1,1,26,0,0.182140," ","integrate((b*x)^p*(c*x)^m,x, algorithm=""giac"")","\frac{x e^{\left(p \log\left(b\right) + m \log\left(c\right) + m \log\left(x\right) + p \log\left(x\right)\right)}}{m + p + 1}"," ",0,"x*e^(p*log(b) + m*log(c) + m*log(x) + p*log(x))/(m + p + 1)","A",0
2,1,10,0,0.147488," ","integrate(x^3*(b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, \sqrt{b} x^{5} \mathrm{sgn}\left(x\right)"," ",0,"1/5*sqrt(b)*x^5*sgn(x)","A",0
3,1,10,0,0.173245," ","integrate(x^2*(b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{b} x^{4} \mathrm{sgn}\left(x\right)"," ",0,"1/4*sqrt(b)*x^4*sgn(x)","A",0
4,1,10,0,0.149533," ","integrate(x*(b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{b} x^{3} \mathrm{sgn}\left(x\right)"," ",0,"1/3*sqrt(b)*x^3*sgn(x)","A",0
5,1,10,0,0.161849," ","integrate((b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{b} x^{2} \mathrm{sgn}\left(x\right)"," ",0,"1/2*sqrt(b)*x^2*sgn(x)","A",0
6,1,7,0,0.207796," ","integrate((b*x^2)^(1/2)/x,x, algorithm=""giac"")","\sqrt{b} x \mathrm{sgn}\left(x\right)"," ",0,"sqrt(b)*x*sgn(x)","A",0
7,1,9,0,0.159582," ","integrate((b*x^2)^(1/2)/x^2,x, algorithm=""giac"")","\sqrt{b} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(x\right)"," ",0,"sqrt(b)*log(abs(x))*sgn(x)","A",0
8,1,10,0,0.169551," ","integrate((b*x^2)^(1/2)/x^3,x, algorithm=""giac"")","-\frac{\sqrt{b} \mathrm{sgn}\left(x\right)}{x}"," ",0,"-sqrt(b)*sgn(x)/x","A",0
9,1,10,0,0.153124," ","integrate((b*x^2)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{\sqrt{b} \mathrm{sgn}\left(x\right)}{2 \, x^{2}}"," ",0,"-1/2*sqrt(b)*sgn(x)/x^2","A",0
10,1,10,0,0.181891," ","integrate((b*x^2)^(1/2)/x^5,x, algorithm=""giac"")","-\frac{\sqrt{b} \mathrm{sgn}\left(x\right)}{3 \, x^{3}}"," ",0,"-1/3*sqrt(b)*sgn(x)/x^3","A",0
11,1,7,0,0.151565," ","integrate(x^2*(x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, x^{4} \mathrm{sgn}\left(x\right)"," ",0,"1/4*x^4*sgn(x)","A",0
12,1,10,0,0.150003," ","integrate(x^2*(b*x^2)^(3/2),x, algorithm=""giac"")","\frac{1}{6} \, b^{\frac{3}{2}} x^{6} \mathrm{sgn}\left(x\right)"," ",0,"1/6*b^(3/2)*x^6*sgn(x)","A",0
13,1,10,0,0.169877," ","integrate(x*(b*x^2)^(3/2),x, algorithm=""giac"")","\frac{1}{5} \, b^{\frac{3}{2}} x^{5} \mathrm{sgn}\left(x\right)"," ",0,"1/5*b^(3/2)*x^5*sgn(x)","A",0
14,1,10,0,0.152368," ","integrate((b*x^2)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, b^{\frac{3}{2}} x^{4} \mathrm{sgn}\left(x\right)"," ",0,"1/4*b^(3/2)*x^4*sgn(x)","A",0
15,1,10,0,0.177524," ","integrate((b*x^2)^(3/2)/x,x, algorithm=""giac"")","\frac{1}{3} \, b^{\frac{3}{2}} x^{3} \mathrm{sgn}\left(x\right)"," ",0,"1/3*b^(3/2)*x^3*sgn(x)","A",0
16,1,10,0,0.154750," ","integrate((b*x^2)^(3/2)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, b^{\frac{3}{2}} x^{2} \mathrm{sgn}\left(x\right)"," ",0,"1/2*b^(3/2)*x^2*sgn(x)","A",0
17,1,7,0,0.182765," ","integrate((b*x^2)^(3/2)/x^3,x, algorithm=""giac"")","b^{\frac{3}{2}} x \mathrm{sgn}\left(x\right)"," ",0,"b^(3/2)*x*sgn(x)","A",0
18,1,9,0,0.187065," ","integrate((b*x^2)^(3/2)/x^4,x, algorithm=""giac"")","b^{\frac{3}{2}} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(x\right)"," ",0,"b^(3/2)*log(abs(x))*sgn(x)","A",0
19,1,10,0,0.158288," ","integrate((b*x^2)^(3/2)/x^5,x, algorithm=""giac"")","-\frac{b^{\frac{3}{2}} \mathrm{sgn}\left(x\right)}{x}"," ",0,"-b^(3/2)*sgn(x)/x","A",0
20,1,10,0,0.176753," ","integrate((b*x^2)^(3/2)/x^6,x, algorithm=""giac"")","-\frac{b^{\frac{3}{2}} \mathrm{sgn}\left(x\right)}{2 \, x^{2}}"," ",0,"-1/2*b^(3/2)*sgn(x)/x^2","A",0
21,1,10,0,0.155021," ","integrate((b*x^2)^(3/2)/x^7,x, algorithm=""giac"")","-\frac{b^{\frac{3}{2}} \mathrm{sgn}\left(x\right)}{3 \, x^{3}}"," ",0,"-1/3*b^(3/2)*sgn(x)/x^3","A",0
22,1,7,0,0.150607," ","integrate((x^2)^(5/2),x, algorithm=""giac"")","\frac{1}{6} \, x^{6} \mathrm{sgn}\left(x\right)"," ",0,"1/6*x^6*sgn(x)","A",0
23,1,10,0,0.146780," ","integrate(x*(b*x^2)^(5/2),x, algorithm=""giac"")","\frac{1}{7} \, b^{\frac{5}{2}} x^{7} \mathrm{sgn}\left(x\right)"," ",0,"1/7*b^(5/2)*x^7*sgn(x)","A",0
24,1,10,0,0.172250," ","integrate((b*x^2)^(5/2),x, algorithm=""giac"")","\frac{1}{6} \, b^{\frac{5}{2}} x^{6} \mathrm{sgn}\left(x\right)"," ",0,"1/6*b^(5/2)*x^6*sgn(x)","A",0
25,1,10,0,0.152415," ","integrate((b*x^2)^(5/2)/x,x, algorithm=""giac"")","\frac{1}{5} \, b^{\frac{5}{2}} x^{5} \mathrm{sgn}\left(x\right)"," ",0,"1/5*b^(5/2)*x^5*sgn(x)","A",0
26,1,10,0,0.166339," ","integrate((b*x^2)^(5/2)/x^2,x, algorithm=""giac"")","\frac{1}{4} \, b^{\frac{5}{2}} x^{4} \mathrm{sgn}\left(x\right)"," ",0,"1/4*b^(5/2)*x^4*sgn(x)","A",0
27,1,10,0,0.177754," ","integrate((b*x^2)^(5/2)/x^3,x, algorithm=""giac"")","\frac{1}{3} \, b^{\frac{5}{2}} x^{3} \mathrm{sgn}\left(x\right)"," ",0,"1/3*b^(5/2)*x^3*sgn(x)","A",0
28,1,10,0,0.153458," ","integrate((b*x^2)^(5/2)/x^4,x, algorithm=""giac"")","\frac{1}{2} \, b^{\frac{5}{2}} x^{2} \mathrm{sgn}\left(x\right)"," ",0,"1/2*b^(5/2)*x^2*sgn(x)","A",0
29,1,7,0,0.169601," ","integrate((b*x^2)^(5/2)/x^5,x, algorithm=""giac"")","b^{\frac{5}{2}} x \mathrm{sgn}\left(x\right)"," ",0,"b^(5/2)*x*sgn(x)","A",0
30,1,9,0,0.173774," ","integrate((b*x^2)^(5/2)/x^6,x, algorithm=""giac"")","b^{\frac{5}{2}} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(x\right)"," ",0,"b^(5/2)*log(abs(x))*sgn(x)","A",0
31,1,10,0,0.154254," ","integrate((b*x^2)^(5/2)/x^7,x, algorithm=""giac"")","-\frac{b^{\frac{5}{2}} \mathrm{sgn}\left(x\right)}{x}"," ",0,"-b^(5/2)*sgn(x)/x","A",0
32,1,10,0,0.155092," ","integrate((b*x^2)^(5/2)/x^8,x, algorithm=""giac"")","-\frac{b^{\frac{5}{2}} \mathrm{sgn}\left(x\right)}{2 \, x^{2}}"," ",0,"-1/2*b^(5/2)*sgn(x)/x^2","A",0
33,1,10,0,0.152974," ","integrate((b*x^2)^(5/2)/x^9,x, algorithm=""giac"")","-\frac{b^{\frac{5}{2}} \mathrm{sgn}\left(x\right)}{3 \, x^{3}}"," ",0,"-1/3*b^(5/2)*sgn(x)/x^3","A",0
34,1,7,0,0.413118," ","integrate((x^2)^(7/2),x, algorithm=""giac"")","\frac{1}{8} \, x^{8} \mathrm{sgn}\left(x\right)"," ",0,"1/8*x^8*sgn(x)","A",0
35,1,15,0,0.155293," ","integrate(x^3/(b*x^2)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2}} x^{2}}{3 \, b}"," ",0,"1/3*sqrt(b*x^2)*x^2/b","A",0
36,1,11,0,0.150541," ","integrate(x/(b*x^2)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2}}}{b}"," ",0,"sqrt(b*x^2)/b","A",0
37,1,9,0,0.154023," ","integrate(1/x/(b*x^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{\sqrt{b x^{2}}}"," ",0,"-1/sqrt(b*x^2)","A",0
38,1,12,0,0.165330," ","integrate(1/x^3/(b*x^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{3 \, \sqrt{b x^{2}} x^{2}}"," ",0,"-1/3/(sqrt(b*x^2)*x^2)","A",0
39,1,13,0,0.220025," ","integrate(x^2/(b*x^2)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2}} x}{2 \, b}"," ",0,"1/2*sqrt(b*x^2)*x/b","A",0
40,1,19,0,0.202887," ","integrate(1/(b*x^2)^(1/2),x, algorithm=""giac"")","\frac{\log\left(\sqrt{{\left| b \right|}} {\left| x \right|} {\left| \mathrm{sgn}\left(x\right) \right|}\right)}{\sqrt{b} \mathrm{sgn}\left(x\right)}"," ",0,"log(sqrt(abs(b))*abs(x)*abs(sgn(x)))/(sqrt(b)*sgn(x))","A",0
41,0,0,0,0.000000," ","integrate(1/x^2/(b*x^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
42,1,15,0,0.153570," ","integrate(x^5/(b*x^2)^(3/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2}} x^{2}}{3 \, b^{2}}"," ",0,"1/3*sqrt(b*x^2)*x^2/b^2","A",0
43,1,11,0,0.150634," ","integrate(x^3/(b*x^2)^(3/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2}}}{b^{2}}"," ",0,"sqrt(b*x^2)/b^2","A",0
44,1,12,0,0.153568," ","integrate(x/(b*x^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{\sqrt{b x^{2}} b}"," ",0,"-1/(sqrt(b*x^2)*b)","A",0
45,1,15,0,0.162125," ","integrate(1/x/(b*x^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{3 \, \sqrt{b x^{2}} b x^{2}}"," ",0,"-1/3/(sqrt(b*x^2)*b*x^2)","A",0
46,1,15,0,0.150005," ","integrate(1/x^3/(b*x^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{5 \, \sqrt{b x^{2}} b x^{4}}"," ",0,"-1/5/(sqrt(b*x^2)*b*x^4)","A",0
47,1,15,0,0.166954," ","integrate(x^6/(b*x^2)^(3/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2}} x^{3}}{4 \, b^{2}}"," ",0,"1/4*sqrt(b*x^2)*x^3/b^2","A",0
48,1,13,0,0.213552," ","integrate(x^4/(b*x^2)^(3/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2}} x}{2 \, b^{2}}"," ",0,"1/2*sqrt(b*x^2)*x/b^2","A",0
49,1,21,0,0.174727," ","integrate(x^2/(b*x^2)^(3/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -\sqrt{b} x + \sqrt{b x^{2}} \right|}\right)}{b^{\frac{3}{2}}}"," ",0,"-log(abs(-sqrt(b)*x + sqrt(b*x^2)))/b^(3/2)","A",0
50,0,0,0,0.000000," ","integrate(1/(b*x^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
51,0,0,0,0.000000," ","integrate(1/x^2/(b*x^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
52,1,15,0,0.153948," ","integrate(x^7/(b*x^2)^(5/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2}} x^{2}}{3 \, b^{3}}"," ",0,"1/3*sqrt(b*x^2)*x^2/b^3","A",0
53,1,11,0,0.165191," ","integrate(x^5/(b*x^2)^(5/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2}}}{b^{3}}"," ",0,"sqrt(b*x^2)/b^3","A",0
54,1,12,0,0.180779," ","integrate(x^3/(b*x^2)^(5/2),x, algorithm=""giac"")","-\frac{1}{\sqrt{b x^{2}} b^{2}}"," ",0,"-1/(sqrt(b*x^2)*b^2)","A",0
55,1,15,0,0.156299," ","integrate(x/(b*x^2)^(5/2),x, algorithm=""giac"")","-\frac{1}{3 \, \sqrt{b x^{2}} b^{2} x^{2}}"," ",0,"-1/3/(sqrt(b*x^2)*b^2*x^2)","A",0
56,1,15,0,0.151791," ","integrate(1/x/(b*x^2)^(5/2),x, algorithm=""giac"")","-\frac{1}{5 \, \sqrt{b x^{2}} b^{2} x^{4}}"," ",0,"-1/5/(sqrt(b*x^2)*b^2*x^4)","A",0
57,1,13,0,0.169250," ","integrate(x^6/(b*x^2)^(5/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2}} x}{2 \, b^{3}}"," ",0,"1/2*sqrt(b*x^2)*x/b^3","A",0
58,1,21,0,0.221615," ","integrate(x^4/(b*x^2)^(5/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -\sqrt{b} x + \sqrt{b x^{2}} \right|}\right)}{b^{\frac{5}{2}}}"," ",0,"-log(abs(-sqrt(b)*x + sqrt(b*x^2)))/b^(5/2)","A",0
59,0,0,0,0.000000," ","integrate(x^2/(b*x^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
60,0,0,0,0.000000," ","integrate(1/(b*x^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
61,0,0,0,0.000000," ","integrate(1/x^2/(b*x^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
62,-2,0,0,0.000000," ","integrate((c*x)^m*(b*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)]Undef/Unsigned Inf encountered in limitLimit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
63,-2,0,0,0.000000," ","integrate((c*x)^m*(b*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)]Undef/Unsigned Inf encountered in limitLimit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
64,0,0,0,0.000000," ","integrate((c*x)^m/(b*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m}}{\sqrt{b x^{2}}}\,{d x}"," ",0,"integrate((c*x)^m/sqrt(b*x^2), x)","F",0
65,0,0,0,0.000000," ","integrate((c*x)^m/(b*x^2)^(3/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m}}{\left(b x^{2}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x)^m/(b*x^2)^(3/2), x)","F",0
66,1,24,0,0.168606," ","integrate(x^m*(b*x^2)^p,x, algorithm=""giac"")","\frac{x x^{m} e^{\left(p \log\left(b\right) + 2 \, p \log\left(x\right)\right)}}{m + 2 \, p + 1}"," ",0,"x*x^m*e^(p*log(b) + 2*p*log(x))/(m + 2*p + 1)","A",0
67,1,29,0,0.165132," ","integrate((c*x)^m*(b*x^2)^p,x, algorithm=""giac"")","\frac{x e^{\left(p \log\left(b\right) + m \log\left(c\right) + m \log\left(x\right) + 2 \, p \log\left(x\right)\right)}}{m + 2 \, p + 1}"," ",0,"x*e^(p*log(b) + m*log(c) + m*log(x) + 2*p*log(x))/(m + 2*p + 1)","A",0
68,0,0,0,0.000000," ","integrate(x^(-1-2*p)*(x^2)^p,x, algorithm=""giac"")","\int {\left(x^{2}\right)}^{p} x^{-2 \, p - 1}\,{d x}"," ",0,"integrate((x^2)^p*x^(-2*p - 1), x)","F",0
69,1,17,0,0.152639," ","integrate(x^3*(b*x^2)^p,x, algorithm=""giac"")","\frac{\left(b x^{2}\right)^{p} x^{4}}{2 \, {\left(p + 2\right)}}"," ",0,"1/2*(b*x^2)^p*x^4/(p + 2)","A",0
70,1,18,0,0.179499," ","integrate(x^2*(b*x^2)^p,x, algorithm=""giac"")","\frac{\left(b x^{2}\right)^{p} x^{3}}{2 \, p + 3}"," ",0,"(b*x^2)^p*x^3/(2*p + 3)","A",0
71,1,19,0,0.157235," ","integrate(x*(b*x^2)^p,x, algorithm=""giac"")","\frac{\left(b x^{2}\right)^{p + 1}}{2 \, b {\left(p + 1\right)}}"," ",0,"1/2*(b*x^2)^(p + 1)/(b*(p + 1))","A",0
72,1,16,0,0.191266," ","integrate((b*x^2)^p,x, algorithm=""giac"")","\frac{\left(b x^{2}\right)^{p} x}{2 \, p + 1}"," ",0,"(b*x^2)^p*x/(2*p + 1)","A",0
73,1,12,0,0.153532," ","integrate((b*x^2)^p/x,x, algorithm=""giac"")","\frac{\left(b x^{2}\right)^{p}}{2 \, p}"," ",0,"1/2*(b*x^2)^p/p","A",0
74,0,0,0,0.000000," ","integrate((b*x^2)^p/x^2,x, algorithm=""giac"")","\int \frac{\left(b x^{2}\right)^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^2)^p/x^2, x)","F",0
75,0,0,0,0.000000," ","integrate((b*x^2)^p/x^3,x, algorithm=""giac"")","\int \frac{\left(b x^{2}\right)^{p}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^2)^p/x^3, x)","F",0
76,0,0,0,0.000000," ","integrate((b*x^2)^p/x^4,x, algorithm=""giac"")","\int \frac{\left(b x^{2}\right)^{p}}{x^{4}}\,{d x}"," ",0,"integrate((b*x^2)^p/x^4, x)","F",0
77,1,12,0,0.165418," ","integrate((b*x^3)^(1/2),x, algorithm=""giac"")","\frac{2}{5} \, \sqrt{b x} x^{2} \mathrm{sgn}\left(x\right)"," ",0,"2/5*sqrt(b*x)*x^2*sgn(x)","A",0
78,1,10,0,0.150084," ","integrate((b*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{b} x^{2} \mathrm{sgn}\left(x\right)"," ",0,"1/2*sqrt(b)*x^2*sgn(x)","A",0
79,1,8,0,0.144059," ","integrate((b*x)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{b x} x"," ",0,"2/3*sqrt(b*x)*x","A",0
80,1,9,0,0.150858," ","integrate((b/x)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{b x} \mathrm{sgn}\left(x\right)"," ",0,"2*sqrt(b*x)*sgn(x)","A",0
81,1,9,0,0.169207," ","integrate((b/x^2)^(1/2),x, algorithm=""giac"")","\sqrt{b} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(x\right)"," ",0,"sqrt(b)*log(abs(x))*sgn(x)","A",0
82,1,8,0,0.153354," ","integrate((b/x^3)^(1/2),x, algorithm=""giac"")","-\frac{2 \, b}{\sqrt{b x}}"," ",0,"-2*b/sqrt(b*x)","A",0
83,1,13,0,0.149858," ","integrate((b*x^3)^(3/2),x, algorithm=""giac"")","\frac{2}{11} \, \sqrt{b x} b x^{5} \mathrm{sgn}\left(x\right)"," ",0,"2/11*sqrt(b*x)*b*x^5*sgn(x)","A",0
84,1,10,0,0.165595," ","integrate((b*x^2)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, b^{\frac{3}{2}} x^{4} \mathrm{sgn}\left(x\right)"," ",0,"1/4*b^(3/2)*x^4*sgn(x)","A",0
85,1,11,0,0.175700," ","integrate((b*x)^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, \sqrt{b x} b x^{2}"," ",0,"2/5*sqrt(b*x)*b*x^2","A",0
86,1,12,0,0.157155," ","integrate((b/x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, b^{2} \mathrm{sgn}\left(x\right)}{\sqrt{b x}}"," ",0,"-2*b^2*sgn(x)/sqrt(b*x)","A",0
87,1,10,0,0.149452," ","integrate((b/x^2)^(3/2),x, algorithm=""giac"")","-\frac{b^{\frac{3}{2}} \mathrm{sgn}\left(x\right)}{2 \, x^{2}}"," ",0,"-1/2*b^(3/2)*sgn(x)/x^2","A",0
88,1,13,0,0.153960," ","integrate((b/x^3)^(3/2),x, algorithm=""giac"")","-\frac{2 \, b^{2}}{7 \, \sqrt{b x} x^{3}}"," ",0,"-2/7*b^2/(sqrt(b*x)*x^3)","A",0
89,1,11,0,0.152762," ","integrate(1/(b*x^3)^(1/2),x, algorithm=""giac"")","-\frac{2}{\sqrt{b x} \mathrm{sgn}\left(x\right)}"," ",0,"-2/(sqrt(b*x)*sgn(x))","A",0
90,1,19,0,0.198038," ","integrate(1/(b*x^2)^(1/2),x, algorithm=""giac"")","\frac{\log\left(\sqrt{{\left| b \right|}} {\left| x \right|} {\left| \mathrm{sgn}\left(x\right) \right|}\right)}{\sqrt{b} \mathrm{sgn}\left(x\right)}"," ",0,"log(sqrt(abs(b))*abs(x)*abs(sgn(x)))/(sqrt(b)*sgn(x))","A",0
91,1,10,0,0.221610," ","integrate(1/(b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{b x}}{b}"," ",0,"2*sqrt(b*x)/b","A",0
92,1,15,0,0.154912," ","integrate(1/(b/x)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{b x} x}{3 \, b \mathrm{sgn}\left(x\right)}"," ",0,"2/3*sqrt(b*x)*x/(b*sgn(x))","A",0
93,1,12,0,0.190837," ","integrate(1/(b/x^2)^(1/2),x, algorithm=""giac"")","\frac{x^{2}}{2 \, \sqrt{b} \mathrm{sgn}\left(x\right)}"," ",0,"1/2*x^2/(sqrt(b)*sgn(x))","A",0
94,1,13,0,0.170689," ","integrate(1/(b/x^3)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{b x} x^{2}}{5 \, b}"," ",0,"2/5*sqrt(b*x)*x^2/b","A",0
95,0,0,0,0.000000," ","integrate(1/(b*x^3)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
96,0,0,0,0.000000," ","integrate(1/(b*x^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
97,1,10,0,0.148233," ","integrate(1/(b*x)^(3/2),x, algorithm=""giac"")","-\frac{2}{\sqrt{b x} b}"," ",0,"-2/(sqrt(b*x)*b)","A",0
98,1,15,0,0.171012," ","integrate(1/(b/x)^(3/2),x, algorithm=""giac"")","\frac{2 \, x^{2}}{5 \, b \sqrt{\frac{b}{x}}}"," ",0,"2/5*x^2/(b*sqrt(b/x))","A",0
99,1,8,0,0.155662," ","integrate(1/(b/x^2)^(3/2),x, algorithm=""giac"")","\frac{x^{4}}{4 \, b^{\frac{3}{2}}}"," ",0,"1/4*x^4/b^(3/2)","A",0
100,0,0,0,0.000000," ","integrate(1/(b/x^3)^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{b}{x^{3}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b/x^3)^(-3/2), x)","F",0
101,0,0,0,0.000000," ","integrate((b*x^n)^(1/3),x, algorithm=""giac"")","\int \left(b x^{n}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*x^n)^(1/3), x)","F",0
102,1,8,0,0.147999," ","integrate((b*x^3)^(1/3),x, algorithm=""giac"")","\frac{1}{2} \, b^{\frac{1}{3}} x^{2}"," ",0,"1/2*b^(1/3)*x^2","A",0
103,1,11,0,0.160978," ","integrate((b*x^2)^(1/3),x, algorithm=""giac"")","\frac{3 \, b x}{5 \, \left(\frac{b}{x}\right)^{\frac{2}{3}}}"," ",0,"3/5*b*x/(b/x)^(2/3)","A",0
104,1,8,0,0.148884," ","integrate((b*x)^(1/3),x, algorithm=""giac"")","\frac{3}{4} \, \left(b x\right)^{\frac{1}{3}} x"," ",0,"3/4*(b*x)^(1/3)*x","A",0
105,1,10,0,0.150300," ","integrate((b/x)^(1/3),x, algorithm=""giac"")","\frac{3 \, b}{2 \, \left(\frac{b}{x}\right)^{\frac{2}{3}}}"," ",0,"3/2*b/(b/x)^(2/3)","A",0
106,0,0,0,0.000000," ","integrate((b/x^2)^(1/3),x, algorithm=""giac"")","\int \left(\frac{b}{x^{2}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b/x^2)^(1/3), x)","F",0
107,0,0,0,0.000000," ","integrate((b/x^3)^(1/3),x, algorithm=""giac"")","\int \left(\frac{b}{x^{3}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b/x^3)^(1/3), x)","F",0
108,0,0,0,0.000000," ","integrate((b/x^4)^(1/3),x, algorithm=""giac"")","\int \left(\frac{b}{x^{4}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b/x^4)^(1/3), x)","F",0
109,0,0,0,0.000000," ","integrate((b*x^n)^(2/3),x, algorithm=""giac"")","\int \left(b x^{n}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*x^n)^(2/3), x)","F",0
110,1,13,0,0.160099," ","integrate((b*x^2)^(2/3),x, algorithm=""giac"")","\frac{3 \, b x^{2}}{7 \, \left(\frac{b}{x}\right)^{\frac{1}{3}}}"," ",0,"3/7*b*x^2/(b/x)^(1/3)","A",0
111,1,8,0,0.155990," ","integrate((b*x)^(2/3),x, algorithm=""giac"")","\frac{3}{5} \, \left(b x\right)^{\frac{2}{3}} x"," ",0,"3/5*(b*x)^(2/3)*x","A",0
112,1,10,0,0.153295," ","integrate((b/x)^(2/3),x, algorithm=""giac"")","\frac{3 \, b}{\left(\frac{b}{x}\right)^{\frac{1}{3}}}"," ",0,"3*b/(b/x)^(1/3)","A",0
113,0,0,0,0.000000," ","integrate((b/x^2)^(2/3),x, algorithm=""giac"")","\int \left(\frac{b}{x^{2}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b/x^2)^(2/3), x)","F",0
114,0,0,0,0.000000," ","integrate((b/x^3)^(2/3),x, algorithm=""giac"")","\int \left(\frac{b}{x^{3}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b/x^3)^(2/3), x)","F",0
115,0,0,0,0.000000," ","integrate((b/x^4)^(2/3),x, algorithm=""giac"")","\int \left(\frac{b}{x^{4}}\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b/x^4)^(2/3), x)","F",0
116,0,0,0,0.000000," ","integrate(1/(b*x^n)^(1/3),x, algorithm=""giac"")","\int \frac{1}{\left(b x^{n}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^n)^(-1/3), x)","F",0
117,0,0,0,0.000000," ","integrate(1/(b*x^4)^(1/3),x, algorithm=""giac"")","\int \frac{1}{\left(b x^{4}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^4)^(-1/3), x)","F",0
118,1,7,0,0.159767," ","integrate(1/(b*x^3)^(1/3),x, algorithm=""giac"")","\frac{\log\left({\left| x \right|}\right)}{b^{\frac{1}{3}}}"," ",0,"log(abs(x))/b^(1/3)","A",0
119,1,9,0,0.197362," ","integrate(1/(b*x^2)^(1/3),x, algorithm=""giac"")","\frac{3}{\left(\frac{b}{x}\right)^{\frac{1}{3}}}"," ",0,"3/(b/x)^(1/3)","A",0
120,1,10,0,0.159968," ","integrate(1/(b*x)^(1/3),x, algorithm=""giac"")","\frac{3 \, \left(b x\right)^{\frac{2}{3}}}{2 \, b}"," ",0,"3/2*(b*x)^(2/3)/b","A",0
121,1,10,0,0.197853," ","integrate(1/(b/x)^(1/3),x, algorithm=""giac"")","\frac{3 \, x}{4 \, \left(\frac{b}{x}\right)^{\frac{1}{3}}}"," ",0,"3/4*x/(b/x)^(1/3)","A",0
122,0,0,0,0.000000," ","integrate(1/(b/x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{b}{x^{2}}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b/x^2)^(-1/3), x)","F",0
123,0,0,0,0.000000," ","integrate(1/(b/x^3)^(1/3),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{b}{x^{3}}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b/x^3)^(-1/3), x)","F",0
124,0,0,0,0.000000," ","integrate(1/(b*x^n)^(2/3),x, algorithm=""giac"")","\int \frac{1}{\left(b x^{n}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*x^n)^(-2/3), x)","F",0
125,1,8,0,0.153852," ","integrate(1/(b*x^3)^(2/3),x, algorithm=""giac"")","-\frac{1}{b^{\frac{2}{3}} x}"," ",0,"-1/(b^(2/3)*x)","A",0
126,1,12,0,0.155684," ","integrate(1/(b*x^2)^(2/3),x, algorithm=""giac"")","-\frac{3 \, \left(\frac{b}{x}\right)^{\frac{1}{3}}}{b}"," ",0,"-3*(b/x)^(1/3)/b","A",0
127,1,10,0,0.175154," ","integrate(1/(b*x)^(2/3),x, algorithm=""giac"")","\frac{3 \, \left(b x\right)^{\frac{1}{3}}}{b}"," ",0,"3*(b*x)^(1/3)/b","A",0
128,1,10,0,0.170983," ","integrate(1/(b/x)^(2/3),x, algorithm=""giac"")","\frac{3 \, x}{5 \, \left(\frac{b}{x}\right)^{\frac{2}{3}}}"," ",0,"3/5*x/(b/x)^(2/3)","A",0
129,0,0,0,0.000000," ","integrate(1/(b/x^2)^(2/3),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{b}{x^{2}}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b/x^2)^(-2/3), x)","F",0
130,0,0,0,0.000000," ","integrate(1/(b/x^3)^(2/3),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{b}{x^{3}}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b/x^3)^(-2/3), x)","F",0
131,0,0,0,0.000000," ","integrate(x^2*(b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n}} x^{2}\,{d x}"," ",0,"integrate(sqrt(b*x^n)*x^2, x)","F",0
132,0,0,0,0.000000," ","integrate(x*(b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n}} x\,{d x}"," ",0,"integrate(sqrt(b*x^n)*x, x)","F",0
133,0,0,0,0.000000," ","integrate((b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n}}\,{d x}"," ",0,"integrate(sqrt(b*x^n), x)","F",0
134,1,12,0,0.176428," ","integrate((b*x^n)^(1/2)/x,x, algorithm=""giac"")","\frac{2 \, \sqrt{b x^{n}}}{n}"," ",0,"2*sqrt(b*x^n)/n","A",0
135,0,0,0,0.000000," ","integrate((b*x^n)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{b x^{n}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(b*x^n)/x^2, x)","F",0
136,0,0,0,0.000000," ","integrate((b*x^n)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{b x^{n}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(b*x^n)/x^3, x)","F",0
137,0,0,0,0.000000," ","integrate(x*(b*x^n)^(3/2),x, algorithm=""giac"")","\int \left(b x^{n}\right)^{\frac{3}{2}} x\,{d x}"," ",0,"integrate((b*x^n)^(3/2)*x, x)","F",0
138,0,0,0,0.000000," ","integrate((b*x^n)^(3/2),x, algorithm=""giac"")","\int \left(b x^{n}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*x^n)^(3/2), x)","F",0
139,0,0,0,0.000000," ","integrate((b*x^n)^(3/2)/x,x, algorithm=""giac"")","\int \frac{\left(b x^{n}\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate((b*x^n)^(3/2)/x, x)","F",0
140,0,0,0,0.000000," ","integrate((b*x^n)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{\left(b x^{n}\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^n)^(3/2)/x^2, x)","F",0
141,0,0,0,0.000000," ","integrate((b*x^n)^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{\left(b x^{n}\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^n)^(3/2)/x^3, x)","F",0
142,0,0,0,0.000000," ","integrate((b*x^n)^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{\left(b x^{n}\right)^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate((b*x^n)^(3/2)/x^4, x)","F",0
143,0,0,0,0.000000," ","integrate(x^2/(b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{b x^{n}}}\,{d x}"," ",0,"integrate(x^2/sqrt(b*x^n), x)","F",0
144,0,0,0,0.000000," ","integrate(x/(b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{b x^{n}}}\,{d x}"," ",0,"integrate(x/sqrt(b*x^n), x)","F",0
145,0,0,0,0.000000," ","integrate(1/(b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{n}}}\,{d x}"," ",0,"integrate(1/sqrt(b*x^n), x)","F",0
146,0,0,0,0.000000," ","integrate(1/x/(b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{n}} x}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^n)*x), x)","F",0
147,0,0,0,0.000000," ","integrate(1/x^2/(b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{n}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^n)*x^2), x)","F",0
148,0,0,0,0.000000," ","integrate(1/x^3/(b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{n}} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^n)*x^3), x)","F",0
149,0,0,0,0.000000," ","integrate(x^2/(b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\left(b x^{n}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(b*x^n)^(3/2), x)","F",0
150,0,0,0,0.000000," ","integrate(x/(b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{x}{\left(b x^{n}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(b*x^n)^(3/2), x)","F",0
151,0,0,0,0.000000," ","integrate(1/(b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(b x^{n}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^n)^(-3/2), x)","F",0
152,0,0,0,0.000000," ","integrate(1/x/(b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(b x^{n}\right)^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((b*x^n)^(3/2)*x), x)","F",0
153,0,0,0,0.000000," ","integrate(1/x^2/(b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(b x^{n}\right)^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^n)^(3/2)*x^2), x)","F",0
154,0,0,0,0.000000," ","integrate(1/x^3/(b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(b x^{n}\right)^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^n)^(3/2)*x^3), x)","F",0
155,0,0,0,0.000000," ","integrate(1/x^4/(b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(b x^{n}\right)^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((b*x^n)^(3/2)*x^4), x)","F",0
156,0,0,0,0.000000," ","integrate(x^m/(a*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\left(a x^{n}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m/(a*x^n)^(3/2), x)","F",0
157,0,0,0,0.000000," ","integrate((c*x)^m/(a*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m}}{\left(a x^{n}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x)^m/(a*x^n)^(3/2), x)","F",0
158,0,0,0,0.000000," ","integrate(x^m*(b*x^n)^(3/2),x, algorithm=""giac"")","\int \left(b x^{n}\right)^{\frac{3}{2}} x^{m}\,{d x}"," ",0,"integrate((b*x^n)^(3/2)*x^m, x)","F",0
159,0,0,0,0.000000," ","integrate(x^m*(b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n}} x^{m}\,{d x}"," ",0,"integrate(sqrt(b*x^n)*x^m, x)","F",0
160,0,0,0,0.000000," ","integrate(x^m/(b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\sqrt{b x^{n}}}\,{d x}"," ",0,"integrate(x^m/sqrt(b*x^n), x)","F",0
161,0,0,0,0.000000," ","integrate(x^m/(b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\left(b x^{n}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m/(b*x^n)^(3/2), x)","F",0
162,0,0,0,0.000000," ","integrate((c*x)^m*(b*x^n)^(5/2),x, algorithm=""giac"")","\int \left(b x^{n}\right)^{\frac{5}{2}} \left(c x\right)^{m}\,{d x}"," ",0,"integrate((b*x^n)^(5/2)*(c*x)^m, x)","F",0
163,0,0,0,0.000000," ","integrate((c*x)^m*(b*x^n)^(3/2),x, algorithm=""giac"")","\int \left(b x^{n}\right)^{\frac{3}{2}} \left(c x\right)^{m}\,{d x}"," ",0,"integrate((b*x^n)^(3/2)*(c*x)^m, x)","F",0
164,0,0,0,0.000000," ","integrate((c*x)^m*(b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n}} \left(c x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(b*x^n)*(c*x)^m, x)","F",0
165,0,0,0,0.000000," ","integrate((c*x)^m/(b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m}}{\sqrt{b x^{n}}}\,{d x}"," ",0,"integrate((c*x)^m/sqrt(b*x^n), x)","F",0
166,0,0,0,0.000000," ","integrate((c*x)^m/(b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m}}{\left(b x^{n}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x)^m/(b*x^n)^(3/2), x)","F",0
167,0,0,0,0.000000," ","integrate((c*x)^m/(b*x^n)^(5/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m}}{\left(b x^{n}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x)^m/(b*x^n)^(5/2), x)","F",0
168,0,0,0,0.000000," ","integrate(x^(-1-3/2*n)*(b*x^n)^(3/2),x, algorithm=""giac"")","\int \left(b x^{n}\right)^{\frac{3}{2}} x^{-\frac{3}{2} \, n - 1}\,{d x}"," ",0,"integrate((b*x^n)^(3/2)*x^(-3/2*n - 1), x)","F",0
169,0,0,0,0.000000," ","integrate(x^(-1-1/2*n)*(b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n}} x^{-\frac{1}{2} \, n - 1}\,{d x}"," ",0,"integrate(sqrt(b*x^n)*x^(-1/2*n - 1), x)","F",0
170,1,14,0,0.212897," ","integrate(x^(-1+1/2*n)/(b*x^n)^(1/2),x, algorithm=""giac"")","\frac{\log\left(x^{n} {\left| b \right|}\right)}{\sqrt{b} n}"," ",0,"log(x^n*abs(b))/(sqrt(b)*n)","A",0
171,0,0,0,0.000000," ","integrate(x^(-1+3/2*n)/(b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{x^{\frac{3}{2} \, n - 1}}{\left(b x^{n}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^(3/2*n - 1)/(b*x^n)^(3/2), x)","F",0
172,1,24,0,0.171932," ","integrate(x^m*(b*x^n)^p,x, algorithm=""giac"")","\frac{x x^{m} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + m + 1}"," ",0,"x*x^m*e^(n*p*log(x) + p*log(b))/(n*p + m + 1)","A",0
173,1,29,0,0.208974," ","integrate((c*x)^m*(b*x^n)^p,x, algorithm=""giac"")","\frac{x e^{\left(n p \log\left(x\right) + p \log\left(b\right) + m \log\left(c\right) + m \log\left(x\right)\right)}}{n p + m + 1}"," ",0,"x*e^(n*p*log(x) + p*log(b) + m*log(c) + m*log(x))/(n*p + m + 1)","A",0
174,1,22,0,0.187444," ","integrate(x^2*(b*x^n)^p,x, algorithm=""giac"")","\frac{x^{3} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 3}"," ",0,"x^3*e^(n*p*log(x) + p*log(b))/(n*p + 3)","A",0
175,1,22,0,0.167401," ","integrate(x*(b*x^n)^p,x, algorithm=""giac"")","\frac{x^{2} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 2}"," ",0,"x^2*e^(n*p*log(x) + p*log(b))/(n*p + 2)","A",0
176,1,20,0,0.213353," ","integrate((b*x^n)^p,x, algorithm=""giac"")","\frac{x e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 1}"," ",0,"x*e^(n*p*log(x) + p*log(b))/(n*p + 1)","A",0
177,1,14,0,0.152098," ","integrate((b*x^n)^p/x,x, algorithm=""giac"")","\frac{\left(b x^{n}\right)^{p}}{n p}"," ",0,"(b*x^n)^p/(n*p)","A",0
178,0,0,0,0.000000," ","integrate((b*x^n)^p/x^2,x, algorithm=""giac"")","\int \frac{\left(b x^{n}\right)^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^n)^p/x^2, x)","F",0
179,0,0,0,0.000000," ","integrate((b*x^n)^p/x^3,x, algorithm=""giac"")","\int \frac{\left(b x^{n}\right)^{p}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^n)^p/x^3, x)","F",0
180,1,14,0,0.212354," ","integrate(x^m/((a*x^n)^(1/n)),x, algorithm=""giac"")","\frac{x^{m}}{a^{\left(\frac{1}{n}\right)} m}"," ",0,"x^m/(a^(1/n)*m)","A",0
181,1,21,0,0.222408," ","integrate((c*x)^m/((a*x^n)^(1/n)),x, algorithm=""giac"")","\frac{e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)}}{a^{\left(\frac{1}{n}\right)} m}"," ",0,"e^(m*log(c) + m*log(x))/(a^(1/n)*m)","A",0
182,1,12,0,0.191501," ","integrate(x^2/((a*x^n)^(1/n)),x, algorithm=""giac"")","\frac{x^{2}}{2 \, a^{\left(\frac{1}{n}\right)}}"," ",0,"1/2*x^2/a^(1/n)","A",0
183,1,9,0,0.172583," ","integrate(x/((a*x^n)^(1/n)),x, algorithm=""giac"")","\frac{x}{a^{\left(\frac{1}{n}\right)}}"," ",0,"x/a^(1/n)","A",0
184,1,10,0,0.179737," ","integrate(1/((a*x^n)^(1/n)),x, algorithm=""giac"")","\frac{\log\left(x\right)}{a^{\left(\frac{1}{n}\right)}}"," ",0,"log(x)/a^(1/n)","A",0
185,1,13,0,0.157001," ","integrate(1/x/((a*x^n)^(1/n)),x, algorithm=""giac"")","-\frac{1}{\left(a x^{n}\right)^{\left(\frac{1}{n}\right)}}"," ",0,"-1/(a*x^n)^(1/n)","A",0
186,0,0,0,0.000000," ","integrate(1/x^2/((a*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{1}{\left(a x^{n}\right)^{\left(\frac{1}{n}\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((a*x^n)^(1/n)*x^2), x)","F",0
187,0,0,0,0.000000," ","integrate(x^m/((a*x^n)^((1+m)/n)),x, algorithm=""giac"")","\int \frac{x^{m}}{\left(a x^{n}\right)^{\frac{m + 1}{n}}}\,{d x}"," ",0,"integrate(x^m/(a*x^n)^((m + 1)/n), x)","F",0
188,0,0,0,0.000000," ","integrate(x^(-n*p-1)*(a*x^n)^p,x, algorithm=""giac"")","\int \left(a x^{n}\right)^{p} x^{-n p - 1}\,{d x}"," ",0,"integrate((a*x^n)^p*x^(-n*p - 1), x)","F",0
189,1,31,0,0.233084," ","integrate(x^m*(a*(b*x^n)^p)^q,x, algorithm=""giac"")","\frac{x x^{m} e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{n p q + m + 1}"," ",0,"x*x^m*e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/(n*p*q + m + 1)","A",0
190,1,29,0,0.262052," ","integrate(x^2*(a*(b*x^n)^p)^q,x, algorithm=""giac"")","\frac{x^{3} e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{n p q + 3}"," ",0,"x^3*e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/(n*p*q + 3)","A",0
191,1,29,0,0.236743," ","integrate(x*(a*(b*x^n)^p)^q,x, algorithm=""giac"")","\frac{x^{2} e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{n p q + 2}"," ",0,"x^2*e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/(n*p*q + 2)","A",0
192,1,27,0,0.192337," ","integrate((a*(b*x^n)^p)^q,x, algorithm=""giac"")","\frac{x e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{n p q + 1}"," ",0,"x*e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/(n*p*q + 1)","A",0
193,1,21,0,0.162755," ","integrate((a*(b*x^n)^p)^q/x,x, algorithm=""giac"")","\frac{\left(\left(b x^{n}\right)^{p} a\right)^{q}}{n p q}"," ",0,"((b*x^n)^p*a)^q/(n*p*q)","A",0
194,0,0,0,0.000000," ","integrate((a*(b*x^n)^p)^q/x^2,x, algorithm=""giac"")","\int \frac{\left(\left(b x^{n}\right)^{p} a\right)^{q}}{x^{2}}\,{d x}"," ",0,"integrate(((b*x^n)^p*a)^q/x^2, x)","F",0
195,0,0,0,0.000000," ","integrate((a*(b*x^n)^p)^q/x^3,x, algorithm=""giac"")","\int \frac{\left(\left(b x^{n}\right)^{p} a\right)^{q}}{x^{3}}\,{d x}"," ",0,"integrate(((b*x^n)^p*a)^q/x^3, x)","F",0
196,1,21,0,0.236271," ","integrate(x^2/((a*(b*x^m)^n)^(1/m/n)),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} e^{\left(-\frac{n \log\left(b\right) + \log\left(a\right)}{m n}\right)}"," ",0,"1/2*x^2*e^(-(n*log(b) + log(a))/(m*n))","A",0
197,1,18,0,0.234496," ","integrate(x/((a*(b*x^m)^n)^(1/m/n)),x, algorithm=""giac"")","x e^{\left(-\frac{n \log\left(b\right) + \log\left(a\right)}{m n}\right)}"," ",0,"x*e^(-(n*log(b) + log(a))/(m*n))","A",0
198,1,19,0,0.202996," ","integrate(1/((a*(b*x^m)^n)^(1/m/n)),x, algorithm=""giac"")","e^{\left(-\frac{n \log\left(b\right) + \log\left(a\right)}{m n}\right)} \log\left(x\right)"," ",0,"e^(-(n*log(b) + log(a))/(m*n))*log(x)","A",0
199,1,21,0,0.168962," ","integrate(1/x/((a*(b*x^m)^n)^(1/m/n)),x, algorithm=""giac"")","-\frac{1}{\left(\left(b x^{m}\right)^{n} a\right)^{\frac{1}{m n}}}"," ",0,"-1/((b*x^m)^n*a)^(1/(m*n))","A",0
200,0,0,0,0.000000," ","integrate(1/x^2/((a*(b*x^m)^n)^(1/m/n)),x, algorithm=""giac"")","\int \frac{1}{\left(\left(b x^{m}\right)^{n} a\right)^{\frac{1}{m n}} x^{2}}\,{d x}"," ",0,"integrate(1/(((b*x^m)^n*a)^(1/(m*n))*x^2), x)","F",0
201,1,18,0,0.276688," ","integrate(x^(-n*p*q+2)*(a*(b*x^n)^p)^q,x, algorithm=""giac"")","\frac{1}{3} \, x e^{\left(p q \log\left(b\right) + q \log\left(a\right) + 2 \, \log\left(x\right)\right)}"," ",0,"1/3*x*e^(p*q*log(b) + q*log(a) + 2*log(x))","A",0
202,1,16,0,0.277501," ","integrate(x^(-n*p*q+1)*(a*(b*x^n)^p)^q,x, algorithm=""giac"")","\frac{1}{2} \, x e^{\left(p q \log\left(b\right) + q \log\left(a\right) + \log\left(x\right)\right)}"," ",0,"1/2*x*e^(p*q*log(b) + q*log(a) + log(x))","A",0
203,1,27,0,0.426270," ","integrate((a*(b*x^n)^p)^q/(x^(n*p*q)),x, algorithm=""giac"")","\frac{x e^{\left(n p q \log\left(x\right) + p q \log\left(b\right) + q \log\left(a\right)\right)}}{x^{n p q}}"," ",0,"x*e^(n*p*q*log(x) + p*q*log(b) + q*log(a))/x^(n*p*q)","A",0
204,0,0,0,0.000000," ","integrate(x^(-n*p*q-1)*(a*(b*x^n)^p)^q,x, algorithm=""giac"")","\int \left(\left(b x^{n}\right)^{p} a\right)^{q} x^{-n p q - 1}\,{d x}"," ",0,"integrate(((b*x^n)^p*a)^q*x^(-n*p*q - 1), x)","F",0
205,1,18,0,0.279830," ","integrate(x^(-n*p*q-2)*(a*(b*x^n)^p)^q,x, algorithm=""giac"")","-x e^{\left(p q \log\left(b\right) + q \log\left(a\right) - 2 \, \log\left(x\right)\right)}"," ",0,"-x*e^(p*q*log(b) + q*log(a) - 2*log(x))","A",0
206,1,13,0,0.149241," ","integrate(x^3*(b*x^3+a),x, algorithm=""giac"")","\frac{1}{7} \, b x^{7} + \frac{1}{4} \, a x^{4}"," ",0,"1/7*b*x^7 + 1/4*a*x^4","A",0
207,1,13,0,0.165145," ","integrate(x^2*(b*x^3+a),x, algorithm=""giac"")","\frac{1}{6} \, b x^{6} + \frac{1}{3} \, a x^{3}"," ",0,"1/6*b*x^6 + 1/3*a*x^3","A",0
208,1,13,0,0.151946," ","integrate(x*(b*x^3+a),x, algorithm=""giac"")","\frac{1}{5} \, b x^{5} + \frac{1}{2} \, a x^{2}"," ",0,"1/5*b*x^5 + 1/2*a*x^2","A",0
209,1,10,0,0.151661," ","integrate(b*x^3+a,x, algorithm=""giac"")","\frac{1}{4} \, b x^{4} + a x"," ",0,"1/4*b*x^4 + a*x","A",0
210,1,12,0,0.160422," ","integrate((b*x^3+a)/x,x, algorithm=""giac"")","\frac{1}{3} \, b x^{3} + a \log\left({\left| x \right|}\right)"," ",0,"1/3*b*x^3 + a*log(abs(x))","A",0
211,1,13,0,0.149689," ","integrate((b*x^3+a)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, b x^{2} - \frac{a}{x}"," ",0,"1/2*b*x^2 - a/x","A",0
212,1,10,0,0.162111," ","integrate((b*x^3+a)/x^3,x, algorithm=""giac"")","b x - \frac{a}{2 \, x^{2}}"," ",0,"b*x - 1/2*a/x^2","A",0
213,1,18,0,0.148627," ","integrate((b*x^3+a)/x^4,x, algorithm=""giac"")","b \log\left({\left| x \right|}\right) - \frac{b x^{3} + a}{3 \, x^{3}}"," ",0,"b*log(abs(x)) - 1/3*(b*x^3 + a)/x^3","A",0
214,1,13,0,0.177073," ","integrate((b*x^3+a)/x^5,x, algorithm=""giac"")","-\frac{4 \, b x^{3} + a}{4 \, x^{4}}"," ",0,"-1/4*(4*b*x^3 + a)/x^4","A",0
215,1,15,0,0.147070," ","integrate((b*x^3+a)/x^6,x, algorithm=""giac"")","-\frac{5 \, b x^{3} + 2 \, a}{10 \, x^{5}}"," ",0,"-1/10*(5*b*x^3 + 2*a)/x^5","A",0
216,1,13,0,0.145705," ","integrate((b*x^3+a)/x^7,x, algorithm=""giac"")","-\frac{2 \, b x^{3} + a}{6 \, x^{6}}"," ",0,"-1/6*(2*b*x^3 + a)/x^6","A",0
217,1,15,0,0.179098," ","integrate((b*x^3+a)/x^8,x, algorithm=""giac"")","-\frac{7 \, b x^{3} + 4 \, a}{28 \, x^{7}}"," ",0,"-1/28*(7*b*x^3 + 4*a)/x^7","A",0
218,1,24,0,0.149121," ","integrate(x^4*(b*x^3+a)^2,x, algorithm=""giac"")","\frac{1}{11} \, b^{2} x^{11} + \frac{1}{4} \, a b x^{8} + \frac{1}{5} \, a^{2} x^{5}"," ",0,"1/11*b^2*x^11 + 1/4*a*b*x^8 + 1/5*a^2*x^5","A",0
219,1,24,0,0.180532," ","integrate(x^3*(b*x^3+a)^2,x, algorithm=""giac"")","\frac{1}{10} \, b^{2} x^{10} + \frac{2}{7} \, a b x^{7} + \frac{1}{4} \, a^{2} x^{4}"," ",0,"1/10*b^2*x^10 + 2/7*a*b*x^7 + 1/4*a^2*x^4","A",0
220,1,14,0,0.157563," ","integrate(x^2*(b*x^3+a)^2,x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{3}}{9 \, b}"," ",0,"1/9*(b*x^3 + a)^3/b","A",0
221,1,24,0,0.167177," ","integrate(x*(b*x^3+a)^2,x, algorithm=""giac"")","\frac{1}{8} \, b^{2} x^{8} + \frac{2}{5} \, a b x^{5} + \frac{1}{2} \, a^{2} x^{2}"," ",0,"1/8*b^2*x^8 + 2/5*a*b*x^5 + 1/2*a^2*x^2","A",0
222,1,21,0,0.149567," ","integrate((b*x^3+a)^2,x, algorithm=""giac"")","\frac{1}{7} \, b^{2} x^{7} + \frac{1}{2} \, a b x^{4} + a^{2} x"," ",0,"1/7*b^2*x^7 + 1/2*a*b*x^4 + a^2*x","A",0
223,1,23,0,0.145579," ","integrate((b*x^3+a)^2/x,x, algorithm=""giac"")","\frac{1}{6} \, b^{2} x^{6} + \frac{2}{3} \, a b x^{3} + a^{2} \log\left({\left| x \right|}\right)"," ",0,"1/6*b^2*x^6 + 2/3*a*b*x^3 + a^2*log(abs(x))","A",0
224,1,23,0,0.148549," ","integrate((b*x^3+a)^2/x^2,x, algorithm=""giac"")","\frac{1}{5} \, b^{2} x^{5} + a b x^{2} - \frac{a^{2}}{x}"," ",0,"1/5*b^2*x^5 + a*b*x^2 - a^2/x","A",0
225,1,22,0,0.164286," ","integrate((b*x^3+a)^2/x^3,x, algorithm=""giac"")","\frac{1}{4} \, b^{2} x^{4} + 2 \, a b x - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/4*b^2*x^4 + 2*a*b*x - 1/2*a^2/x^2","A",0
226,1,32,0,0.185951," ","integrate((b*x^3+a)^2/x^4,x, algorithm=""giac"")","\frac{1}{3} \, b^{2} x^{3} + 2 \, a b \log\left({\left| x \right|}\right) - \frac{2 \, a b x^{3} + a^{2}}{3 \, x^{3}}"," ",0,"1/3*b^2*x^3 + 2*a*b*log(abs(x)) - 1/3*(2*a*b*x^3 + a^2)/x^3","A",0
227,1,25,0,0.151966," ","integrate((b*x^3+a)^2/x^5,x, algorithm=""giac"")","\frac{1}{2} \, b^{2} x^{2} - \frac{8 \, a b x^{3} + a^{2}}{4 \, x^{4}}"," ",0,"1/2*b^2*x^2 - 1/4*(8*a*b*x^3 + a^2)/x^4","A",0
228,1,22,0,0.158862," ","integrate((b*x^3+a)^2/x^6,x, algorithm=""giac"")","b^{2} x - \frac{5 \, a b x^{3} + a^{2}}{5 \, x^{5}}"," ",0,"b^2*x - 1/5*(5*a*b*x^3 + a^2)/x^5","A",0
229,1,32,0,0.147125," ","integrate((b*x^3+a)^2/x^7,x, algorithm=""giac"")","b^{2} \log\left({\left| x \right|}\right) - \frac{3 \, b^{2} x^{6} + 4 \, a b x^{3} + a^{2}}{6 \, x^{6}}"," ",0,"b^2*log(abs(x)) - 1/6*(3*b^2*x^6 + 4*a*b*x^3 + a^2)/x^6","A",0
230,1,26,0,0.233948," ","integrate((b*x^3+a)^2/x^8,x, algorithm=""giac"")","-\frac{14 \, b^{2} x^{6} + 7 \, a b x^{3} + 2 \, a^{2}}{14 \, x^{7}}"," ",0,"-1/14*(14*b^2*x^6 + 7*a*b*x^3 + 2*a^2)/x^7","A",0
231,1,26,0,0.171197," ","integrate((b*x^3+a)^2/x^9,x, algorithm=""giac"")","-\frac{20 \, b^{2} x^{6} + 16 \, a b x^{3} + 5 \, a^{2}}{40 \, x^{8}}"," ",0,"-1/40*(20*b^2*x^6 + 16*a*b*x^3 + 5*a^2)/x^8","A",0
232,1,24,0,0.148704," ","integrate((b*x^3+a)^2/x^10,x, algorithm=""giac"")","-\frac{3 \, b^{2} x^{6} + 3 \, a b x^{3} + a^{2}}{9 \, x^{9}}"," ",0,"-1/9*(3*b^2*x^6 + 3*a*b*x^3 + a^2)/x^9","A",0
233,1,26,0,0.175413," ","integrate((b*x^3+a)^2/x^11,x, algorithm=""giac"")","-\frac{35 \, b^{2} x^{6} + 40 \, a b x^{3} + 14 \, a^{2}}{140 \, x^{10}}"," ",0,"-1/140*(35*b^2*x^6 + 40*a*b*x^3 + 14*a^2)/x^10","A",0
234,1,26,0,0.149493," ","integrate((b*x^3+a)^2/x^12,x, algorithm=""giac"")","-\frac{44 \, b^{2} x^{6} + 55 \, a b x^{3} + 20 \, a^{2}}{220 \, x^{11}}"," ",0,"-1/220*(44*b^2*x^6 + 55*a*b*x^3 + 20*a^2)/x^11","A",0
235,1,26,0,0.151305," ","integrate((b*x^3+a)^2/x^13,x, algorithm=""giac"")","-\frac{6 \, b^{2} x^{6} + 8 \, a b x^{3} + 3 \, a^{2}}{36 \, x^{12}}"," ",0,"-1/36*(6*b^2*x^6 + 8*a*b*x^3 + 3*a^2)/x^12","A",0
236,1,35,0,0.150191," ","integrate(x^14*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{1}{24} \, b^{3} x^{24} + \frac{1}{7} \, a b^{2} x^{21} + \frac{1}{6} \, a^{2} b x^{18} + \frac{1}{15} \, a^{3} x^{15}"," ",0,"1/24*b^3*x^24 + 1/7*a*b^2*x^21 + 1/6*a^2*b*x^18 + 1/15*a^3*x^15","A",0
237,1,35,0,0.264696," ","integrate(x^11*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{1}{21} \, b^{3} x^{21} + \frac{1}{6} \, a b^{2} x^{18} + \frac{1}{5} \, a^{2} b x^{15} + \frac{1}{12} \, a^{3} x^{12}"," ",0,"1/21*b^3*x^21 + 1/6*a*b^2*x^18 + 1/5*a^2*b*x^15 + 1/12*a^3*x^12","A",0
238,1,35,0,0.155051," ","integrate(x^8*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{1}{18} \, b^{3} x^{18} + \frac{1}{5} \, a b^{2} x^{15} + \frac{1}{4} \, a^{2} b x^{12} + \frac{1}{9} \, a^{3} x^{9}"," ",0,"1/18*b^3*x^18 + 1/5*a*b^2*x^15 + 1/4*a^2*b*x^12 + 1/9*a^3*x^9","A",0
239,1,35,0,0.161585," ","integrate(x^5*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{1}{15} \, b^{3} x^{15} + \frac{1}{4} \, a b^{2} x^{12} + \frac{1}{3} \, a^{2} b x^{9} + \frac{1}{6} \, a^{3} x^{6}"," ",0,"1/15*b^3*x^15 + 1/4*a*b^2*x^12 + 1/3*a^2*b*x^9 + 1/6*a^3*x^6","A",0
240,1,14,0,0.148770," ","integrate(x^2*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{4}}{12 \, b}"," ",0,"1/12*(b*x^3 + a)^4/b","A",0
241,1,33,0,0.150407," ","integrate((b*x^3+a)^3/x,x, algorithm=""giac"")","\frac{1}{9} \, b^{3} x^{9} + \frac{1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + a^{3} \log\left({\left| x \right|}\right)"," ",0,"1/9*b^3*x^9 + 1/2*a*b^2*x^6 + a^2*b*x^3 + a^3*log(abs(x))","A",0
242,1,44,0,0.165049," ","integrate((b*x^3+a)^3/x^4,x, algorithm=""giac"")","\frac{1}{6} \, b^{3} x^{6} + a b^{2} x^{3} + 3 \, a^{2} b \log\left({\left| x \right|}\right) - \frac{3 \, a^{2} b x^{3} + a^{3}}{3 \, x^{3}}"," ",0,"1/6*b^3*x^6 + a*b^2*x^3 + 3*a^2*b*log(abs(x)) - 1/3*(3*a^2*b*x^3 + a^3)/x^3","A",0
243,1,45,0,0.187485," ","integrate((b*x^3+a)^3/x^7,x, algorithm=""giac"")","\frac{1}{3} \, b^{3} x^{3} + 3 \, a b^{2} \log\left({\left| x \right|}\right) - \frac{9 \, a b^{2} x^{6} + 6 \, a^{2} b x^{3} + a^{3}}{6 \, x^{6}}"," ",0,"1/3*b^3*x^3 + 3*a*b^2*log(abs(x)) - 1/6*(9*a*b^2*x^6 + 6*a^2*b*x^3 + a^3)/x^6","A",0
244,1,45,0,0.155126," ","integrate((b*x^3+a)^3/x^10,x, algorithm=""giac"")","b^{3} \log\left({\left| x \right|}\right) - \frac{11 \, b^{3} x^{9} + 18 \, a b^{2} x^{6} + 9 \, a^{2} b x^{3} + 2 \, a^{3}}{18 \, x^{9}}"," ",0,"b^3*log(abs(x)) - 1/18*(11*b^3*x^9 + 18*a*b^2*x^6 + 9*a^2*b*x^3 + 2*a^3)/x^9","A",0
245,1,35,0,0.154376," ","integrate((b*x^3+a)^3/x^13,x, algorithm=""giac"")","-\frac{4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}}"," ",0,"-1/12*(4*b^3*x^9 + 6*a*b^2*x^6 + 4*a^2*b*x^3 + a^3)/x^12","B",0
246,1,37,0,0.167840," ","integrate((b*x^3+a)^3/x^16,x, algorithm=""giac"")","-\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}}"," ",0,"-1/60*(10*b^3*x^9 + 20*a*b^2*x^6 + 15*a^2*b*x^3 + 4*a^3)/x^15","A",0
247,1,37,0,0.151342," ","integrate((b*x^3+a)^3/x^19,x, algorithm=""giac"")","-\frac{20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}}"," ",0,"-1/180*(20*b^3*x^9 + 45*a*b^2*x^6 + 36*a^2*b*x^3 + 10*a^3)/x^18","A",0
248,1,37,0,0.150616," ","integrate((b*x^3+a)^3/x^22,x, algorithm=""giac"")","-\frac{35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}}"," ",0,"-1/420*(35*b^3*x^9 + 84*a*b^2*x^6 + 70*a^2*b*x^3 + 20*a^3)/x^21","A",0
249,1,35,0,0.228859," ","integrate(x^4*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{1}{14} \, b^{3} x^{14} + \frac{3}{11} \, a b^{2} x^{11} + \frac{3}{8} \, a^{2} b x^{8} + \frac{1}{5} \, a^{3} x^{5}"," ",0,"1/14*b^3*x^14 + 3/11*a*b^2*x^11 + 3/8*a^2*b*x^8 + 1/5*a^3*x^5","A",0
250,1,35,0,0.178497," ","integrate(x^3*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{3} x^{13} + \frac{3}{10} \, a b^{2} x^{10} + \frac{3}{7} \, a^{2} b x^{7} + \frac{1}{4} \, a^{3} x^{4}"," ",0,"1/13*b^3*x^13 + 3/10*a*b^2*x^10 + 3/7*a^2*b*x^7 + 1/4*a^3*x^4","A",0
251,1,35,0,0.151860," ","integrate(x*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{1}{11} \, b^{3} x^{11} + \frac{3}{8} \, a b^{2} x^{8} + \frac{3}{5} \, a^{2} b x^{5} + \frac{1}{2} \, a^{3} x^{2}"," ",0,"1/11*b^3*x^11 + 3/8*a*b^2*x^8 + 3/5*a^2*b*x^5 + 1/2*a^3*x^2","A",0
252,1,32,0,0.159359," ","integrate((b*x^3+a)^3,x, algorithm=""giac"")","\frac{1}{10} \, b^{3} x^{10} + \frac{3}{7} \, a b^{2} x^{7} + \frac{3}{4} \, a^{2} b x^{4} + a^{3} x"," ",0,"1/10*b^3*x^10 + 3/7*a*b^2*x^7 + 3/4*a^2*b*x^4 + a^3*x","A",0
253,1,35,0,0.193306," ","integrate((b*x^3+a)^3/x^2,x, algorithm=""giac"")","\frac{1}{8} \, b^{3} x^{8} + \frac{3}{5} \, a b^{2} x^{5} + \frac{3}{2} \, a^{2} b x^{2} - \frac{a^{3}}{x}"," ",0,"1/8*b^3*x^8 + 3/5*a*b^2*x^5 + 3/2*a^2*b*x^2 - a^3/x","A",0
254,1,33,0,0.154360," ","integrate((b*x^3+a)^3/x^3,x, algorithm=""giac"")","\frac{1}{7} \, b^{3} x^{7} + \frac{3}{4} \, a b^{2} x^{4} + 3 \, a^{2} b x - \frac{a^{3}}{2 \, x^{2}}"," ",0,"1/7*b^3*x^7 + 3/4*a*b^2*x^4 + 3*a^2*b*x - 1/2*a^3/x^2","A",0
255,1,36,0,0.178421," ","integrate((b*x^3+a)^3/x^5,x, algorithm=""giac"")","\frac{1}{5} \, b^{3} x^{5} + \frac{3}{2} \, a b^{2} x^{2} - \frac{12 \, a^{2} b x^{3} + a^{3}}{4 \, x^{4}}"," ",0,"1/5*b^3*x^5 + 3/2*a*b^2*x^2 - 1/4*(12*a^2*b*x^3 + a^3)/x^4","A",0
256,1,36,0,0.153395," ","integrate((b*x^3+a)^3/x^6,x, algorithm=""giac"")","\frac{1}{4} \, b^{3} x^{4} + 3 \, a b^{2} x - \frac{15 \, a^{2} b x^{3} + 2 \, a^{3}}{10 \, x^{5}}"," ",0,"1/4*b^3*x^4 + 3*a*b^2*x - 1/10*(15*a^2*b*x^3 + 2*a^3)/x^5","A",0
257,1,38,0,0.161113," ","integrate((b*x^3+a)^3/x^8,x, algorithm=""giac"")","\frac{1}{2} \, b^{3} x^{2} - \frac{84 \, a b^{2} x^{6} + 21 \, a^{2} b x^{3} + 4 \, a^{3}}{28 \, x^{7}}"," ",0,"1/2*b^3*x^2 - 1/28*(84*a*b^2*x^6 + 21*a^2*b*x^3 + 4*a^3)/x^7","A",0
258,1,57,0,0.207921," ","integrate(x^17*(b*x^3+a)^5,x, algorithm=""giac"")","\frac{1}{33} \, b^{5} x^{33} + \frac{1}{6} \, a b^{4} x^{30} + \frac{10}{27} \, a^{2} b^{3} x^{27} + \frac{5}{12} \, a^{3} b^{2} x^{24} + \frac{5}{21} \, a^{4} b x^{21} + \frac{1}{18} \, a^{5} x^{18}"," ",0,"1/33*b^5*x^33 + 1/6*a*b^4*x^30 + 10/27*a^2*b^3*x^27 + 5/12*a^3*b^2*x^24 + 5/21*a^4*b*x^21 + 1/18*a^5*x^18","A",0
259,1,57,0,0.166578," ","integrate(x^14*(b*x^3+a)^5,x, algorithm=""giac"")","\frac{1}{30} \, b^{5} x^{30} + \frac{5}{27} \, a b^{4} x^{27} + \frac{5}{12} \, a^{2} b^{3} x^{24} + \frac{10}{21} \, a^{3} b^{2} x^{21} + \frac{5}{18} \, a^{4} b x^{18} + \frac{1}{15} \, a^{5} x^{15}"," ",0,"1/30*b^5*x^30 + 5/27*a*b^4*x^27 + 5/12*a^2*b^3*x^24 + 10/21*a^3*b^2*x^21 + 5/18*a^4*b*x^18 + 1/15*a^5*x^15","A",0
260,1,57,0,0.154105," ","integrate(x^11*(b*x^3+a)^5,x, algorithm=""giac"")","\frac{1}{27} \, b^{5} x^{27} + \frac{5}{24} \, a b^{4} x^{24} + \frac{10}{21} \, a^{2} b^{3} x^{21} + \frac{5}{9} \, a^{3} b^{2} x^{18} + \frac{1}{3} \, a^{4} b x^{15} + \frac{1}{12} \, a^{5} x^{12}"," ",0,"1/27*b^5*x^27 + 5/24*a*b^4*x^24 + 10/21*a^2*b^3*x^21 + 5/9*a^3*b^2*x^18 + 1/3*a^4*b*x^15 + 1/12*a^5*x^12","A",0
261,1,57,0,0.152705," ","integrate(x^8*(b*x^3+a)^5,x, algorithm=""giac"")","\frac{1}{24} \, b^{5} x^{24} + \frac{5}{21} \, a b^{4} x^{21} + \frac{5}{9} \, a^{2} b^{3} x^{18} + \frac{2}{3} \, a^{3} b^{2} x^{15} + \frac{5}{12} \, a^{4} b x^{12} + \frac{1}{9} \, a^{5} x^{9}"," ",0,"1/24*b^5*x^24 + 5/21*a*b^4*x^21 + 5/9*a^2*b^3*x^18 + 2/3*a^3*b^2*x^15 + 5/12*a^4*b*x^12 + 1/9*a^5*x^9","A",0
262,1,57,0,0.153273," ","integrate(x^5*(b*x^3+a)^5,x, algorithm=""giac"")","\frac{1}{21} \, b^{5} x^{21} + \frac{5}{18} \, a b^{4} x^{18} + \frac{2}{3} \, a^{2} b^{3} x^{15} + \frac{5}{6} \, a^{3} b^{2} x^{12} + \frac{5}{9} \, a^{4} b x^{9} + \frac{1}{6} \, a^{5} x^{6}"," ",0,"1/21*b^5*x^21 + 5/18*a*b^4*x^18 + 2/3*a^2*b^3*x^15 + 5/6*a^3*b^2*x^12 + 5/9*a^4*b*x^9 + 1/6*a^5*x^6","A",0
263,1,14,0,0.159398," ","integrate(x^2*(b*x^3+a)^5,x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{6}}{18 \, b}"," ",0,"1/18*(b*x^3 + a)^6/b","A",0
264,1,56,0,0.151614," ","integrate((b*x^3+a)^5/x,x, algorithm=""giac"")","\frac{1}{15} \, b^{5} x^{15} + \frac{5}{12} \, a b^{4} x^{12} + \frac{10}{9} \, a^{2} b^{3} x^{9} + \frac{5}{3} \, a^{3} b^{2} x^{6} + \frac{5}{3} \, a^{4} b x^{3} + a^{5} \log\left({\left| x \right|}\right)"," ",0,"1/15*b^5*x^15 + 5/12*a*b^4*x^12 + 10/9*a^2*b^3*x^9 + 5/3*a^3*b^2*x^6 + 5/3*a^4*b*x^3 + a^5*log(abs(x))","A",0
265,1,67,0,0.149613," ","integrate((b*x^3+a)^5/x^4,x, algorithm=""giac"")","\frac{1}{12} \, b^{5} x^{12} + \frac{5}{9} \, a b^{4} x^{9} + \frac{5}{3} \, a^{2} b^{3} x^{6} + \frac{10}{3} \, a^{3} b^{2} x^{3} + 5 \, a^{4} b \log\left({\left| x \right|}\right) - \frac{5 \, a^{4} b x^{3} + a^{5}}{3 \, x^{3}}"," ",0,"1/12*b^5*x^12 + 5/9*a*b^4*x^9 + 5/3*a^2*b^3*x^6 + 10/3*a^3*b^2*x^3 + 5*a^4*b*log(abs(x)) - 1/3*(5*a^4*b*x^3 + a^5)/x^3","A",0
266,1,69,0,0.152118," ","integrate((b*x^3+a)^5/x^7,x, algorithm=""giac"")","\frac{1}{9} \, b^{5} x^{9} + \frac{5}{6} \, a b^{4} x^{6} + \frac{10}{3} \, a^{2} b^{3} x^{3} + 10 \, a^{3} b^{2} \log\left({\left| x \right|}\right) - \frac{30 \, a^{3} b^{2} x^{6} + 10 \, a^{4} b x^{3} + a^{5}}{6 \, x^{6}}"," ",0,"1/9*b^5*x^9 + 5/6*a*b^4*x^6 + 10/3*a^2*b^3*x^3 + 10*a^3*b^2*log(abs(x)) - 1/6*(30*a^3*b^2*x^6 + 10*a^4*b*x^3 + a^5)/x^6","A",0
267,1,71,0,0.191390," ","integrate((b*x^3+a)^5/x^10,x, algorithm=""giac"")","\frac{1}{6} \, b^{5} x^{6} + \frac{5}{3} \, a b^{4} x^{3} + 10 \, a^{2} b^{3} \log\left({\left| x \right|}\right) - \frac{110 \, a^{2} b^{3} x^{9} + 60 \, a^{3} b^{2} x^{6} + 15 \, a^{4} b x^{3} + 2 \, a^{5}}{18 \, x^{9}}"," ",0,"1/6*b^5*x^6 + 5/3*a*b^4*x^3 + 10*a^2*b^3*log(abs(x)) - 1/18*(110*a^2*b^3*x^9 + 60*a^3*b^2*x^6 + 15*a^4*b*x^3 + 2*a^5)/x^9","A",0
268,1,69,0,0.155265," ","integrate((b*x^3+a)^5/x^13,x, algorithm=""giac"")","\frac{1}{3} \, b^{5} x^{3} + 5 \, a b^{4} \log\left({\left| x \right|}\right) - \frac{125 \, a b^{4} x^{12} + 120 \, a^{2} b^{3} x^{9} + 60 \, a^{3} b^{2} x^{6} + 20 \, a^{4} b x^{3} + 3 \, a^{5}}{36 \, x^{12}}"," ",0,"1/3*b^5*x^3 + 5*a*b^4*log(abs(x)) - 1/36*(125*a*b^4*x^12 + 120*a^2*b^3*x^9 + 60*a^3*b^2*x^6 + 20*a^4*b*x^3 + 3*a^5)/x^12","A",0
269,1,67,0,0.161363," ","integrate((b*x^3+a)^5/x^16,x, algorithm=""giac"")","b^{5} \log\left({\left| x \right|}\right) - \frac{137 \, b^{5} x^{15} + 300 \, a b^{4} x^{12} + 300 \, a^{2} b^{3} x^{9} + 200 \, a^{3} b^{2} x^{6} + 75 \, a^{4} b x^{3} + 12 \, a^{5}}{180 \, x^{15}}"," ",0,"b^5*log(abs(x)) - 1/180*(137*b^5*x^15 + 300*a*b^4*x^12 + 300*a^2*b^3*x^9 + 200*a^3*b^2*x^6 + 75*a^4*b*x^3 + 12*a^5)/x^15","A",0
270,1,57,0,0.255550," ","integrate((b*x^3+a)^5/x^19,x, algorithm=""giac"")","-\frac{6 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 20 \, a^{2} b^{3} x^{9} + 15 \, a^{3} b^{2} x^{6} + 6 \, a^{4} b x^{3} + a^{5}}{18 \, x^{18}}"," ",0,"-1/18*(6*b^5*x^15 + 15*a*b^4*x^12 + 20*a^2*b^3*x^9 + 15*a^3*b^2*x^6 + 6*a^4*b*x^3 + a^5)/x^18","B",0
271,1,59,0,0.173777," ","integrate((b*x^3+a)^5/x^22,x, algorithm=""giac"")","-\frac{21 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 105 \, a^{2} b^{3} x^{9} + 84 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 6 \, a^{5}}{126 \, x^{21}}"," ",0,"-1/126*(21*b^5*x^15 + 70*a*b^4*x^12 + 105*a^2*b^3*x^9 + 84*a^3*b^2*x^6 + 35*a^4*b*x^3 + 6*a^5)/x^21","A",0
272,1,59,0,0.151399," ","integrate((b*x^3+a)^5/x^25,x, algorithm=""giac"")","-\frac{56 \, b^{5} x^{15} + 210 \, a b^{4} x^{12} + 336 \, a^{2} b^{3} x^{9} + 280 \, a^{3} b^{2} x^{6} + 120 \, a^{4} b x^{3} + 21 \, a^{5}}{504 \, x^{24}}"," ",0,"-1/504*(56*b^5*x^15 + 210*a*b^4*x^12 + 336*a^2*b^3*x^9 + 280*a^3*b^2*x^6 + 120*a^4*b*x^3 + 21*a^5)/x^24","A",0
273,1,59,0,0.150922," ","integrate((b*x^3+a)^5/x^28,x, algorithm=""giac"")","-\frac{126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}}"," ",0,"-1/1512*(126*b^5*x^15 + 504*a*b^4*x^12 + 840*a^2*b^3*x^9 + 720*a^3*b^2*x^6 + 315*a^4*b*x^3 + 56*a^5)/x^27","A",0
274,1,59,0,0.171095," ","integrate((b*x^3+a)^5/x^31,x, algorithm=""giac"")","-\frac{252 \, b^{5} x^{15} + 1050 \, a b^{4} x^{12} + 1800 \, a^{2} b^{3} x^{9} + 1575 \, a^{3} b^{2} x^{6} + 700 \, a^{4} b x^{3} + 126 \, a^{5}}{3780 \, x^{30}}"," ",0,"-1/3780*(252*b^5*x^15 + 1050*a*b^4*x^12 + 1800*a^2*b^3*x^9 + 1575*a^3*b^2*x^6 + 700*a^4*b*x^3 + 126*a^5)/x^30","A",0
275,1,57,0,0.148965," ","integrate(x^4*(b*x^3+a)^5,x, algorithm=""giac"")","\frac{1}{20} \, b^{5} x^{20} + \frac{5}{17} \, a b^{4} x^{17} + \frac{5}{7} \, a^{2} b^{3} x^{14} + \frac{10}{11} \, a^{3} b^{2} x^{11} + \frac{5}{8} \, a^{4} b x^{8} + \frac{1}{5} \, a^{5} x^{5}"," ",0,"1/20*b^5*x^20 + 5/17*a*b^4*x^17 + 5/7*a^2*b^3*x^14 + 10/11*a^3*b^2*x^11 + 5/8*a^4*b*x^8 + 1/5*a^5*x^5","A",0
276,1,56,0,0.182271," ","integrate(x^3*(b*x^3+a)^5,x, algorithm=""giac"")","\frac{1}{19} \, b^{5} x^{19} + \frac{5}{16} \, a b^{4} x^{16} + \frac{10}{13} \, a^{2} b^{3} x^{13} + a^{3} b^{2} x^{10} + \frac{5}{7} \, a^{4} b x^{7} + \frac{1}{4} \, a^{5} x^{4}"," ",0,"1/19*b^5*x^19 + 5/16*a*b^4*x^16 + 10/13*a^2*b^3*x^13 + a^3*b^2*x^10 + 5/7*a^4*b*x^7 + 1/4*a^5*x^4","A",0
277,1,56,0,0.207683," ","integrate(x*(b*x^3+a)^5,x, algorithm=""giac"")","\frac{1}{17} \, b^{5} x^{17} + \frac{5}{14} \, a b^{4} x^{14} + \frac{10}{11} \, a^{2} b^{3} x^{11} + \frac{5}{4} \, a^{3} b^{2} x^{8} + a^{4} b x^{5} + \frac{1}{2} \, a^{5} x^{2}"," ",0,"1/17*b^5*x^17 + 5/14*a*b^4*x^14 + 10/11*a^2*b^3*x^11 + 5/4*a^3*b^2*x^8 + a^4*b*x^5 + 1/2*a^5*x^2","A",0
278,1,53,0,0.147198," ","integrate((b*x^3+a)^5,x, algorithm=""giac"")","\frac{1}{16} \, b^{5} x^{16} + \frac{5}{13} \, a b^{4} x^{13} + a^{2} b^{3} x^{10} + \frac{10}{7} \, a^{3} b^{2} x^{7} + \frac{5}{4} \, a^{4} b x^{4} + a^{5} x"," ",0,"1/16*b^5*x^16 + 5/13*a*b^4*x^13 + a^2*b^3*x^10 + 10/7*a^3*b^2*x^7 + 5/4*a^4*b*x^4 + a^5*x","A",0
279,1,57,0,0.181481," ","integrate((b*x^3+a)^5/x^2,x, algorithm=""giac"")","\frac{1}{14} \, b^{5} x^{14} + \frac{5}{11} \, a b^{4} x^{11} + \frac{5}{4} \, a^{2} b^{3} x^{8} + 2 \, a^{3} b^{2} x^{5} + \frac{5}{2} \, a^{4} b x^{2} - \frac{a^{5}}{x}"," ",0,"1/14*b^5*x^14 + 5/11*a*b^4*x^11 + 5/4*a^2*b^3*x^8 + 2*a^3*b^2*x^5 + 5/2*a^4*b*x^2 - a^5/x","A",0
280,1,55,0,0.366383," ","integrate((b*x^3+a)^5/x^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{5} x^{13} + \frac{1}{2} \, a b^{4} x^{10} + \frac{10}{7} \, a^{2} b^{3} x^{7} + \frac{5}{2} \, a^{3} b^{2} x^{4} + 5 \, a^{4} b x - \frac{a^{5}}{2 \, x^{2}}"," ",0,"1/13*b^5*x^13 + 1/2*a*b^4*x^10 + 10/7*a^2*b^3*x^7 + 5/2*a^3*b^2*x^4 + 5*a^4*b*x - 1/2*a^5/x^2","A",0
281,1,58,0,0.153641," ","integrate((b*x^3+a)^5/x^5,x, algorithm=""giac"")","\frac{1}{11} \, b^{5} x^{11} + \frac{5}{8} \, a b^{4} x^{8} + 2 \, a^{2} b^{3} x^{5} + 5 \, a^{3} b^{2} x^{2} - \frac{20 \, a^{4} b x^{3} + a^{5}}{4 \, x^{4}}"," ",0,"1/11*b^5*x^11 + 5/8*a*b^4*x^8 + 2*a^2*b^3*x^5 + 5*a^3*b^2*x^2 - 1/4*(20*a^4*b*x^3 + a^5)/x^4","A",0
282,1,58,0,0.175333," ","integrate((b*x^3+a)^5/x^6,x, algorithm=""giac"")","\frac{1}{10} \, b^{5} x^{10} + \frac{5}{7} \, a b^{4} x^{7} + \frac{5}{2} \, a^{2} b^{3} x^{4} + 10 \, a^{3} b^{2} x - \frac{25 \, a^{4} b x^{3} + 2 \, a^{5}}{10 \, x^{5}}"," ",0,"1/10*b^5*x^10 + 5/7*a*b^4*x^7 + 5/2*a^2*b^3*x^4 + 10*a^3*b^2*x - 1/10*(25*a^4*b*x^3 + 2*a^5)/x^5","A",0
283,1,59,0,0.151183," ","integrate((b*x^3+a)^5/x^8,x, algorithm=""giac"")","\frac{1}{8} \, b^{5} x^{8} + a b^{4} x^{5} + 5 \, a^{2} b^{3} x^{2} - \frac{280 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 4 \, a^{5}}{28 \, x^{7}}"," ",0,"1/8*b^5*x^8 + a*b^4*x^5 + 5*a^2*b^3*x^2 - 1/28*(280*a^3*b^2*x^6 + 35*a^4*b*x^3 + 4*a^5)/x^7","A",0
284,1,56,0,0.152027," ","integrate((b*x^3+a)^5/x^9,x, algorithm=""giac"")","\frac{1}{7} \, b^{5} x^{7} + \frac{5}{4} \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x - \frac{40 \, a^{3} b^{2} x^{6} + 8 \, a^{4} b x^{3} + a^{5}}{8 \, x^{8}}"," ",0,"1/7*b^5*x^7 + 5/4*a*b^4*x^4 + 10*a^2*b^3*x - 1/8*(40*a^3*b^2*x^6 + 8*a^4*b*x^3 + a^5)/x^8","A",0
285,1,90,0,0.148694," ","integrate(x^20*(b*x^3+a)^8,x, algorithm=""giac"")","\frac{1}{45} \, b^{8} x^{45} + \frac{4}{21} \, a b^{7} x^{42} + \frac{28}{39} \, a^{2} b^{6} x^{39} + \frac{14}{9} \, a^{3} b^{5} x^{36} + \frac{70}{33} \, a^{4} b^{4} x^{33} + \frac{28}{15} \, a^{5} b^{3} x^{30} + \frac{28}{27} \, a^{6} b^{2} x^{27} + \frac{1}{3} \, a^{7} b x^{24} + \frac{1}{21} \, a^{8} x^{21}"," ",0,"1/45*b^8*x^45 + 4/21*a*b^7*x^42 + 28/39*a^2*b^6*x^39 + 14/9*a^3*b^5*x^36 + 70/33*a^4*b^4*x^33 + 28/15*a^5*b^3*x^30 + 28/27*a^6*b^2*x^27 + 1/3*a^7*b*x^24 + 1/21*a^8*x^21","A",0
286,1,90,0,0.152155," ","integrate(x^17*(b*x^3+a)^8,x, algorithm=""giac"")","\frac{1}{42} \, b^{8} x^{42} + \frac{8}{39} \, a b^{7} x^{39} + \frac{7}{9} \, a^{2} b^{6} x^{36} + \frac{56}{33} \, a^{3} b^{5} x^{33} + \frac{7}{3} \, a^{4} b^{4} x^{30} + \frac{56}{27} \, a^{5} b^{3} x^{27} + \frac{7}{6} \, a^{6} b^{2} x^{24} + \frac{8}{21} \, a^{7} b x^{21} + \frac{1}{18} \, a^{8} x^{18}"," ",0,"1/42*b^8*x^42 + 8/39*a*b^7*x^39 + 7/9*a^2*b^6*x^36 + 56/33*a^3*b^5*x^33 + 7/3*a^4*b^4*x^30 + 56/27*a^5*b^3*x^27 + 7/6*a^6*b^2*x^24 + 8/21*a^7*b*x^21 + 1/18*a^8*x^18","A",0
287,1,90,0,0.206689," ","integrate(x^14*(b*x^3+a)^8,x, algorithm=""giac"")","\frac{1}{39} \, b^{8} x^{39} + \frac{2}{9} \, a b^{7} x^{36} + \frac{28}{33} \, a^{2} b^{6} x^{33} + \frac{28}{15} \, a^{3} b^{5} x^{30} + \frac{70}{27} \, a^{4} b^{4} x^{27} + \frac{7}{3} \, a^{5} b^{3} x^{24} + \frac{4}{3} \, a^{6} b^{2} x^{21} + \frac{4}{9} \, a^{7} b x^{18} + \frac{1}{15} \, a^{8} x^{15}"," ",0,"1/39*b^8*x^39 + 2/9*a*b^7*x^36 + 28/33*a^2*b^6*x^33 + 28/15*a^3*b^5*x^30 + 70/27*a^4*b^4*x^27 + 7/3*a^5*b^3*x^24 + 4/3*a^6*b^2*x^21 + 4/9*a^7*b*x^18 + 1/15*a^8*x^15","A",0
288,1,90,0,0.151269," ","integrate(x^11*(b*x^3+a)^8,x, algorithm=""giac"")","\frac{1}{36} \, b^{8} x^{36} + \frac{8}{33} \, a b^{7} x^{33} + \frac{14}{15} \, a^{2} b^{6} x^{30} + \frac{56}{27} \, a^{3} b^{5} x^{27} + \frac{35}{12} \, a^{4} b^{4} x^{24} + \frac{8}{3} \, a^{5} b^{3} x^{21} + \frac{14}{9} \, a^{6} b^{2} x^{18} + \frac{8}{15} \, a^{7} b x^{15} + \frac{1}{12} \, a^{8} x^{12}"," ",0,"1/36*b^8*x^36 + 8/33*a*b^7*x^33 + 14/15*a^2*b^6*x^30 + 56/27*a^3*b^5*x^27 + 35/12*a^4*b^4*x^24 + 8/3*a^5*b^3*x^21 + 14/9*a^6*b^2*x^18 + 8/15*a^7*b*x^15 + 1/12*a^8*x^12","A",0
289,1,90,0,0.157352," ","integrate(x^8*(b*x^3+a)^8,x, algorithm=""giac"")","\frac{1}{33} \, b^{8} x^{33} + \frac{4}{15} \, a b^{7} x^{30} + \frac{28}{27} \, a^{2} b^{6} x^{27} + \frac{7}{3} \, a^{3} b^{5} x^{24} + \frac{10}{3} \, a^{4} b^{4} x^{21} + \frac{28}{9} \, a^{5} b^{3} x^{18} + \frac{28}{15} \, a^{6} b^{2} x^{15} + \frac{2}{3} \, a^{7} b x^{12} + \frac{1}{9} \, a^{8} x^{9}"," ",0,"1/33*b^8*x^33 + 4/15*a*b^7*x^30 + 28/27*a^2*b^6*x^27 + 7/3*a^3*b^5*x^24 + 10/3*a^4*b^4*x^21 + 28/9*a^5*b^3*x^18 + 28/15*a^6*b^2*x^15 + 2/3*a^7*b*x^12 + 1/9*a^8*x^9","A",0
290,1,90,0,0.149425," ","integrate(x^5*(b*x^3+a)^8,x, algorithm=""giac"")","\frac{1}{30} \, b^{8} x^{30} + \frac{8}{27} \, a b^{7} x^{27} + \frac{7}{6} \, a^{2} b^{6} x^{24} + \frac{8}{3} \, a^{3} b^{5} x^{21} + \frac{35}{9} \, a^{4} b^{4} x^{18} + \frac{56}{15} \, a^{5} b^{3} x^{15} + \frac{7}{3} \, a^{6} b^{2} x^{12} + \frac{8}{9} \, a^{7} b x^{9} + \frac{1}{6} \, a^{8} x^{6}"," ",0,"1/30*b^8*x^30 + 8/27*a*b^7*x^27 + 7/6*a^2*b^6*x^24 + 8/3*a^3*b^5*x^21 + 35/9*a^4*b^4*x^18 + 56/15*a^5*b^3*x^15 + 7/3*a^6*b^2*x^12 + 8/9*a^7*b*x^9 + 1/6*a^8*x^6","B",0
291,1,14,0,0.176987," ","integrate(x^2*(b*x^3+a)^8,x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{9}}{27 \, b}"," ",0,"1/27*(b*x^3 + a)^9/b","A",0
292,1,89,0,0.163075," ","integrate((b*x^3+a)^8/x,x, algorithm=""giac"")","\frac{1}{24} \, b^{8} x^{24} + \frac{8}{21} \, a b^{7} x^{21} + \frac{14}{9} \, a^{2} b^{6} x^{18} + \frac{56}{15} \, a^{3} b^{5} x^{15} + \frac{35}{6} \, a^{4} b^{4} x^{12} + \frac{56}{9} \, a^{5} b^{3} x^{9} + \frac{14}{3} \, a^{6} b^{2} x^{6} + \frac{8}{3} \, a^{7} b x^{3} + a^{8} \log\left({\left| x \right|}\right)"," ",0,"1/24*b^8*x^24 + 8/21*a*b^7*x^21 + 14/9*a^2*b^6*x^18 + 56/15*a^3*b^5*x^15 + 35/6*a^4*b^4*x^12 + 56/9*a^5*b^3*x^9 + 14/3*a^6*b^2*x^6 + 8/3*a^7*b*x^3 + a^8*log(abs(x))","A",0
293,1,100,0,0.147908," ","integrate((b*x^3+a)^8/x^4,x, algorithm=""giac"")","\frac{1}{21} \, b^{8} x^{21} + \frac{4}{9} \, a b^{7} x^{18} + \frac{28}{15} \, a^{2} b^{6} x^{15} + \frac{14}{3} \, a^{3} b^{5} x^{12} + \frac{70}{9} \, a^{4} b^{4} x^{9} + \frac{28}{3} \, a^{5} b^{3} x^{6} + \frac{28}{3} \, a^{6} b^{2} x^{3} + 8 \, a^{7} b \log\left({\left| x \right|}\right) - \frac{8 \, a^{7} b x^{3} + a^{8}}{3 \, x^{3}}"," ",0,"1/21*b^8*x^21 + 4/9*a*b^7*x^18 + 28/15*a^2*b^6*x^15 + 14/3*a^3*b^5*x^12 + 70/9*a^4*b^4*x^9 + 28/3*a^5*b^3*x^6 + 28/3*a^6*b^2*x^3 + 8*a^7*b*log(abs(x)) - 1/3*(8*a^7*b*x^3 + a^8)/x^3","A",0
294,1,102,0,0.187002," ","integrate((b*x^3+a)^8/x^7,x, algorithm=""giac"")","\frac{1}{18} \, b^{8} x^{18} + \frac{8}{15} \, a b^{7} x^{15} + \frac{7}{3} \, a^{2} b^{6} x^{12} + \frac{56}{9} \, a^{3} b^{5} x^{9} + \frac{35}{3} \, a^{4} b^{4} x^{6} + \frac{56}{3} \, a^{5} b^{3} x^{3} + 28 \, a^{6} b^{2} \log\left({\left| x \right|}\right) - \frac{84 \, a^{6} b^{2} x^{6} + 16 \, a^{7} b x^{3} + a^{8}}{6 \, x^{6}}"," ",0,"1/18*b^8*x^18 + 8/15*a*b^7*x^15 + 7/3*a^2*b^6*x^12 + 56/9*a^3*b^5*x^9 + 35/3*a^4*b^4*x^6 + 56/3*a^5*b^3*x^3 + 28*a^6*b^2*log(abs(x)) - 1/6*(84*a^6*b^2*x^6 + 16*a^7*b*x^3 + a^8)/x^6","A",0
295,1,102,0,0.153850," ","integrate((b*x^3+a)^8/x^10,x, algorithm=""giac"")","\frac{1}{15} \, b^{8} x^{15} + \frac{2}{3} \, a b^{7} x^{12} + \frac{28}{9} \, a^{2} b^{6} x^{9} + \frac{28}{3} \, a^{3} b^{5} x^{6} + \frac{70}{3} \, a^{4} b^{4} x^{3} + 56 \, a^{5} b^{3} \log\left({\left| x \right|}\right) - \frac{308 \, a^{5} b^{3} x^{9} + 84 \, a^{6} b^{2} x^{6} + 12 \, a^{7} b x^{3} + a^{8}}{9 \, x^{9}}"," ",0,"1/15*b^8*x^15 + 2/3*a*b^7*x^12 + 28/9*a^2*b^6*x^9 + 28/3*a^3*b^5*x^6 + 70/3*a^4*b^4*x^3 + 56*a^5*b^3*log(abs(x)) - 1/9*(308*a^5*b^3*x^9 + 84*a^6*b^2*x^6 + 12*a^7*b*x^3 + a^8)/x^9","A",0
296,1,104,0,0.154111," ","integrate((b*x^3+a)^8/x^13,x, algorithm=""giac"")","\frac{1}{12} \, b^{8} x^{12} + \frac{8}{9} \, a b^{7} x^{9} + \frac{14}{3} \, a^{2} b^{6} x^{6} + \frac{56}{3} \, a^{3} b^{5} x^{3} + 70 \, a^{4} b^{4} \log\left({\left| x \right|}\right) - \frac{1750 \, a^{4} b^{4} x^{12} + 672 \, a^{5} b^{3} x^{9} + 168 \, a^{6} b^{2} x^{6} + 32 \, a^{7} b x^{3} + 3 \, a^{8}}{36 \, x^{12}}"," ",0,"1/12*b^8*x^12 + 8/9*a*b^7*x^9 + 14/3*a^2*b^6*x^6 + 56/3*a^3*b^5*x^3 + 70*a^4*b^4*log(abs(x)) - 1/36*(1750*a^4*b^4*x^12 + 672*a^5*b^3*x^9 + 168*a^6*b^2*x^6 + 32*a^7*b*x^3 + 3*a^8)/x^12","A",0
297,1,104,0,0.173720," ","integrate((b*x^3+a)^8/x^16,x, algorithm=""giac"")","\frac{1}{9} \, b^{8} x^{9} + \frac{4}{3} \, a b^{7} x^{6} + \frac{28}{3} \, a^{2} b^{6} x^{3} + 56 \, a^{3} b^{5} \log\left({\left| x \right|}\right) - \frac{1918 \, a^{3} b^{5} x^{15} + 1050 \, a^{4} b^{4} x^{12} + 420 \, a^{5} b^{3} x^{9} + 140 \, a^{6} b^{2} x^{6} + 30 \, a^{7} b x^{3} + 3 \, a^{8}}{45 \, x^{15}}"," ",0,"1/9*b^8*x^9 + 4/3*a*b^7*x^6 + 28/3*a^2*b^6*x^3 + 56*a^3*b^5*log(abs(x)) - 1/45*(1918*a^3*b^5*x^15 + 1050*a^4*b^4*x^12 + 420*a^5*b^3*x^9 + 140*a^6*b^2*x^6 + 30*a^7*b*x^3 + 3*a^8)/x^15","A",0
298,1,104,0,0.160422," ","integrate((b*x^3+a)^8/x^19,x, algorithm=""giac"")","\frac{1}{6} \, b^{8} x^{6} + \frac{8}{3} \, a b^{7} x^{3} + 28 \, a^{2} b^{6} \log\left({\left| x \right|}\right) - \frac{2058 \, a^{2} b^{6} x^{18} + 1680 \, a^{3} b^{5} x^{15} + 1050 \, a^{4} b^{4} x^{12} + 560 \, a^{5} b^{3} x^{9} + 210 \, a^{6} b^{2} x^{6} + 48 \, a^{7} b x^{3} + 5 \, a^{8}}{90 \, x^{18}}"," ",0,"1/6*b^8*x^6 + 8/3*a*b^7*x^3 + 28*a^2*b^6*log(abs(x)) - 1/90*(2058*a^2*b^6*x^18 + 1680*a^3*b^5*x^15 + 1050*a^4*b^4*x^12 + 560*a^5*b^3*x^9 + 210*a^6*b^2*x^6 + 48*a^7*b*x^3 + 5*a^8)/x^18","A",0
299,1,102,0,0.157390," ","integrate((b*x^3+a)^8/x^22,x, algorithm=""giac"")","\frac{1}{3} \, b^{8} x^{3} + 8 \, a b^{7} \log\left({\left| x \right|}\right) - \frac{2178 \, a b^{7} x^{21} + 2940 \, a^{2} b^{6} x^{18} + 2940 \, a^{3} b^{5} x^{15} + 2450 \, a^{4} b^{4} x^{12} + 1470 \, a^{5} b^{3} x^{9} + 588 \, a^{6} b^{2} x^{6} + 140 \, a^{7} b x^{3} + 15 \, a^{8}}{315 \, x^{21}}"," ",0,"1/3*b^8*x^3 + 8*a*b^7*log(abs(x)) - 1/315*(2178*a*b^7*x^21 + 2940*a^2*b^6*x^18 + 2940*a^3*b^5*x^15 + 2450*a^4*b^4*x^12 + 1470*a^5*b^3*x^9 + 588*a^6*b^2*x^6 + 140*a^7*b*x^3 + 15*a^8)/x^21","A",0
300,1,100,0,0.154690," ","integrate((b*x^3+a)^8/x^25,x, algorithm=""giac"")","b^{8} \log\left({\left| x \right|}\right) - \frac{2283 \, b^{8} x^{24} + 6720 \, a b^{7} x^{21} + 11760 \, a^{2} b^{6} x^{18} + 15680 \, a^{3} b^{5} x^{15} + 14700 \, a^{4} b^{4} x^{12} + 9408 \, a^{5} b^{3} x^{9} + 3920 \, a^{6} b^{2} x^{6} + 960 \, a^{7} b x^{3} + 105 \, a^{8}}{2520 \, x^{24}}"," ",0,"b^8*log(abs(x)) - 1/2520*(2283*b^8*x^24 + 6720*a*b^7*x^21 + 11760*a^2*b^6*x^18 + 15680*a^3*b^5*x^15 + 14700*a^4*b^4*x^12 + 9408*a^5*b^3*x^9 + 3920*a^6*b^2*x^6 + 960*a^7*b*x^3 + 105*a^8)/x^24","A",0
301,1,90,0,0.150935," ","integrate((b*x^3+a)^8/x^28,x, algorithm=""giac"")","-\frac{9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}}"," ",0,"-1/27*(9*b^8*x^24 + 36*a*b^7*x^21 + 84*a^2*b^6*x^18 + 126*a^3*b^5*x^15 + 126*a^4*b^4*x^12 + 84*a^5*b^3*x^9 + 36*a^6*b^2*x^6 + 9*a^7*b*x^3 + a^8)/x^27","B",0
302,1,92,0,0.153506," ","integrate((b*x^3+a)^8/x^31,x, algorithm=""giac"")","-\frac{45 \, b^{8} x^{24} + 240 \, a b^{7} x^{21} + 630 \, a^{2} b^{6} x^{18} + 1008 \, a^{3} b^{5} x^{15} + 1050 \, a^{4} b^{4} x^{12} + 720 \, a^{5} b^{3} x^{9} + 315 \, a^{6} b^{2} x^{6} + 80 \, a^{7} b x^{3} + 9 \, a^{8}}{270 \, x^{30}}"," ",0,"-1/270*(45*b^8*x^24 + 240*a*b^7*x^21 + 630*a^2*b^6*x^18 + 1008*a^3*b^5*x^15 + 1050*a^4*b^4*x^12 + 720*a^5*b^3*x^9 + 315*a^6*b^2*x^6 + 80*a^7*b*x^3 + 9*a^8)/x^30","B",0
303,1,92,0,0.163872," ","integrate((b*x^3+a)^8/x^34,x, algorithm=""giac"")","-\frac{165 \, b^{8} x^{24} + 990 \, a b^{7} x^{21} + 2772 \, a^{2} b^{6} x^{18} + 4620 \, a^{3} b^{5} x^{15} + 4950 \, a^{4} b^{4} x^{12} + 3465 \, a^{5} b^{3} x^{9} + 1540 \, a^{6} b^{2} x^{6} + 396 \, a^{7} b x^{3} + 45 \, a^{8}}{1485 \, x^{33}}"," ",0,"-1/1485*(165*b^8*x^24 + 990*a*b^7*x^21 + 2772*a^2*b^6*x^18 + 4620*a^3*b^5*x^15 + 4950*a^4*b^4*x^12 + 3465*a^5*b^3*x^9 + 1540*a^6*b^2*x^6 + 396*a^7*b*x^3 + 45*a^8)/x^33","A",0
304,1,92,0,0.172765," ","integrate((b*x^3+a)^8/x^37,x, algorithm=""giac"")","-\frac{495 \, b^{8} x^{24} + 3168 \, a b^{7} x^{21} + 9240 \, a^{2} b^{6} x^{18} + 15840 \, a^{3} b^{5} x^{15} + 17325 \, a^{4} b^{4} x^{12} + 12320 \, a^{5} b^{3} x^{9} + 5544 \, a^{6} b^{2} x^{6} + 1440 \, a^{7} b x^{3} + 165 \, a^{8}}{5940 \, x^{36}}"," ",0,"-1/5940*(495*b^8*x^24 + 3168*a*b^7*x^21 + 9240*a^2*b^6*x^18 + 15840*a^3*b^5*x^15 + 17325*a^4*b^4*x^12 + 12320*a^5*b^3*x^9 + 5544*a^6*b^2*x^6 + 1440*a^7*b*x^3 + 165*a^8)/x^36","A",0
305,1,92,0,0.153579," ","integrate((b*x^3+a)^8/x^40,x, algorithm=""giac"")","-\frac{1287 \, b^{8} x^{24} + 8580 \, a b^{7} x^{21} + 25740 \, a^{2} b^{6} x^{18} + 45045 \, a^{3} b^{5} x^{15} + 50050 \, a^{4} b^{4} x^{12} + 36036 \, a^{5} b^{3} x^{9} + 16380 \, a^{6} b^{2} x^{6} + 4290 \, a^{7} b x^{3} + 495 \, a^{8}}{19305 \, x^{39}}"," ",0,"-1/19305*(1287*b^8*x^24 + 8580*a*b^7*x^21 + 25740*a^2*b^6*x^18 + 45045*a^3*b^5*x^15 + 50050*a^4*b^4*x^12 + 36036*a^5*b^3*x^9 + 16380*a^6*b^2*x^6 + 4290*a^7*b*x^3 + 495*a^8)/x^39","A",0
306,1,92,0,0.156848," ","integrate((b*x^3+a)^8/x^43,x, algorithm=""giac"")","-\frac{3003 \, b^{8} x^{24} + 20592 \, a b^{7} x^{21} + 63063 \, a^{2} b^{6} x^{18} + 112112 \, a^{3} b^{5} x^{15} + 126126 \, a^{4} b^{4} x^{12} + 91728 \, a^{5} b^{3} x^{9} + 42042 \, a^{6} b^{2} x^{6} + 11088 \, a^{7} b x^{3} + 1287 \, a^{8}}{54054 \, x^{42}}"," ",0,"-1/54054*(3003*b^8*x^24 + 20592*a*b^7*x^21 + 63063*a^2*b^6*x^18 + 112112*a^3*b^5*x^15 + 126126*a^4*b^4*x^12 + 91728*a^5*b^3*x^9 + 42042*a^6*b^2*x^6 + 11088*a^7*b*x^3 + 1287*a^8)/x^42","A",0
307,1,92,0,0.188099," ","integrate((b*x^3+a)^8/x^46,x, algorithm=""giac"")","-\frac{6435 \, b^{8} x^{24} + 45045 \, a b^{7} x^{21} + 140140 \, a^{2} b^{6} x^{18} + 252252 \, a^{3} b^{5} x^{15} + 286650 \, a^{4} b^{4} x^{12} + 210210 \, a^{5} b^{3} x^{9} + 97020 \, a^{6} b^{2} x^{6} + 25740 \, a^{7} b x^{3} + 3003 \, a^{8}}{135135 \, x^{45}}"," ",0,"-1/135135*(6435*b^8*x^24 + 45045*a*b^7*x^21 + 140140*a^2*b^6*x^18 + 252252*a^3*b^5*x^15 + 286650*a^4*b^4*x^12 + 210210*a^5*b^3*x^9 + 97020*a^6*b^2*x^6 + 25740*a^7*b*x^3 + 3003*a^8)/x^45","A",0
308,1,89,0,0.206703," ","integrate(x^4*(b*x^3+a)^8,x, algorithm=""giac"")","\frac{1}{29} \, b^{8} x^{29} + \frac{4}{13} \, a b^{7} x^{26} + \frac{28}{23} \, a^{2} b^{6} x^{23} + \frac{14}{5} \, a^{3} b^{5} x^{20} + \frac{70}{17} \, a^{4} b^{4} x^{17} + 4 \, a^{5} b^{3} x^{14} + \frac{28}{11} \, a^{6} b^{2} x^{11} + a^{7} b x^{8} + \frac{1}{5} \, a^{8} x^{5}"," ",0,"1/29*b^8*x^29 + 4/13*a*b^7*x^26 + 28/23*a^2*b^6*x^23 + 14/5*a^3*b^5*x^20 + 70/17*a^4*b^4*x^17 + 4*a^5*b^3*x^14 + 28/11*a^6*b^2*x^11 + a^7*b*x^8 + 1/5*a^8*x^5","A",0
309,1,90,0,0.149526," ","integrate(x^3*(b*x^3+a)^8,x, algorithm=""giac"")","\frac{1}{28} \, b^{8} x^{28} + \frac{8}{25} \, a b^{7} x^{25} + \frac{14}{11} \, a^{2} b^{6} x^{22} + \frac{56}{19} \, a^{3} b^{5} x^{19} + \frac{35}{8} \, a^{4} b^{4} x^{16} + \frac{56}{13} \, a^{5} b^{3} x^{13} + \frac{14}{5} \, a^{6} b^{2} x^{10} + \frac{8}{7} \, a^{7} b x^{7} + \frac{1}{4} \, a^{8} x^{4}"," ",0,"1/28*b^8*x^28 + 8/25*a*b^7*x^25 + 14/11*a^2*b^6*x^22 + 56/19*a^3*b^5*x^19 + 35/8*a^4*b^4*x^16 + 56/13*a^5*b^3*x^13 + 14/5*a^6*b^2*x^10 + 8/7*a^7*b*x^7 + 1/4*a^8*x^4","A",0
310,1,90,0,0.169711," ","integrate(x*(b*x^3+a)^8,x, algorithm=""giac"")","\frac{1}{26} \, b^{8} x^{26} + \frac{8}{23} \, a b^{7} x^{23} + \frac{7}{5} \, a^{2} b^{6} x^{20} + \frac{56}{17} \, a^{3} b^{5} x^{17} + 5 \, a^{4} b^{4} x^{14} + \frac{56}{11} \, a^{5} b^{3} x^{11} + \frac{7}{2} \, a^{6} b^{2} x^{8} + \frac{8}{5} \, a^{7} b x^{5} + \frac{1}{2} \, a^{8} x^{2}"," ",0,"1/26*b^8*x^26 + 8/23*a*b^7*x^23 + 7/5*a^2*b^6*x^20 + 56/17*a^3*b^5*x^17 + 5*a^4*b^4*x^14 + 56/11*a^5*b^3*x^11 + 7/2*a^6*b^2*x^8 + 8/5*a^7*b*x^5 + 1/2*a^8*x^2","A",0
311,1,87,0,0.154394," ","integrate((b*x^3+a)^8,x, algorithm=""giac"")","\frac{1}{25} \, b^{8} x^{25} + \frac{4}{11} \, a b^{7} x^{22} + \frac{28}{19} \, a^{2} b^{6} x^{19} + \frac{7}{2} \, a^{3} b^{5} x^{16} + \frac{70}{13} \, a^{4} b^{4} x^{13} + \frac{28}{5} \, a^{5} b^{3} x^{10} + 4 \, a^{6} b^{2} x^{7} + 2 \, a^{7} b x^{4} + a^{8} x"," ",0,"1/25*b^8*x^25 + 4/11*a*b^7*x^22 + 28/19*a^2*b^6*x^19 + 7/2*a^3*b^5*x^16 + 70/13*a^4*b^4*x^13 + 28/5*a^5*b^3*x^10 + 4*a^6*b^2*x^7 + 2*a^7*b*x^4 + a^8*x","A",0
312,1,90,0,0.156701," ","integrate((b*x^3+a)^8/x^2,x, algorithm=""giac"")","\frac{1}{23} \, b^{8} x^{23} + \frac{2}{5} \, a b^{7} x^{20} + \frac{28}{17} \, a^{2} b^{6} x^{17} + 4 \, a^{3} b^{5} x^{14} + \frac{70}{11} \, a^{4} b^{4} x^{11} + 7 \, a^{5} b^{3} x^{8} + \frac{28}{5} \, a^{6} b^{2} x^{5} + 4 \, a^{7} b x^{2} - \frac{a^{8}}{x}"," ",0,"1/23*b^8*x^23 + 2/5*a*b^7*x^20 + 28/17*a^2*b^6*x^17 + 4*a^3*b^5*x^14 + 70/11*a^4*b^4*x^11 + 7*a^5*b^3*x^8 + 28/5*a^6*b^2*x^5 + 4*a^7*b*x^2 - a^8/x","A",0
313,1,88,0,0.152705," ","integrate((b*x^3+a)^8/x^3,x, algorithm=""giac"")","\frac{1}{22} \, b^{8} x^{22} + \frac{8}{19} \, a b^{7} x^{19} + \frac{7}{4} \, a^{2} b^{6} x^{16} + \frac{56}{13} \, a^{3} b^{5} x^{13} + 7 \, a^{4} b^{4} x^{10} + 8 \, a^{5} b^{3} x^{7} + 7 \, a^{6} b^{2} x^{4} + 8 \, a^{7} b x - \frac{a^{8}}{2 \, x^{2}}"," ",0,"1/22*b^8*x^22 + 8/19*a*b^7*x^19 + 7/4*a^2*b^6*x^16 + 56/13*a^3*b^5*x^13 + 7*a^4*b^4*x^10 + 8*a^5*b^3*x^7 + 7*a^6*b^2*x^4 + 8*a^7*b*x - 1/2*a^8/x^2","A",0
314,1,91,0,0.164171," ","integrate((b*x^3+a)^8/x^5,x, algorithm=""giac"")","\frac{1}{20} \, b^{8} x^{20} + \frac{8}{17} \, a b^{7} x^{17} + 2 \, a^{2} b^{6} x^{14} + \frac{56}{11} \, a^{3} b^{5} x^{11} + \frac{35}{4} \, a^{4} b^{4} x^{8} + \frac{56}{5} \, a^{5} b^{3} x^{5} + 14 \, a^{6} b^{2} x^{2} - \frac{32 \, a^{7} b x^{3} + a^{8}}{4 \, x^{4}}"," ",0,"1/20*b^8*x^20 + 8/17*a*b^7*x^17 + 2*a^2*b^6*x^14 + 56/11*a^3*b^5*x^11 + 35/4*a^4*b^4*x^8 + 56/5*a^5*b^3*x^5 + 14*a^6*b^2*x^2 - 1/4*(32*a^7*b*x^3 + a^8)/x^4","A",0
315,1,89,0,0.150041," ","integrate((b*x^3+a)^8/x^6,x, algorithm=""giac"")","\frac{1}{19} \, b^{8} x^{19} + \frac{1}{2} \, a b^{7} x^{16} + \frac{28}{13} \, a^{2} b^{6} x^{13} + \frac{28}{5} \, a^{3} b^{5} x^{10} + 10 \, a^{4} b^{4} x^{7} + 14 \, a^{5} b^{3} x^{4} + 28 \, a^{6} b^{2} x - \frac{20 \, a^{7} b x^{3} + a^{8}}{5 \, x^{5}}"," ",0,"1/19*b^8*x^19 + 1/2*a*b^7*x^16 + 28/13*a^2*b^6*x^13 + 28/5*a^3*b^5*x^10 + 10*a^4*b^4*x^7 + 14*a^5*b^3*x^4 + 28*a^6*b^2*x - 1/5*(20*a^7*b*x^3 + a^8)/x^5","A",0
316,1,91,0,0.153142," ","integrate((b*x^3+a)^8/x^8,x, algorithm=""giac"")","\frac{1}{17} \, b^{8} x^{17} + \frac{4}{7} \, a b^{7} x^{14} + \frac{28}{11} \, a^{2} b^{6} x^{11} + 7 \, a^{3} b^{5} x^{8} + 14 \, a^{4} b^{4} x^{5} + 28 \, a^{5} b^{3} x^{2} - \frac{196 \, a^{6} b^{2} x^{6} + 14 \, a^{7} b x^{3} + a^{8}}{7 \, x^{7}}"," ",0,"1/17*b^8*x^17 + 4/7*a*b^7*x^14 + 28/11*a^2*b^6*x^11 + 7*a^3*b^5*x^8 + 14*a^4*b^4*x^5 + 28*a^5*b^3*x^2 - 1/7*(196*a^6*b^2*x^6 + 14*a^7*b*x^3 + a^8)/x^7","A",0
317,1,91,0,0.205850," ","integrate((b*x^3+a)^8/x^9,x, algorithm=""giac"")","\frac{1}{16} \, b^{8} x^{16} + \frac{8}{13} \, a b^{7} x^{13} + \frac{14}{5} \, a^{2} b^{6} x^{10} + 8 \, a^{3} b^{5} x^{7} + \frac{35}{2} \, a^{4} b^{4} x^{4} + 56 \, a^{5} b^{3} x - \frac{560 \, a^{6} b^{2} x^{6} + 64 \, a^{7} b x^{3} + 5 \, a^{8}}{40 \, x^{8}}"," ",0,"1/16*b^8*x^16 + 8/13*a*b^7*x^13 + 14/5*a^2*b^6*x^10 + 8*a^3*b^5*x^7 + 35/2*a^4*b^4*x^4 + 56*a^5*b^3*x - 1/40*(560*a^6*b^2*x^6 + 64*a^7*b*x^3 + 5*a^8)/x^8","A",0
318,1,35,0,0.180324," ","integrate(x^8/(b*x^3+a),x, algorithm=""giac"")","\frac{a^{2} \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{3}} + \frac{b x^{6} - 2 \, a x^{3}}{6 \, b^{2}}"," ",0,"1/3*a^2*log(abs(b*x^3 + a))/b^3 + 1/6*(b*x^6 - 2*a*x^3)/b^2","A",0
319,1,24,0,0.183374," ","integrate(x^5/(b*x^3+a),x, algorithm=""giac"")","\frac{x^{3}}{3 \, b} - \frac{a \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{2}}"," ",0,"1/3*x^3/b - 1/3*a*log(abs(b*x^3 + a))/b^2","A",0
320,1,14,0,0.155322," ","integrate(x^2/(b*x^3+a),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{3} + a \right|}\right)}{3 \, b}"," ",0,"1/3*log(abs(b*x^3 + a))/b","A",0
321,1,22,0,0.152137," ","integrate(1/x/(b*x^3+a),x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{3} + a \right|}\right)}{3 \, a} + \frac{\log\left({\left| x \right|}\right)}{a}"," ",0,"-1/3*log(abs(b*x^3 + a))/a + log(abs(x))/a","A",0
322,1,42,0,0.156822," ","integrate(1/x^4/(b*x^3+a),x, algorithm=""giac"")","\frac{b \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{2}} - \frac{b \log\left({\left| x \right|}\right)}{a^{2}} + \frac{b x^{3} - a}{3 \, a^{2} x^{3}}"," ",0,"1/3*b*log(abs(b*x^3 + a))/a^2 - b*log(abs(x))/a^2 + 1/3*(b*x^3 - a)/(a^2*x^3)","A",0
323,1,114,0,0.192741," ","integrate(x^4/(b*x^3+a),x, algorithm=""giac"")","\frac{x^{2}}{2 \, b} + \frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, b} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{3}} - \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{3}}"," ",0,"1/2*x^2/b + 1/3*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))/b + 1/3*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^3 - 1/6*(-a*b^2)^(2/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^3","A",0
324,1,111,0,0.179632," ","integrate(x^3/(b*x^3+a),x, algorithm=""giac"")","\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, b} + \frac{x}{b} - \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{2}} - \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{2}}"," ",0,"1/3*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/b + x/b - 1/3*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/b^2 - 1/6*(-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/b^2","A",0
325,1,112,0,0.203645," ","integrate(x/(b*x^3+a),x, algorithm=""giac"")","-\frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a} - \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a b^{2}} + \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a b^{2}}"," ",0,"-1/3*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))/a - 1/3*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b^2) + 1/6*(-a*b^2)^(2/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b^2)","A",0
326,1,112,0,0.163356," ","integrate(1/(b*x^3+a),x, algorithm=""giac"")","-\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a b} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a b}"," ",0,"-1/3*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a + 1/3*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b) + 1/6*(-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b)","A",0
327,1,121,0,0.179467," ","integrate(1/x^2/(b*x^3+a),x, algorithm=""giac"")","\frac{b \left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{2}} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{2} b} - \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b} - \frac{1}{a x}"," ",0,"1/3*b*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))/a^2 + 1/3*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b) - 1/6*(-a*b^2)^(2/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b) - 1/(a*x)","A",0
328,1,115,0,0.165545," ","integrate(1/x^3/(b*x^3+a),x, algorithm=""giac"")","\frac{b \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{2}} - \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{2}} - \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{2}} - \frac{1}{2 \, a x^{2}}"," ",0,"1/3*b*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^2 - 1/3*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/a^2 - 1/6*(-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/a^2 - 1/2/(a*x^2)","A",0
329,1,49,0,0.174466," ","integrate(x^8/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{x^{3}}{3 \, b^{2}} - \frac{2 \, a \log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{3}} + \frac{2 \, a b x^{3} + a^{2}}{3 \, {\left(b x^{3} + a\right)} b^{3}}"," ",0,"1/3*x^3/b^2 - 2/3*a*log(abs(b*x^3 + a))/b^3 + 1/3*(2*a*b*x^3 + a^2)/((b*x^3 + a)*b^3)","A",0
330,1,48,0,0.162400," ","integrate(x^5/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\frac{\log\left(\frac{{\left| b x^{3} + a \right|}}{{\left(b x^{3} + a\right)}^{2} {\left| b \right|}}\right)}{b} - \frac{a}{{\left(b x^{3} + a\right)} b}}{3 \, b}"," ",0,"-1/3*(log(abs(b*x^3 + a)/((b*x^3 + a)^2*abs(b)))/b - a/((b*x^3 + a)*b))/b","A",0
331,1,14,0,0.169606," ","integrate(x^2/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{1}{3 \, {\left(b x^{3} + a\right)} b}"," ",0,"-1/3/((b*x^3 + a)*b)","A",0
332,1,45,0,0.154833," ","integrate(1/x/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{2}} + \frac{\log\left({\left| x \right|}\right)}{a^{2}} + \frac{b x^{3} + 2 \, a}{3 \, {\left(b x^{3} + a\right)} a^{2}}"," ",0,"-1/3*log(abs(b*x^3 + a))/a^2 + log(abs(x))/a^2 + 1/3*(b*x^3 + 2*a)/((b*x^3 + a)*a^2)","A",0
333,1,51,0,0.177623," ","integrate(1/x^4/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{2 \, b \log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3}} - \frac{2 \, b \log\left({\left| x \right|}\right)}{a^{3}} - \frac{2 \, b x^{3} + a}{3 \, {\left(b x^{6} + a x^{3}\right)} a^{2}}"," ",0,"2/3*b*log(abs(b*x^3 + a))/a^3 - 2*b*log(abs(x))/a^3 - 1/3*(2*b*x^3 + a)/((b*x^6 + a*x^3)*a^2)","A",0
334,1,132,0,0.163203," ","integrate(x^4/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{x^{2}}{3 \, {\left(b x^{3} + a\right)} b} - \frac{2 \, \left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b} - \frac{2 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a b^{3}} + \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \, a b^{3}}"," ",0,"-1/3*x^2/((b*x^3 + a)*b) - 2/9*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))/(a*b) - 2/9*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b^3) + 1/9*(-a*b^2)^(2/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b^3)","A",0
335,1,130,0,0.243455," ","integrate(x^3/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b} - \frac{x}{3 \, {\left(b x^{3} + a\right)} b} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a b^{2}} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a b^{2}}"," ",0,"-1/9*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b) - 1/3*x/((b*x^3 + a)*b) + 1/9*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b^2) + 1/18*(-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b^2)","A",0
336,1,129,0,0.204010," ","integrate(x/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{x^{2}}{3 \, {\left(b x^{3} + a\right)} a} - \frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2}} - \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{2} b^{2}} + \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a^{2} b^{2}}"," ",0,"1/3*x^2/((b*x^3 + a)*a) - 1/9*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))/a^2 - 1/9*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b^2) + 1/18*(-a*b^2)^(2/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b^2)","A",0
337,1,127,0,0.171409," ","integrate(1/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2}} + \frac{x}{3 \, {\left(b x^{3} + a\right)} a} + \frac{2 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{2} b} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \, a^{2} b}"," ",0,"-2/9*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^2 + 1/3*x/((b*x^3 + a)*a) + 2/9*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b) + 1/9*(-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b)","A",0
338,1,139,0,0.172050," ","integrate(1/x^2/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{4 \, b \left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{3}} + \frac{4 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{3} b} - \frac{4 \, b x^{3} + 3 \, a}{3 \, {\left(b x^{4} + a x\right)} a^{2}} - \frac{2 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \, a^{3} b}"," ",0,"4/9*b*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))/a^3 + 4/9*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^3*b) - 1/3*(4*b*x^3 + 3*a)/((b*x^4 + a*x)*a^2) - 2/9*(-a*b^2)^(2/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^3*b)","A",0
339,1,131,0,0.190774," ","integrate(1/x^3/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{5 \, b \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{3}} - \frac{b x}{3 \, {\left(b x^{3} + a\right)} a^{2}} - \frac{5 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{3}} - \frac{5 \, \left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a^{3}} - \frac{1}{2 \, a^{2} x^{2}}"," ",0,"5/9*b*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^3 - 1/3*b*x/((b*x^3 + a)*a^2) - 5/9*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/a^3 - 5/18*(-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/a^3 - 1/2/(a^2*x^2)","A",0
340,1,62,0,0.166263," ","integrate(x^11/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{x^{3}}{3 \, b^{3}} - \frac{a \log\left({\left| b x^{3} + a \right|}\right)}{b^{4}} + \frac{9 \, a b^{2} x^{6} + 12 \, a^{2} b x^{3} + 4 \, a^{3}}{6 \, {\left(b x^{3} + a\right)}^{2} b^{4}}"," ",0,"1/3*x^3/b^3 - a*log(abs(b*x^3 + a))/b^4 + 1/6*(9*a*b^2*x^6 + 12*a^2*b*x^3 + 4*a^3)/((b*x^3 + a)^2*b^4)","A",0
341,1,42,0,0.204221," ","integrate(x^8/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{\log\left({\left| b x^{3} + a \right|}\right)}{3 \, b^{3}} - \frac{3 \, b x^{6} + 2 \, a x^{3}}{6 \, {\left(b x^{3} + a\right)}^{2} b^{2}}"," ",0,"1/3*log(abs(b*x^3 + a))/b^3 - 1/6*(3*b*x^6 + 2*a*x^3)/((b*x^3 + a)^2*b^2)","A",0
342,1,22,0,0.169433," ","integrate(x^5/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{2 \, b x^{3} + a}{6 \, {\left(b x^{3} + a\right)}^{2} b^{2}}"," ",0,"-1/6*(2*b*x^3 + a)/((b*x^3 + a)^2*b^2)","A",0
343,1,14,0,0.190107," ","integrate(x^2/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{1}{6 \, {\left(b x^{3} + a\right)}^{2} b}"," ",0,"-1/6/((b*x^3 + a)^2*b)","A",0
344,1,57,0,0.159306," ","integrate(1/x/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{3} + a \right|}\right)}{3 \, a^{3}} + \frac{\log\left({\left| x \right|}\right)}{a^{3}} + \frac{3 \, b^{2} x^{6} + 8 \, a b x^{3} + 6 \, a^{2}}{6 \, {\left(b x^{3} + a\right)}^{2} a^{3}}"," ",0,"-1/3*log(abs(b*x^3 + a))/a^3 + log(abs(x))/a^3 + 1/6*(3*b^2*x^6 + 8*a*b*x^3 + 6*a^2)/((b*x^3 + a)^2*a^3)","A",0
345,1,80,0,0.193603," ","integrate(1/x^4/(b*x^3+a)^3,x, algorithm=""giac"")","\frac{b \log\left({\left| b x^{3} + a \right|}\right)}{a^{4}} - \frac{3 \, b \log\left({\left| x \right|}\right)}{a^{4}} - \frac{9 \, b^{3} x^{6} + 22 \, a b^{2} x^{3} + 14 \, a^{2} b}{6 \, {\left(b x^{3} + a\right)}^{2} a^{4}} + \frac{3 \, b x^{3} - a}{3 \, a^{4} x^{3}}"," ",0,"b*log(abs(b*x^3 + a))/a^4 - 3*b*log(abs(x))/a^4 - 1/6*(9*b^3*x^6 + 22*a*b^2*x^3 + 14*a^2*b)/((b*x^3 + a)^2*a^4) + 1/3*(3*b*x^3 - a)/(a^4*x^3)","A",0
346,1,142,0,0.177218," ","integrate(x^7/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{5 \, \left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a b^{2}} - \frac{5 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a b^{4}} - \frac{8 \, b x^{5} + 5 \, a x^{2}}{18 \, {\left(b x^{3} + a\right)}^{2} b^{2}} + \frac{5 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, a b^{4}}"," ",0,"-5/27*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^2) - 5/27*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b^4) - 1/18*(8*b*x^5 + 5*a*x^2)/((b*x^3 + a)^2*b^2) + 5/54*(-a*b^2)^(2/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b^4)","A",0
347,1,140,0,0.179640," ","integrate(x^6/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a b^{2}} + \frac{2 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a b^{3}} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \, a b^{3}} - \frac{7 \, b x^{4} + 4 \, a x}{18 \, {\left(b x^{3} + a\right)}^{2} b^{2}}"," ",0,"-2/27*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^2) + 2/27*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b^3) + 1/27*(-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b^3) - 1/18*(7*b*x^4 + 4*a*x)/((b*x^3 + a)^2*b^2)","A",0
348,1,145,0,0.174527," ","integrate(x^4/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{2} b} - \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a^{2} b^{3}} + \frac{2 \, b x^{5} - a x^{2}}{18 \, {\left(b x^{3} + a\right)}^{2} a b} + \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, a^{2} b^{3}}"," ",0,"-1/27*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b) - 1/27*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b^3) + 1/18*(2*b*x^5 - a*x^2)/((b*x^3 + a)^2*a*b) + 1/54*(-a*b^2)^(2/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b^3)","A",0
349,1,142,0,0.176075," ","integrate(x^3/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{2} b} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a^{2} b^{2}} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, a^{2} b^{2}} + \frac{b x^{4} - 2 \, a x}{18 \, {\left(b x^{3} + a\right)}^{2} a b}"," ",0,"-1/27*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b) + 1/27*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b^2) + 1/54*(-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b^2) + 1/18*(b*x^4 - 2*a*x)/((b*x^3 + a)^2*a*b)","A",0
350,1,139,0,0.172253," ","integrate(x/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{2 \, \left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{3}} - \frac{2 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a^{3} b^{2}} + \frac{4 \, b x^{5} + 7 \, a x^{2}}{18 \, {\left(b x^{3} + a\right)}^{2} a^{2}} + \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \, a^{3} b^{2}}"," ",0,"-2/27*(-a/b)^(2/3)*log(abs(x - (-a/b)^(1/3)))/a^3 - 2/27*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^3*b^2) + 1/18*(4*b*x^5 + 7*a*x^2)/((b*x^3 + a)^2*a^2) + 1/27*(-a*b^2)^(2/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^3*b^2)","A",0
351,1,137,0,0.161228," ","integrate(1/(b*x^3+a)^3,x, algorithm=""giac"")","-\frac{5 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{27 \, a^{3}} + \frac{5 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{27 \, a^{3} b} + \frac{5 \, \left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \, a^{3} b} + \frac{5 \, b x^{4} + 8 \, a x}{18 \, {\left(b x^{3} + a\right)}^{2} a^{2}}"," ",0,"-5/27*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/a^3 + 5/27*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^3*b) + 5/54*(-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^3*b) + 1/18*(5*b*x^4 + 8*a*x)/((b*x^3 + a)^2*a^2)","A",0
352,1,37,0,0.155266," ","integrate(x^8/(-b*x^3+a),x, algorithm=""giac"")","-\frac{a^{2} \log\left({\left| b x^{3} - a \right|}\right)}{3 \, b^{3}} - \frac{b x^{6} + 2 \, a x^{3}}{6 \, b^{2}}"," ",0,"-1/3*a^2*log(abs(b*x^3 - a))/b^3 - 1/6*(b*x^6 + 2*a*x^3)/b^2","A",0
353,1,26,0,0.192548," ","integrate(x^5/(-b*x^3+a),x, algorithm=""giac"")","-\frac{x^{3}}{3 \, b} - \frac{a \log\left({\left| b x^{3} - a \right|}\right)}{3 \, b^{2}}"," ",0,"-1/3*x^3/b - 1/3*a*log(abs(b*x^3 - a))/b^2","A",0
354,1,16,0,0.156924," ","integrate(x^2/(-b*x^3+a),x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{3} - a \right|}\right)}{3 \, b}"," ",0,"-1/3*log(abs(b*x^3 - a))/b","A",0
355,1,24,0,0.161811," ","integrate(1/x/(-b*x^3+a),x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{3} - a \right|}\right)}{3 \, a} + \frac{\log\left({\left| x \right|}\right)}{a}"," ",0,"-1/3*log(abs(b*x^3 - a))/a + log(abs(x))/a","A",0
356,1,41,0,0.208867," ","integrate(1/x^4/(-b*x^3+a),x, algorithm=""giac"")","-\frac{b \log\left({\left| b x^{3} - a \right|}\right)}{3 \, a^{2}} + \frac{b \log\left({\left| x \right|}\right)}{a^{2}} - \frac{b x^{3} + a}{3 \, a^{2} x^{3}}"," ",0,"-1/3*b*log(abs(b*x^3 - a))/a^2 + b*log(abs(x))/a^2 - 1/3*(b*x^3 + a)/(a^2*x^3)","A",0
357,1,106,0,0.176081," ","integrate(x^4/(-b*x^3+a),x, algorithm=""giac"")","-\frac{x^{2}}{2 \, b} - \frac{\left(\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, b} - \frac{\sqrt{3} \left(a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{3}} + \frac{\left(a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{3}}"," ",0,"-1/2*x^2/b - 1/3*(a/b)^(2/3)*log(abs(x - (a/b)^(1/3)))/b - 1/3*sqrt(3)*(a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/b^3 + 1/6*(a*b^2)^(2/3)*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/b^3","A",0
358,1,104,0,0.166821," ","integrate(x^3/(-b*x^3+a),x, algorithm=""giac"")","-\frac{\left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, b} - \frac{x}{b} + \frac{\sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, b^{2}} + \frac{\left(a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, b^{2}}"," ",0,"-1/3*(a/b)^(1/3)*log(abs(x - (a/b)^(1/3)))/b - x/b + 1/3*sqrt(3)*(a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/b^2 + 1/6*(a*b^2)^(1/3)*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/b^2","A",0
359,1,104,0,0.189302," ","integrate(x/(-b*x^3+a),x, algorithm=""giac"")","-\frac{\left(\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a} - \frac{\sqrt{3} \left(a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a b^{2}} + \frac{\left(a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a b^{2}}"," ",0,"-1/3*(a/b)^(2/3)*log(abs(x - (a/b)^(1/3)))/a - 1/3*sqrt(3)*(a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2) + 1/6*(a*b^2)^(2/3)*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b^2)","A",0
360,1,104,0,0.157755," ","integrate(1/(-b*x^3+a),x, algorithm=""giac"")","-\frac{\left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a} + \frac{\sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a b} + \frac{\left(a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a b}"," ",0,"-1/3*(a/b)^(1/3)*log(abs(x - (a/b)^(1/3)))/a + 1/3*sqrt(3)*(a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/(a*b) + 1/6*(a*b^2)^(1/3)*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/(a*b)","A",0
361,1,113,0,0.190689," ","integrate(1/x^2/(-b*x^3+a),x, algorithm=""giac"")","-\frac{b \left(\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{2}} - \frac{\sqrt{3} \left(a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{2} b} + \frac{\left(a b^{2}\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b} - \frac{1}{a x}"," ",0,"-1/3*b*(a/b)^(2/3)*log(abs(x - (a/b)^(1/3)))/a^2 - 1/3*sqrt(3)*(a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/(a^2*b) + 1/6*(a*b^2)^(2/3)*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/(a^2*b) - 1/(a*x)","A",0
362,1,107,0,0.164946," ","integrate(1/x^3/(-b*x^3+a),x, algorithm=""giac"")","-\frac{b \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{2}} + \frac{\sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, a^{2}} + \frac{\left(a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a^{2}} - \frac{1}{2 \, a x^{2}}"," ",0,"-1/3*b*(a/b)^(1/3)*log(abs(x - (a/b)^(1/3)))/a^2 + 1/3*sqrt(3)*(a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (a/b)^(1/3))/(a/b)^(1/3))/a^2 + 1/6*(a*b^2)^(1/3)*log(x^2 + x*(a/b)^(1/3) + (a/b)^(2/3))/a^2 - 1/2/(a*x^2)","A",0
363,1,143,0,0.159706," ","integrate(1/(b*x^3+a+1),x, algorithm=""giac"")","\frac{{\left(-a b^{2} - b^{2}\right)}^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a + 1}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a + 1}{b}\right)^{\frac{1}{3}}}\right)}{\sqrt{3} a b + \sqrt{3} b} + \frac{{\left(-a b^{2} - b^{2}\right)}^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a + 1}{b}\right)^{\frac{1}{3}} + \left(-\frac{a + 1}{b}\right)^{\frac{2}{3}}\right)}{6 \, {\left(a b + b\right)}} - \frac{\left(-\frac{a + 1}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a + 1}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, {\left(a + 1\right)}}"," ",0,"(-a*b^2 - b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-(a + 1)/b)^(1/3))/(-(a + 1)/b)^(1/3))/(sqrt(3)*a*b + sqrt(3)*b) + 1/6*(-a*b^2 - b^2)^(1/3)*log(x^2 + x*(-(a + 1)/b)^(1/3) + (-(a + 1)/b)^(2/3))/(a*b + b) - 1/3*(-(a + 1)/b)^(1/3)*log(abs(x - (-(a + 1)/b)^(1/3)))/(a + 1)","A",0
364,1,131,0,0.158566," ","integrate(1/(-b*x^3+a+1),x, algorithm=""giac"")","\frac{{\left(a b^{2} + b^{2}\right)}^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a + 1}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a + 1}{b}\right)^{\frac{1}{3}}}\right)}{\sqrt{3} a b + \sqrt{3} b} + \frac{{\left(a b^{2} + b^{2}\right)}^{\frac{1}{3}} \log\left(x^{2} + x \left(\frac{a + 1}{b}\right)^{\frac{1}{3}} + \left(\frac{a + 1}{b}\right)^{\frac{2}{3}}\right)}{6 \, {\left(a b + b\right)}} - \frac{\left(\frac{a + 1}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(\frac{a + 1}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, {\left(a + 1\right)}}"," ",0,"(a*b^2 + b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + ((a + 1)/b)^(1/3))/((a + 1)/b)^(1/3))/(sqrt(3)*a*b + sqrt(3)*b) + 1/6*(a*b^2 + b^2)^(1/3)*log(x^2 + x*((a + 1)/b)^(1/3) + ((a + 1)/b)^(2/3))/(a*b + b) - 1/3*((a + 1)/b)^(1/3)*log(abs(x - ((a + 1)/b)^(1/3)))/(a + 1)","A",0
365,1,142,0,0.161264," ","integrate(1/(b*x^3+a-1),x, algorithm=""giac"")","\frac{{\left(-a b^{2} + b^{2}\right)}^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a - 1}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a - 1}{b}\right)^{\frac{1}{3}}}\right)}{\sqrt{3} a b - \sqrt{3} b} + \frac{{\left(-a b^{2} + b^{2}\right)}^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a - 1}{b}\right)^{\frac{1}{3}} + \left(-\frac{a - 1}{b}\right)^{\frac{2}{3}}\right)}{6 \, {\left(a b - b\right)}} - \frac{\left(-\frac{a - 1}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a - 1}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, {\left(a - 1\right)}}"," ",0,"(-a*b^2 + b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-(a - 1)/b)^(1/3))/(-(a - 1)/b)^(1/3))/(sqrt(3)*a*b - sqrt(3)*b) + 1/6*(-a*b^2 + b^2)^(1/3)*log(x^2 + x*(-(a - 1)/b)^(1/3) + (-(a - 1)/b)^(2/3))/(a*b - b) - 1/3*(-(a - 1)/b)^(1/3)*log(abs(x - (-(a - 1)/b)^(1/3)))/(a - 1)","A",0
366,1,138,0,0.204889," ","integrate(1/(-b*x^3+a-1),x, algorithm=""giac"")","\frac{{\left(a b^{2} - b^{2}\right)}^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{a - 1}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a - 1}{b}\right)^{\frac{1}{3}}}\right)}{\sqrt{3} a b - \sqrt{3} b} + \frac{{\left(a b^{2} - b^{2}\right)}^{\frac{1}{3}} \log\left(x^{2} + x \left(\frac{a - 1}{b}\right)^{\frac{1}{3}} + \left(\frac{a - 1}{b}\right)^{\frac{2}{3}}\right)}{6 \, {\left(a b - b\right)}} - \frac{\left(\frac{a - 1}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(\frac{a - 1}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, {\left(a - 1\right)}}"," ",0,"(a*b^2 - b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + ((a - 1)/b)^(1/3))/((a - 1)/b)^(1/3))/(sqrt(3)*a*b - sqrt(3)*b) + 1/6*(a*b^2 - b^2)^(1/3)*log(x^2 + x*((a - 1)/b)^(1/3) + ((a - 1)/b)^(2/3))/(a*b - b) - 1/3*((a - 1)/b)^(1/3)*log(abs(x - ((a - 1)/b)^(1/3)))/(a - 1)","A",0
367,1,6,0,0.150702," ","integrate(x^(1/2)/(x^3+1),x, algorithm=""giac"")","\frac{2}{3} \, \arctan\left(x^{\frac{3}{2}}\right)"," ",0,"2/3*arctan(x^(3/2))","A",0
368,1,57,0,0.157321," ","integrate(x^11*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(35 \, {\left(b x^{3} + a\right)}^{\frac{9}{2}} - 135 \, {\left(b x^{3} + a\right)}^{\frac{7}{2}} a + 189 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}} a^{2} - 105 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} a^{3}\right)}}{945 \, b^{4}}"," ",0,"2/945*(35*(b*x^3 + a)^(9/2) - 135*(b*x^3 + a)^(7/2)*a + 189*(b*x^3 + a)^(5/2)*a^2 - 105*(b*x^3 + a)^(3/2)*a^3)/b^4","A",0
369,1,43,0,0.187706," ","integrate(x^8*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, {\left(b x^{3} + a\right)}^{\frac{7}{2}} - 42 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} a^{2}\right)}}{315 \, b^{3}}"," ",0,"2/315*(15*(b*x^3 + a)^(7/2) - 42*(b*x^3 + a)^(5/2)*a + 35*(b*x^3 + a)^(3/2)*a^2)/b^3","A",0
370,1,29,0,0.151136," ","integrate(x^5*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}} - 5 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} a\right)}}{45 \, b^{2}}"," ",0,"2/45*(3*(b*x^3 + a)^(5/2) - 5*(b*x^3 + a)^(3/2)*a)/b^2","A",0
371,1,14,0,0.148116," ","integrate(x^2*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{9 \, b}"," ",0,"2/9*(b*x^3 + a)^(3/2)/b","A",0
372,1,36,0,0.160547," ","integrate((b*x^3+a)^(1/2)/x,x, algorithm=""giac"")","\frac{2 \, a \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{3 \, \sqrt{-a}} + \frac{2}{3} \, \sqrt{b x^{3} + a}"," ",0,"2/3*a*arctan(sqrt(b*x^3 + a)/sqrt(-a))/sqrt(-a) + 2/3*sqrt(b*x^3 + a)","A",0
373,1,46,0,0.159186," ","integrate((b*x^3+a)^(1/2)/x^4,x, algorithm=""giac"")","\frac{\frac{b^{2} \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{\sqrt{b x^{3} + a} b}{x^{3}}}{3 \, b}"," ",0,"1/3*(b^2*arctan(sqrt(b*x^3 + a)/sqrt(-a))/sqrt(-a) - sqrt(b*x^3 + a)*b/x^3)/b","A",0
374,1,72,0,0.156827," ","integrate((b*x^3+a)^(1/2)/x^7,x, algorithm=""giac"")","-\frac{\frac{b^{3} \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{{\left(b x^{3} + a\right)}^{\frac{3}{2}} b^{3} + \sqrt{b x^{3} + a} a b^{3}}{a b^{2} x^{6}}}{12 \, b}"," ",0,"-1/12*(b^3*arctan(sqrt(b*x^3 + a)/sqrt(-a))/(sqrt(-a)*a) + ((b*x^3 + a)^(3/2)*b^3 + sqrt(b*x^3 + a)*a*b^3)/(a*b^2*x^6))/b","A",0
375,1,92,0,0.180223," ","integrate((b*x^3+a)^(1/2)/x^10,x, algorithm=""giac"")","\frac{\frac{3 \, b^{4} \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{3 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}} b^{4} - 8 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} a b^{4} - 3 \, \sqrt{b x^{3} + a} a^{2} b^{4}}{a^{2} b^{3} x^{9}}}{72 \, b}"," ",0,"1/72*(3*b^4*arctan(sqrt(b*x^3 + a)/sqrt(-a))/(sqrt(-a)*a^2) + (3*(b*x^3 + a)^(5/2)*b^4 - 8*(b*x^3 + a)^(3/2)*a*b^4 - 3*sqrt(b*x^3 + a)*a^2*b^4)/(a^2*b^3*x^9))/b","A",0
376,0,0,0,0.000000," ","integrate(x^6*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{3} + a} x^{6}\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a)*x^6, x)","F",0
377,0,0,0,0.000000," ","integrate(x^3*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{3} + a} x^{3}\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a)*x^3, x)","F",0
378,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{3} + a}\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a), x)","F",0
379,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{b x^{3} + a}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a)/x^3, x)","F",0
380,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{b x^{3} + a}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a)/x^6, x)","F",0
381,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/2)/x^9,x, algorithm=""giac"")","\int \frac{\sqrt{b x^{3} + a}}{x^{9}}\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a)/x^9, x)","F",0
382,0,0,0,0.000000," ","integrate(x^7*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{3} + a} x^{7}\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a)*x^7, x)","F",0
383,0,0,0,0.000000," ","integrate(x^4*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{3} + a} x^{4}\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a)*x^4, x)","F",0
384,0,0,0,0.000000," ","integrate(x*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{3} + a} x\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a)*x, x)","F",0
385,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{b x^{3} + a}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a)/x^2, x)","F",0
386,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{b x^{3} + a}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a)/x^5, x)","F",0
387,1,57,0,0.159715," ","integrate(x^11*(b*x^3+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(105 \, {\left(b x^{3} + a\right)}^{\frac{11}{2}} - 385 \, {\left(b x^{3} + a\right)}^{\frac{9}{2}} a + 495 \, {\left(b x^{3} + a\right)}^{\frac{7}{2}} a^{2} - 231 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}} a^{3}\right)}}{3465 \, b^{4}}"," ",0,"2/3465*(105*(b*x^3 + a)^(11/2) - 385*(b*x^3 + a)^(9/2)*a + 495*(b*x^3 + a)^(7/2)*a^2 - 231*(b*x^3 + a)^(5/2)*a^3)/b^4","A",0
388,1,43,0,0.157964," ","integrate(x^8*(b*x^3+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(35 \, {\left(b x^{3} + a\right)}^{\frac{9}{2}} - 90 \, {\left(b x^{3} + a\right)}^{\frac{7}{2}} a + 63 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}} a^{2}\right)}}{945 \, b^{3}}"," ",0,"2/945*(35*(b*x^3 + a)^(9/2) - 90*(b*x^3 + a)^(7/2)*a + 63*(b*x^3 + a)^(5/2)*a^2)/b^3","A",0
389,1,29,0,0.172979," ","integrate(x^5*(b*x^3+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(5 \, {\left(b x^{3} + a\right)}^{\frac{7}{2}} - 7 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}} a\right)}}{105 \, b^{2}}"," ",0,"2/105*(5*(b*x^3 + a)^(7/2) - 7*(b*x^3 + a)^(5/2)*a)/b^2","A",0
390,1,14,0,0.145349," ","integrate(x^2*(b*x^3+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}}}{15 \, b}"," ",0,"2/15*(b*x^3 + a)^(5/2)/b","A",0
391,1,50,0,0.171093," ","integrate((b*x^3+a)^(3/2)/x,x, algorithm=""giac"")","\frac{2 \, a^{2} \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{3 \, \sqrt{-a}} + \frac{2}{9} \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{b x^{3} + a} a"," ",0,"2/3*a^2*arctan(sqrt(b*x^3 + a)/sqrt(-a))/sqrt(-a) + 2/9*(b*x^3 + a)^(3/2) + 2/3*sqrt(b*x^3 + a)*a","A",0
392,1,63,0,0.182652," ","integrate((b*x^3+a)^(3/2)/x^4,x, algorithm=""giac"")","\frac{\frac{3 \, a b^{2} \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + 2 \, \sqrt{b x^{3} + a} b^{2} - \frac{\sqrt{b x^{3} + a} a b}{x^{3}}}{3 \, b}"," ",0,"1/3*(3*a*b^2*arctan(sqrt(b*x^3 + a)/sqrt(-a))/sqrt(-a) + 2*sqrt(b*x^3 + a)*b^2 - sqrt(b*x^3 + a)*a*b/x^3)/b","A",0
393,1,70,0,0.159677," ","integrate((b*x^3+a)^(3/2)/x^7,x, algorithm=""giac"")","\frac{\frac{3 \, b^{3} \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{5 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} b^{3} - 3 \, \sqrt{b x^{3} + a} a b^{3}}{b^{2} x^{6}}}{12 \, b}"," ",0,"1/12*(3*b^3*arctan(sqrt(b*x^3 + a)/sqrt(-a))/sqrt(-a) - (5*(b*x^3 + a)^(3/2)*b^3 - 3*sqrt(b*x^3 + a)*a*b^3)/(b^2*x^6))/b","A",0
394,0,0,0,0.000000," ","integrate(x^6*(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{6}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/2)*x^6, x)","F",0
395,0,0,0,0.000000," ","integrate(x^3*(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{3}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/2)*x^3, x)","F",0
396,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/2), x)","F",0
397,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/2)/x^3, x)","F",0
398,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)/x^6,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{6}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/2)/x^6, x)","F",0
399,0,0,0,0.000000," ","integrate(x^7*(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{7}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/2)*x^7, x)","F",0
400,0,0,0,0.000000," ","integrate(x^4*(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{4}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/2)*x^4, x)","F",0
401,0,0,0,0.000000," ","integrate(x*(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{3}{2}} x\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/2)*x, x)","F",0
402,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/2)/x^2, x)","F",0
403,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/2)/x^5,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}{x^{5}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/2)/x^5, x)","F",0
404,1,61,0,0.188318," ","integrate(x^11/(b*x^3+a)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{b x^{3} + a} a^{3}}{3 \, b^{4}} + \frac{2 \, {\left(5 \, {\left(b x^{3} + a\right)}^{\frac{7}{2}} - 21 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} a^{2}\right)}}{105 \, b^{4}}"," ",0,"-2/3*sqrt(b*x^3 + a)*a^3/b^4 + 2/105*(5*(b*x^3 + a)^(7/2) - 21*(b*x^3 + a)^(5/2)*a + 35*(b*x^3 + a)^(3/2)*a^2)/b^4","A",0
405,1,47,0,0.157254," ","integrate(x^8/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{b x^{3} + a} a^{2}}{3 \, b^{3}} + \frac{2 \, {\left(3 \, {\left(b x^{3} + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} a\right)}}{45 \, b^{3}}"," ",0,"2/3*sqrt(b*x^3 + a)*a^2/b^3 + 2/45*(3*(b*x^3 + a)^(5/2) - 10*(b*x^3 + a)^(3/2)*a)/b^3","A",0
406,1,30,0,0.147471," ","integrate(x^5/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}}}{9 \, b^{2}} - \frac{2 \, \sqrt{b x^{3} + a} a}{3 \, b^{2}}"," ",0,"2/9*(b*x^3 + a)^(3/2)/b^2 - 2/3*sqrt(b*x^3 + a)*a/b^2","A",0
407,1,14,0,0.156677," ","integrate(x^2/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{b x^{3} + a}}{3 \, b}"," ",0,"2/3*sqrt(b*x^3 + a)/b","A",0
408,1,23,0,0.151567," ","integrate(1/x/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{3 \, \sqrt{-a}}"," ",0,"2/3*arctan(sqrt(b*x^3 + a)/sqrt(-a))/sqrt(-a)","A",0
409,1,51,0,0.195450," ","integrate(1/x^4/(b*x^3+a)^(1/2),x, algorithm=""giac"")","-\frac{\frac{b^{2} \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{\sqrt{b x^{3} + a} b}{a x^{3}}}{3 \, b}"," ",0,"-1/3*(b^2*arctan(sqrt(b*x^3 + a)/sqrt(-a))/(sqrt(-a)*a) + sqrt(b*x^3 + a)*b/(a*x^3))/b","A",0
410,1,75,0,0.166020," ","integrate(1/x^7/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, b^{3} \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{3 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} b^{3} - 5 \, \sqrt{b x^{3} + a} a b^{3}}{a^{2} b^{2} x^{6}}}{12 \, b}"," ",0,"1/12*(3*b^3*arctan(sqrt(b*x^3 + a)/sqrt(-a))/(sqrt(-a)*a^2) + (3*(b*x^3 + a)^(3/2)*b^3 - 5*sqrt(b*x^3 + a)*a*b^3)/(a^2*b^2*x^6))/b","A",0
411,0,0,0,0.000000," ","integrate(x^6/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate(x^6/sqrt(b*x^3 + a), x)","F",0
412,0,0,0,0.000000," ","integrate(x^3/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3}}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate(x^3/sqrt(b*x^3 + a), x)","F",0
413,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*x^3 + a), x)","F",0
414,0,0,0,0.000000," ","integrate(1/x^3/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{3} + a} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^3 + a)*x^3), x)","F",0
415,0,0,0,0.000000," ","integrate(1/x^6/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{3} + a} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^3 + a)*x^6), x)","F",0
416,0,0,0,0.000000," ","integrate(x^7/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{7}}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate(x^7/sqrt(b*x^3 + a), x)","F",0
417,0,0,0,0.000000," ","integrate(x^4/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate(x^4/sqrt(b*x^3 + a), x)","F",0
418,0,0,0,0.000000," ","integrate(x/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate(x/sqrt(b*x^3 + a), x)","F",0
419,0,0,0,0.000000," ","integrate(1/x^2/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{3} + a} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^3 + a)*x^2), x)","F",0
420,0,0,0,0.000000," ","integrate(1/x^5/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{3} + a} x^{5}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^3 + a)*x^5), x)","F",0
421,1,69,0,0.154398," ","integrate(x^11/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, a^{3}}{3 \, \sqrt{b x^{3} + a} b^{4}} + \frac{2 \, {\left({\left(b x^{3} + a\right)}^{\frac{5}{2}} b^{16} - 5 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} a b^{16} + 15 \, \sqrt{b x^{3} + a} a^{2} b^{16}\right)}}{15 \, b^{20}}"," ",0,"2/3*a^3/(sqrt(b*x^3 + a)*b^4) + 2/15*((b*x^3 + a)^(5/2)*b^16 - 5*(b*x^3 + a)^(3/2)*a*b^16 + 15*sqrt(b*x^3 + a)*a^2*b^16)/b^20","A",0
422,1,52,0,0.156178," ","integrate(x^8/(b*x^3+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, a^{2}}{3 \, \sqrt{b x^{3} + a} b^{3}} + \frac{2 \, {\left({\left(b x^{3} + a\right)}^{\frac{3}{2}} b^{6} - 6 \, \sqrt{b x^{3} + a} a b^{6}\right)}}{9 \, b^{9}}"," ",0,"-2/3*a^2/(sqrt(b*x^3 + a)*b^3) + 2/9*((b*x^3 + a)^(3/2)*b^6 - 6*sqrt(b*x^3 + a)*a*b^6)/b^9","A",0
423,1,33,0,0.156901," ","integrate(x^5/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{\sqrt{b x^{3} + a}}{b} + \frac{a}{\sqrt{b x^{3} + a} b}\right)}}{3 \, b}"," ",0,"2/3*(sqrt(b*x^3 + a)/b + a/(sqrt(b*x^3 + a)*b))/b","A",0
424,1,14,0,0.155585," ","integrate(x^2/(b*x^3+a)^(3/2),x, algorithm=""giac"")","-\frac{2}{3 \, \sqrt{b x^{3} + a} b}"," ",0,"-2/3/(sqrt(b*x^3 + a)*b)","A",0
425,1,41,0,0.156315," ","integrate(1/x/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{3 \, \sqrt{-a} a} + \frac{2}{3 \, \sqrt{b x^{3} + a} a}"," ",0,"2/3*arctan(sqrt(b*x^3 + a)/sqrt(-a))/(sqrt(-a)*a) + 2/3/(sqrt(b*x^3 + a)*a)","A",0
426,1,72,0,0.176800," ","integrate(1/x^4/(b*x^3+a)^(3/2),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} - \frac{3 \, {\left(b x^{3} + a\right)} b - 2 \, a b}{3 \, {\left({\left(b x^{3} + a\right)}^{\frac{3}{2}} - \sqrt{b x^{3} + a} a\right)} a^{2}}"," ",0,"-b*arctan(sqrt(b*x^3 + a)/sqrt(-a))/(sqrt(-a)*a^2) - 1/3*(3*(b*x^3 + a)*b - 2*a*b)/(((b*x^3 + a)^(3/2) - sqrt(b*x^3 + a)*a)*a^2)","A",0
427,1,88,0,0.161084," ","integrate(1/x^7/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\frac{5 \, b^{2} \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a} a^{3}} + \frac{2 \, b^{2}}{3 \, \sqrt{b x^{3} + a} a^{3}} + \frac{7 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} b^{2} - 9 \, \sqrt{b x^{3} + a} a b^{2}}{12 \, a^{3} b^{2} x^{6}}"," ",0,"5/4*b^2*arctan(sqrt(b*x^3 + a)/sqrt(-a))/(sqrt(-a)*a^3) + 2/3*b^2/(sqrt(b*x^3 + a)*a^3) + 1/12*(7*(b*x^3 + a)^(3/2)*b^2 - 9*sqrt(b*x^3 + a)*a*b^2)/(a^3*b^2*x^6)","A",0
428,0,0,0,0.000000," ","integrate(x^6/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^6/(b*x^3 + a)^(3/2), x)","F",0
429,0,0,0,0.000000," ","integrate(x^3/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3/(b*x^3 + a)^(3/2), x)","F",0
430,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(-3/2), x)","F",0
431,0,0,0,0.000000," ","integrate(1/x^3/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(3/2)*x^3), x)","F",0
432,0,0,0,0.000000," ","integrate(1/x^6/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{6}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(3/2)*x^6), x)","F",0
433,0,0,0,0.000000," ","integrate(x^7/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{7}}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^7/(b*x^3 + a)^(3/2), x)","F",0
434,0,0,0,0.000000," ","integrate(x^4/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/(b*x^3 + a)^(3/2), x)","F",0
435,0,0,0,0.000000," ","integrate(x/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(b*x^3 + a)^(3/2), x)","F",0
436,0,0,0,0.000000," ","integrate(1/x^2/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(3/2)*x^2), x)","F",0
437,0,0,0,0.000000," ","integrate(1/x^5/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{5}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(3/2)*x^5), x)","F",0
438,1,37,0,0.155683," ","integrate(x^11/(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{21} \, {\left(x^{3} + 1\right)}^{\frac{7}{2}} - \frac{2}{5} \, {\left(x^{3} + 1\right)}^{\frac{5}{2}} + \frac{2}{3} \, {\left(x^{3} + 1\right)}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{x^{3} + 1}"," ",0,"2/21*(x^3 + 1)^(7/2) - 2/5*(x^3 + 1)^(5/2) + 2/3*(x^3 + 1)^(3/2) - 2/3*sqrt(x^3 + 1)","A",0
439,1,28,0,0.156026," ","integrate(x^8/(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(x^{3} + 1\right)}^{\frac{5}{2}} - \frac{4}{9} \, {\left(x^{3} + 1\right)}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{x^{3} + 1}"," ",0,"2/15*(x^3 + 1)^(5/2) - 4/9*(x^3 + 1)^(3/2) + 2/3*sqrt(x^3 + 1)","A",0
440,1,19,0,0.174418," ","integrate(x^5/(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, {\left(x^{3} + 1\right)}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{x^{3} + 1}"," ",0,"2/9*(x^3 + 1)^(3/2) - 2/3*sqrt(x^3 + 1)","A",0
441,1,9,0,0.145652," ","integrate(x^2/(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{x^{3} + 1}"," ",0,"2/3*sqrt(x^3 + 1)","A",0
442,1,26,0,0.149933," ","integrate(1/x/(x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{1}{3} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"-1/3*log(sqrt(x^3 + 1) + 1) + 1/3*log(abs(sqrt(x^3 + 1) - 1))","B",0
443,1,38,0,0.225779," ","integrate(1/x^4/(x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{x^{3} + 1}}{3 \, x^{3}} + \frac{1}{6} \, \log\left(\sqrt{x^{3} + 1} + 1\right) - \frac{1}{6} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"-1/3*sqrt(x^3 + 1)/x^3 + 1/6*log(sqrt(x^3 + 1) + 1) - 1/6*log(abs(sqrt(x^3 + 1) - 1))","A",0
444,1,50,0,0.154309," ","integrate(1/x^7/(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(x^{3} + 1\right)}^{\frac{3}{2}} - 5 \, \sqrt{x^{3} + 1}}{12 \, x^{6}} - \frac{1}{8} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{1}{8} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"1/12*(3*(x^3 + 1)^(3/2) - 5*sqrt(x^3 + 1))/x^6 - 1/8*log(sqrt(x^3 + 1) + 1) + 1/8*log(abs(sqrt(x^3 + 1) - 1))","A",0
445,1,59,0,0.172777," ","integrate(1/x^10/(x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{15 \, {\left(x^{3} + 1\right)}^{\frac{5}{2}} - 40 \, {\left(x^{3} + 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{x^{3} + 1}}{72 \, x^{9}} + \frac{5}{48} \, \log\left(\sqrt{x^{3} + 1} + 1\right) - \frac{5}{48} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"-1/72*(15*(x^3 + 1)^(5/2) - 40*(x^3 + 1)^(3/2) + 33*sqrt(x^3 + 1))/x^9 + 5/48*log(sqrt(x^3 + 1) + 1) - 5/48*log(abs(sqrt(x^3 + 1) - 1))","A",0
446,0,0,0,0.000000," ","integrate(x^6/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(x^6/sqrt(x^3 + 1), x)","F",0
447,0,0,0,0.000000," ","integrate(x^3/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3}}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(x^3/sqrt(x^3 + 1), x)","F",0
448,0,0,0,0.000000," ","integrate(1/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(1/sqrt(x^3 + 1), x)","F",0
449,0,0,0,0.000000," ","integrate(1/x^3/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} + 1} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(x^3 + 1)*x^3), x)","F",0
450,0,0,0,0.000000," ","integrate(1/x^6/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} + 1} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(x^3 + 1)*x^6), x)","F",0
451,0,0,0,0.000000," ","integrate(x^7/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{7}}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(x^7/sqrt(x^3 + 1), x)","F",0
452,0,0,0,0.000000," ","integrate(x^4/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(x^4/sqrt(x^3 + 1), x)","F",0
453,0,0,0,0.000000," ","integrate(x/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(x/sqrt(x^3 + 1), x)","F",0
454,0,0,0,0.000000," ","integrate(1/x^2/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} + 1} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^3 + 1)*x^2), x)","F",0
455,0,0,0,0.000000," ","integrate(1/x^5/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} + 1} x^{5}}\,{d x}"," ",0,"integrate(1/(sqrt(x^3 + 1)*x^5), x)","F",0
456,1,59,0,0.182545," ","integrate(x^11/(-x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{2}{21} \, {\left(x^{3} - 1\right)}^{3} \sqrt{-x^{3} + 1} - \frac{2}{5} \, {\left(x^{3} - 1\right)}^{2} \sqrt{-x^{3} + 1} + \frac{2}{3} \, {\left(-x^{3} + 1\right)}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{-x^{3} + 1}"," ",0,"-2/21*(x^3 - 1)^3*sqrt(-x^3 + 1) - 2/5*(x^3 - 1)^2*sqrt(-x^3 + 1) + 2/3*(-x^3 + 1)^(3/2) - 2/3*sqrt(-x^3 + 1)","A",0
457,1,41,0,0.154288," ","integrate(x^8/(-x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{2}{15} \, {\left(x^{3} - 1\right)}^{2} \sqrt{-x^{3} + 1} + \frac{4}{9} \, {\left(-x^{3} + 1\right)}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{-x^{3} + 1}"," ",0,"-2/15*(x^3 - 1)^2*sqrt(-x^3 + 1) + 4/9*(-x^3 + 1)^(3/2) - 2/3*sqrt(-x^3 + 1)","A",0
458,1,23,0,0.209326," ","integrate(x^5/(-x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, {\left(-x^{3} + 1\right)}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{-x^{3} + 1}"," ",0,"2/9*(-x^3 + 1)^(3/2) - 2/3*sqrt(-x^3 + 1)","A",0
459,1,11,0,0.151576," ","integrate(x^2/(-x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{-x^{3} + 1}"," ",0,"-2/3*sqrt(-x^3 + 1)","A",0
460,1,30,0,0.152539," ","integrate(1/x/(-x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \log\left(\sqrt{-x^{3} + 1} + 1\right) + \frac{1}{3} \, \log\left({\left| \sqrt{-x^{3} + 1} - 1 \right|}\right)"," ",0,"-1/3*log(sqrt(-x^3 + 1) + 1) + 1/3*log(abs(sqrt(-x^3 + 1) - 1))","B",0
461,1,44,0,0.159765," ","integrate(1/x^4/(-x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{3} + 1}}{3 \, x^{3}} - \frac{1}{6} \, \log\left(\sqrt{-x^{3} + 1} + 1\right) + \frac{1}{6} \, \log\left({\left| \sqrt{-x^{3} + 1} - 1 \right|}\right)"," ",0,"-1/3*sqrt(-x^3 + 1)/x^3 - 1/6*log(sqrt(-x^3 + 1) + 1) + 1/6*log(abs(sqrt(-x^3 + 1) - 1))","A",0
462,1,58,0,0.154237," ","integrate(1/x^7/(-x^3+1)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(-x^{3} + 1\right)}^{\frac{3}{2}} - 5 \, \sqrt{-x^{3} + 1}}{12 \, x^{6}} - \frac{1}{8} \, \log\left(\sqrt{-x^{3} + 1} + 1\right) + \frac{1}{8} \, \log\left({\left| \sqrt{-x^{3} + 1} - 1 \right|}\right)"," ",0,"1/12*(3*(-x^3 + 1)^(3/2) - 5*sqrt(-x^3 + 1))/x^6 - 1/8*log(sqrt(-x^3 + 1) + 1) + 1/8*log(abs(sqrt(-x^3 + 1) - 1))","A",0
463,1,76,0,0.171121," ","integrate(1/x^10/(-x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{15 \, {\left(x^{3} - 1\right)}^{2} \sqrt{-x^{3} + 1} - 40 \, {\left(-x^{3} + 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{-x^{3} + 1}}{72 \, x^{9}} - \frac{5}{48} \, \log\left(\sqrt{-x^{3} + 1} + 1\right) + \frac{5}{48} \, \log\left({\left| \sqrt{-x^{3} + 1} - 1 \right|}\right)"," ",0,"-1/72*(15*(x^3 - 1)^2*sqrt(-x^3 + 1) - 40*(-x^3 + 1)^(3/2) + 33*sqrt(-x^3 + 1))/x^9 - 5/48*log(sqrt(-x^3 + 1) + 1) + 5/48*log(abs(sqrt(-x^3 + 1) - 1))","A",0
464,0,0,0,0.000000," ","integrate(x^6/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{-x^{3} + 1}}\,{d x}"," ",0,"integrate(x^6/sqrt(-x^3 + 1), x)","F",0
465,0,0,0,0.000000," ","integrate(x^3/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3}}{\sqrt{-x^{3} + 1}}\,{d x}"," ",0,"integrate(x^3/sqrt(-x^3 + 1), x)","F",0
466,0,0,0,0.000000," ","integrate(1/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} + 1}}\,{d x}"," ",0,"integrate(1/sqrt(-x^3 + 1), x)","F",0
467,0,0,0,0.000000," ","integrate(1/x^3/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} + 1} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^3 + 1)*x^3), x)","F",0
468,0,0,0,0.000000," ","integrate(1/x^6/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} + 1} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^3 + 1)*x^6), x)","F",0
469,0,0,0,0.000000," ","integrate(x^7/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{7}}{\sqrt{-x^{3} + 1}}\,{d x}"," ",0,"integrate(x^7/sqrt(-x^3 + 1), x)","F",0
470,0,0,0,0.000000," ","integrate(x^4/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{-x^{3} + 1}}\,{d x}"," ",0,"integrate(x^4/sqrt(-x^3 + 1), x)","F",0
471,0,0,0,0.000000," ","integrate(x/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{-x^{3} + 1}}\,{d x}"," ",0,"integrate(x/sqrt(-x^3 + 1), x)","F",0
472,0,0,0,0.000000," ","integrate(1/x^2/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} + 1} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^3 + 1)*x^2), x)","F",0
473,0,0,0,0.000000," ","integrate(1/x^5/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} + 1} x^{5}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^3 + 1)*x^5), x)","F",0
474,1,37,0,0.167279," ","integrate(x^11/(x^3-1)^(1/2),x, algorithm=""giac"")","\frac{2}{21} \, {\left(x^{3} - 1\right)}^{\frac{7}{2}} + \frac{2}{5} \, {\left(x^{3} - 1\right)}^{\frac{5}{2}} + \frac{2}{3} \, {\left(x^{3} - 1\right)}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{x^{3} - 1}"," ",0,"2/21*(x^3 - 1)^(7/2) + 2/5*(x^3 - 1)^(5/2) + 2/3*(x^3 - 1)^(3/2) + 2/3*sqrt(x^3 - 1)","A",0
475,1,28,0,0.153273," ","integrate(x^8/(x^3-1)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(x^{3} - 1\right)}^{\frac{5}{2}} + \frac{4}{9} \, {\left(x^{3} - 1\right)}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{x^{3} - 1}"," ",0,"2/15*(x^3 - 1)^(5/2) + 4/9*(x^3 - 1)^(3/2) + 2/3*sqrt(x^3 - 1)","A",0
476,1,19,0,0.162699," ","integrate(x^5/(x^3-1)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, {\left(x^{3} - 1\right)}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{x^{3} - 1}"," ",0,"2/9*(x^3 - 1)^(3/2) + 2/3*sqrt(x^3 - 1)","A",0
477,1,9,0,0.149330," ","integrate(x^2/(x^3-1)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{x^{3} - 1}"," ",0,"2/3*sqrt(x^3 - 1)","A",0
478,1,10,0,0.151895," ","integrate(1/x/(x^3-1)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"2/3*arctan(sqrt(x^3 - 1))","A",0
479,1,23,0,0.149994," ","integrate(1/x^4/(x^3-1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{x^{3} - 1}}{3 \, x^{3}} + \frac{1}{3} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"1/3*sqrt(x^3 - 1)/x^3 + 1/3*arctan(sqrt(x^3 - 1))","A",0
480,1,35,0,0.152478," ","integrate(1/x^7/(x^3-1)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(x^{3} - 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{x^{3} - 1}}{12 \, x^{6}} + \frac{1}{4} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"1/12*(3*(x^3 - 1)^(3/2) + 5*sqrt(x^3 - 1))/x^6 + 1/4*arctan(sqrt(x^3 - 1))","A",0
481,1,44,0,0.151715," ","integrate(1/x^10/(x^3-1)^(1/2),x, algorithm=""giac"")","\frac{15 \, {\left(x^{3} - 1\right)}^{\frac{5}{2}} + 40 \, {\left(x^{3} - 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{x^{3} - 1}}{72 \, x^{9}} + \frac{5}{24} \, \arctan\left(\sqrt{x^{3} - 1}\right)"," ",0,"1/72*(15*(x^3 - 1)^(5/2) + 40*(x^3 - 1)^(3/2) + 33*sqrt(x^3 - 1))/x^9 + 5/24*arctan(sqrt(x^3 - 1))","A",0
482,0,0,0,0.000000," ","integrate(x^6/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{x^{3} - 1}}\,{d x}"," ",0,"integrate(x^6/sqrt(x^3 - 1), x)","F",0
483,0,0,0,0.000000," ","integrate(x^3/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3}}{\sqrt{x^{3} - 1}}\,{d x}"," ",0,"integrate(x^3/sqrt(x^3 - 1), x)","F",0
484,0,0,0,0.000000," ","integrate(1/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} - 1}}\,{d x}"," ",0,"integrate(1/sqrt(x^3 - 1), x)","F",0
485,0,0,0,0.000000," ","integrate(1/x^3/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} - 1} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(x^3 - 1)*x^3), x)","F",0
486,0,0,0,0.000000," ","integrate(1/x^6/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} - 1} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(x^3 - 1)*x^6), x)","F",0
487,0,0,0,0.000000," ","integrate(x^7/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{7}}{\sqrt{x^{3} - 1}}\,{d x}"," ",0,"integrate(x^7/sqrt(x^3 - 1), x)","F",0
488,0,0,0,0.000000," ","integrate(x^4/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{x^{3} - 1}}\,{d x}"," ",0,"integrate(x^4/sqrt(x^3 - 1), x)","F",0
489,0,0,0,0.000000," ","integrate(x/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{3} - 1}}\,{d x}"," ",0,"integrate(x/sqrt(x^3 - 1), x)","F",0
490,0,0,0,0.000000," ","integrate(1/x^2/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} - 1} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^3 - 1)*x^2), x)","F",0
491,0,0,0,0.000000," ","integrate(1/x^5/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} - 1} x^{5}}\,{d x}"," ",0,"integrate(1/(sqrt(x^3 - 1)*x^5), x)","F",0
492,1,59,0,0.173178," ","integrate(x^11/(-x^3-1)^(1/2),x, algorithm=""giac"")","-\frac{2}{21} \, {\left(x^{3} + 1\right)}^{3} \sqrt{-x^{3} - 1} + \frac{2}{5} \, {\left(x^{3} + 1\right)}^{2} \sqrt{-x^{3} - 1} + \frac{2}{3} \, {\left(-x^{3} - 1\right)}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{-x^{3} - 1}"," ",0,"-2/21*(x^3 + 1)^3*sqrt(-x^3 - 1) + 2/5*(x^3 + 1)^2*sqrt(-x^3 - 1) + 2/3*(-x^3 - 1)^(3/2) + 2/3*sqrt(-x^3 - 1)","A",0
493,1,41,0,0.154874," ","integrate(x^8/(-x^3-1)^(1/2),x, algorithm=""giac"")","-\frac{2}{15} \, {\left(x^{3} + 1\right)}^{2} \sqrt{-x^{3} - 1} - \frac{4}{9} \, {\left(-x^{3} - 1\right)}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{-x^{3} - 1}"," ",0,"-2/15*(x^3 + 1)^2*sqrt(-x^3 - 1) - 4/9*(-x^3 - 1)^(3/2) - 2/3*sqrt(-x^3 - 1)","A",0
494,1,23,0,0.150341," ","integrate(x^5/(-x^3-1)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, {\left(-x^{3} - 1\right)}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{-x^{3} - 1}"," ",0,"2/9*(-x^3 - 1)^(3/2) + 2/3*sqrt(-x^3 - 1)","A",0
495,1,11,0,0.149871," ","integrate(x^2/(-x^3-1)^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{-x^{3} - 1}"," ",0,"-2/3*sqrt(-x^3 - 1)","A",0
496,1,12,0,0.155648," ","integrate(1/x/(-x^3-1)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \arctan\left(\sqrt{-x^{3} - 1}\right)"," ",0,"2/3*arctan(sqrt(-x^3 - 1))","A",0
497,1,27,0,0.239924," ","integrate(1/x^4/(-x^3-1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{-x^{3} - 1}}{3 \, x^{3}} - \frac{1}{3} \, \arctan\left(\sqrt{-x^{3} - 1}\right)"," ",0,"1/3*sqrt(-x^3 - 1)/x^3 - 1/3*arctan(sqrt(-x^3 - 1))","A",0
498,1,41,0,0.150258," ","integrate(1/x^7/(-x^3-1)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(-x^{3} - 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{-x^{3} - 1}}{12 \, x^{6}} + \frac{1}{4} \, \arctan\left(\sqrt{-x^{3} - 1}\right)"," ",0,"1/12*(3*(-x^3 - 1)^(3/2) + 5*sqrt(-x^3 - 1))/x^6 + 1/4*arctan(sqrt(-x^3 - 1))","A",0
499,1,59,0,0.173885," ","integrate(1/x^10/(-x^3-1)^(1/2),x, algorithm=""giac"")","\frac{15 \, {\left(x^{3} + 1\right)}^{2} \sqrt{-x^{3} - 1} + 40 \, {\left(-x^{3} - 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{-x^{3} - 1}}{72 \, x^{9}} - \frac{5}{24} \, \arctan\left(\sqrt{-x^{3} - 1}\right)"," ",0,"1/72*(15*(x^3 + 1)^2*sqrt(-x^3 - 1) + 40*(-x^3 - 1)^(3/2) + 33*sqrt(-x^3 - 1))/x^9 - 5/24*arctan(sqrt(-x^3 - 1))","A",0
500,0,0,0,0.000000," ","integrate(x^6/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{-x^{3} - 1}}\,{d x}"," ",0,"integrate(x^6/sqrt(-x^3 - 1), x)","F",0
501,0,0,0,0.000000," ","integrate(x^3/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3}}{\sqrt{-x^{3} - 1}}\,{d x}"," ",0,"integrate(x^3/sqrt(-x^3 - 1), x)","F",0
502,0,0,0,0.000000," ","integrate(1/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} - 1}}\,{d x}"," ",0,"integrate(1/sqrt(-x^3 - 1), x)","F",0
503,0,0,0,0.000000," ","integrate(1/x^3/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} - 1} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^3 - 1)*x^3), x)","F",0
504,0,0,0,0.000000," ","integrate(1/x^6/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} - 1} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^3 - 1)*x^6), x)","F",0
505,0,0,0,0.000000," ","integrate(x^7/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{7}}{\sqrt{-x^{3} - 1}}\,{d x}"," ",0,"integrate(x^7/sqrt(-x^3 - 1), x)","F",0
506,0,0,0,0.000000," ","integrate(x^4/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{-x^{3} - 1}}\,{d x}"," ",0,"integrate(x^4/sqrt(-x^3 - 1), x)","F",0
507,0,0,0,0.000000," ","integrate(x/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{-x^{3} - 1}}\,{d x}"," ",0,"integrate(x/sqrt(-x^3 - 1), x)","F",0
508,0,0,0,0.000000," ","integrate(1/x^2/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} - 1} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^3 - 1)*x^2), x)","F",0
509,0,0,0,0.000000," ","integrate(1/x^5/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} - 1} x^{5}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^3 - 1)*x^5), x)","F",0
510,1,57,0,0.187211," ","integrate(x^11*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\frac{140 \, {\left(b x^{3} + a\right)}^{\frac{13}{3}} - 546 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} a + 780 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a^{2} - 455 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}} a^{3}}{1820 \, b^{4}}"," ",0,"1/1820*(140*(b*x^3 + a)^(13/3) - 546*(b*x^3 + a)^(10/3)*a + 780*(b*x^3 + a)^(7/3)*a^2 - 455*(b*x^3 + a)^(4/3)*a^3)/b^4","A",0
511,1,43,0,0.157120," ","integrate(x^8*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\frac{14 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} - 40 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a + 35 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}} a^{2}}{140 \, b^{3}}"," ",0,"1/140*(14*(b*x^3 + a)^(10/3) - 40*(b*x^3 + a)^(7/3)*a + 35*(b*x^3 + a)^(4/3)*a^2)/b^3","A",0
512,1,29,0,0.156388," ","integrate(x^5*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\frac{4 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} - 7 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}} a}{28 \, b^{2}}"," ",0,"1/28*(4*(b*x^3 + a)^(7/3) - 7*(b*x^3 + a)^(4/3)*a)/b^2","A",0
513,1,14,0,0.150233," ","integrate(x^2*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}{4 \, b}"," ",0,"1/4*(b*x^3 + a)^(4/3)/b","A",0
514,1,96,0,0.671844," ","integrate((b*x^3+a)^(1/3)/x,x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} a^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right) - \frac{1}{6} \, a^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + \frac{1}{3} \, a^{\frac{1}{3}} \log\left({\left| {\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}} \right|}\right) + {\left(b x^{3} + a\right)}^{\frac{1}{3}}"," ",0,"-1/3*sqrt(3)*a^(1/3)*arctan(1/3*sqrt(3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3)) - 1/6*a^(1/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 1/3*a^(1/3)*log(abs((b*x^3 + a)^(1/3) - a^(1/3))) + (b*x^3 + a)^(1/3)","A",0
515,1,115,0,0.694317," ","integrate((b*x^3+a)^(1/3)/x^4,x, algorithm=""giac"")","-\frac{\frac{2 \, \sqrt{3} b^{2} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{a^{\frac{2}{3}}} + \frac{b^{2} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{a^{\frac{2}{3}}} - \frac{2 \, b^{2} \log\left({\left| {\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}} \right|}\right)}{a^{\frac{2}{3}}} + \frac{6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x^{3}}}{18 \, b}"," ",0,"-1/18*(2*sqrt(3)*b^2*arctan(1/3*sqrt(3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3))/a^(2/3) + b^2*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3))/a^(2/3) - 2*b^2*log(abs((b*x^3 + a)^(1/3) - a^(1/3)))/a^(2/3) + 6*(b*x^3 + a)^(1/3)*b/x^3)/b","A",0
516,0,0,0,0.000000," ","integrate(x^4*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} x^{4}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*x^4, x)","F",0
517,0,0,0,0.000000," ","integrate(x*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} x\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*x, x)","F",0
518,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/x^2, x)","F",0
519,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^5,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x^{5}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/x^5, x)","F",0
520,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^8,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x^{8}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/x^8, x)","F",0
521,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^11,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x^{11}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/x^11, x)","F",0
522,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^14,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x^{14}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/x^14, x)","F",0
523,0,0,0,0.000000," ","integrate(x^3*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} x^{3}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*x^3, x)","F",0
524,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3), x)","F",0
525,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/x^3, x)","F",0
526,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^6,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x^{6}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/x^6, x)","F",0
527,1,57,0,0.188873," ","integrate(x^11*(b*x^3+a)^(2/3),x, algorithm=""giac"")","\frac{220 \, {\left(b x^{3} + a\right)}^{\frac{14}{3}} - 840 \, {\left(b x^{3} + a\right)}^{\frac{11}{3}} a + 1155 \, {\left(b x^{3} + a\right)}^{\frac{8}{3}} a^{2} - 616 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{3}}{3080 \, b^{4}}"," ",0,"1/3080*(220*(b*x^3 + a)^(14/3) - 840*(b*x^3 + a)^(11/3)*a + 1155*(b*x^3 + a)^(8/3)*a^2 - 616*(b*x^3 + a)^(5/3)*a^3)/b^4","A",0
528,1,43,0,0.157855," ","integrate(x^8*(b*x^3+a)^(2/3),x, algorithm=""giac"")","\frac{20 \, {\left(b x^{3} + a\right)}^{\frac{11}{3}} - 55 \, {\left(b x^{3} + a\right)}^{\frac{8}{3}} a + 44 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{2}}{220 \, b^{3}}"," ",0,"1/220*(20*(b*x^3 + a)^(11/3) - 55*(b*x^3 + a)^(8/3)*a + 44*(b*x^3 + a)^(5/3)*a^2)/b^3","A",0
529,1,29,0,0.155021," ","integrate(x^5*(b*x^3+a)^(2/3),x, algorithm=""giac"")","\frac{5 \, {\left(b x^{3} + a\right)}^{\frac{8}{3}} - 8 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a}{40 \, b^{2}}"," ",0,"1/40*(5*(b*x^3 + a)^(8/3) - 8*(b*x^3 + a)^(5/3)*a)/b^2","A",0
530,1,14,0,0.169064," ","integrate(x^2*(b*x^3+a)^(2/3),x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}{5 \, b}"," ",0,"1/5*(b*x^3 + a)^(5/3)/b","A",0
531,1,98,0,0.689343," ","integrate((b*x^3+a)^(2/3)/x,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} a^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right) - \frac{1}{6} \, a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + \frac{1}{3} \, a^{\frac{2}{3}} \log\left({\left| {\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}} \right|}\right) + \frac{1}{2} \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}"," ",0,"1/3*sqrt(3)*a^(2/3)*arctan(1/3*sqrt(3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3)) - 1/6*a^(2/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 1/3*a^(2/3)*log(abs((b*x^3 + a)^(1/3) - a^(1/3))) + 1/2*(b*x^3 + a)^(2/3)","A",0
532,1,116,0,0.708543," ","integrate((b*x^3+a)^(2/3)/x^4,x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{3} b^{2} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{a^{\frac{1}{3}}} - \frac{b^{2} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{a^{\frac{1}{3}}} + \frac{2 \, b^{2} \log\left({\left| {\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}} \right|}\right)}{a^{\frac{1}{3}}} - \frac{3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{3}}}{9 \, b}"," ",0,"1/9*(2*sqrt(3)*b^2*arctan(1/3*sqrt(3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3))/a^(1/3) - b^2*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3))/a^(1/3) + 2*b^2*log(abs((b*x^3 + a)^(1/3) - a^(1/3)))/a^(1/3) - 3*(b*x^3 + a)^(2/3)*b/x^3)/b","A",0
533,0,0,0,0.000000," ","integrate(x^4*(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{2}{3}} x^{4}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)*x^4, x)","F",0
534,0,0,0,0.000000," ","integrate(x*(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{2}{3}} x\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)*x, x)","F",0
535,0,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)/x^2, x)","F",0
536,0,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^5,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{5}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)/x^5, x)","F",0
537,0,0,0,0.000000," ","integrate(x^3*(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{2}{3}} x^{3}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)*x^3, x)","F",0
538,0,0,0,0.000000," ","integrate((b*x^3+a)^(2/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3), x)","F",0
539,0,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)/x^3, x)","F",0
540,0,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^6,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{6}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)/x^6, x)","F",0
541,0,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^9,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{9}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)/x^9, x)","F",0
542,0,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^12,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{12}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)/x^12, x)","F",0
543,1,55,0,0.157695," ","integrate(x^8*(-x^3+1)^(6/5),x, algorithm=""giac"")","-\frac{5}{63} \, {\left(x^{3} - 1\right)}^{4} {\left(-x^{3} + 1\right)}^{\frac{1}{5}} - \frac{5}{24} \, {\left(x^{3} - 1\right)}^{3} {\left(-x^{3} + 1\right)}^{\frac{1}{5}} - \frac{5}{33} \, {\left(x^{3} - 1\right)}^{2} {\left(-x^{3} + 1\right)}^{\frac{1}{5}}"," ",0,"-5/63*(x^3 - 1)^4*(-x^3 + 1)^(1/5) - 5/24*(x^3 - 1)^3*(-x^3 + 1)^(1/5) - 5/33*(x^3 - 1)^2*(-x^3 + 1)^(1/5)","A",0
544,1,61,0,0.175382," ","integrate(x^11/(b*x^3+a)^(1/3),x, algorithm=""giac"")","-\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{3}}{2 \, b^{4}} + \frac{40 \, {\left(b x^{3} + a\right)}^{\frac{11}{3}} - 165 \, {\left(b x^{3} + a\right)}^{\frac{8}{3}} a + 264 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a^{2}}{440 \, b^{4}}"," ",0,"-1/2*(b*x^3 + a)^(2/3)*a^3/b^4 + 1/440*(40*(b*x^3 + a)^(11/3) - 165*(b*x^3 + a)^(8/3)*a + 264*(b*x^3 + a)^(5/3)*a^2)/b^4","A",0
545,1,47,0,0.155261," ","integrate(x^8/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{2}}{2 \, b^{3}} + \frac{5 \, {\left(b x^{3} + a\right)}^{\frac{8}{3}} - 16 \, {\left(b x^{3} + a\right)}^{\frac{5}{3}} a}{40 \, b^{3}}"," ",0,"1/2*(b*x^3 + a)^(2/3)*a^2/b^3 + 1/40*(5*(b*x^3 + a)^(8/3) - 16*(b*x^3 + a)^(5/3)*a)/b^3","A",0
546,1,30,0,0.166867," ","integrate(x^5/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}{5 \, b^{2}} - \frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{2 \, b^{2}}"," ",0,"1/5*(b*x^3 + a)^(5/3)/b^2 - 1/2*(b*x^3 + a)^(2/3)*a/b^2","A",0
547,1,14,0,0.167279," ","integrate(x^2/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}{2 \, b}"," ",0,"1/2*(b*x^3 + a)^(2/3)/b","A",0
548,1,87,0,0.719221," ","integrate(1/x/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{3 \, a^{\frac{1}{3}}} - \frac{\log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{6 \, a^{\frac{1}{3}}} + \frac{\log\left({\left| {\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}} \right|}\right)}{3 \, a^{\frac{1}{3}}}"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3))/a^(1/3) - 1/6*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3))/a^(1/3) + 1/3*log(abs((b*x^3 + a)^(1/3) - a^(1/3)))/a^(1/3)","A",0
549,1,119,0,0.710330," ","integrate(1/x^4/(b*x^3+a)^(1/3),x, algorithm=""giac"")","-\frac{\frac{2 \, \sqrt{3} b^{2} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{a^{\frac{4}{3}}} - \frac{b^{2} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{a^{\frac{4}{3}}} + \frac{2 \, b^{2} \log\left({\left| {\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}} \right|}\right)}{a^{\frac{4}{3}}} + \frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{a x^{3}}}{18 \, b}"," ",0,"-1/18*(2*sqrt(3)*b^2*arctan(1/3*sqrt(3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3))/a^(4/3) - b^2*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3))/a^(4/3) + 2*b^2*log(abs((b*x^3 + a)^(1/3) - a^(1/3)))/a^(4/3) + 6*(b*x^3 + a)^(2/3)*b/(a*x^3))/b","A",0
550,0,0,0,0.000000," ","integrate(x^7/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{x^{7}}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^7/(b*x^3 + a)^(1/3), x)","F",0
551,0,0,0,0.000000," ","integrate(x^4/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^4/(b*x^3 + a)^(1/3), x)","F",0
552,0,0,0,0.000000," ","integrate(x/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x/(b*x^3 + a)^(1/3), x)","F",0
553,0,0,0,0.000000," ","integrate(1/x^2/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*x^2), x)","F",0
554,0,0,0,0.000000," ","integrate(1/x^5/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} x^{5}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*x^5), x)","F",0
555,0,0,0,0.000000," ","integrate(x^3/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^3/(b*x^3 + a)^(1/3), x)","F",0
556,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(-1/3), x)","F",0
557,0,0,0,0.000000," ","integrate(1/x^3/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*x^3), x)","F",0
558,0,0,0,0.000000," ","integrate(1/x^6/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} x^{6}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*x^6), x)","F",0
559,0,0,0,0.000000," ","integrate(1/x^9/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} x^{9}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*x^9), x)","F",0
560,0,0,0,0.000000," ","integrate(1/x^12/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} x^{12}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*x^12), x)","F",0
561,1,61,0,0.155142," ","integrate(x^11/(b*x^3+a)^(2/3),x, algorithm=""giac"")","-\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{3}}{b^{4}} + \frac{14 \, {\left(b x^{3} + a\right)}^{\frac{10}{3}} - 60 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} a + 105 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}} a^{2}}{140 \, b^{4}}"," ",0,"-(b*x^3 + a)^(1/3)*a^3/b^4 + 1/140*(14*(b*x^3 + a)^(10/3) - 60*(b*x^3 + a)^(7/3)*a + 105*(b*x^3 + a)^(4/3)*a^2)/b^4","A",0
562,1,46,0,0.154239," ","integrate(x^8/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{2}}{b^{3}} + \frac{2 \, {\left(b x^{3} + a\right)}^{\frac{7}{3}} - 7 \, {\left(b x^{3} + a\right)}^{\frac{4}{3}} a}{14 \, b^{3}}"," ",0,"(b*x^3 + a)^(1/3)*a^2/b^3 + 1/14*(2*(b*x^3 + a)^(7/3) - 7*(b*x^3 + a)^(4/3)*a)/b^3","A",0
563,1,30,0,0.177600," ","integrate(x^5/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}{4 \, b^{2}} - \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} a}{b^{2}}"," ",0,"1/4*(b*x^3 + a)^(4/3)/b^2 - (b*x^3 + a)^(1/3)*a/b^2","A",0
564,1,13,0,0.155051," ","integrate(x^2/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b}"," ",0,"(b*x^3 + a)^(1/3)/b","A",0
565,1,87,0,0.704846," ","integrate(1/x/(b*x^3+a)^(2/3),x, algorithm=""giac"")","-\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{3 \, a^{\frac{2}{3}}} - \frac{\log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{6 \, a^{\frac{2}{3}}} + \frac{\log\left({\left| {\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}} \right|}\right)}{3 \, a^{\frac{2}{3}}}"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3))/a^(2/3) - 1/6*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3))/a^(2/3) + 1/3*log(abs((b*x^3 + a)^(1/3) - a^(1/3)))/a^(2/3)","A",0
566,1,118,0,0.699637," ","integrate(1/x^4/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{3} b^{2} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{a^{\frac{5}{3}}} + \frac{b^{2} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{a^{\frac{5}{3}}} - \frac{2 \, b^{2} \log\left({\left| {\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}} \right|}\right)}{a^{\frac{5}{3}}} - \frac{3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{a x^{3}}}{9 \, b}"," ",0,"1/9*(2*sqrt(3)*b^2*arctan(1/3*sqrt(3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3))/a^(5/3) + b^2*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3))/a^(5/3) - 2*b^2*log(abs((b*x^3 + a)^(1/3) - a^(1/3)))/a^(5/3) - 3*(b*x^3 + a)^(1/3)*b/(a*x^3))/b","A",0
567,0,0,0,0.000000," ","integrate(x^7/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{x^{7}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x^7/(b*x^3 + a)^(2/3), x)","F",0
568,0,0,0,0.000000," ","integrate(x^4/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x^4/(b*x^3 + a)^(2/3), x)","F",0
569,0,0,0,0.000000," ","integrate(x/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x/(b*x^3 + a)^(2/3), x)","F",0
570,0,0,0,0.000000," ","integrate(1/x^2/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*x^2), x)","F",0
571,0,0,0,0.000000," ","integrate(1/x^5/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} x^{5}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*x^5), x)","F",0
572,0,0,0,0.000000," ","integrate(1/x^8/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} x^{8}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*x^8), x)","F",0
573,0,0,0,0.000000," ","integrate(1/x^11/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} x^{11}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*x^11), x)","F",0
574,0,0,0,0.000000," ","integrate(x^6/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x^6/(b*x^3 + a)^(2/3), x)","F",0
575,0,0,0,0.000000," ","integrate(x^3/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x^3/(b*x^3 + a)^(2/3), x)","F",0
576,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(-2/3), x)","F",0
577,0,0,0,0.000000," ","integrate(1/x^3/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*x^3), x)","F",0
578,0,0,0,0.000000," ","integrate(1/x^6/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} x^{6}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*x^6), x)","F",0
579,0,0,0,0.000000," ","integrate(1/(-b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((-b*x^3 + a)^(-1/3), x)","F",0
580,0,0,0,0.000000," ","integrate(1/(x^3+2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} + 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^3 + 2)^(-1/3), x)","F",0
581,0,0,0,0.000000," ","integrate(x/(-x^3+1)^(2/3),x, algorithm=""giac"")","\int \frac{x}{{\left(-x^{3} + 1\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x/(-x^3 + 1)^(2/3), x)","F",0
582,1,9,0,0.152605," ","integrate(x^2/(x^3+2)^(1/4),x, algorithm=""giac"")","\frac{4}{9} \, {\left(x^{3} + 2\right)}^{\frac{3}{4}}"," ",0,"4/9*(x^3 + 2)^(3/4)","A",0
583,1,1269,0,0.316698," ","integrate(x^m*(b*x^3+a)^8,x, algorithm=""giac"")","\frac{b^{8} m^{8} x^{25} x^{m} + 92 \, b^{8} m^{7} x^{25} x^{m} + 3514 \, b^{8} m^{6} x^{25} x^{m} + 8 \, a b^{7} m^{8} x^{22} x^{m} + 72128 \, b^{8} m^{5} x^{25} x^{m} + 760 \, a b^{7} m^{7} x^{22} x^{m} + 859369 \, b^{8} m^{4} x^{25} x^{m} + 29792 \, a b^{7} m^{6} x^{22} x^{m} + 5974388 \, b^{8} m^{3} x^{25} x^{m} + 28 \, a^{2} b^{6} m^{8} x^{19} x^{m} + 624400 \, a b^{7} m^{5} x^{22} x^{m} + 22963996 \, b^{8} m^{2} x^{25} x^{m} + 2744 \, a^{2} b^{6} m^{7} x^{19} x^{m} + 7563752 \, a b^{7} m^{4} x^{22} x^{m} + 42124592 \, b^{8} m x^{25} x^{m} + 110656 \, a^{2} b^{6} m^{6} x^{19} x^{m} + 53266360 \, a b^{7} m^{3} x^{22} x^{m} + 24344320 \, b^{8} x^{25} x^{m} + 56 \, a^{3} b^{5} m^{8} x^{16} x^{m} + 2376920 \, a^{2} b^{6} m^{5} x^{19} x^{m} + 206729648 \, a b^{7} m^{2} x^{22} x^{m} + 5656 \, a^{3} b^{5} m^{7} x^{16} x^{m} + 29390452 \, a^{2} b^{6} m^{4} x^{19} x^{m} + 381743680 \, a b^{7} m x^{22} x^{m} + 235088 \, a^{3} b^{5} m^{6} x^{16} x^{m} + 210422576 \, a^{2} b^{6} m^{3} x^{19} x^{m} + 221312000 \, a b^{7} x^{22} x^{m} + 70 \, a^{4} b^{4} m^{8} x^{13} x^{m} + 5197360 \, a^{3} b^{5} m^{5} x^{16} x^{m} + 827034544 \, a^{2} b^{6} m^{2} x^{19} x^{m} + 7280 \, a^{4} b^{4} m^{7} x^{13} x^{m} + 65946104 \, a^{3} b^{5} m^{4} x^{16} x^{m} + 1540629440 \, a^{2} b^{6} m x^{19} x^{m} + 312340 \, a^{4} b^{4} m^{6} x^{13} x^{m} + 482544664 \, a^{3} b^{5} m^{3} x^{16} x^{m} + 896896000 \, a^{2} b^{6} x^{19} x^{m} + 56 \, a^{5} b^{3} m^{8} x^{10} x^{m} + 7138040 \, a^{4} b^{4} m^{5} x^{13} x^{m} + 1929412352 \, a^{3} b^{5} m^{2} x^{16} x^{m} + 5992 \, a^{5} b^{3} m^{7} x^{10} x^{m} + 93585310 \, a^{4} b^{4} m^{4} x^{13} x^{m} + 3637973920 \, a^{3} b^{5} m x^{16} x^{m} + 265664 \, a^{5} b^{3} m^{6} x^{10} x^{m} + 705493880 \, a^{4} b^{4} m^{3} x^{13} x^{m} + 2130128000 \, a^{3} b^{5} x^{16} x^{m} + 28 \, a^{6} b^{2} m^{8} x^{7} x^{m} + 6302128 \, a^{5} b^{3} m^{5} x^{10} x^{m} + 2891238280 \, a^{4} b^{4} m^{2} x^{13} x^{m} + 3080 \, a^{6} b^{2} m^{7} x^{7} x^{m} + 86082584 \, a^{5} b^{3} m^{4} x^{10} x^{m} + 5549616800 \, a^{4} b^{4} m x^{13} x^{m} + 141232 \, a^{6} b^{2} m^{6} x^{7} x^{m} + 676856488 \, a^{5} b^{3} m^{3} x^{10} x^{m} + 3277120000 \, a^{4} b^{4} x^{13} x^{m} + 8 \, a^{7} b m^{8} x^{4} x^{m} + 3490760 \, a^{6} b^{2} m^{5} x^{7} x^{m} + 2881562096 \, a^{5} b^{3} m^{2} x^{10} x^{m} + 904 \, a^{7} b m^{7} x^{4} x^{m} + 50116612 \, a^{6} b^{2} m^{4} x^{7} x^{m} + 5692950592 \, a^{5} b^{3} m x^{10} x^{m} + 42896 \, a^{7} b m^{6} x^{4} x^{m} + 418024880 \, a^{6} b^{2} m^{3} x^{7} x^{m} + 3408204800 \, a^{5} b^{3} x^{10} x^{m} + a^{8} m^{8} x x^{m} + 1108240 \, a^{7} b m^{5} x^{4} x^{m} + 1898889328 \, a^{6} b^{2} m^{2} x^{7} x^{m} + 116 \, a^{8} m^{7} x x^{m} + 16867592 \, a^{7} b m^{4} x^{4} x^{m} + 3962060480 \, a^{6} b^{2} m x^{7} x^{m} + 5698 \, a^{8} m^{6} x x^{m} + 152198536 \, a^{7} b m^{3} x^{4} x^{m} + 2434432000 \, a^{6} b^{2} x^{7} x^{m} + 154280 \, a^{8} m^{5} x x^{m} + 769795424 \, a^{7} b m^{2} x^{4} x^{m} + 2508289 \, a^{8} m^{4} x x^{m} + 1850614240 \, a^{7} b m x^{4} x^{m} + 24950324 \, a^{8} m^{3} x x^{m} + 1217216000 \, a^{7} b x^{4} x^{m} + 147373372 \, a^{8} m^{2} x x^{m} + 468851120 \, a^{8} m x x^{m} + 608608000 \, a^{8} x x^{m}}{m^{9} + 117 \, m^{8} + 5814 \, m^{7} + 159978 \, m^{6} + 2662569 \, m^{5} + 27458613 \, m^{4} + 172323696 \, m^{3} + 616224492 \, m^{2} + 1077459120 \, m + 608608000}"," ",0,"(b^8*m^8*x^25*x^m + 92*b^8*m^7*x^25*x^m + 3514*b^8*m^6*x^25*x^m + 8*a*b^7*m^8*x^22*x^m + 72128*b^8*m^5*x^25*x^m + 760*a*b^7*m^7*x^22*x^m + 859369*b^8*m^4*x^25*x^m + 29792*a*b^7*m^6*x^22*x^m + 5974388*b^8*m^3*x^25*x^m + 28*a^2*b^6*m^8*x^19*x^m + 624400*a*b^7*m^5*x^22*x^m + 22963996*b^8*m^2*x^25*x^m + 2744*a^2*b^6*m^7*x^19*x^m + 7563752*a*b^7*m^4*x^22*x^m + 42124592*b^8*m*x^25*x^m + 110656*a^2*b^6*m^6*x^19*x^m + 53266360*a*b^7*m^3*x^22*x^m + 24344320*b^8*x^25*x^m + 56*a^3*b^5*m^8*x^16*x^m + 2376920*a^2*b^6*m^5*x^19*x^m + 206729648*a*b^7*m^2*x^22*x^m + 5656*a^3*b^5*m^7*x^16*x^m + 29390452*a^2*b^6*m^4*x^19*x^m + 381743680*a*b^7*m*x^22*x^m + 235088*a^3*b^5*m^6*x^16*x^m + 210422576*a^2*b^6*m^3*x^19*x^m + 221312000*a*b^7*x^22*x^m + 70*a^4*b^4*m^8*x^13*x^m + 5197360*a^3*b^5*m^5*x^16*x^m + 827034544*a^2*b^6*m^2*x^19*x^m + 7280*a^4*b^4*m^7*x^13*x^m + 65946104*a^3*b^5*m^4*x^16*x^m + 1540629440*a^2*b^6*m*x^19*x^m + 312340*a^4*b^4*m^6*x^13*x^m + 482544664*a^3*b^5*m^3*x^16*x^m + 896896000*a^2*b^6*x^19*x^m + 56*a^5*b^3*m^8*x^10*x^m + 7138040*a^4*b^4*m^5*x^13*x^m + 1929412352*a^3*b^5*m^2*x^16*x^m + 5992*a^5*b^3*m^7*x^10*x^m + 93585310*a^4*b^4*m^4*x^13*x^m + 3637973920*a^3*b^5*m*x^16*x^m + 265664*a^5*b^3*m^6*x^10*x^m + 705493880*a^4*b^4*m^3*x^13*x^m + 2130128000*a^3*b^5*x^16*x^m + 28*a^6*b^2*m^8*x^7*x^m + 6302128*a^5*b^3*m^5*x^10*x^m + 2891238280*a^4*b^4*m^2*x^13*x^m + 3080*a^6*b^2*m^7*x^7*x^m + 86082584*a^5*b^3*m^4*x^10*x^m + 5549616800*a^4*b^4*m*x^13*x^m + 141232*a^6*b^2*m^6*x^7*x^m + 676856488*a^5*b^3*m^3*x^10*x^m + 3277120000*a^4*b^4*x^13*x^m + 8*a^7*b*m^8*x^4*x^m + 3490760*a^6*b^2*m^5*x^7*x^m + 2881562096*a^5*b^3*m^2*x^10*x^m + 904*a^7*b*m^7*x^4*x^m + 50116612*a^6*b^2*m^4*x^7*x^m + 5692950592*a^5*b^3*m*x^10*x^m + 42896*a^7*b*m^6*x^4*x^m + 418024880*a^6*b^2*m^3*x^7*x^m + 3408204800*a^5*b^3*x^10*x^m + a^8*m^8*x*x^m + 1108240*a^7*b*m^5*x^4*x^m + 1898889328*a^6*b^2*m^2*x^7*x^m + 116*a^8*m^7*x*x^m + 16867592*a^7*b*m^4*x^4*x^m + 3962060480*a^6*b^2*m*x^7*x^m + 5698*a^8*m^6*x*x^m + 152198536*a^7*b*m^3*x^4*x^m + 2434432000*a^6*b^2*x^7*x^m + 154280*a^8*m^5*x*x^m + 769795424*a^7*b*m^2*x^4*x^m + 2508289*a^8*m^4*x*x^m + 1850614240*a^7*b*m*x^4*x^m + 24950324*a^8*m^3*x*x^m + 1217216000*a^7*b*x^4*x^m + 147373372*a^8*m^2*x*x^m + 468851120*a^8*m*x*x^m + 608608000*a^8*x*x^m)/(m^9 + 117*m^8 + 5814*m^7 + 159978*m^6 + 2662569*m^5 + 27458613*m^4 + 172323696*m^3 + 616224492*m^2 + 1077459120*m + 608608000)","B",0
584,1,540,0,0.217969," ","integrate(x^m*(b*x^3+a)^5,x, algorithm=""giac"")","\frac{b^{5} m^{5} x^{16} x^{m} + 35 \, b^{5} m^{4} x^{16} x^{m} + 445 \, b^{5} m^{3} x^{16} x^{m} + 5 \, a b^{4} m^{5} x^{13} x^{m} + 2485 \, b^{5} m^{2} x^{16} x^{m} + 190 \, a b^{4} m^{4} x^{13} x^{m} + 5714 \, b^{5} m x^{16} x^{m} + 2555 \, a b^{4} m^{3} x^{13} x^{m} + 3640 \, b^{5} x^{16} x^{m} + 10 \, a^{2} b^{3} m^{5} x^{10} x^{m} + 14810 \, a b^{4} m^{2} x^{13} x^{m} + 410 \, a^{2} b^{3} m^{4} x^{10} x^{m} + 34840 \, a b^{4} m x^{13} x^{m} + 5950 \, a^{2} b^{3} m^{3} x^{10} x^{m} + 22400 \, a b^{4} x^{13} x^{m} + 10 \, a^{3} b^{2} m^{5} x^{7} x^{m} + 36550 \, a^{2} b^{3} m^{2} x^{10} x^{m} + 440 \, a^{3} b^{2} m^{4} x^{7} x^{m} + 89240 \, a^{2} b^{3} m x^{10} x^{m} + 6970 \, a^{3} b^{2} m^{3} x^{7} x^{m} + 58240 \, a^{2} b^{3} x^{10} x^{m} + 5 \, a^{4} b m^{5} x^{4} x^{m} + 47260 \, a^{3} b^{2} m^{2} x^{7} x^{m} + 235 \, a^{4} b m^{4} x^{4} x^{m} + 123920 \, a^{3} b^{2} m x^{7} x^{m} + 4085 \, a^{4} b m^{3} x^{4} x^{m} + 83200 \, a^{3} b^{2} x^{7} x^{m} + a^{5} m^{5} x x^{m} + 31685 \, a^{4} b m^{2} x^{4} x^{m} + 50 \, a^{5} m^{4} x x^{m} + 100630 \, a^{4} b m x^{4} x^{m} + 955 \, a^{5} m^{3} x x^{m} + 72800 \, a^{4} b x^{4} x^{m} + 8650 \, a^{5} m^{2} x x^{m} + 36824 \, a^{5} m x x^{m} + 58240 \, a^{5} x x^{m}}{m^{6} + 51 \, m^{5} + 1005 \, m^{4} + 9605 \, m^{3} + 45474 \, m^{2} + 95064 \, m + 58240}"," ",0,"(b^5*m^5*x^16*x^m + 35*b^5*m^4*x^16*x^m + 445*b^5*m^3*x^16*x^m + 5*a*b^4*m^5*x^13*x^m + 2485*b^5*m^2*x^16*x^m + 190*a*b^4*m^4*x^13*x^m + 5714*b^5*m*x^16*x^m + 2555*a*b^4*m^3*x^13*x^m + 3640*b^5*x^16*x^m + 10*a^2*b^3*m^5*x^10*x^m + 14810*a*b^4*m^2*x^13*x^m + 410*a^2*b^3*m^4*x^10*x^m + 34840*a*b^4*m*x^13*x^m + 5950*a^2*b^3*m^3*x^10*x^m + 22400*a*b^4*x^13*x^m + 10*a^3*b^2*m^5*x^7*x^m + 36550*a^2*b^3*m^2*x^10*x^m + 440*a^3*b^2*m^4*x^7*x^m + 89240*a^2*b^3*m*x^10*x^m + 6970*a^3*b^2*m^3*x^7*x^m + 58240*a^2*b^3*x^10*x^m + 5*a^4*b*m^5*x^4*x^m + 47260*a^3*b^2*m^2*x^7*x^m + 235*a^4*b*m^4*x^4*x^m + 123920*a^3*b^2*m*x^7*x^m + 4085*a^4*b*m^3*x^4*x^m + 83200*a^3*b^2*x^7*x^m + a^5*m^5*x*x^m + 31685*a^4*b*m^2*x^4*x^m + 50*a^5*m^4*x*x^m + 100630*a^4*b*m*x^4*x^m + 955*a^5*m^3*x*x^m + 72800*a^4*b*x^4*x^m + 8650*a^5*m^2*x*x^m + 36824*a^5*m*x*x^m + 58240*a^5*x*x^m)/(m^6 + 51*m^5 + 1005*m^4 + 9605*m^3 + 45474*m^2 + 95064*m + 58240)","B",0
585,1,224,0,0.245118," ","integrate(x^m*(b*x^3+a)^3,x, algorithm=""giac"")","\frac{b^{3} m^{3} x^{10} x^{m} + 12 \, b^{3} m^{2} x^{10} x^{m} + 39 \, b^{3} m x^{10} x^{m} + 3 \, a b^{2} m^{3} x^{7} x^{m} + 28 \, b^{3} x^{10} x^{m} + 45 \, a b^{2} m^{2} x^{7} x^{m} + 162 \, a b^{2} m x^{7} x^{m} + 3 \, a^{2} b m^{3} x^{4} x^{m} + 120 \, a b^{2} x^{7} x^{m} + 54 \, a^{2} b m^{2} x^{4} x^{m} + 261 \, a^{2} b m x^{4} x^{m} + a^{3} m^{3} x x^{m} + 210 \, a^{2} b x^{4} x^{m} + 21 \, a^{3} m^{2} x x^{m} + 138 \, a^{3} m x x^{m} + 280 \, a^{3} x x^{m}}{m^{4} + 22 \, m^{3} + 159 \, m^{2} + 418 \, m + 280}"," ",0,"(b^3*m^3*x^10*x^m + 12*b^3*m^2*x^10*x^m + 39*b^3*m*x^10*x^m + 3*a*b^2*m^3*x^7*x^m + 28*b^3*x^10*x^m + 45*a*b^2*m^2*x^7*x^m + 162*a*b^2*m*x^7*x^m + 3*a^2*b*m^3*x^4*x^m + 120*a*b^2*x^7*x^m + 54*a^2*b*m^2*x^4*x^m + 261*a^2*b*m*x^4*x^m + a^3*m^3*x*x^m + 210*a^2*b*x^4*x^m + 21*a^3*m^2*x*x^m + 138*a^3*m*x*x^m + 280*a^3*x*x^m)/(m^4 + 22*m^3 + 159*m^2 + 418*m + 280)","B",0
586,1,117,0,0.168654," ","integrate(x^m*(b*x^3+a)^2,x, algorithm=""giac"")","\frac{b^{2} m^{2} x^{7} x^{m} + 5 \, b^{2} m x^{7} x^{m} + 4 \, b^{2} x^{7} x^{m} + 2 \, a b m^{2} x^{4} x^{m} + 16 \, a b m x^{4} x^{m} + 14 \, a b x^{4} x^{m} + a^{2} m^{2} x x^{m} + 11 \, a^{2} m x x^{m} + 28 \, a^{2} x x^{m}}{m^{3} + 12 \, m^{2} + 39 \, m + 28}"," ",0,"(b^2*m^2*x^7*x^m + 5*b^2*m*x^7*x^m + 4*b^2*x^7*x^m + 2*a*b*m^2*x^4*x^m + 16*a*b*m*x^4*x^m + 14*a*b*x^4*x^m + a^2*m^2*x*x^m + 11*a^2*m*x*x^m + 28*a^2*x*x^m)/(m^3 + 12*m^2 + 39*m + 28)","B",0
587,1,43,0,0.161915," ","integrate(x^m*(b*x^3+a),x, algorithm=""giac"")","\frac{b m x^{4} x^{m} + b x^{4} x^{m} + a m x x^{m} + 4 \, a x x^{m}}{m^{2} + 5 \, m + 4}"," ",0,"(b*m*x^4*x^m + b*x^4*x^m + a*m*x*x^m + 4*a*x*x^m)/(m^2 + 5*m + 4)","A",0
588,0,0,0,0.000000," ","integrate(x^m/(b*x^3+a),x, algorithm=""giac"")","\int \frac{x^{m}}{b x^{3} + a}\,{d x}"," ",0,"integrate(x^m/(b*x^3 + a), x)","F",0
589,0,0,0,0.000000," ","integrate(x^m/(b*x^3+a)^2,x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{3} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^m/(b*x^3 + a)^2, x)","F",0
590,0,0,0,0.000000," ","integrate(x^m/(b*x^3+a)^3,x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{3} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x^m/(b*x^3 + a)^3, x)","F",0
591,0,0,0,0.000000," ","integrate(x^m*(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{3}{2}} x^{m}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/2)*x^m, x)","F",0
592,0,0,0,0.000000," ","integrate(x^m*(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{3} + a} x^{m}\,{d x}"," ",0,"integrate(sqrt(b*x^3 + a)*x^m, x)","F",0
593,0,0,0,0.000000," ","integrate(x^m/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\sqrt{b x^{3} + a}}\,{d x}"," ",0,"integrate(x^m/sqrt(b*x^3 + a), x)","F",0
594,0,0,0,0.000000," ","integrate(x^m/(b*x^3+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{3} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m/(b*x^3 + a)^(3/2), x)","F",0
595,0,0,0,0.000000," ","integrate((c*x)^m*(b*x^3+a)^(4/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{4}{3}} \left(c x\right)^{m}\,{d x}"," ",0,"integrate((b*x^3 + a)^(4/3)*(c*x)^m, x)","F",0
596,0,0,0,0.000000," ","integrate((c*x)^m*(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(c x\right)^{m}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)*(c*x)^m, x)","F",0
597,0,0,0,0.000000," ","integrate((c*x)^m*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(c x\right)^{m}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*(c*x)^m, x)","F",0
598,0,0,0,0.000000," ","integrate((c*x)^m*(b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{p} \left(c x\right)^{m}\,{d x}"," ",0,"integrate((b*x^3 + a)^p*(c*x)^m, x)","F",0
599,1,21,0,0.152803," ","integrate(x^2*(b*x^3+a)^p,x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{p + 1}}{3 \, b {\left(p + 1\right)}}"," ",0,"1/3*(b*x^3 + a)^(p + 1)/(b*(p + 1))","A",0
600,1,94,0,0.171154," ","integrate(x^5*(b*x^3+a)^p,x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{2} {\left(b x^{3} + a\right)}^{p} p - {\left(b x^{3} + a\right)} {\left(b x^{3} + a\right)}^{p} a p + {\left(b x^{3} + a\right)}^{2} {\left(b x^{3} + a\right)}^{p} - 2 \, {\left(b x^{3} + a\right)} {\left(b x^{3} + a\right)}^{p} a}{3 \, {\left(p^{2} + 3 \, p + 2\right)} b^{2}}"," ",0,"1/3*((b*x^3 + a)^2*(b*x^3 + a)^p*p - (b*x^3 + a)*(b*x^3 + a)^p*a*p + (b*x^3 + a)^2*(b*x^3 + a)^p - 2*(b*x^3 + a)*(b*x^3 + a)^p*a)/((p^2 + 3*p + 2)*b^2)","B",0
601,1,231,0,0.163004," ","integrate(x^8*(b*x^3+a)^p,x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{3} {\left(b x^{3} + a\right)}^{p} p^{2} - 2 \, {\left(b x^{3} + a\right)}^{2} {\left(b x^{3} + a\right)}^{p} a p^{2} + {\left(b x^{3} + a\right)} {\left(b x^{3} + a\right)}^{p} a^{2} p^{2} + 3 \, {\left(b x^{3} + a\right)}^{3} {\left(b x^{3} + a\right)}^{p} p - 8 \, {\left(b x^{3} + a\right)}^{2} {\left(b x^{3} + a\right)}^{p} a p + 5 \, {\left(b x^{3} + a\right)} {\left(b x^{3} + a\right)}^{p} a^{2} p + 2 \, {\left(b x^{3} + a\right)}^{3} {\left(b x^{3} + a\right)}^{p} - 6 \, {\left(b x^{3} + a\right)}^{2} {\left(b x^{3} + a\right)}^{p} a + 6 \, {\left(b x^{3} + a\right)} {\left(b x^{3} + a\right)}^{p} a^{2}}{3 \, {\left(b^{2} p^{3} + 6 \, b^{2} p^{2} + 11 \, b^{2} p + 6 \, b^{2}\right)} b}"," ",0,"1/3*((b*x^3 + a)^3*(b*x^3 + a)^p*p^2 - 2*(b*x^3 + a)^2*(b*x^3 + a)^p*a*p^2 + (b*x^3 + a)*(b*x^3 + a)^p*a^2*p^2 + 3*(b*x^3 + a)^3*(b*x^3 + a)^p*p - 8*(b*x^3 + a)^2*(b*x^3 + a)^p*a*p + 5*(b*x^3 + a)*(b*x^3 + a)^p*a^2*p + 2*(b*x^3 + a)^3*(b*x^3 + a)^p - 6*(b*x^3 + a)^2*(b*x^3 + a)^p*a + 6*(b*x^3 + a)*(b*x^3 + a)^p*a^2)/((b^2*p^3 + 6*b^2*p^2 + 11*b^2*p + 6*b^2)*b)","B",0
602,1,410,0,0.192565," ","integrate(x^11*(b*x^3+a)^p,x, algorithm=""giac"")","\frac{{\left(b x^{3} + a\right)}^{4} {\left(b x^{3} + a\right)}^{p} p^{3} - 3 \, {\left(b x^{3} + a\right)}^{3} {\left(b x^{3} + a\right)}^{p} a p^{3} + 3 \, {\left(b x^{3} + a\right)}^{2} {\left(b x^{3} + a\right)}^{p} a^{2} p^{3} - {\left(b x^{3} + a\right)} {\left(b x^{3} + a\right)}^{p} a^{3} p^{3} + 6 \, {\left(b x^{3} + a\right)}^{4} {\left(b x^{3} + a\right)}^{p} p^{2} - 21 \, {\left(b x^{3} + a\right)}^{3} {\left(b x^{3} + a\right)}^{p} a p^{2} + 24 \, {\left(b x^{3} + a\right)}^{2} {\left(b x^{3} + a\right)}^{p} a^{2} p^{2} - 9 \, {\left(b x^{3} + a\right)} {\left(b x^{3} + a\right)}^{p} a^{3} p^{2} + 11 \, {\left(b x^{3} + a\right)}^{4} {\left(b x^{3} + a\right)}^{p} p - 42 \, {\left(b x^{3} + a\right)}^{3} {\left(b x^{3} + a\right)}^{p} a p + 57 \, {\left(b x^{3} + a\right)}^{2} {\left(b x^{3} + a\right)}^{p} a^{2} p - 26 \, {\left(b x^{3} + a\right)} {\left(b x^{3} + a\right)}^{p} a^{3} p + 6 \, {\left(b x^{3} + a\right)}^{4} {\left(b x^{3} + a\right)}^{p} - 24 \, {\left(b x^{3} + a\right)}^{3} {\left(b x^{3} + a\right)}^{p} a + 36 \, {\left(b x^{3} + a\right)}^{2} {\left(b x^{3} + a\right)}^{p} a^{2} - 24 \, {\left(b x^{3} + a\right)} {\left(b x^{3} + a\right)}^{p} a^{3}}{3 \, {\left(b^{3} p^{4} + 10 \, b^{3} p^{3} + 35 \, b^{3} p^{2} + 50 \, b^{3} p + 24 \, b^{3}\right)} b}"," ",0,"1/3*((b*x^3 + a)^4*(b*x^3 + a)^p*p^3 - 3*(b*x^3 + a)^3*(b*x^3 + a)^p*a*p^3 + 3*(b*x^3 + a)^2*(b*x^3 + a)^p*a^2*p^3 - (b*x^3 + a)*(b*x^3 + a)^p*a^3*p^3 + 6*(b*x^3 + a)^4*(b*x^3 + a)^p*p^2 - 21*(b*x^3 + a)^3*(b*x^3 + a)^p*a*p^2 + 24*(b*x^3 + a)^2*(b*x^3 + a)^p*a^2*p^2 - 9*(b*x^3 + a)*(b*x^3 + a)^p*a^3*p^2 + 11*(b*x^3 + a)^4*(b*x^3 + a)^p*p - 42*(b*x^3 + a)^3*(b*x^3 + a)^p*a*p + 57*(b*x^3 + a)^2*(b*x^3 + a)^p*a^2*p - 26*(b*x^3 + a)*(b*x^3 + a)^p*a^3*p + 6*(b*x^3 + a)^4*(b*x^3 + a)^p - 24*(b*x^3 + a)^3*(b*x^3 + a)^p*a + 36*(b*x^3 + a)^2*(b*x^3 + a)^p*a^2 - 24*(b*x^3 + a)*(b*x^3 + a)^p*a^3)/((b^3*p^4 + 10*b^3*p^3 + 35*b^3*p^2 + 50*b^3*p + 24*b^3)*b)","B",0
603,1,43,0,0.170492," ","integrate(x^m*(b*x^4+a),x, algorithm=""giac"")","\frac{b m x^{5} x^{m} + b x^{5} x^{m} + a m x x^{m} + 5 \, a x x^{m}}{m^{2} + 6 \, m + 5}"," ",0,"(b*m*x^5*x^m + b*x^5*x^m + a*m*x*x^m + 5*a*x*x^m)/(m^2 + 6*m + 5)","A",0
604,1,13,0,0.145975," ","integrate(x^5*(b*x^4+a),x, algorithm=""giac"")","\frac{1}{10} \, b x^{10} + \frac{1}{6} \, a x^{6}"," ",0,"1/10*b*x^10 + 1/6*a*x^6","A",0
605,1,13,0,0.145051," ","integrate(x^4*(b*x^4+a),x, algorithm=""giac"")","\frac{1}{9} \, b x^{9} + \frac{1}{5} \, a x^{5}"," ",0,"1/9*b*x^9 + 1/5*a*x^5","A",0
606,1,13,0,0.149831," ","integrate(x^3*(b*x^4+a),x, algorithm=""giac"")","\frac{1}{8} \, b x^{8} + \frac{1}{4} \, a x^{4}"," ",0,"1/8*b*x^8 + 1/4*a*x^4","A",0
607,1,13,0,0.150901," ","integrate(x^2*(b*x^4+a),x, algorithm=""giac"")","\frac{1}{7} \, b x^{7} + \frac{1}{3} \, a x^{3}"," ",0,"1/7*b*x^7 + 1/3*a*x^3","A",0
608,1,13,0,0.147730," ","integrate(x*(b*x^4+a),x, algorithm=""giac"")","\frac{1}{6} \, b x^{6} + \frac{1}{2} \, a x^{2}"," ",0,"1/6*b*x^6 + 1/2*a*x^2","A",0
609,1,10,0,0.147129," ","integrate(b*x^4+a,x, algorithm=""giac"")","\frac{1}{5} \, b x^{5} + a x"," ",0,"1/5*b*x^5 + a*x","A",0
610,1,14,0,0.194503," ","integrate((b*x^4+a)/x,x, algorithm=""giac"")","\frac{1}{4} \, b x^{4} + \frac{1}{4} \, a \log\left(x^{4}\right)"," ",0,"1/4*b*x^4 + 1/4*a*log(x^4)","A",0
611,1,13,0,0.148646," ","integrate((b*x^4+a)/x^2,x, algorithm=""giac"")","\frac{1}{3} \, b x^{3} - \frac{a}{x}"," ",0,"1/3*b*x^3 - a/x","A",0
612,1,13,0,0.174557," ","integrate((b*x^4+a)/x^3,x, algorithm=""giac"")","\frac{1}{2} \, b x^{2} - \frac{a}{2 \, x^{2}}"," ",0,"1/2*b*x^2 - 1/2*a/x^2","A",0
613,1,10,0,0.147021," ","integrate((b*x^4+a)/x^4,x, algorithm=""giac"")","b x - \frac{a}{3 \, x^{3}}"," ",0,"b*x - 1/3*a/x^3","A",0
614,1,20,0,0.148369," ","integrate((b*x^4+a)/x^5,x, algorithm=""giac"")","\frac{1}{4} \, b \log\left(x^{4}\right) - \frac{b x^{4} + a}{4 \, x^{4}}"," ",0,"1/4*b*log(x^4) - 1/4*(b*x^4 + a)/x^4","A",0
615,1,13,0,0.149786," ","integrate((b*x^4+a)/x^6,x, algorithm=""giac"")","-\frac{5 \, b x^{4} + a}{5 \, x^{5}}"," ",0,"-1/5*(5*b*x^4 + a)/x^5","A",0
616,1,13,0,0.144475," ","integrate((b*x^4+a)/x^7,x, algorithm=""giac"")","-\frac{3 \, b x^{4} + a}{6 \, x^{6}}"," ",0,"-1/6*(3*b*x^4 + a)/x^6","A",0
617,1,15,0,0.147509," ","integrate((b*x^4+a)/x^8,x, algorithm=""giac"")","-\frac{7 \, b x^{4} + 3 \, a}{21 \, x^{7}}"," ",0,"-1/21*(7*b*x^4 + 3*a)/x^7","A",0
618,1,13,0,0.175777," ","integrate((b*x^4+a)/x^9,x, algorithm=""giac"")","-\frac{2 \, b x^{4} + a}{8 \, x^{8}}"," ",0,"-1/8*(2*b*x^4 + a)/x^8","A",0
619,1,15,0,0.148093," ","integrate((b*x^4+a)/x^10,x, algorithm=""giac"")","-\frac{9 \, b x^{4} + 5 \, a}{45 \, x^{9}}"," ",0,"-1/45*(9*b*x^4 + 5*a)/x^9","A",0
620,1,117,0,0.162595," ","integrate(x^m*(b*x^4+a)^2,x, algorithm=""giac"")","\frac{b^{2} m^{2} x^{9} x^{m} + 6 \, b^{2} m x^{9} x^{m} + 5 \, b^{2} x^{9} x^{m} + 2 \, a b m^{2} x^{5} x^{m} + 20 \, a b m x^{5} x^{m} + 18 \, a b x^{5} x^{m} + a^{2} m^{2} x x^{m} + 14 \, a^{2} m x x^{m} + 45 \, a^{2} x x^{m}}{m^{3} + 15 \, m^{2} + 59 \, m + 45}"," ",0,"(b^2*m^2*x^9*x^m + 6*b^2*m*x^9*x^m + 5*b^2*x^9*x^m + 2*a*b*m^2*x^5*x^m + 20*a*b*m*x^5*x^m + 18*a*b*x^5*x^m + a^2*m^2*x*x^m + 14*a^2*m*x*x^m + 45*a^2*x*x^m)/(m^3 + 15*m^2 + 59*m + 45)","B",0
621,1,24,0,0.150742," ","integrate(x^5*(b*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{14} \, b^{2} x^{14} + \frac{1}{5} \, a b x^{10} + \frac{1}{6} \, a^{2} x^{6}"," ",0,"1/14*b^2*x^14 + 1/5*a*b*x^10 + 1/6*a^2*x^6","A",0
622,1,24,0,0.154307," ","integrate(x^4*(b*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{13} \, b^{2} x^{13} + \frac{2}{9} \, a b x^{9} + \frac{1}{5} \, a^{2} x^{5}"," ",0,"1/13*b^2*x^13 + 2/9*a*b*x^9 + 1/5*a^2*x^5","A",0
623,1,14,0,0.153794," ","integrate(x^3*(b*x^4+a)^2,x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{3}}{12 \, b}"," ",0,"1/12*(b*x^4 + a)^3/b","A",0
624,1,24,0,0.146563," ","integrate(x^2*(b*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{11} \, b^{2} x^{11} + \frac{2}{7} \, a b x^{7} + \frac{1}{3} \, a^{2} x^{3}"," ",0,"1/11*b^2*x^11 + 2/7*a*b*x^7 + 1/3*a^2*x^3","A",0
625,1,24,0,0.149818," ","integrate(x*(b*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{10} \, b^{2} x^{10} + \frac{1}{3} \, a b x^{6} + \frac{1}{2} \, a^{2} x^{2}"," ",0,"1/10*b^2*x^10 + 1/3*a*b*x^6 + 1/2*a^2*x^2","A",0
626,1,21,0,0.153363," ","integrate((b*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{9} \, b^{2} x^{9} + \frac{2}{5} \, a b x^{5} + a^{2} x"," ",0,"1/9*b^2*x^9 + 2/5*a*b*x^5 + a^2*x","A",0
627,1,25,0,0.148519," ","integrate((b*x^4+a)^2/x,x, algorithm=""giac"")","\frac{1}{8} \, b^{2} x^{8} + \frac{1}{2} \, a b x^{4} + \frac{1}{4} \, a^{2} \log\left(x^{4}\right)"," ",0,"1/8*b^2*x^8 + 1/2*a*b*x^4 + 1/4*a^2*log(x^4)","A",0
628,1,24,0,0.148828," ","integrate((b*x^4+a)^2/x^2,x, algorithm=""giac"")","\frac{1}{7} \, b^{2} x^{7} + \frac{2}{3} \, a b x^{3} - \frac{a^{2}}{x}"," ",0,"1/7*b^2*x^7 + 2/3*a*b*x^3 - a^2/x","A",0
629,1,23,0,0.150870," ","integrate((b*x^4+a)^2/x^3,x, algorithm=""giac"")","\frac{1}{6} \, b^{2} x^{6} + a b x^{2} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/6*b^2*x^6 + a*b*x^2 - 1/2*a^2/x^2","A",0
630,1,22,0,0.148116," ","integrate((b*x^4+a)^2/x^4,x, algorithm=""giac"")","\frac{1}{5} \, b^{2} x^{5} + 2 \, a b x - \frac{a^{2}}{3 \, x^{3}}"," ",0,"1/5*b^2*x^5 + 2*a*b*x - 1/3*a^2/x^3","A",0
631,1,33,0,0.154559," ","integrate((b*x^4+a)^2/x^5,x, algorithm=""giac"")","\frac{1}{4} \, b^{2} x^{4} + \frac{1}{2} \, a b \log\left(x^{4}\right) - \frac{2 \, a b x^{4} + a^{2}}{4 \, x^{4}}"," ",0,"1/4*b^2*x^4 + 1/2*a*b*log(x^4) - 1/4*(2*a*b*x^4 + a^2)/x^4","A",0
632,1,224,0,0.175182," ","integrate(x^m*(b*x^4+a)^3,x, algorithm=""giac"")","\frac{b^{3} m^{3} x^{13} x^{m} + 15 \, b^{3} m^{2} x^{13} x^{m} + 59 \, b^{3} m x^{13} x^{m} + 45 \, b^{3} x^{13} x^{m} + 3 \, a b^{2} m^{3} x^{9} x^{m} + 57 \, a b^{2} m^{2} x^{9} x^{m} + 249 \, a b^{2} m x^{9} x^{m} + 195 \, a b^{2} x^{9} x^{m} + 3 \, a^{2} b m^{3} x^{5} x^{m} + 69 \, a^{2} b m^{2} x^{5} x^{m} + 417 \, a^{2} b m x^{5} x^{m} + 351 \, a^{2} b x^{5} x^{m} + a^{3} m^{3} x x^{m} + 27 \, a^{3} m^{2} x x^{m} + 227 \, a^{3} m x x^{m} + 585 \, a^{3} x x^{m}}{m^{4} + 28 \, m^{3} + 254 \, m^{2} + 812 \, m + 585}"," ",0,"(b^3*m^3*x^13*x^m + 15*b^3*m^2*x^13*x^m + 59*b^3*m*x^13*x^m + 45*b^3*x^13*x^m + 3*a*b^2*m^3*x^9*x^m + 57*a*b^2*m^2*x^9*x^m + 249*a*b^2*m*x^9*x^m + 195*a*b^2*x^9*x^m + 3*a^2*b*m^3*x^5*x^m + 69*a^2*b*m^2*x^5*x^m + 417*a^2*b*m*x^5*x^m + 351*a^2*b*x^5*x^m + a^3*m^3*x*x^m + 27*a^3*m^2*x*x^m + 227*a^3*m*x*x^m + 585*a^3*x*x^m)/(m^4 + 28*m^3 + 254*m^2 + 812*m + 585)","B",0
633,1,35,0,0.181875," ","integrate(x^5*(b*x^4+a)^3,x, algorithm=""giac"")","\frac{1}{18} \, b^{3} x^{18} + \frac{3}{14} \, a b^{2} x^{14} + \frac{3}{10} \, a^{2} b x^{10} + \frac{1}{6} \, a^{3} x^{6}"," ",0,"1/18*b^3*x^18 + 3/14*a*b^2*x^14 + 3/10*a^2*b*x^10 + 1/6*a^3*x^6","A",0
634,1,35,0,0.151503," ","integrate(x^4*(b*x^4+a)^3,x, algorithm=""giac"")","\frac{1}{17} \, b^{3} x^{17} + \frac{3}{13} \, a b^{2} x^{13} + \frac{1}{3} \, a^{2} b x^{9} + \frac{1}{5} \, a^{3} x^{5}"," ",0,"1/17*b^3*x^17 + 3/13*a*b^2*x^13 + 1/3*a^2*b*x^9 + 1/5*a^3*x^5","A",0
635,1,14,0,0.148476," ","integrate(x^3*(b*x^4+a)^3,x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{4}}{16 \, b}"," ",0,"1/16*(b*x^4 + a)^4/b","A",0
636,1,35,0,0.152497," ","integrate(x^2*(b*x^4+a)^3,x, algorithm=""giac"")","\frac{1}{15} \, b^{3} x^{15} + \frac{3}{11} \, a b^{2} x^{11} + \frac{3}{7} \, a^{2} b x^{7} + \frac{1}{3} \, a^{3} x^{3}"," ",0,"1/15*b^3*x^15 + 3/11*a*b^2*x^11 + 3/7*a^2*b*x^7 + 1/3*a^3*x^3","A",0
637,1,35,0,0.158170," ","integrate(x*(b*x^4+a)^3,x, algorithm=""giac"")","\frac{1}{14} \, b^{3} x^{14} + \frac{3}{10} \, a b^{2} x^{10} + \frac{1}{2} \, a^{2} b x^{6} + \frac{1}{2} \, a^{3} x^{2}"," ",0,"1/14*b^3*x^14 + 3/10*a*b^2*x^10 + 1/2*a^2*b*x^6 + 1/2*a^3*x^2","A",0
638,1,32,0,0.171308," ","integrate((b*x^4+a)^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{3} x^{13} + \frac{1}{3} \, a b^{2} x^{9} + \frac{3}{5} \, a^{2} b x^{5} + a^{3} x"," ",0,"1/13*b^3*x^13 + 1/3*a*b^2*x^9 + 3/5*a^2*b*x^5 + a^3*x","A",0
639,1,36,0,0.153114," ","integrate((b*x^4+a)^3/x,x, algorithm=""giac"")","\frac{1}{12} \, b^{3} x^{12} + \frac{3}{8} \, a b^{2} x^{8} + \frac{3}{4} \, a^{2} b x^{4} + \frac{1}{4} \, a^{3} \log\left(x^{4}\right)"," ",0,"1/12*b^3*x^12 + 3/8*a*b^2*x^8 + 3/4*a^2*b*x^4 + 1/4*a^3*log(x^4)","A",0
640,1,34,0,0.230528," ","integrate((b*x^4+a)^3/x^2,x, algorithm=""giac"")","\frac{1}{11} \, b^{3} x^{11} + \frac{3}{7} \, a b^{2} x^{7} + a^{2} b x^{3} - \frac{a^{3}}{x}"," ",0,"1/11*b^3*x^11 + 3/7*a*b^2*x^7 + a^2*b*x^3 - a^3/x","A",0
641,1,35,0,0.154064," ","integrate((b*x^4+a)^3/x^3,x, algorithm=""giac"")","\frac{1}{10} \, b^{3} x^{10} + \frac{1}{2} \, a b^{2} x^{6} + \frac{3}{2} \, a^{2} b x^{2} - \frac{a^{3}}{2 \, x^{2}}"," ",0,"1/10*b^3*x^10 + 1/2*a*b^2*x^6 + 3/2*a^2*b*x^2 - 1/2*a^3/x^2","A",0
642,1,33,0,0.151061," ","integrate((b*x^4+a)^3/x^4,x, algorithm=""giac"")","\frac{1}{9} \, b^{3} x^{9} + \frac{3}{5} \, a b^{2} x^{5} + 3 \, a^{2} b x - \frac{a^{3}}{3 \, x^{3}}"," ",0,"1/9*b^3*x^9 + 3/5*a*b^2*x^5 + 3*a^2*b*x - 1/3*a^3/x^3","A",0
643,1,46,0,0.151535," ","integrate((b*x^4+a)^3/x^5,x, algorithm=""giac"")","\frac{1}{8} \, b^{3} x^{8} + \frac{3}{4} \, a b^{2} x^{4} + \frac{3}{4} \, a^{2} b \log\left(x^{4}\right) - \frac{3 \, a^{2} b x^{4} + a^{3}}{4 \, x^{4}}"," ",0,"1/8*b^3*x^8 + 3/4*a*b^2*x^4 + 3/4*a^2*b*log(x^4) - 1/4*(3*a^2*b*x^4 + a^3)/x^4","A",0
644,1,45,0,0.157862," ","integrate(x^9/(c*x^4+a),x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} c^{2}} + \frac{c^{2} x^{6} - 3 \, a c x^{2}}{6 \, c^{3}}"," ",0,"1/2*a^2*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*c^2) + 1/6*(c^2*x^6 - 3*a*c*x^2)/c^3","A",0
645,1,24,0,0.156156," ","integrate(x^7/(c*x^4+a),x, algorithm=""giac"")","\frac{x^{4}}{4 \, c} - \frac{a \log\left({\left| c x^{4} + a \right|}\right)}{4 \, c^{2}}"," ",0,"1/4*x^4/c - 1/4*a*log(abs(c*x^4 + a))/c^2","A",0
646,1,31,0,0.154551," ","integrate(x^5/(c*x^4+a),x, algorithm=""giac"")","\frac{x^{2}}{2 \, c} - \frac{a \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} c}"," ",0,"1/2*x^2/c - 1/2*a*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*c)","A",0
647,1,14,0,0.165519," ","integrate(x^3/(c*x^4+a),x, algorithm=""giac"")","\frac{\log\left({\left| c x^{4} + a \right|}\right)}{4 \, c}"," ",0,"1/4*log(abs(c*x^4 + a))/c","A",0
648,1,18,0,0.182899," ","integrate(x/(c*x^4+a),x, algorithm=""giac"")","\frac{\arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{2 \, \sqrt{a c}}"," ",0,"1/2*arctan(c*x^2/sqrt(a*c))/sqrt(a*c)","A",0
649,1,24,0,0.155164," ","integrate(1/x/(c*x^4+a),x, algorithm=""giac"")","\frac{\log\left(x^{4}\right)}{4 \, a} - \frac{\log\left({\left| c x^{4} + a \right|}\right)}{4 \, a}"," ",0,"1/4*log(x^4)/a - 1/4*log(abs(c*x^4 + a))/a","A",0
650,1,31,0,0.157096," ","integrate(1/x^3/(c*x^4+a),x, algorithm=""giac"")","-\frac{c \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a} - \frac{1}{2 \, a x^{2}}"," ",0,"-1/2*c*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*a) - 1/2/(a*x^2)","A",0
651,1,43,0,0.153191," ","integrate(1/x^5/(c*x^4+a),x, algorithm=""giac"")","-\frac{c \log\left(x^{4}\right)}{4 \, a^{2}} + \frac{c \log\left({\left| c x^{4} + a \right|}\right)}{4 \, a^{2}} + \frac{c x^{4} - a}{4 \, a^{2} x^{4}}"," ",0,"-1/4*c*log(x^4)/a^2 + 1/4*c*log(abs(c*x^4 + a))/a^2 + 1/4*(c*x^4 - a)/(a^2*x^4)","A",0
652,1,43,0,0.179324," ","integrate(1/x^7/(c*x^4+a),x, algorithm=""giac"")","\frac{c^{2} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a^{2}} + \frac{3 \, c x^{4} - a}{6 \, a^{2} x^{6}}"," ",0,"1/2*c^2*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*a^2) + 1/6*(3*c*x^4 - a)/(a^2*x^6)","A",0
653,1,172,0,0.178087," ","integrate(x^4/(c*x^4+a),x, algorithm=""giac"")","\frac{x}{c} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, c^{2}} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, c^{2}} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, c^{2}} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, c^{2}}"," ",0,"x/c - 1/4*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/c^2 - 1/4*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/c^2 - 1/8*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/c^2 + 1/8*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/c^2","A",0
654,1,179,0,0.162870," ","integrate(x^2/(c*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}}"," ",0,"1/4*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) + 1/4*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) - 1/8*sqrt(2)*(a*c^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3) + 1/8*sqrt(2)*(a*c^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3)","A",0
655,1,179,0,0.171965," ","integrate(1/(c*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c}"," ",0,"1/4*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c) + 1/4*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c) + 1/8*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c) - 1/8*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c)","A",0
656,1,187,0,0.186443," ","integrate(1/x^2/(c*x^4+a),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a^{2} c^{2}} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a^{2} c^{2}} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a^{2} c^{2}} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a^{2} c^{2}} - \frac{1}{a x}"," ",0,"-1/4*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^2) - 1/4*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^2) + 1/8*sqrt(2)*(a*c^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^2) - 1/8*sqrt(2)*(a*c^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^2) - 1/(a*x)","A",0
657,1,175,0,0.159096," ","integrate(1/x^4/(c*x^4+a),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a^{2}} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a^{2}} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a^{2}} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a^{2}} - \frac{1}{3 \, a x^{3}}"," ",0,"-1/4*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/a^2 - 1/4*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/a^2 - 1/8*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/a^2 + 1/8*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/a^2 - 1/3/(a*x^3)","A",0
658,1,49,0,0.188489," ","integrate(x^11/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{x^{4}}{4 \, c^{2}} - \frac{a \log\left({\left| c x^{4} + a \right|}\right)}{2 \, c^{3}} + \frac{2 \, a c x^{4} + a^{2}}{4 \, {\left(c x^{4} + a\right)} c^{3}}"," ",0,"1/4*x^4/c^2 - 1/2*a*log(abs(c*x^4 + a))/c^3 + 1/4*(2*a*c*x^4 + a^2)/((c*x^4 + a)*c^3)","A",0
659,1,49,0,0.159295," ","integrate(x^9/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{a x^{2}}{4 \, {\left(c x^{4} + a\right)} c^{2}} + \frac{x^{2}}{2 \, c^{2}} - \frac{3 \, a \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, \sqrt{a c} c^{2}}"," ",0,"1/4*a*x^2/((c*x^4 + a)*c^2) + 1/2*x^2/c^2 - 3/4*a*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*c^2)","A",0
660,1,48,0,0.199128," ","integrate(x^7/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{\frac{\log\left(\frac{{\left| c x^{4} + a \right|}}{{\left(c x^{4} + a\right)}^{2} {\left| c \right|}}\right)}{c} - \frac{a}{{\left(c x^{4} + a\right)} c}}{4 \, c}"," ",0,"-1/4*(log(abs(c*x^4 + a)/((c*x^4 + a)^2*abs(c)))/c - a/((c*x^4 + a)*c))/c","A",0
661,1,39,0,0.157566," ","integrate(x^5/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{x^{2}}{4 \, {\left(c x^{4} + a\right)} c} + \frac{\arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, \sqrt{a c} c}"," ",0,"-1/4*x^2/((c*x^4 + a)*c) + 1/4*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*c)","A",0
662,1,14,0,0.163049," ","integrate(x^3/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{1}{4 \, {\left(c x^{4} + a\right)} c}"," ",0,"-1/4/((c*x^4 + a)*c)","A",0
663,1,39,0,0.158414," ","integrate(x/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{x^{2}}{4 \, {\left(c x^{4} + a\right)} a} + \frac{\arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, \sqrt{a c} a}"," ",0,"1/4*x^2/((c*x^4 + a)*a) + 1/4*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*a)","A",0
664,1,47,0,0.153741," ","integrate(1/x/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{\log\left(x^{4}\right)}{4 \, a^{2}} - \frac{\log\left({\left| c x^{4} + a \right|}\right)}{4 \, a^{2}} + \frac{c x^{4} + 2 \, a}{4 \, {\left(c x^{4} + a\right)} a^{2}}"," ",0,"1/4*log(x^4)/a^2 - 1/4*log(abs(c*x^4 + a))/a^2 + 1/4*(c*x^4 + 2*a)/((c*x^4 + a)*a^2)","A",0
665,1,51,0,0.193173," ","integrate(1/x^3/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{3 \, c \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, \sqrt{a c} a^{2}} - \frac{3 \, c x^{4} + 2 \, a}{4 \, {\left(c x^{6} + a x^{2}\right)} a^{2}}"," ",0,"-3/4*c*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*a^2) - 1/4*(3*c*x^4 + 2*a)/((c*x^6 + a*x^2)*a^2)","A",0
666,1,196,0,0.183598," ","integrate(x^6/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{x^{3}}{4 \, {\left(c x^{4} + a\right)} c} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a c^{4}} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a c^{4}} - \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a c^{4}} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a c^{4}}"," ",0,"-1/4*x^3/((c*x^4 + a)*c) + 3/16*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^4) + 3/16*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^4) - 3/32*sqrt(2)*(a*c^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^4) + 3/32*sqrt(2)*(a*c^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^4)","A",0
667,1,194,0,0.160976," ","integrate(x^4/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{x}{4 \, {\left(c x^{4} + a\right)} c} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a c^{2}} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a c^{2}} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a c^{2}} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a c^{2}}"," ",0,"-1/4*x/((c*x^4 + a)*c) + 1/16*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^2) + 1/16*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^2) + 1/32*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^2) - 1/32*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^2)","A",0
668,1,196,0,0.181785," ","integrate(x^2/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{x^{3}}{4 \, {\left(c x^{4} + a\right)} a} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{3}} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{3}} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{3}} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{3}}"," ",0,"1/4*x^3/((c*x^4 + a)*a) + 1/16*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^3) + 1/16*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^3) - 1/32*sqrt(2)*(a*c^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^3) + 1/32*sqrt(2)*(a*c^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^3)","A",0
669,1,194,0,0.184941," ","integrate(1/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{x}{4 \, {\left(c x^{4} + a\right)} a} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c} - \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c}"," ",0,"1/4*x/((c*x^4 + a)*a) + 3/16*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c) + 3/16*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c) + 3/32*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c) - 3/32*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c)","A",0
670,1,205,0,0.198996," ","integrate(1/x^2/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{5 \, c x^{4} + 4 \, a}{4 \, {\left(c x^{5} + a x\right)} a^{2}} - \frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{3} c^{2}} - \frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{3} c^{2}} + \frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{3} c^{2}} - \frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{3} c^{2}}"," ",0,"-1/4*(5*c*x^4 + 4*a)/((c*x^5 + a*x)*a^2) - 5/16*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c^2) - 5/16*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c^2) + 5/32*sqrt(2)*(a*c^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^2) - 5/32*sqrt(2)*(a*c^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^2)","A",0
671,1,191,0,0.168457," ","integrate(1/x^4/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{c x}{4 \, {\left(c x^{4} + a\right)} a^{2}} - \frac{7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{3}} - \frac{7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{3}} - \frac{7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{3}} + \frac{7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{3}} - \frac{1}{3 \, a^{2} x^{3}}"," ",0,"-1/4*c*x/((c*x^4 + a)*a^2) - 7/16*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/a^3 - 7/16*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/a^3 - 7/32*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/a^3 + 7/32*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/a^3 - 1/3/(a^2*x^3)","A",0
672,1,42,0,0.268048," ","integrate(x^11/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{\log\left({\left| c x^{4} + a \right|}\right)}{4 \, c^{3}} - \frac{3 \, c x^{8} + 2 \, a x^{4}}{8 \, {\left(c x^{4} + a\right)}^{2} c^{2}}"," ",0,"1/4*log(abs(c*x^4 + a))/c^3 - 1/8*(3*c*x^8 + 2*a*x^4)/((c*x^4 + a)^2*c^2)","A",0
673,1,49,0,0.164734," ","integrate(x^9/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} c^{2}} - \frac{5 \, c x^{6} + 3 \, a x^{2}}{16 \, {\left(c x^{4} + a\right)}^{2} c^{2}}"," ",0,"3/16*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*c^2) - 1/16*(5*c*x^6 + 3*a*x^2)/((c*x^4 + a)^2*c^2)","A",0
674,1,22,0,0.163575," ","integrate(x^7/(c*x^4+a)^3,x, algorithm=""giac"")","-\frac{2 \, c x^{4} + a}{8 \, {\left(c x^{4} + a\right)}^{2} c^{2}}"," ",0,"-1/8*(2*c*x^4 + a)/((c*x^4 + a)^2*c^2)","A",0
675,1,54,0,0.166029," ","integrate(x^5/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{\arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a c} + \frac{c x^{6} - a x^{2}}{16 \, {\left(c x^{4} + a\right)}^{2} a c}"," ",0,"1/16*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*a*c) + 1/16*(c*x^6 - a*x^2)/((c*x^4 + a)^2*a*c)","A",0
676,1,14,0,0.179221," ","integrate(x^3/(c*x^4+a)^3,x, algorithm=""giac"")","-\frac{1}{8 \, {\left(c x^{4} + a\right)}^{2} c}"," ",0,"-1/8/((c*x^4 + a)^2*c)","A",0
677,1,49,0,0.161133," ","integrate(x/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{2}} + \frac{3 \, c x^{6} + 5 \, a x^{2}}{16 \, {\left(c x^{4} + a\right)}^{2} a^{2}}"," ",0,"3/16*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*a^2) + 1/16*(3*c*x^6 + 5*a*x^2)/((c*x^4 + a)^2*a^2)","A",0
678,1,59,0,0.159629," ","integrate(1/x/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{\log\left(x^{4}\right)}{4 \, a^{3}} - \frac{\log\left({\left| c x^{4} + a \right|}\right)}{4 \, a^{3}} + \frac{3 \, c^{2} x^{8} + 8 \, a c x^{4} + 6 \, a^{2}}{8 \, {\left(c x^{4} + a\right)}^{2} a^{3}}"," ",0,"1/4*log(x^4)/a^3 - 1/4*log(abs(c*x^4 + a))/a^3 + 1/8*(3*c^2*x^8 + 8*a*c*x^4 + 6*a^2)/((c*x^4 + a)^2*a^3)","A",0
679,1,61,0,0.159683," ","integrate(1/x^3/(c*x^4+a)^3,x, algorithm=""giac"")","-\frac{15 \, c \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3}} - \frac{7 \, c^{2} x^{6} + 9 \, a c x^{2}}{16 \, {\left(c x^{4} + a\right)}^{2} a^{3}} - \frac{1}{2 \, a^{3} x^{2}}"," ",0,"-15/16*c*arctan(c*x^2/sqrt(a*c))/(sqrt(a*c)*a^3) - 1/16*(7*c^2*x^6 + 9*a*c*x^2)/((c*x^4 + a)^2*a^3) - 1/2/(a^3*x^2)","A",0
680,1,206,0,0.173564," ","integrate(x^10/(c*x^4+a)^3,x, algorithm=""giac"")","-\frac{11 \, c x^{7} + 7 \, a x^{3}}{32 \, {\left(c x^{4} + a\right)}^{2} c^{2}} + \frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a c^{5}} + \frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a c^{5}} - \frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a c^{5}} + \frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a c^{5}}"," ",0,"-1/32*(11*c*x^7 + 7*a*x^3)/((c*x^4 + a)^2*c^2) + 21/128*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^5) + 21/128*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^5) - 21/256*sqrt(2)*(a*c^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^5) + 21/256*sqrt(2)*(a*c^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^5)","A",0
681,1,204,0,0.170229," ","integrate(x^8/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a c^{3}} + \frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a c^{3}} + \frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a c^{3}} - \frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a c^{3}} - \frac{9 \, c x^{5} + 5 \, a x}{32 \, {\left(c x^{4} + a\right)}^{2} c^{2}}"," ",0,"5/128*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) + 5/128*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) + 5/256*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3) - 5/256*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3) - 1/32*(9*c*x^5 + 5*a*x)/((c*x^4 + a)^2*c^2)","A",0
682,1,209,0,0.172078," ","integrate(x^6/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{3 \, c x^{7} - a x^{3}}{32 \, {\left(c x^{4} + a\right)}^{2} a c} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{2} c^{4}} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{2} c^{4}} - \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{2} c^{4}} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{2} c^{4}}"," ",0,"1/32*(3*c*x^7 - a*x^3)/((c*x^4 + a)^2*a*c) + 3/128*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^4) + 3/128*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^4) - 3/256*sqrt(2)*(a*c^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^4) + 3/256*sqrt(2)*(a*c^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^4)","A",0
683,1,206,0,0.170072," ","integrate(x^4/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{2} c^{2}} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{2} c^{2}} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{2} c^{2}} - \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{2} c^{2}} + \frac{c x^{5} - 3 \, a x}{32 \, {\left(c x^{4} + a\right)}^{2} a c}"," ",0,"3/128*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^2) + 3/128*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^2) + 3/256*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^2) - 3/256*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^2) + 1/32*(c*x^5 - 3*a*x)/((c*x^4 + a)^2*a*c)","A",0
684,1,206,0,0.191834," ","integrate(x^2/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{5 \, c x^{7} + 9 \, a x^{3}}{32 \, {\left(c x^{4} + a\right)}^{2} a^{2}} + \frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c^{3}} + \frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c^{3}} - \frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c^{3}} + \frac{5 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c^{3}}"," ",0,"1/32*(5*c*x^7 + 9*a*x^3)/((c*x^4 + a)^2*a^2) + 5/128*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c^3) + 5/128*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c^3) - 5/256*sqrt(2)*(a*c^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^3) + 5/256*sqrt(2)*(a*c^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c^3)","A",0
685,1,204,0,0.159655," ","integrate(1/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c} + \frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{3} c} + \frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c} - \frac{21 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{3} c} + \frac{7 \, c x^{5} + 11 \, a x}{32 \, {\left(c x^{4} + a\right)}^{2} a^{2}}"," ",0,"21/128*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c) + 21/128*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^3*c) + 21/256*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c) - 21/256*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^3*c) + 1/32*(7*c*x^5 + 11*a*x)/((c*x^4 + a)^2*a^2)","A",0
686,1,217,0,0.249475," ","integrate(1/x^2/(c*x^4+a)^3,x, algorithm=""giac"")","-\frac{45 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{4} c^{2}} - \frac{45 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{128 \, a^{4} c^{2}} + \frac{45 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{4} c^{2}} - \frac{45 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{256 \, a^{4} c^{2}} - \frac{13 \, c^{2} x^{7} + 17 \, a c x^{3}}{32 \, {\left(c x^{4} + a\right)}^{2} a^{3}} - \frac{1}{a^{3} x}"," ",0,"-45/128*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^4*c^2) - 45/128*sqrt(2)*(a*c^3)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^4*c^2) + 45/256*sqrt(2)*(a*c^3)^(3/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^4*c^2) - 45/256*sqrt(2)*(a*c^3)^(3/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^4*c^2) - 1/32*(13*c^2*x^7 + 17*a*c*x^3)/((c*x^4 + a)^2*a^3) - 1/(a^3*x)","A",0
687,1,25,0,0.166936," ","integrate(x^9/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{18} \, x^{6} - \frac{1}{9} \, x^{2} + \frac{1}{27} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x^{2}\right)"," ",0,"1/18*x^6 - 1/9*x^2 + 1/27*sqrt(6)*arctan(1/2*sqrt(6)*x^2)","A",0
688,1,16,0,0.167721," ","integrate(x^7/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{12} \, x^{4} - \frac{1}{18} \, \log\left(3 \, x^{4} + 2\right)"," ",0,"1/12*x^4 - 1/18*log(3*x^4 + 2)","A",0
689,1,20,0,0.194739," ","integrate(x^5/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{6} \, x^{2} - \frac{1}{18} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x^{2}\right)"," ",0,"1/6*x^2 - 1/18*sqrt(6)*arctan(1/2*sqrt(6)*x^2)","A",0
690,1,10,0,0.174212," ","integrate(x^3/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{12} \, \log\left(3 \, x^{4} + 2\right)"," ",0,"1/12*log(3*x^4 + 2)","A",0
691,1,14,0,0.165016," ","integrate(x/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x^{2}\right)"," ",0,"1/12*sqrt(6)*arctan(1/2*sqrt(6)*x^2)","A",0
692,1,17,0,0.176358," ","integrate(1/x/(3*x^4+2),x, algorithm=""giac"")","-\frac{1}{8} \, \log\left(3 \, x^{4} + 2\right) + \frac{1}{8} \, \log\left(x^{4}\right)"," ",0,"-1/8*log(3*x^4 + 2) + 1/8*log(x^4)","A",0
693,1,20,0,0.176572," ","integrate(1/x^3/(3*x^4+2),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x^{2}\right) - \frac{1}{4 \, x^{2}}"," ",0,"-1/8*sqrt(6)*arctan(1/2*sqrt(6)*x^2) - 1/4/x^2","A",0
694,1,100,0,0.189258," ","integrate(x^6/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{9} \, x^{3} - \frac{1}{18} \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) - \frac{1}{18} \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{36} \cdot 6^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{36} \cdot 6^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"1/9*x^3 - 1/18*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) - 1/18*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/36*6^(1/4)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/36*6^(1/4)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
695,1,98,0,0.185538," ","integrate(x^4/(3*x^4+2),x, algorithm=""giac"")","-\frac{1}{36} \cdot 6^{\frac{3}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) - \frac{1}{36} \cdot 6^{\frac{3}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) - \frac{1}{72} \cdot 6^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) + \frac{1}{72} \cdot 6^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) + \frac{1}{3} \, x"," ",0,"-1/36*6^(3/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) - 1/36*6^(3/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) - 1/72*6^(3/4)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) + 1/72*6^(3/4)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) + 1/3*x","A",0
696,1,95,0,0.349145," ","integrate(x^2/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{12} \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{12} \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) - \frac{1}{24} \cdot 6^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) + \frac{1}{24} \cdot 6^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"1/12*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/12*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) - 1/24*6^(1/4)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) + 1/24*6^(1/4)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
697,1,95,0,0.200741," ","integrate(1/(3*x^4+2),x, algorithm=""giac"")","\frac{1}{24} \cdot 6^{\frac{3}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{24} \cdot 6^{\frac{3}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{48} \cdot 6^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{48} \cdot 6^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"1/24*6^(3/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/24*6^(3/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/48*6^(3/4)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/48*6^(3/4)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
698,1,100,0,0.193119," ","integrate(1/x^2/(3*x^4+2),x, algorithm=""giac"")","-\frac{1}{8} \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) - \frac{1}{8} \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{16} \cdot 6^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{16} \cdot 6^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{2 \, x}"," ",0,"-1/8*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) - 1/8*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/16*6^(1/4)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/16*6^(1/4)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/2/x","A",0
699,1,11,0,0.206863," ","integrate(x^3/(3*x^4+2)^2,x, algorithm=""giac"")","-\frac{1}{12 \, {\left(3 \, x^{4} + 2\right)}}"," ",0,"-1/12/(3*x^4 + 2)","A",0
700,1,29,0,0.164461," ","integrate(x/(3*x^4+2)^2,x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x^{2}\right) + \frac{x^{2}}{8 \, {\left(3 \, x^{4} + 2\right)}}"," ",0,"1/48*sqrt(6)*arctan(1/2*sqrt(6)*x^2) + 1/8*x^2/(3*x^4 + 2)","A",0
701,1,35,0,0.167275," ","integrate(1/x/(3*x^4+2)^2,x, algorithm=""giac"")","\frac{3 \, x^{4} + 4}{16 \, {\left(3 \, x^{4} + 2\right)}} - \frac{1}{16} \, \log\left(3 \, x^{4} + 2\right) + \frac{1}{16} \, \log\left(x^{4}\right)"," ",0,"1/16*(3*x^4 + 4)/(3*x^4 + 2) - 1/16*log(3*x^4 + 2) + 1/16*log(x^4)","A",0
702,1,37,0,0.174269," ","integrate(1/x^3/(3*x^4+2)^2,x, algorithm=""giac"")","-\frac{3}{32} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x^{2}\right) - \frac{9 \, x^{4} + 4}{16 \, {\left(3 \, x^{6} + 2 \, x^{2}\right)}}"," ",0,"-3/32*sqrt(6)*arctan(1/2*sqrt(6)*x^2) - 1/16*(9*x^4 + 4)/(3*x^6 + 2*x^2)","A",0
703,1,107,0,0.202794," ","integrate(x^4/(3*x^4+2)^2,x, algorithm=""giac"")","\frac{1}{288} \cdot 6^{\frac{3}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{288} \cdot 6^{\frac{3}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{576} \cdot 6^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{576} \cdot 6^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{x}{12 \, {\left(3 \, x^{4} + 2\right)}}"," ",0,"1/288*6^(3/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/288*6^(3/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/576*6^(3/4)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/576*6^(3/4)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/12*x/(3*x^4 + 2)","A",0
704,1,109,0,0.187882," ","integrate(x^2/(3*x^4+2)^2,x, algorithm=""giac"")","\frac{x^{3}}{8 \, {\left(3 \, x^{4} + 2\right)}} + \frac{1}{96} \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{96} \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) - \frac{1}{192} \cdot 6^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) + \frac{1}{192} \cdot 6^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right)"," ",0,"1/8*x^3/(3*x^4 + 2) + 1/96*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/96*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) - 1/192*6^(1/4)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) + 1/192*6^(1/4)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3))","A",0
705,1,107,0,0.198348," ","integrate(1/(3*x^4+2)^2,x, algorithm=""giac"")","\frac{1}{64} \cdot 6^{\frac{3}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{64} \cdot 6^{\frac{3}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{128} \cdot 6^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{1}{128} \cdot 6^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) + \frac{x}{8 \, {\left(3 \, x^{4} + 2\right)}}"," ",0,"1/64*6^(3/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) + 1/64*6^(3/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 1/128*6^(3/4)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/128*6^(3/4)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) + 1/8*x/(3*x^4 + 2)","A",0
706,1,115,0,0.186775," ","integrate(1/x^2/(3*x^4+2)^2,x, algorithm=""giac"")","-\frac{5}{64} \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) - \frac{5}{64} \cdot 6^{\frac{1}{4}} \arctan\left(\frac{3}{4} \, \sqrt{2} \left(\frac{2}{3}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}}\right)}\right) + \frac{5}{128} \cdot 6^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{5}{128} \cdot 6^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} \left(\frac{2}{3}\right)^{\frac{1}{4}} x + \sqrt{\frac{2}{3}}\right) - \frac{15 \, x^{4} + 8}{16 \, {\left(3 \, x^{5} + 2 \, x\right)}}"," ",0,"-5/64*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x + sqrt(2)*(2/3)^(1/4))) - 5/64*6^(1/4)*arctan(3/4*sqrt(2)*(2/3)^(3/4)*(2*x - sqrt(2)*(2/3)^(1/4))) + 5/128*6^(1/4)*log(x^2 + sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 5/128*6^(1/4)*log(x^2 - sqrt(2)*(2/3)^(1/4)*x + sqrt(2/3)) - 1/16*(15*x^4 + 8)/(3*x^5 + 2*x)","A",0
707,1,95,0,0.180062," ","integrate(x^2/(x^4+3),x, algorithm=""giac"")","\frac{1}{12} \cdot 108^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(2 \, x + 3^{\frac{1}{4}} \sqrt{2}\right)}\right) + \frac{1}{12} \cdot 108^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(2 \, x - 3^{\frac{1}{4}} \sqrt{2}\right)}\right) - \frac{1}{24} \cdot 108^{\frac{1}{4}} \log\left(x^{2} + 3^{\frac{1}{4}} \sqrt{2} x + \sqrt{3}\right) + \frac{1}{24} \cdot 108^{\frac{1}{4}} \log\left(x^{2} - 3^{\frac{1}{4}} \sqrt{2} x + \sqrt{3}\right)"," ",0,"1/12*108^(1/4)*arctan(1/6*3^(3/4)*sqrt(2)*(2*x + 3^(1/4)*sqrt(2))) + 1/12*108^(1/4)*arctan(1/6*3^(3/4)*sqrt(2)*(2*x - 3^(1/4)*sqrt(2))) - 1/24*108^(1/4)*log(x^2 + 3^(1/4)*sqrt(2)*x + sqrt(3)) + 1/24*108^(1/4)*log(x^2 - 3^(1/4)*sqrt(2)*x + sqrt(3))","A",0
708,1,267,0,0.165406," ","integrate(1/(1+a+(-1+a)*x^4),x, algorithm=""giac"")","\frac{{\left(a^{4} - 2 \, a^{3} + 2 \, a - 1\right)}^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a + 1}{a - 1}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a + 1}{a - 1}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a^{2} - \sqrt{2}\right)}} + \frac{{\left(a^{4} - 2 \, a^{3} + 2 \, a - 1\right)}^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a + 1}{a - 1}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a + 1}{a - 1}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a^{2} - \sqrt{2}\right)}} + \frac{{\left(a^{4} - 2 \, a^{3} + 2 \, a - 1\right)}^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a + 1}{a - 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a + 1}{a - 1}}\right)}{4 \, {\left(\sqrt{2} a^{2} - \sqrt{2}\right)}} - \frac{{\left(a^{4} - 2 \, a^{3} + 2 \, a - 1\right)}^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a + 1}{a - 1}\right)^{\frac{1}{4}} + \sqrt{\frac{a + 1}{a - 1}}\right)}{4 \, {\left(\sqrt{2} a^{2} - \sqrt{2}\right)}}"," ",0,"1/2*(a^4 - 2*a^3 + 2*a - 1)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*((a + 1)/(a - 1))^(1/4))/((a + 1)/(a - 1))^(1/4))/(sqrt(2)*a^2 - sqrt(2)) + 1/2*(a^4 - 2*a^3 + 2*a - 1)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*((a + 1)/(a - 1))^(1/4))/((a + 1)/(a - 1))^(1/4))/(sqrt(2)*a^2 - sqrt(2)) + 1/4*(a^4 - 2*a^3 + 2*a - 1)^(1/4)*log(x^2 + sqrt(2)*x*((a + 1)/(a - 1))^(1/4) + sqrt((a + 1)/(a - 1)))/(sqrt(2)*a^2 - sqrt(2)) - 1/4*(a^4 - 2*a^3 + 2*a - 1)^(1/4)*log(x^2 - sqrt(2)*x*((a + 1)/(a - 1))^(1/4) + sqrt((a + 1)/(a - 1)))/(sqrt(2)*a^2 - sqrt(2))","B",0
709,1,219,0,0.170847," ","integrate(1/(x^4+2*a+2*b),x, algorithm=""giac"")","\frac{{\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}\right)}}{2 \, {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} + \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}\right)}}{2 \, {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} + \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} x + \sqrt{2 \, a + 2 \, b}\right)}{8 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} - \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} x + \sqrt{2 \, a + 2 \, b}\right)}{8 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}}"," ",0,"1/4*(2*a + 2*b)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(2*a + 2*b)^(1/4))/(2*a + 2*b)^(1/4))/(sqrt(2)*a + sqrt(2)*b) + 1/4*(2*a + 2*b)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(2*a + 2*b)^(1/4))/(2*a + 2*b)^(1/4))/(sqrt(2)*a + sqrt(2)*b) + 1/8*(2*a + 2*b)^(1/4)*log(x^2 + sqrt(2)*(2*a + 2*b)^(1/4)*x + sqrt(2*a + 2*b))/(sqrt(2)*a + sqrt(2)*b) - 1/8*(2*a + 2*b)^(1/4)*log(x^2 - sqrt(2)*(2*a + 2*b)^(1/4)*x + sqrt(2*a + 2*b))/(sqrt(2)*a + sqrt(2)*b)","B",0
710,1,219,0,0.209151," ","integrate(1/(x^4+2*a+2*b),x, algorithm=""giac"")","\frac{{\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}\right)}}{2 \, {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} + \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}\right)}}{2 \, {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} + \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} x + \sqrt{2 \, a + 2 \, b}\right)}{8 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} - \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} x + \sqrt{2 \, a + 2 \, b}\right)}{8 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}}"," ",0,"1/4*(2*a + 2*b)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(2*a + 2*b)^(1/4))/(2*a + 2*b)^(1/4))/(sqrt(2)*a + sqrt(2)*b) + 1/4*(2*a + 2*b)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(2*a + 2*b)^(1/4))/(2*a + 2*b)^(1/4))/(sqrt(2)*a + sqrt(2)*b) + 1/8*(2*a + 2*b)^(1/4)*log(x^2 + sqrt(2)*(2*a + 2*b)^(1/4)*x + sqrt(2*a + 2*b))/(sqrt(2)*a + sqrt(2)*b) - 1/8*(2*a + 2*b)^(1/4)*log(x^2 - sqrt(2)*(2*a + 2*b)^(1/4)*x + sqrt(2*a + 2*b))/(sqrt(2)*a + sqrt(2)*b)","B",0
711,1,24,0,0.155053," ","integrate(x/(x^4+2*a+2*b),x, algorithm=""giac"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} x^{2}}{2 \, \sqrt{a + b}}\right)}{4 \, \sqrt{a + b}}"," ",0,"1/4*sqrt(2)*arctan(1/2*sqrt(2)*x^2/sqrt(a + b))/sqrt(a + b)","A",0
712,1,24,0,0.154018," ","integrate(x/(x^4+2*a+2*b),x, algorithm=""giac"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} x^{2}}{2 \, \sqrt{a + b}}\right)}{4 \, \sqrt{a + b}}"," ",0,"1/4*sqrt(2)*arctan(1/2*sqrt(2)*x^2/sqrt(a + b))/sqrt(a + b)","A",0
713,1,219,0,0.166544," ","integrate(x^2/(x^4+2*a+2*b),x, algorithm=""giac"")","\frac{{\left(2 \, a + 2 \, b\right)}^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}\right)}}{2 \, {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} + \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}\right)}}{2 \, {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} - \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} x + \sqrt{2 \, a + 2 \, b}\right)}{8 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} + \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} x + \sqrt{2 \, a + 2 \, b}\right)}{8 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}}"," ",0,"1/4*(2*a + 2*b)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(2*a + 2*b)^(1/4))/(2*a + 2*b)^(1/4))/(sqrt(2)*a + sqrt(2)*b) + 1/4*(2*a + 2*b)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(2*a + 2*b)^(1/4))/(2*a + 2*b)^(1/4))/(sqrt(2)*a + sqrt(2)*b) - 1/8*(2*a + 2*b)^(3/4)*log(x^2 + sqrt(2)*(2*a + 2*b)^(1/4)*x + sqrt(2*a + 2*b))/(sqrt(2)*a + sqrt(2)*b) + 1/8*(2*a + 2*b)^(3/4)*log(x^2 - sqrt(2)*(2*a + 2*b)^(1/4)*x + sqrt(2*a + 2*b))/(sqrt(2)*a + sqrt(2)*b)","B",0
714,1,219,0,0.186621," ","integrate(x^2/(x^4+2*a+2*b),x, algorithm=""giac"")","\frac{{\left(2 \, a + 2 \, b\right)}^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}\right)}}{2 \, {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} + \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}\right)}}{2 \, {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} - \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{3}{4}} \log\left(x^{2} + \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} x + \sqrt{2 \, a + 2 \, b}\right)}{8 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}} + \frac{{\left(2 \, a + 2 \, b\right)}^{\frac{3}{4}} \log\left(x^{2} - \sqrt{2} {\left(2 \, a + 2 \, b\right)}^{\frac{1}{4}} x + \sqrt{2 \, a + 2 \, b}\right)}{8 \, {\left(\sqrt{2} a + \sqrt{2} b\right)}}"," ",0,"1/4*(2*a + 2*b)^(3/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(2*a + 2*b)^(1/4))/(2*a + 2*b)^(1/4))/(sqrt(2)*a + sqrt(2)*b) + 1/4*(2*a + 2*b)^(3/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(2*a + 2*b)^(1/4))/(2*a + 2*b)^(1/4))/(sqrt(2)*a + sqrt(2)*b) - 1/8*(2*a + 2*b)^(3/4)*log(x^2 + sqrt(2)*(2*a + 2*b)^(1/4)*x + sqrt(2*a + 2*b))/(sqrt(2)*a + sqrt(2)*b) + 1/8*(2*a + 2*b)^(3/4)*log(x^2 - sqrt(2)*(2*a + 2*b)^(1/4)*x + sqrt(2*a + 2*b))/(sqrt(2)*a + sqrt(2)*b)","B",0
715,1,14,0,0.154016," ","integrate(x^3/(x^4+2*a+2*b),x, algorithm=""giac"")","\frac{1}{4} \, \log\left({\left| x^{4} + 2 \, a + 2 \, b \right|}\right)"," ",0,"1/4*log(abs(x^4 + 2*a + 2*b))","A",0
716,1,14,0,0.173276," ","integrate(x^3/(x^4+2*a+2*b),x, algorithm=""giac"")","\frac{1}{4} \, \log\left({\left| x^{4} + 2 \, a + 2 \, b \right|}\right)"," ",0,"1/4*log(abs(x^4 + 2*a + 2*b))","A",0
717,1,13,0,0.172596," ","integrate(x^(5/2)*(c*x^4+a),x, algorithm=""giac"")","\frac{2}{15} \, c x^{\frac{15}{2}} + \frac{2}{7} \, a x^{\frac{7}{2}}"," ",0,"2/15*c*x^(15/2) + 2/7*a*x^(7/2)","A",0
718,1,13,0,0.150525," ","integrate(x^(3/2)*(c*x^4+a),x, algorithm=""giac"")","\frac{2}{13} \, c x^{\frac{13}{2}} + \frac{2}{5} \, a x^{\frac{5}{2}}"," ",0,"2/13*c*x^(13/2) + 2/5*a*x^(5/2)","A",0
719,1,13,0,0.147627," ","integrate((c*x^4+a)*x^(1/2),x, algorithm=""giac"")","\frac{2}{11} \, c x^{\frac{11}{2}} + \frac{2}{3} \, a x^{\frac{3}{2}}"," ",0,"2/11*c*x^(11/2) + 2/3*a*x^(3/2)","A",0
720,1,13,0,0.149015," ","integrate((c*x^4+a)/x^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, c x^{\frac{9}{2}} + 2 \, a \sqrt{x}"," ",0,"2/9*c*x^(9/2) + 2*a*sqrt(x)","A",0
721,1,13,0,0.148287," ","integrate((c*x^4+a)/x^(3/2),x, algorithm=""giac"")","\frac{2}{7} \, c x^{\frac{7}{2}} - \frac{2 \, a}{\sqrt{x}}"," ",0,"2/7*c*x^(7/2) - 2*a/sqrt(x)","A",0
722,1,13,0,0.187830," ","integrate((c*x^4+a)/x^(5/2),x, algorithm=""giac"")","\frac{2}{5} \, c x^{\frac{5}{2}} - \frac{2 \, a}{3 \, x^{\frac{3}{2}}}"," ",0,"2/5*c*x^(5/2) - 2/3*a/x^(3/2)","A",0
723,1,13,0,0.157782," ","integrate((c*x^4+a)/x^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, c x^{\frac{3}{2}} - \frac{2 \, a}{5 \, x^{\frac{5}{2}}}"," ",0,"2/3*c*x^(3/2) - 2/5*a/x^(5/2)","A",0
724,1,24,0,0.150680," ","integrate(x^(5/2)*(c*x^4+a)^2,x, algorithm=""giac"")","\frac{2}{23} \, c^{2} x^{\frac{23}{2}} + \frac{4}{15} \, a c x^{\frac{15}{2}} + \frac{2}{7} \, a^{2} x^{\frac{7}{2}}"," ",0,"2/23*c^2*x^(23/2) + 4/15*a*c*x^(15/2) + 2/7*a^2*x^(7/2)","A",0
725,1,24,0,0.149915," ","integrate(x^(3/2)*(c*x^4+a)^2,x, algorithm=""giac"")","\frac{2}{21} \, c^{2} x^{\frac{21}{2}} + \frac{4}{13} \, a c x^{\frac{13}{2}} + \frac{2}{5} \, a^{2} x^{\frac{5}{2}}"," ",0,"2/21*c^2*x^(21/2) + 4/13*a*c*x^(13/2) + 2/5*a^2*x^(5/2)","A",0
726,1,24,0,0.180071," ","integrate((c*x^4+a)^2*x^(1/2),x, algorithm=""giac"")","\frac{2}{19} \, c^{2} x^{\frac{19}{2}} + \frac{4}{11} \, a c x^{\frac{11}{2}} + \frac{2}{3} \, a^{2} x^{\frac{3}{2}}"," ",0,"2/19*c^2*x^(19/2) + 4/11*a*c*x^(11/2) + 2/3*a^2*x^(3/2)","A",0
727,1,24,0,0.149770," ","integrate((c*x^4+a)^2/x^(1/2),x, algorithm=""giac"")","\frac{2}{17} \, c^{2} x^{\frac{17}{2}} + \frac{4}{9} \, a c x^{\frac{9}{2}} + 2 \, a^{2} \sqrt{x}"," ",0,"2/17*c^2*x^(17/2) + 4/9*a*c*x^(9/2) + 2*a^2*sqrt(x)","A",0
728,1,24,0,0.173397," ","integrate((c*x^4+a)^2/x^(3/2),x, algorithm=""giac"")","\frac{2}{15} \, c^{2} x^{\frac{15}{2}} + \frac{4}{7} \, a c x^{\frac{7}{2}} - \frac{2 \, a^{2}}{\sqrt{x}}"," ",0,"2/15*c^2*x^(15/2) + 4/7*a*c*x^(7/2) - 2*a^2/sqrt(x)","A",0
729,1,24,0,0.152172," ","integrate((c*x^4+a)^2/x^(5/2),x, algorithm=""giac"")","\frac{2}{13} \, c^{2} x^{\frac{13}{2}} + \frac{4}{5} \, a c x^{\frac{5}{2}} - \frac{2 \, a^{2}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/13*c^2*x^(13/2) + 4/5*a*c*x^(5/2) - 2/3*a^2/x^(3/2)","A",0
730,1,24,0,0.191113," ","integrate((c*x^4+a)^2/x^(7/2),x, algorithm=""giac"")","\frac{2}{11} \, c^{2} x^{\frac{11}{2}} + \frac{4}{3} \, a c x^{\frac{3}{2}} - \frac{2 \, a^{2}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/11*c^2*x^(11/2) + 4/3*a*c*x^(3/2) - 2/5*a^2/x^(5/2)","A",0
731,1,35,0,0.150129," ","integrate(x^(5/2)*(c*x^4+a)^3,x, algorithm=""giac"")","\frac{2}{31} \, c^{3} x^{\frac{31}{2}} + \frac{6}{23} \, a c^{2} x^{\frac{23}{2}} + \frac{2}{5} \, a^{2} c x^{\frac{15}{2}} + \frac{2}{7} \, a^{3} x^{\frac{7}{2}}"," ",0,"2/31*c^3*x^(31/2) + 6/23*a*c^2*x^(23/2) + 2/5*a^2*c*x^(15/2) + 2/7*a^3*x^(7/2)","A",0
732,1,35,0,0.152995," ","integrate(x^(3/2)*(c*x^4+a)^3,x, algorithm=""giac"")","\frac{2}{29} \, c^{3} x^{\frac{29}{2}} + \frac{2}{7} \, a c^{2} x^{\frac{21}{2}} + \frac{6}{13} \, a^{2} c x^{\frac{13}{2}} + \frac{2}{5} \, a^{3} x^{\frac{5}{2}}"," ",0,"2/29*c^3*x^(29/2) + 2/7*a*c^2*x^(21/2) + 6/13*a^2*c*x^(13/2) + 2/5*a^3*x^(5/2)","A",0
733,1,35,0,0.172773," ","integrate((c*x^4+a)^3*x^(1/2),x, algorithm=""giac"")","\frac{2}{27} \, c^{3} x^{\frac{27}{2}} + \frac{6}{19} \, a c^{2} x^{\frac{19}{2}} + \frac{6}{11} \, a^{2} c x^{\frac{11}{2}} + \frac{2}{3} \, a^{3} x^{\frac{3}{2}}"," ",0,"2/27*c^3*x^(27/2) + 6/19*a*c^2*x^(19/2) + 6/11*a^2*c*x^(11/2) + 2/3*a^3*x^(3/2)","A",0
734,1,35,0,0.151505," ","integrate((c*x^4+a)^3/x^(1/2),x, algorithm=""giac"")","\frac{2}{25} \, c^{3} x^{\frac{25}{2}} + \frac{6}{17} \, a c^{2} x^{\frac{17}{2}} + \frac{2}{3} \, a^{2} c x^{\frac{9}{2}} + 2 \, a^{3} \sqrt{x}"," ",0,"2/25*c^3*x^(25/2) + 6/17*a*c^2*x^(17/2) + 2/3*a^2*c*x^(9/2) + 2*a^3*sqrt(x)","A",0
735,1,35,0,0.213974," ","integrate((c*x^4+a)^3/x^(3/2),x, algorithm=""giac"")","\frac{2}{23} \, c^{3} x^{\frac{23}{2}} + \frac{2}{5} \, a c^{2} x^{\frac{15}{2}} + \frac{6}{7} \, a^{2} c x^{\frac{7}{2}} - \frac{2 \, a^{3}}{\sqrt{x}}"," ",0,"2/23*c^3*x^(23/2) + 2/5*a*c^2*x^(15/2) + 6/7*a^2*c*x^(7/2) - 2*a^3/sqrt(x)","A",0
736,1,35,0,0.213467," ","integrate((c*x^4+a)^3/x^(5/2),x, algorithm=""giac"")","\frac{2}{21} \, c^{3} x^{\frac{21}{2}} + \frac{6}{13} \, a c^{2} x^{\frac{13}{2}} + \frac{6}{5} \, a^{2} c x^{\frac{5}{2}} - \frac{2 \, a^{3}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/21*c^3*x^(21/2) + 6/13*a*c^2*x^(13/2) + 6/5*a^2*c*x^(5/2) - 2/3*a^3/x^(3/2)","A",0
737,1,35,0,0.191227," ","integrate((c*x^4+a)^3/x^(7/2),x, algorithm=""giac"")","\frac{2}{19} \, c^{3} x^{\frac{19}{2}} + \frac{6}{11} \, a c^{2} x^{\frac{11}{2}} + 2 \, a^{2} c x^{\frac{3}{2}} - \frac{2 \, a^{3}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/19*c^3*x^(19/2) + 6/11*a*c^2*x^(11/2) + 2*a^2*c*x^(3/2) - 2/5*a^3/x^(5/2)","A",0
738,1,453,0,0.641190," ","integrate(x^(9/2)/(c*x^4+a),x, algorithm=""giac"")","\frac{2 \, x^{\frac{3}{2}}}{3 \, c} + \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, c \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, c \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, c \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, c \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, c \sqrt{-2 \, \sqrt{2} + 4}}"," ",0,"2/3*x^(3/2)/c + 1/2*(a/c)^(3/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(c*sqrt(2*sqrt(2) + 4)) + 1/2*(a/c)^(3/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(c*sqrt(2*sqrt(2) + 4)) - 1/2*(a/c)^(3/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(c*sqrt(-2*sqrt(2) + 4)) - 1/2*(a/c)^(3/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(c*sqrt(-2*sqrt(2) + 4)) - 1/4*(a/c)^(3/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(c*sqrt(2*sqrt(2) + 4)) + 1/4*(a/c)^(3/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(c*sqrt(2*sqrt(2) + 4)) + 1/4*(a/c)^(3/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(c*sqrt(-2*sqrt(2) + 4)) - 1/4*(a/c)^(3/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(c*sqrt(-2*sqrt(2) + 4))","B",0
739,1,453,0,0.452140," ","integrate(x^(7/2)/(c*x^4+a),x, algorithm=""giac"")","-\frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, c \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, c \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, c \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, c \sqrt{2 \, \sqrt{2} + 4}} + \frac{2 \, \sqrt{x}}{c}"," ",0,"-1/2*(a/c)^(1/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(c*sqrt(-2*sqrt(2) + 4)) - 1/2*(a/c)^(1/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(c*sqrt(-2*sqrt(2) + 4)) - 1/2*(a/c)^(1/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(c*sqrt(2*sqrt(2) + 4)) - 1/2*(a/c)^(1/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(c*sqrt(2*sqrt(2) + 4)) - 1/4*(a/c)^(1/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(c*sqrt(-2*sqrt(2) + 4)) + 1/4*(a/c)^(1/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(c*sqrt(-2*sqrt(2) + 4)) - 1/4*(a/c)^(1/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(c*sqrt(2*sqrt(2) + 4)) + 1/4*(a/c)^(1/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(c*sqrt(2*sqrt(2) + 4)) + 2*sqrt(x)/c","B",0
740,1,445,0,0.528493," ","integrate(x^(5/2)/(c*x^4+a),x, algorithm=""giac"")","\frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}}"," ",0,"1/2*(a/c)^(7/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/2*(a/c)^(7/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/2*(a/c)^(7/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/2*(a/c)^(7/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) - 1/4*(a/c)^(7/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(a/c)^(7/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) - 1/4*(a/c)^(7/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) + 1/4*(a/c)^(7/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(2*sqrt(2) + 4))","B",0
741,1,445,0,0.545810," ","integrate(x^(3/2)/(c*x^4+a),x, algorithm=""giac"")","-\frac{\left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}}"," ",0,"-1/2*(a/c)^(5/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) - 1/2*(a/c)^(5/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/2*(a/c)^(5/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/2*(a/c)^(5/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) - 1/4*(a/c)^(5/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) + 1/4*(a/c)^(5/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) + 1/4*(a/c)^(5/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) - 1/4*(a/c)^(5/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(-2*sqrt(2) + 4))","B",0
742,1,445,0,0.513433," ","integrate(x^(1/2)/(c*x^4+a),x, algorithm=""giac"")","-\frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}}"," ",0,"-1/2*(a/c)^(3/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) - 1/2*(a/c)^(3/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/2*(a/c)^(3/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/2*(a/c)^(3/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(a/c)^(3/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) - 1/4*(a/c)^(3/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) - 1/4*(a/c)^(3/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(a/c)^(3/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(-2*sqrt(2) + 4))","B",0
743,1,445,0,0.360335," ","integrate(1/(c*x^4+a)/x^(1/2),x, algorithm=""giac"")","\frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}}"," ",0,"1/2*(a/c)^(1/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/2*(a/c)^(1/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/2*(a/c)^(1/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/2*(a/c)^(1/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/4*(a/c)^(1/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) - 1/4*(a/c)^(1/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(a/c)^(1/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) - 1/4*(a/c)^(1/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*sqrt(2*sqrt(2) + 4))","B",0
744,1,461,0,0.552803," ","integrate(1/x^(3/2)/(c*x^4+a),x, algorithm=""giac"")","-\frac{c \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{c \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{c \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{c \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{c \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{c \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{c \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{c \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{2}{a \sqrt{x}}"," ",0,"-1/2*c*(a/c)^(7/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/2*c*(a/c)^(7/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/2*c*(a/c)^(7/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/2*c*(a/c)^(7/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) + 1/4*c*(a/c)^(7/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/4*c*(a/c)^(7/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) + 1/4*c*(a/c)^(7/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/4*c*(a/c)^(7/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 2/(a*sqrt(x))","B",0
745,1,461,0,0.551034," ","integrate(1/x^(5/2)/(c*x^4+a),x, algorithm=""giac"")","\frac{c \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{c \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{c \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{c \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{2 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{c \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{c \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{c \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{c \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{2}{3 \, a x^{\frac{3}{2}}}"," ",0,"1/2*c*(a/c)^(5/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) + 1/2*c*(a/c)^(5/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/2*c*(a/c)^(5/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/2*c*(a/c)^(5/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) + 1/4*c*(a/c)^(5/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/4*c*(a/c)^(5/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/4*c*(a/c)^(5/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) + 1/4*c*(a/c)^(5/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) - 2/3/(a*x^(3/2))","B",0
746,1,486,0,0.736467," ","integrate(x^(13/2)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{x^{\frac{7}{2}}}{4 \, {\left(c x^{4} + a\right)} c} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{2 \, \sqrt{2} + 4}} - \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{2 \, \sqrt{2} + 4}}"," ",0,"-1/4*x^(7/2)/((c*x^4 + a)*c) + 7/16*(a/c)^(7/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(-2*sqrt(2) + 4)) + 7/16*(a/c)^(7/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(-2*sqrt(2) + 4)) + 7/16*(a/c)^(7/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(2*sqrt(2) + 4)) + 7/16*(a/c)^(7/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(2*sqrt(2) + 4)) - 7/32*(a/c)^(7/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(-2*sqrt(2) + 4)) + 7/32*(a/c)^(7/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(-2*sqrt(2) + 4)) - 7/32*(a/c)^(7/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(2*sqrt(2) + 4)) + 7/32*(a/c)^(7/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(2*sqrt(2) + 4))","B",0
747,1,486,0,0.752630," ","integrate(x^(11/2)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{x^{\frac{5}{2}}}{4 \, {\left(c x^{4} + a\right)} c} - \frac{5 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{2 \, \sqrt{2} + 4}} - \frac{5 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{2 \, \sqrt{2} + 4}} + \frac{5 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{5 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{5 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{2 \, \sqrt{2} + 4}} + \frac{5 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{2 \, \sqrt{2} + 4}} + \frac{5 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{5 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{-2 \, \sqrt{2} + 4}}"," ",0,"-1/4*x^(5/2)/((c*x^4 + a)*c) - 5/16*(a/c)^(5/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(2*sqrt(2) + 4)) - 5/16*(a/c)^(5/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(2*sqrt(2) + 4)) + 5/16*(a/c)^(5/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(-2*sqrt(2) + 4)) + 5/16*(a/c)^(5/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(-2*sqrt(2) + 4)) - 5/32*(a/c)^(5/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(2*sqrt(2) + 4)) + 5/32*(a/c)^(5/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(2*sqrt(2) + 4)) + 5/32*(a/c)^(5/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(-2*sqrt(2) + 4)) - 5/32*(a/c)^(5/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(-2*sqrt(2) + 4))","B",0
748,1,486,0,0.733282," ","integrate(x^(9/2)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{x^{\frac{3}{2}}}{4 \, {\left(c x^{4} + a\right)} c} - \frac{3 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{2 \, \sqrt{2} + 4}} - \frac{3 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{2 \, \sqrt{2} + 4}} + \frac{3 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{3 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{3 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{2 \, \sqrt{2} + 4}} - \frac{3 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{2 \, \sqrt{2} + 4}} - \frac{3 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{3 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{-2 \, \sqrt{2} + 4}}"," ",0,"-1/4*x^(3/2)/((c*x^4 + a)*c) - 3/16*(a/c)^(3/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(2*sqrt(2) + 4)) - 3/16*(a/c)^(3/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(2*sqrt(2) + 4)) + 3/16*(a/c)^(3/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(-2*sqrt(2) + 4)) + 3/16*(a/c)^(3/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(-2*sqrt(2) + 4)) + 3/32*(a/c)^(3/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(2*sqrt(2) + 4)) - 3/32*(a/c)^(3/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(2*sqrt(2) + 4)) - 3/32*(a/c)^(3/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(-2*sqrt(2) + 4)) + 3/32*(a/c)^(3/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(-2*sqrt(2) + 4))","B",0
749,1,486,0,0.576950," ","integrate(x^(7/2)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a c \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a c \sqrt{2 \, \sqrt{2} + 4}} - \frac{\sqrt{x}}{4 \, {\left(c x^{4} + a\right)} c}"," ",0,"1/16*(a/c)^(1/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(-2*sqrt(2) + 4)) + 1/16*(a/c)^(1/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(-2*sqrt(2) + 4)) + 1/16*(a/c)^(1/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(2*sqrt(2) + 4)) + 1/16*(a/c)^(1/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c*sqrt(2*sqrt(2) + 4)) + 1/32*(a/c)^(1/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(-2*sqrt(2) + 4)) - 1/32*(a/c)^(1/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(-2*sqrt(2) + 4)) + 1/32*(a/c)^(1/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(2*sqrt(2) + 4)) - 1/32*(a/c)^(1/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c*sqrt(2*sqrt(2) + 4)) - 1/4*sqrt(x)/((c*x^4 + a)*c)","B",0
750,1,462,0,0.727350," ","integrate(x^(5/2)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{x^{\frac{7}{2}}}{4 \, {\left(c x^{4} + a\right)} a} + \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}}"," ",0,"1/4*x^(7/2)/((c*x^4 + a)*a) + 1/16*(a/c)^(7/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) + 1/16*(a/c)^(7/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) + 1/16*(a/c)^(7/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) + 1/16*(a/c)^(7/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/32*(a/c)^(7/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) + 1/32*(a/c)^(7/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/32*(a/c)^(7/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) + 1/32*(a/c)^(7/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4))","B",0
751,1,462,0,0.774479," ","integrate(x^(3/2)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{x^{\frac{5}{2}}}{4 \, {\left(c x^{4} + a\right)} a} - \frac{3 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{3 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{3 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{3 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{3 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{3 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{3 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{3 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}}"," ",0,"1/4*x^(5/2)/((c*x^4 + a)*a) - 3/16*(a/c)^(5/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) - 3/16*(a/c)^(5/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) + 3/16*(a/c)^(5/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) + 3/16*(a/c)^(5/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) - 3/32*(a/c)^(5/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) + 3/32*(a/c)^(5/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) + 3/32*(a/c)^(5/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) - 3/32*(a/c)^(5/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4))","B",0
752,1,462,0,0.722288," ","integrate(x^(1/2)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{x^{\frac{3}{2}}}{4 \, {\left(c x^{4} + a\right)} a} - \frac{5 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{5 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{5 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{5 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{5 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{5 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{5 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{5 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}}"," ",0,"1/4*x^(3/2)/((c*x^4 + a)*a) - 5/16*(a/c)^(3/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) - 5/16*(a/c)^(3/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) + 5/16*(a/c)^(3/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) + 5/16*(a/c)^(3/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) + 5/32*(a/c)^(3/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 5/32*(a/c)^(3/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 5/32*(a/c)^(3/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) + 5/32*(a/c)^(3/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4))","B",0
753,1,462,0,0.567153," ","integrate(1/(c*x^4+a)^2/x^(1/2),x, algorithm=""giac"")","\frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{\sqrt{x}}{4 \, {\left(c x^{4} + a\right)} a}"," ",0,"7/16*(a/c)^(1/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) + 7/16*(a/c)^(1/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) + 7/16*(a/c)^(1/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) + 7/16*(a/c)^(1/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) + 7/32*(a/c)^(1/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) - 7/32*(a/c)^(1/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) + 7/32*(a/c)^(1/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 7/32*(a/c)^(1/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) + 1/4*sqrt(x)/((c*x^4 + a)*a)","B",0
754,1,481,0,0.684649," ","integrate(1/x^(3/2)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{9 \, c \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{9 \, c \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{9 \, c \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} - \frac{9 \, c \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{16 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} + \frac{9 \, c \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{9 \, c \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{9 \, c \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} - \frac{9 \, c \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{32 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} - \frac{9 \, c x^{4} + 8 \, a}{4 \, {\left(c x^{\frac{9}{2}} + a \sqrt{x}\right)} a^{2}}"," ",0,"-9/16*c*(a/c)^(7/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(-2*sqrt(2) + 4)) - 9/16*c*(a/c)^(7/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(-2*sqrt(2) + 4)) - 9/16*c*(a/c)^(7/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(2*sqrt(2) + 4)) - 9/16*c*(a/c)^(7/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(2*sqrt(2) + 4)) + 9/32*c*(a/c)^(7/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(-2*sqrt(2) + 4)) - 9/32*c*(a/c)^(7/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(-2*sqrt(2) + 4)) + 9/32*c*(a/c)^(7/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(2*sqrt(2) + 4)) - 9/32*c*(a/c)^(7/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(2*sqrt(2) + 4)) - 1/4*(9*c*x^4 + 8*a)/((c*x^(9/2) + a*sqrt(x))*a^2)","B",0
755,1,496,0,0.702483," ","integrate(x^(15/2)/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{9 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a c^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{9 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a c^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{9 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a c^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{9 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a c^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{9 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a c^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{9 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a c^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{9 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a c^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{9 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a c^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{17 \, c x^{\frac{9}{2}} + 9 \, a \sqrt{x}}{64 \, {\left(c x^{4} + a\right)}^{2} c^{2}}"," ",0,"9/256*(a/c)^(1/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c^2*sqrt(-2*sqrt(2) + 4)) + 9/256*(a/c)^(1/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a*c^2*sqrt(-2*sqrt(2) + 4)) + 9/256*(a/c)^(1/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c^2*sqrt(2*sqrt(2) + 4)) + 9/256*(a/c)^(1/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a*c^2*sqrt(2*sqrt(2) + 4)) + 9/512*(a/c)^(1/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c^2*sqrt(-2*sqrt(2) + 4)) - 9/512*(a/c)^(1/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c^2*sqrt(-2*sqrt(2) + 4)) + 9/512*(a/c)^(1/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c^2*sqrt(2*sqrt(2) + 4)) - 9/512*(a/c)^(1/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a*c^2*sqrt(2*sqrt(2) + 4)) - 1/64*(17*c*x^(9/2) + 9*a*sqrt(x))/((c*x^4 + a)^2*c^2)","B",0
756,1,499,0,0.875376," ","integrate(x^(13/2)/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} - \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} + \frac{7 \, c x^{\frac{15}{2}} - a x^{\frac{7}{2}}}{64 \, {\left(c x^{4} + a\right)}^{2} a c}"," ",0,"7/256*(a/c)^(7/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 7/256*(a/c)^(7/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 7/256*(a/c)^(7/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(2*sqrt(2) + 4)) + 7/256*(a/c)^(7/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(2*sqrt(2) + 4)) - 7/512*(a/c)^(7/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 7/512*(a/c)^(7/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(-2*sqrt(2) + 4)) - 7/512*(a/c)^(7/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(2*sqrt(2) + 4)) + 7/512*(a/c)^(7/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(2*sqrt(2) + 4)) + 1/64*(7*c*x^(15/2) - a*x^(7/2))/((c*x^4 + a)^2*a*c)","B",0
757,1,499,0,0.874215," ","integrate(x^(11/2)/(c*x^4+a)^3,x, algorithm=""giac"")","-\frac{15 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} - \frac{15 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} + \frac{15 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{15 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{15 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} + \frac{15 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} + \frac{15 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{15 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{5 \, c x^{\frac{13}{2}} - 3 \, a x^{\frac{5}{2}}}{64 \, {\left(c x^{4} + a\right)}^{2} a c}"," ",0,"-15/256*(a/c)^(5/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(2*sqrt(2) + 4)) - 15/256*(a/c)^(5/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(2*sqrt(2) + 4)) + 15/256*(a/c)^(5/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 15/256*(a/c)^(5/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(-2*sqrt(2) + 4)) - 15/512*(a/c)^(5/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(2*sqrt(2) + 4)) + 15/512*(a/c)^(5/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(2*sqrt(2) + 4)) + 15/512*(a/c)^(5/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(-2*sqrt(2) + 4)) - 15/512*(a/c)^(5/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 1/64*(5*c*x^(13/2) - 3*a*x^(5/2))/((c*x^4 + a)^2*a*c)","B",0
758,1,499,0,0.855679," ","integrate(x^(9/2)/(c*x^4+a)^3,x, algorithm=""giac"")","-\frac{15 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} - \frac{15 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} + \frac{15 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{15 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{15 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} - \frac{15 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} - \frac{15 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{15 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{3 \, c x^{\frac{11}{2}} - 5 \, a x^{\frac{3}{2}}}{64 \, {\left(c x^{4} + a\right)}^{2} a c}"," ",0,"-15/256*(a/c)^(3/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(2*sqrt(2) + 4)) - 15/256*(a/c)^(3/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(2*sqrt(2) + 4)) + 15/256*(a/c)^(3/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 15/256*(a/c)^(3/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 15/512*(a/c)^(3/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(2*sqrt(2) + 4)) - 15/512*(a/c)^(3/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(2*sqrt(2) + 4)) - 15/512*(a/c)^(3/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 15/512*(a/c)^(3/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 1/64*(3*c*x^(11/2) - 5*a*x^(3/2))/((c*x^4 + a)^2*a*c)","B",0
759,1,498,0,0.726396," ","integrate(x^(7/2)/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} - \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{-2 \, \sqrt{2} + 4}} + \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} - \frac{7 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{2} c \sqrt{2 \, \sqrt{2} + 4}} + \frac{c x^{\frac{9}{2}} - 7 \, a \sqrt{x}}{64 \, {\left(c x^{4} + a\right)}^{2} a c}"," ",0,"7/256*(a/c)^(1/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 7/256*(a/c)^(1/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 7/256*(a/c)^(1/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(2*sqrt(2) + 4)) + 7/256*(a/c)^(1/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^2*c*sqrt(2*sqrt(2) + 4)) + 7/512*(a/c)^(1/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(-2*sqrt(2) + 4)) - 7/512*(a/c)^(1/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(-2*sqrt(2) + 4)) + 7/512*(a/c)^(1/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(2*sqrt(2) + 4)) - 7/512*(a/c)^(1/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^2*c*sqrt(2*sqrt(2) + 4)) + 1/64*(c*x^(9/2) - 7*a*sqrt(x))/((c*x^4 + a)^2*a*c)","B",0
760,1,472,0,0.857502," ","integrate(x^(5/2)/(c*x^4+a)^3,x, algorithm=""giac"")","\frac{9 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{9 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{9 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} + \frac{9 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} - \frac{9 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{9 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{9 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} + \frac{9 \, \left(\frac{a}{c}\right)^{\frac{7}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} + \frac{9 \, c x^{\frac{15}{2}} + 17 \, a x^{\frac{7}{2}}}{64 \, {\left(c x^{4} + a\right)}^{2} a^{2}}"," ",0,"9/256*(a/c)^(7/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(-2*sqrt(2) + 4)) + 9/256*(a/c)^(7/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(-2*sqrt(2) + 4)) + 9/256*(a/c)^(7/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(2*sqrt(2) + 4)) + 9/256*(a/c)^(7/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(2*sqrt(2) + 4)) - 9/512*(a/c)^(7/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(-2*sqrt(2) + 4)) + 9/512*(a/c)^(7/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(-2*sqrt(2) + 4)) - 9/512*(a/c)^(7/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(2*sqrt(2) + 4)) + 9/512*(a/c)^(7/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(2*sqrt(2) + 4)) + 1/64*(9*c*x^(15/2) + 17*a*x^(7/2))/((c*x^4 + a)^2*a^2)","B",0
761,1,472,0,0.855540," ","integrate(x^(3/2)/(c*x^4+a)^3,x, algorithm=""giac"")","-\frac{33 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} - \frac{33 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} + \frac{33 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{33 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{33 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} + \frac{33 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} + \frac{33 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{33 \, \left(\frac{a}{c}\right)^{\frac{5}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{11 \, c x^{\frac{13}{2}} + 19 \, a x^{\frac{5}{2}}}{64 \, {\left(c x^{4} + a\right)}^{2} a^{2}}"," ",0,"-33/256*(a/c)^(5/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(2*sqrt(2) + 4)) - 33/256*(a/c)^(5/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(2*sqrt(2) + 4)) + 33/256*(a/c)^(5/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(-2*sqrt(2) + 4)) + 33/256*(a/c)^(5/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(-2*sqrt(2) + 4)) - 33/512*(a/c)^(5/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(2*sqrt(2) + 4)) + 33/512*(a/c)^(5/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(2*sqrt(2) + 4)) + 33/512*(a/c)^(5/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(-2*sqrt(2) + 4)) - 33/512*(a/c)^(5/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(-2*sqrt(2) + 4)) + 1/64*(11*c*x^(13/2) + 19*a*x^(5/2))/((c*x^4 + a)^2*a^2)","B",0
762,1,472,0,0.825639," ","integrate(x^(1/2)/(c*x^4+a)^3,x, algorithm=""giac"")","-\frac{65 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} - \frac{65 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} + \frac{65 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{65 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{65 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} - \frac{65 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} - \frac{65 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{65 \, \left(\frac{a}{c}\right)^{\frac{3}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{13 \, c x^{\frac{11}{2}} + 21 \, a x^{\frac{3}{2}}}{64 \, {\left(c x^{4} + a\right)}^{2} a^{2}}"," ",0,"-65/256*(a/c)^(3/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(2*sqrt(2) + 4)) - 65/256*(a/c)^(3/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(2*sqrt(2) + 4)) + 65/256*(a/c)^(3/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(-2*sqrt(2) + 4)) + 65/256*(a/c)^(3/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(-2*sqrt(2) + 4)) + 65/512*(a/c)^(3/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(2*sqrt(2) + 4)) - 65/512*(a/c)^(3/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(2*sqrt(2) + 4)) - 65/512*(a/c)^(3/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(-2*sqrt(2) + 4)) + 65/512*(a/c)^(3/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(-2*sqrt(2) + 4)) + 1/64*(13*c*x^(11/2) + 21*a*x^(3/2))/((c*x^4 + a)^2*a^2)","B",0
763,1,472,0,0.651157," ","integrate(1/(c*x^4+a)^3/x^(1/2),x, algorithm=""giac"")","\frac{105 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{105 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{105 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} + \frac{105 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \arctan\left(-\frac{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} - 2 \, \sqrt{x}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{256 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} + \frac{105 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{105 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{105 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} - \frac{105 \, \left(\frac{a}{c}\right)^{\frac{1}{8}} \log\left(-\sqrt{x} \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + x + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{512 \, a^{3} \sqrt{2 \, \sqrt{2} + 4}} + \frac{15 \, c x^{\frac{9}{2}} + 23 \, a \sqrt{x}}{64 \, {\left(c x^{4} + a\right)}^{2} a^{2}}"," ",0,"105/256*(a/c)^(1/8)*arctan((sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(-2*sqrt(2) + 4)) + 105/256*(a/c)^(1/8)*arctan(-(sqrt(-sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(-2*sqrt(2) + 4)) + 105/256*(a/c)^(1/8)*arctan((sqrt(sqrt(2) + 2)*(a/c)^(1/8) + 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(2*sqrt(2) + 4)) + 105/256*(a/c)^(1/8)*arctan(-(sqrt(sqrt(2) + 2)*(a/c)^(1/8) - 2*sqrt(x))/(sqrt(-sqrt(2) + 2)*(a/c)^(1/8)))/(a^3*sqrt(2*sqrt(2) + 4)) + 105/512*(a/c)^(1/8)*log(sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(-2*sqrt(2) + 4)) - 105/512*(a/c)^(1/8)*log(-sqrt(x)*sqrt(sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(-2*sqrt(2) + 4)) + 105/512*(a/c)^(1/8)*log(sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(2*sqrt(2) + 4)) - 105/512*(a/c)^(1/8)*log(-sqrt(x)*sqrt(-sqrt(2) + 2)*(a/c)^(1/8) + x + (a/c)^(1/4))/(a^3*sqrt(2*sqrt(2) + 4)) + 1/64*(15*c*x^(9/2) + 23*a*sqrt(x))/((c*x^4 + a)^2*a^2)","B",0
764,1,43,0,0.168317," ","integrate(x^11*(c*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{15 \, {\left(c x^{4} + a\right)}^{\frac{7}{2}} - 42 \, {\left(c x^{4} + a\right)}^{\frac{5}{2}} a + 35 \, {\left(c x^{4} + a\right)}^{\frac{3}{2}} a^{2}}{210 \, c^{3}}"," ",0,"1/210*(15*(c*x^4 + a)^(7/2) - 42*(c*x^4 + a)^(5/2)*a + 35*(c*x^4 + a)^(3/2)*a^2)/c^3","A",0
765,1,29,0,0.150912," ","integrate(x^7*(c*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(c x^{4} + a\right)}^{\frac{5}{2}} - 5 \, {\left(c x^{4} + a\right)}^{\frac{3}{2}} a}{30 \, c^{2}}"," ",0,"1/30*(3*(c*x^4 + a)^(5/2) - 5*(c*x^4 + a)^(3/2)*a)/c^2","A",0
766,1,14,0,0.182663," ","integrate(x^3*(c*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}{6 \, c}"," ",0,"1/6*(c*x^4 + a)^(3/2)/c","A",0
767,1,36,0,0.153882," ","integrate((c*x^4+a)^(1/2)/x,x, algorithm=""giac"")","\frac{a \arctan\left(\frac{\sqrt{c x^{4} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a}} + \frac{1}{2} \, \sqrt{c x^{4} + a}"," ",0,"1/2*a*arctan(sqrt(c*x^4 + a)/sqrt(-a))/sqrt(-a) + 1/2*sqrt(c*x^4 + a)","A",0
768,1,46,0,0.158678," ","integrate((c*x^4+a)^(1/2)/x^5,x, algorithm=""giac"")","\frac{\frac{c^{2} \arctan\left(\frac{\sqrt{c x^{4} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{\sqrt{c x^{4} + a} c}{x^{4}}}{4 \, c}"," ",0,"1/4*(c^2*arctan(sqrt(c*x^4 + a)/sqrt(-a))/sqrt(-a) - sqrt(c*x^4 + a)*c/x^4)/c","A",0
769,1,72,0,0.159596," ","integrate((c*x^4+a)^(1/2)/x^9,x, algorithm=""giac"")","-\frac{\frac{c^{3} \arctan\left(\frac{\sqrt{c x^{4} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}} c^{3} + \sqrt{c x^{4} + a} a c^{3}}{a c^{2} x^{8}}}{16 \, c}"," ",0,"-1/16*(c^3*arctan(sqrt(c*x^4 + a)/sqrt(-a))/(sqrt(-a)*a) + ((c*x^4 + a)^(3/2)*c^3 + sqrt(c*x^4 + a)*a*c^3)/(a*c^2*x^8))/c","A",0
770,1,54,0,0.175740," ","integrate(x^5*(c*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{1}{16} \, \sqrt{c x^{4} + a} {\left(2 \, x^{4} + \frac{a}{c}\right)} x^{2} + \frac{a^{2} \log\left({\left| -\sqrt{c} x^{2} + \sqrt{c x^{4} + a} \right|}\right)}{16 \, c^{\frac{3}{2}}}"," ",0,"1/16*sqrt(c*x^4 + a)*(2*x^4 + a/c)*x^2 + 1/16*a^2*log(abs(-sqrt(c)*x^2 + sqrt(c*x^4 + a)))/c^(3/2)","A",0
771,1,41,0,0.193814," ","integrate(x*(c*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{4} + a} x^{2} - \frac{a \log\left({\left| -\sqrt{c} x^{2} + \sqrt{c x^{4} + a} \right|}\right)}{4 \, \sqrt{c}}"," ",0,"1/4*sqrt(c*x^4 + a)*x^2 - 1/4*a*log(abs(-sqrt(c)*x^2 + sqrt(c*x^4 + a)))/sqrt(c)","A",0
772,1,60,0,0.207747," ","integrate((c*x^4+a)^(1/2)/x^3,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{c} \log\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2}\right) + \frac{a \sqrt{c}}{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} - a}"," ",0,"-1/4*sqrt(c)*log((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2) + a*sqrt(c)/((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2 - a)","A",0
773,1,63,0,0.181578," ","integrate((c*x^4+a)^(1/2)/x^7,x, algorithm=""giac"")","\frac{3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{4} c^{\frac{3}{2}} + a^{2} c^{\frac{3}{2}}}{3 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"1/3*(3*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^4*c^(3/2) + a^2*c^(3/2))/((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2 - a)^3","B",0
774,1,120,0,0.206532," ","integrate((c*x^4+a)^(1/2)/x^11,x, algorithm=""giac"")","\frac{2 \, {\left(15 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{6} c^{\frac{5}{2}} + 5 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{4} a c^{\frac{5}{2}} + 5 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} a^{2} c^{\frac{5}{2}} - a^{3} c^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} - a\right)}^{5}}"," ",0,"2/15*(15*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^6*c^(5/2) + 5*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^4*a*c^(5/2) + 5*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^2*a^2*c^(5/2) - a^3*c^(5/2))/((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2 - a)^5","B",0
775,1,148,0,0.195458," ","integrate((c*x^4+a)^(1/2)/x^15,x, algorithm=""giac"")","\frac{8 \, {\left(70 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{8} c^{\frac{7}{2}} + 35 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{6} a c^{\frac{7}{2}} + 21 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{4} a^{2} c^{\frac{7}{2}} - 7 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} a^{3} c^{\frac{7}{2}} + a^{4} c^{\frac{7}{2}}\right)}}{105 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} - a\right)}^{7}}"," ",0,"8/105*(70*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^8*c^(7/2) + 35*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^6*a*c^(7/2) + 21*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^4*a^2*c^(7/2) - 7*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^2*a^3*c^(7/2) + a^4*c^(7/2))/((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2 - a)^7","B",0
776,0,0,0,0.000000," ","integrate(x^4*(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + a} x^{4}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a)*x^4, x)","F",0
777,0,0,0,0.000000," ","integrate((c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + a}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a), x)","F",0
778,0,0,0,0.000000," ","integrate((c*x^4+a)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + a}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a)/x^4, x)","F",0
779,0,0,0,0.000000," ","integrate((c*x^4+a)^(1/2)/x^8,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + a}}{x^{8}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a)/x^8, x)","F",0
780,0,0,0,0.000000," ","integrate(x^2*(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + a} x^{2}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a)*x^2, x)","F",0
781,0,0,0,0.000000," ","integrate((c*x^4+a)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + a}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a)/x^2, x)","F",0
782,0,0,0,0.000000," ","integrate((c*x^4+a)^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + a}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a)/x^6, x)","F",0
783,1,43,0,0.165061," ","integrate(x^11*(c*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{35 \, {\left(c x^{4} + a\right)}^{\frac{9}{2}} - 90 \, {\left(c x^{4} + a\right)}^{\frac{7}{2}} a + 63 \, {\left(c x^{4} + a\right)}^{\frac{5}{2}} a^{2}}{630 \, c^{3}}"," ",0,"1/630*(35*(c*x^4 + a)^(9/2) - 90*(c*x^4 + a)^(7/2)*a + 63*(c*x^4 + a)^(5/2)*a^2)/c^3","A",0
784,1,29,0,0.155261," ","integrate(x^7*(c*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{5 \, {\left(c x^{4} + a\right)}^{\frac{7}{2}} - 7 \, {\left(c x^{4} + a\right)}^{\frac{5}{2}} a}{70 \, c^{2}}"," ",0,"1/70*(5*(c*x^4 + a)^(7/2) - 7*(c*x^4 + a)^(5/2)*a)/c^2","A",0
785,1,14,0,0.152651," ","integrate(x^3*(c*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(c x^{4} + a\right)}^{\frac{5}{2}}}{10 \, c}"," ",0,"1/10*(c*x^4 + a)^(5/2)/c","A",0
786,1,50,0,0.160329," ","integrate((c*x^4+a)^(3/2)/x,x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{\sqrt{c x^{4} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a}} + \frac{1}{6} \, {\left(c x^{4} + a\right)}^{\frac{3}{2}} + \frac{1}{2} \, \sqrt{c x^{4} + a} a"," ",0,"1/2*a^2*arctan(sqrt(c*x^4 + a)/sqrt(-a))/sqrt(-a) + 1/6*(c*x^4 + a)^(3/2) + 1/2*sqrt(c*x^4 + a)*a","A",0
787,1,63,0,0.173651," ","integrate((c*x^4+a)^(3/2)/x^5,x, algorithm=""giac"")","\frac{\frac{3 \, a c^{2} \arctan\left(\frac{\sqrt{c x^{4} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + 2 \, \sqrt{c x^{4} + a} c^{2} - \frac{\sqrt{c x^{4} + a} a c}{x^{4}}}{4 \, c}"," ",0,"1/4*(3*a*c^2*arctan(sqrt(c*x^4 + a)/sqrt(-a))/sqrt(-a) + 2*sqrt(c*x^4 + a)*c^2 - sqrt(c*x^4 + a)*a*c/x^4)/c","A",0
788,1,70,0,0.162434," ","integrate((c*x^4+a)^(3/2)/x^9,x, algorithm=""giac"")","\frac{\frac{3 \, c^{3} \arctan\left(\frac{\sqrt{c x^{4} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{5 \, {\left(c x^{4} + a\right)}^{\frac{3}{2}} c^{3} - 3 \, \sqrt{c x^{4} + a} a c^{3}}{c^{2} x^{8}}}{16 \, c}"," ",0,"1/16*(3*c^3*arctan(sqrt(c*x^4 + a)/sqrt(-a))/sqrt(-a) - (5*(c*x^4 + a)^(3/2)*c^3 - 3*sqrt(c*x^4 + a)*a*c^3)/(c^2*x^8))/c","A",0
789,1,126,0,0.222633," ","integrate(x^5*(c*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{1}{16} \, {\left(\sqrt{c x^{4} + a} {\left(2 \, x^{4} + \frac{a}{c}\right)} x^{2} + \frac{a^{2} \log\left({\left| -\sqrt{c} x^{2} + \sqrt{c x^{4} + a} \right|}\right)}{c^{\frac{3}{2}}}\right)} a + \frac{1}{96} \, {\left({\left(2 \, {\left(4 \, x^{4} + \frac{a}{c}\right)} x^{4} - \frac{3 \, a^{2}}{c^{2}}\right)} \sqrt{c x^{4} + a} x^{2} - \frac{3 \, a^{3} \log\left({\left| -\sqrt{c} x^{2} + \sqrt{c x^{4} + a} \right|}\right)}{c^{\frac{5}{2}}}\right)} c"," ",0,"1/16*(sqrt(c*x^4 + a)*(2*x^4 + a/c)*x^2 + a^2*log(abs(-sqrt(c)*x^2 + sqrt(c*x^4 + a)))/c^(3/2))*a + 1/96*((2*(4*x^4 + a/c)*x^4 - 3*a^2/c^2)*sqrt(c*x^4 + a)*x^2 - 3*a^3*log(abs(-sqrt(c)*x^2 + sqrt(c*x^4 + a)))/c^(5/2))*c","A",0
790,1,99,0,0.213598," ","integrate(x*(c*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(\sqrt{c x^{4} + a} x^{2} - \frac{a \log\left({\left| -\sqrt{c} x^{2} + \sqrt{c x^{4} + a} \right|}\right)}{\sqrt{c}}\right)} a + \frac{1}{16} \, {\left(\sqrt{c x^{4} + a} {\left(2 \, x^{4} + \frac{a}{c}\right)} x^{2} + \frac{a^{2} \log\left({\left| -\sqrt{c} x^{2} + \sqrt{c x^{4} + a} \right|}\right)}{c^{\frac{3}{2}}}\right)} c"," ",0,"1/4*(sqrt(c*x^4 + a)*x^2 - a*log(abs(-sqrt(c)*x^2 + sqrt(c*x^4 + a)))/sqrt(c))*a + 1/16*(sqrt(c*x^4 + a)*(2*x^4 + a/c)*x^2 + a^2*log(abs(-sqrt(c)*x^2 + sqrt(c*x^4 + a)))/c^(3/2))*c","A",0
791,1,78,0,0.218068," ","integrate((c*x^4+a)^(3/2)/x^3,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{4} + a} c x^{2} - \frac{3}{8} \, a \sqrt{c} \log\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2}\right) + \frac{a^{2} \sqrt{c}}{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} - a}"," ",0,"1/4*sqrt(c*x^4 + a)*c*x^2 - 3/8*a*sqrt(c)*log((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2) + a^2*sqrt(c)/((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2 - a)","A",0
792,1,122,0,0.229722," ","integrate((c*x^4+a)^(3/2)/x^7,x, algorithm=""giac"")","-\frac{1}{4} \, c^{\frac{3}{2}} \log\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2}\right) + \frac{2 \, {\left(3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{4} a c^{\frac{3}{2}} - 3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} a^{2} c^{\frac{3}{2}} + 2 \, a^{3} c^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"-1/4*c^(3/2)*log((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2) + 2/3*(3*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^4*a*c^(3/2) - 3*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^2*a^2*c^(3/2) + 2*a^3*c^(3/2))/((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2 - a)^3","B",0
793,1,92,0,0.227705," ","integrate((c*x^4+a)^(3/2)/x^11,x, algorithm=""giac"")","\frac{5 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{8} c^{\frac{5}{2}} + 10 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{4} a^{2} c^{\frac{5}{2}} + a^{4} c^{\frac{5}{2}}}{5 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} - a\right)}^{5}}"," ",0,"1/5*(5*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^8*c^(5/2) + 10*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^4*a^2*c^(5/2) + a^4*c^(5/2))/((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2 - a)^5","B",0
794,1,178,0,0.236142," ","integrate((c*x^4+a)^(3/2)/x^15,x, algorithm=""giac"")","\frac{2 \, {\left(35 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{10} c^{\frac{7}{2}} + 35 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{8} a c^{\frac{7}{2}} + 70 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{6} a^{2} c^{\frac{7}{2}} + 14 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{4} a^{3} c^{\frac{7}{2}} + 7 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} a^{4} c^{\frac{7}{2}} - a^{5} c^{\frac{7}{2}}\right)}}{35 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} - a\right)}^{7}}"," ",0,"2/35*(35*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^10*c^(7/2) + 35*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^8*a*c^(7/2) + 70*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^6*a^2*c^(7/2) + 14*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^4*a^3*c^(7/2) + 7*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^2*a^4*c^(7/2) - a^5*c^(7/2))/((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2 - a)^7","B",0
795,1,206,0,0.252778," ","integrate((c*x^4+a)^(3/2)/x^19,x, algorithm=""giac"")","\frac{8 \, {\left(210 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{12} c^{\frac{9}{2}} + 315 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{10} a c^{\frac{9}{2}} + 441 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{8} a^{2} c^{\frac{9}{2}} + 126 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{6} a^{3} c^{\frac{9}{2}} + 36 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{4} a^{4} c^{\frac{9}{2}} - 9 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} a^{5} c^{\frac{9}{2}} + a^{6} c^{\frac{9}{2}}\right)}}{315 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + a}\right)}^{2} - a\right)}^{9}}"," ",0,"8/315*(210*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^12*c^(9/2) + 315*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^10*a*c^(9/2) + 441*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^8*a^2*c^(9/2) + 126*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^6*a^3*c^(9/2) + 36*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^4*a^4*c^(9/2) - 9*(sqrt(c)*x^2 - sqrt(c*x^4 + a))^2*a^5*c^(9/2) + a^6*c^(9/2))/((sqrt(c)*x^2 - sqrt(c*x^4 + a))^2 - a)^9","B",0
796,0,0,0,0.000000," ","integrate(x^4*(c*x^4+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + a\right)}^{\frac{3}{2}} x^{4}\,{d x}"," ",0,"integrate((c*x^4 + a)^(3/2)*x^4, x)","F",0
797,0,0,0,0.000000," ","integrate((c*x^4+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^4 + a)^(3/2), x)","F",0
798,0,0,0,0.000000," ","integrate((c*x^4+a)^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate((c*x^4 + a)^(3/2)/x^4, x)","F",0
799,0,0,0,0.000000," ","integrate((c*x^4+a)^(3/2)/x^8,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}{x^{8}}\,{d x}"," ",0,"integrate((c*x^4 + a)^(3/2)/x^8, x)","F",0
800,0,0,0,0.000000," ","integrate(x^2*(c*x^4+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + a\right)}^{\frac{3}{2}} x^{2}\,{d x}"," ",0,"integrate((c*x^4 + a)^(3/2)*x^2, x)","F",0
801,0,0,0,0.000000," ","integrate((c*x^4+a)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((c*x^4 + a)^(3/2)/x^2, x)","F",0
802,0,0,0,0.000000," ","integrate((c*x^4+a)^(3/2)/x^6,x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}{x^{6}}\,{d x}"," ",0,"integrate((c*x^4 + a)^(3/2)/x^6, x)","F",0
803,0,0,0,0.000000," ","integrate((x^4+1)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((x^4 + 1)^(3/2), x)","F",0
804,0,0,0,0.000000," ","integrate((-x^4+1)^(3/2),x, algorithm=""giac"")","\int {\left(-x^{4} + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-x^4 + 1)^(3/2), x)","F",0
805,1,23,0,0.149642," ","integrate(x^7*(3*x^4+5)^(1/2),x, algorithm=""giac"")","\frac{1}{90} \, {\left(3 \, x^{4} + 5\right)}^{\frac{5}{2}} - \frac{5}{54} \, {\left(3 \, x^{4} + 5\right)}^{\frac{3}{2}}"," ",0,"1/90*(3*x^4 + 5)^(5/2) - 5/54*(3*x^4 + 5)^(3/2)","A",0
806,1,9,0,0.157296," ","integrate(x^3*(x^4+5)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(x^{4} + 5\right)}^{\frac{3}{2}}"," ",0,"1/6*(x^4 + 5)^(3/2)","A",0
807,1,39,0,0.178919," ","integrate(x*(2*x^4+3)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2 \, x^{4} + 3} x^{2} - \frac{3}{8} \, \sqrt{2} \log\left(-\sqrt{2} x^{2} + \sqrt{2 \, x^{4} + 3}\right)"," ",0,"1/4*sqrt(2*x^4 + 3)*x^2 - 3/8*sqrt(2)*log(-sqrt(2)*x^2 + sqrt(2*x^4 + 3))","A",0
808,1,29,0,0.179181," ","integrate(x*(x^4-2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{x^{4} - 2} x^{2} + \frac{1}{2} \, \log\left(x^{2} - \sqrt{x^{4} - 2}\right)"," ",0,"1/4*sqrt(x^4 - 2)*x^2 + 1/2*log(x^2 - sqrt(x^4 - 2))","A",0
809,0,0,0,0.000000," ","integrate((x^4+1)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 1}\,{d x}"," ",0,"integrate(sqrt(x^4 + 1), x)","F",0
810,0,0,0,0.000000," ","integrate((-x^4+1)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{4} + 1}\,{d x}"," ",0,"integrate(sqrt(-x^4 + 1), x)","F",0
811,1,47,0,0.149589," ","integrate(x^11/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{4} + a} a^{2}}{2 \, b^{3}} + \frac{3 \, {\left(b x^{4} + a\right)}^{\frac{5}{2}} - 10 \, {\left(b x^{4} + a\right)}^{\frac{3}{2}} a}{30 \, b^{3}}"," ",0,"1/2*sqrt(b*x^4 + a)*a^2/b^3 + 1/30*(3*(b*x^4 + a)^(5/2) - 10*(b*x^4 + a)^(3/2)*a)/b^3","A",0
812,1,30,0,0.216260," ","integrate(x^7/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}{6 \, b^{2}} - \frac{\sqrt{b x^{4} + a} a}{2 \, b^{2}}"," ",0,"1/6*(b*x^4 + a)^(3/2)/b^2 - 1/2*sqrt(b*x^4 + a)*a/b^2","A",0
813,1,14,0,0.149219," ","integrate(x^3/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{4} + a}}{2 \, b}"," ",0,"1/2*sqrt(b*x^4 + a)/b","A",0
814,1,23,0,0.168238," ","integrate(1/x/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{b x^{4} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a}}"," ",0,"1/2*arctan(sqrt(b*x^4 + a)/sqrt(-a))/sqrt(-a)","A",0
815,1,51,0,0.169515," ","integrate(1/x^5/(b*x^4+a)^(1/2),x, algorithm=""giac"")","-\frac{\frac{b^{2} \arctan\left(\frac{\sqrt{b x^{4} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{\sqrt{b x^{4} + a} b}{a x^{4}}}{4 \, b}"," ",0,"-1/4*(b^2*arctan(sqrt(b*x^4 + a)/sqrt(-a))/(sqrt(-a)*a) + sqrt(b*x^4 + a)*b/(a*x^4))/b","A",0
816,1,44,0,0.188710," ","integrate(x^5/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{4} + a} x^{2}}{4 \, b} + \frac{a \log\left({\left| -\sqrt{b} x^{2} + \sqrt{b x^{4} + a} \right|}\right)}{4 \, b^{\frac{3}{2}}}"," ",0,"1/4*sqrt(b*x^4 + a)*x^2/b + 1/4*a*log(abs(-sqrt(b)*x^2 + sqrt(b*x^4 + a)))/b^(3/2)","A",0
817,1,25,0,0.175701," ","integrate(x/(b*x^4+a)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -\sqrt{b} x^{2} + \sqrt{b x^{4} + a} \right|}\right)}{2 \, \sqrt{b}}"," ",0,"-1/2*log(abs(-sqrt(b)*x^2 + sqrt(b*x^4 + a)))/sqrt(b)","A",0
818,1,31,0,0.185991," ","integrate(1/x^3/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b}}{{\left(\sqrt{b} x^{2} - \sqrt{b x^{4} + a}\right)}^{2} - a}"," ",0,"sqrt(b)/((sqrt(b)*x^2 - sqrt(b*x^4 + a))^2 - a)","A",0
819,1,59,0,0.202281," ","integrate(1/x^7/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{b} x^{2} - \sqrt{b x^{4} + a}\right)}^{2} - a\right)} b^{\frac{3}{2}}}{3 \, {\left({\left(\sqrt{b} x^{2} - \sqrt{b x^{4} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"2/3*(3*(sqrt(b)*x^2 - sqrt(b*x^4 + a))^2 - a)*b^(3/2)/((sqrt(b)*x^2 - sqrt(b*x^4 + a))^2 - a)^3","A",0
820,1,83,0,0.212212," ","integrate(1/x^11/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{8 \, {\left(10 \, {\left(\sqrt{b} x^{2} - \sqrt{b x^{4} + a}\right)}^{4} - 5 \, {\left(\sqrt{b} x^{2} - \sqrt{b x^{4} + a}\right)}^{2} a + a^{2}\right)} b^{\frac{5}{2}}}{15 \, {\left({\left(\sqrt{b} x^{2} - \sqrt{b x^{4} + a}\right)}^{2} - a\right)}^{5}}"," ",0,"8/15*(10*(sqrt(b)*x^2 - sqrt(b*x^4 + a))^4 - 5*(sqrt(b)*x^2 - sqrt(b*x^4 + a))^2*a + a^2)*b^(5/2)/((sqrt(b)*x^2 - sqrt(b*x^4 + a))^2 - a)^5","A",0
821,0,0,0,0.000000," ","integrate(x^8/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{8}}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate(x^8/sqrt(b*x^4 + a), x)","F",0
822,0,0,0,0.000000," ","integrate(x^4/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate(x^4/sqrt(b*x^4 + a), x)","F",0
823,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*x^4 + a), x)","F",0
824,0,0,0,0.000000," ","integrate(1/x^4/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{4} + a} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^4 + a)*x^4), x)","F",0
825,0,0,0,0.000000," ","integrate(1/x^8/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{4} + a} x^{8}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^4 + a)*x^8), x)","F",0
826,0,0,0,0.000000," ","integrate(x^10/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{10}}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate(x^10/sqrt(b*x^4 + a), x)","F",0
827,0,0,0,0.000000," ","integrate(x^6/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate(x^6/sqrt(b*x^4 + a), x)","F",0
828,0,0,0,0.000000," ","integrate(x^2/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{b x^{4} + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(b*x^4 + a), x)","F",0
829,0,0,0,0.000000," ","integrate(1/x^2/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{4} + a} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^4 + a)*x^2), x)","F",0
830,0,0,0,0.000000," ","integrate(1/x^6/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{4} + a} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^4 + a)*x^6), x)","F",0
831,1,61,0,0.172955," ","integrate(x^11/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{-b x^{4} + a} a^{2}}{2 \, b^{3}} - \frac{3 \, {\left(b x^{4} - a\right)}^{2} \sqrt{-b x^{4} + a} - 10 \, {\left(-b x^{4} + a\right)}^{\frac{3}{2}} a}{30 \, b^{3}}"," ",0,"-1/2*sqrt(-b*x^4 + a)*a^2/b^3 - 1/30*(3*(b*x^4 - a)^2*sqrt(-b*x^4 + a) - 10*(-b*x^4 + a)^(3/2)*a)/b^3","A",0
832,1,32,0,0.153019," ","integrate(x^7/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{2}}}{6 \, b^{2}} - \frac{\sqrt{-b x^{4} + a} a}{2 \, b^{2}}"," ",0,"1/6*(-b*x^4 + a)^(3/2)/b^2 - 1/2*sqrt(-b*x^4 + a)*a/b^2","A",0
833,1,15,0,0.189007," ","integrate(x^3/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{-b x^{4} + a}}{2 \, b}"," ",0,"-1/2*sqrt(-b*x^4 + a)/b","A",0
834,1,24,0,0.156299," ","integrate(1/x/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{-b x^{4} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a}}"," ",0,"1/2*arctan(sqrt(-b*x^4 + a)/sqrt(-a))/sqrt(-a)","A",0
835,1,54,0,0.162608," ","integrate(1/x^5/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{\frac{b^{2} \arctan\left(\frac{\sqrt{-b x^{4} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} - \frac{\sqrt{-b x^{4} + a} b}{a x^{4}}}{4 \, b}"," ",0,"1/4*(b^2*arctan(sqrt(-b*x^4 + a)/sqrt(-a))/(sqrt(-a)*a) - sqrt(-b*x^4 + a)*b/(a*x^4))/b","A",0
836,1,53,0,0.211287," ","integrate(x^5/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{-b x^{4} + a} x^{2}}{4 \, b} - \frac{a \log\left({\left| -\sqrt{-b} x^{2} + \sqrt{-b x^{4} + a} \right|}\right)}{4 \, \sqrt{-b} b}"," ",0,"-1/4*sqrt(-b*x^4 + a)*x^2/b - 1/4*a*log(abs(-sqrt(-b)*x^2 + sqrt(-b*x^4 + a)))/(sqrt(-b)*b)","A",0
837,1,30,0,0.171773," ","integrate(x/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -\sqrt{-b} x^{2} + \sqrt{-b x^{4} + a} \right|}\right)}{2 \, \sqrt{-b}}"," ",0,"-1/2*log(abs(-sqrt(-b)*x^2 + sqrt(-b*x^4 + a)))/sqrt(-b)","A",0
838,1,36,0,0.175581," ","integrate(1/x^3/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{-b}}{{\left(\sqrt{-b} x^{2} - \sqrt{-b x^{4} + a}\right)}^{2} - a}"," ",0,"sqrt(-b)/((sqrt(-b)*x^2 - sqrt(-b*x^4 + a))^2 - a)","A",0
839,1,68,0,0.180649," ","integrate(1/x^7/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, {\left(\sqrt{-b} x^{2} - \sqrt{-b x^{4} + a}\right)}^{2} - a\right)} \sqrt{-b} b}{3 \, {\left({\left(\sqrt{-b} x^{2} - \sqrt{-b x^{4} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"-2/3*(3*(sqrt(-b)*x^2 - sqrt(-b*x^4 + a))^2 - a)*sqrt(-b)*b/((sqrt(-b)*x^2 - sqrt(-b*x^4 + a))^2 - a)^3","A",0
840,1,97,0,0.184389," ","integrate(1/x^11/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\frac{8 \, {\left(10 \, {\left(\sqrt{-b} x^{2} - \sqrt{-b x^{4} + a}\right)}^{4} - 5 \, {\left(\sqrt{-b} x^{2} - \sqrt{-b x^{4} + a}\right)}^{2} a + a^{2}\right)} \sqrt{-b} b^{2}}{15 \, {\left({\left(\sqrt{-b} x^{2} - \sqrt{-b x^{4} + a}\right)}^{2} - a\right)}^{5}}"," ",0,"8/15*(10*(sqrt(-b)*x^2 - sqrt(-b*x^4 + a))^4 - 5*(sqrt(-b)*x^2 - sqrt(-b*x^4 + a))^2*a + a^2)*sqrt(-b)*b^2/((sqrt(-b)*x^2 - sqrt(-b*x^4 + a))^2 - a)^5","A",0
841,0,0,0,0.000000," ","integrate(x^8/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{8}}{\sqrt{-b x^{4} + a}}\,{d x}"," ",0,"integrate(x^8/sqrt(-b*x^4 + a), x)","F",0
842,0,0,0,0.000000," ","integrate(x^4/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{-b x^{4} + a}}\,{d x}"," ",0,"integrate(x^4/sqrt(-b*x^4 + a), x)","F",0
843,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b x^{4} + a}}\,{d x}"," ",0,"integrate(1/sqrt(-b*x^4 + a), x)","F",0
844,0,0,0,0.000000," ","integrate(1/x^4/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b x^{4} + a} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(-b*x^4 + a)*x^4), x)","F",0
845,0,0,0,0.000000," ","integrate(1/x^8/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b x^{4} + a} x^{8}}\,{d x}"," ",0,"integrate(1/(sqrt(-b*x^4 + a)*x^8), x)","F",0
846,0,0,0,0.000000," ","integrate(x^10/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{10}}{\sqrt{-b x^{4} + a}}\,{d x}"," ",0,"integrate(x^10/sqrt(-b*x^4 + a), x)","F",0
847,0,0,0,0.000000," ","integrate(x^6/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{-b x^{4} + a}}\,{d x}"," ",0,"integrate(x^6/sqrt(-b*x^4 + a), x)","F",0
848,0,0,0,0.000000," ","integrate(x^2/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-b x^{4} + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(-b*x^4 + a), x)","F",0
849,0,0,0,0.000000," ","integrate(1/x^2/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b x^{4} + a} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-b*x^4 + a)*x^2), x)","F",0
850,0,0,0,0.000000," ","integrate(1/x^6/(-b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b x^{4} + a} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(-b*x^4 + a)*x^6), x)","F",0
851,1,52,0,0.197768," ","integrate(x^11/(b*x^4+a)^(3/2),x, algorithm=""giac"")","-\frac{a^{2}}{2 \, \sqrt{b x^{4} + a} b^{3}} + \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}} b^{6} - 6 \, \sqrt{b x^{4} + a} a b^{6}}{6 \, b^{9}}"," ",0,"-1/2*a^2/(sqrt(b*x^4 + a)*b^3) + 1/6*((b*x^4 + a)^(3/2)*b^6 - 6*sqrt(b*x^4 + a)*a*b^6)/b^9","A",0
852,1,33,0,0.167382," ","integrate(x^7/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{b x^{4} + a}}{b} + \frac{a}{\sqrt{b x^{4} + a} b}}{2 \, b}"," ",0,"1/2*(sqrt(b*x^4 + a)/b + a/(sqrt(b*x^4 + a)*b))/b","A",0
853,1,14,0,0.151212," ","integrate(x^3/(b*x^4+a)^(3/2),x, algorithm=""giac"")","-\frac{1}{2 \, \sqrt{b x^{4} + a} b}"," ",0,"-1/2/(sqrt(b*x^4 + a)*b)","A",0
854,1,41,0,0.156199," ","integrate(1/x/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{b x^{4} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a} a} + \frac{1}{2 \, \sqrt{b x^{4} + a} a}"," ",0,"1/2*arctan(sqrt(b*x^4 + a)/sqrt(-a))/(sqrt(-a)*a) + 1/2/(sqrt(b*x^4 + a)*a)","A",0
855,1,72,0,0.166224," ","integrate(1/x^5/(b*x^4+a)^(3/2),x, algorithm=""giac"")","-\frac{3 \, b \arctan\left(\frac{\sqrt{b x^{4} + a}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a} a^{2}} - \frac{3 \, {\left(b x^{4} + a\right)} b - 2 \, a b}{4 \, {\left({\left(b x^{4} + a\right)}^{\frac{3}{2}} - \sqrt{b x^{4} + a} a\right)} a^{2}}"," ",0,"-3/4*b*arctan(sqrt(b*x^4 + a)/sqrt(-a))/(sqrt(-a)*a^2) - 1/4*(3*(b*x^4 + a)*b - 2*a*b)/(((b*x^4 + a)^(3/2) - sqrt(b*x^4 + a)*a)*a^2)","A",0
856,1,55,0,0.186896," ","integrate(x^9/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{x^{4}}{b} + \frac{3 \, a}{b^{2}}\right)} x^{2}}{4 \, \sqrt{b x^{4} + a}} + \frac{3 \, a \log\left({\left| -\sqrt{b} x^{2} + \sqrt{b x^{4} + a} \right|}\right)}{4 \, b^{\frac{5}{2}}}"," ",0,"1/4*(x^4/b + 3*a/b^2)*x^2/sqrt(b*x^4 + a) + 3/4*a*log(abs(-sqrt(b)*x^2 + sqrt(b*x^4 + a)))/b^(5/2)","A",0
857,1,43,0,0.192591," ","integrate(x^5/(b*x^4+a)^(3/2),x, algorithm=""giac"")","-\frac{x^{2}}{2 \, \sqrt{b x^{4} + a} b} - \frac{\log\left({\left| -\sqrt{b} x^{2} + \sqrt{b x^{4} + a} \right|}\right)}{2 \, b^{\frac{3}{2}}}"," ",0,"-1/2*x^2/(sqrt(b*x^4 + a)*b) - 1/2*log(abs(-sqrt(b)*x^2 + sqrt(b*x^4 + a)))/b^(3/2)","A",0
858,1,17,0,0.171896," ","integrate(x/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{x^{2}}{2 \, \sqrt{b x^{4} + a} a}"," ",0,"1/2*x^2/(sqrt(b*x^4 + a)*a)","A",0
859,1,53,0,0.188545," ","integrate(1/x^3/(b*x^4+a)^(3/2),x, algorithm=""giac"")","-\frac{b x^{2}}{2 \, \sqrt{b x^{4} + a} a^{2}} + \frac{\sqrt{b}}{{\left({\left(\sqrt{b} x^{2} - \sqrt{b x^{4} + a}\right)}^{2} - a\right)} a}"," ",0,"-1/2*b*x^2/(sqrt(b*x^4 + a)*a^2) + sqrt(b)/(((sqrt(b)*x^2 - sqrt(b*x^4 + a))^2 - a)*a)","A",0
860,1,115,0,0.219515," ","integrate(1/x^7/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\frac{b^{2} x^{2}}{2 \, \sqrt{b x^{4} + a} a^{3}} - \frac{3 \, {\left(\sqrt{b} x^{2} - \sqrt{b x^{4} + a}\right)}^{4} b^{\frac{3}{2}} - 12 \, {\left(\sqrt{b} x^{2} - \sqrt{b x^{4} + a}\right)}^{2} a b^{\frac{3}{2}} + 5 \, a^{2} b^{\frac{3}{2}}}{3 \, {\left({\left(\sqrt{b} x^{2} - \sqrt{b x^{4} + a}\right)}^{2} - a\right)}^{3} a^{2}}"," ",0,"1/2*b^2*x^2/(sqrt(b*x^4 + a)*a^3) - 1/3*(3*(sqrt(b)*x^2 - sqrt(b*x^4 + a))^4*b^(3/2) - 12*(sqrt(b)*x^2 - sqrt(b*x^4 + a))^2*a*b^(3/2) + 5*a^2*b^(3/2))/(((sqrt(b)*x^2 - sqrt(b*x^4 + a))^2 - a)^3*a^2)","B",0
861,0,0,0,0.000000," ","integrate(x^12/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{12}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^12/(b*x^4 + a)^(3/2), x)","F",0
862,0,0,0,0.000000," ","integrate(x^8/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^8/(b*x^4 + a)^(3/2), x)","F",0
863,0,0,0,0.000000," ","integrate(x^4/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/(b*x^4 + a)^(3/2), x)","F",0
864,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(-3/2), x)","F",0
865,0,0,0,0.000000," ","integrate(1/x^4/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/2)*x^4), x)","F",0
866,0,0,0,0.000000," ","integrate(1/x^8/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{2}} x^{8}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/2)*x^8), x)","F",0
867,0,0,0,0.000000," ","integrate(x^14/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{14}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^14/(b*x^4 + a)^(3/2), x)","F",0
868,0,0,0,0.000000," ","integrate(x^10/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{10}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^10/(b*x^4 + a)^(3/2), x)","F",0
869,0,0,0,0.000000," ","integrate(x^6/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^6/(b*x^4 + a)^(3/2), x)","F",0
870,0,0,0,0.000000," ","integrate(x^2/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(b*x^4 + a)^(3/2), x)","F",0
871,0,0,0,0.000000," ","integrate(1/x^2/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/2)*x^2), x)","F",0
872,0,0,0,0.000000," ","integrate(1/x^6/(b*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{2}} x^{6}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/2)*x^6), x)","F",0
873,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(-5/2), x)","F",0
874,1,41,0,0.171221," ","integrate(x^11/(-x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{10} \, {\left(x^{4} - 1\right)}^{2} \sqrt{-x^{4} + 1} + \frac{1}{3} \, {\left(-x^{4} + 1\right)}^{\frac{3}{2}} - \frac{1}{2} \, \sqrt{-x^{4} + 1}"," ",0,"-1/10*(x^4 - 1)^2*sqrt(-x^4 + 1) + 1/3*(-x^4 + 1)^(3/2) - 1/2*sqrt(-x^4 + 1)","A",0
875,1,23,0,0.152687," ","integrate(x^7/(-x^4+1)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(-x^{4} + 1\right)}^{\frac{3}{2}} - \frac{1}{2} \, \sqrt{-x^{4} + 1}"," ",0,"1/6*(-x^4 + 1)^(3/2) - 1/2*sqrt(-x^4 + 1)","A",0
876,1,11,0,0.148453," ","integrate(x^3/(-x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-x^{4} + 1}"," ",0,"-1/2*sqrt(-x^4 + 1)","A",0
877,1,31,0,0.149969," ","integrate(1/x/(-x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \log\left(\sqrt{-x^{4} + 1} + 1\right) + \frac{1}{4} \, \log\left(-\sqrt{-x^{4} + 1} + 1\right)"," ",0,"-1/4*log(sqrt(-x^4 + 1) + 1) + 1/4*log(-sqrt(-x^4 + 1) + 1)","B",0
878,1,45,0,0.150027," ","integrate(1/x^5/(-x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{4} + 1}}{4 \, x^{4}} - \frac{1}{8} \, \log\left(\sqrt{-x^{4} + 1} + 1\right) + \frac{1}{8} \, \log\left(-\sqrt{-x^{4} + 1} + 1\right)"," ",0,"-1/4*sqrt(-x^4 + 1)/x^4 - 1/8*log(sqrt(-x^4 + 1) + 1) + 1/8*log(-sqrt(-x^4 + 1) + 1)","A",0
879,1,21,0,0.180161," ","integrate(x^5/(-x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{-x^{4} + 1} x^{2} + \frac{1}{4} \, \arcsin\left(x^{2}\right)"," ",0,"-1/4*sqrt(-x^4 + 1)*x^2 + 1/4*arcsin(x^2)","A",0
880,1,6,0,0.162047," ","integrate(x/(-x^4+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \arcsin\left(x^{2}\right)"," ",0,"1/2*arcsin(x^2)","A",0
881,1,35,0,0.170423," ","integrate(1/x^3/(-x^4+1)^(1/2),x, algorithm=""giac"")","\frac{x^{2}}{4 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}} - \frac{\sqrt{-x^{4} + 1} - 1}{4 \, x^{2}}"," ",0,"1/4*x^2/(sqrt(-x^4 + 1) - 1) - 1/4*(sqrt(-x^4 + 1) - 1)/x^2","B",0
882,1,73,0,0.195718," ","integrate(1/x^7/(-x^4+1)^(1/2),x, algorithm=""giac"")","\frac{x^{6} {\left(\frac{9 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}^{2}}{x^{4}} + 1\right)}}{48 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}^{3}} - \frac{3 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}}{16 \, x^{2}} - \frac{{\left(\sqrt{-x^{4} + 1} - 1\right)}^{3}}{48 \, x^{6}}"," ",0,"1/48*x^6*(9*(sqrt(-x^4 + 1) - 1)^2/x^4 + 1)/(sqrt(-x^4 + 1) - 1)^3 - 3/16*(sqrt(-x^4 + 1) - 1)/x^2 - 1/48*(sqrt(-x^4 + 1) - 1)^3/x^6","B",0
883,1,109,0,0.174208," ","integrate(1/x^11/(-x^4+1)^(1/2),x, algorithm=""giac"")","\frac{x^{10} {\left(\frac{25 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}^{2}}{x^{4}} + \frac{150 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}^{4}}{x^{8}} + 3\right)}}{960 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}^{5}} - \frac{5 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}}{32 \, x^{2}} - \frac{5 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}^{3}}{192 \, x^{6}} - \frac{{\left(\sqrt{-x^{4} + 1} - 1\right)}^{5}}{320 \, x^{10}}"," ",0,"1/960*x^10*(25*(sqrt(-x^4 + 1) - 1)^2/x^4 + 150*(sqrt(-x^4 + 1) - 1)^4/x^8 + 3)/(sqrt(-x^4 + 1) - 1)^5 - 5/32*(sqrt(-x^4 + 1) - 1)/x^2 - 5/192*(sqrt(-x^4 + 1) - 1)^3/x^6 - 1/320*(sqrt(-x^4 + 1) - 1)^5/x^10","B",0
884,0,0,0,0.000000," ","integrate(x^8/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{8}}{\sqrt{-x^{4} + 1}}\,{d x}"," ",0,"integrate(x^8/sqrt(-x^4 + 1), x)","F",0
885,0,0,0,0.000000," ","integrate(x^4/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{-x^{4} + 1}}\,{d x}"," ",0,"integrate(x^4/sqrt(-x^4 + 1), x)","F",0
886,0,0,0,0.000000," ","integrate(1/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 1}}\,{d x}"," ",0,"integrate(1/sqrt(-x^4 + 1), x)","F",0
887,0,0,0,0.000000," ","integrate(1/x^4/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 1} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^4 + 1)*x^4), x)","F",0
888,0,0,0,0.000000," ","integrate(1/x^8/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 1} x^{8}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^4 + 1)*x^8), x)","F",0
889,0,0,0,0.000000," ","integrate(x^10/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{10}}{\sqrt{-x^{4} + 1}}\,{d x}"," ",0,"integrate(x^10/sqrt(-x^4 + 1), x)","F",0
890,0,0,0,0.000000," ","integrate(x^6/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{-x^{4} + 1}}\,{d x}"," ",0,"integrate(x^6/sqrt(-x^4 + 1), x)","F",0
891,0,0,0,0.000000," ","integrate(x^2/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-x^{4} + 1}}\,{d x}"," ",0,"integrate(x^2/sqrt(-x^4 + 1), x)","F",0
892,0,0,0,0.000000," ","integrate(1/x^2/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 1} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^4 + 1)*x^2), x)","F",0
893,0,0,0,0.000000," ","integrate(1/x^6/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 1} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^4 + 1)*x^6), x)","F",0
894,1,32,0,0.170234," ","integrate(x^11/(-x^4+1)^(3/2),x, algorithm=""giac"")","-\frac{1}{6} \, {\left(-x^{4} + 1\right)}^{\frac{3}{2}} + \sqrt{-x^{4} + 1} + \frac{1}{2 \, \sqrt{-x^{4} + 1}}"," ",0,"-1/6*(-x^4 + 1)^(3/2) + sqrt(-x^4 + 1) + 1/2/sqrt(-x^4 + 1)","A",0
895,1,23,0,0.149247," ","integrate(x^7/(-x^4+1)^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-x^{4} + 1} + \frac{1}{2 \, \sqrt{-x^{4} + 1}}"," ",0,"1/2*sqrt(-x^4 + 1) + 1/2/sqrt(-x^4 + 1)","A",0
896,1,11,0,0.185596," ","integrate(x^3/(-x^4+1)^(3/2),x, algorithm=""giac"")","\frac{1}{2 \, \sqrt{-x^{4} + 1}}"," ",0,"1/2/sqrt(-x^4 + 1)","A",0
897,1,42,0,0.152439," ","integrate(1/x/(-x^4+1)^(3/2),x, algorithm=""giac"")","\frac{1}{2 \, \sqrt{-x^{4} + 1}} - \frac{1}{4} \, \log\left(\sqrt{-x^{4} + 1} + 1\right) + \frac{1}{4} \, \log\left(-\sqrt{-x^{4} + 1} + 1\right)"," ",0,"1/2/sqrt(-x^4 + 1) - 1/4*log(sqrt(-x^4 + 1) + 1) + 1/4*log(-sqrt(-x^4 + 1) + 1)","A",0
898,1,63,0,0.172046," ","integrate(1/x^5/(-x^4+1)^(3/2),x, algorithm=""giac"")","-\frac{3 \, x^{4} - 1}{4 \, {\left({\left(-x^{4} + 1\right)}^{\frac{3}{2}} - \sqrt{-x^{4} + 1}\right)}} - \frac{3}{8} \, \log\left(\sqrt{-x^{4} + 1} + 1\right) + \frac{3}{8} \, \log\left(-\sqrt{-x^{4} + 1} + 1\right)"," ",0,"-1/4*(3*x^4 - 1)/((-x^4 + 1)^(3/2) - sqrt(-x^4 + 1)) - 3/8*log(sqrt(-x^4 + 1) + 1) + 3/8*log(-sqrt(-x^4 + 1) + 1)","A",0
899,1,33,0,0.187269," ","integrate(x^9/(-x^4+1)^(3/2),x, algorithm=""giac"")","\frac{{\left(x^{4} - 3\right)} \sqrt{-x^{4} + 1} x^{2}}{4 \, {\left(x^{4} - 1\right)}} - \frac{3}{4} \, \arcsin\left(x^{2}\right)"," ",0,"1/4*(x^4 - 3)*sqrt(-x^4 + 1)*x^2/(x^4 - 1) - 3/4*arcsin(x^2)","A",0
900,1,28,0,0.177075," ","integrate(x^5/(-x^4+1)^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{4} + 1} x^{2}}{2 \, {\left(x^{4} - 1\right)}} - \frac{1}{2} \, \arcsin\left(x^{2}\right)"," ",0,"-1/2*sqrt(-x^4 + 1)*x^2/(x^4 - 1) - 1/2*arcsin(x^2)","A",0
901,1,21,0,0.182154," ","integrate(x/(-x^4+1)^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{4} + 1} x^{2}}{2 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/2*sqrt(-x^4 + 1)*x^2/(x^4 - 1)","A",0
902,1,56,0,0.185945," ","integrate(1/x^3/(-x^4+1)^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{4} + 1} x^{2}}{2 \, {\left(x^{4} - 1\right)}} + \frac{x^{2}}{4 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}} - \frac{\sqrt{-x^{4} + 1} - 1}{4 \, x^{2}}"," ",0,"-1/2*sqrt(-x^4 + 1)*x^2/(x^4 - 1) + 1/4*x^2/(sqrt(-x^4 + 1) - 1) - 1/4*(sqrt(-x^4 + 1) - 1)/x^2","A",0
903,1,94,0,0.170040," ","integrate(1/x^7/(-x^4+1)^(3/2),x, algorithm=""giac"")","\frac{x^{6} {\left(\frac{21 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}^{2}}{x^{4}} + 1\right)}}{48 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}^{3}} - \frac{\sqrt{-x^{4} + 1} x^{2}}{2 \, {\left(x^{4} - 1\right)}} - \frac{7 \, {\left(\sqrt{-x^{4} + 1} - 1\right)}}{16 \, x^{2}} - \frac{{\left(\sqrt{-x^{4} + 1} - 1\right)}^{3}}{48 \, x^{6}}"," ",0,"1/48*x^6*(21*(sqrt(-x^4 + 1) - 1)^2/x^4 + 1)/(sqrt(-x^4 + 1) - 1)^3 - 1/2*sqrt(-x^4 + 1)*x^2/(x^4 - 1) - 7/16*(sqrt(-x^4 + 1) - 1)/x^2 - 1/48*(sqrt(-x^4 + 1) - 1)^3/x^6","B",0
904,0,0,0,0.000000," ","integrate(x^12/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{12}}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^12/(-x^4 + 1)^(3/2), x)","F",0
905,0,0,0,0.000000," ","integrate(x^8/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^8/(-x^4 + 1)^(3/2), x)","F",0
906,0,0,0,0.000000," ","integrate(x^4/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/(-x^4 + 1)^(3/2), x)","F",0
907,0,0,0,0.000000," ","integrate(1/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-x^4 + 1)^(-3/2), x)","F",0
908,0,0,0,0.000000," ","integrate(1/x^4/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((-x^4 + 1)^(3/2)*x^4), x)","F",0
909,0,0,0,0.000000," ","integrate(1/x^8/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}} x^{8}}\,{d x}"," ",0,"integrate(1/((-x^4 + 1)^(3/2)*x^8), x)","F",0
910,0,0,0,0.000000," ","integrate(x^14/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{14}}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^14/(-x^4 + 1)^(3/2), x)","F",0
911,0,0,0,0.000000," ","integrate(x^10/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{10}}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^10/(-x^4 + 1)^(3/2), x)","F",0
912,0,0,0,0.000000," ","integrate(x^6/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^6/(-x^4 + 1)^(3/2), x)","F",0
913,0,0,0,0.000000," ","integrate(x^2/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(-x^4 + 1)^(3/2), x)","F",0
914,0,0,0,0.000000," ","integrate(1/x^2/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((-x^4 + 1)^(3/2)*x^2), x)","F",0
915,0,0,0,0.000000," ","integrate(1/x^6/(-x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + 1\right)}^{\frac{3}{2}} x^{6}}\,{d x}"," ",0,"integrate(1/((-x^4 + 1)^(3/2)*x^6), x)","F",0
916,0,0,0,0.000000," ","integrate(1/(-x^4+1)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-x^4 + 1)^(-5/2), x)","F",0
917,1,28,0,0.150944," ","integrate(x^11/(x^4+1)^(1/2),x, algorithm=""giac"")","\frac{1}{10} \, {\left(x^{4} + 1\right)}^{\frac{5}{2}} - \frac{1}{3} \, {\left(x^{4} + 1\right)}^{\frac{3}{2}} + \frac{1}{2} \, \sqrt{x^{4} + 1}"," ",0,"1/10*(x^4 + 1)^(5/2) - 1/3*(x^4 + 1)^(3/2) + 1/2*sqrt(x^4 + 1)","A",0
918,1,19,0,0.148812," ","integrate(x^7/(x^4+1)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(x^{4} + 1\right)}^{\frac{3}{2}} - \frac{1}{2} \, \sqrt{x^{4} + 1}"," ",0,"1/6*(x^4 + 1)^(3/2) - 1/2*sqrt(x^4 + 1)","A",0
919,1,9,0,0.183416," ","integrate(x^3/(x^4+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x^{4} + 1}"," ",0,"1/2*sqrt(x^4 + 1)","A",0
920,1,25,0,0.148875," ","integrate(1/x/(x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} + 1\right) + \frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} - 1\right)"," ",0,"-1/4*log(sqrt(x^4 + 1) + 1) + 1/4*log(sqrt(x^4 + 1) - 1)","B",0
921,1,37,0,0.150192," ","integrate(1/x^5/(x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{x^{4} + 1}}{4 \, x^{4}} + \frac{1}{8} \, \log\left(\sqrt{x^{4} + 1} + 1\right) - \frac{1}{8} \, \log\left(\sqrt{x^{4} + 1} - 1\right)"," ",0,"-1/4*sqrt(x^4 + 1)/x^4 + 1/8*log(sqrt(x^4 + 1) + 1) - 1/8*log(sqrt(x^4 + 1) - 1)","A",0
922,1,29,0,0.163211," ","integrate(x^5/(x^4+1)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{x^{4} + 1} x^{2} + \frac{1}{4} \, \log\left(-x^{2} + \sqrt{x^{4} + 1}\right)"," ",0,"1/4*sqrt(x^4 + 1)*x^2 + 1/4*log(-x^2 + sqrt(x^4 + 1))","A",0
923,1,16,0,0.163135," ","integrate(x/(x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 1}\right)"," ",0,"-1/2*log(-x^2 + sqrt(x^4 + 1))","B",0
924,1,19,0,0.155652," ","integrate(1/x^3/(x^4+1)^(1/2),x, algorithm=""giac"")","\frac{1}{{\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} - 1}"," ",0,"1/((x^2 - sqrt(x^4 + 1))^2 - 1)","A",0
925,1,40,0,0.163563," ","integrate(1/x^7/(x^4+1)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} - 1\right)}}{3 \, {\left({\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} - 1\right)}^{3}}"," ",0,"2/3*(3*(x^2 - sqrt(x^4 + 1))^2 - 1)/((x^2 - sqrt(x^4 + 1))^2 - 1)^3","A",0
926,1,57,0,0.183162," ","integrate(1/x^11/(x^4+1)^(1/2),x, algorithm=""giac"")","\frac{8 \, {\left(10 \, {\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{4} - 5 \, {\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} + 1\right)}}{15 \, {\left({\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} - 1\right)}^{5}}"," ",0,"8/15*(10*(x^2 - sqrt(x^4 + 1))^4 - 5*(x^2 - sqrt(x^4 + 1))^2 + 1)/((x^2 - sqrt(x^4 + 1))^2 - 1)^5","A",0
927,0,0,0,0.000000," ","integrate(x^8/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{8}}{\sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(x^8/sqrt(x^4 + 1), x)","F",0
928,0,0,0,0.000000," ","integrate(x^4/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(x^4/sqrt(x^4 + 1), x)","F",0
929,0,0,0,0.000000," ","integrate(1/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(1/sqrt(x^4 + 1), x)","F",0
930,0,0,0,0.000000," ","integrate(1/x^4/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 1} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 1)*x^4), x)","F",0
931,0,0,0,0.000000," ","integrate(1/x^8/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 1} x^{8}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 1)*x^8), x)","F",0
932,0,0,0,0.000000," ","integrate(x^10/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{10}}{\sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(x^10/sqrt(x^4 + 1), x)","F",0
933,0,0,0,0.000000," ","integrate(x^6/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(x^6/sqrt(x^4 + 1), x)","F",0
934,0,0,0,0.000000," ","integrate(x^2/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{x^{4} + 1}}\,{d x}"," ",0,"integrate(x^2/sqrt(x^4 + 1), x)","F",0
935,0,0,0,0.000000," ","integrate(1/x^2/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 1} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 1)*x^2), x)","F",0
936,0,0,0,0.000000," ","integrate(1/x^6/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 1} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 1)*x^6), x)","F",0
937,1,28,0,0.151742," ","integrate(x^11/(x^4+1)^(3/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(x^{4} + 1\right)}^{\frac{3}{2}} - \sqrt{x^{4} + 1} - \frac{1}{2 \, \sqrt{x^{4} + 1}}"," ",0,"1/6*(x^4 + 1)^(3/2) - sqrt(x^4 + 1) - 1/2/sqrt(x^4 + 1)","A",0
938,1,19,0,0.150945," ","integrate(x^7/(x^4+1)^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x^{4} + 1} + \frac{1}{2 \, \sqrt{x^{4} + 1}}"," ",0,"1/2*sqrt(x^4 + 1) + 1/2/sqrt(x^4 + 1)","A",0
939,1,9,0,0.154015," ","integrate(x^3/(x^4+1)^(3/2),x, algorithm=""giac"")","-\frac{1}{2 \, \sqrt{x^{4} + 1}}"," ",0,"-1/2/sqrt(x^4 + 1)","A",0
940,1,34,0,0.167475," ","integrate(1/x/(x^4+1)^(3/2),x, algorithm=""giac"")","\frac{1}{2 \, \sqrt{x^{4} + 1}} - \frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} + 1\right) + \frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} - 1\right)"," ",0,"1/2/sqrt(x^4 + 1) - 1/4*log(sqrt(x^4 + 1) + 1) + 1/4*log(sqrt(x^4 + 1) - 1)","A",0
941,1,53,0,0.151211," ","integrate(1/x^5/(x^4+1)^(3/2),x, algorithm=""giac"")","-\frac{3 \, x^{4} + 1}{4 \, {\left({\left(x^{4} + 1\right)}^{\frac{3}{2}} - \sqrt{x^{4} + 1}\right)}} + \frac{3}{8} \, \log\left(\sqrt{x^{4} + 1} + 1\right) - \frac{3}{8} \, \log\left(\sqrt{x^{4} + 1} - 1\right)"," ",0,"-1/4*(3*x^4 + 1)/((x^4 + 1)^(3/2) - sqrt(x^4 + 1)) + 3/8*log(sqrt(x^4 + 1) + 1) - 3/8*log(sqrt(x^4 + 1) - 1)","A",0
942,1,34,0,0.164840," ","integrate(x^9/(x^4+1)^(3/2),x, algorithm=""giac"")","\frac{{\left(x^{4} + 3\right)} x^{2}}{4 \, \sqrt{x^{4} + 1}} + \frac{3}{4} \, \log\left(-x^{2} + \sqrt{x^{4} + 1}\right)"," ",0,"1/4*(x^4 + 3)*x^2/sqrt(x^4 + 1) + 3/4*log(-x^2 + sqrt(x^4 + 1))","A",0
943,1,29,0,0.180190," ","integrate(x^5/(x^4+1)^(3/2),x, algorithm=""giac"")","-\frac{x^{2}}{2 \, \sqrt{x^{4} + 1}} - \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 1}\right)"," ",0,"-1/2*x^2/sqrt(x^4 + 1) - 1/2*log(-x^2 + sqrt(x^4 + 1))","A",0
944,1,12,0,0.159330," ","integrate(x/(x^4+1)^(3/2),x, algorithm=""giac"")","\frac{x^{2}}{2 \, \sqrt{x^{4} + 1}}"," ",0,"1/2*x^2/sqrt(x^4 + 1)","A",0
945,1,32,0,0.172822," ","integrate(1/x^3/(x^4+1)^(3/2),x, algorithm=""giac"")","-\frac{x^{2}}{2 \, \sqrt{x^{4} + 1}} + \frac{1}{{\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} - 1}"," ",0,"-1/2*x^2/sqrt(x^4 + 1) + 1/((x^2 - sqrt(x^4 + 1))^2 - 1)","A",0
946,1,70,0,0.179306," ","integrate(1/x^7/(x^4+1)^(3/2),x, algorithm=""giac"")","\frac{x^{2}}{2 \, \sqrt{x^{4} + 1}} - \frac{3 \, {\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{4} - 12 \, {\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} + 5}{3 \, {\left({\left(x^{2} - \sqrt{x^{4} + 1}\right)}^{2} - 1\right)}^{3}}"," ",0,"1/2*x^2/sqrt(x^4 + 1) - 1/3*(3*(x^2 - sqrt(x^4 + 1))^4 - 12*(x^2 - sqrt(x^4 + 1))^2 + 5)/((x^2 - sqrt(x^4 + 1))^2 - 1)^3","A",0
947,0,0,0,0.000000," ","integrate(x^12/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{12}}{{\left(x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^12/(x^4 + 1)^(3/2), x)","F",0
948,0,0,0,0.000000," ","integrate(x^8/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^8/(x^4 + 1)^(3/2), x)","F",0
949,0,0,0,0.000000," ","integrate(x^4/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/(x^4 + 1)^(3/2), x)","F",0
950,0,0,0,0.000000," ","integrate(1/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x^4 + 1)^(-3/2), x)","F",0
951,0,0,0,0.000000," ","integrate(1/x^4/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 1\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((x^4 + 1)^(3/2)*x^4), x)","F",0
952,0,0,0,0.000000," ","integrate(1/x^8/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 1\right)}^{\frac{3}{2}} x^{8}}\,{d x}"," ",0,"integrate(1/((x^4 + 1)^(3/2)*x^8), x)","F",0
953,0,0,0,0.000000," ","integrate(x^14/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{14}}{{\left(x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^14/(x^4 + 1)^(3/2), x)","F",0
954,0,0,0,0.000000," ","integrate(x^10/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{10}}{{\left(x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^10/(x^4 + 1)^(3/2), x)","F",0
955,0,0,0,0.000000," ","integrate(x^6/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^6/(x^4 + 1)^(3/2), x)","F",0
956,0,0,0,0.000000," ","integrate(x^2/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{4} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(x^4 + 1)^(3/2), x)","F",0
957,0,0,0,0.000000," ","integrate(1/x^2/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 1\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((x^4 + 1)^(3/2)*x^2), x)","F",0
958,0,0,0,0.000000," ","integrate(1/x^6/(x^4+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 1\right)}^{\frac{3}{2}} x^{6}}\,{d x}"," ",0,"integrate(1/((x^4 + 1)^(3/2)*x^6), x)","F",0
959,0,0,0,0.000000," ","integrate(1/(x^4+1)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((x^4 + 1)^(-5/2), x)","F",0
960,1,23,0,0.149179," ","integrate(x^7/(-x^4+16)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(-x^{4} + 16\right)}^{\frac{3}{2}} - 8 \, \sqrt{-x^{4} + 16}"," ",0,"1/6*(-x^4 + 16)^(3/2) - 8*sqrt(-x^4 + 16)","A",0
961,1,23,0,0.165676," ","integrate(x^5/(-x^4+16)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{-x^{4} + 16} x^{2} + 4 \, \arcsin\left(\frac{1}{4} \, x^{2}\right)"," ",0,"-1/4*sqrt(-x^4 + 16)*x^2 + 4*arcsin(1/4*x^2)","A",0
962,1,11,0,0.158261," ","integrate(x^3/(-x^4+16)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-x^{4} + 16}"," ",0,"-1/2*sqrt(-x^4 + 16)","A",0
963,1,8,0,0.170427," ","integrate(x/(-x^4+16)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \arcsin\left(\frac{1}{4} \, x^{2}\right)"," ",0,"1/2*arcsin(1/4*x^2)","A",0
964,1,31,0,0.147308," ","integrate(1/x/(-x^4+16)^(1/2),x, algorithm=""giac"")","-\frac{1}{16} \, \log\left(\sqrt{-x^{4} + 16} + 4\right) + \frac{1}{16} \, \log\left(-\sqrt{-x^{4} + 16} + 4\right)"," ",0,"-1/16*log(sqrt(-x^4 + 16) + 4) + 1/16*log(-sqrt(-x^4 + 16) + 4)","B",0
965,1,35,0,0.169374," ","integrate(1/x^3/(-x^4+16)^(1/2),x, algorithm=""giac"")","\frac{x^{2}}{64 \, {\left(\sqrt{-x^{4} + 16} - 4\right)}} - \frac{\sqrt{-x^{4} + 16} - 4}{64 \, x^{2}}"," ",0,"1/64*x^2/(sqrt(-x^4 + 16) - 4) - 1/64*(sqrt(-x^4 + 16) - 4)/x^2","B",0
966,1,45,0,0.149926," ","integrate(1/x^5/(-x^4+16)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{4} + 16}}{64 \, x^{4}} - \frac{1}{512} \, \log\left(\sqrt{-x^{4} + 16} + 4\right) + \frac{1}{512} \, \log\left(-\sqrt{-x^{4} + 16} + 4\right)"," ",0,"-1/64*sqrt(-x^4 + 16)/x^4 - 1/512*log(sqrt(-x^4 + 16) + 4) + 1/512*log(-sqrt(-x^4 + 16) + 4)","A",0
967,1,73,0,0.169690," ","integrate(1/x^7/(-x^4+16)^(1/2),x, algorithm=""giac"")","\frac{x^{6} {\left(\frac{9 \, {\left(\sqrt{-x^{4} + 16} - 4\right)}^{2}}{x^{4}} + 1\right)}}{12288 \, {\left(\sqrt{-x^{4} + 16} - 4\right)}^{3}} - \frac{3 \, {\left(\sqrt{-x^{4} + 16} - 4\right)}}{4096 \, x^{2}} - \frac{{\left(\sqrt{-x^{4} + 16} - 4\right)}^{3}}{12288 \, x^{6}}"," ",0,"1/12288*x^6*(9*(sqrt(-x^4 + 16) - 4)^2/x^4 + 1)/(sqrt(-x^4 + 16) - 4)^3 - 3/4096*(sqrt(-x^4 + 16) - 4)/x^2 - 1/12288*(sqrt(-x^4 + 16) - 4)^3/x^6","B",0
968,0,0,0,0.000000," ","integrate(x^6/(-x^4+16)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{-x^{4} + 16}}\,{d x}"," ",0,"integrate(x^6/sqrt(-x^4 + 16), x)","F",0
969,0,0,0,0.000000," ","integrate(x^4/(-x^4+16)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{-x^{4} + 16}}\,{d x}"," ",0,"integrate(x^4/sqrt(-x^4 + 16), x)","F",0
970,0,0,0,0.000000," ","integrate(x^2/(-x^4+16)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-x^{4} + 16}}\,{d x}"," ",0,"integrate(x^2/sqrt(-x^4 + 16), x)","F",0
971,0,0,0,0.000000," ","integrate(1/(-x^4+16)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 16}}\,{d x}"," ",0,"integrate(1/sqrt(-x^4 + 16), x)","F",0
972,0,0,0,0.000000," ","integrate(1/x^2/(-x^4+16)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 16} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^4 + 16)*x^2), x)","F",0
973,0,0,0,0.000000," ","integrate(1/x^4/(-x^4+16)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 16} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^4 + 16)*x^4), x)","F",0
974,1,16,0,0.155930," ","integrate(x/(x^4-4)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(x^{2} - \sqrt{x^{4} - 4}\right)"," ",0,"-1/2*log(x^2 - sqrt(x^4 - 4))","A",0
975,1,16,0,0.195712," ","integrate(x/(x^4+4)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 4}\right)"," ",0,"-1/2*log(-x^2 + sqrt(x^4 + 4))","A",0
976,1,10,0,0.191995," ","integrate(1/x/(x^4-1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(\sqrt{x^{4} - 1}\right)"," ",0,"1/2*arctan(sqrt(x^4 - 1))","A",0
977,0,0,0,0.000000," ","integrate(x^4/(x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{x^{4} - 1}}\,{d x}"," ",0,"integrate(x^4/sqrt(x^4 - 1), x)","F",0
978,0,0,0,0.000000," ","integrate(1/(x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} - 1}}\,{d x}"," ",0,"integrate(1/sqrt(x^4 - 1), x)","F",0
979,0,0,0,0.000000," ","integrate(1/x^4/(x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} - 1} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 - 1)*x^4), x)","F",0
980,0,0,0,0.000000," ","integrate(x^6/(x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{x^{4} - 1}}\,{d x}"," ",0,"integrate(x^6/sqrt(x^4 - 1), x)","F",0
981,0,0,0,0.000000," ","integrate(x^2/(x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{x^{4} - 1}}\,{d x}"," ",0,"integrate(x^2/sqrt(x^4 - 1), x)","F",0
982,0,0,0,0.000000," ","integrate(1/x^2/(x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} - 1} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 - 1)*x^2), x)","F",0
983,0,0,0,0.000000," ","integrate(x^2/(-2*x^4+3)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-2 \, x^{4} + 3}}\,{d x}"," ",0,"integrate(x^2/sqrt(-2*x^4 + 3), x)","F",0
984,0,0,0,0.000000," ","integrate(x^2/(-b*x^4+3)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-b x^{4} + 3}}\,{d x}"," ",0,"integrate(x^2/sqrt(-b*x^4 + 3), x)","F",0
985,1,19,0,0.149146," ","integrate(x^7*(x^4+1)^(1/3),x, algorithm=""giac"")","\frac{3}{28} \, {\left(x^{4} + 1\right)}^{\frac{7}{3}} - \frac{3}{16} \, {\left(x^{4} + 1\right)}^{\frac{4}{3}}"," ",0,"3/28*(x^4 + 1)^(7/3) - 3/16*(x^4 + 1)^(4/3)","A",0
986,1,9,0,0.161787," ","integrate(x^3/(x^4+1)^(4/3),x, algorithm=""giac"")","-\frac{3}{4 \, {\left(x^{4} + 1\right)}^{\frac{1}{3}}}"," ",0,"-3/4/(x^4 + 1)^(1/3)","A",0
987,1,9,0,0.150690," ","integrate(x^3/(x^4+1)^(1/3),x, algorithm=""giac"")","\frac{3}{8} \, {\left(x^{4} + 1\right)}^{\frac{2}{3}}"," ",0,"3/8*(x^4 + 1)^(2/3)","A",0
988,1,71,0,0.165326," ","integrate(x^19*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{3315 \, {\left(b x^{4} + a\right)}^{\frac{21}{4}} - 16380 \, {\left(b x^{4} + a\right)}^{\frac{17}{4}} a + 32130 \, {\left(b x^{4} + a\right)}^{\frac{13}{4}} a^{2} - 30940 \, {\left(b x^{4} + a\right)}^{\frac{9}{4}} a^{3} + 13923 \, {\left(b x^{4} + a\right)}^{\frac{5}{4}} a^{4}}{69615 \, b^{5}}"," ",0,"1/69615*(3315*(b*x^4 + a)^(21/4) - 16380*(b*x^4 + a)^(17/4)*a + 32130*(b*x^4 + a)^(13/4)*a^2 - 30940*(b*x^4 + a)^(9/4)*a^3 + 13923*(b*x^4 + a)^(5/4)*a^4)/b^5","A",0
989,1,57,0,0.158261," ","integrate(x^15*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{195 \, {\left(b x^{4} + a\right)}^{\frac{17}{4}} - 765 \, {\left(b x^{4} + a\right)}^{\frac{13}{4}} a + 1105 \, {\left(b x^{4} + a\right)}^{\frac{9}{4}} a^{2} - 663 \, {\left(b x^{4} + a\right)}^{\frac{5}{4}} a^{3}}{3315 \, b^{4}}"," ",0,"1/3315*(195*(b*x^4 + a)^(17/4) - 765*(b*x^4 + a)^(13/4)*a + 1105*(b*x^4 + a)^(9/4)*a^2 - 663*(b*x^4 + a)^(5/4)*a^3)/b^4","A",0
990,1,43,0,0.163808," ","integrate(x^11*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{45 \, {\left(b x^{4} + a\right)}^{\frac{13}{4}} - 130 \, {\left(b x^{4} + a\right)}^{\frac{9}{4}} a + 117 \, {\left(b x^{4} + a\right)}^{\frac{5}{4}} a^{2}}{585 \, b^{3}}"," ",0,"1/585*(45*(b*x^4 + a)^(13/4) - 130*(b*x^4 + a)^(9/4)*a + 117*(b*x^4 + a)^(5/4)*a^2)/b^3","A",0
991,1,29,0,0.165341," ","integrate(x^7*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{5 \, {\left(b x^{4} + a\right)}^{\frac{9}{4}} - 9 \, {\left(b x^{4} + a\right)}^{\frac{5}{4}} a}{45 \, b^{2}}"," ",0,"1/45*(5*(b*x^4 + a)^(9/4) - 9*(b*x^4 + a)^(5/4)*a)/b^2","A",0
992,1,14,0,0.174200," ","integrate(x^3*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{5 \, b}"," ",0,"1/5*(b*x^4 + a)^(5/4)/b","A",0
993,1,183,0,0.164995," ","integrate((b*x^4+a)^(1/4)/x,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{8} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right) + \frac{1}{8} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right) + {\left(b x^{4} + a\right)}^{\frac{1}{4}}"," ",0,"-1/4*sqrt(2)*(-a)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4)) - 1/4*sqrt(2)*(-a)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4)) - 1/8*sqrt(2)*(-a)^(1/4)*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a)) + 1/8*sqrt(2)*(-a)^(1/4)*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a)) + (b*x^4 + a)^(1/4)","B",0
994,1,207,0,0.176171," ","integrate((b*x^4+a)^(1/4)/x^5,x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{2 \, \sqrt{2} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{\sqrt{2} b^{2} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{a} - \frac{8 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b}{x^{4}}}{32 \, b}"," ",0,"1/32*(2*sqrt(2)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + 2*sqrt(2)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + sqrt(2)*b^2*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/(-a)^(3/4) + sqrt(2)*(-a)^(1/4)*b^2*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a - 8*(b*x^4 + a)^(1/4)*b/x^4)/b","B",0
995,1,243,0,0.178205," ","integrate((b*x^4+a)^(1/4)/x^9,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{6 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{3 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{a^{2}} + \frac{3 \, \sqrt{2} b^{3} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{3}{4}} a} - \frac{8 \, {\left({\left(b x^{4} + a\right)}^{\frac{5}{4}} b^{3} + 3 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} a b^{3}\right)}}{a b^{2} x^{8}}}{256 \, b}"," ",0,"1/256*(6*sqrt(2)*(-a)^(1/4)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 6*sqrt(2)*(-a)^(1/4)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 3*sqrt(2)*(-a)^(1/4)*b^3*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a^2 + 3*sqrt(2)*b^3*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/((-a)^(3/4)*a) - 8*((b*x^4 + a)^(5/4)*b^3 + 3*(b*x^4 + a)^(1/4)*a*b^3)/(a*b^2*x^8))/b","B",0
996,0,0,0,0.000000," ","integrate(x^9*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{9}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)*x^9, x)","F",0
997,0,0,0,0.000000," ","integrate(x^5*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{5}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)*x^5, x)","F",0
998,0,0,0,0.000000," ","integrate(x*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{1}{4}} x\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)*x, x)","F",0
999,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^3, x)","F",0
1000,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^7,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{7}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^7, x)","F",0
1001,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^11,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{11}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^11, x)","F",0
1002,0,0,0,0.000000," ","integrate(x^6*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{6}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)*x^6, x)","F",0
1003,0,0,0,0.000000," ","integrate(x^2*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{2}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)*x^2, x)","F",0
1004,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^2, x)","F",0
1005,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^6,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{6}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^6, x)","F",0
1006,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^10,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{10}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^10, x)","F",0
1007,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^14,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{14}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^14, x)","F",0
1008,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^18,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{18}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^18, x)","F",0
1009,0,0,0,0.000000," ","integrate(x^12*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{12}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)*x^12, x)","F",0
1010,0,0,0,0.000000," ","integrate(x^8*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{8}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)*x^8, x)","F",0
1011,0,0,0,0.000000," ","integrate(x^4*(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{4}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)*x^4, x)","F",0
1012,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{1}{4}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4), x)","F",0
1013,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^4,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{4}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^4, x)","F",0
1014,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^8,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{8}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^8, x)","F",0
1015,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^12,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{12}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^12, x)","F",0
1016,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/x^16,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{x^{16}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/x^16, x)","F",0
1017,1,163,0,0.166047," ","integrate(x^19*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{\frac{23 \, {\left(1155 \, {\left(b x^{4} + a\right)}^{\frac{19}{4}} - 5852 \, {\left(b x^{4} + a\right)}^{\frac{15}{4}} a + 11970 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} a^{2} - 12540 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a^{3} + 7315 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{4}\right)} a}{b^{4}} + \frac{5 \, {\left(4389 \, {\left(b x^{4} + a\right)}^{\frac{23}{4}} - 26565 \, {\left(b x^{4} + a\right)}^{\frac{19}{4}} a + 67298 \, {\left(b x^{4} + a\right)}^{\frac{15}{4}} a^{2} - 91770 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} a^{3} + 72105 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a^{4} - 33649 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{5}\right)}}{b^{4}}}{504735 \, b}"," ",0,"1/504735*(23*(1155*(b*x^4 + a)^(19/4) - 5852*(b*x^4 + a)^(15/4)*a + 11970*(b*x^4 + a)^(11/4)*a^2 - 12540*(b*x^4 + a)^(7/4)*a^3 + 7315*(b*x^4 + a)^(3/4)*a^4)*a/b^4 + 5*(4389*(b*x^4 + a)^(23/4) - 26565*(b*x^4 + a)^(19/4)*a + 67298*(b*x^4 + a)^(15/4)*a^2 - 91770*(b*x^4 + a)^(11/4)*a^3 + 72105*(b*x^4 + a)^(7/4)*a^4 - 33649*(b*x^4 + a)^(3/4)*a^5)/b^4)/b","B",0
1018,1,134,0,0.197701," ","integrate(x^15*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{\frac{19 \, {\left(77 \, {\left(b x^{4} + a\right)}^{\frac{15}{4}} - 315 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} a + 495 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a^{2} - 385 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{3}\right)} a}{b^{3}} + \frac{1155 \, {\left(b x^{4} + a\right)}^{\frac{19}{4}} - 5852 \, {\left(b x^{4} + a\right)}^{\frac{15}{4}} a + 11970 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} a^{2} - 12540 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a^{3} + 7315 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{4}}{b^{3}}}{21945 \, b}"," ",0,"1/21945*(19*(77*(b*x^4 + a)^(15/4) - 315*(b*x^4 + a)^(11/4)*a + 495*(b*x^4 + a)^(7/4)*a^2 - 385*(b*x^4 + a)^(3/4)*a^3)*a/b^3 + (1155*(b*x^4 + a)^(19/4) - 5852*(b*x^4 + a)^(15/4)*a + 11970*(b*x^4 + a)^(11/4)*a^2 - 12540*(b*x^4 + a)^(7/4)*a^3 + 7315*(b*x^4 + a)^(3/4)*a^4)/b^3)/b","B",0
1019,1,106,0,0.160977," ","integrate(x^11*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{\frac{5 \, {\left(21 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} - 66 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a + 77 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{2}\right)} a}{b^{2}} + \frac{77 \, {\left(b x^{4} + a\right)}^{\frac{15}{4}} - 315 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} a + 495 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a^{2} - 385 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{3}}{b^{2}}}{1155 \, b}"," ",0,"1/1155*(5*(21*(b*x^4 + a)^(11/4) - 66*(b*x^4 + a)^(7/4)*a + 77*(b*x^4 + a)^(3/4)*a^2)*a/b^2 + (77*(b*x^4 + a)^(15/4) - 315*(b*x^4 + a)^(11/4)*a + 495*(b*x^4 + a)^(7/4)*a^2 - 385*(b*x^4 + a)^(3/4)*a^3)/b^2)/b","B",0
1020,1,78,0,0.155960," ","integrate(x^7*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{\frac{11 \, {\left(3 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} - 7 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a\right)} a}{b} + \frac{21 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} - 66 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a + 77 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{2}}{b}}{231 \, b}"," ",0,"1/231*(11*(3*(b*x^4 + a)^(7/4) - 7*(b*x^4 + a)^(3/4)*a)*a/b + (21*(b*x^4 + a)^(11/4) - 66*(b*x^4 + a)^(7/4)*a + 77*(b*x^4 + a)^(3/4)*a^2)/b)/b","B",0
1021,1,14,0,0.181937," ","integrate(x^3*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{\frac{7}{4}}}{7 \, b}"," ",0,"1/7*(b*x^4 + a)^(7/4)/b","A",0
1022,1,185,0,0.170538," ","integrate((b*x^4+a)^(3/4)/x,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + \frac{1}{8} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right) - \frac{1}{8} \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right) + \frac{1}{3} \, {\left(b x^{4} + a\right)}^{\frac{3}{4}}"," ",0,"-1/4*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4)) - 1/4*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4)) + 1/8*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a)) - 1/8*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a)) + 1/3*(b*x^4 + a)^(3/4)","B",0
1023,1,209,0,0.210520," ","integrate((b*x^4+a)^(3/4)/x^5,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{1}{4}}} + \frac{6 \, \sqrt{2} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{1}{4}}} + \frac{3 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{2} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{a} + \frac{3 \, \sqrt{2} b^{2} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{1}{4}}} - \frac{8 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} b}{x^{4}}}{32 \, b}"," ",0,"1/32*(6*sqrt(2)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/(-a)^(1/4) + 6*sqrt(2)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/(-a)^(1/4) + 3*sqrt(2)*(-a)^(3/4)*b^2*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a + 3*sqrt(2)*b^2*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/(-a)^(1/4) - 8*(b*x^4 + a)^(3/4)*b/x^4)/b","B",0
1024,1,243,0,0.182481," ","integrate((b*x^4+a)^(3/4)/x^9,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{6 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{3 \, \sqrt{2} b^{3} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{1}{4}} a} + \frac{3 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{3} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{a^{2}} - \frac{8 \, {\left(3 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} b^{3} + {\left(b x^{4} + a\right)}^{\frac{3}{4}} a b^{3}\right)}}{a b^{2} x^{8}}}{256 \, b}"," ",0,"1/256*(6*sqrt(2)*(-a)^(3/4)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 6*sqrt(2)*(-a)^(3/4)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 3*sqrt(2)*b^3*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/((-a)^(1/4)*a) + 3*sqrt(2)*(-a)^(3/4)*b^3*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a^2 - 8*(3*(b*x^4 + a)^(7/4)*b^3 + (b*x^4 + a)^(3/4)*a*b^3)/(a*b^2*x^8))/b","B",0
1025,0,0,0,0.000000," ","integrate(x^9*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{9}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)*x^9, x)","F",0
1026,0,0,0,0.000000," ","integrate(x^5*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{5}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)*x^5, x)","F",0
1027,0,0,0,0.000000," ","integrate(x*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{4}} x\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)*x, x)","F",0
1028,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^3, x)","F",0
1029,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^7,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{7}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^7, x)","F",0
1030,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^11,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{11}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^11, x)","F",0
1031,0,0,0,0.000000," ","integrate(x^12*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{12}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)*x^12, x)","F",0
1032,0,0,0,0.000000," ","integrate(x^8*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{8}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)*x^8, x)","F",0
1033,0,0,0,0.000000," ","integrate(x^4*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{4}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)*x^4, x)","F",0
1034,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{4}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4), x)","F",0
1035,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^4,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{4}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^4, x)","F",0
1036,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^8,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{8}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^8, x)","F",0
1037,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^12,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{12}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^12, x)","F",0
1038,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^16,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{16}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^16, x)","F",0
1039,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^20,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{20}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^20, x)","F",0
1040,0,0,0,0.000000," ","integrate(x^10*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{10}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)*x^10, x)","F",0
1041,0,0,0,0.000000," ","integrate(x^6*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{6}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)*x^6, x)","F",0
1042,0,0,0,0.000000," ","integrate(x^2*(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{2}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)*x^2, x)","F",0
1043,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^2, x)","F",0
1044,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^6,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{6}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^6, x)","F",0
1045,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^10,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{10}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^10, x)","F",0
1046,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/x^14,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{x^{14}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/x^14, x)","F",0
1047,1,71,0,0.202876," ","integrate(x^19*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\frac{13923 \, {\left(b x^{4} + a\right)}^{\frac{25}{4}} - 66300 \, {\left(b x^{4} + a\right)}^{\frac{21}{4}} a + 122850 \, {\left(b x^{4} + a\right)}^{\frac{17}{4}} a^{2} - 107100 \, {\left(b x^{4} + a\right)}^{\frac{13}{4}} a^{3} + 38675 \, {\left(b x^{4} + a\right)}^{\frac{9}{4}} a^{4}}{348075 \, b^{5}}"," ",0,"1/348075*(13923*(b*x^4 + a)^(25/4) - 66300*(b*x^4 + a)^(21/4)*a + 122850*(b*x^4 + a)^(17/4)*a^2 - 107100*(b*x^4 + a)^(13/4)*a^3 + 38675*(b*x^4 + a)^(9/4)*a^4)/b^5","A",0
1048,1,57,0,0.178171," ","integrate(x^15*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\frac{663 \, {\left(b x^{4} + a\right)}^{\frac{21}{4}} - 2457 \, {\left(b x^{4} + a\right)}^{\frac{17}{4}} a + 3213 \, {\left(b x^{4} + a\right)}^{\frac{13}{4}} a^{2} - 1547 \, {\left(b x^{4} + a\right)}^{\frac{9}{4}} a^{3}}{13923 \, b^{4}}"," ",0,"1/13923*(663*(b*x^4 + a)^(21/4) - 2457*(b*x^4 + a)^(17/4)*a + 3213*(b*x^4 + a)^(13/4)*a^2 - 1547*(b*x^4 + a)^(9/4)*a^3)/b^4","A",0
1049,1,43,0,0.161912," ","integrate(x^11*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\frac{117 \, {\left(b x^{4} + a\right)}^{\frac{17}{4}} - 306 \, {\left(b x^{4} + a\right)}^{\frac{13}{4}} a + 221 \, {\left(b x^{4} + a\right)}^{\frac{9}{4}} a^{2}}{1989 \, b^{3}}"," ",0,"1/1989*(117*(b*x^4 + a)^(17/4) - 306*(b*x^4 + a)^(13/4)*a + 221*(b*x^4 + a)^(9/4)*a^2)/b^3","A",0
1050,1,29,0,0.158808," ","integrate(x^7*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\frac{9 \, {\left(b x^{4} + a\right)}^{\frac{13}{4}} - 13 \, {\left(b x^{4} + a\right)}^{\frac{9}{4}} a}{117 \, b^{2}}"," ",0,"1/117*(9*(b*x^4 + a)^(13/4) - 13*(b*x^4 + a)^(9/4)*a)/b^2","A",0
1051,1,14,0,0.173075," ","integrate(x^3*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{\frac{9}{4}}}{9 \, b}"," ",0,"1/9*(b*x^4 + a)^(9/4)/b","A",0
1052,1,200,0,0.178466," ","integrate((b*x^4+a)^(5/4)/x,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{8} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} a \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right) + \frac{1}{8} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} a \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right) + \frac{1}{5} \, {\left(b x^{4} + a\right)}^{\frac{5}{4}} + {\left(b x^{4} + a\right)}^{\frac{1}{4}} a"," ",0,"-1/4*sqrt(2)*(-a)^(1/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4)) - 1/4*sqrt(2)*(-a)^(1/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4)) - 1/8*sqrt(2)*(-a)^(1/4)*a*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a)) + 1/8*sqrt(2)*(-a)^(1/4)*a*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a)) + 1/5*(b*x^4 + a)^(5/4) + (b*x^4 + a)^(1/4)*a","B",0
1053,1,221,0,0.184421," ","integrate((b*x^4+a)^(5/4)/x^5,x, algorithm=""giac"")","-\frac{10 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + 10 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + 5 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right) - 5 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right) - 32 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{2} + \frac{8 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} a b}{x^{4}}}{32 \, b}"," ",0,"-1/32*(10*sqrt(2)*(-a)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4)) + 10*sqrt(2)*(-a)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4)) + 5*sqrt(2)*(-a)^(1/4)*b^2*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a)) - 5*sqrt(2)*(-a)^(1/4)*b^2*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a)) - 32*(b*x^4 + a)^(1/4)*b^2 + 8*(b*x^4 + a)^(1/4)*a*b/x^4)/b","B",0
1054,1,232,0,0.189971," ","integrate((b*x^4+a)^(5/4)/x^9,x, algorithm=""giac"")","\frac{\frac{10 \, \sqrt{2} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{10 \, \sqrt{2} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{5 \, \sqrt{2} b^{3} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{3}{4}}} + \frac{5 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{a} - \frac{8 \, {\left(9 \, {\left(b x^{4} + a\right)}^{\frac{5}{4}} b^{3} - 5 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} a b^{3}\right)}}{b^{2} x^{8}}}{256 \, b}"," ",0,"1/256*(10*sqrt(2)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + 10*sqrt(2)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/(-a)^(3/4) + 5*sqrt(2)*b^3*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/(-a)^(3/4) + 5*sqrt(2)*(-a)^(1/4)*b^3*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a - 8*(9*(b*x^4 + a)^(5/4)*b^3 - 5*(b*x^4 + a)^(1/4)*a*b^3)/(b^2*x^8))/b","B",0
1055,0,0,0,0.000000," ","integrate(x^9*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{9}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)*x^9, x)","F",0
1056,0,0,0,0.000000," ","integrate(x^5*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{5}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)*x^5, x)","F",0
1057,0,0,0,0.000000," ","integrate(x*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{5}{4}} x\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)*x, x)","F",0
1058,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^3, x)","F",0
1059,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^7,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{7}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^7, x)","F",0
1060,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^11,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{11}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^11, x)","F",0
1061,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^15,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{15}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^15, x)","F",0
1062,0,0,0,0.000000," ","integrate(x^10*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{10}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)*x^10, x)","F",0
1063,0,0,0,0.000000," ","integrate(x^6*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{6}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)*x^6, x)","F",0
1064,0,0,0,0.000000," ","integrate(x^2*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{2}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)*x^2, x)","F",0
1065,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^2, x)","F",0
1066,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^6,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{6}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^6, x)","F",0
1067,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^10,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{10}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^10, x)","F",0
1068,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^14,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{14}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^14, x)","F",0
1069,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^18,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{18}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^18, x)","F",0
1070,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^22,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{22}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^22, x)","F",0
1071,0,0,0,0.000000," ","integrate(x^12*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{12}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)*x^12, x)","F",0
1072,0,0,0,0.000000," ","integrate(x^8*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{8}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)*x^8, x)","F",0
1073,0,0,0,0.000000," ","integrate(x^4*(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{4}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)*x^4, x)","F",0
1074,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{5}{4}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4), x)","F",0
1075,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^4,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{4}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^4, x)","F",0
1076,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^8,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{8}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^8, x)","F",0
1077,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^12,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{12}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^12, x)","F",0
1078,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/x^16,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{x^{16}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/x^16, x)","F",0
1079,0,0,0,0.000000," ","integrate((b*x^4+a)^(7/4),x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{\frac{7}{4}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(7/4), x)","F",0
1080,1,71,0,0.156363," ","integrate(x^19/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{1155 \, {\left(b x^{4} + a\right)}^{\frac{19}{4}} - 5852 \, {\left(b x^{4} + a\right)}^{\frac{15}{4}} a + 11970 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} a^{2} - 12540 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a^{3} + 7315 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{4}}{21945 \, b^{5}}"," ",0,"1/21945*(1155*(b*x^4 + a)^(19/4) - 5852*(b*x^4 + a)^(15/4)*a + 11970*(b*x^4 + a)^(11/4)*a^2 - 12540*(b*x^4 + a)^(7/4)*a^3 + 7315*(b*x^4 + a)^(3/4)*a^4)/b^5","A",0
1081,1,57,0,0.174309," ","integrate(x^15/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{77 \, {\left(b x^{4} + a\right)}^{\frac{15}{4}} - 315 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} a + 495 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a^{2} - 385 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{3}}{1155 \, b^{4}}"," ",0,"1/1155*(77*(b*x^4 + a)^(15/4) - 315*(b*x^4 + a)^(11/4)*a + 495*(b*x^4 + a)^(7/4)*a^2 - 385*(b*x^4 + a)^(3/4)*a^3)/b^4","A",0
1082,1,43,0,0.174004," ","integrate(x^11/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{21 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} - 66 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a + 77 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{2}}{231 \, b^{3}}"," ",0,"1/231*(21*(b*x^4 + a)^(11/4) - 66*(b*x^4 + a)^(7/4)*a + 77*(b*x^4 + a)^(3/4)*a^2)/b^3","A",0
1083,1,29,0,0.151598," ","integrate(x^7/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{3 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} - 7 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a}{21 \, b^{2}}"," ",0,"1/21*(3*(b*x^4 + a)^(7/4) - 7*(b*x^4 + a)^(3/4)*a)/b^2","A",0
1084,1,14,0,0.167232," ","integrate(x^3/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{3 \, b}"," ",0,"1/3*(b*x^4 + a)^(3/4)/b","A",0
1085,1,186,0,0.170648," ","integrate(1/x/(b*x^4+a)^(1/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{8 \, a} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{8 \, a}"," ",0,"-1/4*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a - 1/4*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a + 1/8*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a - 1/8*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a","B",0
1086,1,219,0,0.199146," ","integrate(1/x^5/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{2 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{\sqrt{2} b^{2} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{1}{4}} a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{2} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{a^{2}} - \frac{8 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} b}{a x^{4}}}{32 \, b}"," ",0,"1/32*(2*sqrt(2)*(-a)^(3/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 2*sqrt(2)*(-a)^(3/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + sqrt(2)*b^2*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/((-a)^(1/4)*a) + sqrt(2)*(-a)^(3/4)*b^2*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a^2 - 8*(b*x^4 + a)^(3/4)*b/(a*x^4))/b","B",0
1087,1,244,0,0.238447," ","integrate(1/x^9/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{\frac{10 \, \sqrt{2} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{1}{4}} a^{2}} + \frac{10 \, \sqrt{2} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{1}{4}} a^{2}} + \frac{5 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{3} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{a^{3}} + \frac{5 \, \sqrt{2} b^{3} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{1}{4}} a^{2}} + \frac{8 \, {\left(5 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} b^{3} - 9 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a b^{3}\right)}}{a^{2} b^{2} x^{8}}}{256 \, b}"," ",0,"1/256*(10*sqrt(2)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/((-a)^(1/4)*a^2) + 10*sqrt(2)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/((-a)^(1/4)*a^2) + 5*sqrt(2)*(-a)^(3/4)*b^3*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a^3 + 5*sqrt(2)*b^3*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/((-a)^(1/4)*a^2) + 8*(5*(b*x^4 + a)^(7/4)*b^3 - 9*(b*x^4 + a)^(3/4)*a*b^3)/(a^2*b^2*x^8))/b","B",0
1088,0,0,0,0.000000," ","integrate(x^13/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{13}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^13/(b*x^4 + a)^(1/4), x)","F",0
1089,0,0,0,0.000000," ","integrate(x^9/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{9}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^9/(b*x^4 + a)^(1/4), x)","F",0
1090,0,0,0,0.000000," ","integrate(x^5/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{5}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^5/(b*x^4 + a)^(1/4), x)","F",0
1091,0,0,0,0.000000," ","integrate(x/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x/(b*x^4 + a)^(1/4), x)","F",0
1092,0,0,0,0.000000," ","integrate(1/x^3/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^3), x)","F",0
1093,0,0,0,0.000000," ","integrate(1/x^7/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{7}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^7), x)","F",0
1094,0,0,0,0.000000," ","integrate(1/x^11/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{11}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^11), x)","F",0
1095,0,0,0,0.000000," ","integrate(x^8/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^8/(b*x^4 + a)^(1/4), x)","F",0
1096,0,0,0,0.000000," ","integrate(x^4/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/(b*x^4 + a)^(1/4), x)","F",0
1097,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(-1/4), x)","F",0
1098,0,0,0,0.000000," ","integrate(1/x^4/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^4), x)","F",0
1099,0,0,0,0.000000," ","integrate(1/x^8/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{8}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^8), x)","F",0
1100,0,0,0,0.000000," ","integrate(1/x^12/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{12}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^12), x)","F",0
1101,0,0,0,0.000000," ","integrate(1/x^16/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{16}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^16), x)","F",0
1102,0,0,0,0.000000," ","integrate(1/x^20/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{20}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^20), x)","F",0
1103,0,0,0,0.000000," ","integrate(x^10/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{10}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^10/(b*x^4 + a)^(1/4), x)","F",0
1104,0,0,0,0.000000," ","integrate(x^6/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^6/(b*x^4 + a)^(1/4), x)","F",0
1105,0,0,0,0.000000," ","integrate(x^2/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^2/(b*x^4 + a)^(1/4), x)","F",0
1106,0,0,0,0.000000," ","integrate(1/x^2/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^2), x)","F",0
1107,0,0,0,0.000000," ","integrate(1/x^6/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{6}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^6), x)","F",0
1108,0,0,0,0.000000," ","integrate(1/x^10/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{10}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^10), x)","F",0
1109,0,0,0,0.000000," ","integrate(1/x^14/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} x^{14}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*x^14), x)","F",0
1110,1,74,0,0.158115," ","integrate(x^19/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{4}}{b^{5}} + \frac{195 \, {\left(b x^{4} + a\right)}^{\frac{17}{4}} - 1020 \, {\left(b x^{4} + a\right)}^{\frac{13}{4}} a + 2210 \, {\left(b x^{4} + a\right)}^{\frac{9}{4}} a^{2} - 2652 \, {\left(b x^{4} + a\right)}^{\frac{5}{4}} a^{3}}{3315 \, b^{5}}"," ",0,"(b*x^4 + a)^(1/4)*a^4/b^5 + 1/3315*(195*(b*x^4 + a)^(17/4) - 1020*(b*x^4 + a)^(13/4)*a + 2210*(b*x^4 + a)^(9/4)*a^2 - 2652*(b*x^4 + a)^(5/4)*a^3)/b^5","A",0
1111,1,61,0,0.170974," ","integrate(x^15/(b*x^4+a)^(3/4),x, algorithm=""giac"")","-\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3}}{b^{4}} + \frac{15 \, {\left(b x^{4} + a\right)}^{\frac{13}{4}} - 65 \, {\left(b x^{4} + a\right)}^{\frac{9}{4}} a + 117 \, {\left(b x^{4} + a\right)}^{\frac{5}{4}} a^{2}}{195 \, b^{4}}"," ",0,"-(b*x^4 + a)^(1/4)*a^3/b^4 + 1/195*(15*(b*x^4 + a)^(13/4) - 65*(b*x^4 + a)^(9/4)*a + 117*(b*x^4 + a)^(5/4)*a^2)/b^4","A",0
1112,1,46,0,0.153886," ","integrate(x^11/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{2}}{b^{3}} + \frac{5 \, {\left(b x^{4} + a\right)}^{\frac{9}{4}} - 18 \, {\left(b x^{4} + a\right)}^{\frac{5}{4}} a}{45 \, b^{3}}"," ",0,"(b*x^4 + a)^(1/4)*a^2/b^3 + 1/45*(5*(b*x^4 + a)^(9/4) - 18*(b*x^4 + a)^(5/4)*a)/b^3","A",0
1113,1,30,0,0.153106," ","integrate(x^7/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{5 \, b^{2}} - \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a}{b^{2}}"," ",0,"1/5*(b*x^4 + a)^(5/4)/b^2 - (b*x^4 + a)^(1/4)*a/b^2","A",0
1114,1,13,0,0.152450," ","integrate(x^3/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{b}"," ",0,"(b*x^4 + a)^(1/4)/b","A",0
1115,1,186,0,0.159738," ","integrate(1/x/(b*x^4+a)^(3/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a} - \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a} - \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{8 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{8 \, a}"," ",0,"-1/4*sqrt(2)*(-a)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a - 1/4*sqrt(2)*(-a)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a - 1/8*sqrt(2)*(-a)^(1/4)*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a + 1/8*sqrt(2)*(-a)^(1/4)*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a","B",0
1116,1,221,0,0.163922," ","integrate(1/x^5/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{6 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{3 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{a^{2}} + \frac{3 \, \sqrt{2} b^{2} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{3}{4}} a} - \frac{8 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} b}{a x^{4}}}{32 \, b}"," ",0,"1/32*(6*sqrt(2)*(-a)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 6*sqrt(2)*(-a)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 3*sqrt(2)*(-a)^(1/4)*b^2*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a^2 + 3*sqrt(2)*b^2*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/((-a)^(3/4)*a) - 8*(b*x^4 + a)^(1/4)*b/(a*x^4))/b","B",0
1117,1,244,0,0.178871," ","integrate(1/x^9/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{\frac{42 \, \sqrt{2} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{2}} + \frac{42 \, \sqrt{2} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{3}{4}} a^{2}} + \frac{21 \, \sqrt{2} b^{3} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{3}{4}} a^{2}} + \frac{21 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{a^{3}} + \frac{8 \, {\left(7 \, {\left(b x^{4} + a\right)}^{\frac{5}{4}} b^{3} - 11 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}} a b^{3}\right)}}{a^{2} b^{2} x^{8}}}{256 \, b}"," ",0,"1/256*(42*sqrt(2)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^2) + 42*sqrt(2)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/((-a)^(3/4)*a^2) + 21*sqrt(2)*b^3*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/((-a)^(3/4)*a^2) + 21*sqrt(2)*(-a)^(1/4)*b^3*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a^3 + 8*(7*(b*x^4 + a)^(5/4)*b^3 - 11*(b*x^4 + a)^(1/4)*a*b^3)/(a^2*b^2*x^8))/b","B",0
1118,0,0,0,0.000000," ","integrate(x^13/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{13}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^13/(b*x^4 + a)^(3/4), x)","F",0
1119,0,0,0,0.000000," ","integrate(x^9/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{9}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^9/(b*x^4 + a)^(3/4), x)","F",0
1120,0,0,0,0.000000," ","integrate(x^5/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{5}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^5/(b*x^4 + a)^(3/4), x)","F",0
1121,0,0,0,0.000000," ","integrate(x/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x/(b*x^4 + a)^(3/4), x)","F",0
1122,0,0,0,0.000000," ","integrate(1/x^3/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*x^3), x)","F",0
1123,0,0,0,0.000000," ","integrate(1/x^7/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{7}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*x^7), x)","F",0
1124,0,0,0,0.000000," ","integrate(1/x^11/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{11}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*x^11), x)","F",0
1125,0,0,0,0.000000," ","integrate(x^10/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{10}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^10/(b*x^4 + a)^(3/4), x)","F",0
1126,0,0,0,0.000000," ","integrate(x^6/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^6/(b*x^4 + a)^(3/4), x)","F",0
1127,0,0,0,0.000000," ","integrate(x^2/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/(b*x^4 + a)^(3/4), x)","F",0
1128,0,0,0,0.000000," ","integrate(1/x^2/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*x^2), x)","F",0
1129,0,0,0,0.000000," ","integrate(1/x^6/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*x^6), x)","F",0
1130,0,0,0,0.000000," ","integrate(1/x^10/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{10}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*x^10), x)","F",0
1131,0,0,0,0.000000," ","integrate(1/x^14/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{14}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*x^14), x)","F",0
1132,0,0,0,0.000000," ","integrate(x^12/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{12}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^12/(b*x^4 + a)^(3/4), x)","F",0
1133,0,0,0,0.000000," ","integrate(x^8/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^8/(b*x^4 + a)^(3/4), x)","F",0
1134,0,0,0,0.000000," ","integrate(x^4/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^4/(b*x^4 + a)^(3/4), x)","F",0
1135,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(-3/4), x)","F",0
1136,0,0,0,0.000000," ","integrate(1/x^4/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{4}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*x^4), x)","F",0
1137,0,0,0,0.000000," ","integrate(1/x^8/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{8}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*x^8), x)","F",0
1138,0,0,0,0.000000," ","integrate(1/x^12/(b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} x^{12}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*x^12), x)","F",0
1139,1,87,0,0.222653," ","integrate(x^19/(b*x^4+a)^(5/4),x, algorithm=""giac"")","-\frac{a^{4}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{5}} + \frac{77 \, {\left(b x^{4} + a\right)}^{\frac{15}{4}} b^{70} - 420 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} a b^{70} + 990 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a^{2} b^{70} - 1540 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{3} b^{70}}{1155 \, b^{75}}"," ",0,"-a^4/((b*x^4 + a)^(1/4)*b^5) + 1/1155*(77*(b*x^4 + a)^(15/4)*b^70 - 420*(b*x^4 + a)^(11/4)*a*b^70 + 990*(b*x^4 + a)^(7/4)*a^2*b^70 - 1540*(b*x^4 + a)^(3/4)*a^3*b^70)/b^75","A",0
1140,1,69,0,0.161492," ","integrate(x^15/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\frac{a^{3}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{4}} + \frac{7 \, {\left(b x^{4} + a\right)}^{\frac{11}{4}} b^{40} - 33 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} a b^{40} + 77 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a^{2} b^{40}}{77 \, b^{44}}"," ",0,"a^3/((b*x^4 + a)^(1/4)*b^4) + 1/77*(7*(b*x^4 + a)^(11/4)*b^40 - 33*(b*x^4 + a)^(7/4)*a*b^40 + 77*(b*x^4 + a)^(3/4)*a^2*b^40)/b^44","A",0
1141,1,53,0,0.181735," ","integrate(x^11/(b*x^4+a)^(5/4),x, algorithm=""giac"")","-\frac{a^{2}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} b^{3}} + \frac{3 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} b^{18} - 14 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a b^{18}}{21 \, b^{21}}"," ",0,"-a^2/((b*x^4 + a)^(1/4)*b^3) + 1/21*(3*(b*x^4 + a)^(7/4)*b^18 - 14*(b*x^4 + a)^(3/4)*a*b^18)/b^21","A",0
1142,1,34,0,0.186862," ","integrate(x^7/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\frac{\frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{b} + \frac{3 \, a}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} b}}{3 \, b}"," ",0,"1/3*((b*x^4 + a)^(3/4)/b + 3*a/((b*x^4 + a)^(1/4)*b))/b","A",0
1143,1,14,0,0.161540," ","integrate(x^3/(b*x^4+a)^(5/4),x, algorithm=""giac"")","-\frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} b}"," ",0,"-1/((b*x^4 + a)^(1/4)*b)","A",0
1144,1,199,0,0.170940," ","integrate(1/x/(b*x^4+a)^(5/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a^{2}} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a^{2}} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{8 \, a^{2}} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{8 \, a^{2}} + \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a}"," ",0,"-1/4*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 - 1/4*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 1/8*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a^2 - 1/8*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a^2 + 1/((b*x^4 + a)^(1/4)*a)","B",0
1145,1,234,0,0.179106," ","integrate(1/x^5/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\frac{5 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{16 \, a^{3}} + \frac{5 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{16 \, a^{3}} + \frac{5 \, \sqrt{2} b \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{32 \, \left(-a\right)^{\frac{1}{4}} a^{2}} + \frac{5 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{32 \, a^{3}} - \frac{5 \, {\left(b x^{4} + a\right)} b - 4 \, a b}{4 \, {\left({\left(b x^{4} + a\right)}^{\frac{5}{4}} - {\left(b x^{4} + a\right)}^{\frac{1}{4}} a\right)} a^{2}}"," ",0,"5/16*sqrt(2)*(-a)^(3/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^3 + 5/16*sqrt(2)*(-a)^(3/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/a^3 + 5/32*sqrt(2)*b*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/((-a)^(1/4)*a^2) + 5/32*sqrt(2)*(-a)^(3/4)*b*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a^3 - 1/4*(5*(b*x^4 + a)*b - 4*a*b)/(((b*x^4 + a)^(5/4) - (b*x^4 + a)^(1/4)*a)*a^2)","B",0
1146,1,255,0,0.184497," ","integrate(1/x^9/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\frac{45 \, \sqrt{2} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a\right)^{\frac{1}{4}} a^{3}} + \frac{45 \, \sqrt{2} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{128 \, \left(-a\right)^{\frac{1}{4}} a^{3}} + \frac{45 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{2} \log\left(\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{256 \, a^{4}} + \frac{45 \, \sqrt{2} b^{2} \log\left(-\sqrt{2} {\left(b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{4} + a} + \sqrt{-a}\right)}{256 \, \left(-a\right)^{\frac{1}{4}} a^{3}} + \frac{b^{2}}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} a^{3}} + \frac{13 \, {\left(b x^{4} + a\right)}^{\frac{7}{4}} b^{2} - 17 \, {\left(b x^{4} + a\right)}^{\frac{3}{4}} a b^{2}}{32 \, a^{3} b^{2} x^{8}}"," ",0,"45/128*sqrt(2)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/((-a)^(1/4)*a^3) + 45/128*sqrt(2)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^4 + a)^(1/4))/(-a)^(1/4))/((-a)^(1/4)*a^3) + 45/256*sqrt(2)*(-a)^(3/4)*b^2*log(sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/a^4 + 45/256*sqrt(2)*b^2*log(-sqrt(2)*(b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^4 + a) + sqrt(-a))/((-a)^(1/4)*a^3) + b^2/((b*x^4 + a)^(1/4)*a^3) + 1/32*(13*(b*x^4 + a)^(7/4)*b^2 - 17*(b*x^4 + a)^(3/4)*a*b^2)/(a^3*b^2*x^8)","B",0
1147,0,0,0,0.000000," ","integrate(x^13/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x^{13}}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^13/(b*x^4 + a)^(5/4), x)","F",0
1148,0,0,0,0.000000," ","integrate(x^9/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x^{9}}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^9/(b*x^4 + a)^(5/4), x)","F",0
1149,0,0,0,0.000000," ","integrate(x^5/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x^{5}}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^5/(b*x^4 + a)^(5/4), x)","F",0
1150,0,0,0,0.000000," ","integrate(x/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x/(b*x^4 + a)^(5/4), x)","F",0
1151,0,0,0,0.000000," ","integrate(1/x^3/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*x^3), x)","F",0
1152,0,0,0,0.000000," ","integrate(1/x^7/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{7}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*x^7), x)","F",0
1153,0,0,0,0.000000," ","integrate(1/x^11/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{11}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*x^11), x)","F",0
1154,0,0,0,0.000000," ","integrate(x^12/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x^{12}}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^12/(b*x^4 + a)^(5/4), x)","F",0
1155,0,0,0,0.000000," ","integrate(x^8/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^8/(b*x^4 + a)^(5/4), x)","F",0
1156,0,0,0,0.000000," ","integrate(x^4/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^4/(b*x^4 + a)^(5/4), x)","F",0
1157,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(-5/4), x)","F",0
1158,0,0,0,0.000000," ","integrate(1/x^4/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{4}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*x^4), x)","F",0
1159,0,0,0,0.000000," ","integrate(1/x^8/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{8}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*x^8), x)","F",0
1160,0,0,0,0.000000," ","integrate(1/x^12/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{12}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*x^12), x)","F",0
1161,0,0,0,0.000000," ","integrate(1/x^16/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{16}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*x^16), x)","F",0
1162,0,0,0,0.000000," ","integrate(x^14/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x^{14}}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^14/(b*x^4 + a)^(5/4), x)","F",0
1163,0,0,0,0.000000," ","integrate(x^10/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x^{10}}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^10/(b*x^4 + a)^(5/4), x)","F",0
1164,0,0,0,0.000000," ","integrate(x^6/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^6/(b*x^4 + a)^(5/4), x)","F",0
1165,0,0,0,0.000000," ","integrate(x^2/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^2/(b*x^4 + a)^(5/4), x)","F",0
1166,0,0,0,0.000000," ","integrate(1/x^2/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*x^2), x)","F",0
1167,0,0,0,0.000000," ","integrate(1/x^6/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{6}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*x^6), x)","F",0
1168,0,0,0,0.000000," ","integrate(1/x^10/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{10}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*x^10), x)","F",0
1169,0,0,0,0.000000," ","integrate(1/x^14/(b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} x^{14}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*x^14), x)","F",0
1170,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(7/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{7}{4}}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(-7/4), x)","F",0
1171,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(9/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{9}{4}}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(-9/4), x)","F",0
1172,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(11/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{11}{4}}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(-11/4), x)","F",0
1173,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(13/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{13}{4}}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(-13/4), x)","F",0
1174,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(17/4),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{17}{4}}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(-17/4), x)","F",0
1175,1,120,0,0.184503," ","integrate(x^19*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{3315 \, {\left(b x^{4} - a\right)}^{5} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} + 16380 \, {\left(b x^{4} - a\right)}^{4} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a + 32130 \, {\left(b x^{4} - a\right)}^{3} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2} + 30940 \, {\left(b x^{4} - a\right)}^{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{3} - 13923 \, {\left(-b x^{4} + a\right)}^{\frac{5}{4}} a^{4}}{69615 \, b^{5}}"," ",0,"1/69615*(3315*(b*x^4 - a)^5*(-b*x^4 + a)^(1/4) + 16380*(b*x^4 - a)^4*(-b*x^4 + a)^(1/4)*a + 32130*(b*x^4 - a)^3*(-b*x^4 + a)^(1/4)*a^2 + 30940*(b*x^4 - a)^2*(-b*x^4 + a)^(1/4)*a^3 - 13923*(-b*x^4 + a)^(5/4)*a^4)/b^5","A",0
1176,1,94,0,0.163019," ","integrate(x^15*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{195 \, {\left(b x^{4} - a\right)}^{4} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} + 765 \, {\left(b x^{4} - a\right)}^{3} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a + 1105 \, {\left(b x^{4} - a\right)}^{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2} - 663 \, {\left(-b x^{4} + a\right)}^{\frac{5}{4}} a^{3}}{3315 \, b^{4}}"," ",0,"1/3315*(195*(b*x^4 - a)^4*(-b*x^4 + a)^(1/4) + 765*(b*x^4 - a)^3*(-b*x^4 + a)^(1/4)*a + 1105*(b*x^4 - a)^2*(-b*x^4 + a)^(1/4)*a^2 - 663*(-b*x^4 + a)^(5/4)*a^3)/b^4","A",0
1177,1,68,0,0.158709," ","integrate(x^11*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{45 \, {\left(b x^{4} - a\right)}^{3} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} + 130 \, {\left(b x^{4} - a\right)}^{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a - 117 \, {\left(-b x^{4} + a\right)}^{\frac{5}{4}} a^{2}}{585 \, b^{3}}"," ",0,"1/585*(45*(b*x^4 - a)^3*(-b*x^4 + a)^(1/4) + 130*(b*x^4 - a)^2*(-b*x^4 + a)^(1/4)*a - 117*(-b*x^4 + a)^(5/4)*a^2)/b^3","A",0
1178,1,42,0,0.169682," ","integrate(x^7*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{5 \, {\left(b x^{4} - a\right)}^{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} - 9 \, {\left(-b x^{4} + a\right)}^{\frac{5}{4}} a}{45 \, b^{2}}"," ",0,"1/45*(5*(b*x^4 - a)^2*(-b*x^4 + a)^(1/4) - 9*(-b*x^4 + a)^(5/4)*a)/b^2","A",0
1179,1,15,0,0.151145," ","integrate(x^3*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","-\frac{{\left(-b x^{4} + a\right)}^{\frac{5}{4}}}{5 \, b}"," ",0,"-1/5*(-b*x^4 + a)^(5/4)/b","A",0
1180,1,190,0,0.166720," ","integrate((-b*x^4+a)^(1/4)/x,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{4} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - \frac{1}{8} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right) + \frac{1}{8} \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right) + {\left(-b x^{4} + a\right)}^{\frac{1}{4}}"," ",0,"-1/4*sqrt(2)*(-a)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4)) - 1/4*sqrt(2)*(-a)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4)) - 1/8*sqrt(2)*(-a)^(1/4)*log(sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a)) + 1/8*sqrt(2)*(-a)^(1/4)*log(-sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a)) + (-b*x^4 + a)^(1/4)","B",0
1181,1,220,0,0.181765," ","integrate((-b*x^4+a)^(1/4)/x^5,x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{2 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a} + \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{a} + \frac{\sqrt{2} b^{2} \log\left(-\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{3}{4}}} - \frac{8 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b}{x^{4}}}{32 \, b}"," ",0,"1/32*(2*sqrt(2)*(-a)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a + 2*sqrt(2)*(-a)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a + sqrt(2)*(-a)^(1/4)*b^2*log(sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/a + sqrt(2)*b^2*log(-sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/(-a)^(3/4) - 8*(-b*x^4 + a)^(1/4)*b/x^4)/b","B",0
1182,1,251,0,0.207391," ","integrate((-b*x^4+a)^(1/4)/x^9,x, algorithm=""giac"")","\frac{\frac{6 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{6 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{3 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \log\left(\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{a^{2}} + \frac{3 \, \sqrt{2} b^{3} \log\left(-\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{3}{4}} a} - \frac{8 \, {\left({\left(-b x^{4} + a\right)}^{\frac{5}{4}} b^{3} + 3 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a b^{3}\right)}}{a b^{2} x^{8}}}{256 \, b}"," ",0,"1/256*(6*sqrt(2)*(-a)^(1/4)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 6*sqrt(2)*(-a)^(1/4)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 3*sqrt(2)*(-a)^(1/4)*b^3*log(sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/a^2 + 3*sqrt(2)*b^3*log(-sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/((-a)^(3/4)*a) - 8*((-b*x^4 + a)^(5/4)*b^3 + 3*(-b*x^4 + a)^(1/4)*a*b^3)/(a*b^2*x^8))/b","B",0
1183,0,0,0,0.000000," ","integrate(x^9*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{9}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)*x^9, x)","F",0
1184,0,0,0,0.000000," ","integrate(x^5*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{5}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)*x^5, x)","F",0
1185,0,0,0,0.000000," ","integrate(x*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(-b x^{4} + a\right)}^{\frac{1}{4}} x\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)*x, x)","F",0
1186,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^3,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{3}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^3, x)","F",0
1187,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^7,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{7}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^7, x)","F",0
1188,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^11,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{11}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^11, x)","F",0
1189,0,0,0,0.000000," ","integrate(x^6*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{6}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)*x^6, x)","F",0
1190,0,0,0,0.000000," ","integrate(x^2*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{2}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)*x^2, x)","F",0
1191,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^2,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{2}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^2, x)","F",0
1192,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^6,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{6}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^6, x)","F",0
1193,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^10,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{10}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^10, x)","F",0
1194,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^14,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{14}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^14, x)","F",0
1195,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^18,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{18}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^18, x)","F",0
1196,0,0,0,0.000000," ","integrate(x^12*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{12}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)*x^12, x)","F",0
1197,0,0,0,0.000000," ","integrate(x^8*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{8}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)*x^8, x)","F",0
1198,0,0,0,0.000000," ","integrate(x^4*(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{4}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)*x^4, x)","F",0
1199,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4), x)","F",0
1200,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^4,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{4}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^4, x)","F",0
1201,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^8,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{8}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^8, x)","F",0
1202,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^12,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{12}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^12, x)","F",0
1203,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/4)/x^16,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{x^{16}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(1/4)/x^16, x)","F",0
1204,1,109,0,0.164637," ","integrate(x^19/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","-\frac{1155 \, {\left(b x^{4} - a\right)}^{4} {\left(-b x^{4} + a\right)}^{\frac{3}{4}} + 5852 \, {\left(b x^{4} - a\right)}^{3} {\left(-b x^{4} + a\right)}^{\frac{3}{4}} a + 11970 \, {\left(b x^{4} - a\right)}^{2} {\left(-b x^{4} + a\right)}^{\frac{3}{4}} a^{2} - 12540 \, {\left(-b x^{4} + a\right)}^{\frac{7}{4}} a^{3} + 7315 \, {\left(-b x^{4} + a\right)}^{\frac{3}{4}} a^{4}}{21945 \, b^{5}}"," ",0,"-1/21945*(1155*(b*x^4 - a)^4*(-b*x^4 + a)^(3/4) + 5852*(b*x^4 - a)^3*(-b*x^4 + a)^(3/4)*a + 11970*(b*x^4 - a)^2*(-b*x^4 + a)^(3/4)*a^2 - 12540*(-b*x^4 + a)^(7/4)*a^3 + 7315*(-b*x^4 + a)^(3/4)*a^4)/b^5","A",0
1205,1,83,0,0.155855," ","integrate(x^15/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","-\frac{77 \, {\left(b x^{4} - a\right)}^{3} {\left(-b x^{4} + a\right)}^{\frac{3}{4}} + 315 \, {\left(b x^{4} - a\right)}^{2} {\left(-b x^{4} + a\right)}^{\frac{3}{4}} a - 495 \, {\left(-b x^{4} + a\right)}^{\frac{7}{4}} a^{2} + 385 \, {\left(-b x^{4} + a\right)}^{\frac{3}{4}} a^{3}}{1155 \, b^{4}}"," ",0,"-1/1155*(77*(b*x^4 - a)^3*(-b*x^4 + a)^(3/4) + 315*(b*x^4 - a)^2*(-b*x^4 + a)^(3/4)*a - 495*(-b*x^4 + a)^(7/4)*a^2 + 385*(-b*x^4 + a)^(3/4)*a^3)/b^4","A",0
1206,1,57,0,0.152854," ","integrate(x^11/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","-\frac{21 \, {\left(b x^{4} - a\right)}^{2} {\left(-b x^{4} + a\right)}^{\frac{3}{4}} - 66 \, {\left(-b x^{4} + a\right)}^{\frac{7}{4}} a + 77 \, {\left(-b x^{4} + a\right)}^{\frac{3}{4}} a^{2}}{231 \, b^{3}}"," ",0,"-1/231*(21*(b*x^4 - a)^2*(-b*x^4 + a)^(3/4) - 66*(-b*x^4 + a)^(7/4)*a + 77*(-b*x^4 + a)^(3/4)*a^2)/b^3","A",0
1207,1,31,0,0.153145," ","integrate(x^7/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\frac{3 \, {\left(-b x^{4} + a\right)}^{\frac{7}{4}} - 7 \, {\left(-b x^{4} + a\right)}^{\frac{3}{4}} a}{21 \, b^{2}}"," ",0,"1/21*(3*(-b*x^4 + a)^(7/4) - 7*(-b*x^4 + a)^(3/4)*a)/b^2","A",0
1208,1,15,0,0.154684," ","integrate(x^3/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","-\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}{3 \, b}"," ",0,"-1/3*(-b*x^4 + a)^(3/4)/b","A",0
1209,1,192,0,0.166365," ","integrate(1/x/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{8 \, a} - \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{8 \, a}"," ",0,"-1/4*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a - 1/4*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a + 1/8*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/a - 1/8*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/a","B",0
1210,1,226,0,0.178118," ","integrate(1/x^5/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","-\frac{\frac{2 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{2 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{\sqrt{2} b^{2} \log\left(\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{1}{4}} a} + \frac{\sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{2} \log\left(-\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{a^{2}} + \frac{8 \, {\left(-b x^{4} + a\right)}^{\frac{3}{4}} b}{a x^{4}}}{32 \, b}"," ",0,"-1/32*(2*sqrt(2)*(-a)^(3/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 2*sqrt(2)*(-a)^(3/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + sqrt(2)*b^2*log(sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/((-a)^(1/4)*a) + sqrt(2)*(-a)^(3/4)*b^2*log(-sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/a^2 + 8*(-b*x^4 + a)^(3/4)*b/(a*x^4))/b","B",0
1211,1,252,0,0.178814," ","integrate(1/x^9/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","-\frac{\frac{10 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{3}} + \frac{10 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{3}} + \frac{5 \, \sqrt{2} b^{3} \log\left(\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{1}{4}} a^{2}} + \frac{5 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{3} \log\left(-\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{a^{3}} - \frac{8 \, {\left(5 \, {\left(-b x^{4} + a\right)}^{\frac{7}{4}} b^{3} - 9 \, {\left(-b x^{4} + a\right)}^{\frac{3}{4}} a b^{3}\right)}}{a^{2} b^{2} x^{8}}}{256 \, b}"," ",0,"-1/256*(10*sqrt(2)*(-a)^(3/4)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a^3 + 10*sqrt(2)*(-a)^(3/4)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a^3 + 5*sqrt(2)*b^3*log(sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/((-a)^(1/4)*a^2) + 5*sqrt(2)*(-a)^(3/4)*b^3*log(-sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/a^3 - 8*(5*(-b*x^4 + a)^(7/4)*b^3 - 9*(-b*x^4 + a)^(3/4)*a*b^3)/(a^2*b^2*x^8))/b","B",0
1212,0,0,0,0.000000," ","integrate(x^13/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{13}}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^13/(-b*x^4 + a)^(1/4), x)","F",0
1213,0,0,0,0.000000," ","integrate(x^9/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{9}}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^9/(-b*x^4 + a)^(1/4), x)","F",0
1214,0,0,0,0.000000," ","integrate(x^5/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{5}}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^5/(-b*x^4 + a)^(1/4), x)","F",0
1215,0,0,0,0.000000," ","integrate(x/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x/(-b*x^4 + a)^(1/4), x)","F",0
1216,0,0,0,0.000000," ","integrate(1/x^3/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{3}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^3), x)","F",0
1217,0,0,0,0.000000," ","integrate(1/x^7/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{7}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^7), x)","F",0
1218,0,0,0,0.000000," ","integrate(1/x^11/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{11}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^11), x)","F",0
1219,0,0,0,0.000000," ","integrate(x^8/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^8/(-b*x^4 + a)^(1/4), x)","F",0
1220,0,0,0,0.000000," ","integrate(x^4/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^4/(-b*x^4 + a)^(1/4), x)","F",0
1221,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(-1/4), x)","F",0
1222,0,0,0,0.000000," ","integrate(1/x^4/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^4), x)","F",0
1223,0,0,0,0.000000," ","integrate(1/x^8/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{8}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^8), x)","F",0
1224,0,0,0,0.000000," ","integrate(1/x^12/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{12}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^12), x)","F",0
1225,0,0,0,0.000000," ","integrate(1/x^16/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{16}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^16), x)","F",0
1226,0,0,0,0.000000," ","integrate(1/x^20/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{20}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^20), x)","F",0
1227,0,0,0,0.000000," ","integrate(x^10/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{10}}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^10/(-b*x^4 + a)^(1/4), x)","F",0
1228,0,0,0,0.000000," ","integrate(x^6/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^6/(-b*x^4 + a)^(1/4), x)","F",0
1229,0,0,0,0.000000," ","integrate(x^2/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(x^2/(-b*x^4 + a)^(1/4), x)","F",0
1230,0,0,0,0.000000," ","integrate(1/x^2/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{2}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^2), x)","F",0
1231,0,0,0,0.000000," ","integrate(1/x^6/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{6}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^6), x)","F",0
1232,0,0,0,0.000000," ","integrate(1/x^10/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{10}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^10), x)","F",0
1233,0,0,0,0.000000," ","integrate(1/x^14/(-b*x^4+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} x^{14}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(1/4)*x^14), x)","F",0
1234,1,113,0,0.161817," ","integrate(x^19/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{4}}{b^{5}} - \frac{195 \, {\left(b x^{4} - a\right)}^{4} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} + 1020 \, {\left(b x^{4} - a\right)}^{3} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a + 2210 \, {\left(b x^{4} - a\right)}^{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2} - 2652 \, {\left(-b x^{4} + a\right)}^{\frac{5}{4}} a^{3}}{3315 \, b^{5}}"," ",0,"-(-b*x^4 + a)^(1/4)*a^4/b^5 - 1/3315*(195*(b*x^4 - a)^4*(-b*x^4 + a)^(1/4) + 1020*(b*x^4 - a)^3*(-b*x^4 + a)^(1/4)*a + 2210*(b*x^4 - a)^2*(-b*x^4 + a)^(1/4)*a^2 - 2652*(-b*x^4 + a)^(5/4)*a^3)/b^5","A",0
1235,1,87,0,0.158828," ","integrate(x^15/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{3}}{b^{4}} - \frac{15 \, {\left(b x^{4} - a\right)}^{3} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} + 65 \, {\left(b x^{4} - a\right)}^{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a - 117 \, {\left(-b x^{4} + a\right)}^{\frac{5}{4}} a^{2}}{195 \, b^{4}}"," ",0,"-(-b*x^4 + a)^(1/4)*a^3/b^4 - 1/195*(15*(b*x^4 - a)^3*(-b*x^4 + a)^(1/4) + 65*(b*x^4 - a)^2*(-b*x^4 + a)^(1/4)*a - 117*(-b*x^4 + a)^(5/4)*a^2)/b^4","A",0
1236,1,61,0,0.155588," ","integrate(x^11/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a^{2}}{b^{3}} - \frac{5 \, {\left(b x^{4} - a\right)}^{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} - 18 \, {\left(-b x^{4} + a\right)}^{\frac{5}{4}} a}{45 \, b^{3}}"," ",0,"-(-b*x^4 + a)^(1/4)*a^2/b^3 - 1/45*(5*(b*x^4 - a)^2*(-b*x^4 + a)^(1/4) - 18*(-b*x^4 + a)^(5/4)*a)/b^3","A",0
1237,1,32,0,0.158533," ","integrate(x^7/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\frac{{\left(-b x^{4} + a\right)}^{\frac{5}{4}}}{5 \, b^{2}} - \frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}} a}{b^{2}}"," ",0,"1/5*(-b*x^4 + a)^(5/4)/b^2 - (-b*x^4 + a)^(1/4)*a/b^2","A",0
1238,1,15,0,0.187003," ","integrate(x^3/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","-\frac{{\left(-b x^{4} + a\right)}^{\frac{1}{4}}}{b}"," ",0,"-(-b*x^4 + a)^(1/4)/b","A",0
1239,1,192,0,0.161788," ","integrate(1/x/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a} - \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{4 \, a} - \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{8 \, a} + \frac{\sqrt{2} \left(-a\right)^{\frac{1}{4}} \log\left(-\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{8 \, a}"," ",0,"-1/4*sqrt(2)*(-a)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a - 1/4*sqrt(2)*(-a)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a - 1/8*sqrt(2)*(-a)^(1/4)*log(sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/a + 1/8*sqrt(2)*(-a)^(1/4)*log(-sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/a","B",0
1240,1,228,0,0.167846," ","integrate(1/x^5/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","-\frac{\frac{6 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{6 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{2}} + \frac{3 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{a^{2}} + \frac{3 \, \sqrt{2} b^{2} \log\left(-\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{3}{4}} a} + \frac{8 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} b}{a x^{4}}}{32 \, b}"," ",0,"-1/32*(6*sqrt(2)*(-a)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 6*sqrt(2)*(-a)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a^2 + 3*sqrt(2)*(-a)^(1/4)*b^2*log(sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/a^2 + 3*sqrt(2)*b^2*log(-sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/((-a)^(3/4)*a) + 8*(-b*x^4 + a)^(1/4)*b/(a*x^4))/b","B",0
1241,1,252,0,0.170152," ","integrate(1/x^9/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","-\frac{\frac{42 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{3}} + \frac{42 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{a^{3}} + \frac{21 \, \sqrt{2} \left(-a\right)^{\frac{1}{4}} b^{3} \log\left(\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{a^{3}} + \frac{21 \, \sqrt{2} b^{3} \log\left(-\sqrt{2} {\left(-b x^{4} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{-b x^{4} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{3}{4}} a^{2}} - \frac{8 \, {\left(7 \, {\left(-b x^{4} + a\right)}^{\frac{5}{4}} b^{3} - 11 \, {\left(-b x^{4} + a\right)}^{\frac{1}{4}} a b^{3}\right)}}{a^{2} b^{2} x^{8}}}{256 \, b}"," ",0,"-1/256*(42*sqrt(2)*(-a)^(1/4)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a^3 + 42*sqrt(2)*(-a)^(1/4)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(-b*x^4 + a)^(1/4))/(-a)^(1/4))/a^3 + 21*sqrt(2)*(-a)^(1/4)*b^3*log(sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/a^3 + 21*sqrt(2)*b^3*log(-sqrt(2)*(-b*x^4 + a)^(1/4)*(-a)^(1/4) + sqrt(-b*x^4 + a) + sqrt(-a))/((-a)^(3/4)*a^2) - 8*(7*(-b*x^4 + a)^(5/4)*b^3 - 11*(-b*x^4 + a)^(1/4)*a*b^3)/(a^2*b^2*x^8))/b","B",0
1242,0,0,0,0.000000," ","integrate(x^13/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{13}}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^13/(-b*x^4 + a)^(3/4), x)","F",0
1243,0,0,0,0.000000," ","integrate(x^9/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{9}}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^9/(-b*x^4 + a)^(3/4), x)","F",0
1244,0,0,0,0.000000," ","integrate(x^5/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{5}}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^5/(-b*x^4 + a)^(3/4), x)","F",0
1245,0,0,0,0.000000," ","integrate(x/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x/(-b*x^4 + a)^(3/4), x)","F",0
1246,0,0,0,0.000000," ","integrate(1/x^3/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{3}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/4)*x^3), x)","F",0
1247,0,0,0,0.000000," ","integrate(1/x^7/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{7}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/4)*x^7), x)","F",0
1248,0,0,0,0.000000," ","integrate(1/x^11/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{11}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/4)*x^11), x)","F",0
1249,0,0,0,0.000000," ","integrate(x^10/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{10}}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^10/(-b*x^4 + a)^(3/4), x)","F",0
1250,0,0,0,0.000000," ","integrate(x^6/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^6/(-b*x^4 + a)^(3/4), x)","F",0
1251,0,0,0,0.000000," ","integrate(x^2/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/(-b*x^4 + a)^(3/4), x)","F",0
1252,0,0,0,0.000000," ","integrate(1/x^2/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/4)*x^2), x)","F",0
1253,0,0,0,0.000000," ","integrate(1/x^6/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{6}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/4)*x^6), x)","F",0
1254,0,0,0,0.000000," ","integrate(1/x^10/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{10}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/4)*x^10), x)","F",0
1255,0,0,0,0.000000," ","integrate(1/x^14/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{14}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/4)*x^14), x)","F",0
1256,0,0,0,0.000000," ","integrate(x^12/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{12}}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^12/(-b*x^4 + a)^(3/4), x)","F",0
1257,0,0,0,0.000000," ","integrate(x^8/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^8/(-b*x^4 + a)^(3/4), x)","F",0
1258,0,0,0,0.000000," ","integrate(x^4/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^4/(-b*x^4 + a)^(3/4), x)","F",0
1259,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(-3/4), x)","F",0
1260,0,0,0,0.000000," ","integrate(1/x^4/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{4}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/4)*x^4), x)","F",0
1261,0,0,0,0.000000," ","integrate(1/x^8/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{8}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/4)*x^8), x)","F",0
1262,0,0,0,0.000000," ","integrate(1/x^12/(-b*x^4+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{4}} x^{12}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/4)*x^12), x)","F",0
1263,0,0,0,0.000000," ","integrate(x^2/(-b*x^4+a)^(5/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(-b x^{4} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate(x^2/(-b*x^4 + a)^(5/4), x)","F",0
1264,1,94,0,0.169924," ","integrate(x^7*(b*x^4+a)^p,x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{2} {\left(b x^{4} + a\right)}^{p} p - {\left(b x^{4} + a\right)} {\left(b x^{4} + a\right)}^{p} a p + {\left(b x^{4} + a\right)}^{2} {\left(b x^{4} + a\right)}^{p} - 2 \, {\left(b x^{4} + a\right)} {\left(b x^{4} + a\right)}^{p} a}{4 \, {\left(p^{2} + 3 \, p + 2\right)} b^{2}}"," ",0,"1/4*((b*x^4 + a)^2*(b*x^4 + a)^p*p - (b*x^4 + a)*(b*x^4 + a)^p*a*p + (b*x^4 + a)^2*(b*x^4 + a)^p - 2*(b*x^4 + a)*(b*x^4 + a)^p*a)/((p^2 + 3*p + 2)*b^2)","B",0
1265,1,21,0,0.152532," ","integrate(x^3*(b*x^4+a)^p,x, algorithm=""giac"")","\frac{{\left(b x^{4} + a\right)}^{p + 1}}{4 \, b {\left(p + 1\right)}}"," ",0,"1/4*(b*x^4 + a)^(p + 1)/(b*(p + 1))","A",0
1266,0,0,0,0.000000," ","integrate((b*x^4+a)^p/x,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((b*x^4 + a)^p/x, x)","F",0
1267,1,58,0,0.170075," ","integrate(x^24/(b*x^5+a),x, algorithm=""giac"")","\frac{a^{4} \log\left({\left| b x^{5} + a \right|}\right)}{5 \, b^{5}} + \frac{3 \, b^{3} x^{20} - 4 \, a b^{2} x^{15} + 6 \, a^{2} b x^{10} - 12 \, a^{3} x^{5}}{60 \, b^{4}}"," ",0,"1/5*a^4*log(abs(b*x^5 + a))/b^5 + 1/60*(3*b^3*x^20 - 4*a*b^2*x^15 + 6*a^2*b*x^10 - 12*a^3*x^5)/b^4","A",0
1268,1,47,0,0.207843," ","integrate(x^19/(b*x^5+a),x, algorithm=""giac"")","-\frac{a^{3} \log\left({\left| b x^{5} + a \right|}\right)}{5 \, b^{4}} + \frac{2 \, b^{2} x^{15} - 3 \, a b x^{10} + 6 \, a^{2} x^{5}}{30 \, b^{3}}"," ",0,"-1/5*a^3*log(abs(b*x^5 + a))/b^4 + 1/30*(2*b^2*x^15 - 3*a*b*x^10 + 6*a^2*x^5)/b^3","A",0
1269,1,35,0,0.168239," ","integrate(x^14/(b*x^5+a),x, algorithm=""giac"")","\frac{a^{2} \log\left({\left| b x^{5} + a \right|}\right)}{5 \, b^{3}} + \frac{b x^{10} - 2 \, a x^{5}}{10 \, b^{2}}"," ",0,"1/5*a^2*log(abs(b*x^5 + a))/b^3 + 1/10*(b*x^10 - 2*a*x^5)/b^2","A",0
1270,1,24,0,0.182171," ","integrate(x^9/(b*x^5+a),x, algorithm=""giac"")","\frac{x^{5}}{5 \, b} - \frac{a \log\left({\left| b x^{5} + a \right|}\right)}{5 \, b^{2}}"," ",0,"1/5*x^5/b - 1/5*a*log(abs(b*x^5 + a))/b^2","A",0
1271,1,14,0,0.165990," ","integrate(x^4/(b*x^5+a),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{5} + a \right|}\right)}{5 \, b}"," ",0,"1/5*log(abs(b*x^5 + a))/b","A",0
1272,1,22,0,0.206698," ","integrate(1/x/(b*x^5+a),x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{5} + a \right|}\right)}{5 \, a} + \frac{\log\left({\left| x \right|}\right)}{a}"," ",0,"-1/5*log(abs(b*x^5 + a))/a + log(abs(x))/a","A",0
1273,1,42,0,0.169837," ","integrate(1/x^6/(b*x^5+a),x, algorithm=""giac"")","\frac{b \log\left({\left| b x^{5} + a \right|}\right)}{5 \, a^{2}} - \frac{b \log\left({\left| x \right|}\right)}{a^{2}} + \frac{b x^{5} - a}{5 \, a^{2} x^{5}}"," ",0,"1/5*b*log(abs(b*x^5 + a))/a^2 - b*log(abs(x))/a^2 + 1/5*(b*x^5 - a)/(a^2*x^5)","A",0
1274,1,55,0,0.172145," ","integrate(1/x^11/(b*x^5+a),x, algorithm=""giac"")","-\frac{b^{2} \log\left({\left| b x^{5} + a \right|}\right)}{5 \, a^{3}} + \frac{b^{2} \log\left({\left| x \right|}\right)}{a^{3}} - \frac{3 \, b^{2} x^{10} - 2 \, a b x^{5} + a^{2}}{10 \, a^{3} x^{10}}"," ",0,"-1/5*b^2*log(abs(b*x^5 + a))/a^3 + b^2*log(abs(x))/a^3 - 1/10*(3*b^2*x^10 - 2*a*b*x^5 + a^2)/(a^3*x^10)","A",0
1275,1,69,0,0.166584," ","integrate(1/x^16/(b*x^5+a),x, algorithm=""giac"")","\frac{b^{3} \log\left({\left| b x^{5} + a \right|}\right)}{5 \, a^{4}} - \frac{b^{3} \log\left({\left| x \right|}\right)}{a^{4}} + \frac{11 \, b^{3} x^{15} - 6 \, a b^{2} x^{10} + 3 \, a^{2} b x^{5} - 2 \, a^{3}}{30 \, a^{4} x^{15}}"," ",0,"1/5*b^3*log(abs(b*x^5 + a))/a^4 - b^3*log(abs(x))/a^4 + 1/30*(11*b^3*x^15 - 6*a*b^2*x^10 + 3*a^2*b*x^5 - 2*a^3)/(a^4*x^15)","A",0
1276,1,275,0,0.170979," ","integrate(1/(b*x^5+a),x, algorithm=""giac"")","-\frac{\left(-\frac{a}{b}\right)^{\frac{1}{5}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{5}} \right|}\right)}{5 \, a} + \frac{\left(-a b^{4}\right)^{\frac{1}{5}} \sqrt{2 \, \sqrt{5} + 10} \arctan\left(-\frac{{\left(\sqrt{5} - 1\right)} \left(-\frac{a}{b}\right)^{\frac{1}{5}} - 4 \, x}{\sqrt{2 \, \sqrt{5} + 10} \left(-\frac{a}{b}\right)^{\frac{1}{5}}}\right)}{10 \, a b} + \frac{\left(-a b^{4}\right)^{\frac{1}{5}} \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{{\left(\sqrt{5} + 1\right)} \left(-\frac{a}{b}\right)^{\frac{1}{5}} + 4 \, x}{\sqrt{-2 \, \sqrt{5} + 10} \left(-\frac{a}{b}\right)^{\frac{1}{5}}}\right)}{10 \, a b} + \frac{\left(-a b^{4}\right)^{\frac{1}{5}} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} \left(-\frac{a}{b}\right)^{\frac{1}{5}} + \left(-\frac{a}{b}\right)^{\frac{1}{5}}\right)} + \left(-\frac{a}{b}\right)^{\frac{2}{5}}\right)}{5 \, a b {\left(\sqrt{5} - 1\right)}} - \frac{\left(-a b^{4}\right)^{\frac{1}{5}} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} \left(-\frac{a}{b}\right)^{\frac{1}{5}} - \left(-\frac{a}{b}\right)^{\frac{1}{5}}\right)} + \left(-\frac{a}{b}\right)^{\frac{2}{5}}\right)}{5 \, a b {\left(\sqrt{5} + 1\right)}}"," ",0,"-1/5*(-a/b)^(1/5)*log(abs(x - (-a/b)^(1/5)))/a + 1/10*(-a*b^4)^(1/5)*sqrt(2*sqrt(5) + 10)*arctan(-((sqrt(5) - 1)*(-a/b)^(1/5) - 4*x)/(sqrt(2*sqrt(5) + 10)*(-a/b)^(1/5)))/(a*b) + 1/10*(-a*b^4)^(1/5)*sqrt(-2*sqrt(5) + 10)*arctan(((sqrt(5) + 1)*(-a/b)^(1/5) + 4*x)/(sqrt(-2*sqrt(5) + 10)*(-a/b)^(1/5)))/(a*b) + 1/5*(-a*b^4)^(1/5)*log(x^2 + 1/2*x*(sqrt(5)*(-a/b)^(1/5) + (-a/b)^(1/5)) + (-a/b)^(2/5))/(a*b*(sqrt(5) - 1)) - 1/5*(-a*b^4)^(1/5)*log(x^2 - 1/2*x*(sqrt(5)*(-a/b)^(1/5) - (-a/b)^(1/5)) + (-a/b)^(2/5))/(a*b*(sqrt(5) + 1))","A",0
1277,1,80,0,0.171653," ","integrate(x^24/(b*x^5+a)^2,x, algorithm=""giac"")","-\frac{4 \, a^{3} \log\left({\left| b x^{5} + a \right|}\right)}{5 \, b^{5}} + \frac{b^{4} x^{15} - 3 \, a b^{3} x^{10} + 9 \, a^{2} b^{2} x^{5}}{15 \, b^{6}} + \frac{4 \, a^{3} b x^{5} + 3 \, a^{4}}{5 \, {\left(b x^{5} + a\right)} b^{5}}"," ",0,"-4/5*a^3*log(abs(b*x^5 + a))/b^5 + 1/15*(b^4*x^15 - 3*a*b^3*x^10 + 9*a^2*b^2*x^5)/b^6 + 1/5*(4*a^3*b*x^5 + 3*a^4)/((b*x^5 + a)*b^5)","A",0
1278,1,67,0,0.195245," ","integrate(x^19/(b*x^5+a)^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \log\left({\left| b x^{5} + a \right|}\right)}{5 \, b^{4}} + \frac{b^{2} x^{10} - 4 \, a b x^{5}}{10 \, b^{4}} - \frac{3 \, a^{2} b x^{5} + 2 \, a^{3}}{5 \, {\left(b x^{5} + a\right)} b^{4}}"," ",0,"3/5*a^2*log(abs(b*x^5 + a))/b^4 + 1/10*(b^2*x^10 - 4*a*b*x^5)/b^4 - 1/5*(3*a^2*b*x^5 + 2*a^3)/((b*x^5 + a)*b^4)","A",0
1279,1,49,0,0.170924," ","integrate(x^14/(b*x^5+a)^2,x, algorithm=""giac"")","\frac{x^{5}}{5 \, b^{2}} - \frac{2 \, a \log\left({\left| b x^{5} + a \right|}\right)}{5 \, b^{3}} + \frac{2 \, a b x^{5} + a^{2}}{5 \, {\left(b x^{5} + a\right)} b^{3}}"," ",0,"1/5*x^5/b^2 - 2/5*a*log(abs(b*x^5 + a))/b^3 + 1/5*(2*a*b*x^5 + a^2)/((b*x^5 + a)*b^3)","A",0
1280,1,48,0,0.171899," ","integrate(x^9/(b*x^5+a)^2,x, algorithm=""giac"")","-\frac{\frac{\log\left(\frac{{\left| b x^{5} + a \right|}}{{\left(b x^{5} + a\right)}^{2} {\left| b \right|}}\right)}{b} - \frac{a}{{\left(b x^{5} + a\right)} b}}{5 \, b}"," ",0,"-1/5*(log(abs(b*x^5 + a)/((b*x^5 + a)^2*abs(b)))/b - a/((b*x^5 + a)*b))/b","A",0
1281,1,14,0,0.166319," ","integrate(x^4/(b*x^5+a)^2,x, algorithm=""giac"")","-\frac{1}{5 \, {\left(b x^{5} + a\right)} b}"," ",0,"-1/5/((b*x^5 + a)*b)","A",0
1282,1,45,0,0.166154," ","integrate(1/x/(b*x^5+a)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{5} + a \right|}\right)}{5 \, a^{2}} + \frac{\log\left({\left| x \right|}\right)}{a^{2}} + \frac{b x^{5} + 2 \, a}{5 \, {\left(b x^{5} + a\right)} a^{2}}"," ",0,"-1/5*log(abs(b*x^5 + a))/a^2 + log(abs(x))/a^2 + 1/5*(b*x^5 + 2*a)/((b*x^5 + a)*a^2)","A",0
1283,1,51,0,0.238996," ","integrate(1/x^6/(b*x^5+a)^2,x, algorithm=""giac"")","\frac{2 \, b \log\left({\left| b x^{5} + a \right|}\right)}{5 \, a^{3}} - \frac{2 \, b \log\left({\left| x \right|}\right)}{a^{3}} - \frac{2 \, b x^{5} + a}{5 \, {\left(b x^{10} + a x^{5}\right)} a^{2}}"," ",0,"2/5*b*log(abs(b*x^5 + a))/a^3 - 2*b*log(abs(x))/a^3 - 1/5*(2*b*x^5 + a)/((b*x^10 + a*x^5)*a^2)","A",0
1284,1,85,0,0.176962," ","integrate(1/x^11/(b*x^5+a)^2,x, algorithm=""giac"")","-\frac{3 \, b^{2} \log\left({\left| b x^{5} + a \right|}\right)}{5 \, a^{4}} + \frac{3 \, b^{2} \log\left({\left| x \right|}\right)}{a^{4}} + \frac{3 \, b^{3} x^{5} + 4 \, a b^{2}}{5 \, {\left(b x^{5} + a\right)} a^{4}} - \frac{9 \, b^{2} x^{10} - 4 \, a b x^{5} + a^{2}}{10 \, a^{4} x^{10}}"," ",0,"-3/5*b^2*log(abs(b*x^5 + a))/a^4 + 3*b^2*log(abs(x))/a^4 + 1/5*(3*b^3*x^5 + 4*a*b^2)/((b*x^5 + a)*a^4) - 1/10*(9*b^2*x^10 - 4*a*b*x^5 + a^2)/(a^4*x^10)","A",0
1285,1,30,0,0.197536," ","integrate(x^14/(b*x^5+2*b),x, algorithm=""giac"")","\frac{4 \, \log\left({\left| x^{5} + 2 \right|}\right)}{5 \, b} + \frac{b x^{10} - 4 \, b x^{5}}{10 \, b^{2}}"," ",0,"4/5*log(abs(x^5 + 2))/b + 1/10*(b*x^10 - 4*b*x^5)/b^2","A",0
1286,1,21,0,0.227268," ","integrate(x^9/(b*x^5+2*b),x, algorithm=""giac"")","\frac{x^{5}}{5 \, b} - \frac{2 \, \log\left({\left| x^{5} + 2 \right|}\right)}{5 \, b}"," ",0,"1/5*x^5/b - 2/5*log(abs(x^5 + 2))/b","A",0
1287,1,16,0,0.197080," ","integrate(x^4/(b*x^5+2*b),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{5} + 2 \, b \right|}\right)}{5 \, b}"," ",0,"1/5*log(abs(b*x^5 + 2*b))/b","A",0
1288,1,21,0,0.239097," ","integrate(1/x/(b*x^5+2*b),x, algorithm=""giac"")","-\frac{\log\left({\left| x^{5} + 2 \right|}\right)}{10 \, b} + \frac{\log\left({\left| x \right|}\right)}{2 \, b}"," ",0,"-1/10*log(abs(x^5 + 2))/b + 1/2*log(abs(x))/b","A",0
1289,1,34,0,0.231194," ","integrate(1/x^6/(b*x^5+2*b),x, algorithm=""giac"")","\frac{\log\left({\left| x^{5} + 2 \right|}\right)}{20 \, b} - \frac{\log\left({\left| x \right|}\right)}{4 \, b} + \frac{x^{5} - 2}{20 \, b x^{5}}"," ",0,"1/20*log(abs(x^5 + 2))/b - 1/4*log(abs(x))/b + 1/20*(x^5 - 2)/(b*x^5)","A",0
1290,1,31,0,0.674051," ","integrate(x^14/(b*x^5+3),x, algorithm=""giac"")","\frac{b x^{10} - 6 \, x^{5}}{10 \, b^{2}} + \frac{9 \, \log\left({\left| b x^{5} + 3 \right|}\right)}{5 \, b^{3}}"," ",0,"1/10*(b*x^10 - 6*x^5)/b^2 + 9/5*log(abs(b*x^5 + 3))/b^3","A",0
1291,1,23,0,0.667439," ","integrate(x^9/(b*x^5+3),x, algorithm=""giac"")","\frac{x^{5}}{5 \, b} - \frac{3 \, \log\left({\left| b x^{5} + 3 \right|}\right)}{5 \, b^{2}}"," ",0,"1/5*x^5/b - 3/5*log(abs(b*x^5 + 3))/b^2","A",0
1292,1,14,0,0.669971," ","integrate(x^4/(b*x^5+3),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{5} + 3 \right|}\right)}{5 \, b}"," ",0,"1/5*log(abs(b*x^5 + 3))/b","A",0
1293,1,17,0,0.335539," ","integrate(1/x/(b*x^5+3),x, algorithm=""giac"")","-\frac{1}{15} \, \log\left({\left| b x^{5} + 3 \right|}\right) + \frac{1}{3} \, \log\left({\left| x \right|}\right)"," ",0,"-1/15*log(abs(b*x^5 + 3)) + 1/3*log(abs(x))","A",0
1294,1,31,0,0.522082," ","integrate(1/x^6/(b*x^5+3),x, algorithm=""giac"")","\frac{1}{45} \, b \log\left({\left| b x^{5} + 3 \right|}\right) - \frac{1}{9} \, b \log\left({\left| x \right|}\right) + \frac{b x^{5} - 3}{45 \, x^{5}}"," ",0,"1/45*b*log(abs(b*x^5 + 3)) - 1/9*b*log(abs(x)) + 1/45*(b*x^5 - 3)/x^5","A",0
1295,1,20,0,0.156813," ","integrate(x^14/(x^5+1),x, algorithm=""giac"")","\frac{1}{10} \, x^{10} - \frac{1}{5} \, x^{5} + \frac{1}{5} \, \log\left({\left| x^{5} + 1 \right|}\right)"," ",0,"1/10*x^10 - 1/5*x^5 + 1/5*log(abs(x^5 + 1))","A",0
1296,1,15,0,0.156932," ","integrate(x^9/(x^5+1),x, algorithm=""giac"")","\frac{1}{5} \, x^{5} - \frac{1}{5} \, \log\left({\left| x^{5} + 1 \right|}\right)"," ",0,"1/5*x^5 - 1/5*log(abs(x^5 + 1))","A",0
1297,1,9,0,0.205364," ","integrate(x^4/(x^5+1),x, algorithm=""giac"")","\frac{1}{5} \, \log\left({\left| x^{5} + 1 \right|}\right)"," ",0,"1/5*log(abs(x^5 + 1))","A",0
1298,1,13,0,0.157053," ","integrate(1/x/(x^5+1),x, algorithm=""giac"")","-\frac{1}{5} \, \log\left({\left| x^{5} + 1 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"-1/5*log(abs(x^5 + 1)) + log(abs(x))","A",0
1299,1,25,0,0.156556," ","integrate(1/x^6/(x^5+1),x, algorithm=""giac"")","\frac{x^{5} - 1}{5 \, x^{5}} + \frac{1}{5} \, \log\left({\left| x^{5} + 1 \right|}\right) - \log\left({\left| x \right|}\right)"," ",0,"1/5*(x^5 - 1)/x^5 + 1/5*log(abs(x^5 + 1)) - log(abs(x))","A",0
1300,1,128,0,0.176012," ","integrate(x^5/(x^5+1),x, algorithm=""giac"")","-\frac{1}{10} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x + \sqrt{5} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) - \frac{1}{10} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x - \sqrt{5} - 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) + \frac{1}{20} \, \sqrt{5} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) - \frac{1}{20} \, \sqrt{5} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right) + x + \frac{1}{20} \, \log\left(x^{4} - x^{3} + x^{2} - x + 1\right) - \frac{1}{5} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/10*sqrt(2*sqrt(5) + 10)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10)) - 1/10*sqrt(-2*sqrt(5) + 10)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10)) + 1/20*sqrt(5)*log(x^2 - 1/2*x*(sqrt(5) + 1) + 1) - 1/20*sqrt(5)*log(x^2 + 1/2*x*(sqrt(5) - 1) + 1) + x + 1/20*log(x^4 - x^3 + x^2 - x + 1) - 1/5*log(abs(x + 1))","A",0
1301,1,112,0,0.181936," ","integrate(x^3/(x^5+1),x, algorithm=""giac"")","\frac{1}{20} \, {\left(\sqrt{5} + 1\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) - \frac{1}{20} \, {\left(\sqrt{5} - 1\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right) + \frac{1}{10} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x + \sqrt{5} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) + \frac{1}{10} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x - \sqrt{5} - 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) - \frac{1}{5} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/20*(sqrt(5) + 1)*log(x^2 - 1/2*x*(sqrt(5) + 1) + 1) - 1/20*(sqrt(5) - 1)*log(x^2 + 1/2*x*(sqrt(5) - 1) + 1) + 1/10*sqrt(2*sqrt(5) + 10)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10)) + 1/10*sqrt(-2*sqrt(5) + 10)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10)) - 1/5*log(abs(x + 1))","A",0
1302,1,112,0,0.177708," ","integrate(x^2/(x^5+1),x, algorithm=""giac"")","\frac{1}{20} \, {\left(\sqrt{5} - 1\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) - \frac{1}{20} \, {\left(\sqrt{5} + 1\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right) - \frac{1}{10} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x + \sqrt{5} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) + \frac{1}{10} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x - \sqrt{5} - 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) + \frac{1}{5} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/20*(sqrt(5) - 1)*log(x^2 - 1/2*x*(sqrt(5) + 1) + 1) - 1/20*(sqrt(5) + 1)*log(x^2 + 1/2*x*(sqrt(5) - 1) + 1) - 1/10*sqrt(-2*sqrt(5) + 10)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10)) + 1/10*sqrt(2*sqrt(5) + 10)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10)) + 1/5*log(abs(x + 1))","A",0
1303,1,112,0,0.176369," ","integrate(x/(x^5+1),x, algorithm=""giac"")","-\frac{1}{20} \, {\left(\sqrt{5} - 1\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) + \frac{1}{20} \, {\left(\sqrt{5} + 1\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right) - \frac{1}{10} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x + \sqrt{5} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) + \frac{1}{10} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x - \sqrt{5} - 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) - \frac{1}{5} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/20*(sqrt(5) - 1)*log(x^2 - 1/2*x*(sqrt(5) + 1) + 1) + 1/20*(sqrt(5) + 1)*log(x^2 + 1/2*x*(sqrt(5) - 1) + 1) - 1/10*sqrt(-2*sqrt(5) + 10)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10)) + 1/10*sqrt(2*sqrt(5) + 10)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10)) - 1/5*log(abs(x + 1))","A",0
1304,1,112,0,0.163121," ","integrate(1/(x^5+1),x, algorithm=""giac"")","-\frac{1}{20} \, {\left(\sqrt{5} + 1\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) + \frac{1}{20} \, {\left(\sqrt{5} - 1\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right) + \frac{1}{10} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x + \sqrt{5} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) + \frac{1}{10} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x - \sqrt{5} - 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) + \frac{1}{5} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/20*(sqrt(5) + 1)*log(x^2 - 1/2*x*(sqrt(5) + 1) + 1) + 1/20*(sqrt(5) - 1)*log(x^2 + 1/2*x*(sqrt(5) - 1) + 1) + 1/10*sqrt(2*sqrt(5) + 10)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10)) + 1/10*sqrt(-2*sqrt(5) + 10)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10)) + 1/5*log(abs(x + 1))","A",0
1305,1,132,0,0.179919," ","integrate(1/x^2/(x^5+1),x, algorithm=""giac"")","-\frac{1}{10} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x + \sqrt{5} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) - \frac{1}{10} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x - \sqrt{5} - 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) - \frac{1}{20} \, \sqrt{5} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) + \frac{1}{20} \, \sqrt{5} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right) - \frac{1}{x} - \frac{1}{20} \, \log\left(x^{4} - x^{3} + x^{2} - x + 1\right) + \frac{1}{5} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/10*sqrt(2*sqrt(5) + 10)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10)) - 1/10*sqrt(-2*sqrt(5) + 10)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10)) - 1/20*sqrt(5)*log(x^2 - 1/2*x*(sqrt(5) + 1) + 1) + 1/20*sqrt(5)*log(x^2 + 1/2*x*(sqrt(5) - 1) + 1) - 1/x - 1/20*log(x^4 - x^3 + x^2 - x + 1) + 1/5*log(abs(x + 1))","A",0
1306,1,132,0,0.180243," ","integrate(1/x^3/(x^5+1),x, algorithm=""giac"")","\frac{1}{10} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x + \sqrt{5} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) - \frac{1}{10} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x - \sqrt{5} - 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) - \frac{1}{20} \, \sqrt{5} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) + \frac{1}{20} \, \sqrt{5} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right) - \frac{1}{2 \, x^{2}} + \frac{1}{20} \, \log\left(x^{4} - x^{3} + x^{2} - x + 1\right) - \frac{1}{5} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/10*sqrt(-2*sqrt(5) + 10)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10)) - 1/10*sqrt(2*sqrt(5) + 10)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10)) - 1/20*sqrt(5)*log(x^2 - 1/2*x*(sqrt(5) + 1) + 1) + 1/20*sqrt(5)*log(x^2 + 1/2*x*(sqrt(5) - 1) + 1) - 1/2/x^2 + 1/20*log(x^4 - x^3 + x^2 - x + 1) - 1/5*log(abs(x + 1))","A",0
1307,1,132,0,0.178801," ","integrate(1/x^4/(x^5+1),x, algorithm=""giac"")","\frac{1}{10} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x + \sqrt{5} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) - \frac{1}{10} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x - \sqrt{5} - 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) + \frac{1}{20} \, \sqrt{5} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) - \frac{1}{20} \, \sqrt{5} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right) - \frac{1}{3 \, x^{3}} - \frac{1}{20} \, \log\left(x^{4} - x^{3} + x^{2} - x + 1\right) + \frac{1}{5} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/10*sqrt(-2*sqrt(5) + 10)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10)) - 1/10*sqrt(2*sqrt(5) + 10)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10)) + 1/20*sqrt(5)*log(x^2 - 1/2*x*(sqrt(5) + 1) + 1) - 1/20*sqrt(5)*log(x^2 + 1/2*x*(sqrt(5) - 1) + 1) - 1/3/x^3 - 1/20*log(x^4 - x^3 + x^2 - x + 1) + 1/5*log(abs(x + 1))","A",0
1308,1,58,0,0.298149," ","integrate(x^(23/2)/(b*x^5+a)^(1/2),x, algorithm=""giac"")","\frac{1}{20} \, \sqrt{b x^{5} + a} {\left(\frac{2 \, x^{5}}{b} - \frac{3 \, a}{b^{2}}\right)} x^{\frac{5}{2}} - \frac{3 \, a^{2} \log\left({\left| -\sqrt{b} x^{\frac{5}{2}} + \sqrt{b x^{5} + a} \right|}\right)}{20 \, b^{\frac{5}{2}}}"," ",0,"1/20*sqrt(b*x^5 + a)*(2*x^5/b - 3*a/b^2)*x^(5/2) - 3/20*a^2*log(abs(-sqrt(b)*x^(5/2) + sqrt(b*x^5 + a)))/b^(5/2)","A",0
1309,1,44,0,0.294886," ","integrate(x^(13/2)/(b*x^5+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{5} + a} x^{\frac{5}{2}}}{5 \, b} + \frac{a \log\left({\left| -\sqrt{b} x^{\frac{5}{2}} + \sqrt{b x^{5} + a} \right|}\right)}{5 \, b^{\frac{3}{2}}}"," ",0,"1/5*sqrt(b*x^5 + a)*x^(5/2)/b + 1/5*a*log(abs(-sqrt(b)*x^(5/2) + sqrt(b*x^5 + a)))/b^(3/2)","A",0
1310,1,25,0,0.175450," ","integrate(x^(3/2)/(b*x^5+a)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \log\left({\left| -\sqrt{b} x^{\frac{5}{2}} + \sqrt{b x^{5} + a} \right|}\right)}{5 \, \sqrt{b}}"," ",0,"-2/5*log(abs(-sqrt(b)*x^(5/2) + sqrt(b*x^5 + a)))/sqrt(b)","A",0
1311,1,23,0,0.205032," ","integrate(1/x^(7/2)/(b*x^5+a)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{b + \frac{a}{x^{5}}}}{5 \, a} + \frac{2 \, \sqrt{b}}{5 \, a}"," ",0,"-2/5*sqrt(b + a/x^5)/a + 2/5*sqrt(b)/a","A",0
1312,1,38,0,0.209157," ","integrate(1/x^(17/2)/(b*x^5+a)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(b + \frac{a}{x^{5}}\right)}^{\frac{3}{2}}}{15 \, a^{2}} + \frac{2 \, \sqrt{b + \frac{a}{x^{5}}} b}{5 \, a^{2}} - \frac{4 \, b^{\frac{3}{2}}}{15 \, a^{2}}"," ",0,"-2/15*(b + a/x^5)^(3/2)/a^2 + 2/5*sqrt(b + a/x^5)*b/a^2 - 4/15*b^(3/2)/a^2","A",0
1313,1,36,0,0.217910," ","integrate(x^(23/2)/(x^5+1)^(1/2),x, algorithm=""giac"")","\frac{1}{20} \, {\left(2 \, x^{5} - 3\right)} \sqrt{x^{5} + 1} x^{\frac{5}{2}} - \frac{3}{20} \, \log\left(-x^{\frac{5}{2}} + \sqrt{x^{5} + 1}\right)"," ",0,"1/20*(2*x^5 - 3)*sqrt(x^5 + 1)*x^(5/2) - 3/20*log(-x^(5/2) + sqrt(x^5 + 1))","A",0
1314,1,29,0,0.254789," ","integrate(x^(13/2)/(x^5+1)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, \sqrt{x^{5} + 1} x^{\frac{5}{2}} + \frac{1}{5} \, \log\left(-x^{\frac{5}{2}} + \sqrt{x^{5} + 1}\right)"," ",0,"1/5*sqrt(x^5 + 1)*x^(5/2) + 1/5*log(-x^(5/2) + sqrt(x^5 + 1))","A",0
1315,1,16,0,0.165245," ","integrate(x^(3/2)/(x^5+1)^(1/2),x, algorithm=""giac"")","-\frac{2}{5} \, \log\left(-x^{\frac{5}{2}} + \sqrt{x^{5} + 1}\right)"," ",0,"-2/5*log(-x^(5/2) + sqrt(x^5 + 1))","B",0
1316,1,11,0,0.179962," ","integrate(1/x^(7/2)/(x^5+1)^(1/2),x, algorithm=""giac"")","-\frac{2}{5} \, \sqrt{\frac{1}{x^{5}} + 1} + \frac{2}{5}"," ",0,"-2/5*sqrt(1/x^5 + 1) + 2/5","A",0
1317,-2,0,0,0.000000," ","integrate(1/x^(17/2)/(x^5+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)]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
1318,1,31,0,0.154945," ","integrate(x^8/(b*x^6+a),x, algorithm=""giac"")","\frac{x^{3}}{3 \, b} - \frac{a \arctan\left(\frac{b x^{3}}{\sqrt{a b}}\right)}{3 \, \sqrt{a b} b}"," ",0,"1/3*x^3/b - 1/3*a*arctan(b*x^3/sqrt(a*b))/(sqrt(a*b)*b)","A",0
1319,1,120,0,0.163997," ","integrate(x^7/(b*x^6+a),x, algorithm=""giac"")","\frac{x^{2}}{2 \, b} + \frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x^{2} - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{6 \, b} - \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x^{2} + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{6 \, b^{2}} - \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{4} + x^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{12 \, b^{2}}"," ",0,"1/2*x^2/b + 1/6*(-a/b)^(1/3)*log(abs(x^2 - (-a/b)^(1/3)))/b - 1/6*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x^2 + (-a/b)^(1/3))/(-a/b)^(1/3))/b^2 - 1/12*(-a*b^2)^(1/3)*log(x^4 + x^2*(-a/b)^(1/3) + (-a/b)^(2/3))/b^2","A",0
1320,1,180,0,0.159182," ","integrate(x^6/(b*x^6+a),x, algorithm=""giac"")","\frac{x}{b} - \frac{\sqrt{3} \left(a b^{5}\right)^{\frac{1}{6}} \log\left(x^{2} + \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{12 \, b^{2}} + \frac{\sqrt{3} \left(a b^{5}\right)^{\frac{1}{6}} \log\left(x^{2} - \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{12 \, b^{2}} - \frac{\left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, x + \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{6 \, b^{2}} - \frac{\left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, x - \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{6 \, b^{2}} - \frac{\left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 \, b^{2}}"," ",0,"x/b - 1/12*sqrt(3)*(a*b^5)^(1/6)*log(x^2 + sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/b^2 + 1/12*sqrt(3)*(a*b^5)^(1/6)*log(x^2 - sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/b^2 - 1/6*(a*b^5)^(1/6)*arctan((2*x + sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/b^2 - 1/6*(a*b^5)^(1/6)*arctan((2*x - sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/b^2 - 1/3*(a*b^5)^(1/6)*arctan(x/(a/b)^(1/6))/b^2","A",0
1321,1,14,0,0.156235," ","integrate(x^5/(b*x^6+a),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{6} + a \right|}\right)}{6 \, b}"," ",0,"1/6*log(abs(b*x^6 + a))/b","A",0
1322,1,187,0,0.272796," ","integrate(x^4/(b*x^6+a),x, algorithm=""giac"")","\frac{\left(\frac{a}{b}\right)^{\frac{5}{6}} \arctan\left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 \, a} - \frac{\sqrt{3} \left(a b^{5}\right)^{\frac{5}{6}} \log\left(x^{2} + \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{12 \, a b^{5}} + \frac{\sqrt{3} \left(a b^{5}\right)^{\frac{5}{6}} \log\left(x^{2} - \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{12 \, a b^{5}} + \frac{\left(a b^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{2 \, x + \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{6 \, a b^{5}} + \frac{\left(a b^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{2 \, x - \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{6 \, a b^{5}}"," ",0,"1/3*(a/b)^(5/6)*arctan(x/(a/b)^(1/6))/a - 1/12*sqrt(3)*(a*b^5)^(5/6)*log(x^2 + sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a*b^5) + 1/12*sqrt(3)*(a*b^5)^(5/6)*log(x^2 - sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a*b^5) + 1/6*(a*b^5)^(5/6)*arctan((2*x + sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a*b^5) + 1/6*(a*b^5)^(5/6)*arctan((2*x - sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a*b^5)","A",0
1323,1,118,0,0.170749," ","integrate(x^3/(b*x^6+a),x, algorithm=""giac"")","-\frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x^{2} - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{6 \, a} - \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x^{2} + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{6 \, a b^{2}} + \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{4} + x^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{12 \, a b^{2}}"," ",0,"-1/6*(-a/b)^(2/3)*log(abs(x^2 - (-a/b)^(1/3)))/a - 1/6*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x^2 + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b^2) + 1/12*(-a*b^2)^(2/3)*log(x^4 + x^2*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b^2)","A",0
1324,1,18,0,0.160287," ","integrate(x^2/(b*x^6+a),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b x^{3}}{\sqrt{a b}}\right)}{3 \, \sqrt{a b}}"," ",0,"1/3*arctan(b*x^3/sqrt(a*b))/sqrt(a*b)","A",0
1325,1,118,0,0.192073," ","integrate(x/(b*x^6+a),x, algorithm=""giac"")","-\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x^{2} - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{6 \, a} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x^{2} + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{6 \, a b} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{4} + x^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{12 \, a b}"," ",0,"-1/6*(-a/b)^(1/3)*log(abs(x^2 - (-a/b)^(1/3)))/a + 1/6*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x^2 + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b) + 1/12*(-a*b^2)^(1/3)*log(x^4 + x^2*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b)","A",0
1326,1,190,0,0.173560," ","integrate(1/(b*x^6+a),x, algorithm=""giac"")","\frac{\sqrt{3} \left(a b^{5}\right)^{\frac{1}{6}} \log\left(x^{2} + \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{12 \, a b} - \frac{\sqrt{3} \left(a b^{5}\right)^{\frac{1}{6}} \log\left(x^{2} - \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{12 \, a b} + \frac{\left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, x + \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{6 \, a b} + \frac{\left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, x - \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{6 \, a b} + \frac{\left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 \, a b}"," ",0,"1/12*sqrt(3)*(a*b^5)^(1/6)*log(x^2 + sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a*b) - 1/12*sqrt(3)*(a*b^5)^(1/6)*log(x^2 - sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a*b) + 1/6*(a*b^5)^(1/6)*arctan((2*x + sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a*b) + 1/6*(a*b^5)^(1/6)*arctan((2*x - sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a*b) + 1/3*(a*b^5)^(1/6)*arctan(x/(a/b)^(1/6))/(a*b)","A",0
1327,1,24,0,0.158671," ","integrate(1/x/(b*x^6+a),x, algorithm=""giac"")","\frac{\log\left(x^{6}\right)}{6 \, a} - \frac{\log\left({\left| b x^{6} + a \right|}\right)}{6 \, a}"," ",0,"1/6*log(x^6)/a - 1/6*log(abs(b*x^6 + a))/a","A",0
1328,1,196,0,0.264758," ","integrate(1/x^2/(b*x^6+a),x, algorithm=""giac"")","-\frac{b \left(\frac{a}{b}\right)^{\frac{5}{6}} \arctan\left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{3 \, a^{2}} - \frac{1}{a x} + \frac{\sqrt{3} \left(a b^{5}\right)^{\frac{5}{6}} \log\left(x^{2} + \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{12 \, a^{2} b^{4}} - \frac{\sqrt{3} \left(a b^{5}\right)^{\frac{5}{6}} \log\left(x^{2} - \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{12 \, a^{2} b^{4}} - \frac{\left(a b^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{2 \, x + \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{6 \, a^{2} b^{4}} - \frac{\left(a b^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{2 \, x - \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{6 \, a^{2} b^{4}}"," ",0,"-1/3*b*(a/b)^(5/6)*arctan(x/(a/b)^(1/6))/a^2 - 1/(a*x) + 1/12*sqrt(3)*(a*b^5)^(5/6)*log(x^2 + sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a^2*b^4) - 1/12*sqrt(3)*(a*b^5)^(5/6)*log(x^2 - sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a^2*b^4) - 1/6*(a*b^5)^(5/6)*arctan((2*x + sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a^2*b^4) - 1/6*(a*b^5)^(5/6)*arctan((2*x - sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a^2*b^4)","A",0
1329,1,127,0,0.181610," ","integrate(1/x^3/(b*x^6+a),x, algorithm=""giac"")","\frac{b \left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x^{2} - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{6 \, a^{2}} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x^{2} + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{6 \, a^{2} b} - \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{4} + x^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{12 \, a^{2} b} - \frac{1}{2 \, a x^{2}}"," ",0,"1/6*b*(-a/b)^(2/3)*log(abs(x^2 - (-a/b)^(1/3)))/a^2 + 1/6*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x^2 + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b) - 1/12*(-a*b^2)^(2/3)*log(x^4 + x^2*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b) - 1/2/(a*x^2)","A",0
1330,1,31,0,0.182320," ","integrate(1/x^4/(b*x^6+a),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{b x^{3}}{\sqrt{a b}}\right)}{3 \, \sqrt{a b} a} - \frac{1}{3 \, a x^{3}}"," ",0,"-1/3*b*arctan(b*x^3/sqrt(a*b))/(sqrt(a*b)*a) - 1/3/(a*x^3)","A",0
1331,1,39,0,0.165669," ","integrate(x^8/(b*x^6+a)^2,x, algorithm=""giac"")","-\frac{x^{3}}{6 \, {\left(b x^{6} + a\right)} b} + \frac{\arctan\left(\frac{b x^{3}}{\sqrt{a b}}\right)}{6 \, \sqrt{a b} b}"," ",0,"-1/6*x^3/((b*x^6 + a)*b) + 1/6*arctan(b*x^3/sqrt(a*b))/(sqrt(a*b)*b)","A",0
1332,1,138,0,0.201301," ","integrate(x^7/(b*x^6+a)^2,x, algorithm=""giac"")","-\frac{x^{2}}{6 \, {\left(b x^{6} + a\right)} b} - \frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x^{2} - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{18 \, a b} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x^{2} + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{18 \, a b^{2}} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{4} + x^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{36 \, a b^{2}}"," ",0,"-1/6*x^2/((b*x^6 + a)*b) - 1/18*(-a/b)^(1/3)*log(abs(x^2 - (-a/b)^(1/3)))/(a*b) + 1/18*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x^2 + (-a/b)^(1/3))/(-a/b)^(1/3))/(a*b^2) + 1/36*(-a*b^2)^(1/3)*log(x^4 + x^2*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b^2)","A",0
1333,1,205,0,0.206766," ","integrate(x^6/(b*x^6+a)^2,x, algorithm=""giac"")","-\frac{x}{6 \, {\left(b x^{6} + a\right)} b} + \frac{\sqrt{3} \left(a b^{5}\right)^{\frac{1}{6}} \log\left(x^{2} + \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{72 \, a b^{2}} - \frac{\sqrt{3} \left(a b^{5}\right)^{\frac{1}{6}} \log\left(x^{2} - \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{72 \, a b^{2}} + \frac{\left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, x + \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{36 \, a b^{2}} + \frac{\left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, x - \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{36 \, a b^{2}} + \frac{\left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{18 \, a b^{2}}"," ",0,"-1/6*x/((b*x^6 + a)*b) + 1/72*sqrt(3)*(a*b^5)^(1/6)*log(x^2 + sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a*b^2) - 1/72*sqrt(3)*(a*b^5)^(1/6)*log(x^2 - sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a*b^2) + 1/36*(a*b^5)^(1/6)*arctan((2*x + sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a*b^2) + 1/36*(a*b^5)^(1/6)*arctan((2*x - sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a*b^2) + 1/18*(a*b^5)^(1/6)*arctan(x/(a/b)^(1/6))/(a*b^2)","A",0
1334,1,14,0,0.184758," ","integrate(x^5/(b*x^6+a)^2,x, algorithm=""giac"")","-\frac{1}{6 \, {\left(b x^{6} + a\right)} b}"," ",0,"-1/6/((b*x^6 + a)*b)","A",0
1335,1,204,0,0.329936," ","integrate(x^4/(b*x^6+a)^2,x, algorithm=""giac"")","\frac{x^{5}}{6 \, {\left(b x^{6} + a\right)} a} + \frac{\left(\frac{a}{b}\right)^{\frac{5}{6}} \arctan\left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{18 \, a^{2}} - \frac{\sqrt{3} \left(a b^{5}\right)^{\frac{5}{6}} \log\left(x^{2} + \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{72 \, a^{2} b^{5}} + \frac{\sqrt{3} \left(a b^{5}\right)^{\frac{5}{6}} \log\left(x^{2} - \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{72 \, a^{2} b^{5}} + \frac{\left(a b^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{2 \, x + \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{36 \, a^{2} b^{5}} + \frac{\left(a b^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{2 \, x - \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{36 \, a^{2} b^{5}}"," ",0,"1/6*x^5/((b*x^6 + a)*a) + 1/18*(a/b)^(5/6)*arctan(x/(a/b)^(1/6))/a^2 - 1/72*sqrt(3)*(a*b^5)^(5/6)*log(x^2 + sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a^2*b^5) + 1/72*sqrt(3)*(a*b^5)^(5/6)*log(x^2 - sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a^2*b^5) + 1/36*(a*b^5)^(5/6)*arctan((2*x + sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a^2*b^5) + 1/36*(a*b^5)^(5/6)*arctan((2*x - sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a^2*b^5)","A",0
1336,1,135,0,0.184237," ","integrate(x^3/(b*x^6+a)^2,x, algorithm=""giac"")","\frac{x^{4}}{6 \, {\left(b x^{6} + a\right)} a} - \frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x^{2} - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{18 \, a^{2}} - \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x^{2} + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{18 \, a^{2} b^{2}} + \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{4} + x^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{36 \, a^{2} b^{2}}"," ",0,"1/6*x^4/((b*x^6 + a)*a) - 1/18*(-a/b)^(2/3)*log(abs(x^2 - (-a/b)^(1/3)))/a^2 - 1/18*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x^2 + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b^2) + 1/36*(-a*b^2)^(2/3)*log(x^4 + x^2*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b^2)","A",0
1337,1,39,0,0.178049," ","integrate(x^2/(b*x^6+a)^2,x, algorithm=""giac"")","\frac{x^{3}}{6 \, {\left(b x^{6} + a\right)} a} + \frac{\arctan\left(\frac{b x^{3}}{\sqrt{a b}}\right)}{6 \, \sqrt{a b} a}"," ",0,"1/6*x^3/((b*x^6 + a)*a) + 1/6*arctan(b*x^3/sqrt(a*b))/(sqrt(a*b)*a)","A",0
1338,1,135,0,0.202295," ","integrate(x/(b*x^6+a)^2,x, algorithm=""giac"")","\frac{x^{2}}{6 \, {\left(b x^{6} + a\right)} a} - \frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x^{2} - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2}} + \frac{\sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x^{2} + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{2} b} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{4} + x^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, a^{2} b}"," ",0,"1/6*x^2/((b*x^6 + a)*a) - 1/9*(-a/b)^(1/3)*log(abs(x^2 - (-a/b)^(1/3)))/a^2 + 1/9*sqrt(3)*(-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x^2 + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^2*b) + 1/18*(-a*b^2)^(1/3)*log(x^4 + x^2*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b)","A",0
1339,1,205,0,0.158115," ","integrate(1/(b*x^6+a)^2,x, algorithm=""giac"")","\frac{x}{6 \, {\left(b x^{6} + a\right)} a} + \frac{5 \, \sqrt{3} \left(a b^{5}\right)^{\frac{1}{6}} \log\left(x^{2} + \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{72 \, a^{2} b} - \frac{5 \, \sqrt{3} \left(a b^{5}\right)^{\frac{1}{6}} \log\left(x^{2} - \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{72 \, a^{2} b} + \frac{5 \, \left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, x + \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{36 \, a^{2} b} + \frac{5 \, \left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, x - \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{36 \, a^{2} b} + \frac{5 \, \left(a b^{5}\right)^{\frac{1}{6}} \arctan\left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{18 \, a^{2} b}"," ",0,"1/6*x/((b*x^6 + a)*a) + 5/72*sqrt(3)*(a*b^5)^(1/6)*log(x^2 + sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a^2*b) - 5/72*sqrt(3)*(a*b^5)^(1/6)*log(x^2 - sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a^2*b) + 5/36*(a*b^5)^(1/6)*arctan((2*x + sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a^2*b) + 5/36*(a*b^5)^(1/6)*arctan((2*x - sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a^2*b) + 5/18*(a*b^5)^(1/6)*arctan(x/(a/b)^(1/6))/(a^2*b)","A",0
1340,1,47,0,0.157832," ","integrate(1/x/(b*x^6+a)^2,x, algorithm=""giac"")","\frac{\log\left(x^{6}\right)}{6 \, a^{2}} - \frac{\log\left({\left| b x^{6} + a \right|}\right)}{6 \, a^{2}} + \frac{b x^{6} + 2 \, a}{6 \, {\left(b x^{6} + a\right)} a^{2}}"," ",0,"1/6*log(x^6)/a^2 - 1/6*log(abs(b*x^6 + a))/a^2 + 1/6*(b*x^6 + 2*a)/((b*x^6 + a)*a^2)","A",0
1341,1,216,0,0.247477," ","integrate(1/x^2/(b*x^6+a)^2,x, algorithm=""giac"")","-\frac{7 \, b x^{6} + 6 \, a}{6 \, {\left(b x^{7} + a x\right)} a^{2}} + \frac{7 \, \sqrt{3} \left(a b^{5}\right)^{\frac{5}{6}} \log\left(x^{2} + \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{72 \, a^{3} b^{4}} - \frac{7 \, \sqrt{3} \left(a b^{5}\right)^{\frac{5}{6}} \log\left(x^{2} - \sqrt{3} x \left(\frac{a}{b}\right)^{\frac{1}{6}} + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{72 \, a^{3} b^{4}} - \frac{7 \, \left(a b^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{2 \, x + \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{36 \, a^{3} b^{4}} - \frac{7 \, \left(a b^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{2 \, x - \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{6}}}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{36 \, a^{3} b^{4}} - \frac{7 \, \left(a b^{5}\right)^{\frac{5}{6}} \arctan\left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{6}}}\right)}{18 \, a^{3} b^{4}}"," ",0,"-1/6*(7*b*x^6 + 6*a)/((b*x^7 + a*x)*a^2) + 7/72*sqrt(3)*(a*b^5)^(5/6)*log(x^2 + sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a^3*b^4) - 7/72*sqrt(3)*(a*b^5)^(5/6)*log(x^2 - sqrt(3)*x*(a/b)^(1/6) + (a/b)^(1/3))/(a^3*b^4) - 7/36*(a*b^5)^(5/6)*arctan((2*x + sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a^3*b^4) - 7/36*(a*b^5)^(5/6)*arctan((2*x - sqrt(3)*(a/b)^(1/6))/(a/b)^(1/6))/(a^3*b^4) - 7/18*(a*b^5)^(5/6)*arctan(x/(a/b)^(1/6))/(a^3*b^4)","A",0
1342,1,147,0,0.204033," ","integrate(1/x^3/(b*x^6+a)^2,x, algorithm=""giac"")","\frac{2 \, b \left(-\frac{a}{b}\right)^{\frac{2}{3}} \log\left({\left| x^{2} - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{3}} + \frac{2 \, \sqrt{3} \left(-a b^{2}\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x^{2} + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{3} b} - \frac{4 \, b x^{6} + 3 \, a}{6 \, {\left(b x^{8} + a x^{2}\right)} a^{2}} - \frac{\left(-a b^{2}\right)^{\frac{2}{3}} \log\left(x^{4} + x^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \, a^{3} b}"," ",0,"2/9*b*(-a/b)^(2/3)*log(abs(x^2 - (-a/b)^(1/3)))/a^3 + 2/9*sqrt(3)*(-a*b^2)^(2/3)*arctan(1/3*sqrt(3)*(2*x^2 + (-a/b)^(1/3))/(-a/b)^(1/3))/(a^3*b) - 1/6*(4*b*x^6 + 3*a)/((b*x^8 + a*x^2)*a^2) - 1/9*(-a*b^2)^(2/3)*log(x^4 + x^2*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^3*b)","A",0
1343,1,51,0,0.162346," ","integrate(1/x^4/(b*x^6+a)^2,x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{b x^{3}}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2}} - \frac{3 \, b x^{6} + 2 \, a}{6 \, {\left(b x^{9} + a x^{3}\right)} a^{2}}"," ",0,"-1/2*b*arctan(b*x^3/sqrt(a*b))/(sqrt(a*b)*a^2) - 1/6*(3*b*x^6 + 2*a)/((b*x^9 + a*x^3)*a^2)","A",0
1344,1,24,0,0.151668," ","integrate(x^8/(-x^6+1),x, algorithm=""giac"")","-\frac{1}{3} \, x^{3} + \frac{1}{6} \, \log\left({\left| x^{3} + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x^{3} - 1 \right|}\right)"," ",0,"-1/3*x^3 + 1/6*log(abs(x^3 + 1)) - 1/6*log(abs(x^3 - 1))","A",0
1345,1,44,0,0.180599," ","integrate(x^7/(-x^6+1),x, algorithm=""giac"")","-\frac{1}{2} \, x^{2} + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + \frac{1}{12} \, \log\left(x^{4} + x^{2} + 1\right) - \frac{1}{6} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"-1/2*x^2 + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + 1/12*log(x^4 + x^2 + 1) - 1/6*log(abs(x^2 - 1))","A",0
1346,1,70,0,0.159160," ","integrate(x^6/(-x^6+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - x + \frac{1}{12} \, \log\left(x^{2} + x + 1\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - x + 1/12*log(x^2 + x + 1) - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1)) - 1/6*log(abs(x - 1))","A",0
1347,1,9,0,0.162404," ","integrate(x^5/(-x^6+1),x, algorithm=""giac"")","-\frac{1}{6} \, \log\left({\left| x^{6} - 1 \right|}\right)"," ",0,"-1/6*log(abs(x^6 - 1))","A",0
1348,1,67,0,0.188506," ","integrate(x^4/(-x^6+1),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{12} \, \log\left(x^{2} + x + 1\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/12*log(x^2 + x + 1) - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1)) - 1/6*log(abs(x - 1))","A",0
1349,1,39,0,0.155067," ","integrate(x^3/(-x^6+1),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + \frac{1}{12} \, \log\left(x^{4} + x^{2} + 1\right) - \frac{1}{6} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + 1/12*log(x^4 + x^2 + 1) - 1/6*log(abs(x^2 - 1))","A",0
1350,1,19,0,0.149577," ","integrate(x^2/(-x^6+1),x, algorithm=""giac"")","\frac{1}{6} \, \log\left({\left| x^{3} + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x^{3} - 1 \right|}\right)"," ",0,"1/6*log(abs(x^3 + 1)) - 1/6*log(abs(x^3 - 1))","B",0
1351,1,39,0,0.152378," ","integrate(x/(-x^6+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + \frac{1}{12} \, \log\left(x^{4} + x^{2} + 1\right) - \frac{1}{6} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + 1/12*log(x^4 + x^2 + 1) - 1/6*log(abs(x^2 - 1))","A",0
1352,1,67,0,0.208405," ","integrate(1/(-x^6+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{12} \, \log\left(x^{2} + x + 1\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/12*log(x^2 + x + 1) - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1)) - 1/6*log(abs(x - 1))","A",0
1353,1,16,0,0.153270," ","integrate(1/x/(-x^6+1),x, algorithm=""giac"")","\frac{1}{6} \, \log\left(x^{6}\right) - \frac{1}{6} \, \log\left({\left| x^{6} - 1 \right|}\right)"," ",0,"1/6*log(x^6) - 1/6*log(abs(x^6 - 1))","A",0
1354,1,72,0,0.154661," ","integrate(1/x^2/(-x^6+1),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{x} + \frac{1}{12} \, \log\left(x^{2} + x + 1\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/x + 1/12*log(x^2 + x + 1) - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1)) - 1/6*log(abs(x - 1))","A",0
1355,1,44,0,0.150604," ","integrate(1/x^3/(-x^6+1),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) - \frac{1}{2 \, x^{2}} + \frac{1}{12} \, \log\left(x^{4} + x^{2} + 1\right) - \frac{1}{6} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) - 1/2/x^2 + 1/12*log(x^4 + x^2 + 1) - 1/6*log(abs(x^2 - 1))","A",0
1356,1,24,0,0.155502," ","integrate(1/x^4/(-x^6+1),x, algorithm=""giac"")","-\frac{1}{3 \, x^{3}} + \frac{1}{6} \, \log\left({\left| x^{3} + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x^{3} - 1 \right|}\right)"," ",0,"-1/3/x^3 + 1/6*log(abs(x^3 + 1)) - 1/6*log(abs(x^3 - 1))","A",0
1357,1,44,0,0.164689," ","integrate(1/x^5/(-x^6+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) - \frac{1}{4 \, x^{4}} + \frac{1}{12} \, \log\left(x^{4} + x^{2} + 1\right) - \frac{1}{6} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) - 1/4/x^4 + 1/12*log(x^4 + x^2 + 1) - 1/6*log(abs(x^2 - 1))","A",0
1358,1,72,0,0.158492," ","integrate(1/x^6/(-x^6+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{5 \, x^{5}} + \frac{1}{12} \, \log\left(x^{2} + x + 1\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/5/x^5 + 1/12*log(x^2 + x + 1) - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1)) - 1/6*log(abs(x - 1))","A",0
1359,1,26,0,0.170834," ","integrate(1/x^7/(-x^6+1),x, algorithm=""giac"")","-\frac{x^{6} + 1}{6 \, x^{6}} + \frac{1}{6} \, \log\left(x^{6}\right) - \frac{1}{6} \, \log\left({\left| x^{6} - 1 \right|}\right)"," ",0,"-1/6*(x^6 + 1)/x^6 + 1/6*log(x^6) - 1/6*log(abs(x^6 - 1))","A",0
1360,1,79,0,0.156565," ","integrate(1/x^8/(-x^6+1),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{7 \, x^{6} + 1}{7 \, x^{7}} + \frac{1}{12} \, \log\left(x^{2} + x + 1\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/7*(7*x^6 + 1)/x^7 + 1/12*log(x^2 + x + 1) - 1/12*log(x^2 - x + 1) + 1/6*log(abs(x + 1)) - 1/6*log(abs(x - 1))","A",0
1361,1,12,0,0.152222," ","integrate(x^8/(x^6+1),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} - \frac{1}{3} \, \arctan\left(x^{3}\right)"," ",0,"1/3*x^3 - 1/3*arctan(x^3)","A",0
1362,1,45,0,0.150513," ","integrate(x^7/(x^6+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) + \frac{1}{12} \, \log\left(x^{4} - x^{2} + 1\right) - \frac{1}{6} \, \log\left(x^{2} + 1\right)"," ",0,"1/2*x^2 - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) + 1/12*log(x^4 - x^2 + 1) - 1/6*log(x^2 + 1)","A",0
1363,1,61,0,0.161558," ","integrate(x^6/(x^6+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + x - \frac{1}{6} \, \arctan\left(2 \, x + \sqrt{3}\right) - \frac{1}{6} \, \arctan\left(2 \, x - \sqrt{3}\right) - \frac{1}{3} \, \arctan\left(x\right)"," ",0,"-1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + x - 1/6*arctan(2*x + sqrt(3)) - 1/6*arctan(2*x - sqrt(3)) - 1/3*arctan(x)","A",0
1364,1,8,0,0.143150," ","integrate(x^5/(x^6+1),x, algorithm=""giac"")","\frac{1}{6} \, \log\left(x^{6} + 1\right)"," ",0,"1/6*log(x^6 + 1)","A",0
1365,1,60,0,0.173591," ","integrate(x^4/(x^6+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{1}{6} \, \arctan\left(2 \, x + \sqrt{3}\right) + \frac{1}{6} \, \arctan\left(2 \, x - \sqrt{3}\right) + \frac{1}{3} \, \arctan\left(x\right)"," ",0,"-1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/6*arctan(2*x + sqrt(3)) + 1/6*arctan(2*x - sqrt(3)) + 1/3*arctan(x)","A",0
1366,1,40,0,0.153470," ","integrate(x^3/(x^6+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) + \frac{1}{12} \, \log\left(x^{4} - x^{2} + 1\right) - \frac{1}{6} \, \log\left(x^{2} + 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) + 1/12*log(x^4 - x^2 + 1) - 1/6*log(x^2 + 1)","A",0
1367,1,6,0,0.148060," ","integrate(x^2/(x^6+1),x, algorithm=""giac"")","\frac{1}{3} \, \arctan\left(x^{3}\right)"," ",0,"1/3*arctan(x^3)","A",0
1368,1,40,0,0.150157," ","integrate(x/(x^6+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) - \frac{1}{12} \, \log\left(x^{4} - x^{2} + 1\right) + \frac{1}{6} \, \log\left(x^{2} + 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - 1/12*log(x^4 - x^2 + 1) + 1/6*log(x^2 + 1)","A",0
1369,1,60,0,0.179081," ","integrate(1/(x^6+1),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) - \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{1}{6} \, \arctan\left(2 \, x + \sqrt{3}\right) + \frac{1}{6} \, \arctan\left(2 \, x - \sqrt{3}\right) + \frac{1}{3} \, \arctan\left(x\right)"," ",0,"1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) - 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/6*arctan(2*x + sqrt(3)) + 1/6*arctan(2*x - sqrt(3)) + 1/3*arctan(x)","A",0
1370,1,15,0,0.215702," ","integrate(1/x/(x^6+1),x, algorithm=""giac"")","-\frac{1}{6} \, \log\left(x^{6} + 1\right) + \frac{1}{6} \, \log\left(x^{6}\right)"," ",0,"-1/6*log(x^6 + 1) + 1/6*log(x^6)","A",0
1371,1,65,0,0.159599," ","integrate(1/x^2/(x^6+1),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) - \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) - \frac{1}{x} - \frac{1}{6} \, \arctan\left(2 \, x + \sqrt{3}\right) - \frac{1}{6} \, \arctan\left(2 \, x - \sqrt{3}\right) - \frac{1}{3} \, \arctan\left(x\right)"," ",0,"1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) - 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1) - 1/x - 1/6*arctan(2*x + sqrt(3)) - 1/6*arctan(2*x - sqrt(3)) - 1/3*arctan(x)","A",0
1372,1,45,0,0.184398," ","integrate(1/x^3/(x^6+1),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) - \frac{1}{2 \, x^{2}} - \frac{1}{12} \, \log\left(x^{4} - x^{2} + 1\right) + \frac{1}{6} \, \log\left(x^{2} + 1\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - 1/2/x^2 - 1/12*log(x^4 - x^2 + 1) + 1/6*log(x^2 + 1)","A",0
1373,1,12,0,0.149823," ","integrate(1/x^4/(x^6+1),x, algorithm=""giac"")","-\frac{1}{3 \, x^{3}} - \frac{1}{3} \, \arctan\left(x^{3}\right)"," ",0,"-1/3/x^3 - 1/3*arctan(x^3)","A",0
1374,1,45,0,0.169174," ","integrate(1/x^5/(x^6+1),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) - \frac{1}{4 \, x^{4}} + \frac{1}{12} \, \log\left(x^{4} - x^{2} + 1\right) - \frac{1}{6} \, \log\left(x^{2} + 1\right)"," ",0,"-1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - 1/4/x^4 + 1/12*log(x^4 - x^2 + 1) - 1/6*log(x^2 + 1)","A",0
1375,1,65,0,0.207762," ","integrate(1/x^6/(x^6+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) + \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) - \frac{1}{5 \, x^{5}} - \frac{1}{6} \, \arctan\left(2 \, x + \sqrt{3}\right) - \frac{1}{6} \, \arctan\left(2 \, x - \sqrt{3}\right) - \frac{1}{3} \, \arctan\left(x\right)"," ",0,"-1/12*sqrt(3)*log(x^2 + sqrt(3)*x + 1) + 1/12*sqrt(3)*log(x^2 - sqrt(3)*x + 1) - 1/5/x^5 - 1/6*arctan(2*x + sqrt(3)) - 1/6*arctan(2*x - sqrt(3)) - 1/3*arctan(x)","A",0
1376,1,25,0,0.151615," ","integrate(1/x^7/(x^6+1),x, algorithm=""giac"")","\frac{x^{6} - 1}{6 \, x^{6}} + \frac{1}{6} \, \log\left(x^{6} + 1\right) - \frac{1}{6} \, \log\left(x^{6}\right)"," ",0,"1/6*(x^6 - 1)/x^6 + 1/6*log(x^6 + 1) - 1/6*log(x^6)","A",0
1377,1,39,0,0.158437," ","integrate(1/x^8/(x^6+1),x, algorithm=""giac"")","\frac{7 \, x^{6} - 1}{7 \, x^{7}} + \frac{1}{3} \, \arctan\left(2 \, x + \sqrt{3}\right) + \frac{1}{3} \, \arctan\left(2 \, x - \sqrt{3}\right) + \frac{1}{3} \, \arctan\left(x\right)"," ",0,"1/7*(7*x^6 - 1)/x^7 + 1/3*arctan(2*x + sqrt(3)) + 1/3*arctan(2*x - sqrt(3)) + 1/3*arctan(x)","A",0
1378,1,114,0,0.174681," ","integrate(1/(-3*x^6+2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \left(\frac{2}{3}\right)^{\frac{1}{6}} \arctan\left(\frac{1}{2} \, \sqrt{3} \left(\frac{2}{3}\right)^{\frac{5}{6}} {\left(2 \, x + \left(\frac{2}{3}\right)^{\frac{1}{6}}\right)}\right) + \frac{1}{12} \, \sqrt{3} \left(\frac{2}{3}\right)^{\frac{1}{6}} \arctan\left(\frac{1}{2} \, \sqrt{3} \left(\frac{2}{3}\right)^{\frac{5}{6}} {\left(2 \, x - \left(\frac{2}{3}\right)^{\frac{1}{6}}\right)}\right) + \frac{1}{72} \cdot 486^{\frac{1}{6}} \log\left(x^{2} + \left(\frac{2}{3}\right)^{\frac{1}{6}} x + \left(\frac{2}{3}\right)^{\frac{1}{3}}\right) - \frac{1}{72} \cdot 486^{\frac{1}{6}} \log\left(x^{2} - \left(\frac{2}{3}\right)^{\frac{1}{6}} x + \left(\frac{2}{3}\right)^{\frac{1}{3}}\right) + \frac{1}{36} \cdot 486^{\frac{1}{6}} \log\left({\left| x + \left(\frac{2}{3}\right)^{\frac{1}{6}} \right|}\right) - \frac{1}{36} \cdot 486^{\frac{1}{6}} \log\left({\left| x - \left(\frac{2}{3}\right)^{\frac{1}{6}} \right|}\right)"," ",0,"1/12*sqrt(3)*(2/3)^(1/6)*arctan(1/2*sqrt(3)*(2/3)^(5/6)*(2*x + (2/3)^(1/6))) + 1/12*sqrt(3)*(2/3)^(1/6)*arctan(1/2*sqrt(3)*(2/3)^(5/6)*(2*x - (2/3)^(1/6))) + 1/72*486^(1/6)*log(x^2 + (2/3)^(1/6)*x + (2/3)^(1/3)) - 1/72*486^(1/6)*log(x^2 - (2/3)^(1/6)*x + (2/3)^(1/3)) + 1/36*486^(1/6)*log(abs(x + (2/3)^(1/6))) - 1/36*486^(1/6)*log(abs(x - (2/3)^(1/6)))","A",0
1379,1,217,0,3.590638," ","integrate(x^(1/3)/(-x^6+1),x, algorithm=""giac"")","\frac{2}{3} \, \arctan\left(\frac{x^{\frac{2}{3}} - \cos\left(\frac{4}{9} \, \pi\right)}{\sin\left(\frac{4}{9} \, \pi\right)}\right) \cos\left(\frac{4}{9} \, \pi\right) \sin\left(\frac{4}{9} \, \pi\right) + \frac{2}{3} \, \arctan\left(\frac{x^{\frac{2}{3}} - \cos\left(\frac{2}{9} \, \pi\right)}{\sin\left(\frac{2}{9} \, \pi\right)}\right) \cos\left(\frac{2}{9} \, \pi\right) \sin\left(\frac{2}{9} \, \pi\right) - \frac{2}{3} \, \arctan\left(\frac{x^{\frac{2}{3}} + \cos\left(\frac{1}{9} \, \pi\right)}{\sin\left(\frac{1}{9} \, \pi\right)}\right) \cos\left(\frac{1}{9} \, \pi\right) \sin\left(\frac{1}{9} \, \pi\right) - \frac{1}{6} \, {\left(\cos\left(\frac{4}{9} \, \pi\right)^{2} - \sin\left(\frac{4}{9} \, \pi\right)^{2}\right)} \log\left(-2 \, x^{\frac{2}{3}} \cos\left(\frac{4}{9} \, \pi\right) + x^{\frac{4}{3}} + 1\right) - \frac{1}{6} \, {\left(\cos\left(\frac{2}{9} \, \pi\right)^{2} - \sin\left(\frac{2}{9} \, \pi\right)^{2}\right)} \log\left(-2 \, x^{\frac{2}{3}} \cos\left(\frac{2}{9} \, \pi\right) + x^{\frac{4}{3}} + 1\right) - \frac{1}{6} \, {\left(\cos\left(\frac{1}{9} \, \pi\right)^{2} - \sin\left(\frac{1}{9} \, \pi\right)^{2}\right)} \log\left(2 \, x^{\frac{2}{3}} \cos\left(\frac{1}{9} \, \pi\right) + x^{\frac{4}{3}} + 1\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{\frac{2}{3}} + 1\right)}\right) + \frac{1}{12} \, \log\left(x^{\frac{4}{3}} + x^{\frac{2}{3}} + 1\right) - \frac{1}{6} \, \log\left({\left| x^{\frac{2}{3}} - 1 \right|}\right)"," ",0,"2/3*arctan((x^(2/3) - cos(4/9*pi))/sin(4/9*pi))*cos(4/9*pi)*sin(4/9*pi) + 2/3*arctan((x^(2/3) - cos(2/9*pi))/sin(2/9*pi))*cos(2/9*pi)*sin(2/9*pi) - 2/3*arctan((x^(2/3) + cos(1/9*pi))/sin(1/9*pi))*cos(1/9*pi)*sin(1/9*pi) - 1/6*(cos(4/9*pi)^2 - sin(4/9*pi)^2)*log(-2*x^(2/3)*cos(4/9*pi) + x^(4/3) + 1) - 1/6*(cos(2/9*pi)^2 - sin(2/9*pi)^2)*log(-2*x^(2/3)*cos(2/9*pi) + x^(4/3) + 1) - 1/6*(cos(1/9*pi)^2 - sin(1/9*pi)^2)*log(2*x^(2/3)*cos(1/9*pi) + x^(4/3) + 1) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^(2/3) + 1)) + 1/12*log(x^(4/3) + x^(2/3) + 1) - 1/6*log(abs(x^(2/3) - 1))","A",0
1380,0,0,0,0.000000," ","integrate(x^8*(4*x^6-1)^(1/2),x, algorithm=""giac"")","\int \sqrt{4 \, x^{6} - 1} x^{8}\,{d x}"," ",0,"integrate(sqrt(4*x^6 - 1)*x^8, x)","F",0
1381,1,13,0,0.150916," ","integrate(x^5*(a^6-x^6)^(1/2),x, algorithm=""giac"")","-\frac{1}{9} \, {\left(a^{6} - x^{6}\right)}^{\frac{3}{2}}"," ",0,"-1/9*(a^6 - x^6)^(3/2)","A",0
1382,1,30,0,0.177018," ","integrate(x^2*(x^6-2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{x^{6} - 2} x^{3} + \frac{1}{3} \, \log\left({\left| -x^{3} + \sqrt{x^{6} - 2} \right|}\right)"," ",0,"1/6*sqrt(x^6 - 2)*x^3 + 1/3*log(abs(-x^3 + sqrt(x^6 - 2)))","A",0
1383,1,37,0,0.151384," ","integrate(x^23/(x^6+2)^(1/2),x, algorithm=""giac"")","\frac{1}{21} \, {\left(x^{6} + 2\right)}^{\frac{7}{2}} - \frac{2}{5} \, {\left(x^{6} + 2\right)}^{\frac{5}{2}} + \frac{4}{3} \, {\left(x^{6} + 2\right)}^{\frac{3}{2}} - \frac{8}{3} \, \sqrt{x^{6} + 2}"," ",0,"1/21*(x^6 + 2)^(7/2) - 2/5*(x^6 + 2)^(5/2) + 4/3*(x^6 + 2)^(3/2) - 8/3*sqrt(x^6 + 2)","A",0
1384,1,28,0,0.149809," ","integrate(x^17/(x^6+2)^(1/2),x, algorithm=""giac"")","\frac{1}{15} \, {\left(x^{6} + 2\right)}^{\frac{5}{2}} - \frac{4}{9} \, {\left(x^{6} + 2\right)}^{\frac{3}{2}} + \frac{4}{3} \, \sqrt{x^{6} + 2}"," ",0,"1/15*(x^6 + 2)^(5/2) - 4/9*(x^6 + 2)^(3/2) + 4/3*sqrt(x^6 + 2)","A",0
1385,1,19,0,0.152058," ","integrate(x^11/(x^6+2)^(1/2),x, algorithm=""giac"")","\frac{1}{9} \, {\left(x^{6} + 2\right)}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{x^{6} + 2}"," ",0,"1/9*(x^6 + 2)^(3/2) - 2/3*sqrt(x^6 + 2)","A",0
1386,1,9,0,0.148164," ","integrate(x^5/(x^6+2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{6} + 2}"," ",0,"1/3*sqrt(x^6 + 2)","A",0
1387,1,37,0,0.183311," ","integrate(1/x/(x^6+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{2} \log\left(\sqrt{2} + \sqrt{x^{6} + 2}\right) + \frac{1}{12} \, \sqrt{2} \log\left(-\sqrt{2} + \sqrt{x^{6} + 2}\right)"," ",0,"-1/12*sqrt(2)*log(sqrt(2) + sqrt(x^6 + 2)) + 1/12*sqrt(2)*log(-sqrt(2) + sqrt(x^6 + 2))","B",0
1388,1,47,0,0.163248," ","integrate(1/x^7/(x^6+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{48} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \sqrt{x^{6} + 2}}{\sqrt{2} + \sqrt{x^{6} + 2}}\right) - \frac{\sqrt{x^{6} + 2}}{12 \, x^{6}}"," ",0,"-1/48*sqrt(2)*log(-(sqrt(2) - sqrt(x^6 + 2))/(sqrt(2) + sqrt(x^6 + 2))) - 1/12*sqrt(x^6 + 2)/x^6","A",0
1389,1,59,0,0.159780," ","integrate(1/x^13/(x^6+2)^(1/2),x, algorithm=""giac"")","\frac{1}{128} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \sqrt{x^{6} + 2}}{\sqrt{2} + \sqrt{x^{6} + 2}}\right) + \frac{3 \, {\left(x^{6} + 2\right)}^{\frac{3}{2}} - 10 \, \sqrt{x^{6} + 2}}{96 \, x^{12}}"," ",0,"1/128*sqrt(2)*log(-(sqrt(2) - sqrt(x^6 + 2))/(sqrt(2) + sqrt(x^6 + 2))) + 1/96*(3*(x^6 + 2)^(3/2) - 10*sqrt(x^6 + 2))/x^12","A",0
1390,0,0,0,0.000000," ","integrate(x^14/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{14}}{\sqrt{x^{6} + 2}}\,{d x}"," ",0,"integrate(x^14/sqrt(x^6 + 2), x)","F",0
1391,0,0,0,0.000000," ","integrate(x^8/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{8}}{\sqrt{x^{6} + 2}}\,{d x}"," ",0,"integrate(x^8/sqrt(x^6 + 2), x)","F",0
1392,1,16,0,0.208853," ","integrate(x^2/(x^6+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \log\left(-x^{3} + \sqrt{x^{6} + 2}\right)"," ",0,"-1/3*log(-x^3 + sqrt(x^6 + 2))","A",0
1393,1,20,0,0.196020," ","integrate(1/x^4/(x^6+2)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{\frac{2}{x^{6}} + 1}}{6 \, \mathrm{sgn}\left(x\right)} + \frac{1}{6} \, \mathrm{sgn}\left(x\right)"," ",0,"-1/6*sqrt(2/x^6 + 1)/sgn(x) + 1/6*sgn(x)","A",0
1394,-2,0,0,0.000000," ","integrate(1/x^10/(x^6+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(t_nostep)]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
1395,-2,0,0,0.000000," ","integrate(1/x^16/(x^6+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(t_nostep)]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
1396,0,0,0,0.000000," ","integrate(x^7/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{7}}{\sqrt{x^{6} + 2}}\,{d x}"," ",0,"integrate(x^7/sqrt(x^6 + 2), x)","F",0
1397,0,0,0,0.000000," ","integrate(x/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{6} + 2}}\,{d x}"," ",0,"integrate(x/sqrt(x^6 + 2), x)","F",0
1398,0,0,0,0.000000," ","integrate(1/x^5/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{6} + 2} x^{5}}\,{d x}"," ",0,"integrate(1/(sqrt(x^6 + 2)*x^5), x)","F",0
1399,0,0,0,0.000000," ","integrate(x^6/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{x^{6} + 2}}\,{d x}"," ",0,"integrate(x^6/sqrt(x^6 + 2), x)","F",0
1400,0,0,0,0.000000," ","integrate(1/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{6} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(x^6 + 2), x)","F",0
1401,0,0,0,0.000000," ","integrate(1/x^6/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{6} + 2} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(x^6 + 2)*x^6), x)","F",0
1402,0,0,0,0.000000," ","integrate(x^9/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{9}}{\sqrt{x^{6} + 2}}\,{d x}"," ",0,"integrate(x^9/sqrt(x^6 + 2), x)","F",0
1403,0,0,0,0.000000," ","integrate(x^3/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3}}{\sqrt{x^{6} + 2}}\,{d x}"," ",0,"integrate(x^3/sqrt(x^6 + 2), x)","F",0
1404,0,0,0,0.000000," ","integrate(1/x^3/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{6} + 2} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(x^6 + 2)*x^3), x)","F",0
1405,0,0,0,0.000000," ","integrate(x^10/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{10}}{\sqrt{x^{6} + 2}}\,{d x}"," ",0,"integrate(x^10/sqrt(x^6 + 2), x)","F",0
1406,0,0,0,0.000000," ","integrate(x^4/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{x^{6} + 2}}\,{d x}"," ",0,"integrate(x^4/sqrt(x^6 + 2), x)","F",0
1407,0,0,0,0.000000," ","integrate(1/x^2/(x^6+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{6} + 2} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^6 + 2)*x^2), x)","F",0
1408,1,37,0,0.152093," ","integrate(x^23/(x^6+2)^(3/2),x, algorithm=""giac"")","\frac{1}{15} \, {\left(x^{6} + 2\right)}^{\frac{5}{2}} - \frac{2}{3} \, {\left(x^{6} + 2\right)}^{\frac{3}{2}} + 4 \, \sqrt{x^{6} + 2} + \frac{8}{3 \, \sqrt{x^{6} + 2}}"," ",0,"1/15*(x^6 + 2)^(5/2) - 2/3*(x^6 + 2)^(3/2) + 4*sqrt(x^6 + 2) + 8/3/sqrt(x^6 + 2)","A",0
1409,1,28,0,0.149740," ","integrate(x^17/(x^6+2)^(3/2),x, algorithm=""giac"")","\frac{1}{9} \, {\left(x^{6} + 2\right)}^{\frac{3}{2}} - \frac{4}{3} \, \sqrt{x^{6} + 2} - \frac{4}{3 \, \sqrt{x^{6} + 2}}"," ",0,"1/9*(x^6 + 2)^(3/2) - 4/3*sqrt(x^6 + 2) - 4/3/sqrt(x^6 + 2)","A",0
1410,1,19,0,0.162601," ","integrate(x^11/(x^6+2)^(3/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x^{6} + 2} + \frac{2}{3 \, \sqrt{x^{6} + 2}}"," ",0,"1/3*sqrt(x^6 + 2) + 2/3/sqrt(x^6 + 2)","A",0
1411,1,9,0,0.174602," ","integrate(x^5/(x^6+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{3 \, \sqrt{x^{6} + 2}}"," ",0,"-1/3/sqrt(x^6 + 2)","A",0
1412,1,44,0,0.153384," ","integrate(1/x/(x^6+2)^(3/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \sqrt{x^{6} + 2}}{\sqrt{2} + \sqrt{x^{6} + 2}}\right) + \frac{1}{6 \, \sqrt{x^{6} + 2}}"," ",0,"1/24*sqrt(2)*log(-(sqrt(2) - sqrt(x^6 + 2))/(sqrt(2) + sqrt(x^6 + 2))) + 1/6/sqrt(x^6 + 2)","A",0
1413,1,63,0,0.169639," ","integrate(1/x^7/(x^6+2)^(3/2),x, algorithm=""giac"")","-\frac{1}{32} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \sqrt{x^{6} + 2}}{\sqrt{2} + \sqrt{x^{6} + 2}}\right) - \frac{3 \, x^{6} + 2}{24 \, {\left({\left(x^{6} + 2\right)}^{\frac{3}{2}} - 2 \, \sqrt{x^{6} + 2}\right)}}"," ",0,"-1/32*sqrt(2)*log(-(sqrt(2) - sqrt(x^6 + 2))/(sqrt(2) + sqrt(x^6 + 2))) - 1/24*(3*x^6 + 2)/((x^6 + 2)^(3/2) - 2*sqrt(x^6 + 2))","A",0
1414,1,68,0,0.151586," ","integrate(1/x^13/(x^6+2)^(3/2),x, algorithm=""giac"")","\frac{5}{256} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \sqrt{x^{6} + 2}}{\sqrt{2} + \sqrt{x^{6} + 2}}\right) + \frac{1}{24 \, \sqrt{x^{6} + 2}} + \frac{7 \, {\left(x^{6} + 2\right)}^{\frac{3}{2}} - 18 \, \sqrt{x^{6} + 2}}{192 \, x^{12}}"," ",0,"5/256*sqrt(2)*log(-(sqrt(2) - sqrt(x^6 + 2))/(sqrt(2) + sqrt(x^6 + 2))) + 1/24/sqrt(x^6 + 2) + 1/192*(7*(x^6 + 2)^(3/2) - 18*sqrt(x^6 + 2))/x^12","A",0
1415,0,0,0,0.000000," ","integrate(x^14/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{14}}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^14/(x^6 + 2)^(3/2), x)","F",0
1416,0,0,0,0.000000," ","integrate(x^8/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^8/(x^6 + 2)^(3/2), x)","F",0
1417,1,12,0,0.192973," ","integrate(x^2/(x^6+2)^(3/2),x, algorithm=""giac"")","\frac{x^{3}}{6 \, \sqrt{x^{6} + 2}}"," ",0,"1/6*x^3/sqrt(x^6 + 2)","A",0
1418,0,0,0,0.000000," ","integrate(1/x^4/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{6} + 2\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((x^6 + 2)^(3/2)*x^4), x)","F",0
1419,-2,0,0,0.000000," ","integrate(1/x^10/(x^6+2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]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
1420,0,0,0,0.000000," ","integrate(x^13/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{13}}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^13/(x^6 + 2)^(3/2), x)","F",0
1421,0,0,0,0.000000," ","integrate(x^7/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{7}}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^7/(x^6 + 2)^(3/2), x)","F",0
1422,0,0,0,0.000000," ","integrate(x/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(x^6 + 2)^(3/2), x)","F",0
1423,0,0,0,0.000000," ","integrate(1/x^5/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{6} + 2\right)}^{\frac{3}{2}} x^{5}}\,{d x}"," ",0,"integrate(1/((x^6 + 2)^(3/2)*x^5), x)","F",0
1424,0,0,0,0.000000," ","integrate(x^12/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{12}}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^12/(x^6 + 2)^(3/2), x)","F",0
1425,0,0,0,0.000000," ","integrate(x^6/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^6/(x^6 + 2)^(3/2), x)","F",0
1426,0,0,0,0.000000," ","integrate(1/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x^6 + 2)^(-3/2), x)","F",0
1427,0,0,0,0.000000," ","integrate(1/x^6/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{6} + 2\right)}^{\frac{3}{2}} x^{6}}\,{d x}"," ",0,"integrate(1/((x^6 + 2)^(3/2)*x^6), x)","F",0
1428,0,0,0,0.000000," ","integrate(x^15/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{15}}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^15/(x^6 + 2)^(3/2), x)","F",0
1429,0,0,0,0.000000," ","integrate(x^9/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{9}}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^9/(x^6 + 2)^(3/2), x)","F",0
1430,0,0,0,0.000000," ","integrate(x^3/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3/(x^6 + 2)^(3/2), x)","F",0
1431,0,0,0,0.000000," ","integrate(1/x^3/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{6} + 2\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((x^6 + 2)^(3/2)*x^3), x)","F",0
1432,0,0,0,0.000000," ","integrate(x^10/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{10}}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^10/(x^6 + 2)^(3/2), x)","F",0
1433,0,0,0,0.000000," ","integrate(x^4/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(x^{6} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/(x^6 + 2)^(3/2), x)","F",0
1434,0,0,0,0.000000," ","integrate(1/x^2/(x^6+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{6} + 2\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((x^6 + 2)^(3/2)*x^2), x)","F",0
1435,1,43,0,0.159870," ","integrate(x^m*(b*x^7+a),x, algorithm=""giac"")","\frac{b m x^{8} x^{m} + b x^{8} x^{m} + a m x x^{m} + 8 \, a x x^{m}}{m^{2} + 9 \, m + 8}"," ",0,"(b*m*x^8*x^m + b*x^8*x^m + a*m*x*x^m + 8*a*x*x^m)/(m^2 + 9*m + 8)","A",0
1436,1,13,0,0.189508," ","integrate(x^8*(b*x^7+a),x, algorithm=""giac"")","\frac{1}{16} \, b x^{16} + \frac{1}{9} \, a x^{9}"," ",0,"1/16*b*x^16 + 1/9*a*x^9","A",0
1437,1,18,0,0.146501," ","integrate((b*x^7+a)/x^8,x, algorithm=""giac"")","b \log\left({\left| x \right|}\right) - \frac{b x^{7} + a}{7 \, x^{7}}"," ",0,"b*log(abs(x)) - 1/7*(b*x^7 + a)/x^7","A",0
1438,1,117,0,0.172731," ","integrate(x^m*(b*x^7+a)^2,x, algorithm=""giac"")","\frac{b^{2} m^{2} x^{15} x^{m} + 9 \, b^{2} m x^{15} x^{m} + 8 \, b^{2} x^{15} x^{m} + 2 \, a b m^{2} x^{8} x^{m} + 32 \, a b m x^{8} x^{m} + 30 \, a b x^{8} x^{m} + a^{2} m^{2} x x^{m} + 23 \, a^{2} m x x^{m} + 120 \, a^{2} x x^{m}}{m^{3} + 24 \, m^{2} + 143 \, m + 120}"," ",0,"(b^2*m^2*x^15*x^m + 9*b^2*m*x^15*x^m + 8*b^2*x^15*x^m + 2*a*b*m^2*x^8*x^m + 32*a*b*m*x^8*x^m + 30*a*b*x^8*x^m + a^2*m^2*x*x^m + 23*a^2*m*x*x^m + 120*a^2*x*x^m)/(m^3 + 24*m^2 + 143*m + 120)","B",0
1439,1,24,0,0.148867," ","integrate(x^8*(b*x^7+a)^2,x, algorithm=""giac"")","\frac{1}{23} \, b^{2} x^{23} + \frac{1}{8} \, a b x^{16} + \frac{1}{9} \, a^{2} x^{9}"," ",0,"1/23*b^2*x^23 + 1/8*a*b*x^16 + 1/9*a^2*x^9","A",0
1440,1,32,0,0.154092," ","integrate((b*x^7+a)^2/x^8,x, algorithm=""giac"")","\frac{1}{7} \, b^{2} x^{7} + 2 \, a b \log\left({\left| x \right|}\right) - \frac{2 \, a b x^{7} + a^{2}}{7 \, x^{7}}"," ",0,"1/7*b^2*x^7 + 2*a*b*log(abs(x)) - 1/7*(2*a*b*x^7 + a^2)/x^7","A",0
1441,0,0,0,0.000000," ","integrate(x^m/(b*x^7+a),x, algorithm=""giac"")","\int \frac{x^{m}}{b x^{7} + a}\,{d x}"," ",0,"integrate(x^m/(b*x^7 + a), x)","F",0
1442,1,14,0,0.164555," ","integrate(x^6/(b*x^7+a),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{7} + a \right|}\right)}{7 \, b}"," ",0,"1/7*log(abs(b*x^7 + a))/b","A",0
1443,1,310,0,0.246716," ","integrate(1/(b*x^7+a),x, algorithm=""giac"")","\frac{\left(-\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{3}{7} \, \pi\right) \log\left(2 \, x \left(-\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{3}{7} \, \pi\right) + x^{2} + \left(-\frac{a}{b}\right)^{\frac{2}{7}}\right)}{7 \, a} - \frac{\left(-\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{2}{7} \, \pi\right) \log\left(-2 \, x \left(-\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{2}{7} \, \pi\right) + x^{2} + \left(-\frac{a}{b}\right)^{\frac{2}{7}}\right)}{7 \, a} + \frac{\left(-\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{1}{7} \, \pi\right) \log\left(2 \, x \left(-\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{1}{7} \, \pi\right) + x^{2} + \left(-\frac{a}{b}\right)^{\frac{2}{7}}\right)}{7 \, a} + \frac{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{7}} \arctan\left(\frac{\left(-\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{3}{7} \, \pi\right) + x}{\left(-\frac{a}{b}\right)^{\frac{1}{7}} \sin\left(\frac{3}{7} \, \pi\right)}\right) \sin\left(\frac{3}{7} \, \pi\right)}{7 \, a} + \frac{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{7}} \arctan\left(-\frac{\left(-\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{2}{7} \, \pi\right) - x}{\left(-\frac{a}{b}\right)^{\frac{1}{7}} \sin\left(\frac{2}{7} \, \pi\right)}\right) \sin\left(\frac{2}{7} \, \pi\right)}{7 \, a} + \frac{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{7}} \arctan\left(\frac{\left(-\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{1}{7} \, \pi\right) + x}{\left(-\frac{a}{b}\right)^{\frac{1}{7}} \sin\left(\frac{1}{7} \, \pi\right)}\right) \sin\left(\frac{1}{7} \, \pi\right)}{7 \, a} - \frac{\left(-\frac{a}{b}\right)^{\frac{1}{7}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{7}} \right|}\right)}{7 \, a}"," ",0,"1/7*(-a/b)^(1/7)*cos(3/7*pi)*log(2*x*(-a/b)^(1/7)*cos(3/7*pi) + x^2 + (-a/b)^(2/7))/a - 1/7*(-a/b)^(1/7)*cos(2/7*pi)*log(-2*x*(-a/b)^(1/7)*cos(2/7*pi) + x^2 + (-a/b)^(2/7))/a + 1/7*(-a/b)^(1/7)*cos(1/7*pi)*log(2*x*(-a/b)^(1/7)*cos(1/7*pi) + x^2 + (-a/b)^(2/7))/a + 2/7*(-a/b)^(1/7)*arctan(((-a/b)^(1/7)*cos(3/7*pi) + x)/((-a/b)^(1/7)*sin(3/7*pi)))*sin(3/7*pi)/a + 2/7*(-a/b)^(1/7)*arctan(-((-a/b)^(1/7)*cos(2/7*pi) - x)/((-a/b)^(1/7)*sin(2/7*pi)))*sin(2/7*pi)/a + 2/7*(-a/b)^(1/7)*arctan(((-a/b)^(1/7)*cos(1/7*pi) + x)/((-a/b)^(1/7)*sin(1/7*pi)))*sin(1/7*pi)/a - 1/7*(-a/b)^(1/7)*log(abs(x - (-a/b)^(1/7)))/a","A",0
1444,1,22,0,0.159125," ","integrate(1/x/(b*x^7+a),x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{7} + a \right|}\right)}{7 \, a} + \frac{\log\left({\left| x \right|}\right)}{a}"," ",0,"-1/7*log(abs(b*x^7 + a))/a + log(abs(x))/a","A",0
1445,0,0,0,0.000000," ","integrate(x^m/(-b*x^7+a),x, algorithm=""giac"")","\int -\frac{x^{m}}{b x^{7} - a}\,{d x}"," ",0,"integrate(-x^m/(b*x^7 - a), x)","F",0
1446,1,16,0,0.163058," ","integrate(x^6/(-b*x^7+a),x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{7} - a \right|}\right)}{7 \, b}"," ",0,"-1/7*log(abs(b*x^7 - a))/b","A",0
1447,1,290,0,0.176360," ","integrate(1/(-b*x^7+a),x, algorithm=""giac"")","\frac{\left(\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{3}{7} \, \pi\right) \log\left(2 \, x \left(\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{3}{7} \, \pi\right) + x^{2} + \left(\frac{a}{b}\right)^{\frac{2}{7}}\right)}{7 \, a} - \frac{\left(\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{2}{7} \, \pi\right) \log\left(-2 \, x \left(\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{2}{7} \, \pi\right) + x^{2} + \left(\frac{a}{b}\right)^{\frac{2}{7}}\right)}{7 \, a} + \frac{\left(\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{1}{7} \, \pi\right) \log\left(2 \, x \left(\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{1}{7} \, \pi\right) + x^{2} + \left(\frac{a}{b}\right)^{\frac{2}{7}}\right)}{7 \, a} + \frac{2 \, \left(\frac{a}{b}\right)^{\frac{1}{7}} \arctan\left(\frac{\left(\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{3}{7} \, \pi\right) + x}{\left(\frac{a}{b}\right)^{\frac{1}{7}} \sin\left(\frac{3}{7} \, \pi\right)}\right) \sin\left(\frac{3}{7} \, \pi\right)}{7 \, a} + \frac{2 \, \left(\frac{a}{b}\right)^{\frac{1}{7}} \arctan\left(-\frac{\left(\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{2}{7} \, \pi\right) - x}{\left(\frac{a}{b}\right)^{\frac{1}{7}} \sin\left(\frac{2}{7} \, \pi\right)}\right) \sin\left(\frac{2}{7} \, \pi\right)}{7 \, a} + \frac{2 \, \left(\frac{a}{b}\right)^{\frac{1}{7}} \arctan\left(\frac{\left(\frac{a}{b}\right)^{\frac{1}{7}} \cos\left(\frac{1}{7} \, \pi\right) + x}{\left(\frac{a}{b}\right)^{\frac{1}{7}} \sin\left(\frac{1}{7} \, \pi\right)}\right) \sin\left(\frac{1}{7} \, \pi\right)}{7 \, a} - \frac{\left(\frac{a}{b}\right)^{\frac{1}{7}} \log\left({\left| x - \left(\frac{a}{b}\right)^{\frac{1}{7}} \right|}\right)}{7 \, a}"," ",0,"1/7*(a/b)^(1/7)*cos(3/7*pi)*log(2*x*(a/b)^(1/7)*cos(3/7*pi) + x^2 + (a/b)^(2/7))/a - 1/7*(a/b)^(1/7)*cos(2/7*pi)*log(-2*x*(a/b)^(1/7)*cos(2/7*pi) + x^2 + (a/b)^(2/7))/a + 1/7*(a/b)^(1/7)*cos(1/7*pi)*log(2*x*(a/b)^(1/7)*cos(1/7*pi) + x^2 + (a/b)^(2/7))/a + 2/7*(a/b)^(1/7)*arctan(((a/b)^(1/7)*cos(3/7*pi) + x)/((a/b)^(1/7)*sin(3/7*pi)))*sin(3/7*pi)/a + 2/7*(a/b)^(1/7)*arctan(-((a/b)^(1/7)*cos(2/7*pi) - x)/((a/b)^(1/7)*sin(2/7*pi)))*sin(2/7*pi)/a + 2/7*(a/b)^(1/7)*arctan(((a/b)^(1/7)*cos(1/7*pi) + x)/((a/b)^(1/7)*sin(1/7*pi)))*sin(1/7*pi)/a - 1/7*(a/b)^(1/7)*log(abs(x - (a/b)^(1/7)))/a","A",0
1448,1,24,0,0.154844," ","integrate(1/x/(-b*x^7+a),x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{7} - a \right|}\right)}{7 \, a} + \frac{\log\left({\left| x \right|}\right)}{a}"," ",0,"-1/7*log(abs(b*x^7 - a))/a + log(abs(x))/a","A",0
1449,1,127,0,0.158750," ","integrate(1/(-x^7+1),x, algorithm=""giac"")","\frac{1}{7} \, \cos\left(\frac{3}{7} \, \pi\right) \log\left(x^{2} + 2 \, x \cos\left(\frac{3}{7} \, \pi\right) + 1\right) - \frac{1}{7} \, \cos\left(\frac{2}{7} \, \pi\right) \log\left(x^{2} - 2 \, x \cos\left(\frac{2}{7} \, \pi\right) + 1\right) + \frac{1}{7} \, \cos\left(\frac{1}{7} \, \pi\right) \log\left(x^{2} + 2 \, x \cos\left(\frac{1}{7} \, \pi\right) + 1\right) + \frac{2}{7} \, \arctan\left(\frac{x + \cos\left(\frac{3}{7} \, \pi\right)}{\sin\left(\frac{3}{7} \, \pi\right)}\right) \sin\left(\frac{3}{7} \, \pi\right) + \frac{2}{7} \, \arctan\left(\frac{x - \cos\left(\frac{2}{7} \, \pi\right)}{\sin\left(\frac{2}{7} \, \pi\right)}\right) \sin\left(\frac{2}{7} \, \pi\right) + \frac{2}{7} \, \arctan\left(\frac{x + \cos\left(\frac{1}{7} \, \pi\right)}{\sin\left(\frac{1}{7} \, \pi\right)}\right) \sin\left(\frac{1}{7} \, \pi\right) - \frac{1}{7} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/7*cos(3/7*pi)*log(x^2 + 2*x*cos(3/7*pi) + 1) - 1/7*cos(2/7*pi)*log(x^2 - 2*x*cos(2/7*pi) + 1) + 1/7*cos(1/7*pi)*log(x^2 + 2*x*cos(1/7*pi) + 1) + 2/7*arctan((x + cos(3/7*pi))/sin(3/7*pi))*sin(3/7*pi) + 2/7*arctan((x - cos(2/7*pi))/sin(2/7*pi))*sin(2/7*pi) + 2/7*arctan((x + cos(1/7*pi))/sin(1/7*pi))*sin(1/7*pi) - 1/7*log(abs(x - 1))","A",0
1450,1,129,0,0.157204," ","integrate(1/(x^7+1),x, algorithm=""giac"")","-\frac{1}{7} \, \cos\left(\frac{3}{7} \, \pi\right) \log\left(x^{2} - 2 \, x \cos\left(\frac{3}{7} \, \pi\right) + 1\right) + \frac{1}{7} \, \cos\left(\frac{2}{7} \, \pi\right) \log\left(x^{2} + 2 \, x \cos\left(\frac{2}{7} \, \pi\right) + 1\right) - \frac{1}{7} \, \cos\left(\frac{1}{7} \, \pi\right) \log\left(x^{2} - 2 \, x \cos\left(\frac{1}{7} \, \pi\right) + 1\right) + \frac{2}{7} \, \arctan\left(\frac{x - \cos\left(\frac{3}{7} \, \pi\right)}{\sin\left(\frac{3}{7} \, \pi\right)}\right) \sin\left(\frac{3}{7} \, \pi\right) + \frac{2}{7} \, \arctan\left(\frac{x + \cos\left(\frac{2}{7} \, \pi\right)}{\sin\left(\frac{2}{7} \, \pi\right)}\right) \sin\left(\frac{2}{7} \, \pi\right) + \frac{2}{7} \, \arctan\left(\frac{x - \cos\left(\frac{1}{7} \, \pi\right)}{\sin\left(\frac{1}{7} \, \pi\right)}\right) \sin\left(\frac{1}{7} \, \pi\right) + \frac{1}{7} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/7*cos(3/7*pi)*log(x^2 - 2*x*cos(3/7*pi) + 1) + 1/7*cos(2/7*pi)*log(x^2 + 2*x*cos(2/7*pi) + 1) - 1/7*cos(1/7*pi)*log(x^2 - 2*x*cos(1/7*pi) + 1) + 2/7*arctan((x - cos(3/7*pi))/sin(3/7*pi))*sin(3/7*pi) + 2/7*arctan((x + cos(2/7*pi))/sin(2/7*pi))*sin(2/7*pi) + 2/7*arctan((x - cos(1/7*pi))/sin(1/7*pi))*sin(1/7*pi) + 1/7*log(abs(x + 1))","A",0
1451,1,183,0,0.193123," ","integrate(x^9/(b*x^8+a),x, algorithm=""giac"")","\frac{x^{2}}{2 \, b} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x^{2} + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, b^{2}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x^{2} - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, b^{2}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \log\left(x^{4} + \sqrt{2} x^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, b^{2}} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \log\left(x^{4} - \sqrt{2} x^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, b^{2}}"," ",0,"1/2*x^2/b - 1/8*sqrt(2)*(a*b^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x^2 + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/b^2 - 1/8*sqrt(2)*(a*b^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x^2 - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/b^2 - 1/16*sqrt(2)*(a*b^3)^(1/4)*log(x^4 + sqrt(2)*x^2*(a/b)^(1/4) + sqrt(a/b))/b^2 + 1/16*sqrt(2)*(a*b^3)^(1/4)*log(x^4 - sqrt(2)*x^2*(a/b)^(1/4) + sqrt(a/b))/b^2","A",0
1452,1,14,0,0.181592," ","integrate(x^7/(b*x^8+a),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{8} + a \right|}\right)}{8 \, b}"," ",0,"1/8*log(abs(b*x^8 + a))/b","A",0
1453,1,199,0,0.205061," ","integrate(x^5/(b*x^8+a),x, algorithm=""giac"")","\frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} x^{4} \arctan\left(\frac{\sqrt{2} {\left(2 \, x^{2} + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} x^{4} \arctan\left(\frac{\sqrt{2} {\left(2 \, x^{2} - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} x^{4} \log\left(x^{4} + \sqrt{2} x^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, a b} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} x^{4} \log\left(x^{4} - \sqrt{2} x^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, a b}"," ",0,"1/8*sqrt(2)*(a*b^3)^(1/4)*x^4*arctan(1/2*sqrt(2)*(2*x^2 + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b) + 1/8*sqrt(2)*(a*b^3)^(1/4)*x^4*arctan(1/2*sqrt(2)*(2*x^2 - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b) + 1/16*sqrt(2)*(a*b^3)^(1/4)*x^4*log(x^4 + sqrt(2)*x^2*(a/b)^(1/4) + sqrt(a/b))/(a*b) - 1/16*sqrt(2)*(a*b^3)^(1/4)*x^4*log(x^4 - sqrt(2)*x^2*(a/b)^(1/4) + sqrt(a/b))/(a*b)","A",0
1454,1,18,0,0.189927," ","integrate(x^3/(b*x^8+a),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b x^{4}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b}}"," ",0,"1/4*arctan(b*x^4/sqrt(a*b))/sqrt(a*b)","A",0
1455,1,187,0,0.218653," ","integrate(x/(b*x^8+a),x, algorithm=""giac"")","\frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x^{2} + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x^{2} - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \log\left(x^{4} + \sqrt{2} x^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, a b} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \log\left(x^{4} - \sqrt{2} x^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, a b}"," ",0,"1/8*sqrt(2)*(a*b^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x^2 + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b) + 1/8*sqrt(2)*(a*b^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x^2 - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b) + 1/16*sqrt(2)*(a*b^3)^(1/4)*log(x^4 + sqrt(2)*x^2*(a/b)^(1/4) + sqrt(a/b))/(a*b) - 1/16*sqrt(2)*(a*b^3)^(1/4)*log(x^4 - sqrt(2)*x^2*(a/b)^(1/4) + sqrt(a/b))/(a*b)","A",0
1456,1,24,0,0.200378," ","integrate(1/x/(b*x^8+a),x, algorithm=""giac"")","\frac{\log\left(x^{8}\right)}{8 \, a} - \frac{\log\left({\left| b x^{8} + a \right|}\right)}{8 \, a}"," ",0,"1/8*log(x^8)/a - 1/8*log(abs(b*x^8 + a))/a","A",0
1457,1,195,0,0.194400," ","integrate(1/x^3/(b*x^8+a),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} x^{4} \arctan\left(\frac{\sqrt{2} {\left(2 \, x^{2} + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} x^{4} \arctan\left(\frac{\sqrt{2} {\left(2 \, x^{2} - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} x^{4} \log\left(x^{4} + \sqrt{2} x^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2}} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} x^{4} \log\left(x^{4} - \sqrt{2} x^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2}} - \frac{1}{2 \, a x^{2}}"," ",0,"-1/8*sqrt(2)*(a*b^3)^(1/4)*x^4*arctan(1/2*sqrt(2)*(2*x^2 + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/a^2 - 1/8*sqrt(2)*(a*b^3)^(1/4)*x^4*arctan(1/2*sqrt(2)*(2*x^2 - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/a^2 - 1/16*sqrt(2)*(a*b^3)^(1/4)*x^4*log(x^4 + sqrt(2)*x^2*(a/b)^(1/4) + sqrt(a/b))/a^2 + 1/16*sqrt(2)*(a*b^3)^(1/4)*x^4*log(x^4 - sqrt(2)*x^2*(a/b)^(1/4) + sqrt(a/b))/a^2 - 1/2/(a*x^2)","A",0
1458,1,31,0,0.187471," ","integrate(1/x^5/(b*x^8+a),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{b x^{4}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} a} - \frac{1}{4 \, a x^{4}}"," ",0,"-1/4*b*arctan(b*x^4/sqrt(a*b))/(sqrt(a*b)*a) - 1/4/(a*x^4)","A",0
1459,1,183,0,0.225243," ","integrate(1/x^7/(b*x^8+a),x, algorithm=""giac"")","-\frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x^{2} + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x^{2} - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2}} - \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \log\left(x^{4} + \sqrt{2} x^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2}} + \frac{\sqrt{2} \left(a b^{3}\right)^{\frac{1}{4}} \log\left(x^{4} - \sqrt{2} x^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2}} - \frac{1}{6 \, a x^{6}}"," ",0,"-1/8*sqrt(2)*(a*b^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x^2 + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/a^2 - 1/8*sqrt(2)*(a*b^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x^2 - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/a^2 - 1/16*sqrt(2)*(a*b^3)^(1/4)*log(x^4 + sqrt(2)*x^2*(a/b)^(1/4) + sqrt(a/b))/a^2 + 1/16*sqrt(2)*(a*b^3)^(1/4)*log(x^4 - sqrt(2)*x^2*(a/b)^(1/4) + sqrt(a/b))/a^2 - 1/6/(a*x^6)","A",0
1460,1,43,0,0.205421," ","integrate(1/x^9/(b*x^8+a),x, algorithm=""giac"")","-\frac{b \log\left(x^{8}\right)}{8 \, a^{2}} + \frac{b \log\left({\left| b x^{8} + a \right|}\right)}{8 \, a^{2}} + \frac{b x^{8} - a}{8 \, a^{2} x^{8}}"," ",0,"-1/8*b*log(x^8)/a^2 + 1/8*b*log(abs(b*x^8 + a))/a^2 + 1/8*(b*x^8 - a)/(a^2*x^8)","A",0
1461,1,442,0,0.226568," ","integrate(x^8/(b*x^8+a),x, algorithm=""giac"")","\frac{x}{b} - \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, b \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, b \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, b \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, b \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, b \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, b \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, b \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, b \sqrt{2 \, \sqrt{2} + 4}}"," ",0,"x/b - 1/4*(a/b)^(1/8)*arctan((2*x + sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(b*sqrt(-2*sqrt(2) + 4)) - 1/4*(a/b)^(1/8)*arctan((2*x - sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(b*sqrt(-2*sqrt(2) + 4)) - 1/4*(a/b)^(1/8)*arctan((2*x + sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(b*sqrt(2*sqrt(2) + 4)) - 1/4*(a/b)^(1/8)*arctan((2*x - sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(b*sqrt(2*sqrt(2) + 4)) - 1/8*(a/b)^(1/8)*log(x^2 + x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(b*sqrt(-2*sqrt(2) + 4)) + 1/8*(a/b)^(1/8)*log(x^2 - x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(b*sqrt(-2*sqrt(2) + 4)) - 1/8*(a/b)^(1/8)*log(x^2 + x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(b*sqrt(2*sqrt(2) + 4)) + 1/8*(a/b)^(1/8)*log(x^2 - x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(b*sqrt(2*sqrt(2) + 4))","B",0
1462,1,437,0,0.396183," ","integrate(x^6/(b*x^8+a),x, algorithm=""giac"")","\frac{\left(\frac{a}{b}\right)^{\frac{7}{8}} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{7}{8}} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{7}{8}} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{7}{8}} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{7}{8}} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{7}{8}} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{7}{8}} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{7}{8}} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}}"," ",0,"1/4*(a/b)^(7/8)*arctan((2*x + sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(a/b)^(7/8)*arctan((2*x - sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(a/b)^(7/8)*arctan((2*x + sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/4*(a/b)^(7/8)*arctan((2*x - sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) - 1/8*(a/b)^(7/8)*log(x^2 + x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) + 1/8*(a/b)^(7/8)*log(x^2 - x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) - 1/8*(a/b)^(7/8)*log(x^2 + x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) + 1/8*(a/b)^(7/8)*log(x^2 - x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(2*sqrt(2) + 4))","B",0
1463,1,437,0,0.365724," ","integrate(x^4/(b*x^8+a),x, algorithm=""giac"")","-\frac{\left(\frac{a}{b}\right)^{\frac{5}{8}} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{5}{8}} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{5}{8}} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{5}{8}} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{5}{8}} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{5}{8}} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{5}{8}} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{5}{8}} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}}"," ",0,"-1/4*(a/b)^(5/8)*arctan((2*x + sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) - 1/4*(a/b)^(5/8)*arctan((2*x - sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/4*(a/b)^(5/8)*arctan((2*x + sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(a/b)^(5/8)*arctan((2*x - sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) - 1/8*(a/b)^(5/8)*log(x^2 + x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) + 1/8*(a/b)^(5/8)*log(x^2 - x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) + 1/8*(a/b)^(5/8)*log(x^2 + x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) - 1/8*(a/b)^(5/8)*log(x^2 - x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(-2*sqrt(2) + 4))","B",0
1464,1,437,0,0.350095," ","integrate(x^2/(b*x^8+a),x, algorithm=""giac"")","-\frac{\left(\frac{a}{b}\right)^{\frac{3}{8}} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{3}{8}} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{3}{8}} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{3}{8}} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{3}{8}} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{3}{8}} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{3}{8}} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{3}{8}} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}}"," ",0,"-1/4*(a/b)^(3/8)*arctan((2*x + sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) - 1/4*(a/b)^(3/8)*arctan((2*x - sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/4*(a/b)^(3/8)*arctan((2*x + sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(a/b)^(3/8)*arctan((2*x - sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/8*(a/b)^(3/8)*log(x^2 + x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) - 1/8*(a/b)^(3/8)*log(x^2 - x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) - 1/8*(a/b)^(3/8)*log(x^2 + x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) + 1/8*(a/b)^(3/8)*log(x^2 - x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(-2*sqrt(2) + 4))","B",0
1465,1,437,0,0.227389," ","integrate(1/(b*x^8+a),x, algorithm=""giac"")","\frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}}"," ",0,"1/4*(a/b)^(1/8)*arctan((2*x + sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(a/b)^(1/8)*arctan((2*x - sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(a/b)^(1/8)*arctan((2*x + sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/4*(a/b)^(1/8)*arctan((2*x - sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/8*(a/b)^(1/8)*log(x^2 + x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) - 1/8*(a/b)^(1/8)*log(x^2 - x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) + 1/8*(a/b)^(1/8)*log(x^2 + x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) - 1/8*(a/b)^(1/8)*log(x^2 - x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a*sqrt(2*sqrt(2) + 4))","B",0
1466,1,453,0,0.363879," ","integrate(1/x^2/(b*x^8+a),x, algorithm=""giac"")","-\frac{b \left(\frac{a}{b}\right)^{\frac{7}{8}} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{7}{8}} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{7}{8}} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{7}{8}} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{b \left(\frac{a}{b}\right)^{\frac{7}{8}} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{7}{8}} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{b \left(\frac{a}{b}\right)^{\frac{7}{8}} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{7}{8}} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{1}{a x}"," ",0,"-1/4*b*(a/b)^(7/8)*arctan((2*x + sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/4*b*(a/b)^(7/8)*arctan((2*x - sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/4*b*(a/b)^(7/8)*arctan((2*x + sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/4*b*(a/b)^(7/8)*arctan((2*x - sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) + 1/8*b*(a/b)^(7/8)*log(x^2 + x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/8*b*(a/b)^(7/8)*log(x^2 - x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) + 1/8*b*(a/b)^(7/8)*log(x^2 + x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/8*b*(a/b)^(7/8)*log(x^2 - x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/(a*x)","B",0
1467,1,453,0,0.456697," ","integrate(1/x^4/(b*x^8+a),x, algorithm=""giac"")","\frac{b \left(\frac{a}{b}\right)^{\frac{5}{8}} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{b \left(\frac{a}{b}\right)^{\frac{5}{8}} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{5}{8}} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{5}{8}} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{b \left(\frac{a}{b}\right)^{\frac{5}{8}} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{5}{8}} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{5}{8}} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{b \left(\frac{a}{b}\right)^{\frac{5}{8}} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{1}{3 \, a x^{3}}"," ",0,"1/4*b*(a/b)^(5/8)*arctan((2*x + sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) + 1/4*b*(a/b)^(5/8)*arctan((2*x - sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/4*b*(a/b)^(5/8)*arctan((2*x + sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/4*b*(a/b)^(5/8)*arctan((2*x - sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) + 1/8*b*(a/b)^(5/8)*log(x^2 + x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/8*b*(a/b)^(5/8)*log(x^2 - x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/8*b*(a/b)^(5/8)*log(x^2 + x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) + 1/8*b*(a/b)^(5/8)*log(x^2 - x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/3/(a*x^3)","B",0
1468,1,453,0,0.359746," ","integrate(1/x^6/(b*x^8+a),x, algorithm=""giac"")","\frac{b \left(\frac{a}{b}\right)^{\frac{3}{8}} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{b \left(\frac{a}{b}\right)^{\frac{3}{8}} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{3}{8}} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{3}{8}} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{3}{8}} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{b \left(\frac{a}{b}\right)^{\frac{3}{8}} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{b \left(\frac{a}{b}\right)^{\frac{3}{8}} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{3}{8}} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{1}{5 \, a x^{5}}"," ",0,"1/4*b*(a/b)^(3/8)*arctan((2*x + sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) + 1/4*b*(a/b)^(3/8)*arctan((2*x - sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/4*b*(a/b)^(3/8)*arctan((2*x + sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/4*b*(a/b)^(3/8)*arctan((2*x - sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/8*b*(a/b)^(3/8)*log(x^2 + x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) + 1/8*b*(a/b)^(3/8)*log(x^2 - x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) + 1/8*b*(a/b)^(3/8)*log(x^2 + x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/8*b*(a/b)^(3/8)*log(x^2 - x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/5/(a*x^5)","B",0
1469,1,453,0,0.227606," ","integrate(1/x^8/(b*x^8+a),x, algorithm=""giac"")","-\frac{b \left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} + \frac{b \left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{-2 \, \sqrt{2} + 4}} - \frac{b \left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} + \frac{b \left(\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{b}\right)^{\frac{1}{8}} + \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a^{2} \sqrt{2 \, \sqrt{2} + 4}} - \frac{1}{7 \, a x^{7}}"," ",0,"-1/4*b*(a/b)^(1/8)*arctan((2*x + sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/4*b*(a/b)^(1/8)*arctan((2*x - sqrt(-sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/4*b*(a/b)^(1/8)*arctan((2*x + sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/4*b*(a/b)^(1/8)*arctan((2*x - sqrt(sqrt(2) + 2)*(a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(a/b)^(1/8)))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/8*b*(a/b)^(1/8)*log(x^2 + x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) + 1/8*b*(a/b)^(1/8)*log(x^2 - x*sqrt(sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(-2*sqrt(2) + 4)) - 1/8*b*(a/b)^(1/8)*log(x^2 + x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) + 1/8*b*(a/b)^(1/8)*log(x^2 - x*sqrt(-sqrt(2) + 2)*(a/b)^(1/8) + (a/b)^(1/4))/(a^2*sqrt(2*sqrt(2) + 4)) - 1/7/(a*x^7)","B",0
1470,1,461,0,0.207851," ","integrate(1/(-b*x^8+a),x, algorithm=""giac"")","\frac{\left(-\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(-\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(-\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(-\frac{a}{b}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(-\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}} + \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(-\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}} + \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(-\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}} + \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(-\frac{a}{b}\right)^{\frac{1}{8}} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(-\frac{a}{b}\right)^{\frac{1}{8}} + \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}}"," ",0,"1/4*(-a/b)^(1/8)*arctan((2*x + sqrt(-sqrt(2) + 2)*(-a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(-a/b)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(-a/b)^(1/8)*arctan((2*x - sqrt(-sqrt(2) + 2)*(-a/b)^(1/8))/(sqrt(sqrt(2) + 2)*(-a/b)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) + 1/4*(-a/b)^(1/8)*arctan((2*x + sqrt(sqrt(2) + 2)*(-a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(-a/b)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/4*(-a/b)^(1/8)*arctan((2*x - sqrt(sqrt(2) + 2)*(-a/b)^(1/8))/(sqrt(-sqrt(2) + 2)*(-a/b)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) + 1/8*(-a/b)^(1/8)*log(x^2 + x*sqrt(sqrt(2) + 2)*(-a/b)^(1/8) + (-a/b)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) - 1/8*(-a/b)^(1/8)*log(x^2 - x*sqrt(sqrt(2) + 2)*(-a/b)^(1/8) + (-a/b)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) + 1/8*(-a/b)^(1/8)*log(x^2 + x*sqrt(-sqrt(2) + 2)*(-a/b)^(1/8) + (-a/b)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) - 1/8*(-a/b)^(1/8)*log(x^2 - x*sqrt(-sqrt(2) + 2)*(-a/b)^(1/8) + (-a/b)^(1/4))/(a*sqrt(2*sqrt(2) + 4))","B",0
1471,1,29,0,0.153490," ","integrate(x^9/(-x^8+1),x, algorithm=""giac"")","-\frac{1}{2} \, x^{2} + \frac{1}{4} \, \arctan\left(x^{2}\right) + \frac{1}{8} \, \log\left(x^{2} + 1\right) - \frac{1}{8} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"-1/2*x^2 + 1/4*arctan(x^2) + 1/8*log(x^2 + 1) - 1/8*log(abs(x^2 - 1))","A",0
1472,1,9,0,0.163755," ","integrate(x^7/(-x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \log\left({\left| x^{8} - 1 \right|}\right)"," ",0,"-1/8*log(abs(x^8 - 1))","A",0
1473,1,55,0,0.163352," ","integrate(x^5/(-x^8+1),x, algorithm=""giac"")","\frac{1}{4} \, \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) - \frac{1}{4} \, \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{8} \, \log\left(x^{2} + 1\right) - \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/4*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) - 1/4*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/8*log(x^2 + 1) - 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","B",0
1474,1,18,0,0.153808," ","integrate(x^3/(-x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \log\left(x^{4} + 1\right) - \frac{1}{8} \, \log\left({\left| x^{4} - 1 \right|}\right)"," ",0,"1/8*log(x^4 + 1) - 1/8*log(abs(x^4 - 1))","B",0
1475,1,24,0,0.154218," ","integrate(x/(-x^8+1),x, algorithm=""giac"")","\frac{1}{4} \, \arctan\left(x^{2}\right) + \frac{1}{8} \, \log\left(x^{2} + 1\right) - \frac{1}{8} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"1/4*arctan(x^2) + 1/8*log(x^2 + 1) - 1/8*log(abs(x^2 - 1))","A",0
1476,1,16,0,0.153043," ","integrate(1/x/(-x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \log\left(x^{8}\right) - \frac{1}{8} \, \log\left({\left| x^{8} - 1 \right|}\right)"," ",0,"1/8*log(x^8) - 1/8*log(abs(x^8 - 1))","A",0
1477,1,29,0,0.160476," ","integrate(1/x^3/(-x^8+1),x, algorithm=""giac"")","-\frac{1}{2 \, x^{2}} - \frac{1}{4} \, \arctan\left(x^{2}\right) + \frac{1}{8} \, \log\left(x^{2} + 1\right) - \frac{1}{8} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"-1/2/x^2 - 1/4*arctan(x^2) + 1/8*log(x^2 + 1) - 1/8*log(abs(x^2 - 1))","A",0
1478,1,23,0,0.151952," ","integrate(1/x^5/(-x^8+1),x, algorithm=""giac"")","-\frac{1}{4 \, x^{4}} + \frac{1}{8} \, \log\left(x^{4} + 1\right) - \frac{1}{8} \, \log\left({\left| x^{4} - 1 \right|}\right)"," ",0,"-1/4/x^4 + 1/8*log(x^4 + 1) - 1/8*log(abs(x^4 - 1))","A",0
1479,1,29,0,0.316044," ","integrate(1/x^7/(-x^8+1),x, algorithm=""giac"")","-\frac{1}{6 \, x^{6}} + \frac{1}{4} \, \arctan\left(x^{2}\right) + \frac{1}{8} \, \log\left(x^{2} + 1\right) - \frac{1}{8} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"-1/6/x^6 + 1/4*arctan(x^2) + 1/8*log(x^2 + 1) - 1/8*log(abs(x^2 - 1))","A",0
1480,1,26,0,0.157141," ","integrate(1/x^9/(-x^8+1),x, algorithm=""giac"")","-\frac{x^{8} + 1}{8 \, x^{8}} + \frac{1}{8} \, \log\left(x^{8}\right) - \frac{1}{8} \, \log\left({\left| x^{8} - 1 \right|}\right)"," ",0,"-1/8*(x^8 + 1)/x^8 + 1/8*log(x^8) - 1/8*log(abs(x^8 - 1))","A",0
1481,1,93,0,0.155209," ","integrate(x^8/(-x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - x + \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - x + 1/4*arctan(x) + 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","A",0
1482,1,90,0,0.151959," ","integrate(x^6/(-x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) - \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) - 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/4*arctan(x) + 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","A",0
1483,1,90,0,0.170845," ","integrate(x^4/(-x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) - \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) + \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) - 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) - 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) + 1/4*arctan(x) + 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","A",0
1484,1,90,0,0.151057," ","integrate(x^2/(-x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) - 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/4*arctan(x) + 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","A",0
1485,1,90,0,0.147620," ","integrate(1/(-x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) + \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) + 1/4*arctan(x) + 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","A",0
1486,1,95,0,0.170276," ","integrate(1/x^2/(-x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) - \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{1}{x} - \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) - 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/x - 1/4*arctan(x) + 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","A",0
1487,1,95,0,0.153734," ","integrate(1/x^4/(-x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) - \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{1}{3 \, x^{3}} + \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) - 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) - 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/3/x^3 + 1/4*arctan(x) + 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","A",0
1488,1,95,0,0.179189," ","integrate(1/x^6/(-x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{1}{5 \, x^{5}} - \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) - 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) + 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/5/x^5 - 1/4*arctan(x) + 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","A",0
1489,1,95,0,0.152971," ","integrate(1/x^8/(-x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) - \frac{1}{7 \, x^{7}} + \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) - 1/7/x^7 + 1/4*arctan(x) + 1/8*log(abs(x + 1)) - 1/8*log(abs(x - 1))","A",0
1490,1,85,0,0.169338," ","integrate(x^9/(x^8+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x^{2} + \sqrt{2}\right)}\right) - \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x^{2} - \sqrt{2}\right)}\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{4} + \sqrt{2} x^{2} + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{4} - \sqrt{2} x^{2} + 1\right)"," ",0,"1/2*x^2 - 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x^2 + sqrt(2))) - 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x^2 - sqrt(2))) - 1/16*sqrt(2)*log(x^4 + sqrt(2)*x^2 + 1) + 1/16*sqrt(2)*log(x^4 - sqrt(2)*x^2 + 1)","A",0
1491,1,8,0,0.169089," ","integrate(x^7/(x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \log\left(x^{8} + 1\right)"," ",0,"1/8*log(x^8 + 1)","A",0
1492,1,199,0,0.306796," ","integrate(x^5/(x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"-1/8*sqrt(2)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(2)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(2)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/8*sqrt(2)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/16*sqrt(2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) + 1/16*sqrt(2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 1/16*sqrt(2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","B",0
1493,1,6,0,0.170189," ","integrate(x^3/(x^8+1),x, algorithm=""giac"")","\frac{1}{4} \, \arctan\left(x^{4}\right)"," ",0,"1/4*arctan(x^4)","A",0
1494,1,80,0,0.169572," ","integrate(x/(x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x^{2} + \sqrt{2}\right)}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x^{2} - \sqrt{2}\right)}\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{4} + \sqrt{2} x^{2} + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{4} - \sqrt{2} x^{2} + 1\right)"," ",0,"1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x^2 + sqrt(2))) + 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x^2 - sqrt(2))) + 1/16*sqrt(2)*log(x^4 + sqrt(2)*x^2 + 1) - 1/16*sqrt(2)*log(x^4 - sqrt(2)*x^2 + 1)","A",0
1495,1,15,0,0.167753," ","integrate(1/x/(x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \log\left(x^{8} + 1\right) + \frac{1}{8} \, \log\left(x^{8}\right)"," ",0,"-1/8*log(x^8 + 1) + 1/8*log(x^8)","A",0
1496,1,97,0,0.236029," ","integrate(1/x^3/(x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{2} x^{4} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x^{2} + \sqrt{2}\right)}\right) - \frac{1}{8} \, \sqrt{2} x^{4} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x^{2} - \sqrt{2}\right)}\right) - \frac{1}{16} \, \sqrt{2} x^{4} \log\left(x^{4} + \sqrt{2} x^{2} + 1\right) + \frac{1}{16} \, \sqrt{2} x^{4} \log\left(x^{4} - \sqrt{2} x^{2} + 1\right) - \frac{1}{2 \, x^{2}}"," ",0,"-1/8*sqrt(2)*x^4*arctan(1/2*sqrt(2)*(2*x^2 + sqrt(2))) - 1/8*sqrt(2)*x^4*arctan(1/2*sqrt(2)*(2*x^2 - sqrt(2))) - 1/16*sqrt(2)*x^4*log(x^4 + sqrt(2)*x^2 + 1) + 1/16*sqrt(2)*x^4*log(x^4 - sqrt(2)*x^2 + 1) - 1/2/x^2","A",0
1497,1,12,0,0.165713," ","integrate(1/x^5/(x^8+1),x, algorithm=""giac"")","-\frac{1}{4 \, x^{4}} - \frac{1}{4} \, \arctan\left(x^{4}\right)"," ",0,"-1/4/x^4 - 1/4*arctan(x^4)","A",0
1498,1,85,0,0.171108," ","integrate(1/x^7/(x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x^{2} + \sqrt{2}\right)}\right) - \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x^{2} - \sqrt{2}\right)}\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{4} + \sqrt{2} x^{2} + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{4} - \sqrt{2} x^{2} + 1\right) - \frac{1}{6 \, x^{6}}"," ",0,"-1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x^2 + sqrt(2))) - 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x^2 - sqrt(2))) - 1/16*sqrt(2)*log(x^4 + sqrt(2)*x^2 + 1) + 1/16*sqrt(2)*log(x^4 - sqrt(2)*x^2 + 1) - 1/6/x^6","A",0
1499,1,25,0,0.171694," ","integrate(1/x^9/(x^8+1),x, algorithm=""giac"")","\frac{x^{8} - 1}{8 \, x^{8}} + \frac{1}{8} \, \log\left(x^{8} + 1\right) - \frac{1}{8} \, \log\left(x^{8}\right)"," ",0,"1/8*(x^8 - 1)/x^8 + 1/8*log(x^8 + 1) - 1/8*log(x^8)","A",0
1500,1,240,0,0.203996," ","integrate(x^8/(x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right) + x"," ",0,"-1/8*sqrt(sqrt(2) + 2)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(sqrt(2) + 2)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/16*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) + 1/16*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + 1/16*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1) + x","A",0
1501,1,239,0,0.310844," ","integrate(x^6/(x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"1/8*sqrt(sqrt(2) + 2)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(sqrt(2) + 2)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/16*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) + 1/16*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + 1/16*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","A",0
1502,1,239,0,0.311013," ","integrate(x^4/(x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"-1/8*sqrt(-sqrt(2) + 2)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(sqrt(2) + 2)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/8*sqrt(sqrt(2) + 2)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/16*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) + 1/16*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) + 1/16*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 1/16*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","A",0
1503,1,239,0,0.332635," ","integrate(x^2/(x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"-1/8*sqrt(-sqrt(2) + 2)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(sqrt(2) + 2)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/8*sqrt(sqrt(2) + 2)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/16*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + 1/16*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","A",0
1504,1,239,0,0.168564," ","integrate(1/(x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"1/8*sqrt(sqrt(2) + 2)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(sqrt(2) + 2)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/16*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) + 1/16*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 1/16*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","A",0
1505,1,244,0,0.331439," ","integrate(1/x^2/(x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{x}"," ",0,"-1/8*sqrt(sqrt(2) + 2)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(sqrt(2) + 2)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/16*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) + 1/16*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 1/16*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - 1/x","A",0
1506,1,244,0,0.309220," ","integrate(1/x^4/(x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{3 \, x^{3}}"," ",0,"1/8*sqrt(-sqrt(2) + 2)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(sqrt(2) + 2)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(sqrt(2) + 2)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/16*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + 1/16*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - 1/3/x^3","A",0
1507,1,244,0,0.341466," ","integrate(1/x^6/(x^8+1),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{5 \, x^{5}}"," ",0,"1/8*sqrt(-sqrt(2) + 2)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(sqrt(2) + 2)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(sqrt(2) + 2)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/16*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) + 1/16*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) + 1/16*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 1/16*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - 1/5/x^5","A",0
1508,1,244,0,0.188297," ","integrate(1/x^8/(x^8+1),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{16} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{7 \, x^{7}}"," ",0,"-1/8*sqrt(sqrt(2) + 2)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(sqrt(2) + 2)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(-sqrt(2) + 2)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/16*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) + 1/16*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) - 1/16*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + 1/16*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - 1/7/x^7","A",0
1509,1,29,0,0.161601," ","integrate(x^3*(x^8+1)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{x^{8} + 1} x^{4} - \frac{1}{8} \, \log\left(-x^{4} + \sqrt{x^{8} + 1}\right)"," ",0,"1/8*sqrt(x^8 + 1)*x^4 - 1/8*log(-x^4 + sqrt(x^8 + 1))","A",0
1510,0,0,0,0.000000," ","integrate(x*(x^8+1)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{8} + 1} x\,{d x}"," ",0,"integrate(sqrt(x^8 + 1)*x, x)","F",0
1511,1,34,0,0.152111," ","integrate((x^8+1)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{x^{8} + 1} - \frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} + 1\right) + \frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} - 1\right)"," ",0,"1/4*sqrt(x^8 + 1) - 1/8*log(sqrt(x^8 + 1) + 1) + 1/8*log(sqrt(x^8 + 1) - 1)","A",0
1512,0,0,0,0.000000," ","integrate((x^8+1)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{x^{8} + 1}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(x^8 + 1)/x^3, x)","F",0
1513,1,29,0,0.158197," ","integrate(x^3*(x^8-2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{x^{8} - 2} x^{4} + \frac{1}{4} \, \log\left(x^{4} - \sqrt{x^{8} - 2}\right)"," ",0,"1/8*sqrt(x^8 - 2)*x^4 + 1/4*log(x^4 - sqrt(x^8 - 2))","A",0
1514,1,36,0,0.165998," ","integrate(x^19/(x^8+1)^(1/2),x, algorithm=""giac"")","\frac{1}{32} \, {\left(2 \, x^{8} - 3\right)} \sqrt{x^{8} + 1} x^{4} - \frac{3}{32} \, \log\left(-x^{4} + \sqrt{x^{8} + 1}\right)"," ",0,"1/32*(2*x^8 - 3)*sqrt(x^8 + 1)*x^4 - 3/32*log(-x^4 + sqrt(x^8 + 1))","A",0
1515,1,19,0,0.149520," ","integrate(x^15/(x^8+1)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(x^{8} + 1\right)}^{\frac{3}{2}} - \frac{1}{4} \, \sqrt{x^{8} + 1}"," ",0,"1/12*(x^8 + 1)^(3/2) - 1/4*sqrt(x^8 + 1)","A",0
1516,1,29,0,0.163244," ","integrate(x^11/(x^8+1)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{x^{8} + 1} x^{4} + \frac{1}{8} \, \log\left(-x^{4} + \sqrt{x^{8} + 1}\right)"," ",0,"1/8*sqrt(x^8 + 1)*x^4 + 1/8*log(-x^4 + sqrt(x^8 + 1))","A",0
1517,1,9,0,0.146712," ","integrate(x^7/(x^8+1)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{x^{8} + 1}"," ",0,"1/4*sqrt(x^8 + 1)","A",0
1518,1,16,0,0.158989," ","integrate(x^3/(x^8+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \log\left(-x^{4} + \sqrt{x^{8} + 1}\right)"," ",0,"-1/4*log(-x^4 + sqrt(x^8 + 1))","B",0
1519,1,25,0,0.214493," ","integrate(1/x/(x^8+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} + 1\right) + \frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} - 1\right)"," ",0,"-1/8*log(sqrt(x^8 + 1) + 1) + 1/8*log(sqrt(x^8 + 1) - 1)","B",0
1520,1,21,0,0.166721," ","integrate(1/x^5/(x^8+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2 \, {\left({\left(x^{4} - \sqrt{x^{8} + 1}\right)}^{2} - 1\right)}}"," ",0,"1/2/((x^4 - sqrt(x^8 + 1))^2 - 1)","A",0
1521,1,37,0,0.146967," ","integrate(1/x^9/(x^8+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{x^{8} + 1}}{8 \, x^{8}} + \frac{1}{16} \, \log\left(\sqrt{x^{8} + 1} + 1\right) - \frac{1}{16} \, \log\left(\sqrt{x^{8} + 1} - 1\right)"," ",0,"-1/8*sqrt(x^8 + 1)/x^8 + 1/16*log(sqrt(x^8 + 1) + 1) - 1/16*log(sqrt(x^8 + 1) - 1)","A",0
1522,1,40,0,0.168043," ","integrate(1/x^13/(x^8+1)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(x^{4} - \sqrt{x^{8} + 1}\right)}^{2} - 1}{3 \, {\left({\left(x^{4} - \sqrt{x^{8} + 1}\right)}^{2} - 1\right)}^{3}}"," ",0,"1/3*(3*(x^4 - sqrt(x^8 + 1))^2 - 1)/((x^4 - sqrt(x^8 + 1))^2 - 1)^3","A",0
1523,1,49,0,0.149162," ","integrate(1/x^17/(x^8+1)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(x^{8} + 1\right)}^{\frac{3}{2}} - 5 \, \sqrt{x^{8} + 1}}{32 \, x^{16}} - \frac{3}{64} \, \log\left(\sqrt{x^{8} + 1} + 1\right) + \frac{3}{64} \, \log\left(\sqrt{x^{8} + 1} - 1\right)"," ",0,"1/32*(3*(x^8 + 1)^(3/2) - 5*sqrt(x^8 + 1))/x^16 - 3/64*log(sqrt(x^8 + 1) + 1) + 3/64*log(sqrt(x^8 + 1) - 1)","A",0
1524,0,0,0,0.000000," ","integrate(x^13/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{13}}{\sqrt{x^{8} + 1}}\,{d x}"," ",0,"integrate(x^13/sqrt(x^8 + 1), x)","F",0
1525,0,0,0,0.000000," ","integrate(x^9/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{9}}{\sqrt{x^{8} + 1}}\,{d x}"," ",0,"integrate(x^9/sqrt(x^8 + 1), x)","F",0
1526,0,0,0,0.000000," ","integrate(x^5/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{5}}{\sqrt{x^{8} + 1}}\,{d x}"," ",0,"integrate(x^5/sqrt(x^8 + 1), x)","F",0
1527,0,0,0,0.000000," ","integrate(x/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{8} + 1}}\,{d x}"," ",0,"integrate(x/sqrt(x^8 + 1), x)","F",0
1528,0,0,0,0.000000," ","integrate(1/x^3/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{8} + 1} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(x^8 + 1)*x^3), x)","F",0
1529,0,0,0,0.000000," ","integrate(1/x^7/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{8} + 1} x^{7}}\,{d x}"," ",0,"integrate(1/(sqrt(x^8 + 1)*x^7), x)","F",0
1530,0,0,0,0.000000," ","integrate(x^10/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{10}}{\sqrt{x^{8} + 1}}\,{d x}"," ",0,"integrate(x^10/sqrt(x^8 + 1), x)","F",0
1531,0,0,0,0.000000," ","integrate(x^8/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{8}}{\sqrt{x^{8} + 1}}\,{d x}"," ",0,"integrate(x^8/sqrt(x^8 + 1), x)","F",0
1532,0,0,0,0.000000," ","integrate(x^6/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{x^{8} + 1}}\,{d x}"," ",0,"integrate(x^6/sqrt(x^8 + 1), x)","F",0
1533,0,0,0,0.000000," ","integrate(x^4/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{x^{8} + 1}}\,{d x}"," ",0,"integrate(x^4/sqrt(x^8 + 1), x)","F",0
1534,0,0,0,0.000000," ","integrate(x^2/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{x^{8} + 1}}\,{d x}"," ",0,"integrate(x^2/sqrt(x^8 + 1), x)","F",0
1535,0,0,0,0.000000," ","integrate(1/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{8} + 1}}\,{d x}"," ",0,"integrate(1/sqrt(x^8 + 1), x)","F",0
1536,0,0,0,0.000000," ","integrate(1/x^2/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{8} + 1} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^8 + 1)*x^2), x)","F",0
1537,0,0,0,0.000000," ","integrate(1/x^4/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{8} + 1} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(x^8 + 1)*x^4), x)","F",0
1538,0,0,0,0.000000," ","integrate(1/x^6/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{8} + 1} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(x^8 + 1)*x^6), x)","F",0
1539,0,0,0,0.000000," ","integrate(1/x^8/(x^8+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{8} + 1} x^{8}}\,{d x}"," ",0,"integrate(1/(sqrt(x^8 + 1)*x^8), x)","F",0
1540,1,223,0,0.202665," ","integrate(1/(-x^10+1),x, algorithm=""giac"")","\frac{1}{40} \, {\left(\sqrt{5} + 1\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) - \frac{1}{40} \, {\left(\sqrt{5} + 1\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} + 1\right)} + 1\right) + \frac{1}{40} \, {\left(\sqrt{5} - 1\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right) - \frac{1}{40} \, {\left(\sqrt{5} - 1\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} - 1\right)} + 1\right) + \frac{1}{20} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x + \sqrt{5} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) + \frac{1}{20} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x - \sqrt{5} + 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) + \frac{1}{20} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x + \sqrt{5} + 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) + \frac{1}{20} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{4 \, x - \sqrt{5} - 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) + \frac{1}{10} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{10} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/40*(sqrt(5) + 1)*log(x^2 + 1/2*x*(sqrt(5) + 1) + 1) - 1/40*(sqrt(5) + 1)*log(x^2 - 1/2*x*(sqrt(5) + 1) + 1) + 1/40*(sqrt(5) - 1)*log(x^2 + 1/2*x*(sqrt(5) - 1) + 1) - 1/40*(sqrt(5) - 1)*log(x^2 - 1/2*x*(sqrt(5) - 1) + 1) + 1/20*sqrt(2*sqrt(5) + 10)*arctan((4*x + sqrt(5) - 1)/sqrt(2*sqrt(5) + 10)) + 1/20*sqrt(2*sqrt(5) + 10)*arctan((4*x - sqrt(5) + 1)/sqrt(2*sqrt(5) + 10)) + 1/20*sqrt(-2*sqrt(5) + 10)*arctan((4*x + sqrt(5) + 1)/sqrt(-2*sqrt(5) + 10)) + 1/20*sqrt(-2*sqrt(5) + 10)*arctan((4*x - sqrt(5) - 1)/sqrt(-2*sqrt(5) + 10)) + 1/10*log(abs(x + 1)) - 1/10*log(abs(x - 1))","A",0
1541,1,6,0,0.196043," ","integrate(x^4/(-x^10+1)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, \arcsin\left(x^{5}\right)"," ",0,"1/5*arcsin(x^5)","A",0
1542,1,17,0,0.195287," ","integrate(x^4/(x^10-2)^(1/2),x, algorithm=""giac"")","-\frac{1}{5} \, \log\left({\left| -x^{5} + \sqrt{x^{10} - 2} \right|}\right)"," ",0,"-1/5*log(abs(-x^5 + sqrt(x^10 - 2)))","A",0
1543,1,8,0,0.173112," ","integrate(x^5/(x^12+9),x, algorithm=""giac"")","\frac{1}{18} \, \arctan\left(\frac{1}{3} \, x^{6}\right)"," ",0,"1/18*arctan(1/3*x^6)","A",0
1544,1,18,0,0.198573," ","integrate(x^5/(-x^12+9),x, algorithm=""giac"")","\frac{1}{36} \, \log\left(x^{6} + 3\right) - \frac{1}{36} \, \log\left({\left| x^{6} - 3 \right|}\right)"," ",0,"1/36*log(x^6 + 3) - 1/36*log(abs(x^6 - 3))","B",0
1545,1,29,0,0.194459," ","integrate(x^5*(x^12+9)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{x^{12} + 9} x^{6} - \frac{3}{4} \, \log\left(-x^{6} + \sqrt{x^{12} + 9}\right)"," ",0,"1/12*sqrt(x^12 + 9)*x^6 - 3/4*log(-x^6 + sqrt(x^12 + 9))","A",0
1546,1,13,0,0.163302," ","integrate((a+b/x)*x^6,x, algorithm=""giac"")","\frac{1}{7} \, a x^{7} + \frac{1}{6} \, b x^{6}"," ",0,"1/7*a*x^7 + 1/6*b*x^6","A",0
1547,1,13,0,0.186483," ","integrate((a+b/x)*x^5,x, algorithm=""giac"")","\frac{1}{6} \, a x^{6} + \frac{1}{5} \, b x^{5}"," ",0,"1/6*a*x^6 + 1/5*b*x^5","A",0
1548,1,13,0,0.152444," ","integrate((a+b/x)*x^4,x, algorithm=""giac"")","\frac{1}{5} \, a x^{5} + \frac{1}{4} \, b x^{4}"," ",0,"1/5*a*x^5 + 1/4*b*x^4","A",0
1549,1,13,0,0.164288," ","integrate((a+b/x)*x^3,x, algorithm=""giac"")","\frac{1}{4} \, a x^{4} + \frac{1}{3} \, b x^{3}"," ",0,"1/4*a*x^4 + 1/3*b*x^3","A",0
1550,1,13,0,0.146737," ","integrate((a+b/x)*x^2,x, algorithm=""giac"")","\frac{1}{3} \, a x^{3} + \frac{1}{2} \, b x^{2}"," ",0,"1/3*a*x^3 + 1/2*b*x^2","A",0
1551,1,10,0,0.163917," ","integrate((a+b/x)*x,x, algorithm=""giac"")","\frac{1}{2} \, a x^{2} + b x"," ",0,"1/2*a*x^2 + b*x","A",0
1552,1,9,0,0.168707," ","integrate(a+b/x,x, algorithm=""giac"")","a x + b \log\left({\left| x \right|}\right)"," ",0,"a*x + b*log(abs(x))","A",0
1553,1,12,0,0.180283," ","integrate((a+b/x)/x,x, algorithm=""giac"")","a \log\left({\left| x \right|}\right) - \frac{b}{x}"," ",0,"a*log(abs(x)) - b/x","A",0
1554,1,13,0,0.147980," ","integrate((a+b/x)/x^2,x, algorithm=""giac"")","-\frac{a}{x} - \frac{b}{2 \, x^{2}}"," ",0,"-a/x - 1/2*b/x^2","A",0
1555,1,13,0,0.154848," ","integrate((a+b/x)/x^3,x, algorithm=""giac"")","-\frac{3 \, a x + 2 \, b}{6 \, x^{3}}"," ",0,"-1/6*(3*a*x + 2*b)/x^3","A",0
1556,1,13,0,0.147895," ","integrate((a+b/x)/x^4,x, algorithm=""giac"")","-\frac{4 \, a x + 3 \, b}{12 \, x^{4}}"," ",0,"-1/12*(4*a*x + 3*b)/x^4","A",0
1557,1,13,0,0.174336," ","integrate((a+b/x)/x^5,x, algorithm=""giac"")","-\frac{5 \, a x + 4 \, b}{20 \, x^{5}}"," ",0,"-1/20*(5*a*x + 4*b)/x^5","A",0
1558,1,13,0,0.158330," ","integrate((a+b/x)/x^6,x, algorithm=""giac"")","-\frac{6 \, a x + 5 \, b}{30 \, x^{6}}"," ",0,"-1/30*(6*a*x + 5*b)/x^6","A",0
1559,1,24,0,0.160210," ","integrate((a+b/x)^2*x^5,x, algorithm=""giac"")","\frac{1}{6} \, a^{2} x^{6} + \frac{2}{5} \, a b x^{5} + \frac{1}{4} \, b^{2} x^{4}"," ",0,"1/6*a^2*x^6 + 2/5*a*b*x^5 + 1/4*b^2*x^4","A",0
1560,1,24,0,0.151294," ","integrate((a+b/x)^2*x^4,x, algorithm=""giac"")","\frac{1}{5} \, a^{2} x^{5} + \frac{1}{2} \, a b x^{4} + \frac{1}{3} \, b^{2} x^{3}"," ",0,"1/5*a^2*x^5 + 1/2*a*b*x^4 + 1/3*b^2*x^3","A",0
1561,1,24,0,0.182261," ","integrate((a+b/x)^2*x^3,x, algorithm=""giac"")","\frac{1}{4} \, a^{2} x^{4} + \frac{2}{3} \, a b x^{3} + \frac{1}{2} \, b^{2} x^{2}"," ",0,"1/4*a^2*x^4 + 2/3*a*b*x^3 + 1/2*b^2*x^2","A",0
1562,1,20,0,0.154930," ","integrate((a+b/x)^2*x^2,x, algorithm=""giac"")","\frac{1}{3} \, a^{2} x^{3} + a b x^{2} + b^{2} x"," ",0,"1/3*a^2*x^3 + a*b*x^2 + b^2*x","A",0
1563,1,21,0,0.159162," ","integrate((a+b/x)^2*x,x, algorithm=""giac"")","\frac{1}{2} \, a^{2} x^{2} + 2 \, a b x + b^{2} \log\left({\left| x \right|}\right)"," ",0,"1/2*a^2*x^2 + 2*a*b*x + b^2*log(abs(x))","A",0
1564,1,21,0,0.170773," ","integrate((a+b/x)^2,x, algorithm=""giac"")","a^{2} x + 2 \, a b \log\left({\left| x \right|}\right) - \frac{b^{2}}{x}"," ",0,"a^2*x + 2*a*b*log(abs(x)) - b^2/x","A",0
1565,1,22,0,0.153106," ","integrate((a+b/x)^2/x,x, algorithm=""giac"")","a^{2} \log\left({\left| x \right|}\right) - \frac{4 \, a b x + b^{2}}{2 \, x^{2}}"," ",0,"a^2*log(abs(x)) - 1/2*(4*a*b*x + b^2)/x^2","A",0
1566,1,14,0,0.148678," ","integrate((a+b/x)^2/x^2,x, algorithm=""giac"")","-\frac{{\left(a + \frac{b}{x}\right)}^{3}}{3 \, b}"," ",0,"-1/3*(a + b/x)^3/b","A",0
1567,1,24,0,0.149167," ","integrate((a+b/x)^2/x^3,x, algorithm=""giac"")","-\frac{6 \, a^{2} x^{2} + 8 \, a b x + 3 \, b^{2}}{12 \, x^{4}}"," ",0,"-1/12*(6*a^2*x^2 + 8*a*b*x + 3*b^2)/x^4","A",0
1568,1,24,0,0.174783," ","integrate((a+b/x)^2/x^4,x, algorithm=""giac"")","-\frac{10 \, a^{2} x^{2} + 15 \, a b x + 6 \, b^{2}}{30 \, x^{5}}"," ",0,"-1/30*(10*a^2*x^2 + 15*a*b*x + 6*b^2)/x^5","A",0
1569,1,24,0,0.149489," ","integrate((a+b/x)^2/x^5,x, algorithm=""giac"")","-\frac{15 \, a^{2} x^{2} + 24 \, a b x + 10 \, b^{2}}{60 \, x^{6}}"," ",0,"-1/60*(15*a^2*x^2 + 24*a*b*x + 10*b^2)/x^6","A",0
1570,1,35,0,0.163301," ","integrate((a+b/x)^3*x^6,x, algorithm=""giac"")","\frac{1}{7} \, a^{3} x^{7} + \frac{1}{2} \, a^{2} b x^{6} + \frac{3}{5} \, a b^{2} x^{5} + \frac{1}{4} \, b^{3} x^{4}"," ",0,"1/7*a^3*x^7 + 1/2*a^2*b*x^6 + 3/5*a*b^2*x^5 + 1/4*b^3*x^4","A",0
1571,1,35,0,0.170234," ","integrate((a+b/x)^3*x^5,x, algorithm=""giac"")","\frac{1}{6} \, a^{3} x^{6} + \frac{3}{5} \, a^{2} b x^{5} + \frac{3}{4} \, a b^{2} x^{4} + \frac{1}{3} \, b^{3} x^{3}"," ",0,"1/6*a^3*x^6 + 3/5*a^2*b*x^5 + 3/4*a*b^2*x^4 + 1/3*b^3*x^3","A",0
1572,1,34,0,0.148327," ","integrate((a+b/x)^3*x^4,x, algorithm=""giac"")","\frac{1}{5} \, a^{3} x^{5} + \frac{3}{4} \, a^{2} b x^{4} + a b^{2} x^{3} + \frac{1}{2} \, b^{3} x^{2}"," ",0,"1/5*a^3*x^5 + 3/4*a^2*b*x^4 + a*b^2*x^3 + 1/2*b^3*x^2","A",0
1573,1,31,0,0.145755," ","integrate((a+b/x)^3*x^3,x, algorithm=""giac"")","\frac{1}{4} \, a^{3} x^{4} + a^{2} b x^{3} + \frac{3}{2} \, a b^{2} x^{2} + b^{3} x"," ",0,"1/4*a^3*x^4 + a^2*b*x^3 + 3/2*a*b^2*x^2 + b^3*x","B",0
1574,1,32,0,0.151904," ","integrate((a+b/x)^3*x^2,x, algorithm=""giac"")","\frac{1}{3} \, a^{3} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + 3 \, a b^{2} x + b^{3} \log\left({\left| x \right|}\right)"," ",0,"1/3*a^3*x^3 + 3/2*a^2*b*x^2 + 3*a*b^2*x + b^3*log(abs(x))","A",0
1575,1,33,0,0.147269," ","integrate((a+b/x)^3*x,x, algorithm=""giac"")","\frac{1}{2} \, a^{3} x^{2} + 3 \, a^{2} b x + 3 \, a b^{2} \log\left({\left| x \right|}\right) - \frac{b^{3}}{x}"," ",0,"1/2*a^3*x^2 + 3*a^2*b*x + 3*a*b^2*log(abs(x)) - b^3/x","A",0
1576,1,31,0,0.150379," ","integrate((a+b/x)^3,x, algorithm=""giac"")","a^{3} x + 3 \, a^{2} b \log\left({\left| x \right|}\right) - \frac{6 \, a b^{2} x + b^{3}}{2 \, x^{2}}"," ",0,"a^3*x + 3*a^2*b*log(abs(x)) - 1/2*(6*a*b^2*x + b^3)/x^2","A",0
1577,1,35,0,0.190278," ","integrate((a+b/x)^3/x,x, algorithm=""giac"")","a^{3} \log\left({\left| x \right|}\right) - \frac{18 \, a^{2} b x^{2} + 9 \, a b^{2} x + 2 \, b^{3}}{6 \, x^{3}}"," ",0,"a^3*log(abs(x)) - 1/6*(18*a^2*b*x^2 + 9*a*b^2*x + 2*b^3)/x^3","A",0
1578,1,14,0,0.150431," ","integrate((a+b/x)^3/x^2,x, algorithm=""giac"")","-\frac{{\left(a + \frac{b}{x}\right)}^{4}}{4 \, b}"," ",0,"-1/4*(a + b/x)^4/b","A",0
1579,1,35,0,0.149264," ","integrate((a+b/x)^3/x^3,x, algorithm=""giac"")","-\frac{10 \, a^{3} x^{3} + 20 \, a^{2} b x^{2} + 15 \, a b^{2} x + 4 \, b^{3}}{20 \, x^{5}}"," ",0,"-1/20*(10*a^3*x^3 + 20*a^2*b*x^2 + 15*a*b^2*x + 4*b^3)/x^5","A",0
1580,1,35,0,0.149439," ","integrate((a+b/x)^3/x^4,x, algorithm=""giac"")","-\frac{20 \, a^{3} x^{3} + 45 \, a^{2} b x^{2} + 36 \, a b^{2} x + 10 \, b^{3}}{60 \, x^{6}}"," ",0,"-1/60*(20*a^3*x^3 + 45*a^2*b*x^2 + 36*a*b^2*x + 10*b^3)/x^6","A",0
1581,1,35,0,0.154532," ","integrate((a+b/x)^3/x^5,x, algorithm=""giac"")","-\frac{35 \, a^{3} x^{3} + 84 \, a^{2} b x^{2} + 70 \, a b^{2} x + 20 \, b^{3}}{140 \, x^{7}}"," ",0,"-1/140*(35*a^3*x^3 + 84*a^2*b*x^2 + 70*a*b^2*x + 20*b^3)/x^7","A",0
1582,1,35,0,0.152127," ","integrate((a+b/x)^3/x^6,x, algorithm=""giac"")","-\frac{56 \, a^{3} x^{3} + 140 \, a^{2} b x^{2} + 120 \, a b^{2} x + 35 \, b^{3}}{280 \, x^{8}}"," ",0,"-1/280*(56*a^3*x^3 + 140*a^2*b*x^2 + 120*a*b^2*x + 35*b^3)/x^8","A",0
1583,1,90,0,0.154496," ","integrate((a+b/x)^8*x^16,x, algorithm=""giac"")","\frac{1}{17} \, a^{8} x^{17} + \frac{1}{2} \, a^{7} b x^{16} + \frac{28}{15} \, a^{6} b^{2} x^{15} + 4 \, a^{5} b^{3} x^{14} + \frac{70}{13} \, a^{4} b^{4} x^{13} + \frac{14}{3} \, a^{3} b^{5} x^{12} + \frac{28}{11} \, a^{2} b^{6} x^{11} + \frac{4}{5} \, a b^{7} x^{10} + \frac{1}{9} \, b^{8} x^{9}"," ",0,"1/17*a^8*x^17 + 1/2*a^7*b*x^16 + 28/15*a^6*b^2*x^15 + 4*a^5*b^3*x^14 + 70/13*a^4*b^4*x^13 + 14/3*a^3*b^5*x^12 + 28/11*a^2*b^6*x^11 + 4/5*a*b^7*x^10 + 1/9*b^8*x^9","A",0
1584,1,90,0,0.159971," ","integrate((a+b/x)^8*x^15,x, algorithm=""giac"")","\frac{1}{16} \, a^{8} x^{16} + \frac{8}{15} \, a^{7} b x^{15} + 2 \, a^{6} b^{2} x^{14} + \frac{56}{13} \, a^{5} b^{3} x^{13} + \frac{35}{6} \, a^{4} b^{4} x^{12} + \frac{56}{11} \, a^{3} b^{5} x^{11} + \frac{14}{5} \, a^{2} b^{6} x^{10} + \frac{8}{9} \, a b^{7} x^{9} + \frac{1}{8} \, b^{8} x^{8}"," ",0,"1/16*a^8*x^16 + 8/15*a^7*b*x^15 + 2*a^6*b^2*x^14 + 56/13*a^5*b^3*x^13 + 35/6*a^4*b^4*x^12 + 56/11*a^3*b^5*x^11 + 14/5*a^2*b^6*x^10 + 8/9*a*b^7*x^9 + 1/8*b^8*x^8","A",0
1585,1,90,0,0.151771," ","integrate((a+b/x)^8*x^13,x, algorithm=""giac"")","\frac{1}{14} \, a^{8} x^{14} + \frac{8}{13} \, a^{7} b x^{13} + \frac{7}{3} \, a^{6} b^{2} x^{12} + \frac{56}{11} \, a^{5} b^{3} x^{11} + 7 \, a^{4} b^{4} x^{10} + \frac{56}{9} \, a^{3} b^{5} x^{9} + \frac{7}{2} \, a^{2} b^{6} x^{8} + \frac{8}{7} \, a b^{7} x^{7} + \frac{1}{6} \, b^{8} x^{6}"," ",0,"1/14*a^8*x^14 + 8/13*a^7*b*x^13 + 7/3*a^6*b^2*x^12 + 56/11*a^5*b^3*x^11 + 7*a^4*b^4*x^10 + 56/9*a^3*b^5*x^9 + 7/2*a^2*b^6*x^8 + 8/7*a*b^7*x^7 + 1/6*b^8*x^6","A",0
1586,1,90,0,0.156906," ","integrate((a+b/x)^8*x^12,x, algorithm=""giac"")","\frac{1}{13} \, a^{8} x^{13} + \frac{2}{3} \, a^{7} b x^{12} + \frac{28}{11} \, a^{6} b^{2} x^{11} + \frac{28}{5} \, a^{5} b^{3} x^{10} + \frac{70}{9} \, a^{4} b^{4} x^{9} + 7 \, a^{3} b^{5} x^{8} + 4 \, a^{2} b^{6} x^{7} + \frac{4}{3} \, a b^{7} x^{6} + \frac{1}{5} \, b^{8} x^{5}"," ",0,"1/13*a^8*x^13 + 2/3*a^7*b*x^12 + 28/11*a^6*b^2*x^11 + 28/5*a^5*b^3*x^10 + 70/9*a^4*b^4*x^9 + 7*a^3*b^5*x^8 + 4*a^2*b^6*x^7 + 4/3*a*b^7*x^6 + 1/5*b^8*x^5","A",0
1587,1,90,0,0.149650," ","integrate((a+b/x)^8*x^11,x, algorithm=""giac"")","\frac{1}{12} \, a^{8} x^{12} + \frac{8}{11} \, a^{7} b x^{11} + \frac{14}{5} \, a^{6} b^{2} x^{10} + \frac{56}{9} \, a^{5} b^{3} x^{9} + \frac{35}{4} \, a^{4} b^{4} x^{8} + 8 \, a^{3} b^{5} x^{7} + \frac{14}{3} \, a^{2} b^{6} x^{6} + \frac{8}{5} \, a b^{7} x^{5} + \frac{1}{4} \, b^{8} x^{4}"," ",0,"1/12*a^8*x^12 + 8/11*a^7*b*x^11 + 14/5*a^6*b^2*x^10 + 56/9*a^5*b^3*x^9 + 35/4*a^4*b^4*x^8 + 8*a^3*b^5*x^7 + 14/3*a^2*b^6*x^6 + 8/5*a*b^7*x^5 + 1/4*b^8*x^4","A",0
1588,1,90,0,0.164595," ","integrate((a+b/x)^8*x^10,x, algorithm=""giac"")","\frac{1}{11} \, a^{8} x^{11} + \frac{4}{5} \, a^{7} b x^{10} + \frac{28}{9} \, a^{6} b^{2} x^{9} + 7 \, a^{5} b^{3} x^{8} + 10 \, a^{4} b^{4} x^{7} + \frac{28}{3} \, a^{3} b^{5} x^{6} + \frac{28}{5} \, a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + \frac{1}{3} \, b^{8} x^{3}"," ",0,"1/11*a^8*x^11 + 4/5*a^7*b*x^10 + 28/9*a^6*b^2*x^9 + 7*a^5*b^3*x^8 + 10*a^4*b^4*x^7 + 28/3*a^3*b^5*x^6 + 28/5*a^2*b^6*x^5 + 2*a*b^7*x^4 + 1/3*b^8*x^3","B",0
1589,1,90,0,0.167677," ","integrate((a+b/x)^8*x^9,x, algorithm=""giac"")","\frac{1}{10} \, a^{8} x^{10} + \frac{8}{9} \, a^{7} b x^{9} + \frac{7}{2} \, a^{6} b^{2} x^{8} + 8 \, a^{5} b^{3} x^{7} + \frac{35}{3} \, a^{4} b^{4} x^{6} + \frac{56}{5} \, a^{3} b^{5} x^{5} + 7 \, a^{2} b^{6} x^{4} + \frac{8}{3} \, a b^{7} x^{3} + \frac{1}{2} \, b^{8} x^{2}"," ",0,"1/10*a^8*x^10 + 8/9*a^7*b*x^9 + 7/2*a^6*b^2*x^8 + 8*a^5*b^3*x^7 + 35/3*a^4*b^4*x^6 + 56/5*a^3*b^5*x^5 + 7*a^2*b^6*x^4 + 8/3*a*b^7*x^3 + 1/2*b^8*x^2","B",0
1590,1,86,0,0.151048," ","integrate((a+b/x)^8*x^8,x, algorithm=""giac"")","\frac{1}{9} \, a^{8} x^{9} + a^{7} b x^{8} + 4 \, a^{6} b^{2} x^{7} + \frac{28}{3} \, a^{5} b^{3} x^{6} + 14 \, a^{4} b^{4} x^{5} + 14 \, a^{3} b^{5} x^{4} + \frac{28}{3} \, a^{2} b^{6} x^{3} + 4 \, a b^{7} x^{2} + b^{8} x"," ",0,"1/9*a^8*x^9 + a^7*b*x^8 + 4*a^6*b^2*x^7 + 28/3*a^5*b^3*x^6 + 14*a^4*b^4*x^5 + 14*a^3*b^5*x^4 + 28/3*a^2*b^6*x^3 + 4*a*b^7*x^2 + b^8*x","B",0
1591,1,87,0,0.181107," ","integrate((a+b/x)^8*x^7,x, algorithm=""giac"")","\frac{1}{8} \, a^{8} x^{8} + \frac{8}{7} \, a^{7} b x^{7} + \frac{14}{3} \, a^{6} b^{2} x^{6} + \frac{56}{5} \, a^{5} b^{3} x^{5} + \frac{35}{2} \, a^{4} b^{4} x^{4} + \frac{56}{3} \, a^{3} b^{5} x^{3} + 14 \, a^{2} b^{6} x^{2} + 8 \, a b^{7} x + b^{8} \log\left({\left| x \right|}\right)"," ",0,"1/8*a^8*x^8 + 8/7*a^7*b*x^7 + 14/3*a^6*b^2*x^6 + 56/5*a^5*b^3*x^5 + 35/2*a^4*b^4*x^4 + 56/3*a^3*b^5*x^3 + 14*a^2*b^6*x^2 + 8*a*b^7*x + b^8*log(abs(x))","A",0
1592,1,88,0,0.152633," ","integrate((a+b/x)^8*x^6,x, algorithm=""giac"")","\frac{1}{7} \, a^{8} x^{7} + \frac{4}{3} \, a^{7} b x^{6} + \frac{28}{5} \, a^{6} b^{2} x^{5} + 14 \, a^{5} b^{3} x^{4} + \frac{70}{3} \, a^{4} b^{4} x^{3} + 28 \, a^{3} b^{5} x^{2} + 28 \, a^{2} b^{6} x + 8 \, a b^{7} \log\left({\left| x \right|}\right) - \frac{b^{8}}{x}"," ",0,"1/7*a^8*x^7 + 4/3*a^7*b*x^6 + 28/5*a^6*b^2*x^5 + 14*a^5*b^3*x^4 + 70/3*a^4*b^4*x^3 + 28*a^3*b^5*x^2 + 28*a^2*b^6*x + 8*a*b^7*log(abs(x)) - b^8/x","A",0
1593,1,87,0,0.153171," ","integrate((a+b/x)^8*x^5,x, algorithm=""giac"")","\frac{1}{6} \, a^{8} x^{6} + \frac{8}{5} \, a^{7} b x^{5} + 7 \, a^{6} b^{2} x^{4} + \frac{56}{3} \, a^{5} b^{3} x^{3} + 35 \, a^{4} b^{4} x^{2} + 56 \, a^{3} b^{5} x + 28 \, a^{2} b^{6} \log\left({\left| x \right|}\right) - \frac{16 \, a b^{7} x + b^{8}}{2 \, x^{2}}"," ",0,"1/6*a^8*x^6 + 8/5*a^7*b*x^5 + 7*a^6*b^2*x^4 + 56/3*a^5*b^3*x^3 + 35*a^4*b^4*x^2 + 56*a^3*b^5*x + 28*a^2*b^6*log(abs(x)) - 1/2*(16*a*b^7*x + b^8)/x^2","A",0
1594,1,87,0,0.153603," ","integrate((a+b/x)^8*x^4,x, algorithm=""giac"")","\frac{1}{5} \, a^{8} x^{5} + 2 \, a^{7} b x^{4} + \frac{28}{3} \, a^{6} b^{2} x^{3} + 28 \, a^{5} b^{3} x^{2} + 70 \, a^{4} b^{4} x + 56 \, a^{3} b^{5} \log\left({\left| x \right|}\right) - \frac{84 \, a^{2} b^{6} x^{2} + 12 \, a b^{7} x + b^{8}}{3 \, x^{3}}"," ",0,"1/5*a^8*x^5 + 2*a^7*b*x^4 + 28/3*a^6*b^2*x^3 + 28*a^5*b^3*x^2 + 70*a^4*b^4*x + 56*a^3*b^5*log(abs(x)) - 1/3*(84*a^2*b^6*x^2 + 12*a*b^7*x + b^8)/x^3","A",0
1595,1,89,0,0.168653," ","integrate((a+b/x)^8*x^3,x, algorithm=""giac"")","\frac{1}{4} \, a^{8} x^{4} + \frac{8}{3} \, a^{7} b x^{3} + 14 \, a^{6} b^{2} x^{2} + 56 \, a^{5} b^{3} x + 70 \, a^{4} b^{4} \log\left({\left| x \right|}\right) - \frac{672 \, a^{3} b^{5} x^{3} + 168 \, a^{2} b^{6} x^{2} + 32 \, a b^{7} x + 3 \, b^{8}}{12 \, x^{4}}"," ",0,"1/4*a^8*x^4 + 8/3*a^7*b*x^3 + 14*a^6*b^2*x^2 + 56*a^5*b^3*x + 70*a^4*b^4*log(abs(x)) - 1/12*(672*a^3*b^5*x^3 + 168*a^2*b^6*x^2 + 32*a*b^7*x + 3*b^8)/x^4","A",0
1596,1,89,0,0.192864," ","integrate((a+b/x)^8*x^2,x, algorithm=""giac"")","\frac{1}{3} \, a^{8} x^{3} + 4 \, a^{7} b x^{2} + 28 \, a^{6} b^{2} x + 56 \, a^{5} b^{3} \log\left({\left| x \right|}\right) - \frac{1050 \, a^{4} b^{4} x^{4} + 420 \, a^{3} b^{5} x^{3} + 140 \, a^{2} b^{6} x^{2} + 30 \, a b^{7} x + 3 \, b^{8}}{15 \, x^{5}}"," ",0,"1/3*a^8*x^3 + 4*a^7*b*x^2 + 28*a^6*b^2*x + 56*a^5*b^3*log(abs(x)) - 1/15*(1050*a^4*b^4*x^4 + 420*a^3*b^5*x^3 + 140*a^2*b^6*x^2 + 30*a*b^7*x + 3*b^8)/x^5","A",0
1597,1,89,0,0.154864," ","integrate((a+b/x)^8*x,x, algorithm=""giac"")","\frac{1}{2} \, a^{8} x^{2} + 8 \, a^{7} b x + 28 \, a^{6} b^{2} \log\left({\left| x \right|}\right) - \frac{1680 \, a^{5} b^{3} x^{5} + 1050 \, a^{4} b^{4} x^{4} + 560 \, a^{3} b^{5} x^{3} + 210 \, a^{2} b^{6} x^{2} + 48 \, a b^{7} x + 5 \, b^{8}}{30 \, x^{6}}"," ",0,"1/2*a^8*x^2 + 8*a^7*b*x + 28*a^6*b^2*log(abs(x)) - 1/30*(1680*a^5*b^3*x^5 + 1050*a^4*b^4*x^4 + 560*a^3*b^5*x^3 + 210*a^2*b^6*x^2 + 48*a*b^7*x + 5*b^8)/x^6","A",0
1598,1,88,0,0.174265," ","integrate((a+b/x)^8,x, algorithm=""giac"")","a^{8} x + 8 \, a^{7} b \log\left({\left| x \right|}\right) - \frac{2940 \, a^{6} b^{2} x^{6} + 2940 \, a^{5} b^{3} x^{5} + 2450 \, a^{4} b^{4} x^{4} + 1470 \, a^{3} b^{5} x^{3} + 588 \, a^{2} b^{6} x^{2} + 140 \, a b^{7} x + 15 \, b^{8}}{105 \, x^{7}}"," ",0,"a^8*x + 8*a^7*b*log(abs(x)) - 1/105*(2940*a^6*b^2*x^6 + 2940*a^5*b^3*x^5 + 2450*a^4*b^4*x^4 + 1470*a^3*b^5*x^3 + 588*a^2*b^6*x^2 + 140*a*b^7*x + 15*b^8)/x^7","A",0
1599,1,90,0,0.150912," ","integrate((a+b/x)^8/x,x, algorithm=""giac"")","a^{8} \log\left({\left| x \right|}\right) - \frac{6720 \, a^{7} b x^{7} + 11760 \, a^{6} b^{2} x^{6} + 15680 \, a^{5} b^{3} x^{5} + 14700 \, a^{4} b^{4} x^{4} + 9408 \, a^{3} b^{5} x^{3} + 3920 \, a^{2} b^{6} x^{2} + 960 \, a b^{7} x + 105 \, b^{8}}{840 \, x^{8}}"," ",0,"a^8*log(abs(x)) - 1/840*(6720*a^7*b*x^7 + 11760*a^6*b^2*x^6 + 15680*a^5*b^3*x^5 + 14700*a^4*b^4*x^4 + 9408*a^3*b^5*x^3 + 3920*a^2*b^6*x^2 + 960*a*b^7*x + 105*b^8)/x^8","A",0
1600,1,14,0,0.148145," ","integrate((a+b/x)^8/x^2,x, algorithm=""giac"")","-\frac{{\left(a + \frac{b}{x}\right)}^{9}}{9 \, b}"," ",0,"-1/9*(a + b/x)^9/b","A",0
1601,1,90,0,0.214380," ","integrate((a+b/x)^8/x^3,x, algorithm=""giac"")","-\frac{45 \, a^{8} x^{8} + 240 \, a^{7} b x^{7} + 630 \, a^{6} b^{2} x^{6} + 1008 \, a^{5} b^{3} x^{5} + 1050 \, a^{4} b^{4} x^{4} + 720 \, a^{3} b^{5} x^{3} + 315 \, a^{2} b^{6} x^{2} + 80 \, a b^{7} x + 9 \, b^{8}}{90 \, x^{10}}"," ",0,"-1/90*(45*a^8*x^8 + 240*a^7*b*x^7 + 630*a^6*b^2*x^6 + 1008*a^5*b^3*x^5 + 1050*a^4*b^4*x^4 + 720*a^3*b^5*x^3 + 315*a^2*b^6*x^2 + 80*a*b^7*x + 9*b^8)/x^10","B",0
1602,1,90,0,0.165127," ","integrate((a+b/x)^8/x^4,x, algorithm=""giac"")","-\frac{165 \, a^{8} x^{8} + 990 \, a^{7} b x^{7} + 2772 \, a^{6} b^{2} x^{6} + 4620 \, a^{5} b^{3} x^{5} + 4950 \, a^{4} b^{4} x^{4} + 3465 \, a^{3} b^{5} x^{3} + 1540 \, a^{2} b^{6} x^{2} + 396 \, a b^{7} x + 45 \, b^{8}}{495 \, x^{11}}"," ",0,"-1/495*(165*a^8*x^8 + 990*a^7*b*x^7 + 2772*a^6*b^2*x^6 + 4620*a^5*b^3*x^5 + 4950*a^4*b^4*x^4 + 3465*a^3*b^5*x^3 + 1540*a^2*b^6*x^2 + 396*a*b^7*x + 45*b^8)/x^11","A",0
1603,1,90,0,0.173614," ","integrate((a+b/x)^8/x^5,x, algorithm=""giac"")","-\frac{495 \, a^{8} x^{8} + 3168 \, a^{7} b x^{7} + 9240 \, a^{6} b^{2} x^{6} + 15840 \, a^{5} b^{3} x^{5} + 17325 \, a^{4} b^{4} x^{4} + 12320 \, a^{3} b^{5} x^{3} + 5544 \, a^{2} b^{6} x^{2} + 1440 \, a b^{7} x + 165 \, b^{8}}{1980 \, x^{12}}"," ",0,"-1/1980*(495*a^8*x^8 + 3168*a^7*b*x^7 + 9240*a^6*b^2*x^6 + 15840*a^5*b^3*x^5 + 17325*a^4*b^4*x^4 + 12320*a^3*b^5*x^3 + 5544*a^2*b^6*x^2 + 1440*a*b^7*x + 165*b^8)/x^12","A",0
1604,1,90,0,0.151379," ","integrate((a+b/x)^8/x^6,x, algorithm=""giac"")","-\frac{1287 \, a^{8} x^{8} + 8580 \, a^{7} b x^{7} + 25740 \, a^{6} b^{2} x^{6} + 45045 \, a^{5} b^{3} x^{5} + 50050 \, a^{4} b^{4} x^{4} + 36036 \, a^{3} b^{5} x^{3} + 16380 \, a^{2} b^{6} x^{2} + 4290 \, a b^{7} x + 495 \, b^{8}}{6435 \, x^{13}}"," ",0,"-1/6435*(1287*a^8*x^8 + 8580*a^7*b*x^7 + 25740*a^6*b^2*x^6 + 45045*a^5*b^3*x^5 + 50050*a^4*b^4*x^4 + 36036*a^3*b^5*x^3 + 16380*a^2*b^6*x^2 + 4290*a*b^7*x + 495*b^8)/x^13","A",0
1605,1,90,0,0.166093," ","integrate((a+b/x)^8/x^7,x, algorithm=""giac"")","-\frac{3003 \, a^{8} x^{8} + 20592 \, a^{7} b x^{7} + 63063 \, a^{6} b^{2} x^{6} + 112112 \, a^{5} b^{3} x^{5} + 126126 \, a^{4} b^{4} x^{4} + 91728 \, a^{3} b^{5} x^{3} + 42042 \, a^{2} b^{6} x^{2} + 11088 \, a b^{7} x + 1287 \, b^{8}}{18018 \, x^{14}}"," ",0,"-1/18018*(3003*a^8*x^8 + 20592*a^7*b*x^7 + 63063*a^6*b^2*x^6 + 112112*a^5*b^3*x^5 + 126126*a^4*b^4*x^4 + 91728*a^3*b^5*x^3 + 42042*a^2*b^6*x^2 + 11088*a*b^7*x + 1287*b^8)/x^14","A",0
1606,1,90,0,0.153964," ","integrate((a+b/x)^8/x^8,x, algorithm=""giac"")","-\frac{6435 \, a^{8} x^{8} + 45045 \, a^{7} b x^{7} + 140140 \, a^{6} b^{2} x^{6} + 252252 \, a^{5} b^{3} x^{5} + 286650 \, a^{4} b^{4} x^{4} + 210210 \, a^{3} b^{5} x^{3} + 97020 \, a^{2} b^{6} x^{2} + 25740 \, a b^{7} x + 3003 \, b^{8}}{45045 \, x^{15}}"," ",0,"-1/45045*(6435*a^8*x^8 + 45045*a^7*b*x^7 + 140140*a^6*b^2*x^6 + 252252*a^5*b^3*x^5 + 286650*a^4*b^4*x^4 + 210210*a^3*b^5*x^3 + 97020*a^2*b^6*x^2 + 25740*a*b^7*x + 3003*b^8)/x^15","A",0
1607,1,65,0,0.173064," ","integrate(x^4/(a+b/x),x, algorithm=""giac"")","-\frac{b^{5} \log\left({\left| a x + b \right|}\right)}{a^{6}} + \frac{12 \, a^{4} x^{5} - 15 \, a^{3} b x^{4} + 20 \, a^{2} b^{2} x^{3} - 30 \, a b^{3} x^{2} + 60 \, b^{4} x}{60 \, a^{5}}"," ",0,"-b^5*log(abs(a*x + b))/a^6 + 1/60*(12*a^4*x^5 - 15*a^3*b*x^4 + 20*a^2*b^2*x^3 - 30*a*b^3*x^2 + 60*b^4*x)/a^5","A",0
1608,1,53,0,0.172568," ","integrate(x^3/(a+b/x),x, algorithm=""giac"")","\frac{b^{4} \log\left({\left| a x + b \right|}\right)}{a^{5}} + \frac{3 \, a^{3} x^{4} - 4 \, a^{2} b x^{3} + 6 \, a b^{2} x^{2} - 12 \, b^{3} x}{12 \, a^{4}}"," ",0,"b^4*log(abs(a*x + b))/a^5 + 1/12*(3*a^3*x^4 - 4*a^2*b*x^3 + 6*a*b^2*x^2 - 12*b^3*x)/a^4","A",0
1609,1,43,0,0.146646," ","integrate(x^2/(a+b/x),x, algorithm=""giac"")","-\frac{b^{3} \log\left({\left| a x + b \right|}\right)}{a^{4}} + \frac{2 \, a^{2} x^{3} - 3 \, a b x^{2} + 6 \, b^{2} x}{6 \, a^{3}}"," ",0,"-b^3*log(abs(a*x + b))/a^4 + 1/6*(2*a^2*x^3 - 3*a*b*x^2 + 6*b^2*x)/a^3","A",0
1610,1,30,0,0.148626," ","integrate(x/(a+b/x),x, algorithm=""giac"")","\frac{b^{2} \log\left({\left| a x + b \right|}\right)}{a^{3}} + \frac{a x^{2} - 2 \, b x}{2 \, a^{2}}"," ",0,"b^2*log(abs(a*x + b))/a^3 + 1/2*(a*x^2 - 2*b*x)/a^2","A",0
1611,1,19,0,0.175235," ","integrate(1/(a+b/x),x, algorithm=""giac"")","\frac{x}{a} - \frac{b \log\left({\left| a x + b \right|}\right)}{a^{2}}"," ",0,"x/a - b*log(abs(a*x + b))/a^2","A",0
1612,1,11,0,0.148368," ","integrate(1/(a+b/x)/x,x, algorithm=""giac"")","\frac{\log\left({\left| a x + b \right|}\right)}{a}"," ",0,"log(abs(a*x + b))/a","A",0
1613,1,14,0,0.232182," ","integrate(1/(a+b/x)/x^2,x, algorithm=""giac"")","-\frac{\log\left({\left| a + \frac{b}{x} \right|}\right)}{b}"," ",0,"-log(abs(a + b/x))/b","A",0
1614,1,30,0,0.173005," ","integrate(1/(a+b/x)/x^3,x, algorithm=""giac"")","\frac{a \log\left({\left| a x + b \right|}\right)}{b^{2}} - \frac{a \log\left({\left| x \right|}\right)}{b^{2}} - \frac{1}{b x}"," ",0,"a*log(abs(a*x + b))/b^2 - a*log(abs(x))/b^2 - 1/(b*x)","A",0
1615,1,45,0,0.169312," ","integrate(1/(a+b/x)/x^4,x, algorithm=""giac"")","-\frac{a^{2} \log\left({\left| a x + b \right|}\right)}{b^{3}} + \frac{a^{2} \log\left({\left| x \right|}\right)}{b^{3}} + \frac{2 \, a b x - b^{2}}{2 \, b^{3} x^{2}}"," ",0,"-a^2*log(abs(a*x + b))/b^3 + a^2*log(abs(x))/b^3 + 1/2*(2*a*b*x - b^2)/(b^3*x^2)","A",0
1616,1,56,0,0.151717," ","integrate(1/(a+b/x)/x^5,x, algorithm=""giac"")","\frac{a^{3} \log\left({\left| a x + b \right|}\right)}{b^{4}} - \frac{a^{3} \log\left({\left| x \right|}\right)}{b^{4}} - \frac{6 \, a^{2} b x^{2} - 3 \, a b^{2} x + 2 \, b^{3}}{6 \, b^{4} x^{3}}"," ",0,"a^3*log(abs(a*x + b))/b^4 - a^3*log(abs(x))/b^4 - 1/6*(6*a^2*b*x^2 - 3*a*b^2*x + 2*b^3)/(b^4*x^3)","A",0
1617,1,67,0,0.213121," ","integrate(1/(a+b/x)/x^6,x, algorithm=""giac"")","-\frac{a^{4} \log\left({\left| a x + b \right|}\right)}{b^{5}} + \frac{a^{4} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{12 \, a^{3} b x^{3} - 6 \, a^{2} b^{2} x^{2} + 4 \, a b^{3} x - 3 \, b^{4}}{12 \, b^{5} x^{4}}"," ",0,"-a^4*log(abs(a*x + b))/b^5 + a^4*log(abs(x))/b^5 + 1/12*(12*a^3*b*x^3 - 6*a^2*b^2*x^2 + 4*a*b^3*x - 3*b^4)/(b^5*x^4)","A",0
1618,1,78,0,0.167947," ","integrate(1/(a+b/x)/x^7,x, algorithm=""giac"")","\frac{a^{5} \log\left({\left| a x + b \right|}\right)}{b^{6}} - \frac{a^{5} \log\left({\left| x \right|}\right)}{b^{6}} - \frac{60 \, a^{4} b x^{4} - 30 \, a^{3} b^{2} x^{3} + 20 \, a^{2} b^{3} x^{2} - 15 \, a b^{4} x + 12 \, b^{5}}{60 \, b^{6} x^{5}}"," ",0,"a^5*log(abs(a*x + b))/b^6 - a^5*log(abs(x))/b^6 - 1/60*(60*a^4*b*x^4 - 30*a^3*b^2*x^3 + 20*a^2*b^3*x^2 - 15*a*b^4*x + 12*b^5)/(b^6*x^5)","A",0
1619,1,95,0,0.158519," ","integrate(x^5/(a+b/x)^2,x, algorithm=""giac"")","\frac{7 \, b^{6} \log\left({\left| a x + b \right|}\right)}{a^{8}} + \frac{b^{7}}{{\left(a x + b\right)} a^{8}} + \frac{10 \, a^{10} x^{6} - 24 \, a^{9} b x^{5} + 45 \, a^{8} b^{2} x^{4} - 80 \, a^{7} b^{3} x^{3} + 150 \, a^{6} b^{4} x^{2} - 360 \, a^{5} b^{5} x}{60 \, a^{12}}"," ",0,"7*b^6*log(abs(a*x + b))/a^8 + b^7/((a*x + b)*a^8) + 1/60*(10*a^10*x^6 - 24*a^9*b*x^5 + 45*a^8*b^2*x^4 - 80*a^7*b^3*x^3 + 150*a^6*b^4*x^2 - 360*a^5*b^5*x)/a^12","A",0
1620,1,85,0,0.152140," ","integrate(x^4/(a+b/x)^2,x, algorithm=""giac"")","-\frac{6 \, b^{5} \log\left({\left| a x + b \right|}\right)}{a^{7}} - \frac{b^{6}}{{\left(a x + b\right)} a^{7}} + \frac{2 \, a^{8} x^{5} - 5 \, a^{7} b x^{4} + 10 \, a^{6} b^{2} x^{3} - 20 \, a^{5} b^{3} x^{2} + 50 \, a^{4} b^{4} x}{10 \, a^{10}}"," ",0,"-6*b^5*log(abs(a*x + b))/a^7 - b^6/((a*x + b)*a^7) + 1/10*(2*a^8*x^5 - 5*a^7*b*x^4 + 10*a^6*b^2*x^3 - 20*a^5*b^3*x^2 + 50*a^4*b^4*x)/a^10","A",0
1621,1,73,0,0.153721," ","integrate(x^3/(a+b/x)^2,x, algorithm=""giac"")","\frac{5 \, b^{4} \log\left({\left| a x + b \right|}\right)}{a^{6}} + \frac{b^{5}}{{\left(a x + b\right)} a^{6}} + \frac{3 \, a^{6} x^{4} - 8 \, a^{5} b x^{3} + 18 \, a^{4} b^{2} x^{2} - 48 \, a^{3} b^{3} x}{12 \, a^{8}}"," ",0,"5*b^4*log(abs(a*x + b))/a^6 + b^5/((a*x + b)*a^6) + 1/12*(3*a^6*x^4 - 8*a^5*b*x^3 + 18*a^4*b^2*x^2 - 48*a^3*b^3*x)/a^8","A",0
1622,1,62,0,0.180991," ","integrate(x^2/(a+b/x)^2,x, algorithm=""giac"")","-\frac{4 \, b^{3} \log\left({\left| a x + b \right|}\right)}{a^{5}} - \frac{b^{4}}{{\left(a x + b\right)} a^{5}} + \frac{a^{4} x^{3} - 3 \, a^{3} b x^{2} + 9 \, a^{2} b^{2} x}{3 \, a^{6}}"," ",0,"-4*b^3*log(abs(a*x + b))/a^5 - b^4/((a*x + b)*a^5) + 1/3*(a^4*x^3 - 3*a^3*b*x^2 + 9*a^2*b^2*x)/a^6","A",0
1623,1,48,0,0.149224," ","integrate(x/(a+b/x)^2,x, algorithm=""giac"")","\frac{3 \, b^{2} \log\left({\left| a x + b \right|}\right)}{a^{4}} + \frac{b^{3}}{{\left(a x + b\right)} a^{4}} + \frac{a^{2} x^{2} - 4 \, a b x}{2 \, a^{4}}"," ",0,"3*b^2*log(abs(a*x + b))/a^4 + b^3/((a*x + b)*a^4) + 1/2*(a^2*x^2 - 4*a*b*x)/a^4","A",0
1624,1,34,0,0.148576," ","integrate(1/(a+b/x)^2,x, algorithm=""giac"")","\frac{x}{a^{2}} - \frac{2 \, b \log\left({\left| a x + b \right|}\right)}{a^{3}} - \frac{b^{2}}{{\left(a x + b\right)} a^{3}}"," ",0,"x/a^2 - 2*b*log(abs(a*x + b))/a^3 - b^2/((a*x + b)*a^3)","A",0
1625,1,24,0,0.194079," ","integrate(1/(a+b/x)^2/x,x, algorithm=""giac"")","\frac{\log\left({\left| a x + b \right|}\right)}{a^{2}} + \frac{b}{{\left(a x + b\right)} a^{2}}"," ",0,"log(abs(a*x + b))/a^2 + b/((a*x + b)*a^2)","A",0
1626,1,13,0,0.145718," ","integrate(1/(a+b/x)^2/x^2,x, algorithm=""giac"")","\frac{1}{{\left(a + \frac{b}{x}\right)} b}"," ",0,"1/((a + b/x)*b)","A",0
1627,1,31,0,0.154038," ","integrate(1/(a+b/x)^2/x^3,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + b \right|}\right)}{b^{2}} + \frac{\log\left({\left| x \right|}\right)}{b^{2}} + \frac{1}{{\left(a x + b\right)} b}"," ",0,"-log(abs(a*x + b))/b^2 + log(abs(x))/b^2 + 1/((a*x + b)*b)","A",0
1628,1,45,0,0.151477," ","integrate(1/(a+b/x)^2/x^4,x, algorithm=""giac"")","\frac{2 \, a \log\left({\left| a x + b \right|}\right)}{b^{3}} - \frac{2 \, a \log\left({\left| x \right|}\right)}{b^{3}} - \frac{2 \, a x + b}{{\left(a x^{2} + b x\right)} b^{2}}"," ",0,"2*a*log(abs(a*x + b))/b^3 - 2*a*log(abs(x))/b^3 - (2*a*x + b)/((a*x^2 + b*x)*b^2)","A",0
1629,1,64,0,0.148812," ","integrate(1/(a+b/x)^2/x^5,x, algorithm=""giac"")","-\frac{3 \, a^{2} \log\left({\left| a x + b \right|}\right)}{b^{4}} + \frac{3 \, a^{2} \log\left({\left| x \right|}\right)}{b^{4}} + \frac{6 \, a^{2} b x^{2} + 3 \, a b^{2} x - b^{3}}{2 \, {\left(a x + b\right)} b^{4} x^{2}}"," ",0,"-3*a^2*log(abs(a*x + b))/b^4 + 3*a^2*log(abs(x))/b^4 + 1/2*(6*a^2*b*x^2 + 3*a*b^2*x - b^3)/((a*x + b)*b^4*x^2)","A",0
1630,1,73,0,0.155131," ","integrate(1/(a+b/x)^2/x^6,x, algorithm=""giac"")","\frac{4 \, a^{3} \log\left({\left| a x + b \right|}\right)}{b^{5}} - \frac{4 \, a^{3} \log\left({\left| x \right|}\right)}{b^{5}} - \frac{12 \, a^{3} b x^{3} + 6 \, a^{2} b^{2} x^{2} - 2 \, a b^{3} x + b^{4}}{3 \, {\left(a x + b\right)} b^{5} x^{3}}"," ",0,"4*a^3*log(abs(a*x + b))/b^5 - 4*a^3*log(abs(x))/b^5 - 1/3*(12*a^3*b*x^3 + 6*a^2*b^2*x^2 - 2*a*b^3*x + b^4)/((a*x + b)*b^5*x^3)","A",0
1631,1,86,0,0.208521," ","integrate(1/(a+b/x)^2/x^7,x, algorithm=""giac"")","-\frac{5 \, a^{4} \log\left({\left| a x + b \right|}\right)}{b^{6}} + \frac{5 \, a^{4} \log\left({\left| x \right|}\right)}{b^{6}} + \frac{60 \, a^{4} b x^{4} + 30 \, a^{3} b^{2} x^{3} - 10 \, a^{2} b^{3} x^{2} + 5 \, a b^{4} x - 3 \, b^{5}}{12 \, {\left(a x + b\right)} b^{6} x^{4}}"," ",0,"-5*a^4*log(abs(a*x + b))/b^6 + 5*a^4*log(abs(x))/b^6 + 1/12*(60*a^4*b*x^4 + 30*a^3*b^2*x^3 - 10*a^2*b^3*x^2 + 5*a*b^4*x - 3*b^5)/((a*x + b)*b^6*x^4)","A",0
1632,1,97,0,0.151266," ","integrate(1/(a+b/x)^2/x^8,x, algorithm=""giac"")","\frac{6 \, a^{5} \log\left({\left| a x + b \right|}\right)}{b^{7}} - \frac{6 \, a^{5} \log\left({\left| x \right|}\right)}{b^{7}} - \frac{60 \, a^{5} b x^{5} + 30 \, a^{4} b^{2} x^{4} - 10 \, a^{3} b^{3} x^{3} + 5 \, a^{2} b^{4} x^{2} - 3 \, a b^{5} x + 2 \, b^{6}}{10 \, {\left(a x + b\right)} b^{7} x^{5}}"," ",0,"6*a^5*log(abs(a*x + b))/b^7 - 6*a^5*log(abs(x))/b^7 - 1/10*(60*a^5*b*x^5 + 30*a^4*b^2*x^4 - 10*a^3*b^3*x^3 + 5*a^2*b^4*x^2 - 3*a*b^5*x + 2*b^6)/((a*x + b)*b^7*x^5)","A",0
1633,1,95,0,0.154685," ","integrate(x^4/(a+b/x)^3,x, algorithm=""giac"")","-\frac{21 \, b^{5} \log\left({\left| a x + b \right|}\right)}{a^{8}} - \frac{14 \, a b^{6} x + 13 \, b^{7}}{2 \, {\left(a x + b\right)}^{2} a^{8}} + \frac{4 \, a^{12} x^{5} - 15 \, a^{11} b x^{4} + 40 \, a^{10} b^{2} x^{3} - 100 \, a^{9} b^{3} x^{2} + 300 \, a^{8} b^{4} x}{20 \, a^{15}}"," ",0,"-21*b^5*log(abs(a*x + b))/a^8 - 1/2*(14*a*b^6*x + 13*b^7)/((a*x + b)^2*a^8) + 1/20*(4*a^12*x^5 - 15*a^11*b*x^4 + 40*a^10*b^2*x^3 - 100*a^9*b^3*x^2 + 300*a^8*b^4*x)/a^15","A",0
1634,1,83,0,0.178044," ","integrate(x^3/(a+b/x)^3,x, algorithm=""giac"")","\frac{15 \, b^{4} \log\left({\left| a x + b \right|}\right)}{a^{7}} + \frac{12 \, a b^{5} x + 11 \, b^{6}}{2 \, {\left(a x + b\right)}^{2} a^{7}} + \frac{a^{9} x^{4} - 4 \, a^{8} b x^{3} + 12 \, a^{7} b^{2} x^{2} - 40 \, a^{6} b^{3} x}{4 \, a^{12}}"," ",0,"15*b^4*log(abs(a*x + b))/a^7 + 1/2*(12*a*b^5*x + 11*b^6)/((a*x + b)^2*a^7) + 1/4*(a^9*x^4 - 4*a^8*b*x^3 + 12*a^7*b^2*x^2 - 40*a^6*b^3*x)/a^12","A",0
1635,1,73,0,0.150244," ","integrate(x^2/(a+b/x)^3,x, algorithm=""giac"")","-\frac{10 \, b^{3} \log\left({\left| a x + b \right|}\right)}{a^{6}} - \frac{10 \, a b^{4} x + 9 \, b^{5}}{2 \, {\left(a x + b\right)}^{2} a^{6}} + \frac{2 \, a^{6} x^{3} - 9 \, a^{5} b x^{2} + 36 \, a^{4} b^{2} x}{6 \, a^{9}}"," ",0,"-10*b^3*log(abs(a*x + b))/a^6 - 1/2*(10*a*b^4*x + 9*b^5)/((a*x + b)^2*a^6) + 1/6*(2*a^6*x^3 - 9*a^5*b*x^2 + 36*a^4*b^2*x)/a^9","A",0
1636,1,61,0,0.154920," ","integrate(x/(a+b/x)^3,x, algorithm=""giac"")","\frac{6 \, b^{2} \log\left({\left| a x + b \right|}\right)}{a^{5}} + \frac{a^{3} x^{2} - 6 \, a^{2} b x}{2 \, a^{6}} + \frac{8 \, a b^{3} x + 7 \, b^{4}}{2 \, {\left(a x + b\right)}^{2} a^{5}}"," ",0,"6*b^2*log(abs(a*x + b))/a^5 + 1/2*(a^3*x^2 - 6*a^2*b*x)/a^6 + 1/2*(8*a*b^3*x + 7*b^4)/((a*x + b)^2*a^5)","A",0
1637,1,44,0,0.149271," ","integrate(1/(a+b/x)^3,x, algorithm=""giac"")","\frac{x}{a^{3}} - \frac{3 \, b \log\left({\left| a x + b \right|}\right)}{a^{4}} - \frac{6 \, a b^{2} x + 5 \, b^{3}}{2 \, {\left(a x + b\right)}^{2} a^{4}}"," ",0,"x/a^3 - 3*b*log(abs(a*x + b))/a^4 - 1/2*(6*a*b^2*x + 5*b^3)/((a*x + b)^2*a^4)","A",0
1638,1,37,0,0.153891," ","integrate(1/(a+b/x)^3/x,x, algorithm=""giac"")","\frac{\log\left({\left| a x + b \right|}\right)}{a^{3}} + \frac{4 \, b x + \frac{3 \, b^{2}}{a}}{2 \, {\left(a x + b\right)}^{2} a^{2}}"," ",0,"log(abs(a*x + b))/a^3 + 1/2*(4*b*x + 3*b^2/a)/((a*x + b)^2*a^2)","A",0
1639,1,14,0,0.150123," ","integrate(1/(a+b/x)^3/x^2,x, algorithm=""giac"")","\frac{1}{2 \, {\left(a + \frac{b}{x}\right)}^{2} b}"," ",0,"1/2/((a + b/x)^2*b)","A",0
1640,1,12,0,0.151726," ","integrate(1/(a+b/x)^3/x^3,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(a x + b\right)}^{2} a}"," ",0,"-1/2/((a*x + b)^2*a)","A",0
1641,1,43,0,0.152047," ","integrate(1/(a+b/x)^3/x^4,x, algorithm=""giac"")","-\frac{\log\left({\left| a x + b \right|}\right)}{b^{3}} + \frac{\log\left({\left| x \right|}\right)}{b^{3}} + \frac{2 \, a b x + 3 \, b^{2}}{2 \, {\left(a x + b\right)}^{2} b^{3}}"," ",0,"-log(abs(a*x + b))/b^3 + log(abs(x))/b^3 + 1/2*(2*a*b*x + 3*b^2)/((a*x + b)^2*b^3)","A",0
1642,1,60,0,0.154672," ","integrate(1/(a+b/x)^3/x^5,x, algorithm=""giac"")","\frac{3 \, a \log\left({\left| a x + b \right|}\right)}{b^{4}} - \frac{3 \, a \log\left({\left| x \right|}\right)}{b^{4}} - \frac{6 \, a^{2} b x^{2} + 9 \, a b^{2} x + 2 \, b^{3}}{2 \, {\left(a x + b\right)}^{2} b^{4} x}"," ",0,"3*a*log(abs(a*x + b))/b^4 - 3*a*log(abs(x))/b^4 - 1/2*(6*a^2*b*x^2 + 9*a*b^2*x + 2*b^3)/((a*x + b)^2*b^4*x)","A",0
1643,1,73,0,0.156756," ","integrate(1/(a+b/x)^3/x^6,x, algorithm=""giac"")","-\frac{6 \, a^{2} \log\left({\left| a x + b \right|}\right)}{b^{5}} + \frac{6 \, a^{2} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{12 \, a^{3} x^{3} + 18 \, a^{2} b x^{2} + 4 \, a b^{2} x - b^{3}}{2 \, {\left(a x^{2} + b x\right)}^{2} b^{4}}"," ",0,"-6*a^2*log(abs(a*x + b))/b^5 + 6*a^2*log(abs(x))/b^5 + 1/2*(12*a^3*x^3 + 18*a^2*b*x^2 + 4*a*b^2*x - b^3)/((a*x^2 + b*x)^2*b^4)","A",0
1644,1,86,0,0.166894," ","integrate(1/(a+b/x)^3/x^7,x, algorithm=""giac"")","\frac{10 \, a^{3} \log\left({\left| a x + b \right|}\right)}{b^{6}} - \frac{10 \, a^{3} \log\left({\left| x \right|}\right)}{b^{6}} - \frac{60 \, a^{4} b x^{4} + 90 \, a^{3} b^{2} x^{3} + 20 \, a^{2} b^{3} x^{2} - 5 \, a b^{4} x + 2 \, b^{5}}{6 \, {\left(a x + b\right)}^{2} b^{6} x^{3}}"," ",0,"10*a^3*log(abs(a*x + b))/b^6 - 10*a^3*log(abs(x))/b^6 - 1/6*(60*a^4*b*x^4 + 90*a^3*b^2*x^3 + 20*a^2*b^3*x^2 - 5*a*b^4*x + 2*b^5)/((a*x + b)^2*b^6*x^3)","A",0
1645,1,97,0,0.154183," ","integrate(1/(a+b/x)^3/x^8,x, algorithm=""giac"")","-\frac{15 \, a^{4} \log\left({\left| a x + b \right|}\right)}{b^{7}} + \frac{15 \, a^{4} \log\left({\left| x \right|}\right)}{b^{7}} + \frac{60 \, a^{5} b x^{5} + 90 \, a^{4} b^{2} x^{4} + 20 \, a^{3} b^{3} x^{3} - 5 \, a^{2} b^{4} x^{2} + 2 \, a b^{5} x - b^{6}}{4 \, {\left(a x + b\right)}^{2} b^{7} x^{4}}"," ",0,"-15*a^4*log(abs(a*x + b))/b^7 + 15*a^4*log(abs(x))/b^7 + 1/4*(60*a^5*b*x^5 + 90*a^4*b^2*x^4 + 20*a^3*b^3*x^3 - 5*a^2*b^4*x^2 + 2*a*b^5*x - b^6)/((a*x + b)^2*b^7*x^4)","A",0
1646,1,108,0,0.153048," ","integrate(1/(a+b/x)^3/x^9,x, algorithm=""giac"")","\frac{21 \, a^{5} \log\left({\left| a x + b \right|}\right)}{b^{8}} - \frac{21 \, a^{5} \log\left({\left| x \right|}\right)}{b^{8}} - \frac{420 \, a^{6} b x^{6} + 630 \, a^{5} b^{2} x^{5} + 140 \, a^{4} b^{3} x^{4} - 35 \, a^{3} b^{4} x^{3} + 14 \, a^{2} b^{5} x^{2} - 7 \, a b^{6} x + 4 \, b^{7}}{20 \, {\left(a x + b\right)}^{2} b^{8} x^{5}}"," ",0,"21*a^5*log(abs(a*x + b))/b^8 - 21*a^5*log(abs(x))/b^8 - 1/20*(420*a^6*b*x^6 + 630*a^5*b^2*x^5 + 140*a^4*b^3*x^4 - 35*a^3*b^4*x^3 + 14*a^2*b^5*x^2 - 7*a*b^6*x + 4*b^7)/((a*x + b)^2*b^8*x^5)","A",0
1647,1,13,0,0.148772," ","integrate((a+b/x)*x^(5/2),x, algorithm=""giac"")","\frac{2}{7} \, a x^{\frac{7}{2}} + \frac{2}{5} \, b x^{\frac{5}{2}}"," ",0,"2/7*a*x^(7/2) + 2/5*b*x^(5/2)","A",0
1648,1,13,0,0.162026," ","integrate((a+b/x)*x^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, a x^{\frac{5}{2}} + \frac{2}{3} \, b x^{\frac{3}{2}}"," ",0,"2/5*a*x^(5/2) + 2/3*b*x^(3/2)","A",0
1649,1,13,0,0.166601," ","integrate((a+b/x)*x^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, a x^{\frac{3}{2}} + 2 \, b \sqrt{x}"," ",0,"2/3*a*x^(3/2) + 2*b*sqrt(x)","A",0
1650,1,13,0,0.151844," ","integrate((a+b/x)/x^(1/2),x, algorithm=""giac"")","2 \, a \sqrt{x} - \frac{2 \, b}{\sqrt{x}}"," ",0,"2*a*sqrt(x) - 2*b/sqrt(x)","A",0
1651,1,11,0,0.150118," ","integrate((a+b/x)/x^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a x + b\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"-2/3*(3*a*x + b)/x^(3/2)","A",0
1652,1,13,0,0.151536," ","integrate((a+b/x)/x^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(5 \, a x + 3 \, b\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"-2/15*(5*a*x + 3*b)/x^(5/2)","A",0
1653,1,24,0,0.149694," ","integrate((a+b/x)^2*x^(5/2),x, algorithm=""giac"")","\frac{2}{7} \, a^{2} x^{\frac{7}{2}} + \frac{4}{5} \, a b x^{\frac{5}{2}} + \frac{2}{3} \, b^{2} x^{\frac{3}{2}}"," ",0,"2/7*a^2*x^(7/2) + 4/5*a*b*x^(5/2) + 2/3*b^2*x^(3/2)","A",0
1654,1,24,0,0.152678," ","integrate((a+b/x)^2*x^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, a^{2} x^{\frac{5}{2}} + \frac{4}{3} \, a b x^{\frac{3}{2}} + 2 \, b^{2} \sqrt{x}"," ",0,"2/5*a^2*x^(5/2) + 4/3*a*b*x^(3/2) + 2*b^2*sqrt(x)","A",0
1655,1,24,0,0.147458," ","integrate((a+b/x)^2*x^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, a^{2} x^{\frac{3}{2}} + 4 \, a b \sqrt{x} - \frac{2 \, b^{2}}{\sqrt{x}}"," ",0,"2/3*a^2*x^(3/2) + 4*a*b*sqrt(x) - 2*b^2/sqrt(x)","A",0
1656,1,23,0,0.150064," ","integrate((a+b/x)^2/x^(1/2),x, algorithm=""giac"")","2 \, a^{2} \sqrt{x} - \frac{2 \, {\left(6 \, a b x + b^{2}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2*a^2*sqrt(x) - 2/3*(6*a*b*x + b^2)/x^(3/2)","A",0
1657,1,24,0,0.154917," ","integrate((a+b/x)^2/x^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, a^{2} x^{2} + 10 \, a b x + 3 \, b^{2}\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"-2/15*(15*a^2*x^2 + 10*a*b*x + 3*b^2)/x^(5/2)","A",0
1658,1,24,0,0.154160," ","integrate((a+b/x)^2/x^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, a^{2} x^{2} + 42 \, a b x + 15 \, b^{2}\right)}}{105 \, x^{\frac{7}{2}}}"," ",0,"-2/105*(35*a^2*x^2 + 42*a*b*x + 15*b^2)/x^(7/2)","A",0
1659,1,35,0,0.149637," ","integrate((a+b/x)^3*x^(5/2),x, algorithm=""giac"")","\frac{2}{7} \, a^{3} x^{\frac{7}{2}} + \frac{6}{5} \, a^{2} b x^{\frac{5}{2}} + 2 \, a b^{2} x^{\frac{3}{2}} + 2 \, b^{3} \sqrt{x}"," ",0,"2/7*a^3*x^(7/2) + 6/5*a^2*b*x^(5/2) + 2*a*b^2*x^(3/2) + 2*b^3*sqrt(x)","A",0
1660,1,35,0,0.150725," ","integrate((a+b/x)^3*x^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, a^{3} x^{\frac{5}{2}} + 2 \, a^{2} b x^{\frac{3}{2}} + 6 \, a b^{2} \sqrt{x} - \frac{2 \, b^{3}}{\sqrt{x}}"," ",0,"2/5*a^3*x^(5/2) + 2*a^2*b*x^(3/2) + 6*a*b^2*sqrt(x) - 2*b^3/sqrt(x)","A",0
1661,1,34,0,0.176700," ","integrate((a+b/x)^3*x^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, a^{3} x^{\frac{3}{2}} + 6 \, a^{2} b \sqrt{x} - \frac{2 \, {\left(9 \, a b^{2} x + b^{3}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*a^3*x^(3/2) + 6*a^2*b*sqrt(x) - 2/3*(9*a*b^2*x + b^3)/x^(3/2)","A",0
1662,1,34,0,0.162277," ","integrate((a+b/x)^3/x^(1/2),x, algorithm=""giac"")","2 \, a^{3} \sqrt{x} - \frac{2 \, {\left(15 \, a^{2} b x^{2} + 5 \, a b^{2} x + b^{3}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2*a^3*sqrt(x) - 2/5*(15*a^2*b*x^2 + 5*a*b^2*x + b^3)/x^(5/2)","A",0
1663,1,35,0,0.165396," ","integrate((a+b/x)^3/x^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, a^{3} x^{3} + 35 \, a^{2} b x^{2} + 21 \, a b^{2} x + 5 \, b^{3}\right)}}{35 \, x^{\frac{7}{2}}}"," ",0,"-2/35*(35*a^3*x^3 + 35*a^2*b*x^2 + 21*a*b^2*x + 5*b^3)/x^(7/2)","A",0
1664,1,35,0,0.158036," ","integrate((a+b/x)^3/x^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, a^{3} x^{3} + 189 \, a^{2} b x^{2} + 135 \, a b^{2} x + 35 \, b^{3}\right)}}{315 \, x^{\frac{9}{2}}}"," ",0,"-2/315*(105*a^3*x^3 + 189*a^2*b*x^2 + 135*a*b^2*x + 35*b^3)/x^(9/2)","A",0
1665,1,70,0,0.153240," ","integrate(x^(5/2)/(a+b/x),x, algorithm=""giac"")","\frac{2 \, b^{4} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}} + \frac{2 \, {\left(15 \, a^{6} x^{\frac{7}{2}} - 21 \, a^{5} b x^{\frac{5}{2}} + 35 \, a^{4} b^{2} x^{\frac{3}{2}} - 105 \, a^{3} b^{3} \sqrt{x}\right)}}{105 \, a^{7}}"," ",0,"2*b^4*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^4) + 2/105*(15*a^6*x^(7/2) - 21*a^5*b*x^(5/2) + 35*a^4*b^2*x^(3/2) - 105*a^3*b^3*sqrt(x))/a^7","A",0
1666,1,59,0,0.210373," ","integrate(x^(3/2)/(a+b/x),x, algorithm=""giac"")","-\frac{2 \, b^{3} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} + \frac{2 \, {\left(3 \, a^{4} x^{\frac{5}{2}} - 5 \, a^{3} b x^{\frac{3}{2}} + 15 \, a^{2} b^{2} \sqrt{x}\right)}}{15 \, a^{5}}"," ",0,"-2*b^3*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^3) + 2/15*(3*a^4*x^(5/2) - 5*a^3*b*x^(3/2) + 15*a^2*b^2*sqrt(x))/a^5","A",0
1667,1,45,0,0.174450," ","integrate(x^(1/2)/(a+b/x),x, algorithm=""giac"")","\frac{2 \, b^{2} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{2 \, {\left(a^{2} x^{\frac{3}{2}} - 3 \, a b \sqrt{x}\right)}}{3 \, a^{3}}"," ",0,"2*b^2*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^2) + 2/3*(a^2*x^(3/2) - 3*a*b*sqrt(x))/a^3","A",0
1668,1,31,0,0.149641," ","integrate(1/(a+b/x)/x^(1/2),x, algorithm=""giac"")","-\frac{2 \, b \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a} + \frac{2 \, \sqrt{x}}{a}"," ",0,"-2*b*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a) + 2*sqrt(x)/a","A",0
1669,1,18,0,0.149561," ","integrate(1/(a+b/x)/x^(3/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"2*arctan(a*sqrt(x)/sqrt(a*b))/sqrt(a*b)","A",0
1670,1,31,0,0.172983," ","integrate(1/(a+b/x)/x^(5/2),x, algorithm=""giac"")","-\frac{2 \, a \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b} - \frac{2}{b \sqrt{x}}"," ",0,"-2*a*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b) - 2/(b*sqrt(x))","A",0
1671,1,41,0,0.175378," ","integrate(1/(a+b/x)/x^(7/2),x, algorithm=""giac"")","\frac{2 \, a^{2} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{2 \, {\left(3 \, a x - b\right)}}{3 \, b^{2} x^{\frac{3}{2}}}"," ",0,"2*a^2*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^2) + 2/3*(3*a*x - b)/(b^2*x^(3/2))","A",0
1672,1,52,0,0.159323," ","integrate(1/(a+b/x)/x^(9/2),x, algorithm=""giac"")","-\frac{2 \, a^{3} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} - \frac{2 \, {\left(15 \, a^{2} x^{2} - 5 \, a b x + 3 \, b^{2}\right)}}{15 \, b^{3} x^{\frac{5}{2}}}"," ",0,"-2*a^3*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^3) - 2/15*(15*a^2*x^2 - 5*a*b*x + 3*b^2)/(b^3*x^(5/2))","A",0
1673,1,88,0,0.154900," ","integrate(x^(5/2)/(a+b/x)^2,x, algorithm=""giac"")","\frac{9 \, b^{4} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{5}} - \frac{b^{4} \sqrt{x}}{{\left(a x + b\right)} a^{5}} + \frac{2 \, {\left(5 \, a^{12} x^{\frac{7}{2}} - 14 \, a^{11} b x^{\frac{5}{2}} + 35 \, a^{10} b^{2} x^{\frac{3}{2}} - 140 \, a^{9} b^{3} \sqrt{x}\right)}}{35 \, a^{14}}"," ",0,"9*b^4*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^5) - b^4*sqrt(x)/((a*x + b)*a^5) + 2/35*(5*a^12*x^(7/2) - 14*a^11*b*x^(5/2) + 35*a^10*b^2*x^(3/2) - 140*a^9*b^3*sqrt(x))/a^14","A",0
1674,1,76,0,0.159289," ","integrate(x^(3/2)/(a+b/x)^2,x, algorithm=""giac"")","-\frac{7 \, b^{3} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}} + \frac{b^{3} \sqrt{x}}{{\left(a x + b\right)} a^{4}} + \frac{2 \, {\left(3 \, a^{8} x^{\frac{5}{2}} - 10 \, a^{7} b x^{\frac{3}{2}} + 45 \, a^{6} b^{2} \sqrt{x}\right)}}{15 \, a^{10}}"," ",0,"-7*b^3*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^4) + b^3*sqrt(x)/((a*x + b)*a^4) + 2/15*(3*a^8*x^(5/2) - 10*a^7*b*x^(3/2) + 45*a^6*b^2*sqrt(x))/a^10","A",0
1675,1,65,0,0.183678," ","integrate(x^(1/2)/(a+b/x)^2,x, algorithm=""giac"")","\frac{5 \, b^{2} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} - \frac{b^{2} \sqrt{x}}{{\left(a x + b\right)} a^{3}} + \frac{2 \, {\left(a^{4} x^{\frac{3}{2}} - 6 \, a^{3} b \sqrt{x}\right)}}{3 \, a^{6}}"," ",0,"5*b^2*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^3) - b^2*sqrt(x)/((a*x + b)*a^3) + 2/3*(a^4*x^(3/2) - 6*a^3*b*sqrt(x))/a^6","A",0
1676,1,46,0,0.163629," ","integrate(1/(a+b/x)^2/x^(1/2),x, algorithm=""giac"")","-\frac{3 \, b \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{2 \, \sqrt{x}}{a^{2}} + \frac{b \sqrt{x}}{{\left(a x + b\right)} a^{2}}"," ",0,"-3*b*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^2) + 2*sqrt(x)/a^2 + b*sqrt(x)/((a*x + b)*a^2)","A",0
1677,1,36,0,0.152617," ","integrate(1/(a+b/x)^2/x^(3/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} a} - \frac{\sqrt{x}}{{\left(a x + b\right)} a}"," ",0,"arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a) - sqrt(x)/((a*x + b)*a)","A",0
1678,1,35,0,0.161139," ","integrate(1/(a+b/x)^2/x^(5/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b} + \frac{\sqrt{x}}{{\left(a x + b\right)} b}"," ",0,"arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b) + sqrt(x)/((a*x + b)*b)","A",0
1679,1,49,0,0.155451," ","integrate(1/(a+b/x)^2/x^(7/2),x, algorithm=""giac"")","-\frac{3 \, a \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} - \frac{3 \, a x + 2 \, b}{{\left(a x^{\frac{3}{2}} + b \sqrt{x}\right)} b^{2}}"," ",0,"-3*a*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^2) - (3*a*x + 2*b)/((a*x^(3/2) + b*sqrt(x))*b^2)","A",0
1680,1,58,0,0.174173," ","integrate(1/(a+b/x)^2/x^(9/2),x, algorithm=""giac"")","\frac{5 \, a^{2} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{a^{2} \sqrt{x}}{{\left(a x + b\right)} b^{3}} + \frac{2 \, {\left(6 \, a x - b\right)}}{3 \, b^{3} x^{\frac{3}{2}}}"," ",0,"5*a^2*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^3) + a^2*sqrt(x)/((a*x + b)*b^3) + 2/3*(6*a*x - b)/(b^3*x^(3/2))","A",0
1681,1,70,0,0.162143," ","integrate(1/(a+b/x)^2/x^(11/2),x, algorithm=""giac"")","-\frac{7 \, a^{3} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b} b^{4}} - \frac{a^{3} \sqrt{x}}{{\left(a x + b\right)} b^{4}} - \frac{2 \, {\left(45 \, a^{2} x^{2} - 10 \, a b x + 3 \, b^{2}\right)}}{15 \, b^{4} x^{\frac{5}{2}}}"," ",0,"-7*a^3*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^4) - a^3*sqrt(x)/((a*x + b)*b^4) - 2/15*(45*a^2*x^2 - 10*a*b*x + 3*b^2)/(b^4*x^(5/2))","A",0
1682,1,88,0,0.195736," ","integrate(x^(3/2)/(a+b/x)^3,x, algorithm=""giac"")","-\frac{63 \, b^{3} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} a^{5}} + \frac{17 \, a b^{3} x^{\frac{3}{2}} + 15 \, b^{4} \sqrt{x}}{4 \, {\left(a x + b\right)}^{2} a^{5}} + \frac{2 \, {\left(a^{12} x^{\frac{5}{2}} - 5 \, a^{11} b x^{\frac{3}{2}} + 30 \, a^{10} b^{2} \sqrt{x}\right)}}{5 \, a^{15}}"," ",0,"-63/4*b^3*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^5) + 1/4*(17*a*b^3*x^(3/2) + 15*b^4*sqrt(x))/((a*x + b)^2*a^5) + 2/5*(a^12*x^(5/2) - 5*a^11*b*x^(3/2) + 30*a^10*b^2*sqrt(x))/a^15","A",0
1683,1,77,0,0.190688," ","integrate(x^(1/2)/(a+b/x)^3,x, algorithm=""giac"")","\frac{35 \, b^{2} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} a^{4}} - \frac{13 \, a b^{2} x^{\frac{3}{2}} + 11 \, b^{3} \sqrt{x}}{4 \, {\left(a x + b\right)}^{2} a^{4}} + \frac{2 \, {\left(a^{6} x^{\frac{3}{2}} - 9 \, a^{5} b \sqrt{x}\right)}}{3 \, a^{9}}"," ",0,"35/4*b^2*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^4) - 1/4*(13*a*b^2*x^(3/2) + 11*b^3*sqrt(x))/((a*x + b)^2*a^4) + 2/3*(a^6*x^(3/2) - 9*a^5*b*sqrt(x))/a^9","A",0
1684,1,59,0,0.155325," ","integrate(1/(a+b/x)^3/x^(1/2),x, algorithm=""giac"")","-\frac{15 \, b \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} a^{3}} + \frac{2 \, \sqrt{x}}{a^{3}} + \frac{9 \, a b x^{\frac{3}{2}} + 7 \, b^{2} \sqrt{x}}{4 \, {\left(a x + b\right)}^{2} a^{3}}"," ",0,"-15/4*b*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^3) + 2*sqrt(x)/a^3 + 1/4*(9*a*b*x^(3/2) + 7*b^2*sqrt(x))/((a*x + b)^2*a^3)","A",0
1685,1,47,0,0.157223," ","integrate(1/(a+b/x)^3/x^(3/2),x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} a^{2}} - \frac{5 \, a x^{\frac{3}{2}} + 3 \, b \sqrt{x}}{4 \, {\left(a x + b\right)}^{2} a^{2}}"," ",0,"3/4*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a^2) - 1/4*(5*a*x^(3/2) + 3*b*sqrt(x))/((a*x + b)^2*a^2)","A",0
1686,1,52,0,0.156299," ","integrate(1/(a+b/x)^3/x^(5/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} a b} + \frac{a x^{\frac{3}{2}} - b \sqrt{x}}{4 \, {\left(a x + b\right)}^{2} a b}"," ",0,"1/4*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*a*b) + 1/4*(a*x^(3/2) - b*sqrt(x))/((a*x + b)^2*a*b)","A",0
1687,1,47,0,0.151915," ","integrate(1/(a+b/x)^3/x^(7/2),x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} b^{2}} + \frac{3 \, a x^{\frac{3}{2}} + 5 \, b \sqrt{x}}{4 \, {\left(a x + b\right)}^{2} b^{2}}"," ",0,"3/4*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/4*(3*a*x^(3/2) + 5*b*sqrt(x))/((a*x + b)^2*b^2)","A",0
1688,1,59,0,0.158784," ","integrate(1/(a+b/x)^3/x^(9/2),x, algorithm=""giac"")","-\frac{15 \, a \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} b^{3}} - \frac{2}{b^{3} \sqrt{x}} - \frac{7 \, a^{2} x^{\frac{3}{2}} + 9 \, a b \sqrt{x}}{4 \, {\left(a x + b\right)}^{2} b^{3}}"," ",0,"-15/4*a*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^3) - 2/(b^3*sqrt(x)) - 1/4*(7*a^2*x^(3/2) + 9*a*b*sqrt(x))/((a*x + b)^2*b^3)","A",0
1689,1,71,0,0.153390," ","integrate(1/(a+b/x)^3/x^(11/2),x, algorithm=""giac"")","\frac{35 \, a^{2} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} b^{4}} + \frac{2 \, {\left(9 \, a x - b\right)}}{3 \, b^{4} x^{\frac{3}{2}}} + \frac{11 \, a^{3} x^{\frac{3}{2}} + 13 \, a^{2} b \sqrt{x}}{4 \, {\left(a x + b\right)}^{2} b^{4}}"," ",0,"35/4*a^2*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^4) + 2/3*(9*a*x - b)/(b^4*x^(3/2)) + 1/4*(11*a^3*x^(3/2) + 13*a^2*b*sqrt(x))/((a*x + b)^2*b^4)","A",0
1690,1,80,0,0.159728," ","integrate(1/(a+b/x)^3/x^(13/2),x, algorithm=""giac"")","-\frac{63 \, a^{3} \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{4 \, \sqrt{a b} b^{5}} - \frac{15 \, a^{4} x^{\frac{3}{2}} + 17 \, a^{3} b \sqrt{x}}{4 \, {\left(a x + b\right)}^{2} b^{5}} - \frac{2 \, {\left(30 \, a^{2} x^{2} - 5 \, a b x + b^{2}\right)}}{5 \, b^{5} x^{\frac{5}{2}}}"," ",0,"-63/4*a^3*arctan(a*sqrt(x)/sqrt(a*b))/(sqrt(a*b)*b^5) - 1/4*(15*a^4*x^(3/2) + 17*a^3*b*sqrt(x))/((a*x + b)^2*b^5) - 2/5*(30*a^2*x^2 - 5*a*b*x + b^2)/(b^5*x^(5/2))","A",0
1691,1,108,0,0.218544," ","integrate(x^3*(a+b/x)^(1/2),x, algorithm=""giac"")","\frac{5 \, b^{4} \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right) \mathrm{sgn}\left(x\right)}{128 \, a^{\frac{7}{2}}} - \frac{5 \, b^{4} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{128 \, a^{\frac{7}{2}}} + \frac{1}{192} \, \sqrt{a x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, x \mathrm{sgn}\left(x\right) + \frac{b \mathrm{sgn}\left(x\right)}{a}\right)} x - \frac{5 \, b^{2} \mathrm{sgn}\left(x\right)}{a^{2}}\right)} x + \frac{15 \, b^{3} \mathrm{sgn}\left(x\right)}{a^{3}}\right)}"," ",0,"5/128*b^4*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))*sgn(x)/a^(7/2) - 5/128*b^4*log(abs(b))*sgn(x)/a^(7/2) + 1/192*sqrt(a*x^2 + b*x)*(2*(4*(6*x*sgn(x) + b*sgn(x)/a)*x - 5*b^2*sgn(x)/a^2)*x + 15*b^3*sgn(x)/a^3)","A",0
1692,1,94,0,0.304476," ","integrate(x^2*(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{b^{3} \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, a^{\frac{5}{2}}} + \frac{b^{3} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, a^{\frac{5}{2}}} + \frac{1}{24} \, \sqrt{a x^{2} + b x} {\left(2 \, {\left(4 \, x \mathrm{sgn}\left(x\right) + \frac{b \mathrm{sgn}\left(x\right)}{a}\right)} x - \frac{3 \, b^{2} \mathrm{sgn}\left(x\right)}{a^{2}}\right)}"," ",0,"-1/16*b^3*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))*sgn(x)/a^(5/2) + 1/16*b^3*log(abs(b))*sgn(x)/a^(5/2) + 1/24*sqrt(a*x^2 + b*x)*(2*(4*x*sgn(x) + b*sgn(x)/a)*x - 3*b^2*sgn(x)/a^2)","A",0
1693,1,78,0,0.207203," ","integrate(x*(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{b^{2} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{8 \, a^{\frac{3}{2}}} + \frac{1}{8} \, {\left(2 \, \sqrt{a x^{2} + b x} {\left(2 \, x + \frac{b}{a}\right)} + \frac{b^{2} \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right)}{a^{\frac{3}{2}}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"-1/8*b^2*log(abs(b))*sgn(x)/a^(3/2) + 1/8*(2*sqrt(a*x^2 + b*x)*(2*x + b/a) + b^2*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))/a^(3/2))*sgn(x)","A",0
1694,1,64,0,0.204956," ","integrate((a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{b \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right) \mathrm{sgn}\left(x\right)}{2 \, \sqrt{a}} + \frac{b \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{2 \, \sqrt{a}} + \sqrt{a x^{2} + b x} \mathrm{sgn}\left(x\right)"," ",0,"-1/2*b*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))*sgn(x)/sqrt(a) + 1/2*b*log(abs(b))*sgn(x)/sqrt(a) + sqrt(a*x^2 + b*x)*sgn(x)","B",0
1695,-2,0,0,0.000000," ","integrate((a+b/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,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [82.1195442914,26,-89]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [85.3561567818,-64,-30]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [42,43.9628838282,-9]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
1696,1,83,0,0.217120," ","integrate((a+b/x)^(1/2)/x^2,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a \mathrm{sgn}\left(x\right) + 3 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b \mathrm{sgn}\left(x\right) + b^{2} \mathrm{sgn}\left(x\right)\right)}}{3 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3}}"," ",0,"2/3*(3*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*sgn(x) + 3*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b*sgn(x) + b^2*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^3","B",0
1697,1,115,0,0.226234," ","integrate((a+b/x)^(1/2)/x^3,x, algorithm=""giac"")","\frac{2 \, {\left(15 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} \mathrm{sgn}\left(x\right) + 25 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b \mathrm{sgn}\left(x\right) + 15 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{2} \mathrm{sgn}\left(x\right) + 3 \, b^{3} \mathrm{sgn}\left(x\right)\right)}}{15 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5}}"," ",0,"2/15*(15*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*sgn(x) + 25*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b*sgn(x) + 15*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^2*sgn(x) + 3*b^3*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^5","B",0
1698,1,146,0,0.247461," ","integrate((a+b/x)^(1/2)/x^4,x, algorithm=""giac"")","\frac{2 \, {\left(140 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} \mathrm{sgn}\left(x\right) + 315 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b \mathrm{sgn}\left(x\right) + 273 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{2} \mathrm{sgn}\left(x\right) + 105 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{3} \mathrm{sgn}\left(x\right) + 15 \, b^{4} \mathrm{sgn}\left(x\right)\right)}}{105 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{7}}"," ",0,"2/105*(140*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*sgn(x) + 315*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b*sgn(x) + 273*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^2*sgn(x) + 105*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^3*sgn(x) + 15*b^4*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^7","B",0
1699,1,177,0,0.251595," ","integrate((a+b/x)^(1/2)/x^5,x, algorithm=""giac"")","\frac{2 \, {\left(630 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} \mathrm{sgn}\left(x\right) + 1764 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b \mathrm{sgn}\left(x\right) + 1995 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{2} \mathrm{sgn}\left(x\right) + 1125 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{3} \mathrm{sgn}\left(x\right) + 315 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{4} \mathrm{sgn}\left(x\right) + 35 \, b^{5} \mathrm{sgn}\left(x\right)\right)}}{315 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{9}}"," ",0,"2/315*(630*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*sgn(x) + 1764*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b*sgn(x) + 1995*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^2*sgn(x) + 1125*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^3*sgn(x) + 315*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^4*sgn(x) + 35*b^5*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^9","B",0
1700,1,208,0,0.337528," ","integrate((a+b/x)^(1/2)/x^6,x, algorithm=""giac"")","\frac{2 \, {\left(11088 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{6} a^{3} \mathrm{sgn}\left(x\right) + 36960 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} b \mathrm{sgn}\left(x\right) + 51480 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b^{2} \mathrm{sgn}\left(x\right) + 38115 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{3} \mathrm{sgn}\left(x\right) + 15785 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{4} \mathrm{sgn}\left(x\right) + 3465 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{5} \mathrm{sgn}\left(x\right) + 315 \, b^{6} \mathrm{sgn}\left(x\right)\right)}}{3465 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{11}}"," ",0,"2/3465*(11088*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*sgn(x) + 36960*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b*sgn(x) + 51480*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^2*sgn(x) + 38115*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^3*sgn(x) + 15785*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^4*sgn(x) + 3465*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^5*sgn(x) + 315*b^6*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^11","B",0
1701,1,106,0,0.260277," ","integrate((a+b/x)^(3/2)*x^3,x, algorithm=""giac"")","-\frac{3 \, b^{4} \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right) \mathrm{sgn}\left(x\right)}{128 \, a^{\frac{5}{2}}} + \frac{3 \, b^{4} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{128 \, a^{\frac{5}{2}}} + \frac{1}{64} \, \sqrt{a x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, a x \mathrm{sgn}\left(x\right) + 3 \, b \mathrm{sgn}\left(x\right)\right)} x + \frac{b^{2} \mathrm{sgn}\left(x\right)}{a}\right)} x - \frac{3 \, b^{3} \mathrm{sgn}\left(x\right)}{a^{2}}\right)}"," ",0,"-3/128*b^4*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))*sgn(x)/a^(5/2) + 3/128*b^4*log(abs(b))*sgn(x)/a^(5/2) + 1/64*sqrt(a*x^2 + b*x)*(2*(4*(2*a*x*sgn(x) + 3*b*sgn(x))*x + b^2*sgn(x)/a)*x - 3*b^3*sgn(x)/a^2)","A",0
1702,1,93,0,0.219045," ","integrate((a+b/x)^(3/2)*x^2,x, algorithm=""giac"")","\frac{b^{3} \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, a^{\frac{3}{2}}} - \frac{b^{3} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, a^{\frac{3}{2}}} + \frac{1}{24} \, \sqrt{a x^{2} + b x} {\left(2 \, {\left(4 \, a x \mathrm{sgn}\left(x\right) + 7 \, b \mathrm{sgn}\left(x\right)\right)} x + \frac{3 \, b^{2} \mathrm{sgn}\left(x\right)}{a}\right)}"," ",0,"1/16*b^3*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))*sgn(x)/a^(3/2) - 1/16*b^3*log(abs(b))*sgn(x)/a^(3/2) + 1/24*sqrt(a*x^2 + b*x)*(2*(4*a*x*sgn(x) + 7*b*sgn(x))*x + 3*b^2*sgn(x)/a)","A",0
1703,1,79,0,0.221844," ","integrate((a+b/x)^(3/2)*x,x, algorithm=""giac"")","-\frac{3 \, b^{2} \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right) \mathrm{sgn}\left(x\right)}{8 \, \sqrt{a}} + \frac{3 \, b^{2} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{8 \, \sqrt{a}} + \frac{1}{4} \, \sqrt{a x^{2} + b x} {\left(2 \, a x \mathrm{sgn}\left(x\right) + 5 \, b \mathrm{sgn}\left(x\right)\right)}"," ",0,"-3/8*b^2*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))*sgn(x)/sqrt(a) + 3/8*b^2*log(abs(b))*sgn(x)/sqrt(a) + 1/4*sqrt(a*x^2 + b*x)*(2*a*x*sgn(x) + 5*b*sgn(x))","A",0
1704,-2,0,0,0.000000," ","integrate((a+b/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,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [82.1195442914,26,-89]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [85.3561567818,-64,-30]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [42,43.9628838282,-9]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
1705,-2,0,0,0.000000," ","integrate((a+b/x)^(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)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [82.1195442914,26,-89]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [85.3561567818,-64,-30]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [42,43.9628838282,-9]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
1706,1,145,0,0.245241," ","integrate((a+b/x)^(3/2)/x^2,x, algorithm=""giac"")","\frac{2 \, {\left(5 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} \mathrm{sgn}\left(x\right) + 10 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b \mathrm{sgn}\left(x\right) + 10 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{2} \mathrm{sgn}\left(x\right) + 5 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{3} \mathrm{sgn}\left(x\right) + b^{4} \mathrm{sgn}\left(x\right)\right)}}{5 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5}}"," ",0,"2/5*(5*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*sgn(x) + 10*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b*sgn(x) + 10*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^2*sgn(x) + 5*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^3*sgn(x) + b^4*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^5","B",0
1707,1,177,0,0.253879," ","integrate((a+b/x)^(3/2)/x^3,x, algorithm=""giac"")","\frac{2 \, {\left(35 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} \mathrm{sgn}\left(x\right) + 105 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b \mathrm{sgn}\left(x\right) + 140 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{2} \mathrm{sgn}\left(x\right) + 98 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{3} \mathrm{sgn}\left(x\right) + 35 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{4} \mathrm{sgn}\left(x\right) + 5 \, b^{5} \mathrm{sgn}\left(x\right)\right)}}{35 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{7}}"," ",0,"2/35*(35*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*sgn(x) + 105*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b*sgn(x) + 140*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^2*sgn(x) + 98*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^3*sgn(x) + 35*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^4*sgn(x) + 5*b^5*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^7","B",0
1708,1,208,0,0.320864," ","integrate((a+b/x)^(3/2)/x^4,x, algorithm=""giac"")","\frac{2 \, {\left(420 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{6} a^{3} \mathrm{sgn}\left(x\right) + 1575 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} b \mathrm{sgn}\left(x\right) + 2583 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b^{2} \mathrm{sgn}\left(x\right) + 2310 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{3} \mathrm{sgn}\left(x\right) + 1170 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{4} \mathrm{sgn}\left(x\right) + 315 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{5} \mathrm{sgn}\left(x\right) + 35 \, b^{6} \mathrm{sgn}\left(x\right)\right)}}{315 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{9}}"," ",0,"2/315*(420*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*sgn(x) + 1575*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b*sgn(x) + 2583*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^2*sgn(x) + 2310*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^3*sgn(x) + 1170*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^4*sgn(x) + 315*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^5*sgn(x) + 35*b^6*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^9","B",0
1709,1,239,0,0.283217," ","integrate((a+b/x)^(3/2)/x^5,x, algorithm=""giac"")","\frac{2 \, {\left(2310 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{7} a^{\frac{7}{2}} \mathrm{sgn}\left(x\right) + 10164 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{6} a^{3} b \mathrm{sgn}\left(x\right) + 19635 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} b^{2} \mathrm{sgn}\left(x\right) + 21285 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b^{3} \mathrm{sgn}\left(x\right) + 13860 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{4} \mathrm{sgn}\left(x\right) + 5390 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{5} \mathrm{sgn}\left(x\right) + 1155 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{6} \mathrm{sgn}\left(x\right) + 105 \, b^{7} \mathrm{sgn}\left(x\right)\right)}}{1155 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{11}}"," ",0,"2/1155*(2310*(sqrt(a)*x - sqrt(a*x^2 + b*x))^7*a^(7/2)*sgn(x) + 10164*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*b*sgn(x) + 19635*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b^2*sgn(x) + 21285*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^3*sgn(x) + 13860*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^4*sgn(x) + 5390*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^5*sgn(x) + 1155*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^6*sgn(x) + 105*b^7*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^11","B",0
1710,1,270,0,0.333230," ","integrate((a+b/x)^(3/2)/x^6,x, algorithm=""giac"")","\frac{2 \, {\left(48048 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{8} a^{4} \mathrm{sgn}\left(x\right) + 240240 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{7} a^{\frac{7}{2}} b \mathrm{sgn}\left(x\right) + 531960 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{6} a^{3} b^{2} \mathrm{sgn}\left(x\right) + 675675 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} b^{3} \mathrm{sgn}\left(x\right) + 535535 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b^{4} \mathrm{sgn}\left(x\right) + 270270 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{5} \mathrm{sgn}\left(x\right) + 84630 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{6} \mathrm{sgn}\left(x\right) + 15015 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{7} \mathrm{sgn}\left(x\right) + 1155 \, b^{8} \mathrm{sgn}\left(x\right)\right)}}{15015 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{13}}"," ",0,"2/15015*(48048*(sqrt(a)*x - sqrt(a*x^2 + b*x))^8*a^4*sgn(x) + 240240*(sqrt(a)*x - sqrt(a*x^2 + b*x))^7*a^(7/2)*b*sgn(x) + 531960*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*b^2*sgn(x) + 675675*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b^3*sgn(x) + 535535*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^4*sgn(x) + 270270*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^5*sgn(x) + 84630*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^6*sgn(x) + 15015*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^7*sgn(x) + 1155*b^8*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^13","B",0
1711,1,301,0,0.336253," ","integrate((a+b/x)^(3/2)/x^7,x, algorithm=""giac"")","\frac{2 \, {\left(240240 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{9} a^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 1338480 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{8} a^{4} b \mathrm{sgn}\left(x\right) + 3333330 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{7} a^{\frac{7}{2}} b^{2} \mathrm{sgn}\left(x\right) + 4844840 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{6} a^{3} b^{3} \mathrm{sgn}\left(x\right) + 4513509 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} b^{4} \mathrm{sgn}\left(x\right) + 2788695 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b^{5} \mathrm{sgn}\left(x\right) + 1141140 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{6} \mathrm{sgn}\left(x\right) + 297990 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{7} \mathrm{sgn}\left(x\right) + 45045 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{8} \mathrm{sgn}\left(x\right) + 3003 \, b^{9} \mathrm{sgn}\left(x\right)\right)}}{45045 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{15}}"," ",0,"2/45045*(240240*(sqrt(a)*x - sqrt(a*x^2 + b*x))^9*a^(9/2)*sgn(x) + 1338480*(sqrt(a)*x - sqrt(a*x^2 + b*x))^8*a^4*b*sgn(x) + 3333330*(sqrt(a)*x - sqrt(a*x^2 + b*x))^7*a^(7/2)*b^2*sgn(x) + 4844840*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*b^3*sgn(x) + 4513509*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b^4*sgn(x) + 2788695*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^5*sgn(x) + 1141140*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^6*sgn(x) + 297990*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^7*sgn(x) + 45045*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^8*sgn(x) + 3003*b^9*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^15","B",0
1712,1,107,0,0.225881," ","integrate((a+b/x)^(5/2)*x^3,x, algorithm=""giac"")","\frac{5 \, b^{4} \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right) \mathrm{sgn}\left(x\right)}{128 \, a^{\frac{3}{2}}} - \frac{5 \, b^{4} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{128 \, a^{\frac{3}{2}}} + \frac{1}{192} \, \sqrt{a x^{2} + b x} {\left(\frac{15 \, b^{3} \mathrm{sgn}\left(x\right)}{a} + 2 \, {\left(59 \, b^{2} \mathrm{sgn}\left(x\right) + 4 \, {\left(6 \, a^{2} x \mathrm{sgn}\left(x\right) + 17 \, a b \mathrm{sgn}\left(x\right)\right)} x\right)} x\right)}"," ",0,"5/128*b^4*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))*sgn(x)/a^(3/2) - 5/128*b^4*log(abs(b))*sgn(x)/a^(3/2) + 1/192*sqrt(a*x^2 + b*x)*(15*b^3*sgn(x)/a + 2*(59*b^2*sgn(x) + 4*(6*a^2*x*sgn(x) + 17*a*b*sgn(x))*x)*x)","A",0
1713,1,93,0,0.254324," ","integrate((a+b/x)^(5/2)*x^2,x, algorithm=""giac"")","-\frac{5 \, b^{3} \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, \sqrt{a}} + \frac{5 \, b^{3} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, \sqrt{a}} + \frac{1}{24} \, \sqrt{a x^{2} + b x} {\left(33 \, b^{2} \mathrm{sgn}\left(x\right) + 2 \, {\left(4 \, a^{2} x \mathrm{sgn}\left(x\right) + 13 \, a b \mathrm{sgn}\left(x\right)\right)} x\right)}"," ",0,"-5/16*b^3*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))*sgn(x)/sqrt(a) + 5/16*b^3*log(abs(b))*sgn(x)/sqrt(a) + 1/24*sqrt(a*x^2 + b*x)*(33*b^2*sgn(x) + 2*(4*a^2*x*sgn(x) + 13*a*b*sgn(x))*x)","A",0
1714,-2,0,0,0.000000," ","integrate((a+b/x)^(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(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [82.1195442914,26,-89]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [85.3561567818,-64,-30]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [42,43.9628838282,-9]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
1715,-2,0,0,0.000000," ","integrate((a+b/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,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [82.1195442914,26,-89]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [85.3561567818,-64,-30]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [42,43.9628838282,-9]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
1716,-2,0,0,0.000000," ","integrate((a+b/x)^(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(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [82.1195442914,26,-89]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [85.3561567818,-64,-30]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [42,43.9628838282,-9]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
1717,1,207,0,0.273159," ","integrate((a+b/x)^(5/2)/x^2,x, algorithm=""giac"")","\frac{2 \, {\left(7 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{6} a^{3} \mathrm{sgn}\left(x\right) + 21 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} b \mathrm{sgn}\left(x\right) + 35 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b^{2} \mathrm{sgn}\left(x\right) + 35 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{3} \mathrm{sgn}\left(x\right) + 21 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{4} \mathrm{sgn}\left(x\right) + 7 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{5} \mathrm{sgn}\left(x\right) + b^{6} \mathrm{sgn}\left(x\right)\right)}}{7 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{7}}"," ",0,"2/7*(7*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*sgn(x) + 21*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b*sgn(x) + 35*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^2*sgn(x) + 35*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^3*sgn(x) + 21*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^4*sgn(x) + 7*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^5*sgn(x) + b^6*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^7","B",0
1718,1,239,0,0.317338," ","integrate((a+b/x)^(5/2)/x^3,x, algorithm=""giac"")","\frac{2 \, {\left(63 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{7} a^{\frac{7}{2}} \mathrm{sgn}\left(x\right) + 273 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{6} a^{3} b \mathrm{sgn}\left(x\right) + 567 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} b^{2} \mathrm{sgn}\left(x\right) + 693 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b^{3} \mathrm{sgn}\left(x\right) + 525 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{4} \mathrm{sgn}\left(x\right) + 243 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{5} \mathrm{sgn}\left(x\right) + 63 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{6} \mathrm{sgn}\left(x\right) + 7 \, b^{7} \mathrm{sgn}\left(x\right)\right)}}{63 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{9}}"," ",0,"2/63*(63*(sqrt(a)*x - sqrt(a*x^2 + b*x))^7*a^(7/2)*sgn(x) + 273*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*b*sgn(x) + 567*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b^2*sgn(x) + 693*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^3*sgn(x) + 525*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^4*sgn(x) + 243*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^5*sgn(x) + 63*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^6*sgn(x) + 7*b^7*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^9","B",0
1719,1,270,0,0.293217," ","integrate((a+b/x)^(5/2)/x^4,x, algorithm=""giac"")","\frac{2 \, {\left(924 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{8} a^{4} \mathrm{sgn}\left(x\right) + 4851 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{7} a^{\frac{7}{2}} b \mathrm{sgn}\left(x\right) + 11781 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{6} a^{3} b^{2} \mathrm{sgn}\left(x\right) + 16863 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} b^{3} \mathrm{sgn}\left(x\right) + 15345 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b^{4} \mathrm{sgn}\left(x\right) + 9009 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{5} \mathrm{sgn}\left(x\right) + 3311 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{6} \mathrm{sgn}\left(x\right) + 693 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{7} \mathrm{sgn}\left(x\right) + 63 \, b^{8} \mathrm{sgn}\left(x\right)\right)}}{693 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{11}}"," ",0,"2/693*(924*(sqrt(a)*x - sqrt(a*x^2 + b*x))^8*a^4*sgn(x) + 4851*(sqrt(a)*x - sqrt(a*x^2 + b*x))^7*a^(7/2)*b*sgn(x) + 11781*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*b^2*sgn(x) + 16863*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b^3*sgn(x) + 15345*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^4*sgn(x) + 9009*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^5*sgn(x) + 3311*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^6*sgn(x) + 693*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^7*sgn(x) + 63*b^8*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^11","B",0
1720,1,301,0,0.469654," ","integrate((a+b/x)^(5/2)/x^5,x, algorithm=""giac"")","\frac{2 \, {\left(6006 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{9} a^{\frac{9}{2}} \mathrm{sgn}\left(x\right) + 36036 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{8} a^{4} b \mathrm{sgn}\left(x\right) + 99099 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{7} a^{\frac{7}{2}} b^{2} \mathrm{sgn}\left(x\right) + 161733 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{6} a^{3} b^{3} \mathrm{sgn}\left(x\right) + 171171 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} b^{4} \mathrm{sgn}\left(x\right) + 121121 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b^{5} \mathrm{sgn}\left(x\right) + 57057 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{6} \mathrm{sgn}\left(x\right) + 17199 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{7} \mathrm{sgn}\left(x\right) + 3003 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{8} \mathrm{sgn}\left(x\right) + 231 \, b^{9} \mathrm{sgn}\left(x\right)\right)}}{3003 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{13}}"," ",0,"2/3003*(6006*(sqrt(a)*x - sqrt(a*x^2 + b*x))^9*a^(9/2)*sgn(x) + 36036*(sqrt(a)*x - sqrt(a*x^2 + b*x))^8*a^4*b*sgn(x) + 99099*(sqrt(a)*x - sqrt(a*x^2 + b*x))^7*a^(7/2)*b^2*sgn(x) + 161733*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*b^3*sgn(x) + 171171*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b^4*sgn(x) + 121121*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^5*sgn(x) + 57057*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^6*sgn(x) + 17199*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^7*sgn(x) + 3003*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^8*sgn(x) + 231*b^9*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^13","B",0
1721,1,332,0,0.380344," ","integrate((a+b/x)^(5/2)/x^6,x, algorithm=""giac"")","\frac{2 \, {\left(144144 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{10} a^{5} \mathrm{sgn}\left(x\right) + 960960 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{9} a^{\frac{9}{2}} b \mathrm{sgn}\left(x\right) + 2934360 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{8} a^{4} b^{2} \mathrm{sgn}\left(x\right) + 5360355 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{7} a^{\frac{7}{2}} b^{3} \mathrm{sgn}\left(x\right) + 6451445 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{6} a^{3} b^{4} \mathrm{sgn}\left(x\right) + 5324319 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{5} a^{\frac{5}{2}} b^{5} \mathrm{sgn}\left(x\right) + 3042585 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{4} a^{2} b^{6} \mathrm{sgn}\left(x\right) + 1186185 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{7} \mathrm{sgn}\left(x\right) + 301455 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{8} \mathrm{sgn}\left(x\right) + 45045 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{9} \mathrm{sgn}\left(x\right) + 3003 \, b^{10} \mathrm{sgn}\left(x\right)\right)}}{45045 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{15}}"," ",0,"2/45045*(144144*(sqrt(a)*x - sqrt(a*x^2 + b*x))^10*a^5*sgn(x) + 960960*(sqrt(a)*x - sqrt(a*x^2 + b*x))^9*a^(9/2)*b*sgn(x) + 2934360*(sqrt(a)*x - sqrt(a*x^2 + b*x))^8*a^4*b^2*sgn(x) + 5360355*(sqrt(a)*x - sqrt(a*x^2 + b*x))^7*a^(7/2)*b^3*sgn(x) + 6451445*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*b^4*sgn(x) + 5324319*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b^5*sgn(x) + 3042585*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^6*sgn(x) + 1186185*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^7*sgn(x) + 301455*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^8*sgn(x) + 45045*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^9*sgn(x) + 3003*b^10*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^15","B",0
1722,1,141,0,0.183248," ","integrate(x^3/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{1}{192} \, b^{4} {\left(\frac{105 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{4}} - \frac{279 \, a^{3} \sqrt{\frac{a x + b}{x}} - \frac{511 \, {\left(a x + b\right)} a^{2} \sqrt{\frac{a x + b}{x}}}{x} + \frac{385 \, {\left(a x + b\right)}^{2} a \sqrt{\frac{a x + b}{x}}}{x^{2}} - \frac{105 \, {\left(a x + b\right)}^{3} \sqrt{\frac{a x + b}{x}}}{x^{3}}}{{\left(a - \frac{a x + b}{x}\right)}^{4} a^{4}}\right)}"," ",0,"-1/192*b^4*(105*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^4) - (279*a^3*sqrt((a*x + b)/x) - 511*(a*x + b)*a^2*sqrt((a*x + b)/x)/x + 385*(a*x + b)^2*a*sqrt((a*x + b)/x)/x^2 - 105*(a*x + b)^3*sqrt((a*x + b)/x)/x^3)/((a - (a*x + b)/x)^4*a^4))","A",0
1723,1,115,0,0.169565," ","integrate(x^2/(a+b/x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, b^{3} {\left(\frac{15 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} - \frac{33 \, a^{2} \sqrt{\frac{a x + b}{x}} - \frac{40 \, {\left(a x + b\right)} a \sqrt{\frac{a x + b}{x}}}{x} + \frac{15 \, {\left(a x + b\right)}^{2} \sqrt{\frac{a x + b}{x}}}{x^{2}}}{{\left(a - \frac{a x + b}{x}\right)}^{3} a^{3}}\right)}"," ",0,"1/24*b^3*(15*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^3) - (33*a^2*sqrt((a*x + b)/x) - 40*(a*x + b)*a*sqrt((a*x + b)/x)/x + 15*(a*x + b)^2*sqrt((a*x + b)/x)/x^2)/((a - (a*x + b)/x)^3*a^3))","A",0
1724,1,89,0,0.162155," ","integrate(x/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, b^{2} {\left(\frac{3 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} - \frac{5 \, a \sqrt{\frac{a x + b}{x}} - \frac{3 \, {\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}}{{\left(a - \frac{a x + b}{x}\right)}^{2} a^{2}}\right)}"," ",0,"-1/4*b^2*(3*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^2) - (5*a*sqrt((a*x + b)/x) - 3*(a*x + b)*sqrt((a*x + b)/x)/x)/((a - (a*x + b)/x)^2*a^2))","A",0
1725,1,71,0,0.230687," ","integrate(1/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{b \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{2 \, a^{\frac{3}{2}}} + \frac{b \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right)}{2 \, a^{\frac{3}{2}} \mathrm{sgn}\left(x\right)} + \frac{\sqrt{a x^{2} + b x}}{a \mathrm{sgn}\left(x\right)}"," ",0,"-1/2*b*log(abs(b))*sgn(x)/a^(3/2) + 1/2*b*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))/(a^(3/2)*sgn(x)) + sqrt(a*x^2 + b*x)/(a*sgn(x))","B",0
1726,1,25,0,0.177675," ","integrate(1/x/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a}}"," ",0,"-2*arctan(sqrt((a*x + b)/x)/sqrt(-a))/sqrt(-a)","A",0
1727,1,16,0,0.148753," ","integrate(1/x^2/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{\frac{a x + b}{x}}}{b}"," ",0,"-2*sqrt((a*x + b)/x)/b","A",0
1728,1,41,0,0.192339," ","integrate(1/x^3/(a+b/x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, a \sqrt{\frac{a x + b}{x}} - \frac{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)}}{3 \, b^{2}}"," ",0,"2/3*(3*a*sqrt((a*x + b)/x) - (a*x + b)*sqrt((a*x + b)/x)/x)/b^2","A",0
1729,1,67,0,0.165356," ","integrate(1/x^4/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, a^{2} \sqrt{\frac{a x + b}{x}} - \frac{10 \, {\left(a x + b\right)} a \sqrt{\frac{a x + b}{x}}}{x} + \frac{3 \, {\left(a x + b\right)}^{2} \sqrt{\frac{a x + b}{x}}}{x^{2}}\right)}}{15 \, b^{3}}"," ",0,"-2/15*(15*a^2*sqrt((a*x + b)/x) - 10*(a*x + b)*a*sqrt((a*x + b)/x)/x + 3*(a*x + b)^2*sqrt((a*x + b)/x)/x^2)/b^3","A",0
1730,1,93,0,0.200473," ","integrate(1/x^5/(a+b/x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(35 \, a^{3} \sqrt{\frac{a x + b}{x}} - \frac{35 \, {\left(a x + b\right)} a^{2} \sqrt{\frac{a x + b}{x}}}{x} + \frac{21 \, {\left(a x + b\right)}^{2} a \sqrt{\frac{a x + b}{x}}}{x^{2}} - \frac{5 \, {\left(a x + b\right)}^{3} \sqrt{\frac{a x + b}{x}}}{x^{3}}\right)}}{35 \, b^{4}}"," ",0,"2/35*(35*a^3*sqrt((a*x + b)/x) - 35*(a*x + b)*a^2*sqrt((a*x + b)/x)/x + 21*(a*x + b)^2*a*sqrt((a*x + b)/x)/x^2 - 5*(a*x + b)^3*sqrt((a*x + b)/x)/x^3)/b^4","A",0
1731,1,119,0,0.167146," ","integrate(1/x^6/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(315 \, a^{4} \sqrt{\frac{a x + b}{x}} - \frac{420 \, {\left(a x + b\right)} a^{3} \sqrt{\frac{a x + b}{x}}}{x} + \frac{378 \, {\left(a x + b\right)}^{2} a^{2} \sqrt{\frac{a x + b}{x}}}{x^{2}} - \frac{180 \, {\left(a x + b\right)}^{3} a \sqrt{\frac{a x + b}{x}}}{x^{3}} + \frac{35 \, {\left(a x + b\right)}^{4} \sqrt{\frac{a x + b}{x}}}{x^{4}}\right)}}{315 \, b^{5}}"," ",0,"-2/315*(315*a^4*sqrt((a*x + b)/x) - 420*(a*x + b)*a^3*sqrt((a*x + b)/x)/x + 378*(a*x + b)^2*a^2*sqrt((a*x + b)/x)/x^2 - 180*(a*x + b)^3*a*sqrt((a*x + b)/x)/x^3 + 35*(a*x + b)^4*sqrt((a*x + b)/x)/x^4)/b^5","A",0
1732,1,131,0,0.185945," ","integrate(x^2/(a+b/x)^(3/2),x, algorithm=""giac"")","\frac{1}{24} \, b^{3} {\left(\frac{105 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{4}} + \frac{48}{a^{4} \sqrt{\frac{a x + b}{x}}} - \frac{87 \, a^{2} \sqrt{\frac{a x + b}{x}} - \frac{136 \, {\left(a x + b\right)} a \sqrt{\frac{a x + b}{x}}}{x} + \frac{57 \, {\left(a x + b\right)}^{2} \sqrt{\frac{a x + b}{x}}}{x^{2}}}{{\left(a - \frac{a x + b}{x}\right)}^{3} a^{4}}\right)}"," ",0,"1/24*b^3*(105*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^4) + 48/(a^4*sqrt((a*x + b)/x)) - (87*a^2*sqrt((a*x + b)/x) - 136*(a*x + b)*a*sqrt((a*x + b)/x)/x + 57*(a*x + b)^2*sqrt((a*x + b)/x)/x^2)/((a - (a*x + b)/x)^3*a^4))","A",0
1733,1,105,0,0.173628," ","integrate(x/(a+b/x)^(3/2),x, algorithm=""giac"")","-\frac{1}{4} \, b^{2} {\left(\frac{15 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} + \frac{8}{a^{3} \sqrt{\frac{a x + b}{x}}} - \frac{9 \, a \sqrt{\frac{a x + b}{x}} - \frac{7 \, {\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}}{{\left(a - \frac{a x + b}{x}\right)}^{2} a^{3}}\right)}"," ",0,"-1/4*b^2*(15*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^3) + 8/(a^3*sqrt((a*x + b)/x)) - (9*a*sqrt((a*x + b)/x) - 7*(a*x + b)*sqrt((a*x + b)/x)/x)/((a - (a*x + b)/x)^2*a^3))","A",0
1734,1,86,0,0.163574," ","integrate(1/(a+b/x)^(3/2),x, algorithm=""giac"")","b {\left(\frac{3 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{2 \, a - \frac{3 \, {\left(a x + b\right)}}{x}}{{\left(a \sqrt{\frac{a x + b}{x}} - \frac{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)} a^{2}}\right)}"," ",0,"b*(3*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^2) + (2*a - 3*(a*x + b)/x)/((a*sqrt((a*x + b)/x) - (a*x + b)*sqrt((a*x + b)/x)/x)*a^2))","A",0
1735,1,45,0,0.195607," ","integrate(1/(a+b/x)^(3/2)/x,x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a} - \frac{2}{a \sqrt{\frac{a x + b}{x}}}"," ",0,"-2*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a) - 2/(a*sqrt((a*x + b)/x))","A",0
1736,1,16,0,0.155953," ","integrate(1/(a+b/x)^(3/2)/x^2,x, algorithm=""giac"")","\frac{2}{b \sqrt{\frac{a x + b}{x}}}"," ",0,"2/(b*sqrt((a*x + b)/x))","A",0
1737,1,30,0,0.162077," ","integrate(1/(a+b/x)^(3/2)/x^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{a}{\sqrt{\frac{a x + b}{x}}} + \sqrt{\frac{a x + b}{x}}\right)}}{b^{2}}"," ",0,"-2*(a/sqrt((a*x + b)/x) + sqrt((a*x + b)/x))/b^2","A",0
1738,1,57,0,0.174269," ","integrate(1/(a+b/x)^(3/2)/x^4,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, a^{2}}{\sqrt{\frac{a x + b}{x}}} + 6 \, a \sqrt{\frac{a x + b}{x}} - \frac{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)}}{3 \, b^{3}}"," ",0,"2/3*(3*a^2/sqrt((a*x + b)/x) + 6*a*sqrt((a*x + b)/x) - (a*x + b)*sqrt((a*x + b)/x)/x)/b^3","A",0
1739,1,82,0,0.212752," ","integrate(1/(a+b/x)^(3/2)/x^5,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{5 \, a^{3}}{\sqrt{\frac{a x + b}{x}}} + 15 \, a^{2} \sqrt{\frac{a x + b}{x}} - \frac{5 \, {\left(a x + b\right)} a \sqrt{\frac{a x + b}{x}}}{x} + \frac{{\left(a x + b\right)}^{2} \sqrt{\frac{a x + b}{x}}}{x^{2}}\right)}}{5 \, b^{4}}"," ",0,"-2/5*(5*a^3/sqrt((a*x + b)/x) + 15*a^2*sqrt((a*x + b)/x) - 5*(a*x + b)*a*sqrt((a*x + b)/x)/x + (a*x + b)^2*sqrt((a*x + b)/x)/x^2)/b^4","A",0
1740,1,109,0,0.190664," ","integrate(1/(a+b/x)^(3/2)/x^6,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{35 \, a^{4}}{\sqrt{\frac{a x + b}{x}}} + 140 \, a^{3} \sqrt{\frac{a x + b}{x}} - \frac{70 \, {\left(a x + b\right)} a^{2} \sqrt{\frac{a x + b}{x}}}{x} + \frac{28 \, {\left(a x + b\right)}^{2} a \sqrt{\frac{a x + b}{x}}}{x^{2}} - \frac{5 \, {\left(a x + b\right)}^{3} \sqrt{\frac{a x + b}{x}}}{x^{3}}\right)}}{35 \, b^{5}}"," ",0,"2/35*(35*a^4/sqrt((a*x + b)/x) + 140*a^3*sqrt((a*x + b)/x) - 70*(a*x + b)*a^2*sqrt((a*x + b)/x)/x + 28*(a*x + b)^2*a*sqrt((a*x + b)/x)/x^2 - 5*(a*x + b)^3*sqrt((a*x + b)/x)/x^3)/b^5","A",0
1741,1,135,0,0.180303," ","integrate(1/(a+b/x)^(3/2)/x^7,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{63 \, a^{5}}{\sqrt{\frac{a x + b}{x}}} + 315 \, a^{4} \sqrt{\frac{a x + b}{x}} - \frac{210 \, {\left(a x + b\right)} a^{3} \sqrt{\frac{a x + b}{x}}}{x} + \frac{126 \, {\left(a x + b\right)}^{2} a^{2} \sqrt{\frac{a x + b}{x}}}{x^{2}} - \frac{45 \, {\left(a x + b\right)}^{3} a \sqrt{\frac{a x + b}{x}}}{x^{3}} + \frac{7 \, {\left(a x + b\right)}^{4} \sqrt{\frac{a x + b}{x}}}{x^{4}}\right)}}{63 \, b^{6}}"," ",0,"-2/63*(63*a^5/sqrt((a*x + b)/x) + 315*a^4*sqrt((a*x + b)/x) - 210*(a*x + b)*a^3*sqrt((a*x + b)/x)/x + 126*(a*x + b)^2*a^2*sqrt((a*x + b)/x)/x^2 - 45*(a*x + b)^3*a*sqrt((a*x + b)/x)/x^3 + 7*(a*x + b)^4*sqrt((a*x + b)/x)/x^4)/b^6","A",0
1742,1,134,0,0.179484," ","integrate(x^2/(a+b/x)^(5/2),x, algorithm=""giac"")","\frac{1}{24} \, b^{3} {\left(\frac{315 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{5}} + \frac{16 \, a^{4} + \frac{144 \, {\left(a x + b\right)} a^{3}}{x} - \frac{693 \, {\left(a x + b\right)}^{2} a^{2}}{x^{2}} + \frac{840 \, {\left(a x + b\right)}^{3} a}{x^{3}} - \frac{315 \, {\left(a x + b\right)}^{4}}{x^{4}}}{{\left(a \sqrt{\frac{a x + b}{x}} - \frac{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)}^{3} a^{5}}\right)}"," ",0,"1/24*b^3*(315*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^5) + (16*a^4 + 144*(a*x + b)*a^3/x - 693*(a*x + b)^2*a^2/x^2 + 840*(a*x + b)^3*a/x^3 - 315*(a*x + b)^4/x^4)/((a*sqrt((a*x + b)/x) - (a*x + b)*sqrt((a*x + b)/x)/x)^3*a^5))","A",0
1743,1,125,0,0.191971," ","integrate(x/(a+b/x)^(5/2),x, algorithm=""giac"")","-\frac{1}{12} \, b^{2} {\left(\frac{8 \, {\left(a + \frac{9 \, {\left(a x + b\right)}}{x}\right)} x}{{\left(a x + b\right)} a^{4} \sqrt{\frac{a x + b}{x}}} + \frac{105 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{4}} - \frac{3 \, {\left(13 \, a \sqrt{\frac{a x + b}{x}} - \frac{11 \, {\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)}}{{\left(a - \frac{a x + b}{x}\right)}^{2} a^{4}}\right)}"," ",0,"-1/12*b^2*(8*(a + 9*(a*x + b)/x)*x/((a*x + b)*a^4*sqrt((a*x + b)/x)) + 105*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^4) - 3*(13*a*sqrt((a*x + b)/x) - 11*(a*x + b)*sqrt((a*x + b)/x)/x)/((a - (a*x + b)/x)^2*a^4))","A",0
1744,1,98,0,0.169740," ","integrate(1/(a+b/x)^(5/2),x, algorithm=""giac"")","\frac{1}{3} \, b {\left(\frac{2 \, {\left(a + \frac{6 \, {\left(a x + b\right)}}{x}\right)} x}{{\left(a x + b\right)} a^{3} \sqrt{\frac{a x + b}{x}}} + \frac{15 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} - \frac{3 \, \sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a^{3}}\right)}"," ",0,"1/3*b*(2*(a + 6*(a*x + b)/x)*x/((a*x + b)*a^3*sqrt((a*x + b)/x)) + 15*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^3) - 3*sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a^3))","A",0
1745,1,65,0,0.165614," ","integrate(1/(a+b/x)^(5/2)/x,x, algorithm=""giac"")","-\frac{2 \, {\left(a + \frac{3 \, {\left(a x + b\right)}}{x}\right)} x}{3 \, {\left(a x + b\right)} a^{2} \sqrt{\frac{a x + b}{x}}} - \frac{2 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}}"," ",0,"-2/3*(a + 3*(a*x + b)/x)*x/((a*x + b)*a^2*sqrt((a*x + b)/x)) - 2*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^2)","A",0
1746,1,24,0,0.160615," ","integrate(1/(a+b/x)^(5/2)/x^2,x, algorithm=""giac"")","\frac{2 \, x}{3 \, {\left(a x + b\right)} b \sqrt{\frac{a x + b}{x}}}"," ",0,"2/3*x/((a*x + b)*b*sqrt((a*x + b)/x))","A",0
1747,1,36,0,0.163904," ","integrate(1/(a+b/x)^(5/2)/x^3,x, algorithm=""giac"")","-\frac{2 \, {\left(a - \frac{3 \, {\left(a x + b\right)}}{x}\right)} x}{3 \, {\left(a x + b\right)} b^{2} \sqrt{\frac{a x + b}{x}}}"," ",0,"-2/3*(a - 3*(a*x + b)/x)*x/((a*x + b)*b^2*sqrt((a*x + b)/x))","A",0
1748,1,54,0,0.171041," ","integrate(1/(a+b/x)^(5/2)/x^4,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(a^{2} - \frac{6 \, {\left(a x + b\right)} a}{x}\right)} x}{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}} - 3 \, \sqrt{\frac{a x + b}{x}}\right)}}{3 \, b^{3}}"," ",0,"2/3*((a^2 - 6*(a*x + b)*a/x)*x/((a*x + b)*sqrt((a*x + b)/x)) - 3*sqrt((a*x + b)/x))/b^3","A",0
1749,1,79,0,0.239700," ","integrate(1/(a+b/x)^(5/2)/x^5,x, algorithm=""giac"")","\frac{2 \, {\left(9 \, a \sqrt{\frac{a x + b}{x}} - \frac{{\left(a^{3} - \frac{9 \, {\left(a x + b\right)} a^{2}}{x}\right)} x}{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}} - \frac{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)}}{3 \, b^{4}}"," ",0,"2/3*(9*a*sqrt((a*x + b)/x) - (a^3 - 9*(a*x + b)*a^2/x)*x/((a*x + b)*sqrt((a*x + b)/x)) - (a*x + b)*sqrt((a*x + b)/x)/x)/b^4","A",0
1750,1,105,0,0.171182," ","integrate(1/(a+b/x)^(5/2)/x^6,x, algorithm=""giac"")","-\frac{2 \, {\left(90 \, a^{2} \sqrt{\frac{a x + b}{x}} - \frac{20 \, {\left(a x + b\right)} a \sqrt{\frac{a x + b}{x}}}{x} - \frac{5 \, {\left(a^{4} - \frac{12 \, {\left(a x + b\right)} a^{3}}{x}\right)} x}{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}} + \frac{3 \, {\left(a x + b\right)}^{2} \sqrt{\frac{a x + b}{x}}}{x^{2}}\right)}}{15 \, b^{5}}"," ",0,"-2/15*(90*a^2*sqrt((a*x + b)/x) - 20*(a*x + b)*a*sqrt((a*x + b)/x)/x - 5*(a^4 - 12*(a*x + b)*a^3/x)*x/((a*x + b)*sqrt((a*x + b)/x)) + 3*(a*x + b)^2*sqrt((a*x + b)/x)/x^2)/b^5","A",0
1751,1,131,0,0.174994," ","integrate(1/(a+b/x)^(5/2)/x^7,x, algorithm=""giac"")","\frac{2 \, {\left(210 \, a^{3} \sqrt{\frac{a x + b}{x}} - \frac{70 \, {\left(a x + b\right)} a^{2} \sqrt{\frac{a x + b}{x}}}{x} + \frac{21 \, {\left(a x + b\right)}^{2} a \sqrt{\frac{a x + b}{x}}}{x^{2}} - \frac{7 \, {\left(a^{5} - \frac{15 \, {\left(a x + b\right)} a^{4}}{x}\right)} x}{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}} - \frac{3 \, {\left(a x + b\right)}^{3} \sqrt{\frac{a x + b}{x}}}{x^{3}}\right)}}{21 \, b^{6}}"," ",0,"2/21*(210*a^3*sqrt((a*x + b)/x) - 70*(a*x + b)*a^2*sqrt((a*x + b)/x)/x + 21*(a*x + b)^2*a*sqrt((a*x + b)/x)/x^2 - 7*(a^5 - 15*(a*x + b)*a^4/x)*x/((a*x + b)*sqrt((a*x + b)/x)) - 3*(a*x + b)^3*sqrt((a*x + b)/x)/x^3)/b^6","A",0
1752,1,61,0,0.169624," ","integrate((a+b/x)^(1/2)*x^(7/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(\frac{16 \, b^{\frac{9}{2}}}{a^{4}} + \frac{35 \, {\left(a x + b\right)}^{\frac{9}{2}} - 135 \, {\left(a x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(a x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{3}}{a^{4}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"2/315*(16*b^(9/2)/a^4 + (35*(a*x + b)^(9/2) - 135*(a*x + b)^(7/2)*b + 189*(a*x + b)^(5/2)*b^2 - 105*(a*x + b)^(3/2)*b^3)/a^4)*sgn(x)","A",0
1753,1,50,0,0.162272," ","integrate((a+b/x)^(1/2)*x^(5/2),x, algorithm=""giac"")","-\frac{2}{105} \, {\left(\frac{8 \, b^{\frac{7}{2}}}{a^{3}} - \frac{15 \, {\left(a x + b\right)}^{\frac{7}{2}} - 42 \, {\left(a x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{2}}{a^{3}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"-2/105*(8*b^(7/2)/a^3 - (15*(a*x + b)^(7/2) - 42*(a*x + b)^(5/2)*b + 35*(a*x + b)^(3/2)*b^2)/a^3)*sgn(x)","A",0
1754,1,37,0,0.161420," ","integrate((a+b/x)^(1/2)*x^(3/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(\frac{2 \, b^{\frac{5}{2}}}{a^{2}} + \frac{3 \, {\left(a x + b\right)}^{\frac{5}{2}} - 5 \, {\left(a x + b\right)}^{\frac{3}{2}} b}{a^{2}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"2/15*(2*b^(5/2)/a^2 + (3*(a*x + b)^(5/2) - 5*(a*x + b)^(3/2)*b)/a^2)*sgn(x)","A",0
1755,1,24,0,0.194912," ","integrate((a+b/x)^(1/2)*x^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(\frac{{\left(a x + b\right)}^{\frac{3}{2}}}{a} - \frac{b^{\frac{3}{2}}}{a}\right)} \mathrm{sgn}\left(x\right)"," ",0,"2/3*((a*x + b)^(3/2)/a - b^(3/2)/a)*sgn(x)","A",0
1756,1,62,0,0.177227," ","integrate((a+b/x)^(1/2)/x^(1/2),x, algorithm=""giac"")","2 \, {\left(\frac{b \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + \sqrt{a x + b} - \frac{b \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + \sqrt{-b} \sqrt{b}}{\sqrt{-b}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"2*(b*arctan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b) + sqrt(a*x + b) - (b*arctan(sqrt(b)/sqrt(-b)) + sqrt(-b)*sqrt(b))/sqrt(-b))*sgn(x)","A",0
1757,1,43,0,0.256411," ","integrate((a+b/x)^(1/2)/x^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{a^{2} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{\sqrt{a x + b} a}{x}\right)} \mathrm{sgn}\left(x\right)}{a}"," ",0,"(a^2*arctan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b) - sqrt(a*x + b)*a/x)*sgn(x)/a","A",0
1758,1,68,0,0.285504," ","integrate((a+b/x)^(1/2)/x^(5/2),x, algorithm=""giac"")","-\frac{{\left(\frac{a^{3} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} + \frac{{\left(a x + b\right)}^{\frac{3}{2}} a^{3} + \sqrt{a x + b} a^{3} b}{a^{2} b x^{2}}\right)} \mathrm{sgn}\left(x\right)}{4 \, a}"," ",0,"-1/4*(a^3*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b) + ((a*x + b)^(3/2)*a^3 + sqrt(a*x + b)*a^3*b)/(a^2*b*x^2))*sgn(x)/a","A",0
1759,1,86,0,0.323012," ","integrate((a+b/x)^(1/2)/x^(7/2),x, algorithm=""giac"")","\frac{{\left(\frac{3 \, a^{4} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} + \frac{3 \, {\left(a x + b\right)}^{\frac{5}{2}} a^{4} - 8 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{4} b - 3 \, \sqrt{a x + b} a^{4} b^{2}}{a^{3} b^{2} x^{3}}\right)} \mathrm{sgn}\left(x\right)}{24 \, a}"," ",0,"1/24*(3*a^4*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b^2) + (3*(a*x + b)^(5/2)*a^4 - 8*(a*x + b)^(3/2)*a^4*b - 3*sqrt(a*x + b)*a^4*b^2)/(a^3*b^2*x^3))*sgn(x)/a","A",0
1760,1,138,0,0.201330," ","integrate((a+b/x)^(3/2)*x^(9/2),x, algorithm=""giac"")","\frac{2}{315} \, b {\left(\frac{16 \, b^{\frac{9}{2}}}{a^{4}} + \frac{35 \, {\left(a x + b\right)}^{\frac{9}{2}} - 135 \, {\left(a x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(a x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{3}}{a^{4}}\right)} \mathrm{sgn}\left(x\right) - \frac{2}{3465} \, a {\left(\frac{128 \, b^{\frac{11}{2}}}{a^{5}} - \frac{315 \, {\left(a x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(a x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(a x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(a x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{4}}{a^{5}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"2/315*b*(16*b^(9/2)/a^4 + (35*(a*x + b)^(9/2) - 135*(a*x + b)^(7/2)*b + 189*(a*x + b)^(5/2)*b^2 - 105*(a*x + b)^(3/2)*b^3)/a^4)*sgn(x) - 2/3465*a*(128*b^(11/2)/a^5 - (315*(a*x + b)^(11/2) - 1540*(a*x + b)^(9/2)*b + 2970*(a*x + b)^(7/2)*b^2 - 2772*(a*x + b)^(5/2)*b^3 + 1155*(a*x + b)^(3/2)*b^4)/a^5)*sgn(x)","A",0
1761,1,114,0,0.227697," ","integrate((a+b/x)^(3/2)*x^(7/2),x, algorithm=""giac"")","-\frac{2}{105} \, b {\left(\frac{8 \, b^{\frac{7}{2}}}{a^{3}} - \frac{15 \, {\left(a x + b\right)}^{\frac{7}{2}} - 42 \, {\left(a x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{2}}{a^{3}}\right)} \mathrm{sgn}\left(x\right) + \frac{2}{315} \, a {\left(\frac{16 \, b^{\frac{9}{2}}}{a^{4}} + \frac{35 \, {\left(a x + b\right)}^{\frac{9}{2}} - 135 \, {\left(a x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(a x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{3}}{a^{4}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"-2/105*b*(8*b^(7/2)/a^3 - (15*(a*x + b)^(7/2) - 42*(a*x + b)^(5/2)*b + 35*(a*x + b)^(3/2)*b^2)/a^3)*sgn(x) + 2/315*a*(16*b^(9/2)/a^4 + (35*(a*x + b)^(9/2) - 135*(a*x + b)^(7/2)*b + 189*(a*x + b)^(5/2)*b^2 - 105*(a*x + b)^(3/2)*b^3)/a^4)*sgn(x)","B",0
1762,1,90,0,0.178767," ","integrate((a+b/x)^(3/2)*x^(5/2),x, algorithm=""giac"")","\frac{2}{15} \, b {\left(\frac{2 \, b^{\frac{5}{2}}}{a^{2}} + \frac{3 \, {\left(a x + b\right)}^{\frac{5}{2}} - 5 \, {\left(a x + b\right)}^{\frac{3}{2}} b}{a^{2}}\right)} \mathrm{sgn}\left(x\right) - \frac{2}{105} \, a {\left(\frac{8 \, b^{\frac{7}{2}}}{a^{3}} - \frac{15 \, {\left(a x + b\right)}^{\frac{7}{2}} - 42 \, {\left(a x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{2}}{a^{3}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"2/15*b*(2*b^(5/2)/a^2 + (3*(a*x + b)^(5/2) - 5*(a*x + b)^(3/2)*b)/a^2)*sgn(x) - 2/105*a*(8*b^(7/2)/a^3 - (15*(a*x + b)^(7/2) - 42*(a*x + b)^(5/2)*b + 35*(a*x + b)^(3/2)*b^2)/a^3)*sgn(x)","B",0
1763,1,64,0,0.173967," ","integrate((a+b/x)^(3/2)*x^(3/2),x, algorithm=""giac"")","\frac{2}{3} \, b {\left(\frac{{\left(a x + b\right)}^{\frac{3}{2}}}{a} - \frac{b^{\frac{3}{2}}}{a}\right)} \mathrm{sgn}\left(x\right) + \frac{2}{15} \, a {\left(\frac{2 \, b^{\frac{5}{2}}}{a^{2}} + \frac{3 \, {\left(a x + b\right)}^{\frac{5}{2}} - 5 \, {\left(a x + b\right)}^{\frac{3}{2}} b}{a^{2}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"2/3*b*((a*x + b)^(3/2)/a - b^(3/2)/a)*sgn(x) + 2/15*a*(2*b^(5/2)/a^2 + (3*(a*x + b)^(5/2) - 5*(a*x + b)^(3/2)*b)/a^2)*sgn(x)","B",0
1764,1,44,0,0.207625," ","integrate((a+b/x)^(3/2)*x^(1/2),x, algorithm=""giac"")","\frac{2 \, b^{2} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + \frac{2}{3} \, {\left(a x + b\right)}^{\frac{3}{2}} + 2 \, \sqrt{a x + b} b"," ",0,"2*b^2*arctan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b) + 2/3*(a*x + b)^(3/2) + 2*sqrt(a*x + b)*b","A",0
1765,1,56,0,0.274700," ","integrate((a+b/x)^(3/2)/x^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, a^{2} b \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + 2 \, \sqrt{a x + b} a^{2} - \frac{\sqrt{a x + b} a b}{x}}{a}"," ",0,"(3*a^2*b*arctan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b) + 2*sqrt(a*x + b)*a^2 - sqrt(a*x + b)*a*b/x)/a","A",0
1766,1,64,0,0.342601," ","integrate((a+b/x)^(3/2)/x^(3/2),x, algorithm=""giac"")","\frac{\frac{3 \, a^{3} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{5 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{3} - 3 \, \sqrt{a x + b} a^{3} b}{a^{2} x^{2}}}{4 \, a}"," ",0,"1/4*(3*a^3*arctan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b) - (5*(a*x + b)^(3/2)*a^3 - 3*sqrt(a*x + b)*a^3*b)/(a^2*x^2))/a","A",0
1767,1,84,0,0.365867," ","integrate((a+b/x)^(3/2)/x^(5/2),x, algorithm=""giac"")","-\frac{\frac{3 \, a^{4} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} + \frac{3 \, {\left(a x + b\right)}^{\frac{5}{2}} a^{4} + 8 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{4} b - 3 \, \sqrt{a x + b} a^{4} b^{2}}{a^{3} b x^{3}}}{24 \, a}"," ",0,"-1/24*(3*a^4*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b) + (3*(a*x + b)^(5/2)*a^4 + 8*(a*x + b)^(3/2)*a^4*b - 3*sqrt(a*x + b)*a^4*b^2)/(a^3*b*x^3))/a","A",0
1768,1,229,0,0.295787," ","integrate((a+b/x)^(5/2)*x^(11/2),x, algorithm=""giac"")","\frac{2}{315} \, b^{2} {\left(\frac{16 \, b^{\frac{9}{2}}}{a^{4}} + \frac{35 \, {\left(a x + b\right)}^{\frac{9}{2}} - 135 \, {\left(a x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(a x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{3}}{a^{4}}\right)} \mathrm{sgn}\left(x\right) - \frac{4}{3465} \, a b {\left(\frac{128 \, b^{\frac{11}{2}}}{a^{5}} - \frac{315 \, {\left(a x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(a x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(a x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(a x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{4}}{a^{5}}\right)} \mathrm{sgn}\left(x\right) + \frac{2}{9009} \, a^{2} {\left(\frac{256 \, b^{\frac{13}{2}}}{a^{6}} + \frac{693 \, {\left(a x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(a x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(a x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(a x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(a x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{5}}{a^{6}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"2/315*b^2*(16*b^(9/2)/a^4 + (35*(a*x + b)^(9/2) - 135*(a*x + b)^(7/2)*b + 189*(a*x + b)^(5/2)*b^2 - 105*(a*x + b)^(3/2)*b^3)/a^4)*sgn(x) - 4/3465*a*b*(128*b^(11/2)/a^5 - (315*(a*x + b)^(11/2) - 1540*(a*x + b)^(9/2)*b + 2970*(a*x + b)^(7/2)*b^2 - 2772*(a*x + b)^(5/2)*b^3 + 1155*(a*x + b)^(3/2)*b^4)/a^5)*sgn(x) + 2/9009*a^2*(256*b^(13/2)/a^6 + (693*(a*x + b)^(13/2) - 4095*(a*x + b)^(11/2)*b + 10010*(a*x + b)^(9/2)*b^2 - 12870*(a*x + b)^(7/2)*b^3 + 9009*(a*x + b)^(5/2)*b^4 - 3003*(a*x + b)^(3/2)*b^5)/a^6)*sgn(x)","B",0
1769,1,194,0,0.209879," ","integrate((a+b/x)^(5/2)*x^(9/2),x, algorithm=""giac"")","-\frac{2}{105} \, b^{2} {\left(\frac{8 \, b^{\frac{7}{2}}}{a^{3}} - \frac{15 \, {\left(a x + b\right)}^{\frac{7}{2}} - 42 \, {\left(a x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{2}}{a^{3}}\right)} \mathrm{sgn}\left(x\right) + \frac{4}{315} \, a b {\left(\frac{16 \, b^{\frac{9}{2}}}{a^{4}} + \frac{35 \, {\left(a x + b\right)}^{\frac{9}{2}} - 135 \, {\left(a x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(a x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{3}}{a^{4}}\right)} \mathrm{sgn}\left(x\right) - \frac{2}{3465} \, a^{2} {\left(\frac{128 \, b^{\frac{11}{2}}}{a^{5}} - \frac{315 \, {\left(a x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(a x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(a x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(a x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{4}}{a^{5}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"-2/105*b^2*(8*b^(7/2)/a^3 - (15*(a*x + b)^(7/2) - 42*(a*x + b)^(5/2)*b + 35*(a*x + b)^(3/2)*b^2)/a^3)*sgn(x) + 4/315*a*b*(16*b^(9/2)/a^4 + (35*(a*x + b)^(9/2) - 135*(a*x + b)^(7/2)*b + 189*(a*x + b)^(5/2)*b^2 - 105*(a*x + b)^(3/2)*b^3)/a^4)*sgn(x) - 2/3465*a^2*(128*b^(11/2)/a^5 - (315*(a*x + b)^(11/2) - 1540*(a*x + b)^(9/2)*b + 2970*(a*x + b)^(7/2)*b^2 - 2772*(a*x + b)^(5/2)*b^3 + 1155*(a*x + b)^(3/2)*b^4)/a^5)*sgn(x)","B",0
1770,1,157,0,0.197351," ","integrate((a+b/x)^(5/2)*x^(7/2),x, algorithm=""giac"")","\frac{2}{15} \, b^{2} {\left(\frac{2 \, b^{\frac{5}{2}}}{a^{2}} + \frac{3 \, {\left(a x + b\right)}^{\frac{5}{2}} - 5 \, {\left(a x + b\right)}^{\frac{3}{2}} b}{a^{2}}\right)} \mathrm{sgn}\left(x\right) - \frac{4}{105} \, a b {\left(\frac{8 \, b^{\frac{7}{2}}}{a^{3}} - \frac{15 \, {\left(a x + b\right)}^{\frac{7}{2}} - 42 \, {\left(a x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{2}}{a^{3}}\right)} \mathrm{sgn}\left(x\right) + \frac{2}{315} \, a^{2} {\left(\frac{16 \, b^{\frac{9}{2}}}{a^{4}} + \frac{35 \, {\left(a x + b\right)}^{\frac{9}{2}} - 135 \, {\left(a x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(a x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{3}}{a^{4}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"2/15*b^2*(2*b^(5/2)/a^2 + (3*(a*x + b)^(5/2) - 5*(a*x + b)^(3/2)*b)/a^2)*sgn(x) - 4/105*a*b*(8*b^(7/2)/a^3 - (15*(a*x + b)^(7/2) - 42*(a*x + b)^(5/2)*b + 35*(a*x + b)^(3/2)*b^2)/a^3)*sgn(x) + 2/315*a^2*(16*b^(9/2)/a^4 + (35*(a*x + b)^(9/2) - 135*(a*x + b)^(7/2)*b + 189*(a*x + b)^(5/2)*b^2 - 105*(a*x + b)^(3/2)*b^3)/a^4)*sgn(x)","B",0
1771,1,120,0,0.204475," ","integrate((a+b/x)^(5/2)*x^(5/2),x, algorithm=""giac"")","\frac{2}{3} \, b^{2} {\left(\frac{{\left(a x + b\right)}^{\frac{3}{2}}}{a} - \frac{b^{\frac{3}{2}}}{a}\right)} \mathrm{sgn}\left(x\right) + \frac{4}{15} \, a b {\left(\frac{2 \, b^{\frac{5}{2}}}{a^{2}} + \frac{3 \, {\left(a x + b\right)}^{\frac{5}{2}} - 5 \, {\left(a x + b\right)}^{\frac{3}{2}} b}{a^{2}}\right)} \mathrm{sgn}\left(x\right) - \frac{2}{105} \, a^{2} {\left(\frac{8 \, b^{\frac{7}{2}}}{a^{3}} - \frac{15 \, {\left(a x + b\right)}^{\frac{7}{2}} - 42 \, {\left(a x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{2}}{a^{3}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"2/3*b^2*((a*x + b)^(3/2)/a - b^(3/2)/a)*sgn(x) + 4/15*a*b*(2*b^(5/2)/a^2 + (3*(a*x + b)^(5/2) - 5*(a*x + b)^(3/2)*b)/a^2)*sgn(x) - 2/105*a^2*(8*b^(7/2)/a^3 - (15*(a*x + b)^(7/2) - 42*(a*x + b)^(5/2)*b + 35*(a*x + b)^(3/2)*b^2)/a^3)*sgn(x)","B",0
1772,1,56,0,0.260995," ","integrate((a+b/x)^(5/2)*x^(3/2),x, algorithm=""giac"")","\frac{2 \, b^{3} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + \frac{2}{5} \, {\left(a x + b\right)}^{\frac{5}{2}} + \frac{2}{3} \, {\left(a x + b\right)}^{\frac{3}{2}} b + 2 \, \sqrt{a x + b} b^{2}"," ",0,"2*b^3*arctan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b) + 2/5*(a*x + b)^(5/2) + 2/3*(a*x + b)^(3/2)*b + 2*sqrt(a*x + b)*b^2","A",0
1773,1,74,0,0.317232," ","integrate((a+b/x)^(5/2)*x^(1/2),x, algorithm=""giac"")","\frac{\frac{15 \, a^{2} b^{2} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + 2 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{2} + 12 \, \sqrt{a x + b} a^{2} b - \frac{3 \, \sqrt{a x + b} a b^{2}}{x}}{3 \, a}"," ",0,"1/3*(15*a^2*b^2*arctan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b) + 2*(a*x + b)^(3/2)*a^2 + 12*sqrt(a*x + b)*a^2*b - 3*sqrt(a*x + b)*a*b^2/x)/a","A",0
1774,1,80,0,0.303666," ","integrate((a+b/x)^(5/2)/x^(1/2),x, algorithm=""giac"")","\frac{\frac{15 \, a^{3} b \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + 8 \, \sqrt{a x + b} a^{3} - \frac{9 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{3} b - 7 \, \sqrt{a x + b} a^{3} b^{2}}{a^{2} x^{2}}}{4 \, a}"," ",0,"1/4*(15*a^3*b*arctan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b) + 8*sqrt(a*x + b)*a^3 - (9*(a*x + b)^(3/2)*a^3*b - 7*sqrt(a*x + b)*a^3*b^2)/(a^2*x^2))/a","A",0
1775,1,79,0,0.336669," ","integrate((a+b/x)^(5/2)/x^(3/2),x, algorithm=""giac"")","\frac{\frac{15 \, a^{4} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{33 \, {\left(a x + b\right)}^{\frac{5}{2}} a^{4} - 40 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{4} b + 15 \, \sqrt{a x + b} a^{4} b^{2}}{a^{3} x^{3}}}{24 \, a}"," ",0,"1/24*(15*a^4*arctan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b) - (33*(a*x + b)^(5/2)*a^4 - 40*(a*x + b)^(3/2)*a^4*b + 15*sqrt(a*x + b)*a^4*b^2)/(a^3*x^3))/a","A",0
1776,1,99,0,0.372333," ","integrate((a+b/x)^(5/2)/x^(5/2),x, algorithm=""giac"")","-\frac{\frac{15 \, a^{5} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} + \frac{15 \, {\left(a x + b\right)}^{\frac{7}{2}} a^{5} + 73 \, {\left(a x + b\right)}^{\frac{5}{2}} a^{5} b - 55 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{5} b^{2} + 15 \, \sqrt{a x + b} a^{5} b^{3}}{a^{4} b x^{4}}}{192 \, a}"," ",0,"-1/192*(15*a^5*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b) + (15*(a*x + b)^(7/2)*a^5 + 73*(a*x + b)^(5/2)*a^5*b - 55*(a*x + b)^(3/2)*a^5*b^2 + 15*sqrt(a*x + b)*a^5*b^3)/(a^4*b*x^4))/a","A",0
1777,1,73,0,0.164900," ","integrate(x^(7/2)/(a+b/x)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a x + b} b^{4}}{a^{5}} - \frac{256 \, b^{\frac{9}{2}}}{315 \, a^{5}} + \frac{2 \, {\left(35 \, {\left(a x + b\right)}^{\frac{9}{2}} - 180 \, {\left(a x + b\right)}^{\frac{7}{2}} b + 378 \, {\left(a x + b\right)}^{\frac{5}{2}} b^{2} - 420 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{3}\right)}}{315 \, a^{5}}"," ",0,"2*sqrt(a*x + b)*b^4/a^5 - 256/315*b^(9/2)/a^5 + 2/315*(35*(a*x + b)^(9/2) - 180*(a*x + b)^(7/2)*b + 378*(a*x + b)^(5/2)*b^2 - 420*(a*x + b)^(3/2)*b^3)/a^5","A",0
1778,1,61,0,0.166310," ","integrate(x^(5/2)/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{a x + b} b^{3}}{a^{4}} + \frac{32 \, b^{\frac{7}{2}}}{35 \, a^{4}} + \frac{2 \, {\left(5 \, {\left(a x + b\right)}^{\frac{7}{2}} - 21 \, {\left(a x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{2}\right)}}{35 \, a^{4}}"," ",0,"-2*sqrt(a*x + b)*b^3/a^4 + 32/35*b^(7/2)/a^4 + 2/35*(5*(a*x + b)^(7/2) - 21*(a*x + b)^(5/2)*b + 35*(a*x + b)^(3/2)*b^2)/a^4","A",0
1779,1,49,0,0.163372," ","integrate(x^(3/2)/(a+b/x)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a x + b} b^{2}}{a^{3}} - \frac{16 \, b^{\frac{5}{2}}}{15 \, a^{3}} + \frac{2 \, {\left(3 \, {\left(a x + b\right)}^{\frac{5}{2}} - 10 \, {\left(a x + b\right)}^{\frac{3}{2}} b\right)}}{15 \, a^{3}}"," ",0,"2*sqrt(a*x + b)*b^2/a^3 - 16/15*b^(5/2)/a^3 + 2/15*(3*(a*x + b)^(5/2) - 10*(a*x + b)^(3/2)*b)/a^3","A",0
1780,1,34,0,0.192387," ","integrate(x^(1/2)/(a+b/x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(a x + b\right)}^{\frac{3}{2}}}{3 \, a^{2}} - \frac{2 \, \sqrt{a x + b} b}{a^{2}} + \frac{4 \, b^{\frac{3}{2}}}{3 \, a^{2}}"," ",0,"2/3*(a*x + b)^(3/2)/a^2 - 2*sqrt(a*x + b)*b/a^2 + 4/3*b^(3/2)/a^2","A",0
1781,1,21,0,0.177294," ","integrate(1/(a+b/x)^(1/2)/x^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a x + b}}{a} - \frac{2 \, \sqrt{b}}{a}"," ",0,"2*sqrt(a*x + b)/a - 2*sqrt(b)/a","A",0
1782,1,39,0,0.165611," ","integrate(1/(a+b/x)^(1/2)/x^(3/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{2 \, \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right)}{\sqrt{-b}}"," ",0,"2*arctan(sqrt(a*x + b)/sqrt(-b))/sqrt(-b) - 2*arctan(sqrt(b)/sqrt(-b))/sqrt(-b)","A",0
1783,1,47,0,0.206998," ","integrate(1/(a+b/x)^(1/2)/x^(5/2),x, algorithm=""giac"")","-\frac{\frac{a^{2} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} + \frac{\sqrt{a x + b} a}{b x}}{a}"," ",0,"-(a^2*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b) + sqrt(a*x + b)*a/(b*x))/a","A",0
1784,1,69,0,0.320442," ","integrate(1/(a+b/x)^(1/2)/x^(7/2),x, algorithm=""giac"")","\frac{\frac{3 \, a^{3} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} + \frac{3 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{3} - 5 \, \sqrt{a x + b} a^{3} b}{a^{2} b^{2} x^{2}}}{4 \, a}"," ",0,"1/4*(3*a^3*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b^2) + (3*(a*x + b)^(3/2)*a^3 - 5*sqrt(a*x + b)*a^3*b)/(a^2*b^2*x^2))/a","A",0
1785,1,84,0,0.230549," ","integrate(1/(a+b/x)^(1/2)/x^(9/2),x, algorithm=""giac"")","-\frac{\frac{15 \, a^{4} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{3}} + \frac{15 \, {\left(a x + b\right)}^{\frac{5}{2}} a^{4} - 40 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{4} b + 33 \, \sqrt{a x + b} a^{4} b^{2}}{a^{3} b^{3} x^{3}}}{24 \, a}"," ",0,"-1/24*(15*a^4*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b^3) + (15*(a*x + b)^(5/2)*a^4 - 40*(a*x + b)^(3/2)*a^4*b + 33*sqrt(a*x + b)*a^4*b^2)/(a^3*b^3*x^3))/a","A",0
1786,1,85,0,0.177616," ","integrate(x^(5/2)/(a+b/x)^(3/2),x, algorithm=""giac"")","\frac{256 \, b^{\frac{7}{2}}}{35 \, a^{5}} - \frac{2 \, b^{4}}{\sqrt{a x + b} a^{5}} + \frac{2 \, {\left(5 \, {\left(a x + b\right)}^{\frac{7}{2}} a^{30} - 28 \, {\left(a x + b\right)}^{\frac{5}{2}} a^{30} b + 70 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{30} b^{2} - 140 \, \sqrt{a x + b} a^{30} b^{3}\right)}}{35 \, a^{35}}"," ",0,"256/35*b^(7/2)/a^5 - 2*b^4/(sqrt(a*x + b)*a^5) + 2/35*(5*(a*x + b)^(7/2)*a^30 - 28*(a*x + b)^(5/2)*a^30*b + 70*(a*x + b)^(3/2)*a^30*b^2 - 140*sqrt(a*x + b)*a^30*b^3)/a^35","A",0
1787,1,69,0,0.208068," ","integrate(x^(3/2)/(a+b/x)^(3/2),x, algorithm=""giac"")","-\frac{32 \, b^{\frac{5}{2}}}{5 \, a^{4}} + \frac{2 \, b^{3}}{\sqrt{a x + b} a^{4}} + \frac{2 \, {\left({\left(a x + b\right)}^{\frac{5}{2}} a^{16} - 5 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{16} b + 15 \, \sqrt{a x + b} a^{16} b^{2}\right)}}{5 \, a^{20}}"," ",0,"-32/5*b^(5/2)/a^4 + 2*b^3/(sqrt(a*x + b)*a^4) + 2/5*((a*x + b)^(5/2)*a^16 - 5*(a*x + b)^(3/2)*a^16*b + 15*sqrt(a*x + b)*a^16*b^2)/a^20","A",0
1788,1,54,0,0.173961," ","integrate(x^(1/2)/(a+b/x)^(3/2),x, algorithm=""giac"")","\frac{16 \, b^{\frac{3}{2}}}{3 \, a^{3}} - \frac{2 \, b^{2}}{\sqrt{a x + b} a^{3}} + \frac{2 \, {\left({\left(a x + b\right)}^{\frac{3}{2}} a^{6} - 6 \, \sqrt{a x + b} a^{6} b\right)}}{3 \, a^{9}}"," ",0,"16/3*b^(3/2)/a^3 - 2*b^2/(sqrt(a*x + b)*a^3) + 2/3*((a*x + b)^(3/2)*a^6 - 6*sqrt(a*x + b)*a^6*b)/a^9","A",0
1789,1,38,0,0.170382," ","integrate(1/(a+b/x)^(3/2)/x^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{\sqrt{a x + b}}{a} + \frac{b}{\sqrt{a x + b} a}\right)}}{a} - \frac{4 \, \sqrt{b}}{a^{2}}"," ",0,"2*(sqrt(a*x + b)/a + b/(sqrt(a*x + b)*a))/a - 4*sqrt(b)/a^2","A",0
1790,1,21,0,0.165400," ","integrate(1/(a+b/x)^(3/2)/x^(3/2),x, algorithm=""giac"")","-\frac{2}{\sqrt{a x + b} a} + \frac{2}{a \sqrt{b}}"," ",0,"-2/(sqrt(a*x + b)*a) + 2/(a*sqrt(b))","A",0
1791,1,67,0,0.173270," ","integrate(1/(a+b/x)^(3/2)/x^(5/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} - \frac{2 \, {\left(\sqrt{b} \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + \sqrt{-b}\right)}}{\sqrt{-b} b^{\frac{3}{2}}} + \frac{2}{\sqrt{a x + b} b}"," ",0,"2*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b) - 2*(sqrt(b)*arctan(sqrt(b)/sqrt(-b)) + sqrt(-b))/(sqrt(-b)*b^(3/2)) + 2/(sqrt(a*x + b)*b)","A",0
1792,1,64,0,0.267675," ","integrate(1/(a+b/x)^(3/2)/x^(7/2),x, algorithm=""giac"")","-\frac{3 \, a \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} - \frac{3 \, {\left(a x + b\right)} a - 2 \, a b}{{\left({\left(a x + b\right)}^{\frac{3}{2}} - \sqrt{a x + b} b\right)} b^{2}}"," ",0,"-3*a*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b^2) - (3*(a*x + b)*a - 2*a*b)/(((a*x + b)^(3/2) - sqrt(a*x + b)*b)*b^2)","A",0
1793,1,80,0,0.238608," ","integrate(1/(a+b/x)^(3/2)/x^(9/2),x, algorithm=""giac"")","\frac{15 \, a^{2} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{4 \, \sqrt{-b} b^{3}} + \frac{2 \, a^{2}}{\sqrt{a x + b} b^{3}} + \frac{7 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{2} - 9 \, \sqrt{a x + b} a^{2} b}{4 \, a^{2} b^{3} x^{2}}"," ",0,"15/4*a^2*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b^3) + 2*a^2/(sqrt(a*x + b)*b^3) + 1/4*(7*(a*x + b)^(3/2)*a^2 - 9*sqrt(a*x + b)*a^2*b)/(a^2*b^3*x^2)","A",0
1794,1,95,0,0.256725," ","integrate(1/(a+b/x)^(3/2)/x^(11/2),x, algorithm=""giac"")","-\frac{35 \, a^{3} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{8 \, \sqrt{-b} b^{4}} - \frac{2 \, a^{3}}{\sqrt{a x + b} b^{4}} - \frac{57 \, {\left(a x + b\right)}^{\frac{5}{2}} a^{3} - 136 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{3} b + 87 \, \sqrt{a x + b} a^{3} b^{2}}{24 \, a^{3} b^{4} x^{3}}"," ",0,"-35/8*a^3*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b^4) - 2*a^3/(sqrt(a*x + b)*b^4) - 1/24*(57*(a*x + b)^(5/2)*a^3 - 136*(a*x + b)^(3/2)*a^3*b + 87*sqrt(a*x + b)*a^3*b^2)/(a^3*b^4*x^3)","A",0
1795,1,98,0,0.189153," ","integrate(x^(5/2)/(a+b/x)^(5/2),x, algorithm=""giac"")","\frac{512 \, b^{\frac{7}{2}}}{21 \, a^{6}} - \frac{2 \, {\left(15 \, {\left(a x + b\right)} b^{4} - b^{5}\right)}}{3 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{6}} + \frac{2 \, {\left(3 \, {\left(a x + b\right)}^{\frac{7}{2}} a^{36} - 21 \, {\left(a x + b\right)}^{\frac{5}{2}} a^{36} b + 70 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{36} b^{2} - 210 \, \sqrt{a x + b} a^{36} b^{3}\right)}}{21 \, a^{42}}"," ",0,"512/21*b^(7/2)/a^6 - 2/3*(15*(a*x + b)*b^4 - b^5)/((a*x + b)^(3/2)*a^6) + 2/21*(3*(a*x + b)^(7/2)*a^36 - 21*(a*x + b)^(5/2)*a^36*b + 70*(a*x + b)^(3/2)*a^36*b^2 - 210*sqrt(a*x + b)*a^36*b^3)/a^42","A",0
1796,1,83,0,0.183931," ","integrate(x^(3/2)/(a+b/x)^(5/2),x, algorithm=""giac"")","-\frac{256 \, b^{\frac{5}{2}}}{15 \, a^{5}} + \frac{2 \, {\left(12 \, {\left(a x + b\right)} b^{3} - b^{4}\right)}}{3 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{5}} + \frac{2 \, {\left(3 \, {\left(a x + b\right)}^{\frac{5}{2}} a^{20} - 20 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{20} b + 90 \, \sqrt{a x + b} a^{20} b^{2}\right)}}{15 \, a^{25}}"," ",0,"-256/15*b^(5/2)/a^5 + 2/3*(12*(a*x + b)*b^3 - b^4)/((a*x + b)^(3/2)*a^5) + 2/15*(3*(a*x + b)^(5/2)*a^20 - 20*(a*x + b)^(3/2)*a^20*b + 90*sqrt(a*x + b)*a^20*b^2)/a^25","A",0
1797,1,67,0,0.185822," ","integrate(x^(1/2)/(a+b/x)^(5/2),x, algorithm=""giac"")","\frac{32 \, b^{\frac{3}{2}}}{3 \, a^{4}} - \frac{2 \, {\left(9 \, {\left(a x + b\right)} b^{2} - b^{3}\right)}}{3 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{4}} + \frac{2 \, {\left({\left(a x + b\right)}^{\frac{3}{2}} a^{8} - 9 \, \sqrt{a x + b} a^{8} b\right)}}{3 \, a^{12}}"," ",0,"32/3*b^(3/2)/a^4 - 2/3*(9*(a*x + b)*b^2 - b^3)/((a*x + b)^(3/2)*a^4) + 2/3*((a*x + b)^(3/2)*a^8 - 9*sqrt(a*x + b)*a^8*b)/a^12","A",0
1798,1,47,0,0.199569," ","integrate(1/(a+b/x)^(5/2)/x^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a x + b}}{a^{3}} - \frac{16 \, \sqrt{b}}{3 \, a^{3}} + \frac{2 \, {\left(6 \, {\left(a x + b\right)} b - b^{2}\right)}}{3 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{3}}"," ",0,"2*sqrt(a*x + b)/a^3 - 16/3*sqrt(b)/a^3 + 2/3*(6*(a*x + b)*b - b^2)/((a*x + b)^(3/2)*a^3)","A",0
1799,1,29,0,0.187419," ","integrate(1/(a+b/x)^(5/2)/x^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a x + 2 \, b\right)}}{3 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{2}} + \frac{4}{3 \, a^{2} \sqrt{b}}"," ",0,"-2/3*(3*a*x + 2*b)/((a*x + b)^(3/2)*a^2) + 4/3/(a^2*sqrt(b))","A",0
1800,1,21,0,0.175129," ","integrate(1/(a+b/x)^(5/2)/x^(5/2),x, algorithm=""giac"")","-\frac{2}{3 \, {\left(a x + b\right)}^{\frac{3}{2}} a} + \frac{2}{3 \, a b^{\frac{3}{2}}}"," ",0,"-2/3/((a*x + b)^(3/2)*a) + 2/3/(a*b^(3/2))","A",0
1801,1,78,0,0.188314," ","integrate(1/(a+b/x)^(5/2)/x^(7/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} - \frac{2 \, {\left(3 \, \sqrt{b} \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + 4 \, \sqrt{-b}\right)}}{3 \, \sqrt{-b} b^{\frac{5}{2}}} + \frac{2 \, {\left(3 \, a x + 4 \, b\right)}}{3 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{2}}"," ",0,"2*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b^2) - 2/3*(3*sqrt(b)*arctan(sqrt(b)/sqrt(-b)) + 4*sqrt(-b))/(sqrt(-b)*b^(5/2)) + 2/3*(3*a*x + 4*b)/((a*x + b)^(3/2)*b^2)","A",0
1802,1,65,0,0.254175," ","integrate(1/(a+b/x)^(5/2)/x^(9/2),x, algorithm=""giac"")","-\frac{5 \, a \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{3}} - \frac{2 \, {\left(6 \, {\left(a x + b\right)} a + a b\right)}}{3 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{3}} - \frac{\sqrt{a x + b}}{b^{3} x}"," ",0,"-5*a*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b^3) - 2/3*(6*(a*x + b)*a + a*b)/((a*x + b)^(3/2)*b^3) - sqrt(a*x + b)/(b^3*x)","A",0
1803,1,93,0,0.278799," ","integrate(1/(a+b/x)^(5/2)/x^(11/2),x, algorithm=""giac"")","\frac{35 \, a^{2} \arctan\left(\frac{\sqrt{a x + b}}{\sqrt{-b}}\right)}{4 \, \sqrt{-b} b^{4}} + \frac{2 \, {\left(9 \, {\left(a x + b\right)} a^{2} + a^{2} b\right)}}{3 \, {\left(a x + b\right)}^{\frac{3}{2}} b^{4}} + \frac{11 \, {\left(a x + b\right)}^{\frac{3}{2}} a^{2} - 13 \, \sqrt{a x + b} a^{2} b}{4 \, a^{2} b^{4} x^{2}}"," ",0,"35/4*a^2*arctan(sqrt(a*x + b)/sqrt(-b))/(sqrt(-b)*b^4) + 2/3*(9*(a*x + b)*a^2 + a^2*b)/((a*x + b)^(3/2)*b^4) + 1/4*(11*(a*x + b)^(3/2)*a^2 - 13*sqrt(a*x + b)*a^2*b)/(a^2*b^4*x^2)","A",0
1804,1,13,0,0.181346," ","integrate((a+b/x^2)*x^6,x, algorithm=""giac"")","\frac{1}{7} \, a x^{7} + \frac{1}{5} \, b x^{5}"," ",0,"1/7*a*x^7 + 1/5*b*x^5","A",0
1805,1,13,0,0.155305," ","integrate((a+b/x^2)*x^5,x, algorithm=""giac"")","\frac{1}{6} \, a x^{6} + \frac{1}{4} \, b x^{4}"," ",0,"1/6*a*x^6 + 1/4*b*x^4","A",0
1806,1,13,0,0.153150," ","integrate((a+b/x^2)*x^4,x, algorithm=""giac"")","\frac{1}{5} \, a x^{5} + \frac{1}{3} \, b x^{3}"," ",0,"1/5*a*x^5 + 1/3*b*x^3","A",0
1807,1,13,0,0.176797," ","integrate((a+b/x^2)*x^3,x, algorithm=""giac"")","\frac{1}{4} \, a x^{4} + \frac{1}{2} \, b x^{2}"," ",0,"1/4*a*x^4 + 1/2*b*x^2","A",0
1808,1,10,0,0.152060," ","integrate((a+b/x^2)*x^2,x, algorithm=""giac"")","\frac{1}{3} \, a x^{3} + b x"," ",0,"1/3*a*x^3 + b*x","A",0
1809,1,12,0,0.171411," ","integrate((a+b/x^2)*x,x, algorithm=""giac"")","\frac{1}{2} \, a x^{2} + b \log\left({\left| x \right|}\right)"," ",0,"1/2*a*x^2 + b*log(abs(x))","A",0
1810,1,10,0,0.178249," ","integrate(a+b/x^2,x, algorithm=""giac"")","a x - \frac{b}{x}"," ",0,"a*x - b/x","A",0
1811,1,20,0,0.150350," ","integrate((a+b/x^2)/x,x, algorithm=""giac"")","\frac{1}{2} \, a \log\left(x^{2}\right) - \frac{a x^{2} + b}{2 \, x^{2}}"," ",0,"1/2*a*log(x^2) - 1/2*(a*x^2 + b)/x^2","A",0
1812,1,13,0,0.148334," ","integrate((a+b/x^2)/x^2,x, algorithm=""giac"")","-\frac{3 \, a x^{2} + b}{3 \, x^{3}}"," ",0,"-1/3*(3*a*x^2 + b)/x^3","A",0
1813,1,13,0,0.146393," ","integrate((a+b/x^2)/x^3,x, algorithm=""giac"")","-\frac{2 \, a x^{2} + b}{4 \, x^{4}}"," ",0,"-1/4*(2*a*x^2 + b)/x^4","A",0
1814,1,15,0,0.153058," ","integrate((a+b/x^2)/x^4,x, algorithm=""giac"")","-\frac{5 \, a x^{2} + 3 \, b}{15 \, x^{5}}"," ",0,"-1/15*(5*a*x^2 + 3*b)/x^5","A",0
1815,1,15,0,0.198649," ","integrate((a+b/x^2)/x^5,x, algorithm=""giac"")","-\frac{3 \, a x^{2} + 2 \, b}{12 \, x^{6}}"," ",0,"-1/12*(3*a*x^2 + 2*b)/x^6","A",0
1816,1,15,0,0.157668," ","integrate((a+b/x^2)/x^6,x, algorithm=""giac"")","-\frac{7 \, a x^{2} + 5 \, b}{35 \, x^{7}}"," ",0,"-1/35*(7*a*x^2 + 5*b)/x^7","A",0
1817,1,24,0,0.219368," ","integrate((a+b/x^2)^2*x^6,x, algorithm=""giac"")","\frac{1}{7} \, a^{2} x^{7} + \frac{2}{5} \, a b x^{5} + \frac{1}{3} \, b^{2} x^{3}"," ",0,"1/7*a^2*x^7 + 2/5*a*b*x^5 + 1/3*b^2*x^3","A",0
1818,1,24,0,0.161463," ","integrate((a+b/x^2)^2*x^5,x, algorithm=""giac"")","\frac{1}{6} \, a^{2} x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{2} \, b^{2} x^{2}"," ",0,"1/6*a^2*x^6 + 1/2*a*b*x^4 + 1/2*b^2*x^2","A",0
1819,1,21,0,0.183752," ","integrate((a+b/x^2)^2*x^4,x, algorithm=""giac"")","\frac{1}{5} \, a^{2} x^{5} + \frac{2}{3} \, a b x^{3} + b^{2} x"," ",0,"1/5*a^2*x^5 + 2/3*a*b*x^3 + b^2*x","A",0
1820,1,22,0,0.169167," ","integrate((a+b/x^2)^2*x^3,x, algorithm=""giac"")","\frac{1}{4} \, a^{2} x^{4} + a b x^{2} + b^{2} \log\left({\left| x \right|}\right)"," ",0,"1/4*a^2*x^4 + a*b*x^2 + b^2*log(abs(x))","A",0
1821,1,22,0,0.149364," ","integrate((a+b/x^2)^2*x^2,x, algorithm=""giac"")","\frac{1}{3} \, a^{2} x^{3} + 2 \, a b x - \frac{b^{2}}{x}"," ",0,"1/3*a^2*x^3 + 2*a*b*x - b^2/x","A",0
1822,1,24,0,0.164627," ","integrate((a+b/x^2)^2*x,x, algorithm=""giac"")","\frac{1}{2} \, a^{2} x^{2} + 2 \, a b \log\left({\left| x \right|}\right) - \frac{b^{2}}{2 \, x^{2}}"," ",0,"1/2*a^2*x^2 + 2*a*b*log(abs(x)) - 1/2*b^2/x^2","A",0
1823,1,22,0,0.153088," ","integrate((a+b/x^2)^2,x, algorithm=""giac"")","a^{2} x - \frac{6 \, a b x^{2} + b^{2}}{3 \, x^{3}}"," ",0,"a^2*x - 1/3*(6*a*b*x^2 + b^2)/x^3","A",0
1824,1,34,0,0.156531," ","integrate((a+b/x^2)^2/x,x, algorithm=""giac"")","\frac{1}{2} \, a^{2} \log\left(x^{2}\right) - \frac{3 \, a^{2} x^{4} + 4 \, a b x^{2} + b^{2}}{4 \, x^{4}}"," ",0,"1/2*a^2*log(x^2) - 1/4*(3*a^2*x^4 + 4*a*b*x^2 + b^2)/x^4","A",0
1825,1,26,0,0.147867," ","integrate((a+b/x^2)^2/x^2,x, algorithm=""giac"")","-\frac{15 \, a^{2} x^{4} + 10 \, a b x^{2} + 3 \, b^{2}}{15 \, x^{5}}"," ",0,"-1/15*(15*a^2*x^4 + 10*a*b*x^2 + 3*b^2)/x^5","A",0
1826,1,24,0,0.151242," ","integrate((a+b/x^2)^2/x^3,x, algorithm=""giac"")","-\frac{3 \, a^{2} x^{4} + 3 \, a b x^{2} + b^{2}}{6 \, x^{6}}"," ",0,"-1/6*(3*a^2*x^4 + 3*a*b*x^2 + b^2)/x^6","A",0
1827,1,26,0,0.169280," ","integrate((a+b/x^2)^2/x^4,x, algorithm=""giac"")","-\frac{35 \, a^{2} x^{4} + 42 \, a b x^{2} + 15 \, b^{2}}{105 \, x^{7}}"," ",0,"-1/105*(35*a^2*x^4 + 42*a*b*x^2 + 15*b^2)/x^7","A",0
1828,1,26,0,0.154778," ","integrate((a+b/x^2)^2/x^5,x, algorithm=""giac"")","-\frac{6 \, a^{2} x^{4} + 8 \, a b x^{2} + 3 \, b^{2}}{24 \, x^{8}}"," ",0,"-1/24*(6*a^2*x^4 + 8*a*b*x^2 + 3*b^2)/x^8","A",0
1829,1,26,0,0.148633," ","integrate((a+b/x^2)^2/x^6,x, algorithm=""giac"")","-\frac{63 \, a^{2} x^{4} + 90 \, a b x^{2} + 35 \, b^{2}}{315 \, x^{9}}"," ",0,"-1/315*(63*a^2*x^4 + 90*a*b*x^2 + 35*b^2)/x^9","A",0
1830,1,31,0,0.150620," ","integrate((a+b/x^2)^3*x^6,x, algorithm=""giac"")","\frac{1}{7} \, a^{3} x^{7} + \frac{3}{5} \, a^{2} b x^{5} + a b^{2} x^{3} + b^{3} x"," ",0,"1/7*a^3*x^7 + 3/5*a^2*b*x^5 + a*b^2*x^3 + b^3*x","A",0
1831,1,36,0,0.161958," ","integrate((a+b/x^2)^3*x^5,x, algorithm=""giac"")","\frac{1}{6} \, a^{3} x^{6} + \frac{3}{4} \, a^{2} b x^{4} + \frac{3}{2} \, a b^{2} x^{2} + \frac{1}{2} \, b^{3} \log\left(x^{2}\right)"," ",0,"1/6*a^3*x^6 + 3/4*a^2*b*x^4 + 3/2*a*b^2*x^2 + 1/2*b^3*log(x^2)","A",0
1832,1,32,0,0.167170," ","integrate((a+b/x^2)^3*x^4,x, algorithm=""giac"")","\frac{1}{5} \, a^{3} x^{5} + a^{2} b x^{3} + 3 \, a b^{2} x - \frac{b^{3}}{x}"," ",0,"1/5*a^3*x^5 + a^2*b*x^3 + 3*a*b^2*x - b^3/x","A",0
1833,1,35,0,0.152850," ","integrate((a+b/x^2)^3*x^3,x, algorithm=""giac"")","\frac{1}{4} \, a^{3} x^{4} + \frac{3}{2} \, a^{2} b x^{2} + 3 \, a b^{2} \log\left({\left| x \right|}\right) - \frac{b^{3}}{2 \, x^{2}}"," ",0,"1/4*a^3*x^4 + 3/2*a^2*b*x^2 + 3*a*b^2*log(abs(x)) - 1/2*b^3/x^2","A",0
1834,1,34,0,0.189214," ","integrate((a+b/x^2)^3*x^2,x, algorithm=""giac"")","\frac{1}{3} \, a^{3} x^{3} + 3 \, a^{2} b x - \frac{9 \, a b^{2} x^{2} + b^{3}}{3 \, x^{3}}"," ",0,"1/3*a^3*x^3 + 3*a^2*b*x - 1/3*(9*a*b^2*x^2 + b^3)/x^3","A",0
1835,1,36,0,0.150903," ","integrate((a+b/x^2)^3*x,x, algorithm=""giac"")","\frac{1}{2} \, a^{3} x^{2} + 3 \, a^{2} b \log\left({\left| x \right|}\right) - \frac{6 \, a b^{2} x^{2} + b^{3}}{4 \, x^{4}}"," ",0,"1/2*a^3*x^2 + 3*a^2*b*log(abs(x)) - 1/4*(6*a*b^2*x^2 + b^3)/x^4","A",0
1836,1,33,0,0.164851," ","integrate((a+b/x^2)^3,x, algorithm=""giac"")","a^{3} x - \frac{15 \, a^{2} b x^{4} + 5 \, a b^{2} x^{2} + b^{3}}{5 \, x^{5}}"," ",0,"a^3*x - 1/5*(15*a^2*b*x^4 + 5*a*b^2*x^2 + b^3)/x^5","A",0
1837,1,47,0,0.183367," ","integrate((a+b/x^2)^3/x,x, algorithm=""giac"")","\frac{1}{2} \, a^{3} \log\left(x^{2}\right) - \frac{11 \, a^{3} x^{6} + 18 \, a^{2} b x^{4} + 9 \, a b^{2} x^{2} + 2 \, b^{3}}{12 \, x^{6}}"," ",0,"1/2*a^3*log(x^2) - 1/12*(11*a^3*x^6 + 18*a^2*b*x^4 + 9*a*b^2*x^2 + 2*b^3)/x^6","A",0
1838,1,37,0,0.149888," ","integrate((a+b/x^2)^3/x^2,x, algorithm=""giac"")","-\frac{35 \, a^{3} x^{6} + 35 \, a^{2} b x^{4} + 21 \, a b^{2} x^{2} + 5 \, b^{3}}{35 \, x^{7}}"," ",0,"-1/35*(35*a^3*x^6 + 35*a^2*b*x^4 + 21*a*b^2*x^2 + 5*b^3)/x^7","A",0
1839,1,35,0,0.151540," ","integrate((a+b/x^2)^3/x^3,x, algorithm=""giac"")","-\frac{4 \, a^{3} x^{6} + 6 \, a^{2} b x^{4} + 4 \, a b^{2} x^{2} + b^{3}}{8 \, x^{8}}"," ",0,"-1/8*(4*a^3*x^6 + 6*a^2*b*x^4 + 4*a*b^2*x^2 + b^3)/x^8","B",0
1840,1,37,0,0.154518," ","integrate((a+b/x^2)^3/x^4,x, algorithm=""giac"")","-\frac{105 \, a^{3} x^{6} + 189 \, a^{2} b x^{4} + 135 \, a b^{2} x^{2} + 35 \, b^{3}}{315 \, x^{9}}"," ",0,"-1/315*(105*a^3*x^6 + 189*a^2*b*x^4 + 135*a*b^2*x^2 + 35*b^3)/x^9","A",0
1841,1,37,0,0.189179," ","integrate((a+b/x^2)^3/x^5,x, algorithm=""giac"")","-\frac{10 \, a^{3} x^{6} + 20 \, a^{2} b x^{4} + 15 \, a b^{2} x^{2} + 4 \, b^{3}}{40 \, x^{10}}"," ",0,"-1/40*(10*a^3*x^6 + 20*a^2*b*x^4 + 15*a*b^2*x^2 + 4*b^3)/x^10","A",0
1842,1,37,0,0.159118," ","integrate((a+b/x^2)^3/x^6,x, algorithm=""giac"")","-\frac{231 \, a^{3} x^{6} + 495 \, a^{2} b x^{4} + 385 \, a b^{2} x^{2} + 105 \, b^{3}}{1155 \, x^{11}}"," ",0,"-1/1155*(231*a^3*x^6 + 495*a^2*b*x^4 + 385*a*b^2*x^2 + 105*b^3)/x^11","A",0
1843,1,65,0,0.161424," ","integrate(x^6/(a+b/x^2),x, algorithm=""giac"")","\frac{b^{4} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}} + \frac{15 \, a^{6} x^{7} - 21 \, a^{5} b x^{5} + 35 \, a^{4} b^{2} x^{3} - 105 \, a^{3} b^{3} x}{105 \, a^{7}}"," ",0,"b^4*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^4) + 1/105*(15*a^6*x^7 - 21*a^5*b*x^5 + 35*a^4*b^2*x^3 - 105*a^3*b^3*x)/a^7","A",0
1844,1,47,0,0.164942," ","integrate(x^5/(a+b/x^2),x, algorithm=""giac"")","-\frac{b^{3} \log\left({\left| a x^{2} + b \right|}\right)}{2 \, a^{4}} + \frac{2 \, a^{2} x^{6} - 3 \, a b x^{4} + 6 \, b^{2} x^{2}}{12 \, a^{3}}"," ",0,"-1/2*b^3*log(abs(a*x^2 + b))/a^4 + 1/12*(2*a^2*x^6 - 3*a*b*x^4 + 6*b^2*x^2)/a^3","A",0
1845,1,55,0,0.182793," ","integrate(x^4/(a+b/x^2),x, algorithm=""giac"")","-\frac{b^{3} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} + \frac{3 \, a^{4} x^{5} - 5 \, a^{3} b x^{3} + 15 \, a^{2} b^{2} x}{15 \, a^{5}}"," ",0,"-b^3*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^3) + 1/15*(3*a^4*x^5 - 5*a^3*b*x^3 + 15*a^2*b^2*x)/a^5","A",0
1846,1,35,0,0.153411," ","integrate(x^3/(a+b/x^2),x, algorithm=""giac"")","\frac{b^{2} \log\left({\left| a x^{2} + b \right|}\right)}{2 \, a^{3}} + \frac{a x^{4} - 2 \, b x^{2}}{4 \, a^{2}}"," ",0,"1/2*b^2*log(abs(a*x^2 + b))/a^3 + 1/4*(a*x^4 - 2*b*x^2)/a^2","A",0
1847,1,40,0,0.155614," ","integrate(x^2/(a+b/x^2),x, algorithm=""giac"")","\frac{b^{2} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{a^{2} x^{3} - 3 \, a b x}{3 \, a^{3}}"," ",0,"b^2*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^2) + 1/3*(a^2*x^3 - 3*a*b*x)/a^3","A",0
1848,1,24,0,0.183910," ","integrate(x/(a+b/x^2),x, algorithm=""giac"")","\frac{x^{2}}{2 \, a} - \frac{b \log\left({\left| a x^{2} + b \right|}\right)}{2 \, a^{2}}"," ",0,"1/2*x^2/a - 1/2*b*log(abs(a*x^2 + b))/a^2","A",0
1849,1,26,0,0.151160," ","integrate(1/(a+b/x^2),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b} a} + \frac{x}{a}"," ",0,"-b*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a) + x/a","A",0
1850,1,14,0,0.149448," ","integrate(1/(a+b/x^2)/x,x, algorithm=""giac"")","\frac{\log\left({\left| a x^{2} + b \right|}\right)}{2 \, a}"," ",0,"1/2*log(abs(a*x^2 + b))/a","A",0
1851,1,15,0,0.189410," ","integrate(1/(a+b/x^2)/x^2,x, algorithm=""giac"")","\frac{\arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"arctan(a*x/sqrt(a*b))/sqrt(a*b)","A",0
1852,1,24,0,0.165693," ","integrate(1/(a+b/x^2)/x^3,x, algorithm=""giac"")","\frac{\log\left(x^{2}\right)}{2 \, b} - \frac{\log\left({\left| a x^{2} + b \right|}\right)}{2 \, b}"," ",0,"1/2*log(x^2)/b - 1/2*log(abs(a*x^2 + b))/b","A",0
1853,1,29,0,0.148279," ","integrate(1/(a+b/x^2)/x^4,x, algorithm=""giac"")","-\frac{a \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b} b} - \frac{1}{b x}"," ",0,"-a*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*b) - 1/(b*x)","A",0
1854,1,43,0,0.165173," ","integrate(1/(a+b/x^2)/x^5,x, algorithm=""giac"")","-\frac{a \log\left(x^{2}\right)}{2 \, b^{2}} + \frac{a \log\left({\left| a x^{2} + b \right|}\right)}{2 \, b^{2}} + \frac{a x^{2} - b}{2 \, b^{2} x^{2}}"," ",0,"-1/2*a*log(x^2)/b^2 + 1/2*a*log(abs(a*x^2 + b))/b^2 + 1/2*(a*x^2 - b)/(b^2*x^2)","A",0
1855,1,40,0,0.160822," ","integrate(1/(a+b/x^2)/x^6,x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{3 \, a x^{2} - b}{3 \, b^{2} x^{3}}"," ",0,"a^2*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/3*(3*a*x^2 - b)/(b^2*x^3)","A",0
1856,1,57,0,0.152072," ","integrate(1/(a+b/x^2)/x^7,x, algorithm=""giac"")","\frac{a^{2} \log\left(x^{2}\right)}{2 \, b^{3}} - \frac{a^{2} \log\left({\left| a x^{2} + b \right|}\right)}{2 \, b^{3}} - \frac{3 \, a^{2} x^{4} - 2 \, a b x^{2} + b^{2}}{4 \, b^{3} x^{4}}"," ",0,"1/2*a^2*log(x^2)/b^3 - 1/2*a^2*log(abs(a*x^2 + b))/b^3 - 1/4*(3*a^2*x^4 - 2*a*b*x^2 + b^2)/(b^3*x^4)","A",0
1857,1,52,0,0.153407," ","integrate(1/(a+b/x^2)/x^8,x, algorithm=""giac"")","-\frac{a^{3} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} - \frac{15 \, a^{2} x^{4} - 5 \, a b x^{2} + 3 \, b^{2}}{15 \, b^{3} x^{5}}"," ",0,"-a^3*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*b^3) - 1/15*(15*a^2*x^4 - 5*a*b*x^2 + 3*b^2)/(b^3*x^5)","A",0
1858,1,84,0,0.165212," ","integrate(x^6/(a+b/x^2)^2,x, algorithm=""giac"")","\frac{9 \, b^{4} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{5}} - \frac{b^{4} x}{2 \, {\left(a x^{2} + b\right)} a^{5}} + \frac{5 \, a^{12} x^{7} - 14 \, a^{11} b x^{5} + 35 \, a^{10} b^{2} x^{3} - 140 \, a^{9} b^{3} x}{35 \, a^{14}}"," ",0,"9/2*b^4*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^5) - 1/2*b^4*x/((a*x^2 + b)*a^5) + 1/35*(5*a^12*x^7 - 14*a^11*b*x^5 + 35*a^10*b^2*x^3 - 140*a^9*b^3*x)/a^14","A",0
1859,1,80,0,0.158168," ","integrate(x^5/(a+b/x^2)^2,x, algorithm=""giac"")","-\frac{2 \, b^{3} \log\left({\left| a x^{2} + b \right|}\right)}{a^{5}} + \frac{a^{4} x^{6} - 3 \, a^{3} b x^{4} + 9 \, a^{2} b^{2} x^{2}}{6 \, a^{6}} + \frac{4 \, a b^{3} x^{2} + 3 \, b^{4}}{2 \, {\left(a x^{2} + b\right)} a^{5}}"," ",0,"-2*b^3*log(abs(a*x^2 + b))/a^5 + 1/6*(a^4*x^6 - 3*a^3*b*x^4 + 9*a^2*b^2*x^2)/a^6 + 1/2*(4*a*b^3*x^2 + 3*b^4)/((a*x^2 + b)*a^5)","A",0
1860,1,73,0,0.159428," ","integrate(x^4/(a+b/x^2)^2,x, algorithm=""giac"")","-\frac{7 \, b^{3} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{4}} + \frac{b^{3} x}{2 \, {\left(a x^{2} + b\right)} a^{4}} + \frac{3 \, a^{8} x^{5} - 10 \, a^{7} b x^{3} + 45 \, a^{6} b^{2} x}{15 \, a^{10}}"," ",0,"-7/2*b^3*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^4) + 1/2*b^3*x/((a*x^2 + b)*a^4) + 1/15*(3*a^8*x^5 - 10*a^7*b*x^3 + 45*a^6*b^2*x)/a^10","A",0
1861,1,55,0,0.169817," ","integrate(x^3/(a+b/x^2)^2,x, algorithm=""giac"")","\frac{3 \, b^{2} \log\left({\left| a x^{2} + b \right|}\right)}{2 \, a^{4}} + \frac{b^{3}}{2 \, {\left(a x^{2} + b\right)} a^{4}} + \frac{a^{2} x^{4} - 4 \, a b x^{2}}{4 \, a^{4}}"," ",0,"3/2*b^2*log(abs(a*x^2 + b))/a^4 + 1/2*b^3/((a*x^2 + b)*a^4) + 1/4*(a^2*x^4 - 4*a*b*x^2)/a^4","A",0
1862,1,61,0,0.152841," ","integrate(x^2/(a+b/x^2)^2,x, algorithm=""giac"")","\frac{5 \, b^{2} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{3}} - \frac{b^{2} x}{2 \, {\left(a x^{2} + b\right)} a^{3}} + \frac{a^{4} x^{3} - 6 \, a^{3} b x}{3 \, a^{6}}"," ",0,"5/2*b^2*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^3) - 1/2*b^2*x/((a*x^2 + b)*a^3) + 1/3*(a^4*x^3 - 6*a^3*b*x)/a^6","A",0
1863,1,41,0,0.152144," ","integrate(x/(a+b/x^2)^2,x, algorithm=""giac"")","\frac{x^{2}}{2 \, a^{2}} - \frac{b \log\left({\left| a x^{2} + b \right|}\right)}{a^{3}} - \frac{b^{2}}{2 \, {\left(a x^{2} + b\right)} a^{3}}"," ",0,"1/2*x^2/a^2 - b*log(abs(a*x^2 + b))/a^3 - 1/2*b^2/((a*x^2 + b)*a^3)","A",0
1864,1,42,0,0.177289," ","integrate(1/(a+b/x^2)^2,x, algorithm=""giac"")","-\frac{3 \, b \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2}} + \frac{x}{a^{2}} + \frac{b x}{2 \, {\left(a x^{2} + b\right)} a^{2}}"," ",0,"-3/2*b*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^2) + x/a^2 + 1/2*b*x/((a*x^2 + b)*a^2)","A",0
1865,1,32,0,0.150686," ","integrate(1/(a+b/x^2)^2/x,x, algorithm=""giac"")","-\frac{x^{2}}{2 \, {\left(a x^{2} + b\right)} a} + \frac{\log\left({\left| a x^{2} + b \right|}\right)}{2 \, a^{2}}"," ",0,"-1/2*x^2/((a*x^2 + b)*a) + 1/2*log(abs(a*x^2 + b))/a^2","A",0
1866,1,35,0,0.148794," ","integrate(1/(a+b/x^2)^2/x^2,x, algorithm=""giac"")","\frac{\arctan\left(\frac{a x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a} - \frac{x}{2 \, {\left(a x^{2} + b\right)} a}"," ",0,"1/2*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a) - 1/2*x/((a*x^2 + b)*a)","A",0
1867,1,14,0,0.153012," ","integrate(1/(a+b/x^2)^2/x^3,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(a x^{2} + b\right)} a}"," ",0,"-1/2/((a*x^2 + b)*a)","A",0
1868,1,35,0,0.161076," ","integrate(1/(a+b/x^2)^2/x^4,x, algorithm=""giac"")","\frac{\arctan\left(\frac{a x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b} + \frac{x}{2 \, {\left(a x^{2} + b\right)} b}"," ",0,"1/2*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*b) + 1/2*x/((a*x^2 + b)*b)","A",0
1869,1,47,0,0.149980," ","integrate(1/(a+b/x^2)^2/x^5,x, algorithm=""giac"")","\frac{\log\left(x^{2}\right)}{2 \, b^{2}} - \frac{\log\left({\left| a x^{2} + b \right|}\right)}{2 \, b^{2}} + \frac{a x^{2} + 2 \, b}{2 \, {\left(a x^{2} + b\right)} b^{2}}"," ",0,"1/2*log(x^2)/b^2 - 1/2*log(abs(a*x^2 + b))/b^2 + 1/2*(a*x^2 + 2*b)/((a*x^2 + b)*b^2)","A",0
1870,1,47,0,0.152404," ","integrate(1/(a+b/x^2)^2/x^6,x, algorithm=""giac"")","-\frac{3 \, a \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{2}} - \frac{3 \, a x^{2} + 2 \, b}{2 \, {\left(a x^{3} + b x\right)} b^{2}}"," ",0,"-3/2*a*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*b^2) - 1/2*(3*a*x^2 + 2*b)/((a*x^3 + b*x)*b^2)","A",0
1871,1,51,0,0.164028," ","integrate(1/(a+b/x^2)^2/x^7,x, algorithm=""giac"")","-\frac{a \log\left(x^{2}\right)}{b^{3}} + \frac{a \log\left({\left| a x^{2} + b \right|}\right)}{b^{3}} - \frac{2 \, a x^{2} + b}{2 \, {\left(a x^{4} + b x^{2}\right)} b^{2}}"," ",0,"-a*log(x^2)/b^3 + a*log(abs(a*x^2 + b))/b^3 - 1/2*(2*a*x^2 + b)/((a*x^4 + b*x^2)*b^2)","A",0
1872,1,59,0,0.168571," ","integrate(1/(a+b/x^2)^2/x^8,x, algorithm=""giac"")","\frac{5 \, a^{2} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{3}} + \frac{a^{2} x}{2 \, {\left(a x^{2} + b\right)} b^{3}} + \frac{6 \, a x^{2} - b}{3 \, b^{3} x^{3}}"," ",0,"5/2*a^2*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/2*a^2*x/((a*x^2 + b)*b^3) + 1/3*(6*a*x^2 - b)/(b^3*x^3)","A",0
1873,1,86,0,0.151897," ","integrate(1/(a+b/x^2)^2/x^9,x, algorithm=""giac"")","\frac{3 \, a^{2} \log\left(x^{2}\right)}{2 \, b^{4}} - \frac{3 \, a^{2} \log\left({\left| a x^{2} + b \right|}\right)}{2 \, b^{4}} + \frac{3 \, a^{3} x^{2} + 4 \, a^{2} b}{2 \, {\left(a x^{2} + b\right)} b^{4}} - \frac{9 \, a^{2} x^{4} - 4 \, a b x^{2} + b^{2}}{4 \, b^{4} x^{4}}"," ",0,"3/2*a^2*log(x^2)/b^4 - 3/2*a^2*log(abs(a*x^2 + b))/b^4 + 1/2*(3*a^3*x^2 + 4*a^2*b)/((a*x^2 + b)*b^4) - 1/4*(9*a^2*x^4 - 4*a*b*x^2 + b^2)/(b^4*x^4)","A",0
1874,1,92,0,0.166079," ","integrate(x^5/(a+b/x^2)^3,x, algorithm=""giac"")","-\frac{5 \, b^{3} \log\left({\left| a x^{2} + b \right|}\right)}{a^{6}} + \frac{30 \, a^{2} b^{3} x^{4} + 50 \, a b^{4} x^{2} + 21 \, b^{5}}{4 \, {\left(a x^{2} + b\right)}^{2} a^{6}} + \frac{2 \, a^{6} x^{6} - 9 \, a^{5} b x^{4} + 36 \, a^{4} b^{2} x^{2}}{12 \, a^{9}}"," ",0,"-5*b^3*log(abs(a*x^2 + b))/a^6 + 1/4*(30*a^2*b^3*x^4 + 50*a*b^4*x^2 + 21*b^5)/((a*x^2 + b)^2*a^6) + 1/12*(2*a^6*x^6 - 9*a^5*b*x^4 + 36*a^4*b^2*x^2)/a^9","A",0
1875,1,84,0,0.155553," ","integrate(x^4/(a+b/x^2)^3,x, algorithm=""giac"")","-\frac{63 \, b^{3} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{5}} + \frac{17 \, a b^{3} x^{3} + 15 \, b^{4} x}{8 \, {\left(a x^{2} + b\right)}^{2} a^{5}} + \frac{a^{12} x^{5} - 5 \, a^{11} b x^{3} + 30 \, a^{10} b^{2} x}{5 \, a^{15}}"," ",0,"-63/8*b^3*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^5) + 1/8*(17*a*b^3*x^3 + 15*b^4*x)/((a*x^2 + b)^2*a^5) + 1/5*(a^12*x^5 - 5*a^11*b*x^3 + 30*a^10*b^2*x)/a^15","A",0
1876,1,69,0,0.159207," ","integrate(x^3/(a+b/x^2)^3,x, algorithm=""giac"")","\frac{3 \, b^{2} \log\left({\left| a x^{2} + b \right|}\right)}{a^{5}} + \frac{a^{3} x^{4} - 6 \, a^{2} b x^{2}}{4 \, a^{6}} + \frac{8 \, a b^{3} x^{2} + 7 \, b^{4}}{4 \, {\left(a x^{2} + b\right)}^{2} a^{5}}"," ",0,"3*b^2*log(abs(a*x^2 + b))/a^5 + 1/4*(a^3*x^4 - 6*a^2*b*x^2)/a^6 + 1/4*(8*a*b^3*x^2 + 7*b^4)/((a*x^2 + b)^2*a^5)","A",0
1877,1,73,0,0.155992," ","integrate(x^2/(a+b/x^2)^3,x, algorithm=""giac"")","\frac{35 \, b^{2} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{4}} - \frac{13 \, a b^{2} x^{3} + 11 \, b^{3} x}{8 \, {\left(a x^{2} + b\right)}^{2} a^{4}} + \frac{a^{6} x^{3} - 9 \, a^{5} b x}{3 \, a^{9}}"," ",0,"35/8*b^2*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^4) - 1/8*(13*a*b^2*x^3 + 11*b^3*x)/((a*x^2 + b)^2*a^4) + 1/3*(a^6*x^3 - 9*a^5*b*x)/a^9","A",0
1878,1,53,0,0.159038," ","integrate(x/(a+b/x^2)^3,x, algorithm=""giac"")","\frac{x^{2}}{2 \, a^{3}} - \frac{3 \, b \log\left({\left| a x^{2} + b \right|}\right)}{2 \, a^{4}} - \frac{6 \, a b^{2} x^{2} + 5 \, b^{3}}{4 \, {\left(a x^{2} + b\right)}^{2} a^{4}}"," ",0,"1/2*x^2/a^3 - 3/2*b*log(abs(a*x^2 + b))/a^4 - 1/4*(6*a*b^2*x^2 + 5*b^3)/((a*x^2 + b)^2*a^4)","A",0
1879,1,54,0,0.151134," ","integrate(1/(a+b/x^2)^3,x, algorithm=""giac"")","-\frac{15 \, b \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{3}} + \frac{x}{a^{3}} + \frac{9 \, a b x^{3} + 7 \, b^{2} x}{8 \, {\left(a x^{2} + b\right)}^{2} a^{3}}"," ",0,"-15/8*b*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^3) + x/a^3 + 1/8*(9*a*b*x^3 + 7*b^2*x)/((a*x^2 + b)^2*a^3)","A",0
1880,1,42,0,0.153005," ","integrate(1/(a+b/x^2)^3/x,x, algorithm=""giac"")","\frac{\log\left({\left| a x^{2} + b \right|}\right)}{2 \, a^{3}} - \frac{3 \, a x^{4} + 2 \, b x^{2}}{4 \, {\left(a x^{2} + b\right)}^{2} a^{2}}"," ",0,"1/2*log(abs(a*x^2 + b))/a^3 - 1/4*(3*a*x^4 + 2*b*x^2)/((a*x^2 + b)^2*a^2)","A",0
1881,1,45,0,0.165610," ","integrate(1/(a+b/x^2)^3/x^2,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2}} - \frac{5 \, a x^{3} + 3 \, b x}{8 \, {\left(a x^{2} + b\right)}^{2} a^{2}}"," ",0,"3/8*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^2) - 1/8*(5*a*x^3 + 3*b*x)/((a*x^2 + b)^2*a^2)","A",0
1882,1,22,0,0.157051," ","integrate(1/(a+b/x^2)^3/x^3,x, algorithm=""giac"")","-\frac{2 \, a x^{2} + b}{4 \, {\left(a x^{2} + b\right)}^{2} a^{2}}"," ",0,"-1/4*(2*a*x^2 + b)/((a*x^2 + b)^2*a^2)","A",0
1883,1,50,0,0.154319," ","integrate(1/(a+b/x^2)^3/x^4,x, algorithm=""giac"")","\frac{\arctan\left(\frac{a x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a b} + \frac{a x^{3} - b x}{8 \, {\left(a x^{2} + b\right)}^{2} a b}"," ",0,"1/8*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a*b) + 1/8*(a*x^3 - b*x)/((a*x^2 + b)^2*a*b)","A",0
1884,1,14,0,0.154899," ","integrate(1/(a+b/x^2)^3/x^5,x, algorithm=""giac"")","-\frac{1}{4 \, {\left(a x^{2} + b\right)}^{2} a}"," ",0,"-1/4/((a*x^2 + b)^2*a)","A",0
1885,1,45,0,0.220344," ","integrate(1/(a+b/x^2)^3/x^6,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{2}} + \frac{3 \, a x^{3} + 5 \, b x}{8 \, {\left(a x^{2} + b\right)}^{2} b^{2}}"," ",0,"3/8*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/8*(3*a*x^3 + 5*b*x)/((a*x^2 + b)^2*b^2)","A",0
1886,1,59,0,0.154333," ","integrate(1/(a+b/x^2)^3/x^7,x, algorithm=""giac"")","\frac{\log\left(x^{2}\right)}{2 \, b^{3}} - \frac{\log\left({\left| a x^{2} + b \right|}\right)}{2 \, b^{3}} + \frac{3 \, a^{2} x^{4} + 8 \, a b x^{2} + 6 \, b^{2}}{4 \, {\left(a x^{2} + b\right)}^{2} b^{3}}"," ",0,"1/2*log(x^2)/b^3 - 1/2*log(abs(a*x^2 + b))/b^3 + 1/4*(3*a^2*x^4 + 8*a*b*x^2 + 6*b^2)/((a*x^2 + b)^2*b^3)","A",0
1887,1,57,0,0.157908," ","integrate(1/(a+b/x^2)^3/x^8,x, algorithm=""giac"")","-\frac{15 \, a \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{3}} - \frac{7 \, a^{2} x^{3} + 9 \, a b x}{8 \, {\left(a x^{2} + b\right)}^{2} b^{3}} - \frac{1}{b^{3} x}"," ",0,"-15/8*a*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*b^3) - 1/8*(7*a^2*x^3 + 9*a*b*x)/((a*x^2 + b)^2*b^3) - 1/(b^3*x)","A",0
1888,1,82,0,0.156264," ","integrate(1/(a+b/x^2)^3/x^9,x, algorithm=""giac"")","-\frac{3 \, a \log\left(x^{2}\right)}{2 \, b^{4}} + \frac{3 \, a \log\left({\left| a x^{2} + b \right|}\right)}{2 \, b^{4}} - \frac{9 \, a^{3} x^{4} + 22 \, a^{2} b x^{2} + 14 \, a b^{2}}{4 \, {\left(a x^{2} + b\right)}^{2} b^{4}} + \frac{3 \, a x^{2} - b}{2 \, b^{4} x^{2}}"," ",0,"-3/2*a*log(x^2)/b^4 + 3/2*a*log(abs(a*x^2 + b))/b^4 - 1/4*(9*a^3*x^4 + 22*a^2*b*x^2 + 14*a*b^2)/((a*x^2 + b)^2*b^4) + 1/2*(3*a*x^2 - b)/(b^4*x^2)","A",0
1889,1,71,0,0.154811," ","integrate(1/(a+b/x^2)^3/x^10,x, algorithm=""giac"")","\frac{35 \, a^{2} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{4}} + \frac{11 \, a^{3} x^{3} + 13 \, a^{2} b x}{8 \, {\left(a x^{2} + b\right)}^{2} b^{4}} + \frac{9 \, a x^{2} - b}{3 \, b^{4} x^{3}}"," ",0,"35/8*a^2*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/8*(11*a^3*x^3 + 13*a^2*b*x)/((a*x^2 + b)^2*b^4) + 1/3*(9*a*x^2 - b)/(b^4*x^3)","A",0
1890,1,80,0,0.154353," ","integrate(1/(a+b/x^2)^3/x^11,x, algorithm=""giac"")","\frac{3 \, a^{2} \log\left(x^{2}\right)}{b^{5}} - \frac{3 \, a^{2} \log\left({\left| a x^{2} + b \right|}\right)}{b^{5}} + \frac{12 \, a^{3} x^{6} + 18 \, a^{2} b x^{4} + 4 \, a b^{2} x^{2} - b^{3}}{4 \, {\left(a x^{4} + b x^{2}\right)}^{2} b^{4}}"," ",0,"3*a^2*log(x^2)/b^5 - 3*a^2*log(abs(a*x^2 + b))/b^5 + 1/4*(12*a^3*x^6 + 18*a^2*b*x^4 + 4*a*b^2*x^2 - b^3)/((a*x^4 + b*x^2)^2*b^4)","A",0
1891,1,69,0,0.182809," ","integrate((a+b/x^2)^(1/2)*x^3,x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{a x^{2} + b} {\left(2 \, x^{2} \mathrm{sgn}\left(x\right) + \frac{b \mathrm{sgn}\left(x\right)}{a}\right)} x + \frac{b^{2} \log\left({\left| -\sqrt{a} x + \sqrt{a x^{2} + b} \right|}\right) \mathrm{sgn}\left(x\right)}{8 \, a^{\frac{3}{2}}} - \frac{b^{2} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, a^{\frac{3}{2}}}"," ",0,"1/8*sqrt(a*x^2 + b)*(2*x^2*sgn(x) + b*sgn(x)/a)*x + 1/8*b^2*log(abs(-sqrt(a)*x + sqrt(a*x^2 + b)))*sgn(x)/a^(3/2) - 1/16*b^2*log(abs(b))*sgn(x)/a^(3/2)","A",0
1892,1,27,0,0.152991," ","integrate((a+b/x^2)^(1/2)*x^2,x, algorithm=""giac"")","\frac{{\left(a x^{2} + b\right)}^{\frac{3}{2}} \mathrm{sgn}\left(x\right)}{3 \, a} - \frac{b^{\frac{3}{2}} \mathrm{sgn}\left(x\right)}{3 \, a}"," ",0,"1/3*(a*x^2 + b)^(3/2)*sgn(x)/a - 1/3*b^(3/2)*sgn(x)/a","A",0
1893,1,52,0,0.192191," ","integrate((a+b/x^2)^(1/2)*x,x, algorithm=""giac"")","\frac{b \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{4 \, \sqrt{a}} + \frac{1}{2} \, {\left(\sqrt{a x^{2} + b} x - \frac{b \log\left({\left| -\sqrt{a} x + \sqrt{a x^{2} + b} \right|}\right)}{\sqrt{a}}\right)} \mathrm{sgn}\left(x\right)"," ",0,"1/4*b*log(abs(b))*sgn(x)/sqrt(a) + 1/2*(sqrt(a*x^2 + b)*x - b*log(abs(-sqrt(a)*x + sqrt(a*x^2 + b)))/sqrt(a))*sgn(x)","A",0
1894,1,69,0,0.159894," ","integrate((a+b/x^2)^(1/2),x, algorithm=""giac"")","\frac{b \arctan\left(\frac{\sqrt{a x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} + \sqrt{a x^{2} + b} \mathrm{sgn}\left(x\right) - \frac{{\left(b \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + \sqrt{-b} \sqrt{b}\right)} \mathrm{sgn}\left(x\right)}{\sqrt{-b}}"," ",0,"b*arctan(sqrt(a*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) + sqrt(a*x^2 + b)*sgn(x) - (b*arctan(sqrt(b)/sqrt(-b)) + sqrt(-b)*sqrt(b))*sgn(x)/sqrt(-b)","B",0
1895,1,61,0,0.216506," ","integrate((a+b/x^2)^(1/2)/x,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{a} \log\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2}\right) \mathrm{sgn}\left(x\right) + \frac{2 \, \sqrt{a} b \mathrm{sgn}\left(x\right)}{{\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} - b}"," ",0,"-1/2*sqrt(a)*log((sqrt(a)*x - sqrt(a*x^2 + b))^2)*sgn(x) + 2*sqrt(a)*b*sgn(x)/((sqrt(a)*x - sqrt(a*x^2 + b))^2 - b)","B",0
1896,1,50,0,0.208986," ","integrate((a+b/x^2)^(1/2)/x^2,x, algorithm=""giac"")","\frac{\frac{a^{2} \arctan\left(\frac{\sqrt{a x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} - \frac{\sqrt{a x^{2} + b} a \mathrm{sgn}\left(x\right)}{x^{2}}}{2 \, a}"," ",0,"1/2*(a^2*arctan(sqrt(a*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) - sqrt(a*x^2 + b)*a*sgn(x)/x^2)/a","A",0
1897,1,63,0,0.202694," ","integrate((a+b/x^2)^(1/2)/x^3,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{4} a^{\frac{3}{2}} \mathrm{sgn}\left(x\right) + a^{\frac{3}{2}} b^{2} \mathrm{sgn}\left(x\right)\right)}}{3 \, {\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} - b\right)}^{3}}"," ",0,"2/3*(3*(sqrt(a)*x - sqrt(a*x^2 + b))^4*a^(3/2)*sgn(x) + a^(3/2)*b^2*sgn(x))/((sqrt(a)*x - sqrt(a*x^2 + b))^2 - b)^3","B",0
1898,1,78,0,0.225265," ","integrate((a+b/x^2)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{\frac{a^{3} \arctan\left(\frac{\sqrt{a x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b} b} + \frac{{\left(a x^{2} + b\right)}^{\frac{3}{2}} a^{3} \mathrm{sgn}\left(x\right) + \sqrt{a x^{2} + b} a^{3} b \mathrm{sgn}\left(x\right)}{a^{2} b x^{4}}}{8 \, a}"," ",0,"-1/8*(a^3*arctan(sqrt(a*x^2 + b)/sqrt(-b))*sgn(x)/(sqrt(-b)*b) + ((a*x^2 + b)^(3/2)*a^3*sgn(x) + sqrt(a*x^2 + b)*a^3*b*sgn(x))/(a^2*b*x^4))/a","A",0
1899,1,68,0,0.186201," ","integrate((a+b/x^2)^(3/2)*x^3,x, algorithm=""giac"")","-\frac{3 \, b^{2} \log\left({\left| -\sqrt{a} x + \sqrt{a x^{2} + b} \right|}\right) \mathrm{sgn}\left(x\right)}{8 \, \sqrt{a}} + \frac{3 \, b^{2} \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{16 \, \sqrt{a}} + \frac{1}{8} \, {\left(2 \, a x^{2} \mathrm{sgn}\left(x\right) + 5 \, b \mathrm{sgn}\left(x\right)\right)} \sqrt{a x^{2} + b} x"," ",0,"-3/8*b^2*log(abs(-sqrt(a)*x + sqrt(a*x^2 + b)))*sgn(x)/sqrt(a) + 3/16*b^2*log(abs(b))*sgn(x)/sqrt(a) + 1/8*(2*a*x^2*sgn(x) + 5*b*sgn(x))*sqrt(a*x^2 + b)*x","A",0
1900,1,89,0,0.180794," ","integrate((a+b/x^2)^(3/2)*x^2,x, algorithm=""giac"")","\frac{b^{2} \arctan\left(\frac{\sqrt{a x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} + \frac{1}{3} \, {\left(a x^{2} + b\right)}^{\frac{3}{2}} \mathrm{sgn}\left(x\right) + \sqrt{a x^{2} + b} b \mathrm{sgn}\left(x\right) - \frac{{\left(3 \, b^{2} \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + 4 \, \sqrt{-b} b^{\frac{3}{2}}\right)} \mathrm{sgn}\left(x\right)}{3 \, \sqrt{-b}}"," ",0,"b^2*arctan(sqrt(a*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) + 1/3*(a*x^2 + b)^(3/2)*sgn(x) + sqrt(a*x^2 + b)*b*sgn(x) - 1/3*(3*b^2*arctan(sqrt(b)/sqrt(-b)) + 4*sqrt(-b)*b^(3/2))*sgn(x)/sqrt(-b)","A",0
1901,1,79,0,0.279579," ","integrate((a+b/x^2)^(3/2)*x,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{a x^{2} + b} a x \mathrm{sgn}\left(x\right) - \frac{3}{4} \, \sqrt{a} b \log\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2}\right) \mathrm{sgn}\left(x\right) + \frac{2 \, \sqrt{a} b^{2} \mathrm{sgn}\left(x\right)}{{\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} - b}"," ",0,"1/2*sqrt(a*x^2 + b)*a*x*sgn(x) - 3/4*sqrt(a)*b*log((sqrt(a)*x - sqrt(a*x^2 + b))^2)*sgn(x) + 2*sqrt(a)*b^2*sgn(x)/((sqrt(a)*x - sqrt(a*x^2 + b))^2 - b)","A",0
1902,1,69,0,0.208890," ","integrate((a+b/x^2)^(3/2),x, algorithm=""giac"")","\frac{\frac{3 \, a^{2} b \arctan\left(\frac{\sqrt{a x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} + 2 \, \sqrt{a x^{2} + b} a^{2} \mathrm{sgn}\left(x\right) - \frac{\sqrt{a x^{2} + b} a b \mathrm{sgn}\left(x\right)}{x^{2}}}{2 \, a}"," ",0,"1/2*(3*a^2*b*arctan(sqrt(a*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) + 2*sqrt(a*x^2 + b)*a^2*sgn(x) - sqrt(a*x^2 + b)*a*b*sgn(x)/x^2)/a","A",0
1903,1,122,0,0.491676," ","integrate((a+b/x^2)^(3/2)/x,x, algorithm=""giac"")","-\frac{1}{2} \, a^{\frac{3}{2}} \log\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2}\right) \mathrm{sgn}\left(x\right) + \frac{4 \, {\left(3 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{4} a^{\frac{3}{2}} b \mathrm{sgn}\left(x\right) - 3 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} a^{\frac{3}{2}} b^{2} \mathrm{sgn}\left(x\right) + 2 \, a^{\frac{3}{2}} b^{3} \mathrm{sgn}\left(x\right)\right)}}{3 \, {\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} - b\right)}^{3}}"," ",0,"-1/2*a^(3/2)*log((sqrt(a)*x - sqrt(a*x^2 + b))^2)*sgn(x) + 4/3*(3*(sqrt(a)*x - sqrt(a*x^2 + b))^4*a^(3/2)*b*sgn(x) - 3*(sqrt(a)*x - sqrt(a*x^2 + b))^2*a^(3/2)*b^2*sgn(x) + 2*a^(3/2)*b^3*sgn(x))/((sqrt(a)*x - sqrt(a*x^2 + b))^2 - b)^3","B",0
1904,1,76,0,0.272208," ","integrate((a+b/x^2)^(3/2)/x^2,x, algorithm=""giac"")","\frac{\frac{3 \, a^{3} \arctan\left(\frac{\sqrt{a x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} - \frac{5 \, {\left(a x^{2} + b\right)}^{\frac{3}{2}} a^{3} \mathrm{sgn}\left(x\right) - 3 \, \sqrt{a x^{2} + b} a^{3} b \mathrm{sgn}\left(x\right)}{a^{2} x^{4}}}{8 \, a}"," ",0,"1/8*(3*a^3*arctan(sqrt(a*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) - (5*(a*x^2 + b)^(3/2)*a^3*sgn(x) - 3*sqrt(a*x^2 + b)*a^3*b*sgn(x))/(a^2*x^4))/a","A",0
1905,1,92,0,0.222310," ","integrate((a+b/x^2)^(3/2)/x^3,x, algorithm=""giac"")","\frac{2 \, {\left(5 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{8} a^{\frac{5}{2}} \mathrm{sgn}\left(x\right) + 10 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{4} a^{\frac{5}{2}} b^{2} \mathrm{sgn}\left(x\right) + a^{\frac{5}{2}} b^{4} \mathrm{sgn}\left(x\right)\right)}}{5 \, {\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} - b\right)}^{5}}"," ",0,"2/5*(5*(sqrt(a)*x - sqrt(a*x^2 + b))^8*a^(5/2)*sgn(x) + 10*(sqrt(a)*x - sqrt(a*x^2 + b))^4*a^(5/2)*b^2*sgn(x) + a^(5/2)*b^4*sgn(x))/((sqrt(a)*x - sqrt(a*x^2 + b))^2 - b)^5","B",0
1906,1,100,0,0.242346," ","integrate((a+b/x^2)^(3/2)/x^4,x, algorithm=""giac"")","-\frac{\frac{3 \, a^{4} \arctan\left(\frac{\sqrt{a x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b} b} + \frac{3 \, {\left(a x^{2} + b\right)}^{\frac{5}{2}} a^{4} \mathrm{sgn}\left(x\right) + 8 \, {\left(a x^{2} + b\right)}^{\frac{3}{2}} a^{4} b \mathrm{sgn}\left(x\right) - 3 \, \sqrt{a x^{2} + b} a^{4} b^{2} \mathrm{sgn}\left(x\right)}{a^{3} b x^{6}}}{48 \, a}"," ",0,"-1/48*(3*a^4*arctan(sqrt(a*x^2 + b)/sqrt(-b))*sgn(x)/(sqrt(-b)*b) + (3*(a*x^2 + b)^(5/2)*a^4*sgn(x) + 8*(a*x^2 + b)^(3/2)*a^4*b*sgn(x) - 3*sqrt(a*x^2 + b)*a^4*b^2*sgn(x))/(a^3*b*x^6))/a","A",0
1907,1,95,0,0.250958," ","integrate((a+b/x^2)^(5/2)*x^3,x, algorithm=""giac"")","-\frac{15}{16} \, \sqrt{a} b^{2} \log\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2}\right) \mathrm{sgn}\left(x\right) + \frac{2 \, \sqrt{a} b^{3} \mathrm{sgn}\left(x\right)}{{\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} - b} + \frac{1}{8} \, {\left(2 \, a^{2} x^{2} \mathrm{sgn}\left(x\right) + 9 \, a b \mathrm{sgn}\left(x\right)\right)} \sqrt{a x^{2} + b} x"," ",0,"-15/16*sqrt(a)*b^2*log((sqrt(a)*x - sqrt(a*x^2 + b))^2)*sgn(x) + 2*sqrt(a)*b^3*sgn(x)/((sqrt(a)*x - sqrt(a*x^2 + b))^2 - b) + 1/8*(2*a^2*x^2*sgn(x) + 9*a*b*sgn(x))*sqrt(a*x^2 + b)*x","A",0
1908,1,90,0,0.222960," ","integrate((a+b/x^2)^(5/2)*x^2,x, algorithm=""giac"")","\frac{\frac{15 \, a^{2} b^{2} \arctan\left(\frac{\sqrt{a x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} + 2 \, {\left(a x^{2} + b\right)}^{\frac{3}{2}} a^{2} \mathrm{sgn}\left(x\right) + 12 \, \sqrt{a x^{2} + b} a^{2} b \mathrm{sgn}\left(x\right) - \frac{3 \, \sqrt{a x^{2} + b} a b^{2} \mathrm{sgn}\left(x\right)}{x^{2}}}{6 \, a}"," ",0,"1/6*(15*a^2*b^2*arctan(sqrt(a*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) + 2*(a*x^2 + b)^(3/2)*a^2*sgn(x) + 12*sqrt(a*x^2 + b)*a^2*b*sgn(x) - 3*sqrt(a*x^2 + b)*a*b^2*sgn(x)/x^2)/a","A",0
1909,1,142,0,0.500830," ","integrate((a+b/x^2)^(5/2)*x,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{a x^{2} + b} a^{2} x \mathrm{sgn}\left(x\right) - \frac{5}{4} \, a^{\frac{3}{2}} b \log\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2}\right) \mathrm{sgn}\left(x\right) + \frac{2 \, {\left(9 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{4} a^{\frac{3}{2}} b^{2} \mathrm{sgn}\left(x\right) - 12 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} a^{\frac{3}{2}} b^{3} \mathrm{sgn}\left(x\right) + 7 \, a^{\frac{3}{2}} b^{4} \mathrm{sgn}\left(x\right)\right)}}{3 \, {\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} - b\right)}^{3}}"," ",0,"1/2*sqrt(a*x^2 + b)*a^2*x*sgn(x) - 5/4*a^(3/2)*b*log((sqrt(a)*x - sqrt(a*x^2 + b))^2)*sgn(x) + 2/3*(9*(sqrt(a)*x - sqrt(a*x^2 + b))^4*a^(3/2)*b^2*sgn(x) - 12*(sqrt(a)*x - sqrt(a*x^2 + b))^2*a^(3/2)*b^3*sgn(x) + 7*a^(3/2)*b^4*sgn(x))/((sqrt(a)*x - sqrt(a*x^2 + b))^2 - b)^3","B",0
1910,1,96,0,0.222015," ","integrate((a+b/x^2)^(5/2),x, algorithm=""giac"")","\frac{\frac{15 \, a^{3} b \arctan\left(\frac{\sqrt{a x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} + 8 \, \sqrt{a x^{2} + b} a^{3} \mathrm{sgn}\left(x\right) - \frac{9 \, {\left(a x^{2} + b\right)}^{\frac{3}{2}} a^{3} b \mathrm{sgn}\left(x\right) - 7 \, \sqrt{a x^{2} + b} a^{3} b^{2} \mathrm{sgn}\left(x\right)}{a^{2} x^{4}}}{8 \, a}"," ",0,"1/8*(15*a^3*b*arctan(sqrt(a*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) + 8*sqrt(a*x^2 + b)*a^3*sgn(x) - (9*(a*x^2 + b)^(3/2)*a^3*b*sgn(x) - 7*sqrt(a*x^2 + b)*a^3*b^2*sgn(x))/(a^2*x^4))/a","A",0
1911,1,180,0,1.057528," ","integrate((a+b/x^2)^(5/2)/x,x, algorithm=""giac"")","-\frac{1}{2} \, a^{\frac{5}{2}} \log\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2}\right) \mathrm{sgn}\left(x\right) + \frac{2 \, {\left(45 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{8} a^{\frac{5}{2}} b \mathrm{sgn}\left(x\right) - 90 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{6} a^{\frac{5}{2}} b^{2} \mathrm{sgn}\left(x\right) + 140 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{4} a^{\frac{5}{2}} b^{3} \mathrm{sgn}\left(x\right) - 70 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} a^{\frac{5}{2}} b^{4} \mathrm{sgn}\left(x\right) + 23 \, a^{\frac{5}{2}} b^{5} \mathrm{sgn}\left(x\right)\right)}}{15 \, {\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} - b\right)}^{5}}"," ",0,"-1/2*a^(5/2)*log((sqrt(a)*x - sqrt(a*x^2 + b))^2)*sgn(x) + 2/15*(45*(sqrt(a)*x - sqrt(a*x^2 + b))^8*a^(5/2)*b*sgn(x) - 90*(sqrt(a)*x - sqrt(a*x^2 + b))^6*a^(5/2)*b^2*sgn(x) + 140*(sqrt(a)*x - sqrt(a*x^2 + b))^4*a^(5/2)*b^3*sgn(x) - 70*(sqrt(a)*x - sqrt(a*x^2 + b))^2*a^(5/2)*b^4*sgn(x) + 23*a^(5/2)*b^5*sgn(x))/((sqrt(a)*x - sqrt(a*x^2 + b))^2 - b)^5","B",0
1912,1,95,0,0.226955," ","integrate((a+b/x^2)^(5/2)/x^2,x, algorithm=""giac"")","\frac{\frac{15 \, a^{4} \arctan\left(\frac{\sqrt{a x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} - \frac{33 \, {\left(a x^{2} + b\right)}^{\frac{5}{2}} a^{4} \mathrm{sgn}\left(x\right) - 40 \, {\left(a x^{2} + b\right)}^{\frac{3}{2}} a^{4} b \mathrm{sgn}\left(x\right) + 15 \, \sqrt{a x^{2} + b} a^{4} b^{2} \mathrm{sgn}\left(x\right)}{a^{3} x^{6}}}{48 \, a}"," ",0,"1/48*(15*a^4*arctan(sqrt(a*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) - (33*(a*x^2 + b)^(5/2)*a^4*sgn(x) - 40*(a*x^2 + b)^(3/2)*a^4*b*sgn(x) + 15*sqrt(a*x^2 + b)*a^4*b^2*sgn(x))/(a^3*x^6))/a","A",0
1913,1,121,0,0.258763," ","integrate((a+b/x^2)^(5/2)/x^3,x, algorithm=""giac"")","\frac{2 \, {\left(7 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{12} a^{\frac{7}{2}} \mathrm{sgn}\left(x\right) + 35 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{8} a^{\frac{7}{2}} b^{2} \mathrm{sgn}\left(x\right) + 21 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{4} a^{\frac{7}{2}} b^{4} \mathrm{sgn}\left(x\right) + a^{\frac{7}{2}} b^{6} \mathrm{sgn}\left(x\right)\right)}}{7 \, {\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b}\right)}^{2} - b\right)}^{7}}"," ",0,"2/7*(7*(sqrt(a)*x - sqrt(a*x^2 + b))^12*a^(7/2)*sgn(x) + 35*(sqrt(a)*x - sqrt(a*x^2 + b))^8*a^(7/2)*b^2*sgn(x) + 21*(sqrt(a)*x - sqrt(a*x^2 + b))^4*a^(7/2)*b^4*sgn(x) + a^(7/2)*b^6*sgn(x))/((sqrt(a)*x - sqrt(a*x^2 + b))^2 - b)^7","B",0
1914,1,119,0,0.246512," ","integrate((a+b/x^2)^(5/2)/x^4,x, algorithm=""giac"")","-\frac{\frac{15 \, a^{5} \arctan\left(\frac{\sqrt{a x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b} b} + \frac{15 \, {\left(a x^{2} + b\right)}^{\frac{7}{2}} a^{5} \mathrm{sgn}\left(x\right) + 73 \, {\left(a x^{2} + b\right)}^{\frac{5}{2}} a^{5} b \mathrm{sgn}\left(x\right) - 55 \, {\left(a x^{2} + b\right)}^{\frac{3}{2}} a^{5} b^{2} \mathrm{sgn}\left(x\right) + 15 \, \sqrt{a x^{2} + b} a^{5} b^{3} \mathrm{sgn}\left(x\right)}{a^{4} b x^{8}}}{384 \, a}"," ",0,"-1/384*(15*a^5*arctan(sqrt(a*x^2 + b)/sqrt(-b))*sgn(x)/(sqrt(-b)*b) + (15*(a*x^2 + b)^(7/2)*a^5*sgn(x) + 73*(a*x^2 + b)^(5/2)*a^5*b*sgn(x) - 55*(a*x^2 + b)^(3/2)*a^5*b^2*sgn(x) + 15*sqrt(a*x^2 + b)*a^5*b^3*sgn(x))/(a^4*b*x^8))/a","A",0
1915,1,84,0,0.241502," ","integrate(x^3/(a+b/x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{a x^{4} + b x^{2}} {\left(\frac{2 \, x^{2}}{a} - \frac{3 \, b}{a^{2}}\right)} - \frac{3 \, b^{2} \log\left({\left| -2 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} - b \right|}\right)}{16 \, a^{\frac{5}{2}}} + \frac{3 \, b^{2} \log\left({\left| b \right|}\right)}{16 \, a^{\frac{5}{2}}}"," ",0,"1/8*sqrt(a*x^4 + b*x^2)*(2*x^2/a - 3*b/a^2) - 3/16*b^2*log(abs(-2*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) - b))/a^(5/2) + 3/16*b^2*log(abs(b))/a^(5/2)","A",0
1916,1,68,0,0.247760," ","integrate(x/(a+b/x^2)^(1/2),x, algorithm=""giac"")","\frac{b \log\left({\left| -2 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} - b \right|}\right)}{4 \, a^{\frac{3}{2}}} - \frac{b \log\left({\left| b \right|}\right)}{4 \, a^{\frac{3}{2}}} + \frac{\sqrt{a x^{4} + b x^{2}}}{2 \, a}"," ",0,"1/4*b*log(abs(-2*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) - b))/a^(3/2) - 1/4*b*log(abs(b))/a^(3/2) + 1/2*sqrt(a*x^4 + b*x^2)/a","A",0
1917,1,48,0,0.247094," ","integrate(1/(a+b/x^2)^(1/2)/x,x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} - b \right|}\right)}{2 \, \sqrt{a}} + \frac{\log\left({\left| b \right|}\right)}{2 \, \sqrt{a}}"," ",0,"-1/2*log(abs(-2*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) - b))/sqrt(a) + 1/2*log(abs(b))/sqrt(a)","B",0
1918,1,18,0,0.188760," ","integrate(1/(a+b/x^2)^(1/2)/x^3,x, algorithm=""giac"")","-\frac{\sqrt{\frac{a x^{2} + b}{x^{2}}}}{b}"," ",0,"-sqrt((a*x^2 + b)/x^2)/b","A",0
1919,1,57,0,0.205334," ","integrate(1/(a+b/x^2)^(1/2)/x^5,x, algorithm=""giac"")","\frac{3 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} + b}{3 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)}^{3}}"," ",0,"1/3*(3*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) + b)/(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))^3","A",0
1920,1,90,0,0.221742," ","integrate(1/(a+b/x^2)^(1/2)/x^7,x, algorithm=""giac"")","\frac{20 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)}^{2} a + 15 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} b + 3 \, b^{2}}{15 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)}^{5}}"," ",0,"1/15*(20*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))^2*a + 15*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a)*b + 3*b^2)/(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))^5","A",0
1921,1,123,0,0.226170," ","integrate(1/(a+b/x^2)^(1/2)/x^9,x, algorithm=""giac"")","\frac{70 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)}^{3} a^{\frac{3}{2}} + 84 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)}^{2} a b + 35 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} b^{2} + 5 \, b^{3}}{35 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)}^{7}}"," ",0,"1/35*(70*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))^3*a^(3/2) + 84*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))^2*a*b + 35*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a)*b^2 + 5*b^3)/(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))^7","A",0
1922,-2,0,0,0.000000," ","integrate(x^4/(a+b/x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-13,6.59772427287,-13]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [88,60.9680557316,-81]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-43,80.6998703005,-84]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [26,27.1915548402,44]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [56,99.5462650466,-1]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [67,64.8330923682,-48](1/5*a^4*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^5+2*a^2*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^3+2*a*sqrt(b)*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^2*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+b^2*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))-2/3*a^2*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^3-2*b^2*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))-2*a*sqrt(b)*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^2*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+a^3*sqrt(b)*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^4*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))/a^2+b^2/a^2*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))","F(-2)",0
1923,-2,0,0,0.000000," ","integrate(x^2/(a+b/x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-58,43.858863886,56]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [97,57.5616762415,-86]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [25,56.1797324405,2]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [11,64.4576321822,46]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [14,83.5125112212,-22]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-94,31.5331678749,18]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-90,36.3617133629,39]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [35,89.0139720016,56]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [83,3.24575260049,-90]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-10,94.741137628,73]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-36,54.1710346672,-32]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [49,64.8237054832,-70]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [66,42.6786879087,-74]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [22,42.3987513026,-16]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-50,8.71320336033,72]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-50,9.53292093519,-48]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [26,23.6350279255,-29]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-35,43.0853207698,64]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-75,39.8355747634,33]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [43,27.7044391828,74]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [2,63.0726894997,-2]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [28,8.94420680963,99]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-41,5.78430139413,-1]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [2,16.0506848684,66]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-23,15.6387684788,93]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-86,54.2482937952,57]1/a*(-b*sqrt(b)/3/a*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+1/3*(a*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)+sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))/a)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)+sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))/a))^3/a/sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)+sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))/a))-b/a*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))","F(-2)",0
1924,1,28,0,0.155250," ","integrate(1/(a+b/x^2)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{b} \mathrm{sgn}\left(x\right)}{a} + \frac{\sqrt{a x^{2} + b}}{a \mathrm{sgn}\left(x\right)}"," ",0,"-sqrt(b)*sgn(x)/a + sqrt(a*x^2 + b)/(a*sgn(x))","A",0
1925,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(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(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(t_nostep),sign(t_nostep+sqrt(b)/a*sign(t_nostep))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1926,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(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(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(t_nostep),sign(t_nostep+sqrt(b)/a*sign(t_nostep))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1927,1,55,0,0.254333," ","integrate(1/x/(-a+b/x^2)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| 2 \, {\left(\sqrt{-a} x^{2} - \sqrt{-a x^{4} + b x^{2}}\right)} \sqrt{-a} + b \right|}\right)}{2 \, \sqrt{-a}} + \frac{\log\left({\left| b \right|}\right)}{2 \, \sqrt{-a}}"," ",0,"-1/2*log(abs(2*(sqrt(-a)*x^2 - sqrt(-a*x^4 + b*x^2))*sqrt(-a) + b))/sqrt(-a) + 1/2*log(abs(b))/sqrt(-a)","B",0
1928,-2,0,0,0.000000," ","integrate(1/x^2/(2+b/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(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(t_nostep),sign(t_nostep+sqrt(b)/2*sign(t_nostep))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1929,-2,0,0,0.000000," ","integrate(1/x^2/(2-b/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(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(t_nostep),sign(t_nostep+sqrt(-b)/2*sign(t_nostep))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1930,-2,0,0,0.000000," ","integrate(x^3/(a+b/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(t_nostep)]Unable to divide, perhaps due to rounding error%%%{%%%{-2,[1]%%%},[2,1,2]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,3]%%%}+%%%{-2,[0,1,4]%%%} / %%%{%%%{1,[2]%%%},[2,0,0]%%%}+%%%{%%{[%%%{-2,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,1]%%%}+%%%{%%%{1,[1]%%%},[0,0,2]%%%} Error: Bad Argument Value","F(-2)",0
1931,-2,0,0,0.000000," ","integrate(x/(a+b/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(t_nostep)]Unable to divide, perhaps due to rounding error%%%{%%%{-2,[1]%%%},[2,1,2]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,3]%%%}+%%%{-2,[0,1,4]%%%} / %%%{%%%{1,[2]%%%},[2,0,0]%%%}+%%%{%%{[%%%{-2,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,1]%%%}+%%%{%%%{1,[1]%%%},[0,0,2]%%%} Error: Bad Argument Value","F(-2)",0
1932,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(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(t_nostep)]Unable to divide, perhaps due to rounding error%%%{%%%{-2,[1]%%%},[2,1,2]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,3]%%%}+%%%{-2,[0,1,4]%%%} / %%%{%%%{1,[2]%%%},[2,0,0]%%%}+%%%{%%{[%%%{-2,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,1]%%%}+%%%{%%%{1,[1]%%%},[0,0,2]%%%} Error: Bad Argument Value","F(-2)",0
1933,1,44,0,0.191035," ","integrate(1/(a+b/x^2)^(3/2)/x^3,x, algorithm=""giac"")","\frac{1}{{\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} + b\right)} \sqrt{a}} - \frac{1}{\sqrt{a} b}"," ",0,"1/(((sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) + b)*sqrt(a)) - 1/(sqrt(a)*b)","B",0
1934,1,28,0,0.212246," ","integrate(1/(a+b/x^2)^(3/2)/x^5,x, algorithm=""giac"")","-\frac{\frac{2 \, a x^{2}}{b^{2}} + \frac{1}{b}}{\sqrt{a x^{4} + b x^{2}}}"," ",0,"-(2*a*x^2/b^2 + 1/b)/sqrt(a*x^4 + b*x^2)","A",0
1935,0,0,0,0.000000," ","integrate(1/(a+b/x^2)^(3/2)/x^7,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{2}}\right)}^{\frac{3}{2}} x^{7}}\,{d x}"," ",0,"integrate(1/((a + b/x^2)^(3/2)*x^7), x)","F",0
1936,0,0,0,0.000000," ","integrate(1/(a+b/x^2)^(3/2)/x^9,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{2}}\right)}^{\frac{3}{2}} x^{9}}\,{d x}"," ",0,"integrate(1/((a + b/x^2)^(3/2)*x^9), x)","F",0
1937,-2,0,0,0.000000," ","integrate(x^4/(a+b/x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [17,97.031638477,-16]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-30,21.9788511144,56]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [66,51.1688777674,-43]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [28,28.9556208979,28]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-71,67.2689954746,93]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-13,34.9002507734,-2]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-32,42.2093715044,-53]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-68,89.6047224309,-49]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-67,31.1777770203,-77]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [98,37.8441393101,-21]b^3/a^4/(a*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))+(1/5*a^26*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^5+2*a^24*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^3+2*a^23*sqrt(b)*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^2*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+a^22*b^2*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))-a^24*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^3-3*a^22*b^2*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+3*a^22*b^2*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))-3*a^23*sqrt(b)*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^2*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+a^25*sqrt(b)*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^4*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))/a^25-b^2*sqrt(b)/a^4*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))","F(-2)",0
1938,-2,0,0,0.000000," ","integrate(x^2/(a+b/x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [87,11.8623251389,-77]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [42,66.6397423497,-22]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-79,4.84063049592,-53]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-8,67.6494641076,-79]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-5,8.73413453996,60]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [81,31.1594383004,58]1/a*(-b^2/a^2/(a*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))+(1/3*a^10*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^3+a^8*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))-2*a^8*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+a^9*sqrt(b)*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^2*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))/a^9+b*sqrt(b)/a^2*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))","F(-2)",0
1939,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [11,86.0946290595,-72]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [79,97.1729265442,77]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [35,94.710570252,-15]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-46,57.5337947248,-63]b/a^2/(a*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))+(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))/a-sqrt(b)/a^2*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))","F(-2)",0
1940,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(3/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [20,94.4491733639,99]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-9,28.5128403376,-66]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [11,86.0946290595,-72]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [79,97.1729265442,77]a*((b+b)/2/a^2/b/sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))-1/a^2/(a*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))))","F(-2)",0
1941,-2,0,0,0.000000," ","integrate(1/(a+b/x^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(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(t_nostep),sign(t_nostep+sqrt(b)/a*sign(t_nostep))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1942,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(3/2)/x^6,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)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(t_nostep),sign(t_nostep+sqrt(b)/a*sign(t_nostep))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1943,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(3/2)/x^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(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(t_nostep),sign(t_nostep+sqrt(b)/a*sign(t_nostep))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1944,1,196,0,0.369585," ","integrate(x^3/(a+b/x^2)^(5/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{a x^{4} + b x^{2}} {\left(\frac{2 \, x^{2}}{a^{3}} - \frac{11 \, b}{a^{4}}\right)} - \frac{35 \, b^{2} \log\left({\left| -2 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} - b \right|}\right)}{16 \, a^{\frac{9}{2}}} + \frac{5 \, {\left(21 \, b^{2} \log\left({\left| b \right|}\right) + 32 \, b^{2}\right)}}{48 \, a^{\frac{9}{2}}} - \frac{12 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)}^{2} a b^{3} + 21 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} b^{4} + 10 \, b^{5}}{3 \, {\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} + b\right)}^{3} a^{\frac{9}{2}}}"," ",0,"1/8*sqrt(a*x^4 + b*x^2)*(2*x^2/a^3 - 11*b/a^4) - 35/16*b^2*log(abs(-2*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) - b))/a^(9/2) + 5/48*(21*b^2*log(abs(b)) + 32*b^2)/a^(9/2) - 1/3*(12*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))^2*a*b^3 + 21*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a)*b^4 + 10*b^5)/(((sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) + b)^3*a^(9/2))","B",0
1945,1,178,0,0.318723," ","integrate(x/(a+b/x^2)^(5/2),x, algorithm=""giac"")","\frac{5 \, b \log\left({\left| -2 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} - b \right|}\right)}{4 \, a^{\frac{7}{2}}} - \frac{15 \, b \log\left({\left| b \right|}\right) + 28 \, b}{12 \, a^{\frac{7}{2}}} + \frac{\sqrt{a x^{4} + b x^{2}}}{2 \, a^{3}} + \frac{9 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)}^{2} a b^{2} + 15 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} b^{3} + 7 \, b^{4}}{3 \, {\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} + b\right)}^{3} a^{\frac{7}{2}}}"," ",0,"5/4*b*log(abs(-2*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) - b))/a^(7/2) - 1/12*(15*b*log(abs(b)) + 28*b)/a^(7/2) + 1/2*sqrt(a*x^4 + b*x^2)/a^3 + 1/3*(9*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))^2*a*b^2 + 15*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a)*b^3 + 7*b^4)/(((sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) + b)^3*a^(7/2))","B",0
1946,1,154,0,0.333382," ","integrate(1/(a+b/x^2)^(5/2)/x,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| b \right|}\right) + 8}{6 \, a^{\frac{5}{2}}} - \frac{\log\left({\left| -2 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} - b \right|}\right)}{2 \, a^{\frac{5}{2}}} - \frac{6 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)}^{2} a b + 9 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} b^{2} + 4 \, b^{3}}{3 \, {\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} + b\right)}^{3} a^{\frac{5}{2}}}"," ",0,"1/6*(3*log(abs(b)) + 8)/a^(5/2) - 1/2*log(abs(-2*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) - b))/a^(5/2) - 1/3*(6*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))^2*a*b + 9*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a)*b^2 + 4*b^3)/(((sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) + b)^3*a^(5/2))","B",0
1947,1,110,0,0.203736," ","integrate(1/(a+b/x^2)^(5/2)/x^3,x, algorithm=""giac"")","-\frac{1}{3 \, a^{\frac{3}{2}} b} + \frac{3 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)}^{2} a^{\frac{3}{2}} + 3 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} a b + \sqrt{a} b^{2}}{3 \, {\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} + b\right)}^{3} a^{2}}"," ",0,"-1/3/(a^(3/2)*b) + 1/3*(3*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))^2*a^(3/2) + 3*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*a*b + sqrt(a)*b^2)/(((sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) + b)^3*a^2)","B",0
1948,1,78,0,0.240118," ","integrate(1/(a+b/x^2)^(5/2)/x^5,x, algorithm=""giac"")","-\frac{2}{3 \, \sqrt{a} b^{2}} + \frac{3 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} a + 2 \, \sqrt{a} b}{3 \, {\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b x^{2}}\right)} \sqrt{a} + b\right)}^{3} a}"," ",0,"-2/3/(sqrt(a)*b^2) + 1/3*(3*(sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*a + 2*sqrt(a)*b)/(((sqrt(a)*x^2 - sqrt(a*x^4 + b*x^2))*sqrt(a) + b)^3*a)","B",0
1949,0,0,0,0.000000," ","integrate(1/(a+b/x^2)^(5/2)/x^7,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{2}}\right)}^{\frac{5}{2}} x^{7}}\,{d x}"," ",0,"integrate(1/((a + b/x^2)^(5/2)*x^7), x)","F",0
1950,1,58,0,0.219513," ","integrate(1/(a+b/x^2)^(5/2)/x^9,x, algorithm=""giac"")","\frac{2 \, {\left(4 \, x^{2} {\left(\frac{2 \, a^{3} x^{2}}{b^{4}} + \frac{3 \, a^{2}}{b^{3}}\right)} + \frac{3 \, a}{b^{2}}\right)} x^{2} - \frac{1}{b}}{3 \, {\left(a x^{4} + b x^{2}\right)}^{\frac{3}{2}}}"," ",0,"1/3*(2*(4*x^2*(2*a^3*x^2/b^4 + 3*a^2/b^3) + 3*a/b^2)*x^2 - 1/b)/(a*x^4 + b*x^2)^(3/2)","A",0
1951,-2,0,0,0.000000," ","integrate(x^2/(a+b/x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-37,79.8475059881,-6]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [95,91.1380034634,2]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [70,77.1190297226,8]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-26,73.1070263633,63]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-51,40.7394986684,-52]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [42,71.9334104825,-88]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-98,19.1478250967,-53]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-65,12.0642261468,-46]1/a*((1/3*a^18*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^3+a^16*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))-3*a^16*b*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+a^17*sqrt(b)*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^2*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))/a^18+1/3*(-9*a^2*b^2*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^2-9*b^3+b^3-18*a*sqrt(b)*b^2*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))/a^3/(a*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))^3+8*b*sqrt(b)/3/a^3*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))","F(-2)",0
1952,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(t_nostep),sign(t_nostep+sqrt(b)/a*sign(t_nostep))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1953,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(5/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-90,36.3617133629,39]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [35,89.0139720016,56]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [83,3.24575260049,-90]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-10,94.741137628,73]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-36,54.1710346672,-32]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [49,64.8237054832,-70]a*((b+b)/3/a^3/b/sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+1/3*(-3*a^2*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))^2-3*b-6*a*sqrt(b)*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+b)/a^3/(a*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))^3)","F(-2)",0
1954,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(5/2)/x^4,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [32,76.6146142203,-62]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [66,99.6590219955,-30]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-50,17.713730142,-44]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [45,14.5515509131,62](b+b)/6/a/b^2/sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))-1/3/(a*(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x))+sqrt(b)*sign(-sqrt(b)/a*sign(x)+sqrt(a*x^2+b)/a/sign(x)))^3/a","F(-2)",0
1955,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(5/2)/x^6,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)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(t_nostep),sign(t_nostep+sqrt(b)/a*sign(t_nostep))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1956,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(5/2)/x^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(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(t_nostep),sign(t_nostep+sqrt(b)/a*sign(t_nostep))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1957,1,21,0,0.163373," ","integrate((1+1/x^2)^(1/3)/x^3,x, algorithm=""giac"")","-\frac{3 \, {\left(x^{2} + 1\right)} \left(\frac{x^{2} + 1}{x^{2}}\right)^{\frac{1}{3}}}{8 \, x^{2}}"," ",0,"-3/8*(x^2 + 1)*((x^2 + 1)/x^2)^(1/3)/x^2","B",0
1958,1,23,0,0.172606," ","integrate((1+1/x^2)^(5/3)/x^3,x, algorithm=""giac"")","-\frac{3 \, {\left(x^{2} + 1\right)}^{2} \left(\frac{x^{2} + 1}{x^{2}}\right)^{\frac{2}{3}}}{16 \, x^{4}}"," ",0,"-3/16*(x^2 + 1)^2*((x^2 + 1)/x^2)^(2/3)/x^4","B",0
1959,0,0,0,0.000000," ","integrate((1+b/x^2)^(3/2)*(c*x)^m,x, algorithm=""giac"")","\int \left(c x\right)^{m} {\left(\frac{b}{x^{2}} + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x)^m*(b/x^2 + 1)^(3/2), x)","F",0
1960,0,0,0,0.000000," ","integrate((1+b/x^2)^(1/2)*(c*x)^m,x, algorithm=""giac"")","\int \left(c x\right)^{m} \sqrt{\frac{b}{x^{2}} + 1}\,{d x}"," ",0,"integrate((c*x)^m*sqrt(b/x^2 + 1), x)","F",0
1961,0,0,0,0.000000," ","integrate((c*x)^m/(1+b/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m}}{\sqrt{\frac{b}{x^{2}} + 1}}\,{d x}"," ",0,"integrate((c*x)^m/sqrt(b/x^2 + 1), x)","F",0
1962,0,0,0,0.000000," ","integrate((c*x)^m/(1+b/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m}}{{\left(\frac{b}{x^{2}} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x)^m/(b/x^2 + 1)^(3/2), x)","F",0
1963,0,0,0,0.000000," ","integrate((1+b/x^2)^p*(c*x)^m,x, algorithm=""giac"")","\int \left(c x\right)^{m} {\left(\frac{b}{x^{2}} + 1\right)}^{p}\,{d x}"," ",0,"integrate((c*x)^m*(b/x^2 + 1)^p, x)","F",0
1964,0,0,0,0.000000," ","integrate((a+b/x^2)^p*(c*x)^m,x, algorithm=""giac"")","\int \left(c x\right)^{m} {\left(a + \frac{b}{x^{2}}\right)}^{p}\,{d x}"," ",0,"integrate((c*x)^m*(a + b/x^2)^p, x)","F",0
1965,1,35,0,0.158326," ","integrate(x^5/(a+b/x^3),x, algorithm=""giac"")","\frac{b^{2} \log\left({\left| a x^{3} + b \right|}\right)}{3 \, a^{3}} + \frac{a x^{6} - 2 \, b x^{3}}{6 \, a^{2}}"," ",0,"1/3*b^2*log(abs(a*x^3 + b))/a^3 + 1/6*(a*x^6 - 2*b*x^3)/a^2","A",0
1966,1,132,0,0.167641," ","integrate(x^4/(a+b/x^3),x, algorithm=""giac"")","-\frac{b \left(-\frac{b}{a}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{2}} - \frac{\sqrt{3} \left(-a^{2} b\right)^{\frac{2}{3}} b \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{3 \, a^{4}} + \frac{\left(-a^{2} b\right)^{\frac{2}{3}} b \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 \, a^{4}} + \frac{2 \, a^{4} x^{5} - 5 \, a^{3} b x^{2}}{10 \, a^{5}}"," ",0,"-1/3*b*(-b/a)^(2/3)*log(abs(x - (-b/a)^(1/3)))/a^2 - 1/3*sqrt(3)*(-a^2*b)^(2/3)*b*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/a^4 + 1/6*(-a^2*b)^(2/3)*b*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/a^4 + 1/10*(2*a^4*x^5 - 5*a^3*b*x^2)/a^5","A",0
1967,1,129,0,0.171764," ","integrate(x^3/(a+b/x^3),x, algorithm=""giac"")","-\frac{b \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a^{2}} + \frac{\sqrt{3} \left(-a^{2} b\right)^{\frac{1}{3}} b \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{3 \, a^{3}} + \frac{\left(-a^{2} b\right)^{\frac{1}{3}} b \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 \, a^{3}} + \frac{a^{3} x^{4} - 4 \, a^{2} b x}{4 \, a^{4}}"," ",0,"-1/3*b*(-b/a)^(1/3)*log(abs(x - (-b/a)^(1/3)))/a^2 + 1/3*sqrt(3)*(-a^2*b)^(1/3)*b*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/a^3 + 1/6*(-a^2*b)^(1/3)*b*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/a^3 + 1/4*(a^3*x^4 - 4*a^2*b*x)/a^4","A",0
1968,1,24,0,0.203308," ","integrate(x^2/(a+b/x^3),x, algorithm=""giac"")","\frac{x^{3}}{3 \, a} - \frac{b \log\left({\left| a x^{3} + b \right|}\right)}{3 \, a^{2}}"," ",0,"1/3*x^3/a - 1/3*b*log(abs(a*x^3 + b))/a^2","A",0
1969,1,114,0,0.165958," ","integrate(x/(a+b/x^3),x, algorithm=""giac"")","\frac{x^{2}}{2 \, a} + \frac{\left(-\frac{b}{a}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a} + \frac{\sqrt{3} \left(-a^{2} b\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{3 \, a^{3}} - \frac{\left(-a^{2} b\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 \, a^{3}}"," ",0,"1/2*x^2/a + 1/3*(-b/a)^(2/3)*log(abs(x - (-b/a)^(1/3)))/a + 1/3*sqrt(3)*(-a^2*b)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/a^3 - 1/6*(-a^2*b)^(2/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/a^3","A",0
1970,1,111,0,0.159317," ","integrate(1/(a+b/x^3),x, algorithm=""giac"")","\frac{\left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a} + \frac{x}{a} - \frac{\sqrt{3} \left(-a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{3 \, a^{2}} - \frac{\left(-a^{2} b\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 \, a^{2}}"," ",0,"1/3*(-b/a)^(1/3)*log(abs(x - (-b/a)^(1/3)))/a + x/a - 1/3*sqrt(3)*(-a^2*b)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/a^2 - 1/6*(-a^2*b)^(1/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/a^2","A",0
1971,1,14,0,0.152007," ","integrate(1/(a+b/x^3)/x,x, algorithm=""giac"")","\frac{\log\left({\left| a x^{3} + b \right|}\right)}{3 \, a}"," ",0,"1/3*log(abs(a*x^3 + b))/a","A",0
1972,1,112,0,0.214502," ","integrate(1/(a+b/x^3)/x^2,x, algorithm=""giac"")","-\frac{\left(-\frac{b}{a}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{3 \, b} - \frac{\sqrt{3} \left(-a^{2} b\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{3 \, a^{2} b} + \frac{\left(-a^{2} b\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b}"," ",0,"-1/3*(-b/a)^(2/3)*log(abs(x - (-b/a)^(1/3)))/b - 1/3*sqrt(3)*(-a^2*b)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/(a^2*b) + 1/6*(-a^2*b)^(2/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/(a^2*b)","A",0
1973,1,112,0,0.168288," ","integrate(1/(a+b/x^3)/x^3,x, algorithm=""giac"")","-\frac{\left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{3 \, b} + \frac{\sqrt{3} \left(-a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{3 \, a b} + \frac{\left(-a^{2} b\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 \, a b}"," ",0,"-1/3*(-b/a)^(1/3)*log(abs(x - (-b/a)^(1/3)))/b + 1/3*sqrt(3)*(-a^2*b)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/(a*b) + 1/6*(-a^2*b)^(1/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/(a*b)","A",0
1974,1,22,0,0.153491," ","integrate(1/(a+b/x^3)/x^4,x, algorithm=""giac"")","-\frac{\log\left({\left| a x^{3} + b \right|}\right)}{3 \, b} + \frac{\log\left({\left| x \right|}\right)}{b}"," ",0,"-1/3*log(abs(a*x^3 + b))/b + log(abs(x))/b","A",0
1975,1,121,0,0.211036," ","integrate(1/(a+b/x^3)/x^5,x, algorithm=""giac"")","\frac{a \left(-\frac{b}{a}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{3 \, b^{2}} + \frac{\sqrt{3} \left(-a^{2} b\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{3 \, a b^{2}} - \frac{\left(-a^{2} b\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 \, a b^{2}} - \frac{1}{b x}"," ",0,"1/3*a*(-b/a)^(2/3)*log(abs(x - (-b/a)^(1/3)))/b^2 + 1/3*sqrt(3)*(-a^2*b)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/(a*b^2) - 1/6*(-a^2*b)^(2/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/(a*b^2) - 1/(b*x)","A",0
1976,1,115,0,0.164500," ","integrate(1/(a+b/x^3)/x^6,x, algorithm=""giac"")","\frac{a \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{3 \, b^{2}} - \frac{\sqrt{3} \left(-a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{3 \, b^{2}} - \frac{\left(-a^{2} b\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 \, b^{2}} - \frac{1}{2 \, b x^{2}}"," ",0,"1/3*a*(-b/a)^(1/3)*log(abs(x - (-b/a)^(1/3)))/b^2 - 1/3*sqrt(3)*(-a^2*b)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/b^2 - 1/6*(-a^2*b)^(1/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/b^2 - 1/2/(b*x^2)","A",0
1977,1,42,0,0.185812," ","integrate(1/(a+b/x^3)/x^7,x, algorithm=""giac"")","\frac{a \log\left({\left| a x^{3} + b \right|}\right)}{3 \, b^{2}} - \frac{a \log\left({\left| x \right|}\right)}{b^{2}} + \frac{a x^{3} - b}{3 \, b^{2} x^{3}}"," ",0,"1/3*a*log(abs(a*x^3 + b))/b^2 - a*log(abs(x))/b^2 + 1/3*(a*x^3 - b)/(b^2*x^3)","A",0
1978,1,54,0,0.161638," ","integrate(x^5/(a+b/x^3)^2,x, algorithm=""giac"")","\frac{b^{2} \log\left({\left| a x^{3} + b \right|}\right)}{a^{4}} + \frac{b^{3}}{3 \, {\left(a x^{3} + b\right)} a^{4}} + \frac{a^{2} x^{6} - 4 \, a b x^{3}}{6 \, a^{4}}"," ",0,"b^2*log(abs(a*x^3 + b))/a^4 + 1/3*b^3/((a*x^3 + b)*a^4) + 1/6*(a^2*x^6 - 4*a*b*x^3)/a^4","A",0
1979,1,151,0,0.196781," ","integrate(x^4/(a+b/x^3)^2,x, algorithm=""giac"")","-\frac{b^{2} x^{2}}{3 \, {\left(a x^{3} + b\right)} a^{3}} - \frac{8 \, b \left(-\frac{b}{a}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{3}} - \frac{8 \, \sqrt{3} \left(-a^{2} b\right)^{\frac{2}{3}} b \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{9 \, a^{5}} + \frac{4 \, \left(-a^{2} b\right)^{\frac{2}{3}} b \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{9 \, a^{5}} + \frac{a^{8} x^{5} - 5 \, a^{7} b x^{2}}{5 \, a^{10}}"," ",0,"-1/3*b^2*x^2/((a*x^3 + b)*a^3) - 8/9*b*(-b/a)^(2/3)*log(abs(x - (-b/a)^(1/3)))/a^3 - 8/9*sqrt(3)*(-a^2*b)^(2/3)*b*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/a^5 + 4/9*(-a^2*b)^(2/3)*b*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/a^5 + 1/5*(a^8*x^5 - 5*a^7*b*x^2)/a^10","A",0
1980,1,147,0,0.237312," ","integrate(x^3/(a+b/x^3)^2,x, algorithm=""giac"")","-\frac{7 \, b \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{3}} - \frac{b^{2} x}{3 \, {\left(a x^{3} + b\right)} a^{3}} + \frac{7 \, \sqrt{3} \left(-a^{2} b\right)^{\frac{1}{3}} b \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{9 \, a^{4}} + \frac{7 \, \left(-a^{2} b\right)^{\frac{1}{3}} b \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{18 \, a^{4}} + \frac{a^{6} x^{4} - 8 \, a^{5} b x}{4 \, a^{8}}"," ",0,"-7/9*b*(-b/a)^(1/3)*log(abs(x - (-b/a)^(1/3)))/a^3 - 1/3*b^2*x/((a*x^3 + b)*a^3) + 7/9*sqrt(3)*(-a^2*b)^(1/3)*b*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/a^4 + 7/18*(-a^2*b)^(1/3)*b*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/a^4 + 1/4*(a^6*x^4 - 8*a^5*b*x)/a^8","A",0
1981,1,41,0,0.213722," ","integrate(x^2/(a+b/x^3)^2,x, algorithm=""giac"")","\frac{x^{3}}{3 \, a^{2}} - \frac{2 \, b \log\left({\left| a x^{3} + b \right|}\right)}{3 \, a^{3}} - \frac{b^{2}}{3 \, {\left(a x^{3} + b\right)} a^{3}}"," ",0,"1/3*x^3/a^2 - 2/3*b*log(abs(a*x^3 + b))/a^3 - 1/3*b^2/((a*x^3 + b)*a^3)","A",0
1982,1,132,0,0.167135," ","integrate(x/(a+b/x^3)^2,x, algorithm=""giac"")","\frac{x^{2}}{2 \, a^{2}} + \frac{b x^{2}}{3 \, {\left(a x^{3} + b\right)} a^{2}} + \frac{5 \, \left(-\frac{b}{a}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2}} + \frac{5 \, \sqrt{3} \left(-a^{2} b\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{9 \, a^{4}} - \frac{5 \, \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{18 \, a^{4}}"," ",0,"1/2*x^2/a^2 + 1/3*b*x^2/((a*x^3 + b)*a^2) + 5/9*(-b/a)^(2/3)*log(abs(x - (-b/a)^(1/3)))/a^2 + 5/9*sqrt(3)*(-a^2*b)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/a^4 - 5/18*(-a^2*b)^(2/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/a^4","A",0
1983,1,127,0,0.207689," ","integrate(1/(a+b/x^3)^2,x, algorithm=""giac"")","\frac{4 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2}} + \frac{x}{a^{2}} + \frac{b x}{3 \, {\left(a x^{3} + b\right)} a^{2}} - \frac{4 \, \sqrt{3} \left(-a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{9 \, a^{3}} - \frac{2 \, \left(-a^{2} b\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{9 \, a^{3}}"," ",0,"4/9*(-b/a)^(1/3)*log(abs(x - (-b/a)^(1/3)))/a^2 + x/a^2 + 1/3*b*x/((a*x^3 + b)*a^2) - 4/9*sqrt(3)*(-a^2*b)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/a^3 - 2/9*(-a^2*b)^(1/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/a^3","A",0
1984,1,32,0,0.169217," ","integrate(1/(a+b/x^3)^2/x,x, algorithm=""giac"")","-\frac{x^{3}}{3 \, {\left(a x^{3} + b\right)} a} + \frac{\log\left({\left| a x^{3} + b \right|}\right)}{3 \, a^{2}}"," ",0,"-1/3*x^3/((a*x^3 + b)*a) + 1/3*log(abs(a*x^3 + b))/a^2","A",0
1985,1,132,0,0.198376," ","integrate(1/(a+b/x^3)^2/x^2,x, algorithm=""giac"")","-\frac{x^{2}}{3 \, {\left(a x^{3} + b\right)} a} - \frac{2 \, \left(-\frac{b}{a}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b} - \frac{2 \, \sqrt{3} \left(-a^{2} b\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{9 \, a^{3} b} + \frac{\left(-a^{2} b\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{9 \, a^{3} b}"," ",0,"-1/3*x^2/((a*x^3 + b)*a) - 2/9*(-b/a)^(2/3)*log(abs(x - (-b/a)^(1/3)))/(a*b) - 2/9*sqrt(3)*(-a^2*b)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/(a^3*b) + 1/9*(-a^2*b)^(2/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/(a^3*b)","A",0
1986,1,130,0,0.171582," ","integrate(1/(a+b/x^3)^2/x^3,x, algorithm=""giac"")","-\frac{\left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a b} - \frac{x}{3 \, {\left(a x^{3} + b\right)} a} + \frac{\sqrt{3} \left(-a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{9 \, a^{2} b} + \frac{\left(-a^{2} b\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{18 \, a^{2} b}"," ",0,"-1/9*(-b/a)^(1/3)*log(abs(x - (-b/a)^(1/3)))/(a*b) - 1/3*x/((a*x^3 + b)*a) + 1/9*sqrt(3)*(-a^2*b)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/(a^2*b) + 1/18*(-a^2*b)^(1/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/(a^2*b)","A",0
1987,1,14,0,0.163885," ","integrate(1/(a+b/x^3)^2/x^4,x, algorithm=""giac"")","-\frac{1}{3 \, {\left(a x^{3} + b\right)} a}"," ",0,"-1/3/((a*x^3 + b)*a)","A",0
1988,1,129,0,0.181574," ","integrate(1/(a+b/x^3)^2/x^5,x, algorithm=""giac"")","\frac{x^{2}}{3 \, {\left(a x^{3} + b\right)} b} - \frac{\left(-\frac{b}{a}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{9 \, b^{2}} - \frac{\sqrt{3} \left(-a^{2} b\right)^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{9 \, a^{2} b^{2}} + \frac{\left(-a^{2} b\right)^{\frac{2}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{18 \, a^{2} b^{2}}"," ",0,"1/3*x^2/((a*x^3 + b)*b) - 1/9*(-b/a)^(2/3)*log(abs(x - (-b/a)^(1/3)))/b^2 - 1/9*sqrt(3)*(-a^2*b)^(2/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/(a^2*b^2) + 1/18*(-a^2*b)^(2/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/(a^2*b^2)","A",0
1989,1,127,0,0.165483," ","integrate(1/(a+b/x^3)^2/x^6,x, algorithm=""giac"")","-\frac{2 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{3}} \right|}\right)}{9 \, b^{2}} + \frac{x}{3 \, {\left(a x^{3} + b\right)} b} + \frac{2 \, \sqrt{3} \left(-a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{9 \, a b^{2}} + \frac{\left(-a^{2} b\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{9 \, a b^{2}}"," ",0,"-2/9*(-b/a)^(1/3)*log(abs(x - (-b/a)^(1/3)))/b^2 + 1/3*x/((a*x^3 + b)*b) + 2/9*sqrt(3)*(-a^2*b)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-b/a)^(1/3))/(-b/a)^(1/3))/(a*b^2) + 1/9*(-a^2*b)^(1/3)*log(x^2 + x*(-b/a)^(1/3) + (-b/a)^(2/3))/(a*b^2)","A",0
1990,1,45,0,0.158066," ","integrate(1/(a+b/x^3)^2/x^7,x, algorithm=""giac"")","-\frac{\log\left({\left| a x^{3} + b \right|}\right)}{3 \, b^{2}} + \frac{\log\left({\left| x \right|}\right)}{b^{2}} + \frac{a x^{3} + 2 \, b}{3 \, {\left(a x^{3} + b\right)} b^{2}}"," ",0,"-1/3*log(abs(a*x^3 + b))/b^2 + log(abs(x))/b^2 + 1/3*(a*x^3 + 2*b)/((a*x^3 + b)*b^2)","A",0
1991,1,55,0,0.264481," ","integrate(x^5*(a+b/x^3)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{a x^{4} + b x} {\left(2 \, x^{3} + \frac{b}{a}\right)} x + \frac{b^{2} \arctan\left(\frac{\sqrt{a + \frac{b}{x^{3}}}}{\sqrt{-a}}\right)}{12 \, \sqrt{-a} a}"," ",0,"1/12*sqrt(a*x^4 + b*x)*(2*x^3 + b/a)*x + 1/12*b^2*arctan(sqrt(a + b/x^3)/sqrt(-a))/(sqrt(-a)*a)","A",0
1992,1,39,0,0.263640," ","integrate(x^2*(a+b/x^3)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{a x^{4} + b x} x - \frac{b \arctan\left(\frac{\sqrt{a + \frac{b}{x^{3}}}}{\sqrt{-a}}\right)}{3 \, \sqrt{-a}}"," ",0,"1/3*sqrt(a*x^4 + b*x)*x - 1/3*b*arctan(sqrt(a + b/x^3)/sqrt(-a))/sqrt(-a)","A",0
1993,1,36,0,0.244229," ","integrate((a+b/x^3)^(1/2)/x,x, algorithm=""giac"")","-\frac{2 \, a \arctan\left(\frac{\sqrt{a + \frac{b}{x^{3}}}}{\sqrt{-a}}\right)}{3 \, \sqrt{-a}} - \frac{2}{3} \, \sqrt{a + \frac{b}{x^{3}}}"," ",0,"-2/3*a*arctan(sqrt(a + b/x^3)/sqrt(-a))/sqrt(-a) - 2/3*sqrt(a + b/x^3)","A",0
1994,1,14,0,0.176472," ","integrate((a+b/x^3)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}}}{9 \, b}"," ",0,"-2/9*(a + b/x^3)^(3/2)/b","A",0
1995,1,29,0,0.185407," ","integrate((a+b/x^3)^(1/2)/x^7,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{5}{2}} - 5 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} a\right)}}{45 \, b^{2}}"," ",0,"-2/45*(3*(a + b/x^3)^(5/2) - 5*(a + b/x^3)^(3/2)*a)/b^2","A",0
1996,1,43,0,0.221764," ","integrate((a+b/x^3)^(1/2)/x^10,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{2}} - 42 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{5}{2}} a + 35 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} a^{2}\right)}}{315 \, b^{3}}"," ",0,"-2/315*(15*(a + b/x^3)^(7/2) - 42*(a + b/x^3)^(5/2)*a + 35*(a + b/x^3)^(3/2)*a^2)/b^3","A",0
1997,1,57,0,0.196188," ","integrate((a+b/x^3)^(1/2)/x^13,x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{9}{2}} - 135 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{2}} a + 189 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{5}{2}} a^{2} - 105 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} a^{3}\right)}}{945 \, b^{4}}"," ",0,"-2/945*(35*(a + b/x^3)^(9/2) - 135*(a + b/x^3)^(7/2)*a + 189*(a + b/x^3)^(5/2)*a^2 - 105*(a + b/x^3)^(3/2)*a^3)/b^4","A",0
1998,0,0,0,0.000000," ","integrate(x^7*(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{x^{3}}} x^{7}\,{d x}"," ",0,"integrate(sqrt(a + b/x^3)*x^7, x)","F",0
1999,0,0,0,0.000000," ","integrate(x^4*(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{x^{3}}} x^{4}\,{d x}"," ",0,"integrate(sqrt(a + b/x^3)*x^4, x)","F",0
2000,0,0,0,0.000000," ","integrate(x*(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{x^{3}}} x\,{d x}"," ",0,"integrate(sqrt(a + b/x^3)*x, x)","F",0
2001,0,0,0,0.000000," ","integrate((a+b/x^3)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{x^{3}}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^3)/x^2, x)","F",0
2002,0,0,0,0.000000," ","integrate((a+b/x^3)^(1/2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{x^{3}}}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^3)/x^5, x)","F",0
2003,0,0,0,0.000000," ","integrate((a+b/x^3)^(1/2)/x^8,x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{x^{3}}}}{x^{8}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^3)/x^8, x)","F",0
2004,0,0,0,0.000000," ","integrate(x^6*(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{x^{3}}} x^{6}\,{d x}"," ",0,"integrate(sqrt(a + b/x^3)*x^6, x)","F",0
2005,0,0,0,0.000000," ","integrate(x^3*(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{x^{3}}} x^{3}\,{d x}"," ",0,"integrate(sqrt(a + b/x^3)*x^3, x)","F",0
2006,0,0,0,0.000000," ","integrate((a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{x^{3}}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^3), x)","F",0
2007,0,0,0,0.000000," ","integrate((a+b/x^3)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{x^{3}}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^3)/x^3, x)","F",0
2008,0,0,0,0.000000," ","integrate((a+b/x^3)^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{x^{3}}}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^3)/x^6, x)","F",0
2009,0,0,0,0.000000," ","integrate((a+b/x^3)^(1/2)/x^9,x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{x^{3}}}}{x^{9}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^3)/x^9, x)","F",0
2010,1,51,0,0.317596," ","integrate((a+b/x^3)^(3/2)*x^5,x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{a x^{4} + b x} {\left(2 \, a x^{3} + 5 \, b\right)} x - \frac{b^{2} \arctan\left(\frac{\sqrt{a + \frac{b}{x^{3}}}}{\sqrt{-a}}\right)}{4 \, \sqrt{-a}}"," ",0,"1/12*sqrt(a*x^4 + b*x)*(2*a*x^3 + 5*b)*x - 1/4*b^2*arctan(sqrt(a + b/x^3)/sqrt(-a))/sqrt(-a)","A",0
2011,1,55,0,0.352746," ","integrate((a+b/x^3)^(3/2)*x^2,x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{a x^{4} + b x} a x - \frac{1}{3} \, {\left(\frac{3 \, a \arctan\left(\frac{\sqrt{a + \frac{b}{x^{3}}}}{\sqrt{-a}}\right)}{\sqrt{-a}} + 2 \, \sqrt{a + \frac{b}{x^{3}}}\right)} b"," ",0,"1/3*sqrt(a*x^4 + b*x)*a*x - 1/3*(3*a*arctan(sqrt(a + b/x^3)/sqrt(-a))/sqrt(-a) + 2*sqrt(a + b/x^3))*b","A",0
2012,1,50,0,0.275192," ","integrate((a+b/x^3)^(3/2)/x,x, algorithm=""giac"")","-\frac{2 \, a^{2} \arctan\left(\frac{\sqrt{a + \frac{b}{x^{3}}}}{\sqrt{-a}}\right)}{3 \, \sqrt{-a}} - \frac{2}{9} \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{a + \frac{b}{x^{3}}} a"," ",0,"-2/3*a^2*arctan(sqrt(a + b/x^3)/sqrt(-a))/sqrt(-a) - 2/9*(a + b/x^3)^(3/2) - 2/3*sqrt(a + b/x^3)*a","A",0
2013,1,14,0,0.184519," ","integrate((a+b/x^3)^(3/2)/x^4,x, algorithm=""giac"")","-\frac{2 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{5}{2}}}{15 \, b}"," ",0,"-2/15*(a + b/x^3)^(5/2)/b","A",0
2014,1,29,0,0.199210," ","integrate((a+b/x^3)^(3/2)/x^7,x, algorithm=""giac"")","-\frac{2 \, {\left(5 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{2}} - 7 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{5}{2}} a\right)}}{105 \, b^{2}}"," ",0,"-2/105*(5*(a + b/x^3)^(7/2) - 7*(a + b/x^3)^(5/2)*a)/b^2","A",0
2015,1,43,0,0.204144," ","integrate((a+b/x^3)^(3/2)/x^10,x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{9}{2}} - 90 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{2}} a + 63 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{5}{2}} a^{2}\right)}}{945 \, b^{3}}"," ",0,"-2/945*(35*(a + b/x^3)^(9/2) - 90*(a + b/x^3)^(7/2)*a + 63*(a + b/x^3)^(5/2)*a^2)/b^3","A",0
2016,1,57,0,0.204568," ","integrate((a+b/x^3)^(3/2)/x^13,x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{11}{2}} - 385 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{9}{2}} a + 495 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{7}{2}} a^{2} - 231 \, {\left(a + \frac{b}{x^{3}}\right)}^{\frac{5}{2}} a^{3}\right)}}{3465 \, b^{4}}"," ",0,"-2/3465*(105*(a + b/x^3)^(11/2) - 385*(a + b/x^3)^(9/2)*a + 495*(a + b/x^3)^(7/2)*a^2 - 231*(a + b/x^3)^(5/2)*a^3)/b^4","A",0
2017,1,99,0,0.230862," ","integrate(x^5/(a+b/x^3)^(1/2),x, algorithm=""giac"")","-\frac{1}{12} \, b^{2} {\left(\frac{3 \, \arctan\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} - \frac{5 \, a \sqrt{\frac{a x^{3} + b}{x^{3}}} - \frac{3 \, {\left(a x^{3} + b\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{x^{3}}}{{\left(a - \frac{a x^{3} + b}{x^{3}}\right)}^{2} a^{2}}\right)}"," ",0,"-1/12*b^2*(3*arctan(sqrt((a*x^3 + b)/x^3)/sqrt(-a))/(sqrt(-a)*a^2) - (5*a*sqrt((a*x^3 + b)/x^3) - 3*(a*x^3 + b)*sqrt((a*x^3 + b)/x^3)/x^3)/((a - (a*x^3 + b)/x^3)^2*a^2))","A",0
2018,1,67,0,0.247288," ","integrate(x^2/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, b {\left(\frac{\arctan\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{\sqrt{-a}}\right)}{\sqrt{-a} a} - \frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{{\left(a - \frac{a x^{3} + b}{x^{3}}\right)} a}\right)}"," ",0,"1/3*b*(arctan(sqrt((a*x^3 + b)/x^3)/sqrt(-a))/(sqrt(-a)*a) - sqrt((a*x^3 + b)/x^3)/((a - (a*x^3 + b)/x^3)*a))","A",0
2019,0,0,0,0.000000," ","integrate(1/x/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^3)*x), x)","F",0
2020,1,18,0,0.152206," ","integrate(1/x^4/(a+b/x^3)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{\frac{a x^{3} + b}{x^{3}}}}{3 \, b}"," ",0,"-2/3*sqrt((a*x^3 + b)/x^3)/b","A",0
2021,0,0,0,0.000000," ","integrate(1/x^7/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x^{7}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^3)*x^7), x)","F",0
2022,0,0,0,0.000000," ","integrate(1/x^10/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x^{10}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^3)*x^10), x)","F",0
2023,0,0,0,0.000000," ","integrate(1/x^13/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x^{13}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^3)*x^13), x)","F",0
2024,0,0,0,0.000000," ","integrate(x^7/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{x^{7}}{\sqrt{a + \frac{b}{x^{3}}}}\,{d x}"," ",0,"integrate(x^7/sqrt(a + b/x^3), x)","F",0
2025,0,0,0,0.000000," ","integrate(x^4/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{a + \frac{b}{x^{3}}}}\,{d x}"," ",0,"integrate(x^4/sqrt(a + b/x^3), x)","F",0
2026,0,0,0,0.000000," ","integrate(x/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{a + \frac{b}{x^{3}}}}\,{d x}"," ",0,"integrate(x/sqrt(a + b/x^3), x)","F",0
2027,0,0,0,0.000000," ","integrate(1/x^2/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^3)*x^2), x)","F",0
2028,0,0,0,0.000000," ","integrate(1/x^5/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x^{5}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^3)*x^5), x)","F",0
2029,0,0,0,0.000000," ","integrate(1/x^8/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x^{8}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^3)*x^8), x)","F",0
2030,0,0,0,0.000000," ","integrate(x^6/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{a + \frac{b}{x^{3}}}}\,{d x}"," ",0,"integrate(x^6/sqrt(a + b/x^3), x)","F",0
2031,0,0,0,0.000000," ","integrate(x^3/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3}}{\sqrt{a + \frac{b}{x^{3}}}}\,{d x}"," ",0,"integrate(x^3/sqrt(a + b/x^3), x)","F",0
2032,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}}}\,{d x}"," ",0,"integrate(1/sqrt(a + b/x^3), x)","F",0
2033,0,0,0,0.000000," ","integrate(1/x^3/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^3)*x^3), x)","F",0
2034,0,0,0,0.000000," ","integrate(1/x^6/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x^{6}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^3)*x^6), x)","F",0
2035,0,0,0,0.000000," ","integrate(1/x^9/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x^{9}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^3)*x^9), x)","F",0
2036,0,0,0,0.000000," ","integrate(1/x^12/(a+b/x^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x^{12}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^3)*x^12), x)","F",0
2037,1,117,0,0.251501," ","integrate(x^5/(a+b/x^3)^(3/2),x, algorithm=""giac"")","-\frac{1}{12} \, b^{2} {\left(\frac{15 \, \arctan\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} + \frac{8}{a^{3} \sqrt{\frac{a x^{3} + b}{x^{3}}}} - \frac{9 \, a \sqrt{\frac{a x^{3} + b}{x^{3}}} - \frac{7 \, {\left(a x^{3} + b\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{x^{3}}}{{\left(a - \frac{a x^{3} + b}{x^{3}}\right)}^{2} a^{3}}\right)}"," ",0,"-1/12*b^2*(15*arctan(sqrt((a*x^3 + b)/x^3)/sqrt(-a))/(sqrt(-a)*a^3) + 8/(a^3*sqrt((a*x^3 + b)/x^3)) - (9*a*sqrt((a*x^3 + b)/x^3) - 7*(a*x^3 + b)*sqrt((a*x^3 + b)/x^3)/x^3)/((a - (a*x^3 + b)/x^3)^2*a^3))","A",0
2038,1,97,0,0.240545," ","integrate(x^2/(a+b/x^3)^(3/2),x, algorithm=""giac"")","\frac{1}{3} \, b {\left(\frac{3 \, \arctan\left(\frac{\sqrt{\frac{a x^{3} + b}{x^{3}}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{2 \, a - \frac{3 \, {\left(a x^{3} + b\right)}}{x^{3}}}{{\left(a \sqrt{\frac{a x^{3} + b}{x^{3}}} - \frac{{\left(a x^{3} + b\right)} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{x^{3}}\right)} a^{2}}\right)}"," ",0,"1/3*b*(3*arctan(sqrt((a*x^3 + b)/x^3)/sqrt(-a))/(sqrt(-a)*a^2) + (2*a - 3*(a*x^3 + b)/x^3)/((a*sqrt((a*x^3 + b)/x^3) - (a*x^3 + b)*sqrt((a*x^3 + b)/x^3)/x^3)*a^2))","A",0
2039,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x), x)","F",0
2040,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x^4), x)","F",0
2041,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x^7,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x^{7}}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x^7), x)","F",0
2042,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x^10,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x^{10}}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x^10), x)","F",0
2043,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x^13,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x^{13}}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x^13), x)","F",0
2044,0,0,0,0.000000," ","integrate(x^7/(a+b/x^3)^(3/2),x, algorithm=""giac"")","\int \frac{x^{7}}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^7/(a + b/x^3)^(3/2), x)","F",0
2045,0,0,0,0.000000," ","integrate(x^4/(a+b/x^3)^(3/2),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/(a + b/x^3)^(3/2), x)","F",0
2046,0,0,0,0.000000," ","integrate(x/(a+b/x^3)^(3/2),x, algorithm=""giac"")","\int \frac{x}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(a + b/x^3)^(3/2), x)","F",0
2047,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x^2), x)","F",0
2048,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x^5,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x^{5}}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x^5), x)","F",0
2049,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x^8,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x^{8}}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x^8), x)","F",0
2050,0,0,0,0.000000," ","integrate(x^6/(a+b/x^3)^(3/2),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^6/(a + b/x^3)^(3/2), x)","F",0
2051,0,0,0,0.000000," ","integrate(x^3/(a+b/x^3)^(3/2),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3/(a + b/x^3)^(3/2), x)","F",0
2052,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a + b/x^3)^(-3/2), x)","F",0
2053,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x^3), x)","F",0
2054,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x^6,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x^{6}}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x^6), x)","F",0
2055,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x^9,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x^{9}}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x^9), x)","F",0
2056,0,0,0,0.000000," ","integrate(1/(a+b/x^3)^(3/2)/x^12,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{3}}\right)}^{\frac{3}{2}} x^{12}}\,{d x}"," ",0,"integrate(1/((a + b/x^3)^(3/2)*x^12), x)","F",0
2057,1,172,0,0.156442," ","integrate(1/(a+b/x^4),x, algorithm=""giac"")","\frac{x}{a} - \frac{\sqrt{2} \left(a^{3} b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{b}{a}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{b}{a}\right)^{\frac{1}{4}}}\right)}{4 \, a^{2}} - \frac{\sqrt{2} \left(a^{3} b\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{b}{a}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{b}{a}\right)^{\frac{1}{4}}}\right)}{4 \, a^{2}} - \frac{\sqrt{2} \left(a^{3} b\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{b}{a}\right)^{\frac{1}{4}} + \sqrt{\frac{b}{a}}\right)}{8 \, a^{2}} + \frac{\sqrt{2} \left(a^{3} b\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{b}{a}\right)^{\frac{1}{4}} + \sqrt{\frac{b}{a}}\right)}{8 \, a^{2}}"," ",0,"x/a - 1/4*sqrt(2)*(a^3*b)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(b/a)^(1/4))/(b/a)^(1/4))/a^2 - 1/4*sqrt(2)*(a^3*b)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(b/a)^(1/4))/(b/a)^(1/4))/a^2 - 1/8*sqrt(2)*(a^3*b)^(1/4)*log(x^2 + sqrt(2)*x*(b/a)^(1/4) + sqrt(b/a))/a^2 + 1/8*sqrt(2)*(a^3*b)^(1/4)*log(x^2 - sqrt(2)*x*(b/a)^(1/4) + sqrt(b/a))/a^2","A",0
2058,1,41,0,0.167191," ","integrate(x^3*(a+b/x^4)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{a x^{4} + b} x^{2} - \frac{b \log\left({\left| -\sqrt{a} x^{2} + \sqrt{a x^{4} + b} \right|}\right)}{4 \, \sqrt{a}}"," ",0,"1/4*sqrt(a*x^4 + b)*x^2 - 1/4*b*log(abs(-sqrt(a)*x^2 + sqrt(a*x^4 + b)))/sqrt(a)","A",0
2059,1,36,0,0.151873," ","integrate(x*(a+b/x^4)^(1/2),x, algorithm=""giac"")","\frac{b \arctan\left(\frac{\sqrt{a x^{4} + b}}{\sqrt{-b}}\right)}{2 \, \sqrt{-b}} + \frac{1}{2} \, \sqrt{a x^{4} + b}"," ",0,"1/2*b*arctan(sqrt(a*x^4 + b)/sqrt(-b))/sqrt(-b) + 1/2*sqrt(a*x^4 + b)","A",0
2060,1,60,0,0.195034," ","integrate((a+b/x^4)^(1/2)/x,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{a} \log\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2}\right) + \frac{\sqrt{a} b}{{\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2} - b}"," ",0,"-1/4*sqrt(a)*log((sqrt(a)*x^2 - sqrt(a*x^4 + b))^2) + sqrt(a)*b/((sqrt(a)*x^2 - sqrt(a*x^4 + b))^2 - b)","A",0
2061,1,46,0,0.154223," ","integrate((a+b/x^4)^(1/2)/x^3,x, algorithm=""giac"")","\frac{\frac{a^{2} \arctan\left(\frac{\sqrt{a x^{4} + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{\sqrt{a x^{4} + b} a}{x^{4}}}{4 \, a}"," ",0,"1/4*(a^2*arctan(sqrt(a*x^4 + b)/sqrt(-b))/sqrt(-b) - sqrt(a*x^4 + b)*a/x^4)/a","A",0
2062,0,0,0,0.000000," ","integrate(x^2*(a+b/x^4)^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{x^{4}}} x^{2}\,{d x}"," ",0,"integrate(sqrt(a + b/x^4)*x^2, x)","F",0
2063,0,0,0,0.000000," ","integrate((a+b/x^4)^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{x^{4}}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^4), x)","F",0
2064,0,0,0,0.000000," ","integrate((a+b/x^4)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{x^{4}}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^4)/x^2, x)","F",0
2065,0,0,0,0.000000," ","integrate((a+b/x^4)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{x^{4}}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^4)/x^4, x)","F",0
2066,1,78,0,0.221980," ","integrate((a+b/x^4)^(3/2)*x^3,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{a x^{4} + b} a x^{2} - \frac{3}{8} \, \sqrt{a} b \log\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2}\right) + \frac{\sqrt{a} b^{2}}{{\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2} - b}"," ",0,"1/4*sqrt(a*x^4 + b)*a*x^2 - 3/8*sqrt(a)*b*log((sqrt(a)*x^2 - sqrt(a*x^4 + b))^2) + sqrt(a)*b^2/((sqrt(a)*x^2 - sqrt(a*x^4 + b))^2 - b)","A",0
2067,1,63,0,0.162468," ","integrate((a+b/x^4)^(3/2)*x,x, algorithm=""giac"")","\frac{\frac{3 \, a^{2} b \arctan\left(\frac{\sqrt{a x^{4} + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + 2 \, \sqrt{a x^{4} + b} a^{2} - \frac{\sqrt{a x^{4} + b} a b}{x^{4}}}{4 \, a}"," ",0,"1/4*(3*a^2*b*arctan(sqrt(a*x^4 + b)/sqrt(-b))/sqrt(-b) + 2*sqrt(a*x^4 + b)*a^2 - sqrt(a*x^4 + b)*a*b/x^4)/a","A",0
2068,1,122,0,0.254315," ","integrate((a+b/x^4)^(3/2)/x,x, algorithm=""giac"")","-\frac{1}{4} \, a^{\frac{3}{2}} \log\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2}\right) + \frac{2 \, {\left(3 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{4} a^{\frac{3}{2}} b - 3 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2} a^{\frac{3}{2}} b^{2} + 2 \, a^{\frac{3}{2}} b^{3}\right)}}{3 \, {\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2} - b\right)}^{3}}"," ",0,"-1/4*a^(3/2)*log((sqrt(a)*x^2 - sqrt(a*x^4 + b))^2) + 2/3*(3*(sqrt(a)*x^2 - sqrt(a*x^4 + b))^4*a^(3/2)*b - 3*(sqrt(a)*x^2 - sqrt(a*x^4 + b))^2*a^(3/2)*b^2 + 2*a^(3/2)*b^3)/((sqrt(a)*x^2 - sqrt(a*x^4 + b))^2 - b)^3","B",0
2069,1,70,0,0.163815," ","integrate((a+b/x^4)^(3/2)/x^3,x, algorithm=""giac"")","\frac{\frac{3 \, a^{3} \arctan\left(\frac{\sqrt{a x^{4} + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{5 \, {\left(a x^{4} + b\right)}^{\frac{3}{2}} a^{3} - 3 \, \sqrt{a x^{4} + b} a^{3} b}{a^{2} x^{8}}}{16 \, a}"," ",0,"1/16*(3*a^3*arctan(sqrt(a*x^4 + b)/sqrt(-b))/sqrt(-b) - (5*(a*x^4 + b)^(3/2)*a^3 - 3*sqrt(a*x^4 + b)*a^3*b)/(a^2*x^8))/a","A",0
2070,0,0,0,0.000000," ","integrate((a+b/x^4)^(3/2)*x^2,x, algorithm=""giac"")","\int {\left(a + \frac{b}{x^{4}}\right)}^{\frac{3}{2}} x^{2}\,{d x}"," ",0,"integrate((a + b/x^4)^(3/2)*x^2, x)","F",0
2071,0,0,0,0.000000," ","integrate((a+b/x^4)^(3/2),x, algorithm=""giac"")","\int {\left(a + \frac{b}{x^{4}}\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a + b/x^4)^(3/2), x)","F",0
2072,0,0,0,0.000000," ","integrate((a+b/x^4)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((a + b/x^4)^(3/2)/x^2, x)","F",0
2073,0,0,0,0.000000," ","integrate((a+b/x^4)^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate((a + b/x^4)^(3/2)/x^4, x)","F",0
2074,1,142,0,0.270610," ","integrate((a+b/x^4)^(5/2)*x^3,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{a x^{4} + b} a^{2} x^{2} - \frac{5}{8} \, a^{\frac{3}{2}} b \log\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2}\right) + \frac{9 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{4} a^{\frac{3}{2}} b^{2} - 12 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2} a^{\frac{3}{2}} b^{3} + 7 \, a^{\frac{3}{2}} b^{4}}{3 \, {\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2} - b\right)}^{3}}"," ",0,"1/4*sqrt(a*x^4 + b)*a^2*x^2 - 5/8*a^(3/2)*b*log((sqrt(a)*x^2 - sqrt(a*x^4 + b))^2) + 1/3*(9*(sqrt(a)*x^2 - sqrt(a*x^4 + b))^4*a^(3/2)*b^2 - 12*(sqrt(a)*x^2 - sqrt(a*x^4 + b))^2*a^(3/2)*b^3 + 7*a^(3/2)*b^4)/((sqrt(a)*x^2 - sqrt(a*x^4 + b))^2 - b)^3","B",0
2075,1,88,0,0.191360," ","integrate((a+b/x^4)^(5/2)*x,x, algorithm=""giac"")","\frac{\frac{15 \, a^{3} b \arctan\left(\frac{\sqrt{a x^{4} + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + 8 \, \sqrt{a x^{4} + b} a^{3} - \frac{9 \, {\left(a x^{4} + b\right)}^{\frac{3}{2}} a^{3} b - 7 \, \sqrt{a x^{4} + b} a^{3} b^{2}}{a^{2} x^{8}}}{16 \, a}"," ",0,"1/16*(15*a^3*b*arctan(sqrt(a*x^4 + b)/sqrt(-b))/sqrt(-b) + 8*sqrt(a*x^4 + b)*a^3 - (9*(a*x^4 + b)^(3/2)*a^3*b - 7*sqrt(a*x^4 + b)*a^3*b^2)/(a^2*x^8))/a","A",0
2076,1,180,0,0.284364," ","integrate((a+b/x^4)^(5/2)/x,x, algorithm=""giac"")","-\frac{1}{4} \, a^{\frac{5}{2}} \log\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2}\right) + \frac{45 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{8} a^{\frac{5}{2}} b - 90 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{6} a^{\frac{5}{2}} b^{2} + 140 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{4} a^{\frac{5}{2}} b^{3} - 70 \, {\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2} a^{\frac{5}{2}} b^{4} + 23 \, a^{\frac{5}{2}} b^{5}}{15 \, {\left({\left(\sqrt{a} x^{2} - \sqrt{a x^{4} + b}\right)}^{2} - b\right)}^{5}}"," ",0,"-1/4*a^(5/2)*log((sqrt(a)*x^2 - sqrt(a*x^4 + b))^2) + 1/15*(45*(sqrt(a)*x^2 - sqrt(a*x^4 + b))^8*a^(5/2)*b - 90*(sqrt(a)*x^2 - sqrt(a*x^4 + b))^6*a^(5/2)*b^2 + 140*(sqrt(a)*x^2 - sqrt(a*x^4 + b))^4*a^(5/2)*b^3 - 70*(sqrt(a)*x^2 - sqrt(a*x^4 + b))^2*a^(5/2)*b^4 + 23*a^(5/2)*b^5)/((sqrt(a)*x^2 - sqrt(a*x^4 + b))^2 - b)^5","B",0
2077,1,87,0,0.165858," ","integrate((a+b/x^4)^(5/2)/x^3,x, algorithm=""giac"")","\frac{\frac{15 \, a^{4} \arctan\left(\frac{\sqrt{a x^{4} + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{33 \, {\left(a x^{4} + b\right)}^{\frac{5}{2}} a^{4} - 40 \, {\left(a x^{4} + b\right)}^{\frac{3}{2}} a^{4} b + 15 \, \sqrt{a x^{4} + b} a^{4} b^{2}}{a^{3} x^{12}}}{96 \, a}"," ",0,"1/96*(15*a^4*arctan(sqrt(a*x^4 + b)/sqrt(-b))/sqrt(-b) - (33*(a*x^4 + b)^(5/2)*a^4 - 40*(a*x^4 + b)^(3/2)*a^4*b + 15*sqrt(a*x^4 + b)*a^4*b^2)/(a^3*x^12))/a","A",0
2078,0,0,0,0.000000," ","integrate((a+b/x^4)^(5/2)*x^2,x, algorithm=""giac"")","\int {\left(a + \frac{b}{x^{4}}\right)}^{\frac{5}{2}} x^{2}\,{d x}"," ",0,"integrate((a + b/x^4)^(5/2)*x^2, x)","F",0
2079,0,0,0,0.000000," ","integrate((a+b/x^4)^(5/2),x, algorithm=""giac"")","\int {\left(a + \frac{b}{x^{4}}\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a + b/x^4)^(5/2), x)","F",0
2080,0,0,0,0.000000," ","integrate((a+b/x^4)^(5/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{5}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((a + b/x^4)^(5/2)/x^2, x)","F",0
2081,0,0,0,0.000000," ","integrate((a+b/x^4)^(5/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{5}{2}}}{x^{4}}\,{d x}"," ",0,"integrate((a + b/x^4)^(5/2)/x^4, x)","F",0
2082,1,53,0,0.199571," ","integrate(x^3/(a+b/x^4)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{a x^{4} + b} x^{2}}{4 \, a} + \frac{b \log\left({\left| -\sqrt{a} x^{2} + \sqrt{a x^{4} + b} \right|}\right)}{4 \, a^{\frac{3}{2}}} - \frac{b \log\left({\left| b \right|}\right)}{8 \, a^{\frac{3}{2}}}"," ",0,"1/4*sqrt(a*x^4 + b)*x^2/a + 1/4*b*log(abs(-sqrt(a)*x^2 + sqrt(a*x^4 + b)))/a^(3/2) - 1/8*b*log(abs(b))/a^(3/2)","A",0
2083,1,23,0,0.186049," ","integrate(x/(a+b/x^4)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{a x^{4} + b}}{2 \, a} - \frac{\sqrt{b}}{2 \, a}"," ",0,"1/2*sqrt(a*x^4 + b)/a - 1/2*sqrt(b)/a","A",0
2084,1,34,0,0.209583," ","integrate(1/x/(a+b/x^4)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -\sqrt{a} x^{2} + \sqrt{a x^{4} + b} \right|}\right)}{2 \, \sqrt{a}} + \frac{\log\left({\left| b \right|}\right)}{4 \, \sqrt{a}}"," ",0,"-1/2*log(abs(-sqrt(a)*x^2 + sqrt(a*x^4 + b)))/sqrt(a) + 1/4*log(abs(b))/sqrt(a)","A",0
2085,1,41,0,0.172698," ","integrate(1/x^3/(a+b/x^4)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{a x^{4} + b}}{\sqrt{-b}}\right)}{2 \, \sqrt{-b}} - \frac{\arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right)}{2 \, \sqrt{-b}}"," ",0,"1/2*arctan(sqrt(a*x^4 + b)/sqrt(-b))/sqrt(-b) - 1/2*arctan(sqrt(b)/sqrt(-b))/sqrt(-b)","A",0
2086,0,0,0,0.000000," ","integrate(x^2/(a+b/x^4)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{a + \frac{b}{x^{4}}}}\,{d x}"," ",0,"integrate(x^2/sqrt(a + b/x^4), x)","F",0
2087,0,0,0,0.000000," ","integrate(1/(a+b/x^4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{4}}}}\,{d x}"," ",0,"integrate(1/sqrt(a + b/x^4), x)","F",0
2088,0,0,0,0.000000," ","integrate(1/x^2/(a+b/x^4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{4}}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^4)*x^2), x)","F",0
2089,0,0,0,0.000000," ","integrate(1/x^4/(a+b/x^4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{4}}} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^4)*x^4), x)","F",0
2090,1,64,0,0.247012," ","integrate(x^3/(a+b/x^4)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{x^{4}}{a} + \frac{3 \, b}{a^{2}}\right)} x^{2}}{4 \, \sqrt{a x^{4} + b}} + \frac{3 \, b \log\left({\left| -\sqrt{a} x^{2} + \sqrt{a x^{4} + b} \right|}\right)}{4 \, a^{\frac{5}{2}}} - \frac{3 \, b \log\left({\left| b \right|}\right)}{8 \, a^{\frac{5}{2}}}"," ",0,"1/4*(x^4/a + 3*b/a^2)*x^2/sqrt(a*x^4 + b) + 3/4*b*log(abs(-sqrt(a)*x^2 + sqrt(a*x^4 + b)))/a^(5/2) - 3/8*b*log(abs(b))/a^(5/2)","A",0
2091,1,42,0,0.216931," ","integrate(x/(a+b/x^4)^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{a x^{4} + b}}{a} + \frac{b}{\sqrt{a x^{4} + b} a}}{2 \, a} - \frac{\sqrt{b}}{a^{2}}"," ",0,"1/2*(sqrt(a*x^4 + b)/a + b/(sqrt(a*x^4 + b)*a))/a - sqrt(b)/a^2","A",0
2092,1,51,0,0.223868," ","integrate(1/(a+b/x^4)^(3/2)/x,x, algorithm=""giac"")","-\frac{x^{2}}{2 \, \sqrt{a x^{4} + b} a} - \frac{\log\left({\left| -\sqrt{a} x^{2} + \sqrt{a x^{4} + b} \right|}\right)}{2 \, a^{\frac{3}{2}}} + \frac{\log\left({\left| b \right|}\right)}{4 \, a^{\frac{3}{2}}}"," ",0,"-1/2*x^2/(sqrt(a*x^4 + b)*a) - 1/2*log(abs(-sqrt(a)*x^2 + sqrt(a*x^4 + b)))/a^(3/2) + 1/4*log(abs(b))/a^(3/2)","A",0
2093,1,23,0,0.172797," ","integrate(1/(a+b/x^4)^(3/2)/x^3,x, algorithm=""giac"")","-\frac{1}{2 \, \sqrt{a x^{4} + b} a} + \frac{1}{2 \, a \sqrt{b}}"," ",0,"-1/2/(sqrt(a*x^4 + b)*a) + 1/2/(a*sqrt(b))","A",0
2094,0,0,0,0.000000," ","integrate(x^2/(a+b/x^4)^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(a + b/x^4)^(3/2), x)","F",0
2095,0,0,0,0.000000," ","integrate(1/(a+b/x^4)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a + b/x^4)^(-3/2), x)","F",0
2096,0,0,0,0.000000," ","integrate(1/(a+b/x^4)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((a + b/x^4)^(3/2)*x^2), x)","F",0
2097,0,0,0,0.000000," ","integrate(1/(a+b/x^4)^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((a + b/x^4)^(3/2)*x^4), x)","F",0
2098,1,78,0,0.234484," ","integrate(x^3/(a+b/x^4)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{3 \, x^{4}}{a} + \frac{20 \, b}{a^{2}}\right)} x^{4} + \frac{15 \, b^{2}}{a^{3}}\right)} x^{2}}{12 \, {\left(a x^{4} + b\right)}^{\frac{3}{2}}} + \frac{5 \, b \log\left({\left| -\sqrt{a} x^{2} + \sqrt{a x^{4} + b} \right|}\right)}{4 \, a^{\frac{7}{2}}} - \frac{5 \, b \log\left({\left| b \right|}\right)}{8 \, a^{\frac{7}{2}}}"," ",0,"1/12*((3*x^4/a + 20*b/a^2)*x^4 + 15*b^2/a^3)*x^2/(a*x^4 + b)^(3/2) + 5/4*b*log(abs(-sqrt(a)*x^2 + sqrt(a*x^4 + b)))/a^(7/2) - 5/8*b*log(abs(b))/a^(7/2)","A",0
2099,1,53,0,0.194858," ","integrate(x/(a+b/x^4)^(5/2),x, algorithm=""giac"")","\frac{\sqrt{a x^{4} + b}}{2 \, a^{3}} - \frac{4 \, \sqrt{b}}{3 \, a^{3}} + \frac{6 \, {\left(a x^{4} + b\right)} b - b^{2}}{6 \, {\left(a x^{4} + b\right)}^{\frac{3}{2}} a^{3}}"," ",0,"1/2*sqrt(a*x^4 + b)/a^3 - 4/3*sqrt(b)/a^3 + 1/6*(6*(a*x^4 + b)*b - b^2)/((a*x^4 + b)^(3/2)*a^3)","A",0
2100,1,63,0,0.261147," ","integrate(1/(a+b/x^4)^(5/2)/x,x, algorithm=""giac"")","-\frac{{\left(\frac{4 \, x^{4}}{a} + \frac{3 \, b}{a^{2}}\right)} x^{2}}{6 \, {\left(a x^{4} + b\right)}^{\frac{3}{2}}} - \frac{\log\left({\left| -\sqrt{a} x^{2} + \sqrt{a x^{4} + b} \right|}\right)}{2 \, a^{\frac{5}{2}}} + \frac{\log\left({\left| b \right|}\right)}{4 \, a^{\frac{5}{2}}}"," ",0,"-1/6*(4*x^4/a + 3*b/a^2)*x^2/(a*x^4 + b)^(3/2) - 1/2*log(abs(-sqrt(a)*x^2 + sqrt(a*x^4 + b)))/a^(5/2) + 1/4*log(abs(b))/a^(5/2)","A",0
2101,1,33,0,0.192981," ","integrate(1/(a+b/x^4)^(5/2)/x^3,x, algorithm=""giac"")","-\frac{3 \, a x^{4} + 2 \, b}{6 \, {\left(a x^{4} + b\right)}^{\frac{3}{2}} a^{2}} + \frac{1}{3 \, a^{2} \sqrt{b}}"," ",0,"-1/6*(3*a*x^4 + 2*b)/((a*x^4 + b)^(3/2)*a^2) + 1/3/(a^2*sqrt(b))","A",0
2102,0,0,0,0.000000," ","integrate(x^2/(a+b/x^4)^(5/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^2/(a + b/x^4)^(5/2), x)","F",0
2103,0,0,0,0.000000," ","integrate(1/(a+b/x^4)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a + b/x^4)^(-5/2), x)","F",0
2104,0,0,0,0.000000," ","integrate(1/(a+b/x^4)^(5/2)/x^2,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((a + b/x^4)^(5/2)*x^2), x)","F",0
2105,0,0,0,0.000000," ","integrate(1/(a+b/x^4)^(5/2)/x^4,x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{4}}\right)}^{\frac{5}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((a + b/x^4)^(5/2)*x^4), x)","F",0
2106,1,268,0,0.195131," ","integrate(1/(a+b/x^5),x, algorithm=""giac"")","\frac{\left(-\frac{b}{a}\right)^{\frac{1}{5}} \log\left({\left| x - \left(-\frac{b}{a}\right)^{\frac{1}{5}} \right|}\right)}{5 \, a} + \frac{x}{a} - \frac{\left(-a^{4} b\right)^{\frac{1}{5}} \sqrt{2 \, \sqrt{5} + 10} \arctan\left(-\frac{{\left(\sqrt{5} - 1\right)} \left(-\frac{b}{a}\right)^{\frac{1}{5}} - 4 \, x}{\sqrt{2 \, \sqrt{5} + 10} \left(-\frac{b}{a}\right)^{\frac{1}{5}}}\right)}{10 \, a^{2}} - \frac{\left(-a^{4} b\right)^{\frac{1}{5}} \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{{\left(\sqrt{5} + 1\right)} \left(-\frac{b}{a}\right)^{\frac{1}{5}} + 4 \, x}{\sqrt{-2 \, \sqrt{5} + 10} \left(-\frac{b}{a}\right)^{\frac{1}{5}}}\right)}{10 \, a^{2}} - \frac{\left(-a^{4} b\right)^{\frac{1}{5}} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} \left(-\frac{b}{a}\right)^{\frac{1}{5}} + \left(-\frac{b}{a}\right)^{\frac{1}{5}}\right)} + \left(-\frac{b}{a}\right)^{\frac{2}{5}}\right)}{5 \, a^{2} {\left(\sqrt{5} - 1\right)}} + \frac{\left(-a^{4} b\right)^{\frac{1}{5}} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} \left(-\frac{b}{a}\right)^{\frac{1}{5}} - \left(-\frac{b}{a}\right)^{\frac{1}{5}}\right)} + \left(-\frac{b}{a}\right)^{\frac{2}{5}}\right)}{5 \, a^{2} {\left(\sqrt{5} + 1\right)}}"," ",0,"1/5*(-b/a)^(1/5)*log(abs(x - (-b/a)^(1/5)))/a + x/a - 1/10*(-a^4*b)^(1/5)*sqrt(2*sqrt(5) + 10)*arctan(-((sqrt(5) - 1)*(-b/a)^(1/5) - 4*x)/(sqrt(2*sqrt(5) + 10)*(-b/a)^(1/5)))/a^2 - 1/10*(-a^4*b)^(1/5)*sqrt(-2*sqrt(5) + 10)*arctan(((sqrt(5) + 1)*(-b/a)^(1/5) + 4*x)/(sqrt(-2*sqrt(5) + 10)*(-b/a)^(1/5)))/a^2 - 1/5*(-a^4*b)^(1/5)*log(x^2 + 1/2*x*(sqrt(5)*(-b/a)^(1/5) + (-b/a)^(1/5)) + (-b/a)^(2/5))/(a^2*(sqrt(5) - 1)) + 1/5*(-a^4*b)^(1/5)*log(x^2 - 1/2*x*(sqrt(5)*(-b/a)^(1/5) - (-b/a)^(1/5)) + (-b/a)^(2/5))/(a^2*(sqrt(5) + 1))","A",0
2107,0,0,0,0.000000," ","integrate(1/x/(a+b/x^5)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{x^{5}}} x}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/x^5)*x), x)","F",0
2108,0,0,0,0.000000," ","integrate(1/x/(-a+b/x^5)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-a + \frac{b}{x^{5}}} x}\,{d x}"," ",0,"integrate(1/(sqrt(-a + b/x^5)*x), x)","F",0
2109,1,180,0,0.171842," ","integrate(1/(a+b/x^6),x, algorithm=""giac"")","\frac{x}{a} - \frac{\sqrt{3} \left(a^{5} b\right)^{\frac{1}{6}} \log\left(x^{2} + \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{6}} + \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{12 \, a^{2}} + \frac{\sqrt{3} \left(a^{5} b\right)^{\frac{1}{6}} \log\left(x^{2} - \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{6}} + \left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{12 \, a^{2}} - \frac{\left(a^{5} b\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, x + \sqrt{3} \left(\frac{b}{a}\right)^{\frac{1}{6}}}{\left(\frac{b}{a}\right)^{\frac{1}{6}}}\right)}{6 \, a^{2}} - \frac{\left(a^{5} b\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, x - \sqrt{3} \left(\frac{b}{a}\right)^{\frac{1}{6}}}{\left(\frac{b}{a}\right)^{\frac{1}{6}}}\right)}{6 \, a^{2}} - \frac{\left(a^{5} b\right)^{\frac{1}{6}} \arctan\left(\frac{x}{\left(\frac{b}{a}\right)^{\frac{1}{6}}}\right)}{3 \, a^{2}}"," ",0,"x/a - 1/12*sqrt(3)*(a^5*b)^(1/6)*log(x^2 + sqrt(3)*x*(b/a)^(1/6) + (b/a)^(1/3))/a^2 + 1/12*sqrt(3)*(a^5*b)^(1/6)*log(x^2 - sqrt(3)*x*(b/a)^(1/6) + (b/a)^(1/3))/a^2 - 1/6*(a^5*b)^(1/6)*arctan((2*x + sqrt(3)*(b/a)^(1/6))/(b/a)^(1/6))/a^2 - 1/6*(a^5*b)^(1/6)*arctan((2*x - sqrt(3)*(b/a)^(1/6))/(b/a)^(1/6))/a^2 - 1/3*(a^5*b)^(1/6)*arctan(x/(b/a)^(1/6))/a^2","A",0
2110,1,442,0,0.213056," ","integrate(1/(a+b/x^8),x, algorithm=""giac"")","\frac{x}{a} - \frac{\left(\frac{b}{a}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{b}{a}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{b}{a}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{b}{a}\right)^{\frac{1}{8}} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}}}\right)}{4 \, a \sqrt{2 \, \sqrt{2} + 4}} - \frac{\left(\frac{b}{a}\right)^{\frac{1}{8}} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}} + \left(\frac{b}{a}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}} + \frac{\left(\frac{b}{a}\right)^{\frac{1}{8}} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}} + \left(\frac{b}{a}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{-2 \, \sqrt{2} + 4}} - \frac{\left(\frac{b}{a}\right)^{\frac{1}{8}} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}} + \left(\frac{b}{a}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}} + \frac{\left(\frac{b}{a}\right)^{\frac{1}{8}} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{b}{a}\right)^{\frac{1}{8}} + \left(\frac{b}{a}\right)^{\frac{1}{4}}\right)}{8 \, a \sqrt{2 \, \sqrt{2} + 4}}"," ",0,"x/a - 1/4*(b/a)^(1/8)*arctan((2*x + sqrt(-sqrt(2) + 2)*(b/a)^(1/8))/(sqrt(sqrt(2) + 2)*(b/a)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) - 1/4*(b/a)^(1/8)*arctan((2*x - sqrt(-sqrt(2) + 2)*(b/a)^(1/8))/(sqrt(sqrt(2) + 2)*(b/a)^(1/8)))/(a*sqrt(-2*sqrt(2) + 4)) - 1/4*(b/a)^(1/8)*arctan((2*x + sqrt(sqrt(2) + 2)*(b/a)^(1/8))/(sqrt(-sqrt(2) + 2)*(b/a)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) - 1/4*(b/a)^(1/8)*arctan((2*x - sqrt(sqrt(2) + 2)*(b/a)^(1/8))/(sqrt(-sqrt(2) + 2)*(b/a)^(1/8)))/(a*sqrt(2*sqrt(2) + 4)) - 1/8*(b/a)^(1/8)*log(x^2 + x*sqrt(sqrt(2) + 2)*(b/a)^(1/8) + (b/a)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) + 1/8*(b/a)^(1/8)*log(x^2 - x*sqrt(sqrt(2) + 2)*(b/a)^(1/8) + (b/a)^(1/4))/(a*sqrt(-2*sqrt(2) + 4)) - 1/8*(b/a)^(1/8)*log(x^2 + x*sqrt(-sqrt(2) + 2)*(b/a)^(1/8) + (b/a)^(1/4))/(a*sqrt(2*sqrt(2) + 4)) + 1/8*(b/a)^(1/8)*log(x^2 - x*sqrt(-sqrt(2) + 2)*(b/a)^(1/8) + (b/a)^(1/4))/(a*sqrt(2*sqrt(2) + 4))","B",0
2111,1,13,0,0.151238," ","integrate(x^4*(a+b*x^(1/2)),x, algorithm=""giac"")","\frac{2}{11} \, b x^{\frac{11}{2}} + \frac{1}{5} \, a x^{5}"," ",0,"2/11*b*x^(11/2) + 1/5*a*x^5","A",0
2112,1,13,0,0.152696," ","integrate(x^3*(a+b*x^(1/2)),x, algorithm=""giac"")","\frac{2}{9} \, b x^{\frac{9}{2}} + \frac{1}{4} \, a x^{4}"," ",0,"2/9*b*x^(9/2) + 1/4*a*x^4","A",0
2113,1,13,0,0.149448," ","integrate(x^2*(a+b*x^(1/2)),x, algorithm=""giac"")","\frac{2}{7} \, b x^{\frac{7}{2}} + \frac{1}{3} \, a x^{3}"," ",0,"2/7*b*x^(7/2) + 1/3*a*x^3","A",0
2114,1,13,0,0.146312," ","integrate(x*(a+b*x^(1/2)),x, algorithm=""giac"")","\frac{2}{5} \, b x^{\frac{5}{2}} + \frac{1}{2} \, a x^{2}"," ",0,"2/5*b*x^(5/2) + 1/2*a*x^2","A",0
2115,1,10,0,0.155991," ","integrate(a+b*x^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, b x^{\frac{3}{2}} + a x"," ",0,"2/3*b*x^(3/2) + a*x","A",0
2116,1,12,0,0.181412," ","integrate((a+b*x^(1/2))/x,x, algorithm=""giac"")","a \log\left({\left| x \right|}\right) + 2 \, b \sqrt{x}"," ",0,"a*log(abs(x)) + 2*b*sqrt(x)","A",0
2117,1,13,0,0.151800," ","integrate((a+b*x^(1/2))/x^2,x, algorithm=""giac"")","-\frac{2 \, b \sqrt{x} + a}{x}"," ",0,"-(2*b*sqrt(x) + a)/x","A",0
2118,1,15,0,0.166107," ","integrate((a+b*x^(1/2))/x^3,x, algorithm=""giac"")","-\frac{4 \, b \sqrt{x} + 3 \, a}{6 \, x^{2}}"," ",0,"-1/6*(4*b*sqrt(x) + 3*a)/x^2","A",0
2119,1,15,0,0.159132," ","integrate((a+b*x^(1/2))/x^4,x, algorithm=""giac"")","-\frac{6 \, b \sqrt{x} + 5 \, a}{15 \, x^{3}}"," ",0,"-1/15*(6*b*sqrt(x) + 5*a)/x^3","A",0
2120,1,24,0,0.150599," ","integrate(x^4*(a+b*x^(1/2))^2,x, algorithm=""giac"")","\frac{1}{6} \, b^{2} x^{6} + \frac{4}{11} \, a b x^{\frac{11}{2}} + \frac{1}{5} \, a^{2} x^{5}"," ",0,"1/6*b^2*x^6 + 4/11*a*b*x^(11/2) + 1/5*a^2*x^5","A",0
2121,1,24,0,0.153692," ","integrate(x^3*(a+b*x^(1/2))^2,x, algorithm=""giac"")","\frac{1}{5} \, b^{2} x^{5} + \frac{4}{9} \, a b x^{\frac{9}{2}} + \frac{1}{4} \, a^{2} x^{4}"," ",0,"1/5*b^2*x^5 + 4/9*a*b*x^(9/2) + 1/4*a^2*x^4","A",0
2122,1,24,0,0.150026," ","integrate(x^2*(a+b*x^(1/2))^2,x, algorithm=""giac"")","\frac{1}{4} \, b^{2} x^{4} + \frac{4}{7} \, a b x^{\frac{7}{2}} + \frac{1}{3} \, a^{2} x^{3}"," ",0,"1/4*b^2*x^4 + 4/7*a*b*x^(7/2) + 1/3*a^2*x^3","A",0
2123,1,24,0,0.156694," ","integrate(x*(a+b*x^(1/2))^2,x, algorithm=""giac"")","\frac{1}{3} \, b^{2} x^{3} + \frac{4}{5} \, a b x^{\frac{5}{2}} + \frac{1}{2} \, a^{2} x^{2}"," ",0,"1/3*b^2*x^3 + 4/5*a*b*x^(5/2) + 1/2*a^2*x^2","A",0
2124,1,21,0,0.150360," ","integrate((a+b*x^(1/2))^2,x, algorithm=""giac"")","\frac{1}{2} \, b^{2} x^{2} + \frac{4}{3} \, a b x^{\frac{3}{2}} + a^{2} x"," ",0,"1/2*b^2*x^2 + 4/3*a*b*x^(3/2) + a^2*x","A",0
2125,1,20,0,0.153141," ","integrate((a+b*x^(1/2))^2/x,x, algorithm=""giac"")","b^{2} x + a^{2} \log\left({\left| x \right|}\right) + 4 \, a b \sqrt{x}"," ",0,"b^2*x + a^2*log(abs(x)) + 4*a*b*sqrt(x)","A",0
2126,1,24,0,0.154629," ","integrate((a+b*x^(1/2))^2/x^2,x, algorithm=""giac"")","b^{2} \log\left({\left| x \right|}\right) - \frac{4 \, a b \sqrt{x} + a^{2}}{x}"," ",0,"b^2*log(abs(x)) - (4*a*b*sqrt(x) + a^2)/x","A",0
2127,1,24,0,0.155109," ","integrate((a+b*x^(1/2))^2/x^3,x, algorithm=""giac"")","-\frac{6 \, b^{2} x + 8 \, a b \sqrt{x} + 3 \, a^{2}}{6 \, x^{2}}"," ",0,"-1/6*(6*b^2*x + 8*a*b*sqrt(x) + 3*a^2)/x^2","A",0
2128,1,24,0,0.155972," ","integrate((a+b*x^(1/2))^2/x^4,x, algorithm=""giac"")","-\frac{15 \, b^{2} x + 24 \, a b \sqrt{x} + 10 \, a^{2}}{30 \, x^{3}}"," ",0,"-1/30*(15*b^2*x + 24*a*b*sqrt(x) + 10*a^2)/x^3","A",0
2129,1,24,0,0.160009," ","integrate((a+b*x^(1/2))^2/x^5,x, algorithm=""giac"")","-\frac{28 \, b^{2} x + 48 \, a b \sqrt{x} + 21 \, a^{2}}{84 \, x^{4}}"," ",0,"-1/84*(28*b^2*x + 48*a*b*sqrt(x) + 21*a^2)/x^4","A",0
2130,1,35,0,0.152016," ","integrate(x^4*(a+b*x^(1/2))^3,x, algorithm=""giac"")","\frac{2}{13} \, b^{3} x^{\frac{13}{2}} + \frac{1}{2} \, a b^{2} x^{6} + \frac{6}{11} \, a^{2} b x^{\frac{11}{2}} + \frac{1}{5} \, a^{3} x^{5}"," ",0,"2/13*b^3*x^(13/2) + 1/2*a*b^2*x^6 + 6/11*a^2*b*x^(11/2) + 1/5*a^3*x^5","A",0
2131,1,35,0,0.163381," ","integrate(x^3*(a+b*x^(1/2))^3,x, algorithm=""giac"")","\frac{2}{11} \, b^{3} x^{\frac{11}{2}} + \frac{3}{5} \, a b^{2} x^{5} + \frac{2}{3} \, a^{2} b x^{\frac{9}{2}} + \frac{1}{4} \, a^{3} x^{4}"," ",0,"2/11*b^3*x^(11/2) + 3/5*a*b^2*x^5 + 2/3*a^2*b*x^(9/2) + 1/4*a^3*x^4","A",0
2132,1,35,0,0.185485," ","integrate(x^2*(a+b*x^(1/2))^3,x, algorithm=""giac"")","\frac{2}{9} \, b^{3} x^{\frac{9}{2}} + \frac{3}{4} \, a b^{2} x^{4} + \frac{6}{7} \, a^{2} b x^{\frac{7}{2}} + \frac{1}{3} \, a^{3} x^{3}"," ",0,"2/9*b^3*x^(9/2) + 3/4*a*b^2*x^4 + 6/7*a^2*b*x^(7/2) + 1/3*a^3*x^3","A",0
2133,1,34,0,0.163672," ","integrate(x*(a+b*x^(1/2))^3,x, algorithm=""giac"")","\frac{2}{7} \, b^{3} x^{\frac{7}{2}} + a b^{2} x^{3} + \frac{6}{5} \, a^{2} b x^{\frac{5}{2}} + \frac{1}{2} \, a^{3} x^{2}"," ",0,"2/7*b^3*x^(7/2) + a*b^2*x^3 + 6/5*a^2*b*x^(5/2) + 1/2*a^3*x^2","A",0
2134,1,32,0,0.148763," ","integrate((a+b*x^(1/2))^3,x, algorithm=""giac"")","\frac{2}{5} \, b^{3} x^{\frac{5}{2}} + \frac{3}{2} \, a b^{2} x^{2} + 2 \, a^{2} b x^{\frac{3}{2}} + a^{3} x"," ",0,"2/5*b^3*x^(5/2) + 3/2*a*b^2*x^2 + 2*a^2*b*x^(3/2) + a^3*x","A",0
2135,1,32,0,0.155560," ","integrate((a+b*x^(1/2))^3/x,x, algorithm=""giac"")","\frac{2}{3} \, b^{3} x^{\frac{3}{2}} + 3 \, a b^{2} x + a^{3} \log\left({\left| x \right|}\right) + 6 \, a^{2} b \sqrt{x}"," ",0,"2/3*b^3*x^(3/2) + 3*a*b^2*x + a^3*log(abs(x)) + 6*a^2*b*sqrt(x)","A",0
2136,1,36,0,0.154967," ","integrate((a+b*x^(1/2))^3/x^2,x, algorithm=""giac"")","3 \, a b^{2} \log\left({\left| x \right|}\right) + 2 \, b^{3} \sqrt{x} - \frac{6 \, a^{2} b \sqrt{x} + a^{3}}{x}"," ",0,"3*a*b^2*log(abs(x)) + 2*b^3*sqrt(x) - (6*a^2*b*sqrt(x) + a^3)/x","A",0
2137,1,33,0,0.151594," ","integrate((a+b*x^(1/2))^3/x^3,x, algorithm=""giac"")","-\frac{4 \, b^{3} x^{\frac{3}{2}} + 6 \, a b^{2} x + 4 \, a^{2} b \sqrt{x} + a^{3}}{2 \, x^{2}}"," ",0,"-1/2*(4*b^3*x^(3/2) + 6*a*b^2*x + 4*a^2*b*sqrt(x) + a^3)/x^2","A",0
2138,1,35,0,0.151350," ","integrate((a+b*x^(1/2))^3/x^4,x, algorithm=""giac"")","-\frac{20 \, b^{3} x^{\frac{3}{2}} + 45 \, a b^{2} x + 36 \, a^{2} b \sqrt{x} + 10 \, a^{3}}{30 \, x^{3}}"," ",0,"-1/30*(20*b^3*x^(3/2) + 45*a*b^2*x + 36*a^2*b*sqrt(x) + 10*a^3)/x^3","A",0
2139,1,35,0,0.154227," ","integrate((a+b*x^(1/2))^3/x^5,x, algorithm=""giac"")","-\frac{56 \, b^{3} x^{\frac{3}{2}} + 140 \, a b^{2} x + 120 \, a^{2} b \sqrt{x} + 35 \, a^{3}}{140 \, x^{4}}"," ",0,"-1/140*(56*b^3*x^(3/2) + 140*a*b^2*x + 120*a^2*b*sqrt(x) + 35*a^3)/x^4","A",0
2140,1,35,0,0.160384," ","integrate((a+b*x^(1/2))^3/x^6,x, algorithm=""giac"")","-\frac{120 \, b^{3} x^{\frac{3}{2}} + 315 \, a b^{2} x + 280 \, a^{2} b \sqrt{x} + 84 \, a^{3}}{420 \, x^{5}}"," ",0,"-1/420*(120*b^3*x^(3/2) + 315*a*b^2*x + 280*a^2*b*sqrt(x) + 84*a^3)/x^5","A",0
2141,1,57,0,0.152396," ","integrate(x^4*(a+b*x^(1/2))^5,x, algorithm=""giac"")","\frac{2}{15} \, b^{5} x^{\frac{15}{2}} + \frac{5}{7} \, a b^{4} x^{7} + \frac{20}{13} \, a^{2} b^{3} x^{\frac{13}{2}} + \frac{5}{3} \, a^{3} b^{2} x^{6} + \frac{10}{11} \, a^{4} b x^{\frac{11}{2}} + \frac{1}{5} \, a^{5} x^{5}"," ",0,"2/15*b^5*x^(15/2) + 5/7*a*b^4*x^7 + 20/13*a^2*b^3*x^(13/2) + 5/3*a^3*b^2*x^6 + 10/11*a^4*b*x^(11/2) + 1/5*a^5*x^5","A",0
2142,1,57,0,0.155507," ","integrate(x^3*(a+b*x^(1/2))^5,x, algorithm=""giac"")","\frac{2}{13} \, b^{5} x^{\frac{13}{2}} + \frac{5}{6} \, a b^{4} x^{6} + \frac{20}{11} \, a^{2} b^{3} x^{\frac{11}{2}} + 2 \, a^{3} b^{2} x^{5} + \frac{10}{9} \, a^{4} b x^{\frac{9}{2}} + \frac{1}{4} \, a^{5} x^{4}"," ",0,"2/13*b^5*x^(13/2) + 5/6*a*b^4*x^6 + 20/11*a^2*b^3*x^(11/2) + 2*a^3*b^2*x^5 + 10/9*a^4*b*x^(9/2) + 1/4*a^5*x^4","A",0
2143,1,56,0,0.157145," ","integrate(x^2*(a+b*x^(1/2))^5,x, algorithm=""giac"")","\frac{2}{11} \, b^{5} x^{\frac{11}{2}} + a b^{4} x^{5} + \frac{20}{9} \, a^{2} b^{3} x^{\frac{9}{2}} + \frac{5}{2} \, a^{3} b^{2} x^{4} + \frac{10}{7} \, a^{4} b x^{\frac{7}{2}} + \frac{1}{3} \, a^{5} x^{3}"," ",0,"2/11*b^5*x^(11/2) + a*b^4*x^5 + 20/9*a^2*b^3*x^(9/2) + 5/2*a^3*b^2*x^4 + 10/7*a^4*b*x^(7/2) + 1/3*a^5*x^3","A",0
2144,1,57,0,0.162046," ","integrate(x*(a+b*x^(1/2))^5,x, algorithm=""giac"")","\frac{2}{9} \, b^{5} x^{\frac{9}{2}} + \frac{5}{4} \, a b^{4} x^{4} + \frac{20}{7} \, a^{2} b^{3} x^{\frac{7}{2}} + \frac{10}{3} \, a^{3} b^{2} x^{3} + 2 \, a^{4} b x^{\frac{5}{2}} + \frac{1}{2} \, a^{5} x^{2}"," ",0,"2/9*b^5*x^(9/2) + 5/4*a*b^4*x^4 + 20/7*a^2*b^3*x^(7/2) + 10/3*a^3*b^2*x^3 + 2*a^4*b*x^(5/2) + 1/2*a^5*x^2","A",0
2145,1,54,0,0.157349," ","integrate((a+b*x^(1/2))^5,x, algorithm=""giac"")","\frac{2}{7} \, b^{5} x^{\frac{7}{2}} + \frac{5}{3} \, a b^{4} x^{3} + 4 \, a^{2} b^{3} x^{\frac{5}{2}} + 5 \, a^{3} b^{2} x^{2} + \frac{10}{3} \, a^{4} b x^{\frac{3}{2}} + a^{5} x"," ",0,"2/7*b^5*x^(7/2) + 5/3*a*b^4*x^3 + 4*a^2*b^3*x^(5/2) + 5*a^3*b^2*x^2 + 10/3*a^4*b*x^(3/2) + a^5*x","A",0
2146,1,54,0,0.180063," ","integrate((a+b*x^(1/2))^5/x,x, algorithm=""giac"")","\frac{2}{5} \, b^{5} x^{\frac{5}{2}} + \frac{5}{2} \, a b^{4} x^{2} + \frac{20}{3} \, a^{2} b^{3} x^{\frac{3}{2}} + 10 \, a^{3} b^{2} x + a^{5} \log\left({\left| x \right|}\right) + 10 \, a^{4} b \sqrt{x}"," ",0,"2/5*b^5*x^(5/2) + 5/2*a*b^4*x^2 + 20/3*a^2*b^3*x^(3/2) + 10*a^3*b^2*x + a^5*log(abs(x)) + 10*a^4*b*sqrt(x)","A",0
2147,1,56,0,0.162234," ","integrate((a+b*x^(1/2))^5/x^2,x, algorithm=""giac"")","\frac{2}{3} \, b^{5} x^{\frac{3}{2}} + 5 \, a b^{4} x + 10 \, a^{3} b^{2} \log\left({\left| x \right|}\right) + 20 \, a^{2} b^{3} \sqrt{x} - \frac{10 \, a^{4} b \sqrt{x} + a^{5}}{x}"," ",0,"2/3*b^5*x^(3/2) + 5*a*b^4*x + 10*a^3*b^2*log(abs(x)) + 20*a^2*b^3*sqrt(x) - (10*a^4*b*sqrt(x) + a^5)/x","A",0
2148,1,58,0,0.209873," ","integrate((a+b*x^(1/2))^5/x^3,x, algorithm=""giac"")","5 \, a b^{4} \log\left({\left| x \right|}\right) + 2 \, b^{5} \sqrt{x} - \frac{120 \, a^{2} b^{3} x^{\frac{3}{2}} + 60 \, a^{3} b^{2} x + 20 \, a^{4} b \sqrt{x} + 3 \, a^{5}}{6 \, x^{2}}"," ",0,"5*a*b^4*log(abs(x)) + 2*b^5*sqrt(x) - 1/6*(120*a^2*b^3*x^(3/2) + 60*a^3*b^2*x + 20*a^4*b*sqrt(x) + 3*a^5)/x^2","A",0
2149,1,55,0,0.152519," ","integrate((a+b*x^(1/2))^5/x^4,x, algorithm=""giac"")","-\frac{6 \, b^{5} x^{\frac{5}{2}} + 15 \, a b^{4} x^{2} + 20 \, a^{2} b^{3} x^{\frac{3}{2}} + 15 \, a^{3} b^{2} x + 6 \, a^{4} b \sqrt{x} + a^{5}}{3 \, x^{3}}"," ",0,"-1/3*(6*b^5*x^(5/2) + 15*a*b^4*x^2 + 20*a^2*b^3*x^(3/2) + 15*a^3*b^2*x + 6*a^4*b*sqrt(x) + a^5)/x^3","B",0
2150,1,57,0,0.210206," ","integrate((a+b*x^(1/2))^5/x^5,x, algorithm=""giac"")","-\frac{56 \, b^{5} x^{\frac{5}{2}} + 210 \, a b^{4} x^{2} + 336 \, a^{2} b^{3} x^{\frac{3}{2}} + 280 \, a^{3} b^{2} x + 120 \, a^{4} b \sqrt{x} + 21 \, a^{5}}{84 \, x^{4}}"," ",0,"-1/84*(56*b^5*x^(5/2) + 210*a*b^4*x^2 + 336*a^2*b^3*x^(3/2) + 280*a^3*b^2*x + 120*a^4*b*sqrt(x) + 21*a^5)/x^4","A",0
2151,1,57,0,0.179531," ","integrate((a+b*x^(1/2))^5/x^6,x, algorithm=""giac"")","-\frac{252 \, b^{5} x^{\frac{5}{2}} + 1050 \, a b^{4} x^{2} + 1800 \, a^{2} b^{3} x^{\frac{3}{2}} + 1575 \, a^{3} b^{2} x + 700 \, a^{4} b \sqrt{x} + 126 \, a^{5}}{630 \, x^{5}}"," ",0,"-1/630*(252*b^5*x^(5/2) + 1050*a*b^4*x^2 + 1800*a^2*b^3*x^(3/2) + 1575*a^3*b^2*x + 700*a^4*b*sqrt(x) + 126*a^5)/x^5","A",0
2152,1,57,0,0.164043," ","integrate((a+b*x^(1/2))^5/x^7,x, algorithm=""giac"")","-\frac{792 \, b^{5} x^{\frac{5}{2}} + 3465 \, a b^{4} x^{2} + 6160 \, a^{2} b^{3} x^{\frac{3}{2}} + 5544 \, a^{3} b^{2} x + 2520 \, a^{4} b \sqrt{x} + 462 \, a^{5}}{2772 \, x^{6}}"," ",0,"-1/2772*(792*b^5*x^(5/2) + 3465*a*b^4*x^2 + 6160*a^2*b^3*x^(3/2) + 5544*a^3*b^2*x + 2520*a^4*b*sqrt(x) + 462*a^5)/x^6","A",0
2153,1,112,0,0.160197," ","integrate(x^4*(a+b*x^(1/2))^10,x, algorithm=""giac"")","\frac{1}{10} \, b^{10} x^{10} + \frac{20}{19} \, a b^{9} x^{\frac{19}{2}} + 5 \, a^{2} b^{8} x^{9} + \frac{240}{17} \, a^{3} b^{7} x^{\frac{17}{2}} + \frac{105}{4} \, a^{4} b^{6} x^{8} + \frac{168}{5} \, a^{5} b^{5} x^{\frac{15}{2}} + 30 \, a^{6} b^{4} x^{7} + \frac{240}{13} \, a^{7} b^{3} x^{\frac{13}{2}} + \frac{15}{2} \, a^{8} b^{2} x^{6} + \frac{20}{11} \, a^{9} b x^{\frac{11}{2}} + \frac{1}{5} \, a^{10} x^{5}"," ",0,"1/10*b^10*x^10 + 20/19*a*b^9*x^(19/2) + 5*a^2*b^8*x^9 + 240/17*a^3*b^7*x^(17/2) + 105/4*a^4*b^6*x^8 + 168/5*a^5*b^5*x^(15/2) + 30*a^6*b^4*x^7 + 240/13*a^7*b^3*x^(13/2) + 15/2*a^8*b^2*x^6 + 20/11*a^9*b*x^(11/2) + 1/5*a^10*x^5","A",0
2154,1,112,0,0.154920," ","integrate(x^3*(a+b*x^(1/2))^10,x, algorithm=""giac"")","\frac{1}{9} \, b^{10} x^{9} + \frac{20}{17} \, a b^{9} x^{\frac{17}{2}} + \frac{45}{8} \, a^{2} b^{8} x^{8} + 16 \, a^{3} b^{7} x^{\frac{15}{2}} + 30 \, a^{4} b^{6} x^{7} + \frac{504}{13} \, a^{5} b^{5} x^{\frac{13}{2}} + 35 \, a^{6} b^{4} x^{6} + \frac{240}{11} \, a^{7} b^{3} x^{\frac{11}{2}} + 9 \, a^{8} b^{2} x^{5} + \frac{20}{9} \, a^{9} b x^{\frac{9}{2}} + \frac{1}{4} \, a^{10} x^{4}"," ",0,"1/9*b^10*x^9 + 20/17*a*b^9*x^(17/2) + 45/8*a^2*b^8*x^8 + 16*a^3*b^7*x^(15/2) + 30*a^4*b^6*x^7 + 504/13*a^5*b^5*x^(13/2) + 35*a^6*b^4*x^6 + 240/11*a^7*b^3*x^(11/2) + 9*a^8*b^2*x^5 + 20/9*a^9*b*x^(9/2) + 1/4*a^10*x^4","A",0
2155,1,112,0,0.159034," ","integrate(x^2*(a+b*x^(1/2))^10,x, algorithm=""giac"")","\frac{1}{8} \, b^{10} x^{8} + \frac{4}{3} \, a b^{9} x^{\frac{15}{2}} + \frac{45}{7} \, a^{2} b^{8} x^{7} + \frac{240}{13} \, a^{3} b^{7} x^{\frac{13}{2}} + 35 \, a^{4} b^{6} x^{6} + \frac{504}{11} \, a^{5} b^{5} x^{\frac{11}{2}} + 42 \, a^{6} b^{4} x^{5} + \frac{80}{3} \, a^{7} b^{3} x^{\frac{9}{2}} + \frac{45}{4} \, a^{8} b^{2} x^{4} + \frac{20}{7} \, a^{9} b x^{\frac{7}{2}} + \frac{1}{3} \, a^{10} x^{3}"," ",0,"1/8*b^10*x^8 + 4/3*a*b^9*x^(15/2) + 45/7*a^2*b^8*x^7 + 240/13*a^3*b^7*x^(13/2) + 35*a^4*b^6*x^6 + 504/11*a^5*b^5*x^(11/2) + 42*a^6*b^4*x^5 + 80/3*a^7*b^3*x^(9/2) + 45/4*a^8*b^2*x^4 + 20/7*a^9*b*x^(7/2) + 1/3*a^10*x^3","A",0
2156,1,112,0,0.170022," ","integrate(x*(a+b*x^(1/2))^10,x, algorithm=""giac"")","\frac{1}{7} \, b^{10} x^{7} + \frac{20}{13} \, a b^{9} x^{\frac{13}{2}} + \frac{15}{2} \, a^{2} b^{8} x^{6} + \frac{240}{11} \, a^{3} b^{7} x^{\frac{11}{2}} + 42 \, a^{4} b^{6} x^{5} + 56 \, a^{5} b^{5} x^{\frac{9}{2}} + \frac{105}{2} \, a^{6} b^{4} x^{4} + \frac{240}{7} \, a^{7} b^{3} x^{\frac{7}{2}} + 15 \, a^{8} b^{2} x^{3} + 4 \, a^{9} b x^{\frac{5}{2}} + \frac{1}{2} \, a^{10} x^{2}"," ",0,"1/7*b^10*x^7 + 20/13*a*b^9*x^(13/2) + 15/2*a^2*b^8*x^6 + 240/11*a^3*b^7*x^(11/2) + 42*a^4*b^6*x^5 + 56*a^5*b^5*x^(9/2) + 105/2*a^6*b^4*x^4 + 240/7*a^7*b^3*x^(7/2) + 15*a^8*b^2*x^3 + 4*a^9*b*x^(5/2) + 1/2*a^10*x^2","A",0
2157,1,109,0,0.152816," ","integrate((a+b*x^(1/2))^10,x, algorithm=""giac"")","\frac{1}{6} \, b^{10} x^{6} + \frac{20}{11} \, a b^{9} x^{\frac{11}{2}} + 9 \, a^{2} b^{8} x^{5} + \frac{80}{3} \, a^{3} b^{7} x^{\frac{9}{2}} + \frac{105}{2} \, a^{4} b^{6} x^{4} + 72 \, a^{5} b^{5} x^{\frac{7}{2}} + 70 \, a^{6} b^{4} x^{3} + 48 \, a^{7} b^{3} x^{\frac{5}{2}} + \frac{45}{2} \, a^{8} b^{2} x^{2} + \frac{20}{3} \, a^{9} b x^{\frac{3}{2}} + a^{10} x"," ",0,"1/6*b^10*x^6 + 20/11*a*b^9*x^(11/2) + 9*a^2*b^8*x^5 + 80/3*a^3*b^7*x^(9/2) + 105/2*a^4*b^6*x^4 + 72*a^5*b^5*x^(7/2) + 70*a^6*b^4*x^3 + 48*a^7*b^3*x^(5/2) + 45/2*a^8*b^2*x^2 + 20/3*a^9*b*x^(3/2) + a^10*x","B",0
2158,1,109,0,0.163054," ","integrate((a+b*x^(1/2))^10/x,x, algorithm=""giac"")","\frac{1}{5} \, b^{10} x^{5} + \frac{20}{9} \, a b^{9} x^{\frac{9}{2}} + \frac{45}{4} \, a^{2} b^{8} x^{4} + \frac{240}{7} \, a^{3} b^{7} x^{\frac{7}{2}} + 70 \, a^{4} b^{6} x^{3} + \frac{504}{5} \, a^{5} b^{5} x^{\frac{5}{2}} + 105 \, a^{6} b^{4} x^{2} + 80 \, a^{7} b^{3} x^{\frac{3}{2}} + 45 \, a^{8} b^{2} x + a^{10} \log\left({\left| x \right|}\right) + 20 \, a^{9} b \sqrt{x}"," ",0,"1/5*b^10*x^5 + 20/9*a*b^9*x^(9/2) + 45/4*a^2*b^8*x^4 + 240/7*a^3*b^7*x^(7/2) + 70*a^4*b^6*x^3 + 504/5*a^5*b^5*x^(5/2) + 105*a^6*b^4*x^2 + 80*a^7*b^3*x^(3/2) + 45*a^8*b^2*x + a^10*log(abs(x)) + 20*a^9*b*sqrt(x)","A",0
2159,1,111,0,0.174418," ","integrate((a+b*x^(1/2))^10/x^2,x, algorithm=""giac"")","\frac{1}{4} \, b^{10} x^{4} + \frac{20}{7} \, a b^{9} x^{\frac{7}{2}} + 15 \, a^{2} b^{8} x^{3} + 48 \, a^{3} b^{7} x^{\frac{5}{2}} + 105 \, a^{4} b^{6} x^{2} + 168 \, a^{5} b^{5} x^{\frac{3}{2}} + 210 \, a^{6} b^{4} x + 45 \, a^{8} b^{2} \log\left({\left| x \right|}\right) + 240 \, a^{7} b^{3} \sqrt{x} - \frac{20 \, a^{9} b \sqrt{x} + a^{10}}{x}"," ",0,"1/4*b^10*x^4 + 20/7*a*b^9*x^(7/2) + 15*a^2*b^8*x^3 + 48*a^3*b^7*x^(5/2) + 105*a^4*b^6*x^2 + 168*a^5*b^5*x^(3/2) + 210*a^6*b^4*x + 45*a^8*b^2*log(abs(x)) + 240*a^7*b^3*sqrt(x) - (20*a^9*b*sqrt(x) + a^10)/x","A",0
2160,1,111,0,0.167016," ","integrate((a+b*x^(1/2))^10/x^3,x, algorithm=""giac"")","\frac{1}{3} \, b^{10} x^{3} + 4 \, a b^{9} x^{\frac{5}{2}} + \frac{45}{2} \, a^{2} b^{8} x^{2} + 80 \, a^{3} b^{7} x^{\frac{3}{2}} + 210 \, a^{4} b^{6} x + 210 \, a^{6} b^{4} \log\left({\left| x \right|}\right) + 504 \, a^{5} b^{5} \sqrt{x} - \frac{1440 \, a^{7} b^{3} x^{\frac{3}{2}} + 270 \, a^{8} b^{2} x + 40 \, a^{9} b \sqrt{x} + 3 \, a^{10}}{6 \, x^{2}}"," ",0,"1/3*b^10*x^3 + 4*a*b^9*x^(5/2) + 45/2*a^2*b^8*x^2 + 80*a^3*b^7*x^(3/2) + 210*a^4*b^6*x + 210*a^6*b^4*log(abs(x)) + 504*a^5*b^5*sqrt(x) - 1/6*(1440*a^7*b^3*x^(3/2) + 270*a^8*b^2*x + 40*a^9*b*sqrt(x) + 3*a^10)/x^2","A",0
2161,1,111,0,0.247807," ","integrate((a+b*x^(1/2))^10/x^4,x, algorithm=""giac"")","\frac{1}{2} \, b^{10} x^{2} + \frac{20}{3} \, a b^{9} x^{\frac{3}{2}} + 45 \, a^{2} b^{8} x + 210 \, a^{4} b^{6} \log\left({\left| x \right|}\right) + 240 \, a^{3} b^{7} \sqrt{x} - \frac{3024 \, a^{5} b^{5} x^{\frac{5}{2}} + 1260 \, a^{6} b^{4} x^{2} + 480 \, a^{7} b^{3} x^{\frac{3}{2}} + 135 \, a^{8} b^{2} x + 24 \, a^{9} b \sqrt{x} + 2 \, a^{10}}{6 \, x^{3}}"," ",0,"1/2*b^10*x^2 + 20/3*a*b^9*x^(3/2) + 45*a^2*b^8*x + 210*a^4*b^6*log(abs(x)) + 240*a^3*b^7*sqrt(x) - 1/6*(3024*a^5*b^5*x^(5/2) + 1260*a^6*b^4*x^2 + 480*a^7*b^3*x^(3/2) + 135*a^8*b^2*x + 24*a^9*b*sqrt(x) + 2*a^10)/x^3","A",0
2162,1,110,0,0.162675," ","integrate((a+b*x^(1/2))^10/x^5,x, algorithm=""giac"")","b^{10} x + 45 \, a^{2} b^{8} \log\left({\left| x \right|}\right) + 20 \, a b^{9} \sqrt{x} - \frac{6720 \, a^{3} b^{7} x^{\frac{7}{2}} + 5880 \, a^{4} b^{6} x^{3} + 4704 \, a^{5} b^{5} x^{\frac{5}{2}} + 2940 \, a^{6} b^{4} x^{2} + 1344 \, a^{7} b^{3} x^{\frac{3}{2}} + 420 \, a^{8} b^{2} x + 80 \, a^{9} b \sqrt{x} + 7 \, a^{10}}{28 \, x^{4}}"," ",0,"b^10*x + 45*a^2*b^8*log(abs(x)) + 20*a*b^9*sqrt(x) - 1/28*(6720*a^3*b^7*x^(7/2) + 5880*a^4*b^6*x^3 + 4704*a^5*b^5*x^(5/2) + 2940*a^6*b^4*x^2 + 1344*a^7*b^3*x^(3/2) + 420*a^8*b^2*x + 80*a^9*b*sqrt(x) + 7*a^10)/x^4","A",0
2163,1,112,0,0.282453," ","integrate((a+b*x^(1/2))^10/x^6,x, algorithm=""giac"")","b^{10} \log\left({\left| x \right|}\right) - \frac{25200 \, a b^{9} x^{\frac{9}{2}} + 56700 \, a^{2} b^{8} x^{4} + 100800 \, a^{3} b^{7} x^{\frac{7}{2}} + 132300 \, a^{4} b^{6} x^{3} + 127008 \, a^{5} b^{5} x^{\frac{5}{2}} + 88200 \, a^{6} b^{4} x^{2} + 43200 \, a^{7} b^{3} x^{\frac{3}{2}} + 14175 \, a^{8} b^{2} x + 2800 \, a^{9} b \sqrt{x} + 252 \, a^{10}}{1260 \, x^{5}}"," ",0,"b^10*log(abs(x)) - 1/1260*(25200*a*b^9*x^(9/2) + 56700*a^2*b^8*x^4 + 100800*a^3*b^7*x^(7/2) + 132300*a^4*b^6*x^3 + 127008*a^5*b^5*x^(5/2) + 88200*a^6*b^4*x^2 + 43200*a^7*b^3*x^(3/2) + 14175*a^8*b^2*x + 2800*a^9*b*sqrt(x) + 252*a^10)/x^5","A",0
2164,1,112,0,0.164280," ","integrate((a+b*x^(1/2))^10/x^7,x, algorithm=""giac"")","-\frac{66 \, b^{10} x^{5} + 440 \, a b^{9} x^{\frac{9}{2}} + 1485 \, a^{2} b^{8} x^{4} + 3168 \, a^{3} b^{7} x^{\frac{7}{2}} + 4620 \, a^{4} b^{6} x^{3} + 4752 \, a^{5} b^{5} x^{\frac{5}{2}} + 3465 \, a^{6} b^{4} x^{2} + 1760 \, a^{7} b^{3} x^{\frac{3}{2}} + 594 \, a^{8} b^{2} x + 120 \, a^{9} b \sqrt{x} + 11 \, a^{10}}{66 \, x^{6}}"," ",0,"-1/66*(66*b^10*x^5 + 440*a*b^9*x^(9/2) + 1485*a^2*b^8*x^4 + 3168*a^3*b^7*x^(7/2) + 4620*a^4*b^6*x^3 + 4752*a^5*b^5*x^(5/2) + 3465*a^6*b^4*x^2 + 1760*a^7*b^3*x^(3/2) + 594*a^8*b^2*x + 120*a^9*b*sqrt(x) + 11*a^10)/x^6","B",0
2165,1,112,0,0.165142," ","integrate((a+b*x^(1/2))^10/x^8,x, algorithm=""giac"")","-\frac{1001 \, b^{10} x^{5} + 8008 \, a b^{9} x^{\frac{9}{2}} + 30030 \, a^{2} b^{8} x^{4} + 68640 \, a^{3} b^{7} x^{\frac{7}{2}} + 105105 \, a^{4} b^{6} x^{3} + 112112 \, a^{5} b^{5} x^{\frac{5}{2}} + 84084 \, a^{6} b^{4} x^{2} + 43680 \, a^{7} b^{3} x^{\frac{3}{2}} + 15015 \, a^{8} b^{2} x + 3080 \, a^{9} b \sqrt{x} + 286 \, a^{10}}{2002 \, x^{7}}"," ",0,"-1/2002*(1001*b^10*x^5 + 8008*a*b^9*x^(9/2) + 30030*a^2*b^8*x^4 + 68640*a^3*b^7*x^(7/2) + 105105*a^4*b^6*x^3 + 112112*a^5*b^5*x^(5/2) + 84084*a^6*b^4*x^2 + 43680*a^7*b^3*x^(3/2) + 15015*a^8*b^2*x + 3080*a^9*b*sqrt(x) + 286*a^10)/x^7","A",0
2166,1,112,0,0.175546," ","integrate((a+b*x^(1/2))^10/x^9,x, algorithm=""giac"")","-\frac{8008 \, b^{10} x^{5} + 68640 \, a b^{9} x^{\frac{9}{2}} + 270270 \, a^{2} b^{8} x^{4} + 640640 \, a^{3} b^{7} x^{\frac{7}{2}} + 1009008 \, a^{4} b^{6} x^{3} + 1100736 \, a^{5} b^{5} x^{\frac{5}{2}} + 840840 \, a^{6} b^{4} x^{2} + 443520 \, a^{7} b^{3} x^{\frac{3}{2}} + 154440 \, a^{8} b^{2} x + 32032 \, a^{9} b \sqrt{x} + 3003 \, a^{10}}{24024 \, x^{8}}"," ",0,"-1/24024*(8008*b^10*x^5 + 68640*a*b^9*x^(9/2) + 270270*a^2*b^8*x^4 + 640640*a^3*b^7*x^(7/2) + 1009008*a^4*b^6*x^3 + 1100736*a^5*b^5*x^(5/2) + 840840*a^6*b^4*x^2 + 443520*a^7*b^3*x^(3/2) + 154440*a^8*b^2*x + 32032*a^9*b*sqrt(x) + 3003*a^10)/x^8","A",0
2167,1,112,0,0.167167," ","integrate((a+b*x^(1/2))^10/x^10,x, algorithm=""giac"")","-\frac{43758 \, b^{10} x^{5} + 388960 \, a b^{9} x^{\frac{9}{2}} + 1575288 \, a^{2} b^{8} x^{4} + 3818880 \, a^{3} b^{7} x^{\frac{7}{2}} + 6126120 \, a^{4} b^{6} x^{3} + 6785856 \, a^{5} b^{5} x^{\frac{5}{2}} + 5250960 \, a^{6} b^{4} x^{2} + 2800512 \, a^{7} b^{3} x^{\frac{3}{2}} + 984555 \, a^{8} b^{2} x + 205920 \, a^{9} b \sqrt{x} + 19448 \, a^{10}}{175032 \, x^{9}}"," ",0,"-1/175032*(43758*b^10*x^5 + 388960*a*b^9*x^(9/2) + 1575288*a^2*b^8*x^4 + 3818880*a^3*b^7*x^(7/2) + 6126120*a^4*b^6*x^3 + 6785856*a^5*b^5*x^(5/2) + 5250960*a^6*b^4*x^2 + 2800512*a^7*b^3*x^(3/2) + 984555*a^8*b^2*x + 205920*a^9*b*sqrt(x) + 19448*a^10)/x^9","A",0
2168,1,112,0,0.192375," ","integrate((a+b*x^(1/2))^10/x^11,x, algorithm=""giac"")","-\frac{184756 \, b^{10} x^{5} + 1679600 \, a b^{9} x^{\frac{9}{2}} + 6928350 \, a^{2} b^{8} x^{4} + 17054400 \, a^{3} b^{7} x^{\frac{7}{2}} + 27713400 \, a^{4} b^{6} x^{3} + 31039008 \, a^{5} b^{5} x^{\frac{5}{2}} + 24249225 \, a^{6} b^{4} x^{2} + 13041600 \, a^{7} b^{3} x^{\frac{3}{2}} + 4618900 \, a^{8} b^{2} x + 972400 \, a^{9} b \sqrt{x} + 92378 \, a^{10}}{923780 \, x^{10}}"," ",0,"-1/923780*(184756*b^10*x^5 + 1679600*a*b^9*x^(9/2) + 6928350*a^2*b^8*x^4 + 17054400*a^3*b^7*x^(7/2) + 27713400*a^4*b^6*x^3 + 31039008*a^5*b^5*x^(5/2) + 24249225*a^6*b^4*x^2 + 13041600*a^7*b^3*x^(3/2) + 4618900*a^8*b^2*x + 972400*a^9*b*sqrt(x) + 92378*a^10)/x^10","A",0
2169,1,167,0,0.212815," ","integrate(x^5*(a+b*x^(1/2))^15,x, algorithm=""giac"")","\frac{2}{27} \, b^{15} x^{\frac{27}{2}} + \frac{15}{13} \, a b^{14} x^{13} + \frac{42}{5} \, a^{2} b^{13} x^{\frac{25}{2}} + \frac{455}{12} \, a^{3} b^{12} x^{12} + \frac{2730}{23} \, a^{4} b^{11} x^{\frac{23}{2}} + 273 \, a^{5} b^{10} x^{11} + \frac{1430}{3} \, a^{6} b^{9} x^{\frac{21}{2}} + \frac{1287}{2} \, a^{7} b^{8} x^{10} + \frac{12870}{19} \, a^{8} b^{7} x^{\frac{19}{2}} + \frac{5005}{9} \, a^{9} b^{6} x^{9} + \frac{6006}{17} \, a^{10} b^{5} x^{\frac{17}{2}} + \frac{1365}{8} \, a^{11} b^{4} x^{8} + \frac{182}{3} \, a^{12} b^{3} x^{\frac{15}{2}} + 15 \, a^{13} b^{2} x^{7} + \frac{30}{13} \, a^{14} b x^{\frac{13}{2}} + \frac{1}{6} \, a^{15} x^{6}"," ",0,"2/27*b^15*x^(27/2) + 15/13*a*b^14*x^13 + 42/5*a^2*b^13*x^(25/2) + 455/12*a^3*b^12*x^12 + 2730/23*a^4*b^11*x^(23/2) + 273*a^5*b^10*x^11 + 1430/3*a^6*b^9*x^(21/2) + 1287/2*a^7*b^8*x^10 + 12870/19*a^8*b^7*x^(19/2) + 5005/9*a^9*b^6*x^9 + 6006/17*a^10*b^5*x^(17/2) + 1365/8*a^11*b^4*x^8 + 182/3*a^12*b^3*x^(15/2) + 15*a^13*b^2*x^7 + 30/13*a^14*b*x^(13/2) + 1/6*a^15*x^6","A",0
2170,1,167,0,0.171889," ","integrate(x^4*(a+b*x^(1/2))^15,x, algorithm=""giac"")","\frac{2}{25} \, b^{15} x^{\frac{25}{2}} + \frac{5}{4} \, a b^{14} x^{12} + \frac{210}{23} \, a^{2} b^{13} x^{\frac{23}{2}} + \frac{455}{11} \, a^{3} b^{12} x^{11} + 130 \, a^{4} b^{11} x^{\frac{21}{2}} + \frac{3003}{10} \, a^{5} b^{10} x^{10} + \frac{10010}{19} \, a^{6} b^{9} x^{\frac{19}{2}} + 715 \, a^{7} b^{8} x^{9} + \frac{12870}{17} \, a^{8} b^{7} x^{\frac{17}{2}} + \frac{5005}{8} \, a^{9} b^{6} x^{8} + \frac{2002}{5} \, a^{10} b^{5} x^{\frac{15}{2}} + 195 \, a^{11} b^{4} x^{7} + 70 \, a^{12} b^{3} x^{\frac{13}{2}} + \frac{35}{2} \, a^{13} b^{2} x^{6} + \frac{30}{11} \, a^{14} b x^{\frac{11}{2}} + \frac{1}{5} \, a^{15} x^{5}"," ",0,"2/25*b^15*x^(25/2) + 5/4*a*b^14*x^12 + 210/23*a^2*b^13*x^(23/2) + 455/11*a^3*b^12*x^11 + 130*a^4*b^11*x^(21/2) + 3003/10*a^5*b^10*x^10 + 10010/19*a^6*b^9*x^(19/2) + 715*a^7*b^8*x^9 + 12870/17*a^8*b^7*x^(17/2) + 5005/8*a^9*b^6*x^8 + 2002/5*a^10*b^5*x^(15/2) + 195*a^11*b^4*x^7 + 70*a^12*b^3*x^(13/2) + 35/2*a^13*b^2*x^6 + 30/11*a^14*b*x^(11/2) + 1/5*a^15*x^5","A",0
2171,1,167,0,0.160754," ","integrate(x^3*(a+b*x^(1/2))^15,x, algorithm=""giac"")","\frac{2}{23} \, b^{15} x^{\frac{23}{2}} + \frac{15}{11} \, a b^{14} x^{11} + 10 \, a^{2} b^{13} x^{\frac{21}{2}} + \frac{91}{2} \, a^{3} b^{12} x^{10} + \frac{2730}{19} \, a^{4} b^{11} x^{\frac{19}{2}} + \frac{1001}{3} \, a^{5} b^{10} x^{9} + \frac{10010}{17} \, a^{6} b^{9} x^{\frac{17}{2}} + \frac{6435}{8} \, a^{7} b^{8} x^{8} + 858 \, a^{8} b^{7} x^{\frac{15}{2}} + 715 \, a^{9} b^{6} x^{7} + 462 \, a^{10} b^{5} x^{\frac{13}{2}} + \frac{455}{2} \, a^{11} b^{4} x^{6} + \frac{910}{11} \, a^{12} b^{3} x^{\frac{11}{2}} + 21 \, a^{13} b^{2} x^{5} + \frac{10}{3} \, a^{14} b x^{\frac{9}{2}} + \frac{1}{4} \, a^{15} x^{4}"," ",0,"2/23*b^15*x^(23/2) + 15/11*a*b^14*x^11 + 10*a^2*b^13*x^(21/2) + 91/2*a^3*b^12*x^10 + 2730/19*a^4*b^11*x^(19/2) + 1001/3*a^5*b^10*x^9 + 10010/17*a^6*b^9*x^(17/2) + 6435/8*a^7*b^8*x^8 + 858*a^8*b^7*x^(15/2) + 715*a^9*b^6*x^7 + 462*a^10*b^5*x^(13/2) + 455/2*a^11*b^4*x^6 + 910/11*a^12*b^3*x^(11/2) + 21*a^13*b^2*x^5 + 10/3*a^14*b*x^(9/2) + 1/4*a^15*x^4","A",0
2172,1,167,0,0.160581," ","integrate(x^2*(a+b*x^(1/2))^15,x, algorithm=""giac"")","\frac{2}{21} \, b^{15} x^{\frac{21}{2}} + \frac{3}{2} \, a b^{14} x^{10} + \frac{210}{19} \, a^{2} b^{13} x^{\frac{19}{2}} + \frac{455}{9} \, a^{3} b^{12} x^{9} + \frac{2730}{17} \, a^{4} b^{11} x^{\frac{17}{2}} + \frac{3003}{8} \, a^{5} b^{10} x^{8} + \frac{2002}{3} \, a^{6} b^{9} x^{\frac{15}{2}} + \frac{6435}{7} \, a^{7} b^{8} x^{7} + 990 \, a^{8} b^{7} x^{\frac{13}{2}} + \frac{5005}{6} \, a^{9} b^{6} x^{6} + 546 \, a^{10} b^{5} x^{\frac{11}{2}} + 273 \, a^{11} b^{4} x^{5} + \frac{910}{9} \, a^{12} b^{3} x^{\frac{9}{2}} + \frac{105}{4} \, a^{13} b^{2} x^{4} + \frac{30}{7} \, a^{14} b x^{\frac{7}{2}} + \frac{1}{3} \, a^{15} x^{3}"," ",0,"2/21*b^15*x^(21/2) + 3/2*a*b^14*x^10 + 210/19*a^2*b^13*x^(19/2) + 455/9*a^3*b^12*x^9 + 2730/17*a^4*b^11*x^(17/2) + 3003/8*a^5*b^10*x^8 + 2002/3*a^6*b^9*x^(15/2) + 6435/7*a^7*b^8*x^7 + 990*a^8*b^7*x^(13/2) + 5005/6*a^9*b^6*x^6 + 546*a^10*b^5*x^(11/2) + 273*a^11*b^4*x^5 + 910/9*a^12*b^3*x^(9/2) + 105/4*a^13*b^2*x^4 + 30/7*a^14*b*x^(7/2) + 1/3*a^15*x^3","A",0
2173,1,167,0,0.162429," ","integrate(x*(a+b*x^(1/2))^15,x, algorithm=""giac"")","\frac{2}{19} \, b^{15} x^{\frac{19}{2}} + \frac{5}{3} \, a b^{14} x^{9} + \frac{210}{17} \, a^{2} b^{13} x^{\frac{17}{2}} + \frac{455}{8} \, a^{3} b^{12} x^{8} + 182 \, a^{4} b^{11} x^{\frac{15}{2}} + 429 \, a^{5} b^{10} x^{7} + 770 \, a^{6} b^{9} x^{\frac{13}{2}} + \frac{2145}{2} \, a^{7} b^{8} x^{6} + 1170 \, a^{8} b^{7} x^{\frac{11}{2}} + 1001 \, a^{9} b^{6} x^{5} + \frac{2002}{3} \, a^{10} b^{5} x^{\frac{9}{2}} + \frac{1365}{4} \, a^{11} b^{4} x^{4} + 130 \, a^{12} b^{3} x^{\frac{7}{2}} + 35 \, a^{13} b^{2} x^{3} + 6 \, a^{14} b x^{\frac{5}{2}} + \frac{1}{2} \, a^{15} x^{2}"," ",0,"2/19*b^15*x^(19/2) + 5/3*a*b^14*x^9 + 210/17*a^2*b^13*x^(17/2) + 455/8*a^3*b^12*x^8 + 182*a^4*b^11*x^(15/2) + 429*a^5*b^10*x^7 + 770*a^6*b^9*x^(13/2) + 2145/2*a^7*b^8*x^6 + 1170*a^8*b^7*x^(11/2) + 1001*a^9*b^6*x^5 + 2002/3*a^10*b^5*x^(9/2) + 1365/4*a^11*b^4*x^4 + 130*a^12*b^3*x^(7/2) + 35*a^13*b^2*x^3 + 6*a^14*b*x^(5/2) + 1/2*a^15*x^2","B",0
2174,1,164,0,0.157294," ","integrate((a+b*x^(1/2))^15,x, algorithm=""giac"")","\frac{2}{17} \, b^{15} x^{\frac{17}{2}} + \frac{15}{8} \, a b^{14} x^{8} + 14 \, a^{2} b^{13} x^{\frac{15}{2}} + 65 \, a^{3} b^{12} x^{7} + 210 \, a^{4} b^{11} x^{\frac{13}{2}} + \frac{1001}{2} \, a^{5} b^{10} x^{6} + 910 \, a^{6} b^{9} x^{\frac{11}{2}} + 1287 \, a^{7} b^{8} x^{5} + 1430 \, a^{8} b^{7} x^{\frac{9}{2}} + \frac{5005}{4} \, a^{9} b^{6} x^{4} + 858 \, a^{10} b^{5} x^{\frac{7}{2}} + 455 \, a^{11} b^{4} x^{3} + 182 \, a^{12} b^{3} x^{\frac{5}{2}} + \frac{105}{2} \, a^{13} b^{2} x^{2} + 10 \, a^{14} b x^{\frac{3}{2}} + a^{15} x"," ",0,"2/17*b^15*x^(17/2) + 15/8*a*b^14*x^8 + 14*a^2*b^13*x^(15/2) + 65*a^3*b^12*x^7 + 210*a^4*b^11*x^(13/2) + 1001/2*a^5*b^10*x^6 + 910*a^6*b^9*x^(11/2) + 1287*a^7*b^8*x^5 + 1430*a^8*b^7*x^(9/2) + 5005/4*a^9*b^6*x^4 + 858*a^10*b^5*x^(7/2) + 455*a^11*b^4*x^3 + 182*a^12*b^3*x^(5/2) + 105/2*a^13*b^2*x^2 + 10*a^14*b*x^(3/2) + a^15*x","B",0
2175,1,164,0,0.170289," ","integrate((a+b*x^(1/2))^15/x,x, algorithm=""giac"")","\frac{2}{15} \, b^{15} x^{\frac{15}{2}} + \frac{15}{7} \, a b^{14} x^{7} + \frac{210}{13} \, a^{2} b^{13} x^{\frac{13}{2}} + \frac{455}{6} \, a^{3} b^{12} x^{6} + \frac{2730}{11} \, a^{4} b^{11} x^{\frac{11}{2}} + \frac{3003}{5} \, a^{5} b^{10} x^{5} + \frac{10010}{9} \, a^{6} b^{9} x^{\frac{9}{2}} + \frac{6435}{4} \, a^{7} b^{8} x^{4} + \frac{12870}{7} \, a^{8} b^{7} x^{\frac{7}{2}} + \frac{5005}{3} \, a^{9} b^{6} x^{3} + \frac{6006}{5} \, a^{10} b^{5} x^{\frac{5}{2}} + \frac{1365}{2} \, a^{11} b^{4} x^{2} + \frac{910}{3} \, a^{12} b^{3} x^{\frac{3}{2}} + 105 \, a^{13} b^{2} x + a^{15} \log\left({\left| x \right|}\right) + 30 \, a^{14} b \sqrt{x}"," ",0,"2/15*b^15*x^(15/2) + 15/7*a*b^14*x^7 + 210/13*a^2*b^13*x^(13/2) + 455/6*a^3*b^12*x^6 + 2730/11*a^4*b^11*x^(11/2) + 3003/5*a^5*b^10*x^5 + 10010/9*a^6*b^9*x^(9/2) + 6435/4*a^7*b^8*x^4 + 12870/7*a^8*b^7*x^(7/2) + 5005/3*a^9*b^6*x^3 + 6006/5*a^10*b^5*x^(5/2) + 1365/2*a^11*b^4*x^2 + 910/3*a^12*b^3*x^(3/2) + 105*a^13*b^2*x + a^15*log(abs(x)) + 30*a^14*b*sqrt(x)","A",0
2176,1,166,0,0.189229," ","integrate((a+b*x^(1/2))^15/x^2,x, algorithm=""giac"")","\frac{2}{13} \, b^{15} x^{\frac{13}{2}} + \frac{5}{2} \, a b^{14} x^{6} + \frac{210}{11} \, a^{2} b^{13} x^{\frac{11}{2}} + 91 \, a^{3} b^{12} x^{5} + \frac{910}{3} \, a^{4} b^{11} x^{\frac{9}{2}} + \frac{3003}{4} \, a^{5} b^{10} x^{4} + 1430 \, a^{6} b^{9} x^{\frac{7}{2}} + 2145 \, a^{7} b^{8} x^{3} + 2574 \, a^{8} b^{7} x^{\frac{5}{2}} + \frac{5005}{2} \, a^{9} b^{6} x^{2} + 2002 \, a^{10} b^{5} x^{\frac{3}{2}} + 1365 \, a^{11} b^{4} x + 105 \, a^{13} b^{2} \log\left({\left| x \right|}\right) + 910 \, a^{12} b^{3} \sqrt{x} - \frac{30 \, a^{14} b \sqrt{x} + a^{15}}{x}"," ",0,"2/13*b^15*x^(13/2) + 5/2*a*b^14*x^6 + 210/11*a^2*b^13*x^(11/2) + 91*a^3*b^12*x^5 + 910/3*a^4*b^11*x^(9/2) + 3003/4*a^5*b^10*x^4 + 1430*a^6*b^9*x^(7/2) + 2145*a^7*b^8*x^3 + 2574*a^8*b^7*x^(5/2) + 5005/2*a^9*b^6*x^2 + 2002*a^10*b^5*x^(3/2) + 1365*a^11*b^4*x + 105*a^13*b^2*log(abs(x)) + 910*a^12*b^3*sqrt(x) - (30*a^14*b*sqrt(x) + a^15)/x","A",0
2177,1,164,0,0.178234," ","integrate((a+b*x^(1/2))^15/x^3,x, algorithm=""giac"")","\frac{2}{11} \, b^{15} x^{\frac{11}{2}} + 3 \, a b^{14} x^{5} + \frac{70}{3} \, a^{2} b^{13} x^{\frac{9}{2}} + \frac{455}{4} \, a^{3} b^{12} x^{4} + 390 \, a^{4} b^{11} x^{\frac{7}{2}} + 1001 \, a^{5} b^{10} x^{3} + 2002 \, a^{6} b^{9} x^{\frac{5}{2}} + \frac{6435}{2} \, a^{7} b^{8} x^{2} + 4290 \, a^{8} b^{7} x^{\frac{3}{2}} + 5005 \, a^{9} b^{6} x + 1365 \, a^{11} b^{4} \log\left({\left| x \right|}\right) + 6006 \, a^{10} b^{5} \sqrt{x} - \frac{1820 \, a^{12} b^{3} x^{\frac{3}{2}} + 210 \, a^{13} b^{2} x + 20 \, a^{14} b \sqrt{x} + a^{15}}{2 \, x^{2}}"," ",0,"2/11*b^15*x^(11/2) + 3*a*b^14*x^5 + 70/3*a^2*b^13*x^(9/2) + 455/4*a^3*b^12*x^4 + 390*a^4*b^11*x^(7/2) + 1001*a^5*b^10*x^3 + 2002*a^6*b^9*x^(5/2) + 6435/2*a^7*b^8*x^2 + 4290*a^8*b^7*x^(3/2) + 5005*a^9*b^6*x + 1365*a^11*b^4*log(abs(x)) + 6006*a^10*b^5*sqrt(x) - 1/2*(1820*a^12*b^3*x^(3/2) + 210*a^13*b^2*x + 20*a^14*b*sqrt(x) + a^15)/x^2","A",0
2178,1,166,0,0.187060," ","integrate((a+b*x^(1/2))^15/x^4,x, algorithm=""giac"")","\frac{2}{9} \, b^{15} x^{\frac{9}{2}} + \frac{15}{4} \, a b^{14} x^{4} + 30 \, a^{2} b^{13} x^{\frac{7}{2}} + \frac{455}{3} \, a^{3} b^{12} x^{3} + 546 \, a^{4} b^{11} x^{\frac{5}{2}} + \frac{3003}{2} \, a^{5} b^{10} x^{2} + \frac{10010}{3} \, a^{6} b^{9} x^{\frac{3}{2}} + 6435 \, a^{7} b^{8} x + 5005 \, a^{9} b^{6} \log\left({\left| x \right|}\right) + 12870 \, a^{8} b^{7} \sqrt{x} - \frac{36036 \, a^{10} b^{5} x^{\frac{5}{2}} + 8190 \, a^{11} b^{4} x^{2} + 1820 \, a^{12} b^{3} x^{\frac{3}{2}} + 315 \, a^{13} b^{2} x + 36 \, a^{14} b \sqrt{x} + 2 \, a^{15}}{6 \, x^{3}}"," ",0,"2/9*b^15*x^(9/2) + 15/4*a*b^14*x^4 + 30*a^2*b^13*x^(7/2) + 455/3*a^3*b^12*x^3 + 546*a^4*b^11*x^(5/2) + 3003/2*a^5*b^10*x^2 + 10010/3*a^6*b^9*x^(3/2) + 6435*a^7*b^8*x + 5005*a^9*b^6*log(abs(x)) + 12870*a^8*b^7*sqrt(x) - 1/6*(36036*a^10*b^5*x^(5/2) + 8190*a^11*b^4*x^2 + 1820*a^12*b^3*x^(3/2) + 315*a^13*b^2*x + 36*a^14*b*sqrt(x) + 2*a^15)/x^3","A",0
2179,1,166,0,0.173856," ","integrate((a+b*x^(1/2))^15/x^6,x, algorithm=""giac"")","\frac{2}{5} \, b^{15} x^{\frac{5}{2}} + \frac{15}{2} \, a b^{14} x^{2} + 70 \, a^{2} b^{13} x^{\frac{3}{2}} + 455 \, a^{3} b^{12} x + 3003 \, a^{5} b^{10} \log\left({\left| x \right|}\right) + 2730 \, a^{4} b^{11} \sqrt{x} - \frac{600600 \, a^{6} b^{9} x^{\frac{9}{2}} + 386100 \, a^{7} b^{8} x^{4} + 257400 \, a^{8} b^{7} x^{\frac{7}{2}} + 150150 \, a^{9} b^{6} x^{3} + 72072 \, a^{10} b^{5} x^{\frac{5}{2}} + 27300 \, a^{11} b^{4} x^{2} + 7800 \, a^{12} b^{3} x^{\frac{3}{2}} + 1575 \, a^{13} b^{2} x + 200 \, a^{14} b \sqrt{x} + 12 \, a^{15}}{60 \, x^{5}}"," ",0,"2/5*b^15*x^(5/2) + 15/2*a*b^14*x^2 + 70*a^2*b^13*x^(3/2) + 455*a^3*b^12*x + 3003*a^5*b^10*log(abs(x)) + 2730*a^4*b^11*sqrt(x) - 1/60*(600600*a^6*b^9*x^(9/2) + 386100*a^7*b^8*x^4 + 257400*a^8*b^7*x^(7/2) + 150150*a^9*b^6*x^3 + 72072*a^10*b^5*x^(5/2) + 27300*a^11*b^4*x^2 + 7800*a^12*b^3*x^(3/2) + 1575*a^13*b^2*x + 200*a^14*b*sqrt(x) + 12*a^15)/x^5","A",0
2180,1,166,0,0.175359," ","integrate((a+b*x^(1/2))^15/x^7,x, algorithm=""giac"")","\frac{2}{3} \, b^{15} x^{\frac{3}{2}} + 15 \, a b^{14} x + 455 \, a^{3} b^{12} \log\left({\left| x \right|}\right) + 210 \, a^{2} b^{13} \sqrt{x} - \frac{1081080 \, a^{4} b^{11} x^{\frac{11}{2}} + 1189188 \, a^{5} b^{10} x^{5} + 1321320 \, a^{6} b^{9} x^{\frac{9}{2}} + 1274130 \, a^{7} b^{8} x^{4} + 1019304 \, a^{8} b^{7} x^{\frac{7}{2}} + 660660 \, a^{9} b^{6} x^{3} + 339768 \, a^{10} b^{5} x^{\frac{5}{2}} + 135135 \, a^{11} b^{4} x^{2} + 40040 \, a^{12} b^{3} x^{\frac{3}{2}} + 8316 \, a^{13} b^{2} x + 1080 \, a^{14} b \sqrt{x} + 66 \, a^{15}}{396 \, x^{6}}"," ",0,"2/3*b^15*x^(3/2) + 15*a*b^14*x + 455*a^3*b^12*log(abs(x)) + 210*a^2*b^13*sqrt(x) - 1/396*(1081080*a^4*b^11*x^(11/2) + 1189188*a^5*b^10*x^5 + 1321320*a^6*b^9*x^(9/2) + 1274130*a^7*b^8*x^4 + 1019304*a^8*b^7*x^(7/2) + 660660*a^9*b^6*x^3 + 339768*a^10*b^5*x^(5/2) + 135135*a^11*b^4*x^2 + 40040*a^12*b^3*x^(3/2) + 8316*a^13*b^2*x + 1080*a^14*b*sqrt(x) + 66*a^15)/x^6","A",0
2181,1,168,0,0.177863," ","integrate((a+b*x^(1/2))^15/x^8,x, algorithm=""giac"")","15 \, a b^{14} \log\left({\left| x \right|}\right) + 2 \, b^{15} \sqrt{x} - \frac{2522520 \, a^{2} b^{13} x^{\frac{13}{2}} + 5465460 \, a^{3} b^{12} x^{6} + 10930920 \, a^{4} b^{11} x^{\frac{11}{2}} + 18036018 \, a^{5} b^{10} x^{5} + 24048024 \, a^{6} b^{9} x^{\frac{9}{2}} + 25765740 \, a^{7} b^{8} x^{4} + 22084920 \, a^{8} b^{7} x^{\frac{7}{2}} + 15030015 \, a^{9} b^{6} x^{3} + 8016008 \, a^{10} b^{5} x^{\frac{5}{2}} + 3279276 \, a^{11} b^{4} x^{2} + 993720 \, a^{12} b^{3} x^{\frac{3}{2}} + 210210 \, a^{13} b^{2} x + 27720 \, a^{14} b \sqrt{x} + 1716 \, a^{15}}{12012 \, x^{7}}"," ",0,"15*a*b^14*log(abs(x)) + 2*b^15*sqrt(x) - 1/12012*(2522520*a^2*b^13*x^(13/2) + 5465460*a^3*b^12*x^6 + 10930920*a^4*b^11*x^(11/2) + 18036018*a^5*b^10*x^5 + 24048024*a^6*b^9*x^(9/2) + 25765740*a^7*b^8*x^4 + 22084920*a^8*b^7*x^(7/2) + 15030015*a^9*b^6*x^3 + 8016008*a^10*b^5*x^(5/2) + 3279276*a^11*b^4*x^2 + 993720*a^12*b^3*x^(3/2) + 210210*a^13*b^2*x + 27720*a^14*b*sqrt(x) + 1716*a^15)/x^7","A",0
2182,1,165,0,0.188818," ","integrate((a+b*x^(1/2))^15/x^9,x, algorithm=""giac"")","-\frac{16 \, b^{15} x^{\frac{15}{2}} + 120 \, a b^{14} x^{7} + 560 \, a^{2} b^{13} x^{\frac{13}{2}} + 1820 \, a^{3} b^{12} x^{6} + 4368 \, a^{4} b^{11} x^{\frac{11}{2}} + 8008 \, a^{5} b^{10} x^{5} + 11440 \, a^{6} b^{9} x^{\frac{9}{2}} + 12870 \, a^{7} b^{8} x^{4} + 11440 \, a^{8} b^{7} x^{\frac{7}{2}} + 8008 \, a^{9} b^{6} x^{3} + 4368 \, a^{10} b^{5} x^{\frac{5}{2}} + 1820 \, a^{11} b^{4} x^{2} + 560 \, a^{12} b^{3} x^{\frac{3}{2}} + 120 \, a^{13} b^{2} x + 16 \, a^{14} b \sqrt{x} + a^{15}}{8 \, x^{8}}"," ",0,"-1/8*(16*b^15*x^(15/2) + 120*a*b^14*x^7 + 560*a^2*b^13*x^(13/2) + 1820*a^3*b^12*x^6 + 4368*a^4*b^11*x^(11/2) + 8008*a^5*b^10*x^5 + 11440*a^6*b^9*x^(9/2) + 12870*a^7*b^8*x^4 + 11440*a^8*b^7*x^(7/2) + 8008*a^9*b^6*x^3 + 4368*a^10*b^5*x^(5/2) + 1820*a^11*b^4*x^2 + 560*a^12*b^3*x^(3/2) + 120*a^13*b^2*x + 16*a^14*b*sqrt(x) + a^15)/x^8","B",0
2183,1,167,0,0.170481," ","integrate((a+b*x^(1/2))^15/x^10,x, algorithm=""giac"")","-\frac{816 \, b^{15} x^{\frac{15}{2}} + 9180 \, a b^{14} x^{7} + 51408 \, a^{2} b^{13} x^{\frac{13}{2}} + 185640 \, a^{3} b^{12} x^{6} + 477360 \, a^{4} b^{11} x^{\frac{11}{2}} + 918918 \, a^{5} b^{10} x^{5} + 1361360 \, a^{6} b^{9} x^{\frac{9}{2}} + 1575288 \, a^{7} b^{8} x^{4} + 1432080 \, a^{8} b^{7} x^{\frac{7}{2}} + 1021020 \, a^{9} b^{6} x^{3} + 565488 \, a^{10} b^{5} x^{\frac{5}{2}} + 238680 \, a^{11} b^{4} x^{2} + 74256 \, a^{12} b^{3} x^{\frac{3}{2}} + 16065 \, a^{13} b^{2} x + 2160 \, a^{14} b \sqrt{x} + 136 \, a^{15}}{1224 \, x^{9}}"," ",0,"-1/1224*(816*b^15*x^(15/2) + 9180*a*b^14*x^7 + 51408*a^2*b^13*x^(13/2) + 185640*a^3*b^12*x^6 + 477360*a^4*b^11*x^(11/2) + 918918*a^5*b^10*x^5 + 1361360*a^6*b^9*x^(9/2) + 1575288*a^7*b^8*x^4 + 1432080*a^8*b^7*x^(7/2) + 1021020*a^9*b^6*x^3 + 565488*a^10*b^5*x^(5/2) + 238680*a^11*b^4*x^2 + 74256*a^12*b^3*x^(3/2) + 16065*a^13*b^2*x + 2160*a^14*b*sqrt(x) + 136*a^15)/x^9","B",0
2184,1,167,0,0.180592," ","integrate((a+b*x^(1/2))^15/x^11,x, algorithm=""giac"")","-\frac{15504 \, b^{15} x^{\frac{15}{2}} + 193800 \, a b^{14} x^{7} + 1162800 \, a^{2} b^{13} x^{\frac{13}{2}} + 4408950 \, a^{3} b^{12} x^{6} + 11757200 \, a^{4} b^{11} x^{\frac{11}{2}} + 23279256 \, a^{5} b^{10} x^{5} + 35271600 \, a^{6} b^{9} x^{\frac{9}{2}} + 41570100 \, a^{7} b^{8} x^{4} + 38372400 \, a^{8} b^{7} x^{\frac{7}{2}} + 27713400 \, a^{9} b^{6} x^{3} + 15519504 \, a^{10} b^{5} x^{\frac{5}{2}} + 6613425 \, a^{11} b^{4} x^{2} + 2074800 \, a^{12} b^{3} x^{\frac{3}{2}} + 452200 \, a^{13} b^{2} x + 61200 \, a^{14} b \sqrt{x} + 3876 \, a^{15}}{38760 \, x^{10}}"," ",0,"-1/38760*(15504*b^15*x^(15/2) + 193800*a*b^14*x^7 + 1162800*a^2*b^13*x^(13/2) + 4408950*a^3*b^12*x^6 + 11757200*a^4*b^11*x^(11/2) + 23279256*a^5*b^10*x^5 + 35271600*a^6*b^9*x^(9/2) + 41570100*a^7*b^8*x^4 + 38372400*a^8*b^7*x^(7/2) + 27713400*a^9*b^6*x^3 + 15519504*a^10*b^5*x^(5/2) + 6613425*a^11*b^4*x^2 + 2074800*a^12*b^3*x^(3/2) + 452200*a^13*b^2*x + 61200*a^14*b*sqrt(x) + 3876*a^15)/x^10","A",0
2185,1,167,0,0.174343," ","integrate((a+b*x^(1/2))^15/x^12,x, algorithm=""giac"")","-\frac{170544 \, b^{15} x^{\frac{15}{2}} + 2238390 \, a b^{14} x^{7} + 13927760 \, a^{2} b^{13} x^{\frac{13}{2}} + 54318264 \, a^{3} b^{12} x^{6} + 148140720 \, a^{4} b^{11} x^{\frac{11}{2}} + 298750452 \, a^{5} b^{10} x^{5} + 459616080 \, a^{6} b^{9} x^{\frac{9}{2}} + 548725320 \, a^{7} b^{8} x^{4} + 512143632 \, a^{8} b^{7} x^{\frac{7}{2}} + 373438065 \, a^{9} b^{6} x^{3} + 210882672 \, a^{10} b^{5} x^{\frac{5}{2}} + 90530440 \, a^{11} b^{4} x^{2} + 28588560 \, a^{12} b^{3} x^{\frac{3}{2}} + 6267492 \, a^{13} b^{2} x + 852720 \, a^{14} b \sqrt{x} + 54264 \, a^{15}}{596904 \, x^{11}}"," ",0,"-1/596904*(170544*b^15*x^(15/2) + 2238390*a*b^14*x^7 + 13927760*a^2*b^13*x^(13/2) + 54318264*a^3*b^12*x^6 + 148140720*a^4*b^11*x^(11/2) + 298750452*a^5*b^10*x^5 + 459616080*a^6*b^9*x^(9/2) + 548725320*a^7*b^8*x^4 + 512143632*a^8*b^7*x^(7/2) + 373438065*a^9*b^6*x^3 + 210882672*a^10*b^5*x^(5/2) + 90530440*a^11*b^4*x^2 + 28588560*a^12*b^3*x^(3/2) + 6267492*a^13*b^2*x + 852720*a^14*b*sqrt(x) + 54264*a^15)/x^11","A",0
2186,1,167,0,0.175562," ","integrate((a+b*x^(1/2))^15/x^13,x, algorithm=""giac"")","-\frac{1307504 \, b^{15} x^{\frac{15}{2}} + 17651304 \, a b^{14} x^{7} + 112326480 \, a^{2} b^{13} x^{\frac{13}{2}} + 446185740 \, a^{3} b^{12} x^{6} + 1235591280 \, a^{4} b^{11} x^{\frac{11}{2}} + 2524136472 \, a^{5} b^{10} x^{5} + 3926434512 \, a^{6} b^{9} x^{\frac{9}{2}} + 4732755885 \, a^{7} b^{8} x^{4} + 4454358480 \, a^{8} b^{7} x^{\frac{7}{2}} + 3272028760 \, a^{9} b^{6} x^{3} + 1859890032 \, a^{10} b^{5} x^{\frac{5}{2}} + 803134332 \, a^{11} b^{4} x^{2} + 254963280 \, a^{12} b^{3} x^{\frac{3}{2}} + 56163240 \, a^{13} b^{2} x + 7674480 \, a^{14} b \sqrt{x} + 490314 \, a^{15}}{5883768 \, x^{12}}"," ",0,"-1/5883768*(1307504*b^15*x^(15/2) + 17651304*a*b^14*x^7 + 112326480*a^2*b^13*x^(13/2) + 446185740*a^3*b^12*x^6 + 1235591280*a^4*b^11*x^(11/2) + 2524136472*a^5*b^10*x^5 + 3926434512*a^6*b^9*x^(9/2) + 4732755885*a^7*b^8*x^4 + 4454358480*a^8*b^7*x^(7/2) + 3272028760*a^9*b^6*x^3 + 1859890032*a^10*b^5*x^(5/2) + 803134332*a^11*b^4*x^2 + 254963280*a^12*b^3*x^(3/2) + 56163240*a^13*b^2*x + 7674480*a^14*b*sqrt(x) + 490314*a^15)/x^12","A",0
2187,1,167,0,0.195051," ","integrate((a+b*x^(1/2))^15/x^14,x, algorithm=""giac"")","-\frac{7726160 \, b^{15} x^{\frac{15}{2}} + 106234700 \, a b^{14} x^{7} + 686439600 \, a^{2} b^{13} x^{\frac{13}{2}} + 2762102200 \, a^{3} b^{12} x^{6} + 7733886160 \, a^{4} b^{11} x^{\frac{11}{2}} + 15951140205 \, a^{5} b^{10} x^{5} + 25021396400 \, a^{6} b^{9} x^{\frac{9}{2}} + 30383124200 \, a^{7} b^{8} x^{4} + 28784012400 \, a^{8} b^{7} x^{\frac{7}{2}} + 21268186940 \, a^{9} b^{6} x^{3} + 12153249680 \, a^{10} b^{5} x^{\frac{5}{2}} + 5273104200 \, a^{11} b^{4} x^{2} + 1681279600 \, a^{12} b^{3} x^{\frac{3}{2}} + 371821450 \, a^{13} b^{2} x + 50992656 \, a^{14} b \sqrt{x} + 3268760 \, a^{15}}{42493880 \, x^{13}}"," ",0,"-1/42493880*(7726160*b^15*x^(15/2) + 106234700*a*b^14*x^7 + 686439600*a^2*b^13*x^(13/2) + 2762102200*a^3*b^12*x^6 + 7733886160*a^4*b^11*x^(11/2) + 15951140205*a^5*b^10*x^5 + 25021396400*a^6*b^9*x^(9/2) + 30383124200*a^7*b^8*x^4 + 28784012400*a^8*b^7*x^(7/2) + 21268186940*a^9*b^6*x^3 + 12153249680*a^10*b^5*x^(5/2) + 5273104200*a^11*b^4*x^2 + 1681279600*a^12*b^3*x^(3/2) + 371821450*a^13*b^2*x + 50992656*a^14*b*sqrt(x) + 3268760*a^15)/x^13","A",0
2188,1,167,0,0.175070," ","integrate((a+b*x^(1/2))^15/x^15,x, algorithm=""giac"")","-\frac{37442160 \, b^{15} x^{\frac{15}{2}} + 521515800 \, a b^{14} x^{7} + 3407236560 \, a^{2} b^{13} x^{\frac{13}{2}} + 13841898525 \, a^{3} b^{12} x^{6} + 39083007600 \, a^{4} b^{11} x^{\frac{11}{2}} + 81205804680 \, a^{5} b^{10} x^{5} + 128219691600 \, a^{6} b^{9} x^{\frac{9}{2}} + 156611194740 \, a^{7} b^{8} x^{4} + 149153518800 \, a^{8} b^{7} x^{\frac{7}{2}} + 110735188200 \, a^{9} b^{6} x^{3} + 63552368880 \, a^{10} b^{5} x^{\frac{5}{2}} + 27683797050 \, a^{11} b^{4} x^{2} + 8858815056 \, a^{12} b^{3} x^{\frac{3}{2}} + 1965713400 \, a^{13} b^{2} x + 270415600 \, a^{14} b \sqrt{x} + 17383860 \, a^{15}}{243374040 \, x^{14}}"," ",0,"-1/243374040*(37442160*b^15*x^(15/2) + 521515800*a*b^14*x^7 + 3407236560*a^2*b^13*x^(13/2) + 13841898525*a^3*b^12*x^6 + 39083007600*a^4*b^11*x^(11/2) + 81205804680*a^5*b^10*x^5 + 128219691600*a^6*b^9*x^(9/2) + 156611194740*a^7*b^8*x^4 + 149153518800*a^8*b^7*x^(7/2) + 110735188200*a^9*b^6*x^3 + 63552368880*a^10*b^5*x^(5/2) + 27683797050*a^11*b^4*x^2 + 8858815056*a^12*b^3*x^(3/2) + 1965713400*a^13*b^2*x + 270415600*a^14*b*sqrt(x) + 17383860*a^15)/x^14","A",0
2189,1,167,0,0.170865," ","integrate((a+b*x^(1/2))^15/x^16,x, algorithm=""giac"")","-\frac{155117520 \, b^{15} x^{\frac{15}{2}} + 2181340125 \, a b^{14} x^{7} + 14371182000 \, a^{2} b^{13} x^{\frac{13}{2}} + 58815393000 \, a^{3} b^{12} x^{6} + 167159538000 \, a^{4} b^{11} x^{\frac{11}{2}} + 349363434420 \, a^{5} b^{10} x^{5} + 554545134000 \, a^{6} b^{9} x^{\frac{9}{2}} + 680578119000 \, a^{7} b^{8} x^{4} + 650987766000 \, a^{8} b^{7} x^{\frac{7}{2}} + 485226992250 \, a^{9} b^{6} x^{3} + 279490747536 \, a^{10} b^{5} x^{\frac{5}{2}} + 122155047000 \, a^{11} b^{4} x^{2} + 39210262000 \, a^{12} b^{3} x^{\frac{3}{2}} + 8725360500 \, a^{13} b^{2} x + 1203498000 \, a^{14} b \sqrt{x} + 77558760 \, a^{15}}{1163381400 \, x^{15}}"," ",0,"-1/1163381400*(155117520*b^15*x^(15/2) + 2181340125*a*b^14*x^7 + 14371182000*a^2*b^13*x^(13/2) + 58815393000*a^3*b^12*x^6 + 167159538000*a^4*b^11*x^(11/2) + 349363434420*a^5*b^10*x^5 + 554545134000*a^6*b^9*x^(9/2) + 680578119000*a^7*b^8*x^4 + 650987766000*a^8*b^7*x^(7/2) + 485226992250*a^9*b^6*x^3 + 279490747536*a^10*b^5*x^(5/2) + 122155047000*a^11*b^4*x^2 + 39210262000*a^12*b^3*x^(3/2) + 8725360500*a^13*b^2*x + 1203498000*a^14*b*sqrt(x) + 77558760*a^15)/x^15","A",0
2190,1,167,0,0.175620," ","integrate((a+b*x^(1/2))^15/x^17,x, algorithm=""giac"")","-\frac{565722720 \, b^{15} x^{\frac{15}{2}} + 8014405200 \, a b^{14} x^{7} + 53148160800 \, a^{2} b^{13} x^{\frac{13}{2}} + 218793261960 \, a^{3} b^{12} x^{6} + 625123605600 \, a^{4} b^{11} x^{\frac{11}{2}} + 1312759571760 \, a^{5} b^{10} x^{5} + 2092805114400 \, a^{6} b^{9} x^{\frac{9}{2}} + 2578634873100 \, a^{7} b^{8} x^{4} + 2475489478176 \, a^{8} b^{7} x^{\frac{7}{2}} + 1851327601200 \, a^{9} b^{6} x^{3} + 1069655947360 \, a^{10} b^{5} x^{\frac{5}{2}} + 468842704200 \, a^{11} b^{4} x^{2} + 150891904800 \, a^{12} b^{3} x^{\frac{3}{2}} + 33660501840 \, a^{13} b^{2} x + 4653525600 \, a^{14} b \sqrt{x} + 300540195 \, a^{15}}{4808643120 \, x^{16}}"," ",0,"-1/4808643120*(565722720*b^15*x^(15/2) + 8014405200*a*b^14*x^7 + 53148160800*a^2*b^13*x^(13/2) + 218793261960*a^3*b^12*x^6 + 625123605600*a^4*b^11*x^(11/2) + 1312759571760*a^5*b^10*x^5 + 2092805114400*a^6*b^9*x^(9/2) + 2578634873100*a^7*b^8*x^4 + 2475489478176*a^8*b^7*x^(7/2) + 1851327601200*a^9*b^6*x^3 + 1069655947360*a^10*b^5*x^(5/2) + 468842704200*a^11*b^4*x^2 + 150891904800*a^12*b^3*x^(3/2) + 33660501840*a^13*b^2*x + 4653525600*a^14*b*sqrt(x) + 300540195*a^15)/x^16","A",0
2191,1,89,0,0.153513," ","integrate(x^3/(a+b*x^(1/2)),x, algorithm=""giac"")","-\frac{2 \, a^{7} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{8}} + \frac{60 \, b^{6} x^{\frac{7}{2}} - 70 \, a b^{5} x^{3} + 84 \, a^{2} b^{4} x^{\frac{5}{2}} - 105 \, a^{3} b^{3} x^{2} + 140 \, a^{4} b^{2} x^{\frac{3}{2}} - 210 \, a^{5} b x + 420 \, a^{6} \sqrt{x}}{210 \, b^{7}}"," ",0,"-2*a^7*log(abs(b*sqrt(x) + a))/b^8 + 1/210*(60*b^6*x^(7/2) - 70*a*b^5*x^3 + 84*a^2*b^4*x^(5/2) - 105*a^3*b^3*x^2 + 140*a^4*b^2*x^(3/2) - 210*a^5*b*x + 420*a^6*sqrt(x))/b^7","A",0
2192,1,67,0,0.148007," ","integrate(x^2/(a+b*x^(1/2)),x, algorithm=""giac"")","-\frac{2 \, a^{5} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{6}} + \frac{12 \, b^{4} x^{\frac{5}{2}} - 15 \, a b^{3} x^{2} + 20 \, a^{2} b^{2} x^{\frac{3}{2}} - 30 \, a^{3} b x + 60 \, a^{4} \sqrt{x}}{30 \, b^{5}}"," ",0,"-2*a^5*log(abs(b*sqrt(x) + a))/b^6 + 1/30*(12*b^4*x^(5/2) - 15*a*b^3*x^2 + 20*a^2*b^2*x^(3/2) - 30*a^3*b*x + 60*a^4*sqrt(x))/b^5","A",0
2193,1,45,0,0.166912," ","integrate(x/(a+b*x^(1/2)),x, algorithm=""giac"")","-\frac{2 \, a^{3} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{4}} + \frac{2 \, b^{2} x^{\frac{3}{2}} - 3 \, a b x + 6 \, a^{2} \sqrt{x}}{3 \, b^{3}}"," ",0,"-2*a^3*log(abs(b*sqrt(x) + a))/b^4 + 1/3*(2*b^2*x^(3/2) - 3*a*b*x + 6*a^2*sqrt(x))/b^3","A",0
2194,1,24,0,0.185167," ","integrate(1/(a+b*x^(1/2)),x, algorithm=""giac"")","-\frac{2 \, a \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{2}} + \frac{2 \, \sqrt{x}}{b}"," ",0,"-2*a*log(abs(b*sqrt(x) + a))/b^2 + 2*sqrt(x)/b","A",0
2195,1,22,0,0.169111," ","integrate(1/x/(a+b*x^(1/2)),x, algorithm=""giac"")","-\frac{2 \, \log\left({\left| b \sqrt{x} + a \right|}\right)}{a} + \frac{\log\left({\left| x \right|}\right)}{a}"," ",0,"-2*log(abs(b*sqrt(x) + a))/a + log(abs(x))/a","A",0
2196,1,48,0,0.192094," ","integrate(1/x^2/(a+b*x^(1/2)),x, algorithm=""giac"")","-\frac{2 \, b^{2} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{3}} + \frac{b^{2} \log\left({\left| x \right|}\right)}{a^{3}} + \frac{2 \, a b \sqrt{x} - a^{2}}{a^{3} x}"," ",0,"-2*b^2*log(abs(b*sqrt(x) + a))/a^3 + b^2*log(abs(x))/a^3 + (2*a*b*sqrt(x) - a^2)/(a^3*x)","A",0
2197,1,69,0,0.161371," ","integrate(1/x^3/(a+b*x^(1/2)),x, algorithm=""giac"")","-\frac{2 \, b^{4} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{5}} + \frac{b^{4} \log\left({\left| x \right|}\right)}{a^{5}} + \frac{12 \, a b^{3} x^{\frac{3}{2}} - 6 \, a^{2} b^{2} x + 4 \, a^{3} b \sqrt{x} - 3 \, a^{4}}{6 \, a^{5} x^{2}}"," ",0,"-2*b^4*log(abs(b*sqrt(x) + a))/a^5 + b^4*log(abs(x))/a^5 + 1/6*(12*a*b^3*x^(3/2) - 6*a^2*b^2*x + 4*a^3*b*sqrt(x) - 3*a^4)/(a^5*x^2)","A",0
2198,1,91,0,0.154574," ","integrate(1/x^4/(a+b*x^(1/2)),x, algorithm=""giac"")","-\frac{2 \, b^{6} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{7}} + \frac{b^{6} \log\left({\left| x \right|}\right)}{a^{7}} + \frac{60 \, a b^{5} x^{\frac{5}{2}} - 30 \, a^{2} b^{4} x^{2} + 20 \, a^{3} b^{3} x^{\frac{3}{2}} - 15 \, a^{4} b^{2} x + 12 \, a^{5} b \sqrt{x} - 10 \, a^{6}}{30 \, a^{7} x^{3}}"," ",0,"-2*b^6*log(abs(b*sqrt(x) + a))/a^7 + b^6*log(abs(x))/a^7 + 1/30*(60*a*b^5*x^(5/2) - 30*a^2*b^4*x^2 + 20*a^3*b^3*x^(3/2) - 15*a^4*b^2*x + 12*a^5*b*sqrt(x) - 10*a^6)/(a^7*x^3)","A",0
2199,1,100,0,0.208789," ","integrate(x^3/(a+b*x^(1/2))^2,x, algorithm=""giac"")","\frac{14 \, a^{6} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{8}} + \frac{2 \, a^{7}}{{\left(b \sqrt{x} + a\right)} b^{8}} + \frac{10 \, b^{10} x^{3} - 24 \, a b^{9} x^{\frac{5}{2}} + 45 \, a^{2} b^{8} x^{2} - 80 \, a^{3} b^{7} x^{\frac{3}{2}} + 150 \, a^{4} b^{6} x - 360 \, a^{5} b^{5} \sqrt{x}}{30 \, b^{12}}"," ",0,"14*a^6*log(abs(b*sqrt(x) + a))/b^8 + 2*a^7/((b*sqrt(x) + a)*b^8) + 1/30*(10*b^10*x^3 - 24*a*b^9*x^(5/2) + 45*a^2*b^8*x^2 - 80*a^3*b^7*x^(3/2) + 150*a^4*b^6*x - 360*a^5*b^5*sqrt(x))/b^12","A",0
2200,1,78,0,0.213285," ","integrate(x^2/(a+b*x^(1/2))^2,x, algorithm=""giac"")","\frac{10 \, a^{4} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{6}} + \frac{2 \, a^{5}}{{\left(b \sqrt{x} + a\right)} b^{6}} + \frac{3 \, b^{6} x^{2} - 8 \, a b^{5} x^{\frac{3}{2}} + 18 \, a^{2} b^{4} x - 48 \, a^{3} b^{3} \sqrt{x}}{6 \, b^{8}}"," ",0,"10*a^4*log(abs(b*sqrt(x) + a))/b^6 + 2*a^5/((b*sqrt(x) + a)*b^6) + 1/6*(3*b^6*x^2 - 8*a*b^5*x^(3/2) + 18*a^2*b^4*x - 48*a^3*b^3*sqrt(x))/b^8","A",0
2201,1,52,0,0.150021," ","integrate(x/(a+b*x^(1/2))^2,x, algorithm=""giac"")","\frac{6 \, a^{2} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{4}} + \frac{2 \, a^{3}}{{\left(b \sqrt{x} + a\right)} b^{4}} + \frac{b^{2} x - 4 \, a b \sqrt{x}}{b^{4}}"," ",0,"6*a^2*log(abs(b*sqrt(x) + a))/b^4 + 2*a^3/((b*sqrt(x) + a)*b^4) + (b^2*x - 4*a*b*sqrt(x))/b^4","A",0
2202,1,30,0,0.165125," ","integrate(1/(a+b*x^(1/2))^2,x, algorithm=""giac"")","\frac{2 \, \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{2}} + \frac{2 \, a}{{\left(b \sqrt{x} + a\right)} b^{2}}"," ",0,"2*log(abs(b*sqrt(x) + a))/b^2 + 2*a/((b*sqrt(x) + a)*b^2)","A",0
2203,1,36,0,0.216731," ","integrate(1/x/(a+b*x^(1/2))^2,x, algorithm=""giac"")","-\frac{2 \, \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{2}} + \frac{\log\left({\left| x \right|}\right)}{a^{2}} + \frac{2}{{\left(b \sqrt{x} + a\right)} a}"," ",0,"-2*log(abs(b*sqrt(x) + a))/a^2 + log(abs(x))/a^2 + 2/((b*sqrt(x) + a)*a)","A",0
2204,1,67,0,0.213697," ","integrate(1/x^2/(a+b*x^(1/2))^2,x, algorithm=""giac"")","-\frac{6 \, b^{2} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{4}} + \frac{3 \, b^{2} \log\left({\left| x \right|}\right)}{a^{4}} + \frac{6 \, a b^{2} x + 3 \, a^{2} b \sqrt{x} - a^{3}}{{\left(b \sqrt{x} + a\right)} a^{4} x}"," ",0,"-6*b^2*log(abs(b*sqrt(x) + a))/a^4 + 3*b^2*log(abs(x))/a^4 + (6*a*b^2*x + 3*a^2*b*sqrt(x) - a^3)/((b*sqrt(x) + a)*a^4*x)","A",0
2205,1,90,0,0.157446," ","integrate(1/x^3/(a+b*x^(1/2))^2,x, algorithm=""giac"")","-\frac{10 \, b^{4} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{6}} + \frac{5 \, b^{4} \log\left({\left| x \right|}\right)}{a^{6}} + \frac{60 \, a b^{4} x^{2} + 30 \, a^{2} b^{3} x^{\frac{3}{2}} - 10 \, a^{3} b^{2} x + 5 \, a^{4} b \sqrt{x} - 3 \, a^{5}}{6 \, {\left(b \sqrt{x} + a\right)} a^{6} x^{2}}"," ",0,"-10*b^4*log(abs(b*sqrt(x) + a))/a^6 + 5*b^4*log(abs(x))/a^6 + 1/6*(60*a*b^4*x^2 + 30*a^2*b^3*x^(3/2) - 10*a^3*b^2*x + 5*a^4*b*sqrt(x) - 3*a^5)/((b*sqrt(x) + a)*a^6*x^2)","A",0
2206,1,112,0,0.160889," ","integrate(1/x^4/(a+b*x^(1/2))^2,x, algorithm=""giac"")","-\frac{14 \, b^{6} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{8}} + \frac{7 \, b^{6} \log\left({\left| x \right|}\right)}{a^{8}} + \frac{420 \, a b^{6} x^{3} + 210 \, a^{2} b^{5} x^{\frac{5}{2}} - 70 \, a^{3} b^{4} x^{2} + 35 \, a^{4} b^{3} x^{\frac{3}{2}} - 21 \, a^{5} b^{2} x + 14 \, a^{6} b \sqrt{x} - 10 \, a^{7}}{30 \, {\left(b \sqrt{x} + a\right)} a^{8} x^{3}}"," ",0,"-14*b^6*log(abs(b*sqrt(x) + a))/a^8 + 7*b^6*log(abs(x))/a^8 + 1/30*(420*a*b^6*x^3 + 210*a^2*b^5*x^(5/2) - 70*a^3*b^4*x^2 + 35*a^4*b^3*x^(3/2) - 21*a^5*b^2*x + 14*a^6*b*sqrt(x) - 10*a^7)/((b*sqrt(x) + a)*a^8*x^3)","A",0
2207,1,101,0,0.172043," ","integrate(x^3/(a+b*x^(1/2))^3,x, algorithm=""giac"")","-\frac{42 \, a^{5} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{8}} - \frac{14 \, a^{6} b \sqrt{x} + 13 \, a^{7}}{{\left(b \sqrt{x} + a\right)}^{2} b^{8}} + \frac{4 \, b^{12} x^{\frac{5}{2}} - 15 \, a b^{11} x^{2} + 40 \, a^{2} b^{10} x^{\frac{3}{2}} - 100 \, a^{3} b^{9} x + 300 \, a^{4} b^{8} \sqrt{x}}{10 \, b^{15}}"," ",0,"-42*a^5*log(abs(b*sqrt(x) + a))/b^8 - (14*a^6*b*sqrt(x) + 13*a^7)/((b*sqrt(x) + a)^2*b^8) + 1/10*(4*b^12*x^(5/2) - 15*a*b^11*x^2 + 40*a^2*b^10*x^(3/2) - 100*a^3*b^9*x + 300*a^4*b^8*sqrt(x))/b^15","A",0
2208,1,79,0,0.157085," ","integrate(x^2/(a+b*x^(1/2))^3,x, algorithm=""giac"")","-\frac{20 \, a^{3} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{6}} - \frac{10 \, a^{4} b \sqrt{x} + 9 \, a^{5}}{{\left(b \sqrt{x} + a\right)}^{2} b^{6}} + \frac{2 \, b^{6} x^{\frac{3}{2}} - 9 \, a b^{5} x + 36 \, a^{2} b^{4} \sqrt{x}}{3 \, b^{9}}"," ",0,"-20*a^3*log(abs(b*sqrt(x) + a))/b^6 - (10*a^4*b*sqrt(x) + 9*a^5)/((b*sqrt(x) + a)^2*b^6) + 1/3*(2*b^6*x^(3/2) - 9*a*b^5*x + 36*a^2*b^4*sqrt(x))/b^9","A",0
2209,1,53,0,0.154129," ","integrate(x/(a+b*x^(1/2))^3,x, algorithm=""giac"")","-\frac{6 \, a \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{4}} + \frac{2 \, \sqrt{x}}{b^{3}} - \frac{6 \, a^{2} b \sqrt{x} + 5 \, a^{3}}{{\left(b \sqrt{x} + a\right)}^{2} b^{4}}"," ",0,"-6*a*log(abs(b*sqrt(x) + a))/b^4 + 2*sqrt(x)/b^3 - (6*a^2*b*sqrt(x) + 5*a^3)/((b*sqrt(x) + a)^2*b^4)","A",0
2210,1,22,0,0.185730," ","integrate(1/(a+b*x^(1/2))^3,x, algorithm=""giac"")","-\frac{2 \, b \sqrt{x} + a}{{\left(b \sqrt{x} + a\right)}^{2} b^{2}}"," ",0,"-(2*b*sqrt(x) + a)/((b*sqrt(x) + a)^2*b^2)","A",0
2211,1,48,0,0.157871," ","integrate(1/x/(a+b*x^(1/2))^3,x, algorithm=""giac"")","-\frac{2 \, \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{3}} + \frac{\log\left({\left| x \right|}\right)}{a^{3}} + \frac{2 \, a b \sqrt{x} + 3 \, a^{2}}{{\left(b \sqrt{x} + a\right)}^{2} a^{3}}"," ",0,"-2*log(abs(b*sqrt(x) + a))/a^3 + log(abs(x))/a^3 + (2*a*b*sqrt(x) + 3*a^2)/((b*sqrt(x) + a)^2*a^3)","A",0
2212,1,74,0,0.158996," ","integrate(1/x^2/(a+b*x^(1/2))^3,x, algorithm=""giac"")","-\frac{12 \, b^{2} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{5}} + \frac{6 \, b^{2} \log\left({\left| x \right|}\right)}{a^{5}} + \frac{12 \, b^{3} x^{\frac{3}{2}} + 18 \, a b^{2} x + 4 \, a^{2} b \sqrt{x} - a^{3}}{{\left(b x + a \sqrt{x}\right)}^{2} a^{4}}"," ",0,"-12*b^2*log(abs(b*sqrt(x) + a))/a^5 + 6*b^2*log(abs(x))/a^5 + (12*b^3*x^(3/2) + 18*a*b^2*x + 4*a^2*b*sqrt(x) - a^3)/((b*x + a*sqrt(x))^2*a^4)","A",0
2213,1,101,0,0.161379," ","integrate(1/x^3/(a+b*x^(1/2))^3,x, algorithm=""giac"")","-\frac{30 \, b^{4} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{7}} + \frac{15 \, b^{4} \log\left({\left| x \right|}\right)}{a^{7}} + \frac{60 \, a b^{5} x^{\frac{5}{2}} + 90 \, a^{2} b^{4} x^{2} + 20 \, a^{3} b^{3} x^{\frac{3}{2}} - 5 \, a^{4} b^{2} x + 2 \, a^{5} b \sqrt{x} - a^{6}}{2 \, {\left(b \sqrt{x} + a\right)}^{2} a^{7} x^{2}}"," ",0,"-30*b^4*log(abs(b*sqrt(x) + a))/a^7 + 15*b^4*log(abs(x))/a^7 + 1/2*(60*a*b^5*x^(5/2) + 90*a^2*b^4*x^2 + 20*a^3*b^3*x^(3/2) - 5*a^4*b^2*x + 2*a^5*b*sqrt(x) - a^6)/((b*sqrt(x) + a)^2*a^7*x^2)","A",0
2214,1,123,0,0.177963," ","integrate(1/x^4/(a+b*x^(1/2))^3,x, algorithm=""giac"")","-\frac{56 \, b^{6} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{9}} + \frac{28 \, b^{6} \log\left({\left| x \right|}\right)}{a^{9}} + \frac{840 \, a b^{7} x^{\frac{7}{2}} + 1260 \, a^{2} b^{6} x^{3} + 280 \, a^{3} b^{5} x^{\frac{5}{2}} - 70 \, a^{4} b^{4} x^{2} + 28 \, a^{5} b^{3} x^{\frac{3}{2}} - 14 \, a^{6} b^{2} x + 8 \, a^{7} b \sqrt{x} - 5 \, a^{8}}{15 \, {\left(b \sqrt{x} + a\right)}^{2} a^{9} x^{3}}"," ",0,"-56*b^6*log(abs(b*sqrt(x) + a))/a^9 + 28*b^6*log(abs(x))/a^9 + 1/15*(840*a*b^7*x^(7/2) + 1260*a^2*b^6*x^3 + 280*a^3*b^5*x^(5/2) - 70*a^4*b^4*x^2 + 28*a^5*b^3*x^(3/2) - 14*a^6*b^2*x + 8*a^7*b*sqrt(x) - 5*a^8)/((b*sqrt(x) + a)^2*a^9*x^3)","A",0
2215,1,121,0,0.188533," ","integrate(x^4/(a+b*x^(1/2))^5,x, algorithm=""giac"")","-\frac{252 \, a^{5} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{10}} - \frac{336 \, a^{6} b^{3} x^{\frac{3}{2}} + 936 \, a^{7} b^{2} x + 876 \, a^{8} b \sqrt{x} + 275 \, a^{9}}{2 \, {\left(b \sqrt{x} + a\right)}^{4} b^{10}} + \frac{4 \, b^{20} x^{\frac{5}{2}} - 25 \, a b^{19} x^{2} + 100 \, a^{2} b^{18} x^{\frac{3}{2}} - 350 \, a^{3} b^{17} x + 1400 \, a^{4} b^{16} \sqrt{x}}{10 \, b^{25}}"," ",0,"-252*a^5*log(abs(b*sqrt(x) + a))/b^10 - 1/2*(336*a^6*b^3*x^(3/2) + 936*a^7*b^2*x + 876*a^8*b*sqrt(x) + 275*a^9)/((b*sqrt(x) + a)^4*b^10) + 1/10*(4*b^20*x^(5/2) - 25*a*b^19*x^2 + 100*a^2*b^18*x^(3/2) - 350*a^3*b^17*x + 1400*a^4*b^16*sqrt(x))/b^25","A",0
2216,1,99,0,0.160024," ","integrate(x^3/(a+b*x^(1/2))^5,x, algorithm=""giac"")","-\frac{70 \, a^{3} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{8}} - \frac{420 \, a^{4} b^{3} x^{\frac{3}{2}} + 1134 \, a^{5} b^{2} x + 1036 \, a^{6} b \sqrt{x} + 319 \, a^{7}}{6 \, {\left(b \sqrt{x} + a\right)}^{4} b^{8}} + \frac{2 \, b^{10} x^{\frac{3}{2}} - 15 \, a b^{9} x + 90 \, a^{2} b^{8} \sqrt{x}}{3 \, b^{15}}"," ",0,"-70*a^3*log(abs(b*sqrt(x) + a))/b^8 - 1/6*(420*a^4*b^3*x^(3/2) + 1134*a^5*b^2*x + 1036*a^6*b*sqrt(x) + 319*a^7)/((b*sqrt(x) + a)^4*b^8) + 1/3*(2*b^10*x^(3/2) - 15*a*b^9*x + 90*a^2*b^8*sqrt(x))/b^15","A",0
2217,1,73,0,0.154289," ","integrate(x^2/(a+b*x^(1/2))^5,x, algorithm=""giac"")","-\frac{10 \, a \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{6}} + \frac{2 \, \sqrt{x}}{b^{5}} - \frac{120 \, a^{2} b^{3} x^{\frac{3}{2}} + 300 \, a^{3} b^{2} x + 260 \, a^{4} b \sqrt{x} + 77 \, a^{5}}{6 \, {\left(b \sqrt{x} + a\right)}^{4} b^{6}}"," ",0,"-10*a*log(abs(b*sqrt(x) + a))/b^6 + 2*sqrt(x)/b^5 - 1/6*(120*a^2*b^3*x^(3/2) + 300*a^3*b^2*x + 260*a^4*b*sqrt(x) + 77*a^5)/((b*sqrt(x) + a)^4*b^6)","A",0
2218,1,42,0,0.154800," ","integrate(x/(a+b*x^(1/2))^5,x, algorithm=""giac"")","-\frac{4 \, b^{3} x^{\frac{3}{2}} + 6 \, a b^{2} x + 4 \, a^{2} b \sqrt{x} + a^{3}}{2 \, {\left(b \sqrt{x} + a\right)}^{4} b^{4}}"," ",0,"-1/2*(4*b^3*x^(3/2) + 6*a*b^2*x + 4*a^2*b*sqrt(x) + a^3)/((b*sqrt(x) + a)^4*b^4)","B",0
2219,1,22,0,0.155875," ","integrate(1/(a+b*x^(1/2))^5,x, algorithm=""giac"")","-\frac{4 \, b \sqrt{x} + a}{6 \, {\left(b \sqrt{x} + a\right)}^{4} b^{2}}"," ",0,"-1/6*(4*b*sqrt(x) + a)/((b*sqrt(x) + a)^4*b^2)","A",0
2220,1,69,0,0.162761," ","integrate(1/x/(a+b*x^(1/2))^5,x, algorithm=""giac"")","-\frac{2 \, \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{5}} + \frac{\log\left({\left| x \right|}\right)}{a^{5}} + \frac{12 \, a b^{3} x^{\frac{3}{2}} + 42 \, a^{2} b^{2} x + 52 \, a^{3} b \sqrt{x} + 25 \, a^{4}}{6 \, {\left(b \sqrt{x} + a\right)}^{4} a^{5}}"," ",0,"-2*log(abs(b*sqrt(x) + a))/a^5 + log(abs(x))/a^5 + 1/6*(12*a*b^3*x^(3/2) + 42*a^2*b^2*x + 52*a^3*b*sqrt(x) + 25*a^4)/((b*sqrt(x) + a)^4*a^5)","A",0
2221,1,101,0,0.170004," ","integrate(1/x^2/(a+b*x^(1/2))^5,x, algorithm=""giac"")","-\frac{30 \, b^{2} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{7}} + \frac{15 \, b^{2} \log\left({\left| x \right|}\right)}{a^{7}} + \frac{60 \, a b^{5} x^{\frac{5}{2}} + 210 \, a^{2} b^{4} x^{2} + 260 \, a^{3} b^{3} x^{\frac{3}{2}} + 125 \, a^{4} b^{2} x + 12 \, a^{5} b \sqrt{x} - 2 \, a^{6}}{2 \, {\left(b \sqrt{x} + a\right)}^{4} a^{7} x}"," ",0,"-30*b^2*log(abs(b*sqrt(x) + a))/a^7 + 15*b^2*log(abs(x))/a^7 + 1/2*(60*a*b^5*x^(5/2) + 210*a^2*b^4*x^2 + 260*a^3*b^3*x^(3/2) + 125*a^4*b^2*x + 12*a^5*b*sqrt(x) - 2*a^6)/((b*sqrt(x) + a)^4*a^7*x)","A",0
2222,1,119,0,0.168311," ","integrate(1/x^3/(a+b*x^(1/2))^5,x, algorithm=""giac"")","-\frac{140 \, b^{4} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{9}} + \frac{70 \, b^{4} \log\left({\left| x \right|}\right)}{a^{9}} + \frac{840 \, b^{7} x^{\frac{7}{2}} + 2940 \, a b^{6} x^{3} + 3640 \, a^{2} b^{5} x^{\frac{5}{2}} + 1750 \, a^{3} b^{4} x^{2} + 168 \, a^{4} b^{3} x^{\frac{3}{2}} - 28 \, a^{5} b^{2} x + 8 \, a^{6} b \sqrt{x} - 3 \, a^{7}}{6 \, {\left(b x + a \sqrt{x}\right)}^{4} a^{8}}"," ",0,"-140*b^4*log(abs(b*sqrt(x) + a))/a^9 + 70*b^4*log(abs(x))/a^9 + 1/6*(840*b^7*x^(7/2) + 2940*a*b^6*x^3 + 3640*a^2*b^5*x^(5/2) + 1750*a^3*b^4*x^2 + 168*a^4*b^3*x^(3/2) - 28*a^5*b^2*x + 8*a^6*b*sqrt(x) - 3*a^7)/((b*x + a*sqrt(x))^4*a^8)","A",0
2223,1,143,0,0.183311," ","integrate(x^5/(a+b*x^(1/2))^8,x, algorithm=""giac"")","\frac{660 \, a^{4} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{12}} + \frac{38808 \, a^{5} b^{6} x^{3} + 213444 \, a^{6} b^{5} x^{\frac{5}{2}} + 494340 \, a^{7} b^{4} x^{2} + 615615 \, a^{8} b^{3} x^{\frac{3}{2}} + 434049 \, a^{9} b^{2} x + 164087 \, a^{10} b \sqrt{x} + 25961 \, a^{11}}{42 \, {\left(b \sqrt{x} + a\right)}^{7} b^{12}} + \frac{3 \, b^{24} x^{2} - 32 \, a b^{23} x^{\frac{3}{2}} + 216 \, a^{2} b^{22} x - 1440 \, a^{3} b^{21} \sqrt{x}}{6 \, b^{32}}"," ",0,"660*a^4*log(abs(b*sqrt(x) + a))/b^12 + 1/42*(38808*a^5*b^6*x^3 + 213444*a^6*b^5*x^(5/2) + 494340*a^7*b^4*x^2 + 615615*a^8*b^3*x^(3/2) + 434049*a^9*b^2*x + 164087*a^10*b*sqrt(x) + 25961*a^11)/((b*sqrt(x) + a)^7*b^12) + 1/6*(3*b^24*x^2 - 32*a*b^23*x^(3/2) + 216*a^2*b^22*x - 1440*a^3*b^21*sqrt(x))/b^32","A",0
2224,1,119,0,0.166977," ","integrate(x^4/(a+b*x^(1/2))^8,x, algorithm=""giac"")","\frac{72 \, a^{2} \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{10}} + \frac{b^{8} x - 16 \, a b^{7} \sqrt{x}}{b^{16}} + \frac{5880 \, a^{3} b^{6} x^{3} + 30870 \, a^{4} b^{5} x^{\frac{5}{2}} + 69090 \, a^{5} b^{4} x^{2} + 83790 \, a^{6} b^{3} x^{\frac{3}{2}} + 57834 \, a^{7} b^{2} x + 21483 \, a^{8} b \sqrt{x} + 3349 \, a^{9}}{35 \, {\left(b \sqrt{x} + a\right)}^{7} b^{10}}"," ",0,"72*a^2*log(abs(b*sqrt(x) + a))/b^10 + (b^8*x - 16*a*b^7*sqrt(x))/b^16 + 1/35*(5880*a^3*b^6*x^3 + 30870*a^4*b^5*x^(5/2) + 69090*a^5*b^4*x^2 + 83790*a^6*b^3*x^(3/2) + 57834*a^7*b^2*x + 21483*a^8*b*sqrt(x) + 3349*a^9)/((b*sqrt(x) + a)^7*b^10)","A",0
2225,1,95,0,0.159142," ","integrate(x^3/(a+b*x^(1/2))^8,x, algorithm=""giac"")","\frac{2 \, \log\left({\left| b \sqrt{x} + a \right|}\right)}{b^{8}} + \frac{2940 \, a b^{5} x^{3} + 13230 \, a^{2} b^{4} x^{\frac{5}{2}} + 26950 \, a^{3} b^{3} x^{2} + 30625 \, a^{4} b^{2} x^{\frac{3}{2}} + 20139 \, a^{5} b x + 7203 \, a^{6} \sqrt{x} + \frac{1089 \, a^{7}}{b}}{210 \, {\left(b \sqrt{x} + a\right)}^{7} b^{7}}"," ",0,"2*log(abs(b*sqrt(x) + a))/b^8 + 1/210*(2940*a*b^5*x^3 + 13230*a^2*b^4*x^(5/2) + 26950*a^3*b^3*x^2 + 30625*a^4*b^2*x^(3/2) + 20139*a^5*b*x + 7203*a^6*sqrt(x) + 1089*a^7/b)/((b*sqrt(x) + a)^7*b^7)","A",0
2226,1,64,0,0.190996," ","integrate(x^2/(a+b*x^(1/2))^8,x, algorithm=""giac"")","-\frac{21 \, b^{5} x^{\frac{5}{2}} + 35 \, a b^{4} x^{2} + 35 \, a^{2} b^{3} x^{\frac{3}{2}} + 21 \, a^{3} b^{2} x + 7 \, a^{4} b \sqrt{x} + a^{5}}{21 \, {\left(b \sqrt{x} + a\right)}^{7} b^{6}}"," ",0,"-1/21*(21*b^5*x^(5/2) + 35*a*b^4*x^2 + 35*a^2*b^3*x^(3/2) + 21*a^3*b^2*x + 7*a^4*b*sqrt(x) + a^5)/((b*sqrt(x) + a)^7*b^6)","A",0
2227,1,42,0,0.160198," ","integrate(x/(a+b*x^(1/2))^8,x, algorithm=""giac"")","-\frac{35 \, b^{3} x^{\frac{3}{2}} + 21 \, a b^{2} x + 7 \, a^{2} b \sqrt{x} + a^{3}}{70 \, {\left(b \sqrt{x} + a\right)}^{7} b^{4}}"," ",0,"-1/70*(35*b^3*x^(3/2) + 21*a*b^2*x + 7*a^2*b*sqrt(x) + a^3)/((b*sqrt(x) + a)^7*b^4)","A",0
2228,1,22,0,0.183833," ","integrate(1/(a+b*x^(1/2))^8,x, algorithm=""giac"")","-\frac{7 \, b \sqrt{x} + a}{21 \, {\left(b \sqrt{x} + a\right)}^{7} b^{2}}"," ",0,"-1/21*(7*b*sqrt(x) + a)/((b*sqrt(x) + a)^7*b^2)","A",0
2229,1,102,0,0.169185," ","integrate(1/x/(a+b*x^(1/2))^8,x, algorithm=""giac"")","-\frac{2 \, \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{8}} + \frac{\log\left({\left| x \right|}\right)}{a^{8}} + \frac{420 \, a b^{6} x^{3} + 2730 \, a^{2} b^{5} x^{\frac{5}{2}} + 7490 \, a^{3} b^{4} x^{2} + 11165 \, a^{4} b^{3} x^{\frac{3}{2}} + 9639 \, a^{5} b^{2} x + 4683 \, a^{6} b \sqrt{x} + 1089 \, a^{7}}{210 \, {\left(b \sqrt{x} + a\right)}^{7} a^{8}}"," ",0,"-2*log(abs(b*sqrt(x) + a))/a^8 + log(abs(x))/a^8 + 1/210*(420*a*b^6*x^3 + 2730*a^2*b^5*x^(5/2) + 7490*a^3*b^4*x^2 + 11165*a^4*b^3*x^(3/2) + 9639*a^5*b^2*x + 4683*a^6*b*sqrt(x) + 1089*a^7)/((b*sqrt(x) + a)^7*a^8)","A",0
2230,1,134,0,0.206263," ","integrate(1/x^2/(a+b*x^(1/2))^8,x, algorithm=""giac"")","-\frac{72 \, b^{2} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{10}} + \frac{36 \, b^{2} \log\left({\left| x \right|}\right)}{a^{10}} + \frac{2520 \, a b^{8} x^{4} + 16380 \, a^{2} b^{7} x^{\frac{7}{2}} + 44940 \, a^{3} b^{6} x^{3} + 66990 \, a^{4} b^{5} x^{\frac{5}{2}} + 57834 \, a^{5} b^{4} x^{2} + 28098 \, a^{6} b^{3} x^{\frac{3}{2}} + 6534 \, a^{7} b^{2} x + 315 \, a^{8} b \sqrt{x} - 35 \, a^{9}}{35 \, {\left(b \sqrt{x} + a\right)}^{7} a^{10} x}"," ",0,"-72*b^2*log(abs(b*sqrt(x) + a))/a^10 + 36*b^2*log(abs(x))/a^10 + 1/35*(2520*a*b^8*x^4 + 16380*a^2*b^7*x^(7/2) + 44940*a^3*b^6*x^3 + 66990*a^4*b^5*x^(5/2) + 57834*a^5*b^4*x^2 + 28098*a^6*b^3*x^(3/2) + 6534*a^7*b^2*x + 315*a^8*b*sqrt(x) - 35*a^9)/((b*sqrt(x) + a)^7*a^10*x)","A",0
2231,1,156,0,0.168060," ","integrate(1/x^3/(a+b*x^(1/2))^8,x, algorithm=""giac"")","-\frac{660 \, b^{4} \log\left({\left| b \sqrt{x} + a \right|}\right)}{a^{12}} + \frac{330 \, b^{4} \log\left({\left| x \right|}\right)}{a^{12}} + \frac{27720 \, a b^{10} x^{5} + 180180 \, a^{2} b^{9} x^{\frac{9}{2}} + 494340 \, a^{3} b^{8} x^{4} + 736890 \, a^{4} b^{7} x^{\frac{7}{2}} + 636174 \, a^{5} b^{6} x^{3} + 309078 \, a^{6} b^{5} x^{\frac{5}{2}} + 71874 \, a^{7} b^{4} x^{2} + 3465 \, a^{8} b^{3} x^{\frac{3}{2}} - 385 \, a^{9} b^{2} x + 77 \, a^{10} b \sqrt{x} - 21 \, a^{11}}{42 \, {\left(b \sqrt{x} + a\right)}^{7} a^{12} x^{2}}"," ",0,"-660*b^4*log(abs(b*sqrt(x) + a))/a^12 + 330*b^4*log(abs(x))/a^12 + 1/42*(27720*a*b^10*x^5 + 180180*a^2*b^9*x^(9/2) + 494340*a^3*b^8*x^4 + 736890*a^4*b^7*x^(7/2) + 636174*a^5*b^6*x^3 + 309078*a^6*b^5*x^(5/2) + 71874*a^7*b^4*x^2 + 3465*a^8*b^3*x^(3/2) - 385*a^9*b^2*x + 77*a^10*b*sqrt(x) - 21*a^11)/((b*sqrt(x) + a)^7*a^12*x^2)","A",0
2232,1,17,0,0.166395," ","integrate(1/x/(2+b*x^(1/2)),x, algorithm=""giac"")","-\log\left({\left| b \sqrt{x} + 2 \right|}\right) + \frac{1}{2} \, \log\left({\left| x \right|}\right)"," ",0,"-log(abs(b*sqrt(x) + 2)) + 1/2*log(abs(x))","A",0
2233,1,191,0,0.156696," ","integrate(x^2*(a+b*x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(\frac{13 \, {\left(63 \, {\left(b \sqrt{x} + a\right)}^{\frac{11}{2}} - 385 \, {\left(b \sqrt{x} + a\right)}^{\frac{9}{2}} a + 990 \, {\left(b \sqrt{x} + a\right)}^{\frac{7}{2}} a^{2} - 1386 \, {\left(b \sqrt{x} + a\right)}^{\frac{5}{2}} a^{3} + 1155 \, {\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} a^{4} - 693 \, \sqrt{b \sqrt{x} + a} a^{5}\right)} a}{b^{5}} + \frac{3 \, {\left(231 \, {\left(b \sqrt{x} + a\right)}^{\frac{13}{2}} - 1638 \, {\left(b \sqrt{x} + a\right)}^{\frac{11}{2}} a + 5005 \, {\left(b \sqrt{x} + a\right)}^{\frac{9}{2}} a^{2} - 8580 \, {\left(b \sqrt{x} + a\right)}^{\frac{7}{2}} a^{3} + 9009 \, {\left(b \sqrt{x} + a\right)}^{\frac{5}{2}} a^{4} - 6006 \, {\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} a^{5} + 3003 \, \sqrt{b \sqrt{x} + a} a^{6}\right)}}{b^{5}}\right)}}{9009 \, b}"," ",0,"4/9009*(13*(63*(b*sqrt(x) + a)^(11/2) - 385*(b*sqrt(x) + a)^(9/2)*a + 990*(b*sqrt(x) + a)^(7/2)*a^2 - 1386*(b*sqrt(x) + a)^(5/2)*a^3 + 1155*(b*sqrt(x) + a)^(3/2)*a^4 - 693*sqrt(b*sqrt(x) + a)*a^5)*a/b^5 + 3*(231*(b*sqrt(x) + a)^(13/2) - 1638*(b*sqrt(x) + a)^(11/2)*a + 5005*(b*sqrt(x) + a)^(9/2)*a^2 - 8580*(b*sqrt(x) + a)^(7/2)*a^3 + 9009*(b*sqrt(x) + a)^(5/2)*a^4 - 6006*(b*sqrt(x) + a)^(3/2)*a^5 + 3003*sqrt(b*sqrt(x) + a)*a^6)/b^5)/b","A",0
2234,1,134,0,0.183860," ","integrate(x*(a+b*x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(\frac{9 \, {\left(5 \, {\left(b \sqrt{x} + a\right)}^{\frac{7}{2}} - 21 \, {\left(b \sqrt{x} + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b \sqrt{x} + a} a^{3}\right)} a}{b^{3}} + \frac{35 \, {\left(b \sqrt{x} + a\right)}^{\frac{9}{2}} - 180 \, {\left(b \sqrt{x} + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b \sqrt{x} + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b \sqrt{x} + a} a^{4}}{b^{3}}\right)}}{315 \, b}"," ",0,"4/315*(9*(5*(b*sqrt(x) + a)^(7/2) - 21*(b*sqrt(x) + a)^(5/2)*a + 35*(b*sqrt(x) + a)^(3/2)*a^2 - 35*sqrt(b*sqrt(x) + a)*a^3)*a/b^3 + (35*(b*sqrt(x) + a)^(9/2) - 180*(b*sqrt(x) + a)^(7/2)*a + 378*(b*sqrt(x) + a)^(5/2)*a^2 - 420*(b*sqrt(x) + a)^(3/2)*a^3 + 315*sqrt(b*sqrt(x) + a)*a^4)/b^3)/b","B",0
2235,1,76,0,0.173883," ","integrate((a+b*x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(\frac{5 \, {\left({\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{b \sqrt{x} + a} a\right)} a}{b} + \frac{3 \, {\left(b \sqrt{x} + a\right)}^{\frac{5}{2}} - 10 \, {\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b \sqrt{x} + a} a^{2}}{b}\right)}}{15 \, b}"," ",0,"4/15*(5*((b*sqrt(x) + a)^(3/2) - 3*sqrt(b*sqrt(x) + a)*a)*a/b + (3*(b*sqrt(x) + a)^(5/2) - 10*(b*sqrt(x) + a)^(3/2)*a + 15*sqrt(b*sqrt(x) + a)*a^2)/b)/b","B",0
2236,1,41,0,0.173106," ","integrate((a+b*x^(1/2))^(1/2)/x,x, algorithm=""giac"")","\frac{4 \, {\left(\frac{a b \arctan\left(\frac{\sqrt{b \sqrt{x} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + \sqrt{b \sqrt{x} + a} b\right)}}{b}"," ",0,"4*(a*b*arctan(sqrt(b*sqrt(x) + a)/sqrt(-a))/sqrt(-a) + sqrt(b*sqrt(x) + a)*b)/b","A",0
2237,1,72,0,0.162918," ","integrate((a+b*x^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","-\frac{\frac{b^{3} \arctan\left(\frac{\sqrt{b \sqrt{x} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{{\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} b^{3} + \sqrt{b \sqrt{x} + a} a b^{3}}{a b^{2} x}}{2 \, b}"," ",0,"-1/2*(b^3*arctan(sqrt(b*sqrt(x) + a)/sqrt(-a))/(sqrt(-a)*a) + ((b*sqrt(x) + a)^(3/2)*b^3 + sqrt(b*sqrt(x) + a)*a*b^3)/(a*b^2*x))/b","A",0
2238,1,109,0,0.169764," ","integrate((a+b*x^(1/2))^(1/2)/x^3,x, algorithm=""giac"")","-\frac{\frac{15 \, b^{5} \arctan\left(\frac{\sqrt{b \sqrt{x} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} + \frac{15 \, {\left(b \sqrt{x} + a\right)}^{\frac{7}{2}} b^{5} - 55 \, {\left(b \sqrt{x} + a\right)}^{\frac{5}{2}} a b^{5} + 73 \, {\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} a^{2} b^{5} + 15 \, \sqrt{b \sqrt{x} + a} a^{3} b^{5}}{a^{3} b^{4} x^{2}}}{96 \, b}"," ",0,"-1/96*(15*b^5*arctan(sqrt(b*sqrt(x) + a)/sqrt(-a))/(sqrt(-a)*a^3) + (15*(b*sqrt(x) + a)^(7/2)*b^5 - 55*(b*sqrt(x) + a)^(5/2)*a*b^5 + 73*(b*sqrt(x) + a)^(3/2)*a^2*b^5 + 15*sqrt(b*sqrt(x) + a)*a^3*b^5)/(a^3*b^4*x^2))/b","A",0
2239,1,85,0,0.156658," ","integrate(x^2/(a+b*x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(63 \, {\left(b \sqrt{x} + a\right)}^{\frac{11}{2}} - 385 \, {\left(b \sqrt{x} + a\right)}^{\frac{9}{2}} a + 990 \, {\left(b \sqrt{x} + a\right)}^{\frac{7}{2}} a^{2} - 1386 \, {\left(b \sqrt{x} + a\right)}^{\frac{5}{2}} a^{3} + 1155 \, {\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} a^{4} - 693 \, \sqrt{b \sqrt{x} + a} a^{5}\right)}}{693 \, b^{6}}"," ",0,"4/693*(63*(b*sqrt(x) + a)^(11/2) - 385*(b*sqrt(x) + a)^(9/2)*a + 990*(b*sqrt(x) + a)^(7/2)*a^2 - 1386*(b*sqrt(x) + a)^(5/2)*a^3 + 1155*(b*sqrt(x) + a)^(3/2)*a^4 - 693*sqrt(b*sqrt(x) + a)*a^5)/b^6","A",0
2240,1,57,0,0.164095," ","integrate(x/(a+b*x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(5 \, {\left(b \sqrt{x} + a\right)}^{\frac{7}{2}} - 21 \, {\left(b \sqrt{x} + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b \sqrt{x} + a} a^{3}\right)}}{35 \, b^{4}}"," ",0,"4/35*(5*(b*sqrt(x) + a)^(7/2) - 21*(b*sqrt(x) + a)^(5/2)*a + 35*(b*sqrt(x) + a)^(3/2)*a^2 - 35*sqrt(b*sqrt(x) + a)*a^3)/b^4","A",0
2241,1,27,0,0.160887," ","integrate(1/(a+b*x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left({\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{b \sqrt{x} + a} a\right)}}{3 \, b^{2}}"," ",0,"4/3*((b*sqrt(x) + a)^(3/2) - 3*sqrt(b*sqrt(x) + a)*a)/b^2","A",0
2242,1,23,0,0.155703," ","integrate(1/x/(a+b*x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, \arctan\left(\frac{\sqrt{b \sqrt{x} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}}"," ",0,"4*arctan(sqrt(b*sqrt(x) + a)/sqrt(-a))/sqrt(-a)","A",0
2243,1,75,0,0.166619," ","integrate(1/x^2/(a+b*x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, b^{3} \arctan\left(\frac{\sqrt{b \sqrt{x} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{3 \, {\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} b^{3} - 5 \, \sqrt{b \sqrt{x} + a} a b^{3}}{a^{2} b^{2} x}}{2 \, b}"," ",0,"1/2*(3*b^3*arctan(sqrt(b*sqrt(x) + a)/sqrt(-a))/(sqrt(-a)*a^2) + (3*(b*sqrt(x) + a)^(3/2)*b^3 - 5*sqrt(b*sqrt(x) + a)*a*b^3)/(a^2*b^2*x))/b","A",0
2244,1,109,0,0.159948," ","integrate(1/x^3/(a+b*x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{\frac{105 \, b^{5} \arctan\left(\frac{\sqrt{b \sqrt{x} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{4}} + \frac{105 \, {\left(b \sqrt{x} + a\right)}^{\frac{7}{2}} b^{5} - 385 \, {\left(b \sqrt{x} + a\right)}^{\frac{5}{2}} a b^{5} + 511 \, {\left(b \sqrt{x} + a\right)}^{\frac{3}{2}} a^{2} b^{5} - 279 \, \sqrt{b \sqrt{x} + a} a^{3} b^{5}}{a^{4} b^{4} x^{2}}}{96 \, b}"," ",0,"1/96*(105*b^5*arctan(sqrt(b*sqrt(x) + a)/sqrt(-a))/(sqrt(-a)*a^4) + (105*(b*sqrt(x) + a)^(7/2)*b^5 - 385*(b*sqrt(x) + a)^(5/2)*a*b^5 + 511*(b*sqrt(x) + a)^(3/2)*a^2*b^5 - 279*sqrt(b*sqrt(x) + a)*a^3*b^5)/(a^4*b^4*x^2))/b","A",0
2245,1,231,0,0.174713," ","integrate(x^(1/2)*(a+b*x^(1/2))^n,x, algorithm=""giac"")","\frac{2 \, {\left({\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{n} n^{2} - 2 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{n} a n^{2} + {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{n} a^{2} n^{2} + 3 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{n} n - 8 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{n} a n + 5 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{n} a^{2} n + 2 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{n} - 6 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{n} a + 6 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{n} a^{2}\right)}}{{\left(b^{2} n^{3} + 6 \, b^{2} n^{2} + 11 \, b^{2} n + 6 \, b^{2}\right)} b}"," ",0,"2*((b*sqrt(x) + a)^3*(b*sqrt(x) + a)^n*n^2 - 2*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^n*a*n^2 + (b*sqrt(x) + a)*(b*sqrt(x) + a)^n*a^2*n^2 + 3*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^n*n - 8*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^n*a*n + 5*(b*sqrt(x) + a)*(b*sqrt(x) + a)^n*a^2*n + 2*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^n - 6*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^n*a + 6*(b*sqrt(x) + a)*(b*sqrt(x) + a)^n*a^2)/((b^2*n^3 + 6*b^2*n^2 + 11*b^2*n + 6*b^2)*b)","B",0
2246,1,21,0,0.158403," ","integrate((a+b*x^(1/2))^n/x^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(b \sqrt{x} + a\right)}^{n + 1}}{b {\left(n + 1\right)}}"," ",0,"2*(b*sqrt(x) + a)^(n + 1)/(b*(n + 1))","A",0
2247,1,7,0,0.167111," ","integrate((1+x^(1/2))/x^(1/2),x, algorithm=""giac"")","x + 2 \, \sqrt{x}"," ",0,"x + 2*sqrt(x)","A",0
2248,1,14,0,0.153797," ","integrate((1+x^(1/2))^2/x^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, x^{\frac{3}{2}} + 2 \, x + 2 \, \sqrt{x}"," ",0,"2/3*x^(3/2) + 2*x + 2*sqrt(x)","A",0
2249,1,19,0,0.189330," ","integrate((1+x^(1/2))^3/x^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + 2 \, x^{\frac{3}{2}} + 3 \, x + 2 \, \sqrt{x}"," ",0,"1/2*x^2 + 2*x^(3/2) + 3*x + 2*sqrt(x)","B",0
2250,1,15,0,0.173808," ","integrate(x^(1/2)/(1+x^(1/2)),x, algorithm=""giac"")","x - 2 \, \sqrt{x} + 2 \, \log\left(\sqrt{x} + 1\right)"," ",0,"x - 2*sqrt(x) + 2*log(sqrt(x) + 1)","A",0
2251,1,8,0,0.174140," ","integrate(1/x^(1/2)/(1+x^(1/2)),x, algorithm=""giac"")","2 \, \log\left(\sqrt{x} + 1\right)"," ",0,"2*log(sqrt(x) + 1)","A",0
2252,1,9,0,0.155019," ","integrate(1/x^(1/2)/(1+x^(1/2))^2,x, algorithm=""giac"")","-\frac{2}{\sqrt{x} + 1}"," ",0,"-2/(sqrt(x) + 1)","A",0
2253,1,9,0,0.150084," ","integrate(1/x^(1/2)/(1+x^(1/2))^3,x, algorithm=""giac"")","-\frac{1}{{\left(\sqrt{x} + 1\right)}^{2}}"," ",0,"-1/(sqrt(x) + 1)^2","A",0
2254,1,28,0,0.153163," ","integrate(x^(1/2)*(1+x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4}{7} \, {\left(\sqrt{x} + 1\right)}^{\frac{7}{2}} - \frac{8}{5} \, {\left(\sqrt{x} + 1\right)}^{\frac{5}{2}} + \frac{4}{3} \, {\left(\sqrt{x} + 1\right)}^{\frac{3}{2}}"," ",0,"4/7*(sqrt(x) + 1)^(7/2) - 8/5*(sqrt(x) + 1)^(5/2) + 4/3*(sqrt(x) + 1)^(3/2)","A",0
2255,1,9,0,0.185904," ","integrate((1+x^(1/2))^(1/2)/x^(1/2),x, algorithm=""giac"")","\frac{4}{3} \, {\left(\sqrt{x} + 1\right)}^{\frac{3}{2}}"," ",0,"4/3*(sqrt(x) + 1)^(3/2)","A",0
2256,1,48,0,0.160112," ","integrate(x^(1/3)/(1+x^(1/2)),x, algorithm=""giac"")","2 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{\frac{1}{6}} - 1\right)}\right) + \frac{6}{5} \, x^{\frac{5}{6}} - 3 \, x^{\frac{1}{3}} + \log\left(x^{\frac{1}{3}} - x^{\frac{1}{6}} + 1\right) - 2 \, \log\left(x^{\frac{1}{6}} + 1\right)"," ",0,"2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^(1/6) - 1)) + 6/5*x^(5/6) - 3*x^(1/3) + log(x^(1/3) - x^(1/6) + 1) - 2*log(x^(1/6) + 1)","A",0
2257,1,106,0,0.229326," ","integrate(x^m*(a+b*x^(1/2))^4,x, algorithm=""giac"")","\frac{b^{4} x^{3} \sqrt{x}^{2 \, m}}{m + 3} + \frac{8 \, a b^{3} x^{\frac{5}{2}} \sqrt{x}^{2 \, m}}{2 \, m + 5} + \frac{6 \, a^{2} b^{2} x^{2} \sqrt{x}^{2 \, m}}{m + 2} + \frac{8 \, a^{3} b x^{\frac{3}{2}} \sqrt{x}^{2 \, m}}{2 \, m + 3} + \frac{a^{4} x \sqrt{x}^{2 \, m}}{m + 1}"," ",0,"b^4*x^3*sqrt(x)^(2*m)/(m + 3) + 8*a*b^3*x^(5/2)*sqrt(x)^(2*m)/(2*m + 5) + 6*a^2*b^2*x^2*sqrt(x)^(2*m)/(m + 2) + 8*a^3*b*x^(3/2)*sqrt(x)^(2*m)/(2*m + 3) + a^4*x*sqrt(x)^(2*m)/(m + 1)","A",0
2258,1,84,0,0.183008," ","integrate(x^m*(a+b*x^(1/2))^3,x, algorithm=""giac"")","\frac{2 \, b^{3} x^{\frac{5}{2}} \sqrt{x}^{2 \, m}}{2 \, m + 5} + \frac{3 \, a b^{2} x^{2} \sqrt{x}^{2 \, m}}{m + 2} + \frac{6 \, a^{2} b x^{\frac{3}{2}} \sqrt{x}^{2 \, m}}{2 \, m + 3} + \frac{a^{3} x \sqrt{x}^{2 \, m}}{m + 1}"," ",0,"2*b^3*x^(5/2)*sqrt(x)^(2*m)/(2*m + 5) + 3*a*b^2*x^2*sqrt(x)^(2*m)/(m + 2) + 6*a^2*b*x^(3/2)*sqrt(x)^(2*m)/(2*m + 3) + a^3*x*sqrt(x)^(2*m)/(m + 1)","A",0
2259,1,58,0,0.180517," ","integrate(x^m*(a+b*x^(1/2))^2,x, algorithm=""giac"")","\frac{b^{2} x^{2} \sqrt{x}^{2 \, m}}{m + 2} + \frac{4 \, a b x^{\frac{3}{2}} \sqrt{x}^{2 \, m}}{2 \, m + 3} + \frac{a^{2} x \sqrt{x}^{2 \, m}}{m + 1}"," ",0,"b^2*x^2*sqrt(x)^(2*m)/(m + 2) + 4*a*b*x^(3/2)*sqrt(x)^(2*m)/(2*m + 3) + a^2*x*sqrt(x)^(2*m)/(m + 1)","A",0
2260,1,36,0,0.187000," ","integrate(x^m*(a+b*x^(1/2)),x, algorithm=""giac"")","\frac{2 \, b x^{\frac{3}{2}} \sqrt{x}^{2 \, m}}{2 \, m + 3} + \frac{a x \sqrt{x}^{2 \, m}}{m + 1}"," ",0,"2*b*x^(3/2)*sqrt(x)^(2*m)/(2*m + 3) + a*x*sqrt(x)^(2*m)/(m + 1)","A",0
2261,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(1/2)),x, algorithm=""giac"")","\int \frac{x^{m}}{b \sqrt{x} + a}\,{d x}"," ",0,"integrate(x^m/(b*sqrt(x) + a), x)","F",0
2262,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(1/2))^2,x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b \sqrt{x} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^m/(b*sqrt(x) + a)^2, x)","F",0
2263,0,0,0,0.000000," ","integrate(x^m*(a+b*x^(1/2))^p,x, algorithm=""giac"")","\int {\left(b \sqrt{x} + a\right)}^{p} x^{m}\,{d x}"," ",0,"integrate((b*sqrt(x) + a)^p*x^m, x)","F",0
2264,1,1642,0,0.245020," ","integrate(x^3*(a+b*x^(1/2))^p,x, algorithm=""giac"")","\frac{2 \, {\left({\left(b \sqrt{x} + a\right)}^{8} {\left(b \sqrt{x} + a\right)}^{p} p^{7} - 7 \, {\left(b \sqrt{x} + a\right)}^{7} {\left(b \sqrt{x} + a\right)}^{p} a p^{7} + 21 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{7} - 35 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{7} + 35 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p^{7} - 21 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p^{7} + 7 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{6} p^{7} - {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{7} p^{7} + 28 \, {\left(b \sqrt{x} + a\right)}^{8} {\left(b \sqrt{x} + a\right)}^{p} p^{6} - 203 \, {\left(b \sqrt{x} + a\right)}^{7} {\left(b \sqrt{x} + a\right)}^{p} a p^{6} + 630 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{6} - 1085 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{6} + 1120 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p^{6} - 693 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p^{6} + 238 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{6} p^{6} - 35 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{7} p^{6} + 322 \, {\left(b \sqrt{x} + a\right)}^{8} {\left(b \sqrt{x} + a\right)}^{p} p^{5} - 2401 \, {\left(b \sqrt{x} + a\right)}^{7} {\left(b \sqrt{x} + a\right)}^{p} a p^{5} + 7686 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{5} - 13685 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{5} + 14630 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p^{5} - 9387 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p^{5} + 3346 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{6} p^{5} - 511 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{7} p^{5} + 1960 \, {\left(b \sqrt{x} + a\right)}^{8} {\left(b \sqrt{x} + a\right)}^{p} p^{4} - 14945 \, {\left(b \sqrt{x} + a\right)}^{7} {\left(b \sqrt{x} + a\right)}^{p} a p^{4} + 49140 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{4} - 90335 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{4} + 100240 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p^{4} - 67095 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p^{4} + 25060 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{6} p^{4} - 4025 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{7} p^{4} + 6769 \, {\left(b \sqrt{x} + a\right)}^{8} {\left(b \sqrt{x} + a\right)}^{p} p^{3} - 52528 \, {\left(b \sqrt{x} + a\right)}^{7} {\left(b \sqrt{x} + a\right)}^{p} a p^{3} + 176589 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{3} - 334040 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{3} + 384755 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p^{3} - 270144 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p^{3} + 107023 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{6} p^{3} - 18424 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{7} p^{3} + 13132 \, {\left(b \sqrt{x} + a\right)}^{8} {\left(b \sqrt{x} + a\right)}^{p} p^{2} - 103292 \, {\left(b \sqrt{x} + a\right)}^{7} {\left(b \sqrt{x} + a\right)}^{p} a p^{2} + 353430 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{2} - 684740 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{2} + 815920 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p^{2} - 602532 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p^{2} + 256942 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{6} p^{2} - 48860 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{7} p^{2} + 13068 \, {\left(b \sqrt{x} + a\right)}^{8} {\left(b \sqrt{x} + a\right)}^{p} p - 103824 \, {\left(b \sqrt{x} + a\right)}^{7} {\left(b \sqrt{x} + a\right)}^{p} a p + 360024 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p - 710640 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p + 870660 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p - 673008 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p + 312984 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{6} p - 69264 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{7} p + 5040 \, {\left(b \sqrt{x} + a\right)}^{8} {\left(b \sqrt{x} + a\right)}^{p} - 40320 \, {\left(b \sqrt{x} + a\right)}^{7} {\left(b \sqrt{x} + a\right)}^{p} a + 141120 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} a^{2} - 282240 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a^{3} + 352800 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{4} - 282240 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{5} + 141120 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{6} - 40320 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{7}\right)}}{{\left(b^{7} p^{8} + 36 \, b^{7} p^{7} + 546 \, b^{7} p^{6} + 4536 \, b^{7} p^{5} + 22449 \, b^{7} p^{4} + 67284 \, b^{7} p^{3} + 118124 \, b^{7} p^{2} + 109584 \, b^{7} p + 40320 \, b^{7}\right)} b}"," ",0,"2*((b*sqrt(x) + a)^8*(b*sqrt(x) + a)^p*p^7 - 7*(b*sqrt(x) + a)^7*(b*sqrt(x) + a)^p*a*p^7 + 21*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*a^2*p^7 - 35*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a^3*p^7 + 35*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^4*p^7 - 21*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^5*p^7 + 7*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^6*p^7 - (b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^7*p^7 + 28*(b*sqrt(x) + a)^8*(b*sqrt(x) + a)^p*p^6 - 203*(b*sqrt(x) + a)^7*(b*sqrt(x) + a)^p*a*p^6 + 630*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*a^2*p^6 - 1085*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a^3*p^6 + 1120*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^4*p^6 - 693*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^5*p^6 + 238*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^6*p^6 - 35*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^7*p^6 + 322*(b*sqrt(x) + a)^8*(b*sqrt(x) + a)^p*p^5 - 2401*(b*sqrt(x) + a)^7*(b*sqrt(x) + a)^p*a*p^5 + 7686*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*a^2*p^5 - 13685*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a^3*p^5 + 14630*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^4*p^5 - 9387*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^5*p^5 + 3346*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^6*p^5 - 511*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^7*p^5 + 1960*(b*sqrt(x) + a)^8*(b*sqrt(x) + a)^p*p^4 - 14945*(b*sqrt(x) + a)^7*(b*sqrt(x) + a)^p*a*p^4 + 49140*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*a^2*p^4 - 90335*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a^3*p^4 + 100240*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^4*p^4 - 67095*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^5*p^4 + 25060*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^6*p^4 - 4025*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^7*p^4 + 6769*(b*sqrt(x) + a)^8*(b*sqrt(x) + a)^p*p^3 - 52528*(b*sqrt(x) + a)^7*(b*sqrt(x) + a)^p*a*p^3 + 176589*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*a^2*p^3 - 334040*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a^3*p^3 + 384755*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^4*p^3 - 270144*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^5*p^3 + 107023*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^6*p^3 - 18424*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^7*p^3 + 13132*(b*sqrt(x) + a)^8*(b*sqrt(x) + a)^p*p^2 - 103292*(b*sqrt(x) + a)^7*(b*sqrt(x) + a)^p*a*p^2 + 353430*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*a^2*p^2 - 684740*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a^3*p^2 + 815920*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^4*p^2 - 602532*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^5*p^2 + 256942*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^6*p^2 - 48860*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^7*p^2 + 13068*(b*sqrt(x) + a)^8*(b*sqrt(x) + a)^p*p - 103824*(b*sqrt(x) + a)^7*(b*sqrt(x) + a)^p*a*p + 360024*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*a^2*p - 710640*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a^3*p + 870660*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^4*p - 673008*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^5*p + 312984*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^6*p - 69264*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^7*p + 5040*(b*sqrt(x) + a)^8*(b*sqrt(x) + a)^p - 40320*(b*sqrt(x) + a)^7*(b*sqrt(x) + a)^p*a + 141120*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*a^2 - 282240*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a^3 + 352800*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^4 - 282240*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^5 + 141120*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^6 - 40320*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^7)/((b^7*p^8 + 36*b^7*p^7 + 546*b^7*p^6 + 4536*b^7*p^5 + 22449*b^7*p^4 + 67284*b^7*p^3 + 118124*b^7*p^2 + 109584*b^7*p + 40320*b^7)*b)","B",0
2265,1,922,0,0.190884," ","integrate(x^2*(a+b*x^(1/2))^p,x, algorithm=""giac"")","\frac{2 \, {\left({\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} p^{5} - 5 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a p^{5} + 10 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{5} - 10 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{5} + 5 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p^{5} - {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p^{5} + 15 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} p^{4} - 80 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a p^{4} + 170 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{4} - 180 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{4} + 95 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p^{4} - 20 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p^{4} + 85 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} p^{3} - 475 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a p^{3} + 1070 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{3} - 1210 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{3} + 685 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p^{3} - 155 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p^{3} + 225 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} p^{2} - 1300 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a p^{2} + 3070 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{2} - 3720 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{2} + 2305 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p^{2} - 580 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p^{2} + 274 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} p - 1620 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a p + 3960 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p - 5080 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p + 3510 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{4} p - 1044 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{5} p + 120 \, {\left(b \sqrt{x} + a\right)}^{6} {\left(b \sqrt{x} + a\right)}^{p} - 720 \, {\left(b \sqrt{x} + a\right)}^{5} {\left(b \sqrt{x} + a\right)}^{p} a + 1800 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} a^{2} - 2400 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a^{3} + 1800 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{4} - 720 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{5}\right)}}{{\left(b^{5} p^{6} + 21 \, b^{5} p^{5} + 175 \, b^{5} p^{4} + 735 \, b^{5} p^{3} + 1624 \, b^{5} p^{2} + 1764 \, b^{5} p + 720 \, b^{5}\right)} b}"," ",0,"2*((b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*p^5 - 5*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a*p^5 + 10*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^2*p^5 - 10*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^3*p^5 + 5*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^4*p^5 - (b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^5*p^5 + 15*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*p^4 - 80*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a*p^4 + 170*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^2*p^4 - 180*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^3*p^4 + 95*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^4*p^4 - 20*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^5*p^4 + 85*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*p^3 - 475*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a*p^3 + 1070*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^2*p^3 - 1210*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^3*p^3 + 685*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^4*p^3 - 155*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^5*p^3 + 225*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*p^2 - 1300*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a*p^2 + 3070*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^2*p^2 - 3720*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^3*p^2 + 2305*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^4*p^2 - 580*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^5*p^2 + 274*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p*p - 1620*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a*p + 3960*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^2*p - 5080*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^3*p + 3510*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^4*p - 1044*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^5*p + 120*(b*sqrt(x) + a)^6*(b*sqrt(x) + a)^p - 720*(b*sqrt(x) + a)^5*(b*sqrt(x) + a)^p*a + 1800*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*a^2 - 2400*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a^3 + 1800*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^4 - 720*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^5)/((b^5*p^6 + 21*b^5*p^5 + 175*b^5*p^4 + 735*b^5*p^3 + 1624*b^5*p^2 + 1764*b^5*p + 720*b^5)*b)","B",0
2266,1,410,0,0.193797," ","integrate(x*(a+b*x^(1/2))^p,x, algorithm=""giac"")","\frac{2 \, {\left({\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} p^{3} - 3 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a p^{3} + 3 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{3} - {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{3} + 6 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} p^{2} - 21 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a p^{2} + 24 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p^{2} - 9 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p^{2} + 11 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} p - 42 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a p + 57 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{2} p - 26 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{3} p + 6 \, {\left(b \sqrt{x} + a\right)}^{4} {\left(b \sqrt{x} + a\right)}^{p} - 24 \, {\left(b \sqrt{x} + a\right)}^{3} {\left(b \sqrt{x} + a\right)}^{p} a + 36 \, {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} a^{2} - 24 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a^{3}\right)}}{{\left(b^{3} p^{4} + 10 \, b^{3} p^{3} + 35 \, b^{3} p^{2} + 50 \, b^{3} p + 24 \, b^{3}\right)} b}"," ",0,"2*((b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*p^3 - 3*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a*p^3 + 3*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^2*p^3 - (b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^3*p^3 + 6*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*p^2 - 21*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a*p^2 + 24*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^2*p^2 - 9*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^3*p^2 + 11*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p*p - 42*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a*p + 57*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^2*p - 26*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^3*p + 6*(b*sqrt(x) + a)^4*(b*sqrt(x) + a)^p - 24*(b*sqrt(x) + a)^3*(b*sqrt(x) + a)^p*a + 36*(b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*a^2 - 24*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a^3)/((b^3*p^4 + 10*b^3*p^3 + 35*b^3*p^2 + 50*b^3*p + 24*b^3)*b)","B",0
2267,1,94,0,0.156744," ","integrate((a+b*x^(1/2))^p,x, algorithm=""giac"")","\frac{2 \, {\left({\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} p - {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a p + {\left(b \sqrt{x} + a\right)}^{2} {\left(b \sqrt{x} + a\right)}^{p} - 2 \, {\left(b \sqrt{x} + a\right)} {\left(b \sqrt{x} + a\right)}^{p} a\right)}}{{\left(p^{2} + 3 \, p + 2\right)} b^{2}}"," ",0,"2*((b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p*p - (b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a*p + (b*sqrt(x) + a)^2*(b*sqrt(x) + a)^p - 2*(b*sqrt(x) + a)*(b*sqrt(x) + a)^p*a)/((p^2 + 3*p + 2)*b^2)","B",0
2268,0,0,0,0.000000," ","integrate((a+b*x^(1/2))^p/x,x, algorithm=""giac"")","\int \frac{{\left(b \sqrt{x} + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((b*sqrt(x) + a)^p/x, x)","F",0
2269,0,0,0,0.000000," ","integrate((a+b*x^(1/2))^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(b \sqrt{x} + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b*sqrt(x) + a)^p/x^2, x)","F",0
2270,1,20,0,0.155216," ","integrate(x^(1/2)/(1+x^(3/2)),x, algorithm=""giac"")","\frac{2}{3} \, \log\left(x - \sqrt{x} + 1\right) + \frac{2}{3} \, \log\left(\sqrt{x} + 1\right)"," ",0,"2/3*log(x - sqrt(x) + 1) + 2/3*log(sqrt(x) + 1)","B",0
2271,0,0,0,0.000000," ","integrate(x^3/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x^3/(b*x^(3/2) + a)^(2/3), x)","F",0
2272,0,0,0,0.000000," ","integrate(1/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*x^(3/2) + a)^(-2/3), x)","F",0
2273,0,0,0,0.000000," ","integrate(1/x^3/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{2}{3}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^(3/2) + a)^(2/3)*x^3), x)","F",0
2274,0,0,0,0.000000," ","integrate(1/x^6/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{2}{3}} x^{6}}\,{d x}"," ",0,"integrate(1/((b*x^(3/2) + a)^(2/3)*x^6), x)","F",0
2275,0,0,0,0.000000," ","integrate(1/x^9/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{2}{3}} x^{9}}\,{d x}"," ",0,"integrate(1/((b*x^(3/2) + a)^(2/3)*x^9), x)","F",0
2276,1,89,0,0.230086," ","integrate(x^8/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","-\frac{2 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}} a^{5}}{b^{6}} + \frac{91 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{16}{3}} - 560 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{13}{3}} a + 1456 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{10}{3}} a^{2} - 2080 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{7}{3}} a^{3} + 1820 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{4}{3}} a^{4}}{728 \, b^{6}}"," ",0,"-2*(b*x^(3/2) + a)^(1/3)*a^5/b^6 + 1/728*(91*(b*x^(3/2) + a)^(16/3) - 560*(b*x^(3/2) + a)^(13/3)*a + 1456*(b*x^(3/2) + a)^(10/3)*a^2 - 2080*(b*x^(3/2) + a)^(7/3)*a^3 + 1820*(b*x^(3/2) + a)^(4/3)*a^4)/b^6","A",0
2277,1,61,0,0.208325," ","integrate(x^5/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","-\frac{2 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}} a^{3}}{b^{4}} + \frac{14 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{10}{3}} - 60 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{7}{3}} a + 105 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{4}{3}} a^{2}}{70 \, b^{4}}"," ",0,"-2*(b*x^(3/2) + a)^(1/3)*a^3/b^4 + 1/70*(14*(b*x^(3/2) + a)^(10/3) - 60*(b*x^(3/2) + a)^(7/3)*a + 105*(b*x^(3/2) + a)^(4/3)*a^2)/b^4","A",0
2278,1,30,0,0.204960," ","integrate(x^2/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","\frac{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{4}{3}}}{2 \, b^{2}} - \frac{2 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}} a}{b^{2}}"," ",0,"1/2*(b*x^(3/2) + a)^(4/3)/b^2 - 2*(b*x^(3/2) + a)^(1/3)*a/b^2","A",0
2279,1,87,0,2.781551," ","integrate(1/x/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{3 \, a^{\frac{2}{3}}} - \frac{\log\left({\left(b x^{\frac{3}{2}} + a\right)}^{\frac{2}{3}} + {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{3 \, a^{\frac{2}{3}}} + \frac{2 \, \log\left({\left| {\left(b x^{\frac{3}{2}} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}} \right|}\right)}{3 \, a^{\frac{2}{3}}}"," ",0,"-2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(b*x^(3/2) + a)^(1/3) + a^(1/3))/a^(1/3))/a^(2/3) - 1/3*log((b*x^(3/2) + a)^(2/3) + (b*x^(3/2) + a)^(1/3)*a^(1/3) + a^(2/3))/a^(2/3) + 2/3*log(abs((b*x^(3/2) + a)^(1/3) - a^(1/3)))/a^(2/3)","A",0
2280,-2,0,0,0.000000," ","integrate(1/x^4/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage3:=type(sage2):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueDone","F(-2)",0
2281,0,0,0,0.000000," ","integrate(x^4/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x^4/(b*x^(3/2) + a)^(2/3), x)","F",0
2282,0,0,0,0.000000," ","integrate(x/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(x/(b*x^(3/2) + a)^(2/3), x)","F",0
2283,0,0,0,0.000000," ","integrate(1/x^2/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{2}{3}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^(3/2) + a)^(2/3)*x^2), x)","F",0
2284,0,0,0,0.000000," ","integrate(1/x^5/(a+b*x^(3/2))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{\frac{3}{2}} + a\right)}^{\frac{2}{3}} x^{5}}\,{d x}"," ",0,"integrate(1/((b*x^(3/2) + a)^(2/3)*x^5), x)","F",0
2285,1,13,0,0.153486," ","integrate((a+b*x^(1/3))*x^4,x, algorithm=""giac"")","\frac{3}{16} \, b x^{\frac{16}{3}} + \frac{1}{5} \, a x^{5}"," ",0,"3/16*b*x^(16/3) + 1/5*a*x^5","A",0
2286,1,13,0,0.148175," ","integrate((a+b*x^(1/3))*x^3,x, algorithm=""giac"")","\frac{3}{13} \, b x^{\frac{13}{3}} + \frac{1}{4} \, a x^{4}"," ",0,"3/13*b*x^(13/3) + 1/4*a*x^4","A",0
2287,1,13,0,0.150603," ","integrate((a+b*x^(1/3))*x^2,x, algorithm=""giac"")","\frac{3}{10} \, b x^{\frac{10}{3}} + \frac{1}{3} \, a x^{3}"," ",0,"3/10*b*x^(10/3) + 1/3*a*x^3","A",0
2288,1,13,0,0.167091," ","integrate((a+b*x^(1/3))*x,x, algorithm=""giac"")","\frac{3}{7} \, b x^{\frac{7}{3}} + \frac{1}{2} \, a x^{2}"," ",0,"3/7*b*x^(7/3) + 1/2*a*x^2","A",0
2289,1,10,0,0.159065," ","integrate(a+b*x^(1/3),x, algorithm=""giac"")","\frac{3}{4} \, b x^{\frac{4}{3}} + a x"," ",0,"3/4*b*x^(4/3) + a*x","A",0
2290,1,12,0,0.151792," ","integrate((a+b*x^(1/3))/x,x, algorithm=""giac"")","a \log\left({\left| x \right|}\right) + 3 \, b x^{\frac{1}{3}}"," ",0,"a*log(abs(x)) + 3*b*x^(1/3)","A",0
2291,1,15,0,0.192332," ","integrate((a+b*x^(1/3))/x^2,x, algorithm=""giac"")","-\frac{3 \, b x^{\frac{1}{3}} + 2 \, a}{2 \, x}"," ",0,"-1/2*(3*b*x^(1/3) + 2*a)/x","A",0
2292,1,15,0,0.193645," ","integrate((a+b*x^(1/3))/x^3,x, algorithm=""giac"")","-\frac{6 \, b x^{\frac{1}{3}} + 5 \, a}{10 \, x^{2}}"," ",0,"-1/10*(6*b*x^(1/3) + 5*a)/x^2","A",0
2293,1,15,0,0.164503," ","integrate((a+b*x^(1/3))/x^4,x, algorithm=""giac"")","-\frac{9 \, b x^{\frac{1}{3}} + 8 \, a}{24 \, x^{3}}"," ",0,"-1/24*(9*b*x^(1/3) + 8*a)/x^3","A",0
2294,1,24,0,0.199514," ","integrate((a+b*x^(1/3))^2*x^4,x, algorithm=""giac"")","\frac{3}{17} \, b^{2} x^{\frac{17}{3}} + \frac{3}{8} \, a b x^{\frac{16}{3}} + \frac{1}{5} \, a^{2} x^{5}"," ",0,"3/17*b^2*x^(17/3) + 3/8*a*b*x^(16/3) + 1/5*a^2*x^5","A",0
2295,1,24,0,0.152280," ","integrate((a+b*x^(1/3))^2*x^3,x, algorithm=""giac"")","\frac{3}{14} \, b^{2} x^{\frac{14}{3}} + \frac{6}{13} \, a b x^{\frac{13}{3}} + \frac{1}{4} \, a^{2} x^{4}"," ",0,"3/14*b^2*x^(14/3) + 6/13*a*b*x^(13/3) + 1/4*a^2*x^4","A",0
2296,1,24,0,0.152705," ","integrate((a+b*x^(1/3))^2*x^2,x, algorithm=""giac"")","\frac{3}{11} \, b^{2} x^{\frac{11}{3}} + \frac{3}{5} \, a b x^{\frac{10}{3}} + \frac{1}{3} \, a^{2} x^{3}"," ",0,"3/11*b^2*x^(11/3) + 3/5*a*b*x^(10/3) + 1/3*a^2*x^3","A",0
2297,1,24,0,0.158109," ","integrate((a+b*x^(1/3))^2*x,x, algorithm=""giac"")","\frac{3}{8} \, b^{2} x^{\frac{8}{3}} + \frac{6}{7} \, a b x^{\frac{7}{3}} + \frac{1}{2} \, a^{2} x^{2}"," ",0,"3/8*b^2*x^(8/3) + 6/7*a*b*x^(7/3) + 1/2*a^2*x^2","A",0
2298,1,21,0,0.150660," ","integrate((a+b*x^(1/3))^2,x, algorithm=""giac"")","\frac{3}{5} \, b^{2} x^{\frac{5}{3}} + \frac{3}{2} \, a b x^{\frac{4}{3}} + a^{2} x"," ",0,"3/5*b^2*x^(5/3) + 3/2*a*b*x^(4/3) + a^2*x","A",0
2299,1,23,0,0.169283," ","integrate((a+b*x^(1/3))^2/x,x, algorithm=""giac"")","a^{2} \log\left({\left| x \right|}\right) + \frac{3}{2} \, b^{2} x^{\frac{2}{3}} + 6 \, a b x^{\frac{1}{3}}"," ",0,"a^2*log(abs(x)) + 3/2*b^2*x^(2/3) + 6*a*b*x^(1/3)","A",0
2300,1,24,0,0.173118," ","integrate((a+b*x^(1/3))^2/x^2,x, algorithm=""giac"")","-\frac{3 \, b^{2} x^{\frac{2}{3}} + 3 \, a b x^{\frac{1}{3}} + a^{2}}{x}"," ",0,"-(3*b^2*x^(2/3) + 3*a*b*x^(1/3) + a^2)/x","A",0
2301,1,26,0,0.174572," ","integrate((a+b*x^(1/3))^2/x^3,x, algorithm=""giac"")","-\frac{15 \, b^{2} x^{\frac{2}{3}} + 24 \, a b x^{\frac{1}{3}} + 10 \, a^{2}}{20 \, x^{2}}"," ",0,"-1/20*(15*b^2*x^(2/3) + 24*a*b*x^(1/3) + 10*a^2)/x^2","A",0
2302,1,26,0,0.153512," ","integrate((a+b*x^(1/3))^2/x^4,x, algorithm=""giac"")","-\frac{36 \, b^{2} x^{\frac{2}{3}} + 63 \, a b x^{\frac{1}{3}} + 28 \, a^{2}}{84 \, x^{3}}"," ",0,"-1/84*(36*b^2*x^(2/3) + 63*a*b*x^(1/3) + 28*a^2)/x^3","A",0
2303,1,35,0,0.150594," ","integrate((a+b*x^(1/3))^3*x^4,x, algorithm=""giac"")","\frac{1}{6} \, b^{3} x^{6} + \frac{9}{17} \, a b^{2} x^{\frac{17}{3}} + \frac{9}{16} \, a^{2} b x^{\frac{16}{3}} + \frac{1}{5} \, a^{3} x^{5}"," ",0,"1/6*b^3*x^6 + 9/17*a*b^2*x^(17/3) + 9/16*a^2*b*x^(16/3) + 1/5*a^3*x^5","A",0
2304,1,35,0,0.159579," ","integrate((a+b*x^(1/3))^3*x^3,x, algorithm=""giac"")","\frac{1}{5} \, b^{3} x^{5} + \frac{9}{14} \, a b^{2} x^{\frac{14}{3}} + \frac{9}{13} \, a^{2} b x^{\frac{13}{3}} + \frac{1}{4} \, a^{3} x^{4}"," ",0,"1/5*b^3*x^5 + 9/14*a*b^2*x^(14/3) + 9/13*a^2*b*x^(13/3) + 1/4*a^3*x^4","A",0
2305,1,35,0,0.163191," ","integrate((a+b*x^(1/3))^3*x^2,x, algorithm=""giac"")","\frac{1}{4} \, b^{3} x^{4} + \frac{9}{11} \, a b^{2} x^{\frac{11}{3}} + \frac{9}{10} \, a^{2} b x^{\frac{10}{3}} + \frac{1}{3} \, a^{3} x^{3}"," ",0,"1/4*b^3*x^4 + 9/11*a*b^2*x^(11/3) + 9/10*a^2*b*x^(10/3) + 1/3*a^3*x^3","A",0
2306,1,35,0,0.160748," ","integrate((a+b*x^(1/3))^3*x,x, algorithm=""giac"")","\frac{1}{3} \, b^{3} x^{3} + \frac{9}{8} \, a b^{2} x^{\frac{8}{3}} + \frac{9}{7} \, a^{2} b x^{\frac{7}{3}} + \frac{1}{2} \, a^{3} x^{2}"," ",0,"1/3*b^3*x^3 + 9/8*a*b^2*x^(8/3) + 9/7*a^2*b*x^(7/3) + 1/2*a^3*x^2","A",0
2307,1,32,0,0.158019," ","integrate((a+b*x^(1/3))^3,x, algorithm=""giac"")","\frac{1}{2} \, b^{3} x^{2} + \frac{9}{5} \, a b^{2} x^{\frac{5}{3}} + \frac{9}{4} \, a^{2} b x^{\frac{4}{3}} + a^{3} x"," ",0,"1/2*b^3*x^2 + 9/5*a*b^2*x^(5/3) + 9/4*a^2*b*x^(4/3) + a^3*x","A",0
2308,1,31,0,0.152886," ","integrate((a+b*x^(1/3))^3/x,x, algorithm=""giac"")","b^{3} x + a^{3} \log\left({\left| x \right|}\right) + \frac{9}{2} \, a b^{2} x^{\frac{2}{3}} + 9 \, a^{2} b x^{\frac{1}{3}}"," ",0,"b^3*x + a^3*log(abs(x)) + 9/2*a*b^2*x^(2/3) + 9*a^2*b*x^(1/3)","A",0
2309,1,37,0,0.186256," ","integrate((a+b*x^(1/3))^3/x^2,x, algorithm=""giac"")","b^{3} \log\left({\left| x \right|}\right) - \frac{18 \, a b^{2} x^{\frac{2}{3}} + 9 \, a^{2} b x^{\frac{1}{3}} + 2 \, a^{3}}{2 \, x}"," ",0,"b^3*log(abs(x)) - 1/2*(18*a*b^2*x^(2/3) + 9*a^2*b*x^(1/3) + 2*a^3)/x","A",0
2310,1,35,0,0.208170," ","integrate((a+b*x^(1/3))^3/x^3,x, algorithm=""giac"")","-\frac{20 \, b^{3} x + 45 \, a b^{2} x^{\frac{2}{3}} + 36 \, a^{2} b x^{\frac{1}{3}} + 10 \, a^{3}}{20 \, x^{2}}"," ",0,"-1/20*(20*b^3*x + 45*a*b^2*x^(2/3) + 36*a^2*b*x^(1/3) + 10*a^3)/x^2","A",0
2311,1,35,0,0.157314," ","integrate((a+b*x^(1/3))^3/x^4,x, algorithm=""giac"")","-\frac{84 \, b^{3} x + 216 \, a b^{2} x^{\frac{2}{3}} + 189 \, a^{2} b x^{\frac{1}{3}} + 56 \, a^{3}}{168 \, x^{3}}"," ",0,"-1/168*(84*b^3*x + 216*a*b^2*x^(2/3) + 189*a^2*b*x^(1/3) + 56*a^3)/x^3","A",0
2312,1,57,0,0.153231," ","integrate((a+b*x^(1/3))^5*x^4,x, algorithm=""giac"")","\frac{3}{20} \, b^{5} x^{\frac{20}{3}} + \frac{15}{19} \, a b^{4} x^{\frac{19}{3}} + \frac{5}{3} \, a^{2} b^{3} x^{6} + \frac{30}{17} \, a^{3} b^{2} x^{\frac{17}{3}} + \frac{15}{16} \, a^{4} b x^{\frac{16}{3}} + \frac{1}{5} \, a^{5} x^{5}"," ",0,"3/20*b^5*x^(20/3) + 15/19*a*b^4*x^(19/3) + 5/3*a^2*b^3*x^6 + 30/17*a^3*b^2*x^(17/3) + 15/16*a^4*b*x^(16/3) + 1/5*a^5*x^5","A",0
2313,1,57,0,0.167428," ","integrate((a+b*x^(1/3))^5*x^3,x, algorithm=""giac"")","\frac{3}{17} \, b^{5} x^{\frac{17}{3}} + \frac{15}{16} \, a b^{4} x^{\frac{16}{3}} + 2 \, a^{2} b^{3} x^{5} + \frac{15}{7} \, a^{3} b^{2} x^{\frac{14}{3}} + \frac{15}{13} \, a^{4} b x^{\frac{13}{3}} + \frac{1}{4} \, a^{5} x^{4}"," ",0,"3/17*b^5*x^(17/3) + 15/16*a*b^4*x^(16/3) + 2*a^2*b^3*x^5 + 15/7*a^3*b^2*x^(14/3) + 15/13*a^4*b*x^(13/3) + 1/4*a^5*x^4","A",0
2314,1,57,0,0.162482," ","integrate((a+b*x^(1/3))^5*x^2,x, algorithm=""giac"")","\frac{3}{14} \, b^{5} x^{\frac{14}{3}} + \frac{15}{13} \, a b^{4} x^{\frac{13}{3}} + \frac{5}{2} \, a^{2} b^{3} x^{4} + \frac{30}{11} \, a^{3} b^{2} x^{\frac{11}{3}} + \frac{3}{2} \, a^{4} b x^{\frac{10}{3}} + \frac{1}{3} \, a^{5} x^{3}"," ",0,"3/14*b^5*x^(14/3) + 15/13*a*b^4*x^(13/3) + 5/2*a^2*b^3*x^4 + 30/11*a^3*b^2*x^(11/3) + 3/2*a^4*b*x^(10/3) + 1/3*a^5*x^3","A",0
2315,1,57,0,0.163712," ","integrate((a+b*x^(1/3))^5*x,x, algorithm=""giac"")","\frac{3}{11} \, b^{5} x^{\frac{11}{3}} + \frac{3}{2} \, a b^{4} x^{\frac{10}{3}} + \frac{10}{3} \, a^{2} b^{3} x^{3} + \frac{15}{4} \, a^{3} b^{2} x^{\frac{8}{3}} + \frac{15}{7} \, a^{4} b x^{\frac{7}{3}} + \frac{1}{2} \, a^{5} x^{2}"," ",0,"3/11*b^5*x^(11/3) + 3/2*a*b^4*x^(10/3) + 10/3*a^2*b^3*x^3 + 15/4*a^3*b^2*x^(8/3) + 15/7*a^4*b*x^(7/3) + 1/2*a^5*x^2","A",0
2316,1,54,0,0.169403," ","integrate((a+b*x^(1/3))^5,x, algorithm=""giac"")","\frac{3}{8} \, b^{5} x^{\frac{8}{3}} + \frac{15}{7} \, a b^{4} x^{\frac{7}{3}} + 5 \, a^{2} b^{3} x^{2} + 6 \, a^{3} b^{2} x^{\frac{5}{3}} + \frac{15}{4} \, a^{4} b x^{\frac{4}{3}} + a^{5} x"," ",0,"3/8*b^5*x^(8/3) + 15/7*a*b^4*x^(7/3) + 5*a^2*b^3*x^2 + 6*a^3*b^2*x^(5/3) + 15/4*a^4*b*x^(4/3) + a^5*x","A",0
2317,1,54,0,0.153343," ","integrate((a+b*x^(1/3))^5/x,x, algorithm=""giac"")","\frac{3}{5} \, b^{5} x^{\frac{5}{3}} + \frac{15}{4} \, a b^{4} x^{\frac{4}{3}} + 10 \, a^{2} b^{3} x + a^{5} \log\left({\left| x \right|}\right) + 15 \, a^{3} b^{2} x^{\frac{2}{3}} + 15 \, a^{4} b x^{\frac{1}{3}}"," ",0,"3/5*b^5*x^(5/3) + 15/4*a*b^4*x^(4/3) + 10*a^2*b^3*x + a^5*log(abs(x)) + 15*a^3*b^2*x^(2/3) + 15*a^4*b*x^(1/3)","A",0
2318,1,60,0,0.170470," ","integrate((a+b*x^(1/3))^5/x^2,x, algorithm=""giac"")","10 \, a^{2} b^{3} \log\left({\left| x \right|}\right) + \frac{3}{2} \, b^{5} x^{\frac{2}{3}} + 15 \, a b^{4} x^{\frac{1}{3}} - \frac{60 \, a^{3} b^{2} x^{\frac{2}{3}} + 15 \, a^{4} b x^{\frac{1}{3}} + 2 \, a^{5}}{2 \, x}"," ",0,"10*a^2*b^3*log(abs(x)) + 3/2*b^5*x^(2/3) + 15*a*b^4*x^(1/3) - 1/2*(60*a^3*b^2*x^(2/3) + 15*a^4*b*x^(1/3) + 2*a^5)/x","A",0
2319,1,55,0,0.195392," ","integrate((a+b*x^(1/3))^5/x^3,x, algorithm=""giac"")","-\frac{6 \, b^{5} x^{\frac{5}{3}} + 15 \, a b^{4} x^{\frac{4}{3}} + 20 \, a^{2} b^{3} x + 15 \, a^{3} b^{2} x^{\frac{2}{3}} + 6 \, a^{4} b x^{\frac{1}{3}} + a^{5}}{2 \, x^{2}}"," ",0,"-1/2*(6*b^5*x^(5/3) + 15*a*b^4*x^(4/3) + 20*a^2*b^3*x + 15*a^3*b^2*x^(2/3) + 6*a^4*b*x^(1/3) + a^5)/x^2","B",0
2320,1,57,0,0.159656," ","integrate((a+b*x^(1/3))^5/x^4,x, algorithm=""giac"")","-\frac{126 \, b^{5} x^{\frac{5}{3}} + 504 \, a b^{4} x^{\frac{4}{3}} + 840 \, a^{2} b^{3} x + 720 \, a^{3} b^{2} x^{\frac{2}{3}} + 315 \, a^{4} b x^{\frac{1}{3}} + 56 \, a^{5}}{168 \, x^{3}}"," ",0,"-1/168*(126*b^5*x^(5/3) + 504*a*b^4*x^(4/3) + 840*a^2*b^3*x + 720*a^3*b^2*x^(2/3) + 315*a^4*b*x^(1/3) + 56*a^5)/x^3","A",0
2321,1,57,0,0.158743," ","integrate((a+b*x^(1/3))^5/x^5,x, algorithm=""giac"")","-\frac{792 \, b^{5} x^{\frac{5}{3}} + 3465 \, a b^{4} x^{\frac{4}{3}} + 6160 \, a^{2} b^{3} x + 5544 \, a^{3} b^{2} x^{\frac{2}{3}} + 2520 \, a^{4} b x^{\frac{1}{3}} + 462 \, a^{5}}{1848 \, x^{4}}"," ",0,"-1/1848*(792*b^5*x^(5/3) + 3465*a*b^4*x^(4/3) + 6160*a^2*b^3*x + 5544*a^3*b^2*x^(2/3) + 2520*a^4*b*x^(1/3) + 462*a^5)/x^4","A",0
2322,1,57,0,0.157826," ","integrate((a+b*x^(1/3))^5/x^6,x, algorithm=""giac"")","-\frac{3003 \, b^{5} x^{\frac{5}{3}} + 13650 \, a b^{4} x^{\frac{4}{3}} + 25025 \, a^{2} b^{3} x + 23100 \, a^{3} b^{2} x^{\frac{2}{3}} + 10725 \, a^{4} b x^{\frac{1}{3}} + 2002 \, a^{5}}{10010 \, x^{5}}"," ",0,"-1/10010*(3003*b^5*x^(5/3) + 13650*a*b^4*x^(4/3) + 25025*a^2*b^3*x + 23100*a^3*b^2*x^(2/3) + 10725*a^4*b*x^(1/3) + 2002*a^5)/x^5","A",0
2323,1,57,0,0.155916," ","integrate((a+b*x^(1/3))^5/x^7,x, algorithm=""giac"")","-\frac{8568 \, b^{5} x^{\frac{5}{3}} + 39780 \, a b^{4} x^{\frac{4}{3}} + 74256 \, a^{2} b^{3} x + 69615 \, a^{3} b^{2} x^{\frac{2}{3}} + 32760 \, a^{4} b x^{\frac{1}{3}} + 6188 \, a^{5}}{37128 \, x^{6}}"," ",0,"-1/37128*(8568*b^5*x^(5/3) + 39780*a*b^4*x^(4/3) + 74256*a^2*b^3*x + 69615*a^3*b^2*x^(2/3) + 32760*a^4*b*x^(1/3) + 6188*a^5)/x^6","A",0
2324,1,112,0,0.159813," ","integrate((a+b*x^(1/3))^10*x^4,x, algorithm=""giac"")","\frac{3}{25} \, b^{10} x^{\frac{25}{3}} + \frac{5}{4} \, a b^{9} x^{8} + \frac{135}{23} \, a^{2} b^{8} x^{\frac{23}{3}} + \frac{180}{11} \, a^{3} b^{7} x^{\frac{22}{3}} + 30 \, a^{4} b^{6} x^{7} + \frac{189}{5} \, a^{5} b^{5} x^{\frac{20}{3}} + \frac{630}{19} \, a^{6} b^{4} x^{\frac{19}{3}} + 20 \, a^{7} b^{3} x^{6} + \frac{135}{17} \, a^{8} b^{2} x^{\frac{17}{3}} + \frac{15}{8} \, a^{9} b x^{\frac{16}{3}} + \frac{1}{5} \, a^{10} x^{5}"," ",0,"3/25*b^10*x^(25/3) + 5/4*a*b^9*x^8 + 135/23*a^2*b^8*x^(23/3) + 180/11*a^3*b^7*x^(22/3) + 30*a^4*b^6*x^7 + 189/5*a^5*b^5*x^(20/3) + 630/19*a^6*b^4*x^(19/3) + 20*a^7*b^3*x^6 + 135/17*a^8*b^2*x^(17/3) + 15/8*a^9*b*x^(16/3) + 1/5*a^10*x^5","A",0
2325,1,112,0,0.160539," ","integrate((a+b*x^(1/3))^10*x^3,x, algorithm=""giac"")","\frac{3}{22} \, b^{10} x^{\frac{22}{3}} + \frac{10}{7} \, a b^{9} x^{7} + \frac{27}{4} \, a^{2} b^{8} x^{\frac{20}{3}} + \frac{360}{19} \, a^{3} b^{7} x^{\frac{19}{3}} + 35 \, a^{4} b^{6} x^{6} + \frac{756}{17} \, a^{5} b^{5} x^{\frac{17}{3}} + \frac{315}{8} \, a^{6} b^{4} x^{\frac{16}{3}} + 24 \, a^{7} b^{3} x^{5} + \frac{135}{14} \, a^{8} b^{2} x^{\frac{14}{3}} + \frac{30}{13} \, a^{9} b x^{\frac{13}{3}} + \frac{1}{4} \, a^{10} x^{4}"," ",0,"3/22*b^10*x^(22/3) + 10/7*a*b^9*x^7 + 27/4*a^2*b^8*x^(20/3) + 360/19*a^3*b^7*x^(19/3) + 35*a^4*b^6*x^6 + 756/17*a^5*b^5*x^(17/3) + 315/8*a^6*b^4*x^(16/3) + 24*a^7*b^3*x^5 + 135/14*a^8*b^2*x^(14/3) + 30/13*a^9*b*x^(13/3) + 1/4*a^10*x^4","A",0
2326,1,112,0,0.158877," ","integrate((a+b*x^(1/3))^10*x^2,x, algorithm=""giac"")","\frac{3}{19} \, b^{10} x^{\frac{19}{3}} + \frac{5}{3} \, a b^{9} x^{6} + \frac{135}{17} \, a^{2} b^{8} x^{\frac{17}{3}} + \frac{45}{2} \, a^{3} b^{7} x^{\frac{16}{3}} + 42 \, a^{4} b^{6} x^{5} + 54 \, a^{5} b^{5} x^{\frac{14}{3}} + \frac{630}{13} \, a^{6} b^{4} x^{\frac{13}{3}} + 30 \, a^{7} b^{3} x^{4} + \frac{135}{11} \, a^{8} b^{2} x^{\frac{11}{3}} + 3 \, a^{9} b x^{\frac{10}{3}} + \frac{1}{3} \, a^{10} x^{3}"," ",0,"3/19*b^10*x^(19/3) + 5/3*a*b^9*x^6 + 135/17*a^2*b^8*x^(17/3) + 45/2*a^3*b^7*x^(16/3) + 42*a^4*b^6*x^5 + 54*a^5*b^5*x^(14/3) + 630/13*a^6*b^4*x^(13/3) + 30*a^7*b^3*x^4 + 135/11*a^8*b^2*x^(11/3) + 3*a^9*b*x^(10/3) + 1/3*a^10*x^3","A",0
2327,1,112,0,0.188213," ","integrate((a+b*x^(1/3))^10*x,x, algorithm=""giac"")","\frac{3}{16} \, b^{10} x^{\frac{16}{3}} + 2 \, a b^{9} x^{5} + \frac{135}{14} \, a^{2} b^{8} x^{\frac{14}{3}} + \frac{360}{13} \, a^{3} b^{7} x^{\frac{13}{3}} + \frac{105}{2} \, a^{4} b^{6} x^{4} + \frac{756}{11} \, a^{5} b^{5} x^{\frac{11}{3}} + 63 \, a^{6} b^{4} x^{\frac{10}{3}} + 40 \, a^{7} b^{3} x^{3} + \frac{135}{8} \, a^{8} b^{2} x^{\frac{8}{3}} + \frac{30}{7} \, a^{9} b x^{\frac{7}{3}} + \frac{1}{2} \, a^{10} x^{2}"," ",0,"3/16*b^10*x^(16/3) + 2*a*b^9*x^5 + 135/14*a^2*b^8*x^(14/3) + 360/13*a^3*b^7*x^(13/3) + 105/2*a^4*b^6*x^4 + 756/11*a^5*b^5*x^(11/3) + 63*a^6*b^4*x^(10/3) + 40*a^7*b^3*x^3 + 135/8*a^8*b^2*x^(8/3) + 30/7*a^9*b*x^(7/3) + 1/2*a^10*x^2","A",0
2328,1,109,0,0.155525," ","integrate((a+b*x^(1/3))^10,x, algorithm=""giac"")","\frac{3}{13} \, b^{10} x^{\frac{13}{3}} + \frac{5}{2} \, a b^{9} x^{4} + \frac{135}{11} \, a^{2} b^{8} x^{\frac{11}{3}} + 36 \, a^{3} b^{7} x^{\frac{10}{3}} + 70 \, a^{4} b^{6} x^{3} + \frac{189}{2} \, a^{5} b^{5} x^{\frac{8}{3}} + 90 \, a^{6} b^{4} x^{\frac{7}{3}} + 60 \, a^{7} b^{3} x^{2} + 27 \, a^{8} b^{2} x^{\frac{5}{3}} + \frac{15}{2} \, a^{9} b x^{\frac{4}{3}} + a^{10} x"," ",0,"3/13*b^10*x^(13/3) + 5/2*a*b^9*x^4 + 135/11*a^2*b^8*x^(11/3) + 36*a^3*b^7*x^(10/3) + 70*a^4*b^6*x^3 + 189/2*a^5*b^5*x^(8/3) + 90*a^6*b^4*x^(7/3) + 60*a^7*b^3*x^2 + 27*a^8*b^2*x^(5/3) + 15/2*a^9*b*x^(4/3) + a^10*x","B",0
2329,1,109,0,0.188205," ","integrate((a+b*x^(1/3))^10/x,x, algorithm=""giac"")","\frac{3}{10} \, b^{10} x^{\frac{10}{3}} + \frac{10}{3} \, a b^{9} x^{3} + \frac{135}{8} \, a^{2} b^{8} x^{\frac{8}{3}} + \frac{360}{7} \, a^{3} b^{7} x^{\frac{7}{3}} + 105 \, a^{4} b^{6} x^{2} + \frac{756}{5} \, a^{5} b^{5} x^{\frac{5}{3}} + \frac{315}{2} \, a^{6} b^{4} x^{\frac{4}{3}} + 120 \, a^{7} b^{3} x + a^{10} \log\left({\left| x \right|}\right) + \frac{135}{2} \, a^{8} b^{2} x^{\frac{2}{3}} + 30 \, a^{9} b x^{\frac{1}{3}}"," ",0,"3/10*b^10*x^(10/3) + 10/3*a*b^9*x^3 + 135/8*a^2*b^8*x^(8/3) + 360/7*a^3*b^7*x^(7/3) + 105*a^4*b^6*x^2 + 756/5*a^5*b^5*x^(5/3) + 315/2*a^6*b^4*x^(4/3) + 120*a^7*b^3*x + a^10*log(abs(x)) + 135/2*a^8*b^2*x^(2/3) + 30*a^9*b*x^(1/3)","A",0
2330,1,111,0,0.162941," ","integrate((a+b*x^(1/3))^10/x^2,x, algorithm=""giac"")","\frac{3}{7} \, b^{10} x^{\frac{7}{3}} + 5 \, a b^{9} x^{2} + 27 \, a^{2} b^{8} x^{\frac{5}{3}} + 90 \, a^{3} b^{7} x^{\frac{4}{3}} + 210 \, a^{4} b^{6} x + 120 \, a^{7} b^{3} \log\left({\left| x \right|}\right) + 378 \, a^{5} b^{5} x^{\frac{2}{3}} + 630 \, a^{6} b^{4} x^{\frac{1}{3}} - \frac{135 \, a^{8} b^{2} x^{\frac{2}{3}} + 15 \, a^{9} b x^{\frac{1}{3}} + a^{10}}{x}"," ",0,"3/7*b^10*x^(7/3) + 5*a*b^9*x^2 + 27*a^2*b^8*x^(5/3) + 90*a^3*b^7*x^(4/3) + 210*a^4*b^6*x + 120*a^7*b^3*log(abs(x)) + 378*a^5*b^5*x^(2/3) + 630*a^6*b^4*x^(1/3) - (135*a^8*b^2*x^(2/3) + 15*a^9*b*x^(1/3) + a^10)/x","A",0
2331,1,111,0,0.196142," ","integrate((a+b*x^(1/3))^10/x^3,x, algorithm=""giac"")","\frac{3}{4} \, b^{10} x^{\frac{4}{3}} + 10 \, a b^{9} x + 210 \, a^{4} b^{6} \log\left({\left| x \right|}\right) + \frac{135}{2} \, a^{2} b^{8} x^{\frac{2}{3}} + 360 \, a^{3} b^{7} x^{\frac{1}{3}} - \frac{3024 \, a^{5} b^{5} x^{\frac{5}{3}} + 1260 \, a^{6} b^{4} x^{\frac{4}{3}} + 480 \, a^{7} b^{3} x + 135 \, a^{8} b^{2} x^{\frac{2}{3}} + 24 \, a^{9} b x^{\frac{1}{3}} + 2 \, a^{10}}{4 \, x^{2}}"," ",0,"3/4*b^10*x^(4/3) + 10*a*b^9*x + 210*a^4*b^6*log(abs(x)) + 135/2*a^2*b^8*x^(2/3) + 360*a^3*b^7*x^(1/3) - 1/4*(3024*a^5*b^5*x^(5/3) + 1260*a^6*b^4*x^(4/3) + 480*a^7*b^3*x + 135*a^8*b^2*x^(2/3) + 24*a^9*b*x^(1/3) + 2*a^10)/x^2","A",0
2332,1,113,0,0.167708," ","integrate((a+b*x^(1/3))^10/x^4,x, algorithm=""giac"")","10 \, a b^{9} \log\left({\left| x \right|}\right) + 3 \, b^{10} x^{\frac{1}{3}} - \frac{11340 \, a^{2} b^{8} x^{\frac{8}{3}} + 15120 \, a^{3} b^{7} x^{\frac{7}{3}} + 17640 \, a^{4} b^{6} x^{2} + 15876 \, a^{5} b^{5} x^{\frac{5}{3}} + 10584 \, a^{6} b^{4} x^{\frac{4}{3}} + 5040 \, a^{7} b^{3} x + 1620 \, a^{8} b^{2} x^{\frac{2}{3}} + 315 \, a^{9} b x^{\frac{1}{3}} + 28 \, a^{10}}{84 \, x^{3}}"," ",0,"10*a*b^9*log(abs(x)) + 3*b^10*x^(1/3) - 1/84*(11340*a^2*b^8*x^(8/3) + 15120*a^3*b^7*x^(7/3) + 17640*a^4*b^6*x^2 + 15876*a^5*b^5*x^(5/3) + 10584*a^6*b^4*x^(4/3) + 5040*a^7*b^3*x + 1620*a^8*b^2*x^(2/3) + 315*a^9*b*x^(1/3) + 28*a^10)/x^3","A",0
2333,1,112,0,0.181375," ","integrate((a+b*x^(1/3))^10/x^5,x, algorithm=""giac"")","-\frac{66 \, b^{10} x^{\frac{10}{3}} + 440 \, a b^{9} x^{3} + 1485 \, a^{2} b^{8} x^{\frac{8}{3}} + 3168 \, a^{3} b^{7} x^{\frac{7}{3}} + 4620 \, a^{4} b^{6} x^{2} + 4752 \, a^{5} b^{5} x^{\frac{5}{3}} + 3465 \, a^{6} b^{4} x^{\frac{4}{3}} + 1760 \, a^{7} b^{3} x + 594 \, a^{8} b^{2} x^{\frac{2}{3}} + 120 \, a^{9} b x^{\frac{1}{3}} + 11 \, a^{10}}{44 \, x^{4}}"," ",0,"-1/44*(66*b^10*x^(10/3) + 440*a*b^9*x^3 + 1485*a^2*b^8*x^(8/3) + 3168*a^3*b^7*x^(7/3) + 4620*a^4*b^6*x^2 + 4752*a^5*b^5*x^(5/3) + 3465*a^6*b^4*x^(4/3) + 1760*a^7*b^3*x + 594*a^8*b^2*x^(2/3) + 120*a^9*b*x^(1/3) + 11*a^10)/x^4","B",0
2334,1,112,0,0.190486," ","integrate((a+b*x^(1/3))^10/x^6,x, algorithm=""giac"")","-\frac{3003 \, b^{10} x^{\frac{10}{3}} + 25025 \, a b^{9} x^{3} + 96525 \, a^{2} b^{8} x^{\frac{8}{3}} + 225225 \, a^{3} b^{7} x^{\frac{7}{3}} + 350350 \, a^{4} b^{6} x^{2} + 378378 \, a^{5} b^{5} x^{\frac{5}{3}} + 286650 \, a^{6} b^{4} x^{\frac{4}{3}} + 150150 \, a^{7} b^{3} x + 51975 \, a^{8} b^{2} x^{\frac{2}{3}} + 10725 \, a^{9} b x^{\frac{1}{3}} + 1001 \, a^{10}}{5005 \, x^{5}}"," ",0,"-1/5005*(3003*b^10*x^(10/3) + 25025*a*b^9*x^3 + 96525*a^2*b^8*x^(8/3) + 225225*a^3*b^7*x^(7/3) + 350350*a^4*b^6*x^2 + 378378*a^5*b^5*x^(5/3) + 286650*a^6*b^4*x^(4/3) + 150150*a^7*b^3*x + 51975*a^8*b^2*x^(2/3) + 10725*a^9*b*x^(1/3) + 1001*a^10)/x^5","A",0
2335,1,112,0,0.173706," ","integrate((a+b*x^(1/3))^10/x^7,x, algorithm=""giac"")","-\frac{43758 \, b^{10} x^{\frac{10}{3}} + 388960 \, a b^{9} x^{3} + 1575288 \, a^{2} b^{8} x^{\frac{8}{3}} + 3818880 \, a^{3} b^{7} x^{\frac{7}{3}} + 6126120 \, a^{4} b^{6} x^{2} + 6785856 \, a^{5} b^{5} x^{\frac{5}{3}} + 5250960 \, a^{6} b^{4} x^{\frac{4}{3}} + 2800512 \, a^{7} b^{3} x + 984555 \, a^{8} b^{2} x^{\frac{2}{3}} + 205920 \, a^{9} b x^{\frac{1}{3}} + 19448 \, a^{10}}{116688 \, x^{6}}"," ",0,"-1/116688*(43758*b^10*x^(10/3) + 388960*a*b^9*x^3 + 1575288*a^2*b^8*x^(8/3) + 3818880*a^3*b^7*x^(7/3) + 6126120*a^4*b^6*x^2 + 6785856*a^5*b^5*x^(5/3) + 5250960*a^6*b^4*x^(4/3) + 2800512*a^7*b^3*x + 984555*a^8*b^2*x^(2/3) + 205920*a^9*b*x^(1/3) + 19448*a^10)/x^6","A",0
2336,1,112,0,0.171870," ","integrate((a+b*x^(1/3))^10/x^8,x, algorithm=""giac"")","-\frac{352716 \, b^{10} x^{\frac{10}{3}} + 3233230 \, a b^{9} x^{3} + 13430340 \, a^{2} b^{8} x^{\frac{8}{3}} + 33256080 \, a^{3} b^{7} x^{\frac{7}{3}} + 54318264 \, a^{4} b^{6} x^{2} + 61108047 \, a^{5} b^{5} x^{\frac{5}{3}} + 47927880 \, a^{6} b^{4} x^{\frac{4}{3}} + 25865840 \, a^{7} b^{3} x + 9189180 \, a^{8} b^{2} x^{\frac{2}{3}} + 1939938 \, a^{9} b x^{\frac{1}{3}} + 184756 \, a^{10}}{1293292 \, x^{7}}"," ",0,"-1/1293292*(352716*b^10*x^(10/3) + 3233230*a*b^9*x^3 + 13430340*a^2*b^8*x^(8/3) + 33256080*a^3*b^7*x^(7/3) + 54318264*a^4*b^6*x^2 + 61108047*a^5*b^5*x^(5/3) + 47927880*a^6*b^4*x^(4/3) + 25865840*a^7*b^3*x + 9189180*a^8*b^2*x^(2/3) + 1939938*a^9*b*x^(1/3) + 184756*a^10)/x^7","A",0
2337,1,112,0,0.167182," ","integrate((a+b*x^(1/3))^10/x^9,x, algorithm=""giac"")","-\frac{1961256 \, b^{10} x^{\frac{10}{3}} + 18305056 \, a b^{9} x^{3} + 77224455 \, a^{2} b^{8} x^{\frac{8}{3}} + 193818240 \, a^{3} b^{7} x^{\frac{7}{3}} + 320338480 \, a^{4} b^{6} x^{2} + 364174272 \, a^{5} b^{5} x^{\frac{5}{3}} + 288304632 \, a^{6} b^{4} x^{\frac{4}{3}} + 156900480 \, a^{7} b^{3} x + 56163240 \, a^{8} b^{2} x^{\frac{2}{3}} + 11938080 \, a^{9} b x^{\frac{1}{3}} + 1144066 \, a^{10}}{9152528 \, x^{8}}"," ",0,"-1/9152528*(1961256*b^10*x^(10/3) + 18305056*a*b^9*x^3 + 77224455*a^2*b^8*x^(8/3) + 193818240*a^3*b^7*x^(7/3) + 320338480*a^4*b^6*x^2 + 364174272*a^5*b^5*x^(5/3) + 288304632*a^6*b^4*x^(4/3) + 156900480*a^7*b^3*x + 56163240*a^8*b^2*x^(2/3) + 11938080*a^9*b*x^(1/3) + 1144066*a^10)/x^8","A",0
2338,1,112,0,0.197974," ","integrate((a+b*x^(1/3))^10/x^10,x, algorithm=""giac"")","-\frac{8436285 \, b^{10} x^{\frac{10}{3}} + 79676025 \, a b^{9} x^{3} + 339671475 \, a^{2} b^{8} x^{\frac{8}{3}} + 860501070 \, a^{3} b^{7} x^{\frac{7}{3}} + 1434168450 \, a^{4} b^{6} x^{2} + 1642774770 \, a^{5} b^{5} x^{\frac{5}{3}} + 1309458150 \, a^{6} b^{4} x^{\frac{4}{3}} + 717084225 \, a^{7} b^{3} x + 258150321 \, a^{8} b^{2} x^{\frac{2}{3}} + 55160325 \, a^{9} b x^{\frac{1}{3}} + 5311735 \, a^{10}}{47805615 \, x^{9}}"," ",0,"-1/47805615*(8436285*b^10*x^(10/3) + 79676025*a*b^9*x^3 + 339671475*a^2*b^8*x^(8/3) + 860501070*a^3*b^7*x^(7/3) + 1434168450*a^4*b^6*x^2 + 1642774770*a^5*b^5*x^(5/3) + 1309458150*a^6*b^4*x^(4/3) + 717084225*a^7*b^3*x + 258150321*a^8*b^2*x^(2/3) + 55160325*a^9*b*x^(1/3) + 5311735*a^10)/x^9","A",0
2339,1,167,0,0.167273," ","integrate((a+b*x^(1/3))^15*x^5,x, algorithm=""giac"")","\frac{1}{11} \, b^{15} x^{11} + \frac{45}{32} \, a b^{14} x^{\frac{32}{3}} + \frac{315}{31} \, a^{2} b^{13} x^{\frac{31}{3}} + \frac{91}{2} \, a^{3} b^{12} x^{10} + \frac{4095}{29} \, a^{4} b^{11} x^{\frac{29}{3}} + \frac{1287}{4} \, a^{5} b^{10} x^{\frac{28}{3}} + \frac{5005}{9} \, a^{6} b^{9} x^{9} + \frac{1485}{2} \, a^{7} b^{8} x^{\frac{26}{3}} + \frac{3861}{5} \, a^{8} b^{7} x^{\frac{25}{3}} + \frac{5005}{8} \, a^{9} b^{6} x^{8} + \frac{9009}{23} \, a^{10} b^{5} x^{\frac{23}{3}} + \frac{4095}{22} \, a^{11} b^{4} x^{\frac{22}{3}} + 65 \, a^{12} b^{3} x^{7} + \frac{63}{4} \, a^{13} b^{2} x^{\frac{20}{3}} + \frac{45}{19} \, a^{14} b x^{\frac{19}{3}} + \frac{1}{6} \, a^{15} x^{6}"," ",0,"1/11*b^15*x^11 + 45/32*a*b^14*x^(32/3) + 315/31*a^2*b^13*x^(31/3) + 91/2*a^3*b^12*x^10 + 4095/29*a^4*b^11*x^(29/3) + 1287/4*a^5*b^10*x^(28/3) + 5005/9*a^6*b^9*x^9 + 1485/2*a^7*b^8*x^(26/3) + 3861/5*a^8*b^7*x^(25/3) + 5005/8*a^9*b^6*x^8 + 9009/23*a^10*b^5*x^(23/3) + 4095/22*a^11*b^4*x^(22/3) + 65*a^12*b^3*x^7 + 63/4*a^13*b^2*x^(20/3) + 45/19*a^14*b*x^(19/3) + 1/6*a^15*x^6","A",0
2340,1,167,0,0.463100," ","integrate((a+b*x^(1/3))^15*x^4,x, algorithm=""giac"")","\frac{1}{10} \, b^{15} x^{10} + \frac{45}{29} \, a b^{14} x^{\frac{29}{3}} + \frac{45}{4} \, a^{2} b^{13} x^{\frac{28}{3}} + \frac{455}{9} \, a^{3} b^{12} x^{9} + \frac{315}{2} \, a^{4} b^{11} x^{\frac{26}{3}} + \frac{9009}{25} \, a^{5} b^{10} x^{\frac{25}{3}} + \frac{5005}{8} \, a^{6} b^{9} x^{8} + \frac{19305}{23} \, a^{7} b^{8} x^{\frac{23}{3}} + \frac{1755}{2} \, a^{8} b^{7} x^{\frac{22}{3}} + 715 \, a^{9} b^{6} x^{7} + \frac{9009}{20} \, a^{10} b^{5} x^{\frac{20}{3}} + \frac{4095}{19} \, a^{11} b^{4} x^{\frac{19}{3}} + \frac{455}{6} \, a^{12} b^{3} x^{6} + \frac{315}{17} \, a^{13} b^{2} x^{\frac{17}{3}} + \frac{45}{16} \, a^{14} b x^{\frac{16}{3}} + \frac{1}{5} \, a^{15} x^{5}"," ",0,"1/10*b^15*x^10 + 45/29*a*b^14*x^(29/3) + 45/4*a^2*b^13*x^(28/3) + 455/9*a^3*b^12*x^9 + 315/2*a^4*b^11*x^(26/3) + 9009/25*a^5*b^10*x^(25/3) + 5005/8*a^6*b^9*x^8 + 19305/23*a^7*b^8*x^(23/3) + 1755/2*a^8*b^7*x^(22/3) + 715*a^9*b^6*x^7 + 9009/20*a^10*b^5*x^(20/3) + 4095/19*a^11*b^4*x^(19/3) + 455/6*a^12*b^3*x^6 + 315/17*a^13*b^2*x^(17/3) + 45/16*a^14*b*x^(16/3) + 1/5*a^15*x^5","A",0
2341,1,167,0,0.189381," ","integrate((a+b*x^(1/3))^15*x^3,x, algorithm=""giac"")","\frac{1}{9} \, b^{15} x^{9} + \frac{45}{26} \, a b^{14} x^{\frac{26}{3}} + \frac{63}{5} \, a^{2} b^{13} x^{\frac{25}{3}} + \frac{455}{8} \, a^{3} b^{12} x^{8} + \frac{4095}{23} \, a^{4} b^{11} x^{\frac{23}{3}} + \frac{819}{2} \, a^{5} b^{10} x^{\frac{22}{3}} + 715 \, a^{6} b^{9} x^{7} + \frac{3861}{4} \, a^{7} b^{8} x^{\frac{20}{3}} + \frac{19305}{19} \, a^{8} b^{7} x^{\frac{19}{3}} + \frac{5005}{6} \, a^{9} b^{6} x^{6} + \frac{9009}{17} \, a^{10} b^{5} x^{\frac{17}{3}} + \frac{4095}{16} \, a^{11} b^{4} x^{\frac{16}{3}} + 91 \, a^{12} b^{3} x^{5} + \frac{45}{2} \, a^{13} b^{2} x^{\frac{14}{3}} + \frac{45}{13} \, a^{14} b x^{\frac{13}{3}} + \frac{1}{4} \, a^{15} x^{4}"," ",0,"1/9*b^15*x^9 + 45/26*a*b^14*x^(26/3) + 63/5*a^2*b^13*x^(25/3) + 455/8*a^3*b^12*x^8 + 4095/23*a^4*b^11*x^(23/3) + 819/2*a^5*b^10*x^(22/3) + 715*a^6*b^9*x^7 + 3861/4*a^7*b^8*x^(20/3) + 19305/19*a^8*b^7*x^(19/3) + 5005/6*a^9*b^6*x^6 + 9009/17*a^10*b^5*x^(17/3) + 4095/16*a^11*b^4*x^(16/3) + 91*a^12*b^3*x^5 + 45/2*a^13*b^2*x^(14/3) + 45/13*a^14*b*x^(13/3) + 1/4*a^15*x^4","A",0
2342,1,167,0,0.174217," ","integrate((a+b*x^(1/3))^15*x^2,x, algorithm=""giac"")","\frac{1}{8} \, b^{15} x^{8} + \frac{45}{23} \, a b^{14} x^{\frac{23}{3}} + \frac{315}{22} \, a^{2} b^{13} x^{\frac{22}{3}} + 65 \, a^{3} b^{12} x^{7} + \frac{819}{4} \, a^{4} b^{11} x^{\frac{20}{3}} + \frac{9009}{19} \, a^{5} b^{10} x^{\frac{19}{3}} + \frac{5005}{6} \, a^{6} b^{9} x^{6} + \frac{19305}{17} \, a^{7} b^{8} x^{\frac{17}{3}} + \frac{19305}{16} \, a^{8} b^{7} x^{\frac{16}{3}} + 1001 \, a^{9} b^{6} x^{5} + \frac{1287}{2} \, a^{10} b^{5} x^{\frac{14}{3}} + 315 \, a^{11} b^{4} x^{\frac{13}{3}} + \frac{455}{4} \, a^{12} b^{3} x^{4} + \frac{315}{11} \, a^{13} b^{2} x^{\frac{11}{3}} + \frac{9}{2} \, a^{14} b x^{\frac{10}{3}} + \frac{1}{3} \, a^{15} x^{3}"," ",0,"1/8*b^15*x^8 + 45/23*a*b^14*x^(23/3) + 315/22*a^2*b^13*x^(22/3) + 65*a^3*b^12*x^7 + 819/4*a^4*b^11*x^(20/3) + 9009/19*a^5*b^10*x^(19/3) + 5005/6*a^6*b^9*x^6 + 19305/17*a^7*b^8*x^(17/3) + 19305/16*a^8*b^7*x^(16/3) + 1001*a^9*b^6*x^5 + 1287/2*a^10*b^5*x^(14/3) + 315*a^11*b^4*x^(13/3) + 455/4*a^12*b^3*x^4 + 315/11*a^13*b^2*x^(11/3) + 9/2*a^14*b*x^(10/3) + 1/3*a^15*x^3","A",0
2343,1,167,0,0.177891," ","integrate((a+b*x^(1/3))^15*x,x, algorithm=""giac"")","\frac{1}{7} \, b^{15} x^{7} + \frac{9}{4} \, a b^{14} x^{\frac{20}{3}} + \frac{315}{19} \, a^{2} b^{13} x^{\frac{19}{3}} + \frac{455}{6} \, a^{3} b^{12} x^{6} + \frac{4095}{17} \, a^{4} b^{11} x^{\frac{17}{3}} + \frac{9009}{16} \, a^{5} b^{10} x^{\frac{16}{3}} + 1001 \, a^{6} b^{9} x^{5} + \frac{19305}{14} \, a^{7} b^{8} x^{\frac{14}{3}} + 1485 \, a^{8} b^{7} x^{\frac{13}{3}} + \frac{5005}{4} \, a^{9} b^{6} x^{4} + 819 \, a^{10} b^{5} x^{\frac{11}{3}} + \frac{819}{2} \, a^{11} b^{4} x^{\frac{10}{3}} + \frac{455}{3} \, a^{12} b^{3} x^{3} + \frac{315}{8} \, a^{13} b^{2} x^{\frac{8}{3}} + \frac{45}{7} \, a^{14} b x^{\frac{7}{3}} + \frac{1}{2} \, a^{15} x^{2}"," ",0,"1/7*b^15*x^7 + 9/4*a*b^14*x^(20/3) + 315/19*a^2*b^13*x^(19/3) + 455/6*a^3*b^12*x^6 + 4095/17*a^4*b^11*x^(17/3) + 9009/16*a^5*b^10*x^(16/3) + 1001*a^6*b^9*x^5 + 19305/14*a^7*b^8*x^(14/3) + 1485*a^8*b^7*x^(13/3) + 5005/4*a^9*b^6*x^4 + 819*a^10*b^5*x^(11/3) + 819/2*a^11*b^4*x^(10/3) + 455/3*a^12*b^3*x^3 + 315/8*a^13*b^2*x^(8/3) + 45/7*a^14*b*x^(7/3) + 1/2*a^15*x^2","A",0
2344,1,164,0,0.174328," ","integrate((a+b*x^(1/3))^15,x, algorithm=""giac"")","\frac{1}{6} \, b^{15} x^{6} + \frac{45}{17} \, a b^{14} x^{\frac{17}{3}} + \frac{315}{16} \, a^{2} b^{13} x^{\frac{16}{3}} + 91 \, a^{3} b^{12} x^{5} + \frac{585}{2} \, a^{4} b^{11} x^{\frac{14}{3}} + 693 \, a^{5} b^{10} x^{\frac{13}{3}} + \frac{5005}{4} \, a^{6} b^{9} x^{4} + 1755 \, a^{7} b^{8} x^{\frac{11}{3}} + \frac{3861}{2} \, a^{8} b^{7} x^{\frac{10}{3}} + \frac{5005}{3} \, a^{9} b^{6} x^{3} + \frac{9009}{8} \, a^{10} b^{5} x^{\frac{8}{3}} + 585 \, a^{11} b^{4} x^{\frac{7}{3}} + \frac{455}{2} \, a^{12} b^{3} x^{2} + 63 \, a^{13} b^{2} x^{\frac{5}{3}} + \frac{45}{4} \, a^{14} b x^{\frac{4}{3}} + a^{15} x"," ",0,"1/6*b^15*x^6 + 45/17*a*b^14*x^(17/3) + 315/16*a^2*b^13*x^(16/3) + 91*a^3*b^12*x^5 + 585/2*a^4*b^11*x^(14/3) + 693*a^5*b^10*x^(13/3) + 5005/4*a^6*b^9*x^4 + 1755*a^7*b^8*x^(11/3) + 3861/2*a^8*b^7*x^(10/3) + 5005/3*a^9*b^6*x^3 + 9009/8*a^10*b^5*x^(8/3) + 585*a^11*b^4*x^(7/3) + 455/2*a^12*b^3*x^2 + 63*a^13*b^2*x^(5/3) + 45/4*a^14*b*x^(4/3) + a^15*x","B",0
2345,1,164,0,0.212560," ","integrate((a+b*x^(1/3))^15/x,x, algorithm=""giac"")","\frac{1}{5} \, b^{15} x^{5} + \frac{45}{14} \, a b^{14} x^{\frac{14}{3}} + \frac{315}{13} \, a^{2} b^{13} x^{\frac{13}{3}} + \frac{455}{4} \, a^{3} b^{12} x^{4} + \frac{4095}{11} \, a^{4} b^{11} x^{\frac{11}{3}} + \frac{9009}{10} \, a^{5} b^{10} x^{\frac{10}{3}} + \frac{5005}{3} \, a^{6} b^{9} x^{3} + \frac{19305}{8} \, a^{7} b^{8} x^{\frac{8}{3}} + \frac{19305}{7} \, a^{8} b^{7} x^{\frac{7}{3}} + \frac{5005}{2} \, a^{9} b^{6} x^{2} + \frac{9009}{5} \, a^{10} b^{5} x^{\frac{5}{3}} + \frac{4095}{4} \, a^{11} b^{4} x^{\frac{4}{3}} + 455 \, a^{12} b^{3} x + a^{15} \log\left({\left| x \right|}\right) + \frac{315}{2} \, a^{13} b^{2} x^{\frac{2}{3}} + 45 \, a^{14} b x^{\frac{1}{3}}"," ",0,"1/5*b^15*x^5 + 45/14*a*b^14*x^(14/3) + 315/13*a^2*b^13*x^(13/3) + 455/4*a^3*b^12*x^4 + 4095/11*a^4*b^11*x^(11/3) + 9009/10*a^5*b^10*x^(10/3) + 5005/3*a^6*b^9*x^3 + 19305/8*a^7*b^8*x^(8/3) + 19305/7*a^8*b^7*x^(7/3) + 5005/2*a^9*b^6*x^2 + 9009/5*a^10*b^5*x^(5/3) + 4095/4*a^11*b^4*x^(4/3) + 455*a^12*b^3*x + a^15*log(abs(x)) + 315/2*a^13*b^2*x^(2/3) + 45*a^14*b*x^(1/3)","A",0
2346,1,168,0,0.180615," ","integrate((a+b*x^(1/3))^15/x^2,x, algorithm=""giac"")","\frac{1}{4} \, b^{15} x^{4} + \frac{45}{11} \, a b^{14} x^{\frac{11}{3}} + \frac{63}{2} \, a^{2} b^{13} x^{\frac{10}{3}} + \frac{455}{3} \, a^{3} b^{12} x^{3} + \frac{4095}{8} \, a^{4} b^{11} x^{\frac{8}{3}} + 1287 \, a^{5} b^{10} x^{\frac{7}{3}} + \frac{5005}{2} \, a^{6} b^{9} x^{2} + 3861 \, a^{7} b^{8} x^{\frac{5}{3}} + \frac{19305}{4} \, a^{8} b^{7} x^{\frac{4}{3}} + 5005 \, a^{9} b^{6} x + 455 \, a^{12} b^{3} \log\left({\left| x \right|}\right) + \frac{9009}{2} \, a^{10} b^{5} x^{\frac{2}{3}} + 4095 \, a^{11} b^{4} x^{\frac{1}{3}} - \frac{630 \, a^{13} b^{2} x^{\frac{2}{3}} + 45 \, a^{14} b x^{\frac{1}{3}} + 2 \, a^{15}}{2 \, x}"," ",0,"1/4*b^15*x^4 + 45/11*a*b^14*x^(11/3) + 63/2*a^2*b^13*x^(10/3) + 455/3*a^3*b^12*x^3 + 4095/8*a^4*b^11*x^(8/3) + 1287*a^5*b^10*x^(7/3) + 5005/2*a^6*b^9*x^2 + 3861*a^7*b^8*x^(5/3) + 19305/4*a^8*b^7*x^(4/3) + 5005*a^9*b^6*x + 455*a^12*b^3*log(abs(x)) + 9009/2*a^10*b^5*x^(2/3) + 4095*a^11*b^4*x^(1/3) - 1/2*(630*a^13*b^2*x^(2/3) + 45*a^14*b*x^(1/3) + 2*a^15)/x","A",0
2347,1,166,0,0.189487," ","integrate((a+b*x^(1/3))^15/x^3,x, algorithm=""giac"")","\frac{1}{3} \, b^{15} x^{3} + \frac{45}{8} \, a b^{14} x^{\frac{8}{3}} + 45 \, a^{2} b^{13} x^{\frac{7}{3}} + \frac{455}{2} \, a^{3} b^{12} x^{2} + 819 \, a^{4} b^{11} x^{\frac{5}{3}} + \frac{9009}{4} \, a^{5} b^{10} x^{\frac{4}{3}} + 5005 \, a^{6} b^{9} x + 5005 \, a^{9} b^{6} \log\left({\left| x \right|}\right) + \frac{19305}{2} \, a^{7} b^{8} x^{\frac{2}{3}} + 19305 \, a^{8} b^{7} x^{\frac{1}{3}} - \frac{36036 \, a^{10} b^{5} x^{\frac{5}{3}} + 8190 \, a^{11} b^{4} x^{\frac{4}{3}} + 1820 \, a^{12} b^{3} x + 315 \, a^{13} b^{2} x^{\frac{2}{3}} + 36 \, a^{14} b x^{\frac{1}{3}} + 2 \, a^{15}}{4 \, x^{2}}"," ",0,"1/3*b^15*x^3 + 45/8*a*b^14*x^(8/3) + 45*a^2*b^13*x^(7/3) + 455/2*a^3*b^12*x^2 + 819*a^4*b^11*x^(5/3) + 9009/4*a^5*b^10*x^(4/3) + 5005*a^6*b^9*x + 5005*a^9*b^6*log(abs(x)) + 19305/2*a^7*b^8*x^(2/3) + 19305*a^8*b^7*x^(1/3) - 1/4*(36036*a^10*b^5*x^(5/3) + 8190*a^11*b^4*x^(4/3) + 1820*a^12*b^3*x + 315*a^13*b^2*x^(2/3) + 36*a^14*b*x^(1/3) + 2*a^15)/x^2","A",0
2348,1,166,0,0.203022," ","integrate((a+b*x^(1/3))^15/x^4,x, algorithm=""giac"")","\frac{1}{2} \, b^{15} x^{2} + 9 \, a b^{14} x^{\frac{5}{3}} + \frac{315}{4} \, a^{2} b^{13} x^{\frac{4}{3}} + 455 \, a^{3} b^{12} x + 5005 \, a^{6} b^{9} \log\left({\left| x \right|}\right) + \frac{4095}{2} \, a^{4} b^{11} x^{\frac{2}{3}} + 9009 \, a^{5} b^{10} x^{\frac{1}{3}} - \frac{463320 \, a^{7} b^{8} x^{\frac{8}{3}} + 231660 \, a^{8} b^{7} x^{\frac{7}{3}} + 120120 \, a^{9} b^{6} x^{2} + 54054 \, a^{10} b^{5} x^{\frac{5}{3}} + 19656 \, a^{11} b^{4} x^{\frac{4}{3}} + 5460 \, a^{12} b^{3} x + 1080 \, a^{13} b^{2} x^{\frac{2}{3}} + 135 \, a^{14} b x^{\frac{1}{3}} + 8 \, a^{15}}{24 \, x^{3}}"," ",0,"1/2*b^15*x^2 + 9*a*b^14*x^(5/3) + 315/4*a^2*b^13*x^(4/3) + 455*a^3*b^12*x + 5005*a^6*b^9*log(abs(x)) + 4095/2*a^4*b^11*x^(2/3) + 9009*a^5*b^10*x^(1/3) - 1/24*(463320*a^7*b^8*x^(8/3) + 231660*a^8*b^7*x^(7/3) + 120120*a^9*b^6*x^2 + 54054*a^10*b^5*x^(5/3) + 19656*a^11*b^4*x^(4/3) + 5460*a^12*b^3*x + 1080*a^13*b^2*x^(2/3) + 135*a^14*b*x^(1/3) + 8*a^15)/x^3","A",0
2349,1,167,0,0.184322," ","integrate((a+b*x^(1/3))^15/x^6,x, algorithm=""giac"")","b^{15} \log\left({\left| x \right|}\right) - \frac{5405400 \, a b^{14} x^{\frac{14}{3}} + 18918900 \, a^{2} b^{13} x^{\frac{13}{3}} + 54654600 \, a^{3} b^{12} x^{4} + 122972850 \, a^{4} b^{11} x^{\frac{11}{3}} + 216432216 \, a^{5} b^{10} x^{\frac{10}{3}} + 300600300 \, a^{6} b^{9} x^{3} + 331273800 \, a^{7} b^{8} x^{\frac{8}{3}} + 289864575 \, a^{8} b^{7} x^{\frac{7}{3}} + 200400200 \, a^{9} b^{6} x^{2} + 108216108 \, a^{10} b^{5} x^{\frac{5}{3}} + 44717400 \, a^{11} b^{4} x^{\frac{4}{3}} + 13663650 \, a^{12} b^{3} x + 2910600 \, a^{13} b^{2} x^{\frac{2}{3}} + 386100 \, a^{14} b x^{\frac{1}{3}} + 24024 \, a^{15}}{120120 \, x^{5}}"," ",0,"b^15*log(abs(x)) - 1/120120*(5405400*a*b^14*x^(14/3) + 18918900*a^2*b^13*x^(13/3) + 54654600*a^3*b^12*x^4 + 122972850*a^4*b^11*x^(11/3) + 216432216*a^5*b^10*x^(10/3) + 300600300*a^6*b^9*x^3 + 331273800*a^7*b^8*x^(8/3) + 289864575*a^8*b^7*x^(7/3) + 200400200*a^9*b^6*x^2 + 108216108*a^10*b^5*x^(5/3) + 44717400*a^11*b^4*x^(4/3) + 13663650*a^12*b^3*x + 2910600*a^13*b^2*x^(2/3) + 386100*a^14*b*x^(1/3) + 24024*a^15)/x^5","A",0
2350,1,167,0,0.180315," ","integrate((a+b*x^(1/3))^15/x^7,x, algorithm=""giac"")","-\frac{816 \, b^{15} x^{5} + 9180 \, a b^{14} x^{\frac{14}{3}} + 51408 \, a^{2} b^{13} x^{\frac{13}{3}} + 185640 \, a^{3} b^{12} x^{4} + 477360 \, a^{4} b^{11} x^{\frac{11}{3}} + 918918 \, a^{5} b^{10} x^{\frac{10}{3}} + 1361360 \, a^{6} b^{9} x^{3} + 1575288 \, a^{7} b^{8} x^{\frac{8}{3}} + 1432080 \, a^{8} b^{7} x^{\frac{7}{3}} + 1021020 \, a^{9} b^{6} x^{2} + 565488 \, a^{10} b^{5} x^{\frac{5}{3}} + 238680 \, a^{11} b^{4} x^{\frac{4}{3}} + 74256 \, a^{12} b^{3} x + 16065 \, a^{13} b^{2} x^{\frac{2}{3}} + 2160 \, a^{14} b x^{\frac{1}{3}} + 136 \, a^{15}}{816 \, x^{6}}"," ",0,"-1/816*(816*b^15*x^5 + 9180*a*b^14*x^(14/3) + 51408*a^2*b^13*x^(13/3) + 185640*a^3*b^12*x^4 + 477360*a^4*b^11*x^(11/3) + 918918*a^5*b^10*x^(10/3) + 1361360*a^6*b^9*x^3 + 1575288*a^7*b^8*x^(8/3) + 1432080*a^8*b^7*x^(7/3) + 1021020*a^9*b^6*x^2 + 565488*a^10*b^5*x^(5/3) + 238680*a^11*b^4*x^(4/3) + 74256*a^12*b^3*x + 16065*a^13*b^2*x^(2/3) + 2160*a^14*b*x^(1/3) + 136*a^15)/x^6","B",0
2351,1,167,0,0.182819," ","integrate((a+b*x^(1/3))^15/x^8,x, algorithm=""giac"")","-\frac{54264 \, b^{15} x^{5} + 697680 \, a b^{14} x^{\frac{14}{3}} + 4273290 \, a^{2} b^{13} x^{\frac{13}{3}} + 16460080 \, a^{3} b^{12} x^{4} + 44442216 \, a^{4} b^{11} x^{\frac{11}{3}} + 88884432 \, a^{5} b^{10} x^{\frac{10}{3}} + 135795660 \, a^{6} b^{9} x^{3} + 161164080 \, a^{7} b^{8} x^{\frac{8}{3}} + 149652360 \, a^{8} b^{7} x^{\frac{7}{3}} + 108636528 \, a^{9} b^{6} x^{2} + 61108047 \, a^{10} b^{5} x^{\frac{5}{3}} + 26142480 \, a^{11} b^{4} x^{\frac{4}{3}} + 8230040 \, a^{12} b^{3} x + 1799280 \, a^{13} b^{2} x^{\frac{2}{3}} + 244188 \, a^{14} b x^{\frac{1}{3}} + 15504 \, a^{15}}{108528 \, x^{7}}"," ",0,"-1/108528*(54264*b^15*x^5 + 697680*a*b^14*x^(14/3) + 4273290*a^2*b^13*x^(13/3) + 16460080*a^3*b^12*x^4 + 44442216*a^4*b^11*x^(11/3) + 88884432*a^5*b^10*x^(10/3) + 135795660*a^6*b^9*x^3 + 161164080*a^7*b^8*x^(8/3) + 149652360*a^8*b^7*x^(7/3) + 108636528*a^9*b^6*x^2 + 61108047*a^10*b^5*x^(5/3) + 26142480*a^11*b^4*x^(4/3) + 8230040*a^12*b^3*x + 1799280*a^13*b^2*x^(2/3) + 244188*a^14*b*x^(1/3) + 15504*a^15)/x^7","A",0
2352,1,167,0,0.183353," ","integrate((a+b*x^(1/3))^15/x^9,x, algorithm=""giac"")","-\frac{1307504 \, b^{15} x^{5} + 17651304 \, a b^{14} x^{\frac{14}{3}} + 112326480 \, a^{2} b^{13} x^{\frac{13}{3}} + 446185740 \, a^{3} b^{12} x^{4} + 1235591280 \, a^{4} b^{11} x^{\frac{11}{3}} + 2524136472 \, a^{5} b^{10} x^{\frac{10}{3}} + 3926434512 \, a^{6} b^{9} x^{3} + 4732755885 \, a^{7} b^{8} x^{\frac{8}{3}} + 4454358480 \, a^{8} b^{7} x^{\frac{7}{3}} + 3272028760 \, a^{9} b^{6} x^{2} + 1859890032 \, a^{10} b^{5} x^{\frac{5}{3}} + 803134332 \, a^{11} b^{4} x^{\frac{4}{3}} + 254963280 \, a^{12} b^{3} x + 56163240 \, a^{13} b^{2} x^{\frac{2}{3}} + 7674480 \, a^{14} b x^{\frac{1}{3}} + 490314 \, a^{15}}{3922512 \, x^{8}}"," ",0,"-1/3922512*(1307504*b^15*x^5 + 17651304*a*b^14*x^(14/3) + 112326480*a^2*b^13*x^(13/3) + 446185740*a^3*b^12*x^4 + 1235591280*a^4*b^11*x^(11/3) + 2524136472*a^5*b^10*x^(10/3) + 3926434512*a^6*b^9*x^3 + 4732755885*a^7*b^8*x^(8/3) + 4454358480*a^8*b^7*x^(7/3) + 3272028760*a^9*b^6*x^2 + 1859890032*a^10*b^5*x^(5/3) + 803134332*a^11*b^4*x^(4/3) + 254963280*a^12*b^3*x + 56163240*a^13*b^2*x^(2/3) + 7674480*a^14*b*x^(1/3) + 490314*a^15)/x^8","A",0
2353,1,167,0,0.181340," ","integrate((a+b*x^(1/3))^15/x^10,x, algorithm=""giac"")","-\frac{17383860 \, b^{15} x^{5} + 240699600 \, a b^{14} x^{\frac{14}{3}} + 1564547400 \, a^{2} b^{13} x^{\frac{13}{3}} + 6327725040 \, a^{3} b^{12} x^{4} + 17796726675 \, a^{4} b^{11} x^{\frac{11}{3}} + 36849692880 \, a^{5} b^{10} x^{\frac{10}{3}} + 58004146200 \, a^{6} b^{9} x^{3} + 70651666800 \, a^{7} b^{8} x^{\frac{8}{3}} + 67119083460 \, a^{8} b^{7} x^{\frac{7}{3}} + 49717839600 \, a^{9} b^{6} x^{2} + 28474762680 \, a^{10} b^{5} x^{\frac{5}{3}} + 12380331600 \, a^{11} b^{4} x^{\frac{4}{3}} + 3954828150 \, a^{12} b^{3} x + 876146544 \, a^{13} b^{2} x^{\frac{2}{3}} + 120349800 \, a^{14} b x^{\frac{1}{3}} + 7726160 \, a^{15}}{69535440 \, x^{9}}"," ",0,"-1/69535440*(17383860*b^15*x^5 + 240699600*a*b^14*x^(14/3) + 1564547400*a^2*b^13*x^(13/3) + 6327725040*a^3*b^12*x^4 + 17796726675*a^4*b^11*x^(11/3) + 36849692880*a^5*b^10*x^(10/3) + 58004146200*a^6*b^9*x^3 + 70651666800*a^7*b^8*x^(8/3) + 67119083460*a^8*b^7*x^(7/3) + 49717839600*a^9*b^6*x^2 + 28474762680*a^10*b^5*x^(5/3) + 12380331600*a^11*b^4*x^(4/3) + 3954828150*a^12*b^3*x + 876146544*a^13*b^2*x^(2/3) + 120349800*a^14*b*x^(1/3) + 7726160*a^15)/x^9","A",0
2354,1,167,0,0.178801," ","integrate((a+b*x^(1/3))^15/x^11,x, algorithm=""giac"")","-\frac{155117520 \, b^{15} x^{5} + 2181340125 \, a b^{14} x^{\frac{14}{3}} + 14371182000 \, a^{2} b^{13} x^{\frac{13}{3}} + 58815393000 \, a^{3} b^{12} x^{4} + 167159538000 \, a^{4} b^{11} x^{\frac{11}{3}} + 349363434420 \, a^{5} b^{10} x^{\frac{10}{3}} + 554545134000 \, a^{6} b^{9} x^{3} + 680578119000 \, a^{7} b^{8} x^{\frac{8}{3}} + 650987766000 \, a^{8} b^{7} x^{\frac{7}{3}} + 485226992250 \, a^{9} b^{6} x^{2} + 279490747536 \, a^{10} b^{5} x^{\frac{5}{3}} + 122155047000 \, a^{11} b^{4} x^{\frac{4}{3}} + 39210262000 \, a^{12} b^{3} x + 8725360500 \, a^{13} b^{2} x^{\frac{2}{3}} + 1203498000 \, a^{14} b x^{\frac{1}{3}} + 77558760 \, a^{15}}{775587600 \, x^{10}}"," ",0,"-1/775587600*(155117520*b^15*x^5 + 2181340125*a*b^14*x^(14/3) + 14371182000*a^2*b^13*x^(13/3) + 58815393000*a^3*b^12*x^4 + 167159538000*a^4*b^11*x^(11/3) + 349363434420*a^5*b^10*x^(10/3) + 554545134000*a^6*b^9*x^3 + 680578119000*a^7*b^8*x^(8/3) + 650987766000*a^8*b^7*x^(7/3) + 485226992250*a^9*b^6*x^2 + 279490747536*a^10*b^5*x^(5/3) + 122155047000*a^11*b^4*x^(4/3) + 39210262000*a^12*b^3*x + 8725360500*a^13*b^2*x^(2/3) + 1203498000*a^14*b*x^(1/3) + 77558760*a^15)/x^10","A",0
2355,1,167,0,0.202779," ","integrate((a+b*x^(1/3))^15/x^12,x, algorithm=""giac"")","-\frac{1037158320 \, b^{15} x^{5} + 14738565600 \, a b^{14} x^{\frac{14}{3}} + 98011461240 \, a^{2} b^{13} x^{\frac{13}{3}} + 404491744800 \, a^{3} b^{12} x^{4} + 1158317269200 \, a^{4} b^{11} x^{\frac{11}{3}} + 2437502427360 \, a^{5} b^{10} x^{\frac{10}{3}} + 3893233043700 \, a^{6} b^{9} x^{3} + 4805361928224 \, a^{7} b^{8} x^{\frac{8}{3}} + 4620540315600 \, a^{8} b^{7} x^{\frac{7}{3}} + 3460651594400 \, a^{9} b^{6} x^{2} + 2002234136760 \, a^{10} b^{5} x^{\frac{5}{3}} + 878723445600 \, a^{11} b^{4} x^{\frac{4}{3}} + 283144221360 \, a^{12} b^{3} x + 63233200800 \, a^{13} b^{2} x^{\frac{2}{3}} + 8751023325 \, a^{14} b x^{\frac{1}{3}} + 565722720 \, a^{15}}{6222949920 \, x^{11}}"," ",0,"-1/6222949920*(1037158320*b^15*x^5 + 14738565600*a*b^14*x^(14/3) + 98011461240*a^2*b^13*x^(13/3) + 404491744800*a^3*b^12*x^4 + 1158317269200*a^4*b^11*x^(11/3) + 2437502427360*a^5*b^10*x^(10/3) + 3893233043700*a^6*b^9*x^3 + 4805361928224*a^7*b^8*x^(8/3) + 4620540315600*a^8*b^7*x^(7/3) + 3460651594400*a^9*b^6*x^2 + 2002234136760*a^10*b^5*x^(5/3) + 878723445600*a^11*b^4*x^(4/3) + 283144221360*a^12*b^3*x + 63233200800*a^13*b^2*x^(2/3) + 8751023325*a^14*b*x^(1/3) + 565722720*a^15)/x^11","A",0
2356,1,133,0,0.186192," ","integrate(x^3/(a+b*x^(1/3)),x, algorithm=""giac"")","-\frac{3 \, a^{11} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{12}} + \frac{2520 \, b^{10} x^{\frac{11}{3}} - 2772 \, a b^{9} x^{\frac{10}{3}} + 3080 \, a^{2} b^{8} x^{3} - 3465 \, a^{3} b^{7} x^{\frac{8}{3}} + 3960 \, a^{4} b^{6} x^{\frac{7}{3}} - 4620 \, a^{5} b^{5} x^{2} + 5544 \, a^{6} b^{4} x^{\frac{5}{3}} - 6930 \, a^{7} b^{3} x^{\frac{4}{3}} + 9240 \, a^{8} b^{2} x - 13860 \, a^{9} b x^{\frac{2}{3}} + 27720 \, a^{10} x^{\frac{1}{3}}}{9240 \, b^{11}}"," ",0,"-3*a^11*log(abs(b*x^(1/3) + a))/b^12 + 1/9240*(2520*b^10*x^(11/3) - 2772*a*b^9*x^(10/3) + 3080*a^2*b^8*x^3 - 3465*a^3*b^7*x^(8/3) + 3960*a^4*b^6*x^(7/3) - 4620*a^5*b^5*x^2 + 5544*a^6*b^4*x^(5/3) - 6930*a^7*b^3*x^(4/3) + 9240*a^8*b^2*x - 13860*a^9*b*x^(2/3) + 27720*a^10*x^(1/3))/b^11","A",0
2357,1,100,0,0.161464," ","integrate(x^2/(a+b*x^(1/3)),x, algorithm=""giac"")","\frac{3 \, a^{8} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{9}} + \frac{105 \, b^{7} x^{\frac{8}{3}} - 120 \, a b^{6} x^{\frac{7}{3}} + 140 \, a^{2} b^{5} x^{2} - 168 \, a^{3} b^{4} x^{\frac{5}{3}} + 210 \, a^{4} b^{3} x^{\frac{4}{3}} - 280 \, a^{5} b^{2} x + 420 \, a^{6} b x^{\frac{2}{3}} - 840 \, a^{7} x^{\frac{1}{3}}}{280 \, b^{8}}"," ",0,"3*a^8*log(abs(b*x^(1/3) + a))/b^9 + 1/280*(105*b^7*x^(8/3) - 120*a*b^6*x^(7/3) + 140*a^2*b^5*x^2 - 168*a^3*b^4*x^(5/3) + 210*a^4*b^3*x^(4/3) - 280*a^5*b^2*x + 420*a^6*b*x^(2/3) - 840*a^7*x^(1/3))/b^8","A",0
2358,1,67,0,0.208000," ","integrate(x/(a+b*x^(1/3)),x, algorithm=""giac"")","-\frac{3 \, a^{5} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{6}} + \frac{12 \, b^{4} x^{\frac{5}{3}} - 15 \, a b^{3} x^{\frac{4}{3}} + 20 \, a^{2} b^{2} x - 30 \, a^{3} b x^{\frac{2}{3}} + 60 \, a^{4} x^{\frac{1}{3}}}{20 \, b^{5}}"," ",0,"-3*a^5*log(abs(b*x^(1/3) + a))/b^6 + 1/20*(12*b^4*x^(5/3) - 15*a*b^3*x^(4/3) + 20*a^2*b^2*x - 30*a^3*b*x^(2/3) + 60*a^4*x^(1/3))/b^5","A",0
2359,1,35,0,0.161143," ","integrate(1/(a+b*x^(1/3)),x, algorithm=""giac"")","\frac{3 \, a^{2} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{3}} + \frac{3 \, {\left(b x^{\frac{2}{3}} - 2 \, a x^{\frac{1}{3}}\right)}}{2 \, b^{2}}"," ",0,"3*a^2*log(abs(b*x^(1/3) + a))/b^3 + 3/2*(b*x^(2/3) - 2*a*x^(1/3))/b^2","A",0
2360,1,22,0,0.202745," ","integrate(1/(a+b*x^(1/3))/x,x, algorithm=""giac"")","-\frac{3 \, \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a} + \frac{\log\left({\left| x \right|}\right)}{a}"," ",0,"-3*log(abs(b*x^(1/3) + a))/a + log(abs(x))/a","A",0
2361,1,61,0,0.155769," ","integrate(1/(a+b*x^(1/3))/x^2,x, algorithm=""giac"")","\frac{3 \, b^{3} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a^{4}} - \frac{b^{3} \log\left({\left| x \right|}\right)}{a^{4}} - \frac{6 \, a b^{2} x^{\frac{2}{3}} - 3 \, a^{2} b x^{\frac{1}{3}} + 2 \, a^{3}}{2 \, a^{4} x}"," ",0,"3*b^3*log(abs(b*x^(1/3) + a))/a^4 - b^3*log(abs(x))/a^4 - 1/2*(6*a*b^2*x^(2/3) - 3*a^2*b*x^(1/3) + 2*a^3)/(a^4*x)","A",0
2362,1,91,0,0.156563," ","integrate(1/(a+b*x^(1/3))/x^3,x, algorithm=""giac"")","-\frac{3 \, b^{6} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a^{7}} + \frac{b^{6} \log\left({\left| x \right|}\right)}{a^{7}} + \frac{60 \, a b^{5} x^{\frac{5}{3}} - 30 \, a^{2} b^{4} x^{\frac{4}{3}} + 20 \, a^{3} b^{3} x - 15 \, a^{4} b^{2} x^{\frac{2}{3}} + 12 \, a^{5} b x^{\frac{1}{3}} - 10 \, a^{6}}{20 \, a^{7} x^{2}}"," ",0,"-3*b^6*log(abs(b*x^(1/3) + a))/a^7 + b^6*log(abs(x))/a^7 + 1/20*(60*a*b^5*x^(5/3) - 30*a^2*b^4*x^(4/3) + 20*a^3*b^3*x - 15*a^4*b^2*x^(2/3) + 12*a^5*b*x^(1/3) - 10*a^6)/(a^7*x^2)","A",0
2363,1,125,0,0.172991," ","integrate(1/(a+b*x^(1/3))/x^4,x, algorithm=""giac"")","\frac{3 \, b^{9} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a^{10}} - \frac{b^{9} \log\left({\left| x \right|}\right)}{a^{10}} - \frac{2520 \, a b^{8} x^{\frac{8}{3}} - 1260 \, a^{2} b^{7} x^{\frac{7}{3}} + 840 \, a^{3} b^{6} x^{2} - 630 \, a^{4} b^{5} x^{\frac{5}{3}} + 504 \, a^{5} b^{4} x^{\frac{4}{3}} - 420 \, a^{6} b^{3} x + 360 \, a^{7} b^{2} x^{\frac{2}{3}} - 315 \, a^{8} b x^{\frac{1}{3}} + 280 \, a^{9}}{840 \, a^{10} x^{3}}"," ",0,"3*b^9*log(abs(b*x^(1/3) + a))/a^10 - b^9*log(abs(x))/a^10 - 1/840*(2520*a*b^8*x^(8/3) - 1260*a^2*b^7*x^(7/3) + 840*a^3*b^6*x^2 - 630*a^4*b^5*x^(5/3) + 504*a^5*b^4*x^(4/3) - 420*a^6*b^3*x + 360*a^7*b^2*x^(2/3) - 315*a^8*b*x^(1/3) + 280*a^9)/(a^10*x^3)","A",0
2364,1,17,0,0.157195," ","integrate(1/(2+b*x^(1/3))/x,x, algorithm=""giac"")","-\frac{3}{2} \, \log\left({\left| b x^{\frac{1}{3}} + 2 \right|}\right) + \frac{1}{2} \, \log\left({\left| x \right|}\right)"," ",0,"-3/2*log(abs(b*x^(1/3) + 2)) + 1/2*log(abs(x))","A",0
2365,1,144,0,0.167355," ","integrate(x^3/(a+b*x^(1/3))^2,x, algorithm=""giac"")","\frac{33 \, a^{10} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{12}} + \frac{3 \, a^{11}}{{\left(b x^{\frac{1}{3}} + a\right)} b^{12}} + \frac{252 \, b^{18} x^{\frac{10}{3}} - 560 \, a b^{17} x^{3} + 945 \, a^{2} b^{16} x^{\frac{8}{3}} - 1440 \, a^{3} b^{15} x^{\frac{7}{3}} + 2100 \, a^{4} b^{14} x^{2} - 3024 \, a^{5} b^{13} x^{\frac{5}{3}} + 4410 \, a^{6} b^{12} x^{\frac{4}{3}} - 6720 \, a^{7} b^{11} x + 11340 \, a^{8} b^{10} x^{\frac{2}{3}} - 25200 \, a^{9} b^{9} x^{\frac{1}{3}}}{840 \, b^{20}}"," ",0,"33*a^10*log(abs(b*x^(1/3) + a))/b^12 + 3*a^11/((b*x^(1/3) + a)*b^12) + 1/840*(252*b^18*x^(10/3) - 560*a*b^17*x^3 + 945*a^2*b^16*x^(8/3) - 1440*a^3*b^15*x^(7/3) + 2100*a^4*b^14*x^2 - 3024*a^5*b^13*x^(5/3) + 4410*a^6*b^12*x^(4/3) - 6720*a^7*b^11*x + 11340*a^8*b^10*x^(2/3) - 25200*a^9*b^9*x^(1/3))/b^20","A",0
2366,1,111,0,0.173097," ","integrate(x^2/(a+b*x^(1/3))^2,x, algorithm=""giac"")","-\frac{24 \, a^{7} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{9}} - \frac{3 \, a^{8}}{{\left(b x^{\frac{1}{3}} + a\right)} b^{9}} + \frac{15 \, b^{12} x^{\frac{7}{3}} - 35 \, a b^{11} x^{2} + 63 \, a^{2} b^{10} x^{\frac{5}{3}} - 105 \, a^{3} b^{9} x^{\frac{4}{3}} + 175 \, a^{4} b^{8} x - 315 \, a^{5} b^{7} x^{\frac{2}{3}} + 735 \, a^{6} b^{6} x^{\frac{1}{3}}}{35 \, b^{14}}"," ",0,"-24*a^7*log(abs(b*x^(1/3) + a))/b^9 - 3*a^8/((b*x^(1/3) + a)*b^9) + 1/35*(15*b^12*x^(7/3) - 35*a*b^11*x^2 + 63*a^2*b^10*x^(5/3) - 105*a^3*b^9*x^(4/3) + 175*a^4*b^8*x - 315*a^5*b^7*x^(2/3) + 735*a^6*b^6*x^(1/3))/b^14","A",0
2367,1,78,0,0.158183," ","integrate(x/(a+b*x^(1/3))^2,x, algorithm=""giac"")","\frac{15 \, a^{4} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{6}} + \frac{3 \, a^{5}}{{\left(b x^{\frac{1}{3}} + a\right)} b^{6}} + \frac{3 \, b^{6} x^{\frac{4}{3}} - 8 \, a b^{5} x + 18 \, a^{2} b^{4} x^{\frac{2}{3}} - 48 \, a^{3} b^{3} x^{\frac{1}{3}}}{4 \, b^{8}}"," ",0,"15*a^4*log(abs(b*x^(1/3) + a))/b^6 + 3*a^5/((b*x^(1/3) + a)*b^6) + 1/4*(3*b^6*x^(4/3) - 8*a*b^5*x + 18*a^2*b^4*x^(2/3) - 48*a^3*b^3*x^(1/3))/b^8","A",0
2368,1,41,0,0.151895," ","integrate(1/(a+b*x^(1/3))^2,x, algorithm=""giac"")","-\frac{6 \, a \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{3}} + \frac{3 \, x^{\frac{1}{3}}}{b^{2}} - \frac{3 \, a^{2}}{{\left(b x^{\frac{1}{3}} + a\right)} b^{3}}"," ",0,"-6*a*log(abs(b*x^(1/3) + a))/b^3 + 3*x^(1/3)/b^2 - 3*a^2/((b*x^(1/3) + a)*b^3)","A",0
2369,1,36,0,0.159728," ","integrate(1/(a+b*x^(1/3))^2/x,x, algorithm=""giac"")","-\frac{3 \, \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a^{2}} + \frac{\log\left({\left| x \right|}\right)}{a^{2}} + \frac{3}{{\left(b x^{\frac{1}{3}} + a\right)} a}"," ",0,"-3*log(abs(b*x^(1/3) + a))/a^2 + log(abs(x))/a^2 + 3/((b*x^(1/3) + a)*a)","A",0
2370,1,77,0,0.168988," ","integrate(1/(a+b*x^(1/3))^2/x^2,x, algorithm=""giac"")","\frac{12 \, b^{3} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a^{5}} - \frac{4 \, b^{3} \log\left({\left| x \right|}\right)}{a^{5}} - \frac{12 \, a b^{3} x + 6 \, a^{2} b^{2} x^{\frac{2}{3}} - 2 \, a^{3} b x^{\frac{1}{3}} + a^{4}}{{\left(b x^{\frac{1}{3}} + a\right)} a^{5} x}"," ",0,"12*b^3*log(abs(b*x^(1/3) + a))/a^5 - 4*b^3*log(abs(x))/a^5 - (12*a*b^3*x + 6*a^2*b^2*x^(2/3) - 2*a^3*b*x^(1/3) + a^4)/((b*x^(1/3) + a)*a^5*x)","A",0
2371,1,112,0,0.163321," ","integrate(1/(a+b*x^(1/3))^2/x^3,x, algorithm=""giac"")","-\frac{21 \, b^{6} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a^{8}} + \frac{7 \, b^{6} \log\left({\left| x \right|}\right)}{a^{8}} + \frac{420 \, a b^{6} x^{2} + 210 \, a^{2} b^{5} x^{\frac{5}{3}} - 70 \, a^{3} b^{4} x^{\frac{4}{3}} + 35 \, a^{4} b^{3} x - 21 \, a^{5} b^{2} x^{\frac{2}{3}} + 14 \, a^{6} b x^{\frac{1}{3}} - 10 \, a^{7}}{20 \, {\left(b x^{\frac{1}{3}} + a\right)} a^{8} x^{2}}"," ",0,"-21*b^6*log(abs(b*x^(1/3) + a))/a^8 + 7*b^6*log(abs(x))/a^8 + 1/20*(420*a*b^6*x^2 + 210*a^2*b^5*x^(5/3) - 70*a^3*b^4*x^(4/3) + 35*a^4*b^3*x - 21*a^5*b^2*x^(2/3) + 14*a^6*b*x^(1/3) - 10*a^7)/((b*x^(1/3) + a)*a^8*x^2)","A",0
2372,1,145,0,0.186597," ","integrate(1/(a+b*x^(1/3))^2/x^4,x, algorithm=""giac"")","\frac{30 \, b^{9} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a^{11}} - \frac{10 \, b^{9} \log\left({\left| x \right|}\right)}{a^{11}} - \frac{2520 \, a b^{9} x^{3} + 1260 \, a^{2} b^{8} x^{\frac{8}{3}} - 420 \, a^{3} b^{7} x^{\frac{7}{3}} + 210 \, a^{4} b^{6} x^{2} - 126 \, a^{5} b^{5} x^{\frac{5}{3}} + 84 \, a^{6} b^{4} x^{\frac{4}{3}} - 60 \, a^{7} b^{3} x + 45 \, a^{8} b^{2} x^{\frac{2}{3}} - 35 \, a^{9} b x^{\frac{1}{3}} + 28 \, a^{10}}{84 \, {\left(b x^{\frac{1}{3}} + a\right)} a^{11} x^{3}}"," ",0,"30*b^9*log(abs(b*x^(1/3) + a))/a^11 - 10*b^9*log(abs(x))/a^11 - 1/84*(2520*a*b^9*x^3 + 1260*a^2*b^8*x^(8/3) - 420*a^3*b^7*x^(7/3) + 210*a^4*b^6*x^2 - 126*a^5*b^5*x^(5/3) + 84*a^6*b^4*x^(4/3) - 60*a^7*b^3*x + 45*a^8*b^2*x^(2/3) - 35*a^9*b*x^(1/3) + 28*a^10)/((b*x^(1/3) + a)*a^11*x^3)","A",0
2373,1,145,0,0.165033," ","integrate(x^3/(a+b*x^(1/3))^3,x, algorithm=""giac"")","-\frac{165 \, a^{9} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{12}} - \frac{3 \, {\left(22 \, a^{10} b x^{\frac{1}{3}} + 21 \, a^{11}\right)}}{2 \, {\left(b x^{\frac{1}{3}} + a\right)}^{2} b^{12}} + \frac{56 \, b^{24} x^{3} - 189 \, a b^{23} x^{\frac{8}{3}} + 432 \, a^{2} b^{22} x^{\frac{7}{3}} - 840 \, a^{3} b^{21} x^{2} + 1512 \, a^{4} b^{20} x^{\frac{5}{3}} - 2646 \, a^{5} b^{19} x^{\frac{4}{3}} + 4704 \, a^{6} b^{18} x - 9072 \, a^{7} b^{17} x^{\frac{2}{3}} + 22680 \, a^{8} b^{16} x^{\frac{1}{3}}}{168 \, b^{27}}"," ",0,"-165*a^9*log(abs(b*x^(1/3) + a))/b^12 - 3/2*(22*a^10*b*x^(1/3) + 21*a^11)/((b*x^(1/3) + a)^2*b^12) + 1/168*(56*b^24*x^3 - 189*a*b^23*x^(8/3) + 432*a^2*b^22*x^(7/3) - 840*a^3*b^21*x^2 + 1512*a^4*b^20*x^(5/3) - 2646*a^5*b^19*x^(4/3) + 4704*a^6*b^18*x - 9072*a^7*b^17*x^(2/3) + 22680*a^8*b^16*x^(1/3))/b^27","A",0
2374,1,112,0,0.207748," ","integrate(x^2/(a+b*x^(1/3))^3,x, algorithm=""giac"")","\frac{84 \, a^{6} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{9}} + \frac{3 \, {\left(16 \, a^{7} b x^{\frac{1}{3}} + 15 \, a^{8}\right)}}{2 \, {\left(b x^{\frac{1}{3}} + a\right)}^{2} b^{9}} + \frac{5 \, b^{15} x^{2} - 18 \, a b^{14} x^{\frac{5}{3}} + 45 \, a^{2} b^{13} x^{\frac{4}{3}} - 100 \, a^{3} b^{12} x + 225 \, a^{4} b^{11} x^{\frac{2}{3}} - 630 \, a^{5} b^{10} x^{\frac{1}{3}}}{10 \, b^{18}}"," ",0,"84*a^6*log(abs(b*x^(1/3) + a))/b^9 + 3/2*(16*a^7*b*x^(1/3) + 15*a^8)/((b*x^(1/3) + a)^2*b^9) + 1/10*(5*b^15*x^2 - 18*a*b^14*x^(5/3) + 45*a^2*b^13*x^(4/3) - 100*a^3*b^12*x + 225*a^4*b^11*x^(2/3) - 630*a^5*b^10*x^(1/3))/b^18","A",0
2375,1,79,0,0.154461," ","integrate(x/(a+b*x^(1/3))^3,x, algorithm=""giac"")","-\frac{30 \, a^{3} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{6}} - \frac{3 \, {\left(10 \, a^{4} b x^{\frac{1}{3}} + 9 \, a^{5}\right)}}{2 \, {\left(b x^{\frac{1}{3}} + a\right)}^{2} b^{6}} + \frac{2 \, b^{6} x - 9 \, a b^{5} x^{\frac{2}{3}} + 36 \, a^{2} b^{4} x^{\frac{1}{3}}}{2 \, b^{9}}"," ",0,"-30*a^3*log(abs(b*x^(1/3) + a))/b^6 - 3/2*(10*a^4*b*x^(1/3) + 9*a^5)/((b*x^(1/3) + a)^2*b^6) + 1/2*(2*b^6*x - 9*a*b^5*x^(2/3) + 36*a^2*b^4*x^(1/3))/b^9","A",0
2376,1,44,0,0.164072," ","integrate(1/(a+b*x^(1/3))^3,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{b^{3}} + \frac{3 \, {\left(4 \, a x^{\frac{1}{3}} + \frac{3 \, a^{2}}{b}\right)}}{2 \, {\left(b x^{\frac{1}{3}} + a\right)}^{2} b^{2}}"," ",0,"3*log(abs(b*x^(1/3) + a))/b^3 + 3/2*(4*a*x^(1/3) + 3*a^2/b)/((b*x^(1/3) + a)^2*b^2)","A",0
2377,1,49,0,0.167061," ","integrate(1/(a+b*x^(1/3))^3/x,x, algorithm=""giac"")","-\frac{3 \, \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a^{3}} + \frac{\log\left({\left| x \right|}\right)}{a^{3}} + \frac{3 \, {\left(2 \, a b x^{\frac{1}{3}} + 3 \, a^{2}\right)}}{2 \, {\left(b x^{\frac{1}{3}} + a\right)}^{2} a^{3}}"," ",0,"-3*log(abs(b*x^(1/3) + a))/a^3 + log(abs(x))/a^3 + 3/2*(2*a*b*x^(1/3) + 3*a^2)/((b*x^(1/3) + a)^2*a^3)","A",0
2378,1,90,0,0.166459," ","integrate(1/(a+b*x^(1/3))^3/x^2,x, algorithm=""giac"")","\frac{30 \, b^{3} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a^{6}} - \frac{10 \, b^{3} \log\left({\left| x \right|}\right)}{a^{6}} - \frac{60 \, a b^{4} x^{\frac{4}{3}} + 90 \, a^{2} b^{3} x + 20 \, a^{3} b^{2} x^{\frac{2}{3}} - 5 \, a^{4} b x^{\frac{1}{3}} + 2 \, a^{5}}{2 \, {\left(b x^{\frac{1}{3}} + a\right)}^{2} a^{6} x}"," ",0,"30*b^3*log(abs(b*x^(1/3) + a))/a^6 - 10*b^3*log(abs(x))/a^6 - 1/2*(60*a*b^4*x^(4/3) + 90*a^2*b^3*x + 20*a^3*b^2*x^(2/3) - 5*a^4*b*x^(1/3) + 2*a^5)/((b*x^(1/3) + a)^2*a^6*x)","A",0
2379,1,123,0,0.171156," ","integrate(1/(a+b*x^(1/3))^3/x^3,x, algorithm=""giac"")","-\frac{84 \, b^{6} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a^{9}} + \frac{28 \, b^{6} \log\left({\left| x \right|}\right)}{a^{9}} + \frac{840 \, a b^{7} x^{\frac{7}{3}} + 1260 \, a^{2} b^{6} x^{2} + 280 \, a^{3} b^{5} x^{\frac{5}{3}} - 70 \, a^{4} b^{4} x^{\frac{4}{3}} + 28 \, a^{5} b^{3} x - 14 \, a^{6} b^{2} x^{\frac{2}{3}} + 8 \, a^{7} b x^{\frac{1}{3}} - 5 \, a^{8}}{10 \, {\left(b x^{\frac{1}{3}} + a\right)}^{2} a^{9} x^{2}}"," ",0,"-84*b^6*log(abs(b*x^(1/3) + a))/a^9 + 28*b^6*log(abs(x))/a^9 + 1/10*(840*a*b^7*x^(7/3) + 1260*a^2*b^6*x^2 + 280*a^3*b^5*x^(5/3) - 70*a^4*b^4*x^(4/3) + 28*a^5*b^3*x - 14*a^6*b^2*x^(2/3) + 8*a^7*b*x^(1/3) - 5*a^8)/((b*x^(1/3) + a)^2*a^9*x^2)","A",0
2380,1,156,0,0.166161," ","integrate(1/(a+b*x^(1/3))^3/x^4,x, algorithm=""giac"")","\frac{165 \, b^{9} \log\left({\left| b x^{\frac{1}{3}} + a \right|}\right)}{a^{12}} - \frac{55 \, b^{9} \log\left({\left| x \right|}\right)}{a^{12}} - \frac{27720 \, a b^{10} x^{\frac{10}{3}} + 41580 \, a^{2} b^{9} x^{3} + 9240 \, a^{3} b^{8} x^{\frac{8}{3}} - 2310 \, a^{4} b^{7} x^{\frac{7}{3}} + 924 \, a^{5} b^{6} x^{2} - 462 \, a^{6} b^{5} x^{\frac{5}{3}} + 264 \, a^{7} b^{4} x^{\frac{4}{3}} - 165 \, a^{8} b^{3} x + 110 \, a^{9} b^{2} x^{\frac{2}{3}} - 77 \, a^{10} b x^{\frac{1}{3}} + 56 \, a^{11}}{168 \, {\left(b x^{\frac{1}{3}} + a\right)}^{2} a^{12} x^{3}}"," ",0,"165*b^9*log(abs(b*x^(1/3) + a))/a^12 - 55*b^9*log(abs(x))/a^12 - 1/168*(27720*a*b^10*x^(10/3) + 41580*a^2*b^9*x^3 + 9240*a^3*b^8*x^(8/3) - 2310*a^4*b^7*x^(7/3) + 924*a^5*b^6*x^2 - 462*a^6*b^5*x^(5/3) + 264*a^7*b^4*x^(4/3) - 165*a^8*b^3*x + 110*a^9*b^2*x^(2/3) - 77*a^10*b*x^(1/3) + 56*a^11)/((b*x^(1/3) + a)^2*a^12*x^3)","A",0
2381,1,28,0,0.149902," ","integrate(1/(1+x^(1/3))^(1/2),x, algorithm=""giac"")","\frac{6}{5} \, {\left(x^{\frac{1}{3}} + 1\right)}^{\frac{5}{2}} - 4 \, {\left(x^{\frac{1}{3}} + 1\right)}^{\frac{3}{2}} + 6 \, \sqrt{x^{\frac{1}{3}} + 1}"," ",0,"6/5*(x^(1/3) + 1)^(5/2) - 4*(x^(1/3) + 1)^(3/2) + 6*sqrt(x^(1/3) + 1)","A",0
2382,1,19,0,0.154582," ","integrate(1/(1+x^(1/3))/x^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, x^{\frac{1}{3}} - 1\right)}}{\sqrt{x}} + 6 \, \arctan\left(x^{\frac{1}{6}}\right)"," ",0,"2*(3*x^(1/3) - 1)/sqrt(x) + 6*arctan(x^(1/6))","A",0
2383,1,27,0,0.158915," ","integrate(x^(2/3)/(1+x^(1/3)),x, algorithm=""giac"")","\frac{3}{4} \, x^{\frac{4}{3}} - x + \frac{3}{2} \, x^{\frac{2}{3}} - 3 \, x^{\frac{1}{3}} + 3 \, \log\left(x^{\frac{1}{3}} + 1\right)"," ",0,"3/4*x^(4/3) - x + 3/2*x^(2/3) - 3*x^(1/3) + 3*log(x^(1/3) + 1)","A",0
2384,1,12,0,0.154392," ","integrate(1/(1+x^(2/3)),x, algorithm=""giac"")","3 \, x^{\frac{1}{3}} - 3 \, \arctan\left(x^{\frac{1}{3}}\right)"," ",0,"3*x^(1/3) - 3*arctan(x^(1/3))","A",0
2385,1,8,0,0.149205," ","integrate(1/(1+x^(2/3))/x^(1/3),x, algorithm=""giac"")","\frac{3}{2} \, \log\left(x^{\frac{2}{3}} + 1\right)"," ",0,"3/2*log(x^(2/3) + 1)","A",0
2386,1,6,0,0.165473," ","integrate(1/(1+x^(2/3))/x^(2/3),x, algorithm=""giac"")","3 \, \arctan\left(x^{\frac{1}{3}}\right)"," ",0,"3*arctan(x^(1/3))","A",0
2387,1,7,0,0.184478," ","integrate((-1+x^(2/3))^(1/2)/x^(1/3),x, algorithm=""giac"")","{\left(x^{\frac{2}{3}} - 1\right)}^{\frac{3}{2}}"," ",0,"(x^(2/3) - 1)^(3/2)","A",0
2388,1,9,0,0.154398," ","integrate((1+x^(2/3))^(3/2)/x^(1/3),x, algorithm=""giac"")","\frac{3}{5} \, {\left(x^{\frac{2}{3}} + 1\right)}^{\frac{5}{2}}"," ",0,"3/5*(x^(2/3) + 1)^(5/2)","A",0
2389,1,88,0,0.166690," ","integrate(x^(1/2)/(1+x^(2/3)),x, algorithm=""giac"")","\frac{3}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, x^{\frac{1}{6}}\right)}\right) + \frac{3}{2} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, x^{\frac{1}{6}}\right)}\right) + \frac{3}{4} \, \sqrt{2} \log\left(\sqrt{2} x^{\frac{1}{6}} + x^{\frac{1}{3}} + 1\right) - \frac{3}{4} \, \sqrt{2} \log\left(-\sqrt{2} x^{\frac{1}{6}} + x^{\frac{1}{3}} + 1\right) + \frac{6}{5} \, x^{\frac{5}{6}} - 6 \, x^{\frac{1}{6}}"," ",0,"3/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*x^(1/6))) + 3/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*x^(1/6))) + 3/4*sqrt(2)*log(sqrt(2)*x^(1/6) + x^(1/3) + 1) - 3/4*sqrt(2)*log(-sqrt(2)*x^(1/6) + x^(1/3) + 1) + 6/5*x^(5/6) - 6*x^(1/6)","A",0
2390,1,139,0,0.468473," ","integrate(x^(1/3)/(-1+x^(5/6)),x, algorithm=""giac"")","\frac{3}{5} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(-\frac{\sqrt{5} - 4 \, x^{\frac{1}{6}} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) - \frac{3}{5} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{\sqrt{5} + 4 \, x^{\frac{1}{6}} + 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) + \frac{3}{10} \, \sqrt{5} \log\left(\frac{1}{2} \, x^{\frac{1}{6}} {\left(\sqrt{5} + 1\right)} + x^{\frac{1}{3}} + 1\right) - \frac{3}{10} \, \sqrt{5} \log\left(-\frac{1}{2} \, x^{\frac{1}{6}} {\left(\sqrt{5} - 1\right)} + x^{\frac{1}{3}} + 1\right) + 2 \, \sqrt{x} - \frac{3}{10} \, \log\left(x^{\frac{2}{3}} + \sqrt{x} + x^{\frac{1}{3}} + x^{\frac{1}{6}} + 1\right) + \frac{6}{5} \, \log\left({\left| x^{\frac{1}{6}} - 1 \right|}\right)"," ",0,"3/5*sqrt(-2*sqrt(5) + 10)*arctan(-(sqrt(5) - 4*x^(1/6) - 1)/sqrt(2*sqrt(5) + 10)) - 3/5*sqrt(2*sqrt(5) + 10)*arctan((sqrt(5) + 4*x^(1/6) + 1)/sqrt(-2*sqrt(5) + 10)) + 3/10*sqrt(5)*log(1/2*x^(1/6)*(sqrt(5) + 1) + x^(1/3) + 1) - 3/10*sqrt(5)*log(-1/2*x^(1/6)*(sqrt(5) - 1) + x^(1/3) + 1) + 2*sqrt(x) - 3/10*log(x^(2/3) + sqrt(x) + x^(1/3) + x^(1/6) + 1) + 6/5*log(abs(x^(1/6) - 1))","A",0
2391,1,59,0,0.842219," ","integrate((3-1/x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{36} \, {\left(6 \, \sqrt{3 \, x - \sqrt{x}} {\left(6 \, \sqrt{x} - 1\right)} + \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} \sqrt{x} - \sqrt{3 \, x - \sqrt{x}}\right)} + 1 \right|}\right)\right)} \mathrm{sgn}\left(x\right)"," ",0,"1/36*(6*sqrt(3*x - sqrt(x))*(6*sqrt(x) - 1) + sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*sqrt(x) - sqrt(3*x - sqrt(x))) + 1)))*sgn(x)","A",0
2392,1,36,0,0.312865," ","integrate(1/(1+1/x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x + \sqrt{x}} {\left(2 \, \sqrt{x} - 3\right)} - \frac{3}{4} \, \log\left(-2 \, \sqrt{x + \sqrt{x}} + 2 \, \sqrt{x} + 1\right)"," ",0,"1/2*sqrt(x + sqrt(x))*(2*sqrt(x) - 3) - 3/4*log(-2*sqrt(x + sqrt(x)) + 2*sqrt(x) + 1)","A",0
2393,0,0,0,0.000000," ","integrate((a+b/x^(3/2))^(2/3),x, algorithm=""giac"")","\int {\left(a + \frac{b}{x^{\frac{3}{2}}}\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((a + b/x^(3/2))^(2/3), x)","F",0
2394,1,13,0,0.157304," ","integrate((a+b/x^(1/3))*x^4,x, algorithm=""giac"")","\frac{1}{5} \, a x^{5} + \frac{3}{14} \, b x^{\frac{14}{3}}"," ",0,"1/5*a*x^5 + 3/14*b*x^(14/3)","A",0
2395,1,13,0,0.174027," ","integrate((a+b/x^(1/3))*x^3,x, algorithm=""giac"")","\frac{1}{4} \, a x^{4} + \frac{3}{11} \, b x^{\frac{11}{3}}"," ",0,"1/4*a*x^4 + 3/11*b*x^(11/3)","A",0
2396,1,13,0,0.151000," ","integrate((a+b/x^(1/3))*x^2,x, algorithm=""giac"")","\frac{1}{3} \, a x^{3} + \frac{3}{8} \, b x^{\frac{8}{3}}"," ",0,"1/3*a*x^3 + 3/8*b*x^(8/3)","A",0
2397,1,13,0,0.185476," ","integrate((a+b/x^(1/3))*x,x, algorithm=""giac"")","\frac{1}{2} \, a x^{2} + \frac{3}{5} \, b x^{\frac{5}{3}}"," ",0,"1/2*a*x^2 + 3/5*b*x^(5/3)","A",0
2398,1,10,0,0.148126," ","integrate(a+b/x^(1/3),x, algorithm=""giac"")","a x + \frac{3}{2} \, b x^{\frac{2}{3}}"," ",0,"a*x + 3/2*b*x^(2/3)","A",0
2399,1,12,0,0.149424," ","integrate((a+b/x^(1/3))/x,x, algorithm=""giac"")","a \log\left({\left| x \right|}\right) - \frac{3 \, b}{x^{\frac{1}{3}}}"," ",0,"a*log(abs(x)) - 3*b/x^(1/3)","A",0
2400,1,15,0,0.173811," ","integrate((a+b/x^(1/3))/x^2,x, algorithm=""giac"")","-\frac{4 \, a x^{\frac{1}{3}} + 3 \, b}{4 \, x^{\frac{4}{3}}}"," ",0,"-1/4*(4*a*x^(1/3) + 3*b)/x^(4/3)","A",0
2401,1,15,0,0.154116," ","integrate((a+b/x^(1/3))/x^3,x, algorithm=""giac"")","-\frac{7 \, a x^{\frac{1}{3}} + 6 \, b}{14 \, x^{\frac{7}{3}}}"," ",0,"-1/14*(7*a*x^(1/3) + 6*b)/x^(7/3)","A",0
2402,1,15,0,0.192308," ","integrate((a+b/x^(1/3))/x^4,x, algorithm=""giac"")","-\frac{10 \, a x^{\frac{1}{3}} + 9 \, b}{30 \, x^{\frac{10}{3}}}"," ",0,"-1/30*(10*a*x^(1/3) + 9*b)/x^(10/3)","A",0
2403,1,24,0,0.151792," ","integrate((a+b/x^(1/3))^2*x^4,x, algorithm=""giac"")","\frac{1}{5} \, a^{2} x^{5} + \frac{3}{7} \, a b x^{\frac{14}{3}} + \frac{3}{13} \, b^{2} x^{\frac{13}{3}}"," ",0,"1/5*a^2*x^5 + 3/7*a*b*x^(14/3) + 3/13*b^2*x^(13/3)","A",0
2404,1,24,0,0.148494," ","integrate((a+b/x^(1/3))^2*x^3,x, algorithm=""giac"")","\frac{1}{4} \, a^{2} x^{4} + \frac{6}{11} \, a b x^{\frac{11}{3}} + \frac{3}{10} \, b^{2} x^{\frac{10}{3}}"," ",0,"1/4*a^2*x^4 + 6/11*a*b*x^(11/3) + 3/10*b^2*x^(10/3)","A",0
2405,1,24,0,0.157312," ","integrate((a+b/x^(1/3))^2*x^2,x, algorithm=""giac"")","\frac{1}{3} \, a^{2} x^{3} + \frac{3}{4} \, a b x^{\frac{8}{3}} + \frac{3}{7} \, b^{2} x^{\frac{7}{3}}"," ",0,"1/3*a^2*x^3 + 3/4*a*b*x^(8/3) + 3/7*b^2*x^(7/3)","A",0
2406,1,24,0,0.183664," ","integrate((a+b/x^(1/3))^2*x,x, algorithm=""giac"")","\frac{1}{2} \, a^{2} x^{2} + \frac{6}{5} \, a b x^{\frac{5}{3}} + \frac{3}{4} \, b^{2} x^{\frac{4}{3}}"," ",0,"1/2*a^2*x^2 + 6/5*a*b*x^(5/3) + 3/4*b^2*x^(4/3)","A",0
2407,1,21,0,0.158837," ","integrate((a+b/x^(1/3))^2,x, algorithm=""giac"")","a^{2} x + 3 \, a b x^{\frac{2}{3}} + 3 \, b^{2} x^{\frac{1}{3}}"," ",0,"a^2*x + 3*a*b*x^(2/3) + 3*b^2*x^(1/3)","A",0
2408,1,24,0,0.149121," ","integrate((a+b/x^(1/3))^2/x,x, algorithm=""giac"")","a^{2} \log\left({\left| x \right|}\right) - \frac{3 \, {\left(4 \, a b x^{\frac{1}{3}} + b^{2}\right)}}{2 \, x^{\frac{2}{3}}}"," ",0,"a^2*log(abs(x)) - 3/2*(4*a*b*x^(1/3) + b^2)/x^(2/3)","A",0
2409,1,26,0,0.171293," ","integrate((a+b/x^(1/3))^2/x^2,x, algorithm=""giac"")","-\frac{10 \, a^{2} x^{\frac{2}{3}} + 15 \, a b x^{\frac{1}{3}} + 6 \, b^{2}}{10 \, x^{\frac{5}{3}}}"," ",0,"-1/10*(10*a^2*x^(2/3) + 15*a*b*x^(1/3) + 6*b^2)/x^(5/3)","A",0
2410,1,26,0,0.189456," ","integrate((a+b/x^(1/3))^2/x^3,x, algorithm=""giac"")","-\frac{28 \, a^{2} x^{\frac{2}{3}} + 48 \, a b x^{\frac{1}{3}} + 21 \, b^{2}}{56 \, x^{\frac{8}{3}}}"," ",0,"-1/56*(28*a^2*x^(2/3) + 48*a*b*x^(1/3) + 21*b^2)/x^(8/3)","A",0
2411,1,26,0,0.204392," ","integrate((a+b/x^(1/3))^2/x^4,x, algorithm=""giac"")","-\frac{55 \, a^{2} x^{\frac{2}{3}} + 99 \, a b x^{\frac{1}{3}} + 45 \, b^{2}}{165 \, x^{\frac{11}{3}}}"," ",0,"-1/165*(55*a^2*x^(2/3) + 99*a*b*x^(1/3) + 45*b^2)/x^(11/3)","A",0
2412,1,35,0,0.159736," ","integrate((a+b/x^(1/3))^3*x^4,x, algorithm=""giac"")","\frac{1}{5} \, a^{3} x^{5} + \frac{9}{14} \, a^{2} b x^{\frac{14}{3}} + \frac{9}{13} \, a b^{2} x^{\frac{13}{3}} + \frac{1}{4} \, b^{3} x^{4}"," ",0,"1/5*a^3*x^5 + 9/14*a^2*b*x^(14/3) + 9/13*a*b^2*x^(13/3) + 1/4*b^3*x^4","A",0
2413,1,35,0,0.151996," ","integrate((a+b/x^(1/3))^3*x^3,x, algorithm=""giac"")","\frac{1}{4} \, a^{3} x^{4} + \frac{9}{11} \, a^{2} b x^{\frac{11}{3}} + \frac{9}{10} \, a b^{2} x^{\frac{10}{3}} + \frac{1}{3} \, b^{3} x^{3}"," ",0,"1/4*a^3*x^4 + 9/11*a^2*b*x^(11/3) + 9/10*a*b^2*x^(10/3) + 1/3*b^3*x^3","A",0
2414,1,35,0,0.194087," ","integrate((a+b/x^(1/3))^3*x^2,x, algorithm=""giac"")","\frac{1}{3} \, a^{3} x^{3} + \frac{9}{8} \, a^{2} b x^{\frac{8}{3}} + \frac{9}{7} \, a b^{2} x^{\frac{7}{3}} + \frac{1}{2} \, b^{3} x^{2}"," ",0,"1/3*a^3*x^3 + 9/8*a^2*b*x^(8/3) + 9/7*a*b^2*x^(7/3) + 1/2*b^3*x^2","A",0
2415,1,32,0,0.159877," ","integrate((a+b/x^(1/3))^3*x,x, algorithm=""giac"")","\frac{1}{2} \, a^{3} x^{2} + \frac{9}{5} \, a^{2} b x^{\frac{5}{3}} + \frac{9}{4} \, a b^{2} x^{\frac{4}{3}} + b^{3} x"," ",0,"1/2*a^3*x^2 + 9/5*a^2*b*x^(5/3) + 9/4*a*b^2*x^(4/3) + b^3*x","A",0
2416,1,31,0,0.172783," ","integrate((a+b/x^(1/3))^3,x, algorithm=""giac"")","a^{3} x + b^{3} \log\left({\left| x \right|}\right) + \frac{9}{2} \, a^{2} b x^{\frac{2}{3}} + 9 \, a b^{2} x^{\frac{1}{3}}"," ",0,"a^3*x + b^3*log(abs(x)) + 9/2*a^2*b*x^(2/3) + 9*a*b^2*x^(1/3)","A",0
2417,1,37,0,0.156293," ","integrate((a+b/x^(1/3))^3/x,x, algorithm=""giac"")","a^{3} \log\left({\left| x \right|}\right) - \frac{18 \, a^{2} b x^{\frac{2}{3}} + 9 \, a b^{2} x^{\frac{1}{3}} + 2 \, b^{3}}{2 \, x}"," ",0,"a^3*log(abs(x)) - 1/2*(18*a^2*b*x^(2/3) + 9*a*b^2*x^(1/3) + 2*b^3)/x","A",0
2418,1,35,0,0.157639," ","integrate((a+b/x^(1/3))^3/x^2,x, algorithm=""giac"")","-\frac{20 \, a^{3} x + 45 \, a^{2} b x^{\frac{2}{3}} + 36 \, a b^{2} x^{\frac{1}{3}} + 10 \, b^{3}}{20 \, x^{2}}"," ",0,"-1/20*(20*a^3*x + 45*a^2*b*x^(2/3) + 36*a*b^2*x^(1/3) + 10*b^3)/x^2","A",0
2419,1,35,0,0.183104," ","integrate((a+b/x^(1/3))^3/x^3,x, algorithm=""giac"")","-\frac{84 \, a^{3} x + 216 \, a^{2} b x^{\frac{2}{3}} + 189 \, a b^{2} x^{\frac{1}{3}} + 56 \, b^{3}}{168 \, x^{3}}"," ",0,"-1/168*(84*a^3*x + 216*a^2*b*x^(2/3) + 189*a*b^2*x^(1/3) + 56*b^3)/x^3","A",0
2420,1,35,0,0.155460," ","integrate((a+b/x^(1/3))^3/x^4,x, algorithm=""giac"")","-\frac{220 \, a^{3} x + 594 \, a^{2} b x^{\frac{2}{3}} + 540 \, a b^{2} x^{\frac{1}{3}} + 165 \, b^{3}}{660 \, x^{4}}"," ",0,"-1/660*(220*a^3*x + 594*a^2*b*x^(2/3) + 540*a*b^2*x^(1/3) + 165*b^3)/x^4","A",0
2421,1,111,0,0.151136," ","integrate(x^2/(a+b/x^(1/3)),x, algorithm=""giac"")","-\frac{3 \, b^{9} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{10}} + \frac{280 \, a^{8} x^{3} - 315 \, a^{7} b x^{\frac{8}{3}} + 360 \, a^{6} b^{2} x^{\frac{7}{3}} - 420 \, a^{5} b^{3} x^{2} + 504 \, a^{4} b^{4} x^{\frac{5}{3}} - 630 \, a^{3} b^{5} x^{\frac{4}{3}} + 840 \, a^{2} b^{6} x - 1260 \, a b^{7} x^{\frac{2}{3}} + 2520 \, b^{8} x^{\frac{1}{3}}}{840 \, a^{9}}"," ",0,"-3*b^9*log(abs(a*x^(1/3) + b))/a^10 + 1/840*(280*a^8*x^3 - 315*a^7*b*x^(8/3) + 360*a^6*b^2*x^(7/3) - 420*a^5*b^3*x^2 + 504*a^4*b^4*x^(5/3) - 630*a^3*b^5*x^(4/3) + 840*a^2*b^6*x - 1260*a*b^7*x^(2/3) + 2520*b^8*x^(1/3))/a^9","A",0
2422,1,78,0,0.207462," ","integrate(x/(a+b/x^(1/3)),x, algorithm=""giac"")","\frac{3 \, b^{6} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{7}} + \frac{10 \, a^{5} x^{2} - 12 \, a^{4} b x^{\frac{5}{3}} + 15 \, a^{3} b^{2} x^{\frac{4}{3}} - 20 \, a^{2} b^{3} x + 30 \, a b^{4} x^{\frac{2}{3}} - 60 \, b^{5} x^{\frac{1}{3}}}{20 \, a^{6}}"," ",0,"3*b^6*log(abs(a*x^(1/3) + b))/a^7 + 1/20*(10*a^5*x^2 - 12*a^4*b*x^(5/3) + 15*a^3*b^2*x^(4/3) - 20*a^2*b^3*x + 30*a*b^4*x^(2/3) - 60*b^5*x^(1/3))/a^6","A",0
2423,1,45,0,0.155755," ","integrate(1/(a+b/x^(1/3)),x, algorithm=""giac"")","-\frac{3 \, b^{3} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{4}} + \frac{2 \, a^{2} x - 3 \, a b x^{\frac{2}{3}} + 6 \, b^{2} x^{\frac{1}{3}}}{2 \, a^{3}}"," ",0,"-3*b^3*log(abs(a*x^(1/3) + b))/a^4 + 1/2*(2*a^2*x - 3*a*b*x^(2/3) + 6*b^2*x^(1/3))/a^3","A",0
2424,1,14,0,0.155824," ","integrate(1/(a+b/x^(1/3))/x,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a}"," ",0,"3*log(abs(a*x^(1/3) + b))/a","A",0
2425,1,49,0,0.157834," ","integrate(1/(a+b/x^(1/3))/x^2,x, algorithm=""giac"")","-\frac{3 \, a^{2} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{3}} + \frac{a^{2} \log\left({\left| x \right|}\right)}{b^{3}} + \frac{3 \, {\left(2 \, a b x^{\frac{1}{3}} - b^{2}\right)}}{2 \, b^{3} x^{\frac{2}{3}}}"," ",0,"-3*a^2*log(abs(a*x^(1/3) + b))/b^3 + a^2*log(abs(x))/b^3 + 3/2*(2*a*b*x^(1/3) - b^2)/(b^3*x^(2/3))","A",0
2426,1,81,0,0.186482," ","integrate(1/(a+b/x^(1/3))/x^3,x, algorithm=""giac"")","\frac{3 \, a^{5} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{6}} - \frac{a^{5} \log\left({\left| x \right|}\right)}{b^{6}} - \frac{60 \, a^{4} b x^{\frac{4}{3}} - 30 \, a^{3} b^{2} x + 20 \, a^{2} b^{3} x^{\frac{2}{3}} - 15 \, a b^{4} x^{\frac{1}{3}} + 12 \, b^{5}}{20 \, b^{6} x^{\frac{5}{3}}}"," ",0,"3*a^5*log(abs(a*x^(1/3) + b))/b^6 - a^5*log(abs(x))/b^6 - 1/20*(60*a^4*b*x^(4/3) - 30*a^3*b^2*x + 20*a^2*b^3*x^(2/3) - 15*a*b^4*x^(1/3) + 12*b^5)/(b^6*x^(5/3))","A",0
2427,1,113,0,0.178510," ","integrate(1/(a+b/x^(1/3))/x^4,x, algorithm=""giac"")","-\frac{3 \, a^{8} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{9}} + \frac{a^{8} \log\left({\left| x \right|}\right)}{b^{9}} + \frac{840 \, a^{7} b x^{\frac{7}{3}} - 420 \, a^{6} b^{2} x^{2} + 280 \, a^{5} b^{3} x^{\frac{5}{3}} - 210 \, a^{4} b^{4} x^{\frac{4}{3}} + 168 \, a^{3} b^{5} x - 140 \, a^{2} b^{6} x^{\frac{2}{3}} + 120 \, a b^{7} x^{\frac{1}{3}} - 105 \, b^{8}}{280 \, b^{9} x^{\frac{8}{3}}}"," ",0,"-3*a^8*log(abs(a*x^(1/3) + b))/b^9 + a^8*log(abs(x))/b^9 + 1/280*(840*a^7*b*x^(7/3) - 420*a^6*b^2*x^2 + 280*a^5*b^3*x^(5/3) - 210*a^4*b^4*x^(4/3) + 168*a^3*b^5*x - 140*a^2*b^6*x^(2/3) + 120*a*b^7*x^(1/3) - 105*b^8)/(b^9*x^(8/3))","A",0
2428,1,147,0,0.160276," ","integrate(1/(a+b/x^(1/3))/x^5,x, algorithm=""giac"")","\frac{3 \, a^{11} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{12}} - \frac{a^{11} \log\left({\left| x \right|}\right)}{b^{12}} - \frac{27720 \, a^{10} b x^{\frac{10}{3}} - 13860 \, a^{9} b^{2} x^{3} + 9240 \, a^{8} b^{3} x^{\frac{8}{3}} - 6930 \, a^{7} b^{4} x^{\frac{7}{3}} + 5544 \, a^{6} b^{5} x^{2} - 4620 \, a^{5} b^{6} x^{\frac{5}{3}} + 3960 \, a^{4} b^{7} x^{\frac{4}{3}} - 3465 \, a^{3} b^{8} x + 3080 \, a^{2} b^{9} x^{\frac{2}{3}} - 2772 \, a b^{10} x^{\frac{1}{3}} + 2520 \, b^{11}}{9240 \, b^{12} x^{\frac{11}{3}}}"," ",0,"3*a^11*log(abs(a*x^(1/3) + b))/b^12 - a^11*log(abs(x))/b^12 - 1/9240*(27720*a^10*b*x^(10/3) - 13860*a^9*b^2*x^3 + 9240*a^8*b^3*x^(8/3) - 6930*a^7*b^4*x^(7/3) + 5544*a^6*b^5*x^2 - 4620*a^5*b^6*x^(5/3) + 3960*a^4*b^7*x^(4/3) - 3465*a^3*b^8*x + 3080*a^2*b^9*x^(2/3) - 2772*a*b^10*x^(1/3) + 2520*b^11)/(b^12*x^(11/3))","A",0
2429,1,133,0,0.170068," ","integrate(x^2/(a+b/x^(1/3))^2,x, algorithm=""giac"")","-\frac{30 \, b^{9} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{11}} - \frac{3 \, b^{10}}{{\left(a x^{\frac{1}{3}} + b\right)} a^{11}} + \frac{28 \, a^{16} x^{3} - 63 \, a^{15} b x^{\frac{8}{3}} + 108 \, a^{14} b^{2} x^{\frac{7}{3}} - 168 \, a^{13} b^{3} x^{2} + 252 \, a^{12} b^{4} x^{\frac{5}{3}} - 378 \, a^{11} b^{5} x^{\frac{4}{3}} + 588 \, a^{10} b^{6} x - 1008 \, a^{9} b^{7} x^{\frac{2}{3}} + 2268 \, a^{8} b^{8} x^{\frac{1}{3}}}{84 \, a^{18}}"," ",0,"-30*b^9*log(abs(a*x^(1/3) + b))/a^11 - 3*b^10/((a*x^(1/3) + b)*a^11) + 1/84*(28*a^16*x^3 - 63*a^15*b*x^(8/3) + 108*a^14*b^2*x^(7/3) - 168*a^13*b^3*x^2 + 252*a^12*b^4*x^(5/3) - 378*a^11*b^5*x^(4/3) + 588*a^10*b^6*x - 1008*a^9*b^7*x^(2/3) + 2268*a^8*b^8*x^(1/3))/a^18","A",0
2430,1,100,0,0.158187," ","integrate(x/(a+b/x^(1/3))^2,x, algorithm=""giac"")","\frac{21 \, b^{6} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{8}} + \frac{3 \, b^{7}}{{\left(a x^{\frac{1}{3}} + b\right)} a^{8}} + \frac{10 \, a^{10} x^{2} - 24 \, a^{9} b x^{\frac{5}{3}} + 45 \, a^{8} b^{2} x^{\frac{4}{3}} - 80 \, a^{7} b^{3} x + 150 \, a^{6} b^{4} x^{\frac{2}{3}} - 360 \, a^{5} b^{5} x^{\frac{1}{3}}}{20 \, a^{12}}"," ",0,"21*b^6*log(abs(a*x^(1/3) + b))/a^8 + 3*b^7/((a*x^(1/3) + b)*a^8) + 1/20*(10*a^10*x^2 - 24*a^9*b*x^(5/3) + 45*a^8*b^2*x^(4/3) - 80*a^7*b^3*x + 150*a^6*b^4*x^(2/3) - 360*a^5*b^5*x^(1/3))/a^12","A",0
2431,1,65,0,0.175843," ","integrate(1/(a+b/x^(1/3))^2,x, algorithm=""giac"")","-\frac{12 \, b^{3} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{5}} - \frac{3 \, b^{4}}{{\left(a x^{\frac{1}{3}} + b\right)} a^{5}} + \frac{a^{4} x - 3 \, a^{3} b x^{\frac{2}{3}} + 9 \, a^{2} b^{2} x^{\frac{1}{3}}}{a^{6}}"," ",0,"-12*b^3*log(abs(a*x^(1/3) + b))/a^5 - 3*b^4/((a*x^(1/3) + b)*a^5) + (a^4*x - 3*a^3*b*x^(2/3) + 9*a^2*b^2*x^(1/3))/a^6","A",0
2432,1,30,0,0.156798," ","integrate(1/(a+b/x^(1/3))^2/x,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{2}} + \frac{3 \, b}{{\left(a x^{\frac{1}{3}} + b\right)} a^{2}}"," ",0,"3*log(abs(a*x^(1/3) + b))/a^2 + 3*b/((a*x^(1/3) + b)*a^2)","A",0
2433,1,51,0,0.170842," ","integrate(1/(a+b/x^(1/3))^2/x^2,x, algorithm=""giac"")","\frac{6 \, a \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{3}} - \frac{2 \, a \log\left({\left| x \right|}\right)}{b^{3}} - \frac{3 \, {\left(2 \, a x^{\frac{1}{3}} + b\right)}}{{\left(a x^{\frac{2}{3}} + b x^{\frac{1}{3}}\right)} b^{2}}"," ",0,"6*a*log(abs(a*x^(1/3) + b))/b^3 - 2*a*log(abs(x))/b^3 - 3*(2*a*x^(1/3) + b)/((a*x^(2/3) + b*x^(1/3))*b^2)","A",0
2434,1,90,0,0.164368," ","integrate(1/(a+b/x^(1/3))^2/x^3,x, algorithm=""giac"")","-\frac{15 \, a^{4} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{6}} + \frac{5 \, a^{4} \log\left({\left| x \right|}\right)}{b^{6}} + \frac{60 \, a^{4} b x^{\frac{4}{3}} + 30 \, a^{3} b^{2} x - 10 \, a^{2} b^{3} x^{\frac{2}{3}} + 5 \, a b^{4} x^{\frac{1}{3}} - 3 \, b^{5}}{4 \, {\left(a x^{\frac{1}{3}} + b\right)} b^{6} x^{\frac{4}{3}}}"," ",0,"-15*a^4*log(abs(a*x^(1/3) + b))/b^6 + 5*a^4*log(abs(x))/b^6 + 1/4*(60*a^4*b*x^(4/3) + 30*a^3*b^2*x - 10*a^2*b^3*x^(2/3) + 5*a*b^4*x^(1/3) - 3*b^5)/((a*x^(1/3) + b)*b^6*x^(4/3))","A",0
2435,1,123,0,0.167468," ","integrate(1/(a+b/x^(1/3))^2/x^4,x, algorithm=""giac"")","\frac{24 \, a^{7} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{9}} - \frac{8 \, a^{7} \log\left({\left| x \right|}\right)}{b^{9}} - \frac{840 \, a^{7} b x^{\frac{7}{3}} + 420 \, a^{6} b^{2} x^{2} - 140 \, a^{5} b^{3} x^{\frac{5}{3}} + 70 \, a^{4} b^{4} x^{\frac{4}{3}} - 42 \, a^{3} b^{5} x + 28 \, a^{2} b^{6} x^{\frac{2}{3}} - 20 \, a b^{7} x^{\frac{1}{3}} + 15 \, b^{8}}{35 \, {\left(a x^{\frac{1}{3}} + b\right)} b^{9} x^{\frac{7}{3}}}"," ",0,"24*a^7*log(abs(a*x^(1/3) + b))/b^9 - 8*a^7*log(abs(x))/b^9 - 1/35*(840*a^7*b*x^(7/3) + 420*a^6*b^2*x^2 - 140*a^5*b^3*x^(5/3) + 70*a^4*b^4*x^(4/3) - 42*a^3*b^5*x + 28*a^2*b^6*x^(2/3) - 20*a*b^7*x^(1/3) + 15*b^8)/((a*x^(1/3) + b)*b^9*x^(7/3))","A",0
2436,1,156,0,0.193121," ","integrate(1/(a+b/x^(1/3))^2/x^5,x, algorithm=""giac"")","-\frac{33 \, a^{10} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{12}} + \frac{11 \, a^{10} \log\left({\left| x \right|}\right)}{b^{12}} + \frac{27720 \, a^{10} b x^{\frac{10}{3}} + 13860 \, a^{9} b^{2} x^{3} - 4620 \, a^{8} b^{3} x^{\frac{8}{3}} + 2310 \, a^{7} b^{4} x^{\frac{7}{3}} - 1386 \, a^{6} b^{5} x^{2} + 924 \, a^{5} b^{6} x^{\frac{5}{3}} - 660 \, a^{4} b^{7} x^{\frac{4}{3}} + 495 \, a^{3} b^{8} x - 385 \, a^{2} b^{9} x^{\frac{2}{3}} + 308 \, a b^{10} x^{\frac{1}{3}} - 252 \, b^{11}}{840 \, {\left(a x^{\frac{1}{3}} + b\right)} b^{12} x^{\frac{10}{3}}}"," ",0,"-33*a^10*log(abs(a*x^(1/3) + b))/b^12 + 11*a^10*log(abs(x))/b^12 + 1/840*(27720*a^10*b*x^(10/3) + 13860*a^9*b^2*x^3 - 4620*a^8*b^3*x^(8/3) + 2310*a^7*b^4*x^(7/3) - 1386*a^6*b^5*x^2 + 924*a^5*b^6*x^(5/3) - 660*a^4*b^7*x^(4/3) + 495*a^3*b^8*x - 385*a^2*b^9*x^(2/3) + 308*a*b^10*x^(1/3) - 252*b^11)/((a*x^(1/3) + b)*b^12*x^(10/3))","A",0
2437,1,145,0,0.166976," ","integrate(x^2/(a+b/x^(1/3))^3,x, algorithm=""giac"")","-\frac{165 \, b^{9} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{12}} - \frac{3 \, {\left(22 \, a b^{10} x^{\frac{1}{3}} + 21 \, b^{11}\right)}}{2 \, {\left(a x^{\frac{1}{3}} + b\right)}^{2} a^{12}} + \frac{56 \, a^{24} x^{3} - 189 \, a^{23} b x^{\frac{8}{3}} + 432 \, a^{22} b^{2} x^{\frac{7}{3}} - 840 \, a^{21} b^{3} x^{2} + 1512 \, a^{20} b^{4} x^{\frac{5}{3}} - 2646 \, a^{19} b^{5} x^{\frac{4}{3}} + 4704 \, a^{18} b^{6} x - 9072 \, a^{17} b^{7} x^{\frac{2}{3}} + 22680 \, a^{16} b^{8} x^{\frac{1}{3}}}{168 \, a^{27}}"," ",0,"-165*b^9*log(abs(a*x^(1/3) + b))/a^12 - 3/2*(22*a*b^10*x^(1/3) + 21*b^11)/((a*x^(1/3) + b)^2*a^12) + 1/168*(56*a^24*x^3 - 189*a^23*b*x^(8/3) + 432*a^22*b^2*x^(7/3) - 840*a^21*b^3*x^2 + 1512*a^20*b^4*x^(5/3) - 2646*a^19*b^5*x^(4/3) + 4704*a^18*b^6*x - 9072*a^17*b^7*x^(2/3) + 22680*a^16*b^8*x^(1/3))/a^27","A",0
2438,1,112,0,0.157410," ","integrate(x/(a+b/x^(1/3))^3,x, algorithm=""giac"")","\frac{84 \, b^{6} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{9}} + \frac{3 \, {\left(16 \, a b^{7} x^{\frac{1}{3}} + 15 \, b^{8}\right)}}{2 \, {\left(a x^{\frac{1}{3}} + b\right)}^{2} a^{9}} + \frac{5 \, a^{15} x^{2} - 18 \, a^{14} b x^{\frac{5}{3}} + 45 \, a^{13} b^{2} x^{\frac{4}{3}} - 100 \, a^{12} b^{3} x + 225 \, a^{11} b^{4} x^{\frac{2}{3}} - 630 \, a^{10} b^{5} x^{\frac{1}{3}}}{10 \, a^{18}}"," ",0,"84*b^6*log(abs(a*x^(1/3) + b))/a^9 + 3/2*(16*a*b^7*x^(1/3) + 15*b^8)/((a*x^(1/3) + b)^2*a^9) + 1/10*(5*a^15*x^2 - 18*a^14*b*x^(5/3) + 45*a^13*b^2*x^(4/3) - 100*a^12*b^3*x + 225*a^11*b^4*x^(2/3) - 630*a^10*b^5*x^(1/3))/a^18","A",0
2439,1,79,0,0.163090," ","integrate(1/(a+b/x^(1/3))^3,x, algorithm=""giac"")","-\frac{30 \, b^{3} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{6}} - \frac{3 \, {\left(10 \, a b^{4} x^{\frac{1}{3}} + 9 \, b^{5}\right)}}{2 \, {\left(a x^{\frac{1}{3}} + b\right)}^{2} a^{6}} + \frac{2 \, a^{6} x - 9 \, a^{5} b x^{\frac{2}{3}} + 36 \, a^{4} b^{2} x^{\frac{1}{3}}}{2 \, a^{9}}"," ",0,"-30*b^3*log(abs(a*x^(1/3) + b))/a^6 - 3/2*(10*a*b^4*x^(1/3) + 9*b^5)/((a*x^(1/3) + b)^2*a^6) + 1/2*(2*a^6*x - 9*a^5*b*x^(2/3) + 36*a^4*b^2*x^(1/3))/a^9","A",0
2440,1,44,0,0.170776," ","integrate(1/(a+b/x^(1/3))^3/x,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{a^{3}} + \frac{3 \, {\left(4 \, b x^{\frac{1}{3}} + \frac{3 \, b^{2}}{a}\right)}}{2 \, {\left(a x^{\frac{1}{3}} + b\right)}^{2} a^{2}}"," ",0,"3*log(abs(a*x^(1/3) + b))/a^3 + 3/2*(4*b*x^(1/3) + 3*b^2/a)/((a*x^(1/3) + b)^2*a^2)","A",0
2441,1,49,0,0.166254," ","integrate(1/(a+b/x^(1/3))^3/x^2,x, algorithm=""giac"")","-\frac{3 \, \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{3}} + \frac{\log\left({\left| x \right|}\right)}{b^{3}} + \frac{3 \, {\left(2 \, a b x^{\frac{1}{3}} + 3 \, b^{2}\right)}}{2 \, {\left(a x^{\frac{1}{3}} + b\right)}^{2} b^{3}}"," ",0,"-3*log(abs(a*x^(1/3) + b))/b^3 + log(abs(x))/b^3 + 3/2*(2*a*b*x^(1/3) + 3*b^2)/((a*x^(1/3) + b)^2*b^3)","A",0
2442,1,90,0,0.195345," ","integrate(1/(a+b/x^(1/3))^3/x^3,x, algorithm=""giac"")","\frac{30 \, a^{3} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{6}} - \frac{10 \, a^{3} \log\left({\left| x \right|}\right)}{b^{6}} - \frac{60 \, a^{4} b x^{\frac{4}{3}} + 90 \, a^{3} b^{2} x + 20 \, a^{2} b^{3} x^{\frac{2}{3}} - 5 \, a b^{4} x^{\frac{1}{3}} + 2 \, b^{5}}{2 \, {\left(a x^{\frac{1}{3}} + b\right)}^{2} b^{6} x}"," ",0,"30*a^3*log(abs(a*x^(1/3) + b))/b^6 - 10*a^3*log(abs(x))/b^6 - 1/2*(60*a^4*b*x^(4/3) + 90*a^3*b^2*x + 20*a^2*b^3*x^(2/3) - 5*a*b^4*x^(1/3) + 2*b^5)/((a*x^(1/3) + b)^2*b^6*x)","A",0
2443,1,123,0,0.208157," ","integrate(1/(a+b/x^(1/3))^3/x^4,x, algorithm=""giac"")","-\frac{84 \, a^{6} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{9}} + \frac{28 \, a^{6} \log\left({\left| x \right|}\right)}{b^{9}} + \frac{840 \, a^{7} b x^{\frac{7}{3}} + 1260 \, a^{6} b^{2} x^{2} + 280 \, a^{5} b^{3} x^{\frac{5}{3}} - 70 \, a^{4} b^{4} x^{\frac{4}{3}} + 28 \, a^{3} b^{5} x - 14 \, a^{2} b^{6} x^{\frac{2}{3}} + 8 \, a b^{7} x^{\frac{1}{3}} - 5 \, b^{8}}{10 \, {\left(a x^{\frac{1}{3}} + b\right)}^{2} b^{9} x^{2}}"," ",0,"-84*a^6*log(abs(a*x^(1/3) + b))/b^9 + 28*a^6*log(abs(x))/b^9 + 1/10*(840*a^7*b*x^(7/3) + 1260*a^6*b^2*x^2 + 280*a^5*b^3*x^(5/3) - 70*a^4*b^4*x^(4/3) + 28*a^3*b^5*x - 14*a^2*b^6*x^(2/3) + 8*a*b^7*x^(1/3) - 5*b^8)/((a*x^(1/3) + b)^2*b^9*x^2)","A",0
2444,1,156,0,0.172061," ","integrate(1/(a+b/x^(1/3))^3/x^5,x, algorithm=""giac"")","\frac{165 \, a^{9} \log\left({\left| a x^{\frac{1}{3}} + b \right|}\right)}{b^{12}} - \frac{55 \, a^{9} \log\left({\left| x \right|}\right)}{b^{12}} - \frac{27720 \, a^{10} b x^{\frac{10}{3}} + 41580 \, a^{9} b^{2} x^{3} + 9240 \, a^{8} b^{3} x^{\frac{8}{3}} - 2310 \, a^{7} b^{4} x^{\frac{7}{3}} + 924 \, a^{6} b^{5} x^{2} - 462 \, a^{5} b^{6} x^{\frac{5}{3}} + 264 \, a^{4} b^{7} x^{\frac{4}{3}} - 165 \, a^{3} b^{8} x + 110 \, a^{2} b^{9} x^{\frac{2}{3}} - 77 \, a b^{10} x^{\frac{1}{3}} + 56 \, b^{11}}{168 \, {\left(a x^{\frac{1}{3}} + b\right)}^{2} b^{12} x^{3}}"," ",0,"165*a^9*log(abs(a*x^(1/3) + b))/b^12 - 55*a^9*log(abs(x))/b^12 - 1/168*(27720*a^10*b*x^(10/3) + 41580*a^9*b^2*x^3 + 9240*a^8*b^3*x^(8/3) - 2310*a^7*b^4*x^(7/3) + 924*a^6*b^5*x^2 - 462*a^5*b^6*x^(5/3) + 264*a^4*b^7*x^(4/3) - 165*a^3*b^8*x + 110*a^2*b^9*x^(2/3) - 77*a*b^10*x^(1/3) + 56*b^11)/((a*x^(1/3) + b)^2*b^12*x^3)","A",0
2445,1,28,0,0.165768," ","integrate(1/(1+b/x^(1/3)),x, algorithm=""giac"")","-3 \, b^{3} \log\left({\left| b + x^{\frac{1}{3}} \right|}\right) + 3 \, b^{2} x^{\frac{1}{3}} - \frac{3}{2} \, b x^{\frac{2}{3}} + x"," ",0,"-3*b^3*log(abs(b + x^(1/3))) + 3*b^2*x^(1/3) - 3/2*b*x^(2/3) + x","A",0
2446,1,9,0,0.189265," ","integrate(x^(2/3)*(1+x^(5/3))^(2/3),x, algorithm=""giac"")","\frac{9}{25} \, {\left(x^{\frac{5}{3}} + 1\right)}^{\frac{5}{3}}"," ",0,"9/25*(x^(5/3) + 1)^(5/3)","A",0
2447,1,81,0,0.710128," ","integrate(x^(7/3)*(a^(10/3)-x^(10/3))^(19/7),x, algorithm=""giac"")","-\frac{7}{20} \, {\left(a^{\frac{10}{3}} - x^{\frac{10}{3}}\right)}^{\frac{12}{7}} a^{\frac{20}{3}} + \frac{21}{95} \, {\left(a^{\frac{10}{3}} - x^{\frac{10}{3}}\right)}^{\frac{19}{7}} a^{\frac{10}{3}} + \frac{7}{380} \, {\left(19 \, {\left(a^{\frac{10}{3}} - x^{\frac{10}{3}}\right)}^{\frac{12}{7}} a^{\frac{10}{3}} - 12 \, {\left(a^{\frac{10}{3}} - x^{\frac{10}{3}}\right)}^{\frac{19}{7}}\right)} a^{\frac{10}{3}} - \frac{21}{260} \, {\left(a^{\frac{10}{3}} - x^{\frac{10}{3}}\right)}^{\frac{26}{7}}"," ",0,"-7/20*(a^(10/3) - x^(10/3))^(12/7)*a^(20/3) + 21/95*(a^(10/3) - x^(10/3))^(19/7)*a^(10/3) + 7/380*(19*(a^(10/3) - x^(10/3))^(12/7)*a^(10/3) - 12*(a^(10/3) - x^(10/3))^(19/7))*a^(10/3) - 21/260*(a^(10/3) - x^(10/3))^(26/7)","B",0
2448,1,29,0,0.186668," ","integrate(1/(1+x^(1/5)),x, algorithm=""giac"")","\frac{5}{4} \, x^{\frac{4}{5}} - \frac{5}{3} \, x^{\frac{3}{5}} + \frac{5}{2} \, x^{\frac{2}{5}} - 5 \, x^{\frac{1}{5}} + 5 \, \log\left(x^{\frac{1}{5}} + 1\right)"," ",0,"5/4*x^(4/5) - 5/3*x^(3/5) + 5/2*x^(2/5) - 5*x^(1/5) + 5*log(x^(1/5) + 1)","A",0
2449,1,9,0,0.158696," ","integrate(1/x^(1/5)/(1+x^(4/5))^(1/2),x, algorithm=""giac"")","\frac{5}{2} \, \sqrt{x^{\frac{4}{5}} + 1}"," ",0,"5/2*sqrt(x^(4/5) + 1)","A",0
2450,0,0,0,0.000000," ","integrate((a+b/x^(3/5))^(2/3),x, algorithm=""giac"")","\int {\left(a + \frac{b}{x^{\frac{3}{5}}}\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((a + b/x^(3/5))^(2/3), x)","F",0
2451,1,29,0,0.172394," ","integrate(x^3*(a+b*x^n),x, algorithm=""giac"")","\frac{4 \, b x^{4} x^{n} + a n x^{4} + 4 \, a x^{4}}{4 \, {\left(n + 4\right)}}"," ",0,"1/4*(4*b*x^4*x^n + a*n*x^4 + 4*a*x^4)/(n + 4)","A",0
2452,1,29,0,0.186773," ","integrate(x^2*(a+b*x^n),x, algorithm=""giac"")","\frac{3 \, b x^{3} x^{n} + a n x^{3} + 3 \, a x^{3}}{3 \, {\left(n + 3\right)}}"," ",0,"1/3*(3*b*x^3*x^n + a*n*x^3 + 3*a*x^3)/(n + 3)","A",0
2453,1,29,0,0.154955," ","integrate(x*(a+b*x^n),x, algorithm=""giac"")","\frac{2 \, b x^{2} x^{n} + a n x^{2} + 2 \, a x^{2}}{2 \, {\left(n + 2\right)}}"," ",0,"1/2*(2*b*x^2*x^n + a*n*x^2 + 2*a*x^2)/(n + 2)","A",0
2454,1,16,0,0.153637," ","integrate(a+b*x^n,x, algorithm=""giac"")","a x + \frac{b x^{n + 1}}{n + 1}"," ",0,"a*x + b*x^(n + 1)/(n + 1)","A",0
2455,0,0,0,0.000000," ","integrate((a+b*x^n)/x,x, algorithm=""giac"")","\int \frac{b x^{n} + a}{x}\,{d x}"," ",0,"integrate((b*x^n + a)/x, x)","F",0
2456,0,0,0,0.000000," ","integrate((a+b*x^n)/x^2,x, algorithm=""giac"")","\int \frac{b x^{n} + a}{x^{2}}\,{d x}"," ",0,"integrate((b*x^n + a)/x^2, x)","F",0
2457,0,0,0,0.000000," ","integrate((a+b*x^n)/x^3,x, algorithm=""giac"")","\int \frac{b x^{n} + a}{x^{3}}\,{d x}"," ",0,"integrate((b*x^n + a)/x^3, x)","F",0
2458,1,88,0,0.185355," ","integrate(x^3*(a+b*x^n)^2,x, algorithm=""giac"")","\frac{2 \, b^{2} n x^{4} x^{2 \, n} + 8 \, a b n x^{4} x^{n} + a^{2} n^{2} x^{4} + 8 \, b^{2} x^{4} x^{2 \, n} + 16 \, a b x^{4} x^{n} + 6 \, a^{2} n x^{4} + 8 \, a^{2} x^{4}}{4 \, {\left(n^{2} + 6 \, n + 8\right)}}"," ",0,"1/4*(2*b^2*n*x^4*x^(2*n) + 8*a*b*n*x^4*x^n + a^2*n^2*x^4 + 8*b^2*x^4*x^(2*n) + 16*a*b*x^4*x^n + 6*a^2*n*x^4 + 8*a^2*x^4)/(n^2 + 6*n + 8)","B",0
2459,1,91,0,0.165825," ","integrate(x^2*(a+b*x^n)^2,x, algorithm=""giac"")","\frac{3 \, b^{2} n x^{3} x^{2 \, n} + 12 \, a b n x^{3} x^{n} + 2 \, a^{2} n^{2} x^{3} + 9 \, b^{2} x^{3} x^{2 \, n} + 18 \, a b x^{3} x^{n} + 9 \, a^{2} n x^{3} + 9 \, a^{2} x^{3}}{3 \, {\left(2 \, n^{2} + 9 \, n + 9\right)}}"," ",0,"1/3*(3*b^2*n*x^3*x^(2*n) + 12*a*b*n*x^3*x^n + 2*a^2*n^2*x^3 + 9*b^2*x^3*x^(2*n) + 18*a*b*x^3*x^n + 9*a^2*n*x^3 + 9*a^2*x^3)/(2*n^2 + 9*n + 9)","B",0
2460,1,87,0,0.180084," ","integrate(x*(a+b*x^n)^2,x, algorithm=""giac"")","\frac{b^{2} n x^{2} x^{2 \, n} + 4 \, a b n x^{2} x^{n} + a^{2} n^{2} x^{2} + 2 \, b^{2} x^{2} x^{2 \, n} + 4 \, a b x^{2} x^{n} + 3 \, a^{2} n x^{2} + 2 \, a^{2} x^{2}}{2 \, {\left(n^{2} + 3 \, n + 2\right)}}"," ",0,"1/2*(b^2*n*x^2*x^(2*n) + 4*a*b*n*x^2*x^n + a^2*n^2*x^2 + 2*b^2*x^2*x^(2*n) + 4*a*b*x^2*x^n + 3*a^2*n*x^2 + 2*a^2*x^2)/(n^2 + 3*n + 2)","B",0
2461,1,73,0,0.166489," ","integrate((a+b*x^n)^2,x, algorithm=""giac"")","\frac{2 \, a^{2} n^{2} x + b^{2} n x x^{2 \, n} + 4 \, a b n x x^{n} + 3 \, a^{2} n x + b^{2} x x^{2 \, n} + 2 \, a b x x^{n} + a^{2} x}{2 \, n^{2} + 3 \, n + 1}"," ",0,"(2*a^2*n^2*x + b^2*n*x*x^(2*n) + 4*a*b*n*x*x^n + 3*a^2*n*x + b^2*x*x^(2*n) + 2*a*b*x*x^n + a^2*x)/(2*n^2 + 3*n + 1)","A",0
2462,0,0,0,0.000000," ","integrate((a+b*x^n)^2/x,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((b*x^n + a)^2/x, x)","F",0
2463,0,0,0,0.000000," ","integrate((a+b*x^n)^2/x^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{2}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^2/x^2, x)","F",0
2464,0,0,0,0.000000," ","integrate((a+b*x^n)^2/x^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{2}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^n + a)^2/x^3, x)","F",0
2465,1,188,0,0.187379," ","integrate(x^3*(a+b*x^n)^3,x, algorithm=""giac"")","\frac{4 \, b^{3} n^{2} x^{4} x^{3 \, n} + 18 \, a b^{2} n^{2} x^{4} x^{2 \, n} + 36 \, a^{2} b n^{2} x^{4} x^{n} + 3 \, a^{3} n^{3} x^{4} + 24 \, b^{3} n x^{4} x^{3 \, n} + 96 \, a b^{2} n x^{4} x^{2 \, n} + 120 \, a^{2} b n x^{4} x^{n} + 22 \, a^{3} n^{2} x^{4} + 32 \, b^{3} x^{4} x^{3 \, n} + 96 \, a b^{2} x^{4} x^{2 \, n} + 96 \, a^{2} b x^{4} x^{n} + 48 \, a^{3} n x^{4} + 32 \, a^{3} x^{4}}{4 \, {\left(3 \, n^{3} + 22 \, n^{2} + 48 \, n + 32\right)}}"," ",0,"1/4*(4*b^3*n^2*x^4*x^(3*n) + 18*a*b^2*n^2*x^4*x^(2*n) + 36*a^2*b*n^2*x^4*x^n + 3*a^3*n^3*x^4 + 24*b^3*n*x^4*x^(3*n) + 96*a*b^2*n*x^4*x^(2*n) + 120*a^2*b*n*x^4*x^n + 22*a^3*n^2*x^4 + 32*b^3*x^4*x^(3*n) + 96*a*b^2*x^4*x^(2*n) + 96*a^2*b*x^4*x^n + 48*a^3*n*x^4 + 32*a^3*x^4)/(3*n^3 + 22*n^2 + 48*n + 32)","B",0
2466,1,188,0,0.262833," ","integrate(x^2*(a+b*x^n)^3,x, algorithm=""giac"")","\frac{2 \, b^{3} n^{2} x^{3} x^{3 \, n} + 9 \, a b^{2} n^{2} x^{3} x^{2 \, n} + 18 \, a^{2} b n^{2} x^{3} x^{n} + 2 \, a^{3} n^{3} x^{3} + 9 \, b^{3} n x^{3} x^{3 \, n} + 36 \, a b^{2} n x^{3} x^{2 \, n} + 45 \, a^{2} b n x^{3} x^{n} + 11 \, a^{3} n^{2} x^{3} + 9 \, b^{3} x^{3} x^{3 \, n} + 27 \, a b^{2} x^{3} x^{2 \, n} + 27 \, a^{2} b x^{3} x^{n} + 18 \, a^{3} n x^{3} + 9 \, a^{3} x^{3}}{3 \, {\left(2 \, n^{3} + 11 \, n^{2} + 18 \, n + 9\right)}}"," ",0,"1/3*(2*b^3*n^2*x^3*x^(3*n) + 9*a*b^2*n^2*x^3*x^(2*n) + 18*a^2*b*n^2*x^3*x^n + 2*a^3*n^3*x^3 + 9*b^3*n*x^3*x^(3*n) + 36*a*b^2*n*x^3*x^(2*n) + 45*a^2*b*n*x^3*x^n + 11*a^3*n^2*x^3 + 9*b^3*x^3*x^(3*n) + 27*a*b^2*x^3*x^(2*n) + 27*a^2*b*x^3*x^n + 18*a^3*n*x^3 + 9*a^3*x^3)/(2*n^3 + 11*n^2 + 18*n + 9)","B",0
2467,1,188,0,0.184853," ","integrate(x*(a+b*x^n)^3,x, algorithm=""giac"")","\frac{2 \, b^{3} n^{2} x^{2} x^{3 \, n} + 9 \, a b^{2} n^{2} x^{2} x^{2 \, n} + 18 \, a^{2} b n^{2} x^{2} x^{n} + 3 \, a^{3} n^{3} x^{2} + 6 \, b^{3} n x^{2} x^{3 \, n} + 24 \, a b^{2} n x^{2} x^{2 \, n} + 30 \, a^{2} b n x^{2} x^{n} + 11 \, a^{3} n^{2} x^{2} + 4 \, b^{3} x^{2} x^{3 \, n} + 12 \, a b^{2} x^{2} x^{2 \, n} + 12 \, a^{2} b x^{2} x^{n} + 12 \, a^{3} n x^{2} + 4 \, a^{3} x^{2}}{2 \, {\left(3 \, n^{3} + 11 \, n^{2} + 12 \, n + 4\right)}}"," ",0,"1/2*(2*b^3*n^2*x^2*x^(3*n) + 9*a*b^2*n^2*x^2*x^(2*n) + 18*a^2*b*n^2*x^2*x^n + 3*a^3*n^3*x^2 + 6*b^3*n*x^2*x^(3*n) + 24*a*b^2*n*x^2*x^(2*n) + 30*a^2*b*n*x^2*x^n + 11*a^3*n^2*x^2 + 4*b^3*x^2*x^(3*n) + 12*a*b^2*x^2*x^(2*n) + 12*a^2*b*x^2*x^n + 12*a^3*n*x^2 + 4*a^3*x^2)/(3*n^3 + 11*n^2 + 12*n + 4)","B",0
2468,1,159,0,0.162477," ","integrate((a+b*x^n)^3,x, algorithm=""giac"")","\frac{6 \, a^{3} n^{3} x + 2 \, b^{3} n^{2} x x^{3 \, n} + 9 \, a b^{2} n^{2} x x^{2 \, n} + 18 \, a^{2} b n^{2} x x^{n} + 11 \, a^{3} n^{2} x + 3 \, b^{3} n x x^{3 \, n} + 12 \, a b^{2} n x x^{2 \, n} + 15 \, a^{2} b n x x^{n} + 6 \, a^{3} n x + b^{3} x x^{3 \, n} + 3 \, a b^{2} x x^{2 \, n} + 3 \, a^{2} b x x^{n} + a^{3} x}{6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1}"," ",0,"(6*a^3*n^3*x + 2*b^3*n^2*x*x^(3*n) + 9*a*b^2*n^2*x*x^(2*n) + 18*a^2*b*n^2*x*x^n + 11*a^3*n^2*x + 3*b^3*n*x*x^(3*n) + 12*a*b^2*n*x*x^(2*n) + 15*a^2*b*n*x*x^n + 6*a^3*n*x + b^3*x*x^(3*n) + 3*a*b^2*x*x^(2*n) + 3*a^2*b*x*x^n + a^3*x)/(6*n^3 + 11*n^2 + 6*n + 1)","B",0
2469,0,0,0,0.000000," ","integrate((a+b*x^n)^3/x,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{3}}{x}\,{d x}"," ",0,"integrate((b*x^n + a)^3/x, x)","F",0
2470,0,0,0,0.000000," ","integrate((a+b*x^n)^3/x^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{3}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^3/x^2, x)","F",0
2471,0,0,0,0.000000," ","integrate((a+b*x^n)^3/x^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{3}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^n + a)^3/x^3, x)","F",0
2472,0,0,0,0.000000," ","integrate(x/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x}{b x^{n} + a}\,{d x}"," ",0,"integrate(x/(b*x^n + a), x)","F",0
2473,0,0,0,0.000000," ","integrate(1/(a+b*x^n),x, algorithm=""giac"")","\int \frac{1}{b x^{n} + a}\,{d x}"," ",0,"integrate(1/(b*x^n + a), x)","F",0
2474,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*x), x)","F",0
2475,0,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*x^2), x)","F",0
2476,0,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*x^3), x)","F",0
2477,0,0,0,0.000000," ","integrate(x/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x/(b*x^n + a)^2, x)","F",0
2478,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^(-2), x)","F",0
2479,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{2} x}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^2*x), x)","F",0
2480,0,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^2*x^2), x)","F",0
2481,0,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^2*x^3), x)","F",0
2482,0,0,0,0.000000," ","integrate(x/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x/(b*x^n + a)^3, x)","F",0
2483,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^n + a)^(-3), x)","F",0
2484,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{3} x}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^3*x), x)","F",0
2485,0,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^3*x^2), x)","F",0
2486,0,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^3*x^3), x)","F",0
2487,0,0,0,0.000000," ","integrate(x*(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n} + a} x\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)*x, x)","F",0
2488,0,0,0,0.000000," ","integrate((a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n} + a}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a), x)","F",0
2489,0,0,0,0.000000," ","integrate((a+b*x^n)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{b x^{n} + a}}{x}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)/x, x)","F",0
2490,0,0,0,0.000000," ","integrate((a+b*x^n)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{b x^{n} + a}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)/x^2, x)","F",0
2491,0,0,0,0.000000," ","integrate((a+b*x^n)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{b x^{n} + a}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)/x^3, x)","F",0
2492,0,0,0,0.000000," ","integrate(x*(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{\frac{3}{2}} x\,{d x}"," ",0,"integrate((b*x^n + a)^(3/2)*x, x)","F",0
2493,0,0,0,0.000000," ","integrate((a+b*x^n)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^(3/2), x)","F",0
2494,0,0,0,0.000000," ","integrate((a+b*x^n)^(3/2)/x,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate((b*x^n + a)^(3/2)/x, x)","F",0
2495,0,0,0,0.000000," ","integrate((a+b*x^n)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^(3/2)/x^2, x)","F",0
2496,0,0,0,0.000000," ","integrate((a+b*x^n)^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^n + a)^(3/2)/x^3, x)","F",0
2497,0,0,0,0.000000," ","integrate(x*(a+b*x^n)^(5/2),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{\frac{5}{2}} x\,{d x}"," ",0,"integrate((b*x^n + a)^(5/2)*x, x)","F",0
2498,0,0,0,0.000000," ","integrate((a+b*x^n)^(5/2),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^(5/2), x)","F",0
2499,0,0,0,0.000000," ","integrate((a+b*x^n)^(5/2)/x,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{\frac{5}{2}}}{x}\,{d x}"," ",0,"integrate((b*x^n + a)^(5/2)/x, x)","F",0
2500,0,0,0,0.000000," ","integrate((a+b*x^n)^(5/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{\frac{5}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^(5/2)/x^2, x)","F",0
2501,0,0,0,0.000000," ","integrate((a+b*x^n)^(5/2)/x^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{\frac{5}{2}}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^n + a)^(5/2)/x^3, x)","F",0
2502,0,0,0,0.000000," ","integrate(x/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x/sqrt(b*x^n + a), x)","F",0
2503,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*x^n + a), x)","F",0
2504,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{n} + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^n + a)*x), x)","F",0
2505,0,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{n} + a} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^n + a)*x^2), x)","F",0
2506,0,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{n} + a} x^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^n + a)*x^3), x)","F",0
2507,0,0,0,0.000000," ","integrate(x/(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(b*x^n + a)^(3/2), x)","F",0
2508,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^n + a)^(-3/2), x)","F",0
2509,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^(3/2)*x), x)","F",0
2510,0,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^(3/2)*x^2), x)","F",0
2511,0,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^(3/2)*x^3), x)","F",0
2512,0,0,0,0.000000," ","integrate(x/(a+b*x^n)^(5/2),x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{n} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x/(b*x^n + a)^(5/2), x)","F",0
2513,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^n + a)^(-5/2), x)","F",0
2514,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^(5/2)*x), x)","F",0
2515,0,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^(5/2)*x^2), x)","F",0
2516,0,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^(5/2)*x^3), x)","F",0
2517,0,0,0,0.000000," ","integrate((a+b*x^n)^(1/3)/x,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{\frac{1}{3}}}{x}\,{d x}"," ",0,"integrate((b*x^n + a)^(1/3)/x, x)","F",0
2518,0,0,0,0.000000," ","integrate(x^(-1+4*n)*(a+b*x^n),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)} x^{4 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)*x^(4*n - 1), x)","F",0
2519,0,0,0,0.000000," ","integrate(x^(-1+3*n)*(a+b*x^n),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)} x^{3 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)*x^(3*n - 1), x)","F",0
2520,0,0,0,0.000000," ","integrate(x^(-1+2*n)*(a+b*x^n),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)} x^{2 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)*x^(2*n - 1), x)","F",0
2521,1,19,0,0.148849," ","integrate(x^(-1+n)*(a+b*x^n),x, algorithm=""giac"")","\frac{b x^{2 \, n} + 2 \, a x^{n}}{2 \, n}"," ",0,"1/2*(b*x^(2*n) + 2*a*x^n)/n","A",0
2522,0,0,0,0.000000," ","integrate((a+b*x^n)/x,x, algorithm=""giac"")","\int \frac{b x^{n} + a}{x}\,{d x}"," ",0,"integrate((b*x^n + a)/x, x)","F",0
2523,1,21,0,0.179728," ","integrate(x^(-1-n)*(a+b*x^n),x, algorithm=""giac"")","\frac{b n x^{n} \log\left(x\right) - a}{n x^{n}}"," ",0,"(b*n*x^n*log(x) - a)/(n*x^n)","A",0
2524,1,20,0,0.179322," ","integrate(x^(-1-2*n)*(a+b*x^n),x, algorithm=""giac"")","-\frac{2 \, b x^{n} + a}{2 \, n x^{2 \, n}}"," ",0,"-1/2*(2*b*x^n + a)/(n*x^(2*n))","A",0
2525,1,22,0,0.189619," ","integrate(x^(-1-3*n)*(a+b*x^n),x, algorithm=""giac"")","-\frac{3 \, b x^{n} + 2 \, a}{6 \, n x^{3 \, n}}"," ",0,"-1/6*(3*b*x^n + 2*a)/(n*x^(3*n))","A",0
2526,1,22,0,0.164258," ","integrate(x^(-1-4*n)*(a+b*x^n),x, algorithm=""giac"")","-\frac{4 \, b x^{n} + 3 \, a}{12 \, n x^{4 \, n}}"," ",0,"-1/12*(4*b*x^n + 3*a)/(n*x^(4*n))","A",0
2527,1,22,0,0.162918," ","integrate(x^(-1-5*n)*(a+b*x^n),x, algorithm=""giac"")","-\frac{5 \, b x^{n} + 4 \, a}{20 \, n x^{5 \, n}}"," ",0,"-1/20*(5*b*x^n + 4*a)/(n*x^(5*n))","A",0
2528,0,0,0,0.000000," ","integrate(x^(-1+4*n)*(a+b*x^n)^2,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{2} x^{4 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^2*x^(4*n - 1), x)","F",0
2529,0,0,0,0.000000," ","integrate(x^(-1+3*n)*(a+b*x^n)^2,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{2} x^{3 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^2*x^(3*n - 1), x)","F",0
2530,0,0,0,0.000000," ","integrate(x^(-1+2*n)*(a+b*x^n)^2,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{2} x^{2 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^2*x^(2*n - 1), x)","F",0
2531,1,32,0,0.150978," ","integrate(x^(-1+n)*(a+b*x^n)^2,x, algorithm=""giac"")","\frac{b^{2} x^{3 \, n} + 3 \, a b x^{2 \, n} + 3 \, a^{2} x^{n}}{3 \, n}"," ",0,"1/3*(b^2*x^(3*n) + 3*a*b*x^(2*n) + 3*a^2*x^n)/n","A",0
2532,0,0,0,0.000000," ","integrate((a+b*x^n)^2/x,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((b*x^n + a)^2/x, x)","F",0
2533,1,34,0,0.179310," ","integrate(x^(-1-n)*(a+b*x^n)^2,x, algorithm=""giac"")","\frac{2 \, a b n x^{n} \log\left(x\right) + b^{2} x^{2 \, n} - a^{2}}{n x^{n}}"," ",0,"(2*a*b*n*x^n*log(x) + b^2*x^(2*n) - a^2)/(n*x^n)","A",0
2534,1,38,0,0.182853," ","integrate(x^(-1-2*n)*(a+b*x^n)^2,x, algorithm=""giac"")","\frac{2 \, b^{2} n x^{2 \, n} \log\left(x\right) - 4 \, a b x^{n} - a^{2}}{2 \, n x^{2 \, n}}"," ",0,"1/2*(2*b^2*n*x^(2*n)*log(x) - 4*a*b*x^n - a^2)/(n*x^(2*n))","A",0
2535,1,33,0,0.189499," ","integrate(x^(-1-3*n)*(a+b*x^n)^2,x, algorithm=""giac"")","-\frac{3 \, b^{2} x^{2 \, n} + 3 \, a b x^{n} + a^{2}}{3 \, n x^{3 \, n}}"," ",0,"-1/3*(3*b^2*x^(2*n) + 3*a*b*x^n + a^2)/(n*x^(3*n))","A",0
2536,1,35,0,0.186794," ","integrate(x^(-1-4*n)*(a+b*x^n)^2,x, algorithm=""giac"")","-\frac{6 \, b^{2} x^{2 \, n} + 8 \, a b x^{n} + 3 \, a^{2}}{12 \, n x^{4 \, n}}"," ",0,"-1/12*(6*b^2*x^(2*n) + 8*a*b*x^n + 3*a^2)/(n*x^(4*n))","A",0
2537,1,35,0,0.182686," ","integrate(x^(-1-5*n)*(a+b*x^n)^2,x, algorithm=""giac"")","-\frac{10 \, b^{2} x^{2 \, n} + 15 \, a b x^{n} + 6 \, a^{2}}{30 \, n x^{5 \, n}}"," ",0,"-1/30*(10*b^2*x^(2*n) + 15*a*b*x^n + 6*a^2)/(n*x^(5*n))","A",0
2538,1,35,0,0.190536," ","integrate(x^(-1-6*n)*(a+b*x^n)^2,x, algorithm=""giac"")","-\frac{15 \, b^{2} x^{2 \, n} + 24 \, a b x^{n} + 10 \, a^{2}}{60 \, n x^{6 \, n}}"," ",0,"-1/60*(15*b^2*x^(2*n) + 24*a*b*x^n + 10*a^2)/(n*x^(6*n))","A",0
2539,0,0,0,0.000000," ","integrate(x^(-1+4*n)*(a+b*x^n)^3,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{3} x^{4 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^3*x^(4*n - 1), x)","F",0
2540,0,0,0,0.000000," ","integrate(x^(-1+3*n)*(a+b*x^n)^3,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{3} x^{3 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^3*x^(3*n - 1), x)","F",0
2541,0,0,0,0.000000," ","integrate(x^(-1+2*n)*(a+b*x^n)^3,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{3} x^{2 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^3*x^(2*n - 1), x)","F",0
2542,1,45,0,0.154407," ","integrate(x^(-1+n)*(a+b*x^n)^3,x, algorithm=""giac"")","\frac{b^{3} x^{4 \, n} + 4 \, a b^{2} x^{3 \, n} + 6 \, a^{2} b x^{2 \, n} + 4 \, a^{3} x^{n}}{4 \, n}"," ",0,"1/4*(b^3*x^(4*n) + 4*a*b^2*x^(3*n) + 6*a^2*b*x^(2*n) + 4*a^3*x^n)/n","B",0
2543,0,0,0,0.000000," ","integrate((a+b*x^n)^3/x,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{3}}{x}\,{d x}"," ",0,"integrate((b*x^n + a)^3/x, x)","F",0
2544,1,48,0,0.191406," ","integrate(x^(-1-n)*(a+b*x^n)^3,x, algorithm=""giac"")","\frac{6 \, a^{2} b n x^{n} \log\left(x\right) + b^{3} x^{3 \, n} + 6 \, a b^{2} x^{2 \, n} - 2 \, a^{3}}{2 \, n x^{n}}"," ",0,"1/2*(6*a^2*b*n*x^n*log(x) + b^3*x^(3*n) + 6*a*b^2*x^(2*n) - 2*a^3)/(n*x^n)","A",0
2545,1,51,0,0.213740," ","integrate(x^(-1-2*n)*(a+b*x^n)^3,x, algorithm=""giac"")","\frac{6 \, a b^{2} n x^{2 \, n} \log\left(x\right) + 2 \, b^{3} x^{3 \, n} - 6 \, a^{2} b x^{n} - a^{3}}{2 \, n x^{2 \, n}}"," ",0,"1/2*(6*a*b^2*n*x^(2*n)*log(x) + 2*b^3*x^(3*n) - 6*a^2*b*x^n - a^3)/(n*x^(2*n))","A",0
2546,1,51,0,0.199040," ","integrate(x^(-1-3*n)*(a+b*x^n)^3,x, algorithm=""giac"")","\frac{6 \, b^{3} n x^{3 \, n} \log\left(x\right) - 18 \, a b^{2} x^{2 \, n} - 9 \, a^{2} b x^{n} - 2 \, a^{3}}{6 \, n x^{3 \, n}}"," ",0,"1/6*(6*b^3*n*x^(3*n)*log(x) - 18*a*b^2*x^(2*n) - 9*a^2*b*x^n - 2*a^3)/(n*x^(3*n))","A",0
2547,1,46,0,0.211840," ","integrate(x^(-1-4*n)*(a+b*x^n)^3,x, algorithm=""giac"")","-\frac{4 \, b^{3} x^{3 \, n} + 6 \, a b^{2} x^{2 \, n} + 4 \, a^{2} b x^{n} + a^{3}}{4 \, n x^{4 \, n}}"," ",0,"-1/4*(4*b^3*x^(3*n) + 6*a*b^2*x^(2*n) + 4*a^2*b*x^n + a^3)/(n*x^(4*n))","A",0
2548,1,48,0,0.201744," ","integrate(x^(-1-5*n)*(a+b*x^n)^3,x, algorithm=""giac"")","-\frac{10 \, b^{3} x^{3 \, n} + 20 \, a b^{2} x^{2 \, n} + 15 \, a^{2} b x^{n} + 4 \, a^{3}}{20 \, n x^{5 \, n}}"," ",0,"-1/20*(10*b^3*x^(3*n) + 20*a*b^2*x^(2*n) + 15*a^2*b*x^n + 4*a^3)/(n*x^(5*n))","A",0
2549,1,48,0,0.231308," ","integrate(x^(-1-6*n)*(a+b*x^n)^3,x, algorithm=""giac"")","-\frac{20 \, b^{3} x^{3 \, n} + 45 \, a b^{2} x^{2 \, n} + 36 \, a^{2} b x^{n} + 10 \, a^{3}}{60 \, n x^{6 \, n}}"," ",0,"-1/60*(20*b^3*x^(3*n) + 45*a*b^2*x^(2*n) + 36*a^2*b*x^n + 10*a^3)/(n*x^(6*n))","A",0
2550,1,48,0,0.212339," ","integrate(x^(-1-7*n)*(a+b*x^n)^3,x, algorithm=""giac"")","-\frac{35 \, b^{3} x^{3 \, n} + 84 \, a b^{2} x^{2 \, n} + 70 \, a^{2} b x^{n} + 20 \, a^{3}}{140 \, n x^{7 \, n}}"," ",0,"-1/140*(35*b^3*x^(3*n) + 84*a*b^2*x^(2*n) + 70*a^2*b*x^n + 20*a^3)/(n*x^(7*n))","A",0
2551,0,0,0,0.000000," ","integrate(x^(-1+4*n)*(a+b*x^n)^5,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{5} x^{4 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^5*x^(4*n - 1), x)","F",0
2552,0,0,0,0.000000," ","integrate(x^(-1+3*n)*(a+b*x^n)^5,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{5} x^{3 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^5*x^(3*n - 1), x)","F",0
2553,0,0,0,0.000000," ","integrate(x^(-1+2*n)*(a+b*x^n)^5,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{5} x^{2 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^5*x^(2*n - 1), x)","F",0
2554,1,71,0,0.173691," ","integrate(x^(-1+n)*(a+b*x^n)^5,x, algorithm=""giac"")","\frac{b^{5} x^{6 \, n} + 6 \, a b^{4} x^{5 \, n} + 15 \, a^{2} b^{3} x^{4 \, n} + 20 \, a^{3} b^{2} x^{3 \, n} + 15 \, a^{4} b x^{2 \, n} + 6 \, a^{5} x^{n}}{6 \, n}"," ",0,"1/6*(b^5*x^(6*n) + 6*a*b^4*x^(5*n) + 15*a^2*b^3*x^(4*n) + 20*a^3*b^2*x^(3*n) + 15*a^4*b*x^(2*n) + 6*a^5*x^n)/n","B",0
2555,0,0,0,0.000000," ","integrate((a+b*x^n)^5/x,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{5}}{x}\,{d x}"," ",0,"integrate((b*x^n + a)^5/x, x)","F",0
2556,1,75,0,0.282756," ","integrate(x^(-1-n)*(a+b*x^n)^5,x, algorithm=""giac"")","\frac{60 \, a^{4} b n x^{n} \log\left(x\right) + 3 \, b^{5} x^{5 \, n} + 20 \, a b^{4} x^{4 \, n} + 60 \, a^{2} b^{3} x^{3 \, n} + 120 \, a^{3} b^{2} x^{2 \, n} - 12 \, a^{5}}{12 \, n x^{n}}"," ",0,"1/12*(60*a^4*b*n*x^n*log(x) + 3*b^5*x^(5*n) + 20*a*b^4*x^(4*n) + 60*a^2*b^3*x^(3*n) + 120*a^3*b^2*x^(2*n) - 12*a^5)/(n*x^n)","A",0
2557,1,77,0,0.242427," ","integrate(x^(-1-2*n)*(a+b*x^n)^5,x, algorithm=""giac"")","\frac{60 \, a^{3} b^{2} n x^{2 \, n} \log\left(x\right) + 2 \, b^{5} x^{5 \, n} + 15 \, a b^{4} x^{4 \, n} + 60 \, a^{2} b^{3} x^{3 \, n} - 30 \, a^{4} b x^{n} - 3 \, a^{5}}{6 \, n x^{2 \, n}}"," ",0,"1/6*(60*a^3*b^2*n*x^(2*n)*log(x) + 2*b^5*x^(5*n) + 15*a*b^4*x^(4*n) + 60*a^2*b^3*x^(3*n) - 30*a^4*b*x^n - 3*a^5)/(n*x^(2*n))","A",0
2558,1,77,0,0.242917," ","integrate(x^(-1-3*n)*(a+b*x^n)^5,x, algorithm=""giac"")","\frac{60 \, a^{2} b^{3} n x^{3 \, n} \log\left(x\right) + 3 \, b^{5} x^{5 \, n} + 30 \, a b^{4} x^{4 \, n} - 60 \, a^{3} b^{2} x^{2 \, n} - 15 \, a^{4} b x^{n} - 2 \, a^{5}}{6 \, n x^{3 \, n}}"," ",0,"1/6*(60*a^2*b^3*n*x^(3*n)*log(x) + 3*b^5*x^(5*n) + 30*a*b^4*x^(4*n) - 60*a^3*b^2*x^(2*n) - 15*a^4*b*x^n - 2*a^5)/(n*x^(3*n))","A",0
2559,1,77,0,0.240998," ","integrate(x^(-1-4*n)*(a+b*x^n)^5,x, algorithm=""giac"")","\frac{60 \, a b^{4} n x^{4 \, n} \log\left(x\right) + 12 \, b^{5} x^{5 \, n} - 120 \, a^{2} b^{3} x^{3 \, n} - 60 \, a^{3} b^{2} x^{2 \, n} - 20 \, a^{4} b x^{n} - 3 \, a^{5}}{12 \, n x^{4 \, n}}"," ",0,"1/12*(60*a*b^4*n*x^(4*n)*log(x) + 12*b^5*x^(5*n) - 120*a^2*b^3*x^(3*n) - 60*a^3*b^2*x^(2*n) - 20*a^4*b*x^n - 3*a^5)/(n*x^(4*n))","A",0
2560,1,77,0,0.247749," ","integrate(x^(-1-5*n)*(a+b*x^n)^5,x, algorithm=""giac"")","\frac{60 \, b^{5} n x^{5 \, n} \log\left(x\right) - 300 \, a b^{4} x^{4 \, n} - 300 \, a^{2} b^{3} x^{3 \, n} - 200 \, a^{3} b^{2} x^{2 \, n} - 75 \, a^{4} b x^{n} - 12 \, a^{5}}{60 \, n x^{5 \, n}}"," ",0,"1/60*(60*b^5*n*x^(5*n)*log(x) - 300*a*b^4*x^(4*n) - 300*a^2*b^3*x^(3*n) - 200*a^3*b^2*x^(2*n) - 75*a^4*b*x^n - 12*a^5)/(n*x^(5*n))","A",0
2561,1,72,0,0.238582," ","integrate(x^(-1-6*n)*(a+b*x^n)^5,x, algorithm=""giac"")","-\frac{6 \, b^{5} x^{5 \, n} + 15 \, a b^{4} x^{4 \, n} + 20 \, a^{2} b^{3} x^{3 \, n} + 15 \, a^{3} b^{2} x^{2 \, n} + 6 \, a^{4} b x^{n} + a^{5}}{6 \, n x^{6 \, n}}"," ",0,"-1/6*(6*b^5*x^(5*n) + 15*a*b^4*x^(4*n) + 20*a^2*b^3*x^(3*n) + 15*a^3*b^2*x^(2*n) + 6*a^4*b*x^n + a^5)/(n*x^(6*n))","B",0
2562,1,74,0,0.240585," ","integrate(x^(-1-7*n)*(a+b*x^n)^5,x, algorithm=""giac"")","-\frac{21 \, b^{5} x^{5 \, n} + 70 \, a b^{4} x^{4 \, n} + 105 \, a^{2} b^{3} x^{3 \, n} + 84 \, a^{3} b^{2} x^{2 \, n} + 35 \, a^{4} b x^{n} + 6 \, a^{5}}{42 \, n x^{7 \, n}}"," ",0,"-1/42*(21*b^5*x^(5*n) + 70*a*b^4*x^(4*n) + 105*a^2*b^3*x^(3*n) + 84*a^3*b^2*x^(2*n) + 35*a^4*b*x^n + 6*a^5)/(n*x^(7*n))","A",0
2563,1,74,0,0.244338," ","integrate(x^(-1-8*n)*(a+b*x^n)^5,x, algorithm=""giac"")","-\frac{56 \, b^{5} x^{5 \, n} + 210 \, a b^{4} x^{4 \, n} + 336 \, a^{2} b^{3} x^{3 \, n} + 280 \, a^{3} b^{2} x^{2 \, n} + 120 \, a^{4} b x^{n} + 21 \, a^{5}}{168 \, n x^{8 \, n}}"," ",0,"-1/168*(56*b^5*x^(5*n) + 210*a*b^4*x^(4*n) + 336*a^2*b^3*x^(3*n) + 280*a^3*b^2*x^(2*n) + 120*a^4*b*x^n + 21*a^5)/(n*x^(8*n))","A",0
2564,1,74,0,0.323814," ","integrate(x^(-1-9*n)*(a+b*x^n)^5,x, algorithm=""giac"")","-\frac{126 \, b^{5} x^{5 \, n} + 504 \, a b^{4} x^{4 \, n} + 840 \, a^{2} b^{3} x^{3 \, n} + 720 \, a^{3} b^{2} x^{2 \, n} + 315 \, a^{4} b x^{n} + 56 \, a^{5}}{504 \, n x^{9 \, n}}"," ",0,"-1/504*(126*b^5*x^(5*n) + 504*a*b^4*x^(4*n) + 840*a^2*b^3*x^(3*n) + 720*a^3*b^2*x^(2*n) + 315*a^4*b*x^n + 56*a^5)/(n*x^(9*n))","A",0
2565,1,74,0,0.246317," ","integrate(x^(-1-10*n)*(a+b*x^n)^5,x, algorithm=""giac"")","-\frac{252 \, b^{5} x^{5 \, n} + 1050 \, a b^{4} x^{4 \, n} + 1800 \, a^{2} b^{3} x^{3 \, n} + 1575 \, a^{3} b^{2} x^{2 \, n} + 700 \, a^{4} b x^{n} + 126 \, a^{5}}{1260 \, n x^{10 \, n}}"," ",0,"-1/1260*(252*b^5*x^(5*n) + 1050*a*b^4*x^(4*n) + 1800*a^2*b^3*x^(3*n) + 1575*a^3*b^2*x^(2*n) + 700*a^4*b*x^n + 126*a^5)/(n*x^(10*n))","A",0
2566,0,0,0,0.000000," ","integrate(x^(-1+9*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{8} x^{9 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^8*x^(9*n - 1), x)","F",0
2567,0,0,0,0.000000," ","integrate(x^(-1+8*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{8} x^{8 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^8*x^(8*n - 1), x)","F",0
2568,0,0,0,0.000000," ","integrate(x^(-1+7*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{8} x^{7 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^8*x^(7*n - 1), x)","F",0
2569,0,0,0,0.000000," ","integrate(x^(-1+6*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{8} x^{6 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^8*x^(6*n - 1), x)","F",0
2570,0,0,0,0.000000," ","integrate(x^(-1+5*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{8} x^{5 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^8*x^(5*n - 1), x)","F",0
2571,0,0,0,0.000000," ","integrate(x^(-1+4*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{8} x^{4 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^8*x^(4*n - 1), x)","F",0
2572,0,0,0,0.000000," ","integrate(x^(-1+3*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{8} x^{3 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^8*x^(3*n - 1), x)","F",0
2573,0,0,0,0.000000," ","integrate(x^(-1+2*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{8} x^{2 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^8*x^(2*n - 1), x)","F",0
2574,1,110,0,0.165591," ","integrate(x^(-1+n)*(a+b*x^n)^8,x, algorithm=""giac"")","\frac{b^{8} x^{9 \, n} + 9 \, a b^{7} x^{8 \, n} + 36 \, a^{2} b^{6} x^{7 \, n} + 84 \, a^{3} b^{5} x^{6 \, n} + 126 \, a^{4} b^{4} x^{5 \, n} + 126 \, a^{5} b^{3} x^{4 \, n} + 84 \, a^{6} b^{2} x^{3 \, n} + 36 \, a^{7} b x^{2 \, n} + 9 \, a^{8} x^{n}}{9 \, n}"," ",0,"1/9*(b^8*x^(9*n) + 9*a*b^7*x^(8*n) + 36*a^2*b^6*x^(7*n) + 84*a^3*b^5*x^(6*n) + 126*a^4*b^4*x^(5*n) + 126*a^5*b^3*x^(4*n) + 84*a^6*b^2*x^(3*n) + 36*a^7*b*x^(2*n) + 9*a^8*x^n)/n","B",0
2575,0,0,0,0.000000," ","integrate((a+b*x^n)^8/x,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{8}}{x}\,{d x}"," ",0,"integrate((b*x^n + a)^8/x, x)","F",0
2576,1,114,0,0.277110," ","integrate(x^(-1-n)*(a+b*x^n)^8,x, algorithm=""giac"")","\frac{840 \, a^{7} b n x^{n} \log\left(x\right) + 15 \, b^{8} x^{8 \, n} + 140 \, a b^{7} x^{7 \, n} + 588 \, a^{2} b^{6} x^{6 \, n} + 1470 \, a^{3} b^{5} x^{5 \, n} + 2450 \, a^{4} b^{4} x^{4 \, n} + 2940 \, a^{5} b^{3} x^{3 \, n} + 2940 \, a^{6} b^{2} x^{2 \, n} - 105 \, a^{8}}{105 \, n x^{n}}"," ",0,"1/105*(840*a^7*b*n*x^n*log(x) + 15*b^8*x^(8*n) + 140*a*b^7*x^(7*n) + 588*a^2*b^6*x^(6*n) + 1470*a^3*b^5*x^(5*n) + 2450*a^4*b^4*x^(4*n) + 2940*a^5*b^3*x^(3*n) + 2940*a^6*b^2*x^(2*n) - 105*a^8)/(n*x^n)","A",0
2577,1,116,0,0.289469," ","integrate(x^(-1-2*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\frac{840 \, a^{6} b^{2} n x^{2 \, n} \log\left(x\right) + 5 \, b^{8} x^{8 \, n} + 48 \, a b^{7} x^{7 \, n} + 210 \, a^{2} b^{6} x^{6 \, n} + 560 \, a^{3} b^{5} x^{5 \, n} + 1050 \, a^{4} b^{4} x^{4 \, n} + 1680 \, a^{5} b^{3} x^{3 \, n} - 240 \, a^{7} b x^{n} - 15 \, a^{8}}{30 \, n x^{2 \, n}}"," ",0,"1/30*(840*a^6*b^2*n*x^(2*n)*log(x) + 5*b^8*x^(8*n) + 48*a*b^7*x^(7*n) + 210*a^2*b^6*x^(6*n) + 560*a^3*b^5*x^(5*n) + 1050*a^4*b^4*x^(4*n) + 1680*a^5*b^3*x^(3*n) - 240*a^7*b*x^n - 15*a^8)/(n*x^(2*n))","A",0
2578,1,116,0,0.294213," ","integrate(x^(-1-3*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\frac{840 \, a^{5} b^{3} n x^{3 \, n} \log\left(x\right) + 3 \, b^{8} x^{8 \, n} + 30 \, a b^{7} x^{7 \, n} + 140 \, a^{2} b^{6} x^{6 \, n} + 420 \, a^{3} b^{5} x^{5 \, n} + 1050 \, a^{4} b^{4} x^{4 \, n} - 420 \, a^{6} b^{2} x^{2 \, n} - 60 \, a^{7} b x^{n} - 5 \, a^{8}}{15 \, n x^{3 \, n}}"," ",0,"1/15*(840*a^5*b^3*n*x^(3*n)*log(x) + 3*b^8*x^(8*n) + 30*a*b^7*x^(7*n) + 140*a^2*b^6*x^(6*n) + 420*a^3*b^5*x^(5*n) + 1050*a^4*b^4*x^(4*n) - 420*a^6*b^2*x^(2*n) - 60*a^7*b*x^n - 5*a^8)/(n*x^(3*n))","A",0
2579,1,116,0,0.296485," ","integrate(x^(-1-4*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\frac{840 \, a^{4} b^{4} n x^{4 \, n} \log\left(x\right) + 3 \, b^{8} x^{8 \, n} + 32 \, a b^{7} x^{7 \, n} + 168 \, a^{2} b^{6} x^{6 \, n} + 672 \, a^{3} b^{5} x^{5 \, n} - 672 \, a^{5} b^{3} x^{3 \, n} - 168 \, a^{6} b^{2} x^{2 \, n} - 32 \, a^{7} b x^{n} - 3 \, a^{8}}{12 \, n x^{4 \, n}}"," ",0,"1/12*(840*a^4*b^4*n*x^(4*n)*log(x) + 3*b^8*x^(8*n) + 32*a*b^7*x^(7*n) + 168*a^2*b^6*x^(6*n) + 672*a^3*b^5*x^(5*n) - 672*a^5*b^3*x^(3*n) - 168*a^6*b^2*x^(2*n) - 32*a^7*b*x^n - 3*a^8)/(n*x^(4*n))","A",0
2580,1,116,0,0.305225," ","integrate(x^(-1-5*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\frac{840 \, a^{3} b^{5} n x^{5 \, n} \log\left(x\right) + 5 \, b^{8} x^{8 \, n} + 60 \, a b^{7} x^{7 \, n} + 420 \, a^{2} b^{6} x^{6 \, n} - 1050 \, a^{4} b^{4} x^{4 \, n} - 420 \, a^{5} b^{3} x^{3 \, n} - 140 \, a^{6} b^{2} x^{2 \, n} - 30 \, a^{7} b x^{n} - 3 \, a^{8}}{15 \, n x^{5 \, n}}"," ",0,"1/15*(840*a^3*b^5*n*x^(5*n)*log(x) + 5*b^8*x^(8*n) + 60*a*b^7*x^(7*n) + 420*a^2*b^6*x^(6*n) - 1050*a^4*b^4*x^(4*n) - 420*a^5*b^3*x^(3*n) - 140*a^6*b^2*x^(2*n) - 30*a^7*b*x^n - 3*a^8)/(n*x^(5*n))","A",0
2581,1,116,0,0.295963," ","integrate(x^(-1-6*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\frac{840 \, a^{2} b^{6} n x^{6 \, n} \log\left(x\right) + 15 \, b^{8} x^{8 \, n} + 240 \, a b^{7} x^{7 \, n} - 1680 \, a^{3} b^{5} x^{5 \, n} - 1050 \, a^{4} b^{4} x^{4 \, n} - 560 \, a^{5} b^{3} x^{3 \, n} - 210 \, a^{6} b^{2} x^{2 \, n} - 48 \, a^{7} b x^{n} - 5 \, a^{8}}{30 \, n x^{6 \, n}}"," ",0,"1/30*(840*a^2*b^6*n*x^(6*n)*log(x) + 15*b^8*x^(8*n) + 240*a*b^7*x^(7*n) - 1680*a^3*b^5*x^(5*n) - 1050*a^4*b^4*x^(4*n) - 560*a^5*b^3*x^(3*n) - 210*a^6*b^2*x^(2*n) - 48*a^7*b*x^n - 5*a^8)/(n*x^(6*n))","A",0
2582,1,116,0,0.309258," ","integrate(x^(-1-7*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\frac{840 \, a b^{7} n x^{7 \, n} \log\left(x\right) + 105 \, b^{8} x^{8 \, n} - 2940 \, a^{2} b^{6} x^{6 \, n} - 2940 \, a^{3} b^{5} x^{5 \, n} - 2450 \, a^{4} b^{4} x^{4 \, n} - 1470 \, a^{5} b^{3} x^{3 \, n} - 588 \, a^{6} b^{2} x^{2 \, n} - 140 \, a^{7} b x^{n} - 15 \, a^{8}}{105 \, n x^{7 \, n}}"," ",0,"1/105*(840*a*b^7*n*x^(7*n)*log(x) + 105*b^8*x^(8*n) - 2940*a^2*b^6*x^(6*n) - 2940*a^3*b^5*x^(5*n) - 2450*a^4*b^4*x^(4*n) - 1470*a^5*b^3*x^(3*n) - 588*a^6*b^2*x^(2*n) - 140*a^7*b*x^n - 15*a^8)/(n*x^(7*n))","A",0
2583,1,116,0,0.301781," ","integrate(x^(-1-8*n)*(a+b*x^n)^8,x, algorithm=""giac"")","\frac{840 \, b^{8} n x^{8 \, n} \log\left(x\right) - 6720 \, a b^{7} x^{7 \, n} - 11760 \, a^{2} b^{6} x^{6 \, n} - 15680 \, a^{3} b^{5} x^{5 \, n} - 14700 \, a^{4} b^{4} x^{4 \, n} - 9408 \, a^{5} b^{3} x^{3 \, n} - 3920 \, a^{6} b^{2} x^{2 \, n} - 960 \, a^{7} b x^{n} - 105 \, a^{8}}{840 \, n x^{8 \, n}}"," ",0,"1/840*(840*b^8*n*x^(8*n)*log(x) - 6720*a*b^7*x^(7*n) - 11760*a^2*b^6*x^(6*n) - 15680*a^3*b^5*x^(5*n) - 14700*a^4*b^4*x^(4*n) - 9408*a^5*b^3*x^(3*n) - 3920*a^6*b^2*x^(2*n) - 960*a^7*b*x^n - 105*a^8)/(n*x^(8*n))","A",0
2584,1,111,0,0.286056," ","integrate(x^(-1-9*n)*(a+b*x^n)^8,x, algorithm=""giac"")","-\frac{9 \, b^{8} x^{8 \, n} + 36 \, a b^{7} x^{7 \, n} + 84 \, a^{2} b^{6} x^{6 \, n} + 126 \, a^{3} b^{5} x^{5 \, n} + 126 \, a^{4} b^{4} x^{4 \, n} + 84 \, a^{5} b^{3} x^{3 \, n} + 36 \, a^{6} b^{2} x^{2 \, n} + 9 \, a^{7} b x^{n} + a^{8}}{9 \, n x^{9 \, n}}"," ",0,"-1/9*(9*b^8*x^(8*n) + 36*a*b^7*x^(7*n) + 84*a^2*b^6*x^(6*n) + 126*a^3*b^5*x^(5*n) + 126*a^4*b^4*x^(4*n) + 84*a^5*b^3*x^(3*n) + 36*a^6*b^2*x^(2*n) + 9*a^7*b*x^n + a^8)/(n*x^(9*n))","B",0
2585,1,113,0,0.312825," ","integrate(x^(-1-10*n)*(a+b*x^n)^8,x, algorithm=""giac"")","-\frac{45 \, b^{8} x^{8 \, n} + 240 \, a b^{7} x^{7 \, n} + 630 \, a^{2} b^{6} x^{6 \, n} + 1008 \, a^{3} b^{5} x^{5 \, n} + 1050 \, a^{4} b^{4} x^{4 \, n} + 720 \, a^{5} b^{3} x^{3 \, n} + 315 \, a^{6} b^{2} x^{2 \, n} + 80 \, a^{7} b x^{n} + 9 \, a^{8}}{90 \, n x^{10 \, n}}"," ",0,"-1/90*(45*b^8*x^(8*n) + 240*a*b^7*x^(7*n) + 630*a^2*b^6*x^(6*n) + 1008*a^3*b^5*x^(5*n) + 1050*a^4*b^4*x^(4*n) + 720*a^5*b^3*x^(3*n) + 315*a^6*b^2*x^(2*n) + 80*a^7*b*x^n + 9*a^8)/(n*x^(10*n))","B",0
2586,1,113,0,0.329476," ","integrate(x^(-1-11*n)*(a+b*x^n)^8,x, algorithm=""giac"")","-\frac{165 \, b^{8} x^{8 \, n} + 990 \, a b^{7} x^{7 \, n} + 2772 \, a^{2} b^{6} x^{6 \, n} + 4620 \, a^{3} b^{5} x^{5 \, n} + 4950 \, a^{4} b^{4} x^{4 \, n} + 3465 \, a^{5} b^{3} x^{3 \, n} + 1540 \, a^{6} b^{2} x^{2 \, n} + 396 \, a^{7} b x^{n} + 45 \, a^{8}}{495 \, n x^{11 \, n}}"," ",0,"-1/495*(165*b^8*x^(8*n) + 990*a*b^7*x^(7*n) + 2772*a^2*b^6*x^(6*n) + 4620*a^3*b^5*x^(5*n) + 4950*a^4*b^4*x^(4*n) + 3465*a^5*b^3*x^(3*n) + 1540*a^6*b^2*x^(2*n) + 396*a^7*b*x^n + 45*a^8)/(n*x^(11*n))","A",0
2587,1,113,0,0.449880," ","integrate(x^(-1-12*n)*(a+b*x^n)^8,x, algorithm=""giac"")","-\frac{495 \, b^{8} x^{8 \, n} + 3168 \, a b^{7} x^{7 \, n} + 9240 \, a^{2} b^{6} x^{6 \, n} + 15840 \, a^{3} b^{5} x^{5 \, n} + 17325 \, a^{4} b^{4} x^{4 \, n} + 12320 \, a^{5} b^{3} x^{3 \, n} + 5544 \, a^{6} b^{2} x^{2 \, n} + 1440 \, a^{7} b x^{n} + 165 \, a^{8}}{1980 \, n x^{12 \, n}}"," ",0,"-1/1980*(495*b^8*x^(8*n) + 3168*a*b^7*x^(7*n) + 9240*a^2*b^6*x^(6*n) + 15840*a^3*b^5*x^(5*n) + 17325*a^4*b^4*x^(4*n) + 12320*a^5*b^3*x^(3*n) + 5544*a^6*b^2*x^(2*n) + 1440*a^7*b*x^n + 165*a^8)/(n*x^(12*n))","A",0
2588,1,113,0,0.308810," ","integrate(x^(-1-13*n)*(a+b*x^n)^8,x, algorithm=""giac"")","-\frac{1287 \, b^{8} x^{8 \, n} + 8580 \, a b^{7} x^{7 \, n} + 25740 \, a^{2} b^{6} x^{6 \, n} + 45045 \, a^{3} b^{5} x^{5 \, n} + 50050 \, a^{4} b^{4} x^{4 \, n} + 36036 \, a^{5} b^{3} x^{3 \, n} + 16380 \, a^{6} b^{2} x^{2 \, n} + 4290 \, a^{7} b x^{n} + 495 \, a^{8}}{6435 \, n x^{13 \, n}}"," ",0,"-1/6435*(1287*b^8*x^(8*n) + 8580*a*b^7*x^(7*n) + 25740*a^2*b^6*x^(6*n) + 45045*a^3*b^5*x^(5*n) + 50050*a^4*b^4*x^(4*n) + 36036*a^5*b^3*x^(3*n) + 16380*a^6*b^2*x^(2*n) + 4290*a^7*b*x^n + 495*a^8)/(n*x^(13*n))","A",0
2589,1,113,0,0.292788," ","integrate(x^(-1-14*n)*(a+b*x^n)^8,x, algorithm=""giac"")","-\frac{3003 \, b^{8} x^{8 \, n} + 20592 \, a b^{7} x^{7 \, n} + 63063 \, a^{2} b^{6} x^{6 \, n} + 112112 \, a^{3} b^{5} x^{5 \, n} + 126126 \, a^{4} b^{4} x^{4 \, n} + 91728 \, a^{5} b^{3} x^{3 \, n} + 42042 \, a^{6} b^{2} x^{2 \, n} + 11088 \, a^{7} b x^{n} + 1287 \, a^{8}}{18018 \, n x^{14 \, n}}"," ",0,"-1/18018*(3003*b^8*x^(8*n) + 20592*a*b^7*x^(7*n) + 63063*a^2*b^6*x^(6*n) + 112112*a^3*b^5*x^(5*n) + 126126*a^4*b^4*x^(4*n) + 91728*a^5*b^3*x^(3*n) + 42042*a^6*b^2*x^(2*n) + 11088*a^7*b*x^n + 1287*a^8)/(n*x^(14*n))","A",0
2590,1,113,0,0.290323," ","integrate(x^(-1-15*n)*(a+b*x^n)^8,x, algorithm=""giac"")","-\frac{6435 \, b^{8} x^{8 \, n} + 45045 \, a b^{7} x^{7 \, n} + 140140 \, a^{2} b^{6} x^{6 \, n} + 252252 \, a^{3} b^{5} x^{5 \, n} + 286650 \, a^{4} b^{4} x^{4 \, n} + 210210 \, a^{5} b^{3} x^{3 \, n} + 97020 \, a^{6} b^{2} x^{2 \, n} + 25740 \, a^{7} b x^{n} + 3003 \, a^{8}}{45045 \, n x^{15 \, n}}"," ",0,"-1/45045*(6435*b^8*x^(8*n) + 45045*a*b^7*x^(7*n) + 140140*a^2*b^6*x^(6*n) + 252252*a^3*b^5*x^(5*n) + 286650*a^4*b^4*x^(4*n) + 210210*a^5*b^3*x^(3*n) + 97020*a^6*b^2*x^(2*n) + 25740*a^7*b*x^n + 3003*a^8)/(n*x^(15*n))","A",0
2591,1,214,0,0.178483," ","integrate(x^(-1+n)*(a+b*x^n)^16,x, algorithm=""giac"")","\frac{b^{16} x^{17 \, n} + 17 \, a b^{15} x^{16 \, n} + 136 \, a^{2} b^{14} x^{15 \, n} + 680 \, a^{3} b^{13} x^{14 \, n} + 2380 \, a^{4} b^{12} x^{13 \, n} + 6188 \, a^{5} b^{11} x^{12 \, n} + 12376 \, a^{6} b^{10} x^{11 \, n} + 19448 \, a^{7} b^{9} x^{10 \, n} + 24310 \, a^{8} b^{8} x^{9 \, n} + 24310 \, a^{9} b^{7} x^{8 \, n} + 19448 \, a^{10} b^{6} x^{7 \, n} + 12376 \, a^{11} b^{5} x^{6 \, n} + 6188 \, a^{12} b^{4} x^{5 \, n} + 2380 \, a^{13} b^{3} x^{4 \, n} + 680 \, a^{14} b^{2} x^{3 \, n} + 136 \, a^{15} b x^{2 \, n} + 17 \, a^{16} x^{n}}{17 \, n}"," ",0,"1/17*(b^16*x^(17*n) + 17*a*b^15*x^(16*n) + 136*a^2*b^14*x^(15*n) + 680*a^3*b^13*x^(14*n) + 2380*a^4*b^12*x^(13*n) + 6188*a^5*b^11*x^(12*n) + 12376*a^6*b^10*x^(11*n) + 19448*a^7*b^9*x^(10*n) + 24310*a^8*b^8*x^(9*n) + 24310*a^9*b^7*x^(8*n) + 19448*a^10*b^6*x^(7*n) + 12376*a^11*b^5*x^(6*n) + 6188*a^12*b^4*x^(5*n) + 2380*a^13*b^3*x^(4*n) + 680*a^14*b^2*x^(3*n) + 136*a^15*b*x^(2*n) + 17*a^16*x^n)/n","B",0
2592,1,14,0,0.155313," ","integrate(x^12*(b*x^13+a)^12,x, algorithm=""giac"")","\frac{{\left(b x^{13} + a\right)}^{13}}{169 \, b}"," ",0,"1/169*(b*x^13 + a)^13/b","A",0
2593,1,14,0,0.151192," ","integrate(x^24*(b*x^25+a)^12,x, algorithm=""giac"")","\frac{{\left(b x^{25} + a\right)}^{13}}{325 \, b}"," ",0,"1/325*(b*x^25 + a)^13/b","A",0
2594,1,14,0,0.151193," ","integrate(x^36*(b*x^37+a)^12,x, algorithm=""giac"")","\frac{{\left(b x^{37} + a\right)}^{13}}{481 \, b}"," ",0,"1/481*(b*x^37 + a)^13/b","A",0
2595,1,205,0,0.512679," ","integrate(x^(12*m)*(a+b*x^(1+12*m))^12,x, algorithm=""giac"")","\frac{b^{12} x^{13} x^{156 \, m} + 13 \, a b^{11} x^{12} x^{144 \, m} + 78 \, a^{2} b^{10} x^{11} x^{132 \, m} + 286 \, a^{3} b^{9} x^{10} x^{120 \, m} + 715 \, a^{4} b^{8} x^{9} x^{108 \, m} + 1287 \, a^{5} b^{7} x^{8} x^{96 \, m} + 1716 \, a^{6} b^{6} x^{7} x^{84 \, m} + 1716 \, a^{7} b^{5} x^{6} x^{72 \, m} + 1287 \, a^{8} b^{4} x^{5} x^{60 \, m} + 715 \, a^{9} b^{3} x^{4} x^{48 \, m} + 286 \, a^{10} b^{2} x^{3} x^{36 \, m} + 78 \, a^{11} b x^{2} x^{24 \, m} + 13 \, a^{12} x x^{12 \, m}}{13 \, {\left(12 \, m + 1\right)}}"," ",0,"1/13*(b^12*x^13*x^(156*m) + 13*a*b^11*x^12*x^(144*m) + 78*a^2*b^10*x^11*x^(132*m) + 286*a^3*b^9*x^10*x^(120*m) + 715*a^4*b^8*x^9*x^(108*m) + 1287*a^5*b^7*x^8*x^(96*m) + 1716*a^6*b^6*x^7*x^(84*m) + 1716*a^7*b^5*x^6*x^(72*m) + 1287*a^8*b^4*x^5*x^(60*m) + 715*a^9*b^3*x^4*x^(48*m) + 286*a^10*b^2*x^3*x^(36*m) + 78*a^11*b*x^2*x^(24*m) + 13*a^12*x*x^(12*m))/(12*m + 1)","B",0
2596,1,205,0,0.508764," ","integrate(x^(12*m)*(a+b*x^(1+12*m))^12,x, algorithm=""giac"")","\frac{b^{12} x^{13} x^{156 \, m} + 13 \, a b^{11} x^{12} x^{144 \, m} + 78 \, a^{2} b^{10} x^{11} x^{132 \, m} + 286 \, a^{3} b^{9} x^{10} x^{120 \, m} + 715 \, a^{4} b^{8} x^{9} x^{108 \, m} + 1287 \, a^{5} b^{7} x^{8} x^{96 \, m} + 1716 \, a^{6} b^{6} x^{7} x^{84 \, m} + 1716 \, a^{7} b^{5} x^{6} x^{72 \, m} + 1287 \, a^{8} b^{4} x^{5} x^{60 \, m} + 715 \, a^{9} b^{3} x^{4} x^{48 \, m} + 286 \, a^{10} b^{2} x^{3} x^{36 \, m} + 78 \, a^{11} b x^{2} x^{24 \, m} + 13 \, a^{12} x x^{12 \, m}}{13 \, {\left(12 \, m + 1\right)}}"," ",0,"1/13*(b^12*x^13*x^(156*m) + 13*a*b^11*x^12*x^(144*m) + 78*a^2*b^10*x^11*x^(132*m) + 286*a^3*b^9*x^10*x^(120*m) + 715*a^4*b^8*x^9*x^(108*m) + 1287*a^5*b^7*x^8*x^(96*m) + 1716*a^6*b^6*x^7*x^(84*m) + 1716*a^7*b^5*x^6*x^(72*m) + 1287*a^8*b^4*x^5*x^(60*m) + 715*a^9*b^3*x^4*x^(48*m) + 286*a^10*b^2*x^3*x^(36*m) + 78*a^11*b*x^2*x^(24*m) + 13*a^12*x*x^(12*m))/(12*m + 1)","B",0
2597,0,0,0,0.000000," ","integrate(x^(-1+5*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{5 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(5*n - 1)/(b*x^n + a), x)","F",0
2598,0,0,0,0.000000," ","integrate(x^(-1+4*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{4 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(4*n - 1)/(b*x^n + a), x)","F",0
2599,0,0,0,0.000000," ","integrate(x^(-1+3*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{3 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(3*n - 1)/(b*x^n + a), x)","F",0
2600,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(2*n - 1)/(b*x^n + a), x)","F",0
2601,1,16,0,0.150560," ","integrate(x^(-1+n)/(a+b*x^n),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{n} + a \right|}\right)}{b n}"," ",0,"log(abs(b*x^n + a))/(b*n)","A",0
2602,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*x), x)","F",0
2603,0,0,0,0.000000," ","integrate(x^(-1-n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-n - 1)/(b*x^n + a), x)","F",0
2604,0,0,0,0.000000," ","integrate(x^(-1-2*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-2 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-2*n - 1)/(b*x^n + a), x)","F",0
2605,0,0,0,0.000000," ","integrate(x^(-1-3*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-3 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-3*n - 1)/(b*x^n + a), x)","F",0
2606,0,0,0,0.000000," ","integrate(x^(-1+5*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{5 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(5*n - 1)/(b*x^n + a), x)","F",0
2607,0,0,0,0.000000," ","integrate(x^(-1+4*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{4 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(4*n - 1)/(b*x^n + a), x)","F",0
2608,0,0,0,0.000000," ","integrate(x^(-1+3*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{3 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(3*n - 1)/(b*x^n + a), x)","F",0
2609,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(2*n - 1)/(b*x^n + a), x)","F",0
2610,1,16,0,0.151494," ","integrate(x^(-1+n)/(a+b*x^n),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{n} + a \right|}\right)}{b n}"," ",0,"log(abs(b*x^n + a))/(b*n)","A",0
2611,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*x), x)","F",0
2612,0,0,0,0.000000," ","integrate(x^(-1-n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-n - 1)/(b*x^n + a), x)","F",0
2613,0,0,0,0.000000," ","integrate(x^(-1-2*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-2 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-2*n - 1)/(b*x^n + a), x)","F",0
2614,0,0,0,0.000000," ","integrate(x^(-1-3*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-3 \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-3*n - 1)/(b*x^n + a), x)","F",0
2615,0,0,0,0.000000," ","integrate(x^(-1+5*n)/(2+b*x^n),x, algorithm=""giac"")","\int \frac{x^{5 \, n - 1}}{b x^{n} + 2}\,{d x}"," ",0,"integrate(x^(5*n - 1)/(b*x^n + 2), x)","F",0
2616,0,0,0,0.000000," ","integrate(x^(-1+4*n)/(2+b*x^n),x, algorithm=""giac"")","\int \frac{x^{4 \, n - 1}}{b x^{n} + 2}\,{d x}"," ",0,"integrate(x^(4*n - 1)/(b*x^n + 2), x)","F",0
2617,0,0,0,0.000000," ","integrate(x^(-1+3*n)/(2+b*x^n),x, algorithm=""giac"")","\int \frac{x^{3 \, n - 1}}{b x^{n} + 2}\,{d x}"," ",0,"integrate(x^(3*n - 1)/(b*x^n + 2), x)","F",0
2618,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(2+b*x^n),x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{b x^{n} + 2}\,{d x}"," ",0,"integrate(x^(2*n - 1)/(b*x^n + 2), x)","F",0
2619,1,16,0,0.158442," ","integrate(x^(-1+n)/(2+b*x^n),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{n} + 2 \right|}\right)}{b n}"," ",0,"log(abs(b*x^n + 2))/(b*n)","A",0
2620,0,0,0,0.000000," ","integrate(1/x/(2+b*x^n),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + 2\right)} x}\,{d x}"," ",0,"integrate(1/((b*x^n + 2)*x), x)","F",0
2621,0,0,0,0.000000," ","integrate(x^(-1-n)/(2+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-n - 1}}{b x^{n} + 2}\,{d x}"," ",0,"integrate(x^(-n - 1)/(b*x^n + 2), x)","F",0
2622,0,0,0,0.000000," ","integrate(x^(-1-2*n)/(2+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-2 \, n - 1}}{b x^{n} + 2}\,{d x}"," ",0,"integrate(x^(-2*n - 1)/(b*x^n + 2), x)","F",0
2623,0,0,0,0.000000," ","integrate(x^(-1-3*n)/(2+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-3 \, n - 1}}{b x^{n} + 2}\,{d x}"," ",0,"integrate(x^(-3*n - 1)/(b*x^n + 2), x)","F",0
2624,0,0,0,0.000000," ","integrate(x^(-1+4*n)/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{x^{4 \, n - 1}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^(4*n - 1)/(b*x^n + a)^2, x)","F",0
2625,0,0,0,0.000000," ","integrate(x^(-1+3*n)/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{x^{3 \, n - 1}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^(3*n - 1)/(b*x^n + a)^2, x)","F",0
2626,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^(2*n - 1)/(b*x^n + a)^2, x)","F",0
2627,1,17,0,0.150588," ","integrate(x^(-1+n)/(a+b*x^n)^2,x, algorithm=""giac"")","-\frac{1}{{\left(b x^{n} + a\right)} b n}"," ",0,"-1/((b*x^n + a)*b*n)","A",0
2628,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{2} x}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^2*x), x)","F",0
2629,0,0,0,0.000000," ","integrate(x^(-1-n)/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{x^{-n - 1}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^(-n - 1)/(b*x^n + a)^2, x)","F",0
2630,0,0,0,0.000000," ","integrate(x^(-1-2*n)/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{x^{-2 \, n - 1}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^(-2*n - 1)/(b*x^n + a)^2, x)","F",0
2631,0,0,0,0.000000," ","integrate(x^(-1-3*n)/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{x^{-3 \, n - 1}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^(-3*n - 1)/(b*x^n + a)^2, x)","F",0
2632,0,0,0,0.000000," ","integrate(x^(-1+4*n)/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{x^{4 \, n - 1}}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x^(4*n - 1)/(b*x^n + a)^3, x)","F",0
2633,0,0,0,0.000000," ","integrate(x^(-1+3*n)/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{x^{3 \, n - 1}}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x^(3*n - 1)/(b*x^n + a)^3, x)","F",0
2634,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x^(2*n - 1)/(b*x^n + a)^3, x)","F",0
2635,1,17,0,0.152777," ","integrate(x^(-1+n)/(a+b*x^n)^3,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(b x^{n} + a\right)}^{2} b n}"," ",0,"-1/2/((b*x^n + a)^2*b*n)","A",0
2636,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{3} x}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^3*x), x)","F",0
2637,0,0,0,0.000000," ","integrate(x^(-1-n)/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{x^{-n - 1}}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x^(-n - 1)/(b*x^n + a)^3, x)","F",0
2638,0,0,0,0.000000," ","integrate(x^(-1-2*n)/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{x^{-2 \, n - 1}}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x^(-2*n - 1)/(b*x^n + a)^3, x)","F",0
2639,0,0,0,0.000000," ","integrate(x^(-1-1/2*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-\frac{1}{2} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-1/2*n - 1)/(b*x^n + a), x)","F",0
2640,0,0,0,0.000000," ","integrate(x^(-1-2/3*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-\frac{2}{3} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-2/3*n - 1)/(b*x^n + a), x)","F",0
2641,0,0,0,0.000000," ","integrate(x^(-1-3/4*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-\frac{3}{4} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-3/4*n - 1)/(b*x^n + a), x)","F",0
2642,0,0,0,0.000000," ","integrate(x^(-1-n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-n - 1)/(b*x^n + a), x)","F",0
2643,0,0,0,0.000000," ","integrate(x^(-1-1/2*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-\frac{1}{2} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-1/2*n - 1)/(b*x^n + a), x)","F",0
2644,0,0,0,0.000000," ","integrate(x^(-1-1/3*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-\frac{1}{3} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-1/3*n - 1)/(b*x^n + a), x)","F",0
2645,0,0,0,0.000000," ","integrate(x^(-1-1/4*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-\frac{1}{4} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-1/4*n - 1)/(b*x^n + a), x)","F",0
2646,0,0,0,0.000000," ","integrate(x^(-1-3/2*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-\frac{3}{2} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-3/2*n - 1)/(b*x^n + a), x)","F",0
2647,0,0,0,0.000000," ","integrate(x^(-1-4/3*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-\frac{4}{3} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-4/3*n - 1)/(b*x^n + a), x)","F",0
2648,0,0,0,0.000000," ","integrate(x^(-1-5/4*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{-\frac{5}{4} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^(-5/4*n - 1)/(b*x^n + a), x)","F",0
2649,0,0,0,0.000000," ","integrate(x^(-1+4*n)*(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n} + a} x^{4 \, n - 1}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)*x^(4*n - 1), x)","F",0
2650,0,0,0,0.000000," ","integrate(x^(-1+3*n)*(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n} + a} x^{3 \, n - 1}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)*x^(3*n - 1), x)","F",0
2651,0,0,0,0.000000," ","integrate(x^(-1+2*n)*(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n} + a} x^{2 \, n - 1}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)*x^(2*n - 1), x)","F",0
2652,1,17,0,0.162648," ","integrate(x^(-1+n)*(a+b*x^n)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(b x^{n} + a\right)}^{\frac{3}{2}}}{3 \, b n}"," ",0,"2/3*(b*x^n + a)^(3/2)/(b*n)","A",0
2653,0,0,0,0.000000," ","integrate((a+b*x^n)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{b x^{n} + a}}{x}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)/x, x)","F",0
2654,0,0,0,0.000000," ","integrate(x^(-1-n)*(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n} + a} x^{-n - 1}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)*x^(-n - 1), x)","F",0
2655,0,0,0,0.000000," ","integrate(x^(-1-2*n)*(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n} + a} x^{-2 \, n - 1}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)*x^(-2*n - 1), x)","F",0
2656,0,0,0,0.000000," ","integrate(x^(-1-3*n)*(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n} + a} x^{-3 \, n - 1}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)*x^(-3*n - 1), x)","F",0
2657,0,0,0,0.000000," ","integrate(x^(-1-4*n)*(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n} + a} x^{-4 \, n - 1}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)*x^(-4*n - 1), x)","F",0
2658,0,0,0,0.000000," ","integrate(x^(-1+4*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4 \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(4*n - 1)/sqrt(b*x^n + a), x)","F",0
2659,0,0,0,0.000000," ","integrate(x^(-1+3*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3 \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(3*n - 1)/sqrt(b*x^n + a), x)","F",0
2660,0,0,0,0.000000," ","integrate(x^(-1+2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2 \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(2*n - 1)/sqrt(b*x^n + a), x)","F",0
2661,1,17,0,0.157688," ","integrate(x^(-1+n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{b x^{n} + a}}{b n}"," ",0,"2*sqrt(b*x^n + a)/(b*n)","A",0
2662,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{n} + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^n + a)*x), x)","F",0
2663,0,0,0,0.000000," ","integrate(x^(-1-n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{-n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(-n - 1)/sqrt(b*x^n + a), x)","F",0
2664,0,0,0,0.000000," ","integrate(x^(-1-2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{-2 \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(-2*n - 1)/sqrt(b*x^n + a), x)","F",0
2665,0,0,0,0.000000," ","integrate(x^(-1-3*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{-3 \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(-3*n - 1)/sqrt(b*x^n + a), x)","F",0
2666,0,0,0,0.000000," ","integrate(x^(-1-4*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{-4 \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(-4*n - 1)/sqrt(b*x^n + a), x)","F",0
2667,1,622,0,0.209806," ","integrate(x^m*(a+b*x^n)^3,x, algorithm=""giac"")","\frac{b^{3} m^{3} x x^{m} x^{3 \, n} + 3 \, b^{3} m^{2} n x x^{m} x^{3 \, n} + 2 \, b^{3} m n^{2} x x^{m} x^{3 \, n} + 3 \, a b^{2} m^{3} x x^{m} x^{2 \, n} + 12 \, a b^{2} m^{2} n x x^{m} x^{2 \, n} + 9 \, a b^{2} m n^{2} x x^{m} x^{2 \, n} + 3 \, a^{2} b m^{3} x x^{m} x^{n} + 15 \, a^{2} b m^{2} n x x^{m} x^{n} + 18 \, a^{2} b m n^{2} x x^{m} x^{n} + a^{3} m^{3} x x^{m} + 6 \, a^{3} m^{2} n x x^{m} + 11 \, a^{3} m n^{2} x x^{m} + 6 \, a^{3} n^{3} x x^{m} + 3 \, b^{3} m^{2} x x^{m} x^{3 \, n} + 6 \, b^{3} m n x x^{m} x^{3 \, n} + 2 \, b^{3} n^{2} x x^{m} x^{3 \, n} + 9 \, a b^{2} m^{2} x x^{m} x^{2 \, n} + 24 \, a b^{2} m n x x^{m} x^{2 \, n} + 9 \, a b^{2} n^{2} x x^{m} x^{2 \, n} + 9 \, a^{2} b m^{2} x x^{m} x^{n} + 30 \, a^{2} b m n x x^{m} x^{n} + 18 \, a^{2} b n^{2} x x^{m} x^{n} + 3 \, a^{3} m^{2} x x^{m} + 12 \, a^{3} m n x x^{m} + 11 \, a^{3} n^{2} x x^{m} + 3 \, b^{3} m x x^{m} x^{3 \, n} + 3 \, b^{3} n x x^{m} x^{3 \, n} + 9 \, a b^{2} m x x^{m} x^{2 \, n} + 12 \, a b^{2} n x x^{m} x^{2 \, n} + 9 \, a^{2} b m x x^{m} x^{n} + 15 \, a^{2} b n x x^{m} x^{n} + 3 \, a^{3} m x x^{m} + 6 \, a^{3} n x x^{m} + b^{3} x x^{m} x^{3 \, n} + 3 \, a b^{2} x x^{m} x^{2 \, n} + 3 \, a^{2} b x x^{m} x^{n} + a^{3} x x^{m}}{m^{4} + 6 \, m^{3} n + 11 \, m^{2} n^{2} + 6 \, m n^{3} + 4 \, m^{3} + 18 \, m^{2} n + 22 \, m n^{2} + 6 \, n^{3} + 6 \, m^{2} + 18 \, m n + 11 \, n^{2} + 4 \, m + 6 \, n + 1}"," ",0,"(b^3*m^3*x*x^m*x^(3*n) + 3*b^3*m^2*n*x*x^m*x^(3*n) + 2*b^3*m*n^2*x*x^m*x^(3*n) + 3*a*b^2*m^3*x*x^m*x^(2*n) + 12*a*b^2*m^2*n*x*x^m*x^(2*n) + 9*a*b^2*m*n^2*x*x^m*x^(2*n) + 3*a^2*b*m^3*x*x^m*x^n + 15*a^2*b*m^2*n*x*x^m*x^n + 18*a^2*b*m*n^2*x*x^m*x^n + a^3*m^3*x*x^m + 6*a^3*m^2*n*x*x^m + 11*a^3*m*n^2*x*x^m + 6*a^3*n^3*x*x^m + 3*b^3*m^2*x*x^m*x^(3*n) + 6*b^3*m*n*x*x^m*x^(3*n) + 2*b^3*n^2*x*x^m*x^(3*n) + 9*a*b^2*m^2*x*x^m*x^(2*n) + 24*a*b^2*m*n*x*x^m*x^(2*n) + 9*a*b^2*n^2*x*x^m*x^(2*n) + 9*a^2*b*m^2*x*x^m*x^n + 30*a^2*b*m*n*x*x^m*x^n + 18*a^2*b*n^2*x*x^m*x^n + 3*a^3*m^2*x*x^m + 12*a^3*m*n*x*x^m + 11*a^3*n^2*x*x^m + 3*b^3*m*x*x^m*x^(3*n) + 3*b^3*n*x*x^m*x^(3*n) + 9*a*b^2*m*x*x^m*x^(2*n) + 12*a*b^2*n*x*x^m*x^(2*n) + 9*a^2*b*m*x*x^m*x^n + 15*a^2*b*n*x*x^m*x^n + 3*a^3*m*x*x^m + 6*a^3*n*x*x^m + b^3*x*x^m*x^(3*n) + 3*a*b^2*x*x^m*x^(2*n) + 3*a^2*b*x*x^m*x^n + a^3*x*x^m)/(m^4 + 6*m^3*n + 11*m^2*n^2 + 6*m*n^3 + 4*m^3 + 18*m^2*n + 22*m*n^2 + 6*n^3 + 6*m^2 + 18*m*n + 11*n^2 + 4*m + 6*n + 1)","B",0
2668,1,238,0,0.302381," ","integrate(x^m*(a+b*x^n)^2,x, algorithm=""giac"")","\frac{b^{2} m^{2} x x^{m} x^{2 \, n} + b^{2} m n x x^{m} x^{2 \, n} + 2 \, a b m^{2} x x^{m} x^{n} + 4 \, a b m n x x^{m} x^{n} + a^{2} m^{2} x x^{m} + 3 \, a^{2} m n x x^{m} + 2 \, a^{2} n^{2} x x^{m} + 2 \, b^{2} m x x^{m} x^{2 \, n} + b^{2} n x x^{m} x^{2 \, n} + 4 \, a b m x x^{m} x^{n} + 4 \, a b n x x^{m} x^{n} + 2 \, a^{2} m x x^{m} + 3 \, a^{2} n x x^{m} + b^{2} x x^{m} x^{2 \, n} + 2 \, a b x x^{m} x^{n} + a^{2} x x^{m}}{m^{3} + 3 \, m^{2} n + 2 \, m n^{2} + 3 \, m^{2} + 6 \, m n + 2 \, n^{2} + 3 \, m + 3 \, n + 1}"," ",0,"(b^2*m^2*x*x^m*x^(2*n) + b^2*m*n*x*x^m*x^(2*n) + 2*a*b*m^2*x*x^m*x^n + 4*a*b*m*n*x*x^m*x^n + a^2*m^2*x*x^m + 3*a^2*m*n*x*x^m + 2*a^2*n^2*x*x^m + 2*b^2*m*x*x^m*x^(2*n) + b^2*n*x*x^m*x^(2*n) + 4*a*b*m*x*x^m*x^n + 4*a*b*n*x*x^m*x^n + 2*a^2*m*x*x^m + 3*a^2*n*x*x^m + b^2*x*x^m*x^(2*n) + 2*a*b*x*x^m*x^n + a^2*x*x^m)/(m^3 + 3*m^2*n + 2*m*n^2 + 3*m^2 + 6*m*n + 2*n^2 + 3*m + 3*n + 1)","B",0
2669,1,55,0,0.159304," ","integrate(x^m*(a+b*x^n),x, algorithm=""giac"")","\frac{b m x x^{m} x^{n} + a m x x^{m} + a n x x^{m} + b x x^{m} x^{n} + a x x^{m}}{m^{2} + m n + 2 \, m + n + 1}"," ",0,"(b*m*x*x^m*x^n + a*m*x*x^m + a*n*x*x^m + b*x*x^m*x^n + a*x*x^m)/(m^2 + m*n + 2*m + n + 1)","B",0
2670,0,0,0,0.000000," ","integrate(x^m/(a+b*x^n),x, algorithm=""giac"")","\int \frac{x^{m}}{b x^{n} + a}\,{d x}"," ",0,"integrate(x^m/(b*x^n + a), x)","F",0
2671,0,0,0,0.000000," ","integrate(x^m/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^m/(b*x^n + a)^2, x)","F",0
2672,0,0,0,0.000000," ","integrate(x^m/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x^m/(b*x^n + a)^3, x)","F",0
2673,0,0,0,0.000000," ","integrate(x^m*(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{\frac{3}{2}} x^{m}\,{d x}"," ",0,"integrate((b*x^n + a)^(3/2)*x^m, x)","F",0
2674,0,0,0,0.000000," ","integrate(x^m*(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n} + a} x^{m}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)*x^m, x)","F",0
2675,0,0,0,0.000000," ","integrate(x^m/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^m/sqrt(b*x^n + a), x)","F",0
2676,0,0,0,0.000000," ","integrate(x^m/(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m/(b*x^n + a)^(3/2), x)","F",0
2677,0,0,0,0.000000," ","integrate(x^m/(a+b*x^n)^(5/2),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{n} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^m/(b*x^n + a)^(5/2), x)","F",0
2678,0,0,0,0.000000," ","integrate(x^(3+2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2 \, n + 3}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(2*n + 3)/sqrt(b*x^n + a), x)","F",0
2679,0,0,0,0.000000," ","integrate(x^(3+n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{n + 3}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(n + 3)/sqrt(b*x^n + a), x)","F",0
2680,0,0,0,0.000000," ","integrate(x^(3-n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{-n + 3}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(-n + 3)/sqrt(b*x^n + a), x)","F",0
2681,0,0,0,0.000000," ","integrate(x^(3-2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{-2 \, n + 3}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(-2*n + 3)/sqrt(b*x^n + a), x)","F",0
2682,0,0,0,0.000000," ","integrate(x^(m+2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{m + 2 \, n}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(m + 2*n)/sqrt(b*x^n + a), x)","F",0
2683,0,0,0,0.000000," ","integrate(x^(m+n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{m + n}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(m + n)/sqrt(b*x^n + a), x)","F",0
2684,0,0,0,0.000000," ","integrate(x^(m-n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{m - n}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(m - n)/sqrt(b*x^n + a), x)","F",0
2685,0,0,0,0.000000," ","integrate(x^(m-2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{m - 2 \, n}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(m - 2*n)/sqrt(b*x^n + a), x)","F",0
2686,0,0,0,0.000000," ","integrate(-1/2*b*n*x^(-1+m+n)/(a+b*x^n)^(3/2)+m*x^(-1+m)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int -\frac{b n x^{m + n - 1}}{2 \, {\left(b x^{n} + a\right)}^{\frac{3}{2}}} + \frac{m x^{m - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(-1/2*b*n*x^(m + n - 1)/(b*x^n + a)^(3/2) + m*x^(m - 1)/sqrt(b*x^n + a), x)","F",0
2687,0,0,0,0.000000," ","integrate(x^(-1+7/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{\frac{7}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(7/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2688,0,0,0,0.000000," ","integrate(x^(-1+5/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{\frac{5}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(5/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2689,0,0,0,0.000000," ","integrate(x^(-1+3/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{\frac{3}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(3/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2690,-2,0,0,0.000000," ","integrate(x^(-1+1/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueUnable to isolate n in n*sign(x)-n+4*floor(-(n*sign(x)-n-2)/4)-4*n_0, switching to approx. solutionsUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitUnable to isolate n in n*sign(x)-n+4*floor(-(n*sign(x)-n-2)/4)-4*n_1, switching to approx. solutionsUndef/Unsigned Inf encountered in limitUndef/Unsigned Inf encountered in limitEvaluation time: 1.41-2/n/sqrt(b)*ln(sqrt(a+b*abs(x)^n+b*x^n-2*abs(x)^(1/2*n)*sqrt(b)*sqrt(a+b*x^n)*cos(1/2*((1-sign(x))*pi/2*n-2*pi*floor((1-sign(x))*pi/2*n/(2*pi)+1/2)))))","F(-2)",0
2691,0,0,0,0.000000," ","integrate(x^(-1-1/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{-\frac{1}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(-1/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2692,0,0,0,0.000000," ","integrate(x^(-1-3/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{-\frac{3}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(-3/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2693,0,0,0,0.000000," ","integrate(x^(-1-5/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{-\frac{5}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(-5/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2694,0,0,0,0.000000," ","integrate(x^(-1-7/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{x^{-\frac{7}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(x^(-7/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2695,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(-2+m))^(1/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\sqrt{b x^{m - 2} + a}}\,{d x}"," ",0,"integrate(x^m/sqrt(b*x^(m - 2) + a), x)","F",0
2696,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(2-m))^(1/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\sqrt{b x^{-m + 2} + a}}\,{d x}"," ",0,"integrate(x^m/sqrt(b*x^(-m + 2) + a), x)","F",0
2697,0,0,0,0.000000," ","integrate(6*a*x^2/b/(4+m)/(a+b*x^(-2+m))^(1/2)+x^m/(a+b*x^(-2+m))^(1/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\sqrt{b x^{m - 2} + a}} + \frac{6 \, a x^{2}}{\sqrt{b x^{m - 2} + a} b {\left(m + 4\right)}}\,{d x}"," ",0,"integrate(x^m/sqrt(b*x^(m - 2) + a) + 6*a*x^2/(sqrt(b*x^(m - 2) + a)*b*(m + 4)), x)","F",0
2698,0,0,0,0.000000," ","integrate(1/2*x^(-1+m)*(2*a*m+b*(2*m-n)*x^n)/(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b {\left(2 \, m - n\right)} x^{n} + 2 \, a m\right)} x^{m - 1}}{2 \, {\left(b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/2*(b*(2*m - n)*x^n + 2*a*m)*x^(m - 1)/(b*x^n + a)^(3/2), x)","F",0
2699,0,0,0,0.000000," ","integrate(-1/2*b*n*x^(-1+m+n)/(a+b*x^n)^(3/2)+m*x^(-1+m)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int -\frac{b n x^{m + n - 1}}{2 \, {\left(b x^{n} + a\right)}^{\frac{3}{2}}} + \frac{m x^{m - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate(-1/2*b*n*x^(m + n - 1)/(b*x^n + a)^(3/2) + m*x^(m - 1)/sqrt(b*x^n + a), x)","F",0
2700,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(3+3*m))^(1/3),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{3 \, m + 3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^m/(b*x^(3*m + 3) + a)^(1/3), x)","F",0
2701,0,0,0,0.000000," ","integrate(x^m*(a+b/(x^(3/2+3/2*m)))^(2/3),x, algorithm=""giac"")","\int {\left(a + \frac{b}{x^{\frac{3}{2} \, m + \frac{3}{2}}}\right)}^{\frac{2}{3}} x^{m}\,{d x}"," ",0,"integrate((a + b/x^(3/2*m + 3/2))^(2/3)*x^m, x)","F",0
2702,0,0,0,0.000000," ","integrate(x^(-1+1/3*n)/(a+b*x^n)^(1/3),x, algorithm=""giac"")","\int \frac{x^{\frac{1}{3} \, n - 1}}{{\left(b x^{n} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^(1/3*n - 1)/(b*x^n + a)^(1/3), x)","F",0
2703,0,0,0,0.000000," ","integrate(x^(-1-2/3*n)*(a+b*x^n)^(2/3),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{\frac{2}{3}} x^{-\frac{2}{3} \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^(2/3)*x^(-2/3*n - 1), x)","F",0
2704,0,0,0,0.000000," ","integrate(x^m*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} x^{m}\,{d x}"," ",0,"integrate((b*x^n + a)^p*x^m, x)","F",0
2705,0,0,0,0.000000," ","integrate((a+b*x^n)^(-4-1/n),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{-\frac{1}{n} - 4}\,{d x}"," ",0,"integrate((b*x^n + a)^(-1/n - 4), x)","F",0
2706,0,0,0,0.000000," ","integrate((a+b*x^n)^(-3-1/n),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{-\frac{1}{n} - 3}\,{d x}"," ",0,"integrate((b*x^n + a)^(-1/n - 3), x)","F",0
2707,0,0,0,0.000000," ","integrate((a+b*x^n)^(-2-1/n),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{-\frac{1}{n} - 2}\,{d x}"," ",0,"integrate((b*x^n + a)^(-1/n - 2), x)","F",0
2708,0,0,0,0.000000," ","integrate((a+b*x^n)^(-1-1/n),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{-\frac{1}{n} - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^(-1/n - 1), x)","F",0
2709,0,0,0,0.000000," ","integrate(1/((a+b*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\left(\frac{1}{n}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^(1/n)), x)","F",0
2710,0,0,0,0.000000," ","integrate((a+b*x^n)^(1-1/n),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{-\frac{1}{n} + 1}\,{d x}"," ",0,"integrate((b*x^n + a)^(-1/n + 1), x)","F",0
2711,0,0,0,0.000000," ","integrate((a+b*x^n)^(2-1/n),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{-\frac{1}{n} + 2}\,{d x}"," ",0,"integrate((b*x^n + a)^(-1/n + 2), x)","F",0
2712,1,24,0,0.169094," ","integrate(x^m*(b*x^n)^p,x, algorithm=""giac"")","\frac{x x^{m} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + m + 1}"," ",0,"x*x^m*e^(n*p*log(x) + p*log(b))/(n*p + m + 1)","A",0
2713,1,22,0,0.195276," ","integrate(x^2*(b*x^n)^p,x, algorithm=""giac"")","\frac{x^{3} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 3}"," ",0,"x^3*e^(n*p*log(x) + p*log(b))/(n*p + 3)","A",0
2714,1,22,0,0.174075," ","integrate(x*(b*x^n)^p,x, algorithm=""giac"")","\frac{x^{2} e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 2}"," ",0,"x^2*e^(n*p*log(x) + p*log(b))/(n*p + 2)","A",0
2715,1,20,0,0.157289," ","integrate((b*x^n)^p,x, algorithm=""giac"")","\frac{x e^{\left(n p \log\left(x\right) + p \log\left(b\right)\right)}}{n p + 1}"," ",0,"x*e^(n*p*log(x) + p*log(b))/(n*p + 1)","A",0
2716,1,14,0,0.153078," ","integrate((b*x^n)^p/x,x, algorithm=""giac"")","\frac{\left(b x^{n}\right)^{p}}{n p}"," ",0,"(b*x^n)^p/(n*p)","A",0
2717,0,0,0,0.000000," ","integrate((b*x^n)^p/x^2,x, algorithm=""giac"")","\int \frac{\left(b x^{n}\right)^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^n)^p/x^2, x)","F",0
2718,0,0,0,0.000000," ","integrate((b*x^n)^p/x^3,x, algorithm=""giac"")","\int \frac{\left(b x^{n}\right)^{p}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^n)^p/x^3, x)","F",0
2719,0,0,0,0.000000," ","integrate((b*x^n)^p/x^4,x, algorithm=""giac"")","\int \frac{\left(b x^{n}\right)^{p}}{x^{4}}\,{d x}"," ",0,"integrate((b*x^n)^p/x^4, x)","F",0
2720,1,23,0,0.156677," ","integrate(x^(-1+n)*(a+b*x^n)^p,x, algorithm=""giac"")","\frac{{\left(b x^{n} + a\right)}^{p + 1}}{b n {\left(p + 1\right)}}"," ",0,"(b*x^n + a)^(p + 1)/(b*n*(p + 1))","A",0
2721,0,0,0,0.000000," ","integrate(x^(-1+2*n)*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} x^{2 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^p*x^(2*n - 1), x)","F",0
2722,0,0,0,0.000000," ","integrate(x^(-1+3*n)*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} x^{3 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^p*x^(3*n - 1), x)","F",0
2723,0,0,0,0.000000," ","integrate(x^(-1+4*n)*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} x^{4 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^p*x^(4*n - 1), x)","F",0
2724,0,0,0,0.000000," ","integrate(x^(-n*p-n-1)*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} x^{-n p - n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^p*x^(-n*p - n - 1), x)","F",0
2725,1,111,0,0.291447," ","integrate(x^(-1-9*n)*(a+b*x^n)^8,x, algorithm=""giac"")","-\frac{9 \, b^{8} x^{8 \, n} + 36 \, a b^{7} x^{7 \, n} + 84 \, a^{2} b^{6} x^{6 \, n} + 126 \, a^{3} b^{5} x^{5 \, n} + 126 \, a^{4} b^{4} x^{4 \, n} + 84 \, a^{5} b^{3} x^{3 \, n} + 36 \, a^{6} b^{2} x^{2 \, n} + 9 \, a^{7} b x^{n} + a^{8}}{9 \, n x^{9 \, n}}"," ",0,"-1/9*(9*b^8*x^(8*n) + 36*a*b^7*x^(7*n) + 84*a^2*b^6*x^(6*n) + 126*a^3*b^5*x^(5*n) + 126*a^4*b^4*x^(4*n) + 84*a^5*b^3*x^(3*n) + 36*a^6*b^2*x^(2*n) + 9*a^7*b*x^n + a^8)/(n*x^(9*n))","B",0
2726,0,0,0,0.000000," ","integrate(x^(-4-3*p)*(b*x^3+a)^p,x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{p} x^{-3 \, p - 4}\,{d x}"," ",0,"integrate((b*x^3 + a)^p*x^(-3*p - 4), x)","F",0
2727,1,90,0,0.198282," ","integrate((b*x^3+a)^8/x^28,x, algorithm=""giac"")","-\frac{9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}}"," ",0,"-1/27*(9*b^8*x^24 + 36*a*b^7*x^21 + 84*a^2*b^6*x^18 + 126*a^3*b^5*x^15 + 126*a^4*b^4*x^12 + 84*a^5*b^3*x^9 + 36*a^6*b^2*x^6 + 9*a^7*b*x^3 + a^8)/x^27","B",0
2728,0,0,0,0.000000," ","integrate(1/x/(a+b*x^n),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*x), x)","F",0
2729,1,22,0,0.157178," ","integrate(1/x/(b*x^3+a),x, algorithm=""giac"")","-\frac{\log\left({\left| b x^{3} + a \right|}\right)}{3 \, a} + \frac{\log\left({\left| x \right|}\right)}{a}"," ",0,"-1/3*log(abs(b*x^3 + a))/a + log(abs(x))/a","A",0
2730,0,0,0,0.000000," ","integrate(1/((a+b*x^n)^((1+4*n)/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{4 \, n + 1}{n}}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^((4*n + 1)/n)), x)","F",0
2731,0,0,0,0.000000," ","integrate(1/((a+b*x^n)^((1+3*n)/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{3 \, n + 1}{n}}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^((3*n + 1)/n)), x)","F",0
2732,0,0,0,0.000000," ","integrate(1/((a+b*x^n)^((1+2*n)/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{2 \, n + 1}{n}}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^((2*n + 1)/n)), x)","F",0
2733,0,0,0,0.000000," ","integrate(1/((a+b*x^n)^((1+n)/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{n + 1}{n}}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^((n + 1)/n)), x)","F",0
2734,0,0,0,0.000000," ","integrate(1/((a+b*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\left(\frac{1}{n}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^(1/n)), x)","F",0
2735,0,0,0,0.000000," ","integrate(1/((a+b*x^n)^((1-n)/n)),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{\frac{n - 1}{n}}\,{d x}"," ",0,"integrate((b*x^n + a)^((n - 1)/n), x)","F",0
2736,0,0,0,0.000000," ","integrate(1/((a+b*x^n)^((1-2*n)/n)),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{\frac{2 \, n - 1}{n}}\,{d x}"," ",0,"integrate((b*x^n + a)^((2*n - 1)/n), x)","F",0
2737,0,0,0,0.000000," ","integrate(1/x/(a+b/(x^n)),x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{x^{n}}\right)} x}\,{d x}"," ",0,"integrate(1/((a + b/x^n)*x), x)","F",0
2738,1,19,0,0.152096," ","integrate(x^m/(a+b*x^(1+m)),x, algorithm=""giac"")","\frac{\log\left({\left| b x^{m + 1} + a \right|}\right)}{b m + b}"," ",0,"log(abs(b*x^(m + 1) + a))/(b*m + b)","A",0
2739,1,26,0,0.196733," ","integrate(x^m*(a+b*x^(1+m))^n,x, algorithm=""giac"")","\frac{{\left(b x^{m + 1} + a\right)}^{n + 1}}{{\left(b m + b\right)} {\left(n + 1\right)}}"," ",0,"(b*x^(m + 1) + a)^(n + 1)/((b*m + b)*(n + 1))","A",0
2740,1,58,0,0.235404," ","integrate(x^m*(a+b*x^(2+2*m))^3,x, algorithm=""giac"")","\frac{5 \, b^{3} x^{7} x^{7 \, m} + 21 \, a b^{2} x^{5} x^{5 \, m} + 35 \, a^{2} b x^{3} x^{3 \, m} + 35 \, a^{3} x x^{m}}{35 \, {\left(m + 1\right)}}"," ",0,"1/35*(5*b^3*x^7*x^(7*m) + 21*a*b^2*x^5*x^(5*m) + 35*a^2*b*x^3*x^(3*m) + 35*a^3*x*x^m)/(m + 1)","A",0
2741,1,42,0,0.178955," ","integrate(x^m*(a+b*x^(2+2*m))^2,x, algorithm=""giac"")","\frac{3 \, b^{2} x^{5} x^{5 \, m} + 10 \, a b x^{3} x^{3 \, m} + 15 \, a^{2} x x^{m}}{15 \, {\left(m + 1\right)}}"," ",0,"1/15*(3*b^2*x^5*x^(5*m) + 10*a*b*x^3*x^(3*m) + 15*a^2*x*x^m)/(m + 1)","A",0
2742,1,25,0,0.161447," ","integrate(x^m*(a+b*x^(2+2*m)),x, algorithm=""giac"")","\frac{b x^{3} x^{3 \, m} + 3 \, a x x^{m}}{3 \, {\left(m + 1\right)}}"," ",0,"1/3*(b*x^3*x^(3*m) + 3*a*x*x^m)/(m + 1)","A",0
2743,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(2+2*m)),x, algorithm=""giac"")","\int \frac{x^{m}}{b x^{2 \, m + 2} + a}\,{d x}"," ",0,"integrate(x^m/(b*x^(2*m + 2) + a), x)","F",0
2744,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(2+2*m))^2,x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{2 \, m + 2} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^m/(b*x^(2*m + 2) + a)^2, x)","F",0
2745,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(2+2*m))^3,x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{2 \, m + 2} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x^m/(b*x^(2*m + 2) + a)^3, x)","F",0
2746,0,0,0,0.000000," ","integrate(x^m*(a+b*x^(2+2*m))^(5/2),x, algorithm=""giac"")","\int {\left(b x^{2 \, m + 2} + a\right)}^{\frac{5}{2}} x^{m}\,{d x}"," ",0,"integrate((b*x^(2*m + 2) + a)^(5/2)*x^m, x)","F",0
2747,0,0,0,0.000000," ","integrate(x^m*(a+b*x^(2+2*m))^(3/2),x, algorithm=""giac"")","\int {\left(b x^{2 \, m + 2} + a\right)}^{\frac{3}{2}} x^{m}\,{d x}"," ",0,"integrate((b*x^(2*m + 2) + a)^(3/2)*x^m, x)","F",0
2748,0,0,0,0.000000," ","integrate(x^m*(a+b*x^(2+2*m))^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{2 \, m + 2} + a} x^{m}\,{d x}"," ",0,"integrate(sqrt(b*x^(2*m + 2) + a)*x^m, x)","F",0
2749,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(2+2*m))^(1/2),x, algorithm=""giac"")","\int \frac{x^{m}}{\sqrt{b x^{2 \, m + 2} + a}}\,{d x}"," ",0,"integrate(x^m/sqrt(b*x^(2*m + 2) + a), x)","F",0
2750,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(2+2*m))^(3/2),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{2 \, m + 2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m/(b*x^(2*m + 2) + a)^(3/2), x)","F",0
2751,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(2+2*m))^(5/2),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{2 \, m + 2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^m/(b*x^(2*m + 2) + a)^(5/2), x)","F",0
2752,0,0,0,0.000000," ","integrate(x^m/(a+b*x^(2+2*m))^(7/2),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{2 \, m + 2} + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x^m/(b*x^(2*m + 2) + a)^(7/2), x)","F",0
2753,1,16,0,0.154641," ","integrate(x^n*(1+x^(1+n))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(x^{n + 1} + 1\right)}^{\frac{3}{2}}}{3 \, {\left(n + 1\right)}}"," ",0,"2/3*(x^(n + 1) + 1)^(3/2)/(n + 1)","A",0
2754,1,18,0,0.163284," ","integrate(x^n*(a^2+x^(1+n))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(a^{2} + x^{n + 1}\right)}^{\frac{3}{2}}}{3 \, {\left(n + 1\right)}}"," ",0,"2/3*(a^2 + x^(n + 1))^(3/2)/(n + 1)","A",0
2755,1,613,0,0.204817," ","integrate((c*x)^m*(a+b*x^n)^2,x, algorithm=""giac"")","\frac{b^{2} m^{2} x x^{2 \, n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + b^{2} m n x x^{2 \, n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 2 \, a b m^{2} x x^{n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + b^{2} m^{2} x x^{n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 4 \, a b m n x x^{n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + b^{2} m n x x^{n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + a^{2} m^{2} x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 2 \, a b m^{2} x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + b^{2} m^{2} x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 3 \, a^{2} m n x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 4 \, a b m n x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + b^{2} m n x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 2 \, a^{2} n^{2} x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 2 \, b^{2} m x x^{2 \, n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + b^{2} n x x^{2 \, n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 4 \, a b m x x^{n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 2 \, b^{2} m x x^{n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 4 \, a b n x x^{n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + b^{2} n x x^{n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 2 \, a^{2} m x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 4 \, a b m x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 2 \, b^{2} m x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 3 \, a^{2} n x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 4 \, a b n x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + b^{2} n x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + b^{2} x x^{2 \, n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 2 \, a b x x^{n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + b^{2} x x^{n} e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + a^{2} x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + 2 \, a b x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)} + b^{2} x e^{\left(m \log\left(c\right) + m \log\left(x\right)\right)}}{m^{3} + 3 \, m^{2} n + 2 \, m n^{2} + 3 \, m^{2} + 6 \, m n + 2 \, n^{2} + 3 \, m + 3 \, n + 1}"," ",0,"(b^2*m^2*x*x^(2*n)*e^(m*log(c) + m*log(x)) + b^2*m*n*x*x^(2*n)*e^(m*log(c) + m*log(x)) + 2*a*b*m^2*x*x^n*e^(m*log(c) + m*log(x)) + b^2*m^2*x*x^n*e^(m*log(c) + m*log(x)) + 4*a*b*m*n*x*x^n*e^(m*log(c) + m*log(x)) + b^2*m*n*x*x^n*e^(m*log(c) + m*log(x)) + a^2*m^2*x*e^(m*log(c) + m*log(x)) + 2*a*b*m^2*x*e^(m*log(c) + m*log(x)) + b^2*m^2*x*e^(m*log(c) + m*log(x)) + 3*a^2*m*n*x*e^(m*log(c) + m*log(x)) + 4*a*b*m*n*x*e^(m*log(c) + m*log(x)) + b^2*m*n*x*e^(m*log(c) + m*log(x)) + 2*a^2*n^2*x*e^(m*log(c) + m*log(x)) + 2*b^2*m*x*x^(2*n)*e^(m*log(c) + m*log(x)) + b^2*n*x*x^(2*n)*e^(m*log(c) + m*log(x)) + 4*a*b*m*x*x^n*e^(m*log(c) + m*log(x)) + 2*b^2*m*x*x^n*e^(m*log(c) + m*log(x)) + 4*a*b*n*x*x^n*e^(m*log(c) + m*log(x)) + b^2*n*x*x^n*e^(m*log(c) + m*log(x)) + 2*a^2*m*x*e^(m*log(c) + m*log(x)) + 4*a*b*m*x*e^(m*log(c) + m*log(x)) + 2*b^2*m*x*e^(m*log(c) + m*log(x)) + 3*a^2*n*x*e^(m*log(c) + m*log(x)) + 4*a*b*n*x*e^(m*log(c) + m*log(x)) + b^2*n*x*e^(m*log(c) + m*log(x)) + b^2*x*x^(2*n)*e^(m*log(c) + m*log(x)) + 2*a*b*x*x^n*e^(m*log(c) + m*log(x)) + b^2*x*x^n*e^(m*log(c) + m*log(x)) + a^2*x*e^(m*log(c) + m*log(x)) + 2*a*b*x*e^(m*log(c) + m*log(x)) + b^2*x*e^(m*log(c) + m*log(x)))/(m^3 + 3*m^2*n + 2*m*n^2 + 3*m^2 + 6*m*n + 2*n^2 + 3*m + 3*n + 1)","B",0
2756,1,135,0,0.189542," ","integrate((c*x)^m*(b*x^3+a)^2,x, algorithm=""giac"")","\frac{\left(c x\right)^{m} b^{2} m^{2} x^{7} + 5 \, \left(c x\right)^{m} b^{2} m x^{7} + 4 \, \left(c x\right)^{m} b^{2} x^{7} + 2 \, \left(c x\right)^{m} a b m^{2} x^{4} + 16 \, \left(c x\right)^{m} a b m x^{4} + 14 \, \left(c x\right)^{m} a b x^{4} + \left(c x\right)^{m} a^{2} m^{2} x + 11 \, \left(c x\right)^{m} a^{2} m x + 28 \, \left(c x\right)^{m} a^{2} x}{m^{3} + 12 \, m^{2} + 39 \, m + 28}"," ",0,"((c*x)^m*b^2*m^2*x^7 + 5*(c*x)^m*b^2*m*x^7 + 4*(c*x)^m*b^2*x^7 + 2*(c*x)^m*a*b*m^2*x^4 + 16*(c*x)^m*a*b*m*x^4 + 14*(c*x)^m*a*b*x^4 + (c*x)^m*a^2*m^2*x + 11*(c*x)^m*a^2*m*x + 28*(c*x)^m*a^2*x)/(m^3 + 12*m^2 + 39*m + 28)","B",0
2757,1,135,0,0.203290," ","integrate((c*x)^m*(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\left(c x\right)^{m} b^{2} m^{2} x^{5} + 4 \, \left(c x\right)^{m} b^{2} m x^{5} + 2 \, \left(c x\right)^{m} a b m^{2} x^{3} + 3 \, \left(c x\right)^{m} b^{2} x^{5} + 12 \, \left(c x\right)^{m} a b m x^{3} + \left(c x\right)^{m} a^{2} m^{2} x + 10 \, \left(c x\right)^{m} a b x^{3} + 8 \, \left(c x\right)^{m} a^{2} m x + 15 \, \left(c x\right)^{m} a^{2} x}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"((c*x)^m*b^2*m^2*x^5 + 4*(c*x)^m*b^2*m*x^5 + 2*(c*x)^m*a*b*m^2*x^3 + 3*(c*x)^m*b^2*x^5 + 12*(c*x)^m*a*b*m*x^3 + (c*x)^m*a^2*m^2*x + 10*(c*x)^m*a*b*x^3 + 8*(c*x)^m*a^2*m*x + 15*(c*x)^m*a^2*x)/(m^3 + 9*m^2 + 23*m + 15)","B",0
2758,1,135,0,0.157540," ","integrate((c*x)^m*(b*x+a)^2,x, algorithm=""giac"")","\frac{\left(c x\right)^{m} b^{2} m^{2} x^{3} + 2 \, \left(c x\right)^{m} a b m^{2} x^{2} + 3 \, \left(c x\right)^{m} b^{2} m x^{3} + \left(c x\right)^{m} a^{2} m^{2} x + 8 \, \left(c x\right)^{m} a b m x^{2} + 2 \, \left(c x\right)^{m} b^{2} x^{3} + 5 \, \left(c x\right)^{m} a^{2} m x + 6 \, \left(c x\right)^{m} a b x^{2} + 6 \, \left(c x\right)^{m} a^{2} x}{m^{3} + 6 \, m^{2} + 11 \, m + 6}"," ",0,"((c*x)^m*b^2*m^2*x^3 + 2*(c*x)^m*a*b*m^2*x^2 + 3*(c*x)^m*b^2*m*x^3 + (c*x)^m*a^2*m^2*x + 8*(c*x)^m*a*b*m*x^2 + 2*(c*x)^m*b^2*x^3 + 5*(c*x)^m*a^2*m*x + 6*(c*x)^m*a*b*x^2 + 6*(c*x)^m*a^2*x)/(m^3 + 6*m^2 + 11*m + 6)","B",0
2759,0,0,0,0.000000," ","integrate((a+b/x)^2*(c*x)^m,x, algorithm=""giac"")","\int \left(c x\right)^{m} {\left(a + \frac{b}{x}\right)}^{2}\,{d x}"," ",0,"integrate((c*x)^m*(a + b/x)^2, x)","F",0
2760,0,0,0,0.000000," ","integrate((a+b/x^2)^2*(c*x)^m,x, algorithm=""giac"")","\int \left(c x\right)^{m} {\left(a + \frac{b}{x^{2}}\right)}^{2}\,{d x}"," ",0,"integrate((c*x)^m*(a + b/x^2)^2, x)","F",0
2761,0,0,0,0.000000," ","integrate((a+b/x^3)^2*(c*x)^m,x, algorithm=""giac"")","\int \left(c x\right)^{m} {\left(a + \frac{b}{x^{3}}\right)}^{2}\,{d x}"," ",0,"integrate((c*x)^m*(a + b/x^3)^2, x)","F",0
2762,0,0,0,0.000000," ","integrate((c*x)^(-1-1/2*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{1}{2} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(-1/2*n - 1)/(b*x^n + a), x)","F",0
2763,0,0,0,0.000000," ","integrate((c*x)^(-1-2/3*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{2}{3} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(-2/3*n - 1)/(b*x^n + a), x)","F",0
2764,0,0,0,0.000000," ","integrate((c*x)^(-1-3/4*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{3}{4} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(-3/4*n - 1)/(b*x^n + a), x)","F",0
2765,0,0,0,0.000000," ","integrate((c*x)^(-1-n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(-n - 1)/(b*x^n + a), x)","F",0
2766,0,0,0,0.000000," ","integrate((c*x)^(-1-1/2*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{1}{2} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(-1/2*n - 1)/(b*x^n + a), x)","F",0
2767,0,0,0,0.000000," ","integrate((c*x)^(-1-1/3*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{1}{3} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(-1/3*n - 1)/(b*x^n + a), x)","F",0
2768,0,0,0,0.000000," ","integrate((c*x)^(-1-1/4*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{1}{4} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(-1/4*n - 1)/(b*x^n + a), x)","F",0
2769,0,0,0,0.000000," ","integrate((c*x)^(-1-3/2*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{3}{2} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(-3/2*n - 1)/(b*x^n + a), x)","F",0
2770,0,0,0,0.000000," ","integrate((c*x)^(-1-4/3*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{4}{3} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(-4/3*n - 1)/(b*x^n + a), x)","F",0
2771,0,0,0,0.000000," ","integrate((c*x)^(-1-5/4*n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{5}{4} \, n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(-5/4*n - 1)/(b*x^n + a), x)","F",0
2772,0,0,0,0.000000," ","integrate((c*x)^(4+n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{n + 4}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(n + 4)/(b*x^n + a), x)","F",0
2773,0,0,0,0.000000," ","integrate((c*x)^(3+n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{n + 3}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(n + 3)/(b*x^n + a), x)","F",0
2774,0,0,0,0.000000," ","integrate((c*x)^(2+n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{n + 2}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(n + 2)/(b*x^n + a), x)","F",0
2775,0,0,0,0.000000," ","integrate((c*x)^(1+n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{n + 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(n + 1)/(b*x^n + a), x)","F",0
2776,0,0,0,0.000000," ","integrate((c*x)^n/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{n}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^n/(b*x^n + a), x)","F",0
2777,0,0,0,0.000000," ","integrate((c*x)^(-1+n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{n - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(n - 1)/(b*x^n + a), x)","F",0
2778,0,0,0,0.000000," ","integrate((c*x)^(-2+n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{n - 2}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(n - 2)/(b*x^n + a), x)","F",0
2779,0,0,0,0.000000," ","integrate((c*x)^(-3+n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{n - 3}}{b x^{n} + a}\,{d x}"," ",0,"integrate((c*x)^(n - 3)/(b*x^n + a), x)","F",0
2780,0,0,0,0.000000," ","integrate((c*x)^(-1+n)/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{\left(c x\right)^{n - 1}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((c*x)^(n - 1)/(b*x^n + a)^2, x)","F",0
2781,0,0,0,0.000000," ","integrate((c*x)^(-1+7/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{\frac{7}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate((c*x)^(7/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2782,0,0,0,0.000000," ","integrate((c*x)^(-1+5/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{\frac{5}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate((c*x)^(5/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2783,0,0,0,0.000000," ","integrate((c*x)^(-1+3/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{\frac{3}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate((c*x)^(3/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2784,0,0,0,0.000000," ","integrate((c*x)^(-1+1/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{\frac{1}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate((c*x)^(1/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2785,0,0,0,0.000000," ","integrate((c*x)^(-1-1/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{1}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate((c*x)^(-1/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2786,0,0,0,0.000000," ","integrate((c*x)^(-1-3/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{3}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate((c*x)^(-3/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2787,0,0,0,0.000000," ","integrate((c*x)^(-1-5/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{5}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate((c*x)^(-5/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2788,0,0,0,0.000000," ","integrate((c*x)^(-1-7/2*n)/(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{-\frac{7}{2} \, n - 1}}{\sqrt{b x^{n} + a}}\,{d x}"," ",0,"integrate((c*x)^(-7/2*n - 1)/sqrt(b*x^n + a), x)","F",0
2789,0,0,0,0.000000," ","integrate((c*x)^m*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} \left(c x\right)^{m}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(c*x)^m, x)","F",0
2790,-2,0,0,0.000000," ","integrate((c*x)^(3*n)*(a+b*x^n)^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:Simplification assuming x near 0Simplification assuming c near 0Simplification assuming x near 0Simplification assuming c near 0Unable to divide, perhaps due to rounding error%%%{1,[2,0,6,4,2,4,4]%%%}+%%%{4,[2,0,6,4,2,3,4]%%%}+%%%{6,[2,0,6,4,2,2,4]%%%}+%%%{4,[2,0,6,4,2,1,4]%%%}+%%%{1,[2,0,6,4,2,0,4]%%%}+%%%{-1,[1,0,6,4,1,4,5]%%%}+%%%{-4,[1,0,6,4,1,3,5]%%%}+%%%{-6,[1,0,6,4,1,2,5]%%%}+%%%{-4,[1,0,6,4,1,1,5]%%%}+%%%{-1,[1,0,6,4,1,0,5]%%%}+%%%{-1,[0,0,6,3,0,3,6]%%%}+%%%{-3,[0,0,6,3,0,2,6]%%%}+%%%{-3,[0,0,6,3,0,1,6]%%%}+%%%{-1,[0,0,6,3,0,0,6]%%%} / %%%{1,[0,0,7,4,3,4,4]%%%}+%%%{4,[0,0,7,4,3,3,4]%%%}+%%%{6,[0,0,7,4,3,2,4]%%%}+%%%{4,[0,0,7,4,3,1,4]%%%}+%%%{1,[0,0,7,4,3,0,4]%%%} Error: Bad Argument Value","F(-2)",0
2791,-2,0,0,0.000000," ","integrate((c*x)^(2*n)*(a+b*x^n)^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:Simplification assuming x near 0Simplification assuming c near 0Simplification assuming x near 0Simplification assuming c near 0Unable to divide, perhaps due to rounding error%%%{-1,[1,0,4,3,1,3,3]%%%}+%%%{-3,[1,0,4,3,1,2,3]%%%}+%%%{-3,[1,0,4,3,1,1,3]%%%}+%%%{-1,[1,0,4,3,1,0,3]%%%}+%%%{-1,[0,0,4,2,0,2,4]%%%}+%%%{-2,[0,0,4,2,0,1,4]%%%}+%%%{-1,[0,0,4,2,0,0,4]%%%} / %%%{-1,[0,0,5,3,2,3,3]%%%}+%%%{-3,[0,0,5,3,2,2,3]%%%}+%%%{-3,[0,0,5,3,2,1,3]%%%}+%%%{-1,[0,0,5,3,2,0,3]%%%} Error: Bad Argument Value","F(-2)",0
2792,-2,0,0,0.000000," ","integrate((c*x)^n*(a+b*x^n)^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:Simplification assuming x near 0Simplification assuming c near 0Simplification assuming x near 0Simplification assuming c near 0Unable to divide, perhaps due to rounding error%%%{-1,[0,0,2,1,0,1,2]%%%}+%%%{-1,[0,0,2,1,0,0,2]%%%} / %%%{1,[0,0,3,2,1,2,2]%%%}+%%%{2,[0,0,3,2,1,1,2]%%%}+%%%{1,[0,0,3,2,1,0,2]%%%} Error: Bad Argument Value","F(-2)",0
2793,0,0,0,0.000000," ","integrate((a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*x^n + a)^p, x)","F",0
2794,0,0,0,0.000000," ","integrate((a+b*x^n)^p/((c*x)^n),x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{p}}{\left(c x\right)^{n}}\,{d x}"," ",0,"integrate((b*x^n + a)^p/(c*x)^n, x)","F",0
2795,0,0,0,0.000000," ","integrate((a+b*x^n)^p/((c*x)^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{p}}{\left(c x\right)^{2 \, n}}\,{d x}"," ",0,"integrate((b*x^n + a)^p/(c*x)^(2*n), x)","F",0
2796,0,0,0,0.000000," ","integrate((a+b*x^n)^p/((c*x)^(3*n)),x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{p}}{\left(c x\right)^{3 \, n}}\,{d x}"," ",0,"integrate((b*x^n + a)^p/(c*x)^(3*n), x)","F",0
2797,0,0,0,0.000000," ","integrate((c*x)^(-n*p-1)*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} \left(c x\right)^{-n p - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(c*x)^(-n*p - 1), x)","F",0
2798,0,0,0,0.000000," ","integrate((c*x)^(-n*p-n-1)*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} \left(c x\right)^{-n p - n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(c*x)^(-n*p - n - 1), x)","F",0
2799,0,0,0,0.000000," ","integrate((c*x)^(-n*p-2*n-1)*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} \left(c x\right)^{-n p - 2 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(c*x)^(-n*p - 2*n - 1), x)","F",0
2800,0,0,0,0.000000," ","integrate((c*x)^(-n*p-3*n-1)*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} \left(c x\right)^{-n p - 3 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(c*x)^(-n*p - 3*n - 1), x)","F",0
2801,0,0,0,0.000000," ","integrate((c*x)^(-n*p-4*n-1)*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} \left(c x\right)^{-n p - 4 \, n - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(c*x)^(-n*p - 4*n - 1), x)","F",0
2802,1,98,0,0.171616," ","integrate((c*(b*x+a)^2)^(5/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(3 \, {\left(b x^{2} + 2 \, a x\right)} a^{4} c^{2} \mathrm{sgn}\left(b x + a\right) + \frac{a^{6} c^{2} \mathrm{sgn}\left(b x + a\right)}{b} + 3 \, {\left(b x^{2} + 2 \, a x\right)}^{2} a^{2} b c^{2} \mathrm{sgn}\left(b x + a\right) + {\left(b x^{2} + 2 \, a x\right)}^{3} b^{2} c^{2} \mathrm{sgn}\left(b x + a\right)\right)} \sqrt{c}"," ",0,"1/6*(3*(b*x^2 + 2*a*x)*a^4*c^2*sgn(b*x + a) + a^6*c^2*sgn(b*x + a)/b + 3*(b*x^2 + 2*a*x)^2*a^2*b*c^2*sgn(b*x + a) + (b*x^2 + 2*a*x)^3*b^2*c^2*sgn(b*x + a))*sqrt(c)","B",0
2803,1,21,0,0.149205," ","integrate((c*(b*x+a)^2)^(3/2),x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{4} c^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right)}{4 \, b}"," ",0,"1/4*(b*x + a)^4*c^(3/2)*sgn(b*x + a)/b","A",0
2804,1,36,0,0.168231," ","integrate((c*(b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left({\left(b x^{2} + 2 \, a x\right)} \mathrm{sgn}\left(b x + a\right) + \frac{a^{2} \mathrm{sgn}\left(b x + a\right)}{b}\right)} \sqrt{c}"," ",0,"1/2*((b*x^2 + 2*a*x)*sgn(b*x + a) + a^2*sgn(b*x + a)/b)*sqrt(c)","A",0
2805,1,34,0,0.152873," ","integrate(1/(c*(b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| b x + a \right|} \sqrt{{\left| c \right|}} {\left| \mathrm{sgn}\left(b x + a\right) \right|}\right)}{b \sqrt{c} \mathrm{sgn}\left(b x + a\right)}"," ",0,"log(abs(b*x + a)*sqrt(abs(c))*abs(sgn(b*x + a)))/(b*sqrt(c)*sgn(b*x + a))","A",0
2806,0,0,0,0.000000," ","integrate(1/(c*(b*x+a)^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2807,0,0,0,0.000000," ","integrate(1/(c*(b*x+a)^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2808,1,26,0,0.150567," ","integrate(((3+5*x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(5 \, x^{2} + 6 \, x\right)} \mathrm{sgn}\left(5 \, x + 3\right) + \frac{9}{10} \, \mathrm{sgn}\left(5 \, x + 3\right)"," ",0,"1/2*(5*x^2 + 6*x)*sgn(5*x + 3) + 9/10*sgn(5*x + 3)","A",0
2809,1,25,0,0.152319," ","integrate(((6+10*x)^2)^(1/2),x, algorithm=""giac"")","{\left(5 \, x^{2} + 6 \, x\right)} \mathrm{sgn}\left(5 \, x + 3\right) + \frac{9}{5} \, \mathrm{sgn}\left(5 \, x + 3\right)"," ",0,"(5*x^2 + 6*x)*sgn(5*x + 3) + 9/5*sgn(5*x + 3)","A",0
2810,1,15,0,0.151970," ","integrate(1/((3+5*x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, \log\left({\left| 5 \, x + 3 \right|}\right) \mathrm{sgn}\left(5 \, x + 3\right)"," ",0,"1/5*log(abs(5*x + 3))*sgn(5*x + 3)","A",0
2811,1,15,0,0.171806," ","integrate(1/((6+10*x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{10} \, \log\left({\left| 5 \, x + 3 \right|}\right) \mathrm{sgn}\left(5 \, x + 3\right)"," ",0,"1/10*log(abs(5*x + 3))*sgn(5*x + 3)","A",0
2812,1,23,0,0.242633," ","integrate(1/(-(2+3*x)^2)^(1/2),x, algorithm=""giac"")","\frac{i \, \log\left({\left(-3 i \, x - 2 i\right)} \mathrm{sgn}\left(-3 \, x - 2\right)\right)}{3 \, \mathrm{sgn}\left(-3 \, x - 2\right)}"," ",0,"1/3*I*log((-3*I*x - 2*I)*sgn(-3*x - 2))/sgn(-3*x - 2)","C",0
2813,1,851,0,0.251548," ","integrate((c*(b*x+a)^3)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(109395 \, \sqrt{b c x + a c} a^{8} c^{2} \mathrm{sgn}\left(b x + a\right) - 291720 \, {\left(3 \, \sqrt{b c x + a c} a c - {\left(b c x + a c\right)}^{\frac{3}{2}}\right)} a^{7} c \mathrm{sgn}\left(b x + a\right) + 204204 \, {\left(15 \, \sqrt{b c x + a c} a^{2} c^{2} - 10 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a c + 3 \, {\left(b c x + a c\right)}^{\frac{5}{2}}\right)} a^{6} \mathrm{sgn}\left(b x + a\right) - \frac{175032 \, {\left(35 \, \sqrt{b c x + a c} a^{3} c^{3} - 35 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a^{2} c^{2} + 21 \, {\left(b c x + a c\right)}^{\frac{5}{2}} a c - 5 \, {\left(b c x + a c\right)}^{\frac{7}{2}}\right)} a^{5} \mathrm{sgn}\left(b x + a\right)}{c} + \frac{24310 \, {\left(315 \, \sqrt{b c x + a c} a^{4} c^{4} - 420 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a^{3} c^{3} + 378 \, {\left(b c x + a c\right)}^{\frac{5}{2}} a^{2} c^{2} - 180 \, {\left(b c x + a c\right)}^{\frac{7}{2}} a c + 35 \, {\left(b c x + a c\right)}^{\frac{9}{2}}\right)} a^{4} \mathrm{sgn}\left(b x + a\right)}{c^{2}} - \frac{8840 \, {\left(693 \, \sqrt{b c x + a c} a^{5} c^{5} - 1155 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a^{4} c^{4} + 1386 \, {\left(b c x + a c\right)}^{\frac{5}{2}} a^{3} c^{3} - 990 \, {\left(b c x + a c\right)}^{\frac{7}{2}} a^{2} c^{2} + 385 \, {\left(b c x + a c\right)}^{\frac{9}{2}} a c - 63 \, {\left(b c x + a c\right)}^{\frac{11}{2}}\right)} a^{3} \mathrm{sgn}\left(b x + a\right)}{c^{3}} + \frac{1020 \, {\left(3003 \, \sqrt{b c x + a c} a^{6} c^{6} - 6006 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a^{5} c^{5} + 9009 \, {\left(b c x + a c\right)}^{\frac{5}{2}} a^{4} c^{4} - 8580 \, {\left(b c x + a c\right)}^{\frac{7}{2}} a^{3} c^{3} + 5005 \, {\left(b c x + a c\right)}^{\frac{9}{2}} a^{2} c^{2} - 1638 \, {\left(b c x + a c\right)}^{\frac{11}{2}} a c + 231 \, {\left(b c x + a c\right)}^{\frac{13}{2}}\right)} a^{2} \mathrm{sgn}\left(b x + a\right)}{c^{4}} - \frac{136 \, {\left(6435 \, \sqrt{b c x + a c} a^{7} c^{7} - 15015 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a^{6} c^{6} + 27027 \, {\left(b c x + a c\right)}^{\frac{5}{2}} a^{5} c^{5} - 32175 \, {\left(b c x + a c\right)}^{\frac{7}{2}} a^{4} c^{4} + 25025 \, {\left(b c x + a c\right)}^{\frac{9}{2}} a^{3} c^{3} - 12285 \, {\left(b c x + a c\right)}^{\frac{11}{2}} a^{2} c^{2} + 3465 \, {\left(b c x + a c\right)}^{\frac{13}{2}} a c - 429 \, {\left(b c x + a c\right)}^{\frac{15}{2}}\right)} a \mathrm{sgn}\left(b x + a\right)}{c^{5}} + \frac{{\left(109395 \, \sqrt{b c x + a c} a^{8} c^{8} - 291720 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a^{7} c^{7} + 612612 \, {\left(b c x + a c\right)}^{\frac{5}{2}} a^{6} c^{6} - 875160 \, {\left(b c x + a c\right)}^{\frac{7}{2}} a^{5} c^{5} + 850850 \, {\left(b c x + a c\right)}^{\frac{9}{2}} a^{4} c^{4} - 556920 \, {\left(b c x + a c\right)}^{\frac{11}{2}} a^{3} c^{3} + 235620 \, {\left(b c x + a c\right)}^{\frac{13}{2}} a^{2} c^{2} - 58344 \, {\left(b c x + a c\right)}^{\frac{15}{2}} a c + 6435 \, {\left(b c x + a c\right)}^{\frac{17}{2}}\right)} \mathrm{sgn}\left(b x + a\right)}{c^{6}}\right)}}{109395 \, b}"," ",0,"2/109395*(109395*sqrt(b*c*x + a*c)*a^8*c^2*sgn(b*x + a) - 291720*(3*sqrt(b*c*x + a*c)*a*c - (b*c*x + a*c)^(3/2))*a^7*c*sgn(b*x + a) + 204204*(15*sqrt(b*c*x + a*c)*a^2*c^2 - 10*(b*c*x + a*c)^(3/2)*a*c + 3*(b*c*x + a*c)^(5/2))*a^6*sgn(b*x + a) - 175032*(35*sqrt(b*c*x + a*c)*a^3*c^3 - 35*(b*c*x + a*c)^(3/2)*a^2*c^2 + 21*(b*c*x + a*c)^(5/2)*a*c - 5*(b*c*x + a*c)^(7/2))*a^5*sgn(b*x + a)/c + 24310*(315*sqrt(b*c*x + a*c)*a^4*c^4 - 420*(b*c*x + a*c)^(3/2)*a^3*c^3 + 378*(b*c*x + a*c)^(5/2)*a^2*c^2 - 180*(b*c*x + a*c)^(7/2)*a*c + 35*(b*c*x + a*c)^(9/2))*a^4*sgn(b*x + a)/c^2 - 8840*(693*sqrt(b*c*x + a*c)*a^5*c^5 - 1155*(b*c*x + a*c)^(3/2)*a^4*c^4 + 1386*(b*c*x + a*c)^(5/2)*a^3*c^3 - 990*(b*c*x + a*c)^(7/2)*a^2*c^2 + 385*(b*c*x + a*c)^(9/2)*a*c - 63*(b*c*x + a*c)^(11/2))*a^3*sgn(b*x + a)/c^3 + 1020*(3003*sqrt(b*c*x + a*c)*a^6*c^6 - 6006*(b*c*x + a*c)^(3/2)*a^5*c^5 + 9009*(b*c*x + a*c)^(5/2)*a^4*c^4 - 8580*(b*c*x + a*c)^(7/2)*a^3*c^3 + 5005*(b*c*x + a*c)^(9/2)*a^2*c^2 - 1638*(b*c*x + a*c)^(11/2)*a*c + 231*(b*c*x + a*c)^(13/2))*a^2*sgn(b*x + a)/c^4 - 136*(6435*sqrt(b*c*x + a*c)*a^7*c^7 - 15015*(b*c*x + a*c)^(3/2)*a^6*c^6 + 27027*(b*c*x + a*c)^(5/2)*a^5*c^5 - 32175*(b*c*x + a*c)^(7/2)*a^4*c^4 + 25025*(b*c*x + a*c)^(9/2)*a^3*c^3 - 12285*(b*c*x + a*c)^(11/2)*a^2*c^2 + 3465*(b*c*x + a*c)^(13/2)*a*c - 429*(b*c*x + a*c)^(15/2))*a*sgn(b*x + a)/c^5 + (109395*sqrt(b*c*x + a*c)*a^8*c^8 - 291720*(b*c*x + a*c)^(3/2)*a^7*c^7 + 612612*(b*c*x + a*c)^(5/2)*a^6*c^6 - 875160*(b*c*x + a*c)^(7/2)*a^5*c^5 + 850850*(b*c*x + a*c)^(9/2)*a^4*c^4 - 556920*(b*c*x + a*c)^(11/2)*a^3*c^3 + 235620*(b*c*x + a*c)^(13/2)*a^2*c^2 - 58344*(b*c*x + a*c)^(15/2)*a*c + 6435*(b*c*x + a*c)^(17/2))*sgn(b*x + a)/c^6)/b","B",0
2814,1,408,0,0.197024," ","integrate((c*(b*x+a)^3)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(693 \, \sqrt{b c x + a c} a^{5} \mathrm{sgn}\left(b x + a\right) - \frac{1155 \, {\left(3 \, \sqrt{b c x + a c} a c - {\left(b c x + a c\right)}^{\frac{3}{2}}\right)} a^{4} \mathrm{sgn}\left(b x + a\right)}{c} + \frac{462 \, {\left(15 \, \sqrt{b c x + a c} a^{2} c^{2} - 10 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a c + 3 \, {\left(b c x + a c\right)}^{\frac{5}{2}}\right)} a^{3} \mathrm{sgn}\left(b x + a\right)}{c^{2}} - \frac{198 \, {\left(35 \, \sqrt{b c x + a c} a^{3} c^{3} - 35 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a^{2} c^{2} + 21 \, {\left(b c x + a c\right)}^{\frac{5}{2}} a c - 5 \, {\left(b c x + a c\right)}^{\frac{7}{2}}\right)} a^{2} \mathrm{sgn}\left(b x + a\right)}{c^{3}} + \frac{11 \, {\left(315 \, \sqrt{b c x + a c} a^{4} c^{4} - 420 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a^{3} c^{3} + 378 \, {\left(b c x + a c\right)}^{\frac{5}{2}} a^{2} c^{2} - 180 \, {\left(b c x + a c\right)}^{\frac{7}{2}} a c + 35 \, {\left(b c x + a c\right)}^{\frac{9}{2}}\right)} a \mathrm{sgn}\left(b x + a\right)}{c^{4}} - \frac{{\left(693 \, \sqrt{b c x + a c} a^{5} c^{5} - 1155 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a^{4} c^{4} + 1386 \, {\left(b c x + a c\right)}^{\frac{5}{2}} a^{3} c^{3} - 990 \, {\left(b c x + a c\right)}^{\frac{7}{2}} a^{2} c^{2} + 385 \, {\left(b c x + a c\right)}^{\frac{9}{2}} a c - 63 \, {\left(b c x + a c\right)}^{\frac{11}{2}}\right)} \mathrm{sgn}\left(b x + a\right)}{c^{5}}\right)} c}{693 \, b}"," ",0,"2/693*(693*sqrt(b*c*x + a*c)*a^5*sgn(b*x + a) - 1155*(3*sqrt(b*c*x + a*c)*a*c - (b*c*x + a*c)^(3/2))*a^4*sgn(b*x + a)/c + 462*(15*sqrt(b*c*x + a*c)*a^2*c^2 - 10*(b*c*x + a*c)^(3/2)*a*c + 3*(b*c*x + a*c)^(5/2))*a^3*sgn(b*x + a)/c^2 - 198*(35*sqrt(b*c*x + a*c)*a^3*c^3 - 35*(b*c*x + a*c)^(3/2)*a^2*c^2 + 21*(b*c*x + a*c)^(5/2)*a*c - 5*(b*c*x + a*c)^(7/2))*a^2*sgn(b*x + a)/c^3 + 11*(315*sqrt(b*c*x + a*c)*a^4*c^4 - 420*(b*c*x + a*c)^(3/2)*a^3*c^3 + 378*(b*c*x + a*c)^(5/2)*a^2*c^2 - 180*(b*c*x + a*c)^(7/2)*a*c + 35*(b*c*x + a*c)^(9/2))*a*sgn(b*x + a)/c^4 - (693*sqrt(b*c*x + a*c)*a^5*c^5 - 1155*(b*c*x + a*c)^(3/2)*a^4*c^4 + 1386*(b*c*x + a*c)^(5/2)*a^3*c^3 - 990*(b*c*x + a*c)^(7/2)*a^2*c^2 + 385*(b*c*x + a*c)^(9/2)*a*c - 63*(b*c*x + a*c)^(11/2))*sgn(b*x + a)/c^5)*c/b","B",0
2815,1,121,0,0.178871," ","integrate((c*(b*x+a)^3)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \sqrt{b c x + a c} a^{2} \mathrm{sgn}\left(b x + a\right) - \frac{10 \, {\left(3 \, \sqrt{b c x + a c} a c - {\left(b c x + a c\right)}^{\frac{3}{2}}\right)} a \mathrm{sgn}\left(b x + a\right)}{c} + \frac{{\left(15 \, \sqrt{b c x + a c} a^{2} c^{2} - 10 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a c + 3 \, {\left(b c x + a c\right)}^{\frac{5}{2}}\right)} \mathrm{sgn}\left(b x + a\right)}{c^{2}}\right)}}{15 \, b}"," ",0,"2/15*(15*sqrt(b*c*x + a*c)*a^2*sgn(b*x + a) - 10*(3*sqrt(b*c*x + a*c)*a*c - (b*c*x + a*c)^(3/2))*a*sgn(b*x + a)/c + (15*sqrt(b*c*x + a*c)*a^2*c^2 - 10*(b*c*x + a*c)^(3/2)*a*c + 3*(b*c*x + a*c)^(5/2))*sgn(b*x + a)/c^2)/b","B",0
2816,1,23,0,0.155519," ","integrate(1/(c*(b*x+a)^3)^(1/2),x, algorithm=""giac"")","-\frac{2}{\sqrt{b c x + a c} b \mathrm{sgn}\left(b x + a\right)}"," ",0,"-2/(sqrt(b*c*x + a*c)*b*sgn(b*x + a))","A",0
2817,0,0,0,0.000000," ","integrate(1/(c*(b*x+a)^3)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2818,0,0,0,0.000000," ","integrate(1/(c*(b*x+a)^3)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2819,1,24,0,0.155913," ","integrate((c/(b*x+a))^(5/2),x, algorithm=""giac"")","-\frac{2 \, c^{4} \mathrm{sgn}\left(b x + a\right)}{3 \, {\left(b c x + a c\right)}^{\frac{3}{2}} b}"," ",0,"-2/3*c^4*sgn(b*x + a)/((b*c*x + a*c)^(3/2)*b)","A",0
2820,1,24,0,0.200469," ","integrate((c/(b*x+a))^(3/2),x, algorithm=""giac"")","-\frac{2 \, c^{2} \mathrm{sgn}\left(b x + a\right)}{\sqrt{b c x + a c} b}"," ",0,"-2*c^2*sgn(b*x + a)/(sqrt(b*c*x + a*c)*b)","A",0
2821,1,21,0,0.155171," ","integrate((c/(b*x+a))^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{b c x + a c} \mathrm{sgn}\left(b x + a\right)}{b}"," ",0,"2*sqrt(b*c*x + a*c)*sgn(b*x + a)/b","A",0
2822,1,62,0,0.156604," ","integrate(1/(c/(b*x+a))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, \sqrt{b c x + a c} a - \frac{3 \, \sqrt{b c x + a c} a c - {\left(b c x + a c\right)}^{\frac{3}{2}}}{c}\right)}}{3 \, b c \mathrm{sgn}\left(b x + a\right)}"," ",0,"2/3*(3*sqrt(b*c*x + a*c)*a - (3*sqrt(b*c*x + a*c)*a*c - (b*c*x + a*c)^(3/2))/c)/(b*c*sgn(b*x + a))","B",0
2823,1,26,0,0.172058," ","integrate(1/(c/(b*x+a))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(b x + a\right)}^{2}}{5 \, b c \sqrt{\frac{c}{b x + a}}}"," ",0,"2/5*(b*x + a)^2/(b*c*sqrt(c/(b*x + a)))","A",0
2824,1,26,0,0.176497," ","integrate(1/(c/(b*x+a))^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(b x + a\right)}^{3}}{7 \, b c^{2} \sqrt{\frac{c}{b x + a}}}"," ",0,"2/7*(b*x + a)^3/(b*c^2*sqrt(c/(b*x + a)))","A",0
2825,1,21,0,0.201241," ","integrate((c/(b*x+a)^2)^(5/2),x, algorithm=""giac"")","-\frac{c^{\frac{5}{2}} \mathrm{sgn}\left(b x + a\right)}{4 \, {\left(b x + a\right)}^{4} b}"," ",0,"-1/4*c^(5/2)*sgn(b*x + a)/((b*x + a)^4*b)","A",0
2826,1,21,0,0.157745," ","integrate((c/(b*x+a)^2)^(3/2),x, algorithm=""giac"")","-\frac{c^{\frac{3}{2}} \mathrm{sgn}\left(b x + a\right)}{2 \, {\left(b x + a\right)}^{2} b}"," ",0,"-1/2*c^(3/2)*sgn(b*x + a)/((b*x + a)^2*b)","A",0
2827,1,20,0,0.170005," ","integrate((c/(b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c} \log\left({\left| b x + a \right|}\right) \mathrm{sgn}\left(b x + a\right)}{b}"," ",0,"sqrt(c)*log(abs(b*x + a))*sgn(b*x + a)/b","A",0
2828,1,23,0,0.252171," ","integrate(1/(c/(b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{b x^{2} + 2 \, a x}{2 \, \sqrt{c} \mathrm{sgn}\left(b x + a\right)}"," ",0,"1/2*(b*x^2 + 2*a*x)/(sqrt(c)*sgn(b*x + a))","A",0
2829,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)^2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{c}{{\left(b x + a\right)}^{2}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c/(b*x + a)^2)^(-3/2), x)","F",0
2830,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)^2)^(5/2),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{c}{{\left(b x + a\right)}^{2}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c/(b*x + a)^2)^(-5/2), x)","F",0
2831,1,52,0,0.183271," ","integrate((c/(b*x+a)^3)^(5/2),x, algorithm=""giac"")","-\frac{2 \, c^{9} \mathrm{sgn}\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right) \mathrm{sgn}\left(b x + a\right)}{13 \, {\left(b c x + a c\right)}^{\frac{13}{2}} b}"," ",0,"-2/13*c^9*sgn(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*sgn(b*x + a)/((b*c*x + a*c)^(13/2)*b)","A",0
2832,1,52,0,0.184783," ","integrate((c/(b*x+a)^3)^(3/2),x, algorithm=""giac"")","-\frac{2 \, c^{5} \mathrm{sgn}\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right) \mathrm{sgn}\left(b x + a\right)}{7 \, {\left(b c x + a c\right)}^{\frac{7}{2}} b}"," ",0,"-2/7*c^5*sgn(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*sgn(b*x + a)/((b*c*x + a*c)^(7/2)*b)","B",0
2833,1,50,0,0.385381," ","integrate((c/(b*x+a)^3)^(1/2),x, algorithm=""giac"")","-\frac{2 \, c \mathrm{sgn}\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right) \mathrm{sgn}\left(b x + a\right)}{\sqrt{b c x + a c} b}"," ",0,"-2*c*sgn(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*sgn(b*x + a)/(sqrt(b*c*x + a*c)*b)","B",0
2834,1,144,0,0.358039," ","integrate(1/(c/(b*x+a)^3)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \sqrt{b c x + a c} a^{2} - \frac{10 \, {\left(3 \, \sqrt{b c x + a c} a c - {\left(b c x + a c\right)}^{\frac{3}{2}}\right)} a}{c} + \frac{15 \, \sqrt{b c x + a c} a^{2} c^{2} - 10 \, {\left(b c x + a c\right)}^{\frac{3}{2}} a c + 3 \, {\left(b c x + a c\right)}^{\frac{5}{2}}}{c^{2}}\right)}}{15 \, b c \mathrm{sgn}\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right) \mathrm{sgn}\left(b x + a\right)}"," ",0,"2/15*(15*sqrt(b*c*x + a*c)*a^2 - 10*(3*sqrt(b*c*x + a*c)*a*c - (b*c*x + a*c)^(3/2))*a/c + (15*sqrt(b*c*x + a*c)*a^2*c^2 - 10*(b*c*x + a*c)^(3/2)*a*c + 3*(b*c*x + a*c)^(5/2))/c^2)/(b*c*sgn(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*sgn(b*x + a))","B",0
2835,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)^3)^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{c}{{\left(b x + a\right)}^{3}}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c/(b*x + a)^3)^(-3/2), x)","F",0
2836,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)^3)^(5/2),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{c}{{\left(b x + a\right)}^{3}}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c/(b*x + a)^3)^(-5/2), x)","F",0
2837,1,15,0,0.239536," ","integrate((c*(b*x+a)^(3/2))^(2/3),x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{2} c^{\frac{2}{3}}}{2 \, b}"," ",0,"1/2*(b*x + a)^2*c^(2/3)/b","A",0
2838,1,15,0,0.150118," ","integrate((c*(b*x+a)^(2/3))^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} c^{\frac{3}{2}}"," ",0,"1/2*(b*x^2 + 2*a*x)*c^(3/2)","A",0
2839,0,0,0,0.000000," ","integrate(1/(c/(b*x+a)^(3/2))^(2/3),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{c}{{\left(b x + a\right)}^{\frac{3}{2}}}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((c/(b*x + a)^(3/2))^(-2/3), x)","F",0
2840,1,15,0,0.152209," ","integrate(1/(c/(b*x+a)^(2/3))^(3/2),x, algorithm=""giac"")","\frac{b x^{2} + 2 \, a x}{2 \, c^{\frac{3}{2}}}"," ",0,"1/2*(b*x^2 + 2*a*x)/c^(3/2)","A",0
2841,1,86,0,0.165445," ","integrate((d*x+c)^3*(a+b*(d*x+c)^2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(d x^{2} + 2 \, c x\right)} b c^{4} + \frac{1}{2} \, {\left(d x^{2} + 2 \, c x\right)}^{2} b c^{2} d + \frac{1}{6} \, {\left(d x^{2} + 2 \, c x\right)}^{3} b d^{2} + \frac{1}{2} \, {\left(d x^{2} + 2 \, c x\right)} a c^{2} + \frac{1}{4} \, {\left(d x^{2} + 2 \, c x\right)}^{2} a d"," ",0,"1/2*(d*x^2 + 2*c*x)*b*c^4 + 1/2*(d*x^2 + 2*c*x)^2*b*c^2*d + 1/6*(d*x^2 + 2*c*x)^3*b*d^2 + 1/2*(d*x^2 + 2*c*x)*a*c^2 + 1/4*(d*x^2 + 2*c*x)^2*a*d","B",0
2842,1,173,0,0.160545," ","integrate((d*x+c)^3*(a+b*(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(d x^{2} + 2 \, c x\right)} b^{2} c^{6} + \frac{3}{4} \, {\left(d x^{2} + 2 \, c x\right)}^{2} b^{2} c^{4} d + \frac{1}{2} \, {\left(d x^{2} + 2 \, c x\right)}^{3} b^{2} c^{2} d^{2} + \frac{1}{8} \, {\left(d x^{2} + 2 \, c x\right)}^{4} b^{2} d^{3} + {\left(d x^{2} + 2 \, c x\right)} a b c^{4} + {\left(d x^{2} + 2 \, c x\right)}^{2} a b c^{2} d + \frac{1}{3} \, {\left(d x^{2} + 2 \, c x\right)}^{3} a b d^{2} + \frac{1}{2} \, {\left(d x^{2} + 2 \, c x\right)} a^{2} c^{2} + \frac{1}{4} \, {\left(d x^{2} + 2 \, c x\right)}^{2} a^{2} d"," ",0,"1/2*(d*x^2 + 2*c*x)*b^2*c^6 + 3/4*(d*x^2 + 2*c*x)^2*b^2*c^4*d + 1/2*(d*x^2 + 2*c*x)^3*b^2*c^2*d^2 + 1/8*(d*x^2 + 2*c*x)^4*b^2*d^3 + (d*x^2 + 2*c*x)*a*b*c^4 + (d*x^2 + 2*c*x)^2*a*b*c^2*d + 1/3*(d*x^2 + 2*c*x)^3*a*b*d^2 + 1/2*(d*x^2 + 2*c*x)*a^2*c^2 + 1/4*(d*x^2 + 2*c*x)^2*a^2*d","B",0
2843,1,288,0,0.179658," ","integrate((d*x+c)^3*(a+b*(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{1}{2} \, {\left(d x^{2} + 2 \, c x\right)} b^{3} c^{8} + {\left(d x^{2} + 2 \, c x\right)}^{2} b^{3} c^{6} d + {\left(d x^{2} + 2 \, c x\right)}^{3} b^{3} c^{4} d^{2} + \frac{1}{2} \, {\left(d x^{2} + 2 \, c x\right)}^{4} b^{3} c^{2} d^{3} + \frac{1}{10} \, {\left(d x^{2} + 2 \, c x\right)}^{5} b^{3} d^{4} + \frac{3}{2} \, {\left(d x^{2} + 2 \, c x\right)} a b^{2} c^{6} + \frac{9}{4} \, {\left(d x^{2} + 2 \, c x\right)}^{2} a b^{2} c^{4} d + \frac{3}{2} \, {\left(d x^{2} + 2 \, c x\right)}^{3} a b^{2} c^{2} d^{2} + \frac{3}{8} \, {\left(d x^{2} + 2 \, c x\right)}^{4} a b^{2} d^{3} + \frac{3}{2} \, {\left(d x^{2} + 2 \, c x\right)} a^{2} b c^{4} + \frac{3}{2} \, {\left(d x^{2} + 2 \, c x\right)}^{2} a^{2} b c^{2} d + \frac{1}{2} \, {\left(d x^{2} + 2 \, c x\right)}^{3} a^{2} b d^{2} + \frac{1}{2} \, {\left(d x^{2} + 2 \, c x\right)} a^{3} c^{2} + \frac{1}{4} \, {\left(d x^{2} + 2 \, c x\right)}^{2} a^{3} d"," ",0,"1/2*(d*x^2 + 2*c*x)*b^3*c^8 + (d*x^2 + 2*c*x)^2*b^3*c^6*d + (d*x^2 + 2*c*x)^3*b^3*c^4*d^2 + 1/2*(d*x^2 + 2*c*x)^4*b^3*c^2*d^3 + 1/10*(d*x^2 + 2*c*x)^5*b^3*d^4 + 3/2*(d*x^2 + 2*c*x)*a*b^2*c^6 + 9/4*(d*x^2 + 2*c*x)^2*a*b^2*c^4*d + 3/2*(d*x^2 + 2*c*x)^3*a*b^2*c^2*d^2 + 3/8*(d*x^2 + 2*c*x)^4*a*b^2*d^3 + 3/2*(d*x^2 + 2*c*x)*a^2*b*c^4 + 3/2*(d*x^2 + 2*c*x)^2*a^2*b*c^2*d + 1/2*(d*x^2 + 2*c*x)^3*a^2*b*d^2 + 1/2*(d*x^2 + 2*c*x)*a^3*c^2 + 1/4*(d*x^2 + 2*c*x)^2*a^3*d","B",0
2844,1,11,0,0.149811," ","integrate((2+x)/(1+(2+x)^2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(x^{2} + 4 \, x + 5\right)"," ",0,"1/2*log(x^2 + 4*x + 5)","A",0
2845,1,12,0,0.199060," ","integrate((2+x)/(1+(2+x)^2)^2,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(x^{2} + 4 \, x + 5\right)}}"," ",0,"-1/2/(x^2 + 4*x + 5)","A",0
2846,1,12,0,0.172085," ","integrate((2+x)/(1+(2+x)^2)^3,x, algorithm=""giac"")","-\frac{1}{4 \, {\left(x^{2} + 4 \, x + 5\right)}^{2}}"," ",0,"-1/4/(x^2 + 4*x + 5)^2","A",0
2847,1,1290,0,0.254652," ","integrate((d*x+c)^5*(a+b*(d*x+c)^2)^p,x, algorithm=""giac"")","\frac{{\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} d^{6} p^{2} x^{6} + 6 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c d^{5} p^{2} x^{5} + 3 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} d^{6} p x^{6} + 15 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{2} d^{4} p^{2} x^{4} + 18 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c d^{5} p x^{5} + 2 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} d^{6} x^{6} + 20 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{3} d^{3} p^{2} x^{3} + 45 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{2} d^{4} p x^{4} + 12 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c d^{5} x^{5} + 15 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{4} d^{2} p^{2} x^{2} + 60 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{3} d^{3} p x^{3} + 30 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{2} d^{4} x^{4} + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a b^{2} d^{4} p^{2} x^{4} + 6 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{5} d p^{2} x + 45 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{4} d^{2} p x^{2} + 40 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{3} d^{3} x^{3} + 4 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a b^{2} c d^{3} p^{2} x^{3} + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a b^{2} d^{4} p x^{4} + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{6} p^{2} + 18 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{5} d p x + 30 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{4} d^{2} x^{2} + 6 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a b^{2} c^{2} d^{2} p^{2} x^{2} + 4 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a b^{2} c d^{3} p x^{3} + 3 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{6} p + 12 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{5} d x + 4 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a b^{2} c^{3} d p^{2} x + 6 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a b^{2} c^{2} d^{2} p x^{2} + 2 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} b^{3} c^{6} + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a b^{2} c^{4} p^{2} + 4 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a b^{2} c^{3} d p x + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a b^{2} c^{4} p - 2 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a^{2} b d^{2} p x^{2} - 4 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a^{2} b c d p x - 2 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a^{2} b c^{2} p + 2 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p} a^{3}}{2 \, {\left(b^{3} d p^{3} + 6 \, b^{3} d p^{2} + 11 \, b^{3} d p + 6 \, b^{3} d\right)}}"," ",0,"1/2*((b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*d^6*p^2*x^6 + 6*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c*d^5*p^2*x^5 + 3*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*d^6*p*x^6 + 15*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^2*d^4*p^2*x^4 + 18*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c*d^5*p*x^5 + 2*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*d^6*x^6 + 20*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^3*d^3*p^2*x^3 + 45*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^2*d^4*p*x^4 + 12*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c*d^5*x^5 + 15*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^4*d^2*p^2*x^2 + 60*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^3*d^3*p*x^3 + 30*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^2*d^4*x^4 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a*b^2*d^4*p^2*x^4 + 6*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^5*d*p^2*x + 45*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^4*d^2*p*x^2 + 40*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^3*d^3*x^3 + 4*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a*b^2*c*d^3*p^2*x^3 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a*b^2*d^4*p*x^4 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^6*p^2 + 18*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^5*d*p*x + 30*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^4*d^2*x^2 + 6*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a*b^2*c^2*d^2*p^2*x^2 + 4*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a*b^2*c*d^3*p*x^3 + 3*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^6*p + 12*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^5*d*x + 4*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a*b^2*c^3*d*p^2*x + 6*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a*b^2*c^2*d^2*p*x^2 + 2*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*b^3*c^6 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a*b^2*c^4*p^2 + 4*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a*b^2*c^3*d*p*x + (b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a*b^2*c^4*p - 2*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a^2*b*d^2*p*x^2 - 4*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a^2*b*c*d*p*x - 2*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a^2*b*c^2*p + 2*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^p*a^3)/(b^3*d*p^3 + 6*b^3*d*p^2 + 11*b^3*d*p + 6*b^3*d)","B",0
2848,0,0,0,0.000000," ","integrate((d*x+c)^4*(a+b*(d*x+c)^2)^p,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{4} {\left({\left(d x + c\right)}^{2} b + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x + c)^4*((d*x + c)^2*b + a)^p, x)","F",0
2849,1,345,0,0.196354," ","integrate((d*x+c)^3*(a+b*(d*x+c)^2)^p,x, algorithm=""giac"")","\frac{{\left(b c^{2} + {\left(d x^{2} + 2 \, c x\right)} b d + a\right)}^{p} b^{2} c^{4} p + 2 \, {\left(d x^{2} + 2 \, c x\right)} {\left(b c^{2} + {\left(d x^{2} + 2 \, c x\right)} b d + a\right)}^{p} b^{2} c^{2} d p + {\left(d x^{2} + 2 \, c x\right)}^{2} {\left(b c^{2} + {\left(d x^{2} + 2 \, c x\right)} b d + a\right)}^{p} b^{2} d^{2} p + {\left(b c^{2} + {\left(d x^{2} + 2 \, c x\right)} b d + a\right)}^{p} b^{2} c^{4} + 2 \, {\left(d x^{2} + 2 \, c x\right)} {\left(b c^{2} + {\left(d x^{2} + 2 \, c x\right)} b d + a\right)}^{p} b^{2} c^{2} d + {\left(d x^{2} + 2 \, c x\right)}^{2} {\left(b c^{2} + {\left(d x^{2} + 2 \, c x\right)} b d + a\right)}^{p} b^{2} d^{2} + {\left(b c^{2} + {\left(d x^{2} + 2 \, c x\right)} b d + a\right)}^{p} a b c^{2} p + {\left(d x^{2} + 2 \, c x\right)} {\left(b c^{2} + {\left(d x^{2} + 2 \, c x\right)} b d + a\right)}^{p} a b d p - {\left(b c^{2} + {\left(d x^{2} + 2 \, c x\right)} b d + a\right)}^{p} a^{2}}{2 \, {\left(b^{2} d p^{2} + 3 \, b^{2} d p + 2 \, b^{2} d\right)}}"," ",0,"1/2*((b*c^2 + (d*x^2 + 2*c*x)*b*d + a)^p*b^2*c^4*p + 2*(d*x^2 + 2*c*x)*(b*c^2 + (d*x^2 + 2*c*x)*b*d + a)^p*b^2*c^2*d*p + (d*x^2 + 2*c*x)^2*(b*c^2 + (d*x^2 + 2*c*x)*b*d + a)^p*b^2*d^2*p + (b*c^2 + (d*x^2 + 2*c*x)*b*d + a)^p*b^2*c^4 + 2*(d*x^2 + 2*c*x)*(b*c^2 + (d*x^2 + 2*c*x)*b*d + a)^p*b^2*c^2*d + (d*x^2 + 2*c*x)^2*(b*c^2 + (d*x^2 + 2*c*x)*b*d + a)^p*b^2*d^2 + (b*c^2 + (d*x^2 + 2*c*x)*b*d + a)^p*a*b*c^2*p + (d*x^2 + 2*c*x)*(b*c^2 + (d*x^2 + 2*c*x)*b*d + a)^p*a*b*d*p - (b*c^2 + (d*x^2 + 2*c*x)*b*d + a)^p*a^2)/(b^2*d*p^2 + 3*b^2*d*p + 2*b^2*d)","B",0
2850,0,0,0,0.000000," ","integrate((d*x+c)^2*(a+b*(d*x+c)^2)^p,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{2} {\left({\left(d x + c\right)}^{2} b + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x + c)^2*((d*x + c)^2*b + a)^p, x)","F",0
2851,1,38,0,0.165751," ","integrate((d*x+c)*(a+b*(d*x+c)^2)^p,x, algorithm=""giac"")","\frac{{\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}^{p + 1}}{2 \, b d {\left(p + 1\right)}}"," ",0,"1/2*(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)^(p + 1)/(b*d*(p + 1))","A",0
2852,0,0,0,0.000000," ","integrate((a+b*(d*x+c)^2)^p/(d*x+c),x, algorithm=""giac"")","\int \frac{{\left({\left(d x + c\right)}^{2} b + a\right)}^{p}}{d x + c}\,{d x}"," ",0,"integrate(((d*x + c)^2*b + a)^p/(d*x + c), x)","F",0
2853,1,105,0,0.147665," ","integrate((d*x+c)^3*(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{1}{7} \, b d^{6} x^{7} + b c d^{5} x^{6} + 3 \, b c^{2} d^{4} x^{5} + 5 \, b c^{3} d^{3} x^{4} + 5 \, b c^{4} d^{2} x^{3} + 3 \, b c^{5} d x^{2} + b c^{6} x + \frac{1}{4} \, a d^{3} x^{4} + a c d^{2} x^{3} + \frac{3}{2} \, a c^{2} d x^{2} + a c^{3} x"," ",0,"1/7*b*d^6*x^7 + b*c*d^5*x^6 + 3*b*c^2*d^4*x^5 + 5*b*c^3*d^3*x^4 + 5*b*c^4*d^2*x^3 + 3*b*c^5*d*x^2 + b*c^6*x + 1/4*a*d^3*x^4 + a*c*d^2*x^3 + 3/2*a*c^2*d*x^2 + a*c^3*x","B",0
2854,1,248,0,0.160508," ","integrate((d*x+c)^3*(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{1}{10} \, b^{2} d^{9} x^{10} + b^{2} c d^{8} x^{9} + \frac{9}{2} \, b^{2} c^{2} d^{7} x^{8} + 12 \, b^{2} c^{3} d^{6} x^{7} + 21 \, b^{2} c^{4} d^{5} x^{6} + \frac{126}{5} \, b^{2} c^{5} d^{4} x^{5} + 21 \, b^{2} c^{6} d^{3} x^{4} + \frac{2}{7} \, a b d^{6} x^{7} + 12 \, b^{2} c^{7} d^{2} x^{3} + 2 \, a b c d^{5} x^{6} + \frac{9}{2} \, b^{2} c^{8} d x^{2} + 6 \, a b c^{2} d^{4} x^{5} + b^{2} c^{9} x + 10 \, a b c^{3} d^{3} x^{4} + 10 \, a b c^{4} d^{2} x^{3} + 6 \, a b c^{5} d x^{2} + 2 \, a b c^{6} x + \frac{1}{4} \, a^{2} d^{3} x^{4} + a^{2} c d^{2} x^{3} + \frac{3}{2} \, a^{2} c^{2} d x^{2} + a^{2} c^{3} x"," ",0,"1/10*b^2*d^9*x^10 + b^2*c*d^8*x^9 + 9/2*b^2*c^2*d^7*x^8 + 12*b^2*c^3*d^6*x^7 + 21*b^2*c^4*d^5*x^6 + 126/5*b^2*c^5*d^4*x^5 + 21*b^2*c^6*d^3*x^4 + 2/7*a*b*d^6*x^7 + 12*b^2*c^7*d^2*x^3 + 2*a*b*c*d^5*x^6 + 9/2*b^2*c^8*d*x^2 + 6*a*b*c^2*d^4*x^5 + b^2*c^9*x + 10*a*b*c^3*d^3*x^4 + 10*a*b*c^4*d^2*x^3 + 6*a*b*c^5*d*x^2 + 2*a*b*c^6*x + 1/4*a^2*d^3*x^4 + a^2*c*d^2*x^3 + 3/2*a^2*c^2*d*x^2 + a^2*c^3*x","B",0
2855,1,442,0,0.161436," ","integrate((d*x+c)^3*(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{3} d^{12} x^{13} + b^{3} c d^{11} x^{12} + 6 \, b^{3} c^{2} d^{10} x^{11} + 22 \, b^{3} c^{3} d^{9} x^{10} + 55 \, b^{3} c^{4} d^{8} x^{9} + 99 \, b^{3} c^{5} d^{7} x^{8} + 132 \, b^{3} c^{6} d^{6} x^{7} + \frac{3}{10} \, a b^{2} d^{9} x^{10} + 132 \, b^{3} c^{7} d^{5} x^{6} + 3 \, a b^{2} c d^{8} x^{9} + 99 \, b^{3} c^{8} d^{4} x^{5} + \frac{27}{2} \, a b^{2} c^{2} d^{7} x^{8} + 55 \, b^{3} c^{9} d^{3} x^{4} + 36 \, a b^{2} c^{3} d^{6} x^{7} + 22 \, b^{3} c^{10} d^{2} x^{3} + 63 \, a b^{2} c^{4} d^{5} x^{6} + 6 \, b^{3} c^{11} d x^{2} + \frac{378}{5} \, a b^{2} c^{5} d^{4} x^{5} + b^{3} c^{12} x + 63 \, a b^{2} c^{6} d^{3} x^{4} + \frac{3}{7} \, a^{2} b d^{6} x^{7} + 36 \, a b^{2} c^{7} d^{2} x^{3} + 3 \, a^{2} b c d^{5} x^{6} + \frac{27}{2} \, a b^{2} c^{8} d x^{2} + 9 \, a^{2} b c^{2} d^{4} x^{5} + 3 \, a b^{2} c^{9} x + 15 \, a^{2} b c^{3} d^{3} x^{4} + 15 \, a^{2} b c^{4} d^{2} x^{3} + 9 \, a^{2} b c^{5} d x^{2} + 3 \, a^{2} b c^{6} x + \frac{1}{4} \, a^{3} d^{3} x^{4} + a^{3} c d^{2} x^{3} + \frac{3}{2} \, a^{3} c^{2} d x^{2} + a^{3} c^{3} x"," ",0,"1/13*b^3*d^12*x^13 + b^3*c*d^11*x^12 + 6*b^3*c^2*d^10*x^11 + 22*b^3*c^3*d^9*x^10 + 55*b^3*c^4*d^8*x^9 + 99*b^3*c^5*d^7*x^8 + 132*b^3*c^6*d^6*x^7 + 3/10*a*b^2*d^9*x^10 + 132*b^3*c^7*d^5*x^6 + 3*a*b^2*c*d^8*x^9 + 99*b^3*c^8*d^4*x^5 + 27/2*a*b^2*c^2*d^7*x^8 + 55*b^3*c^9*d^3*x^4 + 36*a*b^2*c^3*d^6*x^7 + 22*b^3*c^10*d^2*x^3 + 63*a*b^2*c^4*d^5*x^6 + 6*b^3*c^11*d*x^2 + 378/5*a*b^2*c^5*d^4*x^5 + b^3*c^12*x + 63*a*b^2*c^6*d^3*x^4 + 3/7*a^2*b*d^6*x^7 + 36*a*b^2*c^7*d^2*x^3 + 3*a^2*b*c*d^5*x^6 + 27/2*a*b^2*c^8*d*x^2 + 9*a^2*b*c^2*d^4*x^5 + 3*a*b^2*c^9*x + 15*a^2*b*c^3*d^3*x^4 + 15*a^2*b*c^4*d^2*x^3 + 9*a^2*b*c^5*d*x^2 + 3*a^2*b*c^6*x + 1/4*a^3*d^3*x^4 + a^3*c*d^2*x^3 + 3/2*a^3*c^2*d*x^2 + a^3*c^3*x","B",0
2856,1,127,0,0.152049," ","integrate((d*e*x+c*e)^3*(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{1}{7} \, b d^{6} x^{7} e^{3} + b c d^{5} x^{6} e^{3} + 3 \, b c^{2} d^{4} x^{5} e^{3} + 5 \, b c^{3} d^{3} x^{4} e^{3} + 5 \, b c^{4} d^{2} x^{3} e^{3} + 3 \, b c^{5} d x^{2} e^{3} + b c^{6} x e^{3} + \frac{1}{4} \, a d^{3} x^{4} e^{3} + a c d^{2} x^{3} e^{3} + \frac{3}{2} \, a c^{2} d x^{2} e^{3} + a c^{3} x e^{3}"," ",0,"1/7*b*d^6*x^7*e^3 + b*c*d^5*x^6*e^3 + 3*b*c^2*d^4*x^5*e^3 + 5*b*c^3*d^3*x^4*e^3 + 5*b*c^4*d^2*x^3*e^3 + 3*b*c^5*d*x^2*e^3 + b*c^6*x*e^3 + 1/4*a*d^3*x^4*e^3 + a*c*d^2*x^3*e^3 + 3/2*a*c^2*d*x^2*e^3 + a*c^3*x*e^3","B",0
2857,1,290,0,0.156486," ","integrate((d*e*x+c*e)^3*(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{1}{10} \, b^{2} d^{9} x^{10} e^{3} + b^{2} c d^{8} x^{9} e^{3} + \frac{9}{2} \, b^{2} c^{2} d^{7} x^{8} e^{3} + 12 \, b^{2} c^{3} d^{6} x^{7} e^{3} + 21 \, b^{2} c^{4} d^{5} x^{6} e^{3} + \frac{126}{5} \, b^{2} c^{5} d^{4} x^{5} e^{3} + 21 \, b^{2} c^{6} d^{3} x^{4} e^{3} + \frac{2}{7} \, a b d^{6} x^{7} e^{3} + 12 \, b^{2} c^{7} d^{2} x^{3} e^{3} + 2 \, a b c d^{5} x^{6} e^{3} + \frac{9}{2} \, b^{2} c^{8} d x^{2} e^{3} + 6 \, a b c^{2} d^{4} x^{5} e^{3} + b^{2} c^{9} x e^{3} + 10 \, a b c^{3} d^{3} x^{4} e^{3} + 10 \, a b c^{4} d^{2} x^{3} e^{3} + 6 \, a b c^{5} d x^{2} e^{3} + 2 \, a b c^{6} x e^{3} + \frac{1}{4} \, a^{2} d^{3} x^{4} e^{3} + a^{2} c d^{2} x^{3} e^{3} + \frac{3}{2} \, a^{2} c^{2} d x^{2} e^{3} + a^{2} c^{3} x e^{3}"," ",0,"1/10*b^2*d^9*x^10*e^3 + b^2*c*d^8*x^9*e^3 + 9/2*b^2*c^2*d^7*x^8*e^3 + 12*b^2*c^3*d^6*x^7*e^3 + 21*b^2*c^4*d^5*x^6*e^3 + 126/5*b^2*c^5*d^4*x^5*e^3 + 21*b^2*c^6*d^3*x^4*e^3 + 2/7*a*b*d^6*x^7*e^3 + 12*b^2*c^7*d^2*x^3*e^3 + 2*a*b*c*d^5*x^6*e^3 + 9/2*b^2*c^8*d*x^2*e^3 + 6*a*b*c^2*d^4*x^5*e^3 + b^2*c^9*x*e^3 + 10*a*b*c^3*d^3*x^4*e^3 + 10*a*b*c^4*d^2*x^3*e^3 + 6*a*b*c^5*d*x^2*e^3 + 2*a*b*c^6*x*e^3 + 1/4*a^2*d^3*x^4*e^3 + a^2*c*d^2*x^3*e^3 + 3/2*a^2*c^2*d*x^2*e^3 + a^2*c^3*x*e^3","B",0
2858,1,510,0,0.182123," ","integrate((d*e*x+c*e)^3*(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{3} d^{12} x^{13} e^{3} + b^{3} c d^{11} x^{12} e^{3} + 6 \, b^{3} c^{2} d^{10} x^{11} e^{3} + 22 \, b^{3} c^{3} d^{9} x^{10} e^{3} + 55 \, b^{3} c^{4} d^{8} x^{9} e^{3} + 99 \, b^{3} c^{5} d^{7} x^{8} e^{3} + 132 \, b^{3} c^{6} d^{6} x^{7} e^{3} + \frac{3}{10} \, a b^{2} d^{9} x^{10} e^{3} + 132 \, b^{3} c^{7} d^{5} x^{6} e^{3} + 3 \, a b^{2} c d^{8} x^{9} e^{3} + 99 \, b^{3} c^{8} d^{4} x^{5} e^{3} + \frac{27}{2} \, a b^{2} c^{2} d^{7} x^{8} e^{3} + 55 \, b^{3} c^{9} d^{3} x^{4} e^{3} + 36 \, a b^{2} c^{3} d^{6} x^{7} e^{3} + 22 \, b^{3} c^{10} d^{2} x^{3} e^{3} + 63 \, a b^{2} c^{4} d^{5} x^{6} e^{3} + 6 \, b^{3} c^{11} d x^{2} e^{3} + \frac{378}{5} \, a b^{2} c^{5} d^{4} x^{5} e^{3} + b^{3} c^{12} x e^{3} + 63 \, a b^{2} c^{6} d^{3} x^{4} e^{3} + \frac{3}{7} \, a^{2} b d^{6} x^{7} e^{3} + 36 \, a b^{2} c^{7} d^{2} x^{3} e^{3} + 3 \, a^{2} b c d^{5} x^{6} e^{3} + \frac{27}{2} \, a b^{2} c^{8} d x^{2} e^{3} + 9 \, a^{2} b c^{2} d^{4} x^{5} e^{3} + 3 \, a b^{2} c^{9} x e^{3} + 15 \, a^{2} b c^{3} d^{3} x^{4} e^{3} + 15 \, a^{2} b c^{4} d^{2} x^{3} e^{3} + 9 \, a^{2} b c^{5} d x^{2} e^{3} + 3 \, a^{2} b c^{6} x e^{3} + \frac{1}{4} \, a^{3} d^{3} x^{4} e^{3} + a^{3} c d^{2} x^{3} e^{3} + \frac{3}{2} \, a^{3} c^{2} d x^{2} e^{3} + a^{3} c^{3} x e^{3}"," ",0,"1/13*b^3*d^12*x^13*e^3 + b^3*c*d^11*x^12*e^3 + 6*b^3*c^2*d^10*x^11*e^3 + 22*b^3*c^3*d^9*x^10*e^3 + 55*b^3*c^4*d^8*x^9*e^3 + 99*b^3*c^5*d^7*x^8*e^3 + 132*b^3*c^6*d^6*x^7*e^3 + 3/10*a*b^2*d^9*x^10*e^3 + 132*b^3*c^7*d^5*x^6*e^3 + 3*a*b^2*c*d^8*x^9*e^3 + 99*b^3*c^8*d^4*x^5*e^3 + 27/2*a*b^2*c^2*d^7*x^8*e^3 + 55*b^3*c^9*d^3*x^4*e^3 + 36*a*b^2*c^3*d^6*x^7*e^3 + 22*b^3*c^10*d^2*x^3*e^3 + 63*a*b^2*c^4*d^5*x^6*e^3 + 6*b^3*c^11*d*x^2*e^3 + 378/5*a*b^2*c^5*d^4*x^5*e^3 + b^3*c^12*x*e^3 + 63*a*b^2*c^6*d^3*x^4*e^3 + 3/7*a^2*b*d^6*x^7*e^3 + 36*a*b^2*c^7*d^2*x^3*e^3 + 3*a^2*b*c*d^5*x^6*e^3 + 27/2*a*b^2*c^8*d*x^2*e^3 + 9*a^2*b*c^2*d^4*x^5*e^3 + 3*a*b^2*c^9*x*e^3 + 15*a^2*b*c^3*d^3*x^4*e^3 + 15*a^2*b*c^4*d^2*x^3*e^3 + 9*a^2*b*c^5*d*x^2*e^3 + 3*a^2*b*c^6*x*e^3 + 1/4*a^3*d^3*x^4*e^3 + a^3*c*d^2*x^3*e^3 + 3/2*a^3*c^2*d*x^2*e^3 + a^3*c^3*x*e^3","B",0
2859,1,160,0,0.215991," ","integrate((d*x+c)^4/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{b d^{7} x^{2} + 2 \, b c d^{6} x}{2 \, b^{2} d^{6}} - \frac{2 \, \sqrt{3} \left(a^{2} b d^{15}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(a^{2} b\right)^{\frac{2}{3}}}\right) + \left(a^{2} b d^{15}\right)^{\frac{1}{3}} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(a^{2} b\right)^{\frac{4}{3}}\right) - 2 \, \left(a^{2} b d^{15}\right)^{\frac{1}{3}} \log\left({\left| a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}} \right|}\right)}{6 \, b^{2} d^{6}}"," ",0,"1/2*(b*d^7*x^2 + 2*b*c*d^6*x)/(b^2*d^6) - 1/6*(2*sqrt(3)*(a^2*b*d^15)^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (a^2*b)^(2/3))/(a^2*b)^(2/3)) + (a^2*b*d^15)^(1/3)*log((2*a*b*d*x + 2*a*b*c - (a^2*b)^(2/3))^2 + 3*(a^2*b)^(4/3)) - 2*(a^2*b*d^15)^(1/3)*log(abs(a*b*d*x + a*b*c + (a^2*b)^(2/3))))/(b^2*d^6)","A",0
2860,1,180,0,0.251849," ","integrate((d*x+c)^3/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{x}{b} + \frac{2 \, \sqrt{3} \left(-\frac{a d^{6}}{b}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}}\right) - \left(-\frac{a d^{6}}{b}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(-\frac{a d^{6}}{b}\right)^{\frac{1}{3}} \log\left({\left| -b d x - b c + \left(-a b^{2}\right)^{\frac{1}{3}} \right|}\right)}{6 \, b d^{3}}"," ",0,"x/b + 1/6*(2*sqrt(3)*(-a*d^6/b)^(1/3)*arctan(-(b*d*x + b*c - (-a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))) - (-a*d^6/b)^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))^2 + 4*(b*d*x + b*c - (-a*b^2)^(1/3))^2) + 2*(-a*d^6/b)^(1/3)*log(abs(-b*d*x - b*c + (-a*b^2)^(1/3))))/(b*d^3)","A",0
2861,1,21,0,0.182922," ","integrate((d*x+c)^2/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{\log\left({\left| {\left(d x + c\right)}^{3} b + a \right|}\right)}{3 \, b d}"," ",0,"1/3*log(abs((d*x + c)^3*b + a))/(b*d)","A",0
2862,1,141,0,0.216425," ","integrate((d*x+c)/(a+b*(d*x+c)^3),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(-a^{2} b\right)^{\frac{2}{3}}}\right) - \frac{1}{6} \, \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(-a^{2} b\right)^{\frac{4}{3}}\right) + \frac{1}{3} \, \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| a b d x + a b c + \left(-a^{2} b\right)^{\frac{2}{3}} \right|}\right)"," ",0,"-1/3*sqrt(3)*(-1/(a*b^2*d^3))^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))/(-a^2*b)^(2/3)) - 1/6*(-1/(a*b^2*d^3))^(1/3)*log((2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))^2 + 3*(-a^2*b)^(4/3)) + 1/3*(-1/(a*b^2*d^3))^(1/3)*log(abs(a*b*d*x + a*b*c + (-a^2*b)^(2/3)))","A",0
2863,1,160,0,0.167370," ","integrate(1/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}}\right) - \frac{1}{6} \, \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + \frac{1}{3} \, \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left({\left| b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}} \right|}\right)"," ",0,"1/3*sqrt(3)*(1/(a^2*b*d^3))^(1/3)*arctan(-(b*d*x + b*c + (a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))) - 1/6*(1/(a^2*b*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))^2 + 4*(b*d*x + b*c + (a*b^2)^(1/3))^2) + 1/3*(1/(a^2*b*d^3))^(1/3)*log(abs(b*d*x + b*c + (a*b^2)^(1/3)))","A",0
2864,1,58,0,0.208223," ","integrate(1/(d*x+c)/(a+b*(d*x+c)^3),x, algorithm=""giac"")","-\frac{\log\left({\left| b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a \right|}\right)}{3 \, a d} + \frac{\log\left({\left| d x + c \right|}\right)}{a d}"," ",0,"-1/3*log(abs(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a))/(a*d) + log(abs(d*x + c))/(a*d)","A",0
2865,1,175,0,0.203113," ","integrate(1/(d*x+c)^2/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} \log\left({\left| -\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} - \frac{1}{{\left(d x + c\right)} d} \right|}\right)}{3 \, a} - \frac{\sqrt{3} \left(a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} - \frac{2}{{\left(d x + c\right)} d}\right)}}{3 \, \left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}}}\right)}{3 \, a^{2} d} - \frac{\left(a^{2} b\right)^{\frac{1}{3}} \log\left(\left(\frac{b}{a d^{3}}\right)^{\frac{2}{3}} - \frac{\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}}}{{\left(d x + c\right)} d} + \frac{1}{{\left(d x + c\right)}^{2} d^{2}}\right)}{6 \, a^{2} d} - \frac{1}{{\left(d x + c\right)} a d}"," ",0,"1/3*(b/(a*d^3))^(1/3)*log(abs(-(b/(a*d^3))^(1/3) - 1/((d*x + c)*d)))/a - 1/3*sqrt(3)*(a^2*b)^(1/3)*arctan(1/3*sqrt(3)*((b/(a*d^3))^(1/3) - 2/((d*x + c)*d))/(b/(a*d^3))^(1/3))/(a^2*d) - 1/6*(a^2*b)^(1/3)*log((b/(a*d^3))^(2/3) - (b/(a*d^3))^(1/3)/((d*x + c)*d) + 1/((d*x + c)^2*d^2))/(a^2*d) - 1/((d*x + c)*a*d)","A",0
2866,1,193,0,0.212341," ","integrate(1/(d*x+c)^3/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}}\right) - \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| -b d x - b c + \left(-a b^{2}\right)^{\frac{1}{3}} \right|}\right)}{6 \, a} - \frac{1}{2 \, {\left(d x + c\right)}^{2} a d}"," ",0,"1/6*(2*sqrt(3)*(-b^2/(a^2*d^3))^(1/3)*arctan(-(b*d*x + b*c - (-a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))) - (-b^2/(a^2*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))^2 + 4*(b*d*x + b*c - (-a*b^2)^(1/3))^2) + 2*(-b^2/(a^2*d^3))^(1/3)*log(abs(-b*d*x - b*c + (-a*b^2)^(1/3))))/a - 1/2/((d*x + c)^2*a*d)","A",0
2867,1,41,0,0.209444," ","integrate(1/(d*x+c)^4/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{b \log\left({\left| -b - \frac{a}{{\left(d x + c\right)}^{3}} \right|}\right)}{3 \, a^{2} d} - \frac{1}{3 \, {\left(d x + c\right)}^{3} a d}"," ",0,"1/3*b*log(abs(-b - a/(d*x + c)^3))/(a^2*d) - 1/3/((d*x + c)^3*a*d)","A",0
2868,1,205,0,0.222950," ","integrate((d*x+c)^4/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(-a^{2} b\right)^{\frac{2}{3}}}\right) + \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(-a^{2} b\right)^{\frac{4}{3}}\right) - 2 \, \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| a b d x + a b c + \left(-a^{2} b\right)^{\frac{2}{3}} \right|}\right)}{9 \, b} - \frac{d^{2} x^{2} + 2 \, c d x + c^{2}}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} b d}"," ",0,"-1/9*(2*sqrt(3)*(-1/(a*b^2*d^3))^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))/(-a^2*b)^(2/3)) + (-1/(a*b^2*d^3))^(1/3)*log((2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))^2 + 3*(-a^2*b)^(4/3)) - 2*(-1/(a*b^2*d^3))^(1/3)*log(abs(a*b*d*x + a*b*c + (-a^2*b)^(2/3))))/b - 1/3*(d^2*x^2 + 2*c*d*x + c^2)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*b*d)","A",0
2869,1,214,0,0.249401," ","integrate((d*x+c)^3/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}}\right) - \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left({\left| b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}} \right|}\right)}{18 \, b} - \frac{d x + c}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} b d}"," ",0,"1/18*(2*sqrt(3)*(1/(a^2*b*d^3))^(1/3)*arctan(-(b*d*x + b*c + (a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))) - (1/(a^2*b*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))^2 + 4*(b*d*x + b*c + (a*b^2)^(1/3))^2) + 2*(1/(a^2*b*d^3))^(1/3)*log(abs(b*d*x + b*c + (a*b^2)^(1/3))))/b - 1/3*(d*x + c)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*b*d)","A",0
2870,1,21,0,0.191816," ","integrate((d*x+c)^2/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{1}{3 \, {\left({\left(d x + c\right)}^{3} b + a\right)} b d}"," ",0,"-1/3/(((d*x + c)^3*b + a)*b*d)","A",0
2871,1,205,0,0.285937," ","integrate((d*x+c)/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(-a^{2} b\right)^{\frac{2}{3}}}\right) + \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(-a^{2} b\right)^{\frac{4}{3}}\right) - 2 \, \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| a b d x + a b c + \left(-a^{2} b\right)^{\frac{2}{3}} \right|}\right)}{18 \, a} + \frac{d^{2} x^{2} + 2 \, c d x + c^{2}}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} a d}"," ",0,"-1/18*(2*sqrt(3)*(-1/(a*b^2*d^3))^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))/(-a^2*b)^(2/3)) + (-1/(a*b^2*d^3))^(1/3)*log((2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))^2 + 3*(-a^2*b)^(4/3)) - 2*(-1/(a*b^2*d^3))^(1/3)*log(abs(a*b*d*x + a*b*c + (-a^2*b)^(2/3))))/a + 1/3*(d^2*x^2 + 2*c*d*x + c^2)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*a*d)","A",0
2872,1,214,0,0.234174," ","integrate(1/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}}\right) - \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left({\left| b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a} + \frac{d x + c}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} a d}"," ",0,"1/9*(2*sqrt(3)*(1/(a^2*b*d^3))^(1/3)*arctan(-(b*d*x + b*c + (a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))) - (1/(a^2*b*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))^2 + 4*(b*d*x + b*c + (a*b^2)^(1/3))^2) + 2*(1/(a^2*b*d^3))^(1/3)*log(abs(b*d*x + b*c + (a*b^2)^(1/3))))/a + 1/3*(d*x + c)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*a*d)","A",0
2873,1,101,0,0.191782," ","integrate(1/(d*x+c)/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a \right|}\right)}{3 \, a^{2} d} + \frac{\log\left({\left| d x + c \right|}\right)}{a^{2} d} + \frac{1}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} a d}"," ",0,"-1/3*log(abs(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a))/(a^2*d) + log(abs(d*x + c))/(a^2*d) + 1/3/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*a*d)","A",0
2874,1,204,0,0.235806," ","integrate(1/(d*x+c)^2/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{4 \, \left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} \log\left({\left| -\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} - \frac{1}{{\left(d x + c\right)} d} \right|}\right)}{9 \, a^{2}} - \frac{4 \, \sqrt{3} \left(a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} - \frac{2}{{\left(d x + c\right)} d}\right)}}{3 \, \left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}}}\right)}{9 \, a^{3} d} - \frac{2 \, \left(a^{2} b\right)^{\frac{1}{3}} \log\left(\left(\frac{b}{a d^{3}}\right)^{\frac{2}{3}} - \frac{\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}}}{{\left(d x + c\right)} d} + \frac{1}{{\left(d x + c\right)}^{2} d^{2}}\right)}{9 \, a^{3} d} - \frac{1}{{\left(d x + c\right)} a^{2} d} - \frac{b}{3 \, {\left(d x + c\right)} a^{2} {\left(b + \frac{a}{{\left(d x + c\right)}^{3}}\right)} d}"," ",0,"4/9*(b/(a*d^3))^(1/3)*log(abs(-(b/(a*d^3))^(1/3) - 1/((d*x + c)*d)))/a^2 - 4/9*sqrt(3)*(a^2*b)^(1/3)*arctan(1/3*sqrt(3)*((b/(a*d^3))^(1/3) - 2/((d*x + c)*d))/(b/(a*d^3))^(1/3))/(a^3*d) - 2/9*(a^2*b)^(1/3)*log((b/(a*d^3))^(2/3) - (b/(a*d^3))^(1/3)/((d*x + c)*d) + 1/((d*x + c)^2*d^2))/(a^3*d) - 1/((d*x + c)*a^2*d) - 1/3*b/((d*x + c)*a^2*(b + a/(d*x + c)^3)*d)","A",0
2875,1,244,0,0.224845," ","integrate(1/(d*x+c)^3/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{5 \, {\left(2 \, \sqrt{3} \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}}\right) - \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| -b d x - b c + \left(-a b^{2}\right)^{\frac{1}{3}} \right|}\right)\right)}}{18 \, a^{2}} - \frac{b d x + b c}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} a^{2} d} - \frac{1}{2 \, {\left(d x + c\right)}^{2} a^{2} d}"," ",0,"5/18*(2*sqrt(3)*(-b^2/(a^2*d^3))^(1/3)*arctan(-(b*d*x + b*c - (-a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))) - (-b^2/(a^2*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))^2 + 4*(b*d*x + b*c - (-a*b^2)^(1/3))^2) + 2*(-b^2/(a^2*d^3))^(1/3)*log(abs(-b*d*x - b*c + (-a*b^2)^(1/3))))/a^2 - 1/3*(b*d*x + b*c)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*a^2*d) - 1/2/((d*x + c)^2*a^2*d)","A",0
2876,1,65,0,0.216966," ","integrate(1/(d*x+c)^4/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{2 \, b \log\left({\left| -b - \frac{a}{{\left(d x + c\right)}^{3}} \right|}\right)}{3 \, a^{3} d} + \frac{b^{2}}{3 \, a^{3} {\left(b + \frac{a}{{\left(d x + c\right)}^{3}}\right)} d} - \frac{1}{3 \, {\left(d x + c\right)}^{3} a^{2} d}"," ",0,"2/3*b*log(abs(-b - a/(d*x + c)^3))/(a^3*d) + 1/3*b^2/(a^3*(b + a/(d*x + c)^3)*d) - 1/3/((d*x + c)^3*a^2*d)","A",0
2877,1,274,0,0.262580," ","integrate((d*x+c)^4/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(-a^{2} b\right)^{\frac{2}{3}}}\right) + \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(-a^{2} b\right)^{\frac{4}{3}}\right) - 2 \, \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| a b d x + a b c + \left(-a^{2} b\right)^{\frac{2}{3}} \right|}\right)}{54 \, a b} + \frac{2 \, b d^{5} x^{5} + 10 \, b c d^{4} x^{4} + 20 \, b c^{2} d^{3} x^{3} + 20 \, b c^{3} d^{2} x^{2} + 10 \, b c^{4} d x + 2 \, b c^{5} - a d^{2} x^{2} - 2 \, a c d x - a c^{2}}{18 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}^{2} a b d}"," ",0,"-1/54*(2*sqrt(3)*(-1/(a*b^2*d^3))^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))/(-a^2*b)^(2/3)) + (-1/(a*b^2*d^3))^(1/3)*log((2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))^2 + 3*(-a^2*b)^(4/3)) - 2*(-1/(a*b^2*d^3))^(1/3)*log(abs(a*b*d*x + a*b*c + (-a^2*b)^(2/3))))/(a*b) + 1/18*(2*b*d^5*x^5 + 10*b*c*d^4*x^4 + 20*b*c^2*d^3*x^3 + 20*b*c^3*d^2*x^2 + 10*b*c^4*d*x + 2*b*c^5 - a*d^2*x^2 - 2*a*c*d*x - a*c^2)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)^2*a*b*d)","A",0
2878,1,268,0,0.265810," ","integrate((d*x+c)^3/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}}\right) - \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left({\left| b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}} \right|}\right)}{54 \, a b} + \frac{b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} - 2 \, a d x - 2 \, a c}{18 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}^{2} a b d}"," ",0,"1/54*(2*sqrt(3)*(1/(a^2*b*d^3))^(1/3)*arctan(-(b*d*x + b*c + (a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))) - (1/(a^2*b*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))^2 + 4*(b*d*x + b*c + (a*b^2)^(1/3))^2) + 2*(1/(a^2*b*d^3))^(1/3)*log(abs(b*d*x + b*c + (a*b^2)^(1/3))))/(a*b) + 1/18*(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 - 2*a*d*x - 2*a*c)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)^2*a*b*d)","A",0
2879,1,21,0,0.230339," ","integrate((d*x+c)^2/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{1}{6 \, {\left({\left(d x + c\right)}^{3} b + a\right)}^{2} b d}"," ",0,"-1/6/(((d*x + c)^3*b + a)^2*b*d)","A",0
2880,1,268,0,0.251789," ","integrate((d*x+c)/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(-a^{2} b\right)^{\frac{2}{3}}}\right) + \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(-a^{2} b\right)^{\frac{4}{3}}\right) - 2 \, \left(-\frac{1}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| a b d x + a b c + \left(-a^{2} b\right)^{\frac{2}{3}} \right|}\right)}{27 \, a^{2}} + \frac{4 \, b d^{5} x^{5} + 20 \, b c d^{4} x^{4} + 40 \, b c^{2} d^{3} x^{3} + 40 \, b c^{3} d^{2} x^{2} + 20 \, b c^{4} d x + 4 \, b c^{5} + 7 \, a d^{2} x^{2} + 14 \, a c d x + 7 \, a c^{2}}{18 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}^{2} a^{2} d}"," ",0,"-1/27*(2*sqrt(3)*(-1/(a*b^2*d^3))^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))/(-a^2*b)^(2/3)) + (-1/(a*b^2*d^3))^(1/3)*log((2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))^2 + 3*(-a^2*b)^(4/3)) - 2*(-1/(a*b^2*d^3))^(1/3)*log(abs(a*b*d*x + a*b*c + (-a^2*b)^(2/3))))/a^2 + 1/18*(4*b*d^5*x^5 + 20*b*c*d^4*x^4 + 40*b*c^2*d^3*x^3 + 40*b*c^3*d^2*x^2 + 20*b*c^4*d*x + 4*b*c^5 + 7*a*d^2*x^2 + 14*a*c*d*x + 7*a*c^2)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)^2*a^2*d)","A",0
2881,1,264,0,0.185861," ","integrate(1/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{5 \, {\left(2 \, \sqrt{3} \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}}\right) - \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \log\left({\left| b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}} \right|}\right)\right)}}{54 \, a^{2}} + \frac{5 \, b d^{4} x^{4} + 20 \, b c d^{3} x^{3} + 30 \, b c^{2} d^{2} x^{2} + 20 \, b c^{3} d x + 5 \, b c^{4} + 8 \, a d x + 8 \, a c}{18 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}^{2} a^{2} d}"," ",0,"5/54*(2*sqrt(3)*(1/(a^2*b*d^3))^(1/3)*arctan(-(b*d*x + b*c + (a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))) - (1/(a^2*b*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))^2 + 4*(b*d*x + b*c + (a*b^2)^(1/3))^2) + 2*(1/(a^2*b*d^3))^(1/3)*log(abs(b*d*x + b*c + (a*b^2)^(1/3))))/a^2 + 1/18*(5*b*d^4*x^4 + 20*b*c*d^3*x^3 + 30*b*c^2*d^2*x^2 + 20*b*c^3*d*x + 5*b*c^4 + 8*a*d*x + 8*a*c)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)^2*a^2*d)","A",0
2882,1,144,0,0.239419," ","integrate(1/(d*x+c)/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{\log\left({\left| b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a \right|}\right)}{3 \, a^{3} d} + \frac{\log\left({\left| d x + c \right|}\right)}{a^{3} d} + \frac{2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} + 3 \, a^{2}}{6 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}^{2} a^{3} d}"," ",0,"-1/3*log(abs(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a))/(a^3*d) + log(abs(d*x + c))/(a^3*d) + 1/6*(2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 + 3*a^2)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)^2*a^3*d)","A",0
2883,1,223,0,0.248545," ","integrate(1/(d*x+c)^2/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{14 \, \left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} \log\left({\left| -\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} - \frac{1}{{\left(d x + c\right)} d} \right|}\right)}{27 \, a^{3}} - \frac{14 \, \sqrt{3} \left(a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} - \frac{2}{{\left(d x + c\right)} d}\right)}}{3 \, \left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}}}\right)}{27 \, a^{4} d} - \frac{7 \, \left(a^{2} b\right)^{\frac{1}{3}} \log\left(\left(\frac{b}{a d^{3}}\right)^{\frac{2}{3}} - \frac{\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}}}{{\left(d x + c\right)} d} + \frac{1}{{\left(d x + c\right)}^{2} d^{2}}\right)}{27 \, a^{4} d} - \frac{\frac{10 \, b^{2}}{{\left(d x + c\right)} d} + \frac{13 \, a b}{{\left(d x + c\right)}^{4} d}}{18 \, a^{3} {\left(b + \frac{a}{{\left(d x + c\right)}^{3}}\right)}^{2}} - \frac{1}{{\left(d x + c\right)} a^{3} d}"," ",0,"14/27*(b/(a*d^3))^(1/3)*log(abs(-(b/(a*d^3))^(1/3) - 1/((d*x + c)*d)))/a^3 - 14/27*sqrt(3)*(a^2*b)^(1/3)*arctan(1/3*sqrt(3)*((b/(a*d^3))^(1/3) - 2/((d*x + c)*d))/(b/(a*d^3))^(1/3))/(a^4*d) - 7/27*(a^2*b)^(1/3)*log((b/(a*d^3))^(2/3) - (b/(a*d^3))^(1/3)/((d*x + c)*d) + 1/((d*x + c)^2*d^2))/(a^4*d) - 1/18*(10*b^2/((d*x + c)*d) + 13*a*b/((d*x + c)^4*d))/(a^3*(b + a/(d*x + c)^3)^2) - 1/((d*x + c)*a^3*d)","A",0
2884,1,365,0,0.272515," ","integrate(1/(d*x+c)^3/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{10 \, {\left(2 \, \sqrt{3} \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}}\right) - \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| -b d x - b c + \left(-a b^{2}\right)^{\frac{1}{3}} \right|}\right)\right)}}{27 \, a^{3}} - \frac{20 \, b^{2} d^{6} x^{6} + 120 \, b^{2} c d^{5} x^{5} + 300 \, b^{2} c^{2} d^{4} x^{4} + 400 \, b^{2} c^{3} d^{3} x^{3} + 300 \, b^{2} c^{4} d^{2} x^{2} + 120 \, b^{2} c^{5} d x + 20 \, b^{2} c^{6} + 32 \, a b d^{3} x^{3} + 96 \, a b c d^{2} x^{2} + 96 \, a b c^{2} d x + 32 \, a b c^{3} + 9 \, a^{2}}{18 \, {\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a d x + a c\right)}^{2} a^{3} d}"," ",0,"10/27*(2*sqrt(3)*(-b^2/(a^2*d^3))^(1/3)*arctan(-(b*d*x + b*c - (-a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))) - (-b^2/(a^2*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))^2 + 4*(b*d*x + b*c - (-a*b^2)^(1/3))^2) + 2*(-b^2/(a^2*d^3))^(1/3)*log(abs(-b*d*x - b*c + (-a*b^2)^(1/3))))/a^3 - 1/18*(20*b^2*d^6*x^6 + 120*b^2*c*d^5*x^5 + 300*b^2*c^2*d^4*x^4 + 400*b^2*c^3*d^3*x^3 + 300*b^2*c^4*d^2*x^2 + 120*b^2*c^5*d*x + 20*b^2*c^6 + 32*a*b*d^3*x^3 + 96*a*b*c*d^2*x^2 + 96*a*b*c^2*d*x + 32*a*b*c^3 + 9*a^2)/((b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a*d*x + a*c)^2*a^3*d)","B",0
2885,1,80,0,0.252613," ","integrate(1/(d*x+c)^4/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{b \log\left({\left| -b - \frac{a}{{\left(d x + c\right)}^{3}} \right|}\right)}{a^{4} d} + \frac{5 \, b^{3} + \frac{6 \, a b^{2}}{{\left(d x + c\right)}^{3}}}{6 \, a^{4} {\left(b + \frac{a}{{\left(d x + c\right)}^{3}}\right)}^{2} d} - \frac{1}{3 \, {\left(d x + c\right)}^{3} a^{3} d}"," ",0,"b*log(abs(-b - a/(d*x + c)^3))/(a^4*d) + 1/6*(5*b^3 + 6*a*b^2/(d*x + c)^3)/(a^4*(b + a/(d*x + c)^3)^2*d) - 1/3/((d*x + c)^3*a^3*d)","A",0
2886,1,170,0,0.235547," ","integrate((d*e*x+c*e)^4/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{b d^{7} x^{2} e^{4} + 2 \, b c d^{6} x e^{4}}{2 \, b^{2} d^{6}} - \frac{2 \, \sqrt{3} \left(a^{2} b d^{15}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(a^{2} b\right)^{\frac{2}{3}}}\right) e^{4} + \left(a^{2} b d^{15}\right)^{\frac{1}{3}} e^{4} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(a^{2} b\right)^{\frac{4}{3}}\right) - 2 \, \left(a^{2} b d^{15}\right)^{\frac{1}{3}} e^{4} \log\left({\left| a b d x + a b c + \left(a^{2} b\right)^{\frac{2}{3}} \right|}\right)}{6 \, b^{2} d^{6}}"," ",0,"1/2*(b*d^7*x^2*e^4 + 2*b*c*d^6*x*e^4)/(b^2*d^6) - 1/6*(2*sqrt(3)*(a^2*b*d^15)^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (a^2*b)^(2/3))/(a^2*b)^(2/3))*e^4 + (a^2*b*d^15)^(1/3)*e^4*log((2*a*b*d*x + 2*a*b*c - (a^2*b)^(2/3))^2 + 3*(a^2*b)^(4/3)) - 2*(a^2*b*d^15)^(1/3)*e^4*log(abs(a*b*d*x + a*b*c + (a^2*b)^(2/3))))/(b^2*d^6)","A",0
2887,1,188,0,0.219436," ","integrate((d*e*x+c*e)^3/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{x e^{3}}{b} + \frac{2 \, \sqrt{3} \left(-\frac{a d^{6} e^{9}}{b}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}}\right) - \left(-\frac{a d^{6} e^{9}}{b}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(-\frac{a d^{6} e^{9}}{b}\right)^{\frac{1}{3}} \log\left({\left| -b d x - b c + \left(-a b^{2}\right)^{\frac{1}{3}} \right|}\right)}{6 \, b d^{3}}"," ",0,"x*e^3/b + 1/6*(2*sqrt(3)*(-a*d^6*e^9/b)^(1/3)*arctan(-(b*d*x + b*c - (-a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))) - (-a*d^6*e^9/b)^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))^2 + 4*(b*d*x + b*c - (-a*b^2)^(1/3))^2) + 2*(-a*d^6*e^9/b)^(1/3)*log(abs(-b*d*x - b*c + (-a*b^2)^(1/3))))/(b*d^3)","A",0
2888,1,45,0,0.187230," ","integrate((d*e*x+c*e)^2/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{e^{2} \log\left({\left| b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a \right|}\right)}{3 \, b d}"," ",0,"1/3*e^2*log(abs(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a))/(b*d)","A",0
2889,1,147,0,0.223571," ","integrate((d*e*x+c*e)/(a+b*(d*x+c)^3),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \left(-\frac{e^{3}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(-a^{2} b\right)^{\frac{2}{3}}}\right) - \frac{1}{6} \, \left(-\frac{e^{3}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(-a^{2} b\right)^{\frac{4}{3}}\right) + \frac{1}{3} \, \left(-\frac{e^{3}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| a b d x + a b c + \left(-a^{2} b\right)^{\frac{2}{3}} \right|}\right)"," ",0,"-1/3*sqrt(3)*(-e^3/(a*b^2*d^3))^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))/(-a^2*b)^(2/3)) - 1/6*(-e^3/(a*b^2*d^3))^(1/3)*log((2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))^2 + 3*(-a^2*b)^(4/3)) + 1/3*(-e^3/(a*b^2*d^3))^(1/3)*log(abs(a*b*d*x + a*b*c + (-a^2*b)^(2/3)))","A",0
2890,1,62,0,0.197490," ","integrate(1/(d*e*x+c*e)/(a+b*(d*x+c)^3),x, algorithm=""giac"")","-\frac{e^{\left(-1\right)} \log\left({\left| b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a \right|}\right)}{3 \, a d} + \frac{e^{\left(-1\right)} \log\left({\left| d x + c \right|}\right)}{a d}"," ",0,"-1/3*e^(-1)*log(abs(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a))/(a*d) + e^(-1)*log(abs(d*x + c))/(a*d)","A",0
2891,1,226,0,0.213965," ","integrate(1/(d*e*x+c*e)^2/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-2\right)} \log\left({\left| -\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-2\right)} - \frac{e^{\left(-1\right)}}{{\left(d x e + c e\right)} d} \right|}\right)}{3 \, a} - \frac{\sqrt{3} \left(a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-2\right)} - \frac{2 \, e^{\left(-1\right)}}{{\left(d x e + c e\right)} d}\right)} e^{2}}{3 \, \left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}}}\right) e^{\left(-2\right)}}{3 \, a^{2} d} - \frac{\left(a^{2} b\right)^{\frac{1}{3}} e^{\left(-2\right)} \log\left(\left(\frac{b}{a d^{3}}\right)^{\frac{2}{3}} e^{\left(-4\right)} - \frac{\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-3\right)}}{{\left(d x e + c e\right)} d} + \frac{e^{\left(-2\right)}}{{\left(d x e + c e\right)}^{2} d^{2}}\right)}{6 \, a^{2} d} - \frac{e^{\left(-1\right)}}{{\left(d x e + c e\right)} a d}"," ",0,"1/3*(b/(a*d^3))^(1/3)*e^(-2)*log(abs(-(b/(a*d^3))^(1/3)*e^(-2) - e^(-1)/((d*x*e + c*e)*d)))/a - 1/3*sqrt(3)*(a^2*b)^(1/3)*arctan(1/3*sqrt(3)*((b/(a*d^3))^(1/3)*e^(-2) - 2*e^(-1)/((d*x*e + c*e)*d))*e^2/(b/(a*d^3))^(1/3))*e^(-2)/(a^2*d) - 1/6*(a^2*b)^(1/3)*e^(-2)*log((b/(a*d^3))^(2/3)*e^(-4) - (b/(a*d^3))^(1/3)*e^(-3)/((d*x*e + c*e)*d) + e^(-2)/((d*x*e + c*e)^2*d^2))/(a^2*d) - e^(-1)/((d*x*e + c*e)*a*d)","A",0
2892,1,197,0,0.222461," ","integrate(1/(d*e*x+c*e)^3/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{{\left(2 \, \sqrt{3} \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}}\right) - \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| -b d x - b c + \left(-a b^{2}\right)^{\frac{1}{3}} \right|}\right)\right)} e^{\left(-3\right)}}{6 \, a} - \frac{e^{\left(-3\right)}}{2 \, {\left(d x + c\right)}^{2} a d}"," ",0,"1/6*(2*sqrt(3)*(-b^2/(a^2*d^3))^(1/3)*arctan(-(b*d*x + b*c - (-a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))) - (-b^2/(a^2*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))^2 + 4*(b*d*x + b*c - (-a*b^2)^(1/3))^2) + 2*(-b^2/(a^2*d^3))^(1/3)*log(abs(-b*d*x - b*c + (-a*b^2)^(1/3))))*e^(-3)/a - 1/2*e^(-3)/((d*x + c)^2*a*d)","A",0
2893,1,82,0,0.194382," ","integrate(1/(d*e*x+c*e)^4/(a+b*(d*x+c)^3),x, algorithm=""giac"")","\frac{b e^{\left(-4\right)} \log\left({\left| b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a \right|}\right)}{3 \, a^{2} d} - \frac{b e^{\left(-4\right)} \log\left({\left| d x + c \right|}\right)}{a^{2} d} - \frac{e^{\left(-4\right)}}{3 \, {\left(d x + c\right)}^{3} a d}"," ",0,"1/3*b*e^(-4)*log(abs(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a))/(a^2*d) - b*e^(-4)*log(abs(d*x + c))/(a^2*d) - 1/3*e^(-4)/((d*x + c)^3*a*d)","A",0
2894,1,218,0,0.251606," ","integrate((d*e*x+c*e)^4/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} \left(-\frac{e^{12}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(-a^{2} b\right)^{\frac{2}{3}}}\right) + \left(-\frac{e^{12}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(-a^{2} b\right)^{\frac{4}{3}}\right) - 2 \, \left(-\frac{e^{12}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| a b d x + a b c + \left(-a^{2} b\right)^{\frac{2}{3}} \right|}\right)}{9 \, b} - \frac{d^{2} x^{2} e^{4} + 2 \, c d x e^{4} + c^{2} e^{4}}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} b d}"," ",0,"-1/9*(2*sqrt(3)*(-e^12/(a*b^2*d^3))^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))/(-a^2*b)^(2/3)) + (-e^12/(a*b^2*d^3))^(1/3)*log((2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))^2 + 3*(-a^2*b)^(4/3)) - 2*(-e^12/(a*b^2*d^3))^(1/3)*log(abs(a*b*d*x + a*b*c + (-a^2*b)^(2/3))))/b - 1/3*(d^2*x^2*e^4 + 2*c*d*x*e^4 + c^2*e^4)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*b*d)","A",0
2895,1,225,0,0.248220," ","integrate((d*e*x+c*e)^3/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}}\right) e^{3} - \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} e^{3} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} e^{3} \log\left({\left| b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}} \right|}\right)}{18 \, b} - \frac{d x e^{3} + c e^{3}}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} b d}"," ",0,"1/18*(2*sqrt(3)*(1/(a^2*b*d^3))^(1/3)*arctan(-(b*d*x + b*c + (a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3)))*e^3 - (1/(a^2*b*d^3))^(1/3)*e^3*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))^2 + 4*(b*d*x + b*c + (a*b^2)^(1/3))^2) + 2*(1/(a^2*b*d^3))^(1/3)*e^3*log(abs(b*d*x + b*c + (a*b^2)^(1/3))))/b - 1/3*(d*x*e^3 + c*e^3)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*b*d)","A",0
2896,1,45,0,0.194120," ","integrate((d*e*x+c*e)^2/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{e^{2}}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} b d}"," ",0,"-1/3*e^2/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*b*d)","A",0
2897,1,218,0,0.227325," ","integrate((d*e*x+c*e)/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} \left(-\frac{e^{3}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(-a^{2} b\right)^{\frac{2}{3}}}\right) + \left(-\frac{e^{3}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(-a^{2} b\right)^{\frac{4}{3}}\right) - 2 \, \left(-\frac{e^{3}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| a b d x + a b c + \left(-a^{2} b\right)^{\frac{2}{3}} \right|}\right)}{18 \, a} + \frac{d^{2} x^{2} e + 2 \, c d x e + c^{2} e}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} a d}"," ",0,"-1/18*(2*sqrt(3)*(-e^3/(a*b^2*d^3))^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))/(-a^2*b)^(2/3)) + (-e^3/(a*b^2*d^3))^(1/3)*log((2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))^2 + 3*(-a^2*b)^(4/3)) - 2*(-e^3/(a*b^2*d^3))^(1/3)*log(abs(a*b*d*x + a*b*c + (-a^2*b)^(2/3))))/a + 1/3*(d^2*x^2*e + 2*c*d*x*e + c^2*e)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*a*d)","A",0
2898,1,107,0,0.235746," ","integrate(1/(d*e*x+c*e)/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","-\frac{e^{\left(-1\right)} \log\left({\left| b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a \right|}\right)}{3 \, a^{2} d} + \frac{e^{\left(-1\right)} \log\left({\left| d x + c \right|}\right)}{a^{2} d} + \frac{e^{\left(-1\right)}}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} a d}"," ",0,"-1/3*e^(-1)*log(abs(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a))/(a^2*d) + e^(-1)*log(abs(d*x + c))/(a^2*d) + 1/3*e^(-1)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*a*d)","A",0
2899,1,269,0,0.225693," ","integrate(1/(d*e*x+c*e)^2/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{4 \, \left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-2\right)} \log\left({\left| -\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-2\right)} - \frac{e^{\left(-1\right)}}{{\left(d x e + c e\right)} d} \right|}\right)}{9 \, a^{2}} - \frac{4 \, \sqrt{3} \left(a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-2\right)} - \frac{2 \, e^{\left(-1\right)}}{{\left(d x e + c e\right)} d}\right)} e^{2}}{3 \, \left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}}}\right) e^{\left(-2\right)}}{9 \, a^{3} d} - \frac{2 \, \left(a^{2} b\right)^{\frac{1}{3}} e^{\left(-2\right)} \log\left(\left(\frac{b}{a d^{3}}\right)^{\frac{2}{3}} e^{\left(-4\right)} - \frac{\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-3\right)}}{{\left(d x e + c e\right)} d} + \frac{e^{\left(-2\right)}}{{\left(d x e + c e\right)}^{2} d^{2}}\right)}{9 \, a^{3} d} - \frac{e^{\left(-1\right)}}{{\left(d x e + c e\right)} a^{2} d} - \frac{b e^{\left(-1\right)}}{3 \, {\left(d x e + c e\right)} a^{2} {\left(b + \frac{a e^{3}}{{\left(d x e + c e\right)}^{3}}\right)} d}"," ",0,"4/9*(b/(a*d^3))^(1/3)*e^(-2)*log(abs(-(b/(a*d^3))^(1/3)*e^(-2) - e^(-1)/((d*x*e + c*e)*d)))/a^2 - 4/9*sqrt(3)*(a^2*b)^(1/3)*arctan(1/3*sqrt(3)*((b/(a*d^3))^(1/3)*e^(-2) - 2*e^(-1)/((d*x*e + c*e)*d))*e^2/(b/(a*d^3))^(1/3))*e^(-2)/(a^3*d) - 2/9*(a^2*b)^(1/3)*e^(-2)*log((b/(a*d^3))^(2/3)*e^(-4) - (b/(a*d^3))^(1/3)*e^(-3)/((d*x*e + c*e)*d) + e^(-2)/((d*x*e + c*e)^2*d^2))/(a^3*d) - e^(-1)/((d*x*e + c*e)*a^2*d) - 1/3*b*e^(-1)/((d*x*e + c*e)*a^2*(b + a*e^3/(d*x*e + c*e)^3)*d)","A",0
2900,1,250,0,0.231916," ","integrate(1/(d*e*x+c*e)^3/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{5 \, {\left(2 \, \sqrt{3} \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}}\right) - \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}} \right|}\right)\right)} e^{\left(-3\right)}}{18 \, a^{2}} - \frac{{\left(b d x + b c\right)} e^{\left(-3\right)}}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} a^{2} d} - \frac{e^{\left(-3\right)}}{2 \, {\left(d x + c\right)}^{2} a^{2} d}"," ",0,"5/18*(2*sqrt(3)*(-b^2/(a^2*d^3))^(1/3)*arctan(-(b*d*x + b*c - (-a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))) - (-b^2/(a^2*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))^2 + 4*(b*d*x + b*c - (-a*b^2)^(1/3))^2) + 2*(-b^2/(a^2*d^3))^(1/3)*log(abs(b*d*x + b*c - (-a*b^2)^(1/3))))*e^(-3)/a^2 - 1/3*(b*d*x + b*c)*e^(-3)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*a^2*d) - 1/2*e^(-3)/((d*x + c)^2*a^2*d)","A",0
2901,1,158,0,0.204839," ","integrate(1/(d*e*x+c*e)^4/(a+b*(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{2 \, b e^{\left(-4\right)} \log\left({\left| b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a \right|}\right)}{3 \, a^{3} d} - \frac{2 \, b e^{\left(-4\right)} \log\left({\left| d x + c \right|}\right)}{a^{3} d} - \frac{{\left(2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} + a^{2}\right)} e^{\left(-4\right)}}{3 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)} {\left(d x + c\right)}^{3} a^{3} d}"," ",0,"2/3*b*e^(-4)*log(abs(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a))/(a^3*d) - 2*b*e^(-4)*log(abs(d*x + c))/(a^3*d) - 1/3*(2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 + a^2)*e^(-4)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)*(d*x + c)^3*a^3*d)","A",0
2902,1,298,0,0.287009," ","integrate((d*e*x+c*e)^4/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} \left(-\frac{e^{12}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(-a^{2} b\right)^{\frac{2}{3}}}\right) + \left(-\frac{e^{12}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(-a^{2} b\right)^{\frac{4}{3}}\right) - 2 \, \left(-\frac{e^{12}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| a b d x + a b c + \left(-a^{2} b\right)^{\frac{2}{3}} \right|}\right)}{54 \, a b} + \frac{2 \, b d^{5} x^{5} e^{4} + 10 \, b c d^{4} x^{4} e^{4} + 20 \, b c^{2} d^{3} x^{3} e^{4} + 20 \, b c^{3} d^{2} x^{2} e^{4} + 10 \, b c^{4} d x e^{4} + 2 \, b c^{5} e^{4} - a d^{2} x^{2} e^{4} - 2 \, a c d x e^{4} - a c^{2} e^{4}}{18 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}^{2} a b d}"," ",0,"-1/54*(2*sqrt(3)*(-e^12/(a*b^2*d^3))^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))/(-a^2*b)^(2/3)) + (-e^12/(a*b^2*d^3))^(1/3)*log((2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))^2 + 3*(-a^2*b)^(4/3)) - 2*(-e^12/(a*b^2*d^3))^(1/3)*log(abs(a*b*d*x + a*b*c + (-a^2*b)^(2/3))))/(a*b) + 1/18*(2*b*d^5*x^5*e^4 + 10*b*c*d^4*x^4*e^4 + 20*b*c^2*d^3*x^3*e^4 + 20*b*c^3*d^2*x^2*e^4 + 10*b*c^4*d*x*e^4 + 2*b*c^5*e^4 - a*d^2*x^2*e^4 - 2*a*c*d*x*e^4 - a*c^2*e^4)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)^2*a*b*d)","A",0
2903,1,288,0,0.275191," ","integrate((d*e*x+c*e)^3/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{2 \, \sqrt{3} \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}}\right) e^{3} - \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} e^{3} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c - \sqrt{3} \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(\frac{1}{a^{2} b d^{3}}\right)^{\frac{1}{3}} e^{3} \log\left({\left| b d x + b c + \left(a b^{2}\right)^{\frac{1}{3}} \right|}\right)}{54 \, a b} + \frac{b d^{4} x^{4} e^{3} + 4 \, b c d^{3} x^{3} e^{3} + 6 \, b c^{2} d^{2} x^{2} e^{3} + 4 \, b c^{3} d x e^{3} + b c^{4} e^{3} - 2 \, a d x e^{3} - 2 \, a c e^{3}}{18 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}^{2} a b d}"," ",0,"1/54*(2*sqrt(3)*(1/(a^2*b*d^3))^(1/3)*arctan(-(b*d*x + b*c + (a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3)))*e^3 - (1/(a^2*b*d^3))^(1/3)*e^3*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c - sqrt(3)*(a*b^2)^(1/3))^2 + 4*(b*d*x + b*c + (a*b^2)^(1/3))^2) + 2*(1/(a^2*b*d^3))^(1/3)*e^3*log(abs(b*d*x + b*c + (a*b^2)^(1/3))))/(a*b) + 1/18*(b*d^4*x^4*e^3 + 4*b*c*d^3*x^3*e^3 + 6*b*c^2*d^2*x^2*e^3 + 4*b*c^3*d*x*e^3 + b*c^4*e^3 - 2*a*d*x*e^3 - 2*a*c*e^3)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)^2*a*b*d)","A",0
2904,1,45,0,0.240842," ","integrate((d*e*x+c*e)^2/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{e^{2}}{6 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}^{2} b d}"," ",0,"-1/6*e^2/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)^2*b*d)","A",0
2905,1,292,0,0.275108," ","integrate((d*e*x+c*e)/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} \left(-\frac{e^{3}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}}{3 \, \left(-a^{2} b\right)^{\frac{2}{3}}}\right) + \left(-\frac{e^{3}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \, a b d x + 2 \, a b c - \left(-a^{2} b\right)^{\frac{2}{3}}\right)}^{2} + 3 \, \left(-a^{2} b\right)^{\frac{4}{3}}\right) - 2 \, \left(-\frac{e^{3}}{a b^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| a b d x + a b c + \left(-a^{2} b\right)^{\frac{2}{3}} \right|}\right)}{27 \, a^{2}} + \frac{4 \, b d^{5} x^{5} e + 20 \, b c d^{4} x^{4} e + 40 \, b c^{2} d^{3} x^{3} e + 40 \, b c^{3} d^{2} x^{2} e + 20 \, b c^{4} d x e + 4 \, b c^{5} e + 7 \, a d^{2} x^{2} e + 14 \, a c d x e + 7 \, a c^{2} e}{18 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}^{2} a^{2} d}"," ",0,"-1/27*(2*sqrt(3)*(-e^3/(a*b^2*d^3))^(1/3)*arctan(1/3*sqrt(3)*(2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))/(-a^2*b)^(2/3)) + (-e^3/(a*b^2*d^3))^(1/3)*log((2*a*b*d*x + 2*a*b*c - (-a^2*b)^(2/3))^2 + 3*(-a^2*b)^(4/3)) - 2*(-e^3/(a*b^2*d^3))^(1/3)*log(abs(a*b*d*x + a*b*c + (-a^2*b)^(2/3))))/a^2 + 1/18*(4*b*d^5*x^5*e + 20*b*c*d^4*x^4*e + 40*b*c^2*d^3*x^3*e + 40*b*c^3*d^2*x^2*e + 20*b*c^4*d*x*e + 4*b*c^5*e + 7*a*d^2*x^2*e + 14*a*c*d*x*e + 7*a*c^2*e)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)^2*a^2*d)","A",0
2906,1,150,0,0.241822," ","integrate(1/(d*e*x+c*e)/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","-\frac{e^{\left(-1\right)} \log\left({\left| b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a \right|}\right)}{3 \, a^{3} d} + \frac{e^{\left(-1\right)} \log\left({\left| d x + c \right|}\right)}{a^{3} d} + \frac{{\left(2 \, a b d^{3} x^{3} + 6 \, a b c d^{2} x^{2} + 6 \, a b c^{2} d x + 2 \, a b c^{3} + 3 \, a^{2}\right)} e^{\left(-1\right)}}{6 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}^{2} a^{3} d}"," ",0,"-1/3*e^(-1)*log(abs(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a))/(a^3*d) + e^(-1)*log(abs(d*x + c))/(a^3*d) + 1/6*(2*a*b*d^3*x^3 + 6*a*b*c*d^2*x^2 + 6*a*b*c^2*d*x + 2*a*b*c^3 + 3*a^2)*e^(-1)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)^2*a^3*d)","A",0
2907,1,295,0,0.269157," ","integrate(1/(d*e*x+c*e)^2/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{14 \, \left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-2\right)} \log\left({\left| -\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-2\right)} - \frac{e^{\left(-1\right)}}{{\left(d x e + c e\right)} d} \right|}\right)}{27 \, a^{3}} - \frac{14 \, \sqrt{3} \left(a^{2} b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-2\right)} - \frac{2 \, e^{\left(-1\right)}}{{\left(d x e + c e\right)} d}\right)} e^{2}}{3 \, \left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}}}\right) e^{\left(-2\right)}}{27 \, a^{4} d} - \frac{7 \, \left(a^{2} b\right)^{\frac{1}{3}} e^{\left(-2\right)} \log\left(\left(\frac{b}{a d^{3}}\right)^{\frac{2}{3}} e^{\left(-4\right)} - \frac{\left(\frac{b}{a d^{3}}\right)^{\frac{1}{3}} e^{\left(-3\right)}}{{\left(d x e + c e\right)} d} + \frac{e^{\left(-2\right)}}{{\left(d x e + c e\right)}^{2} d^{2}}\right)}{27 \, a^{4} d} - \frac{\frac{10 \, b^{2} e^{\left(-1\right)}}{{\left(d x e + c e\right)} d} + \frac{13 \, a b e^{2}}{{\left(d x e + c e\right)}^{4} d}}{18 \, a^{3} {\left(b + \frac{a e^{3}}{{\left(d x e + c e\right)}^{3}}\right)}^{2}} - \frac{e^{\left(-1\right)}}{{\left(d x e + c e\right)} a^{3} d}"," ",0,"14/27*(b/(a*d^3))^(1/3)*e^(-2)*log(abs(-(b/(a*d^3))^(1/3)*e^(-2) - e^(-1)/((d*x*e + c*e)*d)))/a^3 - 14/27*sqrt(3)*(a^2*b)^(1/3)*arctan(1/3*sqrt(3)*((b/(a*d^3))^(1/3)*e^(-2) - 2*e^(-1)/((d*x*e + c*e)*d))*e^2/(b/(a*d^3))^(1/3))*e^(-2)/(a^4*d) - 7/27*(a^2*b)^(1/3)*e^(-2)*log((b/(a*d^3))^(2/3)*e^(-4) - (b/(a*d^3))^(1/3)*e^(-3)/((d*x*e + c*e)*d) + e^(-2)/((d*x*e + c*e)^2*d^2))/(a^4*d) - 1/18*(10*b^2*e^(-1)/((d*x*e + c*e)*d) + 13*a*b*e^2/((d*x*e + c*e)^4*d))/(a^3*(b + a*e^3/(d*x*e + c*e)^3)^2) - e^(-1)/((d*x*e + c*e)*a^3*d)","A",0
2908,1,369,0,0.319980," ","integrate(1/(d*e*x+c*e)^3/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{10 \, {\left(2 \, \sqrt{3} \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}}{\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}}\right) - \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, {\left(\sqrt{3} b d x + \sqrt{3} b c + \sqrt{3} \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2} + 4 \, {\left(b d x + b c - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}^{2}\right) + 2 \, \left(-\frac{b^{2}}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left({\left| -b d x - b c + \left(-a b^{2}\right)^{\frac{1}{3}} \right|}\right)\right)} e^{\left(-3\right)}}{27 \, a^{3}} - \frac{{\left(20 \, b^{2} d^{6} x^{6} + 120 \, b^{2} c d^{5} x^{5} + 300 \, b^{2} c^{2} d^{4} x^{4} + 400 \, b^{2} c^{3} d^{3} x^{3} + 300 \, b^{2} c^{4} d^{2} x^{2} + 120 \, b^{2} c^{5} d x + 20 \, b^{2} c^{6} + 32 \, a b d^{3} x^{3} + 96 \, a b c d^{2} x^{2} + 96 \, a b c^{2} d x + 32 \, a b c^{3} + 9 \, a^{2}\right)} e^{\left(-3\right)}}{18 \, {\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a d x + a c\right)}^{2} a^{3} d}"," ",0,"10/27*(2*sqrt(3)*(-b^2/(a^2*d^3))^(1/3)*arctan(-(b*d*x + b*c - (-a*b^2)^(1/3))/(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))) - (-b^2/(a^2*d^3))^(1/3)*log(4*(sqrt(3)*b*d*x + sqrt(3)*b*c + sqrt(3)*(-a*b^2)^(1/3))^2 + 4*(b*d*x + b*c - (-a*b^2)^(1/3))^2) + 2*(-b^2/(a^2*d^3))^(1/3)*log(abs(-b*d*x - b*c + (-a*b^2)^(1/3))))*e^(-3)/a^3 - 1/18*(20*b^2*d^6*x^6 + 120*b^2*c*d^5*x^5 + 300*b^2*c^2*d^4*x^4 + 400*b^2*c^3*d^3*x^3 + 300*b^2*c^4*d^2*x^2 + 120*b^2*c^5*d*x + 20*b^2*c^6 + 32*a*b*d^3*x^3 + 96*a*b*c*d^2*x^2 + 96*a*b*c^2*d*x + 32*a*b*c^3 + 9*a^2)*e^(-3)/((b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a*d*x + a*c)^2*a^3*d)","A",0
2909,1,259,0,0.247343," ","integrate(1/(d*e*x+c*e)^4/(a+b*(d*x+c)^3)^3,x, algorithm=""giac"")","\frac{b e^{\left(-4\right)} \log\left({\left| b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a \right|}\right)}{a^{4} d} - \frac{3 \, b e^{\left(-4\right)} \log\left({\left| d x + c \right|}\right)}{a^{4} d} - \frac{{\left(6 \, a b^{2} d^{6} x^{6} + 36 \, a b^{2} c d^{5} x^{5} + 90 \, a b^{2} c^{2} d^{4} x^{4} + 6 \, a b^{2} c^{6} + 9 \, a^{2} b c^{3} + 3 \, {\left(40 \, a b^{2} c^{3} d^{3} + 3 \, a^{2} b d^{3}\right)} x^{3} + 2 \, a^{3} + 9 \, {\left(10 \, a b^{2} c^{4} d^{2} + 3 \, a^{2} b c d^{2}\right)} x^{2} + 9 \, {\left(4 \, a b^{2} c^{5} d + 3 \, a^{2} b c^{2} d\right)} x\right)} e^{\left(-4\right)}}{6 \, {\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}^{2} {\left(d x + c\right)}^{3} a^{4} d}"," ",0,"b*e^(-4)*log(abs(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a))/(a^4*d) - 3*b*e^(-4)*log(abs(d*x + c))/(a^4*d) - 1/6*(6*a*b^2*d^6*x^6 + 36*a*b^2*c*d^5*x^5 + 90*a*b^2*c^2*d^4*x^4 + 6*a*b^2*c^6 + 9*a^2*b*c^3 + 3*(40*a*b^2*c^3*d^3 + 3*a^2*b*d^3)*x^3 + 2*a^3 + 9*(10*a*b^2*c^4*d^2 + 3*a^2*b*c*d^2)*x^2 + 9*(4*a*b^2*c^5*d + 3*a^2*b*c^2*d)*x)*e^(-4)/((b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)^2*(d*x + c)^3*a^4*d)","B",0
2910,1,62,0,0.175321," ","integrate((d*x+c)^3*(a+b*(d*x+c)^4)^p,x, algorithm=""giac"")","\frac{{\left(b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a\right)}^{p + 1}}{4 \, b d {\left(p + 1\right)}}"," ",0,"1/4*(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a)^(p + 1)/(b*d*(p + 1))","B",0
2911,1,25,0,0.162432," ","integrate((d*x+c)^3*(a+b*(d*x+c)^4),x, algorithm=""giac"")","\frac{{\left(d x + c\right)}^{8} b + 2 \, {\left(d x + c\right)}^{4} a}{8 \, d}"," ",0,"1/8*((d*x + c)^8*b + 2*(d*x + c)^4*a)/d","A",0
2912,1,21,0,0.183426," ","integrate((d*x+c)^3*(a+b*(d*x+c)^4)^2,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{4} b + a\right)}^{3}}{12 \, b d}"," ",0,"1/12*((d*x + c)^4*b + a)^3/(b*d)","A",0
2913,1,21,0,0.218803," ","integrate((d*x+c)^3*(a+b*(d*x+c)^4)^3,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)}^{4} b + a\right)}^{4}}{16 \, b d}"," ",0,"1/16*((d*x + c)^4*b + a)^4/(b*d)","A",0
2914,1,20,0,0.194205," ","integrate((d*x+c)^3/(a+b*(d*x+c)^4),x, algorithm=""giac"")","\frac{\log\left({\left(d x + c\right)}^{4} b + a\right)}{4 \, b d}"," ",0,"1/4*log((d*x + c)^4*b + a)/(b*d)","A",0
2915,1,21,0,0.200149," ","integrate((d*x+c)^3/(a+b*(d*x+c)^4)^2,x, algorithm=""giac"")","-\frac{1}{4 \, {\left({\left(d x + c\right)}^{4} b + a\right)} b d}"," ",0,"-1/4/(((d*x + c)^4*b + a)*b*d)","A",0
2916,1,21,0,0.251050," ","integrate((d*x+c)^3/(a+b*(d*x+c)^4)^3,x, algorithm=""giac"")","-\frac{1}{8 \, {\left({\left(d x + c\right)}^{4} b + a\right)}^{2} b d}"," ",0,"-1/8/(((d*x + c)^4*b + a)^2*b*d)","A",0
2917,0,0,0,0.000000," ","integrate(1/(a+b*(d*x+c)^4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{{\left(d x + c\right)}^{4} b + a}}\,{d x}"," ",0,"integrate(1/sqrt((d*x + c)^4*b + a), x)","F",0
2918,0,0,0,0.000000," ","integrate(x/(a+b*(d*x+c)^4)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{{\left(d x + c\right)}^{4} b + a}}\,{d x}"," ",0,"integrate(x/sqrt((d*x + c)^4*b + a), x)","F",0
2919,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x)^(3/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\left(c x\right)^{\frac{3}{2}} b + a} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(sqrt((c*x)^(3/2)*b + a)*(d*x)^m, x)","F",0
2920,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{c x} b + a} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(sqrt(c*x)*b + a)*(d*x)^m, x)","F",0
2921,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c*x)^(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:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Unable to divide, perhaps due to rounding error%%%{1,[0,1,1,0]%%%} / %%%{1,[0,0,0,1]%%%} Error: Bad Argument Value","F(-2)",0
2922,0,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c*x)^(3/2))^(1/2),x, algorithm=""giac"")","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\left(c x\right)^{\frac{3}{2}}}}\,{d x}"," ",0,"integrate((d*x)^m*sqrt(a + b/(c*x)^(3/2)), x)","F",0
2923,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x)^n)^p,x, algorithm=""giac"")","\int {\left(\left(c x\right)^{n} b + a\right)}^{p} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(((c*x)^n*b + a)^p*(d*x)^m, x)","F",0
2924,0,0,0,0.000000," ","integrate(x^2*(a+b*(c*x)^n)^p,x, algorithm=""giac"")","\int {\left(\left(c x\right)^{n} b + a\right)}^{p} x^{2}\,{d x}"," ",0,"integrate(((c*x)^n*b + a)^p*x^2, x)","F",0
2925,0,0,0,0.000000," ","integrate(x*(a+b*(c*x)^n)^p,x, algorithm=""giac"")","\int {\left(\left(c x\right)^{n} b + a\right)}^{p} x\,{d x}"," ",0,"integrate(((c*x)^n*b + a)^p*x, x)","F",0
2926,0,0,0,0.000000," ","integrate((a+b*(c*x)^n)^p,x, algorithm=""giac"")","\int {\left(\left(c x\right)^{n} b + a\right)}^{p}\,{d x}"," ",0,"integrate(((c*x)^n*b + a)^p, x)","F",0
2927,0,0,0,0.000000," ","integrate((a+b*(c*x)^n)^p/x,x, algorithm=""giac"")","\int \frac{{\left(\left(c x\right)^{n} b + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate(((c*x)^n*b + a)^p/x, x)","F",0
2928,0,0,0,0.000000," ","integrate((a+b*(c*x)^n)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(\left(c x\right)^{n} b + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate(((c*x)^n*b + a)^p/x^2, x)","F",0
2929,1,108,0,0.200538," ","integrate(1/(1+(x^2)^(3/2)),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(-i \, \sqrt{3} - 1\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{1}{\mathrm{sgn}\left(x\right)}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{1}{\mathrm{sgn}\left(x\right)}\right)^{\frac{1}{3}}}\right)}{6 \, \mathrm{sgn}\left(x\right)^{\frac{1}{3}}} - \frac{1}{9} i \, \pi \mathrm{sgn}\left(x\right) - \frac{{\left(-i \, \sqrt{3} - 1\right)} \log\left(x^{2} + x \left(-\frac{1}{\mathrm{sgn}\left(x\right)}\right)^{\frac{1}{3}} + \left(-\frac{1}{\mathrm{sgn}\left(x\right)}\right)^{\frac{2}{3}}\right)}{12 \, \mathrm{sgn}\left(x\right)^{\frac{1}{3}}} - \frac{1}{3} \, \left(-\frac{1}{\mathrm{sgn}\left(x\right)}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{1}{\mathrm{sgn}\left(x\right)}\right)^{\frac{1}{3}} \right|}\right)"," ",0,"-1/6*sqrt(3)*(-I*sqrt(3) - 1)*arctan(1/3*sqrt(3)*(2*x + (-1/sgn(x))^(1/3))/(-1/sgn(x))^(1/3))/sgn(x)^(1/3) - 1/9*I*pi*sgn(x) - 1/12*(-I*sqrt(3) - 1)*log(x^2 + x*(-1/sgn(x))^(1/3) + (-1/sgn(x))^(2/3))/sgn(x)^(1/3) - 1/3*(-1/sgn(x))^(1/3)*log(abs(x - (-1/sgn(x))^(1/3)))","C",0
2930,1,231,0,0.361223," ","integrate(x^5*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{13 \, {\left(63 \, {\left(b \sqrt{c} x + a\right)}^{\frac{11}{2}} \sqrt{c} - 385 \, {\left(b \sqrt{c} x + a\right)}^{\frac{9}{2}} a \sqrt{c} + 990 \, {\left(b \sqrt{c} x + a\right)}^{\frac{7}{2}} a^{2} \sqrt{c} - 1386 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} a^{3} \sqrt{c} + 1155 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a^{4} \sqrt{c} - 693 \, \sqrt{b \sqrt{c} x + a} a^{5} \sqrt{c}\right)} a}{b^{5} c^{3}} + \frac{3 \, {\left(231 \, {\left(b \sqrt{c} x + a\right)}^{\frac{13}{2}} - 1638 \, {\left(b \sqrt{c} x + a\right)}^{\frac{11}{2}} a + 5005 \, {\left(b \sqrt{c} x + a\right)}^{\frac{9}{2}} a^{2} - 8580 \, {\left(b \sqrt{c} x + a\right)}^{\frac{7}{2}} a^{3} + 9009 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} a^{4} - 6006 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a^{5} + 3003 \, \sqrt{b \sqrt{c} x + a} a^{6}\right)}}{b^{5} c^{\frac{5}{2}}}\right)}}{9009 \, b \sqrt{c}}"," ",0,"2/9009*(13*(63*(b*sqrt(c)*x + a)^(11/2)*sqrt(c) - 385*(b*sqrt(c)*x + a)^(9/2)*a*sqrt(c) + 990*(b*sqrt(c)*x + a)^(7/2)*a^2*sqrt(c) - 1386*(b*sqrt(c)*x + a)^(5/2)*a^3*sqrt(c) + 1155*(b*sqrt(c)*x + a)^(3/2)*a^4*sqrt(c) - 693*sqrt(b*sqrt(c)*x + a)*a^5*sqrt(c))*a/(b^5*c^3) + 3*(231*(b*sqrt(c)*x + a)^(13/2) - 1638*(b*sqrt(c)*x + a)^(11/2)*a + 5005*(b*sqrt(c)*x + a)^(9/2)*a^2 - 8580*(b*sqrt(c)*x + a)^(7/2)*a^3 + 9009*(b*sqrt(c)*x + a)^(5/2)*a^4 - 6006*(b*sqrt(c)*x + a)^(3/2)*a^5 + 3003*sqrt(b*sqrt(c)*x + a)*a^6)/(b^5*c^(5/2)))/(b*sqrt(c))","A",0
2931,1,164,0,0.169164," ","integrate(x^3*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{9 \, {\left(5 \, {\left(b \sqrt{c} x + a\right)}^{\frac{7}{2}} \sqrt{c} - 21 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} a \sqrt{c} + 35 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a^{2} \sqrt{c} - 35 \, \sqrt{b \sqrt{c} x + a} a^{3} \sqrt{c}\right)} a}{b^{3} c^{2}} + \frac{35 \, {\left(b \sqrt{c} x + a\right)}^{\frac{9}{2}} - 180 \, {\left(b \sqrt{c} x + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b \sqrt{c} x + a} a^{4}}{b^{3} c^{\frac{3}{2}}}\right)}}{315 \, b \sqrt{c}}"," ",0,"2/315*(9*(5*(b*sqrt(c)*x + a)^(7/2)*sqrt(c) - 21*(b*sqrt(c)*x + a)^(5/2)*a*sqrt(c) + 35*(b*sqrt(c)*x + a)^(3/2)*a^2*sqrt(c) - 35*sqrt(b*sqrt(c)*x + a)*a^3*sqrt(c))*a/(b^3*c^2) + (35*(b*sqrt(c)*x + a)^(9/2) - 180*(b*sqrt(c)*x + a)^(7/2)*a + 378*(b*sqrt(c)*x + a)^(5/2)*a^2 - 420*(b*sqrt(c)*x + a)^(3/2)*a^3 + 315*sqrt(b*sqrt(c)*x + a)*a^4)/(b^3*c^(3/2)))/(b*sqrt(c))","A",0
2932,1,90,0,0.161664," ","integrate(x*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{5 \, {\left({\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{b \sqrt{c} x + a} a\right)} a}{b \sqrt{c}} + \frac{3 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b \sqrt{c} x + a} a^{2}}{b \sqrt{c}}\right)}}{15 \, b \sqrt{c}}"," ",0,"2/15*(5*((b*sqrt(c)*x + a)^(3/2) - 3*sqrt(b*sqrt(c)*x + a)*a)*a/(b*sqrt(c)) + (3*(b*sqrt(c)*x + a)^(5/2) - 10*(b*sqrt(c)*x + a)^(3/2)*a + 15*sqrt(b*sqrt(c)*x + a)*a^2)/(b*sqrt(c)))/(b*sqrt(c))","B",0
2933,1,38,0,0.158473," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x,x, algorithm=""giac"")","\frac{2 \, a \arctan\left(\frac{\sqrt{b \sqrt{c} x + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + 2 \, \sqrt{b \sqrt{c} x + a}"," ",0,"2*a*arctan(sqrt(b*sqrt(c)*x + a)/sqrt(-a))/sqrt(-a) + 2*sqrt(b*sqrt(c)*x + a)","A",0
2934,1,90,0,0.165180," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x^3,x, algorithm=""giac"")","-\frac{\frac{b^{3} c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{b \sqrt{c} x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{{\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} b^{3} c^{\frac{3}{2}} + \sqrt{b \sqrt{c} x + a} a b^{3} c^{\frac{3}{2}}}{a b^{2} c x^{2}}}{4 \, b \sqrt{c}}"," ",0,"-1/4*(b^3*c^(3/2)*arctan(sqrt(b*sqrt(c)*x + a)/sqrt(-a))/(sqrt(-a)*a) + ((b*sqrt(c)*x + a)^(3/2)*b^3*c^(3/2) + sqrt(b*sqrt(c)*x + a)*a*b^3*c^(3/2))/(a*b^2*c*x^2))/(b*sqrt(c))","A",0
2935,1,135,0,0.206270," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x^5,x, algorithm=""giac"")","-\frac{\frac{15 \, b^{5} c^{\frac{5}{2}} \arctan\left(\frac{\sqrt{b \sqrt{c} x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} + \frac{15 \, {\left(b \sqrt{c} x + a\right)}^{\frac{7}{2}} b^{5} c^{\frac{5}{2}} - 55 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} a b^{5} c^{\frac{5}{2}} + 73 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a^{2} b^{5} c^{\frac{5}{2}} + 15 \, \sqrt{b \sqrt{c} x + a} a^{3} b^{5} c^{\frac{5}{2}}}{a^{3} b^{4} c^{2} x^{4}}}{192 \, b \sqrt{c}}"," ",0,"-1/192*(15*b^5*c^(5/2)*arctan(sqrt(b*sqrt(c)*x + a)/sqrt(-a))/(sqrt(-a)*a^3) + (15*(b*sqrt(c)*x + a)^(7/2)*b^5*c^(5/2) - 55*(b*sqrt(c)*x + a)^(5/2)*a*b^5*c^(5/2) + 73*(b*sqrt(c)*x + a)^(3/2)*a^2*b^5*c^(5/2) + 15*sqrt(b*sqrt(c)*x + a)*a^3*b^5*c^(5/2))/(a^3*b^4*c^2*x^4))/(b*sqrt(c))","A",0
2936,1,201,0,0.221978," ","integrate(x^4*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{11 \, {\left(35 \, {\left(b \sqrt{c} x + a\right)}^{\frac{9}{2}} - 180 \, {\left(b \sqrt{c} x + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b \sqrt{c} x + a} a^{4}\right)} a}{b^{4} c^{2}} + \frac{5 \, {\left(63 \, {\left(b \sqrt{c} x + a\right)}^{\frac{11}{2}} \sqrt{c} - 385 \, {\left(b \sqrt{c} x + a\right)}^{\frac{9}{2}} a \sqrt{c} + 990 \, {\left(b \sqrt{c} x + a\right)}^{\frac{7}{2}} a^{2} \sqrt{c} - 1386 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} a^{3} \sqrt{c} + 1155 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a^{4} \sqrt{c} - 693 \, \sqrt{b \sqrt{c} x + a} a^{5} \sqrt{c}\right)}}{b^{4} c^{\frac{5}{2}}}\right)}}{3465 \, b \sqrt{c}}"," ",0,"2/3465*(11*(35*(b*sqrt(c)*x + a)^(9/2) - 180*(b*sqrt(c)*x + a)^(7/2)*a + 378*(b*sqrt(c)*x + a)^(5/2)*a^2 - 420*(b*sqrt(c)*x + a)^(3/2)*a^3 + 315*sqrt(b*sqrt(c)*x + a)*a^4)*a/(b^4*c^2) + 5*(63*(b*sqrt(c)*x + a)^(11/2)*sqrt(c) - 385*(b*sqrt(c)*x + a)^(9/2)*a*sqrt(c) + 990*(b*sqrt(c)*x + a)^(7/2)*a^2*sqrt(c) - 1386*(b*sqrt(c)*x + a)^(5/2)*a^3*sqrt(c) + 1155*(b*sqrt(c)*x + a)^(3/2)*a^4*sqrt(c) - 693*sqrt(b*sqrt(c)*x + a)*a^5*sqrt(c))/(b^4*c^(5/2)))/(b*sqrt(c))","A",0
2937,1,135,0,0.166062," ","integrate(x^2*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{7 \, {\left(3 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} - 10 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b \sqrt{c} x + a} a^{2}\right)} a}{b^{2} c} + \frac{3 \, {\left(5 \, {\left(b \sqrt{c} x + a\right)}^{\frac{7}{2}} \sqrt{c} - 21 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} a \sqrt{c} + 35 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a^{2} \sqrt{c} - 35 \, \sqrt{b \sqrt{c} x + a} a^{3} \sqrt{c}\right)}}{b^{2} c^{\frac{3}{2}}}\right)}}{105 \, b \sqrt{c}}"," ",0,"2/105*(7*(3*(b*sqrt(c)*x + a)^(5/2) - 10*(b*sqrt(c)*x + a)^(3/2)*a + 15*sqrt(b*sqrt(c)*x + a)*a^2)*a/(b^2*c) + 3*(5*(b*sqrt(c)*x + a)^(7/2)*sqrt(c) - 21*(b*sqrt(c)*x + a)^(5/2)*a*sqrt(c) + 35*(b*sqrt(c)*x + a)^(3/2)*a^2*sqrt(c) - 35*sqrt(b*sqrt(c)*x + a)*a^3*sqrt(c))/(b^2*c^(3/2)))/(b*sqrt(c))","A",0
2938,1,18,0,0.159202," ","integrate((a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}}}{3 \, b \sqrt{c}}"," ",0,"2/3*(b*sqrt(c)*x + a)^(3/2)/(b*sqrt(c))","A",0
2939,1,54,0,0.164361," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\frac{\frac{b^{2} c \arctan\left(\frac{\sqrt{b \sqrt{c} x + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{\sqrt{b \sqrt{c} x + a} b \sqrt{c}}{x}}{b \sqrt{c}}"," ",0,"(b^2*c*arctan(sqrt(b*sqrt(c)*x + a)/sqrt(-a))/sqrt(-a) - sqrt(b*sqrt(c)*x + a)*b*sqrt(c)/x)/(b*sqrt(c))","A",0
2940,1,114,0,0.165967," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x^4,x, algorithm=""giac"")","\frac{\frac{3 \, b^{4} c^{2} \arctan\left(\frac{\sqrt{b \sqrt{c} x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{3 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} b^{4} c^{2} - 8 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a b^{4} c^{2} - 3 \, \sqrt{b \sqrt{c} x + a} a^{2} b^{4} c^{2}}{a^{2} b^{3} c^{\frac{3}{2}} x^{3}}}{24 \, b \sqrt{c}}"," ",0,"1/24*(3*b^4*c^2*arctan(sqrt(b*sqrt(c)*x + a)/sqrt(-a))/(sqrt(-a)*a^2) + (3*(b*sqrt(c)*x + a)^(5/2)*b^4*c^2 - 8*(b*sqrt(c)*x + a)^(3/2)*a*b^4*c^2 - 3*sqrt(b*sqrt(c)*x + a)*a^2*b^4*c^2)/(a^2*b^3*c^(3/2)*x^3))/(b*sqrt(c))","A",0
2941,1,156,0,0.172289," ","integrate((a+b*(c*x^2)^(1/2))^(1/2)/x^6,x, algorithm=""giac"")","\frac{\frac{105 \, b^{6} c^{3} \arctan\left(\frac{\sqrt{b \sqrt{c} x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{4}} + \frac{105 \, {\left(b \sqrt{c} x + a\right)}^{\frac{9}{2}} b^{6} c^{3} - 490 \, {\left(b \sqrt{c} x + a\right)}^{\frac{7}{2}} a b^{6} c^{3} + 896 \, {\left(b \sqrt{c} x + a\right)}^{\frac{5}{2}} a^{2} b^{6} c^{3} - 790 \, {\left(b \sqrt{c} x + a\right)}^{\frac{3}{2}} a^{3} b^{6} c^{3} - 105 \, \sqrt{b \sqrt{c} x + a} a^{4} b^{6} c^{3}}{a^{4} b^{5} c^{\frac{5}{2}} x^{5}}}{1920 \, b \sqrt{c}}"," ",0,"1/1920*(105*b^6*c^3*arctan(sqrt(b*sqrt(c)*x + a)/sqrt(-a))/(sqrt(-a)*a^4) + (105*(b*sqrt(c)*x + a)^(9/2)*b^6*c^3 - 490*(b*sqrt(c)*x + a)^(7/2)*a*b^6*c^3 + 896*(b*sqrt(c)*x + a)^(5/2)*a^2*b^6*c^3 - 790*(b*sqrt(c)*x + a)^(3/2)*a^3*b^6*c^3 - 105*sqrt(b*sqrt(c)*x + a)*a^4*b^6*c^3)/(a^4*b^5*c^(5/2)*x^5))/(b*sqrt(c))","A",0
2942,1,64,0,0.178100," ","integrate(x^8*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, {\left(b c^{\frac{3}{2}} x^{3} + a\right)}^{\frac{7}{2}} \sqrt{c} - 42 \, {\left(b c^{\frac{3}{2}} x^{3} + a\right)}^{\frac{5}{2}} a \sqrt{c} + 35 \, {\left(b c^{\frac{3}{2}} x^{3} + a\right)}^{\frac{3}{2}} a^{2} \sqrt{c}\right)}}{315 \, b^{3} c^{5}}"," ",0,"2/315*(15*(b*c^(3/2)*x^3 + a)^(7/2)*sqrt(c) - 42*(b*c^(3/2)*x^3 + a)^(5/2)*a*sqrt(c) + 35*(b*c^(3/2)*x^3 + a)^(3/2)*a^2*sqrt(c))/(b^3*c^5)","A",0
2943,1,38,0,0.177920," ","integrate(x^5*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(b c^{\frac{3}{2}} x^{3} + a\right)}^{\frac{5}{2}} - 5 \, {\left(b c^{\frac{3}{2}} x^{3} + a\right)}^{\frac{3}{2}} a\right)}}{45 \, b^{2} c^{3}}"," ",0,"2/45*(3*(b*c^(3/2)*x^3 + a)^(5/2) - 5*(b*c^(3/2)*x^3 + a)^(3/2)*a)/(b^2*c^3)","A",0
2944,1,20,0,0.155772," ","integrate(x^2*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(b c^{\frac{3}{2}} x^{3} + a\right)}^{\frac{3}{2}}}{9 \, b c^{\frac{3}{2}}}"," ",0,"2/9*(b*c^(3/2)*x^3 + a)^(3/2)/(b*c^(3/2))","A",0
2945,1,42,0,0.166171," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x,x, algorithm=""giac"")","\frac{2 \, a \arctan\left(\frac{\sqrt{b c^{\frac{3}{2}} x^{3} + a}}{\sqrt{-a}}\right)}{3 \, \sqrt{-a}} + \frac{2}{3} \, \sqrt{b c^{\frac{3}{2}} x^{3} + a}"," ",0,"2/3*a*arctan(sqrt(b*c^(3/2)*x^3 + a)/sqrt(-a))/sqrt(-a) + 2/3*sqrt(b*c^(3/2)*x^3 + a)","A",0
2946,1,61,0,0.168845," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x^4,x, algorithm=""giac"")","\frac{\frac{b^{2} c^{3} \arctan\left(\frac{\sqrt{b c^{\frac{3}{2}} x^{3} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{\sqrt{b c^{\frac{3}{2}} x^{3} + a} b c^{\frac{3}{2}}}{x^{3}}}{3 \, b c^{\frac{3}{2}}}"," ",0,"1/3*(b^2*c^3*arctan(sqrt(b*c^(3/2)*x^3 + a)/sqrt(-a))/sqrt(-a) - sqrt(b*c^(3/2)*x^3 + a)*b*c^(3/2)/x^3)/(b*c^(3/2))","A",0
2947,0,0,0,0.000000," ","integrate(x^3*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\left(c x^{2}\right)^{\frac{3}{2}} b + a} x^{3}\,{d x}"," ",0,"integrate(sqrt((c*x^2)^(3/2)*b + a)*x^3, x)","F",0
2948,0,0,0,0.000000," ","integrate((a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\left(c x^{2}\right)^{\frac{3}{2}} b + a}\,{d x}"," ",0,"integrate(sqrt((c*x^2)^(3/2)*b + a), x)","F",0
2949,0,0,0,0.000000," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{\left(c x^{2}\right)^{\frac{3}{2}} b + a}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt((c*x^2)^(3/2)*b + a)/x^3, x)","F",0
2950,0,0,0,0.000000," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{\left(c x^{2}\right)^{\frac{3}{2}} b + a}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt((c*x^2)^(3/2)*b + a)/x^6, x)","F",0
2951,0,0,0,0.000000," ","integrate(x^4*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\left(c x^{2}\right)^{\frac{3}{2}} b + a} x^{4}\,{d x}"," ",0,"integrate(sqrt((c*x^2)^(3/2)*b + a)*x^4, x)","F",0
2952,0,0,0,0.000000," ","integrate(x*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\left(c x^{2}\right)^{\frac{3}{2}} b + a} x\,{d x}"," ",0,"integrate(sqrt((c*x^2)^(3/2)*b + a)*x, x)","F",0
2953,0,0,0,0.000000," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{\left(c x^{2}\right)^{\frac{3}{2}} b + a}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt((c*x^2)^(3/2)*b + a)/x^2, x)","F",0
2954,0,0,0,0.000000," ","integrate((a+b*(c*x^2)^(3/2))^(1/2)/x^5,x, algorithm=""giac"")","\int \frac{\sqrt{\left(c x^{2}\right)^{\frac{3}{2}} b + a}}{x^{5}}\,{d x}"," ",0,"integrate(sqrt((c*x^2)^(3/2)*b + a)/x^5, x)","F",0
2955,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x^2)^(3/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\left(c x^{2}\right)^{\frac{3}{2}} b + a} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(sqrt((c*x^2)^(3/2)*b + a)*(d*x)^m, x)","F",0
2956,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{c x^{2}} b + a} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(sqrt(c*x^2)*b + a)*(d*x)^m, x)","F",0
2957,0,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c*x^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\sqrt{c x^{2}}}}\,{d x}"," ",0,"integrate((d*x)^m*sqrt(a + b/sqrt(c*x^2)), x)","F",0
2958,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c*x^2)^(3/2))^(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 Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Done","F(-2)",0
2959,1,2,0,0.164500," ","integrate(1/(1+(x^3)^(2/3)),x, algorithm=""giac"")","\arctan\left(x\right)"," ",0,"arctan(x)","A",0
2960,1,111,0,0.204175," ","integrate(x^5*(a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(105 \, {\left(\sqrt{c x} b c^{2} x + a c^{2}\right)}^{\frac{3}{2}} a^{3} c^{6} - 189 \, {\left(\sqrt{c x} b c^{2} x + a c^{2}\right)}^{\frac{5}{2}} a^{2} c^{4} + 135 \, {\left(\sqrt{c x} b c^{2} x + a c^{2}\right)}^{\frac{7}{2}} a c^{2} - 35 \, {\left(\sqrt{c x} b c^{2} x + a c^{2}\right)}^{\frac{9}{2}}\right)} {\left| c \right|}}{945 \, b^{4} c^{12}}"," ",0,"-4/945*(105*(sqrt(c*x)*b*c^2*x + a*c^2)^(3/2)*a^3*c^6 - 189*(sqrt(c*x)*b*c^2*x + a*c^2)^(5/2)*a^2*c^4 + 135*(sqrt(c*x)*b*c^2*x + a*c^2)^(7/2)*a*c^2 - 35*(sqrt(c*x)*b*c^2*x + a*c^2)^(9/2))*abs(c)/(b^4*c^12)","A",0
2961,1,57,0,0.182787," ","integrate(x^2*(a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(5 \, {\left(\sqrt{c x} b c^{2} x + a c^{2}\right)}^{\frac{3}{2}} a c^{2} - 3 \, {\left(\sqrt{c x} b c^{2} x + a c^{2}\right)}^{\frac{5}{2}}\right)} {\left| c \right|}}{45 \, b^{2} c^{7}}"," ",0,"-4/45*(5*(sqrt(c*x)*b*c^2*x + a*c^2)^(3/2)*a*c^2 - 3*(sqrt(c*x)*b*c^2*x + a*c^2)^(5/2))*abs(c)/(b^2*c^7)","A",0
2962,1,67,0,0.205896," ","integrate((a+b*(c*x^3)^(1/2))^(1/2)/x,x, algorithm=""giac"")","\frac{4 \, {\left(\frac{a \arctan\left(\frac{\sqrt{\sqrt{c x} b c^{2} x + a c^{2}}}{\sqrt{-a} c}\right)}{\sqrt{-a}} + \frac{\sqrt{\sqrt{c x} b c^{2} x + a c^{2}}}{c}\right)} {\left| c \right|}}{3 \, c}"," ",0,"4/3*(a*arctan(sqrt(sqrt(c*x)*b*c^2*x + a*c^2)/(sqrt(-a)*c))/sqrt(-a) + sqrt(sqrt(c*x)*b*c^2*x + a*c^2)/c)*abs(c)/c","A",0
2963,1,122,0,0.211397," ","integrate((a+b*(c*x^3)^(1/2))^(1/2)/x^4,x, algorithm=""giac"")","-\frac{{\left(\frac{b^{3} c^{3} \arctan\left(\frac{\sqrt{\sqrt{c x} b c^{2} x + a c^{2}}}{\sqrt{-a} c}\right)}{\sqrt{-a} a} + \frac{\sqrt{\sqrt{c x} b c^{2} x + a c^{2}} a b^{3} c^{6} + {\left(\sqrt{c x} b c^{2} x + a c^{2}\right)}^{\frac{3}{2}} b^{3} c^{4}}{a b^{2} c^{5} x^{3}}\right)} {\left| c \right|}}{6 \, b c^{3}}"," ",0,"-1/6*(b^3*c^3*arctan(sqrt(sqrt(c*x)*b*c^2*x + a*c^2)/(sqrt(-a)*c))/(sqrt(-a)*a) + (sqrt(sqrt(c*x)*b*c^2*x + a*c^2)*a*b^3*c^6 + (sqrt(c*x)*b*c^2*x + a*c^2)^(3/2)*b^3*c^4)/(a*b^2*c^5*x^3))*abs(c)/(b*c^3)","A",0
2964,0,0,0,0.000000," ","integrate(x*(a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{c x^{3}} b + a} x\,{d x}"," ",0,"integrate(sqrt(sqrt(c*x^3)*b + a)*x, x)","F",0
2965,-2,0,0,0.000000," ","integrate((a+b*(c*x^3)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 22.1-2*abs(c)/c^2/c*4*c^2/8*sqrt(a*c^2/(c*x)^2+b*c/sqrt(c*x))+integrate(2*abs(c)/c^2/c*6*c^3*b/8/2*c*c/(sqrt(c*x)*sqrt(b*c^2*x*sqrt(c*x)+a*c^2)*abs(c)*sign(x)),x)","F(-2)",0
2966,-2,0,0,0.000000," ","integrate((a+b*(c*x^3)^(1/2))^(1/2)/x^5,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 22.112*abs(c)/c^2/c*2*((-5120*a^4*c^9/81920/a^4/c^4/sqrt(c*x)/sqrt(c*x)/sqrt(c*x)-1536*a^3*c^8*b/81920/a^4/c^4)/sqrt(c*x)/sqrt(c*x)/sqrt(c*x)+2688*a^2*c^7*b^2/81920/a^4/c^4)*sqrt(a*c^2/(c*x)^2+b*c/sqrt(c*x))+integrate(2*abs(c)/c^2/c*2688*a^2*c^8*b^3/81920/a^4/c^4/2*c*c/(sqrt(c*x)*sqrt(b*c^2*x*sqrt(c*x)+a*c^2)*abs(c)*sign(x)),x)","F(-2)",0
2967,0,0,0,0.000000," ","integrate(x^3*(a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{c x^{3}} b + a} x^{3}\,{d x}"," ",0,"integrate(sqrt(sqrt(c*x^3)*b + a)*x^3, x)","F",0
2968,0,0,0,0.000000," ","integrate((a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{c x^{3}} b + a}\,{d x}"," ",0,"integrate(sqrt(sqrt(c*x^3)*b + a), x)","F",0
2969,-2,0,0,0.000000," ","integrate((a+b*(c*x^3)^(1/2))^(1/2)/x^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 22.11-2*abs(c)/c^2/c*16*c^3/64/sqrt(c*x)/sqrt(c*x)*sqrt(a*c^2/(c*x)^2+b*c/sqrt(c*x))+integrate(2*abs(c)/c^2/c*24*c^4*b/64/2*c*c/(sqrt(c*x)*sqrt(b*c^2*x*sqrt(c*x)+a*c^2)*c*x*abs(c)*sign(x)),x)","F(-2)",0
2970,1,121,0,0.283874," ","integrate(x^17*(a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(105 \, {\left(\sqrt{c x} b c^{5} x^{4} + a c^{4}\right)}^{\frac{3}{2}} a^{3} c^{12} - 189 \, {\left(\sqrt{c x} b c^{5} x^{4} + a c^{4}\right)}^{\frac{5}{2}} a^{2} c^{8} + 135 \, {\left(\sqrt{c x} b c^{5} x^{4} + a c^{4}\right)}^{\frac{7}{2}} a c^{4} - 35 \, {\left(\sqrt{c x} b c^{5} x^{4} + a c^{4}\right)}^{\frac{9}{2}}\right)} {\left| c \right|}^{2}}{2835 \, b^{4} c^{26}}"," ",0,"-4/2835*(105*(sqrt(c*x)*b*c^5*x^4 + a*c^4)^(3/2)*a^3*c^12 - 189*(sqrt(c*x)*b*c^5*x^4 + a*c^4)^(5/2)*a^2*c^8 + 135*(sqrt(c*x)*b*c^5*x^4 + a*c^4)^(7/2)*a*c^4 - 35*(sqrt(c*x)*b*c^5*x^4 + a*c^4)^(9/2))*abs(c)^2/(b^4*c^26)","A",0
2971,1,63,0,0.198815," ","integrate(x^8*(a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(5 \, {\left(\sqrt{c x} b c^{5} x^{4} + a c^{4}\right)}^{\frac{3}{2}} a c^{4} - 3 \, {\left(\sqrt{c x} b c^{5} x^{4} + a c^{4}\right)}^{\frac{5}{2}}\right)} {\left| c \right|}^{2}}{135 \, b^{2} c^{15}}"," ",0,"-4/135*(5*(sqrt(c*x)*b*c^5*x^4 + a*c^4)^(3/2)*a*c^4 - 3*(sqrt(c*x)*b*c^5*x^4 + a*c^4)^(5/2))*abs(c)^2/(b^2*c^15)","A",0
2972,1,74,0,0.224392," ","integrate((a+b*(c*x^3)^(3/2))^(1/2)/x,x, algorithm=""giac"")","\frac{4 \, {\left(\frac{a c \arctan\left(\frac{\sqrt{\sqrt{c x} b c^{5} x^{4} + a c^{4}}}{\sqrt{-a} c^{2}}\right)}{\sqrt{-a}} + \frac{\sqrt{\sqrt{c x} b c^{5} x^{4} + a c^{4}}}{c}\right)} {\left| c \right|}^{2}}{9 \, c^{3}}"," ",0,"4/9*(a*c*arctan(sqrt(sqrt(c*x)*b*c^5*x^4 + a*c^4)/(sqrt(-a)*c^2))/sqrt(-a) + sqrt(sqrt(c*x)*b*c^5*x^4 + a*c^4)/c)*abs(c)^2/c^3","A",0
2973,1,130,0,0.247332," ","integrate((a+b*(c*x^3)^(3/2))^(1/2)/x^10,x, algorithm=""giac"")","-\frac{{\left(\frac{b^{3} c^{6} \arctan\left(\frac{\sqrt{\sqrt{c x} b c^{5} x^{4} + a c^{4}}}{\sqrt{-a} c^{2}}\right)}{\sqrt{-a} a} + \frac{\sqrt{\sqrt{c x} b c^{5} x^{4} + a c^{4}} a b^{3} c^{12} + {\left(\sqrt{c x} b c^{5} x^{4} + a c^{4}\right)}^{\frac{3}{2}} b^{3} c^{8}}{a b^{2} c^{11} x^{9}}\right)} {\left| c \right|}^{2}}{18 \, b c^{5}}"," ",0,"-1/18*(b^3*c^6*arctan(sqrt(sqrt(c*x)*b*c^5*x^4 + a*c^4)/(sqrt(-a)*c^2))/(sqrt(-a)*a) + (sqrt(sqrt(c*x)*b*c^5*x^4 + a*c^4)*a*b^3*c^12 + (sqrt(c*x)*b*c^5*x^4 + a*c^4)^(3/2)*b^3*c^8)/(a*b^2*c^11*x^9))*abs(c)^2/(b*c^5)","A",0
2974,0,0,0,0.000000," ","integrate(x^2*(a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\left(c x^{3}\right)^{\frac{3}{2}} b + a} x^{2}\,{d x}"," ",0,"integrate(sqrt((c*x^3)^(3/2)*b + a)*x^2, x)","F",0
2975,0,0,0,0.000000," ","integrate(x^9*(a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\left(c x^{3}\right)^{\frac{3}{2}} b + a} x^{9}\,{d x}"," ",0,"integrate(sqrt((c*x^3)^(3/2)*b + a)*x^9, x)","F",0
2976,0,0,0,0.000000," ","integrate((a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\left(c x^{3}\right)^{\frac{3}{2}} b + a}\,{d x}"," ",0,"integrate(sqrt((c*x^3)^(3/2)*b + a), x)","F",0
2977,0,0,0,0.000000," ","integrate((a+b*(c*x^3)^(3/2))^(1/2)/x^9,x, algorithm=""giac"")","\int \frac{\sqrt{\left(c x^{3}\right)^{\frac{3}{2}} b + a}}{x^{9}}\,{d x}"," ",0,"integrate(sqrt((c*x^3)^(3/2)*b + a)/x^9, x)","F",0
2978,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x^3)^(3/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\left(c x^{3}\right)^{\frac{3}{2}} b + a} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(sqrt((c*x^3)^(3/2)*b + a)*(d*x)^m, x)","F",0
2979,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x^3)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{c x^{3}} b + a} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(sqrt(c*x^3)*b + a)*(d*x)^m, x)","F",0
2980,0,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c*x^3)^(1/2))^(1/2),x, algorithm=""giac"")","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\sqrt{c x^{3}}}}\,{d x}"," ",0,"integrate((d*x)^m*sqrt(a + b/sqrt(c*x^3)), x)","F",0
2981,0,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c*x^3)^(3/2))^(1/2),x, algorithm=""giac"")","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\left(c x^{3}\right)^{\frac{3}{2}}}}\,{d x}"," ",0,"integrate((d*x)^m*sqrt(a + b/(c*x^3)^(3/2)), x)","F",0
2982,-2,0,0,0.000000," ","integrate(x*(a+b*(c/x)^(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: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 ValueWarning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-33]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-70]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [8]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [63]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-64]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [2]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [62]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-37]Algebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueError: Bad Argument TypeWarning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-80]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-23]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [65]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-85]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [28]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-44]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-22]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [93]Algebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofMinimal poly. in rootof must be fraction free Error: Bad Argument ValueEvaluation time: 18Done","F(-2)",0
2983,1,130,0,0.362840," ","integrate((a+b*(c/x)^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{{\left(\frac{b^{2} c^{3} \log\left(c^{2} {\left| b \right|}\right)}{\sqrt{a c} a} - \frac{b^{2} c^{3} \log\left({\left| -b c^{2} - 2 \, \sqrt{a c} {\left(\sqrt{a c} \sqrt{c x} - \sqrt{a c^{2} x + \sqrt{c x} b c^{2}}\right)} \right|}\right)}{\sqrt{a c} a} - 2 \, \sqrt{a c^{2} x + \sqrt{c x} b c^{2}} {\left(\frac{b c}{a} + 2 \, \sqrt{c x}\right)}\right)} \mathrm{sgn}\left(x\right)}{4 \, c^{\frac{3}{2}}}"," ",0,"-1/4*(b^2*c^3*log(c^2*abs(b))/(sqrt(a*c)*a) - b^2*c^3*log(abs(-b*c^2 - 2*sqrt(a*c)*(sqrt(a*c)*sqrt(c*x) - sqrt(a*c^2*x + sqrt(c*x)*b*c^2))))/(sqrt(a*c)*a) - 2*sqrt(a*c^2*x + sqrt(c*x)*b*c^2)*(b*c/a + 2*sqrt(c*x)))*sgn(x)/c^(3/2)","A",0
2984,-2,0,0,0.000000," ","integrate((a+b*(c/x)^(1/2))^(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, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, choosing root of [1,0,%%%{-2,[1,1,2,0]%%%}+%%%{-2,[1,1,0,0]%%%}+%%%{-2,[0,2,1,1]%%%},0,%%%{1,[2,2,4,0]%%%}+%%%{-2,[2,2,2,0]%%%}+%%%{1,[2,2,0,0]%%%}+%%%{2,[1,3,3,1]%%%}+%%%{-2,[1,3,1,1]%%%}+%%%{1,[0,4,2,2]%%%}] at parameters values [-97,-82,7,-27]Sign error (%%%{(-c*sqrt(a*c))*b,0%%%}+%%%{2*a*sqrt(b)*abs(c),1/2%%%}+%%%{-2*a*sqrt(a*c),1%%%}+%%%{a^2*sqrt(b)*abs(c)/(b*c),3/2%%%}+%%%{-a^3*sqrt(b)*abs(c)/(4*b^2*c^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
2985,-1,0,0,0.000000," ","integrate((a+b*(c/x)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2986,0,0,0,0.000000," ","integrate((a+b*(c/x)^(1/2))^(1/2)/x^3,x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2987,-2,0,0,0.000000," ","integrate((a+b*(c/x)^(1/2))^(1/2)/x^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [74.7709350525]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [47.3295757947]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [50.5901726987]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [91.0141688026]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [59.8656459874]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [25.8388736797]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [33.9285577983]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [15.451549686]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [8]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-64]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [2]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[37]Algebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b]=[-56]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b]=[-99]Evaluation time: 5.9index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
2988,0,0,0,0.000000," ","integrate(x/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{b \sqrt{\frac{c}{x}} + a}}\,{d x}"," ",0,"integrate(x/sqrt(b*sqrt(c/x) + a), x)","F",0
2989,1,139,0,0.407794," ","integrate(1/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, b^{2} c^{2} \log\left(c^{2} {\left| b \right|}\right)}{\sqrt{a c} a^{2}} - \frac{3 \, b^{2} c^{2} \log\left({\left| -b c^{2} - 2 \, \sqrt{a c} {\left(\sqrt{a c} \sqrt{c x} - \sqrt{a c^{2} x + \sqrt{c x} b c^{2}}\right)} \right|}\right)}{\sqrt{a c} a^{2}} - 2 \, \sqrt{a c^{2} x + \sqrt{c x} b c^{2}} {\left(\frac{3 \, b}{a^{2}} - \frac{2 \, \sqrt{c x}}{a c}\right)}}{4 \, \sqrt{c} \mathrm{sgn}\left(x\right)}"," ",0,"1/4*(3*b^2*c^2*log(c^2*abs(b))/(sqrt(a*c)*a^2) - 3*b^2*c^2*log(abs(-b*c^2 - 2*sqrt(a*c)*(sqrt(a*c)*sqrt(c*x) - sqrt(a*c^2*x + sqrt(c*x)*b*c^2))))/(sqrt(a*c)*a^2) - 2*sqrt(a*c^2*x + sqrt(c*x)*b*c^2)*(3*b/a^2 - 2*sqrt(c*x)/(a*c)))/(sqrt(c)*sgn(x))","A",0
2990,0,0,0,0.000000," ","integrate(1/x/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sqrt{\frac{c}{x}} + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(b*sqrt(c/x) + a)*x), x)","F",0
2991,1,60,0,0.176575," ","integrate(1/x^2/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left({\left(b \sqrt{\frac{c}{x}} + a\right)}^{\frac{3}{2}} b - 3 \, \sqrt{b \sqrt{\frac{c}{x}} + a} a b\right)} \mathrm{sgn}\left({\left(b \sqrt{\frac{c}{x}} + a\right)} b - a b\right)}{3 \, b^{3} c}"," ",0,"-4/3*((b*sqrt(c/x) + a)^(3/2)*b - 3*sqrt(b*sqrt(c/x) + a)*a*b)*sgn((b*sqrt(c/x) + a)*b - a*b)/(b^3*c)","A",0
2992,1,152,0,0.252039," ","integrate(1/x^3/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(5 \, {\left(b \sqrt{\frac{c}{x}} + a\right)}^{\frac{7}{2}} \mathrm{sgn}\left({\left(b \sqrt{\frac{c}{x}} + a\right)} b - a b\right) - 21 \, {\left(b \sqrt{\frac{c}{x}} + a\right)}^{\frac{5}{2}} a \mathrm{sgn}\left({\left(b \sqrt{\frac{c}{x}} + a\right)} b - a b\right) + 35 \, {\left(b \sqrt{\frac{c}{x}} + a\right)}^{\frac{3}{2}} a^{2} \mathrm{sgn}\left({\left(b \sqrt{\frac{c}{x}} + a\right)} b - a b\right) - 35 \, \sqrt{b \sqrt{\frac{c}{x}} + a} a^{3} \mathrm{sgn}\left({\left(b \sqrt{\frac{c}{x}} + a\right)} b - a b\right)\right)}}{35 \, b^{4} c^{2}}"," ",0,"-4/35*(5*(b*sqrt(c/x) + a)^(7/2)*sgn((b*sqrt(c/x) + a)*b - a*b) - 21*(b*sqrt(c/x) + a)^(5/2)*a*sgn((b*sqrt(c/x) + a)*b - a*b) + 35*(b*sqrt(c/x) + a)^(3/2)*a^2*sgn((b*sqrt(c/x) + a)*b - a*b) - 35*sqrt(b*sqrt(c/x) + a)*a^3*sgn((b*sqrt(c/x) + a)*b - a*b))/(b^4*c^2)","A",0
2993,0,0,0,0.000000," ","integrate(1/x^4/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sqrt{\frac{c}{x}} + a} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sqrt(c/x) + a)*x^4), x)","F",0
2994,1,36,0,0.239847," ","integrate(1/(1+(1/x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x + \sqrt{x}} {\left(2 \, \sqrt{x} - 3\right)} - \frac{3}{4} \, \log\left(-2 \, \sqrt{x + \sqrt{x}} + 2 \, \sqrt{x} + 1\right)"," ",0,"1/2*sqrt(x + sqrt(x))*(2*sqrt(x) - 3) - 3/4*log(-2*sqrt(x + sqrt(x)) + 2*sqrt(x) + 1)","A",0
2995,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c/x)^(3/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \left(\frac{c}{x}\right)^{\frac{3}{2}} + a} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(b*(c/x)^(3/2) + a)*(d*x)^m, x)","F",0
2996,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c/x)^(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:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Unable to divide, perhaps due to rounding error%%%{1,[0,1,1,0]%%%} / %%%{1,[0,0,0,1]%%%} Error: Bad Argument Value","F(-2)",0
2997,0,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c/x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\sqrt{\frac{c}{x}}}}\,{d x}"," ",0,"integrate((d*x)^m*sqrt(a + b/sqrt(c/x)), x)","F",0
2998,0,0,0,0.000000," ","integrate((d*x)^m*(a+b/(c/x)^(3/2))^(1/2),x, algorithm=""giac"")","\int \left(d x\right)^{m} \sqrt{a + \frac{b}{\left(\frac{c}{x}\right)^{\frac{3}{2}}}}\,{d x}"," ",0,"integrate((d*x)^m*sqrt(a + b/(c/x)^(3/2)), x)","F",0
2999,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*(c/x)^(3/2))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{\sqrt{b \left(\frac{c}{x}\right)^{\frac{3}{2}} + a}}\,{d x}"," ",0,"integrate((d*x)^m/sqrt(b*(c/x)^(3/2) + a), x)","F",0
3000,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*(c/x)^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
3001,0,0,0,0.000000," ","integrate((d*x)^m/(a+b/(c/x)^(1/2))^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
3002,0,0,0,0.000000," ","integrate((d*x)^m/(a+b/(c/x)^(3/2))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{\sqrt{a + \frac{b}{\left(\frac{c}{x}\right)^{\frac{3}{2}}}}}\,{d x}"," ",0,"integrate((d*x)^m/sqrt(a + b/(c/x)^(3/2)), x)","F",0
3003,1,15,0,0.162409," ","integrate(a+b*(c*x^n)^(1/n),x, algorithm=""giac"")","\frac{1}{2} \, b c^{\left(\frac{1}{n}\right)} x^{2} + a x"," ",0,"1/2*b*c^(1/n)*x^2 + a*x","A",0
3004,1,32,0,0.189229," ","integrate((a+b*(c*x^n)^(1/n))^2,x, algorithm=""giac"")","\frac{1}{3} \, b^{2} c^{\frac{2}{n}} x^{3} + a b c^{\left(\frac{1}{n}\right)} x^{2} + a^{2} x"," ",0,"1/3*b^2*c^(2/n)*x^3 + a*b*c^(1/n)*x^2 + a^2*x","A",0
3005,1,50,0,0.212080," ","integrate((a+b*(c*x^n)^(1/n))^3,x, algorithm=""giac"")","\frac{1}{4} \, b^{3} c^{\frac{3}{n}} x^{4} + a b^{2} c^{\frac{2}{n}} x^{3} + \frac{3}{2} \, a^{2} b c^{\left(\frac{1}{n}\right)} x^{2} + a^{3} x"," ",0,"1/4*b^3*c^(3/n)*x^4 + a*b^2*c^(2/n)*x^3 + 3/2*a^2*b*c^(1/n)*x^2 + a^3*x","A",0
3006,0,0,0,0.000000," ","integrate(x^3/(a+b*(c*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{x^{3}}{\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a}\,{d x}"," ",0,"integrate(x^3/((c*x^n)^(1/n)*b + a), x)","F",0
3007,0,0,0,0.000000," ","integrate(x^2/(a+b*(c*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{x^{2}}{\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a}\,{d x}"," ",0,"integrate(x^2/((c*x^n)^(1/n)*b + a), x)","F",0
3008,0,0,0,0.000000," ","integrate(x/(a+b*(c*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{x}{\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a}\,{d x}"," ",0,"integrate(x/((c*x^n)^(1/n)*b + a), x)","F",0
3009,0,0,0,0.000000," ","integrate(1/(a+b*(c*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{1}{\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a}\,{d x}"," ",0,"integrate(1/((c*x^n)^(1/n)*b + a), x)","F",0
3010,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)} x}\,{d x}"," ",0,"integrate(1/(((c*x^n)^(1/n)*b + a)*x), x)","F",0
3011,0,0,0,0.000000," ","integrate(1/x^2/(a+b*(c*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/(((c*x^n)^(1/n)*b + a)*x^2), x)","F",0
3012,0,0,0,0.000000," ","integrate(1/x^3/(a+b*(c*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)} x^{3}}\,{d x}"," ",0,"integrate(1/(((c*x^n)^(1/n)*b + a)*x^3), x)","F",0
3013,0,0,0,0.000000," ","integrate(x^3/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^3/((c*x^n)^(1/n)*b + a)^2, x)","F",0
3014,0,0,0,0.000000," ","integrate(x^2/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^2/((c*x^n)^(1/n)*b + a)^2, x)","F",0
3015,0,0,0,0.000000," ","integrate(x/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""giac"")","\int \frac{x}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{2}}\,{d x}"," ",0,"integrate(x/((c*x^n)^(1/n)*b + a)^2, x)","F",0
3016,0,0,0,0.000000," ","integrate(1/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{2}}\,{d x}"," ",0,"integrate(((c*x^n)^(1/n)*b + a)^(-2), x)","F",0
3017,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{2} x}\,{d x}"," ",0,"integrate(1/(((c*x^n)^(1/n)*b + a)^2*x), x)","F",0
3018,0,0,0,0.000000," ","integrate(1/x^2/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate(1/(((c*x^n)^(1/n)*b + a)^2*x^2), x)","F",0
3019,0,0,0,0.000000," ","integrate(1/x^3/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate(1/(((c*x^n)^(1/n)*b + a)^2*x^3), x)","F",0
3020,0,0,0,0.000000," ","integrate(1/(a+b*(c*x^n)^(1/n))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{3}}\,{d x}"," ",0,"integrate(((c*x^n)^(1/n)*b + a)^(-3), x)","F",0
3021,1,11,0,0.168890," ","integrate(x/(1+(x^n)^(1/n))^2,x, algorithm=""giac"")","\frac{1}{x + 1} + \log\left({\left| x + 1 \right|}\right)"," ",0,"1/(x + 1) + log(abs(x + 1))","A",0
3022,1,384,0,0.469351," ","integrate(x^3*(a+b*(c*x^n)^(1/n))^p,x, algorithm=""giac"")","\frac{{\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b^{4} c^{\frac{4}{n}} p^{3} x^{4} + {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a b^{3} c^{\frac{3}{n}} p^{3} x^{3} + 6 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b^{4} c^{\frac{4}{n}} p^{2} x^{4} + 3 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a b^{3} c^{\frac{3}{n}} p^{2} x^{3} + 11 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b^{4} c^{\frac{4}{n}} p x^{4} - 3 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a^{2} b^{2} c^{\frac{2}{n}} p^{2} x^{2} + 2 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a b^{3} c^{\frac{3}{n}} p x^{3} + 6 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b^{4} c^{\frac{4}{n}} x^{4} - 3 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a^{2} b^{2} c^{\frac{2}{n}} p x^{2} + 6 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a^{3} b c^{\left(\frac{1}{n}\right)} p x - 6 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a^{4}}{b^{4} c^{\frac{4}{n}} p^{4} + 10 \, b^{4} c^{\frac{4}{n}} p^{3} + 35 \, b^{4} c^{\frac{4}{n}} p^{2} + 50 \, b^{4} c^{\frac{4}{n}} p + 24 \, b^{4} c^{\frac{4}{n}}}"," ",0,"((b*c^(1/n)*x + a)^p*b^4*c^(4/n)*p^3*x^4 + (b*c^(1/n)*x + a)^p*a*b^3*c^(3/n)*p^3*x^3 + 6*(b*c^(1/n)*x + a)^p*b^4*c^(4/n)*p^2*x^4 + 3*(b*c^(1/n)*x + a)^p*a*b^3*c^(3/n)*p^2*x^3 + 11*(b*c^(1/n)*x + a)^p*b^4*c^(4/n)*p*x^4 - 3*(b*c^(1/n)*x + a)^p*a^2*b^2*c^(2/n)*p^2*x^2 + 2*(b*c^(1/n)*x + a)^p*a*b^3*c^(3/n)*p*x^3 + 6*(b*c^(1/n)*x + a)^p*b^4*c^(4/n)*x^4 - 3*(b*c^(1/n)*x + a)^p*a^2*b^2*c^(2/n)*p*x^2 + 6*(b*c^(1/n)*x + a)^p*a^3*b*c^(1/n)*p*x - 6*(b*c^(1/n)*x + a)^p*a^4)/(b^4*c^(4/n)*p^4 + 10*b^4*c^(4/n)*p^3 + 35*b^4*c^(4/n)*p^2 + 50*b^4*c^(4/n)*p + 24*b^4*c^(4/n))","B",0
3023,1,243,0,0.455126," ","integrate(x^2*(a+b*(c*x^n)^(1/n))^p,x, algorithm=""giac"")","\frac{{\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b^{3} c^{\frac{3}{n}} p^{2} x^{3} + {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a b^{2} c^{\frac{2}{n}} p^{2} x^{2} + 3 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b^{3} c^{\frac{3}{n}} p x^{3} + {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a b^{2} c^{\frac{2}{n}} p x^{2} + 2 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b^{3} c^{\frac{3}{n}} x^{3} - 2 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a^{2} b c^{\left(\frac{1}{n}\right)} p x + 2 \, {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a^{3}}{b^{3} c^{\frac{3}{n}} p^{3} + 6 \, b^{3} c^{\frac{3}{n}} p^{2} + 11 \, b^{3} c^{\frac{3}{n}} p + 6 \, b^{3} c^{\frac{3}{n}}}"," ",0,"((b*c^(1/n)*x + a)^p*b^3*c^(3/n)*p^2*x^3 + (b*c^(1/n)*x + a)^p*a*b^2*c^(2/n)*p^2*x^2 + 3*(b*c^(1/n)*x + a)^p*b^3*c^(3/n)*p*x^3 + (b*c^(1/n)*x + a)^p*a*b^2*c^(2/n)*p*x^2 + 2*(b*c^(1/n)*x + a)^p*b^3*c^(3/n)*x^3 - 2*(b*c^(1/n)*x + a)^p*a^2*b*c^(1/n)*p*x + 2*(b*c^(1/n)*x + a)^p*a^3)/(b^3*c^(3/n)*p^3 + 6*b^3*c^(3/n)*p^2 + 11*b^3*c^(3/n)*p + 6*b^3*c^(3/n))","A",0
3024,1,136,0,0.458409," ","integrate(x*(a+b*(c*x^n)^(1/n))^p,x, algorithm=""giac"")","\frac{{\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b^{2} c^{\frac{2}{n}} p x^{2} + {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a b c^{\left(\frac{1}{n}\right)} p x + {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b^{2} c^{\frac{2}{n}} x^{2} - {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a^{2}}{b^{2} c^{\frac{2}{n}} p^{2} + 3 \, b^{2} c^{\frac{2}{n}} p + 2 \, b^{2} c^{\frac{2}{n}}}"," ",0,"((b*c^(1/n)*x + a)^p*b^2*c^(2/n)*p*x^2 + (b*c^(1/n)*x + a)^p*a*b*c^(1/n)*p*x + (b*c^(1/n)*x + a)^p*b^2*c^(2/n)*x^2 - (b*c^(1/n)*x + a)^p*a^2)/(b^2*c^(2/n)*p^2 + 3*b^2*c^(2/n)*p + 2*b^2*c^(2/n))","A",0
3025,1,54,0,0.305532," ","integrate((a+b*(c*x^n)^(1/n))^p,x, algorithm=""giac"")","\frac{{\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b c^{\left(\frac{1}{n}\right)} x + {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a}{b c^{\left(\frac{1}{n}\right)} p + b c^{\left(\frac{1}{n}\right)}}"," ",0,"((b*c^(1/n)*x + a)^p*b*c^(1/n)*x + (b*c^(1/n)*x + a)^p*a)/(b*c^(1/n)*p + b*c^(1/n))","A",0
3026,0,0,0,0.000000," ","integrate((a+b*(c*x^n)^(1/n))^p/x,x, algorithm=""giac"")","\int \frac{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate(((c*x^n)^(1/n)*b + a)^p/x, x)","F",0
3027,0,0,0,0.000000," ","integrate((a+b*(c*x^n)^(1/n))^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate(((c*x^n)^(1/n)*b + a)^p/x^2, x)","F",0
3028,1,52,0,0.201330," ","integrate((a+b*(c*x^n)^(2/n))^3,x, algorithm=""giac"")","\frac{1}{7} \, b^{3} c^{\frac{6}{n}} x^{7} + \frac{3}{5} \, a b^{2} c^{\frac{4}{n}} x^{5} + a^{2} b c^{\frac{2}{n}} x^{3} + a^{3} x"," ",0,"1/7*b^3*c^(6/n)*x^7 + 3/5*a*b^2*c^(4/n)*x^5 + a^2*b*c^(2/n)*x^3 + a^3*x","A",0
3029,1,35,0,0.194135," ","integrate((a+b*(c*x^n)^(2/n))^2,x, algorithm=""giac"")","\frac{1}{5} \, b^{2} c^{\frac{4}{n}} x^{5} + \frac{2}{3} \, a b c^{\frac{2}{n}} x^{3} + a^{2} x"," ",0,"1/5*b^2*c^(4/n)*x^5 + 2/3*a*b*c^(2/n)*x^3 + a^2*x","A",0
3030,1,17,0,0.163386," ","integrate(a+b*(c*x^n)^(2/n),x, algorithm=""giac"")","\frac{1}{3} \, b c^{\frac{2}{n}} x^{3} + a x"," ",0,"1/3*b*c^(2/n)*x^3 + a*x","A",0
3031,0,0,0,0.000000," ","integrate(1/(a+b*(c*x^n)^(2/n)),x, algorithm=""giac"")","\int \frac{1}{\left(c x^{n}\right)^{\frac{2}{n}} b + a}\,{d x}"," ",0,"integrate(1/((c*x^n)^(2/n)*b + a), x)","F",0
3032,0,0,0,0.000000," ","integrate(1/(a+b*(c*x^n)^(2/n))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\frac{2}{n}} b + a\right)}^{2}}\,{d x}"," ",0,"integrate(((c*x^n)^(2/n)*b + a)^(-2), x)","F",0
3033,0,0,0,0.000000," ","integrate(1/(a+b*(c*x^n)^(2/n))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\frac{2}{n}} b + a\right)}^{3}}\,{d x}"," ",0,"integrate(((c*x^n)^(2/n)*b + a)^(-3), x)","F",0
3034,1,6,0,0.146673," ","integrate(1/(1+4*(x^4)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(2 \, x\right)"," ",0,"1/2*arctan(2*x)","A",0
3035,1,15,0,0.147897," ","integrate(1/(1-4*(x^4)^(1/2)),x, algorithm=""giac"")","\frac{1}{4} \, \log\left({\left| x + \frac{1}{2} \right|}\right) - \frac{1}{4} \, \log\left({\left| x - \frac{1}{2} \right|}\right)"," ",0,"1/4*log(abs(x + 1/2)) - 1/4*log(abs(x - 1/2))","A",0
3036,1,6,0,0.148714," ","integrate(1/(1+4*(x^6)^(1/3)),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(2 \, x\right)"," ",0,"1/2*arctan(2*x)","A",0
3037,1,15,0,0.147612," ","integrate(1/(1-4*(x^6)^(1/3)),x, algorithm=""giac"")","\frac{1}{4} \, \log\left({\left| x + \frac{1}{2} \right|}\right) - \frac{1}{4} \, \log\left({\left| x - \frac{1}{2} \right|}\right)"," ",0,"1/4*log(abs(x + 1/2)) - 1/4*log(abs(x - 1/2))","A",0
3038,1,6,0,0.165436," ","integrate(1/(1+4*(x^(2*n))^(1/n)),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(2 \, x\right)"," ",0,"1/2*arctan(2*x)","A",0
3039,1,15,0,0.151270," ","integrate(1/(1-4*(x^(2*n))^(1/n)),x, algorithm=""giac"")","\frac{1}{4} \, \log\left({\left| x + \frac{1}{2} \right|}\right) - \frac{1}{4} \, \log\left({\left| x - \frac{1}{2} \right|}\right)"," ",0,"1/4*log(abs(x + 1/2)) - 1/4*log(abs(x - 1/2))","A",0
3040,1,53,0,0.398485," ","integrate((a+b*(c*x^n)^(3/n))^3,x, algorithm=""giac"")","\frac{1}{10} \, b^{3} c^{\frac{9}{n}} x^{10} + \frac{3}{7} \, a b^{2} c^{\frac{6}{n}} x^{7} + \frac{3}{4} \, a^{2} b c^{\frac{3}{n}} x^{4} + a^{3} x"," ",0,"1/10*b^3*c^(9/n)*x^10 + 3/7*a*b^2*c^(6/n)*x^7 + 3/4*a^2*b*c^(3/n)*x^4 + a^3*x","A",0
3041,1,35,0,0.198486," ","integrate((a+b*(c*x^n)^(3/n))^2,x, algorithm=""giac"")","\frac{1}{7} \, b^{2} c^{\frac{6}{n}} x^{7} + \frac{1}{2} \, a b c^{\frac{3}{n}} x^{4} + a^{2} x"," ",0,"1/7*b^2*c^(6/n)*x^7 + 1/2*a*b*c^(3/n)*x^4 + a^2*x","A",0
3042,1,17,0,0.166045," ","integrate(a+b*(c*x^n)^(3/n),x, algorithm=""giac"")","\frac{1}{4} \, b c^{\frac{3}{n}} x^{4} + a x"," ",0,"1/4*b*c^(3/n)*x^4 + a*x","A",0
3043,0,0,0,0.000000," ","integrate(1/(a+b*(c*x^n)^(3/n)),x, algorithm=""giac"")","\int \frac{1}{\left(c x^{n}\right)^{\frac{3}{n}} b + a}\,{d x}"," ",0,"integrate(1/((c*x^n)^(3/n)*b + a), x)","F",0
3044,0,0,0,0.000000," ","integrate(1/(a+b*(c*x^n)^(3/n))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\frac{3}{n}} b + a\right)}^{2}}\,{d x}"," ",0,"integrate(((c*x^n)^(3/n)*b + a)^(-2), x)","F",0
3045,0,0,0,0.000000," ","integrate(1/(a+b*(c*x^n)^(3/n))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x^{n}\right)^{\frac{3}{n}} b + a\right)}^{3}}\,{d x}"," ",0,"integrate(((c*x^n)^(3/n)*b + a)^(-3), x)","F",0
3046,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*(c*x^q)^n)^p,x, algorithm=""giac"")","\int {\left(\left(c x^{q}\right)^{n} b + a\right)}^{p} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(((c*x^q)^n*b + a)^p*(d*x)^m, x)","F",0
3047,0,0,0,0.000000," ","integrate(x^2*(a+b*(c*x^q)^n)^p,x, algorithm=""giac"")","\int {\left(\left(c x^{q}\right)^{n} b + a\right)}^{p} x^{2}\,{d x}"," ",0,"integrate(((c*x^q)^n*b + a)^p*x^2, x)","F",0
3048,0,0,0,0.000000," ","integrate(x*(a+b*(c*x^q)^n)^p,x, algorithm=""giac"")","\int {\left(\left(c x^{q}\right)^{n} b + a\right)}^{p} x\,{d x}"," ",0,"integrate(((c*x^q)^n*b + a)^p*x, x)","F",0
3049,0,0,0,0.000000," ","integrate((a+b*(c*x^q)^n)^p,x, algorithm=""giac"")","\int {\left(\left(c x^{q}\right)^{n} b + a\right)}^{p}\,{d x}"," ",0,"integrate(((c*x^q)^n*b + a)^p, x)","F",0
3050,0,0,0,0.000000," ","integrate((a+b*(c*x^q)^n)^p/x,x, algorithm=""giac"")","\int \frac{{\left(\left(c x^{q}\right)^{n} b + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate(((c*x^q)^n*b + a)^p/x, x)","F",0
3051,0,0,0,0.000000," ","integrate((a+b*(c*x^q)^n)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(\left(c x^{q}\right)^{n} b + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate(((c*x^q)^n*b + a)^p/x^2, x)","F",0
3052,0,0,0,0.000000," ","integrate(x^m*(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sqrt{\frac{d}{x}} + a + \frac{c}{x}} x^{m}\,{d x}"," ",0,"integrate(sqrt(b*sqrt(d/x) + a + c/x)*x^m, x)","F",0
3053,-1,0,0,0.000000," ","integrate(x^2*(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3054,-1,0,0,0.000000," ","integrate(x*(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3055,1,213,0,0.986885," ","integrate((a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{{\left(2 \, \sqrt{a d^{2} x + \sqrt{d x} b d^{2} + c d^{2}} {\left(\frac{b d}{a} + 2 \, \sqrt{d x}\right)} + \frac{{\left(b^{2} d^{3} - 4 \, a c d^{2}\right)} \log\left({\left| -b d^{2} - 2 \, \sqrt{a d} {\left(\sqrt{a d} \sqrt{d x} - \sqrt{a d^{2} x + \sqrt{d x} b d^{2} + c d^{2}}\right)} \right|}\right)}{\sqrt{a d} a} - \frac{b^{2} d^{3} \log\left({\left| -b d^{2} + 2 \, \sqrt{c d^{2}} \sqrt{a d} \right|}\right) - 4 \, a c d^{2} \log\left({\left| -b d^{2} + 2 \, \sqrt{c d^{2}} \sqrt{a d} \right|}\right) + 2 \, \sqrt{c d^{2}} \sqrt{a d} b d}{\sqrt{a d} a}\right)} \mathrm{sgn}\left(x\right)}{4 \, d^{\frac{3}{2}}}"," ",0,"1/4*(2*sqrt(a*d^2*x + sqrt(d*x)*b*d^2 + c*d^2)*(b*d/a + 2*sqrt(d*x)) + (b^2*d^3 - 4*a*c*d^2)*log(abs(-b*d^2 - 2*sqrt(a*d)*(sqrt(a*d)*sqrt(d*x) - sqrt(a*d^2*x + sqrt(d*x)*b*d^2 + c*d^2))))/(sqrt(a*d)*a) - (b^2*d^3*log(abs(-b*d^2 + 2*sqrt(c*d^2)*sqrt(a*d))) - 4*a*c*d^2*log(abs(-b*d^2 + 2*sqrt(c*d^2)*sqrt(a*d))) + 2*sqrt(c*d^2)*sqrt(a*d)*b*d)/(sqrt(a*d)*a))*sgn(x)/d^(3/2)","B",0
3056,-2,0,0,0.000000," ","integrate((a+c/x+b*(d/x)^(1/2))^(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, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Sign error (%%%{(-d*sqrt(a*d))*b+2*sqrt(c)*a*abs(d),0%%%}+%%%{(a*b*sqrt(c)*abs(d)-2*a*c*sqrt(a*d))/c,1%%%}+%%%{(4*a^2*c*sqrt(c)*abs(d)-a*b^2*d*sqrt(c)*abs(d))/(4*c^2*d),2%%%}+%%%{undef,3%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
3057,-1,0,0,0.000000," ","integrate((a+c/x+b*(d/x)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3058,-1,0,0,0.000000," ","integrate((a+c/x+b*(d/x)^(1/2))^(1/2)/x^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3059,-1,0,0,0.000000," ","integrate((a+c/x+b*(d/x)^(1/2))^(1/2)/x^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3060,-2,0,0,0.000000," ","integrate(x^m/(a+c/x+b*(d/x)^(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 Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.51Done","F(-2)",0
3061,-2,0,0,0.000000," ","integrate(x^2/(a+c/x+b*(d/x)^(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 Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.53Done","F(-2)",0
3062,-2,0,0,0.000000," ","integrate(x/(a+c/x+b*(d/x)^(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 Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.47Done","F(-2)",0
3063,1,218,0,0.591693," ","integrate(1/(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{a d^{2} x + \sqrt{d x} b d^{2} + c d^{2}} {\left(\frac{3 \, b}{a^{2}} - \frac{2 \, \sqrt{d x}}{a d}\right)} + \frac{{\left(3 \, b^{2} d^{2} - 4 \, a c d\right)} \log\left({\left| -b d^{2} - 2 \, \sqrt{a d} {\left(\sqrt{a d} \sqrt{d x} - \sqrt{a d^{2} x + \sqrt{d x} b d^{2} + c d^{2}}\right)} \right|}\right)}{\sqrt{a d} a^{2}} - \frac{3 \, b^{2} d^{2} \log\left({\left| -b d^{2} + 2 \, \sqrt{c d^{2}} \sqrt{a d} \right|}\right) - 4 \, a c d \log\left({\left| -b d^{2} + 2 \, \sqrt{c d^{2}} \sqrt{a d} \right|}\right) + 6 \, \sqrt{c d^{2}} \sqrt{a d} b}{\sqrt{a d} a^{2}}}{4 \, \sqrt{d} \mathrm{sgn}\left(x\right)}"," ",0,"-1/4*(2*sqrt(a*d^2*x + sqrt(d*x)*b*d^2 + c*d^2)*(3*b/a^2 - 2*sqrt(d*x)/(a*d)) + (3*b^2*d^2 - 4*a*c*d)*log(abs(-b*d^2 - 2*sqrt(a*d)*(sqrt(a*d)*sqrt(d*x) - sqrt(a*d^2*x + sqrt(d*x)*b*d^2 + c*d^2))))/(sqrt(a*d)*a^2) - (3*b^2*d^2*log(abs(-b*d^2 + 2*sqrt(c*d^2)*sqrt(a*d))) - 4*a*c*d*log(abs(-b*d^2 + 2*sqrt(c*d^2)*sqrt(a*d))) + 6*sqrt(c*d^2)*sqrt(a*d)*b)/(sqrt(a*d)*a^2))/(sqrt(d)*sgn(x))","A",0
3064,-2,0,0,0.000000," ","integrate(1/x/(a+c/x+b*(d/x)^(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 Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.42Done","F(-2)",0
3065,-2,0,0,0.000000," ","integrate(1/x^2/(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, checking for positivity of a root depending of parameters might return wrong sign: -dWarning, checking for positivity of a root depending of parameters might return wrong sign: d-1/d/abs(d)*d^2*2*(1/d/c*sqrt(a*d^2+b*d^2*sqrt(d/x)+c*d*d/x)+2*b*d/4/c/sqrt(c*d)*ln(abs(2*sqrt(c*d)*(sqrt(a*d^2+b*d^2*sqrt(d/x)+c*d*d/x)-sqrt(c*d)*sqrt(d/x))-d^2*b)))","F(-2)",0
3066,-2,0,0,0.000000," ","integrate(1/x^3/(a+c/x+b*(d/x)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, checking for positivity of a root depending of parameters might return wrong sign: -dWarning, checking for positivity of a root depending of parameters might return wrong sign: d-1/d/d/abs(d)*d^2*2*(2*((16*c^2/96/d/c^3*sqrt(d/x)-20*d*c*b/96/d/c^3)*sqrt(d/x)+(30*d^2*b^2-32*d*c*a)/96/d/c^3)*sqrt(a*d^2+b*d^2*sqrt(d/x)+c*d*d/x)+2*(-12*a*b*c*d^2+5*b^3*d^3)/32/c^3/sqrt(c*d)*ln(abs(2*sqrt(c*d)*(sqrt(a*d^2+b*d^2*sqrt(d/x)+c*d*d/x)-sqrt(c*d)*sqrt(d/x))-d^2*b)))","F(-2)",0
3067,-2,0,0,0.000000," ","integrate(1/x^4/(a+c/x+b*(d/x)^(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 Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.5Done","F(-2)",0
3068,1,11,0,0.166765," ","integrate((1/x+(1/x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4}{3} \, {\left(\sqrt{x} + 1\right)}^{\frac{3}{2}} - \frac{4}{3}"," ",0,"4/3*(sqrt(x) + 1)^(3/2) - 4/3","A",0
3069,1,74,0,0.199864," ","integrate((2+1/x+(1/x)^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{1}{16} \, \sqrt{2} {\left(2 \, \sqrt{2} - 7 \, \log\left(2 \, \sqrt{2} - 1\right)\right)} + \frac{1}{4} \, \sqrt{2 \, x + \sqrt{x} + 1} {\left(4 \, \sqrt{x} + 1\right)} - \frac{7}{16} \, \sqrt{2} \log\left(-2 \, \sqrt{2} {\left(\sqrt{2} \sqrt{x} - \sqrt{2 \, x + \sqrt{x} + 1}\right)} - 1\right)"," ",0,"-1/16*sqrt(2)*(2*sqrt(2) - 7*log(2*sqrt(2) - 1)) + 1/4*sqrt(2*x + sqrt(x) + 1)*(4*sqrt(x) + 1) - 7/16*sqrt(2)*log(-2*sqrt(2)*(sqrt(2)*sqrt(x) - sqrt(2*x + sqrt(x) + 1)) - 1)","A",0
3070,1,130,0,0.504277," ","integrate((c*x^n)^(1/n)*(a+b*(c*x^n)^(1/n))^p,x, algorithm=""giac"")","\frac{{\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b^{2} c^{\frac{2}{n}} p x^{2} + {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a b c^{\left(\frac{1}{n}\right)} p x + {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} b^{2} c^{\frac{2}{n}} x^{2} - {\left(b c^{\left(\frac{1}{n}\right)} x + a\right)}^{p} a^{2}}{b^{2} c^{\left(\frac{1}{n}\right)} p^{2} + 3 \, b^{2} c^{\left(\frac{1}{n}\right)} p + 2 \, b^{2} c^{\left(\frac{1}{n}\right)}}"," ",0,"((b*c^(1/n)*x + a)^p*b^2*c^(2/n)*p*x^2 + (b*c^(1/n)*x + a)^p*a*b*c^(1/n)*p*x + (b*c^(1/n)*x + a)^p*b^2*c^(2/n)*x^2 - (b*c^(1/n)*x + a)^p*a^2)/(b^2*c^(1/n)*p^2 + 3*b^2*c^(1/n)*p + 2*b^2*c^(1/n))","A",0
3071,1,60,0,0.269470," ","integrate((c*x^n)^(1/n)*(a+b*(c*x^n)^(1/n))^3,x, algorithm=""giac"")","\frac{1}{5} \, b^{3} c^{\frac{4}{n}} x^{5} + \frac{3}{4} \, a b^{2} c^{\frac{3}{n}} x^{4} + a^{2} b c^{\frac{2}{n}} x^{3} + \frac{1}{2} \, a^{3} c^{\left(\frac{1}{n}\right)} x^{2}"," ",0,"1/5*b^3*c^(4/n)*x^5 + 3/4*a*b^2*c^(3/n)*x^4 + a^2*b*c^(2/n)*x^3 + 1/2*a^3*c^(1/n)*x^2","A",0
3072,1,43,0,0.233062," ","integrate((c*x^n)^(1/n)*(a+b*(c*x^n)^(1/n))^2,x, algorithm=""giac"")","\frac{1}{4} \, b^{2} c^{\frac{3}{n}} x^{4} + \frac{2}{3} \, a b c^{\frac{2}{n}} x^{3} + \frac{1}{2} \, a^{2} c^{\left(\frac{1}{n}\right)} x^{2}"," ",0,"1/4*b^2*c^(3/n)*x^4 + 2/3*a*b*c^(2/n)*x^3 + 1/2*a^2*c^(1/n)*x^2","A",0
3073,1,25,0,0.190941," ","integrate((c*x^n)^(1/n)*(a+b*(c*x^n)^(1/n)),x, algorithm=""giac"")","\frac{1}{3} \, b c^{\frac{2}{n}} x^{3} + \frac{1}{2} \, a c^{\left(\frac{1}{n}\right)} x^{2}"," ",0,"1/3*b*c^(2/n)*x^3 + 1/2*a*c^(1/n)*x^2","A",0
3074,0,0,0,0.000000," ","integrate((c*x^n)^(1/n)/(a+b*(c*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{\left(c x^{n}\right)^{\left(\frac{1}{n}\right)}}{\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a}\,{d x}"," ",0,"integrate((c*x^n)^(1/n)/((c*x^n)^(1/n)*b + a), x)","F",0
3075,0,0,0,0.000000," ","integrate((c*x^n)^(1/n)/(a+b*(c*x^n)^(1/n))^2,x, algorithm=""giac"")","\int \frac{\left(c x^{n}\right)^{\left(\frac{1}{n}\right)}}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^n)^(1/n)/((c*x^n)^(1/n)*b + a)^2, x)","F",0
3076,0,0,0,0.000000," ","integrate((c*x^n)^(1/n)/(a+b*(c*x^n)^(1/n))^3,x, algorithm=""giac"")","\int \frac{\left(c x^{n}\right)^{\left(\frac{1}{n}\right)}}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{3}}\,{d x}"," ",0,"integrate((c*x^n)^(1/n)/((c*x^n)^(1/n)*b + a)^3, x)","F",0
3077,0,0,0,0.000000," ","integrate((c*x^n)^(1/n)/(a+b*(c*x^n)^(1/n))^4,x, algorithm=""giac"")","\int \frac{\left(c x^{n}\right)^{\left(\frac{1}{n}\right)}}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{4}}\,{d x}"," ",0,"integrate((c*x^n)^(1/n)/((c*x^n)^(1/n)*b + a)^4, x)","F",0
3078,0,0,0,0.000000," ","integrate((c*x^n)^(1/n)/(a+b*(c*x^n)^(1/n))^5,x, algorithm=""giac"")","\int \frac{\left(c x^{n}\right)^{\left(\frac{1}{n}\right)}}{{\left(\left(c x^{n}\right)^{\left(\frac{1}{n}\right)} b + a\right)}^{5}}\,{d x}"," ",0,"integrate((c*x^n)^(1/n)/((c*x^n)^(1/n)*b + a)^5, x)","F",0
