680,[7,8,5]%%%}+%%%{3840,[6,8,4]%%%}+%%%{-768,[5,8,3]%%%},[2]%%%}+%%%{%%{[%%%{-128,[10,7,7]%%%}+%%%{640,[9,7,6]%%%}+%%%{-1280,[8,7,5]%%%}+%%%{1280,[7,7,4]%%%}+%%%{-640,[6,7,3]%%%}+%%%{128,[5,7,2]%%%},0,%%%{128,[12,8,9]%%%}+%%%{-768,[11,8,8]%%%}+%%%{2048,[10,8,7]%%%}+%%%{-3200,[9,8,6]%%%}+%%%{3200,[8,8,5]%%%}+%%%{-2048,[7,8,4]%%%}+%%%{768,[6,8,3]%%%}+%%%{-128,[5,8,2]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[1]%%%} Error: Bad Argument Value","F(-2)",0
504,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Unable to divide, perhaps due to rounding error%%%{%%%{%%{[-5,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,5]%%%},[6]%%%}+%%%{%%{[%%%{25,[0,4]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[5]%%%}+%%%{%%%{%%{[-50,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,5]%%%}+%%%{%%{[50,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4]%%%},[4]%%%}+%%%{%%{[%%%{50,[2,4]%%%}+%%%{-50,[1,3]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[3]%%%}+%%%{%%%{%%{[-25,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,5]%%%}+%%%{%%{[50,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,4]%%%}+%%%{%%{[-25,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,3]%%%},[2]%%%}+%%%{%%{[%%%{5,[4,4]%%%}+%%%{-10,[3,3]%%%}+%%%{5,[2,2]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[1]%%%} / %%%{%%%{%%{poly1[%%%{5,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,12]%%%}+%%%{%%{poly1[%%%{-30,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,11]%%%}+%%%{%%{poly1[%%%{75,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,10]%%%}+%%%{%%{poly1[%%%{-100,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,9]%%%}+%%%{%%{poly1[%%%{75,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,8]%%%}+%%%{%%{poly1[%%%{-30,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7]%%%}+%%%{%%{poly1[%%%{5,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,6]%%%},[6]%%%}+%%%{%%{[%%%{%%%{-25,[6]%%%},[12,11]%%%}+%%%{%%%{150,[6]%%%},[11,10]%%%}+%%%{%%%{-375,[6]%%%},[10,9]%%%}+%%%{%%%{500,[6]%%%},[9,8]%%%}+%%%{%%%{-375,[6]%%%},[8,7]%%%}+%%%{%%%{150,[6]%%%},[7,6]%%%}+%%%{%%%{-25,[6]%%%},[6,5]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[5]%%%}+%%%{%%%{%%{poly1[%%%{50,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,12]%%%}+%%%{%%{poly1[%%%{-350,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,11]%%%}+%%%{%%{poly1[%%%{1050,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,10]%%%}+%%%{%%{poly1[%%%{-1750,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,9]%%%}+%%%{%%{poly1[%%%{1750,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,8]%%%}+%%%{%%{poly1[%%%{-1050,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,7]%%%}+%%%{%%{poly1[%%%{350,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,6]%%%}+%%%{%%{poly1[%%%{-50,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,5]%%%},[4]%%%}+%%%{%%{[%%%{%%%{-50,[6]%%%},[14,11]%%%}+%%%{%%%{350,[6]%%%},[13,10]%%%}+%%%{%%%{-1050,[6]%%%},[12,9]%%%}+%%%{%%%{1750,[6]%%%},[11,8]%%%}+%%%{%%%{-1750,[6]%%%},[10,7]%%%}+%%%{%%%{1050,[6]%%%},[9,6]%%%}+%%%{%%%{-350,[6]%%%},[8,5]%%%}+%%%{%%%{50,[6]%%%},[7,4]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[3]%%%}+%%%{%%%{%%{poly1[%%%{25,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,12]%%%}+%%%{%%{poly1[%%%{-200,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,11]%%%}+%%%{%%{poly1[%%%{700,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,10]%%%}+%%%{%%{poly1[%%%{-1400,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,9]%%%}+%%%{%%{poly1[%%%{1750,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,8]%%%}+%%%{%%{poly1[%%%{-1400,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,7]%%%}+%%%{%%{poly1[%%%{700,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,6]%%%}+%%%{%%{poly1[%%%{-200,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,5]%%%}+%%%{%%{poly1[%%%{25,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,4]%%%},[2]%%%}+%%%{%%{[%%%{%%%{-5,[6]%%%},[16,11]%%%}+%%%{%%%{40,[6]%%%},[15,10]%%%}+%%%{%%%{-140,[6]%%%},[14,9]%%%}+%%%{%%%{280,[6]%%%},[13,8]%%%}+%%%{%%%{-350,[6]%%%},[12,7]%%%}+%%%{%%%{280,[6]%%%},[11,6]%%%}+%%%{%%%{-140,[6]%%%},[10,5]%%%}+%%%{%%%{40,[6]%%%},[9,4]%%%}+%%%{%%%{-5,[6]%%%},[8,3]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[1]%%%} Error: Bad Argument Value","F(-2)",0
505,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Evaluation time: 0.92Unable to divide, perhaps due to rounding error%%%{%%%{210,[2,1,9]%%%}+%%%{-210,[1,1,8]%%%}+%%%{-210,[0,1,7]%%%},[8]%%%}+%%%{%%{[%%%{-735,[2,0,8]%%%}+%%%{735,[1,0,7]%%%}+%%%{735,[0,0,6]%%%},0,%%%{735,[4,1,10]%%%}+%%%{-1470,[3,1,9]%%%}+%%%{735,[2,1,8]%%%}+%%%{-735,[0,1,6]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[7]%%%}+%%%{%%%{4410,[4,1,9]%%%}+%%%{-8820,[3,1,8]%%%}+%%%{4410,[1,1,6]%%%},[6]%%%}+%%%{%%{[%%%{-3675,[4,0,8]%%%}+%%%{7350,[3,0,7]%%%}+%%%{-3675,[1,0,5]%%%},0,%%%{3675,[6,1,10]%%%}+%%%{-11025,[5,1,9]%%%}+%%%{11025,[4,1,8]%%%}+%%%{-3675,[3,1,7]%%%}+%%%{-3675,[2,1,6]%%%}+%%%{3675,[1,1,5]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[5]%%%}+%%%{%%%{7350,[6,1,9]%%%}+%%%{-22050,[5,1,8]%%%}+%%%{14700,[4,1,7]%%%}+%%%{7350,[3,1,6]%%%}+%%%{-7350,[2,1,5]%%%},[4]%%%}+%%%{%%{[%%%{-2205,[6,0,8]%%%}+%%%{6615,[5,0,7]%%%}+%%%{-4410,[4,0,6]%%%}+%%%{-2205,[3,0,5]%%%}+%%%{2205,[2,0,4]%%%},0,%%%{2205,[8,1,10]%%%}+%%%{-8820,[7,1,9]%%%}+%%%{13230,[6,1,8]%%%}+%%%{-8820,[5,1,7]%%%}+%%%{4410,[3,1,5]%%%}+%%%{-2205,[2,1,4]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[3]%%%}+%%%{%%%{1470,[8,1,9]%%%}+%%%{-5880,[7,1,8]%%%}+%%%{7350,[6,1,7]%%%}+%%%{-1470,[5,1,6]%%%}+%%%{-2940,[4,1,5]%%%}+%%%{1470,[3,1,4]%%%},[2]%%%}+%%%{%%{[%%%{-105,[8,0,8]%%%}+%%%{420,[7,0,7]%%%}+%%%{-525,[6,0,6]%%%}+%%%{105,[5,0,5]%%%}+%%%{210,[4,0,4]%%%}+%%%{-105,[3,0,3]%%%},0,%%%{105,[10,1,10]%%%}+%%%{-525,[9,1,9]%%%}+%%%{1050,[8,1,8]%%%}+%%%{-1050,[7,1,7]%%%}+%%%{420,[6,1,6]%%%}+%%%{210,[5,1,5]%%%}+%%%{-315,[4,1,4]%%%}+%%%{105,[3,1,3]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[1]%%%} / %%%{%%%{65536,[16,16,16]%%%}+%%%{-524288,[15,16,15]%%%}+%%%{1835008,[14,16,14]%%%}+%%%{-3670016,[13,16,13]%%%}+%%%{4587520,[12,16,12]%%%}+%%%{-3670016,[11,16,11]%%%}+%%%{1835008,[10,16,10]%%%}+%%%{-524288,[9,16,9]%%%}+%%%{65536,[8,16,8]%%%},[8]%%%}+%%%{%%{[%%%{-229376,[16,15,15]%%%}+%%%{1835008,[15,15,14]%%%}+%%%{-6422528,[14,15,13]%%%}+%%%{12845056,[13,15,12]%%%}+%%%{-16056320,[12,15,11]%%%}+%%%{12845056,[11,15,10]%%%}+%%%{-6422528,[10,15,9]%%%}+%%%{1835008,[9,15,8]%%%}+%%%{-229376,[8,15,7]%%%},0,%%%{229376,[18,16,17]%%%}+%%%{-2064384,[17,16,16]%%%}+%%%{8486912,[16,16,15]%%%}+%%%{-21102592,[15,16,14]%%%}+%%%{35323904,[14,16,13]%%%}+%%%{-41746432,[13,16,12]%%%}+%%%{35323904,[12,16,11]%%%}+%%%{-21102592,[11,16,10]%%%}+%%%{8486912,[10,16,9]%%%}+%%%{-2064384,[9,16,8]%%%}+%%%{229376,[8,16,7]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[7]%%%}+%%%{%%%{1376256,[18,16,16]%%%}+%%%{-12386304,[17,16,15]%%%}+%%%{49545216,[16,16,14]%%%}+%%%{-115605504,[15,16,13]%%%}+%%%{173408256,[14,16,12]%%%}+%%%{-173408256,[13,16,11]%%%}+%%%{115605504,[12,16,10]%%%}+%%%{-49545216,[11,16,9]%%%}+%%%{12386304,[10,16,8]%%%}+%%%{-1376256,[9,16,7]%%%},[6]%%%}+%%%{%%{[%%%{-1146880,[18,15,15]%%%}+%%%{10321920,[17,15,14]%%%}+%%%{-41287680,[16,15,13]%%%}+%%%{96337920,[15,15,12]%%%}+%%%{-144506880,[14,15,11]%%%}+%%%{144506880,[13,15,10]%%%}+%%%{-96337920,[12,15,9]%%%}+%%%{41287680,[11,15,8]%%%}+%%%{-10321920,[10,15,7]%%%}+%%%{1146880,[9,15,6]%%%},0,%%%{1146880,[20,16,17]%%%}+%%%{-11468800,[19,16,16]%%%}+%%%{52756480,[18,16,15]%%%}+%%%{-147947520,[17,16,14]%%%}+%%%{282132480,[16,16,13]%%%}+%%%{-385351680,[15,16,12]%%%}+%%%{385351680,[14,16,11]%%%}+%%%{-282132480,[13,16,10]%%%}+%%%{147947520,[12,16,9]%%%}+%%%{-52756480,[11,16,8]%%%}+%%%{11468800,[10,16,7]%%%}+%%%{-1146880,[9,16,6]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[5]%%%}+%%%{%%%{2293760,[20,16,16]%%%}+%%%{-22937600,[19,16,15]%%%}+%%%{103219200,[18,16,14]%%%}+%%%{-275251200,[17,16,13]%%%}+%%%{481689600,[16,16,12]%%%}+%%%{-578027520,[15,16,11]%%%}+%%%{481689600,[14,16,10]%%%}+%%%{-275251200,[13,16,9]%%%}+%%%{103219200,[12,16,8]%%%}+%%%{-22937600,[11,16,7]%%%}+%%%{2293760,[10,16,6]%%%},[4]%%%}+%%%{%%{[%%%{-688128,[20,15,15]%%%}+%%%{6881280,[19,15,14]%%%}+%%%{-30965760,[18,15,13]%%%}+%%%{82575360,[17,15,12]%%%}+%%%{-144506880,[16,15,11]%%%}+%%%{173408256,[15,15,10]%%%}+%%%{-144506880,[14,15,9]%%%}+%%%{82575360,[13,15,8]%%%}+%%%{-30965760,[12,15,7]%%%}+%%%{6881280,[11,15,6]%%%}+%%%{-688128,[10,15,5]%%%},0,%%%{688128,[22,16,17]%%%}+%%%{-7569408,[21,16,16]%%%}+%%%{38535168,[20,16,15]%%%}+%%%{-120422400,[19,16,14]%%%}+%%%{258048000,[18,16,13]%%%}+%%%{-400490496,[17,16,12]%%%}+%%%{462422016,[16,16,11]%%%}+%%%{-400490496,[15,16,10]%%%}+%%%{258048000,[14,16,9]%%%}+%%%{-120422400,[13,16,8]%%%}+%%%{38535168,[12,16,7]%%%}+%%%{-7569408,[11,16,6]%%%}+%%%{688128,[10,16,5]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[3]%%%}+%%%{%%%{458752,[22,16,16]%%%}+%%%{-5046272,[21,16,15]%%%}+%%%{25231360,[20,16,14]%%%}+%%%{-75694080,[19,16,13]%%%}+%%%{151388160,[18,16,12]%%%}+%%%{-211943424,[17,16,11]%%%}+%%%{211943424,[16,16,10]%%%}+%%%{-151388160,[15,16,9]%%%}+%%%{75694080,[14,16,8]%%%}+%%%{-25231360,[13,16,7]%%%}+%%%{5046272,[12,16,6]%%%}+%%%{-458752,[11,16,5]%%%},[2]%%%}+%%%{%%{[%%%{-32768,[22,15,15]%%%}+%%%{360448,[21,15,14]%%%}+%%%{-1802240,[20,15,13]%%%}+%%%{5406720,[19,15,12]%%%}+%%%{-10813440,[18,15,11]%%%}+%%%{15138816,[17,15,10]%%%}+%%%{-15138816,[16,15,9]%%%}+%%%{10813440,[15,15,8]%%%}+%%%{-5406720,[14,15,7]%%%}+%%%{1802240,[13,15,6]%%%}+%%%{-360448,[12,15,5]%%%}+%%%{32768,[11,15,4]%%%},0,%%%{32768,[24,16,17]%%%}+%%%{-393216,[23,16,16]%%%}+%%%{2195456,[22,16,15]%%%}+%%%{-7569408,[21,16,14]%%%}+%%%{18022400,[20,16,13]%%%}+%%%{-31358976,[19,16,12]%%%}+%%%{41091072,[18,16,11]%%%}+%%%{-41091072,[17,16,10]%%%}+%%%{31358976,[16,16,9]%%%}+%%%{-18022400,[15,16,8]%%%}+%%%{7569408,[14,16,7]%%%}+%%%{-2195456,[13,16,6]%%%}+%%%{393216,[12,16,5]%%%}+%%%{-32768,[11,16,4]%%%}]:[1,0,%%%{-2,[2,1,2]%%%}+%%%{2,[1,1,1]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[3,2,3]%%%}+%%%{-1,[2,2,2]%%%}+%%%{2,[1,2,1]%%%}+%%%{1,[0,2,0]%%%}]%%},[1]%%%} Error: Bad Argument Value","F(-2)",0
506,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Unable to divide, perhaps due to rounding error%%%{%%%{%%{[-315,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,9]%%%},[10]%%%}+%%%{%%{[%%%{2835,[0,8]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[9]%%%}+%%%{%%%{%%{[-11340,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,9]%%%}+%%%{%%{[11340,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,8]%%%},[8]%%%}+%%%{%%{[%%%{26460,[2,8]%%%}+%%%{-26460,[1,7]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[7]%%%}+%%%{%%%{%%{[-39690,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,9]%%%}+%%%{%%{[79380,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,8]%%%}+%%%{%%{[-39690,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,7]%%%},[6]%%%}+%%%{%%{[%%%{39690,[4,8]%%%}+%%%{-79380,[3,7]%%%}+%%%{39690,[2,6]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[5]%%%}+%%%{%%%{%%{[-26460,0]:[1,0,%%%{-1,[1]%%%}]%%},[6,9]%%%}+%%%{%%{[79380,0]:[1,0,%%%{-1,[1]%%%}]%%},[5,8]%%%}+%%%{%%{[-79380,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,7]%%%}+%%%{%%{[26460,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6]%%%},[4]%%%}+%%%{%%{[%%%{11340,[6,8]%%%}+%%%{-34020,[5,7]%%%}+%%%{34020,[4,6]%%%}+%%%{-11340,[3,5]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[3]%%%}+%%%{%%%{%%{[-2835,0]:[1,0,%%%{-1,[1]%%%}]%%},[8,9]%%%}+%%%{%%{[11340,0]:[1,0,%%%{-1,[1]%%%}]%%},[7,8]%%%}+%%%{%%{[-17010,0]:[1,0,%%%{-1,[1]%%%}]%%},[6,7]%%%}+%%%{%%{[11340,0]:[1,0,%%%{-1,[1]%%%}]%%},[5,6]%%%}+%%%{%%{[-2835,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,5]%%%},[2]%%%}+%%%{%%{[%%%{315,[8,8]%%%}+%%%{-1260,[7,7]%%%}+%%%{1890,[6,6]%%%}+%%%{-1260,[5,5]%%%}+%%%{315,[4,4]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[1]%%%} / %%%{%%%{%%{poly1[%%%{315,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[20,20]%%%}+%%%{%%{poly1[%%%{-3150,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[19,19]%%%}+%%%{%%{poly1[%%%{14175,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[18,18]%%%}+%%%{%%{poly1[%%%{-37800,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,17]%%%}+%%%{%%{poly1[%%%{66150,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,16]%%%}+%%%{%%{poly1[%%%{-79380,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,15]%%%}+%%%{%%{poly1[%%%{66150,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,14]%%%}+%%%{%%{poly1[%%%{-37800,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,13]%%%}+%%%{%%{poly1[%%%{14175,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,12]%%%}+%%%{%%{poly1[%%%{-3150,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,11]%%%}+%%%{%%{poly1[%%%{315,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,10]%%%},[10]%%%}+%%%{%%{[%%%{%%%{-2835,[10]%%%},[20,19]%%%}+%%%{%%%{28350,[10]%%%},[19,18]%%%}+%%%{%%%{-127575,[10]%%%},[18,17]%%%}+%%%{%%%{340200,[10]%%%},[17,16]%%%}+%%%{%%%{-595350,[10]%%%},[16,15]%%%}+%%%{%%%{714420,[10]%%%},[15,14]%%%}+%%%{%%%{-595350,[10]%%%},[14,13]%%%}+%%%{%%%{340200,[10]%%%},[13,12]%%%}+%%%{%%%{-127575,[10]%%%},[12,11]%%%}+%%%{%%%{28350,[10]%%%},[11,10]%%%}+%%%{%%%{-2835,[10]%%%},[10,9]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[9]%%%}+%%%{%%%{%%{poly1[%%%{11340,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[22,20]%%%}+%%%{%%{poly1[%%%{-124740,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[21,19]%%%}+%%%{%%{poly1[%%%{623700,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[20,18]%%%}+%%%{%%{poly1[%%%{-1871100,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[19,17]%%%}+%%%{%%{poly1[%%%{3742200,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[18,16]%%%}+%%%{%%{poly1[%%%{-5239080,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,15]%%%}+%%%{%%{poly1[%%%{5239080,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,14]%%%}+%%%{%%{poly1[%%%{-3742200,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,13]%%%}+%%%{%%{poly1[%%%{1871100,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,12]%%%}+%%%{%%{poly1[%%%{-623700,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,11]%%%}+%%%{%%{poly1[%%%{124740,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,10]%%%}+%%%{%%{poly1[%%%{-11340,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,9]%%%},[8]%%%}+%%%{%%{[%%%{%%%{-26460,[10]%%%},[22,19]%%%}+%%%{%%%{291060,[10]%%%},[21,18]%%%}+%%%{%%%{-1455300,[10]%%%},[20,17]%%%}+%%%{%%%{4365900,[10]%%%},[19,16]%%%}+%%%{%%%{-8731800,[10]%%%},[18,15]%%%}+%%%{%%%{12224520,[10]%%%},[17,14]%%%}+%%%{%%%{-12224520,[10]%%%},[16,13]%%%}+%%%{%%%{8731800,[10]%%%},[15,12]%%%}+%%%{%%%{-4365900,[10]%%%},[14,11]%%%}+%%%{%%%{1455300,[10]%%%},[13,10]%%%}+%%%{%%%{-291060,[10]%%%},[12,9]%%%}+%%%{%%%{26460,[10]%%%},[11,8]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[7]%%%}+%%%{%%%{%%{poly1[%%%{39690,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[24,20]%%%}+%%%{%%{poly1[%%%{-476280,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[23,19]%%%}+%%%{%%{poly1[%%%{2619540,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[22,18]%%%}+%%%{%%{poly1[%%%{-8731800,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[21,17]%%%}+%%%{%%{poly1[%%%{19646550,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[20,16]%%%}+%%%{%%{poly1[%%%{-31434480,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[19,15]%%%}+%%%{%%{poly1[%%%{36673560,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[18,14]%%%}+%%%{%%{poly1[%%%{-31434480,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,13]%%%}+%%%{%%{poly1[%%%{19646550,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,12]%%%}+%%%{%%{poly1[%%%{-8731800,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,11]%%%}+%%%{%%{poly1[%%%{2619540,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,10]%%%}+%%%{%%{poly1[%%%{-476280,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,9]%%%}+%%%{%%{poly1[%%%{39690,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,8]%%%},[6]%%%}+%%%{%%{[%%%{%%%{-39690,[10]%%%},[24,19]%%%}+%%%{%%%{476280,[10]%%%},[23,18]%%%}+%%%{%%%{-2619540,[10]%%%},[22,17]%%%}+%%%{%%%{8731800,[10]%%%},[21,16]%%%}+%%%{%%%{-19646550,[10]%%%},[20,15]%%%}+%%%{%%%{31434480,[10]%%%},[19,14]%%%}+%%%{%%%{-36673560,[10]%%%},[18,13]%%%}+%%%{%%%{31434480,[10]%%%},[17,12]%%%}+%%%{%%%{-19646550,[10]%%%},[16,11]%%%}+%%%{%%%{8731800,[10]%%%},[15,10]%%%}+%%%{%%%{-2619540,[10]%%%},[14,9]%%%}+%%%{%%%{476280,[10]%%%},[13,8]%%%}+%%%{%%%{-39690,[10]%%%},[12,7]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[5]%%%}+%%%{%%%{%%{poly1[%%%{26460,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[26,20]%%%}+%%%{%%{poly1[%%%{-343980,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[25,19]%%%}+%%%{%%{poly1[%%%{2063880,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[24,18]%%%}+%%%{%%{poly1[%%%{-7567560,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[23,17]%%%}+%%%{%%{poly1[%%%{18918900,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[22,16]%%%}+%%%{%%{poly1[%%%{-34054020,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[21,15]%%%}+%%%{%%{poly1[%%%{45405360,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[20,14]%%%}+%%%{%%{poly1[%%%{-45405360,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[19,13]%%%}+%%%{%%{poly1[%%%{34054020,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[18,12]%%%}+%%%{%%{poly1[%%%{-18918900,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,11]%%%}+%%%{%%{poly1[%%%{7567560,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,10]%%%}+%%%{%%{poly1[%%%{-2063880,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,9]%%%}+%%%{%%{poly1[%%%{343980,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,8]%%%}+%%%{%%{poly1[%%%{-26460,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,7]%%%},[4]%%%}+%%%{%%{[%%%{%%%{-11340,[10]%%%},[26,19]%%%}+%%%{%%%{147420,[10]%%%},[25,18]%%%}+%%%{%%%{-884520,[10]%%%},[24,17]%%%}+%%%{%%%{3243240,[10]%%%},[23,16]%%%}+%%%{%%%{-8108100,[10]%%%},[22,15]%%%}+%%%{%%%{14594580,[10]%%%},[21,14]%%%}+%%%{%%%{-19459440,[10]%%%},[20,13]%%%}+%%%{%%%{19459440,[10]%%%},[19,12]%%%}+%%%{%%%{-14594580,[10]%%%},[18,11]%%%}+%%%{%%%{8108100,[10]%%%},[17,10]%%%}+%%%{%%%{-3243240,[10]%%%},[16,9]%%%}+%%%{%%%{884520,[10]%%%},[15,8]%%%}+%%%{%%%{-147420,[10]%%%},[14,7]%%%}+%%%{%%%{11340,[10]%%%},[13,6]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[3]%%%}+%%%{%%%{%%{poly1[%%%{2835,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[28,20]%%%}+%%%{%%{poly1[%%%{-39690,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[27,19]%%%}+%%%{%%{poly1[%%%{257985,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[26,18]%%%}+%%%{%%{poly1[%%%{-1031940,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[25,17]%%%}+%%%{%%{poly1[%%%{2837835,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[24,16]%%%}+%%%{%%{poly1[%%%{-5675670,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[23,15]%%%}+%%%{%%{poly1[%%%{8513505,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[22,14]%%%}+%%%{%%{poly1[%%%{-9729720,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[21,13]%%%}+%%%{%%{poly1[%%%{8513505,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[20,12]%%%}+%%%{%%{poly1[%%%{-5675670,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[19,11]%%%}+%%%{%%{poly1[%%%{2837835,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[18,10]%%%}+%%%{%%{poly1[%%%{-1031940,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,9]%%%}+%%%{%%{poly1[%%%{257985,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,8]%%%}+%%%{%%{poly1[%%%{-39690,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,7]%%%}+%%%{%%{poly1[%%%{2835,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,6]%%%},[2]%%%}+%%%{%%{[%%%{%%%{-315,[10]%%%},[28,19]%%%}+%%%{%%%{4410,[10]%%%},[27,18]%%%}+%%%{%%%{-28665,[10]%%%},[26,17]%%%}+%%%{%%%{114660,[10]%%%},[25,16]%%%}+%%%{%%%{-315315,[10]%%%},[24,15]%%%}+%%%{%%%{630630,[10]%%%},[23,14]%%%}+%%%{%%%{-945945,[10]%%%},[22,13]%%%}+%%%{%%%{1081080,[10]%%%},[21,12]%%%}+%%%{%%%{-945945,[10]%%%},[20,11]%%%}+%%%{%%%{630630,[10]%%%},[19,10]%%%}+%%%{%%%{-315315,[10]%%%},[18,9]%%%}+%%%{%%%{114660,[10]%%%},[17,8]%%%}+%%%{%%%{-28665,[10]%%%},[16,7]%%%}+%%%{%%%{4410,[10]%%%},[15,6]%%%}+%%%{%%%{-315,[10]%%%},[14,5]%%%},0]:[1,0,%%%{%%%{-1,[1]%%%},[2,2]%%%}+%%%{%%%{1,[1]%%%},[1,1]%%%}]%%},[1]%%%} Error: Bad Argument Value","F(-2)",0
507,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a x}} x^{3}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^3/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
508,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
509,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
510,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
511,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
512,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
513,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
514,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
515,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
516,0,0,0,0.000000," ","integrate(x^m*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a x}} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x^m*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
517,-2,0,0,0.000000," ","integrate(x^2*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
518,0,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a x}} x \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*x*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
519,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
520,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}}{x}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1))/x, x)","F",0
521,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1))/x^2, x)","F",0
522,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1))/x^3, x)","F",0
523,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a x}} \sqrt{\frac{a x - 1}{a x + 1}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*sqrt((a*x - 1)/(a*x + 1))/x^4, x)","F",0
524,-2,0,0,0.000000," ","integrate(x^3*(c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Error: Bad Argument Type","F(-2)",0
525,-2,0,0,0.000000," ","integrate(x^2*(c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Error: Bad Argument Type","F(-2)",0
526,-2,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Error: Bad Argument Type","F(-2)",0
527,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Error: Bad Argument Type","F(-2)",0
528,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
529,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
530,1,278,0,0.875994," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^3,x, algorithm=""giac"")","\frac{4 \, \sqrt{2} a^{3} c \arctan\left(\frac{\sqrt{2} {\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)} a + \sqrt{c} {\left| a \right|}\right)}}{2 \, a \sqrt{-c}}\right)}{\sqrt{-c} {\left| a \right|} \mathrm{sgn}\left(x\right)} + \frac{2 \, {\left(60 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{4} a^{5} c - 45 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{3} a^{4} c^{\frac{3}{2}} {\left| a \right|} + 35 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{2} a^{5} c^{2} - 15 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)} a^{4} c^{\frac{5}{2}} {\left| a \right|} + 3 \, a^{5} c^{3}\right)}}{15 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{5} a^{2} {\left| a \right|} \mathrm{sgn}\left(x\right)}"," ",0,"4*sqrt(2)*a^3*c*arctan(1/2*sqrt(2)*((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))*a + sqrt(c)*abs(a))/(a*sqrt(-c)))/(sqrt(-c)*abs(a)*sgn(x)) + 2/15*(60*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^4*a^5*c - 45*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^3*a^4*c^(3/2)*abs(a) + 35*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^2*a^5*c^2 - 15*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))*a^4*c^(5/2)*abs(a) + 3*a^5*c^3)/((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^5*a^2*abs(a)*sgn(x))","B",0
531,1,356,0,1.062575," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^4,x, algorithm=""giac"")","-\frac{4 \, \sqrt{2} a^{4} c \arctan\left(\frac{\sqrt{2} {\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)} a + \sqrt{c} {\left| a \right|}\right)}}{2 \, a \sqrt{-c}}\right)}{\sqrt{-c} {\left| a \right|} \mathrm{sgn}\left(x\right)} - \frac{2 \, {\left(84 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{6} a^{7} c - 84 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{5} a^{6} c^{\frac{3}{2}} {\left| a \right|} + 112 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{4} a^{7} c^{2} - 105 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{3} a^{6} c^{\frac{5}{2}} {\left| a \right|} + 63 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{2} a^{7} c^{3} - 21 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)} a^{6} c^{\frac{7}{2}} {\left| a \right|} + 3 \, a^{7} c^{4}\right)}}{21 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{7} a^{3} {\left| a \right|} \mathrm{sgn}\left(x\right)}"," ",0,"-4*sqrt(2)*a^4*c*arctan(1/2*sqrt(2)*((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))*a + sqrt(c)*abs(a))/(a*sqrt(-c)))/(sqrt(-c)*abs(a)*sgn(x)) - 2/21*(84*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^6*a^7*c - 84*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^5*a^6*c^(3/2)*abs(a) + 112*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^4*a^7*c^2 - 105*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^3*a^6*c^(5/2)*abs(a) + 63*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^2*a^7*c^3 - 21*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))*a^6*c^(7/2)*abs(a) + 3*a^7*c^4)/((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^7*a^3*abs(a)*sgn(x))","B",0
532,1,434,0,1.326784," ","integrate((c-c/a/x)^(1/2)*(a*x-1)/(a*x+1)/x^5,x, algorithm=""giac"")","\frac{4 \, \sqrt{2} a^{5} c \arctan\left(\frac{\sqrt{2} {\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)} a + \sqrt{c} {\left| a \right|}\right)}}{2 \, a \sqrt{-c}}\right)}{\sqrt{-c} {\left| a \right|} \mathrm{sgn}\left(x\right)} + \frac{2 \, {\left(1260 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{8} a^{9} c - 1260 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{7} a^{8} c^{\frac{3}{2}} {\left| a \right|} + 2100 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{6} a^{9} c^{2} - 3150 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{5} a^{8} c^{\frac{5}{2}} {\left| a \right|} + 3528 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{4} a^{9} c^{3} - 2625 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{3} a^{8} c^{\frac{7}{2}} {\left| a \right|} + 1215 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{2} a^{9} c^{4} - 315 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)} a^{8} c^{\frac{9}{2}} {\left| a \right|} + 35 \, a^{9} c^{5}\right)}}{315 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - a c x}\right)}^{9} a^{4} {\left| a \right|} \mathrm{sgn}\left(x\right)}"," ",0,"4*sqrt(2)*a^5*c*arctan(1/2*sqrt(2)*((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))*a + sqrt(c)*abs(a))/(a*sqrt(-c)))/(sqrt(-c)*abs(a)*sgn(x)) + 2/315*(1260*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^8*a^9*c - 1260*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^7*a^8*c^(3/2)*abs(a) + 2100*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^6*a^9*c^2 - 3150*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^5*a^8*c^(5/2)*abs(a) + 3528*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^4*a^9*c^3 - 2625*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^3*a^8*c^(7/2)*abs(a) + 1215*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^2*a^9*c^4 - 315*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))*a^8*c^(9/2)*abs(a) + 35*a^9*c^5)/((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - a*c*x))^9*a^4*abs(a)*sgn(x))","B",0
533,-2,0,0,0.000000," ","integrate(x^3*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
534,-2,0,0,0.000000," ","integrate(x^2*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
535,-2,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
536,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
537,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
538,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
539,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
540,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
541,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x),abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
542,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(c-c/a/x),x, algorithm=""giac"")","\int {\left(c - \frac{c}{a x}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a*x))*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
543,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(c-c/a/x),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{c - \frac{c}{a x}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(c - c/(a*x)), x)","F",0
544,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(c-c/a/x)^2,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(c - \frac{c}{a x}\right)}^{2}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(c - c/(a*x))^2, x)","F",0
545,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(c-c/a/x)^(3/2),x, algorithm=""giac"")","\int {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a*x))^(3/2)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
546,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a x}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(sqrt(c - c/(a*x))*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
547,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{\sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/sqrt(c - c/(a*x)), x)","F",0
548,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(c-c/a/x)^(3/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(c - c/(a*x))^(3/2), x)","F",0
549,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(c-c/a/x)^p,x, algorithm=""giac"")","\int {\left(c - \frac{c}{a x}\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a*x))^p*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
550,0,0,0,0.000000," ","integrate(exp(2*p*arccoth(a*x))*(c-c/a/x)^p,x, algorithm=""giac"")","\int {\left(c - \frac{c}{a x}\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{p}\,{d x}"," ",0,"integrate((c - c/(a*x))^p*((a*x - 1)/(a*x + 1))^p, x)","F",0
551,0,0,0,0.000000," ","integrate((c-c/a/x)^p/exp(2*p*arccoth(a*x)),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{p}}{\left(\frac{a x - 1}{a x + 1}\right)^{p}}\,{d x}"," ",0,"integrate((c - c/(a*x))^p/((a*x - 1)/(a*x + 1))^p, x)","F",0
552,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a/x)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{p}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^p/(a*x - 1), x)","F",0
553,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^p,x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a x}\right)}^{p}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a*x))^p/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
554,0,0,0,0.000000," ","integrate((c-c/a/x)^p*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int {\left(c - \frac{c}{a x}\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((c - c/(a*x))^p*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
555,0,0,0,0.000000," ","integrate((c-c/a/x)^p*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\int \frac{{\left(a x - 1\right)} {\left(c - \frac{c}{a x}\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(c - c/(a*x))^p/(a*x + 1), x)","F",0
556,1,340,0,0.186087," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\frac{1}{1152} \, a c^{4} {\left(\frac{315 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{315 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(\frac{2730 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{10458 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + \frac{23202 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + \frac{32768 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} - \frac{23202 \, {\left(a x - 1\right)}^{5} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{5}} + \frac{10458 \, {\left(a x - 1\right)}^{6} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{6}} - \frac{2730 \, {\left(a x - 1\right)}^{7} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{7}} + \frac{315 \, {\left(a x - 1\right)}^{8} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{8}} - 315 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{9}}\right)}"," ",0,"1/1152*a*c^4*(315*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 315*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 2*(2730*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 10458*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 23202*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 32768*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 - 23202*(a*x - 1)^5*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^5 + 10458*(a*x - 1)^6*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^6 - 2730*(a*x - 1)^7*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^7 + 315*(a*x - 1)^8*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^8 - 315*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^9))","A",0
557,1,278,0,0.186625," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{336} \, a c^{3} {\left(\frac{105 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{105 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(\frac{700 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{1981 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} - \frac{3072 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + \frac{1981 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} - \frac{700 \, {\left(a x - 1\right)}^{5} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{5}} + \frac{105 \, {\left(a x - 1\right)}^{6} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{6}} - 105 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{7}}\right)}"," ",0,"1/336*a*c^3*(105*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 105*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 2*(700*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 1981*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 - 3072*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 1981*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 - 700*(a*x - 1)^5*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^5 + 105*(a*x - 1)^6*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^6 - 105*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^7))","A",0
558,1,216,0,0.184694," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{40} \, a c^{2} {\left(\frac{15 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{15 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(\frac{70 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{128 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} - \frac{70 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + \frac{15 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} - 15 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{5}}\right)}"," ",0,"1/40*a*c^2*(15*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 15*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 2*(70*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 128*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 - 70*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 15*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 - 15*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^5))","A",0
559,1,152,0,0.162722," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{1}{6} \, a c {\left(\frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(\frac{8 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{3 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + 3 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"1/6*a*c*(3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 2*(8*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 3*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 3*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^3))","A",0
560,1,22,0,0.149427," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{1}{a c \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"1/(a*c*sqrt((a*x - 1)/(a*x + 1)))","A",0
561,1,70,0,0.133628," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\frac{\frac{{\left(a x + 1\right)} {\left(\frac{6 \, {\left(a x - 1\right)}}{a x + 1} - 1\right)}}{{\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}} + 3 \, \sqrt{\frac{a x - 1}{a x + 1}}}{12 \, a c^{2}}"," ",0,"1/12*((a*x + 1)*(6*(a*x - 1)/(a*x + 1) - 1)/((a*x - 1)*sqrt((a*x - 1)/(a*x + 1))) + 3*sqrt((a*x - 1)/(a*x + 1)))/(a*c^2)","A",0
562,1,117,0,0.157189," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(a x + 1\right)}^{2} {\left(\frac{20 \, {\left(a x - 1\right)}}{a x + 1} - \frac{90 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 3\right)}}{{\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}} + \frac{5 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - 60 \, \sqrt{\frac{a x - 1}{a x + 1}}}{240 \, a c^{3}}"," ",0,"-1/240*((a*x + 1)^2*(20*(a*x - 1)/(a*x + 1) - 90*(a*x - 1)^2/(a*x + 1)^2 - 3)/((a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))) + 5*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 60*sqrt((a*x - 1)/(a*x + 1)))/(a*c^3)","A",0
563,1,164,0,0.156633," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\frac{\frac{{\left(a x + 1\right)}^{3} {\left(\frac{42 \, {\left(a x - 1\right)}}{a x + 1} - \frac{175 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{700 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 5\right)}}{{\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{70 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{7 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + 525 \, \sqrt{\frac{a x - 1}{a x + 1}}}{2240 \, a c^{4}}"," ",0,"1/2240*((a*x + 1)^3*(42*(a*x - 1)/(a*x + 1) - 175*(a*x - 1)^2/(a*x + 1)^2 + 700*(a*x - 1)^3/(a*x + 1)^3 - 5)/((a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))) - 70*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 7*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 525*sqrt((a*x - 1)/(a*x + 1)))/(a*c^4)","A",0
564,1,113,0,0.138234," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^5,x, algorithm=""giac"")","-\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
565,1,82,0,0.137653," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\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
566,1,70,0,0.138103," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\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
567,1,38,0,0.124560," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\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
568,1,21,0,0.118387," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c),x, algorithm=""giac"")","-\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
569,1,14,0,0.141163," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{1}{{\left(a x - 1\right)} a c}"," ",0,"1/((a*x - 1)*a*c)","A",0
570,1,51,0,0.144200," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a c^{2}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{8 \, a c^{2}} + \frac{a x - 2}{4 \, {\left(a x - 1\right)}^{2} a c^{2}}"," ",0,"-1/8*log(abs(a*x + 1))/(a*c^2) + 1/8*log(abs(a*x - 1))/(a*c^2) + 1/4*(a*x - 2)/((a*x - 1)^2*a*c^2)","A",0
571,1,74,0,0.127705," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a c^{3}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{8 \, a c^{3}} + \frac{3 \, a^{3} x^{3} - 6 \, a^{2} x^{2} + a x + 4}{12 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{3} a c^{3}}"," ",0,"-1/8*log(abs(a*x + 1))/(a*c^3) + 1/8*log(abs(a*x - 1))/(a*c^3) + 1/12*(3*a^3*x^3 - 6*a^2*x^2 + a*x + 4)/((a*x + 1)*(a*x - 1)^3*a*c^3)","A",0
572,1,91,0,0.120985," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","-\frac{15 \, \log\left({\left| a x + 1 \right|}\right)}{128 \, a c^{4}} + \frac{15 \, \log\left({\left| a x - 1 \right|}\right)}{128 \, a c^{4}} + \frac{15 \, a^{5} x^{5} - 30 \, a^{4} x^{4} - 10 \, a^{3} x^{3} + 50 \, a^{2} x^{2} - 17 \, a x - 16}{64 \, {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{4} a c^{4}}"," ",0,"-15/128*log(abs(a*x + 1))/(a*c^4) + 15/128*log(abs(a*x - 1))/(a*c^4) + 1/64*(15*a^5*x^5 - 30*a^4*x^4 - 10*a^3*x^3 + 50*a^2*x^2 - 17*a*x - 16)/((a*x + 1)^2*(a*x - 1)^4*a*c^4)","A",0
573,1,340,0,0.199482," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","-\frac{1}{8064} \, a c^{4} {\left(\frac{3465 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3465 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(\frac{30030 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{115038 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} - \frac{334602 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + \frac{360448 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} - \frac{255222 \, {\left(a x - 1\right)}^{5} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{5}} + \frac{115038 \, {\left(a x - 1\right)}^{6} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{6}} - \frac{30030 \, {\left(a x - 1\right)}^{7} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{7}} + \frac{3465 \, {\left(a x - 1\right)}^{8} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{8}} - 3465 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{9}}\right)}"," ",0,"-1/8064*a*c^4*(3465*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3465*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 2*(30030*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 115038*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 - 334602*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 360448*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 - 255222*(a*x - 1)^5*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^5 + 115038*(a*x - 1)^6*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^6 - 30030*(a*x - 1)^7*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^7 + 3465*(a*x - 1)^8*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^8 - 3465*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^9))","A",0
574,1,278,0,0.198505," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{1}{560} \, a c^{3} {\left(\frac{315 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{315 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(\frac{2100 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{8393 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} - \frac{9216 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + \frac{5943 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} - \frac{2100 \, {\left(a x - 1\right)}^{5} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{5}} + \frac{315 \, {\left(a x - 1\right)}^{6} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{6}} - 315 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{7}}\right)}"," ",0,"-1/560*a*c^3*(315*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 315*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 2*(2100*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 8393*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 - 9216*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 5943*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 - 2100*(a*x - 1)^5*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^5 + 315*(a*x - 1)^6*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^6 - 315*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^7))","A",0
575,1,216,0,0.160867," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{1}{120} \, a c^{2} {\left(\frac{105 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{105 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(\frac{790 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{896 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + \frac{490 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} - \frac{105 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} + 105 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{5}}\right)}"," ",0,"-1/120*a*c^2*(105*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 105*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 2*(790*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 896*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 490*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 - 105*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 + 105*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^5))","A",0
576,1,152,0,0.166058," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{1}{6} \, a c {\left(\frac{15 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{15 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{2 \, {\left(\frac{40 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \frac{15 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} - 33 \, \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}^{3}}\right)}"," ",0,"-1/6*a*c*(15*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 15*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 2*(40*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 15*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 - 33*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) - 1)^3))","A",0
577,1,35,0,0.141126," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{a x + 1}{3 \, {\left(a x - 1\right)} a c \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"1/3*(a*x + 1)/((a*x - 1)*a*c*sqrt((a*x - 1)/(a*x + 1)))","A",0
578,1,69,0,0.149221," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(a x + 1\right)}^{2} {\left(\frac{10 \, {\left(a x - 1\right)}}{a x + 1} - \frac{15 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 3\right)}}{60 \, {\left(a x - 1\right)}^{2} a c^{2} \sqrt{\frac{a x - 1}{a x + 1}}}"," ",0,"1/60*(a*x + 1)^2*(10*(a*x - 1)/(a*x + 1) - 15*(a*x - 1)^2/(a*x + 1)^2 - 3)/((a*x - 1)^2*a*c^2*sqrt((a*x - 1)/(a*x + 1)))","A",0
579,1,104,0,0.184083," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(a x + 1\right)}^{3} {\left(\frac{28 \, {\left(a x - 1\right)}}{a x + 1} - \frac{70 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{140 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - 5\right)}}{{\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}} + 35 \, \sqrt{\frac{a x - 1}{a x + 1}}}{560 \, a c^{3}}"," ",0,"-1/560*((a*x + 1)^3*(28*(a*x - 1)/(a*x + 1) - 70*(a*x - 1)^2/(a*x + 1)^2 + 140*(a*x - 1)^3/(a*x + 1)^3 - 5)/((a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))) + 35*sqrt((a*x - 1)/(a*x + 1)))/(a*c^3)","A",0
580,1,149,0,0.161276," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\frac{\frac{{\left(a x + 1\right)}^{4} {\left(\frac{54 \, {\left(a x - 1\right)}}{a x + 1} - \frac{189 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{420 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} - \frac{945 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} - 7\right)}}{{\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}} + \frac{21 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - 378 \, \sqrt{\frac{a x - 1}{a x + 1}}}{4032 \, a c^{4}}"," ",0,"1/4032*((a*x + 1)^4*(54*(a*x - 1)/(a*x + 1) - 189*(a*x - 1)^2/(a*x + 1)^2 + 420*(a*x - 1)^3/(a*x + 1)^3 - 945*(a*x - 1)^4/(a*x + 1)^4 - 7)/((a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))) + 21*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - 378*sqrt((a*x - 1)/(a*x + 1)))/(a*c^4)","A",0
581,1,102,0,0.127899," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^5,x, algorithm=""giac"")","-\frac{{\left(15 \, c^{5} + \frac{231 \, c^{5}}{a x - 1} + \frac{1540 \, c^{5}}{{\left(a x - 1\right)}^{2}} + \frac{5775 \, c^{5}}{{\left(a x - 1\right)}^{3}} + \frac{13200 \, c^{5}}{{\left(a x - 1\right)}^{4}} + \frac{18480 \, c^{5}}{{\left(a x - 1\right)}^{5}} + \frac{14784 \, c^{5}}{{\left(a x - 1\right)}^{6}} + \frac{5280 \, c^{5}}{{\left(a x - 1\right)}^{7}}\right)} {\left(a x - 1\right)}^{11}}{165 \, a}"," ",0,"-1/165*(15*c^5 + 231*c^5/(a*x - 1) + 1540*c^5/(a*x - 1)^2 + 5775*c^5/(a*x - 1)^3 + 13200*c^5/(a*x - 1)^4 + 18480*c^5/(a*x - 1)^5 + 14784*c^5/(a*x - 1)^6 + 5280*c^5/(a*x - 1)^7)*(a*x - 1)^11/a","A",0
582,1,90,0,0.124259," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\frac{{\left(14 \, c^{4} + \frac{189 \, c^{4}}{a x - 1} + \frac{1080 \, c^{4}}{{\left(a x - 1\right)}^{2}} + \frac{3360 \, c^{4}}{{\left(a x - 1\right)}^{3}} + \frac{6048 \, c^{4}}{{\left(a x - 1\right)}^{4}} + \frac{6048 \, c^{4}}{{\left(a x - 1\right)}^{5}} + \frac{2688 \, c^{4}}{{\left(a x - 1\right)}^{6}}\right)} {\left(a x - 1\right)}^{9}}{126 \, a}"," ",0,"1/126*(14*c^4 + 189*c^4/(a*x - 1) + 1080*c^4/(a*x - 1)^2 + 3360*c^4/(a*x - 1)^3 + 6048*c^4/(a*x - 1)^4 + 6048*c^4/(a*x - 1)^5 + 2688*c^4/(a*x - 1)^6)*(a*x - 1)^9/a","A",0
583,1,78,0,0.125134," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{{\left(3 \, c^{3} + \frac{35 \, c^{3}}{a x - 1} + \frac{168 \, c^{3}}{{\left(a x - 1\right)}^{2}} + \frac{420 \, c^{3}}{{\left(a x - 1\right)}^{3}} + \frac{560 \, c^{3}}{{\left(a x - 1\right)}^{4}} + \frac{336 \, c^{3}}{{\left(a x - 1\right)}^{5}}\right)} {\left(a x - 1\right)}^{7}}{21 \, a}"," ",0,"-1/21*(3*c^3 + 35*c^3/(a*x - 1) + 168*c^3/(a*x - 1)^2 + 420*c^3/(a*x - 1)^3 + 560*c^3/(a*x - 1)^4 + 336*c^3/(a*x - 1)^5)*(a*x - 1)^7/a","B",0
584,1,64,0,0.138947," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(c^{2} + \frac{10 \, c^{2}}{a x - 1} + \frac{40 \, c^{2}}{{\left(a x - 1\right)}^{2}} + \frac{80 \, c^{2}}{{\left(a x - 1\right)}^{3}} + \frac{80 \, c^{2}}{{\left(a x - 1\right)}^{4}}\right)} {\left(a x - 1\right)}^{5}}{5 \, a}"," ",0,"1/5*(c^2 + 10*c^2/(a*x - 1) + 40*c^2/(a*x - 1)^2 + 80*c^2/(a*x - 1)^3 + 80*c^2/(a*x - 1)^4)*(a*x - 1)^5/a","B",0
585,1,60,0,0.137841," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{{\left(a x - 1\right)}^{3} {\left(c + \frac{9 \, c}{a x - 1} + \frac{36 \, c}{{\left(a x - 1\right)}^{2}}\right)}}{3 \, a} + \frac{8 \, c \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a}"," ",0,"-1/3*(a*x - 1)^3*(c + 9*c/(a*x - 1) + 36*c/(a*x - 1)^2)/a + 8*c*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a","A",0
586,1,27,0,0.136589," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{\frac{1}{{\left(a x - 1\right)} a} + \frac{1}{{\left(a x - 1\right)}^{2} a}}{c}"," ",0,"(1/((a*x - 1)*a) + 1/((a*x - 1)^2*a))/c","B",0
587,1,15,0,0.121625," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{1}{3 \, {\left(a x - 1\right)}^{3} a c^{2}}"," ",0,"-1/3/((a*x - 1)^3*a*c^2)","A",0
588,1,91,0,0.139228," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{\log\left({\left| -\frac{2}{a x - 1} - 1 \right|}\right)}{32 \, a c^{3}} - \frac{\frac{3 \, a^{3} c^{9}}{a x - 1} - \frac{3 \, a^{3} c^{9}}{{\left(a x - 1\right)}^{2}} + \frac{4 \, a^{3} c^{9}}{{\left(a x - 1\right)}^{3}} - \frac{6 \, a^{3} c^{9}}{{\left(a x - 1\right)}^{4}}}{48 \, a^{4} c^{12}}"," ",0,"1/32*log(abs(-2/(a*x - 1) - 1))/(a*c^3) - 1/48*(3*a^3*c^9/(a*x - 1) - 3*a^3*c^9/(a*x - 1)^2 + 4*a^3*c^9/(a*x - 1)^3 - 6*a^3*c^9/(a*x - 1)^4)/(a^4*c^12)","A",0
589,1,127,0,0.142305," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| -\frac{2}{a x - 1} - 1 \right|}\right)}{64 \, a c^{4}} + \frac{1}{128 \, a c^{4} {\left(\frac{2}{a x - 1} + 1\right)}} - \frac{\frac{25 \, a^{9} c^{16}}{a x - 1} - \frac{20 \, a^{9} c^{16}}{{\left(a x - 1\right)}^{2}} + \frac{20 \, a^{9} c^{16}}{{\left(a x - 1\right)}^{3}} - \frac{20 \, a^{9} c^{16}}{{\left(a x - 1\right)}^{4}} + \frac{16 \, a^{9} c^{16}}{{\left(a x - 1\right)}^{5}}}{320 \, a^{10} c^{20}}"," ",0,"3/64*log(abs(-2/(a*x - 1) - 1))/(a*c^4) + 1/128/(a*c^4*(2/(a*x - 1) + 1)) - 1/320*(25*a^9*c^16/(a*x - 1) - 20*a^9*c^16/(a*x - 1)^2 + 20*a^9*c^16/(a*x - 1)^3 - 20*a^9*c^16/(a*x - 1)^4 + 16*a^9*c^16/(a*x - 1)^5)/(a^10*c^20)","A",0
590,1,196,0,0.179396," ","integrate((-a^2*c*x^2+c)^4*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{35 \, c^{4} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{128 \, {\left| a \right|}} + \frac{1}{1152} \, \sqrt{a^{2} x^{2} - 1} {\left(\frac{128 \, c^{4} \mathrm{sgn}\left(a x + 1\right)}{a} + {\left(837 \, c^{4} \mathrm{sgn}\left(a x + 1\right) - 2 \, {\left(256 \, a c^{4} \mathrm{sgn}\left(a x + 1\right) + {\left(489 \, a^{2} c^{4} \mathrm{sgn}\left(a x + 1\right) - 4 \, {\left(96 \, a^{3} c^{4} \mathrm{sgn}\left(a x + 1\right) + {\left(75 \, a^{4} c^{4} \mathrm{sgn}\left(a x + 1\right) - 2 \, {\left(32 \, a^{5} c^{4} \mathrm{sgn}\left(a x + 1\right) - {\left(8 \, a^{7} c^{4} x \mathrm{sgn}\left(a x + 1\right) - 9 \, a^{6} c^{4} \mathrm{sgn}\left(a x + 1\right)\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"35/128*c^4*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + 1/1152*sqrt(a^2*x^2 - 1)*(128*c^4*sgn(a*x + 1)/a + (837*c^4*sgn(a*x + 1) - 2*(256*a*c^4*sgn(a*x + 1) + (489*a^2*c^4*sgn(a*x + 1) - 4*(96*a^3*c^4*sgn(a*x + 1) + (75*a^4*c^4*sgn(a*x + 1) - 2*(32*a^5*c^4*sgn(a*x + 1) - (8*a^7*c^4*x*sgn(a*x + 1) - 9*a^6*c^4*sgn(a*x + 1))*x)*x)*x)*x)*x)*x)*x)","A",0
591,1,161,0,0.153726," ","integrate((-a^2*c*x^2+c)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{5 \, c^{3} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{16 \, {\left| a \right|}} + \frac{1}{336} \, \sqrt{a^{2} x^{2} - 1} {\left(\frac{48 \, c^{3} \mathrm{sgn}\left(a x + 1\right)}{a} + {\left(231 \, c^{3} \mathrm{sgn}\left(a x + 1\right) - 2 \, {\left(72 \, a c^{3} \mathrm{sgn}\left(a x + 1\right) + {\left(91 \, a^{2} c^{3} \mathrm{sgn}\left(a x + 1\right) - 4 \, {\left(18 \, a^{3} c^{3} \mathrm{sgn}\left(a x + 1\right) - {\left(6 \, a^{5} c^{3} x \mathrm{sgn}\left(a x + 1\right) - 7 \, a^{4} c^{3} \mathrm{sgn}\left(a x + 1\right)\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"5/16*c^3*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + 1/336*sqrt(a^2*x^2 - 1)*(48*c^3*sgn(a*x + 1)/a + (231*c^3*sgn(a*x + 1) - 2*(72*a*c^3*sgn(a*x + 1) + (91*a^2*c^3*sgn(a*x + 1) - 4*(18*a^3*c^3*sgn(a*x + 1) - (6*a^5*c^3*x*sgn(a*x + 1) - 7*a^4*c^3*sgn(a*x + 1))*x)*x)*x)*x)*x)","A",0
592,1,126,0,0.150585," ","integrate((-a^2*c*x^2+c)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{3 \, c^{2} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{8 \, {\left| a \right|}} + \frac{1}{40} \, \sqrt{a^{2} x^{2} - 1} {\left({\left(25 \, c^{2} \mathrm{sgn}\left(a x + 1\right) - 2 \, {\left(8 \, a c^{2} \mathrm{sgn}\left(a x + 1\right) - {\left(4 \, a^{3} c^{2} x \mathrm{sgn}\left(a x + 1\right) - 5 \, a^{2} c^{2} \mathrm{sgn}\left(a x + 1\right)\right)} x\right)} x\right)} x + \frac{8 \, c^{2} \mathrm{sgn}\left(a x + 1\right)}{a}\right)}"," ",0,"3/8*c^2*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + 1/40*sqrt(a^2*x^2 - 1)*((25*c^2*sgn(a*x + 1) - 2*(8*a*c^2*sgn(a*x + 1) - (4*a^3*c^2*x*sgn(a*x + 1) - 5*a^2*c^2*sgn(a*x + 1))*x)*x)*x + 8*c^2*sgn(a*x + 1)/a)","A",0
593,1,82,0,0.166875," ","integrate((-a^2*c*x^2+c)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\frac{c \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{2 \, {\left| a \right|}} - \frac{1}{6} \, \sqrt{a^{2} x^{2} - 1} {\left({\left(2 \, a c x \mathrm{sgn}\left(a x + 1\right) - 3 \, c \mathrm{sgn}\left(a x + 1\right)\right)} x - \frac{2 \, c \mathrm{sgn}\left(a x + 1\right)}{a}\right)}"," ",0,"1/2*c*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) - 1/6*sqrt(a^2*x^2 - 1)*((2*a*c*x*sgn(a*x + 1) - 3*c*sgn(a*x + 1))*x - 2*c*sgn(a*x + 1)/a)","A",0
594,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
595,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a^{2} c x^{2} - c\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(a^2*c*x^2 - c)^2, x)","F",0
596,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a^{2} c x^{2} - c\right)}^{3}}\,{d x}"," ",0,"integrate(-sqrt((a*x - 1)/(a*x + 1))/(a^2*c*x^2 - c)^3, x)","F",0
597,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a^{2} c x^{2} - c\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(a^2*c*x^2 - c)^4, x)","F",0
598,1,80,0,0.135511," ","integrate((-a^2*c*x^2+c)^4*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\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
599,1,70,0,0.133724," ","integrate((-a^2*c*x^2+c)^3*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\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
600,1,37,0,0.138423," ","integrate((-a^2*c*x^2+c)^2*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\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
601,1,20,0,0.136035," ","integrate((-a^2*c*x^2+c)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\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
602,1,14,0,0.145904," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{1}{{\left(a x + 1\right)} a c}"," ",0,"1/((a*x + 1)*a*c)","A",0
603,1,51,0,0.125797," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a c^{2}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{8 \, a c^{2}} + \frac{a x + 2}{4 \, {\left(a x + 1\right)}^{2} a c^{2}}"," ",0,"-1/8*log(abs(a*x + 1))/(a*c^2) + 1/8*log(abs(a*x - 1))/(a*c^2) + 1/4*(a*x + 2)/((a*x + 1)^2*a*c^2)","A",0
604,1,74,0,0.150228," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a c^{3}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{8 \, a c^{3}} + \frac{3 \, a^{3} x^{3} + 6 \, a^{2} x^{2} + a x - 4}{12 \, {\left(a x + 1\right)}^{3} {\left(a x - 1\right)} a c^{3}}"," ",0,"-1/8*log(abs(a*x + 1))/(a*c^3) + 1/8*log(abs(a*x - 1))/(a*c^3) + 1/12*(3*a^3*x^3 + 6*a^2*x^2 + a*x - 4)/((a*x + 1)^3*(a*x - 1)*a*c^3)","A",0
605,1,91,0,0.148315," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","-\frac{15 \, \log\left({\left| a x + 1 \right|}\right)}{128 \, a c^{4}} + \frac{15 \, \log\left({\left| a x - 1 \right|}\right)}{128 \, a c^{4}} + \frac{15 \, a^{5} x^{5} + 30 \, a^{4} x^{4} - 10 \, a^{3} x^{3} - 50 \, a^{2} x^{2} - 17 \, a x + 16}{64 \, {\left(a x + 1\right)}^{4} {\left(a x - 1\right)}^{2} a c^{4}}"," ",0,"-15/128*log(abs(a*x + 1))/(a*c^4) + 15/128*log(abs(a*x - 1))/(a*c^4) + 1/64*(15*a^5*x^5 + 30*a^4*x^4 - 10*a^3*x^3 - 50*a^2*x^2 - 17*a*x + 16)/((a*x + 1)^4*(a*x - 1)^2*a*c^4)","A",0
606,1,198,0,0.212340," ","integrate((-a^2*c*x^2+c)^4*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","-\frac{55 \, c^{4} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{128 \, {\left| a \right|}} - \frac{1}{8064} \, \sqrt{a^{2} x^{2} - 1} {\left(\frac{3712 \, c^{4} \mathrm{sgn}\left(a x + 1\right)}{a} + {\left(4599 \, c^{4} \mathrm{sgn}\left(a x + 1\right) - 2 \, {\left(5120 \, a c^{4} \mathrm{sgn}\left(a x + 1\right) - {\left(1533 \, a^{2} c^{4} \mathrm{sgn}\left(a x + 1\right) + 4 \, {\left(1056 \, a^{3} c^{4} \mathrm{sgn}\left(a x + 1\right) - {\left(903 \, a^{4} c^{4} \mathrm{sgn}\left(a x + 1\right) + 2 \, {\left(64 \, a^{5} c^{4} \mathrm{sgn}\left(a x + 1\right) + 7 \, {\left(8 \, a^{7} c^{4} x \mathrm{sgn}\left(a x + 1\right) - 27 \, a^{6} c^{4} \mathrm{sgn}\left(a x + 1\right)\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"-55/128*c^4*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) - 1/8064*sqrt(a^2*x^2 - 1)*(3712*c^4*sgn(a*x + 1)/a + (4599*c^4*sgn(a*x + 1) - 2*(5120*a*c^4*sgn(a*x + 1) - (1533*a^2*c^4*sgn(a*x + 1) + 4*(1056*a^3*c^4*sgn(a*x + 1) - (903*a^4*c^4*sgn(a*x + 1) + 2*(64*a^5*c^4*sgn(a*x + 1) + 7*(8*a^7*c^4*x*sgn(a*x + 1) - 27*a^6*c^4*sgn(a*x + 1))*x)*x)*x)*x)*x)*x)*x)","A",0
607,1,162,0,0.206425," ","integrate((-a^2*c*x^2+c)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","-\frac{9 \, c^{3} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{16 \, {\left| a \right|}} - \frac{1}{560} \, \sqrt{a^{2} x^{2} - 1} {\left(\frac{368 \, c^{3} \mathrm{sgn}\left(a x + 1\right)}{a} + {\left(245 \, c^{3} \mathrm{sgn}\left(a x + 1\right) - 2 \, {\left(328 \, a c^{3} \mathrm{sgn}\left(a x + 1\right) - {\left(175 \, a^{2} c^{3} \mathrm{sgn}\left(a x + 1\right) + 4 \, {\left(26 \, a^{3} c^{3} \mathrm{sgn}\left(a x + 1\right) + 5 \, {\left(2 \, a^{5} c^{3} x \mathrm{sgn}\left(a x + 1\right) - 7 \, a^{4} c^{3} \mathrm{sgn}\left(a x + 1\right)\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"-9/16*c^3*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) - 1/560*sqrt(a^2*x^2 - 1)*(368*c^3*sgn(a*x + 1)/a + (245*c^3*sgn(a*x + 1) - 2*(328*a*c^3*sgn(a*x + 1) - (175*a^2*c^3*sgn(a*x + 1) + 4*(26*a^3*c^3*sgn(a*x + 1) + 5*(2*a^5*c^3*x*sgn(a*x + 1) - 7*a^4*c^3*sgn(a*x + 1))*x)*x)*x)*x)*x)","A",0
608,1,126,0,0.179759," ","integrate((-a^2*c*x^2+c)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","-\frac{7 \, c^{2} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{8 \, {\left| a \right|}} - \frac{1}{120} \, \sqrt{a^{2} x^{2} - 1} {\left({\left(15 \, c^{2} \mathrm{sgn}\left(a x + 1\right) - 2 \, {\left(56 \, a c^{2} \mathrm{sgn}\left(a x + 1\right) + 3 \, {\left(4 \, a^{3} c^{2} x \mathrm{sgn}\left(a x + 1\right) - 15 \, a^{2} c^{2} \mathrm{sgn}\left(a x + 1\right)\right)} x\right)} x\right)} x + \frac{136 \, c^{2} \mathrm{sgn}\left(a x + 1\right)}{a}\right)}"," ",0,"-7/8*c^2*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) - 1/120*sqrt(a^2*x^2 - 1)*((15*c^2*sgn(a*x + 1) - 2*(56*a*c^2*sgn(a*x + 1) + 3*(4*a^3*c^2*x*sgn(a*x + 1) - 15*a^2*c^2*sgn(a*x + 1))*x)*x)*x + 136*c^2*sgn(a*x + 1)/a)","A",0
609,1,82,0,0.183420," ","integrate((-a^2*c*x^2+c)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","-\frac{5 \, c \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{2 \, {\left| a \right|}} - \frac{1}{6} \, \sqrt{a^{2} x^{2} - 1} {\left({\left(2 \, a c x \mathrm{sgn}\left(a x + 1\right) - 9 \, c \mathrm{sgn}\left(a x + 1\right)\right)} x + \frac{22 \, c \mathrm{sgn}\left(a x + 1\right)}{a}\right)}"," ",0,"-5/2*c*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) - 1/6*sqrt(a^2*x^2 - 1)*((2*a*c*x*sgn(a*x + 1) - 9*c*sgn(a*x + 1))*x + 22*c*sgn(a*x + 1)/a)","A",0
610,1,49,0,0.194541," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)}^{2} x^{2} + 1\right)}}{3 \, {\left({\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)} x + 1\right)}^{3} a c}"," ",0,"2/3*(3*(a + sqrt(a^2 - 1/x^2))^2*x^2 + 1)/(((a + sqrt(a^2 - 1/x^2))*x + 1)^3*a*c)","B",0
611,1,65,0,0.227884," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{4 \, {\left(10 \, {\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)}^{2} x^{2} + 5 \, {\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)} x + 1\right)}}{15 \, {\left({\left(a + \sqrt{a^{2} - \frac{1}{x^{2}}}\right)} x + 1\right)}^{5} a c^{2}}"," ",0,"-4/15*(10*(a + sqrt(a^2 - 1/x^2))^2*x^2 + 5*(a + sqrt(a^2 - 1/x^2))*x + 1)/(((a + sqrt(a^2 - 1/x^2))*x + 1)^5*a*c^2)","A",0
612,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(a^{2} c x^{2} - c\right)}^{3}}\,{d x}"," ",0,"integrate(-((a*x - 1)/(a*x + 1))^(3/2)/(a^2*c*x^2 - c)^3, x)","F",0
613,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(a^{2} c x^{2} - c\right)}^{4}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(a^2*c*x^2 - c)^4, x)","F",0
614,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(9/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
615,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
616,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
617,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
618,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
619,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*c*x^2 + c)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
620,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
621,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
622,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(7/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
623,1,164,0,0.194818," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(9/2),x, algorithm=""giac"")","\frac{77 \, c^{5} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{256 \, \sqrt{-c} {\left| a \right|}} + \frac{1}{11520} \, \sqrt{-a^{2} c x^{2} + c} {\left(\frac{2560 \, c^{4}}{a} - {\left(8055 \, c^{4} + 2 \, {\left(5120 \, a c^{4} - {\left(3075 \, a^{2} c^{4} + 4 \, {\left(1920 \, a^{3} c^{4} + {\left(39 \, a^{4} c^{4} - 2 \, {\left(640 \, a^{5} c^{4} + {\left(189 \, a^{6} c^{4} - 8 \, {\left(9 \, a^{8} c^{4} x + 20 \, a^{7} c^{4}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"77/256*c^5*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(sqrt(-c)*abs(a)) + 1/11520*sqrt(-a^2*c*x^2 + c)*(2560*c^4/a - (8055*c^4 + 2*(5120*a*c^4 - (3075*a^2*c^4 + 4*(1920*a^3*c^4 + (39*a^4*c^4 - 2*(640*a^5*c^4 + (189*a^6*c^4 - 8*(9*a^8*c^4*x + 20*a^7*c^4)*x)*x)*x)*x)*x)*x)*x)*x)","A",0
624,1,141,0,0.190803," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\frac{45 \, c^{4} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{128 \, \sqrt{-c} {\left| a \right|}} + \frac{1}{896} \, \sqrt{-a^{2} c x^{2} + c} {\left(\frac{256 \, c^{3}}{a} - {\left(581 \, c^{3} + 2 \, {\left(384 \, a c^{3} - {\left(105 \, a^{2} c^{3} + 4 \, {\left(96 \, a^{3} c^{3} + {\left(21 \, a^{4} c^{3} - 2 \, {\left(7 \, a^{6} c^{3} x + 16 \, a^{5} c^{3}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"45/128*c^4*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(sqrt(-c)*abs(a)) + 1/896*sqrt(-a^2*c*x^2 + c)*(256*c^3/a - (581*c^3 + 2*(384*a*c^3 - (105*a^2*c^3 + 4*(96*a^3*c^3 + (21*a^4*c^3 - 2*(7*a^6*c^3*x + 16*a^5*c^3)*x)*x)*x)*x)*x)*x)","A",0
625,1,116,0,0.183063," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{7 \, c^{3} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{16 \, \sqrt{-c} {\left| a \right|}} - \frac{1}{240} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(135 \, c^{2} + 2 \, {\left(96 \, a c^{2} + {\left(5 \, a^{2} c^{2} - 4 \, {\left(5 \, a^{4} c^{2} x + 12 \, a^{3} c^{2}\right)} x\right)} x\right)} x\right)} x - \frac{96 \, c^{2}}{a}\right)}"," ",0,"7/16*c^3*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(sqrt(-c)*abs(a)) - 1/240*sqrt(-a^2*c*x^2 + c)*((135*c^2 + 2*(96*a*c^2 + (5*a^2*c^2 - 4*(5*a^4*c^2*x + 12*a^3*c^2)*x)*x)*x)*x - 96*c^2/a)","A",0
626,1,85,0,0.156590," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{1}{24} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(2 \, {\left(3 \, a^{2} c x + 8 \, a c\right)} x + 9 \, c\right)} x - \frac{16 \, c}{a}\right)} + \frac{5 \, c^{2} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{8 \, \sqrt{-c} {\left| a \right|}}"," ",0,"-1/24*sqrt(-a^2*c*x^2 + c)*((2*(3*a^2*c*x + 8*a*c)*x + 9*c)*x - 16*c/a) + 5/8*c^2*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(sqrt(-c)*abs(a))","A",0
627,1,62,0,0.145472," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-a^{2} c x^{2} + c} {\left(x + \frac{4}{a}\right)} + \frac{3 \, c \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{2 \, \sqrt{-c} {\left| a \right|}}"," ",0,"1/2*sqrt(-a^2*c*x^2 + c)*(x + 4/a) + 3/2*c*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(sqrt(-c)*abs(a))","A",0
628,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
629,1,148,0,0.228018," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(a c - 3 \, \sqrt{-a^{2} c} \sqrt{c}\right)} \mathrm{sgn}\left(x\right)}{3 \, {\left(a^{2} c^{\frac{5}{2}} - \sqrt{-a^{2} c} a c^{2}\right)}} - \frac{2 \, {\left(2 \, a^{2} c + 3 \, a \sqrt{c} {\left(\sqrt{-a^{2} c + \frac{c}{x^{2}}} - \frac{\sqrt{c}}{x}\right)} + 3 \, {\left(\sqrt{-a^{2} c + \frac{c}{x^{2}}} - \frac{\sqrt{c}}{x}\right)}^{2}\right)}}{3 \, {\left(a \sqrt{c} + \sqrt{-a^{2} c + \frac{c}{x^{2}}} - \frac{\sqrt{c}}{x}\right)}^{3} c \mathrm{sgn}\left(x\right)}"," ",0,"1/3*(a*c - 3*sqrt(-a^2*c)*sqrt(c))*sgn(x)/(a^2*c^(5/2) - sqrt(-a^2*c)*a*c^2) - 2/3*(2*a^2*c + 3*a*sqrt(c)*(sqrt(-a^2*c + c/x^2) - sqrt(c)/x) + 3*(sqrt(-a^2*c + c/x^2) - sqrt(c)/x)^2)/((a*sqrt(c) + sqrt(-a^2*c + c/x^2) - sqrt(c)/x)^3*c*sgn(x))","B",0
630,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x - 1\right)}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(5/2)*(a*x - 1)), x)","F",0
631,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} {\left(a x - 1\right)}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(7/2)*(a*x - 1)), x)","F",0
632,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(-a^2*c*x^2+c)^(9/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}} {\left(a x - 1\right)}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(9/2)*(a*x - 1)), x)","F",0
633,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(9/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
634,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
635,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
636,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
637,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
638,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
639,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
640,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
641,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(7/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
642,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(9/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(9/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
643,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
644,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
645,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
646,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
647,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/sqrt(-a^2*c*x^2 + c), x)","F",0
648,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(-a^2*c*x^2 + c)^(3/2), x)","F",0
649,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(-a^2*c*x^2 + c)^(5/2), x)","F",0
650,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(-a^2*c*x^2 + c)^(7/2), x)","F",0
651,1,117,0,0.167994," ","integrate((-a^2*c*x^2+c)^(5/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{7 \, c^{3} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{16 \, \sqrt{-c} {\left| a \right|}} - \frac{1}{240} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(135 \, c^{2} - 2 \, {\left(96 \, a c^{2} - {\left(5 \, a^{2} c^{2} - 4 \, {\left(5 \, a^{4} c^{2} x - 12 \, a^{3} c^{2}\right)} x\right)} x\right)} x\right)} x + \frac{96 \, c^{2}}{a}\right)}"," ",0,"7/16*c^3*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(sqrt(-c)*abs(a)) - 1/240*sqrt(-a^2*c*x^2 + c)*((135*c^2 - 2*(96*a*c^2 - (5*a^2*c^2 - 4*(5*a^4*c^2*x - 12*a^3*c^2)*x)*x)*x)*x + 96*c^2/a)","A",0
652,1,85,0,0.178150," ","integrate((-a^2*c*x^2+c)^(3/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{1}{24} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(2 \, {\left(3 \, a^{2} c x - 8 \, a c\right)} x + 9 \, c\right)} x + \frac{16 \, c}{a}\right)} + \frac{5 \, c^{2} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{8 \, \sqrt{-c} {\left| a \right|}}"," ",0,"-1/24*sqrt(-a^2*c*x^2 + c)*((2*(3*a^2*c*x - 8*a*c)*x + 9*c)*x + 16*c/a) + 5/8*c^2*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(sqrt(-c)*abs(a))","A",0
653,1,62,0,0.152316," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-a^{2} c x^{2} + c} {\left(x - \frac{4}{a}\right)} + \frac{3 \, c \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{2 \, \sqrt{-c} {\left| a \right|}}"," ",0,"1/2*sqrt(-a^2*c*x^2 + c)*(x - 4/a) + 3/2*c*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(sqrt(-c)*abs(a))","A",0
654,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
655,1,148,0,0.231446," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{{\left(a c + 3 \, \sqrt{-a^{2} c} \sqrt{c}\right)} \mathrm{sgn}\left(x\right)}{3 \, {\left(a^{2} c^{\frac{5}{2}} + \sqrt{-a^{2} c} a c^{2}\right)}} + \frac{2 \, {\left(2 \, a^{2} c - 3 \, a \sqrt{c} {\left(\sqrt{-a^{2} c + \frac{c}{x^{2}}} - \frac{\sqrt{c}}{x}\right)} + 3 \, {\left(\sqrt{-a^{2} c + \frac{c}{x^{2}}} - \frac{\sqrt{c}}{x}\right)}^{2}\right)}}{3 \, {\left(a \sqrt{c} - \sqrt{-a^{2} c + \frac{c}{x^{2}}} + \frac{\sqrt{c}}{x}\right)}^{3} c \mathrm{sgn}\left(x\right)}"," ",0,"-1/3*(a*c + 3*sqrt(-a^2*c)*sqrt(c))*sgn(x)/(a^2*c^(5/2) + sqrt(-a^2*c)*a*c^2) + 2/3*(2*a^2*c - 3*a*sqrt(c)*(sqrt(-a^2*c + c/x^2) - sqrt(c)/x) + 3*(sqrt(-a^2*c + c/x^2) - sqrt(c)/x)^2)/((a*sqrt(c) - sqrt(-a^2*c + c/x^2) + sqrt(c)/x)^3*c*sgn(x))","B",0
656,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{a x - 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate((a*x - 1)/((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)), x)","F",0
657,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{a x - 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate((a*x - 1)/((-a^2*c*x^2 + c)^(7/2)*(a*x + 1)), x)","F",0
658,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(-a^2*c*x^2+c)^(9/2),x, algorithm=""giac"")","\int \frac{a x - 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate((a*x - 1)/((-a^2*c*x^2 + c)^(9/2)*(a*x + 1)), x)","F",0
659,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(9/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
660,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
661,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
662,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
663,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
664,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/sqrt(-a^2*c*x^2 + c), x)","F",0
665,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
666,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
667,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(-a^2*c*x^2 + c)^(7/2), x)","F",0
668,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} x^{2}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^2/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
669,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} x}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
670,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
671,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
672,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x^2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
673,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x^3*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
674,1,84,0,0.147592," ","integrate(1/(a*x-1)*(a*x+1)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(2 \, {\left(3 \, x + \frac{8}{a}\right)} x + \frac{21}{a^{2}}\right)} x + \frac{32}{a^{3}}\right)} + \frac{7 \, c \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{8 \, a^{2} \sqrt{-c} {\left| a \right|}}"," ",0,"1/24*sqrt(-a^2*c*x^2 + c)*((2*(3*x + 8/a)*x + 21/a^2)*x + 32/a^3) + 7/8*c*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(a^2*sqrt(-c)*abs(a))","A",0
675,1,72,0,0.144003," ","integrate(1/(a*x-1)*(a*x+1)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(x + \frac{3}{a}\right)} x + \frac{5}{a^{2}}\right)} + \frac{c \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{a \sqrt{-c} {\left| a \right|}}"," ",0,"1/3*sqrt(-a^2*c*x^2 + c)*((x + 3/a)*x + 5/a^2) + c*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(a*sqrt(-c)*abs(a))","A",0
676,1,62,0,0.147557," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-a^{2} c x^{2} + c} {\left(x + \frac{4}{a}\right)} + \frac{3 \, c \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{2 \, \sqrt{-c} {\left| a \right|}}"," ",0,"1/2*sqrt(-a^2*c*x^2 + c)*(x + 4/a) + 3/2*c*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(sqrt(-c)*abs(a))","A",0
677,1,95,0,0.166524," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""giac"")","-\frac{2 \, c \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{2 \, a \sqrt{-c} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{{\left| a \right|}} + \sqrt{-a^{2} c x^{2} + c}"," ",0,"-2*c*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) - 2*a*sqrt(-c)*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) + sqrt(-a^2*c*x^2 + c)","A",0
678,1,134,0,0.164474," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""giac"")","-\frac{4 \, a c \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{a^{2} \sqrt{-c} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{{\left| a \right|}} - \frac{2 \, a^{2} \sqrt{-c} c}{{\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)} {\left| a \right|}}"," ",0,"-4*a*c*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) - a^2*sqrt(-c)*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) - 2*a^2*sqrt(-c)*c/(((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)*abs(a))","A",0
679,1,200,0,0.163070," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""giac"")","-\frac{3 \, a^{2} c \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{{\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a^{2} c - 4 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a \sqrt{-c} c {\left| a \right|} + {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{2} c^{2} + 4 \, a \sqrt{-c} c^{2} {\left| a \right|}}{{\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{2}}"," ",0,"-3*a^2*c*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + ((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a^2*c - 4*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a*sqrt(-c)*c*abs(a) + (sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^2*c^2 + 4*a*sqrt(-c)*c^2*abs(a))/((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^2","B",0
680,1,250,0,0.162327," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{2 \, a^{3} c \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{2 \, {\left(3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{5} a^{3} c - 3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{4} a^{2} \sqrt{-c} c {\left| a \right|} + 12 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{2} \sqrt{-c} c^{2} {\left| a \right|} - 3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{3} c^{3} - 5 \, a^{2} \sqrt{-c} c^{3} {\left| a \right|}\right)}}{3 \, {\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{3}}"," ",0,"-2*a^3*c*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + 2/3*(3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^5*a^3*c - 3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^4*a^2*sqrt(-c)*c*abs(a) + 12*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^2*sqrt(-c)*c^2*abs(a) - 3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^3*c^3 - 5*a^2*sqrt(-c)*c^3*abs(a))/((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^3","B",0
681,1,324,0,0.148968," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^(1/2)/x^5,x, algorithm=""giac"")","-\frac{7 \, a^{4} c \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{4 \, \sqrt{-c}} + \frac{21 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{7} a^{4} c - 45 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{5} a^{4} c^{2} + 96 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{4} a^{3} \sqrt{-c} c^{2} {\left| a \right|} - 45 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a^{4} c^{3} - 128 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{3} \sqrt{-c} c^{3} {\left| a \right|} + 21 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{4} c^{4} + 32 \, a^{3} \sqrt{-c} c^{4} {\left| a \right|}}{12 \, {\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{4}}"," ",0,"-7/4*a^4*c*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + 1/12*(21*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^7*a^4*c - 45*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^5*a^4*c^2 + 96*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^4*a^3*sqrt(-c)*c^2*abs(a) - 45*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a^4*c^3 - 128*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^3*sqrt(-c)*c^3*abs(a) + 21*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^4*c^4 + 32*a^3*sqrt(-c)*c^4*abs(a))/((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^4","B",0
682,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
683,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} x^{2}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^2/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
684,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} x}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
685,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
686,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
687,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x^2*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
688,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x^3*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
689,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x^4*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
690,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{x^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/(x^5*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
691,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^4/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^4/((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
692,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
693,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^2/((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
694,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
695,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
696,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
697,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*x^2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
698,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
699,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^5/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
700,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^4/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^4/((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
701,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
702,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(x^2/((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
703,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
704,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
705,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
706,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*x^2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
707,0,0,0,0.000000," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} x^{2} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^2*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
708,0,0,0,0.000000," ","integrate(x*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} x \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
709,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
710,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{\frac{a x - 1}{a x + 1}}}{x}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt((a*x - 1)/(a*x + 1))/x, x)","F",0
711,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
712,-2,0,0,0.000000," ","integrate(x^3*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
713,1,84,0,0.167844," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(2 \, {\left(3 \, x - \frac{8}{a}\right)} x + \frac{21}{a^{2}}\right)} x - \frac{32}{a^{3}}\right)} + \frac{7 \, c \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{8 \, a^{2} \sqrt{-c} {\left| a \right|}}"," ",0,"1/24*sqrt(-a^2*c*x^2 + c)*((2*(3*x - 8/a)*x + 21/a^2)*x - 32/a^3) + 7/8*c*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(a^2*sqrt(-c)*abs(a))","A",0
714,1,73,0,0.150016," ","integrate(x*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(x - \frac{3}{a}\right)} x + \frac{5}{a^{2}}\right)} - \frac{c \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{a \sqrt{-c} {\left| a \right|}}"," ",0,"1/3*sqrt(-a^2*c*x^2 + c)*((x - 3/a)*x + 5/a^2) - c*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(a*sqrt(-c)*abs(a))","A",0
715,1,62,0,0.165792," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-a^{2} c x^{2} + c} {\left(x - \frac{4}{a}\right)} + \frac{3 \, c \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{2 \, \sqrt{-c} {\left| a \right|}}"," ",0,"1/2*sqrt(-a^2*c*x^2 + c)*(x - 4/a) + 3/2*c*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(sqrt(-c)*abs(a))","A",0
716,1,95,0,0.166228," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x,x, algorithm=""giac"")","-\frac{2 \, c \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{2 \, a \sqrt{-c} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{{\left| a \right|}} + \sqrt{-a^{2} c x^{2} + c}"," ",0,"-2*c*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + 2*a*sqrt(-c)*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) + sqrt(-a^2*c*x^2 + c)","A",0
717,1,134,0,0.154549," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^2,x, algorithm=""giac"")","\frac{4 \, a c \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{a^{2} \sqrt{-c} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{{\left| a \right|}} - \frac{2 \, a^{2} \sqrt{-c} c}{{\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)} {\left| a \right|}}"," ",0,"4*a*c*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) - a^2*sqrt(-c)*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) - 2*a^2*sqrt(-c)*c/(((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)*abs(a))","A",0
718,1,200,0,0.141936," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^3,x, algorithm=""giac"")","-\frac{3 \, a^{2} c \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{{\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a^{2} c + 4 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a \sqrt{-c} c {\left| a \right|} + {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{2} c^{2} - 4 \, a \sqrt{-c} c^{2} {\left| a \right|}}{{\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{2}}"," ",0,"-3*a^2*c*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + ((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a^2*c + 4*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a*sqrt(-c)*c*abs(a) + (sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^2*c^2 - 4*a*sqrt(-c)*c^2*abs(a))/((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^2","B",0
719,1,250,0,0.157125," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^4,x, algorithm=""giac"")","\frac{2 \, a^{3} c \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{2 \, {\left(3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{5} a^{3} c + 3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{4} a^{2} \sqrt{-c} c {\left| a \right|} - 12 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{2} \sqrt{-c} c^{2} {\left| a \right|} - 3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{3} c^{3} + 5 \, a^{2} \sqrt{-c} c^{3} {\left| a \right|}\right)}}{3 \, {\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{3}}"," ",0,"2*a^3*c*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) - 2/3*(3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^5*a^3*c + 3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^4*a^2*sqrt(-c)*c*abs(a) - 12*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^2*sqrt(-c)*c^2*abs(a) - 3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^3*c^3 + 5*a^2*sqrt(-c)*c^3*abs(a))/((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^3","B",0
720,1,324,0,0.148508," ","integrate((-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1)/x^5,x, algorithm=""giac"")","-\frac{7 \, a^{4} c \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{4 \, \sqrt{-c}} + \frac{21 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{7} a^{4} c - 45 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{5} a^{4} c^{2} - 96 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{4} a^{3} \sqrt{-c} c^{2} {\left| a \right|} - 45 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a^{4} c^{3} + 128 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{3} \sqrt{-c} c^{3} {\left| a \right|} + 21 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{4} c^{4} - 32 \, a^{3} \sqrt{-c} c^{4} {\left| a \right|}}{12 \, {\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{4}}"," ",0,"-7/4*a^4*c*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + 1/12*(21*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^7*a^4*c - 45*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^5*a^4*c^2 - 96*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^4*a^3*sqrt(-c)*c^2*abs(a) - 45*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a^4*c^3 + 128*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^3*sqrt(-c)*c^3*abs(a) + 21*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^4*c^4 - 32*a^3*sqrt(-c)*c^4*abs(a))/((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^4","B",0
721,0,0,0,0.000000," ","integrate(x^3*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^3*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
722,0,0,0,0.000000," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^2*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
723,0,0,0,0.000000," ","integrate(x*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
724,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
725,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)/x, x)","F",0
726,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^2, x)","F",0
727,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^3, x)","F",0
728,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^4, x)","F",0
729,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*((a*x - 1)/(a*x + 1))^(3/2)/x^5, x)","F",0
730,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
731,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
732,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
733,0,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^m*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
734,-2,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
735,-2,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
736,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -{\left(a^{2} c x^{2} - c\right)}^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(-(a^2*c*x^2 - c)^3*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
737,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int {\left(a^{2} c x^{2} - c\right)}^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((a^2*c*x^2 - c)^2*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
738,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c),x, algorithm=""giac"")","\int -{\left(a^{2} c x^{2} - c\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(-(a^2*c*x^2 - c)*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
739,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x)),x, algorithm=""giac"")","\int \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
740,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c),x, algorithm=""giac"")","\int -\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}\,{d x}"," ",0,"integrate(-((a*x - 1)/(a*x + 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
741,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{2}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
742,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{3}}\,{d x}"," ",0,"integrate(-((a*x - 1)/(a*x + 1))^(1/2*n)/(a^2*c*x^2 - c)^3, x)","F",0
743,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{4}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(a^2*c*x^2 - c)^4, x)","F",0
744,-2,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
745,-2,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
746,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/sqrt(-a^2*c*x^2 + c), x)","F",0
747,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
748,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
749,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(7/2), x)","F",0
750,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(9/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(9/2), x)","F",0
751,-2,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
752,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2*((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
753,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
754,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
755,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/((-a^2*c*x^2 + c)^(3/2)*x), x)","F",0
756,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*x^4/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^4*((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
757,-2,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
758,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^2*((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
759,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x*((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
760,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(-a^2*c*x^2 + c)^(5/2), x)","F",0
761,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/((-a^2*c*x^2 + c)^(5/2)*x), x)","F",0
762,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
763,0,0,0,0.000000," ","integrate(exp(2*p*arccoth(a*x))*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{p}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p*((a*x - 1)/(a*x + 1))^p, x)","F",0
764,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/exp(2*p*arccoth(a*x)),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{p}}{\left(\frac{a x - 1}{a x + 1}\right)^{p}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p/((a*x - 1)/(a*x + 1))^p, x)","F",0
765,0,0,0,0.000000," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{2} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(a x - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^2*(-a^2*c*x^2 + c)^p/(a*x - 1)^2, x)","F",0
766,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{p}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
767,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{a x - 1}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p/(a*x - 1), x)","F",0
768,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{p}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
769,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{p} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
770,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\int \frac{{\left(a x - 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate((a*x - 1)*(-a^2*c*x^2 + c)^p/(a*x + 1), x)","F",0
771,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
772,1,335,0,0.184565," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^4,x, algorithm=""giac"")","-\frac{1}{840} \, a c^{4} {\left(\frac{3675 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{840 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{840 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{1680 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} + \frac{\frac{1260 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{18921 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + \frac{73152 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + \frac{60151 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} + \frac{23380 \, {\left(a x - 1\right)}^{5} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{5}} + \frac{3675 \, {\left(a x - 1\right)}^{6} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{6}} - 315 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} + 1\right)}^{7}}\right)}"," ",0,"-1/840*a*c^4*(3675*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 840*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 840*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 1680*sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)/(a*x + 1) - 1)) + (1260*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 18921*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 73152*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 60151*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 + 23380*(a*x - 1)^5*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^5 + 3675*(a*x - 1)^6*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^6 - 315*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) + 1)^7))","A",0
773,1,273,0,0.180814," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^3,x, algorithm=""giac"")","-\frac{1}{60} \, a c^{3} {\left(\frac{225 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{60 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{60 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{120 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} + \frac{\frac{310 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{1424 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + \frac{970 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + \frac{225 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} + 15 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} + 1\right)}^{5}}\right)}"," ",0,"-1/60*a*c^3*(225*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 60*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 60*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 120*sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)/(a*x + 1) - 1)) + (310*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 1424*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 970*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 225*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 + 15*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) + 1)^5))","A",0
774,1,211,0,0.169791," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^2,x, algorithm=""giac"")","-\frac{1}{3} \, a c^{2} {\left(\frac{9 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{3 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{6 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} + \frac{\frac{20 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{9 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + 3 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)}"," ",0,"-1/3*a*c^2*(9*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 3*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 6*sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)/(a*x + 1) - 1)) + (20*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 9*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 3*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) + 1)^3))","A",0
775,1,123,0,0.154036," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2),x, algorithm=""giac"")","-a c {\left(\frac{2 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{\log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{4 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)} a^{2} {\left(\frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 1\right)}}\right)}"," ",0,"-a*c*(2*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 4*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/((a*x + 1)*a^2*((a*x - 1)^2/(a*x + 1)^2 - 1)))","A",0
776,1,127,0,0.173025," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2),x, algorithm=""giac"")","a {\left(\frac{\log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{\log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c} - \frac{\frac{3 \, {\left(a x - 1\right)}}{a x + 1} - 1}{a^{2} c {\left(\frac{{\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} - \sqrt{\frac{a x - 1}{a x + 1}}\right)}}\right)}"," ",0,"a*(log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c) - (3*(a*x - 1)/(a*x + 1) - 1)/(a^2*c*((a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) - sqrt((a*x - 1)/(a*x + 1)))))","A",0
777,1,171,0,0.163422," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\frac{1}{12} \, a {\left(\frac{12 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} - \frac{12 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{2}} - \frac{{\left(a x + 1\right)} {\left(\frac{18 \, {\left(a x - 1\right)}}{a x + 1} + 1\right)}}{{\left(a x - 1\right)} a^{2} c^{2} \sqrt{\frac{a x - 1}{a x + 1}}} + \frac{3 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2}} - \frac{24 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/12*a*(12*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) - 12*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^2) - (a*x + 1)*(18*(a*x - 1)/(a*x + 1) + 1)/((a*x - 1)*a^2*c^2*sqrt((a*x - 1)/(a*x + 1))) + 3*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^2) - 24*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^2*((a*x - 1)/(a*x + 1) - 1)))","A",0
778,1,232,0,0.176365," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\frac{1}{240} \, a {\left(\frac{240 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{3}} - \frac{240 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{3}} - \frac{{\left(a x + 1\right)}^{2} {\left(\frac{40 \, {\left(a x - 1\right)}}{a x + 1} + \frac{450 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 3\right)}}{{\left(a x - 1\right)}^{2} a^{2} c^{3} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{480 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} + \frac{5 \, {\left(\frac{{\left(a x - 1\right)} a^{4} c^{6} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + 24 \, a^{4} c^{6} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{6} c^{9}}\right)}"," ",0,"1/240*a*(240*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^3) - 240*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^3) - (a*x + 1)^2*(40*(a*x - 1)/(a*x + 1) + 450*(a*x - 1)^2/(a*x + 1)^2 + 3)/((a*x - 1)^2*a^2*c^3*sqrt((a*x - 1)/(a*x + 1))) - 480*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^3*((a*x - 1)/(a*x + 1) - 1)) + 5*((a*x - 1)*a^4*c^6*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 24*a^4*c^6*sqrt((a*x - 1)/(a*x + 1)))/(a^6*c^9))","A",0
779,1,286,0,0.173630," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\frac{1}{6720} \, a {\left(\frac{6720 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} - \frac{6720 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{4}} - \frac{5 \, {\left(a x + 1\right)}^{3} {\left(\frac{42 \, {\left(a x - 1\right)}}{a x + 1} + \frac{329 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{2940 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 3\right)}}{{\left(a x - 1\right)}^{3} a^{2} c^{4} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{13440 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} + \frac{7 \, {\left(\frac{50 \, {\left(a x - 1\right)} a^{8} c^{16} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{3 \, {\left(a x - 1\right)}^{2} a^{8} c^{16} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + 705 \, a^{8} c^{16} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{10} c^{20}}\right)}"," ",0,"1/6720*a*(6720*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) - 6720*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^4) - 5*(a*x + 1)^3*(42*(a*x - 1)/(a*x + 1) + 329*(a*x - 1)^2/(a*x + 1)^2 + 2940*(a*x - 1)^3/(a*x + 1)^3 + 3)/((a*x - 1)^3*a^2*c^4*sqrt((a*x - 1)/(a*x + 1))) - 13440*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^4*((a*x - 1)/(a*x + 1) - 1)) + 7*(50*(a*x - 1)*a^8*c^16*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 3*(a*x - 1)^2*a^8*c^16*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 705*a^8*c^16*sqrt((a*x - 1)/(a*x + 1)))/(a^10*c^20))","A",0
780,1,115,0,0.134588," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^5,x, algorithm=""giac"")","c^{5} x + \frac{2 \, c^{5} \log\left({\left| x \right|}\right)}{a} + \frac{3780 \, a^{8} c^{5} x^{8} + 5040 \, a^{7} c^{5} x^{7} - 840 \, a^{6} c^{5} x^{6} - 3780 \, a^{5} c^{5} x^{5} - 504 \, a^{4} c^{5} x^{4} + 1680 \, a^{3} c^{5} x^{3} + 540 \, a^{2} c^{5} x^{2} - 315 \, a c^{5} x - 140 \, c^{5}}{1260 \, a^{10} x^{9}}"," ",0,"c^5*x + 2*c^5*log(abs(x))/a + 1/1260*(3780*a^8*c^5*x^8 + 5040*a^7*c^5*x^7 - 840*a^6*c^5*x^6 - 3780*a^5*c^5*x^5 - 504*a^4*c^5*x^4 + 1680*a^3*c^5*x^3 + 540*a^2*c^5*x^2 - 315*a*c^5*x - 140*c^5)/(a^10*x^9)","A",0
781,1,82,0,0.123363," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^4,x, algorithm=""giac"")","c^{4} x + \frac{2 \, c^{4} \log\left({\left| x \right|}\right)}{a} + \frac{420 \, a^{6} c^{4} x^{6} + 630 \, a^{5} c^{4} x^{5} - 315 \, a^{3} c^{4} x^{3} - 84 \, a^{2} c^{4} x^{2} + 70 \, a c^{4} x + 30 \, c^{4}}{210 \, a^{8} x^{7}}"," ",0,"c^4*x + 2*c^4*log(abs(x))/a + 1/210*(420*a^6*c^4*x^6 + 630*a^5*c^4*x^5 - 315*a^3*c^4*x^3 - 84*a^2*c^4*x^2 + 70*a*c^4*x + 30*c^4)/(a^8*x^7)","A",0
782,1,71,0,0.119282," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^3,x, algorithm=""giac"")","c^{3} x + \frac{2 \, c^{3} \log\left({\left| x \right|}\right)}{a} + \frac{30 \, a^{4} c^{3} x^{4} + 60 \, a^{3} c^{3} x^{3} + 10 \, a^{2} c^{3} x^{2} - 15 \, a c^{3} x - 6 \, c^{3}}{30 \, a^{6} x^{5}}"," ",0,"c^3*x + 2*c^3*log(abs(x))/a + 1/30*(30*a^4*c^3*x^4 + 60*a^3*c^3*x^3 + 10*a^2*c^3*x^2 - 15*a*c^3*x - 6*c^3)/(a^6*x^5)","A",0
783,1,36,0,0.136867," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^2,x, algorithm=""giac"")","c^{2} x + \frac{2 \, c^{2} \log\left({\left| x \right|}\right)}{a} + \frac{3 \, a c^{2} x + c^{2}}{3 \, a^{4} x^{3}}"," ",0,"c^2*x + 2*c^2*log(abs(x))/a + 1/3*(3*a*c^2*x + c^2)/(a^4*x^3)","A",0
784,1,22,0,0.121053," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2),x, algorithm=""giac"")","c x + \frac{2 \, c \log\left({\left| x \right|}\right)}{a} - \frac{c}{a^{2} x}"," ",0,"c*x + 2*c*log(abs(x))/a - c/(a^2*x)","A",0
785,1,36,0,0.133502," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2),x, algorithm=""giac"")","\frac{x}{c} + \frac{2 \, \log\left({\left| a x - 1 \right|}\right)}{a c} - \frac{1}{{\left(a x - 1\right)} a c}"," ",0,"x/c + 2*log(abs(a*x - 1))/(a*c) - 1/((a*x - 1)*a*c)","A",0
786,1,57,0,0.143472," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\frac{x}{c^{2}} - \frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a c^{2}} + \frac{17 \, \log\left({\left| a x - 1 \right|}\right)}{8 \, a c^{2}} - \frac{7 \, a x - 6}{4 \, {\left(a x - 1\right)}^{2} a c^{2}}"," ",0,"x/c^2 - 1/8*log(abs(a*x + 1))/(a*c^2) + 17/8*log(abs(a*x - 1))/(a*c^2) - 1/4*(7*a*x - 6)/((a*x - 1)^2*a*c^2)","A",0
787,1,80,0,0.131622," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\frac{x}{c^{3}} - \frac{\log\left({\left| a x + 1 \right|}\right)}{4 \, a c^{3}} + \frac{9 \, \log\left({\left| a x - 1 \right|}\right)}{4 \, a c^{3}} - \frac{15 \, a^{3} x^{3} - 12 \, a^{2} x^{2} - 13 \, a x + 11}{6 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{3} a c^{3}}"," ",0,"x/c^3 - 1/4*log(abs(a*x + 1))/(a*c^3) + 9/4*log(abs(a*x - 1))/(a*c^3) - 1/6*(15*a^3*x^3 - 12*a^2*x^2 - 13*a*x + 11)/((a*x + 1)*(a*x - 1)^3*a*c^3)","A",0
788,1,96,0,0.139786," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\frac{x}{c^{4}} - \frac{47 \, \log\left({\left| a x + 1 \right|}\right)}{128 \, a c^{4}} + \frac{303 \, \log\left({\left| a x - 1 \right|}\right)}{128 \, a c^{4}} - \frac{627 \, a^{5} x^{5} - 486 \, a^{4} x^{4} - 1058 \, a^{3} x^{3} + 874 \, a^{2} x^{2} + 467 \, a x - 400}{192 \, {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{4} a c^{4}}"," ",0,"x/c^4 - 47/128*log(abs(a*x + 1))/(a*c^4) + 303/128*log(abs(a*x - 1))/(a*c^4) - 1/192*(627*a^5*x^5 - 486*a^4*x^4 - 1058*a^3*x^3 + 874*a^2*x^2 + 467*a*x - 400)/((a*x + 1)^2*(a*x - 1)^4*a*c^4)","A",0
789,1,335,0,0.187272," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^4,x, algorithm=""giac"")","-\frac{1}{280} \, a c^{4} {\left(\frac{525 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{840 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{840 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{560 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} + \frac{\frac{13300 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{45871 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + \frac{52672 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + \frac{33201 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} + \frac{11340 \, {\left(a x - 1\right)}^{5} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{5}} + \frac{1645 \, {\left(a x - 1\right)}^{6} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{6}} + 1715 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} + 1\right)}^{7}}\right)}"," ",0,"-1/280*a*c^4*(525*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 840*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 840*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 560*sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)/(a*x + 1) - 1)) + (13300*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 45871*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 52672*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 33201*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 + 11340*(a*x - 1)^5*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^5 + 1645*(a*x - 1)^6*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^6 + 1715*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) + 1)^7))","A",0
790,1,273,0,0.174620," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^3,x, algorithm=""giac"")","-\frac{1}{20} \, a c^{3} {\left(\frac{15 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} - \frac{60 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} + \frac{60 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} + \frac{40 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} + \frac{\frac{810 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{912 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + \frac{470 \, {\left(a x - 1\right)}^{3} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{3}} + \frac{95 \, {\left(a x - 1\right)}^{4} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{4}} + 145 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} + 1\right)}^{5}}\right)}"," ",0,"-1/20*a*c^3*(15*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 - 60*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 + 60*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 + 40*sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)/(a*x + 1) - 1)) + (810*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 912*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 470*(a*x - 1)^3*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^3 + 95*(a*x - 1)^4*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^4 + 145*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) + 1)^5))","A",0
791,1,212,0,0.175216," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\frac{1}{3} \, a c^{2} {\left(\frac{3 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{9 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{6 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} - \frac{\frac{28 \, {\left(a x - 1\right)} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + \frac{9 \, {\left(a x - 1\right)}^{2} \sqrt{\frac{a x - 1}{a x + 1}}}{{\left(a x + 1\right)}^{2}} + 27 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{a x - 1}{a x + 1} + 1\right)}^{3}}\right)}"," ",0,"1/3*a*c^2*(3*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 9*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 6*sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)/(a*x + 1) - 1)) - (28*(a*x - 1)*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 9*(a*x - 1)^2*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1)^2 + 27*sqrt((a*x - 1)/(a*x + 1)))/(a^2*((a*x - 1)/(a*x + 1) + 1)^3))","A",0
792,1,111,0,0.153552," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2),x, algorithm=""giac"")","a c {\left(\frac{6 \, \arctan\left(\sqrt{\frac{a x - 1}{a x + 1}}\right)}{a^{2}} + \frac{3 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2}} - \frac{3 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2}} - \frac{4 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} {\left(\frac{{\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} - 1\right)}}\right)}"," ",0,"a*c*(6*arctan(sqrt((a*x - 1)/(a*x + 1)))/a^2 + 3*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/a^2 - 3*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/a^2 - 4*sqrt((a*x - 1)/(a*x + 1))/(a^2*((a*x - 1)^2/(a*x + 1)^2 - 1)))","A",0
793,1,148,0,0.153237," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2),x, algorithm=""giac"")","\frac{1}{3} \, a {\left(\frac{9 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c} - \frac{9 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c} - \frac{{\left(a x + 1\right)} {\left(\frac{12 \, {\left(a x - 1\right)}}{a x + 1} + 1\right)}}{{\left(a x - 1\right)} a^{2} c \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{6 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/3*a*(9*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c) - 9*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c) - (a*x + 1)*(12*(a*x - 1)/(a*x + 1) + 1)/((a*x - 1)*a^2*c*sqrt((a*x - 1)/(a*x + 1))) - 6*sqrt((a*x - 1)/(a*x + 1))/(a^2*c*((a*x - 1)/(a*x + 1) - 1)))","A",0
794,1,166,0,0.163410," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\frac{1}{20} \, a {\left(\frac{60 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{2}} - \frac{60 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{2}} - \frac{{\left(a x + 1\right)}^{2} {\left(\frac{10 \, {\left(a x - 1\right)}}{a x + 1} + \frac{85 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + 1\right)}}{{\left(a x - 1\right)}^{2} a^{2} c^{2} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{40 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{2} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/20*a*(60*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^2) - 60*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^2) - (a*x + 1)^2*(10*(a*x - 1)/(a*x + 1) + 85*(a*x - 1)^2/(a*x + 1)^2 + 1)/((a*x - 1)^2*a^2*c^2*sqrt((a*x - 1)/(a*x + 1))) - 40*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^2*((a*x - 1)/(a*x + 1) - 1)))","A",0
795,1,205,0,0.166606," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\frac{1}{560} \, a {\left(\frac{1680 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{3}} - \frac{1680 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{3}} - \frac{{\left(a x + 1\right)}^{3} {\left(\frac{56 \, {\left(a x - 1\right)}}{a x + 1} + \frac{350 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{2520 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + 5\right)}}{{\left(a x - 1\right)}^{3} a^{2} c^{3} \sqrt{\frac{a x - 1}{a x + 1}}} + \frac{35 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3}} - \frac{1120 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{3} {\left(\frac{a x - 1}{a x + 1} - 1\right)}}\right)}"," ",0,"1/560*a*(1680*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^3) - 1680*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^3) - (a*x + 1)^3*(56*(a*x - 1)/(a*x + 1) + 350*(a*x - 1)^2/(a*x + 1)^2 + 2520*(a*x - 1)^3/(a*x + 1)^3 + 5)/((a*x - 1)^3*a^2*c^3*sqrt((a*x - 1)/(a*x + 1))) + 35*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^3) - 1120*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^3*((a*x - 1)/(a*x + 1) - 1)))","A",0
796,1,264,0,0.170863," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\frac{1}{20160} \, a {\left(\frac{60480 \, \log\left(\sqrt{\frac{a x - 1}{a x + 1}} + 1\right)}{a^{2} c^{4}} - \frac{60480 \, \log\left({\left| \sqrt{\frac{a x - 1}{a x + 1}} - 1 \right|}\right)}{a^{2} c^{4}} - \frac{{\left(a x + 1\right)}^{4} {\left(\frac{450 \, {\left(a x - 1\right)}}{a x + 1} + \frac{2961 \, {\left(a x - 1\right)}^{2}}{{\left(a x + 1\right)}^{2}} + \frac{14700 \, {\left(a x - 1\right)}^{3}}{{\left(a x + 1\right)}^{3}} + \frac{95445 \, {\left(a x - 1\right)}^{4}}{{\left(a x + 1\right)}^{4}} + 35\right)}}{{\left(a x - 1\right)}^{4} a^{2} c^{4} \sqrt{\frac{a x - 1}{a x + 1}}} - \frac{40320 \, \sqrt{\frac{a x - 1}{a x + 1}}}{a^{2} c^{4} {\left(\frac{a x - 1}{a x + 1} - 1\right)}} + \frac{105 \, {\left(\frac{{\left(a x - 1\right)} a^{4} c^{8} \sqrt{\frac{a x - 1}{a x + 1}}}{a x + 1} + 30 \, a^{4} c^{8} \sqrt{\frac{a x - 1}{a x + 1}}\right)}}{a^{6} c^{12}}\right)}"," ",0,"1/20160*a*(60480*log(sqrt((a*x - 1)/(a*x + 1)) + 1)/(a^2*c^4) - 60480*log(abs(sqrt((a*x - 1)/(a*x + 1)) - 1))/(a^2*c^4) - (a*x + 1)^4*(450*(a*x - 1)/(a*x + 1) + 2961*(a*x - 1)^2/(a*x + 1)^2 + 14700*(a*x - 1)^3/(a*x + 1)^3 + 95445*(a*x - 1)^4/(a*x + 1)^4 + 35)/((a*x - 1)^4*a^2*c^4*sqrt((a*x - 1)/(a*x + 1))) - 40320*sqrt((a*x - 1)/(a*x + 1))/(a^2*c^4*((a*x - 1)/(a*x + 1) - 1)) + 105*((a*x - 1)*a^4*c^8*sqrt((a*x - 1)/(a*x + 1))/(a*x + 1) + 30*a^4*c^8*sqrt((a*x - 1)/(a*x + 1)))/(a^6*c^12))","A",0
797,1,184,0,0.151684," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^5,x, algorithm=""giac"")","-\frac{4 \, c^{5} \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} + \frac{4 \, c^{5} \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right)}{a} + \frac{{\left(630 \, c^{5} + \frac{4049 \, c^{5}}{a x - 1} + \frac{6201 \, c^{5}}{{\left(a x - 1\right)}^{2}} - \frac{18036 \, c^{5}}{{\left(a x - 1\right)}^{3}} - \frac{89124 \, c^{5}}{{\left(a x - 1\right)}^{4}} - \frac{160146 \, c^{5}}{{\left(a x - 1\right)}^{5}} - \frac{153090 \, c^{5}}{{\left(a x - 1\right)}^{6}} - \frac{80220 \, c^{5}}{{\left(a x - 1\right)}^{7}} - \frac{21420 \, c^{5}}{{\left(a x - 1\right)}^{8}} - \frac{2520 \, c^{5}}{{\left(a x - 1\right)}^{9}}\right)} {\left(a x - 1\right)}}{630 \, a {\left(\frac{1}{a x - 1} + 1\right)}^{9}}"," ",0,"-4*c^5*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a + 4*c^5*log(abs(-1/(a*x - 1) - 1))/a + 1/630*(630*c^5 + 4049*c^5/(a*x - 1) + 6201*c^5/(a*x - 1)^2 - 18036*c^5/(a*x - 1)^3 - 89124*c^5/(a*x - 1)^4 - 160146*c^5/(a*x - 1)^5 - 153090*c^5/(a*x - 1)^6 - 80220*c^5/(a*x - 1)^7 - 21420*c^5/(a*x - 1)^8 - 2520*c^5/(a*x - 1)^9)*(a*x - 1)/(a*(1/(a*x - 1) + 1)^9)","A",0
798,1,160,0,0.141755," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^4,x, algorithm=""giac"")","-\frac{4 \, c^{4} \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} + \frac{4 \, c^{4} \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right)}{a} + \frac{{\left(105 \, c^{4} + \frac{659 \, c^{4}}{a x - 1} + \frac{1253 \, c^{4}}{{\left(a x - 1\right)}^{2}} - \frac{231 \, c^{4}}{{\left(a x - 1\right)}^{3}} - \frac{3885 \, c^{4}}{{\left(a x - 1\right)}^{4}} - \frac{5250 \, c^{4}}{{\left(a x - 1\right)}^{5}} - \frac{2730 \, c^{4}}{{\left(a x - 1\right)}^{6}} - \frac{420 \, c^{4}}{{\left(a x - 1\right)}^{7}}\right)} {\left(a x - 1\right)}}{105 \, a {\left(\frac{1}{a x - 1} + 1\right)}^{7}}"," ",0,"-4*c^4*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a + 4*c^4*log(abs(-1/(a*x - 1) - 1))/a + 1/105*(105*c^4 + 659*c^4/(a*x - 1) + 1253*c^4/(a*x - 1)^2 - 231*c^4/(a*x - 1)^3 - 3885*c^4/(a*x - 1)^4 - 5250*c^4/(a*x - 1)^5 - 2730*c^4/(a*x - 1)^6 - 420*c^4/(a*x - 1)^7)*(a*x - 1)/(a*(1/(a*x - 1) + 1)^7)","A",0
799,1,136,0,0.128772," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^3,x, algorithm=""giac"")","-\frac{4 \, c^{3} \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} + \frac{4 \, c^{3} \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right)}{a} + \frac{{\left(15 \, c^{3} + \frac{107 \, c^{3}}{a x - 1} + \frac{235 \, c^{3}}{{\left(a x - 1\right)}^{2}} + \frac{170 \, c^{3}}{{\left(a x - 1\right)}^{3}} - \frac{30 \, c^{3}}{{\left(a x - 1\right)}^{4}} - \frac{60 \, c^{3}}{{\left(a x - 1\right)}^{5}}\right)} {\left(a x - 1\right)}}{15 \, a {\left(\frac{1}{a x - 1} + 1\right)}^{5}}"," ",0,"-4*c^3*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a + 4*c^3*log(abs(-1/(a*x - 1) - 1))/a + 1/15*(15*c^3 + 107*c^3/(a*x - 1) + 235*c^3/(a*x - 1)^2 + 170*c^3/(a*x - 1)^3 - 30*c^3/(a*x - 1)^4 - 60*c^3/(a*x - 1)^5)*(a*x - 1)/(a*(1/(a*x - 1) + 1)^5)","B",0
800,1,112,0,0.121239," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^2,x, algorithm=""giac"")","-\frac{4 \, c^{2} \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} + \frac{4 \, c^{2} \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right)}{a} + \frac{{\left(3 \, c^{2} + \frac{34 \, c^{2}}{a x - 1} + \frac{66 \, c^{2}}{{\left(a x - 1\right)}^{2}} + \frac{36 \, c^{2}}{{\left(a x - 1\right)}^{3}}\right)} {\left(a x - 1\right)}}{3 \, a {\left(\frac{1}{a x - 1} + 1\right)}^{3}}"," ",0,"-4*c^2*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a + 4*c^2*log(abs(-1/(a*x - 1) - 1))/a + 1/3*(3*c^2 + 34*c^2/(a*x - 1) + 66*c^2/(a*x - 1)^2 + 36*c^2/(a*x - 1)^3)*(a*x - 1)/(a*(1/(a*x - 1) + 1)^3)","B",0
801,1,66,0,0.141348," ","integrate(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2),x, algorithm=""giac"")","-\frac{4 \, c \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a} - \frac{4 \, c \log\left({\left| -\frac{1}{a x - 1} - 1 \right|}\right)}{a} + \frac{{\left(a x - 1\right)} c}{a {\left(\frac{1}{a x - 1} + 1\right)}}"," ",0,"-4*c*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/a - 4*c*log(abs(-1/(a*x - 1) - 1))/a + (a*x - 1)*c/(a*(1/(a*x - 1) + 1))","A",0
802,1,74,0,0.118231," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2),x, algorithm=""giac"")","\frac{a x - 1}{a c} - \frac{4 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a c} - \frac{\frac{5 \, a^{3} c}{a x - 1} + \frac{a^{3} c}{{\left(a x - 1\right)}^{2}}}{a^{4} c^{2}}"," ",0,"(a*x - 1)/(a*c) - 4*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/(a*c) - (5*a^3*c/(a*x - 1) + a^3*c/(a*x - 1)^2)/(a^4*c^2)","A",0
803,1,93,0,0.133627," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\frac{a x - 1}{a c^{2}} - \frac{4 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a c^{2}} - \frac{\frac{18 \, a^{5} c^{4}}{a x - 1} + \frac{6 \, a^{5} c^{4}}{{\left(a x - 1\right)}^{2}} + \frac{a^{5} c^{4}}{{\left(a x - 1\right)}^{3}}}{3 \, a^{6} c^{6}}"," ",0,"(a*x - 1)/(a*c^2) - 4*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/(a*c^2) - 1/3*(18*a^5*c^4/(a*x - 1) + 6*a^5*c^4/(a*x - 1)^2 + a^5*c^4/(a*x - 1)^3)/(a^6*c^6)","A",0
804,1,130,0,0.142738," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\frac{a x - 1}{a c^{3}} - \frac{4 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a c^{3}} - \frac{\log\left({\left| -\frac{2}{a x - 1} - 1 \right|}\right)}{32 \, a c^{3}} - \frac{\frac{333 \, a^{11} c^{9}}{a x - 1} + \frac{147 \, a^{11} c^{9}}{{\left(a x - 1\right)}^{2}} + \frac{44 \, a^{11} c^{9}}{{\left(a x - 1\right)}^{3}} + \frac{6 \, a^{11} c^{9}}{{\left(a x - 1\right)}^{4}}}{48 \, a^{12} c^{12}}"," ",0,"(a*x - 1)/(a*c^3) - 4*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/(a*c^3) - 1/32*log(abs(-2/(a*x - 1) - 1))/(a*c^3) - 1/48*(333*a^11*c^9/(a*x - 1) + 147*a^11*c^9/(a*x - 1)^2 + 44*a^11*c^9/(a*x - 1)^3 + 6*a^11*c^9/(a*x - 1)^4)/(a^12*c^12)","A",0
805,1,170,0,0.126792," ","integrate(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\frac{{\left(a x - 1\right)} {\left(\frac{257}{a x - 1} + 128\right)}}{128 \, a c^{4} {\left(\frac{2}{a x - 1} + 1\right)}} - \frac{4 \, \log\left(\frac{{\left| a x - 1 \right|}}{{\left(a x - 1\right)}^{2} {\left| a \right|}}\right)}{a c^{4}} - \frac{5 \, \log\left({\left| -\frac{2}{a x - 1} - 1 \right|}\right)}{64 \, a c^{4}} - \frac{\frac{7515 \, a^{19} c^{16}}{a x - 1} + \frac{4020 \, a^{19} c^{16}}{{\left(a x - 1\right)}^{2}} + \frac{1660 \, a^{19} c^{16}}{{\left(a x - 1\right)}^{3}} + \frac{420 \, a^{19} c^{16}}{{\left(a x - 1\right)}^{4}} + \frac{48 \, a^{19} c^{16}}{{\left(a x - 1\right)}^{5}}}{960 \, a^{20} c^{20}}"," ",0,"1/128*(a*x - 1)*(257/(a*x - 1) + 128)/(a*c^4*(2/(a*x - 1) + 1)) - 4*log(abs(a*x - 1)/((a*x - 1)^2*abs(a)))/(a*c^4) - 5/64*log(abs(-2/(a*x - 1) - 1))/(a*c^4) - 1/960*(7515*a^19*c^16/(a*x - 1) + 4020*a^19*c^16/(a*x - 1)^2 + 1660*a^19*c^16/(a*x - 1)^3 + 420*a^19*c^16/(a*x - 1)^4 + 48*a^19*c^16/(a*x - 1)^5)/(a^20*c^20)","A",0
806,1,524,0,0.188922," ","integrate((c-c/a^2/x^2)^4*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","-\frac{35 \, c^{4} \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{8 \, a} + \frac{c^{4} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c^{4} \mathrm{sgn}\left(a x + 1\right)}{a} - \frac{3045 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{13} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 6720 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{12} a c^{4} \mathrm{sgn}\left(a x + 1\right) + 6860 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{11} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 20160 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{10} a c^{4} \mathrm{sgn}\left(a x + 1\right) + 9065 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{9} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 49280 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{8} a c^{4} \mathrm{sgn}\left(a x + 1\right) - 49280 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{6} a c^{4} \mathrm{sgn}\left(a x + 1\right) - 9065 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{5} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 38976 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{4} a c^{4} \mathrm{sgn}\left(a x + 1\right) - 6860 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{3} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 12992 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} a c^{4} \mathrm{sgn}\left(a x + 1\right) - 3045 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 2816 \, a c^{4} \mathrm{sgn}\left(a x + 1\right)}{840 \, {\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)}^{7} a {\left| a \right|}}"," ",0,"-35/8*c^4*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + c^4*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c^4*sgn(a*x + 1)/a - 1/840*(3045*(x*abs(a) - sqrt(a^2*x^2 - 1))^13*c^4*abs(a)*sgn(a*x + 1) - 6720*(x*abs(a) - sqrt(a^2*x^2 - 1))^12*a*c^4*sgn(a*x + 1) + 6860*(x*abs(a) - sqrt(a^2*x^2 - 1))^11*c^4*abs(a)*sgn(a*x + 1) - 20160*(x*abs(a) - sqrt(a^2*x^2 - 1))^10*a*c^4*sgn(a*x + 1) + 9065*(x*abs(a) - sqrt(a^2*x^2 - 1))^9*c^4*abs(a)*sgn(a*x + 1) - 49280*(x*abs(a) - sqrt(a^2*x^2 - 1))^8*a*c^4*sgn(a*x + 1) - 49280*(x*abs(a) - sqrt(a^2*x^2 - 1))^6*a*c^4*sgn(a*x + 1) - 9065*(x*abs(a) - sqrt(a^2*x^2 - 1))^5*c^4*abs(a)*sgn(a*x + 1) - 38976*(x*abs(a) - sqrt(a^2*x^2 - 1))^4*a*c^4*sgn(a*x + 1) - 6860*(x*abs(a) - sqrt(a^2*x^2 - 1))^3*c^4*abs(a)*sgn(a*x + 1) - 12992*(x*abs(a) - sqrt(a^2*x^2 - 1))^2*a*c^4*sgn(a*x + 1) - 3045*(x*abs(a) - sqrt(a^2*x^2 - 1))*c^4*abs(a)*sgn(a*x + 1) - 2816*a*c^4*sgn(a*x + 1))/(((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)^7*a*abs(a))","A",0
807,1,394,0,0.177207," ","integrate((c-c/a^2/x^2)^3*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","-\frac{15 \, c^{3} \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{4 \, a} + \frac{c^{3} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c^{3} \mathrm{sgn}\left(a x + 1\right)}{a} - \frac{135 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{9} c^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 360 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{8} a c^{3} \mathrm{sgn}\left(a x + 1\right) + 150 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{7} c^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 720 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{6} a c^{3} \mathrm{sgn}\left(a x + 1\right) - 1120 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{4} a c^{3} \mathrm{sgn}\left(a x + 1\right) - 150 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{3} c^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 560 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} a c^{3} \mathrm{sgn}\left(a x + 1\right) - 135 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)} c^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 184 \, a c^{3} \mathrm{sgn}\left(a x + 1\right)}{60 \, {\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)}^{5} a {\left| a \right|}}"," ",0,"-15/4*c^3*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + c^3*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c^3*sgn(a*x + 1)/a - 1/60*(135*(x*abs(a) - sqrt(a^2*x^2 - 1))^9*c^3*abs(a)*sgn(a*x + 1) - 360*(x*abs(a) - sqrt(a^2*x^2 - 1))^8*a*c^3*sgn(a*x + 1) + 150*(x*abs(a) - sqrt(a^2*x^2 - 1))^7*c^3*abs(a)*sgn(a*x + 1) - 720*(x*abs(a) - sqrt(a^2*x^2 - 1))^6*a*c^3*sgn(a*x + 1) - 1120*(x*abs(a) - sqrt(a^2*x^2 - 1))^4*a*c^3*sgn(a*x + 1) - 150*(x*abs(a) - sqrt(a^2*x^2 - 1))^3*c^3*abs(a)*sgn(a*x + 1) - 560*(x*abs(a) - sqrt(a^2*x^2 - 1))^2*a*c^3*sgn(a*x + 1) - 135*(x*abs(a) - sqrt(a^2*x^2 - 1))*c^3*abs(a)*sgn(a*x + 1) - 184*a*c^3*sgn(a*x + 1))/(((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)^5*a*abs(a))","A",0
808,1,264,0,0.183800," ","integrate((c-c/a^2/x^2)^2*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","-\frac{3 \, c^{2} \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{c^{2} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c^{2} \mathrm{sgn}\left(a x + 1\right)}{a} - \frac{3 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{5} c^{2} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 12 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{4} a c^{2} \mathrm{sgn}\left(a x + 1\right) - 12 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} a c^{2} \mathrm{sgn}\left(a x + 1\right) - 3 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)} c^{2} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) - 8 \, a c^{2} \mathrm{sgn}\left(a x + 1\right)}{3 \, {\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)}^{3} a {\left| a \right|}}"," ",0,"-3*c^2*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + c^2*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c^2*sgn(a*x + 1)/a - 1/3*(3*(x*abs(a) - sqrt(a^2*x^2 - 1))^5*c^2*abs(a)*sgn(a*x + 1) - 12*(x*abs(a) - sqrt(a^2*x^2 - 1))^4*a*c^2*sgn(a*x + 1) - 12*(x*abs(a) - sqrt(a^2*x^2 - 1))^2*a*c^2*sgn(a*x + 1) - 3*(x*abs(a) - sqrt(a^2*x^2 - 1))*c^2*abs(a)*sgn(a*x + 1) - 8*a*c^2*sgn(a*x + 1))/(((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)^3*a*abs(a))","A",0
809,1,121,0,0.142894," ","integrate((c-c/a^2/x^2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","-\frac{2 \, c \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{c \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{2 \, c \mathrm{sgn}\left(a x + 1\right)}{{\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)} {\left| a \right|}}"," ",0,"-2*c*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + c*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c*sgn(a*x + 1)/a + 2*c*sgn(a*x + 1)/(((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)*abs(a))","A",0
810,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
811,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(c - c/(a^2*x^2))^2, x)","F",0
812,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(c - c/(a^2*x^2))^3, x)","F",0
813,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x - 1}{a x + 1}}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt((a*x - 1)/(a*x + 1))/(c - c/(a^2*x^2))^4, x)","F",0
814,1,82,0,0.123850," ","integrate((c-c/a^2/x^2)^4*(a*x-1)/(a*x+1),x, algorithm=""giac"")","c^{4} x - \frac{2 \, c^{4} \log\left({\left| x \right|}\right)}{a} + \frac{420 \, a^{6} c^{4} x^{6} - 630 \, a^{5} c^{4} x^{5} + 315 \, a^{3} c^{4} x^{3} - 84 \, a^{2} c^{4} x^{2} - 70 \, a c^{4} x + 30 \, c^{4}}{210 \, a^{8} x^{7}}"," ",0,"c^4*x - 2*c^4*log(abs(x))/a + 1/210*(420*a^6*c^4*x^6 - 630*a^5*c^4*x^5 + 315*a^3*c^4*x^3 - 84*a^2*c^4*x^2 - 70*a*c^4*x + 30*c^4)/(a^8*x^7)","A",0
815,1,71,0,0.120106," ","integrate((c-c/a^2/x^2)^3*(a*x-1)/(a*x+1),x, algorithm=""giac"")","c^{3} x - \frac{2 \, c^{3} \log\left({\left| x \right|}\right)}{a} + \frac{30 \, a^{4} c^{3} x^{4} - 60 \, a^{3} c^{3} x^{3} + 10 \, a^{2} c^{3} x^{2} + 15 \, a c^{3} x - 6 \, c^{3}}{30 \, a^{6} x^{5}}"," ",0,"c^3*x - 2*c^3*log(abs(x))/a + 1/30*(30*a^4*c^3*x^4 - 60*a^3*c^3*x^3 + 10*a^2*c^3*x^2 + 15*a*c^3*x - 6*c^3)/(a^6*x^5)","A",0
816,1,38,0,0.127575," ","integrate((c-c/a^2/x^2)^2*(a*x-1)/(a*x+1),x, algorithm=""giac"")","c^{2} x - \frac{2 \, c^{2} \log\left({\left| x \right|}\right)}{a} - \frac{3 \, a c^{2} x - c^{2}}{3 \, a^{4} x^{3}}"," ",0,"c^2*x - 2*c^2*log(abs(x))/a - 1/3*(3*a*c^2*x - c^2)/(a^4*x^3)","A",0
817,1,22,0,0.132742," ","integrate((c-c/a^2/x^2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","c x - \frac{2 \, c \log\left({\left| x \right|}\right)}{a} - \frac{c}{a^{2} x}"," ",0,"c*x - 2*c*log(abs(x))/a - c/(a^2*x)","A",0
818,1,36,0,0.120451," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2),x, algorithm=""giac"")","\frac{x}{c} - \frac{2 \, \log\left({\left| a x + 1 \right|}\right)}{a c} - \frac{1}{{\left(a x + 1\right)} a c}"," ",0,"x/c - 2*log(abs(a*x + 1))/(a*c) - 1/((a*x + 1)*a*c)","A",0
819,1,57,0,0.130754," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\frac{x}{c^{2}} - \frac{17 \, \log\left({\left| a x + 1 \right|}\right)}{8 \, a c^{2}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{8 \, a c^{2}} - \frac{7 \, a x + 6}{4 \, {\left(a x + 1\right)}^{2} a c^{2}}"," ",0,"x/c^2 - 17/8*log(abs(a*x + 1))/(a*c^2) + 1/8*log(abs(a*x - 1))/(a*c^2) - 1/4*(7*a*x + 6)/((a*x + 1)^2*a*c^2)","A",0
820,1,80,0,0.150408," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\frac{x}{c^{3}} - \frac{9 \, \log\left({\left| a x + 1 \right|}\right)}{4 \, a c^{3}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{4 \, a c^{3}} - \frac{15 \, a^{3} x^{3} + 12 \, a^{2} x^{2} - 13 \, a x - 11}{6 \, {\left(a x + 1\right)}^{3} {\left(a x - 1\right)} a c^{3}}"," ",0,"x/c^3 - 9/4*log(abs(a*x + 1))/(a*c^3) + 1/4*log(abs(a*x - 1))/(a*c^3) - 1/6*(15*a^3*x^3 + 12*a^2*x^2 - 13*a*x - 11)/((a*x + 1)^3*(a*x - 1)*a*c^3)","A",0
821,1,96,0,0.137250," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\frac{x}{c^{4}} - \frac{303 \, \log\left({\left| a x + 1 \right|}\right)}{128 \, a c^{4}} + \frac{47 \, \log\left({\left| a x - 1 \right|}\right)}{128 \, a c^{4}} - \frac{627 \, a^{5} x^{5} + 486 \, a^{4} x^{4} - 1058 \, a^{3} x^{3} - 874 \, a^{2} x^{2} + 467 \, a x + 400}{192 \, {\left(a x + 1\right)}^{4} {\left(a x - 1\right)}^{2} a c^{4}}"," ",0,"x/c^4 - 303/128*log(abs(a*x + 1))/(a*c^4) + 47/128*log(abs(a*x - 1))/(a*c^4) - 1/192*(627*a^5*x^5 + 486*a^4*x^4 - 1058*a^3*x^3 - 874*a^2*x^2 + 467*a*x + 400)/((a*x + 1)^4*(a*x - 1)^2*a*c^4)","A",0
822,1,525,0,0.249512," ","integrate((c-c/a^2/x^2)^4*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","-\frac{15 \, c^{4} \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{8 \, a} + \frac{3 \, c^{4} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c^{4} \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{525 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{13} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 4480 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{12} a c^{4} \mathrm{sgn}\left(a x + 1\right) - 980 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{11} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 20160 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{10} a c^{4} \mathrm{sgn}\left(a x + 1\right) + 945 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{9} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 38080 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{8} a c^{4} \mathrm{sgn}\left(a x + 1\right) + 49280 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{6} a c^{4} \mathrm{sgn}\left(a x + 1\right) - 945 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{5} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 32256 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{4} a c^{4} \mathrm{sgn}\left(a x + 1\right) + 980 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{3} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 12992 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} a c^{4} \mathrm{sgn}\left(a x + 1\right) - 525 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)} c^{4} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 2496 \, a c^{4} \mathrm{sgn}\left(a x + 1\right)}{280 \, {\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)}^{7} a {\left| a \right|}}"," ",0,"-15/8*c^4*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + 3*c^4*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c^4*sgn(a*x + 1)/a + 1/280*(525*(x*abs(a) - sqrt(a^2*x^2 - 1))^13*c^4*abs(a)*sgn(a*x + 1) + 4480*(x*abs(a) - sqrt(a^2*x^2 - 1))^12*a*c^4*sgn(a*x + 1) - 980*(x*abs(a) - sqrt(a^2*x^2 - 1))^11*c^4*abs(a)*sgn(a*x + 1) + 20160*(x*abs(a) - sqrt(a^2*x^2 - 1))^10*a*c^4*sgn(a*x + 1) + 945*(x*abs(a) - sqrt(a^2*x^2 - 1))^9*c^4*abs(a)*sgn(a*x + 1) + 38080*(x*abs(a) - sqrt(a^2*x^2 - 1))^8*a*c^4*sgn(a*x + 1) + 49280*(x*abs(a) - sqrt(a^2*x^2 - 1))^6*a*c^4*sgn(a*x + 1) - 945*(x*abs(a) - sqrt(a^2*x^2 - 1))^5*c^4*abs(a)*sgn(a*x + 1) + 32256*(x*abs(a) - sqrt(a^2*x^2 - 1))^4*a*c^4*sgn(a*x + 1) + 980*(x*abs(a) - sqrt(a^2*x^2 - 1))^3*c^4*abs(a)*sgn(a*x + 1) + 12992*(x*abs(a) - sqrt(a^2*x^2 - 1))^2*a*c^4*sgn(a*x + 1) - 525*(x*abs(a) - sqrt(a^2*x^2 - 1))*c^4*abs(a)*sgn(a*x + 1) + 2496*a*c^4*sgn(a*x + 1))/(((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)^7*a*abs(a))","A",0
823,1,395,0,0.201923," ","integrate((c-c/a^2/x^2)^3*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","-\frac{3 \, c^{3} \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{4 \, a} + \frac{3 \, c^{3} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c^{3} \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{55 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{9} c^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 200 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{8} a c^{3} \mathrm{sgn}\left(a x + 1\right) - 10 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{7} c^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 720 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{6} a c^{3} \mathrm{sgn}\left(a x + 1\right) + 800 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{4} a c^{3} \mathrm{sgn}\left(a x + 1\right) + 10 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{3} c^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 560 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} a c^{3} \mathrm{sgn}\left(a x + 1\right) - 55 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)} c^{3} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 152 \, a c^{3} \mathrm{sgn}\left(a x + 1\right)}{20 \, {\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)}^{5} a {\left| a \right|}}"," ",0,"-3/4*c^3*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + 3*c^3*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c^3*sgn(a*x + 1)/a + 1/20*(55*(x*abs(a) - sqrt(a^2*x^2 - 1))^9*c^3*abs(a)*sgn(a*x + 1) + 200*(x*abs(a) - sqrt(a^2*x^2 - 1))^8*a*c^3*sgn(a*x + 1) - 10*(x*abs(a) - sqrt(a^2*x^2 - 1))^7*c^3*abs(a)*sgn(a*x + 1) + 720*(x*abs(a) - sqrt(a^2*x^2 - 1))^6*a*c^3*sgn(a*x + 1) + 800*(x*abs(a) - sqrt(a^2*x^2 - 1))^4*a*c^3*sgn(a*x + 1) + 10*(x*abs(a) - sqrt(a^2*x^2 - 1))^3*c^3*abs(a)*sgn(a*x + 1) + 560*(x*abs(a) - sqrt(a^2*x^2 - 1))^2*a*c^3*sgn(a*x + 1) - 55*(x*abs(a) - sqrt(a^2*x^2 - 1))*c^3*abs(a)*sgn(a*x + 1) + 152*a*c^3*sgn(a*x + 1))/(((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)^5*a*abs(a))","A",0
824,1,264,0,0.184910," ","integrate((c-c/a^2/x^2)^2*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\frac{c^{2} \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{3 \, c^{2} \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c^{2} \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{9 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{5} c^{2} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 12 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{4} a c^{2} \mathrm{sgn}\left(a x + 1\right) + 36 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} a c^{2} \mathrm{sgn}\left(a x + 1\right) - 9 \, {\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)} c^{2} {\left| a \right|} \mathrm{sgn}\left(a x + 1\right) + 16 \, a c^{2} \mathrm{sgn}\left(a x + 1\right)}{3 \, {\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)}^{3} a {\left| a \right|}}"," ",0,"c^2*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + 3*c^2*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c^2*sgn(a*x + 1)/a + 1/3*(9*(x*abs(a) - sqrt(a^2*x^2 - 1))^5*c^2*abs(a)*sgn(a*x + 1) + 12*(x*abs(a) - sqrt(a^2*x^2 - 1))^4*a*c^2*sgn(a*x + 1) + 36*(x*abs(a) - sqrt(a^2*x^2 - 1))^2*a*c^2*sgn(a*x + 1) - 9*(x*abs(a) - sqrt(a^2*x^2 - 1))*c^2*abs(a)*sgn(a*x + 1) + 16*a*c^2*sgn(a*x + 1))/(((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)^3*a*abs(a))","A",0
825,1,122,0,0.165631," ","integrate((c-c/a^2/x^2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\frac{6 \, c \arctan\left(-x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1}\right) \mathrm{sgn}\left(a x + 1\right)}{a} + \frac{3 \, c \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{{\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} c \mathrm{sgn}\left(a x + 1\right)}{a} - \frac{2 \, c \mathrm{sgn}\left(a x + 1\right)}{{\left({\left(x {\left| a \right|} - \sqrt{a^{2} x^{2} - 1}\right)}^{2} + 1\right)} {\left| a \right|}}"," ",0,"6*c*arctan(-x*abs(a) + sqrt(a^2*x^2 - 1))*sgn(a*x + 1)/a + 3*c*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/abs(a) + sqrt(a^2*x^2 - 1)*c*sgn(a*x + 1)/a - 2*c*sgn(a*x + 1)/(((x*abs(a) - sqrt(a^2*x^2 - 1))^2 + 1)*abs(a))","A",0
826,1,59,0,0.159144," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2),x, algorithm=""giac"")","\frac{3 \, \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{c {\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} \mathrm{sgn}\left(a x + 1\right)}{a c}"," ",0,"3*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/(c*abs(a)) + sqrt(a^2*x^2 - 1)*sgn(a*x + 1)/(a*c)","A",0
827,1,59,0,0.202314," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| -x {\left| a \right|} + \sqrt{a^{2} x^{2} - 1} \right|}\right) \mathrm{sgn}\left(a x + 1\right)}{c^{2} {\left| a \right|}} + \frac{\sqrt{a^{2} x^{2} - 1} \mathrm{sgn}\left(a x + 1\right)}{a c^{2}}"," ",0,"3*log(abs(-x*abs(a) + sqrt(a^2*x^2 - 1)))*sgn(a*x + 1)/(c^2*abs(a)) + sqrt(a^2*x^2 - 1)*sgn(a*x + 1)/(a*c^2)","A",0
828,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{3}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(c - c/(a^2*x^2))^3, x)","F",0
829,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{4}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(3/2)/(c - c/(a^2*x^2))^4, x)","F",0
830,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(7/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
831,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(5/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
832,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(3/2)/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
833,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
834,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c - \frac{c}{a^{2} x^{2}}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/(sqrt(c - c/(a^2*x^2))*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
835,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(3/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
836,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(5/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
837,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(7/2)*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
838,1,561,0,113.348260," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","-\frac{1}{120} \, {\left(\frac{375 \, c^{\frac{7}{2}} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right)}{a^{2}} + \frac{240 \, c^{\frac{7}{2}} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a {\left| a \right|}} - \frac{120 \, \sqrt{a^{2} c x^{2} - c} c^{3} \mathrm{sgn}\left(x\right)}{a^{2}} + \frac{105 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{11} c^{4} {\left| a \right|} \mathrm{sgn}\left(x\right) + 1440 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{10} a c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 595 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{9} c^{5} {\left| a \right|} \mathrm{sgn}\left(x\right) + 4320 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{8} a c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) - 150 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{7} c^{6} {\left| a \right|} \mathrm{sgn}\left(x\right) + 7360 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{6} a c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) + 150 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{5} c^{7} {\left| a \right|} \mathrm{sgn}\left(x\right) + 6720 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} a c^{\frac{15}{2}} \mathrm{sgn}\left(x\right) - 595 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} c^{8} {\left| a \right|} \mathrm{sgn}\left(x\right) + 2976 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a c^{\frac{17}{2}} \mathrm{sgn}\left(x\right) - 105 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} c^{9} {\left| a \right|} \mathrm{sgn}\left(x\right) + 736 \, a c^{\frac{19}{2}} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{6} a^{2} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"-1/120*(375*c^(7/2)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x)/a^2 + 240*c^(7/2)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a*abs(a)) - 120*sqrt(a^2*c*x^2 - c)*c^3*sgn(x)/a^2 + (105*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^11*c^4*abs(a)*sgn(x) + 1440*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^10*a*c^(9/2)*sgn(x) + 595*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^9*c^5*abs(a)*sgn(x) + 4320*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^8*a*c^(11/2)*sgn(x) - 150*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^7*c^6*abs(a)*sgn(x) + 7360*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^6*a*c^(13/2)*sgn(x) + 150*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^5*c^7*abs(a)*sgn(x) + 6720*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*a*c^(15/2)*sgn(x) - 595*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*c^8*abs(a)*sgn(x) + 2976*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a*c^(17/2)*sgn(x) - 105*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*c^9*abs(a)*sgn(x) + 736*a*c^(19/2)*sgn(x))/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^6*a^2*abs(a)))*abs(a)","A",0
839,1,416,0,7.325786," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{27 \, c^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right)}{a^{2}} + \frac{24 \, c^{\frac{5}{2}} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a {\left| a \right|}} - \frac{12 \, \sqrt{a^{2} c x^{2} - c} c^{2} \mathrm{sgn}\left(x\right)}{a^{2}} - \frac{3 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{7} c^{3} {\left| a \right|} \mathrm{sgn}\left(x\right) - 96 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{6} a c^{\frac{7}{2}} \mathrm{sgn}\left(x\right) - 21 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{5} c^{4} {\left| a \right|} \mathrm{sgn}\left(x\right) - 192 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} a c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 21 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} c^{5} {\left| a \right|} \mathrm{sgn}\left(x\right) - 160 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) - 3 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} c^{6} {\left| a \right|} \mathrm{sgn}\left(x\right) - 64 \, a c^{\frac{13}{2}} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{4} a^{2} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"-1/12*(27*c^(5/2)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x)/a^2 + 24*c^(5/2)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a*abs(a)) - 12*sqrt(a^2*c*x^2 - c)*c^2*sgn(x)/a^2 - (3*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^7*c^3*abs(a)*sgn(x) - 96*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^6*a*c^(7/2)*sgn(x) - 21*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^5*c^4*abs(a)*sgn(x) - 192*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*a*c^(9/2)*sgn(x) + 21*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*c^5*abs(a)*sgn(x) - 160*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a*c^(11/2)*sgn(x) - 3*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*c^6*abs(a)*sgn(x) - 64*a*c^(13/2)*sgn(x))/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^4*a^2*abs(a)))*abs(a)","A",0
840,1,266,0,0.504388," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","-{\left(\frac{c^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right)}{a^{2}} + \frac{2 \, c^{\frac{3}{2}} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a {\left| a \right|}} - \frac{\sqrt{a^{2} c x^{2} - c} c \mathrm{sgn}\left(x\right)}{a^{2}} - \frac{{\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} c^{2} {\left| a \right|} \mathrm{sgn}\left(x\right) - 4 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a c^{\frac{5}{2}} \mathrm{sgn}\left(x\right) - {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} c^{3} {\left| a \right|} \mathrm{sgn}\left(x\right) - 4 \, a c^{\frac{7}{2}} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{2} a^{2} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"-(c^(3/2)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x)/a^2 + 2*c^(3/2)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a*abs(a)) - sqrt(a^2*c*x^2 - c)*c*sgn(x)/a^2 - ((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*c^2*abs(a)*sgn(x) - 4*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a*c^(5/2)*sgn(x) - (sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*c^3*abs(a)*sgn(x) - 4*a*c^(7/2)*sgn(x))/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^2*a^2*abs(a)))*abs(a)","A",0
841,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
842,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(a x - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*sqrt(c - c/(a^2*x^2))), x)","F",0
843,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(a x - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*(c - c/(a^2*x^2))^(3/2)), x)","F",0
844,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(a x - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
845,0,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(a x - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/((a*x - 1)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
846,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(9/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
847,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(7/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
848,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(5/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
849,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(3/2)/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
850,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
851,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
852,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(3/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
853,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(5/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
854,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c - c/(a^2*x^2))^(7/2)*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
855,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(7/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
856,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(5/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
857,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(3/2)*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
858,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
859,0,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
860,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
861,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
862,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
863,1,561,0,113.466933," ","integrate((c-c/a^2/x^2)^(7/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{1}{120} \, {\left(\frac{375 \, c^{\frac{7}{2}} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right)}{a^{2}} - \frac{240 \, c^{\frac{7}{2}} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a {\left| a \right|}} - \frac{120 \, \sqrt{a^{2} c x^{2} - c} c^{3} \mathrm{sgn}\left(x\right)}{a^{2}} + \frac{105 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{11} c^{4} {\left| a \right|} \mathrm{sgn}\left(x\right) - 1440 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{10} a c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 595 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{9} c^{5} {\left| a \right|} \mathrm{sgn}\left(x\right) - 4320 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{8} a c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) - 150 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{7} c^{6} {\left| a \right|} \mathrm{sgn}\left(x\right) - 7360 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{6} a c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) + 150 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{5} c^{7} {\left| a \right|} \mathrm{sgn}\left(x\right) - 6720 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} a c^{\frac{15}{2}} \mathrm{sgn}\left(x\right) - 595 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} c^{8} {\left| a \right|} \mathrm{sgn}\left(x\right) - 2976 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a c^{\frac{17}{2}} \mathrm{sgn}\left(x\right) - 105 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} c^{9} {\left| a \right|} \mathrm{sgn}\left(x\right) - 736 \, a c^{\frac{19}{2}} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{6} a^{2} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"-1/120*(375*c^(7/2)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x)/a^2 - 240*c^(7/2)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a*abs(a)) - 120*sqrt(a^2*c*x^2 - c)*c^3*sgn(x)/a^2 + (105*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^11*c^4*abs(a)*sgn(x) - 1440*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^10*a*c^(9/2)*sgn(x) + 595*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^9*c^5*abs(a)*sgn(x) - 4320*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^8*a*c^(11/2)*sgn(x) - 150*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^7*c^6*abs(a)*sgn(x) - 7360*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^6*a*c^(13/2)*sgn(x) + 150*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^5*c^7*abs(a)*sgn(x) - 6720*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*a*c^(15/2)*sgn(x) - 595*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*c^8*abs(a)*sgn(x) - 2976*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a*c^(17/2)*sgn(x) - 105*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*c^9*abs(a)*sgn(x) - 736*a*c^(19/2)*sgn(x))/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^6*a^2*abs(a)))*abs(a)","A",0
864,1,416,0,7.130694," ","integrate((c-c/a^2/x^2)^(5/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{27 \, c^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right)}{a^{2}} - \frac{24 \, c^{\frac{5}{2}} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a {\left| a \right|}} - \frac{12 \, \sqrt{a^{2} c x^{2} - c} c^{2} \mathrm{sgn}\left(x\right)}{a^{2}} - \frac{3 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{7} c^{3} {\left| a \right|} \mathrm{sgn}\left(x\right) + 96 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{6} a c^{\frac{7}{2}} \mathrm{sgn}\left(x\right) - 21 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{5} c^{4} {\left| a \right|} \mathrm{sgn}\left(x\right) + 192 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} a c^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 21 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} c^{5} {\left| a \right|} \mathrm{sgn}\left(x\right) + 160 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) - 3 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} c^{6} {\left| a \right|} \mathrm{sgn}\left(x\right) + 64 \, a c^{\frac{13}{2}} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{4} a^{2} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"-1/12*(27*c^(5/2)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x)/a^2 - 24*c^(5/2)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a*abs(a)) - 12*sqrt(a^2*c*x^2 - c)*c^2*sgn(x)/a^2 - (3*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^7*c^3*abs(a)*sgn(x) + 96*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^6*a*c^(7/2)*sgn(x) - 21*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^5*c^4*abs(a)*sgn(x) + 192*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*a*c^(9/2)*sgn(x) + 21*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*c^5*abs(a)*sgn(x) + 160*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a*c^(11/2)*sgn(x) - 3*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*c^6*abs(a)*sgn(x) + 64*a*c^(13/2)*sgn(x))/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^4*a^2*abs(a)))*abs(a)","A",0
865,1,266,0,0.473837," ","integrate((c-c/a^2/x^2)^(3/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","-{\left(\frac{c^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right)}{a^{2}} - \frac{2 \, c^{\frac{3}{2}} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a {\left| a \right|}} - \frac{\sqrt{a^{2} c x^{2} - c} c \mathrm{sgn}\left(x\right)}{a^{2}} - \frac{{\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} c^{2} {\left| a \right|} \mathrm{sgn}\left(x\right) + 4 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a c^{\frac{5}{2}} \mathrm{sgn}\left(x\right) - {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} c^{3} {\left| a \right|} \mathrm{sgn}\left(x\right) + 4 \, a c^{\frac{7}{2}} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{2} a^{2} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"-(c^(3/2)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x)/a^2 - 2*c^(3/2)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a*abs(a)) - sqrt(a^2*c*x^2 - c)*c*sgn(x)/a^2 - ((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*c^2*abs(a)*sgn(x) + 4*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a*c^(5/2)*sgn(x) - (sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*c^3*abs(a)*sgn(x) + 4*a*c^(7/2)*sgn(x))/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^2*a^2*abs(a)))*abs(a)","A",0
866,-2,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
867,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{a x - 1}{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*sqrt(c - c/(a^2*x^2))), x)","F",0
868,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{a x - 1}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*(c - c/(a^2*x^2))^(3/2)), x)","F",0
869,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{a x - 1}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
870,0,0,0,0.000000," ","integrate((a*x-1)/(a*x+1)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{a x - 1}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x - 1)/((a*x + 1)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
871,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(9/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
872,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(7/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
873,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(5/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
874,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^(3/2)*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
875,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
876,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
877,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
878,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
879,-2,0,0,0.000000," ","integrate(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
880,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
881,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^2/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
882,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} x}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
883,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{\sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/sqrt((a*x - 1)/(a*x + 1)), x)","F",0
884,-2,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*x+1),sign(x)]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[0,1,0]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{-2,[2,2,2]%%%}+%%%{4,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{1,[0,2,0]%%%}+%%%{-2,[0,1,0]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [-89,63,-49]Warning, choosing root of [1,0,%%%{-2,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{2,[0,1,0]%%%}+%%%{2,[0,0,0]%%%},0,%%%{1,[4,2,4]%%%}+%%%{-2,[4,1,4]%%%}+%%%{1,[4,0,4]%%%}+%%%{-2,[2,2,2]%%%}+%%%{4,[2,1,2]%%%}+%%%{-2,[2,0,2]%%%}+%%%{1,[0,2,0]%%%}+%%%{-2,[0,1,0]%%%}+%%%{1,[0,0,0]%%%}] at parameters values [-86,-64,-30]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
885,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x^{2} \sqrt{\frac{a x - 1}{a x + 1}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x^2*sqrt((a*x - 1)/(a*x + 1))), x)","F",0
886,1,128,0,0.181514," ","integrate(1/(a*x-1)*(a*x+1)*x^3*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, \sqrt{a^{2} c x^{2} - c} {\left({\left(2 \, x {\left(\frac{3 \, x \mathrm{sgn}\left(x\right)}{a^{2}} + \frac{8 \, \mathrm{sgn}\left(x\right)}{a^{3}}\right)} + \frac{21 \, \mathrm{sgn}\left(x\right)}{a^{4}}\right)} x + \frac{32 \, \mathrm{sgn}\left(x\right)}{a^{5}}\right)} - \frac{42 \, \sqrt{c} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a^{4} {\left| a \right|}} + \frac{{\left(21 \, a \sqrt{c} \log\left({\left| c \right|}\right) - 64 \, \sqrt{-c} {\left| a \right|}\right)} \mathrm{sgn}\left(x\right)}{a^{5} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"1/48*(2*sqrt(a^2*c*x^2 - c)*((2*x*(3*x*sgn(x)/a^2 + 8*sgn(x)/a^3) + 21*sgn(x)/a^4)*x + 32*sgn(x)/a^5) - 42*sqrt(c)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a^4*abs(a)) + (21*a*sqrt(c)*log(abs(c)) - 64*sqrt(-c)*abs(a))*sgn(x)/(a^5*abs(a)))*abs(a)","A",0
887,1,116,0,0.184881," ","integrate(1/(a*x-1)*(a*x+1)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(2 \, \sqrt{a^{2} c x^{2} - c} {\left(x {\left(\frac{x \mathrm{sgn}\left(x\right)}{a^{2}} + \frac{3 \, \mathrm{sgn}\left(x\right)}{a^{3}}\right)} + \frac{5 \, \mathrm{sgn}\left(x\right)}{a^{4}}\right)} - \frac{6 \, \sqrt{c} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a^{3} {\left| a \right|}} + \frac{{\left(3 \, a \sqrt{c} \log\left({\left| c \right|}\right) - 10 \, \sqrt{-c} {\left| a \right|}\right)} \mathrm{sgn}\left(x\right)}{a^{4} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"1/6*(2*sqrt(a^2*c*x^2 - c)*(x*(x*sgn(x)/a^2 + 3*sgn(x)/a^3) + 5*sgn(x)/a^4) - 6*sqrt(c)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a^3*abs(a)) + (3*a*sqrt(c)*log(abs(c)) - 10*sqrt(-c)*abs(a))*sgn(x)/(a^4*abs(a)))*abs(a)","A",0
888,1,106,0,0.161326," ","integrate(1/(a*x-1)*(a*x+1)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(2 \, \sqrt{a^{2} c x^{2} - c} {\left(\frac{x \mathrm{sgn}\left(x\right)}{a^{2}} + \frac{4 \, \mathrm{sgn}\left(x\right)}{a^{3}}\right)} - \frac{6 \, \sqrt{c} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a^{2} {\left| a \right|}} + \frac{{\left(3 \, a \sqrt{c} \log\left({\left| c \right|}\right) - 8 \, \sqrt{-c} {\left| a \right|}\right)} \mathrm{sgn}\left(x\right)}{a^{3} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"1/4*(2*sqrt(a^2*c*x^2 - c)*(x*sgn(x)/a^2 + 4*sgn(x)/a^3) - 6*sqrt(c)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a^2*abs(a)) + (3*a*sqrt(c)*log(abs(c)) - 8*sqrt(-c)*abs(a))*sgn(x)/(a^3*abs(a)))*abs(a)","A",0
889,-2,0,0,0.000000," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
890,1,127,0,0.305921," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""giac"")","{\left(\frac{4 \, \sqrt{c} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right)}{a} - \frac{\sqrt{c} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{{\left| a \right|}} + \frac{2 \, c^{\frac{3}{2}} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"(4*sqrt(c)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x)/a - sqrt(c)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/abs(a) + 2*c^(3/2)*sgn(x)/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)*abs(a)))*abs(a)","A",0
891,1,194,0,0.334627," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""giac"")","{\left(3 \, \sqrt{c} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right) - \frac{{\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} a c \mathrm{sgn}\left(x\right) - 4 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} c^{\frac{3}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} a c^{2} \mathrm{sgn}\left(x\right) - 4 \, c^{\frac{5}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{2} a}\right)} {\left| a \right|}"," ",0,"(3*sqrt(c)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x) - ((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*a*c*sgn(x) - 4*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*c^(3/2)*abs(a)*sgn(x) - (sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*a*c^2*sgn(x) - 4*c^(5/2)*abs(a)*sgn(x))/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^2*a))*abs(a)","B",0
892,1,231,0,1.884631," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^3,x, algorithm=""giac"")","\frac{2}{3} \, {\left(3 \, a \sqrt{c} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right) - \frac{3 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{5} a c \mathrm{sgn}\left(x\right) - 3 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} c^{\frac{3}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 12 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} c^{\frac{5}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 3 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} a c^{3} \mathrm{sgn}\left(x\right) - 5 \, c^{\frac{7}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{3}}\right)} {\left| a \right|}"," ",0,"2/3*(3*a*sqrt(c)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x) - (3*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^5*a*c*sgn(x) - 3*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*c^(3/2)*abs(a)*sgn(x) - 12*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*c^(5/2)*abs(a)*sgn(x) - 3*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*a*c^3*sgn(x) - 5*c^(7/2)*abs(a)*sgn(x))/((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^3)*abs(a)","A",0
893,1,316,0,7.404266," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^4,x, algorithm=""giac"")","\frac{1}{12} \, {\left(21 \, a^{2} \sqrt{c} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right) - \frac{21 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{7} a^{2} c \mathrm{sgn}\left(x\right) + 45 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{5} a^{2} c^{2} \mathrm{sgn}\left(x\right) - 96 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} a c^{\frac{5}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 45 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} a^{2} c^{3} \mathrm{sgn}\left(x\right) - 128 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a c^{\frac{7}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 21 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} a^{2} c^{4} \mathrm{sgn}\left(x\right) - 32 \, a c^{\frac{9}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{4}}\right)} {\left| a \right|}"," ",0,"1/12*(21*a^2*sqrt(c)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x) - (21*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^7*a^2*c*sgn(x) + 45*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^5*a^2*c^2*sgn(x) - 96*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*a*c^(5/2)*abs(a)*sgn(x) - 45*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*a^2*c^3*sgn(x) - 128*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a*c^(7/2)*abs(a)*sgn(x) - 21*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*a^2*c^4*sgn(x) - 32*a*c^(9/2)*abs(a)*sgn(x))/((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^4)*abs(a)","B",0
894,1,362,0,8.609984," ","integrate(1/(a*x-1)*(a*x+1)*(c-c/a^2/x^2)^(1/2)/x^5,x, algorithm=""giac"")","\frac{1}{10} \, {\left(15 \, a^{3} \sqrt{c} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right) - \frac{15 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{9} a^{3} c \mathrm{sgn}\left(x\right) + 70 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{7} a^{3} c^{2} \mathrm{sgn}\left(x\right) - 40 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{6} a^{2} c^{\frac{5}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 200 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} a^{2} c^{\frac{7}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 70 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} a^{3} c^{4} \mathrm{sgn}\left(x\right) - 120 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a^{2} c^{\frac{9}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 15 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} a^{3} c^{5} \mathrm{sgn}\left(x\right) - 24 \, a^{2} c^{\frac{11}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{5}}\right)} {\left| a \right|}"," ",0,"1/10*(15*a^3*sqrt(c)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x) - (15*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^9*a^3*c*sgn(x) + 70*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^7*a^3*c^2*sgn(x) - 40*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^6*a^2*c^(5/2)*abs(a)*sgn(x) - 200*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*a^2*c^(7/2)*abs(a)*sgn(x) - 70*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*a^3*c^4*sgn(x) - 120*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a^2*c^(9/2)*abs(a)*sgn(x) - 15*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*a^3*c^5*sgn(x) - 24*a^2*c^(11/2)*abs(a)*sgn(x))/((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^5)*abs(a)","B",0
895,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} x^{3}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^3/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
896,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^2/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
897,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} x}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
898,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
899,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
900,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x^2*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
901,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x^3*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
902,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x^{4} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x^4*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
903,0,0,0,0.000000," ","integrate(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}}}{x^{5} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))/(x^5*((a*x - 1)/(a*x + 1))^(3/2)), x)","F",0
904,0,0,0,0.000000," ","integrate(x^m*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{m} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^m*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
905,0,0,0,0.000000," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^2*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
906,0,0,0,0.000000," ","integrate(x*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} x \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
907,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} \sqrt{\frac{a x - 1}{a x + 1}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*sqrt((a*x - 1)/(a*x + 1)), x)","F",0
908,-2,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(x),sign(a*x+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
909,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \sqrt{\frac{a x - 1}{a x + 1}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*sqrt((a*x - 1)/(a*x + 1))/x^2, x)","F",0
910,1,128,0,0.158949," ","integrate(x^3*(c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, \sqrt{a^{2} c x^{2} - c} {\left({\left(2 \, x {\left(\frac{3 \, x \mathrm{sgn}\left(x\right)}{a^{2}} - \frac{8 \, \mathrm{sgn}\left(x\right)}{a^{3}}\right)} + \frac{21 \, \mathrm{sgn}\left(x\right)}{a^{4}}\right)} x - \frac{32 \, \mathrm{sgn}\left(x\right)}{a^{5}}\right)} - \frac{42 \, \sqrt{c} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a^{4} {\left| a \right|}} + \frac{{\left(21 \, a \sqrt{c} \log\left({\left| c \right|}\right) + 64 \, \sqrt{-c} {\left| a \right|}\right)} \mathrm{sgn}\left(x\right)}{a^{5} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"1/48*(2*sqrt(a^2*c*x^2 - c)*((2*x*(3*x*sgn(x)/a^2 - 8*sgn(x)/a^3) + 21*sgn(x)/a^4)*x - 32*sgn(x)/a^5) - 42*sqrt(c)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a^4*abs(a)) + (21*a*sqrt(c)*log(abs(c)) + 64*sqrt(-c)*abs(a))*sgn(x)/(a^5*abs(a)))*abs(a)","A",0
911,1,117,0,0.171699," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{1}{6} \, {\left(2 \, \sqrt{a^{2} c x^{2} - c} {\left(x {\left(\frac{x \mathrm{sgn}\left(x\right)}{a^{2}} - \frac{3 \, \mathrm{sgn}\left(x\right)}{a^{3}}\right)} + \frac{5 \, \mathrm{sgn}\left(x\right)}{a^{4}}\right)} + \frac{6 \, \sqrt{c} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a^{3} {\left| a \right|}} - \frac{{\left(3 \, a \sqrt{c} \log\left({\left| c \right|}\right) + 10 \, \sqrt{-c} {\left| a \right|}\right)} \mathrm{sgn}\left(x\right)}{a^{4} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"1/6*(2*sqrt(a^2*c*x^2 - c)*(x*(x*sgn(x)/a^2 - 3*sgn(x)/a^3) + 5*sgn(x)/a^4) + 6*sqrt(c)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a^3*abs(a)) - (3*a*sqrt(c)*log(abs(c)) + 10*sqrt(-c)*abs(a))*sgn(x)/(a^4*abs(a)))*abs(a)","A",0
912,1,106,0,0.175855," ","integrate(x*(c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\frac{1}{4} \, {\left(2 \, \sqrt{a^{2} c x^{2} - c} {\left(\frac{x \mathrm{sgn}\left(x\right)}{a^{2}} - \frac{4 \, \mathrm{sgn}\left(x\right)}{a^{3}}\right)} - \frac{6 \, \sqrt{c} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{a^{2} {\left| a \right|}} + \frac{{\left(3 \, a \sqrt{c} \log\left({\left| c \right|}\right) + 8 \, \sqrt{-c} {\left| a \right|}\right)} \mathrm{sgn}\left(x\right)}{a^{3} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"1/4*(2*sqrt(a^2*c*x^2 - c)*(x*sgn(x)/a^2 - 4*sgn(x)/a^3) - 6*sqrt(c)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a^2*abs(a)) + (3*a*sqrt(c)*log(abs(c)) + 8*sqrt(-c)*abs(a))*sgn(x)/(a^3*abs(a)))*abs(a)","A",0
913,-2,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
914,1,127,0,0.281368," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x,x, algorithm=""giac"")","-{\left(\frac{4 \, \sqrt{c} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right)}{a} + \frac{\sqrt{c} \log\left({\left| -\sqrt{a^{2} c} x + \sqrt{a^{2} c x^{2} - c} \right|}\right) \mathrm{sgn}\left(x\right)}{{\left| a \right|}} - \frac{2 \, c^{\frac{3}{2}} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"-(4*sqrt(c)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x)/a + sqrt(c)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/abs(a) - 2*c^(3/2)*sgn(x)/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)*abs(a)))*abs(a)","A",0
915,1,194,0,0.350435," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^2,x, algorithm=""giac"")","{\left(3 \, \sqrt{c} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right) - \frac{{\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} a c \mathrm{sgn}\left(x\right) + 4 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} c^{\frac{3}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} a c^{2} \mathrm{sgn}\left(x\right) + 4 \, c^{\frac{5}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{2} a}\right)} {\left| a \right|}"," ",0,"(3*sqrt(c)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x) - ((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*a*c*sgn(x) + 4*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*c^(3/2)*abs(a)*sgn(x) - (sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*a*c^2*sgn(x) + 4*c^(5/2)*abs(a)*sgn(x))/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^2*a))*abs(a)","B",0
916,1,231,0,1.914641," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^3,x, algorithm=""giac"")","-\frac{2}{3} \, {\left(3 \, a \sqrt{c} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right) - \frac{3 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{5} a c \mathrm{sgn}\left(x\right) + 3 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} c^{\frac{3}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) + 12 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} c^{\frac{5}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 3 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} a c^{3} \mathrm{sgn}\left(x\right) + 5 \, c^{\frac{7}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{3}}\right)} {\left| a \right|}"," ",0,"-2/3*(3*a*sqrt(c)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x) - (3*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^5*a*c*sgn(x) + 3*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*c^(3/2)*abs(a)*sgn(x) + 12*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*c^(5/2)*abs(a)*sgn(x) - 3*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*a*c^3*sgn(x) + 5*c^(7/2)*abs(a)*sgn(x))/((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^3)*abs(a)","A",0
917,1,316,0,7.727961," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^4,x, algorithm=""giac"")","\frac{1}{12} \, {\left(21 \, a^{2} \sqrt{c} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right) - \frac{21 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{7} a^{2} c \mathrm{sgn}\left(x\right) + 45 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{5} a^{2} c^{2} \mathrm{sgn}\left(x\right) + 96 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} a c^{\frac{5}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 45 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} a^{2} c^{3} \mathrm{sgn}\left(x\right) + 128 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a c^{\frac{7}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 21 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} a^{2} c^{4} \mathrm{sgn}\left(x\right) + 32 \, a c^{\frac{9}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{4}}\right)} {\left| a \right|}"," ",0,"1/12*(21*a^2*sqrt(c)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x) - (21*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^7*a^2*c*sgn(x) + 45*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^5*a^2*c^2*sgn(x) + 96*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*a*c^(5/2)*abs(a)*sgn(x) - 45*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*a^2*c^3*sgn(x) + 128*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a*c^(7/2)*abs(a)*sgn(x) - 21*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*a^2*c^4*sgn(x) + 32*a*c^(9/2)*abs(a)*sgn(x))/((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^4)*abs(a)","B",0
918,1,362,0,9.781393," ","integrate((c-c/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)/x^5,x, algorithm=""giac"")","-\frac{1}{10} \, {\left(15 \, a^{3} \sqrt{c} \arctan\left(-\frac{\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}}{\sqrt{c}}\right) \mathrm{sgn}\left(x\right) - \frac{15 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{9} a^{3} c \mathrm{sgn}\left(x\right) + 70 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{7} a^{3} c^{2} \mathrm{sgn}\left(x\right) + 40 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{6} a^{2} c^{\frac{5}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) + 200 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} a^{2} c^{\frac{7}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 70 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} a^{3} c^{4} \mathrm{sgn}\left(x\right) + 120 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a^{2} c^{\frac{9}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right) - 15 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} a^{3} c^{5} \mathrm{sgn}\left(x\right) + 24 \, a^{2} c^{\frac{11}{2}} {\left| a \right|} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{5}}\right)} {\left| a \right|}"," ",0,"-1/10*(15*a^3*sqrt(c)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x) - (15*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^9*a^3*c*sgn(x) + 70*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^7*a^3*c^2*sgn(x) + 40*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^6*a^2*c^(5/2)*abs(a)*sgn(x) + 200*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*a^2*c^(7/2)*abs(a)*sgn(x) - 70*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*a^3*c^4*sgn(x) + 120*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a^2*c^(9/2)*abs(a)*sgn(x) - 15*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*a^3*c^5*sgn(x) + 24*a^2*c^(11/2)*abs(a)*sgn(x))/((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^5)*abs(a)","B",0
919,0,0,0,0.000000," ","integrate(x^3*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{3} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^3*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
920,0,0,0,0.000000," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x^2*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
921,0,0,0,0.000000," ","integrate(x*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} x \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*x*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
922,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x, algorithm=""giac"")","\int \sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2), x)","F",0
923,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)/x, x)","F",0
924,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)/x^2, x)","F",0
925,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)/x^3, x)","F",0
926,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)/x^4, x)","F",0
927,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{c - \frac{c}{a^{2} x^{2}}} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{3}{2}}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt(c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(3/2)/x^5, x)","F",0
928,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(c-c/a^2/x^2),x, algorithm=""giac"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
929,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(c-c/a^2/x^2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{c - \frac{c}{a^{2} x^{2}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(c - c/(a^2*x^2)), x)","F",0
930,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/(c - c/(a^2*x^2))^2, x)","F",0
931,-2,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
932,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}}{\sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate(((a*x - 1)/(a*x + 1))^(1/2*n)/sqrt(c - c/(a^2*x^2)), x)","F",0
933,0,0,0,0.000000," ","integrate(exp(n*arccoth(a*x))*(c-c/a^2/x^2)^p,x, algorithm=""giac"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^p*((a*x - 1)/(a*x + 1))^(1/2*n), x)","F",0
934,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^p/exp(2*p*arccoth(a*x)),x, algorithm=""giac"")","\int \frac{{\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{\left(\frac{a x - 1}{a x + 1}\right)^{p}}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^p/((a*x - 1)/(a*x + 1))^p, x)","F",0
935,0,0,0,0.000000," ","integrate(exp(2*p*arccoth(a*x))*(c-c/a^2/x^2)^p,x, algorithm=""giac"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p} \left(\frac{a x - 1}{a x + 1}\right)^{p}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^p*((a*x - 1)/(a*x + 1))^p, x)","F",0
