1,1,17,0,0.0047563,"\int x^2 \left(a x+b x^3\right) \, dx","Int[x^2*(a*x + b*x^3),x]","\frac{a x^4}{4}+\frac{b x^6}{6}","\frac{a x^4}{4}+\frac{b x^6}{6}",1,"(a*x^4)/4 + (b*x^6)/6","A",2,1,13,0.07692,1,"{14}"
2,1,17,0,0.0044615,"\int x \left(a x+b x^3\right) \, dx","Int[x*(a*x + b*x^3),x]","\frac{a x^3}{3}+\frac{b x^5}{5}","\frac{a x^3}{3}+\frac{b x^5}{5}",1,"(a*x^3)/3 + (b*x^5)/5","A",2,1,11,0.09091,1,"{14}"
3,1,17,0,0.0027001,"\int \left(a x+b x^3\right) \, dx","Int[a*x + b*x^3,x]","\frac{a x^2}{2}+\frac{b x^4}{4}","\frac{a x^2}{2}+\frac{b x^4}{4}",1,"(a*x^2)/2 + (b*x^4)/4","A",1,0,9,0,1,"{}"
4,1,12,0,0.0033423,"\int \frac{a x+b x^3}{x} \, dx","Int[(a*x + b*x^3)/x,x]","a x+\frac{b x^3}{3}","a x+\frac{b x^3}{3}",1,"a*x + (b*x^3)/3","A",2,1,13,0.07692,1,"{14}"
5,1,13,0,0.0047781,"\int \frac{a x+b x^3}{x^2} \, dx","Int[(a*x + b*x^3)/x^2,x]","a \log (x)+\frac{b x^2}{2}","a \log (x)+\frac{b x^2}{2}",1,"(b*x^2)/2 + a*Log[x]","A",2,1,13,0.07692,1,"{14}"
6,1,30,0,0.0150718,"\int x^2 \left(a x+b x^3\right)^2 \, dx","Int[x^2*(a*x + b*x^3)^2,x]","\frac{a^2 x^5}{5}+\frac{2}{7} a b x^7+\frac{b^2 x^9}{9}","\frac{a^2 x^5}{5}+\frac{2}{7} a b x^7+\frac{b^2 x^9}{9}",1,"(a^2*x^5)/5 + (2*a*b*x^7)/7 + (b^2*x^9)/9","A",3,2,15,0.1333,1,"{1584, 270}"
7,1,30,0,0.0195837,"\int x \left(a x+b x^3\right)^2 \, dx","Int[x*(a*x + b*x^3)^2,x]","\frac{a^2 x^4}{4}+\frac{1}{3} a b x^6+\frac{b^2 x^8}{8}","\frac{a^2 x^4}{4}+\frac{1}{3} a b x^6+\frac{b^2 x^8}{8}",1,"(a^2*x^4)/4 + (a*b*x^6)/3 + (b^2*x^8)/8","A",4,3,13,0.2308,1,"{1584, 266, 43}"
8,1,30,0,0.0106576,"\int \left(a x+b x^3\right)^2 \, dx","Int[(a*x + b*x^3)^2,x]","\frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7}","\frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7}",1,"(a^2*x^3)/3 + (2*a*b*x^5)/5 + (b^2*x^7)/7","A",3,2,11,0.1818,1,"{1593, 270}"
9,1,16,0,0.0070228,"\int \frac{\left(a x+b x^3\right)^2}{x} \, dx","Int[(a*x + b*x^3)^2/x,x]","\frac{\left(a+b x^2\right)^3}{6 b}","\frac{\left(a+b x^2\right)^3}{6 b}",1,"(a + b*x^2)^3/(6*b)","A",2,2,15,0.1333,1,"{1584, 261}"
10,1,25,0,0.011589,"\int \frac{\left(a x+b x^3\right)^2}{x^2} \, dx","Int[(a*x + b*x^3)^2/x^2,x]","a^2 x+\frac{2}{3} a b x^3+\frac{b^2 x^5}{5}","a^2 x+\frac{2}{3} a b x^3+\frac{b^2 x^5}{5}",1,"a^2*x + (2*a*b*x^3)/3 + (b^2*x^5)/5","A",3,2,15,0.1333,1,"{1584, 194}"
11,1,46,0,0.0157418,"\int \left(-4 x+3 x^3\right)^6 \, dx","Int[(-4*x + 3*x^3)^6,x]","\frac{729 x^{19}}{19}-\frac{5832 x^{17}}{17}+1296 x^{15}-\frac{34560 x^{13}}{13}+\frac{34560 x^{11}}{11}-2048 x^9+\frac{4096 x^7}{7}","\frac{729 x^{19}}{19}-\frac{5832 x^{17}}{17}+1296 x^{15}-\frac{34560 x^{13}}{13}+\frac{34560 x^{11}}{11}-2048 x^9+\frac{4096 x^7}{7}",1,"(4096*x^7)/7 - 2048*x^9 + (34560*x^11)/11 - (34560*x^13)/13 + 1296*x^15 - (5832*x^17)/17 + (729*x^19)/19","A",3,2,11,0.1818,1,"{1593, 270}"
12,1,27,0,0.0227478,"\int \frac{x^4}{a x+b x^3} \, dx","Int[x^4/(a*x + b*x^3),x]","\frac{x^2}{2 b}-\frac{a \log \left(a+b x^2\right)}{2 b^2}","\frac{x^2}{2 b}-\frac{a \log \left(a+b x^2\right)}{2 b^2}",1,"x^2/(2*b) - (a*Log[a + b*x^2])/(2*b^2)","A",4,3,15,0.2000,1,"{1584, 266, 43}"
13,1,31,0,0.0161081,"\int \frac{x^3}{a x+b x^3} \, dx","Int[x^3/(a*x + b*x^3),x]","\frac{x}{b}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}","\frac{x}{b}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}",1,"x/b - (Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(3/2)","A",3,3,15,0.2000,1,"{1584, 321, 205}"
14,1,15,0,0.0074074,"\int \frac{x^2}{a x+b x^3} \, dx","Int[x^2/(a*x + b*x^3),x]","\frac{\log \left(a+b x^2\right)}{2 b}","\frac{\log \left(a+b x^2\right)}{2 b}",1,"Log[a + b*x^2]/(2*b)","A",2,2,15,0.1333,1,"{1584, 260}"
15,1,24,0,0.0089429,"\int \frac{x}{a x+b x^3} \, dx","Int[x/(a*x + b*x^3),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(Sqrt[a]*Sqrt[b])","A",2,2,13,0.1538,1,"{1584, 205}"
16,1,22,0,0.0120126,"\int \frac{1}{a x+b x^3} \, dx","Int[(a*x + b*x^3)^(-1),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^2\right)}{2 a}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^2\right)}{2 a}",1,"Log[x]/a - Log[a + b*x^2]/(2*a)","A",5,5,11,0.4545,1,"{1593, 266, 36, 29, 31}"
17,1,34,0,0.0167518,"\int \frac{1}{x \left(a x+b x^3\right)} \, dx","Int[1/(x*(a*x + b*x^3)),x]","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{1}{a x}","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{1}{a x}",1,"-(1/(a*x)) - (Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(3/2)","A",3,3,15,0.2000,1,"{1584, 325, 205}"
18,1,35,0,0.0259816,"\int \frac{1}{x^2 \left(a x+b x^3\right)} \, dx","Int[1/(x^2*(a*x + b*x^3)),x]","\frac{b \log \left(a+b x^2\right)}{2 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}","\frac{b \log \left(a+b x^2\right)}{2 a^2}-\frac{b \log (x)}{a^2}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) - (b*Log[x])/a^2 + (b*Log[a + b*x^2])/(2*a^2)","A",4,3,15,0.2000,1,"{1584, 266, 44}"
19,1,43,0,0.0259111,"\int \frac{1}{x^3 \left(a x+b x^3\right)} \, dx","Int[1/(x^3*(a*x + b*x^3)),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2}}+\frac{b}{a^2 x}-\frac{1}{3 a x^3}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2}}+\frac{b}{a^2 x}-\frac{1}{3 a x^3}",1,"-1/(3*a*x^3) + b/(a^2*x) + (b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(5/2)","A",4,3,15,0.2000,1,"{1584, 325, 205}"
20,1,49,0,0.0329381,"\int \frac{1}{x^4 \left(a x+b x^3\right)} \, dx","Int[1/(x^4*(a*x + b*x^3)),x]","-\frac{b^2 \log \left(a+b x^2\right)}{2 a^3}+\frac{b^2 \log (x)}{a^3}+\frac{b}{2 a^2 x^2}-\frac{1}{4 a x^4}","-\frac{b^2 \log \left(a+b x^2\right)}{2 a^3}+\frac{b^2 \log (x)}{a^3}+\frac{b}{2 a^2 x^2}-\frac{1}{4 a x^4}",1,"-1/(4*a*x^4) + b/(2*a^2*x^2) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x^2])/(2*a^3)","A",4,3,15,0.2000,1,"{1584, 266, 44}"
21,1,45,0,0.015014,"\int \frac{x^2}{\left(a x+b x^3\right)^2} \, dx","Int[x^2/(a*x + b*x^3)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{x}{2 a \left(a+b x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{x}{2 a \left(a+b x^2\right)}",1,"x/(2*a*(a + b*x^2)) + ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(2*a^(3/2)*Sqrt[b])","A",3,3,15,0.2000,1,"{1584, 199, 205}"
22,1,38,0,0.0283458,"\int \frac{x}{\left(a x+b x^3\right)^2} \, dx","Int[x/(a*x + b*x^3)^2,x]","-\frac{\log \left(a+b x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{1}{2 a \left(a+b x^2\right)}","-\frac{\log \left(a+b x^2\right)}{2 a^2}+\frac{\log (x)}{a^2}+\frac{1}{2 a \left(a+b x^2\right)}",1,"1/(2*a*(a + b*x^2)) + Log[x]/a^2 - Log[a + b*x^2]/(2*a^2)","A",4,3,13,0.2308,1,"{1584, 266, 44}"
23,1,57,0,0.0178089,"\int \frac{1}{\left(a x+b x^3\right)^2} \, dx","Int[(a*x + b*x^3)^(-2),x]","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3}{2 a^2 x}+\frac{1}{2 a x \left(a+b x^2\right)}","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3}{2 a^2 x}+\frac{1}{2 a x \left(a+b x^2\right)}",1,"-3/(2*a^2*x) + 1/(2*a*x*(a + b*x^2)) - (3*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2))","A",4,4,11,0.3636,1,"{1593, 290, 325, 205}"
24,1,49,0,0.0390713,"\int \frac{1}{x \left(a x+b x^3\right)^2} \, dx","Int[1/(x*(a*x + b*x^3)^2),x]","-\frac{b}{2 a^2 \left(a+b x^2\right)}+\frac{b \log \left(a+b x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}-\frac{1}{2 a^2 x^2}","-\frac{b}{2 a^2 \left(a+b x^2\right)}+\frac{b \log \left(a+b x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}-\frac{1}{2 a^2 x^2}",1,"-1/(2*a^2*x^2) - b/(2*a^2*(a + b*x^2)) - (2*b*Log[x])/a^3 + (b*Log[a + b*x^2])/a^3","A",4,3,15,0.2000,1,"{1584, 266, 44}"
25,1,68,0,0.0293549,"\int \frac{1}{x^2 \left(a x+b x^3\right)^2} \, dx","Int[1/(x^2*(a*x + b*x^3)^2),x]","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2}}+\frac{5 b}{2 a^3 x}-\frac{5}{6 a^2 x^3}+\frac{1}{2 a x^3 \left(a+b x^2\right)}","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2}}+\frac{5 b}{2 a^3 x}-\frac{5}{6 a^2 x^3}+\frac{1}{2 a x^3 \left(a+b x^2\right)}",1,"-5/(6*a^2*x^3) + (5*b)/(2*a^3*x) + 1/(2*a*x^3*(a + b*x^2)) + (5*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2))","A",5,4,15,0.2667,1,"{1584, 290, 325, 205}"
26,1,13,0,0.010937,"\int \frac{x^5}{x-x^3} \, dx","Int[x^5/(x - x^3),x]","-\frac{x^3}{3}-x+\tanh ^{-1}(x)","-\frac{x^3}{3}-x+\tanh ^{-1}(x)",1,"-x - x^3/3 + ArcTanh[x]","A",4,3,13,0.2308,1,"{1584, 302, 206}"
27,1,20,0,0.0151658,"\int \frac{x^4}{x-x^3} \, dx","Int[x^4/(x - x^3),x]","-\frac{x^2}{2}-\frac{1}{2} \log \left(1-x^2\right)","-\frac{x^2}{2}-\frac{1}{2} \log \left(1-x^2\right)",1,"-x^2/2 - Log[1 - x^2]/2","A",4,3,13,0.2308,1,"{1584, 266, 43}"
28,1,6,0,0.0080615,"\int \frac{x^3}{x-x^3} \, dx","Int[x^3/(x - x^3),x]","\tanh ^{-1}(x)-x","\tanh ^{-1}(x)-x",1,"-x + ArcTanh[x]","A",3,3,13,0.2308,1,"{1584, 321, 206}"
29,1,12,0,0.0063917,"\int \frac{x^2}{x-x^3} \, dx","Int[x^2/(x - x^3),x]","-\frac{1}{2} \log \left(1-x^2\right)","-\frac{1}{2} \log \left(1-x^2\right)",1,"-Log[1 - x^2]/2","A",2,2,13,0.1538,1,"{1584, 260}"
30,1,2,0,0.0039866,"\int \frac{x}{x-x^3} \, dx","Int[x/(x - x^3),x]","\tanh ^{-1}(x)","\tanh ^{-1}(x)",1,"ArcTanh[x]","A",2,2,11,0.1818,1,"{1584, 206}"
31,1,15,0,0.0082264,"\int \frac{1}{x-x^3} \, dx","Int[(x - x^3)^(-1),x]","\log (x)-\frac{1}{2} \log \left(1-x^2\right)","\log (x)-\frac{1}{2} \log \left(1-x^2\right)",1,"Log[x] - Log[1 - x^2]/2","A",5,5,9,0.5556,1,"{1593, 266, 36, 31, 29}"
32,1,8,0,0.007941,"\int \frac{1}{x \left(x-x^3\right)} \, dx","Int[1/(x*(x - x^3)),x]","\tanh ^{-1}(x)-\frac{1}{x}","\tanh ^{-1}(x)-\frac{1}{x}",1,"-x^(-1) + ArcTanh[x]","A",3,3,13,0.2308,1,"{1584, 325, 206}"
33,1,22,0,0.0146911,"\int \frac{1}{x^2 \left(x-x^3\right)} \, dx","Int[1/(x^2*(x - x^3)),x]","-\frac{1}{2 x^2}-\frac{1}{2} \log \left(1-x^2\right)+\log (x)","-\frac{1}{2 x^2}-\frac{1}{2} \log \left(1-x^2\right)+\log (x)",1,"-1/(2*x^2) + Log[x] - Log[1 - x^2]/2","A",4,3,13,0.2308,1,"{1584, 266, 44}"
34,1,15,0,0.0097331,"\int \frac{1}{x^3 \left(x-x^3\right)} \, dx","Int[1/(x^3*(x - x^3)),x]","-\frac{1}{3 x^3}-\frac{1}{x}+\tanh ^{-1}(x)","-\frac{1}{3 x^3}-\frac{1}{x}+\tanh ^{-1}(x)",1,"-1/(3*x^3) - x^(-1) + ArcTanh[x]","A",4,3,13,0.2308,1,"{1584, 325, 206}"
35,1,29,0,0.0160911,"\int \frac{1}{x^4 \left(x-x^3\right)} \, dx","Int[1/(x^4*(x - x^3)),x]","-\frac{1}{2 x^2}-\frac{1}{4 x^4}-\frac{1}{2} \log \left(1-x^2\right)+\log (x)","-\frac{1}{2 x^2}-\frac{1}{4 x^4}-\frac{1}{2} \log \left(1-x^2\right)+\log (x)",1,"-1/(4*x^4) - 1/(2*x^2) + Log[x] - Log[1 - x^2]/2","A",4,3,13,0.2308,1,"{1584, 266, 44}"
36,1,15,0,0.0094817,"\int \frac{1}{x+b x^3} \, dx","Int[(x + b*x^3)^(-1),x]","\log (x)-\frac{1}{2} \log \left(b x^2+1\right)","\log (x)-\frac{1}{2} \log \left(b x^2+1\right)",1,"Log[x] - Log[1 + b*x^2]/2","A",5,5,9,0.5556,1,"{1593, 266, 36, 29, 31}"
37,1,18,0,0.0102575,"\int \frac{1}{-x+b x^3} \, dx","Int[(-x + b*x^3)^(-1),x]","\frac{1}{2} \log \left(1-b x^2\right)-\log (x)","\frac{1}{2} \log \left(1-b x^2\right)-\log (x)",1,"-Log[x] + Log[1 - b*x^2]/2","A",5,5,11,0.4545,1,"{1593, 266, 36, 29, 31}"
38,1,163,0,0.1883777,"\int x^3 \sqrt{a x+b x^3} \, dx","Int[x^3*Sqrt[a*x + b*x^3],x]","-\frac{20 a^2 \sqrt{a x+b x^3}}{231 b^2}+\frac{10 a^{11/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a x+b x^3}}+\frac{2}{11} x^4 \sqrt{a x+b x^3}+\frac{4 a x^2 \sqrt{a x+b x^3}}{77 b}","-\frac{20 a^2 \sqrt{a x+b x^3}}{231 b^2}+\frac{10 a^{11/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a x+b x^3}}+\frac{2}{11} x^4 \sqrt{a x+b x^3}+\frac{4 a x^2 \sqrt{a x+b x^3}}{77 b}",1,"(-20*a^2*Sqrt[a*x + b*x^3])/(231*b^2) + (4*a*x^2*Sqrt[a*x + b*x^3])/(77*b) + (2*x^4*Sqrt[a*x + b*x^3])/11 + (10*a^(11/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(231*b^(9/4)*Sqrt[a*x + b*x^3])","A",6,5,17,0.2941,1,"{2021, 2024, 2011, 329, 220}"
39,1,281,0,0.26363,"\int x^2 \sqrt{a x+b x^3} \, dx","Int[x^2*Sqrt[a*x + b*x^3],x]","-\frac{4 a^2 x \left(a+b x^2\right)}{15 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{2 a^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a x+b x^3}}+\frac{4 a^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a x+b x^3}}+\frac{2}{9} x^3 \sqrt{a x+b x^3}+\frac{4 a x \sqrt{a x+b x^3}}{45 b}","-\frac{4 a^2 x \left(a+b x^2\right)}{15 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{2 a^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a x+b x^3}}+\frac{4 a^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a x+b x^3}}+\frac{2}{9} x^3 \sqrt{a x+b x^3}+\frac{4 a x \sqrt{a x+b x^3}}{45 b}",1,"(-4*a^2*x*(a + b*x^2))/(15*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) + (4*a*x*Sqrt[a*x + b*x^3])/(45*b) + (2*x^3*Sqrt[a*x + b*x^3])/9 + (4*a^(9/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*b^(7/4)*Sqrt[a*x + b*x^3]) - (2*a^(9/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*b^(7/4)*Sqrt[a*x + b*x^3])","A",7,7,17,0.4118,1,"{2021, 2024, 2032, 329, 305, 220, 1196}"
40,1,137,0,0.1218437,"\int x \sqrt{a x+b x^3} \, dx","Int[x*Sqrt[a*x + b*x^3],x]","-\frac{2 a^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 b^{5/4} \sqrt{a x+b x^3}}+\frac{2}{7} x^2 \sqrt{a x+b x^3}+\frac{4 a \sqrt{a x+b x^3}}{21 b}","-\frac{2 a^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 b^{5/4} \sqrt{a x+b x^3}}+\frac{2}{7} x^2 \sqrt{a x+b x^3}+\frac{4 a \sqrt{a x+b x^3}}{21 b}",1,"(4*a*Sqrt[a*x + b*x^3])/(21*b) + (2*x^2*Sqrt[a*x + b*x^3])/7 - (2*a^(7/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(21*b^(5/4)*Sqrt[a*x + b*x^3])","A",5,5,15,0.3333,1,"{2021, 2024, 2011, 329, 220}"
41,1,255,0,0.1729869,"\int \sqrt{a x+b x^3} \, dx","Int[Sqrt[a*x + b*x^3],x]","\frac{2 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b x^3}}-\frac{4 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b x^3}}+\frac{4 a x \left(a+b x^2\right)}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}+\frac{2}{5} x \sqrt{a x+b x^3}","\frac{2 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b x^3}}-\frac{4 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b x^3}}+\frac{4 a x \left(a+b x^2\right)}{5 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}+\frac{2}{5} x \sqrt{a x+b x^3}",1,"(4*a*x*(a + b*x^2))/(5*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) + (2*x*Sqrt[a*x + b*x^3])/5 - (4*a^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[a*x + b*x^3]) + (2*a^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[a*x + b*x^3])","A",6,6,13,0.4615,1,"{2004, 2032, 329, 305, 220, 1196}"
42,1,113,0,0.0857818,"\int \frac{\sqrt{a x+b x^3}}{x} \, dx","Int[Sqrt[a*x + b*x^3]/x,x]","\frac{2 a^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{a x+b x^3}}+\frac{2}{3} \sqrt{a x+b x^3}","\frac{2 a^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt{a x+b x^3}}+\frac{2}{3} \sqrt{a x+b x^3}",1,"(2*Sqrt[a*x + b*x^3])/3 + (2*a^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*b^(1/4)*Sqrt[a*x + b*x^3])","A",4,4,17,0.2353,1,"{2021, 2011, 329, 220}"
43,1,248,0,0.2013375,"\int \frac{\sqrt{a x+b x^3}}{x^2} \, dx","Int[Sqrt[a*x + b*x^3]/x^2,x]","\frac{4 \sqrt{b} x \left(a+b x^2\right)}{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{2 \sqrt{a x+b x^3}}{x}+\frac{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a x+b x^3}}-\frac{4 \sqrt[4]{a} \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a x+b x^3}}","\frac{4 \sqrt{b} x \left(a+b x^2\right)}{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{2 \sqrt{a x+b x^3}}{x}+\frac{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a x+b x^3}}-\frac{4 \sqrt[4]{a} \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a x+b x^3}}",1,"(4*Sqrt[b]*x*(a + b*x^2))/((Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) - (2*Sqrt[a*x + b*x^3])/x - (4*a^(1/4)*b^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/Sqrt[a*x + b*x^3] + (2*a^(1/4)*b^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/Sqrt[a*x + b*x^3]","A",6,6,17,0.3529,1,"{2020, 2032, 329, 305, 220, 1196}"
44,1,116,0,0.0877961,"\int \frac{\sqrt{a x+b x^3}}{x^3} \, dx","Int[Sqrt[a*x + b*x^3]/x^3,x]","\frac{2 b^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt{a x+b x^3}}-\frac{2 \sqrt{a x+b x^3}}{3 x^2}","\frac{2 b^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt{a x+b x^3}}-\frac{2 \sqrt{a x+b x^3}}{3 x^2}",1,"(-2*Sqrt[a*x + b*x^3])/(3*x^2) + (2*b^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*a^(1/4)*Sqrt[a*x + b*x^3])","A",4,4,17,0.2353,1,"{2020, 2011, 329, 220}"
45,1,283,0,0.2509313,"\int \frac{\sqrt{a x+b x^3}}{x^4} \, dx","Int[Sqrt[a*x + b*x^3]/x^4,x]","\frac{2 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a x+b x^3}}-\frac{4 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a x+b x^3}}+\frac{4 b^{3/2} x \left(a+b x^2\right)}{5 a \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{4 b \sqrt{a x+b x^3}}{5 a x}-\frac{2 \sqrt{a x+b x^3}}{5 x^3}","\frac{2 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a x+b x^3}}-\frac{4 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a x+b x^3}}+\frac{4 b^{3/2} x \left(a+b x^2\right)}{5 a \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{4 b \sqrt{a x+b x^3}}{5 a x}-\frac{2 \sqrt{a x+b x^3}}{5 x^3}",1,"(4*b^(3/2)*x*(a + b*x^2))/(5*a*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) - (2*Sqrt[a*x + b*x^3])/(5*x^3) - (4*b*Sqrt[a*x + b*x^3])/(5*a*x) - (4*b^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*a^(3/4)*Sqrt[a*x + b*x^3]) + (2*b^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*a^(3/4)*Sqrt[a*x + b*x^3])","A",7,7,17,0.4118,1,"{2020, 2025, 2032, 329, 305, 220, 1196}"
46,1,186,0,0.2295452,"\int x^2 \left(a x+b x^3\right)^{3/2} \, dx","Int[x^2*(a*x + b*x^3)^(3/2),x]","-\frac{8 a^3 \sqrt{a x+b x^3}}{231 b^2}+\frac{4 a^{15/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a x+b x^3}}+\frac{8 a^2 x^2 \sqrt{a x+b x^3}}{385 b}+\frac{4}{55} a x^4 \sqrt{a x+b x^3}+\frac{2}{15} x^3 \left(a x+b x^3\right)^{3/2}","-\frac{8 a^3 \sqrt{a x+b x^3}}{231 b^2}+\frac{4 a^{15/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a x+b x^3}}+\frac{8 a^2 x^2 \sqrt{a x+b x^3}}{385 b}+\frac{4}{55} a x^4 \sqrt{a x+b x^3}+\frac{2}{15} x^3 \left(a x+b x^3\right)^{3/2}",1,"(-8*a^3*Sqrt[a*x + b*x^3])/(231*b^2) + (8*a^2*x^2*Sqrt[a*x + b*x^3])/(385*b) + (4*a*x^4*Sqrt[a*x + b*x^3])/55 + (2*x^3*(a*x + b*x^3)^(3/2))/15 + (4*a^(15/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(231*b^(9/4)*Sqrt[a*x + b*x^3])","A",7,5,17,0.2941,1,"{2021, 2024, 2011, 329, 220}"
47,1,304,0,0.2996586,"\int x \left(a x+b x^3\right)^{3/2} \, dx","Int[x*(a*x + b*x^3)^(3/2),x]","-\frac{8 a^3 x \left(a+b x^2\right)}{65 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{4 a^{13/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a x+b x^3}}+\frac{8 a^{13/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a x+b x^3}}+\frac{8 a^2 x \sqrt{a x+b x^3}}{195 b}+\frac{4}{39} a x^3 \sqrt{a x+b x^3}+\frac{2}{13} x^2 \left(a x+b x^3\right)^{3/2}","-\frac{8 a^3 x \left(a+b x^2\right)}{65 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{4 a^{13/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a x+b x^3}}+\frac{8 a^{13/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 b^{7/4} \sqrt{a x+b x^3}}+\frac{8 a^2 x \sqrt{a x+b x^3}}{195 b}+\frac{4}{39} a x^3 \sqrt{a x+b x^3}+\frac{2}{13} x^2 \left(a x+b x^3\right)^{3/2}",1,"(-8*a^3*x*(a + b*x^2))/(65*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) + (8*a^2*x*Sqrt[a*x + b*x^3])/(195*b) + (4*a*x^3*Sqrt[a*x + b*x^3])/39 + (2*x^2*(a*x + b*x^3)^(3/2))/13 + (8*a^(13/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(65*b^(7/4)*Sqrt[a*x + b*x^3]) - (4*a^(13/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(65*b^(7/4)*Sqrt[a*x + b*x^3])","A",8,7,15,0.4667,1,"{2021, 2024, 2032, 329, 305, 220, 1196}"
48,1,158,0,0.1335832,"\int \left(a x+b x^3\right)^{3/2} \, dx","Int[(a*x + b*x^3)^(3/2),x]","-\frac{4 a^{11/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{77 b^{5/4} \sqrt{a x+b x^3}}+\frac{8 a^2 \sqrt{a x+b x^3}}{77 b}+\frac{12}{77} a x^2 \sqrt{a x+b x^3}+\frac{2}{11} x \left(a x+b x^3\right)^{3/2}","-\frac{4 a^{11/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{77 b^{5/4} \sqrt{a x+b x^3}}+\frac{8 a^2 \sqrt{a x+b x^3}}{77 b}+\frac{12}{77} a x^2 \sqrt{a x+b x^3}+\frac{2}{11} x \left(a x+b x^3\right)^{3/2}",1,"(8*a^2*Sqrt[a*x + b*x^3])/(77*b) + (12*a*x^2*Sqrt[a*x + b*x^3])/77 + (2*x*(a*x + b*x^3)^(3/2))/11 - (4*a^(11/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(77*b^(5/4)*Sqrt[a*x + b*x^3])","A",6,6,13,0.4615,1,"{2004, 2021, 2024, 2011, 329, 220}"
49,1,275,0,0.224599,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x} \, dx","Int[(a*x + b*x^3)^(3/2)/x,x]","\frac{4 a^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a x+b x^3}}-\frac{8 a^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a x+b x^3}}+\frac{8 a^2 x \left(a+b x^2\right)}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}+\frac{4}{15} a x \sqrt{a x+b x^3}+\frac{2}{9} \left(a x+b x^3\right)^{3/2}","\frac{4 a^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a x+b x^3}}-\frac{8 a^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{a x+b x^3}}+\frac{8 a^2 x \left(a+b x^2\right)}{15 \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}+\frac{4}{15} a x \sqrt{a x+b x^3}+\frac{2}{9} \left(a x+b x^3\right)^{3/2}",1,"(8*a^2*x*(a + b*x^2))/(15*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) + (4*a*x*Sqrt[a*x + b*x^3])/15 + (2*(a*x + b*x^3)^(3/2))/9 - (8*a^(9/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[a*x + b*x^3]) + (4*a^(9/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[a*x + b*x^3])","A",7,7,17,0.4118,1,"{2021, 2004, 2032, 329, 305, 220, 1196}"
50,1,134,0,0.1319937,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^2} \, dx","Int[(a*x + b*x^3)^(3/2)/x^2,x]","\frac{4 a^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{b} \sqrt{a x+b x^3}}+\frac{4}{7} a \sqrt{a x+b x^3}+\frac{2 \left(a x+b x^3\right)^{3/2}}{7 x}","\frac{4 a^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{b} \sqrt{a x+b x^3}}+\frac{4}{7} a \sqrt{a x+b x^3}+\frac{2 \left(a x+b x^3\right)^{3/2}}{7 x}",1,"(4*a*Sqrt[a*x + b*x^3])/7 + (2*(a*x + b*x^3)^(3/2))/(7*x) + (4*a^(7/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(7*b^(1/4)*Sqrt[a*x + b*x^3])","A",5,4,17,0.2353,1,"{2021, 2011, 329, 220}"
51,1,274,0,0.2325543,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^3} \, dx","Int[(a*x + b*x^3)^(3/2)/x^3,x]","\frac{12 a^{5/4} \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a x+b x^3}}-\frac{24 a^{5/4} \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a x+b x^3}}-\frac{2 \left(a x+b x^3\right)^{3/2}}{x^2}+\frac{12}{5} b x \sqrt{a x+b x^3}+\frac{24 a \sqrt{b} x \left(a+b x^2\right)}{5 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}","\frac{12 a^{5/4} \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a x+b x^3}}-\frac{24 a^{5/4} \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a x+b x^3}}-\frac{2 \left(a x+b x^3\right)^{3/2}}{x^2}+\frac{12}{5} b x \sqrt{a x+b x^3}+\frac{24 a \sqrt{b} x \left(a+b x^2\right)}{5 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}",1,"(24*a*Sqrt[b]*x*(a + b*x^2))/(5*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) + (12*b*x*Sqrt[a*x + b*x^3])/5 - (2*(a*x + b*x^3)^(3/2))/x^2 - (24*a^(5/4)*b^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*Sqrt[a*x + b*x^3]) + (12*a^(5/4)*b^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*Sqrt[a*x + b*x^3])","A",7,7,17,0.4118,1,"{2020, 2004, 2032, 329, 305, 220, 1196}"
52,1,134,0,0.1311368,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^4} \, dx","Int[(a*x + b*x^3)^(3/2)/x^4,x]","\frac{4 a^{3/4} b^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt{a x+b x^3}}-\frac{2 \left(a x+b x^3\right)^{3/2}}{3 x^3}+\frac{4}{3} b \sqrt{a x+b x^3}","\frac{4 a^{3/4} b^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt{a x+b x^3}}-\frac{2 \left(a x+b x^3\right)^{3/2}}{3 x^3}+\frac{4}{3} b \sqrt{a x+b x^3}",1,"(4*b*Sqrt[a*x + b*x^3])/3 - (2*(a*x + b*x^3)^(3/2))/(3*x^3) + (4*a^(3/4)*b^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*Sqrt[a*x + b*x^3])","A",5,5,17,0.2941,1,"{2020, 2021, 2011, 329, 220}"
53,1,277,0,0.2608318,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^5} \, dx","Int[(a*x + b*x^3)^(3/2)/x^5,x]","\frac{24 b^{3/2} x \left(a+b x^2\right)}{5 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}+\frac{12 \sqrt[4]{a} b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a x+b x^3}}-\frac{24 \sqrt[4]{a} b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a x+b x^3}}-\frac{12 b \sqrt{a x+b x^3}}{5 x}-\frac{2 \left(a x+b x^3\right)^{3/2}}{5 x^4}","\frac{24 b^{3/2} x \left(a+b x^2\right)}{5 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}+\frac{12 \sqrt[4]{a} b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a x+b x^3}}-\frac{24 \sqrt[4]{a} b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 \sqrt{a x+b x^3}}-\frac{12 b \sqrt{a x+b x^3}}{5 x}-\frac{2 \left(a x+b x^3\right)^{3/2}}{5 x^4}",1,"(24*b^(3/2)*x*(a + b*x^2))/(5*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) - (12*b*Sqrt[a*x + b*x^3])/(5*x) - (2*(a*x + b*x^3)^(3/2))/(5*x^4) - (24*a^(1/4)*b^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*Sqrt[a*x + b*x^3]) + (12*a^(1/4)*b^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*Sqrt[a*x + b*x^3])","A",7,6,17,0.3529,1,"{2020, 2032, 329, 305, 220, 1196}"
54,1,137,0,0.1342069,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^6} \, dx","Int[(a*x + b*x^3)^(3/2)/x^6,x]","\frac{4 b^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{a} \sqrt{a x+b x^3}}-\frac{4 b \sqrt{a x+b x^3}}{7 x^2}-\frac{2 \left(a x+b x^3\right)^{3/2}}{7 x^5}","\frac{4 b^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{7 \sqrt[4]{a} \sqrt{a x+b x^3}}-\frac{4 b \sqrt{a x+b x^3}}{7 x^2}-\frac{2 \left(a x+b x^3\right)^{3/2}}{7 x^5}",1,"(-4*b*Sqrt[a*x + b*x^3])/(7*x^2) - (2*(a*x + b*x^3)^(3/2))/(7*x^5) + (4*b^(7/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(7*a^(1/4)*Sqrt[a*x + b*x^3])","A",5,4,17,0.2353,1,"{2020, 2011, 329, 220}"
55,1,306,0,0.3119644,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^7} \, dx","Int[(a*x + b*x^3)^(3/2)/x^7,x]","\frac{4 b^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a x+b x^3}}-\frac{8 b^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a x+b x^3}}+\frac{8 b^{5/2} x \left(a+b x^2\right)}{15 a \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{8 b^2 \sqrt{a x+b x^3}}{15 a x}-\frac{4 b \sqrt{a x+b x^3}}{15 x^3}-\frac{2 \left(a x+b x^3\right)^{3/2}}{9 x^6}","\frac{4 b^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a x+b x^3}}-\frac{8 b^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} \sqrt{a x+b x^3}}+\frac{8 b^{5/2} x \left(a+b x^2\right)}{15 a \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{8 b^2 \sqrt{a x+b x^3}}{15 a x}-\frac{4 b \sqrt{a x+b x^3}}{15 x^3}-\frac{2 \left(a x+b x^3\right)^{3/2}}{9 x^6}",1,"(8*b^(5/2)*x*(a + b*x^2))/(15*a*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) - (4*b*Sqrt[a*x + b*x^3])/(15*x^3) - (8*b^2*Sqrt[a*x + b*x^3])/(15*a*x) - (2*(a*x + b*x^3)^(3/2))/(9*x^6) - (8*b^(9/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*a^(3/4)*Sqrt[a*x + b*x^3]) + (4*b^(9/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*a^(3/4)*Sqrt[a*x + b*x^3])","A",8,7,17,0.4118,1,"{2020, 2025, 2032, 329, 305, 220, 1196}"
56,1,163,0,0.1781907,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^8} \, dx","Int[(a*x + b*x^3)^(3/2)/x^8,x]","-\frac{4 b^{11/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{77 a^{5/4} \sqrt{a x+b x^3}}-\frac{8 b^2 \sqrt{a x+b x^3}}{77 a x^2}-\frac{12 b \sqrt{a x+b x^3}}{77 x^4}-\frac{2 \left(a x+b x^3\right)^{3/2}}{11 x^7}","-\frac{4 b^{11/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{77 a^{5/4} \sqrt{a x+b x^3}}-\frac{8 b^2 \sqrt{a x+b x^3}}{77 a x^2}-\frac{12 b \sqrt{a x+b x^3}}{77 x^4}-\frac{2 \left(a x+b x^3\right)^{3/2}}{11 x^7}",1,"(-12*b*Sqrt[a*x + b*x^3])/(77*x^4) - (8*b^2*Sqrt[a*x + b*x^3])/(77*a*x^2) - (2*(a*x + b*x^3)^(3/2))/(11*x^7) - (4*b^(11/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(77*a^(5/4)*Sqrt[a*x + b*x^3])","A",6,5,17,0.2941,1,"{2020, 2025, 2011, 329, 220}"
57,1,140,0,0.1372501,"\int \frac{x^4}{\sqrt{a x+b x^3}} \, dx","Int[x^4/Sqrt[a*x + b*x^3],x]","\frac{5 a^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 b^{9/4} \sqrt{a x+b x^3}}-\frac{10 a \sqrt{a x+b x^3}}{21 b^2}+\frac{2 x^2 \sqrt{a x+b x^3}}{7 b}","\frac{5 a^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 b^{9/4} \sqrt{a x+b x^3}}-\frac{10 a \sqrt{a x+b x^3}}{21 b^2}+\frac{2 x^2 \sqrt{a x+b x^3}}{7 b}",1,"(-10*a*Sqrt[a*x + b*x^3])/(21*b^2) + (2*x^2*Sqrt[a*x + b*x^3])/(7*b) + (5*a^(7/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(21*b^(9/4)*Sqrt[a*x + b*x^3])","A",5,4,17,0.2353,1,"{2024, 2011, 329, 220}"
58,1,258,0,0.2054047,"\int \frac{x^3}{\sqrt{a x+b x^3}} \, dx","Int[x^3/Sqrt[a*x + b*x^3],x]","-\frac{3 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a x+b x^3}}+\frac{6 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a x+b x^3}}-\frac{6 a x \left(a+b x^2\right)}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}+\frac{2 x \sqrt{a x+b x^3}}{5 b}","-\frac{3 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a x+b x^3}}+\frac{6 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a x+b x^3}}-\frac{6 a x \left(a+b x^2\right)}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}+\frac{2 x \sqrt{a x+b x^3}}{5 b}",1,"(-6*a*x*(a + b*x^2))/(5*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) + (2*x*Sqrt[a*x + b*x^3])/(5*b) + (6*a^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*b^(7/4)*Sqrt[a*x + b*x^3]) - (3*a^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*b^(7/4)*Sqrt[a*x + b*x^3])","A",6,6,17,0.3529,1,"{2024, 2032, 329, 305, 220, 1196}"
59,1,116,0,0.091224,"\int \frac{x^2}{\sqrt{a x+b x^3}} \, dx","Int[x^2/Sqrt[a*x + b*x^3],x]","\frac{2 \sqrt{a x+b x^3}}{3 b}-\frac{a^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 b^{5/4} \sqrt{a x+b x^3}}","\frac{2 \sqrt{a x+b x^3}}{3 b}-\frac{a^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 b^{5/4} \sqrt{a x+b x^3}}",1,"(2*Sqrt[a*x + b*x^3])/(3*b) - (a^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*b^(5/4)*Sqrt[a*x + b*x^3])","A",4,4,17,0.2353,1,"{2024, 2011, 329, 220}"
60,1,229,0,0.1496756,"\int \frac{x}{\sqrt{a x+b x^3}} \, dx","Int[x/Sqrt[a*x + b*x^3],x]","\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a x+b x^3}}-\frac{2 \sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a x+b x^3}}+\frac{2 x \left(a+b x^2\right)}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}","\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a x+b x^3}}-\frac{2 \sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a x+b x^3}}+\frac{2 x \left(a+b x^2\right)}{\sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}",1,"(2*x*(a + b*x^2))/(Sqrt[b]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) - (2*a^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(b^(3/4)*Sqrt[a*x + b*x^3]) + (a^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(b^(3/4)*Sqrt[a*x + b*x^3])","A",5,5,15,0.3333,1,"{2032, 329, 305, 220, 1196}"
61,1,92,0,0.0488648,"\int \frac{1}{\sqrt{a x+b x^3}} \, dx","Int[1/Sqrt[a*x + b*x^3],x]","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt[4]{b} \sqrt{a x+b x^3}}","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt[4]{b} \sqrt{a x+b x^3}}",1,"(Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(1/4)*b^(1/4)*Sqrt[a*x + b*x^3])","A",3,3,13,0.2308,1,"{2011, 329, 220}"
62,1,253,0,0.2004933,"\int \frac{1}{x \sqrt{a x+b x^3}} \, dx","Int[1/(x*Sqrt[a*x + b*x^3]),x]","\frac{\sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a x+b x^3}}-\frac{2 \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a x+b x^3}}+\frac{2 \sqrt{b} x \left(a+b x^2\right)}{a \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{2 \sqrt{a x+b x^3}}{a x}","\frac{\sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a x+b x^3}}-\frac{2 \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt{a x+b x^3}}+\frac{2 \sqrt{b} x \left(a+b x^2\right)}{a \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{2 \sqrt{a x+b x^3}}{a x}",1,"(2*Sqrt[b]*x*(a + b*x^2))/(a*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) - (2*Sqrt[a*x + b*x^3])/(a*x) - (2*b^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(3/4)*Sqrt[a*x + b*x^3]) + (b^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(3/4)*Sqrt[a*x + b*x^3])","A",6,6,17,0.3529,1,"{2025, 2032, 329, 305, 220, 1196}"
63,1,119,0,0.0893417,"\int \frac{1}{x^2 \sqrt{a x+b x^3}} \, dx","Int[1/(x^2*Sqrt[a*x + b*x^3]),x]","-\frac{b^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 a^{5/4} \sqrt{a x+b x^3}}-\frac{2 \sqrt{a x+b x^3}}{3 a x^2}","-\frac{b^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 a^{5/4} \sqrt{a x+b x^3}}-\frac{2 \sqrt{a x+b x^3}}{3 a x^2}",1,"(-2*Sqrt[a*x + b*x^3])/(3*a*x^2) - (b^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*a^(5/4)*Sqrt[a*x + b*x^3])","A",4,4,17,0.2353,1,"{2025, 2011, 329, 220}"
64,1,286,0,0.2542955,"\int \frac{1}{x^3 \sqrt{a x+b x^3}} \, dx","Int[1/(x^3*Sqrt[a*x + b*x^3]),x]","-\frac{6 b^{3/2} x \left(a+b x^2\right)}{5 a^2 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{3 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a x+b x^3}}+\frac{6 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a x+b x^3}}+\frac{6 b \sqrt{a x+b x^3}}{5 a^2 x}-\frac{2 \sqrt{a x+b x^3}}{5 a x^3}","-\frac{6 b^{3/2} x \left(a+b x^2\right)}{5 a^2 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{3 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a x+b x^3}}+\frac{6 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a x+b x^3}}+\frac{6 b \sqrt{a x+b x^3}}{5 a^2 x}-\frac{2 \sqrt{a x+b x^3}}{5 a x^3}",1,"(-6*b^(3/2)*x*(a + b*x^2))/(5*a^2*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) - (2*Sqrt[a*x + b*x^3])/(5*a*x^3) + (6*b*Sqrt[a*x + b*x^3])/(5*a^2*x) + (6*b^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*a^(7/4)*Sqrt[a*x + b*x^3]) - (3*b^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*a^(7/4)*Sqrt[a*x + b*x^3])","A",7,6,17,0.3529,1,"{2025, 2032, 329, 305, 220, 1196}"
65,1,161,0,0.1934082,"\int \frac{x^7}{\left(a x+b x^3\right)^{3/2}} \, dx","Int[x^7/(a*x + b*x^3)^(3/2),x]","\frac{15 a^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{14 b^{13/4} \sqrt{a x+b x^3}}+\frac{9 x^2 \sqrt{a x+b x^3}}{7 b^2}-\frac{15 a \sqrt{a x+b x^3}}{7 b^3}-\frac{x^5}{b \sqrt{a x+b x^3}}","\frac{15 a^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{14 b^{13/4} \sqrt{a x+b x^3}}+\frac{9 x^2 \sqrt{a x+b x^3}}{7 b^2}-\frac{15 a \sqrt{a x+b x^3}}{7 b^3}-\frac{x^5}{b \sqrt{a x+b x^3}}",1,"-(x^5/(b*Sqrt[a*x + b*x^3])) - (15*a*Sqrt[a*x + b*x^3])/(7*b^3) + (9*x^2*Sqrt[a*x + b*x^3])/(7*b^2) + (15*a^(7/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(14*b^(13/4)*Sqrt[a*x + b*x^3])","A",6,5,17,0.2941,1,"{2022, 2024, 2011, 329, 220}"
66,1,279,0,0.2688441,"\int \frac{x^6}{\left(a x+b x^3\right)^{3/2}} \, dx","Int[x^6/(a*x + b*x^3)^(3/2),x]","-\frac{21 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 b^{11/4} \sqrt{a x+b x^3}}+\frac{21 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{11/4} \sqrt{a x+b x^3}}+\frac{7 x \sqrt{a x+b x^3}}{5 b^2}-\frac{21 a x \left(a+b x^2\right)}{5 b^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{x^4}{b \sqrt{a x+b x^3}}","-\frac{21 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 b^{11/4} \sqrt{a x+b x^3}}+\frac{21 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 b^{11/4} \sqrt{a x+b x^3}}+\frac{7 x \sqrt{a x+b x^3}}{5 b^2}-\frac{21 a x \left(a+b x^2\right)}{5 b^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{x^4}{b \sqrt{a x+b x^3}}",1,"-(x^4/(b*Sqrt[a*x + b*x^3])) - (21*a*x*(a + b*x^2))/(5*b^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) + (7*x*Sqrt[a*x + b*x^3])/(5*b^2) + (21*a^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*b^(11/4)*Sqrt[a*x + b*x^3]) - (21*a^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(10*b^(11/4)*Sqrt[a*x + b*x^3])","A",7,7,17,0.4118,1,"{2022, 2024, 2032, 329, 305, 220, 1196}"
67,1,137,0,0.147964,"\int \frac{x^5}{\left(a x+b x^3\right)^{3/2}} \, dx","Int[x^5/(a*x + b*x^3)^(3/2),x]","-\frac{5 a^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 b^{9/4} \sqrt{a x+b x^3}}+\frac{5 \sqrt{a x+b x^3}}{3 b^2}-\frac{x^3}{b \sqrt{a x+b x^3}}","-\frac{5 a^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 b^{9/4} \sqrt{a x+b x^3}}+\frac{5 \sqrt{a x+b x^3}}{3 b^2}-\frac{x^3}{b \sqrt{a x+b x^3}}",1,"-(x^3/(b*Sqrt[a*x + b*x^3])) + (5*Sqrt[a*x + b*x^3])/(3*b^2) - (5*a^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(6*b^(9/4)*Sqrt[a*x + b*x^3])","A",5,5,17,0.2941,1,"{2022, 2024, 2011, 329, 220}"
68,1,253,0,0.2132893,"\int \frac{x^4}{\left(a x+b x^3\right)^{3/2}} \, dx","Int[x^4/(a*x + b*x^3)^(3/2),x]","\frac{3 x \left(a+b x^2\right)}{b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}+\frac{3 \sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a x+b x^3}}-\frac{3 \sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{7/4} \sqrt{a x+b x^3}}-\frac{x^2}{b \sqrt{a x+b x^3}}","\frac{3 x \left(a+b x^2\right)}{b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}+\frac{3 \sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 b^{7/4} \sqrt{a x+b x^3}}-\frac{3 \sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{b^{7/4} \sqrt{a x+b x^3}}-\frac{x^2}{b \sqrt{a x+b x^3}}",1,"-(x^2/(b*Sqrt[a*x + b*x^3])) + (3*x*(a + b*x^2))/(b^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) - (3*a^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(b^(7/4)*Sqrt[a*x + b*x^3]) + (3*a^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*b^(7/4)*Sqrt[a*x + b*x^3])","A",6,6,17,0.3529,1,"{2022, 2032, 329, 305, 220, 1196}"
69,1,115,0,0.0998051,"\int \frac{x^3}{\left(a x+b x^3\right)^{3/2}} \, dx","Int[x^3/(a*x + b*x^3)^(3/2),x]","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} b^{5/4} \sqrt{a x+b x^3}}-\frac{x}{b \sqrt{a x+b x^3}}","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} b^{5/4} \sqrt{a x+b x^3}}-\frac{x}{b \sqrt{a x+b x^3}}",1,"-(x/(b*Sqrt[a*x + b*x^3])) + (Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(1/4)*b^(5/4)*Sqrt[a*x + b*x^3])","A",4,4,17,0.2353,1,"{2022, 2011, 329, 220}"
70,1,254,0,0.2090287,"\int \frac{x^2}{\left(a x+b x^3\right)^{3/2}} \, dx","Int[x^2/(a*x + b*x^3)^(3/2),x]","-\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a x+b x^3}}+\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{3/4} \sqrt{a x+b x^3}}+\frac{x^2}{a \sqrt{a x+b x^3}}-\frac{x \left(a+b x^2\right)}{a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}","-\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a x+b x^3}}+\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{3/4} \sqrt{a x+b x^3}}+\frac{x^2}{a \sqrt{a x+b x^3}}-\frac{x \left(a+b x^2\right)}{a \sqrt{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}",1,"x^2/(a*Sqrt[a*x + b*x^3]) - (x*(a + b*x^2))/(a*Sqrt[b]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) + (Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(3/4)*b^(3/4)*Sqrt[a*x + b*x^3]) - (Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(3/4)*b^(3/4)*Sqrt[a*x + b*x^3])","A",6,6,17,0.3529,1,"{2023, 2032, 329, 305, 220, 1196}"
71,1,114,0,0.083586,"\int \frac{x}{\left(a x+b x^3\right)^{3/2}} \, dx","Int[x/(a*x + b*x^3)^(3/2),x]","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{5/4} \sqrt[4]{b} \sqrt{a x+b x^3}}+\frac{x}{a \sqrt{a x+b x^3}}","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{5/4} \sqrt[4]{b} \sqrt{a x+b x^3}}+\frac{x}{a \sqrt{a x+b x^3}}",1,"x/(a*Sqrt[a*x + b*x^3]) + (Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(5/4)*b^(1/4)*Sqrt[a*x + b*x^3])","A",4,4,15,0.2667,1,"{2023, 2011, 329, 220}"
72,1,273,0,0.2238225,"\int \frac{1}{\left(a x+b x^3\right)^{3/2}} \, dx","Int[(a*x + b*x^3)^(-3/2),x]","\frac{3 \sqrt{b} x \left(a+b x^2\right)}{a^2 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{3 \sqrt{a x+b x^3}}{a^2 x}+\frac{3 \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a x+b x^3}}-\frac{3 \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{7/4} \sqrt{a x+b x^3}}+\frac{1}{a \sqrt{a x+b x^3}}","\frac{3 \sqrt{b} x \left(a+b x^2\right)}{a^2 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{3 \sqrt{a x+b x^3}}{a^2 x}+\frac{3 \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt{a x+b x^3}}-\frac{3 \sqrt[4]{b} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{7/4} \sqrt{a x+b x^3}}+\frac{1}{a \sqrt{a x+b x^3}}",1,"1/(a*Sqrt[a*x + b*x^3]) + (3*Sqrt[b]*x*(a + b*x^2))/(a^2*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) - (3*Sqrt[a*x + b*x^3])/(a^2*x) - (3*b^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(7/4)*Sqrt[a*x + b*x^3]) + (3*b^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(7/4)*Sqrt[a*x + b*x^3])","A",7,7,13,0.5385,1,"{2006, 2025, 2032, 329, 305, 220, 1196}"
73,1,139,0,0.1421699,"\int \frac{1}{x \left(a x+b x^3\right)^{3/2}} \, dx","Int[1/(x*(a*x + b*x^3)^(3/2)),x]","-\frac{5 b^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{9/4} \sqrt{a x+b x^3}}-\frac{5 \sqrt{a x+b x^3}}{3 a^2 x^2}+\frac{1}{a x \sqrt{a x+b x^3}}","-\frac{5 b^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{9/4} \sqrt{a x+b x^3}}-\frac{5 \sqrt{a x+b x^3}}{3 a^2 x^2}+\frac{1}{a x \sqrt{a x+b x^3}}",1,"1/(a*x*Sqrt[a*x + b*x^3]) - (5*Sqrt[a*x + b*x^3])/(3*a^2*x^2) - (5*b^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(6*a^(9/4)*Sqrt[a*x + b*x^3])","A",5,5,17,0.2941,1,"{2023, 2025, 2011, 329, 220}"
74,1,306,0,0.3225719,"\int \frac{1}{x^2 \left(a x+b x^3\right)^{3/2}} \, dx","Int[1/(x^2*(a*x + b*x^3)^(3/2)),x]","-\frac{21 b^{3/2} x \left(a+b x^2\right)}{5 a^3 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{21 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 a^{11/4} \sqrt{a x+b x^3}}+\frac{21 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{11/4} \sqrt{a x+b x^3}}+\frac{21 b \sqrt{a x+b x^3}}{5 a^3 x}-\frac{7 \sqrt{a x+b x^3}}{5 a^2 x^3}+\frac{1}{a x^2 \sqrt{a x+b x^3}}","-\frac{21 b^{3/2} x \left(a+b x^2\right)}{5 a^3 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{a x+b x^3}}-\frac{21 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 a^{11/4} \sqrt{a x+b x^3}}+\frac{21 b^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{11/4} \sqrt{a x+b x^3}}+\frac{21 b \sqrt{a x+b x^3}}{5 a^3 x}-\frac{7 \sqrt{a x+b x^3}}{5 a^2 x^3}+\frac{1}{a x^2 \sqrt{a x+b x^3}}",1,"1/(a*x^2*Sqrt[a*x + b*x^3]) - (21*b^(3/2)*x*(a + b*x^2))/(5*a^3*(Sqrt[a] + Sqrt[b]*x)*Sqrt[a*x + b*x^3]) - (7*Sqrt[a*x + b*x^3])/(5*a^2*x^3) + (21*b*Sqrt[a*x + b*x^3])/(5*a^3*x) + (21*b^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*a^(11/4)*Sqrt[a*x + b*x^3]) - (21*b^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(10*a^(11/4)*Sqrt[a*x + b*x^3])","A",8,7,17,0.4118,1,"{2023, 2025, 2032, 329, 305, 220, 1196}"
75,1,159,0,0.2483758,"\int \frac{x^{29/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(29/2)/(a*x + b*x^3)^(9/2),x]","-\frac{9 x^{19/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{3 x^{13/2}}{5 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{3 x^{7/2}}{b^4 \sqrt{a x+b x^3}}+\frac{9 \sqrt{x} \sqrt{a x+b x^3}}{2 b^5}-\frac{9 a \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x+b x^3}}\right)}{2 b^{11/2}}-\frac{x^{25/2}}{7 b \left(a x+b x^3\right)^{7/2}}","-\frac{9 x^{19/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{3 x^{13/2}}{5 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{3 x^{7/2}}{b^4 \sqrt{a x+b x^3}}+\frac{9 \sqrt{x} \sqrt{a x+b x^3}}{2 b^5}-\frac{9 a \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x+b x^3}}\right)}{2 b^{11/2}}-\frac{x^{25/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"-x^(25/2)/(7*b*(a*x + b*x^3)^(7/2)) - (9*x^(19/2))/(35*b^2*(a*x + b*x^3)^(5/2)) - (3*x^(13/2))/(5*b^3*(a*x + b*x^3)^(3/2)) - (3*x^(7/2))/(b^4*Sqrt[a*x + b*x^3]) + (9*Sqrt[x]*Sqrt[a*x + b*x^3])/(2*b^5) - (9*a*ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a*x + b*x^3]])/(2*b^(11/2))","A",7,4,19,0.2105,1,"{2022, 2024, 2029, 206}"
76,1,126,0,0.2002792,"\int \frac{x^{27/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(27/2)/(a*x + b*x^3)^(9/2),x]","-\frac{8 x^{17/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{16 x^{11/2}}{35 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{64 x^{5/2}}{35 b^4 \sqrt{a x+b x^3}}+\frac{128 \sqrt{a x+b x^3}}{35 b^5 \sqrt{x}}-\frac{x^{23/2}}{7 b \left(a x+b x^3\right)^{7/2}}","-\frac{8 x^{17/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{16 x^{11/2}}{35 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{64 x^{5/2}}{35 b^4 \sqrt{a x+b x^3}}+\frac{128 \sqrt{a x+b x^3}}{35 b^5 \sqrt{x}}-\frac{x^{23/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"-x^(23/2)/(7*b*(a*x + b*x^3)^(7/2)) - (8*x^(17/2))/(35*b^2*(a*x + b*x^3)^(5/2)) - (16*x^(11/2))/(35*b^3*(a*x + b*x^3)^(3/2)) - (64*x^(5/2))/(35*b^4*Sqrt[a*x + b*x^3]) + (128*Sqrt[a*x + b*x^3])/(35*b^5*Sqrt[x])","A",5,2,19,0.1053,1,"{2015, 2014}"
77,1,130,0,0.205549,"\int \frac{x^{25/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(25/2)/(a*x + b*x^3)^(9/2),x]","-\frac{x^{15/2}}{5 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{x^{9/2}}{3 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{x^{3/2}}{b^4 \sqrt{a x+b x^3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x+b x^3}}\right)}{b^{9/2}}-\frac{x^{21/2}}{7 b \left(a x+b x^3\right)^{7/2}}","-\frac{x^{15/2}}{5 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{x^{9/2}}{3 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{x^{3/2}}{b^4 \sqrt{a x+b x^3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x+b x^3}}\right)}{b^{9/2}}-\frac{x^{21/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"-x^(21/2)/(7*b*(a*x + b*x^3)^(7/2)) - x^(15/2)/(5*b^2*(a*x + b*x^3)^(5/2)) - x^(9/2)/(3*b^3*(a*x + b*x^3)^(3/2)) - x^(3/2)/(b^4*Sqrt[a*x + b*x^3]) + ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a*x + b*x^3]]/b^(9/2)","A",6,3,19,0.1579,1,"{2022, 2029, 206}"
78,1,101,0,0.1614507,"\int \frac{x^{23/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(23/2)/(a*x + b*x^3)^(9/2),x]","-\frac{6 x^{13/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{8 x^{7/2}}{35 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{16 \sqrt{x}}{35 b^4 \sqrt{a x+b x^3}}-\frac{x^{19/2}}{7 b \left(a x+b x^3\right)^{7/2}}","-\frac{6 x^{13/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{8 x^{7/2}}{35 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{16 \sqrt{x}}{35 b^4 \sqrt{a x+b x^3}}-\frac{x^{19/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"-x^(19/2)/(7*b*(a*x + b*x^3)^(7/2)) - (6*x^(13/2))/(35*b^2*(a*x + b*x^3)^(5/2)) - (8*x^(7/2))/(35*b^3*(a*x + b*x^3)^(3/2)) - (16*Sqrt[x])/(35*b^4*Sqrt[a*x + b*x^3])","A",4,2,19,0.1053,1,"{2015, 2014}"
79,1,25,0,0.0369776,"\int \frac{x^{21/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(21/2)/(a*x + b*x^3)^(9/2),x]","\frac{x^{21/2}}{7 a \left(a x+b x^3\right)^{7/2}}","\frac{x^{21/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"x^(21/2)/(7*a*(a*x + b*x^3)^(7/2))","A",1,1,19,0.05263,1,"{2014}"
80,1,76,0,0.1187755,"\int \frac{x^{19/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(19/2)/(a*x + b*x^3)^(9/2),x]","-\frac{4 x^{9/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{8 x^{3/2}}{105 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{x^{15/2}}{7 b \left(a x+b x^3\right)^{7/2}}","-\frac{4 x^{9/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{8 x^{3/2}}{105 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{x^{15/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"-x^(15/2)/(7*b*(a*x + b*x^3)^(7/2)) - (4*x^(9/2))/(35*b^2*(a*x + b*x^3)^(5/2)) - (8*x^(3/2))/(105*b^3*(a*x + b*x^3)^(3/2))","A",3,2,19,0.1053,1,"{2015, 2014}"
81,1,51,0,0.0747788,"\int \frac{x^{17/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(17/2)/(a*x + b*x^3)^(9/2),x]","\frac{2 x^{15/2}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{x^{17/2}}{7 a \left(a x+b x^3\right)^{7/2}}","\frac{2 x^{15/2}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{x^{17/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"x^(17/2)/(7*a*(a*x + b*x^3)^(7/2)) + (2*x^(15/2))/(35*a^2*(a*x + b*x^3)^(5/2))","A",2,2,19,0.1053,1,"{2015, 2014}"
82,1,51,0,0.0736555,"\int \frac{x^{15/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(15/2)/(a*x + b*x^3)^(9/2),x]","-\frac{2 x^{5/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{x^{11/2}}{7 b \left(a x+b x^3\right)^{7/2}}","-\frac{2 x^{5/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{x^{11/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"-x^(11/2)/(7*b*(a*x + b*x^3)^(7/2)) - (2*x^(5/2))/(35*b^2*(a*x + b*x^3)^(5/2))","A",2,2,19,0.1053,1,"{2015, 2014}"
83,1,76,0,0.112928,"\int \frac{x^{13/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(13/2)/(a*x + b*x^3)^(9/2),x]","\frac{4 x^{11/2}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{8 x^{9/2}}{105 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{x^{13/2}}{7 a \left(a x+b x^3\right)^{7/2}}","\frac{4 x^{11/2}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{8 x^{9/2}}{105 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{x^{13/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"x^(13/2)/(7*a*(a*x + b*x^3)^(7/2)) + (4*x^(11/2))/(35*a^2*(a*x + b*x^3)^(5/2)) + (8*x^(9/2))/(105*a^3*(a*x + b*x^3)^(3/2))","A",3,2,19,0.1053,1,"{2015, 2014}"
84,1,25,0,0.0370535,"\int \frac{x^{11/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(11/2)/(a*x + b*x^3)^(9/2),x]","-\frac{x^{7/2}}{7 b \left(a x+b x^3\right)^{7/2}}","-\frac{x^{7/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"-x^(7/2)/(7*b*(a*x + b*x^3)^(7/2))","A",1,1,19,0.05263,1,"{2014}"
85,1,101,0,0.1572722,"\int \frac{x^{9/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(9/2)/(a*x + b*x^3)^(9/2),x]","\frac{6 x^{7/2}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{8 x^{5/2}}{35 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{16 x^{3/2}}{35 a^4 \sqrt{a x+b x^3}}+\frac{x^{9/2}}{7 a \left(a x+b x^3\right)^{7/2}}","\frac{6 x^{7/2}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{8 x^{5/2}}{35 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{16 x^{3/2}}{35 a^4 \sqrt{a x+b x^3}}+\frac{x^{9/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"x^(9/2)/(7*a*(a*x + b*x^3)^(7/2)) + (6*x^(7/2))/(35*a^2*(a*x + b*x^3)^(5/2)) + (8*x^(5/2))/(35*a^3*(a*x + b*x^3)^(3/2)) + (16*x^(3/2))/(35*a^4*Sqrt[a*x + b*x^3])","A",4,2,19,0.1053,1,"{2015, 2014}"
86,1,130,0,0.2027775,"\int \frac{x^{7/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(7/2)/(a*x + b*x^3)^(9/2),x]","\frac{x^{5/2}}{5 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{x^{3/2}}{3 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{\sqrt{x}}{a^4 \sqrt{a x+b x^3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^3}}\right)}{a^{9/2}}+\frac{x^{7/2}}{7 a \left(a x+b x^3\right)^{7/2}}","\frac{x^{5/2}}{5 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{x^{3/2}}{3 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{\sqrt{x}}{a^4 \sqrt{a x+b x^3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^3}}\right)}{a^{9/2}}+\frac{x^{7/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"x^(7/2)/(7*a*(a*x + b*x^3)^(7/2)) + x^(5/2)/(5*a^2*(a*x + b*x^3)^(5/2)) + x^(3/2)/(3*a^3*(a*x + b*x^3)^(3/2)) + Sqrt[x]/(a^4*Sqrt[a*x + b*x^3]) - ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[a*x + b*x^3]]/a^(9/2)","A",6,3,19,0.1579,1,"{2023, 2029, 206}"
87,1,126,0,0.1924454,"\int \frac{x^{5/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(5/2)/(a*x + b*x^3)^(9/2),x]","\frac{8 x^{3/2}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{16 \sqrt{x}}{35 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{64}{35 a^4 \sqrt{x} \sqrt{a x+b x^3}}-\frac{128 \sqrt{a x+b x^3}}{35 a^5 x^{3/2}}+\frac{x^{5/2}}{7 a \left(a x+b x^3\right)^{7/2}}","\frac{8 x^{3/2}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{16 \sqrt{x}}{35 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{64}{35 a^4 \sqrt{x} \sqrt{a x+b x^3}}-\frac{128 \sqrt{a x+b x^3}}{35 a^5 x^{3/2}}+\frac{x^{5/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"x^(5/2)/(7*a*(a*x + b*x^3)^(7/2)) + (8*x^(3/2))/(35*a^2*(a*x + b*x^3)^(5/2)) + (16*Sqrt[x])/(35*a^3*(a*x + b*x^3)^(3/2)) + 64/(35*a^4*Sqrt[x]*Sqrt[a*x + b*x^3]) - (128*Sqrt[a*x + b*x^3])/(35*a^5*x^(3/2))","A",5,2,19,0.1053,1,"{2015, 2014}"
88,1,159,0,0.2405484,"\int \frac{x^{3/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[x^(3/2)/(a*x + b*x^3)^(9/2),x]","\frac{9 \sqrt{x}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{3}{5 a^3 \sqrt{x} \left(a x+b x^3\right)^{3/2}}+\frac{3}{a^4 x^{3/2} \sqrt{a x+b x^3}}-\frac{9 \sqrt{a x+b x^3}}{2 a^5 x^{5/2}}+\frac{9 b \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^3}}\right)}{2 a^{11/2}}+\frac{x^{3/2}}{7 a \left(a x+b x^3\right)^{7/2}}","\frac{9 \sqrt{x}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{3}{5 a^3 \sqrt{x} \left(a x+b x^3\right)^{3/2}}+\frac{3}{a^4 x^{3/2} \sqrt{a x+b x^3}}-\frac{9 \sqrt{a x+b x^3}}{2 a^5 x^{5/2}}+\frac{9 b \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^3}}\right)}{2 a^{11/2}}+\frac{x^{3/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"x^(3/2)/(7*a*(a*x + b*x^3)^(7/2)) + (9*Sqrt[x])/(35*a^2*(a*x + b*x^3)^(5/2)) + 3/(5*a^3*Sqrt[x]*(a*x + b*x^3)^(3/2)) + 3/(a^4*x^(3/2)*Sqrt[a*x + b*x^3]) - (9*Sqrt[a*x + b*x^3])/(2*a^5*x^(5/2)) + (9*b*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[a*x + b*x^3]])/(2*a^(11/2))","A",7,4,19,0.2105,1,"{2023, 2025, 2029, 206}"
89,1,152,0,0.233374,"\int \frac{\sqrt{x}}{\left(a x+b x^3\right)^{9/2}} \, dx","Int[Sqrt[x]/(a*x + b*x^3)^(9/2),x]","\frac{256 b \sqrt{a x+b x^3}}{21 a^6 x^{3/2}}-\frac{128 \sqrt{a x+b x^3}}{21 a^5 x^{7/2}}+\frac{32}{7 a^4 x^{5/2} \sqrt{a x+b x^3}}+\frac{16}{21 a^3 x^{3/2} \left(a x+b x^3\right)^{3/2}}+\frac{2}{7 a^2 \sqrt{x} \left(a x+b x^3\right)^{5/2}}+\frac{\sqrt{x}}{7 a \left(a x+b x^3\right)^{7/2}}","\frac{256 b \sqrt{a x+b x^3}}{21 a^6 x^{3/2}}-\frac{128 \sqrt{a x+b x^3}}{21 a^5 x^{7/2}}+\frac{32}{7 a^4 x^{5/2} \sqrt{a x+b x^3}}+\frac{16}{21 a^3 x^{3/2} \left(a x+b x^3\right)^{3/2}}+\frac{2}{7 a^2 \sqrt{x} \left(a x+b x^3\right)^{5/2}}+\frac{\sqrt{x}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"Sqrt[x]/(7*a*(a*x + b*x^3)^(7/2)) + 2/(7*a^2*Sqrt[x]*(a*x + b*x^3)^(5/2)) + 16/(21*a^3*x^(3/2)*(a*x + b*x^3)^(3/2)) + 32/(7*a^4*x^(5/2)*Sqrt[a*x + b*x^3]) - (128*Sqrt[a*x + b*x^3])/(21*a^5*x^(7/2)) + (256*b*Sqrt[a*x + b*x^3])/(21*a^6*x^(3/2))","A",6,3,19,0.1579,1,"{2015, 2016, 2014}"
90,1,189,0,0.2927281,"\int \frac{1}{\sqrt{x} \left(a x+b x^3\right)^{9/2}} \, dx","Int[1/(Sqrt[x]*(a*x + b*x^3)^(9/2)),x]","-\frac{99 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^3}}\right)}{8 a^{13/2}}+\frac{99 b \sqrt{a x+b x^3}}{8 a^6 x^{5/2}}-\frac{33 \sqrt{a x+b x^3}}{4 a^5 x^{9/2}}+\frac{33}{5 a^4 x^{7/2} \sqrt{a x+b x^3}}+\frac{33}{35 a^3 x^{5/2} \left(a x+b x^3\right)^{3/2}}+\frac{11}{35 a^2 x^{3/2} \left(a x+b x^3\right)^{5/2}}+\frac{1}{7 a \sqrt{x} \left(a x+b x^3\right)^{7/2}}","-\frac{99 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^3}}\right)}{8 a^{13/2}}+\frac{99 b \sqrt{a x+b x^3}}{8 a^6 x^{5/2}}-\frac{33 \sqrt{a x+b x^3}}{4 a^5 x^{9/2}}+\frac{33}{5 a^4 x^{7/2} \sqrt{a x+b x^3}}+\frac{33}{35 a^3 x^{5/2} \left(a x+b x^3\right)^{3/2}}+\frac{11}{35 a^2 x^{3/2} \left(a x+b x^3\right)^{5/2}}+\frac{1}{7 a \sqrt{x} \left(a x+b x^3\right)^{7/2}}",1,"1/(7*a*Sqrt[x]*(a*x + b*x^3)^(7/2)) + 11/(35*a^2*x^(3/2)*(a*x + b*x^3)^(5/2)) + 33/(35*a^3*x^(5/2)*(a*x + b*x^3)^(3/2)) + 33/(5*a^4*x^(7/2)*Sqrt[a*x + b*x^3]) - (33*Sqrt[a*x + b*x^3])/(4*a^5*x^(9/2)) + (99*b*Sqrt[a*x + b*x^3])/(8*a^6*x^(5/2)) - (99*b^2*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[a*x + b*x^3]])/(8*a^(13/2))","A",8,4,19,0.2105,1,"{2023, 2025, 2029, 206}"
91,1,180,0,0.2849868,"\int \frac{1}{x^{3/2} \left(a x+b x^3\right)^{9/2}} \, dx","Int[1/(x^(3/2)*(a*x + b*x^3)^(9/2)),x]","-\frac{1024 b^2 \sqrt{a x+b x^3}}{35 a^7 x^{3/2}}+\frac{512 b \sqrt{a x+b x^3}}{35 a^6 x^{7/2}}-\frac{384 \sqrt{a x+b x^3}}{35 a^5 x^{11/2}}+\frac{64}{7 a^4 x^{9/2} \sqrt{a x+b x^3}}+\frac{8}{7 a^3 x^{7/2} \left(a x+b x^3\right)^{3/2}}+\frac{12}{35 a^2 x^{5/2} \left(a x+b x^3\right)^{5/2}}+\frac{1}{7 a x^{3/2} \left(a x+b x^3\right)^{7/2}}","-\frac{1024 b^2 \sqrt{a x+b x^3}}{35 a^7 x^{3/2}}+\frac{512 b \sqrt{a x+b x^3}}{35 a^6 x^{7/2}}-\frac{384 \sqrt{a x+b x^3}}{35 a^5 x^{11/2}}+\frac{64}{7 a^4 x^{9/2} \sqrt{a x+b x^3}}+\frac{8}{7 a^3 x^{7/2} \left(a x+b x^3\right)^{3/2}}+\frac{12}{35 a^2 x^{5/2} \left(a x+b x^3\right)^{5/2}}+\frac{1}{7 a x^{3/2} \left(a x+b x^3\right)^{7/2}}",1,"1/(7*a*x^(3/2)*(a*x + b*x^3)^(7/2)) + 12/(35*a^2*x^(5/2)*(a*x + b*x^3)^(5/2)) + 8/(7*a^3*x^(7/2)*(a*x + b*x^3)^(3/2)) + 64/(7*a^4*x^(9/2)*Sqrt[a*x + b*x^3]) - (384*Sqrt[a*x + b*x^3])/(35*a^5*x^(11/2)) + (512*b*Sqrt[a*x + b*x^3])/(35*a^6*x^(7/2)) - (1024*b^2*Sqrt[a*x + b*x^3])/(35*a^7*x^(3/2))","A",7,3,19,0.1579,1,"{2015, 2016, 2014}"
92,1,55,0,0.0698222,"\int \frac{x^4}{\sqrt{a x+b x^4}} \, dx","Int[x^4/Sqrt[a*x + b*x^4],x]","\frac{x \sqrt{a x+b x^4}}{3 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x+b x^4}}\right)}{3 b^{3/2}}","\frac{x \sqrt{a x+b x^4}}{3 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x+b x^4}}\right)}{3 b^{3/2}}",1,"(x*Sqrt[a*x + b*x^4])/(3*b) - (a*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a*x + b*x^4]])/(3*b^(3/2))","A",3,3,17,0.1765,1,"{2024, 2029, 206}"
93,1,32,0,0.0322918,"\int \frac{x}{\sqrt{a x+b x^4}} \, dx","Int[x/Sqrt[a*x + b*x^4],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x+b x^4}}\right)}{3 \sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x+b x^4}}\right)}{3 \sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a*x + b*x^4]])/(3*Sqrt[b])","A",2,2,15,0.1333,1,"{2029, 206}"
94,1,23,0,0.0337861,"\int \frac{1}{x^2 \sqrt{a x+b x^4}} \, dx","Int[1/(x^2*Sqrt[a*x + b*x^4]),x]","-\frac{2 \sqrt{a x+b x^4}}{3 a x^2}","-\frac{2 \sqrt{a x+b x^4}}{3 a x^2}",1,"(-2*Sqrt[a*x + b*x^4])/(3*a*x^2)","A",1,1,17,0.05882,1,"{2014}"
95,1,48,0,0.0664935,"\int \frac{1}{x^5 \sqrt{a x+b x^4}} \, dx","Int[1/(x^5*Sqrt[a*x + b*x^4]),x]","\frac{4 b \sqrt{a x+b x^4}}{9 a^2 x^2}-\frac{2 \sqrt{a x+b x^4}}{9 a x^5}","\frac{4 b \sqrt{a x+b x^4}}{9 a^2 x^2}-\frac{2 \sqrt{a x+b x^4}}{9 a x^5}",1,"(-2*Sqrt[a*x + b*x^4])/(9*a*x^5) + (4*b*Sqrt[a*x + b*x^4])/(9*a^2*x^2)","A",2,2,17,0.1176,1,"{2016, 2014}"
96,1,74,0,0.1016692,"\int \frac{1}{x^8 \sqrt{a x+b x^4}} \, dx","Int[1/(x^8*Sqrt[a*x + b*x^4]),x]","-\frac{16 b^2 \sqrt{a x+b x^4}}{45 a^3 x^2}+\frac{8 b \sqrt{a x+b x^4}}{45 a^2 x^5}-\frac{2 \sqrt{a x+b x^4}}{15 a x^8}","-\frac{16 b^2 \sqrt{a x+b x^4}}{45 a^3 x^2}+\frac{8 b \sqrt{a x+b x^4}}{45 a^2 x^5}-\frac{2 \sqrt{a x+b x^4}}{15 a x^8}",1,"(-2*Sqrt[a*x + b*x^4])/(15*a*x^8) + (8*b*Sqrt[a*x + b*x^4])/(45*a^2*x^5) - (16*b^2*Sqrt[a*x + b*x^4])/(45*a^3*x^2)","A",3,2,17,0.1176,1,"{2016, 2014}"
97,1,224,0,0.2128683,"\int \frac{x^3}{\sqrt{a x+b x^4}} \, dx","Int[x^3/Sqrt[a*x + b*x^4],x]","\frac{\sqrt{a x+b x^4}}{2 b}-\frac{a^{2/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 \sqrt[4]{3} b \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}","\frac{\sqrt{a x+b x^4}}{2 b}-\frac{a^{2/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 \sqrt[4]{3} b \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}",1,"Sqrt[a*x + b*x^4]/(2*b) - (a^(2/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(4*3^(1/4)*b*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x + b*x^4])","A",4,4,17,0.2353,1,"{2024, 2011, 329, 225}"
98,1,197,0,0.1304347,"\int \frac{1}{\sqrt{a x+b x^4}} \, dx","Int[1/Sqrt[a*x + b*x^4],x]","\frac{x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt[3]{a} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}","\frac{x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt[3]{a} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}",1,"(x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(3^(1/4)*a^(1/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x + b*x^4])","A",3,3,13,0.2308,1,"{2011, 329, 225}"
99,1,225,0,0.1868747,"\int \frac{1}{x^3 \sqrt{a x+b x^4}} \, dx","Int[1/(x^3*Sqrt[a*x + b*x^4]),x]","-\frac{2 b x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 \sqrt[4]{3} a^{4/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}-\frac{2 \sqrt{a x+b x^4}}{5 a x^3}","-\frac{2 b x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 \sqrt[4]{3} a^{4/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}-\frac{2 \sqrt{a x+b x^4}}{5 a x^3}",1,"(-2*Sqrt[a*x + b*x^4])/(5*a*x^3) - (2*b*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(5*3^(1/4)*a^(4/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x + b*x^4])","A",4,4,17,0.2353,1,"{2025, 2011, 329, 225}"
100,1,503,0,0.5140973,"\int \frac{x^5}{\sqrt{a x+b x^4}} \, dx","Int[x^5/Sqrt[a*x + b*x^4],x]","\frac{5 \left(1-\sqrt{3}\right) a^{4/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{16 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}+\frac{5 \sqrt[4]{3} a^{4/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}-\frac{5 \left(1+\sqrt{3}\right) a x \left(a+b x^3\right)}{8 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x+b x^4}}+\frac{x^2 \sqrt{a x+b x^4}}{4 b}","\frac{5 \left(1-\sqrt{3}\right) a^{4/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{16 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}+\frac{5 \sqrt[4]{3} a^{4/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}-\frac{5 \left(1+\sqrt{3}\right) a x \left(a+b x^3\right)}{8 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x+b x^4}}+\frac{x^2 \sqrt{a x+b x^4}}{4 b}",1,"(-5*(1 + Sqrt[3])*a*x*(a + b*x^3))/(8*b^(5/3)*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)*Sqrt[a*x + b*x^4]) + (x^2*Sqrt[a*x + b*x^4])/(4*b) + (5*3^(1/4)*a^(4/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(8*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x + b*x^4]) + (5*(1 - Sqrt[3])*a^(4/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(16*3^(1/4)*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x + b*x^4])","A",6,6,17,0.3529,1,"{2024, 2032, 329, 308, 225, 1881}"
101,1,474,0,0.3900818,"\int \frac{x^2}{\sqrt{a x+b x^4}} \, dx","Int[x^2/Sqrt[a*x + b*x^4],x]","-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}-\frac{\sqrt[4]{3} \sqrt[3]{a} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}+\frac{\left(1+\sqrt{3}\right) x \left(a+b x^3\right)}{b^{2/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x+b x^4}}","-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}-\frac{\sqrt[4]{3} \sqrt[3]{a} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}+\frac{\left(1+\sqrt{3}\right) x \left(a+b x^3\right)}{b^{2/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x+b x^4}}",1,"((1 + Sqrt[3])*x*(a + b*x^3))/(b^(2/3)*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)*Sqrt[a*x + b*x^4]) - (3^(1/4)*a^(1/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(b^(2/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x + b*x^4]) - ((1 - Sqrt[3])*a^(1/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(2*3^(1/4)*b^(2/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x + b*x^4])","A",5,5,17,0.2941,1,"{2032, 329, 308, 225, 1881}"
102,1,497,0,0.472092,"\int \frac{1}{x \sqrt{a x+b x^4}} \, dx","Int[1/(x*Sqrt[a*x + b*x^4]),x]","-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}-\frac{2 \sqrt[4]{3} \sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}+\frac{2 \left(1+\sqrt{3}\right) \sqrt[3]{b} x \left(a+b x^3\right)}{a \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x+b x^4}}-\frac{2 \sqrt{a x+b x^4}}{a x}","-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}-\frac{2 \sqrt[4]{3} \sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x+b x^4}}+\frac{2 \left(1+\sqrt{3}\right) \sqrt[3]{b} x \left(a+b x^3\right)}{a \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x+b x^4}}-\frac{2 \sqrt{a x+b x^4}}{a x}",1,"(2*(1 + Sqrt[3])*b^(1/3)*x*(a + b*x^3))/(a*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)*Sqrt[a*x + b*x^4]) - (2*Sqrt[a*x + b*x^4])/(a*x) - (2*3^(1/4)*b^(1/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(a^(2/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x + b*x^4]) - ((1 - Sqrt[3])*b^(1/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(3^(1/4)*a^(2/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x + b*x^4])","A",6,6,17,0.3529,1,"{2025, 2032, 329, 308, 225, 1881}"
103,1,174,0,0.1510432,"\int \frac{x^2}{\sqrt{b \sqrt{x}+a x}} \, dx","Int[x^2/Sqrt[b*Sqrt[x] + a*x],x]","\frac{63 b^4 \sqrt{a x+b \sqrt{x}}}{64 a^5}-\frac{21 b^3 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{32 a^4}+\frac{21 b^2 x \sqrt{a x+b \sqrt{x}}}{40 a^3}-\frac{63 b^5 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{64 a^{11/2}}-\frac{9 b x^{3/2} \sqrt{a x+b \sqrt{x}}}{20 a^2}+\frac{2 x^2 \sqrt{a x+b \sqrt{x}}}{5 a}","\frac{63 b^4 \sqrt{a x+b \sqrt{x}}}{64 a^5}-\frac{21 b^3 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{32 a^4}+\frac{21 b^2 x \sqrt{a x+b \sqrt{x}}}{40 a^3}-\frac{63 b^5 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{64 a^{11/2}}-\frac{9 b x^{3/2} \sqrt{a x+b \sqrt{x}}}{20 a^2}+\frac{2 x^2 \sqrt{a x+b \sqrt{x}}}{5 a}",1,"(63*b^4*Sqrt[b*Sqrt[x] + a*x])/(64*a^5) - (21*b^3*Sqrt[x]*Sqrt[b*Sqrt[x] + a*x])/(32*a^4) + (21*b^2*x*Sqrt[b*Sqrt[x] + a*x])/(40*a^3) - (9*b*x^(3/2)*Sqrt[b*Sqrt[x] + a*x])/(20*a^2) + (2*x^2*Sqrt[b*Sqrt[x] + a*x])/(5*a) - (63*b^5*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/(64*a^(11/2))","A",8,5,19,0.2632,1,"{2018, 670, 640, 620, 206}"
104,1,116,0,0.0868686,"\int \frac{x}{\sqrt{b \sqrt{x}+a x}} \, dx","Int[x/Sqrt[b*Sqrt[x] + a*x],x]","\frac{5 b^2 \sqrt{a x+b \sqrt{x}}}{4 a^3}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{4 a^{7/2}}-\frac{5 b \sqrt{x} \sqrt{a x+b \sqrt{x}}}{6 a^2}+\frac{2 x \sqrt{a x+b \sqrt{x}}}{3 a}","\frac{5 b^2 \sqrt{a x+b \sqrt{x}}}{4 a^3}-\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{4 a^{7/2}}-\frac{5 b \sqrt{x} \sqrt{a x+b \sqrt{x}}}{6 a^2}+\frac{2 x \sqrt{a x+b \sqrt{x}}}{3 a}",1,"(5*b^2*Sqrt[b*Sqrt[x] + a*x])/(4*a^3) - (5*b*Sqrt[x]*Sqrt[b*Sqrt[x] + a*x])/(6*a^2) + (2*x*Sqrt[b*Sqrt[x] + a*x])/(3*a) - (5*b^3*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/(4*a^(7/2))","A",6,5,17,0.2941,1,"{2018, 670, 640, 620, 206}"
105,1,56,0,0.059945,"\int \frac{1}{\sqrt{b \sqrt{x}+a x}} \, dx","Int[1/Sqrt[b*Sqrt[x] + a*x],x]","\frac{2 \sqrt{a x+b \sqrt{x}}}{a}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{a^{3/2}}","\frac{2 \sqrt{a x+b \sqrt{x}}}{a}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{a^{3/2}}",1,"(2*Sqrt[b*Sqrt[x] + a*x])/a - (2*b*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/a^(3/2)","A",4,4,15,0.2667,1,"{2010, 2013, 620, 206}"
106,1,25,0,0.0379828,"\int \frac{1}{x \sqrt{b \sqrt{x}+a x}} \, dx","Int[1/(x*Sqrt[b*Sqrt[x] + a*x]),x]","-\frac{4 \sqrt{a x+b \sqrt{x}}}{b \sqrt{x}}","-\frac{4 \sqrt{a x+b \sqrt{x}}}{b \sqrt{x}}",1,"(-4*Sqrt[b*Sqrt[x] + a*x])/(b*Sqrt[x])","A",1,1,19,0.05263,1,"{2014}"
107,1,84,0,0.1165801,"\int \frac{1}{x^2 \sqrt{b \sqrt{x}+a x}} \, dx","Int[1/(x^2*Sqrt[b*Sqrt[x] + a*x]),x]","-\frac{32 a^2 \sqrt{a x+b \sqrt{x}}}{15 b^3 \sqrt{x}}+\frac{16 a \sqrt{a x+b \sqrt{x}}}{15 b^2 x}-\frac{4 \sqrt{a x+b \sqrt{x}}}{5 b x^{3/2}}","-\frac{32 a^2 \sqrt{a x+b \sqrt{x}}}{15 b^3 \sqrt{x}}+\frac{16 a \sqrt{a x+b \sqrt{x}}}{15 b^2 x}-\frac{4 \sqrt{a x+b \sqrt{x}}}{5 b x^{3/2}}",1,"(-4*Sqrt[b*Sqrt[x] + a*x])/(5*b*x^(3/2)) + (16*a*Sqrt[b*Sqrt[x] + a*x])/(15*b^2*x) - (32*a^2*Sqrt[b*Sqrt[x] + a*x])/(15*b^3*Sqrt[x])","A",3,2,19,0.1053,1,"{2016, 2014}"
108,1,142,0,0.2033787,"\int \frac{1}{x^3 \sqrt{b \sqrt{x}+a x}} \, dx","Int[1/(x^3*Sqrt[b*Sqrt[x] + a*x]),x]","-\frac{64 a^2 \sqrt{a x+b \sqrt{x}}}{105 b^3 x^{3/2}}-\frac{512 a^4 \sqrt{a x+b \sqrt{x}}}{315 b^5 \sqrt{x}}+\frac{256 a^3 \sqrt{a x+b \sqrt{x}}}{315 b^4 x}+\frac{32 a \sqrt{a x+b \sqrt{x}}}{63 b^2 x^2}-\frac{4 \sqrt{a x+b \sqrt{x}}}{9 b x^{5/2}}","-\frac{64 a^2 \sqrt{a x+b \sqrt{x}}}{105 b^3 x^{3/2}}-\frac{512 a^4 \sqrt{a x+b \sqrt{x}}}{315 b^5 \sqrt{x}}+\frac{256 a^3 \sqrt{a x+b \sqrt{x}}}{315 b^4 x}+\frac{32 a \sqrt{a x+b \sqrt{x}}}{63 b^2 x^2}-\frac{4 \sqrt{a x+b \sqrt{x}}}{9 b x^{5/2}}",1,"(-4*Sqrt[b*Sqrt[x] + a*x])/(9*b*x^(5/2)) + (32*a*Sqrt[b*Sqrt[x] + a*x])/(63*b^2*x^2) - (64*a^2*Sqrt[b*Sqrt[x] + a*x])/(105*b^3*x^(3/2)) + (256*a^3*Sqrt[b*Sqrt[x] + a*x])/(315*b^4*x) - (512*a^4*Sqrt[b*Sqrt[x] + a*x])/(315*b^5*Sqrt[x])","A",5,2,19,0.1053,1,"{2016, 2014}"
109,1,200,0,0.2968844,"\int \frac{1}{x^4 \sqrt{b \sqrt{x}+a x}} \, dx","Int[1/(x^4*Sqrt[b*Sqrt[x] + a*x]),x]","-\frac{512 a^4 \sqrt{a x+b \sqrt{x}}}{1001 b^5 x^{3/2}}+\frac{1280 a^3 \sqrt{a x+b \sqrt{x}}}{3003 b^4 x^2}-\frac{160 a^2 \sqrt{a x+b \sqrt{x}}}{429 b^3 x^{5/2}}-\frac{4096 a^6 \sqrt{a x+b \sqrt{x}}}{3003 b^7 \sqrt{x}}+\frac{2048 a^5 \sqrt{a x+b \sqrt{x}}}{3003 b^6 x}+\frac{48 a \sqrt{a x+b \sqrt{x}}}{143 b^2 x^3}-\frac{4 \sqrt{a x+b \sqrt{x}}}{13 b x^{7/2}}","-\frac{512 a^4 \sqrt{a x+b \sqrt{x}}}{1001 b^5 x^{3/2}}+\frac{1280 a^3 \sqrt{a x+b \sqrt{x}}}{3003 b^4 x^2}-\frac{160 a^2 \sqrt{a x+b \sqrt{x}}}{429 b^3 x^{5/2}}-\frac{4096 a^6 \sqrt{a x+b \sqrt{x}}}{3003 b^7 \sqrt{x}}+\frac{2048 a^5 \sqrt{a x+b \sqrt{x}}}{3003 b^6 x}+\frac{48 a \sqrt{a x+b \sqrt{x}}}{143 b^2 x^3}-\frac{4 \sqrt{a x+b \sqrt{x}}}{13 b x^{7/2}}",1,"(-4*Sqrt[b*Sqrt[x] + a*x])/(13*b*x^(7/2)) + (48*a*Sqrt[b*Sqrt[x] + a*x])/(143*b^2*x^3) - (160*a^2*Sqrt[b*Sqrt[x] + a*x])/(429*b^3*x^(5/2)) + (1280*a^3*Sqrt[b*Sqrt[x] + a*x])/(3003*b^4*x^2) - (512*a^4*Sqrt[b*Sqrt[x] + a*x])/(1001*b^5*x^(3/2)) + (2048*a^5*Sqrt[b*Sqrt[x] + a*x])/(3003*b^6*x) - (4096*a^6*Sqrt[b*Sqrt[x] + a*x])/(3003*b^7*Sqrt[x])","A",7,2,19,0.1053,1,"{2016, 2014}"
110,1,197,0,0.1754582,"\int \frac{x^3}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[x^3/(b*Sqrt[x] + a*x)^(3/2),x]","\frac{693 b^4 \sqrt{a x+b \sqrt{x}}}{64 a^6}-\frac{231 b^3 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{32 a^5}+\frac{231 b^2 x \sqrt{a x+b \sqrt{x}}}{40 a^4}-\frac{693 b^5 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{64 a^{13/2}}-\frac{99 b x^{3/2} \sqrt{a x+b \sqrt{x}}}{20 a^3}+\frac{22 x^2 \sqrt{a x+b \sqrt{x}}}{5 a^2}-\frac{4 x^3}{a \sqrt{a x+b \sqrt{x}}}","\frac{693 b^4 \sqrt{a x+b \sqrt{x}}}{64 a^6}-\frac{231 b^3 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{32 a^5}+\frac{231 b^2 x \sqrt{a x+b \sqrt{x}}}{40 a^4}-\frac{693 b^5 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{64 a^{13/2}}-\frac{99 b x^{3/2} \sqrt{a x+b \sqrt{x}}}{20 a^3}+\frac{22 x^2 \sqrt{a x+b \sqrt{x}}}{5 a^2}-\frac{4 x^3}{a \sqrt{a x+b \sqrt{x}}}",1,"(-4*x^3)/(a*Sqrt[b*Sqrt[x] + a*x]) + (693*b^4*Sqrt[b*Sqrt[x] + a*x])/(64*a^6) - (231*b^3*Sqrt[x]*Sqrt[b*Sqrt[x] + a*x])/(32*a^5) + (231*b^2*x*Sqrt[b*Sqrt[x] + a*x])/(40*a^4) - (99*b*x^(3/2)*Sqrt[b*Sqrt[x] + a*x])/(20*a^3) + (22*x^2*Sqrt[b*Sqrt[x] + a*x])/(5*a^2) - (693*b^5*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/(64*a^(13/2))","A",9,6,19,0.3158,1,"{2018, 668, 670, 640, 620, 206}"
111,1,139,0,0.1269712,"\int \frac{x^2}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[x^2/(b*Sqrt[x] + a*x)^(3/2),x]","\frac{35 b^2 \sqrt{a x+b \sqrt{x}}}{4 a^4}-\frac{35 b^3 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{4 a^{9/2}}-\frac{35 b \sqrt{x} \sqrt{a x+b \sqrt{x}}}{6 a^3}+\frac{14 x \sqrt{a x+b \sqrt{x}}}{3 a^2}-\frac{4 x^2}{a \sqrt{a x+b \sqrt{x}}}","\frac{35 b^2 \sqrt{a x+b \sqrt{x}}}{4 a^4}-\frac{35 b^3 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{4 a^{9/2}}-\frac{35 b \sqrt{x} \sqrt{a x+b \sqrt{x}}}{6 a^3}+\frac{14 x \sqrt{a x+b \sqrt{x}}}{3 a^2}-\frac{4 x^2}{a \sqrt{a x+b \sqrt{x}}}",1,"(-4*x^2)/(a*Sqrt[b*Sqrt[x] + a*x]) + (35*b^2*Sqrt[b*Sqrt[x] + a*x])/(4*a^4) - (35*b*Sqrt[x]*Sqrt[b*Sqrt[x] + a*x])/(6*a^3) + (14*x*Sqrt[b*Sqrt[x] + a*x])/(3*a^2) - (35*b^3*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/(4*a^(9/2))","A",7,6,19,0.3158,1,"{2018, 668, 670, 640, 620, 206}"
112,1,77,0,0.0742663,"\int \frac{x}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[x/(b*Sqrt[x] + a*x)^(3/2),x]","\frac{6 \sqrt{a x+b \sqrt{x}}}{a^2}-\frac{6 b \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{a^{5/2}}-\frac{4 x}{a \sqrt{a x+b \sqrt{x}}}","\frac{6 \sqrt{a x+b \sqrt{x}}}{a^2}-\frac{6 b \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{a^{5/2}}-\frac{4 x}{a \sqrt{a x+b \sqrt{x}}}",1,"(-4*x)/(a*Sqrt[b*Sqrt[x] + a*x]) + (6*Sqrt[b*Sqrt[x] + a*x])/a^2 - (6*b*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/a^(5/2)","A",5,5,17,0.2941,1,"{2018, 668, 640, 620, 206}"
113,1,25,0,0.0051318,"\int \frac{1}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[(b*Sqrt[x] + a*x)^(-3/2),x]","\frac{4 \sqrt{x}}{b \sqrt{a x+b \sqrt{x}}}","\frac{4 \sqrt{x}}{b \sqrt{a x+b \sqrt{x}}}",1,"(4*Sqrt[x])/(b*Sqrt[b*Sqrt[x] + a*x])","A",1,1,15,0.06667,1,"{2000}"
114,1,79,0,0.1224785,"\int \frac{1}{x \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[1/(x*(b*Sqrt[x] + a*x)^(3/2)),x]","\frac{32 a \sqrt{a x+b \sqrt{x}}}{3 b^3 \sqrt{x}}-\frac{16 \sqrt{a x+b \sqrt{x}}}{3 b^2 x}+\frac{4}{b \sqrt{x} \sqrt{a x+b \sqrt{x}}}","\frac{32 a \sqrt{a x+b \sqrt{x}}}{3 b^3 \sqrt{x}}-\frac{16 \sqrt{a x+b \sqrt{x}}}{3 b^2 x}+\frac{4}{b \sqrt{x} \sqrt{a x+b \sqrt{x}}}",1,"4/(b*Sqrt[x]*Sqrt[b*Sqrt[x] + a*x]) - (16*Sqrt[b*Sqrt[x] + a*x])/(3*b^2*x) + (32*a*Sqrt[b*Sqrt[x] + a*x])/(3*b^3*Sqrt[x])","A",3,3,19,0.1579,1,"{2015, 2016, 2014}"
115,1,137,0,0.2018791,"\int \frac{1}{x^2 \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[1/(x^2*(b*Sqrt[x] + a*x)^(3/2)),x]","\frac{512 a^3 \sqrt{a x+b \sqrt{x}}}{35 b^5 \sqrt{x}}-\frac{256 a^2 \sqrt{a x+b \sqrt{x}}}{35 b^4 x}+\frac{192 a \sqrt{a x+b \sqrt{x}}}{35 b^3 x^{3/2}}-\frac{32 \sqrt{a x+b \sqrt{x}}}{7 b^2 x^2}+\frac{4}{b x^{3/2} \sqrt{a x+b \sqrt{x}}}","\frac{512 a^3 \sqrt{a x+b \sqrt{x}}}{35 b^5 \sqrt{x}}-\frac{256 a^2 \sqrt{a x+b \sqrt{x}}}{35 b^4 x}+\frac{192 a \sqrt{a x+b \sqrt{x}}}{35 b^3 x^{3/2}}-\frac{32 \sqrt{a x+b \sqrt{x}}}{7 b^2 x^2}+\frac{4}{b x^{3/2} \sqrt{a x+b \sqrt{x}}}",1,"4/(b*x^(3/2)*Sqrt[b*Sqrt[x] + a*x]) - (32*Sqrt[b*Sqrt[x] + a*x])/(7*b^2*x^2) + (192*a*Sqrt[b*Sqrt[x] + a*x])/(35*b^3*x^(3/2)) - (256*a^2*Sqrt[b*Sqrt[x] + a*x])/(35*b^4*x) + (512*a^3*Sqrt[b*Sqrt[x] + a*x])/(35*b^5*Sqrt[x])","A",5,3,19,0.1579,1,"{2015, 2016, 2014}"
116,1,195,0,0.2999994,"\int \frac{1}{x^3 \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[1/(x^3*(b*Sqrt[x] + a*x)^(3/2)),x]","\frac{512 a^3 \sqrt{a x+b \sqrt{x}}}{77 b^5 x^{3/2}}-\frac{1280 a^2 \sqrt{a x+b \sqrt{x}}}{231 b^4 x^2}+\frac{4096 a^5 \sqrt{a x+b \sqrt{x}}}{231 b^7 \sqrt{x}}-\frac{2048 a^4 \sqrt{a x+b \sqrt{x}}}{231 b^6 x}+\frac{160 a \sqrt{a x+b \sqrt{x}}}{33 b^3 x^{5/2}}-\frac{48 \sqrt{a x+b \sqrt{x}}}{11 b^2 x^3}+\frac{4}{b x^{5/2} \sqrt{a x+b \sqrt{x}}}","\frac{512 a^3 \sqrt{a x+b \sqrt{x}}}{77 b^5 x^{3/2}}-\frac{1280 a^2 \sqrt{a x+b \sqrt{x}}}{231 b^4 x^2}+\frac{4096 a^5 \sqrt{a x+b \sqrt{x}}}{231 b^7 \sqrt{x}}-\frac{2048 a^4 \sqrt{a x+b \sqrt{x}}}{231 b^6 x}+\frac{160 a \sqrt{a x+b \sqrt{x}}}{33 b^3 x^{5/2}}-\frac{48 \sqrt{a x+b \sqrt{x}}}{11 b^2 x^3}+\frac{4}{b x^{5/2} \sqrt{a x+b \sqrt{x}}}",1,"4/(b*x^(5/2)*Sqrt[b*Sqrt[x] + a*x]) - (48*Sqrt[b*Sqrt[x] + a*x])/(11*b^2*x^3) + (160*a*Sqrt[b*Sqrt[x] + a*x])/(33*b^3*x^(5/2)) - (1280*a^2*Sqrt[b*Sqrt[x] + a*x])/(231*b^4*x^2) + (512*a^3*Sqrt[b*Sqrt[x] + a*x])/(77*b^5*x^(3/2)) - (2048*a^4*Sqrt[b*Sqrt[x] + a*x])/(231*b^6*x) + (4096*a^5*Sqrt[b*Sqrt[x] + a*x])/(231*b^7*Sqrt[x])","A",7,3,19,0.1579,1,"{2015, 2016, 2014}"
117,1,204,0,0.1715502,"\int \frac{x^{5/2}}{\sqrt{b \sqrt{x}+a x}} \, dx","Int[x^(5/2)/Sqrt[b*Sqrt[x] + a*x],x]","\frac{33 b^2 x^{3/2} \sqrt{a x+b \sqrt{x}}}{80 a^3}-\frac{231 b^5 \sqrt{a x+b \sqrt{x}}}{256 a^6}+\frac{77 b^4 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{128 a^5}-\frac{77 b^3 x \sqrt{a x+b \sqrt{x}}}{160 a^4}+\frac{231 b^6 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{256 a^{13/2}}-\frac{11 b x^2 \sqrt{a x+b \sqrt{x}}}{30 a^2}+\frac{x^{5/2} \sqrt{a x+b \sqrt{x}}}{3 a}","\frac{33 b^2 x^{3/2} \sqrt{a x+b \sqrt{x}}}{80 a^3}-\frac{231 b^5 \sqrt{a x+b \sqrt{x}}}{256 a^6}+\frac{77 b^4 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{128 a^5}-\frac{77 b^3 x \sqrt{a x+b \sqrt{x}}}{160 a^4}+\frac{231 b^6 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{256 a^{13/2}}-\frac{11 b x^2 \sqrt{a x+b \sqrt{x}}}{30 a^2}+\frac{x^{5/2} \sqrt{a x+b \sqrt{x}}}{3 a}",1,"(-231*b^5*Sqrt[b*Sqrt[x] + a*x])/(256*a^6) + (77*b^4*Sqrt[x]*Sqrt[b*Sqrt[x] + a*x])/(128*a^5) - (77*b^3*x*Sqrt[b*Sqrt[x] + a*x])/(160*a^4) + (33*b^2*x^(3/2)*Sqrt[b*Sqrt[x] + a*x])/(80*a^3) - (11*b*x^2*Sqrt[b*Sqrt[x] + a*x])/(30*a^2) + (x^(5/2)*Sqrt[b*Sqrt[x] + a*x])/(3*a) + (231*b^6*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/(256*a^(13/2))","A",9,5,21,0.2381,1,"{2018, 670, 640, 620, 206}"
118,1,146,0,0.1199119,"\int \frac{x^{3/2}}{\sqrt{b \sqrt{x}+a x}} \, dx","Int[x^(3/2)/Sqrt[b*Sqrt[x] + a*x],x]","-\frac{35 b^3 \sqrt{a x+b \sqrt{x}}}{32 a^4}+\frac{35 b^2 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{48 a^3}+\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{32 a^{9/2}}-\frac{7 b x \sqrt{a x+b \sqrt{x}}}{12 a^2}+\frac{x^{3/2} \sqrt{a x+b \sqrt{x}}}{2 a}","-\frac{35 b^3 \sqrt{a x+b \sqrt{x}}}{32 a^4}+\frac{35 b^2 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{48 a^3}+\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{32 a^{9/2}}-\frac{7 b x \sqrt{a x+b \sqrt{x}}}{12 a^2}+\frac{x^{3/2} \sqrt{a x+b \sqrt{x}}}{2 a}",1,"(-35*b^3*Sqrt[b*Sqrt[x] + a*x])/(32*a^4) + (35*b^2*Sqrt[x]*Sqrt[b*Sqrt[x] + a*x])/(48*a^3) - (7*b*x*Sqrt[b*Sqrt[x] + a*x])/(12*a^2) + (x^(3/2)*Sqrt[b*Sqrt[x] + a*x])/(2*a) + (35*b^4*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/(32*a^(9/2))","A",7,5,21,0.2381,1,"{2018, 670, 640, 620, 206}"
119,1,87,0,0.0788138,"\int \frac{\sqrt{x}}{\sqrt{b \sqrt{x}+a x}} \, dx","Int[Sqrt[x]/Sqrt[b*Sqrt[x] + a*x],x]","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{2 a^{5/2}}-\frac{3 b \sqrt{a x+b \sqrt{x}}}{2 a^2}+\frac{\sqrt{x} \sqrt{a x+b \sqrt{x}}}{a}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{2 a^{5/2}}-\frac{3 b \sqrt{a x+b \sqrt{x}}}{2 a^2}+\frac{\sqrt{x} \sqrt{a x+b \sqrt{x}}}{a}",1,"(-3*b*Sqrt[b*Sqrt[x] + a*x])/(2*a^2) + (Sqrt[x]*Sqrt[b*Sqrt[x] + a*x])/a + (3*b^2*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/(2*a^(5/2))","A",5,5,21,0.2381,1,"{2018, 670, 640, 620, 206}"
120,1,34,0,0.0490875,"\int \frac{1}{\sqrt{x} \sqrt{b \sqrt{x}+a x}} \, dx","Int[1/(Sqrt[x]*Sqrt[b*Sqrt[x] + a*x]),x]","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{\sqrt{a}}","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{\sqrt{a}}",1,"(4*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/Sqrt[a]","A",3,3,21,0.1429,1,"{2013, 620, 206}"
121,1,54,0,0.073614,"\int \frac{1}{x^{3/2} \sqrt{b \sqrt{x}+a x}} \, dx","Int[1/(x^(3/2)*Sqrt[b*Sqrt[x] + a*x]),x]","\frac{8 a \sqrt{a x+b \sqrt{x}}}{3 b^2 \sqrt{x}}-\frac{4 \sqrt{a x+b \sqrt{x}}}{3 b x}","\frac{8 a \sqrt{a x+b \sqrt{x}}}{3 b^2 \sqrt{x}}-\frac{4 \sqrt{a x+b \sqrt{x}}}{3 b x}",1,"(-4*Sqrt[b*Sqrt[x] + a*x])/(3*b*x) + (8*a*Sqrt[b*Sqrt[x] + a*x])/(3*b^2*Sqrt[x])","A",2,2,21,0.09524,1,"{2016, 2014}"
122,1,112,0,0.1535517,"\int \frac{1}{x^{5/2} \sqrt{b \sqrt{x}+a x}} \, dx","Int[1/(x^(5/2)*Sqrt[b*Sqrt[x] + a*x]),x]","\frac{64 a^3 \sqrt{a x+b \sqrt{x}}}{35 b^4 \sqrt{x}}-\frac{32 a^2 \sqrt{a x+b \sqrt{x}}}{35 b^3 x}+\frac{24 a \sqrt{a x+b \sqrt{x}}}{35 b^2 x^{3/2}}-\frac{4 \sqrt{a x+b \sqrt{x}}}{7 b x^2}","\frac{64 a^3 \sqrt{a x+b \sqrt{x}}}{35 b^4 \sqrt{x}}-\frac{32 a^2 \sqrt{a x+b \sqrt{x}}}{35 b^3 x}+\frac{24 a \sqrt{a x+b \sqrt{x}}}{35 b^2 x^{3/2}}-\frac{4 \sqrt{a x+b \sqrt{x}}}{7 b x^2}",1,"(-4*Sqrt[b*Sqrt[x] + a*x])/(7*b*x^2) + (24*a*Sqrt[b*Sqrt[x] + a*x])/(35*b^2*x^(3/2)) - (32*a^2*Sqrt[b*Sqrt[x] + a*x])/(35*b^3*x) + (64*a^3*Sqrt[b*Sqrt[x] + a*x])/(35*b^4*Sqrt[x])","A",4,2,21,0.09524,1,"{2016, 2014}"
123,1,170,0,0.2446444,"\int \frac{1}{x^{7/2} \sqrt{b \sqrt{x}+a x}} \, dx","Int[1/(x^(7/2)*Sqrt[b*Sqrt[x] + a*x]),x]","\frac{128 a^3 \sqrt{a x+b \sqrt{x}}}{231 b^4 x^{3/2}}-\frac{320 a^2 \sqrt{a x+b \sqrt{x}}}{693 b^3 x^2}+\frac{1024 a^5 \sqrt{a x+b \sqrt{x}}}{693 b^6 \sqrt{x}}-\frac{512 a^4 \sqrt{a x+b \sqrt{x}}}{693 b^5 x}+\frac{40 a \sqrt{a x+b \sqrt{x}}}{99 b^2 x^{5/2}}-\frac{4 \sqrt{a x+b \sqrt{x}}}{11 b x^3}","\frac{128 a^3 \sqrt{a x+b \sqrt{x}}}{231 b^4 x^{3/2}}-\frac{320 a^2 \sqrt{a x+b \sqrt{x}}}{693 b^3 x^2}+\frac{1024 a^5 \sqrt{a x+b \sqrt{x}}}{693 b^6 \sqrt{x}}-\frac{512 a^4 \sqrt{a x+b \sqrt{x}}}{693 b^5 x}+\frac{40 a \sqrt{a x+b \sqrt{x}}}{99 b^2 x^{5/2}}-\frac{4 \sqrt{a x+b \sqrt{x}}}{11 b x^3}",1,"(-4*Sqrt[b*Sqrt[x] + a*x])/(11*b*x^3) + (40*a*Sqrt[b*Sqrt[x] + a*x])/(99*b^2*x^(5/2)) - (320*a^2*Sqrt[b*Sqrt[x] + a*x])/(693*b^3*x^2) + (128*a^3*Sqrt[b*Sqrt[x] + a*x])/(231*b^4*x^(3/2)) - (512*a^4*Sqrt[b*Sqrt[x] + a*x])/(693*b^5*x) + (1024*a^5*Sqrt[b*Sqrt[x] + a*x])/(693*b^6*Sqrt[x])","A",6,2,21,0.09524,1,"{2016, 2014}"
124,1,171,0,0.1469741,"\int \frac{x^{5/2}}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[x^(5/2)/(b*Sqrt[x] + a*x)^(3/2),x]","-\frac{315 b^3 \sqrt{a x+b \sqrt{x}}}{32 a^5}+\frac{105 b^2 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{16 a^4}+\frac{315 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{32 a^{11/2}}+\frac{9 x^{3/2} \sqrt{a x+b \sqrt{x}}}{2 a^2}-\frac{21 b x \sqrt{a x+b \sqrt{x}}}{4 a^3}-\frac{4 x^{5/2}}{a \sqrt{a x+b \sqrt{x}}}","-\frac{315 b^3 \sqrt{a x+b \sqrt{x}}}{32 a^5}+\frac{105 b^2 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{16 a^4}+\frac{315 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{32 a^{11/2}}+\frac{9 x^{3/2} \sqrt{a x+b \sqrt{x}}}{2 a^2}-\frac{21 b x \sqrt{a x+b \sqrt{x}}}{4 a^3}-\frac{4 x^{5/2}}{a \sqrt{a x+b \sqrt{x}}}",1,"(-4*x^(5/2))/(a*Sqrt[b*Sqrt[x] + a*x]) - (315*b^3*Sqrt[b*Sqrt[x] + a*x])/(32*a^5) + (105*b^2*Sqrt[x]*Sqrt[b*Sqrt[x] + a*x])/(16*a^4) - (21*b*x*Sqrt[b*Sqrt[x] + a*x])/(4*a^3) + (9*x^(3/2)*Sqrt[b*Sqrt[x] + a*x])/(2*a^2) + (315*b^4*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/(32*a^(11/2))","A",8,6,21,0.2857,1,"{2018, 668, 670, 640, 620, 206}"
125,1,113,0,0.1027176,"\int \frac{x^{3/2}}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[x^(3/2)/(b*Sqrt[x] + a*x)^(3/2),x]","\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{2 a^{7/2}}-\frac{15 b \sqrt{a x+b \sqrt{x}}}{2 a^3}+\frac{5 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{a^2}-\frac{4 x^{3/2}}{a \sqrt{a x+b \sqrt{x}}}","\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{2 a^{7/2}}-\frac{15 b \sqrt{a x+b \sqrt{x}}}{2 a^3}+\frac{5 \sqrt{x} \sqrt{a x+b \sqrt{x}}}{a^2}-\frac{4 x^{3/2}}{a \sqrt{a x+b \sqrt{x}}}",1,"(-4*x^(3/2))/(a*Sqrt[b*Sqrt[x] + a*x]) - (15*b*Sqrt[b*Sqrt[x] + a*x])/(2*a^3) + (5*Sqrt[x]*Sqrt[b*Sqrt[x] + a*x])/a^2 + (15*b^2*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/(2*a^(7/2))","A",6,6,21,0.2857,1,"{2018, 668, 670, 640, 620, 206}"
126,1,60,0,0.0671288,"\int \frac{\sqrt{x}}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[Sqrt[x]/(b*Sqrt[x] + a*x)^(3/2),x]","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{a^{3/2}}-\frac{4 \sqrt{x}}{a \sqrt{a x+b \sqrt{x}}}","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{a^{3/2}}-\frac{4 \sqrt{x}}{a \sqrt{a x+b \sqrt{x}}}",1,"(-4*Sqrt[x])/(a*Sqrt[b*Sqrt[x] + a*x]) + (4*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[b*Sqrt[x] + a*x]])/a^(3/2)","A",4,4,21,0.1905,1,"{2018, 652, 620, 206}"
127,1,30,0,0.0471669,"\int \frac{1}{\sqrt{x} \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[1/(Sqrt[x]*(b*Sqrt[x] + a*x)^(3/2)),x]","-\frac{4 \left(2 a \sqrt{x}+b\right)}{b^2 \sqrt{a x+b \sqrt{x}}}","-\frac{4 \left(2 a \sqrt{x}+b\right)}{b^2 \sqrt{a x+b \sqrt{x}}}",1,"(-4*(b + 2*a*Sqrt[x]))/(b^2*Sqrt[b*Sqrt[x] + a*x])","A",2,2,21,0.09524,1,"{2013, 613}"
128,1,107,0,0.1560278,"\int \frac{1}{x^{3/2} \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[1/(x^(3/2)*(b*Sqrt[x] + a*x)^(3/2)),x]","-\frac{64 a^2 \sqrt{a x+b \sqrt{x}}}{5 b^4 \sqrt{x}}-\frac{24 \sqrt{a x+b \sqrt{x}}}{5 b^2 x^{3/2}}+\frac{32 a \sqrt{a x+b \sqrt{x}}}{5 b^3 x}+\frac{4}{b x \sqrt{a x+b \sqrt{x}}}","-\frac{64 a^2 \sqrt{a x+b \sqrt{x}}}{5 b^4 \sqrt{x}}-\frac{24 \sqrt{a x+b \sqrt{x}}}{5 b^2 x^{3/2}}+\frac{32 a \sqrt{a x+b \sqrt{x}}}{5 b^3 x}+\frac{4}{b x \sqrt{a x+b \sqrt{x}}}",1,"4/(b*x*Sqrt[b*Sqrt[x] + a*x]) - (24*Sqrt[b*Sqrt[x] + a*x])/(5*b^2*x^(3/2)) + (32*a*Sqrt[b*Sqrt[x] + a*x])/(5*b^3*x) - (64*a^2*Sqrt[b*Sqrt[x] + a*x])/(5*b^4*Sqrt[x])","A",4,3,21,0.1429,1,"{2015, 2016, 2014}"
129,1,165,0,0.2571457,"\int \frac{1}{x^{5/2} \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[1/(x^(5/2)*(b*Sqrt[x] + a*x)^(3/2)),x]","-\frac{128 a^2 \sqrt{a x+b \sqrt{x}}}{21 b^4 x^{3/2}}-\frac{1024 a^4 \sqrt{a x+b \sqrt{x}}}{63 b^6 \sqrt{x}}+\frac{512 a^3 \sqrt{a x+b \sqrt{x}}}{63 b^5 x}+\frac{320 a \sqrt{a x+b \sqrt{x}}}{63 b^3 x^2}-\frac{40 \sqrt{a x+b \sqrt{x}}}{9 b^2 x^{5/2}}+\frac{4}{b x^2 \sqrt{a x+b \sqrt{x}}}","-\frac{128 a^2 \sqrt{a x+b \sqrt{x}}}{21 b^4 x^{3/2}}-\frac{1024 a^4 \sqrt{a x+b \sqrt{x}}}{63 b^6 \sqrt{x}}+\frac{512 a^3 \sqrt{a x+b \sqrt{x}}}{63 b^5 x}+\frac{320 a \sqrt{a x+b \sqrt{x}}}{63 b^3 x^2}-\frac{40 \sqrt{a x+b \sqrt{x}}}{9 b^2 x^{5/2}}+\frac{4}{b x^2 \sqrt{a x+b \sqrt{x}}}",1,"4/(b*x^2*Sqrt[b*Sqrt[x] + a*x]) - (40*Sqrt[b*Sqrt[x] + a*x])/(9*b^2*x^(5/2)) + (320*a*Sqrt[b*Sqrt[x] + a*x])/(63*b^3*x^2) - (128*a^2*Sqrt[b*Sqrt[x] + a*x])/(21*b^4*x^(3/2)) + (512*a^3*Sqrt[b*Sqrt[x] + a*x])/(63*b^5*x) - (1024*a^4*Sqrt[b*Sqrt[x] + a*x])/(63*b^6*Sqrt[x])","A",6,3,21,0.1429,1,"{2015, 2016, 2014}"
130,1,223,0,0.3531459,"\int \frac{1}{x^{7/2} \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Int[1/(x^(7/2)*(b*Sqrt[x] + a*x)^(3/2)),x]","-\frac{1024 a^4 \sqrt{a x+b \sqrt{x}}}{143 b^6 x^{3/2}}+\frac{2560 a^3 \sqrt{a x+b \sqrt{x}}}{429 b^5 x^2}-\frac{2240 a^2 \sqrt{a x+b \sqrt{x}}}{429 b^4 x^{5/2}}-\frac{8192 a^6 \sqrt{a x+b \sqrt{x}}}{429 b^8 \sqrt{x}}+\frac{4096 a^5 \sqrt{a x+b \sqrt{x}}}{429 b^7 x}+\frac{672 a \sqrt{a x+b \sqrt{x}}}{143 b^3 x^3}-\frac{56 \sqrt{a x+b \sqrt{x}}}{13 b^2 x^{7/2}}+\frac{4}{b x^3 \sqrt{a x+b \sqrt{x}}}","-\frac{1024 a^4 \sqrt{a x+b \sqrt{x}}}{143 b^6 x^{3/2}}+\frac{2560 a^3 \sqrt{a x+b \sqrt{x}}}{429 b^5 x^2}-\frac{2240 a^2 \sqrt{a x+b \sqrt{x}}}{429 b^4 x^{5/2}}-\frac{8192 a^6 \sqrt{a x+b \sqrt{x}}}{429 b^8 \sqrt{x}}+\frac{4096 a^5 \sqrt{a x+b \sqrt{x}}}{429 b^7 x}+\frac{672 a \sqrt{a x+b \sqrt{x}}}{143 b^3 x^3}-\frac{56 \sqrt{a x+b \sqrt{x}}}{13 b^2 x^{7/2}}+\frac{4}{b x^3 \sqrt{a x+b \sqrt{x}}}",1,"4/(b*x^3*Sqrt[b*Sqrt[x] + a*x]) - (56*Sqrt[b*Sqrt[x] + a*x])/(13*b^2*x^(7/2)) + (672*a*Sqrt[b*Sqrt[x] + a*x])/(143*b^3*x^3) - (2240*a^2*Sqrt[b*Sqrt[x] + a*x])/(429*b^4*x^(5/2)) + (2560*a^3*Sqrt[b*Sqrt[x] + a*x])/(429*b^5*x^2) - (1024*a^4*Sqrt[b*Sqrt[x] + a*x])/(143*b^6*x^(3/2)) + (4096*a^5*Sqrt[b*Sqrt[x] + a*x])/(429*b^7*x) - (8192*a^6*Sqrt[b*Sqrt[x] + a*x])/(429*b^8*Sqrt[x])","A",8,3,21,0.1429,1,"{2015, 2016, 2014}"
131,1,301,0,0.5090483,"\int x^3 \sqrt{b \sqrt[3]{x}+a x} \, dx","Int[x^3*Sqrt[b*x^(1/3) + a*x],x]","\frac{884 b^5 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{24035 a^5}-\frac{6188 b^4 x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{216315 a^4}+\frac{476 b^3 x^2 \sqrt{a x+b \sqrt[3]{x}}}{19665 a^3}-\frac{28 b^2 x^{8/3} \sqrt{a x+b \sqrt[3]{x}}}{1311 a^2}+\frac{442 b^{27/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{14421 a^{25/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{884 b^6 \sqrt{a x+b \sqrt[3]{x}}}{14421 a^6}+\frac{4 b x^{10/3} \sqrt{a x+b \sqrt[3]{x}}}{207 a}+\frac{2}{9} x^4 \sqrt{a x+b \sqrt[3]{x}}","\frac{884 b^5 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{24035 a^5}-\frac{6188 b^4 x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{216315 a^4}+\frac{476 b^3 x^2 \sqrt{a x+b \sqrt[3]{x}}}{19665 a^3}-\frac{28 b^2 x^{8/3} \sqrt{a x+b \sqrt[3]{x}}}{1311 a^2}+\frac{442 b^{27/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{14421 a^{25/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{884 b^6 \sqrt{a x+b \sqrt[3]{x}}}{14421 a^6}+\frac{4 b x^{10/3} \sqrt{a x+b \sqrt[3]{x}}}{207 a}+\frac{2}{9} x^4 \sqrt{a x+b \sqrt[3]{x}}",1,"(-884*b^6*Sqrt[b*x^(1/3) + a*x])/(14421*a^6) + (884*b^5*x^(2/3)*Sqrt[b*x^(1/3) + a*x])/(24035*a^5) - (6188*b^4*x^(4/3)*Sqrt[b*x^(1/3) + a*x])/(216315*a^4) + (476*b^3*x^2*Sqrt[b*x^(1/3) + a*x])/(19665*a^3) - (28*b^2*x^(8/3)*Sqrt[b*x^(1/3) + a*x])/(1311*a^2) + (4*b*x^(10/3)*Sqrt[b*x^(1/3) + a*x])/(207*a) + (2*x^4*Sqrt[b*x^(1/3) + a*x])/9 + (442*b^(27/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(14421*a^(25/4)*Sqrt[b*x^(1/3) + a*x])","A",11,6,19,0.3158,1,"{2018, 2021, 2024, 2011, 329, 220}"
132,1,411,0,0.5776513,"\int x^2 \sqrt{b \sqrt[3]{x}+a x} \, dx","Int[x^2*Sqrt[b*x^(1/3) + a*x],x]","\frac{44 b^5 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{221 a^{9/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{60 b^2 x^{5/3} \sqrt{a x+b \sqrt[3]{x}}}{1547 a^2}+\frac{22 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 a^{19/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{44 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 a^{19/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{44 b^4 \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{663 a^4}+\frac{220 b^3 x \sqrt{a x+b \sqrt[3]{x}}}{4641 a^3}+\frac{4 b x^{7/3} \sqrt{a x+b \sqrt[3]{x}}}{119 a}+\frac{2}{7} x^3 \sqrt{a x+b \sqrt[3]{x}}","\frac{44 b^5 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{221 a^{9/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{60 b^2 x^{5/3} \sqrt{a x+b \sqrt[3]{x}}}{1547 a^2}+\frac{22 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 a^{19/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{44 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 a^{19/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{44 b^4 \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{663 a^4}+\frac{220 b^3 x \sqrt{a x+b \sqrt[3]{x}}}{4641 a^3}+\frac{4 b x^{7/3} \sqrt{a x+b \sqrt[3]{x}}}{119 a}+\frac{2}{7} x^3 \sqrt{a x+b \sqrt[3]{x}}",1,"(44*b^5*(b + a*x^(2/3))*x^(1/3))/(221*a^(9/2)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (44*b^4*x^(1/3)*Sqrt[b*x^(1/3) + a*x])/(663*a^4) + (220*b^3*x*Sqrt[b*x^(1/3) + a*x])/(4641*a^3) - (60*b^2*x^(5/3)*Sqrt[b*x^(1/3) + a*x])/(1547*a^2) + (4*b*x^(7/3)*Sqrt[b*x^(1/3) + a*x])/(119*a) + (2*x^3*Sqrt[b*x^(1/3) + a*x])/7 - (44*b^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(221*a^(19/4)*Sqrt[b*x^(1/3) + a*x]) + (22*b^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(221*a^(19/4)*Sqrt[b*x^(1/3) + a*x])","A",11,8,19,0.4211,1,"{2018, 2021, 2024, 2032, 329, 305, 220, 1196}"
133,1,213,0,0.2991552,"\int x \sqrt{b \sqrt[3]{x}+a x} \, dx","Int[x*Sqrt[b*x^(1/3) + a*x],x]","-\frac{36 b^2 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{385 a^2}-\frac{6 b^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 a^{13/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{12 b^3 \sqrt{a x+b \sqrt[3]{x}}}{77 a^3}+\frac{4 b x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{55 a}+\frac{2}{5} x^2 \sqrt{a x+b \sqrt[3]{x}}","-\frac{36 b^2 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{385 a^2}-\frac{6 b^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 a^{13/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{12 b^3 \sqrt{a x+b \sqrt[3]{x}}}{77 a^3}+\frac{4 b x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{55 a}+\frac{2}{5} x^2 \sqrt{a x+b \sqrt[3]{x}}",1,"(12*b^3*Sqrt[b*x^(1/3) + a*x])/(77*a^3) - (36*b^2*x^(2/3)*Sqrt[b*x^(1/3) + a*x])/(385*a^2) + (4*b*x^(4/3)*Sqrt[b*x^(1/3) + a*x])/(55*a) + (2*x^2*Sqrt[b*x^(1/3) + a*x])/5 - (6*b^(15/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(77*a^(13/4)*Sqrt[b*x^(1/3) + a*x])","A",8,6,17,0.3529,1,"{2018, 2021, 2024, 2011, 329, 220}"
134,1,323,0,0.3257121,"\int \sqrt{b \sqrt[3]{x}+a x} \, dx","Int[Sqrt[b*x^(1/3) + a*x],x]","-\frac{4 b^2 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 a^{3/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{2 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4 b \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{15 a}+\frac{2}{3} x \sqrt{a x+b \sqrt[3]{x}}","-\frac{4 b^2 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 a^{3/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{2 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{7/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4 b \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{15 a}+\frac{2}{3} x \sqrt{a x+b \sqrt[3]{x}}",1,"(-4*b^2*(b + a*x^(2/3))*x^(1/3))/(5*a^(3/2)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) + (4*b*x^(1/3)*Sqrt[b*x^(1/3) + a*x])/(15*a) + (2*x*Sqrt[b*x^(1/3) + a*x])/3 + (4*b^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*a^(7/4)*Sqrt[b*x^(1/3) + a*x]) - (2*b^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*a^(7/4)*Sqrt[b*x^(1/3) + a*x])","A",8,8,15,0.5333,1,"{2004, 2018, 2024, 2032, 329, 305, 220, 1196}"
135,1,123,0,0.1462234,"\int \frac{\sqrt{b \sqrt[3]{x}+a x}}{x} \, dx","Int[Sqrt[b*x^(1/3) + a*x]/x,x]","\frac{2 b^{3/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt{a x+b \sqrt[3]{x}}}+2 \sqrt{a x+b \sqrt[3]{x}}","\frac{2 b^{3/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt[4]{a} \sqrt{a x+b \sqrt[3]{x}}}+2 \sqrt{a x+b \sqrt[3]{x}}",1,"2*Sqrt[b*x^(1/3) + a*x] + (2*b^(3/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(a^(1/4)*Sqrt[b*x^(1/3) + a*x])","A",5,5,19,0.2632,1,"{2018, 2021, 2011, 329, 220}"
136,1,325,0,0.3526734,"\int \frac{\sqrt{b \sqrt[3]{x}+a x}}{x^2} \, dx","Int[Sqrt[b*x^(1/3) + a*x]/x^2,x]","\frac{6 a^{5/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{12 a^{5/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{12 a^{3/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 b \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{5 b \sqrt[3]{x}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{5 x}","\frac{6 a^{5/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{12 a^{5/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{12 a^{3/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 b \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{5 b \sqrt[3]{x}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{5 x}",1,"(12*a^(3/2)*(b + a*x^(2/3))*x^(1/3))/(5*b*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (6*Sqrt[b*x^(1/3) + a*x])/(5*x) - (12*a*Sqrt[b*x^(1/3) + a*x])/(5*b*x^(1/3)) - (12*a^(5/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[b*x^(1/3) + a*x]) + (6*a^(5/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[b*x^(1/3) + a*x])","A",8,8,19,0.4211,1,"{2018, 2020, 2025, 2032, 329, 305, 220, 1196}"
137,1,188,0,0.2439342,"\int \frac{\sqrt{b \sqrt[3]{x}+a x}}{x^3} \, dx","Int[Sqrt[b*x^(1/3) + a*x]/x^3,x]","\frac{20 a^2 \sqrt{a x+b \sqrt[3]{x}}}{77 b^2 x^{2/3}}+\frac{10 a^{11/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 b^{9/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{77 b x^{4/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{11 x^2}","\frac{20 a^2 \sqrt{a x+b \sqrt[3]{x}}}{77 b^2 x^{2/3}}+\frac{10 a^{11/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 b^{9/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{77 b x^{4/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{11 x^2}",1,"(-6*Sqrt[b*x^(1/3) + a*x])/(11*x^2) - (12*a*Sqrt[b*x^(1/3) + a*x])/(77*b*x^(4/3)) + (20*a^2*Sqrt[b*x^(1/3) + a*x])/(77*b^2*x^(2/3)) + (10*a^(11/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(77*b^(9/4)*Sqrt[b*x^(1/3) + a*x])","A",7,6,19,0.3158,1,"{2018, 2020, 2025, 2011, 329, 220}"
138,1,413,0,0.5435325,"\int \frac{\sqrt{b \sqrt[3]{x}+a x}}{x^4} \, dx","Int[Sqrt[b*x^(1/3) + a*x]/x^4,x]","-\frac{308 a^{9/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{1105 b^4 \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{44 a^2 \sqrt{a x+b \sqrt[3]{x}}}{663 b^2 x^{5/3}}-\frac{154 a^{17/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{308 a^{17/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{308 a^4 \sqrt{a x+b \sqrt[3]{x}}}{1105 b^4 \sqrt[3]{x}}-\frac{308 a^3 \sqrt{a x+b \sqrt[3]{x}}}{3315 b^3 x}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{221 b x^{7/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{17 x^3}","-\frac{308 a^{9/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{1105 b^4 \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{44 a^2 \sqrt{a x+b \sqrt[3]{x}}}{663 b^2 x^{5/3}}-\frac{154 a^{17/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{308 a^{17/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{308 a^4 \sqrt{a x+b \sqrt[3]{x}}}{1105 b^4 \sqrt[3]{x}}-\frac{308 a^3 \sqrt{a x+b \sqrt[3]{x}}}{3315 b^3 x}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{221 b x^{7/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{17 x^3}",1,"(-308*a^(9/2)*(b + a*x^(2/3))*x^(1/3))/(1105*b^4*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (6*Sqrt[b*x^(1/3) + a*x])/(17*x^3) - (12*a*Sqrt[b*x^(1/3) + a*x])/(221*b*x^(7/3)) + (44*a^2*Sqrt[b*x^(1/3) + a*x])/(663*b^2*x^(5/3)) - (308*a^3*Sqrt[b*x^(1/3) + a*x])/(3315*b^3*x) + (308*a^4*Sqrt[b*x^(1/3) + a*x])/(1105*b^4*x^(1/3)) + (308*a^(17/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(1105*b^(15/4)*Sqrt[b*x^(1/3) + a*x]) - (154*a^(17/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(1105*b^(15/4)*Sqrt[b*x^(1/3) + a*x])","A",11,8,19,0.4211,1,"{2018, 2020, 2025, 2032, 329, 305, 220, 1196}"
139,1,276,0,0.4128993,"\int \frac{\sqrt{b \sqrt[3]{x}+a x}}{x^5} \, dx","Int[Sqrt[b*x^(1/3) + a*x]/x^5,x]","-\frac{2652 a^5 \sqrt{a x+b \sqrt[3]{x}}}{33649 b^5 x^{2/3}}+\frac{7956 a^4 \sqrt{a x+b \sqrt[3]{x}}}{168245 b^4 x^{4/3}}-\frac{884 a^3 \sqrt{a x+b \sqrt[3]{x}}}{24035 b^3 x^2}+\frac{68 a^2 \sqrt{a x+b \sqrt[3]{x}}}{2185 b^2 x^{8/3}}-\frac{1326 a^{23/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{33649 b^{21/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{437 b x^{10/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{23 x^4}","-\frac{2652 a^5 \sqrt{a x+b \sqrt[3]{x}}}{33649 b^5 x^{2/3}}+\frac{7956 a^4 \sqrt{a x+b \sqrt[3]{x}}}{168245 b^4 x^{4/3}}-\frac{884 a^3 \sqrt{a x+b \sqrt[3]{x}}}{24035 b^3 x^2}+\frac{68 a^2 \sqrt{a x+b \sqrt[3]{x}}}{2185 b^2 x^{8/3}}-\frac{1326 a^{23/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{33649 b^{21/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{437 b x^{10/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{23 x^4}",1,"(-6*Sqrt[b*x^(1/3) + a*x])/(23*x^4) - (12*a*Sqrt[b*x^(1/3) + a*x])/(437*b*x^(10/3)) + (68*a^2*Sqrt[b*x^(1/3) + a*x])/(2185*b^2*x^(8/3)) - (884*a^3*Sqrt[b*x^(1/3) + a*x])/(24035*b^3*x^2) + (7956*a^4*Sqrt[b*x^(1/3) + a*x])/(168245*b^4*x^(4/3)) - (2652*a^5*Sqrt[b*x^(1/3) + a*x])/(33649*b^5*x^(2/3)) - (1326*a^(23/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(33649*b^(21/4)*Sqrt[b*x^(1/3) + a*x])","A",10,6,19,0.3158,1,"{2018, 2020, 2025, 2011, 329, 220}"
140,1,298,0,0.5006096,"\int x^2 \left(b \sqrt[3]{x}+a x\right)^{3/2} \, dx","Int[x^2*(b*x^(1/3) + a*x)^(3/2),x]","-\frac{1768 b^5 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{168245 a^4}+\frac{1768 b^4 x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{216315 a^3}-\frac{136 b^3 x^2 \sqrt{a x+b \sqrt[3]{x}}}{19665 a^2}-\frac{884 b^{27/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{100947 a^{21/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{1768 b^6 \sqrt{a x+b \sqrt[3]{x}}}{100947 a^5}+\frac{8 b^2 x^{8/3} \sqrt{a x+b \sqrt[3]{x}}}{1311 a}+\frac{4}{69} b x^{10/3} \sqrt{a x+b \sqrt[3]{x}}+\frac{2}{9} x^3 \left(a x+b \sqrt[3]{x}\right)^{3/2}","-\frac{1768 b^5 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{168245 a^4}+\frac{1768 b^4 x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{216315 a^3}-\frac{136 b^3 x^2 \sqrt{a x+b \sqrt[3]{x}}}{19665 a^2}-\frac{884 b^{27/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{100947 a^{21/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{1768 b^6 \sqrt{a x+b \sqrt[3]{x}}}{100947 a^5}+\frac{8 b^2 x^{8/3} \sqrt{a x+b \sqrt[3]{x}}}{1311 a}+\frac{4}{69} b x^{10/3} \sqrt{a x+b \sqrt[3]{x}}+\frac{2}{9} x^3 \left(a x+b \sqrt[3]{x}\right)^{3/2}",1,"(1768*b^6*Sqrt[b*x^(1/3) + a*x])/(100947*a^5) - (1768*b^5*x^(2/3)*Sqrt[b*x^(1/3) + a*x])/(168245*a^4) + (1768*b^4*x^(4/3)*Sqrt[b*x^(1/3) + a*x])/(216315*a^3) - (136*b^3*x^2*Sqrt[b*x^(1/3) + a*x])/(19665*a^2) + (8*b^2*x^(8/3)*Sqrt[b*x^(1/3) + a*x])/(1311*a) + (4*b*x^(10/3)*Sqrt[b*x^(1/3) + a*x])/69 + (2*x^3*(b*x^(1/3) + a*x)^(3/2))/9 - (884*b^(27/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(100947*a^(21/4)*Sqrt[b*x^(1/3) + a*x])","A",11,6,19,0.3158,1,"{2018, 2021, 2024, 2011, 329, 220}"
141,1,408,0,0.5540654,"\int x \left(b \sqrt[3]{x}+a x\right)^{3/2} \, dx","Int[x*(b*x^(1/3) + a*x)^(3/2),x]","-\frac{88 b^5 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{1105 a^{7/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{44 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 a^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{88 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 a^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{88 b^4 \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{3315 a^3}-\frac{88 b^3 x \sqrt{a x+b \sqrt[3]{x}}}{4641 a^2}+\frac{24 b^2 x^{5/3} \sqrt{a x+b \sqrt[3]{x}}}{1547 a}+\frac{12}{119} b x^{7/3} \sqrt{a x+b \sqrt[3]{x}}+\frac{2}{7} x^2 \left(a x+b \sqrt[3]{x}\right)^{3/2}","-\frac{88 b^5 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{1105 a^{7/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{44 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 a^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{88 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 a^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{88 b^4 \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{3315 a^3}-\frac{88 b^3 x \sqrt{a x+b \sqrt[3]{x}}}{4641 a^2}+\frac{24 b^2 x^{5/3} \sqrt{a x+b \sqrt[3]{x}}}{1547 a}+\frac{12}{119} b x^{7/3} \sqrt{a x+b \sqrt[3]{x}}+\frac{2}{7} x^2 \left(a x+b \sqrt[3]{x}\right)^{3/2}",1,"(-88*b^5*(b + a*x^(2/3))*x^(1/3))/(1105*a^(7/2)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) + (88*b^4*x^(1/3)*Sqrt[b*x^(1/3) + a*x])/(3315*a^3) - (88*b^3*x*Sqrt[b*x^(1/3) + a*x])/(4641*a^2) + (24*b^2*x^(5/3)*Sqrt[b*x^(1/3) + a*x])/(1547*a) + (12*b*x^(7/3)*Sqrt[b*x^(1/3) + a*x])/119 + (2*x^2*(b*x^(1/3) + a*x)^(3/2))/7 + (88*b^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(1105*a^(15/4)*Sqrt[b*x^(1/3) + a*x]) - (44*b^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(1105*a^(15/4)*Sqrt[b*x^(1/3) + a*x])","A",11,8,17,0.4706,1,"{2018, 2021, 2024, 2032, 329, 305, 220, 1196}"
142,1,208,0,0.2707476,"\int \left(b \sqrt[3]{x}+a x\right)^{3/2} \, dx","Int[(b*x^(1/3) + a*x)^(3/2),x]","\frac{4 b^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 a^{9/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{8 b^3 \sqrt{a x+b \sqrt[3]{x}}}{77 a^2}+\frac{24 b^2 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{385 a}+\frac{12}{55} b x^{4/3} \sqrt{a x+b \sqrt[3]{x}}+\frac{2}{5} x \left(a x+b \sqrt[3]{x}\right)^{3/2}","\frac{4 b^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 a^{9/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{8 b^3 \sqrt{a x+b \sqrt[3]{x}}}{77 a^2}+\frac{24 b^2 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{385 a}+\frac{12}{55} b x^{4/3} \sqrt{a x+b \sqrt[3]{x}}+\frac{2}{5} x \left(a x+b \sqrt[3]{x}\right)^{3/2}",1,"(-8*b^3*Sqrt[b*x^(1/3) + a*x])/(77*a^2) + (24*b^2*x^(2/3)*Sqrt[b*x^(1/3) + a*x])/(385*a) + (12*b*x^(4/3)*Sqrt[b*x^(1/3) + a*x])/55 + (2*x*(b*x^(1/3) + a*x)^(3/2))/5 + (4*b^(15/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(77*a^(9/4)*Sqrt[b*x^(1/3) + a*x])","A",8,7,15,0.4667,1,"{2004, 2018, 2021, 2024, 2011, 329, 220}"
143,1,319,0,0.3293396,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x} \, dx","Int[(b*x^(1/3) + a*x)^(3/2)/x,x]","\frac{4 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{8 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{8 b^2 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 \sqrt{a} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{4}{5} b \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}+\frac{2}{3} \left(a x+b \sqrt[3]{x}\right)^{3/2}","\frac{4 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{8 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{3/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{8 b^2 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 \sqrt{a} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{4}{5} b \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}+\frac{2}{3} \left(a x+b \sqrt[3]{x}\right)^{3/2}",1,"(8*b^2*(b + a*x^(2/3))*x^(1/3))/(5*Sqrt[a]*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) + (4*b*x^(1/3)*Sqrt[b*x^(1/3) + a*x])/5 + (2*(b*x^(1/3) + a*x)^(3/2))/3 - (8*b^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*a^(3/4)*Sqrt[b*x^(1/3) + a*x]) + (4*b^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*a^(3/4)*Sqrt[b*x^(1/3) + a*x])","A",8,8,19,0.4211,1,"{2018, 2021, 2004, 2032, 329, 305, 220, 1196}"
144,1,144,0,0.20206,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x^2} \, dx","Int[(b*x^(1/3) + a*x)^(3/2)/x^2,x]","\frac{4 a^{3/4} b^{3/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt{a x+b \sqrt[3]{x}}}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{x}+4 a \sqrt{a x+b \sqrt[3]{x}}","\frac{4 a^{3/4} b^{3/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{\sqrt{a x+b \sqrt[3]{x}}}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{x}+4 a \sqrt{a x+b \sqrt[3]{x}}",1,"4*a*Sqrt[b*x^(1/3) + a*x] - (2*(b*x^(1/3) + a*x)^(3/2))/x + (4*a^(3/4)*b^(3/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/Sqrt[b*x^(1/3) + a*x]","A",6,6,19,0.3158,1,"{2018, 2020, 2021, 2011, 329, 220}"
145,1,350,0,0.4313388,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x^3} \, dx","Int[(b*x^(1/3) + a*x)^(3/2)/x^3,x]","\frac{4 a^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{8 a^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{8 a^{5/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 b \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{8 a^2 \sqrt{a x+b \sqrt[3]{x}}}{5 b \sqrt[3]{x}}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{3 x^2}-\frac{4 a \sqrt{a x+b \sqrt[3]{x}}}{5 x}","\frac{4 a^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{8 a^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{8 a^{5/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 b \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{8 a^2 \sqrt{a x+b \sqrt[3]{x}}}{5 b \sqrt[3]{x}}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{3 x^2}-\frac{4 a \sqrt{a x+b \sqrt[3]{x}}}{5 x}",1,"(8*a^(5/2)*(b + a*x^(2/3))*x^(1/3))/(5*b*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (4*a*Sqrt[b*x^(1/3) + a*x])/(5*x) - (8*a^2*Sqrt[b*x^(1/3) + a*x])/(5*b*x^(1/3)) - (2*(b*x^(1/3) + a*x)^(3/2))/(3*x^2) - (8*a^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[b*x^(1/3) + a*x]) + (4*a^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[b*x^(1/3) + a*x])","A",9,8,19,0.4211,1,"{2018, 2020, 2025, 2032, 329, 305, 220, 1196}"
146,1,213,0,0.3085731,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x^4} \, dx","Int[(b*x^(1/3) + a*x)^(3/2)/x^4,x]","\frac{8 a^3 \sqrt{a x+b \sqrt[3]{x}}}{77 b^2 x^{2/3}}+\frac{4 a^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 b^{9/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{24 a^2 \sqrt{a x+b \sqrt[3]{x}}}{385 b x^{4/3}}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{55 x^2}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{5 x^3}","\frac{8 a^3 \sqrt{a x+b \sqrt[3]{x}}}{77 b^2 x^{2/3}}+\frac{4 a^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 b^{9/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{24 a^2 \sqrt{a x+b \sqrt[3]{x}}}{385 b x^{4/3}}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{55 x^2}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{5 x^3}",1,"(-12*a*Sqrt[b*x^(1/3) + a*x])/(55*x^2) - (24*a^2*Sqrt[b*x^(1/3) + a*x])/(385*b*x^(4/3)) + (8*a^3*Sqrt[b*x^(1/3) + a*x])/(77*b^2*x^(2/3)) - (2*(b*x^(1/3) + a*x)^(3/2))/(5*x^3) + (4*a^(15/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(77*b^(9/4)*Sqrt[b*x^(1/3) + a*x])","A",8,6,19,0.3158,1,"{2018, 2020, 2025, 2011, 329, 220}"
147,1,438,0,0.6404161,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x^5} \, dx","Int[(b*x^(1/3) + a*x)^(3/2)/x^5,x]","-\frac{88 a^{11/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{1105 b^4 \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{88 a^3 \sqrt{a x+b \sqrt[3]{x}}}{4641 b^2 x^{5/3}}-\frac{44 a^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{88 a^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{88 a^5 \sqrt{a x+b \sqrt[3]{x}}}{1105 b^4 \sqrt[3]{x}}-\frac{88 a^4 \sqrt{a x+b \sqrt[3]{x}}}{3315 b^3 x}-\frac{24 a^2 \sqrt{a x+b \sqrt[3]{x}}}{1547 b x^{7/3}}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{119 x^3}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{7 x^4}","-\frac{88 a^{11/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{1105 b^4 \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{88 a^3 \sqrt{a x+b \sqrt[3]{x}}}{4641 b^2 x^{5/3}}-\frac{44 a^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{88 a^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{88 a^5 \sqrt{a x+b \sqrt[3]{x}}}{1105 b^4 \sqrt[3]{x}}-\frac{88 a^4 \sqrt{a x+b \sqrt[3]{x}}}{3315 b^3 x}-\frac{24 a^2 \sqrt{a x+b \sqrt[3]{x}}}{1547 b x^{7/3}}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{119 x^3}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{7 x^4}",1,"(-88*a^(11/2)*(b + a*x^(2/3))*x^(1/3))/(1105*b^4*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (12*a*Sqrt[b*x^(1/3) + a*x])/(119*x^3) - (24*a^2*Sqrt[b*x^(1/3) + a*x])/(1547*b*x^(7/3)) + (88*a^3*Sqrt[b*x^(1/3) + a*x])/(4641*b^2*x^(5/3)) - (88*a^4*Sqrt[b*x^(1/3) + a*x])/(3315*b^3*x) + (88*a^5*Sqrt[b*x^(1/3) + a*x])/(1105*b^4*x^(1/3)) - (2*(b*x^(1/3) + a*x)^(3/2))/(7*x^4) + (88*a^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(1105*b^(15/4)*Sqrt[b*x^(1/3) + a*x]) - (44*a^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(1105*b^(15/4)*Sqrt[b*x^(1/3) + a*x])","A",12,8,19,0.4211,1,"{2018, 2020, 2025, 2032, 329, 305, 220, 1196}"
148,1,301,0,0.4788737,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x^6} \, dx","Int[(b*x^(1/3) + a*x)^(3/2)/x^6,x]","-\frac{1768 a^6 \sqrt{a x+b \sqrt[3]{x}}}{100947 b^5 x^{2/3}}+\frac{1768 a^5 \sqrt{a x+b \sqrt[3]{x}}}{168245 b^4 x^{4/3}}-\frac{1768 a^4 \sqrt{a x+b \sqrt[3]{x}}}{216315 b^3 x^2}+\frac{136 a^3 \sqrt{a x+b \sqrt[3]{x}}}{19665 b^2 x^{8/3}}-\frac{884 a^{27/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{100947 b^{21/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{8 a^2 \sqrt{a x+b \sqrt[3]{x}}}{1311 b x^{10/3}}-\frac{4 a \sqrt{a x+b \sqrt[3]{x}}}{69 x^4}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{9 x^5}","-\frac{1768 a^6 \sqrt{a x+b \sqrt[3]{x}}}{100947 b^5 x^{2/3}}+\frac{1768 a^5 \sqrt{a x+b \sqrt[3]{x}}}{168245 b^4 x^{4/3}}-\frac{1768 a^4 \sqrt{a x+b \sqrt[3]{x}}}{216315 b^3 x^2}+\frac{136 a^3 \sqrt{a x+b \sqrt[3]{x}}}{19665 b^2 x^{8/3}}-\frac{884 a^{27/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{100947 b^{21/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{8 a^2 \sqrt{a x+b \sqrt[3]{x}}}{1311 b x^{10/3}}-\frac{4 a \sqrt{a x+b \sqrt[3]{x}}}{69 x^4}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{9 x^5}",1,"(-4*a*Sqrt[b*x^(1/3) + a*x])/(69*x^4) - (8*a^2*Sqrt[b*x^(1/3) + a*x])/(1311*b*x^(10/3)) + (136*a^3*Sqrt[b*x^(1/3) + a*x])/(19665*b^2*x^(8/3)) - (1768*a^4*Sqrt[b*x^(1/3) + a*x])/(216315*b^3*x^2) + (1768*a^5*Sqrt[b*x^(1/3) + a*x])/(168245*b^4*x^(4/3)) - (1768*a^6*Sqrt[b*x^(1/3) + a*x])/(100947*b^5*x^(2/3)) - (2*(b*x^(1/3) + a*x)^(3/2))/(9*x^5) - (884*a^(27/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(100947*b^(21/4)*Sqrt[b*x^(1/3) + a*x])","A",11,6,19,0.3158,1,"{2018, 2020, 2025, 2011, 329, 220}"
149,1,304,0,0.5060499,"\int \frac{x^4}{\sqrt{b \sqrt[3]{x}+a x}} \, dx","Int[x^4/Sqrt[b*x^(1/3) + a*x],x]","-\frac{2210 b^5 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{4807 a^6}+\frac{15470 b^4 x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{43263 a^5}-\frac{1190 b^3 x^2 \sqrt{a x+b \sqrt[3]{x}}}{3933 a^4}+\frac{350 b^2 x^{8/3} \sqrt{a x+b \sqrt[3]{x}}}{1311 a^3}-\frac{5525 b^{27/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{14421 a^{29/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{11050 b^6 \sqrt{a x+b \sqrt[3]{x}}}{14421 a^7}-\frac{50 b x^{10/3} \sqrt{a x+b \sqrt[3]{x}}}{207 a^2}+\frac{2 x^4 \sqrt{a x+b \sqrt[3]{x}}}{9 a}","-\frac{2210 b^5 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{4807 a^6}+\frac{15470 b^4 x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{43263 a^5}-\frac{1190 b^3 x^2 \sqrt{a x+b \sqrt[3]{x}}}{3933 a^4}+\frac{350 b^2 x^{8/3} \sqrt{a x+b \sqrt[3]{x}}}{1311 a^3}-\frac{5525 b^{27/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{14421 a^{29/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{11050 b^6 \sqrt{a x+b \sqrt[3]{x}}}{14421 a^7}-\frac{50 b x^{10/3} \sqrt{a x+b \sqrt[3]{x}}}{207 a^2}+\frac{2 x^4 \sqrt{a x+b \sqrt[3]{x}}}{9 a}",1,"(11050*b^6*Sqrt[b*x^(1/3) + a*x])/(14421*a^7) - (2210*b^5*x^(2/3)*Sqrt[b*x^(1/3) + a*x])/(4807*a^6) + (15470*b^4*x^(4/3)*Sqrt[b*x^(1/3) + a*x])/(43263*a^5) - (1190*b^3*x^2*Sqrt[b*x^(1/3) + a*x])/(3933*a^4) + (350*b^2*x^(8/3)*Sqrt[b*x^(1/3) + a*x])/(1311*a^3) - (50*b*x^(10/3)*Sqrt[b*x^(1/3) + a*x])/(207*a^2) + (2*x^4*Sqrt[b*x^(1/3) + a*x])/(9*a) - (5525*b^(27/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(14421*a^(29/4)*Sqrt[b*x^(1/3) + a*x])","A",11,5,19,0.2632,1,"{2018, 2024, 2011, 329, 220}"
150,1,414,0,0.5661787,"\int \frac{x^3}{\sqrt{b \sqrt[3]{x}+a x}} \, dx","Int[x^3/Sqrt[b*x^(1/3) + a*x],x]","-\frac{418 b^5 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{221 a^{11/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{570 b^2 x^{5/3} \sqrt{a x+b \sqrt[3]{x}}}{1547 a^3}-\frac{209 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 a^{23/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{418 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 a^{23/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{418 b^4 \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{663 a^5}-\frac{2090 b^3 x \sqrt{a x+b \sqrt[3]{x}}}{4641 a^4}-\frac{38 b x^{7/3} \sqrt{a x+b \sqrt[3]{x}}}{119 a^2}+\frac{2 x^3 \sqrt{a x+b \sqrt[3]{x}}}{7 a}","-\frac{418 b^5 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{221 a^{11/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{570 b^2 x^{5/3} \sqrt{a x+b \sqrt[3]{x}}}{1547 a^3}-\frac{209 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 a^{23/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{418 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 a^{23/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{418 b^4 \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{663 a^5}-\frac{2090 b^3 x \sqrt{a x+b \sqrt[3]{x}}}{4641 a^4}-\frac{38 b x^{7/3} \sqrt{a x+b \sqrt[3]{x}}}{119 a^2}+\frac{2 x^3 \sqrt{a x+b \sqrt[3]{x}}}{7 a}",1,"(-418*b^5*(b + a*x^(2/3))*x^(1/3))/(221*a^(11/2)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) + (418*b^4*x^(1/3)*Sqrt[b*x^(1/3) + a*x])/(663*a^5) - (2090*b^3*x*Sqrt[b*x^(1/3) + a*x])/(4641*a^4) + (570*b^2*x^(5/3)*Sqrt[b*x^(1/3) + a*x])/(1547*a^3) - (38*b*x^(7/3)*Sqrt[b*x^(1/3) + a*x])/(119*a^2) + (2*x^3*Sqrt[b*x^(1/3) + a*x])/(7*a) + (418*b^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(221*a^(23/4)*Sqrt[b*x^(1/3) + a*x]) - (209*b^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(221*a^(23/4)*Sqrt[b*x^(1/3) + a*x])","A",11,7,19,0.3684,1,"{2018, 2024, 2032, 329, 305, 220, 1196}"
151,1,216,0,0.3186916,"\int \frac{x^2}{\sqrt{b \sqrt[3]{x}+a x}} \, dx","Int[x^2/Sqrt[b*x^(1/3) + a*x],x]","\frac{234 b^2 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{385 a^3}+\frac{39 b^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 a^{17/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{78 b^3 \sqrt{a x+b \sqrt[3]{x}}}{77 a^4}-\frac{26 b x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{55 a^2}+\frac{2 x^2 \sqrt{a x+b \sqrt[3]{x}}}{5 a}","\frac{234 b^2 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{385 a^3}+\frac{39 b^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 a^{17/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{78 b^3 \sqrt{a x+b \sqrt[3]{x}}}{77 a^4}-\frac{26 b x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{55 a^2}+\frac{2 x^2 \sqrt{a x+b \sqrt[3]{x}}}{5 a}",1,"(-78*b^3*Sqrt[b*x^(1/3) + a*x])/(77*a^4) + (234*b^2*x^(2/3)*Sqrt[b*x^(1/3) + a*x])/(385*a^3) - (26*b*x^(4/3)*Sqrt[b*x^(1/3) + a*x])/(55*a^2) + (2*x^2*Sqrt[b*x^(1/3) + a*x])/(5*a) + (39*b^(15/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(77*a^(17/4)*Sqrt[b*x^(1/3) + a*x])","A",8,5,19,0.2632,1,"{2018, 2024, 2011, 329, 220}"
152,1,326,0,0.3493934,"\int \frac{x}{\sqrt{b \sqrt[3]{x}+a x}} \, dx","Int[x/Sqrt[b*x^(1/3) + a*x],x]","\frac{14 b^2 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 a^{5/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{7 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{11/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{14 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{11/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{14 b \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{15 a^2}+\frac{2 x \sqrt{a x+b \sqrt[3]{x}}}{3 a}","\frac{14 b^2 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 a^{5/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{7 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{11/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{14 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{11/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{14 b \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{15 a^2}+\frac{2 x \sqrt{a x+b \sqrt[3]{x}}}{3 a}",1,"(14*b^2*(b + a*x^(2/3))*x^(1/3))/(5*a^(5/2)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (14*b*x^(1/3)*Sqrt[b*x^(1/3) + a*x])/(15*a^2) + (2*x*Sqrt[b*x^(1/3) + a*x])/(3*a) - (14*b^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*a^(11/4)*Sqrt[b*x^(1/3) + a*x]) + (7*b^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*a^(11/4)*Sqrt[b*x^(1/3) + a*x])","A",8,7,17,0.4118,1,"{2018, 2024, 2032, 329, 305, 220, 1196}"
153,1,126,0,0.1181104,"\int \frac{1}{\sqrt{b \sqrt[3]{x}+a x}} \, dx","Int[1/Sqrt[b*x^(1/3) + a*x],x]","\frac{2 \sqrt{a x+b \sqrt[3]{x}}}{a}-\frac{b^{3/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{a^{5/4} \sqrt{a x+b \sqrt[3]{x}}}","\frac{2 \sqrt{a x+b \sqrt[3]{x}}}{a}-\frac{b^{3/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{a^{5/4} \sqrt{a x+b \sqrt[3]{x}}}",1,"(2*Sqrt[b*x^(1/3) + a*x])/a - (b^(3/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(a^(5/4)*Sqrt[b*x^(1/3) + a*x])","A",5,5,15,0.3333,1,"{2010, 2013, 2011, 329, 220}"
154,1,294,0,0.2935312,"\int \frac{1}{x \sqrt{b \sqrt[3]{x}+a x}} \, dx","Int[1/(x*Sqrt[b*x^(1/3) + a*x]),x]","\frac{3 \sqrt[4]{a} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{6 \sqrt[4]{a} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{6 \sqrt{a} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{b \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{b \sqrt[3]{x}}","\frac{3 \sqrt[4]{a} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{6 \sqrt[4]{a} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{6 \sqrt{a} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{b \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{b \sqrt[3]{x}}",1,"(6*Sqrt[a]*(b + a*x^(2/3))*x^(1/3))/(b*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (6*Sqrt[b*x^(1/3) + a*x])/(b*x^(1/3)) - (6*a^(1/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(b^(3/4)*Sqrt[b*x^(1/3) + a*x]) + (3*a^(1/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(b^(3/4)*Sqrt[b*x^(1/3) + a*x])","A",7,7,19,0.3684,1,"{2018, 2025, 2032, 329, 305, 220, 1196}"
155,1,163,0,0.2007233,"\int \frac{1}{x^2 \sqrt{b \sqrt[3]{x}+a x}} \, dx","Int[1/(x^2*Sqrt[b*x^(1/3) + a*x]),x]","\frac{5 a^{7/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{7 b^{9/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{10 a \sqrt{a x+b \sqrt[3]{x}}}{7 b^2 x^{2/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{7 b x^{4/3}}","\frac{5 a^{7/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{7 b^{9/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{10 a \sqrt{a x+b \sqrt[3]{x}}}{7 b^2 x^{2/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{7 b x^{4/3}}",1,"(-6*Sqrt[b*x^(1/3) + a*x])/(7*b*x^(4/3)) + (10*a*Sqrt[b*x^(1/3) + a*x])/(7*b^2*x^(2/3)) + (5*a^(7/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(7*b^(9/4)*Sqrt[b*x^(1/3) + a*x])","A",6,5,19,0.2632,1,"{2018, 2025, 2011, 329, 220}"
156,1,388,0,0.4759111,"\int \frac{1}{x^3 \sqrt{b \sqrt[3]{x}+a x}} \, dx","Int[1/(x^3*Sqrt[b*x^(1/3) + a*x]),x]","-\frac{154 a^{7/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{65 b^4 \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{77 a^{13/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{154 a^{13/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{154 a^3 \sqrt{a x+b \sqrt[3]{x}}}{65 b^4 \sqrt[3]{x}}-\frac{154 a^2 \sqrt{a x+b \sqrt[3]{x}}}{195 b^3 x}+\frac{22 a \sqrt{a x+b \sqrt[3]{x}}}{39 b^2 x^{5/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{13 b x^{7/3}}","-\frac{154 a^{7/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{65 b^4 \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}-\frac{77 a^{13/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{154 a^{13/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{65 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{154 a^3 \sqrt{a x+b \sqrt[3]{x}}}{65 b^4 \sqrt[3]{x}}-\frac{154 a^2 \sqrt{a x+b \sqrt[3]{x}}}{195 b^3 x}+\frac{22 a \sqrt{a x+b \sqrt[3]{x}}}{39 b^2 x^{5/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{13 b x^{7/3}}",1,"(-154*a^(7/2)*(b + a*x^(2/3))*x^(1/3))/(65*b^4*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (6*Sqrt[b*x^(1/3) + a*x])/(13*b*x^(7/3)) + (22*a*Sqrt[b*x^(1/3) + a*x])/(39*b^2*x^(5/3)) - (154*a^2*Sqrt[b*x^(1/3) + a*x])/(195*b^3*x) + (154*a^3*Sqrt[b*x^(1/3) + a*x])/(65*b^4*x^(1/3)) + (154*a^(13/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(65*b^(15/4)*Sqrt[b*x^(1/3) + a*x]) - (77*a^(13/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(65*b^(15/4)*Sqrt[b*x^(1/3) + a*x])","A",10,7,19,0.3684,1,"{2018, 2025, 2032, 329, 305, 220, 1196}"
157,1,251,0,0.3454153,"\int \frac{1}{x^4 \sqrt{b \sqrt[3]{x}+a x}} \, dx","Int[1/(x^4*Sqrt[b*x^(1/3) + a*x]),x]","-\frac{1326 a^4 \sqrt{a x+b \sqrt[3]{x}}}{1463 b^5 x^{2/3}}+\frac{3978 a^3 \sqrt{a x+b \sqrt[3]{x}}}{7315 b^4 x^{4/3}}-\frac{442 a^2 \sqrt{a x+b \sqrt[3]{x}}}{1045 b^3 x^2}-\frac{663 a^{19/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1463 b^{21/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{34 a \sqrt{a x+b \sqrt[3]{x}}}{95 b^2 x^{8/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{19 b x^{10/3}}","-\frac{1326 a^4 \sqrt{a x+b \sqrt[3]{x}}}{1463 b^5 x^{2/3}}+\frac{3978 a^3 \sqrt{a x+b \sqrt[3]{x}}}{7315 b^4 x^{4/3}}-\frac{442 a^2 \sqrt{a x+b \sqrt[3]{x}}}{1045 b^3 x^2}-\frac{663 a^{19/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1463 b^{21/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{34 a \sqrt{a x+b \sqrt[3]{x}}}{95 b^2 x^{8/3}}-\frac{6 \sqrt{a x+b \sqrt[3]{x}}}{19 b x^{10/3}}",1,"(-6*Sqrt[b*x^(1/3) + a*x])/(19*b*x^(10/3)) + (34*a*Sqrt[b*x^(1/3) + a*x])/(95*b^2*x^(8/3)) - (442*a^2*Sqrt[b*x^(1/3) + a*x])/(1045*b^3*x^2) + (3978*a^3*Sqrt[b*x^(1/3) + a*x])/(7315*b^4*x^(4/3)) - (1326*a^4*Sqrt[b*x^(1/3) + a*x])/(1463*b^5*x^(2/3)) - (663*a^(19/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(1463*b^(21/4)*Sqrt[b*x^(1/3) + a*x])","A",9,5,19,0.2632,1,"{2018, 2025, 2011, 329, 220}"
158,1,437,0,0.6735873,"\int \frac{x^4}{\left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Int[x^4/(b*x^(1/3) + a*x)^(3/2),x]","-\frac{4807 b^5 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{221 a^{13/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{6555 b^2 x^{5/3} \sqrt{a x+b \sqrt[3]{x}}}{1547 a^4}-\frac{4807 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{442 a^{27/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4807 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 a^{27/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4807 b^4 \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{663 a^6}-\frac{24035 b^3 x \sqrt{a x+b \sqrt[3]{x}}}{4641 a^5}-\frac{437 b x^{7/3} \sqrt{a x+b \sqrt[3]{x}}}{119 a^3}+\frac{23 x^3 \sqrt{a x+b \sqrt[3]{x}}}{7 a^2}-\frac{3 x^4}{a \sqrt{a x+b \sqrt[3]{x}}}","-\frac{4807 b^5 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{221 a^{13/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{6555 b^2 x^{5/3} \sqrt{a x+b \sqrt[3]{x}}}{1547 a^4}-\frac{4807 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{442 a^{27/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4807 b^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 a^{27/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4807 b^4 \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{663 a^6}-\frac{24035 b^3 x \sqrt{a x+b \sqrt[3]{x}}}{4641 a^5}-\frac{437 b x^{7/3} \sqrt{a x+b \sqrt[3]{x}}}{119 a^3}+\frac{23 x^3 \sqrt{a x+b \sqrt[3]{x}}}{7 a^2}-\frac{3 x^4}{a \sqrt{a x+b \sqrt[3]{x}}}",1,"(-4807*b^5*(b + a*x^(2/3))*x^(1/3))/(221*a^(13/2)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (3*x^4)/(a*Sqrt[b*x^(1/3) + a*x]) + (4807*b^4*x^(1/3)*Sqrt[b*x^(1/3) + a*x])/(663*a^6) - (24035*b^3*x*Sqrt[b*x^(1/3) + a*x])/(4641*a^5) + (6555*b^2*x^(5/3)*Sqrt[b*x^(1/3) + a*x])/(1547*a^4) - (437*b*x^(7/3)*Sqrt[b*x^(1/3) + a*x])/(119*a^3) + (23*x^3*Sqrt[b*x^(1/3) + a*x])/(7*a^2) + (4807*b^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(221*a^(27/4)*Sqrt[b*x^(1/3) + a*x]) - (4807*b^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(442*a^(27/4)*Sqrt[b*x^(1/3) + a*x])","A",12,8,19,0.4211,1,"{2018, 2022, 2024, 2032, 329, 305, 220, 1196}"
159,1,239,0,0.3774794,"\int \frac{x^3}{\left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Int[x^3/(b*x^(1/3) + a*x)^(3/2),x]","\frac{1989 b^2 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{385 a^4}+\frac{663 b^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{154 a^{21/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{663 b^3 \sqrt{a x+b \sqrt[3]{x}}}{77 a^5}-\frac{221 b x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{55 a^3}+\frac{17 x^2 \sqrt{a x+b \sqrt[3]{x}}}{5 a^2}-\frac{3 x^3}{a \sqrt{a x+b \sqrt[3]{x}}}","\frac{1989 b^2 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{385 a^4}+\frac{663 b^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{154 a^{21/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{663 b^3 \sqrt{a x+b \sqrt[3]{x}}}{77 a^5}-\frac{221 b x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}{55 a^3}+\frac{17 x^2 \sqrt{a x+b \sqrt[3]{x}}}{5 a^2}-\frac{3 x^3}{a \sqrt{a x+b \sqrt[3]{x}}}",1,"(-3*x^3)/(a*Sqrt[b*x^(1/3) + a*x]) - (663*b^3*Sqrt[b*x^(1/3) + a*x])/(77*a^5) + (1989*b^2*x^(2/3)*Sqrt[b*x^(1/3) + a*x])/(385*a^4) - (221*b*x^(4/3)*Sqrt[b*x^(1/3) + a*x])/(55*a^3) + (17*x^2*Sqrt[b*x^(1/3) + a*x])/(5*a^2) + (663*b^(15/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(154*a^(21/4)*Sqrt[b*x^(1/3) + a*x])","A",9,6,19,0.3158,1,"{2018, 2022, 2024, 2011, 329, 220}"
160,1,349,0,0.4262361,"\int \frac{x^2}{\left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Int[x^2/(b*x^(1/3) + a*x)^(3/2),x]","\frac{77 b^2 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 a^{7/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{77 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 a^{15/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{77 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{15/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{77 b \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{15 a^3}+\frac{11 x \sqrt{a x+b \sqrt[3]{x}}}{3 a^2}-\frac{3 x^2}{a \sqrt{a x+b \sqrt[3]{x}}}","\frac{77 b^2 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 a^{7/2} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{77 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 a^{15/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{77 b^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 a^{15/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{77 b \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}{15 a^3}+\frac{11 x \sqrt{a x+b \sqrt[3]{x}}}{3 a^2}-\frac{3 x^2}{a \sqrt{a x+b \sqrt[3]{x}}}",1,"(77*b^2*(b + a*x^(2/3))*x^(1/3))/(5*a^(7/2)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (3*x^2)/(a*Sqrt[b*x^(1/3) + a*x]) - (77*b*x^(1/3)*Sqrt[b*x^(1/3) + a*x])/(15*a^3) + (11*x*Sqrt[b*x^(1/3) + a*x])/(3*a^2) - (77*b^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*a^(15/4)*Sqrt[b*x^(1/3) + a*x]) + (77*b^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(10*a^(15/4)*Sqrt[b*x^(1/3) + a*x])","A",9,8,19,0.4211,1,"{2018, 2022, 2024, 2032, 329, 305, 220, 1196}"
161,1,149,0,0.2086977,"\int \frac{x}{\left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Int[x/(b*x^(1/3) + a*x)^(3/2),x]","-\frac{5 b^{3/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 a^{9/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{5 \sqrt{a x+b \sqrt[3]{x}}}{a^2}-\frac{3 x}{a \sqrt{a x+b \sqrt[3]{x}}}","-\frac{5 b^{3/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 a^{9/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{5 \sqrt{a x+b \sqrt[3]{x}}}{a^2}-\frac{3 x}{a \sqrt{a x+b \sqrt[3]{x}}}",1,"(-3*x)/(a*Sqrt[b*x^(1/3) + a*x]) + (5*Sqrt[b*x^(1/3) + a*x])/a^2 - (5*b^(3/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(2*a^(9/4)*Sqrt[b*x^(1/3) + a*x])","A",6,6,17,0.3529,1,"{2018, 2022, 2024, 2011, 329, 220}"
162,1,296,0,0.2599598,"\int \frac{1}{\left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Int[(b*x^(1/3) + a*x)^(-3/2),x]","-\frac{3 \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{3 \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{3 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{\sqrt{a} b \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{3 x^{2/3}}{b \sqrt{a x+b \sqrt[3]{x}}}","-\frac{3 \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{3 \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{3/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{3 \sqrt[3]{x} \left(a x^{2/3}+b\right)}{\sqrt{a} b \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{3 x^{2/3}}{b \sqrt{a x+b \sqrt[3]{x}}}",1,"(-3*(b + a*x^(2/3))*x^(1/3))/(Sqrt[a]*b*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) + (3*x^(2/3))/(b*Sqrt[b*x^(1/3) + a*x]) + (3*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(a^(3/4)*b^(3/4)*Sqrt[b*x^(1/3) + a*x]) - (3*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(2*a^(3/4)*b^(3/4)*Sqrt[b*x^(1/3) + a*x])","A",7,7,15,0.4667,1,"{2006, 2018, 2032, 329, 305, 220, 1196}"
163,1,158,0,0.2052317,"\int \frac{1}{x \left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Int[1/(x*(b*x^(1/3) + a*x)^(3/2)),x]","-\frac{5 a^{3/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{9/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{5 \sqrt{a x+b \sqrt[3]{x}}}{b^2 x^{2/3}}+\frac{3}{b \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}","-\frac{5 a^{3/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{9/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{5 \sqrt{a x+b \sqrt[3]{x}}}{b^2 x^{2/3}}+\frac{3}{b \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}}}",1,"3/(b*x^(1/3)*Sqrt[b*x^(1/3) + a*x]) - (5*Sqrt[b*x^(1/3) + a*x])/(b^2*x^(2/3)) - (5*a^(3/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(2*b^(9/4)*Sqrt[b*x^(1/3) + a*x])","A",6,6,19,0.3158,1,"{2018, 2023, 2025, 2011, 329, 220}"
164,1,383,0,0.4785059,"\int \frac{1}{x^2 \left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Int[1/(x^2*(b*x^(1/3) + a*x)^(3/2)),x]","\frac{77 a^{5/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 b^4 \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{77 a^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{77 a^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{77 a^2 \sqrt{a x+b \sqrt[3]{x}}}{5 b^4 \sqrt[3]{x}}-\frac{11 \sqrt{a x+b \sqrt[3]{x}}}{3 b^2 x^{5/3}}+\frac{77 a \sqrt{a x+b \sqrt[3]{x}}}{15 b^3 x}+\frac{3}{b x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}","\frac{77 a^{5/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{5 b^4 \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{77 a^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{77 a^{9/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{15/4} \sqrt{a x+b \sqrt[3]{x}}}-\frac{77 a^2 \sqrt{a x+b \sqrt[3]{x}}}{5 b^4 \sqrt[3]{x}}-\frac{11 \sqrt{a x+b \sqrt[3]{x}}}{3 b^2 x^{5/3}}+\frac{77 a \sqrt{a x+b \sqrt[3]{x}}}{15 b^3 x}+\frac{3}{b x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}",1,"3/(b*x^(4/3)*Sqrt[b*x^(1/3) + a*x]) + (77*a^(5/2)*(b + a*x^(2/3))*x^(1/3))/(5*b^4*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (11*Sqrt[b*x^(1/3) + a*x])/(3*b^2*x^(5/3)) + (77*a*Sqrt[b*x^(1/3) + a*x])/(15*b^3*x) - (77*a^2*Sqrt[b*x^(1/3) + a*x])/(5*b^4*x^(1/3)) - (77*a^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(5*b^(15/4)*Sqrt[b*x^(1/3) + a*x]) + (77*a^(9/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(10*b^(15/4)*Sqrt[b*x^(1/3) + a*x])","A",10,8,19,0.4211,1,"{2018, 2023, 2025, 2032, 329, 305, 220, 1196}"
165,1,246,0,0.3647469,"\int \frac{1}{x^3 \left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Int[1/(x^3*(b*x^(1/3) + a*x)^(3/2)),x]","\frac{663 a^3 \sqrt{a x+b \sqrt[3]{x}}}{77 b^5 x^{2/3}}-\frac{1989 a^2 \sqrt{a x+b \sqrt[3]{x}}}{385 b^4 x^{4/3}}+\frac{663 a^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{154 b^{21/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{221 a \sqrt{a x+b \sqrt[3]{x}}}{55 b^3 x^2}-\frac{17 \sqrt{a x+b \sqrt[3]{x}}}{5 b^2 x^{8/3}}+\frac{3}{b x^{7/3} \sqrt{a x+b \sqrt[3]{x}}}","\frac{663 a^3 \sqrt{a x+b \sqrt[3]{x}}}{77 b^5 x^{2/3}}-\frac{1989 a^2 \sqrt{a x+b \sqrt[3]{x}}}{385 b^4 x^{4/3}}+\frac{663 a^{15/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{154 b^{21/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{221 a \sqrt{a x+b \sqrt[3]{x}}}{55 b^3 x^2}-\frac{17 \sqrt{a x+b \sqrt[3]{x}}}{5 b^2 x^{8/3}}+\frac{3}{b x^{7/3} \sqrt{a x+b \sqrt[3]{x}}}",1,"3/(b*x^(7/3)*Sqrt[b*x^(1/3) + a*x]) - (17*Sqrt[b*x^(1/3) + a*x])/(5*b^2*x^(8/3)) + (221*a*Sqrt[b*x^(1/3) + a*x])/(55*b^3*x^2) - (1989*a^2*Sqrt[b*x^(1/3) + a*x])/(385*b^4*x^(4/3)) + (663*a^3*Sqrt[b*x^(1/3) + a*x])/(77*b^5*x^(2/3)) + (663*a^(15/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(154*b^(21/4)*Sqrt[b*x^(1/3) + a*x])","A",9,6,19,0.3158,1,"{2018, 2023, 2025, 2011, 329, 220}"
166,1,471,0,0.6938253,"\int \frac{1}{x^4 \left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Int[1/(x^4*(b*x^(1/3) + a*x)^(3/2)),x]","-\frac{4807 a^{11/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{221 b^7 \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{24035 a^3 \sqrt{a x+b \sqrt[3]{x}}}{4641 b^5 x^{5/3}}-\frac{6555 a^2 \sqrt{a x+b \sqrt[3]{x}}}{1547 b^4 x^{7/3}}-\frac{4807 a^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{442 b^{27/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4807 a^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 b^{27/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4807 a^5 \sqrt{a x+b \sqrt[3]{x}}}{221 b^7 \sqrt[3]{x}}-\frac{4807 a^4 \sqrt{a x+b \sqrt[3]{x}}}{663 b^6 x}+\frac{437 a \sqrt{a x+b \sqrt[3]{x}}}{119 b^3 x^3}-\frac{23 \sqrt{a x+b \sqrt[3]{x}}}{7 b^2 x^{11/3}}+\frac{3}{b x^{10/3} \sqrt{a x+b \sqrt[3]{x}}}","-\frac{4807 a^{11/2} \sqrt[3]{x} \left(a x^{2/3}+b\right)}{221 b^7 \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{a x+b \sqrt[3]{x}}}+\frac{24035 a^3 \sqrt{a x+b \sqrt[3]{x}}}{4641 b^5 x^{5/3}}-\frac{6555 a^2 \sqrt{a x+b \sqrt[3]{x}}}{1547 b^4 x^{7/3}}-\frac{4807 a^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{442 b^{27/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4807 a^{21/4} \sqrt[6]{x} \left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right) \sqrt{\frac{a x^{2/3}+b}{\left(\sqrt{a} \sqrt[3]{x}+\sqrt{b}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt[6]{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{221 b^{27/4} \sqrt{a x+b \sqrt[3]{x}}}+\frac{4807 a^5 \sqrt{a x+b \sqrt[3]{x}}}{221 b^7 \sqrt[3]{x}}-\frac{4807 a^4 \sqrt{a x+b \sqrt[3]{x}}}{663 b^6 x}+\frac{437 a \sqrt{a x+b \sqrt[3]{x}}}{119 b^3 x^3}-\frac{23 \sqrt{a x+b \sqrt[3]{x}}}{7 b^2 x^{11/3}}+\frac{3}{b x^{10/3} \sqrt{a x+b \sqrt[3]{x}}}",1,"3/(b*x^(10/3)*Sqrt[b*x^(1/3) + a*x]) - (4807*a^(11/2)*(b + a*x^(2/3))*x^(1/3))/(221*b^7*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[b*x^(1/3) + a*x]) - (23*Sqrt[b*x^(1/3) + a*x])/(7*b^2*x^(11/3)) + (437*a*Sqrt[b*x^(1/3) + a*x])/(119*b^3*x^3) - (6555*a^2*Sqrt[b*x^(1/3) + a*x])/(1547*b^4*x^(7/3)) + (24035*a^3*Sqrt[b*x^(1/3) + a*x])/(4641*b^5*x^(5/3)) - (4807*a^4*Sqrt[b*x^(1/3) + a*x])/(663*b^6*x) + (4807*a^5*Sqrt[b*x^(1/3) + a*x])/(221*b^7*x^(1/3)) + (4807*a^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticE[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(221*b^(27/4)*Sqrt[b*x^(1/3) + a*x]) - (4807*a^(21/4)*(Sqrt[b] + Sqrt[a]*x^(1/3))*Sqrt[(b + a*x^(2/3))/(Sqrt[b] + Sqrt[a]*x^(1/3))^2]*x^(1/6)*EllipticF[2*ArcTan[(a^(1/4)*x^(1/6))/b^(1/4)], 1/2])/(442*b^(27/4)*Sqrt[b*x^(1/3) + a*x])","A",13,8,19,0.4211,1,"{2018, 2023, 2025, 2032, 329, 305, 220, 1196}"
167,1,371,0,0.6272823,"\int x^3 \sqrt{b x^{2/3}+a x} \, dx","Int[x^3*Sqrt[b*x^(2/3) + a*x],x]","\frac{8388608 b^{12} \left(a x+b x^{2/3}\right)^{3/2}}{152108775 a^{13} x}-\frac{4194304 b^{11} \left(a x+b x^{2/3}\right)^{3/2}}{50702925 a^{12} x^{2/3}}+\frac{1048576 b^{10} \left(a x+b x^{2/3}\right)^{3/2}}{10140585 a^{11} \sqrt[3]{x}}-\frac{524288 b^9 \left(a x+b x^{2/3}\right)^{3/2}}{4345965 a^{10}}+\frac{65536 b^8 \sqrt[3]{x} \left(a x+b x^{2/3}\right)^{3/2}}{482885 a^9}-\frac{360448 b^7 x^{2/3} \left(a x+b x^{2/3}\right)^{3/2}}{2414425 a^8}+\frac{90112 b^6 x \left(a x+b x^{2/3}\right)^{3/2}}{557175 a^7}-\frac{45056 b^5 x^{4/3} \left(a x+b x^{2/3}\right)^{3/2}}{260015 a^6}+\frac{2816 b^4 x^{5/3} \left(a x+b x^{2/3}\right)^{3/2}}{15295 a^5}-\frac{1408 b^3 x^2 \left(a x+b x^{2/3}\right)^{3/2}}{7245 a^4}+\frac{352 b^2 x^{7/3} \left(a x+b x^{2/3}\right)^{3/2}}{1725 a^3}-\frac{16 b x^{8/3} \left(a x+b x^{2/3}\right)^{3/2}}{75 a^2}+\frac{2 x^3 \left(a x+b x^{2/3}\right)^{3/2}}{9 a}","\frac{8388608 b^{12} \left(a x+b x^{2/3}\right)^{3/2}}{152108775 a^{13} x}-\frac{4194304 b^{11} \left(a x+b x^{2/3}\right)^{3/2}}{50702925 a^{12} x^{2/3}}+\frac{1048576 b^{10} \left(a x+b x^{2/3}\right)^{3/2}}{10140585 a^{11} \sqrt[3]{x}}-\frac{524288 b^9 \left(a x+b x^{2/3}\right)^{3/2}}{4345965 a^{10}}+\frac{65536 b^8 \sqrt[3]{x} \left(a x+b x^{2/3}\right)^{3/2}}{482885 a^9}-\frac{360448 b^7 x^{2/3} \left(a x+b x^{2/3}\right)^{3/2}}{2414425 a^8}+\frac{90112 b^6 x \left(a x+b x^{2/3}\right)^{3/2}}{557175 a^7}-\frac{45056 b^5 x^{4/3} \left(a x+b x^{2/3}\right)^{3/2}}{260015 a^6}+\frac{2816 b^4 x^{5/3} \left(a x+b x^{2/3}\right)^{3/2}}{15295 a^5}-\frac{1408 b^3 x^2 \left(a x+b x^{2/3}\right)^{3/2}}{7245 a^4}+\frac{352 b^2 x^{7/3} \left(a x+b x^{2/3}\right)^{3/2}}{1725 a^3}-\frac{16 b x^{8/3} \left(a x+b x^{2/3}\right)^{3/2}}{75 a^2}+\frac{2 x^3 \left(a x+b x^{2/3}\right)^{3/2}}{9 a}",1,"(-524288*b^9*(b*x^(2/3) + a*x)^(3/2))/(4345965*a^10) + (8388608*b^12*(b*x^(2/3) + a*x)^(3/2))/(152108775*a^13*x) - (4194304*b^11*(b*x^(2/3) + a*x)^(3/2))/(50702925*a^12*x^(2/3)) + (1048576*b^10*(b*x^(2/3) + a*x)^(3/2))/(10140585*a^11*x^(1/3)) + (65536*b^8*x^(1/3)*(b*x^(2/3) + a*x)^(3/2))/(482885*a^9) - (360448*b^7*x^(2/3)*(b*x^(2/3) + a*x)^(3/2))/(2414425*a^8) + (90112*b^6*x*(b*x^(2/3) + a*x)^(3/2))/(557175*a^7) - (45056*b^5*x^(4/3)*(b*x^(2/3) + a*x)^(3/2))/(260015*a^6) + (2816*b^4*x^(5/3)*(b*x^(2/3) + a*x)^(3/2))/(15295*a^5) - (1408*b^3*x^2*(b*x^(2/3) + a*x)^(3/2))/(7245*a^4) + (352*b^2*x^(7/3)*(b*x^(2/3) + a*x)^(3/2))/(1725*a^3) - (16*b*x^(8/3)*(b*x^(2/3) + a*x)^(3/2))/(75*a^2) + (2*x^3*(b*x^(2/3) + a*x)^(3/2))/(9*a)","A",13,3,19,0.1579,1,"{2016, 2002, 2014}"
168,1,283,0,0.4410852,"\int x^2 \sqrt{b x^{2/3}+a x} \, dx","Int[x^2*Sqrt[b*x^(2/3) + a*x],x]","-\frac{131072 b^9 \left(a x+b x^{2/3}\right)^{3/2}}{1616615 a^{10} x}+\frac{196608 b^8 \left(a x+b x^{2/3}\right)^{3/2}}{1616615 a^9 x^{2/3}}-\frac{49152 b^7 \left(a x+b x^{2/3}\right)^{3/2}}{323323 a^8 \sqrt[3]{x}}+\frac{8192 b^6 \left(a x+b x^{2/3}\right)^{3/2}}{46189 a^7}-\frac{9216 b^5 \sqrt[3]{x} \left(a x+b x^{2/3}\right)^{3/2}}{46189 a^6}+\frac{4608 b^4 x^{2/3} \left(a x+b x^{2/3}\right)^{3/2}}{20995 a^5}-\frac{384 b^3 x \left(a x+b x^{2/3}\right)^{3/2}}{1615 a^4}+\frac{576 b^2 x^{4/3} \left(a x+b x^{2/3}\right)^{3/2}}{2261 a^3}-\frac{36 b x^{5/3} \left(a x+b x^{2/3}\right)^{3/2}}{133 a^2}+\frac{2 x^2 \left(a x+b x^{2/3}\right)^{3/2}}{7 a}","-\frac{131072 b^9 \left(a x+b x^{2/3}\right)^{3/2}}{1616615 a^{10} x}+\frac{196608 b^8 \left(a x+b x^{2/3}\right)^{3/2}}{1616615 a^9 x^{2/3}}-\frac{49152 b^7 \left(a x+b x^{2/3}\right)^{3/2}}{323323 a^8 \sqrt[3]{x}}+\frac{8192 b^6 \left(a x+b x^{2/3}\right)^{3/2}}{46189 a^7}-\frac{9216 b^5 \sqrt[3]{x} \left(a x+b x^{2/3}\right)^{3/2}}{46189 a^6}+\frac{4608 b^4 x^{2/3} \left(a x+b x^{2/3}\right)^{3/2}}{20995 a^5}-\frac{384 b^3 x \left(a x+b x^{2/3}\right)^{3/2}}{1615 a^4}+\frac{576 b^2 x^{4/3} \left(a x+b x^{2/3}\right)^{3/2}}{2261 a^3}-\frac{36 b x^{5/3} \left(a x+b x^{2/3}\right)^{3/2}}{133 a^2}+\frac{2 x^2 \left(a x+b x^{2/3}\right)^{3/2}}{7 a}",1,"(8192*b^6*(b*x^(2/3) + a*x)^(3/2))/(46189*a^7) - (131072*b^9*(b*x^(2/3) + a*x)^(3/2))/(1616615*a^10*x) + (196608*b^8*(b*x^(2/3) + a*x)^(3/2))/(1616615*a^9*x^(2/3)) - (49152*b^7*(b*x^(2/3) + a*x)^(3/2))/(323323*a^8*x^(1/3)) - (9216*b^5*x^(1/3)*(b*x^(2/3) + a*x)^(3/2))/(46189*a^6) + (4608*b^4*x^(2/3)*(b*x^(2/3) + a*x)^(3/2))/(20995*a^5) - (384*b^3*x*(b*x^(2/3) + a*x)^(3/2))/(1615*a^4) + (576*b^2*x^(4/3)*(b*x^(2/3) + a*x)^(3/2))/(2261*a^3) - (36*b*x^(5/3)*(b*x^(2/3) + a*x)^(3/2))/(133*a^2) + (2*x^2*(b*x^(2/3) + a*x)^(3/2))/(7*a)","A",10,3,19,0.1579,1,"{2016, 2002, 2014}"
169,1,195,0,0.273272,"\int x \sqrt{b x^{2/3}+a x} \, dx","Int[x*Sqrt[b*x^(2/3) + a*x],x]","\frac{2048 b^6 \left(a x+b x^{2/3}\right)^{3/2}}{15015 a^7 x}-\frac{1024 b^5 \left(a x+b x^{2/3}\right)^{3/2}}{5005 a^6 x^{2/3}}+\frac{256 b^4 \left(a x+b x^{2/3}\right)^{3/2}}{1001 a^5 \sqrt[3]{x}}-\frac{128 b^3 \left(a x+b x^{2/3}\right)^{3/2}}{429 a^4}+\frac{48 b^2 \sqrt[3]{x} \left(a x+b x^{2/3}\right)^{3/2}}{143 a^3}-\frac{24 b x^{2/3} \left(a x+b x^{2/3}\right)^{3/2}}{65 a^2}+\frac{2 x \left(a x+b x^{2/3}\right)^{3/2}}{5 a}","\frac{2048 b^6 \left(a x+b x^{2/3}\right)^{3/2}}{15015 a^7 x}-\frac{1024 b^5 \left(a x+b x^{2/3}\right)^{3/2}}{5005 a^6 x^{2/3}}+\frac{256 b^4 \left(a x+b x^{2/3}\right)^{3/2}}{1001 a^5 \sqrt[3]{x}}-\frac{128 b^3 \left(a x+b x^{2/3}\right)^{3/2}}{429 a^4}+\frac{48 b^2 \sqrt[3]{x} \left(a x+b x^{2/3}\right)^{3/2}}{143 a^3}-\frac{24 b x^{2/3} \left(a x+b x^{2/3}\right)^{3/2}}{65 a^2}+\frac{2 x \left(a x+b x^{2/3}\right)^{3/2}}{5 a}",1,"(-128*b^3*(b*x^(2/3) + a*x)^(3/2))/(429*a^4) + (2048*b^6*(b*x^(2/3) + a*x)^(3/2))/(15015*a^7*x) - (1024*b^5*(b*x^(2/3) + a*x)^(3/2))/(5005*a^6*x^(2/3)) + (256*b^4*(b*x^(2/3) + a*x)^(3/2))/(1001*a^5*x^(1/3)) + (48*b^2*x^(1/3)*(b*x^(2/3) + a*x)^(3/2))/(143*a^3) - (24*b*x^(2/3)*(b*x^(2/3) + a*x)^(3/2))/(65*a^2) + (2*x*(b*x^(2/3) + a*x)^(3/2))/(5*a)","A",7,3,17,0.1765,1,"{2016, 2002, 2014}"
170,1,109,0,0.1367365,"\int \sqrt{b x^{2/3}+a x} \, dx","Int[Sqrt[b*x^(2/3) + a*x],x]","-\frac{32 b^3 \left(a x+b x^{2/3}\right)^{3/2}}{105 a^4 x}+\frac{16 b^2 \left(a x+b x^{2/3}\right)^{3/2}}{35 a^3 x^{2/3}}-\frac{4 b \left(a x+b x^{2/3}\right)^{3/2}}{7 a^2 \sqrt[3]{x}}+\frac{2 \left(a x+b x^{2/3}\right)^{3/2}}{3 a}","-\frac{32 b^3 \left(a x+b x^{2/3}\right)^{3/2}}{105 a^4 x}+\frac{16 b^2 \left(a x+b x^{2/3}\right)^{3/2}}{35 a^3 x^{2/3}}-\frac{4 b \left(a x+b x^{2/3}\right)^{3/2}}{7 a^2 \sqrt[3]{x}}+\frac{2 \left(a x+b x^{2/3}\right)^{3/2}}{3 a}",1,"(2*(b*x^(2/3) + a*x)^(3/2))/(3*a) - (32*b^3*(b*x^(2/3) + a*x)^(3/2))/(105*a^4*x) + (16*b^2*(b*x^(2/3) + a*x)^(3/2))/(35*a^3*x^(2/3)) - (4*b*(b*x^(2/3) + a*x)^(3/2))/(7*a^2*x^(1/3))","A",4,3,15,0.2000,1,"{2002, 2016, 2014}"
171,1,23,0,0.0404968,"\int \frac{\sqrt{b x^{2/3}+a x}}{x} \, dx","Int[Sqrt[b*x^(2/3) + a*x]/x,x]","\frac{2 \left(a x+b x^{2/3}\right)^{3/2}}{a x}","\frac{2 \left(a x+b x^{2/3}\right)^{3/2}}{a x}",1,"(2*(b*x^(2/3) + a*x)^(3/2))/(a*x)","A",1,1,19,0.05263,1,"{2014}"
172,1,90,0,0.1385823,"\int \frac{\sqrt{b x^{2/3}+a x}}{x^2} \, dx","Int[Sqrt[b*x^(2/3) + a*x]/x^2,x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{4 b^{3/2}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{4 b x^{2/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{2 x}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{4 b^{3/2}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{4 b x^{2/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{2 x}",1,"(-3*Sqrt[b*x^(2/3) + a*x])/(2*x) - (3*a*Sqrt[b*x^(2/3) + a*x])/(4*b*x^(2/3)) + (3*a^2*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(4*b^(3/2))","A",4,4,19,0.2105,1,"{2020, 2025, 2029, 206}"
173,1,178,0,0.2959093,"\int \frac{\sqrt{b x^{2/3}+a x}}{x^3} \, dx","Int[Sqrt[b*x^(2/3) + a*x]/x^3,x]","\frac{21 a^4 \sqrt{a x+b x^{2/3}}}{128 b^4 x^{2/3}}-\frac{7 a^3 \sqrt{a x+b x^{2/3}}}{64 b^3 x}+\frac{7 a^2 \sqrt{a x+b x^{2/3}}}{80 b^2 x^{4/3}}-\frac{21 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{128 b^{9/2}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{40 b x^{5/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{5 x^2}","\frac{21 a^4 \sqrt{a x+b x^{2/3}}}{128 b^4 x^{2/3}}-\frac{7 a^3 \sqrt{a x+b x^{2/3}}}{64 b^3 x}+\frac{7 a^2 \sqrt{a x+b x^{2/3}}}{80 b^2 x^{4/3}}-\frac{21 a^5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{128 b^{9/2}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{40 b x^{5/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{5 x^2}",1,"(-3*Sqrt[b*x^(2/3) + a*x])/(5*x^2) - (3*a*Sqrt[b*x^(2/3) + a*x])/(40*b*x^(5/3)) + (7*a^2*Sqrt[b*x^(2/3) + a*x])/(80*b^2*x^(4/3)) - (7*a^3*Sqrt[b*x^(2/3) + a*x])/(64*b^3*x) + (21*a^4*Sqrt[b*x^(2/3) + a*x])/(128*b^4*x^(2/3)) - (21*a^5*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(128*b^(9/2))","A",7,4,19,0.2105,1,"{2020, 2025, 2029, 206}"
174,1,266,0,0.4750033,"\int \frac{\sqrt{b x^{2/3}+a x}}{x^4} \, dx","Int[Sqrt[b*x^(2/3) + a*x]/x^4,x]","-\frac{1287 a^7 \sqrt{a x+b x^{2/3}}}{16384 b^7 x^{2/3}}+\frac{429 a^6 \sqrt{a x+b x^{2/3}}}{8192 b^6 x}-\frac{429 a^5 \sqrt{a x+b x^{2/3}}}{10240 b^5 x^{4/3}}+\frac{1287 a^4 \sqrt{a x+b x^{2/3}}}{35840 b^4 x^{5/3}}-\frac{143 a^3 \sqrt{a x+b x^{2/3}}}{4480 b^3 x^2}+\frac{13 a^2 \sqrt{a x+b x^{2/3}}}{448 b^2 x^{7/3}}+\frac{1287 a^8 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{16384 b^{15/2}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{112 b x^{8/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{8 x^3}","-\frac{1287 a^7 \sqrt{a x+b x^{2/3}}}{16384 b^7 x^{2/3}}+\frac{429 a^6 \sqrt{a x+b x^{2/3}}}{8192 b^6 x}-\frac{429 a^5 \sqrt{a x+b x^{2/3}}}{10240 b^5 x^{4/3}}+\frac{1287 a^4 \sqrt{a x+b x^{2/3}}}{35840 b^4 x^{5/3}}-\frac{143 a^3 \sqrt{a x+b x^{2/3}}}{4480 b^3 x^2}+\frac{13 a^2 \sqrt{a x+b x^{2/3}}}{448 b^2 x^{7/3}}+\frac{1287 a^8 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{16384 b^{15/2}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{112 b x^{8/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{8 x^3}",1,"(-3*Sqrt[b*x^(2/3) + a*x])/(8*x^3) - (3*a*Sqrt[b*x^(2/3) + a*x])/(112*b*x^(8/3)) + (13*a^2*Sqrt[b*x^(2/3) + a*x])/(448*b^2*x^(7/3)) - (143*a^3*Sqrt[b*x^(2/3) + a*x])/(4480*b^3*x^2) + (1287*a^4*Sqrt[b*x^(2/3) + a*x])/(35840*b^4*x^(5/3)) - (429*a^5*Sqrt[b*x^(2/3) + a*x])/(10240*b^5*x^(4/3)) + (429*a^6*Sqrt[b*x^(2/3) + a*x])/(8192*b^6*x) - (1287*a^7*Sqrt[b*x^(2/3) + a*x])/(16384*b^7*x^(2/3)) + (1287*a^8*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(16384*b^(15/2))","A",10,4,19,0.2105,1,"{2020, 2025, 2029, 206}"
175,1,354,0,0.6600359,"\int \frac{\sqrt{b x^{2/3}+a x}}{x^5} \, dx","Int[Sqrt[b*x^(2/3) + a*x]/x^5,x]","\frac{12597 a^{10} \sqrt{a x+b x^{2/3}}}{262144 b^{10} x^{2/3}}-\frac{4199 a^9 \sqrt{a x+b x^{2/3}}}{131072 b^9 x}+\frac{4199 a^8 \sqrt{a x+b x^{2/3}}}{163840 b^8 x^{4/3}}-\frac{12597 a^7 \sqrt{a x+b x^{2/3}}}{573440 b^7 x^{5/3}}+\frac{4199 a^6 \sqrt{a x+b x^{2/3}}}{215040 b^6 x^2}-\frac{4199 a^5 \sqrt{a x+b x^{2/3}}}{236544 b^5 x^{7/3}}+\frac{323 a^4 \sqrt{a x+b x^{2/3}}}{19712 b^4 x^{8/3}}-\frac{323 a^3 \sqrt{a x+b x^{2/3}}}{21120 b^3 x^3}+\frac{19 a^2 \sqrt{a x+b x^{2/3}}}{1320 b^2 x^{10/3}}-\frac{12597 a^{11} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{262144 b^{21/2}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{220 b x^{11/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{11 x^4}","\frac{12597 a^{10} \sqrt{a x+b x^{2/3}}}{262144 b^{10} x^{2/3}}-\frac{4199 a^9 \sqrt{a x+b x^{2/3}}}{131072 b^9 x}+\frac{4199 a^8 \sqrt{a x+b x^{2/3}}}{163840 b^8 x^{4/3}}-\frac{12597 a^7 \sqrt{a x+b x^{2/3}}}{573440 b^7 x^{5/3}}+\frac{4199 a^6 \sqrt{a x+b x^{2/3}}}{215040 b^6 x^2}-\frac{4199 a^5 \sqrt{a x+b x^{2/3}}}{236544 b^5 x^{7/3}}+\frac{323 a^4 \sqrt{a x+b x^{2/3}}}{19712 b^4 x^{8/3}}-\frac{323 a^3 \sqrt{a x+b x^{2/3}}}{21120 b^3 x^3}+\frac{19 a^2 \sqrt{a x+b x^{2/3}}}{1320 b^2 x^{10/3}}-\frac{12597 a^{11} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{262144 b^{21/2}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{220 b x^{11/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{11 x^4}",1,"(-3*Sqrt[b*x^(2/3) + a*x])/(11*x^4) - (3*a*Sqrt[b*x^(2/3) + a*x])/(220*b*x^(11/3)) + (19*a^2*Sqrt[b*x^(2/3) + a*x])/(1320*b^2*x^(10/3)) - (323*a^3*Sqrt[b*x^(2/3) + a*x])/(21120*b^3*x^3) + (323*a^4*Sqrt[b*x^(2/3) + a*x])/(19712*b^4*x^(8/3)) - (4199*a^5*Sqrt[b*x^(2/3) + a*x])/(236544*b^5*x^(7/3)) + (4199*a^6*Sqrt[b*x^(2/3) + a*x])/(215040*b^6*x^2) - (12597*a^7*Sqrt[b*x^(2/3) + a*x])/(573440*b^7*x^(5/3)) + (4199*a^8*Sqrt[b*x^(2/3) + a*x])/(163840*b^8*x^(4/3)) - (4199*a^9*Sqrt[b*x^(2/3) + a*x])/(131072*b^9*x) + (12597*a^10*Sqrt[b*x^(2/3) + a*x])/(262144*b^10*x^(2/3)) - (12597*a^11*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(262144*b^(21/2))","A",13,4,19,0.2105,1,"{2020, 2025, 2029, 206}"
176,1,343,0,0.6162859,"\int x^2 \left(b x^{2/3}+a x\right)^{3/2} \, dx","Int[x^2*(b*x^(2/3) + a*x)^(3/2),x]","-\frac{1048576 b^{11} \left(a x+b x^{2/3}\right)^{5/2}}{152108775 a^{12} x^{5/3}}+\frac{524288 b^{10} \left(a x+b x^{2/3}\right)^{5/2}}{30421755 a^{11} x^{4/3}}-\frac{131072 b^9 \left(a x+b x^{2/3}\right)^{5/2}}{4345965 a^{10} x}+\frac{65536 b^8 \left(a x+b x^{2/3}\right)^{5/2}}{1448655 a^9 x^{2/3}}-\frac{90112 b^7 \left(a x+b x^{2/3}\right)^{5/2}}{1448655 a^8 \sqrt[3]{x}}+\frac{45056 b^6 \left(a x+b x^{2/3}\right)^{5/2}}{557175 a^7}-\frac{11264 b^5 \sqrt[3]{x} \left(a x+b x^{2/3}\right)^{5/2}}{111435 a^6}+\frac{5632 b^4 x^{2/3} \left(a x+b x^{2/3}\right)^{5/2}}{45885 a^5}-\frac{352 b^3 x \left(a x+b x^{2/3}\right)^{5/2}}{2415 a^4}+\frac{176 b^2 x^{4/3} \left(a x+b x^{2/3}\right)^{5/2}}{1035 a^3}-\frac{44 b x^{5/3} \left(a x+b x^{2/3}\right)^{5/2}}{225 a^2}+\frac{2 x^2 \left(a x+b x^{2/3}\right)^{5/2}}{9 a}","-\frac{1048576 b^{11} \left(a x+b x^{2/3}\right)^{5/2}}{152108775 a^{12} x^{5/3}}+\frac{524288 b^{10} \left(a x+b x^{2/3}\right)^{5/2}}{30421755 a^{11} x^{4/3}}-\frac{131072 b^9 \left(a x+b x^{2/3}\right)^{5/2}}{4345965 a^{10} x}+\frac{65536 b^8 \left(a x+b x^{2/3}\right)^{5/2}}{1448655 a^9 x^{2/3}}-\frac{90112 b^7 \left(a x+b x^{2/3}\right)^{5/2}}{1448655 a^8 \sqrt[3]{x}}+\frac{45056 b^6 \left(a x+b x^{2/3}\right)^{5/2}}{557175 a^7}-\frac{11264 b^5 \sqrt[3]{x} \left(a x+b x^{2/3}\right)^{5/2}}{111435 a^6}+\frac{5632 b^4 x^{2/3} \left(a x+b x^{2/3}\right)^{5/2}}{45885 a^5}-\frac{352 b^3 x \left(a x+b x^{2/3}\right)^{5/2}}{2415 a^4}+\frac{176 b^2 x^{4/3} \left(a x+b x^{2/3}\right)^{5/2}}{1035 a^3}-\frac{44 b x^{5/3} \left(a x+b x^{2/3}\right)^{5/2}}{225 a^2}+\frac{2 x^2 \left(a x+b x^{2/3}\right)^{5/2}}{9 a}",1,"(45056*b^6*(b*x^(2/3) + a*x)^(5/2))/(557175*a^7) - (1048576*b^11*(b*x^(2/3) + a*x)^(5/2))/(152108775*a^12*x^(5/3)) + (524288*b^10*(b*x^(2/3) + a*x)^(5/2))/(30421755*a^11*x^(4/3)) - (131072*b^9*(b*x^(2/3) + a*x)^(5/2))/(4345965*a^10*x) + (65536*b^8*(b*x^(2/3) + a*x)^(5/2))/(1448655*a^9*x^(2/3)) - (90112*b^7*(b*x^(2/3) + a*x)^(5/2))/(1448655*a^8*x^(1/3)) - (11264*b^5*x^(1/3)*(b*x^(2/3) + a*x)^(5/2))/(111435*a^6) + (5632*b^4*x^(2/3)*(b*x^(2/3) + a*x)^(5/2))/(45885*a^5) - (352*b^3*x*(b*x^(2/3) + a*x)^(5/2))/(2415*a^4) + (176*b^2*x^(4/3)*(b*x^(2/3) + a*x)^(5/2))/(1035*a^3) - (44*b*x^(5/3)*(b*x^(2/3) + a*x)^(5/2))/(225*a^2) + (2*x^2*(b*x^(2/3) + a*x)^(5/2))/(9*a)","A",12,3,19,0.1579,1,"{2016, 2002, 2014}"
177,1,255,0,0.4220497,"\int x \left(b x^{2/3}+a x\right)^{3/2} \, dx","Int[x*(b*x^(2/3) + a*x)^(3/2),x]","\frac{65536 b^8 \left(a x+b x^{2/3}\right)^{5/2}}{4849845 a^9 x^{5/3}}-\frac{32768 b^7 \left(a x+b x^{2/3}\right)^{5/2}}{969969 a^8 x^{4/3}}+\frac{8192 b^6 \left(a x+b x^{2/3}\right)^{5/2}}{138567 a^7 x}-\frac{4096 b^5 \left(a x+b x^{2/3}\right)^{5/2}}{46189 a^6 x^{2/3}}+\frac{512 b^4 \left(a x+b x^{2/3}\right)^{5/2}}{4199 a^5 \sqrt[3]{x}}-\frac{256 b^3 \left(a x+b x^{2/3}\right)^{5/2}}{1615 a^4}+\frac{64 b^2 \sqrt[3]{x} \left(a x+b x^{2/3}\right)^{5/2}}{323 a^3}-\frac{32 b x^{2/3} \left(a x+b x^{2/3}\right)^{5/2}}{133 a^2}+\frac{2 x \left(a x+b x^{2/3}\right)^{5/2}}{7 a}","\frac{65536 b^8 \left(a x+b x^{2/3}\right)^{5/2}}{4849845 a^9 x^{5/3}}-\frac{32768 b^7 \left(a x+b x^{2/3}\right)^{5/2}}{969969 a^8 x^{4/3}}+\frac{8192 b^6 \left(a x+b x^{2/3}\right)^{5/2}}{138567 a^7 x}-\frac{4096 b^5 \left(a x+b x^{2/3}\right)^{5/2}}{46189 a^6 x^{2/3}}+\frac{512 b^4 \left(a x+b x^{2/3}\right)^{5/2}}{4199 a^5 \sqrt[3]{x}}-\frac{256 b^3 \left(a x+b x^{2/3}\right)^{5/2}}{1615 a^4}+\frac{64 b^2 \sqrt[3]{x} \left(a x+b x^{2/3}\right)^{5/2}}{323 a^3}-\frac{32 b x^{2/3} \left(a x+b x^{2/3}\right)^{5/2}}{133 a^2}+\frac{2 x \left(a x+b x^{2/3}\right)^{5/2}}{7 a}",1,"(-256*b^3*(b*x^(2/3) + a*x)^(5/2))/(1615*a^4) + (65536*b^8*(b*x^(2/3) + a*x)^(5/2))/(4849845*a^9*x^(5/3)) - (32768*b^7*(b*x^(2/3) + a*x)^(5/2))/(969969*a^8*x^(4/3)) + (8192*b^6*(b*x^(2/3) + a*x)^(5/2))/(138567*a^7*x) - (4096*b^5*(b*x^(2/3) + a*x)^(5/2))/(46189*a^6*x^(2/3)) + (512*b^4*(b*x^(2/3) + a*x)^(5/2))/(4199*a^5*x^(1/3)) + (64*b^2*x^(1/3)*(b*x^(2/3) + a*x)^(5/2))/(323*a^3) - (32*b*x^(2/3)*(b*x^(2/3) + a*x)^(5/2))/(133*a^2) + (2*x*(b*x^(2/3) + a*x)^(5/2))/(7*a)","A",9,3,17,0.1765,1,"{2016, 2002, 2014}"
178,1,169,0,0.2494761,"\int \left(b x^{2/3}+a x\right)^{3/2} \, dx","Int[(b*x^(2/3) + a*x)^(3/2),x]","-\frac{512 b^5 \left(a x+b x^{2/3}\right)^{5/2}}{15015 a^6 x^{5/3}}+\frac{256 b^4 \left(a x+b x^{2/3}\right)^{5/2}}{3003 a^5 x^{4/3}}-\frac{64 b^3 \left(a x+b x^{2/3}\right)^{5/2}}{429 a^4 x}+\frac{32 b^2 \left(a x+b x^{2/3}\right)^{5/2}}{143 a^3 x^{2/3}}-\frac{4 b \left(a x+b x^{2/3}\right)^{5/2}}{13 a^2 \sqrt[3]{x}}+\frac{2 \left(a x+b x^{2/3}\right)^{5/2}}{5 a}","-\frac{512 b^5 \left(a x+b x^{2/3}\right)^{5/2}}{15015 a^6 x^{5/3}}+\frac{256 b^4 \left(a x+b x^{2/3}\right)^{5/2}}{3003 a^5 x^{4/3}}-\frac{64 b^3 \left(a x+b x^{2/3}\right)^{5/2}}{429 a^4 x}+\frac{32 b^2 \left(a x+b x^{2/3}\right)^{5/2}}{143 a^3 x^{2/3}}-\frac{4 b \left(a x+b x^{2/3}\right)^{5/2}}{13 a^2 \sqrt[3]{x}}+\frac{2 \left(a x+b x^{2/3}\right)^{5/2}}{5 a}",1,"(2*(b*x^(2/3) + a*x)^(5/2))/(5*a) - (512*b^5*(b*x^(2/3) + a*x)^(5/2))/(15015*a^6*x^(5/3)) + (256*b^4*(b*x^(2/3) + a*x)^(5/2))/(3003*a^5*x^(4/3)) - (64*b^3*(b*x^(2/3) + a*x)^(5/2))/(429*a^4*x) + (32*b^2*(b*x^(2/3) + a*x)^(5/2))/(143*a^3*x^(2/3)) - (4*b*(b*x^(2/3) + a*x)^(5/2))/(13*a^2*x^(1/3))","A",6,3,15,0.2000,1,"{2002, 2016, 2014}"
179,1,84,0,0.1387792,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x} \, dx","Int[(b*x^(2/3) + a*x)^(3/2)/x,x]","\frac{16 b^2 \left(a x+b x^{2/3}\right)^{5/2}}{105 a^3 x^{5/3}}-\frac{8 b \left(a x+b x^{2/3}\right)^{5/2}}{21 a^2 x^{4/3}}+\frac{2 \left(a x+b x^{2/3}\right)^{5/2}}{3 a x}","\frac{16 b^2 \left(a x+b x^{2/3}\right)^{5/2}}{105 a^3 x^{5/3}}-\frac{8 b \left(a x+b x^{2/3}\right)^{5/2}}{21 a^2 x^{4/3}}+\frac{2 \left(a x+b x^{2/3}\right)^{5/2}}{3 a x}",1,"(16*b^2*(b*x^(2/3) + a*x)^(5/2))/(105*a^3*x^(5/3)) - (8*b*(b*x^(2/3) + a*x)^(5/2))/(21*a^2*x^(4/3)) + (2*(b*x^(2/3) + a*x)^(5/2))/(3*a*x)","A",3,2,19,0.1053,1,"{2016, 2014}"
180,1,78,0,0.1369976,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x^2} \, dx","Int[(b*x^(2/3) + a*x)^(3/2)/x^2,x]","-6 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)+\frac{6 b \sqrt{a x+b x^{2/3}}}{\sqrt[3]{x}}+\frac{2 \left(a x+b x^{2/3}\right)^{3/2}}{x}","-6 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)+\frac{6 b \sqrt{a x+b x^{2/3}}}{\sqrt[3]{x}}+\frac{2 \left(a x+b x^{2/3}\right)^{3/2}}{x}",1,"(6*b*Sqrt[b*x^(2/3) + a*x])/x^(1/3) + (2*(b*x^(2/3) + a*x)^(3/2))/x - 6*b^(3/2)*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]]","A",4,3,19,0.1579,1,"{2021, 2029, 206}"
181,1,113,0,0.183797,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x^3} \, dx","Int[(b*x^(2/3) + a*x)^(3/2)/x^3,x]","\frac{3 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{8 b^{3/2}}-\frac{3 a^2 \sqrt{a x+b x^{2/3}}}{8 b x^{2/3}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{4 x}-\frac{\left(a x+b x^{2/3}\right)^{3/2}}{x^2}","\frac{3 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{8 b^{3/2}}-\frac{3 a^2 \sqrt{a x+b x^{2/3}}}{8 b x^{2/3}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{4 x}-\frac{\left(a x+b x^{2/3}\right)^{3/2}}{x^2}",1,"(-3*a*Sqrt[b*x^(2/3) + a*x])/(4*x) - (3*a^2*Sqrt[b*x^(2/3) + a*x])/(8*b*x^(2/3)) - (b*x^(2/3) + a*x)^(3/2)/x^2 + (3*a^3*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(8*b^(3/2))","A",5,4,19,0.2105,1,"{2020, 2025, 2029, 206}"
182,1,203,0,0.3403697,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x^4} \, dx","Int[(b*x^(2/3) + a*x)^(3/2)/x^4,x]","\frac{21 a^5 \sqrt{a x+b x^{2/3}}}{512 b^4 x^{2/3}}-\frac{7 a^4 \sqrt{a x+b x^{2/3}}}{256 b^3 x}+\frac{7 a^3 \sqrt{a x+b x^{2/3}}}{320 b^2 x^{4/3}}-\frac{21 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{512 b^{9/2}}-\frac{3 a^2 \sqrt{a x+b x^{2/3}}}{160 b x^{5/3}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{20 x^2}-\frac{\left(a x+b x^{2/3}\right)^{3/2}}{2 x^3}","\frac{21 a^5 \sqrt{a x+b x^{2/3}}}{512 b^4 x^{2/3}}-\frac{7 a^4 \sqrt{a x+b x^{2/3}}}{256 b^3 x}+\frac{7 a^3 \sqrt{a x+b x^{2/3}}}{320 b^2 x^{4/3}}-\frac{21 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{512 b^{9/2}}-\frac{3 a^2 \sqrt{a x+b x^{2/3}}}{160 b x^{5/3}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{20 x^2}-\frac{\left(a x+b x^{2/3}\right)^{3/2}}{2 x^3}",1,"(-3*a*Sqrt[b*x^(2/3) + a*x])/(20*x^2) - (3*a^2*Sqrt[b*x^(2/3) + a*x])/(160*b*x^(5/3)) + (7*a^3*Sqrt[b*x^(2/3) + a*x])/(320*b^2*x^(4/3)) - (7*a^4*Sqrt[b*x^(2/3) + a*x])/(256*b^3*x) + (21*a^5*Sqrt[b*x^(2/3) + a*x])/(512*b^4*x^(2/3)) - (b*x^(2/3) + a*x)^(3/2)/(2*x^3) - (21*a^6*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(512*b^(9/2))","A",8,4,19,0.2105,1,"{2020, 2025, 2029, 206}"
183,1,291,0,0.5215618,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x^5} \, dx","Int[(b*x^(2/3) + a*x)^(3/2)/x^5,x]","-\frac{429 a^8 \sqrt{a x+b x^{2/3}}}{32768 b^7 x^{2/3}}+\frac{143 a^7 \sqrt{a x+b x^{2/3}}}{16384 b^6 x}-\frac{143 a^6 \sqrt{a x+b x^{2/3}}}{20480 b^5 x^{4/3}}+\frac{429 a^5 \sqrt{a x+b x^{2/3}}}{71680 b^4 x^{5/3}}-\frac{143 a^4 \sqrt{a x+b x^{2/3}}}{26880 b^3 x^2}+\frac{13 a^3 \sqrt{a x+b x^{2/3}}}{2688 b^2 x^{7/3}}+\frac{429 a^9 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{32768 b^{15/2}}-\frac{a^2 \sqrt{a x+b x^{2/3}}}{224 b x^{8/3}}-\frac{a \sqrt{a x+b x^{2/3}}}{16 x^3}-\frac{\left(a x+b x^{2/3}\right)^{3/2}}{3 x^4}","-\frac{429 a^8 \sqrt{a x+b x^{2/3}}}{32768 b^7 x^{2/3}}+\frac{143 a^7 \sqrt{a x+b x^{2/3}}}{16384 b^6 x}-\frac{143 a^6 \sqrt{a x+b x^{2/3}}}{20480 b^5 x^{4/3}}+\frac{429 a^5 \sqrt{a x+b x^{2/3}}}{71680 b^4 x^{5/3}}-\frac{143 a^4 \sqrt{a x+b x^{2/3}}}{26880 b^3 x^2}+\frac{13 a^3 \sqrt{a x+b x^{2/3}}}{2688 b^2 x^{7/3}}+\frac{429 a^9 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{32768 b^{15/2}}-\frac{a^2 \sqrt{a x+b x^{2/3}}}{224 b x^{8/3}}-\frac{a \sqrt{a x+b x^{2/3}}}{16 x^3}-\frac{\left(a x+b x^{2/3}\right)^{3/2}}{3 x^4}",1,"-(a*Sqrt[b*x^(2/3) + a*x])/(16*x^3) - (a^2*Sqrt[b*x^(2/3) + a*x])/(224*b*x^(8/3)) + (13*a^3*Sqrt[b*x^(2/3) + a*x])/(2688*b^2*x^(7/3)) - (143*a^4*Sqrt[b*x^(2/3) + a*x])/(26880*b^3*x^2) + (429*a^5*Sqrt[b*x^(2/3) + a*x])/(71680*b^4*x^(5/3)) - (143*a^6*Sqrt[b*x^(2/3) + a*x])/(20480*b^5*x^(4/3)) + (143*a^7*Sqrt[b*x^(2/3) + a*x])/(16384*b^6*x) - (429*a^8*Sqrt[b*x^(2/3) + a*x])/(32768*b^7*x^(2/3)) - (b*x^(2/3) + a*x)^(3/2)/(3*x^4) + (429*a^9*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(32768*b^(15/2))","A",11,4,19,0.2105,1,"{2020, 2025, 2029, 206}"
184,1,379,0,0.7184151,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x^6} \, dx","Int[(b*x^(2/3) + a*x)^(3/2)/x^6,x]","\frac{12597 a^{11} \sqrt{a x+b x^{2/3}}}{2097152 b^{10} x^{2/3}}-\frac{4199 a^{10} \sqrt{a x+b x^{2/3}}}{1048576 b^9 x}+\frac{4199 a^9 \sqrt{a x+b x^{2/3}}}{1310720 b^8 x^{4/3}}-\frac{12597 a^8 \sqrt{a x+b x^{2/3}}}{4587520 b^7 x^{5/3}}+\frac{4199 a^7 \sqrt{a x+b x^{2/3}}}{1720320 b^6 x^2}-\frac{4199 a^6 \sqrt{a x+b x^{2/3}}}{1892352 b^5 x^{7/3}}+\frac{323 a^5 \sqrt{a x+b x^{2/3}}}{157696 b^4 x^{8/3}}-\frac{323 a^4 \sqrt{a x+b x^{2/3}}}{168960 b^3 x^3}+\frac{19 a^3 \sqrt{a x+b x^{2/3}}}{10560 b^2 x^{10/3}}-\frac{12597 a^{12} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{2097152 b^{21/2}}-\frac{3 a^2 \sqrt{a x+b x^{2/3}}}{1760 b x^{11/3}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{88 x^4}-\frac{\left(a x+b x^{2/3}\right)^{3/2}}{4 x^5}","\frac{12597 a^{11} \sqrt{a x+b x^{2/3}}}{2097152 b^{10} x^{2/3}}-\frac{4199 a^{10} \sqrt{a x+b x^{2/3}}}{1048576 b^9 x}+\frac{4199 a^9 \sqrt{a x+b x^{2/3}}}{1310720 b^8 x^{4/3}}-\frac{12597 a^8 \sqrt{a x+b x^{2/3}}}{4587520 b^7 x^{5/3}}+\frac{4199 a^7 \sqrt{a x+b x^{2/3}}}{1720320 b^6 x^2}-\frac{4199 a^6 \sqrt{a x+b x^{2/3}}}{1892352 b^5 x^{7/3}}+\frac{323 a^5 \sqrt{a x+b x^{2/3}}}{157696 b^4 x^{8/3}}-\frac{323 a^4 \sqrt{a x+b x^{2/3}}}{168960 b^3 x^3}+\frac{19 a^3 \sqrt{a x+b x^{2/3}}}{10560 b^2 x^{10/3}}-\frac{12597 a^{12} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{2097152 b^{21/2}}-\frac{3 a^2 \sqrt{a x+b x^{2/3}}}{1760 b x^{11/3}}-\frac{3 a \sqrt{a x+b x^{2/3}}}{88 x^4}-\frac{\left(a x+b x^{2/3}\right)^{3/2}}{4 x^5}",1,"(-3*a*Sqrt[b*x^(2/3) + a*x])/(88*x^4) - (3*a^2*Sqrt[b*x^(2/3) + a*x])/(1760*b*x^(11/3)) + (19*a^3*Sqrt[b*x^(2/3) + a*x])/(10560*b^2*x^(10/3)) - (323*a^4*Sqrt[b*x^(2/3) + a*x])/(168960*b^3*x^3) + (323*a^5*Sqrt[b*x^(2/3) + a*x])/(157696*b^4*x^(8/3)) - (4199*a^6*Sqrt[b*x^(2/3) + a*x])/(1892352*b^5*x^(7/3)) + (4199*a^7*Sqrt[b*x^(2/3) + a*x])/(1720320*b^6*x^2) - (12597*a^8*Sqrt[b*x^(2/3) + a*x])/(4587520*b^7*x^(5/3)) + (4199*a^9*Sqrt[b*x^(2/3) + a*x])/(1310720*b^8*x^(4/3)) - (4199*a^10*Sqrt[b*x^(2/3) + a*x])/(1048576*b^9*x) + (12597*a^11*Sqrt[b*x^(2/3) + a*x])/(2097152*b^10*x^(2/3)) - (b*x^(2/3) + a*x)^(3/2)/(4*x^5) - (12597*a^12*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(2097152*b^(21/2))","A",14,4,19,0.2105,1,"{2020, 2025, 2029, 206}"
185,1,401,0,0.7281132,"\int \frac{x^4}{\sqrt{b x^{2/3}+a x}} \, dx","Int[x^4/Sqrt[b*x^(2/3) + a*x],x]","-\frac{16777216 b^{13} \sqrt{a x+b x^{2/3}}}{11700675 a^{14} \sqrt[3]{x}}+\frac{8388608 b^{12} \sqrt{a x+b x^{2/3}}}{11700675 a^{13}}-\frac{2097152 b^{11} \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{3900225 a^{12}}+\frac{1048576 b^{10} x^{2/3} \sqrt{a x+b x^{2/3}}}{2340135 a^{11}}-\frac{131072 b^9 x \sqrt{a x+b x^{2/3}}}{334305 a^{10}}+\frac{65536 b^8 x^{4/3} \sqrt{a x+b x^{2/3}}}{185725 a^9}-\frac{180224 b^7 x^{5/3} \sqrt{a x+b x^{2/3}}}{557175 a^8}+\frac{1171456 b^6 x^2 \sqrt{a x+b x^{2/3}}}{3900225 a^7}-\frac{73216 b^5 x^{7/3} \sqrt{a x+b x^{2/3}}}{260015 a^6}+\frac{36608 b^4 x^{8/3} \sqrt{a x+b x^{2/3}}}{137655 a^5}-\frac{9152 b^3 x^3 \sqrt{a x+b x^{2/3}}}{36225 a^4}+\frac{416 b^2 x^{10/3} \sqrt{a x+b x^{2/3}}}{1725 a^3}-\frac{52 b x^{11/3} \sqrt{a x+b x^{2/3}}}{225 a^2}+\frac{2 x^4 \sqrt{a x+b x^{2/3}}}{9 a}","-\frac{16777216 b^{13} \sqrt{a x+b x^{2/3}}}{11700675 a^{14} \sqrt[3]{x}}+\frac{8388608 b^{12} \sqrt{a x+b x^{2/3}}}{11700675 a^{13}}-\frac{2097152 b^{11} \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{3900225 a^{12}}+\frac{1048576 b^{10} x^{2/3} \sqrt{a x+b x^{2/3}}}{2340135 a^{11}}-\frac{131072 b^9 x \sqrt{a x+b x^{2/3}}}{334305 a^{10}}+\frac{65536 b^8 x^{4/3} \sqrt{a x+b x^{2/3}}}{185725 a^9}-\frac{180224 b^7 x^{5/3} \sqrt{a x+b x^{2/3}}}{557175 a^8}+\frac{1171456 b^6 x^2 \sqrt{a x+b x^{2/3}}}{3900225 a^7}-\frac{73216 b^5 x^{7/3} \sqrt{a x+b x^{2/3}}}{260015 a^6}+\frac{36608 b^4 x^{8/3} \sqrt{a x+b x^{2/3}}}{137655 a^5}-\frac{9152 b^3 x^3 \sqrt{a x+b x^{2/3}}}{36225 a^4}+\frac{416 b^2 x^{10/3} \sqrt{a x+b x^{2/3}}}{1725 a^3}-\frac{52 b x^{11/3} \sqrt{a x+b x^{2/3}}}{225 a^2}+\frac{2 x^4 \sqrt{a x+b x^{2/3}}}{9 a}",1,"(8388608*b^12*Sqrt[b*x^(2/3) + a*x])/(11700675*a^13) - (16777216*b^13*Sqrt[b*x^(2/3) + a*x])/(11700675*a^14*x^(1/3)) - (2097152*b^11*x^(1/3)*Sqrt[b*x^(2/3) + a*x])/(3900225*a^12) + (1048576*b^10*x^(2/3)*Sqrt[b*x^(2/3) + a*x])/(2340135*a^11) - (131072*b^9*x*Sqrt[b*x^(2/3) + a*x])/(334305*a^10) + (65536*b^8*x^(4/3)*Sqrt[b*x^(2/3) + a*x])/(185725*a^9) - (180224*b^7*x^(5/3)*Sqrt[b*x^(2/3) + a*x])/(557175*a^8) + (1171456*b^6*x^2*Sqrt[b*x^(2/3) + a*x])/(3900225*a^7) - (73216*b^5*x^(7/3)*Sqrt[b*x^(2/3) + a*x])/(260015*a^6) + (36608*b^4*x^(8/3)*Sqrt[b*x^(2/3) + a*x])/(137655*a^5) - (9152*b^3*x^3*Sqrt[b*x^(2/3) + a*x])/(36225*a^4) + (416*b^2*x^(10/3)*Sqrt[b*x^(2/3) + a*x])/(1725*a^3) - (52*b*x^(11/3)*Sqrt[b*x^(2/3) + a*x])/(225*a^2) + (2*x^4*Sqrt[b*x^(2/3) + a*x])/(9*a)","A",14,3,19,0.1579,1,"{2016, 2002, 2014}"
186,1,313,0,0.5309203,"\int \frac{x^3}{\sqrt{b x^{2/3}+a x}} \, dx","Int[x^3/Sqrt[b*x^(2/3) + a*x],x]","\frac{524288 b^{10} \sqrt{a x+b x^{2/3}}}{323323 a^{11} \sqrt[3]{x}}-\frac{262144 b^9 \sqrt{a x+b x^{2/3}}}{323323 a^{10}}+\frac{196608 b^8 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{323323 a^9}-\frac{163840 b^7 x^{2/3} \sqrt{a x+b x^{2/3}}}{323323 a^8}+\frac{20480 b^6 x \sqrt{a x+b x^{2/3}}}{46189 a^7}-\frac{18432 b^5 x^{4/3} \sqrt{a x+b x^{2/3}}}{46189 a^6}+\frac{1536 b^4 x^{5/3} \sqrt{a x+b x^{2/3}}}{4199 a^5}-\frac{768 b^3 x^2 \sqrt{a x+b x^{2/3}}}{2261 a^4}+\frac{720 b^2 x^{7/3} \sqrt{a x+b x^{2/3}}}{2261 a^3}-\frac{40 b x^{8/3} \sqrt{a x+b x^{2/3}}}{133 a^2}+\frac{2 x^3 \sqrt{a x+b x^{2/3}}}{7 a}","\frac{524288 b^{10} \sqrt{a x+b x^{2/3}}}{323323 a^{11} \sqrt[3]{x}}-\frac{262144 b^9 \sqrt{a x+b x^{2/3}}}{323323 a^{10}}+\frac{196608 b^8 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{323323 a^9}-\frac{163840 b^7 x^{2/3} \sqrt{a x+b x^{2/3}}}{323323 a^8}+\frac{20480 b^6 x \sqrt{a x+b x^{2/3}}}{46189 a^7}-\frac{18432 b^5 x^{4/3} \sqrt{a x+b x^{2/3}}}{46189 a^6}+\frac{1536 b^4 x^{5/3} \sqrt{a x+b x^{2/3}}}{4199 a^5}-\frac{768 b^3 x^2 \sqrt{a x+b x^{2/3}}}{2261 a^4}+\frac{720 b^2 x^{7/3} \sqrt{a x+b x^{2/3}}}{2261 a^3}-\frac{40 b x^{8/3} \sqrt{a x+b x^{2/3}}}{133 a^2}+\frac{2 x^3 \sqrt{a x+b x^{2/3}}}{7 a}",1,"(-262144*b^9*Sqrt[b*x^(2/3) + a*x])/(323323*a^10) + (524288*b^10*Sqrt[b*x^(2/3) + a*x])/(323323*a^11*x^(1/3)) + (196608*b^8*x^(1/3)*Sqrt[b*x^(2/3) + a*x])/(323323*a^9) - (163840*b^7*x^(2/3)*Sqrt[b*x^(2/3) + a*x])/(323323*a^8) + (20480*b^6*x*Sqrt[b*x^(2/3) + a*x])/(46189*a^7) - (18432*b^5*x^(4/3)*Sqrt[b*x^(2/3) + a*x])/(46189*a^6) + (1536*b^4*x^(5/3)*Sqrt[b*x^(2/3) + a*x])/(4199*a^5) - (768*b^3*x^2*Sqrt[b*x^(2/3) + a*x])/(2261*a^4) + (720*b^2*x^(7/3)*Sqrt[b*x^(2/3) + a*x])/(2261*a^3) - (40*b*x^(8/3)*Sqrt[b*x^(2/3) + a*x])/(133*a^2) + (2*x^3*Sqrt[b*x^(2/3) + a*x])/(7*a)","A",11,3,19,0.1579,1,"{2016, 2002, 2014}"
187,1,225,0,0.3457798,"\int \frac{x^2}{\sqrt{b x^{2/3}+a x}} \, dx","Int[x^2/Sqrt[b*x^(2/3) + a*x],x]","-\frac{4096 b^7 \sqrt{a x+b x^{2/3}}}{2145 a^8 \sqrt[3]{x}}+\frac{2048 b^6 \sqrt{a x+b x^{2/3}}}{2145 a^7}-\frac{512 b^5 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{715 a^6}+\frac{256 b^4 x^{2/3} \sqrt{a x+b x^{2/3}}}{429 a^5}-\frac{224 b^3 x \sqrt{a x+b x^{2/3}}}{429 a^4}+\frac{336 b^2 x^{4/3} \sqrt{a x+b x^{2/3}}}{715 a^3}-\frac{28 b x^{5/3} \sqrt{a x+b x^{2/3}}}{65 a^2}+\frac{2 x^2 \sqrt{a x+b x^{2/3}}}{5 a}","-\frac{4096 b^7 \sqrt{a x+b x^{2/3}}}{2145 a^8 \sqrt[3]{x}}+\frac{2048 b^6 \sqrt{a x+b x^{2/3}}}{2145 a^7}-\frac{512 b^5 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{715 a^6}+\frac{256 b^4 x^{2/3} \sqrt{a x+b x^{2/3}}}{429 a^5}-\frac{224 b^3 x \sqrt{a x+b x^{2/3}}}{429 a^4}+\frac{336 b^2 x^{4/3} \sqrt{a x+b x^{2/3}}}{715 a^3}-\frac{28 b x^{5/3} \sqrt{a x+b x^{2/3}}}{65 a^2}+\frac{2 x^2 \sqrt{a x+b x^{2/3}}}{5 a}",1,"(2048*b^6*Sqrt[b*x^(2/3) + a*x])/(2145*a^7) - (4096*b^7*Sqrt[b*x^(2/3) + a*x])/(2145*a^8*x^(1/3)) - (512*b^5*x^(1/3)*Sqrt[b*x^(2/3) + a*x])/(715*a^6) + (256*b^4*x^(2/3)*Sqrt[b*x^(2/3) + a*x])/(429*a^5) - (224*b^3*x*Sqrt[b*x^(2/3) + a*x])/(429*a^4) + (336*b^2*x^(4/3)*Sqrt[b*x^(2/3) + a*x])/(715*a^3) - (28*b*x^(5/3)*Sqrt[b*x^(2/3) + a*x])/(65*a^2) + (2*x^2*Sqrt[b*x^(2/3) + a*x])/(5*a)","A",8,3,19,0.1579,1,"{2016, 2002, 2014}"
188,1,137,0,0.1798585,"\int \frac{x}{\sqrt{b x^{2/3}+a x}} \, dx","Int[x/Sqrt[b*x^(2/3) + a*x],x]","\frac{256 b^4 \sqrt{a x+b x^{2/3}}}{105 a^5 \sqrt[3]{x}}-\frac{128 b^3 \sqrt{a x+b x^{2/3}}}{105 a^4}+\frac{32 b^2 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{35 a^3}-\frac{16 b x^{2/3} \sqrt{a x+b x^{2/3}}}{21 a^2}+\frac{2 x \sqrt{a x+b x^{2/3}}}{3 a}","\frac{256 b^4 \sqrt{a x+b x^{2/3}}}{105 a^5 \sqrt[3]{x}}-\frac{128 b^3 \sqrt{a x+b x^{2/3}}}{105 a^4}+\frac{32 b^2 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{35 a^3}-\frac{16 b x^{2/3} \sqrt{a x+b x^{2/3}}}{21 a^2}+\frac{2 x \sqrt{a x+b x^{2/3}}}{3 a}",1,"(-128*b^3*Sqrt[b*x^(2/3) + a*x])/(105*a^4) + (256*b^4*Sqrt[b*x^(2/3) + a*x])/(105*a^5*x^(1/3)) + (32*b^2*x^(1/3)*Sqrt[b*x^(2/3) + a*x])/(35*a^3) - (16*b*x^(2/3)*Sqrt[b*x^(2/3) + a*x])/(21*a^2) + (2*x*Sqrt[b*x^(2/3) + a*x])/(3*a)","A",5,3,17,0.1765,1,"{2016, 2002, 2014}"
189,1,47,0,0.0495725,"\int \frac{1}{\sqrt{b x^{2/3}+a x}} \, dx","Int[1/Sqrt[b*x^(2/3) + a*x],x]","\frac{2 \sqrt{a x+b x^{2/3}}}{a}-\frac{4 b \sqrt{a x+b x^{2/3}}}{a^2 \sqrt[3]{x}}","\frac{2 \sqrt{a x+b x^{2/3}}}{a}-\frac{4 b \sqrt{a x+b x^{2/3}}}{a^2 \sqrt[3]{x}}",1,"(2*Sqrt[b*x^(2/3) + a*x])/a - (4*b*Sqrt[b*x^(2/3) + a*x])/(a^2*x^(1/3))","A",2,2,15,0.1333,1,"{2002, 2014}"
190,1,61,0,0.0934507,"\int \frac{1}{x \sqrt{b x^{2/3}+a x}} \, dx","Int[1/(x*Sqrt[b*x^(2/3) + a*x]),x]","\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{b^{3/2}}-\frac{3 \sqrt{a x+b x^{2/3}}}{b x^{2/3}}","\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{b^{3/2}}-\frac{3 \sqrt{a x+b x^{2/3}}}{b x^{2/3}}",1,"(-3*Sqrt[b*x^(2/3) + a*x])/(b*x^(2/3)) + (3*a*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/b^(3/2)","A",3,3,19,0.1579,1,"{2025, 2029, 206}"
191,1,153,0,0.239309,"\int \frac{1}{x^2 \sqrt{b x^{2/3}+a x}} \, dx","Int[1/(x^2*Sqrt[b*x^(2/3) + a*x]),x]","\frac{105 a^3 \sqrt{a x+b x^{2/3}}}{64 b^4 x^{2/3}}-\frac{35 a^2 \sqrt{a x+b x^{2/3}}}{32 b^3 x}-\frac{105 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{64 b^{9/2}}+\frac{7 a \sqrt{a x+b x^{2/3}}}{8 b^2 x^{4/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{4 b x^{5/3}}","\frac{105 a^3 \sqrt{a x+b x^{2/3}}}{64 b^4 x^{2/3}}-\frac{35 a^2 \sqrt{a x+b x^{2/3}}}{32 b^3 x}-\frac{105 a^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{64 b^{9/2}}+\frac{7 a \sqrt{a x+b x^{2/3}}}{8 b^2 x^{4/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{4 b x^{5/3}}",1,"(-3*Sqrt[b*x^(2/3) + a*x])/(4*b*x^(5/3)) + (7*a*Sqrt[b*x^(2/3) + a*x])/(8*b^2*x^(4/3)) - (35*a^2*Sqrt[b*x^(2/3) + a*x])/(32*b^3*x) + (105*a^3*Sqrt[b*x^(2/3) + a*x])/(64*b^4*x^(2/3)) - (105*a^4*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(64*b^(9/2))","A",6,3,19,0.1579,1,"{2025, 2029, 206}"
192,1,241,0,0.407532,"\int \frac{1}{x^3 \sqrt{b x^{2/3}+a x}} \, dx","Int[1/(x^3*Sqrt[b*x^(2/3) + a*x]),x]","-\frac{1287 a^6 \sqrt{a x+b x^{2/3}}}{1024 b^7 x^{2/3}}+\frac{429 a^5 \sqrt{a x+b x^{2/3}}}{512 b^6 x}-\frac{429 a^4 \sqrt{a x+b x^{2/3}}}{640 b^5 x^{4/3}}+\frac{1287 a^3 \sqrt{a x+b x^{2/3}}}{2240 b^4 x^{5/3}}-\frac{143 a^2 \sqrt{a x+b x^{2/3}}}{280 b^3 x^2}+\frac{1287 a^7 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{1024 b^{15/2}}+\frac{13 a \sqrt{a x+b x^{2/3}}}{28 b^2 x^{7/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{7 b x^{8/3}}","-\frac{1287 a^6 \sqrt{a x+b x^{2/3}}}{1024 b^7 x^{2/3}}+\frac{429 a^5 \sqrt{a x+b x^{2/3}}}{512 b^6 x}-\frac{429 a^4 \sqrt{a x+b x^{2/3}}}{640 b^5 x^{4/3}}+\frac{1287 a^3 \sqrt{a x+b x^{2/3}}}{2240 b^4 x^{5/3}}-\frac{143 a^2 \sqrt{a x+b x^{2/3}}}{280 b^3 x^2}+\frac{1287 a^7 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{1024 b^{15/2}}+\frac{13 a \sqrt{a x+b x^{2/3}}}{28 b^2 x^{7/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{7 b x^{8/3}}",1,"(-3*Sqrt[b*x^(2/3) + a*x])/(7*b*x^(8/3)) + (13*a*Sqrt[b*x^(2/3) + a*x])/(28*b^2*x^(7/3)) - (143*a^2*Sqrt[b*x^(2/3) + a*x])/(280*b^3*x^2) + (1287*a^3*Sqrt[b*x^(2/3) + a*x])/(2240*b^4*x^(5/3)) - (429*a^4*Sqrt[b*x^(2/3) + a*x])/(640*b^5*x^(4/3)) + (429*a^5*Sqrt[b*x^(2/3) + a*x])/(512*b^6*x) - (1287*a^6*Sqrt[b*x^(2/3) + a*x])/(1024*b^7*x^(2/3)) + (1287*a^7*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(1024*b^(15/2))","A",9,3,19,0.1579,1,"{2025, 2029, 206}"
193,1,329,0,0.5771388,"\int \frac{1}{x^4 \sqrt{b x^{2/3}+a x}} \, dx","Int[1/(x^4*Sqrt[b*x^(2/3) + a*x]),x]","\frac{138567 a^9 \sqrt{a x+b x^{2/3}}}{131072 b^{10} x^{2/3}}-\frac{46189 a^8 \sqrt{a x+b x^{2/3}}}{65536 b^9 x}+\frac{46189 a^7 \sqrt{a x+b x^{2/3}}}{81920 b^8 x^{4/3}}-\frac{138567 a^6 \sqrt{a x+b x^{2/3}}}{286720 b^7 x^{5/3}}+\frac{46189 a^5 \sqrt{a x+b x^{2/3}}}{107520 b^6 x^2}-\frac{4199 a^4 \sqrt{a x+b x^{2/3}}}{10752 b^5 x^{7/3}}+\frac{323 a^3 \sqrt{a x+b x^{2/3}}}{896 b^4 x^{8/3}}-\frac{323 a^2 \sqrt{a x+b x^{2/3}}}{960 b^3 x^3}-\frac{138567 a^{10} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{131072 b^{21/2}}+\frac{19 a \sqrt{a x+b x^{2/3}}}{60 b^2 x^{10/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{10 b x^{11/3}}","\frac{138567 a^9 \sqrt{a x+b x^{2/3}}}{131072 b^{10} x^{2/3}}-\frac{46189 a^8 \sqrt{a x+b x^{2/3}}}{65536 b^9 x}+\frac{46189 a^7 \sqrt{a x+b x^{2/3}}}{81920 b^8 x^{4/3}}-\frac{138567 a^6 \sqrt{a x+b x^{2/3}}}{286720 b^7 x^{5/3}}+\frac{46189 a^5 \sqrt{a x+b x^{2/3}}}{107520 b^6 x^2}-\frac{4199 a^4 \sqrt{a x+b x^{2/3}}}{10752 b^5 x^{7/3}}+\frac{323 a^3 \sqrt{a x+b x^{2/3}}}{896 b^4 x^{8/3}}-\frac{323 a^2 \sqrt{a x+b x^{2/3}}}{960 b^3 x^3}-\frac{138567 a^{10} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{131072 b^{21/2}}+\frac{19 a \sqrt{a x+b x^{2/3}}}{60 b^2 x^{10/3}}-\frac{3 \sqrt{a x+b x^{2/3}}}{10 b x^{11/3}}",1,"(-3*Sqrt[b*x^(2/3) + a*x])/(10*b*x^(11/3)) + (19*a*Sqrt[b*x^(2/3) + a*x])/(60*b^2*x^(10/3)) - (323*a^2*Sqrt[b*x^(2/3) + a*x])/(960*b^3*x^3) + (323*a^3*Sqrt[b*x^(2/3) + a*x])/(896*b^4*x^(8/3)) - (4199*a^4*Sqrt[b*x^(2/3) + a*x])/(10752*b^5*x^(7/3)) + (46189*a^5*Sqrt[b*x^(2/3) + a*x])/(107520*b^6*x^2) - (138567*a^6*Sqrt[b*x^(2/3) + a*x])/(286720*b^7*x^(5/3)) + (46189*a^7*Sqrt[b*x^(2/3) + a*x])/(81920*b^8*x^(4/3)) - (46189*a^8*Sqrt[b*x^(2/3) + a*x])/(65536*b^9*x) + (138567*a^9*Sqrt[b*x^(2/3) + a*x])/(131072*b^10*x^(2/3)) - (138567*a^10*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(131072*b^(21/2))","A",12,3,19,0.1579,1,"{2025, 2029, 206}"
194,1,336,0,0.5992246,"\int \frac{x^4}{\left(b x^{2/3}+a x\right)^{3/2}} \, dx","Int[x^4/(b*x^(2/3) + a*x)^(3/2),x]","\frac{1048576 b^{10} \sqrt{a x+b x^{2/3}}}{29393 a^{12} \sqrt[3]{x}}-\frac{524288 b^9 \sqrt{a x+b x^{2/3}}}{29393 a^{11}}+\frac{393216 b^8 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{29393 a^{10}}-\frac{327680 b^7 x^{2/3} \sqrt{a x+b x^{2/3}}}{29393 a^9}+\frac{40960 b^6 x \sqrt{a x+b x^{2/3}}}{4199 a^8}-\frac{36864 b^5 x^{4/3} \sqrt{a x+b x^{2/3}}}{4199 a^7}+\frac{33792 b^4 x^{5/3} \sqrt{a x+b x^{2/3}}}{4199 a^6}-\frac{16896 b^3 x^2 \sqrt{a x+b x^{2/3}}}{2261 a^5}+\frac{15840 b^2 x^{7/3} \sqrt{a x+b x^{2/3}}}{2261 a^4}-\frac{880 b x^{8/3} \sqrt{a x+b x^{2/3}}}{133 a^3}+\frac{44 x^3 \sqrt{a x+b x^{2/3}}}{7 a^2}-\frac{6 x^4}{a \sqrt{a x+b x^{2/3}}}","\frac{1048576 b^{10} \sqrt{a x+b x^{2/3}}}{29393 a^{12} \sqrt[3]{x}}-\frac{524288 b^9 \sqrt{a x+b x^{2/3}}}{29393 a^{11}}+\frac{393216 b^8 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{29393 a^{10}}-\frac{327680 b^7 x^{2/3} \sqrt{a x+b x^{2/3}}}{29393 a^9}+\frac{40960 b^6 x \sqrt{a x+b x^{2/3}}}{4199 a^8}-\frac{36864 b^5 x^{4/3} \sqrt{a x+b x^{2/3}}}{4199 a^7}+\frac{33792 b^4 x^{5/3} \sqrt{a x+b x^{2/3}}}{4199 a^6}-\frac{16896 b^3 x^2 \sqrt{a x+b x^{2/3}}}{2261 a^5}+\frac{15840 b^2 x^{7/3} \sqrt{a x+b x^{2/3}}}{2261 a^4}-\frac{880 b x^{8/3} \sqrt{a x+b x^{2/3}}}{133 a^3}+\frac{44 x^3 \sqrt{a x+b x^{2/3}}}{7 a^2}-\frac{6 x^4}{a \sqrt{a x+b x^{2/3}}}",1,"(-6*x^4)/(a*Sqrt[b*x^(2/3) + a*x]) - (524288*b^9*Sqrt[b*x^(2/3) + a*x])/(29393*a^11) + (1048576*b^10*Sqrt[b*x^(2/3) + a*x])/(29393*a^12*x^(1/3)) + (393216*b^8*x^(1/3)*Sqrt[b*x^(2/3) + a*x])/(29393*a^10) - (327680*b^7*x^(2/3)*Sqrt[b*x^(2/3) + a*x])/(29393*a^9) + (40960*b^6*x*Sqrt[b*x^(2/3) + a*x])/(4199*a^8) - (36864*b^5*x^(4/3)*Sqrt[b*x^(2/3) + a*x])/(4199*a^7) + (33792*b^4*x^(5/3)*Sqrt[b*x^(2/3) + a*x])/(4199*a^6) - (16896*b^3*x^2*Sqrt[b*x^(2/3) + a*x])/(2261*a^5) + (15840*b^2*x^(7/3)*Sqrt[b*x^(2/3) + a*x])/(2261*a^4) - (880*b*x^(8/3)*Sqrt[b*x^(2/3) + a*x])/(133*a^3) + (44*x^3*Sqrt[b*x^(2/3) + a*x])/(7*a^2)","A",12,4,19,0.2105,1,"{2015, 2016, 2002, 2014}"
195,1,248,0,0.4139677,"\int \frac{x^3}{\left(b x^{2/3}+a x\right)^{3/2}} \, dx","Int[x^3/(b*x^(2/3) + a*x)^(3/2),x]","-\frac{65536 b^7 \sqrt{a x+b x^{2/3}}}{2145 a^9 \sqrt[3]{x}}+\frac{32768 b^6 \sqrt{a x+b x^{2/3}}}{2145 a^8}-\frac{8192 b^5 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{715 a^7}+\frac{4096 b^4 x^{2/3} \sqrt{a x+b x^{2/3}}}{429 a^6}-\frac{3584 b^3 x \sqrt{a x+b x^{2/3}}}{429 a^5}+\frac{5376 b^2 x^{4/3} \sqrt{a x+b x^{2/3}}}{715 a^4}-\frac{448 b x^{5/3} \sqrt{a x+b x^{2/3}}}{65 a^3}+\frac{32 x^2 \sqrt{a x+b x^{2/3}}}{5 a^2}-\frac{6 x^3}{a \sqrt{a x+b x^{2/3}}}","-\frac{65536 b^7 \sqrt{a x+b x^{2/3}}}{2145 a^9 \sqrt[3]{x}}+\frac{32768 b^6 \sqrt{a x+b x^{2/3}}}{2145 a^8}-\frac{8192 b^5 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{715 a^7}+\frac{4096 b^4 x^{2/3} \sqrt{a x+b x^{2/3}}}{429 a^6}-\frac{3584 b^3 x \sqrt{a x+b x^{2/3}}}{429 a^5}+\frac{5376 b^2 x^{4/3} \sqrt{a x+b x^{2/3}}}{715 a^4}-\frac{448 b x^{5/3} \sqrt{a x+b x^{2/3}}}{65 a^3}+\frac{32 x^2 \sqrt{a x+b x^{2/3}}}{5 a^2}-\frac{6 x^3}{a \sqrt{a x+b x^{2/3}}}",1,"(-6*x^3)/(a*Sqrt[b*x^(2/3) + a*x]) + (32768*b^6*Sqrt[b*x^(2/3) + a*x])/(2145*a^8) - (65536*b^7*Sqrt[b*x^(2/3) + a*x])/(2145*a^9*x^(1/3)) - (8192*b^5*x^(1/3)*Sqrt[b*x^(2/3) + a*x])/(715*a^7) + (4096*b^4*x^(2/3)*Sqrt[b*x^(2/3) + a*x])/(429*a^6) - (3584*b^3*x*Sqrt[b*x^(2/3) + a*x])/(429*a^5) + (5376*b^2*x^(4/3)*Sqrt[b*x^(2/3) + a*x])/(715*a^4) - (448*b*x^(5/3)*Sqrt[b*x^(2/3) + a*x])/(65*a^3) + (32*x^2*Sqrt[b*x^(2/3) + a*x])/(5*a^2)","A",9,4,19,0.2105,1,"{2015, 2016, 2002, 2014}"
196,1,160,0,0.242094,"\int \frac{x^2}{\left(b x^{2/3}+a x\right)^{3/2}} \, dx","Int[x^2/(b*x^(2/3) + a*x)^(3/2),x]","\frac{512 b^4 \sqrt{a x+b x^{2/3}}}{21 a^6 \sqrt[3]{x}}-\frac{256 b^3 \sqrt{a x+b x^{2/3}}}{21 a^5}+\frac{64 b^2 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{7 a^4}-\frac{160 b x^{2/3} \sqrt{a x+b x^{2/3}}}{21 a^3}+\frac{20 x \sqrt{a x+b x^{2/3}}}{3 a^2}-\frac{6 x^2}{a \sqrt{a x+b x^{2/3}}}","\frac{512 b^4 \sqrt{a x+b x^{2/3}}}{21 a^6 \sqrt[3]{x}}-\frac{256 b^3 \sqrt{a x+b x^{2/3}}}{21 a^5}+\frac{64 b^2 \sqrt[3]{x} \sqrt{a x+b x^{2/3}}}{7 a^4}-\frac{160 b x^{2/3} \sqrt{a x+b x^{2/3}}}{21 a^3}+\frac{20 x \sqrt{a x+b x^{2/3}}}{3 a^2}-\frac{6 x^2}{a \sqrt{a x+b x^{2/3}}}",1,"(-6*x^2)/(a*Sqrt[b*x^(2/3) + a*x]) - (256*b^3*Sqrt[b*x^(2/3) + a*x])/(21*a^5) + (512*b^4*Sqrt[b*x^(2/3) + a*x])/(21*a^6*x^(1/3)) + (64*b^2*x^(1/3)*Sqrt[b*x^(2/3) + a*x])/(7*a^4) - (160*b*x^(2/3)*Sqrt[b*x^(2/3) + a*x])/(21*a^3) + (20*x*Sqrt[b*x^(2/3) + a*x])/(3*a^2)","A",6,4,19,0.2105,1,"{2015, 2016, 2002, 2014}"
197,1,68,0,0.0838576,"\int \frac{x}{\left(b x^{2/3}+a x\right)^{3/2}} \, dx","Int[x/(b*x^(2/3) + a*x)^(3/2),x]","-\frac{16 b \sqrt{a x+b x^{2/3}}}{a^3 \sqrt[3]{x}}+\frac{8 \sqrt{a x+b x^{2/3}}}{a^2}-\frac{6 x}{a \sqrt{a x+b x^{2/3}}}","-\frac{16 b \sqrt{a x+b x^{2/3}}}{a^3 \sqrt[3]{x}}+\frac{8 \sqrt{a x+b x^{2/3}}}{a^2}-\frac{6 x}{a \sqrt{a x+b x^{2/3}}}",1,"(-6*x)/(a*Sqrt[b*x^(2/3) + a*x]) + (8*Sqrt[b*x^(2/3) + a*x])/a^2 - (16*b*Sqrt[b*x^(2/3) + a*x])/(a^3*x^(1/3))","A",3,3,17,0.1765,1,"{2015, 2002, 2014}"
198,1,60,0,0.0560228,"\int \frac{1}{\left(b x^{2/3}+a x\right)^{3/2}} \, dx","Int[(b*x^(2/3) + a*x)^(-3/2),x]","\frac{6 \sqrt[3]{x}}{b \sqrt{a x+b x^{2/3}}}-\frac{6 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{b^{3/2}}","\frac{6 \sqrt[3]{x}}{b \sqrt{a x+b x^{2/3}}}-\frac{6 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{b^{3/2}}",1,"(6*x^(1/3))/(b*Sqrt[b*x^(2/3) + a*x]) - (6*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/b^(3/2)","A",3,3,15,0.2000,1,"{2006, 2029, 206}"
199,1,146,0,0.2405217,"\int \frac{1}{x \left(b x^{2/3}+a x\right)^{3/2}} \, dx","Int[1/(x*(b*x^(2/3) + a*x)^(3/2)),x]","-\frac{105 a^2 \sqrt{a x+b x^{2/3}}}{8 b^4 x^{2/3}}+\frac{105 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{8 b^{9/2}}+\frac{35 a \sqrt{a x+b x^{2/3}}}{4 b^3 x}-\frac{7 \sqrt{a x+b x^{2/3}}}{b^2 x^{4/3}}+\frac{6}{b x^{2/3} \sqrt{a x+b x^{2/3}}}","-\frac{105 a^2 \sqrt{a x+b x^{2/3}}}{8 b^4 x^{2/3}}+\frac{105 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{8 b^{9/2}}+\frac{35 a \sqrt{a x+b x^{2/3}}}{4 b^3 x}-\frac{7 \sqrt{a x+b x^{2/3}}}{b^2 x^{4/3}}+\frac{6}{b x^{2/3} \sqrt{a x+b x^{2/3}}}",1,"6/(b*x^(2/3)*Sqrt[b*x^(2/3) + a*x]) - (7*Sqrt[b*x^(2/3) + a*x])/(b^2*x^(4/3)) + (35*a*Sqrt[b*x^(2/3) + a*x])/(4*b^3*x) - (105*a^2*Sqrt[b*x^(2/3) + a*x])/(8*b^4*x^(2/3)) + (105*a^3*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(8*b^(9/2))","A",6,4,19,0.2105,1,"{2023, 2025, 2029, 206}"
200,1,236,0,0.4104415,"\int \frac{1}{x^2 \left(b x^{2/3}+a x\right)^{3/2}} \, dx","Int[1/(x^2*(b*x^(2/3) + a*x)^(3/2)),x]","\frac{9009 a^5 \sqrt{a x+b x^{2/3}}}{512 b^7 x^{2/3}}-\frac{3003 a^4 \sqrt{a x+b x^{2/3}}}{256 b^6 x}+\frac{3003 a^3 \sqrt{a x+b x^{2/3}}}{320 b^5 x^{4/3}}-\frac{1287 a^2 \sqrt{a x+b x^{2/3}}}{160 b^4 x^{5/3}}-\frac{9009 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{512 b^{15/2}}+\frac{143 a \sqrt{a x+b x^{2/3}}}{20 b^3 x^2}-\frac{13 \sqrt{a x+b x^{2/3}}}{2 b^2 x^{7/3}}+\frac{6}{b x^{5/3} \sqrt{a x+b x^{2/3}}}","\frac{9009 a^5 \sqrt{a x+b x^{2/3}}}{512 b^7 x^{2/3}}-\frac{3003 a^4 \sqrt{a x+b x^{2/3}}}{256 b^6 x}+\frac{3003 a^3 \sqrt{a x+b x^{2/3}}}{320 b^5 x^{4/3}}-\frac{1287 a^2 \sqrt{a x+b x^{2/3}}}{160 b^4 x^{5/3}}-\frac{9009 a^6 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{512 b^{15/2}}+\frac{143 a \sqrt{a x+b x^{2/3}}}{20 b^3 x^2}-\frac{13 \sqrt{a x+b x^{2/3}}}{2 b^2 x^{7/3}}+\frac{6}{b x^{5/3} \sqrt{a x+b x^{2/3}}}",1,"6/(b*x^(5/3)*Sqrt[b*x^(2/3) + a*x]) - (13*Sqrt[b*x^(2/3) + a*x])/(2*b^2*x^(7/3)) + (143*a*Sqrt[b*x^(2/3) + a*x])/(20*b^3*x^2) - (1287*a^2*Sqrt[b*x^(2/3) + a*x])/(160*b^4*x^(5/3)) + (3003*a^3*Sqrt[b*x^(2/3) + a*x])/(320*b^5*x^(4/3)) - (3003*a^4*Sqrt[b*x^(2/3) + a*x])/(256*b^6*x) + (9009*a^5*Sqrt[b*x^(2/3) + a*x])/(512*b^7*x^(2/3)) - (9009*a^6*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(512*b^(15/2))","A",9,4,19,0.2105,1,"{2023, 2025, 2029, 206}"
201,1,324,0,0.597076,"\int \frac{1}{x^3 \left(b x^{2/3}+a x\right)^{3/2}} \, dx","Int[1/(x^3*(b*x^(2/3) + a*x)^(3/2)),x]","-\frac{692835 a^8 \sqrt{a x+b x^{2/3}}}{32768 b^{10} x^{2/3}}+\frac{230945 a^7 \sqrt{a x+b x^{2/3}}}{16384 b^9 x}-\frac{46189 a^6 \sqrt{a x+b x^{2/3}}}{4096 b^8 x^{4/3}}+\frac{138567 a^5 \sqrt{a x+b x^{2/3}}}{14336 b^7 x^{5/3}}-\frac{46189 a^4 \sqrt{a x+b x^{2/3}}}{5376 b^6 x^2}+\frac{20995 a^3 \sqrt{a x+b x^{2/3}}}{2688 b^5 x^{7/3}}-\frac{1615 a^2 \sqrt{a x+b x^{2/3}}}{224 b^4 x^{8/3}}+\frac{692835 a^9 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{32768 b^{21/2}}+\frac{323 a \sqrt{a x+b x^{2/3}}}{48 b^3 x^3}-\frac{19 \sqrt{a x+b x^{2/3}}}{3 b^2 x^{10/3}}+\frac{6}{b x^{8/3} \sqrt{a x+b x^{2/3}}}","-\frac{692835 a^8 \sqrt{a x+b x^{2/3}}}{32768 b^{10} x^{2/3}}+\frac{230945 a^7 \sqrt{a x+b x^{2/3}}}{16384 b^9 x}-\frac{46189 a^6 \sqrt{a x+b x^{2/3}}}{4096 b^8 x^{4/3}}+\frac{138567 a^5 \sqrt{a x+b x^{2/3}}}{14336 b^7 x^{5/3}}-\frac{46189 a^4 \sqrt{a x+b x^{2/3}}}{5376 b^6 x^2}+\frac{20995 a^3 \sqrt{a x+b x^{2/3}}}{2688 b^5 x^{7/3}}-\frac{1615 a^2 \sqrt{a x+b x^{2/3}}}{224 b^4 x^{8/3}}+\frac{692835 a^9 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{32768 b^{21/2}}+\frac{323 a \sqrt{a x+b x^{2/3}}}{48 b^3 x^3}-\frac{19 \sqrt{a x+b x^{2/3}}}{3 b^2 x^{10/3}}+\frac{6}{b x^{8/3} \sqrt{a x+b x^{2/3}}}",1,"6/(b*x^(8/3)*Sqrt[b*x^(2/3) + a*x]) - (19*Sqrt[b*x^(2/3) + a*x])/(3*b^2*x^(10/3)) + (323*a*Sqrt[b*x^(2/3) + a*x])/(48*b^3*x^3) - (1615*a^2*Sqrt[b*x^(2/3) + a*x])/(224*b^4*x^(8/3)) + (20995*a^3*Sqrt[b*x^(2/3) + a*x])/(2688*b^5*x^(7/3)) - (46189*a^4*Sqrt[b*x^(2/3) + a*x])/(5376*b^6*x^2) + (138567*a^5*Sqrt[b*x^(2/3) + a*x])/(14336*b^7*x^(5/3)) - (46189*a^6*Sqrt[b*x^(2/3) + a*x])/(4096*b^8*x^(4/3)) + (230945*a^7*Sqrt[b*x^(2/3) + a*x])/(16384*b^9*x) - (692835*a^8*Sqrt[b*x^(2/3) + a*x])/(32768*b^10*x^(2/3)) + (692835*a^9*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(32768*b^(21/2))","A",12,4,19,0.2105,1,"{2023, 2025, 2029, 206}"
202,1,412,0,0.8399899,"\int \frac{1}{x^4 \left(b x^{2/3}+a x\right)^{3/2}} \, dx","Int[1/(x^4*(b*x^(2/3) + a*x)^(3/2)),x]","\frac{50702925 a^{11} \sqrt{a x+b x^{2/3}}}{2097152 b^{13} x^{2/3}}-\frac{16900975 a^{10} \sqrt{a x+b x^{2/3}}}{1048576 b^{12} x}+\frac{3380195 a^9 \sqrt{a x+b x^{2/3}}}{262144 b^{11} x^{4/3}}-\frac{1448655 a^8 \sqrt{a x+b x^{2/3}}}{131072 b^{10} x^{5/3}}+\frac{482885 a^7 \sqrt{a x+b x^{2/3}}}{49152 b^9 x^2}-\frac{2414425 a^6 \sqrt{a x+b x^{2/3}}}{270336 b^8 x^{7/3}}+\frac{185725 a^5 \sqrt{a x+b x^{2/3}}}{22528 b^7 x^{8/3}}-\frac{260015 a^4 \sqrt{a x+b x^{2/3}}}{33792 b^6 x^3}+\frac{15295 a^3 \sqrt{a x+b x^{2/3}}}{2112 b^5 x^{10/3}}-\frac{2415 a^2 \sqrt{a x+b x^{2/3}}}{352 b^4 x^{11/3}}-\frac{50702925 a^{12} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{2097152 b^{27/2}}+\frac{575 a \sqrt{a x+b x^{2/3}}}{88 b^3 x^4}-\frac{25 \sqrt{a x+b x^{2/3}}}{4 b^2 x^{13/3}}+\frac{6}{b x^{11/3} \sqrt{a x+b x^{2/3}}}","\frac{50702925 a^{11} \sqrt{a x+b x^{2/3}}}{2097152 b^{13} x^{2/3}}-\frac{16900975 a^{10} \sqrt{a x+b x^{2/3}}}{1048576 b^{12} x}+\frac{3380195 a^9 \sqrt{a x+b x^{2/3}}}{262144 b^{11} x^{4/3}}-\frac{1448655 a^8 \sqrt{a x+b x^{2/3}}}{131072 b^{10} x^{5/3}}+\frac{482885 a^7 \sqrt{a x+b x^{2/3}}}{49152 b^9 x^2}-\frac{2414425 a^6 \sqrt{a x+b x^{2/3}}}{270336 b^8 x^{7/3}}+\frac{185725 a^5 \sqrt{a x+b x^{2/3}}}{22528 b^7 x^{8/3}}-\frac{260015 a^4 \sqrt{a x+b x^{2/3}}}{33792 b^6 x^3}+\frac{15295 a^3 \sqrt{a x+b x^{2/3}}}{2112 b^5 x^{10/3}}-\frac{2415 a^2 \sqrt{a x+b x^{2/3}}}{352 b^4 x^{11/3}}-\frac{50702925 a^{12} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[3]{x}}{\sqrt{a x+b x^{2/3}}}\right)}{2097152 b^{27/2}}+\frac{575 a \sqrt{a x+b x^{2/3}}}{88 b^3 x^4}-\frac{25 \sqrt{a x+b x^{2/3}}}{4 b^2 x^{13/3}}+\frac{6}{b x^{11/3} \sqrt{a x+b x^{2/3}}}",1,"6/(b*x^(11/3)*Sqrt[b*x^(2/3) + a*x]) - (25*Sqrt[b*x^(2/3) + a*x])/(4*b^2*x^(13/3)) + (575*a*Sqrt[b*x^(2/3) + a*x])/(88*b^3*x^4) - (2415*a^2*Sqrt[b*x^(2/3) + a*x])/(352*b^4*x^(11/3)) + (15295*a^3*Sqrt[b*x^(2/3) + a*x])/(2112*b^5*x^(10/3)) - (260015*a^4*Sqrt[b*x^(2/3) + a*x])/(33792*b^6*x^3) + (185725*a^5*Sqrt[b*x^(2/3) + a*x])/(22528*b^7*x^(8/3)) - (2414425*a^6*Sqrt[b*x^(2/3) + a*x])/(270336*b^8*x^(7/3)) + (482885*a^7*Sqrt[b*x^(2/3) + a*x])/(49152*b^9*x^2) - (1448655*a^8*Sqrt[b*x^(2/3) + a*x])/(131072*b^10*x^(5/3)) + (3380195*a^9*Sqrt[b*x^(2/3) + a*x])/(262144*b^11*x^(4/3)) - (16900975*a^10*Sqrt[b*x^(2/3) + a*x])/(1048576*b^12*x) + (50702925*a^11*Sqrt[b*x^(2/3) + a*x])/(2097152*b^13*x^(2/3)) - (50702925*a^12*ArcTanh[(Sqrt[b]*x^(1/3))/Sqrt[b*x^(2/3) + a*x]])/(2097152*b^(27/2))","A",15,4,19,0.2105,1,"{2023, 2025, 2029, 206}"
203,1,17,0,0.0088074,"\int x^2 \left(a x^2+b x^3\right) \, dx","Int[x^2*(a*x^2 + b*x^3),x]","\frac{a x^5}{5}+\frac{b x^6}{6}","\frac{a x^5}{5}+\frac{b x^6}{6}",1,"(a*x^5)/5 + (b*x^6)/6","A",2,1,15,0.06667,1,"{14}"
204,1,17,0,0.0079168,"\int x \left(a x^2+b x^3\right) \, dx","Int[x*(a*x^2 + b*x^3),x]","\frac{a x^4}{4}+\frac{b x^5}{5}","\frac{a x^4}{4}+\frac{b x^5}{5}",1,"(a*x^4)/4 + (b*x^5)/5","A",2,1,13,0.07692,1,"{14}"
205,1,17,0,0.0029354,"\int \left(a x^2+b x^3\right) \, dx","Int[a*x^2 + b*x^3,x]","\frac{a x^3}{3}+\frac{b x^4}{4}","\frac{a x^3}{3}+\frac{b x^4}{4}",1,"(a*x^3)/3 + (b*x^4)/4","A",1,0,11,0,1,"{}"
206,1,17,0,0.006029,"\int \frac{a x^2+b x^3}{x} \, dx","Int[(a*x^2 + b*x^3)/x,x]","\frac{a x^2}{2}+\frac{b x^3}{3}","\frac{a x^2}{2}+\frac{b x^3}{3}",1,"(a*x^2)/2 + (b*x^3)/3","A",2,1,15,0.06667,1,"{14}"
207,1,12,0,0.0035858,"\int \frac{a x^2+b x^3}{x^2} \, dx","Int[(a*x^2 + b*x^3)/x^2,x]","a x+\frac{b x^2}{2}","a x+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2","A",2,1,15,0.06667,1,"{14}"
208,1,30,0,0.0314118,"\int x^2 \left(a x^2+b x^3\right)^2 \, dx","Int[x^2*(a*x^2 + b*x^3)^2,x]","\frac{a^2 x^7}{7}+\frac{1}{4} a b x^8+\frac{b^2 x^9}{9}","\frac{a^2 x^7}{7}+\frac{1}{4} a b x^8+\frac{b^2 x^9}{9}",1,"(a^2*x^7)/7 + (a*b*x^8)/4 + (b^2*x^9)/9","A",3,2,17,0.1176,1,"{1584, 43}"
209,1,30,0,0.0170845,"\int x \left(a x^2+b x^3\right)^2 \, dx","Int[x*(a*x^2 + b*x^3)^2,x]","\frac{a^2 x^6}{6}+\frac{2}{7} a b x^7+\frac{b^2 x^8}{8}","\frac{a^2 x^6}{6}+\frac{2}{7} a b x^7+\frac{b^2 x^8}{8}",1,"(a^2*x^6)/6 + (2*a*b*x^7)/7 + (b^2*x^8)/8","A",3,2,15,0.1333,1,"{1584, 43}"
210,1,30,0,0.0134057,"\int \left(a x^2+b x^3\right)^2 \, dx","Int[(a*x^2 + b*x^3)^2,x]","\frac{a^2 x^5}{5}+\frac{1}{3} a b x^6+\frac{b^2 x^7}{7}","\frac{a^2 x^5}{5}+\frac{1}{3} a b x^6+\frac{b^2 x^7}{7}",1,"(a^2*x^5)/5 + (a*b*x^6)/3 + (b^2*x^7)/7","A",3,2,13,0.1538,1,"{1593, 43}"
211,1,30,0,0.0174214,"\int \frac{\left(a x^2+b x^3\right)^2}{x} \, dx","Int[(a*x^2 + b*x^3)^2/x,x]","\frac{a^2 x^4}{4}+\frac{2}{5} a b x^5+\frac{b^2 x^6}{6}","\frac{a^2 x^4}{4}+\frac{2}{5} a b x^5+\frac{b^2 x^6}{6}",1,"(a^2*x^4)/4 + (2*a*b*x^5)/5 + (b^2*x^6)/6","A",3,2,17,0.1176,1,"{1584, 43}"
212,1,30,0,0.0163855,"\int \frac{\left(a x^2+b x^3\right)^2}{x^2} \, dx","Int[(a*x^2 + b*x^3)^2/x^2,x]","\frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5}","\frac{a^2 x^3}{3}+\frac{1}{2} a b x^4+\frac{b^2 x^5}{5}",1,"(a^2*x^3)/3 + (a*b*x^4)/2 + (b^2*x^5)/5","A",3,2,17,0.1176,1,"{1584, 43}"
213,1,57,0,0.0355117,"\int \frac{x^6}{a x^2+b x^3} \, dx","Int[x^6/(a*x^2 + b*x^3),x]","\frac{a^2 x^2}{2 b^3}-\frac{a^3 x}{b^4}+\frac{a^4 \log (a+b x)}{b^5}-\frac{a x^3}{3 b^2}+\frac{x^4}{4 b}","\frac{a^2 x^2}{2 b^3}-\frac{a^3 x}{b^4}+\frac{a^4 \log (a+b x)}{b^5}-\frac{a x^3}{3 b^2}+\frac{x^4}{4 b}",1,"-((a^3*x)/b^4) + (a^2*x^2)/(2*b^3) - (a*x^3)/(3*b^2) + x^4/(4*b) + (a^4*Log[a + b*x])/b^5","A",3,2,17,0.1176,1,"{1584, 43}"
214,1,44,0,0.0270089,"\int \frac{x^5}{a x^2+b x^3} \, dx","Int[x^5/(a*x^2 + b*x^3),x]","\frac{a^2 x}{b^3}-\frac{a^3 \log (a+b x)}{b^4}-\frac{a x^2}{2 b^2}+\frac{x^3}{3 b}","\frac{a^2 x}{b^3}-\frac{a^3 \log (a+b x)}{b^4}-\frac{a x^2}{2 b^2}+\frac{x^3}{3 b}",1,"(a^2*x)/b^3 - (a*x^2)/(2*b^2) + x^3/(3*b) - (a^3*Log[a + b*x])/b^4","A",3,2,17,0.1176,1,"{1584, 43}"
215,1,31,0,0.0205414,"\int \frac{x^4}{a x^2+b x^3} \, dx","Int[x^4/(a*x^2 + b*x^3),x]","\frac{a^2 \log (a+b x)}{b^3}-\frac{a x}{b^2}+\frac{x^2}{2 b}","\frac{a^2 \log (a+b x)}{b^3}-\frac{a x}{b^2}+\frac{x^2}{2 b}",1,"-((a*x)/b^2) + x^2/(2*b) + (a^2*Log[a + b*x])/b^3","A",3,2,17,0.1176,1,"{1584, 43}"
216,1,18,0,0.0163976,"\int \frac{x^3}{a x^2+b x^3} \, dx","Int[x^3/(a*x^2 + b*x^3),x]","\frac{x}{b}-\frac{a \log (a+b x)}{b^2}","\frac{x}{b}-\frac{a \log (a+b x)}{b^2}",1,"x/b - (a*Log[a + b*x])/b^2","A",3,2,17,0.1176,1,"{1584, 43}"
217,1,10,0,0.0072511,"\int \frac{x^2}{a x^2+b x^3} \, dx","Int[x^2/(a*x^2 + b*x^3),x]","\frac{\log (a+b x)}{b}","\frac{\log (a+b x)}{b}",1,"Log[a + b*x]/b","A",2,2,17,0.1176,1,"{1584, 31}"
218,1,18,0,0.0074465,"\int \frac{x}{a x^2+b x^3} \, dx","Int[x/(a*x^2 + b*x^3),x]","\frac{\log (x)}{a}-\frac{\log (a+b x)}{a}","\frac{\log (x)}{a}-\frac{\log (a+b x)}{a}",1,"Log[x]/a - Log[a + b*x]/a","A",4,4,15,0.2667,1,"{1584, 36, 29, 31}"
219,1,28,0,0.0146112,"\int \frac{1}{a x^2+b x^3} \, dx","Int[(a*x^2 + b*x^3)^(-1),x]","-\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x}","-\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x}",1,"-(1/(a*x)) - (b*Log[x])/a^2 + (b*Log[a + b*x])/a^2","A",3,2,13,0.1538,1,"{1593, 44}"
220,1,42,0,0.0212892,"\int \frac{1}{x \left(a x^2+b x^3\right)} \, dx","Int[1/(x*(a*x^2 + b*x^3)),x]","\frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}","\frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + b/(a^2*x) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x])/a^3","A",3,2,17,0.1176,1,"{1584, 44}"
221,1,56,0,0.0267151,"\int \frac{1}{x^2 \left(a x^2+b x^3\right)} \, dx","Int[1/(x^2*(a*x^2 + b*x^3)),x]","-\frac{b^2}{a^3 x}-\frac{b^3 \log (x)}{a^4}+\frac{b^3 \log (a+b x)}{a^4}+\frac{b}{2 a^2 x^2}-\frac{1}{3 a x^3}","-\frac{b^2}{a^3 x}-\frac{b^3 \log (x)}{a^4}+\frac{b^3 \log (a+b x)}{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^3*x) - (b^3*Log[x])/a^4 + (b^3*Log[a + b*x])/a^4","A",3,2,17,0.1176,1,"{1584, 44}"
222,1,58,0,0.040053,"\int \frac{x^8}{\left(a x^2+b x^3\right)^2} \, dx","Int[x^8/(a*x^2 + b*x^3)^2,x]","-\frac{a^4}{b^5 (a+b x)}+\frac{3 a^2 x}{b^4}-\frac{4 a^3 \log (a+b x)}{b^5}-\frac{a x^2}{b^3}+\frac{x^3}{3 b^2}","-\frac{a^4}{b^5 (a+b x)}+\frac{3 a^2 x}{b^4}-\frac{4 a^3 \log (a+b x)}{b^5}-\frac{a x^2}{b^3}+\frac{x^3}{3 b^2}",1,"(3*a^2*x)/b^4 - (a*x^2)/b^3 + x^3/(3*b^2) - a^4/(b^5*(a + b*x)) - (4*a^3*Log[a + b*x])/b^5","A",3,2,17,0.1176,1,"{1584, 43}"
223,1,46,0,0.0301855,"\int \frac{x^7}{\left(a x^2+b x^3\right)^2} \, dx","Int[x^7/(a*x^2 + b*x^3)^2,x]","\frac{a^3}{b^4 (a+b x)}+\frac{3 a^2 \log (a+b x)}{b^4}-\frac{2 a x}{b^3}+\frac{x^2}{2 b^2}","\frac{a^3}{b^4 (a+b x)}+\frac{3 a^2 \log (a+b x)}{b^4}-\frac{2 a x}{b^3}+\frac{x^2}{2 b^2}",1,"(-2*a*x)/b^3 + x^2/(2*b^2) + a^3/(b^4*(a + b*x)) + (3*a^2*Log[a + b*x])/b^4","A",3,2,17,0.1176,1,"{1584, 43}"
224,1,33,0,0.023916,"\int \frac{x^6}{\left(a x^2+b x^3\right)^2} \, dx","Int[x^6/(a*x^2 + b*x^3)^2,x]","-\frac{a^2}{b^3 (a+b x)}-\frac{2 a \log (a+b x)}{b^3}+\frac{x}{b^2}","-\frac{a^2}{b^3 (a+b x)}-\frac{2 a \log (a+b x)}{b^3}+\frac{x}{b^2}",1,"x/b^2 - a^2/(b^3*(a + b*x)) - (2*a*Log[a + b*x])/b^3","A",3,2,17,0.1176,1,"{1584, 43}"
225,1,23,0,0.0180811,"\int \frac{x^5}{\left(a x^2+b x^3\right)^2} \, dx","Int[x^5/(a*x^2 + b*x^3)^2,x]","\frac{a}{b^2 (a+b x)}+\frac{\log (a+b x)}{b^2}","\frac{a}{b^2 (a+b x)}+\frac{\log (a+b x)}{b^2}",1,"a/(b^2*(a + b*x)) + Log[a + b*x]/b^2","A",3,2,17,0.1176,1,"{1584, 43}"
226,1,12,0,0.0073729,"\int \frac{x^4}{\left(a x^2+b x^3\right)^2} \, dx","Int[x^4/(a*x^2 + b*x^3)^2,x]","-\frac{1}{b (a+b x)}","-\frac{1}{b (a+b x)}",1,"-(1/(b*(a + b*x)))","A",2,2,17,0.1176,1,"{1584, 32}"
227,1,29,0,0.0188643,"\int \frac{x^3}{\left(a x^2+b x^3\right)^2} \, dx","Int[x^3/(a*x^2 + b*x^3)^2,x]","-\frac{\log (a+b x)}{a^2}+\frac{\log (x)}{a^2}+\frac{1}{a (a+b x)}","-\frac{\log (a+b x)}{a^2}+\frac{\log (x)}{a^2}+\frac{1}{a (a+b x)}",1,"1/(a*(a + b*x)) + Log[x]/a^2 - Log[a + b*x]/a^2","A",3,2,17,0.1176,1,"{1584, 44}"
228,1,42,0,0.0239151,"\int \frac{x^2}{\left(a x^2+b x^3\right)^2} \, dx","Int[x^2/(a*x^2 + b*x^3)^2,x]","-\frac{b}{a^2 (a+b x)}-\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}-\frac{1}{a^2 x}","-\frac{b}{a^2 (a+b x)}-\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}-\frac{1}{a^2 x}",1,"-(1/(a^2*x)) - b/(a^2*(a + b*x)) - (2*b*Log[x])/a^3 + (2*b*Log[a + b*x])/a^3","A",3,2,17,0.1176,1,"{1584, 44}"
229,1,58,0,0.0315931,"\int \frac{x}{\left(a x^2+b x^3\right)^2} \, dx","Int[x/(a*x^2 + b*x^3)^2,x]","\frac{b^2}{a^3 (a+b x)}+\frac{3 b^2 \log (x)}{a^4}-\frac{3 b^2 \log (a+b x)}{a^4}+\frac{2 b}{a^3 x}-\frac{1}{2 a^2 x^2}","\frac{b^2}{a^3 (a+b x)}+\frac{3 b^2 \log (x)}{a^4}-\frac{3 b^2 \log (a+b x)}{a^4}+\frac{2 b}{a^3 x}-\frac{1}{2 a^2 x^2}",1,"-1/(2*a^2*x^2) + (2*b)/(a^3*x) + b^2/(a^3*(a + b*x)) + (3*b^2*Log[x])/a^4 - (3*b^2*Log[a + b*x])/a^4","A",3,2,15,0.1333,1,"{1584, 44}"
230,1,69,0,0.0389185,"\int \frac{1}{\left(a x^2+b x^3\right)^2} \, dx","Int[(a*x^2 + b*x^3)^(-2),x]","-\frac{b^3}{a^4 (a+b x)}-\frac{3 b^2}{a^4 x}-\frac{4 b^3 \log (x)}{a^5}+\frac{4 b^3 \log (a+b x)}{a^5}+\frac{b}{a^3 x^2}-\frac{1}{3 a^2 x^3}","-\frac{b^3}{a^4 (a+b x)}-\frac{3 b^2}{a^4 x}-\frac{4 b^3 \log (x)}{a^5}+\frac{4 b^3 \log (a+b x)}{a^5}+\frac{b}{a^3 x^2}-\frac{1}{3 a^2 x^3}",1,"-1/(3*a^2*x^3) + b/(a^3*x^2) - (3*b^2)/(a^4*x) - b^3/(a^4*(a + b*x)) - (4*b^3*Log[x])/a^5 + (4*b^3*Log[a + b*x])/a^5","A",3,2,13,0.1538,1,"{1593, 44}"
231,1,84,0,0.052285,"\int \frac{1}{x \left(a x^2+b x^3\right)^2} \, dx","Int[1/(x*(a*x^2 + b*x^3)^2),x]","-\frac{3 b^2}{2 a^4 x^2}+\frac{b^4}{a^5 (a+b x)}+\frac{4 b^3}{a^5 x}+\frac{5 b^4 \log (x)}{a^6}-\frac{5 b^4 \log (a+b x)}{a^6}+\frac{2 b}{3 a^3 x^3}-\frac{1}{4 a^2 x^4}","-\frac{3 b^2}{2 a^4 x^2}+\frac{b^4}{a^5 (a+b x)}+\frac{4 b^3}{a^5 x}+\frac{5 b^4 \log (x)}{a^6}-\frac{5 b^4 \log (a+b x)}{a^6}+\frac{2 b}{3 a^3 x^3}-\frac{1}{4 a^2 x^4}",1,"-1/(4*a^2*x^4) + (2*b)/(3*a^3*x^3) - (3*b^2)/(2*a^4*x^2) + (4*b^3)/(a^5*x) + b^4/(a^5*(a + b*x)) + (5*b^4*Log[x])/a^6 - (5*b^4*Log[a + b*x])/a^6","A",3,2,17,0.1176,1,"{1584, 44}"
232,1,105,0,0.1197289,"\int x^2 \sqrt{a x^2+b x^3} \, dx","Int[x^2*Sqrt[a*x^2 + b*x^3],x]","-\frac{32 a^3 \left(a x^2+b x^3\right)^{3/2}}{315 b^4 x^3}+\frac{16 a^2 \left(a x^2+b x^3\right)^{3/2}}{105 b^3 x^2}-\frac{4 a \left(a x^2+b x^3\right)^{3/2}}{21 b^2 x}+\frac{2 \left(a x^2+b x^3\right)^{3/2}}{9 b}","-\frac{32 a^3 \left(a x^2+b x^3\right)^{3/2}}{315 b^4 x^3}+\frac{16 a^2 \left(a x^2+b x^3\right)^{3/2}}{105 b^3 x^2}-\frac{4 a \left(a x^2+b x^3\right)^{3/2}}{21 b^2 x}+\frac{2 \left(a x^2+b x^3\right)^{3/2}}{9 b}",1,"(2*(a*x^2 + b*x^3)^(3/2))/(9*b) - (32*a^3*(a*x^2 + b*x^3)^(3/2))/(315*b^4*x^3) + (16*a^2*(a*x^2 + b*x^3)^(3/2))/(105*b^3*x^2) - (4*a*(a*x^2 + b*x^3)^(3/2))/(21*b^2*x)","A",4,3,19,0.1579,1,"{2016, 2002, 2014}"
233,1,80,0,0.073556,"\int x \sqrt{a x^2+b x^3} \, dx","Int[x*Sqrt[a*x^2 + b*x^3],x]","\frac{16 a^2 \left(a x^2+b x^3\right)^{3/2}}{105 b^3 x^3}-\frac{8 a \left(a x^2+b x^3\right)^{3/2}}{35 b^2 x^2}+\frac{2 \left(a x^2+b x^3\right)^{3/2}}{7 b x}","\frac{16 a^2 \left(a x^2+b x^3\right)^{3/2}}{105 b^3 x^3}-\frac{8 a \left(a x^2+b x^3\right)^{3/2}}{35 b^2 x^2}+\frac{2 \left(a x^2+b x^3\right)^{3/2}}{7 b x}",1,"(16*a^2*(a*x^2 + b*x^3)^(3/2))/(105*b^3*x^3) - (8*a*(a*x^2 + b*x^3)^(3/2))/(35*b^2*x^2) + (2*(a*x^2 + b*x^3)^(3/2))/(7*b*x)","A",3,3,17,0.1765,1,"{2016, 2002, 2014}"
234,1,52,0,0.0430886,"\int \sqrt{a x^2+b x^3} \, dx","Int[Sqrt[a*x^2 + b*x^3],x]","\frac{2 \left(a x^2+b x^3\right)^{3/2}}{5 b x^2}-\frac{4 a \left(a x^2+b x^3\right)^{3/2}}{15 b^2 x^3}","\frac{2 \left(a x^2+b x^3\right)^{3/2}}{5 b x^2}-\frac{4 a \left(a x^2+b x^3\right)^{3/2}}{15 b^2 x^3}",1,"(-4*a*(a*x^2 + b*x^3)^(3/2))/(15*b^2*x^3) + (2*(a*x^2 + b*x^3)^(3/2))/(5*b*x^2)","A",2,2,15,0.1333,1,"{2002, 2014}"
235,1,25,0,0.0358451,"\int \frac{\sqrt{a x^2+b x^3}}{x} \, dx","Int[Sqrt[a*x^2 + b*x^3]/x,x]","\frac{2 \left(a x^2+b x^3\right)^{3/2}}{3 b x^3}","\frac{2 \left(a x^2+b x^3\right)^{3/2}}{3 b x^3}",1,"(2*(a*x^2 + b*x^3)^(3/2))/(3*b*x^3)","A",1,1,19,0.05263,1,"{2014}"
236,1,51,0,0.0490906,"\int \frac{\sqrt{a x^2+b x^3}}{x^2} \, dx","Int[Sqrt[a*x^2 + b*x^3]/x^2,x]","\frac{2 \sqrt{a x^2+b x^3}}{x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)","\frac{2 \sqrt{a x^2+b x^3}}{x}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)",1,"(2*Sqrt[a*x^2 + b*x^3])/x - 2*Sqrt[a]*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]]","A",3,3,19,0.1579,1,"{2021, 2008, 206}"
237,1,52,0,0.0519346,"\int \frac{\sqrt{a x^2+b x^3}}{x^3} \, dx","Int[Sqrt[a*x^2 + b*x^3]/x^3,x]","-\frac{\sqrt{a x^2+b x^3}}{x^2}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{\sqrt{a}}","-\frac{\sqrt{a x^2+b x^3}}{x^2}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{\sqrt{a}}",1,"-(Sqrt[a*x^2 + b*x^3]/x^2) - (b*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/Sqrt[a]","A",3,3,19,0.1579,1,"{2020, 2008, 206}"
238,1,84,0,0.0915473,"\int \frac{\sqrt{a x^2+b x^3}}{x^4} \, dx","Int[Sqrt[a*x^2 + b*x^3]/x^4,x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{4 a^{3/2}}-\frac{b \sqrt{a x^2+b x^3}}{4 a x^2}-\frac{\sqrt{a x^2+b x^3}}{2 x^3}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{4 a^{3/2}}-\frac{b \sqrt{a x^2+b x^3}}{4 a x^2}-\frac{\sqrt{a x^2+b x^3}}{2 x^3}",1,"-Sqrt[a*x^2 + b*x^3]/(2*x^3) - (b*Sqrt[a*x^2 + b*x^3])/(4*a*x^2) + (b^2*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/(4*a^(3/2))","A",4,4,19,0.2105,1,"{2020, 2025, 2008, 206}"
239,1,112,0,0.1378768,"\int \frac{\sqrt{a x^2+b x^3}}{x^5} \, dx","Int[Sqrt[a*x^2 + b*x^3]/x^5,x]","\frac{b^2 \sqrt{a x^2+b x^3}}{8 a^2 x^2}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{8 a^{5/2}}-\frac{b \sqrt{a x^2+b x^3}}{12 a x^3}-\frac{\sqrt{a x^2+b x^3}}{3 x^4}","\frac{b^2 \sqrt{a x^2+b x^3}}{8 a^2 x^2}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{8 a^{5/2}}-\frac{b \sqrt{a x^2+b x^3}}{12 a x^3}-\frac{\sqrt{a x^2+b x^3}}{3 x^4}",1,"-Sqrt[a*x^2 + b*x^3]/(3*x^4) - (b*Sqrt[a*x^2 + b*x^3])/(12*a*x^3) + (b^2*Sqrt[a*x^2 + b*x^3])/(8*a^2*x^2) - (b^3*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/(8*a^(5/2))","A",5,4,19,0.2105,1,"{2020, 2025, 2008, 206}"
240,1,161,0,0.2312204,"\int x^2 \left(a x^2+b x^3\right)^{3/2} \, dx","Int[x^2*(a*x^2 + b*x^3)^(3/2),x]","-\frac{512 a^5 \left(a x^2+b x^3\right)^{5/2}}{45045 b^6 x^5}+\frac{256 a^4 \left(a x^2+b x^3\right)^{5/2}}{9009 b^5 x^4}-\frac{64 a^3 \left(a x^2+b x^3\right)^{5/2}}{1287 b^4 x^3}+\frac{32 a^2 \left(a x^2+b x^3\right)^{5/2}}{429 b^3 x^2}-\frac{4 a \left(a x^2+b x^3\right)^{5/2}}{39 b^2 x}+\frac{2 \left(a x^2+b x^3\right)^{5/2}}{15 b}","-\frac{512 a^5 \left(a x^2+b x^3\right)^{5/2}}{45045 b^6 x^5}+\frac{256 a^4 \left(a x^2+b x^3\right)^{5/2}}{9009 b^5 x^4}-\frac{64 a^3 \left(a x^2+b x^3\right)^{5/2}}{1287 b^4 x^3}+\frac{32 a^2 \left(a x^2+b x^3\right)^{5/2}}{429 b^3 x^2}-\frac{4 a \left(a x^2+b x^3\right)^{5/2}}{39 b^2 x}+\frac{2 \left(a x^2+b x^3\right)^{5/2}}{15 b}",1,"(2*(a*x^2 + b*x^3)^(5/2))/(15*b) - (512*a^5*(a*x^2 + b*x^3)^(5/2))/(45045*b^6*x^5) + (256*a^4*(a*x^2 + b*x^3)^(5/2))/(9009*b^5*x^4) - (64*a^3*(a*x^2 + b*x^3)^(5/2))/(1287*b^4*x^3) + (32*a^2*(a*x^2 + b*x^3)^(5/2))/(429*b^3*x^2) - (4*a*(a*x^2 + b*x^3)^(5/2))/(39*b^2*x)","A",6,3,19,0.1579,1,"{2016, 2002, 2014}"
241,1,136,0,0.1716237,"\int x \left(a x^2+b x^3\right)^{3/2} \, dx","Int[x*(a*x^2 + b*x^3)^(3/2),x]","\frac{256 a^4 \left(a x^2+b x^3\right)^{5/2}}{15015 b^5 x^5}-\frac{128 a^3 \left(a x^2+b x^3\right)^{5/2}}{3003 b^4 x^4}+\frac{32 a^2 \left(a x^2+b x^3\right)^{5/2}}{429 b^3 x^3}-\frac{16 a \left(a x^2+b x^3\right)^{5/2}}{143 b^2 x^2}+\frac{2 \left(a x^2+b x^3\right)^{5/2}}{13 b x}","\frac{256 a^4 \left(a x^2+b x^3\right)^{5/2}}{15015 b^5 x^5}-\frac{128 a^3 \left(a x^2+b x^3\right)^{5/2}}{3003 b^4 x^4}+\frac{32 a^2 \left(a x^2+b x^3\right)^{5/2}}{429 b^3 x^3}-\frac{16 a \left(a x^2+b x^3\right)^{5/2}}{143 b^2 x^2}+\frac{2 \left(a x^2+b x^3\right)^{5/2}}{13 b x}",1,"(256*a^4*(a*x^2 + b*x^3)^(5/2))/(15015*b^5*x^5) - (128*a^3*(a*x^2 + b*x^3)^(5/2))/(3003*b^4*x^4) + (32*a^2*(a*x^2 + b*x^3)^(5/2))/(429*b^3*x^3) - (16*a*(a*x^2 + b*x^3)^(5/2))/(143*b^2*x^2) + (2*(a*x^2 + b*x^3)^(5/2))/(13*b*x)","A",5,3,17,0.1765,1,"{2016, 2002, 2014}"
242,1,108,0,0.1412189,"\int \left(a x^2+b x^3\right)^{3/2} \, dx","Int[(a*x^2 + b*x^3)^(3/2),x]","-\frac{32 a^3 \left(a x^2+b x^3\right)^{5/2}}{1155 b^4 x^5}+\frac{16 a^2 \left(a x^2+b x^3\right)^{5/2}}{231 b^3 x^4}-\frac{4 a \left(a x^2+b x^3\right)^{5/2}}{33 b^2 x^3}+\frac{2 \left(a x^2+b x^3\right)^{5/2}}{11 b x^2}","-\frac{32 a^3 \left(a x^2+b x^3\right)^{5/2}}{1155 b^4 x^5}+\frac{16 a^2 \left(a x^2+b x^3\right)^{5/2}}{231 b^3 x^4}-\frac{4 a \left(a x^2+b x^3\right)^{5/2}}{33 b^2 x^3}+\frac{2 \left(a x^2+b x^3\right)^{5/2}}{11 b x^2}",1,"(-32*a^3*(a*x^2 + b*x^3)^(5/2))/(1155*b^4*x^5) + (16*a^2*(a*x^2 + b*x^3)^(5/2))/(231*b^3*x^4) - (4*a*(a*x^2 + b*x^3)^(5/2))/(33*b^2*x^3) + (2*(a*x^2 + b*x^3)^(5/2))/(11*b*x^2)","A",4,3,15,0.2000,1,"{2002, 2016, 2014}"
243,1,80,0,0.132562,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x} \, dx","Int[(a*x^2 + b*x^3)^(3/2)/x,x]","\frac{16 a^2 \left(a x^2+b x^3\right)^{5/2}}{315 b^3 x^5}-\frac{8 a \left(a x^2+b x^3\right)^{5/2}}{63 b^2 x^4}+\frac{2 \left(a x^2+b x^3\right)^{5/2}}{9 b x^3}","\frac{16 a^2 \left(a x^2+b x^3\right)^{5/2}}{315 b^3 x^5}-\frac{8 a \left(a x^2+b x^3\right)^{5/2}}{63 b^2 x^4}+\frac{2 \left(a x^2+b x^3\right)^{5/2}}{9 b x^3}",1,"(16*a^2*(a*x^2 + b*x^3)^(5/2))/(315*b^3*x^5) - (8*a*(a*x^2 + b*x^3)^(5/2))/(63*b^2*x^4) + (2*(a*x^2 + b*x^3)^(5/2))/(9*b*x^3)","A",3,2,19,0.1053,1,"{2016, 2014}"
244,1,52,0,0.0826054,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^2} \, dx","Int[(a*x^2 + b*x^3)^(3/2)/x^2,x]","\frac{2 \left(a x^2+b x^3\right)^{5/2}}{7 b x^4}-\frac{4 a \left(a x^2+b x^3\right)^{5/2}}{35 b^2 x^5}","\frac{2 \left(a x^2+b x^3\right)^{5/2}}{7 b x^4}-\frac{4 a \left(a x^2+b x^3\right)^{5/2}}{35 b^2 x^5}",1,"(-4*a*(a*x^2 + b*x^3)^(5/2))/(35*b^2*x^5) + (2*(a*x^2 + b*x^3)^(5/2))/(7*b*x^4)","A",2,2,19,0.1053,1,"{2016, 2014}"
245,1,25,0,0.0406793,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^3} \, dx","Int[(a*x^2 + b*x^3)^(3/2)/x^3,x]","\frac{2 \left(a x^2+b x^3\right)^{5/2}}{5 b x^5}","\frac{2 \left(a x^2+b x^3\right)^{5/2}}{5 b x^5}",1,"(2*(a*x^2 + b*x^3)^(5/2))/(5*b*x^5)","A",1,1,19,0.05263,1,"{2014}"
246,1,74,0,0.0958373,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^4} \, dx","Int[(a*x^2 + b*x^3)^(3/2)/x^4,x]","-2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)+\frac{2 a \sqrt{a x^2+b x^3}}{x}+\frac{2 \left(a x^2+b x^3\right)^{3/2}}{3 x^3}","-2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)+\frac{2 a \sqrt{a x^2+b x^3}}{x}+\frac{2 \left(a x^2+b x^3\right)^{3/2}}{3 x^3}",1,"(2*a*Sqrt[a*x^2 + b*x^3])/x + (2*(a*x^2 + b*x^3)^(3/2))/(3*x^3) - 2*a^(3/2)*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]]","A",4,3,19,0.1579,1,"{2021, 2008, 206}"
247,1,73,0,0.0931158,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^5} \, dx","Int[(a*x^2 + b*x^3)^(3/2)/x^5,x]","-\frac{\left(a x^2+b x^3\right)^{3/2}}{x^4}+\frac{3 b \sqrt{a x^2+b x^3}}{x}-3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)","-\frac{\left(a x^2+b x^3\right)^{3/2}}{x^4}+\frac{3 b \sqrt{a x^2+b x^3}}{x}-3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)",1,"(3*b*Sqrt[a*x^2 + b*x^3])/x - (a*x^2 + b*x^3)^(3/2)/x^4 - 3*Sqrt[a]*b*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]]","A",4,4,19,0.2105,1,"{2020, 2021, 2008, 206}"
248,1,81,0,0.0921833,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^6} \, dx","Int[(a*x^2 + b*x^3)^(3/2)/x^6,x]","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{4 \sqrt{a}}-\frac{3 b \sqrt{a x^2+b x^3}}{4 x^2}-\frac{\left(a x^2+b x^3\right)^{3/2}}{2 x^5}","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{4 \sqrt{a}}-\frac{3 b \sqrt{a x^2+b x^3}}{4 x^2}-\frac{\left(a x^2+b x^3\right)^{3/2}}{2 x^5}",1,"(-3*b*Sqrt[a*x^2 + b*x^3])/(4*x^2) - (a*x^2 + b*x^3)^(3/2)/(2*x^5) - (3*b^2*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/(4*Sqrt[a])","A",4,3,19,0.1579,1,"{2020, 2008, 206}"
249,1,109,0,0.1341519,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^7} \, dx","Int[(a*x^2 + b*x^3)^(3/2)/x^7,x]","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{8 a^{3/2}}-\frac{b^2 \sqrt{a x^2+b x^3}}{8 a x^2}-\frac{b \sqrt{a x^2+b x^3}}{4 x^3}-\frac{\left(a x^2+b x^3\right)^{3/2}}{3 x^6}","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{8 a^{3/2}}-\frac{b^2 \sqrt{a x^2+b x^3}}{8 a x^2}-\frac{b \sqrt{a x^2+b x^3}}{4 x^3}-\frac{\left(a x^2+b x^3\right)^{3/2}}{3 x^6}",1,"-(b*Sqrt[a*x^2 + b*x^3])/(4*x^3) - (b^2*Sqrt[a*x^2 + b*x^3])/(8*a*x^2) - (a*x^2 + b*x^3)^(3/2)/(3*x^6) + (b^3*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/(8*a^(3/2))","A",5,4,19,0.2105,1,"{2020, 2025, 2008, 206}"
250,1,137,0,0.1841904,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^8} \, dx","Int[(a*x^2 + b*x^3)^(3/2)/x^8,x]","\frac{3 b^3 \sqrt{a x^2+b x^3}}{64 a^2 x^2}-\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{64 a^{5/2}}-\frac{b^2 \sqrt{a x^2+b x^3}}{32 a x^3}-\frac{b \sqrt{a x^2+b x^3}}{8 x^4}-\frac{\left(a x^2+b x^3\right)^{3/2}}{4 x^7}","\frac{3 b^3 \sqrt{a x^2+b x^3}}{64 a^2 x^2}-\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{64 a^{5/2}}-\frac{b^2 \sqrt{a x^2+b x^3}}{32 a x^3}-\frac{b \sqrt{a x^2+b x^3}}{8 x^4}-\frac{\left(a x^2+b x^3\right)^{3/2}}{4 x^7}",1,"-(b*Sqrt[a*x^2 + b*x^3])/(8*x^4) - (b^2*Sqrt[a*x^2 + b*x^3])/(32*a*x^3) + (3*b^3*Sqrt[a*x^2 + b*x^3])/(64*a^2*x^2) - (a*x^2 + b*x^3)^(3/2)/(4*x^7) - (3*b^4*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/(64*a^(5/2))","A",6,4,19,0.2105,1,"{2020, 2025, 2008, 206}"
251,1,165,0,0.2361052,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^9} \, dx","Int[(a*x^2 + b*x^3)^(3/2)/x^9,x]","-\frac{3 b^4 \sqrt{a x^2+b x^3}}{128 a^3 x^2}+\frac{b^3 \sqrt{a x^2+b x^3}}{64 a^2 x^3}+\frac{3 b^5 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{128 a^{7/2}}-\frac{b^2 \sqrt{a x^2+b x^3}}{80 a x^4}-\frac{3 b \sqrt{a x^2+b x^3}}{40 x^5}-\frac{\left(a x^2+b x^3\right)^{3/2}}{5 x^8}","-\frac{3 b^4 \sqrt{a x^2+b x^3}}{128 a^3 x^2}+\frac{b^3 \sqrt{a x^2+b x^3}}{64 a^2 x^3}+\frac{3 b^5 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{128 a^{7/2}}-\frac{b^2 \sqrt{a x^2+b x^3}}{80 a x^4}-\frac{3 b \sqrt{a x^2+b x^3}}{40 x^5}-\frac{\left(a x^2+b x^3\right)^{3/2}}{5 x^8}",1,"(-3*b*Sqrt[a*x^2 + b*x^3])/(40*x^5) - (b^2*Sqrt[a*x^2 + b*x^3])/(80*a*x^4) + (b^3*Sqrt[a*x^2 + b*x^3])/(64*a^2*x^3) - (3*b^4*Sqrt[a*x^2 + b*x^3])/(128*a^3*x^2) - (a*x^2 + b*x^3)^(3/2)/(5*x^8) + (3*b^5*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/(128*a^(7/2))","A",7,4,19,0.2105,1,"{2020, 2025, 2008, 206}"
252,1,103,0,0.1484664,"\int \frac{x^4}{\sqrt{a x^2+b x^3}} \, dx","Int[x^4/Sqrt[a*x^2 + b*x^3],x]","-\frac{32 a^3 \sqrt{a x^2+b x^3}}{35 b^4 x}+\frac{16 a^2 \sqrt{a x^2+b x^3}}{35 b^3}-\frac{12 a x \sqrt{a x^2+b x^3}}{35 b^2}+\frac{2 x^2 \sqrt{a x^2+b x^3}}{7 b}","-\frac{32 a^3 \sqrt{a x^2+b x^3}}{35 b^4 x}+\frac{16 a^2 \sqrt{a x^2+b x^3}}{35 b^3}-\frac{12 a x \sqrt{a x^2+b x^3}}{35 b^2}+\frac{2 x^2 \sqrt{a x^2+b x^3}}{7 b}",1,"(16*a^2*Sqrt[a*x^2 + b*x^3])/(35*b^3) - (32*a^3*Sqrt[a*x^2 + b*x^3])/(35*b^4*x) - (12*a*x*Sqrt[a*x^2 + b*x^3])/(35*b^2) + (2*x^2*Sqrt[a*x^2 + b*x^3])/(7*b)","A",4,2,19,0.1053,1,"{2016, 1588}"
253,1,75,0,0.0999528,"\int \frac{x^3}{\sqrt{a x^2+b x^3}} \, dx","Int[x^3/Sqrt[a*x^2 + b*x^3],x]","\frac{16 a^2 \sqrt{a x^2+b x^3}}{15 b^3 x}-\frac{8 a \sqrt{a x^2+b x^3}}{15 b^2}+\frac{2 x \sqrt{a x^2+b x^3}}{5 b}","\frac{16 a^2 \sqrt{a x^2+b x^3}}{15 b^3 x}-\frac{8 a \sqrt{a x^2+b x^3}}{15 b^2}+\frac{2 x \sqrt{a x^2+b x^3}}{5 b}",1,"(-8*a*Sqrt[a*x^2 + b*x^3])/(15*b^2) + (16*a^2*Sqrt[a*x^2 + b*x^3])/(15*b^3*x) + (2*x*Sqrt[a*x^2 + b*x^3])/(5*b)","A",3,2,19,0.1053,1,"{2016, 1588}"
254,1,49,0,0.0545702,"\int \frac{x^2}{\sqrt{a x^2+b x^3}} \, dx","Int[x^2/Sqrt[a*x^2 + b*x^3],x]","\frac{2 \sqrt{a x^2+b x^3}}{3 b}-\frac{4 a \sqrt{a x^2+b x^3}}{3 b^2 x}","\frac{2 \sqrt{a x^2+b x^3}}{3 b}-\frac{4 a \sqrt{a x^2+b x^3}}{3 b^2 x}",1,"(2*Sqrt[a*x^2 + b*x^3])/(3*b) - (4*a*Sqrt[a*x^2 + b*x^3])/(3*b^2*x)","A",2,2,19,0.1053,1,"{2016, 1588}"
255,1,23,0,0.0101149,"\int \frac{x}{\sqrt{a x^2+b x^3}} \, dx","Int[x/Sqrt[a*x^2 + b*x^3],x]","\frac{2 \sqrt{a x^2+b x^3}}{b x}","\frac{2 \sqrt{a x^2+b x^3}}{b x}",1,"(2*Sqrt[a*x^2 + b*x^3])/(b*x)","A",1,1,17,0.05882,1,"{1588}"
256,1,30,0,0.0105473,"\int \frac{1}{\sqrt{a x^2+b x^3}} \, dx","Int[1/Sqrt[a*x^2 + b*x^3],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{\sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{\sqrt{a}}",1,"(-2*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/Sqrt[a]","A",2,2,15,0.1333,1,"{2008, 206}"
257,1,54,0,0.0489975,"\int \frac{1}{x \sqrt{a x^2+b x^3}} \, dx","Int[1/(x*Sqrt[a*x^2 + b*x^3]),x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{a^{3/2}}-\frac{\sqrt{a x^2+b x^3}}{a x^2}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{a^{3/2}}-\frac{\sqrt{a x^2+b x^3}}{a x^2}",1,"-(Sqrt[a*x^2 + b*x^3]/(a*x^2)) + (b*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/a^(3/2)","A",3,3,19,0.1579,1,"{2025, 2008, 206}"
258,1,87,0,0.0911053,"\int \frac{1}{x^2 \sqrt{a x^2+b x^3}} \, dx","Int[1/(x^2*Sqrt[a*x^2 + b*x^3]),x]","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{4 a^{5/2}}+\frac{3 b \sqrt{a x^2+b x^3}}{4 a^2 x^2}-\frac{\sqrt{a x^2+b x^3}}{2 a x^3}","-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{4 a^{5/2}}+\frac{3 b \sqrt{a x^2+b x^3}}{4 a^2 x^2}-\frac{\sqrt{a x^2+b x^3}}{2 a x^3}",1,"-Sqrt[a*x^2 + b*x^3]/(2*a*x^3) + (3*b*Sqrt[a*x^2 + b*x^3])/(4*a^2*x^2) - (3*b^2*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/(4*a^(5/2))","A",4,3,19,0.1579,1,"{2025, 2008, 206}"
259,1,115,0,0.1353883,"\int \frac{1}{x^3 \sqrt{a x^2+b x^3}} \, dx","Int[1/(x^3*Sqrt[a*x^2 + b*x^3]),x]","-\frac{5 b^2 \sqrt{a x^2+b x^3}}{8 a^3 x^2}+\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{8 a^{7/2}}+\frac{5 b \sqrt{a x^2+b x^3}}{12 a^2 x^3}-\frac{\sqrt{a x^2+b x^3}}{3 a x^4}","-\frac{5 b^2 \sqrt{a x^2+b x^3}}{8 a^3 x^2}+\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{8 a^{7/2}}+\frac{5 b \sqrt{a x^2+b x^3}}{12 a^2 x^3}-\frac{\sqrt{a x^2+b x^3}}{3 a x^4}",1,"-Sqrt[a*x^2 + b*x^3]/(3*a*x^4) + (5*b*Sqrt[a*x^2 + b*x^3])/(12*a^2*x^3) - (5*b^2*Sqrt[a*x^2 + b*x^3])/(8*a^3*x^2) + (5*b^3*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/(8*a^(7/2))","A",5,3,19,0.1579,1,"{2025, 2008, 206}"
260,1,98,0,0.1508822,"\int \frac{x^6}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Int[x^6/(a*x^2 + b*x^3)^(3/2),x]","\frac{32 a^2 \sqrt{a x^2+b x^3}}{5 b^4 x}+\frac{12 x \sqrt{a x^2+b x^3}}{5 b^2}-\frac{16 a \sqrt{a x^2+b x^3}}{5 b^3}-\frac{2 x^4}{b \sqrt{a x^2+b x^3}}","\frac{32 a^2 \sqrt{a x^2+b x^3}}{5 b^4 x}+\frac{12 x \sqrt{a x^2+b x^3}}{5 b^2}-\frac{16 a \sqrt{a x^2+b x^3}}{5 b^3}-\frac{2 x^4}{b \sqrt{a x^2+b x^3}}",1,"(-2*x^4)/(b*Sqrt[a*x^2 + b*x^3]) - (16*a*Sqrt[a*x^2 + b*x^3])/(5*b^3) + (32*a^2*Sqrt[a*x^2 + b*x^3])/(5*b^4*x) + (12*x*Sqrt[a*x^2 + b*x^3])/(5*b^2)","A",4,3,19,0.1579,1,"{2015, 2016, 1588}"
261,1,72,0,0.1052151,"\int \frac{x^5}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Int[x^5/(a*x^2 + b*x^3)^(3/2),x]","\frac{8 \sqrt{a x^2+b x^3}}{3 b^2}-\frac{16 a \sqrt{a x^2+b x^3}}{3 b^3 x}-\frac{2 x^3}{b \sqrt{a x^2+b x^3}}","\frac{8 \sqrt{a x^2+b x^3}}{3 b^2}-\frac{16 a \sqrt{a x^2+b x^3}}{3 b^3 x}-\frac{2 x^3}{b \sqrt{a x^2+b x^3}}",1,"(-2*x^3)/(b*Sqrt[a*x^2 + b*x^3]) + (8*Sqrt[a*x^2 + b*x^3])/(3*b^2) - (16*a*Sqrt[a*x^2 + b*x^3])/(3*b^3*x)","A",3,3,19,0.1579,1,"{2015, 2016, 1588}"
262,1,47,0,0.0567734,"\int \frac{x^4}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Int[x^4/(a*x^2 + b*x^3)^(3/2),x]","\frac{4 \sqrt{a x^2+b x^3}}{b^2 x}-\frac{2 x^2}{b \sqrt{a x^2+b x^3}}","\frac{4 \sqrt{a x^2+b x^3}}{b^2 x}-\frac{2 x^2}{b \sqrt{a x^2+b x^3}}",1,"(-2*x^2)/(b*Sqrt[a*x^2 + b*x^3]) + (4*Sqrt[a*x^2 + b*x^3])/(b^2*x)","A",2,2,19,0.1053,1,"{2015, 1588}"
263,1,21,0,0.0175054,"\int \frac{x^3}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Int[x^3/(a*x^2 + b*x^3)^(3/2),x]","-\frac{2 x}{b \sqrt{a x^2+b x^3}}","-\frac{2 x}{b \sqrt{a x^2+b x^3}}",1,"(-2*x)/(b*Sqrt[a*x^2 + b*x^3])","A",1,1,19,0.05263,1,"{1588}"
264,1,52,0,0.0583374,"\int \frac{x^2}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Int[x^2/(a*x^2 + b*x^3)^(3/2),x]","\frac{2 x}{a \sqrt{a x^2+b x^3}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{a^{3/2}}","\frac{2 x}{a \sqrt{a x^2+b x^3}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{a^{3/2}}",1,"(2*x)/(a*Sqrt[a*x^2 + b*x^3]) - (2*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/a^(3/2)","A",3,3,19,0.1579,1,"{2023, 2008, 206}"
265,1,75,0,0.0857002,"\int \frac{x}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Int[x/(a*x^2 + b*x^3)^(3/2),x]","-\frac{3 \sqrt{a x^2+b x^3}}{a^2 x^2}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{a^{5/2}}+\frac{2}{a \sqrt{a x^2+b x^3}}","-\frac{3 \sqrt{a x^2+b x^3}}{a^2 x^2}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{a^{5/2}}+\frac{2}{a \sqrt{a x^2+b x^3}}",1,"2/(a*Sqrt[a*x^2 + b*x^3]) - (3*Sqrt[a*x^2 + b*x^3])/(a^2*x^2) + (3*b*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/a^(5/2)","A",4,4,17,0.2353,1,"{2023, 2025, 2008, 206}"
266,1,110,0,0.1051748,"\int \frac{1}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Int[(a*x^2 + b*x^3)^(-3/2),x]","-\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{4 a^{7/2}}+\frac{15 b \sqrt{a x^2+b x^3}}{4 a^3 x^2}-\frac{5 \sqrt{a x^2+b x^3}}{2 a^2 x^3}+\frac{2}{a x \sqrt{a x^2+b x^3}}","-\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{4 a^{7/2}}+\frac{15 b \sqrt{a x^2+b x^3}}{4 a^3 x^2}-\frac{5 \sqrt{a x^2+b x^3}}{2 a^2 x^3}+\frac{2}{a x \sqrt{a x^2+b x^3}}",1,"2/(a*x*Sqrt[a*x^2 + b*x^3]) - (5*Sqrt[a*x^2 + b*x^3])/(2*a^2*x^3) + (15*b*Sqrt[a*x^2 + b*x^3])/(4*a^3*x^2) - (15*b^2*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/(4*a^(7/2))","A",5,4,15,0.2667,1,"{2006, 2025, 2008, 206}"
267,1,138,0,0.1862718,"\int \frac{1}{x \left(a x^2+b x^3\right)^{3/2}} \, dx","Int[1/(x*(a*x^2 + b*x^3)^(3/2)),x]","-\frac{35 b^2 \sqrt{a x^2+b x^3}}{8 a^4 x^2}+\frac{35 b^3 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{8 a^{9/2}}+\frac{35 b \sqrt{a x^2+b x^3}}{12 a^3 x^3}-\frac{7 \sqrt{a x^2+b x^3}}{3 a^2 x^4}+\frac{2}{a x^2 \sqrt{a x^2+b x^3}}","-\frac{35 b^2 \sqrt{a x^2+b x^3}}{8 a^4 x^2}+\frac{35 b^3 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{8 a^{9/2}}+\frac{35 b \sqrt{a x^2+b x^3}}{12 a^3 x^3}-\frac{7 \sqrt{a x^2+b x^3}}{3 a^2 x^4}+\frac{2}{a x^2 \sqrt{a x^2+b x^3}}",1,"2/(a*x^2*Sqrt[a*x^2 + b*x^3]) - (7*Sqrt[a*x^2 + b*x^3])/(3*a^2*x^4) + (35*b*Sqrt[a*x^2 + b*x^3])/(12*a^3*x^3) - (35*b^2*Sqrt[a*x^2 + b*x^3])/(8*a^4*x^2) + (35*b^3*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/(8*a^(9/2))","A",6,4,19,0.2105,1,"{2023, 2025, 2008, 206}"
268,1,166,0,0.2324475,"\int \frac{1}{x^2 \left(a x^2+b x^3\right)^{3/2}} \, dx","Int[1/(x^2*(a*x^2 + b*x^3)^(3/2)),x]","\frac{315 b^3 \sqrt{a x^2+b x^3}}{64 a^5 x^2}-\frac{105 b^2 \sqrt{a x^2+b x^3}}{32 a^4 x^3}-\frac{315 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{64 a^{11/2}}+\frac{21 b \sqrt{a x^2+b x^3}}{8 a^3 x^4}-\frac{9 \sqrt{a x^2+b x^3}}{4 a^2 x^5}+\frac{2}{a x^3 \sqrt{a x^2+b x^3}}","\frac{315 b^3 \sqrt{a x^2+b x^3}}{64 a^5 x^2}-\frac{105 b^2 \sqrt{a x^2+b x^3}}{32 a^4 x^3}-\frac{315 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{64 a^{11/2}}+\frac{21 b \sqrt{a x^2+b x^3}}{8 a^3 x^4}-\frac{9 \sqrt{a x^2+b x^3}}{4 a^2 x^5}+\frac{2}{a x^3 \sqrt{a x^2+b x^3}}",1,"2/(a*x^3*Sqrt[a*x^2 + b*x^3]) - (9*Sqrt[a*x^2 + b*x^3])/(4*a^2*x^5) + (21*b*Sqrt[a*x^2 + b*x^3])/(8*a^3*x^4) - (105*b^2*Sqrt[a*x^2 + b*x^3])/(32*a^4*x^3) + (315*b^3*Sqrt[a*x^2 + b*x^3])/(64*a^5*x^2) - (315*b^4*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^3]])/(64*a^(11/2))","A",7,4,19,0.2105,1,"{2023, 2025, 2008, 206}"
269,1,125,0,0.1694489,"\int \frac{x^{7/2}}{\sqrt{a x^2+b x^3}} \, dx","Int[x^(7/2)/Sqrt[a*x^2 + b*x^3],x]","\frac{5 a^2 \sqrt{a x^2+b x^3}}{8 b^3 \sqrt{x}}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x^2+b x^3}}\right)}{8 b^{7/2}}-\frac{5 a \sqrt{x} \sqrt{a x^2+b x^3}}{12 b^2}+\frac{x^{3/2} \sqrt{a x^2+b x^3}}{3 b}","\frac{5 a^2 \sqrt{a x^2+b x^3}}{8 b^3 \sqrt{x}}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x^2+b x^3}}\right)}{8 b^{7/2}}-\frac{5 a \sqrt{x} \sqrt{a x^2+b x^3}}{12 b^2}+\frac{x^{3/2} \sqrt{a x^2+b x^3}}{3 b}",1,"(5*a^2*Sqrt[a*x^2 + b*x^3])/(8*b^3*Sqrt[x]) - (5*a*Sqrt[x]*Sqrt[a*x^2 + b*x^3])/(12*b^2) + (x^(3/2)*Sqrt[a*x^2 + b*x^3])/(3*b) - (5*a^3*ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a*x^2 + b*x^3]])/(8*b^(7/2))","A",5,3,21,0.1429,1,"{2024, 2029, 206}"
270,1,95,0,0.1254405,"\int \frac{x^{5/2}}{\sqrt{a x^2+b x^3}} \, dx","Int[x^(5/2)/Sqrt[a*x^2 + b*x^3],x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x^2+b x^3}}\right)}{4 b^{5/2}}-\frac{3 a \sqrt{a x^2+b x^3}}{4 b^2 \sqrt{x}}+\frac{\sqrt{x} \sqrt{a x^2+b x^3}}{2 b}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x^2+b x^3}}\right)}{4 b^{5/2}}-\frac{3 a \sqrt{a x^2+b x^3}}{4 b^2 \sqrt{x}}+\frac{\sqrt{x} \sqrt{a x^2+b x^3}}{2 b}",1,"(-3*a*Sqrt[a*x^2 + b*x^3])/(4*b^2*Sqrt[x]) + (Sqrt[x]*Sqrt[a*x^2 + b*x^3])/(2*b) + (3*a^2*ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a*x^2 + b*x^3]])/(4*b^(5/2))","A",4,3,21,0.1429,1,"{2024, 2029, 206}"
271,1,60,0,0.0833389,"\int \frac{x^{3/2}}{\sqrt{a x^2+b x^3}} \, dx","Int[x^(3/2)/Sqrt[a*x^2 + b*x^3],x]","\frac{\sqrt{a x^2+b x^3}}{b \sqrt{x}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x^2+b x^3}}\right)}{b^{3/2}}","\frac{\sqrt{a x^2+b x^3}}{b \sqrt{x}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x^2+b x^3}}\right)}{b^{3/2}}",1,"Sqrt[a*x^2 + b*x^3]/(b*Sqrt[x]) - (a*ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a*x^2 + b*x^3]])/b^(3/2)","A",3,3,21,0.1429,1,"{2024, 2029, 206}"
272,1,34,0,0.0424737,"\int \frac{\sqrt{x}}{\sqrt{a x^2+b x^3}} \, dx","Int[Sqrt[x]/Sqrt[a*x^2 + b*x^3],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x^2+b x^3}}\right)}{\sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x^2+b x^3}}\right)}{\sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a*x^2 + b*x^3]])/Sqrt[b]","A",2,2,21,0.09524,1,"{2029, 206}"
273,1,25,0,0.0377593,"\int \frac{1}{\sqrt{x} \sqrt{a x^2+b x^3}} \, dx","Int[1/(Sqrt[x]*Sqrt[a*x^2 + b*x^3]),x]","-\frac{2 \sqrt{a x^2+b x^3}}{a x^{3/2}}","-\frac{2 \sqrt{a x^2+b x^3}}{a x^{3/2}}",1,"(-2*Sqrt[a*x^2 + b*x^3])/(a*x^(3/2))","A",1,1,21,0.04762,1,"{2014}"
274,1,56,0,0.0766247,"\int \frac{1}{x^{3/2} \sqrt{a x^2+b x^3}} \, dx","Int[1/(x^(3/2)*Sqrt[a*x^2 + b*x^3]),x]","\frac{4 b \sqrt{a x^2+b x^3}}{3 a^2 x^{3/2}}-\frac{2 \sqrt{a x^2+b x^3}}{3 a x^{5/2}}","\frac{4 b \sqrt{a x^2+b x^3}}{3 a^2 x^{3/2}}-\frac{2 \sqrt{a x^2+b x^3}}{3 a x^{5/2}}",1,"(-2*Sqrt[a*x^2 + b*x^3])/(3*a*x^(5/2)) + (4*b*Sqrt[a*x^2 + b*x^3])/(3*a^2*x^(3/2))","A",2,2,21,0.09524,1,"{2016, 2014}"
275,1,86,0,0.1178004,"\int \frac{1}{x^{5/2} \sqrt{a x^2+b x^3}} \, dx","Int[1/(x^(5/2)*Sqrt[a*x^2 + b*x^3]),x]","-\frac{16 b^2 \sqrt{a x^2+b x^3}}{15 a^3 x^{3/2}}+\frac{8 b \sqrt{a x^2+b x^3}}{15 a^2 x^{5/2}}-\frac{2 \sqrt{a x^2+b x^3}}{5 a x^{7/2}}","-\frac{16 b^2 \sqrt{a x^2+b x^3}}{15 a^3 x^{3/2}}+\frac{8 b \sqrt{a x^2+b x^3}}{15 a^2 x^{5/2}}-\frac{2 \sqrt{a x^2+b x^3}}{5 a x^{7/2}}",1,"(-2*Sqrt[a*x^2 + b*x^3])/(5*a*x^(7/2)) + (8*b*Sqrt[a*x^2 + b*x^3])/(15*a^2*x^(5/2)) - (16*b^2*Sqrt[a*x^2 + b*x^3])/(15*a^3*x^(3/2))","A",3,2,21,0.09524,1,"{2016, 2014}"
276,1,116,0,0.1627655,"\int \frac{1}{x^{7/2} \sqrt{a x^2+b x^3}} \, dx","Int[1/(x^(7/2)*Sqrt[a*x^2 + b*x^3]),x]","\frac{32 b^3 \sqrt{a x^2+b x^3}}{35 a^4 x^{3/2}}-\frac{16 b^2 \sqrt{a x^2+b x^3}}{35 a^3 x^{5/2}}+\frac{12 b \sqrt{a x^2+b x^3}}{35 a^2 x^{7/2}}-\frac{2 \sqrt{a x^2+b x^3}}{7 a x^{9/2}}","\frac{32 b^3 \sqrt{a x^2+b x^3}}{35 a^4 x^{3/2}}-\frac{16 b^2 \sqrt{a x^2+b x^3}}{35 a^3 x^{5/2}}+\frac{12 b \sqrt{a x^2+b x^3}}{35 a^2 x^{7/2}}-\frac{2 \sqrt{a x^2+b x^3}}{7 a x^{9/2}}",1,"(-2*Sqrt[a*x^2 + b*x^3])/(7*a*x^(9/2)) + (12*b*Sqrt[a*x^2 + b*x^3])/(35*a^2*x^(7/2)) - (16*b^2*Sqrt[a*x^2 + b*x^3])/(35*a^3*x^(5/2)) + (32*b^3*Sqrt[a*x^2 + b*x^3])/(35*a^4*x^(3/2))","A",4,2,21,0.09524,1,"{2016, 2014}"
277,1,61,0,0.038824,"\int x^{1-3 n} \left(a x^2+b x^3\right)^n \, dx","Int[x^(1 - 3*n)*(a*x^2 + b*x^3)^n,x]","\frac{x^{2-3 n} \left(\frac{b x}{a}+1\right)^{-n} \left(a x^2+b x^3\right)^n \, _2F_1\left(2-n,-n;3-n;-\frac{b x}{a}\right)}{2-n}","\frac{x^{2-3 n} \left(\frac{b x}{a}+1\right)^{-n} \left(a x^2+b x^3\right)^n \, _2F_1\left(2-n,-n;3-n;-\frac{b x}{a}\right)}{2-n}",1,"(x^(2 - 3*n)*(a*x^2 + b*x^3)^n*Hypergeometric2F1[2 - n, -n, 3 - n, -((b*x)/a)])/((2 - n)*(1 + (b*x)/a)^n)","A",3,3,21,0.1429,1,"{2032, 66, 64}"
278,1,61,0,0.0371099,"\int x^{-3 n} \left(a x^2+b x^3\right)^n \, dx","Int[(a*x^2 + b*x^3)^n/x^(3*n),x]","\frac{x^{1-3 n} \left(\frac{b x}{a}+1\right)^{-n} \left(a x^2+b x^3\right)^n \, _2F_1\left(1-n,-n;2-n;-\frac{b x}{a}\right)}{1-n}","\frac{x^{-3 n-1} \left(a x^2+b x^3\right)^{n+1} \, _2F_1\left(1,2;2-n;-\frac{b x}{a}\right)}{a (1-n)}",1,"(x^(1 - 3*n)*(a*x^2 + b*x^3)^n*Hypergeometric2F1[1 - n, -n, 2 - n, -((b*x)/a)])/((1 - n)*(1 + (b*x)/a)^n)","A",3,3,19,0.1579,1,"{2032, 66, 64}"
279,1,54,0,0.0382429,"\int x^{-1-3 n} \left(a x^2+b x^3\right)^n \, dx","Int[x^(-1 - 3*n)*(a*x^2 + b*x^3)^n,x]","-\frac{x^{-3 n} \left(\frac{b x}{a}+1\right)^{-n} \left(a x^2+b x^3\right)^n \, _2F_1\left(-n,-n;1-n;-\frac{b x}{a}\right)}{n}","-\frac{x^{-3 n} \left(\frac{b x}{a}+1\right)^{-n} \left(a x^2+b x^3\right)^n \, _2F_1\left(-n,-n;1-n;-\frac{b x}{a}\right)}{n}",1,"-(((a*x^2 + b*x^3)^n*Hypergeometric2F1[-n, -n, 1 - n, -((b*x)/a)])/(n*x^(3*n)*(1 + (b*x)/a)^n))","A",3,3,21,0.1429,1,"{2032, 66, 64}"
280,1,32,0,0.0251077,"\int x^{-2-3 n} \left(a x^2+b x^3\right)^n \, dx","Int[x^(-2 - 3*n)*(a*x^2 + b*x^3)^n,x]","-\frac{x^{-3 (n+1)} \left(a x^2+b x^3\right)^{n+1}}{a (n+1)}","-\frac{x^{-3 (n+1)} \left(a x^2+b x^3\right)^{n+1}}{a (n+1)}",1,"-((a*x^2 + b*x^3)^(1 + n)/(a*(1 + n)*x^(3*(1 + n))))","A",1,1,21,0.04762,1,"{2014}"
281,1,70,0,0.0543414,"\int x^{-3-3 n} \left(a x^2+b x^3\right)^n \, dx","Int[x^(-3 - 3*n)*(a*x^2 + b*x^3)^n,x]","\frac{b x^{-3 (n+1)} \left(a x^2+b x^3\right)^{n+1}}{a^2 (n+1) (n+2)}-\frac{x^{-3 n-4} \left(a x^2+b x^3\right)^{n+1}}{a (n+2)}","\frac{b x^{-3 (n+1)} \left(a x^2+b x^3\right)^{n+1}}{a^2 (n+1) (n+2)}-\frac{x^{-3 n-4} \left(a x^2+b x^3\right)^{n+1}}{a (n+2)}",1,"-((x^(-4 - 3*n)*(a*x^2 + b*x^3)^(1 + n))/(a*(2 + n))) + (b*(a*x^2 + b*x^3)^(1 + n))/(a^2*(1 + n)*(2 + n)*x^(3*(1 + n)))","A",2,2,21,0.09524,1,"{2016, 2014}"
282,1,116,0,0.0914168,"\int x^{-4-3 n} \left(a x^2+b x^3\right)^n \, dx","Int[x^(-4 - 3*n)*(a*x^2 + b*x^3)^n,x]","-\frac{2 b^2 x^{-3 (n+1)} \left(a x^2+b x^3\right)^{n+1}}{a^3 (n+1) (n+2) (n+3)}+\frac{2 b x^{-3 n-4} \left(a x^2+b x^3\right)^{n+1}}{a^2 (n+2) (n+3)}-\frac{x^{-3 n-5} \left(a x^2+b x^3\right)^{n+1}}{a (n+3)}","-\frac{2 b^2 x^{-3 (n+1)} \left(a x^2+b x^3\right)^{n+1}}{a^3 (n+1) (n+2) (n+3)}+\frac{2 b x^{-3 n-4} \left(a x^2+b x^3\right)^{n+1}}{a^2 (n+2) (n+3)}-\frac{x^{-3 n-5} \left(a x^2+b x^3\right)^{n+1}}{a (n+3)}",1,"-((x^(-5 - 3*n)*(a*x^2 + b*x^3)^(1 + n))/(a*(3 + n))) + (2*b*x^(-4 - 3*n)*(a*x^2 + b*x^3)^(1 + n))/(a^2*(2 + n)*(3 + n)) - (2*b^2*(a*x^2 + b*x^3)^(1 + n))/(a^3*(1 + n)*(2 + n)*(3 + n)*x^(3*(1 + n)))","A",3,2,21,0.09524,1,"{2016, 2014}"
283,1,19,0,0.0100698,"\int \frac{x^{11}}{\left(a x^2+b x^5\right)^3} \, dx","Int[x^11/(a*x^2 + b*x^5)^3,x]","\frac{x^6}{6 a \left(a+b x^3\right)^2}","\frac{x^6}{6 a \left(a+b x^3\right)^2}",1,"x^6/(6*a*(a + b*x^3)^2)","A",2,2,17,0.1176,1,"{1584, 264}"
284,1,80,0,0.1148125,"\int \frac{x^9}{\sqrt{a x^2+b x^5}} \, dx","Int[x^9/Sqrt[a*x^2 + b*x^5],x]","\frac{16 a^2 \sqrt{a x^2+b x^5}}{45 b^3 x}-\frac{8 a x^2 \sqrt{a x^2+b x^5}}{45 b^2}+\frac{2 x^5 \sqrt{a x^2+b x^5}}{15 b}","\frac{16 a^2 \sqrt{a x^2+b x^5}}{45 b^3 x}-\frac{8 a x^2 \sqrt{a x^2+b x^5}}{45 b^2}+\frac{2 x^5 \sqrt{a x^2+b x^5}}{15 b}",1,"(16*a^2*Sqrt[a*x^2 + b*x^5])/(45*b^3*x) - (8*a*x^2*Sqrt[a*x^2 + b*x^5])/(45*b^2) + (2*x^5*Sqrt[a*x^2 + b*x^5])/(15*b)","A",3,2,19,0.1053,1,"{2016, 1588}"
285,1,52,0,0.0649265,"\int \frac{x^6}{\sqrt{a x^2+b x^5}} \, dx","Int[x^6/Sqrt[a*x^2 + b*x^5],x]","\frac{2 x^2 \sqrt{a x^2+b x^5}}{9 b}-\frac{4 a \sqrt{a x^2+b x^5}}{9 b^2 x}","\frac{2 x^2 \sqrt{a x^2+b x^5}}{9 b}-\frac{4 a \sqrt{a x^2+b x^5}}{9 b^2 x}",1,"(-4*a*Sqrt[a*x^2 + b*x^5])/(9*b^2*x) + (2*x^2*Sqrt[a*x^2 + b*x^5])/(9*b)","A",2,2,19,0.1053,1,"{2016, 1588}"
286,1,25,0,0.016886,"\int \frac{x^3}{\sqrt{a x^2+b x^5}} \, dx","Int[x^3/Sqrt[a*x^2 + b*x^5],x]","\frac{2 \sqrt{a x^2+b x^5}}{3 b x}","\frac{2 \sqrt{a x^2+b x^5}}{3 b x}",1,"(2*Sqrt[a*x^2 + b*x^5])/(3*b*x)","A",1,1,19,0.05263,1,"{1588}"
287,1,32,0,0.0109513,"\int \frac{1}{\sqrt{a x^2+b x^5}} \, dx","Int[1/Sqrt[a*x^2 + b*x^5],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^5}}\right)}{3 \sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^5}}\right)}{3 \sqrt{a}}",1,"(-2*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^5]])/(3*Sqrt[a])","A",2,2,15,0.1333,1,"{2008, 206}"
288,1,59,0,0.0545933,"\int \frac{1}{x^3 \sqrt{a x^2+b x^5}} \, dx","Int[1/(x^3*Sqrt[a*x^2 + b*x^5]),x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^5}}\right)}{3 a^{3/2}}-\frac{\sqrt{a x^2+b x^5}}{3 a x^4}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^5}}\right)}{3 a^{3/2}}-\frac{\sqrt{a x^2+b x^5}}{3 a x^4}",1,"-Sqrt[a*x^2 + b*x^5]/(3*a*x^4) + (b*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^5]])/(3*a^(3/2))","A",3,3,19,0.1579,1,"{2025, 2008, 206}"
289,1,238,0,0.1415681,"\int \frac{x^4}{\sqrt{a x^2+b x^5}} \, dx","Int[x^4/Sqrt[a*x^2 + b*x^5],x]","\frac{2 \sqrt{a x^2+b x^5}}{5 b}-\frac{4 \sqrt{2+\sqrt{3}} a x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}","\frac{2 \sqrt{a x^2+b x^5}}{5 b}-\frac{4 \sqrt{2+\sqrt{3}} a x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}",1,"(2*Sqrt[a*x^2 + b*x^5])/(5*b) - (4*Sqrt[2 + Sqrt[3]]*a*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(5*3^(1/4)*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",3,3,19,0.1579,1,"{2024, 2032, 218}"
290,1,212,0,0.0667158,"\int \frac{x}{\sqrt{a x^2+b x^5}} \, dx","Int[x/Sqrt[a*x^2 + b*x^5],x]","\frac{2 \sqrt{2+\sqrt{3}} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}","\frac{2 \sqrt{2+\sqrt{3}} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}",1,"(2*Sqrt[2 + Sqrt[3]]*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",2,2,17,0.1176,1,"{2032, 218}"
291,1,243,0,0.1286268,"\int \frac{1}{x^2 \sqrt{a x^2+b x^5}} \, dx","Int[1/(x^2*Sqrt[a*x^2 + b*x^5]),x]","-\frac{\sqrt{2+\sqrt{3}} b^{2/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{\sqrt{a x^2+b x^5}}{2 a x^3}","-\frac{\sqrt{2+\sqrt{3}} b^{2/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{\sqrt{a x^2+b x^5}}{2 a x^3}",1,"-Sqrt[a*x^2 + b*x^5]/(2*a*x^3) - (Sqrt[2 + Sqrt[3]]*b^(2/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*3^(1/4)*a*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",3,3,19,0.1579,1,"{2025, 2032, 218}"
292,1,514,0,0.308019,"\int \frac{x^5}{\sqrt{a x^2+b x^5}} \, dx","Int[x^5/Sqrt[a*x^2 + b*x^5],x]","-\frac{8 \sqrt{2} a^{4/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{8 a x \left(a+b x^3\right)}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}+\frac{2 x \sqrt{a x^2+b x^5}}{7 b}","-\frac{8 \sqrt{2} a^{4/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{8 a x \left(a+b x^3\right)}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}+\frac{2 x \sqrt{a x^2+b x^5}}{7 b}",1,"(-8*a*x*(a + b*x^3))/(7*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)*Sqrt[a*x^2 + b*x^5]) + (2*x*Sqrt[a*x^2 + b*x^5])/(7*b) + (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5]) - (8*Sqrt[2]*a^(4/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*3^(1/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",5,5,19,0.2632,1,"{2024, 2032, 303, 218, 1877}"
293,1,484,0,0.1896966,"\int \frac{x^2}{\sqrt{a x^2+b x^5}} \, dx","Int[x^2/Sqrt[a*x^2 + b*x^5],x]","\frac{2 \sqrt{2} \sqrt[3]{a} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{2 x \left(a+b x^3\right)}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}","\frac{2 \sqrt{2} \sqrt[3]{a} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{2 x \left(a+b x^3\right)}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}",1,"(2*x*(a + b*x^3))/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)*Sqrt[a*x^2 + b*x^5]) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5]) + (2*Sqrt[2]*a^(1/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",4,4,19,0.2105,1,"{2032, 303, 218, 1877}"
294,1,510,0,0.2734081,"\int \frac{1}{x \sqrt{a x^2+b x^5}} \, dx","Int[1/(x*Sqrt[a*x^2 + b*x^5]),x]","\frac{\sqrt{2} \sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{\sqrt[3]{b} x \left(a+b x^3\right)}{a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}-\frac{\sqrt{a x^2+b x^5}}{a x^2}","\frac{\sqrt{2} \sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{\sqrt[3]{b} x \left(a+b x^3\right)}{a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}-\frac{\sqrt{a x^2+b x^5}}{a x^2}",1,"(b^(1/3)*x*(a + b*x^3))/(a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)*Sqrt[a*x^2 + b*x^5]) - Sqrt[a*x^2 + b*x^5]/(a*x^2) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5]) + (Sqrt[2]*b^(1/3)*x*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",5,5,19,0.2632,1,"{2025, 2032, 303, 218, 1877}"
295,1,265,0,0.2818674,"\int \frac{x^{13/2}}{\sqrt{a x^2+b x^5}} \, dx","Int[x^(13/2)/Sqrt[a*x^2 + b*x^5],x]","\frac{7 a^{5/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 \sqrt[4]{3} b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{7 a \sqrt{a x^2+b x^5}}{20 b^2 \sqrt{x}}+\frac{x^{5/2} \sqrt{a x^2+b x^5}}{5 b}","\frac{7 a^{5/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 \sqrt[4]{3} b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{7 a \sqrt{a x^2+b x^5}}{20 b^2 \sqrt{x}}+\frac{x^{5/2} \sqrt{a x^2+b x^5}}{5 b}",1,"(-7*a*Sqrt[a*x^2 + b*x^5])/(20*b^2*Sqrt[x]) + (x^(5/2)*Sqrt[a*x^2 + b*x^5])/(5*b) + (7*a^(5/3)*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(40*3^(1/4)*b^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",5,4,21,0.1905,1,"{2024, 2032, 329, 225}"
296,1,525,0,0.5000058,"\int \frac{x^{11/2}}{\sqrt{a x^2+b x^5}} \, dx","Int[x^(11/2)/Sqrt[a*x^2 + b*x^5],x]","\frac{5 \left(1-\sqrt{3}\right) a^{4/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{16 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{5 \sqrt[4]{3} a^{4/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{5 \left(1+\sqrt{3}\right) a x^{3/2} \left(a+b x^3\right)}{8 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}+\frac{x^{3/2} \sqrt{a x^2+b x^5}}{4 b}","\frac{5 \left(1-\sqrt{3}\right) a^{4/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{16 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{5 \sqrt[4]{3} a^{4/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{5 \left(1+\sqrt{3}\right) a x^{3/2} \left(a+b x^3\right)}{8 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}+\frac{x^{3/2} \sqrt{a x^2+b x^5}}{4 b}",1,"(-5*(1 + Sqrt[3])*a*x^(3/2)*(a + b*x^3))/(8*b^(5/3)*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)*Sqrt[a*x^2 + b*x^5]) + (x^(3/2)*Sqrt[a*x^2 + b*x^5])/(4*b) + (5*3^(1/4)*a^(4/3)*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(8*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5]) + (5*(1 - Sqrt[3])*a^(4/3)*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(16*3^(1/4)*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",6,6,21,0.2857,1,"{2024, 2032, 329, 308, 225, 1881}"
297,1,65,0,0.0896446,"\int \frac{x^{9/2}}{\sqrt{a x^2+b x^5}} \, dx","Int[x^(9/2)/Sqrt[a*x^2 + b*x^5],x]","\frac{\sqrt{x} \sqrt{a x^2+b x^5}}{3 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a x^2+b x^5}}\right)}{3 b^{3/2}}","\frac{\sqrt{x} \sqrt{a x^2+b x^5}}{3 b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a x^2+b x^5}}\right)}{3 b^{3/2}}",1,"(Sqrt[x]*Sqrt[a*x^2 + b*x^5])/(3*b) - (a*ArcTanh[(Sqrt[b]*x^(5/2))/Sqrt[a*x^2 + b*x^5]])/(3*b^(3/2))","A",3,3,21,0.1429,1,"{2024, 2029, 206}"
298,1,237,0,0.225232,"\int \frac{x^{7/2}}{\sqrt{a x^2+b x^5}} \, dx","Int[x^(7/2)/Sqrt[a*x^2 + b*x^5],x]","\frac{\sqrt{a x^2+b x^5}}{2 b \sqrt{x}}-\frac{a^{2/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 \sqrt[4]{3} b \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}","\frac{\sqrt{a x^2+b x^5}}{2 b \sqrt{x}}-\frac{a^{2/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 \sqrt[4]{3} b \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}",1,"Sqrt[a*x^2 + b*x^5]/(2*b*Sqrt[x]) - (a^(2/3)*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(4*3^(1/4)*b*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",4,4,21,0.1905,1,"{2024, 2032, 329, 225}"
299,1,492,0,0.3983775,"\int \frac{x^{5/2}}{\sqrt{a x^2+b x^5}} \, dx","Int[x^(5/2)/Sqrt[a*x^2 + b*x^5],x]","-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{\sqrt[4]{3} \sqrt[3]{a} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{\left(1+\sqrt{3}\right) x^{3/2} \left(a+b x^3\right)}{b^{2/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}","-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{\sqrt[4]{3} \sqrt[3]{a} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{\left(1+\sqrt{3}\right) x^{3/2} \left(a+b x^3\right)}{b^{2/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}",1,"((1 + Sqrt[3])*x^(3/2)*(a + b*x^3))/(b^(2/3)*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)*Sqrt[a*x^2 + b*x^5]) - (3^(1/4)*a^(1/3)*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(b^(2/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5]) - ((1 - Sqrt[3])*a^(1/3)*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(2*3^(1/4)*b^(2/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",5,5,21,0.2381,1,"{2032, 329, 308, 225, 1881}"
300,1,36,0,0.0475052,"\int \frac{x^{3/2}}{\sqrt{a x^2+b x^5}} \, dx","Int[x^(3/2)/Sqrt[a*x^2 + b*x^5],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a x^2+b x^5}}\right)}{3 \sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a x^2+b x^5}}\right)}{3 \sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x^(5/2))/Sqrt[a*x^2 + b*x^5]])/(3*Sqrt[b])","A",2,2,21,0.09524,1,"{2029, 206}"
301,1,203,0,0.1657111,"\int \frac{\sqrt{x}}{\sqrt{a x^2+b x^5}} \, dx","Int[Sqrt[x]/Sqrt[a*x^2 + b*x^5],x]","\frac{x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt[3]{a} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}","\frac{x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt[3]{a} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}",1,"(x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(3^(1/4)*a^(1/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",3,3,21,0.1429,1,"{2032, 329, 225}"
302,1,519,0,0.4868236,"\int \frac{1}{\sqrt{x} \sqrt{a x^2+b x^5}} \, dx","Int[1/(Sqrt[x]*Sqrt[a*x^2 + b*x^5]),x]","-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{2 \sqrt[4]{3} \sqrt[3]{b} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{2 \left(1+\sqrt{3}\right) \sqrt[3]{b} x^{3/2} \left(a+b x^3\right)}{a \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}-\frac{2 \sqrt{a x^2+b x^5}}{a x^{3/2}}","-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{2 \sqrt[4]{3} \sqrt[3]{b} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{2 \left(1+\sqrt{3}\right) \sqrt[3]{b} x^{3/2} \left(a+b x^3\right)}{a \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}-\frac{2 \sqrt{a x^2+b x^5}}{a x^{3/2}}",1,"(2*(1 + Sqrt[3])*b^(1/3)*x^(3/2)*(a + b*x^3))/(a*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)*Sqrt[a*x^2 + b*x^5]) - (2*Sqrt[a*x^2 + b*x^5])/(a*x^(3/2)) - (2*3^(1/4)*b^(1/3)*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(a^(2/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5]) - ((1 - Sqrt[3])*b^(1/3)*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(3^(1/4)*a^(2/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",6,6,21,0.2857,1,"{2025, 2032, 329, 308, 225, 1881}"
303,1,27,0,0.0400189,"\int \frac{1}{x^{3/2} \sqrt{a x^2+b x^5}} \, dx","Int[1/(x^(3/2)*Sqrt[a*x^2 + b*x^5]),x]","-\frac{2 \sqrt{a x^2+b x^5}}{3 a x^{5/2}}","-\frac{2 \sqrt{a x^2+b x^5}}{3 a x^{5/2}}",1,"(-2*Sqrt[a*x^2 + b*x^5])/(3*a*x^(5/2))","A",1,1,21,0.04762,1,"{2014}"
304,1,235,0,0.2210221,"\int \frac{1}{x^{5/2} \sqrt{a x^2+b x^5}} \, dx","Int[1/(x^(5/2)*Sqrt[a*x^2 + b*x^5]),x]","-\frac{2 b x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 \sqrt[4]{3} a^{4/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{2 \sqrt{a x^2+b x^5}}{5 a x^{7/2}}","-\frac{2 b x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 \sqrt[4]{3} a^{4/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}-\frac{2 \sqrt{a x^2+b x^5}}{5 a x^{7/2}}",1,"(-2*Sqrt[a*x^2 + b*x^5])/(5*a*x^(7/2)) - (2*b*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(5*3^(1/4)*a^(4/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",4,4,21,0.1905,1,"{2025, 2032, 329, 225}"
305,1,555,0,0.5731814,"\int \frac{1}{x^{7/2} \sqrt{a x^2+b x^5}} \, dx","Int[1/(x^(7/2)*Sqrt[a*x^2 + b*x^5]),x]","-\frac{8 \left(1+\sqrt{3}\right) b^{4/3} x^{3/2} \left(a+b x^3\right)}{7 a^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}+\frac{4 \left(1-\sqrt{3}\right) b^{4/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{7 \sqrt[4]{3} a^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{8 \sqrt[4]{3} b^{4/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{7 a^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{8 b \sqrt{a x^2+b x^5}}{7 a^2 x^{3/2}}-\frac{2 \sqrt{a x^2+b x^5}}{7 a x^{9/2}}","-\frac{8 \left(1+\sqrt{3}\right) b^{4/3} x^{3/2} \left(a+b x^3\right)}{7 a^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right) \sqrt{a x^2+b x^5}}+\frac{4 \left(1-\sqrt{3}\right) b^{4/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{7 \sqrt[4]{3} a^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{8 \sqrt[4]{3} b^{4/3} x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{7 a^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{8 b \sqrt{a x^2+b x^5}}{7 a^2 x^{3/2}}-\frac{2 \sqrt{a x^2+b x^5}}{7 a x^{9/2}}",1,"(-8*(1 + Sqrt[3])*b^(4/3)*x^(3/2)*(a + b*x^3))/(7*a^2*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)*Sqrt[a*x^2 + b*x^5]) - (2*Sqrt[a*x^2 + b*x^5])/(7*a*x^(9/2)) + (8*b*Sqrt[a*x^2 + b*x^5])/(7*a^2*x^(3/2)) + (8*3^(1/4)*b^(4/3)*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(7*a^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5]) + (4*(1 - Sqrt[3])*b^(4/3)*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(7*3^(1/4)*a^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",7,6,21,0.2857,1,"{2025, 2032, 329, 308, 225, 1881}"
306,1,56,0,0.0830774,"\int \frac{1}{x^{9/2} \sqrt{a x^2+b x^5}} \, dx","Int[1/(x^(9/2)*Sqrt[a*x^2 + b*x^5]),x]","\frac{4 b \sqrt{a x^2+b x^5}}{9 a^2 x^{5/2}}-\frac{2 \sqrt{a x^2+b x^5}}{9 a x^{11/2}}","\frac{4 b \sqrt{a x^2+b x^5}}{9 a^2 x^{5/2}}-\frac{2 \sqrt{a x^2+b x^5}}{9 a x^{11/2}}",1,"(-2*Sqrt[a*x^2 + b*x^5])/(9*a*x^(11/2)) + (4*b*Sqrt[a*x^2 + b*x^5])/(9*a^2*x^(5/2))","A",2,2,21,0.09524,1,"{2016, 2014}"
307,1,265,0,0.284104,"\int \frac{1}{x^{11/2} \sqrt{a x^2+b x^5}} \, dx","Int[1/(x^(11/2)*Sqrt[a*x^2 + b*x^5]),x]","\frac{16 b^2 x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{55 \sqrt[4]{3} a^{7/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{16 b \sqrt{a x^2+b x^5}}{55 a^2 x^{7/2}}-\frac{2 \sqrt{a x^2+b x^5}}{11 a x^{13/2}}","\frac{16 b^2 x^{3/2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{55 \sqrt[4]{3} a^{7/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a x^2+b x^5}}+\frac{16 b \sqrt{a x^2+b x^5}}{55 a^2 x^{7/2}}-\frac{2 \sqrt{a x^2+b x^5}}{11 a x^{13/2}}",1,"(-2*Sqrt[a*x^2 + b*x^5])/(11*a*x^(13/2)) + (16*b*Sqrt[a*x^2 + b*x^5])/(55*a^2*x^(7/2)) + (16*b^2*x^(3/2)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(55*3^(1/4)*a^(7/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a*x^2 + b*x^5])","A",5,4,21,0.1905,1,"{2025, 2032, 329, 225}"
308,1,28,0,0.0169484,"\int \frac{x}{a x^3+b x^4} \, dx","Int[x/(a*x^3 + b*x^4),x]","-\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x}","-\frac{b \log (x)}{a^2}+\frac{b \log (a+b x)}{a^2}-\frac{1}{a x}",1,"-(1/(a*x)) - (b*Log[x])/a^2 + (b*Log[a + b*x])/a^2","A",3,2,15,0.1333,1,"{1584, 44}"
309,1,42,0,0.0191524,"\int \frac{1}{a x^3+b x^4} \, dx","Int[(a*x^3 + b*x^4)^(-1),x]","\frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}","\frac{b^2 \log (x)}{a^3}-\frac{b^2 \log (a+b x)}{a^3}+\frac{b}{a^2 x}-\frac{1}{2 a x^2}",1,"-1/(2*a*x^2) + b/(a^2*x) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x])/a^3","A",3,2,13,0.1538,1,"{1593, 44}"
310,1,112,0,0.1788224,"\int \frac{x^4}{\sqrt{a x^3+b x^4}} \, dx","Int[x^4/Sqrt[a*x^3 + b*x^4],x]","\frac{5 a^2 \sqrt{a x^3+b x^4}}{8 b^3 x}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^3+b x^4}}\right)}{8 b^{7/2}}-\frac{5 a \sqrt{a x^3+b x^4}}{12 b^2}+\frac{x \sqrt{a x^3+b x^4}}{3 b}","\frac{5 a^2 \sqrt{a x^3+b x^4}}{8 b^3 x}-\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^3+b x^4}}\right)}{8 b^{7/2}}-\frac{5 a \sqrt{a x^3+b x^4}}{12 b^2}+\frac{x \sqrt{a x^3+b x^4}}{3 b}",1,"(-5*a*Sqrt[a*x^3 + b*x^4])/(12*b^2) + (5*a^2*Sqrt[a*x^3 + b*x^4])/(8*b^3*x) + (x*Sqrt[a*x^3 + b*x^4])/(3*b) - (5*a^3*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a*x^3 + b*x^4]])/(8*b^(7/2))","A",5,3,19,0.1579,1,"{2024, 2029, 206}"
311,1,86,0,0.127086,"\int \frac{x^3}{\sqrt{a x^3+b x^4}} \, dx","Int[x^3/Sqrt[a*x^3 + b*x^4],x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^3+b x^4}}\right)}{4 b^{5/2}}-\frac{3 a \sqrt{a x^3+b x^4}}{4 b^2 x}+\frac{\sqrt{a x^3+b x^4}}{2 b}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^3+b x^4}}\right)}{4 b^{5/2}}-\frac{3 a \sqrt{a x^3+b x^4}}{4 b^2 x}+\frac{\sqrt{a x^3+b x^4}}{2 b}",1,"Sqrt[a*x^3 + b*x^4]/(2*b) - (3*a*Sqrt[a*x^3 + b*x^4])/(4*b^2*x) + (3*a^2*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a*x^3 + b*x^4]])/(4*b^(5/2))","A",4,3,19,0.1579,1,"{2024, 2029, 206}"
312,1,56,0,0.0823131,"\int \frac{x^2}{\sqrt{a x^3+b x^4}} \, dx","Int[x^2/Sqrt[a*x^3 + b*x^4],x]","\frac{\sqrt{a x^3+b x^4}}{b x}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^3+b x^4}}\right)}{b^{3/2}}","\frac{\sqrt{a x^3+b x^4}}{b x}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^3+b x^4}}\right)}{b^{3/2}}",1,"Sqrt[a*x^3 + b*x^4]/(b*x) - (a*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a*x^3 + b*x^4]])/b^(3/2)","A",3,3,19,0.1579,1,"{2024, 2029, 206}"
313,1,32,0,0.0343985,"\int \frac{x}{\sqrt{a x^3+b x^4}} \, dx","Int[x/Sqrt[a*x^3 + b*x^4],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^3+b x^4}}\right)}{\sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^3+b x^4}}\right)}{\sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a*x^3 + b*x^4]])/Sqrt[b]","A",2,2,17,0.1176,1,"{2029, 206}"
314,1,23,0,0.0050791,"\int \frac{1}{\sqrt{a x^3+b x^4}} \, dx","Int[1/Sqrt[a*x^3 + b*x^4],x]","-\frac{2 \sqrt{a x^3+b x^4}}{a x^2}","-\frac{2 \sqrt{a x^3+b x^4}}{a x^2}",1,"(-2*Sqrt[a*x^3 + b*x^4])/(a*x^2)","A",1,1,15,0.06667,1,"{2000}"
315,1,52,0,0.0450667,"\int \frac{1}{x \sqrt{a x^3+b x^4}} \, dx","Int[1/(x*Sqrt[a*x^3 + b*x^4]),x]","\frac{4 b \sqrt{a x^3+b x^4}}{3 a^2 x^2}-\frac{2 \sqrt{a x^3+b x^4}}{3 a x^3}","\frac{4 b \sqrt{a x^3+b x^4}}{3 a^2 x^2}-\frac{2 \sqrt{a x^3+b x^4}}{3 a x^3}",1,"(-2*Sqrt[a*x^3 + b*x^4])/(3*a*x^3) + (4*b*Sqrt[a*x^3 + b*x^4])/(3*a^2*x^2)","A",2,2,19,0.1053,1,"{2016, 2000}"
316,1,80,0,0.0860185,"\int \frac{1}{x^2 \sqrt{a x^3+b x^4}} \, dx","Int[1/(x^2*Sqrt[a*x^3 + b*x^4]),x]","-\frac{16 b^2 \sqrt{a x^3+b x^4}}{15 a^3 x^2}+\frac{8 b \sqrt{a x^3+b x^4}}{15 a^2 x^3}-\frac{2 \sqrt{a x^3+b x^4}}{5 a x^4}","-\frac{16 b^2 \sqrt{a x^3+b x^4}}{15 a^3 x^2}+\frac{8 b \sqrt{a x^3+b x^4}}{15 a^2 x^3}-\frac{2 \sqrt{a x^3+b x^4}}{5 a x^4}",1,"(-2*Sqrt[a*x^3 + b*x^4])/(5*a*x^4) + (8*b*Sqrt[a*x^3 + b*x^4])/(15*a^2*x^3) - (16*b^2*Sqrt[a*x^3 + b*x^4])/(15*a^3*x^2)","A",3,2,19,0.1053,1,"{2016, 2000}"
317,1,108,0,0.1341978,"\int \frac{1}{x^3 \sqrt{a x^3+b x^4}} \, dx","Int[1/(x^3*Sqrt[a*x^3 + b*x^4]),x]","\frac{32 b^3 \sqrt{a x^3+b x^4}}{35 a^4 x^2}-\frac{16 b^2 \sqrt{a x^3+b x^4}}{35 a^3 x^3}+\frac{12 b \sqrt{a x^3+b x^4}}{35 a^2 x^4}-\frac{2 \sqrt{a x^3+b x^4}}{7 a x^5}","\frac{32 b^3 \sqrt{a x^3+b x^4}}{35 a^4 x^2}-\frac{16 b^2 \sqrt{a x^3+b x^4}}{35 a^3 x^3}+\frac{12 b \sqrt{a x^3+b x^4}}{35 a^2 x^4}-\frac{2 \sqrt{a x^3+b x^4}}{7 a x^5}",1,"(-2*Sqrt[a*x^3 + b*x^4])/(7*a*x^5) + (12*b*Sqrt[a*x^3 + b*x^4])/(35*a^2*x^4) - (16*b^2*Sqrt[a*x^3 + b*x^4])/(35*a^3*x^3) + (32*b^3*Sqrt[a*x^3 + b*x^4])/(35*a^4*x^2)","A",4,2,19,0.1053,1,"{2016, 2000}"
318,1,136,0,0.1744205,"\int \frac{1}{x^4 \sqrt{a x^3+b x^4}} \, dx","Int[1/(x^4*Sqrt[a*x^3 + b*x^4]),x]","-\frac{256 b^4 \sqrt{a x^3+b x^4}}{315 a^5 x^2}+\frac{128 b^3 \sqrt{a x^3+b x^4}}{315 a^4 x^3}-\frac{32 b^2 \sqrt{a x^3+b x^4}}{105 a^3 x^4}+\frac{16 b \sqrt{a x^3+b x^4}}{63 a^2 x^5}-\frac{2 \sqrt{a x^3+b x^4}}{9 a x^6}","-\frac{256 b^4 \sqrt{a x^3+b x^4}}{315 a^5 x^2}+\frac{128 b^3 \sqrt{a x^3+b x^4}}{315 a^4 x^3}-\frac{32 b^2 \sqrt{a x^3+b x^4}}{105 a^3 x^4}+\frac{16 b \sqrt{a x^3+b x^4}}{63 a^2 x^5}-\frac{2 \sqrt{a x^3+b x^4}}{9 a x^6}",1,"(-2*Sqrt[a*x^3 + b*x^4])/(9*a*x^6) + (16*b*Sqrt[a*x^3 + b*x^4])/(63*a^2*x^5) - (32*b^2*Sqrt[a*x^3 + b*x^4])/(105*a^3*x^4) + (128*b^3*Sqrt[a*x^3 + b*x^4])/(315*a^4*x^3) - (256*b^4*Sqrt[a*x^3 + b*x^4])/(315*a^5*x^2)","A",5,2,19,0.1053,1,"{2016, 2000}"
319,1,26,0,0.0176425,"\int \frac{1}{x^3+b x^5} \, dx","Int[(x^3 + b*x^5)^(-1),x]","\frac{1}{2} b \log \left(b x^2+1\right)-b \log (x)-\frac{1}{2 x^2}","\frac{1}{2} b \log \left(b x^2+1\right)-b \log (x)-\frac{1}{2 x^2}",1,"-1/(2*x^2) - b*Log[x] + (b*Log[1 + b*x^2])/2","A",4,3,11,0.2727,1,"{1593, 266, 44}"
320,1,27,0,0.0184613,"\int \frac{1}{-x^3+b x^5} \, dx","Int[(-x^3 + b*x^5)^(-1),x]","\frac{1}{2} b \log \left(1-b x^2\right)-b \log (x)+\frac{1}{2 x^2}","\frac{1}{2} b \log \left(1-b x^2\right)-b \log (x)+\frac{1}{2 x^2}",1,"1/(2*x^2) - b*Log[x] + (b*Log[1 - b*x^2])/2","A",4,3,13,0.2308,1,"{1593, 266, 44}"
321,1,8,0,0.0031854,"\int \frac{1}{a x+b x} \, dx","Int[(a*x + b*x)^(-1),x]","\frac{\log (x)}{a+b}","\frac{\log (x)}{a+b}",1,"Log[x]/(a + b)","A",3,3,9,0.3333,1,"{6, 12, 29}"
322,1,10,0,0.0032584,"\int \frac{1}{(a x+b x)^2} \, dx","Int[(a*x + b*x)^(-2),x]","-\frac{1}{x (a+b)^2}","-\frac{1}{x (a+b)^2}",1,"-(1/((a + b)^2*x))","A",3,3,9,0.3333,1,"{6, 12, 30}"
323,1,12,0,0.0030896,"\int \frac{1}{(a x+b x)^3} \, dx","Int[(a*x + b*x)^(-3),x]","-\frac{1}{2 x^2 (a+b)^3}","-\frac{1}{2 x^2 (a+b)^3}",1,"-1/(2*(a + b)^3*x^2)","A",3,3,9,0.3333,1,"{6, 12, 30}"
324,1,10,0,0.0016056,"\int \frac{1}{a x^2+b x^2} \, dx","Int[(a*x^2 + b*x^2)^(-1),x]","-\frac{1}{x (a+b)}","-\frac{1}{x (a+b)}",1,"-(1/((a + b)*x))","A",3,3,13,0.2308,1,"{6, 12, 30}"
325,1,20,0,0.0058103,"\int \frac{1}{a x^n+b x^n} \, dx","Int[(a*x^n + b*x^n)^(-1),x]","\frac{x^{1-n}}{(1-n) (a+b)}","\frac{x^{1-n}}{(1-n) (a+b)}",1,"x^(1 - n)/((a + b)*(1 - n))","A",3,3,13,0.2308,1,"{6, 12, 30}"
326,1,20,0,0.0082571,"\int \frac{1}{\left(a x^n+b x^n\right)^2} \, dx","Int[(a*x^n + b*x^n)^(-2),x]","\frac{x^{1-2 n}}{(1-2 n) (a+b)^2}","\frac{x^{1-2 n}}{(1-2 n) (a+b)^2}",1,"x^(1 - 2*n)/((a + b)^2*(1 - 2*n))","A",3,3,13,0.2308,1,"{6, 12, 30}"
327,1,20,0,0.0089884,"\int \frac{1}{\left(a x^n+b x^n\right)^3} \, dx","Int[(a*x^n + b*x^n)^(-3),x]","\frac{x^{1-3 n}}{(1-3 n) (a+b)^3}","\frac{x^{1-3 n}}{(1-3 n) (a+b)^3}",1,"x^(1 - 3*n)/((a + b)^3*(1 - 3*n))","A",3,3,13,0.2308,1,"{6, 12, 30}"
328,1,16,0,0.0044672,"\int \left(a x+b x^{14}\right)^{12} \, dx","Int[(a*x + b*x^14)^12,x]","\frac{\left(a+b x^{13}\right)^{13}}{169 b}","\frac{\left(a+b x^{13}\right)^{13}}{169 b}",1,"(a + b*x^13)^13/(169*b)","A",2,2,11,0.1818,1,"{1593, 261}"
329,1,16,0,0.0114282,"\int x^{12} \left(a x+b x^{26}\right)^{12} \, dx","Int[x^12*(a*x + b*x^26)^12,x]","\frac{\left(a+b x^{25}\right)^{13}}{325 b}","\frac{\left(a+b x^{25}\right)^{13}}{325 b}",1,"(a + b*x^25)^13/(325*b)","A",2,2,15,0.1333,1,"{1584, 261}"
330,1,16,0,0.0117595,"\int x^{24} \left(a x+b x^{38}\right)^{12} \, dx","Int[x^24*(a*x + b*x^38)^12,x]","\frac{\left(a+b x^{37}\right)^{13}}{481 b}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a + b*x^37)^13/(481*b)","A",2,2,15,0.1333,1,"{1584, 261}"
331,1,27,0,0.0147372,"\int x^{12 (-1+m)} \left(a x+b x^{2+12 m}\right)^{12} \, dx","Int[x^(12*(-1 + m))*(a*x + b*x^(2 + 12*m))^12,x]","\frac{\left(a+b x^{12 m+1}\right)^{13}}{13 b (12 m+1)}","\frac{\left(a+b x^{12 m+1}\right)^{13}}{13 b (12 m+1)}",1,"(a + b*x^(1 + 12*m))^13/(13*b*(1 + 12*m))","A",2,2,23,0.08696,1,"{1584, 261}"
332,1,16,0,0.0044802,"\int \left(a x+b x^{14}\right)^{12} \, dx","Int[(a*x + b*x^14)^12,x]","\frac{\left(a+b x^{13}\right)^{13}}{169 b}","\frac{\left(a+b x^{13}\right)^{13}}{169 b}",1,"(a + b*x^13)^13/(169*b)","A",2,2,11,0.1818,1,"{1593, 261}"
333,1,16,0,0.0045659,"\int \left(a x^2+b x^{27}\right)^{12} \, dx","Int[(a*x^2 + b*x^27)^12,x]","\frac{\left(a+b x^{25}\right)^{13}}{325 b}","\frac{\left(a+b x^{25}\right)^{13}}{325 b}",1,"(a + b*x^25)^13/(325*b)","A",2,2,13,0.1538,1,"{1593, 261}"
334,1,16,0,0.0044845,"\int \left(a x^3+b x^{40}\right)^{12} \, dx","Int[(a*x^3 + b*x^40)^12,x]","\frac{\left(a+b x^{37}\right)^{13}}{481 b}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a + b*x^37)^13/(481*b)","A",2,2,13,0.1538,1,"{1593, 261}"
335,1,27,0,0.0077874,"\int \left(a x^m+b x^{1+13 m}\right)^{12} \, dx","Int[(a*x^m + b*x^(1 + 13*m))^12,x]","\frac{\left(a+b x^{12 m+1}\right)^{13}}{13 b (12 m+1)}","\frac{\left(a+b x^{12 m+1}\right)^{13}}{13 b (12 m+1)}",1,"(a + b*x^(1 + 12*m))^13/(13*b*(1 + 12*m))","A",2,2,17,0.1176,1,"{1593, 261}"
336,1,27,0,0.0102364,"\int \left(a x^m+b x^{1+6 m}\right)^5 \, dx","Int[(a*x^m + b*x^(1 + 6*m))^5,x]","\frac{\left(a+b x^{5 m+1}\right)^6}{6 b (5 m+1)}","\frac{\left(a+b x^{5 m+1}\right)^6}{6 b (5 m+1)}",1,"(a + b*x^(1 + 5*m))^6/(6*b*(1 + 5*m))","A",2,2,17,0.1176,1,"{1593, 261}"
337,1,27,0,0.0137646,"\int \frac{1}{\left(b x^{1-2 m}+a x^m\right)^3} \, dx","Int[(b*x^(1 - 2*m) + a*x^m)^(-3),x]","-\frac{1}{2 b (1-3 m) \left(a+b x^{1-3 m}\right)^2}","-\frac{1}{2 b (1-3 m) \left(a+b x^{1-3 m}\right)^2}",1,"-1/(2*b*(1 - 3*m)*(a + b*x^(1 - 3*m))^2)","A",2,2,17,0.1176,1,"{1593, 261}"
338,1,15,0,0.004795,"\int \frac{1}{\frac{b}{x}+a x} \, dx","Int[(b/x + a*x)^(-1),x]","\frac{\log \left(a x^2+b\right)}{2 a}","\frac{\log \left(a x^2+b\right)}{2 a}",1,"Log[b + a*x^2]/(2*a)","A",2,2,11,0.1818,1,"{1593, 260}"
339,1,15,0,0.0060296,"\int \frac{1}{\frac{b}{x^2}+a x} \, dx","Int[(b/x^2 + a*x)^(-1),x]","\frac{\log \left(a x^3+b\right)}{3 a}","\frac{\log \left(a x^3+b\right)}{3 a}",1,"Log[b + a*x^3]/(3*a)","A",2,2,11,0.1818,1,"{1593, 260}"
340,1,15,0,0.0053283,"\int \frac{1}{\frac{b}{x^3}+a x} \, dx","Int[(b/x^3 + a*x)^(-1),x]","\frac{\log \left(a x^4+b\right)}{4 a}","\frac{\log \left(a x^4+b\right)}{4 a}",1,"Log[b + a*x^4]/(4*a)","A",2,2,11,0.1818,1,"{1593, 260}"
341,1,19,0,0.0054465,"\int \frac{1}{\left(\frac{b}{x}+a x\right)^3} \, dx","Int[(b/x + a*x)^(-3),x]","\frac{x^4}{4 b \left(a x^2+b\right)^2}","\frac{x^4}{4 b \left(a x^2+b\right)^2}",1,"x^4/(4*b*(b + a*x^2)^2)","A",2,2,11,0.1818,1,"{1593, 264}"
342,1,19,0,0.006112,"\int \frac{1}{\left(\frac{b}{x^3}+a x^2\right)^3} \, dx","Int[(b/x^3 + a*x^2)^(-3),x]","\frac{x^{10}}{10 b \left(a x^5+b\right)^2}","\frac{x^{10}}{10 b \left(a x^5+b\right)^2}",1,"x^10/(10*b*(b + a*x^5)^2)","A",2,2,13,0.1538,1,"{1593, 264}"
343,1,19,0,0.0057949,"\int \frac{1}{\left(\frac{b}{x^5}+a x^3\right)^3} \, dx","Int[(b/x^5 + a*x^3)^(-3),x]","\frac{x^{16}}{16 b \left(a x^8+b\right)^2}","\frac{x^{16}}{16 b \left(a x^8+b\right)^2}",1,"x^16/(16*b*(b + a*x^8)^2)","A",2,2,13,0.1538,1,"{1593, 264}"
344,1,24,0,0.0109929,"\int \left(\frac{a}{x}+b x\right)^2 \, dx","Int[(a/x + b*x)^2,x]","-\frac{a^2}{x}+2 a b x+\frac{b^2 x^3}{3}","-\frac{a^2}{x}+2 a b x+\frac{b^2 x^3}{3}",1,"-(a^2/x) + 2*a*b*x + (b^2*x^3)/3","A",3,2,11,0.1818,1,"{1593, 270}"
345,1,40,0,0.0225053,"\int \left(\frac{a}{x}+b x\right)^3 \, dx","Int[(a/x + b*x)^3,x]","3 a^2 b \log (x)-\frac{a^3}{2 x^2}+\frac{3}{2} a b^2 x^2+\frac{b^3 x^4}{4}","3 a^2 b \log (x)-\frac{a^3}{2 x^2}+\frac{3}{2} a b^2 x^2+\frac{b^3 x^4}{4}",1,"-a^3/(2*x^2) + (3*a*b^2*x^2)/2 + (b^3*x^4)/4 + 3*a^2*b*Log[x]","A",4,3,11,0.2727,1,"{1593, 266, 43}"
346,1,50,0,0.0211109,"\int \left(\frac{a}{x}+b x\right)^4 \, dx","Int[(a/x + b*x)^4,x]","6 a^2 b^2 x-\frac{4 a^3 b}{x}-\frac{a^4}{3 x^3}+\frac{4}{3} a b^3 x^3+\frac{b^4 x^5}{5}","6 a^2 b^2 x-\frac{4 a^3 b}{x}-\frac{a^4}{3 x^3}+\frac{4}{3} a b^3 x^3+\frac{b^4 x^5}{5}",1,"-a^4/(3*x^3) - (4*a^3*b)/x + 6*a^2*b^2*x + (4*a*b^3*x^3)/3 + (b^4*x^5)/5","A",3,2,11,0.1818,1,"{1593, 270}"
347,1,185,0,0.3455425,"\int \frac{1}{\frac{1}{x^2}+x^3} \, dx","Int[(x^(-2) + x^3)^(-1),x]","-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+\frac{1}{5} \log (x+1)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)","-\frac{1}{20} \left(1+\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1-\sqrt{5}\right) x+1\right)-\frac{1}{20} \left(1-\sqrt{5}\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+\frac{1}{5} \log (x+1)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)} \tan ^{-1}\left(2 \sqrt{\frac{2}{5+\sqrt{5}}} x+\sqrt{\frac{1}{5} \left(5-2 \sqrt{5}\right)}\right)-\frac{1}{5} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{1}{5} \left(5+2 \sqrt{5}\right)}-\sqrt{\frac{2}{5} \left(5+\sqrt{5}\right)} x\right)",1,"-(Sqrt[(5 - Sqrt[5])/2]*ArcTan[Sqrt[(5 - 2*Sqrt[5])/5] + 2*Sqrt[2/(5 + Sqrt[5])]*x])/5 - (Sqrt[(5 + Sqrt[5])/2]*ArcTan[Sqrt[(5 + 2*Sqrt[5])/5] - Sqrt[(2*(5 + Sqrt[5]))/5]*x])/5 + Log[1 + x]/5 - ((1 + Sqrt[5])*Log[1 - ((1 - Sqrt[5])*x)/2 + x^2])/20 - ((1 - Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",7,7,9,0.7778,1,"{1593, 293, 634, 618, 204, 628, 31}"
348,1,29,0,0.0172572,"\int x^p \left(a x^n+b x^{1+13 n+p}\right)^{12} \, dx","Int[x^p*(a*x^n + b*x^(1 + 13*n + p))^12,x]","\frac{\left(a+b x^{12 n+p+1}\right)^{13}}{13 b (12 n+p+1)}","\frac{\left(a+b x^{12 n+p+1}\right)^{13}}{13 b (12 n+p+1)}",1,"(a + b*x^(1 + 12*n + p))^13/(13*b*(1 + 12*n + p))","A",2,2,22,0.09091,1,"{1584, 261}"
349,1,16,0,0.0029452,"\int x^{12} \left(a+b x^{13}\right)^{12} \, dx","Int[x^12*(a + b*x^13)^12,x]","\frac{\left(a+b x^{13}\right)^{13}}{169 b}","\frac{\left(a+b x^{13}\right)^{13}}{169 b}",1,"(a + b*x^13)^13/(169*b)","A",1,1,13,0.07692,1,"{261}"
350,1,16,0,0.0086186,"\int x^{12} \left(a x+b x^{26}\right)^{12} \, dx","Int[x^12*(a*x + b*x^26)^12,x]","\frac{\left(a+b x^{25}\right)^{13}}{325 b}","\frac{\left(a+b x^{25}\right)^{13}}{325 b}",1,"(a + b*x^25)^13/(325*b)","A",2,2,15,0.1333,1,"{1584, 261}"
351,1,16,0,0.0119976,"\int x^{12} \left(a x^2+b x^{39}\right)^{12} \, dx","Int[x^12*(a*x^2 + b*x^39)^12,x]","\frac{\left(a+b x^{37}\right)^{13}}{481 b}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a + b*x^37)^13/(481*b)","A",2,2,17,0.1176,1,"{1584, 261}"
352,1,16,0,0.0027836,"\int x^{24} \left(a+b x^{25}\right)^{12} \, dx","Int[x^24*(a + b*x^25)^12,x]","\frac{\left(a+b x^{25}\right)^{13}}{325 b}","\frac{\left(a+b x^{25}\right)^{13}}{325 b}",1,"(a + b*x^25)^13/(325*b)","A",1,1,13,0.07692,1,"{261}"
353,1,16,0,0.0083321,"\int x^{24} \left(a x+b x^{38}\right)^{12} \, dx","Int[x^24*(a*x + b*x^38)^12,x]","\frac{\left(a+b x^{37}\right)^{13}}{481 b}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a + b*x^37)^13/(481*b)","A",2,2,15,0.1333,1,"{1584, 261}"
354,1,16,0,0.0029089,"\int x^{36} \left(a+b x^{37}\right)^{12} \, dx","Int[x^36*(a + b*x^37)^12,x]","\frac{\left(a+b x^{37}\right)^{13}}{481 b}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a + b*x^37)^13/(481*b)","A",1,1,13,0.07692,1,"{261}"
355,1,23,0,0.0108914,"\int \frac{1}{a x+b x^n} \, dx","Int[(a*x + b*x^n)^(-1),x]","\frac{\log \left(a x^{1-n}+b\right)}{a (1-n)}","\frac{\log \left(a x^{1-n}+b\right)}{a (1-n)}",1,"Log[b + a*x^(1 - n)]/(a*(1 - n))","A",2,2,11,0.1818,1,"{1593, 260}"
356,1,23,0,0.0131801,"\int \frac{1}{a x+b x^{1+n}} \, dx","Int[(a*x + b*x^(1 + n))^(-1),x]","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}",1,"Log[x]/a - Log[a + b*x^n]/(a*n)","A",5,5,13,0.3846,1,"{1593, 266, 36, 29, 31}"
357,1,15,0,0.0076386,"\int \frac{1}{a x+b x^{1-n}} \, dx","Int[(a*x + b*x^(1 - n))^(-1),x]","\frac{\log \left(a x^n+b\right)}{a n}","\frac{\log \left(a x^n+b\right)}{a n}",1,"Log[b + a*x^n]/(a*n)","A",2,2,15,0.1333,1,"{1593, 260}"
358,1,22,0,0.0097024,"\int \frac{1}{2 x+3 x^{1+n}} \, dx","Int[(2*x + 3*x^(1 + n))^(-1),x]","\frac{\log (x)}{2}-\frac{\log \left(3 x^n+2\right)}{2 n}","\frac{\log (x)}{2}-\frac{\log \left(3 x^n+2\right)}{2 n}",1,"Log[x]/2 - Log[2 + 3*x^n]/(2*n)","A",5,5,13,0.3846,1,"{1593, 266, 36, 29, 31}"
359,1,15,0,0.0063023,"\int \frac{1}{2 x+3 x^{1-n}} \, dx","Int[(2*x + 3*x^(1 - n))^(-1),x]","\frac{\log \left(2 x^n+3\right)}{2 n}","\frac{\log \left(2 x^n+3\right)}{2 n}",1,"Log[3 + 2*x^n]/(2*n)","A",2,2,15,0.1333,1,"{1593, 260}"
360,1,12,0,0.003826,"\int \frac{1}{-\sqrt{x}+x} \, dx","Int[(-Sqrt[x] + x)^(-1),x]","2 \log \left(1-\sqrt{x}\right)","2 \log \left(1-\sqrt{x}\right)",1,"2*Log[1 - Sqrt[x]]","A",2,2,11,0.1818,1,"{1593, 260}"
361,1,14,0,0.0046696,"\int \frac{1}{-x^{3/5}+x} \, dx","Int[(-x^(3/5) + x)^(-1),x]","\frac{5}{2} \log \left(1-x^{2/5}\right)","\frac{5}{2} \log \left(1-x^{2/5}\right)",1,"(5*Log[1 - x^(2/5)])/2","A",2,2,11,0.1818,1,"{1593, 260}"
362,1,12,0,0.0035075,"\int \frac{1}{\frac{1}{\sqrt[3]{x}}+x} \, dx","Int[(x^(-1/3) + x)^(-1),x]","\frac{3}{4} \log \left(x^{4/3}+1\right)","\frac{3}{4} \log \left(x^{4/3}+1\right)",1,"(3*Log[1 + x^(4/3)])/4","A",2,2,9,0.2222,1,"{1593, 260}"
363,1,24,0,0.0163587,"\int \frac{1}{x+x^{\sqrt{2}}} \, dx","Int[(x + x^Sqrt[2])^(-1),x]","\log (x)-\left(1+\sqrt{2}\right) \log \left(x^{\sqrt{2}-1}+1\right)","\log (x)-\left(1+\sqrt{2}\right) \log \left(x^{\sqrt{2}-1}+1\right)",1,"Log[x] - (1 + Sqrt[2])*Log[1 + x^(-1 + Sqrt[2])]","A",5,5,11,0.4545,1,"{1593, 266, 36, 29, 31}"
364,1,75,0,0.1142468,"\int x^{-1-\frac{j}{2}} \sqrt{a x^j+b x^n} \, dx","Int[x^(-1 - j/2)*Sqrt[a*x^j + b*x^n],x]","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} x^{j/2}}{\sqrt{a x^j+b x^n}}\right)}{j-n}-\frac{2 x^{-j/2} \sqrt{a x^j+b x^n}}{j-n}","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} x^{j/2}}{\sqrt{a x^j+b x^n}}\right)}{j-n}-\frac{2 x^{-j/2} \sqrt{a x^j+b x^n}}{j-n}",1,"(-2*Sqrt[a*x^j + b*x^n])/((j - n)*x^(j/2)) + (2*Sqrt[a]*ArcTanh[(Sqrt[a]*x^(j/2))/Sqrt[a*x^j + b*x^n]])/(j - n)","A",3,3,25,0.1200,1,"{2028, 2029, 206}"
365,1,99,0,0.1573384,"\int (c x)^{-1-\frac{j}{2}} \sqrt{a x^j+b x^n} \, dx","Int[(c*x)^(-1 - j/2)*Sqrt[a*x^j + b*x^n],x]","\frac{2 \sqrt{a} x^{j/2} (c x)^{-j/2} \tanh ^{-1}\left(\frac{\sqrt{a} x^{j/2}}{\sqrt{a x^j+b x^n}}\right)}{c (j-n)}-\frac{2 (c x)^{-j/2} \sqrt{a x^j+b x^n}}{c (j-n)}","\frac{2 \sqrt{a} x^{j/2} (c x)^{-j/2} \tanh ^{-1}\left(\frac{\sqrt{a} x^{j/2}}{\sqrt{a x^j+b x^n}}\right)}{c (j-n)}-\frac{2 (c x)^{-j/2} \sqrt{a x^j+b x^n}}{c (j-n)}",1,"(-2*Sqrt[a*x^j + b*x^n])/(c*(j - n)*(c*x)^(j/2)) + (2*Sqrt[a]*x^(j/2)*ArcTanh[(Sqrt[a]*x^(j/2))/Sqrt[a*x^j + b*x^n]])/(c*(j - n)*(c*x)^(j/2))","A",4,4,27,0.1481,1,"{2031, 2028, 2029, 206}"
366,1,91,0,0.1554867,"\int \frac{\sqrt{a x^3+b x^n}}{(c x)^{5/2}} \, dx","Int[Sqrt[a*x^3 + b*x^n]/(c*x)^(5/2),x]","\frac{2 \sqrt{a} \sqrt{c x} \tanh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b x^n}}\right)}{c^3 (3-n) \sqrt{x}}-\frac{2 \sqrt{a x^3+b x^n}}{c (3-n) (c x)^{3/2}}","\frac{2 \sqrt{a} \sqrt{c x} \tanh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b x^n}}\right)}{c^3 (3-n) \sqrt{x}}-\frac{2 \sqrt{a x^3+b x^n}}{c (3-n) (c x)^{3/2}}",1,"(-2*Sqrt[a*x^3 + b*x^n])/(c*(3 - n)*(c*x)^(3/2)) + (2*Sqrt[a]*Sqrt[c*x]*ArcTanh[(Sqrt[a]*x^(3/2))/Sqrt[a*x^3 + b*x^n]])/(c^3*(3 - n)*Sqrt[x])","A",4,4,23,0.1739,1,"{2028, 2031, 2029, 206}"
367,1,71,0,0.0755826,"\int \frac{\sqrt{a x^2+b x^n}}{c^2 x^2} \, dx","Int[Sqrt[a*x^2 + b*x^n]/(c^2*x^2),x]","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^n}}\right)}{c^2 (2-n)}-\frac{2 \sqrt{a x^2+b x^n}}{c^2 (2-n) x}","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^n}}\right)}{c^2 (2-n)}-\frac{2 \sqrt{a x^2+b x^n}}{c^2 (2-n) x}",1,"(-2*Sqrt[a*x^2 + b*x^n])/(c^2*(2 - n)*x) + (2*Sqrt[a]*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^n]])/(c^2*(2 - n))","A",4,4,22,0.1818,1,"{12, 2028, 2008, 206}"
368,1,87,0,0.1376525,"\int \frac{\sqrt{a x+b x^n}}{(c x)^{3/2}} \, dx","Int[Sqrt[a*x + b*x^n]/(c*x)^(3/2),x]","\frac{2 \sqrt{a} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^n}}\right)}{c (1-n) \sqrt{c x}}-\frac{2 \sqrt{a x+b x^n}}{c (1-n) \sqrt{c x}}","\frac{2 \sqrt{a} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^n}}\right)}{c (1-n) \sqrt{c x}}-\frac{2 \sqrt{a x+b x^n}}{c (1-n) \sqrt{c x}}",1,"(-2*Sqrt[a*x + b*x^n])/(c*(1 - n)*Sqrt[c*x]) + (2*Sqrt[a]*Sqrt[x]*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[a*x + b*x^n]])/(c*(1 - n)*Sqrt[c*x])","A",4,4,21,0.1905,1,"{2028, 2031, 2029, 206}"
369,1,51,0,0.0291036,"\int \frac{\sqrt{a+b x^n}}{c x} \, dx","Int[Sqrt[a + b*x^n]/(c*x),x]","\frac{2 \sqrt{a+b x^n}}{c n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{c n}","\frac{2 \sqrt{a+b x^n}}{c n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{c n}",1,"(2*Sqrt[a + b*x^n])/(c*n) - (2*Sqrt[a]*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(c*n)","A",5,5,18,0.2778,1,"{12, 266, 50, 63, 208}"
370,1,84,0,0.1710022,"\int \frac{\sqrt{\frac{a}{x}+b x^n}}{\sqrt{c x}} \, dx","Int[Sqrt[a/x + b*x^n]/Sqrt[c*x],x]","\frac{2 \sqrt{c x} \sqrt{\frac{a}{x}+b x^n}}{c (n+1)}-\frac{2 \sqrt{a} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{\sqrt{x} \sqrt{\frac{a}{x}+b x^n}}\right)}{(n+1) \sqrt{c x}}","\frac{2 \sqrt{c x} \sqrt{\frac{a}{x}+b x^n}}{c (n+1)}-\frac{2 \sqrt{a} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{\sqrt{x} \sqrt{\frac{a}{x}+b x^n}}\right)}{(n+1) \sqrt{c x}}",1,"(2*Sqrt[c*x]*Sqrt[a/x + b*x^n])/(c*(1 + n)) - (2*Sqrt[a]*Sqrt[x]*ArcTanh[Sqrt[a]/(Sqrt[x]*Sqrt[a/x + b*x^n])])/((1 + n)*Sqrt[c*x])","A",4,4,23,0.1739,1,"{2028, 2031, 2029, 206}"
371,1,61,0,0.0834905,"\int \sqrt{\frac{a}{x^2}+b x^n} \, dx","Int[Sqrt[a/x^2 + b*x^n],x]","\frac{2 x \sqrt{\frac{a}{x^2}+b x^n}}{n+2}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x^n}}\right)}{n+2}","\frac{2 x \sqrt{\frac{a}{x^2}+b x^n}}{n+2}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x^n}}\right)}{n+2}",1,"(2*x*Sqrt[a/x^2 + b*x^n])/(2 + n) - (2*Sqrt[a]*ArcTanh[Sqrt[a]/(x*Sqrt[a/x^2 + b*x^n])])/(2 + n)","A",3,3,15,0.2000,1,"{2007, 2029, 206}"
372,1,85,0,0.1986219,"\int \sqrt{c x} \sqrt{\frac{a}{x^3}+b x^n} \, dx","Int[Sqrt[c*x]*Sqrt[a/x^3 + b*x^n],x]","\frac{2 (c x)^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}{c (n+3)}-\frac{2 \sqrt{a} c \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{x^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}\right)}{(n+3) \sqrt{c x}}","\frac{2 (c x)^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}{c (n+3)}-\frac{2 \sqrt{a} c \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{x^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}\right)}{(n+3) \sqrt{c x}}",1,"(2*(c*x)^(3/2)*Sqrt[a/x^3 + b*x^n])/(c*(3 + n)) - (2*Sqrt[a]*c*Sqrt[x]*ArcTanh[Sqrt[a]/(x^(3/2)*Sqrt[a/x^3 + b*x^n])])/((3 + n)*Sqrt[c*x])","A",4,4,23,0.1739,1,"{2028, 2031, 2029, 206}"
373,1,141,0,0.2253555,"\int (c x)^{-1-\frac{3 j}{2}} \left(a x^j+b x^n\right)^{3/2} \, dx","Int[(c*x)^(-1 - (3*j)/2)*(a*x^j + b*x^n)^(3/2),x]","\frac{2 a^{3/2} x^{3 j/2} (c x)^{-3 j/2} \tanh ^{-1}\left(\frac{\sqrt{a} x^{j/2}}{\sqrt{a x^j+b x^n}}\right)}{c (j-n)}-\frac{2 (c x)^{-3 j/2} \left(a x^j+b x^n\right)^{3/2}}{3 c (j-n)}-\frac{2 a x^j (c x)^{-3 j/2} \sqrt{a x^j+b x^n}}{c (j-n)}","\frac{2 a^{3/2} x^{3 j/2} (c x)^{-3 j/2} \tanh ^{-1}\left(\frac{\sqrt{a} x^{j/2}}{\sqrt{a x^j+b x^n}}\right)}{c (j-n)}-\frac{2 (c x)^{-3 j/2} \left(a x^j+b x^n\right)^{3/2}}{3 c (j-n)}-\frac{2 a x^j (c x)^{-3 j/2} \sqrt{a x^j+b x^n}}{c (j-n)}",1,"(-2*a*x^j*Sqrt[a*x^j + b*x^n])/(c*(j - n)*(c*x)^((3*j)/2)) - (2*(a*x^j + b*x^n)^(3/2))/(3*c*(j - n)*(c*x)^((3*j)/2)) + (2*a^(3/2)*x^((3*j)/2)*ArcTanh[(Sqrt[a]*x^(j/2))/Sqrt[a*x^j + b*x^n]])/(c*(j - n)*(c*x)^((3*j)/2))","A",5,4,27,0.1481,1,"{2031, 2028, 2029, 206}"
374,1,128,0,0.2088715,"\int \frac{\left(a x^3+b x^n\right)^{3/2}}{(c x)^{11/2}} \, dx","Int[(a*x^3 + b*x^n)^(3/2)/(c*x)^(11/2),x]","\frac{2 a^{3/2} \sqrt{c x} \tanh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b x^n}}\right)}{c^6 (3-n) \sqrt{x}}-\frac{2 a \sqrt{a x^3+b x^n}}{c^4 (3-n) (c x)^{3/2}}-\frac{2 \left(a x^3+b x^n\right)^{3/2}}{3 c (3-n) (c x)^{9/2}}","\frac{2 a^{3/2} \sqrt{c x} \tanh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b x^n}}\right)}{c^6 (3-n) \sqrt{x}}-\frac{2 a \sqrt{a x^3+b x^n}}{c^4 (3-n) (c x)^{3/2}}-\frac{2 \left(a x^3+b x^n\right)^{3/2}}{3 c (3-n) (c x)^{9/2}}",1,"(-2*a*Sqrt[a*x^3 + b*x^n])/(c^4*(3 - n)*(c*x)^(3/2)) - (2*(a*x^3 + b*x^n)^(3/2))/(3*c*(3 - n)*(c*x)^(9/2)) + (2*a^(3/2)*Sqrt[c*x]*ArcTanh[(Sqrt[a]*x^(3/2))/Sqrt[a*x^3 + b*x^n]])/(c^6*(3 - n)*Sqrt[x])","A",5,4,23,0.1739,1,"{2028, 2031, 2029, 206}"
375,1,104,0,0.1331964,"\int \frac{\left(a x^2+b x^n\right)^{3/2}}{c^4 x^4} \, dx","Int[(a*x^2 + b*x^n)^(3/2)/(c^4*x^4),x]","\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^n}}\right)}{c^4 (2-n)}-\frac{2 a \sqrt{a x^2+b x^n}}{c^4 (2-n) x}-\frac{2 \left(a x^2+b x^n\right)^{3/2}}{3 c^4 (2-n) x^3}","\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^n}}\right)}{c^4 (2-n)}-\frac{2 a \sqrt{a x^2+b x^n}}{c^4 (2-n) x}-\frac{2 \left(a x^2+b x^n\right)^{3/2}}{3 c^4 (2-n) x^3}",1,"(-2*a*Sqrt[a*x^2 + b*x^n])/(c^4*(2 - n)*x) - (2*(a*x^2 + b*x^n)^(3/2))/(3*c^4*(2 - n)*x^3) + (2*a^(3/2)*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^n]])/(c^4*(2 - n))","A",5,4,22,0.1818,1,"{12, 2028, 2008, 206}"
376,1,122,0,0.1883078,"\int \frac{\left(a x+b x^n\right)^{3/2}}{(c x)^{5/2}} \, dx","Int[(a*x + b*x^n)^(3/2)/(c*x)^(5/2),x]","\frac{2 a^{3/2} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^n}}\right)}{c^2 (1-n) \sqrt{c x}}-\frac{2 a \sqrt{a x+b x^n}}{c^2 (1-n) \sqrt{c x}}-\frac{2 \left(a x+b x^n\right)^{3/2}}{3 c (1-n) (c x)^{3/2}}","\frac{2 a^{3/2} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^n}}\right)}{c^2 (1-n) \sqrt{c x}}-\frac{2 a \sqrt{a x+b x^n}}{c^2 (1-n) \sqrt{c x}}-\frac{2 \left(a x+b x^n\right)^{3/2}}{3 c (1-n) (c x)^{3/2}}",1,"(-2*a*Sqrt[a*x + b*x^n])/(c^2*(1 - n)*Sqrt[c*x]) - (2*(a*x + b*x^n)^(3/2))/(3*c*(1 - n)*(c*x)^(3/2)) + (2*a^(3/2)*Sqrt[x]*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[a*x + b*x^n]])/(c^2*(1 - n)*Sqrt[c*x])","A",5,4,21,0.1905,1,"{2028, 2031, 2029, 206}"
377,1,73,0,0.0408936,"\int \frac{\left(a+b x^n\right)^{3/2}}{c x} \, dx","Int[(a + b*x^n)^(3/2)/(c*x),x]","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{c n}+\frac{2 a \sqrt{a+b x^n}}{c n}+\frac{2 \left(a+b x^n\right)^{3/2}}{3 c n}","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{c n}+\frac{2 a \sqrt{a+b x^n}}{c n}+\frac{2 \left(a+b x^n\right)^{3/2}}{3 c n}",1,"(2*a*Sqrt[a + b*x^n])/(c*n) + (2*(a + b*x^n)^(3/2))/(3*c*n) - (2*a^(3/2)*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(c*n)","A",6,5,18,0.2778,1,"{12, 266, 50, 63, 208}"
378,1,117,0,0.2301011,"\int \sqrt{c x} \left(\frac{a}{x}+b x^n\right)^{3/2} \, dx","Int[Sqrt[c*x]*(a/x + b*x^n)^(3/2),x]","-\frac{2 a^{3/2} c \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{\sqrt{x} \sqrt{\frac{a}{x}+b x^n}}\right)}{(n+1) \sqrt{c x}}+\frac{2 a \sqrt{c x} \sqrt{\frac{a}{x}+b x^n}}{n+1}+\frac{2 (c x)^{3/2} \left(\frac{a}{x}+b x^n\right)^{3/2}}{3 c (n+1)}","-\frac{2 a^{3/2} c \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{\sqrt{x} \sqrt{\frac{a}{x}+b x^n}}\right)}{(n+1) \sqrt{c x}}+\frac{2 a \sqrt{c x} \sqrt{\frac{a}{x}+b x^n}}{n+1}+\frac{2 (c x)^{3/2} \left(\frac{a}{x}+b x^n\right)^{3/2}}{3 c (n+1)}",1,"(2*a*Sqrt[c*x]*Sqrt[a/x + b*x^n])/(1 + n) + (2*(c*x)^(3/2)*(a/x + b*x^n)^(3/2))/(3*c*(1 + n)) - (2*a^(3/2)*c*Sqrt[x]*ArcTanh[Sqrt[a]/(Sqrt[x]*Sqrt[a/x + b*x^n])])/((1 + n)*Sqrt[c*x])","A",5,4,23,0.1739,1,"{2028, 2031, 2029, 206}"
379,1,98,0,0.171814,"\int c^2 x^2 \left(\frac{a}{x^2}+b x^n\right)^{3/2} \, dx","Int[c^2*x^2*(a/x^2 + b*x^n)^(3/2),x]","-\frac{2 a^{3/2} c^2 \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x^n}}\right)}{n+2}+\frac{2 c^2 x^3 \left(\frac{a}{x^2}+b x^n\right)^{3/2}}{3 (n+2)}+\frac{2 a c^2 x \sqrt{\frac{a}{x^2}+b x^n}}{n+2}","-\frac{2 a^{3/2} c^2 \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x^n}}\right)}{n+2}+\frac{2 c^2 x^3 \left(\frac{a}{x^2}+b x^n\right)^{3/2}}{3 (n+2)}+\frac{2 a c^2 x \sqrt{\frac{a}{x^2}+b x^n}}{n+2}",1,"(2*a*c^2*x*Sqrt[a/x^2 + b*x^n])/(2 + n) + (2*c^2*x^3*(a/x^2 + b*x^n)^(3/2))/(3*(2 + n)) - (2*a^(3/2)*c^2*ArcTanh[Sqrt[a]/(x*Sqrt[a/x^2 + b*x^n])])/(2 + n)","A",5,5,22,0.2273,1,"{12, 2028, 2007, 2029, 206}"
380,1,122,0,0.2760273,"\int (c x)^{7/2} \left(\frac{a}{x^3}+b x^n\right)^{3/2} \, dx","Int[(c*x)^(7/2)*(a/x^3 + b*x^n)^(3/2),x]","-\frac{2 a^{3/2} c^4 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{x^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}\right)}{(n+3) \sqrt{c x}}+\frac{2 a c^2 (c x)^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}{n+3}+\frac{2 (c x)^{9/2} \left(\frac{a}{x^3}+b x^n\right)^{3/2}}{3 c (n+3)}","-\frac{2 a^{3/2} c^4 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{x^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}\right)}{(n+3) \sqrt{c x}}+\frac{2 a c^2 (c x)^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}{n+3}+\frac{2 (c x)^{9/2} \left(\frac{a}{x^3}+b x^n\right)^{3/2}}{3 c (n+3)}",1,"(2*a*c^2*(c*x)^(3/2)*Sqrt[a/x^3 + b*x^n])/(3 + n) + (2*(c*x)^(9/2)*(a/x^3 + b*x^n)^(3/2))/(3*c*(3 + n)) - (2*a^(3/2)*c^4*Sqrt[x]*ArcTanh[Sqrt[a]/(x^(3/2)*Sqrt[a/x^3 + b*x^n])])/((3 + n)*Sqrt[c*x])","A",5,4,23,0.1739,1,"{2028, 2031, 2029, 206}"
381,1,100,0,0.2120585,"\int c^5 x^5 \left(\frac{a}{x^4}+b x^n\right)^{3/2} \, dx","Int[c^5*x^5*(a/x^4 + b*x^n)^(3/2),x]","-\frac{2 a^{3/2} c^5 \tanh ^{-1}\left(\frac{\sqrt{a}}{x^2 \sqrt{\frac{a}{x^4}+b x^n}}\right)}{n+4}+\frac{2 c^5 x^6 \left(\frac{a}{x^4}+b x^n\right)^{3/2}}{3 (n+4)}+\frac{2 a c^5 x^2 \sqrt{\frac{a}{x^4}+b x^n}}{n+4}","-\frac{2 a^{3/2} c^5 \tanh ^{-1}\left(\frac{\sqrt{a}}{x^2 \sqrt{\frac{a}{x^4}+b x^n}}\right)}{n+4}+\frac{2 c^5 x^6 \left(\frac{a}{x^4}+b x^n\right)^{3/2}}{3 (n+4)}+\frac{2 a c^5 x^2 \sqrt{\frac{a}{x^4}+b x^n}}{n+4}",1,"(2*a*c^5*x^2*Sqrt[a/x^4 + b*x^n])/(4 + n) + (2*c^5*x^6*(a/x^4 + b*x^n)^(3/2))/(3*(4 + n)) - (2*a^(3/2)*c^5*ArcTanh[Sqrt[a]/(x^2*Sqrt[a/x^4 + b*x^n])])/(4 + n)","A",5,4,22,0.1818,1,"{12, 2028, 2029, 206}"
382,1,51,0,0.0765409,"\int \sqrt{\frac{a+b x}{x^2}} \, dx","Int[Sqrt[(a + b*x)/x^2],x]","2 x \sqrt{\frac{a}{x^2}+\frac{b}{x}}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+\frac{b}{x}}}\right)","2 x \sqrt{\frac{a}{x^2}+\frac{b}{x}}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+\frac{b}{x}}}\right)",1,"2*Sqrt[a/x^2 + b/x]*x - 2*Sqrt[a]*ArcTanh[Sqrt[a]/(Sqrt[a/x^2 + b/x]*x)]","A",5,5,13,0.3846,1,"{1979, 2007, 2013, 620, 206}"
383,1,42,0,0.0229586,"\int \sqrt{\frac{a+b x^2}{x^2}} \, dx","Int[Sqrt[(a + b*x^2)/x^2],x]","x \sqrt{\frac{a}{x^2}+b}-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b}}\right)","x \sqrt{\frac{a}{x^2}+b}-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b}}\right)",1,"Sqrt[b + a/x^2]*x - Sqrt[a]*ArcTanh[Sqrt[a]/(Sqrt[b + a/x^2]*x)]","A",5,5,15,0.3333,1,"{1972, 242, 277, 217, 206}"
384,1,51,0,0.0649497,"\int \sqrt{\frac{a+b x^3}{x^2}} \, dx","Int[Sqrt[(a + b*x^3)/x^2],x]","\frac{2}{3} x \sqrt{\frac{a}{x^2}+b x}-\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x}}\right)","\frac{2}{3} x \sqrt{\frac{a}{x^2}+b x}-\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x}}\right)",1,"(2*x*Sqrt[a/x^2 + b*x])/3 - (2*Sqrt[a]*ArcTanh[Sqrt[a]/(x*Sqrt[a/x^2 + b*x])])/3","A",4,4,15,0.2667,1,"{1979, 2007, 2029, 206}"
385,1,61,0,0.0799542,"\int \sqrt{\frac{a+b x^n}{x^2}} \, dx","Int[Sqrt[(a + b*x^n)/x^2],x]","\frac{2 x \sqrt{\frac{a}{x^2}+b x^{n-2}}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x^{n-2}}}\right)}{n}","\frac{2 x \sqrt{\frac{a}{x^2}+b x^{n-2}}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x^{n-2}}}\right)}{n}",1,"(2*x*Sqrt[a/x^2 + b*x^(-2 + n)])/n - (2*Sqrt[a]*ArcTanh[Sqrt[a]/(x*Sqrt[a/x^2 + b*x^(-2 + n)])])/n","A",4,4,15,0.2667,1,"{1979, 2007, 2029, 206}"
386,1,53,0,0.0789457,"\int \sqrt{\frac{-a+b x}{x^2}} \, dx","Int[Sqrt[(-a + b*x)/x^2],x]","2 x \sqrt{\frac{b}{x}-\frac{a}{x^2}}+2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{b}{x}-\frac{a}{x^2}}}\right)","2 x \sqrt{\frac{b}{x}-\frac{a}{x^2}}+2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{b}{x}-\frac{a}{x^2}}}\right)",1,"2*Sqrt[-(a/x^2) + b/x]*x + 2*Sqrt[a]*ArcTan[Sqrt[a]/(Sqrt[-(a/x^2) + b/x]*x)]","A",5,5,15,0.3333,1,"{1979, 2007, 2013, 620, 203}"
387,1,43,0,0.023209,"\int \sqrt{\frac{-a+b x^2}{x^2}} \, dx","Int[Sqrt[(-a + b*x^2)/x^2],x]","x \sqrt{b-\frac{a}{x^2}}+\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{b-\frac{a}{x^2}}}\right)","x \sqrt{b-\frac{a}{x^2}}+\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{b-\frac{a}{x^2}}}\right)",1,"Sqrt[b - a/x^2]*x + Sqrt[a]*ArcTan[Sqrt[a]/(Sqrt[b - a/x^2]*x)]","A",5,5,17,0.2941,1,"{1972, 242, 277, 217, 203}"
388,1,53,0,0.0679645,"\int \sqrt{\frac{-a+b x^3}{x^2}} \, dx","Int[Sqrt[(-a + b*x^3)/x^2],x]","\frac{2}{3} x \sqrt{b x-\frac{a}{x^2}}+\frac{2}{3} \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{b x-\frac{a}{x^2}}}\right)","\frac{2}{3} x \sqrt{b x-\frac{a}{x^2}}+\frac{2}{3} \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{b x-\frac{a}{x^2}}}\right)",1,"(2*x*Sqrt[-(a/x^2) + b*x])/3 + (2*Sqrt[a]*ArcTan[Sqrt[a]/(x*Sqrt[-(a/x^2) + b*x])])/3","A",4,4,17,0.2353,1,"{1979, 2007, 2029, 203}"
389,1,63,0,0.0804348,"\int \sqrt{\frac{-a+b x^n}{x^2}} \, dx","Int[Sqrt[(-a + b*x^n)/x^2],x]","\frac{2 x \sqrt{b x^{n-2}-\frac{a}{x^2}}}{n}+\frac{2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{b x^{n-2}-\frac{a}{x^2}}}\right)}{n}","\frac{2 x \sqrt{b x^{n-2}-\frac{a}{x^2}}}{n}+\frac{2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{b x^{n-2}-\frac{a}{x^2}}}\right)}{n}",1,"(2*x*Sqrt[-(a/x^2) + b*x^(-2 + n)])/n + (2*Sqrt[a]*ArcTan[Sqrt[a]/(x*Sqrt[-(a/x^2) + b*x^(-2 + n)])])/n","A",4,4,17,0.2353,1,"{1979, 2007, 2029, 203}"
390,1,62,0,0.1079952,"\int \frac{(c x)^{-1+\frac{j}{2}}}{\sqrt{a x^j+b x^n}} \, dx","Int[(c*x)^(-1 + j/2)/Sqrt[a*x^j + b*x^n],x]","\frac{2 x^{-j/2} (c x)^{j/2} \tanh ^{-1}\left(\frac{\sqrt{a} x^{j/2}}{\sqrt{a x^j+b x^n}}\right)}{\sqrt{a} c (j-n)}","\frac{2 x^{-j/2} (c x)^{j/2} \tanh ^{-1}\left(\frac{\sqrt{a} x^{j/2}}{\sqrt{a x^j+b x^n}}\right)}{\sqrt{a} c (j-n)}",1,"(2*(c*x)^(j/2)*ArcTanh[(Sqrt[a]*x^(j/2))/Sqrt[a*x^j + b*x^n]])/(Sqrt[a]*c*(j - n)*x^(j/2))","A",3,3,27,0.1111,1,"{2031, 2029, 206}"
391,1,53,0,0.0987987,"\int \frac{\sqrt{c x}}{\sqrt{a x^3+b x^n}} \, dx","Int[Sqrt[c*x]/Sqrt[a*x^3 + b*x^n],x]","\frac{2 \sqrt{c x} \tanh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b x^n}}\right)}{\sqrt{a} (3-n) \sqrt{x}}","\frac{2 \sqrt{c x} \tanh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b x^n}}\right)}{\sqrt{a} (3-n) \sqrt{x}}",1,"(2*Sqrt[c*x]*ArcTanh[(Sqrt[a]*x^(3/2))/Sqrt[a*x^3 + b*x^n]])/(Sqrt[a]*(3 - n)*Sqrt[x])","A",3,3,23,0.1304,1,"{2031, 2029, 206}"
392,1,37,0,0.015101,"\int \frac{1}{\sqrt{a x^2+b x^n}} \, dx","Int[1/Sqrt[a*x^2 + b*x^n],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^n}}\right)}{\sqrt{a} (2-n)}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^n}}\right)}{\sqrt{a} (2-n)}",1,"(2*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^n]])/(Sqrt[a]*(2 - n))","A",2,2,15,0.1333,1,"{2008, 206}"
393,1,51,0,0.0852557,"\int \frac{1}{\sqrt{c x} \sqrt{a x+b x^n}} \, dx","Int[1/(Sqrt[c*x]*Sqrt[a*x + b*x^n]),x]","\frac{2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^n}}\right)}{\sqrt{a} (1-n) \sqrt{c x}}","\frac{2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^n}}\right)}{\sqrt{a} (1-n) \sqrt{c x}}",1,"(2*Sqrt[x]*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[a*x + b*x^n]])/(Sqrt[a]*(1 - n)*Sqrt[c*x])","A",3,3,21,0.1429,1,"{2031, 2029, 206}"
394,1,31,0,0.0204733,"\int \frac{1}{c x \sqrt{a+b x^n}} \, dx","Int[1/(c*x*Sqrt[a + b*x^n]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{\sqrt{a} c n}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{\sqrt{a} c n}",1,"(-2*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(Sqrt[a]*c*n)","A",4,4,18,0.2222,1,"{12, 266, 63, 208}"
395,1,54,0,0.110832,"\int \frac{1}{(c x)^{3/2} \sqrt{\frac{a}{x}+b x^n}} \, dx","Int[1/((c*x)^(3/2)*Sqrt[a/x + b*x^n]),x]","-\frac{2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{\sqrt{x} \sqrt{\frac{a}{x}+b x^n}}\right)}{\sqrt{a} c (n+1) \sqrt{c x}}","-\frac{2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{\sqrt{x} \sqrt{\frac{a}{x}+b x^n}}\right)}{\sqrt{a} c (n+1) \sqrt{c x}}",1,"(-2*Sqrt[x]*ArcTanh[Sqrt[a]/(Sqrt[x]*Sqrt[a/x + b*x^n])])/(Sqrt[a]*c*(1 + n)*Sqrt[c*x])","A",3,3,23,0.1304,1,"{2031, 2029, 206}"
396,1,40,0,0.0737836,"\int \frac{1}{c^2 x^2 \sqrt{\frac{a}{x^2}+b x^n}} \, dx","Int[1/(c^2*x^2*Sqrt[a/x^2 + b*x^n]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x^n}}\right)}{\sqrt{a} c^2 (n+2)}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x^n}}\right)}{\sqrt{a} c^2 (n+2)}",1,"(-2*ArcTanh[Sqrt[a]/(x*Sqrt[a/x^2 + b*x^n])])/(Sqrt[a]*c^2*(2 + n))","A",3,3,22,0.1364,1,"{12, 2029, 206}"
397,1,54,0,0.1357929,"\int \frac{1}{(c x)^{5/2} \sqrt{\frac{a}{x^3}+b x^n}} \, dx","Int[1/((c*x)^(5/2)*Sqrt[a/x^3 + b*x^n]),x]","-\frac{2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{x^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}\right)}{\sqrt{a} c^2 (n+3) \sqrt{c x}}","-\frac{2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{x^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}\right)}{\sqrt{a} c^2 (n+3) \sqrt{c x}}",1,"(-2*Sqrt[x]*ArcTanh[Sqrt[a]/(x^(3/2)*Sqrt[a/x^3 + b*x^n])])/(Sqrt[a]*c^2*(3 + n)*Sqrt[c*x])","A",3,3,23,0.1304,1,"{2031, 2029, 206}"
398,1,107,0,0.1871962,"\int \frac{(c x)^{-1+\frac{3 j}{2}}}{\left(a x^j+b x^n\right)^{3/2}} \, dx","Int[(c*x)^(-1 + (3*j)/2)/(a*x^j + b*x^n)^(3/2),x]","\frac{2 x^{-3 j/2} (c x)^{3 j/2} \tanh ^{-1}\left(\frac{\sqrt{a} x^{j/2}}{\sqrt{a x^j+b x^n}}\right)}{a^{3/2} c (j-n)}-\frac{2 x^{-j} (c x)^{3 j/2}}{a c (j-n) \sqrt{a x^j+b x^n}}","\frac{2 x^{-3 j/2} (c x)^{3 j/2} \tanh ^{-1}\left(\frac{\sqrt{a} x^{j/2}}{\sqrt{a x^j+b x^n}}\right)}{a^{3/2} c (j-n)}-\frac{2 x^{-j} (c x)^{3 j/2}}{a c (j-n) \sqrt{a x^j+b x^n}}",1,"(-2*(c*x)^((3*j)/2))/(a*c*(j - n)*x^j*Sqrt[a*x^j + b*x^n]) + (2*(c*x)^((3*j)/2)*ArcTanh[(Sqrt[a]*x^(j/2))/Sqrt[a*x^j + b*x^n]])/(a^(3/2)*c*(j - n)*x^((3*j)/2))","A",4,4,27,0.1481,1,"{2031, 2030, 2029, 206}"
399,1,94,0,0.1595721,"\int \frac{(c x)^{7/2}}{\left(a x^3+b x^n\right)^{3/2}} \, dx","Int[(c*x)^(7/2)/(a*x^3 + b*x^n)^(3/2),x]","\frac{2 c^3 \sqrt{c x} \tanh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b x^n}}\right)}{a^{3/2} (3-n) \sqrt{x}}-\frac{2 c^2 (c x)^{3/2}}{a (3-n) \sqrt{a x^3+b x^n}}","\frac{2 c^3 \sqrt{c x} \tanh ^{-1}\left(\frac{\sqrt{a} x^{3/2}}{\sqrt{a x^3+b x^n}}\right)}{a^{3/2} (3-n) \sqrt{x}}-\frac{2 c^2 (c x)^{3/2}}{a (3-n) \sqrt{a x^3+b x^n}}",1,"(-2*c^2*(c*x)^(3/2))/(a*(3 - n)*Sqrt[a*x^3 + b*x^n]) + (2*c^3*Sqrt[c*x]*ArcTanh[(Sqrt[a]*x^(3/2))/Sqrt[a*x^3 + b*x^n]])/(a^(3/2)*(3 - n)*Sqrt[x])","A",4,4,23,0.1739,1,"{2030, 2031, 2029, 206}"
400,1,72,0,0.0880041,"\int \frac{c^2 x^2}{\left(a x^2+b x^n\right)^{3/2}} \, dx","Int[(c^2*x^2)/(a*x^2 + b*x^n)^(3/2),x]","\frac{2 c^2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^n}}\right)}{a^{3/2} (2-n)}-\frac{2 c^2 x}{a (2-n) \sqrt{a x^2+b x^n}}","\frac{2 c^2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^n}}\right)}{a^{3/2} (2-n)}-\frac{2 c^2 x}{a (2-n) \sqrt{a x^2+b x^n}}",1,"(-2*c^2*x)/(a*(2 - n)*Sqrt[a*x^2 + b*x^n]) + (2*c^2*ArcTanh[(Sqrt[a]*x)/Sqrt[a*x^2 + b*x^n]])/(a^(3/2)*(2 - n))","A",4,4,22,0.1818,1,"{12, 2030, 2008, 206}"
401,1,85,0,0.1378935,"\int \frac{\sqrt{c x}}{\left(a x+b x^n\right)^{3/2}} \, dx","Int[Sqrt[c*x]/(a*x + b*x^n)^(3/2),x]","\frac{2 c \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^n}}\right)}{a^{3/2} (1-n) \sqrt{c x}}-\frac{2 \sqrt{c x}}{a (1-n) \sqrt{a x+b x^n}}","\frac{2 c \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^n}}\right)}{a^{3/2} (1-n) \sqrt{c x}}-\frac{2 \sqrt{c x}}{a (1-n) \sqrt{a x+b x^n}}",1,"(-2*Sqrt[c*x])/(a*(1 - n)*Sqrt[a*x + b*x^n]) + (2*c*Sqrt[x]*ArcTanh[(Sqrt[a]*Sqrt[x])/Sqrt[a*x + b*x^n]])/(a^(3/2)*(1 - n)*Sqrt[c*x])","A",4,4,21,0.1905,1,"{2030, 2031, 2029, 206}"
402,1,54,0,0.0332688,"\int \frac{1}{c x \left(a+b x^n\right)^{3/2}} \, dx","Int[1/(c*x*(a + b*x^n)^(3/2)),x]","\frac{2}{a c n \sqrt{a+b x^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{a^{3/2} c n}","\frac{2}{a c n \sqrt{a+b x^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{a^{3/2} c n}",1,"2/(a*c*n*Sqrt[a + b*x^n]) - (2*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(a^(3/2)*c*n)","A",5,5,18,0.2778,1,"{12, 266, 51, 63, 208}"
403,1,90,0,0.1935091,"\int \frac{1}{(c x)^{5/2} \left(\frac{a}{x}+b x^n\right)^{3/2}} \, dx","Int[1/((c*x)^(5/2)*(a/x + b*x^n)^(3/2)),x]","\frac{2}{a c^2 (n+1) \sqrt{c x} \sqrt{\frac{a}{x}+b x^n}}-\frac{2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{\sqrt{x} \sqrt{\frac{a}{x}+b x^n}}\right)}{a^{3/2} c^2 (n+1) \sqrt{c x}}","\frac{2}{a c^2 (n+1) \sqrt{c x} \sqrt{\frac{a}{x}+b x^n}}-\frac{2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{\sqrt{x} \sqrt{\frac{a}{x}+b x^n}}\right)}{a^{3/2} c^2 (n+1) \sqrt{c x}}",1,"2/(a*c^2*(1 + n)*Sqrt[c*x]*Sqrt[a/x + b*x^n]) - (2*Sqrt[x]*ArcTanh[Sqrt[a]/(Sqrt[x]*Sqrt[a/x + b*x^n])])/(a^(3/2)*c^2*(1 + n)*Sqrt[c*x])","A",4,4,23,0.1739,1,"{2030, 2031, 2029, 206}"
404,1,72,0,0.1559988,"\int \frac{1}{c^4 x^4 \left(\frac{a}{x^2}+b x^n\right)^{3/2}} \, dx","Int[1/(c^4*x^4*(a/x^2 + b*x^n)^(3/2)),x]","\frac{2}{a c^4 (n+2) x \sqrt{\frac{a}{x^2}+b x^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x^n}}\right)}{a^{3/2} c^4 (n+2)}","\frac{2}{a c^4 (n+2) x \sqrt{\frac{a}{x^2}+b x^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a}}{x \sqrt{\frac{a}{x^2}+b x^n}}\right)}{a^{3/2} c^4 (n+2)}",1,"2/(a*c^4*(2 + n)*x*Sqrt[a/x^2 + b*x^n]) - (2*ArcTanh[Sqrt[a]/(x*Sqrt[a/x^2 + b*x^n])])/(a^(3/2)*c^4*(2 + n))","A",4,4,22,0.1818,1,"{12, 2030, 2029, 206}"
405,1,90,0,0.2166979,"\int \frac{1}{(c x)^{11/2} \left(\frac{a}{x^3}+b x^n\right)^{3/2}} \, dx","Int[1/((c*x)^(11/2)*(a/x^3 + b*x^n)^(3/2)),x]","\frac{2}{a c^4 (n+3) (c x)^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}-\frac{2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{x^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}\right)}{a^{3/2} c^5 (n+3) \sqrt{c x}}","\frac{2}{a c^4 (n+3) (c x)^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}-\frac{2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{a}}{x^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}\right)}{a^{3/2} c^5 (n+3) \sqrt{c x}}",1,"2/(a*c^4*(3 + n)*(c*x)^(3/2)*Sqrt[a/x^3 + b*x^n]) - (2*Sqrt[x]*ArcTanh[Sqrt[a]/(x^(3/2)*Sqrt[a/x^3 + b*x^n])])/(a^(3/2)*c^5*(3 + n)*Sqrt[c*x])","A",4,4,23,0.1739,1,"{2030, 2031, 2029, 206}"
406,1,72,0,0.1521609,"\int \frac{1}{c^7 x^7 \left(\frac{a}{x^4}+b x^n\right)^{3/2}} \, dx","Int[1/(c^7*x^7*(a/x^4 + b*x^n)^(3/2)),x]","\frac{2}{a c^7 (n+4) x^2 \sqrt{\frac{a}{x^4}+b x^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a}}{x^2 \sqrt{\frac{a}{x^4}+b x^n}}\right)}{a^{3/2} c^7 (n+4)}","\frac{2}{a c^7 (n+4) x^2 \sqrt{\frac{a}{x^4}+b x^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a}}{x^2 \sqrt{\frac{a}{x^4}+b x^n}}\right)}{a^{3/2} c^7 (n+4)}",1,"2/(a*c^7*(4 + n)*x^2*Sqrt[a/x^4 + b*x^n]) - (2*ArcTanh[Sqrt[a]/(x^2*Sqrt[a/x^4 + b*x^n])])/(a^(3/2)*c^7*(4 + n))","A",4,4,22,0.1818,1,"{12, 2030, 2029, 206}"
407,1,32,0,0.0144815,"\int \frac{1}{\sqrt{\frac{a+b x^3}{x}}} \, dx","Int[1/Sqrt[(a + b*x^3)/x],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x}+b x^2}}\right)}{3 \sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x}+b x^2}}\right)}{3 \sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[a/x + b*x^2]])/(3*Sqrt[b])","A",3,3,15,0.2000,1,"{1979, 2008, 206}"
408,1,32,0,0.0159634,"\int \frac{1}{\sqrt{\frac{a+b x^4}{x^2}}} \, dx","Int[1/Sqrt[(a + b*x^4)/x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^2}+b x^2}}\right)}{2 \sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^2}+b x^2}}\right)}{2 \sqrt{b}}",1,"ArcTanh[(Sqrt[b]*x)/Sqrt[a/x^2 + b*x^2]]/(2*Sqrt[b])","A",3,3,15,0.2000,1,"{1979, 2008, 206}"
409,1,32,0,0.0158393,"\int \frac{1}{\sqrt{\frac{a+b x^5}{x^3}}} \, dx","Int[1/Sqrt[(a + b*x^5)/x^3],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^3}+b x^2}}\right)}{5 \sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^3}+b x^2}}\right)}{5 \sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[a/x^3 + b*x^2]])/(5*Sqrt[b])","A",3,3,15,0.2000,1,"{1979, 2008, 206}"
410,1,37,0,0.0239837,"\int \frac{1}{\sqrt{x^{2-n} \left(a+b x^n\right)}} \, dx","Int[1/Sqrt[x^(2 - n)*(a + b*x^n)],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^{2-n}+b x^2}}\right)}{\sqrt{b} n}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^{2-n}+b x^2}}\right)}{\sqrt{b} n}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + a*x^(2 - n)]])/(Sqrt[b]*n)","A",3,3,19,0.1579,1,"{1979, 2008, 206}"
411,1,33,0,0.0140644,"\int \frac{1}{\sqrt{\frac{a-b x^3}{x}}} \, dx","Int[1/Sqrt[(a - b*x^3)/x],x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x}-b x^2}}\right)}{3 \sqrt{b}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x}-b x^2}}\right)}{3 \sqrt{b}}",1,"(2*ArcTan[(Sqrt[b]*x)/Sqrt[a/x - b*x^2]])/(3*Sqrt[b])","A",3,3,16,0.1875,1,"{1979, 2008, 203}"
412,1,33,0,0.0149095,"\int \frac{1}{\sqrt{\frac{a-b x^4}{x^2}}} \, dx","Int[1/Sqrt[(a - b*x^4)/x^2],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^2}-b x^2}}\right)}{2 \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^2}-b x^2}}\right)}{2 \sqrt{b}}",1,"ArcTan[(Sqrt[b]*x)/Sqrt[a/x^2 - b*x^2]]/(2*Sqrt[b])","A",3,3,16,0.1875,1,"{1979, 2008, 203}"
413,1,33,0,0.0161781,"\int \frac{1}{\sqrt{\frac{a-b x^5}{x^3}}} \, dx","Int[1/Sqrt[(a - b*x^5)/x^3],x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^3}-b x^2}}\right)}{5 \sqrt{b}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^3}-b x^2}}\right)}{5 \sqrt{b}}",1,"(2*ArcTan[(Sqrt[b]*x)/Sqrt[a/x^3 - b*x^2]])/(5*Sqrt[b])","A",3,3,16,0.1875,1,"{1979, 2008, 203}"
414,1,38,0,0.0226047,"\int \frac{1}{\sqrt{x^{2-n} \left(a-b x^n\right)}} \, dx","Int[1/Sqrt[x^(2 - n)*(a - b*x^n)],x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^{2-n}-b x^2}}\right)}{\sqrt{b} n}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^{2-n}-b x^2}}\right)}{\sqrt{b} n}",1,"(2*ArcTan[(Sqrt[b]*x)/Sqrt[-(b*x^2) + a*x^(2 - n)]])/(Sqrt[b]*n)","A",3,3,20,0.1500,1,"{1979, 2008, 203}"
415,1,37,0,0.0233351,"\int \frac{1}{\sqrt{x^n \left(a+b x^{2-n}\right)}} \, dx","Int[1/Sqrt[x^n*(a + b*x^(2 - n))],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n+b x^2}}\right)}{\sqrt{b} (2-n)}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n+b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + a*x^n]])/(Sqrt[b]*(2 - n))","A",3,3,19,0.1579,1,"{1979, 2008, 206}"
416,1,37,0,0.0193817,"\int \frac{1}{\sqrt{x^2 \left(b+a x^{-2+n}\right)}} \, dx","Int[1/Sqrt[x^2*(b + a*x^(-2 + n))],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n+b x^2}}\right)}{\sqrt{b} (2-n)}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n+b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + a*x^n]])/(Sqrt[b]*(2 - n))","A",3,3,17,0.1765,1,"{1979, 2008, 206}"
417,1,37,0,0.0183542,"\int \frac{1}{\sqrt{x \left(b x+a x^{-1+n}\right)}} \, dx","Int[1/Sqrt[x*(b*x + a*x^(-1 + n))],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n+b x^2}}\right)}{\sqrt{b} (2-n)}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n+b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + a*x^n]])/(Sqrt[b]*(2 - n))","A",3,3,17,0.1765,1,"{1979, 2008, 206}"
418,1,38,0,0.0209641,"\int \frac{1}{\sqrt{x^n \left(a-b x^{2-n}\right)}} \, dx","Int[1/Sqrt[x^n*(a - b*x^(2 - n))],x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n-b x^2}}\right)}{\sqrt{b} (2-n)}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n-b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(2*ArcTan[(Sqrt[b]*x)/Sqrt[-(b*x^2) + a*x^n]])/(Sqrt[b]*(2 - n))","A",3,3,20,0.1500,1,"{1979, 2008, 203}"
419,1,38,0,0.0198648,"\int \frac{1}{\sqrt{x^2 \left(-b+a x^{-2+n}\right)}} \, dx","Int[1/Sqrt[x^2*(-b + a*x^(-2 + n))],x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n-b x^2}}\right)}{\sqrt{b} (2-n)}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n-b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(2*ArcTan[(Sqrt[b]*x)/Sqrt[-(b*x^2) + a*x^n]])/(Sqrt[b]*(2 - n))","A",3,3,19,0.1579,1,"{1979, 2008, 203}"
420,1,38,0,0.0188031,"\int \frac{1}{\sqrt{x \left(-b x+a x^{-1+n}\right)}} \, dx","Int[1/Sqrt[x*(-(b*x) + a*x^(-1 + n))],x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n-b x^2}}\right)}{\sqrt{b} (2-n)}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n-b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(2*ArcTan[(Sqrt[b]*x)/Sqrt[-(b*x^2) + a*x^n]])/(Sqrt[b]*(2 - n))","A",3,3,18,0.1667,1,"{1979, 2008, 203}"
421,1,107,0,0.1021145,"\int (c x)^m \left(a x^j+b x^n\right)^{3/2} \, dx","Int[(c*x)^m*(a*x^j + b*x^n)^(3/2),x]","\frac{2 b x^{n+1} (c x)^m \sqrt{a x^j+b x^n} \, _2F_1\left(-\frac{3}{2},\frac{m+\frac{3 n}{2}+1}{j-n};\frac{m+\frac{3 n}{2}+1}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{(2 m+3 n+2) \sqrt{\frac{a x^{j-n}}{b}+1}}","\frac{2 b x^{n+1} (c x)^m \sqrt{a x^j+b x^n} \, _2F_1\left(-\frac{3}{2},\frac{m+\frac{3 n}{2}+1}{j-n};\frac{m+\frac{3 n}{2}+1}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{(2 m+3 n+2) \sqrt{\frac{a x^{j-n}}{b}+1}}",1,"(2*b*x^(1 + n)*(c*x)^m*Sqrt[a*x^j + b*x^n]*Hypergeometric2F1[-3/2, (1 + m + (3*n)/2)/(j - n), 1 + (1 + m + (3*n)/2)/(j - n), -((a*x^(j - n))/b)])/((2 + 2*m + 3*n)*Sqrt[1 + (a*x^(j - n))/b])","A",3,3,21,0.1429,1,"{2032, 365, 364}"
422,1,100,0,0.094578,"\int (c x)^m \sqrt{a x^j+b x^n} \, dx","Int[(c*x)^m*Sqrt[a*x^j + b*x^n],x]","\frac{2 x (c x)^m \sqrt{a x^j+b x^n} \, _2F_1\left(-\frac{1}{2},\frac{m+\frac{n}{2}+1}{j-n};\frac{2 m+n+2}{2 j-2 n}+1;-\frac{a x^{j-n}}{b}\right)}{(2 m+n+2) \sqrt{\frac{a x^{j-n}}{b}+1}}","\frac{2 x (c x)^m \sqrt{a x^j+b x^n} \, _2F_1\left(-\frac{1}{2},\frac{m+\frac{n}{2}+1}{j-n};\frac{2 m+n+2}{2 j-2 n}+1;-\frac{a x^{j-n}}{b}\right)}{(2 m+n+2) \sqrt{\frac{a x^{j-n}}{b}+1}}",1,"(2*x*(c*x)^m*Sqrt[a*x^j + b*x^n]*Hypergeometric2F1[-1/2, (1 + m + n/2)/(j - n), 1 + (2 + 2*m + n)/(2*j - 2*n), -((a*x^(j - n))/b)])/((2 + 2*m + n)*Sqrt[1 + (a*x^(j - n))/b])","A",3,3,21,0.1429,1,"{2032, 365, 364}"
423,1,102,0,0.097152,"\int \frac{(c x)^m}{\sqrt{a x^j+b x^n}} \, dx","Int[(c*x)^m/Sqrt[a*x^j + b*x^n],x]","\frac{2 x (c x)^m \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{m-\frac{n}{2}+1}{j-n};\frac{m-\frac{n}{2}+1}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{(2 m-n+2) \sqrt{a x^j+b x^n}}","\frac{2 x (c x)^m \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{m-\frac{n}{2}+1}{j-n};\frac{m-\frac{n}{2}+1}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{(2 m-n+2) \sqrt{a x^j+b x^n}}",1,"(2*x*(c*x)^m*Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[1/2, (1 + m - n/2)/(j - n), 1 + (1 + m - n/2)/(j - n), -((a*x^(j - n))/b)])/((2 + 2*m - n)*Sqrt[a*x^j + b*x^n])","A",3,3,21,0.1429,1,"{2032, 365, 364}"
424,1,111,0,0.1077651,"\int \frac{(c x)^m}{\left(a x^j+b x^n\right)^{3/2}} \, dx","Int[(c*x)^m/(a*x^j + b*x^n)^(3/2),x]","\frac{2 x^{1-n} (c x)^m \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{3}{2},\frac{m-\frac{3 n}{2}+1}{j-n};\frac{m-\frac{3 n}{2}+1}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{b (2 m-3 n+2) \sqrt{a x^j+b x^n}}","\frac{2 x^{1-n} (c x)^m \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{3}{2},\frac{m-\frac{3 n}{2}+1}{j-n};\frac{m-\frac{3 n}{2}+1}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{b (2 m-3 n+2) \sqrt{a x^j+b x^n}}",1,"(2*x^(1 - n)*(c*x)^m*Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[3/2, (1 + m - (3*n)/2)/(j - n), 1 + (1 + m - (3*n)/2)/(j - n), -((a*x^(j - n))/b)])/(b*(2 + 2*m - 3*n)*Sqrt[a*x^j + b*x^n])","A",3,3,21,0.1429,1,"{2032, 365, 364}"
425,1,111,0,0.1064847,"\int \frac{(c x)^m}{\left(a x^j+b x^n\right)^{5/2}} \, dx","Int[(c*x)^m/(a*x^j + b*x^n)^(5/2),x]","\frac{2 x^{1-2 n} (c x)^m \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{5}{2},\frac{m-\frac{5 n}{2}+1}{j-n};\frac{m-\frac{5 n}{2}+1}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{b^2 (2 m-5 n+2) \sqrt{a x^j+b x^n}}","\frac{2 x^{1-2 n} (c x)^m \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{5}{2},\frac{m-\frac{5 n}{2}+1}{j-n};\frac{m-\frac{5 n}{2}+1}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{b^2 (2 m-5 n+2) \sqrt{a x^j+b x^n}}",1,"(2*x^(1 - 2*n)*(c*x)^m*Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[5/2, (1 + m - (5*n)/2)/(j - n), 1 + (1 + m - (5*n)/2)/(j - n), -((a*x^(j - n))/b)])/(b^2*(2 + 2*m - 5*n)*Sqrt[a*x^j + b*x^n])","A",3,3,21,0.1429,1,"{2032, 365, 364}"
426,1,97,0,0.05521,"\int \left(a x^j+b x^n\right)^{3/2} \, dx","Int[(a*x^j + b*x^n)^(3/2),x]","\frac{2 b x^{n+1} \sqrt{a x^j+b x^n} \, _2F_1\left(-\frac{3}{2},\frac{\frac{3 n}{2}+1}{j-n};\frac{2 j+n+2}{2 (j-n)};-\frac{a x^{j-n}}{b}\right)}{(3 n+2) \sqrt{\frac{a x^{j-n}}{b}+1}}","\frac{2 b x^{n+1} \sqrt{a x^j+b x^n} \, _2F_1\left(-\frac{3}{2},\frac{\frac{3 n}{2}+1}{j-n};\frac{2 j+n+2}{2 (j-n)};-\frac{a x^{j-n}}{b}\right)}{(3 n+2) \sqrt{\frac{a x^{j-n}}{b}+1}}",1,"(2*b*x^(1 + n)*Sqrt[a*x^j + b*x^n]*Hypergeometric2F1[-3/2, (1 + (3*n)/2)/(j - n), (2 + 2*j + n)/(2*(j - n)), -((a*x^(j - n))/b)])/((2 + 3*n)*Sqrt[1 + (a*x^(j - n))/b])","A",3,3,15,0.2000,1,"{2011, 365, 364}"
427,1,87,0,0.0525132,"\int \sqrt{a x^j+b x^n} \, dx","Int[Sqrt[a*x^j + b*x^n],x]","\frac{2 x \sqrt{a x^j+b x^n} \, _2F_1\left(-\frac{1}{2},\frac{n+2}{2 (j-n)};\frac{n+2}{2 j-2 n}+1;-\frac{a x^{j-n}}{b}\right)}{(n+2) \sqrt{\frac{a x^{j-n}}{b}+1}}","\frac{2 x \sqrt{a x^j+b x^n} \, _2F_1\left(-\frac{1}{2},\frac{n+2}{2 (j-n)};\frac{n+2}{2 j-2 n}+1;-\frac{a x^{j-n}}{b}\right)}{(n+2) \sqrt{\frac{a x^{j-n}}{b}+1}}",1,"(2*x*Sqrt[a*x^j + b*x^n]*Hypergeometric2F1[-1/2, (2 + n)/(2*(j - n)), 1 + (2 + n)/(2*j - 2*n), -((a*x^(j - n))/b)])/((2 + n)*Sqrt[1 + (a*x^(j - n))/b])","A",3,3,15,0.2000,1,"{2011, 365, 364}"
428,1,93,0,0.0511551,"\int \frac{1}{\sqrt{a x^j+b x^n}} \, dx","Int[1/Sqrt[a*x^j + b*x^n],x]","\frac{2 x \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{2-n}{2 (j-n)};\frac{1-\frac{n}{2}}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{(2-n) \sqrt{a x^j+b x^n}}","\frac{2 x \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{2-n}{2 (j-n)};\frac{1-\frac{n}{2}}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{(2-n) \sqrt{a x^j+b x^n}}",1,"(2*x*Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[1/2, (2 - n)/(2*(j - n)), 1 + (1 - n/2)/(j - n), -((a*x^(j - n))/b)])/((2 - n)*Sqrt[a*x^j + b*x^n])","A",3,3,15,0.2000,1,"{2011, 365, 364}"
429,1,101,0,0.0568401,"\int \frac{1}{\left(a x^j+b x^n\right)^{3/2}} \, dx","Int[(a*x^j + b*x^n)^(-3/2),x]","\frac{2 x^{1-n} \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{3}{2},\frac{1-\frac{3 n}{2}}{j-n};\frac{1-\frac{3 n}{2}}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{b (2-3 n) \sqrt{a x^j+b x^n}}","\frac{2 x^{1-n} \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{3}{2},\frac{1-\frac{3 n}{2}}{j-n};\frac{1-\frac{3 n}{2}}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{b (2-3 n) \sqrt{a x^j+b x^n}}",1,"(2*x^(1 - n)*Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[3/2, (1 - (3*n)/2)/(j - n), 1 + (1 - (3*n)/2)/(j - n), -((a*x^(j - n))/b)])/(b*(2 - 3*n)*Sqrt[a*x^j + b*x^n])","A",3,3,15,0.2000,1,"{2011, 365, 364}"
430,1,101,0,0.0565193,"\int \frac{1}{\left(a x^j+b x^n\right)^{5/2}} \, dx","Int[(a*x^j + b*x^n)^(-5/2),x]","\frac{2 x^{1-2 n} \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{5}{2},\frac{1-\frac{5 n}{2}}{j-n};\frac{1-\frac{5 n}{2}}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{b^2 (2-5 n) \sqrt{a x^j+b x^n}}","\frac{2 x^{1-2 n} \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{5}{2},\frac{1-\frac{5 n}{2}}{j-n};\frac{1-\frac{5 n}{2}}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{b^2 (2-5 n) \sqrt{a x^j+b x^n}}",1,"(2*x^(1 - 2*n)*Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[5/2, (1 - (5*n)/2)/(j - n), 1 + (1 - (5*n)/2)/(j - n), -((a*x^(j - n))/b)])/(b^2*(2 - 5*n)*Sqrt[a*x^j + b*x^n])","A",3,3,15,0.2000,1,"{2011, 365, 364}"
431,1,18,0,0.006895,"\int \sqrt{\frac{1+x}{x^5}} \, dx","Int[Sqrt[(1 + x)/x^5],x]","-\frac{2}{3} \left(\frac{1}{x^4}+\frac{1}{x^5}\right)^{3/2} x^6","-\frac{2}{3} \left(\frac{1}{x^4}+\frac{1}{x^5}\right)^{3/2} x^6",1,"(-2*(x^(-5) + x^(-4))^(3/2)*x^6)/3","A",2,2,11,0.1818,1,"{1979, 2000}"
432,1,20,0,0.003314,"\int \sqrt{x+x^{5/2}} \, dx","Int[Sqrt[x + x^(5/2)],x]","\frac{4 \left(x^{5/2}+x\right)^{3/2}}{9 x^{3/2}}","\frac{4 \left(x^{5/2}+x\right)^{3/2}}{9 x^{3/2}}",1,"(4*(x + x^(5/2))^(3/2))/(9*x^(3/2))","A",1,1,11,0.09091,1,"{2000}"
433,1,8,0,0.003541,"\int \frac{1}{\sqrt{x}+x^{3/2}} \, dx","Int[(Sqrt[x] + x^(3/2))^(-1),x]","2 \tan ^{-1}\left(\sqrt{x}\right)","2 \tan ^{-1}\left(\sqrt{x}\right)",1,"2*ArcTan[Sqrt[x]]","A",3,3,13,0.2308,1,"{1593, 63, 203}"
434,1,25,0,0.010443,"\int x \sqrt{x^2 \left(a+b x^3\right)} \, dx","Int[x*Sqrt[x^2*(a + b*x^3)],x]","\frac{2 \left(x^2 \left(a+b x^3\right)\right)^{3/2}}{9 b x^3}","\frac{2 \left(x^2 \left(a+b x^3\right)\right)^{3/2}}{9 b x^3}",1,"(2*(x^2*(a + b*x^3))^(3/2))/(9*b*x^3)","A",1,1,17,0.05882,1,"{1588}"
435,1,25,0,0.0105747,"\int x \sqrt{a x^2+b x^5} \, dx","Int[x*Sqrt[a*x^2 + b*x^5],x]","\frac{2 \left(a x^2+b x^5\right)^{3/2}}{9 b x^3}","\frac{2 \left(a x^2+b x^5\right)^{3/2}}{9 b x^3}",1,"(2*(a*x^2 + b*x^5)^(3/2))/(9*b*x^3)","A",1,1,17,0.05882,1,"{1588}"
436,1,25,0,0.0078477,"\int \sqrt{x^4 \left(a+b x^3\right)} \, dx","Int[Sqrt[x^4*(a + b*x^3)],x]","\frac{2 \left(a x^4+b x^7\right)^{3/2}}{9 b x^6}","\frac{2 \left(a x^4+b x^7\right)^{3/2}}{9 b x^6}",1,"(2*(a*x^4 + b*x^7)^(3/2))/(9*b*x^6)","A",2,2,15,0.1333,1,"{1979, 2000}"
437,1,988,0,2.2454481,"\int \frac{1}{\sqrt[3]{a \sqrt[3]{x}+b x^{2/3}}} \, dx","Int[(a*x^(1/3) + b*x^(2/3))^(-1/3),x]","-\frac{45 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1\right)^2}} \sqrt[3]{-\frac{b \left(\sqrt[3]{x} a+b x^{2/3}\right)}{a^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) a^4}{28 \sqrt[3]{2} b^3 \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1\right)^2}} \left(a+2 b \sqrt[3]{x}\right) \sqrt[3]{\sqrt[3]{x} a+b x^{2/3}}}+\frac{15\ 3^{3/4} \left(1-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1\right)^2}} \sqrt[3]{-\frac{b \left(\sqrt[3]{x} a+b x^{2/3}\right)}{a^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) a^4}{7\ 2^{5/6} b^3 \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1\right)^2}} \left(a+2 b \sqrt[3]{x}\right) \sqrt[3]{\sqrt[3]{x} a+b x^{2/3}}}-\frac{45 \left(a+2 b \sqrt[3]{x}\right) \sqrt[3]{-\frac{b \left(\sqrt[3]{x} a+b x^{2/3}\right)}{a^2}} a^2}{14 \sqrt[3]{2} b^3 \left(-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1\right) \sqrt[3]{\sqrt[3]{x} a+b x^{2/3}}}-\frac{45 \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x} a}{28 b^2 \sqrt[3]{\sqrt[3]{x} a+b x^{2/3}}}+\frac{9 \left(a+b \sqrt[3]{x}\right) x^{2/3}}{7 b \sqrt[3]{\sqrt[3]{x} a+b x^{2/3}}}","-\frac{45 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1\right)^2}} \sqrt[3]{-\frac{b \left(\sqrt[3]{x} a+b x^{2/3}\right)}{a^2}} E\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) a^4}{28 \sqrt[3]{2} b^3 \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1\right)^2}} \left(a+2 b \sqrt[3]{x}\right) \sqrt[3]{\sqrt[3]{x} a+b x^{2/3}}}+\frac{15\ 3^{3/4} \left(1-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1\right)^2}} \sqrt[3]{-\frac{b \left(\sqrt[3]{x} a+b x^{2/3}\right)}{a^2}} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right) a^4}{7\ 2^{5/6} b^3 \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1\right)^2}} \left(a+2 b \sqrt[3]{x}\right) \sqrt[3]{\sqrt[3]{x} a+b x^{2/3}}}-\frac{45 \left(a+2 b \sqrt[3]{x}\right) \sqrt[3]{-\frac{b \left(\sqrt[3]{x} a+b x^{2/3}\right)}{a^2}} a^2}{14 \sqrt[3]{2} b^3 \left(-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1\right) \sqrt[3]{\sqrt[3]{x} a+b x^{2/3}}}-\frac{45 \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x} a}{28 b^2 \sqrt[3]{\sqrt[3]{x} a+b x^{2/3}}}+\frac{9 \left(a+b \sqrt[3]{x}\right) x^{2/3}}{7 b \sqrt[3]{\sqrt[3]{x} a+b x^{2/3}}}",1,"(-45*a^2*(a + 2*b*x^(1/3))*(-((b*(a*x^(1/3) + b*x^(2/3)))/a^2))^(1/3))/(14*2^(1/3)*b^3*(1 - Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))*(a*x^(1/3) + b*x^(2/3))^(1/3)) - (45*a*(a + b*x^(1/3))*x^(1/3))/(28*b^2*(a*x^(1/3) + b*x^(2/3))^(1/3)) + (9*(a + b*x^(1/3))*x^(2/3))/(7*b*(a*x^(1/3) + b*x^(2/3))^(1/3)) - (45*3^(1/4)*Sqrt[2 + Sqrt[3]]*a^4*(1 - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3) + 2*2^(1/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))^2]*(-((b*(a*x^(1/3) + b*x^(2/3)))/a^2))^(1/3)*EllipticE[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))], -7 + 4*Sqrt[3]])/(28*2^(1/3)*b^3*Sqrt[-((1 - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))^2)]*(a + 2*b*x^(1/3))*(a*x^(1/3) + b*x^(2/3))^(1/3)) + (15*3^(3/4)*a^4*(1 - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3) + 2*2^(1/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))^2]*(-((b*(a*x^(1/3) + b*x^(2/3)))/a^2))^(1/3)*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))], -7 + 4*Sqrt[3]])/(7*2^(5/6)*b^3*Sqrt[-((1 - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))^2)]*(a + 2*b*x^(1/3))*(a*x^(1/3) + b*x^(2/3))^(1/3))","A",11,10,19,0.5263,1,"{2011, 341, 50, 61, 622, 619, 235, 304, 219, 1879}"
438,1,487,0,0.9738749,"\int \frac{1}{\left(a \sqrt[3]{x}+b x^{2/3}\right)^{2/3}} \, dx","Int[(a*x^(1/3) + b*x^(2/3))^(-2/3),x]","\frac{6 \sqrt[3]{2} 3^{3/4} \sqrt{2-\sqrt{3}} a^4 \left(1-2^{2/3} \sqrt[3]{-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}}-\sqrt{3}+1\right)^2}} \left(-\frac{b \left(a \sqrt[3]{x}+b x^{2/3}\right)}{a^2}\right)^{2/3} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5 b^3 \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}}-\sqrt{3}+1\right)^2}} \left(a+2 b \sqrt[3]{x}\right) \left(a \sqrt[3]{x}+b x^{2/3}\right)^{2/3}}-\frac{18 a \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{5 b^2 \left(a \sqrt[3]{x}+b x^{2/3}\right)^{2/3}}+\frac{9 x^{2/3} \left(a+b \sqrt[3]{x}\right)}{5 b \left(a \sqrt[3]{x}+b x^{2/3}\right)^{2/3}}","\frac{6 \sqrt[3]{2} 3^{3/4} \sqrt{2-\sqrt{3}} a^4 \left(1-2^{2/3} \sqrt[3]{-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}}\right) \sqrt{\frac{2 \sqrt[3]{2} \left(-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}\right)^{2/3}+2^{2/3} \sqrt[3]{-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}}+1}{\left(-2^{2/3} \sqrt[3]{-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}}-\sqrt{3}+1\right)^2}} \left(-\frac{b \left(a \sqrt[3]{x}+b x^{2/3}\right)}{a^2}\right)^{2/3} F\left(\sin ^{-1}\left(\frac{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}+\sqrt{3}+1}{-2^{2/3} \sqrt[3]{-\frac{b \left(a+b \sqrt[3]{x}\right) \sqrt[3]{x}}{a^2}}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{5 b^3 \sqrt{-\frac{1-2^{2/3} \sqrt[3]{-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}}}{\left(-2^{2/3} \sqrt[3]{-\frac{b \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{a^2}}-\sqrt{3}+1\right)^2}} \left(a+2 b \sqrt[3]{x}\right) \left(a \sqrt[3]{x}+b x^{2/3}\right)^{2/3}}-\frac{18 a \sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}{5 b^2 \left(a \sqrt[3]{x}+b x^{2/3}\right)^{2/3}}+\frac{9 x^{2/3} \left(a+b \sqrt[3]{x}\right)}{5 b \left(a \sqrt[3]{x}+b x^{2/3}\right)^{2/3}}",1,"(-18*a*(a + b*x^(1/3))*x^(1/3))/(5*b^2*(a*x^(1/3) + b*x^(2/3))^(2/3)) + (9*(a + b*x^(1/3))*x^(2/3))/(5*b*(a*x^(1/3) + b*x^(2/3))^(2/3)) + (6*2^(1/3)*3^(3/4)*Sqrt[2 - Sqrt[3]]*a^4*(1 - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))*Sqrt[(1 + 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3) + 2*2^(1/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(2/3))/(1 - Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))^2]*(-((b*(a*x^(1/3) + b*x^(2/3)))/a^2))^(2/3)*EllipticF[ArcSin[(1 + Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))], -7 + 4*Sqrt[3]])/(5*b^3*Sqrt[-((1 - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))/(1 - Sqrt[3] - 2^(2/3)*(-((b*(a + b*x^(1/3))*x^(1/3))/a^2))^(1/3))^2)]*(a + 2*b*x^(1/3))*(a*x^(1/3) + b*x^(2/3))^(2/3))","A",9,8,19,0.4211,1,"{2011, 341, 50, 61, 622, 619, 236, 219}"
439,1,92,0,0.0683331,"\int x^m \left(a x^j+b x^n\right)^p \, dx","Int[x^m*(a*x^j + b*x^n)^p,x]","\frac{x^{m+1} \left(\frac{a x^{j-n}}{b}+1\right)^{-p} \left(a x^j+b x^n\right)^p \, _2F_1\left(-p,\frac{m+n p+1}{j-n};\frac{m+n p+1}{j-n}+1;-\frac{a x^{j-n}}{b}\right)}{m+n p+1}","\frac{x^{m+1} \left(a+b x^{n-j}\right) \left(a x^j+b x^n\right)^p \, _2F_1\left(1,p+\frac{m+j p+1}{n-j}+1;\frac{m+j p+1}{n-j}+1;-\frac{b x^{n-j}}{a}\right)}{a (j p+m+1)}",1,"(x^(1 + m)*(a*x^j + b*x^n)^p*Hypergeometric2F1[-p, (1 + m + n*p)/(j - n), 1 + (1 + m + n*p)/(j - n), -((a*x^(j - n))/b)])/((1 + m + n*p)*(1 + (a*x^(j - n))/b)^p)","A",3,3,17,0.1765,1,"{2032, 365, 364}"
440,1,69,0,0.0683911,"\int x^{-1-p q} \left(b x^n+a x^q\right)^p \, dx","Int[x^(-1 - p*q)*(b*x^n + a*x^q)^p,x]","-\frac{x^{-p q} \left(a+b x^{n-q}\right) \left(a x^q+b x^n\right)^p \, _2F_1\left(1,p+1;p+2;\frac{b x^{n-q}}{a}+1\right)}{a (p+1) (n-q)}","-\frac{x^{-p q} \left(a+b x^{n-q}\right) \left(a x^q+b x^n\right)^p \, _2F_1\left(1,p+1;p+2;\frac{b x^{n-q}}{a}+1\right)}{a (p+1) (n-q)}",1,"-(((a + b*x^(n - q))*(b*x^n + a*x^q)^p*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*x^(n - q))/a])/(a*(1 + p)*(n - q)*x^(p*q)))","A",3,3,22,0.1364,1,"{2032, 266, 65}"
441,1,74,0,0.0675878,"\int x^{-1-n p} \left(b x^n+a x^q\right)^p \, dx","Int[x^(-1 - n*p)*(b*x^n + a*x^q)^p,x]","-\frac{x^{-n p} \left(\frac{b x^{n-q}}{a}+1\right)^{-p} \left(a x^q+b x^n\right)^p \, _2F_1\left(-p,-p;1-p;-\frac{b x^{n-q}}{a}\right)}{p (n-q)}","-\frac{x^{-n p} \left(a+b x^{n-q}\right) \left(a x^q+b x^n\right)^p \, _2F_1\left(1,1;1-p;-\frac{b x^{n-q}}{a}\right)}{a p (n-q)}",1,"-(((b*x^n + a*x^q)^p*Hypergeometric2F1[-p, -p, 1 - p, -((b*x^(n - q))/a)])/(p*(n - q)*x^(n*p)*(1 + (b*x^(n - q))/a)^p))","A",3,3,22,0.1364,1,"{2032, 365, 364}"
442,1,69,0,0.077541,"\int x^{-1-n-(-1+p) q} \left(b x^n+a x^q\right)^p \, dx","Int[x^(-1 - n - (-1 + p)*q)*(b*x^n + a*x^q)^p,x]","\frac{b x^{-p q} \left(a+b x^{n-q}\right) \left(a x^q+b x^n\right)^p \, _2F_1\left(2,p+1;p+2;\frac{b x^{n-q}}{a}+1\right)}{a^2 (p+1) (n-q)}","\frac{b x^{-p q} \left(a+b x^{n-q}\right) \left(a x^q+b x^n\right)^p \, _2F_1\left(2,p+1;p+2;\frac{b x^{n-q}}{a}+1\right)}{a^2 (p+1) (n-q)}",1,"(b*(a + b*x^(n - q))*(b*x^n + a*x^q)^p*Hypergeometric2F1[2, 1 + p, 2 + p, 1 + (b*x^(n - q))/a])/(a^2*(1 + p)*(n - q)*x^(p*q))","A",3,3,27,0.1111,1,"{2032, 266, 65}"
443,1,84,0,0.081219,"\int x^{-1-n (-1+p)-q} \left(b x^n+a x^q\right)^p \, dx","Int[x^(-1 - n*(-1 + p) - q)*(b*x^n + a*x^q)^p,x]","\frac{x^{n (-p)+n-q} \left(\frac{b x^{n-q}}{a}+1\right)^{-p} \left(a x^q+b x^n\right)^p \, _2F_1\left(1-p,-p;2-p;-\frac{b x^{n-q}}{a}\right)}{(1-p) (n-q)}","\frac{x^{n (-p)+n-q} \left(\frac{b x^{n-q}}{a}+1\right)^{-p} \left(a x^q+b x^n\right)^p \, _2F_1\left(1-p,-p;2-p;-\frac{b x^{n-q}}{a}\right)}{(1-p) (n-q)}",1,"(x^(n - n*p - q)*(b*x^n + a*x^q)^p*Hypergeometric2F1[1 - p, -p, 2 - p, -((b*x^(n - q))/a)])/((1 - p)*(n - q)*(1 + (b*x^(n - q))/a)^p)","A",3,3,27,0.1111,1,"{2032, 365, 364}"
444,1,44,0,0.0154702,"\int \left(a x^m+b x^{1+m+m p}\right)^p \, dx","Int[(a*x^m + b*x^(1 + m + m*p))^p,x]","\frac{x^{-m (p+1)} \left(a x^m+b x^{m p+m+1}\right)^{p+1}}{b (p+1) (m p+1)}","\frac{x^{-m (p+1)} \left(a x^m+b x^{m p+m+1}\right)^{p+1}}{b (p+1) (m p+1)}",1,"(a*x^m + b*x^(1 + m + m*p))^(1 + p)/(b*(1 + p)*(1 + m*p)*x^(m*(1 + p)))","A",1,1,18,0.05556,1,"{2000}"
445,1,44,0,0.0150384,"\int \left(x^m \left(a+b x^{1+m p}\right)\right)^p \, dx","Int[(x^m*(a + b*x^(1 + m*p)))^p,x]","\frac{x^{-m (p+1)} \left(a x^m+b x^{m p+m+1}\right)^{p+1}}{b (p+1) (m p+1)}","\frac{x^{-m (p+1)} \left(a x^m+b x^{m p+m+1}\right)^{p+1}}{b (p+1) (m p+1)}",1,"(a*x^m + b*x^(1 + m + m*p))^(1 + p)/(b*(1 + p)*(1 + m*p)*x^(m*(1 + p)))","A",2,2,17,0.1176,1,"{1979, 2000}"
446,1,46,0,0.0753067,"\int x^n \left(x^m \left(a+b x^{1+n+m p}\right)\right)^p \, dx","Int[x^n*(x^m*(a + b*x^(1 + n + m*p)))^p,x]","\frac{x^{-m (p+1)} \left(a x^m+b x^{m p+m+n+1}\right)^{p+1}}{b (p+1) (m p+n+1)}","\frac{x^{-m (p+1)} \left(a x^m+b x^{m p+m+n+1}\right)^{p+1}}{b (p+1) (m p+n+1)}",1,"(a*x^m + b*x^(1 + m + n + m*p))^(1 + p)/(b*(1 + p)*(1 + n + m*p)*x^(m*(1 + p)))","A",2,2,22,0.09091,1,"{1980, 2014}"
447,1,46,0,0.0453976,"\int x^n \left(a x^m+b x^{1+m+n+m p}\right)^p \, dx","Int[x^n*(a*x^m + b*x^(1 + m + n + m*p))^p,x]","\frac{x^{-m (p+1)} \left(a x^m+b x^{m p+m+n+1}\right)^{p+1}}{b (p+1) (m p+n+1)}","\frac{x^{-m (p+1)} \left(a x^m+b x^{m p+m+n+1}\right)^{p+1}}{b (p+1) (m p+n+1)}",1,"(a*x^m + b*x^(1 + m + n + m*p))^(1 + p)/(b*(1 + p)*(1 + n + m*p)*x^(m*(1 + p)))","A",1,1,23,0.04348,1,"{2014}"
448,1,44,0,0.0181042,"\int \sqrt{x^{2 (-1+n)} \left(a+b x^n\right)} \, dx","Int[Sqrt[x^(2*(-1 + n))*(a + b*x^n)],x]","\frac{2 x^{3 (1-n)} \left(a x^{-2 (1-n)}+b x^{3 n-2}\right)^{3/2}}{3 b n}","\frac{2 x^{3 (1-n)} \left(a x^{-2 (1-n)}+b x^{3 n-2}\right)^{3/2}}{3 b n}",1,"(2*x^(3*(1 - n))*(a/x^(2*(1 - n)) + b*x^(-2 + 3*n))^(3/2))/(3*b*n)","A",2,2,19,0.1053,1,"{1979, 2000}"
449,1,44,0,0.0172021,"\int \sqrt[3]{x^{3 (-1+n)} \left(a+b x^n\right)} \, dx","Int[(x^(3*(-1 + n))*(a + b*x^n))^(1/3),x]","\frac{3 x^{4 (1-n)} \left(a x^{-3 (1-n)}+b x^{4 n-3}\right)^{4/3}}{4 b n}","\frac{3 x^{4 (1-n)} \left(a x^{-3 (1-n)}+b x^{4 n-3}\right)^{4/3}}{4 b n}",1,"(3*x^(4*(1 - n))*(a/x^(3*(1 - n)) + b*x^(-3 + 4*n))^(4/3))/(4*b*n)","A",2,2,19,0.1053,1,"{1979, 2000}"
450,1,44,0,0.0183645,"\int \sqrt[4]{x^{4 (-1+n)} \left(a+b x^n\right)} \, dx","Int[(x^(4*(-1 + n))*(a + b*x^n))^(1/4),x]","\frac{4 x^{5 (1-n)} \left(a x^{-4 (1-n)}+b x^{5 n-4}\right)^{5/4}}{5 b n}","\frac{4 x^{5 (1-n)} \left(a x^{-4 (1-n)}+b x^{5 n-4}\right)^{5/4}}{5 b n}",1,"(4*x^(5*(1 - n))*(a/x^(4*(1 - n)) + b*x^(-4 + 5*n))^(5/4))/(5*b*n)","A",2,2,19,0.1053,1,"{1979, 2000}"
451,1,57,0,0.0277425,"\int \left(x^{(-1+n) p} \left(a+b x^n\right)\right)^{\frac{1}{p}} \, dx","Int[(x^((-1 + n)*p)*(a + b*x^n))^p^(-1),x]","\frac{p x^{(1-n) (p+1)} \left(a x^{-(1-n) p}+b x^{n-(1-n) p}\right)^{\frac{1}{p}+1}}{b n (p+1)}","\frac{p x^{(1-n) (p+1)} \left(a x^{-(1-n) p}+b x^{n-(1-n) p}\right)^{\frac{1}{p}+1}}{b n (p+1)}",1,"(p*x^((1 - n)*(1 + p))*(a/x^((1 - n)*p) + b*x^(n - (1 - n)*p))^(1 + p^(-1)))/(b*n*(1 + p))","A",2,2,19,0.1053,1,"{1979, 2000}"
452,1,61,0,0.0248845,"\int \left(x^{\frac{-1+n}{p}} \left(a+b x^n\right)\right)^p \, dx","Int[(x^((-1 + n)/p)*(a + b*x^n))^p,x]","\frac{x^{\frac{(1-n) (p+1)}{p}} \left(a x^{-\frac{1-n}{p}}+b x^{n-\frac{1-n}{p}}\right)^{p+1}}{b n (p+1)}","\frac{x^{\frac{(1-n) (p+1)}{p}} \left(a x^{-\frac{1-n}{p}}+b x^{n-\frac{1-n}{p}}\right)^{p+1}}{b n (p+1)}",1,"(x^(((1 - n)*(1 + p))/p)*(b*x^(n - (1 - n)/p) + a/x^((1 - n)/p))^(1 + p))/(b*n*(1 + p))","A",2,2,19,0.1053,1,"{1979, 2000}"
453,1,39,0,0.0498496,"\int x^{-1+n-p (1+q)} \left(a x^n+b x^p\right)^q \, dx","Int[x^(-1 + n - p*(1 + q))*(a*x^n + b*x^p)^q,x]","\frac{x^{-p (q+1)} \left(a x^n+b x^p\right)^{q+1}}{a (q+1) (n-p)}","\frac{x^{-p (q+1)} \left(a x^n+b x^p\right)^{q+1}}{a (q+1) (n-p)}",1,"(a*x^n + b*x^p)^(1 + q)/(a*(n - p)*(1 + q)*x^(p*(1 + q)))","A",1,1,25,0.04000,1,"{2014}"
454,1,40,0,0.0738037,"\int x^{-1-n q-p (1+q)} \left(x^n \left(a+b x^p\right)\right)^q \, dx","Int[x^(-1 - n*q - p*(1 + q))*(x^n*(a + b*x^p))^q,x]","-\frac{x^{(q+1) (-(n+p))} \left(a x^n+b x^{n+p}\right)^{q+1}}{a p (q+1)}","-\frac{x^{(q+1) (-(n+p))} \left(a x^n+b x^{n+p}\right)^{q+1}}{a p (q+1)}",1,"-((a*x^n + b*x^(n + p))^(1 + q)/(a*p*(1 + q)*x^((n + p)*(1 + q))))","A",2,2,28,0.07143,1,"{1980, 2014}"