1,1,52,0,0.0482703,"\int \left(a x^3+b x^6\right)^{5/3} \, dx","Int[(a*x^3 + b*x^6)^(5/3),x]","\frac{\left(a x^3+b x^6\right)^{8/3}}{11 b x^5}-\frac{3 a \left(a x^3+b x^6\right)^{8/3}}{88 b^2 x^8}","\frac{\left(a x^3+b x^6\right)^{8/3}}{11 b x^5}-\frac{3 a \left(a x^3+b x^6\right)^{8/3}}{88 b^2 x^8}",1,"(-3*a*(a*x^3 + b*x^6)^(8/3))/(88*b^2*x^8) + (a*x^3 + b*x^6)^(8/3)/(11*b*x^5)","A",2,2,15,0.1333,1,"{2002, 2014}"
2,1,25,0,0.0048654,"\int \left(a x^3+b x^6\right)^{2/3} \, dx","Int[(a*x^3 + b*x^6)^(2/3),x]","\frac{\left(a x^3+b x^6\right)^{5/3}}{5 b x^5}","\frac{\left(a x^3+b x^6\right)^{5/3}}{5 b x^5}",1,"(a*x^3 + b*x^6)^(5/3)/(5*b*x^5)","A",1,1,15,0.06667,1,"{2000}"
3,1,23,0,0.0049352,"\int \frac{1}{\left(a x^3+b x^6\right)^{2/3}} \, dx","Int[(a*x^3 + b*x^6)^(-2/3),x]","-\frac{\sqrt[3]{a x^3+b x^6}}{a x^2}","-\frac{\sqrt[3]{a x^3+b x^6}}{a x^2}",1,"-((a*x^3 + b*x^6)^(1/3)/(a*x^2))","A",1,1,15,0.06667,1,"{2000}"
4,1,77,0,0.0566138,"\int \frac{1}{\left(a x^3+b x^6\right)^{5/3}} \, dx","Int[(a*x^3 + b*x^6)^(-5/3),x]","\frac{9 b \sqrt[3]{a x^3+b x^6}}{4 a^3 x^2}-\frac{3 \sqrt[3]{a x^3+b x^6}}{4 a^2 x^5}+\frac{1}{2 a x^2 \left(a x^3+b x^6\right)^{2/3}}","\frac{9 b \sqrt[3]{a x^3+b x^6}}{4 a^3 x^2}-\frac{3 \sqrt[3]{a x^3+b x^6}}{4 a^2 x^5}+\frac{1}{2 a x^2 \left(a x^3+b x^6\right)^{2/3}}",1,"1/(2*a*x^2*(a*x^3 + b*x^6)^(2/3)) - (3*(a*x^3 + b*x^6)^(1/3))/(4*a^2*x^5) + (9*b*(a*x^3 + b*x^6)^(1/3))/(4*a^3*x^2)","A",3,3,15,0.2000,1,"{2001, 2016, 2000}"
5,1,48,0,0.023464,"\int \frac{1}{-x^3+x^6} \, dx","Int[(-x^3 + x^6)^(-1),x]","\frac{1}{2 x^2}-\frac{1}{6} \log \left(x^2+x+1\right)+\frac{1}{3} \log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{2 x^2}-\frac{1}{6} \log \left(x^2+x+1\right)+\frac{1}{3} \log (1-x)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"1/(2*x^2) - ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3] + Log[1 - x]/3 - Log[1 + x + x^2]/6","A",8,8,11,0.7273,1,"{1593, 325, 200, 31, 634, 618, 204, 628}"
6,1,79,0,0.0230703,"\int x^5 \sqrt{a^2+2 a b x^3+b^2 x^6} \, dx","Int[x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{b x^9 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 \left(a+b x^3\right)}+\frac{a x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 \left(a+b x^3\right)}","\frac{b x^9 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 \left(a+b x^3\right)}+\frac{a x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 \left(a+b x^3\right)}",1,"(a*x^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(6*(a + b*x^3)) + (b*x^9*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(9*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 14}"
7,1,79,0,0.0233265,"\int x^4 \sqrt{a^2+2 a b x^3+b^2 x^6} \, dx","Int[x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{b x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{a x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}","\frac{b x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{a x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}",1,"(a*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*(a + b*x^3)) + (b*x^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 14}"
8,1,79,0,0.0235534,"\int x^3 \sqrt{a^2+2 a b x^3+b^2 x^6} \, dx","Int[x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{b x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{a x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}","\frac{b x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{a x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}",1,"(a*x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3)) + (b*x^7*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 14}"
9,1,36,0,0.0275715,"\int x^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \, dx","Int[x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{\left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 b}","\frac{\left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 b}",1,"((a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(6*b)","A",2,2,26,0.07692,1,"{1352, 609}"
10,1,79,0,0.0180364,"\int x \sqrt{a^2+2 a b x^3+b^2 x^6} \, dx","Int[x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{b x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}+\frac{a x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}","\frac{b x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}+\frac{a x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}",1,"(a*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (b*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*(a + b*x^3))","A",3,2,24,0.08333,1,"{1355, 14}"
11,1,74,0,0.0123292,"\int \sqrt{a^2+2 a b x^3+b^2 x^6} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{b x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{a x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","\frac{b x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{a x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"(a*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (b*x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3))","A",2,1,22,0.04545,1,"{1343}"
12,1,75,0,0.0195575,"\int \frac{\sqrt{a^2+2 a b x^3+b^2 x^6}}{x} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]/x,x]","\frac{b x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{a \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","\frac{b x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{a \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"(b*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*(a + b*x^3)) + (a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",3,2,26,0.07692,1,"{1355, 14}"
13,1,77,0,0.021185,"\int \frac{\sqrt{a^2+2 a b x^3+b^2 x^6}}{x^2} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]/x^2,x]","\frac{b x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}","\frac{b x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}",1,"-((a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3))) + (b*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 14}"
14,1,74,0,0.020172,"\int \frac{\sqrt{a^2+2 a b x^3+b^2 x^6}}{x^3} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]/x^3,x]","\frac{b x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}","\frac{b x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^2*(a + b*x^3)) + (b*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3)","A",3,2,26,0.07692,1,"{1355, 14}"
15,1,75,0,0.0209114,"\int \frac{\sqrt{a^2+2 a b x^3+b^2 x^6}}{x^4} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]/x^4,x]","\frac{b \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}","\frac{b \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*x^3*(a + b*x^3)) + (b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",3,2,26,0.07692,1,"{1355, 14}"
16,1,77,0,0.0209954,"\int \frac{\sqrt{a^2+2 a b x^3+b^2 x^6}}{x^5} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]/x^5,x]","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^4*(a + b*x^3)) - (b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 14}"
17,1,79,0,0.0221565,"\int \frac{\sqrt{a^2+2 a b x^3+b^2 x^6}}{x^6} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]/x^6,x]","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*x^5*(a + b*x^3)) - (b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^2*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 14}"
18,1,79,0,0.0216519,"\int \frac{\sqrt{a^2+2 a b x^3+b^2 x^6}}{x^7} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]/x^7,x]","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 x^6 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 x^6 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(6*x^6*(a + b*x^3)) - (b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*x^3*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 14}"
19,1,79,0,0.0223182,"\int \frac{\sqrt{a^2+2 a b x^3+b^2 x^6}}{x^8} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]/x^8,x]","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3)) - (b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^4*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 14}"
20,1,79,0,0.0211998,"\int \frac{\sqrt{a^2+2 a b x^3+b^2 x^6}}{x^9} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]/x^9,x]","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*x^8*(a + b*x^3)) - (b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*x^5*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 14}"
21,1,79,0,0.0216881,"\int \frac{\sqrt{a^2+2 a b x^3+b^2 x^6}}{x^{10}} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]/x^10,x]","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 x^9 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 x^6 \left(a+b x^3\right)}","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 x^9 \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 x^6 \left(a+b x^3\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(9*x^9*(a + b*x^3)) - (b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(6*x^6*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 14}"
22,1,79,0,0.0222281,"\int \frac{\sqrt{a^2+2 a b x^3+b^2 x^6}}{x^{11}} \, dx","Int[Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]/x^11,x]","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 x^{10} \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}","-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 x^{10} \left(a+b x^3\right)}-\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(10*x^10*(a + b*x^3)) - (b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 14}"
23,1,167,0,0.042637,"\int x^9 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2} \, dx","Int[x^9*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{b^3 x^{19} \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 \left(a+b x^3\right)}+\frac{3 a b^2 x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 \left(a+b x^3\right)}+\frac{3 a^2 b x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{a^3 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 \left(a+b x^3\right)}","\frac{b^3 x^{19} \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 \left(a+b x^3\right)}+\frac{3 a b^2 x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 \left(a+b x^3\right)}+\frac{3 a^2 b x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{a^3 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 \left(a+b x^3\right)}",1,"(a^3*x^10*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(10*(a + b*x^3)) + (3*a^2*b*x^13*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*(a + b*x^3)) + (3*a*b^2*x^16*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(16*(a + b*x^3)) + (b^3*x^19*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(19*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
24,1,167,0,0.0532489,"\int x^8 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2} \, dx","Int[x^8*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{b^3 x^{18} \sqrt{a^2+2 a b x^3+b^2 x^6}}{18 \left(a+b x^3\right)}+\frac{a b^2 x^{15} \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}+\frac{a^2 b x^{12} \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{a^3 x^9 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 \left(a+b x^3\right)}","\frac{\sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^5}{18 b^3}-\frac{2 a \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^4}{15 b^3}+\frac{a^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^3}{12 b^3}",1,"(a^3*x^9*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(9*(a + b*x^3)) + (a^2*b*x^12*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3)) + (a*b^2*x^15*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*(a + b*x^3)) + (b^3*x^18*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(18*(a + b*x^3))","A",4,3,26,0.1154,1,"{1355, 266, 43}"
25,1,167,0,0.0426231,"\int x^7 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2} \, dx","Int[x^7*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{b^3 x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{3 a b^2 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}+\frac{3 a^2 b x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{a^3 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}","\frac{b^3 x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{3 a b^2 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}+\frac{3 a^2 b x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{a^3 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}",1,"(a^3*x^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*(a + b*x^3)) + (3*a^2*b*x^11*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*(a + b*x^3)) + (3*a*b^2*x^14*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(14*(a + b*x^3)) + (b^3*x^17*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(17*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
26,1,167,0,0.0408195,"\int x^6 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2} \, dx","Int[x^6*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{b^3 x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 \left(a+b x^3\right)}+\frac{3 a b^2 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{3 a^2 b x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 \left(a+b x^3\right)}+\frac{a^3 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}","\frac{b^3 x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 \left(a+b x^3\right)}+\frac{3 a b^2 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{3 a^2 b x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 \left(a+b x^3\right)}+\frac{a^3 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}",1,"(a^3*x^7*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*(a + b*x^3)) + (3*a^2*b*x^10*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(10*(a + b*x^3)) + (3*a*b^2*x^13*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*(a + b*x^3)) + (b^3*x^16*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(16*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
27,1,78,0,0.050472,"\int x^5 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2} \, dx","Int[x^5*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{\left(a+b x^3\right)^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{15 b^2}-\frac{a \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 b^2}","\frac{\left(a+b x^3\right)^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{15 b^2}-\frac{a \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 b^2}",1,"-(a*(a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(12*b^2) + ((a + b*x^3)^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(15*b^2)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
28,1,167,0,0.0413745,"\int x^4 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2} \, dx","Int[x^4*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{b^3 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}+\frac{3 a b^2 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{3 a^2 b x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{a^3 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}","\frac{b^3 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}+\frac{3 a b^2 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{3 a^2 b x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{a^3 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}",1,"(a^3*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*(a + b*x^3)) + (3*a^2*b*x^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*(a + b*x^3)) + (3*a*b^2*x^11*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*(a + b*x^3)) + (b^3*x^14*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(14*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
29,1,167,0,0.0409833,"\int x^3 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2} \, dx","Int[x^3*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{b^3 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{3 a b^2 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 \left(a+b x^3\right)}+\frac{3 a^2 b x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{a^3 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}","\frac{b^3 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{3 a b^2 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 \left(a+b x^3\right)}+\frac{3 a^2 b x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{a^3 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}",1,"(a^3*x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3)) + (3*a^2*b*x^7*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*(a + b*x^3)) + (3*a*b^2*x^10*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(10*(a + b*x^3)) + (b^3*x^13*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
30,1,36,0,0.02958,"\int x^2 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2} \, dx","Int[x^2*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{\left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{12 b}","\frac{\left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{12 b}",1,"((a + b*x^3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2))/(12*b)","A",2,2,26,0.07692,1,"{1352, 609}"
31,1,167,0,0.0378921,"\int x \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2} \, dx","Int[x*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{b^3 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{3 a b^2 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{3 a^2 b x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}+\frac{a^3 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}","\frac{b^3 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{3 a b^2 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{3 a^2 b x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}+\frac{a^3 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}",1,"(a^3*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (3*a^2*b*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*(a + b*x^3)) + (3*a*b^2*x^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*(a + b*x^3)) + (b^3*x^11*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*(a + b*x^3))","A",3,2,24,0.08333,1,"{1355, 270}"
32,1,162,0,0.0327202,"\int \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{b^3 x^{10} \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{10 \left(a+b x^3\right)^3}+\frac{3 a b^2 x^7 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{7 \left(a+b x^3\right)^3}+\frac{3 a^2 b x^4 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{4 \left(a+b x^3\right)^3}+\frac{a^3 x \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{\left(a+b x^3\right)^3}","\frac{b^3 x^{10} \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{10 \left(a+b x^3\right)^3}+\frac{3 a b^2 x^7 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{7 \left(a+b x^3\right)^3}+\frac{3 a^2 b x^4 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{4 \left(a+b x^3\right)^3}+\frac{a^3 x \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{\left(a+b x^3\right)^3}",1,"(a^3*x*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2))/(a + b*x^3)^3 + (3*a^2*b*x^4*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2))/(4*(a + b*x^3)^3) + (3*a*b^2*x^7*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2))/(7*(a + b*x^3)^3) + (b^3*x^10*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2))/(10*(a + b*x^3)^3)","A",3,2,22,0.09091,1,"{1343, 194}"
33,1,160,0,0.0477448,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x,x]","\frac{b^3 x^9 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 \left(a+b x^3\right)}+\frac{a b^2 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{a^2 b x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{a^3 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","\frac{b^3 x^9 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 \left(a+b x^3\right)}+\frac{a b^2 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{a^2 b x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{a^3 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"(a^2*b*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (a*b^2*x^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (b^3*x^9*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(9*(a + b*x^3)) + (a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
34,1,165,0,0.0424294,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^2} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^2,x]","\frac{b^3 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{3 a b^2 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}+\frac{3 a^2 b x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}","\frac{b^3 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{3 a b^2 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}+\frac{3 a^2 b x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}",1,"-((a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3))) + (3*a^2*b*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (3*a*b^2*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*(a + b*x^3)) + (b^3*x^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
35,1,163,0,0.042097,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^3} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^3,x]","\frac{b^3 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{3 a b^2 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{3 a^2 b x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}","\frac{b^3 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{3 a b^2 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{3 a^2 b x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^2*(a + b*x^3)) + (3*a^2*b*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (3*a*b^2*x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3)) + (b^3*x^7*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
36,1,161,0,0.0475871,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^4} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^4,x]","\frac{b^3 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 \left(a+b x^3\right)}+\frac{a b^2 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}+\frac{3 a^2 b \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","\frac{b^3 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 \left(a+b x^3\right)}+\frac{a b^2 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}+\frac{3 a^2 b \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*x^3*(a + b*x^3)) + (a*b^2*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (b^3*x^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(6*(a + b*x^3)) + (3*a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
37,1,165,0,0.041809,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^5} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^5,x]","\frac{b^3 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}+\frac{3 a b^2 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}","\frac{b^3 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}+\frac{3 a b^2 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^4*(a + b*x^3)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3)) + (3*a*b^2*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (b^3*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
38,1,163,0,0.0407628,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^6} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^6,x]","\frac{b^3 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{3 a b^2 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}","\frac{b^3 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{3 a b^2 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*x^5*(a + b*x^3)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^2*(a + b*x^3)) + (3*a*b^2*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (b^3*x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
39,1,162,0,0.0465453,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^7} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^7,x]","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 x^6 \left(a+b x^3\right)}-\frac{a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^3 \left(a+b x^3\right)}+\frac{b^3 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{3 a b^2 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 x^6 \left(a+b x^3\right)}-\frac{a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^3 \left(a+b x^3\right)}+\frac{b^3 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{3 a b^2 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(6*x^6*(a + b*x^3)) - (a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x^3*(a + b*x^3)) + (b^3*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*(a + b*x^3)) + (3*a*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
40,1,165,0,0.040594,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^8} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^8,x]","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}+\frac{b^3 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}+\frac{b^3 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^4*(a + b*x^3)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3)) + (b^3*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
41,1,162,0,0.0409398,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^9} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^9,x]","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}+\frac{b^3 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}+\frac{b^3 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*x^8*(a + b*x^3)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*x^5*(a + b*x^3)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^2*(a + b*x^3)) + (b^3*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3)","A",3,2,26,0.07692,1,"{1355, 270}"
42,1,161,0,0.0464384,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^{10}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^10,x]","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 x^9 \left(a+b x^3\right)}-\frac{a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^6 \left(a+b x^3\right)}-\frac{a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^3 \left(a+b x^3\right)}+\frac{b^3 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 x^9 \left(a+b x^3\right)}-\frac{a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^6 \left(a+b x^3\right)}-\frac{a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^3 \left(a+b x^3\right)}+\frac{b^3 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(9*x^9*(a + b*x^3)) - (a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^6*(a + b*x^3)) - (a*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x^3*(a + b*x^3)) + (b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
43,1,165,0,0.0402338,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^{11}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^11,x]","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 x^{10} \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}-\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 x^{10} \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}-\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(10*x^10*(a + b*x^3)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^4*(a + b*x^3)) - (b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
44,1,167,0,0.040581,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^{12}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^12,x]","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}-\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}-\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*x^11*(a + b*x^3)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*x^8*(a + b*x^3)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*x^5*(a + b*x^3)) - (b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^2*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
45,1,41,0,0.0182668,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^{13}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^13,x]","-\frac{\left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 a x^{12}}","-\frac{\left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 a x^{12}}",1,"-((a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(12*a*x^12)","A",2,2,26,0.07692,1,"{1355, 264}"
46,1,167,0,0.0412958,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^{14}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^14,x]","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 x^{10} \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 x^{10} \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*x^13*(a + b*x^3)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(10*x^10*(a + b*x^3)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3)) - (b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^4*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
47,1,167,0,0.0409204,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^{15}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^15,x]","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 x^{14} \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 x^{14} \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(14*x^14*(a + b*x^3)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*x^11*(a + b*x^3)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*x^8*(a + b*x^3)) - (b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*x^5*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
48,1,84,0,0.0396448,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^{16}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^16,x]","\frac{b \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{60 a^2 x^{12}}-\frac{\left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{15 a x^{15}}","\frac{b \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{60 a^2 x^{12}}-\frac{\left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{15 a x^{15}}",1,"-((a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(15*a*x^15) + (b*(a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(60*a^2*x^12)","A",4,4,26,0.1538,1,"{1355, 266, 45, 37}"
49,1,167,0,0.0401521,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}{x^{17}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)/x^17,x]","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 x^{16} \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 x^{10} \left(a+b x^3\right)}-\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}","-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 x^{16} \left(a+b x^3\right)}-\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 x^{10} \left(a+b x^3\right)}-\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(16*x^16*(a + b*x^3)) - (3*a^2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*x^13*(a + b*x^3)) - (3*a*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(10*x^10*(a + b*x^3)) - (b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
50,1,255,0,0.0636303,"\int x^{13} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^13*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{b^5 x^{29} \sqrt{a^2+2 a b x^3+b^2 x^6}}{29 \left(a+b x^3\right)}+\frac{5 a b^4 x^{26} \sqrt{a^2+2 a b x^3+b^2 x^6}}{26 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^{23} \sqrt{a^2+2 a b x^3+b^2 x^6}}{23 \left(a+b x^3\right)}+\frac{a^3 b^2 x^{20} \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{5 a^4 b x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{a^5 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}","\frac{b^5 x^{29} \sqrt{a^2+2 a b x^3+b^2 x^6}}{29 \left(a+b x^3\right)}+\frac{5 a b^4 x^{26} \sqrt{a^2+2 a b x^3+b^2 x^6}}{26 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^{23} \sqrt{a^2+2 a b x^3+b^2 x^6}}{23 \left(a+b x^3\right)}+\frac{a^3 b^2 x^{20} \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{5 a^4 b x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{a^5 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}",1,"(a^5*x^14*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(14*(a + b*x^3)) + (5*a^4*b*x^17*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(17*(a + b*x^3)) + (a^3*b^2*x^20*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (10*a^2*b^3*x^23*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(23*(a + b*x^3)) + (5*a*b^4*x^26*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(26*(a + b*x^3)) + (b^5*x^29*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(29*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
51,1,255,0,0.0584196,"\int x^{12} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^12*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{b^5 x^{28} \sqrt{a^2+2 a b x^3+b^2 x^6}}{28 \left(a+b x^3\right)}+\frac{a b^4 x^{25} \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^{22} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x^{19} \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 \left(a+b x^3\right)}+\frac{5 a^4 b x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 \left(a+b x^3\right)}+\frac{a^5 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}","\frac{b^5 x^{28} \sqrt{a^2+2 a b x^3+b^2 x^6}}{28 \left(a+b x^3\right)}+\frac{a b^4 x^{25} \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^{22} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x^{19} \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 \left(a+b x^3\right)}+\frac{5 a^4 b x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 \left(a+b x^3\right)}+\frac{a^5 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}",1,"(a^5*x^13*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*(a + b*x^3)) + (5*a^4*b*x^16*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(16*(a + b*x^3)) + (10*a^3*b^2*x^19*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(19*(a + b*x^3)) + (5*a^2*b^3*x^22*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*(a + b*x^3)) + (a*b^4*x^25*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*(a + b*x^3)) + (b^5*x^28*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(28*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
52,1,160,0,0.120288,"\int x^{11} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^11*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{\sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^8}{27 b^4}-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^7}{8 b^4}+\frac{a^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^6}{7 b^4}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^5}{18 b^4}","\frac{\sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^8}{27 b^4}-\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^7}{8 b^4}+\frac{a^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^6}{7 b^4}-\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^5}{18 b^4}",1,"-(a^3*(a + b*x^3)^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(18*b^4) + (a^2*(a + b*x^3)^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*b^4) - (a*(a + b*x^3)^7*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*b^4) + ((a + b*x^3)^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(27*b^4)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
53,1,255,0,0.0608434,"\int x^{10} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^10*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{b^5 x^{26} \sqrt{a^2+2 a b x^3+b^2 x^6}}{26 \left(a+b x^3\right)}+\frac{5 a b^4 x^{23} \sqrt{a^2+2 a b x^3+b^2 x^6}}{23 \left(a+b x^3\right)}+\frac{a^2 b^3 x^{20} \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{5 a^4 b x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}+\frac{a^5 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}","\frac{b^5 x^{26} \sqrt{a^2+2 a b x^3+b^2 x^6}}{26 \left(a+b x^3\right)}+\frac{5 a b^4 x^{23} \sqrt{a^2+2 a b x^3+b^2 x^6}}{23 \left(a+b x^3\right)}+\frac{a^2 b^3 x^{20} \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{5 a^4 b x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}+\frac{a^5 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}",1,"(a^5*x^11*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*(a + b*x^3)) + (5*a^4*b*x^14*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(14*(a + b*x^3)) + (10*a^3*b^2*x^17*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(17*(a + b*x^3)) + (a^2*b^3*x^20*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (5*a*b^4*x^23*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(23*(a + b*x^3)) + (b^5*x^26*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(26*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
54,1,255,0,0.0573355,"\int x^9 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^9*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{b^5 x^{25} \sqrt{a^2+2 a b x^3+b^2 x^6}}{25 \left(a+b x^3\right)}+\frac{5 a b^4 x^{22} \sqrt{a^2+2 a b x^3+b^2 x^6}}{22 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^{19} \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 \left(a+b x^3\right)}+\frac{5 a^3 b^2 x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{5 a^4 b x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{a^5 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 \left(a+b x^3\right)}","\frac{b^5 x^{25} \sqrt{a^2+2 a b x^3+b^2 x^6}}{25 \left(a+b x^3\right)}+\frac{5 a b^4 x^{22} \sqrt{a^2+2 a b x^3+b^2 x^6}}{22 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^{19} \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 \left(a+b x^3\right)}+\frac{5 a^3 b^2 x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{5 a^4 b x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{a^5 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 \left(a+b x^3\right)}",1,"(a^5*x^10*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(10*(a + b*x^3)) + (5*a^4*b*x^13*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*(a + b*x^3)) + (5*a^3*b^2*x^16*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*(a + b*x^3)) + (10*a^2*b^3*x^19*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(19*(a + b*x^3)) + (5*a*b^4*x^22*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(22*(a + b*x^3)) + (b^5*x^25*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(25*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
55,1,119,0,0.0903906,"\int x^8 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^8*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{\sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^7}{24 b^3}-\frac{2 a \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^6}{21 b^3}+\frac{a^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^5}{18 b^3}","\frac{\sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^7}{24 b^3}-\frac{2 a \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^6}{21 b^3}+\frac{a^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^5}{18 b^3}",1,"(a^2*(a + b*x^3)^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(18*b^3) - (2*a*(a + b*x^3)^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(21*b^3) + ((a + b*x^3)^7*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(24*b^3)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
56,1,255,0,0.0602653,"\int x^7 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^7*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{b^5 x^{23} \sqrt{a^2+2 a b x^3+b^2 x^6}}{23 \left(a+b x^3\right)}+\frac{a b^4 x^{20} \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{5 a^3 b^2 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{5 a^4 b x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{a^5 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}","\frac{b^5 x^{23} \sqrt{a^2+2 a b x^3+b^2 x^6}}{23 \left(a+b x^3\right)}+\frac{a b^4 x^{20} \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{5 a^3 b^2 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{5 a^4 b x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{a^5 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}",1,"(a^5*x^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*(a + b*x^3)) + (5*a^4*b*x^11*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*(a + b*x^3)) + (5*a^3*b^2*x^14*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*(a + b*x^3)) + (10*a^2*b^3*x^17*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(17*(a + b*x^3)) + (a*b^4*x^20*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3)) + (b^5*x^23*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(23*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
57,1,255,0,0.0594273,"\int x^6 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^6*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{b^5 x^{22} \sqrt{a^2+2 a b x^3+b^2 x^6}}{22 \left(a+b x^3\right)}+\frac{5 a b^4 x^{19} \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{a^4 b x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{a^5 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}","\frac{b^5 x^{22} \sqrt{a^2+2 a b x^3+b^2 x^6}}{22 \left(a+b x^3\right)}+\frac{5 a b^4 x^{19} \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{a^4 b x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{a^5 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}",1,"(a^5*x^7*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*(a + b*x^3)) + (a^4*b*x^10*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (10*a^3*b^2*x^13*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*(a + b*x^3)) + (5*a^2*b^3*x^16*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*(a + b*x^3)) + (5*a*b^4*x^19*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(19*(a + b*x^3)) + (b^5*x^22*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(22*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
58,1,78,0,0.056291,"\int x^5 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^5*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{\left(a+b x^3\right)^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{21 b^2}-\frac{a \left(a+b x^3\right)^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{18 b^2}","\frac{\left(a+b x^3\right)^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{21 b^2}-\frac{a \left(a+b x^3\right)^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{18 b^2}",1,"-(a*(a + b*x^3)^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(18*b^2) + ((a + b*x^3)^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(21*b^2)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
59,1,255,0,0.0588751,"\int x^4 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^4*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{b^5 x^{20} \sqrt{a^2+2 a b x^3+b^2 x^6}}{20 \left(a+b x^3\right)}+\frac{5 a b^4 x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{5 a^4 b x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{a^5 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}","\frac{b^5 x^{20} \sqrt{a^2+2 a b x^3+b^2 x^6}}{20 \left(a+b x^3\right)}+\frac{5 a b^4 x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{5 a^4 b x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{a^5 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}",1,"(a^5*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*(a + b*x^3)) + (5*a^4*b*x^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*(a + b*x^3)) + (10*a^3*b^2*x^11*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*(a + b*x^3)) + (5*a^2*b^3*x^14*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*(a + b*x^3)) + (5*a*b^4*x^17*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(17*(a + b*x^3)) + (b^5*x^20*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(20*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
60,1,252,0,0.0573269,"\int x^3 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^3*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{b^5 x^{19} \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 \left(a+b x^3\right)}+\frac{5 a b^4 x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{a^3 b^2 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{5 a^4 b x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{a^5 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}","\frac{b^5 x^{19} \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 \left(a+b x^3\right)}+\frac{5 a b^4 x^{16} \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{a^3 b^2 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{5 a^4 b x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{a^5 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}",1,"(a^5*x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3)) + (5*a^4*b*x^7*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*(a + b*x^3)) + (a^3*b^2*x^10*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (10*a^2*b^3*x^13*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*(a + b*x^3)) + (5*a*b^4*x^16*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(16*(a + b*x^3)) + (b^5*x^19*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(19*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
61,1,36,0,0.0289644,"\int x^2 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x^2*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{\left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{18 b}","\frac{\left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{18 b}",1,"((a + b*x^3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2))/(18*b)","A",2,2,26,0.07692,1,"{1352, 609}"
62,1,252,0,0.0544888,"\int x \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[x*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{b^5 x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{5 a b^4 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{5 a^3 b^2 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{a^4 b x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{a^5 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}","\frac{b^5 x^{17} \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 \left(a+b x^3\right)}+\frac{5 a b^4 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{5 a^3 b^2 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{a^4 b x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{a^5 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}",1,"(a^5*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (a^4*b*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (5*a^3*b^2*x^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3)) + (10*a^2*b^3*x^11*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*(a + b*x^3)) + (5*a*b^4*x^14*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(14*(a + b*x^3)) + (b^5*x^17*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(17*(a + b*x^3))","A",3,2,24,0.08333,1,"{1355, 270}"
63,1,247,0,0.0508262,"\int \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{b^5 x^{16} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{16 \left(a+b x^3\right)^5}+\frac{5 a b^4 x^{13} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{13 \left(a+b x^3\right)^5}+\frac{a^2 b^3 x^{10} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{\left(a+b x^3\right)^5}+\frac{10 a^3 b^2 x^7 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{7 \left(a+b x^3\right)^5}+\frac{5 a^4 b x^4 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{4 \left(a+b x^3\right)^5}+\frac{a^5 x \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{\left(a+b x^3\right)^5}","\frac{b^5 x^{16} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{16 \left(a+b x^3\right)^5}+\frac{5 a b^4 x^{13} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{13 \left(a+b x^3\right)^5}+\frac{a^2 b^3 x^{10} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{\left(a+b x^3\right)^5}+\frac{10 a^3 b^2 x^7 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{7 \left(a+b x^3\right)^5}+\frac{5 a^4 b x^4 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{4 \left(a+b x^3\right)^5}+\frac{a^5 x \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{\left(a+b x^3\right)^5}",1,"(a^5*x*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2))/(a + b*x^3)^5 + (5*a^4*b*x^4*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2))/(4*(a + b*x^3)^5) + (10*a^3*b^2*x^7*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2))/(7*(a + b*x^3)^5) + (a^2*b^3*x^10*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2))/(a + b*x^3)^5 + (5*a*b^4*x^13*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2))/(13*(a + b*x^3)^5) + (b^5*x^16*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2))/(16*(a + b*x^3)^5)","A",3,2,22,0.09091,1,"{1343, 194}"
64,1,251,0,0.0686626,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x,x]","\frac{b^5 x^{15} \sqrt{a^2+2 a b x^3+b^2 x^6}}{15 \left(a+b x^3\right)}+\frac{5 a b^4 x^{12} \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^9 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 \left(a+b x^3\right)}+\frac{5 a^3 b^2 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{5 a^4 b x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{a^5 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","\frac{b^5 x^{15} \sqrt{a^2+2 a b x^3+b^2 x^6}}{15 \left(a+b x^3\right)}+\frac{5 a b^4 x^{12} \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^9 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 \left(a+b x^3\right)}+\frac{5 a^3 b^2 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{5 a^4 b x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{a^5 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"(5*a^4*b*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*(a + b*x^3)) + (5*a^3*b^2*x^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*(a + b*x^3)) + (10*a^2*b^3*x^9*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(9*(a + b*x^3)) + (5*a*b^4*x^12*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(12*(a + b*x^3)) + (b^5*x^15*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(15*(a + b*x^3)) + (a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
65,1,251,0,0.0605986,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^2} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^2,x]","\frac{b^5 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}+\frac{5 a b^4 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{2 a^3 b^2 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{5 a^4 b x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}","\frac{b^5 x^{14} \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 \left(a+b x^3\right)}+\frac{5 a b^4 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{2 a^3 b^2 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{5 a^4 b x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}",1,"-((a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3))) + (5*a^4*b*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (2*a^3*b^2*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (5*a^2*b^3*x^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3)) + (5*a*b^4*x^11*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*(a + b*x^3)) + (b^5*x^14*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(14*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
66,1,251,0,0.0589937,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^3} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^3,x]","\frac{b^5 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{a b^4 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{5 a^3 b^2 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{5 a^4 b x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}","\frac{b^5 x^{13} \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 \left(a+b x^3\right)}+\frac{a b^4 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{5 a^3 b^2 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{5 a^4 b x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^2*(a + b*x^3)) + (5*a^4*b*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (5*a^3*b^2*x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (10*a^2*b^3*x^7*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*(a + b*x^3)) + (a*b^4*x^10*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (b^5*x^13*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
67,1,252,0,0.0735974,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^4} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^4,x]","\frac{b^5 x^{12} \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 \left(a+b x^3\right)}+\frac{5 a b^4 x^9 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}+\frac{5 a^4 b \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","\frac{b^5 x^{12} \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 \left(a+b x^3\right)}+\frac{5 a b^4 x^9 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}+\frac{5 a^4 b \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*x^3*(a + b*x^3)) + (10*a^3*b^2*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*(a + b*x^3)) + (5*a^2*b^3*x^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*(a + b*x^3)) + (5*a*b^4*x^9*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(9*(a + b*x^3)) + (b^5*x^12*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(12*(a + b*x^3)) + (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
68,1,249,0,0.0593276,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^5} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^5,x]","\frac{b^5 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{5 a b^4 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{2 a^2 b^3 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{5 a^3 b^2 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}","\frac{b^5 x^{11} \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 \left(a+b x^3\right)}+\frac{5 a b^4 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{2 a^2 b^3 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{5 a^3 b^2 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^4*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3)) + (5*a^3*b^2*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (2*a^2*b^3*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (5*a*b^4*x^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*(a + b*x^3)) + (b^5*x^11*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
69,1,251,0,0.0575716,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^6} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^6,x]","\frac{b^5 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 \left(a+b x^3\right)}+\frac{5 a b^4 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}","\frac{b^5 x^{10} \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 \left(a+b x^3\right)}+\frac{5 a b^4 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{5 a^2 b^3 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{10 a^3 b^2 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*x^5*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^2*(a + b*x^3)) + (10*a^3*b^2*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (5*a^2*b^3*x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (5*a*b^4*x^7*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*(a + b*x^3)) + (b^5*x^10*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(10*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
70,1,252,0,0.0733688,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^7} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^7,x]","\frac{b^5 x^9 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 \left(a+b x^3\right)}+\frac{5 a b^4 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 x^6 \left(a+b x^3\right)}+\frac{10 a^3 b^2 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","\frac{b^5 x^9 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 \left(a+b x^3\right)}+\frac{5 a b^4 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 x^6 \left(a+b x^3\right)}+\frac{10 a^3 b^2 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(6*x^6*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*x^3*(a + b*x^3)) + (10*a^2*b^3*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*(a + b*x^3)) + (5*a*b^4*x^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(6*(a + b*x^3)) + (b^5*x^9*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(9*(a + b*x^3)) + (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
71,1,248,0,0.058232,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^8} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^8,x]","\frac{b^5 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{a b^4 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{5 a^2 b^3 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}","\frac{b^5 x^8 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 \left(a+b x^3\right)}+\frac{a b^4 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{5 a^2 b^3 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^4*(a + b*x^3)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3)) + (5*a^2*b^3*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (a*b^4*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (b^5*x^8*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
72,1,247,0,0.059024,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^9} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^9,x]","\frac{b^5 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{5 a b^4 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^2 \left(a+b x^3\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^5 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}","\frac{b^5 x^7 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 \left(a+b x^3\right)}+\frac{5 a b^4 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}+\frac{10 a^2 b^3 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^2 \left(a+b x^3\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^5 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*x^8*(a + b*x^3)) - (a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x^5*(a + b*x^3)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x^2*(a + b*x^3)) + (10*a^2*b^3*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (5*a*b^4*x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3)) + (b^5*x^7*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
73,1,252,0,0.0711647,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{10}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^10,x]","\frac{b^5 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 \left(a+b x^3\right)}+\frac{5 a b^4 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 x^6 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 x^9 \left(a+b x^3\right)}+\frac{10 a^2 b^3 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","\frac{b^5 x^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 \left(a+b x^3\right)}+\frac{5 a b^4 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{6 x^6 \left(a+b x^3\right)}-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 x^9 \left(a+b x^3\right)}+\frac{10 a^2 b^3 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(9*x^9*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(6*x^6*(a + b*x^3)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*x^3*(a + b*x^3)) + (5*a*b^4*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*(a + b*x^3)) + (b^5*x^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(6*(a + b*x^3)) + (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
74,1,253,0,0.0623355,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{11}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^11,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 x^{10} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^4 \left(a+b x^3\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}+\frac{5 a b^4 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{b^5 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{10 x^{10} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^4 \left(a+b x^3\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}+\frac{5 a b^4 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}+\frac{b^5 x^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(10*x^10*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^4*(a + b*x^3)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3)) + (5*a*b^4*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3)) + (b^5*x^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
75,1,247,0,0.0601738,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{12}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^12,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{2 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^5 \left(a+b x^3\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^2 \left(a+b x^3\right)}+\frac{5 a b^4 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{b^5 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{2 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^5 \left(a+b x^3\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^2 \left(a+b x^3\right)}+\frac{5 a b^4 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}+\frac{b^5 x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*x^11*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*x^8*(a + b*x^3)) - (2*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x^5*(a + b*x^3)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x^2*(a + b*x^3)) + (5*a*b^4*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3) + (b^5*x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
76,1,252,0,0.0705895,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{13}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^13,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 x^{12} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 x^9 \left(a+b x^3\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^6 \left(a+b x^3\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}+\frac{b^5 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{5 a b^4 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 x^{12} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 x^9 \left(a+b x^3\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^6 \left(a+b x^3\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}+\frac{b^5 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 \left(a+b x^3\right)}+\frac{5 a b^4 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(12*x^12*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(9*x^9*(a + b*x^3)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*x^6*(a + b*x^3)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*x^3*(a + b*x^3)) + (b^5*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*(a + b*x^3)) + (5*a*b^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
77,1,253,0,0.0594934,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{14}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^14,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^{10} \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^4 \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}+\frac{b^5 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^{10} \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^4 \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}+\frac{b^5 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*x^13*(a + b*x^3)) - (a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^10*(a + b*x^3)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^4*(a + b*x^3)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3)) + (b^5*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
78,1,248,0,0.0598894,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{15}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^15,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 x^{14} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^8 \left(a+b x^3\right)}-\frac{2 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^5 \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}+\frac{b^5 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 x^{14} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^8 \left(a+b x^3\right)}-\frac{2 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^5 \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}+\frac{b^5 x \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(14*x^14*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*x^11*(a + b*x^3)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^8*(a + b*x^3)) - (2*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x^5*(a + b*x^3)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^2*(a + b*x^3)) + (b^5*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(a + b*x^3)","A",3,2,26,0.07692,1,"{1355, 270}"
79,1,251,0,0.069104,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{16}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^16,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{15 x^{15} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 x^{12} \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 x^9 \left(a+b x^3\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^6 \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}+\frac{b^5 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{15 x^{15} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{12 x^{12} \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{9 x^9 \left(a+b x^3\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^6 \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{3 x^3 \left(a+b x^3\right)}+\frac{b^5 \log (x) \sqrt{a^2+2 a b x^3+b^2 x^6}}{a+b x^3}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(15*x^15*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(12*x^12*(a + b*x^3)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(9*x^9*(a + b*x^3)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*x^6*(a + b*x^3)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(3*x^3*(a + b*x^3)) + (b^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]*Log[x])/(a + b*x^3)","A",4,3,26,0.1154,1,"{1355, 266, 43}"
80,1,251,0,0.0581628,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{17}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^17,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 x^{16} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^{10} \left(a+b x^3\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 x^{16} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^{10} \left(a+b x^3\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(16*x^16*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*x^13*(a + b*x^3)) - (a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x^10*(a + b*x^3)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^4*(a + b*x^3)) - (b^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
81,1,253,0,0.0580731,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{18}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^18,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 x^{17} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 x^{14} \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^8 \left(a+b x^3\right)}-\frac{a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^5 \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 x^{17} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{14 x^{14} \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^8 \left(a+b x^3\right)}-\frac{a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^5 \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^2 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(17*x^17*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(14*x^14*(a + b*x^3)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*x^11*(a + b*x^3)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^8*(a + b*x^3)) - (a*b^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x^5*(a + b*x^3)) - (b^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^2*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
82,1,41,0,0.0184203,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{19}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^19,x]","-\frac{\left(a+b x^3\right)^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{18 a x^{18}}","-\frac{\left(a+b x^3\right)^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{18 a x^{18}}",1,"-((a + b*x^3)^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(18*a*x^18)","A",2,2,26,0.07692,1,"{1355, 264}"
83,1,253,0,0.0614571,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{20}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^20,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 x^{19} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 x^{16} \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^{10} \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 x^{19} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{16 x^{16} \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{x^{10} \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^4 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(19*x^19*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(16*x^16*(a + b*x^3)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*x^13*(a + b*x^3)) - (a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(x^10*(a + b*x^3)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3)) - (b^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^4*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
84,1,255,0,0.0563872,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{21}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^21,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{20 x^{20} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 x^{17} \left(a+b x^3\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^{14} \left(a+b x^3\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{20 x^{20} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 x^{17} \left(a+b x^3\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^{14} \left(a+b x^3\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{5 x^5 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(20*x^20*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(17*x^17*(a + b*x^3)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^14*(a + b*x^3)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*x^11*(a + b*x^3)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*x^8*(a + b*x^3)) - (b^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(5*x^5*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
85,1,84,0,0.0400933,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{22}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^22,x]","\frac{b \left(a+b x^3\right)^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{126 a^2 x^{18}}-\frac{\left(a+b x^3\right)^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{21 a x^{21}}","\frac{b \left(a+b x^3\right)^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{126 a^2 x^{18}}-\frac{\left(a+b x^3\right)^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{21 a x^{21}}",1,"-((a + b*x^3)^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(21*a*x^21) + (b*(a + b*x^3)^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(126*a^2*x^18)","A",4,4,26,0.1538,1,"{1355, 266, 45, 37}"
86,1,255,0,0.0580603,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{23}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^23,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{22 x^{22} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 x^{19} \left(a+b x^3\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^{16} \left(a+b x^3\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^{10} \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{22 x^{22} \left(a+b x^3\right)}-\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{19 x^{19} \left(a+b x^3\right)}-\frac{5 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^{16} \left(a+b x^3\right)}-\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{13 x^{13} \left(a+b x^3\right)}-\frac{a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{2 x^{10} \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^7 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(22*x^22*(a + b*x^3)) - (5*a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(19*x^19*(a + b*x^3)) - (5*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*x^16*(a + b*x^3)) - (10*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(13*x^13*(a + b*x^3)) - (a*b^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(2*x^10*(a + b*x^3)) - (b^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^7*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
87,1,255,0,0.0564672,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{24}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^24,x]","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{23 x^{23} \left(a+b x^3\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^{20} \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 x^{17} \left(a+b x^3\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^{14} \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}","-\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{23 x^{23} \left(a+b x^3\right)}-\frac{a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6}}{4 x^{20} \left(a+b x^3\right)}-\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}{17 x^{17} \left(a+b x^3\right)}-\frac{5 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}{7 x^{14} \left(a+b x^3\right)}-\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}{11 x^{11} \left(a+b x^3\right)}-\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{8 x^8 \left(a+b x^3\right)}",1,"-(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(23*x^23*(a + b*x^3)) - (a^4*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(4*x^20*(a + b*x^3)) - (10*a^3*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(17*x^17*(a + b*x^3)) - (5*a^2*b^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(7*x^14*(a + b*x^3)) - (5*a*b^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(11*x^11*(a + b*x^3)) - (b^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(8*x^8*(a + b*x^3))","A",3,2,26,0.07692,1,"{1355, 270}"
88,1,128,0,0.0566844,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}{x^{25}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)/x^25,x]","-\frac{b^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^5}{504 a^3 x^{18}}+\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^5}{84 a^2 x^{21}}-\frac{\sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^5}{24 a x^{24}}","-\frac{b^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^5}{504 a^3 x^{18}}+\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^5}{84 a^2 x^{21}}-\frac{\sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^5}{24 a x^{24}}",1,"-((a + b*x^3)^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(24*a*x^24) + (b*(a + b*x^3)^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(84*a^2*x^21) - (b^2*(a + b*x^3)^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(504*a^3*x^18)","A",5,4,26,0.1538,1,"{1355, 266, 45, 37}"
89,1,240,0,0.1239018,"\int \frac{x^4}{\sqrt{a^2+2 a b x^3+b^2 x^6}} \, dx","Int[x^4/Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{x^2 \left(a+b x^3\right)}{2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{a^{2/3} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{a^{2/3} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{a^{2/3} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{x^2 \left(a+b x^3\right)}{2 b \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{a^{2/3} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{a^{2/3} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{a^{2/3} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"(x^2*(a + b*x^3))/(2*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (a^(2/3)*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (a^(2/3)*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (a^(2/3)*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",8,8,26,0.3077,1,"{1355, 321, 292, 31, 634, 617, 204, 628}"
90,1,235,0,0.1136817,"\int \frac{x^3}{\sqrt{a^2+2 a b x^3+b^2 x^6}} \, dx","Int[x^3/Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{x \left(a+b x^3\right)}{b \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\sqrt[3]{a} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\sqrt[3]{a} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\sqrt[3]{a} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{x \left(a+b x^3\right)}{b \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\sqrt[3]{a} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\sqrt[3]{a} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\sqrt[3]{a} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"(x*(a + b*x^3))/(b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (a^(1/3)*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (a^(1/3)*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (a^(1/3)*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",8,8,26,0.3077,1,"{1355, 321, 200, 31, 634, 617, 204, 628}"
91,1,44,0,0.034893,"\int \frac{x^2}{\sqrt{a^2+2 a b x^3+b^2 x^6}} \, dx","Int[x^2/Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{\left(a+b x^3\right) \log \left(a+b x^3\right)}{3 b \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{\left(a+b x^3\right) \log \left(a+b x^3\right)}{3 b \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"((a + b*x^3)*Log[a + b*x^3])/(3*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",3,3,26,0.1154,1,"{1352, 608, 31}"
92,1,202,0,0.0849865,"\int \frac{x}{\sqrt{a^2+2 a b x^3+b^2 x^6}} \, dx","Int[x/Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","-\frac{\left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{\left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"-(((a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*b^(2/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])) - ((a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(1/3)*b^(2/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + ((a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(1/3)*b^(2/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",7,7,24,0.2917,1,"{1355, 292, 31, 634, 617, 204, 628}"
93,1,202,0,0.1174906,"\int \frac{1}{\sqrt{a^2+2 a b x^3+b^2 x^6}} \, dx","Int[1/Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{\left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} \sqrt[3]{b} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b} \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{\left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} \sqrt[3]{b} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} \sqrt[3]{b} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} \sqrt[3]{b} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"-(((a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(1/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])) + ((a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(1/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - ((a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(1/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",7,7,22,0.3182,1,"{1343, 200, 31, 634, 617, 204, 628}"
94,1,80,0,0.0339088,"\int \frac{1}{x \sqrt{a^2+2 a b x^3+b^2 x^6}} \, dx","Int[1/(x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]),x]","\frac{\log (x) \left(a+b x^3\right)}{a \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(a+b x^3\right)}{3 a \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{\log (x) \left(a+b x^3\right)}{a \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(a+b x^3\right)}{3 a \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"((a + b*x^3)*Log[x])/(a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - ((a + b*x^3)*Log[a + b*x^3])/(3*a*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",5,5,26,0.1923,1,"{1355, 266, 36, 29, 31}"
95,1,238,0,0.1075944,"\int \frac{1}{x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}} \, dx","Int[1/(x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]),x]","-\frac{a+b x^3}{a x \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\sqrt[3]{b} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\sqrt[3]{b} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\sqrt[3]{b} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{a+b x^3}{a x \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\sqrt[3]{b} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\sqrt[3]{b} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\sqrt[3]{b} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"-((a + b*x^3)/(a*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])) + (b^(1/3)*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (b^(1/3)*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (b^(1/3)*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",8,8,26,0.3077,1,"{1355, 325, 292, 31, 634, 617, 204, 628}"
96,1,240,0,0.1070532,"\int \frac{1}{x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}} \, dx","Int[1/(x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]),x]","-\frac{a+b x^3}{2 a x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{b^{2/3} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{b^{2/3} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{b^{2/3} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{a+b x^3}{2 a x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{b^{2/3} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{b^{2/3} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{b^{2/3} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"-(a + b*x^3)/(2*a*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (b^(2/3)*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (b^(2/3)*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (b^(2/3)*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",8,8,26,0.3077,1,"{1355, 325, 200, 31, 634, 617, 204, 628}"
97,1,122,0,0.0505751,"\int \frac{1}{x^4 \sqrt{a^2+2 a b x^3+b^2 x^6}} \, dx","Int[1/(x^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]),x]","-\frac{a+b x^3}{3 a x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{b \log (x) \left(a+b x^3\right)}{a^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{b \left(a+b x^3\right) \log \left(a+b x^3\right)}{3 a^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{a+b x^3}{3 a x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{b \log (x) \left(a+b x^3\right)}{a^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{b \left(a+b x^3\right) \log \left(a+b x^3\right)}{3 a^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"-(a + b*x^3)/(3*a*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (b*(a + b*x^3)*Log[x])/(a^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (b*(a + b*x^3)*Log[a + b*x^3])/(3*a^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",4,3,26,0.1154,1,"{1355, 266, 44}"
98,1,280,0,0.1352532,"\int \frac{x^4}{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}} \, dx","Int[x^4/(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{x^2}{9 a b \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{x^2}{6 b \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{4/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{4/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{x^2}{9 a b \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{x^2}{6 b \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{4/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{4/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"x^2/(9*a*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - x^2/(6*b*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - ((a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(4/3)*b^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - ((a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(4/3)*b^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + ((a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(4/3)*b^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",9,9,26,0.3462,1,"{1355, 288, 290, 292, 31, 634, 617, 204, 628}"
99,1,276,0,0.133187,"\int \frac{x^3}{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}} \, dx","Int[x^3/(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{x}{18 a b \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{x}{6 b \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{5/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{5/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{x}{18 a b \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{x}{6 b \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{5/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{5/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"x/(18*a*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - x/(6*b*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - ((a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(5/3)*b^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + ((a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(5/3)*b^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - ((a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(5/3)*b^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",9,9,26,0.3462,1,"{1355, 288, 199, 200, 31, 634, 617, 204, 628}"
100,1,38,0,0.0293781,"\int \frac{x^2}{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}} \, dx","Int[x^2/(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","-\frac{1}{6 b \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{1}{6 b \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"-1/(6*b*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",2,2,26,0.07692,1,"{1352, 607}"
101,1,277,0,0.1404896,"\int \frac{x}{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}} \, dx","Int[x/(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{x^2}{6 a \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{2 x^2}{9 a^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{2 \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{7/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{7/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{2 \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{x^2}{6 a \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{2 x^2}{9 a^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{2 \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{7/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{7/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{2 \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"(2*x^2)/(9*a^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + x^2/(6*a*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (2*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(7/3)*b^(2/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (2*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(7/3)*b^(2/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + ((a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(27*a^(7/3)*b^(2/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",9,8,24,0.3333,1,"{1355, 290, 292, 31, 634, 617, 204, 628}"
102,1,286,0,0.1467657,"\int \frac{1}{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(-3/2),x]","\frac{5 x \left(a+b x^3\right)^2}{18 a^2 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}+\frac{x \left(a+b x^3\right)}{6 a \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}+\frac{5 \left(a+b x^3\right)^3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}-\frac{5 \left(a+b x^3\right)^3 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}-\frac{5 \left(a+b x^3\right)^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}","\frac{5 x \left(a+b x^3\right)^2}{18 a^2 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}+\frac{x \left(a+b x^3\right)}{6 a \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}+\frac{5 \left(a+b x^3\right)^3 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}-\frac{5 \left(a+b x^3\right)^3 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}-\frac{5 \left(a+b x^3\right)^3 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}",1,"(x*(a + b*x^3))/(6*a*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)) + (5*x*(a + b*x^3)^2)/(18*a^2*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)) - (5*(a + b*x^3)^3*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*b^(1/3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)) + (5*(a + b*x^3)^3*Log[a^(1/3) + b^(1/3)*x])/(27*a^(8/3)*b^(1/3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)) - (5*(a + b*x^3)^3*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(8/3)*b^(1/3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2))","A",9,8,22,0.3636,1,"{1343, 199, 200, 31, 634, 617, 204, 628}"
103,1,147,0,0.0827271,"\int \frac{1}{x \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}} \, dx","Int[1/(x*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)),x]","\frac{1}{6 a \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{3 a^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\log (x) \left(a+b x^3\right)}{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(a+b x^3\right)}{3 a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{1}{6 a \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{3 a^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\log (x) \left(a+b x^3\right)}{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(a+b x^3\right)}{3 a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"1/(3*a^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 1/(6*a*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + ((a + b*x^3)*Log[x])/(a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - ((a + b*x^3)*Log[a + b*x^3])/(3*a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",4,3,26,0.1154,1,"{1355, 266, 44}"
104,1,316,0,0.1603813,"\int \frac{1}{x^2 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)),x]","-\frac{14 \left(a+b x^3\right)}{9 a^3 x \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{7}{18 a^2 x \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{6 a x \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)}+\frac{14 \sqrt[3]{b} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{10/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{7 \sqrt[3]{b} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{10/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{14 \sqrt[3]{b} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{10/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{14 \left(a+b x^3\right)}{9 a^3 x \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{7}{18 a^2 x \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{6 a x \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)}+\frac{14 \sqrt[3]{b} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{10/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{7 \sqrt[3]{b} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{10/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{14 \sqrt[3]{b} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{10/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"7/(18*a^2*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 1/(6*a*x*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (14*(a + b*x^3))/(9*a^3*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (14*b^(1/3)*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(10/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (14*b^(1/3)*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(10/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (7*b^(1/3)*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(27*a^(10/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",10,9,26,0.3462,1,"{1355, 290, 325, 292, 31, 634, 617, 204, 628}"
105,1,316,0,0.1586609,"\int \frac{1}{x^3 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}} \, dx","Int[1/(x^3*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)),x]","-\frac{10 \left(a+b x^3\right)}{9 a^3 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{4}{9 a^2 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{6 a x^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)}-\frac{20 b^{2/3} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{11/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{10 b^{2/3} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{11/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{20 b^{2/3} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{10 \left(a+b x^3\right)}{9 a^3 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{4}{9 a^2 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{6 a x^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)}-\frac{20 b^{2/3} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{11/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{10 b^{2/3} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{11/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{20 b^{2/3} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"4/(9*a^2*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 1/(6*a*x^2*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (10*(a + b*x^3))/(9*a^3*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (20*b^(2/3)*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(11/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (20*b^(2/3)*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(11/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (10*b^(2/3)*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(27*a^(11/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",10,9,26,0.3462,1,"{1355, 290, 325, 200, 31, 634, 617, 204, 628}"
106,1,188,0,0.0972588,"\int \frac{1}{x^4 \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}} \, dx","Int[1/(x^4*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2)),x]","-\frac{b}{6 a^2 \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{2 b}{3 a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{a+b x^3}{3 a^3 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{3 b \log (x) \left(a+b x^3\right)}{a^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{b \left(a+b x^3\right) \log \left(a+b x^3\right)}{a^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{b}{6 a^2 \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{2 b}{3 a^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{a+b x^3}{3 a^3 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{3 b \log (x) \left(a+b x^3\right)}{a^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{b \left(a+b x^3\right) \log \left(a+b x^3\right)}{a^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"(-2*b)/(3*a^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - b/(6*a^2*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (a + b*x^3)/(3*a^3*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (3*b*(a + b*x^3)*Log[x])/(a^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (b*(a + b*x^3)*Log[a + b*x^3])/(a^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",4,3,26,0.1154,1,"{1355, 266, 44}"
107,1,359,0,0.1850646,"\int \frac{x^6}{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[x^6/(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","-\frac{x^4}{12 b \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{x}{162 a b^2 \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{5 x}{486 a^2 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{x}{27 b^2 \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{5 \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{8/3} b^{7/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{5 \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{1458 a^{8/3} b^{7/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{5 \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{8/3} b^{7/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{x^4}{12 b \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{x}{162 a b^2 \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{5 x}{486 a^2 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{x}{27 b^2 \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{5 \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{8/3} b^{7/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{5 \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{1458 a^{8/3} b^{7/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{5 \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{8/3} b^{7/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"(5*x)/(486*a^2*b^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - x^4/(12*b*(a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - x/(27*b^2*(a + b*x^3)^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + x/(162*a*b^2*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (5*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(243*Sqrt[3]*a^(8/3)*b^(7/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (5*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(729*a^(8/3)*b^(7/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (5*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(1458*a^(8/3)*b^(7/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",11,9,26,0.3462,1,"{1355, 288, 199, 200, 31, 634, 617, 204, 628}"
108,1,78,0,0.0526029,"\int \frac{x^5}{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[x^5/(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{a}{12 b^2 \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{1}{9 b^2 \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{a}{12 b^2 \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{1}{9 b^2 \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"a/(12*b^2*(a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - 1/(9*b^2*(a + b*x^3)^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",4,3,26,0.1154,1,"{1355, 266, 43}"
109,1,368,0,0.1908958,"\int \frac{x^4}{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[x^4/(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{7 x^2}{243 a^3 b \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{7 x^2}{324 a^2 b \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{x^2}{54 a b \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{x^2}{12 b \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{7 \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{10/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{7 \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{1458 a^{10/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{7 \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{10/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{7 x^2}{243 a^3 b \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{7 x^2}{324 a^2 b \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{x^2}{54 a b \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{x^2}{12 b \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{7 \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{10/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{7 \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{1458 a^{10/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{7 \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{10/3} b^{5/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"(7*x^2)/(243*a^3*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - x^2/(12*b*(a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + x^2/(54*a*b*(a + b*x^3)^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (7*x^2)/(324*a^2*b*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (7*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(243*Sqrt[3]*a^(10/3)*b^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (7*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(729*a^(10/3)*b^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (7*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(1458*a^(10/3)*b^(5/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",11,9,26,0.3462,1,"{1355, 288, 290, 292, 31, 634, 617, 204, 628}"
110,1,360,0,0.1799091,"\int \frac{x^3}{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[x^3/(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{5 x}{243 a^3 b \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{x}{81 a^2 b \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{x}{108 a b \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{x}{12 b \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{10 \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{11/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{5 \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{729 a^{11/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{10 \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{11/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{5 x}{243 a^3 b \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{x}{81 a^2 b \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{x}{108 a b \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{x}{12 b \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{10 \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{11/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{5 \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{729 a^{11/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{10 \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{11/3} b^{4/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"(5*x)/(243*a^3*b*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - x/(12*b*(a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + x/(108*a*b*(a + b*x^3)^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + x/(81*a^2*b*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (10*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(243*Sqrt[3]*a^(11/3)*b^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (10*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(729*a^(11/3)*b^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (5*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(729*a^(11/3)*b^(4/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",11,9,26,0.3462,1,"{1355, 288, 199, 200, 31, 634, 617, 204, 628}"
111,1,38,0,0.0295249,"\int \frac{x^2}{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[x^2/(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","-\frac{1}{12 b \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}","-\frac{1}{12 b \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}}",1,"-1/(12*b*(a + b*x^3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2))","A",2,2,26,0.07692,1,"{1352, 607}"
112,1,359,0,0.1927506,"\int \frac{x}{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[x/(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{35 x^2}{324 a^3 \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{5 x^2}{54 a^2 \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{x^2}{12 a \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{35 x^2}{243 a^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{35 \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{13/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{35 \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{1458 a^{13/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{35 \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{13/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{35 x^2}{324 a^3 \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{5 x^2}{54 a^2 \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{x^2}{12 a \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{35 x^2}{243 a^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{35 \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{13/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{35 \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{1458 a^{13/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{35 \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{13/3} b^{2/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"(35*x^2)/(243*a^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + x^2/(12*a*(a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (5*x^2)/(54*a^2*(a + b*x^3)^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (35*x^2)/(324*a^3*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (35*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(243*Sqrt[3]*a^(13/3)*b^(2/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (35*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(729*a^(13/3)*b^(2/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (35*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(1458*a^(13/3)*b^(2/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",11,8,24,0.3333,1,"{1355, 290, 292, 31, 634, 617, 204, 628}"
113,1,364,0,0.1991206,"\int \frac{1}{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^(-5/2),x]","\frac{55 x \left(a+b x^3\right)^4}{243 a^4 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}+\frac{11 x \left(a+b x^3\right)^3}{81 a^3 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}+\frac{11 x \left(a+b x^3\right)^2}{108 a^2 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}+\frac{x \left(a+b x^3\right)}{12 a \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}+\frac{110 \left(a+b x^3\right)^5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{14/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}-\frac{55 \left(a+b x^3\right)^5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{729 a^{14/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}-\frac{110 \left(a+b x^3\right)^5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{14/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}","\frac{55 x \left(a+b x^3\right)^4}{243 a^4 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}+\frac{11 x \left(a+b x^3\right)^3}{81 a^3 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}+\frac{11 x \left(a+b x^3\right)^2}{108 a^2 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}+\frac{x \left(a+b x^3\right)}{12 a \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}+\frac{110 \left(a+b x^3\right)^5 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{14/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}-\frac{55 \left(a+b x^3\right)^5 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{729 a^{14/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}-\frac{110 \left(a+b x^3\right)^5 \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{14/3} \sqrt[3]{b} \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}}",1,"(x*(a + b*x^3))/(12*a*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)) + (11*x*(a + b*x^3)^2)/(108*a^2*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)) + (11*x*(a + b*x^3)^3)/(81*a^3*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)) + (55*x*(a + b*x^3)^4)/(243*a^4*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)) - (110*(a + b*x^3)^5*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(243*Sqrt[3]*a^(14/3)*b^(1/3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)) + (110*(a + b*x^3)^5*Log[a^(1/3) + b^(1/3)*x])/(729*a^(14/3)*b^(1/3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)) - (55*(a + b*x^3)^5*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(729*a^(14/3)*b^(1/3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2))","A",11,8,22,0.3636,1,"{1343, 199, 200, 31, 634, 617, 204, 628}"
114,1,223,0,0.1239052,"\int \frac{1}{x \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[1/(x*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)),x]","\frac{1}{6 a^3 \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{9 a^2 \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{12 a \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{3 a^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\log (x) \left(a+b x^3\right)}{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(a+b x^3\right)}{3 a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{1}{6 a^3 \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{9 a^2 \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{12 a \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{1}{3 a^4 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{\log (x) \left(a+b x^3\right)}{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{\left(a+b x^3\right) \log \left(a+b x^3\right)}{3 a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"1/(3*a^4*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 1/(12*a*(a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 1/(9*a^2*(a + b*x^3)^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 1/(6*a^3*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + ((a + b*x^3)*Log[x])/(a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - ((a + b*x^3)*Log[a + b*x^3])/(3*a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",4,3,26,0.1154,1,"{1355, 266, 44}"
115,1,398,0,0.2163112,"\int \frac{1}{x^2 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)),x]","-\frac{455 \left(a+b x^3\right)}{243 a^5 x \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{455}{972 a^4 x \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{65}{324 a^3 x \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)}+\frac{13}{108 a^2 x \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^2}+\frac{1}{12 a x \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^3}+\frac{455 \sqrt[3]{b} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{16/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{455 \sqrt[3]{b} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{1458 a^{16/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{455 \sqrt[3]{b} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{16/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{455 \left(a+b x^3\right)}{243 a^5 x \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{455}{972 a^4 x \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{65}{324 a^3 x \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)}+\frac{13}{108 a^2 x \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^2}+\frac{1}{12 a x \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^3}+\frac{455 \sqrt[3]{b} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{16/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{455 \sqrt[3]{b} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{1458 a^{16/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{455 \sqrt[3]{b} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{16/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"455/(972*a^4*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 1/(12*a*x*(a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 13/(108*a^2*x*(a + b*x^3)^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 65/(324*a^3*x*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (455*(a + b*x^3))/(243*a^5*x*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (455*b^(1/3)*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(243*Sqrt[3]*a^(16/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (455*b^(1/3)*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(729*a^(16/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (455*b^(1/3)*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(1458*a^(16/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",12,9,26,0.3462,1,"{1355, 290, 325, 292, 31, 634, 617, 204, 628}"
116,1,398,0,0.2106283,"\int \frac{1}{x^3 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[1/(x^3*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)),x]","-\frac{385 \left(a+b x^3\right)}{243 a^5 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{154}{243 a^4 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{77}{324 a^3 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)}+\frac{7}{54 a^2 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^2}+\frac{1}{12 a x^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^3}-\frac{770 b^{2/3} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{17/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{385 b^{2/3} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{729 a^{17/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{770 b^{2/3} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{17/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{385 \left(a+b x^3\right)}{243 a^5 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{154}{243 a^4 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{77}{324 a^3 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)}+\frac{7}{54 a^2 x^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^2}+\frac{1}{12 a x^2 \sqrt{a^2+2 a b x^3+b^2 x^6} \left(a+b x^3\right)^3}-\frac{770 b^{2/3} \left(a+b x^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{729 a^{17/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{385 b^{2/3} \left(a+b x^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{729 a^{17/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{770 b^{2/3} \left(a+b x^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{243 \sqrt{3} a^{17/3} \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"154/(243*a^4*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 1/(12*a*x^2*(a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 7/(54*a^2*x^2*(a + b*x^3)^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + 77/(324*a^3*x^2*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (385*(a + b*x^3))/(243*a^5*x^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (770*b^(2/3)*(a + b*x^3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(243*Sqrt[3]*a^(17/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (770*b^(2/3)*(a + b*x^3)*Log[a^(1/3) + b^(1/3)*x])/(729*a^(17/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (385*b^(2/3)*(a + b*x^3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(729*a^(17/3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",12,9,26,0.3462,1,"{1355, 290, 325, 200, 31, 634, 617, 204, 628}"
117,1,269,0,0.1425279,"\int \frac{1}{x^4 \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[1/(x^4*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2)),x]","-\frac{b}{2 a^4 \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{2 b}{9 a^3 \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{b}{12 a^2 \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{4 b}{3 a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{a+b x^3}{3 a^5 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{5 b \log (x) \left(a+b x^3\right)}{a^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{5 b \left(a+b x^3\right) \log \left(a+b x^3\right)}{3 a^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}","-\frac{b}{2 a^4 \left(a+b x^3\right) \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{2 b}{9 a^3 \left(a+b x^3\right)^2 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{b}{12 a^2 \left(a+b x^3\right)^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{4 b}{3 a^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{a+b x^3}{3 a^5 x^3 \sqrt{a^2+2 a b x^3+b^2 x^6}}-\frac{5 b \log (x) \left(a+b x^3\right)}{a^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}+\frac{5 b \left(a+b x^3\right) \log \left(a+b x^3\right)}{3 a^6 \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"(-4*b)/(3*a^5*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - b/(12*a^2*(a + b*x^3)^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (2*b)/(9*a^3*(a + b*x^3)^2*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - b/(2*a^4*(a + b*x^3)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (a + b*x^3)/(3*a^5*x^3*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) - (5*b*(a + b*x^3)*Log[x])/(a^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6]) + (5*b*(a + b*x^3)*Log[a + b*x^3])/(3*a^6*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",4,3,26,0.1154,1,"{1355, 266, 44}"
118,1,313,0,0.1378612,"\int (d x)^m \left(a^2+2 a b x^3+b^2 x^6\right)^{5/2} \, dx","Int[(d*x)^m*(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+4}}{d^4 (m+4) \left(a+b x^3\right)}+\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+7}}{d^7 (m+7) \left(a+b x^3\right)}+\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+10}}{d^{10} (m+10) \left(a+b x^3\right)}+\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+13}}{d^{13} (m+13) \left(a+b x^3\right)}+\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+16}}{d^{16} (m+16) \left(a+b x^3\right)}+\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+1}}{d (m+1) \left(a+b x^3\right)}","\frac{5 a^4 b \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+4}}{d^4 (m+4) \left(a+b x^3\right)}+\frac{10 a^3 b^2 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+7}}{d^7 (m+7) \left(a+b x^3\right)}+\frac{10 a^2 b^3 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+10}}{d^{10} (m+10) \left(a+b x^3\right)}+\frac{5 a b^4 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+13}}{d^{13} (m+13) \left(a+b x^3\right)}+\frac{b^5 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+16}}{d^{16} (m+16) \left(a+b x^3\right)}+\frac{a^5 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+1}}{d (m+1) \left(a+b x^3\right)}",1,"(a^5*(d*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d*(1 + m)*(a + b*x^3)) + (5*a^4*b*(d*x)^(4 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d^4*(4 + m)*(a + b*x^3)) + (10*a^3*b^2*(d*x)^(7 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d^7*(7 + m)*(a + b*x^3)) + (10*a^2*b^3*(d*x)^(10 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d^10*(10 + m)*(a + b*x^3)) + (5*a*b^4*(d*x)^(13 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d^13*(13 + m)*(a + b*x^3)) + (b^5*(d*x)^(16 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d^16*(16 + m)*(a + b*x^3))","A",3,2,28,0.07143,1,"{1355, 270}"
119,1,205,0,0.0851968,"\int (d x)^m \left(a^2+2 a b x^3+b^2 x^6\right)^{3/2} \, dx","Int[(d*x)^m*(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+4}}{d^4 (m+4) \left(a+b x^3\right)}+\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+7}}{d^7 (m+7) \left(a+b x^3\right)}+\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+10}}{d^{10} (m+10) \left(a+b x^3\right)}+\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+1}}{d (m+1) \left(a+b x^3\right)}","\frac{3 a^2 b \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+4}}{d^4 (m+4) \left(a+b x^3\right)}+\frac{3 a b^2 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+7}}{d^7 (m+7) \left(a+b x^3\right)}+\frac{b^3 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+10}}{d^{10} (m+10) \left(a+b x^3\right)}+\frac{a^3 \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+1}}{d (m+1) \left(a+b x^3\right)}",1,"(a^3*(d*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d*(1 + m)*(a + b*x^3)) + (3*a^2*b*(d*x)^(4 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d^4*(4 + m)*(a + b*x^3)) + (3*a*b^2*(d*x)^(7 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d^7*(7 + m)*(a + b*x^3)) + (b^3*(d*x)^(10 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d^10*(10 + m)*(a + b*x^3))","A",3,2,28,0.07143,1,"{1355, 270}"
120,1,97,0,0.0378413,"\int (d x)^m \sqrt{a^2+2 a b x^3+b^2 x^6} \, dx","Int[(d*x)^m*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+4}}{d^4 (m+4) \left(a+b x^3\right)}+\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+1}}{d (m+1) \left(a+b x^3\right)}","\frac{b \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+4}}{d^4 (m+4) \left(a+b x^3\right)}+\frac{a \sqrt{a^2+2 a b x^3+b^2 x^6} (d x)^{m+1}}{d (m+1) \left(a+b x^3\right)}",1,"(a*(d*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d*(1 + m)*(a + b*x^3)) + (b*(d*x)^(4 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])/(d^4*(4 + m)*(a + b*x^3))","A",3,2,28,0.07143,1,"{1355, 14}"
121,1,73,0,0.033872,"\int \frac{(d x)^m}{\sqrt{a^2+2 a b x^3+b^2 x^6}} \, dx","Int[(d*x)^m/Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6],x]","\frac{\left(a+b x^3\right) (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a d (m+1) \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{\left(a+b x^3\right) (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a d (m+1) \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"((d*x)^(1 + m)*(a + b*x^3)*Hypergeometric2F1[1, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(a*d*(1 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",2,2,28,0.07143,1,"{1355, 364}"
122,1,73,0,0.0345446,"\int \frac{(d x)^m}{\left(a^2+2 a b x^3+b^2 x^6\right)^{3/2}} \, dx","Int[(d*x)^m/(a^2 + 2*a*b*x^3 + b^2*x^6)^(3/2),x]","\frac{\left(a+b x^3\right) (d x)^{m+1} \, _2F_1\left(3,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a^3 d (m+1) \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{\left(a+b x^3\right) (d x)^{m+1} \, _2F_1\left(3,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a^3 d (m+1) \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"((d*x)^(1 + m)*(a + b*x^3)*Hypergeometric2F1[3, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(a^3*d*(1 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",2,2,28,0.07143,1,"{1355, 364}"
123,1,73,0,0.0349544,"\int \frac{(d x)^m}{\left(a^2+2 a b x^3+b^2 x^6\right)^{5/2}} \, dx","Int[(d*x)^m/(a^2 + 2*a*b*x^3 + b^2*x^6)^(5/2),x]","\frac{\left(a+b x^3\right) (d x)^{m+1} \, _2F_1\left(5,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a^5 d (m+1) \sqrt{a^2+2 a b x^3+b^2 x^6}}","\frac{\left(a+b x^3\right) (d x)^{m+1} \, _2F_1\left(5,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a^5 d (m+1) \sqrt{a^2+2 a b x^3+b^2 x^6}}",1,"((d*x)^(1 + m)*(a + b*x^3)*Hypergeometric2F1[5, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(a^5*d*(1 + m)*Sqrt[a^2 + 2*a*b*x^3 + b^2*x^6])","A",2,2,28,0.07143,1,"{1355, 364}"
124,1,77,0,0.0253913,"\int (d x)^m \left(a^2+2 a b x^3+b^2 x^6\right)^p \, dx","Int[(d*x)^m*(a^2 + 2*a*b*x^3 + b^2*x^6)^p,x]","\frac{(d x)^{m+1} \left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(\frac{m+1}{3},-2 p;\frac{m+4}{3};-\frac{b x^3}{a}\right)}{d (m+1)}","\frac{(d x)^{m+1} \left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(\frac{m+1}{3},-2 p;\frac{m+4}{3};-\frac{b x^3}{a}\right)}{d (m+1)}",1,"((d*x)^(1 + m)*(a^2 + 2*a*b*x^3 + b^2*x^6)^p*Hypergeometric2F1[(1 + m)/3, -2*p, (4 + m)/3, -((b*x^3)/a)])/(d*(1 + m)*(1 + (b*x^3)/a)^(2*p))","A",2,2,26,0.07692,1,"{1356, 364}"
125,1,172,0,0.1126721,"\int x^{11} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, dx","Int[x^11*(a^2 + 2*a*b*x^3 + b^2*x^6)^p,x]","\frac{\left(a+b x^3\right)^4 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{6 b^4 (p+2)}-\frac{a \left(a+b x^3\right)^3 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{b^4 (2 p+3)}+\frac{a^2 \left(a+b x^3\right)^2 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{2 b^4 (p+1)}-\frac{a^3 \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b^4 (2 p+1)}","\frac{\left(a+b x^3\right)^4 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{6 b^4 (p+2)}-\frac{a \left(a+b x^3\right)^3 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{b^4 (2 p+3)}+\frac{a^2 \left(a+b x^3\right)^2 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{2 b^4 (p+1)}-\frac{a^3 \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b^4 (2 p+1)}",1,"-(a^3*(a + b*x^3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^p)/(3*b^4*(1 + 2*p)) + (a^2*(a + b*x^3)^2*(a^2 + 2*a*b*x^3 + b^2*x^6)^p)/(2*b^4*(1 + p)) - (a*(a + b*x^3)^3*(a^2 + 2*a*b*x^3 + b^2*x^6)^p)/(b^4*(3 + 2*p)) + ((a + b*x^3)^4*(a^2 + 2*a*b*x^3 + b^2*x^6)^p)/(6*b^4*(2 + p))","A",4,3,24,0.1250,1,"{1356, 266, 43}"
126,1,130,0,0.0788709,"\int x^8 \left(a^2+2 a b x^3+b^2 x^6\right)^p \, dx","Int[x^8*(a^2 + 2*a*b*x^3 + b^2*x^6)^p,x]","\frac{\left(a+b x^3\right)^3 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b^3 (2 p+3)}-\frac{a \left(a+b x^3\right)^2 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b^3 (p+1)}+\frac{a^2 \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b^3 (2 p+1)}","\frac{\left(a+b x^3\right)^3 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b^3 (2 p+3)}-\frac{a \left(a+b x^3\right)^2 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b^3 (p+1)}+\frac{a^2 \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b^3 (2 p+1)}",1,"(a^2*(a + b*x^3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^p)/(3*b^3*(1 + 2*p)) - (a*(a + b*x^3)^2*(a^2 + 2*a*b*x^3 + b^2*x^6)^p)/(3*b^3*(1 + p)) + ((a + b*x^3)^3*(a^2 + 2*a*b*x^3 + b^2*x^6)^p)/(3*b^3*(3 + 2*p))","A",4,3,24,0.1250,1,"{1356, 266, 43}"
127,1,84,0,0.055235,"\int x^5 \left(a^2+2 a b x^3+b^2 x^6\right)^p \, dx","Int[x^5*(a^2 + 2*a*b*x^3 + b^2*x^6)^p,x]","\frac{\left(a+b x^3\right)^2 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{6 b^2 (p+1)}-\frac{a \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b^2 (2 p+1)}","\frac{\left(a+b x^3\right)^2 \left(a^2+2 a b x^3+b^2 x^6\right)^p}{6 b^2 (p+1)}-\frac{a \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b^2 (2 p+1)}",1,"-(a*(a + b*x^3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^p)/(3*b^2*(1 + 2*p)) + ((a + b*x^3)^2*(a^2 + 2*a*b*x^3 + b^2*x^6)^p)/(6*b^2*(1 + p))","A",4,3,24,0.1250,1,"{1356, 266, 43}"
128,1,60,0,0.0192857,"\int x^4 \left(a^2+2 a b x^3+b^2 x^6\right)^p \, dx","Int[x^4*(a^2 + 2*a*b*x^3 + b^2*x^6)^p,x]","\frac{1}{5} x^5 \left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(\frac{5}{3},-2 p;\frac{8}{3};-\frac{b x^3}{a}\right)","\frac{1}{5} x^5 \left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(\frac{5}{3},-2 p;\frac{8}{3};-\frac{b x^3}{a}\right)",1,"(x^5*(a^2 + 2*a*b*x^3 + b^2*x^6)^p*Hypergeometric2F1[5/3, -2*p, 8/3, -((b*x^3)/a)])/(5*(1 + (b*x^3)/a)^(2*p))","A",2,2,24,0.08333,1,"{1356, 364}"
129,1,60,0,0.0193485,"\int x^3 \left(a^2+2 a b x^3+b^2 x^6\right)^p \, dx","Int[x^3*(a^2 + 2*a*b*x^3 + b^2*x^6)^p,x]","\frac{1}{4} x^4 \left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(\frac{4}{3},-2 p;\frac{7}{3};-\frac{b x^3}{a}\right)","\frac{1}{4} x^4 \left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(\frac{4}{3},-2 p;\frac{7}{3};-\frac{b x^3}{a}\right)",1,"(x^4*(a^2 + 2*a*b*x^3 + b^2*x^6)^p*Hypergeometric2F1[4/3, -2*p, 7/3, -((b*x^3)/a)])/(4*(1 + (b*x^3)/a)^(2*p))","A",2,2,24,0.08333,1,"{1356, 364}"
130,1,41,0,0.0276851,"\int x^2 \left(a^2+2 a b x^3+b^2 x^6\right)^p \, dx","Int[x^2*(a^2 + 2*a*b*x^3 + b^2*x^6)^p,x]","\frac{\left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b (2 p+1)}","\frac{\left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p}{3 b (2 p+1)}",1,"((a + b*x^3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^p)/(3*b*(1 + 2*p))","A",2,2,24,0.08333,1,"{1352, 609}"
131,1,60,0,0.0151618,"\int x \left(a^2+2 a b x^3+b^2 x^6\right)^p \, dx","Int[x*(a^2 + 2*a*b*x^3 + b^2*x^6)^p,x]","\frac{1}{2} x^2 \left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(\frac{2}{3},-2 p;\frac{5}{3};-\frac{b x^3}{a}\right)","\frac{x^2 \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(1,2 p+\frac{5}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 a}",1,"(x^2*(a^2 + 2*a*b*x^3 + b^2*x^6)^p*Hypergeometric2F1[2/3, -2*p, 5/3, -((b*x^3)/a)])/(2*(1 + (b*x^3)/a)^(2*p))","A",2,2,22,0.09091,1,"{1356, 364}"
132,1,55,0,0.019247,"\int \left(a^2+2 a b x^3+b^2 x^6\right)^p \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^p,x]","x \left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(\frac{1}{3},-2 p;\frac{4}{3};-\frac{b x^3}{a}\right)","\frac{x \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(1,2 p+\frac{4}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{a}",1,"(x*(a^2 + 2*a*b*x^3 + b^2*x^6)^p*Hypergeometric2F1[1/3, -2*p, 4/3, -((b*x^3)/a)])/(1 + (b*x^3)/a)^(2*p)","A",3,3,20,0.1500,1,"{1343, 246, 245}"
133,1,63,0,0.0373573,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^p}{x} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^p/x,x]","-\frac{\left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(1,2 p+1;2 (p+1);\frac{b x^3}{a}+1\right)}{3 a (2 p+1)}","-\frac{\left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(1,2 p+1;2 (p+1);\frac{b x^3}{a}+1\right)}{3 a (2 p+1)}",1,"-((a + b*x^3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^p*Hypergeometric2F1[1, 1 + 2*p, 2*(1 + p), 1 + (b*x^3)/a])/(3*a*(1 + 2*p))","A",3,3,24,0.1250,1,"{1356, 266, 65}"
134,1,58,0,0.0183031,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^p}{x^2} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^p/x^2,x]","-\frac{\left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(-\frac{1}{3},-2 p;\frac{2}{3};-\frac{b x^3}{a}\right)}{x}","-\frac{\left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(-\frac{1}{3},-2 p;\frac{2}{3};-\frac{b x^3}{a}\right)}{x}",1,"-(((a^2 + 2*a*b*x^3 + b^2*x^6)^p*Hypergeometric2F1[-1/3, -2*p, 2/3, -((b*x^3)/a)])/(x*(1 + (b*x^3)/a)^(2*p)))","A",2,2,24,0.08333,1,"{1356, 364}"
135,1,60,0,0.0188288,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^p}{x^3} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^p/x^3,x]","-\frac{\left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(-\frac{2}{3},-2 p;\frac{1}{3};-\frac{b x^3}{a}\right)}{2 x^2}","-\frac{\left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(-\frac{2}{3},-2 p;\frac{1}{3};-\frac{b x^3}{a}\right)}{2 x^2}",1,"-((a^2 + 2*a*b*x^3 + b^2*x^6)^p*Hypergeometric2F1[-2/3, -2*p, 1/3, -((b*x^3)/a)])/(2*x^2*(1 + (b*x^3)/a)^(2*p))","A",2,2,24,0.08333,1,"{1356, 364}"
136,1,64,0,0.0411508,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^p}{x^4} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^p/x^4,x]","\frac{b \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(2,2 p+1;2 (p+1);\frac{b x^3}{a}+1\right)}{3 a^2 (2 p+1)}","\frac{b \left(a+b x^3\right) \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(2,2 p+1;2 (p+1);\frac{b x^3}{a}+1\right)}{3 a^2 (2 p+1)}",1,"(b*(a + b*x^3)*(a^2 + 2*a*b*x^3 + b^2*x^6)^p*Hypergeometric2F1[2, 1 + 2*p, 2*(1 + p), 1 + (b*x^3)/a])/(3*a^2*(1 + 2*p))","A",3,3,24,0.1250,1,"{1356, 266, 65}"
137,1,60,0,0.0197642,"\int \frac{\left(a^2+2 a b x^3+b^2 x^6\right)^p}{x^5} \, dx","Int[(a^2 + 2*a*b*x^3 + b^2*x^6)^p/x^5,x]","-\frac{\left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(-\frac{4}{3},-2 p;-\frac{1}{3};-\frac{b x^3}{a}\right)}{4 x^4}","-\frac{\left(\frac{b x^3}{a}+1\right)^{-2 p} \left(a^2+2 a b x^3+b^2 x^6\right)^p \, _2F_1\left(-\frac{4}{3},-2 p;-\frac{1}{3};-\frac{b x^3}{a}\right)}{4 x^4}",1,"-((a^2 + 2*a*b*x^3 + b^2*x^6)^p*Hypergeometric2F1[-4/3, -2*p, -1/3, -((b*x^3)/a)])/(4*x^4*(1 + (b*x^3)/a)^(2*p))","A",2,2,24,0.08333,1,"{1356, 364}"
138,1,81,0,0.0827972,"\int \frac{x^8}{a+b x^3+c x^6} \, dx","Int[x^8/(a + b*x^3 + c*x^6),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x^3+c x^6\right)}{6 c^2}+\frac{x^3}{3 c}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x^3+c x^6\right)}{6 c^2}+\frac{x^3}{3 c}",1,"x^3/(3*c) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x^3)/Sqrt[b^2 - 4*a*c]])/(3*c^2*Sqrt[b^2 - 4*a*c]) - (b*Log[a + b*x^3 + c*x^6])/(6*c^2)","A",6,6,18,0.3333,1,"{1357, 703, 634, 618, 206, 628}"
139,1,63,0,0.0578286,"\int \frac{x^5}{a+b x^3+c x^6} \, dx","Int[x^5/(a + b*x^3 + c*x^6),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^3+c x^6\right)}{6 c}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^3+c x^6\right)}{6 c}",1,"(b*ArcTanh[(b + 2*c*x^3)/Sqrt[b^2 - 4*a*c]])/(3*c*Sqrt[b^2 - 4*a*c]) + Log[a + b*x^3 + c*x^6]/(6*c)","A",5,5,18,0.2778,1,"{1357, 634, 618, 206, 628}"
140,1,38,0,0.0357311,"\int \frac{x^2}{a+b x^3+c x^6} \, dx","Int[x^2/(a + b*x^3 + c*x^6),x]","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 \sqrt{b^2-4 a c}}","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 \sqrt{b^2-4 a c}}",1,"(-2*ArcTanh[(b + 2*c*x^3)/Sqrt[b^2 - 4*a*c]])/(3*Sqrt[b^2 - 4*a*c])","A",3,3,18,0.1667,1,"{1352, 618, 206}"
141,1,69,0,0.0695275,"\int \frac{1}{x \left(a+b x^3+c x^6\right)} \, dx","Int[1/(x*(a + b*x^3 + c*x^6)),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x^3+c x^6\right)}{6 a}+\frac{\log (x)}{a}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x^3+c x^6\right)}{6 a}+\frac{\log (x)}{a}",1,"(b*ArcTanh[(b + 2*c*x^3)/Sqrt[b^2 - 4*a*c]])/(3*a*Sqrt[b^2 - 4*a*c]) + Log[x]/a - Log[a + b*x^3 + c*x^6]/(6*a)","A",7,7,18,0.3889,1,"{1357, 705, 29, 634, 618, 206, 628}"
142,1,89,0,0.1250236,"\int \frac{1}{x^4 \left(a+b x^3+c x^6\right)} \, dx","Int[1/(x^4*(a + b*x^3 + c*x^6)),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x^3+c x^6\right)}{6 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{3 a x^3}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{\sqrt{b^2-4 a c}}\right)}{3 a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x^3+c x^6\right)}{6 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x^3)/Sqrt[b^2 - 4*a*c]])/(3*a^2*Sqrt[b^2 - 4*a*c]) - (b*Log[x])/a^2 + (b*Log[a + b*x^3 + c*x^6])/(6*a^2)","A",8,7,18,0.3889,1,"{1357, 709, 800, 634, 618, 206, 628}"
143,1,636,0,1.2489884,"\int \frac{x^7}{a+b x^3+c x^6} \, dx","Int[x^7/(a + b*x^3 + c*x^6),x]","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{x^2}{2 c}","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{5/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{5/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{x^2}{2 c}",1,"x^2/(2*c) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*c^(5/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*c^(5/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*c^(5/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*c^(5/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)) - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*c^(5/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*c^(5/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3))","A",14,8,18,0.4444,1,"{1367, 1510, 292, 31, 634, 617, 204, 628}"
144,1,631,0,1.0240853,"\int \frac{x^6}{a+b x^3+c x^6} \, dx","Int[x^6/(a + b*x^3 + c*x^6),x]","\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{x}{c}","\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{x}{c}",1,"x/c + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*c^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*c^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3)) - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*c^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*c^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*c^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*c^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3))","A",14,8,18,0.4444,1,"{1367, 1422, 200, 31, 634, 617, 204, 628}"
145,1,558,0,0.519725,"\int \frac{x^4}{a+b x^3+c x^6} \, dx","Int[x^4/(a + b*x^3 + c*x^6),x]","-\frac{\left(b-\sqrt{b^2-4 a c}\right)^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{2/3} \sqrt{b^2-4 a c}}+\frac{\left(\sqrt{b^2-4 a c}+b\right)^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{2/3} \sqrt{b^2-4 a c}}+\frac{\left(b-\sqrt{b^2-4 a c}\right)^{2/3} \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{2/3} \sqrt{b^2-4 a c}}-\frac{\left(\sqrt{b^2-4 a c}+b\right)^{2/3} \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{2/3} \sqrt{b^2-4 a c}}+\frac{\left(b-\sqrt{b^2-4 a c}\right)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{2/3} \sqrt{b^2-4 a c}}-\frac{\left(\sqrt{b^2-4 a c}+b\right)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{2/3} \sqrt{b^2-4 a c}}","-\frac{\left(b-\sqrt{b^2-4 a c}\right)^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{2/3} \sqrt{b^2-4 a c}}+\frac{\left(\sqrt{b^2-4 a c}+b\right)^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} c^{2/3} \sqrt{b^2-4 a c}}+\frac{\left(b-\sqrt{b^2-4 a c}\right)^{2/3} \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{2/3} \sqrt{b^2-4 a c}}-\frac{\left(\sqrt{b^2-4 a c}+b\right)^{2/3} \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} c^{2/3} \sqrt{b^2-4 a c}}+\frac{\left(b-\sqrt{b^2-4 a c}\right)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{2/3} \sqrt{b^2-4 a c}}-\frac{\left(\sqrt{b^2-4 a c}+b\right)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} c^{2/3} \sqrt{b^2-4 a c}}",1,"((b - Sqrt[b^2 - 4*a*c])^(2/3)*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*c^(2/3)*Sqrt[b^2 - 4*a*c]) - ((b + Sqrt[b^2 - 4*a*c])^(2/3)*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*c^(2/3)*Sqrt[b^2 - 4*a*c]) + ((b - Sqrt[b^2 - 4*a*c])^(2/3)*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*c^(2/3)*Sqrt[b^2 - 4*a*c]) - ((b + Sqrt[b^2 - 4*a*c])^(2/3)*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*c^(2/3)*Sqrt[b^2 - 4*a*c]) - ((b - Sqrt[b^2 - 4*a*c])^(2/3)*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*c^(2/3)*Sqrt[b^2 - 4*a*c]) + ((b + Sqrt[b^2 - 4*a*c])^(2/3)*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*c^(2/3)*Sqrt[b^2 - 4*a*c])","A",13,7,18,0.3889,1,"{1374, 292, 31, 634, 617, 204, 628}"
146,1,558,0,0.5736054,"\int \frac{x^3}{a+b x^3+c x^6} \, dx","Int[x^3/(a + b*x^3 + c*x^6),x]","\frac{\sqrt[3]{b-\sqrt{b^2-4 a c}} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} \sqrt[3]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[3]{\sqrt{b^2-4 a c}+b} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} \sqrt[3]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[3]{b-\sqrt{b^2-4 a c}} \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} \sqrt[3]{c} \sqrt{b^2-4 a c}}+\frac{\sqrt[3]{\sqrt{b^2-4 a c}+b} \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} \sqrt[3]{c} \sqrt{b^2-4 a c}}+\frac{\sqrt[3]{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[3]{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{c} \sqrt{b^2-4 a c}}","\frac{\sqrt[3]{b-\sqrt{b^2-4 a c}} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} \sqrt[3]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[3]{\sqrt{b^2-4 a c}+b} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} \sqrt[3]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[3]{b-\sqrt{b^2-4 a c}} \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} \sqrt[3]{c} \sqrt{b^2-4 a c}}+\frac{\sqrt[3]{\sqrt{b^2-4 a c}+b} \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} \sqrt[3]{c} \sqrt{b^2-4 a c}}+\frac{\sqrt[3]{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[3]{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} \sqrt[3]{c} \sqrt{b^2-4 a c}}",1,"((b - Sqrt[b^2 - 4*a*c])^(1/3)*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*c^(1/3)*Sqrt[b^2 - 4*a*c]) - ((b + Sqrt[b^2 - 4*a*c])^(1/3)*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*c^(1/3)*Sqrt[b^2 - 4*a*c]) - ((b - Sqrt[b^2 - 4*a*c])^(1/3)*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*c^(1/3)*Sqrt[b^2 - 4*a*c]) + ((b + Sqrt[b^2 - 4*a*c])^(1/3)*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*c^(1/3)*Sqrt[b^2 - 4*a*c]) + ((b - Sqrt[b^2 - 4*a*c])^(1/3)*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*c^(1/3)*Sqrt[b^2 - 4*a*c]) - ((b + Sqrt[b^2 - 4*a*c])^(1/3)*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*c^(1/3)*Sqrt[b^2 - 4*a*c])","A",13,7,18,0.3889,1,"{1374, 200, 31, 634, 617, 204, 628}"
147,1,558,0,0.471834,"\int \frac{x}{a+b x^3+c x^6} \, dx","Int[x/(a + b*x^3 + c*x^6),x]","\frac{\sqrt[3]{c} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{3\ 2^{2/3} \sqrt{b^2-4 a c} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt[3]{c} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{3\ 2^{2/3} \sqrt{b^2-4 a c} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt[3]{2} \sqrt[3]{c} \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt{b^2-4 a c} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{2} \sqrt[3]{c} \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt{b^2-4 a c} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt[3]{2} \sqrt[3]{c} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt{b^2-4 a c} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{2} \sqrt[3]{c} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt{b^2-4 a c} \sqrt[3]{\sqrt{b^2-4 a c}+b}}","\frac{\sqrt[3]{c} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{3\ 2^{2/3} \sqrt{b^2-4 a c} \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt[3]{c} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{3\ 2^{2/3} \sqrt{b^2-4 a c} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt[3]{2} \sqrt[3]{c} \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt{b^2-4 a c} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{2} \sqrt[3]{c} \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt{b^2-4 a c} \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt[3]{2} \sqrt[3]{c} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt{b^2-4 a c} \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{2} \sqrt[3]{c} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt{b^2-4 a c} \sqrt[3]{\sqrt{b^2-4 a c}+b}}",1,"-((2^(1/3)*c^(1/3)*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(Sqrt[3]*Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])^(1/3))) + (2^(1/3)*c^(1/3)*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(Sqrt[3]*Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])^(1/3)) - (2^(1/3)*c^(1/3)*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])^(1/3)) + (2^(1/3)*c^(1/3)*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])^(1/3)) + (c^(1/3)*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(3*2^(2/3)*Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])^(1/3)) - (c^(1/3)*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(3*2^(2/3)*Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])^(1/3))","A",13,7,16,0.4375,1,"{1375, 292, 31, 634, 617, 204, 628}"
148,1,558,0,0.5954392,"\int \frac{1}{a+b x^3+c x^6} \, dx","Int[(a + b*x^3 + c*x^6)^(-1),x]","-\frac{c^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{3 \sqrt[3]{2} \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{3 \sqrt[3]{2} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{2^{2/3} c^{2/3} \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{2^{2/3} c^{2/3} \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{2^{2/3} c^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{2^{2/3} c^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}","-\frac{c^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{3 \sqrt[3]{2} \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{3 \sqrt[3]{2} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{2^{2/3} c^{2/3} \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{2^{2/3} c^{2/3} \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{2^{2/3} c^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{2^{2/3} c^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}",1,"-((2^(2/3)*c^(2/3)*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(Sqrt[3]*Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])^(2/3))) + (2^(2/3)*c^(2/3)*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(Sqrt[3]*Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])^(2/3)) + (2^(2/3)*c^(2/3)*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])^(2/3)) - (2^(2/3)*c^(2/3)*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])^(2/3)) - (c^(2/3)*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(3*2^(1/3)*Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])^(2/3)) + (c^(2/3)*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(3*2^(1/3)*Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])^(2/3))","A",13,7,14,0.5000,1,"{1347, 200, 31, 634, 617, 204, 628}"
149,1,610,0,0.8181175,"\int \frac{1}{x^2 \left(a+b x^3+c x^6\right)} \, dx","Int[1/(x^2*(a + b*x^3 + c*x^6)),x]","-\frac{\sqrt[3]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt[3]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt[3]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt[3]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{1}{a x}","-\frac{\sqrt[3]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt[3]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6\ 2^{2/3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt[3]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3\ 2^{2/3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt[3]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} a \sqrt[3]{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt[3]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} a \sqrt[3]{\sqrt{b^2-4 a c}+b}}-\frac{1}{a x}",1,"-(1/(a*x)) + (c^(1/3)*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*a*(b - Sqrt[b^2 - 4*a*c])^(1/3)) + (c^(1/3)*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(2/3)*Sqrt[3]*a*(b + Sqrt[b^2 - 4*a*c])^(1/3)) + (c^(1/3)*(1 + b/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*a*(b - Sqrt[b^2 - 4*a*c])^(1/3)) + (c^(1/3)*(1 - b/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(2/3)*a*(b + Sqrt[b^2 - 4*a*c])^(1/3)) - (c^(1/3)*(1 + b/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*a*(b - Sqrt[b^2 - 4*a*c])^(1/3)) - (c^(1/3)*(1 - b/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(2/3)*a*(b + Sqrt[b^2 - 4*a*c])^(1/3))","A",14,8,18,0.4444,1,"{1368, 1510, 292, 31, 634, 617, 204, 628}"
150,1,612,0,0.8150989,"\int \frac{1}{x^3 \left(a+b x^3+c x^6\right)} \, dx","Int[1/(x^3*(a + b*x^3 + c*x^6)),x]","\frac{c^{2/3} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{c^{2/3} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{c^{2/3} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{c^{2/3} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{1}{2 a x^2}","\frac{c^{2/3} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{c^{2/3} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{c^{2/3} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{c^{2/3} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} a \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} a \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + (c^(2/3)*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*a*(b - Sqrt[b^2 - 4*a*c])^(2/3)) + (c^(2/3)*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*a*(b + Sqrt[b^2 - 4*a*c])^(2/3)) - (c^(2/3)*(1 + b/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*a*(b - Sqrt[b^2 - 4*a*c])^(2/3)) - (c^(2/3)*(1 - b/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*a*(b + Sqrt[b^2 - 4*a*c])^(2/3)) + (c^(2/3)*(1 + b/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*a*(b - Sqrt[b^2 - 4*a*c])^(2/3)) + (c^(2/3)*(1 - b/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*a*(b + Sqrt[b^2 - 4*a*c])^(2/3))","A",14,8,18,0.4444,1,"{1368, 1422, 200, 31, 634, 617, 204, 628}"
151,1,35,0,0.024081,"\int \frac{x^{11}}{3+4 x^3+x^6} \, dx","Int[x^11/(3 + 4*x^3 + x^6),x]","\frac{x^6}{6}-\frac{4 x^3}{3}-\frac{1}{6} \log \left(x^3+1\right)+\frac{9}{2} \log \left(x^3+3\right)","\frac{x^6}{6}-\frac{4 x^3}{3}-\frac{1}{6} \log \left(x^3+1\right)+\frac{9}{2} \log \left(x^3+3\right)",1,"(-4*x^3)/3 + x^6/6 - Log[1 + x^3]/6 + (9*Log[3 + x^3])/2","A",6,4,16,0.2500,1,"{1357, 701, 632, 31}"
152,1,28,0,0.0187006,"\int \frac{x^8}{3+4 x^3+x^6} \, dx","Int[x^8/(3 + 4*x^3 + x^6),x]","\frac{x^3}{3}+\frac{1}{6} \log \left(x^3+1\right)-\frac{3}{2} \log \left(x^3+3\right)","\frac{x^3}{3}+\frac{1}{6} \log \left(x^3+1\right)-\frac{3}{2} \log \left(x^3+3\right)",1,"x^3/3 + Log[1 + x^3]/6 - (3*Log[3 + x^3])/2","A",5,4,16,0.2500,1,"{1357, 703, 632, 31}"
153,1,21,0,0.0141699,"\int \frac{x^5}{3+4 x^3+x^6} \, dx","Int[x^5/(3 + 4*x^3 + x^6),x]","\frac{1}{2} \log \left(x^3+3\right)-\frac{1}{6} \log \left(x^3+1\right)","\frac{1}{2} \log \left(x^3+3\right)-\frac{1}{6} \log \left(x^3+1\right)",1,"-Log[1 + x^3]/6 + Log[3 + x^3]/2","A",4,3,16,0.1875,1,"{1357, 632, 31}"
154,1,21,0,0.0139787,"\int \frac{x^2}{3+4 x^3+x^6} \, dx","Int[x^2/(3 + 4*x^3 + x^6),x]","\frac{1}{6} \log \left(x^3+1\right)-\frac{1}{6} \log \left(x^3+3\right)","-\frac{1}{3} \tanh ^{-1}\left(x^3+2\right)",1,"Log[1 + x^3]/6 - Log[3 + x^3]/6","B",4,3,16,0.1875,1,"{1352, 616, 31}"
155,1,27,0,0.0189696,"\int \frac{1}{x \left(3+4 x^3+x^6\right)} \, dx","Int[1/(x*(3 + 4*x^3 + x^6)),x]","-\frac{1}{6} \log \left(x^3+1\right)+\frac{1}{18} \log \left(x^3+3\right)+\frac{\log (x)}{3}","-\frac{1}{6} \log \left(x^3+1\right)+\frac{1}{18} \log \left(x^3+3\right)+\frac{\log (x)}{3}",1,"Log[x]/3 - Log[1 + x^3]/6 + Log[3 + x^3]/18","A",6,5,16,0.3125,1,"{1357, 705, 29, 632, 31}"
156,1,34,0,0.0318425,"\int \frac{1}{x^4 \left(3+4 x^3+x^6\right)} \, dx","Int[1/(x^4*(3 + 4*x^3 + x^6)),x]","-\frac{1}{9 x^3}+\frac{1}{6} \log \left(x^3+1\right)-\frac{1}{54} \log \left(x^3+3\right)-\frac{4 \log (x)}{9}","-\frac{1}{9 x^3}+\frac{1}{6} \log \left(x^3+1\right)-\frac{1}{54} \log \left(x^3+3\right)-\frac{4 \log (x)}{9}",1,"-1/(9*x^3) - (4*Log[x])/9 + Log[1 + x^3]/6 - Log[3 + x^3]/54","A",4,3,16,0.1875,1,"{1357, 709, 800}"
157,1,41,0,0.03602,"\int \frac{1}{x^7 \left(3+4 x^3+x^6\right)} \, dx","Int[1/(x^7*(3 + 4*x^3 + x^6)),x]","\frac{4}{27 x^3}-\frac{1}{18 x^6}-\frac{1}{6} \log \left(x^3+1\right)+\frac{1}{162} \log \left(x^3+3\right)+\frac{13 \log (x)}{27}","\frac{4}{27 x^3}-\frac{1}{18 x^6}-\frac{1}{6} \log \left(x^3+1\right)+\frac{1}{162} \log \left(x^3+3\right)+\frac{13 \log (x)}{27}",1,"-1/(18*x^6) + 4/(27*x^3) + (13*Log[x])/27 - Log[1 + x^3]/6 + Log[3 + x^3]/162","A",4,3,16,0.1875,1,"{1357, 709, 800}"
158,1,124,0,0.1141431,"\int \frac{x^{10}}{3+4 x^3+x^6} \, dx","Int[x^10/(3 + 4*x^3 + x^6),x]","\frac{x^5}{5}-2 x^2-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{3}{4} 3^{2/3} \log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)+\frac{1}{6} \log (x+1)-\frac{3}{2} 3^{2/3} \log \left(x+\sqrt[3]{3}\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{9}{2} \sqrt[6]{3} \tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)","\frac{x^5}{5}-2 x^2-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{3}{4} 3^{2/3} \log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)+\frac{1}{6} \log (x+1)-\frac{3}{2} 3^{2/3} \log \left(x+\sqrt[3]{3}\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{9}{2} \sqrt[6]{3} \tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)",1,"-2*x^2 + x^5/5 + ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) - (9*3^(1/6)*ArcTan[(3^(1/3) - 2*x)/3^(5/6)])/2 + Log[1 + x]/6 - (3*3^(2/3)*Log[3^(1/3) + x])/2 - Log[1 - x + x^2]/12 + (3*3^(2/3)*Log[3^(2/3) - 3^(1/3)*x + x^2])/4","A",15,10,16,0.6250,1,"{1367, 1502, 1510, 292, 31, 634, 618, 204, 628, 617}"
159,1,122,0,0.0936454,"\int \frac{x^9}{3+4 x^3+x^6} \, dx","Int[x^9/(3 + 4*x^3 + x^6),x]","\frac{x^4}{4}+\frac{1}{12} \log \left(x^2-x+1\right)-\frac{3}{4} \sqrt[3]{3} \log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)-4 x-\frac{1}{6} \log (x+1)+\frac{3}{2} \sqrt[3]{3} \log \left(x+\sqrt[3]{3}\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{3}{2} 3^{5/6} \tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)","\frac{x^4}{4}+\frac{1}{12} \log \left(x^2-x+1\right)-\frac{3}{4} \sqrt[3]{3} \log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)-4 x-\frac{1}{6} \log (x+1)+\frac{3}{2} \sqrt[3]{3} \log \left(x+\sqrt[3]{3}\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{3}{2} 3^{5/6} \tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)",1,"-4*x + x^4/4 + ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) - (3*3^(5/6)*ArcTan[(3^(1/3) - 2*x)/3^(5/6)])/2 - Log[1 + x]/6 + (3*3^(1/3)*Log[3^(1/3) + x])/2 + Log[1 - x + x^2]/12 - (3*3^(1/3)*Log[3^(2/3) - 3^(1/3)*x + x^2])/4","A",15,10,16,0.6250,1,"{1367, 1502, 1422, 200, 31, 634, 618, 204, 628, 617}"
160,1,119,0,0.081783,"\int \frac{x^7}{3+4 x^3+x^6} \, dx","Int[x^7/(3 + 4*x^3 + x^6),x]","\frac{x^2}{2}+\frac{1}{12} \log \left(x^2-x+1\right)-\frac{1}{4} 3^{2/3} \log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)-\frac{1}{6} \log (x+1)+\frac{1}{2} 3^{2/3} \log \left(x+\sqrt[3]{3}\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{3}{2} \sqrt[6]{3} \tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)","\frac{x^2}{2}+\frac{1}{12} \log \left(x^2-x+1\right)-\frac{1}{4} 3^{2/3} \log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)-\frac{1}{6} \log (x+1)+\frac{1}{2} 3^{2/3} \log \left(x+\sqrt[3]{3}\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{3}{2} \sqrt[6]{3} \tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)",1,"x^2/2 - ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + (3*3^(1/6)*ArcTan[(3^(1/3) - 2*x)/3^(5/6)])/2 - Log[1 + x]/6 + (3^(2/3)*Log[3^(1/3) + x])/2 + Log[1 - x + x^2]/12 - (3^(2/3)*Log[3^(2/3) - 3^(1/3)*x + x^2])/4","A",14,9,16,0.5625,1,"{1367, 1510, 292, 31, 634, 618, 204, 628, 617}"
161,1,113,0,0.0739025,"\int \frac{x^6}{3+4 x^3+x^6} \, dx","Int[x^6/(3 + 4*x^3 + x^6),x]","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{1}{4} \sqrt[3]{3} \log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)+x+\frac{1}{6} \log (x+1)-\frac{1}{2} \sqrt[3]{3} \log \left(x+\sqrt[3]{3}\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{2} 3^{5/6} \tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{1}{4} \sqrt[3]{3} \log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)+x+\frac{1}{6} \log (x+1)-\frac{1}{2} \sqrt[3]{3} \log \left(x+\sqrt[3]{3}\right)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{2} 3^{5/6} \tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)",1,"x - ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + (3^(5/6)*ArcTan[(3^(1/3) - 2*x)/3^(5/6)])/2 + Log[1 + x]/6 - (3^(1/3)*Log[3^(1/3) + x])/2 - Log[1 - x + x^2]/12 + (3^(1/3)*Log[3^(2/3) - 3^(1/3)*x + x^2])/4","A",14,9,16,0.5625,1,"{1367, 1422, 200, 31, 634, 618, 204, 628, 617}"
162,1,112,0,0.0680056,"\int \frac{x^4}{3+4 x^3+x^6} \, dx","Int[x^4/(3 + 4*x^3 + x^6),x]","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{4 \sqrt[3]{3}}+\frac{1}{6} \log (x+1)-\frac{\log \left(x+\sqrt[3]{3}\right)}{2 \sqrt[3]{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{2} \sqrt[6]{3} \tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{4 \sqrt[3]{3}}+\frac{1}{6} \log (x+1)-\frac{\log \left(x+\sqrt[3]{3}\right)}{2 \sqrt[3]{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{2} \sqrt[6]{3} \tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)",1,"ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) - (3^(1/6)*ArcTan[(3^(1/3) - 2*x)/3^(5/6)])/2 + Log[1 + x]/6 - Log[3^(1/3) + x]/(2*3^(1/3)) - Log[1 - x + x^2]/12 + Log[3^(2/3) - 3^(1/3)*x + x^2]/(4*3^(1/3))","A",13,8,16,0.5000,1,"{1374, 292, 31, 634, 617, 204, 628, 618}"
163,1,112,0,0.0693467,"\int \frac{x^3}{3+4 x^3+x^6} \, dx","Int[x^3/(3 + 4*x^3 + x^6),x]","\frac{1}{12} \log \left(x^2-x+1\right)-\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{4\ 3^{2/3}}-\frac{1}{6} \log (x+1)+\frac{\log \left(x+\sqrt[3]{3}\right)}{2\ 3^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{2 \sqrt[6]{3}}","\frac{1}{12} \log \left(x^2-x+1\right)-\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{4\ 3^{2/3}}-\frac{1}{6} \log (x+1)+\frac{\log \left(x+\sqrt[3]{3}\right)}{2\ 3^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{2 \sqrt[6]{3}}",1,"ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTan[(3^(1/3) - 2*x)/3^(5/6)]/(2*3^(1/6)) - Log[1 + x]/6 + Log[3^(1/3) + x]/(2*3^(2/3)) + Log[1 - x + x^2]/12 - Log[3^(2/3) - 3^(1/3)*x + x^2]/(4*3^(2/3))","A",13,8,16,0.5000,1,"{1374, 200, 31, 634, 617, 204, 628, 618}"
164,1,112,0,0.0690096,"\int \frac{x}{3+4 x^3+x^6} \, dx","Int[x/(3 + 4*x^3 + x^6),x]","\frac{1}{12} \log \left(x^2-x+1\right)-\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{12 \sqrt[3]{3}}-\frac{1}{6} \log (x+1)+\frac{\log \left(x+\sqrt[3]{3}\right)}{6 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{2\ 3^{5/6}}","\frac{1}{12} \log \left(x^2-x+1\right)-\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{12 \sqrt[3]{3}}-\frac{1}{6} \log (x+1)+\frac{\log \left(x+\sqrt[3]{3}\right)}{6 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{2\ 3^{5/6}}",1,"-ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTan[(3^(1/3) - 2*x)/3^(5/6)]/(2*3^(5/6)) - Log[1 + x]/6 + Log[3^(1/3) + x]/(6*3^(1/3)) + Log[1 - x + x^2]/12 - Log[3^(2/3) - 3^(1/3)*x + x^2]/(12*3^(1/3))","A",13,8,14,0.5714,1,"{1375, 292, 31, 634, 618, 204, 628, 617}"
165,1,112,0,0.0652153,"\int \frac{1}{3+4 x^3+x^6} \, dx","Int[(3 + 4*x^3 + x^6)^(-1),x]","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{12\ 3^{2/3}}+\frac{1}{6} \log (x+1)-\frac{\log \left(x+\sqrt[3]{3}\right)}{6\ 3^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{6 \sqrt[6]{3}}","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{12\ 3^{2/3}}+\frac{1}{6} \log (x+1)-\frac{\log \left(x+\sqrt[3]{3}\right)}{6\ 3^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{6 \sqrt[6]{3}}",1,"-ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTan[(3^(1/3) - 2*x)/3^(5/6)]/(6*3^(1/6)) + Log[1 + x]/6 - Log[3^(1/3) + x]/(6*3^(2/3)) - Log[1 - x + x^2]/12 + Log[3^(2/3) - 3^(1/3)*x + x^2]/(12*3^(2/3))","A",13,8,12,0.6667,1,"{1347, 200, 31, 634, 618, 204, 628, 617}"
166,1,119,0,0.0822884,"\int \frac{1}{x^2 \left(3+4 x^3+x^6\right)} \, dx","Int[1/(x^2*(3 + 4*x^3 + x^6)),x]","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{36 \sqrt[3]{3}}-\frac{1}{3 x}+\frac{1}{6} \log (x+1)-\frac{\log \left(x+\sqrt[3]{3}\right)}{18 \sqrt[3]{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{6\ 3^{5/6}}","-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{36 \sqrt[3]{3}}-\frac{1}{3 x}+\frac{1}{6} \log (x+1)-\frac{\log \left(x+\sqrt[3]{3}\right)}{18 \sqrt[3]{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{6\ 3^{5/6}}",1,"-1/(3*x) + ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTan[(3^(1/3) - 2*x)/3^(5/6)]/(6*3^(5/6)) + Log[1 + x]/6 - Log[3^(1/3) + x]/(18*3^(1/3)) - Log[1 - x + x^2]/12 + Log[3^(2/3) - 3^(1/3)*x + x^2]/(36*3^(1/3))","A",14,9,16,0.5625,1,"{1368, 1510, 292, 31, 634, 618, 204, 628, 617}"
167,1,119,0,0.0775538,"\int \frac{1}{x^3 \left(3+4 x^3+x^6\right)} \, dx","Int[1/(x^3*(3 + 4*x^3 + x^6)),x]","-\frac{1}{6 x^2}+\frac{1}{12} \log \left(x^2-x+1\right)-\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{36\ 3^{2/3}}-\frac{1}{6} \log (x+1)+\frac{\log \left(x+\sqrt[3]{3}\right)}{18\ 3^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{18 \sqrt[6]{3}}","-\frac{1}{6 x^2}+\frac{1}{12} \log \left(x^2-x+1\right)-\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{36\ 3^{2/3}}-\frac{1}{6} \log (x+1)+\frac{\log \left(x+\sqrt[3]{3}\right)}{18\ 3^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{18 \sqrt[6]{3}}",1,"-1/(6*x^2) + ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTan[(3^(1/3) - 2*x)/3^(5/6)]/(18*3^(1/6)) - Log[1 + x]/6 + Log[3^(1/3) + x]/(18*3^(2/3)) + Log[1 - x + x^2]/12 - Log[3^(2/3) - 3^(1/3)*x + x^2]/(36*3^(2/3))","A",14,9,16,0.5625,1,"{1368, 1422, 200, 31, 634, 618, 204, 628, 617}"
168,1,126,0,0.1029802,"\int \frac{1}{x^5 \left(3+4 x^3+x^6\right)} \, dx","Int[1/(x^5*(3 + 4*x^3 + x^6)),x]","-\frac{1}{12 x^4}+\frac{1}{12} \log \left(x^2-x+1\right)-\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{108 \sqrt[3]{3}}+\frac{4}{9 x}-\frac{1}{6} \log (x+1)+\frac{\log \left(x+\sqrt[3]{3}\right)}{54 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{18\ 3^{5/6}}","-\frac{1}{12 x^4}+\frac{1}{12} \log \left(x^2-x+1\right)-\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{108 \sqrt[3]{3}}+\frac{4}{9 x}-\frac{1}{6} \log (x+1)+\frac{\log \left(x+\sqrt[3]{3}\right)}{54 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{18\ 3^{5/6}}",1,"-1/(12*x^4) + 4/(9*x) - ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTan[(3^(1/3) - 2*x)/3^(5/6)]/(18*3^(5/6)) - Log[1 + x]/6 + Log[3^(1/3) + x]/(54*3^(1/3)) + Log[1 - x + x^2]/12 - Log[3^(2/3) - 3^(1/3)*x + x^2]/(108*3^(1/3))","A",15,10,16,0.6250,1,"{1368, 1504, 1510, 292, 31, 634, 618, 204, 628, 617}"
169,1,126,0,0.0985897,"\int \frac{1}{x^6 \left(3+4 x^3+x^6\right)} \, dx","Int[1/(x^6*(3 + 4*x^3 + x^6)),x]","\frac{2}{9 x^2}-\frac{1}{15 x^5}-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{108\ 3^{2/3}}+\frac{1}{6} \log (x+1)-\frac{\log \left(x+\sqrt[3]{3}\right)}{54\ 3^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{54 \sqrt[6]{3}}","\frac{2}{9 x^2}-\frac{1}{15 x^5}-\frac{1}{12} \log \left(x^2-x+1\right)+\frac{\log \left(x^2-\sqrt[3]{3} x+3^{2/3}\right)}{108\ 3^{2/3}}+\frac{1}{6} \log (x+1)-\frac{\log \left(x+\sqrt[3]{3}\right)}{54\ 3^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{3}-2 x}{3^{5/6}}\right)}{54 \sqrt[6]{3}}",1,"-1/(15*x^5) + 2/(9*x^2) - ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTan[(3^(1/3) - 2*x)/3^(5/6)]/(54*3^(1/6)) + Log[1 + x]/6 - Log[3^(1/3) + x]/(54*3^(2/3)) - Log[1 - x + x^2]/12 + Log[3^(2/3) - 3^(1/3)*x + x^2]/(108*3^(2/3))","A",15,10,16,0.6250,1,"{1368, 1504, 1422, 200, 31, 634, 618, 204, 628, 617}"
170,1,412,0,0.4283215,"\int \frac{x^6}{1-x^3+x^6} \, dx","Int[x^6/(1 - x^3 + x^6),x]","-\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}+x+\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}","-\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}+x+\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}",1,"x + ((I - Sqrt[3])*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) - ((I + Sqrt[3])*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) + ((3 - I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) + ((3 + I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) - ((3 - I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) - ((3 + I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 + I*Sqrt[3])^(2/3))","A",14,8,16,0.5000,1,"{1367, 1422, 200, 31, 634, 617, 204, 628}"
171,1,39,0,0.0354415,"\int \frac{x^5}{1-x^3+x^6} \, dx","Int[x^5/(1 - x^3 + x^6),x]","\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-ArcTan[(1 - 2*x^3)/Sqrt[3]]/(3*Sqrt[3]) + Log[1 - x^3 + x^6]/6","A",5,5,16,0.3125,1,"{1357, 634, 618, 204, 628}"
172,1,411,0,0.2805915,"\int \frac{x^4}{1-x^3+x^6} \, dx","Int[x^4/(1 - x^3 + x^6),x]","-\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}+\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}+\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}","-\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}+\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}+\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}",1,"((I + Sqrt[3])*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) - ((I - Sqrt[3])*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(2/3)*(1 + I*Sqrt[3])^(1/3)) + ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) + ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(2/3)*(1 + I*Sqrt[3])^(1/3)) - ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) - ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(2/3)*(1 + I*Sqrt[3])^(1/3))","A",13,7,16,0.4375,1,"{1374, 292, 31, 634, 617, 204, 628}"
173,1,411,0,0.277631,"\int \frac{x^3}{1-x^3+x^6} \, dx","Int[x^3/(1 - x^3 + x^6),x]","-\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}+\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}","-\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}+\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}",1,"-((I + Sqrt[3])*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) + ((I - Sqrt[3])*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) + ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) + ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) - ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) - ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 + I*Sqrt[3])^(2/3))","A",13,7,16,0.4375,1,"{1374, 200, 31, 634, 617, 204, 628}"
174,1,23,0,0.0230573,"\int \frac{x^2}{1-x^3+x^6} \, dx","Int[x^2/(1 - x^3 + x^6),x]","-\frac{2 \tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{2 \tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(-2*ArcTan[(1 - 2*x^3)/Sqrt[3]])/(3*Sqrt[3])","A",3,3,16,0.1875,1,"{1352, 618, 204}"
175,1,375,0,0.2503896,"\int \frac{x}{1-x^3+x^6} \, dx","Int[x/(1 - x^3 + x^6),x]","-\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{3\ 2^{2/3} \sqrt{3} \sqrt[3]{1-i \sqrt{3}}}+\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{3\ 2^{2/3} \sqrt{3} \sqrt[3]{1+i \sqrt{3}}}+\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}-\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}+\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}-\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}","-\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{3\ 2^{2/3} \sqrt{3} \sqrt[3]{1-i \sqrt{3}}}+\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{3\ 2^{2/3} \sqrt{3} \sqrt[3]{1+i \sqrt{3}}}+\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}-\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}+\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}-\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}",1,"((I/3)*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/((1 - I*Sqrt[3])/2)^(1/3) - ((I/3)*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/((1 + I*Sqrt[3])/2)^(1/3) + ((I/3)*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(Sqrt[3]*((1 - I*Sqrt[3])/2)^(1/3)) - ((I/3)*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(Sqrt[3]*((1 + I*Sqrt[3])/2)^(1/3)) - ((I/3)*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(2^(2/3)*Sqrt[3]*(1 - I*Sqrt[3])^(1/3)) + ((I/3)*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(2^(2/3)*Sqrt[3]*(1 + I*Sqrt[3])^(1/3))","A",13,7,14,0.5000,1,"{1375, 292, 31, 634, 617, 204, 628}"
176,1,375,0,0.2424503,"\int \frac{1}{1-x^3+x^6} \, dx","Int[(1 - x^3 + x^6)^(-1),x]","-\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{3 \sqrt[3]{2} \sqrt{3} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{i \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{3 \sqrt[3]{2} \sqrt{3} \left(1+i \sqrt{3}\right)^{2/3}}+\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{3 \sqrt{3} \left(\frac{1}{2} \left(1-i \sqrt{3}\right)\right)^{2/3}}-\frac{i \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{3 \sqrt{3} \left(\frac{1}{2} \left(1+i \sqrt{3}\right)\right)^{2/3}}-\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \left(\frac{1}{2} \left(1-i \sqrt{3}\right)\right)^{2/3}}+\frac{i \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \left(\frac{1}{2} \left(1+i \sqrt{3}\right)\right)^{2/3}}","-\frac{(-1)^{5/18} \left(3 \log \left(\sqrt[9]{-1}-x\right)+\log (2)\right)}{9 \sqrt{3}}+\frac{(-1)^{13/18} \log \left(-\sqrt[3]{2} \left(x+(-1)^{8/9}\right)\right)}{3 \sqrt{3}}-\frac{(-1)^{13/18} \log \left(-2^{2/3} \left(\left((-1)^{8/9}-x\right) x+(-1)^{7/9}\right)\right)}{6 \sqrt{3}}+\frac{(-1)^{5/18} \log \left(2^{2/3} \left(x \left(x+\sqrt[9]{-1}\right)+(-1)^{2/9}\right)\right)}{6 \sqrt{3}}-\frac{1}{3} (-1)^{13/18} \tan ^{-1}\left(\frac{2 \sqrt[9]{-1} x+1}{\sqrt{3}}\right)+\frac{1}{3} (-1)^{5/18} \tan ^{-1}\left(\frac{1-2 (-1)^{8/9} x}{\sqrt{3}}\right)",1,"((-I/3)*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/((1 - I*Sqrt[3])/2)^(2/3) + ((I/3)*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/((1 + I*Sqrt[3])/2)^(2/3) + ((I/3)*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(Sqrt[3]*((1 - I*Sqrt[3])/2)^(2/3)) - ((I/3)*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(Sqrt[3]*((1 + I*Sqrt[3])/2)^(2/3)) - ((I/3)*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(2^(1/3)*Sqrt[3]*(1 - I*Sqrt[3])^(2/3)) + ((I/3)*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(2^(1/3)*Sqrt[3]*(1 + I*Sqrt[3])^(2/3))","C",13,7,12,0.5833,1,"{1347, 200, 31, 634, 617, 204, 628}"
177,1,41,0,0.0394801,"\int \frac{1}{x \left(1-x^3+x^6\right)} \, dx","Int[1/(x*(1 - x^3 + x^6)),x]","-\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}+\log (x)","-\frac{1}{6} \log \left(x^6-x^3+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}+\log (x)",1,"-ArcTan[(1 - 2*x^3)/Sqrt[3]]/(3*Sqrt[3]) + Log[x] - Log[1 - x^3 + x^6]/6","A",7,7,16,0.4375,1,"{1357, 705, 29, 634, 618, 204, 628}"
178,1,416,0,0.2997148,"\int \frac{1}{x^2 \left(1-x^3+x^6\right)} \, dx","Int[1/(x^2*(1 - x^3 + x^6)),x]","\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{1}{x}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}","\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{1}{x}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}",1,"-x^(-1) + ((I - Sqrt[3])*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) - ((I + Sqrt[3])*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(2/3)*(1 + I*Sqrt[3])^(1/3)) - ((3 - I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) - ((3 + I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(2/3)*(1 + I*Sqrt[3])^(1/3)) + ((3 - I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) + ((3 + I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(2/3)*(1 + I*Sqrt[3])^(1/3))","A",14,8,16,0.5000,1,"{1368, 1510, 292, 31, 634, 617, 204, 628}"
179,1,418,0,0.3424751,"\int \frac{1}{x^3 \left(1-x^3+x^6\right)} \, dx","Int[1/(x^3*(1 - x^3 + x^6)),x]","-\frac{1}{2 x^2}+\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}","-\frac{1}{2 x^2}+\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}-\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1-i \sqrt{3}\right)^{2/3}}+\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3 \sqrt[3]{2} \left(1+i \sqrt{3}\right)^{2/3}}",1,"-1/(2*x^2) - ((I - Sqrt[3])*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) + ((I + Sqrt[3])*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) - ((3 - I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) - ((3 + I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(1/3)*(1 + I*Sqrt[3])^(2/3)) + ((3 - I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 - I*Sqrt[3])^(2/3)) + ((3 + I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(1/3)*(1 + I*Sqrt[3])^(2/3))","A",14,8,16,0.5000,1,"{1368, 1422, 200, 31, 634, 617, 204, 628}"
180,1,48,0,0.0520241,"\int \frac{1}{x^4 \left(1-x^3+x^6\right)} \, dx","Int[1/(x^4*(1 - x^3 + x^6)),x]","-\frac{1}{3 x^3}-\frac{1}{6} \log \left(x^6-x^3+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}+\log (x)","-\frac{1}{3 x^3}-\frac{1}{6} \log \left(x^6-x^3+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^3}{\sqrt{3}}\right)}{3 \sqrt{3}}+\log (x)",1,"-1/(3*x^3) + ArcTan[(1 - 2*x^3)/Sqrt[3]]/(3*Sqrt[3]) + Log[x] - Log[1 - x^3 + x^6]/6","A",8,7,16,0.4375,1,"{1357, 709, 800, 634, 618, 204, 628}"
181,1,423,0,0.3691714,"\int \frac{1}{x^5 \left(1-x^3+x^6\right)} \, dx","Int[1/(x^5*(1 - x^3 + x^6)),x]","-\frac{1}{4 x^4}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{1}{x}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}","-\frac{1}{4 x^4}+\frac{\left(3+i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1-i \sqrt{3}\right)} x+\left(1-i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(3-i \sqrt{3}\right) \log \left(2^{2/3} x^2+\sqrt[3]{2 \left(1+i \sqrt{3}\right)} x+\left(1+i \sqrt{3}\right)^{2/3}\right)}{18\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{1}{x}-\frac{\left(3+i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}-\frac{\left(3-i \sqrt{3}\right) \log \left(-\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{3}}\right)}{9\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}-\frac{\left(\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1-i \sqrt{3}}}+\frac{\left(-\sqrt{3}+i\right) \tan ^{-1}\left(\frac{1+\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{3}\right)}}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt[3]{1+i \sqrt{3}}}",1,"-1/(4*x^4) - x^(-1) - ((I + Sqrt[3])*ArcTan[(1 + (2*x)/((1 - I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) + ((I - Sqrt[3])*ArcTan[(1 + (2*x)/((1 + I*Sqrt[3])/2)^(1/3))/Sqrt[3]])/(3*2^(2/3)*(1 + I*Sqrt[3])^(1/3)) - ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) - ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(1/3) - 2^(1/3)*x])/(9*2^(2/3)*(1 + I*Sqrt[3])^(1/3)) + ((3 + I*Sqrt[3])*Log[(1 - I*Sqrt[3])^(2/3) + (2*(1 - I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(2/3)*(1 - I*Sqrt[3])^(1/3)) + ((3 - I*Sqrt[3])*Log[(1 + I*Sqrt[3])^(2/3) + (2*(1 + I*Sqrt[3]))^(1/3)*x + 2^(2/3)*x^2])/(18*2^(2/3)*(1 + I*Sqrt[3])^(1/3))","A",16,10,16,0.6250,1,"{1368, 1504, 12, 1374, 292, 31, 634, 617, 204, 628}"
182,1,381,0,0.4027228,"\int \frac{1}{2+x^3+x^6} \, dx","Int[(2 + x^3 + x^6)^(-1),x]","\frac{i \log \left(2^{2/3} x^2-\sqrt[3]{2 \left(1-i \sqrt{7}\right)} x+\left(1-i \sqrt{7}\right)^{2/3}\right)}{3 \sqrt[3]{2} \sqrt{7} \left(1-i \sqrt{7}\right)^{2/3}}-\frac{i \log \left(2^{2/3} x^2-\sqrt[3]{2 \left(1+i \sqrt{7}\right)} x+\left(1+i \sqrt{7}\right)^{2/3}\right)}{3 \sqrt[3]{2} \sqrt{7} \left(1+i \sqrt{7}\right)^{2/3}}-\frac{i \log \left(\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{7}}\right)}{3 \sqrt{7} \left(\frac{1}{2} \left(1-i \sqrt{7}\right)\right)^{2/3}}+\frac{i \log \left(\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{7}}\right)}{3 \sqrt{7} \left(\frac{1}{2} \left(1+i \sqrt{7}\right)\right)^{2/3}}+\frac{i \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{7}\right)}}}{\sqrt{3}}\right)}{\sqrt{21} \left(\frac{1}{2} \left(1-i \sqrt{7}\right)\right)^{2/3}}-\frac{i \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{7}\right)}}}{\sqrt{3}}\right)}{\sqrt{21} \left(\frac{1}{2} \left(1+i \sqrt{7}\right)\right)^{2/3}}","\frac{i \log \left(2^{2/3} x^2-\sqrt[3]{2 \left(1-i \sqrt{7}\right)} x+\left(1-i \sqrt{7}\right)^{2/3}\right)}{3 \sqrt[3]{2} \sqrt{7} \left(1-i \sqrt{7}\right)^{2/3}}-\frac{i \log \left(2^{2/3} x^2-\sqrt[3]{2 \left(1+i \sqrt{7}\right)} x+\left(1+i \sqrt{7}\right)^{2/3}\right)}{3 \sqrt[3]{2} \sqrt{7} \left(1+i \sqrt{7}\right)^{2/3}}-\frac{i \log \left(\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{7}}\right)}{3 \sqrt{7} \left(\frac{1}{2} \left(1-i \sqrt{7}\right)\right)^{2/3}}+\frac{i \log \left(\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{7}}\right)}{3 \sqrt{7} \left(\frac{1}{2} \left(1+i \sqrt{7}\right)\right)^{2/3}}+\frac{i \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{7}\right)}}}{\sqrt{3}}\right)}{\sqrt{21} \left(\frac{1}{2} \left(1-i \sqrt{7}\right)\right)^{2/3}}-\frac{i \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{7}\right)}}}{\sqrt{3}}\right)}{\sqrt{21} \left(\frac{1}{2} \left(1+i \sqrt{7}\right)\right)^{2/3}}",1,"(I*ArcTan[(1 - (2*x)/((1 - I*Sqrt[7])/2)^(1/3))/Sqrt[3]])/(Sqrt[21]*((1 - I*Sqrt[7])/2)^(2/3)) - (I*ArcTan[(1 - (2*x)/((1 + I*Sqrt[7])/2)^(1/3))/Sqrt[3]])/(Sqrt[21]*((1 + I*Sqrt[7])/2)^(2/3)) - ((I/3)*Log[(1 - I*Sqrt[7])^(1/3) + 2^(1/3)*x])/(Sqrt[7]*((1 - I*Sqrt[7])/2)^(2/3)) + ((I/3)*Log[(1 + I*Sqrt[7])^(1/3) + 2^(1/3)*x])/(Sqrt[7]*((1 + I*Sqrt[7])/2)^(2/3)) + ((I/3)*Log[(1 - I*Sqrt[7])^(2/3) - (2*(1 - I*Sqrt[7]))^(1/3)*x + 2^(2/3)*x^2])/(2^(1/3)*Sqrt[7]*(1 - I*Sqrt[7])^(2/3)) - ((I/3)*Log[(1 + I*Sqrt[7])^(2/3) - (2*(1 + I*Sqrt[7]))^(1/3)*x + 2^(2/3)*x^2])/(2^(1/3)*Sqrt[7]*(1 + I*Sqrt[7])^(2/3))","A",13,7,10,0.7000,1,"{1347, 200, 31, 634, 617, 204, 628}"
183,1,23,0,0.0241188,"\int \frac{x^2}{2+x^3+x^6} \, dx","Int[x^2/(2 + x^3 + x^6),x]","\frac{2 \tan ^{-1}\left(\frac{2 x^3+1}{\sqrt{7}}\right)}{3 \sqrt{7}}","\frac{2 \tan ^{-1}\left(\frac{2 x^3+1}{\sqrt{7}}\right)}{3 \sqrt{7}}",1,"(2*ArcTan[(1 + 2*x^3)/Sqrt[7]])/(3*Sqrt[7])","A",3,3,14,0.2143,1,"{1352, 618, 204}"
184,1,399,0,0.3050935,"\int \frac{x^3}{2+x^3+x^6} \, dx","Int[x^3/(2 + x^3 + x^6),x]","-\frac{\left(7+i \sqrt{7}\right) \log \left(2^{2/3} x^2-\sqrt[3]{2 \left(1-i \sqrt{7}\right)} x+\left(1-i \sqrt{7}\right)^{2/3}\right)}{42 \sqrt[3]{2} \left(1-i \sqrt{7}\right)^{2/3}}-\frac{\left(7-i \sqrt{7}\right) \log \left(2^{2/3} x^2-\sqrt[3]{2 \left(1+i \sqrt{7}\right)} x+\left(1+i \sqrt{7}\right)^{2/3}\right)}{42 \sqrt[3]{2} \left(1+i \sqrt{7}\right)^{2/3}}+\frac{\left(7+i \sqrt{7}\right) \log \left(\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{7}}\right)}{21 \sqrt[3]{2} \left(1-i \sqrt{7}\right)^{2/3}}+\frac{\left(7-i \sqrt{7}\right) \log \left(\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{7}}\right)}{21 \sqrt[3]{2} \left(1+i \sqrt{7}\right)^{2/3}}-\frac{i \sqrt[3]{\frac{1}{2} \left(1-i \sqrt{7}\right)} \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{7}\right)}}}{\sqrt{3}}\right)}{\sqrt{21}}+\frac{i \sqrt[3]{\frac{1}{2} \left(1+i \sqrt{7}\right)} \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{7}\right)}}}{\sqrt{3}}\right)}{\sqrt{21}}","-\frac{\left(7+i \sqrt{7}\right) \log \left(2^{2/3} x^2-\sqrt[3]{2 \left(1-i \sqrt{7}\right)} x+\left(1-i \sqrt{7}\right)^{2/3}\right)}{42 \sqrt[3]{2} \left(1-i \sqrt{7}\right)^{2/3}}-\frac{\left(7-i \sqrt{7}\right) \log \left(2^{2/3} x^2-\sqrt[3]{2 \left(1+i \sqrt{7}\right)} x+\left(1+i \sqrt{7}\right)^{2/3}\right)}{42 \sqrt[3]{2} \left(1+i \sqrt{7}\right)^{2/3}}+\frac{\left(7+i \sqrt{7}\right) \log \left(\sqrt[3]{2} x+\sqrt[3]{1-i \sqrt{7}}\right)}{21 \sqrt[3]{2} \left(1-i \sqrt{7}\right)^{2/3}}+\frac{\left(7-i \sqrt{7}\right) \log \left(\sqrt[3]{2} x+\sqrt[3]{1+i \sqrt{7}}\right)}{21 \sqrt[3]{2} \left(1+i \sqrt{7}\right)^{2/3}}-\frac{i \sqrt[3]{\frac{1}{2} \left(1-i \sqrt{7}\right)} \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1-i \sqrt{7}\right)}}}{\sqrt{3}}\right)}{\sqrt{21}}+\frac{i \sqrt[3]{\frac{1}{2} \left(1+i \sqrt{7}\right)} \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{\frac{1}{2} \left(1+i \sqrt{7}\right)}}}{\sqrt{3}}\right)}{\sqrt{21}}",1,"((-I)*((1 - I*Sqrt[7])/2)^(1/3)*ArcTan[(1 - (2*x)/((1 - I*Sqrt[7])/2)^(1/3))/Sqrt[3]])/Sqrt[21] + (I*((1 + I*Sqrt[7])/2)^(1/3)*ArcTan[(1 - (2*x)/((1 + I*Sqrt[7])/2)^(1/3))/Sqrt[3]])/Sqrt[21] + ((7 + I*Sqrt[7])*Log[(1 - I*Sqrt[7])^(1/3) + 2^(1/3)*x])/(21*2^(1/3)*(1 - I*Sqrt[7])^(2/3)) + ((7 - I*Sqrt[7])*Log[(1 + I*Sqrt[7])^(1/3) + 2^(1/3)*x])/(21*2^(1/3)*(1 + I*Sqrt[7])^(2/3)) - ((7 + I*Sqrt[7])*Log[(1 - I*Sqrt[7])^(2/3) - (2*(1 - I*Sqrt[7]))^(1/3)*x + 2^(2/3)*x^2])/(42*2^(1/3)*(1 - I*Sqrt[7])^(2/3)) - ((7 - I*Sqrt[7])*Log[(1 + I*Sqrt[7])^(2/3) - (2*(1 + I*Sqrt[7]))^(1/3)*x + 2^(2/3)*x^2])/(42*2^(1/3)*(1 + I*Sqrt[7])^(2/3))","A",13,7,14,0.5000,1,"{1374, 200, 31, 634, 617, 204, 628}"
185,1,231,0,0.2996631,"\int x^{14} \sqrt{a+b x^3+c x^6} \, dx","Int[x^14*Sqrt[a + b*x^3 + c*x^6],x]","\frac{\left(16 a^2 c^2-56 a b^2 c+21 b^4\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{1536 c^5}-\frac{\left(b^2-4 a c\right) \left(16 a^2 c^2-56 a b^2 c+21 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{3072 c^{11/2}}-\frac{\left(7 b \left(15 b^2-28 a c\right)-6 c x^3 \left(21 b^2-20 a c\right)\right) \left(a+b x^3+c x^6\right)^{3/2}}{2880 c^4}-\frac{b x^6 \left(a+b x^3+c x^6\right)^{3/2}}{20 c^2}+\frac{x^9 \left(a+b x^3+c x^6\right)^{3/2}}{18 c}","\frac{\left(16 a^2 c^2-56 a b^2 c+21 b^4\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{1536 c^5}-\frac{\left(b^2-4 a c\right) \left(16 a^2 c^2-56 a b^2 c+21 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{3072 c^{11/2}}-\frac{\left(7 b \left(15 b^2-28 a c\right)-6 c x^3 \left(21 b^2-20 a c\right)\right) \left(a+b x^3+c x^6\right)^{3/2}}{2880 c^4}-\frac{b x^6 \left(a+b x^3+c x^6\right)^{3/2}}{20 c^2}+\frac{x^9 \left(a+b x^3+c x^6\right)^{3/2}}{18 c}",1,"((21*b^4 - 56*a*b^2*c + 16*a^2*c^2)*(b + 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(1536*c^5) - (b*x^6*(a + b*x^3 + c*x^6)^(3/2))/(20*c^2) + (x^9*(a + b*x^3 + c*x^6)^(3/2))/(18*c) - ((7*b*(15*b^2 - 28*a*c) - 6*c*(21*b^2 - 20*a*c)*x^3)*(a + b*x^3 + c*x^6)^(3/2))/(2880*c^4) - ((b^2 - 4*a*c)*(21*b^4 - 56*a*b^2*c + 16*a^2*c^2)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(3072*c^(11/2))","A",7,7,20,0.3500,1,"{1357, 742, 832, 779, 612, 621, 206}"
186,1,171,0,0.1518177,"\int x^{11} \sqrt{a+b x^3+c x^6} \, dx","Int[x^11*Sqrt[a + b*x^3 + c*x^6],x]","\frac{\left(-32 a c+35 b^2-42 b c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{720 c^3}-\frac{b \left(7 b^2-12 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{384 c^4}+\frac{b \left(7 b^2-12 a c\right) \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{768 c^{9/2}}+\frac{x^6 \left(a+b x^3+c x^6\right)^{3/2}}{15 c}","\frac{\left(-32 a c+35 b^2-42 b c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{720 c^3}-\frac{b \left(7 b^2-12 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{384 c^4}+\frac{b \left(7 b^2-12 a c\right) \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{768 c^{9/2}}+\frac{x^6 \left(a+b x^3+c x^6\right)^{3/2}}{15 c}",1,"-(b*(7*b^2 - 12*a*c)*(b + 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(384*c^4) + (x^6*(a + b*x^3 + c*x^6)^(3/2))/(15*c) + ((35*b^2 - 32*a*c - 42*b*c*x^3)*(a + b*x^3 + c*x^6)^(3/2))/(720*c^3) + (b*(7*b^2 - 12*a*c)*(b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(768*c^(9/2))","A",6,6,20,0.3000,1,"{1357, 742, 779, 612, 621, 206}"
187,1,153,0,0.1358406,"\int x^8 \sqrt{a+b x^3+c x^6} \, dx","Int[x^8*Sqrt[a + b*x^3 + c*x^6],x]","\frac{\left(5 b^2-4 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{192 c^3}-\frac{\left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{384 c^{7/2}}-\frac{5 b \left(a+b x^3+c x^6\right)^{3/2}}{72 c^2}+\frac{x^3 \left(a+b x^3+c x^6\right)^{3/2}}{12 c}","\frac{\left(5 b^2-4 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{192 c^3}-\frac{\left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{384 c^{7/2}}-\frac{5 b \left(a+b x^3+c x^6\right)^{3/2}}{72 c^2}+\frac{x^3 \left(a+b x^3+c x^6\right)^{3/2}}{12 c}",1,"((5*b^2 - 4*a*c)*(b + 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(192*c^3) - (5*b*(a + b*x^3 + c*x^6)^(3/2))/(72*c^2) + (x^3*(a + b*x^3 + c*x^6)^(3/2))/(12*c) - ((b^2 - 4*a*c)*(5*b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(384*c^(7/2))","A",6,6,20,0.3000,1,"{1357, 742, 640, 612, 621, 206}"
188,1,108,0,0.0853352,"\int x^5 \sqrt{a+b x^3+c x^6} \, dx","Int[x^5*Sqrt[a + b*x^3 + c*x^6],x]","\frac{b \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{48 c^{5/2}}-\frac{b \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{24 c^2}+\frac{\left(a+b x^3+c x^6\right)^{3/2}}{9 c}","\frac{b \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{48 c^{5/2}}-\frac{b \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{24 c^2}+\frac{\left(a+b x^3+c x^6\right)^{3/2}}{9 c}",1,"-(b*(b + 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(24*c^2) + (a + b*x^3 + c*x^6)^(3/2)/(9*c) + (b*(b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(48*c^(5/2))","A",5,5,20,0.2500,1,"{1357, 640, 612, 621, 206}"
189,1,83,0,0.0601921,"\int x^2 \sqrt{a+b x^3+c x^6} \, dx","Int[x^2*Sqrt[a + b*x^3 + c*x^6],x]","\frac{\left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{12 c}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{24 c^{3/2}}","\frac{\left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{12 c}-\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{24 c^{3/2}}",1,"((b + 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(12*c) - ((b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(24*c^(3/2))","A",4,4,20,0.2000,1,"{1352, 612, 621, 206}"
190,1,109,0,0.1113792,"\int \frac{\sqrt{a+b x^3+c x^6}}{x} \, dx","Int[Sqrt[a + b*x^3 + c*x^6]/x,x]","\frac{1}{3} \sqrt{a+b x^3+c x^6}-\frac{1}{3} \sqrt{a} \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)+\frac{b \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{6 \sqrt{c}}","\frac{1}{3} \sqrt{a+b x^3+c x^6}-\frac{1}{3} \sqrt{a} \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)+\frac{b \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{6 \sqrt{c}}",1,"Sqrt[a + b*x^3 + c*x^6]/3 - (Sqrt[a]*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/3 + (b*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(6*Sqrt[c])","A",7,6,20,0.3000,1,"{1357, 734, 843, 621, 206, 724}"
191,1,112,0,0.1142907,"\int \frac{\sqrt{a+b x^3+c x^6}}{x^4} \, dx","Int[Sqrt[a + b*x^3 + c*x^6]/x^4,x]","-\frac{\sqrt{a+b x^3+c x^6}}{3 x^3}-\frac{b \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{6 \sqrt{a}}+\frac{1}{3} \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)","-\frac{\sqrt{a+b x^3+c x^6}}{3 x^3}-\frac{b \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{6 \sqrt{a}}+\frac{1}{3} \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)",1,"-Sqrt[a + b*x^3 + c*x^6]/(3*x^3) - (b*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(6*Sqrt[a]) + (Sqrt[c]*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/3","A",7,6,20,0.3000,1,"{1357, 732, 843, 621, 206, 724}"
192,1,88,0,0.0727628,"\int \frac{\sqrt{a+b x^3+c x^6}}{x^7} \, dx","Int[Sqrt[a + b*x^3 + c*x^6]/x^7,x]","\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{24 a^{3/2}}-\frac{\left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{12 a x^6}","\frac{\left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{24 a^{3/2}}-\frac{\left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{12 a x^6}",1,"-((2*a + b*x^3)*Sqrt[a + b*x^3 + c*x^6])/(12*a*x^6) + ((b^2 - 4*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(24*a^(3/2))","A",4,4,20,0.2000,1,"{1357, 720, 724, 206}"
193,1,116,0,0.0954686,"\int \frac{\sqrt{a+b x^3+c x^6}}{x^{10}} \, dx","Int[Sqrt[a + b*x^3 + c*x^6]/x^10,x]","-\frac{b \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{48 a^{5/2}}+\frac{b \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{24 a^2 x^6}-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{9 a x^9}","-\frac{b \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{48 a^{5/2}}+\frac{b \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{24 a^2 x^6}-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{9 a x^9}",1,"(b*(2*a + b*x^3)*Sqrt[a + b*x^3 + c*x^6])/(24*a^2*x^6) - (a + b*x^3 + c*x^6)^(3/2)/(9*a*x^9) - (b*(b^2 - 4*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(48*a^(5/2))","A",5,5,20,0.2500,1,"{1357, 730, 720, 724, 206}"
194,1,161,0,0.1470088,"\int \frac{\sqrt{a+b x^3+c x^6}}{x^{13}} \, dx","Int[Sqrt[a + b*x^3 + c*x^6]/x^13,x]","-\frac{\left(5 b^2-4 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{192 a^3 x^6}+\frac{\left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{384 a^{7/2}}+\frac{5 b \left(a+b x^3+c x^6\right)^{3/2}}{72 a^2 x^9}-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{12 a x^{12}}","-\frac{\left(5 b^2-4 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{192 a^3 x^6}+\frac{\left(b^2-4 a c\right) \left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{384 a^{7/2}}+\frac{5 b \left(a+b x^3+c x^6\right)^{3/2}}{72 a^2 x^9}-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{12 a x^{12}}",1,"-((5*b^2 - 4*a*c)*(2*a + b*x^3)*Sqrt[a + b*x^3 + c*x^6])/(192*a^3*x^6) - (a + b*x^3 + c*x^6)^(3/2)/(12*a*x^12) + (5*b*(a + b*x^3 + c*x^6)^(3/2))/(72*a^2*x^9) + ((b^2 - 4*a*c)*(5*b^2 - 4*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(384*a^(7/2))","A",6,6,20,0.3000,1,"{1357, 744, 806, 720, 724, 206}"
195,1,199,0,0.2267678,"\int \frac{\sqrt{a+b x^3+c x^6}}{x^{16}} \, dx","Int[Sqrt[a + b*x^3 + c*x^6]/x^16,x]","-\frac{\left(35 b^2-32 a c\right) \left(a+b x^3+c x^6\right)^{3/2}}{720 a^3 x^9}+\frac{b \left(7 b^2-12 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{384 a^4 x^6}-\frac{b \left(7 b^2-12 a c\right) \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{768 a^{9/2}}+\frac{7 b \left(a+b x^3+c x^6\right)^{3/2}}{120 a^2 x^{12}}-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{15 a x^{15}}","-\frac{\left(35 b^2-32 a c\right) \left(a+b x^3+c x^6\right)^{3/2}}{720 a^3 x^9}+\frac{b \left(7 b^2-12 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{384 a^4 x^6}-\frac{b \left(7 b^2-12 a c\right) \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{768 a^{9/2}}+\frac{7 b \left(a+b x^3+c x^6\right)^{3/2}}{120 a^2 x^{12}}-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{15 a x^{15}}",1,"(b*(7*b^2 - 12*a*c)*(2*a + b*x^3)*Sqrt[a + b*x^3 + c*x^6])/(384*a^4*x^6) - (a + b*x^3 + c*x^6)^(3/2)/(15*a*x^15) + (7*b*(a + b*x^3 + c*x^6)^(3/2))/(120*a^2*x^12) - ((35*b^2 - 32*a*c)*(a + b*x^3 + c*x^6)^(3/2))/(720*a^3*x^9) - (b*(7*b^2 - 12*a*c)*(b^2 - 4*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(768*a^(9/2))","A",7,7,20,0.3500,1,"{1357, 744, 834, 806, 720, 724, 206}"
196,1,140,0,0.1494813,"\int x^3 \sqrt{a+b x^3+c x^6} \, dx","Int[x^3*Sqrt[a + b*x^3 + c*x^6],x]","\frac{x^4 \sqrt{a+b x^3+c x^6} F_1\left(\frac{4}{3};-\frac{1}{2},-\frac{1}{2};\frac{7}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","\frac{x^4 \sqrt{a+b x^3+c x^6} F_1\left(\frac{4}{3};-\frac{1}{2},-\frac{1}{2};\frac{7}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"(x^4*Sqrt[a + b*x^3 + c*x^6]*AppellF1[4/3, -1/2, -1/2, 7/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(4*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,20,0.1000,1,"{1385, 510}"
197,1,140,0,0.0988441,"\int x \sqrt{a+b x^3+c x^6} \, dx","Int[x*Sqrt[a + b*x^3 + c*x^6],x]","\frac{x^2 \sqrt{a+b x^3+c x^6} F_1\left(\frac{2}{3};-\frac{1}{2},-\frac{1}{2};\frac{5}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","\frac{x^2 \sqrt{a+b x^3+c x^6} F_1\left(\frac{2}{3};-\frac{1}{2},-\frac{1}{2};\frac{5}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"(x^2*Sqrt[a + b*x^3 + c*x^6]*AppellF1[2/3, -1/2, -1/2, 5/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(2*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,18,0.1111,1,"{1385, 510}"
198,1,135,0,0.0646869,"\int \sqrt{a+b x^3+c x^6} \, dx","Int[Sqrt[a + b*x^3 + c*x^6],x]","\frac{x \sqrt{a+b x^3+c x^6} F_1\left(\frac{1}{3};-\frac{1}{2},-\frac{1}{2};\frac{4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","\frac{x \sqrt{a+b x^3+c x^6} F_1\left(\frac{1}{3};-\frac{1}{2},-\frac{1}{2};\frac{4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"(x*Sqrt[a + b*x^3 + c*x^6]*AppellF1[1/3, -1/2, -1/2, 4/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,16,0.1250,1,"{1348, 429}"
199,1,138,0,0.1237166,"\int \frac{\sqrt{a+b x^3+c x^6}}{x^2} \, dx","Int[Sqrt[a + b*x^3 + c*x^6]/x^2,x]","-\frac{\sqrt{a+b x^3+c x^6} F_1\left(-\frac{1}{3};-\frac{1}{2},-\frac{1}{2};\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","-\frac{\sqrt{a+b x^3+c x^6} F_1\left(-\frac{1}{3};-\frac{1}{2},-\frac{1}{2};\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"-((Sqrt[a + b*x^3 + c*x^6]*AppellF1[-1/3, -1/2, -1/2, 2/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(x*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]))","A",2,2,20,0.1000,1,"{1385, 510}"
200,1,140,0,0.1227095,"\int \frac{\sqrt{a+b x^3+c x^6}}{x^3} \, dx","Int[Sqrt[a + b*x^3 + c*x^6]/x^3,x]","-\frac{\sqrt{a+b x^3+c x^6} F_1\left(-\frac{2}{3};-\frac{1}{2},-\frac{1}{2};\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","-\frac{\sqrt{a+b x^3+c x^6} F_1\left(-\frac{2}{3};-\frac{1}{2},-\frac{1}{2};\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"-(Sqrt[a + b*x^3 + c*x^6]*AppellF1[-2/3, -1/2, -1/2, 1/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(2*x^2*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,20,0.1000,1,"{1385, 510}"
201,1,293,0,0.402334,"\int x^{14} \left(a+b x^3+c x^6\right)^{3/2} \, dx","Int[x^14*(a + b*x^3 + c*x^6)^(3/2),x]","\frac{\left(16 a^2 c^2-72 a b^2 c+33 b^4\right) \left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{6144 c^5}-\frac{\left(b^2-4 a c\right) \left(16 a^2 c^2-72 a b^2 c+33 b^4\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{16384 c^6}+\frac{\left(b^2-4 a c\right)^2 \left(16 a^2 c^2-72 a b^2 c+33 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{32768 c^{13/2}}-\frac{\left(3 b \left(77 b^2-124 a c\right)-10 c x^3 \left(33 b^2-28 a c\right)\right) \left(a+b x^3+c x^6\right)^{5/2}}{13440 c^4}-\frac{11 b x^6 \left(a+b x^3+c x^6\right)^{5/2}}{336 c^2}+\frac{x^9 \left(a+b x^3+c x^6\right)^{5/2}}{24 c}","\frac{\left(16 a^2 c^2-72 a b^2 c+33 b^4\right) \left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{6144 c^5}-\frac{\left(b^2-4 a c\right) \left(16 a^2 c^2-72 a b^2 c+33 b^4\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{16384 c^6}+\frac{\left(b^2-4 a c\right)^2 \left(16 a^2 c^2-72 a b^2 c+33 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{32768 c^{13/2}}-\frac{\left(3 b \left(77 b^2-124 a c\right)-10 c x^3 \left(33 b^2-28 a c\right)\right) \left(a+b x^3+c x^6\right)^{5/2}}{13440 c^4}-\frac{11 b x^6 \left(a+b x^3+c x^6\right)^{5/2}}{336 c^2}+\frac{x^9 \left(a+b x^3+c x^6\right)^{5/2}}{24 c}",1,"-((b^2 - 4*a*c)*(33*b^4 - 72*a*b^2*c + 16*a^2*c^2)*(b + 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(16384*c^6) + ((33*b^4 - 72*a*b^2*c + 16*a^2*c^2)*(b + 2*c*x^3)*(a + b*x^3 + c*x^6)^(3/2))/(6144*c^5) - (11*b*x^6*(a + b*x^3 + c*x^6)^(5/2))/(336*c^2) + (x^9*(a + b*x^3 + c*x^6)^(5/2))/(24*c) - ((3*b*(77*b^2 - 124*a*c) - 10*c*(33*b^2 - 28*a*c)*x^3)*(a + b*x^3 + c*x^6)^(5/2))/(13440*c^4) + ((b^2 - 4*a*c)^2*(33*b^4 - 72*a*b^2*c + 16*a^2*c^2)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(32768*c^(13/2))","A",8,7,20,0.3500,1,"{1357, 742, 832, 779, 612, 621, 206}"
202,1,223,0,0.2059777,"\int x^{11} \left(a+b x^3+c x^6\right)^{3/2} \, dx","Int[x^11*(a + b*x^3 + c*x^6)^(3/2),x]","\frac{\left(-16 a c+21 b^2-30 b c x^3\right) \left(a+b x^3+c x^6\right)^{5/2}}{840 c^3}-\frac{b \left(3 b^2-4 a c\right) \left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{384 c^4}+\frac{b \left(b^2-4 a c\right) \left(3 b^2-4 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{1024 c^5}-\frac{b \left(b^2-4 a c\right)^2 \left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{2048 c^{11/2}}+\frac{x^6 \left(a+b x^3+c x^6\right)^{5/2}}{21 c}","\frac{\left(-16 a c+21 b^2-30 b c x^3\right) \left(a+b x^3+c x^6\right)^{5/2}}{840 c^3}-\frac{b \left(3 b^2-4 a c\right) \left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{384 c^4}+\frac{b \left(b^2-4 a c\right) \left(3 b^2-4 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{1024 c^5}-\frac{b \left(b^2-4 a c\right)^2 \left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{2048 c^{11/2}}+\frac{x^6 \left(a+b x^3+c x^6\right)^{5/2}}{21 c}",1,"(b*(b^2 - 4*a*c)*(3*b^2 - 4*a*c)*(b + 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(1024*c^5) - (b*(3*b^2 - 4*a*c)*(b + 2*c*x^3)*(a + b*x^3 + c*x^6)^(3/2))/(384*c^4) + (x^6*(a + b*x^3 + c*x^6)^(5/2))/(21*c) + ((21*b^2 - 16*a*c - 30*b*c*x^3)*(a + b*x^3 + c*x^6)^(5/2))/(840*c^3) - (b*(b^2 - 4*a*c)^2*(3*b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(2048*c^(11/2))","A",7,6,20,0.3000,1,"{1357, 742, 779, 612, 621, 206}"
203,1,204,0,0.1876118,"\int x^8 \left(a+b x^3+c x^6\right)^{3/2} \, dx","Int[x^8*(a + b*x^3 + c*x^6)^(3/2),x]","\frac{\left(7 b^2-4 a c\right) \left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{576 c^3}-\frac{\left(b^2-4 a c\right) \left(7 b^2-4 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{1536 c^4}+\frac{\left(b^2-4 a c\right)^2 \left(7 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{3072 c^{9/2}}-\frac{7 b \left(a+b x^3+c x^6\right)^{5/2}}{180 c^2}+\frac{x^3 \left(a+b x^3+c x^6\right)^{5/2}}{18 c}","\frac{\left(7 b^2-4 a c\right) \left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{576 c^3}-\frac{\left(b^2-4 a c\right) \left(7 b^2-4 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{1536 c^4}+\frac{\left(b^2-4 a c\right)^2 \left(7 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{3072 c^{9/2}}-\frac{7 b \left(a+b x^3+c x^6\right)^{5/2}}{180 c^2}+\frac{x^3 \left(a+b x^3+c x^6\right)^{5/2}}{18 c}",1,"-((b^2 - 4*a*c)*(7*b^2 - 4*a*c)*(b + 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(1536*c^4) + ((7*b^2 - 4*a*c)*(b + 2*c*x^3)*(a + b*x^3 + c*x^6)^(3/2))/(576*c^3) - (7*b*(a + b*x^3 + c*x^6)^(5/2))/(180*c^2) + (x^3*(a + b*x^3 + c*x^6)^(5/2))/(18*c) + ((b^2 - 4*a*c)^2*(7*b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(3072*c^(9/2))","A",7,6,20,0.3000,1,"{1357, 742, 640, 612, 621, 206}"
204,1,150,0,0.1162505,"\int x^5 \left(a+b x^3+c x^6\right)^{3/2} \, dx","Int[x^5*(a + b*x^3 + c*x^6)^(3/2),x]","\frac{b \left(b^2-4 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{128 c^3}-\frac{b \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{256 c^{7/2}}-\frac{b \left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{48 c^2}+\frac{\left(a+b x^3+c x^6\right)^{5/2}}{15 c}","\frac{b \left(b^2-4 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{128 c^3}-\frac{b \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{256 c^{7/2}}-\frac{b \left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{48 c^2}+\frac{\left(a+b x^3+c x^6\right)^{5/2}}{15 c}",1,"(b*(b^2 - 4*a*c)*(b + 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(128*c^3) - (b*(b + 2*c*x^3)*(a + b*x^3 + c*x^6)^(3/2))/(48*c^2) + (a + b*x^3 + c*x^6)^(5/2)/(15*c) - (b*(b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(256*c^(7/2))","A",6,5,20,0.2500,1,"{1357, 640, 612, 621, 206}"
205,1,124,0,0.086428,"\int x^2 \left(a+b x^3+c x^6\right)^{3/2} \, dx","Int[x^2*(a + b*x^3 + c*x^6)^(3/2),x]","-\frac{\left(b^2-4 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{64 c^2}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{128 c^{5/2}}+\frac{\left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{24 c}","-\frac{\left(b^2-4 a c\right) \left(b+2 c x^3\right) \sqrt{a+b x^3+c x^6}}{64 c^2}+\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{128 c^{5/2}}+\frac{\left(b+2 c x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{24 c}",1,"-((b^2 - 4*a*c)*(b + 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(64*c^2) + ((b + 2*c*x^3)*(a + b*x^3 + c*x^6)^(3/2))/(24*c) + ((b^2 - 4*a*c)^2*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(128*c^(5/2))","A",5,4,20,0.2000,1,"{1352, 612, 621, 206}"
206,1,155,0,0.1789065,"\int \frac{\left(a+b x^3+c x^6\right)^{3/2}}{x} \, dx","Int[(a + b*x^3 + c*x^6)^(3/2)/x,x]","-\frac{1}{3} a^{3/2} \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)-\frac{b \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{48 c^{3/2}}+\frac{\left(8 a c+b^2+2 b c x^3\right) \sqrt{a+b x^3+c x^6}}{24 c}+\frac{1}{9} \left(a+b x^3+c x^6\right)^{3/2}","-\frac{1}{3} a^{3/2} \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)-\frac{b \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{48 c^{3/2}}+\frac{\left(8 a c+b^2+2 b c x^3\right) \sqrt{a+b x^3+c x^6}}{24 c}+\frac{1}{9} \left(a+b x^3+c x^6\right)^{3/2}",1,"((b^2 + 8*a*c + 2*b*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(24*c) + (a + b*x^3 + c*x^6)^(3/2)/9 - (a^(3/2)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/3 - (b*(b^2 - 12*a*c)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(48*c^(3/2))","A",8,7,20,0.3500,1,"{1357, 734, 814, 843, 621, 206, 724}"
207,1,150,0,0.1698178,"\int \frac{\left(a+b x^3+c x^6\right)^{3/2}}{x^4} \, dx","Int[(a + b*x^3 + c*x^6)^(3/2)/x^4,x]","\frac{\left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{8 \sqrt{c}}-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{3 x^3}+\frac{1}{4} \left(3 b+2 c x^3\right) \sqrt{a+b x^3+c x^6}-\frac{1}{2} \sqrt{a} b \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)","\frac{\left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{8 \sqrt{c}}-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{3 x^3}+\frac{1}{4} \left(3 b+2 c x^3\right) \sqrt{a+b x^3+c x^6}-\frac{1}{2} \sqrt{a} b \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)",1,"((3*b + 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/4 - (a + b*x^3 + c*x^6)^(3/2)/(3*x^3) - (Sqrt[a]*b*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/2 + ((b^2 + 4*a*c)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(8*Sqrt[c])","A",8,7,20,0.3500,1,"{1357, 732, 814, 843, 621, 206, 724}"
208,1,151,0,0.162014,"\int \frac{\left(a+b x^3+c x^6\right)^{3/2}}{x^7} \, dx","Int[(a + b*x^3 + c*x^6)^(3/2)/x^7,x]","-\frac{\left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{8 \sqrt{a}}-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{6 x^6}-\frac{\left(b-2 c x^3\right) \sqrt{a+b x^3+c x^6}}{4 x^3}+\frac{1}{2} b \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)","-\frac{\left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{8 \sqrt{a}}-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{6 x^6}-\frac{\left(b-2 c x^3\right) \sqrt{a+b x^3+c x^6}}{4 x^3}+\frac{1}{2} b \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)",1,"-((b - 2*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(4*x^3) - (a + b*x^3 + c*x^6)^(3/2)/(6*x^6) - ((b^2 + 4*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(8*Sqrt[a]) + (b*Sqrt[c]*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/2","A",8,7,20,0.3500,1,"{1357, 732, 812, 843, 621, 206, 724}"
209,1,163,0,0.1755295,"\int \frac{\left(a+b x^3+c x^6\right)^{3/2}}{x^{10}} \, dx","Int[(a + b*x^3 + c*x^6)^(3/2)/x^10,x]","\frac{b \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{48 a^{3/2}}-\frac{\left(x^3 \left(8 a c+b^2\right)+2 a b\right) \sqrt{a+b x^3+c x^6}}{24 a x^6}+\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{9 x^9}","\frac{b \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{48 a^{3/2}}-\frac{\left(x^3 \left(8 a c+b^2\right)+2 a b\right) \sqrt{a+b x^3+c x^6}}{24 a x^6}+\frac{1}{3} c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)-\frac{\left(a+b x^3+c x^6\right)^{3/2}}{9 x^9}",1,"-((2*a*b + (b^2 + 8*a*c)*x^3)*Sqrt[a + b*x^3 + c*x^6])/(24*a*x^6) - (a + b*x^3 + c*x^6)^(3/2)/(9*x^9) + (b*(b^2 - 12*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(48*a^(3/2)) + (c^(3/2)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/3","A",8,7,20,0.3500,1,"{1357, 732, 810, 843, 621, 206, 724}"
210,1,133,0,0.1076,"\int \frac{\left(a+b x^3+c x^6\right)^{3/2}}{x^{13}} \, dx","Int[(a + b*x^3 + c*x^6)^(3/2)/x^13,x]","\frac{\left(b^2-4 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{64 a^2 x^6}-\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{128 a^{5/2}}-\frac{\left(2 a+b x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{24 a x^{12}}","\frac{\left(b^2-4 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{64 a^2 x^6}-\frac{\left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{128 a^{5/2}}-\frac{\left(2 a+b x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{24 a x^{12}}",1,"((b^2 - 4*a*c)*(2*a + b*x^3)*Sqrt[a + b*x^3 + c*x^6])/(64*a^2*x^6) - ((2*a + b*x^3)*(a + b*x^3 + c*x^6)^(3/2))/(24*a*x^12) - ((b^2 - 4*a*c)^2*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(128*a^(5/2))","A",5,4,20,0.2000,1,"{1357, 720, 724, 206}"
211,1,162,0,0.1455842,"\int \frac{\left(a+b x^3+c x^6\right)^{3/2}}{x^{16}} \, dx","Int[(a + b*x^3 + c*x^6)^(3/2)/x^16,x]","-\frac{b \left(b^2-4 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{128 a^3 x^6}+\frac{b \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{256 a^{7/2}}+\frac{b \left(2 a+b x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{48 a^2 x^{12}}-\frac{\left(a+b x^3+c x^6\right)^{5/2}}{15 a x^{15}}","-\frac{b \left(b^2-4 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{128 a^3 x^6}+\frac{b \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{256 a^{7/2}}+\frac{b \left(2 a+b x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{48 a^2 x^{12}}-\frac{\left(a+b x^3+c x^6\right)^{5/2}}{15 a x^{15}}",1,"-(b*(b^2 - 4*a*c)*(2*a + b*x^3)*Sqrt[a + b*x^3 + c*x^6])/(128*a^3*x^6) + (b*(2*a + b*x^3)*(a + b*x^3 + c*x^6)^(3/2))/(48*a^2*x^12) - (a + b*x^3 + c*x^6)^(5/2)/(15*a*x^15) + (b*(b^2 - 4*a*c)^2*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(256*a^(7/2))","A",6,5,20,0.2500,1,"{1357, 730, 720, 724, 206}"
212,1,216,0,0.2072415,"\int \frac{\left(a+b x^3+c x^6\right)^{3/2}}{x^{19}} \, dx","Int[(a + b*x^3 + c*x^6)^(3/2)/x^19,x]","-\frac{\left(7 b^2-4 a c\right) \left(2 a+b x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{576 a^3 x^{12}}+\frac{\left(b^2-4 a c\right) \left(7 b^2-4 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{1536 a^4 x^6}-\frac{\left(b^2-4 a c\right)^2 \left(7 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{3072 a^{9/2}}+\frac{7 b \left(a+b x^3+c x^6\right)^{5/2}}{180 a^2 x^{15}}-\frac{\left(a+b x^3+c x^6\right)^{5/2}}{18 a x^{18}}","-\frac{\left(7 b^2-4 a c\right) \left(2 a+b x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{576 a^3 x^{12}}+\frac{\left(b^2-4 a c\right) \left(7 b^2-4 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{1536 a^4 x^6}-\frac{\left(b^2-4 a c\right)^2 \left(7 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{3072 a^{9/2}}+\frac{7 b \left(a+b x^3+c x^6\right)^{5/2}}{180 a^2 x^{15}}-\frac{\left(a+b x^3+c x^6\right)^{5/2}}{18 a x^{18}}",1,"((b^2 - 4*a*c)*(7*b^2 - 4*a*c)*(2*a + b*x^3)*Sqrt[a + b*x^3 + c*x^6])/(1536*a^4*x^6) - ((7*b^2 - 4*a*c)*(2*a + b*x^3)*(a + b*x^3 + c*x^6)^(3/2))/(576*a^3*x^12) - (a + b*x^3 + c*x^6)^(5/2)/(18*a*x^18) + (7*b*(a + b*x^3 + c*x^6)^(5/2))/(180*a^2*x^15) - ((b^2 - 4*a*c)^2*(7*b^2 - 4*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(3072*a^(9/2))","A",7,6,20,0.3000,1,"{1357, 744, 806, 720, 724, 206}"
213,1,255,0,0.3117329,"\int \frac{\left(a+b x^3+c x^6\right)^{3/2}}{x^{22}} \, dx","Int[(a + b*x^3 + c*x^6)^(3/2)/x^22,x]","-\frac{\left(21 b^2-16 a c\right) \left(a+b x^3+c x^6\right)^{5/2}}{840 a^3 x^{15}}+\frac{b \left(3 b^2-4 a c\right) \left(2 a+b x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{384 a^4 x^{12}}-\frac{b \left(b^2-4 a c\right) \left(3 b^2-4 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{1024 a^5 x^6}+\frac{b \left(b^2-4 a c\right)^2 \left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{2048 a^{11/2}}+\frac{b \left(a+b x^3+c x^6\right)^{5/2}}{28 a^2 x^{18}}-\frac{\left(a+b x^3+c x^6\right)^{5/2}}{21 a x^{21}}","-\frac{\left(21 b^2-16 a c\right) \left(a+b x^3+c x^6\right)^{5/2}}{840 a^3 x^{15}}+\frac{b \left(3 b^2-4 a c\right) \left(2 a+b x^3\right) \left(a+b x^3+c x^6\right)^{3/2}}{384 a^4 x^{12}}-\frac{b \left(b^2-4 a c\right) \left(3 b^2-4 a c\right) \left(2 a+b x^3\right) \sqrt{a+b x^3+c x^6}}{1024 a^5 x^6}+\frac{b \left(b^2-4 a c\right)^2 \left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{2048 a^{11/2}}+\frac{b \left(a+b x^3+c x^6\right)^{5/2}}{28 a^2 x^{18}}-\frac{\left(a+b x^3+c x^6\right)^{5/2}}{21 a x^{21}}",1,"-(b*(b^2 - 4*a*c)*(3*b^2 - 4*a*c)*(2*a + b*x^3)*Sqrt[a + b*x^3 + c*x^6])/(1024*a^5*x^6) + (b*(3*b^2 - 4*a*c)*(2*a + b*x^3)*(a + b*x^3 + c*x^6)^(3/2))/(384*a^4*x^12) - (a + b*x^3 + c*x^6)^(5/2)/(21*a*x^21) + (b*(a + b*x^3 + c*x^6)^(5/2))/(28*a^2*x^18) - ((21*b^2 - 16*a*c)*(a + b*x^3 + c*x^6)^(5/2))/(840*a^3*x^15) + (b*(b^2 - 4*a*c)^2*(3*b^2 - 4*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(2048*a^(11/2))","A",8,7,20,0.3500,1,"{1357, 744, 834, 806, 720, 724, 206}"
214,1,141,0,0.1294062,"\int x^3 \left(a+b x^3+c x^6\right)^{3/2} \, dx","Int[x^3*(a + b*x^3 + c*x^6)^(3/2),x]","\frac{a x^4 \sqrt{a+b x^3+c x^6} F_1\left(\frac{4}{3};-\frac{3}{2},-\frac{3}{2};\frac{7}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","\frac{a x^4 \sqrt{a+b x^3+c x^6} F_1\left(\frac{4}{3};-\frac{3}{2},-\frac{3}{2};\frac{7}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"(a*x^4*Sqrt[a + b*x^3 + c*x^6]*AppellF1[4/3, -3/2, -3/2, 7/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(4*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,20,0.1000,1,"{1385, 510}"
215,1,141,0,0.0962197,"\int x \left(a+b x^3+c x^6\right)^{3/2} \, dx","Int[x*(a + b*x^3 + c*x^6)^(3/2),x]","\frac{a x^2 \sqrt{a+b x^3+c x^6} F_1\left(\frac{2}{3};-\frac{3}{2},-\frac{3}{2};\frac{5}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","\frac{a x^2 \sqrt{a+b x^3+c x^6} F_1\left(\frac{2}{3};-\frac{3}{2},-\frac{3}{2};\frac{5}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"(a*x^2*Sqrt[a + b*x^3 + c*x^6]*AppellF1[2/3, -3/2, -3/2, 5/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(2*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,18,0.1111,1,"{1385, 510}"
216,1,136,0,0.0664819,"\int \left(a+b x^3+c x^6\right)^{3/2} \, dx","Int[(a + b*x^3 + c*x^6)^(3/2),x]","\frac{a x \sqrt{a+b x^3+c x^6} F_1\left(\frac{1}{3};-\frac{3}{2},-\frac{3}{2};\frac{4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","\frac{a x \sqrt{a+b x^3+c x^6} F_1\left(\frac{1}{3};-\frac{3}{2},-\frac{3}{2};\frac{4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"(a*x*Sqrt[a + b*x^3 + c*x^6]*AppellF1[1/3, -3/2, -3/2, 4/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,16,0.1250,1,"{1348, 429}"
217,1,139,0,0.1282205,"\int \frac{\left(a+b x^3+c x^6\right)^{3/2}}{x^2} \, dx","Int[(a + b*x^3 + c*x^6)^(3/2)/x^2,x]","-\frac{a \sqrt{a+b x^3+c x^6} F_1\left(-\frac{1}{3};-\frac{3}{2},-\frac{3}{2};\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","-\frac{a \sqrt{a+b x^3+c x^6} F_1\left(-\frac{1}{3};-\frac{3}{2},-\frac{3}{2};\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"-((a*Sqrt[a + b*x^3 + c*x^6]*AppellF1[-1/3, -3/2, -3/2, 2/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(x*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]))","A",2,2,20,0.1000,1,"{1385, 510}"
218,1,141,0,0.1271854,"\int \frac{\left(a+b x^3+c x^6\right)^{3/2}}{x^3} \, dx","Int[(a + b*x^3 + c*x^6)^(3/2)/x^3,x]","-\frac{a \sqrt{a+b x^3+c x^6} F_1\left(-\frac{2}{3};-\frac{3}{2},-\frac{3}{2};\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","-\frac{a \sqrt{a+b x^3+c x^6} F_1\left(-\frac{2}{3};-\frac{3}{2},-\frac{3}{2};\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"-(a*Sqrt[a + b*x^3 + c*x^6]*AppellF1[-2/3, -3/2, -3/2, 1/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(2*x^2*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,20,0.1000,1,"{1385, 510}"
219,1,171,0,0.2162408,"\int \frac{x^{14}}{\sqrt{a+b x^3+c x^6}} \, dx","Int[x^14/Sqrt[a + b*x^3 + c*x^6],x]","\frac{\left(48 a^2 c^2-120 a b^2 c+35 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{384 c^{9/2}}-\frac{\left(5 b \left(21 b^2-44 a c\right)-2 c x^3 \left(35 b^2-36 a c\right)\right) \sqrt{a+b x^3+c x^6}}{576 c^4}-\frac{7 b x^6 \sqrt{a+b x^3+c x^6}}{72 c^2}+\frac{x^9 \sqrt{a+b x^3+c x^6}}{12 c}","\frac{\left(48 a^2 c^2-120 a b^2 c+35 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{384 c^{9/2}}-\frac{\left(5 b \left(21 b^2-44 a c\right)-2 c x^3 \left(35 b^2-36 a c\right)\right) \sqrt{a+b x^3+c x^6}}{576 c^4}-\frac{7 b x^6 \sqrt{a+b x^3+c x^6}}{72 c^2}+\frac{x^9 \sqrt{a+b x^3+c x^6}}{12 c}",1,"(-7*b*x^6*Sqrt[a + b*x^3 + c*x^6])/(72*c^2) + (x^9*Sqrt[a + b*x^3 + c*x^6])/(12*c) - ((5*b*(21*b^2 - 44*a*c) - 2*c*(35*b^2 - 36*a*c)*x^3)*Sqrt[a + b*x^3 + c*x^6])/(576*c^4) + ((35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(384*c^(9/2))","A",6,6,20,0.3000,1,"{1357, 742, 832, 779, 621, 206}"
220,1,121,0,0.105398,"\int \frac{x^{11}}{\sqrt{a+b x^3+c x^6}} \, dx","Int[x^11/Sqrt[a + b*x^3 + c*x^6],x]","\frac{\left(-16 a c+15 b^2-10 b c x^3\right) \sqrt{a+b x^3+c x^6}}{72 c^3}-\frac{b \left(5 b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{48 c^{7/2}}+\frac{x^6 \sqrt{a+b x^3+c x^6}}{9 c}","\frac{\left(-16 a c+15 b^2-10 b c x^3\right) \sqrt{a+b x^3+c x^6}}{72 c^3}-\frac{b \left(5 b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{48 c^{7/2}}+\frac{x^6 \sqrt{a+b x^3+c x^6}}{9 c}",1,"(x^6*Sqrt[a + b*x^3 + c*x^6])/(9*c) + ((15*b^2 - 16*a*c - 10*b*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(72*c^3) - (b*(5*b^2 - 12*a*c)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(48*c^(7/2))","A",5,5,20,0.2500,1,"{1357, 742, 779, 621, 206}"
221,1,104,0,0.0886356,"\int \frac{x^8}{\sqrt{a+b x^3+c x^6}} \, dx","Int[x^8/Sqrt[a + b*x^3 + c*x^6],x]","\frac{\left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{24 c^{5/2}}-\frac{b \sqrt{a+b x^3+c x^6}}{4 c^2}+\frac{x^3 \sqrt{a+b x^3+c x^6}}{6 c}","\frac{\left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{24 c^{5/2}}-\frac{b \sqrt{a+b x^3+c x^6}}{4 c^2}+\frac{x^3 \sqrt{a+b x^3+c x^6}}{6 c}",1,"-(b*Sqrt[a + b*x^3 + c*x^6])/(4*c^2) + (x^3*Sqrt[a + b*x^3 + c*x^6])/(6*c) + ((3*b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(24*c^(5/2))","A",5,5,20,0.2500,1,"{1357, 742, 640, 621, 206}"
222,1,68,0,0.0565937,"\int \frac{x^5}{\sqrt{a+b x^3+c x^6}} \, dx","Int[x^5/Sqrt[a + b*x^3 + c*x^6],x]","\frac{\sqrt{a+b x^3+c x^6}}{3 c}-\frac{b \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{6 c^{3/2}}","\frac{\sqrt{a+b x^3+c x^6}}{3 c}-\frac{b \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{6 c^{3/2}}",1,"Sqrt[a + b*x^3 + c*x^6]/(3*c) - (b*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(6*c^(3/2))","A",4,4,20,0.2000,1,"{1357, 640, 621, 206}"
223,1,43,0,0.0341713,"\int \frac{x^2}{\sqrt{a+b x^3+c x^6}} \, dx","Int[x^2/Sqrt[a + b*x^3 + c*x^6],x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{3 \sqrt{c}}","\frac{\tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{3 \sqrt{c}}",1,"ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])]/(3*Sqrt[c])","A",3,3,20,0.1500,1,"{1352, 621, 206}"
224,1,44,0,0.0401252,"\int \frac{1}{x \sqrt{a+b x^3+c x^6}} \, dx","Int[1/(x*Sqrt[a + b*x^3 + c*x^6]),x]","-\frac{\tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{3 \sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{3 \sqrt{a}}",1,"-ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])]/(3*Sqrt[a])","A",3,3,20,0.1500,1,"{1357, 724, 206}"
225,1,72,0,0.0600472,"\int \frac{1}{x^4 \sqrt{a+b x^3+c x^6}} \, dx","Int[1/(x^4*Sqrt[a + b*x^3 + c*x^6]),x]","\frac{b \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{6 a^{3/2}}-\frac{\sqrt{a+b x^3+c x^6}}{3 a x^3}","\frac{b \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{6 a^{3/2}}-\frac{\sqrt{a+b x^3+c x^6}}{3 a x^3}",1,"-Sqrt[a + b*x^3 + c*x^6]/(3*a*x^3) + (b*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(6*a^(3/2))","A",4,4,20,0.2000,1,"{1357, 730, 724, 206}"
226,1,108,0,0.1005075,"\int \frac{1}{x^7 \sqrt{a+b x^3+c x^6}} \, dx","Int[1/(x^7*Sqrt[a + b*x^3 + c*x^6]),x]","-\frac{\left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{24 a^{5/2}}+\frac{b \sqrt{a+b x^3+c x^6}}{4 a^2 x^3}-\frac{\sqrt{a+b x^3+c x^6}}{6 a x^6}","-\frac{\left(3 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{24 a^{5/2}}+\frac{b \sqrt{a+b x^3+c x^6}}{4 a^2 x^3}-\frac{\sqrt{a+b x^3+c x^6}}{6 a x^6}",1,"-Sqrt[a + b*x^3 + c*x^6]/(6*a*x^6) + (b*Sqrt[a + b*x^3 + c*x^6])/(4*a^2*x^3) - ((3*b^2 - 4*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(24*a^(5/2))","A",5,5,20,0.2500,1,"{1357, 744, 806, 724, 206}"
227,1,145,0,0.1576192,"\int \frac{1}{x^{10} \sqrt{a+b x^3+c x^6}} \, dx","Int[1/(x^10*Sqrt[a + b*x^3 + c*x^6]),x]","-\frac{\left(15 b^2-16 a c\right) \sqrt{a+b x^3+c x^6}}{72 a^3 x^3}+\frac{b \left(5 b^2-12 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{48 a^{7/2}}+\frac{5 b \sqrt{a+b x^3+c x^6}}{36 a^2 x^6}-\frac{\sqrt{a+b x^3+c x^6}}{9 a x^9}","-\frac{\left(15 b^2-16 a c\right) \sqrt{a+b x^3+c x^6}}{72 a^3 x^3}+\frac{b \left(5 b^2-12 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{48 a^{7/2}}+\frac{5 b \sqrt{a+b x^3+c x^6}}{36 a^2 x^6}-\frac{\sqrt{a+b x^3+c x^6}}{9 a x^9}",1,"-Sqrt[a + b*x^3 + c*x^6]/(9*a*x^9) + (5*b*Sqrt[a + b*x^3 + c*x^6])/(36*a^2*x^6) - ((15*b^2 - 16*a*c)*Sqrt[a + b*x^3 + c*x^6])/(72*a^3*x^3) + (b*(5*b^2 - 12*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(48*a^(7/2))","A",6,6,20,0.3000,1,"{1357, 744, 834, 806, 724, 206}"
228,1,192,0,0.233341,"\int \frac{1}{x^{13} \sqrt{a+b x^3+c x^6}} \, dx","Int[1/(x^13*Sqrt[a + b*x^3 + c*x^6]),x]","-\frac{\left(48 a^2 c^2-120 a b^2 c+35 b^4\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{384 a^{9/2}}+\frac{5 b \left(21 b^2-44 a c\right) \sqrt{a+b x^3+c x^6}}{576 a^4 x^3}-\frac{\left(35 b^2-36 a c\right) \sqrt{a+b x^3+c x^6}}{288 a^3 x^6}+\frac{7 b \sqrt{a+b x^3+c x^6}}{72 a^2 x^9}-\frac{\sqrt{a+b x^3+c x^6}}{12 a x^{12}}","-\frac{\left(48 a^2 c^2-120 a b^2 c+35 b^4\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{384 a^{9/2}}+\frac{5 b \left(21 b^2-44 a c\right) \sqrt{a+b x^3+c x^6}}{576 a^4 x^3}-\frac{\left(35 b^2-36 a c\right) \sqrt{a+b x^3+c x^6}}{288 a^3 x^6}+\frac{7 b \sqrt{a+b x^3+c x^6}}{72 a^2 x^9}-\frac{\sqrt{a+b x^3+c x^6}}{12 a x^{12}}",1,"-Sqrt[a + b*x^3 + c*x^6]/(12*a*x^12) + (7*b*Sqrt[a + b*x^3 + c*x^6])/(72*a^2*x^9) - ((35*b^2 - 36*a*c)*Sqrt[a + b*x^3 + c*x^6])/(288*a^3*x^6) + (5*b*(21*b^2 - 44*a*c)*Sqrt[a + b*x^3 + c*x^6])/(576*a^4*x^3) - ((35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(384*a^(9/2))","A",7,6,20,0.3000,1,"{1357, 744, 834, 806, 724, 206}"
229,1,140,0,0.1256739,"\int \frac{x^3}{\sqrt{a+b x^3+c x^6}} \, dx","Int[x^3/Sqrt[a + b*x^3 + c*x^6],x]","\frac{x^4 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{4}{3};\frac{1}{2},\frac{1}{2};\frac{7}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{a+b x^3+c x^6}}","\frac{x^4 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{4}{3};\frac{1}{2},\frac{1}{2};\frac{7}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{a+b x^3+c x^6}}",1,"(x^4*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[4/3, 1/2, 1/2, 7/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(4*Sqrt[a + b*x^3 + c*x^6])","A",2,2,20,0.1000,1,"{1385, 510}"
230,1,140,0,0.0909508,"\int \frac{x}{\sqrt{a+b x^3+c x^6}} \, dx","Int[x/Sqrt[a + b*x^3 + c*x^6],x]","\frac{x^2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{5}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{a+b x^3+c x^6}}","\frac{x^2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{5}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{a+b x^3+c x^6}}",1,"(x^2*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[2/3, 1/2, 1/2, 5/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(2*Sqrt[a + b*x^3 + c*x^6])","A",2,2,18,0.1111,1,"{1385, 510}"
231,1,135,0,0.0639999,"\int \frac{1}{\sqrt{a+b x^3+c x^6}} \, dx","Int[1/Sqrt[a + b*x^3 + c*x^6],x]","\frac{x \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{a+b x^3+c x^6}}","\frac{x \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{a+b x^3+c x^6}}",1,"(x*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[1/3, 1/2, 1/2, 4/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[a + b*x^3 + c*x^6]","A",2,2,16,0.1250,1,"{1348, 429}"
232,1,138,0,0.1187183,"\int \frac{1}{x^2 \sqrt{a+b x^3+c x^6}} \, dx","Int[1/(x^2*Sqrt[a + b*x^3 + c*x^6]),x]","-\frac{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{a+b x^3+c x^6}}","-\frac{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{a+b x^3+c x^6}}",1,"-((Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-1/3, 1/2, 1/2, 2/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(x*Sqrt[a + b*x^3 + c*x^6]))","A",2,2,20,0.1000,1,"{1385, 510}"
233,1,140,0,0.1195389,"\int \frac{1}{x^3 \sqrt{a+b x^3+c x^6}} \, dx","Int[1/(x^3*Sqrt[a + b*x^3 + c*x^6]),x]","-\frac{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{a+b x^3+c x^6}}","-\frac{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{a+b x^3+c x^6}}",1,"-(Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-2/3, 1/2, 1/2, 1/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(2*x^2*Sqrt[a + b*x^3 + c*x^6])","A",2,2,20,0.1000,1,"{1385, 510}"
234,1,195,0,0.2285352,"\int \frac{x^{14}}{\left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[x^14/(a + b*x^3 + c*x^6)^(3/2),x]","-\frac{\left(b \left(15 b^2-52 a c\right)-2 c x^3 \left(5 b^2-12 a c\right)\right) \sqrt{a+b x^3+c x^6}}{12 c^3 \left(b^2-4 a c\right)}+\frac{\left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{8 c^{7/2}}+\frac{2 x^9 \left(2 a+b x^3\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}-\frac{2 b x^6 \sqrt{a+b x^3+c x^6}}{3 c \left(b^2-4 a c\right)}","-\frac{\left(b \left(15 b^2-52 a c\right)-2 c x^3 \left(5 b^2-12 a c\right)\right) \sqrt{a+b x^3+c x^6}}{12 c^3 \left(b^2-4 a c\right)}+\frac{\left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{8 c^{7/2}}+\frac{2 x^9 \left(2 a+b x^3\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}-\frac{2 b x^6 \sqrt{a+b x^3+c x^6}}{3 c \left(b^2-4 a c\right)}",1,"(2*x^9*(2*a + b*x^3))/(3*(b^2 - 4*a*c)*Sqrt[a + b*x^3 + c*x^6]) - (2*b*x^6*Sqrt[a + b*x^3 + c*x^6])/(3*c*(b^2 - 4*a*c)) - ((b*(15*b^2 - 52*a*c) - 2*c*(5*b^2 - 12*a*c)*x^3)*Sqrt[a + b*x^3 + c*x^6])/(12*c^3*(b^2 - 4*a*c)) + ((5*b^2 - 4*a*c)*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(8*c^(7/2))","A",6,6,20,0.3000,1,"{1357, 738, 832, 779, 621, 206}"
235,1,137,0,0.1105734,"\int \frac{x^{11}}{\left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[x^11/(a + b*x^3 + c*x^6)^(3/2),x]","\frac{\left(-8 a c+3 b^2-2 b c x^3\right) \sqrt{a+b x^3+c x^6}}{3 c^2 \left(b^2-4 a c\right)}+\frac{2 x^6 \left(2 a+b x^3\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}-\frac{b \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{2 c^{5/2}}","\frac{\left(-8 a c+3 b^2-2 b c x^3\right) \sqrt{a+b x^3+c x^6}}{3 c^2 \left(b^2-4 a c\right)}+\frac{2 x^6 \left(2 a+b x^3\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}-\frac{b \tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{2 c^{5/2}}",1,"(2*x^6*(2*a + b*x^3))/(3*(b^2 - 4*a*c)*Sqrt[a + b*x^3 + c*x^6]) + ((3*b^2 - 8*a*c - 2*b*c*x^3)*Sqrt[a + b*x^3 + c*x^6])/(3*c^2*(b^2 - 4*a*c)) - (b*ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])])/(2*c^(5/2))","A",5,5,20,0.2500,1,"{1357, 738, 779, 621, 206}"
236,1,120,0,0.0895328,"\int \frac{x^8}{\left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[x^8/(a + b*x^3 + c*x^6)^(3/2),x]","\frac{2 x^3 \left(2 a+b x^3\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}-\frac{2 b \sqrt{a+b x^3+c x^6}}{3 c \left(b^2-4 a c\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{3 c^{3/2}}","\frac{2 x^3 \left(2 a+b x^3\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}-\frac{2 b \sqrt{a+b x^3+c x^6}}{3 c \left(b^2-4 a c\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^3}{2 \sqrt{c} \sqrt{a+b x^3+c x^6}}\right)}{3 c^{3/2}}",1,"(2*x^3*(2*a + b*x^3))/(3*(b^2 - 4*a*c)*Sqrt[a + b*x^3 + c*x^6]) - (2*b*Sqrt[a + b*x^3 + c*x^6])/(3*c*(b^2 - 4*a*c)) + ArcTanh[(b + 2*c*x^3)/(2*Sqrt[c]*Sqrt[a + b*x^3 + c*x^6])]/(3*c^(3/2))","A",5,5,20,0.2500,1,"{1357, 738, 640, 621, 206}"
237,1,39,0,0.0293345,"\int \frac{x^5}{\left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[x^5/(a + b*x^3 + c*x^6)^(3/2),x]","\frac{2 \left(2 a+b x^3\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}","\frac{2 \left(2 a+b x^3\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}",1,"(2*(2*a + b*x^3))/(3*(b^2 - 4*a*c)*Sqrt[a + b*x^3 + c*x^6])","A",2,2,20,0.1000,1,"{1357, 636}"
238,1,38,0,0.0247371,"\int \frac{x^2}{\left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[x^2/(a + b*x^3 + c*x^6)^(3/2),x]","-\frac{2 \left(b+2 c x^3\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}","-\frac{2 \left(b+2 c x^3\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}",1,"(-2*(b + 2*c*x^3))/(3*(b^2 - 4*a*c)*Sqrt[a + b*x^3 + c*x^6])","A",2,2,20,0.1000,1,"{1352, 613}"
239,1,92,0,0.077819,"\int \frac{1}{x \left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[1/(x*(a + b*x^3 + c*x^6)^(3/2)),x]","\frac{2 \left(-2 a c+b^2+b c x^3\right)}{3 a \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}-\frac{\tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{3 a^{3/2}}","\frac{2 \left(-2 a c+b^2+b c x^3\right)}{3 a \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}-\frac{\tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{3 a^{3/2}}",1,"(2*(b^2 - 2*a*c + b*c*x^3))/(3*a*(b^2 - 4*a*c)*Sqrt[a + b*x^3 + c*x^6]) - ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])]/(3*a^(3/2))","A",5,5,20,0.2500,1,"{1357, 740, 12, 724, 206}"
240,1,142,0,0.1240313,"\int \frac{1}{x^4 \left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[1/(x^4*(a + b*x^3 + c*x^6)^(3/2)),x]","-\frac{\left(3 b^2-8 a c\right) \sqrt{a+b x^3+c x^6}}{3 a^2 x^3 \left(b^2-4 a c\right)}+\frac{b \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{2 a^{5/2}}+\frac{2 \left(-2 a c+b^2+b c x^3\right)}{3 a x^3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}","-\frac{\left(3 b^2-8 a c\right) \sqrt{a+b x^3+c x^6}}{3 a^2 x^3 \left(b^2-4 a c\right)}+\frac{b \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{2 a^{5/2}}+\frac{2 \left(-2 a c+b^2+b c x^3\right)}{3 a x^3 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}",1,"(2*(b^2 - 2*a*c + b*c*x^3))/(3*a*(b^2 - 4*a*c)*x^3*Sqrt[a + b*x^3 + c*x^6]) - ((3*b^2 - 8*a*c)*Sqrt[a + b*x^3 + c*x^6])/(3*a^2*(b^2 - 4*a*c)*x^3) + (b*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(2*a^(5/2))","A",5,5,20,0.2500,1,"{1357, 740, 806, 724, 206}"
241,1,198,0,0.2042596,"\int \frac{1}{x^7 \left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[1/(x^7*(a + b*x^3 + c*x^6)^(3/2)),x]","\frac{b \left(15 b^2-52 a c\right) \sqrt{a+b x^3+c x^6}}{12 a^3 x^3 \left(b^2-4 a c\right)}-\frac{\left(5 b^2-12 a c\right) \sqrt{a+b x^3+c x^6}}{6 a^2 x^6 \left(b^2-4 a c\right)}-\frac{\left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{8 a^{7/2}}+\frac{2 \left(-2 a c+b^2+b c x^3\right)}{3 a x^6 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}","\frac{b \left(15 b^2-52 a c\right) \sqrt{a+b x^3+c x^6}}{12 a^3 x^3 \left(b^2-4 a c\right)}-\frac{\left(5 b^2-12 a c\right) \sqrt{a+b x^3+c x^6}}{6 a^2 x^6 \left(b^2-4 a c\right)}-\frac{\left(5 b^2-4 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{8 a^{7/2}}+\frac{2 \left(-2 a c+b^2+b c x^3\right)}{3 a x^6 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}",1,"(2*(b^2 - 2*a*c + b*c*x^3))/(3*a*(b^2 - 4*a*c)*x^6*Sqrt[a + b*x^3 + c*x^6]) - ((5*b^2 - 12*a*c)*Sqrt[a + b*x^3 + c*x^6])/(6*a^2*(b^2 - 4*a*c)*x^6) + (b*(15*b^2 - 52*a*c)*Sqrt[a + b*x^3 + c*x^6])/(12*a^3*(b^2 - 4*a*c)*x^3) - ((5*b^2 - 4*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(8*a^(7/2))","A",6,6,20,0.3000,1,"{1357, 740, 834, 806, 724, 206}"
242,1,256,0,0.2859433,"\int \frac{1}{x^{10} \left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[1/(x^10*(a + b*x^3 + c*x^6)^(3/2)),x]","-\frac{\left(256 a^2 c^2-460 a b^2 c+105 b^4\right) \sqrt{a+b x^3+c x^6}}{72 a^4 x^3 \left(b^2-4 a c\right)}+\frac{b \left(35 b^2-116 a c\right) \sqrt{a+b x^3+c x^6}}{36 a^3 x^6 \left(b^2-4 a c\right)}-\frac{\left(7 b^2-16 a c\right) \sqrt{a+b x^3+c x^6}}{9 a^2 x^9 \left(b^2-4 a c\right)}+\frac{5 b \left(7 b^2-12 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{48 a^{9/2}}+\frac{2 \left(-2 a c+b^2+b c x^3\right)}{3 a x^9 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}","-\frac{\left(256 a^2 c^2-460 a b^2 c+105 b^4\right) \sqrt{a+b x^3+c x^6}}{72 a^4 x^3 \left(b^2-4 a c\right)}+\frac{b \left(35 b^2-116 a c\right) \sqrt{a+b x^3+c x^6}}{36 a^3 x^6 \left(b^2-4 a c\right)}-\frac{\left(7 b^2-16 a c\right) \sqrt{a+b x^3+c x^6}}{9 a^2 x^9 \left(b^2-4 a c\right)}+\frac{5 b \left(7 b^2-12 a c\right) \tanh ^{-1}\left(\frac{2 a+b x^3}{2 \sqrt{a} \sqrt{a+b x^3+c x^6}}\right)}{48 a^{9/2}}+\frac{2 \left(-2 a c+b^2+b c x^3\right)}{3 a x^9 \left(b^2-4 a c\right) \sqrt{a+b x^3+c x^6}}",1,"(2*(b^2 - 2*a*c + b*c*x^3))/(3*a*(b^2 - 4*a*c)*x^9*Sqrt[a + b*x^3 + c*x^6]) - ((7*b^2 - 16*a*c)*Sqrt[a + b*x^3 + c*x^6])/(9*a^2*(b^2 - 4*a*c)*x^9) + (b*(35*b^2 - 116*a*c)*Sqrt[a + b*x^3 + c*x^6])/(36*a^3*(b^2 - 4*a*c)*x^6) - ((105*b^4 - 460*a*b^2*c + 256*a^2*c^2)*Sqrt[a + b*x^3 + c*x^6])/(72*a^4*(b^2 - 4*a*c)*x^3) + (5*b*(7*b^2 - 12*a*c)*ArcTanh[(2*a + b*x^3)/(2*Sqrt[a]*Sqrt[a + b*x^3 + c*x^6])])/(48*a^(9/2))","A",7,6,20,0.3000,1,"{1357, 740, 834, 806, 724, 206}"
243,1,143,0,0.1321405,"\int \frac{x^3}{\left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[x^3/(a + b*x^3 + c*x^6)^(3/2),x]","\frac{x^4 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{4}{3};\frac{3}{2},\frac{3}{2};\frac{7}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{4 a \sqrt{a+b x^3+c x^6}}","\frac{x^4 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{4}{3};\frac{3}{2},\frac{3}{2};\frac{7}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{4 a \sqrt{a+b x^3+c x^6}}",1,"(x^4*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[4/3, 3/2, 3/2, 7/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(4*a*Sqrt[a + b*x^3 + c*x^6])","A",2,2,20,0.1000,1,"{1385, 510}"
244,1,143,0,0.0967523,"\int \frac{x}{\left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[x/(a + b*x^3 + c*x^6)^(3/2),x]","\frac{x^2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{3};\frac{3}{2},\frac{3}{2};\frac{5}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{a+b x^3+c x^6}}","\frac{x^2 \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{3};\frac{3}{2},\frac{3}{2};\frac{5}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{a+b x^3+c x^6}}",1,"(x^2*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[2/3, 3/2, 3/2, 5/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(2*a*Sqrt[a + b*x^3 + c*x^6])","A",2,2,18,0.1111,1,"{1385, 510}"
245,1,138,0,0.0672494,"\int \frac{1}{\left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[(a + b*x^3 + c*x^6)^(-3/2),x]","\frac{x \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{3};\frac{3}{2},\frac{3}{2};\frac{4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{a \sqrt{a+b x^3+c x^6}}","\frac{x \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{3};\frac{3}{2},\frac{3}{2};\frac{4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{a \sqrt{a+b x^3+c x^6}}",1,"(x*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[1/3, 3/2, 3/2, 4/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(a*Sqrt[a + b*x^3 + c*x^6])","A",2,2,16,0.1250,1,"{1348, 429}"
246,1,141,0,0.1277453,"\int \frac{1}{x^2 \left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*x^3 + c*x^6)^(3/2)),x]","-\frac{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{3};\frac{3}{2},\frac{3}{2};\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{a x \sqrt{a+b x^3+c x^6}}","-\frac{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{3};\frac{3}{2},\frac{3}{2};\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{a x \sqrt{a+b x^3+c x^6}}",1,"-((Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-1/3, 3/2, 3/2, 2/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(a*x*Sqrt[a + b*x^3 + c*x^6]))","A",2,2,20,0.1000,1,"{1385, 510}"
247,1,143,0,0.1284235,"\int \frac{1}{x^3 \left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[1/(x^3*(a + b*x^3 + c*x^6)^(3/2)),x]","-\frac{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{2}{3};\frac{3}{2},\frac{3}{2};\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 a x^2 \sqrt{a+b x^3+c x^6}}","-\frac{\sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{2}{3};\frac{3}{2},\frac{3}{2};\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 a x^2 \sqrt{a+b x^3+c x^6}}",1,"-(Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-2/3, 3/2, 3/2, 1/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(2*a*x^2*Sqrt[a + b*x^3 + c*x^6])","A",2,2,20,0.1000,1,"{1385, 510}"
248,1,101,0,0.0609639,"\int (d x)^m \left(a+b x^3+c x^6\right)^2 \, dx","Int[(d*x)^m*(a + b*x^3 + c*x^6)^2,x]","\frac{a^2 (d x)^{m+1}}{d (m+1)}+\frac{\left(2 a c+b^2\right) (d x)^{m+7}}{d^7 (m+7)}+\frac{2 a b (d x)^{m+4}}{d^4 (m+4)}+\frac{2 b c (d x)^{m+10}}{d^{10} (m+10)}+\frac{c^2 (d x)^{m+13}}{d^{13} (m+13)}","\frac{a^2 (d x)^{m+1}}{d (m+1)}+\frac{\left(2 a c+b^2\right) (d x)^{m+7}}{d^7 (m+7)}+\frac{2 a b (d x)^{m+4}}{d^4 (m+4)}+\frac{2 b c (d x)^{m+10}}{d^{10} (m+10)}+\frac{c^2 (d x)^{m+13}}{d^{13} (m+13)}",1,"(a^2*(d*x)^(1 + m))/(d*(1 + m)) + (2*a*b*(d*x)^(4 + m))/(d^4*(4 + m)) + ((b^2 + 2*a*c)*(d*x)^(7 + m))/(d^7*(7 + m)) + (2*b*c*(d*x)^(10 + m))/(d^10*(10 + m)) + (c^2*(d*x)^(13 + m))/(d^13*(13 + m))","A",2,1,20,0.05000,1,"{1353}"
249,1,52,0,0.0206515,"\int (d x)^m \left(a+b x^3+c x^6\right) \, dx","Int[(d*x)^m*(a + b*x^3 + c*x^6),x]","\frac{a (d x)^{m+1}}{d (m+1)}+\frac{b (d x)^{m+4}}{d^4 (m+4)}+\frac{c (d x)^{m+7}}{d^7 (m+7)}","\frac{a (d x)^{m+1}}{d (m+1)}+\frac{b (d x)^{m+4}}{d^4 (m+4)}+\frac{c (d x)^{m+7}}{d^7 (m+7)}",1,"(a*(d*x)^(1 + m))/(d*(1 + m)) + (b*(d*x)^(4 + m))/(d^4*(4 + m)) + (c*(d*x)^(7 + m))/(d^7*(7 + m))","A",2,1,18,0.05556,1,"{14}"
250,1,173,0,0.2375438,"\int \frac{(d x)^m}{a+b x^3+c x^6} \, dx","Int[(d*x)^m/(a + b*x^3 + c*x^6),x]","\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}","\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}",1,"(2*c*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/3, (4 + m)/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*d*(1 + m)) - (2*c*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/3, (4 + m)/3, (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*d*(1 + m))","A",3,2,20,0.1000,1,"{1375, 364}"
251,1,315,0,0.7130229,"\int \frac{(d x)^m}{\left(a+b x^3+c x^6\right)^2} \, dx","Int[(d*x)^m/(a + b*x^3 + c*x^6)^2,x]","\frac{c (d x)^{m+1} \left(b (2-m) \sqrt{b^2-4 a c}-4 a c (5-m)+b^2 (2-m)\right) \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}\right)}{3 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (d x)^{m+1} \left(-b (2-m) \sqrt{b^2-4 a c}-4 a c (5-m)+b^2 (2-m)\right) \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{3 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(d x)^{m+1} \left(-2 a c+b^2+b c x^3\right)}{3 a d \left(b^2-4 a c\right) \left(a+b x^3+c x^6\right)}","\frac{c (d x)^{m+1} \left(b (2-m) \sqrt{b^2-4 a c}-4 a c (5-m)+b^2 (2-m)\right) \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}\right)}{3 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (d x)^{m+1} \left(-b (2-m) \sqrt{b^2-4 a c}-4 a c (5-m)+b^2 (2-m)\right) \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{3 a d (m+1) \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(d x)^{m+1} \left(-2 a c+b^2+b c x^3\right)}{3 a d \left(b^2-4 a c\right) \left(a+b x^3+c x^6\right)}",1,"((d*x)^(1 + m)*(b^2 - 2*a*c + b*c*x^3))/(3*a*(b^2 - 4*a*c)*d*(a + b*x^3 + c*x^6)) + (c*(b^2*(2 - m) + b*Sqrt[b^2 - 4*a*c]*(2 - m) - 4*a*c*(5 - m))*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/3, (4 + m)/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])])/(3*a*(b^2 - 4*a*c)^(3/2)*(b - Sqrt[b^2 - 4*a*c])*d*(1 + m)) - (c*(b^2*(2 - m) - b*Sqrt[b^2 - 4*a*c]*(2 - m) - 4*a*c*(5 - m))*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/3, (4 + m)/3, (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(3*a*(b^2 - 4*a*c)^(3/2)*(b + Sqrt[b^2 - 4*a*c])*d*(1 + m))","A",4,3,20,0.1500,1,"{1366, 1510, 364}"
252,1,158,0,0.1524427,"\int (d x)^m \left(a+b x^3+c x^6\right)^{3/2} \, dx","Int[(d*x)^m*(a + b*x^3 + c*x^6)^(3/2),x]","\frac{a (d x)^{m+1} \sqrt{a+b x^3+c x^6} F_1\left(\frac{m+1}{3};-\frac{3}{2},-\frac{3}{2};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","\frac{a (d x)^{m+1} \sqrt{a+b x^3+c x^6} F_1\left(\frac{m+1}{3};-\frac{3}{2},-\frac{3}{2};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"(a*(d*x)^(1 + m)*Sqrt[a + b*x^3 + c*x^6]*AppellF1[(1 + m)/3, -3/2, -3/2, (4 + m)/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,22,0.09091,1,"{1385, 510}"
253,1,157,0,0.1392263,"\int (d x)^m \sqrt{a+b x^3+c x^6} \, dx","Int[(d*x)^m*Sqrt[a + b*x^3 + c*x^6],x]","\frac{(d x)^{m+1} \sqrt{a+b x^3+c x^6} F_1\left(\frac{m+1}{3};-\frac{1}{2},-\frac{1}{2};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}","\frac{(d x)^{m+1} \sqrt{a+b x^3+c x^6} F_1\left(\frac{m+1}{3};-\frac{1}{2},-\frac{1}{2};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1}}",1,"((d*x)^(1 + m)*Sqrt[a + b*x^3 + c*x^6]*AppellF1[(1 + m)/3, -1/2, -1/2, (4 + m)/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,22,0.09091,1,"{1385, 510}"
254,1,157,0,0.1329576,"\int \frac{(d x)^m}{\sqrt{a+b x^3+c x^6}} \, dx","Int[(d*x)^m/Sqrt[a + b*x^3 + c*x^6],x]","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{3};\frac{1}{2},\frac{1}{2};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{a+b x^3+c x^6}}","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{3};\frac{1}{2},\frac{1}{2};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{a+b x^3+c x^6}}",1,"((d*x)^(1 + m)*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[(1 + m)/3, 1/2, 1/2, (4 + m)/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*Sqrt[a + b*x^3 + c*x^6])","A",2,2,22,0.09091,1,"{1385, 510}"
255,1,160,0,0.1408204,"\int \frac{(d x)^m}{\left(a+b x^3+c x^6\right)^{3/2}} \, dx","Int[(d*x)^m/(a + b*x^3 + c*x^6)^(3/2),x]","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{3};\frac{3}{2},\frac{3}{2};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{a d (m+1) \sqrt{a+b x^3+c x^6}}","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{3};\frac{3}{2},\frac{3}{2};\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{a d (m+1) \sqrt{a+b x^3+c x^6}}",1,"((d*x)^(1 + m)*Sqrt[1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[(1 + m)/3, 3/2, 3/2, (4 + m)/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(a*d*(1 + m)*Sqrt[a + b*x^3 + c*x^6])","A",2,2,22,0.09091,1,"{1385, 510}"
256,1,155,0,0.101441,"\int (d x)^m \left(a+b x^3+c x^6\right)^p \, dx","Int[(d*x)^m*(a + b*x^3 + c*x^6)^p,x]","\frac{(d x)^{m+1} \left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(\frac{m+1}{3};-p,-p;\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1)}","\frac{(d x)^{m+1} \left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(\frac{m+1}{3};-p,-p;\frac{m+4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1)}",1,"((d*x)^(1 + m)*(a + b*x^3 + c*x^6)^p*AppellF1[(1 + m)/3, -p, -p, (4 + m)/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*(1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,20,0.1000,1,"{1385, 510}"
257,1,224,0,0.2434921,"\int x^8 \left(a+b x^3+c x^6\right)^p \, dx","Int[x^8*(a + b*x^3 + c*x^6)^p,x]","\frac{2^p \left(2 a c-b^2 (p+2)\right) \left(a+b x^3+c x^6\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^3+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{3 c^2 (p+1) (2 p+3) \sqrt{b^2-4 a c}}-\frac{b (p+2) \left(a+b x^3+c x^6\right)^{p+1}}{6 c^2 (p+1) (2 p+3)}+\frac{x^3 \left(a+b x^3+c x^6\right)^{p+1}}{3 c (2 p+3)}","\frac{2^p \left(2 a c-b^2 (p+2)\right) \left(a+b x^3+c x^6\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^3+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{3 c^2 (p+1) (2 p+3) \sqrt{b^2-4 a c}}-\frac{b (p+2) \left(a+b x^3+c x^6\right)^{p+1}}{6 c^2 (p+1) (2 p+3)}+\frac{x^3 \left(a+b x^3+c x^6\right)^{p+1}}{3 c (2 p+3)}",1,"-(b*(2 + p)*(a + b*x^3 + c*x^6)^(1 + p))/(6*c^2*(1 + p)*(3 + 2*p)) + (x^3*(a + b*x^3 + c*x^6)^(1 + p))/(3*c*(3 + 2*p)) + (2^p*(2*a*c - b^2*(2 + p))*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x^3)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x^3 + c*x^6)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x^3)/(2*Sqrt[b^2 - 4*a*c])])/(3*c^2*Sqrt[b^2 - 4*a*c]*(1 + p)*(3 + 2*p))","A",4,4,18,0.2222,1,"{1357, 742, 640, 624}"
258,1,161,0,0.1169843,"\int x^5 \left(a+b x^3+c x^6\right)^p \, dx","Int[x^5*(a + b*x^3 + c*x^6)^p,x]","\frac{b 2^p \left(a+b x^3+c x^6\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^3+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{3 c (p+1) \sqrt{b^2-4 a c}}+\frac{\left(a+b x^3+c x^6\right)^{p+1}}{6 c (p+1)}","\frac{b 2^p \left(a+b x^3+c x^6\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^3+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{3 c (p+1) \sqrt{b^2-4 a c}}+\frac{\left(a+b x^3+c x^6\right)^{p+1}}{6 c (p+1)}",1,"(a + b*x^3 + c*x^6)^(1 + p)/(6*c*(1 + p)) + (2^p*b*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x^3)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x^3 + c*x^6)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x^3)/(2*Sqrt[b^2 - 4*a*c])])/(3*c*Sqrt[b^2 - 4*a*c]*(1 + p))","A",3,3,18,0.1667,1,"{1357, 640, 624}"
259,1,130,0,0.0733837,"\int x^2 \left(a+b x^3+c x^6\right)^p \, dx","Int[x^2*(a + b*x^3 + c*x^6)^p,x]","-\frac{2^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x^3+c x^6\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^3+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{3 (p+1) \sqrt{b^2-4 a c}}","-\frac{2^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x^3+c x^6\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{2 c x^3+b+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{3 (p+1) \sqrt{b^2-4 a c}}",1,"-(2^(1 + p)*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x^3)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x^3 + c*x^6)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x^3)/(2*Sqrt[b^2 - 4*a*c])])/(3*Sqrt[b^2 - 4*a*c]*(1 + p))","A",2,2,18,0.1111,1,"{1352, 624}"
260,1,138,0,0.0954244,"\int x^4 \left(a+b x^3+c x^6\right)^p \, dx","Int[x^4*(a + b*x^3 + c*x^6)^p,x]","\frac{1}{5} x^5 \left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(\frac{5}{3};-p,-p;\frac{8}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)","\frac{1}{5} x^5 \left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(\frac{5}{3};-p,-p;\frac{8}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)",1,"(x^5*(a + b*x^3 + c*x^6)^p*AppellF1[5/3, -p, -p, 8/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(5*(1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,18,0.1111,1,"{1385, 510}"
261,1,138,0,0.0909034,"\int x^3 \left(a+b x^3+c x^6\right)^p \, dx","Int[x^3*(a + b*x^3 + c*x^6)^p,x]","\frac{1}{4} x^4 \left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(\frac{4}{3};-p,-p;\frac{7}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)","\frac{1}{4} x^4 \left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(\frac{4}{3};-p,-p;\frac{7}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)",1,"(x^4*(a + b*x^3 + c*x^6)^p*AppellF1[4/3, -p, -p, 7/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(4*(1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,18,0.1111,1,"{1385, 510}"
262,1,138,0,0.0699415,"\int x \left(a+b x^3+c x^6\right)^p \, dx","Int[x*(a + b*x^3 + c*x^6)^p,x]","\frac{1}{2} x^2 \left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(\frac{2}{3};-p,-p;\frac{5}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)","\frac{1}{2} x^2 \left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(\frac{2}{3};-p,-p;\frac{5}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)",1,"(x^2*(a + b*x^3 + c*x^6)^p*AppellF1[2/3, -p, -p, 5/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(2*(1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,16,0.1250,1,"{1385, 510}"
263,1,133,0,0.0588891,"\int \left(a+b x^3+c x^6\right)^p \, dx","Int[(a + b*x^3 + c*x^6)^p,x]","x \left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(\frac{1}{3};-p,-p;\frac{4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)","x \left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(\frac{1}{3};-p,-p;\frac{4}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)",1,"(x*(a + b*x^3 + c*x^6)^p*AppellF1[1/3, -p, -p, 4/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/((1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,14,0.1429,1,"{1348, 429}"
264,1,157,0,0.1415805,"\int \frac{\left(a+b x^3+c x^6\right)^p}{x} \, dx","Int[(a + b*x^3 + c*x^6)^p/x,x]","\frac{2^{2 p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(-2 p;-p,-p;1-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x^3},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^3}\right)}{3 p}","\frac{2^{2 p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(-2 p;-p,-p;1-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x^3},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^3}\right)}{3 p}",1,"(2^(-1 + 2*p)*(a + b*x^3 + c*x^6)^p*AppellF1[-2*p, -p, -p, 1 - 2*p, -(b - Sqrt[b^2 - 4*a*c])/(2*c*x^3), -(b + Sqrt[b^2 - 4*a*c])/(2*c*x^3)])/(3*p*((b - Sqrt[b^2 - 4*a*c] + 2*c*x^3)/(c*x^3))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x^3)/(c*x^3))^p)","A",3,3,18,0.1667,1,"{1357, 758, 133}"
265,1,136,0,0.0891608,"\int \frac{\left(a+b x^3+c x^6\right)^p}{x^2} \, dx","Int[(a + b*x^3 + c*x^6)^p/x^2,x]","-\frac{\left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(-\frac{1}{3};-p,-p;\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{x}","-\frac{\left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(-\frac{1}{3};-p,-p;\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{x}",1,"-(((a + b*x^3 + c*x^6)^p*AppellF1[-1/3, -p, -p, 2/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(x*(1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c]))^p))","A",2,2,18,0.1111,1,"{1385, 510}"
266,1,138,0,0.0893756,"\int \frac{\left(a+b x^3+c x^6\right)^p}{x^3} \, dx","Int[(a + b*x^3 + c*x^6)^p/x^3,x]","-\frac{\left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(-\frac{2}{3};-p,-p;\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2}","-\frac{\left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(-\frac{2}{3};-p,-p;\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2}",1,"-((a + b*x^3 + c*x^6)^p*AppellF1[-2/3, -p, -p, 1/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(2*x^2*(1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,18,0.1111,1,"{1385, 510}"
267,1,164,0,0.1266536,"\int \frac{\left(a+b x^3+c x^6\right)^p}{x^4} \, dx","Int[(a + b*x^3 + c*x^6)^p/x^4,x]","-\frac{4^p \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(1-2 p;-p,-p;2 (1-p);-\frac{b-\sqrt{b^2-4 a c}}{2 c x^3},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^3}\right)}{3 (1-2 p) x^3}","-\frac{4^p \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(1-2 p;-p,-p;2 (1-p);-\frac{b-\sqrt{b^2-4 a c}}{2 c x^3},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^3}\right)}{3 (1-2 p) x^3}",1,"-(4^p*(a + b*x^3 + c*x^6)^p*AppellF1[1 - 2*p, -p, -p, 2*(1 - p), -(b - Sqrt[b^2 - 4*a*c])/(2*c*x^3), -(b + Sqrt[b^2 - 4*a*c])/(2*c*x^3)])/(3*(1 - 2*p)*x^3*((b - Sqrt[b^2 - 4*a*c] + 2*c*x^3)/(c*x^3))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x^3)/(c*x^3))^p)","A",3,3,18,0.1667,1,"{1357, 758, 133}"
268,1,138,0,0.090244,"\int \frac{\left(a+b x^3+c x^6\right)^p}{x^5} \, dx","Int[(a + b*x^3 + c*x^6)^p/x^5,x]","-\frac{\left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(-\frac{4}{3};-p,-p;-\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{4 x^4}","-\frac{\left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(-\frac{4}{3};-p,-p;-\frac{1}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{4 x^4}",1,"-((a + b*x^3 + c*x^6)^p*AppellF1[-4/3, -p, -p, -1/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(4*x^4*(1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,18,0.1111,1,"{1385, 510}"
269,1,138,0,0.0886634,"\int \frac{\left(a+b x^3+c x^6\right)^p}{x^6} \, dx","Int[(a + b*x^3 + c*x^6)^p/x^6,x]","-\frac{\left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(-\frac{5}{3};-p,-p;-\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{5 x^5}","-\frac{\left(\frac{2 c x^3}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^3}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(-\frac{5}{3};-p,-p;-\frac{2}{3};-\frac{2 c x^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^3}{b+\sqrt{b^2-4 a c}}\right)}{5 x^5}",1,"-((a + b*x^3 + c*x^6)^p*AppellF1[-5/3, -p, -p, -2/3, (-2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^3)/(b + Sqrt[b^2 - 4*a*c])])/(5*x^5*(1 + (2*c*x^3)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^3)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,18,0.1111,1,"{1385, 510}"
270,1,168,0,0.1260967,"\int \frac{\left(a+b x^3+c x^6\right)^p}{x^7} \, dx","Int[(a + b*x^3 + c*x^6)^p/x^7,x]","-\frac{2^{2 p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(2 (1-p);-p,-p;3-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x^3},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^3}\right)}{3 (1-p) x^6}","-\frac{2^{2 p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x^3}{c x^3}\right)^{-p} \left(a+b x^3+c x^6\right)^p F_1\left(2 (1-p);-p,-p;3-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x^3},-\frac{b+\sqrt{b^2-4 a c}}{2 c x^3}\right)}{3 (1-p) x^6}",1,"-(2^(-1 + 2*p)*(a + b*x^3 + c*x^6)^p*AppellF1[2*(1 - p), -p, -p, 3 - 2*p, -(b - Sqrt[b^2 - 4*a*c])/(2*c*x^3), -(b + Sqrt[b^2 - 4*a*c])/(2*c*x^3)])/(3*(1 - p)*x^6*((b - Sqrt[b^2 - 4*a*c] + 2*c*x^3)/(c*x^3))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x^3)/(c*x^3))^p)","A",3,3,18,0.1667,1,"{1357, 758, 133}"
271,1,32,0,0.0077789,"\int \frac{x^m}{1+2 x^4+x^8} \, dx","Int[x^m/(1 + 2*x^4 + x^8),x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{4};\frac{m+5}{4};-x^4\right)}{m+1}","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{4};\frac{m+5}{4};-x^4\right)}{m+1}",1,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/4, (5 + m)/4, -x^4])/(1 + m)","A",2,2,16,0.1250,1,"{28, 364}"
272,1,30,0,0.0123403,"\int \frac{x^9}{1+2 x^4+x^8} \, dx","Int[x^9/(1 + 2*x^4 + x^8),x]","-\frac{x^6}{4 \left(x^4+1\right)}+\frac{3 x^2}{4}-\frac{3}{4} \tan ^{-1}\left(x^2\right)","-\frac{x^6}{4 \left(x^4+1\right)}+\frac{3 x^2}{4}-\frac{3}{4} \tan ^{-1}\left(x^2\right)",1,"(3*x^2)/4 - x^6/(4*(1 + x^4)) - (3*ArcTan[x^2])/4","A",5,5,16,0.3125,1,"{28, 275, 288, 321, 203}"
273,1,22,0,0.01037,"\int \frac{x^7}{1+2 x^4+x^8} \, dx","Int[x^7/(1 + 2*x^4 + x^8),x]","\frac{1}{4 \left(x^4+1\right)}+\frac{1}{4} \log \left(x^4+1\right)","\frac{1}{4 \left(x^4+1\right)}+\frac{1}{4} \log \left(x^4+1\right)",1,"1/(4*(1 + x^4)) + Log[1 + x^4]/4","A",4,3,16,0.1875,1,"{28, 266, 43}"
274,1,23,0,0.0093071,"\int \frac{x^5}{1+2 x^4+x^8} \, dx","Int[x^5/(1 + 2*x^4 + x^8),x]","\frac{1}{4} \tan ^{-1}\left(x^2\right)-\frac{x^2}{4 \left(x^4+1\right)}","\frac{1}{4} \tan ^{-1}\left(x^2\right)-\frac{x^2}{4 \left(x^4+1\right)}",1,"-x^2/(4*(1 + x^4)) + ArcTan[x^2]/4","A",4,4,16,0.2500,1,"{28, 275, 288, 203}"
275,1,11,0,0.0028654,"\int \frac{x^3}{1+2 x^4+x^8} \, dx","Int[x^3/(1 + 2*x^4 + x^8),x]","-\frac{1}{4 \left(x^4+1\right)}","-\frac{1}{4 \left(x^4+1\right)}",1,"-1/(4*(1 + x^4))","A",2,2,16,0.1250,1,"{28, 261}"
276,1,23,0,0.0070609,"\int \frac{x}{1+2 x^4+x^8} \, dx","Int[x/(1 + 2*x^4 + x^8),x]","\frac{x^2}{4 \left(x^4+1\right)}+\frac{1}{4} \tan ^{-1}\left(x^2\right)","\frac{x^2}{4 \left(x^4+1\right)}+\frac{1}{4} \tan ^{-1}\left(x^2\right)",1,"x^2/(4*(1 + x^4)) + ArcTan[x^2]/4","A",4,4,14,0.2857,1,"{28, 275, 199, 203}"
277,1,24,0,0.0118203,"\int \frac{1}{x \left(1+2 x^4+x^8\right)} \, dx","Int[1/(x*(1 + 2*x^4 + x^8)),x]","\frac{1}{4 \left(x^4+1\right)}-\frac{1}{4} \log \left(x^4+1\right)+\log (x)","\frac{1}{4 \left(x^4+1\right)}-\frac{1}{4} \log \left(x^4+1\right)+\log (x)",1,"1/(4*(1 + x^4)) + Log[x] - Log[1 + x^4]/4","A",4,3,16,0.1875,1,"{28, 266, 44}"
278,1,30,0,0.0123191,"\int \frac{1}{x^3 \left(1+2 x^4+x^8\right)} \, dx","Int[1/(x^3*(1 + 2*x^4 + x^8)),x]","\frac{1}{4 x^2 \left(x^4+1\right)}-\frac{3}{4 x^2}-\frac{3}{4} \tan ^{-1}\left(x^2\right)","\frac{1}{4 x^2 \left(x^4+1\right)}-\frac{3}{4 x^2}-\frac{3}{4} \tan ^{-1}\left(x^2\right)",1,"-3/(4*x^2) + 1/(4*x^2*(1 + x^4)) - (3*ArcTan[x^2])/4","A",5,5,16,0.3125,1,"{28, 275, 290, 325, 203}"
279,1,33,0,0.0162449,"\int \frac{1}{x^5 \left(1+2 x^4+x^8\right)} \, dx","Int[1/(x^5*(1 + 2*x^4 + x^8)),x]","-\frac{1}{4 \left(x^4+1\right)}-\frac{1}{4 x^4}+\frac{1}{2} \log \left(x^4+1\right)-2 \log (x)","-\frac{1}{4 \left(x^4+1\right)}-\frac{1}{4 x^4}+\frac{1}{2} \log \left(x^4+1\right)-2 \log (x)",1,"-1/(4*x^4) - 1/(4*(1 + x^4)) - 2*Log[x] + Log[1 + x^4]/2","A",4,3,16,0.1875,1,"{28, 266, 44}"
280,1,37,0,0.0157296,"\int \frac{1}{x^7 \left(1+2 x^4+x^8\right)} \, dx","Int[1/(x^7*(1 + 2*x^4 + x^8)),x]","\frac{1}{4 x^6 \left(x^4+1\right)}+\frac{5}{4 x^2}-\frac{5}{12 x^6}+\frac{5}{4} \tan ^{-1}\left(x^2\right)","\frac{1}{4 x^6 \left(x^4+1\right)}+\frac{5}{4 x^2}-\frac{5}{12 x^6}+\frac{5}{4} \tan ^{-1}\left(x^2\right)",1,"-5/(12*x^6) + 5/(4*x^2) + 1/(4*x^6*(1 + x^4)) + (5*ArcTan[x^2])/4","A",6,5,16,0.3125,1,"{28, 275, 290, 325, 203}"
281,1,104,0,0.054602,"\int \frac{x^8}{1+2 x^4+x^8} \, dx","Int[x^8/(1 + 2*x^4 + x^8),x]","-\frac{x^5}{4 \left(x^4+1\right)}+\frac{5 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{5 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{5 x}{4}+\frac{5 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}-\frac{5 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}","-\frac{x^5}{4 \left(x^4+1\right)}+\frac{5 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{5 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{5 x}{4}+\frac{5 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}-\frac{5 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}",1,"(5*x)/4 - x^5/(4*(1 + x^4)) + (5*ArcTan[1 - Sqrt[2]*x])/(8*Sqrt[2]) - (5*ArcTan[1 + Sqrt[2]*x])/(8*Sqrt[2]) + (5*Log[1 - Sqrt[2]*x + x^2])/(16*Sqrt[2]) - (5*Log[1 + Sqrt[2]*x + x^2])/(16*Sqrt[2])","A",12,9,16,0.5625,1,"{28, 288, 321, 211, 1165, 628, 1162, 617, 204}"
282,1,99,0,0.0509516,"\int \frac{x^6}{1+2 x^4+x^8} \, dx","Int[x^6/(1 + 2*x^4 + x^8),x]","-\frac{x^3}{4 \left(x^4+1\right)}+\frac{3 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{3 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}","-\frac{x^3}{4 \left(x^4+1\right)}+\frac{3 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{3 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}",1,"-x^3/(4*(1 + x^4)) - (3*ArcTan[1 - Sqrt[2]*x])/(8*Sqrt[2]) + (3*ArcTan[1 + Sqrt[2]*x])/(8*Sqrt[2]) + (3*Log[1 - Sqrt[2]*x + x^2])/(16*Sqrt[2]) - (3*Log[1 + Sqrt[2]*x + x^2])/(16*Sqrt[2])","A",11,8,16,0.5000,1,"{28, 288, 297, 1162, 617, 204, 1165, 628}"
283,1,97,0,0.0511466,"\int \frac{x^4}{1+2 x^4+x^8} \, dx","Int[x^4/(1 + 2*x^4 + x^8),x]","-\frac{x}{4 \left(x^4+1\right)}-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}","-\frac{x}{4 \left(x^4+1\right)}-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}",1,"-x/(4*(1 + x^4)) - ArcTan[1 - Sqrt[2]*x]/(8*Sqrt[2]) + ArcTan[1 + Sqrt[2]*x]/(8*Sqrt[2]) - Log[1 - Sqrt[2]*x + x^2]/(16*Sqrt[2]) + Log[1 + Sqrt[2]*x + x^2]/(16*Sqrt[2])","A",11,8,16,0.5000,1,"{28, 288, 211, 1165, 628, 1162, 617, 204}"
284,1,99,0,0.050228,"\int \frac{x^2}{1+2 x^4+x^8} \, dx","Int[x^2/(1 + 2*x^4 + x^8),x]","\frac{x^3}{4 \left(x^4+1\right)}+\frac{\log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}","\frac{x^3}{4 \left(x^4+1\right)}+\frac{\log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{\log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}",1,"x^3/(4*(1 + x^4)) - ArcTan[1 - Sqrt[2]*x]/(8*Sqrt[2]) + ArcTan[1 + Sqrt[2]*x]/(8*Sqrt[2]) + Log[1 - Sqrt[2]*x + x^2]/(16*Sqrt[2]) - Log[1 + Sqrt[2]*x + x^2]/(16*Sqrt[2])","A",11,8,16,0.5000,1,"{28, 290, 297, 1162, 617, 204, 1165, 628}"
285,1,97,0,0.0469694,"\int \frac{1}{1+2 x^4+x^8} \, dx","Int[(1 + 2*x^4 + x^8)^(-1),x]","\frac{x}{4 \left(x^4+1\right)}-\frac{3 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{3 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}","\frac{x}{4 \left(x^4+1\right)}-\frac{3 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{3 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{3 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}",1,"x/(4*(1 + x^4)) - (3*ArcTan[1 - Sqrt[2]*x])/(8*Sqrt[2]) + (3*ArcTan[1 + Sqrt[2]*x])/(8*Sqrt[2]) - (3*Log[1 - Sqrt[2]*x + x^2])/(16*Sqrt[2]) + (3*Log[1 + Sqrt[2]*x + x^2])/(16*Sqrt[2])","A",11,8,12,0.6667,1,"{28, 199, 211, 1165, 628, 1162, 617, 204}"
286,1,106,0,0.0515349,"\int \frac{1}{x^2 \left(1+2 x^4+x^8\right)} \, dx","Int[1/(x^2*(1 + 2*x^4 + x^8)),x]","\frac{1}{4 x \left(x^4+1\right)}-\frac{5 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{5 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{5}{4 x}+\frac{5 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}-\frac{5 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}","\frac{1}{4 x \left(x^4+1\right)}-\frac{5 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{5 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{5}{4 x}+\frac{5 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}-\frac{5 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}",1,"-5/(4*x) + 1/(4*x*(1 + x^4)) + (5*ArcTan[1 - Sqrt[2]*x])/(8*Sqrt[2]) - (5*ArcTan[1 + Sqrt[2]*x])/(8*Sqrt[2]) - (5*Log[1 - Sqrt[2]*x + x^2])/(16*Sqrt[2]) + (5*Log[1 + Sqrt[2]*x + x^2])/(16*Sqrt[2])","A",12,9,16,0.5625,1,"{28, 290, 325, 297, 1162, 617, 204, 1165, 628}"
287,1,106,0,0.0521337,"\int \frac{1}{x^4 \left(1+2 x^4+x^8\right)} \, dx","Int[1/(x^4*(1 + 2*x^4 + x^8)),x]","\frac{1}{4 x^3 \left(x^4+1\right)}-\frac{7}{12 x^3}+\frac{7 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{7 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{7 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}-\frac{7 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}","\frac{1}{4 x^3 \left(x^4+1\right)}-\frac{7}{12 x^3}+\frac{7 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{7 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{7 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}-\frac{7 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}",1,"-7/(12*x^3) + 1/(4*x^3*(1 + x^4)) + (7*ArcTan[1 - Sqrt[2]*x])/(8*Sqrt[2]) - (7*ArcTan[1 + Sqrt[2]*x])/(8*Sqrt[2]) + (7*Log[1 - Sqrt[2]*x + x^2])/(16*Sqrt[2]) - (7*Log[1 + Sqrt[2]*x + x^2])/(16*Sqrt[2])","A",12,9,16,0.5625,1,"{28, 290, 325, 211, 1165, 628, 1162, 617, 204}"
288,1,113,0,0.0543694,"\int \frac{1}{x^6 \left(1+2 x^4+x^8\right)} \, dx","Int[1/(x^6*(1 + 2*x^4 + x^8)),x]","\frac{1}{4 x^5 \left(x^4+1\right)}-\frac{9}{20 x^5}+\frac{9 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{9 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{9}{4 x}-\frac{9 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{9 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}","\frac{1}{4 x^5 \left(x^4+1\right)}-\frac{9}{20 x^5}+\frac{9 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{9 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{9}{4 x}-\frac{9 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{9 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}",1,"-9/(20*x^5) + 9/(4*x) + 1/(4*x^5*(1 + x^4)) - (9*ArcTan[1 - Sqrt[2]*x])/(8*Sqrt[2]) + (9*ArcTan[1 + Sqrt[2]*x])/(8*Sqrt[2]) + (9*Log[1 - Sqrt[2]*x + x^2])/(16*Sqrt[2]) - (9*Log[1 + Sqrt[2]*x + x^2])/(16*Sqrt[2])","A",13,9,16,0.5625,1,"{28, 290, 325, 297, 1162, 617, 204, 1165, 628}"
289,1,113,0,0.0548459,"\int \frac{1}{x^8 \left(1+2 x^4+x^8\right)} \, dx","Int[1/(x^8*(1 + 2*x^4 + x^8)),x]","\frac{1}{4 x^7 \left(x^4+1\right)}+\frac{11}{12 x^3}-\frac{11}{28 x^7}-\frac{11 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{11 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{11 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{11 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}","\frac{1}{4 x^7 \left(x^4+1\right)}+\frac{11}{12 x^3}-\frac{11}{28 x^7}-\frac{11 \log \left(x^2-\sqrt{2} x+1\right)}{16 \sqrt{2}}+\frac{11 \log \left(x^2+\sqrt{2} x+1\right)}{16 \sqrt{2}}-\frac{11 \tan ^{-1}\left(1-\sqrt{2} x\right)}{8 \sqrt{2}}+\frac{11 \tan ^{-1}\left(\sqrt{2} x+1\right)}{8 \sqrt{2}}",1,"-11/(28*x^7) + 11/(12*x^3) + 1/(4*x^7*(1 + x^4)) - (11*ArcTan[1 - Sqrt[2]*x])/(8*Sqrt[2]) + (11*ArcTan[1 + Sqrt[2]*x])/(8*Sqrt[2]) - (11*Log[1 - Sqrt[2]*x + x^2])/(16*Sqrt[2]) + (11*Log[1 + Sqrt[2]*x + x^2])/(16*Sqrt[2])","A",13,9,16,0.5625,1,"{28, 290, 325, 211, 1165, 628, 1162, 617, 204}"
290,1,30,0,0.0056888,"\int \frac{x^m}{1-2 x^4+x^8} \, dx","Int[x^m/(1 - 2*x^4 + x^8),x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{4};\frac{m+5}{4};x^4\right)}{m+1}","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{4};\frac{m+5}{4};x^4\right)}{m+1}",1,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/4, (5 + m)/4, x^4])/(1 + m)","A",2,2,16,0.1250,1,"{28, 364}"
291,1,32,0,0.0130546,"\int \frac{x^9}{1-2 x^4+x^8} \, dx","Int[x^9/(1 - 2*x^4 + x^8),x]","\frac{x^6}{4 \left(1-x^4\right)}+\frac{3 x^2}{4}-\frac{3}{4} \tanh ^{-1}\left(x^2\right)","\frac{x^6}{4 \left(1-x^4\right)}+\frac{3 x^2}{4}-\frac{3}{4} \tanh ^{-1}\left(x^2\right)",1,"(3*x^2)/4 + x^6/(4*(1 - x^4)) - (3*ArcTanh[x^2])/4","A",5,5,16,0.3125,1,"{28, 275, 288, 321, 207}"
292,1,26,0,0.0128445,"\int \frac{x^7}{1-2 x^4+x^8} \, dx","Int[x^7/(1 - 2*x^4 + x^8),x]","\frac{1}{4 \left(1-x^4\right)}+\frac{1}{4} \log \left(1-x^4\right)","\frac{1}{4 \left(1-x^4\right)}+\frac{1}{4} \log \left(1-x^4\right)",1,"1/(4*(1 - x^4)) + Log[1 - x^4]/4","A",4,3,16,0.1875,1,"{28, 266, 43}"
293,1,25,0,0.0101594,"\int \frac{x^5}{1-2 x^4+x^8} \, dx","Int[x^5/(1 - 2*x^4 + x^8),x]","\frac{x^2}{4 \left(1-x^4\right)}-\frac{1}{4} \tanh ^{-1}\left(x^2\right)","\frac{x^2}{4 \left(1-x^4\right)}-\frac{1}{4} \tanh ^{-1}\left(x^2\right)",1,"x^2/(4*(1 - x^4)) - ArcTanh[x^2]/4","A",4,4,16,0.2500,1,"{28, 275, 288, 207}"
294,1,13,0,0.0025553,"\int \frac{x^3}{1-2 x^4+x^8} \, dx","Int[x^3/(1 - 2*x^4 + x^8),x]","\frac{1}{4 \left(1-x^4\right)}","\frac{1}{4 \left(1-x^4\right)}",1,"1/(4*(1 - x^4))","A",2,2,16,0.1250,1,"{28, 261}"
295,1,25,0,0.0081537,"\int \frac{x}{1-2 x^4+x^8} \, dx","Int[x/(1 - 2*x^4 + x^8),x]","\frac{x^2}{4 \left(1-x^4\right)}+\frac{1}{4} \tanh ^{-1}\left(x^2\right)","\frac{x^2}{4 \left(1-x^4\right)}+\frac{1}{4} \tanh ^{-1}\left(x^2\right)",1,"x^2/(4*(1 - x^4)) + ArcTanh[x^2]/4","A",4,4,14,0.2857,1,"{28, 275, 199, 207}"
296,1,28,0,0.0147175,"\int \frac{1}{x \left(1-2 x^4+x^8\right)} \, dx","Int[1/(x*(1 - 2*x^4 + x^8)),x]","\frac{1}{4 \left(1-x^4\right)}-\frac{1}{4} \log \left(1-x^4\right)+\log (x)","\frac{1}{4 \left(1-x^4\right)}-\frac{1}{4} \log \left(1-x^4\right)+\log (x)",1,"1/(4*(1 - x^4)) + Log[x] - Log[1 - x^4]/4","A",4,3,16,0.1875,1,"{28, 266, 44}"
297,1,32,0,0.0126115,"\int \frac{1}{x^3 \left(1-2 x^4+x^8\right)} \, dx","Int[1/(x^3*(1 - 2*x^4 + x^8)),x]","\frac{1}{4 x^2 \left(1-x^4\right)}-\frac{3}{4 x^2}+\frac{3}{4} \tanh ^{-1}\left(x^2\right)","\frac{1}{4 x^2 \left(1-x^4\right)}-\frac{3}{4 x^2}+\frac{3}{4} \tanh ^{-1}\left(x^2\right)",1,"-3/(4*x^2) + 1/(4*x^2*(1 - x^4)) + (3*ArcTanh[x^2])/4","A",5,5,16,0.3125,1,"{28, 275, 290, 325, 207}"
298,1,37,0,0.0185109,"\int \frac{1}{x^5 \left(1-2 x^4+x^8\right)} \, dx","Int[1/(x^5*(1 - 2*x^4 + x^8)),x]","\frac{1}{4 \left(1-x^4\right)}-\frac{1}{4 x^4}-\frac{1}{2} \log \left(1-x^4\right)+2 \log (x)","\frac{1}{4 \left(1-x^4\right)}-\frac{1}{4 x^4}-\frac{1}{2} \log \left(1-x^4\right)+2 \log (x)",1,"-1/(4*x^4) + 1/(4*(1 - x^4)) + 2*Log[x] - Log[1 - x^4]/2","A",4,3,16,0.1875,1,"{28, 266, 44}"
299,1,39,0,0.0171345,"\int \frac{1}{x^7 \left(1-2 x^4+x^8\right)} \, dx","Int[1/(x^7*(1 - 2*x^4 + x^8)),x]","\frac{1}{4 x^6 \left(1-x^4\right)}-\frac{5}{4 x^2}-\frac{5}{12 x^6}+\frac{5}{4} \tanh ^{-1}\left(x^2\right)","\frac{1}{4 x^6 \left(1-x^4\right)}-\frac{5}{4 x^2}-\frac{5}{12 x^6}+\frac{5}{4} \tanh ^{-1}\left(x^2\right)",1,"-5/(12*x^6) - 5/(4*x^2) + 1/(4*x^6*(1 - x^4)) + (5*ArcTanh[x^2])/4","A",6,5,16,0.3125,1,"{28, 275, 290, 325, 207}"
300,1,34,0,0.0090223,"\int \frac{x^8}{1-2 x^4+x^8} \, dx","Int[x^8/(1 - 2*x^4 + x^8),x]","\frac{x^5}{4 \left(1-x^4\right)}+\frac{5 x}{4}-\frac{5}{8} \tan ^{-1}(x)-\frac{5}{8} \tanh ^{-1}(x)","\frac{x^5}{4 \left(1-x^4\right)}+\frac{5 x}{4}-\frac{5}{8} \tan ^{-1}(x)-\frac{5}{8} \tanh ^{-1}(x)",1,"(5*x)/4 + x^5/(4*(1 - x^4)) - (5*ArcTan[x])/8 - (5*ArcTanh[x])/8","A",6,6,16,0.3750,1,"{28, 288, 321, 212, 206, 203}"
301,1,29,0,0.0077958,"\int \frac{x^6}{1-2 x^4+x^8} \, dx","Int[x^6/(1 - 2*x^4 + x^8),x]","\frac{x^3}{4 \left(1-x^4\right)}+\frac{3}{8} \tan ^{-1}(x)-\frac{3}{8} \tanh ^{-1}(x)","\frac{x^3}{4 \left(1-x^4\right)}+\frac{3}{8} \tan ^{-1}(x)-\frac{3}{8} \tanh ^{-1}(x)",1,"x^3/(4*(1 - x^4)) + (3*ArcTan[x])/8 - (3*ArcTanh[x])/8","A",5,5,16,0.3125,1,"{28, 288, 298, 203, 206}"
302,1,27,0,0.0073036,"\int \frac{x^4}{1-2 x^4+x^8} \, dx","Int[x^4/(1 - 2*x^4 + x^8),x]","\frac{x}{4 \left(1-x^4\right)}-\frac{1}{8} \tan ^{-1}(x)-\frac{1}{8} \tanh ^{-1}(x)","\frac{x}{4 \left(1-x^4\right)}-\frac{1}{8} \tan ^{-1}(x)-\frac{1}{8} \tanh ^{-1}(x)",1,"x/(4*(1 - x^4)) - ArcTan[x]/8 - ArcTanh[x]/8","A",5,5,16,0.3125,1,"{28, 288, 212, 206, 203}"
303,1,29,0,0.0083581,"\int \frac{x^2}{1-2 x^4+x^8} \, dx","Int[x^2/(1 - 2*x^4 + x^8),x]","\frac{x^3}{4 \left(1-x^4\right)}-\frac{1}{8} \tan ^{-1}(x)+\frac{1}{8} \tanh ^{-1}(x)","\frac{x^3}{4 \left(1-x^4\right)}-\frac{1}{8} \tan ^{-1}(x)+\frac{1}{8} \tanh ^{-1}(x)",1,"x^3/(4*(1 - x^4)) - ArcTan[x]/8 + ArcTanh[x]/8","A",5,5,16,0.3125,1,"{28, 290, 298, 203, 206}"
304,1,27,0,0.0053873,"\int \frac{1}{1-2 x^4+x^8} \, dx","Int[(1 - 2*x^4 + x^8)^(-1),x]","\frac{x}{4 \left(1-x^4\right)}+\frac{3}{8} \tan ^{-1}(x)+\frac{3}{8} \tanh ^{-1}(x)","\frac{x}{4 \left(1-x^4\right)}+\frac{3}{8} \tan ^{-1}(x)+\frac{3}{8} \tanh ^{-1}(x)",1,"x/(4*(1 - x^4)) + (3*ArcTan[x])/8 + (3*ArcTanh[x])/8","A",5,5,12,0.4167,1,"{28, 199, 212, 206, 203}"
305,1,36,0,0.0101916,"\int \frac{1}{x^2 \left(1-2 x^4+x^8\right)} \, dx","Int[1/(x^2*(1 - 2*x^4 + x^8)),x]","\frac{1}{4 x \left(1-x^4\right)}-\frac{5}{4 x}-\frac{5}{8} \tan ^{-1}(x)+\frac{5}{8} \tanh ^{-1}(x)","\frac{1}{4 x \left(1-x^4\right)}-\frac{5}{4 x}-\frac{5}{8} \tan ^{-1}(x)+\frac{5}{8} \tanh ^{-1}(x)",1,"-5/(4*x) + 1/(4*x*(1 - x^4)) - (5*ArcTan[x])/8 + (5*ArcTanh[x])/8","A",6,6,16,0.3750,1,"{28, 290, 325, 298, 203, 206}"
306,1,36,0,0.0088647,"\int \frac{1}{x^4 \left(1-2 x^4+x^8\right)} \, dx","Int[1/(x^4*(1 - 2*x^4 + x^8)),x]","\frac{1}{4 x^3 \left(1-x^4\right)}-\frac{7}{12 x^3}+\frac{7}{8} \tan ^{-1}(x)+\frac{7}{8} \tanh ^{-1}(x)","\frac{1}{4 x^3 \left(1-x^4\right)}-\frac{7}{12 x^3}+\frac{7}{8} \tan ^{-1}(x)+\frac{7}{8} \tanh ^{-1}(x)",1,"-7/(12*x^3) + 1/(4*x^3*(1 - x^4)) + (7*ArcTan[x])/8 + (7*ArcTanh[x])/8","A",6,6,16,0.3750,1,"{28, 290, 325, 212, 206, 203}"
307,1,43,0,0.0122302,"\int \frac{1}{x^6 \left(1-2 x^4+x^8\right)} \, dx","Int[1/(x^6*(1 - 2*x^4 + x^8)),x]","\frac{1}{4 x^5 \left(1-x^4\right)}-\frac{9}{20 x^5}-\frac{9}{4 x}-\frac{9}{8} \tan ^{-1}(x)+\frac{9}{8} \tanh ^{-1}(x)","\frac{1}{4 x^5 \left(1-x^4\right)}-\frac{9}{20 x^5}-\frac{9}{4 x}-\frac{9}{8} \tan ^{-1}(x)+\frac{9}{8} \tanh ^{-1}(x)",1,"-9/(20*x^5) - 9/(4*x) + 1/(4*x^5*(1 - x^4)) - (9*ArcTan[x])/8 + (9*ArcTanh[x])/8","A",7,6,16,0.3750,1,"{28, 290, 325, 298, 203, 206}"
308,1,43,0,0.0120157,"\int \frac{1}{x^8 \left(1-2 x^4+x^8\right)} \, dx","Int[1/(x^8*(1 - 2*x^4 + x^8)),x]","\frac{1}{4 x^7 \left(1-x^4\right)}-\frac{11}{12 x^3}-\frac{11}{28 x^7}+\frac{11}{8} \tan ^{-1}(x)+\frac{11}{8} \tanh ^{-1}(x)","\frac{1}{4 x^7 \left(1-x^4\right)}-\frac{11}{12 x^3}-\frac{11}{28 x^7}+\frac{11}{8} \tan ^{-1}(x)+\frac{11}{8} \tanh ^{-1}(x)",1,"-11/(28*x^7) - 11/(12*x^3) + 1/(4*x^7*(1 - x^4)) + (11*ArcTan[x])/8 + (11*ArcTanh[x])/8","A",7,6,16,0.3750,1,"{28, 290, 325, 212, 206, 203}"
309,1,163,0,0.1409947,"\int \frac{x^m}{a+b x^4+c x^8} \, dx","Int[x^m/(a + b*x^4 + c*x^8),x]","\frac{2 c x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 c x^4}{b-\sqrt{b^2-4 a c}}\right)}{(m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 c x^4}{b+\sqrt{b^2-4 a c}}\right)}{(m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}","\frac{2 c x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 c x^4}{b-\sqrt{b^2-4 a c}}\right)}{(m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 c x^4}{b+\sqrt{b^2-4 a c}}\right)}{(m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}",1,"(2*c*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, (-2*c*x^4)/(b - Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*(1 + m)) - (2*c*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, (-2*c*x^4)/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*(1 + m))","A",3,2,18,0.1111,1,"{1375, 364}"
310,1,81,0,0.0837916,"\int \frac{x^{11}}{a+b x^4+c x^8} \, dx","Int[x^11/(a + b*x^4 + c*x^8),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x^4+c x^8\right)}{8 c^2}+\frac{x^4}{4 c}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x^4+c x^8\right)}{8 c^2}+\frac{x^4}{4 c}",1,"x^4/(4*c) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x^4)/Sqrt[b^2 - 4*a*c]])/(4*c^2*Sqrt[b^2 - 4*a*c]) - (b*Log[a + b*x^4 + c*x^8])/(8*c^2)","A",6,6,18,0.3333,1,"{1357, 703, 634, 618, 206, 628}"
311,1,192,0,0.3389142,"\int \frac{x^9}{a+b x^4+c x^8} \, dx","Int[x^9/(a + b*x^4 + c*x^8),x]","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^2}{2 c}","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^2}{2 c}",1,"x^2/(2*c) - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,18,0.2222,1,"{1359, 1122, 1166, 205}"
312,1,63,0,0.0578285,"\int \frac{x^7}{a+b x^4+c x^8} \, dx","Int[x^7/(a + b*x^4 + c*x^8),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^4+c x^8\right)}{8 c}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^4+c x^8\right)}{8 c}",1,"(b*ArcTanh[(b + 2*c*x^4)/Sqrt[b^2 - 4*a*c]])/(4*c*Sqrt[b^2 - 4*a*c]) + Log[a + b*x^4 + c*x^8]/(8*c)","A",5,5,18,0.2778,1,"{1357, 634, 618, 206, 628}"
313,1,159,0,0.1262109,"\int \frac{x^5}{a+b x^4+c x^8} \, dx","Int[x^5/(a + b*x^4 + c*x^8),x]","\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}","\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}",1,"-(Sqrt[b - Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c]) + (Sqrt[b + Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])","A",4,3,18,0.1667,1,"{1359, 1130, 205}"
314,1,38,0,0.034339,"\int \frac{x^3}{a+b x^4+c x^8} \, dx","Int[x^3/(a + b*x^4 + c*x^8),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{2 \sqrt{b^2-4 a c}}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{2 \sqrt{b^2-4 a c}}",1,"-ArcTanh[(b + 2*c*x^4)/Sqrt[b^2 - 4*a*c]]/(2*Sqrt[b^2 - 4*a*c])","A",3,3,18,0.1667,1,"{1352, 618, 206}"
315,1,154,0,0.0940859,"\int \frac{x}{a+b x^4+c x^8} \, dx","Int[x/(a + b*x^4 + c*x^8),x]","\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(Sqrt[c]*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,16,0.1875,1,"{1359, 1093, 205}"
316,1,69,0,0.0683157,"\int \frac{1}{x \left(a+b x^4+c x^8\right)} \, dx","Int[1/(x*(a + b*x^4 + c*x^8)),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x^4+c x^8\right)}{8 a}+\frac{\log (x)}{a}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x^4+c x^8\right)}{8 a}+\frac{\log (x)}{a}",1,"(b*ArcTanh[(b + 2*c*x^4)/Sqrt[b^2 - 4*a*c]])/(4*a*Sqrt[b^2 - 4*a*c]) + Log[x]/a - Log[a + b*x^4 + c*x^8]/(8*a)","A",7,7,18,0.3889,1,"{1357, 705, 29, 634, 618, 206, 628}"
317,1,184,0,0.2243782,"\int \frac{1}{x^3 \left(a+b x^4+c x^8\right)} \, dx","Int[1/(x^3*(a + b*x^4 + c*x^8)),x]","-\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{2 a x^2}","-\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^2}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) - (Sqrt[c]*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x^2)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,18,0.2222,1,"{1359, 1123, 1166, 205}"
318,1,89,0,0.1236293,"\int \frac{1}{x^5 \left(a+b x^4+c x^8\right)} \, dx","Int[1/(x^5*(a + b*x^4 + c*x^8)),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x^4+c x^8\right)}{8 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{4 a x^4}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^4}{\sqrt{b^2-4 a c}}\right)}{4 a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x^4+c x^8\right)}{8 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{4 a x^4}",1,"-1/(4*a*x^4) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x^4)/Sqrt[b^2 - 4*a*c]])/(4*a^2*Sqrt[b^2 - 4*a*c]) - (b*Log[x])/a^2 + (b*Log[a + b*x^4 + c*x^8])/(8*a^2)","A",8,7,18,0.3889,1,"{1357, 709, 800, 634, 618, 206, 628}"
319,1,381,0,0.6472296,"\int \frac{x^{10}}{a+b x^4+c x^8} \, dx","Int[x^10/(a + b*x^4 + c*x^8),x]","-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{7/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{7/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{7/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{7/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{x^3}{3 c}","-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{7/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{7/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{7/4} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{7/4} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{x^3}{3 c}",1,"x^3/(3*c) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(7/4)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(7/4)*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(7/4)*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(7/4)*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",8,5,18,0.2778,1,"{1367, 1510, 298, 205, 208}"
320,1,376,0,0.5738542,"\int \frac{x^8}{a+b x^4+c x^8} \, dx","Int[x^8/(a + b*x^4 + c*x^8),x]","\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{x}{c}","\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{x}{c}",1,"x/c + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",8,5,18,0.2778,1,"{1367, 1422, 212, 208, 205}"
321,1,325,0,0.3068957,"\int \frac{x^6}{a+b x^4+c x^8} \, dx","Int[x^6/(a + b*x^4 + c*x^8),x]","-\frac{\left(-\sqrt{b^2-4 a c}-b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}+\frac{\left(\sqrt{b^2-4 a c}-b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}+\frac{\left(-\sqrt{b^2-4 a c}-b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}-\frac{\left(\sqrt{b^2-4 a c}-b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}","-\frac{\left(-\sqrt{b^2-4 a c}-b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}+\frac{\left(\sqrt{b^2-4 a c}-b\right)^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}+\frac{\left(-\sqrt{b^2-4 a c}-b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}-\frac{\left(\sqrt{b^2-4 a c}-b\right)^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} c^{3/4} \sqrt{b^2-4 a c}}",1,"-((-b - Sqrt[b^2 - 4*a*c])^(3/4)*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(3/4)*Sqrt[b^2 - 4*a*c]) + ((-b + Sqrt[b^2 - 4*a*c])^(3/4)*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(3/4)*Sqrt[b^2 - 4*a*c]) + ((-b - Sqrt[b^2 - 4*a*c])^(3/4)*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(3/4)*Sqrt[b^2 - 4*a*c]) - ((-b + Sqrt[b^2 - 4*a*c])^(3/4)*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*c^(3/4)*Sqrt[b^2 - 4*a*c])","A",7,4,18,0.2222,1,"{1374, 298, 205, 208}"
322,1,325,0,0.2958404,"\int \frac{x^4}{a+b x^4+c x^8} \, dx","Int[x^4/(a + b*x^4 + c*x^8),x]","\frac{\sqrt[4]{-\sqrt{b^2-4 a c}-b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[4]{\sqrt{b^2-4 a c}-b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}+\frac{\sqrt[4]{-\sqrt{b^2-4 a c}-b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[4]{\sqrt{b^2-4 a c}-b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}","\frac{\sqrt[4]{-\sqrt{b^2-4 a c}-b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[4]{\sqrt{b^2-4 a c}-b} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}+\frac{\sqrt[4]{-\sqrt{b^2-4 a c}-b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}-\frac{\sqrt[4]{\sqrt{b^2-4 a c}-b} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} \sqrt[4]{c} \sqrt{b^2-4 a c}}",1,"((-b - Sqrt[b^2 - 4*a*c])^(1/4)*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(1/4)*Sqrt[b^2 - 4*a*c]) - ((-b + Sqrt[b^2 - 4*a*c])^(1/4)*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(1/4)*Sqrt[b^2 - 4*a*c]) + ((-b - Sqrt[b^2 - 4*a*c])^(1/4)*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(1/4)*Sqrt[b^2 - 4*a*c]) - ((-b + Sqrt[b^2 - 4*a*c])^(1/4)*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(1/4)*Sqrt[b^2 - 4*a*c])","A",7,4,18,0.2222,1,"{1374, 212, 208, 205}"
323,1,315,0,0.2898912,"\int \frac{x^2}{a+b x^4+c x^8} \, dx","Int[x^2/(a + b*x^4 + c*x^8),x]","-\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} \sqrt{b^2-4 a c} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} \sqrt{b^2-4 a c} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} \sqrt{b^2-4 a c} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} \sqrt{b^2-4 a c} \sqrt[4]{\sqrt{b^2-4 a c}-b}}","-\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} \sqrt{b^2-4 a c} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} \sqrt{b^2-4 a c} \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} \sqrt{b^2-4 a c} \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2^{3/4} \sqrt{b^2-4 a c} \sqrt[4]{\sqrt{b^2-4 a c}-b}}",1,"-((c^(1/4)*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(1/4))) + (c^(1/4)*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(3/4)*Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",7,4,18,0.2222,1,"{1375, 298, 205, 208}"
324,1,315,0,0.3040074,"\int \frac{1}{a+b x^4+c x^8} \, dx","Int[(a + b*x^4 + c*x^8)^(-1),x]","\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}","\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}",1,"(c^(3/4)*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (c^(3/4)*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) - (c^(3/4)*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",7,4,14,0.2857,1,"{1347, 212, 208, 205}"
325,1,363,0,0.4116789,"\int \frac{1}{x^2 \left(a+b x^4+c x^8\right)} \, dx","Int[1/(x^2*(a + b*x^4 + c*x^8)),x]","-\frac{\sqrt[4]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{1}{a x}","-\frac{\sqrt[4]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}-\frac{\sqrt[4]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{-\sqrt{b^2-4 a c}-b}}+\frac{\sqrt[4]{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2\ 2^{3/4} a \sqrt[4]{\sqrt{b^2-4 a c}-b}}-\frac{1}{a x}",1,"-(1/(a*x)) - (c^(1/4)*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) - (c^(1/4)*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(1/4)) + (c^(1/4)*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(3/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(1/4))","A",8,5,18,0.2778,1,"{1368, 1510, 298, 205, 208}"
326,1,365,0,0.3989784,"\int \frac{1}{x^4 \left(a+b x^4+c x^8\right)} \, dx","Int[1/(x^4*(a + b*x^4 + c*x^8)),x]","\frac{c^{3/4} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{1}{3 a x^3}","\frac{c^{3/4} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{c^{3/4} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} a \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) + (c^(3/4)*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*a*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + (c^(3/4)*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*a*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",8,5,18,0.2778,1,"{1368, 1422, 212, 208, 205}"
327,1,127,0,0.0779896,"\int \frac{x^m}{1+x^4+x^8} \, dx","Int[x^m/(1 + x^4 + x^8),x]","\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 x^4}{1-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+i\right) (m+1)}-\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 x^4}{1+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+i\right) (m+1)}","\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 x^4}{1-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+i\right) (m+1)}-\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 x^4}{1+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+i\right) (m+1)}",1,"(2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, (-2*x^4)/(1 - I*Sqrt[3])])/(Sqrt[3]*(I + Sqrt[3])*(1 + m)) - (2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, (-2*x^4)/(1 + I*Sqrt[3])])/(Sqrt[3]*(I - Sqrt[3])*(1 + m))","A",3,2,14,0.1429,1,"{1375, 364}"
328,1,44,0,0.0367014,"\int \frac{x^{11}}{1+x^4+x^8} \, dx","Int[x^11/(1 + x^4 + x^8),x]","\frac{x^4}{4}-\frac{1}{8} \log \left(x^8+x^4+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^4+1}{\sqrt{3}}\right)}{4 \sqrt{3}}","\frac{x^4}{4}-\frac{1}{8} \log \left(x^8+x^4+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^4+1}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"x^4/4 - ArcTan[(1 + 2*x^4)/Sqrt[3]]/(4*Sqrt[3]) - Log[1 + x^4 + x^8]/8","A",6,6,14,0.4286,1,"{1357, 703, 634, 618, 204, 628}"
329,1,54,0,0.0577644,"\int \frac{x^9}{1+x^4+x^8} \, dx","Int[x^9/(1 + x^4 + x^8),x]","\frac{x^2}{2}+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","\frac{x^2}{2}+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"x^2/2 + ArcTan[(1 - 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) - ArcTan[(1 + 2*x^2)/Sqrt[3]]/(2*Sqrt[3])","A",7,5,14,0.3571,1,"{1359, 1122, 1161, 618, 204}"
330,1,37,0,0.0310579,"\int \frac{x^7}{1+x^4+x^8} \, dx","Int[x^7/(1 + x^4 + x^8),x]","\frac{1}{8} \log \left(x^8+x^4+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^4+1}{\sqrt{3}}\right)}{4 \sqrt{3}}","\frac{1}{8} \log \left(x^8+x^4+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^4+1}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"-ArcTan[(1 + 2*x^4)/Sqrt[3]]/(4*Sqrt[3]) + Log[1 + x^4 + x^8]/8","A",5,5,14,0.3571,1,"{1357, 634, 618, 204, 628}"
331,1,75,0,0.0765716,"\int \frac{x^5}{1+x^4+x^8} \, dx","Int[x^5/(1 + x^4 + x^8),x]","\frac{1}{8} \log \left(x^4-x^2+1\right)-\frac{1}{8} \log \left(x^4+x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{4 \sqrt{3}}","\frac{1}{8} \log \left(x^4-x^2+1\right)-\frac{1}{8} \log \left(x^4+x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"-ArcTan[(1 - 2*x^2)/Sqrt[3]]/(4*Sqrt[3]) + ArcTan[(1 + 2*x^2)/Sqrt[3]]/(4*Sqrt[3]) + Log[1 - x^2 + x^4]/8 - Log[1 + x^2 + x^4]/8","A",10,7,14,0.5000,1,"{1359, 1127, 1161, 618, 204, 1164, 628}"
332,1,23,0,0.0212884,"\int \frac{x^3}{1+x^4+x^8} \, dx","Int[x^3/(1 + x^4 + x^8),x]","\frac{\tan ^{-1}\left(\frac{2 x^4+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","\frac{\tan ^{-1}\left(\frac{2 x^4+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"ArcTan[(1 + 2*x^4)/Sqrt[3]]/(2*Sqrt[3])","A",3,3,14,0.2143,1,"{1352, 618, 204}"
333,1,75,0,0.0636766,"\int \frac{x}{1+x^4+x^8} \, dx","Int[x/(1 + x^4 + x^8),x]","-\frac{1}{8} \log \left(x^4-x^2+1\right)+\frac{1}{8} \log \left(x^4+x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{4 \sqrt{3}}","-\frac{1}{8} \log \left(x^4-x^2+1\right)+\frac{1}{8} \log \left(x^4+x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"-ArcTan[(1 - 2*x^2)/Sqrt[3]]/(4*Sqrt[3]) + ArcTan[(1 + 2*x^2)/Sqrt[3]]/(4*Sqrt[3]) - Log[1 - x^2 + x^4]/8 + Log[1 + x^2 + x^4]/8","A",10,6,12,0.5000,1,"{1359, 1094, 634, 618, 204, 628}"
334,1,39,0,0.0347782,"\int \frac{1}{x \left(1+x^4+x^8\right)} \, dx","Int[1/(x*(1 + x^4 + x^8)),x]","-\frac{1}{8} \log \left(x^8+x^4+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^4+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\log (x)","-\frac{1}{8} \log \left(x^8+x^4+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^4+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\log (x)",1,"-ArcTan[(1 + 2*x^4)/Sqrt[3]]/(4*Sqrt[3]) + Log[x] - Log[1 + x^4 + x^8]/8","A",7,7,14,0.5000,1,"{1357, 705, 29, 634, 618, 204, 628}"
335,1,54,0,0.0515594,"\int \frac{1}{x^3 \left(1+x^4+x^8\right)} \, dx","Int[1/(x^3*(1 + x^4 + x^8)),x]","-\frac{1}{2 x^2}+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{2 x^2}+\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-1/(2*x^2) + ArcTan[(1 - 2*x^2)/Sqrt[3]]/(2*Sqrt[3]) - ArcTan[(1 + 2*x^2)/Sqrt[3]]/(2*Sqrt[3])","A",7,5,14,0.3571,1,"{1359, 1123, 1161, 618, 204}"
336,1,48,0,0.0512834,"\int \frac{1}{x^5 \left(1+x^4+x^8\right)} \, dx","Int[1/(x^5*(1 + x^4 + x^8)),x]","-\frac{1}{4 x^4}+\frac{1}{8} \log \left(x^8+x^4+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^4+1}{\sqrt{3}}\right)}{4 \sqrt{3}}-\log (x)","-\frac{1}{4 x^4}+\frac{1}{8} \log \left(x^8+x^4+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^4+1}{\sqrt{3}}\right)}{4 \sqrt{3}}-\log (x)",1,"-1/(4*x^4) - ArcTan[(1 + 2*x^4)/Sqrt[3]]/(4*Sqrt[3]) - Log[x] + Log[1 + x^4 + x^8]/8","A",8,7,14,0.5000,1,"{1357, 709, 800, 634, 618, 204, 628}"
337,1,89,0,0.0962304,"\int \frac{1}{x^7 \left(1+x^4+x^8\right)} \, dx","Int[1/(x^7*(1 + x^4 + x^8)),x]","\frac{1}{2 x^2}-\frac{1}{6 x^6}+\frac{1}{8} \log \left(x^4-x^2+1\right)-\frac{1}{8} \log \left(x^4+x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{4 \sqrt{3}}","\frac{1}{2 x^2}-\frac{1}{6 x^6}+\frac{1}{8} \log \left(x^4-x^2+1\right)-\frac{1}{8} \log \left(x^4+x^2+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"-1/(6*x^6) + 1/(2*x^2) - ArcTan[(1 - 2*x^2)/Sqrt[3]]/(4*Sqrt[3]) + ArcTan[(1 + 2*x^2)/Sqrt[3]]/(4*Sqrt[3]) + Log[1 - x^2 + x^4]/8 - Log[1 + x^2 + x^4]/8","A",13,10,14,0.7143,1,"{1359, 1123, 1281, 12, 1127, 1161, 618, 204, 1164, 628}"
338,1,141,0,0.0973638,"\int \frac{x^8}{1+x^4+x^8} \, dx","Int[x^8/(1 + x^4 + x^8),x]","\frac{1}{8} \log \left(x^2-x+1\right)-\frac{1}{8} \log \left(x^2+x+1\right)+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}+x+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)","\frac{1}{8} \log \left(x^2-x+1\right)-\frac{1}{8} \log \left(x^2+x+1\right)+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}+x+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"x + ArcTan[(1 - 2*x)/Sqrt[3]]/(4*Sqrt[3]) + ArcTan[Sqrt[3] - 2*x]/4 - ArcTan[(1 + 2*x)/Sqrt[3]]/(4*Sqrt[3]) - ArcTan[Sqrt[3] + 2*x]/4 + Log[1 - x + x^2]/8 - Log[1 + x + x^2]/8 + Log[1 - Sqrt[3]*x + x^2]/(8*Sqrt[3]) - Log[1 + Sqrt[3]*x + x^2]/(8*Sqrt[3])","A",20,7,14,0.5000,1,"{1367, 1419, 1094, 634, 618, 204, 628}"
339,1,88,0,0.0578484,"\int \frac{x^6}{1+x^4+x^8} \, dx","Int[x^6/(1 + x^4 + x^8),x]","\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTan[(1 + 2*x)/Sqrt[3]]/(2*Sqrt[3]) + Log[1 - Sqrt[3]*x + x^2]/(4*Sqrt[3]) - Log[1 + Sqrt[3]*x + x^2]/(4*Sqrt[3])","A",9,6,14,0.4286,1,"{1372, 1164, 628, 1161, 618, 204}"
340,1,140,0,0.1065388,"\int \frac{x^4}{1+x^4+x^8} \, dx","Int[x^4/(1 + x^4 + x^8),x]","-\frac{1}{8} \log \left(x^2-x+1\right)+\frac{1}{8} \log \left(x^2+x+1\right)+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)","-\frac{1}{8} \log \left(x^2-x+1\right)+\frac{1}{8} \log \left(x^2+x+1\right)+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"ArcTan[(1 - 2*x)/Sqrt[3]]/(4*Sqrt[3]) - ArcTan[Sqrt[3] - 2*x]/4 - ArcTan[(1 + 2*x)/Sqrt[3]]/(4*Sqrt[3]) + ArcTan[Sqrt[3] + 2*x]/4 - Log[1 - x + x^2]/8 + Log[1 + x + x^2]/8 + Log[1 - Sqrt[3]*x + x^2]/(8*Sqrt[3]) - Log[1 + Sqrt[3]*x + x^2]/(8*Sqrt[3])","A",19,7,14,0.5000,1,"{1373, 1127, 1161, 618, 204, 1164, 628}"
341,1,140,0,0.0831656,"\int \frac{x^2}{1+x^4+x^8} \, dx","Int[x^2/(1 + x^4 + x^8),x]","\frac{1}{8} \log \left(x^2-x+1\right)-\frac{1}{8} \log \left(x^2+x+1\right)-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)","\frac{1}{8} \log \left(x^2-x+1\right)-\frac{1}{8} \log \left(x^2+x+1\right)-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"ArcTan[(1 - 2*x)/Sqrt[3]]/(4*Sqrt[3]) - ArcTan[Sqrt[3] - 2*x]/4 - ArcTan[(1 + 2*x)/Sqrt[3]]/(4*Sqrt[3]) + ArcTan[Sqrt[3] + 2*x]/4 + Log[1 - x + x^2]/8 - Log[1 + x + x^2]/8 - Log[1 - Sqrt[3]*x + x^2]/(8*Sqrt[3]) + Log[1 + Sqrt[3]*x + x^2]/(8*Sqrt[3])","A",19,6,14,0.4286,1,"{1373, 1094, 634, 618, 204, 628}"
342,1,88,0,0.0516773,"\int \frac{1}{1+x^4+x^8} \, dx","Int[(1 + x^4 + x^8)^(-1),x]","-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTan[(1 + 2*x)/Sqrt[3]]/(2*Sqrt[3]) - Log[1 - Sqrt[3]*x + x^2]/(4*Sqrt[3]) + Log[1 + Sqrt[3]*x + x^2]/(4*Sqrt[3])","A",9,6,10,0.6000,1,"{1346, 1164, 628, 1161, 618, 204}"
343,1,145,0,0.1116334,"\int \frac{1}{x^2 \left(1+x^4+x^8\right)} \, dx","Int[1/(x^2*(1 + x^4 + x^8)),x]","-\frac{1}{8} \log \left(x^2-x+1\right)+\frac{1}{8} \log \left(x^2+x+1\right)-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)","-\frac{1}{8} \log \left(x^2-x+1\right)+\frac{1}{8} \log \left(x^2+x+1\right)-\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"-x^(-1) + ArcTan[(1 - 2*x)/Sqrt[3]]/(4*Sqrt[3]) + ArcTan[Sqrt[3] - 2*x]/4 - ArcTan[(1 + 2*x)/Sqrt[3]]/(4*Sqrt[3]) - ArcTan[Sqrt[3] + 2*x]/4 - Log[1 - x + x^2]/8 + Log[1 + x + x^2]/8 - Log[1 - Sqrt[3]*x + x^2]/(8*Sqrt[3]) + Log[1 + Sqrt[3]*x + x^2]/(8*Sqrt[3])","A",20,8,14,0.5714,1,"{1368, 1506, 1127, 1161, 618, 204, 1164, 628}"
344,1,147,0,0.0991428,"\int \frac{1}{x^4 \left(1+x^4+x^8\right)} \, dx","Int[1/(x^4*(1 + x^4 + x^8)),x]","-\frac{1}{3 x^3}+\frac{1}{8} \log \left(x^2-x+1\right)-\frac{1}{8} \log \left(x^2+x+1\right)+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)","-\frac{1}{3 x^3}+\frac{1}{8} \log \left(x^2-x+1\right)-\frac{1}{8} \log \left(x^2+x+1\right)+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"-1/(3*x^3) + ArcTan[(1 - 2*x)/Sqrt[3]]/(4*Sqrt[3]) + ArcTan[Sqrt[3] - 2*x]/4 - ArcTan[(1 + 2*x)/Sqrt[3]]/(4*Sqrt[3]) - ArcTan[Sqrt[3] + 2*x]/4 + Log[1 - x + x^2]/8 - Log[1 + x + x^2]/8 + Log[1 - Sqrt[3]*x + x^2]/(8*Sqrt[3]) - Log[1 + Sqrt[3]*x + x^2]/(8*Sqrt[3])","A",20,7,14,0.5000,1,"{1368, 1419, 1094, 634, 618, 204, 628}"
345,1,98,0,0.0838172,"\int \frac{1}{x^6 \left(1+x^4+x^8\right)} \, dx","Int[1/(x^6*(1 + x^4 + x^8)),x]","-\frac{1}{5 x^5}+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{1}{x}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{1}{5 x^5}+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{4 \sqrt{3}}+\frac{1}{x}-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-1/(5*x^5) + x^(-1) - ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) + ArcTan[(1 + 2*x)/Sqrt[3]]/(2*Sqrt[3]) + Log[1 - Sqrt[3]*x + x^2]/(4*Sqrt[3]) - Log[1 + Sqrt[3]*x + x^2]/(4*Sqrt[3])","A",12,9,14,0.6429,1,"{1368, 1504, 12, 1372, 1164, 628, 1161, 618, 204}"
346,1,154,0,0.1418259,"\int \frac{1}{x^8 \left(1+x^4+x^8\right)} \, dx","Int[1/(x^8*(1 + x^4 + x^8)),x]","\frac{1}{3 x^3}-\frac{1}{7 x^7}-\frac{1}{8} \log \left(x^2-x+1\right)+\frac{1}{8} \log \left(x^2+x+1\right)+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)","\frac{1}{3 x^3}-\frac{1}{7 x^7}-\frac{1}{8} \log \left(x^2-x+1\right)+\frac{1}{8} \log \left(x^2+x+1\right)+\frac{\log \left(x^2-\sqrt{3} x+1\right)}{8 \sqrt{3}}-\frac{\log \left(x^2+\sqrt{3} x+1\right)}{8 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{4 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x\right)-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(2 x+\sqrt{3}\right)",1,"-1/(7*x^7) + 1/(3*x^3) + ArcTan[(1 - 2*x)/Sqrt[3]]/(4*Sqrt[3]) - ArcTan[Sqrt[3] - 2*x]/4 - ArcTan[(1 + 2*x)/Sqrt[3]]/(4*Sqrt[3]) + ArcTan[Sqrt[3] + 2*x]/4 - Log[1 - x + x^2]/8 + Log[1 + x + x^2]/8 + Log[1 - Sqrt[3]*x + x^2]/(8*Sqrt[3]) - Log[1 + Sqrt[3]*x + x^2]/(8*Sqrt[3])","A",22,10,14,0.7143,1,"{1368, 1504, 12, 1373, 1127, 1161, 618, 204, 1164, 628}"
347,1,127,0,0.0486989,"\int \frac{x^m}{1-x^4+x^8} \, dx","Int[x^m/(1 - x^4 + x^8),x]","\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};\frac{2 x^4}{1-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+i\right) (m+1)}-\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};\frac{2 x^4}{1+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+i\right) (m+1)}","\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};\frac{2 x^4}{1-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+i\right) (m+1)}-\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};\frac{2 x^4}{1+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+i\right) (m+1)}",1,"(2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, (2*x^4)/(1 - I*Sqrt[3])])/(Sqrt[3]*(I + Sqrt[3])*(1 + m)) - (2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, (2*x^4)/(1 + I*Sqrt[3])])/(Sqrt[3]*(I - Sqrt[3])*(1 + m))","A",3,2,16,0.1250,1,"{1375, 364}"
348,1,46,0,0.0401795,"\int \frac{x^{11}}{1-x^4+x^8} \, dx","Int[x^11/(1 - x^4 + x^8),x]","\frac{x^4}{4}+\frac{1}{8} \log \left(x^8-x^4+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}","\frac{x^4}{4}+\frac{1}{8} \log \left(x^8-x^4+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"x^4/4 + ArcTan[(1 - 2*x^4)/Sqrt[3]]/(4*Sqrt[3]) + Log[1 - x^4 + x^8]/8","A",6,6,16,0.3750,1,"{1357, 703, 634, 618, 204, 628}"
349,1,57,0,0.0431245,"\int \frac{x^9}{1-x^4+x^8} \, dx","Int[x^9/(1 - x^4 + x^8),x]","\frac{x^2}{2}+\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{4 \sqrt{3}}","\frac{x^2}{2}+\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{4 \sqrt{3}}-\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{4 \sqrt{3}}",1,"x^2/2 + Log[1 - Sqrt[3]*x^2 + x^4]/(4*Sqrt[3]) - Log[1 + Sqrt[3]*x^2 + x^4]/(4*Sqrt[3])","A",5,4,16,0.2500,1,"{1359, 1122, 1164, 628}"
350,1,39,0,0.0329002,"\int \frac{x^7}{1-x^4+x^8} \, dx","Int[x^7/(1 - x^4 + x^8),x]","\frac{1}{8} \log \left(x^8-x^4+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}","\frac{1}{8} \log \left(x^8-x^4+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"-ArcTan[(1 - 2*x^4)/Sqrt[3]]/(4*Sqrt[3]) + Log[1 - x^4 + x^8]/8","A",5,5,16,0.3125,1,"{1357, 634, 618, 204, 628}"
351,1,82,0,0.0710082,"\int \frac{x^5}{1-x^4+x^8} \, dx","Int[x^5/(1 - x^4 + x^8),x]","\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{8 \sqrt{3}}-\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{8 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x^2\right)+\frac{1}{4} \tan ^{-1}\left(2 x^2+\sqrt{3}\right)","\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{8 \sqrt{3}}-\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{8 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x^2\right)+\frac{1}{4} \tan ^{-1}\left(2 x^2+\sqrt{3}\right)",1,"-ArcTan[Sqrt[3] - 2*x^2]/4 + ArcTan[Sqrt[3] + 2*x^2]/4 + Log[1 - Sqrt[3]*x^2 + x^4]/(8*Sqrt[3]) - Log[1 + Sqrt[3]*x^2 + x^4]/(8*Sqrt[3])","A",10,7,16,0.4375,1,"{1359, 1127, 1161, 618, 204, 1164, 628}"
352,1,23,0,0.0223594,"\int \frac{x^3}{1-x^4+x^8} \, dx","Int[x^3/(1 - x^4 + x^8),x]","-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{2 \sqrt{3}}","-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"-ArcTan[(1 - 2*x^4)/Sqrt[3]]/(2*Sqrt[3])","A",3,3,16,0.1875,1,"{1352, 618, 204}"
353,1,82,0,0.0571404,"\int \frac{x}{1-x^4+x^8} \, dx","Int[x/(1 - x^4 + x^8),x]","-\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{8 \sqrt{3}}+\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{8 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x^2\right)+\frac{1}{4} \tan ^{-1}\left(2 x^2+\sqrt{3}\right)","-\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{8 \sqrt{3}}+\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{8 \sqrt{3}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x^2\right)+\frac{1}{4} \tan ^{-1}\left(2 x^2+\sqrt{3}\right)",1,"-ArcTan[Sqrt[3] - 2*x^2]/4 + ArcTan[Sqrt[3] + 2*x^2]/4 - Log[1 - Sqrt[3]*x^2 + x^4]/(8*Sqrt[3]) + Log[1 + Sqrt[3]*x^2 + x^4]/(8*Sqrt[3])","A",10,6,14,0.4286,1,"{1359, 1094, 634, 618, 204, 628}"
354,1,41,0,0.0378776,"\int \frac{1}{x \left(1-x^4+x^8\right)} \, dx","Int[1/(x*(1 - x^4 + x^8)),x]","-\frac{1}{8} \log \left(x^8-x^4+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}+\log (x)","-\frac{1}{8} \log \left(x^8-x^4+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}+\log (x)",1,"-ArcTan[(1 - 2*x^4)/Sqrt[3]]/(4*Sqrt[3]) + Log[x] - Log[1 - x^4 + x^8]/8","A",7,7,16,0.4375,1,"{1357, 705, 29, 634, 618, 204, 628}"
355,1,57,0,0.0419199,"\int \frac{1}{x^3 \left(1-x^4+x^8\right)} \, dx","Int[1/(x^3*(1 - x^4 + x^8)),x]","-\frac{1}{2 x^2}-\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{4 \sqrt{3}}+\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{4 \sqrt{3}}","-\frac{1}{2 x^2}-\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{4 \sqrt{3}}+\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{4 \sqrt{3}}",1,"-1/(2*x^2) - Log[1 - Sqrt[3]*x^2 + x^4]/(4*Sqrt[3]) + Log[1 + Sqrt[3]*x^2 + x^4]/(4*Sqrt[3])","A",5,4,16,0.2500,1,"{1359, 1123, 1164, 628}"
356,1,48,0,0.0536337,"\int \frac{1}{x^5 \left(1-x^4+x^8\right)} \, dx","Int[1/(x^5*(1 - x^4 + x^8)),x]","-\frac{1}{4 x^4}-\frac{1}{8} \log \left(x^8-x^4+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}+\log (x)","-\frac{1}{4 x^4}-\frac{1}{8} \log \left(x^8-x^4+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}+\log (x)",1,"-1/(4*x^4) + ArcTan[(1 - 2*x^4)/Sqrt[3]]/(4*Sqrt[3]) + Log[x] - Log[1 - x^4 + x^8]/8","A",8,7,16,0.4375,1,"{1357, 709, 800, 634, 618, 204, 628}"
357,1,96,0,0.0943797,"\int \frac{1}{x^7 \left(1-x^4+x^8\right)} \, dx","Int[1/(x^7*(1 - x^4 + x^8)),x]","-\frac{1}{2 x^2}-\frac{1}{6 x^6}-\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{8 \sqrt{3}}+\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{8 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x^2\right)-\frac{1}{4} \tan ^{-1}\left(2 x^2+\sqrt{3}\right)","-\frac{1}{2 x^2}-\frac{1}{6 x^6}-\frac{\log \left(x^4-\sqrt{3} x^2+1\right)}{8 \sqrt{3}}+\frac{\log \left(x^4+\sqrt{3} x^2+1\right)}{8 \sqrt{3}}+\frac{1}{4} \tan ^{-1}\left(\sqrt{3}-2 x^2\right)-\frac{1}{4} \tan ^{-1}\left(2 x^2+\sqrt{3}\right)",1,"-1/(6*x^6) - 1/(2*x^2) + ArcTan[Sqrt[3] - 2*x^2]/4 - ArcTan[Sqrt[3] + 2*x^2]/4 - Log[1 - Sqrt[3]*x^2 + x^4]/(8*Sqrt[3]) + Log[1 + Sqrt[3]*x^2 + x^4]/(8*Sqrt[3])","A",13,10,16,0.6250,1,"{1359, 1123, 1281, 12, 1127, 1161, 618, 204, 1164, 628}"
358,1,356,0,0.3326629,"\int \frac{x^8}{1-x^4+x^8} \, dx","Int[x^8/(1 - x^4 + x^8),x]","-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)+x+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}","-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)+x+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}",1,"x + ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]]/(4*Sqrt[3*(2 - Sqrt[3])]) - ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]]/(4*Sqrt[3*(2 + Sqrt[3])]) - ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]]/(4*Sqrt[3*(2 - Sqrt[3])]) + ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]]/(4*Sqrt[3*(2 + Sqrt[3])]) - (Sqrt[(2 - Sqrt[3])/3]*Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2])/8 + (Sqrt[(2 - Sqrt[3])/3]*Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2])/8 + (Sqrt[(2 + Sqrt[3])/3]*Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 + Sqrt[3])/3]*Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2])/8","A",20,7,16,0.4375,1,"{1367, 1421, 1169, 634, 618, 204, 628}"
359,1,275,0,0.2426652,"\int \frac{x^6}{1-x^4+x^8} \, dx","Int[x^6/(1 - x^4 + x^8),x]","\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}","\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}",1,"-ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[6]) - ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[6]) + ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[6]) + ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[6]) + Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2]/(4*Sqrt[6]) - Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2]/(4*Sqrt[6]) + Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2]/(4*Sqrt[6]) - Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2]/(4*Sqrt[6])","A",19,6,16,0.3750,1,"{1372, 1169, 634, 618, 204, 628}"
360,1,347,0,0.2087701,"\int \frac{x^4}{1-x^4+x^8} \, dx","Int[x^4/(1 - x^4 + x^8),x]","-\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2+\sqrt{3}\right)}}-\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2+\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}","-\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2+\sqrt{3}\right)}}-\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2+\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}",1,"ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]]/(4*Sqrt[3*(2 + Sqrt[3])]) - ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]]/(4*Sqrt[3*(2 - Sqrt[3])]) - ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]]/(4*Sqrt[3*(2 + Sqrt[3])]) + ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]]/(4*Sqrt[3*(2 - Sqrt[3])]) - Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2]/(8*Sqrt[3*(2 - Sqrt[3])]) + Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2]/(8*Sqrt[3*(2 - Sqrt[3])]) + Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2]/(8*Sqrt[3*(2 + Sqrt[3])]) - Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2]/(8*Sqrt[3*(2 + Sqrt[3])])","A",19,7,16,0.4375,1,"{1373, 1127, 1161, 618, 204, 1164, 628}"
361,1,355,0,0.1996687,"\int \frac{x^2}{1-x^4+x^8} \, dx","Int[x^2/(1 - x^4 + x^8),x]","\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2+\sqrt{3}\right)}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2+\sqrt{3}\right)}}+\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)","\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2+\sqrt{3}\right)}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{8 \sqrt{3 \left(2+\sqrt{3}\right)}}+\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)",1,"(Sqrt[(2 - Sqrt[3])/3]*ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]])/4 - (Sqrt[(2 + Sqrt[3])/3]*ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]])/4 - (Sqrt[(2 - Sqrt[3])/3]*ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]])/4 + (Sqrt[(2 + Sqrt[3])/3]*ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]])/4 + Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2]/(8*Sqrt[3*(2 - Sqrt[3])]) - Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2]/(8*Sqrt[3*(2 - Sqrt[3])]) - Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2]/(8*Sqrt[3*(2 + Sqrt[3])]) + Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2]/(8*Sqrt[3*(2 + Sqrt[3])])","A",19,6,16,0.3750,1,"{1373, 1094, 634, 618, 204, 628}"
362,1,275,0,0.2105478,"\int \frac{1}{1-x^4+x^8} \, dx","Int[(1 - x^4 + x^8)^(-1),x]","-\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}","-\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}",1,"-ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[6]) - ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[6]) + ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[6]) + ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[6]) - Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2]/(4*Sqrt[6]) + Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2]/(4*Sqrt[6]) - Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2]/(4*Sqrt[6]) + Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2]/(4*Sqrt[6])","A",19,6,12,0.5000,1,"{1346, 1169, 634, 618, 204, 628}"
363,1,360,0,0.2385851,"\int \frac{1}{x^2 \left(1-x^4+x^8\right)} \, dx","Int[1/(x^2*(1 - x^4 + x^8)),x]","\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}","\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{4 \sqrt{3 \left(2-\sqrt{3}\right)}}+\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{4 \sqrt{3 \left(2+\sqrt{3}\right)}}",1,"-x^(-1) + ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]]/(4*Sqrt[3*(2 - Sqrt[3])]) - ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]]/(4*Sqrt[3*(2 + Sqrt[3])]) - ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]]/(4*Sqrt[3*(2 - Sqrt[3])]) + ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]]/(4*Sqrt[3*(2 + Sqrt[3])]) + (Sqrt[(2 - Sqrt[3])/3]*Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 - Sqrt[3])/3]*Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 + Sqrt[3])/3]*Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2])/8 + (Sqrt[(2 + Sqrt[3])/3]*Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2])/8","A",22,8,16,0.5000,1,"{1368, 1506, 1279, 1169, 634, 618, 204, 628}"
364,1,370,0,0.2355337,"\int \frac{1}{x^4 \left(1-x^4+x^8\right)} \, dx","Int[1/(x^4*(1 - x^4 + x^8)),x]","-\frac{1}{3 x^3}+\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)","-\frac{1}{3 x^3}+\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)",1,"-1/(3*x^3) - (Sqrt[(2 + Sqrt[3])/3]*ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]])/4 + (Sqrt[(2 - Sqrt[3])/3]*ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]])/4 + (Sqrt[(2 + Sqrt[3])/3]*ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]])/4 - (Sqrt[(2 - Sqrt[3])/3]*ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]])/4 + (Sqrt[(2 - Sqrt[3])/3]*Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 - Sqrt[3])/3]*Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 + Sqrt[3])/3]*Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2])/8 + (Sqrt[(2 + Sqrt[3])/3]*Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2])/8","A",20,7,16,0.4375,1,"{1368, 1421, 1169, 634, 618, 204, 628}"
365,1,287,0,0.2410939,"\int \frac{1}{x^6 \left(1-x^4+x^8\right)} \, dx","Int[1/(x^6*(1 - x^4 + x^8)),x]","-\frac{1}{5 x^5}-\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}","-\frac{1}{5 x^5}-\frac{\log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{\log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}+\frac{\log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)}{4 \sqrt{6}}-\frac{1}{x}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)}{2 \sqrt{6}}-\frac{\tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)}{2 \sqrt{6}}",1,"-1/(5*x^5) - x^(-1) + ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[6]) + ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[6]) - ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]]/(2*Sqrt[6]) - ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]]/(2*Sqrt[6]) - Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2]/(4*Sqrt[6]) + Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2]/(4*Sqrt[6]) - Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2]/(4*Sqrt[6]) + Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2]/(4*Sqrt[6])","A",22,9,16,0.5625,1,"{1368, 1504, 12, 1372, 1169, 634, 618, 204, 628}"
366,1,377,0,0.2864035,"\int \frac{1}{x^8 \left(1-x^4+x^8\right)} \, dx","Int[1/(x^8*(1 - x^4 + x^8)),x]","-\frac{1}{3 x^3}-\frac{1}{7 x^7}+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)","-\frac{1}{3 x^3}-\frac{1}{7 x^7}+\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2-\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \log \left(x^2+\sqrt{2-\sqrt{3}} x+1\right)-\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2-\sqrt{2+\sqrt{3}} x+1\right)+\frac{1}{8} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \log \left(x^2+\sqrt{2+\sqrt{3}} x+1\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{3}}-2 x}{\sqrt{2+\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{3}}-2 x}{\sqrt{2-\sqrt{3}}}\right)+\frac{1}{4} \sqrt{\frac{1}{3} \left(2-\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\right)-\frac{1}{4} \sqrt{\frac{1}{3} \left(2+\sqrt{3}\right)} \tan ^{-1}\left(\frac{2 x+\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}\right)",1,"-1/(7*x^7) - 1/(3*x^3) - (Sqrt[(2 - Sqrt[3])/3]*ArcTan[(Sqrt[2 - Sqrt[3]] - 2*x)/Sqrt[2 + Sqrt[3]]])/4 + (Sqrt[(2 + Sqrt[3])/3]*ArcTan[(Sqrt[2 + Sqrt[3]] - 2*x)/Sqrt[2 - Sqrt[3]]])/4 + (Sqrt[(2 - Sqrt[3])/3]*ArcTan[(Sqrt[2 - Sqrt[3]] + 2*x)/Sqrt[2 + Sqrt[3]]])/4 - (Sqrt[(2 + Sqrt[3])/3]*ArcTan[(Sqrt[2 + Sqrt[3]] + 2*x)/Sqrt[2 - Sqrt[3]]])/4 + (Sqrt[(2 + Sqrt[3])/3]*Log[1 - Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 + Sqrt[3])/3]*Log[1 + Sqrt[2 - Sqrt[3]]*x + x^2])/8 - (Sqrt[(2 - Sqrt[3])/3]*Log[1 - Sqrt[2 + Sqrt[3]]*x + x^2])/8 + (Sqrt[(2 - Sqrt[3])/3]*Log[1 + Sqrt[2 + Sqrt[3]]*x + x^2])/8","A",22,10,16,0.6250,1,"{1368, 1504, 12, 1373, 1127, 1161, 618, 204, 1164, 628}"
367,1,117,0,0.0837868,"\int \frac{x^m}{1+3 x^4+x^8} \, dx","Int[x^m/(1 + 3*x^4 + x^8),x]","\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 x^4}{3-\sqrt{5}}\right)}{\sqrt{5} \left(3-\sqrt{5}\right) (m+1)}-\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 x^4}{3+\sqrt{5}}\right)}{\sqrt{5} \left(3+\sqrt{5}\right) (m+1)}","\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 x^4}{3-\sqrt{5}}\right)}{\sqrt{5} \left(3-\sqrt{5}\right) (m+1)}-\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};-\frac{2 x^4}{3+\sqrt{5}}\right)}{\sqrt{5} \left(3+\sqrt{5}\right) (m+1)}",1,"(2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, (-2*x^4)/(3 - Sqrt[5])])/(Sqrt[5]*(3 - Sqrt[5])*(1 + m)) - (2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, (-2*x^4)/(3 + Sqrt[5])])/(Sqrt[5]*(3 + Sqrt[5])*(1 + m))","A",3,2,16,0.1250,1,"{1375, 364}"
368,1,62,0,0.0562573,"\int \frac{x^{11}}{1+3 x^4+x^8} \, dx","Int[x^11/(1 + 3*x^4 + x^8),x]","\frac{x^4}{4}-\frac{1}{40} \left(15-7 \sqrt{5}\right) \log \left(2 x^4-\sqrt{5}+3\right)-\frac{1}{40} \left(15+7 \sqrt{5}\right) \log \left(2 x^4+\sqrt{5}+3\right)","\frac{x^4}{4}-\frac{1}{40} \left(15-7 \sqrt{5}\right) \log \left(2 x^4-\sqrt{5}+3\right)-\frac{1}{40} \left(15+7 \sqrt{5}\right) \log \left(2 x^4+\sqrt{5}+3\right)",1,"x^4/4 - ((15 - 7*Sqrt[5])*Log[3 - Sqrt[5] + 2*x^4])/40 - ((15 + 7*Sqrt[5])*Log[3 + Sqrt[5] + 2*x^4])/40","A",5,4,16,0.2500,1,"{1357, 703, 632, 31}"
369,1,90,0,0.1421505,"\int \frac{x^9}{1+3 x^4+x^8} \, dx","Int[x^9/(1 + 3*x^4 + x^8),x]","\frac{x^2}{2}-\frac{1}{2} \sqrt{\frac{1}{5} \left(9+4 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)+\frac{1}{2} \sqrt{\frac{1}{5} \left(9-4 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)","\frac{x^2}{2}-\frac{1}{2} \sqrt{\frac{1}{5} \left(9+4 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)+\frac{1}{2} \sqrt{\frac{1}{5} \left(9-4 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)",1,"x^2/2 - (Sqrt[(9 + 4*Sqrt[5])/5]*ArcTan[Sqrt[2/(3 + Sqrt[5])]*x^2])/2 + (Sqrt[(9 - 4*Sqrt[5])/5]*ArcTan[Sqrt[(3 + Sqrt[5])/2]*x^2])/2","A",5,4,16,0.2500,1,"{1359, 1122, 1166, 203}"
370,1,55,0,0.0329384,"\int \frac{x^7}{1+3 x^4+x^8} \, dx","Int[x^7/(1 + 3*x^4 + x^8),x]","\frac{1}{40} \left(5-3 \sqrt{5}\right) \log \left(2 x^4-\sqrt{5}+3\right)+\frac{1}{40} \left(5+3 \sqrt{5}\right) \log \left(2 x^4+\sqrt{5}+3\right)","\frac{1}{40} \left(5-3 \sqrt{5}\right) \log \left(2 x^4-\sqrt{5}+3\right)+\frac{1}{40} \left(5+3 \sqrt{5}\right) \log \left(2 x^4+\sqrt{5}+3\right)",1,"((5 - 3*Sqrt[5])*Log[3 - Sqrt[5] + 2*x^4])/40 + ((5 + 3*Sqrt[5])*Log[3 + Sqrt[5] + 2*x^4])/40","A",4,3,16,0.1875,1,"{1357, 632, 31}"
371,1,81,0,0.084069,"\int \frac{x^5}{1+3 x^4+x^8} \, dx","Int[x^5/(1 + 3*x^4 + x^8),x]","\frac{1}{2} \sqrt{\frac{1}{10} \left(3+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(3-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)","\frac{1}{2} \sqrt{\frac{1}{10} \left(3+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(3-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)",1,"(Sqrt[(3 + Sqrt[5])/10]*ArcTan[Sqrt[2/(3 + Sqrt[5])]*x^2])/2 - (Sqrt[(3 - Sqrt[5])/10]*ArcTan[Sqrt[(3 + Sqrt[5])/2]*x^2])/2","A",4,3,16,0.1875,1,"{1359, 1130, 203}"
372,1,23,0,0.0256436,"\int \frac{x^3}{1+3 x^4+x^8} \, dx","Int[x^3/(1 + 3*x^4 + x^8),x]","-\frac{\tanh ^{-1}\left(\frac{2 x^4+3}{\sqrt{5}}\right)}{2 \sqrt{5}}","-\frac{\tanh ^{-1}\left(\frac{2 x^4+3}{\sqrt{5}}\right)}{2 \sqrt{5}}",1,"-ArcTanh[(3 + 2*x^4)/Sqrt[5]]/(2*Sqrt[5])","A",3,3,16,0.1875,1,"{1352, 618, 206}"
373,1,75,0,0.058168,"\int \frac{x}{1+3 x^4+x^8} \, dx","Int[x/(1 + 3*x^4 + x^8),x]","\frac{1}{2} \sqrt{\frac{1}{10} \left(3+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)-\frac{\tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)}{\sqrt{10 \left(3+\sqrt{5}\right)}}","\frac{1}{2} \sqrt{\frac{1}{10} \left(3+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)-\frac{\tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)}{\sqrt{10 \left(3+\sqrt{5}\right)}}",1,"-(ArcTan[Sqrt[2/(3 + Sqrt[5])]*x^2]/Sqrt[10*(3 + Sqrt[5])]) + (Sqrt[(3 + Sqrt[5])/10]*ArcTan[Sqrt[(3 + Sqrt[5])/2]*x^2])/2","A",4,3,14,0.2143,1,"{1359, 1093, 203}"
374,1,57,0,0.0342272,"\int \frac{1}{x \left(1+3 x^4+x^8\right)} \, dx","Int[1/(x*(1 + 3*x^4 + x^8)),x]","-\frac{1}{40} \left(5+3 \sqrt{5}\right) \log \left(2 x^4-\sqrt{5}+3\right)-\frac{1}{40} \left(5-3 \sqrt{5}\right) \log \left(2 x^4+\sqrt{5}+3\right)+\log (x)","-\frac{1}{40} \left(5+3 \sqrt{5}\right) \log \left(2 x^4-\sqrt{5}+3\right)-\frac{1}{40} \left(5-3 \sqrt{5}\right) \log \left(2 x^4+\sqrt{5}+3\right)+\log (x)",1,"Log[x] - ((5 + 3*Sqrt[5])*Log[3 - Sqrt[5] + 2*x^4])/40 - ((5 - 3*Sqrt[5])*Log[3 + Sqrt[5] + 2*x^4])/40","A",6,5,16,0.3125,1,"{1357, 705, 29, 632, 31}"
375,1,89,0,0.0724102,"\int \frac{1}{x^3 \left(1+3 x^4+x^8\right)} \, dx","Int[1/(x^3*(1 + 3*x^4 + x^8)),x]","-\frac{1}{2 x^2}+\frac{1}{2} \sqrt{\frac{1}{5} \left(9-4 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)-\frac{\left(3+\sqrt{5}\right)^{3/2} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)}{4 \sqrt{10}}","-\frac{1}{2 x^2}+\frac{1}{2} \sqrt{\frac{1}{5} \left(9-4 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)-\frac{\left(3+\sqrt{5}\right)^{3/2} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)}{4 \sqrt{10}}",1,"-1/(2*x^2) + (Sqrt[(9 - 4*Sqrt[5])/5]*ArcTan[Sqrt[2/(3 + Sqrt[5])]*x^2])/2 - ((3 + Sqrt[5])^(3/2)*ArcTan[Sqrt[(3 + Sqrt[5])/2]*x^2])/(4*Sqrt[10])","A",5,4,16,0.2500,1,"{1359, 1123, 1166, 203}"
376,1,66,0,0.06666,"\int \frac{1}{x^5 \left(1+3 x^4+x^8\right)} \, dx","Int[1/(x^5*(1 + 3*x^4 + x^8)),x]","-\frac{1}{4 x^4}+\frac{1}{40} \left(15+7 \sqrt{5}\right) \log \left(2 x^4-\sqrt{5}+3\right)+\frac{1}{40} \left(15-7 \sqrt{5}\right) \log \left(2 x^4+\sqrt{5}+3\right)-3 \log (x)","-\frac{1}{4 x^4}+\frac{1}{40} \left(15+7 \sqrt{5}\right) \log \left(2 x^4-\sqrt{5}+3\right)+\frac{1}{40} \left(15-7 \sqrt{5}\right) \log \left(2 x^4+\sqrt{5}+3\right)-3 \log (x)",1,"-1/(4*x^4) - 3*Log[x] + ((15 + 7*Sqrt[5])*Log[3 - Sqrt[5] + 2*x^4])/40 + ((15 - 7*Sqrt[5])*Log[3 + Sqrt[5] + 2*x^4])/40","A",7,5,16,0.3125,1,"{1357, 709, 800, 632, 31}"
377,1,97,0,0.1344027,"\int \frac{1}{x^7 \left(1+3 x^4+x^8\right)} \, dx","Int[1/(x^7*(1 + 3*x^4 + x^8)),x]","\frac{3}{2 x^2}-\frac{1}{6 x^6}-\frac{1}{2} \sqrt{\frac{1}{10} \left(123-55 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)+\frac{1}{2} \sqrt{\frac{1}{10} \left(123+55 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)","\frac{3}{2 x^2}-\frac{1}{6 x^6}-\frac{1}{2} \sqrt{\frac{1}{10} \left(123-55 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)+\frac{1}{2} \sqrt{\frac{1}{10} \left(123+55 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)",1,"-1/(6*x^6) + 3/(2*x^2) - (Sqrt[(123 - 55*Sqrt[5])/10]*ArcTan[Sqrt[2/(3 + Sqrt[5])]*x^2])/2 + (Sqrt[(123 + 55*Sqrt[5])/10]*ArcTan[Sqrt[(3 + Sqrt[5])/2]*x^2])/2","A",6,5,16,0.3125,1,"{1359, 1123, 1281, 1166, 203}"
378,1,440,0,0.4162555,"\int \frac{x^8}{1+3 x^4+x^8} \, dx","Int[x^8/(1 + 3*x^4 + x^8),x]","-\frac{\sqrt[4]{984-440 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{8 \sqrt{10}}+\frac{\sqrt[4]{984-440 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{8 \sqrt{10}}+\frac{\sqrt[4]{123+55 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{123+55 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+x-\frac{\sqrt[4]{984-440 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{4 \sqrt{10}}+\frac{\sqrt[4]{984-440 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{4 \sqrt{10}}+\frac{\sqrt[4]{123+55 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{123+55 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}","-\frac{\sqrt[4]{123-55 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{123-55 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{123+55 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{123+55 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+x-\frac{\sqrt[4]{123-55 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{123-55 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{123+55 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{123+55 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}",1,"x - ((984 - 440*Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(4*Sqrt[10]) + ((984 - 440*Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(4*Sqrt[10]) + ((123 + 55*Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) - ((123 + 55*Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) - ((984 - 440*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] - 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(8*Sqrt[10]) + ((984 - 440*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] + 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(8*Sqrt[10]) + ((123 + 55*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 + Sqrt[5])] - 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5]) - ((123 + 55*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 + Sqrt[5])] + 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5])","A",20,8,16,0.5000,1,"{1367, 1422, 211, 1165, 628, 1162, 617, 204}"
379,1,431,0,0.2946075,"\int \frac{x^6}{1+3 x^4+x^8} \, dx","Int[x^6/(1 + 3*x^4 + x^8),x]","-\frac{\sqrt[4]{9-4 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\sqrt[4]{9-4 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\left(3+\sqrt{5}\right)^{3/4} \log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{8 \sqrt[4]{2} \sqrt{5}}-\frac{\left(3+\sqrt{5}\right)^{3/4} \log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{8 \sqrt[4]{2} \sqrt{5}}+\frac{\sqrt[4]{9-4 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{2 \sqrt{10}}-\frac{\sqrt[4]{9-4 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{2 \sqrt{10}}-\frac{\left(3+\sqrt{5}\right)^{3/4} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{4 \sqrt[4]{2} \sqrt{5}}+\frac{\left(3+\sqrt{5}\right)^{3/4} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{4 \sqrt[4]{2} \sqrt{5}}","-\frac{\sqrt[4]{9-4 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\sqrt[4]{9-4 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\left(3+\sqrt{5}\right)^{3/4} \log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{8 \sqrt[4]{2} \sqrt{5}}-\frac{\left(3+\sqrt{5}\right)^{3/4} \log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{8 \sqrt[4]{2} \sqrt{5}}+\frac{\sqrt[4]{9-4 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{2 \sqrt{10}}-\frac{\sqrt[4]{9-4 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{2 \sqrt{10}}-\frac{\left(3+\sqrt{5}\right)^{3/4} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{4 \sqrt[4]{2} \sqrt{5}}+\frac{\left(3+\sqrt{5}\right)^{3/4} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{4 \sqrt[4]{2} \sqrt{5}}",1,"((9 - 4*Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(2*Sqrt[10]) - ((9 - 4*Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(2*Sqrt[10]) - ((3 + Sqrt[5])^(3/4)*ArcTan[1 - (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)])/(4*2^(1/4)*Sqrt[5]) + ((3 + Sqrt[5])^(3/4)*ArcTan[1 + (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)])/(4*2^(1/4)*Sqrt[5]) - ((9 - 4*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] - 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(4*Sqrt[10]) + ((9 - 4*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] + 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(4*Sqrt[10]) + ((3 + Sqrt[5])^(3/4)*Log[Sqrt[2*(3 + Sqrt[5])] - 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2])/(8*2^(1/4)*Sqrt[5]) - ((3 + Sqrt[5])^(3/4)*Log[Sqrt[2*(3 + Sqrt[5])] + 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2])/(8*2^(1/4)*Sqrt[5])","A",19,7,16,0.4375,1,"{1374, 297, 1162, 617, 204, 1165, 628}"
380,1,451,0,0.2800805,"\int \frac{x^4}{1+3 x^4+x^8} \, dx","Int[x^4/(1 + 3*x^4 + x^8),x]","\frac{\sqrt[4]{3-\sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{3-\sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{3+\sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{3+\sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{3-\sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{3-\sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{3+\sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{3+\sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}","\frac{\sqrt[4]{3-\sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{3-\sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{3+\sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{3+\sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{3-\sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{3-\sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{3+\sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{3+\sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}",1,"((3 - Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) - ((3 - Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) - ((3 + Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) + ((3 + Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) + ((3 - Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] - 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5]) - ((3 - Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] + 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5]) - ((3 + Sqrt[5])^(1/4)*Log[Sqrt[2*(3 + Sqrt[5])] - 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5]) + ((3 + Sqrt[5])^(1/4)*Log[Sqrt[2*(3 + Sqrt[5])] + 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5])","A",19,7,16,0.4375,1,"{1374, 211, 1165, 628, 1162, 617, 204}"
381,1,431,0,0.2591095,"\int \frac{x^2}{1+3 x^4+x^8} \, dx","Int[x^2/(1 + 3*x^4 + x^8),x]","\frac{\sqrt[4]{3+\sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{3+\sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4 \sqrt{5} \sqrt[4]{2 \left(3+\sqrt{5}\right)}}+\frac{\log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4 \sqrt{5} \sqrt[4]{2 \left(3+\sqrt{5}\right)}}-\frac{\sqrt[4]{3+\sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{3+\sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}+\frac{\tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{2 \sqrt{5} \sqrt[4]{2 \left(3+\sqrt{5}\right)}}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{2 \sqrt{5} \sqrt[4]{2 \left(3+\sqrt{5}\right)}}","\frac{\log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4 \sqrt{5} \sqrt[4]{2 \left(3-\sqrt{5}\right)}}-\frac{\log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4 \sqrt{5} \sqrt[4]{2 \left(3-\sqrt{5}\right)}}-\frac{\log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4 \sqrt{5} \sqrt[4]{2 \left(3+\sqrt{5}\right)}}+\frac{\log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4 \sqrt{5} \sqrt[4]{2 \left(3+\sqrt{5}\right)}}-\frac{\tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{2 \sqrt{5} \sqrt[4]{2 \left(3-\sqrt{5}\right)}}+\frac{\tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{2 \sqrt{5} \sqrt[4]{2 \left(3-\sqrt{5}\right)}}+\frac{\tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{2 \sqrt{5} \sqrt[4]{2 \left(3+\sqrt{5}\right)}}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{2 \sqrt{5} \sqrt[4]{2 \left(3+\sqrt{5}\right)}}",1,"-((3 + Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) + ((3 + Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) + ArcTan[1 - (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)]/(2*Sqrt[5]*(2*(3 + Sqrt[5]))^(1/4)) - ArcTan[1 + (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)]/(2*Sqrt[5]*(2*(3 + Sqrt[5]))^(1/4)) + ((3 + Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] - 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5]) - ((3 + Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] + 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5]) - Log[Sqrt[2*(3 + Sqrt[5])] - 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2]/(4*Sqrt[5]*(2*(3 + Sqrt[5]))^(1/4)) + Log[Sqrt[2*(3 + Sqrt[5])] + 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2]/(4*Sqrt[5]*(2*(3 + Sqrt[5]))^(1/4))","A",19,7,16,0.4375,1,"{1375, 297, 1162, 617, 204, 1165, 628}"
382,1,414,0,0.2568826,"\int \frac{1}{1+3 x^4+x^8} \, dx","Int[(1 + 3*x^4 + x^8)^(-1),x]","-\frac{\sqrt[4]{9+4 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\sqrt[4]{9+4 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{2 \sqrt{5} \left(2 \left(3+\sqrt{5}\right)\right)^{3/4}}-\frac{\log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{2 \sqrt{5} \left(2 \left(3+\sqrt{5}\right)\right)^{3/4}}-\frac{\sqrt[4]{9+4 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{2 \sqrt{10}}+\frac{\sqrt[4]{9+4 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{2 \sqrt{10}}+\frac{\tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{\sqrt{5} \left(2 \left(3+\sqrt{5}\right)\right)^{3/4}}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{\sqrt{5} \left(2 \left(3+\sqrt{5}\right)\right)^{3/4}}","-\frac{\sqrt[4]{9+4 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\sqrt[4]{9+4 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4 \sqrt{10}}+\frac{\log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{2 \sqrt{5} \left(2 \left(3+\sqrt{5}\right)\right)^{3/4}}-\frac{\log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{2 \sqrt{5} \left(2 \left(3+\sqrt{5}\right)\right)^{3/4}}-\frac{\sqrt[4]{9+4 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{2 \sqrt{10}}+\frac{\sqrt[4]{9+4 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{2 \sqrt{10}}+\frac{\tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{\sqrt{5} \left(2 \left(3+\sqrt{5}\right)\right)^{3/4}}-\frac{\tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{\sqrt{5} \left(2 \left(3+\sqrt{5}\right)\right)^{3/4}}",1,"-((9 + 4*Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(2*Sqrt[10]) + ((9 + 4*Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(2*Sqrt[10]) + ArcTan[1 - (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)]/(Sqrt[5]*(2*(3 + Sqrt[5]))^(3/4)) - ArcTan[1 + (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)]/(Sqrt[5]*(2*(3 + Sqrt[5]))^(3/4)) - ((9 + 4*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] - 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(4*Sqrt[10]) + ((9 + 4*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] + 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(4*Sqrt[10]) + Log[Sqrt[2*(3 + Sqrt[5])] - 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2]/(2*Sqrt[5]*(2*(3 + Sqrt[5]))^(3/4)) - Log[Sqrt[2*(3 + Sqrt[5])] + 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2]/(2*Sqrt[5]*(2*(3 + Sqrt[5]))^(3/4))","A",19,7,12,0.5833,1,"{1347, 211, 1165, 628, 1162, 617, 204}"
383,1,416,0,0.2854763,"\int \frac{1}{x^2 \left(1+3 x^4+x^8\right)} \, dx","Int[1/(x^2*(1 + 3*x^4 + x^8)),x]","-\frac{\left(3+\sqrt{5}\right)^{5/4} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{8\ 2^{3/4} \sqrt{5}}+\frac{\left(3+\sqrt{5}\right)^{5/4} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{8\ 2^{3/4} \sqrt{5}}+\frac{1}{40} \sqrt[4]{6150-2750 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)-\frac{1}{40} \sqrt[4]{6150-2750 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)-\frac{1}{x}+\frac{\left(3+\sqrt{5}\right)^{5/4} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\left(3+\sqrt{5}\right)^{5/4} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{1}{20} \sqrt[4]{6150-2750 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)+\frac{1}{20} \sqrt[4]{6150-2750 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)","-\frac{\left(3+\sqrt{5}\right)^{5/4} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{8\ 2^{3/4} \sqrt{5}}+\frac{\left(3+\sqrt{5}\right)^{5/4} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{8\ 2^{3/4} \sqrt{5}}+\frac{1}{40} \sqrt[4]{6150-2750 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)-\frac{1}{40} \sqrt[4]{6150-2750 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)-\frac{1}{x}+\frac{\left(3+\sqrt{5}\right)^{5/4} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\left(3+\sqrt{5}\right)^{5/4} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{1}{20} \sqrt[4]{6150-2750 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)+\frac{1}{20} \sqrt[4]{6150-2750 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)",1,"-x^(-1) + ((3 + Sqrt[5])^(5/4)*ArcTan[1 - (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(4*2^(3/4)*Sqrt[5]) - ((3 + Sqrt[5])^(5/4)*ArcTan[1 + (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(4*2^(3/4)*Sqrt[5]) - ((6150 - 2750*Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)])/20 + ((6150 - 2750*Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)])/20 - ((3 + Sqrt[5])^(5/4)*Log[Sqrt[2*(3 - Sqrt[5])] - 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(8*2^(3/4)*Sqrt[5]) + ((3 + Sqrt[5])^(5/4)*Log[Sqrt[2*(3 - Sqrt[5])] + 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(8*2^(3/4)*Sqrt[5]) + ((6150 - 2750*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 + Sqrt[5])] - 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2])/40 - ((6150 - 2750*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 + Sqrt[5])] + 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2])/40","A",20,8,16,0.5000,1,"{1368, 1510, 297, 1162, 617, 204, 1165, 628}"
384,1,466,0,0.3671449,"\int \frac{1}{x^4 \left(1+3 x^4+x^8\right)} \, dx","Int[1/(x^4*(1 + 3*x^4 + x^8)),x]","-\frac{1}{3 x^3}+\frac{\sqrt[4]{843+377 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{843+377 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{843-377 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{843-377 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{843+377 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{843+377 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{843-377 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{843-377 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}","-\frac{1}{3 x^3}+\frac{\sqrt[4]{843+377 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{843+377 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3-\sqrt{5}\right)} x+\sqrt{2 \left(3-\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{843-377 \sqrt{5}} \log \left(2 x^2-2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{843-377 \sqrt{5}} \log \left(2 x^2+2 \sqrt[4]{2 \left(3+\sqrt{5}\right)} x+\sqrt{2 \left(3+\sqrt{5}\right)}\right)}{4\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{843+377 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{843+377 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3-\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{843-377 \sqrt{5}} \tan ^{-1}\left(1-\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}\right)}{2\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{843-377 \sqrt{5}} \tan ^{-1}\left(\frac{2^{3/4} x}{\sqrt[4]{3+\sqrt{5}}}+1\right)}{2\ 2^{3/4} \sqrt{5}}",1,"-1/(3*x^3) + ((843 + 377*Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) - ((843 + 377*Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/(3 - Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) - ((843 - 377*Sqrt[5])^(1/4)*ArcTan[1 - (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) + ((843 - 377*Sqrt[5])^(1/4)*ArcTan[1 + (2^(3/4)*x)/(3 + Sqrt[5])^(1/4)])/(2*2^(3/4)*Sqrt[5]) + ((843 + 377*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] - 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5]) - ((843 + 377*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 - Sqrt[5])] + 2*(2*(3 - Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5]) - ((843 - 377*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 + Sqrt[5])] - 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5]) + ((843 - 377*Sqrt[5])^(1/4)*Log[Sqrt[2*(3 + Sqrt[5])] + 2*(2*(3 + Sqrt[5]))^(1/4)*x + 2*x^2])/(4*2^(3/4)*Sqrt[5])","A",20,8,16,0.5000,1,"{1368, 1422, 211, 1165, 628, 1162, 617, 204}"
385,1,117,0,0.0646287,"\int \frac{x^m}{1-3 x^4+x^8} \, dx","Int[x^m/(1 - 3*x^4 + x^8),x]","\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};\frac{2 x^4}{3-\sqrt{5}}\right)}{\sqrt{5} \left(3-\sqrt{5}\right) (m+1)}-\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};\frac{2 x^4}{3+\sqrt{5}}\right)}{\sqrt{5} \left(3+\sqrt{5}\right) (m+1)}","\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};\frac{2 x^4}{3-\sqrt{5}}\right)}{\sqrt{5} \left(3-\sqrt{5}\right) (m+1)}-\frac{2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};\frac{2 x^4}{3+\sqrt{5}}\right)}{\sqrt{5} \left(3+\sqrt{5}\right) (m+1)}",1,"(2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, (2*x^4)/(3 - Sqrt[5])])/(Sqrt[5]*(3 - Sqrt[5])*(1 + m)) - (2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/4, (5 + m)/4, (2*x^4)/(3 + Sqrt[5])])/(Sqrt[5]*(3 + Sqrt[5])*(1 + m))","A",3,2,16,0.1250,1,"{1375, 364}"
386,1,62,0,0.045602,"\int \frac{x^{11}}{1-3 x^4+x^8} \, dx","Int[x^11/(1 - 3*x^4 + x^8),x]","\frac{x^4}{4}+\frac{1}{40} \left(15-7 \sqrt{5}\right) \log \left(-2 x^4-\sqrt{5}+3\right)+\frac{1}{40} \left(15+7 \sqrt{5}\right) \log \left(-2 x^4+\sqrt{5}+3\right)","\frac{x^4}{4}+\frac{1}{40} \left(15-7 \sqrt{5}\right) \log \left(-2 x^4-\sqrt{5}+3\right)+\frac{1}{40} \left(15+7 \sqrt{5}\right) \log \left(-2 x^4+\sqrt{5}+3\right)",1,"x^4/4 + ((15 - 7*Sqrt[5])*Log[3 - Sqrt[5] - 2*x^4])/40 + ((15 + 7*Sqrt[5])*Log[3 + Sqrt[5] - 2*x^4])/40","A",5,4,16,0.2500,1,"{1357, 703, 632, 31}"
387,1,90,0,0.0720074,"\int \frac{x^9}{1-3 x^4+x^8} \, dx","Int[x^9/(1 - 3*x^4 + x^8),x]","\frac{x^2}{2}-\frac{1}{2} \sqrt{\frac{1}{5} \left(9+4 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)+\frac{1}{2} \sqrt{\frac{1}{5} \left(9-4 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)","\frac{x^2}{2}-\frac{1}{2} \sqrt{\frac{1}{5} \left(9+4 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)+\frac{1}{2} \sqrt{\frac{1}{5} \left(9-4 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)",1,"x^2/2 - (Sqrt[(9 + 4*Sqrt[5])/5]*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*x^2])/2 + (Sqrt[(9 - 4*Sqrt[5])/5]*ArcTanh[Sqrt[(3 + Sqrt[5])/2]*x^2])/2","A",5,4,16,0.2500,1,"{1359, 1122, 1166, 207}"
388,1,55,0,0.0318653,"\int \frac{x^7}{1-3 x^4+x^8} \, dx","Int[x^7/(1 - 3*x^4 + x^8),x]","\frac{1}{40} \left(5-3 \sqrt{5}\right) \log \left(-2 x^4-\sqrt{5}+3\right)+\frac{1}{40} \left(5+3 \sqrt{5}\right) \log \left(-2 x^4+\sqrt{5}+3\right)","\frac{1}{40} \left(5-3 \sqrt{5}\right) \log \left(-2 x^4-\sqrt{5}+3\right)+\frac{1}{40} \left(5+3 \sqrt{5}\right) \log \left(-2 x^4+\sqrt{5}+3\right)",1,"((5 - 3*Sqrt[5])*Log[3 - Sqrt[5] - 2*x^4])/40 + ((5 + 3*Sqrt[5])*Log[3 + Sqrt[5] - 2*x^4])/40","A",4,3,16,0.1875,1,"{1357, 632, 31}"
389,1,81,0,0.0532177,"\int \frac{x^5}{1-3 x^4+x^8} \, dx","Int[x^5/(1 - 3*x^4 + x^8),x]","\frac{1}{2} \sqrt{\frac{1}{10} \left(3-\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)","\frac{1}{2} \sqrt{\frac{1}{10} \left(3-\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)-\frac{1}{2} \sqrt{\frac{1}{10} \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)",1,"-(Sqrt[(3 + Sqrt[5])/10]*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*x^2])/2 + (Sqrt[(3 - Sqrt[5])/10]*ArcTanh[Sqrt[(3 + Sqrt[5])/2]*x^2])/2","A",4,3,16,0.1875,1,"{1359, 1130, 207}"
390,1,23,0,0.0269306,"\int \frac{x^3}{1-3 x^4+x^8} \, dx","Int[x^3/(1 - 3*x^4 + x^8),x]","\frac{\tanh ^{-1}\left(\frac{3-2 x^4}{\sqrt{5}}\right)}{2 \sqrt{5}}","\frac{\tanh ^{-1}\left(\frac{3-2 x^4}{\sqrt{5}}\right)}{2 \sqrt{5}}",1,"ArcTanh[(3 - 2*x^4)/Sqrt[5]]/(2*Sqrt[5])","A",3,3,16,0.1875,1,"{1352, 618, 206}"
391,1,75,0,0.0377546,"\int \frac{x}{1-3 x^4+x^8} \, dx","Int[x/(1 - 3*x^4 + x^8),x]","\frac{1}{2} \sqrt{\frac{1}{10} \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)-\frac{\tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)}{\sqrt{10 \left(3+\sqrt{5}\right)}}","\frac{1}{2} \sqrt{\frac{1}{10} \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)-\frac{\tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)}{\sqrt{10 \left(3+\sqrt{5}\right)}}",1,"-(ArcTanh[Sqrt[2/(3 + Sqrt[5])]*x^2]/Sqrt[10*(3 + Sqrt[5])]) + (Sqrt[(3 + Sqrt[5])/10]*ArcTanh[Sqrt[(3 + Sqrt[5])/2]*x^2])/2","A",4,3,14,0.2143,1,"{1359, 1093, 207}"
392,1,57,0,0.0302591,"\int \frac{1}{x \left(1-3 x^4+x^8\right)} \, dx","Int[1/(x*(1 - 3*x^4 + x^8)),x]","-\frac{1}{40} \left(5+3 \sqrt{5}\right) \log \left(-2 x^4-\sqrt{5}+3\right)-\frac{1}{40} \left(5-3 \sqrt{5}\right) \log \left(-2 x^4+\sqrt{5}+3\right)+\log (x)","-\frac{1}{40} \left(5+3 \sqrt{5}\right) \log \left(-2 x^4-\sqrt{5}+3\right)-\frac{1}{40} \left(5-3 \sqrt{5}\right) \log \left(-2 x^4+\sqrt{5}+3\right)+\log (x)",1,"Log[x] - ((5 + 3*Sqrt[5])*Log[3 - Sqrt[5] - 2*x^4])/40 - ((5 - 3*Sqrt[5])*Log[3 + Sqrt[5] - 2*x^4])/40","A",6,5,16,0.3125,1,"{1357, 705, 29, 632, 31}"
393,1,89,0,0.0576259,"\int \frac{1}{x^3 \left(1-3 x^4+x^8\right)} \, dx","Int[1/(x^3*(1 - 3*x^4 + x^8)),x]","-\frac{1}{2 x^2}-\frac{1}{2} \sqrt{\frac{1}{5} \left(9-4 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)+\frac{\left(3+\sqrt{5}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)}{4 \sqrt{10}}","-\frac{1}{2 x^2}-\frac{1}{2} \sqrt{\frac{1}{5} \left(9-4 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)+\frac{\left(3+\sqrt{5}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)}{4 \sqrt{10}}",1,"-1/(2*x^2) - (Sqrt[(9 - 4*Sqrt[5])/5]*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*x^2])/2 + ((3 + Sqrt[5])^(3/2)*ArcTanh[Sqrt[(3 + Sqrt[5])/2]*x^2])/(4*Sqrt[10])","A",5,4,16,0.2500,1,"{1359, 1123, 1166, 207}"
394,1,66,0,0.0626971,"\int \frac{1}{x^5 \left(1-3 x^4+x^8\right)} \, dx","Int[1/(x^5*(1 - 3*x^4 + x^8)),x]","-\frac{1}{4 x^4}-\frac{1}{40} \left(15+7 \sqrt{5}\right) \log \left(-2 x^4-\sqrt{5}+3\right)-\frac{1}{40} \left(15-7 \sqrt{5}\right) \log \left(-2 x^4+\sqrt{5}+3\right)+3 \log (x)","-\frac{1}{4 x^4}-\frac{1}{40} \left(15+7 \sqrt{5}\right) \log \left(-2 x^4-\sqrt{5}+3\right)-\frac{1}{40} \left(15-7 \sqrt{5}\right) \log \left(-2 x^4+\sqrt{5}+3\right)+3 \log (x)",1,"-1/(4*x^4) + 3*Log[x] - ((15 + 7*Sqrt[5])*Log[3 - Sqrt[5] - 2*x^4])/40 - ((15 - 7*Sqrt[5])*Log[3 + Sqrt[5] - 2*x^4])/40","A",7,5,16,0.3125,1,"{1357, 709, 800, 632, 31}"
395,1,97,0,0.0904821,"\int \frac{1}{x^7 \left(1-3 x^4+x^8\right)} \, dx","Int[1/(x^7*(1 - 3*x^4 + x^8)),x]","-\frac{3}{2 x^2}-\frac{1}{6 x^6}-\frac{1}{2} \sqrt{\frac{1}{10} \left(123-55 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)+\frac{1}{2} \sqrt{\frac{1}{10} \left(123+55 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)","-\frac{3}{2 x^2}-\frac{1}{6 x^6}-\frac{1}{2} \sqrt{\frac{1}{10} \left(123-55 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{3+\sqrt{5}}} x^2\right)+\frac{1}{2} \sqrt{\frac{1}{10} \left(123+55 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{1}{2} \left(3+\sqrt{5}\right)} x^2\right)",1,"-1/(6*x^6) - 3/(2*x^2) - (Sqrt[(123 - 55*Sqrt[5])/10]*ArcTanh[Sqrt[2/(3 + Sqrt[5])]*x^2])/2 + (Sqrt[(123 + 55*Sqrt[5])/10]*ArcTanh[Sqrt[(3 + Sqrt[5])/2]*x^2])/2","A",6,5,16,0.3125,1,"{1359, 1123, 1281, 1166, 207}"
396,1,170,0,0.1144061,"\int \frac{x^8}{1-3 x^4+x^8} \, dx","Int[x^8/(1 - 3*x^4 + x^8),x]","x-\frac{\sqrt[4]{\frac{1}{2} \left(123+55 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{984-440 \sqrt{5}} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt{5}}-\frac{\sqrt[4]{\frac{1}{2} \left(123+55 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{984-440 \sqrt{5}} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt{5}}","x-\frac{\sqrt[4]{\frac{1}{2} \left(123+55 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{984-440 \sqrt{5}} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt{5}}-\frac{\sqrt[4]{\frac{1}{2} \left(123+55 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{984-440 \sqrt{5}} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt{5}}",1,"x - (((123 + 55*Sqrt[5])/2)^(1/4)*ArcTan[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*Sqrt[5]) + ((984 - 440*Sqrt[5])^(1/4)*ArcTan[((3 + Sqrt[5])/2)^(1/4)*x])/(4*Sqrt[5]) - (((123 + 55*Sqrt[5])/2)^(1/4)*ArcTanh[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*Sqrt[5]) + ((984 - 440*Sqrt[5])^(1/4)*ArcTanh[((3 + Sqrt[5])/2)^(1/4)*x])/(4*Sqrt[5])","A",8,5,16,0.3125,1,"{1367, 1422, 212, 206, 203}"
397,1,167,0,0.0783492,"\int \frac{x^6}{1-3 x^4+x^8} \, dx","Int[x^6/(1 - 3*x^4 + x^8),x]","\frac{\left(3+\sqrt{5}\right)^{3/4} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{144-64 \sqrt{5}} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt{5}}-\frac{\left(3+\sqrt{5}\right)^{3/4} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{144-64 \sqrt{5}} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt{5}}","\frac{\left(3+\sqrt{5}\right)^{3/4} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{144-64 \sqrt{5}} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt{5}}-\frac{\left(3+\sqrt{5}\right)^{3/4} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2\ 2^{3/4} \sqrt{5}}+\frac{\sqrt[4]{144-64 \sqrt{5}} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt{5}}",1,"((3 + Sqrt[5])^(3/4)*ArcTan[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*2^(3/4)*Sqrt[5]) - ((144 - 64*Sqrt[5])^(1/4)*ArcTan[((3 + Sqrt[5])/2)^(1/4)*x])/(4*Sqrt[5]) - ((3 + Sqrt[5])^(3/4)*ArcTanh[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*2^(3/4)*Sqrt[5]) + ((144 - 64*Sqrt[5])^(1/4)*ArcTanh[((3 + Sqrt[5])/2)^(1/4)*x])/(4*Sqrt[5])","A",7,4,16,0.2500,1,"{1374, 298, 203, 206}"
398,1,173,0,0.075094,"\int \frac{x^4}{1-3 x^4+x^8} \, dx","Int[x^4/(1 - 3*x^4 + x^8),x]","-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}","-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(3-\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}",1,"-(((3 + Sqrt[5])/2)^(1/4)*ArcTan[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*Sqrt[5]) + (((3 - Sqrt[5])/2)^(1/4)*ArcTan[((3 + Sqrt[5])/2)^(1/4)*x])/(2*Sqrt[5]) - (((3 + Sqrt[5])/2)^(1/4)*ArcTanh[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*Sqrt[5]) + (((3 - Sqrt[5])/2)^(1/4)*ArcTanh[((3 + Sqrt[5])/2)^(1/4)*x])/(2*Sqrt[5])","A",7,4,16,0.2500,1,"{1374, 212, 206, 203}"
399,1,166,0,0.0599003,"\int \frac{x^2}{1-3 x^4+x^8} \, dx","Int[x^2/(1 - 3*x^4 + x^8),x]","\frac{\tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2^{3/4} \sqrt{5} \sqrt[4]{3+\sqrt{5}}}-\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}-\frac{\tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2^{3/4} \sqrt{5} \sqrt[4]{3+\sqrt{5}}}+\frac{\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}","\frac{1}{20} \sqrt{10 \sqrt{5}-10} \tan ^{-1}\left(\frac{1}{2} \sqrt{2 \sqrt{5}-2} x\right)-\frac{1}{20} \sqrt{10+10 \sqrt{5}} \tan ^{-1}\left(\frac{1}{2} \sqrt{2+2 \sqrt{5}} x\right)-\frac{1}{20} \sqrt{10 \sqrt{5}-10} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2 \sqrt{5}-2} x\right)+\frac{1}{20} \sqrt{10+10 \sqrt{5}} \tanh ^{-1}\left(\frac{1}{2} \sqrt{2+2 \sqrt{5}} x\right)",1,"ArcTan[(2/(3 + Sqrt[5]))^(1/4)*x]/(2^(3/4)*Sqrt[5]*(3 + Sqrt[5])^(1/4)) - (((3 + Sqrt[5])/2)^(1/4)*ArcTan[((3 + Sqrt[5])/2)^(1/4)*x])/(2*Sqrt[5]) - ArcTanh[(2/(3 + Sqrt[5]))^(1/4)*x]/(2^(3/4)*Sqrt[5]*(3 + Sqrt[5])^(1/4)) + (((3 + Sqrt[5])/2)^(1/4)*ArcTanh[((3 + Sqrt[5])/2)^(1/4)*x])/(2*Sqrt[5])","A",7,4,16,0.2500,1,"{1375, 298, 203, 206}"
400,1,169,0,0.0596203,"\int \frac{1}{1-3 x^4+x^8} \, dx","Int[(1 - 3*x^4 + x^8)^(-1),x]","-\frac{\tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{\sqrt[4]{2} \sqrt{5} \left(3+\sqrt{5}\right)^{3/4}}+\frac{\left(3+\sqrt{5}\right)^{3/4} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{\sqrt[4]{2} \sqrt{5} \left(3+\sqrt{5}\right)^{3/4}}+\frac{\left(3+\sqrt{5}\right)^{3/4} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2\ 2^{3/4} \sqrt{5}}","-\frac{\tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{\sqrt[4]{2} \sqrt{5} \left(3+\sqrt{5}\right)^{3/4}}+\frac{\left(3+\sqrt{5}\right)^{3/4} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2\ 2^{3/4} \sqrt{5}}-\frac{\tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{\sqrt[4]{2} \sqrt{5} \left(3+\sqrt{5}\right)^{3/4}}+\frac{\left(3+\sqrt{5}\right)^{3/4} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2\ 2^{3/4} \sqrt{5}}",1,"-(ArcTan[(2/(3 + Sqrt[5]))^(1/4)*x]/(2^(1/4)*Sqrt[5]*(3 + Sqrt[5])^(3/4))) + ((3 + Sqrt[5])^(3/4)*ArcTan[((3 + Sqrt[5])/2)^(1/4)*x])/(2*2^(3/4)*Sqrt[5]) - ArcTanh[(2/(3 + Sqrt[5]))^(1/4)*x]/(2^(1/4)*Sqrt[5]*(3 + Sqrt[5])^(3/4)) + ((3 + Sqrt[5])^(3/4)*ArcTanh[((3 + Sqrt[5])/2)^(1/4)*x])/(2*2^(3/4)*Sqrt[5])","A",7,4,12,0.3333,1,"{1347, 212, 206, 203}"
401,1,172,0,0.0887916,"\int \frac{1}{x^2 \left(1-3 x^4+x^8\right)} \, dx","Int[1/(x^2*(1 - 3*x^4 + x^8)),x]","-\frac{1}{x}+\frac{\sqrt[4]{984-440 \sqrt{5}} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{4 \sqrt{5}}-\frac{\left(3+\sqrt{5}\right)^{5/4} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt[4]{2} \sqrt{5}}-\frac{\sqrt[4]{984-440 \sqrt{5}} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{4 \sqrt{5}}+\frac{\left(3+\sqrt{5}\right)^{5/4} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt[4]{2} \sqrt{5}}","-\frac{1}{x}+\frac{\sqrt[4]{984-440 \sqrt{5}} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{4 \sqrt{5}}-\frac{\left(3+\sqrt{5}\right)^{5/4} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt[4]{2} \sqrt{5}}-\frac{\sqrt[4]{984-440 \sqrt{5}} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{4 \sqrt{5}}+\frac{\left(3+\sqrt{5}\right)^{5/4} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4 \sqrt[4]{2} \sqrt{5}}",1,"-x^(-1) + ((984 - 440*Sqrt[5])^(1/4)*ArcTan[(2/(3 + Sqrt[5]))^(1/4)*x])/(4*Sqrt[5]) - ((3 + Sqrt[5])^(5/4)*ArcTan[((3 + Sqrt[5])/2)^(1/4)*x])/(4*2^(1/4)*Sqrt[5]) - ((984 - 440*Sqrt[5])^(1/4)*ArcTanh[(2/(3 + Sqrt[5]))^(1/4)*x])/(4*Sqrt[5]) + ((3 + Sqrt[5])^(5/4)*ArcTanh[((3 + Sqrt[5])/2)^(1/4)*x])/(4*2^(1/4)*Sqrt[5])","A",8,5,16,0.3125,1,"{1368, 1510, 298, 203, 206}"
402,1,182,0,0.1178538,"\int \frac{1}{x^4 \left(1-3 x^4+x^8\right)} \, dx","Int[1/(x^4*(1 - 3*x^4 + x^8)),x]","-\frac{1}{3 x^3}-\frac{\sqrt[4]{\frac{1}{2} \left(843-377 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\left(3+\sqrt{5}\right)^{7/4} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{\frac{1}{2} \left(843-377 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\left(3+\sqrt{5}\right)^{7/4} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4\ 2^{3/4} \sqrt{5}}","-\frac{1}{3 x^3}-\frac{\sqrt[4]{\frac{1}{2} \left(843-377 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\left(3+\sqrt{5}\right)^{7/4} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4\ 2^{3/4} \sqrt{5}}-\frac{\sqrt[4]{\frac{1}{2} \left(843-377 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\left(3+\sqrt{5}\right)^{7/4} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{4\ 2^{3/4} \sqrt{5}}",1,"-1/(3*x^3) - (((843 - 377*Sqrt[5])/2)^(1/4)*ArcTan[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*Sqrt[5]) + ((3 + Sqrt[5])^(7/4)*ArcTan[((3 + Sqrt[5])/2)^(1/4)*x])/(4*2^(3/4)*Sqrt[5]) - (((843 - 377*Sqrt[5])/2)^(1/4)*ArcTanh[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*Sqrt[5]) + ((3 + Sqrt[5])^(7/4)*ArcTanh[((3 + Sqrt[5])/2)^(1/4)*x])/(4*2^(3/4)*Sqrt[5])","A",8,5,16,0.3125,1,"{1368, 1422, 212, 206, 203}"
403,1,173,0,0.1402604,"\int \frac{1}{x^6 \left(1-3 x^4+x^8\right)} \, dx","Int[1/(x^6*(1 - 3*x^4 + x^8)),x]","-\frac{1}{5 x^5}-\frac{3}{x}+\frac{\sqrt[4]{2889-1292 \sqrt{5}} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{2889+1292 \sqrt{5}} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{2889-1292 \sqrt{5}} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{2889+1292 \sqrt{5}} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}","-\frac{1}{5 x^5}-\frac{3}{x}+\frac{\sqrt[4]{2889-1292 \sqrt{5}} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{2889+1292 \sqrt{5}} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{2889-1292 \sqrt{5}} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{2889+1292 \sqrt{5}} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}",1,"-1/(5*x^5) - 3/x + ((2889 - 1292*Sqrt[5])^(1/4)*ArcTan[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*Sqrt[5]) - ((2889 + 1292*Sqrt[5])^(1/4)*ArcTan[((3 + Sqrt[5])/2)^(1/4)*x])/(2*Sqrt[5]) - ((2889 - 1292*Sqrt[5])^(1/4)*ArcTanh[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*Sqrt[5]) + ((2889 + 1292*Sqrt[5])^(1/4)*ArcTanh[((3 + Sqrt[5])/2)^(1/4)*x])/(2*Sqrt[5])","A",9,6,16,0.3750,1,"{1368, 1504, 1510, 298, 203, 206}"
404,1,189,0,0.1627223,"\int \frac{1}{x^8 \left(1-3 x^4+x^8\right)} \, dx","Int[1/(x^8*(1 - 3*x^4 + x^8)),x]","-\frac{1}{x^3}-\frac{1}{7 x^7}-\frac{\sqrt[4]{\frac{1}{2} \left(39603-17711 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(39603+17711 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{\frac{1}{2} \left(39603-17711 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(39603+17711 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}","-\frac{1}{x^3}-\frac{1}{7 x^7}-\frac{\sqrt[4]{\frac{1}{2} \left(39603-17711 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(39603+17711 \sqrt{5}\right)} \tan ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}-\frac{\sqrt[4]{\frac{1}{2} \left(39603-17711 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{2}{3+\sqrt{5}}} x\right)}{2 \sqrt{5}}+\frac{\sqrt[4]{\frac{1}{2} \left(39603+17711 \sqrt{5}\right)} \tanh ^{-1}\left(\sqrt[4]{\frac{1}{2} \left(3+\sqrt{5}\right)} x\right)}{2 \sqrt{5}}",1,"-1/(7*x^7) - x^(-3) - (((39603 - 17711*Sqrt[5])/2)^(1/4)*ArcTan[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*Sqrt[5]) + (((39603 + 17711*Sqrt[5])/2)^(1/4)*ArcTan[((3 + Sqrt[5])/2)^(1/4)*x])/(2*Sqrt[5]) - (((39603 - 17711*Sqrt[5])/2)^(1/4)*ArcTanh[(2/(3 + Sqrt[5]))^(1/4)*x])/(2*Sqrt[5]) + (((39603 + 17711*Sqrt[5])/2)^(1/4)*ArcTanh[((3 + Sqrt[5])/2)^(1/4)*x])/(2*Sqrt[5])","A",9,6,16,0.3750,1,"{1368, 1504, 1422, 212, 206, 203}"
405,1,21,0,0.0127365,"\int \frac{x^3}{2+3 x^4+x^8} \, dx","Int[x^3/(2 + 3*x^4 + x^8),x]","\frac{1}{4} \log \left(x^4+1\right)-\frac{1}{4} \log \left(x^4+2\right)","\frac{1}{4} \log \left(x^4+1\right)-\frac{1}{4} \log \left(x^4+2\right)",1,"Log[1 + x^4]/4 - Log[2 + x^4]/4","A",4,3,16,0.1875,1,"{1352, 616, 31}"
406,1,26,0,0.0189562,"\int \frac{x^{11}}{2+3 x^4+x^8} \, dx","Int[x^11/(2 + 3*x^4 + x^8),x]","\frac{x^4}{4}+\frac{1}{4} \log \left(x^4+1\right)-\log \left(x^4+2\right)","\frac{x^4}{4}+\frac{1}{4} \log \left(x^4+1\right)-\log \left(x^4+2\right)",1,"x^4/4 + Log[1 + x^4]/4 - Log[2 + x^4]","A",5,4,16,0.2500,1,"{1357, 703, 632, 31}"
407,1,37,0,0.0342108,"\int \frac{x^9}{2+x^5+x^{10}} \, dx","Int[x^9/(2 + x^5 + x^10),x]","\frac{1}{10} \log \left(x^{10}+x^5+2\right)-\frac{\tan ^{-1}\left(\frac{2 x^5+1}{\sqrt{7}}\right)}{5 \sqrt{7}}","\frac{1}{10} \log \left(x^{10}+x^5+2\right)-\frac{\tan ^{-1}\left(\frac{2 x^5+1}{\sqrt{7}}\right)}{5 \sqrt{7}}",1,"-ArcTan[(1 + 2*x^5)/Sqrt[7]]/(5*Sqrt[7]) + Log[2 + x^5 + x^10]/10","A",5,5,14,0.3571,1,"{1357, 634, 618, 204, 628}"
408,1,23,0,0.0218787,"\int \frac{x^4}{2+x^5+x^{10}} \, dx","Int[x^4/(2 + x^5 + x^10),x]","\frac{2 \tan ^{-1}\left(\frac{2 x^5+1}{\sqrt{7}}\right)}{5 \sqrt{7}}","\frac{2 \tan ^{-1}\left(\frac{2 x^5+1}{\sqrt{7}}\right)}{5 \sqrt{7}}",1,"(2*ArcTan[(1 + 2*x^5)/Sqrt[7]])/(5*Sqrt[7])","A",3,3,14,0.2143,1,"{1352, 618, 204}"
409,1,39,0,0.0353901,"\int \frac{1}{x \left(1+x^5+x^{10}\right)} \, dx","Int[1/(x*(1 + x^5 + x^10)),x]","-\frac{1}{10} \log \left(x^{10}+x^5+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^5+1}{\sqrt{3}}\right)}{5 \sqrt{3}}+\log (x)","-\frac{1}{10} \log \left(x^{10}+x^5+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^5+1}{\sqrt{3}}\right)}{5 \sqrt{3}}+\log (x)",1,"-ArcTan[(1 + 2*x^5)/Sqrt[3]]/(5*Sqrt[3]) + Log[x] - Log[1 + x^5 + x^10]/10","A",7,7,14,0.5000,1,"{1357, 705, 29, 634, 618, 204, 628}"
410,1,48,0,0.0512029,"\int \frac{1}{x^6 \left(1+x^5+x^{10}\right)} \, dx","Int[1/(x^6*(1 + x^5 + x^10)),x]","-\frac{1}{5 x^5}+\frac{1}{10} \log \left(x^{10}+x^5+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^5+1}{\sqrt{3}}\right)}{5 \sqrt{3}}-\log (x)","-\frac{1}{5 x^5}+\frac{1}{10} \log \left(x^{10}+x^5+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^5+1}{\sqrt{3}}\right)}{5 \sqrt{3}}-\log (x)",1,"-1/(5*x^5) - ArcTan[(1 + 2*x^5)/Sqrt[3]]/(5*Sqrt[3]) - Log[x] + Log[1 + x^5 + x^10]/10","A",8,7,14,0.5000,1,"{1357, 709, 800, 634, 618, 204, 628}"
411,1,39,0,0.0356537,"\int \frac{1}{x+x^6+x^{11}} \, dx","Int[(x + x^6 + x^11)^(-1),x]","-\frac{1}{10} \log \left(x^{10}+x^5+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^5+1}{\sqrt{3}}\right)}{5 \sqrt{3}}+\log (x)","-\frac{1}{10} \log \left(x^{10}+x^5+1\right)-\frac{\tan ^{-1}\left(\frac{2 x^5+1}{\sqrt{3}}\right)}{5 \sqrt{3}}+\log (x)",1,"-ArcTan[(1 + 2*x^5)/Sqrt[3]]/(5*Sqrt[3]) + Log[x] - Log[1 + x^5 + x^10]/10","A",8,8,10,0.8000,1,"{1594, 1357, 705, 29, 634, 618, 204, 628}"
412,1,147,0,0.1365131,"\int \frac{x^3}{c+\frac{a}{x^2}+\frac{b}{x}} \, dx","Int[x^3/(c + a/x^2 + b/x),x]","\frac{\left(a^2 c^2-3 a b^2 c+b^4\right) \log \left(a+b x+c x^2\right)}{2 c^5}+\frac{b \left(5 a^2 c^2-5 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^5 \sqrt{b^2-4 a c}}+\frac{x^2 \left(b^2-a c\right)}{2 c^3}-\frac{b x \left(b^2-2 a c\right)}{c^4}-\frac{b x^3}{3 c^2}+\frac{x^4}{4 c}","\frac{\left(a^2 c^2-3 a b^2 c+b^4\right) \log \left(a+b x+c x^2\right)}{2 c^5}+\frac{b \left(5 a^2 c^2-5 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^5 \sqrt{b^2-4 a c}}+\frac{x^2 \left(b^2-a c\right)}{2 c^3}-\frac{b x \left(b^2-2 a c\right)}{c^4}-\frac{b x^3}{3 c^2}+\frac{x^4}{4 c}",1,"-((b*(b^2 - 2*a*c)*x)/c^4) + ((b^2 - a*c)*x^2)/(2*c^3) - (b*x^3)/(3*c^2) + x^4/(4*c) + (b*(b^4 - 5*a*b^2*c + 5*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^5*Sqrt[b^2 - 4*a*c]) + ((b^4 - 3*a*b^2*c + a^2*c^2)*Log[a + b*x + c*x^2])/(2*c^5)","A",7,6,18,0.3333,1,"{1354, 701, 634, 618, 206, 628}"
413,1,118,0,0.1047794,"\int \frac{x^2}{c+\frac{a}{x^2}+\frac{b}{x}} \, dx","Int[x^2/(c + a/x^2 + b/x),x]","-\frac{\left(2 a^2 c^2-4 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \sqrt{b^2-4 a c}}-\frac{b \left(b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 c^4}+\frac{x \left(b^2-a c\right)}{c^3}-\frac{b x^2}{2 c^2}+\frac{x^3}{3 c}","-\frac{\left(2 a^2 c^2-4 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \sqrt{b^2-4 a c}}-\frac{b \left(b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 c^4}+\frac{x \left(b^2-a c\right)}{c^3}-\frac{b x^2}{2 c^2}+\frac{x^3}{3 c}",1,"((b^2 - a*c)*x)/c^3 - (b*x^2)/(2*c^2) + x^3/(3*c) - ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^4*Sqrt[b^2 - 4*a*c]) - (b*(b^2 - 2*a*c)*Log[a + b*x + c*x^2])/(2*c^4)","A",7,6,18,0.3333,1,"{1354, 701, 634, 618, 206, 628}"
414,1,89,0,0.0861381,"\int \frac{x}{c+\frac{a}{x^2}+\frac{b}{x}} \, dx","Int[x/(c + a/x^2 + b/x),x]","\frac{\left(b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 c^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c}}-\frac{b x}{c^2}+\frac{x^2}{2 c}","\frac{\left(b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 c^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c}}-\frac{b x}{c^2}+\frac{x^2}{2 c}",1,"-((b*x)/c^2) + x^2/(2*c) + (b*(b^2 - 3*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*Sqrt[b^2 - 4*a*c]) + ((b^2 - a*c)*Log[a + b*x + c*x^2])/(2*c^3)","A",7,6,16,0.3750,1,"{1354, 701, 634, 618, 206, 628}"
415,1,70,0,0.0490922,"\int \frac{1}{c+\frac{a}{x^2}+\frac{b}{x}} \, dx","Int[(c + a/x^2 + b/x)^(-1),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{x}{c}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{x}{c}",1,"x/c - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c]) - (b*Log[a + b*x + c*x^2])/(2*c^2)","A",6,6,14,0.4286,1,"{1340, 703, 634, 618, 206, 628}"
416,1,56,0,0.0362539,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right) x} \, dx","Int[1/((c + a/x^2 + b/x)*x),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x+c x^2\right)}{2 c}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x+c x^2\right)}{2 c}",1,"(b*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c*Sqrt[b^2 - 4*a*c]) + Log[a + b*x + c*x^2]/(2*c)","A",5,5,18,0.2778,1,"{1354, 634, 618, 206, 628}"
417,1,36,0,0.0324579,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right) x^2} \, dx","Int[1/((c + a/x^2 + b/x)*x^2),x]","\frac{2 \tanh ^{-1}\left(\frac{\frac{2 a}{x}+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","\frac{2 \tanh ^{-1}\left(\frac{\frac{2 a}{x}+b}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"(2*ArcTanh[(b + (2*a)/x)/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",3,3,18,0.1667,1,"{1352, 618, 206}"
418,1,62,0,0.0476562,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right) x^3} \, dx","Int[1/((c + a/x^2 + b/x)*x^3),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x+c x^2\right)}{2 a}+\frac{\log (x)}{a}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x+c x^2\right)}{2 a}+\frac{\log (x)}{a}",1,"(b*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]) + Log[x]/a - Log[a + b*x + c*x^2]/(2*a)","A",7,7,18,0.3889,1,"{1354, 705, 29, 634, 618, 206, 628}"
419,1,81,0,0.1024174,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right) x^4} \, dx","Int[1/((c + a/x^2 + b/x)*x^4),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x+c x^2\right)}{2 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{a x}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x+c x^2\right)}{2 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{a x}",1,"-(1/(a*x)) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^2*Sqrt[b^2 - 4*a*c]) - (b*Log[x])/a^2 + (b*Log[a + b*x + c*x^2])/(2*a^2)","A",8,7,18,0.3889,1,"{1354, 709, 800, 634, 618, 206, 628}"
420,1,104,0,0.1525419,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right) x^5} \, dx","Int[1/((c + a/x^2 + b/x)*x^5),x]","-\frac{\left(b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 a^3}+\frac{\log (x) \left(b^2-a c\right)}{a^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \sqrt{b^2-4 a c}}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}","-\frac{\left(b^2-a c\right) \log \left(a+b x+c x^2\right)}{2 a^3}+\frac{\log (x) \left(b^2-a c\right)}{a^3}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \sqrt{b^2-4 a c}}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + b/(a^2*x) + (b*(b^2 - 3*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^3*Sqrt[b^2 - 4*a*c]) + ((b^2 - a*c)*Log[x])/a^3 - ((b^2 - a*c)*Log[a + b*x + c*x^2])/(2*a^3)","A",8,7,18,0.3889,1,"{1354, 709, 800, 634, 618, 206, 628}"
421,1,137,0,0.1928001,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right) x^6} \, dx","Int[1/((c + a/x^2 + b/x)*x^6),x]","-\frac{\left(2 a^2 c^2-4 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \sqrt{b^2-4 a c}}+\frac{b \left(b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 a^4}-\frac{b^2-a c}{a^3 x}-\frac{b \log (x) \left(b^2-2 a c\right)}{a^4}+\frac{b}{2 a^2 x^2}-\frac{1}{3 a x^3}","-\frac{\left(2 a^2 c^2-4 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \sqrt{b^2-4 a c}}+\frac{b \left(b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 a^4}-\frac{b^2-a c}{a^3 x}-\frac{b \log (x) \left(b^2-2 a c\right)}{a^4}+\frac{b}{2 a^2 x^2}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) + b/(2*a^2*x^2) - (b^2 - a*c)/(a^3*x) - ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^4*Sqrt[b^2 - 4*a*c]) - (b*(b^2 - 2*a*c)*Log[x])/a^4 + (b*(b^2 - 2*a*c)*Log[a + b*x + c*x^2])/(2*a^4)","A",8,7,18,0.3889,1,"{1354, 709, 800, 634, 618, 206, 628}"
422,1,196,0,0.2047864,"\int \frac{x}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^2} \, dx","Int[x/(c + a/x^2 + b/x)^2,x]","\frac{b \left(30 a^2 c^2-20 a b^2 c+3 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{3/2}}+\frac{x^2 \left(3 b^2-8 a c\right)}{2 c^2 \left(b^2-4 a c\right)}+\frac{\left(3 b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 c^4}-\frac{b x \left(3 b^2-11 a c\right)}{c^3 \left(b^2-4 a c\right)}+\frac{x^4 (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{b x^3}{c \left(b^2-4 a c\right)}","\frac{b \left(30 a^2 c^2-20 a b^2 c+3 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{3/2}}+\frac{x^2 \left(3 b^2-8 a c\right)}{2 c^2 \left(b^2-4 a c\right)}+\frac{\left(3 b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 c^4}-\frac{b x \left(3 b^2-11 a c\right)}{c^3 \left(b^2-4 a c\right)}+\frac{x^4 (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{b x^3}{c \left(b^2-4 a c\right)}",1,"-((b*(3*b^2 - 11*a*c)*x)/(c^3*(b^2 - 4*a*c))) + ((3*b^2 - 8*a*c)*x^2)/(2*c^2*(b^2 - 4*a*c)) - (b*x^3)/(c*(b^2 - 4*a*c)) + (x^4*(2*a + b*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + (b*(3*b^4 - 20*a*b^2*c + 30*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^4*(b^2 - 4*a*c)^(3/2)) + ((3*b^2 - 2*a*c)*Log[a + b*x + c*x^2])/(2*c^4)","A",8,7,16,0.4375,1,"{1354, 738, 800, 634, 618, 206, 628}"
423,1,150,0,0.1481079,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^2} \, dx","Int[(c + a/x^2 + b/x)^(-2),x]","-\frac{2 \left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{2 x \left(b^2-3 a c\right)}{c^2 \left(b^2-4 a c\right)}+\frac{x^3 (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{b x^2}{c \left(b^2-4 a c\right)}-\frac{b \log \left(a+b x+c x^2\right)}{c^3}","-\frac{2 \left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{2 x \left(b^2-3 a c\right)}{c^2 \left(b^2-4 a c\right)}+\frac{x^3 (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{b x^2}{c \left(b^2-4 a c\right)}-\frac{b \log \left(a+b x+c x^2\right)}{c^3}",1,"(2*(b^2 - 3*a*c)*x)/(c^2*(b^2 - 4*a*c)) - (b*x^2)/(c*(b^2 - 4*a*c)) + (x^3*(2*a + b*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) - (2*(b^4 - 6*a*b^2*c + 6*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*(b^2 - 4*a*c)^(3/2)) - (b*Log[a + b*x + c*x^2])/c^3","A",8,7,14,0.5000,1,"{1340, 738, 800, 634, 618, 206, 628}"
424,1,114,0,0.1002897,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^2 x} \, dx","Int[1/((c + a/x^2 + b/x)^2*x),x]","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x^2 (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{b x}{c \left(b^2-4 a c\right)}+\frac{\log \left(a+b x+c x^2\right)}{2 c^2}","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x^2 (2 a+b x)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{b x}{c \left(b^2-4 a c\right)}+\frac{\log \left(a+b x+c x^2\right)}{2 c^2}",1,"-((b*x)/(c*(b^2 - 4*a*c))) + (x^2*(2*a + b*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + (b*(b^2 - 6*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*(b^2 - 4*a*c)^(3/2)) + Log[a + b*x + c*x^2]/(2*c^2)","A",7,7,18,0.3889,1,"{1354, 738, 773, 634, 618, 206, 628}"
425,1,71,0,0.0421379,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^2 x^2} \, dx","Int[1/((c + a/x^2 + b/x)^2*x^2),x]","\frac{\frac{2 a}{x}+b}{\left(b^2-4 a c\right) \left(\frac{a}{x^2}+\frac{b}{x}+c\right)}-\frac{4 a \tanh ^{-1}\left(\frac{\frac{2 a}{x}+b}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","\frac{\frac{2 a}{x}+b}{\left(b^2-4 a c\right) \left(\frac{a}{x^2}+\frac{b}{x}+c\right)}-\frac{4 a \tanh ^{-1}\left(\frac{\frac{2 a}{x}+b}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(b + (2*a)/x)/((b^2 - 4*a*c)*(c + a/x^2 + b/x)) - (4*a*ArcTanh[(b + (2*a)/x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,18,0.2222,1,"{1352, 614, 618, 206}"
426,1,66,0,0.033888,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^2 x^3} \, dx","Int[1/((c + a/x^2 + b/x)^2*x^3),x]","\frac{2 a+b x}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{2 b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","\frac{2 a+b x}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{2 b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(2*a + b*x)/((b^2 - 4*a*c)*(a + b*x + c*x^2)) - (2*b*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,18,0.2222,1,"{1354, 638, 618, 206}"
427,1,66,0,0.032642,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^2 x^4} \, dx","Int[1/((c + a/x^2 + b/x)^2*x^4),x]","\frac{4 c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c x}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{4 c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c x}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-((b + 2*c*x)/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + (4*c*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,18,0.2222,1,"{1354, 614, 618, 206}"
428,1,108,0,0.1447338,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^2 x^5} \, dx","Int[1/((c + a/x^2 + b/x)^2*x^5),x]","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b x+c x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{-2 a c+b^2+b c x}{a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b x+c x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{-2 a c+b^2+b c x}{a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"(b^2 - 2*a*c + b*c*x)/(a*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (b*(b^2 - 6*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^2*(b^2 - 4*a*c)^(3/2)) + Log[x]/a^2 - Log[a + b*x + c*x^2]/(2*a^2)","A",8,7,18,0.3889,1,"{1354, 740, 800, 634, 618, 206, 628}"
429,1,148,0,0.1821219,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^2 x^6} \, dx","Int[1/((c + a/x^2 + b/x)^2*x^6),x]","-\frac{2 \left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{2 \left(b^2-3 a c\right)}{a^2 x \left(b^2-4 a c\right)}+\frac{b \log \left(a+b x+c x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}+\frac{-2 a c+b^2+b c x}{a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","-\frac{2 \left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{2 \left(b^2-3 a c\right)}{a^2 x \left(b^2-4 a c\right)}+\frac{b \log \left(a+b x+c x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}+\frac{-2 a c+b^2+b c x}{a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"(-2*(b^2 - 3*a*c))/(a^2*(b^2 - 4*a*c)*x) + (b^2 - 2*a*c + b*c*x)/(a*(b^2 - 4*a*c)*x*(a + b*x + c*x^2)) - (2*(b^4 - 6*a*b^2*c + 6*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^3*(b^2 - 4*a*c)^(3/2)) - (2*b*Log[x])/a^3 + (b*Log[a + b*x + c*x^2])/a^3","A",8,7,18,0.3889,1,"{1354, 740, 800, 634, 618, 206, 628}"
430,1,202,0,0.2388145,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^2 x^7} \, dx","Int[1/((c + a/x^2 + b/x)^2*x^7),x]","\frac{b \left(30 a^2 c^2-20 a b^2 c+3 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \left(b^2-4 a c\right)^{3/2}}-\frac{3 b^2-8 a c}{2 a^2 x^2 \left(b^2-4 a c\right)}-\frac{\left(3 b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 a^4}+\frac{b \left(3 b^2-11 a c\right)}{a^3 x \left(b^2-4 a c\right)}+\frac{\log (x) \left(3 b^2-2 a c\right)}{a^4}+\frac{-2 a c+b^2+b c x}{a x^2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{b \left(30 a^2 c^2-20 a b^2 c+3 b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \left(b^2-4 a c\right)^{3/2}}-\frac{3 b^2-8 a c}{2 a^2 x^2 \left(b^2-4 a c\right)}-\frac{\left(3 b^2-2 a c\right) \log \left(a+b x+c x^2\right)}{2 a^4}+\frac{b \left(3 b^2-11 a c\right)}{a^3 x \left(b^2-4 a c\right)}+\frac{\log (x) \left(3 b^2-2 a c\right)}{a^4}+\frac{-2 a c+b^2+b c x}{a x^2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-(3*b^2 - 8*a*c)/(2*a^2*(b^2 - 4*a*c)*x^2) + (b*(3*b^2 - 11*a*c))/(a^3*(b^2 - 4*a*c)*x) + (b^2 - 2*a*c + b*c*x)/(a*(b^2 - 4*a*c)*x^2*(a + b*x + c*x^2)) + (b*(3*b^4 - 20*a*b^2*c + 30*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^4*(b^2 - 4*a*c)^(3/2)) + ((3*b^2 - 2*a*c)*Log[x])/a^4 - ((3*b^2 - 2*a*c)*Log[a + b*x + c*x^2])/(2*a^4)","A",8,7,18,0.3889,1,"{1354, 740, 800, 634, 618, 206, 628}"
431,1,238,0,0.291033,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^3} \, dx","Int[(c + a/x^2 + b/x)^(-3),x]","\frac{3 x \left(10 a^2 c^2-7 a b^2 c+b^4\right)}{c^3 \left(b^2-4 a c\right)^2}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{5/2}}-\frac{3 b x^2 \left(b^2-6 a c\right)}{2 c^2 \left(b^2-4 a c\right)^2}+\frac{x^5 (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{x^3 \left(b x \left(b^2-7 a c\right)+a \left(b^2-10 a c\right)\right)}{c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 b \log \left(a+b x+c x^2\right)}{2 c^4}","\frac{3 x \left(10 a^2 c^2-7 a b^2 c+b^4\right)}{c^3 \left(b^2-4 a c\right)^2}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{5/2}}-\frac{3 b x^2 \left(b^2-6 a c\right)}{2 c^2 \left(b^2-4 a c\right)^2}+\frac{x^5 (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{x^3 \left(b x \left(b^2-7 a c\right)+a \left(b^2-10 a c\right)\right)}{c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 b \log \left(a+b x+c x^2\right)}{2 c^4}",1,"(3*(b^4 - 7*a*b^2*c + 10*a^2*c^2)*x)/(c^3*(b^2 - 4*a*c)^2) - (3*b*(b^2 - 6*a*c)*x^2)/(2*c^2*(b^2 - 4*a*c)^2) + (x^5*(2*a + b*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (x^3*(a*(b^2 - 10*a*c) + b*(b^2 - 7*a*c)*x))/(c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^4*(b^2 - 4*a*c)^(5/2)) - (3*b*Log[a + b*x + c*x^2])/(2*c^4)","A",9,8,14,0.5714,1,"{1340, 738, 818, 800, 634, 618, 206, 628}"
432,1,190,0,0.2794203,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^3 x} \, dx","Int[1/((c + a/x^2 + b/x)^3*x),x]","\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{5/2}}-\frac{b x \left(b^2-7 a c\right)}{c^2 \left(b^2-4 a c\right)^2}+\frac{x^4 (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{x^2 \left(b x \left(b^2-10 a c\right)+a \left(b^2-16 a c\right)\right)}{2 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{\log \left(a+b x+c x^2\right)}{2 c^3}","\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{5/2}}-\frac{b x \left(b^2-7 a c\right)}{c^2 \left(b^2-4 a c\right)^2}+\frac{x^4 (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{x^2 \left(b x \left(b^2-10 a c\right)+a \left(b^2-16 a c\right)\right)}{2 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{\log \left(a+b x+c x^2\right)}{2 c^3}",1,"-((b*(b^2 - 7*a*c)*x)/(c^2*(b^2 - 4*a*c)^2)) + (x^4*(2*a + b*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (x^2*(a*(b^2 - 16*a*c) + b*(b^2 - 10*a*c)*x))/(2*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + (b*(b^4 - 10*a*b^2*c + 30*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*(b^2 - 4*a*c)^(5/2)) + Log[a + b*x + c*x^2]/(2*c^3)","A",8,8,18,0.4444,1,"{1354, 738, 818, 773, 634, 618, 206, 628}"
433,1,111,0,0.0665031,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^3 x^2} \, dx","Int[1/((c + a/x^2 + b/x)^3*x^2),x]","\frac{12 a^2 \tanh ^{-1}\left(\frac{\frac{2 a}{x}+b}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}-\frac{3 a \left(\frac{2 a}{x}+b\right)}{\left(b^2-4 a c\right)^2 \left(\frac{a}{x^2}+\frac{b}{x}+c\right)}+\frac{\frac{2 a}{x}+b}{2 \left(b^2-4 a c\right) \left(\frac{a}{x^2}+\frac{b}{x}+c\right)^2}","\frac{12 a^2 \tanh ^{-1}\left(\frac{\frac{2 a}{x}+b}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}-\frac{3 a \left(\frac{2 a}{x}+b\right)}{\left(b^2-4 a c\right)^2 \left(\frac{a}{x^2}+\frac{b}{x}+c\right)}+\frac{\frac{2 a}{x}+b}{2 \left(b^2-4 a c\right) \left(\frac{a}{x^2}+\frac{b}{x}+c\right)^2}",1,"(b + (2*a)/x)/(2*(b^2 - 4*a*c)*(c + a/x^2 + b/x)^2) - (3*a*(b + (2*a)/x))/((b^2 - 4*a*c)^2*(c + a/x^2 + b/x)) + (12*a^2*ArcTanh[(b + (2*a)/x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,4,18,0.2222,1,"{1352, 614, 618, 206}"
434,1,107,0,0.0500256,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^3 x^3} \, dx","Int[1/((c + a/x^2 + b/x)^3*x^3),x]","-\frac{x^3 (b+2 c x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{3 b x (2 a+b x)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{6 a b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","-\frac{x^3 (b+2 c x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{3 b x (2 a+b x)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{6 a b \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"-(x^3*(b + 2*c*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (3*b*x*(2*a + b*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + (6*a*b*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,5,18,0.2778,1,"{1354, 728, 722, 618, 206}"
435,1,115,0,0.0682724,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^3 x^4} \, dx","Int[1/((c + a/x^2 + b/x)^3*x^4),x]","\frac{x (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{x \left(2 a c+b^2\right)+3 a b}{\left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{2 \left(2 a c+b^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","\frac{x (2 a+b x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{x \left(2 a c+b^2\right)+3 a b}{\left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{2 \left(2 a c+b^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"(x*(2*a + b*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (3*a*b + (b^2 + 2*a*c)*x)/((b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (2*(b^2 + 2*a*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,5,18,0.2778,1,"{1354, 738, 638, 618, 206}"
436,1,103,0,0.0412466,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^3 x^5} \, dx","Int[1/((c + a/x^2 + b/x)^3*x^5),x]","\frac{2 a+b x}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{3 b (b+2 c x)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{6 b c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","\frac{2 a+b x}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{3 b (b+2 c x)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{6 b c \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"(2*a + b*x)/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) - (3*b*(b + 2*c*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + (6*b*c*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,5,18,0.2778,1,"{1354, 638, 614, 618, 206}"
437,1,101,0,0.0412279,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^3 x^6} \, dx","Int[1/((c + a/x^2 + b/x)^3*x^6),x]","-\frac{12 c^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{3 c (b+2 c x)}{\left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{b+2 c x}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","-\frac{12 c^2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{3 c (b+2 c x)}{\left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{b+2 c x}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-(b + 2*c*x)/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (3*c*(b + 2*c*x))/((b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (12*c^2*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,4,18,0.2222,1,"{1354, 614, 618, 206}"
438,1,185,0,0.2203151,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^3 x^7} \, dx","Int[1/((c + a/x^2 + b/x)^3*x^7),x]","\frac{16 a^2 c^2+2 b c x \left(b^2-7 a c\right)-15 a b^2 c+2 b^4}{2 a^2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{5/2}}-\frac{\log \left(a+b x+c x^2\right)}{2 a^3}+\frac{\log (x)}{a^3}+\frac{-2 a c+b^2+b c x}{2 a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{16 a^2 c^2+2 b c x \left(b^2-7 a c\right)-15 a b^2 c+2 b^4}{2 a^2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{5/2}}-\frac{\log \left(a+b x+c x^2\right)}{2 a^3}+\frac{\log (x)}{a^3}+\frac{-2 a c+b^2+b c x}{2 a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"(b^2 - 2*a*c + b*c*x)/(2*a*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (2*b^4 - 15*a*b^2*c + 16*a^2*c^2 + 2*b*c*(b^2 - 7*a*c)*x)/(2*a^2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + (b*(b^4 - 10*a*b^2*c + 30*a^2*c^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^3*(b^2 - 4*a*c)^(5/2)) + Log[x]/a^3 - Log[a + b*x + c*x^2]/(2*a^3)","A",9,8,18,0.4444,1,"{1354, 740, 822, 800, 634, 618, 206, 628}"
439,1,239,0,0.277369,"\int \frac{1}{\left(c+\frac{a}{x^2}+\frac{b}{x}\right)^3 x^8} \, dx","Int[1/((c + a/x^2 + b/x)^3*x^8),x]","\frac{20 a^2 c^2+3 b c x \left(b^2-6 a c\right)-20 a b^2 c+3 b^4}{2 a^2 x \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(b^2-5 a c\right) \left(b^2-2 a c\right)}{a^3 x \left(b^2-4 a c\right)^2}+\frac{3 b \log \left(a+b x+c x^2\right)}{2 a^4}-\frac{3 b \log (x)}{a^4}+\frac{-2 a c+b^2+b c x}{2 a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{20 a^2 c^2+3 b c x \left(b^2-6 a c\right)-20 a b^2 c+3 b^4}{2 a^2 x \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(b^2-5 a c\right) \left(b^2-2 a c\right)}{a^3 x \left(b^2-4 a c\right)^2}+\frac{3 b \log \left(a+b x+c x^2\right)}{2 a^4}-\frac{3 b \log (x)}{a^4}+\frac{-2 a c+b^2+b c x}{2 a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"(-3*(b^2 - 5*a*c)*(b^2 - 2*a*c))/(a^3*(b^2 - 4*a*c)^2*x) + (b^2 - 2*a*c + b*c*x)/(2*a*(b^2 - 4*a*c)*x*(a + b*x + c*x^2)^2) + (3*b^4 - 20*a*b^2*c + 20*a^2*c^2 + 3*b*c*(b^2 - 6*a*c)*x)/(2*a^2*(b^2 - 4*a*c)^2*x*(a + b*x + c*x^2)) - (3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^4*(b^2 - 4*a*c)^(5/2)) - (3*b*Log[x])/a^4 + (3*b*Log[a + b*x + c*x^2])/(2*a^4)","A",9,8,18,0.4444,1,"{1354, 740, 822, 800, 634, 618, 206, 628}"
440,1,40,0,0.0223199,"\int \frac{x^2}{15+\frac{2}{x^2}+\frac{13}{x}} \, dx","Int[x^2/(15 + 2/x^2 + 13/x),x]","\frac{x^3}{45}-\frac{13 x^2}{450}+\frac{139 x}{3375}-\frac{16}{567} \log (3 x+2)+\frac{\log (5 x+1)}{4375}","\frac{x^3}{45}-\frac{13 x^2}{450}+\frac{139 x}{3375}-\frac{16}{567} \log (3 x+2)+\frac{\log (5 x+1)}{4375}",1,"(139*x)/3375 - (13*x^2)/450 + x^3/45 - (16*Log[2 + 3*x])/567 + Log[1 + 5*x]/4375","A",6,4,18,0.2222,1,"{1354, 701, 632, 31}"
441,1,33,0,0.0195103,"\int \frac{x}{15+\frac{2}{x^2}+\frac{13}{x}} \, dx","Int[x/(15 + 2/x^2 + 13/x),x]","\frac{x^2}{30}-\frac{13 x}{225}+\frac{8}{189} \log (3 x+2)-\frac{1}{875} \log (5 x+1)","\frac{x^2}{30}-\frac{13 x}{225}+\frac{8}{189} \log (3 x+2)-\frac{1}{875} \log (5 x+1)",1,"(-13*x)/225 + x^2/30 + (8*Log[2 + 3*x])/189 - Log[1 + 5*x]/875","A",6,4,16,0.2500,1,"{1354, 701, 632, 31}"
442,1,26,0,0.0147211,"\int \frac{1}{15+\frac{2}{x^2}+\frac{13}{x}} \, dx","Int[(15 + 2/x^2 + 13/x)^(-1),x]","\frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1)","\frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1)",1,"x/15 - (4*Log[2 + 3*x])/63 + Log[1 + 5*x]/175","A",5,4,14,0.2857,1,"{1340, 703, 632, 31}"
443,1,21,0,0.0112666,"\int \frac{1}{\left(15+\frac{2}{x^2}+\frac{13}{x}\right) x} \, dx","Int[1/((15 + 2/x^2 + 13/x)*x),x]","\frac{2}{21} \log (3 x+2)-\frac{1}{35} \log (5 x+1)","\frac{2}{21} \log (3 x+2)-\frac{1}{35} \log (5 x+1)",1,"(2*Log[2 + 3*x])/21 - Log[1 + 5*x]/35","A",4,3,18,0.1667,1,"{1354, 632, 31}"
444,1,23,0,0.0141307,"\int \frac{1}{\left(15+\frac{2}{x^2}+\frac{13}{x}\right) x^2} \, dx","Int[1/((15 + 2/x^2 + 13/x)*x^2),x]","\frac{1}{7} \log \left(\frac{1}{x}+5\right)-\frac{1}{7} \log \left(\frac{2}{x}+3\right)","\frac{1}{7} \log \left(\frac{1}{x}+5\right)-\frac{1}{7} \log \left(\frac{2}{x}+3\right)",1,"Log[5 + x^(-1)]/7 - Log[3 + 2/x]/7","A",4,3,18,0.1667,1,"{1352, 616, 31}"
445,1,27,0,0.0168466,"\int \frac{1}{\left(15+\frac{2}{x^2}+\frac{13}{x}\right) x^3} \, dx","Int[1/((15 + 2/x^2 + 13/x)*x^3),x]","\frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1)","\frac{\log (x)}{2}+\frac{3}{14} \log (3 x+2)-\frac{5}{7} \log (5 x+1)",1,"Log[x]/2 + (3*Log[2 + 3*x])/14 - (5*Log[1 + 5*x])/7","A",6,5,18,0.2778,1,"{1354, 705, 29, 632, 31}"
446,1,34,0,0.0314264,"\int \frac{1}{\left(15+\frac{2}{x^2}+\frac{13}{x}\right) x^4} \, dx","Int[1/((15 + 2/x^2 + 13/x)*x^4),x]","-\frac{1}{2 x}-\frac{13 \log (x)}{4}-\frac{9}{28} \log (3 x+2)+\frac{25}{7} \log (5 x+1)","-\frac{1}{2 x}-\frac{13 \log (x)}{4}-\frac{9}{28} \log (3 x+2)+\frac{25}{7} \log (5 x+1)",1,"-1/(2*x) - (13*Log[x])/4 - (9*Log[2 + 3*x])/28 + (25*Log[1 + 5*x])/7","A",4,3,18,0.1667,1,"{1354, 709, 800}"
447,1,41,0,0.0348749,"\int \frac{1}{\left(15+\frac{2}{x^2}+\frac{13}{x}\right) x^5} \, dx","Int[1/((15 + 2/x^2 + 13/x)*x^5),x]","-\frac{1}{4 x^2}+\frac{13}{4 x}+\frac{139 \log (x)}{8}+\frac{27}{56} \log (3 x+2)-\frac{125}{7} \log (5 x+1)","-\frac{1}{4 x^2}+\frac{13}{4 x}+\frac{139 \log (x)}{8}+\frac{27}{56} \log (3 x+2)-\frac{125}{7} \log (5 x+1)",1,"-1/(4*x^2) + 13/(4*x) + (139*Log[x])/8 + (27*Log[2 + 3*x])/56 - (125*Log[1 + 5*x])/7","A",4,3,18,0.1667,1,"{1354, 709, 800}"
448,1,48,0,0.0423328,"\int \frac{1}{\left(15+\frac{2}{x^2}+\frac{13}{x}\right) x^6} \, dx","Int[1/((15 + 2/x^2 + 13/x)*x^6),x]","\frac{13}{8 x^2}-\frac{1}{6 x^3}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1)","\frac{13}{8 x^2}-\frac{1}{6 x^3}-\frac{139}{8 x}-\frac{1417 \log (x)}{16}-\frac{81}{112} \log (3 x+2)+\frac{625}{7} \log (5 x+1)",1,"-1/(6*x^3) + 13/(8*x^2) - 139/(8*x) - (1417*Log[x])/16 - (81*Log[2 + 3*x])/112 + (625*Log[1 + 5*x])/7","A",4,3,18,0.1667,1,"{1354, 709, 800}"
449,1,204,0,0.2306793,"\int \left(a+\frac{c}{x^2}+\frac{b}{x}\right)^{5/2} \, dx","Int[(a + c/x^2 + b/x)^(5/2),x]","\frac{5 \left(-48 a^2 c^2-24 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+\frac{2 c}{x}}{2 \sqrt{c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{128 c^{3/2}}+\frac{5}{2} a^{3/2} b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)-\frac{5 \left(\frac{2 c \left(12 a c+b^2\right)}{x}+b \left(44 a c+b^2\right)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}{64 c}+x \left(a+\frac{b}{x}+\frac{c}{x^2}\right)^{5/2}-\frac{5}{24} \left(7 b+\frac{6 c}{x}\right) \left(a+\frac{b}{x}+\frac{c}{x^2}\right)^{3/2}","\frac{5 \left(-48 a^2 c^2-24 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+\frac{2 c}{x}}{2 \sqrt{c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{128 c^{3/2}}+\frac{5}{2} a^{3/2} b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)-\frac{5 \left(\frac{2 c \left(12 a c+b^2\right)}{x}+b \left(44 a c+b^2\right)\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}{64 c}+x \left(a+\frac{b}{x}+\frac{c}{x^2}\right)^{5/2}-\frac{5}{24} \left(7 b+\frac{6 c}{x}\right) \left(a+\frac{b}{x}+\frac{c}{x^2}\right)^{3/2}",1,"(-5*(a + c/x^2 + b/x)^(3/2)*(7*b + (6*c)/x))/24 - (5*Sqrt[a + c/x^2 + b/x]*(b*(b^2 + 44*a*c) + (2*c*(b^2 + 12*a*c))/x))/(64*c) + (a + c/x^2 + b/x)^(5/2)*x + (5*a^(3/2)*b*ArcTanh[(2*a + b/x)/(2*Sqrt[a]*Sqrt[a + c/x^2 + b/x])])/2 + (5*(b^4 - 24*a*b^2*c - 48*a^2*c^2)*ArcTanh[(b + (2*c)/x)/(2*Sqrt[c]*Sqrt[a + c/x^2 + b/x])])/(128*c^(3/2))","A",9,7,16,0.4375,1,"{1342, 732, 814, 843, 621, 206, 724}"
450,1,145,0,0.1344514,"\int \left(a+\frac{c}{x^2}+\frac{b}{x}\right)^{3/2} \, dx","Int[(a + c/x^2 + b/x)^(3/2),x]","-\frac{3 \left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{b+\frac{2 c}{x}}{2 \sqrt{c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{8 \sqrt{c}}+x \left(a+\frac{b}{x}+\frac{c}{x^2}\right)^{3/2}-\frac{3}{4} \left(3 b+\frac{2 c}{x}\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}+\frac{3}{2} \sqrt{a} b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)","-\frac{3 \left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{b+\frac{2 c}{x}}{2 \sqrt{c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{8 \sqrt{c}}+x \left(a+\frac{b}{x}+\frac{c}{x^2}\right)^{3/2}-\frac{3}{4} \left(3 b+\frac{2 c}{x}\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}+\frac{3}{2} \sqrt{a} b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)",1,"(-3*Sqrt[a + c/x^2 + b/x]*(3*b + (2*c)/x))/4 + (a + c/x^2 + b/x)^(3/2)*x + (3*Sqrt[a]*b*ArcTanh[(2*a + b/x)/(2*Sqrt[a]*Sqrt[a + c/x^2 + b/x])])/2 - (3*(b^2 + 4*a*c)*ArcTanh[(b + (2*c)/x)/(2*Sqrt[c]*Sqrt[a + c/x^2 + b/x])])/(8*Sqrt[c])","A",8,7,16,0.4375,1,"{1342, 732, 814, 843, 621, 206, 724}"
451,1,105,0,0.0827327,"\int \sqrt{a+\frac{c}{x^2}+\frac{b}{x}} \, dx","Int[Sqrt[a + c/x^2 + b/x],x]","x \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}+\frac{b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{2 \sqrt{a}}-\sqrt{c} \tanh ^{-1}\left(\frac{b+\frac{2 c}{x}}{2 \sqrt{c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)","x \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}+\frac{b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{2 \sqrt{a}}-\sqrt{c} \tanh ^{-1}\left(\frac{b+\frac{2 c}{x}}{2 \sqrt{c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)",1,"Sqrt[a + c/x^2 + b/x]*x + (b*ArcTanh[(2*a + b/x)/(2*Sqrt[a]*Sqrt[a + c/x^2 + b/x])])/(2*Sqrt[a]) - Sqrt[c]*ArcTanh[(b + (2*c)/x)/(2*Sqrt[c]*Sqrt[a + c/x^2 + b/x])]","A",7,6,16,0.3750,1,"{1342, 732, 843, 621, 206, 724}"
452,1,67,0,0.0405132,"\int \frac{1}{\sqrt{a+\frac{c}{x^2}+\frac{b}{x}}} \, dx","Int[1/Sqrt[a + c/x^2 + b/x],x]","\frac{x \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}{a}-\frac{b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{2 a^{3/2}}","\frac{x \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}{a}-\frac{b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{2 a^{3/2}}",1,"(Sqrt[a + c/x^2 + b/x]*x)/a - (b*ArcTanh[(2*a + b/x)/(2*Sqrt[a]*Sqrt[a + c/x^2 + b/x])])/(2*a^(3/2))","A",4,4,16,0.2500,1,"{1342, 730, 724, 206}"
453,1,133,0,0.0992594,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right)^{3/2}} \, dx","Int[(a + c/x^2 + b/x)^(-3/2),x]","\frac{x \left(3 b^2-8 a c\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}{a^2 \left(b^2-4 a c\right)}-\frac{3 b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{2 a^{5/2}}-\frac{2 x \left(-2 a c+b^2+\frac{b c}{x}\right)}{a \left(b^2-4 a c\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}","\frac{x \left(3 b^2-8 a c\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}{a^2 \left(b^2-4 a c\right)}-\frac{3 b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{2 a^{5/2}}-\frac{2 x \left(-2 a c+b^2+\frac{b c}{x}\right)}{a \left(b^2-4 a c\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}",1,"((3*b^2 - 8*a*c)*Sqrt[a + c/x^2 + b/x]*x)/(a^2*(b^2 - 4*a*c)) - (2*(b^2 - 2*a*c + (b*c)/x)*x)/(a*(b^2 - 4*a*c)*Sqrt[a + c/x^2 + b/x]) - (3*b*ArcTanh[(2*a + b/x)/(2*Sqrt[a]*Sqrt[a + c/x^2 + b/x])])/(2*a^(5/2))","A",5,5,16,0.3125,1,"{1342, 740, 806, 724, 206}"
454,1,220,0,0.1936865,"\int \frac{1}{\left(a+\frac{c}{x^2}+\frac{b}{x}\right)^{5/2}} \, dx","Int[(a + c/x^2 + b/x)^(-5/2),x]","-\frac{2 x \left(32 a^2 c^2+\frac{b c \left(5 b^2-28 a c\right)}{x}-32 a b^2 c+5 b^4\right)}{3 a^2 \left(b^2-4 a c\right)^2 \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}+\frac{x \left(128 a^2 c^2-100 a b^2 c+15 b^4\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}{3 a^3 \left(b^2-4 a c\right)^2}-\frac{5 b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{2 a^{7/2}}-\frac{2 x \left(-2 a c+b^2+\frac{b c}{x}\right)}{3 a \left(b^2-4 a c\right) \left(a+\frac{b}{x}+\frac{c}{x^2}\right)^{3/2}}","-\frac{2 x \left(32 a^2 c^2+\frac{b c \left(5 b^2-28 a c\right)}{x}-32 a b^2 c+5 b^4\right)}{3 a^2 \left(b^2-4 a c\right)^2 \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}+\frac{x \left(128 a^2 c^2-100 a b^2 c+15 b^4\right) \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}{3 a^3 \left(b^2-4 a c\right)^2}-\frac{5 b \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{2 a^{7/2}}-\frac{2 x \left(-2 a c+b^2+\frac{b c}{x}\right)}{3 a \left(b^2-4 a c\right) \left(a+\frac{b}{x}+\frac{c}{x^2}\right)^{3/2}}",1,"((15*b^4 - 100*a*b^2*c + 128*a^2*c^2)*Sqrt[a + c/x^2 + b/x]*x)/(3*a^3*(b^2 - 4*a*c)^2) - (2*(b^2 - 2*a*c + (b*c)/x)*x)/(3*a*(b^2 - 4*a*c)*(a + c/x^2 + b/x)^(3/2)) - (2*(5*b^4 - 32*a*b^2*c + 32*a^2*c^2 + (b*c*(5*b^2 - 28*a*c))/x)*x)/(3*a^2*(b^2 - 4*a*c)^2*Sqrt[a + c/x^2 + b/x]) - (5*b*ArcTanh[(2*a + b/x)/(2*Sqrt[a]*Sqrt[a + c/x^2 + b/x])])/(2*a^(7/2))","A",6,6,16,0.3750,1,"{1342, 740, 822, 806, 724, 206}"
455,1,73,0,0.0357841,"\int \sqrt{a^2+\frac{b^2}{x^2}+\frac{2 a b}{x}} \, dx","Int[Sqrt[a^2 + b^2/x^2 + (2*a*b)/x],x]","\frac{a x \sqrt{a^2+\frac{2 a b}{x}+\frac{b^2}{x^2}}}{a+\frac{b}{x}}-\frac{b \log \left(\frac{1}{x}\right) \sqrt{a^2+\frac{2 a b}{x}+\frac{b^2}{x^2}}}{a+\frac{b}{x}}","\frac{a x \sqrt{a^2+\frac{2 a b}{x}+\frac{b^2}{x^2}}}{a+\frac{b}{x}}-\frac{b \log \left(\frac{1}{x}\right) \sqrt{a^2+\frac{2 a b}{x}+\frac{b^2}{x^2}}}{a+\frac{b}{x}}",1,"(a*Sqrt[a^2 + b^2/x^2 + (2*a*b)/x]*x)/(a + b/x) - (b*Sqrt[a^2 + b^2/x^2 + (2*a*b)/x]*Log[x^(-1)])/(a + b/x)","A",4,3,22,0.1364,1,"{1342, 646, 43}"
456,1,179,0,0.2912448,"\int \frac{1}{c+\frac{a}{x^4}+\frac{b}{x^2}} \, dx","Int[(c + a/x^4 + b/x^2)^(-1),x]","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x}{c}","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x}{c}",1,"x/c - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,14,0.2857,1,"{1340, 1122, 1166, 205}"
457,1,631,0,1.1698362,"\int \frac{1}{c+\frac{a}{x^6}+\frac{b}{x^3}} \, dx","Int[(c + a/x^6 + b/x^3)^(-1),x]","\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{x}{c}","\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(-\sqrt[3]{2} \sqrt[3]{c} x \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^2\right)}{6 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x\right)}{3 \sqrt[3]{2} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} c^{4/3} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}+\frac{x}{c}",1,"x/c + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*c^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x)/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(2^(1/3)*Sqrt[3]*c^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3)) - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*c^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x])/(3*2^(1/3)*c^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*c^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x + 2^(2/3)*c^(2/3)*x^2])/(6*2^(1/3)*c^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3))","A",15,9,14,0.6429,1,"{1340, 1367, 1422, 200, 31, 634, 617, 204, 628}"
458,1,376,0,0.6663613,"\int \frac{1}{c+\frac{a}{x^8}+\frac{b}{x^4}} \, dx","Int[(c + a/x^8 + b/x^4)^(-1),x]","\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{x}{c}","\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{2 \sqrt[4]{2} c^{5/4} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{x}{c}",1,"x/c + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*c^(1/4)*x)/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(2*2^(1/4)*c^(5/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4))","A",9,6,14,0.4286,1,"{1340, 1367, 1422, 212, 208, 205}"
459,1,106,0,0.0915753,"\int \frac{\sqrt{a+b \sqrt{x}+c x}}{x} \, dx","Int[Sqrt[a + b*Sqrt[x] + c*x]/x,x]","2 \sqrt{a+b \sqrt{x}+c x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{2 a+b \sqrt{x}}{2 \sqrt{a} \sqrt{a+b \sqrt{x}+c x}}\right)+\frac{b \tanh ^{-1}\left(\frac{b+2 c \sqrt{x}}{2 \sqrt{c} \sqrt{a+b \sqrt{x}+c x}}\right)}{\sqrt{c}}","2 \sqrt{a+b \sqrt{x}+c x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{2 a+b \sqrt{x}}{2 \sqrt{a} \sqrt{a+b \sqrt{x}+c x}}\right)+\frac{b \tanh ^{-1}\left(\frac{b+2 c \sqrt{x}}{2 \sqrt{c} \sqrt{a+b \sqrt{x}+c x}}\right)}{\sqrt{c}}",1,"2*Sqrt[a + b*Sqrt[x] + c*x] - 2*Sqrt[a]*ArcTanh[(2*a + b*Sqrt[x])/(2*Sqrt[a]*Sqrt[a + b*Sqrt[x] + c*x])] + (b*ArcTanh[(b + 2*c*Sqrt[x])/(2*Sqrt[c]*Sqrt[a + b*Sqrt[x] + c*x])])/Sqrt[c]","A",7,6,20,0.3000,1,"{1357, 734, 843, 621, 206, 724}"
460,1,40,0,0.019456,"\int \left(\frac{b^2}{4 c}+b \sqrt{x}+c x\right)^2 \, dx","Int[(b^2/(4*c) + b*Sqrt[x] + c*x)^2,x]","\frac{\left(b+2 c \sqrt{x}\right)^6}{192 c^4}-\frac{b \left(b+2 c \sqrt{x}\right)^5}{160 c^4}","\frac{\left(b+2 c \sqrt{x}\right)^6}{192 c^4}-\frac{b \left(b+2 c \sqrt{x}\right)^5}{160 c^4}",1,"-(b*(b + 2*c*Sqrt[x])^5)/(160*c^4) + (b + 2*c*Sqrt[x])^6/(192*c^4)","A",4,3,23,0.1304,1,"{28, 190, 43}"
461,1,75,0,0.039791,"\int \frac{1}{\sqrt{a^2+2 a b \sqrt{x}+b^2 x}} \, dx","Int[1/Sqrt[a^2 + 2*a*b*Sqrt[x] + b^2*x],x]","\frac{2 \sqrt{a^2+2 a b \sqrt{x}+b^2 x}}{b^2}-\frac{2 a \left(a+b \sqrt{x}\right) \log \left(a+b \sqrt{x}\right)}{b^2 \sqrt{a^2+2 a b \sqrt{x}+b^2 x}}","\frac{2 \sqrt{a^2+2 a b \sqrt{x}+b^2 x}}{b^2}-\frac{2 a \left(a+b \sqrt{x}\right) \log \left(a+b \sqrt{x}\right)}{b^2 \sqrt{a^2+2 a b \sqrt{x}+b^2 x}}",1,"(2*Sqrt[a^2 + 2*a*b*Sqrt[x] + b^2*x])/b^2 - (2*a*(a + b*Sqrt[x])*Log[a + b*Sqrt[x]])/(b^2*Sqrt[a^2 + 2*a*b*Sqrt[x] + b^2*x])","A",4,4,22,0.1818,1,"{1341, 640, 608, 31}"
462,1,137,0,0.0812464,"\int \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^{7/2} \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^(7/2),x]","\frac{3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^9}{10 b^3}-\frac{2 a \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^8}{3 b^3}+\frac{3 a^2 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^7}{8 b^3}","\frac{3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^9}{10 b^3}-\frac{2 a \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^8}{3 b^3}+\frac{3 a^2 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^7}{8 b^3}",1,"(3*a^2*(a + b*x^(1/3))^7*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])/(8*b^3) - (2*a*(a + b*x^(1/3))^8*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])/(3*b^3) + (3*(a + b*x^(1/3))^9*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])/(10*b^3)","A",4,3,26,0.1154,1,"{1341, 646, 43}"
463,1,137,0,0.0706979,"\int \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^{5/2} \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^(5/2),x]","\frac{3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^7}{8 b^3}-\frac{6 a \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^6}{7 b^3}+\frac{a^2 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^5}{2 b^3}","\frac{3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^7}{8 b^3}-\frac{6 a \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^6}{7 b^3}+\frac{a^2 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^5}{2 b^3}",1,"(a^2*(a + b*x^(1/3))^5*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])/(2*b^3) - (6*a*(a + b*x^(1/3))^6*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])/(7*b^3) + (3*(a + b*x^(1/3))^7*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])/(8*b^3)","A",4,3,26,0.1154,1,"{1341, 646, 43}"
464,1,137,0,0.0558239,"\int \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^{3/2} \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^(3/2),x]","\frac{\sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^5}{2 b^3}-\frac{6 a \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^4}{5 b^3}+\frac{3 a^2 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^3}{4 b^3}","\frac{\sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^5}{2 b^3}-\frac{6 a \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^4}{5 b^3}+\frac{3 a^2 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \left(a+b \sqrt[3]{x}\right)^3}{4 b^3}",1,"(3*a^2*(a + b*x^(1/3))^3*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])/(4*b^3) - (6*a*(a + b*x^(1/3))^4*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])/(5*b^3) + ((a + b*x^(1/3))^5*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])/(2*b^3)","A",3,2,26,0.07692,1,"{1341, 645}"
465,1,88,0,0.0398336,"\int \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}} \, dx","Int[Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)],x]","\frac{3 b x^{4/3} \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}{4 \left(a+b \sqrt[3]{x}\right)}+\frac{a x \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}{a+b \sqrt[3]{x}}","\frac{3 b x^{4/3} \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}{4 \left(a+b \sqrt[3]{x}\right)}+\frac{a x \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}{a+b \sqrt[3]{x}}",1,"(a*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]*x)/(a + b*x^(1/3)) + (3*b*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]*x^(4/3))/(4*(a + b*x^(1/3)))","A",4,3,26,0.1154,1,"{1341, 646, 43}"
466,1,147,0,0.0703464,"\int \frac{1}{\sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}} \, dx","Int[1/Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)],x]","-\frac{3 a \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{b^2 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{3 x^{2/3} \left(a+b \sqrt[3]{x}\right)}{2 b \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{3 a^2 \left(a+b \sqrt[3]{x}\right) \log \left(a+b \sqrt[3]{x}\right)}{b^3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}","-\frac{3 a \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{b^2 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{3 x^{2/3} \left(a+b \sqrt[3]{x}\right)}{2 b \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{3 a^2 \left(a+b \sqrt[3]{x}\right) \log \left(a+b \sqrt[3]{x}\right)}{b^3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}",1,"(-3*a*(a + b*x^(1/3))*x^(1/3))/(b^2*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) + (3*(a + b*x^(1/3))*x^(2/3))/(2*b*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) + (3*a^2*(a + b*x^(1/3))*Log[a + b*x^(1/3)])/(b^3*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])","A",4,3,26,0.1154,1,"{1341, 646, 43}"
467,1,130,0,0.0720178,"\int \frac{1}{\left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^(-3/2),x]","-\frac{3 a^2}{2 b^3 \left(a+b \sqrt[3]{x}\right) \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{6 a}{b^3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{3 \left(a+b \sqrt[3]{x}\right) \log \left(a+b \sqrt[3]{x}\right)}{b^3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}","-\frac{3 a^2}{2 b^3 \left(a+b \sqrt[3]{x}\right) \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{6 a}{b^3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{3 \left(a+b \sqrt[3]{x}\right) \log \left(a+b \sqrt[3]{x}\right)}{b^3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}",1,"(6*a)/(b^3*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) - (3*a^2)/(2*b^3*(a + b*x^(1/3))*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) + (3*(a + b*x^(1/3))*Log[a + b*x^(1/3)])/(b^3*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])","A",4,3,26,0.1154,1,"{1341, 646, 43}"
468,1,135,0,0.0746981,"\int \frac{1}{\left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^(-5/2),x]","-\frac{3 a^2}{4 b^3 \left(a+b \sqrt[3]{x}\right)^3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{2 a}{b^3 \left(a+b \sqrt[3]{x}\right)^2 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}-\frac{3}{2 b^3 \left(a+b \sqrt[3]{x}\right) \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}","-\frac{3 a^2}{4 b^3 \left(a+b \sqrt[3]{x}\right)^3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{2 a}{b^3 \left(a+b \sqrt[3]{x}\right)^2 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}-\frac{3}{2 b^3 \left(a+b \sqrt[3]{x}\right) \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}",1,"(-3*a^2)/(4*b^3*(a + b*x^(1/3))^3*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) + (2*a)/(b^3*(a + b*x^(1/3))^2*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) - 3/(2*b^3*(a + b*x^(1/3))*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])","A",4,3,26,0.1154,1,"{1341, 646, 43}"
469,1,137,0,0.0779012,"\int \frac{1}{\left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^{7/2}} \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^(-7/2),x]","-\frac{a^2}{2 b^3 \left(a+b \sqrt[3]{x}\right)^5 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{6 a}{5 b^3 \left(a+b \sqrt[3]{x}\right)^4 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}-\frac{3}{4 b^3 \left(a+b \sqrt[3]{x}\right)^3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}","-\frac{a^2}{2 b^3 \left(a+b \sqrt[3]{x}\right)^5 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{6 a}{5 b^3 \left(a+b \sqrt[3]{x}\right)^4 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}-\frac{3}{4 b^3 \left(a+b \sqrt[3]{x}\right)^3 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}",1,"-a^2/(2*b^3*(a + b*x^(1/3))^5*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) + (6*a)/(5*b^3*(a + b*x^(1/3))^4*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) - 3/(4*b^3*(a + b*x^(1/3))^3*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])","A",4,3,26,0.1154,1,"{1341, 646, 43}"
470,1,137,0,0.0787639,"\int \frac{1}{\left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^{9/2}} \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^(-9/2),x]","-\frac{3 a^2}{8 b^3 \left(a+b \sqrt[3]{x}\right)^7 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{6 a}{7 b^3 \left(a+b \sqrt[3]{x}\right)^6 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}-\frac{1}{2 b^3 \left(a+b \sqrt[3]{x}\right)^5 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}","-\frac{3 a^2}{8 b^3 \left(a+b \sqrt[3]{x}\right)^7 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{6 a}{7 b^3 \left(a+b \sqrt[3]{x}\right)^6 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}-\frac{1}{2 b^3 \left(a+b \sqrt[3]{x}\right)^5 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}",1,"(-3*a^2)/(8*b^3*(a + b*x^(1/3))^7*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) + (6*a)/(7*b^3*(a + b*x^(1/3))^6*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) - 1/(2*b^3*(a + b*x^(1/3))^5*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])","A",4,3,26,0.1154,1,"{1341, 646, 43}"
471,1,137,0,0.0780041,"\int \frac{1}{\left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^{11/2}} \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^(-11/2),x]","-\frac{3 a^2}{10 b^3 \left(a+b \sqrt[3]{x}\right)^9 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{2 a}{3 b^3 \left(a+b \sqrt[3]{x}\right)^8 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}-\frac{3}{8 b^3 \left(a+b \sqrt[3]{x}\right)^7 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}","-\frac{3 a^2}{10 b^3 \left(a+b \sqrt[3]{x}\right)^9 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}+\frac{2 a}{3 b^3 \left(a+b \sqrt[3]{x}\right)^8 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}-\frac{3}{8 b^3 \left(a+b \sqrt[3]{x}\right)^7 \sqrt{a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}}}",1,"(-3*a^2)/(10*b^3*(a + b*x^(1/3))^9*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) + (2*a)/(3*b^3*(a + b*x^(1/3))^8*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)]) - 3/(8*b^3*(a + b*x^(1/3))^7*Sqrt[a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3)])","A",4,3,26,0.1154,1,"{1341, 646, 43}"
472,1,77,0,0.0367421,"\int \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p (d x)^m \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p*(d*x)^m,x]","\frac{x (d x)^m \left(\frac{b \sqrt[3]{x}}{a}+1\right)^{-2 p} \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p \, _2F_1\left(3 (m+1),-2 p;3 m+4;-\frac{b \sqrt[3]{x}}{a}\right)}{m+1}","\frac{x (d x)^m \left(\frac{b \sqrt[3]{x}}{a}+1\right)^{-2 p} \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p \, _2F_1\left(3 (m+1),-2 p;3 m+4;-\frac{b \sqrt[3]{x}}{a}\right)}{m+1}",1,"((a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p*x*(d*x)^m*Hypergeometric2F1[3*(1 + m), -2*p, 4 + 3*m, -((b*x^(1/3))/a)])/((1 + m)*(1 + (b*x^(1/3))/a)^(2*p))","A",4,4,30,0.1333,1,"{1356, 343, 341, 64}"
473,1,468,0,0.224245,"\int \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p x^2 \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p*x^2,x]","\frac{3 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^9 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (2 p+9)}-\frac{12 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^8 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (p+4)}+\frac{84 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^7 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (2 p+7)}-\frac{84 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^6 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (p+3)}+\frac{210 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^5 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (2 p+5)}-\frac{84 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^4 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (p+2)}+\frac{84 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^3 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (2 p+3)}-\frac{12 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^2 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (p+1)}+\frac{3 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (2 p+1)}","\frac{3 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^9 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (2 p+9)}-\frac{12 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^8 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (p+4)}+\frac{84 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^7 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (2 p+7)}-\frac{84 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^6 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (p+3)}+\frac{210 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^5 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (2 p+5)}-\frac{84 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^4 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (p+2)}+\frac{84 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^3 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (2 p+3)}-\frac{12 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^2 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (p+1)}+\frac{3 a^9 \left(\frac{b \sqrt[3]{x}}{a}+1\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^9 (2 p+1)}",1,"(3*a^9*(1 + (b*x^(1/3))/a)*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^9*(1 + 2*p)) - (12*a^9*(1 + (b*x^(1/3))/a)^2*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^9*(1 + p)) + (84*a^9*(1 + (b*x^(1/3))/a)^3*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^9*(3 + 2*p)) - (84*a^9*(1 + (b*x^(1/3))/a)^4*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^9*(2 + p)) + (210*a^9*(1 + (b*x^(1/3))/a)^5*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^9*(5 + 2*p)) - (84*a^9*(1 + (b*x^(1/3))/a)^6*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^9*(3 + p)) + (84*a^9*(1 + (b*x^(1/3))/a)^7*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^9*(7 + 2*p)) - (12*a^9*(1 + (b*x^(1/3))/a)^8*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^9*(4 + p)) + (3*a^9*(1 + (b*x^(1/3))/a)^9*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^9*(9 + 2*p))","A",4,3,28,0.1071,1,"{1356, 266, 43}"
474,1,315,0,0.1396512,"\int \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p x \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p*x,x]","\frac{3 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^6 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{2 b^6 (p+3)}-\frac{15 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^5 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^6 (2 p+5)}+\frac{15 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^4 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^6 (p+2)}-\frac{30 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^3 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^6 (2 p+3)}+\frac{15 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^2 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{2 b^6 (p+1)}-\frac{3 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^6 (2 p+1)}","\frac{3 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^6 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{2 b^6 (p+3)}-\frac{15 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^5 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^6 (2 p+5)}+\frac{15 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^4 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^6 (p+2)}-\frac{30 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^3 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^6 (2 p+3)}+\frac{15 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right)^2 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{2 b^6 (p+1)}-\frac{3 a^6 \left(\frac{b \sqrt[3]{x}}{a}+1\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^6 (2 p+1)}",1,"(-3*a^6*(1 + (b*x^(1/3))/a)*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^6*(1 + 2*p)) + (15*a^6*(1 + (b*x^(1/3))/a)^2*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(2*b^6*(1 + p)) - (30*a^6*(1 + (b*x^(1/3))/a)^3*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^6*(3 + 2*p)) + (15*a^6*(1 + (b*x^(1/3))/a)^4*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^6*(2 + p)) - (15*a^6*(1 + (b*x^(1/3))/a)^5*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^6*(5 + 2*p)) + (3*a^6*(1 + (b*x^(1/3))/a)^6*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(2*b^6*(3 + p))","A",4,3,26,0.1154,1,"{1356, 266, 43}"
475,1,142,0,0.0677279,"\int \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p,x]","\frac{3 \left(a+b \sqrt[3]{x}\right)^3 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^3 (2 p+3)}-\frac{3 a \left(a+b \sqrt[3]{x}\right)^2 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^3 (p+1)}+\frac{3 a^2 \left(a+b \sqrt[3]{x}\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^3 (2 p+1)}","\frac{3 \left(a+b \sqrt[3]{x}\right)^3 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^3 (2 p+3)}-\frac{3 a \left(a+b \sqrt[3]{x}\right)^2 \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^3 (p+1)}+\frac{3 a^2 \left(a+b \sqrt[3]{x}\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{b^3 (2 p+1)}",1,"(3*a^2*(a + b*x^(1/3))*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^3*(1 + 2*p)) - (3*a*(a + b*x^(1/3))^2*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^3*(1 + p)) + (3*(a + b*x^(1/3))^3*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(b^3*(3 + 2*p))","A",4,3,24,0.1250,1,"{1341, 646, 43}"
476,1,69,0,0.0312997,"\int \frac{\left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{x} \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p/x,x]","-\frac{3 \left(\frac{b \sqrt[3]{x}}{a}+1\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p \, _2F_1\left(1,2 p+1;2 (p+1);\frac{\sqrt[3]{x} b}{a}+1\right)}{2 p+1}","-\frac{3 \left(\frac{b \sqrt[3]{x}}{a}+1\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p \, _2F_1\left(1,2 p+1;2 (p+1);\frac{\sqrt[3]{x} b}{a}+1\right)}{2 p+1}",1,"(-3*(1 + (b*x^(1/3))/a)*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p*Hypergeometric2F1[1, 1 + 2*p, 2*(1 + p), 1 + (b*x^(1/3))/a])/(1 + 2*p)","A",3,3,28,0.1071,1,"{1356, 266, 65}"
477,1,75,0,0.0364101,"\int \frac{\left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{x^2} \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p/x^2,x]","\frac{3 b^3 \left(\frac{b \sqrt[3]{x}}{a}+1\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p \, _2F_1\left(4,2 p+1;2 (p+1);\frac{\sqrt[3]{x} b}{a}+1\right)}{a^3 (2 p+1)}","\frac{3 b^3 \left(\frac{b \sqrt[3]{x}}{a}+1\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p \, _2F_1\left(4,2 p+1;2 (p+1);\frac{\sqrt[3]{x} b}{a}+1\right)}{a^3 (2 p+1)}",1,"(3*b^3*(1 + (b*x^(1/3))/a)*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p*Hypergeometric2F1[4, 1 + 2*p, 2*(1 + p), 1 + (b*x^(1/3))/a])/(a^3*(1 + 2*p))","A",3,3,28,0.1071,1,"{1356, 266, 65}"
478,1,162,0,0.0985437,"\int \left(\frac{\left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{x^2}-\frac{2 b^3 (1-2 p) (1-p) p \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{3 a^3 x}\right) \, dx","Int[(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p/x^2 - (2*b^3*(1 - 2*p)*(1 - p)*p*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p)/(3*a^3*x),x]","\frac{2 b^3 (1-2 p) (1-p) p \left(\frac{b \sqrt[3]{x}}{a}+1\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p \, _2F_1\left(1,2 p+1;2 (p+1);\frac{\sqrt[3]{x} b}{a}+1\right)}{a^3 (2 p+1)}+\frac{3 b^3 \left(\frac{b \sqrt[3]{x}}{a}+1\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p \, _2F_1\left(4,2 p+1;2 (p+1);\frac{\sqrt[3]{x} b}{a}+1\right)}{a^3 (2 p+1)}","-\frac{b^2 (1-2 p) (1-p) \left(a+b \sqrt[3]{x}\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{a^3 \sqrt[3]{x}}+\frac{b (1-p) \left(a+b \sqrt[3]{x}\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{a^2 x^{2/3}}-\frac{\left(a+b \sqrt[3]{x}\right) \left(a^2+2 a b \sqrt[3]{x}+b^2 x^{2/3}\right)^p}{a x}",1,"(2*b^3*(1 - 2*p)*(1 - p)*p*(1 + (b*x^(1/3))/a)*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p*Hypergeometric2F1[1, 1 + 2*p, 2*(1 + p), 1 + (b*x^(1/3))/a])/(a^3*(1 + 2*p)) + (3*b^3*(1 + (b*x^(1/3))/a)*(a^2 + 2*a*b*x^(1/3) + b^2*x^(2/3))^p*Hypergeometric2F1[4, 1 + 2*p, 2*(1 + p), 1 + (b*x^(1/3))/a])/(a^3*(1 + 2*p))","C",7,3,77,0.03896,1,"{1356, 266, 65}"
479,1,176,0,0.1037828,"\int \frac{1}{\left(a^2+2 a b \sqrt[4]{x}+b^2 \sqrt{x}\right)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x^(1/4) + b^2*Sqrt[x])^(-3/2),x]","\frac{2 a^3}{b^4 \left(a+b \sqrt[4]{x}\right) \sqrt{a^2+2 a b \sqrt[4]{x}+b^2 \sqrt{x}}}-\frac{12 a^2}{b^4 \sqrt{a^2+2 a b \sqrt[4]{x}+b^2 \sqrt{x}}}+\frac{4 \sqrt[4]{x} \left(a+b \sqrt[4]{x}\right)}{b^3 \sqrt{a^2+2 a b \sqrt[4]{x}+b^2 \sqrt{x}}}-\frac{12 a \left(a+b \sqrt[4]{x}\right) \log \left(a+b \sqrt[4]{x}\right)}{b^4 \sqrt{a^2+2 a b \sqrt[4]{x}+b^2 \sqrt{x}}}","\frac{2 a^3}{b^4 \left(a+b \sqrt[4]{x}\right) \sqrt{a^2+2 a b \sqrt[4]{x}+b^2 \sqrt{x}}}-\frac{12 a^2}{b^4 \sqrt{a^2+2 a b \sqrt[4]{x}+b^2 \sqrt{x}}}+\frac{4 \sqrt[4]{x} \left(a+b \sqrt[4]{x}\right)}{b^3 \sqrt{a^2+2 a b \sqrt[4]{x}+b^2 \sqrt{x}}}-\frac{12 a \left(a+b \sqrt[4]{x}\right) \log \left(a+b \sqrt[4]{x}\right)}{b^4 \sqrt{a^2+2 a b \sqrt[4]{x}+b^2 \sqrt{x}}}",1,"(-12*a^2)/(b^4*Sqrt[a^2 + 2*a*b*x^(1/4) + b^2*Sqrt[x]]) + (2*a^3)/(b^4*(a + b*x^(1/4))*Sqrt[a^2 + 2*a*b*x^(1/4) + b^2*Sqrt[x]]) + (4*(a + b*x^(1/4))*x^(1/4))/(b^3*Sqrt[a^2 + 2*a*b*x^(1/4) + b^2*Sqrt[x]]) - (12*a*(a + b*x^(1/4))*Log[a + b*x^(1/4)])/(b^4*Sqrt[a^2 + 2*a*b*x^(1/4) + b^2*Sqrt[x]])","A",4,3,26,0.1154,1,"{1341, 646, 43}"
480,1,268,0,0.1509195,"\int \frac{1}{\left(a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}\right)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x^(1/6) + b^2*x^(1/3))^(-5/2),x]","\frac{3 a^5}{2 b^6 \left(a+b \sqrt[6]{x}\right)^3 \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}-\frac{10 a^4}{b^6 \left(a+b \sqrt[6]{x}\right)^2 \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}+\frac{30 a^3}{b^6 \left(a+b \sqrt[6]{x}\right) \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}-\frac{60 a^2}{b^6 \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}+\frac{6 \sqrt[6]{x} \left(a+b \sqrt[6]{x}\right)}{b^5 \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}-\frac{30 a \left(a+b \sqrt[6]{x}\right) \log \left(a+b \sqrt[6]{x}\right)}{b^6 \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}","\frac{3 a^5}{2 b^6 \left(a+b \sqrt[6]{x}\right)^3 \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}-\frac{10 a^4}{b^6 \left(a+b \sqrt[6]{x}\right)^2 \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}+\frac{30 a^3}{b^6 \left(a+b \sqrt[6]{x}\right) \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}-\frac{60 a^2}{b^6 \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}+\frac{6 \sqrt[6]{x} \left(a+b \sqrt[6]{x}\right)}{b^5 \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}-\frac{30 a \left(a+b \sqrt[6]{x}\right) \log \left(a+b \sqrt[6]{x}\right)}{b^6 \sqrt{a^2+2 a b \sqrt[6]{x}+b^2 \sqrt[3]{x}}}",1,"(-60*a^2)/(b^6*Sqrt[a^2 + 2*a*b*x^(1/6) + b^2*x^(1/3)]) + (3*a^5)/(2*b^6*(a + b*x^(1/6))^3*Sqrt[a^2 + 2*a*b*x^(1/6) + b^2*x^(1/3)]) - (10*a^4)/(b^6*(a + b*x^(1/6))^2*Sqrt[a^2 + 2*a*b*x^(1/6) + b^2*x^(1/3)]) + (30*a^3)/(b^6*(a + b*x^(1/6))*Sqrt[a^2 + 2*a*b*x^(1/6) + b^2*x^(1/3)]) + (6*(a + b*x^(1/6))*x^(1/6))/(b^5*Sqrt[a^2 + 2*a*b*x^(1/6) + b^2*x^(1/3)]) - (30*a*(a + b*x^(1/6))*Log[a + b*x^(1/6)])/(b^6*Sqrt[a^2 + 2*a*b*x^(1/6) + b^2*x^(1/3)])","A",4,3,26,0.1154,1,"{1341, 646, 43}"
481,1,179,0,0.0922638,"\int \left(a^2+\frac{b^2}{x}+\frac{2 a b}{\sqrt{x}}\right)^{3/2} \, dx","Int[(a^2 + b^2/x + (2*a*b)/Sqrt[x])^(3/2),x]","\frac{a^3 x \sqrt{a^2+\frac{2 a b}{\sqrt{x}}+\frac{b^2}{x}}}{a+\frac{b}{\sqrt{x}}}+\frac{6 a^2 b \sqrt{x} \sqrt{a^2+\frac{2 a b}{\sqrt{x}}+\frac{b^2}{x}}}{a+\frac{b}{\sqrt{x}}}-\frac{2 b^3 \sqrt{a^2+\frac{2 a b}{\sqrt{x}}+\frac{b^2}{x}}}{\sqrt{x} \left(a+\frac{b}{\sqrt{x}}\right)}+\frac{6 a b^2 \log \left(\sqrt{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt{x}}+\frac{b^2}{x}}}{a+\frac{b}{\sqrt{x}}}","\frac{a^3 x \sqrt{a^2+\frac{2 a b}{\sqrt{x}}+\frac{b^2}{x}}}{a+\frac{b}{\sqrt{x}}}+\frac{6 a^2 b \sqrt{x} \sqrt{a^2+\frac{2 a b}{\sqrt{x}}+\frac{b^2}{x}}}{a+\frac{b}{\sqrt{x}}}-\frac{2 b^3 \sqrt{a^2+\frac{2 a b}{\sqrt{x}}+\frac{b^2}{x}}}{\sqrt{x} \left(a+\frac{b}{\sqrt{x}}\right)}+\frac{6 a b^2 \log \left(\sqrt{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt{x}}+\frac{b^2}{x}}}{a+\frac{b}{\sqrt{x}}}",1,"(-2*b^3*Sqrt[a^2 + b^2/x + (2*a*b)/Sqrt[x]])/((a + b/Sqrt[x])*Sqrt[x]) + (6*a^2*b*Sqrt[a^2 + b^2/x + (2*a*b)/Sqrt[x]]*Sqrt[x])/(a + b/Sqrt[x]) + (a^3*Sqrt[a^2 + b^2/x + (2*a*b)/Sqrt[x]]*x)/(a + b/Sqrt[x]) + (6*a*b^2*Sqrt[a^2 + b^2/x + (2*a*b)/Sqrt[x]]*Log[Sqrt[x]])/(a + b/Sqrt[x])","A",5,4,24,0.1667,1,"{1341, 1355, 263, 43}"
482,1,391,0,0.1871713,"\int \left(a^2+\frac{b^2}{x^{2/3}}+\frac{2 a b}{\sqrt[3]{x}}\right)^{7/2} \, dx","Int[(a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3))^(7/2),x]","\frac{a^7 x \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}+\frac{21 a^6 b x^{2/3} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{63 a^5 b^2 \sqrt[3]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}-\frac{105 a^3 b^4 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{\sqrt[3]{x} \left(a+\frac{b}{\sqrt[3]{x}}\right)}-\frac{63 a^2 b^5 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 x^{2/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}-\frac{7 a b^6 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{x \left(a+\frac{b}{\sqrt[3]{x}}\right)}-\frac{3 b^7 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{4 x^{4/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{105 a^4 b^3 \log \left(\sqrt[3]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}","\frac{a^7 x \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}+\frac{21 a^6 b x^{2/3} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{63 a^5 b^2 \sqrt[3]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}-\frac{105 a^3 b^4 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{\sqrt[3]{x} \left(a+\frac{b}{\sqrt[3]{x}}\right)}-\frac{63 a^2 b^5 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 x^{2/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}-\frac{7 a b^6 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{x \left(a+\frac{b}{\sqrt[3]{x}}\right)}-\frac{3 b^7 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{4 x^{4/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{105 a^4 b^3 \log \left(\sqrt[3]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}",1,"(-3*b^7*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)])/(4*(a + b/x^(1/3))*x^(4/3)) - (7*a*b^6*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)])/((a + b/x^(1/3))*x) - (63*a^2*b^5*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)])/(2*(a + b/x^(1/3))*x^(2/3)) - (105*a^3*b^4*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)])/((a + b/x^(1/3))*x^(1/3)) + (63*a^5*b^2*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*x^(1/3))/(a + b/x^(1/3)) + (21*a^6*b*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*x^(2/3))/(2*(a + b/x^(1/3))) + (a^7*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*x)/(a + b/x^(1/3)) + (105*a^4*b^3*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*Log[x^(1/3)])/(a + b/x^(1/3))","A",5,4,26,0.1538,1,"{1341, 1355, 263, 43}"
483,1,291,0,0.1373369,"\int \left(a^2+\frac{b^2}{x^{2/3}}+\frac{2 a b}{\sqrt[3]{x}}\right)^{5/2} \, dx","Int[(a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3))^(5/2),x]","\frac{a^5 x \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}+\frac{15 a^4 b x^{2/3} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{30 a^3 b^2 \sqrt[3]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}-\frac{15 a b^4 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{\sqrt[3]{x} \left(a+\frac{b}{\sqrt[3]{x}}\right)}-\frac{3 b^5 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 x^{2/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{30 a^2 b^3 \log \left(\sqrt[3]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}","\frac{a^5 x \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}+\frac{15 a^4 b x^{2/3} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{30 a^3 b^2 \sqrt[3]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}-\frac{15 a b^4 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{\sqrt[3]{x} \left(a+\frac{b}{\sqrt[3]{x}}\right)}-\frac{3 b^5 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 x^{2/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{30 a^2 b^3 \log \left(\sqrt[3]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}",1,"(-3*b^5*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)])/(2*(a + b/x^(1/3))*x^(2/3)) - (15*a*b^4*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)])/((a + b/x^(1/3))*x^(1/3)) + (30*a^3*b^2*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*x^(1/3))/(a + b/x^(1/3)) + (15*a^4*b*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*x^(2/3))/(2*(a + b/x^(1/3))) + (a^5*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*x)/(a + b/x^(1/3)) + (30*a^2*b^3*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*Log[x^(1/3)])/(a + b/x^(1/3))","A",5,4,26,0.1538,1,"{1341, 1355, 263, 43}"
484,1,189,0,0.0906669,"\int \left(a^2+\frac{b^2}{x^{2/3}}+\frac{2 a b}{\sqrt[3]{x}}\right)^{3/2} \, dx","Int[(a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3))^(3/2),x]","\frac{a^3 x \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}+\frac{9 a^2 b x^{2/3} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{9 a b^2 \sqrt[3]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}+\frac{3 b^3 \log \left(\sqrt[3]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}","\frac{a^3 x \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}+\frac{9 a^2 b x^{2/3} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{9 a b^2 \sqrt[3]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}+\frac{3 b^3 \log \left(\sqrt[3]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}",1,"(9*a*b^2*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*x^(1/3))/(a + b/x^(1/3)) + (9*a^2*b*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*x^(2/3))/(2*(a + b/x^(1/3))) + (a^3*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*x)/(a + b/x^(1/3)) + (3*b^3*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*Log[x^(1/3)])/(a + b/x^(1/3))","A",5,4,26,0.1538,1,"{1341, 1355, 263, 43}"
485,1,88,0,0.0525367,"\int \sqrt{a^2+\frac{b^2}{x^{2/3}}+\frac{2 a b}{\sqrt[3]{x}}} \, dx","Int[Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)],x]","\frac{3 b x^{2/3} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{a x \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}","\frac{3 b x^{2/3} \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{2 \left(a+\frac{b}{\sqrt[3]{x}}\right)}+\frac{a x \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}{a+\frac{b}{\sqrt[3]{x}}}",1,"(3*b*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*x^(2/3))/(2*(a + b/x^(1/3))) + (a*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*x)/(a + b/x^(1/3))","A",4,3,26,0.1154,1,"{1341, 1355, 14}"
486,1,190,0,0.1180629,"\int \frac{1}{\sqrt{a^2+\frac{b^2}{x^{2/3}}+\frac{2 a b}{\sqrt[3]{x}}}} \, dx","Int[1/Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)],x]","\frac{3 b^2 \sqrt[3]{x} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^3 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{3 b x^{2/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{2 a^2 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}+\frac{x \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{3 b^3 \left(a+\frac{b}{\sqrt[3]{x}}\right) \log \left(a \sqrt[3]{x}+b\right)}{a^4 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}","\frac{3 b^2 \sqrt[3]{x} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^3 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{3 b x^{2/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{2 a^2 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}+\frac{x \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{3 b^3 \left(a+\frac{b}{\sqrt[3]{x}}\right) \log \left(a \sqrt[3]{x}+b\right)}{a^4 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}",1,"(3*b^2*(a + b/x^(1/3))*x^(1/3))/(a^3*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]) - (3*b*(a + b/x^(1/3))*x^(2/3))/(2*a^2*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]) + ((a + b/x^(1/3))*x)/(a*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]) - (3*b^3*(a + b/x^(1/3))*Log[b + a*x^(1/3)])/(a^4*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)])","A",5,4,26,0.1538,1,"{1341, 1355, 263, 43}"
487,1,300,0,0.1874664,"\int \frac{1}{\left(a^2+\frac{b^2}{x^{2/3}}+\frac{2 a b}{\sqrt[3]{x}}\right)^{3/2}} \, dx","Int[(a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3))^(-3/2),x]","\frac{3 b^5 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{2 a^6 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)^2}-\frac{15 b^4 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^6 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)}+\frac{18 b^2 \sqrt[3]{x} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^5 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{9 b x^{2/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{2 a^4 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}+\frac{x \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^3 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{30 b^3 \left(a+\frac{b}{\sqrt[3]{x}}\right) \log \left(a \sqrt[3]{x}+b\right)}{a^6 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}","\frac{3 b^5 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{2 a^6 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)^2}-\frac{15 b^4 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^6 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)}+\frac{18 b^2 \sqrt[3]{x} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^5 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{9 b x^{2/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{2 a^4 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}+\frac{x \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^3 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{30 b^3 \left(a+\frac{b}{\sqrt[3]{x}}\right) \log \left(a \sqrt[3]{x}+b\right)}{a^6 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}",1,"(3*b^5*(a + b/x^(1/3)))/(2*a^6*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*(b + a*x^(1/3))^2) - (15*b^4*(a + b/x^(1/3)))/(a^6*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*(b + a*x^(1/3))) + (18*b^2*(a + b/x^(1/3))*x^(1/3))/(a^5*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]) - (9*b*(a + b/x^(1/3))*x^(2/3))/(2*a^4*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]) + ((a + b/x^(1/3))*x)/(a^3*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]) - (30*b^3*(a + b/x^(1/3))*Log[b + a*x^(1/3)])/(a^6*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)])","A",5,4,26,0.1538,1,"{1341, 1355, 263, 43}"
488,1,410,0,0.2677212,"\int \frac{1}{\left(a^2+\frac{b^2}{x^{2/3}}+\frac{2 a b}{\sqrt[3]{x}}\right)^{5/2}} \, dx","Int[(a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3))^(-5/2),x]","\frac{3 b^7 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{4 a^8 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)^4}-\frac{7 b^6 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^8 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)^3}+\frac{63 b^5 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{2 a^8 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)^2}-\frac{105 b^4 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^8 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)}+\frac{45 b^2 \sqrt[3]{x} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^7 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{15 b x^{2/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{2 a^6 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}+\frac{x \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^5 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{105 b^3 \left(a+\frac{b}{\sqrt[3]{x}}\right) \log \left(a \sqrt[3]{x}+b\right)}{a^8 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}","\frac{3 b^7 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{4 a^8 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)^4}-\frac{7 b^6 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^8 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)^3}+\frac{63 b^5 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{2 a^8 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)^2}-\frac{105 b^4 \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^8 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}} \left(a \sqrt[3]{x}+b\right)}+\frac{45 b^2 \sqrt[3]{x} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^7 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{15 b x^{2/3} \left(a+\frac{b}{\sqrt[3]{x}}\right)}{2 a^6 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}+\frac{x \left(a+\frac{b}{\sqrt[3]{x}}\right)}{a^5 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}-\frac{105 b^3 \left(a+\frac{b}{\sqrt[3]{x}}\right) \log \left(a \sqrt[3]{x}+b\right)}{a^8 \sqrt{a^2+\frac{2 a b}{\sqrt[3]{x}}+\frac{b^2}{x^{2/3}}}}",1,"(3*b^7*(a + b/x^(1/3)))/(4*a^8*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*(b + a*x^(1/3))^4) - (7*b^6*(a + b/x^(1/3)))/(a^8*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*(b + a*x^(1/3))^3) + (63*b^5*(a + b/x^(1/3)))/(2*a^8*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*(b + a*x^(1/3))^2) - (105*b^4*(a + b/x^(1/3)))/(a^8*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]*(b + a*x^(1/3))) + (45*b^2*(a + b/x^(1/3))*x^(1/3))/(a^7*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]) - (15*b*(a + b/x^(1/3))*x^(2/3))/(2*a^6*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]) + ((a + b/x^(1/3))*x)/(a^5*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)]) - (105*b^3*(a + b/x^(1/3))*Log[b + a*x^(1/3)])/(a^8*Sqrt[a^2 + b^2/x^(2/3) + (2*a*b)/x^(1/3)])","A",5,4,26,0.1538,1,"{1341, 1355, 263, 43}"
489,1,289,0,0.1380809,"\int \left(a^2+\frac{b^2}{\sqrt{x}}+\frac{2 a b}{\sqrt[4]{x}}\right)^{5/2} \, dx","Int[(a^2 + b^2/Sqrt[x] + (2*a*b)/x^(1/4))^(5/2),x]","\frac{20 a^4 b x^{3/4} \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{3 \left(a+\frac{b}{\sqrt[4]{x}}\right)}+\frac{a^5 x \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{a+\frac{b}{\sqrt[4]{x}}}+\frac{20 a^3 b^2 \sqrt{x} \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{a+\frac{b}{\sqrt[4]{x}}}+\frac{40 a^2 b^3 \sqrt[4]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{a+\frac{b}{\sqrt[4]{x}}}-\frac{4 b^5 \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{\sqrt[4]{x} \left(a+\frac{b}{\sqrt[4]{x}}\right)}+\frac{20 a b^4 \log \left(\sqrt[4]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{a+\frac{b}{\sqrt[4]{x}}}","\frac{20 a^4 b x^{3/4} \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{3 \left(a+\frac{b}{\sqrt[4]{x}}\right)}+\frac{a^5 x \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{a+\frac{b}{\sqrt[4]{x}}}+\frac{20 a^3 b^2 \sqrt{x} \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{a+\frac{b}{\sqrt[4]{x}}}+\frac{40 a^2 b^3 \sqrt[4]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{a+\frac{b}{\sqrt[4]{x}}}-\frac{4 b^5 \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{\sqrt[4]{x} \left(a+\frac{b}{\sqrt[4]{x}}\right)}+\frac{20 a b^4 \log \left(\sqrt[4]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[4]{x}}+\frac{b^2}{\sqrt{x}}}}{a+\frac{b}{\sqrt[4]{x}}}",1,"(-4*b^5*Sqrt[a^2 + b^2/Sqrt[x] + (2*a*b)/x^(1/4)])/((a + b/x^(1/4))*x^(1/4)) + (40*a^2*b^3*Sqrt[a^2 + b^2/Sqrt[x] + (2*a*b)/x^(1/4)]*x^(1/4))/(a + b/x^(1/4)) + (20*a^3*b^2*Sqrt[a^2 + b^2/Sqrt[x] + (2*a*b)/x^(1/4)]*Sqrt[x])/(a + b/x^(1/4)) + (20*a^4*b*Sqrt[a^2 + b^2/Sqrt[x] + (2*a*b)/x^(1/4)]*x^(3/4))/(3*(a + b/x^(1/4))) + (a^5*Sqrt[a^2 + b^2/Sqrt[x] + (2*a*b)/x^(1/4)]*x)/(a + b/x^(1/4)) + (20*a*b^4*Sqrt[a^2 + b^2/Sqrt[x] + (2*a*b)/x^(1/4)]*Log[x^(1/4)])/(a + b/x^(1/4))","A",5,4,26,0.1538,1,"{1341, 1355, 263, 43}"
490,1,291,0,0.1369134,"\int \left(a^2+\frac{b^2}{x^{2/5}}+\frac{2 a b}{\sqrt[5]{x}}\right)^{5/2} \, dx","Int[(a^2 + b^2/x^(2/5) + (2*a*b)/x^(1/5))^(5/2),x]","\frac{a^5 x \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{a+\frac{b}{\sqrt[5]{x}}}+\frac{25 a^4 b x^{4/5} \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{4 \left(a+\frac{b}{\sqrt[5]{x}}\right)}+\frac{50 a^3 b^2 x^{3/5} \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{3 \left(a+\frac{b}{\sqrt[5]{x}}\right)}+\frac{25 a^2 b^3 x^{2/5} \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{a+\frac{b}{\sqrt[5]{x}}}+\frac{25 a b^4 \sqrt[5]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{a+\frac{b}{\sqrt[5]{x}}}+\frac{5 b^5 \log \left(\sqrt[5]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{a+\frac{b}{\sqrt[5]{x}}}","\frac{a^5 x \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{a+\frac{b}{\sqrt[5]{x}}}+\frac{25 a^4 b x^{4/5} \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{4 \left(a+\frac{b}{\sqrt[5]{x}}\right)}+\frac{50 a^3 b^2 x^{3/5} \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{3 \left(a+\frac{b}{\sqrt[5]{x}}\right)}+\frac{25 a^2 b^3 x^{2/5} \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{a+\frac{b}{\sqrt[5]{x}}}+\frac{25 a b^4 \sqrt[5]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{a+\frac{b}{\sqrt[5]{x}}}+\frac{5 b^5 \log \left(\sqrt[5]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[5]{x}}+\frac{b^2}{x^{2/5}}}}{a+\frac{b}{\sqrt[5]{x}}}",1,"(25*a*b^4*Sqrt[a^2 + b^2/x^(2/5) + (2*a*b)/x^(1/5)]*x^(1/5))/(a + b/x^(1/5)) + (25*a^2*b^3*Sqrt[a^2 + b^2/x^(2/5) + (2*a*b)/x^(1/5)]*x^(2/5))/(a + b/x^(1/5)) + (50*a^3*b^2*Sqrt[a^2 + b^2/x^(2/5) + (2*a*b)/x^(1/5)]*x^(3/5))/(3*(a + b/x^(1/5))) + (25*a^4*b*Sqrt[a^2 + b^2/x^(2/5) + (2*a*b)/x^(1/5)]*x^(4/5))/(4*(a + b/x^(1/5))) + (a^5*Sqrt[a^2 + b^2/x^(2/5) + (2*a*b)/x^(1/5)]*x)/(a + b/x^(1/5)) + (5*b^5*Sqrt[a^2 + b^2/x^(2/5) + (2*a*b)/x^(1/5)]*Log[x^(1/5)])/(a + b/x^(1/5))","A",5,4,26,0.1538,1,"{1341, 1355, 263, 43}"
491,1,222,0,0.1259475,"\int \frac{1}{\left(a^2+2 a b \sqrt[5]{x}+b^2 x^{2/5}\right)^{5/2}} \, dx","Int[(a^2 + 2*a*b*x^(1/5) + b^2*x^(2/5))^(-5/2),x]","-\frac{5 a^4}{4 b^5 \left(a+b \sqrt[5]{x}\right)^3 \sqrt{a^2+2 a b \sqrt[5]{x}+b^2 x^{2/5}}}+\frac{20 a^3}{3 b^5 \left(a+b \sqrt[5]{x}\right)^2 \sqrt{a^2+2 a b \sqrt[5]{x}+b^2 x^{2/5}}}-\frac{15 a^2}{b^5 \left(a+b \sqrt[5]{x}\right) \sqrt{a^2+2 a b \sqrt[5]{x}+b^2 x^{2/5}}}+\frac{20 a}{b^5 \sqrt{a^2+2 a b \sqrt[5]{x}+b^2 x^{2/5}}}+\frac{5 \left(a+b \sqrt[5]{x}\right) \log \left(a+b \sqrt[5]{x}\right)}{b^5 \sqrt{a^2+2 a b \sqrt[5]{x}+b^2 x^{2/5}}}","-\frac{5 a^4}{4 b^5 \left(a+b \sqrt[5]{x}\right)^3 \sqrt{a^2+2 a b \sqrt[5]{x}+b^2 x^{2/5}}}+\frac{20 a^3}{3 b^5 \left(a+b \sqrt[5]{x}\right)^2 \sqrt{a^2+2 a b \sqrt[5]{x}+b^2 x^{2/5}}}-\frac{15 a^2}{b^5 \left(a+b \sqrt[5]{x}\right) \sqrt{a^2+2 a b \sqrt[5]{x}+b^2 x^{2/5}}}+\frac{20 a}{b^5 \sqrt{a^2+2 a b \sqrt[5]{x}+b^2 x^{2/5}}}+\frac{5 \left(a+b \sqrt[5]{x}\right) \log \left(a+b \sqrt[5]{x}\right)}{b^5 \sqrt{a^2+2 a b \sqrt[5]{x}+b^2 x^{2/5}}}",1,"(20*a)/(b^5*Sqrt[a^2 + 2*a*b*x^(1/5) + b^2*x^(2/5)]) - (5*a^4)/(4*b^5*(a + b*x^(1/5))^3*Sqrt[a^2 + 2*a*b*x^(1/5) + b^2*x^(2/5)]) + (20*a^3)/(3*b^5*(a + b*x^(1/5))^2*Sqrt[a^2 + 2*a*b*x^(1/5) + b^2*x^(2/5)]) - (15*a^2)/(b^5*(a + b*x^(1/5))*Sqrt[a^2 + 2*a*b*x^(1/5) + b^2*x^(2/5)]) + (5*(a + b*x^(1/5))*Log[a + b*x^(1/5)])/(b^5*Sqrt[a^2 + 2*a*b*x^(1/5) + b^2*x^(2/5)])","A",4,3,26,0.1154,1,"{1341, 646, 43}"
492,1,391,0,0.179674,"\int \left(a^2+\frac{b^2}{\sqrt[3]{x}}+\frac{2 a b}{\sqrt[6]{x}}\right)^{7/2} \, dx","Int[(a^2 + b^2/x^(1/3) + (2*a*b)/x^(1/6))^(7/2),x]","\frac{42 a^6 b x^{5/6} \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{5 \left(a+\frac{b}{\sqrt[6]{x}}\right)}+\frac{63 a^5 b^2 x^{2/3} \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{2 \left(a+\frac{b}{\sqrt[6]{x}}\right)}+\frac{a^7 x \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{a+\frac{b}{\sqrt[6]{x}}}+\frac{70 a^4 b^3 \sqrt{x} \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{a+\frac{b}{\sqrt[6]{x}}}+\frac{105 a^3 b^4 \sqrt[3]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{a+\frac{b}{\sqrt[6]{x}}}+\frac{126 a^2 b^5 \sqrt[6]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{a+\frac{b}{\sqrt[6]{x}}}-\frac{6 b^7 \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{\sqrt[6]{x} \left(a+\frac{b}{\sqrt[6]{x}}\right)}+\frac{42 a b^6 \log \left(\sqrt[6]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{a+\frac{b}{\sqrt[6]{x}}}","\frac{42 a^6 b x^{5/6} \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{5 \left(a+\frac{b}{\sqrt[6]{x}}\right)}+\frac{63 a^5 b^2 x^{2/3} \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{2 \left(a+\frac{b}{\sqrt[6]{x}}\right)}+\frac{a^7 x \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{a+\frac{b}{\sqrt[6]{x}}}+\frac{70 a^4 b^3 \sqrt{x} \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{a+\frac{b}{\sqrt[6]{x}}}+\frac{105 a^3 b^4 \sqrt[3]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{a+\frac{b}{\sqrt[6]{x}}}+\frac{126 a^2 b^5 \sqrt[6]{x} \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{a+\frac{b}{\sqrt[6]{x}}}-\frac{6 b^7 \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{\sqrt[6]{x} \left(a+\frac{b}{\sqrt[6]{x}}\right)}+\frac{42 a b^6 \log \left(\sqrt[6]{x}\right) \sqrt{a^2+\frac{2 a b}{\sqrt[6]{x}}+\frac{b^2}{\sqrt[3]{x}}}}{a+\frac{b}{\sqrt[6]{x}}}",1,"(-6*b^7*Sqrt[a^2 + b^2/x^(1/3) + (2*a*b)/x^(1/6)])/((a + b/x^(1/6))*x^(1/6)) + (126*a^2*b^5*Sqrt[a^2 + b^2/x^(1/3) + (2*a*b)/x^(1/6)]*x^(1/6))/(a + b/x^(1/6)) + (105*a^3*b^4*Sqrt[a^2 + b^2/x^(1/3) + (2*a*b)/x^(1/6)]*x^(1/3))/(a + b/x^(1/6)) + (70*a^4*b^3*Sqrt[a^2 + b^2/x^(1/3) + (2*a*b)/x^(1/6)]*Sqrt[x])/(a + b/x^(1/6)) + (63*a^5*b^2*Sqrt[a^2 + b^2/x^(1/3) + (2*a*b)/x^(1/6)]*x^(2/3))/(2*(a + b/x^(1/6))) + (42*a^6*b*Sqrt[a^2 + b^2/x^(1/3) + (2*a*b)/x^(1/6)]*x^(5/6))/(5*(a + b/x^(1/6))) + (a^7*Sqrt[a^2 + b^2/x^(1/3) + (2*a*b)/x^(1/6)]*x)/(a + b/x^(1/6)) + (42*a*b^6*Sqrt[a^2 + b^2/x^(1/3) + (2*a*b)/x^(1/6)]*Log[x^(1/6)])/(a + b/x^(1/6))","A",5,4,26,0.1538,1,"{1341, 1355, 263, 43}"
493,1,46,0,0.036353,"\int \frac{x^{-1+4 n}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 + 4*n)/(b*x^n + c*x^(2*n)),x]","\frac{b^2 \log \left(b+c x^n\right)}{c^3 n}-\frac{b x^n}{c^2 n}+\frac{x^{2 n}}{2 c n}","\frac{b^2 \log \left(b+c x^n\right)}{c^3 n}-\frac{b x^n}{c^2 n}+\frac{x^{2 n}}{2 c n}",1,"-((b*x^n)/(c^2*n)) + x^(2*n)/(2*c*n) + (b^2*Log[b + c*x^n])/(c^3*n)","A",4,3,23,0.1304,1,"{1584, 266, 43}"
494,1,28,0,0.0258639,"\int \frac{x^{-1+3 n}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 + 3*n)/(b*x^n + c*x^(2*n)),x]","\frac{x^n}{c n}-\frac{b \log \left(b+c x^n\right)}{c^2 n}","\frac{x^n}{c n}-\frac{b \log \left(b+c x^n\right)}{c^2 n}",1,"x^n/(c*n) - (b*Log[b + c*x^n])/(c^2*n)","A",4,3,23,0.1304,1,"{1584, 266, 43}"
495,1,15,0,0.0124989,"\int \frac{x^{-1+2 n}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 + 2*n)/(b*x^n + c*x^(2*n)),x]","\frac{\log \left(b+c x^n\right)}{c n}","\frac{\log \left(b+c x^n\right)}{c n}",1,"Log[b + c*x^n]/(c*n)","A",2,2,23,0.08696,1,"{1584, 260}"
496,1,23,0,0.0185387,"\int \frac{x^{-1+n}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 + n)/(b*x^n + c*x^(2*n)),x]","\frac{\log (x)}{b}-\frac{\log \left(b+c x^n\right)}{b n}","\frac{\log (x)}{b}-\frac{\log \left(b+c x^n\right)}{b n}",1,"Log[x]/b - Log[b + c*x^n]/(b*n)","A",5,5,21,0.2381,1,"{1584, 266, 36, 29, 31}"
497,1,57,0,0.0421494,"\int \frac{x^{-1-n}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 - n)/(b*x^n + c*x^(2*n)),x]","-\frac{c^2 \log \left(b+c x^n\right)}{b^3 n}+\frac{c^2 \log (x)}{b^3}+\frac{c x^{-n}}{b^2 n}-\frac{x^{-2 n}}{2 b n}","-\frac{c^2 \log \left(b+c x^n\right)}{b^3 n}+\frac{c^2 \log (x)}{b^3}+\frac{c x^{-n}}{b^2 n}-\frac{x^{-2 n}}{2 b n}",1,"-1/(2*b*n*x^(2*n)) + c/(b^2*n*x^n) + (c^2*Log[x])/b^3 - (c^2*Log[b + c*x^n])/(b^3*n)","A",4,3,23,0.1304,1,"{1584, 266, 44}"
498,1,76,0,0.0471033,"\int \frac{x^{-1-2 n}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 - 2*n)/(b*x^n + c*x^(2*n)),x]","-\frac{c^2 x^{-n}}{b^3 n}+\frac{c^3 \log \left(b+c x^n\right)}{b^4 n}-\frac{c^3 \log (x)}{b^4}+\frac{c x^{-2 n}}{2 b^2 n}-\frac{x^{-3 n}}{3 b n}","-\frac{c^2 x^{-n}}{b^3 n}+\frac{c^3 \log \left(b+c x^n\right)}{b^4 n}-\frac{c^3 \log (x)}{b^4}+\frac{c x^{-2 n}}{2 b^2 n}-\frac{x^{-3 n}}{3 b n}",1,"-1/(3*b*n*x^(3*n)) + c/(2*b^2*n*x^(2*n)) - c^2/(b^3*n*x^n) - (c^3*Log[x])/b^4 + (c^3*Log[b + c*x^n])/(b^4*n)","A",4,3,23,0.1304,1,"{1584, 266, 44}"
499,1,93,0,0.0538467,"\int \frac{x^{-1-3 n}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 - 3*n)/(b*x^n + c*x^(2*n)),x]","-\frac{c^2 x^{-2 n}}{2 b^3 n}+\frac{c^3 x^{-n}}{b^4 n}-\frac{c^4 \log \left(b+c x^n\right)}{b^5 n}+\frac{c^4 \log (x)}{b^5}+\frac{c x^{-3 n}}{3 b^2 n}-\frac{x^{-4 n}}{4 b n}","-\frac{c^2 x^{-2 n}}{2 b^3 n}+\frac{c^3 x^{-n}}{b^4 n}-\frac{c^4 \log \left(b+c x^n\right)}{b^5 n}+\frac{c^4 \log (x)}{b^5}+\frac{c x^{-3 n}}{3 b^2 n}-\frac{x^{-4 n}}{4 b n}",1,"-1/(4*b*n*x^(4*n)) + c/(3*b^2*n*x^(3*n)) - c^2/(2*b^3*n*x^(2*n)) + c^3/(b^4*n*x^n) + (c^4*Log[x])/b^5 - (c^4*Log[b + c*x^n])/(b^5*n)","A",4,3,23,0.1304,1,"{1584, 266, 44}"
500,1,236,0,0.2063005,"\int \frac{x^{-1+\frac{n}{4}}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 + n/4)/(b*x^n + c*x^(2*n)),x]","\frac{c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} x^{n/4}+\sqrt{b}+\sqrt{c} x^{n/2}\right)}{\sqrt{2} b^{7/4} n}-\frac{c^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} x^{n/4}+\sqrt{b}+\sqrt{c} x^{n/2}\right)}{\sqrt{2} b^{7/4} n}+\frac{\sqrt{2} c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{b}}\right)}{b^{7/4} n}-\frac{\sqrt{2} c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{b}}+1\right)}{b^{7/4} n}-\frac{4 x^{-3 n/4}}{3 b n}","\frac{c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} x^{n/4}+\sqrt{b}+\sqrt{c} x^{n/2}\right)}{\sqrt{2} b^{7/4} n}-\frac{c^{3/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} x^{n/4}+\sqrt{b}+\sqrt{c} x^{n/2}\right)}{\sqrt{2} b^{7/4} n}+\frac{\sqrt{2} c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{b}}\right)}{b^{7/4} n}-\frac{\sqrt{2} c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{b}}+1\right)}{b^{7/4} n}-\frac{4 x^{-3 n/4}}{3 b n}",1,"-4/(3*b*n*x^((3*n)/4)) + (Sqrt[2]*c^(3/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x^(n/4))/b^(1/4)])/(b^(7/4)*n) - (Sqrt[2]*c^(3/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x^(n/4))/b^(1/4)])/(b^(7/4)*n) + (c^(3/4)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*x^(n/4) + Sqrt[c]*x^(n/2)])/(Sqrt[2]*b^(7/4)*n) - (c^(3/4)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*x^(n/4) + Sqrt[c]*x^(n/2)])/(Sqrt[2]*b^(7/4)*n)","A",12,9,25,0.3600,1,"{1584, 362, 345, 211, 1165, 628, 1162, 617, 204}"
501,1,160,0,0.1321471,"\int \frac{x^{-1+\frac{n}{3}}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 + n/3)/(b*x^n + c*x^(2*n)),x]","-\frac{c^{2/3} \log \left(\sqrt[3]{b}+\sqrt[3]{c} x^{n/3}\right)}{b^{5/3} n}+\frac{c^{2/3} \log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{c} x^{n/3}+c^{2/3} x^{2 n/3}\right)}{2 b^{5/3} n}+\frac{\sqrt{3} c^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{c} x^{n/3}}{\sqrt{3} \sqrt[3]{b}}\right)}{b^{5/3} n}-\frac{3 x^{-2 n/3}}{2 b n}","-\frac{c^{2/3} \log \left(\sqrt[3]{b}+\sqrt[3]{c} x^{n/3}\right)}{b^{5/3} n}+\frac{c^{2/3} \log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{c} x^{n/3}+c^{2/3} x^{2 n/3}\right)}{2 b^{5/3} n}+\frac{\sqrt{3} c^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{c} x^{n/3}}{\sqrt{3} \sqrt[3]{b}}\right)}{b^{5/3} n}-\frac{3 x^{-2 n/3}}{2 b n}",1,"-3/(2*b*n*x^((2*n)/3)) + (Sqrt[3]*c^(2/3)*ArcTan[(b^(1/3) - 2*c^(1/3)*x^(n/3))/(Sqrt[3]*b^(1/3))])/(b^(5/3)*n) - (c^(2/3)*Log[b^(1/3) + c^(1/3)*x^(n/3)])/(b^(5/3)*n) + (c^(2/3)*Log[b^(2/3) - b^(1/3)*c^(1/3)*x^(n/3) + c^(2/3)*x^((2*n)/3)])/(2*b^(5/3)*n)","A",9,9,25,0.3600,1,"{1584, 362, 345, 200, 31, 634, 617, 204, 628}"
502,1,50,0,0.0347027,"\int \frac{x^{-1+\frac{n}{2}}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 + n/2)/(b*x^n + c*x^(2*n)),x]","\frac{2 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{b} x^{-n/2}}{\sqrt{c}}\right)}{b^{3/2} n}-\frac{2 x^{-n/2}}{b n}","\frac{2 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{b} x^{-n/2}}{\sqrt{c}}\right)}{b^{3/2} n}-\frac{2 x^{-n/2}}{b n}",1,"-2/(b*n*x^(n/2)) + (2*Sqrt[c]*ArcTan[Sqrt[b]/(Sqrt[c]*x^(n/2))])/(b^(3/2)*n)","A",5,5,25,0.2000,1,"{1584, 345, 193, 321, 205}"
503,1,68,0,0.0408412,"\int \frac{x^{-1-\frac{n}{2}}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 - n/2)/(b*x^n + c*x^(2*n)),x]","-\frac{2 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x^{-n/2}}{\sqrt{c}}\right)}{b^{5/2} n}+\frac{2 c x^{-n/2}}{b^2 n}-\frac{2 x^{-3 n/2}}{3 b n}","-\frac{2 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x^{-n/2}}{\sqrt{c}}\right)}{b^{5/2} n}+\frac{2 c x^{-n/2}}{b^2 n}-\frac{2 x^{-3 n/2}}{3 b n}",1,"-2/(3*b*n*x^((3*n)/2)) + (2*c)/(b^2*n*x^(n/2)) - (2*c^(3/2)*ArcTan[Sqrt[b]/(Sqrt[c]*x^(n/2))])/(b^(5/2)*n)","A",6,6,25,0.2400,1,"{1584, 362, 345, 193, 321, 205}"
504,1,176,0,0.1424916,"\int \frac{x^{-1-\frac{n}{3}}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 - n/3)/(b*x^n + c*x^(2*n)),x]","-\frac{c^{4/3} \log \left(\sqrt[3]{b} x^{-n/3}+\sqrt[3]{c}\right)}{b^{7/3} n}+\frac{c^{4/3} \log \left(b^{2/3} x^{-2 n/3}-\sqrt[3]{b} \sqrt[3]{c} x^{-n/3}+c^{2/3}\right)}{2 b^{7/3} n}+\frac{\sqrt{3} c^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{b} x^{-n/3}}{\sqrt{3} \sqrt[3]{c}}\right)}{b^{7/3} n}+\frac{3 c x^{-n/3}}{b^2 n}-\frac{3 x^{-4 n/3}}{4 b n}","-\frac{c^{4/3} \log \left(\sqrt[3]{b} x^{-n/3}+\sqrt[3]{c}\right)}{b^{7/3} n}+\frac{c^{4/3} \log \left(b^{2/3} x^{-2 n/3}-\sqrt[3]{b} \sqrt[3]{c} x^{-n/3}+c^{2/3}\right)}{2 b^{7/3} n}+\frac{\sqrt{3} c^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{b} x^{-n/3}}{\sqrt{3} \sqrt[3]{c}}\right)}{b^{7/3} n}+\frac{3 c x^{-n/3}}{b^2 n}-\frac{3 x^{-4 n/3}}{4 b n}",1,"-3/(4*b*n*x^((4*n)/3)) + (3*c)/(b^2*n*x^(n/3)) + (Sqrt[3]*c^(4/3)*ArcTan[(c^(1/3) - (2*b^(1/3))/x^(n/3))/(Sqrt[3]*c^(1/3))])/(b^(7/3)*n) - (c^(4/3)*Log[c^(1/3) + b^(1/3)/x^(n/3)])/(b^(7/3)*n) + (c^(4/3)*Log[c^(2/3) + b^(2/3)/x^((2*n)/3) - (b^(1/3)*c^(1/3))/x^(n/3)])/(2*b^(7/3)*n)","A",11,11,25,0.4400,1,"{1584, 362, 345, 193, 321, 200, 31, 634, 617, 204, 628}"
505,1,252,0,0.2245051,"\int \frac{x^{-1-\frac{n}{4}}}{b x^n+c x^{2 n}} \, dx","Int[x^(-1 - n/4)/(b*x^n + c*x^(2*n)),x]","\frac{c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} x^{-n/4}+\sqrt{b} x^{-n/2}+\sqrt{c}\right)}{\sqrt{2} b^{9/4} n}-\frac{c^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} x^{-n/4}+\sqrt{b} x^{-n/2}+\sqrt{c}\right)}{\sqrt{2} b^{9/4} n}+\frac{\sqrt{2} c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^{-n/4}}{\sqrt[4]{c}}\right)}{b^{9/4} n}-\frac{\sqrt{2} c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^{-n/4}}{\sqrt[4]{c}}+1\right)}{b^{9/4} n}+\frac{4 c x^{-n/4}}{b^2 n}-\frac{4 x^{-5 n/4}}{5 b n}","\frac{c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} x^{-n/4}+\sqrt{b} x^{-n/2}+\sqrt{c}\right)}{\sqrt{2} b^{9/4} n}-\frac{c^{5/4} \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} x^{-n/4}+\sqrt{b} x^{-n/2}+\sqrt{c}\right)}{\sqrt{2} b^{9/4} n}+\frac{\sqrt{2} c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x^{-n/4}}{\sqrt[4]{c}}\right)}{b^{9/4} n}-\frac{\sqrt{2} c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x^{-n/4}}{\sqrt[4]{c}}+1\right)}{b^{9/4} n}+\frac{4 c x^{-n/4}}{b^2 n}-\frac{4 x^{-5 n/4}}{5 b n}",1,"-4/(5*b*n*x^((5*n)/4)) + (4*c)/(b^2*n*x^(n/4)) + (Sqrt[2]*c^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4))/(c^(1/4)*x^(n/4))])/(b^(9/4)*n) - (Sqrt[2]*c^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4))/(c^(1/4)*x^(n/4))])/(b^(9/4)*n) + (c^(5/4)*Log[Sqrt[c] + Sqrt[b]/x^(n/2) - (Sqrt[2]*b^(1/4)*c^(1/4))/x^(n/4)])/(Sqrt[2]*b^(9/4)*n) - (c^(5/4)*Log[Sqrt[c] + Sqrt[b]/x^(n/2) + (Sqrt[2]*b^(1/4)*c^(1/4))/x^(n/4)])/(Sqrt[2]*b^(9/4)*n)","A",14,11,25,0.4400,1,"{1584, 362, 345, 193, 321, 211, 1165, 628, 1162, 617, 204}"
506,1,37,0,0.0395401,"\int x^{-1-n (-1+p)} \left(b x^n+c x^{2 n}\right)^p \, dx","Int[x^(-1 - n*(-1 + p))*(b*x^n + c*x^(2*n))^p,x]","\frac{x^{-n (p+1)} \left(b x^n+c x^{2 n}\right)^{p+1}}{c n (p+1)}","\frac{x^{-n (p+1)} \left(b x^n+c x^{2 n}\right)^{p+1}}{c n (p+1)}",1,"(b*x^n + c*x^(2*n))^(1 + p)/(c*n*(1 + p)*x^(n*(1 + p)))","A",1,1,26,0.03846,1,"{2014}"
507,1,38,0,0.0389941,"\int x^{-1-n (1+2 p)} \left(b x^n+c x^{2 n}\right)^p \, dx","Int[x^(-1 - n*(1 + 2*p))*(b*x^n + c*x^(2*n))^p,x]","-\frac{x^{-2 n (p+1)} \left(b x^n+c x^{2 n}\right)^{p+1}}{b n (p+1)}","-\frac{x^{-2 n (p+1)} \left(b x^n+c x^{2 n}\right)^{p+1}}{b n (p+1)}",1,"-((b*x^n + c*x^(2*n))^(1 + p)/(b*n*(1 + p)*x^(2*n*(1 + p))))","A",1,1,28,0.03571,1,"{2014}"
508,1,112,0,0.0416955,"\int x^{-1+2 n} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{5/2} \, dx","Int[x^(-1 + 2*n)*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(5/2),x]","\frac{\left(a+b x^n\right)^7 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{7 n \left(a b^2+b^3 x^n\right)}-\frac{a \left(a+b x^n\right)^6 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{6 n \left(a b^2+b^3 x^n\right)}","\frac{\left(a+b x^n\right)^7 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{7 n \left(a b^2+b^3 x^n\right)}-\frac{a \left(a+b x^n\right)^6 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{6 n \left(a b^2+b^3 x^n\right)}",1,"-(a*(a + b*x^n)^6*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(6*n*(a*b^2 + b^3*x^n)) + ((a + b*x^n)^7*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(7*n*(a*b^2 + b^3*x^n))","A",4,3,32,0.09375,1,"{1355, 266, 43}"
509,1,112,0,0.0396355,"\int x^{-1+2 n} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2} \, dx","Int[x^(-1 + 2*n)*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2),x]","\frac{\left(a+b x^n\right)^5 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{5 n \left(a b^2+b^3 x^n\right)}-\frac{a \left(a+b x^n\right)^4 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{4 n \left(a b^2+b^3 x^n\right)}","\frac{\left(a+b x^n\right)^5 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{5 n \left(a b^2+b^3 x^n\right)}-\frac{a \left(a+b x^n\right)^4 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{4 n \left(a b^2+b^3 x^n\right)}",1,"-(a*(a + b*x^n)^4*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(4*n*(a*b^2 + b^3*x^n)) + ((a + b*x^n)^5*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(5*n*(a*b^2 + b^3*x^n))","A",4,3,32,0.09375,1,"{1355, 266, 43}"
510,1,99,0,0.0310233,"\int x^{-1+2 n} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}} \, dx","Int[x^(-1 + 2*n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)],x]","\frac{a x^{2 n} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 n \left(a+b x^n\right)}+\frac{b^2 x^{3 n} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{3 n \left(a b+b^2 x^n\right)}","\frac{a x^{2 n} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 n \left(a+b x^n\right)}+\frac{b^2 x^{3 n} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{3 n \left(a b+b^2 x^n\right)}",1,"(a*x^(2*n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(2*n*(a + b*x^n)) + (b^2*x^(3*n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(3*n*(a*b + b^2*x^n))","A",3,2,32,0.06250,1,"{1355, 14}"
511,1,90,0,0.0438885,"\int \frac{x^{-1+2 n}}{\sqrt{a^2+2 a b x^n+b^2 x^{2 n}}} \, dx","Int[x^(-1 + 2*n)/Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)],x]","\frac{x^n \left(a+b x^n\right)}{b n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}-\frac{a \left(a+b x^n\right) \log \left(a+b x^n\right)}{b^2 n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{x^n \left(a+b x^n\right)}{b n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}-\frac{a \left(a+b x^n\right) \log \left(a+b x^n\right)}{b^2 n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"(x^n*(a + b*x^n))/(b*n*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]) - (a*(a + b*x^n)*Log[a + b*x^n])/(b^2*n*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",4,3,32,0.09375,1,"{1355, 266, 43}"
512,1,48,0,0.0268692,"\int \frac{x^{-1+2 n}}{\left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}} \, dx","Int[x^(-1 + 2*n)/(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2),x]","\frac{x^{2 n}}{2 a n \left(a+b x^n\right) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{x^{2 n}}{2 a n \left(a+b x^n\right) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"x^(2*n)/(2*a*n*(a + b*x^n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",2,2,32,0.06250,1,"{1355, 264}"
513,1,88,0,0.0515943,"\int \frac{x^{-1+2 n}}{\left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{5/2}} \, dx","Int[x^(-1 + 2*n)/(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(5/2),x]","\frac{a}{4 b^2 n \left(a+b x^n\right)^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}-\frac{1}{3 b^2 n \left(a+b x^n\right)^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{a}{4 b^2 n \left(a+b x^n\right)^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}-\frac{1}{3 b^2 n \left(a+b x^n\right)^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"a/(4*b^2*n*(a + b*x^n)^3*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]) - 1/(3*b^2*n*(a + b*x^n)^2*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",4,3,32,0.09375,1,"{1355, 266, 43}"
514,1,88,0,0.0513487,"\int \frac{x^{-1+2 n}}{\left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{7/2}} \, dx","Int[x^(-1 + 2*n)/(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(7/2),x]","\frac{a}{6 b^2 n \left(a+b x^n\right)^5 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}-\frac{1}{5 b^2 n \left(a+b x^n\right)^4 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{a}{6 b^2 n \left(a+b x^n\right)^5 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}-\frac{1}{5 b^2 n \left(a+b x^n\right)^4 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"a/(6*b^2*n*(a + b*x^n)^5*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]) - 1/(5*b^2*n*(a + b*x^n)^4*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",4,3,32,0.09375,1,"{1355, 266, 43}"
515,1,108,0,0.0415609,"\int (d x)^m \sqrt{a^2+2 a b x^n+b^2 x^{2 n}} \, dx","Int[(d*x)^m*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)],x]","\frac{b^2 x^{n+1} (d x)^m \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(m+n+1) \left(a b+b^2 x^n\right)}+\frac{a (d x)^{m+1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{d (m+1) \left(a+b x^n\right)}","\frac{b^2 x^{n+1} (d x)^m \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(m+n+1) \left(a b+b^2 x^n\right)}+\frac{a (d x)^{m+1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{d (m+1) \left(a+b x^n\right)}",1,"(a*(d*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(d*(1 + m)*(a + b*x^n)) + (b^2*x^(1 + n)*(d*x)^m*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((1 + m + n)*(a*b + b^2*x^n))","A",5,4,30,0.1333,1,"{1355, 14, 20, 30}"
516,1,93,0,0.0283172,"\int x^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}} \, dx","Int[x^2*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)],x]","\frac{b^2 x^{n+3} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(n+3) \left(a b+b^2 x^n\right)}+\frac{a x^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{3 \left(a+b x^n\right)}","\frac{b^2 x^{n+3} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(n+3) \left(a b+b^2 x^n\right)}+\frac{a x^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{3 \left(a+b x^n\right)}",1,"(a*x^3*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(3*(a + b*x^n)) + (b^2*x^(3 + n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((3 + n)*(a*b + b^2*x^n))","A",3,2,28,0.07143,1,"{1355, 14}"
517,1,93,0,0.0247172,"\int x \sqrt{a^2+2 a b x^n+b^2 x^{2 n}} \, dx","Int[x*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)],x]","\frac{b^2 x^{n+2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(n+2) \left(a b+b^2 x^n\right)}+\frac{a x^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 \left(a+b x^n\right)}","\frac{b^2 x^{n+2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(n+2) \left(a b+b^2 x^n\right)}+\frac{a x^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 \left(a+b x^n\right)}",1,"(a*x^2*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(2*(a + b*x^n)) + (b^2*x^(2 + n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((2 + n)*(a*b + b^2*x^n))","A",3,2,26,0.07692,1,"{1355, 14}"
518,1,88,0,0.0185866,"\int \sqrt{a^2+2 a b x^n+b^2 x^{2 n}} \, dx","Int[Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)],x]","\frac{b^2 x^{n+1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(n+1) \left(a b+b^2 x^n\right)}+\frac{a x \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{a+b x^n}","\frac{b^2 x^{n+1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(n+1) \left(a b+b^2 x^n\right)}+\frac{a x \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{a+b x^n}",1,"(a*x*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(a + b*x^n) + (b^2*x^(1 + n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((1 + n)*(a*b + b^2*x^n))","A",2,1,24,0.04167,1,"{1343}"
519,1,85,0,0.0261973,"\int \frac{\sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{x} \, dx","Int[Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]/x,x]","\frac{b^2 x^n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{n \left(a b+b^2 x^n\right)}+\frac{a \log (x) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{a+b x^n}","\frac{b^2 x^n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{n \left(a b+b^2 x^n\right)}+\frac{a \log (x) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{a+b x^n}",1,"(b^2*x^n*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(n*(a*b + b^2*x^n)) + (a*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]*Log[x])/(a + b*x^n)","A",3,2,28,0.07143,1,"{1355, 14}"
520,1,94,0,0.0330818,"\int \frac{\sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{x^2} \, dx","Int[Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]/x^2,x]","-\frac{b^2 x^{n-1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(1-n) \left(a b+b^2 x^n\right)}-\frac{a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{x \left(a+b x^n\right)}","-\frac{b^2 x^{n-1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(1-n) \left(a b+b^2 x^n\right)}-\frac{a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{x \left(a+b x^n\right)}",1,"-((a*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(x*(a + b*x^n))) - (b^2*x^(-1 + n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((1 - n)*(a*b + b^2*x^n))","A",3,2,28,0.07143,1,"{1355, 14}"
521,1,96,0,0.0293044,"\int \frac{\sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{x^3} \, dx","Int[Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]/x^3,x]","-\frac{b^2 x^{n-2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(2-n) \left(a b+b^2 x^n\right)}-\frac{a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 x^2 \left(a+b x^n\right)}","-\frac{b^2 x^{n-2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(2-n) \left(a b+b^2 x^n\right)}-\frac{a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 x^2 \left(a+b x^n\right)}",1,"-(a*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(2*x^2*(a + b*x^n)) - (b^2*x^(-2 + n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((2 - n)*(a*b + b^2*x^n))","A",3,2,28,0.07143,1,"{1355, 14}"
522,1,238,0,0.0980303,"\int (d x)^m \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2} \, dx","Int[(d*x)^m*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2),x]","\frac{3 a^2 b^2 x^{n+1} (d x)^m \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(m+n+1) \left(a b+b^2 x^n\right)}+\frac{3 a b^3 x^{2 n+1} (d x)^m \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(m+2 n+1) \left(a b+b^2 x^n\right)}+\frac{b^4 x^{3 n+1} (d x)^m \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(m+3 n+1) \left(a b+b^2 x^n\right)}+\frac{a^3 (d x)^{m+1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{d (m+1) \left(a+b x^n\right)}","\frac{3 a^2 b^2 x^{n+1} (d x)^m \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(m+n+1) \left(a b+b^2 x^n\right)}+\frac{3 a b^3 x^{2 n+1} (d x)^m \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(m+2 n+1) \left(a b+b^2 x^n\right)}+\frac{b^4 x^{3 n+1} (d x)^m \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(m+3 n+1) \left(a b+b^2 x^n\right)}+\frac{a^3 (d x)^{m+1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{d (m+1) \left(a+b x^n\right)}",1,"(a^3*(d*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(d*(1 + m)*(a + b*x^n)) + (3*a^2*b^2*x^(1 + n)*(d*x)^m*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((1 + m + n)*(a*b + b^2*x^n)) + (3*a*b^3*x^(1 + 2*n)*(d*x)^m*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((1 + m + 2*n)*(a*b + b^2*x^n)) + (b^4*x^(1 + 3*n)*(d*x)^m*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((1 + m + 3*n)*(a*b + b^2*x^n))","A",9,4,30,0.1333,1,"{1355, 270, 20, 30}"
523,1,212,0,0.0624851,"\int x^2 \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2} \, dx","Int[x^2*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2),x]","\frac{b^4 x^{3 (n+1)} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{3 (n+1) \left(a b+b^2 x^n\right)}+\frac{3 a^2 b^2 x^{n+3} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(n+3) \left(a b+b^2 x^n\right)}+\frac{3 a b^3 x^{2 n+3} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(2 n+3) \left(a b+b^2 x^n\right)}+\frac{a^3 x^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{3 \left(a+b x^n\right)}","\frac{b^4 x^{3 (n+1)} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{3 (n+1) \left(a b+b^2 x^n\right)}+\frac{3 a^2 b^2 x^{n+3} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(n+3) \left(a b+b^2 x^n\right)}+\frac{3 a b^3 x^{2 n+3} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(2 n+3) \left(a b+b^2 x^n\right)}+\frac{a^3 x^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{3 \left(a+b x^n\right)}",1,"(a^3*x^3*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(3*(a + b*x^n)) + (b^4*x^(3*(1 + n))*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(3*(1 + n)*(a*b + b^2*x^n)) + (3*a^2*b^2*x^(3 + n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((3 + n)*(a*b + b^2*x^n)) + (3*a*b^3*x^(3 + 2*n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((3 + 2*n)*(a*b + b^2*x^n))","A",3,2,28,0.07143,1,"{1355, 270}"
524,1,211,0,0.0581511,"\int x \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2} \, dx","Int[x*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2),x]","\frac{3 a b^3 x^{2 (n+1)} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 (n+1) \left(a b+b^2 x^n\right)}+\frac{3 a^2 b^2 x^{n+2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(n+2) \left(a b+b^2 x^n\right)}+\frac{b^4 x^{3 n+2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(3 n+2) \left(a b+b^2 x^n\right)}+\frac{a^3 x^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 \left(a+b x^n\right)}","\frac{3 a b^3 x^{2 (n+1)} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 (n+1) \left(a b+b^2 x^n\right)}+\frac{3 a^2 b^2 x^{n+2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(n+2) \left(a b+b^2 x^n\right)}+\frac{b^4 x^{3 n+2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(3 n+2) \left(a b+b^2 x^n\right)}+\frac{a^3 x^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 \left(a+b x^n\right)}",1,"(a^3*x^2*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(2*(a + b*x^n)) + (3*a*b^3*x^(2*(1 + n))*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(2*(1 + n)*(a*b + b^2*x^n)) + (3*a^2*b^2*x^(2 + n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((2 + n)*(a*b + b^2*x^n)) + (b^4*x^(2 + 3*n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((2 + 3*n)*(a*b + b^2*x^n))","A",3,2,26,0.07692,1,"{1355, 270}"
525,1,206,0,0.0518595,"\int \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2} \, dx","Int[(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2),x]","\frac{3 a^2 b^4 x^{n+1} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}{(n+1) \left(a b+b^2 x^n\right)^3}+\frac{3 a b^5 x^{2 n+1} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}{(2 n+1) \left(a b+b^2 x^n\right)^3}+\frac{b^6 x^{3 n+1} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}{(3 n+1) \left(a b+b^2 x^n\right)^3}+\frac{a^3 x \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}{\left(a+b x^n\right)^3}","\frac{3 a^2 b^4 x^{n+1} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}{(n+1) \left(a b+b^2 x^n\right)^3}+\frac{3 a b^5 x^{2 n+1} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}{(2 n+1) \left(a b+b^2 x^n\right)^3}+\frac{b^6 x^{3 n+1} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}{(3 n+1) \left(a b+b^2 x^n\right)^3}+\frac{a^3 x \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}{\left(a+b x^n\right)^3}",1,"(a^3*x*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2))/(a + b*x^n)^3 + (3*a^2*b^4*x^(1 + n)*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2))/((1 + n)*(a*b + b^2*x^n)^3) + (3*a*b^5*x^(1 + 2*n)*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2))/((1 + 2*n)*(a*b + b^2*x^n)^3) + (b^6*x^(1 + 3*n)*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2))/((1 + 3*n)*(a*b + b^2*x^n)^3)","A",3,2,24,0.08333,1,"{1343, 244}"
526,1,196,0,0.0516225,"\int \frac{\left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}{x} \, dx","Int[(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2)/x,x]","\frac{3 a^2 b^2 x^n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{n \left(a b+b^2 x^n\right)}+\frac{3 a b^3 x^{2 n} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 n \left(a b+b^2 x^n\right)}+\frac{b^4 x^{3 n} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{3 n \left(a b+b^2 x^n\right)}+\frac{a^3 \log (x) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{a+b x^n}","\frac{3 a^2 b^2 x^n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{n \left(a b+b^2 x^n\right)}+\frac{3 a b^3 x^{2 n} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 n \left(a b+b^2 x^n\right)}+\frac{b^4 x^{3 n} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{3 n \left(a b+b^2 x^n\right)}+\frac{a^3 \log (x) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{a+b x^n}",1,"(3*a^2*b^2*x^n*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(n*(a*b + b^2*x^n)) + (3*a*b^3*x^(2*n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(2*n*(a*b + b^2*x^n)) + (b^4*x^(3*n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(3*n*(a*b + b^2*x^n)) + (a^3*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]*Log[x])/(a + b*x^n)","A",4,3,28,0.1071,1,"{1355, 266, 43}"
527,1,212,0,0.0698802,"\int \frac{\left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}{x^2} \, dx","Int[(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2)/x^2,x]","-\frac{3 a^2 b^2 x^{n-1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(1-n) \left(a b+b^2 x^n\right)}-\frac{3 a b^3 x^{2 n-1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(1-2 n) \left(a b+b^2 x^n\right)}-\frac{b^4 x^{3 n-1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(1-3 n) \left(a b+b^2 x^n\right)}-\frac{a^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{x \left(a+b x^n\right)}","-\frac{3 a^2 b^2 x^{n-1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(1-n) \left(a b+b^2 x^n\right)}-\frac{3 a b^3 x^{2 n-1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(1-2 n) \left(a b+b^2 x^n\right)}-\frac{b^4 x^{3 n-1} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(1-3 n) \left(a b+b^2 x^n\right)}-\frac{a^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{x \left(a+b x^n\right)}",1,"-((a^3*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(x*(a + b*x^n))) - (3*a^2*b^2*x^(-1 + n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((1 - n)*(a*b + b^2*x^n)) - (3*a*b^3*x^(-1 + 2*n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((1 - 2*n)*(a*b + b^2*x^n)) - (b^4*x^(-1 + 3*n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((1 - 3*n)*(a*b + b^2*x^n))","A",3,2,28,0.07143,1,"{1355, 270}"
528,1,218,0,0.0698201,"\int \frac{\left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}{x^3} \, dx","Int[(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2)/x^3,x]","-\frac{3 a b^3 x^{-2 (1-n)} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 (1-n) \left(a b+b^2 x^n\right)}-\frac{3 a^2 b^2 x^{n-2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(2-n) \left(a b+b^2 x^n\right)}-\frac{b^4 x^{3 n-2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(2-3 n) \left(a b+b^2 x^n\right)}-\frac{a^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 x^2 \left(a+b x^n\right)}","-\frac{3 a b^3 x^{-2 (1-n)} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 (1-n) \left(a b+b^2 x^n\right)}-\frac{3 a^2 b^2 x^{n-2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(2-n) \left(a b+b^2 x^n\right)}-\frac{b^4 x^{3 n-2} \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{(2-3 n) \left(a b+b^2 x^n\right)}-\frac{a^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}{2 x^2 \left(a+b x^n\right)}",1,"-(a^3*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(2*x^2*(a + b*x^n)) - (3*a*b^3*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/(2*(1 - n)*x^(2*(1 - n))*(a*b + b^2*x^n)) - (3*a^2*b^2*x^(-2 + n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((2 - n)*(a*b + b^2*x^n)) - (b^4*x^(-2 + 3*n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])/((2 - 3*n)*(a*b + b^2*x^n))","A",3,2,28,0.07143,1,"{1355, 270}"
529,1,76,0,0.0389876,"\int \frac{(d x)^m}{\sqrt{a^2+2 a b x^n+b^2 x^{2 n}}} \, dx","Int[(d*x)^m/Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)],x]","\frac{(d x)^{m+1} \left(a+b x^n\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a d (m+1) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{(d x)^{m+1} \left(a+b x^n\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a d (m+1) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"((d*x)^(1 + m)*(a + b*x^n)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*d*(1 + m)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",2,2,30,0.06667,1,"{1355, 364}"
530,1,64,0,0.0267265,"\int \frac{x^2}{\sqrt{a^2+2 a b x^n+b^2 x^{2 n}}} \, dx","Int[x^2/Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)],x]","\frac{x^3 \left(a+b x^n\right) \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{b x^n}{a}\right)}{3 a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{x^3 \left(a+b x^n\right) \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{b x^n}{a}\right)}{3 a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"(x^3*(a + b*x^n)*Hypergeometric2F1[1, 3/n, (3 + n)/n, -((b*x^n)/a)])/(3*a*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",2,2,28,0.07143,1,"{1355, 364}"
531,1,64,0,0.0218741,"\int \frac{x}{\sqrt{a^2+2 a b x^n+b^2 x^{2 n}}} \, dx","Int[x/Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)],x]","\frac{x^2 \left(a+b x^n\right) \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{x^2 \left(a+b x^n\right) \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"(x^2*(a + b*x^n)*Hypergeometric2F1[1, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*a*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",2,2,26,0.07692,1,"{1355, 364}"
532,1,55,0,0.0173405,"\int \frac{1}{\sqrt{a^2+2 a b x^n+b^2 x^{2 n}}} \, dx","Int[1/Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)],x]","\frac{x \left(a+b x^n\right) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{x \left(a+b x^n\right) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"(x*(a + b*x^n)*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",2,2,24,0.08333,1,"{1343, 245}"
533,1,85,0,0.0361088,"\int \frac{1}{x \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}} \, dx","Int[1/(x*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]),x]","\frac{\log (x) \left(a+b x^n\right)}{a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}-\frac{\left(a+b x^n\right) \log \left(a+b x^n\right)}{a n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{\log (x) \left(a+b x^n\right)}{a \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}-\frac{\left(a+b x^n\right) \log \left(a+b x^n\right)}{a n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"((a + b*x^n)*Log[x])/(a*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]) - ((a + b*x^n)*Log[a + b*x^n])/(a*n*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",5,5,28,0.1786,1,"{1355, 266, 36, 29, 31}"
534,1,65,0,0.0258666,"\int \frac{1}{x^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}} \, dx","Int[1/(x^2*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]),x]","-\frac{\left(a+b x^n\right) \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","-\frac{\left(a+b x^n\right) \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"-(((a + b*x^n)*Hypergeometric2F1[1, -n^(-1), -((1 - n)/n), -((b*x^n)/a)])/(a*x*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]))","A",2,2,28,0.07143,1,"{1355, 364}"
535,1,67,0,0.0261127,"\int \frac{1}{x^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}} \, dx","Int[1/(x^3*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]),x]","-\frac{\left(a+b x^n\right) \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","-\frac{\left(a+b x^n\right) \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"-((a + b*x^n)*Hypergeometric2F1[1, -2/n, -((2 - n)/n), -((b*x^n)/a)])/(2*a*x^2*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",2,2,28,0.07143,1,"{1355, 364}"
536,1,76,0,0.0372914,"\int \frac{(d x)^m}{\left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}} \, dx","Int[(d*x)^m/(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2),x]","\frac{(d x)^{m+1} \left(a+b x^n\right) \, _2F_1\left(3,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a^3 d (m+1) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{(d x)^{m+1} \left(a+b x^n\right) \, _2F_1\left(3,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a^3 d (m+1) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"((d*x)^(1 + m)*(a + b*x^n)*Hypergeometric2F1[3, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^3*d*(1 + m)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",2,2,30,0.06667,1,"{1355, 364}"
537,1,64,0,0.0266486,"\int \frac{x^2}{\left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}} \, dx","Int[x^2/(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2),x]","\frac{x^3 \left(a+b x^n\right) \, _2F_1\left(3,\frac{3}{n};\frac{n+3}{n};-\frac{b x^n}{a}\right)}{3 a^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{x^3 \left(a+b x^n\right) \, _2F_1\left(3,\frac{3}{n};\frac{n+3}{n};-\frac{b x^n}{a}\right)}{3 a^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"(x^3*(a + b*x^n)*Hypergeometric2F1[3, 3/n, (3 + n)/n, -((b*x^n)/a)])/(3*a^3*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",2,2,28,0.07143,1,"{1355, 364}"
538,1,64,0,0.0223194,"\int \frac{x}{\left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}} \, dx","Int[x/(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2),x]","\frac{x^2 \left(a+b x^n\right) \, _2F_1\left(3,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{x^2 \left(a+b x^n\right) \, _2F_1\left(3,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"(x^2*(a + b*x^n)*Hypergeometric2F1[3, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*a^3*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",2,2,26,0.07692,1,"{1355, 364}"
539,1,57,0,0.0158974,"\int \frac{1}{\left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}} \, dx","Int[(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(-3/2),x]","\frac{x \left(a+b x^n\right)^3 \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^3 \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}","\frac{x \left(a+b x^n\right)^3 \, _2F_1\left(3,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^3 \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}}",1,"(x*(a + b*x^n)^3*Hypergeometric2F1[3, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^3*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2))","A",2,2,24,0.08333,1,"{1343, 245}"
540,1,159,0,0.0830614,"\int \frac{1}{x \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}} \, dx","Int[1/(x*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2)),x]","\frac{1}{a^2 n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}+\frac{1}{2 a n \left(a+b x^n\right) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}+\frac{\log (x) \left(a+b x^n\right)}{a^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}-\frac{\left(a+b x^n\right) \log \left(a+b x^n\right)}{a^3 n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","\frac{1}{a^2 n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}+\frac{1}{2 a n \left(a+b x^n\right) \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}+\frac{\log (x) \left(a+b x^n\right)}{a^3 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}-\frac{\left(a+b x^n\right) \log \left(a+b x^n\right)}{a^3 n \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"1/(a^2*n*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]) + 1/(2*a*n*(a + b*x^n)*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]) + ((a + b*x^n)*Log[x])/(a^3*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]) - ((a + b*x^n)*Log[a + b*x^n])/(a^3*n*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",4,3,28,0.1071,1,"{1355, 266, 44}"
541,1,65,0,0.0259398,"\int \frac{1}{x^2 \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}} \, dx","Int[1/(x^2*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2)),x]","-\frac{\left(a+b x^n\right) \, _2F_1\left(3,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a^3 x \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","-\frac{\left(a+b x^n\right) \, _2F_1\left(3,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a^3 x \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"-(((a + b*x^n)*Hypergeometric2F1[3, -n^(-1), -((1 - n)/n), -((b*x^n)/a)])/(a^3*x*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)]))","A",2,2,28,0.07143,1,"{1355, 364}"
542,1,67,0,0.0275665,"\int \frac{1}{x^3 \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{3/2}} \, dx","Int[1/(x^3*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(3/2)),x]","-\frac{\left(a+b x^n\right) \, _2F_1\left(3,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a^3 x^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}","-\frac{\left(a+b x^n\right) \, _2F_1\left(3,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a^3 x^2 \sqrt{a^2+2 a b x^n+b^2 x^{2 n}}}",1,"-((a + b*x^n)*Hypergeometric2F1[3, -2/n, -((2 - n)/n), -((b*x^n)/a)])/(2*a^3*x^2*Sqrt[a^2 + 2*a*b*x^n + b^2*x^(2*n)])","A",2,2,28,0.07143,1,"{1355, 364}"
543,1,52,0,0.0195689,"\int \left(a^2+b^2 x^{-\frac{2}{1+2 p}}+2 a b x^{-\frac{1}{1+2 p}}\right)^p \, dx","Int[(a^2 + b^2/x^(2/(1 + 2*p)) + (2*a*b)/x^(1 + 2*p)^(-1))^p,x]","\frac{x \left(a+b x^{\frac{1}{-2 p-1}}\right) \left(a^2+2 a b x^{\frac{1}{-2 p-1}}+b^2 x^{-\frac{2}{2 p+1}}\right)^p}{a}","\frac{x \left(a+b x^{\frac{1}{-2 p-1}}\right) \left(a^2+2 a b x^{\frac{1}{-2 p-1}}+b^2 x^{-\frac{2}{2 p+1}}\right)^p}{a}",1,"(x*(a + b*x^(-1 - 2*p)^(-1))*(a^2 + 2*a*b*x^(-1 - 2*p)^(-1) + b^2/x^(2/(1 + 2*p)))^p)/a","A",2,2,36,0.05556,1,"{1343, 191}"
544,1,43,0,0.0134285,"\int \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{-\frac{1+n}{2 n}} \, dx","Int[(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(-(1 + n)/(2*n)),x]","\frac{x \left(a+b x^n\right) \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{-\frac{n+1}{2 n}}}{a}","\frac{x \left(a+b x^n\right) \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{-\frac{n+1}{2 n}}}{a}",1,"(x*(a + b*x^n))/(a*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^((1 + n)/(2*n)))","A",2,2,31,0.06452,1,"{1343, 191}"
545,1,130,0,0.0552074,"\int \left(a^2+b^2 x^{-\frac{1}{1+p}}+2 a b x^{-\frac{1}{2 (1+p)}}\right)^p \, dx","Int[(a^2 + b^2/x^(1 + p)^(-1) + (2*a*b)/x^(1/(2*(1 + p))))^p,x]","\frac{2 (p+1) x \left(a+b x^{-\frac{1}{2 (p+1)}}\right) \left(a^2+2 a b x^{-\frac{1}{2 (p+1)}}+b^2 x^{-\frac{1}{p+1}}\right)^p}{a (2 p+1)}-\frac{x \left(a+b x^{-\frac{1}{2 (p+1)}}\right)^2 \left(a^2+2 a b x^{-\frac{1}{2 (p+1)}}+b^2 x^{-\frac{1}{p+1}}\right)^p}{a^2 (2 p+1)}","\frac{2 (p+1) x \left(a+b x^{-\frac{1}{2 (p+1)}}\right) \left(a^2+2 a b x^{-\frac{1}{2 (p+1)}}+b^2 x^{-\frac{1}{p+1}}\right)^p}{a (2 p+1)}-\frac{x \left(a+b x^{-\frac{1}{2 (p+1)}}\right)^2 \left(a^2+2 a b x^{-\frac{1}{2 (p+1)}}+b^2 x^{-\frac{1}{p+1}}\right)^p}{a^2 (2 p+1)}",1,"(2*(1 + p)*x*(a + b/x^(1/(2*(1 + p))))*(a^2 + b^2/x^(1 + p)^(-1) + (2*a*b)/x^(1/(2*(1 + p))))^p)/(a*(1 + 2*p)) - (x*(a + b/x^(1/(2*(1 + p))))^2*(a^2 + b^2/x^(1 + p)^(-1) + (2*a*b)/x^(1/(2*(1 + p))))^p)/(a^2*(1 + 2*p))","A",3,3,34,0.08824,1,"{1343, 192, 191}"
546,1,102,0,0.0442048,"\int \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{-\frac{1+2 n}{2 n}} \, dx","Int[(a^2 + 2*a*b*x^n + b^2*x^(2*n))^(-(1 + 2*n)/(2*n)),x]","\frac{n x \left(a+b x^n\right)^2 \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{\frac{1}{2} \left(-\frac{1}{n}-2\right)}}{a^2 (n+1)}+\frac{x \left(a+b x^n\right) \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{\frac{1}{2} \left(-\frac{1}{n}-2\right)}}{a (n+1)}","\frac{n x \left(a+b x^n\right)^2 \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{\frac{1}{2} \left(-\frac{1}{n}-2\right)}}{a^2 (n+1)}+\frac{x \left(a+b x^n\right) \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{\frac{1}{2} \left(-\frac{1}{n}-2\right)}}{a (n+1)}",1,"(x*(a + b*x^n)*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^((-2 - n^(-1))/2))/(a*(1 + n)) + (n*x*(a + b*x^n)^2*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^((-2 - n^(-1))/2))/(a^2*(1 + n))","A",3,3,33,0.09091,1,"{1343, 192, 191}"
547,1,124,0,0.0642789,"\int (d x)^{-1-2 n (1+p)} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^p \, dx","Int[(d*x)^(-1 - 2*n*(1 + p))*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^p,x]","\frac{\left(\frac{b x^n}{a}+1\right)^2 (d x)^{-2 n (p+1)} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^p}{2 d n \left(2 p^2+3 p+1\right)}-\frac{\left(\frac{b x^n}{a}+1\right) (d x)^{-2 n (p+1)} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^p}{d n (2 p+1)}","\frac{(d x)^{-2 n (p+1)} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^{p+1}}{2 a^2 d n (p+1) (2 p+1)}-\frac{\left(a+b x^n\right) (d x)^{-2 n (p+1)} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^p}{a d n (2 p+1)}",1,"-(((1 + (b*x^n)/a)*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^p)/(d*n*(1 + 2*p)*(d*x)^(2*n*(1 + p)))) + ((1 + (b*x^n)/a)^2*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^p)/(2*d*n*(1 + 3*p + 2*p^2)*(d*x)^(2*n*(1 + p)))","A",3,3,35,0.08571,1,"{1356, 273, 264}"
548,1,103,0,0.0647758,"\int x^{-1+2 n} \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^p \, dx","Int[x^(-1 + 2*n)*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^p,x]","\frac{a^2 \left(\frac{b x^n}{a}+1\right)^2 \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^p}{2 b^2 n (p+1)}-\frac{a^2 \left(\frac{b x^n}{a}+1\right) \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^p}{b^2 n (2 p+1)}","\frac{a^2 \left(\frac{b x^n}{a}+1\right)^2 \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^p}{2 b^2 n (p+1)}-\frac{a^2 \left(\frac{b x^n}{a}+1\right) \left(a^2+2 a b x^n+b^2 x^{2 n}\right)^p}{b^2 n (2 p+1)}",1,"-((a^2*(1 + (b*x^n)/a)*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^p)/(b^2*n*(1 + 2*p))) + (a^2*(1 + (b*x^n)/a)^2*(a^2 + 2*a*b*x^n + b^2*x^(2*n))^p)/(2*b^2*n*(1 + p))","A",4,3,30,0.1000,1,"{1356, 266, 43}"
549,1,111,0,0.1217265,"\int \frac{x^{-1+4 n}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 + 4*n)/(a + b*x^n + c*x^(2*n)),x]","\frac{\left(b^2-a c\right) \log \left(a+b x^n+c x^{2 n}\right)}{2 c^3 n}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{c^3 n \sqrt{b^2-4 a c}}-\frac{b x^n}{c^2 n}+\frac{x^{2 n}}{2 c n}","\frac{\left(b^2-a c\right) \log \left(a+b x^n+c x^{2 n}\right)}{2 c^3 n}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{c^3 n \sqrt{b^2-4 a c}}-\frac{b x^n}{c^2 n}+\frac{x^{2 n}}{2 c n}",1,"-((b*x^n)/(c^2*n)) + x^(2*n)/(2*c*n) + (b*(b^2 - 3*a*c)*ArcTanh[(b + 2*c*x^n)/Sqrt[b^2 - 4*a*c]])/(c^3*Sqrt[b^2 - 4*a*c]*n) + ((b^2 - a*c)*Log[a + b*x^n + c*x^(2*n)])/(2*c^3*n)","A",7,6,24,0.2500,1,"{1357, 701, 634, 618, 206, 628}"
550,1,87,0,0.074099,"\int \frac{x^{-1+3 n}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 + 3*n)/(a + b*x^n + c*x^(2*n)),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{c^2 n \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x^n+c x^{2 n}\right)}{2 c^2 n}+\frac{x^n}{c n}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{c^2 n \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b x^n+c x^{2 n}\right)}{2 c^2 n}+\frac{x^n}{c n}",1,"x^n/(c*n) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x^n)/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c]*n) - (b*Log[a + b*x^n + c*x^(2*n)])/(2*c^2*n)","A",6,6,24,0.2500,1,"{1357, 703, 634, 618, 206, 628}"
551,1,68,0,0.0505273,"\int \frac{x^{-1+2 n}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 + 2*n)/(a + b*x^n + c*x^(2*n)),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{c n \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^n+c x^{2 n}\right)}{2 c n}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{c n \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^n+c x^{2 n}\right)}{2 c n}",1,"(b*ArcTanh[(b + 2*c*x^n)/Sqrt[b^2 - 4*a*c]])/(c*Sqrt[b^2 - 4*a*c]*n) + Log[a + b*x^n + c*x^(2*n)]/(2*c*n)","A",5,5,24,0.2083,1,"{1357, 634, 618, 206, 628}"
552,1,39,0,0.0329309,"\int \frac{x^{-1+n}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 + n)/(a + b*x^n + c*x^(2*n)),x]","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{n \sqrt{b^2-4 a c}}","-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{n \sqrt{b^2-4 a c}}",1,"(-2*ArcTanh[(b + 2*c*x^n)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*n)","A",3,3,22,0.1364,1,"{1352, 618, 206}"
553,1,98,0,0.1260378,"\int \frac{x^{-1-n}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 - n)/(a + b*x^n + c*x^(2*n)),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{a^2 n \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x^n+c x^{2 n}\right)}{2 a^2 n}-\frac{b \log (x)}{a^2}-\frac{x^{-n}}{a n}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{a^2 n \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b x^n+c x^{2 n}\right)}{2 a^2 n}-\frac{b \log (x)}{a^2}-\frac{x^{-n}}{a n}",1,"-(1/(a*n*x^n)) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*x^n)/Sqrt[b^2 - 4*a*c]])/(a^2*Sqrt[b^2 - 4*a*c]*n) - (b*Log[x])/a^2 + (b*Log[a + b*x^n + c*x^(2*n)])/(2*a^2*n)","A",8,7,24,0.2917,1,"{1357, 709, 800, 634, 618, 206, 628}"
554,1,126,0,0.1709707,"\int \frac{x^{-1-2 n}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 - 2*n)/(a + b*x^n + c*x^(2*n)),x]","-\frac{\left(b^2-a c\right) \log \left(a+b x^n+c x^{2 n}\right)}{2 a^3 n}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{a^3 n \sqrt{b^2-4 a c}}+\frac{\log (x) \left(b^2-a c\right)}{a^3}+\frac{b x^{-n}}{a^2 n}-\frac{x^{-2 n}}{2 a n}","-\frac{\left(b^2-a c\right) \log \left(a+b x^n+c x^{2 n}\right)}{2 a^3 n}+\frac{b \left(b^2-3 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{a^3 n \sqrt{b^2-4 a c}}+\frac{\log (x) \left(b^2-a c\right)}{a^3}+\frac{b x^{-n}}{a^2 n}-\frac{x^{-2 n}}{2 a n}",1,"-1/(2*a*n*x^(2*n)) + b/(a^2*n*x^n) + (b*(b^2 - 3*a*c)*ArcTanh[(b + 2*c*x^n)/Sqrt[b^2 - 4*a*c]])/(a^3*Sqrt[b^2 - 4*a*c]*n) + ((b^2 - a*c)*Log[x])/a^3 - ((b^2 - a*c)*Log[a + b*x^n + c*x^(2*n)])/(2*a^3*n)","A",8,7,24,0.2917,1,"{1357, 709, 800, 634, 618, 206, 628}"
555,1,164,0,0.2312625,"\int \frac{x^{-1-3 n}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 - 3*n)/(a + b*x^n + c*x^(2*n)),x]","-\frac{\left(2 a^2 c^2-4 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{a^4 n \sqrt{b^2-4 a c}}-\frac{x^{-n} \left(b^2-a c\right)}{a^3 n}+\frac{b \left(b^2-2 a c\right) \log \left(a+b x^n+c x^{2 n}\right)}{2 a^4 n}-\frac{b \log (x) \left(b^2-2 a c\right)}{a^4}+\frac{b x^{-2 n}}{2 a^2 n}-\frac{x^{-3 n}}{3 a n}","-\frac{\left(2 a^2 c^2-4 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{a^4 n \sqrt{b^2-4 a c}}-\frac{x^{-n} \left(b^2-a c\right)}{a^3 n}+\frac{b \left(b^2-2 a c\right) \log \left(a+b x^n+c x^{2 n}\right)}{2 a^4 n}-\frac{b \log (x) \left(b^2-2 a c\right)}{a^4}+\frac{b x^{-2 n}}{2 a^2 n}-\frac{x^{-3 n}}{3 a n}",1,"-1/(3*a*n*x^(3*n)) + b/(2*a^2*n*x^(2*n)) - (b^2 - a*c)/(a^3*n*x^n) - ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*ArcTanh[(b + 2*c*x^n)/Sqrt[b^2 - 4*a*c]])/(a^4*Sqrt[b^2 - 4*a*c]*n) - (b*(b^2 - 2*a*c)*Log[x])/a^4 + (b*(b^2 - 2*a*c)*Log[a + b*x^n + c*x^(2*n)])/(2*a^4*n)","A",8,7,24,0.2917,1,"{1357, 709, 800, 634, 618, 206, 628}"
556,1,353,0,0.6269604,"\int \frac{x^{-1+\frac{n}{4}}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 + n/4)/(a + b*x^n + c*x^(2*n)),x]","\frac{2\ 2^{3/4} c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{n \sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2\ 2^{3/4} c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{n \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{2\ 2^{3/4} c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{n \sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2\ 2^{3/4} c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{n \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}","\frac{2\ 2^{3/4} c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{n \sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2\ 2^{3/4} c^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{n \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}+\frac{2\ 2^{3/4} c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{n \sqrt{b^2-4 a c} \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2\ 2^{3/4} c^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} x^{n/4}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{n \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}",1,"(2*2^(3/4)*c^(3/4)*ArcTan[(2^(1/4)*c^(1/4)*x^(n/4))/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(3/4)*n) - (2*2^(3/4)*c^(3/4)*ArcTan[(2^(1/4)*c^(1/4)*x^(n/4))/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(3/4)*n) + (2*2^(3/4)*c^(3/4)*ArcTanh[(2^(1/4)*c^(1/4)*x^(n/4))/(-b - Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(3/4)*n) - (2*2^(3/4)*c^(3/4)*ArcTanh[(2^(1/4)*c^(1/4)*x^(n/4))/(-b + Sqrt[b^2 - 4*a*c])^(1/4)])/(Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(3/4)*n)","A",8,5,26,0.1923,1,"{1381, 1347, 212, 208, 205}"
557,1,610,0,1.1522947,"\int \frac{x^{-1+\frac{n}{3}}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 + n/3)/(a + b*x^n + c*x^(2*n)),x]","\frac{2^{2/3} c^{2/3} \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x^{n/3}\right)}{n \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{2^{2/3} c^{2/3} \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x^{n/3}\right)}{n \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{c^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x^{n/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^{2 n/3}\right)}{\sqrt[3]{2} n \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x^{n/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^{2 n/3}\right)}{\sqrt[3]{2} n \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{2^{2/3} \sqrt{3} c^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x^{n/3}}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{n \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{2^{2/3} \sqrt{3} c^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x^{n/3}}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{n \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}","\frac{2^{2/3} c^{2/3} \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{c} x^{n/3}\right)}{n \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{2^{2/3} c^{2/3} \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{c} x^{n/3}\right)}{n \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{c^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x^{n/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}+2^{2/3} c^{2/3} x^{2 n/3}\right)}{\sqrt[3]{2} n \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{c^{2/3} \log \left(-\sqrt[3]{2} \sqrt[3]{c} x^{n/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}+2^{2/3} c^{2/3} x^{2 n/3}\right)}{\sqrt[3]{2} n \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{2^{2/3} \sqrt{3} c^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x^{n/3}}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{n \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{2^{2/3} \sqrt{3} c^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{c} x^{n/3}}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{n \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}",1,"-((2^(2/3)*Sqrt[3]*c^(2/3)*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x^(n/3))/(b - Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])^(2/3)*n)) + (2^(2/3)*Sqrt[3]*c^(2/3)*ArcTan[(1 - (2*2^(1/3)*c^(1/3)*x^(n/3))/(b + Sqrt[b^2 - 4*a*c])^(1/3))/Sqrt[3]])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])^(2/3)*n) + (2^(2/3)*c^(2/3)*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x^(n/3)])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])^(2/3)*n) - (2^(2/3)*c^(2/3)*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + 2^(1/3)*c^(1/3)*x^(n/3)])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])^(2/3)*n) - (c^(2/3)*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3)*x^(n/3) + 2^(2/3)*c^(2/3)*x^((2*n)/3)])/(2^(1/3)*Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])^(2/3)*n) + (c^(2/3)*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) - 2^(1/3)*c^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3)*x^(n/3) + 2^(2/3)*c^(2/3)*x^((2*n)/3)])/(2^(1/3)*Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])^(2/3)*n)","A",14,8,26,0.3077,1,"{1381, 1347, 200, 31, 634, 617, 204, 628}"
558,1,169,0,0.1918174,"\int \frac{x^{-1+\frac{n}{2}}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 + n/2)/(a + b*x^n + c*x^(2*n)),x]","\frac{2 \sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^{n/2}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{n \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{2 \sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^{n/2}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{n \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{2 \sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^{n/2}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{n \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{2 \sqrt{2} \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x^{n/2}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{n \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(2*Sqrt[2]*Sqrt[c]*ArcTan[(Sqrt[2]*Sqrt[c]*x^(n/2))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]*n) - (2*Sqrt[2]*Sqrt[c]*ArcTan[(Sqrt[2]*Sqrt[c]*x^(n/2))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]*n)","A",4,3,26,0.1154,1,"{1381, 1093, 205}"
559,1,205,0,0.395062,"\int \frac{x^{-1-\frac{n}{2}}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 - n/2)/(a + b*x^n + c*x^(2*n)),x]","\frac{\sqrt{2} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x^{-n/2}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a^{3/2} n \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x^{-n/2}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a^{3/2} n \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 x^{-n/2}}{a n}","\frac{\sqrt{2} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x^{-n/2}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a^{3/2} n \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{a} x^{-n/2}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a^{3/2} n \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 x^{-n/2}}{a n}",1,"-2/(a*n*x^(n/2)) + (Sqrt[2]*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[a])/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*x^(n/2))])/(a^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*n) + (Sqrt[2]*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[a])/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*x^(n/2))])/(a^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*n)","A",6,5,26,0.1923,1,"{1381, 1340, 1122, 1166, 205}"
560,1,699,0,1.4929304,"\int \frac{x^{-1-\frac{n}{3}}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 - n/3)/(a + b*x^n + c*x^(2*n)),x]","\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{a} x^{-n/3}\right)}{\sqrt[3]{2} a^{4/3} n \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{a} x^{-n/3}\right)}{\sqrt[3]{2} a^{4/3} n \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(2^{2/3} a^{2/3} x^{-2 n/3}-\sqrt[3]{2} \sqrt[3]{a} x^{-n/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}\right)}{2 \sqrt[3]{2} a^{4/3} n \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(2^{2/3} a^{2/3} x^{-2 n/3}-\sqrt[3]{2} \sqrt[3]{a} x^{-n/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}\right)}{2 \sqrt[3]{2} a^{4/3} n \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\sqrt{3} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{a} x^{-n/3}}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} a^{4/3} n \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\sqrt{3} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{a} x^{-n/3}}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} a^{4/3} n \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{3 x^{-n/3}}{a n}","\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(\sqrt[3]{b-\sqrt{b^2-4 a c}}+\sqrt[3]{2} \sqrt[3]{a} x^{-n/3}\right)}{\sqrt[3]{2} a^{4/3} n \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(\sqrt[3]{\sqrt{b^2-4 a c}+b}+\sqrt[3]{2} \sqrt[3]{a} x^{-n/3}\right)}{\sqrt[3]{2} a^{4/3} n \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \log \left(2^{2/3} a^{2/3} x^{-2 n/3}-\sqrt[3]{2} \sqrt[3]{a} x^{-n/3} \sqrt[3]{b-\sqrt{b^2-4 a c}}+\left(b-\sqrt{b^2-4 a c}\right)^{2/3}\right)}{2 \sqrt[3]{2} a^{4/3} n \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \log \left(2^{2/3} a^{2/3} x^{-2 n/3}-\sqrt[3]{2} \sqrt[3]{a} x^{-n/3} \sqrt[3]{\sqrt{b^2-4 a c}+b}+\left(\sqrt{b^2-4 a c}+b\right)^{2/3}\right)}{2 \sqrt[3]{2} a^{4/3} n \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{\sqrt{3} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{a} x^{-n/3}}{\sqrt[3]{b-\sqrt{b^2-4 a c}}}}{\sqrt{3}}\right)}{\sqrt[3]{2} a^{4/3} n \left(b-\sqrt{b^2-4 a c}\right)^{2/3}}-\frac{\sqrt{3} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \sqrt[3]{a} x^{-n/3}}{\sqrt[3]{\sqrt{b^2-4 a c}+b}}}{\sqrt{3}}\right)}{\sqrt[3]{2} a^{4/3} n \left(\sqrt{b^2-4 a c}+b\right)^{2/3}}-\frac{3 x^{-n/3}}{a n}",1,"-3/(a*n*x^(n/3)) - (Sqrt[3]*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*a^(1/3))/((b - Sqrt[b^2 - 4*a*c])^(1/3)*x^(n/3)))/Sqrt[3]])/(2^(1/3)*a^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)*n) - (Sqrt[3]*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(1 - (2*2^(1/3)*a^(1/3))/((b + Sqrt[b^2 - 4*a*c])^(1/3)*x^(n/3)))/Sqrt[3]])/(2^(1/3)*a^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3)*n) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(1/3) + (2^(1/3)*a^(1/3))/x^(n/3)])/(2^(1/3)*a^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)*n) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(1/3) + (2^(1/3)*a^(1/3))/x^(n/3)])/(2^(1/3)*a^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3)*n) - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b - Sqrt[b^2 - 4*a*c])^(2/3) + (2^(2/3)*a^(2/3))/x^((2*n)/3) - (2^(1/3)*a^(1/3)*(b - Sqrt[b^2 - 4*a*c])^(1/3))/x^(n/3)])/(2*2^(1/3)*a^(4/3)*(b - Sqrt[b^2 - 4*a*c])^(2/3)*n) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*Log[(b + Sqrt[b^2 - 4*a*c])^(2/3) + (2^(2/3)*a^(2/3))/x^((2*n)/3) - (2^(1/3)*a^(1/3)*(b + Sqrt[b^2 - 4*a*c])^(1/3))/x^(n/3)])/(2*2^(1/3)*a^(4/3)*(b + Sqrt[b^2 - 4*a*c])^(2/3)*n)","A",16,10,26,0.3846,1,"{1381, 1340, 1367, 1422, 200, 31, 634, 617, 204, 628}"
561,1,414,0,0.7868854,"\int \frac{x^{-1-\frac{n}{4}}}{a+b x^n+c x^{2 n}} \, dx","Int[x^(-1 - n/4)/(a + b*x^n + c*x^(2*n)),x]","-\frac{2^{3/4} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{a^{5/4} n \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2^{3/4} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{a^{5/4} n \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2^{3/4} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{a^{5/4} n \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2^{3/4} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{a^{5/4} n \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{4 x^{-n/4}}{a n}","-\frac{2^{3/4} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{a^{5/4} n \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2^{3/4} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{a^{5/4} n \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2^{3/4} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{-\sqrt{b^2-4 a c}-b}}\right)}{a^{5/4} n \left(-\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{2^{3/4} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{a} x^{-n/4}}{\sqrt[4]{\sqrt{b^2-4 a c}-b}}\right)}{a^{5/4} n \left(\sqrt{b^2-4 a c}-b\right)^{3/4}}-\frac{4 x^{-n/4}}{a n}",1,"-4/(a*n*x^(n/4)) - (2^(3/4)*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*a^(1/4))/((-b - Sqrt[b^2 - 4*a*c])^(1/4)*x^(n/4))])/(a^(5/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)*n) - (2^(3/4)*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(2^(1/4)*a^(1/4))/((-b + Sqrt[b^2 - 4*a*c])^(1/4)*x^(n/4))])/(a^(5/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)*n) - (2^(3/4)*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*a^(1/4))/((-b - Sqrt[b^2 - 4*a*c])^(1/4)*x^(n/4))])/(a^(5/4)*(-b - Sqrt[b^2 - 4*a*c])^(3/4)*n) - (2^(3/4)*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(2^(1/4)*a^(1/4))/((-b + Sqrt[b^2 - 4*a*c])^(1/4)*x^(n/4))])/(a^(5/4)*(-b + Sqrt[b^2 - 4*a*c])^(3/4)*n)","A",10,7,26,0.2692,1,"{1381, 1340, 1367, 1422, 212, 208, 205}"
562,1,140,0,0.1184536,"\int \frac{x^2}{a+b x^n+c x^{2 n}} \, dx","Int[x^2/(a + b*x^n + c*x^(2*n)),x]","-\frac{2 c x^3 \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{3 \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}-\frac{2 c x^3 \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{3 \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}","-\frac{2 c x^3 \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{3 \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}-\frac{2 c x^3 \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{3 \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}",1,"(-2*c*x^3*Hypergeometric2F1[1, 3/n, (3 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])])/(3*(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])) - (2*c*x^3*Hypergeometric2F1[1, 3/n, (3 + n)/n, (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(3*(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c]))","A",3,2,20,0.1000,1,"{1383, 364}"
563,1,136,0,0.0401216,"\int \frac{x}{a+b x^n+c x^{2 n}} \, dx","Int[x/(a + b*x^n + c*x^(2*n)),x]","-\frac{c x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{c x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}","-\frac{c x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{c x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}",1,"-((c*x^2*Hypergeometric2F1[1, 2/n, (2 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])) - (c*x^2*Hypergeometric2F1[1, 2/n, (2 + n)/n, (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])","A",3,2,18,0.1111,1,"{1383, 364}"
564,1,124,0,0.0629608,"\int \frac{1}{a+b x^n+c x^{2 n}} \, dx","Int[(a + b*x^n + c*x^(2*n))^(-1),x]","-\frac{2 c x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{2 c x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}","-\frac{2 c x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{2 c x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}",1,"(-2*c*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c]) - (2*c*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])","A",3,2,16,0.1250,1,"{1347, 245}"
565,1,74,0,0.0658304,"\int \frac{1}{x \left(a+b x^n+c x^{2 n}\right)} \, dx","Int[1/(x*(a + b*x^n + c*x^(2*n))),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{a n \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x^n+c x^{2 n}\right)}{2 a n}+\frac{\log (x)}{a}","\frac{b \tanh ^{-1}\left(\frac{b+2 c x^n}{\sqrt{b^2-4 a c}}\right)}{a n \sqrt{b^2-4 a c}}-\frac{\log \left(a+b x^n+c x^{2 n}\right)}{2 a n}+\frac{\log (x)}{a}",1,"(b*ArcTanh[(b + 2*c*x^n)/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]*n) + Log[x]/a - Log[a + b*x^n + c*x^(2*n)]/(2*a*n)","A",7,7,20,0.3500,1,"{1357, 705, 29, 634, 618, 206, 628}"
566,1,142,0,0.0462026,"\int \frac{1}{x^2 \left(a+b x^n+c x^{2 n}\right)} \, dx","Int[1/(x^2*(a + b*x^n + c*x^(2*n))),x]","\frac{2 c \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{x \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}+\frac{2 c \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{x \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}","\frac{2 c \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{x \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}+\frac{2 c \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{x \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}",1,"(2*c*Hypergeometric2F1[1, -n^(-1), -((1 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])])/((b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])*x) + (2*c*Hypergeometric2F1[1, -n^(-1), -((1 - n)/n), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/((b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])*x)","A",3,2,20,0.1000,1,"{1383, 364}"
567,1,140,0,0.0481798,"\int \frac{1}{x^3 \left(a+b x^n+c x^{2 n}\right)} \, dx","Int[1/(x^3*(a + b*x^n + c*x^(2*n))),x]","\frac{c \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{x^2 \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}+\frac{c \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{x^2 \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}","\frac{c \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{x^2 \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}+\frac{c \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{x^2 \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}",1,"(c*Hypergeometric2F1[1, -2/n, -((2 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])])/((b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])*x^2) + (c*Hypergeometric2F1[1, -2/n, -((2 - n)/n), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/((b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])*x^2)","A",3,2,20,0.1000,1,"{1383, 364}"
568,1,148,0,0.177984,"\int x^3 \sqrt{a+b x^n+c x^{2 n}} \, dx","Int[x^3*Sqrt[a + b*x^n + c*x^(2*n)],x]","\frac{x^4 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{4}{n};-\frac{1}{2},-\frac{1}{2};\frac{n+4}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","\frac{x^4 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{4}{n};-\frac{1}{2},-\frac{1}{2};\frac{n+4}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"(x^4*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[4/n, -1/2, -1/2, (4 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(4*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,22,0.09091,1,"{1385, 510}"
569,1,148,0,0.1472396,"\int x^2 \sqrt{a+b x^n+c x^{2 n}} \, dx","Int[x^2*Sqrt[a + b*x^n + c*x^(2*n)],x]","\frac{x^3 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{3}{n};-\frac{1}{2},-\frac{1}{2};\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{3 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","\frac{x^3 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{3}{n};-\frac{1}{2},-\frac{1}{2};\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{3 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"(x^3*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[3/n, -1/2, -1/2, (3 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(3*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,22,0.09091,1,"{1385, 510}"
570,1,148,0,0.1138899,"\int x \sqrt{a+b x^n+c x^{2 n}} \, dx","Int[x*Sqrt[a + b*x^n + c*x^(2*n)],x]","\frac{x^2 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{2}{n};-\frac{1}{2},-\frac{1}{2};\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","\frac{x^2 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{2}{n};-\frac{1}{2},-\frac{1}{2};\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"(x^2*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[2/n, -1/2, -1/2, (2 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(2*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,20,0.1000,1,"{1385, 510}"
571,1,139,0,0.0840802,"\int \sqrt{a+b x^n+c x^{2 n}} \, dx","Int[Sqrt[a + b*x^n + c*x^(2*n)],x]","\frac{x \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{1}{n};-\frac{1}{2},-\frac{1}{2};1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","\frac{x \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{1}{n};-\frac{1}{2},-\frac{1}{2};1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"(x*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[n^(-1), -1/2, -1/2, 1 + n^(-1), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,18,0.1111,1,"{1348, 429}"
572,1,119,0,0.0952366,"\int \frac{\sqrt{a+b x^n+c x^{2 n}}}{x} \, dx","Int[Sqrt[a + b*x^n + c*x^(2*n)]/x,x]","\frac{\sqrt{a+b x^n+c x^{2 n}}}{n}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{2 a+b x^n}{2 \sqrt{a} \sqrt{a+b x^n+c x^{2 n}}}\right)}{n}+\frac{b \tanh ^{-1}\left(\frac{b+2 c x^n}{2 \sqrt{c} \sqrt{a+b x^n+c x^{2 n}}}\right)}{2 \sqrt{c} n}","\frac{\sqrt{a+b x^n+c x^{2 n}}}{n}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{2 a+b x^n}{2 \sqrt{a} \sqrt{a+b x^n+c x^{2 n}}}\right)}{n}+\frac{b \tanh ^{-1}\left(\frac{b+2 c x^n}{2 \sqrt{c} \sqrt{a+b x^n+c x^{2 n}}}\right)}{2 \sqrt{c} n}",1,"Sqrt[a + b*x^n + c*x^(2*n)]/n - (Sqrt[a]*ArcTanh[(2*a + b*x^n)/(2*Sqrt[a]*Sqrt[a + b*x^n + c*x^(2*n)])])/n + (b*ArcTanh[(b + 2*c*x^n)/(2*Sqrt[c]*Sqrt[a + b*x^n + c*x^(2*n)])])/(2*Sqrt[c]*n)","A",7,6,22,0.2727,1,"{1357, 734, 843, 621, 206, 724}"
573,1,149,0,0.1496985,"\int \frac{\sqrt{a+b x^n+c x^{2 n}}}{x^2} \, dx","Int[Sqrt[a + b*x^n + c*x^(2*n)]/x^2,x]","-\frac{\sqrt{a+b x^n+c x^{2 n}} F_1\left(-\frac{1}{n};-\frac{1}{2},-\frac{1}{2};-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","-\frac{\sqrt{a+b x^n+c x^{2 n}} F_1\left(-\frac{1}{n};-\frac{1}{2},-\frac{1}{2};-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"-((Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[-n^(-1), -1/2, -1/2, -((1 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(x*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]))","A",2,2,22,0.09091,1,"{1385, 510}"
574,1,151,0,0.1485331,"\int \frac{\sqrt{a+b x^n+c x^{2 n}}}{x^3} \, dx","Int[Sqrt[a + b*x^n + c*x^(2*n)]/x^3,x]","-\frac{\sqrt{a+b x^n+c x^{2 n}} F_1\left(-\frac{2}{n};-\frac{1}{2},-\frac{1}{2};-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","-\frac{\sqrt{a+b x^n+c x^{2 n}} F_1\left(-\frac{2}{n};-\frac{1}{2},-\frac{1}{2};-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"-(Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[-2/n, -1/2, -1/2, -((2 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(2*x^2*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,22,0.09091,1,"{1385, 510}"
575,1,149,0,0.1538122,"\int x^3 \left(a+b x^n+c x^{2 n}\right)^{3/2} \, dx","Int[x^3*(a + b*x^n + c*x^(2*n))^(3/2),x]","\frac{a x^4 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{4}{n};-\frac{3}{2},-\frac{3}{2};\frac{n+4}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","\frac{a x^4 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{4}{n};-\frac{3}{2},-\frac{3}{2};\frac{n+4}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"(a*x^4*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[4/n, -3/2, -3/2, (4 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(4*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,22,0.09091,1,"{1385, 510}"
576,1,149,0,0.1508043,"\int x^2 \left(a+b x^n+c x^{2 n}\right)^{3/2} \, dx","Int[x^2*(a + b*x^n + c*x^(2*n))^(3/2),x]","\frac{a x^3 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{3}{n};-\frac{3}{2},-\frac{3}{2};\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{3 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","\frac{a x^3 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{3}{n};-\frac{3}{2},-\frac{3}{2};\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{3 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"(a*x^3*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[3/n, -3/2, -3/2, (3 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(3*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,22,0.09091,1,"{1385, 510}"
577,1,149,0,0.113792,"\int x \left(a+b x^n+c x^{2 n}\right)^{3/2} \, dx","Int[x*(a + b*x^n + c*x^(2*n))^(3/2),x]","\frac{a x^2 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{2}{n};-\frac{3}{2},-\frac{3}{2};\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","\frac{a x^2 \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{2}{n};-\frac{3}{2},-\frac{3}{2};\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"(a*x^2*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[2/n, -3/2, -3/2, (2 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(2*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,20,0.1000,1,"{1385, 510}"
578,1,140,0,0.0827008,"\int \left(a+b x^n+c x^{2 n}\right)^{3/2} \, dx","Int[(a + b*x^n + c*x^(2*n))^(3/2),x]","\frac{a x \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{1}{n};-\frac{3}{2},-\frac{3}{2};1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","\frac{a x \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{1}{n};-\frac{3}{2},-\frac{3}{2};1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"(a*x*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[n^(-1), -3/2, -3/2, 1 + n^(-1), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,18,0.1111,1,"{1348, 429}"
579,1,173,0,0.1586209,"\int \frac{\left(a+b x^n+c x^{2 n}\right)^{3/2}}{x} \, dx","Int[(a + b*x^n + c*x^(2*n))^(3/2)/x,x]","-\frac{a^{3/2} \tanh ^{-1}\left(\frac{2 a+b x^n}{2 \sqrt{a} \sqrt{a+b x^n+c x^{2 n}}}\right)}{n}-\frac{b \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{2 \sqrt{c} \sqrt{a+b x^n+c x^{2 n}}}\right)}{16 c^{3/2} n}+\frac{\left(8 a c+b^2+2 b c x^n\right) \sqrt{a+b x^n+c x^{2 n}}}{8 c n}+\frac{\left(a+b x^n+c x^{2 n}\right)^{3/2}}{3 n}","-\frac{a^{3/2} \tanh ^{-1}\left(\frac{2 a+b x^n}{2 \sqrt{a} \sqrt{a+b x^n+c x^{2 n}}}\right)}{n}-\frac{b \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^n}{2 \sqrt{c} \sqrt{a+b x^n+c x^{2 n}}}\right)}{16 c^{3/2} n}+\frac{\left(8 a c+b^2+2 b c x^n\right) \sqrt{a+b x^n+c x^{2 n}}}{8 c n}+\frac{\left(a+b x^n+c x^{2 n}\right)^{3/2}}{3 n}",1,"((b^2 + 8*a*c + 2*b*c*x^n)*Sqrt[a + b*x^n + c*x^(2*n)])/(8*c*n) + (a + b*x^n + c*x^(2*n))^(3/2)/(3*n) - (a^(3/2)*ArcTanh[(2*a + b*x^n)/(2*Sqrt[a]*Sqrt[a + b*x^n + c*x^(2*n)])])/n - (b*(b^2 - 12*a*c)*ArcTanh[(b + 2*c*x^n)/(2*Sqrt[c]*Sqrt[a + b*x^n + c*x^(2*n)])])/(16*c^(3/2)*n)","A",8,7,22,0.3182,1,"{1357, 734, 814, 843, 621, 206, 724}"
580,1,150,0,0.1506765,"\int \frac{\left(a+b x^n+c x^{2 n}\right)^{3/2}}{x^2} \, dx","Int[(a + b*x^n + c*x^(2*n))^(3/2)/x^2,x]","-\frac{a \sqrt{a+b x^n+c x^{2 n}} F_1\left(-\frac{1}{n};-\frac{3}{2},-\frac{3}{2};-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","-\frac{a \sqrt{a+b x^n+c x^{2 n}} F_1\left(-\frac{1}{n};-\frac{3}{2},-\frac{3}{2};-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"-((a*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[-n^(-1), -3/2, -3/2, -((1 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(x*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]))","A",2,2,22,0.09091,1,"{1385, 510}"
581,1,152,0,0.1521108,"\int \frac{\left(a+b x^n+c x^{2 n}\right)^{3/2}}{x^3} \, dx","Int[(a + b*x^n + c*x^(2*n))^(3/2)/x^3,x]","-\frac{a \sqrt{a+b x^n+c x^{2 n}} F_1\left(-\frac{2}{n};-\frac{3}{2},-\frac{3}{2};-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","-\frac{a \sqrt{a+b x^n+c x^{2 n}} F_1\left(-\frac{2}{n};-\frac{3}{2},-\frac{3}{2};-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"-(a*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[-2/n, -3/2, -3/2, -((2 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(2*x^2*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,22,0.09091,1,"{1385, 510}"
582,1,148,0,0.152993,"\int \frac{x^3}{\sqrt{a+b x^n+c x^{2 n}}} \, dx","Int[x^3/Sqrt[a + b*x^n + c*x^(2*n)],x]","\frac{x^4 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{4}{n};\frac{1}{2},\frac{1}{2};\frac{n+4}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{a+b x^n+c x^{2 n}}}","\frac{x^4 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{4}{n};\frac{1}{2},\frac{1}{2};\frac{n+4}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{4 \sqrt{a+b x^n+c x^{2 n}}}",1,"(x^4*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[4/n, 1/2, 1/2, (4 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(4*Sqrt[a + b*x^n + c*x^(2*n)])","A",2,2,22,0.09091,1,"{1385, 510}"
583,1,148,0,0.1479512,"\int \frac{x^2}{\sqrt{a+b x^n+c x^{2 n}}} \, dx","Int[x^2/Sqrt[a + b*x^n + c*x^(2*n)],x]","\frac{x^3 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{n};\frac{1}{2},\frac{1}{2};\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{3 \sqrt{a+b x^n+c x^{2 n}}}","\frac{x^3 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{n};\frac{1}{2},\frac{1}{2};\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{3 \sqrt{a+b x^n+c x^{2 n}}}",1,"(x^3*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[3/n, 1/2, 1/2, (3 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(3*Sqrt[a + b*x^n + c*x^(2*n)])","A",2,2,22,0.09091,1,"{1385, 510}"
584,1,148,0,0.1106209,"\int \frac{x}{\sqrt{a+b x^n+c x^{2 n}}} \, dx","Int[x/Sqrt[a + b*x^n + c*x^(2*n)],x]","\frac{x^2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{n};\frac{1}{2},\frac{1}{2};\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{a+b x^n+c x^{2 n}}}","\frac{x^2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{n};\frac{1}{2},\frac{1}{2};\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 \sqrt{a+b x^n+c x^{2 n}}}",1,"(x^2*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[2/n, 1/2, 1/2, (2 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(2*Sqrt[a + b*x^n + c*x^(2*n)])","A",2,2,20,0.1000,1,"{1385, 510}"
585,1,139,0,0.083524,"\int \frac{1}{\sqrt{a+b x^n+c x^{2 n}}} \, dx","Int[1/Sqrt[a + b*x^n + c*x^(2*n)],x]","\frac{x \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{n};\frac{1}{2},\frac{1}{2};1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{a+b x^n+c x^{2 n}}}","\frac{x \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{n};\frac{1}{2},\frac{1}{2};1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{\sqrt{a+b x^n+c x^{2 n}}}",1,"(x*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[n^(-1), 1/2, 1/2, 1 + n^(-1), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/Sqrt[a + b*x^n + c*x^(2*n)]","A",2,2,18,0.1111,1,"{1348, 429}"
586,1,47,0,0.0334797,"\int \frac{1}{x \sqrt{a+b x^n+c x^{2 n}}} \, dx","Int[1/(x*Sqrt[a + b*x^n + c*x^(2*n)]),x]","-\frac{\tanh ^{-1}\left(\frac{2 a+b x^n}{2 \sqrt{a} \sqrt{a+b x^n+c x^{2 n}}}\right)}{\sqrt{a} n}","-\frac{\tanh ^{-1}\left(\frac{2 a+b x^n}{2 \sqrt{a} \sqrt{a+b x^n+c x^{2 n}}}\right)}{\sqrt{a} n}",1,"-(ArcTanh[(2*a + b*x^n)/(2*Sqrt[a]*Sqrt[a + b*x^n + c*x^(2*n)])]/(Sqrt[a]*n))","A",3,3,22,0.1364,1,"{1357, 724, 206}"
587,1,149,0,0.1470358,"\int \frac{1}{x^2 \sqrt{a+b x^n+c x^{2 n}}} \, dx","Int[1/(x^2*Sqrt[a + b*x^n + c*x^(2*n)]),x]","-\frac{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{n};\frac{1}{2},\frac{1}{2};-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{a+b x^n+c x^{2 n}}}","-\frac{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{n};\frac{1}{2},\frac{1}{2};-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{x \sqrt{a+b x^n+c x^{2 n}}}",1,"-((Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-n^(-1), 1/2, 1/2, -((1 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(x*Sqrt[a + b*x^n + c*x^(2*n)]))","A",2,2,22,0.09091,1,"{1385, 510}"
588,1,151,0,0.146022,"\int \frac{1}{x^3 \sqrt{a+b x^n+c x^{2 n}}} \, dx","Int[1/(x^3*Sqrt[a + b*x^n + c*x^(2*n)]),x]","-\frac{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{2}{n};\frac{1}{2},\frac{1}{2};-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{a+b x^n+c x^{2 n}}}","-\frac{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{2}{n};\frac{1}{2},\frac{1}{2};-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 x^2 \sqrt{a+b x^n+c x^{2 n}}}",1,"-(Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-2/n, 1/2, 1/2, -((2 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(2*x^2*Sqrt[a + b*x^n + c*x^(2*n)])","A",2,2,22,0.09091,1,"{1385, 510}"
589,1,151,0,0.1512053,"\int \frac{x^3}{\left(a+b x^n+c x^{2 n}\right)^{3/2}} \, dx","Int[x^3/(a + b*x^n + c*x^(2*n))^(3/2),x]","\frac{x^4 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{4}{n};\frac{3}{2},\frac{3}{2};\frac{n+4}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{4 a \sqrt{a+b x^n+c x^{2 n}}}","\frac{x^4 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{4}{n};\frac{3}{2},\frac{3}{2};\frac{n+4}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{4 a \sqrt{a+b x^n+c x^{2 n}}}",1,"(x^4*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[4/n, 3/2, 3/2, (4 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(4*a*Sqrt[a + b*x^n + c*x^(2*n)])","A",2,2,22,0.09091,1,"{1385, 510}"
590,1,151,0,0.1491511,"\int \frac{x^2}{\left(a+b x^n+c x^{2 n}\right)^{3/2}} \, dx","Int[x^2/(a + b*x^n + c*x^(2*n))^(3/2),x]","\frac{x^3 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{n};\frac{3}{2},\frac{3}{2};\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{3 a \sqrt{a+b x^n+c x^{2 n}}}","\frac{x^3 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{n};\frac{3}{2},\frac{3}{2};\frac{n+3}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{3 a \sqrt{a+b x^n+c x^{2 n}}}",1,"(x^3*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[3/n, 3/2, 3/2, (3 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(3*a*Sqrt[a + b*x^n + c*x^(2*n)])","A",2,2,22,0.09091,1,"{1385, 510}"
591,1,151,0,0.1121069,"\int \frac{x}{\left(a+b x^n+c x^{2 n}\right)^{3/2}} \, dx","Int[x/(a + b*x^n + c*x^(2*n))^(3/2),x]","\frac{x^2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{n};\frac{3}{2},\frac{3}{2};\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{a+b x^n+c x^{2 n}}}","\frac{x^2 \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{n};\frac{3}{2},\frac{3}{2};\frac{n+2}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{a+b x^n+c x^{2 n}}}",1,"(x^2*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[2/n, 3/2, 3/2, (2 + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(2*a*Sqrt[a + b*x^n + c*x^(2*n)])","A",2,2,20,0.1000,1,"{1385, 510}"
592,1,142,0,0.0822772,"\int \frac{1}{\left(a+b x^n+c x^{2 n}\right)^{3/2}} \, dx","Int[(a + b*x^n + c*x^(2*n))^(-3/2),x]","\frac{x \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{n};\frac{3}{2},\frac{3}{2};1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{a \sqrt{a+b x^n+c x^{2 n}}}","\frac{x \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{n};\frac{3}{2},\frac{3}{2};1+\frac{1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{a \sqrt{a+b x^n+c x^{2 n}}}",1,"(x*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[n^(-1), 3/2, 3/2, 1 + n^(-1), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(a*Sqrt[a + b*x^n + c*x^(2*n)])","A",2,2,18,0.1111,1,"{1348, 429}"
593,1,98,0,0.0729641,"\int \frac{1}{x \left(a+b x^n+c x^{2 n}\right)^{3/2}} \, dx","Int[1/(x*(a + b*x^n + c*x^(2*n))^(3/2)),x]","\frac{2 \left(-2 a c+b^2+b c x^n\right)}{a n \left(b^2-4 a c\right) \sqrt{a+b x^n+c x^{2 n}}}-\frac{\tanh ^{-1}\left(\frac{2 a+b x^n}{2 \sqrt{a} \sqrt{a+b x^n+c x^{2 n}}}\right)}{a^{3/2} n}","\frac{2 \left(-2 a c+b^2+b c x^n\right)}{a n \left(b^2-4 a c\right) \sqrt{a+b x^n+c x^{2 n}}}-\frac{\tanh ^{-1}\left(\frac{2 a+b x^n}{2 \sqrt{a} \sqrt{a+b x^n+c x^{2 n}}}\right)}{a^{3/2} n}",1,"(2*(b^2 - 2*a*c + b*c*x^n))/(a*(b^2 - 4*a*c)*n*Sqrt[a + b*x^n + c*x^(2*n)]) - ArcTanh[(2*a + b*x^n)/(2*Sqrt[a]*Sqrt[a + b*x^n + c*x^(2*n)])]/(a^(3/2)*n)","A",5,5,22,0.2273,1,"{1357, 740, 12, 724, 206}"
594,1,152,0,0.1570287,"\int \frac{1}{x^2 \left(a+b x^n+c x^{2 n}\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*x^n + c*x^(2*n))^(3/2)),x]","-\frac{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{n};\frac{3}{2},\frac{3}{2};-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{a x \sqrt{a+b x^n+c x^{2 n}}}","-\frac{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{n};\frac{3}{2},\frac{3}{2};-\frac{1-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{a x \sqrt{a+b x^n+c x^{2 n}}}",1,"-((Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-n^(-1), 3/2, 3/2, -((1 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(a*x*Sqrt[a + b*x^n + c*x^(2*n)]))","A",2,2,22,0.09091,1,"{1385, 510}"
595,1,154,0,0.1541472,"\int \frac{1}{x^3 \left(a+b x^n+c x^{2 n}\right)^{3/2}} \, dx","Int[1/(x^3*(a + b*x^n + c*x^(2*n))^(3/2)),x]","-\frac{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{2}{n};\frac{3}{2},\frac{3}{2};-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 a x^2 \sqrt{a+b x^n+c x^{2 n}}}","-\frac{\sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{2}{n};\frac{3}{2},\frac{3}{2};-\frac{2-n}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 a x^2 \sqrt{a+b x^n+c x^{2 n}}}",1,"-(Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-2/n, 3/2, 3/2, -((2 - n)/n), (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(2*a*x^2*Sqrt[a + b*x^n + c*x^(2*n)])","A",2,2,22,0.09091,1,"{1385, 510}"
596,1,182,0,0.1557611,"\int (d x)^m \left(a+b x^n+c x^{2 n}\right)^3 \, dx","Int[(d*x)^m*(a + b*x^n + c*x^(2*n))^3,x]","\frac{3 a^2 b x^{n+1} (d x)^m}{m+n+1}+\frac{a^3 (d x)^{m+1}}{d (m+1)}+\frac{3 a x^{2 n+1} \left(a c+b^2\right) (d x)^m}{m+2 n+1}+\frac{b x^{3 n+1} \left(6 a c+b^2\right) (d x)^m}{m+3 n+1}+\frac{3 c x^{4 n+1} \left(a c+b^2\right) (d x)^m}{m+4 n+1}+\frac{3 b c^2 x^{5 n+1} (d x)^m}{m+5 n+1}+\frac{c^3 x^{6 n+1} (d x)^m}{m+6 n+1}","\frac{3 a^2 b x^{n+1} (d x)^m}{m+n+1}+\frac{a^3 (d x)^{m+1}}{d (m+1)}+\frac{3 a x^{2 n+1} \left(a c+b^2\right) (d x)^m}{m+2 n+1}+\frac{b x^{3 n+1} \left(6 a c+b^2\right) (d x)^m}{m+3 n+1}+\frac{3 c x^{4 n+1} \left(a c+b^2\right) (d x)^m}{m+4 n+1}+\frac{3 b c^2 x^{5 n+1} (d x)^m}{m+5 n+1}+\frac{c^3 x^{6 n+1} (d x)^m}{m+6 n+1}",1,"(3*a^2*b*x^(1 + n)*(d*x)^m)/(1 + m + n) + (3*a*(b^2 + a*c)*x^(1 + 2*n)*(d*x)^m)/(1 + m + 2*n) + (b*(b^2 + 6*a*c)*x^(1 + 3*n)*(d*x)^m)/(1 + m + 3*n) + (3*c*(b^2 + a*c)*x^(1 + 4*n)*(d*x)^m)/(1 + m + 4*n) + (3*b*c^2*x^(1 + 5*n)*(d*x)^m)/(1 + m + 5*n) + (c^3*x^(1 + 6*n)*(d*x)^m)/(1 + m + 6*n) + (a^3*(d*x)^(1 + m))/(d*(1 + m))","A",14,3,22,0.1364,1,"{1353, 20, 30}"
597,1,117,0,0.0690006,"\int (d x)^m \left(a+b x^n+c x^{2 n}\right)^2 \, dx","Int[(d*x)^m*(a + b*x^n + c*x^(2*n))^2,x]","\frac{a^2 (d x)^{m+1}}{d (m+1)}+\frac{x^{2 n+1} \left(2 a c+b^2\right) (d x)^m}{m+2 n+1}+\frac{2 a b x^{n+1} (d x)^m}{m+n+1}+\frac{2 b c x^{3 n+1} (d x)^m}{m+3 n+1}+\frac{c^2 x^{4 n+1} (d x)^m}{m+4 n+1}","\frac{a^2 (d x)^{m+1}}{d (m+1)}+\frac{x^{2 n+1} \left(2 a c+b^2\right) (d x)^m}{m+2 n+1}+\frac{2 a b x^{n+1} (d x)^m}{m+n+1}+\frac{2 b c x^{3 n+1} (d x)^m}{m+3 n+1}+\frac{c^2 x^{4 n+1} (d x)^m}{m+4 n+1}",1,"(2*a*b*x^(1 + n)*(d*x)^m)/(1 + m + n) + ((b^2 + 2*a*c)*x^(1 + 2*n)*(d*x)^m)/(1 + m + 2*n) + (2*b*c*x^(1 + 3*n)*(d*x)^m)/(1 + m + 3*n) + (c^2*x^(1 + 4*n)*(d*x)^m)/(1 + m + 4*n) + (a^2*(d*x)^(1 + m))/(d*(1 + m))","A",10,3,22,0.1364,1,"{1353, 20, 30}"
598,1,58,0,0.0242398,"\int (d x)^m \left(a+b x^n+c x^{2 n}\right) \, dx","Int[(d*x)^m*(a + b*x^n + c*x^(2*n)),x]","\frac{a (d x)^{m+1}}{d (m+1)}+\frac{b x^{n+1} (d x)^m}{m+n+1}+\frac{c x^{2 n+1} (d x)^m}{m+2 n+1}","\frac{a (d x)^{m+1}}{d (m+1)}+\frac{b x^{n+1} (d x)^m}{m+n+1}+\frac{c x^{2 n+1} (d x)^m}{m+2 n+1}",1,"(b*x^(1 + n)*(d*x)^m)/(1 + m + n) + (c*x^(1 + 2*n)*(d*x)^m)/(1 + m + 2*n) + (a*(d*x)^(1 + m))/(d*(1 + m))","A",6,3,20,0.1500,1,"{14, 20, 30}"
599,1,175,0,0.1853463,"\int \frac{(d x)^m}{a+b x^n+c x^{2 n}} \, dx","Int[(d*x)^m/(a + b*x^n + c*x^(2*n)),x]","\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}","\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c (d x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}",1,"(2*c*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*d*(1 + m)) - (2*c*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*d*(1 + m))","A",3,2,22,0.09091,1,"{1383, 364}"
600,1,328,0,0.9612825,"\int \frac{(d x)^m}{\left(a+b x^n+c x^{2 n}\right)^2} \, dx","Int[(d*x)^m/(a + b*x^n + c*x^(2*n))^2,x]","\frac{c (d x)^{m+1} \left(\frac{4 a c (m-2 n+1)-b^2 (m-n+1)}{\sqrt{b^2-4 a c}}-b (m-n+1)\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{a d (m+1) n \left(b^2-4 a c\right) \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (d x)^{m+1} \left(b (m-n+1) \sqrt{b^2-4 a c}+4 a c (m-2 n+1)+b^2 (-(m-n+1))\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{a d (m+1) n \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(d x)^{m+1} \left(-2 a c+b^2+b c x^n\right)}{a d n \left(b^2-4 a c\right) \left(a+b x^n+c x^{2 n}\right)}","\frac{c (d x)^{m+1} \left(\frac{4 a c (m-2 n+1)-b^2 (m-n+1)}{\sqrt{b^2-4 a c}}-b (m-n+1)\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{a d (m+1) n \left(b^2-4 a c\right) \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (d x)^{m+1} \left(b (m-n+1) \sqrt{b^2-4 a c}+4 a c (m-2 n+1)+b^2 (-(m-n+1))\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{a d (m+1) n \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(d x)^{m+1} \left(-2 a c+b^2+b c x^n\right)}{a d n \left(b^2-4 a c\right) \left(a+b x^n+c x^{2 n}\right)}",1,"((d*x)^(1 + m)*(b^2 - 2*a*c + b*c*x^n))/(a*(b^2 - 4*a*c)*d*n*(a + b*x^n + c*x^(2*n))) + (c*((4*a*c*(1 + m - 2*n) - b^2*(1 + m - n))/Sqrt[b^2 - 4*a*c] - b*(1 + m - n))*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])])/(a*(b^2 - 4*a*c)*(b - Sqrt[b^2 - 4*a*c])*d*(1 + m)*n) - (c*(4*a*c*(1 + m - 2*n) - b^2*(1 + m - n) + b*Sqrt[b^2 - 4*a*c]*(1 + m - n))*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(a*(b^2 - 4*a*c)^(3/2)*(b + Sqrt[b^2 - 4*a*c])*d*(1 + m)*n)","A",5,3,22,0.1364,1,"{1384, 1560, 364}"
601,1,615,0,10.723782,"\int \frac{(d x)^m}{\left(a+b x^n+c x^{2 n}\right)^3} \, dx","Int[(d*x)^m/(a + b*x^n + c*x^(2*n))^3,x]","-\frac{c (d x)^{m+1} \left(-8 a^2 c^2 \left(m^2+m (2-6 n)+8 n^2-6 n+1\right)+6 a b^2 c \left(m^2+m (2-4 n)+3 n^2-4 n+1\right)+b (m-n+1) \sqrt{b^2-4 a c} \left(2 a c (2 m-7 n+2)-b^2 (m-2 n+1)\right)+b^4 \left(-\left(m^2+m (2-3 n)+2 n^2-3 n+1\right)\right)\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{2 a^2 d (m+1) n^2 \left(b^2-4 a c\right)^{5/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (d x)^{m+1} \left(8 a^2 c^2 \left(m^2+m (2-6 n)+8 n^2-6 n+1\right)-6 a b^2 c \left(m^2+m (2-4 n)+3 n^2-4 n+1\right)+b (m-n+1) \sqrt{b^2-4 a c} \left(2 a c (2 m-7 n+2)-b^2 (m-2 n+1)\right)+b^4 \left(m^2+m (2-3 n)+2 n^2-3 n+1\right)\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 a^2 d (m+1) n^2 \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}+b\right)}-\frac{(d x)^{m+1} \left(4 a^2 c^2 (m-4 n+1)-b c x^n \left(2 a c (2 m-7 n+2)-b^2 (m-2 n+1)\right)-5 a b^2 c (m-3 n+1)+b^4 (m-2 n+1)\right)}{2 a^2 d n^2 \left(b^2-4 a c\right)^2 \left(a+b x^n+c x^{2 n}\right)}+\frac{(d x)^{m+1} \left(-2 a c+b^2+b c x^n\right)}{2 a d n \left(b^2-4 a c\right) \left(a+b x^n+c x^{2 n}\right)^2}","-\frac{c (d x)^{m+1} \left(-8 a^2 c^2 \left(m^2+m (2-6 n)+8 n^2-6 n+1\right)+6 a b^2 c \left(m^2+m (2-4 n)+3 n^2-4 n+1\right)+b (m-n+1) \sqrt{b^2-4 a c} \left(2 a c (2 m-7 n+2)-b^2 (m-2 n+1)\right)+b^4 \left(-\left(m^2+m (2-3 n)+2 n^2-3 n+1\right)\right)\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}\right)}{2 a^2 d (m+1) n^2 \left(b^2-4 a c\right)^{5/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (d x)^{m+1} \left(8 a^2 c^2 \left(m^2+m (2-6 n)+8 n^2-6 n+1\right)-6 a b^2 c \left(m^2+m (2-4 n)+3 n^2-4 n+1\right)+b (m-n+1) \sqrt{b^2-4 a c} \left(2 a c (2 m-7 n+2)-b^2 (m-2 n+1)\right)+b^4 \left(m^2+m (2-3 n)+2 n^2-3 n+1\right)\right) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{2 a^2 d (m+1) n^2 \left(b^2-4 a c\right)^{5/2} \left(\sqrt{b^2-4 a c}+b\right)}-\frac{(d x)^{m+1} \left(4 a^2 c^2 (m-4 n+1)-b c x^n \left(2 a c (2 m-7 n+2)-b^2 (m-2 n+1)\right)-5 a b^2 c (m-3 n+1)+b^4 (m-2 n+1)\right)}{2 a^2 d n^2 \left(b^2-4 a c\right)^2 \left(a+b x^n+c x^{2 n}\right)}+\frac{(d x)^{m+1} \left(-2 a c+b^2+b c x^n\right)}{2 a d n \left(b^2-4 a c\right) \left(a+b x^n+c x^{2 n}\right)^2}",1,"((d*x)^(1 + m)*(b^2 - 2*a*c + b*c*x^n))/(2*a*(b^2 - 4*a*c)*d*n*(a + b*x^n + c*x^(2*n))^2) - ((d*x)^(1 + m)*(4*a^2*c^2*(1 + m - 4*n) - 5*a*b^2*c*(1 + m - 3*n) + b^4*(1 + m - 2*n) - b*c*(2*a*c*(2 + 2*m - 7*n) - b^2*(1 + m - 2*n))*x^n))/(2*a^2*(b^2 - 4*a*c)^2*d*n^2*(a + b*x^n + c*x^(2*n))) - (c*(b*Sqrt[b^2 - 4*a*c]*(2*a*c*(2 + 2*m - 7*n) - b^2*(1 + m - 2*n))*(1 + m - n) - b^4*(1 + m^2 + m*(2 - 3*n) - 3*n + 2*n^2) + 6*a*b^2*c*(1 + m^2 + m*(2 - 4*n) - 4*n + 3*n^2) - 8*a^2*c^2*(1 + m^2 + m*(2 - 6*n) - 6*n + 8*n^2))*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])])/(2*a^2*(b^2 - 4*a*c)^(5/2)*(b - Sqrt[b^2 - 4*a*c])*d*(1 + m)*n^2) - (c*(b*Sqrt[b^2 - 4*a*c]*(2*a*c*(2 + 2*m - 7*n) - b^2*(1 + m - 2*n))*(1 + m - n) + b^4*(1 + m^2 + m*(2 - 3*n) - 3*n + 2*n^2) - 6*a*b^2*c*(1 + m^2 + m*(2 - 4*n) - 4*n + 3*n^2) + 8*a^2*c^2*(1 + m^2 + m*(2 - 6*n) - 6*n + 8*n^2))*(d*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(2*a^2*(b^2 - 4*a*c)^(5/2)*(b + Sqrt[b^2 - 4*a*c])*d*(1 + m)*n^2)","A",6,4,22,0.1818,1,"{1384, 1558, 1560, 364}"
602,1,161,0,0.1792602,"\int (d x)^m \left(a+b x^n+c x^{2 n}\right)^{3/2} \, dx","Int[(d*x)^m*(a + b*x^n + c*x^(2*n))^(3/2),x]","\frac{a (d x)^{m+1} \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{m+1}{n};-\frac{3}{2},-\frac{3}{2};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","\frac{a (d x)^{m+1} \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{m+1}{n};-\frac{3}{2},-\frac{3}{2};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"(a*(d*x)^(1 + m)*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[(1 + m)/n, -3/2, -3/2, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,24,0.08333,1,"{1385, 510}"
603,1,160,0,0.1678164,"\int (d x)^m \sqrt{a+b x^n+c x^{2 n}} \, dx","Int[(d*x)^m*Sqrt[a + b*x^n + c*x^(2*n)],x]","\frac{(d x)^{m+1} \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{m+1}{n};-\frac{1}{2},-\frac{1}{2};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}","\frac{(d x)^{m+1} \sqrt{a+b x^n+c x^{2 n}} F_1\left(\frac{m+1}{n};-\frac{1}{2},-\frac{1}{2};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1}}",1,"((d*x)^(1 + m)*Sqrt[a + b*x^n + c*x^(2*n)]*AppellF1[(1 + m)/n, -1/2, -1/2, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])","A",2,2,24,0.08333,1,"{1385, 510}"
604,1,160,0,0.1691889,"\int \frac{(d x)^m}{\sqrt{a+b x^n+c x^{2 n}}} \, dx","Int[(d*x)^m/Sqrt[a + b*x^n + c*x^(2*n)],x]","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{n};\frac{1}{2},\frac{1}{2};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{a+b x^n+c x^{2 n}}}","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{n};\frac{1}{2},\frac{1}{2};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1) \sqrt{a+b x^n+c x^{2 n}}}",1,"((d*x)^(1 + m)*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[(1 + m)/n, 1/2, 1/2, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*Sqrt[a + b*x^n + c*x^(2*n)])","A",2,2,24,0.08333,1,"{1385, 510}"
605,1,163,0,0.1733553,"\int \frac{(d x)^m}{\left(a+b x^n+c x^{2 n}\right)^{3/2}} \, dx","Int[(d*x)^m/(a + b*x^n + c*x^(2*n))^(3/2),x]","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{n};\frac{3}{2},\frac{3}{2};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{a d (m+1) \sqrt{a+b x^n+c x^{2 n}}}","\frac{(d x)^{m+1} \sqrt{\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{n};\frac{3}{2},\frac{3}{2};\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{a d (m+1) \sqrt{a+b x^n+c x^{2 n}}}",1,"((d*x)^(1 + m)*Sqrt[1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[(1 + m)/n, 3/2, 3/2, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(a*d*(1 + m)*Sqrt[a + b*x^n + c*x^(2*n)])","A",2,2,24,0.08333,1,"{1385, 510}"
606,1,158,0,0.1290942,"\int (d x)^m \left(a+b x^n+c x^{2 n}\right)^p \, dx","Int[(d*x)^m*(a + b*x^n + c*x^(2*n))^p,x]","\frac{(d x)^{m+1} \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+1}{n};-p,-p;\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1)}","\frac{(d x)^{m+1} \left(\frac{2 c x^n}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x^n}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x^n+c x^{2 n}\right)^p F_1\left(\frac{m+1}{n};-p,-p;\frac{m+n+1}{n};-\frac{2 c x^n}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^n}{b+\sqrt{b^2-4 a c}}\right)}{d (m+1)}",1,"((d*x)^(1 + m)*(a + b*x^n + c*x^(2*n))^p*AppellF1[(1 + m)/n, -p, -p, (1 + m + n)/n, (-2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^n)/(b + Sqrt[b^2 - 4*a*c])])/(d*(1 + m)*(1 + (2*c*x^n)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x^n)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",2,2,22,0.09091,1,"{1385, 510}"
607,1,46,0,0.0536108,"\int (d+e x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right) \, dx","Int[(d + e*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4),x]","\frac{a (d+e x)^4}{4 e}+\frac{b (d+e x)^6}{6 e}+\frac{c (d+e x)^8}{8 e}","\frac{a (d+e x)^4}{4 e}+\frac{b (d+e x)^6}{6 e}+\frac{c (d+e x)^8}{8 e}",1,"(a*(d + e*x)^4)/(4*e) + (b*(d + e*x)^6)/(6*e) + (c*(d + e*x)^8)/(8*e)","A",3,2,28,0.07143,1,"{1142, 14}"
608,1,89,0,0.1870726,"\int (d+e x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2 \, dx","Int[(d + e*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2,x]","\frac{a^2 (d+e x)^4}{4 e}+\frac{\left(2 a c+b^2\right) (d+e x)^8}{8 e}+\frac{a b (d+e x)^6}{3 e}+\frac{b c (d+e x)^{10}}{5 e}+\frac{c^2 (d+e x)^{12}}{12 e}","\frac{a^2 (d+e x)^4}{4 e}+\frac{\left(2 a c+b^2\right) (d+e x)^8}{8 e}+\frac{a b (d+e x)^6}{3 e}+\frac{b c (d+e x)^{10}}{5 e}+\frac{c^2 (d+e x)^{12}}{12 e}",1,"(a^2*(d + e*x)^4)/(4*e) + (a*b*(d + e*x)^6)/(3*e) + ((b^2 + 2*a*c)*(d + e*x)^8)/(8*e) + (b*c*(d + e*x)^10)/(5*e) + (c^2*(d + e*x)^12)/(12*e)","A",4,3,30,0.1000,1,"{1142, 1114, 631}"
609,1,138,0,0.3732535,"\int (d+e x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)^3 \, dx","Int[(d + e*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3,x]","\frac{a^2 b (d+e x)^6}{2 e}+\frac{a^3 (d+e x)^4}{4 e}+\frac{c \left(a c+b^2\right) (d+e x)^{12}}{4 e}+\frac{b \left(6 a c+b^2\right) (d+e x)^{10}}{10 e}+\frac{3 a \left(a c+b^2\right) (d+e x)^8}{8 e}+\frac{3 b c^2 (d+e x)^{14}}{14 e}+\frac{c^3 (d+e x)^{16}}{16 e}","\frac{a^2 b (d+e x)^6}{2 e}+\frac{a^3 (d+e x)^4}{4 e}+\frac{c \left(a c+b^2\right) (d+e x)^{12}}{4 e}+\frac{b \left(6 a c+b^2\right) (d+e x)^{10}}{10 e}+\frac{3 a \left(a c+b^2\right) (d+e x)^8}{8 e}+\frac{3 b c^2 (d+e x)^{14}}{14 e}+\frac{c^3 (d+e x)^{16}}{16 e}",1,"(a^3*(d + e*x)^4)/(4*e) + (a^2*b*(d + e*x)^6)/(2*e) + (3*a*(b^2 + a*c)*(d + e*x)^8)/(8*e) + (b*(b^2 + 6*a*c)*(d + e*x)^10)/(10*e) + (c*(b^2 + a*c)*(d + e*x)^12)/(4*e) + (3*b*c^2*(d + e*x)^14)/(14*e) + (c^3*(d + e*x)^16)/(16*e)","A",4,3,30,0.1000,1,"{1142, 1114, 631}"
610,1,55,0,0.0530198,"\int (d f+e f x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right) \, dx","Int[(d*f + e*f*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4),x]","\frac{a f^3 (d+e x)^4}{4 e}+\frac{b f^3 (d+e x)^6}{6 e}+\frac{c f^3 (d+e x)^8}{8 e}","\frac{a f^3 (d+e x)^4}{4 e}+\frac{b f^3 (d+e x)^6}{6 e}+\frac{c f^3 (d+e x)^8}{8 e}",1,"(a*f^3*(d + e*x)^4)/(4*e) + (b*f^3*(d + e*x)^6)/(6*e) + (c*f^3*(d + e*x)^8)/(8*e)","A",3,2,31,0.06452,1,"{1142, 14}"
611,1,104,0,0.1641755,"\int (d f+e f x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2 \, dx","Int[(d*f + e*f*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2,x]","\frac{a^2 f^3 (d+e x)^4}{4 e}+\frac{f^3 \left(2 a c+b^2\right) (d+e x)^8}{8 e}+\frac{a b f^3 (d+e x)^6}{3 e}+\frac{b c f^3 (d+e x)^{10}}{5 e}+\frac{c^2 f^3 (d+e x)^{12}}{12 e}","\frac{a^2 f^3 (d+e x)^4}{4 e}+\frac{f^3 \left(2 a c+b^2\right) (d+e x)^8}{8 e}+\frac{a b f^3 (d+e x)^6}{3 e}+\frac{b c f^3 (d+e x)^{10}}{5 e}+\frac{c^2 f^3 (d+e x)^{12}}{12 e}",1,"(a^2*f^3*(d + e*x)^4)/(4*e) + (a*b*f^3*(d + e*x)^6)/(3*e) + ((b^2 + 2*a*c)*f^3*(d + e*x)^8)/(8*e) + (b*c*f^3*(d + e*x)^10)/(5*e) + (c^2*f^3*(d + e*x)^12)/(12*e)","A",4,3,33,0.09091,1,"{1142, 1114, 631}"
612,1,159,0,0.3153005,"\int (d f+e f x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)^3 \, dx","Int[(d*f + e*f*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3,x]","\frac{a^2 b f^3 (d+e x)^6}{2 e}+\frac{a^3 f^3 (d+e x)^4}{4 e}+\frac{c f^3 \left(a c+b^2\right) (d+e x)^{12}}{4 e}+\frac{b f^3 \left(6 a c+b^2\right) (d+e x)^{10}}{10 e}+\frac{3 a f^3 \left(a c+b^2\right) (d+e x)^8}{8 e}+\frac{3 b c^2 f^3 (d+e x)^{14}}{14 e}+\frac{c^3 f^3 (d+e x)^{16}}{16 e}","\frac{a^2 b f^3 (d+e x)^6}{2 e}+\frac{a^3 f^3 (d+e x)^4}{4 e}+\frac{c f^3 \left(a c+b^2\right) (d+e x)^{12}}{4 e}+\frac{b f^3 \left(6 a c+b^2\right) (d+e x)^{10}}{10 e}+\frac{3 a f^3 \left(a c+b^2\right) (d+e x)^8}{8 e}+\frac{3 b c^2 f^3 (d+e x)^{14}}{14 e}+\frac{c^3 f^3 (d+e x)^{16}}{16 e}",1,"(a^3*f^3*(d + e*x)^4)/(4*e) + (a^2*b*f^3*(d + e*x)^6)/(2*e) + (3*a*(b^2 + a*c)*f^3*(d + e*x)^8)/(8*e) + (b*(b^2 + 6*a*c)*f^3*(d + e*x)^10)/(10*e) + (c*(b^2 + a*c)*f^3*(d + e*x)^12)/(4*e) + (3*b*c^2*f^3*(d + e*x)^14)/(14*e) + (c^3*f^3*(d + e*x)^16)/(16*e)","A",4,3,33,0.09091,1,"{1142, 1114, 631}"
613,1,193,0,0.4383319,"\int \frac{(d+e x)^4}{a+b (d+e x)^2+c (d+e x)^4} \, dx","Int[(d + e*x)^4/(a + b*(d + e*x)^2 + c*(d + e*x)^4),x]","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} e \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} e \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x}{c}","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} e \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} e \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x}{c}",1,"x/c - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",5,4,30,0.1333,1,"{1142, 1122, 1166, 205}"
614,1,81,0,0.1285358,"\int \frac{(d+e x)^3}{a+b (d+e x)^2+c (d+e x)^4} \, dx","Int[(d + e*x)^3/(a + b*(d + e*x)^2 + c*(d + e*x)^4),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 c e \sqrt{b^2-4 a c}}+\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 c e}","\frac{b \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 c e \sqrt{b^2-4 a c}}+\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 c e}",1,"(b*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*c*Sqrt[b^2 - 4*a*c]*e) + Log[a + b*(d + e*x)^2 + c*(d + e*x)^4]/(4*c*e)","A",6,6,30,0.2000,1,"{1142, 1114, 634, 618, 206, 628}"
615,1,164,0,0.1548394,"\int \frac{(d+e x)^2}{a+b (d+e x)^2+c (d+e x)^4} \, dx","Int[(d + e*x)^2/(a + b*(d + e*x)^2 + c*(d + e*x)^4),x]","\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} e \sqrt{b^2-4 a c}}-\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} e \sqrt{b^2-4 a c}}","\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} e \sqrt{b^2-4 a c}}-\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} e \sqrt{b^2-4 a c}}",1,"-((Sqrt[b - Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c]*e)) + (Sqrt[b + Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c]*e)","A",4,3,30,0.1000,1,"{1142, 1130, 205}"
616,1,43,0,0.0612972,"\int \frac{d+e x}{a+b (d+e x)^2+c (d+e x)^4} \, dx","Int[(d + e*x)/(a + b*(d + e*x)^2 + c*(d + e*x)^4),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \sqrt{b^2-4 a c}}","-\frac{\tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \sqrt{b^2-4 a c}}",1,"-(ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]]/(Sqrt[b^2 - 4*a*c]*e))","A",4,4,28,0.1429,1,"{1142, 1107, 618, 206}"
617,1,94,0,0.1322914,"\int \frac{1}{(d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)} \, dx","Int[1/((d + e*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a e \sqrt{b^2-4 a c}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a e}+\frac{\log (d+e x)}{a e}","\frac{b \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a e \sqrt{b^2-4 a c}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a e}+\frac{\log (d+e x)}{a e}",1,"(b*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*a*Sqrt[b^2 - 4*a*c]*e) + Log[d + e*x]/(a*e) - Log[a + b*(d + e*x)^2 + c*(d + e*x)^4]/(4*a*e)","A",8,8,30,0.2667,1,"{1142, 1114, 705, 29, 634, 618, 206, 628}"
618,1,195,0,0.2863614,"\int \frac{1}{(d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)} \, dx","Int[1/((d + e*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)),x]","-\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a e \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a e \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{a e (d+e x)}","-\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a e \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a e \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{a e (d+e x)}",1,"-(1/(a*e*(d + e*x))) - (Sqrt[c]*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) - (Sqrt[c]*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",5,4,30,0.1333,1,"{1142, 1123, 1166, 205}"
619,1,121,0,0.1984839,"\int \frac{1}{(d+e x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)} \, dx","Int[1/((d + e*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 e \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^2 e}-\frac{b \log (d+e x)}{a^2 e}-\frac{1}{2 a e (d+e x)^2}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 e \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^2 e}-\frac{b \log (d+e x)}{a^2 e}-\frac{1}{2 a e (d+e x)^2}",1,"-1/(2*a*e*(d + e*x)^2) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*Sqrt[b^2 - 4*a*c]*e) - (b*Log[d + e*x])/(a^2*e) + (b*Log[a + b*(d + e*x)^2 + c*(d + e*x)^4])/(4*a^2*e)","A",9,8,30,0.2667,1,"{1142, 1114, 709, 800, 634, 618, 206, 628}"
620,1,224,0,0.4967649,"\int \frac{1}{(d+e x)^4 \left(a+b (d+e x)^2+c (d+e x)^4\right)} \, dx","Int[1/((d + e*x)^4*(a + b*(d + e*x)^2 + c*(d + e*x)^4)),x]","\frac{\sqrt{c} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^2 e \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^2 e \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b}{a^2 e (d+e x)}-\frac{1}{3 a e (d+e x)^3}","\frac{\sqrt{c} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^2 e \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^2 e \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b}{a^2 e (d+e x)}-\frac{1}{3 a e (d+e x)^3}",1,"-1/(3*a*e*(d + e*x)^3) + b/(a^2*e*(d + e*x)) + (Sqrt[c]*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) + (Sqrt[c]*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",6,5,30,0.1667,1,"{1142, 1123, 1281, 1166, 205}"
621,1,270,0,0.5792246,"\int \frac{(d+e x)^4}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[(d + e*x)^4/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2,x]","\frac{(d+e x) \left(2 a+b (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{\left(b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} e \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(b \sqrt{b^2-4 a c}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{(d+e x) \left(2 a+b (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{\left(b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} e \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(b \sqrt{b^2-4 a c}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"((d + e*x)*(2*a + b*(d + e*x)^2))/(2*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + ((b - (b^2 + 4*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) + ((b^2 + 4*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",5,4,30,0.1333,1,"{1142, 1120, 1166, 205}"
622,1,97,0,0.1351435,"\int \frac{(d+e x)^3}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[(d + e*x)^3/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2,x]","\frac{2 a+b (d+e x)^2}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{b \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{3/2}}","\frac{2 a+b (d+e x)^2}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{b \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{3/2}}",1,"(2*a + b*(d + e*x)^2)/(2*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - (b*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(3/2)*e)","A",5,5,30,0.1667,1,"{1142, 1114, 638, 618, 206}"
623,1,254,0,0.3880644,"\int \frac{(d+e x)^2}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[(d + e*x)^2/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2,x]","-\frac{(d+e x) \left(b+2 c (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{\sqrt{c} \left(2 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} e \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(\sqrt{b^2-4 a c}+2 b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{(d+e x) \left(b+2 c (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{\sqrt{c} \left(2 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} e \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(\sqrt{b^2-4 a c}+2 b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-((d + e*x)*(b + 2*c*(d + e*x)^2))/(2*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (Sqrt[c]*(2*b - Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) - (Sqrt[c]*(2*b + Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",5,4,30,0.1333,1,"{1142, 1119, 1166, 205}"
624,1,96,0,0.1224843,"\int \frac{d+e x}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[(d + e*x)/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2,x]","\frac{2 c \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c (d+e x)^2}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}","\frac{2 c \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{3/2}}-\frac{b+2 c (d+e x)^2}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}",1,"-(b + 2*c*(d + e*x)^2)/(2*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (2*c*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(3/2)*e)","A",5,5,28,0.1786,1,"{1142, 1107, 614, 618, 206}"
625,1,299,0,0.701916,"\int \frac{1}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[(a + b*(d + e*x)^2 + c*(d + e*x)^4)^(-2),x]","\frac{\left(\frac{d}{e}+x\right) \left(-2 a c+b^2+b c e^2 \left(\frac{d}{e}+x\right)^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b e^2 \left(\frac{d}{e}+x\right)^2+c e^4 \left(\frac{d}{e}+x\right)^4\right)}+\frac{\sqrt{c} \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a e \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\left(\frac{d}{e}+x\right) \left(-2 a c+b^2+b c e^2 \left(\frac{d}{e}+x\right)^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b e^2 \left(\frac{d}{e}+x\right)^2+c e^4 \left(\frac{d}{e}+x\right)^4\right)}+\frac{\sqrt{c} \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a e \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"((d/e + x)*(b^2 - 2*a*c + b*c*e^2*(d/e + x)^2))/(2*a*(b^2 - 4*a*c)*(a + b*e^2*(d/e + x)^2 + c*e^4*(d/e + x)^4)) + (Sqrt[c]*(b^2 - 12*a*c + b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) - (Sqrt[c]*(b^2 - 12*a*c - b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",5,4,22,0.1818,1,"{1106, 1092, 1166, 205}"
626,1,162,0,0.2942154,"\int \frac{1}{(d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[1/((d + e*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2),x]","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 e \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^2 e}+\frac{\log (d+e x)}{a^2 e}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 e \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^2 e}+\frac{\log (d+e x)}{a^2 e}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}",1,"(b^2 - 2*a*c + b*c*(d + e*x)^2)/(2*a*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (b*(b^2 - 6*a*c)*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*(b^2 - 4*a*c)^(3/2)*e) + Log[d + e*x]/(a^2*e) - Log[a + b*(d + e*x)^2 + c*(d + e*x)^4]/(4*a^2*e)","A",9,8,30,0.2667,1,"{1142, 1114, 740, 800, 634, 618, 206, 628}"
627,1,348,0,1.6528562,"\int \frac{1}{(d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[1/((d + e*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2),x]","-\frac{3 b^2-10 a c}{2 a^2 e \left(b^2-4 a c\right) (d+e x)}-\frac{\sqrt{c} \left(\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 e \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e \left(b^2-4 a c\right) (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)}","-\frac{3 b^2-10 a c}{2 a^2 e \left(b^2-4 a c\right) (d+e x)}-\frac{\sqrt{c} \left(\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 e \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e \left(b^2-4 a c\right) (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)}",1,"-(3*b^2 - 10*a*c)/(2*a^2*(b^2 - 4*a*c)*e*(d + e*x)) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/(2*a*(b^2 - 4*a*c)*e*(d + e*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - (Sqrt[c]*(3*b^3 - 16*a*b*c + (3*b^2 - 10*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) + (Sqrt[c]*(3*b^3 - 16*a*b*c - (3*b^2 - 10*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",6,5,30,0.1667,1,"{1142, 1121, 1281, 1166, 205}"
628,1,213,0,0.3901069,"\int \frac{1}{(d+e x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[1/((d + e*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2),x]","-\frac{\left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{a^3 e \left(b^2-4 a c\right)^{3/2}}-\frac{b^2-3 a c}{a^2 e \left(b^2-4 a c\right) (d+e x)^2}+\frac{b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{2 a^3 e}-\frac{2 b \log (d+e x)}{a^3 e}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e \left(b^2-4 a c\right) (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}","-\frac{\left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{a^3 e \left(b^2-4 a c\right)^{3/2}}-\frac{b^2-3 a c}{a^2 e \left(b^2-4 a c\right) (d+e x)^2}+\frac{b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{2 a^3 e}-\frac{2 b \log (d+e x)}{a^3 e}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e \left(b^2-4 a c\right) (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}",1,"-((b^2 - 3*a*c)/(a^2*(b^2 - 4*a*c)*e*(d + e*x)^2)) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/(2*a*(b^2 - 4*a*c)*e*(d + e*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - ((b^4 - 6*a*b^2*c + 6*a^2*c^2)*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(a^3*(b^2 - 4*a*c)^(3/2)*e) - (2*b*Log[d + e*x])/(a^3*e) + (b*Log[a + b*(d + e*x)^2 + c*(d + e*x)^4])/(2*a^3*e)","A",9,8,30,0.2667,1,"{1142, 1114, 740, 800, 634, 618, 206, 628}"
629,1,408,0,3.6755012,"\int \frac{1}{(d+e x)^4 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[1/((d + e*x)^4*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2),x]","\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c+b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^3 e \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c-b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^3 e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b \left(5 b^2-19 a c\right)}{2 a^3 e \left(b^2-4 a c\right) (d+e x)}-\frac{5 b^2-14 a c}{6 a^2 e \left(b^2-4 a c\right) (d+e x)^3}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e \left(b^2-4 a c\right) (d+e x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)}","\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c+b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^3 e \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c-b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^3 e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b \left(5 b^2-19 a c\right)}{2 a^3 e \left(b^2-4 a c\right) (d+e x)}-\frac{5 b^2-14 a c}{6 a^2 e \left(b^2-4 a c\right) (d+e x)^3}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e \left(b^2-4 a c\right) (d+e x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)}",1,"-(5*b^2 - 14*a*c)/(6*a^2*(b^2 - 4*a*c)*e*(d + e*x)^3) + (b*(5*b^2 - 19*a*c))/(2*a^3*(b^2 - 4*a*c)*e*(d + e*x)) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/(2*a*(b^2 - 4*a*c)*e*(d + e*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (Sqrt[c]*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 + b*(5*b^2 - 19*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) - (Sqrt[c]*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 - b*(5*b^2 - 19*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",7,5,30,0.1667,1,"{1142, 1121, 1281, 1166, 205}"
630,1,341,0,0.9505792,"\int \frac{(d+e x)^4}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[(d + e*x)^4/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3,x]","\frac{(d+e x) \left(2 a+b (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}-\frac{(d+e x) \left(-4 a c+7 b^2+12 b c (d+e x)^2\right)}{8 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{3 \sqrt{c} \left(-2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} e \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} e \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{(d+e x) \left(2 a+b (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}-\frac{(d+e x) \left(-4 a c+7 b^2+12 b c (d+e x)^2\right)}{8 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{3 \sqrt{c} \left(-2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} e \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} e \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"((d + e*x)*(2*a + b*(d + e*x)^2))/(4*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) - ((d + e*x)*(7*b^2 - 4*a*c + 12*b*c*(d + e*x)^2))/(8*(b^2 - 4*a*c)^2*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (3*Sqrt[c]*(3*b^2 + 4*a*c - 2*b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) - (3*Sqrt[c]*(3*b^2 + 4*a*c + 2*b*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",6,5,30,0.1667,1,"{1142, 1120, 1178, 1166, 205}"
631,1,150,0,0.1961409,"\int \frac{(d+e x)^3}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[(d + e*x)^3/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3,x]","\frac{2 a+b (d+e x)^2}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}-\frac{3 b \left(b+2 c (d+e x)^2\right)}{4 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{3 b c \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{5/2}}","\frac{2 a+b (d+e x)^2}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}-\frac{3 b \left(b+2 c (d+e x)^2\right)}{4 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{3 b c \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{5/2}}",1,"(2*a + b*(d + e*x)^2)/(4*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) - (3*b*(b + 2*c*(d + e*x)^2))/(4*(b^2 - 4*a*c)^2*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (3*b*c*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*e)","A",6,6,30,0.2000,1,"{1142, 1114, 638, 614, 618, 206}"
632,1,363,0,1.03918,"\int \frac{(d+e x)^2}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[(d + e*x)^2/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3,x]","-\frac{(d+e x) \left(b+2 c (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}+\frac{(d+e x) \left(c \left(20 a c+b^2\right) (d+e x)^2+b \left(8 a c+b^2\right)\right)}{8 a e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{\sqrt{c} \left(\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a e \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a e \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{(d+e x) \left(b+2 c (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}+\frac{(d+e x) \left(c \left(20 a c+b^2\right) (d+e x)^2+b \left(8 a c+b^2\right)\right)}{8 a e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{\sqrt{c} \left(\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a e \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a e \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-((d + e*x)*(b + 2*c*(d + e*x)^2))/(4*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + ((d + e*x)*(b*(b^2 + 8*a*c) + c*(b^2 + 20*a*c)*(d + e*x)^2))/(8*a*(b^2 - 4*a*c)^2*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (Sqrt[c]*(b^2 + 20*a*c + (b*(b^2 - 52*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) + (Sqrt[c]*(b^2 + 20*a*c - (b*(b^2 - 52*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",6,5,30,0.1667,1,"{1142, 1119, 1178, 1166, 205}"
633,1,150,0,0.1848648,"\int \frac{d+e x}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[(d + e*x)/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3,x]","-\frac{6 c^2 \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{5/2}}+\frac{3 c \left(b+2 c (d+e x)^2\right)}{2 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{b+2 c (d+e x)^2}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}","-\frac{6 c^2 \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{5/2}}+\frac{3 c \left(b+2 c (d+e x)^2\right)}{2 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{b+2 c (d+e x)^2}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}",1,"-(b + 2*c*(d + e*x)^2)/(4*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (3*c*(b + 2*c*(d + e*x)^2))/(2*(b^2 - 4*a*c)^2*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - (6*c^2*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*e)","A",6,5,28,0.1786,1,"{1142, 1107, 614, 618, 206}"
634,1,437,0,5.3610513,"\int \frac{1}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[(a + b*(d + e*x)^2 + c*(d + e*x)^4)^(-3),x]","\frac{3 \sqrt{c} \left(56 a^2 c^2-10 a b^2 c+b \left(b^2-8 a c\right) \sqrt{b^2-4 a c}+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 e \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(56 a^2 c^2-10 a b^2 c-b \left(b^2-8 a c\right) \sqrt{b^2-4 a c}+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^2 e \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\left(\frac{d}{e}+x\right) \left(3 b c e^2 \left(b^2-8 a c\right) \left(\frac{d}{e}+x\right)^2+\left(b^2-7 a c\right) \left(3 b^2-4 a c\right)\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b e^2 \left(\frac{d}{e}+x\right)^2+c e^4 \left(\frac{d}{e}+x\right)^4\right)}+\frac{\left(\frac{d}{e}+x\right) \left(-2 a c+b^2+b c e^2 \left(\frac{d}{e}+x\right)^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b e^2 \left(\frac{d}{e}+x\right)^2+c e^4 \left(\frac{d}{e}+x\right)^4\right)^2}","\frac{3 \sqrt{c} \left(56 a^2 c^2-10 a b^2 c+b \left(b^2-8 a c\right) \sqrt{b^2-4 a c}+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 e \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(56 a^2 c^2-10 a b^2 c-b \left(b^2-8 a c\right) \sqrt{b^2-4 a c}+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^2 e \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\left(\frac{d}{e}+x\right) \left(3 b c e^2 \left(b^2-8 a c\right) \left(\frac{d}{e}+x\right)^2+\left(b^2-7 a c\right) \left(3 b^2-4 a c\right)\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b e^2 \left(\frac{d}{e}+x\right)^2+c e^4 \left(\frac{d}{e}+x\right)^4\right)}+\frac{\left(\frac{d}{e}+x\right) \left(-2 a c+b^2+b c e^2 \left(\frac{d}{e}+x\right)^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b e^2 \left(\frac{d}{e}+x\right)^2+c e^4 \left(\frac{d}{e}+x\right)^4\right)^2}",1,"((d/e + x)*(b^2 - 2*a*c + b*c*e^2*(d/e + x)^2))/(4*a*(b^2 - 4*a*c)*(a + b*e^2*(d/e + x)^2 + c*e^4*(d/e + x)^4)^2) + ((d/e + x)*((b^2 - 7*a*c)*(3*b^2 - 4*a*c) + 3*b*c*(b^2 - 8*a*c)*e^2*(d/e + x)^2))/(8*a^2*(b^2 - 4*a*c)^2*(a + b*e^2*(d/e + x)^2 + c*e^4*(d/e + x)^4)) + (3*Sqrt[c]*(b^4 - 10*a*b^2*c + 56*a^2*c^2 + b*(b^2 - 8*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) - (3*Sqrt[c]*(b^4 - 10*a*b^2*c + 56*a^2*c^2 - b*(b^2 - 8*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*(b^2 - 4*a*c)^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",6,5,22,0.2273,1,"{1106, 1092, 1178, 1166, 205}"
635,1,255,0,0.485574,"\int \frac{1}{(d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[1/((d + e*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x]","\frac{16 a^2 c^2+2 b c \left(b^2-7 a c\right) (d+e x)^2-15 a b^2 c+2 b^4}{4 a^2 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 e \left(b^2-4 a c\right)^{5/2}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^3 e}+\frac{\log (d+e x)}{a^3 e}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}","\frac{16 a^2 c^2+2 b c \left(b^2-7 a c\right) (d+e x)^2-15 a b^2 c+2 b^4}{4 a^2 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 e \left(b^2-4 a c\right)^{5/2}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^3 e}+\frac{\log (d+e x)}{a^3 e}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}",1,"(b^2 - 2*a*c + b*c*(d + e*x)^2)/(4*a*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (2*b^4 - 15*a*b^2*c + 16*a^2*c^2 + 2*b*c*(b^2 - 7*a*c)*(d + e*x)^2)/(4*a^2*(b^2 - 4*a*c)^2*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (b*(b^4 - 10*a*b^2*c + 30*a^2*c^2)*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*a^3*(b^2 - 4*a*c)^(5/2)*e) + Log[d + e*x]/(a^3*e) - Log[a + b*(d + e*x)^2 + c*(d + e*x)^4]/(4*a^3*e)","A",10,9,30,0.3000,1,"{1142, 1114, 740, 822, 800, 634, 618, 206, 628}"
636,1,484,0,1.2267618,"\int \frac{1}{(d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[1/((d + e*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x]","\frac{36 a^2 c^2+b c \left(5 b^2-32 a c\right) (d+e x)^2-35 a b^2 c+5 b^4}{8 a^2 e \left(b^2-4 a c\right)^2 (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{3 \sqrt{c} \left(\frac{b \left(124 a^2 c^2-47 a b^2 c+5 b^4\right)}{\sqrt{b^2-4 a c}}+\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^3 e \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)-\frac{124 a^2 b c^2-47 a b^3 c+5 b^5}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^3 e \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 \left(5 b^2-12 a c\right) \left(b^2-5 a c\right)}{8 a^3 e \left(b^2-4 a c\right)^2 (d+e x)}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e \left(b^2-4 a c\right) (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}","\frac{36 a^2 c^2+b c \left(5 b^2-32 a c\right) (d+e x)^2-35 a b^2 c+5 b^4}{8 a^2 e \left(b^2-4 a c\right)^2 (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{3 \sqrt{c} \left(\frac{b \left(124 a^2 c^2-47 a b^2 c+5 b^4\right)}{\sqrt{b^2-4 a c}}+\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^3 e \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)-\frac{124 a^2 b c^2-47 a b^3 c+5 b^5}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^3 e \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 \left(5 b^2-12 a c\right) \left(b^2-5 a c\right)}{8 a^3 e \left(b^2-4 a c\right)^2 (d+e x)}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e \left(b^2-4 a c\right) (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}",1,"(-3*(5*b^2 - 12*a*c)*(b^2 - 5*a*c))/(8*a^3*(b^2 - 4*a*c)^2*e*(d + e*x)) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/(4*a*(b^2 - 4*a*c)*e*(d + e*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (5*b^4 - 35*a*b^2*c + 36*a^2*c^2 + b*c*(5*b^2 - 32*a*c)*(d + e*x)^2)/(8*a^2*(b^2 - 4*a*c)^2*e*(d + e*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - (3*Sqrt[c]*((5*b^2 - 12*a*c)*(b^2 - 5*a*c) + (b*(5*b^4 - 47*a*b^2*c + 124*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^3*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) - (3*Sqrt[c]*((5*b^2 - 12*a*c)*(b^2 - 5*a*c) - (5*b^5 - 47*a*b^3*c + 124*a^2*b*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^3*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",7,6,30,0.2000,1,"{1142, 1121, 1277, 1281, 1166, 205}"
637,1,325,0,0.5848298,"\int \frac{1}{(d+e x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[1/((d + e*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x]","\frac{20 a^2 c^2+3 b c \left(b^2-6 a c\right) (d+e x)^2-20 a b^2 c+3 b^4}{4 a^2 e \left(b^2-4 a c\right)^2 (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^4 e \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(b^2-5 a c\right) \left(b^2-2 a c\right)}{2 a^3 e \left(b^2-4 a c\right)^2 (d+e x)^2}+\frac{3 b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^4 e}-\frac{3 b \log (d+e x)}{a^4 e}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e \left(b^2-4 a c\right) (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}","\frac{20 a^2 c^2+3 b c \left(b^2-6 a c\right) (d+e x)^2-20 a b^2 c+3 b^4}{4 a^2 e \left(b^2-4 a c\right)^2 (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^4 e \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(b^2-5 a c\right) \left(b^2-2 a c\right)}{2 a^3 e \left(b^2-4 a c\right)^2 (d+e x)^2}+\frac{3 b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^4 e}-\frac{3 b \log (d+e x)}{a^4 e}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e \left(b^2-4 a c\right) (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}",1,"(-3*(b^2 - 5*a*c)*(b^2 - 2*a*c))/(2*a^3*(b^2 - 4*a*c)^2*e*(d + e*x)^2) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/(4*a*(b^2 - 4*a*c)*e*(d + e*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (3*b^4 - 20*a*b^2*c + 20*a^2*c^2 + 3*b*c*(b^2 - 6*a*c)*(d + e*x)^2)/(4*a^2*(b^2 - 4*a*c)^2*e*(d + e*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - (3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*a^4*(b^2 - 4*a*c)^(5/2)*e) - (3*b*Log[d + e*x])/(a^4*e) + (3*b*Log[a + b*(d + e*x)^2 + c*(d + e*x)^4])/(4*a^4*e)","A",10,9,30,0.3000,1,"{1142, 1114, 740, 822, 800, 634, 618, 206, 628}"
638,1,202,0,0.3619435,"\int \frac{(d f+e f x)^4}{a+b (d+e x)^2+c (d+e x)^4} \, dx","Int[(d*f + e*f*x)^4/(a + b*(d + e*x)^2 + c*(d + e*x)^4),x]","-\frac{f^4 \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} e \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{f^4 \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} e \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{f^4 x}{c}","-\frac{f^4 \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} e \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{f^4 \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} e \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{f^4 x}{c}",1,"(f^4*x)/c - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*f^4*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*f^4*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",5,4,33,0.1212,1,"{1142, 1122, 1166, 205}"
639,1,87,0,0.1274769,"\int \frac{(d f+e f x)^3}{a+b (d+e x)^2+c (d+e x)^4} \, dx","Int[(d*f + e*f*x)^3/(a + b*(d + e*x)^2 + c*(d + e*x)^4),x]","\frac{b f^3 \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 c e \sqrt{b^2-4 a c}}+\frac{f^3 \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 c e}","\frac{b f^3 \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 c e \sqrt{b^2-4 a c}}+\frac{f^3 \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 c e}",1,"(b*f^3*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*c*Sqrt[b^2 - 4*a*c]*e) + (f^3*Log[a + b*(d + e*x)^2 + c*(d + e*x)^4])/(4*c*e)","A",6,6,33,0.1818,1,"{1142, 1114, 634, 618, 206, 628}"
640,1,170,0,0.1525507,"\int \frac{(d f+e f x)^2}{a+b (d+e x)^2+c (d+e x)^4} \, dx","Int[(d*f + e*f*x)^2/(a + b*(d + e*x)^2 + c*(d + e*x)^4),x]","\frac{f^2 \sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} e \sqrt{b^2-4 a c}}-\frac{f^2 \sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} e \sqrt{b^2-4 a c}}","\frac{f^2 \sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} e \sqrt{b^2-4 a c}}-\frac{f^2 \sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} e \sqrt{b^2-4 a c}}",1,"-((Sqrt[b - Sqrt[b^2 - 4*a*c]]*f^2*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c]*e)) + (Sqrt[b + Sqrt[b^2 - 4*a*c]]*f^2*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c]*e)","A",4,3,33,0.09091,1,"{1142, 1130, 205}"
641,1,44,0,0.0631629,"\int \frac{d f+e f x}{a+b (d+e x)^2+c (d+e x)^4} \, dx","Int[(d*f + e*f*x)/(a + b*(d + e*x)^2 + c*(d + e*x)^4),x]","-\frac{f \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \sqrt{b^2-4 a c}}","-\frac{f \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \sqrt{b^2-4 a c}}",1,"-((f*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*e))","A",4,4,31,0.1290,1,"{1142, 1107, 618, 206}"
642,1,103,0,0.1382907,"\int \frac{1}{(d f+e f x) \left(a+b (d+e x)^2+c (d+e x)^4\right)} \, dx","Int[1/((d*f + e*f*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)),x]","\frac{b \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a e f \sqrt{b^2-4 a c}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a e f}+\frac{\log (d+e x)}{a e f}","\frac{b \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a e f \sqrt{b^2-4 a c}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a e f}+\frac{\log (d+e x)}{a e f}",1,"(b*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*a*Sqrt[b^2 - 4*a*c]*e*f) + Log[d + e*x]/(a*e*f) - Log[a + b*(d + e*x)^2 + c*(d + e*x)^4]/(4*a*e*f)","A",8,8,33,0.2424,1,"{1142, 1114, 705, 29, 634, 618, 206, 628}"
643,1,204,0,0.2732813,"\int \frac{1}{(d f+e f x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)} \, dx","Int[1/((d*f + e*f*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)),x]","-\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a e f^2 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a e f^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{a e f^2 (d+e x)}","-\frac{\sqrt{c} \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a e f^2 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a e f^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{1}{a e f^2 (d+e x)}",1,"-(1/(a*e*f^2*(d + e*x))) - (Sqrt[c]*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e*f^2) - (Sqrt[c]*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e*f^2)","A",5,4,33,0.1212,1,"{1142, 1123, 1166, 205}"
644,1,133,0,0.1953097,"\int \frac{1}{(d f+e f x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)} \, dx","Int[1/((d*f + e*f*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)),x]","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 e f^3 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^2 e f^3}-\frac{b \log (d+e x)}{a^2 e f^3}-\frac{1}{2 a e f^3 (d+e x)^2}","-\frac{\left(b^2-2 a c\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 e f^3 \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^2 e f^3}-\frac{b \log (d+e x)}{a^2 e f^3}-\frac{1}{2 a e f^3 (d+e x)^2}",1,"-1/(2*a*e*f^3*(d + e*x)^2) - ((b^2 - 2*a*c)*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*Sqrt[b^2 - 4*a*c]*e*f^3) - (b*Log[d + e*x])/(a^2*e*f^3) + (b*Log[a + b*(d + e*x)^2 + c*(d + e*x)^4])/(4*a^2*e*f^3)","A",9,8,33,0.2424,1,"{1142, 1114, 709, 800, 634, 618, 206, 628}"
645,1,236,0,0.4881495,"\int \frac{1}{(d f+e f x)^4 \left(a+b (d+e x)^2+c (d+e x)^4\right)} \, dx","Int[1/((d*f + e*f*x)^4*(a + b*(d + e*x)^2 + c*(d + e*x)^4)),x]","\frac{\sqrt{c} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^2 e f^4 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^2 e f^4 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b}{a^2 e f^4 (d+e x)}-\frac{1}{3 a e f^4 (d+e x)^3}","\frac{\sqrt{c} \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^2 e f^4 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^2 e f^4 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b}{a^2 e f^4 (d+e x)}-\frac{1}{3 a e f^4 (d+e x)^3}",1,"-1/(3*a*e*f^4*(d + e*x)^3) + b/(a^2*e*f^4*(d + e*x)) + (Sqrt[c]*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e*f^4) + (Sqrt[c]*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e*f^4)","A",6,5,33,0.1515,1,"{1142, 1123, 1281, 1166, 205}"
646,1,279,0,0.5385984,"\int \frac{(d f+e f x)^4}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[(d*f + e*f*x)^4/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2,x]","\frac{f^4 (d+e x) \left(2 a+b (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{f^4 \left(b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} e \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{f^4 \left(b \sqrt{b^2-4 a c}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{f^4 (d+e x) \left(2 a+b (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{f^4 \left(b-\frac{4 a c+b^2}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} e \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{f^4 \left(b \sqrt{b^2-4 a c}+4 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(f^4*(d + e*x)*(2*a + b*(d + e*x)^2))/(2*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + ((b - (b^2 + 4*a*c)/Sqrt[b^2 - 4*a*c])*f^4*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) + ((b^2 + 4*a*c + b*Sqrt[b^2 - 4*a*c])*f^4*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",5,4,33,0.1212,1,"{1142, 1120, 1166, 205}"
647,1,103,0,0.1376048,"\int \frac{(d f+e f x)^3}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[(d*f + e*f*x)^3/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2,x]","\frac{f^3 \left(2 a+b (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{b f^3 \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{3/2}}","\frac{f^3 \left(2 a+b (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{b f^3 \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{3/2}}",1,"(f^3*(2*a + b*(d + e*x)^2))/(2*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - (b*f^3*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(3/2)*e)","A",5,5,33,0.1515,1,"{1142, 1114, 638, 618, 206}"
648,1,263,0,0.3679748,"\int \frac{(d f+e f x)^2}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[(d*f + e*f*x)^2/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2,x]","-\frac{f^2 (d+e x) \left(b+2 c (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{\sqrt{c} f^2 \left(2 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} e \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} f^2 \left(\sqrt{b^2-4 a c}+2 b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{f^2 (d+e x) \left(b+2 c (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{\sqrt{c} f^2 \left(2 b-\sqrt{b^2-4 a c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} e \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} f^2 \left(\sqrt{b^2-4 a c}+2 b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} e \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-(f^2*(d + e*x)*(b + 2*c*(d + e*x)^2))/(2*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (Sqrt[c]*(2*b - Sqrt[b^2 - 4*a*c])*f^2*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) - (Sqrt[c]*(2*b + Sqrt[b^2 - 4*a*c])*f^2*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",5,4,33,0.1212,1,"{1142, 1119, 1166, 205}"
649,1,98,0,0.1270713,"\int \frac{d f+e f x}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[(d*f + e*f*x)/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2,x]","\frac{2 c f \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{3/2}}-\frac{f \left(b+2 c (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}","\frac{2 c f \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{3/2}}-\frac{f \left(b+2 c (d+e x)^2\right)}{2 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}",1,"-(f*(b + 2*c*(d + e*x)^2))/(2*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (2*c*f*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(3/2)*e)","A",5,5,31,0.1613,1,"{1142, 1107, 614, 618, 206}"
650,1,174,0,0.2953723,"\int \frac{1}{(d f+e f x) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[1/((d*f + e*f*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2),x]","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 e f \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^2 e f}+\frac{\log (d+e x)}{a^2 e f}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e f \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}","\frac{b \left(b^2-6 a c\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 e f \left(b^2-4 a c\right)^{3/2}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^2 e f}+\frac{\log (d+e x)}{a^2 e f}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e f \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)}",1,"(b^2 - 2*a*c + b*c*(d + e*x)^2)/(2*a*(b^2 - 4*a*c)*e*f*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (b*(b^2 - 6*a*c)*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*(b^2 - 4*a*c)^(3/2)*e*f) + Log[d + e*x]/(a^2*e*f) - Log[a + b*(d + e*x)^2 + c*(d + e*x)^4]/(4*a^2*e*f)","A",9,8,33,0.2424,1,"{1142, 1114, 740, 800, 634, 618, 206, 628}"
651,1,360,0,1.5992627,"\int \frac{1}{(d f+e f x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[1/((d*f + e*f*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2),x]","-\frac{3 b^2-10 a c}{2 a^2 e f^2 \left(b^2-4 a c\right) (d+e x)}-\frac{\sqrt{c} \left(\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 e f^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 e f^2 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e f^2 \left(b^2-4 a c\right) (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)}","-\frac{3 b^2-10 a c}{2 a^2 e f^2 \left(b^2-4 a c\right) (d+e x)}-\frac{\sqrt{c} \left(\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 e f^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\left(3 b^2-10 a c\right) \sqrt{b^2-4 a c}-16 a b c+3 b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^2 e f^2 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e f^2 \left(b^2-4 a c\right) (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)}",1,"-(3*b^2 - 10*a*c)/(2*a^2*(b^2 - 4*a*c)*e*f^2*(d + e*x)) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/(2*a*(b^2 - 4*a*c)*e*f^2*(d + e*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - (Sqrt[c]*(3*b^3 - 16*a*b*c + (3*b^2 - 10*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e*f^2) + (Sqrt[c]*(3*b^3 - 16*a*b*c - (3*b^2 - 10*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e*f^2)","A",6,5,33,0.1515,1,"{1142, 1121, 1281, 1166, 205}"
652,1,228,0,0.3688734,"\int \frac{1}{(d f+e f x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[1/((d*f + e*f*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2),x]","-\frac{\left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{a^3 e f^3 \left(b^2-4 a c\right)^{3/2}}-\frac{b^2-3 a c}{a^2 e f^3 \left(b^2-4 a c\right) (d+e x)^2}+\frac{b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{2 a^3 e f^3}-\frac{2 b \log (d+e x)}{a^3 e f^3}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e f^3 \left(b^2-4 a c\right) (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}","-\frac{\left(6 a^2 c^2-6 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{a^3 e f^3 \left(b^2-4 a c\right)^{3/2}}-\frac{b^2-3 a c}{a^2 e f^3 \left(b^2-4 a c\right) (d+e x)^2}+\frac{b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{2 a^3 e f^3}-\frac{2 b \log (d+e x)}{a^3 e f^3}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e f^3 \left(b^2-4 a c\right) (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}",1,"-((b^2 - 3*a*c)/(a^2*(b^2 - 4*a*c)*e*f^3*(d + e*x)^2)) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/(2*a*(b^2 - 4*a*c)*e*f^3*(d + e*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - ((b^4 - 6*a*b^2*c + 6*a^2*c^2)*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(a^3*(b^2 - 4*a*c)^(3/2)*e*f^3) - (2*b*Log[d + e*x])/(a^3*e*f^3) + (b*Log[a + b*(d + e*x)^2 + c*(d + e*x)^4])/(2*a^3*e*f^3)","A",9,8,33,0.2424,1,"{1142, 1114, 740, 800, 634, 618, 206, 628}"
653,1,423,0,3.5502973,"\int \frac{1}{(d f+e f x)^4 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2} \, dx","Int[1/((d*f + e*f*x)^4*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2),x]","\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c+b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^3 e f^4 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c-b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^3 e f^4 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b \left(5 b^2-19 a c\right)}{2 a^3 e f^4 \left(b^2-4 a c\right) (d+e x)}-\frac{5 b^2-14 a c}{6 a^2 e f^4 \left(b^2-4 a c\right) (d+e x)^3}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e f^4 \left(b^2-4 a c\right) (d+e x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)}","\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c+b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^3 e f^4 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(28 a^2 c^2-29 a b^2 c-b \left(5 b^2-19 a c\right) \sqrt{b^2-4 a c}+5 b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^3 e f^4 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{b \left(5 b^2-19 a c\right)}{2 a^3 e f^4 \left(b^2-4 a c\right) (d+e x)}-\frac{5 b^2-14 a c}{6 a^2 e f^4 \left(b^2-4 a c\right) (d+e x)^3}+\frac{-2 a c+b^2+b c (d+e x)^2}{2 a e f^4 \left(b^2-4 a c\right) (d+e x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)}",1,"-(5*b^2 - 14*a*c)/(6*a^2*(b^2 - 4*a*c)*e*f^4*(d + e*x)^3) + (b*(5*b^2 - 19*a*c))/(2*a^3*(b^2 - 4*a*c)*e*f^4*(d + e*x)) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/(2*a*(b^2 - 4*a*c)*e*f^4*(d + e*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (Sqrt[c]*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 + b*(5*b^2 - 19*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e*f^4) - (Sqrt[c]*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 - b*(5*b^2 - 19*a*c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e*f^4)","A",7,5,33,0.1515,1,"{1142, 1121, 1281, 1166, 205}"
654,1,353,0,0.8700265,"\int \frac{(d f+e f x)^4}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[(d*f + e*f*x)^4/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3,x]","-\frac{f^4 (d+e x) \left(-4 a c+7 b^2+12 b c (d+e x)^2\right)}{8 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{f^4 (d+e x) \left(2 a+b (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}+\frac{3 \sqrt{c} f^4 \left(-2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} e \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} f^4 \left(2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} e \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{f^4 (d+e x) \left(-4 a c+7 b^2+12 b c (d+e x)^2\right)}{8 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{f^4 (d+e x) \left(2 a+b (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}+\frac{3 \sqrt{c} f^4 \left(-2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} e \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} f^4 \left(2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} e \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(f^4*(d + e*x)*(2*a + b*(d + e*x)^2))/(4*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) - (f^4*(d + e*x)*(7*b^2 - 4*a*c + 12*b*c*(d + e*x)^2))/(8*(b^2 - 4*a*c)^2*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (3*Sqrt[c]*(3*b^2 + 4*a*c - 2*b*Sqrt[b^2 - 4*a*c])*f^4*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) - (3*Sqrt[c]*(3*b^2 + 4*a*c + 2*b*Sqrt[b^2 - 4*a*c])*f^4*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",6,5,33,0.1515,1,"{1142, 1120, 1178, 1166, 205}"
655,1,159,0,0.1997501,"\int \frac{(d f+e f x)^3}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[(d*f + e*f*x)^3/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3,x]","-\frac{3 b f^3 \left(b+2 c (d+e x)^2\right)}{4 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{f^3 \left(2 a+b (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}+\frac{3 b c f^3 \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{5/2}}","-\frac{3 b f^3 \left(b+2 c (d+e x)^2\right)}{4 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{f^3 \left(2 a+b (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}+\frac{3 b c f^3 \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{5/2}}",1,"(f^3*(2*a + b*(d + e*x)^2))/(4*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) - (3*b*f^3*(b + 2*c*(d + e*x)^2))/(4*(b^2 - 4*a*c)^2*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (3*b*c*f^3*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*e)","A",6,6,33,0.1818,1,"{1142, 1114, 638, 614, 618, 206}"
656,1,375,0,0.972237,"\int \frac{(d f+e f x)^2}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[(d*f + e*f*x)^2/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3,x]","\frac{f^2 (d+e x) \left(c \left(20 a c+b^2\right) (d+e x)^2+b \left(8 a c+b^2\right)\right)}{8 a e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{f^2 (d+e x) \left(b+2 c (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}+\frac{\sqrt{c} f^2 \left(\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a e \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} f^2 \left(-\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a e \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{f^2 (d+e x) \left(c \left(20 a c+b^2\right) (d+e x)^2+b \left(8 a c+b^2\right)\right)}{8 a e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{f^2 (d+e x) \left(b+2 c (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}+\frac{\sqrt{c} f^2 \left(\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a e \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} f^2 \left(-\frac{b \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+20 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a e \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-(f^2*(d + e*x)*(b + 2*c*(d + e*x)^2))/(4*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (f^2*(d + e*x)*(b*(b^2 + 8*a*c) + c*(b^2 + 20*a*c)*(d + e*x)^2))/(8*a*(b^2 - 4*a*c)^2*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (Sqrt[c]*(b^2 + 20*a*c + (b*(b^2 - 52*a*c))/Sqrt[b^2 - 4*a*c])*f^2*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e) + (Sqrt[c]*(b^2 + 20*a*c - (b*(b^2 - 52*a*c))/Sqrt[b^2 - 4*a*c])*f^2*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e)","A",6,5,33,0.1515,1,"{1142, 1119, 1178, 1166, 205}"
657,1,153,0,0.1919416,"\int \frac{d f+e f x}{\left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[(d*f + e*f*x)/(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3,x]","-\frac{6 c^2 f \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{5/2}}+\frac{3 c f \left(b+2 c (d+e x)^2\right)}{2 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{f \left(b+2 c (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}","-\frac{6 c^2 f \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{e \left(b^2-4 a c\right)^{5/2}}+\frac{3 c f \left(b+2 c (d+e x)^2\right)}{2 e \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{f \left(b+2 c (d+e x)^2\right)}{4 e \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}",1,"-(f*(b + 2*c*(d + e*x)^2))/(4*(b^2 - 4*a*c)*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (3*c*f*(b + 2*c*(d + e*x)^2))/(2*(b^2 - 4*a*c)^2*e*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - (6*c^2*f*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*e)","A",6,5,31,0.1613,1,"{1142, 1107, 614, 618, 206}"
658,1,270,0,0.4963734,"\int \frac{1}{(d f+e f x) \left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[1/((d*f + e*f*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x]","\frac{16 a^2 c^2+2 b c \left(b^2-7 a c\right) (d+e x)^2-15 a b^2 c+2 b^4}{4 a^2 e f \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 e f \left(b^2-4 a c\right)^{5/2}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^3 e f}+\frac{\log (d+e x)}{a^3 e f}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e f \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}","\frac{16 a^2 c^2+2 b c \left(b^2-7 a c\right) (d+e x)^2-15 a b^2 c+2 b^4}{4 a^2 e f \left(b^2-4 a c\right)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}+\frac{b \left(30 a^2 c^2-10 a b^2 c+b^4\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 e f \left(b^2-4 a c\right)^{5/2}}-\frac{\log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^3 e f}+\frac{\log (d+e x)}{a^3 e f}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e f \left(b^2-4 a c\right) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}",1,"(b^2 - 2*a*c + b*c*(d + e*x)^2)/(4*a*(b^2 - 4*a*c)*e*f*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (2*b^4 - 15*a*b^2*c + 16*a^2*c^2 + 2*b*c*(b^2 - 7*a*c)*(d + e*x)^2)/(4*a^2*(b^2 - 4*a*c)^2*e*f*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) + (b*(b^4 - 10*a*b^2*c + 30*a^2*c^2)*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*a^3*(b^2 - 4*a*c)^(5/2)*e*f) + Log[d + e*x]/(a^3*e*f) - Log[a + b*(d + e*x)^2 + c*(d + e*x)^4]/(4*a^3*e*f)","A",10,9,33,0.2727,1,"{1142, 1114, 740, 822, 800, 634, 618, 206, 628}"
659,1,499,0,1.0935875,"\int \frac{1}{(d f+e f x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[1/((d*f + e*f*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x]","\frac{36 a^2 c^2+b c \left(5 b^2-32 a c\right) (d+e x)^2-35 a b^2 c+5 b^4}{8 a^2 e f^2 \left(b^2-4 a c\right)^2 (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{3 \sqrt{c} \left(\frac{b \left(124 a^2 c^2-47 a b^2 c+5 b^4\right)}{\sqrt{b^2-4 a c}}+\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^3 e f^2 \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)-\frac{124 a^2 b c^2-47 a b^3 c+5 b^5}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^3 e f^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 \left(5 b^2-12 a c\right) \left(b^2-5 a c\right)}{8 a^3 e f^2 \left(b^2-4 a c\right)^2 (d+e x)}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e f^2 \left(b^2-4 a c\right) (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}","\frac{36 a^2 c^2+b c \left(5 b^2-32 a c\right) (d+e x)^2-35 a b^2 c+5 b^4}{8 a^2 e f^2 \left(b^2-4 a c\right)^2 (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{3 \sqrt{c} \left(\frac{b \left(124 a^2 c^2-47 a b^2 c+5 b^4\right)}{\sqrt{b^2-4 a c}}+\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^3 e f^2 \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(\left(5 b^2-12 a c\right) \left(b^2-5 a c\right)-\frac{124 a^2 b c^2-47 a b^3 c+5 b^5}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} (d+e x)}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^3 e f^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{3 \left(5 b^2-12 a c\right) \left(b^2-5 a c\right)}{8 a^3 e f^2 \left(b^2-4 a c\right)^2 (d+e x)}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e f^2 \left(b^2-4 a c\right) (d+e x) \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}",1,"(-3*(5*b^2 - 12*a*c)*(b^2 - 5*a*c))/(8*a^3*(b^2 - 4*a*c)^2*e*f^2*(d + e*x)) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/(4*a*(b^2 - 4*a*c)*e*f^2*(d + e*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (5*b^4 - 35*a*b^2*c + 36*a^2*c^2 + b*c*(5*b^2 - 32*a*c)*(d + e*x)^2)/(8*a^2*(b^2 - 4*a*c)^2*e*f^2*(d + e*x)*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - (3*Sqrt[c]*((5*b^2 - 12*a*c)*(b^2 - 5*a*c) + (b*(5*b^4 - 47*a*b^2*c + 124*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^3*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*e*f^2) - (3*Sqrt[c]*((5*b^2 - 12*a*c)*(b^2 - 5*a*c) - (5*b^5 - 47*a*b^3*c + 124*a^2*b*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*(d + e*x))/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^3*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*e*f^2)","A",7,6,33,0.1818,1,"{1142, 1121, 1277, 1281, 1166, 205}"
660,1,343,0,0.5887062,"\int \frac{1}{(d f+e f x)^3 \left(a+b (d+e x)^2+c (d+e x)^4\right)^3} \, dx","Int[1/((d*f + e*f*x)^3*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^3),x]","\frac{20 a^2 c^2+3 b c \left(b^2-6 a c\right) (d+e x)^2-20 a b^2 c+3 b^4}{4 a^2 e f^3 \left(b^2-4 a c\right)^2 (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^4 e f^3 \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(b^2-5 a c\right) \left(b^2-2 a c\right)}{2 a^3 e f^3 \left(b^2-4 a c\right)^2 (d+e x)^2}+\frac{3 b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^4 e f^3}-\frac{3 b \log (d+e x)}{a^4 e f^3}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e f^3 \left(b^2-4 a c\right) (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}","\frac{20 a^2 c^2+3 b c \left(b^2-6 a c\right) (d+e x)^2-20 a b^2 c+3 b^4}{4 a^2 e f^3 \left(b^2-4 a c\right)^2 (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)}-\frac{3 \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right) \tanh ^{-1}\left(\frac{b+2 c (d+e x)^2}{\sqrt{b^2-4 a c}}\right)}{2 a^4 e f^3 \left(b^2-4 a c\right)^{5/2}}-\frac{3 \left(b^2-5 a c\right) \left(b^2-2 a c\right)}{2 a^3 e f^3 \left(b^2-4 a c\right)^2 (d+e x)^2}+\frac{3 b \log \left(a+b (d+e x)^2+c (d+e x)^4\right)}{4 a^4 e f^3}-\frac{3 b \log (d+e x)}{a^4 e f^3}+\frac{-2 a c+b^2+b c (d+e x)^2}{4 a e f^3 \left(b^2-4 a c\right) (d+e x)^2 \left(a+b (d+e x)^2+c (d+e x)^4\right)^2}",1,"(-3*(b^2 - 5*a*c)*(b^2 - 2*a*c))/(2*a^3*(b^2 - 4*a*c)^2*e*f^3*(d + e*x)^2) + (b^2 - 2*a*c + b*c*(d + e*x)^2)/(4*a*(b^2 - 4*a*c)*e*f^3*(d + e*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)^2) + (3*b^4 - 20*a*b^2*c + 20*a^2*c^2 + 3*b*c*(b^2 - 6*a*c)*(d + e*x)^2)/(4*a^2*(b^2 - 4*a*c)^2*e*f^3*(d + e*x)^2*(a + b*(d + e*x)^2 + c*(d + e*x)^4)) - (3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*ArcTanh[(b + 2*c*(d + e*x)^2)/Sqrt[b^2 - 4*a*c]])/(2*a^4*(b^2 - 4*a*c)^(5/2)*e*f^3) - (3*b*Log[d + e*x])/(a^4*e*f^3) + (3*b*Log[a + b*(d + e*x)^2 + c*(d + e*x)^4])/(4*a^4*e*f^3)","A",10,9,33,0.2727,1,"{1142, 1114, 740, 822, 800, 634, 618, 206, 628}"
661,1,340,0,0.6910034,"\int \frac{x}{\sqrt{a+b (d+e x)^3+c (d+e x)^6}} \, dx","Int[x/Sqrt[a + b*(d + e*x)^3 + c*(d + e*x)^6],x]","\frac{(d+e x)^2 \sqrt{\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c (d+e x)^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{5}{3};-\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c (d+e x)^3}{b+\sqrt{b^2-4 a c}}\right)}{2 e^2 \sqrt{a+b (d+e x)^3+c (d+e x)^6}}-\frac{d (d+e x) \sqrt{\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c (d+e x)^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{4}{3};-\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c (d+e x)^3}{b+\sqrt{b^2-4 a c}}\right)}{e^2 \sqrt{a+b (d+e x)^3+c (d+e x)^6}}","\frac{(d+e x)^2 \sqrt{\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c (d+e x)^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{5}{3};-\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c (d+e x)^3}{b+\sqrt{b^2-4 a c}}\right)}{2 e^2 \sqrt{a+b (d+e x)^3+c (d+e x)^6}}-\frac{d (d+e x) \sqrt{\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c (d+e x)^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{4}{3};-\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c (d+e x)^3}{b+\sqrt{b^2-4 a c}}\right)}{e^2 \sqrt{a+b (d+e x)^3+c (d+e x)^6}}",1,"-((d*(d + e*x)*Sqrt[1 + (2*c*(d + e*x)^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*(d + e*x)^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[1/3, 1/2, 1/2, 4/3, (-2*c*(d + e*x)^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*(d + e*x)^3)/(b + Sqrt[b^2 - 4*a*c])])/(e^2*Sqrt[a + b*(d + e*x)^3 + c*(d + e*x)^6])) + ((d + e*x)^2*Sqrt[1 + (2*c*(d + e*x)^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*(d + e*x)^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[2/3, 1/2, 1/2, 5/3, (-2*c*(d + e*x)^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*(d + e*x)^3)/(b + Sqrt[b^2 - 4*a*c])])/(2*e^2*Sqrt[a + b*(d + e*x)^3 + c*(d + e*x)^6])","A",7,6,26,0.2308,1,"{1389, 1790, 1348, 429, 1385, 510}"
662,1,398,0,0.6870492,"\int \frac{x^2}{\sqrt{a+b (d+e x)^3+c (d+e x)^6}} \, dx","Int[x^2/Sqrt[a + b*(d + e*x)^3 + c*(d + e*x)^6],x]","\frac{d^2 (d+e x) \sqrt{\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c (d+e x)^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{4}{3};-\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c (d+e x)^3}{b+\sqrt{b^2-4 a c}}\right)}{e^3 \sqrt{a+b (d+e x)^3+c (d+e x)^6}}-\frac{d (d+e x)^2 \sqrt{\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c (d+e x)^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{5}{3};-\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c (d+e x)^3}{b+\sqrt{b^2-4 a c}}\right)}{e^3 \sqrt{a+b (d+e x)^3+c (d+e x)^6}}+\frac{\tanh ^{-1}\left(\frac{b+2 c (d+e x)^3}{2 \sqrt{c} \sqrt{a+b (d+e x)^3+c (d+e x)^6}}\right)}{3 \sqrt{c} e^3}","\frac{d^2 (d+e x) \sqrt{\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c (d+e x)^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{4}{3};-\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c (d+e x)^3}{b+\sqrt{b^2-4 a c}}\right)}{e^3 \sqrt{a+b (d+e x)^3+c (d+e x)^6}}-\frac{d (d+e x)^2 \sqrt{\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c (d+e x)^3}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{5}{3};-\frac{2 c (d+e x)^3}{b-\sqrt{b^2-4 a c}},-\frac{2 c (d+e x)^3}{b+\sqrt{b^2-4 a c}}\right)}{e^3 \sqrt{a+b (d+e x)^3+c (d+e x)^6}}+\frac{\tanh ^{-1}\left(\frac{b+2 c (d+e x)^3}{2 \sqrt{c} \sqrt{a+b (d+e x)^3+c (d+e x)^6}}\right)}{3 \sqrt{c} e^3}",1,"(d^2*(d + e*x)*Sqrt[1 + (2*c*(d + e*x)^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*(d + e*x)^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[1/3, 1/2, 1/2, 4/3, (-2*c*(d + e*x)^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*(d + e*x)^3)/(b + Sqrt[b^2 - 4*a*c])])/(e^3*Sqrt[a + b*(d + e*x)^3 + c*(d + e*x)^6]) - (d*(d + e*x)^2*Sqrt[1 + (2*c*(d + e*x)^3)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*(d + e*x)^3)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[2/3, 1/2, 1/2, 5/3, (-2*c*(d + e*x)^3)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*(d + e*x)^3)/(b + Sqrt[b^2 - 4*a*c])])/(e^3*Sqrt[a + b*(d + e*x)^3 + c*(d + e*x)^6]) + ArcTanh[(b + 2*c*(d + e*x)^3)/(2*Sqrt[c]*Sqrt[a + b*(d + e*x)^3 + c*(d + e*x)^6])]/(3*Sqrt[c]*e^3)","A",10,9,28,0.3214,1,"{1389, 1790, 1348, 429, 1385, 510, 1352, 621, 206}"
663,1,34,0,0.0356623,"\int (2+3 x)^6 \left(1+(2+3 x)^7+(2+3 x)^{14}\right) \, dx","Int[(2 + 3*x)^6*(1 + (2 + 3*x)^7 + (2 + 3*x)^14),x]","\frac{1}{63} (3 x+2)^{21}+\frac{1}{42} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7","\frac{1}{63} (3 x+2)^{21}+\frac{1}{42} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7",1,"(2 + 3*x)^7/21 + (2 + 3*x)^14/42 + (2 + 3*x)^21/63","A",3,2,24,0.08333,1,"{1390, 14}"
664,1,56,0,0.0957482,"\int (2+3 x)^6 \left(1+(2+3 x)^7+(2+3 x)^{14}\right)^2 \, dx","Int[(2 + 3*x)^6*(1 + (2 + 3*x)^7 + (2 + 3*x)^14)^2,x]","\frac{1}{105} (3 x+2)^{35}+\frac{1}{42} (3 x+2)^{28}+\frac{1}{21} (3 x+2)^{21}+\frac{1}{21} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7","\frac{1}{105} (3 x+2)^{35}+\frac{1}{42} (3 x+2)^{28}+\frac{1}{21} (3 x+2)^{21}+\frac{1}{21} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7",1,"(2 + 3*x)^7/21 + (2 + 3*x)^14/21 + (2 + 3*x)^21/21 + (2 + 3*x)^28/42 + (2 + 3*x)^35/105","A",4,3,26,0.1154,1,"{1390, 1352, 611}"