1,1,17,17,0.0016688,"\int x^2 \left(a x+b x^3\right) \, dx","Integrate[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",1
2,1,17,17,0.0016004,"\int x \left(a x+b x^3\right) \, dx","Integrate[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",1
3,1,17,17,0.0000874,"\int \left(a x+b x^3\right) \, dx","Integrate[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
4,1,12,12,0.0004199,"\int \frac{a x+b x^3}{x} \, dx","Integrate[(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",1
5,1,13,13,0.0012583,"\int \frac{a x+b x^3}{x^2} \, dx","Integrate[(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",1
6,1,30,30,0.0011088,"\int x^2 \left(a x+b x^3\right)^2 \, dx","Integrate[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",1
7,1,30,30,0.0010746,"\int x \left(a x+b x^3\right)^2 \, dx","Integrate[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",1
8,1,30,30,0.0017165,"\int \left(a x+b x^3\right)^2 \, dx","Integrate[(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",1
9,1,16,16,0.0023151,"\int \frac{\left(a x+b x^3\right)^2}{x} \, dx","Integrate[(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",1
10,1,25,25,0.001131,"\int \frac{\left(a x+b x^3\right)^2}{x^2} \, dx","Integrate[(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",1
11,1,46,46,0.0021759,"\int \left(-4 x+3 x^3\right)^6 \, dx","Integrate[(-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",1
12,1,27,27,0.0048965,"\int \frac{x^4}{a x+b x^3} \, dx","Integrate[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",1
13,1,31,31,0.0094971,"\int \frac{x^3}{a x+b x^3} \, dx","Integrate[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",1
14,1,15,15,0.0024311,"\int \frac{x^2}{a x+b x^3} \, dx","Integrate[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",1
15,1,24,24,0.0042617,"\int \frac{x}{a x+b x^3} \, dx","Integrate[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",1
16,1,22,22,0.0048163,"\int \frac{1}{a x+b x^3} \, dx","Integrate[(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",1
17,1,34,34,0.0129383,"\int \frac{1}{x \left(a x+b x^3\right)} \, dx","Integrate[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",1
18,1,35,35,0.0073981,"\int \frac{1}{x^2 \left(a x+b x^3\right)} \, dx","Integrate[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*1/(a*x^2) - (b*Log[x])/a^2 + (b*Log[a + b*x^2])/(2*a^2)","A",1
19,1,43,43,0.0229705,"\int \frac{1}{x^3 \left(a x+b x^3\right)} \, dx","Integrate[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*1/(a*x^3) + b/(a^2*x) + (b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(5/2)","A",1
20,1,49,49,0.0074934,"\int \frac{1}{x^4 \left(a x+b x^3\right)} \, dx","Integrate[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*1/(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",1
21,1,45,45,0.026906,"\int \frac{x^2}{\left(a x+b x^3\right)^2} \, dx","Integrate[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",1
22,1,33,38,0.0176882,"\int \frac{x}{\left(a x+b x^3\right)^2} \, dx","Integrate[x/(a*x + b*x^3)^2,x]","\frac{\frac{a}{a+b x^2}-\log \left(a+b x^2\right)+2 \log (x)}{2 a^2}","-\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,"(a/(a + b*x^2) + 2*Log[x] - Log[a + b*x^2])/(2*a^2)","A",1
23,1,54,57,0.0379011,"\int \frac{1}{\left(a x+b x^3\right)^2} \, dx","Integrate[(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{b x}{2 a^2 \left(a+b x^2\right)}-\frac{1}{a^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)}",1,"-(1/(a^2*x)) - (b*x)/(2*a^2*(a + b*x^2)) - (3*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2))","A",1
24,1,41,49,0.0373141,"\int \frac{1}{x \left(a x+b x^3\right)^2} \, dx","Integrate[1/(x*(a*x + b*x^3)^2),x]","-\frac{a \left(\frac{b}{a+b x^2}+\frac{1}{x^2}\right)-2 b \log \left(a+b x^2\right)+4 b \log (x)}{2 a^3}","\frac{b \log \left(a+b x^2\right)}{a^3}-\frac{2 b \log (x)}{a^3}-\frac{b}{2 a^2 \left(a+b x^2\right)}-\frac{1}{2 a^2 x^2}",1,"-1/2*(a*(x^(-2) + b/(a + b*x^2)) + 4*b*Log[x] - 2*b*Log[a + b*x^2])/a^3","A",1
25,1,67,68,0.0400207,"\int \frac{1}{x^2 \left(a x+b x^3\right)^2} \, dx","Integrate[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{b^2 x}{2 a^3 \left(a+b x^2\right)}+\frac{2 b}{a^3 x}-\frac{1}{3 a^2 x^3}","\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,"-1/3*1/(a^2*x^3) + (2*b)/(a^3*x) + (b^2*x)/(2*a^3*(a + b*x^2)) + (5*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2))","A",1
26,1,29,13,0.0049028,"\int \frac{x^5}{x-x^3} \, dx","Integrate[x^5/(x - x^3),x]","-\frac{x^3}{3}-x-\frac{1}{2} \log (1-x)+\frac{1}{2} \log (x+1)","-\frac{x^3}{3}-x+\tanh ^{-1}(x)",1,"-x - x^3/3 - Log[1 - x]/2 + Log[1 + x]/2","B",1
27,1,18,20,0.0033279,"\int \frac{x^4}{x-x^3} \, dx","Integrate[x^4/(x - x^3),x]","-\frac{x^2}{2}-\frac{1}{2} \log \left(x^2-1\right)","-\frac{x^2}{2}-\frac{1}{2} \log \left(1-x^2\right)",1,"-1/2*x^2 - Log[-1 + x^2]/2","A",1
28,1,22,6,0.0032683,"\int \frac{x^3}{x-x^3} \, dx","Integrate[x^3/(x - x^3),x]","-x-\frac{1}{2} \log (1-x)+\frac{1}{2} \log (x+1)","\tanh ^{-1}(x)-x",1,"-x - Log[1 - x]/2 + Log[1 + x]/2","B",1
29,1,12,12,0.0022054,"\int \frac{x^2}{x-x^3} \, dx","Integrate[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,"-1/2*Log[1 - x^2]","A",1
30,1,19,2,0.0024683,"\int \frac{x}{x-x^3} \, dx","Integrate[x/(x - x^3),x]","\frac{1}{2} \log (x+1)-\frac{1}{2} \log (1-x)","\tanh ^{-1}(x)",1,"-1/2*Log[1 - x] + Log[1 + x]/2","B",1
31,1,15,15,0.0026806,"\int \frac{1}{x-x^3} \, dx","Integrate[(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",1
32,1,24,8,0.0033391,"\int \frac{1}{x \left(x-x^3\right)} \, dx","Integrate[1/(x*(x - x^3)),x]","-\frac{1}{x}-\frac{1}{2} \log (1-x)+\frac{1}{2} \log (x+1)","\tanh ^{-1}(x)-\frac{1}{x}",1,"-x^(-1) - Log[1 - x]/2 + Log[1 + x]/2","B",1
33,1,22,22,0.0037268,"\int \frac{1}{x^2 \left(x-x^3\right)} \, dx","Integrate[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*1/x^2 + Log[x] - Log[1 - x^2]/2","A",1
34,1,31,15,0.0043721,"\int \frac{1}{x^3 \left(x-x^3\right)} \, dx","Integrate[1/(x^3*(x - x^3)),x]","-\frac{1}{3 x^3}-\frac{1}{x}-\frac{1}{2} \log (1-x)+\frac{1}{2} \log (x+1)","-\frac{1}{3 x^3}-\frac{1}{x}+\tanh ^{-1}(x)",1,"-1/3*1/x^3 - x^(-1) - Log[1 - x]/2 + Log[1 + x]/2","B",1
35,1,29,29,0.0039049,"\int \frac{1}{x^4 \left(x-x^3\right)} \, dx","Integrate[1/(x^4*(x - x^3)),x]","-\frac{1}{4 x^4}-\frac{1}{2 x^2}-\frac{1}{2} \log \left(1-x^2\right)+\log (x)","-\frac{1}{4 x^4}-\frac{1}{2 x^2}-\frac{1}{2} \log \left(1-x^2\right)+\log (x)",1,"-1/4*1/x^4 - 1/(2*x^2) + Log[x] - Log[1 - x^2]/2","A",1
36,1,15,15,0.0039498,"\int \frac{1}{x+b x^3} \, dx","Integrate[(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",1
37,1,18,18,0.0037886,"\int \frac{1}{-x+b x^3} \, dx","Integrate[(-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",1
38,1,95,163,0.059359,"\int x^3 \sqrt{a x+b x^3} \, dx","Integrate[x^3*Sqrt[a*x + b*x^3],x]","\frac{2 \sqrt{x \left(a+b x^2\right)} \left(\sqrt{\frac{b x^2}{a}+1} \left(-5 a^2+2 a b x^2+7 b^2 x^4\right)+5 a^2 \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{b x^2}{a}\right)\right)}{77 b^2 \sqrt{\frac{b x^2}{a}+1}}","\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{20 a^2 \sqrt{a x+b x^3}}{231 b^2}+\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,"(2*Sqrt[x*(a + b*x^2)]*(Sqrt[1 + (b*x^2)/a]*(-5*a^2 + 2*a*b*x^2 + 7*b^2*x^4) + 5*a^2*Hypergeometric2F1[-1/2, 1/4, 5/4, -((b*x^2)/a)]))/(77*b^2*Sqrt[1 + (b*x^2)/a])","C",1
39,1,80,281,0.0558203,"\int x^2 \sqrt{a x+b x^3} \, dx","Integrate[x^2*Sqrt[a*x + b*x^3],x]","\frac{2 x \sqrt{x \left(a+b x^2\right)} \left(\left(a+b x^2\right) \sqrt{\frac{b x^2}{a}+1}-a \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{b x^2}{a}\right)\right)}{9 b \sqrt{\frac{b x^2}{a}+1}}","-\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{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}{9} x^3 \sqrt{a x+b x^3}+\frac{4 a x \sqrt{a x+b x^3}}{45 b}",1,"(2*x*Sqrt[x*(a + b*x^2)]*((a + b*x^2)*Sqrt[1 + (b*x^2)/a] - a*Hypergeometric2F1[-1/2, 3/4, 7/4, -((b*x^2)/a)]))/(9*b*Sqrt[1 + (b*x^2)/a])","C",1
40,1,79,137,0.0331921,"\int x \sqrt{a x+b x^3} \, dx","Integrate[x*Sqrt[a*x + b*x^3],x]","\frac{2 \sqrt{x \left(a+b x^2\right)} \left(\left(a+b x^2\right) \sqrt{\frac{b x^2}{a}+1}-a \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{b x^2}{a}\right)\right)}{7 b \sqrt{\frac{b x^2}{a}+1}}","-\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{4 a \sqrt{a x+b x^3}}{21 b}+\frac{2}{7} x^2 \sqrt{a x+b x^3}",1,"(2*Sqrt[x*(a + b*x^2)]*((a + b*x^2)*Sqrt[1 + (b*x^2)/a] - a*Hypergeometric2F1[-1/2, 1/4, 5/4, -((b*x^2)/a)]))/(7*b*Sqrt[1 + (b*x^2)/a])","C",1
41,1,51,255,0.0123099,"\int \sqrt{a x+b x^3} \, dx","Integrate[Sqrt[a*x + b*x^3],x]","\frac{2 x \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{b x^2}{a}\right)}{3 \sqrt{\frac{b x^2}{a}+1}}","\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{2}{5} x \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}}",1,"(2*x*Sqrt[x*(a + b*x^2)]*Hypergeometric2F1[-1/2, 3/4, 7/4, -((b*x^2)/a)])/(3*Sqrt[1 + (b*x^2)/a])","C",1
42,1,48,113,0.0099285,"\int \frac{\sqrt{a x+b x^3}}{x} \, dx","Integrate[Sqrt[a*x + b*x^3]/x,x]","\frac{2 \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{b x^2}{a}\right)}{\sqrt{\frac{b x^2}{a}+1}}","\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[x*(a + b*x^2)]*Hypergeometric2F1[-1/2, 1/4, 5/4, -((b*x^2)/a)])/Sqrt[1 + (b*x^2)/a]","C",1
43,1,51,248,0.0126239,"\int \frac{\sqrt{a x+b x^3}}{x^2} \, dx","Integrate[Sqrt[a*x + b*x^3]/x^2,x]","-\frac{2 \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{1}{2},-\frac{1}{4};\frac{3}{4};-\frac{b x^2}{a}\right)}{x \sqrt{\frac{b x^2}{a}+1}}","-\frac{2 \sqrt{a x+b x^3}}{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[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,"(-2*Sqrt[x*(a + b*x^2)]*Hypergeometric2F1[-1/2, -1/4, 3/4, -((b*x^2)/a)])/(x*Sqrt[1 + (b*x^2)/a])","C",1
44,1,53,116,0.0139453,"\int \frac{\sqrt{a x+b x^3}}{x^3} \, dx","Integrate[Sqrt[a*x + b*x^3]/x^3,x]","-\frac{2 \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{3}{4},-\frac{1}{2};\frac{1}{4};-\frac{b x^2}{a}\right)}{3 x^2 \sqrt{\frac{b x^2}{a}+1}}","\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[x*(a + b*x^2)]*Hypergeometric2F1[-3/4, -1/2, 1/4, -((b*x^2)/a)])/(3*x^2*Sqrt[1 + (b*x^2)/a])","C",1
45,1,53,283,0.0148763,"\int \frac{\sqrt{a x+b x^3}}{x^4} \, dx","Integrate[Sqrt[a*x + b*x^3]/x^4,x]","-\frac{2 \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{5}{4},-\frac{1}{2};-\frac{1}{4};-\frac{b x^2}{a}\right)}{5 x^3 \sqrt{\frac{b x^2}{a}+1}}","\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,"(-2*Sqrt[x*(a + b*x^2)]*Hypergeometric2F1[-5/4, -1/2, -1/4, -((b*x^2)/a)])/(5*x^3*Sqrt[1 + (b*x^2)/a])","C",1
46,1,94,186,0.0892421,"\int x^2 \left(a x+b x^3\right)^{3/2} \, dx","Integrate[x^2*(a*x + b*x^3)^(3/2),x]","\frac{2 \sqrt{x \left(a+b x^2\right)} \left(5 a^3 \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{b x^2}{a}\right)-\left(5 a-11 b x^2\right) \left(a+b x^2\right)^2 \sqrt{\frac{b x^2}{a}+1}\right)}{165 b^2 \sqrt{\frac{b x^2}{a}+1}}","\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^3 \sqrt{a x+b x^3}}{231 b^2}+\frac{8 a^2 x^2 \sqrt{a x+b x^3}}{385 b}+\frac{2}{15} x^3 \left(a x+b x^3\right)^{3/2}+\frac{4}{55} a x^4 \sqrt{a x+b x^3}",1,"(2*Sqrt[x*(a + b*x^2)]*(-((5*a - 11*b*x^2)*(a + b*x^2)^2*Sqrt[1 + (b*x^2)/a]) + 5*a^3*Hypergeometric2F1[-3/2, 1/4, 5/4, -((b*x^2)/a)]))/(165*b^2*Sqrt[1 + (b*x^2)/a])","C",1
47,1,84,304,0.0462092,"\int x \left(a x+b x^3\right)^{3/2} \, dx","Integrate[x*(a*x + b*x^3)^(3/2),x]","\frac{2 x \sqrt{x \left(a+b x^2\right)} \left(\left(a+b x^2\right)^2 \sqrt{\frac{b x^2}{a}+1}-a^2 \, _2F_1\left(-\frac{3}{2},\frac{3}{4};\frac{7}{4};-\frac{b x^2}{a}\right)\right)}{13 b \sqrt{\frac{b x^2}{a}+1}}","-\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^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{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,"(2*x*Sqrt[x*(a + b*x^2)]*((a + b*x^2)^2*Sqrt[1 + (b*x^2)/a] - a^2*Hypergeometric2F1[-3/2, 3/4, 7/4, -((b*x^2)/a)]))/(13*b*Sqrt[1 + (b*x^2)/a])","C",1
48,1,83,158,0.0347613,"\int \left(a x+b x^3\right)^{3/2} \, dx","Integrate[(a*x + b*x^3)^(3/2),x]","\frac{2 \sqrt{x \left(a+b x^2\right)} \left(\left(a+b x^2\right)^2 \sqrt{\frac{b x^2}{a}+1}-a^2 \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{b x^2}{a}\right)\right)}{11 b \sqrt{\frac{b x^2}{a}+1}}","-\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{2}{11} x \left(a x+b x^3\right)^{3/2}+\frac{12}{77} a x^2 \sqrt{a x+b x^3}",1,"(2*Sqrt[x*(a + b*x^2)]*((a + b*x^2)^2*Sqrt[1 + (b*x^2)/a] - a^2*Hypergeometric2F1[-3/2, 1/4, 5/4, -((b*x^2)/a)]))/(11*b*Sqrt[1 + (b*x^2)/a])","C",1
49,1,52,275,0.0160301,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x} \, dx","Integrate[(a*x + b*x^3)^(3/2)/x,x]","\frac{2 a x \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{3}{2},\frac{3}{4};\frac{7}{4};-\frac{b x^2}{a}\right)}{3 \sqrt{\frac{b x^2}{a}+1}}","\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,"(2*a*x*Sqrt[x*(a + b*x^2)]*Hypergeometric2F1[-3/2, 3/4, 7/4, -((b*x^2)/a)])/(3*Sqrt[1 + (b*x^2)/a])","C",1
50,1,49,134,0.0161455,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^2} \, dx","Integrate[(a*x + b*x^3)^(3/2)/x^2,x]","\frac{2 a \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{b x^2}{a}\right)}{\sqrt{\frac{b x^2}{a}+1}}","\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,"(2*a*Sqrt[x*(a + b*x^2)]*Hypergeometric2F1[-3/2, 1/4, 5/4, -((b*x^2)/a)])/Sqrt[1 + (b*x^2)/a]","C",1
51,1,52,274,0.0160856,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^3} \, dx","Integrate[(a*x + b*x^3)^(3/2)/x^3,x]","-\frac{2 a \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{3}{2},-\frac{1}{4};\frac{3}{4};-\frac{b x^2}{a}\right)}{x \sqrt{\frac{b x^2}{a}+1}}","\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{12}{5} b x \sqrt{a x+b x^3}-\frac{2 \left(a x+b x^3\right)^{3/2}}{x^2}+\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,"(-2*a*Sqrt[x*(a + b*x^2)]*Hypergeometric2F1[-3/2, -1/4, 3/4, -((b*x^2)/a)])/(x*Sqrt[1 + (b*x^2)/a])","C",1
52,1,54,134,0.0168784,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^4} \, dx","Integrate[(a*x + b*x^3)^(3/2)/x^4,x]","-\frac{2 a \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{3}{2},-\frac{3}{4};\frac{1}{4};-\frac{b x^2}{a}\right)}{3 x^2 \sqrt{\frac{b x^2}{a}+1}}","\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,"(-2*a*Sqrt[x*(a + b*x^2)]*Hypergeometric2F1[-3/2, -3/4, 1/4, -((b*x^2)/a)])/(3*x^2*Sqrt[1 + (b*x^2)/a])","C",1
53,1,54,277,0.0152828,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^5} \, dx","Integrate[(a*x + b*x^3)^(3/2)/x^5,x]","-\frac{2 a \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{3}{2},-\frac{5}{4};-\frac{1}{4};-\frac{b x^2}{a}\right)}{5 x^3 \sqrt{\frac{b x^2}{a}+1}}","\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,"(-2*a*Sqrt[x*(a + b*x^2)]*Hypergeometric2F1[-3/2, -5/4, -1/4, -((b*x^2)/a)])/(5*x^3*Sqrt[1 + (b*x^2)/a])","C",1
54,1,54,137,0.0199001,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^6} \, dx","Integrate[(a*x + b*x^3)^(3/2)/x^6,x]","-\frac{2 a \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{7}{4},-\frac{3}{2};-\frac{3}{4};-\frac{b x^2}{a}\right)}{7 x^4 \sqrt{\frac{b x^2}{a}+1}}","\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{2 \left(a x+b x^3\right)^{3/2}}{7 x^5}-\frac{4 b \sqrt{a x+b x^3}}{7 x^2}",1,"(-2*a*Sqrt[x*(a + b*x^2)]*Hypergeometric2F1[-7/4, -3/2, -3/4, -((b*x^2)/a)])/(7*x^4*Sqrt[1 + (b*x^2)/a])","C",1
55,1,54,306,0.017101,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^7} \, dx","Integrate[(a*x + b*x^3)^(3/2)/x^7,x]","-\frac{2 a \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{9}{4},-\frac{3}{2};-\frac{5}{4};-\frac{b x^2}{a}\right)}{9 x^5 \sqrt{\frac{b x^2}{a}+1}}","\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,"(-2*a*Sqrt[x*(a + b*x^2)]*Hypergeometric2F1[-9/4, -3/2, -5/4, -((b*x^2)/a)])/(9*x^5*Sqrt[1 + (b*x^2)/a])","C",1
56,1,54,163,0.0161873,"\int \frac{\left(a x+b x^3\right)^{3/2}}{x^8} \, dx","Integrate[(a*x + b*x^3)^(3/2)/x^8,x]","-\frac{2 a \sqrt{x \left(a+b x^2\right)} \, _2F_1\left(-\frac{11}{4},-\frac{3}{2};-\frac{7}{4};-\frac{b x^2}{a}\right)}{11 x^6 \sqrt{\frac{b x^2}{a}+1}}","-\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{2 \left(a x+b x^3\right)^{3/2}}{11 x^7}-\frac{12 b \sqrt{a x+b x^3}}{77 x^4}",1,"(-2*a*Sqrt[x*(a + b*x^2)]*Hypergeometric2F1[-11/4, -3/2, -7/4, -((b*x^2)/a)])/(11*x^6*Sqrt[1 + (b*x^2)/a])","C",1
57,1,80,140,0.0342849,"\int \frac{x^4}{\sqrt{a x+b x^3}} \, dx","Integrate[x^4/Sqrt[a*x + b*x^3],x]","\frac{2 x \left(5 a^2 \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^2}{a}\right)-5 a^2-2 a b x^2+3 b^2 x^4\right)}{21 b^2 \sqrt{x \left(a+b x^2\right)}}","\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,"(2*x*(-5*a^2 - 2*a*b*x^2 + 3*b^2*x^4 + 5*a^2*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^2)/a)]))/(21*b^2*Sqrt[x*(a + b*x^2)])","C",1
58,1,66,258,0.0338634,"\int \frac{x^3}{\sqrt{a x+b x^3}} \, dx","Integrate[x^3/Sqrt[a*x + b*x^3],x]","\frac{2 x^2 \left(-a \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{b x^2}{a}\right)+a+b x^2\right)}{5 b \sqrt{x \left(a+b x^2\right)}}","-\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,"(2*x^2*(a + b*x^2 - a*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((b*x^2)/a)]))/(5*b*Sqrt[x*(a + b*x^2)])","C",1
59,1,64,116,0.0421688,"\int \frac{x^2}{\sqrt{a x+b x^3}} \, dx","Integrate[x^2/Sqrt[a*x + b*x^3],x]","\frac{2 x \left(-a \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^2}{a}\right)+a+b x^2\right)}{3 b \sqrt{x \left(a+b x^2\right)}}","\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*x*(a + b*x^2 - a*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^2)/a)]))/(3*b*Sqrt[x*(a + b*x^2)])","C",1
60,1,53,229,0.0206943,"\int \frac{x}{\sqrt{a x+b x^3}} \, dx","Integrate[x/Sqrt[a*x + b*x^3],x]","\frac{2 x^2 \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{b x^2}{a}\right)}{3 \sqrt{x \left(a+b x^2\right)}}","\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^2*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/2, 3/4, 7/4, -((b*x^2)/a)])/(3*Sqrt[x*(a + b*x^2)])","C",1
61,1,49,92,0.0167302,"\int \frac{1}{\sqrt{a x+b x^3}} \, dx","Integrate[1/Sqrt[a*x + b*x^3],x]","\frac{2 x \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^2}{a}\right)}{\sqrt{x \left(a+b x^2\right)}}","\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,"(2*x*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^2)/a)])/Sqrt[x*(a + b*x^2)]","C",1
62,1,48,253,0.0133176,"\int \frac{1}{x \sqrt{a x+b x^3}} \, dx","Integrate[1/(x*Sqrt[a*x + b*x^3]),x]","-\frac{2 \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-\frac{b x^2}{a}\right)}{\sqrt{x \left(a+b x^2\right)}}","\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{a x+b x^3}}{a x}+\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}}",1,"(-2*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[-1/4, 1/2, 3/4, -((b*x^2)/a)])/Sqrt[x*(a + b*x^2)]","C",1
63,1,53,119,0.0247471,"\int \frac{1}{x^2 \sqrt{a x+b x^3}} \, dx","Integrate[1/(x^2*Sqrt[a*x + b*x^3]),x]","-\frac{2 \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-\frac{b x^2}{a}\right)}{3 x \sqrt{x \left(a+b x^2\right)}}","-\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[1 + (b*x^2)/a]*Hypergeometric2F1[-3/4, 1/2, 1/4, -((b*x^2)/a)])/(3*x*Sqrt[x*(a + b*x^2)])","C",1
64,1,53,286,0.014958,"\int \frac{1}{x^3 \sqrt{a x+b x^3}} \, dx","Integrate[1/(x^3*Sqrt[a*x + b*x^3]),x]","-\frac{2 \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(-\frac{5}{4},\frac{1}{2};-\frac{1}{4};-\frac{b x^2}{a}\right)}{5 x^2 \sqrt{x \left(a+b x^2\right)}}","-\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^{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{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,"(-2*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[-5/4, 1/2, -1/4, -((b*x^2)/a)])/(5*x^2*Sqrt[x*(a + b*x^2)])","C",1
65,1,80,161,0.0385555,"\int \frac{x^7}{\left(a x+b x^3\right)^{3/2}} \, dx","Integrate[x^7/(a*x + b*x^3)^(3/2),x]","\frac{x \left(15 a^2 \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^2}{a}\right)-15 a^2-6 a b x^2+2 b^2 x^4\right)}{7 b^3 \sqrt{x \left(a+b x^2\right)}}","\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{15 a \sqrt{a x+b x^3}}{7 b^3}+\frac{9 x^2 \sqrt{a x+b x^3}}{7 b^2}-\frac{x^5}{b \sqrt{a x+b x^3}}",1,"(x*(-15*a^2 - 6*a*b*x^2 + 2*b^2*x^4 + 15*a^2*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^2)/a)]))/(7*b^3*Sqrt[x*(a + b*x^2)])","C",1
66,1,68,279,0.0294443,"\int \frac{x^6}{\left(a x+b x^3\right)^{3/2}} \, dx","Integrate[x^6/(a*x + b*x^3)^(3/2),x]","\frac{2 x^2 \left(7 a \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{b x^2}{a}\right)-7 a+b x^2\right)}{5 b^2 \sqrt{x \left(a+b x^2\right)}}","-\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{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{7 x \sqrt{a x+b x^3}}{5 b^2}-\frac{x^4}{b \sqrt{a x+b x^3}}",1,"(2*x^2*(-7*a + b*x^2 + 7*a*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[3/4, 3/2, 7/4, -((b*x^2)/a)]))/(5*b^2*Sqrt[x*(a + b*x^2)])","C",1
67,1,67,137,0.0336026,"\int \frac{x^5}{\left(a x+b x^3\right)^{3/2}} \, dx","Integrate[x^5/(a*x + b*x^3)^(3/2),x]","\frac{x \left(-5 a \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^2}{a}\right)+5 a+2 b x^2\right)}{3 b^2 \sqrt{x \left(a+b x^2\right)}}","-\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*(5*a + 2*b*x^2 - 5*a*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^2)/a)]))/(3*b^2*Sqrt[x*(a + b*x^2)])","C",1
68,1,57,253,0.0251569,"\int \frac{x^4}{\left(a x+b x^3\right)^{3/2}} \, dx","Integrate[x^4/(a*x + b*x^3)^(3/2),x]","-\frac{2 x^2 \left(\sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{b x^2}{a}\right)-1\right)}{b \sqrt{x \left(a+b x^2\right)}}","\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,"(-2*x^2*(-1 + Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[3/4, 3/2, 7/4, -((b*x^2)/a)]))/(b*Sqrt[x*(a + b*x^2)])","C",1
69,1,54,115,0.0288524,"\int \frac{x^3}{\left(a x+b x^3\right)^{3/2}} \, dx","Integrate[x^3/(a*x + b*x^3)^(3/2),x]","\frac{x \left(\sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^2}{a}\right)-1\right)}{b \sqrt{x \left(a+b x^2\right)}}","\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*(-1 + Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^2)/a)]))/(b*Sqrt[x*(a + b*x^2)])","C",1
70,1,56,254,0.0157032,"\int \frac{x^2}{\left(a x+b x^3\right)^{3/2}} \, dx","Integrate[x^2/(a*x + b*x^3)^(3/2),x]","\frac{2 x^2 \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{b x^2}{a}\right)}{3 a \sqrt{x \left(a+b x^2\right)}}","-\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,"(2*x^2*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[3/4, 3/2, 7/4, -((b*x^2)/a)])/(3*a*Sqrt[x*(a + b*x^2)])","C",1
71,1,54,114,0.031718,"\int \frac{x}{\left(a x+b x^3\right)^{3/2}} \, dx","Integrate[x/(a*x + b*x^3)^(3/2),x]","\frac{x \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{b x^2}{a}\right)+x}{a \sqrt{x \left(a+b x^2\right)}}","\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 + x*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[1/4, 1/2, 5/4, -((b*x^2)/a)])/(a*Sqrt[x*(a + b*x^2)])","C",1
72,1,51,273,0.0257649,"\int \frac{1}{\left(a x+b x^3\right)^{3/2}} \, dx","Integrate[(a*x + b*x^3)^(-3/2),x]","-\frac{2 \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(-\frac{1}{4},\frac{3}{2};\frac{3}{4};-\frac{b x^2}{a}\right)}{a \sqrt{x \left(a+b x^2\right)}}","\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{3 \sqrt{a x+b x^3}}{a^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{1}{a \sqrt{a x+b x^3}}",1,"(-2*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[-1/4, 3/2, 3/4, -((b*x^2)/a)])/(a*Sqrt[x*(a + b*x^2)])","C",1
73,1,56,139,0.0175373,"\int \frac{1}{x \left(a x+b x^3\right)^{3/2}} \, dx","Integrate[1/(x*(a*x + b*x^3)^(3/2)),x]","-\frac{2 \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(-\frac{3}{4},\frac{3}{2};\frac{1}{4};-\frac{b x^2}{a}\right)}{3 a x \sqrt{x \left(a+b x^2\right)}}","-\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,"(-2*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[-3/4, 3/2, 1/4, -((b*x^2)/a)])/(3*a*x*Sqrt[x*(a + b*x^2)])","C",1
74,1,56,306,0.017161,"\int \frac{1}{x^2 \left(a x+b x^3\right)^{3/2}} \, dx","Integrate[1/(x^2*(a*x + b*x^3)^(3/2)),x]","-\frac{2 \sqrt{\frac{b x^2}{a}+1} \, _2F_1\left(-\frac{5}{4},\frac{3}{2};-\frac{1}{4};-\frac{b x^2}{a}\right)}{5 a x^2 \sqrt{x \left(a+b x^2\right)}}","-\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^{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 \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,"(-2*Sqrt[1 + (b*x^2)/a]*Hypergeometric2F1[-5/4, 3/2, -1/4, -((b*x^2)/a)])/(5*a*x^2*Sqrt[x*(a + b*x^2)])","C",1
75,1,130,159,0.212589,"\int \frac{x^{29/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(29/2)/(a*x + b*x^3)^(9/2),x]","\frac{\sqrt{x} \left(\sqrt{b} x \left(315 a^4+1050 a^3 b x^2+1218 a^2 b^2 x^4+528 a b^3 x^6+35 b^4 x^8\right)-\frac{315 \sqrt{a} \left(a+b x^2\right)^4 \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{\frac{b x^2}{a}+1}}\right)}{70 b^{11/2} \left(a+b x^2\right)^3 \sqrt{x \left(a+b x^2\right)}}","-\frac{9 a \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x+b x^3}}\right)}{2 b^{11/2}}+\frac{9 \sqrt{x} \sqrt{a x+b x^3}}{2 b^5}-\frac{3 x^{7/2}}{b^4 \sqrt{a x+b x^3}}-\frac{3 x^{13/2}}{5 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{9 x^{19/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{x^{25/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"(Sqrt[x]*(Sqrt[b]*x*(315*a^4 + 1050*a^3*b*x^2 + 1218*a^2*b^2*x^4 + 528*a*b^3*x^6 + 35*b^4*x^8) - (315*Sqrt[a]*(a + b*x^2)^4*ArcSinh[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[1 + (b*x^2)/a]))/(70*b^(11/2)*(a + b*x^2)^3*Sqrt[x*(a + b*x^2)])","A",1
76,1,77,126,0.0418576,"\int \frac{x^{27/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(27/2)/(a*x + b*x^3)^(9/2),x]","\frac{\sqrt{x} \left(128 a^4+448 a^3 b x^2+560 a^2 b^2 x^4+280 a b^3 x^6+35 b^4 x^8\right)}{35 b^5 \left(a+b x^2\right)^3 \sqrt{x \left(a+b x^2\right)}}","\frac{128 \sqrt{a x+b x^3}}{35 b^5 \sqrt{x}}-\frac{64 x^{5/2}}{35 b^4 \sqrt{a x+b x^3}}-\frac{16 x^{11/2}}{35 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{8 x^{17/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{x^{23/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"(Sqrt[x]*(128*a^4 + 448*a^3*b*x^2 + 560*a^2*b^2*x^4 + 280*a*b^3*x^6 + 35*b^4*x^8))/(35*b^5*(a + b*x^2)^3*Sqrt[x*(a + b*x^2)])","A",1
77,1,120,130,0.2860101,"\int \frac{x^{25/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(25/2)/(a*x + b*x^3)^(9/2),x]","\frac{\sqrt{x} \left(105 \sqrt{a} \left(a+b x^2\right)^3 \sqrt{\frac{b x^2}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)-\sqrt{b} x \left(105 a^3+350 a^2 b x^2+406 a b^2 x^4+176 b^3 x^6\right)\right)}{105 b^{9/2} \left(a+b x^2\right)^3 \sqrt{x \left(a+b x^2\right)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x+b x^3}}\right)}{b^{9/2}}-\frac{x^{3/2}}{b^4 \sqrt{a x+b x^3}}-\frac{x^{9/2}}{3 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{x^{15/2}}{5 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{x^{21/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"(Sqrt[x]*(-(Sqrt[b]*x*(105*a^3 + 350*a^2*b*x^2 + 406*a*b^2*x^4 + 176*b^3*x^6)) + 105*Sqrt[a]*(a + b*x^2)^3*Sqrt[1 + (b*x^2)/a]*ArcSinh[(Sqrt[b]*x)/Sqrt[a]]))/(105*b^(9/2)*(a + b*x^2)^3*Sqrt[x*(a + b*x^2)])","A",1
78,1,66,101,0.0344562,"\int \frac{x^{23/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(23/2)/(a*x + b*x^3)^(9/2),x]","-\frac{\sqrt{x} \left(16 a^3+56 a^2 b x^2+70 a b^2 x^4+35 b^3 x^6\right)}{35 b^4 \left(a+b x^2\right)^3 \sqrt{x \left(a+b x^2\right)}}","-\frac{16 \sqrt{x}}{35 b^4 \sqrt{a x+b x^3}}-\frac{8 x^{7/2}}{35 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{6 x^{13/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{x^{19/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"-1/35*(Sqrt[x]*(16*a^3 + 56*a^2*b*x^2 + 70*a*b^2*x^4 + 35*b^3*x^6))/(b^4*(a + b*x^2)^3*Sqrt[x*(a + b*x^2)])","A",1
79,1,25,25,0.0194042,"\int \frac{x^{21/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(21/2)/(a*x + b*x^3)^(9/2),x]","\frac{x^{21/2}}{7 a \left(x \left(a+b x^2\right)\right)^{7/2}}","\frac{x^{21/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"x^(21/2)/(7*a*(x*(a + b*x^2))^(7/2))","A",1
80,1,55,76,0.027506,"\int \frac{x^{19/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(19/2)/(a*x + b*x^3)^(9/2),x]","-\frac{\sqrt{x} \left(8 a^2+28 a b x^2+35 b^2 x^4\right)}{105 b^3 \left(a+b x^2\right)^3 \sqrt{x \left(a+b x^2\right)}}","-\frac{8 x^{3/2}}{105 b^3 \left(a x+b x^3\right)^{3/2}}-\frac{4 x^{9/2}}{35 b^2 \left(a x+b x^3\right)^{5/2}}-\frac{x^{15/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"-1/105*(Sqrt[x]*(8*a^2 + 28*a*b*x^2 + 35*b^2*x^4))/(b^3*(a + b*x^2)^3*Sqrt[x*(a + b*x^2)])","A",1
81,1,44,51,0.0236696,"\int \frac{x^{17/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(17/2)/(a*x + b*x^3)^(9/2),x]","\frac{x^{9/2} \sqrt{x \left(a+b x^2\right)} \left(7 a+2 b x^2\right)}{35 a^2 \left(a+b x^2\right)^4}","\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^(9/2)*Sqrt[x*(a + b*x^2)]*(7*a + 2*b*x^2))/(35*a^2*(a + b*x^2)^4)","A",1
82,1,44,51,0.0229634,"\int \frac{x^{15/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(15/2)/(a*x + b*x^3)^(9/2),x]","-\frac{\sqrt{x} \left(2 a+7 b x^2\right)}{35 b^2 \left(a+b x^2\right)^3 \sqrt{x \left(a+b x^2\right)}}","-\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,"-1/35*(Sqrt[x]*(2*a + 7*b*x^2))/(b^2*(a + b*x^2)^3*Sqrt[x*(a + b*x^2)])","A",1
83,1,55,76,0.0229222,"\int \frac{x^{13/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(13/2)/(a*x + b*x^3)^(9/2),x]","\frac{x^{5/2} \sqrt{x \left(a+b x^2\right)} \left(35 a^2+28 a b x^2+8 b^2 x^4\right)}{105 a^3 \left(a+b x^2\right)^4}","\frac{8 x^{9/2}}{105 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{4 x^{11/2}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{x^{13/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"(x^(5/2)*Sqrt[x*(a + b*x^2)]*(35*a^2 + 28*a*b*x^2 + 8*b^2*x^4))/(105*a^3*(a + b*x^2)^4)","A",1
84,1,25,25,0.016286,"\int \frac{x^{11/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(11/2)/(a*x + b*x^3)^(9/2),x]","-\frac{x^{7/2}}{7 b \left(x \left(a+b x^2\right)\right)^{7/2}}","-\frac{x^{7/2}}{7 b \left(a x+b x^3\right)^{7/2}}",1,"-1/7*x^(7/2)/(b*(x*(a + b*x^2))^(7/2))","A",1
85,1,66,101,0.0253914,"\int \frac{x^{9/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(9/2)/(a*x + b*x^3)^(9/2),x]","\frac{\sqrt{x} \sqrt{x \left(a+b x^2\right)} \left(35 a^3+70 a^2 b x^2+56 a b^2 x^4+16 b^3 x^6\right)}{35 a^4 \left(a+b x^2\right)^4}","\frac{16 x^{3/2}}{35 a^4 \sqrt{a x+b x^3}}+\frac{8 x^{5/2}}{35 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{6 x^{7/2}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{x^{9/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"(Sqrt[x]*Sqrt[x*(a + b*x^2)]*(35*a^3 + 70*a^2*b*x^2 + 56*a*b^2*x^4 + 16*b^3*x^6))/(35*a^4*(a + b*x^2)^4)","A",1
86,1,43,130,0.0140979,"\int \frac{x^{7/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(7/2)/(a*x + b*x^3)^(9/2),x]","\frac{x^{7/2} \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};\frac{b x^2}{a}+1\right)}{7 a \left(x \left(a+b x^2\right)\right)^{7/2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^3}}\right)}{a^{9/2}}+\frac{\sqrt{x}}{a^4 \sqrt{a x+b x^3}}+\frac{x^{3/2}}{3 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{x^{5/2}}{5 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{x^{7/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"(x^(7/2)*Hypergeometric2F1[-7/2, 1, -5/2, 1 + (b*x^2)/a])/(7*a*(x*(a + b*x^2))^(7/2))","C",1
87,1,77,126,0.0409454,"\int \frac{x^{5/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(5/2)/(a*x + b*x^3)^(9/2),x]","-\frac{\sqrt{x \left(a+b x^2\right)} \left(35 a^4+280 a^3 b x^2+560 a^2 b^2 x^4+448 a b^3 x^6+128 b^4 x^8\right)}{35 a^5 x^{3/2} \left(a+b x^2\right)^4}","-\frac{128 \sqrt{a x+b x^3}}{35 a^5 x^{3/2}}+\frac{64}{35 a^4 \sqrt{x} \sqrt{a x+b x^3}}+\frac{16 \sqrt{x}}{35 a^3 \left(a x+b x^3\right)^{3/2}}+\frac{8 x^{3/2}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{x^{5/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"-1/35*(Sqrt[x*(a + b*x^2)]*(35*a^4 + 280*a^3*b*x^2 + 560*a^2*b^2*x^4 + 448*a*b^3*x^6 + 128*b^4*x^8))/(a^5*x^(3/2)*(a + b*x^2)^4)","A",1
88,1,44,159,0.0228729,"\int \frac{x^{3/2}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[x^(3/2)/(a*x + b*x^3)^(9/2),x]","-\frac{b x^{7/2} \, _2F_1\left(-\frac{7}{2},2;-\frac{5}{2};\frac{b x^2}{a}+1\right)}{7 a^2 \left(x \left(a+b x^2\right)\right)^{7/2}}","\frac{9 b \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b x^3}}\right)}{2 a^{11/2}}-\frac{9 \sqrt{a x+b x^3}}{2 a^5 x^{5/2}}+\frac{3}{a^4 x^{3/2} \sqrt{a x+b x^3}}+\frac{3}{5 a^3 \sqrt{x} \left(a x+b x^3\right)^{3/2}}+\frac{9 \sqrt{x}}{35 a^2 \left(a x+b x^3\right)^{5/2}}+\frac{x^{3/2}}{7 a \left(a x+b x^3\right)^{7/2}}",1,"-1/7*(b*x^(7/2)*Hypergeometric2F1[-7/2, 2, -5/2, 1 + (b*x^2)/a])/(a^2*(x*(a + b*x^2))^(7/2))","C",1
89,1,88,152,0.045219,"\int \frac{\sqrt{x}}{\left(a x+b x^3\right)^{9/2}} \, dx","Integrate[Sqrt[x]/(a*x + b*x^3)^(9/2),x]","\frac{\sqrt{x \left(a+b x^2\right)} \left(-7 a^5+70 a^4 b x^2+560 a^3 b^2 x^4+1120 a^2 b^3 x^6+896 a b^4 x^8+256 b^5 x^{10}\right)}{21 a^6 x^{7/2} \left(a+b x^2\right)^4}","\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*(a + b*x^2)]*(-7*a^5 + 70*a^4*b*x^2 + 560*a^3*b^2*x^4 + 1120*a^2*b^3*x^6 + 896*a*b^4*x^8 + 256*b^5*x^10))/(21*a^6*x^(7/2)*(a + b*x^2)^4)","A",1
90,1,46,189,0.0270754,"\int \frac{1}{\sqrt{x} \left(a x+b x^3\right)^{9/2}} \, dx","Integrate[1/(Sqrt[x]*(a*x + b*x^3)^(9/2)),x]","\frac{b^2 x^{7/2} \, _2F_1\left(-\frac{7}{2},3;-\frac{5}{2};\frac{b x^2}{a}+1\right)}{7 a^3 \left(x \left(a+b x^2\right)\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,"(b^2*x^(7/2)*Hypergeometric2F1[-7/2, 3, -5/2, 1 + (b*x^2)/a])/(7*a^3*(x*(a + b*x^2))^(7/2))","C",1
91,1,99,180,0.042526,"\int \frac{1}{x^{3/2} \left(a x+b x^3\right)^{9/2}} \, dx","Integrate[1/(x^(3/2)*(a*x + b*x^3)^(9/2)),x]","-\frac{\sqrt{x \left(a+b x^2\right)} \left(7 a^6-28 a^5 b x^2+280 a^4 b^2 x^4+2240 a^3 b^3 x^6+4480 a^2 b^4 x^8+3584 a b^5 x^{10}+1024 b^6 x^{12}\right)}{35 a^7 x^{11/2} \left(a+b x^2\right)^4}","-\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,"-1/35*(Sqrt[x*(a + b*x^2)]*(7*a^6 - 28*a^5*b*x^2 + 280*a^4*b^2*x^4 + 2240*a^3*b^3*x^6 + 4480*a^2*b^4*x^8 + 3584*a*b^5*x^10 + 1024*b^6*x^12))/(a^7*x^(11/2)*(a + b*x^2)^4)","A",1
92,1,81,55,0.0503166,"\int \frac{x^4}{\sqrt{a x+b x^4}} \, dx","Integrate[x^4/Sqrt[a*x + b*x^4],x]","\frac{\sqrt{b} x^2 \left(a+b x^3\right)-a \sqrt{x} \sqrt{a+b x^3} \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a+b x^3}}\right)}{3 b^{3/2} \sqrt{x \left(a+b x^3\right)}}","\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,"(Sqrt[b]*x^2*(a + b*x^3) - a*Sqrt[x]*Sqrt[a + b*x^3]*ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a + b*x^3]])/(3*b^(3/2)*Sqrt[x*(a + b*x^3)])","A",1
93,1,61,32,0.0317619,"\int \frac{x}{\sqrt{a x+b x^4}} \, dx","Integrate[x/Sqrt[a*x + b*x^4],x]","\frac{2 \sqrt{x} \sqrt{a+b x^3} \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a+b x^3}}\right)}{3 \sqrt{b} \sqrt{x \left(a+b x^3\right)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x+b x^4}}\right)}{3 \sqrt{b}}",1,"(2*Sqrt[x]*Sqrt[a + b*x^3]*ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a + b*x^3]])/(3*Sqrt[b]*Sqrt[x*(a + b*x^3)])","A",1
94,1,23,23,0.0288826,"\int \frac{1}{x^2 \sqrt{a x+b x^4}} \, dx","Integrate[1/(x^2*Sqrt[a*x + b*x^4]),x]","-\frac{2 \sqrt{x \left(a+b x^3\right)}}{3 a x^2}","-\frac{2 \sqrt{a x+b x^4}}{3 a x^2}",1,"(-2*Sqrt[x*(a + b*x^3)])/(3*a*x^2)","A",1
95,1,31,48,0.027936,"\int \frac{1}{x^5 \sqrt{a x+b x^4}} \, dx","Integrate[1/(x^5*Sqrt[a*x + b*x^4]),x]","-\frac{2 \left(a-2 b x^3\right) \sqrt{x \left(a+b x^3\right)}}{9 a^2 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*(a - 2*b*x^3)*Sqrt[x*(a + b*x^3)])/(9*a^2*x^5)","A",1
96,1,44,74,0.0281023,"\int \frac{1}{x^8 \sqrt{a x+b x^4}} \, dx","Integrate[1/(x^8*Sqrt[a*x + b*x^4]),x]","-\frac{2 \sqrt{x \left(a+b x^3\right)} \left(3 a^2-4 a b x^3+8 b^2 x^6\right)}{45 a^3 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[x*(a + b*x^3)]*(3*a^2 - 4*a*b*x^3 + 8*b^2*x^6))/(45*a^3*x^8)","A",1
97,1,64,224,0.0362775,"\int \frac{x^3}{\sqrt{a x+b x^4}} \, dx","Integrate[x^3/Sqrt[a*x + b*x^4],x]","\frac{x \left(-a \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{b x^3}{a}\right)+a+b x^3\right)}{2 b \sqrt{x \left(a+b x^3\right)}}","\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,"(x*(a + b*x^3 - a*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/6, 1/2, 7/6, -((b*x^3)/a)]))/(2*b*Sqrt[x*(a + b*x^3)])","C",1
98,1,49,197,0.0107287,"\int \frac{1}{\sqrt{a x+b x^4}} \, dx","Integrate[1/Sqrt[a*x + b*x^4],x]","\frac{2 x \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{b x^3}{a}\right)}{\sqrt{x \left(a+b x^3\right)}}","\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,"(2*x*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/6, 1/2, 7/6, -((b*x^3)/a)])/Sqrt[x*(a + b*x^3)]","C",1
99,1,53,225,0.0144682,"\int \frac{1}{x^3 \sqrt{a x+b x^4}} \, dx","Integrate[1/(x^3*Sqrt[a*x + b*x^4]),x]","-\frac{2 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{1}{6};-\frac{b x^3}{a}\right)}{5 x^2 \sqrt{x \left(a+b x^3\right)}}","-\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[1 + (b*x^3)/a]*Hypergeometric2F1[-5/6, 1/2, 1/6, -((b*x^3)/a)])/(5*x^2*Sqrt[x*(a + b*x^3)])","C",1
100,1,66,503,0.0297244,"\int \frac{x^5}{\sqrt{a x+b x^4}} \, dx","Integrate[x^5/Sqrt[a*x + b*x^4],x]","\frac{x^3 \left(-a \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};-\frac{b x^3}{a}\right)+a+b x^3\right)}{4 b \sqrt{x \left(a+b x^3\right)}}","\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,"(x^3*(a + b*x^3 - a*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, 5/6, 11/6, -((b*x^3)/a)]))/(4*b*Sqrt[x*(a + b*x^3)])","C",1
101,1,53,474,0.0131184,"\int \frac{x^2}{\sqrt{a x+b x^4}} \, dx","Integrate[x^2/Sqrt[a*x + b*x^4],x]","\frac{2 x^3 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};-\frac{b x^3}{a}\right)}{5 \sqrt{x \left(a+b x^3\right)}}","-\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,"(2*x^3*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, 5/6, 11/6, -((b*x^3)/a)])/(5*Sqrt[x*(a + b*x^3)])","C",1
102,1,48,497,0.0127073,"\int \frac{1}{x \sqrt{a x+b x^4}} \, dx","Integrate[1/(x*Sqrt[a*x + b*x^4]),x]","-\frac{2 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};-\frac{b x^3}{a}\right)}{\sqrt{x \left(a+b x^3\right)}}","-\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 \sqrt{a x+b x^4}}{a x}+\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}}",1,"(-2*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-1/6, 1/2, 5/6, -((b*x^3)/a)])/Sqrt[x*(a + b*x^3)]","C",1
103,1,151,174,0.1868536,"\int \frac{x^2}{\sqrt{b \sqrt{x}+a x}} \, dx","Integrate[x^2/Sqrt[b*Sqrt[x] + a*x],x]","\frac{\left(a \sqrt{x}+b\right) \left(\sqrt{a} \sqrt{x} \sqrt{\frac{a \sqrt{x}}{b}+1} \left(128 a^4 x^2-144 a^3 b x^{3/2}+168 a^2 b^2 x-210 a b^3 \sqrt{x}+315 b^4\right)-315 b^{9/2} \sqrt[4]{x} \sinh ^{-1}\left(\frac{\sqrt{a} \sqrt[4]{x}}{\sqrt{b}}\right)\right)}{320 a^{11/2} \sqrt{\frac{a \sqrt{x}}{b}+1} \sqrt{a x+b \sqrt{x}}}","-\frac{63 b^5 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{64 a^{11/2}}+\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{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,"((b + a*Sqrt[x])*(Sqrt[a]*Sqrt[1 + (a*Sqrt[x])/b]*Sqrt[x]*(315*b^4 - 210*a*b^3*Sqrt[x] + 168*a^2*b^2*x - 144*a^3*b*x^(3/2) + 128*a^4*x^2) - 315*b^(9/2)*x^(1/4)*ArcSinh[(Sqrt[a]*x^(1/4))/Sqrt[b]]))/(320*a^(11/2)*Sqrt[1 + (a*Sqrt[x])/b]*Sqrt[b*Sqrt[x] + a*x])","A",1
104,1,129,116,0.1163957,"\int \frac{x}{\sqrt{b \sqrt{x}+a x}} \, dx","Integrate[x/Sqrt[b*Sqrt[x] + a*x],x]","\frac{5 b^4 \left(\frac{a \sqrt{x}}{b}+1\right) \left(\frac{16 a^3 x^{3/2}}{15 b^3}-\frac{4 a^2 x}{3 b^2}+\frac{2 a \sqrt{x}}{b}-\frac{2 \sqrt{a} \sqrt[4]{x} \sinh ^{-1}\left(\frac{\sqrt{a} \sqrt[4]{x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{\frac{a \sqrt{x}}{b}+1}}\right)}{8 a^4 \sqrt{\sqrt{x} \left(a \sqrt{x}+b\right)}}","-\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^2 \sqrt{a x+b \sqrt{x}}}{4 a^3}-\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^4*(1 + (a*Sqrt[x])/b)*((2*a*Sqrt[x])/b - (4*a^2*x)/(3*b^2) + (16*a^3*x^(3/2))/(15*b^3) - (2*Sqrt[a]*x^(1/4)*ArcSinh[(Sqrt[a]*x^(1/4))/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (a*Sqrt[x])/b])))/(8*a^4*Sqrt[(b + a*Sqrt[x])*Sqrt[x]])","A",1
105,1,88,56,0.0527072,"\int \frac{1}{\sqrt{b \sqrt{x}+a x}} \, dx","Integrate[1/Sqrt[b*Sqrt[x] + a*x],x]","\frac{2 \sqrt{a} \sqrt{x} \left(a \sqrt{x}+b\right)-2 b^{3/2} \sqrt[4]{x} \sqrt{\frac{a \sqrt{x}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} \sqrt[4]{x}}{\sqrt{b}}\right)}{a^{3/2} \sqrt{a x+b \sqrt{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}}",1,"(2*Sqrt[a]*(b + a*Sqrt[x])*Sqrt[x] - 2*b^(3/2)*Sqrt[1 + (a*Sqrt[x])/b]*x^(1/4)*ArcSinh[(Sqrt[a]*x^(1/4))/Sqrt[b]])/(a^(3/2)*Sqrt[b*Sqrt[x] + a*x])","A",1
106,1,25,25,0.008841,"\int \frac{1}{x \sqrt{b \sqrt{x}+a x}} \, dx","Integrate[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
107,1,48,84,0.0516419,"\int \frac{1}{x^2 \sqrt{b \sqrt{x}+a x}} \, dx","Integrate[1/(x^2*Sqrt[b*Sqrt[x] + a*x]),x]","-\frac{4 \sqrt{a x+b \sqrt{x}} \left(8 a^2 x-4 a b \sqrt{x}+3 b^2\right)}{15 b^3 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]*(3*b^2 - 4*a*b*Sqrt[x] + 8*a^2*x))/(15*b^3*x^(3/2))","A",1
108,1,72,142,0.0537308,"\int \frac{1}{x^3 \sqrt{b \sqrt{x}+a x}} \, dx","Integrate[1/(x^3*Sqrt[b*Sqrt[x] + a*x]),x]","-\frac{4 \sqrt{a x+b \sqrt{x}} \left(128 a^4 x^2-64 a^3 b x^{3/2}+48 a^2 b^2 x-40 a b^3 \sqrt{x}+35 b^4\right)}{315 b^5 x^{5/2}}","-\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{64 a^2 \sqrt{a x+b \sqrt{x}}}{105 b^3 x^{3/2}}+\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]*(35*b^4 - 40*a*b^3*Sqrt[x] + 48*a^2*b^2*x - 64*a^3*b*x^(3/2) + 128*a^4*x^2))/(315*b^5*x^(5/2))","A",1
109,1,96,200,0.0620266,"\int \frac{1}{x^4 \sqrt{b \sqrt{x}+a x}} \, dx","Integrate[1/(x^4*Sqrt[b*Sqrt[x] + a*x]),x]","-\frac{4 \sqrt{a x+b \sqrt{x}} \left(1024 a^6 x^3-512 a^5 b x^{5/2}+384 a^4 b^2 x^2-320 a^3 b^3 x^{3/2}+280 a^2 b^4 x-252 a b^5 \sqrt{x}+231 b^6\right)}{3003 b^7 x^{7/2}}","-\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{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{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]*(231*b^6 - 252*a*b^5*Sqrt[x] + 280*a^2*b^4*x - 320*a^3*b^3*x^(3/2) + 384*a^4*b^2*x^2 - 512*a^5*b*x^(5/2) + 1024*a^6*x^3))/(3003*b^7*x^(7/2))","A",1
110,1,64,197,0.0649548,"\int \frac{x^3}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[x^3/(b*Sqrt[x] + a*x)^(3/2),x]","\frac{4 x^{7/2} \sqrt{\frac{a \sqrt{x}}{b}+1} \, _2F_1\left(\frac{3}{2},\frac{13}{2};\frac{15}{2};-\frac{a \sqrt{x}}{b}\right)}{13 b \sqrt{a x+b \sqrt{x}}}","-\frac{693 b^5 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{64 a^{13/2}}+\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{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*Sqrt[1 + (a*Sqrt[x])/b]*x^(7/2)*Hypergeometric2F1[3/2, 13/2, 15/2, -((a*Sqrt[x])/b)])/(13*b*Sqrt[b*Sqrt[x] + a*x])","C",1
111,1,64,139,0.0751769,"\int \frac{x^2}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[x^2/(b*Sqrt[x] + a*x)^(3/2),x]","\frac{4 x^{5/2} \sqrt{\frac{a \sqrt{x}}{b}+1} \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};-\frac{a \sqrt{x}}{b}\right)}{9 b \sqrt{a x+b \sqrt{x}}}","-\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^2 \sqrt{a x+b \sqrt{x}}}{4 a^4}-\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*Sqrt[1 + (a*Sqrt[x])/b]*x^(5/2)*Hypergeometric2F1[3/2, 9/2, 11/2, -((a*Sqrt[x])/b)])/(9*b*Sqrt[b*Sqrt[x] + a*x])","C",1
112,1,64,77,0.0431537,"\int \frac{x}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[x/(b*Sqrt[x] + a*x)^(3/2),x]","\frac{4 x^{3/2} \sqrt{\frac{a \sqrt{x}}{b}+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-\frac{a \sqrt{x}}{b}\right)}{5 b \sqrt{a x+b \sqrt{x}}}","-\frac{6 b \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{a^{5/2}}+\frac{6 \sqrt{a x+b \sqrt{x}}}{a^2}-\frac{4 x}{a \sqrt{a x+b \sqrt{x}}}",1,"(4*Sqrt[1 + (a*Sqrt[x])/b]*x^(3/2)*Hypergeometric2F1[3/2, 5/2, 7/2, -((a*Sqrt[x])/b)])/(5*b*Sqrt[b*Sqrt[x] + a*x])","C",1
113,1,25,25,0.0190664,"\int \frac{1}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[(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
114,1,48,79,0.0822708,"\int \frac{1}{x \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[1/(x*(b*Sqrt[x] + a*x)^(3/2)),x]","\frac{4 \left(8 a^2 x+4 a b \sqrt{x}-b^2\right)}{3 b^3 \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^2 + 4*a*b*Sqrt[x] + 8*a^2*x))/(3*b^3*Sqrt[x]*Sqrt[b*Sqrt[x] + a*x])","A",1
115,1,72,137,0.077711,"\int \frac{1}{x^2 \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[1/(x^2*(b*Sqrt[x] + a*x)^(3/2)),x]","\frac{4 \left(128 a^4 x^2+64 a^3 b x^{3/2}-16 a^2 b^2 x+8 a b^3 \sqrt{x}-5 b^4\right)}{35 b^5 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*(-5*b^4 + 8*a*b^3*Sqrt[x] - 16*a^2*b^2*x + 64*a^3*b*x^(3/2) + 128*a^4*x^2))/(35*b^5*x^(3/2)*Sqrt[b*Sqrt[x] + a*x])","A",1
116,1,96,195,0.0854718,"\int \frac{1}{x^3 \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[1/(x^3*(b*Sqrt[x] + a*x)^(3/2)),x]","\frac{4 \left(1024 a^6 x^3+512 a^5 b x^{5/2}-128 a^4 b^2 x^2+64 a^3 b^3 x^{3/2}-40 a^2 b^4 x+28 a b^5 \sqrt{x}-21 b^6\right)}{231 b^7 x^{5/2} \sqrt{a x+b \sqrt{x}}}","\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{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{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*(-21*b^6 + 28*a*b^5*Sqrt[x] - 40*a^2*b^4*x + 64*a^3*b^3*x^(3/2) - 128*a^4*b^2*x^2 + 512*a^5*b*x^(5/2) + 1024*a^6*x^3))/(231*b^7*x^(5/2)*Sqrt[b*Sqrt[x] + a*x])","A",1
117,1,164,204,0.264089,"\int \frac{x^{5/2}}{\sqrt{b \sqrt{x}+a x}} \, dx","Integrate[x^(5/2)/Sqrt[b*Sqrt[x] + a*x],x]","\frac{\left(a \sqrt{x}+b\right) \left(\sqrt{a} \sqrt{x} \sqrt{\frac{a \sqrt{x}}{b}+1} \left(1280 a^5 x^{5/2}-1408 a^4 b x^2+1584 a^3 b^2 x^{3/2}-1848 a^2 b^3 x+2310 a b^4 \sqrt{x}-3465 b^5\right)+3465 b^{11/2} \sqrt[4]{x} \sinh ^{-1}\left(\frac{\sqrt{a} \sqrt[4]{x}}{\sqrt{b}}\right)\right)}{3840 a^{13/2} \sqrt{\frac{a \sqrt{x}}{b}+1} \sqrt{a x+b \sqrt{x}}}","\frac{231 b^6 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{256 a^{13/2}}-\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{33 b^2 x^{3/2} \sqrt{a x+b \sqrt{x}}}{80 a^3}-\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,"((b + a*Sqrt[x])*(Sqrt[a]*Sqrt[1 + (a*Sqrt[x])/b]*Sqrt[x]*(-3465*b^5 + 2310*a*b^4*Sqrt[x] - 1848*a^2*b^3*x + 1584*a^3*b^2*x^(3/2) - 1408*a^4*b*x^2 + 1280*a^5*x^(5/2)) + 3465*b^(11/2)*x^(1/4)*ArcSinh[(Sqrt[a]*x^(1/4))/Sqrt[b]]))/(3840*a^(13/2)*Sqrt[1 + (a*Sqrt[x])/b]*Sqrt[b*Sqrt[x] + a*x])","A",1
118,1,142,146,0.2093076,"\int \frac{x^{3/2}}{\sqrt{b \sqrt{x}+a x}} \, dx","Integrate[x^(3/2)/Sqrt[b*Sqrt[x] + a*x],x]","-\frac{35 b^5 \left(\frac{a \sqrt{x}}{b}+1\right) \left(-\frac{32 a^4 x^2}{35 b^4}+\frac{16 a^3 x^{3/2}}{15 b^3}-\frac{4 a^2 x}{3 b^2}+\frac{2 a \sqrt{x}}{b}-\frac{2 \sqrt{a} \sqrt[4]{x} \sinh ^{-1}\left(\frac{\sqrt{a} \sqrt[4]{x}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{\frac{a \sqrt{x}}{b}+1}}\right)}{64 a^5 \sqrt{\sqrt{x} \left(a \sqrt{x}+b\right)}}","\frac{35 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{32 a^{9/2}}-\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{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^5*(1 + (a*Sqrt[x])/b)*((2*a*Sqrt[x])/b - (4*a^2*x)/(3*b^2) + (16*a^3*x^(3/2))/(15*b^3) - (32*a^4*x^2)/(35*b^4) - (2*Sqrt[a]*x^(1/4)*ArcSinh[(Sqrt[a]*x^(1/4))/Sqrt[b]])/(Sqrt[b]*Sqrt[1 + (a*Sqrt[x])/b])))/(64*a^5*Sqrt[(b + a*Sqrt[x])*Sqrt[x]])","A",1
119,1,102,87,0.1171129,"\int \frac{\sqrt{x}}{\sqrt{b \sqrt{x}+a x}} \, dx","Integrate[Sqrt[x]/Sqrt[b*Sqrt[x] + a*x],x]","\frac{\sqrt{a} \sqrt{x} \left(2 a^2 x-a b \sqrt{x}-3 b^2\right)+3 b^{5/2} \sqrt[4]{x} \sqrt{\frac{a \sqrt{x}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} \sqrt[4]{x}}{\sqrt{b}}\right)}{2 a^{5/2} \sqrt{a x+b \sqrt{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}",1,"(Sqrt[a]*Sqrt[x]*(-3*b^2 - a*b*Sqrt[x] + 2*a^2*x) + 3*b^(5/2)*Sqrt[1 + (a*Sqrt[x])/b]*x^(1/4)*ArcSinh[(Sqrt[a]*x^(1/4))/Sqrt[b]])/(2*a^(5/2)*Sqrt[b*Sqrt[x] + a*x])","A",1
120,1,65,34,0.0740162,"\int \frac{1}{\sqrt{x} \sqrt{b \sqrt{x}+a x}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[b*Sqrt[x] + a*x]),x]","\frac{4 \sqrt{b} \sqrt[4]{x} \sqrt{\frac{a \sqrt{x}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} \sqrt[4]{x}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{a x+b \sqrt{x}}}","\frac{4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{\sqrt{a}}",1,"(4*Sqrt[b]*Sqrt[1 + (a*Sqrt[x])/b]*x^(1/4)*ArcSinh[(Sqrt[a]*x^(1/4))/Sqrt[b]])/(Sqrt[a]*Sqrt[b*Sqrt[x] + a*x])","A",1
121,1,37,54,0.0608786,"\int \frac{1}{x^{3/2} \sqrt{b \sqrt{x}+a x}} \, dx","Integrate[1/(x^(3/2)*Sqrt[b*Sqrt[x] + a*x]),x]","\frac{4 \left(2 a \sqrt{x}-b\right) \sqrt{a x+b \sqrt{x}}}{3 b^2 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*(-b + 2*a*Sqrt[x])*Sqrt[b*Sqrt[x] + a*x])/(3*b^2*x)","A",1
122,1,59,112,0.0692037,"\int \frac{1}{x^{5/2} \sqrt{b \sqrt{x}+a x}} \, dx","Integrate[1/(x^(5/2)*Sqrt[b*Sqrt[x] + a*x]),x]","\frac{4 \sqrt{a x+b \sqrt{x}} \left(16 a^3 x^{3/2}-8 a^2 b x+6 a b^2 \sqrt{x}-5 b^3\right)}{35 b^4 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]*(-5*b^3 + 6*a*b^2*Sqrt[x] - 8*a^2*b*x + 16*a^3*x^(3/2)))/(35*b^4*x^2)","A",1
123,1,83,170,0.0862878,"\int \frac{1}{x^{7/2} \sqrt{b \sqrt{x}+a x}} \, dx","Integrate[1/(x^(7/2)*Sqrt[b*Sqrt[x] + a*x]),x]","\frac{4 \sqrt{a x+b \sqrt{x}} \left(256 a^5 x^{5/2}-128 a^4 b x^2+96 a^3 b^2 x^{3/2}-80 a^2 b^3 x+70 a b^4 \sqrt{x}-63 b^5\right)}{693 b^6 x^3}","\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{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{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]*(-63*b^5 + 70*a*b^4*Sqrt[x] - 80*a^2*b^3*x + 96*a^3*b^2*x^(3/2) - 128*a^4*b*x^2 + 256*a^5*x^(5/2)))/(693*b^6*x^3)","A",1
124,1,62,171,0.0833185,"\int \frac{x^{5/2}}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[x^(5/2)/(b*Sqrt[x] + a*x)^(3/2),x]","\frac{4 x^3 \sqrt{\frac{a \sqrt{x}}{b}+1} \, _2F_1\left(\frac{3}{2},\frac{11}{2};\frac{13}{2};-\frac{a \sqrt{x}}{b}\right)}{11 b \sqrt{a x+b \sqrt{x}}}","\frac{315 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{x}}{\sqrt{a x+b \sqrt{x}}}\right)}{32 a^{11/2}}-\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{21 b x \sqrt{a x+b \sqrt{x}}}{4 a^3}+\frac{9 x^{3/2} \sqrt{a x+b \sqrt{x}}}{2 a^2}-\frac{4 x^{5/2}}{a \sqrt{a x+b \sqrt{x}}}",1,"(4*Sqrt[1 + (a*Sqrt[x])/b]*x^3*Hypergeometric2F1[3/2, 11/2, 13/2, -((a*Sqrt[x])/b)])/(11*b*Sqrt[b*Sqrt[x] + a*x])","C",1
125,1,62,113,0.0676132,"\int \frac{x^{3/2}}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[x^(3/2)/(b*Sqrt[x] + a*x)^(3/2),x]","\frac{4 x^2 \sqrt{\frac{a \sqrt{x}}{b}+1} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};-\frac{a \sqrt{x}}{b}\right)}{7 b \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*Sqrt[1 + (a*Sqrt[x])/b]*x^2*Hypergeometric2F1[3/2, 7/2, 9/2, -((a*Sqrt[x])/b)])/(7*b*Sqrt[b*Sqrt[x] + a*x])","C",1
126,1,79,60,0.1134981,"\int \frac{\sqrt{x}}{\left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[Sqrt[x]/(b*Sqrt[x] + a*x)^(3/2),x]","\frac{4 \sqrt[4]{x} \left(\sqrt{b} \sqrt{\frac{a \sqrt{x}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} \sqrt[4]{x}}{\sqrt{b}}\right)-\sqrt{a} \sqrt[4]{x}\right)}{a^{3/2} \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*x^(1/4)*(-(Sqrt[a]*x^(1/4)) + Sqrt[b]*Sqrt[1 + (a*Sqrt[x])/b]*ArcSinh[(Sqrt[a]*x^(1/4))/Sqrt[b]]))/(a^(3/2)*Sqrt[b*Sqrt[x] + a*x])","A",1
127,1,45,30,0.0417134,"\int \frac{1}{\sqrt{x} \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[1/(Sqrt[x]*(b*Sqrt[x] + a*x)^(3/2)),x]","-\frac{4 \left(2 a \sqrt{x}+b\right) \sqrt{a x+b \sqrt{x}}}{a b^2 x+b^3 \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])*Sqrt[b*Sqrt[x] + a*x])/(b^3*Sqrt[x] + a*b^2*x)","A",1
128,1,57,107,0.0509536,"\int \frac{1}{x^{3/2} \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[1/(x^(3/2)*(b*Sqrt[x] + a*x)^(3/2)),x]","-\frac{4 \left(16 a^3 x^{3/2}+8 a^2 b x-2 a b^2 \sqrt{x}+b^3\right)}{5 b^4 x \sqrt{a x+b \sqrt{x}}}","-\frac{64 a^2 \sqrt{a x+b \sqrt{x}}}{5 b^4 \sqrt{x}}+\frac{32 a \sqrt{a x+b \sqrt{x}}}{5 b^3 x}-\frac{24 \sqrt{a x+b \sqrt{x}}}{5 b^2 x^{3/2}}+\frac{4}{b x \sqrt{a x+b \sqrt{x}}}",1,"(-4*(b^3 - 2*a*b^2*Sqrt[x] + 8*a^2*b*x + 16*a^3*x^(3/2)))/(5*b^4*x*Sqrt[b*Sqrt[x] + a*x])","A",1
129,1,83,165,0.0686594,"\int \frac{1}{x^{5/2} \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[1/(x^(5/2)*(b*Sqrt[x] + a*x)^(3/2)),x]","-\frac{4 \left(256 a^5 x^{5/2}+128 a^4 b x^2-32 a^3 b^2 x^{3/2}+16 a^2 b^3 x-10 a b^4 \sqrt{x}+7 b^5\right)}{63 b^6 x^2 \sqrt{a x+b \sqrt{x}}}","-\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{128 a^2 \sqrt{a x+b \sqrt{x}}}{21 b^4 x^{3/2}}+\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*(7*b^5 - 10*a*b^4*Sqrt[x] + 16*a^2*b^3*x - 32*a^3*b^2*x^(3/2) + 128*a^4*b*x^2 + 256*a^5*x^(5/2)))/(63*b^6*x^2*Sqrt[b*Sqrt[x] + a*x])","A",1
130,1,107,223,0.0663254,"\int \frac{1}{x^{7/2} \left(b \sqrt{x}+a x\right)^{3/2}} \, dx","Integrate[1/(x^(7/2)*(b*Sqrt[x] + a*x)^(3/2)),x]","-\frac{4 \left(2048 a^7 x^{7/2}+1024 a^6 b x^3-256 a^5 b^2 x^{5/2}+128 a^4 b^3 x^2-80 a^3 b^4 x^{3/2}+56 a^2 b^5 x-42 a b^6 \sqrt{x}+33 b^7\right)}{429 b^8 x^3 \sqrt{a x+b \sqrt{x}}}","-\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{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{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*(33*b^7 - 42*a*b^6*Sqrt[x] + 56*a^2*b^5*x - 80*a^3*b^4*x^(3/2) + 128*a^4*b^3*x^2 - 256*a^5*b^2*x^(5/2) + 1024*a^6*b*x^3 + 2048*a^7*x^(7/2)))/(429*b^8*x^3*Sqrt[b*Sqrt[x] + a*x])","A",1
131,1,155,301,0.1784027,"\int x^3 \sqrt{b \sqrt[3]{x}+a x} \, dx","Integrate[x^3*Sqrt[b*x^(1/3) + a*x],x]","\frac{2 \sqrt{a x+b \sqrt[3]{x}} \left(\sqrt{\frac{a x^{2/3}}{b}+1} \left(24035 a^6 x^4+2090 a^5 b x^{10/3}-2310 a^4 b^2 x^{8/3}+2618 a^3 b^3 x^2-3094 a^2 b^4 x^{4/3}+3978 a b^5 x^{2/3}-9945 b^6\right)+9945 b^6 \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{a x^{2/3}}{b}\right)\right)}{216315 a^6 \sqrt{\frac{a x^{2/3}}{b}+1}}","\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{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{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,"(2*Sqrt[b*x^(1/3) + a*x]*(Sqrt[1 + (a*x^(2/3))/b]*(-9945*b^6 + 3978*a*b^5*x^(2/3) - 3094*a^2*b^4*x^(4/3) + 2618*a^3*b^3*x^2 - 2310*a^4*b^2*x^(8/3) + 2090*a^5*b*x^(10/3) + 24035*a^6*x^4) + 9945*b^6*Hypergeometric2F1[-1/2, 1/4, 5/4, -((a*x^(2/3))/b)]))/(216315*a^6*Sqrt[1 + (a*x^(2/3))/b])","C",1
132,1,136,411,0.1286106,"\int x^2 \sqrt{b \sqrt[3]{x}+a x} \, dx","Integrate[x^2*Sqrt[b*x^(1/3) + a*x],x]","\frac{2 \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}} \left(\sqrt{\frac{a x^{2/3}}{b}+1} \left(663 a^4 x^{8/3}+78 a^3 b x^2-90 a^2 b^2 x^{4/3}+110 a b^3 x^{2/3}-385 b^4\right)+385 b^4 \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{a x^{2/3}}{b}\right)\right)}{4641 a^4 \sqrt{\frac{a x^{2/3}}{b}+1}}","\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^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{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{60 b^2 x^{5/3} \sqrt{a x+b \sqrt[3]{x}}}{1547 a^2}+\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,"(2*x^(1/3)*Sqrt[b*x^(1/3) + a*x]*(Sqrt[1 + (a*x^(2/3))/b]*(-385*b^4 + 110*a*b^3*x^(2/3) - 90*a^2*b^2*x^(4/3) + 78*a^3*b*x^2 + 663*a^4*x^(8/3)) + 385*b^4*Hypergeometric2F1[-1/2, 3/4, 7/4, -((a*x^(2/3))/b)]))/(4641*a^4*Sqrt[1 + (a*x^(2/3))/b])","C",1
133,1,118,213,0.1037592,"\int x \sqrt{b \sqrt[3]{x}+a x} \, dx","Integrate[x*Sqrt[b*x^(1/3) + a*x],x]","\frac{2 \sqrt{a x+b \sqrt[3]{x}} \left(\sqrt{\frac{a x^{2/3}}{b}+1} \left(77 a^3 x^2+14 a^2 b x^{4/3}-18 a b^2 x^{2/3}+45 b^3\right)-45 b^3 \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{a x^{2/3}}{b}\right)\right)}{385 a^3 \sqrt{\frac{a x^{2/3}}{b}+1}}","-\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{36 b^2 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{385 a^2}+\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,"(2*Sqrt[b*x^(1/3) + a*x]*(Sqrt[1 + (a*x^(2/3))/b]*(45*b^3 - 18*a*b^2*x^(2/3) + 14*a^2*b*x^(4/3) + 77*a^3*x^2) - 45*b^3*Hypergeometric2F1[-1/2, 1/4, 5/4, -((a*x^(2/3))/b)]))/(385*a^3*Sqrt[1 + (a*x^(2/3))/b])","C",1
134,1,94,323,0.0590316,"\int \sqrt{b \sqrt[3]{x}+a x} \, dx","Integrate[Sqrt[b*x^(1/3) + a*x],x]","\frac{2 \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}} \left(\left(a x^{2/3}+b\right) \sqrt{\frac{a x^{2/3}}{b}+1}-b \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{a x^{2/3}}{b}\right)\right)}{3 a \sqrt{\frac{a x^{2/3}}{b}+1}}","-\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^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{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,"(2*x^(1/3)*Sqrt[b*x^(1/3) + a*x]*((b + a*x^(2/3))*Sqrt[1 + (a*x^(2/3))/b] - b*Hypergeometric2F1[-1/2, 3/4, 7/4, -((a*x^(2/3))/b)]))/(3*a*Sqrt[1 + (a*x^(2/3))/b])","C",1
135,1,54,123,0.0475664,"\int \frac{\sqrt{b \sqrt[3]{x}+a x}}{x} \, dx","Integrate[Sqrt[b*x^(1/3) + a*x]/x,x]","\frac{6 \sqrt{a x+b \sqrt[3]{x}} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-\frac{a x^{2/3}}{b}\right)}{\sqrt{\frac{a x^{2/3}}{b}+1}}","\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,"(6*Sqrt[b*x^(1/3) + a*x]*Hypergeometric2F1[-1/2, 1/4, 5/4, -((a*x^(2/3))/b)])/Sqrt[1 + (a*x^(2/3))/b]","C",1
136,1,59,325,0.0717443,"\int \frac{\sqrt{b \sqrt[3]{x}+a x}}{x^2} \, dx","Integrate[Sqrt[b*x^(1/3) + a*x]/x^2,x]","-\frac{6 \sqrt{a x+b \sqrt[3]{x}} \, _2F_1\left(-\frac{5}{4},-\frac{1}{2};-\frac{1}{4};-\frac{a x^{2/3}}{b}\right)}{5 x \sqrt{\frac{a x^{2/3}}{b}+1}}","\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,"(-6*Sqrt[b*x^(1/3) + a*x]*Hypergeometric2F1[-5/4, -1/2, -1/4, -((a*x^(2/3))/b)])/(5*Sqrt[1 + (a*x^(2/3))/b]*x)","C",1
137,1,59,188,0.0521328,"\int \frac{\sqrt{b \sqrt[3]{x}+a x}}{x^3} \, dx","Integrate[Sqrt[b*x^(1/3) + a*x]/x^3,x]","-\frac{6 \sqrt{a x+b \sqrt[3]{x}} \, _2F_1\left(-\frac{11}{4},-\frac{1}{2};-\frac{7}{4};-\frac{a x^{2/3}}{b}\right)}{11 x^2 \sqrt{\frac{a x^{2/3}}{b}+1}}","\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{20 a^2 \sqrt{a x+b \sqrt[3]{x}}}{77 b^2 x^{2/3}}-\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]*Hypergeometric2F1[-11/4, -1/2, -7/4, -((a*x^(2/3))/b)])/(11*Sqrt[1 + (a*x^(2/3))/b]*x^2)","C",1
138,1,59,413,0.0513423,"\int \frac{\sqrt{b \sqrt[3]{x}+a x}}{x^4} \, dx","Integrate[Sqrt[b*x^(1/3) + a*x]/x^4,x]","-\frac{6 \sqrt{a x+b \sqrt[3]{x}} \, _2F_1\left(-\frac{17}{4},-\frac{1}{2};-\frac{13}{4};-\frac{a x^{2/3}}{b}\right)}{17 x^3 \sqrt{\frac{a x^{2/3}}{b}+1}}","-\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^{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{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{44 a^2 \sqrt{a x+b \sqrt[3]{x}}}{663 b^2 x^{5/3}}-\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,"(-6*Sqrt[b*x^(1/3) + a*x]*Hypergeometric2F1[-17/4, -1/2, -13/4, -((a*x^(2/3))/b)])/(17*Sqrt[1 + (a*x^(2/3))/b]*x^3)","C",1
139,1,59,276,0.0599589,"\int \frac{\sqrt{b \sqrt[3]{x}+a x}}{x^5} \, dx","Integrate[Sqrt[b*x^(1/3) + a*x]/x^5,x]","-\frac{6 \sqrt{a x+b \sqrt[3]{x}} \, _2F_1\left(-\frac{23}{4},-\frac{1}{2};-\frac{19}{4};-\frac{a x^{2/3}}{b}\right)}{23 x^4 \sqrt{\frac{a x^{2/3}}{b}+1}}","-\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{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{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]*Hypergeometric2F1[-23/4, -1/2, -19/4, -((a*x^(2/3))/b)])/(23*Sqrt[1 + (a*x^(2/3))/b]*x^4)","C",1
140,1,142,298,0.1535526,"\int x^2 \left(b \sqrt[3]{x}+a x\right)^{3/2} \, dx","Integrate[x^2*(b*x^(1/3) + a*x)^(3/2),x]","\frac{2 \sqrt{a x+b \sqrt[3]{x}} \left(\left(a x^{2/3}+b\right)^2 \sqrt{\frac{a x^{2/3}}{b}+1} \left(24035 a^4 x^{8/3}-17765 a^3 b x^2+12155 a^2 b^2 x^{4/3}-7293 a b^3 x^{2/3}+3315 b^4\right)-3315 b^6 \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{a x^{2/3}}{b}\right)\right)}{216315 a^5 \sqrt{\frac{a x^{2/3}}{b}+1}}","-\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{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{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,"(2*Sqrt[b*x^(1/3) + a*x]*((b + a*x^(2/3))^2*Sqrt[1 + (a*x^(2/3))/b]*(3315*b^4 - 7293*a*b^3*x^(2/3) + 12155*a^2*b^2*x^(4/3) - 17765*a^3*b*x^2 + 24035*a^4*x^(8/3)) - 3315*b^6*Hypergeometric2F1[-3/2, 1/4, 5/4, -((a*x^(2/3))/b)]))/(216315*a^5*Sqrt[1 + (a*x^(2/3))/b])","C",1
141,1,123,408,0.1093419,"\int x \left(b \sqrt[3]{x}+a x\right)^{3/2} \, dx","Integrate[x*(b*x^(1/3) + a*x)^(3/2),x]","\frac{2 \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}} \left(\left(a x^{2/3}+b\right)^2 \sqrt{\frac{a x^{2/3}}{b}+1} \left(221 a^2 x^{4/3}-143 a b x^{2/3}+77 b^2\right)-77 b^4 \, _2F_1\left(-\frac{3}{2},\frac{3}{4};\frac{7}{4};-\frac{a x^{2/3}}{b}\right)\right)}{1547 a^3 \sqrt{\frac{a x^{2/3}}{b}+1}}","-\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^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{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,"(2*x^(1/3)*Sqrt[b*x^(1/3) + a*x]*((b + a*x^(2/3))^2*Sqrt[1 + (a*x^(2/3))/b]*(77*b^2 - 143*a*b*x^(2/3) + 221*a^2*x^(4/3)) - 77*b^4*Hypergeometric2F1[-3/2, 3/4, 7/4, -((a*x^(2/3))/b)]))/(1547*a^3*Sqrt[1 + (a*x^(2/3))/b])","C",1
142,1,106,208,0.1009669,"\int \left(b \sqrt[3]{x}+a x\right)^{3/2} \, dx","Integrate[(b*x^(1/3) + a*x)^(3/2),x]","\frac{2 \sqrt{a x+b \sqrt[3]{x}} \left(5 b^3 \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-\frac{a x^{2/3}}{b}\right)-\left(5 b-11 a x^{2/3}\right) \left(a x^{2/3}+b\right)^2 \sqrt{\frac{a x^{2/3}}{b}+1}\right)}{55 a^2 \sqrt{\frac{a x^{2/3}}{b}+1}}","\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,"(2*Sqrt[b*x^(1/3) + a*x]*(-((5*b - 11*a*x^(2/3))*(b + a*x^(2/3))^2*Sqrt[1 + (a*x^(2/3))/b]) + 5*b^3*Hypergeometric2F1[-3/2, 1/4, 5/4, -((a*x^(2/3))/b)]))/(55*a^2*Sqrt[1 + (a*x^(2/3))/b])","C",1
143,1,60,319,0.0483663,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x} \, dx","Integrate[(b*x^(1/3) + a*x)^(3/2)/x,x]","\frac{2 b \sqrt[3]{x} \sqrt{a x+b \sqrt[3]{x}} \, _2F_1\left(-\frac{3}{2},\frac{3}{4};\frac{7}{4};-\frac{a x^{2/3}}{b}\right)}{\sqrt{\frac{a x^{2/3}}{b}+1}}","\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,"(2*b*x^(1/3)*Sqrt[b*x^(1/3) + a*x]*Hypergeometric2F1[-3/2, 3/4, 7/4, -((a*x^(2/3))/b)])/Sqrt[1 + (a*x^(2/3))/b]","C",1
144,1,60,144,0.059699,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x^2} \, dx","Integrate[(b*x^(1/3) + a*x)^(3/2)/x^2,x]","-\frac{2 b \sqrt{a x+b \sqrt[3]{x}} \, _2F_1\left(-\frac{3}{2},-\frac{3}{4};\frac{1}{4};-\frac{a x^{2/3}}{b}\right)}{x^{2/3} \sqrt{\frac{a x^{2/3}}{b}+1}}","\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,"(-2*b*Sqrt[b*x^(1/3) + a*x]*Hypergeometric2F1[-3/2, -3/4, 1/4, -((a*x^(2/3))/b)])/(Sqrt[1 + (a*x^(2/3))/b]*x^(2/3))","C",1
145,1,62,350,0.0603249,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x^3} \, dx","Integrate[(b*x^(1/3) + a*x)^(3/2)/x^3,x]","-\frac{2 b \sqrt{a x+b \sqrt[3]{x}} \, _2F_1\left(-\frac{9}{4},-\frac{3}{2};-\frac{5}{4};-\frac{a x^{2/3}}{b}\right)}{3 x^{5/3} \sqrt{\frac{a x^{2/3}}{b}+1}}","\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,"(-2*b*Sqrt[b*x^(1/3) + a*x]*Hypergeometric2F1[-9/4, -3/2, -5/4, -((a*x^(2/3))/b)])/(3*Sqrt[1 + (a*x^(2/3))/b]*x^(5/3))","C",1
146,1,62,213,0.0662999,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x^4} \, dx","Integrate[(b*x^(1/3) + a*x)^(3/2)/x^4,x]","-\frac{2 b \sqrt{a x+b \sqrt[3]{x}} \, _2F_1\left(-\frac{15}{4},-\frac{3}{2};-\frac{11}{4};-\frac{a x^{2/3}}{b}\right)}{5 x^{8/3} \sqrt{\frac{a x^{2/3}}{b}+1}}","\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{8 a^3 \sqrt{a x+b \sqrt[3]{x}}}{77 b^2 x^{2/3}}-\frac{24 a^2 \sqrt{a x+b \sqrt[3]{x}}}{385 b x^{4/3}}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{5 x^3}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{55 x^2}",1,"(-2*b*Sqrt[b*x^(1/3) + a*x]*Hypergeometric2F1[-15/4, -3/2, -11/4, -((a*x^(2/3))/b)])/(5*Sqrt[1 + (a*x^(2/3))/b]*x^(8/3))","C",1
147,1,62,438,0.0580649,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x^5} \, dx","Integrate[(b*x^(1/3) + a*x)^(3/2)/x^5,x]","-\frac{2 b \sqrt{a x+b \sqrt[3]{x}} \, _2F_1\left(-\frac{21}{4},-\frac{3}{2};-\frac{17}{4};-\frac{a x^{2/3}}{b}\right)}{7 x^{11/3} \sqrt{\frac{a x^{2/3}}{b}+1}}","-\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^{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^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{88 a^3 \sqrt{a x+b \sqrt[3]{x}}}{4641 b^2 x^{5/3}}-\frac{24 a^2 \sqrt{a x+b \sqrt[3]{x}}}{1547 b x^{7/3}}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{7 x^4}-\frac{12 a \sqrt{a x+b \sqrt[3]{x}}}{119 x^3}",1,"(-2*b*Sqrt[b*x^(1/3) + a*x]*Hypergeometric2F1[-21/4, -3/2, -17/4, -((a*x^(2/3))/b)])/(7*Sqrt[1 + (a*x^(2/3))/b]*x^(11/3))","C",1
148,1,62,301,0.0690321,"\int \frac{\left(b \sqrt[3]{x}+a x\right)^{3/2}}{x^6} \, dx","Integrate[(b*x^(1/3) + a*x)^(3/2)/x^6,x]","-\frac{2 b \sqrt{a x+b \sqrt[3]{x}} \, _2F_1\left(-\frac{27}{4},-\frac{3}{2};-\frac{23}{4};-\frac{a x^{2/3}}{b}\right)}{9 x^{14/3} \sqrt{\frac{a x^{2/3}}{b}+1}}","-\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{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{8 a^2 \sqrt{a x+b \sqrt[3]{x}}}{1311 b x^{10/3}}-\frac{2 \left(a x+b \sqrt[3]{x}\right)^{3/2}}{9 x^5}-\frac{4 a \sqrt{a x+b \sqrt[3]{x}}}{69 x^4}",1,"(-2*b*Sqrt[b*x^(1/3) + a*x]*Hypergeometric2F1[-27/4, -3/2, -23/4, -((a*x^(2/3))/b)])/(9*Sqrt[1 + (a*x^(2/3))/b]*x^(14/3))","C",1
149,1,161,304,0.1012237,"\int \frac{x^4}{\sqrt{b \sqrt[3]{x}+a x}} \, dx","Integrate[x^4/Sqrt[b*x^(1/3) + a*x],x]","\frac{2 \sqrt{a x+b \sqrt[3]{x}} \left(4807 a^7 x^{14/3}-418 a^6 b x^4+550 a^5 b^2 x^{10/3}-770 a^4 b^3 x^{8/3}+1190 a^3 b^4 x^2-2210 a^2 b^5 x^{4/3}-16575 b^7 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{a x^{2/3}}{b}\right)+6630 a b^6 x^{2/3}+16575 b^7\right)}{43263 a^7 \left(a x^{2/3}+b\right)}","-\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{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{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,"(2*Sqrt[b*x^(1/3) + a*x]*(16575*b^7 + 6630*a*b^6*x^(2/3) - 2210*a^2*b^5*x^(4/3) + 1190*a^3*b^4*x^2 - 770*a^4*b^3*x^(8/3) + 550*a^5*b^2*x^(10/3) - 418*a^6*b*x^4 + 4807*a^7*x^(14/3) - 16575*b^7*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[1/4, 1/2, 5/4, -((a*x^(2/3))/b)]))/(43263*a^7*(b + a*x^(2/3)))","C",1
150,1,143,414,0.0771792,"\int \frac{x^3}{\sqrt{b \sqrt[3]{x}+a x}} \, dx","Integrate[x^3/Sqrt[b*x^(1/3) + a*x],x]","\frac{2 \sqrt{a x+b \sqrt[3]{x}} \left(663 a^5 x^{11/3}-78 a^4 b x^3+114 a^3 b^2 x^{7/3}-190 a^2 b^3 x^{5/3}-1463 b^5 \sqrt[3]{x} \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{a x^{2/3}}{b}\right)+418 a b^4 x+1463 b^5 \sqrt[3]{x}\right)}{4641 a^5 \left(a x^{2/3}+b\right)}","-\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^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{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{570 b^2 x^{5/3} \sqrt{a x+b \sqrt[3]{x}}}{1547 a^3}-\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,"(2*Sqrt[b*x^(1/3) + a*x]*(1463*b^5*x^(1/3) + 418*a*b^4*x - 190*a^2*b^3*x^(5/3) + 114*a^3*b^2*x^(7/3) - 78*a^4*b*x^3 + 663*a^5*x^(11/3) - 1463*b^5*Sqrt[1 + (a*x^(2/3))/b]*x^(1/3)*Hypergeometric2F1[1/2, 3/4, 7/4, -((a*x^(2/3))/b)]))/(4641*a^5*(b + a*x^(2/3)))","C",1
151,1,124,216,0.0720042,"\int \frac{x^2}{\sqrt{b \sqrt[3]{x}+a x}} \, dx","Integrate[x^2/Sqrt[b*x^(1/3) + a*x],x]","\frac{2 \sqrt{a x+b \sqrt[3]{x}} \left(77 a^4 x^{8/3}-14 a^3 b x^2+26 a^2 b^2 x^{4/3}+195 b^4 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{a x^{2/3}}{b}\right)-78 a b^3 x^{2/3}-195 b^4\right)}{385 a^4 \left(a x^{2/3}+b\right)}","\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{234 b^2 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{385 a^3}-\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,"(2*Sqrt[b*x^(1/3) + a*x]*(-195*b^4 - 78*a*b^3*x^(2/3) + 26*a^2*b^2*x^(4/3) - 14*a^3*b*x^2 + 77*a^4*x^(8/3) + 195*b^4*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[1/4, 1/2, 5/4, -((a*x^(2/3))/b)]))/(385*a^4*(b + a*x^(2/3)))","C",1
152,1,106,326,0.0894049,"\int \frac{x}{\sqrt{b \sqrt[3]{x}+a x}} \, dx","Integrate[x/Sqrt[b*x^(1/3) + a*x],x]","\frac{2 \sqrt{a x+b \sqrt[3]{x}} \left(5 a^2 x^{5/3}+7 b^2 \sqrt[3]{x} \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{a x^{2/3}}{b}\right)-2 a b x-7 b^2 \sqrt[3]{x}\right)}{15 a^2 \left(a x^{2/3}+b\right)}","\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^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{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,"(2*Sqrt[b*x^(1/3) + a*x]*(-7*b^2*x^(1/3) - 2*a*b*x + 5*a^2*x^(5/3) + 7*b^2*Sqrt[1 + (a*x^(2/3))/b]*x^(1/3)*Hypergeometric2F1[1/2, 3/4, 7/4, -((a*x^(2/3))/b)]))/(15*a^2*(b + a*x^(2/3)))","C",1
153,1,80,126,0.0389954,"\int \frac{1}{\sqrt{b \sqrt[3]{x}+a x}} \, dx","Integrate[1/Sqrt[b*x^(1/3) + a*x],x]","\frac{2 \sqrt{a x+b \sqrt[3]{x}} \left(-b \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{a x^{2/3}}{b}\right)+a x^{2/3}+b\right)}{a \left(a x^{2/3}+b\right)}","\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]*(b + a*x^(2/3) - b*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[1/4, 1/2, 5/4, -((a*x^(2/3))/b)]))/(a*(b + a*x^(2/3)))","C",1
154,1,54,294,0.0708259,"\int \frac{1}{x \sqrt{b \sqrt[3]{x}+a x}} \, dx","Integrate[1/(x*Sqrt[b*x^(1/3) + a*x]),x]","-\frac{6 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-\frac{a x^{2/3}}{b}\right)}{\sqrt{a 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[1 + (a*x^(2/3))/b]*Hypergeometric2F1[-1/4, 1/2, 3/4, -((a*x^(2/3))/b)])/Sqrt[b*x^(1/3) + a*x]","C",1
155,1,59,163,0.0620921,"\int \frac{1}{x^2 \sqrt{b \sqrt[3]{x}+a x}} \, dx","Integrate[1/(x^2*Sqrt[b*x^(1/3) + a*x]),x]","-\frac{6 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(-\frac{7}{4},\frac{1}{2};-\frac{3}{4};-\frac{a x^{2/3}}{b}\right)}{7 x \sqrt{a x+b \sqrt[3]{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}}",1,"(-6*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[-7/4, 1/2, -3/4, -((a*x^(2/3))/b)])/(7*x*Sqrt[b*x^(1/3) + a*x])","C",1
156,1,59,388,0.0568687,"\int \frac{1}{x^3 \sqrt{b \sqrt[3]{x}+a x}} \, dx","Integrate[1/(x^3*Sqrt[b*x^(1/3) + a*x]),x]","-\frac{6 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(-\frac{13}{4},\frac{1}{2};-\frac{9}{4};-\frac{a x^{2/3}}{b}\right)}{13 x^2 \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^{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{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,"(-6*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[-13/4, 1/2, -9/4, -((a*x^(2/3))/b)])/(13*x^2*Sqrt[b*x^(1/3) + a*x])","C",1
157,1,59,251,0.0905976,"\int \frac{1}{x^4 \sqrt{b \sqrt[3]{x}+a x}} \, dx","Integrate[1/(x^4*Sqrt[b*x^(1/3) + a*x]),x]","-\frac{6 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(-\frac{19}{4},\frac{1}{2};-\frac{15}{4};-\frac{a x^{2/3}}{b}\right)}{19 x^3 \sqrt{a x+b \sqrt[3]{x}}}","-\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{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{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[1 + (a*x^(2/3))/b]*Hypergeometric2F1[-19/4, 1/2, -15/4, -((a*x^(2/3))/b)])/(19*x^3*Sqrt[b*x^(1/3) + a*x])","C",1
158,1,131,437,0.1091554,"\int \frac{x^4}{\left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Integrate[x^4/(b*x^(1/3) + a*x)^(3/2),x]","\frac{2 x^{2/3} \left(663 a^5 x^{10/3}-897 a^4 b x^{8/3}+1311 a^3 b^2 x^2-2185 a^2 b^3 x^{4/3}+33649 b^5 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{a x^{2/3}}{b}\right)+4807 a b^4 x^{2/3}-33649 b^5\right)}{4641 a^6 \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}} 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^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{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{6555 b^2 x^{5/3} \sqrt{a x+b \sqrt[3]{x}}}{1547 a^4}-\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,"(2*x^(2/3)*(-33649*b^5 + 4807*a*b^4*x^(2/3) - 2185*a^2*b^3*x^(4/3) + 1311*a^3*b^2*x^2 - 897*a^4*b*x^(8/3) + 663*a^5*x^(10/3) + 33649*b^5*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[3/4, 3/2, 7/4, -((a*x^(2/3))/b)]))/(4641*a^6*Sqrt[b*x^(1/3) + a*x])","C",1
159,1,124,239,0.131858,"\int \frac{x^3}{\left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Integrate[x^3/(b*x^(1/3) + a*x)^(3/2),x]","\frac{\sqrt{a x+b \sqrt[3]{x}} \left(154 a^4 x^{8/3}-238 a^3 b x^2+442 a^2 b^2 x^{4/3}+3315 b^4 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{a x^{2/3}}{b}\right)-1326 a b^3 x^{2/3}-3315 b^4\right)}{385 a^5 \left(a x^{2/3}+b\right)}","\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{1989 b^2 x^{2/3} \sqrt{a x+b \sqrt[3]{x}}}{385 a^4}-\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,"(Sqrt[b*x^(1/3) + a*x]*(-3315*b^4 - 1326*a*b^3*x^(2/3) + 442*a^2*b^2*x^(4/3) - 238*a^3*b*x^2 + 154*a^4*x^(8/3) + 3315*b^4*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[1/4, 1/2, 5/4, -((a*x^(2/3))/b)]))/(385*a^5*(b + a*x^(2/3)))","C",1
160,1,94,349,0.0934078,"\int \frac{x^2}{\left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Integrate[x^2/(b*x^(1/3) + a*x)^(3/2),x]","\frac{2 x^{2/3} \left(5 a^2 x^{4/3}-77 b^2 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{a x^{2/3}}{b}\right)-11 a b x^{2/3}+77 b^2\right)}{15 a^3 \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^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 \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,"(2*x^(2/3)*(77*b^2 - 11*a*b*x^(2/3) + 5*a^2*x^(4/3) - 77*b^2*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[3/4, 3/2, 7/4, -((a*x^(2/3))/b)]))/(15*a^3*Sqrt[b*x^(1/3) + a*x])","C",1
161,1,82,149,0.0893443,"\int \frac{x}{\left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Integrate[x/(b*x^(1/3) + a*x)^(3/2),x]","\frac{\sqrt{a x+b \sqrt[3]{x}} \left(-5 b \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\frac{a x^{2/3}}{b}\right)+2 a x^{2/3}+5 b\right)}{a^2 \left(a x^{2/3}+b\right)}","-\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,"(Sqrt[b*x^(1/3) + a*x]*(5*b + 2*a*x^(2/3) - 5*b*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[1/4, 1/2, 5/4, -((a*x^(2/3))/b)]))/(a^2*(b + a*x^(2/3)))","C",1
162,1,62,296,0.0440125,"\int \frac{1}{\left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Integrate[(b*x^(1/3) + a*x)^(-3/2),x]","\frac{2 x^{2/3} \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(\frac{3}{4},\frac{3}{2};\frac{7}{4};-\frac{a x^{2/3}}{b}\right)}{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,"(2*Sqrt[1 + (a*x^(2/3))/b]*x^(2/3)*Hypergeometric2F1[3/4, 3/2, 7/4, -((a*x^(2/3))/b)])/(b*Sqrt[b*x^(1/3) + a*x])","C",1
163,1,62,158,0.0702602,"\int \frac{1}{x \left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Integrate[1/(x*(b*x^(1/3) + a*x)^(3/2)),x]","-\frac{2 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(-\frac{3}{4},\frac{3}{2};\frac{1}{4};-\frac{a x^{2/3}}{b}\right)}{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,"(-2*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[-3/4, 3/2, 1/4, -((a*x^(2/3))/b)])/(b*x^(1/3)*Sqrt[b*x^(1/3) + a*x])","C",1
164,1,64,383,0.078159,"\int \frac{1}{x^2 \left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Integrate[1/(x^2*(b*x^(1/3) + a*x)^(3/2)),x]","-\frac{2 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(-\frac{9}{4},\frac{3}{2};-\frac{5}{4};-\frac{a x^{2/3}}{b}\right)}{3 b x^{4/3} \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^{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^2 \sqrt{a x+b \sqrt[3]{x}}}{5 b^4 \sqrt[3]{x}}+\frac{77 a \sqrt{a x+b \sqrt[3]{x}}}{15 b^3 x}-\frac{11 \sqrt{a x+b \sqrt[3]{x}}}{3 b^2 x^{5/3}}+\frac{3}{b x^{4/3} \sqrt{a x+b \sqrt[3]{x}}}",1,"(-2*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[-9/4, 3/2, -5/4, -((a*x^(2/3))/b)])/(3*b*x^(4/3)*Sqrt[b*x^(1/3) + a*x])","C",1
165,1,64,246,0.0723816,"\int \frac{1}{x^3 \left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Integrate[1/(x^3*(b*x^(1/3) + a*x)^(3/2)),x]","-\frac{2 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(-\frac{15}{4},\frac{3}{2};-\frac{11}{4};-\frac{a x^{2/3}}{b}\right)}{5 b x^{7/3} \sqrt{a x+b \sqrt[3]{x}}}","\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{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{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,"(-2*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[-15/4, 3/2, -11/4, -((a*x^(2/3))/b)])/(5*b*x^(7/3)*Sqrt[b*x^(1/3) + a*x])","C",1
166,1,64,471,0.0831113,"\int \frac{1}{x^4 \left(b \sqrt[3]{x}+a x\right)^{3/2}} \, dx","Integrate[1/(x^4*(b*x^(1/3) + a*x)^(3/2)),x]","-\frac{2 \sqrt{\frac{a x^{2/3}}{b}+1} \, _2F_1\left(-\frac{21}{4},\frac{3}{2};-\frac{17}{4};-\frac{a x^{2/3}}{b}\right)}{7 b x^{10/3} \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}} 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^{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{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{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{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,"(-2*Sqrt[1 + (a*x^(2/3))/b]*Hypergeometric2F1[-21/4, 3/2, -17/4, -((a*x^(2/3))/b)])/(7*b*x^(10/3)*Sqrt[b*x^(1/3) + a*x])","C",1
167,1,181,371,0.1842069,"\int x^3 \sqrt{b x^{2/3}+a x} \, dx","Integrate[x^3*Sqrt[b*x^(2/3) + a*x],x]","\frac{2 \left(a \sqrt[3]{x}+b\right) \sqrt{a x+b x^{2/3}} \left(16900975 a^{12} x^4-16224936 a^{11} b x^{11/3}+15519504 a^{10} b^2 x^{10/3}-14780480 a^9 b^3 x^3+14002560 a^8 b^4 x^{8/3}-13178880 a^7 b^5 x^{7/3}+12300288 a^6 b^6 x^2-11354112 a^5 b^7 x^{5/3}+10321920 a^4 b^8 x^{4/3}-9175040 a^3 b^9 x+7864320 a^2 b^{10} x^{2/3}-6291456 a b^{11} \sqrt[3]{x}+4194304 b^{12}\right)}{152108775 a^{13} \sqrt[3]{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}",1,"(2*(b + a*x^(1/3))*Sqrt[b*x^(2/3) + a*x]*(4194304*b^12 - 6291456*a*b^11*x^(1/3) + 7864320*a^2*b^10*x^(2/3) - 9175040*a^3*b^9*x + 10321920*a^4*b^8*x^(4/3) - 11354112*a^5*b^7*x^(5/3) + 12300288*a^6*b^6*x^2 - 13178880*a^7*b^5*x^(7/3) + 14002560*a^8*b^4*x^(8/3) - 14780480*a^9*b^3*x^3 + 15519504*a^10*b^2*x^(10/3) - 16224936*a^11*b*x^(11/3) + 16900975*a^12*x^4))/(152108775*a^13*x^(1/3))","A",1
168,1,144,283,0.1299642,"\int x^2 \sqrt{b x^{2/3}+a x} \, dx","Integrate[x^2*Sqrt[b*x^(2/3) + a*x],x]","\frac{2 \left(a \sqrt[3]{x}+b\right) \sqrt{a x+b x^{2/3}} \left(230945 a^9 x^3-218790 a^8 b x^{8/3}+205920 a^7 b^2 x^{7/3}-192192 a^6 b^3 x^2+177408 a^5 b^4 x^{5/3}-161280 a^4 b^5 x^{4/3}+143360 a^3 b^6 x-122880 a^2 b^7 x^{2/3}+98304 a b^8 \sqrt[3]{x}-65536 b^9\right)}{1616615 a^{10} \sqrt[3]{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}",1,"(2*(b + a*x^(1/3))*Sqrt[b*x^(2/3) + a*x]*(-65536*b^9 + 98304*a*b^8*x^(1/3) - 122880*a^2*b^7*x^(2/3) + 143360*a^3*b^6*x - 161280*a^4*b^5*x^(4/3) + 177408*a^5*b^4*x^(5/3) - 192192*a^6*b^3*x^2 + 205920*a^7*b^2*x^(7/3) - 218790*a^8*b*x^(8/3) + 230945*a^9*x^3))/(1616615*a^10*x^(1/3))","A",1
169,1,107,195,0.090129,"\int x \sqrt{b x^{2/3}+a x} \, dx","Integrate[x*Sqrt[b*x^(2/3) + a*x],x]","\frac{2 \left(a \sqrt[3]{x}+b\right) \sqrt{a x+b x^{2/3}} \left(3003 a^6 x^2-2772 a^5 b x^{5/3}+2520 a^4 b^2 x^{4/3}-2240 a^3 b^3 x+1920 a^2 b^4 x^{2/3}-1536 a b^5 \sqrt[3]{x}+1024 b^6\right)}{15015 a^7 \sqrt[3]{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}",1,"(2*(b + a*x^(1/3))*Sqrt[b*x^(2/3) + a*x]*(1024*b^6 - 1536*a*b^5*x^(1/3) + 1920*a^2*b^4*x^(2/3) - 2240*a^3*b^3*x + 2520*a^4*b^2*x^(4/3) - 2772*a^5*b*x^(5/3) + 3003*a^6*x^2))/(15015*a^7*x^(1/3))","A",1
170,1,70,109,0.0466563,"\int \sqrt{b x^{2/3}+a x} \, dx","Integrate[Sqrt[b*x^(2/3) + a*x],x]","\frac{2 \left(a \sqrt[3]{x}+b\right) \sqrt{a x+b x^{2/3}} \left(35 a^3 x-30 a^2 b x^{2/3}+24 a b^2 \sqrt[3]{x}-16 b^3\right)}{105 a^4 \sqrt[3]{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}",1,"(2*(b + a*x^(1/3))*Sqrt[b*x^(2/3) + a*x]*(-16*b^3 + 24*a*b^2*x^(1/3) - 30*a^2*b*x^(2/3) + 35*a^3*x))/(105*a^4*x^(1/3))","A",1
171,1,23,23,0.0115582,"\int \frac{\sqrt{b x^{2/3}+a x}}{x} \, dx","Integrate[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
172,1,57,90,0.0551726,"\int \frac{\sqrt{b x^{2/3}+a x}}{x^2} \, dx","Integrate[Sqrt[b*x^(2/3) + a*x]/x^2,x]","-\frac{2 a^2 \left(a \sqrt[3]{x}+b\right) \sqrt{a x+b x^{2/3}} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b^3 \sqrt[3]{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,"(-2*a^2*(b + a*x^(1/3))*Sqrt[b*x^(2/3) + a*x]*Hypergeometric2F1[3/2, 3, 5/2, 1 + (a*x^(1/3))/b])/(b^3*x^(1/3))","C",1
173,1,57,178,0.0749909,"\int \frac{\sqrt{b x^{2/3}+a x}}{x^3} \, dx","Integrate[Sqrt[b*x^(2/3) + a*x]/x^3,x]","\frac{2 a^5 \left(a \sqrt[3]{x}+b\right) \sqrt{a x+b x^{2/3}} \, _2F_1\left(\frac{3}{2},6;\frac{5}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b^6 \sqrt[3]{x}}","-\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{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{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,"(2*a^5*(b + a*x^(1/3))*Sqrt[b*x^(2/3) + a*x]*Hypergeometric2F1[3/2, 6, 5/2, 1 + (a*x^(1/3))/b])/(b^6*x^(1/3))","C",1
174,1,57,266,0.0495065,"\int \frac{\sqrt{b x^{2/3}+a x}}{x^4} \, dx","Integrate[Sqrt[b*x^(2/3) + a*x]/x^4,x]","-\frac{2 a^8 \left(a \sqrt[3]{x}+b\right) \sqrt{a x+b x^{2/3}} \, _2F_1\left(\frac{3}{2},9;\frac{5}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b^9 \sqrt[3]{x}}","\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{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{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,"(-2*a^8*(b + a*x^(1/3))*Sqrt[b*x^(2/3) + a*x]*Hypergeometric2F1[3/2, 9, 5/2, 1 + (a*x^(1/3))/b])/(b^9*x^(1/3))","C",1
175,1,57,354,0.052217,"\int \frac{\sqrt{b x^{2/3}+a x}}{x^5} \, dx","Integrate[Sqrt[b*x^(2/3) + a*x]/x^5,x]","\frac{2 a^{11} \left(a \sqrt[3]{x}+b\right) \sqrt{a x+b x^{2/3}} \, _2F_1\left(\frac{3}{2},12;\frac{5}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b^{12} \sqrt[3]{x}}","-\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{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{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,"(2*a^11*(b + a*x^(1/3))*Sqrt[b*x^(2/3) + a*x]*Hypergeometric2F1[3/2, 12, 5/2, 1 + (a*x^(1/3))/b])/(b^12*x^(1/3))","C",1
176,1,172,343,0.1613851,"\int x^2 \left(b x^{2/3}+a x\right)^{3/2} \, dx","Integrate[x^2*(b*x^(2/3) + a*x)^(3/2),x]","\frac{2 \left(a \sqrt[3]{x}+b\right)^2 \sqrt{a x+b x^{2/3}} \left(16900975 a^{11} x^{11/3}-14872858 a^{10} b x^{10/3}+12932920 a^9 b^2 x^3-11085360 a^8 b^3 x^{8/3}+9335040 a^7 b^4 x^{7/3}-7687680 a^6 b^5 x^2+6150144 a^5 b^6 x^{5/3}-4730880 a^4 b^7 x^{4/3}+3440640 a^3 b^8 x-2293760 a^2 b^9 x^{2/3}+1310720 a b^{10} \sqrt[3]{x}-524288 b^{11}\right)}{152108775 a^{12} \sqrt[3]{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}",1,"(2*(b + a*x^(1/3))^2*Sqrt[b*x^(2/3) + a*x]*(-524288*b^11 + 1310720*a*b^10*x^(1/3) - 2293760*a^2*b^9*x^(2/3) + 3440640*a^3*b^8*x - 4730880*a^4*b^7*x^(4/3) + 6150144*a^5*b^6*x^(5/3) - 7687680*a^6*b^5*x^2 + 9335040*a^7*b^4*x^(7/3) - 11085360*a^8*b^3*x^(8/3) + 12932920*a^9*b^2*x^3 - 14872858*a^10*b*x^(10/3) + 16900975*a^11*x^(11/3)))/(152108775*a^12*x^(1/3))","A",1
177,1,135,255,0.1123876,"\int x \left(b x^{2/3}+a x\right)^{3/2} \, dx","Integrate[x*(b*x^(2/3) + a*x)^(3/2),x]","\frac{2 \left(a \sqrt[3]{x}+b\right)^2 \sqrt{a x+b x^{2/3}} \left(692835 a^8 x^{8/3}-583440 a^7 b x^{7/3}+480480 a^6 b^2 x^2-384384 a^5 b^3 x^{5/3}+295680 a^4 b^4 x^{4/3}-215040 a^3 b^5 x+143360 a^2 b^6 x^{2/3}-81920 a b^7 \sqrt[3]{x}+32768 b^8\right)}{4849845 a^9 \sqrt[3]{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}",1,"(2*(b + a*x^(1/3))^2*Sqrt[b*x^(2/3) + a*x]*(32768*b^8 - 81920*a*b^7*x^(1/3) + 143360*a^2*b^6*x^(2/3) - 215040*a^3*b^5*x + 295680*a^4*b^4*x^(4/3) - 384384*a^5*b^3*x^(5/3) + 480480*a^6*b^2*x^2 - 583440*a^7*b*x^(7/3) + 692835*a^8*x^(8/3)))/(4849845*a^9*x^(1/3))","A",1
178,1,98,169,0.0698931,"\int \left(b x^{2/3}+a x\right)^{3/2} \, dx","Integrate[(b*x^(2/3) + a*x)^(3/2),x]","\frac{2 \left(a \sqrt[3]{x}+b\right)^2 \sqrt{a x+b x^{2/3}} \left(3003 a^5 x^{5/3}-2310 a^4 b x^{4/3}+1680 a^3 b^2 x-1120 a^2 b^3 x^{2/3}+640 a b^4 \sqrt[3]{x}-256 b^5\right)}{15015 a^6 \sqrt[3]{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}",1,"(2*(b + a*x^(1/3))^2*Sqrt[b*x^(2/3) + a*x]*(-256*b^5 + 640*a*b^4*x^(1/3) - 1120*a^2*b^3*x^(2/3) + 1680*a^3*b^2*x - 2310*a^4*b*x^(4/3) + 3003*a^5*x^(5/3)))/(15015*a^6*x^(1/3))","A",1
179,1,63,84,0.0804807,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x} \, dx","Integrate[(b*x^(2/3) + a*x)^(3/2)/x,x]","\frac{2 \left(a \sqrt[3]{x}+b\right)^2 \left(35 a^2 x^{2/3}-20 a b \sqrt[3]{x}+8 b^2\right) \sqrt{a x+b x^{2/3}}}{105 a^3 \sqrt[3]{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,"(2*(b + a*x^(1/3))^2*(8*b^2 - 20*a*b*x^(1/3) + 35*a^2*x^(2/3))*Sqrt[b*x^(2/3) + a*x])/(105*a^3*x^(1/3))","A",1
180,1,88,78,0.1039339,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x^2} \, dx","Integrate[(b*x^(2/3) + a*x)^(3/2)/x^2,x]","\frac{2 \sqrt{a x+b x^{2/3}} \left(\sqrt{a \sqrt[3]{x}+b} \left(a \sqrt[3]{x}+4 b\right)-3 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a \sqrt[3]{x}+b}}{\sqrt{b}}\right)\right)}{\sqrt[3]{x} \sqrt{a \sqrt[3]{x}+b}}","-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,"(2*Sqrt[b*x^(2/3) + a*x]*(Sqrt[b + a*x^(1/3)]*(4*b + a*x^(1/3)) - 3*b^(3/2)*ArcTanh[Sqrt[b + a*x^(1/3)]/Sqrt[b]]))/(Sqrt[b + a*x^(1/3)]*x^(1/3))","A",1
181,1,61,113,0.0742066,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x^3} \, dx","Integrate[(b*x^(2/3) + a*x)^(3/2)/x^3,x]","\frac{6 a^3 \left(a \sqrt[3]{x}+b\right)^2 \sqrt{a x+b x^{2/3}} \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{5 b^4 \sqrt[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}",1,"(6*a^3*(b + a*x^(1/3))^2*Sqrt[b*x^(2/3) + a*x]*Hypergeometric2F1[5/2, 4, 7/2, 1 + (a*x^(1/3))/b])/(5*b^4*x^(1/3))","C",1
182,1,61,203,0.0537726,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x^4} \, dx","Integrate[(b*x^(2/3) + a*x)^(3/2)/x^4,x]","-\frac{6 a^6 \left(a \sqrt[3]{x}+b\right)^2 \sqrt{a x+b x^{2/3}} \, _2F_1\left(\frac{5}{2},7;\frac{7}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{5 b^7 \sqrt[3]{x}}","-\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{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{3 a^2 \sqrt{a x+b x^{2/3}}}{160 b x^{5/3}}-\frac{\left(a x+b x^{2/3}\right)^{3/2}}{2 x^3}-\frac{3 a \sqrt{a x+b x^{2/3}}}{20 x^2}",1,"(-6*a^6*(b + a*x^(1/3))^2*Sqrt[b*x^(2/3) + a*x]*Hypergeometric2F1[5/2, 7, 7/2, 1 + (a*x^(1/3))/b])/(5*b^7*x^(1/3))","C",1
183,1,61,291,0.0600149,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x^5} \, dx","Integrate[(b*x^(2/3) + a*x)^(3/2)/x^5,x]","\frac{6 a^9 \left(a \sqrt[3]{x}+b\right)^2 \sqrt{a x+b x^{2/3}} \, _2F_1\left(\frac{5}{2},10;\frac{7}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{5 b^{10} \sqrt[3]{x}}","\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{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{a^2 \sqrt{a x+b x^{2/3}}}{224 b x^{8/3}}-\frac{\left(a x+b x^{2/3}\right)^{3/2}}{3 x^4}-\frac{a \sqrt{a x+b x^{2/3}}}{16 x^3}",1,"(6*a^9*(b + a*x^(1/3))^2*Sqrt[b*x^(2/3) + a*x]*Hypergeometric2F1[5/2, 10, 7/2, 1 + (a*x^(1/3))/b])/(5*b^10*x^(1/3))","C",1
184,1,61,379,0.0963873,"\int \frac{\left(b x^{2/3}+a x\right)^{3/2}}{x^6} \, dx","Integrate[(b*x^(2/3) + a*x)^(3/2)/x^6,x]","-\frac{6 a^{12} \left(a \sqrt[3]{x}+b\right)^2 \sqrt{a x+b x^{2/3}} \, _2F_1\left(\frac{5}{2},13;\frac{7}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{5 b^{13} \sqrt[3]{x}}","-\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{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{3 a^2 \sqrt{a x+b x^{2/3}}}{1760 b x^{11/3}}-\frac{\left(a x+b x^{2/3}\right)^{3/2}}{4 x^5}-\frac{3 a \sqrt{a x+b x^{2/3}}}{88 x^4}",1,"(-6*a^12*(b + a*x^(1/3))^2*Sqrt[b*x^(2/3) + a*x]*Hypergeometric2F1[5/2, 13, 7/2, 1 + (a*x^(1/3))/b])/(5*b^13*x^(1/3))","C",1
185,1,185,401,0.228872,"\int \frac{x^4}{\sqrt{b x^{2/3}+a x}} \, dx","Integrate[x^4/Sqrt[b*x^(2/3) + a*x],x]","\frac{2 \sqrt{a x+b x^{2/3}} \left(1300075 a^{13} x^{13/3}-1352078 a^{12} b x^4+1410864 a^{11} b^2 x^{11/3}-1478048 a^{10} b^3 x^{10/3}+1555840 a^9 b^4 x^3-1647360 a^8 b^5 x^{8/3}+1757184 a^7 b^6 x^{7/3}-1892352 a^6 b^7 x^2+2064384 a^5 b^8 x^{5/3}-2293760 a^4 b^9 x^{4/3}+2621440 a^3 b^{10} x-3145728 a^2 b^{11} x^{2/3}+4194304 a b^{12} \sqrt[3]{x}-8388608 b^{13}\right)}{11700675 a^{14} \sqrt[3]{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}",1,"(2*Sqrt[b*x^(2/3) + a*x]*(-8388608*b^13 + 4194304*a*b^12*x^(1/3) - 3145728*a^2*b^11*x^(2/3) + 2621440*a^3*b^10*x - 2293760*a^4*b^9*x^(4/3) + 2064384*a^5*b^8*x^(5/3) - 1892352*a^6*b^7*x^2 + 1757184*a^7*b^6*x^(7/3) - 1647360*a^8*b^5*x^(8/3) + 1555840*a^9*b^4*x^3 - 1478048*a^10*b^3*x^(10/3) + 1410864*a^11*b^2*x^(11/3) - 1352078*a^12*b*x^4 + 1300075*a^13*x^(13/3)))/(11700675*a^14*x^(1/3))","A",1
186,1,148,313,0.1408359,"\int \frac{x^3}{\sqrt{b x^{2/3}+a x}} \, dx","Integrate[x^3/Sqrt[b*x^(2/3) + a*x],x]","\frac{2 \sqrt{a x+b x^{2/3}} \left(46189 a^{10} x^{10/3}-48620 a^9 b x^3+51480 a^8 b^2 x^{8/3}-54912 a^7 b^3 x^{7/3}+59136 a^6 b^4 x^2-64512 a^5 b^5 x^{5/3}+71680 a^4 b^6 x^{4/3}-81920 a^3 b^7 x+98304 a^2 b^8 x^{2/3}-131072 a b^9 \sqrt[3]{x}+262144 b^{10}\right)}{323323 a^{11} \sqrt[3]{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}",1,"(2*Sqrt[b*x^(2/3) + a*x]*(262144*b^10 - 131072*a*b^9*x^(1/3) + 98304*a^2*b^8*x^(2/3) - 81920*a^3*b^7*x + 71680*a^4*b^6*x^(4/3) - 64512*a^5*b^5*x^(5/3) + 59136*a^6*b^4*x^2 - 54912*a^7*b^3*x^(7/3) + 51480*a^8*b^2*x^(8/3) - 48620*a^9*b*x^3 + 46189*a^10*x^(10/3)))/(323323*a^11*x^(1/3))","A",1
187,1,111,225,0.1280764,"\int \frac{x^2}{\sqrt{b x^{2/3}+a x}} \, dx","Integrate[x^2/Sqrt[b*x^(2/3) + a*x],x]","\frac{2 \sqrt{a x+b x^{2/3}} \left(429 a^7 x^{7/3}-462 a^6 b x^2+504 a^5 b^2 x^{5/3}-560 a^4 b^3 x^{4/3}+640 a^3 b^4 x-768 a^2 b^5 x^{2/3}+1024 a b^6 \sqrt[3]{x}-2048 b^7\right)}{2145 a^8 \sqrt[3]{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}",1,"(2*Sqrt[b*x^(2/3) + a*x]*(-2048*b^7 + 1024*a*b^6*x^(1/3) - 768*a^2*b^5*x^(2/3) + 640*a^3*b^4*x - 560*a^4*b^3*x^(4/3) + 504*a^5*b^2*x^(5/3) - 462*a^6*b*x^2 + 429*a^7*x^(7/3)))/(2145*a^8*x^(1/3))","A",1
188,1,74,137,0.0835721,"\int \frac{x}{\sqrt{b x^{2/3}+a x}} \, dx","Integrate[x/Sqrt[b*x^(2/3) + a*x],x]","\frac{2 \sqrt{a x+b x^{2/3}} \left(35 a^4 x^{4/3}-40 a^3 b x+48 a^2 b^2 x^{2/3}-64 a b^3 \sqrt[3]{x}+128 b^4\right)}{105 a^5 \sqrt[3]{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}",1,"(2*Sqrt[b*x^(2/3) + a*x]*(128*b^4 - 64*a*b^3*x^(1/3) + 48*a^2*b^2*x^(2/3) - 40*a^3*b*x + 35*a^4*x^(4/3)))/(105*a^5*x^(1/3))","A",1
189,1,36,47,0.0382327,"\int \frac{1}{\sqrt{b x^{2/3}+a x}} \, dx","Integrate[1/Sqrt[b*x^(2/3) + a*x],x]","\frac{2 \left(a \sqrt[3]{x}-2 b\right) \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*(-2*b + a*x^(1/3))*Sqrt[b*x^(2/3) + a*x])/(a^2*x^(1/3))","A",1
190,1,90,61,0.1301265,"\int \frac{1}{x \sqrt{b x^{2/3}+a x}} \, dx","Integrate[1/(x*Sqrt[b*x^(2/3) + a*x]),x]","\frac{6 a \sqrt[3]{x} \left(a \sqrt[3]{x}+b\right) \left(\frac{\tanh ^{-1}\left(\sqrt{\frac{a \sqrt[3]{x}}{b}+1}\right)}{2 \sqrt{\frac{a \sqrt[3]{x}}{b}+1}}-\frac{b}{2 a \sqrt[3]{x}}\right)}{b^2 \sqrt{x^{2/3} \left(a \sqrt[3]{x}+b\right)}}","\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,"(6*a*(b + a*x^(1/3))*x^(1/3)*(-1/2*b/(a*x^(1/3)) + ArcTanh[Sqrt[1 + (a*x^(1/3))/b]]/(2*Sqrt[1 + (a*x^(1/3))/b])))/(b^2*Sqrt[(b + a*x^(1/3))*x^(2/3)])","A",1
191,1,48,153,0.0631864,"\int \frac{1}{x^2 \sqrt{b x^{2/3}+a x}} \, dx","Integrate[1/(x^2*Sqrt[b*x^(2/3) + a*x]),x]","-\frac{6 a^4 \sqrt{a x+b x^{2/3}} \, _2F_1\left(\frac{1}{2},5;\frac{3}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b^5 \sqrt[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{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{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,"(-6*a^4*Sqrt[b*x^(2/3) + a*x]*Hypergeometric2F1[1/2, 5, 3/2, 1 + (a*x^(1/3))/b])/(b^5*x^(1/3))","C",1
192,1,48,241,0.0785123,"\int \frac{1}{x^3 \sqrt{b x^{2/3}+a x}} \, dx","Integrate[1/(x^3*Sqrt[b*x^(2/3) + a*x]),x]","\frac{6 a^7 \sqrt{a x+b x^{2/3}} \, _2F_1\left(\frac{1}{2},8;\frac{3}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b^8 \sqrt[3]{x}}","\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{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{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,"(6*a^7*Sqrt[b*x^(2/3) + a*x]*Hypergeometric2F1[1/2, 8, 3/2, 1 + (a*x^(1/3))/b])/(b^8*x^(1/3))","C",1
193,1,48,329,0.0707915,"\int \frac{1}{x^4 \sqrt{b x^{2/3}+a x}} \, dx","Integrate[1/(x^4*Sqrt[b*x^(2/3) + a*x]),x]","-\frac{6 a^{10} \sqrt{a x+b x^{2/3}} \, _2F_1\left(\frac{1}{2},11;\frac{3}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b^{11} \sqrt[3]{x}}","-\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{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{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,"(-6*a^10*Sqrt[b*x^(2/3) + a*x]*Hypergeometric2F1[1/2, 11, 3/2, 1 + (a*x^(1/3))/b])/(b^11*x^(1/3))","C",1
194,1,161,336,0.1922261,"\int \frac{x^4}{\left(b x^{2/3}+a x\right)^{3/2}} \, dx","Integrate[x^4/(b*x^(2/3) + a*x)^(3/2),x]","\frac{2 \sqrt[3]{x} \left(4199 a^{11} x^{11/3}-4862 a^{10} b x^{10/3}+5720 a^9 b^2 x^3-6864 a^8 b^3 x^{8/3}+8448 a^7 b^4 x^{7/3}-10752 a^6 b^5 x^2+14336 a^5 b^6 x^{5/3}-20480 a^4 b^7 x^{4/3}+32768 a^3 b^8 x-65536 a^2 b^9 x^{2/3}+262144 a b^{10} \sqrt[3]{x}+524288 b^{11}\right)}{29393 a^{12} \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,"(2*x^(1/3)*(524288*b^11 + 262144*a*b^10*x^(1/3) - 65536*a^2*b^9*x^(2/3) + 32768*a^3*b^8*x - 20480*a^4*b^7*x^(4/3) + 14336*a^5*b^6*x^(5/3) - 10752*a^6*b^5*x^2 + 8448*a^7*b^4*x^(7/3) - 6864*a^8*b^3*x^(8/3) + 5720*a^9*b^2*x^3 - 4862*a^10*b*x^(10/3) + 4199*a^11*x^(11/3)))/(29393*a^12*Sqrt[b*x^(2/3) + a*x])","A",1
195,1,122,248,0.1271971,"\int \frac{x^3}{\left(b x^{2/3}+a x\right)^{3/2}} \, dx","Integrate[x^3/(b*x^(2/3) + a*x)^(3/2),x]","\frac{2 \left(429 a^8 x^3-528 a^7 b x^{8/3}+672 a^6 b^2 x^{7/3}-896 a^5 b^3 x^2+1280 a^4 b^4 x^{5/3}-2048 a^3 b^5 x^{4/3}+4096 a^2 b^6 x-16384 a b^7 x^{2/3}-32768 b^8 \sqrt[3]{x}\right)}{2145 a^9 \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,"(2*(-32768*b^8*x^(1/3) - 16384*a*b^7*x^(2/3) + 4096*a^2*b^6*x - 2048*a^3*b^5*x^(4/3) + 1280*a^4*b^4*x^(5/3) - 896*a^5*b^3*x^2 + 672*a^6*b^2*x^(7/3) - 528*a^7*b*x^(8/3) + 429*a^8*x^3))/(2145*a^9*Sqrt[b*x^(2/3) + a*x])","A",1
196,1,85,160,0.1002503,"\int \frac{x^2}{\left(b x^{2/3}+a x\right)^{3/2}} \, dx","Integrate[x^2/(b*x^(2/3) + a*x)^(3/2),x]","\frac{14 a^5 x^2-20 a^4 b x^{5/3}+32 a^3 b^2 x^{4/3}-64 a^2 b^3 x+256 a b^4 x^{2/3}+512 b^5 \sqrt[3]{x}}{21 a^6 \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,"(512*b^5*x^(1/3) + 256*a*b^4*x^(2/3) - 64*a^2*b^3*x + 32*a^3*b^2*x^(4/3) - 20*a^4*b*x^(5/3) + 14*a^5*x^2)/(21*a^6*Sqrt[b*x^(2/3) + a*x])","A",1
197,1,60,68,0.0634825,"\int \frac{x}{\left(b x^{2/3}+a x\right)^{3/2}} \, dx","Integrate[x/(b*x^(2/3) + a*x)^(3/2),x]","\frac{2 \left(a^2 x^{2/3}-4 a b \sqrt[3]{x}-8 b^2\right) \sqrt{a x+b x^{2/3}}}{a^3 \sqrt[3]{x} \left(a \sqrt[3]{x}+b\right)}","-\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,"(2*(-8*b^2 - 4*a*b*x^(1/3) + a^2*x^(2/3))*Sqrt[b*x^(2/3) + a*x])/(a^3*(b + a*x^(1/3))*x^(1/3))","A",1
198,1,45,60,0.0415175,"\int \frac{1}{\left(b x^{2/3}+a x\right)^{3/2}} \, dx","Integrate[(b*x^(2/3) + a*x)^(-3/2),x]","\frac{6 \sqrt[3]{x} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b \sqrt{a x+b x^{2/3}}}","\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)*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (a*x^(1/3))/b])/(b*Sqrt[b*x^(2/3) + a*x])","C",1
199,1,48,146,0.0881306,"\int \frac{1}{x \left(b x^{2/3}+a x\right)^{3/2}} \, dx","Integrate[1/(x*(b*x^(2/3) + a*x)^(3/2)),x]","-\frac{6 a^3 \sqrt[3]{x} \, _2F_1\left(-\frac{1}{2},4;\frac{1}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b^4 \sqrt{a x+b 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{105 a^2 \sqrt{a x+b x^{2/3}}}{8 b^4 x^{2/3}}+\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*a^3*x^(1/3)*Hypergeometric2F1[-1/2, 4, 1/2, 1 + (a*x^(1/3))/b])/(b^4*Sqrt[b*x^(2/3) + a*x])","C",1
200,1,48,236,0.0764359,"\int \frac{1}{x^2 \left(b x^{2/3}+a x\right)^{3/2}} \, dx","Integrate[1/(x^2*(b*x^(2/3) + a*x)^(3/2)),x]","\frac{6 a^6 \sqrt[3]{x} \, _2F_1\left(-\frac{1}{2},7;\frac{1}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b^7 \sqrt{a x+b x^{2/3}}}","-\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{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{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*a^6*x^(1/3)*Hypergeometric2F1[-1/2, 7, 1/2, 1 + (a*x^(1/3))/b])/(b^7*Sqrt[b*x^(2/3) + a*x])","C",1
201,1,48,324,0.0748896,"\int \frac{1}{x^3 \left(b x^{2/3}+a x\right)^{3/2}} \, dx","Integrate[1/(x^3*(b*x^(2/3) + a*x)^(3/2)),x]","-\frac{6 a^9 \sqrt[3]{x} \, _2F_1\left(-\frac{1}{2},10;\frac{1}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b^{10} \sqrt{a x+b x^{2/3}}}","\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{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{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*a^9*x^(1/3)*Hypergeometric2F1[-1/2, 10, 1/2, 1 + (a*x^(1/3))/b])/(b^10*Sqrt[b*x^(2/3) + a*x])","C",1
202,1,48,412,0.0890745,"\int \frac{1}{x^4 \left(b x^{2/3}+a x\right)^{3/2}} \, dx","Integrate[1/(x^4*(b*x^(2/3) + a*x)^(3/2)),x]","\frac{6 a^{12} \sqrt[3]{x} \, _2F_1\left(-\frac{1}{2},13;\frac{1}{2};\frac{\sqrt[3]{x} a}{b}+1\right)}{b^{13} \sqrt{a x+b x^{2/3}}}","-\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{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{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*a^12*x^(1/3)*Hypergeometric2F1[-1/2, 13, 1/2, 1 + (a*x^(1/3))/b])/(b^13*Sqrt[b*x^(2/3) + a*x])","C",1
203,1,17,17,0.001402,"\int x^2 \left(a x^2+b x^3\right) \, dx","Integrate[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",1
204,1,17,17,0.0011184,"\int x \left(a x^2+b x^3\right) \, dx","Integrate[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",1
205,1,17,17,0.0000826,"\int \left(a x^2+b x^3\right) \, dx","Integrate[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
206,1,17,17,0.0011329,"\int \frac{a x^2+b x^3}{x} \, dx","Integrate[(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",1
207,1,12,12,0.0006254,"\int \frac{a x^2+b x^3}{x^2} \, dx","Integrate[(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",1
208,1,30,30,0.0018799,"\int x^2 \left(a x^2+b x^3\right)^2 \, dx","Integrate[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",1
209,1,30,30,0.0021528,"\int x \left(a x^2+b x^3\right)^2 \, dx","Integrate[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",1
210,1,30,30,0.0017691,"\int \left(a x^2+b x^3\right)^2 \, dx","Integrate[(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",1
211,1,30,30,0.0018138,"\int \frac{\left(a x^2+b x^3\right)^2}{x} \, dx","Integrate[(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",1
212,1,30,30,0.0019163,"\int \frac{\left(a x^2+b x^3\right)^2}{x^2} \, dx","Integrate[(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",1
213,1,57,57,0.0283934,"\int \frac{x^6}{a x^2+b x^3} \, dx","Integrate[x^6/(a*x^2 + b*x^3),x]","\frac{a^4 \log (a+b x)}{b^5}-\frac{a^3 x}{b^4}+\frac{a^2 x^2}{2 b^3}-\frac{a x^3}{3 b^2}+\frac{x^4}{4 b}","\frac{a^4 \log (a+b x)}{b^5}-\frac{a^3 x}{b^4}+\frac{a^2 x^2}{2 b^3}-\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",1
214,1,44,44,0.0040935,"\int \frac{x^5}{a x^2+b x^3} \, dx","Integrate[x^5/(a*x^2 + b*x^3),x]","-\frac{a^3 \log (a+b x)}{b^4}+\frac{a^2 x}{b^3}-\frac{a x^2}{2 b^2}+\frac{x^3}{3 b}","-\frac{a^3 \log (a+b x)}{b^4}+\frac{a^2 x}{b^3}-\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",1
215,1,31,31,0.0038035,"\int \frac{x^4}{a x^2+b x^3} \, dx","Integrate[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",1
216,1,18,18,0.0029657,"\int \frac{x^3}{a x^2+b x^3} \, dx","Integrate[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",1
217,1,10,10,0.0011498,"\int \frac{x^2}{a x^2+b x^3} \, dx","Integrate[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",1
218,1,18,18,0.0039569,"\int \frac{x}{a x^2+b x^3} \, dx","Integrate[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",1
219,1,28,28,0.0047183,"\int \frac{1}{a x^2+b x^3} \, dx","Integrate[(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",1
220,1,42,42,0.0316044,"\int \frac{1}{x \left(a x^2+b x^3\right)} \, dx","Integrate[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*1/(a*x^2) + b/(a^2*x) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x])/a^3","A",1
221,1,56,56,0.0057912,"\int \frac{1}{x^2 \left(a x^2+b x^3\right)} \, dx","Integrate[1/(x^2*(a*x^2 + b*x^3)),x]","-\frac{b^3 \log (x)}{a^4}+\frac{b^3 \log (a+b x)}{a^4}-\frac{b^2}{a^3 x}+\frac{b}{2 a^2 x^2}-\frac{1}{3 a x^3}","-\frac{b^3 \log (x)}{a^4}+\frac{b^3 \log (a+b x)}{a^4}-\frac{b^2}{a^3 x}+\frac{b}{2 a^2 x^2}-\frac{1}{3 a x^3}",1,"-1/3*1/(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",1
222,1,54,58,0.0227747,"\int \frac{x^8}{\left(a x^2+b x^3\right)^2} \, dx","Integrate[x^8/(a*x^2 + b*x^3)^2,x]","\frac{-\frac{3 a^4}{a+b x}-12 a^3 \log (a+b x)+9 a^2 b x-3 a b^2 x^2+b^3 x^3}{3 b^5}","-\frac{a^4}{b^5 (a+b x)}-\frac{4 a^3 \log (a+b x)}{b^5}+\frac{3 a^2 x}{b^4}-\frac{a x^2}{b^3}+\frac{x^3}{3 b^2}",1,"(9*a^2*b*x - 3*a*b^2*x^2 + b^3*x^3 - (3*a^4)/(a + b*x) - 12*a^3*Log[a + b*x])/(3*b^5)","A",1
223,1,43,46,0.0145616,"\int \frac{x^7}{\left(a x^2+b x^3\right)^2} \, dx","Integrate[x^7/(a*x^2 + b*x^3)^2,x]","\frac{\frac{2 a^3}{a+b x}+6 a^2 \log (a+b x)-4 a b x+b^2 x^2}{2 b^4}","\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,"(-4*a*b*x + b^2*x^2 + (2*a^3)/(a + b*x) + 6*a^2*Log[a + b*x])/(2*b^4)","A",1
224,1,29,33,0.0141582,"\int \frac{x^6}{\left(a x^2+b x^3\right)^2} \, dx","Integrate[x^6/(a*x^2 + b*x^3)^2,x]","\frac{-\frac{a^2}{a+b x}-2 a \log (a+b x)+b x}{b^3}","-\frac{a^2}{b^3 (a+b x)}-\frac{2 a \log (a+b x)}{b^3}+\frac{x}{b^2}",1,"(b*x - a^2/(a + b*x) - 2*a*Log[a + b*x])/b^3","A",1
225,1,20,23,0.006791,"\int \frac{x^5}{\left(a x^2+b x^3\right)^2} \, dx","Integrate[x^5/(a*x^2 + b*x^3)^2,x]","\frac{\frac{a}{a+b x}+\log (a+b x)}{b^2}","\frac{a}{b^2 (a+b x)}+\frac{\log (a+b x)}{b^2}",1,"(a/(a + b*x) + Log[a + b*x])/b^2","A",1
226,1,12,12,0.0029273,"\int \frac{x^4}{\left(a x^2+b x^3\right)^2} \, dx","Integrate[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",1
227,1,24,29,0.0130963,"\int \frac{x^3}{\left(a x^2+b x^3\right)^2} \, dx","Integrate[x^3/(a*x^2 + b*x^3)^2,x]","\frac{\frac{a}{a+b x}-\log (a+b x)+\log (x)}{a^2}","-\frac{\log (a+b x)}{a^2}+\frac{\log (x)}{a^2}+\frac{1}{a (a+b x)}",1,"(a/(a + b*x) + Log[x] - Log[a + b*x])/a^2","A",1
228,1,35,42,0.0511522,"\int \frac{x^2}{\left(a x^2+b x^3\right)^2} \, dx","Integrate[x^2/(a*x^2 + b*x^3)^2,x]","-\frac{a \left(\frac{b}{a+b x}+\frac{1}{x}\right)-2 b \log (a+b x)+2 b \log (x)}{a^3}","-\frac{2 b \log (x)}{a^3}+\frac{2 b \log (a+b x)}{a^3}-\frac{b}{a^2 (a+b x)}-\frac{1}{a^2 x}",1,"-((a*(x^(-1) + b/(a + b*x)) + 2*b*Log[x] - 2*b*Log[a + b*x])/a^3)","A",1
229,1,53,58,0.0889623,"\int \frac{x}{\left(a x^2+b x^3\right)^2} \, dx","Integrate[x/(a*x^2 + b*x^3)^2,x]","\frac{a \left(\frac{2 b^2}{a+b x}-\frac{a}{x^2}+\frac{4 b}{x}\right)-6 b^2 \log (a+b x)+6 b^2 \log (x)}{2 a^4}","\frac{3 b^2 \log (x)}{a^4}-\frac{3 b^2 \log (a+b x)}{a^4}+\frac{b^2}{a^3 (a+b x)}+\frac{2 b}{a^3 x}-\frac{1}{2 a^2 x^2}",1,"(a*(-(a/x^2) + (4*b)/x + (2*b^2)/(a + b*x)) + 6*b^2*Log[x] - 6*b^2*Log[a + b*x])/(2*a^4)","A",1
230,1,66,69,0.0703674,"\int \frac{1}{\left(a x^2+b x^3\right)^2} \, dx","Integrate[(a*x^2 + b*x^3)^(-2),x]","-\frac{\frac{a \left(a^3-2 a^2 b x+6 a b^2 x^2+12 b^3 x^3\right)}{x^3 (a+b x)}-12 b^3 \log (a+b x)+12 b^3 \log (x)}{3 a^5}","-\frac{4 b^3 \log (x)}{a^5}+\frac{4 b^3 \log (a+b x)}{a^5}-\frac{b^3}{a^4 (a+b x)}-\frac{3 b^2}{a^4 x}+\frac{b}{a^3 x^2}-\frac{1}{3 a^2 x^3}",1,"-1/3*((a*(a^3 - 2*a^2*b*x + 6*a*b^2*x^2 + 12*b^3*x^3))/(x^3*(a + b*x)) + 12*b^3*Log[x] - 12*b^3*Log[a + b*x])/a^5","A",1
231,1,79,84,0.0472494,"\int \frac{1}{x \left(a x^2+b x^3\right)^2} \, dx","Integrate[1/(x*(a*x^2 + b*x^3)^2),x]","\frac{\frac{a \left(-3 a^4+5 a^3 b x-10 a^2 b^2 x^2+30 a b^3 x^3+60 b^4 x^4\right)}{x^4 (a+b x)}-60 b^4 \log (a+b x)+60 b^4 \log (x)}{12 a^6}","\frac{5 b^4 \log (x)}{a^6}-\frac{5 b^4 \log (a+b x)}{a^6}+\frac{b^4}{a^5 (a+b x)}+\frac{4 b^3}{a^5 x}-\frac{3 b^2}{2 a^4 x^2}+\frac{2 b}{3 a^3 x^3}-\frac{1}{4 a^2 x^4}",1,"((a*(-3*a^4 + 5*a^3*b*x - 10*a^2*b^2*x^2 + 30*a*b^3*x^3 + 60*b^4*x^4))/(x^4*(a + b*x)) + 60*b^4*Log[x] - 60*b^4*Log[a + b*x])/(12*a^6)","A",1
232,1,53,105,0.0415792,"\int x^2 \sqrt{a x^2+b x^3} \, dx","Integrate[x^2*Sqrt[a*x^2 + b*x^3],x]","\frac{2 \left(x^2 (a+b x)\right)^{3/2} \left(-16 a^3+24 a^2 b x-30 a b^2 x^2+35 b^3 x^3\right)}{315 b^4 x^3}","-\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*(x^2*(a + b*x))^(3/2)*(-16*a^3 + 24*a^2*b*x - 30*a*b^2*x^2 + 35*b^3*x^3))/(315*b^4*x^3)","A",1
233,1,42,80,0.0436624,"\int x \sqrt{a x^2+b x^3} \, dx","Integrate[x*Sqrt[a*x^2 + b*x^3],x]","\frac{2 \left(x^2 (a+b x)\right)^{3/2} \left(8 a^2-12 a b x+15 b^2 x^2\right)}{105 b^3 x^3}","\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,"(2*(x^2*(a + b*x))^(3/2)*(8*a^2 - 12*a*b*x + 15*b^2*x^2))/(105*b^3*x^3)","A",1
234,1,31,52,0.0244249,"\int \sqrt{a x^2+b x^3} \, dx","Integrate[Sqrt[a*x^2 + b*x^3],x]","\frac{2 \left(x^2 (a+b x)\right)^{3/2} (3 b x-2 a)}{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,"(2*(x^2*(a + b*x))^(3/2)*(-2*a + 3*b*x))/(15*b^2*x^3)","A",1
235,1,23,25,0.0107468,"\int \frac{\sqrt{a x^2+b x^3}}{x} \, dx","Integrate[Sqrt[a*x^2 + b*x^3]/x,x]","\frac{2 \left(x^2 (a+b x)\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*(x^2*(a + b*x))^(3/2))/(3*b*x^3)","A",1
236,1,53,51,0.0325247,"\int \frac{\sqrt{a x^2+b x^3}}{x^2} \, dx","Integrate[Sqrt[a*x^2 + b*x^3]/x^2,x]","\frac{2 x \left(-\sqrt{a} \sqrt{a+b x} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)+a+b x\right)}{\sqrt{x^2 (a+b 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)",1,"(2*x*(a + b*x - Sqrt[a]*Sqrt[a + b*x]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]))/Sqrt[x^2*(a + b*x)]","A",1
237,1,48,52,0.0539589,"\int \frac{\sqrt{a x^2+b x^3}}{x^3} \, dx","Integrate[Sqrt[a*x^2 + b*x^3]/x^3,x]","-\frac{b x \sqrt{\frac{b x}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)+a+b x}{\sqrt{x^2 (a+b 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}}",1,"-((a + b*x + b*x*Sqrt[1 + (b*x)/a]*ArcTanh[Sqrt[1 + (b*x)/a]])/Sqrt[x^2*(a + b*x)])","A",1
238,1,42,84,0.0132003,"\int \frac{\sqrt{a x^2+b x^3}}{x^4} \, dx","Integrate[Sqrt[a*x^2 + b*x^3]/x^4,x]","-\frac{2 b^2 \left(x^2 (a+b x)\right)^{3/2} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{b x}{a}+1\right)}{3 a^3 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,"(-2*b^2*(x^2*(a + b*x))^(3/2)*Hypergeometric2F1[3/2, 3, 5/2, 1 + (b*x)/a])/(3*a^3*x^3)","C",1
239,1,42,112,0.0136026,"\int \frac{\sqrt{a x^2+b x^3}}{x^5} \, dx","Integrate[Sqrt[a*x^2 + b*x^3]/x^5,x]","\frac{2 b^3 \left(x^2 (a+b x)\right)^{3/2} \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{b x}{a}+1\right)}{3 a^4 x^3}","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{8 a^{5/2}}+\frac{b^2 \sqrt{a x^2+b x^3}}{8 a^2 x^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,"(2*b^3*(x^2*(a + b*x))^(3/2)*Hypergeometric2F1[3/2, 4, 5/2, 1 + (b*x)/a])/(3*a^4*x^3)","C",1
240,1,80,161,0.0481566,"\int x^2 \left(a x^2+b x^3\right)^{3/2} \, dx","Integrate[x^2*(a*x^2 + b*x^3)^(3/2),x]","\frac{2 x (a+b x)^3 \left(-256 a^5+640 a^4 b x-1120 a^3 b^2 x^2+1680 a^2 b^3 x^3-2310 a b^4 x^4+3003 b^5 x^5\right)}{45045 b^6 \sqrt{x^2 (a+b 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}",1,"(2*x*(a + b*x)^3*(-256*a^5 + 640*a^4*b*x - 1120*a^3*b^2*x^2 + 1680*a^2*b^3*x^3 - 2310*a*b^4*x^4 + 3003*b^5*x^5))/(45045*b^6*Sqrt[x^2*(a + b*x)])","A",1
241,1,69,136,0.0400002,"\int x \left(a x^2+b x^3\right)^{3/2} \, dx","Integrate[x*(a*x^2 + b*x^3)^(3/2),x]","\frac{2 x (a+b x)^3 \left(128 a^4-320 a^3 b x+560 a^2 b^2 x^2-840 a b^3 x^3+1155 b^4 x^4\right)}{15015 b^5 \sqrt{x^2 (a+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,"(2*x*(a + b*x)^3*(128*a^4 - 320*a^3*b*x + 560*a^2*b^2*x^2 - 840*a*b^3*x^3 + 1155*b^4*x^4))/(15015*b^5*Sqrt[x^2*(a + b*x)])","A",1
242,1,58,108,0.0288623,"\int \left(a x^2+b x^3\right)^{3/2} \, dx","Integrate[(a*x^2 + b*x^3)^(3/2),x]","\frac{2 x (a+b x)^3 \left(-16 a^3+40 a^2 b x-70 a b^2 x^2+105 b^3 x^3\right)}{1155 b^4 \sqrt{x^2 (a+b 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}",1,"(2*x*(a + b*x)^3*(-16*a^3 + 40*a^2*b*x - 70*a*b^2*x^2 + 105*b^3*x^3))/(1155*b^4*Sqrt[x^2*(a + b*x)])","A",1
243,1,47,80,0.026509,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x} \, dx","Integrate[(a*x^2 + b*x^3)^(3/2)/x,x]","\frac{2 x (a+b x)^3 \left(8 a^2-20 a b x+35 b^2 x^2\right)}{315 b^3 \sqrt{x^2 (a+b 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}",1,"(2*x*(a + b*x)^3*(8*a^2 - 20*a*b*x + 35*b^2*x^2))/(315*b^3*Sqrt[x^2*(a + b*x)])","A",1
244,1,36,52,0.0206783,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^2} \, dx","Integrate[(a*x^2 + b*x^3)^(3/2)/x^2,x]","\frac{2 x (a+b x)^3 (5 b x-2 a)}{35 b^2 \sqrt{x^2 (a+b 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}",1,"(2*x*(a + b*x)^3*(-2*a + 5*b*x))/(35*b^2*Sqrt[x^2*(a + b*x)])","A",1
245,1,23,25,0.0143473,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^3} \, dx","Integrate[(a*x^2 + b*x^3)^(3/2)/x^3,x]","\frac{2 \left(x^2 (a+b x)\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*(x^2*(a + b*x))^(5/2))/(5*b*x^5)","A",1
246,1,68,74,0.0471329,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^4} \, dx","Integrate[(a*x^2 + b*x^3)^(3/2)/x^4,x]","\frac{2 x \sqrt{a+b x} \left(\sqrt{a+b x} (4 a+b x)-3 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)\right)}{3 \sqrt{x^2 (a+b 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}",1,"(2*x*Sqrt[a + b*x]*(Sqrt[a + b*x]*(4*a + b*x) - 3*a^(3/2)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]))/(3*Sqrt[x^2*(a + b*x)])","A",1
247,1,40,73,0.0145723,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^5} \, dx","Integrate[(a*x^2 + b*x^3)^(3/2)/x^5,x]","\frac{2 b \left(x^2 (a+b x)\right)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{b x}{a}+1\right)}{5 a^2 x^5}","\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}",1,"(2*b*(x^2*(a + b*x))^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, 1 + (b*x)/a])/(5*a^2*x^5)","C",1
248,1,72,81,0.0506097,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^6} \, dx","Integrate[(a*x^2 + b*x^3)^(3/2)/x^6,x]","-\frac{2 a^2+3 b^2 x^2 \sqrt{\frac{b x}{a}+1} \tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)+7 a b x+5 b^2 x^2}{4 x \sqrt{x^2 (a+b 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}",1,"-1/4*(2*a^2 + 7*a*b*x + 5*b^2*x^2 + 3*b^2*x^2*Sqrt[1 + (b*x)/a]*ArcTanh[Sqrt[1 + (b*x)/a]])/(x*Sqrt[x^2*(a + b*x)])","A",1
249,1,42,109,0.0220659,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^7} \, dx","Integrate[(a*x^2 + b*x^3)^(3/2)/x^7,x]","\frac{2 b^3 \left(x^2 (a+b x)\right)^{5/2} \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{b x}{a}+1\right)}{5 a^4 x^5}","\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,"(2*b^3*(x^2*(a + b*x))^(5/2)*Hypergeometric2F1[5/2, 4, 7/2, 1 + (b*x)/a])/(5*a^4*x^5)","C",1
250,1,42,137,0.0174989,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^8} \, dx","Integrate[(a*x^2 + b*x^3)^(3/2)/x^8,x]","-\frac{2 b^4 \left(x^2 (a+b x)\right)^{5/2} \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};\frac{b x}{a}+1\right)}{5 a^5 x^5}","-\frac{3 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{64 a^{5/2}}+\frac{3 b^3 \sqrt{a x^2+b x^3}}{64 a^2 x^2}-\frac{b^2 \sqrt{a x^2+b x^3}}{32 a x^3}-\frac{\left(a x^2+b x^3\right)^{3/2}}{4 x^7}-\frac{b \sqrt{a x^2+b x^3}}{8 x^4}",1,"(-2*b^4*(x^2*(a + b*x))^(5/2)*Hypergeometric2F1[5/2, 5, 7/2, 1 + (b*x)/a])/(5*a^5*x^5)","C",1
251,1,42,165,0.0285738,"\int \frac{\left(a x^2+b x^3\right)^{3/2}}{x^9} \, dx","Integrate[(a*x^2 + b*x^3)^(3/2)/x^9,x]","\frac{2 b^5 \left(x^2 (a+b x)\right)^{5/2} \, _2F_1\left(\frac{5}{2},6;\frac{7}{2};\frac{b x}{a}+1\right)}{5 a^6 x^5}","\frac{3 b^5 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{128 a^{7/2}}-\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{b^2 \sqrt{a x^2+b x^3}}{80 a x^4}-\frac{\left(a x^2+b x^3\right)^{3/2}}{5 x^8}-\frac{3 b \sqrt{a x^2+b x^3}}{40 x^5}",1,"(2*b^5*(x^2*(a + b*x))^(5/2)*Hypergeometric2F1[5/2, 6, 7/2, 1 + (b*x)/a])/(5*a^6*x^5)","C",1
252,1,53,103,0.0412782,"\int \frac{x^4}{\sqrt{a x^2+b x^3}} \, dx","Integrate[x^4/Sqrt[a*x^2 + b*x^3],x]","\frac{2 \sqrt{x^2 (a+b x)} \left(-16 a^3+8 a^2 b x-6 a b^2 x^2+5 b^3 x^3\right)}{35 b^4 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}",1,"(2*Sqrt[x^2*(a + b*x)]*(-16*a^3 + 8*a^2*b*x - 6*a*b^2*x^2 + 5*b^3*x^3))/(35*b^4*x)","A",1
253,1,42,75,0.0273461,"\int \frac{x^3}{\sqrt{a x^2+b x^3}} \, dx","Integrate[x^3/Sqrt[a*x^2 + b*x^3],x]","\frac{2 \sqrt{x^2 (a+b x)} \left(8 a^2-4 a b x+3 b^2 x^2\right)}{15 b^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}",1,"(2*Sqrt[x^2*(a + b*x)]*(8*a^2 - 4*a*b*x + 3*b^2*x^2))/(15*b^3*x)","A",1
254,1,30,49,0.0214033,"\int \frac{x^2}{\sqrt{a x^2+b x^3}} \, dx","Integrate[x^2/Sqrt[a*x^2 + b*x^3],x]","\frac{2 (b x-2 a) \sqrt{x^2 (a+b x)}}{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*(-2*a + b*x)*Sqrt[x^2*(a + b*x)])/(3*b^2*x)","A",1
255,1,21,23,0.0082036,"\int \frac{x}{\sqrt{a x^2+b x^3}} \, dx","Integrate[x/Sqrt[a*x^2 + b*x^3],x]","\frac{2 \sqrt{x^2 (a+b x)}}{b x}","\frac{2 \sqrt{a x^2+b x^3}}{b x}",1,"(2*Sqrt[x^2*(a + b*x)])/(b*x)","A",1
256,1,46,30,0.0101774,"\int \frac{1}{\sqrt{a x^2+b x^3}} \, dx","Integrate[1/Sqrt[a*x^2 + b*x^3],x]","-\frac{2 x \sqrt{a+b x} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{x^2 (a+b x)}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{\sqrt{a}}",1,"(-2*x*Sqrt[a + b*x]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(Sqrt[a]*Sqrt[x^2*(a + b*x)])","A",1
257,1,66,54,0.0638109,"\int \frac{1}{x \sqrt{a x^2+b x^3}} \, dx","Integrate[1/(x*Sqrt[a*x^2 + b*x^3]),x]","\frac{2 b x (a+b x) \left(\frac{\tanh ^{-1}\left(\sqrt{\frac{b x}{a}+1}\right)}{2 \sqrt{\frac{b x}{a}+1}}-\frac{a}{2 b x}\right)}{a^2 \sqrt{x^2 (a+b 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}",1,"(2*b*x*(a + b*x)*(-1/2*a/(b*x) + ArcTanh[Sqrt[1 + (b*x)/a]]/(2*Sqrt[1 + (b*x)/a])))/(a^2*Sqrt[x^2*(a + b*x)])","A",1
258,1,40,87,0.0108928,"\int \frac{1}{x^2 \sqrt{a x^2+b x^3}} \, dx","Integrate[1/(x^2*Sqrt[a*x^2 + b*x^3]),x]","-\frac{2 b^2 \sqrt{x^2 (a+b x)} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{b x}{a}+1\right)}{a^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}",1,"(-2*b^2*Sqrt[x^2*(a + b*x)]*Hypergeometric2F1[1/2, 3, 3/2, 1 + (b*x)/a])/(a^3*x)","C",1
259,1,40,115,0.0112867,"\int \frac{1}{x^3 \sqrt{a x^2+b x^3}} \, dx","Integrate[1/(x^3*Sqrt[a*x^2 + b*x^3]),x]","\frac{2 b^3 \sqrt{x^2 (a+b x)} \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};\frac{b x}{a}+1\right)}{a^4 x}","\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^2 \sqrt{a x^2+b x^3}}{8 a^3 x^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,"(2*b^3*Sqrt[x^2*(a + b*x)]*Hypergeometric2F1[1/2, 4, 3/2, 1 + (b*x)/a])/(a^4*x)","C",1
260,1,50,98,0.0345694,"\int \frac{x^6}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Integrate[x^6/(a*x^2 + b*x^3)^(3/2),x]","\frac{2 x \left(16 a^3+8 a^2 b x-2 a b^2 x^2+b^3 x^3\right)}{5 b^4 \sqrt{x^2 (a+b x)}}","\frac{32 a^2 \sqrt{a x^2+b x^3}}{5 b^4 x}-\frac{16 a \sqrt{a x^2+b x^3}}{5 b^3}+\frac{12 x \sqrt{a x^2+b x^3}}{5 b^2}-\frac{2 x^4}{b \sqrt{a x^2+b x^3}}",1,"(2*x*(16*a^3 + 8*a^2*b*x - 2*a*b^2*x^2 + b^3*x^3))/(5*b^4*Sqrt[x^2*(a + b*x)])","A",1
261,1,39,72,0.0183379,"\int \frac{x^5}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Integrate[x^5/(a*x^2 + b*x^3)^(3/2),x]","\frac{2 x \left(-8 a^2-4 a b x+b^2 x^2\right)}{3 b^3 \sqrt{x^2 (a+b x)}}","-\frac{16 a \sqrt{a x^2+b x^3}}{3 b^3 x}+\frac{8 \sqrt{a x^2+b x^3}}{3 b^2}-\frac{2 x^3}{b \sqrt{a x^2+b x^3}}",1,"(2*x*(-8*a^2 - 4*a*b*x + b^2*x^2))/(3*b^3*Sqrt[x^2*(a + b*x)])","A",1
262,1,26,47,0.0135163,"\int \frac{x^4}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Integrate[x^4/(a*x^2 + b*x^3)^(3/2),x]","\frac{2 x (2 a+b x)}{b^2 \sqrt{x^2 (a+b 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}}",1,"(2*x*(2*a + b*x))/(b^2*Sqrt[x^2*(a + b*x)])","A",1
263,1,19,21,0.0066686,"\int \frac{x^3}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Integrate[x^3/(a*x^2 + b*x^3)^(3/2),x]","-\frac{2 x}{b \sqrt{x^2 (a+b x)}}","-\frac{2 x}{b \sqrt{a x^2+b x^3}}",1,"(-2*x)/(b*Sqrt[x^2*(a + b*x)])","A",1
264,1,35,52,0.0289716,"\int \frac{x^2}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Integrate[x^2/(a*x^2 + b*x^3)^(3/2),x]","\frac{2 x \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x}{a}+1\right)}{a \sqrt{x^2 (a+b 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}}",1,"(2*x*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x)/a])/(a*Sqrt[x^2*(a + b*x)])","C",1
265,1,36,75,0.0097447,"\int \frac{x}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Integrate[x/(a*x^2 + b*x^3)^(3/2),x]","-\frac{2 b x \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{b x}{a}+1\right)}{a^2 \sqrt{x^2 (a+b x)}}","\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{a^{5/2}}-\frac{3 \sqrt{a x^2+b x^3}}{a^2 x^2}+\frac{2}{a \sqrt{a x^2+b x^3}}",1,"(-2*b*x*Hypergeometric2F1[-1/2, 2, 1/2, 1 + (b*x)/a])/(a^2*Sqrt[x^2*(a + b*x)])","C",1
266,1,38,110,0.018513,"\int \frac{1}{\left(a x^2+b x^3\right)^{3/2}} \, dx","Integrate[(a*x^2 + b*x^3)^(-3/2),x]","\frac{2 b^2 x \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{b x}{a}+1\right)}{a^3 \sqrt{x^2 (a+b 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}}",1,"(2*b^2*x*Hypergeometric2F1[-1/2, 3, 1/2, 1 + (b*x)/a])/(a^3*Sqrt[x^2*(a + b*x)])","C",1
267,1,38,138,0.0099064,"\int \frac{1}{x \left(a x^2+b x^3\right)^{3/2}} \, dx","Integrate[1/(x*(a*x^2 + b*x^3)^(3/2)),x]","-\frac{2 b^3 x \, _2F_1\left(-\frac{1}{2},4;\frac{1}{2};\frac{b x}{a}+1\right)}{a^4 \sqrt{x^2 (a+b x)}}","\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^2 \sqrt{a x^2+b x^3}}{8 a^4 x^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*b^3*x*Hypergeometric2F1[-1/2, 4, 1/2, 1 + (b*x)/a])/(a^4*Sqrt[x^2*(a + b*x)])","C",1
268,1,38,166,0.0118132,"\int \frac{1}{x^2 \left(a x^2+b x^3\right)^{3/2}} \, dx","Integrate[1/(x^2*(a*x^2 + b*x^3)^(3/2)),x]","\frac{2 b^4 x \, _2F_1\left(-\frac{1}{2},5;\frac{1}{2};\frac{b x}{a}+1\right)}{a^5 \sqrt{x^2 (a+b x)}}","-\frac{315 b^4 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^3}}\right)}{64 a^{11/2}}+\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{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*b^4*x*Hypergeometric2F1[-1/2, 5, 1/2, 1 + (b*x)/a])/(a^5*Sqrt[x^2*(a + b*x)])","C",1
269,1,104,125,0.1347366,"\int \frac{x^{7/2}}{\sqrt{a x^2+b x^3}} \, dx","Integrate[x^(7/2)/Sqrt[a*x^2 + b*x^3],x]","\frac{\sqrt{x^2 (a+b x)} \left(\sqrt{b} \sqrt{x} \sqrt{\frac{b x}{a}+1} \left(15 a^2-10 a b x+8 b^2 x^2\right)-15 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)\right)}{24 b^{7/2} x \sqrt{\frac{b x}{a}+1}}","-\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^2 \sqrt{a x^2+b x^3}}{8 b^3 \sqrt{x}}-\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,"(Sqrt[x^2*(a + b*x)]*(Sqrt[b]*Sqrt[x]*Sqrt[1 + (b*x)/a]*(15*a^2 - 10*a*b*x + 8*b^2*x^2) - 15*a^(5/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]]))/(24*b^(7/2)*x*Sqrt[1 + (b*x)/a])","A",1
270,1,90,95,0.0545585,"\int \frac{x^{5/2}}{\sqrt{a x^2+b x^3}} \, dx","Integrate[x^(5/2)/Sqrt[a*x^2 + b*x^3],x]","\frac{3 a^{5/2} x \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\sqrt{b} x^{3/2} \left(-3 a^2-a b x+2 b^2 x^2\right)}{4 b^{5/2} \sqrt{x^2 (a+b 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}",1,"(Sqrt[b]*x^(3/2)*(-3*a^2 - a*b*x + 2*b^2*x^2) + 3*a^(5/2)*x*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(5/2)*Sqrt[x^2*(a + b*x)])","A",1
271,1,73,60,0.0433457,"\int \frac{x^{3/2}}{\sqrt{a x^2+b x^3}} \, dx","Integrate[x^(3/2)/Sqrt[a*x^2 + b*x^3],x]","\frac{\sqrt{b} x^{3/2} (a+b x)-a^{3/2} x \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{3/2} \sqrt{x^2 (a+b 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}}",1,"(Sqrt[b]*x^(3/2)*(a + b*x) - a^(3/2)*x*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(b^(3/2)*Sqrt[x^2*(a + b*x)])","A",1
272,1,55,34,0.0178519,"\int \frac{\sqrt{x}}{\sqrt{a x^2+b x^3}} \, dx","Integrate[Sqrt[x]/Sqrt[a*x^2 + b*x^3],x]","\frac{2 \sqrt{a} x \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b} \sqrt{x^2 (a+b x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a x^2+b x^3}}\right)}{\sqrt{b}}",1,"(2*Sqrt[a]*x*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[b]*Sqrt[x^2*(a + b*x)])","A",1
273,1,23,25,0.0103254,"\int \frac{1}{\sqrt{x} \sqrt{a x^2+b x^3}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[a*x^2 + b*x^3]),x]","-\frac{2 \sqrt{x^2 (a+b x)}}{a x^{3/2}}","-\frac{2 \sqrt{a x^2+b x^3}}{a x^{3/2}}",1,"(-2*Sqrt[x^2*(a + b*x)])/(a*x^(3/2))","A",1
274,1,31,56,0.0159241,"\int \frac{1}{x^{3/2} \sqrt{a x^2+b x^3}} \, dx","Integrate[1/(x^(3/2)*Sqrt[a*x^2 + b*x^3]),x]","-\frac{2 (a-2 b x) \sqrt{x^2 (a+b x)}}{3 a^2 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*(a - 2*b*x)*Sqrt[x^2*(a + b*x)])/(3*a^2*x^(5/2))","A",1
275,1,44,86,0.0164251,"\int \frac{1}{x^{5/2} \sqrt{a x^2+b x^3}} \, dx","Integrate[1/(x^(5/2)*Sqrt[a*x^2 + b*x^3]),x]","-\frac{2 \sqrt{x^2 (a+b x)} \left(3 a^2-4 a b x+8 b^2 x^2\right)}{15 a^3 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[x^2*(a + b*x)]*(3*a^2 - 4*a*b*x + 8*b^2*x^2))/(15*a^3*x^(7/2))","A",1
276,1,55,116,0.0201432,"\int \frac{1}{x^{7/2} \sqrt{a x^2+b x^3}} \, dx","Integrate[1/(x^(7/2)*Sqrt[a*x^2 + b*x^3]),x]","\frac{2 \sqrt{x^2 (a+b x)} \left(-5 a^3+6 a^2 b x-8 a b^2 x^2+16 b^3 x^3\right)}{35 a^4 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[x^2*(a + b*x)]*(-5*a^3 + 6*a^2*b*x - 8*a*b^2*x^2 + 16*b^3*x^3))/(35*a^4*x^(9/2))","A",1
277,1,59,61,0.0216307,"\int x^{1-3 n} \left(a x^2+b x^3\right)^n \, dx","Integrate[x^(1 - 3*n)*(a*x^2 + b*x^3)^n,x]","\frac{x^{2-3 n} \left(x^2 (a+b x)\right)^n \left(\frac{b x}{a}+1\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)*(x^2*(a + b*x))^n*Hypergeometric2F1[2 - n, -n, 3 - n, -((b*x)/a)])/((2 - n)*(1 + (b*x)/a)^n)","A",1
278,1,59,48,0.0135315,"\int x^{-3 n} \left(a x^2+b x^3\right)^n \, dx","Integrate[(a*x^2 + b*x^3)^n/x^(3*n),x]","\frac{x^{1-3 n} \left(x^2 (a+b x)\right)^n \left(\frac{b x}{a}+1\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)*(x^2*(a + b*x))^n*Hypergeometric2F1[1 - n, -n, 2 - n, -((b*x)/a)])/((1 - n)*(1 + (b*x)/a)^n)","A",1
279,1,52,54,0.0083837,"\int x^{-1-3 n} \left(a x^2+b x^3\right)^n \, dx","Integrate[x^(-1 - 3*n)*(a*x^2 + b*x^3)^n,x]","-\frac{x^{-3 n} \left(x^2 (a+b x)\right)^n \left(\frac{b x}{a}+1\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,"-(((x^2*(a + b*x))^n*Hypergeometric2F1[-n, -n, 1 - n, -((b*x)/a)])/(n*x^(3*n)*(1 + (b*x)/a)^n))","A",1
280,1,30,32,0.0162845,"\int x^{-2-3 n} \left(a x^2+b x^3\right)^n \, dx","Integrate[x^(-2 - 3*n)*(a*x^2 + b*x^3)^n,x]","-\frac{x^{-3 (n+1)} \left(x^2 (a+b x)\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,"-((x^2*(a + b*x))^(1 + n)/(a*(1 + n)*x^(3*(1 + n))))","A",1
281,1,44,70,0.0233577,"\int x^{-3-3 n} \left(a x^2+b x^3\right)^n \, dx","Integrate[x^(-3 - 3*n)*(a*x^2 + b*x^3)^n,x]","-\frac{x^{-3 n-4} (a n+a-b x) \left(x^2 (a+b x)\right)^{n+1}}{a^2 (n+1) (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 + a*n - b*x)*(x^2*(a + b*x))^(1 + n))/(a^2*(1 + n)*(2 + n)))","A",1
282,1,72,116,0.031794,"\int x^{-4-3 n} \left(a x^2+b x^3\right)^n \, dx","Integrate[x^(-4 - 3*n)*(a*x^2 + b*x^3)^n,x]","-\frac{x^{-3 (n+1)} (a+b x) \left(x^2 (a+b x)\right)^n \left(a^2 \left(n^2+3 n+2\right)-2 a b (n+1) x+2 b^2 x^2\right)}{a^3 (n+1) (n+2) (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,"-(((a + b*x)*(x^2*(a + b*x))^n*(a^2*(2 + 3*n + n^2) - 2*a*b*(1 + n)*x + 2*b^2*x^2))/(a^3*(1 + n)*(2 + n)*(3 + n)*x^(3*(1 + n))))","A",1
283,1,24,19,0.0081934,"\int \frac{x^{11}}{\left(a x^2+b x^5\right)^3} \, dx","Integrate[x^11/(a*x^2 + b*x^5)^3,x]","-\frac{a+2 b x^3}{6 b^2 \left(a+b x^3\right)^2}","\frac{x^6}{6 a \left(a+b x^3\right)^2}",1,"-1/6*(a + 2*b*x^3)/(b^2*(a + b*x^3)^2)","A",1
284,1,46,80,0.0335628,"\int \frac{x^9}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^9/Sqrt[a*x^2 + b*x^5],x]","\frac{2 \sqrt{x^2 \left(a+b x^3\right)} \left(8 a^2-4 a b x^3+3 b^2 x^6\right)}{45 b^3 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}",1,"(2*Sqrt[x^2*(a + b*x^3)]*(8*a^2 - 4*a*b*x^3 + 3*b^2*x^6))/(45*b^3*x)","A",1
285,1,34,52,0.018712,"\int \frac{x^6}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^6/Sqrt[a*x^2 + b*x^5],x]","\frac{2 \left(b x^3-2 a\right) \sqrt{x^2 \left(a+b x^3\right)}}{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,"(2*(-2*a + b*x^3)*Sqrt[x^2*(a + b*x^3)])/(9*b^2*x)","A",1
286,1,25,25,0.0084607,"\int \frac{x^3}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^3/Sqrt[a*x^2 + b*x^5],x]","\frac{2 \sqrt{x^2 \left(a+b x^3\right)}}{3 b x}","\frac{2 \sqrt{a x^2+b x^5}}{3 b x}",1,"(2*Sqrt[x^2*(a + b*x^3)])/(3*b*x)","A",1
287,1,54,32,0.0109349,"\int \frac{1}{\sqrt{a x^2+b x^5}} \, dx","Integrate[1/Sqrt[a*x^2 + b*x^5],x]","-\frac{2 x \sqrt{a+b x^3} \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a} \sqrt{x^2 \left(a+b x^3\right)}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^5}}\right)}{3 \sqrt{a}}",1,"(-2*x*Sqrt[a + b*x^3]*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a]*Sqrt[x^2*(a + b*x^3)])","A",1
288,1,71,59,0.0708832,"\int \frac{1}{x^3 \sqrt{a x^2+b x^5}} \, dx","Integrate[1/(x^3*Sqrt[a*x^2 + b*x^5]),x]","\frac{2 b \sqrt{x^2 \left(a+b x^3\right)} \left(\frac{\tanh ^{-1}\left(\sqrt{\frac{b x^3}{a}+1}\right)}{2 \sqrt{\frac{b x^3}{a}+1}}-\frac{a}{2 b x^3}\right)}{3 a^2 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}",1,"(2*b*Sqrt[x^2*(a + b*x^3)]*(-1/2*a/(b*x^3) + ArcTanh[Sqrt[1 + (b*x^3)/a]]/(2*Sqrt[1 + (b*x^3)/a])))/(3*a^2*x)","A",1
289,1,68,238,0.0279363,"\int \frac{x^4}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^4/Sqrt[a*x^2 + b*x^5],x]","\frac{2 x^2 \left(-a \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a}\right)+a+b x^3\right)}{5 b \sqrt{x^2 \left(a+b x^3\right)}}","\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*x^2*(a + b*x^3 - a*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/3, 1/2, 4/3, -((b*x^3)/a)]))/(5*b*Sqrt[x^2*(a + b*x^3)])","C",1
290,1,52,212,0.0098253,"\int \frac{x}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x/Sqrt[a*x^2 + b*x^5],x]","\frac{x^2 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a}\right)}{\sqrt{x^2 \left(a+b x^3\right)}}","\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,"(x^2*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/3, 1/2, 4/3, -((b*x^3)/a)])/Sqrt[x^2*(a + b*x^3)]","C",1
291,1,55,243,0.0134587,"\int \frac{1}{x^2 \sqrt{a x^2+b x^5}} \, dx","Integrate[1/(x^2*Sqrt[a*x^2 + b*x^5]),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a}\right)}{2 x \sqrt{x^2 \left(a+b x^3\right)}}","-\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,"-1/2*(Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-2/3, 1/2, 1/3, -((b*x^3)/a)])/(x*Sqrt[x^2*(a + b*x^3)])","C",1
292,1,68,514,0.0252621,"\int \frac{x^5}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^5/Sqrt[a*x^2 + b*x^5],x]","\frac{2 x^3 \left(-a \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)+a+b x^3\right)}{7 b \sqrt{x^2 \left(a+b x^3\right)}}","-\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,"(2*x^3*(a + b*x^3 - a*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, 2/3, 5/3, -((b*x^3)/a)]))/(7*b*Sqrt[x^2*(a + b*x^3)])","C",1
293,1,55,484,0.0299785,"\int \frac{x^2}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^2/Sqrt[a*x^2 + b*x^5],x]","\frac{x^3 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 \sqrt{x^2 \left(a+b x^3\right)}}","\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,"(x^3*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, 2/3, 5/3, -((b*x^3)/a)])/(2*Sqrt[x^2*(a + b*x^3)])","C",1
294,1,50,510,0.0113506,"\int \frac{1}{x \sqrt{a x^2+b x^5}} \, dx","Integrate[1/(x*Sqrt[a*x^2 + b*x^5]),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a}\right)}{\sqrt{x^2 \left(a+b x^3\right)}}","\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{a x^2+b x^5}}{a x^2}+\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}}",1,"-((Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-1/3, 1/2, 2/3, -((b*x^3)/a)])/Sqrt[x^2*(a + b*x^3)])","C",1
295,1,86,265,0.052651,"\int \frac{x^{13/2}}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^(13/2)/Sqrt[a*x^2 + b*x^5],x]","\frac{x^{3/2} \left(7 a^2 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{b x^3}{a}\right)-7 a^2-3 a b x^3+4 b^2 x^6\right)}{20 b^2 \sqrt{x^2 \left(a+b x^3\right)}}","\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,"(x^(3/2)*(-7*a^2 - 3*a*b*x^3 + 4*b^2*x^6 + 7*a^2*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/6, 1/2, 7/6, -((b*x^3)/a)]))/(20*b^2*Sqrt[x^2*(a + b*x^3)])","C",1
296,1,70,525,0.0294186,"\int \frac{x^{11/2}}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^(11/2)/Sqrt[a*x^2 + b*x^5],x]","\frac{x^{7/2} \left(-a \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};-\frac{b x^3}{a}\right)+a+b x^3\right)}{4 b \sqrt{x^2 \left(a+b x^3\right)}}","\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,"(x^(7/2)*(a + b*x^3 - a*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, 5/6, 11/6, -((b*x^3)/a)]))/(4*b*Sqrt[x^2*(a + b*x^3)])","C",1
297,1,81,65,0.0421054,"\int \frac{x^{9/2}}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^(9/2)/Sqrt[a*x^2 + b*x^5],x]","\frac{\sqrt{b} x^{5/2} \left(a+b x^3\right)-a x \sqrt{a+b x^3} \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a+b x^3}}\right)}{3 b^{3/2} \sqrt{x^2 \left(a+b x^3\right)}}","\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[b]*x^(5/2)*(a + b*x^3) - a*x*Sqrt[a + b*x^3]*ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a + b*x^3]])/(3*b^(3/2)*Sqrt[x^2*(a + b*x^3)])","A",1
298,1,70,237,0.0350269,"\int \frac{x^{7/2}}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^(7/2)/Sqrt[a*x^2 + b*x^5],x]","\frac{x^{3/2} \left(-a \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{b x^3}{a}\right)+a+b x^3\right)}{2 b \sqrt{x^2 \left(a+b x^3\right)}}","\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,"(x^(3/2)*(a + b*x^3 - a*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/6, 1/2, 7/6, -((b*x^3)/a)]))/(2*b*Sqrt[x^2*(a + b*x^3)])","C",1
299,1,57,492,0.0240594,"\int \frac{x^{5/2}}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^(5/2)/Sqrt[a*x^2 + b*x^5],x]","\frac{2 x^{7/2} \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};-\frac{b x^3}{a}\right)}{5 \sqrt{x^2 \left(a+b x^3\right)}}","-\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,"(2*x^(7/2)*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, 5/6, 11/6, -((b*x^3)/a)])/(5*Sqrt[x^2*(a + b*x^3)])","C",1
300,1,59,36,0.0232377,"\int \frac{x^{3/2}}{\sqrt{a x^2+b x^5}} \, dx","Integrate[x^(3/2)/Sqrt[a*x^2 + b*x^5],x]","\frac{2 x \sqrt{a+b x^3} \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a+b x^3}}\right)}{3 \sqrt{b} \sqrt{x^2 \left(a+b x^3\right)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a x^2+b x^5}}\right)}{3 \sqrt{b}}",1,"(2*x*Sqrt[a + b*x^3]*ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a + b*x^3]])/(3*Sqrt[b]*Sqrt[x^2*(a + b*x^3)])","A",1
301,1,55,203,0.0141989,"\int \frac{\sqrt{x}}{\sqrt{a x^2+b x^5}} \, dx","Integrate[Sqrt[x]/Sqrt[a*x^2 + b*x^5],x]","\frac{2 x^{3/2} \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{b x^3}{a}\right)}{\sqrt{x^2 \left(a+b x^3\right)}}","\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,"(2*x^(3/2)*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/6, 1/2, 7/6, -((b*x^3)/a)])/Sqrt[x^2*(a + b*x^3)]","C",1
302,1,55,519,0.0252234,"\int \frac{1}{\sqrt{x} \sqrt{a x^2+b x^5}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[a*x^2 + b*x^5]),x]","-\frac{2 \sqrt{x} \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};-\frac{b x^3}{a}\right)}{\sqrt{x^2 \left(a+b x^3\right)}}","-\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 \sqrt{a x^2+b x^5}}{a x^{3/2}}+\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}}",1,"(-2*Sqrt[x]*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-1/6, 1/2, 5/6, -((b*x^3)/a)])/Sqrt[x^2*(a + b*x^3)]","C",1
303,1,27,27,0.011732,"\int \frac{1}{x^{3/2} \sqrt{a x^2+b x^5}} \, dx","Integrate[1/(x^(3/2)*Sqrt[a*x^2 + b*x^5]),x]","-\frac{2 \sqrt{x^2 \left(a+b x^3\right)}}{3 a x^{5/2}}","-\frac{2 \sqrt{a x^2+b x^5}}{3 a x^{5/2}}",1,"(-2*Sqrt[x^2*(a + b*x^3)])/(3*a*x^(5/2))","A",1
304,1,57,235,0.0157208,"\int \frac{1}{x^{5/2} \sqrt{a x^2+b x^5}} \, dx","Integrate[1/(x^(5/2)*Sqrt[a*x^2 + b*x^5]),x]","-\frac{2 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{1}{6};-\frac{b x^3}{a}\right)}{5 x^{3/2} \sqrt{x^2 \left(a+b x^3\right)}}","-\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[1 + (b*x^3)/a]*Hypergeometric2F1[-5/6, 1/2, 1/6, -((b*x^3)/a)])/(5*x^(3/2)*Sqrt[x^2*(a + b*x^3)])","C",1
305,1,57,555,0.0262633,"\int \frac{1}{x^{7/2} \sqrt{a x^2+b x^5}} \, dx","Integrate[1/(x^(7/2)*Sqrt[a*x^2 + b*x^5]),x]","-\frac{2 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{7}{6},\frac{1}{2};-\frac{1}{6};-\frac{b x^3}{a}\right)}{7 x^{5/2} \sqrt{x^2 \left(a+b x^3\right)}}","\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 \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{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,"(-2*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[-7/6, 1/2, -1/6, -((b*x^3)/a)])/(7*x^(5/2)*Sqrt[x^2*(a + b*x^3)])","C",1
306,1,35,56,0.0185764,"\int \frac{1}{x^{9/2} \sqrt{a x^2+b x^5}} \, dx","Integrate[1/(x^(9/2)*Sqrt[a*x^2 + b*x^5]),x]","-\frac{2 \left(a-2 b x^3\right) \sqrt{x^2 \left(a+b x^3\right)}}{9 a^2 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*(a - 2*b*x^3)*Sqrt[x^2*(a + b*x^3)])/(9*a^2*x^(11/2))","A",1
307,1,57,265,0.0165155,"\int \frac{1}{x^{11/2} \sqrt{a x^2+b x^5}} \, dx","Integrate[1/(x^(11/2)*Sqrt[a*x^2 + b*x^5]),x]","-\frac{2 \sqrt{\frac{b x^3}{a}+1} \, _2F_1\left(-\frac{11}{6},\frac{1}{2};-\frac{5}{6};-\frac{b x^3}{a}\right)}{11 x^{9/2} \sqrt{x^2 \left(a+b x^3\right)}}","\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[1 + (b*x^3)/a]*Hypergeometric2F1[-11/6, 1/2, -5/6, -((b*x^3)/a)])/(11*x^(9/2)*Sqrt[x^2*(a + b*x^3)])","C",1
308,1,28,28,0.0051659,"\int \frac{x}{a x^3+b x^4} \, dx","Integrate[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",1
309,1,42,42,0.0049213,"\int \frac{1}{a x^3+b x^4} \, dx","Integrate[(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*1/(a*x^2) + b/(a^2*x) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x])/a^3","A",1
310,1,94,112,0.1955084,"\int \frac{x^4}{\sqrt{a x^3+b x^4}} \, dx","Integrate[x^4/Sqrt[a*x^3 + b*x^4],x]","\frac{\sqrt{x^3 (a+b x)} \left(\sqrt{b} \sqrt{x} \left(15 a^2-10 a b x+8 b^2 x^2\right)-\frac{15 a^{5/2} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{\frac{b x}{a}+1}}\right)}{24 b^{7/2} x^{3/2}}","-\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^2 \sqrt{a x^3+b x^4}}{8 b^3 x}-\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,"(Sqrt[x^3*(a + b*x)]*(Sqrt[b]*Sqrt[x]*(15*a^2 - 10*a*b*x + 8*b^2*x^2) - (15*a^(5/2)*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/Sqrt[1 + (b*x)/a]))/(24*b^(7/2)*x^(3/2))","A",1
311,1,92,86,0.0728465,"\int \frac{x^3}{\sqrt{a x^3+b x^4}} \, dx","Integrate[x^3/Sqrt[a*x^3 + b*x^4],x]","\frac{3 a^{5/2} x^{3/2} \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)+\sqrt{b} x^2 \left(-3 a^2-a b x+2 b^2 x^2\right)}{4 b^{5/2} \sqrt{x^3 (a+b 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}",1,"(Sqrt[b]*x^2*(-3*a^2 - a*b*x + 2*b^2*x^2) + 3*a^(5/2)*x^(3/2)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(5/2)*Sqrt[x^3*(a + b*x)])","A",1
312,1,75,56,0.0504219,"\int \frac{x^2}{\sqrt{a x^3+b x^4}} \, dx","Integrate[x^2/Sqrt[a*x^3 + b*x^4],x]","\frac{\sqrt{b} x^2 (a+b x)-a^{3/2} x^{3/2} \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{3/2} \sqrt{x^3 (a+b 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}}",1,"(Sqrt[b]*x^2*(a + b*x) - a^(3/2)*x^(3/2)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(b^(3/2)*Sqrt[x^3*(a + b*x)])","A",1
313,1,59,32,0.0180798,"\int \frac{x}{\sqrt{a x^3+b x^4}} \, dx","Integrate[x/Sqrt[a*x^3 + b*x^4],x]","\frac{2 \sqrt{a} x^{3/2} \sqrt{\frac{b x}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{b} \sqrt{x^3 (a+b x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a x^3+b x^4}}\right)}{\sqrt{b}}",1,"(2*Sqrt[a]*x^(3/2)*Sqrt[1 + (b*x)/a]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[b]*Sqrt[x^3*(a + b*x)])","A",1
314,1,21,23,0.0079451,"\int \frac{1}{\sqrt{a x^3+b x^4}} \, dx","Integrate[1/Sqrt[a*x^3 + b*x^4],x]","-\frac{2 \sqrt{x^3 (a+b x)}}{a x^2}","-\frac{2 \sqrt{a x^3+b x^4}}{a x^2}",1,"(-2*Sqrt[x^3*(a + b*x)])/(a*x^2)","A",1
315,1,29,52,0.0151686,"\int \frac{1}{x \sqrt{a x^3+b x^4}} \, dx","Integrate[1/(x*Sqrt[a*x^3 + b*x^4]),x]","-\frac{2 (a-2 b x) \sqrt{x^3 (a+b x)}}{3 a^2 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*(a - 2*b*x)*Sqrt[x^3*(a + b*x)])/(3*a^2*x^3)","A",1
316,1,42,80,0.0209232,"\int \frac{1}{x^2 \sqrt{a x^3+b x^4}} \, dx","Integrate[1/(x^2*Sqrt[a*x^3 + b*x^4]),x]","-\frac{2 \sqrt{x^3 (a+b x)} \left(3 a^2-4 a b x+8 b^2 x^2\right)}{15 a^3 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[x^3*(a + b*x)]*(3*a^2 - 4*a*b*x + 8*b^2*x^2))/(15*a^3*x^4)","A",1
317,1,53,108,0.0239654,"\int \frac{1}{x^3 \sqrt{a x^3+b x^4}} \, dx","Integrate[1/(x^3*Sqrt[a*x^3 + b*x^4]),x]","\frac{2 \sqrt{x^3 (a+b x)} \left(-5 a^3+6 a^2 b x-8 a b^2 x^2+16 b^3 x^3\right)}{35 a^4 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[x^3*(a + b*x)]*(-5*a^3 + 6*a^2*b*x - 8*a*b^2*x^2 + 16*b^3*x^3))/(35*a^4*x^5)","A",1
318,1,64,136,0.0209051,"\int \frac{1}{x^4 \sqrt{a x^3+b x^4}} \, dx","Integrate[1/(x^4*Sqrt[a*x^3 + b*x^4]),x]","-\frac{2 \sqrt{x^3 (a+b x)} \left(35 a^4-40 a^3 b x+48 a^2 b^2 x^2-64 a b^3 x^3+128 b^4 x^4\right)}{315 a^5 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[x^3*(a + b*x)]*(35*a^4 - 40*a^3*b*x + 48*a^2*b^2*x^2 - 64*a*b^3*x^3 + 128*b^4*x^4))/(315*a^5*x^6)","A",1
319,1,26,26,0.0141373,"\int \frac{1}{x^3+b x^5} \, dx","Integrate[(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*1/x^2 - b*Log[x] + (b*Log[1 + b*x^2])/2","A",1
320,1,27,27,0.0056224,"\int \frac{1}{-x^3+b x^5} \, dx","Integrate[(-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",1
321,1,14,8,0.0051144,"\int \frac{1}{a x+b x} \, dx","Integrate[(a*x + b*x)^(-1),x]","\frac{\log (a x+b x)}{a+b}","\frac{\log (x)}{a+b}",1,"Log[a*x + b*x]/(a + b)","A",1
322,1,10,10,0.0029073,"\int \frac{1}{(a x+b x)^2} \, dx","Integrate[(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",1
323,1,12,12,0.0042903,"\int \frac{1}{(a x+b x)^3} \, dx","Integrate[(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*1/((a + b)^3*x^2)","A",1
324,1,10,10,0.000821,"\int \frac{1}{a x^2+b x^2} \, dx","Integrate[(a*x^2 + b*x^2)^(-1),x]","-\frac{1}{x (a+b)}","-\frac{1}{x (a+b)}",1,"-(1/((a + b)*x))","A",1
325,1,20,20,0.0039098,"\int \frac{1}{a x^n+b x^n} \, dx","Integrate[(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",1
326,1,20,20,0.0036001,"\int \frac{1}{\left(a x^n+b x^n\right)^2} \, dx","Integrate[(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",1
327,1,20,20,0.0037267,"\int \frac{1}{\left(a x^n+b x^n\right)^3} \, dx","Integrate[(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",1
328,1,160,16,0.0049447,"\int \left(a x+b x^{14}\right)^{12} \, dx","Integrate[(a*x + b*x^14)^12,x]","\frac{a^{12} x^{13}}{13}+\frac{6}{13} a^{11} b x^{26}+\frac{22}{13} a^{10} b^2 x^{39}+\frac{55}{13} a^9 b^3 x^{52}+\frac{99}{13} a^8 b^4 x^{65}+\frac{132}{13} a^7 b^5 x^{78}+\frac{132}{13} a^6 b^6 x^{91}+\frac{99}{13} a^5 b^7 x^{104}+\frac{55}{13} a^4 b^8 x^{117}+\frac{22}{13} a^3 b^9 x^{130}+\frac{6}{13} a^2 b^{10} x^{143}+\frac{1}{13} a b^{11} x^{156}+\frac{b^{12} x^{169}}{169}","\frac{\left(a+b x^{13}\right)^{13}}{169 b}",1,"(a^12*x^13)/13 + (6*a^11*b*x^26)/13 + (22*a^10*b^2*x^39)/13 + (55*a^9*b^3*x^52)/13 + (99*a^8*b^4*x^65)/13 + (132*a^7*b^5*x^78)/13 + (132*a^6*b^6*x^91)/13 + (99*a^5*b^7*x^104)/13 + (55*a^4*b^8*x^117)/13 + (22*a^3*b^9*x^130)/13 + (6*a^2*b^10*x^143)/13 + (a*b^11*x^156)/13 + (b^12*x^169)/169","B",1
329,1,160,16,0.0198292,"\int x^{12} \left(a x+b x^{26}\right)^{12} \, dx","Integrate[x^12*(a*x + b*x^26)^12,x]","\frac{a^{12} x^{25}}{25}+\frac{6}{25} a^{11} b x^{50}+\frac{22}{25} a^{10} b^2 x^{75}+\frac{11}{5} a^9 b^3 x^{100}+\frac{99}{25} a^8 b^4 x^{125}+\frac{132}{25} a^7 b^5 x^{150}+\frac{132}{25} a^6 b^6 x^{175}+\frac{99}{25} a^5 b^7 x^{200}+\frac{11}{5} a^4 b^8 x^{225}+\frac{22}{25} a^3 b^9 x^{250}+\frac{6}{25} a^2 b^{10} x^{275}+\frac{1}{25} a b^{11} x^{300}+\frac{b^{12} x^{325}}{325}","\frac{\left(a+b x^{25}\right)^{13}}{325 b}",1,"(a^12*x^25)/25 + (6*a^11*b*x^50)/25 + (22*a^10*b^2*x^75)/25 + (11*a^9*b^3*x^100)/5 + (99*a^8*b^4*x^125)/25 + (132*a^7*b^5*x^150)/25 + (132*a^6*b^6*x^175)/25 + (99*a^5*b^7*x^200)/25 + (11*a^4*b^8*x^225)/5 + (22*a^3*b^9*x^250)/25 + (6*a^2*b^10*x^275)/25 + (a*b^11*x^300)/25 + (b^12*x^325)/325","B",1
330,1,160,16,0.0143891,"\int x^{24} \left(a x+b x^{38}\right)^{12} \, dx","Integrate[x^24*(a*x + b*x^38)^12,x]","\frac{a^{12} x^{37}}{37}+\frac{6}{37} a^{11} b x^{74}+\frac{22}{37} a^{10} b^2 x^{111}+\frac{55}{37} a^9 b^3 x^{148}+\frac{99}{37} a^8 b^4 x^{185}+\frac{132}{37} a^7 b^5 x^{222}+\frac{132}{37} a^6 b^6 x^{259}+\frac{99}{37} a^5 b^7 x^{296}+\frac{55}{37} a^4 b^8 x^{333}+\frac{22}{37} a^3 b^9 x^{370}+\frac{6}{37} a^2 b^{10} x^{407}+\frac{1}{37} a b^{11} x^{444}+\frac{b^{12} x^{481}}{481}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a^12*x^37)/37 + (6*a^11*b*x^74)/37 + (22*a^10*b^2*x^111)/37 + (55*a^9*b^3*x^148)/37 + (99*a^8*b^4*x^185)/37 + (132*a^7*b^5*x^222)/37 + (132*a^6*b^6*x^259)/37 + (99*a^5*b^7*x^296)/37 + (55*a^4*b^8*x^333)/37 + (22*a^3*b^9*x^370)/37 + (6*a^2*b^10*x^407)/37 + (a*b^11*x^444)/37 + (b^12*x^481)/481","B",1
331,1,24,27,0.0313807,"\int x^{12 (-1+m)} \left(a x+b x^{2+12 m}\right)^{12} \, dx","Integrate[x^(12*(-1 + m))*(a*x + b*x^(2 + 12*m))^12,x]","\frac{\left(a+b x^{12 m+1}\right)^{13}}{156 b m+13 b}","\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 + 156*b*m)","A",1
332,1,160,16,0.0036647,"\int \left(a x+b x^{14}\right)^{12} \, dx","Integrate[(a*x + b*x^14)^12,x]","\frac{a^{12} x^{13}}{13}+\frac{6}{13} a^{11} b x^{26}+\frac{22}{13} a^{10} b^2 x^{39}+\frac{55}{13} a^9 b^3 x^{52}+\frac{99}{13} a^8 b^4 x^{65}+\frac{132}{13} a^7 b^5 x^{78}+\frac{132}{13} a^6 b^6 x^{91}+\frac{99}{13} a^5 b^7 x^{104}+\frac{55}{13} a^4 b^8 x^{117}+\frac{22}{13} a^3 b^9 x^{130}+\frac{6}{13} a^2 b^{10} x^{143}+\frac{1}{13} a b^{11} x^{156}+\frac{b^{12} x^{169}}{169}","\frac{\left(a+b x^{13}\right)^{13}}{169 b}",1,"(a^12*x^13)/13 + (6*a^11*b*x^26)/13 + (22*a^10*b^2*x^39)/13 + (55*a^9*b^3*x^52)/13 + (99*a^8*b^4*x^65)/13 + (132*a^7*b^5*x^78)/13 + (132*a^6*b^6*x^91)/13 + (99*a^5*b^7*x^104)/13 + (55*a^4*b^8*x^117)/13 + (22*a^3*b^9*x^130)/13 + (6*a^2*b^10*x^143)/13 + (a*b^11*x^156)/13 + (b^12*x^169)/169","B",1
333,1,160,16,0.0059397,"\int \left(a x^2+b x^{27}\right)^{12} \, dx","Integrate[(a*x^2 + b*x^27)^12,x]","\frac{a^{12} x^{25}}{25}+\frac{6}{25} a^{11} b x^{50}+\frac{22}{25} a^{10} b^2 x^{75}+\frac{11}{5} a^9 b^3 x^{100}+\frac{99}{25} a^8 b^4 x^{125}+\frac{132}{25} a^7 b^5 x^{150}+\frac{132}{25} a^6 b^6 x^{175}+\frac{99}{25} a^5 b^7 x^{200}+\frac{11}{5} a^4 b^8 x^{225}+\frac{22}{25} a^3 b^9 x^{250}+\frac{6}{25} a^2 b^{10} x^{275}+\frac{1}{25} a b^{11} x^{300}+\frac{b^{12} x^{325}}{325}","\frac{\left(a+b x^{25}\right)^{13}}{325 b}",1,"(a^12*x^25)/25 + (6*a^11*b*x^50)/25 + (22*a^10*b^2*x^75)/25 + (11*a^9*b^3*x^100)/5 + (99*a^8*b^4*x^125)/25 + (132*a^7*b^5*x^150)/25 + (132*a^6*b^6*x^175)/25 + (99*a^5*b^7*x^200)/25 + (11*a^4*b^8*x^225)/5 + (22*a^3*b^9*x^250)/25 + (6*a^2*b^10*x^275)/25 + (a*b^11*x^300)/25 + (b^12*x^325)/325","B",1
334,1,160,16,0.006799,"\int \left(a x^3+b x^{40}\right)^{12} \, dx","Integrate[(a*x^3 + b*x^40)^12,x]","\frac{a^{12} x^{37}}{37}+\frac{6}{37} a^{11} b x^{74}+\frac{22}{37} a^{10} b^2 x^{111}+\frac{55}{37} a^9 b^3 x^{148}+\frac{99}{37} a^8 b^4 x^{185}+\frac{132}{37} a^7 b^5 x^{222}+\frac{132}{37} a^6 b^6 x^{259}+\frac{99}{37} a^5 b^7 x^{296}+\frac{55}{37} a^4 b^8 x^{333}+\frac{22}{37} a^3 b^9 x^{370}+\frac{6}{37} a^2 b^{10} x^{407}+\frac{1}{37} a b^{11} x^{444}+\frac{b^{12} x^{481}}{481}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a^12*x^37)/37 + (6*a^11*b*x^74)/37 + (22*a^10*b^2*x^111)/37 + (55*a^9*b^3*x^148)/37 + (99*a^8*b^4*x^185)/37 + (132*a^7*b^5*x^222)/37 + (132*a^6*b^6*x^259)/37 + (99*a^5*b^7*x^296)/37 + (55*a^4*b^8*x^333)/37 + (22*a^3*b^9*x^370)/37 + (6*a^2*b^10*x^407)/37 + (a*b^11*x^444)/37 + (b^12*x^481)/481","B",1
335,1,24,27,0.0045288,"\int \left(a x^m+b x^{1+13 m}\right)^{12} \, dx","Integrate[(a*x^m + b*x^(1 + 13*m))^12,x]","\frac{\left(a+b x^{12 m+1}\right)^{13}}{156 b m+13 b}","\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 + 156*b*m)","A",1
336,1,27,27,0.0137524,"\int \left(a x^m+b x^{1+6 m}\right)^5 \, dx","Integrate[(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",1
337,1,27,27,0.0216972,"\int \frac{1}{\left(b x^{1-2 m}+a x^m\right)^3} \, dx","Integrate[(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*1/(b*(1 - 3*m)*(a + b*x^(1 - 3*m))^2)","A",1
338,1,15,15,0.0028966,"\int \frac{1}{\frac{b}{x}+a x} \, dx","Integrate[(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",1
339,1,15,15,0.0043177,"\int \frac{1}{\frac{b}{x^2}+a x} \, dx","Integrate[(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",1
340,1,15,15,0.0049517,"\int \frac{1}{\frac{b}{x^3}+a x} \, dx","Integrate[(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",1
341,1,24,19,0.009568,"\int \frac{1}{\left(\frac{b}{x}+a x\right)^3} \, dx","Integrate[(b/x + a*x)^(-3),x]","-\frac{2 a x^2+b}{4 a^2 \left(a x^2+b\right)^2}","\frac{x^4}{4 b \left(a x^2+b\right)^2}",1,"-1/4*(b + 2*a*x^2)/(a^2*(b + a*x^2)^2)","A",1
342,1,24,19,0.0173679,"\int \frac{1}{\left(\frac{b}{x^3}+a x^2\right)^3} \, dx","Integrate[(b/x^3 + a*x^2)^(-3),x]","-\frac{2 a x^5+b}{10 a^2 \left(a x^5+b\right)^2}","\frac{x^{10}}{10 b \left(a x^5+b\right)^2}",1,"-1/10*(b + 2*a*x^5)/(a^2*(b + a*x^5)^2)","A",1
343,1,24,19,0.0133634,"\int \frac{1}{\left(\frac{b}{x^5}+a x^3\right)^3} \, dx","Integrate[(b/x^5 + a*x^3)^(-3),x]","-\frac{2 a x^8+b}{16 a^2 \left(a x^8+b\right)^2}","\frac{x^{16}}{16 b \left(a x^8+b\right)^2}",1,"-1/16*(b + 2*a*x^8)/(a^2*(b + a*x^8)^2)","A",1
344,1,24,24,0.0016246,"\int \left(\frac{a}{x}+b x\right)^2 \, dx","Integrate[(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",1
345,1,40,40,0.0076772,"\int \left(\frac{a}{x}+b x\right)^3 \, dx","Integrate[(a/x + b*x)^3,x]","-\frac{a^3}{2 x^2}+3 a^2 b \log (x)+\frac{3}{2} a b^2 x^2+\frac{b^3 x^4}{4}","-\frac{a^3}{2 x^2}+3 a^2 b \log (x)+\frac{3}{2} a b^2 x^2+\frac{b^3 x^4}{4}",1,"-1/2*a^3/x^2 + (3*a*b^2*x^2)/2 + (b^3*x^4)/4 + 3*a^2*b*Log[x]","A",1
346,1,50,50,0.0070004,"\int \left(\frac{a}{x}+b x\right)^4 \, dx","Integrate[(a/x + b*x)^4,x]","-\frac{a^4}{3 x^3}-\frac{4 a^3 b}{x}+6 a^2 b^2 x+\frac{4}{3} a b^3 x^3+\frac{b^4 x^5}{5}","-\frac{a^4}{3 x^3}-\frac{4 a^3 b}{x}+6 a^2 b^2 x+\frac{4}{3} a b^3 x^3+\frac{b^4 x^5}{5}",1,"-1/3*a^4/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",1
347,1,144,185,0.1434902,"\int \frac{1}{\frac{1}{x^2}+x^3} \, dx","Integrate[(x^(-2) + x^3)^(-1),x]","\frac{1}{20} \left(-\left(1+\sqrt{5}\right) \log \left(x^2+\frac{1}{2} \left(\sqrt{5}-1\right) x+1\right)+\left(\sqrt{5}-1\right) \log \left(x^2-\frac{1}{2} \left(1+\sqrt{5}\right) x+1\right)+4 \log (x+1)-2 \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{-4 x+\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}}\right)-2 \sqrt{10-2 \sqrt{5}} \tan ^{-1}\left(\frac{4 x+\sqrt{5}-1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)\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,"(-2*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(1 + Sqrt[5] - 4*x)/Sqrt[10 - 2*Sqrt[5]]] - 2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(-1 + Sqrt[5] + 4*x)/Sqrt[2*(5 + Sqrt[5])]] + 4*Log[1 + x] - (1 + Sqrt[5])*Log[1 + ((-1 + Sqrt[5])*x)/2 + x^2] + (-1 + Sqrt[5])*Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20","A",0
348,1,29,29,0.0174649,"\int x^p \left(a x^n+b x^{1+13 n+p}\right)^{12} \, dx","Integrate[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",1
349,1,160,16,0.005966,"\int x^{12} \left(a+b x^{13}\right)^{12} \, dx","Integrate[x^12*(a + b*x^13)^12,x]","\frac{a^{12} x^{13}}{13}+\frac{6}{13} a^{11} b x^{26}+\frac{22}{13} a^{10} b^2 x^{39}+\frac{55}{13} a^9 b^3 x^{52}+\frac{99}{13} a^8 b^4 x^{65}+\frac{132}{13} a^7 b^5 x^{78}+\frac{132}{13} a^6 b^6 x^{91}+\frac{99}{13} a^5 b^7 x^{104}+\frac{55}{13} a^4 b^8 x^{117}+\frac{22}{13} a^3 b^9 x^{130}+\frac{6}{13} a^2 b^{10} x^{143}+\frac{1}{13} a b^{11} x^{156}+\frac{b^{12} x^{169}}{169}","\frac{\left(a+b x^{13}\right)^{13}}{169 b}",1,"(a^12*x^13)/13 + (6*a^11*b*x^26)/13 + (22*a^10*b^2*x^39)/13 + (55*a^9*b^3*x^52)/13 + (99*a^8*b^4*x^65)/13 + (132*a^7*b^5*x^78)/13 + (132*a^6*b^6*x^91)/13 + (99*a^5*b^7*x^104)/13 + (55*a^4*b^8*x^117)/13 + (22*a^3*b^9*x^130)/13 + (6*a^2*b^10*x^143)/13 + (a*b^11*x^156)/13 + (b^12*x^169)/169","B",1
350,1,160,16,0.0063552,"\int x^{12} \left(a x+b x^{26}\right)^{12} \, dx","Integrate[x^12*(a*x + b*x^26)^12,x]","\frac{a^{12} x^{25}}{25}+\frac{6}{25} a^{11} b x^{50}+\frac{22}{25} a^{10} b^2 x^{75}+\frac{11}{5} a^9 b^3 x^{100}+\frac{99}{25} a^8 b^4 x^{125}+\frac{132}{25} a^7 b^5 x^{150}+\frac{132}{25} a^6 b^6 x^{175}+\frac{99}{25} a^5 b^7 x^{200}+\frac{11}{5} a^4 b^8 x^{225}+\frac{22}{25} a^3 b^9 x^{250}+\frac{6}{25} a^2 b^{10} x^{275}+\frac{1}{25} a b^{11} x^{300}+\frac{b^{12} x^{325}}{325}","\frac{\left(a+b x^{25}\right)^{13}}{325 b}",1,"(a^12*x^25)/25 + (6*a^11*b*x^50)/25 + (22*a^10*b^2*x^75)/25 + (11*a^9*b^3*x^100)/5 + (99*a^8*b^4*x^125)/25 + (132*a^7*b^5*x^150)/25 + (132*a^6*b^6*x^175)/25 + (99*a^5*b^7*x^200)/25 + (11*a^4*b^8*x^225)/5 + (22*a^3*b^9*x^250)/25 + (6*a^2*b^10*x^275)/25 + (a*b^11*x^300)/25 + (b^12*x^325)/325","B",1
351,1,160,16,0.0075485,"\int x^{12} \left(a x^2+b x^{39}\right)^{12} \, dx","Integrate[x^12*(a*x^2 + b*x^39)^12,x]","\frac{a^{12} x^{37}}{37}+\frac{6}{37} a^{11} b x^{74}+\frac{22}{37} a^{10} b^2 x^{111}+\frac{55}{37} a^9 b^3 x^{148}+\frac{99}{37} a^8 b^4 x^{185}+\frac{132}{37} a^7 b^5 x^{222}+\frac{132}{37} a^6 b^6 x^{259}+\frac{99}{37} a^5 b^7 x^{296}+\frac{55}{37} a^4 b^8 x^{333}+\frac{22}{37} a^3 b^9 x^{370}+\frac{6}{37} a^2 b^{10} x^{407}+\frac{1}{37} a b^{11} x^{444}+\frac{b^{12} x^{481}}{481}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a^12*x^37)/37 + (6*a^11*b*x^74)/37 + (22*a^10*b^2*x^111)/37 + (55*a^9*b^3*x^148)/37 + (99*a^8*b^4*x^185)/37 + (132*a^7*b^5*x^222)/37 + (132*a^6*b^6*x^259)/37 + (99*a^5*b^7*x^296)/37 + (55*a^4*b^8*x^333)/37 + (22*a^3*b^9*x^370)/37 + (6*a^2*b^10*x^407)/37 + (a*b^11*x^444)/37 + (b^12*x^481)/481","B",1
352,1,160,16,0.0050981,"\int x^{24} \left(a+b x^{25}\right)^{12} \, dx","Integrate[x^24*(a + b*x^25)^12,x]","\frac{a^{12} x^{25}}{25}+\frac{6}{25} a^{11} b x^{50}+\frac{22}{25} a^{10} b^2 x^{75}+\frac{11}{5} a^9 b^3 x^{100}+\frac{99}{25} a^8 b^4 x^{125}+\frac{132}{25} a^7 b^5 x^{150}+\frac{132}{25} a^6 b^6 x^{175}+\frac{99}{25} a^5 b^7 x^{200}+\frac{11}{5} a^4 b^8 x^{225}+\frac{22}{25} a^3 b^9 x^{250}+\frac{6}{25} a^2 b^{10} x^{275}+\frac{1}{25} a b^{11} x^{300}+\frac{b^{12} x^{325}}{325}","\frac{\left(a+b x^{25}\right)^{13}}{325 b}",1,"(a^12*x^25)/25 + (6*a^11*b*x^50)/25 + (22*a^10*b^2*x^75)/25 + (11*a^9*b^3*x^100)/5 + (99*a^8*b^4*x^125)/25 + (132*a^7*b^5*x^150)/25 + (132*a^6*b^6*x^175)/25 + (99*a^5*b^7*x^200)/25 + (11*a^4*b^8*x^225)/5 + (22*a^3*b^9*x^250)/25 + (6*a^2*b^10*x^275)/25 + (a*b^11*x^300)/25 + (b^12*x^325)/325","B",1
353,1,160,16,0.006672,"\int x^{24} \left(a x+b x^{38}\right)^{12} \, dx","Integrate[x^24*(a*x + b*x^38)^12,x]","\frac{a^{12} x^{37}}{37}+\frac{6}{37} a^{11} b x^{74}+\frac{22}{37} a^{10} b^2 x^{111}+\frac{55}{37} a^9 b^3 x^{148}+\frac{99}{37} a^8 b^4 x^{185}+\frac{132}{37} a^7 b^5 x^{222}+\frac{132}{37} a^6 b^6 x^{259}+\frac{99}{37} a^5 b^7 x^{296}+\frac{55}{37} a^4 b^8 x^{333}+\frac{22}{37} a^3 b^9 x^{370}+\frac{6}{37} a^2 b^{10} x^{407}+\frac{1}{37} a b^{11} x^{444}+\frac{b^{12} x^{481}}{481}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a^12*x^37)/37 + (6*a^11*b*x^74)/37 + (22*a^10*b^2*x^111)/37 + (55*a^9*b^3*x^148)/37 + (99*a^8*b^4*x^185)/37 + (132*a^7*b^5*x^222)/37 + (132*a^6*b^6*x^259)/37 + (99*a^5*b^7*x^296)/37 + (55*a^4*b^8*x^333)/37 + (22*a^3*b^9*x^370)/37 + (6*a^2*b^10*x^407)/37 + (a*b^11*x^444)/37 + (b^12*x^481)/481","B",1
354,1,160,16,0.0061216,"\int x^{36} \left(a+b x^{37}\right)^{12} \, dx","Integrate[x^36*(a + b*x^37)^12,x]","\frac{a^{12} x^{37}}{37}+\frac{6}{37} a^{11} b x^{74}+\frac{22}{37} a^{10} b^2 x^{111}+\frac{55}{37} a^9 b^3 x^{148}+\frac{99}{37} a^8 b^4 x^{185}+\frac{132}{37} a^7 b^5 x^{222}+\frac{132}{37} a^6 b^6 x^{259}+\frac{99}{37} a^5 b^7 x^{296}+\frac{55}{37} a^4 b^8 x^{333}+\frac{22}{37} a^3 b^9 x^{370}+\frac{6}{37} a^2 b^{10} x^{407}+\frac{1}{37} a b^{11} x^{444}+\frac{b^{12} x^{481}}{481}","\frac{\left(a+b x^{37}\right)^{13}}{481 b}",1,"(a^12*x^37)/37 + (6*a^11*b*x^74)/37 + (22*a^10*b^2*x^111)/37 + (55*a^9*b^3*x^148)/37 + (99*a^8*b^4*x^185)/37 + (132*a^7*b^5*x^222)/37 + (132*a^6*b^6*x^259)/37 + (99*a^5*b^7*x^296)/37 + (55*a^4*b^8*x^333)/37 + (22*a^3*b^9*x^370)/37 + (6*a^2*b^10*x^407)/37 + (a*b^11*x^444)/37 + (b^12*x^481)/481","B",1
355,1,23,23,0.0087277,"\int \frac{1}{a x+b x^n} \, dx","Integrate[(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",1
356,1,22,23,0.00649,"\int \frac{1}{a x+b x^{1+n}} \, dx","Integrate[(a*x + b*x^(1 + n))^(-1),x]","\frac{n \log (x)-\log \left(a+b x^n\right)}{a n}","\frac{\log (x)}{a}-\frac{\log \left(a+b x^n\right)}{a n}",1,"(n*Log[x] - Log[a + b*x^n])/(a*n)","A",1
357,1,15,15,0.0048215,"\int \frac{1}{a x+b x^{1-n}} \, dx","Integrate[(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",1
358,1,22,22,0.006416,"\int \frac{1}{2 x+3 x^{1+n}} \, dx","Integrate[(2*x + 3*x^(1 + n))^(-1),x]","\frac{n \log (x)-\log \left(3 x^n+2\right)}{2 n}","\frac{\log (x)}{2}-\frac{\log \left(3 x^n+2\right)}{2 n}",1,"(n*Log[x] - Log[2 + 3*x^n])/(2*n)","A",1
359,1,15,15,0.0036065,"\int \frac{1}{2 x+3 x^{1-n}} \, dx","Integrate[(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",1
360,1,12,12,0.0025846,"\int \frac{1}{-\sqrt{x}+x} \, dx","Integrate[(-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",1
361,1,14,14,0.0031101,"\int \frac{1}{-x^{3/5}+x} \, dx","Integrate[(-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",1
362,1,12,12,0.0024235,"\int \frac{1}{\frac{1}{\sqrt[3]{x}}+x} \, dx","Integrate[(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",1
363,1,24,24,0.0243144,"\int \frac{1}{x+x^{\sqrt{2}}} \, dx","Integrate[(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",1
364,1,104,75,0.2260044,"\int x^{-1-\frac{j}{2}} \sqrt{a x^j+b x^n} \, dx","Integrate[x^(-1 - j/2)*Sqrt[a*x^j + b*x^n],x]","-\frac{2 x^{-j/2} \left(-\sqrt{a} \sqrt{b} x^{\frac{j+n}{2}} \sqrt{\frac{a x^{j-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{j-n}{2}}}{\sqrt{b}}\right)+a x^j+b x^n\right)}{(j-n) \sqrt{a x^j+b x^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*(a*x^j + b*x^n - Sqrt[a]*Sqrt[b]*x^((j + n)/2)*Sqrt[1 + (a*x^(j - n))/b]*ArcSinh[(Sqrt[a]*x^((j - n)/2))/Sqrt[b]]))/((j - n)*x^(j/2)*Sqrt[a*x^j + b*x^n])","A",1
365,1,109,99,0.0666337,"\int (c x)^{-1-\frac{j}{2}} \sqrt{a x^j+b x^n} \, dx","Integrate[(c*x)^(-1 - j/2)*Sqrt[a*x^j + b*x^n],x]","-\frac{2 (c x)^{-j/2} \left(-\sqrt{a} \sqrt{b} x^{\frac{j+n}{2}} \sqrt{\frac{a x^{j-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{j-n}{2}}}{\sqrt{b}}\right)+a x^j+b x^n\right)}{c (j-n) \sqrt{a x^j+b x^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*(a*x^j + b*x^n - Sqrt[a]*Sqrt[b]*x^((j + n)/2)*Sqrt[1 + (a*x^(j - n))/b]*ArcSinh[(Sqrt[a]*x^((j - n)/2))/Sqrt[b]]))/(c*(j - n)*(c*x)^(j/2)*Sqrt[a*x^j + b*x^n])","A",1
366,1,103,91,0.2700895,"\int \frac{\sqrt{a x^3+b x^n}}{(c x)^{5/2}} \, dx","Integrate[Sqrt[a*x^3 + b*x^n]/(c*x)^(5/2),x]","\frac{2 x \left(-\sqrt{a} \sqrt{b} x^{\frac{n+3}{2}} \sqrt{\frac{a x^{3-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{3}{2}-\frac{n}{2}}}{\sqrt{b}}\right)+a x^3+b x^n\right)}{(n-3) (c x)^{5/2} \sqrt{a x^3+b x^n}}","\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*x*(a*x^3 + b*x^n - Sqrt[a]*Sqrt[b]*x^((3 + n)/2)*Sqrt[1 + (a*x^(3 - n))/b]*ArcSinh[(Sqrt[a]*x^(3/2 - n/2))/Sqrt[b]]))/((-3 + n)*(c*x)^(5/2)*Sqrt[a*x^3 + b*x^n])","A",1
367,1,99,71,0.159653,"\int \frac{\sqrt{a x^2+b x^n}}{c^2 x^2} \, dx","Integrate[Sqrt[a*x^2 + b*x^n]/(c^2*x^2),x]","\frac{2 \left(-\sqrt{a} \sqrt{b} x^{\frac{n}{2}+1} \sqrt{\frac{a x^{2-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{1-\frac{n}{2}}}{\sqrt{b}}\right)+a x^2+b x^n\right)}{c^2 (n-2) x \sqrt{a x^2+b x^n}}","\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*(a*x^2 + b*x^n - Sqrt[a]*Sqrt[b]*x^(1 + n/2)*Sqrt[1 + (a*x^(2 - n))/b]*ArcSinh[(Sqrt[a]*x^(1 - n/2))/Sqrt[b]]))/(c^2*(-2 + n)*x*Sqrt[a*x^2 + b*x^n])","A",1
368,1,100,87,0.2855218,"\int \frac{\sqrt{a x+b x^n}}{(c x)^{3/2}} \, dx","Integrate[Sqrt[a*x + b*x^n]/(c*x)^(3/2),x]","\frac{x \left(-2 \sqrt{a} \sqrt{b} x^{\frac{n+1}{2}} \sqrt{\frac{a x^{1-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{1}{2}-\frac{n}{2}}}{\sqrt{b}}\right)+2 a x+2 b x^n\right)}{(n-1) (c x)^{3/2} \sqrt{a x+b x^n}}","\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,"(x*(2*a*x + 2*b*x^n - 2*Sqrt[a]*Sqrt[b]*x^((1 + n)/2)*Sqrt[1 + (a*x^(1 - n))/b]*ArcSinh[(Sqrt[a]*x^(1/2 - n/2))/Sqrt[b]]))/((-1 + n)*(c*x)^(3/2)*Sqrt[a*x + b*x^n])","A",1
369,1,46,51,0.0139412,"\int \frac{\sqrt{a+b x^n}}{c x} \, dx","Integrate[Sqrt[a + b*x^n]/(c*x),x]","\frac{2 \sqrt{a+b x^n}-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] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(c*n)","A",1
370,1,85,84,0.0676076,"\int \frac{\sqrt{\frac{a}{x}+b x^n}}{\sqrt{c x}} \, dx","Integrate[Sqrt[a/x + b*x^n]/Sqrt[c*x],x]","\frac{x \sqrt{\frac{a}{x}+b x^n} \left(2 \sqrt{a+b x^{n+1}}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^{n+1}}}{\sqrt{a}}\right)\right)}{(n+1) \sqrt{c x} \sqrt{a+b x^{n+1}}}","\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,"(x*Sqrt[a/x + b*x^n]*(2*Sqrt[a + b*x^(1 + n)] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x^(1 + n)]/Sqrt[a]]))/((1 + n)*Sqrt[c*x]*Sqrt[a + b*x^(1 + n)])","A",1
371,1,78,61,0.0559457,"\int \sqrt{\frac{a}{x^2}+b x^n} \, dx","Integrate[Sqrt[a/x^2 + b*x^n],x]","\frac{x \sqrt{\frac{a}{x^2}+b x^n} \left(2 \sqrt{a+b x^{n+2}}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^{n+2}}}{\sqrt{a}}\right)\right)}{(n+2) \sqrt{a+b x^{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,"(x*Sqrt[a/x^2 + b*x^n]*(2*Sqrt[a + b*x^(2 + n)] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x^(2 + n)]/Sqrt[a]]))/((2 + n)*Sqrt[a + b*x^(2 + n)])","A",1
372,1,85,85,0.0742956,"\int \sqrt{c x} \sqrt{\frac{a}{x^3}+b x^n} \, dx","Integrate[Sqrt[c*x]*Sqrt[a/x^3 + b*x^n],x]","\frac{x \sqrt{c x} \sqrt{\frac{a}{x^3}+b x^n} \left(2 \sqrt{a+b x^{n+3}}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^{n+3}}}{\sqrt{a}}\right)\right)}{(n+3) \sqrt{a+b x^{n+3}}}","\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,"(x*Sqrt[c*x]*Sqrt[a/x^3 + b*x^n]*(2*Sqrt[a + b*x^(3 + n)] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x^(3 + n)]/Sqrt[a]]))/((3 + n)*Sqrt[a + b*x^(3 + n)])","A",1
373,1,131,141,0.2631972,"\int (c x)^{-1-\frac{3 j}{2}} \left(a x^j+b x^n\right)^{3/2} \, dx","Integrate[(c*x)^(-1 - (3*j)/2)*(a*x^j + b*x^n)^(3/2),x]","-\frac{2 (c x)^{-3 j/2} \left(-3 a^{3/2} \sqrt{b} x^{\frac{1}{2} (3 j+n)} \sqrt{\frac{a x^{j-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{j-n}{2}}}{\sqrt{b}}\right)+4 a^2 x^{2 j}+5 a b x^{j+n}+b^2 x^{2 n}\right)}{3 c (j-n) \sqrt{a x^j+b x^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*(4*a^2*x^(2*j) + b^2*x^(2*n) + 5*a*b*x^(j + n) - 3*a^(3/2)*Sqrt[b]*x^((3*j + n)/2)*Sqrt[1 + (a*x^(j - n))/b]*ArcSinh[(Sqrt[a]*x^((j - n)/2))/Sqrt[b]]))/(3*c*(j - n)*(c*x)^((3*j)/2)*Sqrt[a*x^j + b*x^n])","A",1
374,1,126,128,0.3261648,"\int \frac{\left(a x^3+b x^n\right)^{3/2}}{(c x)^{11/2}} \, dx","Integrate[(a*x^3 + b*x^n)^(3/2)/(c*x)^(11/2),x]","\frac{2 \sqrt{c x} \left(-3 a^{3/2} \sqrt{b} x^{\frac{n+9}{2}} \sqrt{\frac{a x^{3-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{3}{2}-\frac{n}{2}}}{\sqrt{b}}\right)+4 a^2 x^6+5 a b x^{n+3}+b^2 x^{2 n}\right)}{3 c^6 (n-3) x^5 \sqrt{a x^3+b x^n}}","\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*Sqrt[c*x]*(4*a^2*x^6 + b^2*x^(2*n) + 5*a*b*x^(3 + n) - 3*a^(3/2)*Sqrt[b]*x^((9 + n)/2)*Sqrt[1 + (a*x^(3 - n))/b]*ArcSinh[(Sqrt[a]*x^(3/2 - n/2))/Sqrt[b]]))/(3*c^6*(-3 + n)*x^5*Sqrt[a*x^3 + b*x^n])","A",1
375,1,117,104,0.1730015,"\int \frac{\left(a x^2+b x^n\right)^{3/2}}{c^4 x^4} \, dx","Integrate[(a*x^2 + b*x^n)^(3/2)/(c^4*x^4),x]","\frac{2 \left(-3 a^{3/2} \sqrt{b} x^{\frac{n}{2}+3} \sqrt{\frac{a x^{2-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{1-\frac{n}{2}}}{\sqrt{b}}\right)+4 a^2 x^4+5 a b x^{n+2}+b^2 x^{2 n}\right)}{3 c^4 (n-2) x^3 \sqrt{a x^2+b x^n}}","\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*(4*a^2*x^4 + b^2*x^(2*n) + 5*a*b*x^(2 + n) - 3*a^(3/2)*Sqrt[b]*x^(3 + n/2)*Sqrt[1 + (a*x^(2 - n))/b]*ArcSinh[(Sqrt[a]*x^(1 - n/2))/Sqrt[b]]))/(3*c^4*(-2 + n)*x^3*Sqrt[a*x^2 + b*x^n])","A",1
376,1,120,122,0.2759578,"\int \frac{\left(a x+b x^n\right)^{3/2}}{(c x)^{5/2}} \, dx","Integrate[(a*x + b*x^n)^(3/2)/(c*x)^(5/2),x]","\frac{x \left(-6 a^{3/2} \sqrt{b} x^{\frac{n+3}{2}} \sqrt{\frac{a x^{1-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{1}{2}-\frac{n}{2}}}{\sqrt{b}}\right)+8 a^2 x^2+10 a b x^{n+1}+2 b^2 x^{2 n}\right)}{3 (n-1) (c x)^{5/2} \sqrt{a x+b x^n}}","\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,"(x*(8*a^2*x^2 + 2*b^2*x^(2*n) + 10*a*b*x^(1 + n) - 6*a^(3/2)*Sqrt[b]*x^((3 + n)/2)*Sqrt[1 + (a*x^(1 - n))/b]*ArcSinh[(Sqrt[a]*x^(1/2 - n/2))/Sqrt[b]]))/(3*(-1 + n)*(c*x)^(5/2)*Sqrt[a*x + b*x^n])","A",1
377,1,58,73,0.028036,"\int \frac{\left(a+b x^n\right)^{3/2}}{c x} \, dx","Integrate[(a + b*x^n)^(3/2)/(c*x),x]","\frac{2 \sqrt{a+b x^n} \left(4 a+b x^n\right)-6 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)}{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*Sqrt[a + b*x^n]*(4*a + b*x^n) - 6*a^(3/2)*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]])/(3*c*n)","A",1
378,1,97,117,0.078149,"\int \sqrt{c x} \left(\frac{a}{x}+b x^n\right)^{3/2} \, dx","Integrate[Sqrt[c*x]*(a/x + b*x^n)^(3/2),x]","\frac{2 \sqrt{c x} \sqrt{\frac{a}{x}+b x^n} \left(\sqrt{a+b x^{n+1}} \left(4 a+b x^{n+1}\right)-3 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^{n+1}}}{\sqrt{a}}\right)\right)}{3 (n+1) \sqrt{a+b x^{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*Sqrt[c*x]*Sqrt[a/x + b*x^n]*(Sqrt[a + b*x^(1 + n)]*(4*a + b*x^(1 + n)) - 3*a^(3/2)*ArcTanh[Sqrt[a + b*x^(1 + n)]/Sqrt[a]]))/(3*(1 + n)*Sqrt[a + b*x^(1 + n)])","A",1
379,1,94,98,0.0718391,"\int c^2 x^2 \left(\frac{a}{x^2}+b x^n\right)^{3/2} \, dx","Integrate[c^2*x^2*(a/x^2 + b*x^n)^(3/2),x]","\frac{2 c^2 x \sqrt{\frac{a}{x^2}+b x^n} \left(\sqrt{a+b x^{n+2}} \left(4 a+b x^{n+2}\right)-3 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^{n+2}}}{\sqrt{a}}\right)\right)}{3 (n+2) \sqrt{a+b x^{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 a c^2 x \sqrt{\frac{a}{x^2}+b x^n}}{n+2}+\frac{2 c^2 x^3 \left(\frac{a}{x^2}+b x^n\right)^{3/2}}{3 (n+2)}",1,"(2*c^2*x*Sqrt[a/x^2 + b*x^n]*(Sqrt[a + b*x^(2 + n)]*(4*a + b*x^(2 + n)) - 3*a^(3/2)*ArcTanh[Sqrt[a + b*x^(2 + n)]/Sqrt[a]]))/(3*(2 + n)*Sqrt[a + b*x^(2 + n)])","A",1
380,1,100,122,0.0900346,"\int (c x)^{7/2} \left(\frac{a}{x^3}+b x^n\right)^{3/2} \, dx","Integrate[(c*x)^(7/2)*(a/x^3 + b*x^n)^(3/2),x]","\frac{2 c^2 (c x)^{3/2} \sqrt{\frac{a}{x^3}+b x^n} \left(\sqrt{a+b x^{n+3}} \left(4 a+b x^{n+3}\right)-3 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^{n+3}}}{\sqrt{a}}\right)\right)}{3 (n+3) \sqrt{a+b x^{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*c^2*(c*x)^(3/2)*Sqrt[a/x^3 + b*x^n]*(Sqrt[a + b*x^(3 + n)]*(4*a + b*x^(3 + n)) - 3*a^(3/2)*ArcTanh[Sqrt[a + b*x^(3 + n)]/Sqrt[a]]))/(3*(3 + n)*Sqrt[a + b*x^(3 + n)])","A",1
381,1,96,100,0.078612,"\int c^5 x^5 \left(\frac{a}{x^4}+b x^n\right)^{3/2} \, dx","Integrate[c^5*x^5*(a/x^4 + b*x^n)^(3/2),x]","\frac{2 c^5 x^2 \sqrt{\frac{a}{x^4}+b x^n} \left(\sqrt{a+b x^{n+4}} \left(4 a+b x^{n+4}\right)-3 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x^{n+4}}}{\sqrt{a}}\right)\right)}{3 (n+4) \sqrt{a+b x^{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*c^5*x^2*Sqrt[a/x^4 + b*x^n]*(Sqrt[a + b*x^(4 + n)]*(4*a + b*x^(4 + n)) - 3*a^(3/2)*ArcTanh[Sqrt[a + b*x^(4 + n)]/Sqrt[a]]))/(3*(4 + n)*Sqrt[a + b*x^(4 + n)])","A",1
382,1,58,51,0.0288064,"\int \sqrt{\frac{a+b x}{x^2}} \, dx","Integrate[Sqrt[(a + b*x)/x^2],x]","\frac{2 x \sqrt{\frac{a+b x}{x^2}} \left(\sqrt{a+b x}-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)\right)}{\sqrt{a+b 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)",1,"(2*x*Sqrt[(a + b*x)/x^2]*(Sqrt[a + b*x] - Sqrt[a]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]]))/Sqrt[a + b*x]","A",1
383,1,62,42,0.0319595,"\int \sqrt{\frac{a+b x^2}{x^2}} \, dx","Integrate[Sqrt[(a + b*x^2)/x^2],x]","x \sqrt{\frac{a}{x^2}+b}-\frac{\sqrt{a} x \sqrt{\frac{a}{x^2}+b} \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a+b x^2}}","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]*Sqrt[b + a/x^2]*x*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/Sqrt[a + b*x^2]","A",1
384,1,66,51,0.0375356,"\int \sqrt{\frac{a+b x^3}{x^2}} \, dx","Integrate[Sqrt[(a + b*x^3)/x^2],x]","\frac{2 x \sqrt{\frac{a}{x^2}+b x} \left(\sqrt{a+b x^3}-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)\right)}{3 \sqrt{a+b x^3}}","\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]*(Sqrt[a + b*x^3] - Sqrt[a]*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]]))/(3*Sqrt[a + b*x^3])","A",1
385,1,70,61,0.0224128,"\int \sqrt{\frac{a+b x^n}{x^2}} \, dx","Integrate[Sqrt[(a + b*x^n)/x^2],x]","\frac{x \sqrt{\frac{a+b x^n}{x^2}} \left(2 \sqrt{a+b x^n}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x^n}}{\sqrt{a}}\right)\right)}{n \sqrt{a+b x^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,"(x*Sqrt[(a + b*x^n)/x^2]*(2*Sqrt[a + b*x^n] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*x^n]/Sqrt[a]]))/(n*Sqrt[a + b*x^n])","A",1
386,1,66,53,0.0314389,"\int \sqrt{\frac{-a+b x}{x^2}} \, dx","Integrate[Sqrt[(-a + b*x)/x^2],x]","\frac{2 x \sqrt{\frac{b x-a}{x^2}} \left(\sqrt{b x-a}-\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b x-a}}{\sqrt{a}}\right)\right)}{\sqrt{b x-a}}","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*x*Sqrt[(-a + b*x)/x^2]*(Sqrt[-a + b*x] - Sqrt[a]*ArcTan[Sqrt[-a + b*x]/Sqrt[a]]))/Sqrt[-a + b*x]","A",1
387,1,68,43,0.0344247,"\int \sqrt{\frac{-a+b x^2}{x^2}} \, dx","Integrate[Sqrt[(-a + b*x^2)/x^2],x]","x \sqrt{b-\frac{a}{x^2}}-\frac{\sqrt{a} x \sqrt{b-\frac{a}{x^2}} \tan ^{-1}\left(\frac{\sqrt{b x^2-a}}{\sqrt{a}}\right)}{\sqrt{b x^2-a}}","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]*Sqrt[b - a/x^2]*x*ArcTan[Sqrt[-a + b*x^2]/Sqrt[a]])/Sqrt[-a + b*x^2]","A",1
388,1,73,53,0.0423565,"\int \sqrt{\frac{-a+b x^3}{x^2}} \, dx","Integrate[Sqrt[(-a + b*x^3)/x^2],x]","\frac{2 x \sqrt{b x-\frac{a}{x^2}} \left(\sqrt{b x^3-a}-\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b x^3-a}}{\sqrt{a}}\right)\right)}{3 \sqrt{b x^3-a}}","\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]*(Sqrt[-a + b*x^3] - Sqrt[a]*ArcTan[Sqrt[-a + b*x^3]/Sqrt[a]]))/(3*Sqrt[-a + b*x^3])","A",1
389,1,78,63,0.0316654,"\int \sqrt{\frac{-a+b x^n}{x^2}} \, dx","Integrate[Sqrt[(-a + b*x^n)/x^2],x]","\frac{x \sqrt{\frac{b x^n-a}{x^2}} \left(2 \sqrt{b x^n-a}-2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b x^n-a}}{\sqrt{a}}\right)\right)}{n \sqrt{b x^n-a}}","\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,"(x*Sqrt[(-a + b*x^n)/x^2]*(2*Sqrt[-a + b*x^n] - 2*Sqrt[a]*ArcTan[Sqrt[-a + b*x^n]/Sqrt[a]]))/(n*Sqrt[-a + b*x^n])","A",1
390,1,98,62,0.1608026,"\int \frac{(c x)^{-1+\frac{j}{2}}}{\sqrt{a x^j+b x^n}} \, dx","Integrate[(c*x)^(-1 + j/2)/Sqrt[a*x^j + b*x^n],x]","\frac{2 \sqrt{b} (c x)^{j/2} x^{\frac{n-j}{2}} \sqrt{\frac{a x^{j-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{j-n}{2}}}{\sqrt{b}}\right)}{\sqrt{a} c (j-n) \sqrt{a x^j+b x^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*Sqrt[b]*x^((-j + n)/2)*(c*x)^(j/2)*Sqrt[1 + (a*x^(j - n))/b]*ArcSinh[(Sqrt[a]*x^((j - n)/2))/Sqrt[b]])/(Sqrt[a]*c*(j - n)*Sqrt[a*x^j + b*x^n])","A",1
391,1,89,53,0.1692078,"\int \frac{\sqrt{c x}}{\sqrt{a x^3+b x^n}} \, dx","Integrate[Sqrt[c*x]/Sqrt[a*x^3 + b*x^n],x]","-\frac{2 \sqrt{b} \sqrt{c x} x^{\frac{n-1}{2}} \sqrt{\frac{a x^{3-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{3}{2}-\frac{n}{2}}}{\sqrt{b}}\right)}{\sqrt{a} (n-3) \sqrt{a x^3+b x^n}}","\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[b]*x^((-1 + n)/2)*Sqrt[c*x]*Sqrt[1 + (a*x^(3 - n))/b]*ArcSinh[(Sqrt[a]*x^(3/2 - n/2))/Sqrt[b]])/(Sqrt[a]*(-3 + n)*Sqrt[a*x^3 + b*x^n])","A",1
392,1,78,37,0.0739359,"\int \frac{1}{\sqrt{a x^2+b x^n}} \, dx","Integrate[1/Sqrt[a*x^2 + b*x^n],x]","-\frac{2 \sqrt{b} x^{n/2} \sqrt{\frac{a x^{2-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{1-\frac{n}{2}}}{\sqrt{b}}\right)}{\sqrt{a} (n-2) \sqrt{a x^2+b x^n}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{a x^2+b x^n}}\right)}{\sqrt{a} (2-n)}",1,"(-2*Sqrt[b]*x^(n/2)*Sqrt[1 + (a*x^(2 - n))/b]*ArcSinh[(Sqrt[a]*x^(1 - n/2))/Sqrt[b]])/(Sqrt[a]*(-2 + n)*Sqrt[a*x^2 + b*x^n])","B",1
393,1,87,51,0.134756,"\int \frac{1}{\sqrt{c x} \sqrt{a x+b x^n}} \, dx","Integrate[1/(Sqrt[c*x]*Sqrt[a*x + b*x^n]),x]","-\frac{2 \sqrt{b} x^{\frac{n+1}{2}} \sqrt{\frac{a x^{1-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{1}{2}-\frac{n}{2}}}{\sqrt{b}}\right)}{\sqrt{a} (n-1) \sqrt{c x} \sqrt{a x+b x^n}}","\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[b]*x^((1 + n)/2)*Sqrt[1 + (a*x^(1 - n))/b]*ArcSinh[(Sqrt[a]*x^(1/2 - n/2))/Sqrt[b]])/(Sqrt[a]*(-1 + n)*Sqrt[c*x]*Sqrt[a*x + b*x^n])","A",1
394,1,31,31,0.007074,"\int \frac{1}{c x \sqrt{a+b x^n}} \, dx","Integrate[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",1
395,1,68,54,0.0496841,"\int \frac{1}{(c x)^{3/2} \sqrt{\frac{a}{x}+b x^n}} \, dx","Integrate[1/((c*x)^(3/2)*Sqrt[a/x + b*x^n]),x]","-\frac{2 x \sqrt{a+b x^{n+1}} \tanh ^{-1}\left(\frac{\sqrt{a+b x^{n+1}}}{\sqrt{a}}\right)}{\sqrt{a} (n+1) (c x)^{3/2} \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)}{\sqrt{a} c (n+1) \sqrt{c x}}",1,"(-2*x*Sqrt[a + b*x^(1 + n)]*ArcTanh[Sqrt[a + b*x^(1 + n)]/Sqrt[a]])/(Sqrt[a]*(1 + n)*(c*x)^(3/2)*Sqrt[a/x + b*x^n])","A",1
396,1,66,40,0.0478402,"\int \frac{1}{c^2 x^2 \sqrt{\frac{a}{x^2}+b x^n}} \, dx","Integrate[1/(c^2*x^2*Sqrt[a/x^2 + b*x^n]),x]","-\frac{2 \sqrt{a+b x^{n+2}} \tanh ^{-1}\left(\frac{\sqrt{a+b x^{n+2}}}{\sqrt{a}}\right)}{\sqrt{a} c^2 (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)}{\sqrt{a} c^2 (n+2)}",1,"(-2*Sqrt[a + b*x^(2 + n)]*ArcTanh[Sqrt[a + b*x^(2 + n)]/Sqrt[a]])/(Sqrt[a]*c^2*(2 + n)*x*Sqrt[a/x^2 + b*x^n])","A",1
397,1,68,54,0.0570644,"\int \frac{1}{(c x)^{5/2} \sqrt{\frac{a}{x^3}+b x^n}} \, dx","Integrate[1/((c*x)^(5/2)*Sqrt[a/x^3 + b*x^n]),x]","-\frac{2 x \sqrt{a+b x^{n+3}} \tanh ^{-1}\left(\frac{\sqrt{a+b x^{n+3}}}{\sqrt{a}}\right)}{\sqrt{a} (n+3) (c x)^{5/2} \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)}{\sqrt{a} c^2 (n+3) \sqrt{c x}}",1,"(-2*x*Sqrt[a + b*x^(3 + n)]*ArcTanh[Sqrt[a + b*x^(3 + n)]/Sqrt[a]])/(Sqrt[a]*(3 + n)*(c*x)^(5/2)*Sqrt[a/x^3 + b*x^n])","A",1
398,1,117,107,0.1994156,"\int \frac{(c x)^{-1+\frac{3 j}{2}}}{\left(a x^j+b x^n\right)^{3/2}} \, dx","Integrate[(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} \left(\sqrt{a} x^{j/2}-\sqrt{b} x^{n/2} \sqrt{\frac{a x^{j-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{j-n}{2}}}{\sqrt{b}}\right)\right)}{a^{3/2} 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)*(Sqrt[a]*x^(j/2) - Sqrt[b]*x^(n/2)*Sqrt[1 + (a*x^(j - n))/b]*ArcSinh[(Sqrt[a]*x^((j - n)/2))/Sqrt[b]]))/(a^(3/2)*c*(j - n)*x^((3*j)/2)*Sqrt[a*x^j + b*x^n])","A",1
399,1,109,94,0.2087609,"\int \frac{(c x)^{7/2}}{\left(a x^3+b x^n\right)^{3/2}} \, dx","Integrate[(c*x)^(7/2)/(a*x^3 + b*x^n)^(3/2),x]","\frac{2 c^3 \sqrt{c x} \left(\sqrt{a} x^{3/2}-\sqrt{b} x^{n/2} \sqrt{\frac{a x^{3-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{3}{2}-\frac{n}{2}}}{\sqrt{b}}\right)\right)}{a^{3/2} (n-3) \sqrt{x} \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^3*Sqrt[c*x]*(Sqrt[a]*x^(3/2) - Sqrt[b]*x^(n/2)*Sqrt[1 + (a*x^(3 - n))/b]*ArcSinh[(Sqrt[a]*x^(3/2 - n/2))/Sqrt[b]]))/(a^(3/2)*(-3 + n)*Sqrt[x]*Sqrt[a*x^3 + b*x^n])","A",1
400,1,91,72,0.1520217,"\int \frac{c^2 x^2}{\left(a x^2+b x^n\right)^{3/2}} \, dx","Integrate[(c^2*x^2)/(a*x^2 + b*x^n)^(3/2),x]","\frac{2 c^2 \left(\sqrt{a} x-\sqrt{b} x^{n/2} \sqrt{\frac{a x^{2-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{1-\frac{n}{2}}}{\sqrt{b}}\right)\right)}{a^{3/2} (n-2) \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*(Sqrt[a]*x - Sqrt[b]*x^(n/2)*Sqrt[1 + (a*x^(2 - n))/b]*ArcSinh[(Sqrt[a]*x^(1 - n/2))/Sqrt[b]]))/(a^(3/2)*(-2 + n)*Sqrt[a*x^2 + b*x^n])","A",1
401,1,104,85,0.2007701,"\int \frac{\sqrt{c x}}{\left(a x+b x^n\right)^{3/2}} \, dx","Integrate[Sqrt[c*x]/(a*x + b*x^n)^(3/2),x]","\frac{2 \sqrt{c x} \left(\sqrt{a} \sqrt{x}-\sqrt{b} x^{n/2} \sqrt{\frac{a x^{1-n}}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} x^{\frac{1}{2}-\frac{n}{2}}}{\sqrt{b}}\right)\right)}{a^{3/2} (n-1) \sqrt{x} \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]*(Sqrt[a]*Sqrt[x] - Sqrt[b]*x^(n/2)*Sqrt[1 + (a*x^(1 - n))/b]*ArcSinh[(Sqrt[a]*x^(1/2 - n/2))/Sqrt[b]]))/(a^(3/2)*(-1 + n)*Sqrt[x]*Sqrt[a*x + b*x^n])","A",1
402,1,40,54,0.0138631,"\int \frac{1}{c x \left(a+b x^n\right)^{3/2}} \, dx","Integrate[1/(c*x*(a + b*x^n)^(3/2)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x^n}{a}+1\right)}{a c n \sqrt{a+b x^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*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x^n)/a])/(a*c*n*Sqrt[a + b*x^n])","C",1
403,1,55,90,0.0485999,"\int \frac{1}{(c x)^{5/2} \left(\frac{a}{x}+b x^n\right)^{3/2}} \, dx","Integrate[1/((c*x)^(5/2)*(a/x + b*x^n)^(3/2)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x^{n+1}}{a}+1\right)}{a c^2 (n+1) \sqrt{c x} \sqrt{\frac{a}{x}+b x^n}}","\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*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x^(1 + n))/a])/(a*c^2*(1 + n)*Sqrt[c*x]*Sqrt[a/x + b*x^n])","C",1
404,1,51,72,0.0434972,"\int \frac{1}{c^4 x^4 \left(\frac{a}{x^2}+b x^n\right)^{3/2}} \, dx","Integrate[1/(c^4*x^4*(a/x^2 + b*x^n)^(3/2)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x^{n+2}}{a}+1\right)}{a c^4 (n+2) x \sqrt{\frac{a}{x^2}+b x^n}}","\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*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x^(2 + n))/a])/(a*c^4*(2 + n)*x*Sqrt[a/x^2 + b*x^n])","C",1
405,1,55,90,0.0546719,"\int \frac{1}{(c x)^{11/2} \left(\frac{a}{x^3}+b x^n\right)^{3/2}} \, dx","Integrate[1/((c*x)^(11/2)*(a/x^3 + b*x^n)^(3/2)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x^{n+3}}{a}+1\right)}{a c^4 (n+3) (c x)^{3/2} \sqrt{\frac{a}{x^3}+b x^n}}","\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*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x^(3 + n))/a])/(a*c^4*(3 + n)*(c*x)^(3/2)*Sqrt[a/x^3 + b*x^n])","C",1
406,1,51,72,0.0651209,"\int \frac{1}{c^7 x^7 \left(\frac{a}{x^4}+b x^n\right)^{3/2}} \, dx","Integrate[1/(c^7*x^7*(a/x^4 + b*x^n)^(3/2)),x]","\frac{2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{b x^{n+4}}{a}+1\right)}{a c^7 (n+4) x^2 \sqrt{\frac{a}{x^4}+b x^n}}","\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*Hypergeometric2F1[-1/2, 1, 1/2, 1 + (b*x^(4 + n))/a])/(a*c^7*(4 + n)*x^2*Sqrt[a/x^4 + b*x^n])","C",1
407,1,63,32,0.025465,"\int \frac{1}{\sqrt{\frac{a+b x^3}{x}}} \, dx","Integrate[1/Sqrt[(a + b*x^3)/x],x]","\frac{2 \sqrt{a+b x^3} \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a+b x^3}}\right)}{3 \sqrt{b} \sqrt{x} \sqrt{\frac{a+b x^3}{x}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x}+b x^2}}\right)}{3 \sqrt{b}}",1,"(2*Sqrt[a + b*x^3]*ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a + b*x^3]])/(3*Sqrt[b]*Sqrt[x]*Sqrt[(a + b*x^3)/x])","A",1
408,1,59,32,0.0197464,"\int \frac{1}{\sqrt{\frac{a+b x^4}{x^2}}} \, dx","Integrate[1/Sqrt[(a + b*x^4)/x^2],x]","\frac{\sqrt{a+b x^4} \tanh ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a+b x^4}}\right)}{2 \sqrt{b} x \sqrt{\frac{a+b x^4}{x^2}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^2}+b x^2}}\right)}{2 \sqrt{b}}",1,"(Sqrt[a + b*x^4]*ArcTanh[(Sqrt[b]*x^2)/Sqrt[a + b*x^4]])/(2*Sqrt[b]*x*Sqrt[(a + b*x^4)/x^2])","A",1
409,1,63,32,0.029305,"\int \frac{1}{\sqrt{\frac{a+b x^5}{x^3}}} \, dx","Integrate[1/Sqrt[(a + b*x^5)/x^3],x]","\frac{2 \sqrt{a+b x^5} \tanh ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a+b x^5}}\right)}{5 \sqrt{b} x^{3/2} \sqrt{\frac{a+b x^5}{x^3}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^3}+b x^2}}\right)}{5 \sqrt{b}}",1,"(2*Sqrt[a + b*x^5]*ArcTanh[(Sqrt[b]*x^(5/2))/Sqrt[a + b*x^5]])/(5*Sqrt[b]*x^(3/2)*Sqrt[(a + b*x^5)/x^3])","A",1
410,1,76,37,0.0500871,"\int \frac{1}{\sqrt{x^{2-n} \left(a+b x^n\right)}} \, dx","Integrate[1/Sqrt[x^(2 - n)*(a + b*x^n)],x]","\frac{2 \sqrt{a} x^{1-\frac{n}{2}} \sqrt{\frac{b x^n}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a}}\right)}{\sqrt{b} n \sqrt{x^{2-n} \left(a+b x^n\right)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^{2-n}+b x^2}}\right)}{\sqrt{b} n}",1,"(2*Sqrt[a]*x^(1 - n/2)*Sqrt[1 + (b*x^n)/a]*ArcSinh[(Sqrt[b]*x^(n/2))/Sqrt[a]])/(Sqrt[b]*n*Sqrt[x^(2 - n)*(a + b*x^n)])","B",1
411,1,66,33,0.0325246,"\int \frac{1}{\sqrt{\frac{a-b x^3}{x}}} \, dx","Integrate[1/Sqrt[(a - b*x^3)/x],x]","\frac{2 \sqrt{a-b x^3} \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a-b x^3}}\right)}{3 \sqrt{b} \sqrt{x} \sqrt{\frac{a-b x^3}{x}}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x}-b x^2}}\right)}{3 \sqrt{b}}",1,"(2*Sqrt[a - b*x^3]*ArcTan[(Sqrt[b]*x^(3/2))/Sqrt[a - b*x^3]])/(3*Sqrt[b]*Sqrt[x]*Sqrt[(a - b*x^3)/x])","A",1
412,1,62,33,0.0229549,"\int \frac{1}{\sqrt{\frac{a-b x^4}{x^2}}} \, dx","Integrate[1/Sqrt[(a - b*x^4)/x^2],x]","\frac{\sqrt{a-b x^4} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a-b x^4}}\right)}{2 \sqrt{b} x \sqrt{\frac{a-b x^4}{x^2}}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^2}-b x^2}}\right)}{2 \sqrt{b}}",1,"(Sqrt[a - b*x^4]*ArcTan[(Sqrt[b]*x^2)/Sqrt[a - b*x^4]])/(2*Sqrt[b]*x*Sqrt[(a - b*x^4)/x^2])","A",1
413,1,66,33,0.0284028,"\int \frac{1}{\sqrt{\frac{a-b x^5}{x^3}}} \, dx","Integrate[1/Sqrt[(a - b*x^5)/x^3],x]","\frac{2 \sqrt{a-b x^5} \tan ^{-1}\left(\frac{\sqrt{b} x^{5/2}}{\sqrt{a-b x^5}}\right)}{5 \sqrt{b} x^{3/2} \sqrt{\frac{a-b x^5}{x^3}}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{\frac{a}{x^3}-b x^2}}\right)}{5 \sqrt{b}}",1,"(2*Sqrt[a - b*x^5]*ArcTan[(Sqrt[b]*x^(5/2))/Sqrt[a - b*x^5]])/(5*Sqrt[b]*x^(3/2)*Sqrt[(a - b*x^5)/x^3])","A",1
414,1,78,38,0.0591615,"\int \frac{1}{\sqrt{x^{2-n} \left(a-b x^n\right)}} \, dx","Integrate[1/Sqrt[x^(2 - n)*(a - b*x^n)],x]","\frac{2 \sqrt{a} x^{1-\frac{n}{2}} \sqrt{1-\frac{b x^n}{a}} \sin ^{-1}\left(\frac{\sqrt{b} x^{n/2}}{\sqrt{a}}\right)}{\sqrt{b} n \sqrt{x^{2-n} \left(a-b x^n\right)}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^{2-n}-b x^2}}\right)}{\sqrt{b} n}",1,"(2*Sqrt[a]*x^(1 - n/2)*Sqrt[1 - (b*x^n)/a]*ArcSin[(Sqrt[b]*x^(n/2))/Sqrt[a]])/(Sqrt[b]*n*Sqrt[x^(2 - n)*(a - b*x^n)])","B",1
415,1,78,37,0.1026622,"\int \frac{1}{\sqrt{x^n \left(a+b x^{2-n}\right)}} \, dx","Integrate[1/Sqrt[x^n*(a + b*x^(2 - n))],x]","-\frac{2 \sqrt{a} x^{n/2} \sqrt{\frac{b x^{2-n}}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x^{1-\frac{n}{2}}}{\sqrt{a}}\right)}{\sqrt{b} (n-2) \sqrt{a x^n+b x^2}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n+b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(-2*Sqrt[a]*x^(n/2)*Sqrt[1 + (b*x^(2 - n))/a]*ArcSinh[(Sqrt[b]*x^(1 - n/2))/Sqrt[a]])/(Sqrt[b]*(-2 + n)*Sqrt[b*x^2 + a*x^n])","B",1
416,1,78,37,0.0401665,"\int \frac{1}{\sqrt{x^2 \left(b+a x^{-2+n}\right)}} \, dx","Integrate[1/Sqrt[x^2*(b + a*x^(-2 + n))],x]","-\frac{2 \sqrt{a} x^{n/2} \sqrt{\frac{b x^{2-n}}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x^{1-\frac{n}{2}}}{\sqrt{a}}\right)}{\sqrt{b} (n-2) \sqrt{a x^n+b x^2}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n+b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(-2*Sqrt[a]*x^(n/2)*Sqrt[1 + (b*x^(2 - n))/a]*ArcSinh[(Sqrt[b]*x^(1 - n/2))/Sqrt[a]])/(Sqrt[b]*(-2 + n)*Sqrt[b*x^2 + a*x^n])","B",1
417,1,78,37,0.0285789,"\int \frac{1}{\sqrt{x \left(b x+a x^{-1+n}\right)}} \, dx","Integrate[1/Sqrt[x*(b*x + a*x^(-1 + n))],x]","-\frac{2 \sqrt{a} x^{n/2} \sqrt{\frac{b x^{2-n}}{a}+1} \sinh ^{-1}\left(\frac{\sqrt{b} x^{1-\frac{n}{2}}}{\sqrt{a}}\right)}{\sqrt{b} (n-2) \sqrt{a x^n+b x^2}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n+b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(-2*Sqrt[a]*x^(n/2)*Sqrt[1 + (b*x^(2 - n))/a]*ArcSinh[(Sqrt[b]*x^(1 - n/2))/Sqrt[a]])/(Sqrt[b]*(-2 + n)*Sqrt[b*x^2 + a*x^n])","B",1
418,1,80,38,0.1055493,"\int \frac{1}{\sqrt{x^n \left(a-b x^{2-n}\right)}} \, dx","Integrate[1/Sqrt[x^n*(a - b*x^(2 - n))],x]","-\frac{2 \sqrt{a} x^{n/2} \sqrt{1-\frac{b x^{2-n}}{a}} \sin ^{-1}\left(\frac{\sqrt{b} x^{1-\frac{n}{2}}}{\sqrt{a}}\right)}{\sqrt{b} (n-2) \sqrt{a x^n-b x^2}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n-b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(-2*Sqrt[a]*x^(n/2)*Sqrt[1 - (b*x^(2 - n))/a]*ArcSin[(Sqrt[b]*x^(1 - n/2))/Sqrt[a]])/(Sqrt[b]*(-2 + n)*Sqrt[-(b*x^2) + a*x^n])","B",1
419,1,80,38,0.0249841,"\int \frac{1}{\sqrt{x^2 \left(-b+a x^{-2+n}\right)}} \, dx","Integrate[1/Sqrt[x^2*(-b + a*x^(-2 + n))],x]","-\frac{2 \sqrt{a} x^{n/2} \sqrt{1-\frac{b x^{2-n}}{a}} \sin ^{-1}\left(\frac{\sqrt{b} x^{1-\frac{n}{2}}}{\sqrt{a}}\right)}{\sqrt{b} (n-2) \sqrt{a x^n-b x^2}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n-b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(-2*Sqrt[a]*x^(n/2)*Sqrt[1 - (b*x^(2 - n))/a]*ArcSin[(Sqrt[b]*x^(1 - n/2))/Sqrt[a]])/(Sqrt[b]*(-2 + n)*Sqrt[-(b*x^2) + a*x^n])","B",1
420,1,80,38,0.0284851,"\int \frac{1}{\sqrt{x \left(-b x+a x^{-1+n}\right)}} \, dx","Integrate[1/Sqrt[x*(-(b*x) + a*x^(-1 + n))],x]","-\frac{2 \sqrt{a} x^{n/2} \sqrt{1-\frac{b x^{2-n}}{a}} \sin ^{-1}\left(\frac{\sqrt{b} x^{1-\frac{n}{2}}}{\sqrt{a}}\right)}{\sqrt{b} (n-2) \sqrt{a x^n-b x^2}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x^n-b x^2}}\right)}{\sqrt{b} (2-n)}",1,"(-2*Sqrt[a]*x^(n/2)*Sqrt[1 - (b*x^(2 - n))/a]*ArcSin[(Sqrt[b]*x^(1 - n/2))/Sqrt[a]])/(Sqrt[b]*(-2 + n)*Sqrt[-(b*x^2) + a*x^n])","B",1
421,1,218,107,0.4117076,"\int (c x)^m \left(a x^j+b x^n\right)^{3/2} \, dx","Integrate[(c*x)^m*(a*x^j + b*x^n)^(3/2),x]","\frac{2 (c x)^m \left(3 a^2 (j-n)^2 x^{2 j+1} \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{4 j+2 m-n+2}{2 j-2 n};\frac{6 j+2 m-3 n+2}{2 j-2 n};-\frac{a x^{j-n}}{b}\right)+x^{-m} (4 j+2 m-n+2) \left(a x^j+b x^n\right) \left(a (-j+2 m+4 n+2) x^{j+m+1}+b (2 j+2 m+n+2) x^{m+n+1}\right)\right)}{(2 m+3 n+2) (4 j+2 m-n+2) (2 j+2 m+n+2) \sqrt{a x^j+b x^n}}","\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*(c*x)^m*(((2 + 4*j + 2*m - n)*(a*x^j + b*x^n)*(a*(2 - j + 2*m + 4*n)*x^(1 + j + m) + b*(2 + 2*j + 2*m + n)*x^(1 + m + n)))/x^m + 3*a^2*(j - n)^2*x^(1 + 2*j)*Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[1/2, (2 + 4*j + 2*m - n)/(2*j - 2*n), (2 + 6*j + 2*m - 3*n)/(2*j - 2*n), -((a*x^(j - n))/b)]))/((2 + 4*j + 2*m - n)*(2 + 2*j + 2*m + n)*(2 + 2*m + 3*n)*Sqrt[a*x^j + b*x^n])","B",1
422,1,156,100,0.2101385,"\int (c x)^m \sqrt{a x^j+b x^n} \, dx","Integrate[(c*x)^m*Sqrt[a*x^j + b*x^n],x]","\frac{2 x (c x)^m \left((2 j+2 m-n+2) \left(a x^j+b x^n\right)-a (j-n) x^j \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{2 j+2 m-n+2}{2 j-2 n};\frac{4 j+2 m-3 n+2}{2 j-2 n};-\frac{a x^{j-n}}{b}\right)\right)}{(2 m+n+2) (2 j+2 m-n+2) \sqrt{a x^j+b x^n}}","\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*((2 + 2*j + 2*m - n)*(a*x^j + b*x^n) - a*(j - n)*x^j*Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[1/2, (2 + 2*j + 2*m - n)/(2*j - 2*n), (2 + 4*j + 2*m - 3*n)/(2*j - 2*n), -((a*x^(j - n))/b)]))/((2 + 2*j + 2*m - n)*(2 + 2*m + n)*Sqrt[a*x^j + b*x^n])","A",1
423,1,106,102,0.0906603,"\int \frac{(c x)^m}{\sqrt{a x^j+b x^n}} \, dx","Integrate[(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{2 m-n+2}{2 j-2 n};\frac{2 m-n+2}{2 j-2 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, (2 + 2*m - n)/(2*j - 2*n), 1 + (2 + 2*m - n)/(2*j - 2*n), -((a*x^(j - n))/b)])/((2 + 2*m - n)*Sqrt[a*x^j + b*x^n])","A",1
424,1,116,111,0.1451467,"\int \frac{(c x)^m}{\left(a x^j+b x^n\right)^{3/2}} \, dx","Integrate[(c*x)^m/(a*x^j + b*x^n)^(3/2),x]","\frac{2 x^{1-j} (c x)^m \left(\sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{-2 j+2 m-n+2}{2 j-2 n};\frac{2 m-3 n+2}{2 j-2 n};-\frac{a x^{j-n}}{b}\right)-1\right)}{a (j-n) \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 - j)*(c*x)^m*(-1 + Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[1/2, (2 - 2*j + 2*m - n)/(2*j - 2*n), (2 + 2*m - 3*n)/(2*j - 2*n), -((a*x^(j - n))/b)]))/(a*(j - n)*Sqrt[a*x^j + b*x^n])","A",1
425,1,166,111,0.5511022,"\int \frac{(c x)^m}{\left(a x^j+b x^n\right)^{5/2}} \, dx","Integrate[(c*x)^m/(a*x^j + b*x^n)^(5/2),x]","\frac{2 x^{1-2 j} (c x)^m \left(-(2 j-2 m+3 n-2) \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{-4 j+2 m-n+2}{2 j-2 n};\frac{-2 j+2 m-3 n+2}{2 j-2 n};-\frac{a x^{j-n}}{b}\right)-\frac{a (j-n) x^j}{a x^j+b x^n}+2 j-2 m+3 n-2\right)}{3 a^2 (j-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*j)*(c*x)^m*(-2 + 2*j - 2*m + 3*n - (a*(j - n)*x^j)/(a*x^j + b*x^n) - (-2 + 2*j - 2*m + 3*n)*Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[1/2, (2 - 4*j + 2*m - n)/(2*j - 2*n), (2 - 2*j + 2*m - 3*n)/(2*j - 2*n), -((a*x^(j - n))/b)]))/(3*a^2*(j - n)^2*Sqrt[a*x^j + b*x^n])","A",1
426,1,177,97,0.2286365,"\int \left(a x^j+b x^n\right)^{3/2} \, dx","Integrate[(a*x^j + b*x^n)^(3/2),x]","\frac{2 x \left(3 a^2 (j-n)^2 x^{2 j} \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{4 j-n+2}{2 j-2 n};\frac{6 j-3 n+2}{2 j-2 n};-\frac{a x^{j-n}}{b}\right)+(4 j-n+2) \left(a x^j+b x^n\right) \left(a (-j+4 n+2) x^j+b (2 j+n+2) x^n\right)\right)}{(3 n+2) (4 j-n+2) (2 j+n+2) \sqrt{a x^j+b x^n}}","\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*x*((2 + 4*j - n)*(a*x^j + b*x^n)*(a*(2 - j + 4*n)*x^j + b*(2 + 2*j + n)*x^n) + 3*a^2*(j - n)^2*x^(2*j)*Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[1/2, (2 + 4*j - n)/(2*j - 2*n), (2 + 6*j - 3*n)/(2*j - 2*n), -((a*x^(j - n))/b)]))/((2 + 4*j - n)*(2 + 2*j + n)*(2 + 3*n)*Sqrt[a*x^j + b*x^n])","A",1
427,1,134,87,0.1659759,"\int \sqrt{a x^j+b x^n} \, dx","Integrate[Sqrt[a*x^j + b*x^n],x]","\frac{2 x \left(a (j-n) x^j \sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{1}{2},\frac{2 j-n+2}{2 j-2 n};\frac{4 j-3 n+2}{2 j-2 n};-\frac{a x^{j-n}}{b}\right)-(2 j-n+2) \left(a x^j+b x^n\right)\right)}{(n+2) (-2 j+n-2) \sqrt{a x^j+b x^n}}","\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*(-((2 + 2*j - n)*(a*x^j + b*x^n)) + a*(j - n)*x^j*Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[1/2, (2 + 2*j - n)/(2*j - 2*n), (2 + 4*j - 3*n)/(2*j - 2*n), -((a*x^(j - n))/b)]))/((2 + n)*(-2 - 2*j + n)*Sqrt[a*x^j + b*x^n])","A",1
428,1,88,93,0.0581695,"\int \frac{1}{\sqrt{a x^j+b x^n}} \, dx","Integrate[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{n-2}{2 (n-j)};\frac{n-2}{2 (n-j)}+1;-\frac{a x^{j-n}}{b}\right)}{(n-2) \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 + (-2 + n)/(2*(-j + n)), -((a*x^(j - n))/b)])/((-2 + n)*Sqrt[a*x^j + b*x^n])","A",1
429,1,104,101,0.1230498,"\int \frac{1}{\left(a x^j+b x^n\right)^{3/2}} \, dx","Integrate[(a*x^j + b*x^n)^(-3/2),x]","\frac{2 x^{1-j} \left(\sqrt{\frac{a x^{j-n}}{b}+1} \, _2F_1\left(\frac{1}{2},-\frac{2 j+n-2}{2 (j-n)};\frac{2-3 n}{2 j-2 n};-\frac{a x^{j-n}}{b}\right)-1\right)}{a (j-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 - j)*(-1 + Sqrt[1 + (a*x^(j - n))/b]*Hypergeometric2F1[1/2, -1/2*(-2 + 2*j + n)/(j - n), (2 - 3*n)/(2*j - 2*n), -((a*x^(j - n))/b)]))/(a*(j - n)*Sqrt[a*x^j + b*x^n])","A",1
430,1,185,101,0.3817564,"\int \frac{1}{\left(a x^j+b x^n\right)^{5/2}} \, dx","Integrate[(a*x^j + b*x^n)^(-5/2),x]","\frac{2 x^{1-2 j} \left(\left(8 j^2+2 j (7 n-6)+3 n^2-8 n+4\right) \sqrt{\frac{a x^{j-n}}{b}+1} \left(a x^j+b x^n\right) \, _2F_1\left(\frac{1}{2},-\frac{4 j+n-2}{2 (j-n)};\frac{-2 j-3 n+2}{2 j-2 n};-\frac{a x^{j-n}}{b}\right)-(4 j+n-2) \left(a (j+4 n-2) x^j+b (2 j+3 n-2) x^n\right)\right)}{3 a^2 (-4 j-n+2) (j-n)^2 \left(a x^j+b x^n\right)^{3/2}}","\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*j)*(-((-2 + 4*j + n)*(a*(-2 + j + 4*n)*x^j + b*(-2 + 2*j + 3*n)*x^n)) + (4 + 8*j^2 - 8*n + 3*n^2 + 2*j*(-6 + 7*n))*Sqrt[1 + (a*x^(j - n))/b]*(a*x^j + b*x^n)*Hypergeometric2F1[1/2, -1/2*(-2 + 4*j + n)/(j - n), (2 - 2*j - 3*n)/(2*j - 2*n), -((a*x^(j - n))/b)]))/(3*a^2*(2 - 4*j - n)*(j - n)^2*(a*x^j + b*x^n)^(3/2))","A",1
431,1,19,18,0.0056492,"\int \sqrt{\frac{1+x}{x^5}} \, dx","Integrate[Sqrt[(1 + x)/x^5],x]","-\frac{2}{3} x (x+1) \sqrt{\frac{x+1}{x^5}}","-\frac{2}{3} \left(\frac{1}{x^5}+\frac{1}{x^4}\right)^{3/2} x^6",1,"(-2*x*(1 + x)*Sqrt[(1 + x)/x^5])/3","A",1
432,1,20,20,0.0100367,"\int \sqrt{x+x^{5/2}} \, dx","Integrate[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
433,1,8,8,0.0021485,"\int \frac{1}{\sqrt{x}+x^{3/2}} \, dx","Integrate[(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",1
434,1,25,25,0.0128101,"\int x \sqrt{x^2 \left(a+b x^3\right)} \, dx","Integrate[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
435,1,25,25,0.0027697,"\int x \sqrt{a x^2+b x^5} \, dx","Integrate[x*Sqrt[a*x^2 + b*x^5],x]","\frac{2 \left(x^2 \left(a+b x^3\right)\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*(x^2*(a + b*x^3))^(3/2))/(9*b*x^3)","A",1
436,1,25,25,0.0121895,"\int \sqrt{x^4 \left(a+b x^3\right)} \, dx","Integrate[Sqrt[x^4*(a + b*x^3)],x]","\frac{2 \left(x^4 \left(a+b x^3\right)\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*(x^4*(a + b*x^3))^(3/2))/(9*b*x^6)","A",1
437,1,61,988,0.0211651,"\int \frac{1}{\sqrt[3]{a \sqrt[3]{x}+b x^{2/3}}} \, dx","Integrate[(a*x^(1/3) + b*x^(2/3))^(-1/3),x]","\frac{9 x \sqrt[3]{\frac{b \sqrt[3]{x}}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{8}{3};\frac{11}{3};-\frac{b \sqrt[3]{x}}{a}\right)}{8 \sqrt[3]{\sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)}}","-\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,"(9*(1 + (b*x^(1/3))/a)^(1/3)*x*Hypergeometric2F1[1/3, 8/3, 11/3, -((b*x^(1/3))/a)])/(8*((a + b*x^(1/3))*x^(1/3))^(1/3))","C",1
438,1,61,487,0.0170448,"\int \frac{1}{\left(a \sqrt[3]{x}+b x^{2/3}\right)^{2/3}} \, dx","Integrate[(a*x^(1/3) + b*x^(2/3))^(-2/3),x]","\frac{9 x \left(\frac{b \sqrt[3]{x}}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{7}{3};\frac{10}{3};-\frac{b \sqrt[3]{x}}{a}\right)}{7 \left(\sqrt[3]{x} \left(a+b \sqrt[3]{x}\right)\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,"(9*(1 + (b*x^(1/3))/a)^(2/3)*x*Hypergeometric2F1[2/3, 7/3, 10/3, -((b*x^(1/3))/a)])/(7*((a + b*x^(1/3))*x^(1/3))^(2/3))","C",1
439,1,92,89,0.1346048,"\int x^m \left(a x^j+b x^n\right)^p \, dx","Integrate[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",1
440,1,73,69,0.1745974,"\int x^{-1-p q} \left(b x^n+a x^q\right)^p \, dx","Integrate[x^(-1 - p*q)*(b*x^n + a*x^q)^p,x]","\frac{x^{-p q} \left(a x^q+b x^n\right)^p \left(\frac{a x^{q-n}}{b}+1\right)^{-p} \, _2F_1\left(-p,-p;1-p;-\frac{a x^{q-n}}{b}\right)}{p (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,"((b*x^n + a*x^q)^p*Hypergeometric2F1[-p, -p, 1 - p, -((a*x^(-n + q))/b)])/(p*(n - q)*x^(p*q)*(1 + (a*x^(-n + q))/b)^p)","A",1
441,1,74,66,0.1289191,"\int x^{-1-n p} \left(b x^n+a x^q\right)^p \, dx","Integrate[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",1
442,1,82,69,0.1983476,"\int x^{-1-n-(-1+p) q} \left(b x^n+a x^q\right)^p \, dx","Integrate[x^(-1 - n - (-1 + p)*q)*(b*x^n + a*x^q)^p,x]","\frac{x^{-n-p q+q} \left(a x^q+b x^n\right)^p \left(\frac{a x^{q-n}}{b}+1\right)^{-p} \, _2F_1\left(1-p,-p;2-p;-\frac{a x^{q-n}}{b}\right)}{(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,"(x^(-n + q - p*q)*(b*x^n + a*x^q)^p*Hypergeometric2F1[1 - p, -p, 2 - p, -((a*x^(-n + q))/b)])/((-1 + p)*(n - q)*(1 + (a*x^(-n + q))/b)^p)","A",1
443,1,83,84,0.1465886,"\int x^{-1-n (-1+p)-q} \left(b x^n+a x^q\right)^p \, dx","Integrate[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)}{(p-1) (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",1
444,1,43,44,0.0394373,"\int \left(a x^m+b x^{1+m+m p}\right)^p \, dx","Integrate[(a*x^m + b*x^(1 + m + m*p))^p,x]","\frac{x^{-m (p+1)} \left(x^m \left(a+b x^{m p+1}\right)\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,"(x^m*(a + b*x^(1 + m*p)))^(1 + p)/(b*(1 + p)*(1 + m*p)*x^(m*(1 + p)))","A",1
445,1,43,44,0.0027953,"\int \left(x^m \left(a+b x^{1+m p}\right)\right)^p \, dx","Integrate[(x^m*(a + b*x^(1 + m*p)))^p,x]","\frac{x^{-m (p+1)} \left(x^m \left(a+b x^{m p+1}\right)\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,"(x^m*(a + b*x^(1 + m*p)))^(1 + p)/(b*(1 + p)*(1 + m*p)*x^(m*(1 + p)))","A",1
446,1,45,46,0.046388,"\int x^n \left(x^m \left(a+b x^{1+n+m p}\right)\right)^p \, dx","Integrate[x^n*(x^m*(a + b*x^(1 + n + m*p)))^p,x]","\frac{x^{-m (p+1)} \left(x^m \left(a+b x^{m p+n+1}\right)\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,"(x^m*(a + b*x^(1 + n + m*p)))^(1 + p)/(b*(1 + p)*(1 + n + m*p)*x^(m*(1 + p)))","A",1
447,1,45,46,0.0048956,"\int x^n \left(a x^m+b x^{1+m+n+m p}\right)^p \, dx","Integrate[x^n*(a*x^m + b*x^(1 + m + n + m*p))^p,x]","\frac{x^{-m (p+1)} \left(x^m \left(a+b x^{m p+n+1}\right)\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,"(x^m*(a + b*x^(1 + n + m*p)))^(1 + p)/(b*(1 + p)*(1 + n + m*p)*x^(m*(1 + p)))","A",1
448,1,36,44,0.0329164,"\int \sqrt{x^{2 (-1+n)} \left(a+b x^n\right)} \, dx","Integrate[Sqrt[x^(2*(-1 + n))*(a + b*x^n)],x]","\frac{2 x^{3-3 n} \left(x^{2 n-2} \left(a+b x^n\right)\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 - 3*n)*(x^(-2 + 2*n)*(a + b*x^n))^(3/2))/(3*b*n)","A",1
449,1,36,44,0.0326887,"\int \sqrt[3]{x^{3 (-1+n)} \left(a+b x^n\right)} \, dx","Integrate[(x^(3*(-1 + n))*(a + b*x^n))^(1/3),x]","\frac{3 x^{4-4 n} \left(x^{3 n-3} \left(a+b x^n\right)\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 - 4*n)*(x^(-3 + 3*n)*(a + b*x^n))^(4/3))/(4*b*n)","A",1
450,1,36,44,0.0327112,"\int \sqrt[4]{x^{4 (-1+n)} \left(a+b x^n\right)} \, dx","Integrate[(x^(4*(-1 + n))*(a + b*x^n))^(1/4),x]","\frac{4 x^{5-5 n} \left(x^{4 n-4} \left(a+b x^n\right)\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 - 5*n)*(x^(-4 + 4*n)*(a + b*x^n))^(5/4))/(5*b*n)","A",1
451,1,47,57,0.0234416,"\int \left(x^{(-1+n) p} \left(a+b x^n\right)\right)^{\frac{1}{p}} \, dx","Integrate[(x^((-1 + n)*p)*(a + b*x^n))^p^(-1),x]","\frac{x^{1-n} \left(a+b x^n\right) \left(x^{(n-1) p} \left(a+b x^n\right)\right)^{\frac{1}{p}}}{b n \left(\frac{1}{p}+1\right)}","\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,"(x^(1 - n)*(a + b*x^n)*(x^((-1 + n)*p)*(a + b*x^n))^p^(-1))/(b*n*(1 + p^(-1)))","A",1
452,1,45,61,0.0267005,"\int \left(x^{\frac{-1+n}{p}} \left(a+b x^n\right)\right)^p \, dx","Integrate[(x^((-1 + n)/p)*(a + b*x^n))^p,x]","\frac{x^{1-n} \left(a+b x^n\right) \left(x^{\frac{n-1}{p}} \left(a+b x^n\right)\right)^p}{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)*(a + b*x^n)*(x^((-1 + n)/p)*(a + b*x^n))^p)/(b*n*(1 + p))","A",1
453,1,40,39,0.026182,"\int x^{-1+n-p (1+q)} \left(a x^n+b x^p\right)^q \, dx","Integrate[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) (p-n)}","\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
454,1,38,40,0.044636,"\int x^{-1-n q-p (1+q)} \left(x^n \left(a+b x^p\right)\right)^q \, dx","Integrate[x^(-1 - n*q - p*(1 + q))*(x^n*(a + b*x^p))^q,x]","-\frac{x^{-((q+1) (n+p))} \left(x^n \left(a+b x^p\right)\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,"-((x^n*(a + b*x^p))^(1 + q)/(a*p*(1 + q)*x^((n + p)*(1 + q))))","A",1