1,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
2,1,59,0,1.177661," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3,x, algorithm=""giac"")","-\frac{1}{24} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, x {\left(\frac{3 \, x}{a} + \frac{4}{a^{2}}\right)} + \frac{9}{a^{3}}\right)} x + \frac{16}{a^{4}}\right)} + \frac{3 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, a^{3} {\left| a \right|}}"," ",0,"-1/24*sqrt(-a^2*x^2 + 1)*((2*x*(3*x/a + 4/a^2) + 9/a^3)*x + 16/a^4) + 3/8*arcsin(a*x)*sgn(a)/(a^3*abs(a))","A",0
3,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
4,1,41,0,1.113710," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{x}{a} + \frac{2}{a^{2}}\right)} + \frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, a {\left| a \right|}}"," ",0,"-1/2*sqrt(-a^2*x^2 + 1)*(x/a + 2/a^2) + 1/2*arcsin(a*x)*sgn(a)/(a*abs(a))","A",0
5,1,29,0,0.215488," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a}"," ",0,"arcsin(a*x)*sgn(a)/abs(a) - sqrt(-a^2*x^2 + 1)/a","A",0
6,1,51,0,0.225546," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x,x, algorithm=""giac"")","\frac{a \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{a \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}}"," ",0,"a*arcsin(a*x)*sgn(a)/abs(a) - a*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a)","B",0
7,1,96,0,0.415085," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""giac"")","\frac{a^{4} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} - \frac{a^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{2 \, x {\left| a \right|}}"," ",0,"1/2*a^4*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) - a^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(x*abs(a))","B",0
8,1,158,0,0.408046," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""giac"")","\frac{{\left(a^{3} + \frac{4 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a}{x}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}} - \frac{a^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\frac{4 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a {\left| a \right|}}{x} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}}{a x^{2}}}{8 \, a^{2}}"," ",0,"1/8*(a^3 + 4*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a/x)*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)) - 1/2*a^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/8*(4*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*abs(a)/x + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)/(a*x^2))/a^2","B",0
9,1,210,0,0.212750," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""giac"")","\frac{{\left(a^{4} + \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2}}{x} + \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} - \frac{a^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4}}{x} + \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2}}{x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(a^4 + 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2/x + 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/x^2)*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) - 1/2*a^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/24*(9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4/x + 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2/x^2 + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/x^3)/(a^2*abs(a))","B",0
10,1,273,0,0.176104," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^5,x, algorithm=""giac"")","\frac{{\left(3 \, a^{5} + \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{3}}{x} + \frac{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a}{x^{2}} + \frac{72 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a x^{3}}\right)} a^{8} x^{4}}{192 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} {\left| a \right|}} - \frac{3 \, a^{5} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} - \frac{\frac{72 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{5} {\left| a \right|}}{x} + \frac{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{3} {\left| a \right|}}{x^{2}} + \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a {\left| a \right|}}{x^{3}} + \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} {\left| a \right|}}{a x^{4}}}{192 \, a^{4}}"," ",0,"1/192*(3*a^5 + 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^3/x + 24*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a/x^2 + 72*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a*x^3))*a^8*x^4/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*abs(a)) - 3/8*a^5*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/192*(72*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^5*abs(a)/x + 24*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^3*abs(a)/x^2 + 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a*abs(a)/x^3 + 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*abs(a)/(a*x^4))/a^4","B",0
11,1,47,0,0.934972," ","integrate((a*x+1)^2/(-a^2*x^2+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
12,1,38,0,0.166025," ","integrate((a*x+1)^2/(-a^2*x^2+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
13,1,30,0,0.156075," ","integrate((a*x+1)^2/(-a^2*x^2+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
14,1,16,0,0.241266," ","integrate((a*x+1)^2/(-a^2*x^2+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
15,1,13,0,0.342019," ","integrate((a*x+1)^2/(-a^2*x^2+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
16,1,22,0,0.245393," ","integrate((a*x+1)^2/(-a^2*x^2+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
17,1,32,0,0.245965," ","integrate((a*x+1)^2/(-a^2*x^2+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
18,1,40,0,0.191543," ","integrate((a*x+1)^2/(-a^2*x^2+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
19,1,87,0,0.235084," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2,x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left(x {\left(\frac{2 \, x}{a} + \frac{9}{a^{2}}\right)} + \frac{28}{a^{3}}\right)} - \frac{11 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, a^{2} {\left| a \right|}} + \frac{8}{a^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"1/6*sqrt(-a^2*x^2 + 1)*(x*(2*x/a + 9/a^2) + 28/a^3) - 11/2*arcsin(a*x)*sgn(a)/(a^2*abs(a)) + 8/(a^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
20,1,78,0,0.219705," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{x}{a} + \frac{6}{a^{2}}\right)} - \frac{9 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, a {\left| a \right|}} + \frac{8}{a {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"1/2*sqrt(-a^2*x^2 + 1)*(x/a + 6/a^2) - 9/2*arcsin(a*x)*sgn(a)/(a*abs(a)) + 8/(a*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
21,1,63,0,0.231223," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{3 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a} + \frac{8}{{\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"-3*arcsin(a*x)*sgn(a)/abs(a) + sqrt(-a^2*x^2 + 1)/a + 8/(((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
22,1,87,0,0.215655," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x,x, algorithm=""giac"")","-\frac{a \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{a \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} + \frac{8 \, a}{{\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"-a*arcsin(a*x)*sgn(a)/abs(a) - a*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 8*a/(((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","B",0
23,1,150,0,0.214963," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""giac"")","-\frac{3 \, a^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{{\left(a^{2} - \frac{17 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{x}\right)} a^{2} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{2 \, x {\left| a \right|}}"," ",0,"-3*a^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/2*(a^2 - 17*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/x)*a^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a)) - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(x*abs(a))","B",0
24,1,213,0,0.421895," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""giac"")","-\frac{{\left(a^{3} + \frac{11 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a}{x} - \frac{76 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a x^{2}}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}} - \frac{9 \, a^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\frac{12 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a {\left| a \right|}}{x} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}}{a x^{2}}}{8 \, a^{2}}"," ",0,"-1/8*(a^3 + 11*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a/x - 76*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a*x^2))*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a)) - 9/2*a^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/8*(12*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*abs(a)/x + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)/(a*x^2))/a^2","B",0
25,1,265,0,0.402004," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""giac"")","-\frac{{\left(a^{4} + \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2}}{x} + \frac{48 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{x^{2}} - \frac{249 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{2} x^{3}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}} - \frac{11 \, a^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\frac{57 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4}}{x} + \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2}}{x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"-1/24*(a^4 + 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2/x + 48*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/x^2 - 249*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^2*x^3))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a)) - 11/2*a^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/24*(57*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4/x + 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2/x^2 + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/x^3)/(a^2*abs(a))","B",0
26,1,61,0,0.244361," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*x^3,x, algorithm=""giac"")","\frac{16 \, \log\left({\left| a x - 1 \right|}\right)}{a^{4}} - \frac{4}{{\left(a x - 1\right)} a^{4}} + \frac{3 \, a^{8} x^{4} + 16 \, a^{7} x^{3} + 48 \, a^{6} x^{2} + 144 \, a^{5} x}{12 \, a^{8}}"," ",0,"16*log(abs(a*x - 1))/a^4 - 4/((a*x - 1)*a^4) + 1/12*(3*a^8*x^4 + 16*a^7*x^3 + 48*a^6*x^2 + 144*a^5*x)/a^8","A",0
27,1,52,0,0.197422," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*x^2,x, algorithm=""giac"")","\frac{12 \, \log\left({\left| a x - 1 \right|}\right)}{a^{3}} - \frac{4}{{\left(a x - 1\right)} a^{3}} + \frac{a^{6} x^{3} + 6 \, a^{5} x^{2} + 24 \, a^{4} x}{3 \, a^{6}}"," ",0,"12*log(abs(a*x - 1))/a^3 - 4/((a*x - 1)*a^3) + 1/3*(a^6*x^3 + 6*a^5*x^2 + 24*a^4*x)/a^6","A",0
28,1,44,0,0.169307," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*x,x, algorithm=""giac"")","\frac{8 \, \log\left({\left| a x - 1 \right|}\right)}{a^{2}} + \frac{a^{4} x^{2} + 8 \, a^{3} x}{2 \, a^{4}} - \frac{4}{{\left(a x - 1\right)} a^{2}}"," ",0,"8*log(abs(a*x - 1))/a^2 + 1/2*(a^4*x^2 + 8*a^3*x)/a^4 - 4/((a*x - 1)*a^2)","A",0
29,1,26,0,0.171666," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2,x, algorithm=""giac"")","x + \frac{4 \, \log\left({\left| a x - 1 \right|}\right)}{a} - \frac{4}{{\left(a x - 1\right)} a}"," ",0,"x + 4*log(abs(a*x - 1))/a - 4/((a*x - 1)*a)","A",0
30,1,13,0,0.157902," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/x,x, algorithm=""giac"")","-\frac{4}{a x - 1} + \log\left({\left| x \right|}\right)"," ",0,"-4/(a*x - 1) + log(abs(x))","A",0
31,1,36,0,1.093673," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/x^2,x, algorithm=""giac"")","-4 \, a \log\left({\left| a x - 1 \right|}\right) + 4 \, a \log\left({\left| x \right|}\right) - \frac{5 \, a x - 1}{a x^{2} - x}"," ",0,"-4*a*log(abs(a*x - 1)) + 4*a*log(abs(x)) - (5*a*x - 1)/(a*x^2 - x)","A",0
32,1,47,0,0.388879," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/x^3,x, algorithm=""giac"")","-8 \, a^{2} \log\left({\left| a x - 1 \right|}\right) + 8 \, a^{2} \log\left({\left| x \right|}\right) - \frac{16 \, a^{2} x^{2} - 7 \, a x - 1}{2 \, {\left(a x - 1\right)} x^{2}}"," ",0,"-8*a^2*log(abs(a*x - 1)) + 8*a^2*log(abs(x)) - 1/2*(16*a^2*x^2 - 7*a*x - 1)/((a*x - 1)*x^2)","A",0
33,1,55,0,0.175149," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/x^4,x, algorithm=""giac"")","-12 \, a^{3} \log\left({\left| a x - 1 \right|}\right) + 12 \, a^{3} \log\left({\left| x \right|}\right) - \frac{36 \, a^{3} x^{3} - 18 \, a^{2} x^{2} - 5 \, a x - 1}{3 \, {\left(a x - 1\right)} x^{3}}"," ",0,"-12*a^3*log(abs(a*x - 1)) + 12*a^3*log(abs(x)) - 1/3*(36*a^3*x^3 - 18*a^2*x^2 - 5*a*x - 1)/((a*x - 1)*x^3)","A",0
34,-2,0,0,0.000000," ","integrate(x^3/(a*x+1)*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
35,-2,0,0,0.000000," ","integrate(x^2/(a*x+1)*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
36,1,41,0,0.171638," ","integrate(x/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{x}{a} - \frac{2}{a^{2}}\right)} - \frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, a {\left| a \right|}}"," ",0,"1/2*sqrt(-a^2*x^2 + 1)*(x/a - 2/a^2) - 1/2*arcsin(a*x)*sgn(a)/(a*abs(a))","A",0
37,1,28,0,0.593103," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a}"," ",0,"arcsin(a*x)*sgn(a)/abs(a) + sqrt(-a^2*x^2 + 1)/a","A",0
38,1,52,0,0.174585," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""giac"")","-\frac{a \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{a \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}}"," ",0,"-a*arcsin(a*x)*sgn(a)/abs(a) - a*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a)","B",0
39,-2,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
40,1,159,0,1.598887," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""giac"")","\frac{{\left(a^{3} - \frac{4 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a}{x}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}} - \frac{a^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} + \frac{\frac{4 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a {\left| a \right|}}{x} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}}{a x^{2}}}{8 \, a^{2}}"," ",0,"1/8*(a^3 - 4*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a/x)*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)) - 1/2*a^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/8*(4*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*abs(a)/x - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)/(a*x^2))/a^2","B",0
41,-2,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
42,1,273,0,0.202991," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^5,x, algorithm=""giac"")","\frac{{\left(3 \, a^{5} - \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{3}}{x} + \frac{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a}{x^{2}} - \frac{72 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a x^{3}}\right)} a^{8} x^{4}}{192 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} {\left| a \right|}} - \frac{3 \, a^{5} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} + \frac{\frac{72 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{5} {\left| a \right|}}{x} - \frac{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{3} {\left| a \right|}}{x^{2}} + \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a {\left| a \right|}}{x^{3}} - \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} {\left| a \right|}}{a x^{4}}}{192 \, a^{4}}"," ",0,"1/192*(3*a^5 - 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^3/x + 24*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a/x^2 - 72*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a*x^3))*a^8*x^4/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*abs(a)) - 3/8*a^5*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/192*(72*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^5*abs(a)/x - 24*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^3*abs(a)/x^2 + 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a*abs(a)/x^3 - 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*abs(a)/(a*x^4))/a^4","B",0
43,1,66,0,0.387853," ","integrate(x^3/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\frac{{\left(a x + 1\right)}^{4} {\left(\frac{20}{a x + 1} - \frac{54}{{\left(a x + 1\right)}^{2}} + \frac{84}{{\left(a x + 1\right)}^{3}} - 3\right)}}{12 \, a^{4}} + \frac{2 \, \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a^{4}}"," ",0,"1/12*(a*x + 1)^4*(20/(a*x + 1) - 54/(a*x + 1)^2 + 84/(a*x + 1)^3 - 3)/a^4 + 2*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a^4","A",0
44,1,57,0,0.200344," ","integrate(x^2/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\frac{{\left(a x + 1\right)}^{3} {\left(\frac{6}{a x + 1} - \frac{15}{{\left(a x + 1\right)}^{2}} - 1\right)}}{3 \, a^{3}} - \frac{2 \, \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a^{3}}"," ",0,"1/3*(a*x + 1)^3*(6/(a*x + 1) - 15/(a*x + 1)^2 - 1)/a^3 - 2*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a^3","A",0
45,1,52,0,0.177625," ","integrate(x/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\frac{\frac{{\left(a x + 1\right)}^{2} {\left(\frac{6}{a x + 1} - 1\right)}}{a} + \frac{4 \, \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a}}{2 \, a}"," ",0,"1/2*((a*x + 1)^2*(6/(a*x + 1) - 1)/a + 4*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a)/a","B",0
46,1,64,0,0.155582," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-a^{2} {\left(\frac{a x + 1}{a^{3}} + \frac{2 \, \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a^{3}} - \frac{1}{{\left(a x + 1\right)} a^{3}}\right)} - \frac{1}{{\left(a x + 1\right)} a}"," ",0,"-a^2*((a*x + 1)/a^3 + 2*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a^3 - 1/((a*x + 1)*a^3)) - 1/((a*x + 1)*a)","B",0
47,1,43,0,0.359780," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/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}\right)}"," ",0,"a*(log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a + log(abs(-1/(a*x + 1) + 1))/a)","B",0
48,1,30,0,0.173661," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/x^2,x, algorithm=""giac"")","-2 \, a \log\left({\left| -\frac{1}{a x + 1} + 1 \right|}\right) + \frac{a}{\frac{1}{a x + 1} - 1}"," ",0,"-2*a*log(abs(-1/(a*x + 1) + 1)) + a/(1/(a*x + 1) - 1)","A",0
49,1,50,0,0.183393," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/x^3,x, algorithm=""giac"")","2 \, a^{2} \log\left({\left| -\frac{1}{a x + 1} + 1 \right|}\right) + \frac{5 \, a^{2} - \frac{6 \, a^{2}}{a x + 1}}{2 \, {\left(\frac{1}{a x + 1} - 1\right)}^{2}}"," ",0,"2*a^2*log(abs(-1/(a*x + 1) + 1)) + 1/2*(5*a^2 - 6*a^2/(a*x + 1))/(1/(a*x + 1) - 1)^2","A",0
50,1,62,0,0.156291," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/x^4,x, algorithm=""giac"")","-2 \, a^{3} \log\left({\left| -\frac{1}{a x + 1} + 1 \right|}\right) + \frac{10 \, a^{3} - \frac{24 \, a^{3}}{a x + 1} + \frac{15 \, a^{3}}{{\left(a x + 1\right)}^{2}}}{3 \, {\left(\frac{1}{a x + 1} - 1\right)}^{3}}"," ",0,"-2*a^3*log(abs(-1/(a*x + 1) + 1)) + 1/3*(10*a^3 - 24*a^3/(a*x + 1) + 15*a^3/(a*x + 1)^2)/(1/(a*x + 1) - 1)^3","A",0
51,-2,0,0,0.000000," ","integrate(x^3/(a*x+1)^3*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
52,1,87,0,0.638899," ","integrate(x^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left(x {\left(\frac{2 \, x}{a} - \frac{9}{a^{2}}\right)} + \frac{28}{a^{3}}\right)} - \frac{11 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, a^{2} {\left| a \right|}} + \frac{8}{a^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"-1/6*sqrt(-a^2*x^2 + 1)*(x*(2*x/a - 9/a^2) + 28/a^3) - 11/2*arcsin(a*x)*sgn(a)/(a^2*abs(a)) + 8/(a^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
53,1,78,0,0.222291," ","integrate(x/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{x}{a} - \frac{6}{a^{2}}\right)} + \frac{9 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, a {\left| a \right|}} - \frac{8}{a {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"-1/2*sqrt(-a^2*x^2 + 1)*(x/a - 6/a^2) + 9/2*arcsin(a*x)*sgn(a)/(a*abs(a)) - 8/(a*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
54,1,64,0,0.200203," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{3 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a} + \frac{8}{{\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"-3*arcsin(a*x)*sgn(a)/abs(a) - sqrt(-a^2*x^2 + 1)/a + 8/(((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
55,1,86,0,0.219002," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x, algorithm=""giac"")","\frac{a \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{a \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{8 \, a}{{\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"a*arcsin(a*x)*sgn(a)/abs(a) - a*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 8*a/(((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","B",0
56,1,150,0,0.199598," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} + \frac{{\left(a^{2} + \frac{17 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{x}\right)} a^{2} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{2 \, x {\left| a \right|}}"," ",0,"3*a^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/2*(a^2 + 17*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/x)*a^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a)) - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(x*abs(a))","B",0
57,1,214,0,0.218319," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""giac"")","\frac{{\left(a^{3} - \frac{11 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a}{x} - \frac{76 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a x^{2}}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}} - \frac{9 \, a^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} + \frac{\frac{12 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a {\left| a \right|}}{x} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}}{a x^{2}}}{8 \, a^{2}}"," ",0,"1/8*(a^3 - 11*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a/x - 76*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a*x^2))*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a)) - 9/2*a^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/8*(12*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*abs(a)/x - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)/(a*x^2))/a^2","B",0
58,1,265,0,0.195123," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""giac"")","\frac{{\left(a^{4} - \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2}}{x} + \frac{48 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{x^{2}} + \frac{249 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{2} x^{3}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}} + \frac{11 \, a^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\frac{57 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4}}{x} - \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2}}{x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(a^4 - 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2/x + 48*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/x^2 + 249*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^2*x^3))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a)) + 11/2*a^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/24*(57*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4/x - 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2/x^2 + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/x^3)/(a^2*abs(a))","B",0
59,1,326,0,0.187207," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x, algorithm=""giac"")","\frac{{\left(a^{5} - \frac{7 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{3}}{x} + \frac{32 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a}{x^{2}} - \frac{160 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a x^{3}} - \frac{712 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{3} x^{4}}\right)} a^{8} x^{4}}{64 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}} - \frac{51 \, a^{5} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} + \frac{\frac{200 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{5} {\left| a \right|}}{x} - \frac{40 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{3} {\left| a \right|}}{x^{2}} + \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a {\left| a \right|}}{x^{3}} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} {\left| a \right|}}{a x^{4}}}{64 \, a^{4}}"," ",0,"1/64*(a^5 - 7*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^3/x + 32*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a/x^2 - 160*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a*x^3) - 712*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^3*x^4))*a^8*x^4/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a)) - 51/8*a^5*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/64*(200*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^5*abs(a)/x - 40*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^3*abs(a)/x^2 + 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a*abs(a)/x^3 - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*abs(a)/(a*x^4))/a^4","B",0
60,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^m,x, algorithm=""giac"")","\int x^{m} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(x^m*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
61,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^2,x, algorithm=""giac"")","\int x^{2} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(x^2*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
62,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x,x, algorithm=""giac"")","\int x \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(x*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
63,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
64,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x, x)","F",0
65,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x^2, x)","F",0
66,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x^3, x)","F",0
67,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x^4, x)","F",0
68,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x^5, x)","F",0
69,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/x^6, x)","F",0
70,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x^m,x, algorithm=""giac"")","\int x^{m} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^m*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
71,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x^3,x, algorithm=""giac"")","\int x^{3} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x^3*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
72,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(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
73,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)*x,x, algorithm=""giac"")","\int x \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
74,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""giac"")","\int \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
75,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x,x, algorithm=""giac"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)/x, x)","F",0
76,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(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)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,x]=[0,0]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,x]=[0,0]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
77,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)/x^3, x)","F",0
78,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(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)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,x]=[0,0]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,x]=[0,0]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
79,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^5,x, algorithm=""giac"")","\int \frac{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{5}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)/x^5, x)","F",0
80,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*x^m,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
81,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*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
82,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*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
83,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)*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
84,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(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)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
85,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/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
86,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/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
87,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/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
88,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/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
89,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/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
90,0,0,0,0.000000," ","integrate(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(x^m/sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
91,-2,0,0,0.000000," ","integrate(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
92,0,0,0,0.000000," ","integrate(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(x^2/sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
93,0,0,0,0.000000," ","integrate(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(x/sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
94,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
95,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x,x, algorithm=""giac"")","\int \frac{1}{x \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))), x)","F",0
96,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{1}{x^{2} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^2*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))), x)","F",0
97,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{1}{x^{3} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^3*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))), x)","F",0
98,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{1}{x^{4} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^4*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))), x)","F",0
99,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^5,x, algorithm=""giac"")","\int \frac{1}{x^{5} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}\,{d x}"," ",0,"integrate(1/(x^5*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))), x)","F",0
100,0,0,0,0.000000," ","integrate(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m/((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2), x)","F",0
101,-2,0,0,0.000000," ","integrate(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
102,-2,0,0,0.000000," ","integrate(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
103,-2,0,0,0.000000," ","integrate(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(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, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,x]=[0,0]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,x]=[0,0]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*t_nostep-1)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,x]=[0,0]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,x]=[0,0]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a*t_nostep-1)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,t_nostep]=[0,0]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,t_nostep]=[0,0]Evaluation time: 0.75sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
104,-2,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
105,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x,x, algorithm=""giac"")","\int \frac{1}{x \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)), x)","F",0
106,-2,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
107,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{1}{x^{3} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x^3*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)), x)","F",0
108,-2,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
109,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(3/2)/x^5,x, algorithm=""giac"")","\int \frac{1}{x^{5} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x^5*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(3/2)), x)","F",0
110,0,0,0,0.000000," ","integrate(x^m/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^m/((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2), x)","F",0
111,-2,0,0,0.000000," ","integrate(x^3/((a*x+1)/(-a^2*x^2+1)^(1/2))^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
112,0,0,0,0.000000," ","integrate(x^2/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^2/((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2), x)","F",0
113,-2,0,0,0.000000," ","integrate(x/((a*x+1)/(-a^2*x^2+1)^(1/2))^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
114,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/sqrt(-a^2*x^2 + 1))^(-5/2), x)","F",0
115,-2,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
116,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^2,x, algorithm=""giac"")","\int \frac{1}{x^{2} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x^2*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)), x)","F",0
117,-2,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
118,0,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/x^4,x, algorithm=""giac"")","\int \frac{1}{x^{4} \left(\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(x^4*((a*x + 1)/sqrt(-a^2*x^2 + 1))^(5/2)), x)","F",0
119,-2,0,0,0.000000," ","integrate(1/((a*x+1)/(-a^2*x^2+1)^(1/2))^(5/2)/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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
120,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)*x^m,x, algorithm=""giac"")","\int x^{m} \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(x^m*((x + 1)/sqrt(-x^2 + 1))^(1/3), x)","F",0
121,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)*x^2,x, algorithm=""giac"")","\int x^{2} \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(x^2*((x + 1)/sqrt(-x^2 + 1))^(1/3), x)","F",0
122,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)*x,x, algorithm=""giac"")","\int x \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(x*((x + 1)/sqrt(-x^2 + 1))^(1/3), x)","F",0
123,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3),x, algorithm=""giac"")","\int \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(1/3), x)","F",0
124,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)/x,x, algorithm=""giac"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}}{x}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(1/3)/x, x)","F",0
125,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)/x^2,x, algorithm=""giac"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}}{x^{2}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(1/3)/x^2, x)","F",0
126,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(1/3)/x^3,x, algorithm=""giac"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{1}{3}}}{x^{3}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(1/3)/x^3, x)","F",0
127,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)*x^m,x, algorithm=""giac"")","\int x^{m} \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(x^m*((x + 1)/sqrt(-x^2 + 1))^(2/3), x)","F",0
128,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)*x^2,x, algorithm=""giac"")","\int x^{2} \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(x^2*((x + 1)/sqrt(-x^2 + 1))^(2/3), x)","F",0
129,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)*x,x, algorithm=""giac"")","\int x \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(x*((x + 1)/sqrt(-x^2 + 1))^(2/3), x)","F",0
130,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3),x, algorithm=""giac"")","\int \left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(2/3), x)","F",0
131,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)/x,x, algorithm=""giac"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}}{x}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(2/3)/x, x)","F",0
132,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)/x^2,x, algorithm=""giac"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}}{x^{2}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(2/3)/x^2, x)","F",0
133,0,0,0,0.000000," ","integrate(((1+x)/(-x^2+1)^(1/2))^(2/3)/x^3,x, algorithm=""giac"")","\int \frac{\left(\frac{x + 1}{\sqrt{-x^{2} + 1}}\right)^{\frac{2}{3}}}{x^{3}}\,{d x}"," ",0,"integrate(((x + 1)/sqrt(-x^2 + 1))^(2/3)/x^3, x)","F",0
134,-1,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x^m,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,-1,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)*x,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,-1,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-1,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/4)/x^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,0,0,0,0.000000," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*x^m,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{4} x^{m}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^4*x^m/(a^2*x^2 - 1)^2, x)","F",0
142,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^m,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
143,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2} x^{m}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(a*x + 1)^2*x^m/(a^2*x^2 - 1), x)","F",0
144,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
145,0,0,0,0.000000," ","integrate(x^m/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*x^m/(a*x + 1), x)","F",0
146,0,0,0,0.000000," ","integrate(x^m/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} x^{m}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*x^m/(a*x + 1)^2, x)","F",0
147,-2,0,0,0.000000," ","integrate(x^m/(a*x+1)^3*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
148,0,0,0,0.000000," ","integrate(exp(n*arctanh(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*arctanh(a*x))*x^3,x, algorithm=""giac"")","\int x^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^3*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
150,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2,x, algorithm=""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
151,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
152,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
153,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
154,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
155,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
156,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
157,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a c x + c\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a*c*x + c)^p/sqrt(-a^2*x^2 + 1), x)","F",0
158,1,78,0,0.214681," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4,x, algorithm=""giac"")","\frac{7 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} + \frac{1}{120} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{136 \, c^{4}}{a} + {\left(15 \, c^{4} - 2 \, {\left(56 \, a c^{4} + 3 \, {\left(4 \, a^{3} c^{4} x - 15 \, a^{2} c^{4}\right)} x\right)} x\right)} x\right)}"," ",0,"7/8*c^4*arcsin(a*x)*sgn(a)/abs(a) + 1/120*sqrt(-a^2*x^2 + 1)*(136*c^4/a + (15*c^4 - 2*(56*a*c^4 + 3*(4*a^3*c^4*x - 15*a^2*c^4)*x)*x)*x)","A",0
159,1,66,0,0.216407," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{5 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} + \frac{1}{24} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{16 \, c^{3}}{a} + {\left(9 \, c^{3} + 2 \, {\left(3 \, a^{2} c^{3} x - 8 \, a c^{3}\right)} x\right)} x\right)}"," ",0,"5/8*c^3*arcsin(a*x)*sgn(a)/abs(a) + 1/24*sqrt(-a^2*x^2 + 1)*(16*c^3/a + (9*c^3 + 2*(3*a^2*c^3*x - 8*a*c^3)*x)*x)","A",0
160,1,54,0,0.172909," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2,x, algorithm=""giac"")","\frac{c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} - \frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, a c^{2} x - 3 \, c^{2}\right)} x - \frac{2 \, c^{2}}{a}\right)}"," ",0,"1/2*c^2*arcsin(a*x)*sgn(a)/abs(a) - 1/6*sqrt(-a^2*x^2 + 1)*((2*a*c^2*x - 3*c^2)*x - 2*c^2/a)","A",0
161,1,30,0,0.293640," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} c x + \frac{c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}}"," ",0,"1/2*sqrt(-a^2*x^2 + 1)*c*x + 1/2*c*arcsin(a*x)*sgn(a)/abs(a)","A",0
162,1,53,0,0.207160," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c),x, algorithm=""giac"")","-\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c {\left| a \right|}} + \frac{4}{c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"-arcsin(a*x)*sgn(a)/(c*abs(a)) + 4/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
163,1,66,0,0.345028," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{i \, \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right) + \frac{{\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}}}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}}{3 \, c^{2} {\left| a \right|}}"," ",0,"-1/3*(I*sgn(1/(a*c*x - c))*sgn(a)*sgn(c) + (-2*c/(a*c*x - c) - 1)^(3/2)/(sgn(1/(a*c*x - c))*sgn(a)*sgn(c)))/(c^2*abs(a))","C",0
164,1,145,0,0.358700," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{25 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} - 4\right)}}{15 \, c^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"-2/15*(5*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 25*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) - 4)/(c^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","B",0
165,1,199,0,0.223155," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{56 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{273 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{350 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{455 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} + \frac{210 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{10} x^{5}} - \frac{105 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{12} x^{6}} - 23\right)}}{105 \, c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{7} {\left| a \right|}}"," ",0,"-2/105*(56*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 273*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 350*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 455*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) + 210*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^10*x^5) - 105*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^12*x^6) - 23)/(c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^7*abs(a))","B",0
166,1,321,0,0.261449," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^5,x, algorithm=""giac"")","\frac{-\frac{16 i \, \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}{c^{3}} - \frac{\frac{35 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{4} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 180 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{3} \sqrt{-\frac{2 \, c}{a c x - c} - 1} + 378 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1} + 420 \, {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} + 315 \, \sqrt{-\frac{2 \, c}{a c x - c} - 1}}{c^{3}} + \frac{9 \, {\left(5 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{3} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 21 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 35 \, {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} - 35 \, \sqrt{-\frac{2 \, c}{a c x - c} - 1}\right)}}{c^{3}}}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}}{2520 \, c^{2} {\left| a \right|}}"," ",0,"1/2520*(-16*I*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)/c^3 - ((35*(2*c/(a*c*x - c) + 1)^4*sqrt(-2*c/(a*c*x - c) - 1) - 180*(2*c/(a*c*x - c) + 1)^3*sqrt(-2*c/(a*c*x - c) - 1) + 378*(2*c/(a*c*x - c) + 1)^2*sqrt(-2*c/(a*c*x - c) - 1) + 420*(-2*c/(a*c*x - c) - 1)^(3/2) + 315*sqrt(-2*c/(a*c*x - c) - 1))/c^3 + 9*(5*(2*c/(a*c*x - c) + 1)^3*sqrt(-2*c/(a*c*x - c) - 1) - 21*(2*c/(a*c*x - c) + 1)^2*sqrt(-2*c/(a*c*x - c) - 1) - 35*(-2*c/(a*c*x - c) - 1)^(3/2) - 35*sqrt(-2*c/(a*c*x - c) - 1))/c^3)/(sgn(1/(a*c*x - c))*sgn(a)*sgn(c)))/(c^2*abs(a))","C",0
167,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a*c*x+c)^p,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2} {\left(-a c x + c\right)}^{p}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(a*x + 1)^2*(-a*c*x + c)^p/(a^2*x^2 - 1), x)","F",0
168,1,59,0,0.161949," ","integrate((a*x+1)^2/(-a^2*x^2+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
169,1,37,0,0.160199," ","integrate((a*x+1)^2/(-a^2*x^2+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
170,1,37,0,0.169385," ","integrate((a*x+1)^2/(-a^2*x^2+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
171,1,17,0,0.328356," ","integrate((a*x+1)^2/(-a^2*x^2+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
172,1,11,0,1.272346," ","integrate((a*x+1)^2/(-a^2*x^2+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
173,1,30,0,0.174010," ","integrate((a*x+1)^2/(-a^2*x^2+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
174,1,32,0,0.243443," ","integrate((a*x+1)^2/(-a^2*x^2+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
175,1,21,0,0.153055," ","integrate((a*x+1)^2/(-a^2*x^2+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
176,1,21,0,0.177822," ","integrate((a*x+1)^2/(-a^2*x^2+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,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^p,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
178,1,78,0,0.358584," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^4,x, algorithm=""giac"")","\frac{3 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} + \frac{1}{40} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{8 \, c^{4}}{a} + {\left(25 \, c^{4} - 2 \, {\left(8 \, a c^{4} - {\left(4 \, a^{3} c^{4} x - 5 \, a^{2} c^{4}\right)} x\right)} x\right)} x\right)}"," ",0,"3/8*c^4*arcsin(a*x)*sgn(a)/abs(a) + 1/40*sqrt(-a^2*x^2 + 1)*(8*c^4/a + (25*c^4 - 2*(8*a*c^4 - (4*a^3*c^4*x - 5*a^2*c^4)*x)*x)*x)","A",0
179,1,48,0,0.288064," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{3 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} - \frac{1}{8} \, {\left(2 \, a^{2} c^{3} x^{2} - 5 \, c^{3}\right)} \sqrt{-a^{2} x^{2} + 1} x"," ",0,"3/8*c^3*arcsin(a*x)*sgn(a)/abs(a) - 1/8*(2*a^2*c^3*x^2 - 5*c^3)*sqrt(-a^2*x^2 + 1)*x","A",0
180,1,54,0,1.183692," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^2,x, algorithm=""giac"")","\frac{c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} + \frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, a c^{2} x + 3 \, c^{2}\right)} x - \frac{2 \, c^{2}}{a}\right)}"," ",0,"1/2*c^2*arcsin(a*x)*sgn(a)/abs(a) + 1/6*sqrt(-a^2*x^2 + 1)*((2*a*c^2*x + 3*c^2)*x - 2*c^2/a)","A",0
181,1,38,0,0.193332," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c),x, algorithm=""giac"")","\frac{3 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} - \frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} {\left(c x + \frac{4 \, c}{a}\right)}"," ",0,"3/2*c*arcsin(a*x)*sgn(a)/abs(a) - 1/2*sqrt(-a^2*x^2 + 1)*(c*x + 4*c/a)","A",0
182,1,79,0,0.251943," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c),x, algorithm=""giac"")","\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c {\left| a \right|}} + \frac{8 \, {\left(\frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - 1\right)}}{3 \, c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{3} {\left| a \right|}}"," ",0,"arcsin(a*x)*sgn(a)/(c*abs(a)) + 8/3*(3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^3*abs(a))","A",0
183,1,83,0,0.313479," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{-i \, \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right) + \frac{{\left(\frac{2 \, c}{a c x - c} + 1\right)}^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1}}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}}{5 \, c^{2} {\left| a \right|}}"," ",0,"-1/5*(-I*sgn(1/(a*c*x - c))*sgn(a)*sgn(c) + (2*c/(a*c*x - c) + 1)^2*sqrt(-2*c/(a*c*x - c) - 1)/(sgn(1/(a*c*x - c))*sgn(a)*sgn(c)))/(c^2*abs(a))","C",0
184,1,199,0,0.206132," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{7 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{91 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{70 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{140 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} + \frac{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{10} x^{5}} - \frac{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{12} x^{6}} - 6\right)}}{35 \, c^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{7} {\left| a \right|}}"," ",0,"-2/35*(7*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 91*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 70*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 140*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) + 35*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^10*x^5) - 35*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^12*x^6) - 6)/(c^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^7*abs(a))","B",0
185,1,253,0,0.232731," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{108 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{1062 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{1638 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{3402 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} + \frac{2520 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{10} x^{5}} - \frac{2310 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{12} x^{6}} + \frac{630 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7}}{a^{14} x^{7}} - \frac{315 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{8}}{a^{16} x^{8}} - 47\right)}}{315 \, c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{9} {\left| a \right|}}"," ",0,"-2/315*(108*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1062*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 1638*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 3402*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) + 2520*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^10*x^5) - 2310*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^12*x^6) + 630*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^7/(a^14*x^7) - 315*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^8/(a^16*x^8) - 47)/(c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^9*abs(a))","B",0
186,1,509,0,0.574965," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^5,x, algorithm=""giac"")","\frac{\frac{48 i \, \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}{c^{3}} + \frac{\frac{5 \, {\left(63 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{5} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 385 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{4} \sqrt{-\frac{2 \, c}{a c x - c} - 1} + 990 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{3} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 1386 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 1155 \, {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} - 693 \, \sqrt{-\frac{2 \, c}{a c x - c} - 1}\right)}}{c^{3}} + \frac{22 \, {\left(35 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{4} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 180 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{3} \sqrt{-\frac{2 \, c}{a c x - c} - 1} + 378 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1} + 420 \, {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} + 315 \, \sqrt{-\frac{2 \, c}{a c x - c} - 1}\right)}}{c^{3}} + \frac{99 \, {\left(5 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{3} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 21 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 35 \, {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} - 35 \, \sqrt{-\frac{2 \, c}{a c x - c} - 1}\right)}}{c^{3}}}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}}{27720 \, c^{2} {\left| a \right|}}"," ",0,"1/27720*(48*I*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)/c^3 + (5*(63*(2*c/(a*c*x - c) + 1)^5*sqrt(-2*c/(a*c*x - c) - 1) - 385*(2*c/(a*c*x - c) + 1)^4*sqrt(-2*c/(a*c*x - c) - 1) + 990*(2*c/(a*c*x - c) + 1)^3*sqrt(-2*c/(a*c*x - c) - 1) - 1386*(2*c/(a*c*x - c) + 1)^2*sqrt(-2*c/(a*c*x - c) - 1) - 1155*(-2*c/(a*c*x - c) - 1)^(3/2) - 693*sqrt(-2*c/(a*c*x - c) - 1))/c^3 + 22*(35*(2*c/(a*c*x - c) + 1)^4*sqrt(-2*c/(a*c*x - c) - 1) - 180*(2*c/(a*c*x - c) + 1)^3*sqrt(-2*c/(a*c*x - c) - 1) + 378*(2*c/(a*c*x - c) + 1)^2*sqrt(-2*c/(a*c*x - c) - 1) + 420*(-2*c/(a*c*x - c) - 1)^(3/2) + 315*sqrt(-2*c/(a*c*x - c) - 1))/c^3 + 99*(5*(2*c/(a*c*x - c) + 1)^3*sqrt(-2*c/(a*c*x - c) - 1) - 21*(2*c/(a*c*x - c) + 1)^2*sqrt(-2*c/(a*c*x - c) - 1) - 35*(-2*c/(a*c*x - c) - 1)^(3/2) - 35*sqrt(-2*c/(a*c*x - c) - 1))/c^3)/(sgn(1/(a*c*x - c))*sgn(a)*sgn(c)))/(c^2*abs(a))","C",0
187,0,0,0,0.000000," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{4} {\left(-a c x + c\right)}^{p}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^4*(-a*c*x + c)^p/(a^2*x^2 - 1)^2, x)","F",0
188,1,59,0,0.203349," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^5,x, algorithm=""giac"")","-\frac{1}{6} \, a^{5} c^{5} x^{6} + \frac{1}{5} \, a^{4} c^{5} x^{5} + \frac{1}{2} \, a^{3} c^{5} x^{4} - \frac{2}{3} \, a^{2} c^{5} x^{3} - \frac{1}{2} \, a c^{5} x^{2} + c^{5} x"," ",0,"-1/6*a^5*c^5*x^6 + 1/5*a^4*c^5*x^5 + 1/2*a^3*c^5*x^4 - 2/3*a^2*c^5*x^3 - 1/2*a*c^5*x^2 + c^5*x","A",0
189,1,28,0,0.187036," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^4,x, algorithm=""giac"")","\frac{1}{5} \, a^{4} c^{4} x^{5} - \frac{2}{3} \, a^{2} c^{4} x^{3} + c^{4} x"," ",0,"1/5*a^4*c^4*x^5 - 2/3*a^2*c^4*x^3 + c^4*x","A",0
190,1,37,0,0.173877," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-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
191,1,25,0,0.159142," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c)^2,x, algorithm=""giac"")","\frac{1}{3} \, a^{2} c^{2} x^{3} + a c^{2} x^{2} + c^{2} x"," ",0,"1/3*a^2*c^2*x^3 + a*c^2*x^2 + c^2*x","A",0
192,1,35,0,0.170604," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a*c*x+c),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
193,1,37,0,0.175987," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a*c*x+c),x, algorithm=""giac"")","-\frac{\log\left({\left| a x - 1 \right|}\right)}{a c} + \frac{2 \, {\left(2 \, a x - 1\right)}}{{\left(a x - 1\right)}^{2} a c}"," ",0,"-log(abs(a*x - 1))/(a*c) + 2*(2*a*x - 1)/((a*x - 1)^2*a*c)","A",0
194,1,50,0,0.187089," ","integrate((a*x+1)^4/(-a^2*x^2+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
195,1,29,0,0.158915," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{3 \, a^{2} x^{2} + 2 \, a x + 1}{6 \, {\left(a x - 1\right)}^{4} a c^{3}}"," ",0,"1/6*(3*a^2*x^2 + 2*a*x + 1)/((a*x - 1)^4*a*c^3)","A",0
196,1,29,0,0.130641," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{5 \, a^{2} x^{2} + 5 \, a x + 2}{15 \, {\left(a x - 1\right)}^{5} a c^{4}}"," ",0,"-1/15*(5*a^2*x^2 + 5*a*x + 2)/((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^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a c x + c\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a*c*x + c)^p/(a*x + 1), x)","F",0
198,1,67,0,0.782045," ","integrate((-a*c*x+c)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{35 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} + \frac{1}{24} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{160 \, c^{3}}{a} - {\left(81 \, c^{3} + 2 \, {\left(3 \, a^{2} c^{3} x - 16 \, a c^{3}\right)} x\right)} x\right)}"," ",0,"35/8*c^3*arcsin(a*x)*sgn(a)/abs(a) + 1/24*sqrt(-a^2*x^2 + 1)*(160*c^3/a - (81*c^3 + 2*(3*a^2*c^3*x - 16*a*c^3)*x)*x)","A",0
199,1,54,0,0.757038," ","integrate((-a*c*x+c)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{5 \, c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} + \frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, a c^{2} x - 9 \, c^{2}\right)} x + \frac{22 \, c^{2}}{a}\right)}"," ",0,"5/2*c^2*arcsin(a*x)*sgn(a)/abs(a) + 1/6*sqrt(-a^2*x^2 + 1)*((2*a*c^2*x - 9*c^2)*x + 22*c^2/a)","A",0
200,1,38,0,0.182268," ","integrate((-a*c*x+c)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{3 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} - \frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} {\left(c x - \frac{4 \, c}{a}\right)}"," ",0,"3/2*c*arcsin(a*x)*sgn(a)/abs(a) - 1/2*sqrt(-a^2*x^2 + 1)*(c*x - 4*c/a)","A",0
201,1,14,0,0.221534," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c),x, algorithm=""giac"")","\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c {\left| a \right|}}"," ",0,"arcsin(a*x)*sgn(a)/(c*abs(a))","A",0
202,1,70,0,0.241479," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^2,x, algorithm=""giac"")","-c^{2} {\left(\frac{\sqrt{-\frac{2 \, c}{a c x - c} - 1} \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}{a^{2} c^{4}} - \frac{i \, \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}{a^{2} c^{4}}\right)} {\left| a \right|}"," ",0,"-c^2*(sqrt(-2*c/(a*c*x - c) - 1)*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)/(a^2*c^4) - I*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)/(a^2*c^4))*abs(a)","C",0
203,1,91,0,0.411875," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} - 2\right)}}{3 \, c^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{3} {\left| a \right|}}"," ",0,"-2/3*(3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) - 2)/(c^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^3*abs(a))","A",0
204,1,145,0,0.247093," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{20 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{40 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{30 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} - 7\right)}}{15 \, c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"-2/15*(20*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 40*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 30*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) - 7)/(c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","A",0
205,1,164,0,0.209602," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^5,x, algorithm=""giac"")","\frac{1}{280} \, c^{2} {\left(\frac{{\left(5 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{3} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 21 \, {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 35 \, {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} - 35 \, \sqrt{-\frac{2 \, c}{a c x - c} - 1}\right)} \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}{a^{2} c^{7}} + \frac{16 i \, \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}{a^{2} c^{7}}\right)} {\left| a \right|}"," ",0,"1/280*c^2*((5*(2*c/(a*c*x - c) + 1)^3*sqrt(-2*c/(a*c*x - c) - 1) - 21*(2*c/(a*c*x - c) + 1)^2*sqrt(-2*c/(a*c*x - c) - 1) - 35*(-2*c/(a*c*x - c) - 1)^(3/2) - 35*sqrt(-2*c/(a*c*x - c) - 1))*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)/(a^2*c^7) + 16*I*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)/(a^2*c^7))*abs(a)","C",0
206,0,0,0,0.000000," ","integrate((-a*c*x+c)^p/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} {\left(-a c x + c\right)}^{p}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*(-a*c*x + c)^p/(a*x + 1)^2, x)","F",0
207,1,94,0,0.211794," ","integrate((-a*c*x+c)^4/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{{\left(6 \, c^{4} - \frac{75 \, c^{4}}{a x + 1} + \frac{400 \, c^{4}}{{\left(a x + 1\right)}^{2}} - \frac{1200 \, c^{4}}{{\left(a x + 1\right)}^{3}} + \frac{2400 \, c^{4}}{{\left(a x + 1\right)}^{4}}\right)} {\left(a x + 1\right)}^{5}}{30 \, a} - \frac{32 \, c^{4} \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a}"," ",0,"-1/30*(6*c^4 - 75*c^4/(a*x + 1) + 400*c^4/(a*x + 1)^2 - 1200*c^4/(a*x + 1)^3 + 2400*c^4/(a*x + 1)^4)*(a*x + 1)^5/a - 32*c^4*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a","A",0
208,1,82,0,0.177991," ","integrate((-a*c*x+c)^3/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\frac{{\left(3 \, c^{3} - \frac{32 \, c^{3}}{a x + 1} + \frac{144 \, c^{3}}{{\left(a x + 1\right)}^{2}} - \frac{384 \, c^{3}}{{\left(a x + 1\right)}^{3}}\right)} {\left(a x + 1\right)}^{4}}{12 \, a} - \frac{16 \, c^{3} \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a}"," ",0,"1/12*(3*c^3 - 32*c^3/(a*x + 1) + 144*c^3/(a*x + 1)^2 - 384*c^3/(a*x + 1)^3)*(a*x + 1)^4/a - 16*c^3*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a","A",0
209,1,68,0,0.191129," ","integrate((-a*c*x+c)^2/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{{\left(c^{2} - \frac{9 \, c^{2}}{a x + 1} + \frac{36 \, c^{2}}{{\left(a x + 1\right)}^{2}}\right)} {\left(a x + 1\right)}^{3}}{3 \, a} - \frac{8 \, c^{2} \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a}"," ",0,"-1/3*(c^2 - 9*c^2/(a*x + 1) + 36*c^2/(a*x + 1)^2)*(a*x + 1)^3/a - 8*c^2*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a","A",0
210,1,50,0,0.160057," ","integrate((-a*c*x+c)/(a*x+1)^2*(-a^2*x^2+1),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","B",0
211,1,27,0,0.755556," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-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}"," ",0,"-log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/(a*c)","B",0
212,1,25,0,0.283829," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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
213,1,43,0,0.186186," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{\log\left({\left| -\frac{2}{a x + 1} + 1 \right|}\right)}{4 \, a c^{3}} + \frac{1}{4 \, a c^{3} {\left(\frac{2}{a x + 1} - 1\right)}}"," ",0,"-1/4*log(abs(-2/(a*x + 1) + 1))/(a*c^3) + 1/4/(a*c^3*(2/(a*x + 1) - 1))","A",0
214,1,58,0,0.575482," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{\log\left({\left| -\frac{2}{a x + 1} + 1 \right|}\right)}{8 \, a c^{4}} - \frac{\frac{3}{a} - \frac{8}{{\left(a x + 1\right)} a}}{16 \, c^{4} {\left(\frac{2}{a x + 1} - 1\right)}^{2}}"," ",0,"-1/8*log(abs(-2/(a*x + 1) + 1))/(a*c^4) - 1/16*(3/a - 8/((a*x + 1)*a))/(c^4*(2/(a*x + 1) - 1)^2)","A",0
215,1,89,0,0.200779," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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)^3*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
217,1,103,0,0.254660," ","integrate((-a*c*x+c)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{315 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} - \frac{1}{8} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{240 \, c^{3}}{a} - {\left(67 \, c^{3} + 2 \, {\left(a^{2} c^{3} x - 8 \, a c^{3}\right)} x\right)} x\right)} + \frac{64 \, c^{3}}{{\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"-315/8*c^3*arcsin(a*x)*sgn(a)/abs(a) - 1/8*sqrt(-a^2*x^2 + 1)*(240*c^3/a - (67*c^3 + 2*(a^2*c^3*x - 8*a*c^3)*x)*x) + 64*c^3/(((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
218,1,91,0,0.189173," ","integrate((-a*c*x+c)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{35 \, c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} - \frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, a c^{2} x - 15 \, c^{2}\right)} x + \frac{70 \, c^{2}}{a}\right)} + \frac{32 \, c^{2}}{{\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"-35/2*c^2*arcsin(a*x)*sgn(a)/abs(a) - 1/6*sqrt(-a^2*x^2 + 1)*((2*a*c^2*x - 15*c^2)*x + 70*c^2/a) + 32*c^2/(((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
219,1,73,0,0.202575," ","integrate((-a*c*x+c)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{15 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} + \frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} {\left(c x - \frac{8 \, c}{a}\right)} + \frac{16 \, c}{{\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"-15/2*c*arcsin(a*x)*sgn(a)/abs(a) + 1/2*sqrt(-a^2*x^2 + 1)*(c*x - 8*c/a) + 16*c/(((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
220,1,53,0,0.274269," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c),x, algorithm=""giac"")","-\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c {\left| a \right|}} + \frac{4}{c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"-arcsin(a*x)*sgn(a)/(c*abs(a)) + 4/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
221,1,69,0,0.291219," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^2,x, algorithm=""giac"")","c^{2} {\left(\frac{i \, \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}{a^{2} c^{4}} + \frac{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}{a^{2} c^{4} \sqrt{-\frac{2 \, c}{a c x - c} - 1}}\right)} {\left| a \right|}"," ",0,"c^2*(I*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)/(a^2*c^4) + sgn(1/(a*c*x - c))*sgn(a)*sgn(c)/(a^2*c^4*sqrt(-2*c/(a*c*x - c) - 1)))*abs(a)","C",0
222,1,29,0,0.300718," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{\sqrt{-a^{2} x^{2} + 1} x}{{\left(a^{2} x^{2} - 1\right)} c^{3}}"," ",0,"-sqrt(-a^2*x^2 + 1)*x/((a^2*x^2 - 1)*c^3)","A",0
223,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^4,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a c x - c\right)}^{4} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*c*x - c)^4*(a*x + 1)^3), x)","F",0
224,1,174,0,0.336949," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^5,x, algorithm=""giac"")","\frac{1}{40} \, {\left(a {\left(\frac{5}{a^{3} c^{7} \sqrt{-\frac{2 \, c}{a c x - c} - 1}} - \frac{a^{12} c^{28} {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1} + 5 \, a^{12} c^{28} {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} + 15 \, a^{12} c^{28} \sqrt{-\frac{2 \, c}{a c x - c} - 1}}{a^{15} c^{35}}\right)} \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right) + \frac{16 i \, \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}{a^{2} c^{7}}\right)} c^{2} {\left| a \right|}"," ",0,"1/40*(a*(5/(a^3*c^7*sqrt(-2*c/(a*c*x - c) - 1)) - (a^12*c^28*(2*c/(a*c*x - c) + 1)^2*sqrt(-2*c/(a*c*x - c) - 1) + 5*a^12*c^28*(-2*c/(a*c*x - c) - 1)^(3/2) + 15*a^12*c^28*sqrt(-2*c/(a*c*x - c) - 1))/(a^15*c^35))*sgn(1/(a*c*x - c))*sgn(a)*sgn(c) + 16*I*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)/(a^2*c^7))*c^2*abs(a)","C",0
225,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^6,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a c x - c\right)}^{6} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*c*x - c)^6*(a*x + 1)^3), x)","F",0
226,1,87,0,0.270633," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(9/2),x, algorithm=""giac"")","-\frac{2 \, {\left(4096 \, \sqrt{2} c^{\frac{7}{2}} - \frac{315 \, {\left(a c x + c\right)}^{\frac{11}{2}} - 3080 \, {\left(a c x + c\right)}^{\frac{9}{2}} c + 11880 \, {\left(a c x + c\right)}^{\frac{7}{2}} c^{2} - 22176 \, {\left(a c x + c\right)}^{\frac{5}{2}} c^{3} + 18480 \, {\left(a c x + c\right)}^{\frac{3}{2}} c^{4}}{c^{2}}\right)} c^{2}}{3465 \, a {\left| c \right|}}"," ",0,"-2/3465*(4096*sqrt(2)*c^(7/2) - (315*(a*c*x + c)^(11/2) - 3080*(a*c*x + c)^(9/2)*c + 11880*(a*c*x + c)^(7/2)*c^2 - 22176*(a*c*x + c)^(5/2)*c^3 + 18480*(a*c*x + c)^(3/2)*c^4)/c^2)*c^2/(a*abs(c))","A",0
227,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
228,1,61,0,0.198593," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(64 \, \sqrt{2} c^{\frac{3}{2}} - \frac{15 \, {\left(a c x + c\right)}^{\frac{7}{2}} - 84 \, {\left(a c x + c\right)}^{\frac{5}{2}} c + 140 \, {\left(a c x + c\right)}^{\frac{3}{2}} c^{2}}{c^{2}}\right)} c^{2}}{105 \, a {\left| c \right|}}"," ",0,"-2/105*(64*sqrt(2)*c^(3/2) - (15*(a*c*x + c)^(7/2) - 84*(a*c*x + c)^(5/2)*c + 140*(a*c*x + c)^(3/2)*c^2)/c^2)*c^2/(a*abs(c))","A",0
229,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
230,1,34,0,0.174042," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, c^{2} {\left(\frac{2 \, \sqrt{2}}{\sqrt{c}} - \frac{{\left(a c x + c\right)}^{\frac{3}{2}}}{c^{2}}\right)}}{3 \, a {\left| c \right|}}"," ",0,"-2/3*c^2*(2*sqrt(2)/sqrt(c) - (a*c*x + c)^(3/2)/c^2)/(a*abs(c))","A",0
231,1,88,0,0.155682," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, c {\left(\frac{\frac{\sqrt{2} c \arctan\left(\frac{\sqrt{2} \sqrt{a c x + c}}{2 \, \sqrt{-c}}\right)}{\sqrt{-c}} + \sqrt{a c x + c}}{c} - \frac{\sqrt{2} {\left(c \arctan\left(\frac{\sqrt{c}}{\sqrt{-c}}\right) + \sqrt{-c} \sqrt{c}\right)}}{\sqrt{-c} c}\right)}}{a {\left| c \right|}}"," ",0,"-2*c*((sqrt(2)*c*arctan(1/2*sqrt(2)*sqrt(a*c*x + c)/sqrt(-c))/sqrt(-c) + sqrt(a*c*x + c))/c - sqrt(2)*(c*arctan(sqrt(c)/sqrt(-c)) + sqrt(-c)*sqrt(c))/(sqrt(-c)*c))/(a*abs(c))","A",0
232,1,58,0,0.334555," ","integrate((a*x+1)/(-a^2*x^2+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 {\left| 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*abs(c))","A",0
233,1,76,0,0.245005," ","integrate((a*x+1)/(-a^2*x^2+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)}{\sqrt{-c} c} + \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 {\left| c \right|}}"," ",0,"1/16*(sqrt(2)*arctan(1/2*sqrt(2)*sqrt(a*c*x + c)/sqrt(-c))/(sqrt(-c)*c) + 2*((a*c*x + c)^(3/2) + 2*sqrt(a*c*x + c)*c)/((a*c*x - c)^2*c))/(a*abs(c))","A",0
234,1,92,0,0.312360," ","integrate((a*x+1)/(-a^2*x^2+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)}{\sqrt{-c} c^{2}} + \frac{2 \, {\left(3 \, {\left(a c x + c\right)}^{\frac{5}{2}} - 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 {\left| c \right|}}"," ",0,"1/192*(3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(a*c*x + c)/sqrt(-c))/(sqrt(-c)*c^2) + 2*(3*(a*c*x + c)^(5/2) - 16*(a*c*x + c)^(3/2)*c - 12*sqrt(a*c*x + c)*c^2)/((a*c*x - c)^3*c^2))/(a*abs(c))","A",0
235,1,205,0,0.178843," ","integrate((a*x+1)^2/(-a^2*x^2+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
236,1,141,0,0.178018," ","integrate((a*x+1)^2/(-a^2*x^2+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
237,1,71,0,0.174320," ","integrate((a*x+1)^2/(-a^2*x^2+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
238,1,44,0,0.296153," ","integrate((a*x+1)^2/(-a^2*x^2+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
239,1,32,0,0.249734," ","integrate((a*x+1)^2/(-a^2*x^2+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
240,1,36,0,0.231931," ","integrate((a*x+1)^2/(-a^2*x^2+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
241,1,34,0,0.178544," ","integrate((a*x+1)^2/(-a^2*x^2+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
242,1,36,0,0.215708," ","integrate((a*x+1)^2/(-a^2*x^2+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
243,1,73,0,0.221444," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(9/2),x, algorithm=""giac"")","-\frac{2 \, {\left(512 \, \sqrt{2} c^{\frac{7}{2}} + \frac{105 \, {\left(a c x + c\right)}^{\frac{11}{2}} - 770 \, {\left(a c x + c\right)}^{\frac{9}{2}} c + 1980 \, {\left(a c x + c\right)}^{\frac{7}{2}} c^{2} - 1848 \, {\left(a c x + c\right)}^{\frac{5}{2}} c^{3}}{c^{2}}\right)} c^{2}}{1155 \, a {\left| c \right|}}"," ",0,"-2/1155*(512*sqrt(2)*c^(7/2) + (105*(a*c*x + c)^(11/2) - 770*(a*c*x + c)^(9/2)*c + 1980*(a*c*x + c)^(7/2)*c^2 - 1848*(a*c*x + c)^(5/2)*c^3)/c^2)*c^2/(a*abs(c))","A",0
244,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
245,1,47,0,0.161013," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(16 \, \sqrt{2} c^{\frac{3}{2}} + \frac{5 \, {\left(a c x + c\right)}^{\frac{7}{2}} - 14 \, {\left(a c x + c\right)}^{\frac{5}{2}} c}{c^{2}}\right)} c^{2}}{35 \, a {\left| c \right|}}"," ",0,"-2/35*(16*sqrt(2)*c^(3/2) + (5*(a*c*x + c)^(7/2) - 14*(a*c*x + c)^(5/2)*c)/c^2)*c^2/(a*abs(c))","A",0
246,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
247,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
248,1,70,0,0.224404," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, \sqrt{2} c \arctan\left(\frac{\sqrt{2} \sqrt{a c x + c}}{2 \, \sqrt{-c}}\right)}{\sqrt{-c}} + 2 \, \sqrt{a c x + c} - \frac{2 \, \sqrt{a c x + c} c}{a c x - c}}{a {\left| c \right|}}"," ",0,"(3*sqrt(2)*c*arctan(1/2*sqrt(2)*sqrt(a*c*x + c)/sqrt(-c))/sqrt(-c) + 2*sqrt(a*c*x + c) - 2*sqrt(a*c*x + c)*c/(a*c*x - c))/(a*abs(c))","A",0
249,1,73,0,0.413849," ","integrate((a*x+1)^3/(-a^2*x^2+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 {\left| 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*abs(c))","A",0
250,1,92,0,0.228529," ","integrate((a*x+1)^3/(-a^2*x^2+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)}{\sqrt{-c} c} + \frac{2 \, {\left(3 \, {\left(a c x + c\right)}^{\frac{5}{2}} + 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 {\left| c \right|}}"," ",0,"-1/96*(3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(a*c*x + c)/sqrt(-c))/(sqrt(-c)*c) + 2*(3*(a*c*x + c)^(5/2) + 16*(a*c*x + c)^(3/2)*c - 12*sqrt(a*c*x + c)*c^2)/((a*c*x - c)^3*c))/(a*abs(c))","A",0
251,1,105,0,0.318671," ","integrate((a*x+1)^3/(-a^2*x^2+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)}{\sqrt{-c} c^{2}} + \frac{2 \, {\left(3 \, {\left(a c x + c\right)}^{\frac{7}{2}} - 22 \, {\left(a c x + c\right)}^{\frac{5}{2}} 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 {\left| c \right|}}"," ",0,"-1/512*(3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(a*c*x + c)/sqrt(-c))/(sqrt(-c)*c^2) + 2*(3*(a*c*x + c)^(7/2) - 22*(a*c*x + c)^(5/2)*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*abs(c))","A",0
252,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(9/2)/(a*x+1)*(-a^2*x^2+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: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^2*x^2+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: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^2*x^2+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: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^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
256,1,50,0,0.182278," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{8 \, \sqrt{2} {\left| c \right|}}{3 \, a \sqrt{c}} - \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,"-8/3*sqrt(2)*abs(c)/(a*sqrt(c)) - 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(1/(a*x+1)*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
258,1,62,0,0.173754," ","integrate(1/(a*x+1)*(-a^2*x^2+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|}}{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)/c^2","A",0
259,-2,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
260,1,80,0,0.637733," ","integrate(1/(a*x+1)*(-a^2*x^2+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)}{\sqrt{-c} c^{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|}}{32 \, a c^{2}}"," ",0,"-1/32*(3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(a*c*x + c)/sqrt(-c))/(sqrt(-c)*c^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)/(a*c^2)","A",0
261,1,161,0,0.195112," ","integrate((-a*c*x+c)^(7/2)/(a*x+1)^2*(-a^2*x^2+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
262,1,134,0,0.185643," ","integrate((-a*c*x+c)^(5/2)/(a*x+1)^2*(-a^2*x^2+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
263,1,107,0,0.243279," ","integrate((-a*c*x+c)^(3/2)/(a*x+1)^2*(-a^2*x^2+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
264,1,77,0,0.192416," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
265,1,51,0,0.180074," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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
266,1,35,0,0.747996," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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
267,1,53,0,2.866599," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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
268,1,73,0,0.139533," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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
269,1,93,0,0.174828," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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)^(5/2)/(a*x+1)^3*(-a^2*x^2+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: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)^(3/2)/(a*x+1)^3*(-a^2*x^2+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: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)^(1/2)/(a*x+1)^3*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
273,1,50,0,0.252343," ","integrate(1/(a*x+1)^3*(-a^2*x^2+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|} + \frac{4 \, \sqrt{2} {\left| c \right|}}{a c^{\frac{3}{2}}}"," ",0,"-2*(sqrt(a*c*x + c)/(a*c^2) + 2/(sqrt(a*c*x + c)*a*c))*abs(c) + 4*sqrt(2)*abs(c)/(a*c^(3/2))","A",0
274,1,30,0,0.199383," ","integrate(1/(a*x+1)^3*(-a^2*x^2+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|}}{c^{2}}"," ",0,"(sqrt(2)/(a*sqrt(c)) - 2/(sqrt(a*c*x + c)*a))*abs(c)/c^2","A",0
275,-2,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(5/2),x, algorithm=""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
276,1,82,0,0.266196," ","integrate(1/(a*x+1)^3*(-a^2*x^2+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 \sqrt{-c} c^{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|}}{8 \, c^{2}}"," ",0,"-1/8*(3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(a*c*x + c)/sqrt(-c))/(a*sqrt(-c)*c^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)/c^2","A",0
277,-2,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a*c*x+c)^(9/2),x, algorithm=""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
278,-2,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a*c*x+c)^(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:Unable to divide, perhaps due to rounding error%%%{1,[0,8,1,0,0]%%%}+%%%{-4,[0,6,1,1,0]%%%}+%%%{6,[0,4,1,2,0]%%%}+%%%{-4,[0,2,1,3,0]%%%}+%%%{1,[0,0,1,4,0]%%%} / %%%{1,[0,0,0,4,4]%%%} Error: Bad Argument Value","F(-2)",0
279,-2,0,0,0.000000," ","integrate(exp(n*arctanh(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
280,-2,0,0,0.000000," ","integrate(exp(n*arctanh(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
281,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
282,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
283,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
284,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
285,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
286,1,57,0,0.224044," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4*(-a*c*x+c),x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{-a^{2} x^{2} + 1} {\left(2 \, {\left(4 \, c x^{2} - \frac{c}{a^{2}}\right)} x^{2} - \frac{3 \, c}{a^{4}}\right)} x + \frac{c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{16 \, a^{4} {\left| a \right|}}"," ",0,"1/48*sqrt(-a^2*x^2 + 1)*(2*(4*c*x^2 - c/a^2)*x^2 - 3*c/a^4)*x + 1/16*c*arcsin(a*x)*sgn(a)/(a^4*abs(a))","A",0
287,1,47,0,0.164786," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c),x, algorithm=""giac"")","\frac{3 \, {\left(a^{2} x^{2} - 1\right)}^{2} \sqrt{-a^{2} x^{2} + 1} c - 5 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c}{15 \, a^{4}}"," ",0,"1/15*(3*(a^2*x^2 - 1)^2*sqrt(-a^2*x^2 + 1)*c - 5*(-a^2*x^2 + 1)^(3/2)*c)/a^4","A",0
288,1,45,0,0.188963," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{-a^{2} x^{2} + 1} {\left(2 \, c x^{2} - \frac{c}{a^{2}}\right)} x + \frac{c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, a^{2} {\left| a \right|}}"," ",0,"1/8*sqrt(-a^2*x^2 + 1)*(2*c*x^2 - c/a^2)*x + 1/8*c*arcsin(a*x)*sgn(a)/(a^2*abs(a))","A",0
289,1,18,0,0.183591," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c),x, algorithm=""giac"")","-\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c}{3 \, a^{2}}"," ",0,"-1/3*(-a^2*x^2 + 1)^(3/2)*c/a^2","A",0
290,1,30,0,0.198063," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} c x + \frac{c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}}"," ",0,"1/2*sqrt(-a^2*x^2 + 1)*c*x + 1/2*c*arcsin(a*x)*sgn(a)/abs(a)","A",0
291,1,53,0,0.159564," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x,x, algorithm=""giac"")","-\frac{1}{2} \, c \log\left(\sqrt{-a^{2} x^{2} + 1} + 1\right) + \frac{1}{2} \, c \log\left(-\sqrt{-a^{2} x^{2} + 1} + 1\right) + \sqrt{-a^{2} x^{2} + 1} c"," ",0,"-1/2*c*log(sqrt(-a^2*x^2 + 1) + 1) + 1/2*c*log(-sqrt(-a^2*x^2 + 1) + 1) + sqrt(-a^2*x^2 + 1)*c","A",0
292,1,74,0,0.198725," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x^2,x, algorithm=""giac"")","\frac{a^{4} c x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} - \frac{a^{2} c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c}{2 \, x {\left| a \right|}}"," ",0,"1/2*a^4*c*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) - a^2*c*arcsin(a*x)*sgn(a)/abs(a) - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c/(x*abs(a))","B",0
293,1,70,0,0.160437," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x^3,x, algorithm=""giac"")","\frac{a^{4} c \log\left(\sqrt{-a^{2} x^{2} + 1} + 1\right) - a^{4} c \log\left(-\sqrt{-a^{2} x^{2} + 1} + 1\right) - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c}{x^{2}}}{4 \, a^{2}}"," ",0,"1/4*(a^4*c*log(sqrt(-a^2*x^2 + 1) + 1) - a^4*c*log(-sqrt(-a^2*x^2 + 1) + 1) - 2*sqrt(-a^2*x^2 + 1)*a^2*c/x^2)/a^2","A",0
294,1,124,0,0.187509," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)/x^4,x, algorithm=""giac"")","\frac{{\left(a^{4} c - \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c}{x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} + \frac{\frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c}{x} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c}{x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(a^4*c - 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c/x^2)*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) + 1/24*(3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c/x - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c/x^3)/(a^2*abs(a))","B",0
295,1,92,0,0.178692," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{1}{240} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, a c^{2} x - 6 \, c^{2}\right)} x - \frac{5 \, c^{2}}{a}\right)} x + \frac{8 \, c^{2}}{a^{2}}\right)} x - \frac{15 \, c^{2}}{a^{3}}\right)} x + \frac{32 \, c^{2}}{a^{4}}\right)} - \frac{c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{16 \, a^{3} {\left| a \right|}}"," ",0,"-1/240*sqrt(-a^2*x^2 + 1)*((2*((4*(5*a*c^2*x - 6*c^2)*x - 5*c^2/a)*x + 8*c^2/a^2)*x - 15*c^2/a^3)*x + 32*c^2/a^4) - 1/16*c^2*arcsin(a*x)*sgn(a)/(a^3*abs(a))","A",0
296,1,81,0,0.253230," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{1}{120} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, {\left(3 \, {\left(4 \, a c^{2} x - 5 \, c^{2}\right)} x - \frac{4 \, c^{2}}{a}\right)} x + \frac{15 \, c^{2}}{a^{2}}\right)} x - \frac{16 \, c^{2}}{a^{3}}\right)} + \frac{c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, a^{2} {\left| a \right|}}"," ",0,"-1/120*sqrt(-a^2*x^2 + 1)*((2*(3*(4*a*c^2*x - 5*c^2)*x - 4*c^2/a)*x + 15*c^2/a^2)*x - 16*c^2/a^3) + 1/8*c^2*arcsin(a*x)*sgn(a)/(a^2*abs(a))","A",0
297,1,69,0,0.304705," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, a {\left| a \right|}} - \frac{1}{24} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, {\left(3 \, a c^{2} x - 4 \, c^{2}\right)} x - \frac{3 \, c^{2}}{a}\right)} x + \frac{8 \, c^{2}}{a^{2}}\right)}"," ",0,"-1/8*c^2*arcsin(a*x)*sgn(a)/(a*abs(a)) - 1/24*sqrt(-a^2*x^2 + 1)*((2*(3*a*c^2*x - 4*c^2)*x - 3*c^2/a)*x + 8*c^2/a^2)","A",0
298,1,54,0,0.198769," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2,x, algorithm=""giac"")","\frac{c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} - \frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, a c^{2} x - 3 \, c^{2}\right)} x - \frac{2 \, c^{2}}{a}\right)}"," ",0,"1/2*c^2*arcsin(a*x)*sgn(a)/abs(a) - 1/6*sqrt(-a^2*x^2 + 1)*((2*a*c^2*x - 3*c^2)*x - 2*c^2/a)","A",0
299,1,84,0,0.720860," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x,x, algorithm=""giac"")","-\frac{a c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} - \frac{a c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{1}{2} \, {\left(a c^{2} x - 2 \, c^{2}\right)} \sqrt{-a^{2} x^{2} + 1}"," ",0,"-1/2*a*c^2*arcsin(a*x)*sgn(a)/abs(a) - a*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/2*(a*c^2*x - 2*c^2)*sqrt(-a^2*x^2 + 1)","A",0
300,1,140,0,0.228436," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^2,x, algorithm=""giac"")","\frac{a^{4} c^{2} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} - \frac{a^{2} c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{a^{2} c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \sqrt{-a^{2} x^{2} + 1} a c^{2} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{2 \, x {\left| a \right|}}"," ",0,"1/2*a^4*c^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) - a^2*c^2*arcsin(a*x)*sgn(a)/abs(a) + a^2*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*a*c^2 - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/(x*abs(a))","B",0
301,1,192,0,0.223870," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^3,x, algorithm=""giac"")","\frac{a^{3} c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{a^{3} c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} + \frac{{\left(a^{3} c^{2} - \frac{4 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c^{2}}{x}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}} + \frac{\frac{4 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c^{2} {\left| a \right|}}{x} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{2} {\left| a \right|}}{a x^{2}}}{8 \, a^{2}}"," ",0,"a^3*c^2*arcsin(a*x)*sgn(a)/abs(a) + 1/2*a^3*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/8*(a^3*c^2 - 4*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c^2/x)*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)) + 1/8*(4*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c^2*abs(a)/x - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^2*abs(a)/(a*x^2))/a^2","B",0
302,1,233,0,0.535044," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^4,x, algorithm=""giac"")","\frac{{\left(a^{4} c^{2} - \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2} c^{2}}{x} - \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{2}}{x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} - \frac{a^{4} c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} + \frac{\frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{2}}{x} + \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{2}}{x^{2}} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{2}}{x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(a^4*c^2 - 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2*c^2/x - 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^2/x^2)*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) - 1/2*a^4*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/24*(3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^2/x + 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^2/x^2 - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^2/x^3)/(a^2*abs(a))","B",0
303,1,240,0,0.301851," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^5,x, algorithm=""giac"")","\frac{{\left(3 \, a^{5} c^{2} - \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{3} c^{2}}{x} + \frac{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{2}}{a x^{3}}\right)} a^{8} x^{4}}{192 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} {\left| a \right|}} + \frac{a^{5} c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} - \frac{\frac{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{5} c^{2} {\left| a \right|}}{x} - \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a c^{2} {\left| a \right|}}{x^{3}} + \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{2} {\left| a \right|}}{a x^{4}}}{192 \, a^{4}}"," ",0,"1/192*(3*a^5*c^2 - 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^3*c^2/x + 24*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^2/(a*x^3))*a^8*x^4/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*abs(a)) + 1/8*a^5*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/192*(24*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^5*c^2*abs(a)/x - 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a*c^2*abs(a)/x^3 + 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^2*abs(a)/(a*x^4))/a^4","B",0
304,1,297,0,0.296986," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^6,x, algorithm=""giac"")","\frac{{\left(6 \, a^{6} c^{2} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{2}}{x} + \frac{10 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{2}}{x^{2}} - \frac{60 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{2}}{a^{2} x^{4}}\right)} a^{10} x^{5}}{960 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} {\left| a \right|}} - \frac{a^{6} c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} + \frac{\frac{60 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{8} c^{2}}{x} - \frac{10 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a^{4} c^{2}}{x^{3}} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} a^{2} c^{2}}{x^{4}} - \frac{6 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{2}}{x^{5}}}{960 \, a^{4} {\left| a \right|}}"," ",0,"1/960*(6*a^6*c^2 - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^2/x + 10*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^2/x^2 - 60*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^2/(a^2*x^4))*a^10*x^5/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*abs(a)) - 1/8*a^6*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/960*(60*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^8*c^2/x - 10*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a^4*c^2/x^3 + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*a^2*c^2/x^4 - 6*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^2/x^5)/(a^4*abs(a))","B",0
305,1,424,0,0.651206," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^2/x^7,x, algorithm=""giac"")","\frac{{\left(5 \, a^{7} c^{2} - \frac{12 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{5} c^{2}}{x} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{3} c^{2}}{x^{2}} - \frac{20 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a c^{2}}{x^{3}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{2}}{a x^{4}} + \frac{120 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{2}}{a^{3} x^{5}}\right)} a^{12} x^{6}}{1920 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} {\left| a \right|}} + \frac{a^{7} c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{16 \, {\left| a \right|}} - \frac{\frac{120 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{9} c^{2} {\left| a \right|}}{x} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{7} c^{2} {\left| a \right|}}{x^{2}} - \frac{20 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a^{5} c^{2} {\left| a \right|}}{x^{3}} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} a^{3} c^{2} {\left| a \right|}}{x^{4}} - \frac{12 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} a c^{2} {\left| a \right|}}{x^{5}} + \frac{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} c^{2} {\left| a \right|}}{a x^{6}}}{1920 \, a^{6}}"," ",0,"1/1920*(5*a^7*c^2 - 12*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^5*c^2/x + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^3*c^2/x^2 - 20*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a*c^2/x^3 - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^2/(a*x^4) + 120*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^2/(a^3*x^5))*a^12*x^6/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*abs(a)) + 1/16*a^7*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/1920*(120*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^9*c^2*abs(a)/x - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^7*c^2*abs(a)/x^2 - 20*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a^5*c^2*abs(a)/x^3 + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*a^3*c^2*abs(a)/x^4 - 12*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*a*c^2*abs(a)/x^5 + 5*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*c^2*abs(a)/(a*x^6))/a^6","B",0
306,1,104,0,0.212194," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{1}{840} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, {\left({\left(\frac{35 \, c^{3}}{a} + 4 \, {\left(18 \, c^{3} + 5 \, {\left(3 \, a^{2} c^{3} x - 7 \, a c^{3}\right)} x\right)} x\right)} x - \frac{44 \, c^{3}}{a^{2}}\right)} x + \frac{105 \, c^{3}}{a^{3}}\right)} x - \frac{176 \, c^{3}}{a^{4}}\right)} - \frac{c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, a^{3} {\left| a \right|}}"," ",0,"1/840*sqrt(-a^2*x^2 + 1)*((2*((35*c^3/a + 4*(18*c^3 + 5*(3*a^2*c^3*x - 7*a*c^3)*x)*x)*x - 44*c^3/a^2)*x + 105*c^3/a^3)*x - 176*c^3/a^4) - 1/8*c^3*arcsin(a*x)*sgn(a)/(a^3*abs(a))","A",0
307,1,92,0,0.530950," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{3 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{16 \, a^{2} {\left| a \right|}} + \frac{1}{240} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, {\left(\frac{16 \, c^{3}}{a} + {\left(25 \, c^{3} + 4 \, {\left(5 \, a^{2} c^{3} x - 12 \, a c^{3}\right)} x\right)} x\right)} x - \frac{45 \, c^{3}}{a^{2}}\right)} x + \frac{64 \, c^{3}}{a^{3}}\right)}"," ",0,"3/16*c^3*arcsin(a*x)*sgn(a)/(a^2*abs(a)) + 1/240*sqrt(-a^2*x^2 + 1)*((2*(16*c^3/a + (25*c^3 + 4*(5*a^2*c^3*x - 12*a*c^3)*x)*x)*x - 45*c^3/a^2)*x + 64*c^3/a^3)","A",0
308,1,81,0,0.370483," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{4 \, a {\left| a \right|}} + \frac{1}{60} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(\frac{15 \, c^{3}}{a} + 2 \, {\left(8 \, c^{3} + 3 \, {\left(2 \, a^{2} c^{3} x - 5 \, a c^{3}\right)} x\right)} x\right)} x - \frac{28 \, c^{3}}{a^{2}}\right)}"," ",0,"-1/4*c^3*arcsin(a*x)*sgn(a)/(a*abs(a)) + 1/60*sqrt(-a^2*x^2 + 1)*((15*c^3/a + 2*(8*c^3 + 3*(2*a^2*c^3*x - 5*a*c^3)*x)*x)*x - 28*c^3/a^2)","A",0
309,1,66,0,0.298386," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{5 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} + \frac{1}{24} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{16 \, c^{3}}{a} + {\left(9 \, c^{3} + 2 \, {\left(3 \, a^{2} c^{3} x - 8 \, a c^{3}\right)} x\right)} x\right)}"," ",0,"5/8*c^3*arcsin(a*x)*sgn(a)/abs(a) + 1/24*sqrt(-a^2*x^2 + 1)*(16*c^3/a + (9*c^3 + 2*(3*a^2*c^3*x - 8*a*c^3)*x)*x)","A",0
310,1,95,0,0.411292," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x,x, algorithm=""giac"")","-\frac{a c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{a c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} + \frac{1}{3} \, \sqrt{-a^{2} x^{2} + 1} {\left(2 \, c^{3} + {\left(a^{2} c^{3} x - 3 \, a c^{3}\right)} x\right)}"," ",0,"-a*c^3*arcsin(a*x)*sgn(a)/abs(a) - a*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/3*sqrt(-a^2*x^2 + 1)*(2*c^3 + (a^2*c^3*x - 3*a*c^3)*x)","A",0
311,1,152,0,0.266603," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^2,x, algorithm=""giac"")","\frac{a^{4} c^{3} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} - \frac{a^{2} c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} + \frac{2 \, a^{2} c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3}}{2 \, x {\left| a \right|}} + \frac{1}{2} \, {\left(a^{2} c^{3} x - 4 \, a c^{3}\right)} \sqrt{-a^{2} x^{2} + 1}"," ",0,"1/2*a^4*c^3*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) - 1/2*a^2*c^3*arcsin(a*x)*sgn(a)/abs(a) + 2*a^2*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3/(x*abs(a)) + 1/2*(a^2*c^3*x - 4*a*c^3)*sqrt(-a^2*x^2 + 1)","B",0
312,1,212,0,0.224914," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^3,x, algorithm=""giac"")","\frac{2 \, a^{3} c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{a^{3} c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} + \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} + \frac{{\left(a^{3} c^{3} - \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c^{3}}{x}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}} + \frac{\frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c^{3} {\left| a \right|}}{x} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3} {\left| a \right|}}{a x^{2}}}{8 \, a^{2}}"," ",0,"2*a^3*c^3*arcsin(a*x)*sgn(a)/abs(a) - 1/2*a^3*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*a^2*c^3 + 1/8*(a^3*c^3 - 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c^3/x)*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)) + 1/8*(8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c^3*abs(a)/x - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3*abs(a)/(a*x^2))/a^2","B",0
313,1,250,0,0.202024," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^4,x, algorithm=""giac"")","-\frac{a^{4} c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{a^{4} c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} + \frac{{\left(a^{4} c^{3} - \frac{6 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2} c^{3}}{x} + \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3}}{x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} - \frac{\frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{3}}{x} - \frac{6 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{3}}{x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{3}}{x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"-a^4*c^3*arcsin(a*x)*sgn(a)/abs(a) - a^4*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/24*(a^4*c^3 - 6*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2*c^3/x + 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3/x^2)*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) - 1/24*(9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^3/x - 6*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^3/x^2 + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^3/x^3)/(a^2*abs(a))","B",0
314,1,300,0,0.422896," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^5,x, algorithm=""giac"")","\frac{{\left(3 \, a^{5} c^{3} - \frac{16 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{3} c^{3}}{x} + \frac{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a c^{3}}{x^{2}} + \frac{48 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{3}}{a x^{3}}\right)} a^{8} x^{4}}{192 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} {\left| a \right|}} + \frac{5 \, a^{5} c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} - \frac{\frac{48 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{5} c^{3} {\left| a \right|}}{x} + \frac{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{3} c^{3} {\left| a \right|}}{x^{2}} - \frac{16 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a c^{3} {\left| a \right|}}{x^{3}} + \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{3} {\left| a \right|}}{a x^{4}}}{192 \, a^{4}}"," ",0,"1/192*(3*a^5*c^3 - 16*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^3*c^3/x + 24*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a*c^3/x^2 + 48*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^3/(a*x^3))*a^8*x^4/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*abs(a)) + 5/8*a^5*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/192*(48*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^5*c^3*abs(a)/x + 24*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^3*c^3*abs(a)/x^2 - 16*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a*c^3*abs(a)/x^3 + 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^3*abs(a)/(a*x^4))/a^4","B",0
315,1,297,0,0.241724," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^3/x^6,x, algorithm=""giac"")","\frac{{\left(3 \, a^{6} c^{3} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{3}}{x} + \frac{25 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{3}}{x^{2}} - \frac{90 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{3}}{a^{2} x^{4}}\right)} a^{10} x^{5}}{480 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} {\left| a \right|}} - \frac{a^{6} c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{4 \, {\left| a \right|}} + \frac{\frac{90 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{8} c^{3}}{x} - \frac{25 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a^{4} c^{3}}{x^{3}} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} a^{2} c^{3}}{x^{4}} - \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{3}}{x^{5}}}{480 \, a^{4} {\left| a \right|}}"," ",0,"1/480*(3*a^6*c^3 - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^3/x + 25*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^3/x^2 - 90*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^3/(a^2*x^4))*a^10*x^5/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*abs(a)) - 1/4*a^6*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/480*(90*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^8*c^3/x - 25*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a^4*c^3/x^3 + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*a^2*c^3/x^4 - 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^3/x^5)/(a^4*abs(a))","B",0
316,1,117,0,0.214823," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{29 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{128 \, a^{3} {\left| a \right|}} - \frac{1}{13440} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, {\left(\frac{1216 \, c^{4}}{a^{2}} - {\left(\frac{1015 \, c^{4}}{a} + 4 \, {\left(192 \, c^{4} - 5 \, {\left(161 \, a c^{4} + 6 \, {\left(7 \, a^{3} c^{4} x - 24 \, a^{2} c^{4}\right)} x\right)} x\right)} x\right)} x\right)} x - \frac{3045 \, c^{4}}{a^{3}}\right)} x + \frac{4864 \, c^{4}}{a^{4}}\right)}"," ",0,"-29/128*c^4*arcsin(a*x)*sgn(a)/(a^3*abs(a)) - 1/13440*sqrt(-a^2*x^2 + 1)*((2*(1216*c^4/a^2 - (1015*c^4/a + 4*(192*c^4 - 5*(161*a*c^4 + 6*(7*a^3*c^4*x - 24*a^2*c^4)*x)*x)*x)*x)*x - 3045*c^4/a^3)*x + 4864*c^4/a^4)","A",0
317,1,104,0,0.267046," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a*c*x+c)^4,x, algorithm=""giac"")","\frac{5 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{16 \, a^{2} {\left| a \right|}} - \frac{1}{336} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(\frac{105 \, c^{4}}{a^{2}} - 2 \, {\left(\frac{40 \, c^{4}}{a} + 3 \, {\left(7 \, c^{4} - 4 \, {\left(8 \, a c^{4} + {\left(2 \, a^{3} c^{4} x - 7 \, a^{2} c^{4}\right)} x\right)} x\right)} x\right)} x\right)} x - \frac{160 \, c^{4}}{a^{3}}\right)}"," ",0,"5/16*c^4*arcsin(a*x)*sgn(a)/(a^2*abs(a)) - 1/336*sqrt(-a^2*x^2 + 1)*((105*c^4/a^2 - 2*(40*c^4/a + 3*(7*c^4 - 4*(8*a*c^4 + (2*a^3*c^4*x - 7*a^2*c^4)*x)*x)*x)*x)*x - 160*c^4/a^3)","A",0
318,1,94,0,0.181013," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{7 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{16 \, a {\left| a \right|}} - \frac{1}{240} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{176 \, c^{4}}{a^{2}} - {\left(\frac{105 \, c^{4}}{a} + 2 \, {\left(16 \, c^{4} - {\left(85 \, a c^{4} + 4 \, {\left(5 \, a^{3} c^{4} x - 18 \, a^{2} c^{4}\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"-7/16*c^4*arcsin(a*x)*sgn(a)/(a*abs(a)) - 1/240*sqrt(-a^2*x^2 + 1)*(176*c^4/a^2 - (105*c^4/a + 2*(16*c^4 - (85*a*c^4 + 4*(5*a^3*c^4*x - 18*a^2*c^4)*x)*x)*x)*x)","A",0
319,1,78,0,0.188142," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4,x, algorithm=""giac"")","\frac{7 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} + \frac{1}{120} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{136 \, c^{4}}{a} + {\left(15 \, c^{4} - 2 \, {\left(56 \, a c^{4} + 3 \, {\left(4 \, a^{3} c^{4} x - 15 \, a^{2} c^{4}\right)} x\right)} x\right)} x\right)}"," ",0,"7/8*c^4*arcsin(a*x)*sgn(a)/abs(a) + 1/120*sqrt(-a^2*x^2 + 1)*(136*c^4/a + (15*c^4 - 2*(56*a*c^4 + 3*(4*a^3*c^4*x - 15*a^2*c^4)*x)*x)*x)","A",0
320,1,100,0,0.291024," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x,x, algorithm=""giac"")","-\frac{13 \, a c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} - \frac{a c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{1}{8} \, {\left(11 \, a c^{4} + 2 \, {\left(a^{3} c^{4} x - 4 \, a^{2} c^{4}\right)} x\right)} \sqrt{-a^{2} x^{2} + 1} x"," ",0,"-13/8*a*c^4*arcsin(a*x)*sgn(a)/abs(a) - a*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/8*(11*a*c^4 + 2*(a^3*c^4*x - 4*a^2*c^4)*x)*sqrt(-a^2*x^2 + 1)*x","A",0
321,1,164,0,0.254032," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^2,x, algorithm=""giac"")","\frac{a^{4} c^{4} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} + \frac{a^{2} c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} + \frac{3 \, a^{2} c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4}}{2 \, x {\left| a \right|}} - \frac{1}{6} \, {\left(16 \, a c^{4} + {\left(2 \, a^{3} c^{4} x - 9 \, a^{2} c^{4}\right)} x\right)} \sqrt{-a^{2} x^{2} + 1}"," ",0,"1/2*a^4*c^4*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) + 1/2*a^2*c^4*arcsin(a*x)*sgn(a)/abs(a) + 3*a^2*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4/(x*abs(a)) - 1/6*(16*a*c^4 + (2*a^3*c^4*x - 9*a^2*c^4)*x)*sqrt(-a^2*x^2 + 1)","A",0
322,1,224,0,0.227405," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^3,x, algorithm=""giac"")","\frac{5 \, a^{3} c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} - \frac{5 \, a^{3} c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} + \frac{{\left(a^{3} c^{4} - \frac{12 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c^{4}}{x}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}} - \frac{1}{2} \, {\left(a^{3} c^{4} x - 6 \, a^{2} c^{4}\right)} \sqrt{-a^{2} x^{2} + 1} + \frac{\frac{12 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c^{4} {\left| a \right|}}{x} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4} {\left| a \right|}}{a x^{2}}}{8 \, a^{2}}"," ",0,"5/2*a^3*c^4*arcsin(a*x)*sgn(a)/abs(a) - 5/2*a^3*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/8*(a^3*c^4 - 12*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c^4/x)*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)) - 1/2*(a^3*c^4*x - 6*a^2*c^4)*sqrt(-a^2*x^2 + 1) + 1/8*(12*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c^4*abs(a)/x - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4*abs(a)/(a*x^2))/a^2","B",0
323,1,270,0,0.416456," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^4,x, algorithm=""giac"")","-\frac{3 \, a^{4} c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{a^{4} c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \sqrt{-a^{2} x^{2} + 1} a^{3} c^{4} + \frac{{\left(a^{4} c^{4} - \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2} c^{4}}{x} + \frac{33 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4}}{x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} - \frac{\frac{33 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{4}}{x} - \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{4}}{x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"-3*a^4*c^4*arcsin(a*x)*sgn(a)/abs(a) - 1/2*a^4*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*a^3*c^4 + 1/24*(a^4*c^4 - 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2*c^4/x + 33*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4/x^2)*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) - 1/24*(33*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^4/x - 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^4/x^2 + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/x^3)/(a^2*abs(a))","B",0
324,1,316,0,0.197398," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^5,x, algorithm=""giac"")","\frac{a^{5} c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{13 \, a^{5} c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} + \frac{{\left(a^{5} c^{4} - \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{3} c^{4}}{x} + \frac{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a c^{4}}{x^{2}} - \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{a x^{3}}\right)} a^{8} x^{4}}{64 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} {\left| a \right|}} + \frac{\frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{5} c^{4} {\left| a \right|}}{x} - \frac{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{3} c^{4} {\left| a \right|}}{x^{2}} + \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a c^{4} {\left| a \right|}}{x^{3}} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{4} {\left| a \right|}}{a x^{4}}}{64 \, a^{4}}"," ",0,"a^5*c^4*arcsin(a*x)*sgn(a)/abs(a) + 13/8*a^5*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/64*(a^5*c^4 - 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^3*c^4/x + 24*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a*c^4/x^2 - 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/(a*x^3))*a^8*x^4/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*abs(a)) + 1/64*(8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^5*c^4*abs(a)/x - 24*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^3*c^4*abs(a)/x^2 + 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a*c^4*abs(a)/x^3 - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^4*abs(a)/(a*x^4))/a^4","B",0
325,1,354,0,0.231089," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^6,x, algorithm=""giac"")","\frac{{\left(6 \, a^{6} c^{4} - \frac{45 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{4}}{x} + \frac{130 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{4}}{x^{2}} - \frac{120 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{x^{3}} - \frac{420 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{4}}{a^{2} x^{4}}\right)} a^{10} x^{5}}{960 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} {\left| a \right|}} - \frac{7 \, a^{6} c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} + \frac{\frac{420 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{8} c^{4}}{x} + \frac{120 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{6} c^{4}}{x^{2}} - \frac{130 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a^{4} c^{4}}{x^{3}} + \frac{45 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} a^{2} c^{4}}{x^{4}} - \frac{6 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{4}}{x^{5}}}{960 \, a^{4} {\left| a \right|}}"," ",0,"1/960*(6*a^6*c^4 - 45*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^4/x + 130*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^4/x^2 - 120*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/x^3 - 420*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^4/(a^2*x^4))*a^10*x^5/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*abs(a)) - 7/8*a^6*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 1/960*(420*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^8*c^4/x + 120*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^6*c^4/x^2 - 130*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a^4*c^4/x^3 + 45*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*a^2*c^4/x^4 - 6*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^4/x^5)/(a^4*abs(a))","B",0
326,1,424,0,0.238777," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^4/x^7,x, algorithm=""giac"")","\frac{{\left(5 \, a^{7} c^{4} - \frac{36 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{5} c^{4}}{x} + \frac{105 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{3} c^{4}}{x^{2}} - \frac{140 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a c^{4}}{x^{3}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{4}}{a x^{4}} + \frac{600 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{4}}{a^{3} x^{5}}\right)} a^{12} x^{6}}{1920 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} {\left| a \right|}} + \frac{7 \, a^{7} c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{16 \, {\left| a \right|}} - \frac{\frac{600 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{9} c^{4} {\left| a \right|}}{x} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{7} c^{4} {\left| a \right|}}{x^{2}} - \frac{140 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a^{5} c^{4} {\left| a \right|}}{x^{3}} + \frac{105 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} a^{3} c^{4} {\left| a \right|}}{x^{4}} - \frac{36 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} a c^{4} {\left| a \right|}}{x^{5}} + \frac{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} c^{4} {\left| a \right|}}{a x^{6}}}{1920 \, a^{6}}"," ",0,"1/1920*(5*a^7*c^4 - 36*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^5*c^4/x + 105*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^3*c^4/x^2 - 140*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a*c^4/x^3 - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^4/(a*x^4) + 600*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^4/(a^3*x^5))*a^12*x^6/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*abs(a)) + 7/16*a^7*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/1920*(600*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^9*c^4*abs(a)/x - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^7*c^4*abs(a)/x^2 - 140*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a^5*c^4*abs(a)/x^3 + 105*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*a^3*c^4*abs(a)/x^4 - 36*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*a*c^4*abs(a)/x^5 + 5*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*c^4*abs(a)/(a*x^6))/a^6","B",0
327,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c),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
328,1,101,0,0.208363," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{-a^{2} x^{2} + 1} {\left(x {\left(\frac{x}{a^{2} c} + \frac{3}{a^{3} c}\right)} + \frac{8}{a^{4} c}\right)} - \frac{3 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{a^{3} c {\left| a \right|}} + \frac{4}{a^{3} c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"1/3*sqrt(-a^2*x^2 + 1)*(x*(x/(a^2*c) + 3/(a^3*c)) + 8/(a^4*c)) - 3*arcsin(a*x)*sgn(a)/(a^3*c*abs(a)) + 4/(a^3*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
329,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c),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
330,1,78,0,0.244382," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c),x, algorithm=""giac"")","-\frac{2 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{a c {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{2} c} + \frac{4}{a c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"-2*arcsin(a*x)*sgn(a)/(a*c*abs(a)) + sqrt(-a^2*x^2 + 1)/(a^2*c) + 4/(a*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
331,1,53,0,0.259474," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c),x, algorithm=""giac"")","-\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c {\left| a \right|}} + \frac{4}{c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"-arcsin(a*x)*sgn(a)/(c*abs(a)) + 4/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
332,1,80,0,0.186943," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c),x, algorithm=""giac"")","-\frac{a \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{c {\left| a \right|}} + \frac{4 \, a}{c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"-a*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c*abs(a)) + 4*a/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
333,1,159,0,0.201546," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c),x, algorithm=""giac"")","-\frac{2 \, a^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{c {\left| a \right|}} - \frac{{\left(a^{2} - \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{x}\right)} a^{2} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{2 \, c x {\left| a \right|}}"," ",0,"-2*a^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c*abs(a)) - 1/2*(a^2 - 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/x)*a^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a)) - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(c*x*abs(a))","B",0
334,1,224,0,0.204135," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c),x, algorithm=""giac"")","-\frac{{\left(a^{3} + \frac{7 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a}{x} - \frac{40 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a x^{2}}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}} - \frac{5 \, a^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, c {\left| a \right|}} - \frac{\frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c {\left| a \right|}}{x} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c {\left| a \right|}}{a x^{2}}}{8 \, a^{2} c^{2}}"," ",0,"-1/8*(a^3 + 7*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a/x - 40*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a*x^2))*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a)) - 5/2*a^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c*abs(a)) - 1/8*(8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c*abs(a)/x + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c*abs(a)/(a*x^2))/(a^2*c^2)","B",0
335,1,283,0,0.189338," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a*c*x+c),x, algorithm=""giac"")","-\frac{{\left(a^{4} + \frac{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2}}{x} + \frac{27 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{x^{2}} - \frac{129 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{2} x^{3}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}} - \frac{3 \, a^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{c {\left| a \right|}} - \frac{\frac{33 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{2}}{x} + \frac{6 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{2}}{x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{2}}{x^{3}}}{24 \, a^{2} c^{3} {\left| a \right|}}"," ",0,"-1/24*(a^4 + 5*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2/x + 27*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/x^2 - 129*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^2*x^3))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a)) - 3*a^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c*abs(a)) - 1/24*(33*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^2/x + 6*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^2/x^2 + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^2/x^3)/(a^2*c^3*abs(a))","B",0
336,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c)^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
337,1,176,0,0.239381," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{4 \, a^{3} c^{6} {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} + 132 \, a^{3} c^{6} \arctan\left(\sqrt{-\frac{2 \, c}{a c x - c} - 1}\right) - 72 \, a^{3} c^{6} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - \frac{3 \, {\left(7 \, a^{3} c^{6} {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} + 5 \, a^{3} c^{6} \sqrt{-\frac{2 \, c}{a c x - c} - 1}\right)} {\left(a c x - c\right)}^{2}}{c^{2}}}{12 \, a^{6} c^{8} {\left| a \right|} \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}"," ",0,"-1/12*(4*a^3*c^6*(-2*c/(a*c*x - c) - 1)^(3/2) + 132*a^3*c^6*arctan(sqrt(-2*c/(a*c*x - c) - 1)) - 72*a^3*c^6*sqrt(-2*c/(a*c*x - c) - 1) - 3*(7*a^3*c^6*(-2*c/(a*c*x - c) - 1)^(3/2) + 5*a^3*c^6*sqrt(-2*c/(a*c*x - c) - 1))*(a*c*x - c)^2/c^2)/(a^6*c^8*abs(a)*sgn(1/(a*c*x - c))*sgn(a)*sgn(c))","A",0
338,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c)^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
339,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 1/abs(a)/c^2/a/c*(-(-6*c*atan(i)-(-7*i)*c)/3*sign((a*c*x-c)^-1)*sign(a)*sign(c)-2*a*c^2*(1/8*(4/3*sqrt(-2*a*c^2*(a*c*x-c)^-1/a/c-1)*(-2*a*c^2*(a*c*x-c)^-1/a/c-1)-8*sqrt(-2*a*c^2*(a*c*x-c)^-1/a/c-1))+atan(sqrt(-2*a*c^2*(a*c*x-c)^-1/a/c-1)))/a/c/sign((a*c*x-c)^-1)/sign(a)/sign(c))","F(-2)",0
340,1,66,0,0.240955," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^2,x, algorithm=""giac"")","-\frac{i \, \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right) + \frac{{\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}}}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}}{3 \, c^{2} {\left| a \right|}}"," ",0,"-1/3*(I*sgn(1/(a*c*x - c))*sgn(a)*sgn(c) + (-2*c/(a*c*x - c) - 1)^(3/2)/(sgn(1/(a*c*x - c))*sgn(a)*sgn(c)))/(c^2*abs(a))","C",0
341,1,245,0,0.279740," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c)^2,x, algorithm=""giac"")","\frac{{\left(\frac{{\left(3 \, \log\left(2\right) - 6 \, \log\left(i + 1\right) + 10 i\right)} \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)}{c} + \frac{6 \, \log\left(\sqrt{-\frac{2 \, c}{a c x - c} - 1} + 1\right)}{c \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)} - \frac{6 \, \log\left({\left| \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 1 \right|}\right)}{c \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)} - \frac{2 \, {\left(c^{2} {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{2} \mathrm{sgn}\left(a\right)^{2} \mathrm{sgn}\left(c\right)^{2} + 6 \, c^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1} \mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{2} \mathrm{sgn}\left(a\right)^{2} \mathrm{sgn}\left(c\right)^{2}\right)}}{c^{3} \mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{3} \mathrm{sgn}\left(a\right)^{3} \mathrm{sgn}\left(c\right)^{3}}\right)} a}{6 \, c {\left| a \right|}}"," ",0,"1/6*((3*log(2) - 6*log(I + 1) + 10*I)*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)/c + 6*log(sqrt(-2*c/(a*c*x - c) - 1) + 1)/(c*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)) - 6*log(abs(sqrt(-2*c/(a*c*x - c) - 1) - 1))/(c*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)) - 2*(c^2*(-2*c/(a*c*x - c) - 1)^(3/2)*sgn(1/(a*c*x - c))^2*sgn(a)^2*sgn(c)^2 + 6*c^2*sqrt(-2*c/(a*c*x - c) - 1)*sgn(1/(a*c*x - c))^2*sgn(a)^2*sgn(c)^2)/(c^3*sgn(1/(a*c*x - c))^3*sgn(a)^3*sgn(c)^3))*a/(c*abs(a))","C",0
342,1,307,0,0.240400," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c)^2,x, algorithm=""giac"")","\frac{{\left(9 \, a^{2} \log\left(2\right) - 18 \, a^{2} \log\left(i + 1\right) + 28 i \, a^{2}\right)} \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right) + \frac{18 \, a^{2} \log\left(\sqrt{-\frac{2 \, c}{a c x - c} - 1} + 1\right)}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)} - \frac{18 \, a^{2} \log\left({\left| \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 1 \right|}\right)}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)} - \frac{6 \, a^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1}}{{\left(\frac{c}{a c x - c} + 1\right)} \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)} - \frac{2 \, {\left(a^{2} {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{2} \mathrm{sgn}\left(a\right)^{2} \mathrm{sgn}\left(c\right)^{2} + 12 \, a^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1} \mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{2} \mathrm{sgn}\left(a\right)^{2} \mathrm{sgn}\left(c\right)^{2}\right)}}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{3} \mathrm{sgn}\left(a\right)^{3} \mathrm{sgn}\left(c\right)^{3}}}{6 \, c^{2} {\left| a \right|}}"," ",0,"1/6*((9*a^2*log(2) - 18*a^2*log(I + 1) + 28*I*a^2)*sgn(1/(a*c*x - c))*sgn(a)*sgn(c) + 18*a^2*log(sqrt(-2*c/(a*c*x - c) - 1) + 1)/(sgn(1/(a*c*x - c))*sgn(a)*sgn(c)) - 18*a^2*log(abs(sqrt(-2*c/(a*c*x - c) - 1) - 1))/(sgn(1/(a*c*x - c))*sgn(a)*sgn(c)) - 6*a^2*sqrt(-2*c/(a*c*x - c) - 1)/((c/(a*c*x - c) + 1)*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)) - 2*(a^2*(-2*c/(a*c*x - c) - 1)^(3/2)*sgn(1/(a*c*x - c))^2*sgn(a)^2*sgn(c)^2 + 12*a^2*sqrt(-2*c/(a*c*x - c) - 1)*sgn(1/(a*c*x - c))^2*sgn(a)^2*sgn(c)^2)/(sgn(1/(a*c*x - c))^3*sgn(a)^3*sgn(c)^3))/(c^2*abs(a))","C",0
343,1,332,0,0.274662," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c)^2,x, algorithm=""giac"")","\frac{{\left(33 \, a^{3} \log\left(2\right) - 66 \, a^{3} \log\left(i + 1\right) + 104 i \, a^{3}\right)} \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right) + \frac{66 \, a^{3} \log\left(\sqrt{-\frac{2 \, c}{a c x - c} - 1} + 1\right)}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)} - \frac{66 \, a^{3} \log\left({\left| \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 1 \right|}\right)}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)} + \frac{3 \, {\left(7 \, a^{3} {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} - 5 \, a^{3} \sqrt{-\frac{2 \, c}{a c x - c} - 1}\right)}}{{\left(\frac{c}{a c x - c} + 1\right)}^{2} \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)} - \frac{4 \, {\left(a^{3} {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{2} \mathrm{sgn}\left(a\right)^{2} \mathrm{sgn}\left(c\right)^{2} + 18 \, a^{3} \sqrt{-\frac{2 \, c}{a c x - c} - 1} \mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{2} \mathrm{sgn}\left(a\right)^{2} \mathrm{sgn}\left(c\right)^{2}\right)}}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{3} \mathrm{sgn}\left(a\right)^{3} \mathrm{sgn}\left(c\right)^{3}}}{12 \, c^{2} {\left| a \right|}}"," ",0,"1/12*((33*a^3*log(2) - 66*a^3*log(I + 1) + 104*I*a^3)*sgn(1/(a*c*x - c))*sgn(a)*sgn(c) + 66*a^3*log(sqrt(-2*c/(a*c*x - c) - 1) + 1)/(sgn(1/(a*c*x - c))*sgn(a)*sgn(c)) - 66*a^3*log(abs(sqrt(-2*c/(a*c*x - c) - 1) - 1))/(sgn(1/(a*c*x - c))*sgn(a)*sgn(c)) + 3*(7*a^3*(-2*c/(a*c*x - c) - 1)^(3/2) - 5*a^3*sqrt(-2*c/(a*c*x - c) - 1))/((c/(a*c*x - c) + 1)^2*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)) - 4*(a^3*(-2*c/(a*c*x - c) - 1)^(3/2)*sgn(1/(a*c*x - c))^2*sgn(a)^2*sgn(c)^2 + 18*a^3*sqrt(-2*c/(a*c*x - c) - 1)*sgn(1/(a*c*x - c))^2*sgn(a)^2*sgn(c)^2)/(sgn(1/(a*c*x - c))^3*sgn(a)^3*sgn(c)^3))/(c^2*abs(a))","C",0
344,1,372,0,0.297416," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a*c*x+c)^2,x, algorithm=""giac"")","\frac{2 \, {\left(51 \, a^{4} \log\left(2\right) - 102 \, a^{4} \log\left(i + 1\right) + 160 i \, a^{4}\right)} \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right) + \frac{204 \, a^{4} \log\left(\sqrt{-\frac{2 \, c}{a c x - c} - 1} + 1\right)}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)} - \frac{204 \, a^{4} \log\left({\left| \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 1 \right|}\right)}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)} - \frac{45 \, a^{4} {\left(\frac{2 \, c}{a c x - c} + 1\right)}^{2} \sqrt{-\frac{2 \, c}{a c x - c} - 1} - 64 \, a^{4} {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} + 27 \, a^{4} \sqrt{-\frac{2 \, c}{a c x - c} - 1}}{{\left(\frac{c}{a c x - c} + 1\right)}^{3} \mathrm{sgn}\left(\frac{1}{a c x - c}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(c\right)} - \frac{8 \, {\left(a^{4} {\left(-\frac{2 \, c}{a c x - c} - 1\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{2} \mathrm{sgn}\left(a\right)^{2} \mathrm{sgn}\left(c\right)^{2} + 24 \, a^{4} \sqrt{-\frac{2 \, c}{a c x - c} - 1} \mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{2} \mathrm{sgn}\left(a\right)^{2} \mathrm{sgn}\left(c\right)^{2}\right)}}{\mathrm{sgn}\left(\frac{1}{a c x - c}\right)^{3} \mathrm{sgn}\left(a\right)^{3} \mathrm{sgn}\left(c\right)^{3}}}{24 \, c^{2} {\left| a \right|}}"," ",0,"1/24*(2*(51*a^4*log(2) - 102*a^4*log(I + 1) + 160*I*a^4)*sgn(1/(a*c*x - c))*sgn(a)*sgn(c) + 204*a^4*log(sqrt(-2*c/(a*c*x - c) - 1) + 1)/(sgn(1/(a*c*x - c))*sgn(a)*sgn(c)) - 204*a^4*log(abs(sqrt(-2*c/(a*c*x - c) - 1) - 1))/(sgn(1/(a*c*x - c))*sgn(a)*sgn(c)) - (45*a^4*(2*c/(a*c*x - c) + 1)^2*sqrt(-2*c/(a*c*x - c) - 1) - 64*a^4*(-2*c/(a*c*x - c) - 1)^(3/2) + 27*a^4*sqrt(-2*c/(a*c*x - c) - 1))/((c/(a*c*x - c) + 1)^3*sgn(1/(a*c*x - c))*sgn(a)*sgn(c)) - 8*(a^4*(-2*c/(a*c*x - c) - 1)^(3/2)*sgn(1/(a*c*x - c))^2*sgn(a)^2*sgn(c)^2 + 24*a^4*sqrt(-2*c/(a*c*x - c) - 1)*sgn(1/(a*c*x - c))^2*sgn(a)^2*sgn(c)^2)/(sgn(1/(a*c*x - c))^3*sgn(a)^3*sgn(c)^3))/(c^2*abs(a))","C",0
345,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c)^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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
346,1,186,0,0.194873," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{4 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{a^{3} c^{3} {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{4} c^{3}} - \frac{2 \, {\left(\frac{335 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{505 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{285 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{60 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} - 79\right)}}{15 \, a^{3} c^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"-4*arcsin(a*x)*sgn(a)/(a^3*c^3*abs(a)) + sqrt(-a^2*x^2 + 1)/(a^4*c^3) - 2/15*(335*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 505*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 285*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 60*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) - 79)/(a^3*c^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","A",0
347,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c)^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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
348,1,121,0,0.203294," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c)^3,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} + \frac{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - 1\right)}}{15 \, a c^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"2/15*(5*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 5*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 1)/(a*c^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","B",0
349,1,145,0,0.215944," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{25 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} - 4\right)}}{15 \, c^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"-2/15*(5*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 25*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) - 4)/(c^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","B",0
350,1,189,0,0.221568," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{a \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{c^{3} {\left| a \right|}} + \frac{2 \, {\left(13 \, a - \frac{45 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a x} + \frac{75 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{3} x^{2}} - \frac{55 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{5} x^{3}} + \frac{20 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{7} x^{4}}\right)}}{5 \, c^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"-a*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c^3*abs(a)) + 2/5*(13*a - 45*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a*x) + 75*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^3*x^2) - 55*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^5*x^3) + 20*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^7*x^4))/(c^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","B",0
351,1,269,0,0.246245," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{4 \, a^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{c^{3} {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{2 \, c^{3} x {\left| a \right|}} - \frac{{\left(15 \, a^{2} - \frac{491 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{x} + \frac{1690 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{2} x^{2}} - \frac{2570 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{4} x^{3}} + \frac{1815 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{6} x^{4}} - \frac{555 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{8} x^{5}}\right)} a^{2} x}{30 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"-4*a^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c^3*abs(a)) - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(c^3*x*abs(a)) - 1/30*(15*a^2 - 491*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/x + 1690*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^2*x^2) - 2570*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^4*x^3) + 1815*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^6*x^4) - 555*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^8*x^5))*a^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","B",0
352,1,338,0,0.253834," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{19 \, a^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, c^{3} {\left| a \right|}} - \frac{{\left(15 \, a^{3} + \frac{165 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a}{x} - \frac{4234 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a x^{2}} + \frac{14330 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{3} x^{3}} - \frac{20965 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{5} x^{4}} + \frac{14385 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{7} x^{5}} - \frac{4080 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{9} x^{6}}\right)} a^{4} x^{2}}{120 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}} - \frac{\frac{16 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c^{3} {\left| a \right|}}{x} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3} {\left| a \right|}}{a x^{2}}}{8 \, a^{2} c^{6}}"," ",0,"-19/2*a^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c^3*abs(a)) - 1/120*(15*a^3 + 165*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a/x - 4234*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a*x^2) + 14330*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^3*x^3) - 20965*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^5*x^4) + 14385*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^7*x^5) - 4080*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^9*x^6))*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a)) - 1/8*(16*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c^3*abs(a)/x + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3*abs(a)/(a*x^2))/(a^2*c^6)","B",0
353,1,393,0,0.400388," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a*c*x+c)^3,x, algorithm=""giac"")","-\frac{18 \, a^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{c^{3} {\left| a \right|}} - \frac{{\left(5 \, a^{4} + \frac{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2}}{x} + \frac{335 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{x^{2}} - \frac{7559 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{2} x^{3}} + \frac{25195 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{4} x^{4}} - \frac{36035 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{6} x^{5}} + \frac{24225 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{8} x^{6}} - \frac{6585 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7}}{a^{10} x^{7}}\right)} a^{6} x^{3}}{120 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}} - \frac{\frac{117 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{6}}{x} + \frac{12 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{6}}{x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{6}}{x^{3}}}{24 \, a^{2} c^{9} {\left| a \right|}}"," ",0,"-18*a^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c^3*abs(a)) - 1/120*(5*a^4 + 35*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2/x + 335*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/x^2 - 7559*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^2*x^3) + 25195*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^4*x^4) - 36035*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^6*x^5) + 24225*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^8*x^6) - 6585*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^7/(a^10*x^7))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a)) - 1/24*(117*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^6/x + 12*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^6/x^2 + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^6/x^3)/(a^2*c^9*abs(a))","B",0
354,1,252,0,0.169039," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{x}{a^{5} c^{4}} + \frac{10}{a^{6} c^{4}}\right)} + \frac{29 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, a^{5} c^{4} {\left| a \right|}} + \frac{2 \, {\left(\frac{11599 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{29442 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{38500 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{26845 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} + \frac{9765 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{10} x^{5}} - \frac{1470 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{12} x^{6}} - 1867\right)}}{105 \, a^{5} c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{7} {\left| a \right|}}"," ",0,"-1/2*sqrt(-a^2*x^2 + 1)*(x/(a^5*c^4) + 10/(a^6*c^4)) + 29/2*arcsin(a*x)*sgn(a)/(a^5*c^4*abs(a)) + 2/105*(11599*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 29442*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 38500*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 26845*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) + 9765*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^10*x^5) - 1470*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^12*x^6) - 1867)/(a^5*c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^7*abs(a))","A",0
355,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a*c*x+c)^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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
356,1,220,0,0.203629," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a*c*x+c)^4,x, algorithm=""giac"")","\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{a^{3} c^{4} {\left| a \right|}} + \frac{2 \, {\left(\frac{1057 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{2751 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{3640 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{2170 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} + \frac{735 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{10} x^{5}} - \frac{105 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{12} x^{6}} - 166\right)}}{105 \, a^{3} c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{7} {\left| a \right|}}"," ",0,"arcsin(a*x)*sgn(a)/(a^3*c^4*abs(a)) + 2/105*(1057*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 2751*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 3640*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 2170*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) + 735*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^10*x^5) - 105*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^12*x^6) - 166)/(a^3*c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^7*abs(a))","A",0
357,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a*c*x+c)^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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
358,1,148,0,0.506385," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a*c*x+c)^4,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{7 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} + \frac{28 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{7 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} + \frac{21 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{10} x^{5}} - 1\right)}}{21 \, a c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{7} {\left| a \right|}}"," ",0,"2/21*(7*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 28*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 7*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) + 21*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^10*x^5) - 1)/(a*c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^7*abs(a))","A",0
359,1,199,0,0.264893," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{56 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{273 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{350 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{455 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} + \frac{210 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{10} x^{5}} - \frac{105 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{12} x^{6}} - 23\right)}}{105 \, c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{7} {\left| a \right|}}"," ",0,"-2/105*(56*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 273*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 350*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 455*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) + 210*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^10*x^5) - 105*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^12*x^6) - 23)/(c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^7*abs(a))","B",0
360,1,243,0,0.260660," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{a \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{c^{4} {\left| a \right|}} + \frac{2 \, {\left(296 \, a - \frac{1547 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a x} + \frac{4011 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{3} x^{2}} - \frac{5600 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{5} x^{3}} + \frac{4760 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{7} x^{4}} - \frac{2205 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{9} x^{5}} + \frac{525 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{11} x^{6}}\right)}}{105 \, c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{7} {\left| a \right|}}"," ",0,"-a*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c^4*abs(a)) + 2/105*(296*a - 1547*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a*x) + 4011*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^3*x^2) - 5600*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^5*x^3) + 4760*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^7*x^4) - 2205*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^9*x^5) + 525*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^11*x^6))/(c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^7*abs(a))","B",0
361,1,323,0,0.230577," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{5 \, a^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{c^{4} {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{2 \, c^{4} x {\left| a \right|}} - \frac{{\left(105 \, a^{2} - \frac{4831 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{x} + \frac{24997 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{2} x^{2}} - \frac{61131 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{4} x^{3}} + \frac{82915 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{6} x^{4}} - \frac{66325 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{8} x^{5}} + \frac{29295 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{10} x^{6}} - \frac{5985 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7}}{a^{12} x^{7}}\right)} a^{2} x}{210 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{7} {\left| a \right|}}"," ",0,"-5*a^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c^4*abs(a)) - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(c^4*x*abs(a)) - 1/210*(105*a^2 - 4831*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/x + 24997*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^2*x^2) - 61131*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^4*x^3) + 82915*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^6*x^4) - 66325*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^8*x^5) + 29295*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^10*x^6) - 5985*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^7/(a^12*x^7))*a^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^7*abs(a))","B",0
362,1,392,0,0.523901," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a*c*x+c)^4,x, algorithm=""giac"")","-\frac{29 \, a^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, c^{4} {\left| a \right|}} - \frac{{\left(105 \, a^{3} + \frac{1365 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a}{x} - \frac{51167 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a x^{2}} + \frac{260729 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{3} x^{3}} - \frac{621537 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{5} x^{4}} + \frac{826175 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{7} x^{5}} - \frac{642005 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{9} x^{6}} + \frac{274995 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7}}{a^{11} x^{7}} - \frac{52500 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{8}}{a^{13} x^{8}}\right)} a^{4} x^{2}}{840 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{7} {\left| a \right|}} - \frac{\frac{20 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c^{4} {\left| a \right|}}{x} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4} {\left| a \right|}}{a x^{2}}}{8 \, a^{2} c^{8}}"," ",0,"-29/2*a^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c^4*abs(a)) - 1/840*(105*a^3 + 1365*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a/x - 51167*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a*x^2) + 260729*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^3*x^3) - 621537*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^5*x^4) + 826175*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^7*x^5) - 642005*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^9*x^6) + 274995*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^7/(a^11*x^7) - 52500*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^8/(a^13*x^8))*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^7*abs(a)) - 1/8*(20*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c^4*abs(a)/x + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4*abs(a)/(a*x^2))/(a^2*c^8)","B",0
363,1,21,0,0.184427," ","integrate((1+x)^2/(-x^2+1)^(1/2)*x,x, algorithm=""giac"")","-\frac{1}{3} \, {\left({\left(x + 3\right)} x + 5\right)} \sqrt{-x^{2} + 1} + \arcsin\left(x\right)"," ",0,"-1/3*((x + 3)*x + 5)*sqrt(-x^2 + 1) + arcsin(x)","A",0
364,1,19,0,0.185058," ","integrate((1+x)^2/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-x^{2} + 1} {\left(x + 4\right)} + \frac{3}{2} \, \arcsin\left(x\right)"," ",0,"-1/2*sqrt(-x^2 + 1)*(x + 4) + 3/2*arcsin(x)","A",0
365,1,28,0,0.244036," ","integrate((1+x)^3/(-x^2+1)^(1/2)*x,x, algorithm=""giac"")","-\frac{1}{8} \, {\left({\left(2 \, {\left(x + 4\right)} x + 15\right)} x + 24\right)} \sqrt{-x^{2} + 1} + \frac{15}{8} \, \arcsin\left(x\right)"," ",0,"-1/8*((2*(x + 4)*x + 15)*x + 24)*sqrt(-x^2 + 1) + 15/8*arcsin(x)","A",0
366,1,25,0,0.181233," ","integrate((1+x)^3/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{6} \, {\left({\left(2 \, x + 9\right)} x + 22\right)} \sqrt{-x^{2} + 1} + \frac{5}{2} \, \arcsin\left(x\right)"," ",0,"-1/6*((2*x + 9)*x + 22)*sqrt(-x^2 + 1) + 5/2*arcsin(x)","A",0
367,1,11,0,0.288583," ","integrate(x/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\sqrt{-x^{2} + 1}"," ",0,"-sqrt(-x^2 + 1)","C",0
368,1,2,0,0.181124," ","integrate(1/(-x^2+1)^(1/2),x, algorithm=""giac"")","\arcsin\left(x\right)"," ",0,"arcsin(x)","A",0
369,1,24,0,0.179625," ","integrate(1/(1+x)/(-x^2+1)^(1/2)*x,x, algorithm=""giac"")","-\frac{2}{\frac{\sqrt{-x^{2} + 1} - 1}{x} - 1} + \arcsin\left(x\right)"," ",0,"-2/((sqrt(-x^2 + 1) - 1)/x - 1) + arcsin(x)","A",0
370,1,21,0,0.157879," ","integrate(1/(1+x)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{2}{\frac{\sqrt{-x^{2} + 1} - 1}{x} - 1}"," ",0,"2/((sqrt(-x^2 + 1) - 1)/x - 1)","A",0
371,-2,0,0,0.000000," ","integrate((1+x)^(5/2)/(-x^2+1)^(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(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
372,-2,0,0,0.000000," ","integrate((1+x)^(5/2)/(-x^2+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(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
373,1,27,0,0.432284," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2)*x,x, algorithm=""giac"")","-\frac{2}{7} \, {\left(x + 1\right)}^{\frac{7}{2}} + \frac{6}{5} \, {\left(x + 1\right)}^{\frac{5}{2}} - \frac{4}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} + \frac{16}{105} \, \sqrt{2}"," ",0,"-2/7*(x + 1)^(7/2) + 6/5*(x + 1)^(5/2) - 4/3*(x + 1)^(3/2) + 16/105*sqrt(2)","A",0
374,1,20,0,0.221494," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2),x, algorithm=""giac"")","-\frac{2}{5} \, {\left(x + 1\right)}^{\frac{5}{2}} + \frac{4}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} - \frac{16}{15} \, \sqrt{2}"," ",0,"-2/5*(x + 1)^(5/2) + 4/3*(x + 1)^(3/2) - 16/15*sqrt(2)","A",0
375,-2,0,0,0.000000," ","integrate((1+x)^(3/2)/(-x^2+1)^(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(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
376,-2,0,0,0.000000," ","integrate((1+x)^(3/2)/(-x^2+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(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
377,1,20,0,0.157614," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2)*x,x, algorithm=""giac"")","\frac{2}{5} \, {\left(x + 1\right)}^{\frac{5}{2}} - \frac{2}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} - \frac{4}{15} \, \sqrt{2}"," ",0,"2/5*(x + 1)^(5/2) - 2/3*(x + 1)^(3/2) - 4/15*sqrt(2)","A",0
378,1,13,0,0.404075," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} - \frac{4}{3} \, \sqrt{2}"," ",0,"2/3*(x + 1)^(3/2) - 4/3*sqrt(2)","A",0
379,-2,0,0,0.000000," ","integrate((1+x)^(1/2)/(-x^2+1)^(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(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
380,1,15,0,0.179699," ","integrate((1+x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{2} - 2 \, \sqrt{-x + 1}"," ",0,"2*sqrt(2) - 2*sqrt(-x + 1)","A",0
381,1,44,0,0.172045," ","integrate((1+x)/(-x^2+1)^(1/2)*x/(1-x)^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} - \sqrt{2} \log\left(\frac{\sqrt{2} - \sqrt{x + 1}}{\sqrt{2} + \sqrt{x + 1}}\right) - 2 \, \sqrt{x + 1}"," ",0,"-2/3*(x + 1)^(3/2) - sqrt(2)*log((sqrt(2) - sqrt(x + 1))/(sqrt(2) + sqrt(x + 1))) - 2*sqrt(x + 1)","A",0
382,1,37,0,0.234369," ","integrate((1+x)/(-x^2+1)^(1/2)/(1-x)^(1/2),x, algorithm=""giac"")","-\sqrt{2} \log\left(\frac{\sqrt{2} - \sqrt{x + 1}}{\sqrt{2} + \sqrt{x + 1}}\right) - 2 \, \sqrt{x + 1}"," ",0,"-sqrt(2)*log((sqrt(2) - sqrt(x + 1))/(sqrt(2) + sqrt(x + 1))) - 2*sqrt(x + 1)","A",0
383,1,43,0,0.501187," ","integrate(1/(1+x)^(1/2)/(-x^2+1)^(1/2)*x,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(\frac{\sqrt{2} - \sqrt{-x + 1}}{\sqrt{2} + \sqrt{-x + 1}}\right) - 2 \, \sqrt{-x + 1}"," ",0,"-1/2*sqrt(2)*log((sqrt(2) - sqrt(-x + 1))/(sqrt(2) + sqrt(-x + 1))) - 2*sqrt(-x + 1)","A",0
384,1,37,0,0.311156," ","integrate(1/(1+x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(\sqrt{2} + \sqrt{-x + 1}\right) + \frac{1}{2} \, \sqrt{2} \log\left(\sqrt{2} - \sqrt{-x + 1}\right)"," ",0,"-1/2*sqrt(2)*log(sqrt(2) + sqrt(-x + 1)) + 1/2*sqrt(2)*log(sqrt(2) - sqrt(-x + 1))","B",0
385,1,49,0,0.186613," ","integrate((1+x)/(-x^2+1)^(1/2)*x/(1-x)^(3/2),x, algorithm=""giac"")","\frac{5}{4} \, \sqrt{2} \log\left(\frac{\sqrt{2} - \sqrt{x + 1}}{\sqrt{2} + \sqrt{x + 1}}\right) + 2 \, \sqrt{x + 1} - \frac{\sqrt{x + 1}}{x - 1}"," ",0,"5/4*sqrt(2)*log((sqrt(2) - sqrt(x + 1))/(sqrt(2) + sqrt(x + 1))) + 2*sqrt(x + 1) - sqrt(x + 1)/(x - 1)","A",0
386,1,42,0,0.193459," ","integrate((1+x)/(-x^2+1)^(1/2)/(1-x)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{\sqrt{2} - \sqrt{x + 1}}{\sqrt{2} + \sqrt{x + 1}}\right) - \frac{\sqrt{x + 1}}{x - 1}"," ",0,"1/4*sqrt(2)*log((sqrt(2) - sqrt(x + 1))/(sqrt(2) + sqrt(x + 1))) - sqrt(x + 1)/(x - 1)","A",0
387,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a c x + c} {\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(-a*c*x + c)*(a*x + 1)*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
388,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
389,1,54,0,0.197193," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, c^{2} {\left(\frac{2 \, \sqrt{2}}{a \sqrt{c}} - \frac{3 \, {\left(a c x + c\right)}^{\frac{5}{2}} - 5 \, {\left(a c x + c\right)}^{\frac{3}{2}} c}{a c^{3}}\right)}}{15 \, a {\left| c \right|}}"," ",0,"-2/15*c^2*(2*sqrt(2)/(a*sqrt(c)) - (3*(a*c*x + c)^(5/2) - 5*(a*c*x + c)^(3/2)*c)/(a*c^3))/(a*abs(c))","A",0
390,1,34,0,0.206695," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, c^{2} {\left(\frac{2 \, \sqrt{2}}{\sqrt{c}} - \frac{{\left(a c x + c\right)}^{\frac{3}{2}}}{c^{2}}\right)}}{3 \, a {\left| c \right|}}"," ",0,"-2/3*c^2*(2*sqrt(2)/sqrt(c) - (a*c*x + c)^(3/2)/c^2)/(a*abs(c))","A",0
391,1,83,0,0.157418," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2)/x,x, algorithm=""giac"")","\frac{2 \, c^{3} {\left(\frac{\arctan\left(\frac{\sqrt{a c x + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c} - \frac{\sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{c}}{\sqrt{-c}}\right) + \sqrt{2} \sqrt{-c}}{\sqrt{-c} c^{\frac{3}{2}}} + \frac{\sqrt{a c x + c}}{c^{2}}\right)}}{{\left| c \right|}}"," ",0,"2*c^3*(arctan(sqrt(a*c*x + c)/sqrt(-c))/(sqrt(-c)*c) - (sqrt(c)*arctan(sqrt(2)*sqrt(c)/sqrt(-c)) + sqrt(2)*sqrt(-c))/(sqrt(-c)*c^(3/2)) + sqrt(a*c*x + c)/c^2)/abs(c)","A",0
392,1,97,0,0.169128," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""giac"")","\frac{{\left(\frac{a^{2} \arctan\left(\frac{\sqrt{a c x + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{a^{2} \sqrt{c} \arctan\left(\frac{\sqrt{2} \sqrt{c}}{\sqrt{-c}}\right) - \sqrt{2} a^{2} \sqrt{-c}}{\sqrt{-c} \sqrt{c}} - \frac{\sqrt{a c x + c} a}{c x}\right)} c^{2}}{a {\left| c \right|}}"," ",0,"(a^2*arctan(sqrt(a*c*x + c)/sqrt(-c))/sqrt(-c) - (a^2*sqrt(c)*arctan(sqrt(2)*sqrt(c)/sqrt(-c)) - sqrt(2)*a^2*sqrt(-c))/(sqrt(-c)*sqrt(c)) - sqrt(a*c*x + c)*a/(c*x))*c^2/(a*abs(c))","A",0
393,1,189,0,0.482334," ","integrate((a*x+1)^2/(-a^2*x^2+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
394,1,142,0,0.166286," ","integrate((a*x+1)^2/(-a^2*x^2+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
395,1,92,0,0.156410," ","integrate((a*x+1)^2/(-a^2*x^2+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
396,1,44,0,0.156349," ","integrate((a*x+1)^2/(-a^2*x^2+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
397,1,40,0,0.200078," ","integrate((a*x+1)^2/(-a^2*x^2+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
398,1,47,0,0.169831," ","integrate((a*x+1)^2/(-a^2*x^2+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
399,1,76,0,0.184755," ","integrate((a*x+1)^2/(-a^2*x^2+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
400,1,104,0,0.166766," ","integrate((a*x+1)^2/(-a^2*x^2+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
401,1,131,0,0.389328," ","integrate((a*x+1)^2/(-a^2*x^2+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
402,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a*c*x+c)^(1/2),x, algorithm=""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
403,1,130,0,0.248065," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a*c*x+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, c^{2} {\left(\frac{2 \, \sqrt{2} {\left(21 \, c \arctan\left(\frac{\sqrt{c}}{\sqrt{-c}}\right) + 40 \, \sqrt{-c} \sqrt{c}\right)}}{a^{2} \sqrt{-c} c} - \frac{\frac{42 \, \sqrt{2} c^{4} \arctan\left(\frac{\sqrt{2} \sqrt{a c x + c}}{2 \, \sqrt{-c}}\right)}{\sqrt{-c}} + 3 \, {\left(a c x + c\right)}^{\frac{7}{2}} + 7 \, {\left(a c x + c\right)}^{\frac{3}{2}} c^{2} + 42 \, \sqrt{a c x + c} c^{3}}{a^{2} c^{4}}\right)}}{21 \, a {\left| c \right|}}"," ",0,"2/21*c^2*(2*sqrt(2)*(21*c*arctan(sqrt(c)/sqrt(-c)) + 40*sqrt(-c)*sqrt(c))/(a^2*sqrt(-c)*c) - (42*sqrt(2)*c^4*arctan(1/2*sqrt(2)*sqrt(a*c*x + c)/sqrt(-c))/sqrt(-c) + 3*(a*c*x + c)^(7/2) + 7*(a*c*x + c)^(3/2)*c^2 + 42*sqrt(a*c*x + c)*c^3)/(a^2*c^4))/(a*abs(c))","A",0
404,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a*c*x+c)^(1/2),x, algorithm=""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
405,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
406,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x,x, algorithm=""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
407,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^2,x, algorithm=""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
408,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^3,x, algorithm=""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
409,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^4,x, algorithm=""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
410,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a*c*x+c)^(1/2)/x^5,x, algorithm=""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
411,0,0,0,0.000000," ","integrate(x^m*(-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{-a c x + c} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(-a*c*x + c)*x^m/(a*x + 1), x)","F",0
412,-2,0,0,0.000000," ","integrate(x^2*(-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
413,1,65,0,0.947396," ","integrate(x*(-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{8 \, \sqrt{2} {\left| c \right|}}{5 \, a^{2} \sqrt{c}} - \frac{4 \, \sqrt{a c x + c} {\left| c \right|}}{a^{2} c} - \frac{2 \, {\left({\left(a c x + c\right)}^{\frac{5}{2}} {\left| c \right|} - 5 \, {\left(a c x + c\right)}^{\frac{3}{2}} c {\left| c \right|}\right)}}{5 \, a^{2} c^{3}}"," ",0,"8/5*sqrt(2)*abs(c)/(a^2*sqrt(c)) - 4*sqrt(a*c*x + c)*abs(c)/(a^2*c) - 2/5*((a*c*x + c)^(5/2)*abs(c) - 5*(a*c*x + c)^(3/2)*c*abs(c))/(a^2*c^3)","A",0
414,1,50,0,0.376967," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{8 \, \sqrt{2} {\left| c \right|}}{3 \, a \sqrt{c}} - \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,"-8/3*sqrt(2)*abs(c)/(a*sqrt(c)) - 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
415,1,82,0,0.154156," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+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|} - \frac{2 \, {\left(\sqrt{c} {\left| c \right|} \arctan\left(\frac{\sqrt{2} \sqrt{c}}{\sqrt{-c}}\right) - \sqrt{2} \sqrt{-c} {\left| c \right|}\right)}}{\sqrt{-c} \sqrt{c}}"," ",0,"2*(arctan(sqrt(a*c*x + c)/sqrt(-c))/sqrt(-c) - sqrt(a*c*x + c)/c)*abs(c) - 2*(sqrt(c)*abs(c)*arctan(sqrt(2)*sqrt(c)/sqrt(-c)) - sqrt(2)*sqrt(-c)*abs(c))/(sqrt(-c)*sqrt(c))","A",0
416,1,90,0,1.017327," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+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|} + \frac{3 \, a \sqrt{c} {\left| c \right|} \arctan\left(\frac{\sqrt{2} \sqrt{c}}{\sqrt{-c}}\right) + \sqrt{2} a \sqrt{-c} {\left| c \right|}}{\sqrt{-c} \sqrt{c}}"," ",0,"-a*(3*arctan(sqrt(a*c*x + c)/sqrt(-c))/sqrt(-c) + sqrt(a*c*x + c)/(a*c*x))*abs(c) + (3*a*sqrt(c)*abs(c)*arctan(sqrt(2)*sqrt(c)/sqrt(-c)) + sqrt(2)*a*sqrt(-c)*abs(c))/(sqrt(-c)*sqrt(c))","A",0
417,1,117,0,0.207413," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""giac"")","\frac{1}{4} \, a^{2} c {\left(\frac{7 \, \arctan\left(\frac{\sqrt{a c x + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c} + \frac{7 \, {\left(a c x + c\right)}^{\frac{3}{2}} - 9 \, \sqrt{a c x + c} c}{a^{2} c^{3} x^{2}}\right)} {\left| c \right|} - \frac{7 \, a^{2} c {\left| c \right|} \arctan\left(\frac{\sqrt{2} \sqrt{c}}{\sqrt{-c}}\right) + 5 \, \sqrt{2} a^{2} \sqrt{-c} \sqrt{c} {\left| c \right|}}{4 \, \sqrt{-c} c}"," ",0,"1/4*a^2*c*(7*arctan(sqrt(a*c*x + c)/sqrt(-c))/(sqrt(-c)*c) + (7*(a*c*x + c)^(3/2) - 9*sqrt(a*c*x + c)*c)/(a^2*c^3*x^2))*abs(c) - 1/4*(7*a^2*c*abs(c)*arctan(sqrt(2)*sqrt(c)/sqrt(-c)) + 5*sqrt(2)*a^2*sqrt(-c)*sqrt(c)*abs(c))/(sqrt(-c)*c)","A",0
418,1,132,0,0.259759," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{1}{24} \, a^{3} c^{2} {\left(\frac{33 \, \arctan\left(\frac{\sqrt{a c x + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c^{2}} + \frac{33 \, {\left(a c x + c\right)}^{\frac{5}{2}} - 88 \, {\left(a c x + c\right)}^{\frac{3}{2}} c + 63 \, \sqrt{a c x + c} c^{2}}{a^{3} c^{5} x^{3}}\right)} {\left| c \right|} + \frac{33 \, a^{3} c {\left| c \right|} \arctan\left(\frac{\sqrt{2} \sqrt{c}}{\sqrt{-c}}\right) + 19 \, \sqrt{2} a^{3} \sqrt{-c} \sqrt{c} {\left| c \right|}}{24 \, \sqrt{-c} c}"," ",0,"-1/24*a^3*c^2*(33*arctan(sqrt(a*c*x + c)/sqrt(-c))/(sqrt(-c)*c^2) + (33*(a*c*x + c)^(5/2) - 88*(a*c*x + c)^(3/2)*c + 63*sqrt(a*c*x + c)*c^2)/(a^3*c^5*x^3))*abs(c) + 1/24*(33*a^3*c*abs(c)*arctan(sqrt(2)*sqrt(c)/sqrt(-c)) + 19*sqrt(2)*a^3*sqrt(-c)*sqrt(c)*abs(c))/(sqrt(-c)*c)","A",0
419,1,159,0,0.188655," ","integrate(x^3*(-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
420,1,105,0,0.166065," ","integrate(x^2*(-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
421,1,105,0,0.267354," ","integrate(x*(-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
422,1,77,0,0.172888," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
423,1,67,0,0.174067," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
424,1,72,0,0.184931," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
425,1,106,0,0.195820," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
426,1,133,0,0.150931," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
427,1,160,0,0.179483," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
428,-2,0,0,0.000000," ","integrate(x^3*(-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
429,-2,0,0,0.000000," ","integrate(x^2*(-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
430,-2,0,0,0.000000," ","integrate(x*(-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
431,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
432,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x, algorithm=""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
433,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""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
434,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""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
435,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""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
436,-2,0,0,0.000000," ","integrate((-a*c*x+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x, algorithm=""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
437,0,0,0,0.000000," ","integrate((-a*c*x+c)^p/exp(2*p*arctanh(a*x)),x, algorithm=""giac"")","\int \frac{{\left(-a c x + c\right)}^{p}}{\left(\frac{a x + 1}{a x - 1}\right)^{p}}\,{d x}"," ",0,"integrate((-a*c*x + c)^p/((a*x + 1)/(a*x - 1))^p, x)","F",0
438,0,0,0,0.000000," ","integrate(exp(2*p*arctanh(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)^{p}\,{d x}"," ",0,"integrate((-a*c*x + c)^p*((a*x + 1)/(a*x - 1))^p, x)","F",0
439,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
440,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
441,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
442,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
443,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
444,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
445,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
446,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
447,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^p/sqrt(-a^2*x^2 + 1), x)","F",0
448,1,263,0,0.431186," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^4,x, algorithm=""giac"")","\frac{{\left(c^{4} - \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4}}{a^{2} x} + \frac{33 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4}}{a^{4} x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} - \frac{3 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{a} - \frac{\frac{33 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4}}{x} - \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4}}{a^{2} x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{a^{4} x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(c^4 - 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4/(a^2*x) + 33*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4/(a^4*x^2))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) - 3*c^4*arcsin(a*x)*sgn(a)/abs(a) - 1/2*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c^4/a - 1/24*(33*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4/x - 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4/(a^2*x^2) + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/(a^4*x^3))/(a^2*abs(a))","B",0
449,1,207,0,0.379286," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^3,x, algorithm=""giac"")","-\frac{{\left(c^{3} - \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3}}{a^{2} x}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}} - \frac{2 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{a} - \frac{\frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3} {\left| a \right|}}{a^{2} x} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3} {\left| a \right|}}{a^{4} x^{2}}}{8 \, a^{2}}"," ",0,"-1/8*(c^3 - 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3/(a^2*x))*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)) - 2*c^3*arcsin(a*x)*sgn(a)/abs(a) + 1/2*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c^3/a - 1/8*(8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3*abs(a)/(a^2*x) - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3*abs(a)/(a^4*x^2))/a^2","B",0
450,1,139,0,0.440543," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^2,x, algorithm=""giac"")","\frac{a^{2} c^{2} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} - \frac{c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{2 \, a^{2} x {\left| a \right|}}"," ",0,"1/2*a^2*c^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) - c^2*arcsin(a*x)*sgn(a)/abs(a) + c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c^2/a - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/(a^2*x*abs(a))","B",0
451,1,58,0,0.216318," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x),x, algorithm=""giac"")","\frac{c \log\left(\sqrt{-a^{2} x^{2} + 1} + 1\right) - c \log\left(-\sqrt{-a^{2} x^{2} + 1} + 1\right) - 2 \, \sqrt{-a^{2} x^{2} + 1} c}{2 \, a}"," ",0,"1/2*(c*log(sqrt(-a^2*x^2 + 1) + 1) - c*log(-sqrt(-a^2*x^2 + 1) + 1) - 2*sqrt(-a^2*x^2 + 1)*c)/a","A",0
452,1,73,0,0.193148," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x),x, algorithm=""giac"")","\frac{2 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a c} - \frac{4}{c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"2*arcsin(a*x)*sgn(a)/(c*abs(a)) - sqrt(-a^2*x^2 + 1)/(a*c) - 4/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
453,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
454,1,181,0,0.200956," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^3,x, algorithm=""giac"")","\frac{4 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c^{3} {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a c^{3}} + \frac{2 \, {\left(\frac{335 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{505 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{285 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{60 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} - 79\right)}}{15 \, c^{3} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"4*arcsin(a*x)*sgn(a)/(c^3*abs(a)) - sqrt(-a^2*x^2 + 1)/(a*c^3) + 2/15*(335*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 505*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 285*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 60*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) - 79)/(c^3*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","A",0
455,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
456,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a/x)^p,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a x}\right)}^{p}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(a*x + 1)^2*(c - c/(a*x))^p/(a^2*x^2 - 1), x)","F",0
457,1,59,0,0.158493," ","integrate((a*x+1)^2/(-a^2*x^2+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
458,1,39,0,0.198159," ","integrate((a*x+1)^2/(-a^2*x^2+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
459,1,38,0,0.203992," ","integrate((a*x+1)^2/(-a^2*x^2+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
460,1,18,0,0.200712," ","integrate((a*x+1)^2/(-a^2*x^2+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
461,1,14,0,0.175211," ","integrate((a*x+1)^2/(-a^2*x^2+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
462,1,37,0,0.362651," ","integrate((a*x+1)^2/(-a^2*x^2+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
463,1,42,0,0.159437," ","integrate((a*x+1)^2/(-a^2*x^2+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
464,1,51,0,0.184432," ","integrate((a*x+1)^2/(-a^2*x^2+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
465,1,59,0,0.168563," ","integrate((a*x+1)^2/(-a^2*x^2+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
466,1,262,0,0.223712," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^4,x, algorithm=""giac"")","\frac{{\left(c^{4} - \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4}}{a^{2} x} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4}}{a^{4} x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} + \frac{c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{3 \, c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{a} + \frac{\frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4}}{x} + \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4}}{a^{2} x^{2}} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{a^{4} x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(c^4 - 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4/(a^2*x) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4/(a^4*x^2))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) + c^4*arcsin(a*x)*sgn(a)/abs(a) - 3/2*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c^4/a + 1/24*(15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4/x + 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4/(a^2*x^2) - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/(a^4*x^3))/(a^2*abs(a))","B",0
467,1,97,0,0.359763," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^3,x, algorithm=""giac"")","-\frac{3 \, a^{4} c^{3} \log\left(\sqrt{-a^{2} x^{2} + 1} + 1\right) - 3 \, a^{4} c^{3} \log\left(-\sqrt{-a^{2} x^{2} + 1} + 1\right) - 4 \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{3} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3}}{x^{2}}}{4 \, a^{5}}"," ",0,"-1/4*(3*a^4*c^3*log(sqrt(-a^2*x^2 + 1) + 1) - 3*a^4*c^3*log(-sqrt(-a^2*x^2 + 1) + 1) - 4*sqrt(-a^2*x^2 + 1)*a^4*c^3 - 2*sqrt(-a^2*x^2 + 1)*a^2*c^3/x^2)/a^5","A",0
468,1,139,0,0.252395," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^2,x, algorithm=""giac"")","\frac{a^{2} c^{2} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} - \frac{c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{2 \, a^{2} x {\left| a \right|}}"," ",0,"1/2*a^2*c^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) - c^2*arcsin(a*x)*sgn(a)/abs(a) - c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c^2/a - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/(a^2*x*abs(a))","B",0
469,1,68,0,2.095616," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x),x, algorithm=""giac"")","-\frac{2 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c}{a}"," ",0,"-2*c*arcsin(a*x)*sgn(a)/abs(a) + c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c/a","A",0
470,1,126,0,0.196826," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x),x, algorithm=""giac"")","-\frac{4 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a c} - \frac{8 \, {\left(\frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} - 4\right)}}{3 \, c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{3} {\left| a \right|}}"," ",0,"-4*arcsin(a*x)*sgn(a)/(c*abs(a)) + sqrt(-a^2*x^2 + 1)/(a*c) - 8/3*(9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) - 4)/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^3*abs(a))","A",0
471,1,180,0,0.207673," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^2,x, algorithm=""giac"")","-\frac{5 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c^{2} {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a c^{2}} - \frac{2 \, {\left(\frac{440 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{670 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{360 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{75 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} - 103\right)}}{15 \, c^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"-5*arcsin(a*x)*sgn(a)/(c^2*abs(a)) + sqrt(-a^2*x^2 + 1)/(a*c^2) - 2/15*(440*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 670*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 360*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 75*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) - 103)/(c^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","A",0
472,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
473,1,288,0,0.670408," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^4,x, algorithm=""giac"")","-\frac{7 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c^{4} {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a c^{4}} - \frac{2 \, {\left(\frac{26136 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{93834 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{188706 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{229194 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} + \frac{167580 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5}}{a^{10} x^{5}} - \frac{75810 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6}}{a^{12} x^{6}} + \frac{19530 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7}}{a^{14} x^{7}} - \frac{2205 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{8}}{a^{16} x^{8}} - 3149\right)}}{315 \, c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{9} {\left| a \right|}}"," ",0,"-7*arcsin(a*x)*sgn(a)/(c^4*abs(a)) + sqrt(-a^2*x^2 + 1)/(a*c^4) - 2/315*(26136*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 93834*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 188706*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 229194*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) + 167580*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5/(a^10*x^5) - 75810*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6/(a^12*x^6) + 19530*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^7/(a^14*x^7) - 2205*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^8/(a^16*x^8) - 3149)/(c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^9*abs(a))","A",0
474,0,0,0,0.000000," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{4} {\left(c - \frac{c}{a x}\right)}^{p}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^4*(c - c/(a*x))^p/(a^2*x^2 - 1)^2, x)","F",0
475,1,60,0,0.198591," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^5,x, algorithm=""giac"")","c^{5} x - \frac{c^{5} \log\left({\left| x \right|}\right)}{a} + \frac{24 \, a^{3} c^{5} x^{3} - 12 \, a^{2} c^{5} x^{2} - 4 \, a c^{5} x + 3 \, c^{5}}{12 \, a^{5} x^{4}}"," ",0,"c^5*x - c^5*log(abs(x))/a + 1/12*(24*a^3*c^5*x^3 - 12*a^2*c^5*x^2 - 4*a*c^5*x + 3*c^5)/(a^5*x^4)","A",0
476,1,31,0,0.233947," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^4,x, algorithm=""giac"")","c^{4} x + \frac{6 \, a^{2} c^{4} x^{2} - c^{4}}{3 \, a^{4} x^{3}}"," ",0,"c^4*x + 1/3*(6*a^2*c^4*x^2 - c^4)/(a^4*x^3)","A",0
477,1,35,0,0.180943," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(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
478,1,28,0,0.200461," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x)^2,x, algorithm=""giac"")","c^{2} x + \frac{2 \, c^{2} \log\left({\left| x \right|}\right)}{a} - \frac{c^{2}}{a^{2} x}"," ",0,"c^2*x + 2*c^2*log(abs(x))/a - c^2/(a^2*x)","A",0
479,1,26,0,0.194287," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a/x),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
480,1,42,0,0.181915," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x),x, algorithm=""giac"")","\frac{x}{c} + \frac{5 \, \log\left({\left| a x - 1 \right|}\right)}{a c} - \frac{2 \, {\left(4 \, a x - 3\right)}}{{\left(a x - 1\right)}^{2} a c}"," ",0,"x/c + 5*log(abs(a*x - 1))/(a*c) - 2*(4*a*x - 3)/((a*x - 1)^2*a*c)","A",0
481,1,50,0,0.133711," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x)^2,x, algorithm=""giac"")","\frac{x}{c^{2}} + \frac{6 \, \log\left({\left| a x - 1 \right|}\right)}{a c^{2}} - \frac{39 \, a^{2} x^{2} - 60 \, a x + 25}{3 \, {\left(a x - 1\right)}^{3} a c^{2}}"," ",0,"x/c^2 + 6*log(abs(a*x - 1))/(a*c^2) - 1/3*(39*a^2*x^2 - 60*a*x + 25)/((a*x - 1)^3*a*c^2)","A",0
482,1,58,0,0.329698," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x)^3,x, algorithm=""giac"")","\frac{x}{c^{3}} + \frac{7 \, \log\left({\left| a x - 1 \right|}\right)}{a c^{3}} - \frac{114 \, a^{3} x^{3} - 267 \, a^{2} x^{2} + 224 \, a x - 65}{6 \, {\left(a x - 1\right)}^{4} a c^{3}}"," ",0,"x/c^3 + 7*log(abs(a*x - 1))/(a*c^3) - 1/6*(114*a^3*x^3 - 267*a^2*x^2 + 224*a*x - 65)/((a*x - 1)^4*a*c^3)","A",0
483,1,66,0,0.208937," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a/x)^4,x, algorithm=""giac"")","\frac{x}{c^{4}} + \frac{8 \, \log\left({\left| a x - 1 \right|}\right)}{a c^{4}} - \frac{390 \, a^{4} x^{4} - 1230 \, a^{3} x^{3} + 1555 \, a^{2} x^{2} - 905 \, a x + 202}{15 \, {\left(a x - 1\right)}^{5} a c^{4}}"," ",0,"x/c^4 + 8*log(abs(a*x - 1))/(a*c^4) - 1/15*(390*a^4*x^4 - 1230*a^3*x^3 + 1555*a^2*x^2 - 905*a*x + 202)/((a*x - 1)^5*a*c^4)","A",0
484,0,0,0,0.000000," ","integrate((c-c/a/x)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^p/(a*x + 1), x)","F",0
485,1,262,0,0.204174," ","integrate((c-c/a/x)^4/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{{\left(c^{4} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4}}{a^{2} x} + \frac{129 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4}}{a^{4} x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} + \frac{5 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{25 \, c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{a} - \frac{\frac{129 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4}}{x} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4}}{a^{2} x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{a^{4} x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(c^4 - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4/(a^2*x) + 129*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4/(a^4*x^2))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) + 5*c^4*arcsin(a*x)*sgn(a)/abs(a) + 25/2*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c^4/a - 1/24*(129*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4/x - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4/(a^2*x^2) + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/(a^4*x^3))/(a^2*abs(a))","B",0
486,1,206,0,0.208930," ","integrate((c-c/a/x)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{{\left(c^{3} - \frac{16 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3}}{a^{2} x}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}} + \frac{4 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{13 \, c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{a} - \frac{\frac{16 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3} {\left| a \right|}}{a^{2} x} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3} {\left| a \right|}}{a^{4} x^{2}}}{8 \, a^{2}}"," ",0,"-1/8*(c^3 - 16*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3/(a^2*x))*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)) + 4*c^3*arcsin(a*x)*sgn(a)/abs(a) + 13/2*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c^3/a - 1/8*(16*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3*abs(a)/(a^2*x) - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3*abs(a)/(a^4*x^2))/a^2","B",0
487,1,139,0,0.430603," ","integrate((c-c/a/x)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{a^{2} c^{2} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} + \frac{3 \, c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{3 \, c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{2 \, a^{2} x {\left| a \right|}}"," ",0,"1/2*a^2*c^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) + 3*c^2*arcsin(a*x)*sgn(a)/abs(a) + 3*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c^2/a - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/(a^2*x*abs(a))","A",0
488,1,68,0,0.208576," ","integrate((c-c/a/x)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{2 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c}{a}"," ",0,"2*c*arcsin(a*x)*sgn(a)/abs(a) + c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c/a","A",0
489,1,19,0,0.160326," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x),x, algorithm=""giac"")","\frac{\sqrt{-a^{2} x^{2} + 1}}{a c}"," ",0,"sqrt(-a^2*x^2 + 1)/(a*c)","A",0
490,1,72,0,2.107229," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^2,x, algorithm=""giac"")","-\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c^{2} {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a c^{2}} + \frac{2}{c^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"-arcsin(a*x)*sgn(a)/(c^2*abs(a)) + sqrt(-a^2*x^2 + 1)/(a*c^2) + 2/(c^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
491,-2,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
492,1,180,0,0.187972," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^4,x, algorithm=""giac"")","-\frac{3 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c^{4} {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a c^{4}} - \frac{2 \, {\left(\frac{80 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{120 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{70 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} - 19\right)}}{5 \, c^{4} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"-3*arcsin(a*x)*sgn(a)/(c^4*abs(a)) + sqrt(-a^2*x^2 + 1)/(a*c^4) - 2/5*(80*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 120*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 70*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) - 19)/(c^4*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","A",0
493,0,0,0,0.000000," ","integrate((c-c/a/x)^p/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a x}\right)}^{p}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*(c - c/(a*x))^p/(a*x + 1)^2, x)","F",0
494,1,112,0,0.167313," ","integrate((c-c/a/x)^4/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{6 \, c^{4} \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a} - \frac{26 \, c^{4} \log\left({\left| -\frac{1}{a x + 1} + 1 \right|}\right)}{a} + \frac{{\left(3 \, c^{4} + \frac{49 \, c^{4}}{a x + 1} - \frac{117 \, c^{4}}{{\left(a x + 1\right)}^{2}} + \frac{66 \, c^{4}}{{\left(a x + 1\right)}^{3}}\right)} {\left(a x + 1\right)}}{3 \, a {\left(\frac{1}{a x + 1} - 1\right)}^{3}}"," ",0,"-6*c^4*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a - 26*c^4*log(abs(-1/(a*x + 1) + 1))/a + 1/3*(3*c^4 + 49*c^4/(a*x + 1) - 117*c^4/(a*x + 1)^2 + 66*c^4/(a*x + 1)^3)*(a*x + 1)/(a*(1/(a*x + 1) - 1)^3)","A",0
495,1,100,0,3.792539," ","integrate((c-c/a/x)^3/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{5 \, c^{3} \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a} - \frac{11 \, c^{3} \log\left({\left| -\frac{1}{a x + 1} + 1 \right|}\right)}{a} - \frac{{\left(2 \, c^{3} + \frac{7 \, c^{3}}{a x + 1} - \frac{10 \, 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,"-5*c^3*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a - 11*c^3*log(abs(-1/(a*x + 1) + 1))/a - 1/2*(2*c^3 + 7*c^3/(a*x + 1) - 10*c^3/(a*x + 1)^2)*(a*x + 1)/(a*(1/(a*x + 1) - 1)^2)","A",0
496,1,72,0,1.984814," ","integrate((c-c/a/x)^2/(a*x+1)^2*(-a^2*x^2+1),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(a x + 1\right)} c^{2}}{a {\left(\frac{1}{a x + 1} - 1\right)}}"," ",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 + (a*x + 1)*c^2/(a*(1/(a*x + 1) - 1))","A",0
497,1,56,0,0.163373," ","integrate((c-c/a/x)/(a*x+1)^2*(-a^2*x^2+1),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
498,1,41,0,1.766683," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x),x, algorithm=""giac"")","-\frac{a x + 1}{a c} - \frac{\log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a c}"," ",0,"-(a*x + 1)/(a*c) - log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/(a*c)","B",0
499,1,35,0,0.163985," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^2,x, algorithm=""giac"")","-\frac{a x + 1}{a c^{2}} - \frac{\log\left({\left| -\frac{2}{a x + 1} + 1 \right|}\right)}{2 \, a c^{2}}"," ",0,"-(a*x + 1)/(a*c^2) - 1/2*log(abs(-2/(a*x + 1) + 1))/(a*c^2)","A",0
500,1,85,0,0.202235," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^3,x, algorithm=""giac"")","-\frac{{\left(a x + 1\right)} {\left(\frac{9}{a x + 1} - 4\right)}}{4 \, a c^{3} {\left(\frac{2}{a x + 1} - 1\right)}} + \frac{\log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a c^{3}} - \frac{5 \, \log\left({\left| -\frac{2}{a x + 1} + 1 \right|}\right)}{4 \, a c^{3}}"," ",0,"-1/4*(a*x + 1)*(9/(a*x + 1) - 4)/(a*c^3*(2/(a*x + 1) - 1)) + log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/(a*c^3) - 5/4*log(abs(-2/(a*x + 1) + 1))/(a*c^3)","A",0
501,1,95,0,0.177252," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a/x)^4,x, algorithm=""giac"")","\frac{2 \, \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a c^{4}} - \frac{17 \, \log\left({\left| -\frac{2}{a x + 1} + 1 \right|}\right)}{8 \, a c^{4}} + \frac{{\left(a x + 1\right)} {\left(\frac{77}{a x + 1} - \frac{88}{{\left(a x + 1\right)}^{2}} - 16\right)}}{16 \, a c^{4} {\left(\frac{2}{a x + 1} - 1\right)}^{2}}"," ",0,"2*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/(a*c^4) - 17/8*log(abs(-2/(a*x + 1) + 1))/(a*c^4) + 1/16*(a*x + 1)*(77/(a*x + 1) - 88/(a*x + 1)^2 - 16)/(a*c^4*(2/(a*x + 1) - 1)^2)","A",0
502,1,265,0,0.197903," ","integrate((c-c/a/x)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{6 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{{\left(c^{3} - \frac{23 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3}}{a^{2} x} - \frac{536 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3}}{a^{4} x^{2}}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}} + \frac{33 \, c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{a} - \frac{\frac{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3} {\left| a \right|}}{a^{2} x} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3} {\left| a \right|}}{a^{4} x^{2}}}{8 \, a^{2}}"," ",0,"-6*c^3*arcsin(a*x)*sgn(a)/abs(a) - 1/8*(c^3 - 23*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3/(a^2*x) - 536*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3/(a^4*x^2))*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a)) + 33/2*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c^3/a - 1/8*(24*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3*abs(a)/(a^2*x) - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3*abs(a)/(a^4*x^2))/a^2","B",0
503,1,197,0,0.201016," ","integrate((c-c/a/x)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{5 \, c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{5 \, c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a} + \frac{{\left(c^{2} + \frac{65 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{a^{2} x}\right)} a^{2} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{2 \, a^{2} x {\left| a \right|}}"," ",0,"-5*c^2*arcsin(a*x)*sgn(a)/abs(a) + 5*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c^2/a + 1/2*(c^2 + 65*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/(a^2*x))*a^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a)) - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/(a^2*x*abs(a))","A",0
504,1,104,0,4.041085," ","integrate((c-c/a/x)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{4 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c}{a} + \frac{16 \, c}{{\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"-4*c*arcsin(a*x)*sgn(a)/abs(a) + c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c/a + 16*c/(((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
505,1,73,0,1.816623," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x),x, algorithm=""giac"")","-\frac{2 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a c} + \frac{4}{c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"-2*arcsin(a*x)*sgn(a)/(c*abs(a)) - sqrt(-a^2*x^2 + 1)/(a*c) + 4/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
506,1,73,0,0.181122," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^2,x, algorithm=""giac"")","-\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c^{2} {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a c^{2}} + \frac{2}{c^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"-arcsin(a*x)*sgn(a)/(c^2*abs(a)) - sqrt(-a^2*x^2 + 1)/(a*c^2) + 2/(c^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
507,1,38,0,0.257040," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^3,x, algorithm=""giac"")","-\frac{\frac{\sqrt{-a^{2} x^{2} + 1}}{c^{3}} + \frac{1}{\sqrt{-a^{2} x^{2} + 1} c^{3}}}{a}"," ",0,"-(sqrt(-a^2*x^2 + 1)/c^3 + 1/(sqrt(-a^2*x^2 + 1)*c^3))/a","A",0
508,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^4,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{4}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a*x))^4), x)","F",0
509,-2,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
510,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^(9/2)/sqrt(-a^2*x^2 + 1), x)","F",0
511,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+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(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
512,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a*x))^(5/2)/sqrt(-a^2*x^2 + 1), x)","F",0
513,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+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(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
514,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/sqrt(-a^2*x^2 + 1), x)","F",0
515,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))), x)","F",0
516,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(3/2),x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a*x))^(3/2)), x)","F",0
517,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
518,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+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: 1.79Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
519,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+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%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
520,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+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
521,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+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
522,1,97,0,4.940351," ","integrate((a*x+1)^2/(-a^2*x^2+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
523,1,123,0,2.170737," ","integrate((a*x+1)^2/(-a^2*x^2+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
524,1,136,0,0.195296," ","integrate((a*x+1)^2/(-a^2*x^2+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
525,1,165,0,0.194665," ","integrate((a*x+1)^2/(-a^2*x^2+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
526,1,187,0,0.226813," ","integrate((a*x+1)^2/(-a^2*x^2+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
527,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{\frac{9}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a*x))^(9/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
528,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+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(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
529,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a*x))^(5/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
530,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+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(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
531,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+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(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
532,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a*x))), x)","F",0
533,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^(3/2)), x)","F",0
534,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a*x))^(5/2)), x)","F",0
535,-2,0,0,0.000000," ","integrate((c-c/a/x)^(9/2)/(a*x+1)*(-a^2*x^2+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)]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)^(7/2)/(a*x+1)*(-a^2*x^2+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)]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)^(5/2)/(a*x+1)*(-a^2*x^2+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)]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)^(3/2)/(a*x+1)*(-a^2*x^2+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)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
539,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/(a*x + 1), x)","F",0
540,-2,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+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: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(1/(a*x+1)*(-a^2*x^2+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: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(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a/x)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a*x))^(5/2)), x)","F",0
543,-2,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
544,-2,0,0,0.000000," ","integrate((c-c/a/x)^(9/2)/(a*x+1)^2*(-a^2*x^2+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
545,-2,0,0,0.000000," ","integrate((c-c/a/x)^(7/2)/(a*x+1)^2*(-a^2*x^2+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
546,-2,0,0,0.000000," ","integrate((c-c/a/x)^(5/2)/(a*x+1)^2*(-a^2*x^2+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
547,-2,0,0,0.000000," ","integrate((c-c/a/x)^(3/2)/(a*x+1)^2*(-a^2*x^2+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
548,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
549,1,130,0,0.219260," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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
550,1,129,0,0.178634," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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
551,1,166,0,0.196972," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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
552,1,187,0,0.191821," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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
553,1,207,0,0.192575," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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
554,-2,0,0,0.000000," ","integrate((c-c/a/x)^(9/2)/(a*x+1)^3*(-a^2*x^2+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)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
555,-2,0,0,0.000000," ","integrate((c-c/a/x)^(7/2)/(a*x+1)^3*(-a^2*x^2+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)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
556,-2,0,0,0.000000," ","integrate((c-c/a/x)^(5/2)/(a*x+1)^3*(-a^2*x^2+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)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
557,-2,0,0,0.000000," ","integrate((c-c/a/x)^(3/2)/(a*x+1)^3*(-a^2*x^2+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)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
558,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+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)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
559,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*sqrt(c - c/(a*x))), x)","F",0
560,-2,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(3/2),x, algorithm=""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
561,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a x}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a*x))^(5/2)), x)","F",0
562,-2,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a/x)^(7/2),x, algorithm=""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
563,1,217,0,0.217815," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a/x)/x^3,x, algorithm=""giac"")","\frac{4 \, a^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{c {\left| a \right|}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a}{2 \, c x {\left| a \right|}} + \frac{{\left(3 \, a^{3} - \frac{89 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a}{x} + \frac{153 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a x^{2}} - \frac{99 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{3} x^{3}}\right)} a^{2} x}{6 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{3} {\left| a \right|}}"," ",0,"4*a^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c*abs(a)) + 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a/(c*x*abs(a)) + 1/6*(3*a^3 - 89*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a/x + 153*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a*x^2) - 99*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^3*x^3))*a^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^3*abs(a))","B",0
564,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
565,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}} x^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))*x^2/sqrt(-a^2*x^2 + 1), x)","F",0
566,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}} x}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))*x/sqrt(-a^2*x^2 + 1), x)","F",0
567,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/sqrt(-a^2*x^2 + 1), x)","F",0
568,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
569,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
570,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
571,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(sqrt(-a^2*x^2 + 1)*x^4), x)","F",0
572,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a x}}}{\sqrt{-a^{2} x^{2} + 1} x^{5}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a*x))/(sqrt(-a^2*x^2 + 1)*x^5), x)","F",0
573,1,142,0,0.208801," ","integrate((a*x+1)^2/(-a^2*x^2+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
574,1,127,0,0.253350," ","integrate((a*x+1)^2/(-a^2*x^2+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
575,1,112,0,0.224705," ","integrate((a*x+1)^2/(-a^2*x^2+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
576,1,97,0,0.227118," ","integrate((a*x+1)^2/(-a^2*x^2+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
577,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+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
578,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+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
579,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+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
580,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+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: 0.45Unable 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
581,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+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
582,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(c-c/a/x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a x}} x^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a*x))*x^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
583,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(c-c/a/x)^(1/2),x, algorithm=""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
584,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(c-c/a/x)^(1/2),x, algorithm=""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
585,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+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(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
586,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x,x, algorithm=""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
587,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^2,x, algorithm=""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
588,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^3,x, algorithm=""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
589,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^4,x, algorithm=""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
590,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a/x)^(1/2)/x^5,x, algorithm=""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
591,0,0,0,0.000000," ","integrate(x^m*(c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))*x^m/(a*x + 1), x)","F",0
592,-2,0,0,0.000000," ","integrate(x^2*(c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""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]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
593,0,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}} x}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))*x/(a*x + 1), x)","F",0
594,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/(a*x + 1), x)","F",0
595,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/((a*x + 1)*x), x)","F",0
596,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/((a*x + 1)*x^2), x)","F",0
597,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/((a*x + 1)*x^3), x)","F",0
598,0,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a x}}}{{\left(a x + 1\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a*x))/((a*x + 1)*x^4), x)","F",0
599,-2,0,0,0.000000," ","integrate(x^3*(c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
600,-2,0,0,0.000000," ","integrate(x^2*(c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
601,-2,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
602,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
603,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
604,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
605,1,278,0,1.181347," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
606,1,356,0,1.231466," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
607,1,434,0,2.349996," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
608,-2,0,0,0.000000," ","integrate(x^3*(c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""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
609,-2,0,0,0.000000," ","integrate(x^2*(c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+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)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
610,-2,0,0,0.000000," ","integrate(x*(c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""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
611,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+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)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
612,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x, algorithm=""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
613,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""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
614,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""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
615,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""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
616,-2,0,0,0.000000," ","integrate((c-c/a/x)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x, algorithm=""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
617,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
618,0,0,0,0.000000," ","integrate((c-c/a/x)^p/exp(2*p*arctanh(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
619,0,0,0,0.000000," ","integrate(exp(2*p*arctanh(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
620,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a/x)^2,x, algorithm=""giac"")","\int {\left(c - \frac{c}{a x}\right)}^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a*x))^2*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
621,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a/x),x, algorithm=""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
622,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
623,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
624,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
625,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
626,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
627,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
628,1,505,0,0.211084," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\frac{{\left(15 \, c^{4} + \frac{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4}}{a^{2} x} - \frac{189 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4}}{a^{4} x^{2}} - \frac{525 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{a^{6} x^{3}} + \frac{1295 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{4}}{a^{8} x^{4}} + \frac{4935 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{4}}{a^{10} x^{5}} - \frac{9765 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} c^{4}}{a^{12} x^{6}}\right)} a^{14} x^{7}}{13440 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7} {\left| a \right|}} + \frac{c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{35 \, c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{16 \, {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{a} + \frac{\frac{9765 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{4}}{x} - \frac{4935 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{4}}{x^{2}} - \frac{1295 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{x^{3}} + \frac{525 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{4}}{a^{2} x^{4}} + \frac{189 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{4}}{a^{4} x^{5}} - \frac{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} c^{4}}{a^{6} x^{6}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7} c^{4}}{a^{8} x^{7}}}{13440 \, a^{6} {\left| a \right|}}"," ",0,"1/13440*(15*c^4 + 35*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4/(a^2*x) - 189*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4/(a^4*x^2) - 525*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/(a^6*x^3) + 1295*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^4/(a^8*x^4) + 4935*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^4/(a^10*x^5) - 9765*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*c^4/(a^12*x^6))*a^14*x^7/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^7*abs(a)) + c^4*arcsin(a*x)*sgn(a)/abs(a) + 35/16*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c^4/a + 1/13440*(9765*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^4/x - 4935*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^4/x^2 - 1295*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/x^3 + 525*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^4/(a^2*x^4) + 189*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^4/(a^4*x^5) - 35*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*c^4/(a^6*x^6) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^7*c^4/(a^8*x^7))/(a^6*abs(a))","B",0
629,1,385,0,0.273476," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^3,x, algorithm=""giac"")","-\frac{{\left(6 \, c^{3} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3}}{a^{2} x} - \frac{70 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3}}{a^{4} x^{2}} - \frac{240 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{3}}{a^{6} x^{3}} + \frac{660 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{3}}{a^{8} x^{4}}\right)} a^{10} x^{5}}{960 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} {\left| a \right|}} + \frac{c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{15 \, c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{a} + \frac{\frac{660 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2} c^{3}}{x} - \frac{240 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3}}{x^{2}} - \frac{70 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{3}}{a^{2} x^{3}} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{3}}{a^{4} x^{4}} + \frac{6 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{3}}{a^{6} x^{5}}}{960 \, a^{4} {\left| a \right|}}"," ",0,"-1/960*(6*c^3 + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3/(a^2*x) - 70*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3/(a^4*x^2) - 240*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^3/(a^6*x^3) + 660*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^3/(a^8*x^4))*a^10*x^5/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*abs(a)) + c^3*arcsin(a*x)*sgn(a)/abs(a) + 15/8*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c^3/a + 1/960*(660*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2*c^3/x - 240*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3/x^2 - 70*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^3/(a^2*x^3) + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^3/(a^4*x^4) + 6*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^3/(a^6*x^5))/(a^4*abs(a))","B",0
630,1,263,0,0.574924," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\frac{{\left(c^{2} + \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{a^{2} x} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{2}}{a^{4} x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} + \frac{c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{3 \, c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a} + \frac{\frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{x} - \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{2}}{a^{2} x^{2}} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{2}}{a^{4} x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(c^2 + 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/(a^2*x) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^2/(a^4*x^2))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) + c^2*arcsin(a*x)*sgn(a)/abs(a) + 3/2*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c^2/a + 1/24*(15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/x - 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^2/(a^2*x^2) - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^2/(a^4*x^3))/(a^2*abs(a))","B",0
631,1,128,0,0.256219," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2),x, algorithm=""giac"")","-\frac{a^{2} c x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} + \frac{c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c}{a} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c}{2 \, a^{2} x {\left| a \right|}}"," ",0,"-1/2*a^2*c*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) + c*arcsin(a*x)*sgn(a)/abs(a) + c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c/a + 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c/(a^2*x*abs(a))","B",0
632,1,72,0,0.202058," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2),x, algorithm=""giac"")","\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a c} - \frac{2}{c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"arcsin(a*x)*sgn(a)/(c*abs(a)) - sqrt(-a^2*x^2 + 1)/(a*c) - 2/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
633,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^2), x)","F",0
634,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^3), x)","F",0
635,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{4}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^4), x)","F",0
636,1,116,0,0.188954," ","integrate((a*x+1)^2/(-a^2*x^2+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
637,1,83,0,0.202288," ","integrate((a*x+1)^2/(-a^2*x^2+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
638,1,72,0,0.192825," ","integrate((a*x+1)^2/(-a^2*x^2+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
639,1,37,0,0.189736," ","integrate((a*x+1)^2/(-a^2*x^2+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
640,1,22,0,0.188813," ","integrate((a*x+1)^2/(-a^2*x^2+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
641,1,36,0,0.182726," ","integrate((a*x+1)^2/(-a^2*x^2+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
642,1,58,0,0.178421," ","integrate((a*x+1)^2/(-a^2*x^2+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
643,1,81,0,0.173812," ","integrate((a*x+1)^2/(-a^2*x^2+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
644,1,97,0,0.396065," ","integrate((a*x+1)^2/(-a^2*x^2+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
645,1,505,0,0.242898," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\frac{{\left(5 \, c^{4} + \frac{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4}}{a^{2} x} + \frac{49 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4}}{a^{4} x^{2}} - \frac{245 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{a^{6} x^{3}} - \frac{875 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{4}}{a^{8} x^{4}} + \frac{455 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{4}}{a^{10} x^{5}} + \frac{9065 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} c^{4}}{a^{12} x^{6}}\right)} a^{14} x^{7}}{4480 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7} {\left| a \right|}} - \frac{3 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{15 \, c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{16 \, {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{a} - \frac{\frac{9065 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{4}}{x} + \frac{455 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{4}}{x^{2}} - \frac{875 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{x^{3}} - \frac{245 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{4}}{a^{2} x^{4}} + \frac{49 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{4}}{a^{4} x^{5}} + \frac{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} c^{4}}{a^{6} x^{6}} + \frac{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7} c^{4}}{a^{8} x^{7}}}{4480 \, a^{6} {\left| a \right|}}"," ",0,"1/4480*(5*c^4 + 35*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4/(a^2*x) + 49*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4/(a^4*x^2) - 245*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/(a^6*x^3) - 875*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^4/(a^8*x^4) + 455*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^4/(a^10*x^5) + 9065*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*c^4/(a^12*x^6))*a^14*x^7/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^7*abs(a)) - 3*c^4*arcsin(a*x)*sgn(a)/abs(a) - 15/16*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c^4/a - 1/4480*(9065*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^4/x + 455*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^4/x^2 - 875*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/x^3 - 245*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^4/(a^2*x^4) + 49*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^4/(a^4*x^5) + 35*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*c^4/(a^6*x^6) + 5*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^7*c^4/(a^8*x^7))/(a^6*abs(a))","B",0
646,1,385,0,0.508645," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^3,x, algorithm=""giac"")","-\frac{{\left(2 \, c^{3} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3}}{a^{2} x} + \frac{30 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3}}{a^{4} x^{2}} - \frac{80 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{3}}{a^{6} x^{3}} - \frac{580 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{3}}{a^{8} x^{4}}\right)} a^{10} x^{5}}{320 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} {\left| a \right|}} - \frac{3 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{3 \, c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{a} - \frac{\frac{580 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2} c^{3}}{x} + \frac{80 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3}}{x^{2}} - \frac{30 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{3}}{a^{2} x^{3}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{3}}{a^{4} x^{4}} - \frac{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{3}}{a^{6} x^{5}}}{320 \, a^{4} {\left| a \right|}}"," ",0,"-1/320*(2*c^3 + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3/(a^2*x) + 30*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3/(a^4*x^2) - 80*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^3/(a^6*x^3) - 580*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^3/(a^8*x^4))*a^10*x^5/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*abs(a)) - 3*c^3*arcsin(a*x)*sgn(a)/abs(a) - 3/8*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c^3/a - 1/320*(580*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2*c^3/x + 80*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3/x^2 - 30*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^3/(a^2*x^3) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^3/(a^4*x^4) - 2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^3/(a^6*x^5))/(a^4*abs(a))","B",0
647,1,262,0,0.308514," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\frac{{\left(c^{2} + \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{a^{2} x} + \frac{33 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{2}}{a^{4} x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} - \frac{3 \, c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a} - \frac{\frac{33 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{x} + \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{2}}{a^{2} x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{2}}{a^{4} x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(c^2 + 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/(a^2*x) + 33*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^2/(a^4*x^2))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) - 3*c^2*arcsin(a*x)*sgn(a)/abs(a) + 1/2*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c^2/a - 1/24*(33*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/x + 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^2/(a^2*x^2) + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^2/(a^4*x^3))/(a^2*abs(a))","B",0
648,1,129,0,0.251214," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2),x, algorithm=""giac"")","-\frac{a^{2} c x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} - \frac{3 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{3 \, c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c}{a} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c}{2 \, a^{2} x {\left| a \right|}}"," ",0,"-1/2*a^2*c*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) - 3*c*arcsin(a*x)*sgn(a)/abs(a) + 3*c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c/a + 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c/(a^2*x*abs(a))","A",0
649,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
650,1,180,0,0.240203," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","-\frac{3 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c^{2} {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a c^{2}} - \frac{2 \, {\left(\frac{80 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{120 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{70 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} - 19\right)}}{5 \, c^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"-3*arcsin(a*x)*sgn(a)/(c^2*abs(a)) + sqrt(-a^2*x^2 + 1)/(a*c^2) - 2/5*(80*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 120*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 70*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) - 19)/(c^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","A",0
651,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{3}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^3), x)","F",0
652,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{4}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^4), x)","F",0
653,1,104,0,0.195946," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^5,x, algorithm=""giac"")","c^{5} x + \frac{4 \, c^{5} \log\left({\left| x \right|}\right)}{a} - \frac{1890 \, a^{8} c^{5} x^{8} - 2520 \, a^{7} c^{5} x^{7} - 2940 \, a^{6} c^{5} x^{6} + 1764 \, a^{4} c^{5} x^{4} + 840 \, a^{3} c^{5} x^{3} - 270 \, a^{2} c^{5} x^{2} - 315 \, a c^{5} x - 70 \, c^{5}}{630 \, a^{10} x^{9}}"," ",0,"c^5*x + 4*c^5*log(abs(x))/a - 1/630*(1890*a^8*c^5*x^8 - 2520*a^7*c^5*x^7 - 2940*a^6*c^5*x^6 + 1764*a^4*c^5*x^4 + 840*a^3*c^5*x^3 - 270*a^2*c^5*x^2 - 315*a*c^5*x - 70*c^5)/(a^10*x^9)","A",0
654,1,93,0,0.182037," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^4,x, algorithm=""giac"")","c^{4} x + \frac{4 \, c^{4} \log\left({\left| x \right|}\right)}{a} - \frac{420 \, a^{6} c^{4} x^{6} - 210 \, a^{5} c^{4} x^{5} - 350 \, a^{4} c^{4} x^{4} - 105 \, a^{3} c^{4} x^{3} + 84 \, a^{2} c^{4} x^{2} + 70 \, a c^{4} x + 15 \, c^{4}}{105 \, a^{8} x^{7}}"," ",0,"c^4*x + 4*c^4*log(abs(x))/a - 1/105*(420*a^6*c^4*x^6 - 210*a^5*c^4*x^5 - 350*a^4*c^4*x^4 - 105*a^3*c^4*x^3 + 84*a^2*c^4*x^2 + 70*a*c^4*x + 15*c^4)/(a^8*x^7)","A",0
655,1,60,0,0.139835," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^3,x, algorithm=""giac"")","c^{3} x + \frac{4 \, c^{3} \log\left({\left| x \right|}\right)}{a} - \frac{75 \, a^{4} c^{3} x^{4} - 25 \, a^{2} c^{3} x^{2} - 15 \, a c^{3} x - 3 \, c^{3}}{15 \, a^{6} x^{5}}"," ",0,"c^3*x + 4*c^3*log(abs(x))/a - 1/15*(75*a^4*c^3*x^4 - 25*a^2*c^3*x^2 - 15*a*c^3*x - 3*c^3)/(a^6*x^5)","A",0
656,1,47,0,0.203934," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^2,x, algorithm=""giac"")","c^{2} x + \frac{4 \, c^{2} \log\left({\left| x \right|}\right)}{a} - \frac{18 \, a^{2} c^{2} x^{2} + 6 \, a c^{2} x + c^{2}}{3 \, a^{4} x^{3}}"," ",0,"c^2*x + 4*c^2*log(abs(x))/a - 1/3*(18*a^2*c^2*x^2 + 6*a*c^2*x + c^2)/(a^4*x^3)","A",0
657,1,34,0,0.153193," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2),x, algorithm=""giac"")","c x + \frac{8 \, c \log\left({\left| a x - 1 \right|}\right)}{a} - \frac{4 \, c \log\left({\left| x \right|}\right)}{a} + \frac{c}{a^{2} x}"," ",0,"c*x + 8*c*log(abs(a*x - 1))/a - 4*c*log(abs(x))/a + c/(a^2*x)","A",0
658,1,42,0,0.167090," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2),x, algorithm=""giac"")","\frac{x}{c} + \frac{4 \, \log\left({\left| a x - 1 \right|}\right)}{a c} - \frac{5 \, a x - 4}{{\left(a x - 1\right)}^{2} a c}"," ",0,"x/c + 4*log(abs(a*x - 1))/(a*c) - (5*a*x - 4)/((a*x - 1)^2*a*c)","A",0
659,1,50,0,0.165724," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\frac{x}{c^{2}} + \frac{4 \, \log\left({\left| a x - 1 \right|}\right)}{a c^{2}} - \frac{18 \, a^{2} x^{2} - 30 \, a x + 13}{3 \, {\left(a x - 1\right)}^{3} a c^{2}}"," ",0,"x/c^2 + 4*log(abs(a*x - 1))/(a*c^2) - 1/3*(18*a^2*x^2 - 30*a*x + 13)/((a*x - 1)^3*a*c^2)","A",0
660,1,73,0,0.156139," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\frac{x}{c^{3}} - \frac{\log\left({\left| a x + 1 \right|}\right)}{32 \, a c^{3}} + \frac{129 \, \log\left({\left| a x - 1 \right|}\right)}{32 \, a c^{3}} - \frac{333 \, a^{3} x^{3} - 852 \, a^{2} x^{2} + 749 \, a x - 224}{48 \, {\left(a x - 1\right)}^{4} a c^{3}}"," ",0,"x/c^3 - 1/32*log(abs(a*x + 1))/(a*c^3) + 129/32*log(abs(a*x - 1))/(a*c^3) - 1/48*(333*a^3*x^3 - 852*a^2*x^2 + 749*a*x - 224)/((a*x - 1)^4*a*c^3)","A",0
661,1,96,0,0.182583," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\frac{x}{c^{4}} - \frac{5 \, \log\left({\left| a x + 1 \right|}\right)}{64 \, a c^{4}} + \frac{261 \, \log\left({\left| a x - 1 \right|}\right)}{64 \, a c^{4}} - \frac{3765 \, a^{5} x^{5} - 9300 \, a^{4} x^{4} + 4400 \, a^{3} x^{3} + 6820 \, a^{2} x^{2} - 8021 \, a x + 2384}{480 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{5} a c^{4}}"," ",0,"x/c^4 - 5/64*log(abs(a*x + 1))/(a*c^4) + 261/64*log(abs(a*x - 1))/(a*c^4) - 1/480*(3765*a^5*x^5 - 9300*a^4*x^4 + 4400*a^3*x^3 + 6820*a^2*x^2 - 8021*a*x + 2384)/((a*x + 1)*(a*x - 1)^5*a*c^4)","A",0
662,1,504,0,0.172455," ","integrate((c-c/a^2/x^2)^4/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{{\left(15 \, c^{4} - \frac{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4}}{a^{2} x} - \frac{189 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4}}{a^{4} x^{2}} + \frac{525 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{a^{6} x^{3}} + \frac{1295 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{4}}{a^{8} x^{4}} - \frac{4935 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{4}}{a^{10} x^{5}} - \frac{9765 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} c^{4}}{a^{12} x^{6}}\right)} a^{14} x^{7}}{13440 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7} {\left| a \right|}} + \frac{c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{35 \, c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{16 \, {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{a} + \frac{\frac{9765 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{4}}{x} + \frac{4935 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{4}}{x^{2}} - \frac{1295 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{x^{3}} - \frac{525 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{4}}{a^{2} x^{4}} + \frac{189 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{4}}{a^{4} x^{5}} + \frac{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} c^{4}}{a^{6} x^{6}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7} c^{4}}{a^{8} x^{7}}}{13440 \, a^{6} {\left| a \right|}}"," ",0,"1/13440*(15*c^4 - 35*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4/(a^2*x) - 189*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4/(a^4*x^2) + 525*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/(a^6*x^3) + 1295*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^4/(a^8*x^4) - 4935*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^4/(a^10*x^5) - 9765*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*c^4/(a^12*x^6))*a^14*x^7/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^7*abs(a)) + c^4*arcsin(a*x)*sgn(a)/abs(a) - 35/16*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c^4/a + 1/13440*(9765*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^4/x + 4935*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^4/x^2 - 1295*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/x^3 - 525*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^4/(a^2*x^4) + 189*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^4/(a^4*x^5) + 35*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*c^4/(a^6*x^6) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^7*c^4/(a^8*x^7))/(a^6*abs(a))","B",0
663,1,384,0,0.218528," ","integrate((c-c/a^2/x^2)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{{\left(6 \, c^{3} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3}}{a^{2} x} - \frac{70 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3}}{a^{4} x^{2}} + \frac{240 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{3}}{a^{6} x^{3}} + \frac{660 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{3}}{a^{8} x^{4}}\right)} a^{10} x^{5}}{960 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} {\left| a \right|}} + \frac{c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{15 \, c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{a} + \frac{\frac{660 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2} c^{3}}{x} + \frac{240 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3}}{x^{2}} - \frac{70 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{3}}{a^{2} x^{3}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{3}}{a^{4} x^{4}} + \frac{6 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{3}}{a^{6} x^{5}}}{960 \, a^{4} {\left| a \right|}}"," ",0,"-1/960*(6*c^3 - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3/(a^2*x) - 70*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3/(a^4*x^2) + 240*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^3/(a^6*x^3) + 660*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^3/(a^8*x^4))*a^10*x^5/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*abs(a)) + c^3*arcsin(a*x)*sgn(a)/abs(a) - 15/8*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c^3/a + 1/960*(660*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2*c^3/x + 240*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3/x^2 - 70*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^3/(a^2*x^3) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^3/(a^4*x^4) + 6*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^3/(a^6*x^5))/(a^4*abs(a))","B",0
664,1,262,0,0.239007," ","integrate((c-c/a^2/x^2)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{{\left(c^{2} - \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{a^{2} x} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{2}}{a^{4} x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} + \frac{c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{3 \, c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a} + \frac{\frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{x} + \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{2}}{a^{2} x^{2}} - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{2}}{a^{4} x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(c^2 - 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/(a^2*x) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^2/(a^4*x^2))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) + c^2*arcsin(a*x)*sgn(a)/abs(a) - 3/2*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c^2/a + 1/24*(15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/x + 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^2/(a^2*x^2) - (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^2/(a^4*x^3))/(a^2*abs(a))","B",0
665,1,128,0,0.427467," ","integrate((c-c/a^2/x^2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{a^{2} c x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} + \frac{c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1} c}{a} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c}{2 \, a^{2} x {\left| a \right|}}"," ",0,"-1/2*a^2*c*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) + c*arcsin(a*x)*sgn(a)/abs(a) - c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + sqrt(-a^2*x^2 + 1)*c/a + 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c/(a^2*x*abs(a))","B",0
666,1,71,0,0.202986," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2),x, algorithm=""giac"")","\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a c} - \frac{2}{c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"arcsin(a*x)*sgn(a)/(c*abs(a)) + sqrt(-a^2*x^2 + 1)/(a*c) - 2/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
667,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^2), x)","F",0
668,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^3), x)","F",0
669,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^4), x)","F",0
670,1,160,0,0.177233," ","integrate((c-c/a^2/x^2)^4/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{2 \, c^{4} \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a} + \frac{2 \, c^{4} \log\left({\left| -\frac{1}{a x + 1} + 1 \right|}\right)}{a} + \frac{{\left(210 \, c^{4} - \frac{719 \, c^{4}}{a x + 1} - \frac{427 \, c^{4}}{{\left(a x + 1\right)}^{2}} + \frac{5271 \, c^{4}}{{\left(a x + 1\right)}^{3}} - \frac{9485 \, c^{4}}{{\left(a x + 1\right)}^{4}} + \frac{7490 \, 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)}}{210 \, a {\left(\frac{1}{a x + 1} - 1\right)}^{7}}"," ",0,"-2*c^4*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a + 2*c^4*log(abs(-1/(a*x + 1) + 1))/a + 1/210*(210*c^4 - 719*c^4/(a*x + 1) - 427*c^4/(a*x + 1)^2 + 5271*c^4/(a*x + 1)^3 - 9485*c^4/(a*x + 1)^4 + 7490*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
671,1,136,0,0.287425," ","integrate((c-c/a^2/x^2)^3/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{2 \, c^{3} \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a} + \frac{2 \, c^{3} \log\left({\left| -\frac{1}{a x + 1} + 1 \right|}\right)}{a} + \frac{{\left(30 \, c^{3} - \frac{71 \, c^{3}}{a x + 1} - \frac{65 \, c^{3}}{{\left(a x + 1\right)}^{2}} + \frac{310 \, c^{3}}{{\left(a x + 1\right)}^{3}} - \frac{270 \, c^{3}}{{\left(a x + 1\right)}^{4}} + \frac{60 \, c^{3}}{{\left(a x + 1\right)}^{5}}\right)} {\left(a x + 1\right)}}{30 \, a {\left(\frac{1}{a x + 1} - 1\right)}^{5}}"," ",0,"-2*c^3*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a + 2*c^3*log(abs(-1/(a*x + 1) + 1))/a + 1/30*(30*c^3 - 71*c^3/(a*x + 1) - 65*c^3/(a*x + 1)^2 + 310*c^3/(a*x + 1)^3 - 270*c^3/(a*x + 1)^4 + 60*c^3/(a*x + 1)^5)*(a*x + 1)/(a*(1/(a*x + 1) - 1)^5)","A",0
672,1,112,0,0.216129," ","integrate((c-c/a^2/x^2)^2/(a*x+1)^2*(-a^2*x^2+1),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{{\left(3 \, c^{2} - \frac{5 \, c^{2}}{a x + 1} - \frac{3 \, c^{2}}{{\left(a x + 1\right)}^{2}} + \frac{6 \, 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,"-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 + 1/3*(3*c^2 - 5*c^2/(a*x + 1) - 3*c^2/(a*x + 1)^2 + 6*c^2/(a*x + 1)^3)*(a*x + 1)/(a*(1/(a*x + 1) - 1)^3)","B",0
673,1,88,0,0.166060," ","integrate((c-c/a^2/x^2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{2 \, c \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a} + \frac{2 \, c \log\left({\left| -\frac{1}{a x + 1} + 1 \right|}\right)}{a} - \frac{c - \frac{2 \, c}{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*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/a + 2*c*log(abs(-1/(a*x + 1) + 1))/a - (c - 2*c/(a*x + 1))/(a^2*(1/((a*x + 1)*a) - 1/((a*x + 1)^2*a)))","B",0
674,1,55,0,0.183481," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2),x, algorithm=""giac"")","-\frac{a x + 1}{a c} - \frac{2 \, \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a c} + \frac{1}{{\left(a x + 1\right)} a c}"," ",0,"-(a*x + 1)/(a*c) - 2*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/(a*c) + 1/((a*x + 1)*a*c)","A",0
675,1,101,0,0.160192," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","-\frac{a x + 1}{a c^{2}} - \frac{2 \, \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a c^{2}} - \frac{\log\left({\left| -\frac{2}{a x + 1} + 1 \right|}\right)}{8 \, a c^{2}} + \frac{\frac{7 \, a^{5} c^{2}}{a x + 1} - \frac{a^{5} c^{2}}{{\left(a x + 1\right)}^{2}}}{4 \, a^{6} c^{4}}"," ",0,"-(a*x + 1)/(a*c^2) - 2*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/(a*c^2) - 1/8*log(abs(-2/(a*x + 1) + 1))/(a*c^2) + 1/4*(7*a^5*c^2/(a*x + 1) - a^5*c^2/(a*x + 1)^2)/(a^6*c^4)","A",0
676,1,140,0,0.172437," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","-\frac{{\left(a x + 1\right)} {\left(\frac{65}{a x + 1} - 32\right)}}{32 \, a c^{3} {\left(\frac{2}{a x + 1} - 1\right)}} - \frac{2 \, \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)}{4 \, a c^{3}} + \frac{\frac{117 \, a^{11} c^{6}}{a x + 1} - \frac{30 \, a^{11} c^{6}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, a^{11} c^{6}}{{\left(a x + 1\right)}^{3}}}{48 \, a^{12} c^{9}}"," ",0,"-1/32*(a*x + 1)*(65/(a*x + 1) - 32)/(a*c^3*(2/(a*x + 1) - 1)) - 2*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/(a*c^3) - 1/4*log(abs(-2/(a*x + 1) + 1))/(a*c^3) + 1/48*(117*a^11*c^6/(a*x + 1) - 30*a^11*c^6/(a*x + 1)^2 + 4*a^11*c^6/(a*x + 1)^3)/(a^12*c^9)","A",0
677,1,164,0,0.174576," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","-\frac{2 \, \log\left(\frac{{\left| a x + 1 \right|}}{{\left(a x + 1\right)}^{2} {\left| a \right|}}\right)}{a c^{4}} - \frac{47 \, \log\left({\left| -\frac{2}{a x + 1} + 1 \right|}\right)}{128 \, a c^{4}} + \frac{{\left(a x + 1\right)} {\left(\frac{1045}{a x + 1} - \frac{1064}{{\left(a x + 1\right)}^{2}} - 256\right)}}{256 \, a c^{4} {\left(\frac{2}{a x + 1} - 1\right)}^{2}} + \frac{\frac{297 \, a^{19} c^{12}}{a x + 1} - \frac{105 \, a^{19} c^{12}}{{\left(a x + 1\right)}^{2}} + \frac{26 \, a^{19} c^{12}}{{\left(a x + 1\right)}^{3}} - \frac{3 \, a^{19} c^{12}}{{\left(a x + 1\right)}^{4}}}{96 \, a^{20} c^{16}}"," ",0,"-2*log(abs(a*x + 1)/((a*x + 1)^2*abs(a)))/(a*c^4) - 47/128*log(abs(-2/(a*x + 1) + 1))/(a*c^4) + 1/256*(a*x + 1)*(1045/(a*x + 1) - 1064/(a*x + 1)^2 - 256)/(a*c^4*(2/(a*x + 1) - 1)^2) + 1/96*(297*a^19*c^12/(a*x + 1) - 105*a^19*c^12/(a*x + 1)^2 + 26*a^19*c^12/(a*x + 1)^3 - 3*a^19*c^12/(a*x + 1)^4)/(a^20*c^16)","A",0
678,1,506,0,0.301321," ","integrate((c-c/a^2/x^2)^4/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\frac{{\left(5 \, c^{4} - \frac{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{4}}{a^{2} x} + \frac{49 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{4}}{a^{4} x^{2}} + \frac{245 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{a^{6} x^{3}} - \frac{875 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{4}}{a^{8} x^{4}} - \frac{455 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{4}}{a^{10} x^{5}} + \frac{9065 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} c^{4}}{a^{12} x^{6}}\right)} a^{14} x^{7}}{4480 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7} {\left| a \right|}} - \frac{3 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{15 \, c^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{16 \, {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{a} - \frac{\frac{9065 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{4}}{x} - \frac{455 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{4}}{x^{2}} - \frac{875 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{4}}{x^{3}} + \frac{245 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{4}}{a^{2} x^{4}} + \frac{49 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{4}}{a^{4} x^{5}} - \frac{35 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{6} c^{4}}{a^{6} x^{6}} + \frac{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{7} c^{4}}{a^{8} x^{7}}}{4480 \, a^{6} {\left| a \right|}}"," ",0,"1/4480*(5*c^4 - 35*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^4/(a^2*x) + 49*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^4/(a^4*x^2) + 245*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/(a^6*x^3) - 875*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^4/(a^8*x^4) - 455*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^4/(a^10*x^5) + 9065*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*c^4/(a^12*x^6))*a^14*x^7/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^7*abs(a)) - 3*c^4*arcsin(a*x)*sgn(a)/abs(a) + 15/16*c^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c^4/a - 1/4480*(9065*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^4/x - 455*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^4/x^2 - 875*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^4/x^3 + 245*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^4/(a^2*x^4) + 49*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^4/(a^4*x^5) - 35*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^6*c^4/(a^6*x^6) + 5*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^7*c^4/(a^8*x^7))/(a^6*abs(a))","B",0
679,1,386,0,0.206233," ","integrate((c-c/a^2/x^2)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{{\left(2 \, c^{3} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{3}}{a^{2} x} + \frac{30 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3}}{a^{4} x^{2}} + \frac{80 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{3}}{a^{6} x^{3}} - \frac{580 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{3}}{a^{8} x^{4}}\right)} a^{10} x^{5}}{320 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} {\left| a \right|}} - \frac{3 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{3 \, c^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{a} - \frac{\frac{580 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2} c^{3}}{x} - \frac{80 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{3}}{x^{2}} - \frac{30 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{3}}{a^{2} x^{3}} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c^{3}}{a^{4} x^{4}} - \frac{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c^{3}}{a^{6} x^{5}}}{320 \, a^{4} {\left| a \right|}}"," ",0,"-1/320*(2*c^3 - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^3/(a^2*x) + 30*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3/(a^4*x^2) + 80*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^3/(a^6*x^3) - 580*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^3/(a^8*x^4))*a^10*x^5/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*abs(a)) - 3*c^3*arcsin(a*x)*sgn(a)/abs(a) + 3/8*c^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c^3/a - 1/320*(580*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2*c^3/x - 80*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^3/x^2 - 30*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^3/(a^2*x^3) + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c^3/(a^4*x^4) - 2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c^3/(a^6*x^5))/(a^4*abs(a))","B",0
680,1,263,0,0.182522," ","integrate((c-c/a^2/x^2)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\frac{{\left(c^{2} - \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{a^{2} x} + \frac{33 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{2}}{a^{4} x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} - \frac{3 \, c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{c^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a} - \frac{\frac{33 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c^{2}}{x} - \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c^{2}}{a^{2} x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{2}}{a^{4} x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(c^2 - 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/(a^2*x) + 33*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^2/(a^4*x^2))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) - 3*c^2*arcsin(a*x)*sgn(a)/abs(a) - 1/2*c^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c^2/a - 1/24*(33*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c^2/x - 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c^2/(a^2*x^2) + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^2/(a^4*x^3))/(a^2*abs(a))","B",0
681,1,130,0,0.234514," ","integrate((c-c/a^2/x^2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{a^{2} c x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} - \frac{3 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{3 \, c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} c}{a} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c}{2 \, a^{2} x {\left| a \right|}}"," ",0,"-1/2*a^2*c*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) - 3*c*arcsin(a*x)*sgn(a)/abs(a) - 3*c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*c/a + 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c/(a^2*x*abs(a))","A",0
682,-2,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2),x, algorithm=""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
683,1,181,0,0.237673," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^2,x, algorithm=""giac"")","-\frac{3 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{c^{2} {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1}}{a c^{2}} + \frac{2 \, {\left(\frac{80 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} + \frac{120 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{70 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} + 19\right)}}{5 \, c^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)}^{5} {\left| a \right|}}"," ",0,"-3*arcsin(a*x)*sgn(a)/(c^2*abs(a)) - sqrt(-a^2*x^2 + 1)/(a*c^2) + 2/5*(80*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 120*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 70*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) + 19)/(c^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)^5*abs(a))","A",0
684,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^3,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a^2*x^2))^3), x)","F",0
685,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^4,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{4}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a^2*x^2))^4), x)","F",0
686,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^(9/2)/sqrt(-a^2*x^2 + 1), x)","F",0
687,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^(7/2)/sqrt(-a^2*x^2 + 1), x)","F",0
688,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^(5/2)/sqrt(-a^2*x^2 + 1), x)","F",0
689,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^(3/2)/sqrt(-a^2*x^2 + 1), x)","F",0
690,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))/sqrt(-a^2*x^2 + 1), x)","F",0
691,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a^2*x^2))), x)","F",0
692,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(3/2)), x)","F",0
693,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
694,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
695,1,707,0,137.056804," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(9/2),x, algorithm=""giac"")","\frac{1}{6720} \, {\left(\frac{25725 \, c^{\frac{9}{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{13440 \, c^{\frac{9}{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{6720 \, \sqrt{a^{2} c x^{2} - c} c^{4} \mathrm{sgn}\left(x\right)}{a^{2}} + \frac{14595 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{15} c^{5} {\left| a \right|} \mathrm{sgn}\left(x\right) + 107520 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{14} a c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) + 76055 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{13} c^{6} {\left| a \right|} \mathrm{sgn}\left(x\right) + 430080 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{12} a c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) + 64435 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{11} c^{7} {\left| a \right|} \mathrm{sgn}\left(x\right) + 1111040 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{10} a c^{\frac{15}{2}} \mathrm{sgn}\left(x\right) + 110495 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{9} c^{8} {\left| a \right|} \mathrm{sgn}\left(x\right) + 1576960 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{8} a c^{\frac{17}{2}} \mathrm{sgn}\left(x\right) - 110495 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{7} c^{9} {\left| a \right|} \mathrm{sgn}\left(x\right) + 1412096 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{6} a c^{\frac{19}{2}} \mathrm{sgn}\left(x\right) - 64435 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{5} c^{10} {\left| a \right|} \mathrm{sgn}\left(x\right) + 831488 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} a c^{\frac{21}{2}} \mathrm{sgn}\left(x\right) - 76055 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} c^{11} {\left| a \right|} \mathrm{sgn}\left(x\right) + 252928 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a c^{\frac{23}{2}} \mathrm{sgn}\left(x\right) - 14595 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} c^{12} {\left| a \right|} \mathrm{sgn}\left(x\right) + 45056 \, a c^{\frac{25}{2}} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{8} a^{2} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"1/6720*(25725*c^(9/2)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x)/a^2 + 13440*c^(9/2)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a*abs(a)) - 6720*sqrt(a^2*c*x^2 - c)*c^4*sgn(x)/a^2 + (14595*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^15*c^5*abs(a)*sgn(x) + 107520*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^14*a*c^(11/2)*sgn(x) + 76055*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^13*c^6*abs(a)*sgn(x) + 430080*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^12*a*c^(13/2)*sgn(x) + 64435*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^11*c^7*abs(a)*sgn(x) + 1111040*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^10*a*c^(15/2)*sgn(x) + 110495*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^9*c^8*abs(a)*sgn(x) + 1576960*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^8*a*c^(17/2)*sgn(x) - 110495*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^7*c^9*abs(a)*sgn(x) + 1412096*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^6*a*c^(19/2)*sgn(x) - 64435*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^5*c^10*abs(a)*sgn(x) + 831488*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*a*c^(21/2)*sgn(x) - 76055*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*c^11*abs(a)*sgn(x) + 252928*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a*c^(23/2)*sgn(x) - 14595*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*c^12*abs(a)*sgn(x) + 45056*a*c^(25/2)*sgn(x))/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^8*a^2*abs(a)))*abs(a)","A",0
696,-1,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
697,1,416,0,6.540628," ","integrate((a*x+1)^2/(-a^2*x^2+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
698,1,265,0,0.449785," ","integrate((a*x+1)^2/(-a^2*x^2+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
699,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+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
700,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate(-(a*x + 1)^2/((a^2*x^2 - 1)*sqrt(c - c/(a^2*x^2))), x)","F",0
701,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(a*x + 1)^2/((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(3/2)), x)","F",0
702,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(a*x + 1)^2/((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
703,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(a*x + 1)^2/((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
704,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(c-c/a^2/x^2)^(9/2),x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2}}{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(-(a*x + 1)^2/((a^2*x^2 - 1)*(c - c/(a^2*x^2))^(9/2)), x)","F",0
705,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a^2*x^2))^(9/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
706,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a^2*x^2))^(7/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
707,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a^2*x^2))^(5/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
708,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a^2*x^2))^(3/2)/(-a^2*x^2 + 1)^(3/2), x)","F",0
709,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a^2*x^2))/(-a^2*x^2 + 1)^(3/2), x)","F",0
710,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))), x)","F",0
711,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""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
712,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
713,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
714,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(9/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(9/2)/(a*x + 1), x)","F",0
715,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(7/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(7/2)/(a*x + 1), x)","F",0
716,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(5/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(5/2)/(a*x + 1), x)","F",0
717,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(3/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^(3/2)/(a*x + 1), x)","F",0
718,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a^2*x^2))/(a*x + 1), x)","F",0
719,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*sqrt(c - c/(a^2*x^2))), x)","F",0
720,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^(3/2)), x)","F",0
721,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^(5/2)), x)","F",0
722,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a*x + 1)*(c - c/(a^2*x^2))^(7/2)), x)","F",0
723,1,707,0,101.601252," ","integrate((c-c/a^2/x^2)^(9/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\frac{1}{6720} \, {\left(\frac{25725 \, c^{\frac{9}{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{13440 \, c^{\frac{9}{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{6720 \, \sqrt{a^{2} c x^{2} - c} c^{4} \mathrm{sgn}\left(x\right)}{a^{2}} + \frac{14595 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{15} c^{5} {\left| a \right|} \mathrm{sgn}\left(x\right) - 107520 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{14} a c^{\frac{11}{2}} \mathrm{sgn}\left(x\right) + 76055 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{13} c^{6} {\left| a \right|} \mathrm{sgn}\left(x\right) - 430080 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{12} a c^{\frac{13}{2}} \mathrm{sgn}\left(x\right) + 64435 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{11} c^{7} {\left| a \right|} \mathrm{sgn}\left(x\right) - 1111040 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{10} a c^{\frac{15}{2}} \mathrm{sgn}\left(x\right) + 110495 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{9} c^{8} {\left| a \right|} \mathrm{sgn}\left(x\right) - 1576960 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{8} a c^{\frac{17}{2}} \mathrm{sgn}\left(x\right) - 110495 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{7} c^{9} {\left| a \right|} \mathrm{sgn}\left(x\right) - 1412096 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{6} a c^{\frac{19}{2}} \mathrm{sgn}\left(x\right) - 64435 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{5} c^{10} {\left| a \right|} \mathrm{sgn}\left(x\right) - 831488 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{4} a c^{\frac{21}{2}} \mathrm{sgn}\left(x\right) - 76055 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{3} c^{11} {\left| a \right|} \mathrm{sgn}\left(x\right) - 252928 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} a c^{\frac{23}{2}} \mathrm{sgn}\left(x\right) - 14595 \, {\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)} c^{12} {\left| a \right|} \mathrm{sgn}\left(x\right) - 45056 \, a c^{\frac{25}{2}} \mathrm{sgn}\left(x\right)}{{\left({\left(\sqrt{a^{2} c} x - \sqrt{a^{2} c x^{2} - c}\right)}^{2} + c\right)}^{8} a^{2} {\left| a \right|}}\right)} {\left| a \right|}"," ",0,"1/6720*(25725*c^(9/2)*arctan(-(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))/sqrt(c))*sgn(x)/a^2 - 13440*c^(9/2)*log(abs(-sqrt(a^2*c)*x + sqrt(a^2*c*x^2 - c)))*sgn(x)/(a*abs(a)) - 6720*sqrt(a^2*c*x^2 - c)*c^4*sgn(x)/a^2 + (14595*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^15*c^5*abs(a)*sgn(x) - 107520*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^14*a*c^(11/2)*sgn(x) + 76055*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^13*c^6*abs(a)*sgn(x) - 430080*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^12*a*c^(13/2)*sgn(x) + 64435*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^11*c^7*abs(a)*sgn(x) - 1111040*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^10*a*c^(15/2)*sgn(x) + 110495*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^9*c^8*abs(a)*sgn(x) - 1576960*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^8*a*c^(17/2)*sgn(x) - 110495*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^7*c^9*abs(a)*sgn(x) - 1412096*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^6*a*c^(19/2)*sgn(x) - 64435*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^5*c^10*abs(a)*sgn(x) - 831488*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^4*a*c^(21/2)*sgn(x) - 76055*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^3*c^11*abs(a)*sgn(x) - 252928*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2*a*c^(23/2)*sgn(x) - 14595*(sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))*c^12*abs(a)*sgn(x) - 45056*a*c^(25/2)*sgn(x))/(((sqrt(a^2*c)*x - sqrt(a^2*c*x^2 - c))^2 + c)^8*a^2*abs(a)))*abs(a)","A",0
724,-1,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(7/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
725,1,416,0,13.718471," ","integrate((c-c/a^2/x^2)^(5/2)/(a*x+1)^2*(-a^2*x^2+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
726,1,265,0,4.417456," ","integrate((c-c/a^2/x^2)^(3/2)/(a*x+1)^2*(-a^2*x^2+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
727,-2,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
728,1,97,0,0.207390," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(a x + 1\right)} a^{2} \sqrt{c - \frac{2 \, c}{a x + 1}} + \frac{4 \, a^{2} c \arctan\left(\frac{\sqrt{c - \frac{2 \, c}{a x + 1}}}{\sqrt{-c}}\right)}{\sqrt{-c}} + 2 \, a^{2} \sqrt{c - \frac{2 \, c}{a x + 1}}}{a^{3} c \mathrm{sgn}\left(-\frac{1}{a x + 1} + 1\right)}"," ",0,"-((a*x + 1)*a^2*sqrt(c - 2*c/(a*x + 1)) + 4*a^2*c*arctan(sqrt(c - 2*c/(a*x + 1))/sqrt(-c))/sqrt(-c) + 2*a^2*sqrt(c - 2*c/(a*x + 1)))/(a^3*c*sgn(-1/(a*x + 1) + 1))","A",0
729,1,127,0,0.219639," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(3/2),x, algorithm=""giac"")","-\frac{6 \, {\left(a x + 1\right)} a^{2} \sqrt{c - \frac{2 \, c}{a x + 1}} + \frac{24 \, a^{2} c \arctan\left(\frac{\sqrt{c - \frac{2 \, c}{a x + 1}}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{a^{2} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} c^{2} + 15 \, a^{2} \sqrt{c - \frac{2 \, c}{a x + 1}} c^{3}}{c^{3}}}{6 \, a^{3} c^{2} \mathrm{sgn}\left(-\frac{1}{a x + 1} + 1\right)}"," ",0,"-1/6*(6*(a*x + 1)*a^2*sqrt(c - 2*c/(a*x + 1)) + 24*a^2*c*arctan(sqrt(c - 2*c/(a*x + 1))/sqrt(-c))/sqrt(-c) + (a^2*(c - 2*c/(a*x + 1))^(3/2)*c^2 + 15*a^2*sqrt(c - 2*c/(a*x + 1))*c^3)/c^3)/(a^3*c^2*sgn(-1/(a*x + 1) + 1))","A",0
730,1,208,0,0.253914," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","-\frac{4 \, \arctan\left(\frac{\sqrt{c - \frac{2 \, c}{a x + 1}}}{\sqrt{-c}}\right)}{a \sqrt{-c} c^{2} \mathrm{sgn}\left(-\frac{1}{a x + 1} + 1\right)} + \frac{8 \, c - \frac{17 \, c}{a x + 1}}{4 \, {\left({\left(c - \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} - \sqrt{c - \frac{2 \, c}{a x + 1}} c\right)} a c^{2} \mathrm{sgn}\left(-\frac{1}{a x + 1} + 1\right)} - \frac{3 \, a^{4} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{\frac{5}{2}} c^{20} + 35 \, a^{4} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} c^{21} + 345 \, a^{4} \sqrt{c - \frac{2 \, c}{a x + 1}} c^{22}}{120 \, a^{5} c^{25} \mathrm{sgn}\left(-\frac{1}{a x + 1} + 1\right)}"," ",0,"-4*arctan(sqrt(c - 2*c/(a*x + 1))/sqrt(-c))/(a*sqrt(-c)*c^2*sgn(-1/(a*x + 1) + 1)) + 1/4*(8*c - 17*c/(a*x + 1))/(((c - 2*c/(a*x + 1))^(3/2) - sqrt(c - 2*c/(a*x + 1))*c)*a*c^2*sgn(-1/(a*x + 1) + 1)) - 1/120*(3*a^4*(c - 2*c/(a*x + 1))^(5/2)*c^20 + 35*a^4*(c - 2*c/(a*x + 1))^(3/2)*c^21 + 345*a^4*sqrt(c - 2*c/(a*x + 1))*c^22)/(a^5*c^25*sgn(-1/(a*x + 1) + 1))","A",0
731,1,251,0,3.817989," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","-\frac{{\left(a x + 1\right)} \sqrt{c - \frac{2 \, c}{a x + 1}}}{a c^{4} \mathrm{sgn}\left(-\frac{1}{a x + 1} + 1\right)} - \frac{4 \, \arctan\left(\frac{\sqrt{c - \frac{2 \, c}{a x + 1}}}{\sqrt{-c}}\right)}{a \sqrt{-c} c^{3} \mathrm{sgn}\left(-\frac{1}{a x + 1} + 1\right)} + \frac{14 \, c - \frac{27 \, c}{a x + 1}}{48 \, a {\left(c - \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} c^{3} \mathrm{sgn}\left(-\frac{1}{a x + 1} + 1\right)} - \frac{15 \, a^{6} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{\frac{7}{2}} c^{42} + 189 \, a^{6} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{\frac{5}{2}} c^{43} + 1330 \, a^{6} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} c^{44} + 10710 \, a^{6} \sqrt{c - \frac{2 \, c}{a x + 1}} c^{45}}{3360 \, a^{7} c^{49} \mathrm{sgn}\left(-\frac{1}{a x + 1} + 1\right)}"," ",0,"-(a*x + 1)*sqrt(c - 2*c/(a*x + 1))/(a*c^4*sgn(-1/(a*x + 1) + 1)) - 4*arctan(sqrt(c - 2*c/(a*x + 1))/sqrt(-c))/(a*sqrt(-c)*c^3*sgn(-1/(a*x + 1) + 1)) + 1/48*(14*c - 27*c/(a*x + 1))/(a*(c - 2*c/(a*x + 1))^(3/2)*c^3*sgn(-1/(a*x + 1) + 1)) - 1/3360*(15*a^6*(c - 2*c/(a*x + 1))^(7/2)*c^42 + 189*a^6*(c - 2*c/(a*x + 1))^(5/2)*c^43 + 1330*a^6*(c - 2*c/(a*x + 1))^(3/2)*c^44 + 10710*a^6*sqrt(c - 2*c/(a*x + 1))*c^45)/(a^7*c^49*sgn(-1/(a*x + 1) + 1))","A",0
732,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(9/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{9}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(9/2)/(a*x + 1)^3, x)","F",0
733,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(7/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(7/2)/(a*x + 1)^3, x)","F",0
734,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(5/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(5/2)/(a*x + 1)^3, x)","F",0
735,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(3/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^(3/2)/(a*x + 1)^3, x)","F",0
736,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/(a*x + 1)^3, x)","F",0
737,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a^{2} x^{2}}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*sqrt(c - c/(a^2*x^2))), x)","F",0
738,-2,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(3/2),x, algorithm=""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
739,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a^2*x^2))^(5/2)), x)","F",0
740,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(c-c/a^2/x^2)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*(c - c/(a^2*x^2))^(7/2)), x)","F",0
741,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
742,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))*x^2/sqrt(-a^2*x^2 + 1), x)","F",0
743,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}} x}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))*x/sqrt(-a^2*x^2 + 1), x)","F",0
744,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))/sqrt(-a^2*x^2 + 1), x)","F",0
745,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
746,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*sqrt(c - c/(a^2*x^2))/(sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
747,1,128,0,3.087207," ","integrate((a*x+1)^2/(-a^2*x^2+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
748,1,116,0,0.189868," ","integrate((a*x+1)^2/(-a^2*x^2+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
749,1,106,0,0.216297," ","integrate((a*x+1)^2/(-a^2*x^2+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
750,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+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
751,1,128,0,0.318315," ","integrate((a*x+1)^2/(-a^2*x^2+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
752,1,195,0,3.007526," ","integrate((a*x+1)^2/(-a^2*x^2+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
753,1,231,0,11.137765," ","integrate((a*x+1)^2/(-a^2*x^2+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
754,1,316,0,6.416517," ","integrate((a*x+1)^2/(-a^2*x^2+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
755,1,362,0,5.489470," ","integrate((a*x+1)^2/(-a^2*x^2+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
756,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a^2*x^2))*x^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
757,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a^2*x^2))*x^2/(-a^2*x^2 + 1)^(3/2), x)","F",0
758,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a^{2} x^{2}}} x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a^2*x^2))*x/(-a^2*x^2 + 1)^(3/2), x)","F",0
759,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a^2*x^2))/(-a^2*x^2 + 1)^(3/2), x)","F",0
760,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a^2*x^2))/((-a^2*x^2 + 1)^(3/2)*x), x)","F",0
761,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a^2*x^2))/((-a^2*x^2 + 1)^(3/2)*x^2), x)","F",0
762,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a^2*x^2))/((-a^2*x^2 + 1)^(3/2)*x^3), x)","F",0
763,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a^2*x^2))/((-a^2*x^2 + 1)^(3/2)*x^4), x)","F",0
764,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^(1/2)/x^5,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{5}}\,{d x}"," ",0,"integrate((a*x + 1)^3*sqrt(c - c/(a^2*x^2))/((-a^2*x^2 + 1)^(3/2)*x^5), x)","F",0
765,0,0,0,0.000000," ","integrate(x^m*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a^2*x^2))*x^m/(a*x + 1), x)","F",0
766,0,0,0,0.000000," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a^2*x^2))*x^2/(a*x + 1), x)","F",0
767,0,0,0,0.000000," ","integrate(x*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a^{2} x^{2}}} x}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a^2*x^2))*x/(a*x + 1), x)","F",0
768,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a^2*x^2))/(a*x + 1), x)","F",0
769,-2,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""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)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
770,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt(c - c/(a^2*x^2))/((a*x + 1)*x^2), x)","F",0
771,1,128,0,0.266636," ","integrate(x^3*(c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
772,1,117,0,0.235480," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
773,1,106,0,0.182378," ","integrate(x*(c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
774,-2,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
775,1,126,0,0.342024," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
776,1,195,0,0.380651," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
777,1,231,0,2.776435," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
778,1,316,0,6.169247," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
779,1,362,0,7.928822," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
780,0,0,0,0.000000," ","integrate(x^3*(c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{3}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))*x^3/(a*x + 1)^3, x)","F",0
781,0,0,0,0.000000," ","integrate(x^2*(c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}} x^{2}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))*x^2/(a*x + 1)^3, x)","F",0
782,0,0,0,0.000000," ","integrate(x*(c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}} x}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))*x/(a*x + 1)^3, x)","F",0
783,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/(a*x + 1)^3, x)","F",0
784,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3} x}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^3*x), x)","F",0
785,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^3*x^2), x)","F",0
786,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^3*x^3), x)","F",0
787,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3} x^{4}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^3*x^4), x)","F",0
788,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c - \frac{c}{a^{2} x^{2}}}}{{\left(a x + 1\right)}^{3} x^{5}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt(c - c/(a^2*x^2))/((a*x + 1)^3*x^5), x)","F",0
789,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^p/exp(2*p*arctanh(a*x)),x, algorithm=""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
790,0,0,0,0.000000," ","integrate(exp(2*p*arctanh(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
791,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^2,x, algorithm=""giac"")","\int {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((c - c/(a^2*x^2))^2*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
792,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a^2/x^2),x, algorithm=""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
793,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
794,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
795,-2,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(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(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
796,-2,0,0,0.000000," ","integrate(exp(n*arctanh(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
797,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
798,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^(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^{2} x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(c - c/(a^2*x^2))^(3/2), x)","F",0
799,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(c-c/a^2/x^2)^(5/2),x, algorithm=""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)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(c - c/(a^2*x^2))^(5/2), x)","F",0
800,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(c-c/a^2/x^2)^p,x, algorithm=""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
801,0,0,0,0.000000," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(c-c/a^2/x^2)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{4} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^4*(c - c/(a^2*x^2))^p/(a^2*x^2 - 1)^2, x)","F",0
802,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(c-c/a^2/x^2)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(c - c/(a^2*x^2))^p/(-a^2*x^2 + 1)^(3/2), x)","F",0
803,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(c-c/a^2/x^2)^p,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(a*x + 1)^2*(c - c/(a^2*x^2))^p/(a^2*x^2 - 1), x)","F",0
804,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(c-c/a^2/x^2)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(c - c/(a^2*x^2))^p/sqrt(-a^2*x^2 + 1), x)","F",0
805,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(c - c/(a^2*x^2))^p/(a*x + 1), x)","F",0
806,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^p/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*(c - c/(a^2*x^2))^p/(a*x + 1)^2, x)","F",0
807,0,0,0,0.000000," ","integrate((c-c/a^2/x^2)^p/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(c - \frac{c}{a^{2} x^{2}}\right)}^{p}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(c - c/(a^2*x^2))^p/(a*x + 1)^3, x)","F",0
808,1,124,0,0.195456," ","integrate((1+x)^(3/2)/(-x^2+1)^(1/2)*x*sin(x),x, algorithm=""giac"")","-\left(\frac{11}{16} i - \frac{1}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{i} + \left(\frac{11}{16} i + \frac{1}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{\left(-i\right)} - \frac{1}{4} i \, {\left(-2 i \, {\left(-x + 1\right)}^{\frac{3}{2}} + \left(4 i - 3\right) \, \sqrt{-x + 1}\right)} e^{\left(i \, x\right)} - \frac{1}{4} i \, {\left(-2 i \, {\left(-x + 1\right)}^{\frac{3}{2}} + \left(4 i + 3\right) \, \sqrt{-x + 1}\right)} e^{\left(-i \, x\right)} + \frac{1}{2} \, \sqrt{-x + 1} e^{\left(i \, x\right)} + \frac{1}{2} \, \sqrt{-x + 1} e^{\left(-i \, x\right)} + 1.79526793396000"," ",0,"-(11/16*I - 1/16)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(-x + 1))*e^I + (11/16*I + 1/16)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(-x + 1))*e^(-I) - 1/4*I*(-2*I*(-x + 1)^(3/2) + (4*I - 3)*sqrt(-x + 1))*e^(I*x) - 1/4*I*(-2*I*(-x + 1)^(3/2) + (4*I + 3)*sqrt(-x + 1))*e^(-I*x) + 1/2*sqrt(-x + 1)*e^(I*x) + 1/2*sqrt(-x + 1)*e^(-I*x) + 1.79526793396000","C",0
809,1,74,0,0.178303," ","integrate((1+x)^(3/2)/(-x^2+1)^(1/2)*sin(x),x, algorithm=""giac"")","-\left(\frac{5}{8} i + \frac{3}{8}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{i} + \left(\frac{5}{8} i - \frac{3}{8}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{\left(-i\right)} + \frac{1}{2} \, \sqrt{-x + 1} e^{\left(i \, x\right)} + \frac{1}{2} \, \sqrt{-x + 1} e^{\left(-i \, x\right)} + 1.99284503743000"," ",0,"-(5/8*I + 3/8)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(-x + 1))*e^I + (5/8*I - 3/8)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(-x + 1))*e^(-I) + 1/2*sqrt(-x + 1)*e^(I*x) + 1/2*sqrt(-x + 1)*e^(-I*x) + 1.99284503743000","C",0
810,1,108,0,0.189964," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2)*x*sin(x),x, algorithm=""giac"")","\left(\frac{1}{16} i + \frac{5}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{x + 1}\right) e^{i} - \left(\frac{1}{16} i - \frac{5}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{x + 1}\right) e^{\left(-i\right)} + \frac{1}{4} i \, {\left(2 i \, {\left(x + 1\right)}^{\frac{3}{2}} - \left(4 i + 3\right) \, \sqrt{x + 1}\right)} e^{\left(i \, x\right)} + \frac{1}{4} i \, {\left(2 i \, {\left(x + 1\right)}^{\frac{3}{2}} - \left(4 i - 3\right) \, \sqrt{x + 1}\right)} e^{\left(-i \, x\right)} - \frac{1}{2} \, \sqrt{x + 1} e^{\left(i \, x\right)} - \frac{1}{2} \, \sqrt{x + 1} e^{\left(-i \, x\right)} - 0.537182832596000"," ",0,"(1/16*I + 5/16)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(x + 1))*e^I - (1/16*I - 5/16)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(x + 1))*e^(-I) + 1/4*I*(2*I*(x + 1)^(3/2) - (4*I + 3)*sqrt(x + 1))*e^(I*x) + 1/4*I*(2*I*(x + 1)^(3/2) - (4*I - 3)*sqrt(x + 1))*e^(-I*x) - 1/2*sqrt(x + 1)*e^(I*x) - 1/2*sqrt(x + 1)*e^(-I*x) - 0.537182832596000","C",0
811,1,66,0,0.179970," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(1/2)*sin(x),x, algorithm=""giac"")","\left(\frac{1}{8} i - \frac{1}{8}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{x + 1}\right) e^{i} - \left(\frac{1}{8} i + \frac{1}{8}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{x + 1}\right) e^{\left(-i\right)} - \frac{1}{2} \, \sqrt{x + 1} e^{\left(i \, x\right)} - \frac{1}{2} \, \sqrt{x + 1} e^{\left(-i \, x\right)} - 0.339605729125000"," ",0,"(1/8*I - 1/8)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(x + 1))*e^I - (1/8*I + 1/8)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(x + 1))*e^(-I) - 1/2*sqrt(x + 1)*e^(I*x) - 1/2*sqrt(x + 1)*e^(-I*x) - 0.339605729125000","C",0
812,1,202,0,0.235777," ","integrate((1+x)^(5/2)/(-x^2+1)^(1/2)*x*sin(x),x, algorithm=""giac"")","-\left(\frac{19}{32} i - \frac{15}{32}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{i} + \left(\frac{19}{32} i + \frac{15}{32}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{\left(-i\right)} - \frac{1}{8} i \, {\left(4 i \, {\left(x - 1\right)}^{2} \sqrt{-x + 1} - \left(12 i - 10\right) \, {\left(-x + 1\right)}^{\frac{3}{2}} - \left(3 i + 18\right) \, \sqrt{-x + 1}\right)} e^{\left(i \, x\right)} - \frac{1}{2} i \, {\left(-2 i \, {\left(-x + 1\right)}^{\frac{3}{2}} + \left(4 i - 3\right) \, \sqrt{-x + 1}\right)} e^{\left(i \, x\right)} - \frac{1}{8} i \, {\left(4 i \, {\left(x - 1\right)}^{2} \sqrt{-x + 1} - \left(12 i + 10\right) \, {\left(-x + 1\right)}^{\frac{3}{2}} - \left(3 i - 18\right) \, \sqrt{-x + 1}\right)} e^{\left(-i \, x\right)} - \frac{1}{2} i \, {\left(-2 i \, {\left(-x + 1\right)}^{\frac{3}{2}} + \left(4 i + 3\right) \, \sqrt{-x + 1}\right)} e^{\left(-i \, x\right)} + \frac{1}{2} \, \sqrt{-x + 1} e^{\left(i \, x\right)} + \frac{1}{2} \, \sqrt{-x + 1} e^{\left(-i \, x\right)} + 3.25954715712000"," ",0,"-(19/32*I - 15/32)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(-x + 1))*e^I + (19/32*I + 15/32)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(-x + 1))*e^(-I) - 1/8*I*(4*I*(x - 1)^2*sqrt(-x + 1) - (12*I - 10)*(-x + 1)^(3/2) - (3*I + 18)*sqrt(-x + 1))*e^(I*x) - 1/2*I*(-2*I*(-x + 1)^(3/2) + (4*I - 3)*sqrt(-x + 1))*e^(I*x) - 1/8*I*(4*I*(x - 1)^2*sqrt(-x + 1) - (12*I + 10)*(-x + 1)^(3/2) - (3*I - 18)*sqrt(-x + 1))*e^(-I*x) - 1/2*I*(-2*I*(-x + 1)^(3/2) + (4*I + 3)*sqrt(-x + 1))*e^(-I*x) + 1/2*sqrt(-x + 1)*e^(I*x) + 1/2*sqrt(-x + 1)*e^(-I*x) + 3.25954715712000","C",0
813,1,122,0,0.219571," ","integrate((1+x)^(5/2)/(-x^2+1)^(1/2)*sin(x),x, algorithm=""giac"")","-\left(\frac{21}{16} i + \frac{5}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{i} + \left(\frac{21}{16} i - \frac{5}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{\left(-i\right)} - \frac{1}{4} i \, {\left(-2 i \, {\left(-x + 1\right)}^{\frac{3}{2}} + \left(4 i - 3\right) \, \sqrt{-x + 1}\right)} e^{\left(i \, x\right)} - \frac{1}{4} i \, {\left(-2 i \, {\left(-x + 1\right)}^{\frac{3}{2}} + \left(4 i + 3\right) \, \sqrt{-x + 1}\right)} e^{\left(-i \, x\right)} + \sqrt{-x + 1} e^{\left(i \, x\right)} + \sqrt{-x + 1} e^{\left(-i \, x\right)} + 3.78811297138000"," ",0,"-(21/16*I + 5/16)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(-x + 1))*e^I + (21/16*I - 5/16)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(-x + 1))*e^(-I) - 1/4*I*(-2*I*(-x + 1)^(3/2) + (4*I - 3)*sqrt(-x + 1))*e^(I*x) - 1/4*I*(-2*I*(-x + 1)^(3/2) + (4*I + 3)*sqrt(-x + 1))*e^(-I*x) + sqrt(-x + 1)*e^(I*x) + sqrt(-x + 1)*e^(-I*x) + 3.78811297138000","C",0
814,1,122,0,0.215715," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2)*x*sin(x),x, algorithm=""giac"")","\left(\frac{25}{32} i + \frac{11}{32}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{x + 1}\right) e^{i} - \left(\frac{25}{32} i - \frac{11}{32}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{x + 1}\right) e^{\left(-i\right)} - \frac{1}{8} i \, {\left(4 i \, {\left(x + 1\right)}^{\frac{5}{2}} - \left(12 i + 10\right) \, {\left(x + 1\right)}^{\frac{3}{2}} - \left(3 i - 18\right) \, \sqrt{x + 1}\right)} e^{\left(i \, x\right)} - \frac{1}{8} i \, {\left(4 i \, {\left(x + 1\right)}^{\frac{5}{2}} - \left(12 i - 10\right) \, {\left(x + 1\right)}^{\frac{3}{2}} - \left(3 i + 18\right) \, \sqrt{x + 1}\right)} e^{\left(-i \, x\right)} - \frac{1}{2} \, \sqrt{x + 1} e^{\left(i \, x\right)} - \frac{1}{2} \, \sqrt{x + 1} e^{\left(-i \, x\right)} - 0.330988710799000"," ",0,"(25/32*I + 11/32)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(x + 1))*e^I - (25/32*I - 11/32)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(x + 1))*e^(-I) - 1/8*I*(4*I*(x + 1)^(5/2) - (12*I + 10)*(x + 1)^(3/2) - (3*I - 18)*sqrt(x + 1))*e^(I*x) - 1/8*I*(4*I*(x + 1)^(5/2) - (12*I - 10)*(x + 1)^(3/2) - (3*I + 18)*sqrt(x + 1))*e^(-I*x) - 1/2*sqrt(x + 1)*e^(I*x) - 1/2*sqrt(x + 1)*e^(-I*x) - 0.330988710799000","C",0
815,1,86,0,0.188635," ","integrate((1+x)/(-x^2+1)^(1/2)*(1-x)^(3/2)*sin(x),x, algorithm=""giac"")","\left(\frac{1}{16} i - \frac{7}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{x + 1}\right) e^{i} - \left(\frac{1}{16} i + \frac{7}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{x + 1}\right) e^{\left(-i\right)} - \frac{1}{4} i \, {\left(2 i \, {\left(x + 1\right)}^{\frac{3}{2}} - \left(4 i + 3\right) \, \sqrt{x + 1}\right)} e^{\left(i \, x\right)} - \frac{1}{4} i \, {\left(2 i \, {\left(x + 1\right)}^{\frac{3}{2}} - \left(4 i - 3\right) \, \sqrt{x + 1}\right)} e^{\left(-i \, x\right)} + 0.197577103470000"," ",0,"(1/16*I - 7/16)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(x + 1))*e^I - (1/16*I + 7/16)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(x + 1))*e^(-I) - 1/4*I*(2*I*(x + 1)^(3/2) - (4*I + 3)*sqrt(x + 1))*e^(I*x) - 1/4*I*(2*I*(x + 1)^(3/2) - (4*I - 3)*sqrt(x + 1))*e^(-I*x) + 0.197577103470000","C",0
816,1,74,0,0.521144," ","integrate((1+x)^(1/2)/(-x^2+1)^(1/2)*x*sin(x),x, algorithm=""giac"")","-\left(\frac{3}{8} i + \frac{1}{8}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{i} + \left(\frac{3}{8} i - \frac{1}{8}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{\left(-i\right)} + \frac{1}{2} \, \sqrt{-x + 1} e^{\left(i \, x\right)} + \frac{1}{2} \, \sqrt{-x + 1} e^{\left(-i \, x\right)} + 1.16622538328000"," ",0,"-(3/8*I + 1/8)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(-x + 1))*e^I + (3/8*I - 1/8)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(-x + 1))*e^(-I) + 1/2*sqrt(-x + 1)*e^(I*x) + 1/2*sqrt(-x + 1)*e^(-I*x) + 1.16622538328000","C",0
817,1,48,0,0.182291," ","integrate((1+x)^(1/2)/(-x^2+1)^(1/2)*sin(x),x, algorithm=""giac"")","-\left(\frac{1}{4} i + \frac{1}{4}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{i} + \left(\frac{1}{4} i - \frac{1}{4}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{-x + 1}\right) e^{\left(-i\right)} + 0.826619654151000"," ",0,"-(1/4*I + 1/4)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(-x + 1))*e^I + (1/4*I - 1/4)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(-x + 1))*e^(-I) + 0.826619654151000","C",0
818,1,139,0,0.231788," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x^3,x, algorithm=""giac"")","-\frac{1}{24} \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left({\left(2 \, x {\left(\frac{3 \, x}{b} - \frac{3 \, a b^{5} - 4 \, b^{5}}{b^{7}}\right)} + \frac{6 \, a^{2} b^{4} - 20 \, a b^{4} + 9 \, b^{4}}{b^{7}}\right)} x - \frac{6 \, a^{3} b^{3} - 44 \, a^{2} b^{3} + 39 \, a b^{3} - 16 \, b^{3}}{b^{7}}\right)} + \frac{{\left(8 \, a^{3} - 12 \, a^{2} + 12 \, a - 3\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{8 \, b^{3} {\left| b \right|}}"," ",0,"-1/24*sqrt(-(b*x + a)^2 + 1)*((2*x*(3*x/b - (3*a*b^5 - 4*b^5)/b^7) + (6*a^2*b^4 - 20*a*b^4 + 9*b^4)/b^7)*x - (6*a^3*b^3 - 44*a^2*b^3 + 39*a*b^3 - 16*b^3)/b^7) + 1/8*(8*a^3 - 12*a^2 + 12*a - 3)*arcsin(-b*x - a)*sgn(b)/(b^3*abs(b))","A",0
819,1,97,0,0.212621," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x^2,x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(x {\left(\frac{2 \, x}{b} - \frac{2 \, a b^{3} - 3 \, b^{3}}{b^{5}}\right)} + \frac{2 \, a^{2} b^{2} - 9 \, a b^{2} + 4 \, b^{2}}{b^{5}}\right)} - \frac{{\left(2 \, a^{2} - 2 \, a + 1\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{2 \, b^{2} {\left| b \right|}}"," ",0,"-1/6*sqrt(-(b*x + a)^2 + 1)*(x*(2*x/b - (2*a*b^3 - 3*b^3)/b^5) + (2*a^2*b^2 - 9*a*b^2 + 4*b^2)/b^5) - 1/2*(2*a^2 - 2*a + 1)*arcsin(-b*x - a)*sgn(b)/(b^2*abs(b))","A",0
820,1,59,0,0.393366," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(\frac{x}{b} - \frac{a b - 2 \, b}{b^{3}}\right)} + \frac{{\left(2 \, a - 1\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{2 \, b {\left| b \right|}}"," ",0,"-1/2*sqrt(-(b*x + a)^2 + 1)*(x/b - (a*b - 2*b)/b^3) + 1/2*(2*a - 1)*arcsin(-b*x - a)*sgn(b)/(b*abs(b))","A",0
821,1,36,0,0.214571," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{\arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} - \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1}}{b}"," ",0,"-arcsin(-b*x - a)*sgn(b)/abs(b) - sqrt(-(b*x + a)^2 + 1)/b","A",0
822,1,79,0,0.230415," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x,x, algorithm=""giac"")","-\frac{b \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} + \frac{2 \, {\left(a b + b\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{\sqrt{a^{2} - 1} {\left| b \right|}}"," ",0,"-b*arcsin(-b*x - a)*sgn(b)/abs(b) + 2*(a*b + b)*arctan(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/(sqrt(a^2 - 1)*abs(b))","A",0
823,1,190,0,0.254470," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^2,x, algorithm=""giac"")","-\frac{2 \, b^{2} \arctan\left(\frac{\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{\sqrt{a^{2} - 1} {\left(a {\left| b \right|} - {\left| b \right|}\right)}} + \frac{2 \, {\left(a b^{2} - \frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} b^{2}}{b^{2} x + a b}\right)}}{{\left(a^{2} {\left| b \right|} - a {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}}"," ",0,"-2*b^2*arctan(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/(sqrt(a^2 - 1)*(a*abs(b) - abs(b))) + 2*(a*b^2 - (sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*b^2/(b^2*x + a*b))/((a^2*abs(b) - a*abs(b))*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b)))","B",0
824,1,622,0,0.386396," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^3,x, algorithm=""giac"")","\frac{{\left(2 \, a b^{3} + b^{3}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{3} {\left| b \right|} - a^{2} {\left| b \right|} - a {\left| b \right|} + {\left| b \right|}\right)} \sqrt{a^{2} - 1}} - \frac{\frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{4} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} + 2 \, a^{4} b^{3} - \frac{5 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{3} b^{3}}{b^{2} x + a b} + \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{3} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{3 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{3} b^{3}}{{\left(b^{2} x + a b\right)}^{3}} + 2 \, a^{3} b^{3} - \frac{6 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{3}}{b^{2} x + a b} + \frac{3 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{3}} - a^{2} b^{3} + \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a b^{3}}{b^{2} x + a b} + \frac{4 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a b^{3}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a b^{3}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{2}}}{{\left(a^{5} {\left| b \right|} - a^{4} {\left| b \right|} - a^{3} {\left| b \right|} + a^{2} {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}^{2}}"," ",0,"(2*a*b^3 + b^3)*arctan(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^3*abs(b) - a^2*abs(b) - a*abs(b) + abs(b))*sqrt(a^2 - 1)) - (2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^4*b^3/(b^2*x + a*b)^2 + 2*a^4*b^3 - 5*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^3*b^3/(b^2*x + a*b) + 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^3*b^3/(b^2*x + a*b)^2 - 3*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^3*b^3/(b^2*x + a*b)^3 + 2*a^3*b^3 - 6*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^2*b^3/(b^2*x + a*b) + 3*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^2*b^3/(b^2*x + a*b)^2 - 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^2*b^3/(b^2*x + a*b)^3 - a^2*b^3 + 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a*b^3/(b^2*x + a*b) + 4*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a*b^3/(b^2*x + a*b)^2 + 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a*b^3/(b^2*x + a*b)^3 - 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*b^3/(b^2*x + a*b)^2)/((a^5*abs(b) - a^4*abs(b) - a^3*abs(b) + a^2*abs(b))*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b))^2)","B",0
825,1,1376,0,1.054952," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{{\left(2 \, a^{2} b^{4} + 2 \, a b^{4} + b^{4}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{5} {\left| b \right|} - a^{4} {\left| b \right|} - 2 \, a^{3} {\left| b \right|} + 2 \, a^{2} {\left| b \right|} + a {\left| b \right|} - {\left| b \right|}\right)} \sqrt{a^{2} - 1}} + \frac{\frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{7} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{6 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{7} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + 6 \, a^{7} b^{4} - \frac{24 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{6} b^{4}}{b^{2} x + a b} + \frac{24 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{36 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + 12 \, a^{6} b^{4} - \frac{57 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{5} b^{4}}{b^{2} x + a b} + \frac{36 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{72 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{30 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{15 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} - 2 \, a^{5} b^{4} + \frac{84 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{51 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} - 3 \, a^{4} b^{4} + \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{3} b^{4}}{b^{2} x + a b} - \frac{30 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{18 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + \frac{6 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + 2 \, a^{3} b^{4} - \frac{6 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{4}}{b^{2} x + a b} - \frac{18 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{4 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{18 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{6 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{8 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{3}}}{3 \, {\left(a^{8} {\left| b \right|} - a^{7} {\left| b \right|} - 2 \, a^{6} {\left| b \right|} + 2 \, a^{5} {\left| b \right|} + a^{4} {\left| b \right|} - a^{3} {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}^{3}}"," ",0,"-(2*a^2*b^4 + 2*a*b^4 + b^4)*arctan(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^5*abs(b) - a^4*abs(b) - 2*a^3*abs(b) + 2*a^2*abs(b) + a*abs(b) - abs(b))*sqrt(a^2 - 1)) + 1/3*(12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^7*b^4/(b^2*x + a*b)^2 + 6*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^7*b^4/(b^2*x + a*b)^4 + 6*a^7*b^4 - 24*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^6*b^4/(b^2*x + a*b) + 24*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^6*b^4/(b^2*x + a*b)^2 - 36*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^6*b^4/(b^2*x + a*b)^3 + 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^6*b^4/(b^2*x + a*b)^4 - 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^5*a^6*b^4/(b^2*x + a*b)^5 + 12*a^6*b^4 - 57*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^5*b^4/(b^2*x + a*b) + 36*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^5*b^4/(b^2*x + a*b)^2 - 72*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^5*b^4/(b^2*x + a*b)^3 + 30*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^5*b^4/(b^2*x + a*b)^4 - 15*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^5*a^5*b^4/(b^2*x + a*b)^5 - 2*a^5*b^4 + 84*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^4*b^4/(b^2*x + a*b)^2 - 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^4*b^4/(b^2*x + a*b)^3 + 51*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^4*b^4/(b^2*x + a*b)^4 + 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^5*a^4*b^4/(b^2*x + a*b)^5 - 3*a^4*b^4 + 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^3*b^4/(b^2*x + a*b) - 30*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^3*b^4/(b^2*x + a*b)^3 - 18*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^3*b^4/(b^2*x + a*b)^4 + 6*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^5*a^3*b^4/(b^2*x + a*b)^5 + 2*a^3*b^4 - 6*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^2*b^4/(b^2*x + a*b) - 18*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^2*b^4/(b^2*x + a*b)^2 - 4*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^2*b^4/(b^2*x + a*b)^3 - 18*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^2*b^4/(b^2*x + a*b)^4 - 6*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^5*a^2*b^4/(b^2*x + a*b)^5 + 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a*b^4/(b^2*x + a*b)^2 + 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a*b^4/(b^2*x + a*b)^3 + 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a*b^4/(b^2*x + a*b)^4 - 8*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*b^4/(b^2*x + a*b)^3)/((a^8*abs(b) - a^7*abs(b) - 2*a^6*abs(b) + 2*a^5*abs(b) + a^4*abs(b) - a^3*abs(b))*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b))^3)","B",0
826,1,122,0,0.178645," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)*x^4,x, algorithm=""giac"")","-\frac{2 \, {\left(a^{4} - 4 \, a^{3} + 6 \, a^{2} - 4 \, a + 1\right)} \log\left({\left| b x + a - 1 \right|}\right)}{b^{5}} - \frac{6 \, b^{5} x^{5} + 15 \, b^{4} x^{4} - 20 \, a b^{3} x^{3} + 30 \, a^{2} b^{2} x^{2} + 20 \, b^{3} x^{3} - 60 \, a^{3} b x - 60 \, a b^{2} x^{2} + 180 \, a^{2} b x + 30 \, b^{2} x^{2} - 180 \, a b x + 60 \, b x}{30 \, b^{5}}"," ",0,"-2*(a^4 - 4*a^3 + 6*a^2 - 4*a + 1)*log(abs(b*x + a - 1))/b^5 - 1/30*(6*b^5*x^5 + 15*b^4*x^4 - 20*a*b^3*x^3 + 30*a^2*b^2*x^2 + 20*b^3*x^3 - 60*a^3*b*x - 60*a*b^2*x^2 + 180*a^2*b*x + 30*b^2*x^2 - 180*a*b*x + 60*b*x)/b^5","A",0
827,1,82,0,0.151323," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)*x^3,x, algorithm=""giac"")","\frac{2 \, {\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)} \log\left({\left| b x + a - 1 \right|}\right)}{b^{4}} - \frac{3 \, b^{4} x^{4} + 8 \, b^{3} x^{3} - 12 \, a b^{2} x^{2} + 24 \, a^{2} b x + 12 \, b^{2} x^{2} - 48 \, a b x + 24 \, b x}{12 \, b^{4}}"," ",0,"2*(a^3 - 3*a^2 + 3*a - 1)*log(abs(b*x + a - 1))/b^4 - 1/12*(3*b^4*x^4 + 8*b^3*x^3 - 12*a*b^2*x^2 + 24*a^2*b*x + 12*b^2*x^2 - 48*a*b*x + 24*b*x)/b^4","A",0
828,1,52,0,0.148487," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)*x^2,x, algorithm=""giac"")","-\frac{2 \, {\left(a^{2} - 2 \, a + 1\right)} \log\left({\left| b x + a - 1 \right|}\right)}{b^{3}} - \frac{b^{3} x^{3} + 3 \, b^{2} x^{2} - 6 \, a b x + 6 \, b x}{3 \, b^{3}}"," ",0,"-2*(a^2 - 2*a + 1)*log(abs(b*x + a - 1))/b^3 - 1/3*(b^3*x^3 + 3*b^2*x^2 - 6*a*b*x + 6*b*x)/b^3","A",0
829,1,34,0,0.151700," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)*x,x, algorithm=""giac"")","\frac{2 \, {\left(a - 1\right)} \log\left({\left| b x + a - 1 \right|}\right)}{b^{2}} - \frac{b^{2} x^{2} + 4 \, b x}{2 \, b^{2}}"," ",0,"2*(a - 1)*log(abs(b*x + a - 1))/b^2 - 1/2*(b^2*x^2 + 4*b*x)/b^2","A",0
830,1,17,0,0.239664," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2),x, algorithm=""giac"")","-x - \frac{2 \, \log\left({\left| b x + a - 1 \right|}\right)}{b}"," ",0,"-x - 2*log(abs(b*x + a - 1))/b","A",0
831,1,34,0,0.188272," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)/x,x, algorithm=""giac"")","\frac{2 \, b \log\left({\left| b x + a - 1 \right|}\right)}{a b - b} - \frac{{\left(a + 1\right)} \log\left({\left| x \right|}\right)}{a - 1}"," ",0,"2*b*log(abs(b*x + a - 1))/(a*b - b) - (a + 1)*log(abs(x))/(a - 1)","A",0
832,1,57,0,0.144053," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)/x^2,x, algorithm=""giac"")","-\frac{2 \, b^{2} \log\left({\left| b x + a - 1 \right|}\right)}{a^{2} b - 2 \, a b + b} + \frac{2 \, b \log\left({\left| x \right|}\right)}{a^{2} - 2 \, a + 1} + \frac{a^{2} - 1}{{\left(a - 1\right)}^{2} x}"," ",0,"-2*b^2*log(abs(b*x + a - 1))/(a^2*b - 2*a*b + b) + 2*b*log(abs(x))/(a^2 - 2*a + 1) + (a^2 - 1)/((a - 1)^2*x)","A",0
833,1,91,0,0.178505," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)/x^3,x, algorithm=""giac"")","\frac{2 \, b^{3} \log\left({\left| b x + a - 1 \right|}\right)}{a^{3} b - 3 \, a^{2} b + 3 \, a b - b} - \frac{2 \, b^{2} \log\left({\left| x \right|}\right)}{a^{3} - 3 \, a^{2} + 3 \, a - 1} + \frac{a^{3} - a^{2} - 4 \, {\left(a b - b\right)} x - a + 1}{2 \, {\left(a - 1\right)}^{3} x^{2}}"," ",0,"2*b^3*log(abs(b*x + a - 1))/(a^3*b - 3*a^2*b + 3*a*b - b) - 2*b^2*log(abs(x))/(a^3 - 3*a^2 + 3*a - 1) + 1/2*(a^3 - a^2 - 4*(a*b - b)*x - a + 1)/((a - 1)^3*x^2)","A",0
834,1,120,0,0.174491," ","integrate((b*x+a+1)^2/(1-(b*x+a)^2)/x^4,x, algorithm=""giac"")","-\frac{2 \, b^{4} \log\left({\left| b x + a - 1 \right|}\right)}{a^{4} b - 4 \, a^{3} b + 6 \, a^{2} b - 4 \, a b + b} + \frac{2 \, b^{3} \log\left({\left| x \right|}\right)}{a^{4} - 4 \, a^{3} + 6 \, a^{2} - 4 \, a + 1} + \frac{a^{4} - 2 \, a^{3} + 6 \, {\left(a b^{2} - b^{2}\right)} x^{2} - 3 \, {\left(a^{2} b - 2 \, a b + b\right)} x + 2 \, a - 1}{3 \, {\left(a - 1\right)}^{4} x^{3}}"," ",0,"-2*b^4*log(abs(b*x + a - 1))/(a^4*b - 4*a^3*b + 6*a^2*b - 4*a*b + b) + 2*b^3*log(abs(x))/(a^4 - 4*a^3 + 6*a^2 - 4*a + 1) + 1/3*(a^4 - 2*a^3 + 6*(a*b^2 - b^2)*x^2 - 3*(a^2*b - 2*a*b + b)*x + 2*a - 1)/((a - 1)^4*x^3)","A",0
835,1,193,0,0.515948," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)*x^3,x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left({\left(2 \, x {\left(\frac{x}{b} - \frac{a b^{11} - 4 \, b^{11}}{b^{13}}\right)} + \frac{2 \, a^{2} b^{10} - 20 \, a b^{10} + 19 \, b^{10}}{b^{13}}\right)} x - \frac{2 \, a^{3} b^{9} - 44 \, a^{2} b^{9} + 93 \, a b^{9} - 48 \, b^{9}}{b^{13}}\right)} - \frac{3 \, {\left(8 \, a^{3} - 36 \, a^{2} + 44 \, a - 17\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{8 \, b^{3} {\left| b \right|}} - \frac{8 \, {\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)}}{b^{3} {\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)} {\left| b \right|}}"," ",0,"1/8*sqrt(-(b*x + a)^2 + 1)*((2*x*(x/b - (a*b^11 - 4*b^11)/b^13) + (2*a^2*b^10 - 20*a*b^10 + 19*b^10)/b^13)*x - (2*a^3*b^9 - 44*a^2*b^9 + 93*a*b^9 - 48*b^9)/b^13) - 3/8*(8*a^3 - 36*a^2 + 44*a - 17)*arcsin(-b*x - a)*sgn(b)/(b^3*abs(b)) - 8*(a^3 - 3*a^2 + 3*a - 1)/(b^3*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1)*abs(b))","A",0
836,1,148,0,0.299575," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)*x^2,x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(x {\left(\frac{2 \, x}{b} - \frac{2 \, a b^{6} - 9 \, b^{6}}{b^{8}}\right)} + \frac{2 \, a^{2} b^{5} - 27 \, a b^{5} + 28 \, b^{5}}{b^{8}}\right)} + \frac{{\left(6 \, a^{2} - 18 \, a + 11\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{2 \, b^{2} {\left| b \right|}} + \frac{8 \, {\left(a^{2} - 2 \, a + 1\right)}}{b^{2} {\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)} {\left| b \right|}}"," ",0,"1/6*sqrt(-(b*x + a)^2 + 1)*(x*(2*x/b - (2*a*b^6 - 9*b^6)/b^8) + (2*a^2*b^5 - 27*a*b^5 + 28*b^5)/b^8) + 1/2*(6*a^2 - 18*a + 11)*arcsin(-b*x - a)*sgn(b)/(b^2*abs(b)) + 8*(a^2 - 2*a + 1)/(b^2*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1)*abs(b))","A",0
837,1,109,0,0.254725," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)*x,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(\frac{x}{b} - \frac{a b^{2} - 6 \, b^{2}}{b^{4}}\right)} - \frac{3 \, {\left(2 \, a - 3\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{2 \, b {\left| b \right|}} - \frac{8 \, {\left(a - 1\right)}}{b {\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)} {\left| b \right|}}"," ",0,"1/2*sqrt(-(b*x + a)^2 + 1)*(x/b - (a*b^2 - 6*b^2)/b^4) - 3/2*(2*a - 3)*arcsin(-b*x - a)*sgn(b)/(b*abs(b)) - 8*(a - 1)/(b*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1)*abs(b))","A",0
838,1,75,0,0.312089," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2),x, algorithm=""giac"")","\frac{3 \, \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1}}{b} + \frac{8}{{\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)} {\left| b \right|}}"," ",0,"3*arcsin(-b*x - a)*sgn(b)/abs(b) + sqrt(-(b*x + a)^2 + 1)/b + 8/(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1)*abs(b))","A",0
839,1,139,0,0.319372," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x,x, algorithm=""giac"")","\frac{b \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} - \frac{2 \, {\left(a^{2} b + 2 \, a b + b\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{\sqrt{a^{2} - 1} {\left(a {\left| b \right|} - {\left| b \right|}\right)}} - \frac{8 \, b}{{\left(a {\left| b \right|} - {\left| b \right|}\right)} {\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)}}"," ",0,"b*arcsin(-b*x - a)*sgn(b)/abs(b) - 2*(a^2*b + 2*a*b + b)*arctan(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/(sqrt(a^2 - 1)*(a*abs(b) - abs(b))) - 8*b/((a*abs(b) - abs(b))*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1))","A",0
840,1,498,0,0.225981," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^2,x, algorithm=""giac"")","\frac{6 \, {\left(a b^{2} + b^{2}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{2} {\left| b \right|} - 2 \, a {\left| b \right|} + {\left| b \right|}\right)} \sqrt{a^{2} - 1}} - \frac{2 \, {\left(\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{2}}{b^{2} x + a b} - \frac{4 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{2}}{{\left(b^{2} x + a b\right)}^{2}} - 5 \, a^{2} b^{2} + \frac{10 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a b^{2}}{b^{2} x + a b} - \frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a b^{2}}{{\left(b^{2} x + a b\right)}^{2}} - a b^{2} + \frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} b^{2}}{b^{2} x + a b} - \frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} b^{2}}{{\left(b^{2} x + a b\right)}^{2}}\right)}}{{\left(a^{3} {\left| b \right|} - 2 \, a^{2} {\left| b \right|} + a {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - \frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + \frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a}{{\left(b^{2} x + a b\right)}^{3}} - a + \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b} - \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2}}{{\left(b^{2} x + a b\right)}^{2}}\right)}}"," ",0,"6*(a*b^2 + b^2)*arctan(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^2*abs(b) - 2*a*abs(b) + abs(b))*sqrt(a^2 - 1)) - 2*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^2*b^2/(b^2*x + a*b) - 4*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^2*b^2/(b^2*x + a*b)^2 - 5*a^2*b^2 + 10*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a*b^2/(b^2*x + a*b) - (sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a*b^2/(b^2*x + a*b)^2 - a*b^2 + (sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*b^2/(b^2*x + a*b) - (sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*b^2/(b^2*x + a*b)^2)/((a^3*abs(b) - 2*a^2*abs(b) + a*abs(b))*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - (sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + (sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a/(b^2*x + a*b)^3 - a + 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2/(b^2*x + a*b)^2))","B",0
841,1,691,0,0.452016," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^3,x, algorithm=""giac"")","-\frac{8 \, b^{3}}{{\left(a^{3} {\left| b \right|} - 3 \, a^{2} {\left| b \right|} + 3 \, a {\left| b \right|} - {\left| b \right|}\right)} {\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)}} - \frac{3 \, {\left(2 \, a b^{3} + 3 \, b^{3}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{3} {\left| b \right|} - 3 \, a^{2} {\left| b \right|} + 3 \, a {\left| b \right|} - {\left| b \right|}\right)} \sqrt{a^{2} - 1}} + \frac{\frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{4} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} + 2 \, a^{4} b^{3} - \frac{5 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{3} b^{3}}{b^{2} x + a b} + \frac{6 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{3} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{3 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{3} b^{3}}{{\left(b^{2} x + a b\right)}^{3}} + 6 \, a^{3} b^{3} - \frac{18 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{3}}{b^{2} x + a b} + \frac{3 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{6 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{3}} - a^{2} b^{3} + \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a b^{3}}{b^{2} x + a b} + \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a b^{3}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a b^{3}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{2}}}{{\left(a^{5} {\left| b \right|} - 3 \, a^{4} {\left| b \right|} + 3 \, a^{3} {\left| b \right|} - a^{2} {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}^{2}}"," ",0,"-8*b^3/((a^3*abs(b) - 3*a^2*abs(b) + 3*a*abs(b) - abs(b))*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1)) - 3*(2*a*b^3 + 3*b^3)*arctan(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^3*abs(b) - 3*a^2*abs(b) + 3*a*abs(b) - abs(b))*sqrt(a^2 - 1)) + (2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^4*b^3/(b^2*x + a*b)^2 + 2*a^4*b^3 - 5*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^3*b^3/(b^2*x + a*b) + 6*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^3*b^3/(b^2*x + a*b)^2 - 3*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^3*b^3/(b^2*x + a*b)^3 + 6*a^3*b^3 - 18*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^2*b^3/(b^2*x + a*b) + 3*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^2*b^3/(b^2*x + a*b)^2 - 6*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^2*b^3/(b^2*x + a*b)^3 - a^2*b^3 + 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a*b^3/(b^2*x + a*b) + 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a*b^3/(b^2*x + a*b)^2 + 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a*b^3/(b^2*x + a*b)^3 - 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*b^3/(b^2*x + a*b)^2)/((a^5*abs(b) - 3*a^4*abs(b) + 3*a^3*abs(b) - a^2*abs(b))*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b))^2)","B",0
842,1,1521,0,0.278276," ","integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^4,x, algorithm=""giac"")","\frac{8 \, b^{4}}{{\left(a^{4} {\left| b \right|} - 4 \, a^{3} {\left| b \right|} + 6 \, a^{2} {\left| b \right|} - 4 \, a {\left| b \right|} + {\left| b \right|}\right)} {\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)}} + \frac{{\left(6 \, a^{2} b^{4} + 18 \, a b^{4} + 11 \, b^{4}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{5} {\left| b \right|} - 3 \, a^{4} {\left| b \right|} + 2 \, a^{3} {\left| b \right|} + 2 \, a^{2} {\left| b \right|} - 3 \, a {\left| b \right|} + {\left| b \right|}\right)} \sqrt{a^{2} - 1}} - \frac{\frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{7} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{6 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{7} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + 6 \, a^{7} b^{4} - \frac{24 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{6} b^{4}}{b^{2} x + a b} + \frac{72 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{36 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{36 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + 36 \, a^{6} b^{4} - \frac{171 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{5} b^{4}}{b^{2} x + a b} + \frac{84 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{216 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{54 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{45 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + 22 \, a^{5} b^{4} - \frac{120 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{4} b^{4}}{b^{2} x + a b} + \frac{252 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{156 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{153 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} - 9 \, a^{4} b^{4} + \frac{36 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{3} b^{4}}{b^{2} x + a b} + \frac{192 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{90 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{78 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + \frac{18 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + 2 \, a^{3} b^{4} - \frac{6 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{4}}{b^{2} x + a b} - \frac{54 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{100 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{54 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{6 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{36 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{12 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{4} a b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{8 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{3}}}{3 \, {\left(a^{8} {\left| b \right|} - 3 \, a^{7} {\left| b \right|} + 2 \, a^{6} {\left| b \right|} + 2 \, a^{5} {\left| b \right|} - 3 \, a^{4} {\left| b \right|} + a^{3} {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}^{3}}"," ",0,"8*b^4/((a^4*abs(b) - 4*a^3*abs(b) + 6*a^2*abs(b) - 4*a*abs(b) + abs(b))*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1)) + (6*a^2*b^4 + 18*a*b^4 + 11*b^4)*arctan(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^5*abs(b) - 3*a^4*abs(b) + 2*a^3*abs(b) + 2*a^2*abs(b) - 3*a*abs(b) + abs(b))*sqrt(a^2 - 1)) - 1/3*(12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^7*b^4/(b^2*x + a*b)^2 + 6*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^7*b^4/(b^2*x + a*b)^4 + 6*a^7*b^4 - 24*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^6*b^4/(b^2*x + a*b) + 72*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^6*b^4/(b^2*x + a*b)^2 - 36*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^6*b^4/(b^2*x + a*b)^3 + 36*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^6*b^4/(b^2*x + a*b)^4 - 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^5*a^6*b^4/(b^2*x + a*b)^5 + 36*a^6*b^4 - 171*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^5*b^4/(b^2*x + a*b) + 84*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^5*b^4/(b^2*x + a*b)^2 - 216*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^5*b^4/(b^2*x + a*b)^3 + 54*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^5*b^4/(b^2*x + a*b)^4 - 45*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^5*a^5*b^4/(b^2*x + a*b)^5 + 22*a^5*b^4 - 120*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^4*b^4/(b^2*x + a*b) + 252*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^4*b^4/(b^2*x + a*b)^2 - 156*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^4*b^4/(b^2*x + a*b)^3 + 153*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^4*b^4/(b^2*x + a*b)^4 - 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^5*a^4*b^4/(b^2*x + a*b)^5 - 9*a^4*b^4 + 36*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^3*b^4/(b^2*x + a*b) + 192*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^3*b^4/(b^2*x + a*b)^2 - 90*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^3*b^4/(b^2*x + a*b)^3 + 78*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^3*b^4/(b^2*x + a*b)^4 + 18*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^5*a^3*b^4/(b^2*x + a*b)^5 + 2*a^3*b^4 - 6*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^2*b^4/(b^2*x + a*b) - 54*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^2*b^4/(b^2*x + a*b)^2 - 100*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a^2*b^4/(b^2*x + a*b)^3 - 54*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a^2*b^4/(b^2*x + a*b)^4 - 6*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^5*a^2*b^4/(b^2*x + a*b)^5 + 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a*b^4/(b^2*x + a*b)^2 + 36*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a*b^4/(b^2*x + a*b)^3 + 12*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^4*a*b^4/(b^2*x + a*b)^4 - 8*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*b^4/(b^2*x + a*b)^3)/((a^8*abs(b) - 3*a^7*abs(b) + 2*a^6*abs(b) + 2*a^5*abs(b) - 3*a^4*abs(b) + a^3*abs(b))*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b))^3)","B",0
843,1,148,0,0.219558," ","integrate(x^3/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left({\left(2 \, x {\left(\frac{3 \, x}{b} - \frac{3 \, a b^{5} + 4 \, b^{5}}{b^{7}}\right)} + \frac{6 \, a^{2} b^{4} + 20 \, a b^{4} + 9 \, b^{4}}{b^{7}}\right)} x - \frac{6 \, a^{3} b^{3} + 44 \, a^{2} b^{3} + 39 \, a b^{3} + 16 \, b^{3}}{b^{7}}\right)} + \frac{{\left(8 \, a^{3} + 12 \, a^{2} + 12 \, a + 3\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{8 \, b^{3} {\left| b \right|}}"," ",0,"1/24*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*((2*x*(3*x/b - (3*a*b^5 + 4*b^5)/b^7) + (6*a^2*b^4 + 20*a*b^4 + 9*b^4)/b^7)*x - (6*a^3*b^3 + 44*a^2*b^3 + 39*a*b^3 + 16*b^3)/b^7) + 1/8*(8*a^3 + 12*a^2 + 12*a + 3)*arcsin(-b*x - a)*sgn(b)/(b^3*abs(b))","A",0
844,1,106,0,0.837692," ","integrate(x^2/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(x {\left(\frac{2 \, x}{b} - \frac{2 \, a b^{3} + 3 \, b^{3}}{b^{5}}\right)} + \frac{2 \, a^{2} b^{2} + 9 \, a b^{2} + 4 \, b^{2}}{b^{5}}\right)} - \frac{{\left(2 \, a^{2} + 2 \, a + 1\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{2 \, b^{2} {\left| b \right|}}"," ",0,"1/6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(x*(2*x/b - (2*a*b^3 + 3*b^3)/b^5) + (2*a^2*b^2 + 9*a*b^2 + 4*b^2)/b^5) - 1/2*(2*a^2 + 2*a + 1)*arcsin(-b*x - a)*sgn(b)/(b^2*abs(b))","A",0
845,1,68,0,0.176165," ","integrate(x/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(\frac{x}{b} - \frac{a b + 2 \, b}{b^{3}}\right)} + \frac{{\left(2 \, a + 1\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{2 \, b {\left| b \right|}}"," ",0,"1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(x/b - (a*b + 2*b)/b^3) + 1/2*(2*a + 1)*arcsin(-b*x - a)*sgn(b)/(b*abs(b))","A",0
846,1,44,0,0.180505," ","integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{\arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} + \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b}"," ",0,"-arcsin(-b*x - a)*sgn(b)/abs(b) + sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b","A",0
847,1,89,0,0.406966," ","integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x,x, algorithm=""giac"")","\frac{b \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} - \frac{2 \, {\left(a b - b\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{\sqrt{a^{2} - 1} {\left| b \right|}}"," ",0,"b*arcsin(-b*x - a)*sgn(b)/abs(b) - 2*(a*b - b)*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/(sqrt(a^2 - 1)*abs(b))","A",0
848,1,223,0,0.273139," ","integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x^2,x, algorithm=""giac"")","-\frac{2 \, b^{2} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{\sqrt{a^{2} - 1} {\left(a {\left| b \right|} + {\left| b \right|}\right)}} - \frac{2 \, {\left(a b^{2} - \frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} b^{2}}{b^{2} x + a b}\right)}}{{\left(a^{2} {\left| b \right|} + a {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}}"," ",0,"-2*b^2*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/(sqrt(a^2 - 1)*(a*abs(b) + abs(b))) - 2*(a*b^2 - (sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*b^2/(b^2*x + a*b))/((a^2*abs(b) + a*abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b)))","B",0
849,1,750,0,0.290102," ","integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x^3,x, algorithm=""giac"")","\frac{{\left(2 \, a b^{3} - b^{3}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{3} {\left| b \right|} + a^{2} {\left| b \right|} - a {\left| b \right|} - {\left| b \right|}\right)} \sqrt{a^{2} - 1}} + \frac{\frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{4} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} + 2 \, a^{4} b^{3} - \frac{5 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{3} b^{3}}{b^{2} x + a b} - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{3} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{3 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{3} b^{3}}{{\left(b^{2} x + a b\right)}^{3}} - 2 \, a^{3} b^{3} + \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{3}}{b^{2} x + a b} + \frac{3 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{3}} - a^{2} b^{3} + \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a b^{3}}{b^{2} x + a b} - \frac{4 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a b^{3}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a b^{3}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{2}}}{{\left(a^{5} {\left| b \right|} + a^{4} {\left| b \right|} - a^{3} {\left| b \right|} - a^{2} {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}^{2}}"," ",0,"(2*a*b^3 - b^3)*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^3*abs(b) + a^2*abs(b) - a*abs(b) - abs(b))*sqrt(a^2 - 1)) + (2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^4*b^3/(b^2*x + a*b)^2 + 2*a^4*b^3 - 5*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^3*b^3/(b^2*x + a*b) - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^3*b^3/(b^2*x + a*b)^2 - 3*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^3*b^3/(b^2*x + a*b)^3 - 2*a^3*b^3 + 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^2*b^3/(b^2*x + a*b) + 3*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^2*b^3/(b^2*x + a*b)^2 + 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^2*b^3/(b^2*x + a*b)^3 - a^2*b^3 + 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a*b^3/(b^2*x + a*b) - 4*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a*b^3/(b^2*x + a*b)^2 + 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a*b^3/(b^2*x + a*b)^3 - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*b^3/(b^2*x + a*b)^2)/((a^5*abs(b) + a^4*abs(b) - a^3*abs(b) - a^2*abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b))^2)","B",0
850,1,1659,0,0.253316," ","integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{{\left(2 \, a^{2} b^{4} - 2 \, a b^{4} + b^{4}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{5} {\left| b \right|} + a^{4} {\left| b \right|} - 2 \, a^{3} {\left| b \right|} - 2 \, a^{2} {\left| b \right|} + a {\left| b \right|} + {\left| b \right|}\right)} \sqrt{a^{2} - 1}} - \frac{\frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{7} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{7} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + 6 \, a^{7} b^{4} - \frac{24 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{6} b^{4}}{b^{2} x + a b} - \frac{24 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{36 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} - 12 \, a^{6} b^{4} + \frac{57 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{5} b^{4}}{b^{2} x + a b} + \frac{36 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{72 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{30 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + \frac{15 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} - 2 \, a^{5} b^{4} - \frac{84 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{51 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + 3 \, a^{4} b^{4} - \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{3} b^{4}}{b^{2} x + a b} + \frac{30 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{18 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + 2 \, a^{3} b^{4} - \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{4}}{b^{2} x + a b} + \frac{18 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{4 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{18 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{8 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{3}}}{3 \, {\left(a^{8} {\left| b \right|} + a^{7} {\left| b \right|} - 2 \, a^{6} {\left| b \right|} - 2 \, a^{5} {\left| b \right|} + a^{4} {\left| b \right|} + a^{3} {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}^{3}}"," ",0,"-(2*a^2*b^4 - 2*a*b^4 + b^4)*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^5*abs(b) + a^4*abs(b) - 2*a^3*abs(b) - 2*a^2*abs(b) + a*abs(b) + abs(b))*sqrt(a^2 - 1)) - 1/3*(12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^7*b^4/(b^2*x + a*b)^2 + 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^7*b^4/(b^2*x + a*b)^4 + 6*a^7*b^4 - 24*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^6*b^4/(b^2*x + a*b) - 24*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^6*b^4/(b^2*x + a*b)^2 - 36*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^6*b^4/(b^2*x + a*b)^3 - 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^6*b^4/(b^2*x + a*b)^4 - 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^6*b^4/(b^2*x + a*b)^5 - 12*a^6*b^4 + 57*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^5*b^4/(b^2*x + a*b) + 36*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^5*b^4/(b^2*x + a*b)^2 + 72*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^5*b^4/(b^2*x + a*b)^3 + 30*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^5*b^4/(b^2*x + a*b)^4 + 15*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^5*b^4/(b^2*x + a*b)^5 - 2*a^5*b^4 - 84*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^4*b^4/(b^2*x + a*b)^2 - 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^4*b^4/(b^2*x + a*b)^3 - 51*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^4*b^4/(b^2*x + a*b)^4 + 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^4*b^4/(b^2*x + a*b)^5 + 3*a^4*b^4 - 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^3*b^4/(b^2*x + a*b) + 30*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^3*b^4/(b^2*x + a*b)^3 - 18*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^3*b^4/(b^2*x + a*b)^4 - 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^3*b^4/(b^2*x + a*b)^5 + 2*a^3*b^4 - 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^2*b^4/(b^2*x + a*b) + 18*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^2*b^4/(b^2*x + a*b)^2 - 4*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^2*b^4/(b^2*x + a*b)^3 + 18*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^2*b^4/(b^2*x + a*b)^4 - 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^2*b^4/(b^2*x + a*b)^5 + 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a*b^4/(b^2*x + a*b)^2 - 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a*b^4/(b^2*x + a*b)^3 + 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a*b^4/(b^2*x + a*b)^4 - 8*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*b^4/(b^2*x + a*b)^3)/((a^8*abs(b) + a^7*abs(b) - 2*a^6*abs(b) - 2*a^5*abs(b) + a^4*abs(b) + a^3*abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b))^3)","B",0
851,1,202,0,0.308700," ","integrate(x^4/(b*x+a+1)^2*(1-(b*x+a)^2),x, algorithm=""giac"")","\frac{{\left(b x + a + 1\right)}^{5} {\left(\frac{15 \, {\left(2 \, a b + 3 \, b\right)}}{{\left(b x + a + 1\right)} b} - \frac{20 \, {\left(3 \, a^{2} b^{2} + 10 \, a b^{2} + 7 \, b^{2}\right)}}{{\left(b x + a + 1\right)}^{2} b^{2}} + \frac{60 \, {\left(a^{3} b^{3} + 6 \, a^{2} b^{3} + 9 \, a b^{3} + 4 \, b^{3}\right)}}{{\left(b x + a + 1\right)}^{3} b^{3}} - \frac{30 \, {\left(a^{4} b^{4} + 12 \, a^{3} b^{4} + 30 \, a^{2} b^{4} + 28 \, a b^{4} + 9 \, b^{4}\right)}}{{\left(b x + a + 1\right)}^{4} b^{4}} - 6\right)}}{30 \, b^{5}} - \frac{2 \, {\left(a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1\right)} \log\left(\frac{{\left| b x + a + 1 \right|}}{{\left(b x + a + 1\right)}^{2} {\left| b \right|}}\right)}{b^{5}}"," ",0,"1/30*(b*x + a + 1)^5*(15*(2*a*b + 3*b)/((b*x + a + 1)*b) - 20*(3*a^2*b^2 + 10*a*b^2 + 7*b^2)/((b*x + a + 1)^2*b^2) + 60*(a^3*b^3 + 6*a^2*b^3 + 9*a*b^3 + 4*b^3)/((b*x + a + 1)^3*b^3) - 30*(a^4*b^4 + 12*a^3*b^4 + 30*a^2*b^4 + 28*a*b^4 + 9*b^4)/((b*x + a + 1)^4*b^4) - 6)/b^5 - 2*(a^4 + 4*a^3 + 6*a^2 + 4*a + 1)*log(abs(b*x + a + 1)/((b*x + a + 1)^2*abs(b)))/b^5","B",0
852,1,148,0,0.260774," ","integrate(x^3/(b*x+a+1)^2*(1-(b*x+a)^2),x, algorithm=""giac"")","\frac{{\left(b x + a + 1\right)}^{4} {\left(\frac{4 \, {\left(3 \, a b + 5 \, b\right)}}{{\left(b x + a + 1\right)} b} - \frac{18 \, {\left(a^{2} b^{2} + 4 \, a b^{2} + 3 \, b^{2}\right)}}{{\left(b x + a + 1\right)}^{2} b^{2}} + \frac{12 \, {\left(a^{3} b^{3} + 9 \, a^{2} b^{3} + 15 \, a b^{3} + 7 \, b^{3}\right)}}{{\left(b x + a + 1\right)}^{3} b^{3}} - 3\right)}}{12 \, b^{4}} + \frac{2 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} \log\left(\frac{{\left| b x + a + 1 \right|}}{{\left(b x + a + 1\right)}^{2} {\left| b \right|}}\right)}{b^{4}}"," ",0,"1/12*(b*x + a + 1)^4*(4*(3*a*b + 5*b)/((b*x + a + 1)*b) - 18*(a^2*b^2 + 4*a*b^2 + 3*b^2)/((b*x + a + 1)^2*b^2) + 12*(a^3*b^3 + 9*a^2*b^3 + 15*a*b^3 + 7*b^3)/((b*x + a + 1)^3*b^3) - 3)/b^4 + 2*(a^3 + 3*a^2 + 3*a + 1)*log(abs(b*x + a + 1)/((b*x + a + 1)^2*abs(b)))/b^4","B",0
853,1,102,0,0.160168," ","integrate(x^2/(b*x+a+1)^2*(1-(b*x+a)^2),x, algorithm=""giac"")","\frac{{\left(b x + a + 1\right)}^{3} {\left(\frac{3 \, {\left(a b + 2 \, b\right)}}{{\left(b x + a + 1\right)} b} - \frac{3 \, {\left(a^{2} b^{2} + 6 \, a b^{2} + 5 \, b^{2}\right)}}{{\left(b x + a + 1\right)}^{2} b^{2}} - 1\right)}}{3 \, b^{3}} - \frac{2 \, {\left(a^{2} + 2 \, a + 1\right)} \log\left(\frac{{\left| b x + a + 1 \right|}}{{\left(b x + a + 1\right)}^{2} {\left| b \right|}}\right)}{b^{3}}"," ",0,"1/3*(b*x + a + 1)^3*(3*(a*b + 2*b)/((b*x + a + 1)*b) - 3*(a^2*b^2 + 6*a*b^2 + 5*b^2)/((b*x + a + 1)^2*b^2) - 1)/b^3 - 2*(a^2 + 2*a + 1)*log(abs(b*x + a + 1)/((b*x + a + 1)^2*abs(b)))/b^3","B",0
854,1,69,0,0.168751," ","integrate(x/(b*x+a+1)^2*(1-(b*x+a)^2),x, algorithm=""giac"")","\frac{\frac{{\left(b x + a + 1\right)}^{2} {\left(\frac{2 \, {\left(a b + 3 \, b\right)}}{{\left(b x + a + 1\right)} b} - 1\right)}}{b} + \frac{4 \, {\left(a + 1\right)} \log\left(\frac{{\left| b x + a + 1 \right|}}{{\left(b x + a + 1\right)}^{2} {\left| b \right|}}\right)}{b}}{2 \, b}"," ",0,"1/2*((b*x + a + 1)^2*(2*(a*b + 3*b)/((b*x + a + 1)*b) - 1)/b + 4*(a + 1)*log(abs(b*x + a + 1)/((b*x + a + 1)^2*abs(b)))/b)/b","B",0
855,1,38,0,0.526961," ","integrate(1/(b*x+a+1)^2*(1-(b*x+a)^2),x, algorithm=""giac"")","-\frac{b x + a + 1}{b} - \frac{2 \, \log\left(\frac{{\left| b x + a + 1 \right|}}{{\left(b x + a + 1\right)}^{2} {\left| b \right|}}\right)}{b}"," ",0,"-(b*x + a + 1)/b - 2*log(abs(b*x + a + 1)/((b*x + a + 1)^2*abs(b)))/b","B",0
856,1,66,0,0.321490," ","integrate(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x,x, algorithm=""giac"")","-b {\left(\frac{{\left(a - 1\right)} \log\left({\left| -\frac{a}{b x + a + 1} - \frac{1}{b x + a + 1} + 1 \right|}\right)}{a b + b} - \frac{\log\left(\frac{{\left| b x + a + 1 \right|}}{{\left(b x + a + 1\right)}^{2} {\left| b \right|}}\right)}{b}\right)}"," ",0,"-b*((a - 1)*log(abs(-a/(b*x + a + 1) - 1/(b*x + a + 1) + 1))/(a*b + b) - log(abs(b*x + a + 1)/((b*x + a + 1)^2*abs(b)))/b)","B",0
857,1,80,0,0.186401," ","integrate(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x^2,x, algorithm=""giac"")","-\frac{2 \, b^{2} \log\left({\left| -\frac{a}{b x + a + 1} - \frac{1}{b x + a + 1} + 1 \right|}\right)}{a^{2} b + 2 \, a b + b} - \frac{a b - b}{{\left(a + 1\right)}^{2} {\left(\frac{a}{b x + a + 1} + \frac{1}{b x + a + 1} - 1\right)}}"," ",0,"-2*b^2*log(abs(-a/(b*x + a + 1) - 1/(b*x + a + 1) + 1))/(a^2*b + 2*a*b + b) - (a*b - b)/((a + 1)^2*(a/(b*x + a + 1) + 1/(b*x + a + 1) - 1))","B",0
858,1,121,0,0.181218," ","integrate(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x^3,x, algorithm=""giac"")","\frac{2 \, b^{3} \log\left({\left| -\frac{a}{b x + a + 1} - \frac{1}{b x + a + 1} + 1 \right|}\right)}{a^{3} b + 3 \, a^{2} b + 3 \, a b + b} - \frac{\frac{a b^{2} - 5 \, b^{2}}{a + 1} - \frac{2 \, {\left(a b^{3} - 3 \, b^{3}\right)}}{{\left(b x + a + 1\right)} b}}{2 \, {\left(a + 1\right)}^{2} {\left(\frac{a}{b x + a + 1} + \frac{1}{b x + a + 1} - 1\right)}^{2}}"," ",0,"2*b^3*log(abs(-a/(b*x + a + 1) - 1/(b*x + a + 1) + 1))/(a^3*b + 3*a^2*b + 3*a*b + b) - 1/2*((a*b^2 - 5*b^2)/(a + 1) - 2*(a*b^3 - 3*b^3)/((b*x + a + 1)*b))/((a + 1)^2*(a/(b*x + a + 1) + 1/(b*x + a + 1) - 1)^2)","B",0
859,1,159,0,0.438697," ","integrate(1/(b*x+a+1)^2*(1-(b*x+a)^2)/x^4,x, algorithm=""giac"")","-\frac{2 \, b^{4} \log\left({\left| -\frac{a}{b x + a + 1} - \frac{1}{b x + a + 1} + 1 \right|}\right)}{a^{4} b + 4 \, a^{3} b + 6 \, a^{2} b + 4 \, a b + b} - \frac{\frac{a b^{3} - 10 \, b^{3}}{a + 1} - \frac{3 \, {\left(a b^{4} - 8 \, b^{4}\right)}}{{\left(b x + a + 1\right)} b} + \frac{3 \, {\left(a^{2} b^{5} - 4 \, a b^{5} - 5 \, b^{5}\right)}}{{\left(b x + a + 1\right)}^{2} b^{2}}}{3 \, {\left(a + 1\right)}^{3} {\left(\frac{a}{b x + a + 1} + \frac{1}{b x + a + 1} - 1\right)}^{3}}"," ",0,"-2*b^4*log(abs(-a/(b*x + a + 1) - 1/(b*x + a + 1) + 1))/(a^4*b + 4*a^3*b + 6*a^2*b + 4*a*b + b) - 1/3*((a*b^3 - 10*b^3)/(a + 1) - 3*(a*b^4 - 8*b^4)/((b*x + a + 1)*b) + 3*(a^2*b^5 - 4*a*b^5 - 5*b^5)/((b*x + a + 1)^2*b^2))/((a + 1)^3*(a/(b*x + a + 1) + 1/(b*x + a + 1) - 1)^3)","B",0
860,1,211,0,0.234798," ","integrate(x^3/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left({\left(2 \, x {\left(\frac{x}{b} - \frac{a b^{11} + 4 \, b^{11}}{b^{13}}\right)} + \frac{2 \, a^{2} b^{10} + 20 \, a b^{10} + 19 \, b^{10}}{b^{13}}\right)} x - \frac{2 \, a^{3} b^{9} + 44 \, a^{2} b^{9} + 93 \, a b^{9} + 48 \, b^{9}}{b^{13}}\right)} - \frac{3 \, {\left(8 \, a^{3} + 36 \, a^{2} + 44 \, a + 17\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{8 \, b^{3} {\left| b \right|}} - \frac{8 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)}}{b^{3} {\left(\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} + 1\right)} {\left| b \right|}}"," ",0,"-1/8*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*((2*x*(x/b - (a*b^11 + 4*b^11)/b^13) + (2*a^2*b^10 + 20*a*b^10 + 19*b^10)/b^13)*x - (2*a^3*b^9 + 44*a^2*b^9 + 93*a*b^9 + 48*b^9)/b^13) - 3/8*(8*a^3 + 36*a^2 + 44*a + 17)*arcsin(-b*x - a)*sgn(b)/(b^3*abs(b)) - 8*(a^3 + 3*a^2 + 3*a + 1)/(b^3*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b) + 1)*abs(b))","A",0
861,1,166,0,0.210405," ","integrate(x^2/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(x {\left(\frac{2 \, x}{b} - \frac{2 \, a b^{6} + 9 \, b^{6}}{b^{8}}\right)} + \frac{2 \, a^{2} b^{5} + 27 \, a b^{5} + 28 \, b^{5}}{b^{8}}\right)} + \frac{{\left(6 \, a^{2} + 18 \, a + 11\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{2 \, b^{2} {\left| b \right|}} + \frac{8 \, {\left(a^{2} + 2 \, a + 1\right)}}{b^{2} {\left(\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} + 1\right)} {\left| b \right|}}"," ",0,"-1/6*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(x*(2*x/b - (2*a*b^6 + 9*b^6)/b^8) + (2*a^2*b^5 + 27*a*b^5 + 28*b^5)/b^8) + 1/2*(6*a^2 + 18*a + 11)*arcsin(-b*x - a)*sgn(b)/(b^2*abs(b)) + 8*(a^2 + 2*a + 1)/(b^2*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b) + 1)*abs(b))","A",0
862,1,127,0,0.240051," ","integrate(x/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left(\frac{x}{b} - \frac{a b^{2} + 6 \, b^{2}}{b^{4}}\right)} - \frac{3 \, {\left(2 \, a + 3\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{2 \, b {\left| b \right|}} - \frac{8 \, {\left(a + 1\right)}}{b {\left(\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} + 1\right)} {\left| b \right|}}"," ",0,"-1/2*sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*(x/b - (a*b^2 + 6*b^2)/b^4) - 3/2*(2*a + 3)*arcsin(-b*x - a)*sgn(b)/(b*abs(b)) - 8*(a + 1)/(b*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b) + 1)*abs(b))","A",0
863,1,94,0,0.207858," ","integrate(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2),x, algorithm=""giac"")","\frac{3 \, \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} - \frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1}}{b} + \frac{8}{{\left(\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} + 1\right)} {\left| b \right|}}"," ",0,"3*arcsin(-b*x - a)*sgn(b)/abs(b) - sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)/b + 8/(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b) + 1)*abs(b))","A",0
864,1,154,0,0.218943," ","integrate(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x,x, algorithm=""giac"")","-\frac{b \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} + \frac{2 \, {\left(a^{2} b - 2 \, a b + b\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{\sqrt{a^{2} - 1} {\left(a {\left| b \right|} + {\left| b \right|}\right)}} - \frac{8 \, b}{{\left(a {\left| b \right|} + {\left| b \right|}\right)} {\left(\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} + 1\right)}}"," ",0,"-b*arcsin(-b*x - a)*sgn(b)/abs(b) + 2*(a^2*b - 2*a*b + b)*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/(sqrt(a^2 - 1)*(a*abs(b) + abs(b))) - 8*b/((a*abs(b) + abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b) + 1))","A",0
865,1,604,0,0.212610," ","integrate(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x^2,x, algorithm=""giac"")","\frac{6 \, {\left(a b^{2} - b^{2}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{2} {\left| b \right|} + 2 \, a {\left| b \right|} + {\left| b \right|}\right)} \sqrt{a^{2} - 1}} + \frac{2 \, {\left(\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{2}}{b^{2} x + a b} + \frac{4 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{2}}{{\left(b^{2} x + a b\right)}^{2}} + 5 \, a^{2} b^{2} - \frac{10 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a b^{2}}{b^{2} x + a b} - \frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a b^{2}}{{\left(b^{2} x + a b\right)}^{2}} - a b^{2} + \frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} b^{2}}{b^{2} x + a b} + \frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} b^{2}}{{\left(b^{2} x + a b\right)}^{2}}\right)}}{{\left(a^{3} {\left| b \right|} + 2 \, a^{2} {\left| b \right|} + a {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} + \frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + \frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a}{{\left(b^{2} x + a b\right)}^{3}} + a - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b} - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2}}{{\left(b^{2} x + a b\right)}^{2}}\right)}}"," ",0,"6*(a*b^2 - b^2)*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^2*abs(b) + 2*a*abs(b) + abs(b))*sqrt(a^2 - 1)) + 2*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^2*b^2/(b^2*x + a*b) + 4*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^2*b^2/(b^2*x + a*b)^2 + 5*a^2*b^2 - 10*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a*b^2/(b^2*x + a*b) - (sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a*b^2/(b^2*x + a*b)^2 - a*b^2 + (sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*b^2/(b^2*x + a*b) + (sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*b^2/(b^2*x + a*b)^2)/((a^3*abs(b) + 2*a^2*abs(b) + a*abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) + (sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + (sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a/(b^2*x + a*b)^3 + a - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2/(b^2*x + a*b)^2))","B",0
866,1,822,0,0.435471," ","integrate(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x^3,x, algorithm=""giac"")","-\frac{8 \, b^{3}}{{\left(a^{3} {\left| b \right|} + 3 \, a^{2} {\left| b \right|} + 3 \, a {\left| b \right|} + {\left| b \right|}\right)} {\left(\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} + 1\right)}} - \frac{3 \, {\left(2 \, a b^{3} - 3 \, b^{3}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{3} {\left| b \right|} + 3 \, a^{2} {\left| b \right|} + 3 \, a {\left| b \right|} + {\left| b \right|}\right)} \sqrt{a^{2} - 1}} - \frac{\frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{4} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} + 2 \, a^{4} b^{3} - \frac{5 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{3} b^{3}}{b^{2} x + a b} - \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{3} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{3 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{3} b^{3}}{{\left(b^{2} x + a b\right)}^{3}} - 6 \, a^{3} b^{3} + \frac{18 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{3}}{b^{2} x + a b} + \frac{3 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{3}} - a^{2} b^{3} + \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a b^{3}}{b^{2} x + a b} - \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a b^{3}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a b^{3}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} b^{3}}{{\left(b^{2} x + a b\right)}^{2}}}{{\left(a^{5} {\left| b \right|} + 3 \, a^{4} {\left| b \right|} + 3 \, a^{3} {\left| b \right|} + a^{2} {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}^{2}}"," ",0,"-8*b^3/((a^3*abs(b) + 3*a^2*abs(b) + 3*a*abs(b) + abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b) + 1)) - 3*(2*a*b^3 - 3*b^3)*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^3*abs(b) + 3*a^2*abs(b) + 3*a*abs(b) + abs(b))*sqrt(a^2 - 1)) - (2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^4*b^3/(b^2*x + a*b)^2 + 2*a^4*b^3 - 5*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^3*b^3/(b^2*x + a*b) - 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^3*b^3/(b^2*x + a*b)^2 - 3*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^3*b^3/(b^2*x + a*b)^3 - 6*a^3*b^3 + 18*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^2*b^3/(b^2*x + a*b) + 3*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^2*b^3/(b^2*x + a*b)^2 + 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^2*b^3/(b^2*x + a*b)^3 - a^2*b^3 + 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a*b^3/(b^2*x + a*b) - 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a*b^3/(b^2*x + a*b)^2 + 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a*b^3/(b^2*x + a*b)^3 - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*b^3/(b^2*x + a*b)^2)/((a^5*abs(b) + 3*a^4*abs(b) + 3*a^3*abs(b) + a^2*abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b))^2)","B",0
867,1,1839,0,0.255405," ","integrate(1/(b*x+a+1)^3*(1-(b*x+a)^2)^(3/2)/x^4,x, algorithm=""giac"")","\frac{8 \, b^{4}}{{\left(a^{4} {\left| b \right|} + 4 \, a^{3} {\left| b \right|} + 6 \, a^{2} {\left| b \right|} + 4 \, a {\left| b \right|} + {\left| b \right|}\right)} {\left(\frac{\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} + 1\right)}} + \frac{{\left(6 \, a^{2} b^{4} - 18 \, a b^{4} + 11 \, b^{4}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{5} {\left| b \right|} + 3 \, a^{4} {\left| b \right|} + 2 \, a^{3} {\left| b \right|} - 2 \, a^{2} {\left| b \right|} - 3 \, a {\left| b \right|} - {\left| b \right|}\right)} \sqrt{a^{2} - 1}} + \frac{\frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{7} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{7} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + 6 \, a^{7} b^{4} - \frac{24 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{6} b^{4}}{b^{2} x + a b} - \frac{72 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{36 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{36 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{6} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} - 36 \, a^{6} b^{4} + \frac{171 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{5} b^{4}}{b^{2} x + a b} + \frac{84 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{216 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{54 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} + \frac{45 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{5} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + 22 \, a^{5} b^{4} - \frac{120 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{4} b^{4}}{b^{2} x + a b} - \frac{252 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{156 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} - \frac{153 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{4} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + 9 \, a^{4} b^{4} - \frac{36 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{3} b^{4}}{b^{2} x + a b} + \frac{192 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} + \frac{90 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{78 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{18 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + 2 \, a^{3} b^{4} - \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{4}}{b^{2} x + a b} + \frac{54 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{100 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{54 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{6 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{5} a^{2} b^{4}}{{\left(b^{2} x + a b\right)}^{5}} + \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a b^{4}}{{\left(b^{2} x + a b\right)}^{2}} - \frac{36 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} a b^{4}}{{\left(b^{2} x + a b\right)}^{3}} + \frac{12 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{4} a b^{4}}{{\left(b^{2} x + a b\right)}^{4}} - \frac{8 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{3} b^{4}}{{\left(b^{2} x + a b\right)}^{3}}}{3 \, {\left(a^{8} {\left| b \right|} + 3 \, a^{7} {\left| b \right|} + 2 \, a^{6} {\left| b \right|} - 2 \, a^{5} {\left| b \right|} - 3 \, a^{4} {\left| b \right|} - a^{3} {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + a - \frac{2 \, {\left(\sqrt{-b^{2} x^{2} - 2 \, a b x - a^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b}\right)}^{3}}"," ",0,"8*b^4/((a^4*abs(b) + 4*a^3*abs(b) + 6*a^2*abs(b) + 4*a*abs(b) + abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b) + 1)) + (6*a^2*b^4 - 18*a*b^4 + 11*b^4)*arctan(((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^5*abs(b) + 3*a^4*abs(b) + 2*a^3*abs(b) - 2*a^2*abs(b) - 3*a*abs(b) - abs(b))*sqrt(a^2 - 1)) + 1/3*(12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^7*b^4/(b^2*x + a*b)^2 + 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^7*b^4/(b^2*x + a*b)^4 + 6*a^7*b^4 - 24*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^6*b^4/(b^2*x + a*b) - 72*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^6*b^4/(b^2*x + a*b)^2 - 36*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^6*b^4/(b^2*x + a*b)^3 - 36*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^6*b^4/(b^2*x + a*b)^4 - 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^6*b^4/(b^2*x + a*b)^5 - 36*a^6*b^4 + 171*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^5*b^4/(b^2*x + a*b) + 84*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^5*b^4/(b^2*x + a*b)^2 + 216*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^5*b^4/(b^2*x + a*b)^3 + 54*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^5*b^4/(b^2*x + a*b)^4 + 45*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^5*b^4/(b^2*x + a*b)^5 + 22*a^5*b^4 - 120*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^4*b^4/(b^2*x + a*b) - 252*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^4*b^4/(b^2*x + a*b)^2 - 156*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^4*b^4/(b^2*x + a*b)^3 - 153*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^4*b^4/(b^2*x + a*b)^4 - 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^4*b^4/(b^2*x + a*b)^5 + 9*a^4*b^4 - 36*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^3*b^4/(b^2*x + a*b) + 192*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^3*b^4/(b^2*x + a*b)^2 + 90*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^3*b^4/(b^2*x + a*b)^3 + 78*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^3*b^4/(b^2*x + a*b)^4 - 18*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^3*b^4/(b^2*x + a*b)^5 + 2*a^3*b^4 - 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)*a^2*b^4/(b^2*x + a*b) + 54*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a^2*b^4/(b^2*x + a*b)^2 - 100*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a^2*b^4/(b^2*x + a*b)^3 + 54*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a^2*b^4/(b^2*x + a*b)^4 - 6*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^5*a^2*b^4/(b^2*x + a*b)^5 + 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a*b^4/(b^2*x + a*b)^2 - 36*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*a*b^4/(b^2*x + a*b)^3 + 12*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^4*a*b^4/(b^2*x + a*b)^4 - 8*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^3*b^4/(b^2*x + a*b)^3)/((a^8*abs(b) + 3*a^7*abs(b) + 2*a^6*abs(b) - 2*a^5*abs(b) - 3*a^4*abs(b) - a^3*abs(b))*((sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + a - 2*(sqrt(-b^2*x^2 - 2*a*b*x - a^2 + 1)*abs(b) + b)/(b^2*x + a*b))^3)","B",0
868,1,15,0,0.192459," ","integrate(1/(1-(b*x+1)^2)^(1/2),x, algorithm=""giac"")","-\frac{\arcsin\left(-b x - 1\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}}"," ",0,"-arcsin(-b*x - 1)*sgn(b)/abs(b)","A",0
869,1,125,0,0.244862," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x^3/(-b^2*x^2-2*a*b*x-a^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-{\left(b x + a\right)}^{2} + 1} {\left(\frac{x}{b^{3}} - \frac{5 \, a b^{6} - 2 \, b^{6}}{b^{10}}\right)} + \frac{3 \, {\left(2 \, a^{2} - 2 \, a + 1\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{2 \, b^{3} {\left| b \right|}} - \frac{2 \, {\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)}}{b^{3} {\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)} {\left| b \right|}}"," ",0,"1/2*sqrt(-(b*x + a)^2 + 1)*(x/b^3 - (5*a*b^6 - 2*b^6)/b^10) + 3/2*(2*a^2 - 2*a + 1)*arcsin(-b*x - a)*sgn(b)/(b^3*abs(b)) - 2*(a^3 - 3*a^2 + 3*a - 1)/(b^3*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1)*abs(b))","A",0
870,1,94,0,0.248732," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x^2/(-b^2*x^2-2*a*b*x-a^2+1),x, algorithm=""giac"")","-\frac{{\left(2 \, a - 1\right)} \arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{b^{2} {\left| b \right|}} + \frac{\sqrt{-{\left(b x + a\right)}^{2} + 1}}{b^{3}} + \frac{2 \, {\left(a^{2} - 2 \, a + 1\right)}}{b^{2} {\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)} {\left| b \right|}}"," ",0,"-(2*a - 1)*arcsin(-b*x - a)*sgn(b)/(b^2*abs(b)) + sqrt(-(b*x + a)^2 + 1)/b^3 + 2*(a^2 - 2*a + 1)/(b^2*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1)*abs(b))","A",0
871,1,66,0,0.277085," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)*x/(-b^2*x^2-2*a*b*x-a^2+1),x, algorithm=""giac"")","\frac{\arcsin\left(-b x - a\right) \mathrm{sgn}\left(b\right)}{b {\left| b \right|}} - \frac{2 \, {\left(a - 1\right)}}{b {\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)} {\left| b \right|}}"," ",0,"arcsin(-b*x - a)*sgn(b)/(b*abs(b)) - 2*(a - 1)/(b*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1)*abs(b))","A",0
872,1,40,0,0.396452," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/(-b^2*x^2-2*a*b*x-a^2+1),x, algorithm=""giac"")","\frac{2}{{\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)} {\left| b \right|}}"," ",0,"2/(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1)*abs(b))","A",0
873,1,112,0,0.371383," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x/(-b^2*x^2-2*a*b*x-a^2+1),x, algorithm=""giac"")","-\frac{2 \, b \arctan\left(\frac{\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{\sqrt{a^{2} - 1} {\left(a {\left| b \right|} - {\left| b \right|}\right)}} - \frac{2 \, b}{{\left(a {\left| b \right|} - {\left| b \right|}\right)} {\left(\frac{\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b}{b^{2} x + a b} - 1\right)}}"," ",0,"-2*b*arctan(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/(sqrt(a^2 - 1)*(a*abs(b) - abs(b))) - 2*b/((a*abs(b) - abs(b))*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 1))","A",0
874,1,519,0,0.202377," ","integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^2/(-b^2*x^2-2*a*b*x-a^2+1),x, algorithm=""giac"")","\frac{2 \, {\left(2 \, a b^{2} + b^{2}\right)} \arctan\left(\frac{\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - 1}{\sqrt{a^{2} - 1}}\right)}{{\left(a^{3} {\left| b \right|} - a^{2} {\left| b \right|} - a {\left| b \right|} + {\left| b \right|}\right)} \sqrt{a^{2} - 1}} + \frac{2 \, {\left(\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{3} b^{2}}{{\left(b^{2} x + a b\right)}^{2}} + a^{3} b^{2} - \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a^{2} b^{2}}{b^{2} x + a b} + \frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a^{2} b^{2}}{{\left(b^{2} x + a b\right)}^{2}} + a^{2} b^{2} - \frac{3 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a b^{2}}{b^{2} x + a b} + a b^{2} - \frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} b^{2}}{b^{2} x + a b} + \frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} b^{2}}{{\left(b^{2} x + a b\right)}^{2}}\right)}}{{\left(a^{4} {\left| b \right|} - a^{3} {\left| b \right|} - a^{2} {\left| b \right|} + a {\left| b \right|}\right)} {\left(\frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)} a}{b^{2} x + a b} - \frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2} a}{{\left(b^{2} x + a b\right)}^{2}} + \frac{{\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{3} a}{{\left(b^{2} x + a b\right)}^{3}} - a + \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}}{b^{2} x + a b} - \frac{2 \, {\left(\sqrt{-{\left(b x + a\right)}^{2} + 1} {\left| b \right|} + b\right)}^{2}}{{\left(b^{2} x + a b\right)}^{2}}\right)}}"," ",0,"2*(2*a*b^2 + b^2)*arctan(((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - 1)/sqrt(a^2 - 1))/((a^3*abs(b) - a^2*abs(b) - a*abs(b) + abs(b))*sqrt(a^2 - 1)) + 2*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^3*b^2/(b^2*x + a*b)^2 + a^3*b^2 - 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a^2*b^2/(b^2*x + a*b) + (sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a^2*b^2/(b^2*x + a*b)^2 + a^2*b^2 - 3*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a*b^2/(b^2*x + a*b) + a*b^2 - (sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*b^2/(b^2*x + a*b) + (sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*b^2/(b^2*x + a*b)^2)/((a^4*abs(b) - a^3*abs(b) - a^2*abs(b) + a*abs(b))*((sqrt(-(b*x + a)^2 + 1)*abs(b) + b)*a/(b^2*x + a*b) - (sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2*a/(b^2*x + a*b)^2 + (sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^3*a/(b^2*x + a*b)^3 - a + 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)/(b^2*x + a*b) - 2*(sqrt(-(b*x + a)^2 + 1)*abs(b) + b)^2/(b^2*x + a*b)^2))","B",0
875,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))*x^m,x, algorithm=""giac"")","\int x^{m} \left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^m*((b*x + a + 1)/(b*x + a - 1))^(1/2*n), x)","F",0
876,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))*x^3,x, algorithm=""giac"")","\int x^{3} \left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^3*((b*x + a + 1)/(b*x + a - 1))^(1/2*n), x)","F",0
877,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))*x^2,x, algorithm=""giac"")","\int x^{2} \left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x^2*((b*x + a + 1)/(b*x + a - 1))^(1/2*n), x)","F",0
878,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))*x,x, algorithm=""giac"")","\int x \left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(x*((b*x + a + 1)/(b*x + a - 1))^(1/2*n), x)","F",0
879,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a)),x, algorithm=""giac"")","\int \left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(((b*x + a + 1)/(b*x + a - 1))^(1/2*n), x)","F",0
880,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))/x,x, algorithm=""giac"")","\int \frac{\left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}}{x}\,{d x}"," ",0,"integrate(((b*x + a + 1)/(b*x + a - 1))^(1/2*n)/x, x)","F",0
881,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))/x^2,x, algorithm=""giac"")","\int \frac{\left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}}{x^{2}}\,{d x}"," ",0,"integrate(((b*x + a + 1)/(b*x + a - 1))^(1/2*n)/x^2, x)","F",0
882,0,0,0,0.000000," ","integrate(exp(n*arctanh(b*x+a))/x^3,x, algorithm=""giac"")","\int \frac{\left(\frac{b x + a + 1}{b x + a - 1}\right)^{\frac{1}{2} \, n}}{x^{3}}\,{d x}"," ",0,"integrate(((b*x + a + 1)/(b*x + a - 1))^(1/2*n)/x^3, x)","F",0
883,1,127,0,0.198489," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\frac{35 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{128 \, {\left| a \right|}} - \frac{1}{1152} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{128 \, c^{4}}{a} - {\left(837 \, c^{4} + 2 \, {\left(256 \, a c^{4} - {\left(489 \, a^{2} c^{4} + 4 \, {\left(96 \, a^{3} c^{4} - {\left(75 \, a^{4} c^{4} + 2 \, {\left(32 \, a^{5} c^{4} - {\left(8 \, a^{7} c^{4} x + 9 \, a^{6} c^{4}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"35/128*c^4*arcsin(a*x)*sgn(a)/abs(a) - 1/1152*sqrt(-a^2*x^2 + 1)*(128*c^4/a - (837*c^4 + 2*(256*a*c^4 - (489*a^2*c^4 + 4*(96*a^3*c^4 - (75*a^4*c^4 + 2*(32*a^5*c^4 - (8*a^7*c^4*x + 9*a^6*c^4)*x)*x)*x)*x)*x)*x)*x)","A",0
884,1,103,0,0.189659," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{5 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{16 \, {\left| a \right|}} - \frac{1}{336} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{48 \, c^{3}}{a} - {\left(231 \, c^{3} + 2 \, {\left(72 \, a c^{3} - {\left(91 \, a^{2} c^{3} + 4 \, {\left(18 \, a^{3} c^{3} - {\left(6 \, a^{5} c^{3} x + 7 \, a^{4} c^{3}\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"5/16*c^3*arcsin(a*x)*sgn(a)/abs(a) - 1/336*sqrt(-a^2*x^2 + 1)*(48*c^3/a - (231*c^3 + 2*(72*a*c^3 - (91*a^2*c^3 + 4*(18*a^3*c^3 - (6*a^5*c^3*x + 7*a^4*c^3)*x)*x)*x)*x)*x)","A",0
885,1,78,0,0.209242," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\frac{3 \, c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} + \frac{1}{40} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(25 \, c^{2} + 2 \, {\left(8 \, a c^{2} - {\left(4 \, a^{3} c^{2} x + 5 \, a^{2} c^{2}\right)} x\right)} x\right)} x - \frac{8 \, c^{2}}{a}\right)}"," ",0,"3/8*c^2*arcsin(a*x)*sgn(a)/abs(a) + 1/40*sqrt(-a^2*x^2 + 1)*((25*c^2 + 2*(8*a*c^2 - (4*a^3*c^2*x + 5*a^2*c^2)*x)*x)*x - 8*c^2/a)","A",0
886,1,46,0,0.206805," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} + \frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, a c x + 3 \, c\right)} x - \frac{2 \, c}{a}\right)}"," ",0,"1/2*c*arcsin(a*x)*sgn(a)/abs(a) + 1/6*sqrt(-a^2*x^2 + 1)*((2*a*c*x + 3*c)*x - 2*c/a)","A",0
887,1,102,0,0.208956," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left(x {\left(\frac{2 \, x}{a^{3} c} + \frac{3}{a^{4} c}\right)} + \frac{10}{a^{5} c}\right)} - \frac{3 \, \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, a^{4} c {\left| a \right|}} + \frac{2}{a^{4} c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"1/6*sqrt(-a^2*x^2 + 1)*(x*(2*x/(a^3*c) + 3/(a^4*c)) + 10/(a^5*c)) - 3/2*arcsin(a*x)*sgn(a)/(a^4*c*abs(a)) + 2/(a^4*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
888,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c),x, algorithm=""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
889,1,78,0,0.495445," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{a^{2} c {\left| a \right|}} + \frac{\sqrt{-a^{2} x^{2} + 1}}{a^{3} c} + \frac{2}{a^{2} c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"-arcsin(a*x)*sgn(a)/(a^2*c*abs(a)) + sqrt(-a^2*x^2 + 1)/(a^3*c) + 2/(a^2*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
890,1,59,0,0.220294," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{a c {\left| a \right|}} + \frac{2}{a c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"-arcsin(a*x)*sgn(a)/(a*c*abs(a)) + 2/(a*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
891,1,37,0,0.210150," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{2}{c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"2/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
892,1,80,0,0.192547," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{a \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{c {\left| a \right|}} + \frac{2 \, a}{c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"-a*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c*abs(a)) + 2*a/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","A",0
893,1,159,0,0.628328," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{a^{2} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{c {\left| a \right|}} - \frac{{\left(a^{2} - \frac{5 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{x}\right)} a^{2} x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}} - \frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{2 \, c x {\left| a \right|}}"," ",0,"-a^2*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c*abs(a)) - 1/2*(a^2 - 5*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/x)*a^2*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a)) - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(c*x*abs(a))","B",0
894,1,224,0,0.215724," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{{\left(a^{3} + \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a}{x} - \frac{20 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a x^{2}}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}} - \frac{3 \, a^{3} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, c {\left| a \right|}} - \frac{\frac{4 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c {\left| a \right|}}{x} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c {\left| a \right|}}{a x^{2}}}{8 \, a^{2} c^{2}}"," ",0,"-1/8*(a^3 + 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a/x - 20*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a*x^2))*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a)) - 3/2*a^3*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c*abs(a)) - 1/8*(4*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c*abs(a)/x + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c*abs(a)/(a*x^2))/(a^2*c^2)","B",0
895,1,283,0,0.211522," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{{\left(a^{4} + \frac{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2}}{x} + \frac{18 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{x^{2}} - \frac{69 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{2} x^{3}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}} - \frac{3 \, a^{4} \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, c {\left| a \right|}} - \frac{\frac{21 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c^{2}}{x} + \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c^{2}}{x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c^{2}}{x^{3}}}{24 \, a^{2} c^{3} {\left| a \right|}}"," ",0,"-1/24*(a^4 + 2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2/x + 18*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/x^2 - 69*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^2*x^3))*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a)) - 3/2*a^4*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/(c*abs(a)) - 1/24*(21*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c^2/x + 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c^2/x^2 + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c^2/x^3)/(a^2*c^3*abs(a))","B",0
896,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^6/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{6}}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^6/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)), x)","F",0
897,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^2,x, algorithm=""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
898,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{4}}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^4/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)), x)","F",0
899,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^2,x, algorithm=""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
900,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{2}}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^2/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)), x)","F",0
901,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)), x)","F",0
902,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)), x)","F",0
903,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)*x), x)","F",0
904,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
905,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
906,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)*x^4), x)","F",0
907,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^7/(-a^2*c*x^2+c)^3,x, algorithm=""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
908,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^6/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)} x^{6}}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(-(a*x + 1)*x^6/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)), x)","F",0
909,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^3,x, algorithm=""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
910,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)} x^{4}}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(-(a*x + 1)*x^4/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)), x)","F",0
911,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^3,x, algorithm=""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
912,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)} x^{2}}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(-(a*x + 1)*x^2/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)), x)","F",0
913,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)} x}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(-(a*x + 1)*x/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)), x)","F",0
914,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(-(a*x + 1)/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)), x)","F",0
915,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(-(a*x + 1)/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)*x), x)","F",0
916,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate(-(a*x + 1)/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
917,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(-(a*x + 1)/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
918,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{4} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/((a^2*c*x^2 - c)^4*sqrt(-a^2*x^2 + 1)), x)","F",0
919,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^5,x, algorithm=""giac"")","\int -\frac{a x + 1}{{\left(a^{2} c x^{2} - c\right)}^{5} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(-(a*x + 1)/((a^2*c*x^2 - c)^5*sqrt(-a^2*x^2 + 1)), x)","F",0
920,1,44,0,0.259220," ","integrate((a*x+1)/(-a^2*x^2+1)*x^4,x, algorithm=""giac"")","-\frac{3 \, a^{3} x^{4} + 4 \, a^{2} x^{3} + 6 \, a x^{2} + 12 \, x}{12 \, a^{4}} - \frac{\log\left({\left| a x - 1 \right|}\right)}{a^{5}}"," ",0,"-1/12*(3*a^3*x^4 + 4*a^2*x^3 + 6*a*x^2 + 12*x)/a^4 - log(abs(a*x - 1))/a^5","A",0
921,1,36,0,0.158941," ","integrate((a*x+1)/(-a^2*x^2+1)*x^3,x, algorithm=""giac"")","-\frac{2 \, a^{2} x^{3} + 3 \, a x^{2} + 6 \, x}{6 \, a^{3}} - \frac{\log\left({\left| a x - 1 \right|}\right)}{a^{4}}"," ",0,"-1/6*(2*a^2*x^3 + 3*a*x^2 + 6*x)/a^3 - log(abs(a*x - 1))/a^4","A",0
922,1,27,0,0.198678," ","integrate((a*x+1)/(-a^2*x^2+1)*x^2,x, algorithm=""giac"")","-\frac{a x^{2} + 2 \, x}{2 \, a^{2}} - \frac{\log\left({\left| a x - 1 \right|}\right)}{a^{3}}"," ",0,"-1/2*(a*x^2 + 2*x)/a^2 - log(abs(a*x - 1))/a^3","A",0
923,1,19,0,0.152840," ","integrate((a*x+1)/(-a^2*x^2+1)*x,x, algorithm=""giac"")","-\frac{x}{a} - \frac{\log\left({\left| a x - 1 \right|}\right)}{a^{2}}"," ",0,"-x/a - log(abs(a*x - 1))/a^2","A",0
924,1,12,0,0.200853," ","integrate((a*x+1)/(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{\log\left({\left| a x - 1 \right|}\right)}{a}"," ",0,"-log(abs(a*x - 1))/a","A",0
925,1,13,0,0.191089," ","integrate((a*x+1)/(-a^2*x^2+1)/x,x, algorithm=""giac"")","-\log\left({\left| a x - 1 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"-log(abs(a*x - 1)) + log(abs(x))","A",0
926,1,21,0,0.191222," ","integrate((a*x+1)/(-a^2*x^2+1)/x^2,x, algorithm=""giac"")","-a \log\left({\left| a x - 1 \right|}\right) + a \log\left({\left| x \right|}\right) - \frac{1}{x}"," ",0,"-a*log(abs(a*x - 1)) + a*log(abs(x)) - 1/x","A",0
927,1,31,0,0.143672," ","integrate((a*x+1)/(-a^2*x^2+1)/x^3,x, algorithm=""giac"")","-a^{2} \log\left({\left| a x - 1 \right|}\right) + a^{2} \log\left({\left| x \right|}\right) - \frac{2 \, a x + 1}{2 \, x^{2}}"," ",0,"-a^2*log(abs(a*x - 1)) + a^2*log(abs(x)) - 1/2*(2*a*x + 1)/x^2","A",0
928,1,39,0,0.173667," ","integrate((a*x+1)/(-a^2*x^2+1)/x^4,x, algorithm=""giac"")","-a^{3} \log\left({\left| a x - 1 \right|}\right) + a^{3} \log\left({\left| x \right|}\right) - \frac{6 \, a^{2} x^{2} + 3 \, a x + 2}{6 \, x^{3}}"," ",0,"-a^3*log(abs(a*x - 1)) + a^3*log(abs(x)) - 1/6*(6*a^2*x^2 + 3*a*x + 2)/x^3","A",0
929,1,56,0,0.146343," ","integrate((a*x+1)/(-a^2*x^2+1)^2*x^4,x, algorithm=""giac"")","\frac{\log\left({\left| a x + 1 \right|}\right)}{4 \, a^{5}} + \frac{7 \, \log\left({\left| a x - 1 \right|}\right)}{4 \, a^{5}} + \frac{a^{3} x^{2} + 2 \, a^{2} x}{2 \, a^{6}} - \frac{1}{2 \, {\left(a x - 1\right)} a^{5}}"," ",0,"1/4*log(abs(a*x + 1))/a^5 + 7/4*log(abs(a*x - 1))/a^5 + 1/2*(a^3*x^2 + 2*a^2*x)/a^6 - 1/2/((a*x - 1)*a^5)","A",0
930,1,42,0,0.191502," ","integrate((a*x+1)/(-a^2*x^2+1)^2*x^3,x, algorithm=""giac"")","\frac{x}{a^{3}} - \frac{\log\left({\left| a x + 1 \right|}\right)}{4 \, a^{4}} + \frac{5 \, \log\left({\left| a x - 1 \right|}\right)}{4 \, a^{4}} - \frac{1}{2 \, {\left(a x - 1\right)} a^{4}}"," ",0,"x/a^3 - 1/4*log(abs(a*x + 1))/a^4 + 5/4*log(abs(a*x - 1))/a^4 - 1/2/((a*x - 1)*a^4)","A",0
931,1,37,0,0.167938," ","integrate((a*x+1)/(-a^2*x^2+1)^2*x^2,x, algorithm=""giac"")","\frac{\log\left({\left| a x + 1 \right|}\right)}{4 \, a^{3}} + \frac{3 \, \log\left({\left| a x - 1 \right|}\right)}{4 \, a^{3}} - \frac{1}{2 \, {\left(a x - 1\right)} a^{3}}"," ",0,"1/4*log(abs(a*x + 1))/a^3 + 3/4*log(abs(a*x - 1))/a^3 - 1/2/((a*x - 1)*a^3)","A",0
932,1,37,0,0.173354," ","integrate((a*x+1)/(-a^2*x^2+1)^2*x,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{4 \, a^{2}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{4 \, a^{2}} - \frac{1}{2 \, {\left(a x - 1\right)} a^{2}}"," ",0,"-1/4*log(abs(a*x + 1))/a^2 + 1/4*log(abs(a*x - 1))/a^2 - 1/2/((a*x - 1)*a^2)","A",0
933,1,37,0,0.488730," ","integrate((a*x+1)/(-a^2*x^2+1)^2,x, algorithm=""giac"")","\frac{\log\left({\left| a x + 1 \right|}\right)}{4 \, a} - \frac{\log\left({\left| a x - 1 \right|}\right)}{4 \, a} - \frac{1}{2 \, {\left(a x - 1\right)} a}"," ",0,"1/4*log(abs(a*x + 1))/a - 1/4*log(abs(a*x - 1))/a - 1/2/((a*x - 1)*a)","A",0
934,1,31,0,0.192130," ","integrate((a*x+1)/(-a^2*x^2+1)^2/x,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(a x - 1\right)}} - \frac{1}{4} \, \log\left({\left| a x + 1 \right|}\right) - \frac{3}{4} \, \log\left({\left| a x - 1 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"-1/2/(a*x - 1) - 1/4*log(abs(a*x + 1)) - 3/4*log(abs(a*x - 1)) + log(abs(x))","A",0
935,1,44,0,0.201116," ","integrate((a*x+1)/(-a^2*x^2+1)^2/x^2,x, algorithm=""giac"")","\frac{1}{4} \, a \log\left({\left| a x + 1 \right|}\right) - \frac{5}{4} \, a \log\left({\left| a x - 1 \right|}\right) + a \log\left({\left| x \right|}\right) - \frac{3 \, a x - 2}{2 \, {\left(a x - 1\right)} x}"," ",0,"1/4*a*log(abs(a*x + 1)) - 5/4*a*log(abs(a*x - 1)) + a*log(abs(x)) - 1/2*(3*a*x - 2)/((a*x - 1)*x)","A",0
936,1,59,0,0.187941," ","integrate((a*x+1)/(-a^2*x^2+1)^2/x^3,x, algorithm=""giac"")","-\frac{1}{4} \, a^{2} \log\left({\left| a x + 1 \right|}\right) - \frac{7}{4} \, a^{2} \log\left({\left| a x - 1 \right|}\right) + 2 \, a^{2} \log\left({\left| x \right|}\right) - \frac{3 \, a^{2} x^{2} - a x - 1}{2 \, {\left(a x - 1\right)} x^{2}}"," ",0,"-1/4*a^2*log(abs(a*x + 1)) - 7/4*a^2*log(abs(a*x - 1)) + 2*a^2*log(abs(x)) - 1/2*(3*a^2*x^2 - a*x - 1)/((a*x - 1)*x^2)","A",0
937,1,67,0,0.153442," ","integrate((a*x+1)/(-a^2*x^2+1)^2/x^4,x, algorithm=""giac"")","\frac{1}{4} \, a^{3} \log\left({\left| a x + 1 \right|}\right) - \frac{9}{4} \, a^{3} \log\left({\left| a x - 1 \right|}\right) + 2 \, a^{3} \log\left({\left| x \right|}\right) - \frac{15 \, a^{3} x^{3} - 9 \, a^{2} x^{2} - a x - 2}{6 \, {\left(a x - 1\right)} x^{3}}"," ",0,"1/4*a^3*log(abs(a*x + 1)) - 9/4*a^3*log(abs(a*x - 1)) + 2*a^3*log(abs(x)) - 1/6*(15*a^3*x^3 - 9*a^2*x^2 - a*x - 2)/((a*x - 1)*x^3)","A",0
938,1,77,0,0.189432," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^6,x, algorithm=""giac"")","-\frac{9 \, \log\left({\left| a x + 1 \right|}\right)}{16 \, a^{7}} - \frac{39 \, \log\left({\left| a x - 1 \right|}\right)}{16 \, a^{7}} - \frac{a^{5} x^{2} + 2 \, a^{4} x}{2 \, a^{10}} + \frac{9 \, a^{2} x^{2} + 3 \, a x - 10}{8 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{2} a^{7}}"," ",0,"-9/16*log(abs(a*x + 1))/a^7 - 39/16*log(abs(a*x - 1))/a^7 - 1/2*(a^5*x^2 + 2*a^4*x)/a^10 + 1/8*(9*a^2*x^2 + 3*a*x - 10)/((a*x + 1)*(a*x - 1)^2*a^7)","A",0
939,1,64,0,0.165430," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^5,x, algorithm=""giac"")","-\frac{x}{a^{5}} + \frac{7 \, \log\left({\left| a x + 1 \right|}\right)}{16 \, a^{6}} - \frac{23 \, \log\left({\left| a x - 1 \right|}\right)}{16 \, a^{6}} + \frac{9 \, a^{2} x^{2} - a x - 6}{8 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{2} a^{6}}"," ",0,"-x/a^5 + 7/16*log(abs(a*x + 1))/a^6 - 23/16*log(abs(a*x - 1))/a^6 + 1/8*(9*a^2*x^2 - a*x - 6)/((a*x + 1)*(a*x - 1)^2*a^6)","A",0
940,1,58,0,0.272505," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^4,x, algorithm=""giac"")","-\frac{5 \, \log\left({\left| a x + 1 \right|}\right)}{16 \, a^{5}} - \frac{11 \, \log\left({\left| a x - 1 \right|}\right)}{16 \, a^{5}} + \frac{5 \, a^{2} x^{2} + 3 \, a x - 6}{8 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{2} a^{5}}"," ",0,"-5/16*log(abs(a*x + 1))/a^5 - 11/16*log(abs(a*x - 1))/a^5 + 1/8*(5*a^2*x^2 + 3*a*x - 6)/((a*x + 1)*(a*x - 1)^2*a^5)","A",0
941,1,58,0,0.192245," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^3,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| a x + 1 \right|}\right)}{16 \, a^{4}} - \frac{3 \, \log\left({\left| a x - 1 \right|}\right)}{16 \, a^{4}} + \frac{5 \, a^{2} x^{2} - a x - 2}{8 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{2} a^{4}}"," ",0,"3/16*log(abs(a*x + 1))/a^4 - 3/16*log(abs(a*x - 1))/a^4 + 1/8*(5*a^2*x^2 - a*x - 2)/((a*x + 1)*(a*x - 1)^2*a^4)","A",0
942,1,57,0,0.161955," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^2,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{16 \, a^{3}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{16 \, a^{3}} + \frac{a^{2} x^{2} + 3 \, a x - 2}{8 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{2} a^{3}}"," ",0,"-1/16*log(abs(a*x + 1))/a^3 + 1/16*log(abs(a*x - 1))/a^3 + 1/8*(a^2*x^2 + 3*a*x - 2)/((a*x + 1)*(a*x - 1)^2*a^3)","A",0
943,1,57,0,0.164201," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{16 \, a^{2}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{16 \, a^{2}} + \frac{a^{2} x^{2} - a x + 2}{8 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{2} a^{2}}"," ",0,"-1/16*log(abs(a*x + 1))/a^2 + 1/16*log(abs(a*x - 1))/a^2 + 1/8*(a^2*x^2 - a*x + 2)/((a*x + 1)*(a*x - 1)^2*a^2)","A",0
944,1,58,0,0.325859," ","integrate((a*x+1)/(-a^2*x^2+1)^3,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| a x + 1 \right|}\right)}{16 \, a} - \frac{3 \, \log\left({\left| a x - 1 \right|}\right)}{16 \, a} - \frac{3 \, a^{2} x^{2} - 3 \, a x - 2}{8 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{2} a}"," ",0,"3/16*log(abs(a*x + 1))/a - 3/16*log(abs(a*x - 1))/a - 1/8*(3*a^2*x^2 - 3*a*x - 2)/((a*x + 1)*(a*x - 1)^2*a)","A",0
945,1,51,0,0.181036," ","integrate((a*x+1)/(-a^2*x^2+1)^3/x,x, algorithm=""giac"")","-\frac{3 \, a^{2} x^{2} + a x - 6}{8 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{2}} - \frac{5}{16} \, \log\left({\left| a x + 1 \right|}\right) - \frac{11}{16} \, \log\left({\left| a x - 1 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"-1/8*(3*a^2*x^2 + a*x - 6)/((a*x + 1)*(a*x - 1)^2) - 5/16*log(abs(a*x + 1)) - 11/16*log(abs(a*x - 1)) + log(abs(x))","A",0
946,1,67,0,0.163228," ","integrate((a*x+1)/(-a^2*x^2+1)^3/x^2,x, algorithm=""giac"")","\frac{7}{16} \, a \log\left({\left| a x + 1 \right|}\right) - \frac{23}{16} \, a \log\left({\left| a x - 1 \right|}\right) + a \log\left({\left| x \right|}\right) - \frac{15 \, a^{3} x^{3} - 11 \, a^{2} x^{2} - 14 \, a x + 8}{8 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{2} x}"," ",0,"7/16*a*log(abs(a*x + 1)) - 23/16*a*log(abs(a*x - 1)) + a*log(abs(x)) - 1/8*(15*a^3*x^3 - 11*a^2*x^2 - 14*a*x + 8)/((a*x + 1)*(a*x - 1)^2*x)","A",0
947,1,82,0,0.401003," ","integrate((a*x+1)/(-a^2*x^2+1)^3/x^3,x, algorithm=""giac"")","-\frac{9}{16} \, a^{2} \log\left({\left| a x + 1 \right|}\right) - \frac{39}{16} \, a^{2} \log\left({\left| a x - 1 \right|}\right) + 3 \, a^{2} \log\left({\left| x \right|}\right) - \frac{15 \, a^{4} x^{4} - 3 \, a^{3} x^{3} - 22 \, a^{2} x^{2} + 4 \, a x + 4}{8 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{2} x^{2}}"," ",0,"-9/16*a^2*log(abs(a*x + 1)) - 39/16*a^2*log(abs(a*x - 1)) + 3*a^2*log(abs(x)) - 1/8*(15*a^4*x^4 - 3*a^3*x^3 - 22*a^2*x^2 + 4*a*x + 4)/((a*x + 1)*(a*x - 1)^2*x^2)","A",0
948,1,90,0,0.255549," ","integrate((a*x+1)/(-a^2*x^2+1)^3/x^4,x, algorithm=""giac"")","\frac{11}{16} \, a^{3} \log\left({\left| a x + 1 \right|}\right) - \frac{59}{16} \, a^{3} \log\left({\left| a x - 1 \right|}\right) + 3 \, a^{3} \log\left({\left| x \right|}\right) - \frac{105 \, a^{5} x^{5} - 69 \, a^{4} x^{4} - 106 \, a^{3} x^{3} + 52 \, a^{2} x^{2} + 4 \, a x + 8}{24 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{2} x^{3}}"," ",0,"11/16*a^3*log(abs(a*x + 1)) - 59/16*a^3*log(abs(a*x - 1)) + 3*a^3*log(abs(x)) - 1/24*(105*a^5*x^5 - 69*a^4*x^4 - 106*a^3*x^3 + 52*a^2*x^2 + 4*a*x + 8)/((a*x + 1)*(a*x - 1)^2*x^3)","A",0
949,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""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
950,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)} x}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)*x/sqrt(-a^2*x^2 + 1), x)","F",0
951,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)/sqrt(-a^2*x^2 + 1), x)","F",0
952,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
953,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)/(sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
954,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)/sqrt(-a^2*x^2 + 1), x)","F",0
955,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)/sqrt(-a^2*x^2 + 1), x)","F",0
956,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} {\left(a x + 1\right)}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)*(a*x + 1)/sqrt(-a^2*x^2 + 1), x)","F",0
957,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^(1/2),x, algorithm=""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
958,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{3}}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^3/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)), x)","F",0
959,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""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
960,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)), x)","F",0
961,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)), x)","F",0
962,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)*x), x)","F",0
963,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
964,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
965,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{a x + 1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)*x^4), x)","F",0
966,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^(3/2),x, algorithm=""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
967,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{4}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^4/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
968,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""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
969,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^2/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
970,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
971,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
972,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)*x), x)","F",0
973,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
974,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
975,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^4/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1} x^{4}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)*x^4), x)","F",0
976,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^6/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{6}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^6/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
977,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^5/(-a^2*c*x^2+c)^(5/2),x, algorithm=""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
978,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^4/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{4}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^4/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
979,-2,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""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
980,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^2/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
981,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
982,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
983,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)*x), x)","F",0
984,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
985,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
986,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{a x + 1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)/((-a^2*c*x^2 + c)^(7/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
987,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(a^{2} c x^{2} - c\right)}^{2} {\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a^2*c*x^2 - c)^2*(a*x + 1)*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
988,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c),x, algorithm=""giac"")","\int -\frac{{\left(a^{2} c x^{2} - c\right)} {\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(-(a^2*c*x^2 - c)*(a*x + 1)*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
989,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c),x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)} x^{m}}{{\left(a^{2} c x^{2} - c\right)} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(-(a*x + 1)*x^m/((a^2*c*x^2 - c)*sqrt(-a^2*x^2 + 1)), x)","F",0
990,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(a^{2} c x^{2} - c\right)}^{2} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/((a^2*c*x^2 - c)^2*sqrt(-a^2*x^2 + 1)), x)","F",0
991,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)} x^{m}}{{\left(a^{2} c x^{2} - c\right)}^{3} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(-(a*x + 1)*x^m/((a^2*c*x^2 - c)^3*sqrt(-a^2*x^2 + 1)), x)","F",0
992,1,460,0,0.220757," ","integrate((a*x+1)*(-a^2*x^2+1)^2*x^m,x, algorithm=""giac"")","\frac{a^{5} m^{5} x^{6} x^{m} + 15 \, a^{5} m^{4} x^{6} x^{m} + a^{4} m^{5} x^{5} x^{m} + 85 \, a^{5} m^{3} x^{6} x^{m} + 16 \, a^{4} m^{4} x^{5} x^{m} + 225 \, a^{5} m^{2} x^{6} x^{m} - 2 \, a^{3} m^{5} x^{4} x^{m} + 95 \, a^{4} m^{3} x^{5} x^{m} + 274 \, a^{5} m x^{6} x^{m} - 34 \, a^{3} m^{4} x^{4} x^{m} + 260 \, a^{4} m^{2} x^{5} x^{m} + 120 \, a^{5} x^{6} x^{m} - 2 \, a^{2} m^{5} x^{3} x^{m} - 214 \, a^{3} m^{3} x^{4} x^{m} + 324 \, a^{4} m x^{5} x^{m} - 36 \, a^{2} m^{4} x^{3} x^{m} - 614 \, a^{3} m^{2} x^{4} x^{m} + 144 \, a^{4} x^{5} x^{m} + a m^{5} x^{2} x^{m} - 242 \, a^{2} m^{3} x^{3} x^{m} - 792 \, a^{3} m x^{4} x^{m} + 19 \, a m^{4} x^{2} x^{m} - 744 \, a^{2} m^{2} x^{3} x^{m} - 360 \, a^{3} x^{4} x^{m} + m^{5} x x^{m} + 137 \, a m^{3} x^{2} x^{m} - 1016 \, a^{2} m x^{3} x^{m} + 20 \, m^{4} x x^{m} + 461 \, a m^{2} x^{2} x^{m} - 480 \, a^{2} x^{3} x^{m} + 155 \, m^{3} x x^{m} + 702 \, a m x^{2} x^{m} + 580 \, m^{2} x x^{m} + 360 \, a x^{2} x^{m} + 1044 \, m x x^{m} + 720 \, x x^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720}"," ",0,"(a^5*m^5*x^6*x^m + 15*a^5*m^4*x^6*x^m + a^4*m^5*x^5*x^m + 85*a^5*m^3*x^6*x^m + 16*a^4*m^4*x^5*x^m + 225*a^5*m^2*x^6*x^m - 2*a^3*m^5*x^4*x^m + 95*a^4*m^3*x^5*x^m + 274*a^5*m*x^6*x^m - 34*a^3*m^4*x^4*x^m + 260*a^4*m^2*x^5*x^m + 120*a^5*x^6*x^m - 2*a^2*m^5*x^3*x^m - 214*a^3*m^3*x^4*x^m + 324*a^4*m*x^5*x^m - 36*a^2*m^4*x^3*x^m - 614*a^3*m^2*x^4*x^m + 144*a^4*x^5*x^m + a*m^5*x^2*x^m - 242*a^2*m^3*x^3*x^m - 792*a^3*m*x^4*x^m + 19*a*m^4*x^2*x^m - 744*a^2*m^2*x^3*x^m - 360*a^3*x^4*x^m + m^5*x*x^m + 137*a*m^3*x^2*x^m - 1016*a^2*m*x^3*x^m + 20*m^4*x*x^m + 461*a*m^2*x^2*x^m - 480*a^2*x^3*x^m + 155*m^3*x*x^m + 702*a*m*x^2*x^m + 580*m^2*x*x^m + 360*a*x^2*x^m + 1044*m*x*x^m + 720*x*x^m)/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)","B",0
993,1,197,0,0.182914," ","integrate((a*x+1)*(-a^2*x^2+1)*x^m,x, algorithm=""giac"")","-\frac{a^{3} m^{3} x^{4} x^{m} + 6 \, a^{3} m^{2} x^{4} x^{m} + a^{2} m^{3} x^{3} x^{m} + 11 \, a^{3} m x^{4} x^{m} + 7 \, a^{2} m^{2} x^{3} x^{m} + 6 \, a^{3} x^{4} x^{m} - a m^{3} x^{2} x^{m} + 14 \, a^{2} m x^{3} x^{m} - 8 \, a m^{2} x^{2} x^{m} + 8 \, a^{2} x^{3} x^{m} - m^{3} x x^{m} - 19 \, a m x^{2} x^{m} - 9 \, m^{2} x x^{m} - 12 \, a x^{2} x^{m} - 26 \, m x x^{m} - 24 \, x x^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"-(a^3*m^3*x^4*x^m + 6*a^3*m^2*x^4*x^m + a^2*m^3*x^3*x^m + 11*a^3*m*x^4*x^m + 7*a^2*m^2*x^3*x^m + 6*a^3*x^4*x^m - a*m^3*x^2*x^m + 14*a^2*m*x^3*x^m - 8*a*m^2*x^2*x^m + 8*a^2*x^3*x^m - m^3*x*x^m - 19*a*m*x^2*x^m - 9*m^2*x*x^m - 12*a*x^2*x^m - 26*m*x*x^m - 24*x*x^m)/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","B",0
994,1,41,0,0.235979," ","integrate((a*x+1)*x^m,x, algorithm=""giac"")","\frac{a m x^{2} x^{m} + a x^{2} x^{m} + m x x^{m} + 2 \, x x^{m}}{m^{2} + 3 \, m + 2}"," ",0,"(a*m*x^2*x^m + a*x^2*x^m + m*x*x^m + 2*x*x^m)/(m^2 + 3*m + 2)","A",0
995,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)*x^m,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)} x^{m}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(a*x + 1)*x^m/(a^2*x^2 - 1), x)","F",0
996,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^2*x^m,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/(a^2*x^2 - 1)^2, x)","F",0
997,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^3*x^m,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)} x^{m}}{{\left(a^{2} x^{2} - 1\right)}^{3}}\,{d x}"," ",0,"integrate(-(a*x + 1)*x^m/(a^2*x^2 - 1)^3, x)","F",0
998,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
999,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
1000,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
1001,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{m}}{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)), x)","F",0
1002,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
1003,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{m}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^m/((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
1004,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^m*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{m}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p*x^m/sqrt(-a^2*x^2 + 1), x)","F",0
1005,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a^2*x^2+1)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p} x^{3}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^p*x^3/sqrt(-a^2*x^2 + 1), x)","F",0
1006,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*x^2+1)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p} x^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^p*x^2/sqrt(-a^2*x^2 + 1), x)","F",0
1007,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*x^2+1)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p} x}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^p*x/sqrt(-a^2*x^2 + 1), x)","F",0
1008,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^p/sqrt(-a^2*x^2 + 1), x)","F",0
1009,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p/x,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^p/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
1010,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^p/(sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
1011,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*x^2+1)^p/x^3,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} x^{2} + 1\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*x^2 + 1)^p/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
1012,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^3*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{3}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p*x^3/sqrt(-a^2*x^2 + 1), x)","F",0
1013,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p*x^2/sqrt(-a^2*x^2 + 1), x)","F",0
1014,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p} x}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p*x/sqrt(-a^2*x^2 + 1), x)","F",0
1015,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p/sqrt(-a^2*x^2 + 1), x)","F",0
1016,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
1017,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p/(sqrt(-a^2*x^2 + 1)*x^2), x)","F",0
1018,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^p/x^3,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)*(-a^2*c*x^2 + c)^p/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
1019,1,23,0,0.157813," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4*(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{1}{7} \, a^{2} c x^{7} + \frac{1}{3} \, a c x^{6} + \frac{1}{5} \, c x^{5}"," ",0,"1/7*a^2*c*x^7 + 1/3*a*c*x^6 + 1/5*c*x^5","A",0
1020,1,23,0,0.189142," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{1}{6} \, a^{2} c x^{6} + \frac{2}{5} \, a c x^{5} + \frac{1}{4} \, c x^{4}"," ",0,"1/6*a^2*c*x^6 + 2/5*a*c*x^5 + 1/4*c*x^4","A",0
1021,1,23,0,0.208987," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{1}{5} \, a^{2} c x^{5} + \frac{1}{2} \, a c x^{4} + \frac{1}{3} \, c x^{3}"," ",0,"1/5*a^2*c*x^5 + 1/2*a*c*x^4 + 1/3*c*x^3","A",0
1022,1,23,0,0.211217," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{1}{4} \, a^{2} c x^{4} + \frac{2}{3} \, a c x^{3} + \frac{1}{2} \, c x^{2}"," ",0,"1/4*a^2*c*x^4 + 2/3*a*c*x^3 + 1/2*c*x^2","A",0
1023,1,19,0,0.177739," ","integrate((a*x+1)^2/(-a^2*x^2+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
1024,1,20,0,0.287743," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x,x, algorithm=""giac"")","\frac{1}{2} \, a^{2} c x^{2} + 2 \, a c x + c \log\left({\left| x \right|}\right)"," ",0,"1/2*a^2*c*x^2 + 2*a*c*x + c*log(abs(x))","A",0
1025,1,20,0,0.185774," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x^2,x, algorithm=""giac"")","a^{2} c x + 2 \, a c \log\left({\left| x \right|}\right) - \frac{c}{x}"," ",0,"a^2*c*x + 2*a*c*log(abs(x)) - c/x","A",0
1026,1,21,0,0.197507," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x^3,x, algorithm=""giac"")","a^{2} c \log\left({\left| x \right|}\right) - \frac{4 \, a c x + c}{2 \, x^{2}}"," ",0,"a^2*c*log(abs(x)) - 1/2*(4*a*c*x + c)/x^2","A",0
1027,1,21,0,0.351827," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)/x^4,x, algorithm=""giac"")","-\frac{3 \, a^{2} c x^{2} + 3 \, a c x + c}{3 \, x^{3}}"," ",0,"-1/3*(3*a^2*c*x^2 + 3*a*c*x + c)/x^3","A",0
1028,1,40,0,0.166510," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{1}{9} \, a^{4} c^{2} x^{9} - \frac{1}{4} \, a^{3} c^{2} x^{8} + \frac{1}{3} \, a c^{2} x^{6} + \frac{1}{5} \, c^{2} x^{5}"," ",0,"-1/9*a^4*c^2*x^9 - 1/4*a^3*c^2*x^8 + 1/3*a*c^2*x^6 + 1/5*c^2*x^5","A",0
1029,1,40,0,0.399259," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{1}{8} \, a^{4} c^{2} x^{8} - \frac{2}{7} \, a^{3} c^{2} x^{7} + \frac{2}{5} \, a c^{2} x^{5} + \frac{1}{4} \, c^{2} x^{4}"," ",0,"-1/8*a^4*c^2*x^8 - 2/7*a^3*c^2*x^7 + 2/5*a*c^2*x^5 + 1/4*c^2*x^4","A",0
1030,1,40,0,0.164502," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{1}{7} \, a^{4} c^{2} x^{7} - \frac{1}{3} \, a^{3} c^{2} x^{6} + \frac{1}{2} \, a c^{2} x^{4} + \frac{1}{3} \, c^{2} x^{3}"," ",0,"-1/7*a^4*c^2*x^7 - 1/3*a^3*c^2*x^6 + 1/2*a*c^2*x^4 + 1/3*c^2*x^3","A",0
1031,1,40,0,0.198278," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{1}{6} \, a^{4} c^{2} x^{6} - \frac{2}{5} \, a^{3} c^{2} x^{5} + \frac{2}{3} \, a c^{2} x^{3} + \frac{1}{2} \, c^{2} x^{2}"," ",0,"-1/6*a^4*c^2*x^6 - 2/5*a^3*c^2*x^5 + 2/3*a*c^2*x^3 + 1/2*c^2*x^2","A",0
1032,1,36,0,1.406069," ","integrate((a*x+1)^2/(-a^2*x^2+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
1033,1,37,0,0.155005," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x,x, algorithm=""giac"")","-\frac{1}{4} \, a^{4} c^{2} x^{4} - \frac{2}{3} \, a^{3} c^{2} x^{3} + 2 \, a c^{2} x + c^{2} \log\left({\left| x \right|}\right)"," ",0,"-1/4*a^4*c^2*x^4 - 2/3*a^3*c^2*x^3 + 2*a*c^2*x + c^2*log(abs(x))","A",0
1034,1,40,0,0.218531," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^2,x, algorithm=""giac"")","-\frac{1}{3} \, a^{4} c^{2} x^{3} - a^{3} c^{2} x^{2} + 2 \, a c^{2} \log\left({\left| x \right|}\right) - \frac{c^{2}}{x}"," ",0,"-1/3*a^4*c^2*x^3 - a^3*c^2*x^2 + 2*a*c^2*log(abs(x)) - c^2/x","A",0
1035,1,37,0,0.562909," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^3,x, algorithm=""giac"")","-\frac{1}{2} \, a^{4} c^{2} x^{2} - 2 \, a^{3} c^{2} x - \frac{4 \, a c^{2} x + c^{2}}{2 \, x^{2}}"," ",0,"-1/2*a^4*c^2*x^2 - 2*a^3*c^2*x - 1/2*(4*a*c^2*x + c^2)/x^2","B",0
1036,1,37,0,0.448266," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^4,x, algorithm=""giac"")","-a^{4} c^{2} x - 2 \, a^{3} c^{2} \log\left({\left| x \right|}\right) - \frac{3 \, a c^{2} x + c^{2}}{3 \, x^{3}}"," ",0,"-a^4*c^2*x - 2*a^3*c^2*log(abs(x)) - 1/3*(3*a*c^2*x + c^2)/x^3","A",0
1037,1,41,0,0.226098," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^5,x, algorithm=""giac"")","-a^{4} c^{2} \log\left({\left| x \right|}\right) + \frac{24 \, a^{3} c^{2} x^{3} - 8 \, a c^{2} x - 3 \, c^{2}}{12 \, x^{4}}"," ",0,"-a^4*c^2*log(abs(x)) + 1/12*(24*a^3*c^2*x^3 - 8*a*c^2*x - 3*c^2)/x^4","A",0
1038,1,40,0,0.177362," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^2/x^6,x, algorithm=""giac"")","\frac{10 \, a^{4} c^{2} x^{4} + 10 \, a^{3} c^{2} x^{3} - 5 \, a c^{2} x - 2 \, c^{2}}{10 \, x^{5}}"," ",0,"1/10*(10*a^4*c^2*x^4 + 10*a^3*c^2*x^3 - 5*a*c^2*x - 2*c^2)/x^5","A",0
1039,1,73,0,0.226235," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{11} \, a^{6} c^{3} x^{11} + \frac{1}{5} \, a^{5} c^{3} x^{10} - \frac{1}{9} \, a^{4} c^{3} x^{9} - \frac{1}{2} \, a^{3} c^{3} x^{8} - \frac{1}{7} \, a^{2} c^{3} x^{7} + \frac{1}{3} \, a c^{3} x^{6} + \frac{1}{5} \, c^{3} x^{5}"," ",0,"1/11*a^6*c^3*x^11 + 1/5*a^5*c^3*x^10 - 1/9*a^4*c^3*x^9 - 1/2*a^3*c^3*x^8 - 1/7*a^2*c^3*x^7 + 1/3*a*c^3*x^6 + 1/5*c^3*x^5","A",0
1040,1,73,0,0.185625," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{10} \, a^{6} c^{3} x^{10} + \frac{2}{9} \, a^{5} c^{3} x^{9} - \frac{1}{8} \, a^{4} c^{3} x^{8} - \frac{4}{7} \, a^{3} c^{3} x^{7} - \frac{1}{6} \, a^{2} c^{3} x^{6} + \frac{2}{5} \, a c^{3} x^{5} + \frac{1}{4} \, c^{3} x^{4}"," ",0,"1/10*a^6*c^3*x^10 + 2/9*a^5*c^3*x^9 - 1/8*a^4*c^3*x^8 - 4/7*a^3*c^3*x^7 - 1/6*a^2*c^3*x^6 + 2/5*a*c^3*x^5 + 1/4*c^3*x^4","A",0
1041,1,73,0,1.730046," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{9} \, a^{6} c^{3} x^{9} + \frac{1}{4} \, a^{5} c^{3} x^{8} - \frac{1}{7} \, a^{4} c^{3} x^{7} - \frac{2}{3} \, a^{3} c^{3} x^{6} - \frac{1}{5} \, a^{2} c^{3} x^{5} + \frac{1}{2} \, a c^{3} x^{4} + \frac{1}{3} \, c^{3} x^{3}"," ",0,"1/9*a^6*c^3*x^9 + 1/4*a^5*c^3*x^8 - 1/7*a^4*c^3*x^7 - 2/3*a^3*c^3*x^6 - 1/5*a^2*c^3*x^5 + 1/2*a*c^3*x^4 + 1/3*c^3*x^3","A",0
1042,1,73,0,0.172691," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{8} \, a^{6} c^{3} x^{8} + \frac{2}{7} \, a^{5} c^{3} x^{7} - \frac{1}{6} \, a^{4} c^{3} x^{6} - \frac{4}{5} \, a^{3} c^{3} x^{5} - \frac{1}{4} \, a^{2} c^{3} x^{4} + \frac{2}{3} \, a c^{3} x^{3} + \frac{1}{2} \, c^{3} x^{2}"," ",0,"1/8*a^6*c^3*x^8 + 2/7*a^5*c^3*x^7 - 1/6*a^4*c^3*x^6 - 4/5*a^3*c^3*x^5 - 1/4*a^2*c^3*x^4 + 2/3*a*c^3*x^3 + 1/2*c^3*x^2","A",0
1043,1,69,0,0.182739," ","integrate((a*x+1)^2/(-a^2*x^2+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
1044,1,70,0,0.149967," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x,x, algorithm=""giac"")","\frac{1}{6} \, a^{6} c^{3} x^{6} + \frac{2}{5} \, a^{5} c^{3} x^{5} - \frac{1}{4} \, a^{4} c^{3} x^{4} - \frac{4}{3} \, a^{3} c^{3} x^{3} - \frac{1}{2} \, a^{2} c^{3} x^{2} + 2 \, a c^{3} x + c^{3} \log\left({\left| x \right|}\right)"," ",0,"1/6*a^6*c^3*x^6 + 2/5*a^5*c^3*x^5 - 1/4*a^4*c^3*x^4 - 4/3*a^3*c^3*x^3 - 1/2*a^2*c^3*x^2 + 2*a*c^3*x + c^3*log(abs(x))","A",0
1045,1,71,0,0.195048," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x^2,x, algorithm=""giac"")","\frac{1}{5} \, a^{6} c^{3} x^{5} + \frac{1}{2} \, a^{5} c^{3} x^{4} - \frac{1}{3} \, a^{4} c^{3} x^{3} - 2 \, a^{3} c^{3} x^{2} - a^{2} c^{3} x + 2 \, a c^{3} \log\left({\left| x \right|}\right) - \frac{c^{3}}{x}"," ",0,"1/5*a^6*c^3*x^5 + 1/2*a^5*c^3*x^4 - 1/3*a^4*c^3*x^3 - 2*a^3*c^3*x^2 - a^2*c^3*x + 2*a*c^3*log(abs(x)) - c^3/x","A",0
1046,1,70,0,1.036671," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x^3,x, algorithm=""giac"")","\frac{1}{4} \, a^{6} c^{3} x^{4} + \frac{2}{3} \, a^{5} c^{3} x^{3} - \frac{1}{2} \, a^{4} c^{3} x^{2} - 4 \, a^{3} c^{3} x - a^{2} c^{3} \log\left({\left| x \right|}\right) - \frac{4 \, a c^{3} x + c^{3}}{2 \, x^{2}}"," ",0,"1/4*a^6*c^3*x^4 + 2/3*a^5*c^3*x^3 - 1/2*a^4*c^3*x^2 - 4*a^3*c^3*x - a^2*c^3*log(abs(x)) - 1/2*(4*a*c^3*x + c^3)/x^2","A",0
1047,1,71,0,0.205299," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^3/x^4,x, algorithm=""giac"")","\frac{1}{3} \, a^{6} c^{3} x^{3} + a^{5} c^{3} x^{2} - a^{4} c^{3} x - 4 \, a^{3} c^{3} \log\left({\left| x \right|}\right) + \frac{3 \, a^{2} c^{3} x^{2} - 3 \, a c^{3} x - c^{3}}{3 \, x^{3}}"," ",0,"1/3*a^6*c^3*x^3 + a^5*c^3*x^2 - a^4*c^3*x - 4*a^3*c^3*log(abs(x)) + 1/3*(3*a^2*c^3*x^2 - 3*a*c^3*x - c^3)/x^3","A",0
1048,1,79,0,0.307457," ","integrate((a*x+1)^2/(-a^2*x^2+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
1049,1,70,0,0.184708," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{4 \, \log\left({\left| a x - 1 \right|}\right)}{a^{5} c} - \frac{1}{{\left(a x - 1\right)} a^{5} c} + \frac{a^{4} c^{2} x^{3} + 3 \, a^{3} c^{2} x^{2} + 9 \, a^{2} c^{2} x}{3 \, a^{6} c^{3}}"," ",0,"4*log(abs(a*x - 1))/(a^5*c) - 1/((a*x - 1)*a^5*c) + 1/3*(a^4*c^2*x^3 + 3*a^3*c^2*x^2 + 9*a^2*c^2*x)/(a^6*c^3)","A",0
1050,1,53,0,0.234752," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{3 \, \log\left({\left| a x - 1 \right|}\right)}{a^{4} c} + \frac{a^{2} c x^{2} + 4 \, a c x}{2 \, a^{4} c^{2}} - \frac{1}{{\left(a x - 1\right)} a^{4} c}"," ",0,"3*log(abs(a*x - 1))/(a^4*c) + 1/2*(a^2*c*x^2 + 4*a*c*x)/(a^4*c^2) - 1/((a*x - 1)*a^4*c)","A",0
1051,1,39,0,0.883932," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{x}{a^{2} c} + \frac{2 \, \log\left({\left| a x - 1 \right|}\right)}{a^{3} c} - \frac{1}{{\left(a x - 1\right)} a^{3} c}"," ",0,"x/(a^2*c) + 2*log(abs(a*x - 1))/(a^3*c) - 1/((a*x - 1)*a^3*c)","A",0
1052,1,30,0,0.230759," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{\log\left({\left| a x - 1 \right|}\right)}{a^{2} c} - \frac{1}{{\left(a x - 1\right)} a^{2} c}"," ",0,"log(abs(a*x - 1))/(a^2*c) - 1/((a*x - 1)*a^2*c)","A",0
1053,1,15,0,0.174416," ","integrate((a*x+1)^2/(-a^2*x^2+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
1054,1,32,0,0.210049," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{\log\left({\left| a x - 1 \right|}\right)}{c} + \frac{\log\left({\left| x \right|}\right)}{c} - \frac{1}{{\left(a x - 1\right)} c}"," ",0,"-log(abs(a*x - 1))/c + log(abs(x))/c - 1/((a*x - 1)*c)","A",0
1055,1,45,0,0.446983," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{2 \, a \log\left({\left| a x - 1 \right|}\right)}{c} + \frac{2 \, a \log\left({\left| x \right|}\right)}{c} - \frac{2 \, a x - 1}{{\left(a x^{2} - x\right)} c}"," ",0,"-2*a*log(abs(a*x - 1))/c + 2*a*log(abs(x))/c - (2*a*x - 1)/((a*x^2 - x)*c)","A",0
1056,1,56,0,0.425379," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{3 \, a^{2} \log\left({\left| a x - 1 \right|}\right)}{c} + \frac{3 \, a^{2} \log\left({\left| x \right|}\right)}{c} - \frac{6 \, a^{2} x^{2} - 3 \, a x - 1}{2 \, {\left(a x - 1\right)} c x^{2}}"," ",0,"-3*a^2*log(abs(a*x - 1))/c + 3*a^2*log(abs(x))/c - 1/2*(6*a^2*x^2 - 3*a*x - 1)/((a*x - 1)*c*x^2)","A",0
1057,1,64,0,0.311094," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^4/(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{4 \, a^{3} \log\left({\left| a x - 1 \right|}\right)}{c} + \frac{4 \, a^{3} \log\left({\left| x \right|}\right)}{c} - \frac{12 \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 2 \, a x - 1}{3 \, {\left(a x - 1\right)} c x^{3}}"," ",0,"-4*a^3*log(abs(a*x - 1))/c + 4*a^3*log(abs(x))/c - 1/3*(12*a^3*x^3 - 6*a^2*x^2 - 2*a*x - 1)/((a*x - 1)*c*x^3)","A",0
1058,1,61,0,0.156441," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{x}{a^{4} c^{2}} + \frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a^{5} c^{2}} - \frac{17 \, \log\left({\left| a x - 1 \right|}\right)}{8 \, a^{5} c^{2}} + \frac{7 \, a x - 6}{4 \, {\left(a x - 1\right)}^{2} a^{5} c^{2}}"," ",0,"-x/(a^4*c^2) + 1/8*log(abs(a*x + 1))/(a^5*c^2) - 17/8*log(abs(a*x - 1))/(a^5*c^2) + 1/4*(7*a*x - 6)/((a*x - 1)^2*a^5*c^2)","A",0
1059,1,52,0,0.341115," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a^{4} c^{2}} - \frac{7 \, \log\left({\left| a x - 1 \right|}\right)}{8 \, a^{4} c^{2}} + \frac{5 \, a x - 4}{4 \, {\left(a x - 1\right)}^{2} a^{4} c^{2}}"," ",0,"-1/8*log(abs(a*x + 1))/(a^4*c^2) - 7/8*log(abs(a*x - 1))/(a^4*c^2) + 1/4*(5*a*x - 4)/((a*x - 1)^2*a^4*c^2)","A",0
1060,1,52,0,0.301190," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a^{3} c^{2}} - \frac{\log\left({\left| a x - 1 \right|}\right)}{8 \, a^{3} c^{2}} + \frac{3 \, a x - 2}{4 \, {\left(a x - 1\right)}^{2} a^{3} c^{2}}"," ",0,"1/8*log(abs(a*x + 1))/(a^3*c^2) - 1/8*log(abs(a*x - 1))/(a^3*c^2) + 1/4*(3*a*x - 2)/((a*x - 1)^2*a^3*c^2)","A",0
1061,1,47,0,0.207743," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a^{2} c^{2}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{8 \, a^{2} c^{2}} + \frac{x}{4 \, {\left(a x - 1\right)}^{2} a c^{2}}"," ",0,"-1/8*log(abs(a*x + 1))/(a^2*c^2) + 1/8*log(abs(a*x - 1))/(a^2*c^2) + 1/4*x/((a*x - 1)^2*a*c^2)","A",0
1062,1,51,0,0.341443," ","integrate((a*x+1)^2/(-a^2*x^2+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
1063,1,50,0,0.183685," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, c^{2}} - \frac{7 \, \log\left({\left| a x - 1 \right|}\right)}{8 \, c^{2}} + \frac{\log\left({\left| x \right|}\right)}{c^{2}} - \frac{3 \, a x - 4}{4 \, {\left(a x - 1\right)}^{2} c^{2}}"," ",0,"-1/8*log(abs(a*x + 1))/c^2 - 7/8*log(abs(a*x - 1))/c^2 + log(abs(x))/c^2 - 1/4*(3*a*x - 4)/((a*x - 1)^2*c^2)","A",0
1064,1,65,0,0.199166," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\frac{a \log\left({\left| a x + 1 \right|}\right)}{8 \, c^{2}} - \frac{17 \, a \log\left({\left| a x - 1 \right|}\right)}{8 \, c^{2}} + \frac{2 \, a \log\left({\left| x \right|}\right)}{c^{2}} - \frac{9 \, a^{2} x^{2} - 14 \, a x + 4}{4 \, {\left(a x - 1\right)}^{2} c^{2} x}"," ",0,"1/8*a*log(abs(a*x + 1))/c^2 - 17/8*a*log(abs(a*x - 1))/c^2 + 2*a*log(abs(x))/c^2 - 1/4*(9*a^2*x^2 - 14*a*x + 4)/((a*x - 1)^2*c^2*x)","A",0
1065,1,79,0,1.085574," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{a^{2} \log\left({\left| a x + 1 \right|}\right)}{8 \, c^{2}} - \frac{31 \, a^{2} \log\left({\left| a x - 1 \right|}\right)}{8 \, c^{2}} + \frac{4 \, a^{2} \log\left({\left| x \right|}\right)}{c^{2}} - \frac{15 \, a^{3} x^{3} - 22 \, a^{2} x^{2} + 4 \, a x + 2}{4 \, {\left(a x - 1\right)}^{2} c^{2} x^{2}}"," ",0,"-1/8*a^2*log(abs(a*x + 1))/c^2 - 31/8*a^2*log(abs(a*x - 1))/c^2 + 4*a^2*log(abs(x))/c^2 - 1/4*(15*a^3*x^3 - 22*a^2*x^2 + 4*a*x + 2)/((a*x - 1)^2*c^2*x^2)","A",0
1066,1,87,0,0.160158," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^4/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\frac{a^{3} \log\left({\left| a x + 1 \right|}\right)}{8 \, c^{2}} - \frac{49 \, a^{3} \log\left({\left| a x - 1 \right|}\right)}{8 \, c^{2}} + \frac{6 \, a^{3} \log\left({\left| x \right|}\right)}{c^{2}} - \frac{75 \, a^{4} x^{4} - 114 \, a^{3} x^{3} + 28 \, a^{2} x^{2} + 4 \, a x + 4}{12 \, {\left(a x - 1\right)}^{2} c^{2} x^{3}}"," ",0,"1/8*a^3*log(abs(a*x + 1))/c^2 - 49/8*a^3*log(abs(a*x - 1))/c^2 + 6*a^3*log(abs(x))/c^2 - 1/12*(75*a^4*x^4 - 114*a^3*x^3 + 28*a^2*x^2 + 4*a*x + 4)/((a*x - 1)^2*c^2*x^3)","A",0
1067,1,75,0,0.726080," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^5/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| a x + 1 \right|}\right)}{16 \, a^{6} c^{3}} + \frac{13 \, \log\left({\left| a x - 1 \right|}\right)}{16 \, a^{6} c^{3}} - \frac{33 \, a^{3} x^{3} - 18 \, a^{2} x^{2} - 37 \, a x + 26}{24 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{3} a^{6} c^{3}}"," ",0,"3/16*log(abs(a*x + 1))/(a^6*c^3) + 13/16*log(abs(a*x - 1))/(a^6*c^3) - 1/24*(33*a^3*x^3 - 18*a^2*x^2 - 37*a*x + 26)/((a*x + 1)*(a*x - 1)^3*a^6*c^3)","A",0
1068,1,75,0,0.187819," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^4/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{8 \, a^{5} c^{3}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{8 \, a^{5} c^{3}} - \frac{9 \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 5 \, a x + 4}{12 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{3} a^{5} c^{3}}"," ",0,"-1/8*log(abs(a*x + 1))/(a^5*c^3) + 1/8*log(abs(a*x - 1))/(a^5*c^3) - 1/12*(9*a^3*x^3 - 6*a^2*x^2 - 5*a*x + 4)/((a*x + 1)*(a*x - 1)^3*a^5*c^3)","A",0
1069,1,75,0,0.185554," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{\log\left({\left| a x + 1 \right|}\right)}{16 \, a^{4} c^{3}} - \frac{\log\left({\left| a x - 1 \right|}\right)}{16 \, a^{4} c^{3}} - \frac{3 \, a^{3} x^{3} + 6 \, a^{2} x^{2} - 7 \, a x + 2}{24 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{3} a^{4} c^{3}}"," ",0,"1/16*log(abs(a*x + 1))/(a^4*c^3) - 1/16*log(abs(a*x - 1))/(a^4*c^3) - 1/24*(3*a^3*x^3 + 6*a^2*x^2 - 7*a*x + 2)/((a*x + 1)*(a*x - 1)^3*a^4*c^3)","A",0
1070,1,45,0,0.192825," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{1}{16 \, {\left(a x + 1\right)} a^{3} c^{3}} + \frac{3 \, a^{2} x^{2} - 12 \, a x + 5}{48 \, {\left(a x - 1\right)}^{3} a^{3} c^{3}}"," ",0,"-1/16/((a*x + 1)*a^3*c^3) + 1/48*(3*a^2*x^2 - 12*a*x + 5)/((a*x - 1)^3*a^3*c^3)","A",0
1071,1,74,0,0.178111," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + 1 \right|}\right)}{16 \, a^{2} c^{3}} + \frac{\log\left({\left| a x - 1 \right|}\right)}{16 \, a^{2} c^{3}} + \frac{3 \, a^{3} x^{3} - 6 \, a^{2} x^{2} + a x - 2}{24 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{3} a^{2} c^{3}}"," ",0,"-1/16*log(abs(a*x + 1))/(a^2*c^3) + 1/16*log(abs(a*x - 1))/(a^2*c^3) + 1/24*(3*a^3*x^3 - 6*a^2*x^2 + a*x - 2)/((a*x + 1)*(a*x - 1)^3*a^2*c^3)","A",0
1072,1,74,0,0.208461," ","integrate((a*x+1)^2/(-a^2*x^2+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
1073,1,73,0,0.362141," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{3 \, \log\left({\left| a x + 1 \right|}\right)}{16 \, c^{3}} - \frac{13 \, \log\left({\left| a x - 1 \right|}\right)}{16 \, c^{3}} + \frac{\log\left({\left| x \right|}\right)}{c^{3}} - \frac{15 \, a^{3} x^{3} - 18 \, a^{2} x^{2} - 19 \, a x + 26}{24 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{3} c^{3}}"," ",0,"-3/16*log(abs(a*x + 1))/c^3 - 13/16*log(abs(a*x - 1))/c^3 + log(abs(x))/c^3 - 1/24*(15*a^3*x^3 - 18*a^2*x^2 - 19*a*x + 26)/((a*x + 1)*(a*x - 1)^3*c^3)","A",0
1074,1,88,0,0.189861," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{a \log\left({\left| a x + 1 \right|}\right)}{4 \, c^{3}} - \frac{9 \, a \log\left({\left| a x - 1 \right|}\right)}{4 \, c^{3}} + \frac{2 \, a \log\left({\left| x \right|}\right)}{c^{3}} - \frac{15 \, a^{4} x^{4} - 24 \, a^{3} x^{3} - 7 \, a^{2} x^{2} + 23 \, a x - 6}{6 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{3} c^{3} x}"," ",0,"1/4*a*log(abs(a*x + 1))/c^3 - 9/4*a*log(abs(a*x - 1))/c^3 + 2*a*log(abs(x))/c^3 - 1/6*(15*a^4*x^4 - 24*a^3*x^3 - 7*a^2*x^2 + 23*a*x - 6)/((a*x + 1)*(a*x - 1)^3*c^3*x)","A",0
1075,1,102,0,0.185571," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{5 \, a^{2} \log\left({\left| a x + 1 \right|}\right)}{16 \, c^{3}} - \frac{75 \, a^{2} \log\left({\left| a x - 1 \right|}\right)}{16 \, c^{3}} + \frac{5 \, a^{2} \log\left({\left| x \right|}\right)}{c^{3}} - \frac{105 \, a^{5} x^{5} - 150 \, a^{4} x^{4} - 85 \, a^{3} x^{3} + 170 \, a^{2} x^{2} - 24 \, a x - 12}{24 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{3} c^{3} x^{2}}"," ",0,"-5/16*a^2*log(abs(a*x + 1))/c^3 - 75/16*a^2*log(abs(a*x - 1))/c^3 + 5*a^2*log(abs(x))/c^3 - 1/24*(105*a^5*x^5 - 150*a^4*x^4 - 85*a^3*x^3 + 170*a^2*x^2 - 24*a*x - 12)/((a*x + 1)*(a*x - 1)^3*c^3*x^2)","A",0
1076,1,91,0,1.119116," ","integrate((a*x+1)^2/(-a^2*x^2+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
1077,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^(1/2),x, algorithm=""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
1078,1,84,0,0.192639," ","integrate((a*x+1)^2/(-a^2*x^2+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
1079,1,73,0,0.233364," ","integrate((a*x+1)^2/(-a^2*x^2+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
1080,1,62,0,0.230026," ","integrate((a*x+1)^2/(-a^2*x^2+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
1081,1,97,0,0.186770," ","integrate((a*x+1)^2/(-a^2*x^2+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
1082,1,133,0,1.843107," ","integrate((a*x+1)^2/(-a^2*x^2+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
1083,1,201,0,0.187953," ","integrate((a*x+1)^2/(-a^2*x^2+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
1084,1,250,0,0.833824," ","integrate((a*x+1)^2/(-a^2*x^2+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
1085,1,324,0,0.199088," ","integrate((a*x+1)^2/(-a^2*x^2+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
1086,1,117,0,0.345187," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{1}{840} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, {\left(3 \, a^{2} c x + 7 \, a c\right)} x + 18 \, c\right)} x - \frac{35 \, c}{a}\right)} x - \frac{44 \, c}{a^{2}}\right)} x - \frac{105 \, c}{a^{3}}\right)} x - \frac{176 \, c}{a^{4}}\right)} - \frac{c^{2} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{8 \, a^{3} \sqrt{-c} {\left| a \right|}}"," ",0,"1/840*sqrt(-a^2*c*x^2 + c)*((2*((4*(5*(3*a^2*c*x + 7*a*c)*x + 18*c)*x - 35*c/a)*x - 44*c/a^2)*x - 105*c/a^3)*x - 176*c/a^4) - 1/8*c^2*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(a^3*sqrt(-c)*abs(a))","A",0
1087,1,107,0,0.208127," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{1}{240} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, a^{2} c x + 12 \, a c\right)} x + 25 \, c\right)} x - \frac{16 \, c}{a}\right)} x - \frac{45 \, c}{a^{2}}\right)} x - \frac{64 \, c}{a^{3}}\right)} - \frac{3 \, c^{2} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{16 \, a^{2} \sqrt{-c} {\left| a \right|}}"," ",0,"1/240*sqrt(-a^2*c*x^2 + c)*((2*((4*(5*a^2*c*x + 12*a*c)*x + 25*c)*x - 16*c/a)*x - 45*c/a^2)*x - 64*c/a^3) - 3/16*c^2*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(a^2*sqrt(-c)*abs(a))","A",0
1088,1,98,0,0.203465," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{1}{60} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(2 \, {\left(3 \, {\left(2 \, a^{2} c x + 5 \, a c\right)} x + 8 \, c\right)} x - \frac{15 \, c}{a}\right)} x - \frac{28 \, c}{a^{2}}\right)} - \frac{c^{2} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{4 \, a \sqrt{-c} {\left| a \right|}}"," ",0,"1/60*sqrt(-a^2*c*x^2 + c)*((2*(3*(2*a^2*c*x + 5*a*c)*x + 8*c)*x - 15*c/a)*x - 28*c/a^2) - 1/4*c^2*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(a*sqrt(-c)*abs(a))","A",0
1089,1,85,0,0.762105," ","integrate((a*x+1)^2/(-a^2*x^2+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
1090,1,116,0,1.060372," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x,x, algorithm=""giac"")","\frac{2 \, c^{2} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{a \sqrt{-c} c \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{{\left| a \right|}} + \frac{1}{3} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(a^{2} c x + 3 \, a c\right)} x + 2 \, c\right)}"," ",0,"2*c^2*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + a*sqrt(-c)*c*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) + 1/3*sqrt(-a^2*c*x^2 + c)*((a^2*c*x + 3*a*c)*x + 2*c)","A",0
1091,1,165,0,0.999356," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^2,x, algorithm=""giac"")","\frac{4 \, a c^{2} \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} c \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{2 \, {\left| a \right|}} + \frac{2 \, a^{2} \sqrt{-c} c^{2}}{{\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)} {\left| a \right|}} + \frac{1}{2} \, \sqrt{-a^{2} c x^{2} + c} {\left(a^{2} c x + 4 \, a c\right)}"," ",0,"4*a*c^2*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) - 1/2*a^2*sqrt(-c)*c*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) + 2*a^2*sqrt(-c)*c^2/(((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)*abs(a)) + 1/2*sqrt(-a^2*c*x^2 + c)*(a^2*c*x + 4*a*c)","A",0
1092,1,274,0,0.226446," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^3,x, algorithm=""giac"")","\frac{a^{2} c^{2} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{2 \, a^{3} \sqrt{-c} 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} a^{2} c - \frac{{\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a^{2} c^{2} {\left| a \right|} - 4 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{3} \sqrt{-c} c^{2} + {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{2} c^{3} {\left| a \right|} + 4 \, a^{3} \sqrt{-c} c^{3}}{{\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{2} {\left| a \right|}}"," ",0,"a^2*c^2*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) - 2*a^3*sqrt(-c)*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^2*c - ((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a^2*c^2*abs(a) - 4*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^3*sqrt(-c)*c^2 + (sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^2*c^3*abs(a) + 4*a^3*sqrt(-c)*c^3)/(((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^2*abs(a))","B",0
1093,1,259,0,0.548865," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^4,x, algorithm=""giac"")","-\frac{2 \, a^{3} c^{2} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{a^{4} \sqrt{-c} c \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{{\left| a \right|}} - \frac{2 \, {\left(3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{5} a^{3} c^{2} {\left| a \right|} + 6 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{4} \sqrt{-c} c^{3} - 3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{3} c^{4} {\left| a \right|} - 2 \, a^{4} \sqrt{-c} c^{4}\right)}}{3 \, {\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{3} {\left| a \right|}}"," ",0,"-2*a^3*c^2*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) - a^4*sqrt(-c)*c*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) - 2/3*(3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^5*a^3*c^2*abs(a) + 6*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^4*sqrt(-c)*c^3 - 3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^3*c^4*abs(a) - 2*a^4*sqrt(-c)*c^4)/(((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^3*abs(a))","B",0
1094,1,371,0,0.217410," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^5,x, algorithm=""giac"")","-\frac{5 \, a^{4} c^{2} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{4 \, \sqrt{-c}} - \frac{9 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{7} a^{4} c^{2} + 48 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{6} a^{3} \sqrt{-c} c^{2} {\left| a \right|} - 33 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{5} a^{4} c^{3} - 48 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{4} a^{3} \sqrt{-c} c^{3} {\left| a \right|} - 33 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a^{4} c^{4} + 16 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{3} \sqrt{-c} c^{4} {\left| a \right|} + 9 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{4} c^{5} - 16 \, a^{3} \sqrt{-c} c^{5} {\left| a \right|}}{12 \, {\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{4}}"," ",0,"-5/4*a^4*c^2*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) - 1/12*(9*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^7*a^4*c^2 + 48*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^6*a^3*sqrt(-c)*c^2*abs(a) - 33*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^5*a^4*c^3 - 48*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^4*a^3*sqrt(-c)*c^3*abs(a) - 33*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a^4*c^4 + 16*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^3*sqrt(-c)*c^4*abs(a) + 9*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^4*c^5 - 16*a^3*sqrt(-c)*c^5*abs(a))/((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^4","B",0
1095,1,414,0,0.212531," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^6,x, algorithm=""giac"")","-\frac{a^{5} c^{2} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{2 \, \sqrt{-c}} + \frac{15 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{9} a^{5} c^{2} - 60 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{8} a^{4} \sqrt{-c} c^{2} {\left| a \right|} + 90 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{7} a^{5} c^{3} + 240 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{6} a^{4} \sqrt{-c} c^{3} {\left| a \right|} - 40 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{4} a^{4} \sqrt{-c} c^{4} {\left| a \right|} - 90 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a^{5} c^{5} + 80 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{4} \sqrt{-c} c^{5} {\left| a \right|} - 15 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{5} c^{6} - 28 \, a^{4} \sqrt{-c} c^{6} {\left| a \right|}}{30 \, {\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{5}}"," ",0,"-1/2*a^5*c^2*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + 1/30*(15*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^9*a^5*c^2 - 60*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^8*a^4*sqrt(-c)*c^2*abs(a) + 90*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^7*a^5*c^3 + 240*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^6*a^4*sqrt(-c)*c^3*abs(a) - 40*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^4*a^4*sqrt(-c)*c^4*abs(a) - 90*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a^5*c^5 + 80*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^4*sqrt(-c)*c^5*abs(a) - 15*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^5*c^6 - 28*a^4*sqrt(-c)*c^6*abs(a))/((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^5","B",0
1096,1,443,0,0.571281," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^7,x, algorithm=""giac"")","-\frac{3 \, a^{6} c^{2} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{8 \, \sqrt{-c}} + \frac{45 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{11} a^{6} c^{2} + 65 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{9} a^{6} c^{3} + 960 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{8} a^{5} \sqrt{-c} c^{3} {\left| a \right|} - 750 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{7} a^{6} c^{4} - 640 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{6} a^{5} \sqrt{-c} c^{4} {\left| a \right|} - 750 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{5} a^{6} c^{5} + 65 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a^{6} c^{6} - 384 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{5} \sqrt{-c} c^{6} {\left| a \right|} + 45 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{6} c^{7} + 64 \, a^{5} \sqrt{-c} c^{7} {\left| a \right|}}{120 \, {\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{6}}"," ",0,"-3/8*a^6*c^2*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + 1/120*(45*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^11*a^6*c^2 + 65*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^9*a^6*c^3 + 960*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^8*a^5*sqrt(-c)*c^3*abs(a) - 750*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^7*a^6*c^4 - 640*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^6*a^5*sqrt(-c)*c^4*abs(a) - 750*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^5*a^6*c^5 + 65*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a^6*c^6 - 384*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^5*sqrt(-c)*c^6*abs(a) + 45*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^6*c^7 + 64*a^5*sqrt(-c)*c^7*abs(a))/((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^6","B",0
1097,1,529,0,0.270279," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(3/2)/x^8,x, algorithm=""giac"")","-\frac{a^{7} c^{2} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{4 \, \sqrt{-c}} + \frac{105 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{13} a^{7} c^{2} - 700 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{11} a^{7} c^{3} + 1680 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{10} a^{6} \sqrt{-c} c^{3} {\left| a \right|} - 3395 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{9} a^{7} c^{4} - 7280 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{8} a^{6} \sqrt{-c} c^{4} {\left| a \right|} - 1120 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{6} a^{6} \sqrt{-c} c^{5} {\left| a \right|} + 3395 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{5} a^{7} c^{6} - 2016 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{4} a^{6} \sqrt{-c} c^{6} {\left| a \right|} + 700 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a^{7} c^{7} + 1232 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{6} \sqrt{-c} c^{7} {\left| a \right|} - 105 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{7} c^{8} - 176 \, a^{6} \sqrt{-c} c^{8} {\left| a \right|}}{420 \, {\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{7}}"," ",0,"-1/4*a^7*c^2*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + 1/420*(105*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^13*a^7*c^2 - 700*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^11*a^7*c^3 + 1680*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^10*a^6*sqrt(-c)*c^3*abs(a) - 3395*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^9*a^7*c^4 - 7280*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^8*a^6*sqrt(-c)*c^4*abs(a) - 1120*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^6*a^6*sqrt(-c)*c^5*abs(a) + 3395*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^5*a^7*c^6 - 2016*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^4*a^6*sqrt(-c)*c^6*abs(a) + 700*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a^7*c^7 + 1232*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^6*sqrt(-c)*c^7*abs(a) - 105*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^7*c^8 - 176*a^6*sqrt(-c)*c^8*abs(a))/((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^7","B",0
1098,1,155,0,0.390364," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3*(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{1}{20160} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(2 \, {\left({\left(4 \, {\left(552 \, c^{2} + 5 \, {\left(189 \, a c^{2} + 2 \, {\left(4 \, a^{2} c^{2} - 7 \, {\left(4 \, a^{4} c^{2} x + 9 \, a^{3} c^{2}\right)} x\right)} x\right)} x\right)} x - \frac{315 \, c^{2}}{a}\right)} x - \frac{416 \, c^{2}}{a^{2}}\right)} x - \frac{945 \, c^{2}}{a^{3}}\right)} x - \frac{1664 \, c^{2}}{a^{4}}\right)} - \frac{3 \, c^{3} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{64 \, a^{3} \sqrt{-c} {\left| a \right|}}"," ",0,"1/20160*sqrt(-a^2*c*x^2 + c)*((2*((4*(552*c^2 + 5*(189*a*c^2 + 2*(4*a^2*c^2 - 7*(4*a^4*c^2*x + 9*a^3*c^2)*x)*x)*x)*x - 315*c^2/a)*x - 416*c^2/a^2)*x - 945*c^2/a^3)*x - 1664*c^2/a^4) - 3/64*c^3*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(a^3*sqrt(-c)*abs(a))","A",0
1099,1,143,0,0.277565," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{1}{13440} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(2 \, {\left({\left(1855 \, c^{2} + 4 \, {\left(768 \, a c^{2} + 5 \, {\left(7 \, a^{2} c^{2} - 6 \, {\left(7 \, a^{4} c^{2} x + 16 \, a^{3} c^{2}\right)} x\right)} x\right)} x\right)} x - \frac{384 \, c^{2}}{a}\right)} x - \frac{1155 \, c^{2}}{a^{2}}\right)} x - \frac{1536 \, c^{2}}{a^{3}}\right)} - \frac{11 \, c^{3} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{128 \, a^{2} \sqrt{-c} {\left| a \right|}}"," ",0,"1/13440*sqrt(-a^2*c*x^2 + c)*((2*((1855*c^2 + 4*(768*a*c^2 + 5*(7*a^2*c^2 - 6*(7*a^4*c^2*x + 16*a^3*c^2)*x)*x)*x)*x - 384*c^2/a)*x - 1155*c^2/a^2)*x - 1536*c^2/a^3) - 11/128*c^3*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(a^2*sqrt(-c)*abs(a))","A",0
1100,1,131,0,0.892828," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x*(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{1}{840} \, \sqrt{-a^{2} c x^{2} + c} {\left({\left(2 \, {\left(156 \, c^{2} + {\left(245 \, a c^{2} + 4 \, {\left(3 \, a^{2} c^{2} - 5 \, {\left(3 \, a^{4} c^{2} x + 7 \, a^{3} c^{2}\right)} x\right)} x\right)} x\right)} x - \frac{105 \, c^{2}}{a}\right)} x - \frac{216 \, c^{2}}{a^{2}}\right)} - \frac{c^{3} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{8 \, a \sqrt{-c} {\left| a \right|}}"," ",0,"1/840*sqrt(-a^2*c*x^2 + c)*((2*(156*c^2 + (245*a*c^2 + 4*(3*a^2*c^2 - 5*(3*a^4*c^2*x + 7*a^3*c^2)*x)*x)*x)*x - 105*c^2/a)*x - 216*c^2/a^2) - 1/8*c^3*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(a*sqrt(-c)*abs(a))","A",0
1101,1,116,0,0.251883," ","integrate((a*x+1)^2/(-a^2*x^2+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
1102,1,150,0,0.704209," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x,x, algorithm=""giac"")","\frac{2 \, c^{3} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{3 \, a \sqrt{-c} c^{2} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{4 \, {\left| a \right|}} + \frac{1}{60} \, \sqrt{-a^{2} c x^{2} + c} {\left(68 \, c^{2} + {\left(75 \, a c^{2} + 2 \, {\left(2 \, a^{2} c^{2} - 3 \, {\left(2 \, a^{4} c^{2} x + 5 \, a^{3} c^{2}\right)} x\right)} x\right)} x\right)}"," ",0,"2*c^3*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + 3/4*a*sqrt(-c)*c^2*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) + 1/60*sqrt(-a^2*c*x^2 + c)*(68*c^2 + (75*a*c^2 + 2*(2*a^2*c^2 - 3*(2*a^4*c^2*x + 5*a^3*c^2)*x)*x)*x)","A",0
1103,1,195,0,0.979992," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^2,x, algorithm=""giac"")","\frac{4 \, a c^{3} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{9 \, a^{2} \sqrt{-c} c^{2} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{8 \, {\left| a \right|}} + \frac{2 \, a^{2} \sqrt{-c} c^{3}}{{\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)} {\left| a \right|}} + \frac{1}{24} \, \sqrt{-a^{2} c x^{2} + c} {\left(64 \, a c^{2} + {\left(3 \, a^{2} c^{2} - 2 \, {\left(3 \, a^{4} c^{2} x + 8 \, a^{3} c^{2}\right)} x\right)} x\right)}"," ",0,"4*a*c^3*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) - 9/8*a^2*sqrt(-c)*c^2*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) + 2*a^2*sqrt(-c)*c^3/(((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)*abs(a)) + 1/24*sqrt(-a^2*c*x^2 + c)*(64*a*c^2 + (3*a^2*c^2 - 2*(3*a^4*c^2*x + 8*a^3*c^2)*x)*x)","A",0
1104,1,302,0,0.994877," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^3,x, algorithm=""giac"")","-\frac{a^{2} c^{3} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{3 \, a^{3} \sqrt{-c} c^{2} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{{\left| a \right|}} + \frac{1}{3} \, \sqrt{-a^{2} c x^{2} + c} {\left(a^{2} c^{2} - {\left(a^{4} c^{2} x + 3 \, a^{3} c^{2}\right)} x\right)} - \frac{{\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a^{2} c^{3} {\left| a \right|} - 4 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{3} \sqrt{-c} c^{3} + {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{2} c^{4} {\left| a \right|} + 4 \, a^{3} \sqrt{-c} c^{4}}{{\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{2} {\left| a \right|}}"," ",0,"-a^2*c^3*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) - 3*a^3*sqrt(-c)*c^2*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) + 1/3*sqrt(-a^2*c*x^2 + c)*(a^2*c^2 - (a^4*c^2*x + 3*a^3*c^2)*x) - ((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a^2*c^3*abs(a) - 4*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^3*sqrt(-c)*c^3 + (sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^2*c^4*abs(a) + 4*a^3*sqrt(-c)*c^4)/(((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^2*abs(a))","B",0
1105,1,292,0,0.231892," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^4,x, algorithm=""giac"")","-\frac{6 \, a^{3} c^{3} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{a^{4} \sqrt{-c} c^{2} \log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{2 \, {\left| a \right|}} - \frac{1}{2} \, {\left(a^{4} c^{2} x + 4 \, a^{3} c^{2}\right)} \sqrt{-a^{2} c x^{2} + 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| a \right|} + 3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{4} a^{4} \sqrt{-c} c^{3} - 3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{3} c^{5} {\left| a \right|} + a^{4} \sqrt{-c} c^{5}\right)}}{3 \, {\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{3} {\left| a \right|}}"," ",0,"-6*a^3*c^3*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) - 1/2*a^4*sqrt(-c)*c^2*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) - 1/2*(a^4*c^2*x + 4*a^3*c^2)*sqrt(-a^2*c*x^2 + c) - 2/3*(3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^5*a^3*c^3*abs(a) + 3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^4*a^4*sqrt(-c)*c^3 - 3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^3*c^5*abs(a) + a^4*sqrt(-c)*c^5)/(((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^3*abs(a))","B",0
1106,1,440,0,0.374004," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^(5/2)/x^5,x, algorithm=""giac"")","-\frac{9 \, a^{4} c^{3} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{4 \, \sqrt{-c}} + \frac{2 \, a^{5} \sqrt{-c} c^{2} \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} a^{4} c^{2} + \frac{3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{7} a^{4} c^{3} {\left| a \right|} - 96 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{6} a^{5} \sqrt{-c} c^{3} + 21 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{5} a^{4} c^{4} {\left| a \right|} + 192 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{4} a^{5} \sqrt{-c} c^{4} + 21 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a^{4} c^{5} {\left| a \right|} - 160 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} a^{5} \sqrt{-c} c^{5} + 3 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a^{4} c^{6} {\left| a \right|} + 64 \, a^{5} \sqrt{-c} c^{6}}{12 \, {\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{4} {\left| a \right|}}"," ",0,"-9/4*a^4*c^3*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/sqrt(-c) + 2*a^5*sqrt(-c)*c^2*log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/abs(a) - sqrt(-a^2*c*x^2 + c)*a^4*c^2 + 1/12*(3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^7*a^4*c^3*abs(a) - 96*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^6*a^5*sqrt(-c)*c^3 + 21*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^5*a^4*c^4*abs(a) + 192*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^4*a^5*sqrt(-c)*c^4 + 21*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a^4*c^5*abs(a) - 160*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*a^5*sqrt(-c)*c^5 + 3*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a^4*c^6*abs(a) + 64*a^5*sqrt(-c)*c^6)/(((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^4*abs(a))","B",0
1107,1,141,0,0.342843," ","integrate((a*x+1)^2/(-a^2*x^2+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
1108,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
1109,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""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
1110,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
1111,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
1112,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
1113,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
1114,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
1115,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^4/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
1116,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""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
1117,1,44,0,0.643080," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -\sqrt{-a^{2} c} x + \sqrt{-a^{2} c x^{2} + c} \right|}\right)}{a^{2} \sqrt{-c} c {\left| a \right|}}"," ",0,"-log(abs(-sqrt(-a^2*c)*x + sqrt(-a^2*c*x^2 + c)))/(a^2*sqrt(-c)*c*abs(a))","A",0
1118,1,117,0,0.309698," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x/(-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^{3} c^{\frac{5}{2}} - \sqrt{-a^{2} c} a^{2} c^{2}\right)}} - \frac{2 \, {\left(a \sqrt{c} + 3 \, \sqrt{-a^{2} c + \frac{c}{x^{2}}} - \frac{3 \, \sqrt{c}}{x}\right)}}{3 \, {\left(a \sqrt{c} + \sqrt{-a^{2} c + \frac{c}{x^{2}}} - \frac{\sqrt{c}}{x}\right)}^{3} \sqrt{c} \mathrm{sgn}\left(x\right)}"," ",0,"-1/3*(a*c + 3*sqrt(-a^2*c)*sqrt(c))*sgn(x)/(a^3*c^(5/2) - sqrt(-a^2*c)*a^2*c^2) - 2/3*(a*sqrt(c) + 3*sqrt(-a^2*c + c/x^2) - 3*sqrt(c)/x)/((a*sqrt(c) + sqrt(-a^2*c + c/x^2) - sqrt(c)/x)^3*sqrt(c)*sgn(x))","B",0
1119,1,148,0,0.351876," ","integrate((a*x+1)^2/(-a^2*x^2+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
1120,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x/(-a^2*c*x^2+c)^(3/2),x, algorithm=""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
1121,1,100,0,0.446973," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","-2 \, a^{2} \sqrt{-c} c {\left(\frac{2 \, {\left| a \right|} \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{a^{3} c^{3}} - \frac{1}{{\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)} a^{2} c^{2}}\right)} {\left| a \right|}"," ",0,"-2*a^2*sqrt(-c)*c*(2*abs(a)*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/(a^3*c^3) - 1/(((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)*a^2*c^2))*abs(a)","A",0
1122,1,204,0,0.410359," ","integrate((a*x+1)^2/(-a^2*x^2+1)/x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","a^{4} c^{2} {\left(\frac{7 \, \arctan\left(-\frac{\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c} c^{3}} - \frac{{\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{3} a - 4 \, {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} \sqrt{-c} {\left| a \right|} + {\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)} a c + 4 \, \sqrt{-c} c {\left| a \right|}}{{\left({\left(\sqrt{-a^{2} c} x - \sqrt{-a^{2} c x^{2} + c}\right)}^{2} - c\right)}^{2} a^{3} c^{3}}\right)}"," ",0,"a^4*c^2*(7*arctan(-(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))/sqrt(-c))/(a^2*sqrt(-c)*c^3) - ((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^3*a - 4*(sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2*sqrt(-c)*abs(a) + (sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))*a*c + 4*sqrt(-c)*c*abs(a))/(((sqrt(-a^2*c)*x - sqrt(-a^2*c*x^2 + c))^2 - c)^2*a^3*c^3))","A",0
1123,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-(a*x + 1)^2/((-a^2*c*x^2 + c)^(5/2)*(a^2*x^2 - 1)), x)","F",0
1124,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-(a*x + 1)^2/((-a^2*c*x^2 + c)^(7/2)*(a^2*x^2 - 1)), x)","F",0
1125,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int \frac{{\left(a^{2} c x^{2} - c\right)}^{3} {\left(a x + 1\right)}^{2} x^{m}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate((a^2*c*x^2 - c)^3*(a*x + 1)^2*x^m/(a^2*x^2 - 1), x)","F",0
1126,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int -\frac{{\left(a^{2} c x^{2} - c\right)}^{2} {\left(a x + 1\right)}^{2} x^{m}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(a^2*c*x^2 - c)^2*(a*x + 1)^2*x^m/(a^2*x^2 - 1), x)","F",0
1127,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c),x, algorithm=""giac"")","\int \frac{{\left(a^{2} c x^{2} - c\right)} {\left(a x + 1\right)}^{2} x^{m}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate((a^2*c*x^2 - c)*(a*x + 1)^2*x^m/(a^2*x^2 - 1), x)","F",0
1128,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{2} x^{m}}{{\left(a^{2} c x^{2} - c\right)} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((a*x + 1)^2*x^m/((a^2*c*x^2 - c)*(a^2*x^2 - 1)), x)","F",0
1129,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2} x^{m}}{{\left(a^{2} c x^{2} - c\right)}^{2} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-(a*x + 1)^2*x^m/((a^2*c*x^2 - c)^2*(a^2*x^2 - 1)), x)","F",0
1130,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{2} x^{m}}{{\left(a^{2} c x^{2} - c\right)}^{3} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"integrate((a*x + 1)^2*x^m/((a^2*c*x^2 - c)^3*(a^2*x^2 - 1)), x)","F",0
1131,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(5/2),x, algorithm=""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
1132,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(3/2),x, algorithm=""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
1133,-2,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""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
1134,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2} x^{m}}{\sqrt{-a^{2} c x^{2} + c} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-(a*x + 1)^2*x^m/(sqrt(-a^2*c*x^2 + c)*(a^2*x^2 - 1)), x)","F",0
1135,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^m/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2} x^{m}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-(a*x + 1)^2*x^m/((-a^2*c*x^2 + c)^(3/2)*(a^2*x^2 - 1)), x)","F",0
1136,0,0,0,0.000000," ","integrate((a*x+1)^2/(-a^2*x^2+1)*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{2} {\left(-a^{2} c x^{2} + c\right)}^{p}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(a*x + 1)^2*(-a^2*c*x^2 + c)^p/(a^2*x^2 - 1), x)","F",0
1137,1,78,0,0.200155," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{1}{240} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, a c x + 18 \, c\right)} x + \frac{115 \, c}{a}\right)} x + \frac{136 \, c}{a^{2}}\right)} x + \frac{345 \, c}{a^{3}}\right)} x + \frac{544 \, c}{a^{4}}\right)} + \frac{23 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{16 \, a^{3} {\left| a \right|}}"," ",0,"-1/240*sqrt(-a^2*x^2 + 1)*((2*((4*(5*a*c*x + 18*c)*x + 115*c/a)*x + 136*c/a^2)*x + 345*c/a^3)*x + 544*c/a^4) + 23/16*c*arcsin(a*x)*sgn(a)/(a^3*abs(a))","A",0
1138,1,69,0,0.231967," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{1}{120} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, {\left(3 \, {\left(4 \, a c x + 15 \, c\right)} x + \frac{76 \, c}{a}\right)} x + \frac{195 \, c}{a^{2}}\right)} x + \frac{304 \, c}{a^{3}}\right)} + \frac{13 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, a^{2} {\left| a \right|}}"," ",0,"-1/120*sqrt(-a^2*x^2 + 1)*((2*(3*(4*a*c*x + 15*c)*x + 76*c/a)*x + 195*c/a^2)*x + 304*c/a^3) + 13/8*c*arcsin(a*x)*sgn(a)/(a^2*abs(a))","A",0
1139,1,58,0,1.606582," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, {\left(a c x + 4 \, c\right)} x + \frac{15 \, c}{a}\right)} x + \frac{24 \, c}{a^{2}}\right)} + \frac{15 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, a {\left| a \right|}}"," ",0,"-1/8*sqrt(-a^2*x^2 + 1)*((2*(a*c*x + 4*c)*x + 15*c/a)*x + 24*c/a^2) + 15/8*c*arcsin(a*x)*sgn(a)/(a*abs(a))","A",0
1140,1,46,0,0.287219," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{5 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} - \frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, a c x + 9 \, c\right)} x + \frac{22 \, c}{a}\right)}"," ",0,"5/2*c*arcsin(a*x)*sgn(a)/abs(a) - 1/6*sqrt(-a^2*x^2 + 1)*((2*a*c*x + 9*c)*x + 22*c/a)","A",0
1141,1,76,0,0.211297," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x,x, algorithm=""giac"")","\frac{7 \, a c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} - \frac{a c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} {\left(a c x + 6 \, c\right)}"," ",0,"7/2*a*c*arcsin(a*x)*sgn(a)/abs(a) - a*c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/2*sqrt(-a^2*x^2 + 1)*(a*c*x + 6*c)","A",0
1142,1,131,0,0.232306," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^2,x, algorithm=""giac"")","\frac{a^{4} c x}{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} {\left| a \right|}} + \frac{3 \, a^{2} c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{3 \, a^{2} c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} - \sqrt{-a^{2} x^{2} + 1} a c - \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} c}{2 \, x {\left| a \right|}}"," ",0,"1/2*a^4*c*x/((sqrt(-a^2*x^2 + 1)*abs(a) + a)*abs(a)) + 3*a^2*c*arcsin(a*x)*sgn(a)/abs(a) - 3*a^2*c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - sqrt(-a^2*x^2 + 1)*a*c - 1/2*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*c/(x*abs(a))","B",0
1143,1,179,0,0.389065," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^3,x, algorithm=""giac"")","\frac{a^{3} c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} + \frac{{\left(a^{3} c + \frac{12 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c}{x}\right)} a^{4} x^{2}}{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} {\left| a \right|}} - \frac{7 \, a^{3} c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\frac{12 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a c {\left| a \right|}}{x} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c {\left| a \right|}}{a x^{2}}}{8 \, a^{2}}"," ",0,"a^3*c*arcsin(a*x)*sgn(a)/abs(a) + 1/8*(a^3*c + 12*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c/x)*a^4*x^2/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*abs(a)) - 7/2*a^3*c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/8*(12*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a*c*abs(a)/x + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c*abs(a)/(a*x^2))/a^2","B",0
1144,1,218,0,0.229527," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^4,x, algorithm=""giac"")","\frac{{\left(a^{4} c + \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{2} c}{x} + \frac{45 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} c}{x^{2}}\right)} a^{6} x^{3}}{24 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} {\left| a \right|}} - \frac{5 \, a^{4} c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{2 \, {\left| a \right|}} - \frac{\frac{45 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c}{x} + \frac{9 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c}{x^{2}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c}{x^{3}}}{24 \, a^{2} {\left| a \right|}}"," ",0,"1/24*(a^4*c + 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^2*c/x + 45*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*c/x^2)*a^6*x^3/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*abs(a)) - 5/2*a^4*c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/24*(45*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c/x + 9*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c/x^2 + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c/x^3)/(a^2*abs(a))","B",0
1145,1,280,0,0.182447," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^5,x, algorithm=""giac"")","\frac{{\left(a^{5} c + \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{3} c}{x} + \frac{32 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a c}{x^{2}} + \frac{104 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c}{a x^{3}}\right)} a^{8} x^{4}}{64 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} {\left| a \right|}} - \frac{15 \, a^{5} c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} - \frac{\frac{104 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{5} c {\left| a \right|}}{x} + \frac{32 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{3} c {\left| a \right|}}{x^{2}} + \frac{8 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a c {\left| a \right|}}{x^{3}} + \frac{{\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c {\left| a \right|}}{a x^{4}}}{64 \, a^{4}}"," ",0,"1/64*(a^5*c + 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^3*c/x + 32*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a*c/x^2 + 104*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c/(a*x^3))*a^8*x^4/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*abs(a)) - 15/8*a^5*c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/64*(104*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^5*c*abs(a)/x + 32*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^3*c*abs(a)/x^2 + 8*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a*c*abs(a)/x^3 + (sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c*abs(a)/(a*x^4))/a^4","B",0
1146,1,332,0,0.571778," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)/x^6,x, algorithm=""giac"")","\frac{{\left(6 \, a^{6} c + \frac{45 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{4} c}{x} + \frac{170 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{2} c}{x^{2}} + \frac{480 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} c}{x^{3}} + \frac{1380 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} c}{a^{2} x^{4}}\right)} a^{10} x^{5}}{960 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} {\left| a \right|}} - \frac{13 \, a^{6} c \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{8 \, {\left| a \right|}} - \frac{\frac{1380 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)} a^{8} c}{x} + \frac{480 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2} a^{6} c}{x^{2}} + \frac{170 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3} a^{4} c}{x^{3}} + \frac{45 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4} a^{2} c}{x^{4}} + \frac{6 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{5} c}{x^{5}}}{960 \, a^{4} {\left| a \right|}}"," ",0,"1/960*(6*a^6*c + 45*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^4*c/x + 170*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^2*c/x^2 + 480*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*c/x^3 + 1380*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*c/(a^2*x^4))*a^10*x^5/((sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*abs(a)) - 13/8*a^6*c*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) - 1/960*(1380*(sqrt(-a^2*x^2 + 1)*abs(a) + a)*a^8*c/x + 480*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2*a^6*c/x^2 + 170*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3*a^4*c/x^3 + 45*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4*a^2*c/x^4 + 6*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^5*c/x^5)/(a^4*abs(a))","B",0
1147,1,78,0,0.234721," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\frac{7 \, c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} + \frac{1}{120} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(15 \, c^{2} + 2 \, {\left(56 \, a c^{2} + 3 \, {\left(4 \, a^{3} c^{2} x + 15 \, a^{2} c^{2}\right)} x\right)} x\right)} x - \frac{136 \, c^{2}}{a}\right)}"," ",0,"7/8*c^2*arcsin(a*x)*sgn(a)/abs(a) + 1/120*sqrt(-a^2*x^2 + 1)*((15*c^2 + 2*(56*a*c^2 + 3*(4*a^3*c^2*x + 15*a^2*c^2)*x)*x)*x - 136*c^2/a)","A",0
1148,1,102,0,0.224929," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{9 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{16 \, {\left| a \right|}} - \frac{1}{560} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{368 \, c^{3}}{a} - {\left(245 \, c^{3} + 2 \, {\left(328 \, a c^{3} + {\left(175 \, a^{2} c^{3} - 4 \, {\left(26 \, a^{3} c^{3} + 5 \, {\left(2 \, a^{5} c^{3} x + 7 \, a^{4} c^{3}\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"9/16*c^3*arcsin(a*x)*sgn(a)/abs(a) - 1/560*sqrt(-a^2*x^2 + 1)*(368*c^3/a - (245*c^3 + 2*(328*a*c^3 + (175*a^2*c^3 - 4*(26*a^3*c^3 + 5*(2*a^5*c^3*x + 7*a^4*c^3)*x)*x)*x)*x)*x)","A",0
1149,1,125,0,1.012280," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\frac{55 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{128 \, {\left| a \right|}} - \frac{1}{8064} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{3712 \, c^{4}}{a} - {\left(4599 \, c^{4} + 2 \, {\left(5120 \, a c^{4} + {\left(1533 \, a^{2} c^{4} - 4 \, {\left(1056 \, a^{3} c^{4} + {\left(903 \, a^{4} c^{4} - 2 \, {\left(64 \, a^{5} c^{4} + 7 \, {\left(8 \, a^{7} c^{4} x + 27 \, a^{6} c^{4}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"55/128*c^4*arcsin(a*x)*sgn(a)/abs(a) - 1/8064*sqrt(-a^2*x^2 + 1)*(3712*c^4/a - (4599*c^4 + 2*(5120*a*c^4 + (1533*a^2*c^4 - 4*(1056*a^3*c^4 + (903*a^4*c^4 - 2*(64*a^5*c^4 + 7*(8*a^7*c^4*x + 27*a^6*c^4)*x)*x)*x)*x)*x)*x)*x)","A",0
1150,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2/(-a^2*c*x^2+c),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
1151,1,112,0,0.345232," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{\arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{a c {\left| a \right|}} + \frac{2 \, {\left(\frac{12 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} - 5\right)}}{3 \, a c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{3} {\left| a \right|}}"," ",0,"arcsin(a*x)*sgn(a)/(a*c*abs(a)) + 2/3*(12*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) - 5)/(a*c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^3*abs(a))","A",0
1152,1,66,0,0.339730," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + 1\right)}}{3 \, c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{3} {\left| a \right|}}"," ",0,"2/3*(3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 1)/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^3*abs(a))","B",0
1153,1,145,0,0.275681," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{20 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} - \frac{40 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{30 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} - \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} - 7\right)}}{15 \, c^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)}^{5} {\left| a \right|}}"," ",0,"-2/15*(20*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 40*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 30*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) - 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) - 7)/(c^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)^5*abs(a))","A",0
1154,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{{\left(a x + 1\right)}^{3}}{{\left(a^{2} c x^{2} - c\right)}^{3} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(a*x + 1)^3/((a^2*c*x^2 - c)^3*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1155,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(a^{2} c x^{2} - c\right)}^{4} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((a^2*c*x^2 - c)^4*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1156,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{3} x^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^3*x^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
1157,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""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
1158,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{3} x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^3*x/(-a^2*x^2 + 1)^(3/2), x)","F",0
1159,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
1160,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*x), x)","F",0
1161,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*x^2), x)","F",0
1162,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*x^3), x)","F",0
1163,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*x^4), x)","F",0
1164,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{5}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^3/((-a^2*x^2 + 1)^(3/2)*x^5), x)","F",0
1165,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
1166,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
1167,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} {\left(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)*(a*x + 1)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
1168,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+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(a x + 1\right)}^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(9/2)*(a*x + 1)^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
1169,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1170,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*c*x^2 + c)^(3/2)*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1171,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*c*x^2 + c)^(5/2)*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1172,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3/((-a^2*c*x^2 + c)^(7/2)*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1173,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^m*(-a^2*c*x^2+c)^(1/2),x, algorithm=""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
1174,-2,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^m*(-a^2*c*x^2+c)^p,x, algorithm=""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
1175,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{3}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p*x^3/(-a^2*x^2 + 1)^(3/2), x)","F",0
1176,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{2}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p*x^2/(-a^2*x^2 + 1)^(3/2), x)","F",0
1177,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(-a^{2} c x^{2} + c\right)}^{p} x}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p*x/(-a^2*x^2 + 1)^(3/2), x)","F",0
1178,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p/(-a^2*x^2 + 1)^(3/2), x)","F",0
1179,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p/((-a^2*x^2 + 1)^(3/2)*x), x)","F",0
1180,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p/((-a^2*x^2 + 1)^(3/2)*x^2), x)","F",0
1181,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^p/x^3,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate((a*x + 1)^3*(-a^2*c*x^2 + c)^p/((-a^2*x^2 + 1)^(3/2)*x^3), x)","F",0
1182,1,101,0,0.268724," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^5,x, algorithm=""giac"")","-\frac{1}{11} \, a^{10} c^{5} x^{11} - \frac{2}{5} \, a^{9} c^{5} x^{10} - \frac{1}{3} \, a^{8} c^{5} x^{9} + a^{7} c^{5} x^{8} + 2 \, a^{6} c^{5} x^{7} - \frac{14}{5} \, a^{4} c^{5} x^{5} - 2 \, a^{3} c^{5} x^{4} + a^{2} c^{5} x^{3} + 2 \, a c^{5} x^{2} + c^{5} x"," ",0,"-1/11*a^10*c^5*x^11 - 2/5*a^9*c^5*x^10 - 1/3*a^8*c^5*x^9 + a^7*c^5*x^8 + 2*a^6*c^5*x^7 - 14/5*a^4*c^5*x^5 - 2*a^3*c^5*x^4 + a^2*c^5*x^3 + 2*a*c^5*x^2 + c^5*x","A",0
1183,1,92,0,0.345188," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\frac{1}{9} \, a^{8} c^{4} x^{9} + \frac{1}{2} \, a^{7} c^{4} x^{8} + \frac{4}{7} \, a^{6} c^{4} x^{7} - \frac{2}{3} \, a^{5} c^{4} x^{6} - 2 \, a^{4} c^{4} x^{5} - a^{3} c^{4} x^{4} + \frac{4}{3} \, a^{2} c^{4} x^{3} + 2 \, a c^{4} x^{2} + c^{4} x"," ",0,"1/9*a^8*c^4*x^9 + 1/2*a^7*c^4*x^8 + 4/7*a^6*c^4*x^7 - 2/3*a^5*c^4*x^6 - 2*a^4*c^4*x^5 - a^3*c^4*x^4 + 4/3*a^2*c^4*x^3 + 2*a*c^4*x^2 + c^4*x","A",0
1184,1,59,0,0.162438," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{1}{7} \, a^{6} c^{3} x^{7} - \frac{2}{3} \, a^{5} c^{3} x^{6} - a^{4} c^{3} x^{5} + \frac{5}{3} \, a^{2} c^{3} x^{3} + 2 \, a c^{3} x^{2} + c^{3} x"," ",0,"-1/7*a^6*c^3*x^7 - 2/3*a^5*c^3*x^6 - a^4*c^3*x^5 + 5/3*a^2*c^3*x^3 + 2*a*c^3*x^2 + c^3*x","A",0
1185,1,47,0,0.158759," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{5} \, a^{4} c^{2} x^{5} + a^{3} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{3} + 2 \, a c^{2} x^{2} + c^{2} x"," ",0,"1/5*a^4*c^2*x^5 + a^3*c^2*x^4 + 2*a^2*c^2*x^3 + 2*a*c^2*x^2 + c^2*x","B",0
1186,1,44,0,0.341902," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c),x, algorithm=""giac"")","-\frac{8 \, c \log\left({\left| a x - 1 \right|}\right)}{a} - \frac{a^{5} c x^{3} + 6 \, a^{4} c x^{2} + 21 \, a^{3} c x}{3 \, a^{3}}"," ",0,"-8*c*log(abs(a*x - 1))/a - 1/3*(a^5*c*x^3 + 6*a^4*c*x^2 + 21*a^3*c*x)/a^3","A",0
1187,1,12,0,0.157290," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{x}{{\left(a x - 1\right)}^{2} c}"," ",0,"x/((a*x - 1)^2*c)","A",0
1188,1,15,0,0.627299," ","integrate((a*x+1)^4/(-a^2*x^2+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
1189,1,68,0,0.189177," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{\log\left({\left| a x + 1 \right|}\right)}{32 \, a c^{3}} - \frac{\log\left({\left| a x - 1 \right|}\right)}{32 \, a c^{3}} - \frac{3 \, a^{3} x^{3} - 12 \, a^{2} x^{2} + 19 \, a x - 16}{48 \, {\left(a x - 1\right)}^{4} a c^{3}}"," ",0,"1/32*log(abs(a*x + 1))/(a*c^3) - 1/32*log(abs(a*x - 1))/(a*c^3) - 1/48*(3*a^3*x^3 - 12*a^2*x^2 + 19*a*x - 16)/((a*x - 1)^4*a*c^3)","A",0
1190,1,91,0,0.179294," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| a x + 1 \right|}\right)}{64 \, a c^{4}} - \frac{3 \, \log\left({\left| a x - 1 \right|}\right)}{64 \, a c^{4}} - \frac{15 \, a^{5} x^{5} - 60 \, a^{4} x^{4} + 80 \, a^{3} x^{3} - 20 \, a^{2} x^{2} - 47 \, a x + 48}{160 \, {\left(a x + 1\right)} {\left(a x - 1\right)}^{5} a c^{4}}"," ",0,"3/64*log(abs(a*x + 1))/(a*c^4) - 3/64*log(abs(a*x - 1))/(a*c^4) - 1/160*(15*a^5*x^5 - 60*a^4*x^4 + 80*a^3*x^3 - 20*a^2*x^2 - 47*a*x + 48)/((a*x + 1)*(a*x - 1)^5*a*c^4)","A",0
1191,0,0,0,0.000000," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{4} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(a^{2} x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((a*x + 1)^4*(-a^2*c*x^2 + c)^p/(a^2*x^2 - 1)^2, x)","F",0
1192,1,124,0,0.198393," ","integrate((-a^2*c*x^2+c)^4/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{35 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{128 \, {\left| a \right|}} + \frac{1}{1152} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{128 \, c^{4}}{a} + {\left(837 \, c^{4} - 2 \, {\left(256 \, a c^{4} + {\left(489 \, a^{2} c^{4} - 4 \, {\left(96 \, a^{3} c^{4} + {\left(75 \, a^{4} c^{4} - 2 \, {\left(32 \, a^{5} c^{4} - {\left(8 \, a^{7} c^{4} x - 9 \, a^{6} c^{4}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"35/128*c^4*arcsin(a*x)*sgn(a)/abs(a) + 1/1152*sqrt(-a^2*x^2 + 1)*(128*c^4/a + (837*c^4 - 2*(256*a*c^4 + (489*a^2*c^4 - 4*(96*a^3*c^4 + (75*a^4*c^4 - 2*(32*a^5*c^4 - (8*a^7*c^4*x - 9*a^6*c^4)*x)*x)*x)*x)*x)*x)*x)","A",0
1193,1,101,0,0.206954," ","integrate((-a^2*c*x^2+c)^3/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{5 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{16 \, {\left| a \right|}} + \frac{1}{336} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{48 \, c^{3}}{a} + {\left(231 \, c^{3} - 2 \, {\left(72 \, a c^{3} + {\left(91 \, a^{2} c^{3} - 4 \, {\left(18 \, a^{3} c^{3} - {\left(6 \, a^{5} c^{3} x - 7 \, a^{4} c^{3}\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"5/16*c^3*arcsin(a*x)*sgn(a)/abs(a) + 1/336*sqrt(-a^2*x^2 + 1)*(48*c^3/a + (231*c^3 - 2*(72*a*c^3 + (91*a^2*c^3 - 4*(18*a^3*c^3 - (6*a^5*c^3*x - 7*a^4*c^3)*x)*x)*x)*x)*x)","A",0
1194,1,78,0,0.201780," ","integrate((-a^2*c*x^2+c)^2/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{3 \, c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} + \frac{1}{40} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(25 \, c^{2} - 2 \, {\left(8 \, a c^{2} - {\left(4 \, a^{3} c^{2} x - 5 \, a^{2} c^{2}\right)} x\right)} x\right)} x + \frac{8 \, c^{2}}{a}\right)}"," ",0,"3/8*c^2*arcsin(a*x)*sgn(a)/abs(a) + 1/40*sqrt(-a^2*x^2 + 1)*((25*c^2 - 2*(8*a*c^2 - (4*a^3*c^2*x - 5*a^2*c^2)*x)*x)*x + 8*c^2/a)","A",0
1195,1,46,0,0.665033," ","integrate((-a^2*c*x^2+c)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\frac{c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} - \frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, a c x - 3 \, c\right)} x - \frac{2 \, c}{a}\right)}"," ",0,"1/2*c*arcsin(a*x)*sgn(a)/abs(a) - 1/6*sqrt(-a^2*x^2 + 1)*((2*a*c*x - 3*c)*x - 2*c/a)","A",0
1196,1,37,0,0.219743," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{2}{c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)} {\left| a \right|}}"," ",0,"2/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)*abs(a))","A",0
1197,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} c x^{2} - c\right)}^{2} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a^2*c*x^2 - c)^2*(a*x + 1)), x)","F",0
1198,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} c x^{2} - c\right)}^{3} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(-sqrt(-a^2*x^2 + 1)/((a^2*c*x^2 - c)^3*(a*x + 1)), x)","F",0
1199,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} c x^{2} - c\right)}^{4} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((a^2*c*x^2 - c)^4*(a*x + 1)), x)","F",0
1200,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^5,x, algorithm=""giac"")","\int -\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} c x^{2} - c\right)}^{5} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(-sqrt(-a^2*x^2 + 1)/((a^2*c*x^2 - c)^5*(a*x + 1)), x)","F",0
1201,0,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)*x^m/(a*x + 1), x)","F",0
1202,0,0,0,0.000000," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1} x^{2}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)*x^2/(a*x + 1), x)","F",0
1203,0,0,0,0.000000," ","integrate(x*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1} x}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)*x/(a*x + 1), x)","F",0
1204,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)/(a*x + 1), x)","F",0
1205,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)/((a*x + 1)*x), x)","F",0
1206,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""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
1207,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)/(a*x + 1), x)","F",0
1208,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{-a^{2} x^{2} + 1}}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*sqrt(-a^2*x^2 + 1)/(a*x + 1), x)","F",0
1209,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(7/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} \sqrt{-a^{2} x^{2} + 1}}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)*sqrt(-a^2*x^2 + 1)/(a*x + 1), x)","F",0
1210,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(9/2)/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}} \sqrt{-a^{2} x^{2} + 1}}{a x + 1}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(9/2)*sqrt(-a^2*x^2 + 1)/(a*x + 1), x)","F",0
1211,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/(sqrt(-a^2*c*x^2 + c)*(a*x + 1)), x)","F",0
1212,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)), x)","F",0
1213,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)), x)","F",0
1214,0,0,0,0.000000," ","integrate(1/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)/((-a^2*c*x^2 + c)^(7/2)*(a*x + 1)), x)","F",0
1215,0,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{m}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p*x^m/(a*x + 1), x)","F",0
1216,0,0,0,0.000000," ","integrate(x^3*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} x^{2} + 1\right)}^{p} x^{3}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*x^2 + 1)^p*x^3/(a*x + 1), x)","F",0
1217,0,0,0,0.000000," ","integrate(x^2*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} x^{2} + 1\right)}^{p} x^{2}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*x^2 + 1)^p*x^2/(a*x + 1), x)","F",0
1218,0,0,0,0.000000," ","integrate(x*(-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} x^{2} + 1\right)}^{p} x}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*x^2 + 1)^p*x/(a*x + 1), x)","F",0
1219,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} x^{2} + 1\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*x^2 + 1)^p/(a*x + 1), x)","F",0
1220,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} x^{2} + 1\right)}^{p}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*x^2 + 1)^p/((a*x + 1)*x), x)","F",0
1221,0,0,0,0.000000," ","integrate((-a^2*x^2+1)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} x^{2} + 1\right)}^{p}}{{\left(a x + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*x^2 + 1)^p/((a*x + 1)*x^2), x)","F",0
1222,-2,0,0,0.000000," ","integrate(x^3*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""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
1223,0,0,0,0.000000," ","integrate(x^2*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p} x^{2}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p*x^2/(a*x + 1), x)","F",0
1224,0,0,0,0.000000," ","integrate(x*(-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p} x}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p*x/(a*x + 1), x)","F",0
1225,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p}}{a x + 1}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p/(a*x + 1), x)","F",0
1226,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(a x + 1\right)} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*(-a^2*c*x^2 + c)^p/((a*x + 1)*x), x)","F",0
1227,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/(a*x+1)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""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
1228,1,78,0,1.649323," ","integrate((-a^2*c*x^2+c)^4/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{{\left(28 \, c^{4} - \frac{315 \, c^{4}}{a x + 1} + \frac{1440 \, c^{4}}{{\left(a x + 1\right)}^{2}} - \frac{3360 \, c^{4}}{{\left(a x + 1\right)}^{3}} + \frac{4032 \, c^{4}}{{\left(a x + 1\right)}^{4}} - \frac{2016 \, c^{4}}{{\left(a x + 1\right)}^{5}}\right)} {\left(a x + 1\right)}^{9}}{252 \, a}"," ",0,"-1/252*(28*c^4 - 315*c^4/(a*x + 1) + 1440*c^4/(a*x + 1)^2 - 3360*c^4/(a*x + 1)^3 + 4032*c^4/(a*x + 1)^4 - 2016*c^4/(a*x + 1)^5)*(a*x + 1)^9/a","A",0
1229,1,66,0,0.166914," ","integrate((-a^2*c*x^2+c)^3/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\frac{{\left(15 \, c^{3} - \frac{140 \, c^{3}}{a x + 1} + \frac{504 \, c^{3}}{{\left(a x + 1\right)}^{2}} - \frac{840 \, c^{3}}{{\left(a x + 1\right)}^{3}} + \frac{560 \, c^{3}}{{\left(a x + 1\right)}^{4}}\right)} {\left(a x + 1\right)}^{7}}{105 \, a}"," ",0,"1/105*(15*c^3 - 140*c^3/(a*x + 1) + 504*c^3/(a*x + 1)^2 - 840*c^3/(a*x + 1)^3 + 560*c^3/(a*x + 1)^4)*(a*x + 1)^7/a","A",0
1230,1,54,0,0.148852," ","integrate((-a^2*c*x^2+c)^2/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{{\left(2 \, c^{2} - \frac{15 \, c^{2}}{a x + 1} + \frac{40 \, c^{2}}{{\left(a x + 1\right)}^{2}} - \frac{40 \, c^{2}}{{\left(a x + 1\right)}^{3}}\right)} {\left(a x + 1\right)}^{5}}{10 \, a}"," ",0,"-1/10*(2*c^2 - 15*c^2/(a*x + 1) + 40*c^2/(a*x + 1)^2 - 40*c^2/(a*x + 1)^3)*(a*x + 1)^5/a","A",0
1231,1,34,0,0.181830," ","integrate((-a^2*c*x^2+c)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\frac{{\left(a x + 1\right)}^{3} {\left(c - \frac{6 \, c}{a x + 1} + \frac{12 \, c}{{\left(a x + 1\right)}^{2}}\right)}}{3 \, a}"," ",0,"1/3*(a*x + 1)^3*(c - 6*c/(a*x + 1) + 12*c/(a*x + 1)^2)/a","B",0
1232,1,15,0,0.166143," ","integrate(1/(a*x+1)^2*(-a^2*x^2+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
1233,1,55,0,0.279882," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| -\frac{2}{a x + 1} + 1 \right|}\right)}{8 \, a c^{2}} - \frac{\frac{a c^{2}}{a x + 1} + \frac{a c^{2}}{{\left(a x + 1\right)}^{2}}}{4 \, a^{2} c^{4}}"," ",0,"-1/8*log(abs(-2/(a*x + 1) + 1))/(a*c^2) - 1/4*(a*c^2/(a*x + 1) + a*c^2/(a*x + 1)^2)/(a^2*c^4)","A",0
1234,1,97,0,0.350945," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{\log\left({\left| -\frac{2}{a x + 1} + 1 \right|}\right)}{8 \, a c^{3}} + \frac{1}{32 \, a c^{3} {\left(\frac{2}{a x + 1} - 1\right)}} - \frac{\frac{9 \, a^{5} c^{6}}{a x + 1} + \frac{6 \, a^{5} c^{6}}{{\left(a x + 1\right)}^{2}} + \frac{4 \, a^{5} c^{6}}{{\left(a x + 1\right)}^{3}}}{48 \, a^{6} c^{9}}"," ",0,"-1/8*log(abs(-2/(a*x + 1) + 1))/(a*c^3) + 1/32/(a*c^3*(2/(a*x + 1) - 1)) - 1/48*(9*a^5*c^6/(a*x + 1) + 6*a^5*c^6/(a*x + 1)^2 + 4*a^5*c^6/(a*x + 1)^3)/(a^6*c^9)","A",0
1235,1,122,0,0.177714," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","-\frac{15 \, \log\left({\left| -\frac{2}{a x + 1} + 1 \right|}\right)}{128 \, a c^{4}} + \frac{\frac{24}{a x + 1} - 11}{256 \, a c^{4} {\left(\frac{2}{a x + 1} - 1\right)}^{2}} - \frac{\frac{5 \, a^{11} c^{12}}{a x + 1} + \frac{3 \, a^{11} c^{12}}{{\left(a x + 1\right)}^{2}} + \frac{2 \, a^{11} c^{12}}{{\left(a x + 1\right)}^{3}} + \frac{a^{11} c^{12}}{{\left(a x + 1\right)}^{4}}}{32 \, a^{12} c^{16}}"," ",0,"-15/128*log(abs(-2/(a*x + 1) + 1))/(a*c^4) + 1/256*(24/(a*x + 1) - 11)/(a*c^4*(2/(a*x + 1) - 1)^2) - 1/32*(5*a^11*c^12/(a*x + 1) + 3*a^11*c^12/(a*x + 1)^2 + 2*a^11*c^12/(a*x + 1)^3 + a^11*c^12/(a*x + 1)^4)/(a^12*c^16)","A",0
1236,-2,0,0,0.000000," ","integrate(x^3*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+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
1237,1,221,0,0.411104," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{{\left(336 \, a^{5} \sqrt{c} \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + \frac{{\left(75 \, a^{5} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{3} c \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - 83 \, a^{5} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{2} c^{2} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - 21 \, a^{5} c^{4} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - 77 \, a^{5} c^{3} {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)\right)} {\left(a x + 1\right)}^{4}}{c^{4}}\right)} {\left| a \right|}}{192 \, a^{9}}"," ",0,"-1/192*(336*a^5*sqrt(c)*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(c))*sgn(1/(a*x + 1))*sgn(a) + (75*a^5*(c - 2*c/(a*x + 1))^3*c*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) - 83*a^5*(c - 2*c/(a*x + 1))^2*c^2*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) - 21*a^5*c^4*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) - 77*a^5*c^3*(-c + 2*c/(a*x + 1))^(3/2)*sgn(1/(a*x + 1))*sgn(a))*(a*x + 1)^4/c^4)*abs(a)/a^9","B",0
1238,1,174,0,0.413059," ","integrate(x*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\frac{{\left(24 \, a^{4} \sqrt{c} \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - \frac{{\left(9 \, a^{4} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{2} c \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 3 \, a^{4} c^{3} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 8 \, a^{4} c^{2} {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)\right)} {\left(a x + 1\right)}^{3}}{c^{3}}\right)} {\left| a \right|}}{12 \, a^{7}}"," ",0,"1/12*(24*a^4*sqrt(c)*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(c))*sgn(1/(a*x + 1))*sgn(a) - (9*a^4*(c - 2*c/(a*x + 1))^2*c*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 3*a^4*c^3*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 8*a^4*c^2*(-c + 2*c/(a*x + 1))^(3/2)*sgn(1/(a*x + 1))*sgn(a))*(a*x + 1)^3/c^3)*abs(a)/a^7","B",0
1239,1,126,0,0.401830," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{{\left(12 \, a^{3} \sqrt{c} \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - \frac{{\left(3 \, a^{3} c^{2} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 5 \, a^{3} c {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)\right)} {\left(a x + 1\right)}^{2}}{c^{2}}\right)} {\left| a \right|}}{4 \, a^{5}}"," ",0,"-1/4*(12*a^3*sqrt(c)*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(c))*sgn(1/(a*x + 1))*sgn(a) - (3*a^3*c^2*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 5*a^3*c*(-c + 2*c/(a*x + 1))^(3/2)*sgn(1/(a*x + 1))*sgn(a))*(a*x + 1)^2/c^2)*abs(a)/a^5","A",0
1240,1,124,0,0.330895," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x,x, algorithm=""giac"")","-{\left(\frac{{\left(a x + 1\right)} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{a^{2}} - \frac{2 \, c \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{-c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{a^{2} \sqrt{-c}} - \frac{4 \, \sqrt{c} \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{a^{2}}\right)} a {\left| a \right|}"," ",0,"-((a*x + 1)*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a)/a^2 - 2*c*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(-c))*sgn(1/(a*x + 1))*sgn(a)/(a^2*sqrt(-c)) - 4*sqrt(c)*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(c))*sgn(1/(a*x + 1))*sgn(a)/a^2)*a*abs(a)","A",0
1241,1,168,0,0.230331," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^2,x, algorithm=""giac"")","-{\left(\frac{4 \, c \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{-c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{\sqrt{-c}} + 2 \, \sqrt{c} \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - \frac{{\left(\pi c + 2 \, \sqrt{-c} \sqrt{c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{c}}\right) - c\right)} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{\sqrt{-c}} + \frac{c \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{c - \frac{c}{a x + 1}}\right)} {\left| a \right|}"," ",0,"-(4*c*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(-c))*sgn(1/(a*x + 1))*sgn(a)/sqrt(-c) + 2*sqrt(c)*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(c))*sgn(1/(a*x + 1))*sgn(a) - (pi*c + 2*sqrt(-c)*sqrt(c)*arctan(sqrt(-c)/sqrt(c)) - c)*sgn(1/(a*x + 1))*sgn(a)/sqrt(-c) + c*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a)/(c - c/(a*x + 1)))*abs(a)","B",0
1242,1,152,0,3.094450," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^3,x, algorithm=""giac"")","\frac{1}{4} \, {\left(\frac{12 \, a c \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{-c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{\sqrt{-c}} - \frac{{\left(3 \, \pi a c - 8 \, a c\right)} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{\sqrt{-c}} + \frac{3 \, a c^{2} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - 5 \, a c {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{{\left(c - \frac{c}{a x + 1}\right)}^{2}}\right)} {\left| a \right|}"," ",0,"1/4*(12*a*c*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(-c))*sgn(1/(a*x + 1))*sgn(a)/sqrt(-c) - (3*pi*a*c - 8*a*c)*sgn(1/(a*x + 1))*sgn(a)/sqrt(-c) + (3*a*c^2*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) - 5*a*c*(-c + 2*c/(a*x + 1))^(3/2)*sgn(1/(a*x + 1))*sgn(a))/(c - c/(a*x + 1))^2)*abs(a)","B",0
1243,1,210,0,0.387367," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^4,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{24 \, a^{2} c \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{-c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{\sqrt{-c}} - \frac{2 \, {\left(3 \, \pi a^{2} c - 10 \, a^{2} c\right)} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{\sqrt{-c}} + \frac{9 \, a^{2} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{2} c \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 3 \, a^{2} c^{3} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - 8 \, a^{2} c^{2} {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{{\left(c - \frac{c}{a x + 1}\right)}^{3}}\right)} {\left| a \right|}"," ",0,"-1/12*(24*a^2*c*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(-c))*sgn(1/(a*x + 1))*sgn(a)/sqrt(-c) - 2*(3*pi*a^2*c - 10*a^2*c)*sgn(1/(a*x + 1))*sgn(a)/sqrt(-c) + (9*a^2*(c - 2*c/(a*x + 1))^2*c*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 3*a^2*c^3*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) - 8*a^2*c^2*(-c + 2*c/(a*x + 1))^(3/2)*sgn(1/(a*x + 1))*sgn(a))/(c - c/(a*x + 1))^3)*abs(a)","B",0
1244,1,258,0,0.234479," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1)/x^5,x, algorithm=""giac"")","\frac{1}{192} \, {\left(\frac{336 \, a^{3} c \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{-c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{\sqrt{-c}} - \frac{4 \, {\left(21 \, \pi a^{3} c - 64 \, a^{3} c\right)} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{\sqrt{-c}} + \frac{75 \, a^{3} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{3} c \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 83 \, a^{3} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{2} c^{2} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 21 \, a^{3} c^{4} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - 77 \, a^{3} c^{3} {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{{\left(c - \frac{c}{a x + 1}\right)}^{4}}\right)} {\left| a \right|}"," ",0,"1/192*(336*a^3*c*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(-c))*sgn(1/(a*x + 1))*sgn(a)/sqrt(-c) - 4*(21*pi*a^3*c - 64*a^3*c)*sgn(1/(a*x + 1))*sgn(a)/sqrt(-c) + (75*a^3*(c - 2*c/(a*x + 1))^3*c*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 83*a^3*(c - 2*c/(a*x + 1))^2*c^2*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 21*a^3*c^4*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) - 77*a^3*c^3*(-c + 2*c/(a*x + 1))^(3/2)*sgn(1/(a*x + 1))*sgn(a))/(c - c/(a*x + 1))^4)*abs(a)","B",0
1245,1,224,0,0.281039," ","integrate((-a^2*c*x^2+c)^(3/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{{\left(240 \, a^{5} c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - \frac{{\left(15 \, a^{5} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{3} c^{2} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 73 \, a^{5} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{2} c^{3} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 15 \, a^{5} c^{5} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 55 \, a^{5} c^{4} {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)\right)} {\left(a x + 1\right)}^{4}}{c^{4}}\right)} {\left| a \right|}}{192 \, a^{7}}"," ",0,"-1/192*(240*a^5*c^(3/2)*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(c))*sgn(1/(a*x + 1))*sgn(a) - (15*a^5*(c - 2*c/(a*x + 1))^3*c^2*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 73*a^5*(c - 2*c/(a*x + 1))^2*c^3*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 15*a^5*c^5*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 55*a^5*c^4*(-c + 2*c/(a*x + 1))^(3/2)*sgn(1/(a*x + 1))*sgn(a))*(a*x + 1)^4/c^4)*abs(a)/a^7","B",0
1246,1,320,0,0.282641," ","integrate((-a^2*c*x^2+c)^(5/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{{\left(6720 \, a^{7} c^{\frac{5}{2}} \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - \frac{{\left(105 \, a^{7} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{5} c^{3} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - 595 \, a^{7} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{4} c^{4} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - 1686 \, a^{7} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{3} c^{5} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 1386 \, a^{7} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{2} c^{6} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 105 \, a^{7} c^{8} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 595 \, a^{7} c^{7} {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)\right)} {\left(a x + 1\right)}^{6}}{c^{6}}\right)} {\left| a \right|}}{7680 \, a^{9}}"," ",0,"-1/7680*(6720*a^7*c^(5/2)*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(c))*sgn(1/(a*x + 1))*sgn(a) - (105*a^7*(c - 2*c/(a*x + 1))^5*c^3*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) - 595*a^7*(c - 2*c/(a*x + 1))^4*c^4*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) - 1686*a^7*(c - 2*c/(a*x + 1))^3*c^5*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 1386*a^7*(c - 2*c/(a*x + 1))^2*c^6*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 105*a^7*c^8*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 595*a^7*c^7*(-c + 2*c/(a*x + 1))^(3/2)*sgn(1/(a*x + 1))*sgn(a))*(a*x + 1)^6/c^6)*abs(a)/a^9","B",0
1247,1,416,0,0.435731," ","integrate((-a^2*c*x^2+c)^(7/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","-\frac{{\left(80640 \, a^{9} c^{\frac{7}{2}} \arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{c}}\right) \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - \frac{{\left(315 \, a^{9} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{7} c^{4} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - 2415 \, a^{9} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{6} c^{5} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 8043 \, a^{9} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{5} c^{6} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 17609 \, a^{9} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{4} c^{7} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) - 15159 \, a^{9} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{3} c^{8} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 8043 \, a^{9} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{2} c^{9} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 315 \, a^{9} c^{11} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right) + 2415 \, a^{9} c^{10} {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)\right)} {\left(a x + 1\right)}^{8}}{c^{8}}\right)} {\left| a \right|}}{114688 \, a^{11}}"," ",0,"-1/114688*(80640*a^9*c^(7/2)*arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(c))*sgn(1/(a*x + 1))*sgn(a) - (315*a^9*(c - 2*c/(a*x + 1))^7*c^4*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) - 2415*a^9*(c - 2*c/(a*x + 1))^6*c^5*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 8043*a^9*(c - 2*c/(a*x + 1))^5*c^6*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 17609*a^9*(c - 2*c/(a*x + 1))^4*c^7*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) - 15159*a^9*(c - 2*c/(a*x + 1))^3*c^8*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 8043*a^9*(c - 2*c/(a*x + 1))^2*c^9*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 315*a^9*c^11*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a) + 2415*a^9*c^10*(-c + 2*c/(a*x + 1))^(3/2)*sgn(1/(a*x + 1))*sgn(a))*(a*x + 1)^8/c^8)*abs(a)/a^11","B",0
1248,1,107,0,0.210602," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(c \arctan\left(\frac{\sqrt{-c}}{\sqrt{c}}\right) - \sqrt{-c} \sqrt{c}\right)} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{c^{\frac{3}{2}}} - \frac{\frac{\arctan\left(\frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{\sqrt{c}}\right)}{\sqrt{c}} - \frac{\sqrt{-c + \frac{2 \, c}{a x + 1}}}{c}}{\mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}\right)}}{{\left| a \right|}}"," ",0,"-2*((c*arctan(sqrt(-c)/sqrt(c)) - sqrt(-c)*sqrt(c))*sgn(1/(a*x + 1))*sgn(a)/c^(3/2) - (arctan(sqrt(-c + 2*c/(a*x + 1))/sqrt(c))/sqrt(c) - sqrt(-c + 2*c/(a*x + 1))/c)/(sgn(1/(a*x + 1))*sgn(a)))/abs(a)","B",0
1249,1,82,0,0.978159," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{-c} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{c^{2}} - \frac{3 \, c \sqrt{-c + \frac{2 \, c}{a x + 1}} + {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}}}{c^{3} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}}{6 \, {\left| a \right|}}"," ",0,"1/6*(2*sqrt(-c)*sgn(1/(a*x + 1))*sgn(a)/c^2 - (3*c*sqrt(-c + 2*c/(a*x + 1)) + (-c + 2*c/(a*x + 1))^(3/2))/(c^3*sgn(1/(a*x + 1))*sgn(a)))/abs(a)","A",0
1250,1,220,0,0.279571," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{a^{3} {\left(\frac{5}{a^{3} c^{2} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)} - \frac{a^{12} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{2} c^{20} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right)^{4} \mathrm{sgn}\left(a\right)^{4} + 15 \, a^{12} c^{22} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right)^{4} \mathrm{sgn}\left(a\right)^{4} + 5 \, a^{12} c^{21} {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right)^{4} \mathrm{sgn}\left(a\right)^{4}}{a^{15} c^{25} \mathrm{sgn}\left(\frac{1}{a x + 1}\right)^{5} \mathrm{sgn}\left(a\right)^{5}}\right)} - \frac{16 \, \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{\sqrt{-c} c^{2}}}{40 \, {\left| a \right|}}"," ",0,"1/40*(a^3*(5/(a^3*c^2*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a)) - (a^12*(c - 2*c/(a*x + 1))^2*c^20*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))^4*sgn(a)^4 + 15*a^12*c^22*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))^4*sgn(a)^4 + 5*a^12*c^21*(-c + 2*c/(a*x + 1))^(3/2)*sgn(1/(a*x + 1))^4*sgn(a)^4)/(a^15*c^25*sgn(1/(a*x + 1))^5*sgn(a)^5)) - 16*sgn(1/(a*x + 1))*sgn(a)/(sqrt(-c)*c^2))/abs(a)","B",0
1251,1,300,0,0.618665," ","integrate(1/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\frac{a^{5} {\left(\frac{14 \, {\left(7 \, c - \frac{15 \, c}{a x + 1}\right)}}{a^{5} {\left(c - \frac{2 \, c}{a x + 1}\right)} c^{3} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)} + \frac{3 \, a^{30} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{3} c^{42} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right)^{6} \mathrm{sgn}\left(a\right)^{6} - 21 \, a^{30} {\left(c - \frac{2 \, c}{a x + 1}\right)}^{2} c^{43} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right)^{6} \mathrm{sgn}\left(a\right)^{6} - 210 \, a^{30} c^{45} \sqrt{-c + \frac{2 \, c}{a x + 1}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right)^{6} \mathrm{sgn}\left(a\right)^{6} - 70 \, a^{30} c^{44} {\left(-c + \frac{2 \, c}{a x + 1}\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{a x + 1}\right)^{6} \mathrm{sgn}\left(a\right)^{6}}{a^{35} c^{49} \mathrm{sgn}\left(\frac{1}{a x + 1}\right)^{7} \mathrm{sgn}\left(a\right)^{7}}\right)} - \frac{256 \, \mathrm{sgn}\left(\frac{1}{a x + 1}\right) \mathrm{sgn}\left(a\right)}{\sqrt{-c} c^{3}}}{672 \, {\left| a \right|}}"," ",0,"1/672*(a^5*(14*(7*c - 15*c/(a*x + 1))/(a^5*(c - 2*c/(a*x + 1))*c^3*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))*sgn(a)) + (3*a^30*(c - 2*c/(a*x + 1))^3*c^42*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))^6*sgn(a)^6 - 21*a^30*(c - 2*c/(a*x + 1))^2*c^43*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))^6*sgn(a)^6 - 210*a^30*c^45*sqrt(-c + 2*c/(a*x + 1))*sgn(1/(a*x + 1))^6*sgn(a)^6 - 70*a^30*c^44*(-c + 2*c/(a*x + 1))^(3/2)*sgn(1/(a*x + 1))^6*sgn(a)^6)/(a^35*c^49*sgn(1/(a*x + 1))^7*sgn(a)^7)) - 256*sgn(1/(a*x + 1))*sgn(a)/(sqrt(-c)*c^3))/abs(a)","B",0
1252,-2,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""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
1253,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/(a*x+1)^2*(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{{\left(a^{2} x^{2} - 1\right)} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(a x + 1\right)}^{2}}\,{d x}"," ",0,"integrate(-(a^2*x^2 - 1)*(-a^2*c*x^2 + c)^p/(a*x + 1)^2, x)","F",0
1254,1,126,0,0.322890," ","integrate((-a^2*c*x^2+c)^4/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\frac{55 \, c^{4} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{128 \, {\left| a \right|}} + \frac{1}{8064} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{3712 \, c^{4}}{a} + {\left(4599 \, c^{4} - 2 \, {\left(5120 \, a c^{4} - {\left(1533 \, a^{2} c^{4} + 4 \, {\left(1056 \, a^{3} c^{4} - {\left(903 \, a^{4} c^{4} + 2 \, {\left(64 \, a^{5} c^{4} + 7 \, {\left(8 \, a^{7} c^{4} x - 27 \, a^{6} c^{4}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"55/128*c^4*arcsin(a*x)*sgn(a)/abs(a) + 1/8064*sqrt(-a^2*x^2 + 1)*(3712*c^4/a + (4599*c^4 - 2*(5120*a*c^4 - (1533*a^2*c^4 + 4*(1056*a^3*c^4 - (903*a^4*c^4 + 2*(64*a^5*c^4 + 7*(8*a^7*c^4*x - 27*a^6*c^4)*x)*x)*x)*x)*x)*x)*x)","A",0
1255,1,102,0,0.197196," ","integrate((-a^2*c*x^2+c)^3/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\frac{9 \, c^{3} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{16 \, {\left| a \right|}} + \frac{1}{560} \, \sqrt{-a^{2} x^{2} + 1} {\left(\frac{368 \, c^{3}}{a} + {\left(245 \, c^{3} - 2 \, {\left(328 \, a c^{3} - {\left(175 \, a^{2} c^{3} + 4 \, {\left(26 \, a^{3} c^{3} + 5 \, {\left(2 \, a^{5} c^{3} x - 7 \, a^{4} c^{3}\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"9/16*c^3*arcsin(a*x)*sgn(a)/abs(a) + 1/560*sqrt(-a^2*x^2 + 1)*(368*c^3/a + (245*c^3 - 2*(328*a*c^3 - (175*a^2*c^3 + 4*(26*a^3*c^3 + 5*(2*a^5*c^3*x - 7*a^4*c^3)*x)*x)*x)*x)*x)","A",0
1256,1,78,0,0.209105," ","integrate((-a^2*c*x^2+c)^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\frac{7 \, c^{2} \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{8 \, {\left| a \right|}} + \frac{1}{120} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(15 \, c^{2} - 2 \, {\left(56 \, a c^{2} + 3 \, {\left(4 \, a^{3} c^{2} x - 15 \, a^{2} c^{2}\right)} x\right)} x\right)} x + \frac{136 \, c^{2}}{a}\right)}"," ",0,"7/8*c^2*arcsin(a*x)*sgn(a)/abs(a) + 1/120*sqrt(-a^2*x^2 + 1)*((15*c^2 - 2*(56*a*c^2 + 3*(4*a^3*c^2*x - 15*a^2*c^2)*x)*x)*x + 136*c^2/a)","A",0
1257,1,46,0,0.267224," ","integrate((-a^2*c*x^2+c)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\frac{5 \, c \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{2 \, {\left| a \right|}} + \frac{1}{6} \, \sqrt{-a^{2} x^{2} + 1} {\left({\left(2 \, a c x - 9 \, c\right)} x + \frac{22 \, c}{a}\right)}"," ",0,"5/2*c*arcsin(a*x)*sgn(a)/abs(a) + 1/6*sqrt(-a^2*x^2 + 1)*((2*a*c*x - 9*c)*x + 22*c/a)","A",0
1258,1,66,0,0.382809," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + 1\right)}}{3 \, c {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)}^{3} {\left| a \right|}}"," ",0,"2/3*(3*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 1)/(c*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)^3*abs(a))","B",0
1259,1,145,0,0.233651," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{20 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}}{a^{2} x} + \frac{40 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{2}}{a^{4} x^{2}} + \frac{30 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{3}}{a^{6} x^{3}} + \frac{15 \, {\left(\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a\right)}^{4}}{a^{8} x^{4}} + 7\right)}}{15 \, c^{2} {\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} + 1\right)}^{5} {\left| a \right|}}"," ",0,"2/15*(20*(sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 40*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^2/(a^4*x^2) + 30*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^3/(a^6*x^3) + 15*(sqrt(-a^2*x^2 + 1)*abs(a) + a)^4/(a^8*x^4) + 7)/(c^2*((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) + 1)^5*abs(a))","A",0
1260,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\int -\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a^{2} c x^{2} - c\right)}^{3} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate(-(-a^2*x^2 + 1)^(3/2)/((a^2*c*x^2 - c)^3*(a*x + 1)^3), x)","F",0
1261,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^4,x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a^{2} c x^{2} - c\right)}^{4} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((a^2*c*x^2 - c)^4*(a*x + 1)^3), x)","F",0
1262,0,0,0,0.000000," ","integrate(x^3*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)*x^3/(a*x + 1)^3, x)","F",0
1263,0,0,0,0.000000," ","integrate(x^2*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)*x^2/(a*x + 1)^3, x)","F",0
1264,0,0,0,0.000000," ","integrate(x*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)*x/(a*x + 1)^3, x)","F",0
1265,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/(a*x + 1)^3, x)","F",0
1266,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x), x)","F",0
1267,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^2), x)","F",0
1268,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^3), x)","F",0
1269,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^4), x)","F",0
1270,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} c x^{2} + c} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3} x^{5}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*(-a^2*x^2 + 1)^(3/2)/((a*x + 1)^3*x^5), x)","F",0
1271,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(9/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(9/2)*(-a^2*x^2 + 1)^(3/2)/(a*x + 1)^3, x)","F",0
1272,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(7/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(7/2)*(-a^2*x^2 + 1)^(3/2)/(a*x + 1)^3, x)","F",0
1273,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*(-a^2*x^2 + 1)^(3/2)/(a*x + 1)^3, x)","F",0
1274,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*(-a^2*x^2 + 1)^(3/2)/(a*x + 1)^3, x)","F",0
1275,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{\sqrt{-a^{2} c x^{2} + c} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/(sqrt(-a^2*c*x^2 + c)*(a*x + 1)^3), x)","F",0
1276,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)^3), x)","F",0
1277,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((-a^2*c*x^2 + c)^(5/2)*(a*x + 1)^3), x)","F",0
1278,0,0,0,0.000000," ","integrate(1/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)/((-a^2*c*x^2 + c)^(7/2)*(a*x + 1)^3), x)","F",0
1279,-2,0,0,0.000000," ","integrate(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""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
1280,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/(a*x+1)^3*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(-a^{2} c x^{2} + c\right)}^{p}}{{\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*(-a^2*c*x^2 + c)^p/(a*x + 1)^3, x)","F",0
1281,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(5/2),x, algorithm=""giac"")","\int {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(5/2)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1282,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1283,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} x^{2} + 1} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1284,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/sqrt(-a^2*x^2 + 1), x)","F",0
1285,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*x^2 + 1)^(3/2), x)","F",0
1286,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*x^2 + 1)^(5/2), x)","F",0
1287,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*x^2 + 1)^(7/2), x)","F",0
1288,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*x^2+1)^(9/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} x^{2} + 1\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*x^2 + 1)^(9/2), x)","F",0
1289,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1290,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1291,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1)), x)","F",0
1292,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/sqrt(-a^2*c*x^2 + c), x)","F",0
1293,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(3/2), x)","F",0
1294,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(5/2), x)","F",0
1295,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(7/2), x)","F",0
1296,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(9/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(9/2), x)","F",0
1297,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^3/(-a^2*c*x^2+c)^(5/4),x, algorithm=""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
1298,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^2/(-a^2*c*x^2+c)^(5/4),x, algorithm=""giac"")","\int \frac{x^{2} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^2*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(5/4), x)","F",0
1299,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x/(-a^2*c*x^2+c)^(5/4),x, algorithm=""giac"")","\int \frac{x \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(5/4), x)","F",0
1300,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(5/4),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(5/4), x)","F",0
1301,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x/(-a^2*c*x^2+c)^(5/4),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{4}} x}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/((-a^2*c*x^2 + c)^(5/4)*x), x)","F",0
1302,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x^2/(-a^2*c*x^2+c)^(5/4),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{4}} x^{2}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/((-a^2*c*x^2 + c)^(5/4)*x^2), x)","F",0
1303,-2,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^3/(-a^2*c*x^2+c)^(9/8),x, algorithm=""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
1304,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x^2/(-a^2*c*x^2+c)^(9/8),x, algorithm=""giac"")","\int \frac{x^{2} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{8}}}\,{d x}"," ",0,"integrate(x^2*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(9/8), x)","F",0
1305,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)*x/(-a^2*c*x^2+c)^(9/8),x, algorithm=""giac"")","\int \frac{x \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{8}}}\,{d x}"," ",0,"integrate(x*sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(9/8), x)","F",0
1306,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(9/8),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{8}}}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/(-a^2*c*x^2 + c)^(9/8), x)","F",0
1307,0,0,0,0.000000," ","integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/x/(-a^2*c*x^2+c)^(9/8),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{9}{8}} x}\,{d x}"," ",0,"integrate(sqrt((a*x + 1)/sqrt(-a^2*x^2 + 1))/((-a^2*c*x^2 + c)^(9/8)*x), x)","F",0
1308,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c),x, algorithm=""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
1309,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1310,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1311,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^4/(-a^2*c*x^2+c),x, algorithm=""giac"")","\int -\frac{x^{4} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}\,{d x}"," ",0,"integrate(-x^4*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
1312,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c),x, algorithm=""giac"")","\int -\frac{x^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}\,{d x}"," ",0,"integrate(-x^3*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
1313,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c),x, algorithm=""giac"")","\int -\frac{x^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}\,{d x}"," ",0,"integrate(-x^2*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
1314,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c),x, algorithm=""giac"")","\int -\frac{x \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}\,{d x}"," ",0,"integrate(-x*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
1315,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1316,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/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}}{{\left(a^{2} c x^{2} - c\right)} x}\,{d x}"," ",0,"integrate(-((a*x + 1)/(a*x - 1))^(1/2*n)/((a^2*c*x^2 - c)*x), x)","F",0
1317,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c),x, algorithm=""giac"")","\int -\frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)} x^{2}}\,{d x}"," ",0,"integrate(-((a*x + 1)/(a*x - 1))^(1/2*n)/((a^2*c*x^2 - c)*x^2), x)","F",0
1318,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^4/(-a^2*c*x^2+c)^2,x, algorithm=""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)}^{2}}\,{d x}"," ",0,"integrate(x^4*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
1319,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^3/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{x^{3} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
1320,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^2,x, algorithm=""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)}^{2}}\,{d x}"," ",0,"integrate(x^2*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
1321,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c)^2,x, algorithm=""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)}^{2}}\,{d x}"," ",0,"integrate(x*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
1322,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^2,x, algorithm=""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
1323,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/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} x}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((a^2*c*x^2 - c)^2*x), x)","F",0
1324,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^2,x, algorithm=""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} x^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((a^2*c*x^2 - c)^2*x^2), x)","F",0
1325,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^3,x, algorithm=""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
1326,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1327,-2,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*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
1328,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \sqrt{-a^{2} c x^{2} + c} x^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*x^2*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1329,-2,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*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
1330,-2,0,0,0.000000," ","integrate(exp(n*arctanh(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
1331,-2,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1332,-2,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^(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:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1333,-2,0,0,0.000000," ","integrate(exp(n*arctanh(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
1334,-2,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*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
1335,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^2*((a*x + 1)/(a*x - 1))^(1/2*n)/sqrt(-a^2*c*x^2 + c), x)","F",0
1336,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{x \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x*((a*x + 1)/(a*x - 1))^(1/2*n)/sqrt(-a^2*c*x^2 + c), x)","F",0
1337,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^(1/2),x, algorithm=""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
1338,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/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} x}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(sqrt(-a^2*c*x^2 + c)*x), x)","F",0
1339,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c} x^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(sqrt(-a^2*c*x^2 + c)*x^2), x)","F",0
1340,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{\sqrt{-a^{2} c x^{2} + c} x^{3}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/(sqrt(-a^2*c*x^2 + c)*x^3), x)","F",0
1341,-2,0,0,0.000000," ","integrate(exp(n*arctanh(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
1342,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1343,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1344,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1345,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1346,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^2/(-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^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((-a^2*c*x^2 + c)^(3/2)*x^2), x)","F",0
1347,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""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^{3}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((-a^2*c*x^2 + c)^(3/2)*x^3), x)","F",0
1348,-2,0,0,0.000000," ","integrate(exp(n*arctanh(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
1349,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1350,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1351,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1352,0,0,0,0.000000," ","integrate(exp(n*arctanh(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
1353,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^2/(-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^{2}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((-a^2*c*x^2 + c)^(5/2)*x^2), x)","F",0
1354,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/x^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""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^{3}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(1/2*n)/((-a^2*c*x^2 + c)^(5/2)*x^3), x)","F",0
1355,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))/(-a^2*c*x^2+c)^(7/2),x, algorithm=""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
1356,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int {\left(a^{2} c x^{2} - c\right)}^{2} x^{m} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((a^2*c*x^2 - c)^2*x^m*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1357,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c),x, algorithm=""giac"")","\int -{\left(a^{2} c x^{2} - c\right)} x^{m} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate(-(a^2*c*x^2 - c)*x^m*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1358,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^m/(-a^2*c*x^2+c),x, algorithm=""giac"")","\int -\frac{x^{m} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{a^{2} c x^{2} - c}\,{d x}"," ",0,"integrate(-x^m*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c), x)","F",0
1359,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^m/(-a^2*c*x^2+c)^2,x, algorithm=""giac"")","\int \frac{x^{m} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}}{{\left(a^{2} c x^{2} - c\right)}^{2}}\,{d x}"," ",0,"integrate(x^m*((a*x + 1)/(a*x - 1))^(1/2*n)/(a^2*c*x^2 - c)^2, x)","F",0
1360,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^m*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{p} x^{m} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p*x^m*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1361,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x*(-a^2*c*x^2+c)^p,x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{p} x \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^p*x*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1362,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*(-a^2*c*x^2+c)^p,x, algorithm=""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
1363,0,0,0,0.000000," ","integrate(exp(2*(1+p)*arctanh(a*x))/((-a^2*x^2+1)^p),x, algorithm=""giac"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{p + 1}}{{\left(-a^{2} x^{2} + 1\right)}^{p}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(p + 1)/(-a^2*x^2 + 1)^p, x)","F",0
1364,0,0,0,0.000000," ","integrate(exp(2*(1+p)*arctanh(a*x))/((-a^2*c*x^2+c)^p),x, algorithm=""giac"")","\int \frac{\left(\frac{a x + 1}{a x - 1}\right)^{p + 1}}{{\left(-a^{2} c x^{2} + c\right)}^{p}}\,{d x}"," ",0,"integrate(((a*x + 1)/(a*x - 1))^(p + 1)/(-a^2*c*x^2 + c)^p, x)","F",0
1365,0,0,0,0.000000," ","integrate(exp(2*p*arctanh(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
1366,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^p/exp(2*p*arctanh(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
1367,0,0,0,0.000000," ","integrate(exp(n*arctanh(a*x))*x^2*(-a^2*c*x^2+c)^(-1-1/2*n^2),x, algorithm=""giac"")","\int {\left(-a^{2} c x^{2} + c\right)}^{-\frac{1}{2} \, n^{2} - 1} x^{2} \left(\frac{a x + 1}{a x - 1}\right)^{\frac{1}{2} \, n}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(-1/2*n^2 - 1)*x^2*((a*x + 1)/(a*x - 1))^(1/2*n), x)","F",0
1368,1,299,0,0.252175," ","integrate((a*x+1)^6/(-a^2*x^2+1)^3*x^2/(-a^2*c*x^2+c)^19,x, algorithm=""giac"")","-\frac{358229025 \, a^{14} x^{14} + 5340869100 \, a^{13} x^{13} + 37114698075 \, a^{12} x^{12} + 159416118225 \, a^{11} x^{11} + 473088806190 \, a^{10} x^{10} + 1026819468675 \, a^{9} x^{9} + 1682288472150 \, a^{8} x^{8} + 2115551402250 \, a^{7} x^{7} + 2054435046125 \, a^{6} x^{6} + 1535397250002 \, a^{5} x^{5} + 870854759775 \, a^{4} x^{4} + 364307533205 \, a^{3} x^{3} + 106553746740 \, a^{2} x^{2} + 19571887695 \, a x + 1710785408}{901943132160 \, {\left(a x + 1\right)}^{15} a^{3} c^{19}} + \frac{358229025 \, a^{20} x^{20} - 7555375800 \, a^{19} x^{19} + 75901131600 \, a^{18} x^{18} - 483051354975 \, a^{17} x^{17} + 2184946607340 \, a^{16} x^{16} - 7469205450840 \, a^{15} x^{15} + 20031221295000 \, a^{14} x^{14} - 43177004037300 \, a^{13} x^{13} + 76013078916950 \, a^{12} x^{12} - 110448380006328 \, a^{11} x^{11} + 133277726128008 \, a^{10} x^{10} - 133908931763530 \, a^{9} x^{9} + 111933156213900 \, a^{8} x^{8} - 77492989590120 \, a^{7} x^{7} + 44041557267624 \, a^{6} x^{6} - 20244576347604 \, a^{5} x^{5} + 7349182966545 \, a^{4} x^{4} - 2026362494800 \, a^{3} x^{3} + 396520754280 \, a^{2} x^{2} - 48177926223 \, a x + 2584181888}{901943132160 \, {\left(a x - 1\right)}^{21} a^{3} c^{19}}"," ",0,"-1/901943132160*(358229025*a^14*x^14 + 5340869100*a^13*x^13 + 37114698075*a^12*x^12 + 159416118225*a^11*x^11 + 473088806190*a^10*x^10 + 1026819468675*a^9*x^9 + 1682288472150*a^8*x^8 + 2115551402250*a^7*x^7 + 2054435046125*a^6*x^6 + 1535397250002*a^5*x^5 + 870854759775*a^4*x^4 + 364307533205*a^3*x^3 + 106553746740*a^2*x^2 + 19571887695*a*x + 1710785408)/((a*x + 1)^15*a^3*c^19) + 1/901943132160*(358229025*a^20*x^20 - 7555375800*a^19*x^19 + 75901131600*a^18*x^18 - 483051354975*a^17*x^17 + 2184946607340*a^16*x^16 - 7469205450840*a^15*x^15 + 20031221295000*a^14*x^14 - 43177004037300*a^13*x^13 + 76013078916950*a^12*x^12 - 110448380006328*a^11*x^11 + 133277726128008*a^10*x^10 - 133908931763530*a^9*x^9 + 111933156213900*a^8*x^8 - 77492989590120*a^7*x^7 + 44041557267624*a^6*x^6 - 20244576347604*a^5*x^5 + 7349182966545*a^4*x^4 - 2026362494800*a^3*x^3 + 396520754280*a^2*x^2 - 48177926223*a*x + 2584181888)/((a*x - 1)^21*a^3*c^19)","B",0
1369,1,139,0,0.189905," ","integrate((a*x+1)^4/(-a^2*x^2+1)^2*x^2/(-a^2*c*x^2+c)^9,x, algorithm=""giac"")","-\frac{2145 \, a^{5} x^{5} + 12540 \, a^{4} x^{4} + 30030 \, a^{3} x^{3} + 37080 \, a^{2} x^{2} + 23841 \, a x + 6476}{983040 \, {\left(a x + 1\right)}^{6} a^{3} c^{9}} + \frac{2145 \, a^{9} x^{9} - 21780 \, a^{8} x^{8} + 99660 \, a^{7} x^{7} - 270480 \, a^{6} x^{6} + 481446 \, a^{5} x^{5} - 584920 \, a^{4} x^{4} + 486220 \, a^{3} x^{3} - 265680 \, a^{2} x^{2} + 84065 \, a x - 9908}{983040 \, {\left(a x - 1\right)}^{10} a^{3} c^{9}}"," ",0,"-1/983040*(2145*a^5*x^5 + 12540*a^4*x^4 + 30030*a^3*x^3 + 37080*a^2*x^2 + 23841*a*x + 6476)/((a*x + 1)^6*a^3*c^9) + 1/983040*(2145*a^9*x^9 - 21780*a^8*x^8 + 99660*a^7*x^7 - 270480*a^6*x^6 + 481446*a^5*x^5 - 584920*a^4*x^4 + 486220*a^3*x^3 - 265680*a^2*x^2 + 84065*a*x - 9908)/((a*x - 1)^10*a^3*c^9)","B",0
1370,1,45,0,0.224109," ","integrate((a*x+1)^2/(-a^2*x^2+1)*x^2/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","-\frac{1}{16 \, {\left(a x + 1\right)} a^{3} c^{3}} + \frac{3 \, a^{2} x^{2} - 12 \, a x + 5}{48 \, {\left(a x - 1\right)}^{3} a^{3} c^{3}}"," ",0,"-1/16/((a*x + 1)*a^3*c^3) + 1/48*(3*a^2*x^2 - 12*a*x + 5)/((a*x - 1)^3*a^3*c^3)","A",0
1371,1,76,0,0.167042," ","integrate(x^2/(a*x+1)^2*(-a^2*x^2+1)/(-a^2*c*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{32 \, a^{3} c^{3} {\left(\frac{2}{a x + 1} - 1\right)}} + \frac{\frac{3 \, a^{3} c^{6}}{a x + 1} + \frac{6 \, a^{3} c^{6}}{{\left(a x + 1\right)}^{2}} - \frac{4 \, a^{3} c^{6}}{{\left(a x + 1\right)}^{3}}}{48 \, a^{6} c^{9}}"," ",0,"1/32/(a^3*c^3*(2/(a*x + 1) - 1)) + 1/48*(3*a^3*c^6/(a*x + 1) + 6*a^3*c^6/(a*x + 1)^2 - 4*a^3*c^6/(a*x + 1)^3)/(a^6*c^9)","B",0
1372,1,139,0,0.196265," ","integrate(x^2/(a*x+1)^4*(-a^2*x^2+1)^2/(-a^2*c*x^2+c)^9,x, algorithm=""giac"")","-\frac{2145 \, a^{5} x^{5} - 12540 \, a^{4} x^{4} + 30030 \, a^{3} x^{3} - 37080 \, a^{2} x^{2} + 23841 \, a x - 6476}{983040 \, {\left(a x - 1\right)}^{6} a^{3} c^{9}} + \frac{2145 \, a^{9} x^{9} + 21780 \, a^{8} x^{8} + 99660 \, a^{7} x^{7} + 270480 \, a^{6} x^{6} + 481446 \, a^{5} x^{5} + 584920 \, a^{4} x^{4} + 486220 \, a^{3} x^{3} + 265680 \, a^{2} x^{2} + 84065 \, a x + 9908}{983040 \, {\left(a x + 1\right)}^{10} a^{3} c^{9}}"," ",0,"-1/983040*(2145*a^5*x^5 - 12540*a^4*x^4 + 30030*a^3*x^3 - 37080*a^2*x^2 + 23841*a*x - 6476)/((a*x - 1)^6*a^3*c^9) + 1/983040*(2145*a^9*x^9 + 21780*a^8*x^8 + 99660*a^7*x^7 + 270480*a^6*x^6 + 481446*a^5*x^5 + 584920*a^4*x^4 + 486220*a^3*x^3 + 265680*a^2*x^2 + 84065*a*x + 9908)/((a*x + 1)^10*a^3*c^9)","B",0
1373,0,0,0,0.000000," ","integrate((a*x+1)^5/(-a^2*x^2+1)^(5/2)*x^2/(-a^2*c*x^2+c)^(27/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{5} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{27}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^5*x^2/((-a^2*c*x^2 + c)^(27/2)*(-a^2*x^2 + 1)^(5/2)), x)","F",0
1374,0,0,0,0.000000," ","integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2/(-a^2*c*x^2+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)}^{3} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{11}{2}} {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*x + 1)^3*x^2/((-a^2*c*x^2 + c)^(11/2)*(-a^2*x^2 + 1)^(3/2)), x)","F",0
1375,0,0,0,0.000000," ","integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a x + 1\right)} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((a*x + 1)*x^2/((-a^2*c*x^2 + c)^(3/2)*sqrt(-a^2*x^2 + 1)), x)","F",0
1376,0,0,0,0.000000," ","integrate(x^2/(a*x+1)*(-a^2*x^2+1)^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} {\left(a x + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*x^2 + 1)*x^2/((-a^2*c*x^2 + c)^(3/2)*(a*x + 1)), x)","F",0
1377,0,0,0,0.000000," ","integrate(x^2/(a*x+1)^3*(-a^2*x^2+1)^(3/2)/(-a^2*c*x^2+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{11}{2}} {\left(a x + 1\right)}^{3}}\,{d x}"," ",0,"integrate((-a^2*x^2 + 1)^(3/2)*x^2/((-a^2*c*x^2 + c)^(11/2)*(a*x + 1)^3), x)","F",0
1378,1,489,0,5.602478," ","integrate(x^2/(a*x+1)^5*(-a^2*x^2+1)^(5/2)/(-a^2*c*x^2+c)^(27/2),x, algorithm=""giac"")","\frac{2451570 \, \sqrt{c} {\left(\frac{2}{a x + 1} - 1\right)}^{9} + 1514205 \, \sqrt{c} {\left(\frac{2}{a x + 1} - 1\right)}^{8} + 769120 \, \sqrt{c} {\left(\frac{2}{a x + 1} - 1\right)}^{7} + 318780 \, \sqrt{c} {\left(\frac{2}{a x + 1} - 1\right)}^{6} + 106260 \, \sqrt{c} {\left(\frac{2}{a x + 1} - 1\right)}^{5} + 27830 \, \sqrt{c} {\left(\frac{2}{a x + 1} - 1\right)}^{4} + 5520 \, \sqrt{c} {\left(\frac{2}{a x + 1} - 1\right)}^{3} + 780 \, \sqrt{c} {\left(\frac{2}{a x + 1} - 1\right)}^{2} + 70 \, \sqrt{c} {\left(\frac{2}{a x + 1} - 1\right)} + 3 \, \sqrt{c}}{2013265920 \, a^{3} c^{14} {\left(\frac{2}{a x + 1} - 1\right)}^{10}} - \frac{2 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{15} + 45 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{14} + 480 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{13} + 3220 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{12} + 15180 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{11} + 53130 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{10} + 141680 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{9} + 288420 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{8} + 432630 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{7} + 408595 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{6} - 891480 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{4} - 2080120 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{3} - 3120180 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}^{2} - 3565920 \, a^{42} c^{\frac{393}{2}} {\left(\frac{2}{a x + 1} - 1\right)}}{2013265920 \, a^{45} c^{210}}"," ",0,"1/2013265920*(2451570*sqrt(c)*(2/(a*x + 1) - 1)^9 + 1514205*sqrt(c)*(2/(a*x + 1) - 1)^8 + 769120*sqrt(c)*(2/(a*x + 1) - 1)^7 + 318780*sqrt(c)*(2/(a*x + 1) - 1)^6 + 106260*sqrt(c)*(2/(a*x + 1) - 1)^5 + 27830*sqrt(c)*(2/(a*x + 1) - 1)^4 + 5520*sqrt(c)*(2/(a*x + 1) - 1)^3 + 780*sqrt(c)*(2/(a*x + 1) - 1)^2 + 70*sqrt(c)*(2/(a*x + 1) - 1) + 3*sqrt(c))/(a^3*c^14*(2/(a*x + 1) - 1)^10) - 1/2013265920*(2*a^42*c^(393/2)*(2/(a*x + 1) - 1)^15 + 45*a^42*c^(393/2)*(2/(a*x + 1) - 1)^14 + 480*a^42*c^(393/2)*(2/(a*x + 1) - 1)^13 + 3220*a^42*c^(393/2)*(2/(a*x + 1) - 1)^12 + 15180*a^42*c^(393/2)*(2/(a*x + 1) - 1)^11 + 53130*a^42*c^(393/2)*(2/(a*x + 1) - 1)^10 + 141680*a^42*c^(393/2)*(2/(a*x + 1) - 1)^9 + 288420*a^42*c^(393/2)*(2/(a*x + 1) - 1)^8 + 432630*a^42*c^(393/2)*(2/(a*x + 1) - 1)^7 + 408595*a^42*c^(393/2)*(2/(a*x + 1) - 1)^6 - 891480*a^42*c^(393/2)*(2/(a*x + 1) - 1)^4 - 2080120*a^42*c^(393/2)*(2/(a*x + 1) - 1)^3 - 3120180*a^42*c^(393/2)*(2/(a*x + 1) - 1)^2 - 3565920*a^42*c^(393/2)*(2/(a*x + 1) - 1))/(a^45*c^210)","B",0
