1,1,14,13,0.039000," ","int(x^2*(b*x^3+a*x),x)","\frac{1}{6} b \,x^{6}+\frac{1}{4} a \,x^{4}"," ",0,"1/4*a*x^4+1/6*b*x^6","A"
2,1,14,13,0.041000," ","int(x*(b*x^3+a*x),x)","\frac{1}{5} b \,x^{5}+\frac{1}{3} a \,x^{3}"," ",0,"1/3*a*x^3+1/5*b*x^5","A"
3,1,14,13,0.043000," ","int(b*x^3+a*x,x)","\frac{1}{4} b \,x^{4}+\frac{1}{2} a \,x^{2}"," ",0,"1/2*a*x^2+1/4*b*x^4","A"
4,1,11,10,0.045000," ","int((b*x^3+a*x)/x,x)","\frac{1}{3} b \,x^{3}+a x"," ",0,"a*x+1/3*b*x^3","A"
5,1,12,11,0.052000," ","int((b*x^3+a*x)/x^2,x)","\frac{b \,x^{2}}{2}+a \ln \left(x \right)"," ",0,"1/2*b*x^2+a*ln(x)","A"
6,1,25,24,0.040000," ","int(x^2*(b*x^3+a*x)^2,x)","\frac{1}{9} b^{2} x^{9}+\frac{2}{7} a b \,x^{7}+\frac{1}{5} a^{2} x^{5}"," ",0,"1/5*a^2*x^5+2/7*a*b*x^7+1/9*b^2*x^9","A"
7,1,25,24,0.038000," ","int(x*(b*x^3+a*x)^2,x)","\frac{1}{8} b^{2} x^{8}+\frac{1}{3} a b \,x^{6}+\frac{1}{4} a^{2} x^{4}"," ",0,"1/4*a^2*x^4+1/3*a*b*x^6+1/8*b^2*x^8","A"
8,1,25,24,0.043000," ","int((b*x^3+a*x)^2,x)","\frac{1}{7} b^{2} x^{7}+\frac{2}{5} a b \,x^{5}+\frac{1}{3} a^{2} x^{3}"," ",0,"1/3*a^2*x^3+2/5*a*b*x^5+1/7*b^2*x^7","A"
9,1,25,14,0.042000," ","int((b*x^3+a*x)^2/x,x)","\frac{1}{6} b^{2} x^{6}+\frac{1}{2} a b \,x^{4}+\frac{1}{2} a^{2} x^{2}"," ",0,"1/6*b^2*x^6+1/2*a*b*x^4+1/2*a^2*x^2","A"
10,1,22,21,0.051000," ","int((b*x^3+a*x)^2/x^2,x)","\frac{1}{5} b^{2} x^{5}+\frac{2}{3} a b \,x^{3}+a^{2} x"," ",0,"a^2*x+2/3*a*b*x^3+1/5*b^2*x^5","A"
11,1,37,36,0.036000," ","int((3*x^3-4*x)^6,x)","\frac{729}{19} x^{19}-\frac{5832}{17} x^{17}+1296 x^{15}-\frac{34560}{13} x^{13}+\frac{34560}{11} x^{11}-2048 x^{9}+\frac{4096}{7} x^{7}"," ",0,"4096/7*x^7-2048*x^9+34560/11*x^11-34560/13*x^13+1296*x^15-5832/17*x^17+729/19*x^19","A"
12,1,24,23,0.043000," ","int(x^4/(b*x^3+a*x),x)","\frac{x^{2}}{2 b}-\frac{a \ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/2/b*x^2-1/2*a*ln(b*x^2+a)/b^2","A"
13,1,27,23,0.044000," ","int(x^3/(b*x^3+a*x),x)","-\frac{a \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{x}{b}"," ",0,"1/b*x-a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
14,1,14,13,0.044000," ","int(x^2/(b*x^3+a*x),x)","\frac{\ln \left(b \,x^{2}+a \right)}{2 b}"," ",0,"1/2*ln(b*x^2+a)/b","A"
15,1,16,16,0.044000," ","int(x/(b*x^3+a*x),x)","\frac{\arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"1/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
16,1,21,20,0.046000," ","int(1/(b*x^3+a*x),x)","\frac{\ln \left(x \right)}{a}-\frac{\ln \left(b \,x^{2}+a \right)}{2 a}"," ",0,"1/a*ln(x)-1/2*ln(b*x^2+a)/a","A"
17,1,30,26,0.049000," ","int(1/x/(b*x^3+a*x),x)","-\frac{b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a}-\frac{1}{a x}"," ",0,"-1/a*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-1/a/x","A"
18,1,32,31,0.051000," ","int(1/x^2/(b*x^3+a*x),x)","-\frac{b \ln \left(x \right)}{a^{2}}+\frac{b \ln \left(b \,x^{2}+a \right)}{2 a^{2}}-\frac{1}{2 a \,x^{2}}"," ",0,"-1/2/a/x^2-1/a^2*b*ln(x)+1/2*b*ln(b*x^2+a)/a^2","A"
19,1,39,33,0.047000," ","int(1/x^3/(b*x^3+a*x),x)","\frac{b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, a^{2}}+\frac{b}{a^{2} x}-\frac{1}{3 a \,x^{3}}"," ",0,"1/a^2*b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-1/3/a/x^3+b/a^2/x","A"
20,1,44,43,0.054000," ","int(1/x^4/(b*x^3+a*x),x)","\frac{b^{2} \ln \left(x \right)}{a^{3}}-\frac{b^{2} \ln \left(b \,x^{2}+a \right)}{2 a^{3}}+\frac{b}{2 a^{2} x^{2}}-\frac{1}{4 a \,x^{4}}"," ",0,"-1/4/a/x^4+1/2*b/a^2/x^2+1/a^3*b^2*ln(x)-1/2*b^2*ln(b*x^2+a)/a^3","A"
21,1,36,33,0.049000," ","int(x^2/(b*x^3+a*x)^2,x)","\frac{x}{2 \left(b \,x^{2}+a \right) a}+\frac{\arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}"," ",0,"1/2*x/a/(b*x^2+a)+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
22,1,35,34,0.054000," ","int(x/(b*x^3+a*x)^2,x)","\frac{1}{2 \left(b \,x^{2}+a \right) a}+\frac{\ln \left(x \right)}{a^{2}}-\frac{\ln \left(b \,x^{2}+a \right)}{2 a^{2}}"," ",0,"1/2/a/(b*x^2+a)+1/a^2*ln(x)-1/2*ln(b*x^2+a)/a^2","A"
23,1,46,43,0.055000," ","int(1/(b*x^3+a*x)^2,x)","-\frac{b x}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{3 b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{2}}-\frac{1}{a^{2} x}"," ",0,"-1/2/a^2*b*x/(b*x^2+a)-3/2/a^2*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-1/a^2/x","A"
24,1,46,45,0.054000," ","int(1/x/(b*x^3+a*x)^2,x)","-\frac{b}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{2 b \ln \left(x \right)}{a^{3}}+\frac{b \ln \left(b \,x^{2}+a \right)}{a^{3}}-\frac{1}{2 a^{2} x^{2}}"," ",0,"-1/2/a^2/x^2-1/2*b/a^2/(b*x^2+a)-2/a^3*b*ln(x)+b*ln(b*x^2+a)/a^3","A"
25,1,59,52,0.061000," ","int(1/x^2/(b*x^3+a*x)^2,x)","\frac{b^{2} x}{2 \left(b \,x^{2}+a \right) a^{3}}+\frac{5 b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{3}}+\frac{2 b}{a^{3} x}-\frac{1}{3 a^{2} x^{3}}"," ",0,"1/2/a^3*b^2*x/(b*x^2+a)+5/2/a^3*b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)-1/3/a^2/x^3+2*b/a^3/x","A"
26,1,22,11,0.046000," ","int(x^5/(-x^3+x),x)","-\frac{x^{3}}{3}-x -\frac{\ln \left(x -1\right)}{2}+\frac{\ln \left(x +1\right)}{2}"," ",0,"-1/3*x^3-x-1/2*ln(x-1)+1/2*ln(x+1)","A"
27,1,19,16,0.041000," ","int(x^4/(-x^3+x),x)","-\frac{x^{2}}{2}-\frac{\ln \left(x -1\right)}{2}-\frac{\ln \left(x +1\right)}{2}"," ",0,"-1/2*x^2-1/2*ln(x-1)-1/2*ln(x+1)","A"
28,1,17,6,0.049000," ","int(x^3/(-x^3+x),x)","-x -\frac{\ln \left(x -1\right)}{2}+\frac{\ln \left(x +1\right)}{2}"," ",0,"-x-1/2*ln(x-1)+1/2*ln(x+1)","B"
29,1,14,10,0.046000," ","int(x^2/(-x^3+x),x)","-\frac{\ln \left(x -1\right)}{2}-\frac{\ln \left(x +1\right)}{2}"," ",0,"-1/2*ln(x-1)-1/2*ln(x+1)","A"
30,1,3,2,0.039000," ","int(x/(-x^3+x),x)","\arctanh \left(x \right)"," ",0,"arctanh(x)","A"
31,1,16,13,0.057000," ","int(1/(-x^3+x),x)","\ln \left(x \right)-\frac{\ln \left(x -1\right)}{2}-\frac{\ln \left(x +1\right)}{2}"," ",0,"-1/2*ln(x-1)-1/2*ln(x+1)+ln(x)","A"
32,1,19,8,0.051000," ","int(1/x/(-x^3+x),x)","-\frac{\ln \left(x -1\right)}{2}+\frac{\ln \left(x +1\right)}{2}-\frac{1}{x}"," ",0,"-1/2*ln(x-1)-1/x+1/2*ln(x+1)","B"
33,1,21,18,0.049000," ","int(1/x^2/(-x^3+x),x)","\ln \left(x \right)-\frac{\ln \left(x -1\right)}{2}-\frac{\ln \left(x +1\right)}{2}-\frac{1}{2 x^{2}}"," ",0,"-1/2*ln(x-1)-1/2*ln(x+1)-1/2/x^2+ln(x)","A"
34,1,24,13,0.057000," ","int(1/x^3/(-x^3+x),x)","-\frac{\ln \left(x -1\right)}{2}+\frac{\ln \left(x +1\right)}{2}-\frac{1}{x}-\frac{1}{3 x^{3}}"," ",0,"-1/2*ln(x-1)+1/2*ln(x+1)-1/3/x^3-1/x","A"
35,1,26,23,0.046000," ","int(1/x^4/(-x^3+x),x)","\ln \left(x \right)-\frac{\ln \left(x -1\right)}{2}-\frac{\ln \left(x +1\right)}{2}-\frac{1}{2 x^{2}}-\frac{1}{4 x^{4}}"," ",0,"-1/2*ln(x-1)-1/2*ln(x+1)-1/4/x^4-1/2/x^2+ln(x)","A"
36,1,14,13,0.045000," ","int(1/(b*x^3+x),x)","\ln \left(x \right)-\frac{\ln \left(b \,x^{2}+1\right)}{2}"," ",0,"ln(x)-1/2*ln(b*x^2+1)","A"
37,1,16,16,0.047000," ","int(1/(b*x^3-x),x)","-\ln \left(x \right)+\frac{\ln \left(b \,x^{2}-1\right)}{2}"," ",0,"1/2*ln(b*x^2-1)-ln(x)","A"
38,1,168,162,0.096000," ","int(x^3*(b*x^3+a*x)^(1/2),x)","\frac{2 \sqrt{b \,x^{3}+a x}\, x^{4}}{11}+\frac{4 \sqrt{b \,x^{3}+a x}\, a \,x^{2}}{77 b}+\frac{10 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, a^{3} \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{231 \sqrt{b \,x^{3}+a x}\, b^{3}}-\frac{20 \sqrt{b \,x^{3}+a x}\, a^{2}}{231 b^{2}}"," ",0,"2/11*x^4*(b*x^3+a*x)^(1/2)+4/77*a*x^2*(b*x^3+a*x)^(1/2)/b-20/231*a^2*(b*x^3+a*x)^(1/2)/b^2+10/231*a^3/b^3*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
39,1,197,285,0.063000," ","int(x^2*(b*x^3+a*x)^(1/2),x)","\frac{2 \sqrt{b \,x^{3}+a x}\, x^{3}}{9}+\frac{4 \sqrt{b \,x^{3}+a x}\, a x}{45 b}-\frac{2 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) a^{2}}{15 \sqrt{b \,x^{3}+a x}\, b^{2}}"," ",0,"2/9*x^3*(b*x^3+a*x)^(1/2)+4/45*a*x*(b*x^3+a*x)^(1/2)/b-2/15*a^2/b^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
40,1,146,140,0.067000," ","int(x*(b*x^3+a*x)^(1/2),x)","\frac{2 \sqrt{b \,x^{3}+a x}\, x^{2}}{7}-\frac{2 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, a^{2} \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{21 \sqrt{b \,x^{3}+a x}\, b^{2}}+\frac{4 \sqrt{b \,x^{3}+a x}\, a}{21 b}"," ",0,"2/7*x^2*(b*x^3+a*x)^(1/2)+4/21*a*(b*x^3+a*x)^(1/2)/b-2/21*a^2/b^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
41,1,175,263,0.068000," ","int((b*x^3+a*x)^(1/2),x)","\frac{2 \sqrt{b \,x^{3}+a x}\, x}{5}+\frac{2 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) a}{5 \sqrt{b \,x^{3}+a x}\, b}"," ",0,"2/5*x*(b*x^3+a*x)^(1/2)+2/5*a*(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
42,1,124,120,0.066000," ","int((b*x^3+a*x)^(1/2)/x,x)","\frac{2 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, a \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3 \sqrt{b \,x^{3}+a x}\, b}+\frac{2 \sqrt{b \,x^{3}+a x}}{3}"," ",0,"2/3*(b*x^3+a*x)^(1/2)+2/3*a*(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
43,1,177,264,0.083000," ","int((b*x^3+a*x)^(1/2)/x^2,x)","-\frac{2 \left(b \,x^{2}+a \right)}{\sqrt{\left(b \,x^{2}+a \right) x}}+\frac{2 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right)}{\sqrt{b \,x^{3}+a x}}"," ",0,"-2*(b*x^2+a)/(x*(b*x^2+a))^(1/2)+2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
44,1,123,123,0.041000," ","int((b*x^3+a*x)^(1/2)/x^3,x)","\frac{2 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3 \sqrt{b \,x^{3}+a x}}-\frac{2 \sqrt{b \,x^{3}+a x}}{3 x^{2}}"," ",0,"-2/3*(b*x^3+a*x)^(1/2)/x^2+2/3*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
45,1,201,287,0.044000," ","int((b*x^3+a*x)^(1/2)/x^4,x)","-\frac{4 \left(b \,x^{2}+a \right) b}{5 \sqrt{\left(b \,x^{2}+a \right) x}\, a}+\frac{2 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) b}{5 \sqrt{b \,x^{3}+a x}\, a}-\frac{2 \sqrt{b \,x^{3}+a x}}{5 x^{3}}"," ",0,"-2/5*(b*x^3+a*x)^(1/2)/x^3-4/5*(b*x^2+a)*b/a/((b*x^2+a)*x)^(1/2)+2/5*b/a*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
46,1,188,181,0.073000," ","int(x^2*(b*x^3+a*x)^(3/2),x)","\frac{2 \sqrt{b \,x^{3}+a x}\, b \,x^{6}}{15}+\frac{34 \sqrt{b \,x^{3}+a x}\, a \,x^{4}}{165}+\frac{8 \sqrt{b \,x^{3}+a x}\, a^{2} x^{2}}{385 b}+\frac{4 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, a^{4} \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{231 \sqrt{b \,x^{3}+a x}\, b^{3}}-\frac{8 \sqrt{b \,x^{3}+a x}\, a^{3}}{231 b^{2}}"," ",0,"2/15*b*x^6*(b*x^3+a*x)^(1/2)+34/165*a*x^4*(b*x^3+a*x)^(1/2)+8/385*a^2*x^2*(b*x^3+a*x)^(1/2)/b-8/231*a^3*(b*x^3+a*x)^(1/2)/b^2+4/231*a^4/b^3*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
47,1,217,304,0.075000," ","int(x*(b*x^3+a*x)^(3/2),x)","\frac{2 \sqrt{b \,x^{3}+a x}\, b \,x^{5}}{13}+\frac{10 \sqrt{b \,x^{3}+a x}\, a \,x^{3}}{39}+\frac{8 \sqrt{b \,x^{3}+a x}\, a^{2} x}{195 b}-\frac{4 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) a^{3}}{65 \sqrt{b \,x^{3}+a x}\, b^{2}}"," ",0,"2/13*b*x^5*(b*x^3+a*x)^(1/2)+10/39*a*x^3*(b*x^3+a*x)^(1/2)+8/195*a^2*x*(b*x^3+a*x)^(1/2)/b-4/65*a^3/b^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
48,1,166,157,0.073000," ","int((b*x^3+a*x)^(3/2),x)","\frac{2 \sqrt{b \,x^{3}+a x}\, b \,x^{4}}{11}+\frac{26 \sqrt{b \,x^{3}+a x}\, a \,x^{2}}{77}-\frac{4 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, a^{3} \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{77 \sqrt{b \,x^{3}+a x}\, b^{2}}+\frac{8 \sqrt{b \,x^{3}+a x}\, a^{2}}{77 b}"," ",0,"2/11*b*x^4*(b*x^3+a*x)^(1/2)+26/77*a*x^2*(b*x^3+a*x)^(1/2)+8/77*a^2*(b*x^3+a*x)^(1/2)/b-4/77*a^3/b^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
49,1,195,279,0.068000," ","int((b*x^3+a*x)^(3/2)/x,x)","\frac{2 \sqrt{b \,x^{3}+a x}\, b \,x^{3}}{9}+\frac{22 \sqrt{b \,x^{3}+a x}\, a x}{45}+\frac{4 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) a^{2}}{15 \sqrt{b \,x^{3}+a x}\, b}"," ",0,"2/9*b*x^3*(b*x^3+a*x)^(1/2)+22/45*a*x*(b*x^3+a*x)^(1/2)+4/15*a^2*(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
50,1,144,137,0.077000," ","int((b*x^3+a*x)^(3/2)/x^2,x)","\frac{2 \sqrt{b \,x^{3}+a x}\, b \,x^{2}}{7}+\frac{4 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, a^{2} \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{7 \sqrt{b \,x^{3}+a x}\, b}+\frac{6 \sqrt{b \,x^{3}+a x}\, a}{7}"," ",0,"2/7*b*x^2*(b*x^3+a*x)^(1/2)+6/7*a*(b*x^3+a*x)^(1/2)+4/7*a^2*(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
51,1,194,280,0.069000," ","int((b*x^3+a*x)^(3/2)/x^3,x)","\frac{2 \sqrt{b \,x^{3}+a x}\, b x}{5}-\frac{2 \left(b \,x^{2}+a \right) a}{\sqrt{\left(b \,x^{2}+a \right) x}}+\frac{12 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) a}{5 \sqrt{b \,x^{3}+a x}}"," ",0,"-2*(b*x^2+a)*a/((b*x^2+a)*x)^(1/2)+2/5*b*x*(b*x^3+a*x)^(1/2)+12/5*a*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
52,1,139,137,0.073000," ","int((b*x^3+a*x)^(3/2)/x^4,x)","\frac{4 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, a \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3 \sqrt{b \,x^{3}+a x}}+\frac{2 \sqrt{b \,x^{3}+a x}\, b}{3}-\frac{2 \sqrt{b \,x^{3}+a x}\, a}{3 x^{2}}"," ",0,"-2/3*a*(b*x^3+a*x)^(1/2)/x^2+2/3*b*(b*x^3+a*x)^(1/2)+4/3*a*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
53,1,196,281,0.077000," ","int((b*x^3+a*x)^(3/2)/x^5,x)","-\frac{14 \left(b \,x^{2}+a \right) b}{5 \sqrt{\left(b \,x^{2}+a \right) x}}+\frac{12 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) b}{5 \sqrt{b \,x^{3}+a x}}-\frac{2 \sqrt{b \,x^{3}+a x}\, a}{5 x^{3}}"," ",0,"-2/5*a*(b*x^3+a*x)^(1/2)/x^3-14/5*(b*x^2+a)*b/((b*x^2+a)*x)^(1/2)+12/5*b*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
54,1,142,140,0.081000," ","int((b*x^3+a*x)^(3/2)/x^6,x)","\frac{4 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, b \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{7 \sqrt{b \,x^{3}+a x}}-\frac{6 \sqrt{b \,x^{3}+a x}\, b}{7 x^{2}}-\frac{2 \sqrt{b \,x^{3}+a x}\, a}{7 x^{4}}"," ",0,"-2/7*a*(b*x^3+a*x)^(1/2)/x^4-6/7*b*(b*x^3+a*x)^(1/2)/x^2+4/7*b*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
55,1,223,306,0.081000," ","int((b*x^3+a*x)^(3/2)/x^7,x)","-\frac{8 \left(b \,x^{2}+a \right) b^{2}}{15 \sqrt{\left(b \,x^{2}+a \right) x}\, a}+\frac{4 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) b^{2}}{15 \sqrt{b \,x^{3}+a x}\, a}-\frac{22 \sqrt{b \,x^{3}+a x}\, b}{45 x^{3}}-\frac{2 \sqrt{b \,x^{3}+a x}\, a}{9 x^{5}}"," ",0,"-2/9*a*(b*x^3+a*x)^(1/2)/x^5-22/45*b*(b*x^3+a*x)^(1/2)/x^3-8/15*(b*x^2+a)*b^2/a/((b*x^2+a)*x)^(1/2)+4/15/a*b^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
56,1,169,162,0.083000," ","int((b*x^3+a*x)^(3/2)/x^8,x)","-\frac{4 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, b^{2} \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{77 \sqrt{b \,x^{3}+a x}\, a}-\frac{8 \sqrt{b \,x^{3}+a x}\, b^{2}}{77 a \,x^{2}}-\frac{26 \sqrt{b \,x^{3}+a x}\, b}{77 x^{4}}-\frac{2 \sqrt{b \,x^{3}+a x}\, a}{11 x^{6}}"," ",0,"-2/11*a*(b*x^3+a*x)^(1/2)/x^6-26/77*b*(b*x^3+a*x)^(1/2)/x^4-8/77*b^2*(b*x^3+a*x)^(1/2)/a/x^2-4/77/a*b^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
57,1,149,143,0.067000," ","int(x^4/(b*x^3+a*x)^(1/2),x)","\frac{2 \sqrt{b \,x^{3}+a x}\, x^{2}}{7 b}+\frac{5 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, a^{2} \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{21 \sqrt{b \,x^{3}+a x}\, b^{3}}-\frac{10 \sqrt{b \,x^{3}+a x}\, a}{21 b^{2}}"," ",0,"2/7*x^2*(b*x^3+a*x)^(1/2)/b-10/21*a*(b*x^3+a*x)^(1/2)/b^2+5/21*a^2/b^3*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
58,1,178,266,0.072000," ","int(x^3/(b*x^3+a*x)^(1/2),x)","\frac{2 \sqrt{b \,x^{3}+a x}\, x}{5 b}-\frac{3 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) a}{5 \sqrt{b \,x^{3}+a x}\, b^{2}}"," ",0,"2/5*x*(b*x^3+a*x)^(1/2)/b-3/5*a/b^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
59,1,127,123,0.063000," ","int(x^2/(b*x^3+a*x)^(1/2),x)","-\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, a \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3 \sqrt{b \,x^{3}+a x}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a x}}{3 b}"," ",0,"2/3*(b*x^3+a*x)^(1/2)/b-1/3*a/b^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
60,1,158,247,0.067000," ","int(x/(b*x^3+a*x)^(1/2),x)","\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right)}{\sqrt{b \,x^{3}+a x}\, b}"," ",0,"(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
61,1,108,105,0.066000," ","int(1/(b*x^3+a*x)^(1/2),x)","\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{b \,x^{3}+a x}\, b}"," ",0,"(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
62,1,182,269,0.072000," ","int(1/x/(b*x^3+a*x)^(1/2),x)","-\frac{2 \left(b \,x^{2}+a \right)}{\sqrt{\left(b \,x^{2}+a \right) x}\, a}+\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right)}{\sqrt{b \,x^{3}+a x}\, a}"," ",0,"-2*(b*x^2+a)/a/((b*x^2+a)*x)^(1/2)+1/a*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
63,1,129,126,0.071000," ","int(1/x^2/(b*x^3+a*x)^(1/2),x)","-\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3 \sqrt{b \,x^{3}+a x}\, a}-\frac{2 \sqrt{b \,x^{3}+a x}}{3 a \,x^{2}}"," ",0,"-2/3*(b*x^3+a*x)^(1/2)/a/x^2-1/3/a*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
64,1,204,290,0.072000," ","int(1/x^3/(b*x^3+a*x)^(1/2),x)","\frac{6 \left(b \,x^{2}+a \right) b}{5 \sqrt{\left(b \,x^{2}+a \right) x}\, a^{2}}-\frac{3 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) b}{5 \sqrt{b \,x^{3}+a x}\, a^{2}}-\frac{2 \sqrt{b \,x^{3}+a x}}{5 a \,x^{3}}"," ",0,"-2/5*(b*x^3+a*x)^(1/2)/a/x^3+6/5*(b*x^2+a)/a^2*b/((b*x^2+a)*x)^(1/2)-3/5/a^2*b*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
65,1,172,162,0.095000," ","int(x^7/(b*x^3+a*x)^(3/2),x)","-\frac{a^{2} x}{\sqrt{\left(x^{2}+\frac{a}{b}\right) b x}\, b^{3}}+\frac{2 \sqrt{b \,x^{3}+a x}\, x^{2}}{7 b^{2}}+\frac{15 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, a^{2} \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{14 \sqrt{b \,x^{3}+a x}\, b^{4}}-\frac{8 \sqrt{b \,x^{3}+a x}\, a}{7 b^{3}}"," ",0,"-x/b^3*a^2/((x^2+a/b)*x*b)^(1/2)+2/7*x^2*(b*x^3+a*x)^(1/2)/b^2-8/7*a*(b*x^3+a*x)^(1/2)/b^3+15/14*a^2/b^4*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
66,1,200,285,0.073000," ","int(x^6/(b*x^3+a*x)^(3/2),x)","\frac{a \,x^{2}}{\sqrt{\left(x^{2}+\frac{a}{b}\right) b x}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a x}\, x}{5 b^{2}}-\frac{21 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) a}{10 \sqrt{b \,x^{3}+a x}\, b^{3}}"," ",0,"x^2/b^2*a/((x^2+a/b)*b*x)^(1/2)+2/5*x*(b*x^3+a*x)^(1/2)/b^2-21/10*a/b^3*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
67,1,147,142,0.073000," ","int(x^5/(b*x^3+a*x)^(3/2),x)","\frac{a x}{\sqrt{\left(x^{2}+\frac{a}{b}\right) b x}\, b^{2}}-\frac{5 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, a \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{6 \sqrt{b \,x^{3}+a x}\, b^{3}}+\frac{2 \sqrt{b \,x^{3}+a x}}{3 b^{2}}"," ",0,"x/b^2*a/((x^2+a/b)*b*x)^(1/2)+2/3*(b*x^3+a*x)^(1/2)/b^2-5/6*a/b^3*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
68,1,182,267,0.073000," ","int(x^4/(b*x^3+a*x)^(3/2),x)","-\frac{x^{2}}{\sqrt{\left(x^{2}+\frac{a}{b}\right) b x}\, b}+\frac{3 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right)}{2 \sqrt{b \,x^{3}+a x}\, b^{2}}"," ",0,"-x^2/b/((x^2+a/b)*b*x)^(1/2)+3/2/b^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
69,1,130,124,0.071000," ","int(x^3/(b*x^3+a*x)^(3/2),x)","-\frac{x}{\sqrt{\left(x^{2}+\frac{a}{b}\right) b x}\, b}+\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{b \,x^{3}+a x}\, b^{2}}"," ",0,"-x/b/((x^2+a/b)*b*x)^(1/2)+1/2/b^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
70,1,184,268,0.074000," ","int(x^2/(b*x^3+a*x)^(3/2),x)","\frac{x^{2}}{\sqrt{\left(x^{2}+\frac{a}{b}\right) b x}\, a}-\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right)}{2 \sqrt{b \,x^{3}+a x}\, a b}"," ",0,"x^2/a/((x^2+a/b)*b*x)^(1/2)-1/2/a*(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
71,1,132,123,0.068000," ","int(x/(b*x^3+a*x)^(3/2),x)","\frac{x}{\sqrt{\left(x^{2}+\frac{a}{b}\right) b x}\, a}+\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{b \,x^{3}+a x}\, a b}"," ",0,"x/a/((x^2+a/b)*b*x)^(1/2)+1/2/a*(-a*b)^(1/2)/b*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
72,1,206,285,0.074000," ","int(1/(b*x^3+a*x)^(3/2),x)","-\frac{b \,x^{2}}{\sqrt{\left(x^{2}+\frac{a}{b}\right) b x}\, a^{2}}-\frac{2 \left(b \,x^{2}+a \right)}{\sqrt{\left(b \,x^{2}+a \right) x}\, a^{2}}+\frac{3 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right)}{2 \sqrt{b \,x^{3}+a x}\, a^{2}}"," ",0,"-x^2*b/a^2/((x^2+a/b)*b*x)^(1/2)-2*(b*x^2+a)/a^2/((b*x^2+a)*x)^(1/2)+3/2/a^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
73,1,150,144,0.074000," ","int(1/x/(b*x^3+a*x)^(3/2),x)","-\frac{b x}{\sqrt{\left(x^{2}+\frac{a}{b}\right) b x}\, a^{2}}-\frac{5 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{6 \sqrt{b \,x^{3}+a x}\, a^{2}}-\frac{2 \sqrt{b \,x^{3}+a x}}{3 a^{2} x^{2}}"," ",0,"-x*b/a^2/((x^2+a/b)*b*x)^(1/2)-2/3*(b*x^3+a*x)^(1/2)/a^2/x^2-5/6/a^2*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))","A"
74,1,228,308,0.080000," ","int(1/x^2/(b*x^3+a*x)^(3/2),x)","\frac{b^{2} x^{2}}{\sqrt{\left(x^{2}+\frac{a}{b}\right) b x}\, a^{3}}+\frac{16 \left(b \,x^{2}+a \right) b}{5 \sqrt{\left(b \,x^{2}+a \right) x}\, a^{3}}-\frac{21 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}\, \sqrt{-\frac{b x}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{b}\right) b}{10 \sqrt{b \,x^{3}+a x}\, a^{3}}-\frac{2 \sqrt{b \,x^{3}+a x}}{5 a^{2} x^{3}}"," ",0,"x^2*b^2/a^3/((x^2+a/b)*b*x)^(1/2)-2/5*(b*x^3+a*x)^(1/2)/a^2/x^3+16/5*(b*x^2+a)*b/a^3/((b*x^2+a)*x)^(1/2)-21/10/a^3*b*(-a*b)^(1/2)*((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-2*(x-(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2)*(-1/(-a*b)^(1/2)*b*x)^(1/2)/(b*x^3+a*x)^(1/2)*(-2*(-a*b)^(1/2)/b*EllipticE(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/b*EllipticF(((x+(-a*b)^(1/2)/b)/(-a*b)^(1/2)*b)^(1/2),1/2*2^(1/2)))","A"
75,1,212,121,0.092000," ","int(x^(29/2)/(b*x^3+a*x)^(9/2),x)","-\frac{\sqrt{\left(b \,x^{2}+a \right) x}\, \left(-35 b^{\frac{9}{2}} x^{9}-528 a \,b^{\frac{7}{2}} x^{7}+315 \sqrt{b \,x^{2}+a}\, a \,b^{3} x^{6} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)-1218 a^{2} b^{\frac{5}{2}} x^{5}+945 \sqrt{b \,x^{2}+a}\, a^{2} b^{2} x^{4} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)-1050 a^{3} b^{\frac{3}{2}} x^{3}+945 \sqrt{b \,x^{2}+a}\, a^{3} b \,x^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)-315 a^{4} \sqrt{b}\, x +315 \sqrt{b \,x^{2}+a}\, a^{4} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)\right)}{70 \left(b \,x^{2}+a \right)^{4} b^{\frac{11}{2}} \sqrt{x}}"," ",0,"-1/70*((b*x^2+a)*x)^(1/2)/b^(11/2)*(-35*x^9*b^(9/2)+315*ln(b^(1/2)*x+(b*x^2+a)^(1/2))*x^6*a*b^3*(b*x^2+a)^(1/2)-528*b^(7/2)*x^7*a+945*ln(b^(1/2)*x+(b*x^2+a)^(1/2))*x^4*a^2*b^2*(b*x^2+a)^(1/2)-1218*b^(5/2)*x^5*a^2+945*ln(b^(1/2)*x+(b*x^2+a)^(1/2))*x^2*a^3*b*(b*x^2+a)^(1/2)-1050*b^(3/2)*x^3*a^3+315*ln(b^(1/2)*x+(b*x^2+a)^(1/2))*a^4*(b*x^2+a)^(1/2)-315*b^(1/2)*x*a^4)/x^(1/2)/(b*x^2+a)^4","A"
76,1,70,96,0.044000," ","int(x^(27/2)/(b*x^3+a*x)^(9/2),x)","\frac{\left(b \,x^{2}+a \right) \left(35 x^{8} b^{4}+280 a \,x^{6} b^{3}+560 a^{2} x^{4} b^{2}+448 a^{3} x^{2} b +128 a^{4}\right) x^{\frac{9}{2}}}{35 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} b^{5}}"," ",0,"1/35*(b*x^2+a)*(35*b^4*x^8+280*a*b^3*x^6+560*a^2*b^2*x^4+448*a^3*b*x^2+128*a^4)*x^(9/2)/b^5/(b*x^3+a*x)^(9/2)","A"
77,1,198,100,0.078000," ","int(x^(25/2)/(b*x^3+a*x)^(9/2),x)","\frac{\sqrt{\left(b \,x^{2}+a \right) x}\, \left(-176 b^{\frac{7}{2}} x^{7}+105 \sqrt{b \,x^{2}+a}\, b^{3} x^{6} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)-406 a \,b^{\frac{5}{2}} x^{5}+315 \sqrt{b \,x^{2}+a}\, a \,b^{2} x^{4} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)-350 a^{2} b^{\frac{3}{2}} x^{3}+315 \sqrt{b \,x^{2}+a}\, a^{2} b \,x^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)-105 a^{3} \sqrt{b}\, x +105 \sqrt{b \,x^{2}+a}\, a^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)\right)}{105 \left(b \,x^{2}+a \right)^{4} b^{\frac{9}{2}} \sqrt{x}}"," ",0,"1/105*((b*x^2+a)*x)^(1/2)/b^(9/2)*(105*ln(b^(1/2)*x+(b*x^2+a)^(1/2))*x^6*b^3*(b*x^2+a)^(1/2)-176*x^7*b^(7/2)+315*ln(b^(1/2)*x+(b*x^2+a)^(1/2))*x^4*a*b^2*(b*x^2+a)^(1/2)-406*b^(5/2)*x^5*a+315*ln(b^(1/2)*x+(b*x^2+a)^(1/2))*x^2*a^2*b*(b*x^2+a)^(1/2)-350*b^(3/2)*x^3*a^2+105*ln(b^(1/2)*x+(b*x^2+a)^(1/2))*a^3*(b*x^2+a)^(1/2)-105*b^(1/2)*x*a^3)/x^(1/2)/(b*x^2+a)^4","A"
78,1,59,77,0.046000," ","int(x^(23/2)/(b*x^3+a*x)^(9/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(35 b^{3} x^{6}+70 a \,b^{2} x^{4}+56 a^{2} b \,x^{2}+16 a^{3}\right) x^{\frac{9}{2}}}{35 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} b^{4}}"," ",0,"-1/35*(b*x^2+a)*(35*b^3*x^6+70*a*b^2*x^4+56*a^2*b*x^2+16*a^3)*x^(9/2)/b^4/(b*x^3+a*x)^(9/2)","A"
79,1,27,19,0.048000," ","int(x^(21/2)/(b*x^3+a*x)^(9/2),x)","\frac{\left(b \,x^{2}+a \right) x^{\frac{23}{2}}}{7 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} a}"," ",0,"1/7*(b*x^2+a)/a*x^(23/2)/(b*x^3+a*x)^(9/2)","A"
80,1,48,58,0.047000," ","int(x^(19/2)/(b*x^3+a*x)^(9/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(35 b^{2} x^{4}+28 a b \,x^{2}+8 a^{2}\right) x^{\frac{9}{2}}}{105 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} b^{3}}"," ",0,"-1/105*(b*x^2+a)*(35*b^2*x^4+28*a*b*x^2+8*a^2)*x^(9/2)/b^3/(b*x^3+a*x)^(9/2)","A"
81,1,37,39,0.063000," ","int(x^(17/2)/(b*x^3+a*x)^(9/2),x)","\frac{\left(b \,x^{2}+a \right) \left(2 b \,x^{2}+7 a \right) x^{\frac{19}{2}}}{35 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} a^{2}}"," ",0,"1/35*(b*x^2+a)*x^(19/2)*(2*b*x^2+7*a)/a^2/(b*x^3+a*x)^(9/2)","A"
82,1,37,39,0.058000," ","int(x^(15/2)/(b*x^3+a*x)^(9/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(7 b \,x^{2}+2 a \right) x^{\frac{9}{2}}}{35 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} b^{2}}"," ",0,"-1/35*(b*x^2+a)*(7*b*x^2+2*a)*x^(9/2)/b^2/(b*x^3+a*x)^(9/2)","A"
83,1,48,58,0.048000," ","int(x^(13/2)/(b*x^3+a*x)^(9/2),x)","\frac{\left(b \,x^{2}+a \right) \left(8 b^{2} x^{4}+28 a b \,x^{2}+35 a^{2}\right) x^{\frac{15}{2}}}{105 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} a^{3}}"," ",0,"1/105*(b*x^2+a)*x^(15/2)*(8*b^2*x^4+28*a*b*x^2+35*a^2)/a^3/(b*x^3+a*x)^(9/2)","A"
84,1,27,19,0.042000," ","int(x^(11/2)/(b*x^3+a*x)^(9/2),x)","-\frac{\left(b \,x^{2}+a \right) x^{\frac{9}{2}}}{7 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} b}"," ",0,"-1/7*(b*x^2+a)/b*x^(9/2)/(b*x^3+a*x)^(9/2)","A"
85,1,59,77,0.043000," ","int(x^(9/2)/(b*x^3+a*x)^(9/2),x)","\frac{\left(b \,x^{2}+a \right) \left(16 b^{3} x^{6}+56 a \,b^{2} x^{4}+70 a^{2} b \,x^{2}+35 a^{3}\right) x^{\frac{11}{2}}}{35 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} a^{4}}"," ",0,"1/35*(b*x^2+a)*x^(11/2)*(16*b^3*x^6+56*a*b^2*x^4+70*a^2*b*x^2+35*a^3)/a^4/(b*x^3+a*x)^(9/2)","A"
86,1,217,100,0.054000," ","int(x^(7/2)/(b*x^3+a*x)^(9/2),x)","-\frac{\sqrt{\left(b \,x^{2}+a \right) x}\, \left(105 \sqrt{b \,x^{2}+a}\, b^{3} x^{6} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-105 \sqrt{a}\, b^{3} x^{6}+315 \sqrt{b \,x^{2}+a}\, a \,b^{2} x^{4} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-350 a^{\frac{3}{2}} b^{2} x^{4}+315 \sqrt{b \,x^{2}+a}\, a^{2} b \,x^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-406 a^{\frac{5}{2}} b \,x^{2}+105 \sqrt{b \,x^{2}+a}\, a^{3} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-176 a^{\frac{7}{2}}\right)}{105 \left(b \,x^{2}+a \right)^{4} a^{\frac{9}{2}} \sqrt{x}}"," ",0,"-1/105*((b*x^2+a)*x)^(1/2)/a^(9/2)*(105*ln(2*((b*x^2+a)^(1/2)*a^(1/2)+a)/x)*x^6*b^3*(b*x^2+a)^(1/2)-105*a^(1/2)*x^6*b^3+315*ln(2*((b*x^2+a)^(1/2)*a^(1/2)+a)/x)*x^4*a*b^2*(b*x^2+a)^(1/2)-350*a^(3/2)*x^4*b^2+315*ln(2*((b*x^2+a)^(1/2)*a^(1/2)+a)/x)*x^2*a^2*b*(b*x^2+a)^(1/2)-406*a^(5/2)*x^2*b+105*ln(2*((b*x^2+a)^(1/2)*a^(1/2)+a)/x)*a^3*(b*x^2+a)^(1/2)-176*a^(7/2))/x^(1/2)/(b*x^2+a)^4","B"
87,1,70,96,0.049000," ","int(x^(5/2)/(b*x^3+a*x)^(9/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(128 x^{8} b^{4}+448 a \,x^{6} b^{3}+560 a^{2} x^{4} b^{2}+280 a^{3} x^{2} b +35 a^{4}\right) x^{\frac{7}{2}}}{35 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} a^{5}}"," ",0,"-1/35*(b*x^2+a)*x^(7/2)*(128*b^4*x^8+448*a*b^3*x^6+560*a^2*b^2*x^4+280*a^3*b*x^2+35*a^4)/a^5/(b*x^3+a*x)^(9/2)","A"
88,1,234,121,0.057000," ","int(x^(3/2)/(b*x^3+a*x)^(9/2),x)","\frac{\sqrt{\left(b \,x^{2}+a \right) x}\, \left(315 \sqrt{b \,x^{2}+a}\, b^{4} x^{8} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-315 \sqrt{a}\, b^{4} x^{8}+945 \sqrt{b \,x^{2}+a}\, a \,b^{3} x^{6} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-1050 a^{\frac{3}{2}} b^{3} x^{6}+945 \sqrt{b \,x^{2}+a}\, a^{2} b^{2} x^{4} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-1218 a^{\frac{5}{2}} b^{2} x^{4}+315 \sqrt{b \,x^{2}+a}\, a^{3} b \,x^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-528 a^{\frac{7}{2}} b \,x^{2}-35 a^{\frac{9}{2}}\right)}{70 \left(b \,x^{2}+a \right)^{4} a^{\frac{11}{2}} x^{\frac{5}{2}}}"," ",0,"1/70*((b*x^2+a)*x)^(1/2)/a^(11/2)*(315*ln(2*(a+(b*x^2+a)^(1/2)*a^(1/2))/x)*x^8*b^4*(b*x^2+a)^(1/2)-315*a^(1/2)*x^8*b^4+945*ln(2*(a+(b*x^2+a)^(1/2)*a^(1/2))/x)*x^6*a*b^3*(b*x^2+a)^(1/2)-1050*a^(3/2)*x^6*b^3+945*ln(2*(a+(b*x^2+a)^(1/2)*a^(1/2))/x)*x^4*a^2*b^2*(b*x^2+a)^(1/2)-1218*a^(5/2)*x^4*b^2+315*ln(2*(a+(b*x^2+a)^(1/2)*a^(1/2))/x)*x^2*a^3*b*(b*x^2+a)^(1/2)-528*a^(7/2)*x^2*b-35*a^(9/2))/x^(5/2)/(b*x^2+a)^4","A"
89,1,81,116,0.045000," ","int(x^(1/2)/(b*x^3+a*x)^(9/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(-256 b^{5} x^{10}-896 a \,b^{4} x^{8}-1120 a^{2} b^{3} x^{6}-560 a^{3} b^{2} x^{4}-70 a^{4} b \,x^{2}+7 a^{5}\right) x^{\frac{3}{2}}}{21 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} a^{6}}"," ",0,"-1/21*(b*x^2+a)*x^(3/2)*(-256*b^5*x^10-896*a*b^4*x^8-1120*a^2*b^3*x^6-560*a^3*b^2*x^4-70*a^4*b*x^2+7*a^5)/a^6/(b*x^3+a*x)^(9/2)","A"
90,1,247,143,0.061000," ","int(1/x^(1/2)/(b*x^3+a*x)^(9/2),x)","-\frac{\sqrt{\left(b \,x^{2}+a \right) x}\, \left(3465 \sqrt{b \,x^{2}+a}\, b^{5} x^{10} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-3465 \sqrt{a}\, b^{5} x^{10}+10395 \sqrt{b \,x^{2}+a}\, a \,b^{4} x^{8} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-11550 a^{\frac{3}{2}} b^{4} x^{8}+10395 \sqrt{b \,x^{2}+a}\, a^{2} b^{3} x^{6} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-13398 a^{\frac{5}{2}} b^{3} x^{6}+3465 \sqrt{b \,x^{2}+a}\, a^{3} b^{2} x^{4} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-5808 a^{\frac{7}{2}} b^{2} x^{4}-385 a^{\frac{9}{2}} b \,x^{2}+70 a^{\frac{11}{2}}\right)}{280 \left(b \,x^{2}+a \right)^{4} a^{\frac{13}{2}} x^{\frac{9}{2}}}"," ",0,"-1/280*((b*x^2+a)*x)^(1/2)/a^(13/2)*(3465*ln(2*(a+(b*x^2+a)^(1/2)*a^(1/2))/x)*x^10*b^5*(b*x^2+a)^(1/2)-3465*a^(1/2)*x^10*b^5+10395*ln(2*(a+(b*x^2+a)^(1/2)*a^(1/2))/x)*x^8*a*b^4*(b*x^2+a)^(1/2)-11550*a^(3/2)*x^8*b^4+10395*ln(2*(a+(b*x^2+a)^(1/2)*a^(1/2))/x)*x^6*a^2*b^3*(b*x^2+a)^(1/2)-13398*a^(5/2)*x^6*b^3+3465*ln(2*(a+(b*x^2+a)^(1/2)*a^(1/2))/x)*x^4*a^3*b^2*(b*x^2+a)^(1/2)-5808*a^(7/2)*x^4*b^2-385*a^(9/2)*x^2*b+70*a^(11/2))/x^(9/2)/(b*x^2+a)^4","A"
91,1,92,138,0.046000," ","int(1/x^(3/2)/(b*x^3+a*x)^(9/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(1024 b^{6} x^{12}+3584 b^{5} x^{10} a +4480 x^{8} b^{4} a^{2}+2240 b^{3} x^{6} a^{3}+280 b^{2} x^{4} a^{4}-28 b \,x^{2} a^{5}+7 a^{6}\right)}{35 \left(b \,x^{3}+a x \right)^{\frac{9}{2}} a^{7} \sqrt{x}}"," ",0,"-1/35*(b*x^2+a)*(1024*b^6*x^12+3584*a*b^5*x^10+4480*a^2*b^4*x^8+2240*a^3*b^3*x^6+280*a^4*b^2*x^4-28*a^5*b*x^2+7*a^6)/x^(1/2)/a^7/(b*x^3+a*x)^(9/2)","A"
92,1,997,43,0.089000," ","int(x^4/(b*x^4+a*x)^(1/2),x)","-\frac{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}\, \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)^{2} \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{b}-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticPi \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \frac{-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{b}\right) a}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b x}}+\frac{\sqrt{b \,x^{4}+a x}\, x}{3 b}"," ",0,"1/3*x*(b*x^4+a*x)^(1/2)/b-a*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*x/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b))^(1/2)*(x-(-a*b^2)^(1/3)/b)^2*((-a*b^2)^(1/3)/b*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b))^(1/2)*((-a*b^2)^(1/3)/b*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b))^(1/2)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-a*b^2)^(1/3)/(b*x*(x-(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*((-a*b^2)^(1/3)/b*EllipticF(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*x/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b))^(1/2),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2))-(-a*b^2)^(1/3)/b*EllipticPi(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*x/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b))^(1/2),(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)))","C"
93,1,979,24,0.087000," ","int(x/(b*x^4+a*x)^(1/2),x)","\frac{2 \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}\, \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)^{2} \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{b}-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticPi \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \frac{-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{b}\right) b}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b x}}"," ",0,"2*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2)*(x-(-a*b^2)^(1/3)/b)^2*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-a*b^2)^(1/3)*b/((x-(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*b*x)^(1/2)*((-a*b^2)^(1/3)/b*EllipticF(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2))-(-a*b^2)^(1/3)/b*EllipticPi(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2),(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)))","C"
94,1,27,19,0.041000," ","int(1/x^2/(b*x^4+a*x)^(1/2),x)","-\frac{2 \left(b \,x^{3}+a \right)}{3 \sqrt{b \,x^{4}+a x}\, a x}"," ",0,"-2/3/x*(b*x^3+a)/a/(b*x^4+a*x)^(1/2)","A"
95,1,35,40,0.040000," ","int(1/x^5/(b*x^4+a*x)^(1/2),x)","-\frac{2 \left(b \,x^{3}+a \right) \left(-2 b \,x^{3}+a \right)}{9 \sqrt{b \,x^{4}+a x}\, a^{2} x^{4}}"," ",0,"-2/9*(b*x^3+a)*(-2*b*x^3+a)/x^4/a^2/(b*x^4+a*x)^(1/2)","A"
96,1,48,62,0.046000," ","int(1/x^8/(b*x^4+a*x)^(1/2),x)","-\frac{2 \left(b \,x^{3}+a \right) \left(8 b^{2} x^{6}-4 a b \,x^{3}+3 a^{2}\right)}{45 \sqrt{b \,x^{4}+a x}\, a^{3} x^{7}}"," ",0,"-2/45*(b*x^3+a)*(8*b^2*x^6-4*a*b*x^3+3*a^2)/x^7/a^3/(b*x^4+a*x)^(1/2)","A"
97,1,688,241,0.096000," ","int(x^3/(b*x^4+a*x)^(1/2),x)","-\frac{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}\, \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)^{2} \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, a \EllipticF \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{2 \left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b x}}+\frac{\sqrt{b \,x^{4}+a x}}{2 b}"," ",0,"1/2*(b*x^4+a*x)^(1/2)/b-1/2*a*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2)*(x-(-a*b^2)^(1/3)/b)^2*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-a*b^2)^(1/3)/((x-(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*b*x)^(1/2)*EllipticF(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2))","C"
98,1,671,221,0.086000," ","int(1/(b*x^4+a*x)^(1/2),x)","\frac{2 \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}\, \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)^{2} \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, b \EllipticF \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b x}}"," ",0,"2*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2)*(x-(-a*b^2)^(1/3)/b)^2*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-a*b^2)^(1/3)*b/((x-(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*b*x)^(1/2)*EllipticF(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2))","C"
99,1,696,242,0.093000," ","int(1/x^3/(b*x^4+a*x)^(1/2),x)","-\frac{4 \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}\, \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)^{2} \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, b^{2} \EllipticF \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{5 \left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b x}\, a}-\frac{2 \sqrt{b \,x^{4}+a x}}{5 a \,x^{3}}"," ",0,"-2/5*(b*x^4+a*x)^(1/2)/a/x^3-4/5/a*b^2*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2)*(x-(-a*b^2)^(1/3)/b)^2*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-a*b^2)^(1/3)/((x-(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*b*x)^(1/2)*EllipticF(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2))","C"
100,1,1079,521,0.087000," ","int(x^5/(b*x^4+a*x)^(1/2),x)","\frac{\sqrt{b \,x^{4}+a x}\, x^{2}}{4 b}-\frac{5 \left(\left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x +\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}\, \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)^{2} \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \left(\frac{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b \EllipticE \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}+\frac{\left(\frac{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}+\frac{\left(-a \,b^{2}\right)^{\frac{2}{3}}}{b^{2}}\right) b \EllipticF \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(-a \,b^{2}\right)^{\frac{1}{3}}}\right)\right) a}{8 \sqrt{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b x}\, b}"," ",0,"1/4*x^2*(b*x^4+a*x)^(1/2)/b-5/8*a/b*(x*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)+(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2)*(x-(-a*b^2)^(1/3)/b)^2*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)*(((-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(-a*b^2)^(1/3)/b+(-a*b^2)^(2/3)/b^2)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-a*b^2)^(1/3)*b*EllipticF(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2))+(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2))/(-a*b^2)^(1/3)*b))/((x-(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*b*x)^(1/2)","C"
101,1,1054,500,0.095000," ","int(x^2/(b*x^4+a*x)^(1/2),x)","\frac{\left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x +\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}\, \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)^{2} \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \left(\frac{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b \EllipticE \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}+\frac{\left(\frac{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}+\frac{\left(-a \,b^{2}\right)^{\frac{2}{3}}}{b^{2}}\right) b \EllipticF \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(-a \,b^{2}\right)^{\frac{1}{3}}}\right)}{\sqrt{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b x}}"," ",0,"((x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*x+(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2)*(x-(-a*b^2)^(1/3)/b)^2*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)*(((-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(-a*b^2)^(1/3)/b+(-a*b^2)^(2/3)/b^2)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-a*b^2)^(1/3)*b*EllipticF(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2))+(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2))/(-a*b^2)^(1/3)*b))/((x-(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*b*x)^(1/2)","C"
102,1,1083,523,0.094000," ","int(1/x/(b*x^4+a*x)^(1/2),x)","\frac{2 \left(\left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x +\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}\, \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)^{2} \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \sqrt{\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}}\, \left(\frac{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b \EllipticE \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}+\frac{\left(\frac{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}+\frac{\left(-a \,b^{2}\right)^{\frac{2}{3}}}{b^{2}}\right) b \EllipticF \left(\sqrt{\frac{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) x}{\left(-\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right)}}, \sqrt{\frac{\left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}{\left(\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right)}}\right)}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(-a \,b^{2}\right)^{\frac{1}{3}}}\right)\right) b}{\sqrt{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b x}\, a}-\frac{2 \left(b \,x^{3}+a \right)}{\sqrt{\left(b \,x^{3}+a \right) x}\, a}"," ",0,"-2*(b*x^3+a)/a/(x*(b*x^3+a))^(1/2)+2/a*b*((x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*x+(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2)*(x-(-a*b^2)^(1/3)/b)^2*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)*((-a*b^2)^(1/3)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)/b)^(1/2)*(((-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(-a*b^2)^(1/3)/b+(-a*b^2)^(2/3)/b^2)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-a*b^2)^(1/3)*b*EllipticF(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2))+(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(-1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(x-(-a*b^2)^(1/3)/b)*x)^(1/2),((3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/(3/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2))/(-a*b^2)^(1/3)*b))/((x-(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*b*x)^(1/2)","C"
103,1,223,128,0.093000," ","int(x^2/(b*x^(1/2)+a*x)^(1/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(-640 a \,b^{5} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+325 a \,b^{5} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-1300 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} b^{3} \sqrt{x}+256 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} x +1280 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b^{4}-650 \sqrt{a x +b \sqrt{x}}\, a^{\frac{3}{2}} b^{4}-544 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b \sqrt{x}+880 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{2}\right)}{640 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{13}{2}}}"," ",0,"1/640*(b*x^(1/2)+a*x)^(1/2)*(256*x*(b*x^(1/2)+a*x)^(3/2)*a^(9/2)-544*a^(7/2)*x^(1/2)*(b*x^(1/2)+a*x)^(3/2)*b-1300*a^(5/2)*x^(1/2)*(b*x^(1/2)+a*x)^(1/2)*b^3+880*a^(5/2)*(b*x^(1/2)+a*x)^(3/2)*b^2+1280*a^(3/2)*(x^(1/2)*(b+a*x^(1/2)))^(1/2)*b^4-650*a^(3/2)*(b*x^(1/2)+a*x)^(1/2)*b^4+325*ln(1/2*(2*(b*x^(1/2)+a*x)^(1/2)*a^(1/2)+2*a*x^(1/2)+b)/a^(1/2))*a*b^5-640*a*ln(1/2*(2*(x^(1/2)*(b+a*x^(1/2)))^(1/2)*a^(1/2)+2*a*x^(1/2)+b)/a^(1/2))*b^5)/(x^(1/2)*(b+a*x^(1/2)))^(1/2)/a^(13/2)","A"
104,1,181,84,0.051000," ","int(x/(a*x+b*x^(1/2))^(1/2),x)","-\frac{\sqrt{a x +b \sqrt{x}}\, \left(24 a \,b^{3} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-9 a \,b^{3} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+36 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} b \sqrt{x}-48 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b^{2}+18 \sqrt{a x +b \sqrt{x}}\, a^{\frac{3}{2}} b^{2}-16 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}}\right)}{24 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{9}{2}}}"," ",0,"-1/24*(a*x+b*x^(1/2))^(1/2)/a^(9/2)*(36*x^(1/2)*(a*x+b*x^(1/2))^(1/2)*a^(5/2)*b-16*(a*x+b*x^(1/2))^(3/2)*a^(5/2)-48*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(3/2)*b^2+18*(a*x+b*x^(1/2))^(1/2)*a^(3/2)*b^2+24*a*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*b^3-9*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a*b^3)/((a*x^(1/2)+b)*x^(1/2))^(1/2)","B"
105,1,83,42,0.049000," ","int(1/(a*x+b*x^(1/2))^(1/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(-b \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\right)}{\sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}}}"," ",0,"(a*x+b*x^(1/2))^(1/2)*(2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2)-b*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2)))/((a*x^(1/2)+b)*x^(1/2))^(1/2)/a^(3/2)","A"
106,1,159,19,0.055000," ","int(1/x/(a*x+b*x^(1/2))^(1/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(-a b x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+a b x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} x +2 \sqrt{a x +b \sqrt{x}}\, a^{\frac{3}{2}} x -4 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\right)}{\sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\, b^{2} x}"," ",0,"(a*x+b*x^(1/2))^(1/2)*(2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(3/2)*x-4*(a*x+b*x^(1/2))^(3/2)*a^(1/2)+2*(a*x+b*x^(1/2))^(1/2)*a^(3/2)*x-ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x*a*b+ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x*a*b)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^2/x/a^(1/2)","C"
107,1,218,62,0.066000," ","int(1/x^2/(a*x+b*x^(1/2))^(1/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(-15 a^{3} b \,x^{\frac{7}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+15 a^{3} b \,x^{\frac{7}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+30 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{7}{2}} x^{\frac{7}{2}}+30 \sqrt{a x +b \sqrt{x}}\, a^{\frac{7}{2}} x^{\frac{7}{2}}-60 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} x^{\frac{5}{2}}+28 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} b \,x^{2}-12 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b^{2} x^{\frac{3}{2}}\right)}{15 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\, b^{4} x^{\frac{7}{2}}}"," ",0,"1/15*(a*x+b*x^(1/2))^(1/2)*(30*x^(7/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(7/2)-60*x^(5/2)*(a*x+b*x^(1/2))^(3/2)*a^(5/2)+30*x^(7/2)*(a*x+b*x^(1/2))^(1/2)*a^(7/2)-15*x^(7/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^3*b+15*x^(7/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^3*b-12*x^(3/2)*(a*x+b*x^(1/2))^(3/2)*a^(1/2)*b^2+28*a^(3/2)*(a*x+b*x^(1/2))^(3/2)*b*x^2)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^4/x^(7/2)/a^(1/2)","C"
108,1,262,106,0.065000," ","int(1/x^3/(a*x+b*x^(1/2))^(1/2),x)","-\frac{\sqrt{a x +b \sqrt{x}}\, \left(315 a^{5} b \,x^{\frac{11}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-315 a^{5} b \,x^{\frac{11}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-630 \sqrt{a x +b \sqrt{x}}\, a^{\frac{11}{2}} x^{\frac{11}{2}}-630 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{11}{2}} x^{\frac{11}{2}}+1260 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} x^{\frac{9}{2}}-748 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b \,x^{4}+492 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{2} x^{\frac{7}{2}}-300 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{3} x^{3}+140 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b^{4} x^{\frac{5}{2}}\right)}{315 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\, b^{6} x^{\frac{11}{2}}}"," ",0,"-1/315*(a*x+b*x^(1/2))^(1/2)*(1260*(a*x+b*x^(1/2))^(3/2)*a^(9/2)*x^(9/2)-630*(a*x+b*x^(1/2))^(1/2)*a^(11/2)*x^(11/2)+315*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(11/2)*a^5*b-630*a^(11/2)*x^(11/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)-315*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(11/2)*a^5*b+492*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*x^(7/2)*b^2+140*(a*x+b*x^(1/2))^(3/2)*a^(1/2)*x^(5/2)*b^4-748*a^(7/2)*(a*x+b*x^(1/2))^(3/2)*b*x^4-300*(a*x+b*x^(1/2))^(3/2)*a^(3/2)*x^3*b^3)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^6/x^(11/2)/a^(1/2)","C"
109,1,306,150,0.068000," ","int(1/x^4/(a*x+b*x^(1/2))^(1/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(-3003 a^{7} b \,x^{\frac{15}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+3003 a^{7} b \,x^{\frac{15}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+6006 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{15}{2}} x^{\frac{15}{2}}+6006 \sqrt{a x +b \sqrt{x}}\, a^{\frac{15}{2}} x^{\frac{15}{2}}-12012 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{13}{2}} x^{\frac{13}{2}}+7916 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{11}{2}} b \,x^{6}-5868 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} b^{2} x^{\frac{11}{2}}+4332 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b^{3} x^{5}-3052 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{4} x^{\frac{9}{2}}+1932 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{5} x^{4}-924 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b^{6} x^{\frac{7}{2}}\right)}{3003 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\, b^{8} x^{\frac{15}{2}}}"," ",0,"1/3003*(a*x+b*x^(1/2))^(1/2)*(6006*x^(15/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(15/2)-12012*x^(13/2)*(a*x+b*x^(1/2))^(3/2)*a^(13/2)+6006*x^(15/2)*(a*x+b*x^(1/2))^(1/2)*a^(15/2)-3003*x^(15/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^7*b+3003*x^(15/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^7*b-5868*x^(11/2)*(a*x+b*x^(1/2))^(3/2)*a^(9/2)*b^2-3052*x^(9/2)*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*b^4+7916*a^(11/2)*(a*x+b*x^(1/2))^(3/2)*b*x^6-924*x^(7/2)*(a*x+b*x^(1/2))^(3/2)*a^(1/2)*b^6+4332*x^5*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*b^3+1932*(a*x+b*x^(1/2))^(3/2)*a^(3/2)*x^4*b^5)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^8/x^(15/2)/a^(1/2)","C"
110,1,549,147,0.062000," ","int(x^3/(a*x+b*x^(1/2))^(3/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(-4480 a^{3} b^{5} x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+1015 a^{3} b^{5} x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-8960 a^{2} b^{6} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+2030 a^{2} b^{6} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-4060 \sqrt{a x +b \sqrt{x}}\, a^{\frac{9}{2}} b^{3} x^{\frac{3}{2}}-4480 a \,b^{7} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+1015 a \,b^{7} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+256 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{13}{2}} x^{2}-10150 \sqrt{a x +b \sqrt{x}}\, a^{\frac{7}{2}} b^{4} x +8960 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{7}{2}} b^{4} x -352 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{11}{2}} b \,x^{\frac{3}{2}}-8120 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} b^{5} \sqrt{x}+17920 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{5}{2}} b^{5} \sqrt{x}+528 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} b^{2} x -2030 \sqrt{a x +b \sqrt{x}}\, a^{\frac{3}{2}} b^{6}+8960 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b^{6}+3136 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b^{3} \sqrt{x}+2000 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{4}-2560 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{4}\right)}{640 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} a^{\frac{15}{2}}}"," ",0,"1/640*(a*x+b*x^(1/2))^(1/2)*(256*(a*x+b*x^(1/2))^(3/2)*a^(13/2)*x^2-352*(a*x+b*x^(1/2))^(3/2)*a^(11/2)*x^(3/2)*b-4060*(a*x+b*x^(1/2))^(1/2)*a^(9/2)*x^(3/2)*b^3+528*(a*x+b*x^(1/2))^(3/2)*a^(9/2)*x*b^2+3136*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*x^(1/2)*b^3-10150*(a*x+b*x^(1/2))^(1/2)*a^(7/2)*x*b^4+8960*a^(7/2)*x*((a*x^(1/2)+b)*x^(1/2))^(1/2)*b^4+2000*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*b^4-8120*(a*x+b*x^(1/2))^(1/2)*a^(5/2)*x^(1/2)*b^5+17920*a^(5/2)*x^(1/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*b^5-2560*a^(5/2)*((a*x^(1/2)+b)*x^(1/2))^(3/2)*b^4-2030*(a*x+b*x^(1/2))^(1/2)*a^(3/2)*b^6+8960*a^(3/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*b^6+2030*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(1/2)*a^2*b^6+1015*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x*a^3*b^5-8960*a^2*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(1/2)*b^6-4480*a^3*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x*b^5+1015*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a*b^7-4480*a*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*b^7)/a^(15/2)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/(a*x^(1/2)+b)^2","B"
111,1,503,103,0.064000," ","int(x^2/(a*x+b*x^(1/2))^(3/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(-120 a^{3} b^{3} x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+15 a^{3} b^{3} x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-240 a^{2} b^{4} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+30 a^{2} b^{4} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-60 \sqrt{a x +b \sqrt{x}}\, a^{\frac{9}{2}} b \,x^{\frac{3}{2}}-120 a \,b^{5} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+15 a \,b^{5} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-150 \sqrt{a x +b \sqrt{x}}\, a^{\frac{7}{2}} b^{2} x +240 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{7}{2}} b^{2} x -120 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} b^{3} \sqrt{x}+480 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{5}{2}} b^{3} \sqrt{x}+16 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} x -30 \sqrt{a x +b \sqrt{x}}\, a^{\frac{3}{2}} b^{4}+240 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b^{4}+32 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b \sqrt{x}+16 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{2}-96 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{2}\right)}{24 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} a^{\frac{11}{2}}}"," ",0,"1/24*(a*x+b*x^(1/2))^(1/2)/a^(11/2)*(16*(a*x+b*x^(1/2))^(3/2)*a^(9/2)*x-60*(a*x+b*x^(1/2))^(1/2)*a^(9/2)*x^(3/2)*b-120*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^3*x*b^3+32*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*b*x^(1/2)-150*(a*x+b*x^(1/2))^(1/2)*a^(7/2)*x*b^2+240*a^(7/2)*x*((a*x^(1/2)+b)*x^(1/2))^(1/2)*b^2+15*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x*a^3*b^3-240*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^2*x^(1/2)*b^4+16*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*b^2-120*(a*x+b*x^(1/2))^(1/2)*a^(5/2)*b^3*x^(1/2)+480*a^(5/2)*x^(1/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*b^3-96*a^(5/2)*((a*x^(1/2)+b)*x^(1/2))^(3/2)*b^2+30*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(1/2)*a^2*b^4-120*a*b^5*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))-30*(a*x+b*x^(1/2))^(1/2)*a^(3/2)*b^4+240*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(3/2)*b^4+15*a*b^5*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2)))/((a*x^(1/2)+b)*x^(1/2))^(1/2)/(a*x^(1/2)+b)^2","B"
112,1,236,59,0.048000," ","int(x/(a*x+b*x^(1/2))^(3/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(-3 a^{2} b x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 a \,b^{2} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 b^{3} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+6 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{5}{2}} x +12 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b \sqrt{x}+6 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\, b^{2}-4 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}}\right)}{\sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} a^{\frac{5}{2}}}"," ",0,"(a*x+b*x^(1/2))^(1/2)/a^(5/2)*(6*x*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(5/2)-3*x*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^2*b+12*x^(1/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(3/2)*b-6*x^(1/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a*b^2-4*a^(3/2)*((a*x^(1/2)+b)*x^(1/2))^(3/2)+6*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2)*b^2-3*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*b^3)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/(a*x^(1/2)+b)^2","B"
113,1,404,19,0.059000," ","int(1/(a*x+b*x^(1/2))^(3/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(-a^{2} b x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+a^{2} b x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 a \,b^{2} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 a \,b^{2} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-b^{3} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+b^{3} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{5}{2}} x +2 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} x +4 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b \sqrt{x}+4 \sqrt{a x +b \sqrt{x}}\, a^{\frac{3}{2}} b \sqrt{x}+2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\, b^{2}+2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}\, b^{2}-4 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}}\right)}{\sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} \sqrt{a}\, b^{2}}"," ",0,"(a*x+b*x^(1/2))^(1/2)*(2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(5/2)*x+2*x*(a*x+b*x^(1/2))^(1/2)*a^(5/2)-a^2*b*x*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))+x*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^2*b+4*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(3/2)*b*x^(1/2)+4*x^(1/2)*(a*x+b*x^(1/2))^(1/2)*a^(3/2)*b-2*a*b^2*x^(1/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))+2*x^(1/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a*b^2-4*((a*x^(1/2)+b)*x^(1/2))^(3/2)*a^(3/2)+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2)*b^2+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2)*b^2-b^3*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))+ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*b^3)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^2/(a*x^(1/2)+b)^2/a^(1/2)","C"
114,1,524,59,0.066000," ","int(1/x/(a*x+b*x^(1/2))^(3/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(3 a^{4} b \,x^{\frac{7}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 a^{4} b \,x^{\frac{7}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+6 a^{3} b^{2} x^{3} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 a^{3} b^{2} x^{3} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+3 a^{2} b^{3} x^{\frac{5}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 a^{2} b^{3} x^{\frac{5}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 \sqrt{a x +b \sqrt{x}}\, a^{\frac{9}{2}} x^{\frac{7}{2}}-6 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{9}{2}} x^{\frac{7}{2}}-12 \sqrt{a x +b \sqrt{x}}\, a^{\frac{7}{2}} b \,x^{3}-12 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{7}{2}} b \,x^{3}-6 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} b^{2} x^{\frac{5}{2}}-6 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{5}{2}} b^{2} x^{\frac{5}{2}}+24 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} x^{\frac{5}{2}}-12 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} x^{\frac{5}{2}}+44 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b \,x^{2}+16 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{2} x^{\frac{3}{2}}-4 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b^{3} x \right)}{3 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} \sqrt{a}\, b^{4} x^{\frac{5}{2}}}"," ",0,"1/3*(a*x+b*x^(1/2))^(1/2)*(24*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*x^(5/2)-6*(a*x+b*x^(1/2))^(1/2)*a^(9/2)*x^(7/2)+3*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(7/2)*a^4*b-6*a^(9/2)*x^(7/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)-3*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(7/2)*a^4*b+44*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*x^2*b-12*(a*x+b*x^(1/2))^(1/2)*a^(7/2)*x^3*b+6*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^3*a^3*b^2-12*a^(7/2)*x^3*((a*x^(1/2)+b)*x^(1/2))^(1/2)*b-12*a^(7/2)*x^(5/2)*((a*x^(1/2)+b)*x^(1/2))^(3/2)-6*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^3*a^3*b^2+16*(a*x+b*x^(1/2))^(3/2)*a^(3/2)*x^(3/2)*b^2-6*(a*x+b*x^(1/2))^(1/2)*a^(5/2)*x^(5/2)*b^2+3*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(5/2)*a^2*b^3-6*a^(5/2)*x^(5/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*b^2-3*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(5/2)*a^2*b^3-4*(a*x+b*x^(1/2))^(3/2)*a^(1/2)*x*b^3)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^4/a^(1/2)/x^(5/2)/(a*x^(1/2)+b)^2","C"
115,1,570,103,0.064000," ","int(1/x^2/(a*x+b*x^(1/2))^(3/2),x)","-\frac{\sqrt{a x +b \sqrt{x}}\, \left(-105 a^{6} b \,x^{\frac{11}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+105 a^{6} b \,x^{\frac{11}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-210 a^{5} b^{2} x^{5} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+210 a^{5} b^{2} x^{5} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-105 a^{4} b^{3} x^{\frac{9}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+105 a^{4} b^{3} x^{\frac{9}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+210 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{13}{2}} x^{\frac{11}{2}}+210 \sqrt{a x +b \sqrt{x}}\, a^{\frac{13}{2}} x^{\frac{11}{2}}+420 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{11}{2}} b \,x^{5}+420 \sqrt{a x +b \sqrt{x}}\, a^{\frac{11}{2}} b \,x^{5}+210 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{9}{2}} b^{2} x^{\frac{9}{2}}+210 \sqrt{a x +b \sqrt{x}}\, a^{\frac{9}{2}} b^{2} x^{\frac{9}{2}}-560 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{11}{2}} x^{\frac{9}{2}}+140 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{11}{2}} x^{\frac{9}{2}}-932 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} b \,x^{4}-256 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b^{2} x^{\frac{7}{2}}+64 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{3} x^{3}-32 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{4} x^{\frac{5}{2}}+20 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b^{5} x^{2}\right)}{35 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} \sqrt{a}\, b^{6} x^{\frac{9}{2}}}"," ",0,"-1/35*(a*x+b*x^(1/2))^(1/2)*(210*x^(11/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(13/2)-560*x^(9/2)*(a*x+b*x^(1/2))^(3/2)*a^(11/2)+210*x^(11/2)*(a*x+b*x^(1/2))^(1/2)*a^(13/2)-105*x^(11/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^6*b+105*x^(11/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^6*b-256*x^(7/2)*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*b^2+420*x^5*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(11/2)*b-932*x^4*(a*x+b*x^(1/2))^(3/2)*a^(9/2)*b+420*x^5*(a*x+b*x^(1/2))^(1/2)*a^(11/2)*b-210*x^5*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^5*b^2+210*x^5*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^5*b^2+140*x^(9/2)*((a*x^(1/2)+b)*x^(1/2))^(3/2)*a^(11/2)+64*x^3*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*b^3+210*x^(9/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(9/2)*b^2+210*x^(9/2)*(a*x+b*x^(1/2))^(1/2)*a^(9/2)*b^2-105*x^(9/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^4*b^3+105*x^(9/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^4*b^3-32*x^(5/2)*(a*x+b*x^(1/2))^(3/2)*a^(3/2)*b^4+20*(a*x+b*x^(1/2))^(3/2)*a^(1/2)*x^2*b^5)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^6/x^(9/2)/a^(1/2)/(a*x^(1/2)+b)^2","C"
116,1,614,147,0.067000," ","int(1/x^3/(a*x+b*x^(1/2))^(3/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(1155 a^{8} b \,x^{\frac{15}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-1155 a^{8} b \,x^{\frac{15}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+2310 a^{7} b^{2} x^{7} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-2310 a^{7} b^{2} x^{7} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+1155 a^{6} b^{3} x^{\frac{13}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-1155 a^{6} b^{3} x^{\frac{13}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-2310 \sqrt{a x +b \sqrt{x}}\, a^{\frac{17}{2}} x^{\frac{15}{2}}-2310 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{17}{2}} x^{\frac{15}{2}}-4620 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{15}{2}} b \,x^{7}-4620 \sqrt{a x +b \sqrt{x}}\, a^{\frac{15}{2}} b \,x^{7}-2310 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{13}{2}} b^{2} x^{\frac{13}{2}}-2310 \sqrt{a x +b \sqrt{x}}\, a^{\frac{13}{2}} b^{2} x^{\frac{13}{2}}+5544 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{15}{2}} x^{\frac{13}{2}}-924 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{15}{2}} x^{\frac{13}{2}}+8716 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{13}{2}} b \,x^{6}+2048 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{11}{2}} b^{2} x^{\frac{11}{2}}-512 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} b^{3} x^{5}+256 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b^{4} x^{\frac{9}{2}}-160 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{5} x^{4}+112 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{6} x^{\frac{7}{2}}-84 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b^{7} x^{3}\right)}{231 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} \sqrt{a}\, b^{8} x^{\frac{13}{2}}}"," ",0,"1/231*(a*x+b*x^(1/2))^(1/2)*(-2310*a^(13/2)*x^(13/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*b^2-2310*(a*x+b*x^(1/2))^(1/2)*a^(13/2)*x^(13/2)*b^2-512*(a*x+b*x^(1/2))^(3/2)*a^(9/2)*x^5*b^3-4620*a^(15/2)*x^7*((a*x^(1/2)+b)*x^(1/2))^(1/2)*b-4620*(a*x+b*x^(1/2))^(1/2)*a^(15/2)*x^7*b+2048*(a*x+b*x^(1/2))^(3/2)*a^(11/2)*x^(11/2)*b^2+8716*(a*x+b*x^(1/2))^(3/2)*a^(13/2)*x^6*b-84*(a*x+b*x^(1/2))^(3/2)*a^(1/2)*x^3*b^7+5544*(a*x+b*x^(1/2))^(3/2)*a^(15/2)*x^(13/2)-2310*(a*x+b*x^(1/2))^(1/2)*a^(17/2)*x^(15/2)+1155*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(15/2)*a^8*b-2310*a^(17/2)*x^(15/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)-1155*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(15/2)*a^8*b+2310*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^7*a^7*b^2-924*a^(15/2)*x^(13/2)*((a*x^(1/2)+b)*x^(1/2))^(3/2)-2310*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^7*a^7*b^2+256*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*x^(9/2)*b^4+1155*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(13/2)*a^6*b^3-1155*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(13/2)*a^6*b^3-160*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*x^4*b^5+112*(a*x+b*x^(1/2))^(3/2)*a^(3/2)*x^(7/2)*b^6)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^8/x^(13/2)/a^(1/2)/(a*x^(1/2)+b)^2","C"
117,1,245,150,0.055000," ","int(x^(5/2)/(a*x+b*x^(1/2))^(1/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(7680 a \,b^{6} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-4215 a \,b^{6} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+2560 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{11}{2}} x^{\frac{3}{2}}+16860 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} b^{4} \sqrt{x}-5376 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} b x -15360 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b^{5}+8430 \sqrt{a x +b \sqrt{x}}\, a^{\frac{3}{2}} b^{5}+8544 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b^{2} \sqrt{x}-12240 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{3}\right)}{7680 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{15}{2}}}"," ",0,"1/7680*(a*x+b*x^(1/2))^(1/2)*(2560*x^(3/2)*(a*x+b*x^(1/2))^(3/2)*a^(11/2)+8544*x^(1/2)*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*b^2-5376*(a*x+b*x^(1/2))^(3/2)*a^(9/2)*x*b+16860*x^(1/2)*(a*x+b*x^(1/2))^(1/2)*a^(5/2)*b^4-12240*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*b^3-15360*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(3/2)*b^5+8430*(a*x+b*x^(1/2))^(1/2)*a^(3/2)*b^5+7680*a*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*b^6-4215*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a*b^6)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/a^(15/2)","A"
118,1,203,106,0.054000," ","int(x^(3/2)/(a*x+b*x^(1/2))^(1/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(192 a \,b^{4} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-87 a \,b^{4} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+348 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} b^{2} \sqrt{x}-384 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b^{3}+174 \sqrt{a x +b \sqrt{x}}\, a^{\frac{3}{2}} b^{3}+96 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} \sqrt{x}-208 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b \right)}{192 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{11}{2}}}"," ",0,"1/192*(a*x+b*x^(1/2))^(1/2)*(96*x^(1/2)*(a*x+b*x^(1/2))^(3/2)*a^(7/2)+348*x^(1/2)*(a*x+b*x^(1/2))^(1/2)*a^(5/2)*b^2-208*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*b-384*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(3/2)*b^3+174*(a*x+b*x^(1/2))^(1/2)*a^(3/2)*b^3+192*a*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*b^4-87*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a*b^4)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/a^(11/2)","A"
119,1,160,63,0.051000," ","int(x^(1/2)/(a*x+b*x^(1/2))^(1/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(4 a \,b^{2} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-a \,b^{2} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} \sqrt{x}-8 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b +2 \sqrt{a x +b \sqrt{x}}\, a^{\frac{3}{2}} b \right)}{4 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{7}{2}}}"," ",0,"1/4*(a*x+b*x^(1/2))^(1/2)*(4*x^(1/2)*(a*x+b*x^(1/2))^(1/2)*a^(5/2)-8*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(3/2)*b+2*(a*x+b*x^(1/2))^(1/2)*a^(3/2)*b+4*a*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*b^2-b^2*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/a^(7/2)","B"
120,1,136,24,0.050000," ","int(1/x^(1/2)/(a*x+b*x^(1/2))^(1/2),x)","-\frac{\sqrt{a x +b \sqrt{x}}\, \left(-b \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-b \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}-2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}\right)}{\sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\, b}"," ",0,"-(a*x+b*x^(1/2))^(1/2)*(2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2)-2*(a*x+b*x^(1/2))^(1/2)*a^(1/2)-b*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))-b*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2)))/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b/a^(1/2)","B"
121,1,194,40,0.063000," ","int(1/x^(3/2)/(a*x+b*x^(1/2))^(1/2),x)","-\frac{\sqrt{a x +b \sqrt{x}}\, \left(-3 a^{2} b \,x^{\frac{5}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+3 a^{2} b \,x^{\frac{5}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+6 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{5}{2}} x^{\frac{5}{2}}+6 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} x^{\frac{5}{2}}-12 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} x^{\frac{3}{2}}+4 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b x \right)}{3 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\, b^{3} x^{\frac{5}{2}}}"," ",0,"-1/3*(a*x+b*x^(1/2))^(1/2)*(6*x^(5/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(5/2)-12*x^(3/2)*(a*x+b*x^(1/2))^(3/2)*a^(3/2)+6*x^(5/2)*(a*x+b*x^(1/2))^(1/2)*a^(5/2)-3*x^(5/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^2*b+3*x^(5/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^2*b+4*(a*x+b*x^(1/2))^(3/2)*b*a^(1/2)*x)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^3/a^(1/2)/x^(5/2)","C"
122,1,240,84,0.060000," ","int(1/x^(5/2)/(a*x+b*x^(1/2))^(1/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(35 a^{4} b \,x^{\frac{9}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-35 a^{4} b \,x^{\frac{9}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-70 \sqrt{a x +b \sqrt{x}}\, a^{\frac{9}{2}} x^{\frac{9}{2}}-70 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{9}{2}} x^{\frac{9}{2}}+140 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} x^{\frac{7}{2}}-76 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b \,x^{3}+44 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{2} x^{\frac{5}{2}}-20 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b^{3} x^{2}\right)}{35 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\, b^{5} x^{\frac{9}{2}}}"," ",0,"1/35*(a*x+b*x^(1/2))^(1/2)*(140*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*x^(7/2)-70*(a*x+b*x^(1/2))^(1/2)*a^(9/2)*x^(9/2)+35*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(9/2)*a^4*b-70*a^(9/2)*x^(9/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)-35*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(9/2)*a^4*b+44*(a*x+b*x^(1/2))^(3/2)*a^(3/2)*x^(5/2)*b^2-76*a^(5/2)*(a*x+b*x^(1/2))^(3/2)*b*x^3-20*(a*x+b*x^(1/2))^(3/2)*a^(1/2)*x^2*b^3)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^5/x^(9/2)/a^(1/2)","C"
123,1,284,128,0.065000," ","int(1/x^(7/2)/(a*x+b*x^(1/2))^(1/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(693 a^{6} b \,x^{\frac{13}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-693 a^{6} b \,x^{\frac{13}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-1386 \sqrt{a x +b \sqrt{x}}\, a^{\frac{13}{2}} x^{\frac{13}{2}}-1386 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{13}{2}} x^{\frac{13}{2}}+2772 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{11}{2}} x^{\frac{11}{2}}-1748 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} b \,x^{5}+1236 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b^{2} x^{\frac{9}{2}}-852 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{3} x^{4}+532 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{4} x^{\frac{7}{2}}-252 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b^{5} x^{3}\right)}{693 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\, b^{7} x^{\frac{13}{2}}}"," ",0,"1/693*(a*x+b*x^(1/2))^(1/2)*(2772*(a*x+b*x^(1/2))^(3/2)*a^(11/2)*x^(11/2)-1386*(a*x+b*x^(1/2))^(1/2)*a^(13/2)*x^(13/2)+693*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(13/2)*a^6*b-1386*a^(13/2)*x^(13/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)-693*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(13/2)*a^6*b+1236*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*x^(9/2)*b^2+532*(a*x+b*x^(1/2))^(3/2)*a^(3/2)*x^(7/2)*b^4-1748*a^(9/2)*(a*x+b*x^(1/2))^(3/2)*b*x^5-852*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*x^4*b^3-252*(a*x+b*x^(1/2))^(3/2)*a^(1/2)*x^3*b^5)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^7/x^(13/2)/a^(1/2)","C"
124,1,527,125,0.064000," ","int(x^(5/2)/(a*x+b*x^(1/2))^(3/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(384 a^{3} b^{4} x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-69 a^{3} b^{4} x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+768 a^{2} b^{5} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-138 a^{2} b^{5} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+276 \sqrt{a x +b \sqrt{x}}\, a^{\frac{9}{2}} b^{2} x^{\frac{3}{2}}+384 a \,b^{6} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-69 a \,b^{6} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-768 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{7}{2}} b^{3} x +690 \sqrt{a x +b \sqrt{x}}\, a^{\frac{7}{2}} b^{3} x +32 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{11}{2}} x^{\frac{3}{2}}-1536 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{5}{2}} b^{4} \sqrt{x}+552 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} b^{4} \sqrt{x}-48 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} b x -768 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b^{5}+138 \sqrt{a x +b \sqrt{x}}\, a^{\frac{3}{2}} b^{5}-192 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b^{2} \sqrt{x}+256 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{3}-112 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{3}\right)}{64 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} a^{\frac{13}{2}}}"," ",0,"1/64*(a*x+b*x^(1/2))^(1/2)/a^(13/2)*(32*(a*x+b*x^(1/2))^(3/2)*a^(11/2)*x^(3/2)+276*x^(3/2)*(a*x+b*x^(1/2))^(1/2)*a^(9/2)*b^2-48*(a*x+b*x^(1/2))^(3/2)*a^(9/2)*b*x-768*x*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(7/2)*b^3+690*x*(a*x+b*x^(1/2))^(1/2)*a^(7/2)*b^3+384*x*a^3*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*b^4-192*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*b^2*x^(1/2)-69*x*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^3*b^4-1536*x^(1/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(5/2)*b^4+552*(a*x+b*x^(1/2))^(1/2)*a^(5/2)*b^4*x^(1/2)+768*x^(1/2)*a^2*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*b^5+256*((a*x^(1/2)+b)*x^(1/2))^(3/2)*a^(5/2)*b^3-112*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*b^3-138*x^(1/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^2*b^5-768*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(3/2)*b^5+138*(a*x+b*x^(1/2))^(1/2)*a^(3/2)*b^5+384*a*b^6*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))-69*a*b^6*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2)))/((a*x^(1/2)+b)*x^(1/2))^(1/2)/(a*x^(1/2)+b)^2","B"
125,1,440,83,0.060000," ","int(x^(3/2)/(a*x+b*x^(1/2))^(3/2),x)","\frac{\sqrt{a x +b \sqrt{x}}\, \left(16 a^{3} b^{2} x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-a^{3} b^{2} x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+32 a^{2} b^{3} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 a^{2} b^{3} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 \sqrt{a x +b \sqrt{x}}\, a^{\frac{9}{2}} x^{\frac{3}{2}}+16 a \,b^{4} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-a \,b^{4} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-32 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{7}{2}} b x +10 \sqrt{a x +b \sqrt{x}}\, a^{\frac{7}{2}} b x -64 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{5}{2}} b^{2} \sqrt{x}+8 \sqrt{a x +b \sqrt{x}}\, a^{\frac{5}{2}} b^{2} \sqrt{x}-32 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b^{3}+2 \sqrt{a x +b \sqrt{x}}\, a^{\frac{3}{2}} b^{3}+16 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b \right)}{4 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} a^{\frac{9}{2}}}"," ",0,"1/4*(a*x+b*x^(1/2))^(1/2)/a^(9/2)*(4*x^(3/2)*(a*x+b*x^(1/2))^(1/2)*a^(9/2)-32*x*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(7/2)*b+10*x*(a*x+b*x^(1/2))^(1/2)*a^(7/2)*b+16*x*a^3*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*b^2-x*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^3*b^2-64*x^(1/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(5/2)*b^2+8*(a*x+b*x^(1/2))^(1/2)*a^(5/2)*b^2*x^(1/2)+32*x^(1/2)*a^2*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*b^3+16*((a*x^(1/2)+b)*x^(1/2))^(3/2)*a^(5/2)*b-2*x^(1/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^2*b^3-32*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(3/2)*b^3+2*(a*x+b*x^(1/2))^(1/2)*a^(3/2)*b^3+16*a*b^4*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))-a*b^4*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2)))/((a*x^(1/2)+b)*x^(1/2))^(1/2)/(a*x^(1/2)+b)^2","B"
126,1,240,44,0.049000," ","int(x^(1/2)/(a*x+b*x^(1/2))^(3/2),x)","-\frac{2 \sqrt{a x +b \sqrt{x}}\, \left(-a^{2} b x \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 a \,b^{2} \sqrt{x}\, \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-b^{3} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{5}{2}} x +4 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{3}{2}} b \sqrt{x}+2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}\, b^{2}-2 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}}\right)}{\sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} a^{\frac{3}{2}} b}"," ",0,"-2*(a*x+b*x^(1/2))^(1/2)/a^(3/2)*(2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(5/2)*x-a^2*b*x*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))+4*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(3/2)*b*x^(1/2)-2*a*b^2*x^(1/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))-2*((a*x^(1/2)+b)*x^(1/2))^(3/2)*a^(3/2)+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2)*b^2-b^3*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2)))/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b/(a*x^(1/2)+b)^2","B"
127,1,111,24,0.059000," ","int(1/x^(1/2)/(a*x+b*x^(1/2))^(3/2),x)","-\frac{4 \sqrt{a x +b \sqrt{x}}\, \left(\left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{2} x -\left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{2} x +2 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a b \sqrt{x}+\left(a x +b \sqrt{x}\right)^{\frac{3}{2}} b^{2}\right)}{\sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} b^{3} x}"," ",0,"-4*(a*x+b*x^(1/2))^(1/2)*((a*x+b*x^(1/2))^(3/2)*x*a^2+2*(a*x+b*x^(1/2))^(3/2)*x^(1/2)*a*b-((a*x^(1/2)+b)*x^(1/2))^(3/2)*x*a^2+(a*x+b*x^(1/2))^(3/2)*b^2)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^3/(a*x^(1/2)+b)^2/x","B"
128,1,548,81,0.063000," ","int(1/x^(3/2)/(a*x+b*x^(1/2))^(3/2),x)","\frac{2 \sqrt{a x +b \sqrt{x}}\, \left(-5 a^{5} b \,x^{\frac{9}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+5 a^{5} b \,x^{\frac{9}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-10 a^{4} b^{2} x^{4} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+10 a^{4} b^{2} x^{4} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-5 a^{3} b^{3} x^{\frac{7}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+5 a^{3} b^{3} x^{\frac{7}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+10 \sqrt{a x +b \sqrt{x}}\, a^{\frac{11}{2}} x^{\frac{9}{2}}+10 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{11}{2}} x^{\frac{9}{2}}+20 \sqrt{a x +b \sqrt{x}}\, a^{\frac{9}{2}} b \,x^{4}+20 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{9}{2}} b \,x^{4}+10 \sqrt{a x +b \sqrt{x}}\, a^{\frac{7}{2}} b^{2} x^{\frac{7}{2}}+10 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{7}{2}} b^{2} x^{\frac{7}{2}}-30 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} x^{\frac{7}{2}}+10 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} x^{\frac{7}{2}}-52 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b \,x^{3}-16 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{2} x^{\frac{5}{2}}+4 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{3} x^{2}-2 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b^{4} x^{\frac{3}{2}}\right)}{5 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} \sqrt{a}\, b^{5} x^{\frac{7}{2}}}"," ",0,"2/5*(a*x+b*x^(1/2))^(1/2)*(5*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(9/2)*a^5*b-30*(a*x+b*x^(1/2))^(3/2)*a^(9/2)*x^(7/2)+10*(a*x+b*x^(1/2))^(1/2)*a^(11/2)*x^(9/2)-5*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(9/2)*a^5*b+10*a^(11/2)*x^(9/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)+10*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^4*a^4*b^2-16*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*x^(5/2)*b^2-52*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*x^3*b+20*(a*x+b*x^(1/2))^(1/2)*a^(9/2)*x^4*b-10*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^4*a^4*b^2+20*a^(9/2)*x^4*((a*x^(1/2)+b)*x^(1/2))^(1/2)*b+10*a^(9/2)*x^(7/2)*((a*x^(1/2)+b)*x^(1/2))^(3/2)+5*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(7/2)*a^3*b^3+4*(a*x+b*x^(1/2))^(3/2)*a^(3/2)*x^2*b^3+10*(a*x+b*x^(1/2))^(1/2)*a^(7/2)*x^(7/2)*b^2-5*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*x^(7/2)*a^3*b^3+10*a^(7/2)*x^(7/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*b^2-2*(a*x+b*x^(1/2))^(3/2)*a^(1/2)*x^(3/2)*b^4)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^5/x^(7/2)/a^(1/2)/(a*x^(1/2)+b)^2","C"
129,1,592,125,0.067000," ","int(1/x^(5/2)/(a*x+b*x^(1/2))^(3/2),x)","\frac{4 \sqrt{a x +b \sqrt{x}}\, \left(-63 a^{7} b \,x^{\frac{13}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+63 a^{7} b \,x^{\frac{13}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-126 a^{6} b^{2} x^{6} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+126 a^{6} b^{2} x^{6} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-63 a^{5} b^{3} x^{\frac{11}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+63 a^{5} b^{3} x^{\frac{11}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+126 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{15}{2}} x^{\frac{13}{2}}+126 \sqrt{a x +b \sqrt{x}}\, a^{\frac{15}{2}} x^{\frac{13}{2}}+252 \sqrt{a x +b \sqrt{x}}\, a^{\frac{13}{2}} b \,x^{6}+252 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{13}{2}} b \,x^{6}+126 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{11}{2}} b^{2} x^{\frac{11}{2}}+126 \sqrt{a x +b \sqrt{x}}\, a^{\frac{11}{2}} b^{2} x^{\frac{11}{2}}+63 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{13}{2}} x^{\frac{11}{2}}-315 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{13}{2}} x^{\frac{11}{2}}-508 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{11}{2}} b \,x^{5}-128 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} b^{2} x^{\frac{9}{2}}+32 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b^{3} x^{4}-16 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{4} x^{\frac{7}{2}}+10 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{5} x^{3}-7 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b^{6} x^{\frac{5}{2}}\right)}{63 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} \sqrt{a}\, b^{7} x^{\frac{11}{2}}}"," ",0,"4/63*(a*x+b*x^(1/2))^(1/2)*(126*x^6*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^6*b^2+63*x^(11/2)*((a*x^(1/2)+b)*x^(1/2))^(3/2)*a^(13/2)-16*x^(7/2)*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*b^4-63*x^(11/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^5*b^3+63*x^(11/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^5*b^3+10*x^3*(a*x+b*x^(1/2))^(3/2)*a^(3/2)*b^5+126*x^(11/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(11/2)*b^2+126*x^(11/2)*(a*x+b*x^(1/2))^(1/2)*a^(11/2)*b^2+252*x^6*(a*x+b*x^(1/2))^(1/2)*a^(13/2)*b+32*x^4*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*b^3-508*x^5*(a*x+b*x^(1/2))^(3/2)*a^(11/2)*b-128*x^(9/2)*(a*x+b*x^(1/2))^(3/2)*a^(9/2)*b^2+252*x^6*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(13/2)*b-7*x^(5/2)*(a*x+b*x^(1/2))^(3/2)*a^(1/2)*b^6+126*x^(13/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(15/2)-315*x^(11/2)*(a*x+b*x^(1/2))^(3/2)*a^(13/2)+126*x^(13/2)*(a*x+b*x^(1/2))^(1/2)*a^(15/2)-63*x^(13/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^7*b+63*x^(13/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^7*b-126*x^6*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^6*b^2)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^7/x^(11/2)/a^(1/2)/(a*x^(1/2)+b)^2","C"
130,1,636,169,0.094000," ","int(1/x^(7/2)/(a*x+b*x^(1/2))^(3/2),x)","\frac{2 \sqrt{a x +b \sqrt{x}}\, \left(-1287 a^{9} b \,x^{\frac{17}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+1287 a^{9} b \,x^{\frac{17}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-2574 a^{8} b^{2} x^{8} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+2574 a^{8} b^{2} x^{8} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)-1287 a^{7} b^{3} x^{\frac{15}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+1287 a^{7} b^{3} x^{\frac{15}{2}} \ln \left(\frac{2 a \sqrt{x}+b +2 \sqrt{a x +b \sqrt{x}}\, \sqrt{a}}{2 \sqrt{a}}\right)+2574 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{19}{2}} x^{\frac{17}{2}}+2574 \sqrt{a x +b \sqrt{x}}\, a^{\frac{19}{2}} x^{\frac{17}{2}}+5148 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{17}{2}} b \,x^{8}+5148 \sqrt{a x +b \sqrt{x}}\, a^{\frac{17}{2}} b \,x^{8}+2574 \sqrt{a x +b \sqrt{x}}\, a^{\frac{15}{2}} b^{2} x^{\frac{15}{2}}+2574 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, a^{\frac{15}{2}} b^{2} x^{\frac{15}{2}}-6006 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{17}{2}} x^{\frac{15}{2}}+858 \left(\left(a \sqrt{x}+b \right) \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{17}{2}} x^{\frac{15}{2}}-9244 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{15}{2}} b \,x^{7}-2048 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{13}{2}} b^{2} x^{\frac{13}{2}}+512 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{11}{2}} b^{3} x^{6}-256 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{9}{2}} b^{4} x^{\frac{11}{2}}+160 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{7}{2}} b^{5} x^{5}-112 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{6} x^{\frac{9}{2}}+84 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{7} x^{4}-66 \left(a x +b \sqrt{x}\right)^{\frac{3}{2}} \sqrt{a}\, b^{8} x^{\frac{7}{2}}\right)}{429 \sqrt{\left(a \sqrt{x}+b \right) \sqrt{x}}\, \left(a \sqrt{x}+b \right)^{2} \sqrt{a}\, b^{9} x^{\frac{15}{2}}}"," ",0,"2/429*(a*x+b*x^(1/2))^(1/2)*(2574*x^(15/2)*(a*x+b*x^(1/2))^(1/2)*a^(15/2)*b^2+160*x^5*(a*x+b*x^(1/2))^(3/2)*a^(7/2)*b^5-2048*x^(13/2)*(a*x+b*x^(1/2))^(3/2)*a^(13/2)*b^2+5148*x^8*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(17/2)*b-9244*x^7*(a*x+b*x^(1/2))^(3/2)*a^(15/2)*b+5148*x^8*(a*x+b*x^(1/2))^(1/2)*a^(17/2)*b-256*x^(11/2)*(a*x+b*x^(1/2))^(3/2)*a^(9/2)*b^4+512*x^6*(a*x+b*x^(1/2))^(3/2)*a^(11/2)*b^3+2574*x^(15/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(15/2)*b^2+2574*x^(17/2)*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(19/2)-66*x^(7/2)*(a*x+b*x^(1/2))^(3/2)*a^(1/2)*b^8-6006*x^(15/2)*(a*x+b*x^(1/2))^(3/2)*a^(17/2)+2574*x^(17/2)*(a*x+b*x^(1/2))^(1/2)*a^(19/2)-1287*x^(17/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^9*b+1287*x^(17/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^9*b-2574*x^8*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^8*b^2+2574*x^8*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^8*b^2+858*x^(15/2)*((a*x^(1/2)+b)*x^(1/2))^(3/2)*a^(17/2)-1287*x^(15/2)*ln(1/2*(2*a*x^(1/2)+b+2*((a*x^(1/2)+b)*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^7*b^3+1287*x^(15/2)*ln(1/2*(2*a*x^(1/2)+b+2*(a*x+b*x^(1/2))^(1/2)*a^(1/2))/a^(1/2))*a^7*b^3-112*x^(9/2)*(a*x+b*x^(1/2))^(3/2)*a^(5/2)*b^6+84*x^4*(a*x+b*x^(1/2))^(3/2)*a^(3/2)*b^7)/((a*x^(1/2)+b)*x^(1/2))^(1/2)/b^9/x^(15/2)/a^(1/2)/(a*x^(1/2)+b)^2","C"
131,1,264,254,0.115000," ","int(x^3*(b*x^(1/3)+a*x)^(1/2),x)","\frac{2 \sqrt{a x +b \,x^{\frac{1}{3}}}\, x^{4}}{9}+\frac{4 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b \,x^{\frac{10}{3}}}{207 a}-\frac{28 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{2} x^{\frac{8}{3}}}{1311 a^{2}}+\frac{476 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{3} x^{2}}{19665 a^{3}}-\frac{6188 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{4} x^{\frac{4}{3}}}{216315 a^{4}}+\frac{442 \sqrt{-a b}\, \sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x^{\frac{1}{3}}-\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{7} \EllipticF \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{14421 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{7}}+\frac{884 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{5} x^{\frac{2}{3}}}{24035 a^{5}}-\frac{884 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{6}}{14421 a^{6}}"," ",0,"2/9*x^4*(b*x^(1/3)+a*x)^(1/2)+4/207*b*x^(10/3)*(b*x^(1/3)+a*x)^(1/2)/a-28/1311*b^2*x^(8/3)*(b*x^(1/3)+a*x)^(1/2)/a^2+476/19665*b^3*x^2*(b*x^(1/3)+a*x)^(1/2)/a^3-6188/216315*b^4*x^(4/3)*(b*x^(1/3)+a*x)^(1/2)/a^4+884/24035*b^5*x^(2/3)*(b*x^(1/3)+a*x)^(1/2)/a^5-884/14421*b^6*(b*x^(1/3)+a*x)^(1/2)/a^6+442/14421*b^7/a^7*(-a*b)^(1/2)*((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-2*(x^(1/3)-(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-x^(1/3)/(-a*b)^(1/2)*a)^(1/2)/(b*x^(1/3)+a*x)^(1/2)*EllipticF(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2))","A"
132,1,273,363,0.073000," ","int(x^2*(a*x+b*x^(1/3))^(1/2),x)","\frac{2 \sqrt{a x +b \,x^{\frac{1}{3}}}\, x^{3}}{7}+\frac{4 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b \,x^{\frac{7}{3}}}{119 a}-\frac{60 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{2} x^{\frac{5}{3}}}{1547 a^{2}}+\frac{220 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{3} x}{4641 a^{3}}-\frac{44 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{4} x^{\frac{1}{3}}}{663 a^{4}}+\frac{22 \sqrt{-a b}\, \sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x^{\frac{1}{3}}-\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}\right) b^{5}}{221 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{5}}"," ",0,"2/7*x^3*(a*x+b*x^(1/3))^(1/2)+4/119*b*x^(7/3)*(a*x+b*x^(1/3))^(1/2)/a-60/1547*b^2*x^(5/3)*(a*x+b*x^(1/3))^(1/2)/a^2+220/4641*b^3*x*(a*x+b*x^(1/3))^(1/2)/a^3-44/663*b^4*x^(1/3)*(a*x+b*x^(1/3))^(1/2)/a^4+22/221*b^5/a^5*(-a*b)^(1/2)*((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-2*(x^(1/3)-(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)/(a*x+b*x^(1/3))^(1/2)*(-2*(-a*b)^(1/2)/a*EllipticE(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/a*EllipticF(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2)))","A"
133,1,198,188,0.076000," ","int(x*(a*x+b*x^(1/3))^(1/2),x)","\frac{2 \sqrt{a x +b \,x^{\frac{1}{3}}}\, x^{2}}{5}+\frac{4 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b \,x^{\frac{4}{3}}}{55 a}-\frac{6 \sqrt{-a b}\, \sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x^{\frac{1}{3}}-\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{4} \EllipticF \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{77 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{4}}-\frac{36 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{2} x^{\frac{2}{3}}}{385 a^{2}}+\frac{12 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{3}}{77 a^{3}}"," ",0,"2/5*x^2*(a*x+b*x^(1/3))^(1/2)+4/55*b*x^(4/3)*(a*x+b*x^(1/3))^(1/2)/a-36/385*b^2*x^(2/3)*(a*x+b*x^(1/3))^(1/2)/a^2+12/77*b^3*(a*x+b*x^(1/3))^(1/2)/a^3-6/77/a^4*b^4*(-a*b)^(1/2)*((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-2*(x^(1/3)-(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)/(a*x+b*x^(1/3))^(1/2)*EllipticF(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2))","A"
134,1,207,297,0.071000," ","int((a*x+b*x^(1/3))^(1/2),x)","\frac{2 \sqrt{a x +b \,x^{\frac{1}{3}}}\, x}{3}+\frac{4 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b \,x^{\frac{1}{3}}}{15 a}-\frac{2 \sqrt{-a b}\, \sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x^{\frac{1}{3}}-\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}\right) b^{2}}{5 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{2}}"," ",0,"2/3*x*(a*x+b*x^(1/3))^(1/2)+4/15*b*x^(1/3)*(a*x+b*x^(1/3))^(1/2)/a-2/5*b^2/a^2*(-a*b)^(1/2)*((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-2*(x^(1/3)-(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)/(a*x+b*x^(1/3))^(1/2)*(-2*(-a*b)^(1/2)/a*EllipticE(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/a*EllipticF(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2)))","A"
135,1,132,124,0.065000," ","int((a*x+b*x^(1/3))^(1/2)/x,x)","\frac{2 \sqrt{-a b}\, \sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x^{\frac{1}{3}}-\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b \EllipticF \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{a x +b \,x^{\frac{1}{3}}}\, a}+2 \sqrt{a x +b \,x^{\frac{1}{3}}}"," ",0,"2*(a*x+b*x^(1/3))^(1/2)+2*b*(-a*b)^(1/2)/a*((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-2*(x^(1/3)-(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)/(a*x+b*x^(1/3))^(1/2)*EllipticF(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2))","A"
136,1,213,299,0.096000," ","int((a*x+b*x^(1/3))^(1/2)/x^2,x)","-\frac{12 \left(a \,x^{\frac{2}{3}}+b \right) a}{5 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b}+\frac{6 \sqrt{-a b}\, \sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x^{\frac{1}{3}}-\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}\right) a}{5 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b}-\frac{6 \sqrt{a x +b \,x^{\frac{1}{3}}}}{5 x}"," ",0,"-6/5*(a*x+b*x^(1/3))^(1/2)/x-12/5*(b+a*x^(2/3))*a/b/(x^(1/3)*(b+a*x^(2/3)))^(1/2)+6/5*a/b*(-a*b)^(1/2)*((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-2*(x^(1/3)-(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)/(a*x+b*x^(1/3))^(1/2)*(-2*(-a*b)^(1/2)/a*EllipticE(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/a*EllipticF(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2)))","A"
137,1,179,169,0.077000," ","int((a*x+b*x^(1/3))^(1/2)/x^3,x)","\frac{10 \sqrt{-a b}\, \sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x^{\frac{1}{3}}-\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, a^{2} \EllipticF \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{77 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{2}}+\frac{20 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{2}}{77 b^{2} x^{\frac{2}{3}}}-\frac{12 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a}{77 b \,x^{\frac{4}{3}}}-\frac{6 \sqrt{a x +b \,x^{\frac{1}{3}}}}{11 x^{2}}"," ",0,"-6/11*(a*x+b*x^(1/3))^(1/2)/x^2-12/77*a*(a*x+b*x^(1/3))^(1/2)/b/x^(4/3)+20/77*a^2*(a*x+b*x^(1/3))^(1/2)/b^2/x^(2/3)+10/77*a^2/b^2*(-a*b)^(1/2)*((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-2*(x^(1/3)-(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)/(a*x+b*x^(1/3))^(1/2)*EllipticF(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2))","A"
138,1,281,365,0.082000," ","int((a*x+b*x^(1/3))^(1/2)/x^4,x)","\frac{308 \left(a \,x^{\frac{2}{3}}+b \right) a^{4}}{1105 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{4}}-\frac{154 \sqrt{-a b}\, \sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x^{\frac{1}{3}}-\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}\right) a^{4}}{1105 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{4}}-\frac{308 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{3}}{3315 b^{3} x}+\frac{44 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{2}}{663 b^{2} x^{\frac{5}{3}}}-\frac{12 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a}{221 b \,x^{\frac{7}{3}}}-\frac{6 \sqrt{a x +b \,x^{\frac{1}{3}}}}{17 x^{3}}"," ",0,"-6/17*(a*x+b*x^(1/3))^(1/2)/x^3-12/221*a*(a*x+b*x^(1/3))^(1/2)/b/x^(7/3)+44/663*a^2*(a*x+b*x^(1/3))^(1/2)/b^2/x^(5/3)-308/3315*a^3*(a*x+b*x^(1/3))^(1/2)/b^3/x+308/1105*(a*x^(2/3)+b)*a^4/b^4/((a*x^(2/3)+b)*x^(1/3))^(1/2)-154/1105*a^4/b^4*(-a*b)^(1/2)*((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-2*(x^(1/3)-(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)/(a*x+b*x^(1/3))^(1/2)*(-2*(-a*b)^(1/2)/a*EllipticE(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2))+(-a*b)^(1/2)/a*EllipticF(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2)))","A"
139,1,245,235,0.085000," ","int((a*x+b*x^(1/3))^(1/2)/x^5,x)","-\frac{1326 \sqrt{-a b}\, \sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x^{\frac{1}{3}}-\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, a^{5} \EllipticF \left(\sqrt{\frac{\left(x^{\frac{1}{3}}+\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{33649 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b^{5}}-\frac{2652 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{5}}{33649 b^{5} x^{\frac{2}{3}}}+\frac{7956 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{4}}{168245 b^{4} x^{\frac{4}{3}}}-\frac{884 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{3}}{24035 b^{3} x^{2}}+\frac{68 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{2}}{2185 b^{2} x^{\frac{8}{3}}}-\frac{12 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a}{437 b \,x^{\frac{10}{3}}}-\frac{6 \sqrt{a x +b \,x^{\frac{1}{3}}}}{23 x^{4}}"," ",0,"-6/23*(a*x+b*x^(1/3))^(1/2)/x^4-12/437*a*(a*x+b*x^(1/3))^(1/2)/b/x^(10/3)+68/2185*a^2*(a*x+b*x^(1/3))^(1/2)/b^2/x^(8/3)-884/24035*a^3*(a*x+b*x^(1/3))^(1/2)/b^3/x^2+7956/168245*a^4*(a*x+b*x^(1/3))^(1/2)/b^4/x^(4/3)-2652/33649*a^5*(a*x+b*x^(1/3))^(1/2)/b^5/x^(2/3)-1326/33649*a^5/b^5*(-a*b)^(1/2)*((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-2*(x^(1/3)-(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)/(a*x+b*x^(1/3))^(1/2)*EllipticF(((x^(1/3)+(-a*b)^(1/2)/a)/(-a*b)^(1/2)*a)^(1/2),1/2*2^(1/2))","A"
140,1,196,251,0.144000," ","int(x^2*(a*x+b*x^(1/3))^(3/2),x)","\frac{\frac{2 a^{8} x^{5}}{9}+\frac{104 a^{7} b \,x^{\frac{13}{3}}}{207}+\frac{1126 a^{6} b^{2} x^{\frac{11}{3}}}{3933}-\frac{16 a^{5} b^{3} x^{3}}{19665}+\frac{272 a^{4} b^{4} x^{\frac{7}{3}}}{216315}-\frac{3536 a^{3} b^{5} x^{\frac{5}{3}}}{1514205}+\frac{3536 a^{2} b^{6} x}{504735}+\frac{1768 a \,b^{7} x^{\frac{1}{3}}}{100947}-\frac{884 \sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{7} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{100947}}{\sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{6}}"," ",0,"2/1514205*(216755*x^(11/3)*a^6*b^2+380380*x^(13/3)*a^7*b-616*a^5*b^3*x^3-1768*x^(5/3)*a^3*b^5+952*x^(7/3)*a^4*b^4+168245*a^8*x^5-6630*b^7*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+5304*a^2*b^6*x+13260*x^(1/3)*a*b^7)/a^6/((a*x^(2/3)+b)*x^(1/3))^(1/2)","A"
141,1,261,360,0.079000," ","int(x*(a*x+b*x^(1/3))^(3/2),x)","\frac{\frac{2 a^{6} x^{4}}{7}+\frac{80 a^{5} b \,x^{\frac{10}{3}}}{119}+\frac{622 a^{4} b^{2} x^{\frac{8}{3}}}{1547}-\frac{16 a^{3} b^{3} x^{2}}{4641}+\frac{176 a^{2} b^{4} x^{\frac{4}{3}}}{23205}-\frac{88 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{6} \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{1105}+\frac{44 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{6} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{1105}+\frac{88 a \,b^{5} x^{\frac{2}{3}}}{3315}}{\sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{4}}"," ",0,"2/23205/a^4*(4665*x^(8/3)*a^4*b^2+7800*x^(10/3)*a^5*b-40*x^2*a^3*b^3-924*b^6*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+462*b^6*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+3315*x^4*a^6+308*x^(2/3)*a*b^5+88*x^(4/3)*a^2*b^4)/((a*x^(2/3)+b)*x^(1/3))^(1/2)","A"
142,1,164,183,0.107000," ","int((a*x+b*x^(1/3))^(3/2),x)","\frac{\frac{2 a^{5} x^{3}}{5}+\frac{56 a^{4} b \,x^{\frac{7}{3}}}{55}+\frac{262 a^{3} b^{2} x^{\frac{5}{3}}}{385}-\frac{16 a^{2} b^{3} x}{385}-\frac{8 a \,b^{4} x^{\frac{1}{3}}}{77}+\frac{4 \sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{4} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{77}}{\sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{3}}"," ",0,"2/385*(10*b^4*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+131*a^3*b^2*x^(5/3)+196*a^4*b*x^(7/3)-8*a^2*b^3*x+77*a^5*x^3-20*a*b^4*x^(1/3))/a^3/((a*x^(2/3)+b)*x^(1/3))^(1/2)","A"
143,1,228,293,0.085000," ","int((a*x+b*x^(1/3))^(3/2)/x,x)","\frac{\frac{2 a^{3} x^{2}}{3}+\frac{32 a^{2} b \,x^{\frac{4}{3}}}{15}+\frac{8 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{3} \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}-\frac{4 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{3} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{5}+\frac{22 a \,b^{2} x^{\frac{2}{3}}}{15}}{\sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a}"," ",0,"2/15/a*(12*b^3*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))-6*b^3*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+11*a*b^2*x^(2/3)+16*a^2*b*x^(4/3)+5*a^3*x^2)/((a*x^(2/3)+b)*x^(1/3))^(1/2)","A"
144,1,130,141,0.074000," ","int((a*x+b*x^(1/3))^(3/2)/x^2,x)","\frac{2 a^{2} x^{\frac{4}{3}}+4 \sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b \,x^{\frac{1}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-2 b^{2}}{\sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, x^{\frac{1}{3}}}"," ",0,"2/x^(1/3)*(2*x^(1/3)*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*b+x^(4/3)*a^2-b^2)/((a*x^(2/3)+b)*x^(1/3))^(1/2)","A"
145,1,339,318,0.081000," ","int((a*x+b*x^(1/3))^(3/2)/x^3,x)","-\frac{2 \left(-12 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b \,x^{\frac{8}{3}} \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b \,x^{\frac{8}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+12 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{3} x^{\frac{10}{3}}+12 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{2} b \,x^{\frac{8}{3}}+11 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b \,x^{\frac{8}{3}}+16 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a \,b^{2} x^{2}+5 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{3} x^{\frac{4}{3}}\right)}{15 \left(a \,x^{\frac{2}{3}}+b \right) b \,x^{3}}"," ",0,"-2/15*(-12*a^2*b*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*x^(8/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+6*a^2*b*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*x^(8/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+12*x^(10/3)*(a*x+b*x^(1/3))^(1/2)*a^3+12*x^(8/3)*(a*x+b*x^(1/3))^(1/2)*a^2*b+16*x^2*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a*b^2+11*x^(8/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^2*b+5*x^(4/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*b^3)/b/x^3/(a*x^(2/3)+b)","A"
146,1,168,188,0.086000," ","int((a*x+b*x^(1/3))^(3/2)/x^4,x)","\frac{\frac{8 a^{4} x^{5}}{77}+\frac{4 \sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, a^{3} x^{\frac{14}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{77}+\frac{16 a^{3} b \,x^{\frac{13}{3}}}{385}-\frac{262 a^{2} b^{2} x^{\frac{11}{3}}}{385}-\frac{56 a \,b^{3} x^{3}}{55}-\frac{2 b^{4} x^{\frac{7}{3}}}{5}}{\sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{2} x^{\frac{14}{3}}}"," ",0,"2/385*(10*a^3*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^(14/3)-131*x^(11/3)*a^2*b^2+8*x^(13/3)*a^3*b-196*a*b^3*x^3+20*x^5*a^4-77*x^(7/3)*b^4)/b^2/((a*x^(2/3)+b)*x^(1/3))^(1/2)/x^(14/3)","A"
147,1,411,384,0.088000," ","int((a*x+b*x^(1/3))^(3/2)/x^5,x)","\frac{-\frac{88 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{5} b \,x^{\frac{20}{3}} \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{1105}+\frac{44 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{5} b \,x^{\frac{20}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{1105}+\frac{88 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{6} x^{\frac{22}{3}}}{1105}+\frac{88 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{5} b \,x^{\frac{20}{3}}}{1105}-\frac{88 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{5} b \,x^{\frac{20}{3}}}{3315}-\frac{176 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{4} b^{2} x^{6}}{23205}+\frac{16 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{3} b^{3} x^{\frac{16}{3}}}{4641}-\frac{622 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b^{4} x^{\frac{14}{3}}}{1547}-\frac{80 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a \,b^{5} x^{4}}{119}-\frac{2 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{6} x^{\frac{10}{3}}}{7}}{\left(a \,x^{\frac{2}{3}}+b \right) b^{4} x^{7}}"," ",0,"2/23205*(-924*a^5*b*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*x^(20/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+462*a^5*b*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*x^(20/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+924*(a*x+b*x^(1/3))^(1/2)*x^(22/3)*a^6+924*(a*x+b*x^(1/3))^(1/2)*x^(20/3)*a^5*b-88*x^6*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^4*b^2-308*x^(20/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^5*b-4665*x^(14/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^2*b^4+40*x^(16/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^3*b^3-7800*x^4*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a*b^5-3315*x^(10/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*b^6)/b^4/x^7/(a*x^(2/3)+b)","A"
148,1,201,254,0.089000," ","int((a*x+b*x^(1/3))^(3/2)/x^6,x)","-\frac{2 \left(13260 a^{7} x^{9}+6630 \sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, a^{6} x^{\frac{26}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+5304 a^{6} b \,x^{\frac{25}{3}}-1768 a^{5} b^{2} x^{\frac{23}{3}}+952 a^{4} b^{3} x^{7}-616 a^{3} b^{4} x^{\frac{19}{3}}+216755 a^{2} b^{5} x^{\frac{17}{3}}+380380 a \,b^{6} x^{5}+168245 b^{7} x^{\frac{13}{3}}\right)}{1514205 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{5} x^{\frac{26}{3}}}"," ",0,"-2/1514205*(6630*a^6*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^(26/3)-1768*x^(23/3)*a^5*b^2+5304*x^(25/3)*a^6*b+952*x^7*a^4*b^3+216755*x^(17/3)*a^2*b^5-616*x^(19/3)*a^3*b^4+380380*x^5*a*b^6+13260*x^9*a^7+168245*x^(13/3)*b^7)/b^5/((a*x^(2/3)+b)*x^(1/3))^(1/2)/x^(26/3)","A"
149,1,196,257,0.105000," ","int(x^4/(a*x+b*x^(1/3))^(1/2),x)","-\frac{-9614 a^{8} x^{5}+836 a^{7} b \,x^{\frac{13}{3}}-1100 a^{6} b^{2} x^{\frac{11}{3}}+1540 a^{5} b^{3} x^{3}-2380 a^{4} b^{4} x^{\frac{7}{3}}+4420 a^{3} b^{5} x^{\frac{5}{3}}-13260 a^{2} b^{6} x -33150 a \,b^{7} x^{\frac{1}{3}}+16575 \sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{7} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{43263 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{8}}"," ",0,"-1/43263*(-1100*a^6*b^2*x^(11/3)+836*a^7*b*x^(13/3)+1540*a^5*b^3*x^3+4420*a^3*b^5*x^(5/3)-2380*a^4*b^4*x^(7/3)-9614*a^8*x^5+16575*b^7*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))-13260*a^2*b^6*x-33150*a*b^7*x^(1/3))/((a*x^(2/3)+b)*x^(1/3))^(1/2)/a^8","A"
150,1,263,366,0.087000," ","int(x^3/(a*x+b*x^(1/3))^(1/2),x)","-\frac{-1326 a^{6} x^{4}+156 a^{5} b \,x^{\frac{10}{3}}-228 a^{4} b^{2} x^{\frac{8}{3}}+380 a^{3} b^{3} x^{2}-836 a^{2} b^{4} x^{\frac{4}{3}}+8778 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{6} \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-4389 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{6} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-2926 a \,b^{5} x^{\frac{2}{3}}}{4641 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{6}}"," ",0,"-1/4641/a^6*(-228*a^4*b^2*x^(8/3)+156*a^5*b*x^(10/3)+380*a^3*b^3*x^2+8778*b^6*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))-4389*b^6*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))-1326*a^6*x^4-2926*a*b^5*x^(2/3)-836*a^2*b^4*x^(4/3))/((a*x^(2/3)+b)*x^(1/3))^(1/2)","A"
151,1,163,191,0.054000," ","int(x^2/(a*x+b*x^(1/3))^(1/2),x)","\frac{154 a^{5} x^{3}-28 a^{4} b \,x^{\frac{7}{3}}+52 a^{3} b^{2} x^{\frac{5}{3}}-156 a^{2} b^{3} x -390 a \,b^{4} x^{\frac{1}{3}}+195 \sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{4} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{385 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{5}}"," ",0,"1/385*(52*a^3*b^2*x^(5/3)-28*a^4*b*x^(7/3)+195*b^4*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))-156*a^2*b^3*x+154*a^5*x^3-390*a*b^4*x^(1/3))/((a*x^(2/3)+b)*x^(1/3))^(1/2)/a^5","A"
152,1,228,300,0.057000," ","int(x/(a*x+b*x^(1/3))^(1/2),x)","-\frac{-10 a^{3} x^{2}+4 a^{2} b \,x^{\frac{4}{3}}-42 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{3} \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{3} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+14 a \,b^{2} x^{\frac{2}{3}}}{15 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{3}}"," ",0,"-1/15/a^3*(-42*b^3*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+21*b^3*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+14*a*b^2*x^(2/3)+4*a^2*b*x^(4/3)-10*a^3*x^2)/((a*x^(2/3)+b)*x^(1/3))^(1/2)","A"
153,1,127,127,0.050000," ","int(1/(a*x+b*x^(1/3))^(1/2),x)","\frac{2 a^{2} x +2 a b \,x^{\frac{1}{3}}-\sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2}}"," ",0,"(-b*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+2*a*b*x^(1/3)+2*a^2*x)/((a*x^(2/3)+b)*x^(1/3))^(1/2)/a^2","A"
154,1,253,282,0.077000," ","int(1/x/(a*x+b*x^(1/3))^(1/2),x)","-\frac{3 \left(-2 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a \,x^{\frac{2}{3}}+2 \sqrt{a x +b \,x^{\frac{1}{3}}}\, b \right)}{\left(a \,x^{\frac{2}{3}}+b \right) b \,x^{\frac{1}{3}}}"," ",0,"-3*(-2*((a*x^(2/3)+b)*x^(1/3))^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*b+((a*x^(2/3)+b)*x^(1/3))^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*b+2*x^(2/3)*(a*x+b*x^(1/3))^(1/2)*a+2*(a*x+b*x^(1/3))^(1/2)*b)/x^(1/3)/(a*x^(2/3)+b)/b","A"
155,1,142,150,0.092000," ","int(1/x^2/(a*x+b*x^(1/3))^(1/2),x)","\frac{10 a^{2} x^{\frac{5}{3}}+5 \sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, a \,x^{\frac{4}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+4 a b x -6 b^{2} x^{\frac{1}{3}}}{7 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{2} x^{\frac{4}{3}}}"," ",0,"1/7*(5*a*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^(4/3)+4*a*b*x+10*x^(5/3)*a^2-6*b^2*x^(1/3))/b^2/((a*x^(2/3)+b)*x^(1/3))^(1/2)/x^(4/3)","A"
156,1,365,346,0.087000," ","int(1/x^3/(a*x+b*x^(1/3))^(1/2),x)","-\frac{462 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{3} b \,x^{\frac{10}{3}} \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-231 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{3} b \,x^{\frac{10}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-462 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{4} x^{4}-462 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{3} b \,x^{\frac{10}{3}}+154 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{3} b \,x^{\frac{10}{3}}+44 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b^{2} x^{\frac{8}{3}}-20 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a \,b^{3} x^{2}+90 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{4} x^{\frac{4}{3}}}{195 \left(a \,x^{\frac{2}{3}}+b \right) b^{4} x^{\frac{11}{3}}}"," ",0,"-1/195*(462*a^3*b*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*x^(10/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))-231*a^3*b*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*x^(10/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))-462*x^(10/3)*(a*x+b*x^(1/3))^(1/2)*a^3*b+44*x^(8/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^2*b^2+154*x^(10/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^3*b-20*x^2*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a*b^3-462*x^4*(a*x+b*x^(1/3))^(1/2)*a^4+90*x^(4/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*b^4)/x^(11/3)/(a*x^(2/3)+b)/b^4","A"
157,1,179,216,0.101000," ","int(1/x^4/(a*x+b*x^(1/3))^(1/2),x)","-\frac{6630 a^{5} x^{\frac{17}{3}}+3315 \sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, a^{4} x^{\frac{16}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+2652 a^{4} b \,x^{5}-884 a^{3} b^{2} x^{\frac{13}{3}}+476 a^{2} b^{3} x^{\frac{11}{3}}-308 a \,b^{4} x^{3}+2310 b^{5} x^{\frac{7}{3}}}{7315 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{5} x^{\frac{16}{3}}}"," ",0,"-1/7315*(3315*a^4*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^(16/3)+2652*a^4*b*x^5+6630*x^(17/3)*a^5+476*x^(11/3)*a^2*b^3-884*x^(13/3)*a^3*b^2-308*a*b^4*x^3+2310*x^(7/3)*b^5)/b^5/((a*x^(2/3)+b)*x^(1/3))^(1/2)/x^(16/3)","A"
158,1,384,385,0.115000," ","int(x^4/(a*x+b*x^(1/3))^(3/2),x)","-\frac{-2652 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{6} x^{4}+3588 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{5} b \,x^{\frac{10}{3}}-5244 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{4} b^{2} x^{\frac{8}{3}}+8740 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{3} b^{3} x^{2}-19228 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b^{4} x^{\frac{4}{3}}+201894 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{6} \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-100947 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{6} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)-39452 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a \,b^{5} x^{\frac{2}{3}}-27846 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a \,b^{5} x^{\frac{2}{3}}}{9282 \left(a \,x^{\frac{2}{3}}+b \right) a^{7} x^{\frac{1}{3}}}"," ",0,"-1/9282/a^7*(-5244*x^(8/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^4*b^2+3588*x^(10/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^5*b+8740*x^2*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^3*b^3+201894*b^6*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))-100947*b^6*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))-2652*((a*x^(2/3)+b)*x^(1/3))^(1/2)*x^4*a^6-39452*x^(2/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a*b^5-27846*x^(2/3)*(a*x+b*x^(1/3))^(1/2)*a*b^5-19228*x^(4/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^2*b^4)/x^(1/3)/(a*x^(2/3)+b)","A"
159,1,260,210,0.088000," ","int(x^3/(a*x+b*x^(1/3))^(3/2),x)","-\frac{-308 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{5} x^{3}+476 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{4} b \,x^{\frac{7}{3}}-884 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{3} b^{2} x^{\frac{5}{3}}+2652 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b^{3} x +4320 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a \,b^{4} x^{\frac{1}{3}}+2310 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a \,b^{4} x^{\frac{1}{3}}-3315 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, \sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b^{4} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{770 \left(a \,x^{\frac{2}{3}}+b \right) a^{6} x^{\frac{1}{3}}}"," ",0,"-1/770*(-884*x^(5/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^3*b^2+476*x^(7/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^4*b-3315*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*b^4+2652*x*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^2*b^3-308*((a*x^(2/3)+b)*x^(1/3))^(1/2)*x^3*a^5+4320*x^(1/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a*b^4+2310*x^(1/3)*(a*x+b*x^(1/3))^(1/2)*a*b^4)/x^(1/3)/(a*x^(2/3)+b)/a^6","A"
160,1,312,319,0.067000," ","int(x^2/(a*x+b*x^(1/3))^(3/2),x)","-\frac{-20 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{3} x^{2}+44 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b \,x^{\frac{4}{3}}-462 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{3} \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+231 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{3} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+64 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a \,b^{2} x^{\frac{2}{3}}+90 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a \,b^{2} x^{\frac{2}{3}}}{30 \left(a \,x^{\frac{2}{3}}+b \right) a^{4} x^{\frac{1}{3}}}"," ",0,"-1/30/a^4*(-462*b^3*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+231*b^3*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+64*x^(2/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a*b^2+90*x^(2/3)*(a*x+b*x^(1/3))^(1/2)*a*b^2+44*x^(4/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^2*b-20*((a*x^(2/3)+b)*x^(1/3))^(1/2)*x^2*a^3)/x^(1/3)/(a*x^(2/3)+b)","A"
161,1,184,144,0.063000," ","int(x/(a*x+b*x^(1/3))^(3/2),x)","\frac{4 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} x +4 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a b \,x^{\frac{1}{3}}+6 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a b \,x^{\frac{1}{3}}-5 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, \sqrt{-a b}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, b \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{2 \left(a \,x^{\frac{2}{3}}+b \right) a^{3} x^{\frac{1}{3}}}"," ",0,"1/2*(-5*((a*x^(2/3)+b)*x^(1/3))^(1/2)*(-a*b)^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*b+4*x^(1/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a*b+6*x^(1/3)*(a*x+b*x^(1/3))^(1/2)*a*b+4*((a*x^(2/3)+b)*x^(1/3))^(1/2)*x*a^2)/x^(1/3)/(a*x^(2/3)+b)/a^3","A"
162,1,242,282,0.059000," ","int(1/(a*x+b*x^(1/3))^(3/2),x)","\frac{-3 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+\frac{3 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, b \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{2}+3 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a \,x^{\frac{2}{3}}}{\left(a \,x^{\frac{2}{3}}+b \right) a b \,x^{\frac{1}{3}}}"," ",0,"3/2/a*(-2*((a*x^(2/3)+b)*x^(1/3))^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*b+((a*x^(2/3)+b)*x^(1/3))^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*b+2*(a*x+b*x^(1/3))^(1/2)*a*x^(2/3))/x^(1/3)/(a*x^(2/3)+b)/b","A"
163,1,181,149,0.069000," ","int(1/x/(a*x+b*x^(1/3))^(3/2),x)","-\frac{6 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a x +4 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a x +5 \sqrt{-a b}\, \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{2}\, \sqrt{\frac{-a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, x^{\frac{2}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+4 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b \,x^{\frac{1}{3}}}{2 \left(a \,x^{\frac{2}{3}}+b \right) b^{2} x}"," ",0,"-1/2*(5*(-a*b)^(1/2)*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*2^(1/2)*((-a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^(2/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)+6*(a*x+b*x^(1/3))^(1/2)*x*a+4*x^(1/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*b+4*((a*x^(2/3)+b)*x^(1/3))^(1/2)*x*a)/b^2/x/(a*x^(2/3)+b)","A"
164,1,339,343,0.066000," ","int(1/x^2/(a*x+b*x^(1/3))^(3/2),x)","-\frac{-462 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b \,x^{\frac{8}{3}} \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+231 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b \,x^{\frac{8}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+462 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{3} x^{\frac{10}{3}}+372 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{2} b \,x^{\frac{8}{3}}-64 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b \,x^{\frac{8}{3}}-44 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a \,b^{2} x^{2}+20 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{3} x^{\frac{4}{3}}}{30 \left(a \,x^{\frac{2}{3}}+b \right) b^{4} x^{3}}"," ",0,"-1/30*(-462*a^2*b*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*x^(8/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+231*a^2*b*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*x^(8/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+462*(a*x+b*x^(1/3))^(1/2)*a^3*x^(10/3)+372*(a*x+b*x^(1/3))^(1/2)*a^2*b*x^(8/3)-44*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a*b^2*x^2-64*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^2*b*x^(8/3)+20*((a*x^(2/3)+b)*x^(1/3))^(1/2)*b^3*x^(4/3))/x^3/(a*x^(2/3)+b)/b^4","A"
165,1,261,213,0.079000," ","int(1/x^3/(a*x+b*x^(1/3))^(3/2),x)","\frac{2310 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{4} x^{5}+4320 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{4} x^{5}+3315 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, \sqrt{-a b}\, a^{3} x^{\frac{14}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+2652 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{3} b \,x^{\frac{13}{3}}-884 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b^{2} x^{\frac{11}{3}}+476 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a \,b^{3} x^{3}-308 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{4} x^{\frac{7}{3}}}{770 \left(a \,x^{\frac{2}{3}}+b \right) b^{5} x^{5}}"," ",0,"1/770*(3315*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))*x^(14/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*(-a*b)^(1/2)*a^3-884*x^(11/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^2*b^2+2652*x^(13/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^3*b+476*x^3*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a*b^3+2310*(a*x+b*x^(1/3))^(1/2)*x^5*a^4+4320*((a*x^(2/3)+b)*x^(1/3))^(1/2)*x^5*a^4-308*x^(7/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*b^4)/b^5/x^5/(a*x^(2/3)+b)","A"
166,1,411,409,0.067000," ","int(1/x^4/(a*x+b*x^(1/3))^(3/2),x)","\frac{-201894 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{5} b \,x^{\frac{20}{3}} \EllipticE \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+100947 \sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(a \,x^{\frac{1}{3}}-\sqrt{-a b}\right)}{\sqrt{-a b}}}\, \sqrt{-\frac{a \,x^{\frac{1}{3}}}{\sqrt{-a b}}}\, \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{5} b \,x^{\frac{20}{3}} \EllipticF \left(\sqrt{\frac{a \,x^{\frac{1}{3}}+\sqrt{-a b}}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)+201894 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{6} x^{\frac{22}{3}}+174048 \sqrt{a x +b \,x^{\frac{1}{3}}}\, a^{5} b \,x^{\frac{20}{3}}-39452 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{5} b \,x^{\frac{20}{3}}-19228 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{4} b^{2} x^{6}+8740 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{3} b^{3} x^{\frac{16}{3}}-5244 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a^{2} b^{4} x^{\frac{14}{3}}+3588 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, a \,b^{5} x^{4}-2652 \sqrt{\left(a \,x^{\frac{2}{3}}+b \right) x^{\frac{1}{3}}}\, b^{6} x^{\frac{10}{3}}}{9282 \left(a \,x^{\frac{2}{3}}+b \right) b^{7} x^{7}}"," ",0,"1/9282*(-201894*a^5*b*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*x^(20/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticE(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+100947*a^5*b*((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-2*(a*x^(1/3)-(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2)*(-1/(-a*b)^(1/2)*a*x^(1/3))^(1/2)*x^(20/3)*((a*x^(2/3)+b)*x^(1/3))^(1/2)*EllipticF(((a*x^(1/3)+(-a*b)^(1/2))/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+201894*(a*x+b*x^(1/3))^(1/2)*a^6*x^(22/3)+174048*(a*x+b*x^(1/3))^(1/2)*a^5*b*x^(20/3)-19228*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^4*b^2*x^6-39452*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^5*b*x^(20/3)-5244*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^2*b^4*x^(14/3)+8740*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a^3*b^3*x^(16/3)+3588*((a*x^(2/3)+b)*x^(1/3))^(1/2)*a*b^5*x^4-2652*((a*x^(2/3)+b)*x^(1/3))^(1/2)*b^6*x^(10/3))/x^7/(a*x^(2/3)+b)/b^7","A"
167,1,156,277,0.070000," ","int(x^3*(b*x^(2/3)+a*x)^(1/2),x)","-\frac{2 \sqrt{a x +b \,x^{\frac{2}{3}}}\, \left(a \,x^{\frac{1}{3}}+b \right) \left(-16900975 a^{12} x^{4}+16224936 a^{11} b \,x^{\frac{11}{3}}-15519504 a^{10} b^{2} x^{\frac{10}{3}}+14780480 a^{9} b^{3} x^{3}-14002560 a^{8} b^{4} x^{\frac{8}{3}}+13178880 a^{7} b^{5} x^{\frac{7}{3}}-12300288 a^{6} b^{6} x^{2}+11354112 a^{5} b^{7} x^{\frac{5}{3}}-10321920 a^{4} b^{8} x^{\frac{4}{3}}+9175040 a^{3} b^{9} x -7864320 a^{2} b^{10} x^{\frac{2}{3}}+6291456 a \,b^{11} x^{\frac{1}{3}}-4194304 b^{12}\right)}{152108775 a^{13} x^{\frac{1}{3}}}"," ",0,"-2/152108775*(b*x^(2/3)+a*x)^(1/2)*(a*x^(1/3)+b)*(16224936*x^(11/3)*a^11*b-15519504*x^(10/3)*a^10*b^2-14002560*x^(8/3)*a^8*b^4+13178880*x^(7/3)*a^7*b^5+11354112*x^(5/3)*a^5*b^7-10321920*x^(4/3)*a^4*b^8-16900975*x^4*a^12+14780480*x^3*a^9*b^3-7864320*x^(2/3)*a^2*b^10-12300288*x^2*a^6*b^6+6291456*x^(1/3)*a*b^11+9175040*x*a^3*b^9-4194304*b^12)/x^(1/3)/a^13","A"
168,1,123,211,0.048000," ","int(x^2*(a*x+b*x^(2/3))^(1/2),x)","-\frac{2 \sqrt{a x +b \,x^{\frac{2}{3}}}\, \left(a \,x^{\frac{1}{3}}+b \right) \left(-230945 a^{9} x^{3}+218790 a^{8} b \,x^{\frac{8}{3}}-205920 a^{7} b^{2} x^{\frac{7}{3}}+192192 a^{6} b^{3} x^{2}-177408 a^{5} b^{4} x^{\frac{5}{3}}+161280 a^{4} b^{5} x^{\frac{4}{3}}-143360 a^{3} b^{6} x +122880 a^{2} b^{7} x^{\frac{2}{3}}-98304 a \,b^{8} x^{\frac{1}{3}}+65536 b^{9}\right)}{1616615 a^{10} x^{\frac{1}{3}}}"," ",0,"-2/1616615*(a*x+b*x^(2/3))^(1/2)*(a*x^(1/3)+b)*(218790*x^(8/3)*a^8*b-205920*x^(7/3)*a^7*b^2-177408*x^(5/3)*a^5*b^4+161280*x^(4/3)*a^4*b^5-230945*x^3*a^9+122880*x^(2/3)*a^2*b^7+192192*x^2*a^6*b^3-98304*x^(1/3)*a*b^8-143360*x*a^3*b^6+65536*b^9)/x^(1/3)/a^10","A"
169,1,90,145,0.049000," ","int(x*(a*x+b*x^(2/3))^(1/2),x)","-\frac{2 \sqrt{a x +b \,x^{\frac{2}{3}}}\, \left(a \,x^{\frac{1}{3}}+b \right) \left(-3003 a^{6} x^{2}+2772 a^{5} b \,x^{\frac{5}{3}}-2520 a^{4} b^{2} x^{\frac{4}{3}}+2240 a^{3} b^{3} x -1920 a^{2} b^{4} x^{\frac{2}{3}}+1536 a \,b^{5} x^{\frac{1}{3}}-1024 b^{6}\right)}{15015 a^{7} x^{\frac{1}{3}}}"," ",0,"-2/15015*(a*x+b*x^(2/3))^(1/2)*(a*x^(1/3)+b)*(2772*x^(5/3)*a^5*b-2520*x^(4/3)*a^4*b^2-1920*x^(2/3)*a^2*b^4-3003*x^2*a^6+1536*x^(1/3)*a*b^5+2240*x*a^3*b^3-1024*b^6)/x^(1/3)/a^7","A"
170,1,57,81,0.045000," ","int((a*x+b*x^(2/3))^(1/2),x)","-\frac{2 \sqrt{a x +b \,x^{\frac{2}{3}}}\, \left(a \,x^{\frac{1}{3}}+b \right) \left(-35 a^{3} x +30 a^{2} b \,x^{\frac{2}{3}}-24 a \,b^{2} x^{\frac{1}{3}}+16 b^{3}\right)}{105 a^{4} x^{\frac{1}{3}}}"," ",0,"-2/105*(a*x+b*x^(2/3))^(1/2)*(a*x^(1/3)+b)*(30*a^2*b*x^(2/3)-24*a*b^2*x^(1/3)-35*a^3*x+16*b^3)/x^(1/3)/a^4","A"
171,1,27,19,0.039000," ","int((a*x+b*x^(2/3))^(1/2)/x,x)","\frac{2 \sqrt{a x +b \,x^{\frac{2}{3}}}\, \left(a \,x^{\frac{1}{3}}+b \right)}{a \,x^{\frac{1}{3}}}"," ",0,"2*(a*x+b*x^(2/3))^(1/2)/x^(1/3)*(a*x^(1/3)+b)/a","A"
172,1,80,64,0.049000," ","int((a*x+b*x^(2/3))^(1/2)/x^2,x)","\frac{3 \sqrt{a x +b \,x^{\frac{2}{3}}}\, \left(a^{2} b \,x^{\frac{2}{3}} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-\sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{5}{2}}-\left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{3}{2}}\right)}{4 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{5}{2}} x}"," ",0,"3/4*(a*x+b*x^(2/3))^(1/2)*(arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*b*x^(2/3)*a^2-(a*x^(1/3)+b)^(3/2)*b^(3/2)-(a*x^(1/3)+b)^(1/2)*b^(5/2))/x/(a*x^(1/3)+b)^(1/2)/b^(5/2)","A"
173,1,125,130,0.061000," ","int((a*x+b*x^(2/3))^(1/2)/x^3,x)","-\frac{\sqrt{a x +b \,x^{\frac{2}{3}}}\, \left(105 a^{5} b^{4} x^{\frac{5}{3}} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)+105 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{17}{2}}+790 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{15}{2}}-896 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{5}{2}} b^{\frac{13}{2}}+490 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{7}{2}} b^{\frac{11}{2}}-105 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{9}{2}} b^{\frac{9}{2}}\right)}{640 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{17}{2}} x^{2}}"," ",0,"-1/640*(a*x+b*x^(2/3))^(1/2)*(-105*(a*x^(1/3)+b)^(9/2)*b^(9/2)+490*(a*x^(1/3)+b)^(7/2)*b^(11/2)-896*(a*x^(1/3)+b)^(5/2)*b^(13/2)+105*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*b^4*x^(5/3)*a^5+790*(a*x^(1/3)+b)^(3/2)*b^(15/2)+105*(a*x^(1/3)+b)^(1/2)*b^(17/2))/x^2/(a*x^(1/3)+b)^(1/2)/b^(17/2)","A"
174,1,167,196,0.059000," ","int((a*x+b*x^(2/3))^(1/2)/x^4,x)","-\frac{\sqrt{a x +b \,x^{\frac{2}{3}}}\, \left(-45045 a^{8} b^{7} x^{\frac{8}{3}} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)+45045 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{29}{2}}+801535 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{27}{2}}-1831739 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{5}{2}} b^{\frac{25}{2}}+2518087 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{7}{2}} b^{\frac{23}{2}}-2167737 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{9}{2}} b^{\frac{21}{2}}+1150149 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{11}{2}} b^{\frac{19}{2}}-345345 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{13}{2}} b^{\frac{17}{2}}+45045 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{15}{2}} b^{\frac{15}{2}}\right)}{573440 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{29}{2}} x^{3}}"," ",0,"-1/573440*(a*x+b*x^(2/3))^(1/2)*(45045*b^(15/2)*(a*x^(1/3)+b)^(15/2)-345345*b^(17/2)*(a*x^(1/3)+b)^(13/2)+1150149*b^(19/2)*(a*x^(1/3)+b)^(11/2)-2167737*b^(21/2)*(a*x^(1/3)+b)^(9/2)+2518087*b^(23/2)*(a*x^(1/3)+b)^(7/2)-1831739*b^(25/2)*(a*x^(1/3)+b)^(5/2)+801535*b^(27/2)*(a*x^(1/3)+b)^(3/2)-45045*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*b^7*x^(8/3)*a^8+45045*b^(29/2)*(a*x^(1/3)+b)^(1/2))/x^3/(a*x^(1/3)+b)^(1/2)/b^(29/2)","A"
175,1,209,262,0.061000," ","int((a*x+b*x^(2/3))^(1/2)/x^5,x)","-\frac{\sqrt{a x +b \,x^{\frac{2}{3}}}\, \left(14549535 a^{11} b^{10} x^{\frac{11}{3}} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)+14549535 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{41}{2}}+450357600 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{39}{2}}-1551313995 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{5}{2}} b^{\frac{37}{2}}+3424523520 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{7}{2}} b^{\frac{35}{2}}-5174056250 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{9}{2}} b^{\frac{33}{2}}+5503713280 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{11}{2}} b^{\frac{31}{2}}-4139920070 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{13}{2}} b^{\frac{29}{2}}+2163862272 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{15}{2}} b^{\frac{27}{2}}-749786037 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{17}{2}} b^{\frac{25}{2}}+155195040 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{19}{2}} b^{\frac{23}{2}}-14549535 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{21}{2}} b^{\frac{21}{2}}\right)}{302776320 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{41}{2}} x^{4}}"," ",0,"-1/302776320*(a*x+b*x^(2/3))^(1/2)*(-14549535*(a*x^(1/3)+b)^(21/2)*b^(21/2)+155195040*(a*x^(1/3)+b)^(19/2)*b^(23/2)-749786037*(a*x^(1/3)+b)^(17/2)*b^(25/2)+2163862272*(a*x^(1/3)+b)^(15/2)*b^(27/2)-4139920070*(a*x^(1/3)+b)^(13/2)*b^(29/2)+5503713280*(a*x^(1/3)+b)^(11/2)*b^(31/2)-5174056250*(a*x^(1/3)+b)^(9/2)*b^(33/2)+3424523520*(a*x^(1/3)+b)^(7/2)*b^(35/2)-1551313995*(a*x^(1/3)+b)^(5/2)*b^(37/2)+14549535*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*b^10*x^(11/3)*a^11+450357600*(a*x^(1/3)+b)^(3/2)*b^(39/2)+14549535*(a*x^(1/3)+b)^(1/2)*b^(41/2))/x^4/(a*x^(1/3)+b)^(1/2)/b^(41/2)","A"
176,1,145,255,0.048000," ","int(x^2*(a*x+b*x^(2/3))^(3/2),x)","\frac{2 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} \left(a \,x^{\frac{1}{3}}+b \right) \left(16900975 a^{11} x^{\frac{11}{3}}-14872858 a^{10} b \,x^{\frac{10}{3}}+12932920 a^{9} b^{2} x^{3}-11085360 a^{8} b^{3} x^{\frac{8}{3}}+9335040 a^{7} b^{4} x^{\frac{7}{3}}-7687680 a^{6} b^{5} x^{2}+6150144 a^{5} b^{6} x^{\frac{5}{3}}-4730880 a^{4} b^{7} x^{\frac{4}{3}}+3440640 a^{3} b^{8} x -2293760 a^{2} b^{9} x^{\frac{2}{3}}+1310720 a \,b^{10} x^{\frac{1}{3}}-524288 b^{11}\right)}{152108775 a^{12} x}"," ",0,"2/152108775*(a*x+b*x^(2/3))^(3/2)*(a*x^(1/3)+b)*(16900975*x^(11/3)*a^11-14872858*x^(10/3)*a^10*b+12932920*x^3*a^9*b^2-11085360*x^(8/3)*a^8*b^3+9335040*x^(7/3)*a^7*b^4-7687680*x^2*a^6*b^5+6150144*x^(5/3)*a^5*b^6-4730880*x^(4/3)*a^4*b^7+3440640*x*a^3*b^8-2293760*x^(2/3)*a^2*b^9+1310720*x^(1/3)*a*b^10-524288*b^11)/x/a^12","A"
177,1,112,189,0.051000," ","int(x*(a*x+b*x^(2/3))^(3/2),x)","\frac{2 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} \left(a \,x^{\frac{1}{3}}+b \right) \left(692835 a^{8} x^{\frac{8}{3}}-583440 a^{7} b \,x^{\frac{7}{3}}+480480 a^{6} b^{2} x^{2}-384384 a^{5} b^{3} x^{\frac{5}{3}}+295680 a^{4} b^{4} x^{\frac{4}{3}}-215040 a^{3} b^{5} x +143360 a^{2} b^{6} x^{\frac{2}{3}}-81920 a \,b^{7} x^{\frac{1}{3}}+32768 b^{8}\right)}{4849845 a^{9} x}"," ",0,"2/4849845*(a*x+b*x^(2/3))^(3/2)*(a*x^(1/3)+b)*(692835*x^(8/3)*a^8-583440*x^(7/3)*a^7*b+480480*a^6*b^2*x^2-384384*x^(5/3)*a^5*b^3+295680*x^(4/3)*a^4*b^4-215040*a^3*b^5*x+143360*x^(2/3)*a^2*b^6-81920*x^(1/3)*a*b^7+32768*b^8)/x/a^9","A"
178,1,79,125,0.049000," ","int((a*x+b*x^(2/3))^(3/2),x)","\frac{2 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} \left(a \,x^{\frac{1}{3}}+b \right) \left(3003 a^{5} x^{\frac{5}{3}}-2310 a^{4} b \,x^{\frac{4}{3}}+1680 a^{3} b^{2} x -1120 a^{2} b^{3} x^{\frac{2}{3}}+640 a \,b^{4} x^{\frac{1}{3}}-256 b^{5}\right)}{15015 a^{6} x}"," ",0,"2/15015*(a*x+b*x^(2/3))^(3/2)*(a*x^(1/3)+b)*(3003*x^(5/3)*a^5-2310*a^4*b*x^(4/3)+1680*a^3*b^2*x-1120*x^(2/3)*a^2*b^3+640*a*b^4*x^(1/3)-256*b^5)/x/a^6","A"
179,1,48,62,0.051000," ","int((a*x+b*x^(2/3))^(3/2)/x,x)","\frac{2 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} \left(a \,x^{\frac{1}{3}}+b \right) \left(35 a^{2} x^{\frac{2}{3}}-20 a b \,x^{\frac{1}{3}}+8 b^{2}\right)}{105 a^{3} x}"," ",0,"2/105*(a*x+b*x^(2/3))^(3/2)*(a*x^(1/3)+b)*(35*a^2*x^(2/3)-20*a*b*x^(1/3)+8*b^2)/x/a^3","A"
180,1,69,58,0.051000," ","int((a*x+b*x^(2/3))^(3/2)/x^2,x)","-\frac{2 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} \left(3 b^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-3 \sqrt{a \,x^{\frac{1}{3}}+b}\, b -\left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}}\right)}{\left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} x}"," ",0,"-2*(a*x+b*x^(2/3))^(3/2)*(3*b^(3/2)*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))-(a*x^(1/3)+b)^(3/2)-3*(a*x^(1/3)+b)^(1/2)*b)/x/(a*x^(1/3)+b)^(3/2)","A"
181,1,93,83,0.061000," ","int((a*x+b*x^(2/3))^(3/2)/x^3,x)","-\frac{\left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} \left(-3 a^{3} b x \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-3 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{7}{2}}+8 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{5}{2}}+3 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{5}{2}} b^{\frac{3}{2}}\right)}{8 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{5}{2}} x^{2}}"," ",0,"-1/8*(a*x+b*x^(2/3))^(3/2)*(3*(a*x^(1/3)+b)^(5/2)*b^(3/2)+8*(a*x^(1/3)+b)^(3/2)*b^(5/2)-3*(a*x^(1/3)+b)^(1/2)*b^(7/2)-3*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*x*a^3*b)/x^2/(a*x^(1/3)+b)^(3/2)/b^(5/2)","A"
182,1,139,149,0.062000," ","int((a*x+b*x^(2/3))^(3/2)/x^4,x)","\frac{\left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} \left(-105 a^{6} b^{4} x^{2} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)+105 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{19}{2}}-595 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{17}{2}}-1686 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{5}{2}} b^{\frac{15}{2}}+1386 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{7}{2}} b^{\frac{13}{2}}-595 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{9}{2}} b^{\frac{11}{2}}+105 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{11}{2}} b^{\frac{9}{2}}\right)}{2560 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{17}{2}} x^{3}}"," ",0,"1/2560*(a*x+b*x^(2/3))^(3/2)*(105*b^(9/2)*(a*x^(1/3)+b)^(11/2)-595*b^(11/2)*(a*x^(1/3)+b)^(9/2)+1386*b^(13/2)*(a*x^(1/3)+b)^(7/2)-1686*b^(15/2)*(a*x^(1/3)+b)^(5/2)-595*b^(17/2)*(a*x^(1/3)+b)^(3/2)+105*b^(19/2)*(a*x^(1/3)+b)^(1/2)-105*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*b^4*x^2*a^6)/x^3/(a*x^(1/3)+b)^(3/2)/b^(17/2)","A"
183,1,181,215,0.059000," ","int((a*x+b*x^(2/3))^(3/2)/x^5,x)","-\frac{\left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} \left(-45045 a^{9} b^{7} x^{3} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-45045 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{31}{2}}+390390 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{29}{2}}+2633274 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{5}{2}} b^{\frac{27}{2}}-4349826 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{7}{2}} b^{\frac{25}{2}}+4685824 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{9}{2}} b^{\frac{23}{2}}-3317886 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{11}{2}} b^{\frac{21}{2}}+1495494 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{13}{2}} b^{\frac{19}{2}}-390390 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{15}{2}} b^{\frac{17}{2}}+45045 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{17}{2}} b^{\frac{15}{2}}\right)}{3440640 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{29}{2}} x^{4}}"," ",0,"-1/3440640*(a*x+b*x^(2/3))^(3/2)*(45045*(a*x^(1/3)+b)^(17/2)*b^(15/2)-390390*(a*x^(1/3)+b)^(15/2)*b^(17/2)+1495494*(a*x^(1/3)+b)^(13/2)*b^(19/2)-3317886*(a*x^(1/3)+b)^(11/2)*b^(21/2)+4685824*(a*x^(1/3)+b)^(9/2)*b^(23/2)-4349826*(a*x^(1/3)+b)^(7/2)*b^(25/2)+2633274*(a*x^(1/3)+b)^(5/2)*b^(27/2)+390390*(a*x^(1/3)+b)^(3/2)*b^(29/2)-45045*(a*x^(1/3)+b)^(1/2)*b^(31/2)-45045*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*b^7*x^3*a^9)/x^4/(a*x^(1/3)+b)^(3/2)/b^(29/2)","A"
184,1,223,281,0.069000," ","int((a*x+b*x^(2/3))^(3/2)/x^6,x)","\frac{\left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} \left(-14549535 a^{12} b^{10} x^{4} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)+14549535 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{43}{2}}-169744575 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{41}{2}}-2001671595 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{5}{2}} b^{\frac{39}{2}}+4975837515 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{7}{2}} b^{\frac{37}{2}}-8598579770 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{9}{2}} b^{\frac{35}{2}}+10677769530 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{11}{2}} b^{\frac{33}{2}}-9643633350 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{13}{2}} b^{\frac{31}{2}}+6303782342 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{15}{2}} b^{\frac{29}{2}}-2913648309 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{17}{2}} b^{\frac{27}{2}}+904981077 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{19}{2}} b^{\frac{25}{2}}-169744575 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{21}{2}} b^{\frac{23}{2}}+14549535 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{23}{2}} b^{\frac{21}{2}}\right)}{2422210560 \left(a \,x^{\frac{1}{3}}+b \right)^{\frac{3}{2}} b^{\frac{41}{2}} x^{5}}"," ",0,"1/2422210560*(a*x+b*x^(2/3))^(3/2)*(14549535*(a*x^(1/3)+b)^(23/2)*b^(21/2)-169744575*(a*x^(1/3)+b)^(21/2)*b^(23/2)+904981077*(a*x^(1/3)+b)^(19/2)*b^(25/2)-2913648309*(a*x^(1/3)+b)^(17/2)*b^(27/2)+6303782342*(a*x^(1/3)+b)^(15/2)*b^(29/2)-9643633350*(a*x^(1/3)+b)^(13/2)*b^(31/2)+10677769530*(a*x^(1/3)+b)^(11/2)*b^(33/2)-8598579770*(a*x^(1/3)+b)^(9/2)*b^(35/2)+4975837515*(a*x^(1/3)+b)^(7/2)*b^(37/2)-2001671595*(a*x^(1/3)+b)^(5/2)*b^(39/2)-169744575*(a*x^(1/3)+b)^(3/2)*b^(41/2)+14549535*(a*x^(1/3)+b)^(1/2)*b^(43/2)-14549535*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*b^10*x^4*a^12)/x^5/(a*x^(1/3)+b)^(3/2)/b^(41/2)","A"
185,1,167,299,0.051000," ","int(x^4/(a*x+b*x^(2/3))^(1/2),x)","\frac{2 \left(a \,x^{\frac{1}{3}}+b \right) \left(1300075 a^{13} x^{\frac{13}{3}}-1352078 a^{12} b \,x^{4}+1410864 a^{11} b^{2} x^{\frac{11}{3}}-1478048 a^{10} b^{3} x^{\frac{10}{3}}+1555840 a^{9} b^{4} x^{3}-1647360 a^{8} b^{5} x^{\frac{8}{3}}+1757184 a^{7} b^{6} x^{\frac{7}{3}}-1892352 a^{6} b^{7} x^{2}+2064384 a^{5} b^{8} x^{\frac{5}{3}}-2293760 a^{4} b^{9} x^{\frac{4}{3}}+2621440 a^{3} b^{10} x -3145728 a^{2} b^{11} x^{\frac{2}{3}}+4194304 a \,b^{12} x^{\frac{1}{3}}-8388608 b^{13}\right) x^{\frac{1}{3}}}{11700675 \sqrt{a x +b \,x^{\frac{2}{3}}}\, a^{14}}"," ",0,"2/11700675*x^(1/3)*(a*x^(1/3)+b)*(1300075*x^(13/3)*a^13-1352078*x^4*a^12*b+1410864*x^(11/3)*a^11*b^2-1478048*x^(10/3)*a^10*b^3+1555840*x^3*a^9*b^4-1647360*x^(8/3)*a^8*b^5+1757184*x^(7/3)*a^7*b^6-1892352*x^2*a^6*b^7+2064384*x^(5/3)*a^5*b^8-2293760*x^(4/3)*a^4*b^9+2621440*x*a^3*b^10-3145728*x^(2/3)*a^2*b^11+4194304*x^(1/3)*a*b^12-8388608*b^13)/(a*x+b*x^(2/3))^(1/2)/a^14","A"
186,1,134,233,0.044000," ","int(x^3/(a*x+b*x^(2/3))^(1/2),x)","\frac{2 \left(a \,x^{\frac{1}{3}}+b \right) \left(46189 a^{10} x^{\frac{10}{3}}-48620 a^{9} b \,x^{3}+51480 a^{8} b^{2} x^{\frac{8}{3}}-54912 a^{7} b^{3} x^{\frac{7}{3}}+59136 a^{6} b^{4} x^{2}-64512 a^{5} b^{5} x^{\frac{5}{3}}+71680 a^{4} b^{6} x^{\frac{4}{3}}-81920 a^{3} b^{7} x +98304 a^{2} b^{8} x^{\frac{2}{3}}-131072 a \,b^{9} x^{\frac{1}{3}}+262144 b^{10}\right) x^{\frac{1}{3}}}{323323 \sqrt{a x +b \,x^{\frac{2}{3}}}\, a^{11}}"," ",0,"2/323323*x^(1/3)*(a*x^(1/3)+b)*(46189*x^(10/3)*a^10-48620*x^3*a^9*b+51480*a^8*b^2*x^(8/3)-54912*x^(7/3)*a^7*b^3+59136*a^6*b^4*x^2-64512*a^5*b^5*x^(5/3)+71680*x^(4/3)*a^4*b^6-81920*x*a^3*b^7+98304*a^2*b^8*x^(2/3)-131072*x^(1/3)*a*b^9+262144*b^10)/(a*x+b*x^(2/3))^(1/2)/a^11","A"
187,1,101,167,0.046000," ","int(x^2/(a*x+b*x^(2/3))^(1/2),x)","\frac{2 \left(a \,x^{\frac{1}{3}}+b \right) \left(429 a^{7} x^{\frac{7}{3}}-462 a^{6} b \,x^{2}+504 a^{5} b^{2} x^{\frac{5}{3}}-560 a^{4} b^{3} x^{\frac{4}{3}}+640 a^{3} b^{4} x -768 a^{2} b^{5} x^{\frac{2}{3}}+1024 a \,b^{6} x^{\frac{1}{3}}-2048 b^{7}\right) x^{\frac{1}{3}}}{2145 \sqrt{a x +b \,x^{\frac{2}{3}}}\, a^{8}}"," ",0,"2/2145*x^(1/3)*(a*x^(1/3)+b)*(429*x^(7/3)*a^7-462*x^2*a^6*b+504*x^(5/3)*a^5*b^2-560*a^4*x^(4/3)*b^3+640*x*a^3*b^4-768*x^(2/3)*a^2*b^5+1024*x^(1/3)*a*b^6-2048*b^7)/(a*x+b*x^(2/3))^(1/2)/a^8","A"
188,1,68,101,0.049000," ","int(x/(a*x+b*x^(2/3))^(1/2),x)","\frac{2 \left(a \,x^{\frac{1}{3}}+b \right) \left(35 a^{4} x^{\frac{4}{3}}-40 a^{3} b x +48 a^{2} b^{2} x^{\frac{2}{3}}-64 a \,b^{3} x^{\frac{1}{3}}+128 b^{4}\right) x^{\frac{1}{3}}}{105 \sqrt{a x +b \,x^{\frac{2}{3}}}\, a^{5}}"," ",0,"2/105*x^(1/3)*(a*x^(1/3)+b)*(35*x^(4/3)*a^4-40*x*a^3*b+48*x^(2/3)*a^2*b^2-64*x^(1/3)*a*b^3+128*b^4)/(a*x+b*x^(2/3))^(1/2)/a^5","A"
189,1,36,37,0.044000," ","int(1/(a*x+b*x^(2/3))^(1/2),x)","\frac{2 \left(a \,x^{\frac{1}{3}}+b \right) \left(a \,x^{\frac{1}{3}}-2 b \right) x^{\frac{1}{3}}}{\sqrt{a x +b \,x^{\frac{2}{3}}}\, a^{2}}"," ",0,"2*x^(1/3)*(a*x^(1/3)+b)*(a*x^(1/3)-2*b)/(a*x+b*x^(2/3))^(1/2)/a^2","A"
190,1,61,45,0.050000," ","int(1/x/(a*x+b*x^(2/3))^(1/2),x)","\frac{3 \sqrt{a \,x^{\frac{1}{3}}+b}\, \left(a b \,x^{\frac{1}{3}} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-\sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{3}{2}}\right)}{\sqrt{a x +b \,x^{\frac{2}{3}}}\, b^{\frac{5}{2}}}"," ",0,"3*(a*x^(1/3)+b)^(1/2)*(arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*b*x^(1/3)*a-(a*x^(1/3)+b)^(1/2)*b^(3/2))/(a*x+b*x^(2/3))^(1/2)/b^(5/2)","A"
191,1,126,111,0.048000," ","int(1/x^2/(a*x+b*x^(2/3))^(1/2),x)","-\frac{\sqrt{a \,x^{\frac{1}{3}}+b}\, \left(105 a^{4} b \,x^{\frac{7}{3}} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-105 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{3} b^{\frac{3}{2}} x^{2}+70 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{2} b^{\frac{5}{2}} x^{\frac{5}{3}}-56 \sqrt{a \,x^{\frac{1}{3}}+b}\, a \,b^{\frac{7}{2}} x^{\frac{4}{3}}+48 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{9}{2}} x \right)}{64 \sqrt{a x +b \,x^{\frac{2}{3}}}\, b^{\frac{11}{2}} x^{2}}"," ",0,"-1/64*(a*x^(1/3)+b)^(1/2)*(105*x^(7/3)*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*a^4*b+70*x^(5/3)*(a*x^(1/3)+b)^(1/2)*b^(5/2)*a^2-56*x^(4/3)*(a*x^(1/3)+b)^(1/2)*b^(7/2)*a+48*(a*x^(1/3)+b)^(1/2)*b^(9/2)*x-105*x^2*(a*x^(1/3)+b)^(1/2)*b^(3/2)*a^3)/x^2/(a*x+b*x^(2/3))^(1/2)/b^(11/2)","A"
192,1,188,177,0.050000," ","int(1/x^3/(a*x+b*x^(2/3))^(1/2),x)","\frac{\sqrt{a \,x^{\frac{1}{3}}+b}\, \left(45045 a^{7} b \,x^{\frac{13}{3}} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-45045 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{6} b^{\frac{3}{2}} x^{4}+30030 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{5} b^{\frac{5}{2}} x^{\frac{11}{3}}-24024 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{4} b^{\frac{7}{2}} x^{\frac{10}{3}}+20592 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{3} b^{\frac{9}{2}} x^{3}-18304 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{2} b^{\frac{11}{2}} x^{\frac{8}{3}}+16640 \sqrt{a \,x^{\frac{1}{3}}+b}\, a \,b^{\frac{13}{2}} x^{\frac{7}{3}}-15360 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{15}{2}} x^{2}\right)}{35840 \sqrt{a x +b \,x^{\frac{2}{3}}}\, b^{\frac{17}{2}} x^{4}}"," ",0,"1/35840*(a*x^(1/3)+b)^(1/2)*(45045*x^(13/3)*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*a^7*b+30030*x^(11/3)*(a*x^(1/3)+b)^(1/2)*b^(5/2)*a^5-24024*x^(10/3)*(a*x^(1/3)+b)^(1/2)*b^(7/2)*a^4-18304*x^(8/3)*(a*x^(1/3)+b)^(1/2)*b^(11/2)*a^2+16640*x^(7/3)*(a*x^(1/3)+b)^(1/2)*b^(13/2)*a-15360*(a*x^(1/3)+b)^(1/2)*b^(15/2)*x^2+20592*x^3*(a*x^(1/3)+b)^(1/2)*b^(9/2)*a^3-45045*x^4*(a*x^(1/3)+b)^(1/2)*b^(3/2)*a^6)/x^4/(a*x+b*x^(2/3))^(1/2)/b^(17/2)","A"
193,1,248,243,0.053000," ","int(1/x^4/(a*x+b*x^(2/3))^(1/2),x)","-\frac{\sqrt{a \,x^{\frac{1}{3}}+b}\, \left(14549535 a^{10} b \,x^{\frac{19}{3}} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-14549535 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{9} b^{\frac{3}{2}} x^{6}+9699690 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{8} b^{\frac{5}{2}} x^{\frac{17}{3}}-7759752 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{7} b^{\frac{7}{2}} x^{\frac{16}{3}}+6651216 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{6} b^{\frac{9}{2}} x^{5}-5912192 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{5} b^{\frac{11}{2}} x^{\frac{14}{3}}+5374720 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{4} b^{\frac{13}{2}} x^{\frac{13}{3}}-4961280 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{3} b^{\frac{15}{2}} x^{4}+4630528 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{2} b^{\frac{17}{2}} x^{\frac{11}{3}}-4358144 \sqrt{a \,x^{\frac{1}{3}}+b}\, a \,b^{\frac{19}{2}} x^{\frac{10}{3}}+4128768 \sqrt{a \,x^{\frac{1}{3}}+b}\, b^{\frac{21}{2}} x^{3}\right)}{13762560 \sqrt{a x +b \,x^{\frac{2}{3}}}\, b^{\frac{23}{2}} x^{6}}"," ",0,"-1/13762560*(a*x^(1/3)+b)^(1/2)*(14549535*x^(19/3)*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*a^10*b+9699690*x^(17/3)*(a*x^(1/3)+b)^(1/2)*b^(5/2)*a^8-7759752*x^(16/3)*(a*x^(1/3)+b)^(1/2)*b^(7/2)*a^7-5912192*x^(14/3)*(a*x^(1/3)+b)^(1/2)*b^(11/2)*a^5+5374720*x^(13/3)*(a*x^(1/3)+b)^(1/2)*b^(13/2)*a^4+4630528*x^(11/3)*(a*x^(1/3)+b)^(1/2)*b^(17/2)*a^2-4358144*x^(10/3)*(a*x^(1/3)+b)^(1/2)*b^(19/2)*a+4128768*(a*x^(1/3)+b)^(1/2)*b^(21/2)*x^3-4961280*x^4*(a*x^(1/3)+b)^(1/2)*b^(15/2)*a^3+6651216*x^5*(a*x^(1/3)+b)^(1/2)*b^(9/2)*a^6-14549535*x^6*(a*x^(1/3)+b)^(1/2)*b^(3/2)*a^9)/x^6/(a*x+b*x^(2/3))^(1/2)/b^(23/2)","A"
194,1,143,252,0.050000," ","int(x^4/(a*x+b*x^(2/3))^(3/2),x)","\frac{2 \left(a \,x^{\frac{1}{3}}+b \right) \left(4199 a^{11} x^{\frac{11}{3}}-4862 a^{10} b \,x^{\frac{10}{3}}+5720 a^{9} b^{2} x^{3}-6864 a^{8} b^{3} x^{\frac{8}{3}}+8448 a^{7} b^{4} x^{\frac{7}{3}}-10752 a^{6} b^{5} x^{2}+14336 a^{5} b^{6} x^{\frac{5}{3}}-20480 a^{4} b^{7} x^{\frac{4}{3}}+32768 a^{3} b^{8} x -65536 a^{2} b^{9} x^{\frac{2}{3}}+262144 a \,b^{10} x^{\frac{1}{3}}+524288 b^{11}\right) x}{29393 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} a^{12}}"," ",0,"2/29393*x*(a*x^(1/3)+b)*(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*x^(1/3)+524288*b^11)/(a*x+b*x^(2/3))^(3/2)/a^12","A"
195,1,110,186,0.052000," ","int(x^3/(a*x+b*x^(2/3))^(3/2),x)","\frac{2 \left(a \,x^{\frac{1}{3}}+b \right) \left(429 a^{8} x^{\frac{8}{3}}-528 a^{7} b \,x^{\frac{7}{3}}+672 a^{6} b^{2} x^{2}-896 a^{5} b^{3} x^{\frac{5}{3}}+1280 a^{4} b^{4} x^{\frac{4}{3}}-2048 a^{3} b^{5} x +4096 a^{2} b^{6} x^{\frac{2}{3}}-16384 a \,b^{7} x^{\frac{1}{3}}-32768 b^{8}\right) x}{2145 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} a^{9}}"," ",0,"2/2145*x*(a*x^(1/3)+b)*(429*a^8*x^(8/3)-528*a^7*b*x^(7/3)+672*a^6*b^2*x^2-896*a^5*b^3*x^(5/3)+1280*x^(4/3)*a^4*b^4-2048*a^3*b^5*x+4096*x^(2/3)*a^2*b^6-16384*x^(1/3)*a*b^7-32768*b^8)/(a*x+b*x^(2/3))^(3/2)/a^9","A"
196,1,77,120,0.052000," ","int(x^2/(a*x+b*x^(2/3))^(3/2),x)","\frac{2 \left(a \,x^{\frac{1}{3}}+b \right) \left(7 a^{5} x^{\frac{5}{3}}-10 a^{4} b \,x^{\frac{4}{3}}+16 a^{3} b^{2} x -32 a^{2} b^{3} x^{\frac{2}{3}}+128 a \,b^{4} x^{\frac{1}{3}}+256 b^{5}\right) x}{21 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} a^{6}}"," ",0,"2/21*x*(a*x^(1/3)+b)*(7*a^5*x^(5/3)-10*a^4*b*x^(4/3)+16*a^3*b^2*x-32*a^2*b^3*x^(2/3)+128*a*b^4*x^(1/3)+256*b^5)/(a*x+b*x^(2/3))^(3/2)/a^6","A"
197,1,45,54,0.047000," ","int(x/(a*x+b*x^(2/3))^(3/2),x)","\frac{2 \left(a \,x^{\frac{1}{3}}+b \right) \left(a^{2} x^{\frac{2}{3}}-4 a b \,x^{\frac{1}{3}}-8 b^{2}\right) x}{\left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} a^{3}}"," ",0,"2*x*(a*x^(1/3)+b)*(a^2*x^(2/3)-4*a*b*x^(1/3)-8*b^2)/(a*x+b*x^(2/3))^(3/2)/a^3","A"
198,1,56,44,0.051000," ","int(1/(a*x+b*x^(2/3))^(3/2),x)","-\frac{6 \left(a \,x^{\frac{1}{3}}+b \right) \left(\sqrt{a \,x^{\frac{1}{3}}+b}\, b \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-b^{\frac{3}{2}}\right) x}{\left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} b^{\frac{5}{2}}}"," ",0,"-6*x*(a*x^(1/3)+b)*(arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*b*(a*x^(1/3)+b)^(1/2)-b^(3/2))/(a*x+b*x^(2/3))^(3/2)/b^(5/2)","A"
199,1,88,108,0.057000," ","int(1/x/(a*x+b*x^(2/3))^(3/2),x)","-\frac{\left(a \,x^{\frac{1}{3}}+b \right) \left(-105 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{3} x \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)+105 a^{3} \sqrt{b}\, x +35 a^{2} b^{\frac{3}{2}} x^{\frac{2}{3}}-14 a \,b^{\frac{5}{2}} x^{\frac{1}{3}}+8 b^{\frac{7}{2}}\right)}{8 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} b^{\frac{9}{2}}}"," ",0,"-1/8*(a*x^(1/3)+b)*(-14*b^(5/2)*x^(1/3)*a+35*b^(3/2)*x^(2/3)*a^2+105*x*a^3*b^(1/2)+8*b^(7/2)-105*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*(a*x^(1/3)+b)^(1/2)*x*a^3)/(a*x+b*x^(2/3))^(3/2)/b^(9/2)","A"
200,1,126,174,0.064000," ","int(1/x^2/(a*x+b*x^(2/3))^(3/2),x)","-\frac{\left(a \,x^{\frac{1}{3}}+b \right) \left(45045 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{6} x^{2} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-45045 a^{6} \sqrt{b}\, x^{2}-15015 a^{5} b^{\frac{3}{2}} x^{\frac{5}{3}}+6006 a^{4} b^{\frac{5}{2}} x^{\frac{4}{3}}-3432 a^{3} b^{\frac{7}{2}} x +2288 a^{2} b^{\frac{9}{2}} x^{\frac{2}{3}}-1664 a \,b^{\frac{11}{2}} x^{\frac{1}{3}}+1280 b^{\frac{13}{2}}\right)}{2560 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} b^{\frac{15}{2}} x}"," ",0,"-1/2560*(a*x^(1/3)+b)*(1280*b^(13/2)+45045*(a*x^(1/3)+b)^(1/2)*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*x^2*a^6+6006*x^(4/3)*b^(5/2)*a^4-3432*x*b^(7/2)*a^3+2288*x^(2/3)*b^(9/2)*a^2-1664*x^(1/3)*b^(11/2)*a-45045*x^2*a^6*b^(1/2)-15015*x^(5/3)*b^(3/2)*a^5)/x/(a*x+b*x^(2/3))^(3/2)/b^(15/2)","A"
201,1,159,240,0.069000," ","int(1/x^3/(a*x+b*x^(2/3))^(3/2),x)","\frac{\left(a \,x^{\frac{1}{3}}+b \right) \left(14549535 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{9} x^{3} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-14549535 a^{9} \sqrt{b}\, x^{3}-4849845 a^{8} b^{\frac{3}{2}} x^{\frac{8}{3}}+1939938 a^{7} b^{\frac{5}{2}} x^{\frac{7}{3}}-1108536 a^{6} b^{\frac{7}{2}} x^{2}+739024 a^{5} b^{\frac{9}{2}} x^{\frac{5}{3}}-537472 a^{4} b^{\frac{11}{2}} x^{\frac{4}{3}}+413440 a^{3} b^{\frac{13}{2}} x -330752 a^{2} b^{\frac{15}{2}} x^{\frac{2}{3}}+272384 a \,b^{\frac{17}{2}} x^{\frac{1}{3}}-229376 b^{\frac{19}{2}}\right)}{688128 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} b^{\frac{21}{2}} x^{2}}"," ",0,"1/688128*(a*x^(1/3)+b)*(14549535*(a*x^(1/3)+b)^(1/2)*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*x^3*a^9-229376*b^(19/2)-537472*b^(11/2)*x^(4/3)*a^4-4849845*b^(3/2)*x^(8/3)*a^8+272384*b^(17/2)*x^(1/3)*a+413440*b^(13/2)*x*a^3-330752*b^(15/2)*x^(2/3)*a^2+739024*b^(9/2)*x^(5/3)*a^5-14549535*x^3*a^9*b^(1/2)+1939938*b^(5/2)*x^(7/3)*a^7-1108536*b^(7/2)*x^2*a^6)/x^2/(a*x+b*x^(2/3))^(3/2)/b^(21/2)","A"
202,1,192,306,0.079000," ","int(1/x^4/(a*x+b*x^(2/3))^(3/2),x)","-\frac{\left(a \,x^{\frac{1}{3}}+b \right) \left(1673196525 \sqrt{a \,x^{\frac{1}{3}}+b}\, a^{12} x^{4} \arctanh \left(\frac{\sqrt{a \,x^{\frac{1}{3}}+b}}{\sqrt{b}}\right)-1673196525 a^{12} \sqrt{b}\, x^{4}-557732175 a^{11} b^{\frac{3}{2}} x^{\frac{11}{3}}+223092870 a^{10} b^{\frac{5}{2}} x^{\frac{10}{3}}-127481640 a^{9} b^{\frac{7}{2}} x^{3}+84987760 a^{8} b^{\frac{9}{2}} x^{\frac{8}{3}}-61809280 a^{7} b^{\frac{11}{2}} x^{\frac{7}{3}}+47545600 a^{6} b^{\frac{13}{2}} x^{2}-38036480 a^{5} b^{\frac{15}{2}} x^{\frac{5}{3}}+31324160 a^{4} b^{\frac{17}{2}} x^{\frac{4}{3}}-26378240 a^{3} b^{\frac{19}{2}} x +22609920 a^{2} b^{\frac{21}{2}} x^{\frac{2}{3}}-19660800 a \,b^{\frac{23}{2}} x^{\frac{1}{3}}+17301504 b^{\frac{25}{2}}\right)}{69206016 \left(a x +b \,x^{\frac{2}{3}}\right)^{\frac{3}{2}} b^{\frac{27}{2}} x^{3}}"," ",0,"-1/69206016*(a*x^(1/3)+b)*(17301504*b^(25/2)-1673196525*x^4*a^12*b^(1/2)-19660800*b^(23/2)*x^(1/3)*a+22609920*b^(21/2)*x^(2/3)*a^2+1673196525*(a*x^(1/3)+b)^(1/2)*arctanh((a*x^(1/3)+b)^(1/2)/b^(1/2))*x^4*a^12-26378240*b^(19/2)*x*a^3+31324160*b^(17/2)*x^(4/3)*a^4-38036480*b^(15/2)*x^(5/3)*a^5+47545600*b^(13/2)*x^2*a^6-61809280*b^(11/2)*x^(7/3)*a^7+84987760*b^(9/2)*x^(8/3)*a^8-127481640*b^(7/2)*x^3*a^9+223092870*b^(5/2)*x^(10/3)*a^10-557732175*b^(3/2)*x^(11/3)*a^11)/x^3/(a*x+b*x^(2/3))^(3/2)/b^(27/2)","A"
203,1,14,13,0.037000," ","int(x^2*(b*x^3+a*x^2),x)","\frac{1}{6} b \,x^{6}+\frac{1}{5} a \,x^{5}"," ",0,"1/5*a*x^5+1/6*b*x^6","A"
204,1,14,13,0.040000," ","int(x*(b*x^3+a*x^2),x)","\frac{1}{5} b \,x^{5}+\frac{1}{4} a \,x^{4}"," ",0,"1/4*a*x^4+1/5*b*x^5","A"
205,1,14,13,0.045000," ","int(b*x^3+a*x^2,x)","\frac{1}{4} b \,x^{4}+\frac{1}{3} a \,x^{3}"," ",0,"1/3*a*x^3+1/4*b*x^4","A"
206,1,14,13,0.055000," ","int((b*x^3+a*x^2)/x,x)","\frac{1}{3} b \,x^{3}+\frac{1}{2} a \,x^{2}"," ",0,"1/2*a*x^2+1/3*b*x^3","A"
207,1,11,10,0.046000," ","int((b*x^3+a*x^2)/x^2,x)","\frac{1}{2} b \,x^{2}+a x"," ",0,"a*x+1/2*b*x^2","A"
208,1,25,24,0.045000," ","int(x^2*(b*x^3+a*x^2)^2,x)","\frac{1}{9} b^{2} x^{9}+\frac{1}{4} a b \,x^{8}+\frac{1}{7} a^{2} x^{7}"," ",0,"1/7*a^2*x^7+1/4*a*b*x^8+1/9*b^2*x^9","A"
209,1,25,24,0.056000," ","int(x*(b*x^3+a*x^2)^2,x)","\frac{1}{8} b^{2} x^{8}+\frac{2}{7} a b \,x^{7}+\frac{1}{6} a^{2} x^{6}"," ",0,"1/6*a^2*x^6+2/7*a*b*x^7+1/8*b^2*x^8","A"
210,1,25,24,0.043000," ","int((b*x^3+a*x^2)^2,x)","\frac{1}{7} b^{2} x^{7}+\frac{1}{3} a b \,x^{6}+\frac{1}{5} a^{2} x^{5}"," ",0,"1/5*a^2*x^5+1/3*a*b*x^6+1/7*b^2*x^7","A"
211,1,25,24,0.038000," ","int((b*x^3+a*x^2)^2/x,x)","\frac{1}{6} b^{2} x^{6}+\frac{2}{5} a b \,x^{5}+\frac{1}{4} a^{2} x^{4}"," ",0,"1/4*a^2*x^4+2/5*a*b*x^5+1/6*b^2*x^6","A"
212,1,25,24,0.046000," ","int((b*x^3+a*x^2)^2/x^2,x)","\frac{1}{5} b^{2} x^{5}+\frac{1}{2} a b \,x^{4}+\frac{1}{3} a^{2} x^{3}"," ",0,"1/3*a^2*x^3+1/2*a*b*x^4+1/5*b^2*x^5","A"
213,1,52,51,0.043000," ","int(x^6/(b*x^3+a*x^2),x)","\frac{x^{4}}{4 b}-\frac{a \,x^{3}}{3 b^{2}}+\frac{a^{2} x^{2}}{2 b^{3}}+\frac{a^{4} \ln \left(b x +a \right)}{b^{5}}-\frac{a^{3} x}{b^{4}}"," ",0,"-a^3/b^4*x+1/2*a^2/b^3*x^2-1/3*a/b^2*x^3+1/4*x^4/b+a^4*ln(b*x+a)/b^5","A"
214,1,41,40,0.043000," ","int(x^5/(b*x^3+a*x^2),x)","\frac{x^{3}}{3 b}-\frac{a \,x^{2}}{2 b^{2}}-\frac{a^{3} \ln \left(b x +a \right)}{b^{4}}+\frac{a^{2} x}{b^{3}}"," ",0,"a^2/b^3*x-1/2*a/b^2*x^2+1/3/b*x^3-a^3*ln(b*x+a)/b^4","A"
215,1,30,29,0.045000," ","int(x^4/(b*x^3+a*x^2),x)","\frac{x^{2}}{2 b}+\frac{a^{2} \ln \left(b x +a \right)}{b^{3}}-\frac{a x}{b^{2}}"," ",0,"-a/b^2*x+1/2/b*x^2+a^2*ln(b*x+a)/b^3","A"
216,1,19,18,0.049000," ","int(x^3/(b*x^3+a*x^2),x)","-\frac{a \ln \left(b x +a \right)}{b^{2}}+\frac{x}{b}"," ",0,"1/b*x-a*ln(b*x+a)/b^2","A"
217,1,11,10,0.042000," ","int(x^2/(b*x^3+a*x^2),x)","\frac{\ln \left(b x +a \right)}{b}"," ",0,"1/b*ln(b*x+a)","A"
218,1,19,18,0.047000," ","int(x/(b*x^3+a*x^2),x)","\frac{\ln \left(x \right)}{a}-\frac{\ln \left(b x +a \right)}{a}"," ",0,"1/a*ln(x)-ln(b*x+a)/a","A"
219,1,29,28,0.050000," ","int(1/(b*x^3+a*x^2),x)","-\frac{b \ln \left(x \right)}{a^{2}}+\frac{b \ln \left(b x +a \right)}{a^{2}}-\frac{1}{a x}"," ",0,"-1/a/x-1/a^2*b*ln(x)+b*ln(b*x+a)/a^2","A"
220,1,41,40,0.053000," ","int(1/x/(b*x^3+a*x^2),x)","\frac{b^{2} \ln \left(x \right)}{a^{3}}-\frac{b^{2} \ln \left(b x +a \right)}{a^{3}}+\frac{b}{a^{2} x}-\frac{1}{2 a \,x^{2}}"," ",0,"-1/2/a/x^2+1/a^2*b/x+1/a^3*b^2*ln(x)-b^2*ln(b*x+a)/a^3","A"
221,1,53,52,0.053000," ","int(1/x^2/(b*x^3+a*x^2),x)","-\frac{b^{3} \ln \left(x \right)}{a^{4}}+\frac{b^{3} \ln \left(b x +a \right)}{a^{4}}-\frac{b^{2}}{a^{3} x}+\frac{b}{2 a^{2} x^{2}}-\frac{1}{3 a \,x^{3}}"," ",0,"-1/3/a/x^3+1/2/a^2*b/x^2-1/a^3*b^2/x-1/a^4*b^3*ln(x)+b^3*ln(b*x+a)/a^4","A"
222,1,57,56,0.052000," ","int(x^8/(b*x^3+a*x^2)^2,x)","\frac{x^{3}}{3 b^{2}}-\frac{a \,x^{2}}{b^{3}}-\frac{a^{4}}{\left(b x +a \right) b^{5}}-\frac{4 a^{3} \ln \left(b x +a \right)}{b^{5}}+\frac{3 a^{2} x}{b^{4}}"," ",0,"3*a^2/b^4*x-a/b^3*x^2+1/3/b^2*x^3-a^4/b^5/(b*x+a)-4*a^3*ln(b*x+a)/b^5","A"
223,1,45,44,0.048000," ","int(x^7/(b*x^3+a*x^2)^2,x)","\frac{x^{2}}{2 b^{2}}+\frac{a^{3}}{\left(b x +a \right) b^{4}}+\frac{3 a^{2} \ln \left(b x +a \right)}{b^{4}}-\frac{2 a x}{b^{3}}"," ",0,"-2*a/b^3*x+1/2/b^2*x^2+a^3/b^4/(b*x+a)+3*a^2*ln(b*x+a)/b^4","A"
224,1,34,33,0.050000," ","int(x^6/(b*x^3+a*x^2)^2,x)","-\frac{a^{2}}{\left(b x +a \right) b^{3}}-\frac{2 a \ln \left(b x +a \right)}{b^{3}}+\frac{x}{b^{2}}"," ",0,"1/b^2*x-a^2/b^3/(b*x+a)-2*a*ln(b*x+a)/b^3","A"
225,1,24,23,0.049000," ","int(x^5/(b*x^3+a*x^2)^2,x)","\frac{a}{\left(b x +a \right) b^{2}}+\frac{\ln \left(b x +a \right)}{b^{2}}"," ",0,"a/b^2/(b*x+a)+ln(b*x+a)/b^2","A"
226,1,13,12,0.049000," ","int(x^4/(b*x^3+a*x^2)^2,x)","-\frac{1}{\left(b x +a \right) b}"," ",0,"-1/b/(b*x+a)","A"
227,1,30,29,0.065000," ","int(x^3/(b*x^3+a*x^2)^2,x)","\frac{1}{\left(b x +a \right) a}+\frac{\ln \left(x \right)}{a^{2}}-\frac{\ln \left(b x +a \right)}{a^{2}}"," ",0,"1/a/(b*x+a)+1/a^2*ln(x)-ln(b*x+a)/a^2","A"
228,1,43,42,0.051000," ","int(x^2/(b*x^3+a*x^2)^2,x)","-\frac{b}{\left(b x +a \right) a^{2}}-\frac{2 b \ln \left(x \right)}{a^{3}}+\frac{2 b \ln \left(b x +a \right)}{a^{3}}-\frac{1}{a^{2} x}"," ",0,"-1/a^2/x-b/a^2/(b*x+a)-2/a^3*b*ln(x)+2*b*ln(b*x+a)/a^3","A"
229,1,57,56,0.059000," ","int(x/(b*x^3+a*x^2)^2,x)","\frac{b^{2}}{\left(b x +a \right) a^{3}}+\frac{3 b^{2} \ln \left(x \right)}{a^{4}}-\frac{3 b^{2} \ln \left(b x +a \right)}{a^{4}}+\frac{2 b}{a^{3} x}-\frac{1}{2 a^{2} x^{2}}"," ",0,"-1/2/a^2/x^2+2/a^3*b/x+b^2/a^3/(b*x+a)+3/a^4*b^2*ln(x)-3*b^2*ln(b*x+a)/a^4","A"
230,1,68,67,0.051000," ","int(1/(b*x^3+a*x^2)^2,x)","-\frac{b^{3}}{\left(b x +a \right) a^{4}}-\frac{4 b^{3} \ln \left(x \right)}{a^{5}}+\frac{4 b^{3} \ln \left(b x +a \right)}{a^{5}}-\frac{3 b^{2}}{a^{4} x}+\frac{b}{a^{3} x^{2}}-\frac{1}{3 a^{2} x^{3}}"," ",0,"-1/3/a^2/x^3+b/a^3/x^2-3/a^4*b^2/x-b^3/a^4/(b*x+a)-4/a^5*b^3*ln(x)+4*b^3*ln(b*x+a)/a^5","A"
231,1,79,78,0.054000," ","int(1/x/(b*x^3+a*x^2)^2,x)","\frac{b^{4}}{\left(b x +a \right) a^{5}}+\frac{5 b^{4} \ln \left(x \right)}{a^{6}}-\frac{5 b^{4} \ln \left(b x +a \right)}{a^{6}}+\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}}"," ",0,"-1/4/a^2/x^4+2/3*b/a^3/x^3-3/2/a^4*b^2/x^2+4/a^5*b^3/x+b^4/a^5/(b*x+a)+5/a^6*b^4*ln(x)-5*b^4*ln(b*x+a)/a^6","A"
232,1,57,89,0.043000," ","int(x^2*(b*x^3+a*x^2)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(-35 b^{3} x^{3}+30 a \,b^{2} x^{2}-24 a^{2} b x +16 a^{3}\right) \sqrt{b \,x^{3}+a \,x^{2}}}{315 b^{4} x}"," ",0,"-2/315*(b*x+a)*(-35*b^3*x^3+30*a*b^2*x^2-24*a^2*b*x+16*a^3)*(b*x^3+a*x^2)^(1/2)/b^4/x","A"
233,1,46,68,0.046000," ","int(x*(b*x^3+a*x^2)^(1/2),x)","\frac{2 \left(b x +a \right) \left(15 b^{2} x^{2}-12 a b x +8 a^{2}\right) \sqrt{b \,x^{3}+a \,x^{2}}}{105 b^{3} x}"," ",0,"2/105*(b*x+a)*(15*b^2*x^2-12*a*b*x+8*a^2)*(b*x^3+a*x^2)^(1/2)/b^3/x","A"
234,1,35,44,0.049000," ","int((b*x^3+a*x^2)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(-3 b x +2 a \right) \sqrt{b \,x^{3}+a \,x^{2}}}{15 b^{2} x}"," ",0,"-2/15*(b*x+a)*(-3*b*x+2*a)*(b*x^3+a*x^2)^(1/2)/b^2/x","A"
235,1,27,21,0.041000," ","int((b*x^3+a*x^2)^(1/2)/x,x)","\frac{2 \left(b x +a \right) \sqrt{b \,x^{3}+a \,x^{2}}}{3 b x}"," ",0,"2/3*(b*x+a)*(b*x^3+a*x^2)^(1/2)/b/x","A"
236,1,51,43,0.043000," ","int((b*x^3+a*x^2)^(1/2)/x^2,x)","\frac{2 \sqrt{b \,x^{3}+a \,x^{2}}\, \left(-\sqrt{a}\, \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+\sqrt{b x +a}\right)}{\sqrt{b x +a}\, x}"," ",0,"2*(b*x^3+a*x^2)^(1/2)*(-a^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2))+(b*x+a)^(1/2))/x/(b*x+a)^(1/2)","A"
237,1,56,44,0.053000," ","int((b*x^3+a*x^2)^(1/2)/x^3,x)","-\frac{\sqrt{b \,x^{3}+a \,x^{2}}\, \left(b x \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+\sqrt{b x +a}\, \sqrt{a}\right)}{\sqrt{b x +a}\, \sqrt{a}\, x^{2}}"," ",0,"-(b*x^3+a*x^2)^(1/2)*(arctanh((b*x+a)^(1/2)/a^(1/2))*x*b+(b*x+a)^(1/2)*a^(1/2))/x^2/(b*x+a)^(1/2)/a^(1/2)","A"
238,1,73,68,0.055000," ","int((b*x^3+a*x^2)^(1/2)/x^4,x)","-\frac{\sqrt{b \,x^{3}+a \,x^{2}}\, \left(-a \,b^{2} x^{2} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+\sqrt{b x +a}\, a^{\frac{5}{2}}+\left(b x +a \right)^{\frac{3}{2}} a^{\frac{3}{2}}\right)}{4 \sqrt{b x +a}\, a^{\frac{5}{2}} x^{3}}"," ",0,"-1/4*(b*x^3+a*x^2)^(1/2)*((b*x+a)^(3/2)*a^(3/2)-arctanh((b*x+a)^(1/2)/a^(1/2))*a*x^2*b^2+(b*x+a)^(1/2)*a^(5/2))/x^3/(b*x+a)^(1/2)/a^(5/2)","A"
239,1,89,92,0.056000," ","int((b*x^3+a*x^2)^(1/2)/x^5,x)","\frac{\sqrt{b \,x^{3}+a \,x^{2}}\, \left(-3 a^{2} b^{3} x^{3} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)-3 \sqrt{b x +a}\, a^{\frac{9}{2}}-8 \left(b x +a \right)^{\frac{3}{2}} a^{\frac{7}{2}}+3 \left(b x +a \right)^{\frac{5}{2}} a^{\frac{5}{2}}\right)}{24 \sqrt{b x +a}\, a^{\frac{9}{2}} x^{4}}"," ",0,"1/24*(b*x^3+a*x^2)^(1/2)*(3*(b*x+a)^(5/2)*a^(5/2)-8*(b*x+a)^(3/2)*a^(7/2)-3*arctanh((b*x+a)^(1/2)/a^(1/2))*a^2*b^3*x^3-3*(b*x+a)^(1/2)*a^(9/2))/x^4/(b*x+a)^(1/2)/a^(9/2)","A"
240,1,79,137,0.048000," ","int(x^2*(b*x^3+a*x^2)^(3/2),x)","-\frac{2 \left(b x +a \right) \left(-3003 x^{5} b^{5}+2310 a \,b^{4} x^{4}-1680 a^{2} b^{3} x^{3}+1120 a^{3} b^{2} x^{2}-640 a^{4} b x +256 a^{5}\right) \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}}}{45045 b^{6} x^{3}}"," ",0,"-2/45045*(b*x+a)*(-3003*b^5*x^5+2310*a*b^4*x^4-1680*a^2*b^3*x^3+1120*a^3*b^2*x^2-640*a^4*b*x+256*a^5)*(b*x^3+a*x^2)^(3/2)/b^6/x^3","A"
241,1,68,116,0.051000," ","int(x*(b*x^3+a*x^2)^(3/2),x)","\frac{2 \left(b x +a \right) \left(1155 x^{4} b^{4}-840 a \,b^{3} x^{3}+560 a^{2} x^{2} b^{2}-320 a^{3} x b +128 a^{4}\right) \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}}}{15015 b^{5} x^{3}}"," ",0,"2/15015*(b*x+a)*(1155*b^4*x^4-840*a*b^3*x^3+560*a^2*b^2*x^2-320*a^3*b*x+128*a^4)*(b*x^3+a*x^2)^(3/2)/b^5/x^3","A"
242,1,57,92,0.043000," ","int((b*x^3+a*x^2)^(3/2),x)","-\frac{2 \left(b x +a \right) \left(-105 b^{3} x^{3}+70 a \,b^{2} x^{2}-40 a^{2} b x +16 a^{3}\right) \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}}}{1155 b^{4} x^{3}}"," ",0,"-2/1155*(b*x+a)*(-105*b^3*x^3+70*a*b^2*x^2-40*a^2*b*x+16*a^3)*(b*x^3+a*x^2)^(3/2)/b^4/x^3","A"
243,1,46,68,0.045000," ","int((b*x^3+a*x^2)^(3/2)/x,x)","\frac{2 \left(b x +a \right) \left(35 b^{2} x^{2}-20 a b x +8 a^{2}\right) \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}}}{315 b^{3} x^{3}}"," ",0,"2/315*(b*x+a)*(35*b^2*x^2-20*a*b*x+8*a^2)*(b*x^3+a*x^2)^(3/2)/b^3/x^3","A"
244,1,35,44,0.039000," ","int((b*x^3+a*x^2)^(3/2)/x^2,x)","-\frac{2 \left(b x +a \right) \left(-5 b x +2 a \right) \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}}}{35 b^{2} x^{3}}"," ",0,"-2/35*(b*x+a)*(-5*b*x+2*a)*(b*x^3+a*x^2)^(3/2)/b^2/x^3","A"
245,1,27,21,0.041000," ","int((b*x^3+a*x^2)^(3/2)/x^3,x)","\frac{2 \left(b x +a \right) \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}}}{5 b \,x^{3}}"," ",0,"2/5*(b*x+a)*(b*x^3+a*x^2)^(3/2)/b/x^3","A"
246,1,61,62,0.048000," ","int((b*x^3+a*x^2)^(3/2)/x^4,x)","\frac{2 \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(-3 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+3 \sqrt{b x +a}\, a +\left(b x +a \right)^{\frac{3}{2}}\right)}{3 \left(b x +a \right)^{\frac{3}{2}} x^{3}}"," ",0,"2/3*(b*x^3+a*x^2)^(3/2)*(-3*a^(3/2)*arctanh((b*x+a)^(1/2)/a^(1/2))+(b*x+a)^(3/2)+3*(b*x+a)^(1/2)*a)/x^3/(b*x+a)^(3/2)","A"
247,1,72,63,0.055000," ","int((b*x^3+a*x^2)^(3/2)/x^5,x)","-\frac{\left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(3 a b x \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)-2 \sqrt{b x +a}\, \sqrt{a}\, b x +\sqrt{b x +a}\, a^{\frac{3}{2}}\right)}{\left(b x +a \right)^{\frac{3}{2}} \sqrt{a}\, x^{4}}"," ",0,"-(b*x^3+a*x^2)^(3/2)*((b*x+a)^(1/2)*a^(3/2)-2*(b*x+a)^(1/2)*x*b*a^(1/2)+3*arctanh((b*x+a)^(1/2)/a^(1/2))*x*a*b)/x^4/(b*x+a)^(3/2)/a^(1/2)","A"
248,1,74,65,0.059000," ","int((b*x^3+a*x^2)^(3/2)/x^6,x)","-\frac{\left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(3 b^{2} x^{2} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)-3 \sqrt{b x +a}\, a^{\frac{3}{2}}+5 \left(b x +a \right)^{\frac{3}{2}} \sqrt{a}\right)}{4 \left(b x +a \right)^{\frac{3}{2}} \sqrt{a}\, x^{5}}"," ",0,"-1/4*(b*x^3+a*x^2)^(3/2)*(3*arctanh((b*x+a)^(1/2)/a^(1/2))*x^2*b^2+5*(b*x+a)^(3/2)*a^(1/2)-3*(b*x+a)^(1/2)*a^(3/2))/x^5/(b*x+a)^(3/2)/a^(1/2)","A"
249,1,87,89,0.056000," ","int((b*x^3+a*x^2)^(3/2)/x^7,x)","-\frac{\left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(-3 a \,b^{3} x^{3} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)-3 \sqrt{b x +a}\, a^{\frac{7}{2}}+8 \left(b x +a \right)^{\frac{3}{2}} a^{\frac{5}{2}}+3 \left(b x +a \right)^{\frac{5}{2}} a^{\frac{3}{2}}\right)}{24 \left(b x +a \right)^{\frac{3}{2}} a^{\frac{5}{2}} x^{6}}"," ",0,"-1/24*(b*x^3+a*x^2)^(3/2)*(3*(b*x+a)^(5/2)*a^(3/2)-3*arctanh((b*x+a)^(1/2)/a^(1/2))*x^3*a*b^3+8*(b*x+a)^(3/2)*a^(5/2)-3*(b*x+a)^(1/2)*a^(7/2))/x^6/(b*x+a)^(3/2)/a^(5/2)","A"
250,1,101,113,0.053000," ","int((b*x^3+a*x^2)^(3/2)/x^8,x)","\frac{\left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(-3 a^{2} b^{4} x^{4} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+3 \sqrt{b x +a}\, a^{\frac{11}{2}}-11 \left(b x +a \right)^{\frac{3}{2}} a^{\frac{9}{2}}-11 \left(b x +a \right)^{\frac{5}{2}} a^{\frac{7}{2}}+3 \left(b x +a \right)^{\frac{7}{2}} a^{\frac{5}{2}}\right)}{64 \left(b x +a \right)^{\frac{3}{2}} a^{\frac{9}{2}} x^{7}}"," ",0,"1/64*(b*x^3+a*x^2)^(3/2)*(3*(b*x+a)^(7/2)*a^(5/2)-11*(b*x+a)^(5/2)*a^(7/2)-3*arctanh((b*x+a)^(1/2)/a^(1/2))*a^2*x^4*b^4-11*(b*x+a)^(3/2)*a^(9/2)+3*(b*x+a)^(1/2)*a^(11/2))/x^7/(b*x+a)^(3/2)/a^(9/2)","A"
251,1,113,137,0.054000," ","int((b*x^3+a*x^2)^(3/2)/x^9,x)","-\frac{\left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(-15 a^{3} b^{5} x^{5} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)-15 \sqrt{b x +a}\, a^{\frac{15}{2}}+70 \left(b x +a \right)^{\frac{3}{2}} a^{\frac{13}{2}}+128 \left(b x +a \right)^{\frac{5}{2}} a^{\frac{11}{2}}-70 \left(b x +a \right)^{\frac{7}{2}} a^{\frac{9}{2}}+15 \left(b x +a \right)^{\frac{9}{2}} a^{\frac{7}{2}}\right)}{640 \left(b x +a \right)^{\frac{3}{2}} a^{\frac{13}{2}} x^{8}}"," ",0,"-1/640*(b*x^3+a*x^2)^(3/2)*(15*(b*x+a)^(9/2)*a^(7/2)-70*(b*x+a)^(7/2)*a^(9/2)+128*(b*x+a)^(5/2)*a^(11/2)-15*arctanh((b*x+a)^(1/2)/a^(1/2))*a^3*x^5*b^5+70*(b*x+a)^(3/2)*a^(13/2)-15*(b*x+a)^(1/2)*a^(15/2))/x^8/(b*x+a)^(3/2)/a^(13/2)","A"
252,1,55,87,0.048000," ","int(x^4/(b*x^3+a*x^2)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(-5 b^{3} x^{3}+6 a \,b^{2} x^{2}-8 a^{2} b x +16 a^{3}\right) x}{35 \sqrt{b \,x^{3}+a \,x^{2}}\, b^{4}}"," ",0,"-2/35*(b*x+a)*(-5*b^3*x^3+6*a*b^2*x^2-8*a^2*b*x+16*a^3)*x/b^4/(b*x^3+a*x^2)^(1/2)","A"
253,1,44,63,0.046000," ","int(x^3/(b*x^3+a*x^2)^(1/2),x)","\frac{2 \left(b x +a \right) \left(3 b^{2} x^{2}-4 a b x +8 a^{2}\right) x}{15 \sqrt{b \,x^{3}+a \,x^{2}}\, b^{3}}"," ",0,"2/15*(b*x+a)*(3*b^2*x^2-4*a*b*x+8*a^2)*x/b^3/(b*x^3+a*x^2)^(1/2)","A"
254,1,33,41,0.043000," ","int(x^2/(b*x^3+a*x^2)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(-b x +2 a \right) x}{3 \sqrt{b \,x^{3}+a \,x^{2}}\, b^{2}}"," ",0,"-2/3*(b*x+a)*(-b*x+2*a)*x/b^2/(b*x^3+a*x^2)^(1/2)","A"
255,1,25,21,0.043000," ","int(x/(b*x^3+a*x^2)^(1/2),x)","\frac{2 \left(b x +a \right) x}{\sqrt{b \,x^{3}+a \,x^{2}}\, b}"," ",0,"2*x*(b*x+a)/b/(b*x^3+a*x^2)^(1/2)","A"
256,1,39,24,0.044000," ","int(1/(b*x^3+a*x^2)^(1/2),x)","-\frac{2 \sqrt{b x +a}\, x \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)}{\sqrt{b \,x^{3}+a \,x^{2}}\, \sqrt{a}}"," ",0,"-2/(b*x^3+a*x^2)^(1/2)*x*(b*x+a)^(1/2)/a^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2))","A"
257,1,55,46,0.048000," ","int(1/x/(b*x^3+a*x^2)^(1/2),x)","-\frac{\sqrt{b x +a}\, \left(-a b x \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+\sqrt{b x +a}\, a^{\frac{3}{2}}\right)}{\sqrt{b \,x^{3}+a \,x^{2}}\, a^{\frac{5}{2}}}"," ",0,"-(b*x+a)^(1/2)*((b*x+a)^(1/2)*a^(3/2)-arctanh((b*x+a)^(1/2)/a^(1/2))*x*a*b)/(b*x^3+a*x^2)^(1/2)/a^(5/2)","A"
258,1,77,71,0.046000," ","int(1/x^2/(b*x^3+a*x^2)^(1/2),x)","-\frac{\sqrt{b x +a}\, \left(3 a \,b^{2} x^{2} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)-3 \sqrt{b x +a}\, a^{\frac{3}{2}} b x +2 \sqrt{b x +a}\, a^{\frac{5}{2}}\right)}{4 \sqrt{b \,x^{3}+a \,x^{2}}\, a^{\frac{7}{2}} x}"," ",0,"-1/4*(b*x+a)^(1/2)*(2*(b*x+a)^(1/2)*a^(5/2)-3*(b*x+a)^(1/2)*a^(3/2)*x*b+3*arctanh((b*x+a)^(1/2)/a^(1/2))*a*x^2*b^2)/x/(b*x^3+a*x^2)^(1/2)/a^(7/2)","A"
259,1,95,95,0.055000," ","int(1/x^3/(b*x^3+a*x^2)^(1/2),x)","-\frac{\sqrt{b x +a}\, \left(-15 a \,b^{3} x^{3} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+15 \sqrt{b x +a}\, a^{\frac{3}{2}} b^{2} x^{2}-10 \sqrt{b x +a}\, a^{\frac{5}{2}} b x +8 \sqrt{b x +a}\, a^{\frac{7}{2}}\right)}{24 \sqrt{b \,x^{3}+a \,x^{2}}\, a^{\frac{9}{2}} x^{2}}"," ",0,"-1/24/x^2*(b*x+a)^(1/2)*(15*(b*x+a)^(1/2)*a^(3/2)*x^2*b^2-15*arctanh((b*x+a)^(1/2)/a^(1/2))*x^3*a*b^3-10*(b*x+a)^(1/2)*a^(5/2)*x*b+8*(b*x+a)^(1/2)*a^(7/2))/(b*x^3+a*x^2)^(1/2)/a^(9/2)","A"
260,1,56,84,0.046000," ","int(x^6/(b*x^3+a*x^2)^(3/2),x)","\frac{2 \left(b x +a \right) \left(b^{3} x^{3}-2 a \,b^{2} x^{2}+8 a^{2} b x +16 a^{3}\right) x^{3}}{5 \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} b^{4}}"," ",0,"2/5*(b*x+a)*(b^3*x^3-2*a*b^2*x^2+8*a^2*b*x+16*a^3)*x^3/b^4/(b*x^3+a*x^2)^(3/2)","A"
261,1,46,62,0.048000," ","int(x^5/(b*x^3+a*x^2)^(3/2),x)","-\frac{2 \left(b x +a \right) \left(-b^{2} x^{2}+4 a b x +8 a^{2}\right) x^{3}}{3 \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} b^{3}}"," ",0,"-2/3*(b*x+a)*(-b^2*x^2+4*a*b*x+8*a^2)*x^3/b^3/(b*x^3+a*x^2)^(3/2)","A"
262,1,34,43,0.047000," ","int(x^4/(b*x^3+a*x^2)^(3/2),x)","\frac{2 \left(b x +a \right) \left(b x +2 a \right) x^{3}}{\left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} b^{2}}"," ",0,"2*(b*x+a)*(b*x+2*a)*x^3/b^2/(b*x^3+a*x^2)^(3/2)","A"
263,1,27,19,0.044000," ","int(x^3/(b*x^3+a*x^2)^(3/2),x)","-\frac{2 \left(b x +a \right) x^{3}}{\left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} b}"," ",0,"-2*(b*x+a)*x^3/b/(b*x^3+a*x^2)^(3/2)","A"
264,1,54,44,0.053000," ","int(x^2/(b*x^3+a*x^2)^(3/2),x)","-\frac{2 \left(b x +a \right) \left(\sqrt{b x +a}\, a \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)-a^{\frac{3}{2}}\right) x^{3}}{\left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} a^{\frac{5}{2}}}"," ",0,"-2*x^3*(b*x+a)*(arctanh((b*x+a)^(1/2)/a^(1/2))*a*(b*x+a)^(1/2)-a^(3/2))/(b*x^3+a*x^2)^(3/2)/a^(5/2)","A"
265,1,62,65,0.059000," ","int(x/(b*x^3+a*x^2)^(3/2),x)","\frac{\left(b x +a \right) \left(3 \sqrt{b x +a}\, b x \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)-3 \sqrt{a}\, b x -a^{\frac{3}{2}}\right) x^{2}}{\left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} a^{\frac{5}{2}}}"," ",0,"x^2*(b*x+a)*(3*(b*x+a)^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2))*x*b-3*x*b*a^(1/2)-a^(3/2))/(b*x^3+a*x^2)^(3/2)/a^(5/2)","A"
266,1,76,92,0.057000," ","int(1/(b*x^3+a*x^2)^(3/2),x)","-\frac{\left(b x +a \right) \left(15 \sqrt{b x +a}\, b^{2} x^{2} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)-15 \sqrt{a}\, b^{2} x^{2}-5 a^{\frac{3}{2}} b x +2 a^{\frac{5}{2}}\right) x}{4 \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} a^{\frac{7}{2}}}"," ",0,"-1/4*x*(b*x+a)*(15*arctanh((b*x+a)^(1/2)/a^(1/2))*(b*x+a)^(1/2)*x^2*b^2-5*a^(3/2)*x*b-15*x^2*b^2*a^(1/2)+2*a^(5/2))/(b*x^3+a*x^2)^(3/2)/a^(7/2)","A"
267,1,86,116,0.061000," ","int(1/x/(b*x^3+a*x^2)^(3/2),x)","-\frac{\left(b x +a \right) \left(-105 \sqrt{b x +a}\, b^{3} x^{3} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+105 \sqrt{a}\, b^{3} x^{3}+35 a^{\frac{3}{2}} b^{2} x^{2}-14 a^{\frac{5}{2}} b x +8 a^{\frac{7}{2}}\right)}{24 \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} a^{\frac{9}{2}}}"," ",0,"-1/24*(b*x+a)*(-105*arctanh((b*x+a)^(1/2)/a^(1/2))*(b*x+a)^(1/2)*x^3*b^3-14*a^(5/2)*x*b+35*a^(3/2)*x^2*b^2+105*b^3*x^3*a^(1/2)+8*a^(7/2))/(b*x^3+a*x^2)^(3/2)/a^(9/2)","A"
268,1,100,140,0.064000," ","int(1/x^2/(b*x^3+a*x^2)^(3/2),x)","-\frac{\left(b x +a \right) \left(315 \sqrt{b x +a}\, b^{4} x^{4} \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)-315 \sqrt{a}\, b^{4} x^{4}-105 a^{\frac{3}{2}} b^{3} x^{3}+42 a^{\frac{5}{2}} b^{2} x^{2}-24 a^{\frac{7}{2}} b x +16 a^{\frac{9}{2}}\right)}{64 \left(b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} a^{\frac{11}{2}} x}"," ",0,"-1/64*(b*x+a)*(315*arctanh((b*x+a)^(1/2)/a^(1/2))*(b*x+a)^(1/2)*x^4*b^4-24*a^(7/2)*x*b+42*a^(5/2)*x^2*b^2-105*a^(3/2)*x^3*b^3-315*x^4*b^4*a^(1/2)+16*a^(9/2))/x/(b*x^3+a*x^2)^(3/2)/a^(11/2)","A"
269,1,103,97,0.069000," ","int(x^(7/2)/(b*x^3+a*x^2)^(1/2),x)","-\frac{\left(-16 b^{\frac{9}{2}} x^{4}+4 a \,b^{\frac{7}{2}} x^{3}-10 a^{2} b^{\frac{5}{2}} x^{2}-30 a^{3} b^{\frac{3}{2}} x +15 \sqrt{\left(b x +a \right) x}\, a^{3} b \ln \left(\frac{2 b x +a +2 \sqrt{b \,x^{2}+a x}\, \sqrt{b}}{2 \sqrt{b}}\right)\right) \sqrt{x}}{48 \sqrt{b \,x^{3}+a \,x^{2}}\, b^{\frac{9}{2}}}"," ",0,"-1/48*x^(1/2)*(-16*b^(9/2)*x^4+4*b^(7/2)*x^3*a-10*b^(5/2)*x^2*a^2-30*b^(3/2)*x*a^3+15*(x*(b*x+a))^(1/2)*ln(1/2*(2*(b*x^2+a*x)^(1/2)*b^(1/2)+2*b*x+a)/b^(1/2))*a^3*b)/(b*x^3+a*x^2)^(1/2)/b^(9/2)","A"
270,1,92,73,0.048000," ","int(x^(5/2)/(b*x^3+a*x^2)^(1/2),x)","\frac{\left(4 b^{\frac{7}{2}} x^{3}-2 a \,b^{\frac{5}{2}} x^{2}-6 a^{2} b^{\frac{3}{2}} x +3 \sqrt{\left(b x +a \right) x}\, a^{2} b \ln \left(\frac{2 b x +a +2 \sqrt{b \,x^{2}+a x}\, \sqrt{b}}{2 \sqrt{b}}\right)\right) \sqrt{x}}{8 \sqrt{b \,x^{3}+a \,x^{2}}\, b^{\frac{7}{2}}}"," ",0,"1/8*x^(1/2)*(4*b^(7/2)*x^3-2*b^(5/2)*x^2*a-6*b^(3/2)*x*a^2+3*((b*x+a)*x)^(1/2)*ln(1/2*(2*b*x+a+2*(b*x^2+a*x)^(1/2)*b^(1/2))/b^(1/2))*a^2*b)/(b*x^3+a*x^2)^(1/2)/b^(7/2)","A"
271,1,78,48,0.049000," ","int(x^(3/2)/(b*x^3+a*x^2)^(1/2),x)","-\frac{\left(-2 b^{\frac{5}{2}} x^{2}-2 a \,b^{\frac{3}{2}} x +\sqrt{\left(b x +a \right) x}\, a b \ln \left(\frac{2 b x +a +2 \sqrt{b \,x^{2}+a x}\, \sqrt{b}}{2 \sqrt{b}}\right)\right) \sqrt{x}}{2 \sqrt{b \,x^{3}+a \,x^{2}}\, b^{\frac{5}{2}}}"," ",0,"-1/2*x^(1/2)*(-2*b^(5/2)*x^2-2*a*b^(3/2)*x+a*((b*x+a)*x)^(1/2)*ln(1/2*(2*b*x+a+2*(b*x^2+a*x)^(1/2)*b^(1/2))/b^(1/2))*b)/(b*x^3+a*x^2)^(1/2)/b^(5/2)","A"
272,1,58,26,0.047000," ","int(x^(1/2)/(b*x^3+a*x^2)^(1/2),x)","\frac{\sqrt{\left(b x +a \right) x}\, \sqrt{x}\, \ln \left(\frac{2 b x +a +2 \sqrt{b \,x^{2}+a x}\, \sqrt{b}}{2 \sqrt{b}}\right)}{\sqrt{b \,x^{3}+a \,x^{2}}\, \sqrt{b}}"," ",0,"1/(b*x^3+a*x^2)^(1/2)*x^(1/2)*((b*x+a)*x)^(1/2)*ln(1/2*(2*b*x+a+2*(b*x^2+a*x)^(1/2)*b^(1/2))/b^(1/2))/b^(1/2)","B"
273,1,27,21,0.037000," ","int(1/x^(1/2)/(b*x^3+a*x^2)^(1/2),x)","-\frac{2 \left(b x +a \right) \sqrt{x}}{\sqrt{b \,x^{3}+a \,x^{2}}\, a}"," ",0,"-2*(b*x+a)*x^(1/2)/a/(b*x^3+a*x^2)^(1/2)","A"
274,1,33,44,0.063000," ","int(1/x^(3/2)/(b*x^3+a*x^2)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(-2 b x +a \right)}{3 \sqrt{b \,x^{3}+a \,x^{2}}\, a^{2} \sqrt{x}}"," ",0,"-2/3*(b*x+a)*(-2*b*x+a)/x^(1/2)/a^2/(b*x^3+a*x^2)^(1/2)","A"
275,1,46,68,0.045000," ","int(1/x^(5/2)/(b*x^3+a*x^2)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(8 b^{2} x^{2}-4 a b x +3 a^{2}\right)}{15 \sqrt{b \,x^{3}+a \,x^{2}}\, a^{3} x^{\frac{3}{2}}}"," ",0,"-2/15*(b*x+a)*(8*b^2*x^2-4*a*b*x+3*a^2)/x^(3/2)/a^3/(b*x^3+a*x^2)^(1/2)","A"
276,1,57,92,0.045000," ","int(1/x^(7/2)/(b*x^3+a*x^2)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(-16 b^{3} x^{3}+8 a \,b^{2} x^{2}-6 a^{2} b x +5 a^{3}\right)}{35 \sqrt{b \,x^{3}+a \,x^{2}}\, a^{4} x^{\frac{5}{2}}}"," ",0,"-2/35*(b*x+a)*(-16*b^3*x^3+8*a*b^2*x^2-6*a^2*b*x+5*a^3)/x^(5/2)/a^4/(b*x^3+a*x^2)^(1/2)","A"
277,0,0,63,0.497000," ","int(x^(1-3*n)*(b*x^3+a*x^2)^n,x)","\int x^{-3 n +1} \left(b \,x^{3}+a \,x^{2}\right)^{n}\, dx"," ",0,"int(x^(1-3*n)*(b*x^3+a*x^2)^n,x)","F"
278,0,0,50,0.508000," ","int((b*x^3+a*x^2)^n/(x^(3*n)),x)","\int x^{-3 n} \left(b \,x^{3}+a \,x^{2}\right)^{n}\, dx"," ",0,"int((b*x^3+a*x^2)^n/(x^(3*n)),x)","F"
279,0,0,58,0.500000," ","int(x^(-3*n-1)*(b*x^3+a*x^2)^n,x)","\int x^{-3 n -1} \left(b \,x^{3}+a \,x^{2}\right)^{n}\, dx"," ",0,"int(x^(-3*n-1)*(b*x^3+a*x^2)^n,x)","F"
280,1,36,34,0.046000," ","int(x^(-2-3*n)*(b*x^3+a*x^2)^n,x)","-\frac{\left(b x +a \right) x^{-3 n -1} \left(b \,x^{3}+a \,x^{2}\right)^{n}}{\left(n +1\right) a}"," ",0,"-(b*x+a)*x^(-3*n-1)/a/(n+1)*(b*x^3+a*x^2)^n","A"
281,1,50,72,0.048000," ","int(x^(-3-3*n)*(b*x^3+a*x^2)^n,x)","-\frac{\left(a n -b x +a \right) \left(b x +a \right) x^{-3 n -2} \left(b \,x^{3}+a \,x^{2}\right)^{n}}{\left(n +2\right) \left(n +1\right) a^{2}}"," ",0,"-(b*x^3+a*x^2)^n*x^(-2-3*n)*(a*n-b*x+a)*(b*x+a)/(n+2)/(n+1)/a^2","A"
282,1,84,118,0.049000," ","int(x^(-4-3*n)*(b*x^3+a*x^2)^n,x)","-\frac{\left(b x +a \right) \left(a^{2} n^{2}-2 a b n x +2 b^{2} x^{2}+3 a^{2} n -2 a b x +2 a^{2}\right) x^{-3 n -3} \left(b \,x^{3}+a \,x^{2}\right)^{n}}{\left(n +3\right) \left(n +2\right) \left(n +1\right) a^{3}}"," ",0,"-x^(-3-3*n)*(b*x+a)*(a^2*n^2-2*a*b*n*x+2*b^2*x^2+3*a^2*n-2*a*b*x+2*a^2)*(b*x^3+a*x^2)^n/(n+3)/(n+2)/(n+1)/a^3","A"
283,1,31,17,0.056000," ","int(x^11/(b*x^5+a*x^2)^3,x)","\frac{a}{6 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{1}{3 \left(b \,x^{3}+a \right) b^{2}}"," ",0,"1/6*a/b^2/(b*x^3+a)^2-1/3/b^2/(b*x^3+a)","A"
284,1,48,68,0.050000," ","int(x^9/(b*x^5+a*x^2)^(1/2),x)","\frac{2 \left(b \,x^{3}+a \right) \left(3 b^{2} x^{6}-4 a b \,x^{3}+8 a^{2}\right) x}{45 \sqrt{b \,x^{5}+a \,x^{2}}\, b^{3}}"," ",0,"2/45*(b*x^3+a)*(3*b^2*x^6-4*a*b*x^3+8*a^2)*x/b^3/(b*x^5+a*x^2)^(1/2)","A"
285,1,37,44,0.056000," ","int(x^6/(b*x^5+a*x^2)^(1/2),x)","-\frac{2 \left(b \,x^{3}+a \right) \left(-b \,x^{3}+2 a \right) x}{9 \sqrt{b \,x^{5}+a \,x^{2}}\, b^{2}}"," ",0,"-2/9*(b*x^3+a)*(-b*x^3+2*a)*x/b^2/(b*x^5+a*x^2)^(1/2)","A"
286,1,27,21,0.048000," ","int(x^3/(b*x^5+a*x^2)^(1/2),x)","\frac{2 \left(b \,x^{3}+a \right) x}{3 \sqrt{b \,x^{5}+a \,x^{2}}\, b}"," ",0,"2/3*(b*x^3+a)*x/b/(b*x^5+a*x^2)^(1/2)","A"
287,1,43,24,0.048000," ","int(1/(b*x^5+a*x^2)^(1/2),x)","-\frac{2 \sqrt{b \,x^{3}+a}\, x \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{b \,x^{5}+a \,x^{2}}\, \sqrt{a}}"," ",0,"-2/3/(b*x^5+a*x^2)^(1/2)*x*(b*x^3+a)^(1/2)*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)","A"
288,1,66,47,0.051000," ","int(1/x^3/(b*x^5+a*x^2)^(1/2),x)","-\frac{\sqrt{b \,x^{3}+a}\, \left(-a b \,x^{3} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)+\sqrt{b \,x^{3}+a}\, a^{\frac{3}{2}}\right)}{3 \sqrt{b \,x^{5}+a \,x^{2}}\, a^{\frac{5}{2}} x^{2}}"," ",0,"-1/3/x^2*(b*x^3+a)^(1/2)*(-b*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a*x^3+(b*x^3+a)^(1/2)*a^(3/2))/(b*x^5+a*x^2)^(1/2)/a^(5/2)","A"
289,1,248,179,1.292000," ","int(x^4/(b*x^5+a*x^2)^(1/2),x)","\frac{2 \left(3 b^{2} x^{4}+3 a b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{2 \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(i \sqrt{3}-3\right)}}\, \sqrt{-\frac{i \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)\right) x}{15 \sqrt{b \,x^{5}+a \,x^{2}}\, b^{2}}"," ",0,"2/15*x*(I*a*3^(1/2)*(-a*b^2)^(1/3)*(-I*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*(-2*(-b*x+(-a*b^2)^(1/3))/(-a*b^2)^(1/3)/(I*3^(1/2)-3))^(1/2)*(-I*(I*3^(1/2)*(-a*b^2)^(1/3)+2*b*x+(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*EllipticF(1/6*3^(1/2)*2^(1/2)*(-I*(I*3^(1/2)*(-a*b^2)^(1/3)-2*b*x-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2))+3*b^2*x^4+3*a*b*x)/(b*x^5+a*x^2)^(1/2)/b^2","A"
290,1,231,159,0.049000," ","int(x/(b*x^5+a*x^2)^(1/2),x)","-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{2 \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(i \sqrt{3}-3\right)}}\, \sqrt{-\frac{i \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, x \EllipticF \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)}{3 \sqrt{b \,x^{5}+a \,x^{2}}\, b}"," ",0,"-1/3*I/(b*x^5+a*x^2)^(1/2)*x*3^(1/2)*(-a*b^2)^(1/3)/b*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*(-2*(-b*x+(-a*b^2)^(1/3))/(-a*b^2)^(1/3)/(I*3^(1/2)-3))^(1/2)*(-I*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*EllipticF(1/6*3^(1/2)*2^(1/2)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2))","A"
291,1,248,184,0.524000," ","int(1/x^2/(b*x^5+a*x^2)^(1/2),x)","\frac{-6 b \,x^{3}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{2 \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(i \sqrt{3}-3\right)}}\, \sqrt{-\frac{i \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, x^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)-6 a}{12 \sqrt{b \,x^{5}+a \,x^{2}}\, a x}"," ",0,"1/12/x*(I*3^(1/2)*(-a*b^2)^(1/3)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*(-2*(-b*x+(-a*b^2)^(1/3))/(-a*b^2)^(1/3)/(I*3^(1/2)-3))^(1/2)*(-I*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*EllipticF(1/6*3^(1/2)*2^(1/2)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2))*x^2-6*b*x^3-6*a)/(b*x^5+a*x^2)^(1/2)/a","A"
292,1,676,380,0.539000," ","int(x^5/(b*x^5+a*x^2)^(1/2),x)","-\frac{2 \left(-3 b^{3} x^{5}-3 a \,b^{2} x^{2}+3 i \sqrt{-\frac{2 \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(i \sqrt{3}-3\right)}}\, \sqrt{-\frac{i \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, a \EllipticE \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)+3 \sqrt{-\frac{2 \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(i \sqrt{3}-3\right)}}\, \sqrt{-\frac{i \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} a \EllipticE \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)-2 i \sqrt{-\frac{2 \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(i \sqrt{3}-3\right)}}\, \sqrt{-\frac{i \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)\right) x}{21 \sqrt{b \,x^{5}+a \,x^{2}}\, b^{3}}"," ",0,"-2/21*x*(3*I*(-2*(-b*x+(-a*b^2)^(1/3))/(-a*b^2)^(1/3)/(I*3^(1/2)-3))^(1/2)*(-I*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*EllipticE(1/6*3^(1/2)*2^(1/2)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2))*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*(-a*b^2)^(2/3)*3^(1/2)*a-2*I*(-2*(-b*x+(-a*b^2)^(1/3))/(-a*b^2)^(1/3)/(I*3^(1/2)-3))^(1/2)*(-I*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*EllipticF(1/6*3^(1/2)*2^(1/2)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2))*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*(-a*b^2)^(2/3)*3^(1/2)*a-3*b^3*x^5+3*(-2*(-b*x+(-a*b^2)^(1/3))/(-a*b^2)^(1/3)/(I*3^(1/2)-3))^(1/2)*(-I*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*EllipticE(1/6*3^(1/2)*2^(1/2)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2))*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*(-a*b^2)^(2/3)*a-3*a*b^2*x^2)/(b*x^5+a*x^2)^(1/2)/b^3","A"
293,1,394,360,0.059000," ","int(x^2/(b*x^5+a*x^2)^(1/2),x)","-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{2 \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(i \sqrt{3}-3\right)}}\, \sqrt{-\frac{i \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(i \sqrt{3}\, \EllipticE \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)-3 \EllipticE \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)+2 \EllipticF \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)\right) x}{6 \sqrt{b \,x^{5}+a \,x^{2}}\, b^{2}}"," ",0,"-1/6*I*x*3^(1/2)*(-a*b^2)^(2/3)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*(-2*(-b*x+(-a*b^2)^(1/3))/(-a*b^2)^(1/3)/(I*3^(1/2)-3))^(1/2)*(-I*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*(I*EllipticE(1/6*3^(1/2)*2^(1/2)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2))*3^(1/2)-3*EllipticE(1/6*3^(1/2)*2^(1/2)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2))+2*EllipticF(1/6*3^(1/2)*2^(1/2)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2)))/(b*x^5+a*x^2)^(1/2)/b^2","A"
294,1,673,383,0.545000," ","int(1/x/(b*x^5+a*x^2)^(1/2),x)","\frac{-12 b^{2} x^{3}-12 a b +3 i \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{2 \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(i \sqrt{3}-3\right)}}\, \sqrt{-\frac{i \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, x \EllipticE \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)+3 \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{2 \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(i \sqrt{3}-3\right)}}\, \sqrt{-\frac{i \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} x \EllipticE \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)-2 i \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{2 \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}} \left(i \sqrt{3}-3\right)}}\, \sqrt{-\frac{i \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, x \EllipticF \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{6}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{i \sqrt{3}-3}}\right)}{12 \sqrt{b \,x^{5}+a \,x^{2}}\, a b}"," ",0,"1/12*(3*I*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*(-2*(-b*x+(-a*b^2)^(1/3))/(-a*b^2)^(1/3)/(I*3^(1/2)-3))^(1/2)*(-I*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*EllipticE(1/6*3^(1/2)*2^(1/2)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*3^(1/2)*x-2*I*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*(-2*(-b*x+(-a*b^2)^(1/3))/(-a*b^2)^(1/3)/(I*3^(1/2)-3))^(1/2)*(-I*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*EllipticF(1/6*3^(1/2)*2^(1/2)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*3^(1/2)*x+3*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*(-2*(-b*x+(-a*b^2)^(1/3))/(-a*b^2)^(1/3)/(I*3^(1/2)-3))^(1/2)*(-I*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2)*EllipticE(1/6*3^(1/2)*2^(1/2)*(-I*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))*3^(1/2)/(-a*b^2)^(1/3))^(1/2),2^(1/2)*(I*3^(1/2)/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x-12*b^2*x^3-12*a*b)/(b*x^5+a*x^2)^(1/2)/a/b","A"
295,1,2017,272,0.846000," ","int(x^(13/2)/(b*x^5+a*x^2)^(1/2),x)","-\frac{\left(b \,x^{3}+a \right) \left(14 i \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{3}\, a^{2} b^{2} x^{2} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-14 \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, a^{2} b^{2} x^{2} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-28 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{3}\, a^{2} b x \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)+28 \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, a^{2} b x \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-4 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(b \,x^{3}+a \right) x}\, \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, \sqrt{3}\, b^{2} x^{3}+12 \sqrt{\left(b \,x^{3}+a \right) x}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, b^{2} x^{3}+14 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{3}\, a^{2} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-14 \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, a^{2} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)+7 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(b \,x^{3}+a \right) x}\, \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, \sqrt{3}\, a b -21 \sqrt{\left(b \,x^{3}+a \right) x}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, a b \right) x^{\frac{3}{2}}}{20 \sqrt{b \,x^{5}+a \,x^{2}}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(b \,x^{3}+a \right) x}\, \left(i \sqrt{3}-3\right) \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, b^{3}}"," ",0,"-1/20/(b*x^5+a*x^2)^(1/2)*x^(3/2)*(b*x^3+a)/b^3/(-a*b^2)^(1/3)*(14*I*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*x^2*a^2*b^2-28*I*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*x*a^2*b+14*I*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*a^2-4*I*(-a*b^2)^(1/3)*((b*x^3+a)*x)^(1/2)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3)))^(1/2)*3^(1/2)*x^3*b^2-14*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a^2*b^2+28*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a^2*b-14*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)*x*b/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a^2+12*x^3*((b*x^3+a)*x)^(1/2)*b^2*(-a*b^2)^(1/3)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3)))^(1/2)+7*I*(-a*b^2)^(1/3)*((b*x^3+a)*x)^(1/2)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3)))^(1/2)*3^(1/2)*a*b-21*a*((b*x^3+a)*x)^(1/2)*b*(-a*b^2)^(1/3)*(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3)))^(1/2))/((b*x^3+a)*x)^(1/2)/(I*3^(1/2)-3)/(1/b^2*x*(-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3)))^(1/2)","C"
296,1,2586,535,0.668000," ","int(x^(11/2)/(b*x^5+a*x^2)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/4*x^(3/2)*(b*x^3+a)*(-5*I*(-a*b^2)^(1/3)*3^(1/2)*x^2*a*b-5*I*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*x^2*a*b-10*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b+15*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b-5*I*(-a*b^2)^(2/3)*3^(1/2)*x*a+20*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a-30*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a+10*I*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*x*a-5*I*3^(1/2)*x^3*a*b^2+5*I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*a^2*b+10*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a^2*b-15*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a^2*b+I*((b*x^3+a)*x)^(1/2)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*3^(1/2)*x^2*b^2-3*((b*x^3+a)*x)^(1/2)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*x^2*b^2+15*a*b^2*x^3+15*(-a*b^2)^(1/3)*x^2*a*b+15*(-a*b^2)^(2/3)*x*a)/(b*x^5+a*x^2)^(1/2)/b^3/((b*x^3+a)*x)^(1/2)/(I*3^(1/2)-3)/((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)","C"
297,1,3347,49,1.140000," ","int(x^(9/2)/(b*x^5+a*x^2)^(1/2),x)","\text{output too large to display}"," ",0,"1/3/(b*x^5+a*x^2)^(1/2)*x^(3/2)*(b*x^3+a)/b^3*(6*I*3^(1/2)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b^2-6*I*3^(1/2)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b^2-12*I*3^(1/2)*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a*b+12*I*3^(1/2)*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a*b+6*I*3^(1/2)*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a-6*I*3^(1/2)*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a-6*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b^2+6*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b^2+12*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a*b-12*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a*b+I*3^(1/2)*((b*x^3+a)*x)^(1/2)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*x*b^2-6*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a+6*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticPi((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a-3*x*((b*x^3+a)*x)^(1/2)*b^2*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2))/((b*x^3+a)*x)^(1/2)/(I*3^(1/2)-3)/((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)","C"
298,1,1793,250,1.135000," ","int(x^(7/2)/(b*x^5+a*x^2)^(1/2),x)","\frac{\left(b \,x^{3}+a \right) \left(2 i \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{3}\, a \,b^{2} x^{2} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-2 \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, a \,b^{2} x^{2} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-4 i \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, a b x \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)+4 \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, a b x \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)+2 i \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, a \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-2 \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, a \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)+i \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \sqrt{\left(b \,x^{3}+a \right) x}\, b -3 \sqrt{\left(b \,x^{3}+a \right) x}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, b \right) x^{\frac{3}{2}}}{2 \sqrt{b \,x^{5}+a \,x^{2}}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(b \,x^{3}+a \right) x}\, \left(i \sqrt{3}-3\right) \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, b^{2}}"," ",0,"1/2/(b*x^5+a*x^2)^(1/2)*x^(3/2)*(b*x^3+a)/b^2/(-a*b^2)^(1/3)*(2*I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*x^2*a*b^2-4*I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*3^(1/2)*x*a*b+2*I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*3^(1/2)*a-2*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^2*a*b^2+4*(-a*b^2)^(1/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x*a*b-2*(-a*b^2)^(2/3)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a+I*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*(-a*b^2)^(1/3)*3^(1/2)*((b*x^3+a)*x)^(1/2)*b-3*((b*x^3+a)*x)^(1/2)*b*(-a*b^2)^(1/3)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2))/((b*x^3+a)*x)^(1/2)/(I*3^(1/2)-3)/((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)","C"
299,1,2374,512,1.166000," ","int(x^(5/2)/(b*x^5+a*x^2)^(1/2),x)","\text{Expression too large to display}"," ",0,"-2*x^(3/2)*(b*x^3+a)*(-I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*3^(1/2)*x^2*b+2*I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*3^(1/2)*x-2*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^2*b+3*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^2*b+I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*a*b+4*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x-6*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x-I*3^(1/2)*x^3*b^2+2*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a*b-3*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*a*b-I*(-a*b^2)^(1/3)*3^(1/2)*x^2*b-I*(-a*b^2)^(2/3)*3^(1/2)*x+3*b^2*x^3+3*(-a*b^2)^(1/3)*x^2*b+3*(-a*b^2)^(2/3)*x)/(b*x^5+a*x^2)^(1/2)/b^2/((b*x^3+a)*x)^(1/2)/(I*3^(1/2)-3)/((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)","C"
300,1,480,26,1.237000," ","int(x^(3/2)/(b*x^5+a*x^2)^(1/2),x)","-\frac{4 \left(b \,x^{3}+a \right) \left(i \sqrt{3}-1\right) \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)^{2} \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(\EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-\EllipticPi \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \frac{i \sqrt{3}-1}{i \sqrt{3}-3}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)\right) x^{\frac{3}{2}}}{\sqrt{b \,x^{5}+a \,x^{2}}\, \sqrt{\left(b \,x^{3}+a \right) x}\, \left(i \sqrt{3}-3\right) \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, b^{2}}"," ",0,"-4*x^(3/2)*(b*x^3+a)*(I*3^(1/2)-1)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*(-b*x+(-a*b^2)^(1/3))^2*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*(EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))-EllipticPi((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2)))/(b*x^5+a*x^2)^(1/2)/b^2/((b*x^3+a)*x)^(1/2)/(I*3^(1/2)-3)/((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)","C"
301,1,437,225,1.225000," ","int(x^(1/2)/(b*x^5+a*x^2)^(1/2),x)","-\frac{4 \left(b \,x^{3}+a \right) \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(i \sqrt{3}\, b^{2} x^{2}-b^{2} x^{2}-2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, b x +2 \left(-a \,b^{2}\right)^{\frac{1}{3}} b x +i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) x^{\frac{3}{2}} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)}{\sqrt{b \,x^{5}+a \,x^{2}}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(b \,x^{3}+a \right) x}\, \left(i \sqrt{3}-3\right) \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, b}"," ",0,"-4/(b*x^5+a*x^2)^(1/2)*x^(3/2)*(b*x^3+a)/(-a*b^2)^(1/3)/b*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(I*3^(1/2)*x^2*b^2-2*I*(-a*b^2)^(1/3)*3^(1/2)*x*b+I*(-a*b^2)^(2/3)*3^(1/2)-b^2*x^2+2*(-a*b^2)^(1/3)*x*b-(-a*b^2)^(2/3))/((b*x^3+a)*x)^(1/2)/(I*3^(1/2)-3)/((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)","C"
302,1,2860,537,0.910000," ","int(1/x^(1/2)/(b*x^5+a*x^2)^(1/2),x)","\text{output too large to display}"," ",0,"-2*x^(1/2)*(4*I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*((b*x^3+a)*x)^(1/2)*(-a*b^2)^(2/3)*3^(1/2)*x+2*I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*((b*x^3+a)*x)^(1/2)*3^(1/2)*a*b-4*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*((b*x^3+a)*x)^(1/2)*(-a*b^2)^(1/3)*x^2*b+6*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*((b*x^3+a)*x)^(1/2)*(-a*b^2)^(1/3)*x^2*b-2*I*((b*x^3+a)*x)^(1/2)*(-a*b^2)^(1/3)*3^(1/2)*x^2*b+8*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*((b*x^3+a)*x)^(1/2)*(-a*b^2)^(2/3)*x-12*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*((b*x^3+a)*x)^(1/2)*(-a*b^2)^(2/3)*x+I*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*3^(1/2)*x^3*b^2-2*I*((b*x^3+a)*x)^(1/2)*(-a*b^2)^(2/3)*3^(1/2)*x+4*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*((b*x^3+a)*x)^(1/2)*a*b-6*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*((b*x^3+a)*x)^(1/2)*a*b-2*I*((b*x^3+a)*x)^(1/2)*3^(1/2)*x^3*b^2-3*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*x^3*b^2-2*I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*((b*x^3+a)*x)^(1/2)*(-a*b^2)^(1/3)*3^(1/2)*x^2*b+6*((b*x^3+a)*x)^(1/2)*x^3*b^2+I*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*3^(1/2)*a*b+6*((b*x^3+a)*x)^(1/2)*(-a*b^2)^(1/3)*x^2*b+6*((b*x^3+a)*x)^(1/2)*(-a*b^2)^(2/3)*x-3*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*a*b)/(b*x^5+a*x^2)^(1/2)/b/a/(I*3^(1/2)-3)/((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)","C"
303,1,29,21,0.045000," ","int(1/x^(3/2)/(b*x^5+a*x^2)^(1/2),x)","-\frac{2 \left(b \,x^{3}+a \right)}{3 \sqrt{b \,x^{5}+a \,x^{2}}\, a \sqrt{x}}"," ",0,"-2/3*(b*x^3+a)/x^(1/2)/a/(b*x^5+a*x^2)^(1/2)","A"
304,1,1795,248,1.081000," ","int(1/x^(5/2)/(b*x^5+a*x^2)^(1/2),x)","\frac{2 \left(b \,x^{3}+a \right) \left(4 i \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{3}\, b^{2} x^{5} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-4 \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, b^{2} x^{5} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-8 i \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, b \,x^{4} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)+8 \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} b \,x^{4} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)+4 i \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, x^{3} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-4 \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(-a \,b^{2}\right)^{\frac{2}{3}} x^{3} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-i \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \sqrt{\left(b \,x^{3}+a \right) x}+3 \sqrt{\left(b \,x^{3}+a \right) x}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\right)}{5 \sqrt{b \,x^{5}+a \,x^{2}}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(b \,x^{3}+a \right) x}\, \left(i \sqrt{3}-3\right) \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, a \,x^{\frac{3}{2}}}"," ",0,"2/5/(b*x^5+a*x^2)^(1/2)/x^(3/2)*(b*x^3+a)/(-a*b^2)^(1/3)/a*(4*I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*3^(1/2)*x^5*b^2-8*I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*3^(1/2)*x^4*b+4*I*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*3^(1/2)*x^3-4*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*b^2+8*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(1/3)*x^4*b-4*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-a*b^2)^(2/3)*x^3-I*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*(-a*b^2)^(1/3)*3^(1/2)*((b*x^3+a)*x)^(1/2)+3*((b*x^3+a)*x)^(1/2)*(-a*b^2)^(1/3)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2))/((b*x^3+a)*x)^(1/2)/(I*3^(1/2)-3)/((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)","C"
305,1,3048,559,1.086000," ","int(1/x^(7/2)/(b*x^5+a*x^2)^(1/2),x)","\text{output too large to display}"," ",0,"2/7*(-8*I*3^(1/2)*((b*x^3+a)*x)^(1/2)*x^6*b^2+16*I*(-a*b^2)^(2/3)*3^(1/2)*((b*x^3+a)*x)^(1/2)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4-16*(-a*b^2)^(1/3)*((b*x^3+a)*x)^(1/2)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*b+24*(-a*b^2)^(1/3)*((b*x^3+a)*x)^(1/2)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*b+4*I*3^(1/2)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*x^6*b^2+32*(-a*b^2)^(2/3)*((b*x^3+a)*x)^(1/2)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4-48*(-a*b^2)^(2/3)*((b*x^3+a)*x)^(1/2)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^4-8*I*(-a*b^2)^(2/3)*3^(1/2)*((b*x^3+a)*x)^(1/2)*x^4+3*I*3^(1/2)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*x^3*a*b-8*I*(-a*b^2)^(1/3)*3^(1/2)*((b*x^3+a)*x)^(1/2)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^5*b+16*((b*x^3+a)*x)^(1/2)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^3*a*b-24*((b*x^3+a)*x)^(1/2)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^3*a*b-I*3^(1/2)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*a^2+24*((b*x^3+a)*x)^(1/2)*x^6*b^2-12*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*x^6*b^2+24*(-a*b^2)^(1/3)*((b*x^3+a)*x)^(1/2)*x^5*b+8*I*3^(1/2)*((b*x^3+a)*x)^(1/2)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*EllipticE((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*x^3*a*b+24*(-a*b^2)^(2/3)*((b*x^3+a)*x)^(1/2)*x^4-9*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*x^3*a*b-8*I*(-a*b^2)^(1/3)*3^(1/2)*((b*x^3+a)*x)^(1/2)*x^5*b+3*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*a^2)/(b*x^5+a*x^2)^(1/2)/x^(5/2)/a^2/(I*3^(1/2)-3)/((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)","C"
306,1,37,44,0.043000," ","int(1/x^(9/2)/(b*x^5+a*x^2)^(1/2),x)","-\frac{2 \left(b \,x^{3}+a \right) \left(-2 b \,x^{3}+a \right)}{9 \sqrt{b \,x^{5}+a \,x^{2}}\, a^{2} x^{\frac{7}{2}}}"," ",0,"-2/9*(b*x^3+a)*(-2*b*x^3+a)/x^(7/2)/a^2/(b*x^5+a*x^2)^(1/2)","A"
307,1,2009,272,1.235000," ","int(1/x^(11/2)/(b*x^5+a*x^2)^(1/2),x)","-\frac{2 \left(b \,x^{3}+a \right) \left(32 i \sqrt{3}\, \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, b^{3} x^{8} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-32 \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, b^{3} x^{8} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-64 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, b^{2} x^{7} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)+64 \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, b^{2} x^{7} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)+32 i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, b \,x^{6} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-32 \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, b \,x^{6} \EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-8 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \sqrt{\left(b \,x^{3}+a \right) x}\, \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, b \,x^{3}+24 \sqrt{\left(b \,x^{3}+a \right) x}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, b \,x^{3}+5 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \sqrt{\left(b \,x^{3}+a \right) x}\, \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, a -15 \sqrt{\left(b \,x^{3}+a \right) x}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, a \right)}{55 \sqrt{b \,x^{5}+a \,x^{2}}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\left(b \,x^{3}+a \right) x}\, \left(i \sqrt{3}-3\right) \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, a^{2} x^{\frac{9}{2}}}"," ",0,"-2/55/(b*x^5+a*x^2)^(1/2)/x^(9/2)*(b*x^3+a)/(-a*b^2)^(1/3)/a^2*(32*I*3^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*x^8*b^3-64*I*(-a*b^2)^(1/3)*3^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*x^7*b^2+32*I*(-a*b^2)^(2/3)*3^(1/2)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*x^6*b-32*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*x^8*b^3+64*(-a*b^2)^(1/3)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*x^7*b^2-32*(-a*b^2)^(2/3)*EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)*x^6*b-8*I*(-a*b^2)^(1/3)*3^(1/2)*((b*x^3+a)*x)^(1/2)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*x^3*b+24*b*((b*x^3+a)*x)^(1/2)*x^3*(-a*b^2)^(1/3)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)+5*I*(-a*b^2)^(1/3)*3^(1/2)*((b*x^3+a)*x)^(1/2)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)*a-15*((b*x^3+a)*x)^(1/2)*a*(-a*b^2)^(1/3)*((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2))/((b*x^3+a)*x)^(1/2)/(I*3^(1/2)-3)/((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)","C"
308,1,29,28,0.048000," ","int(x/(b*x^4+a*x^3),x)","-\frac{b \ln \left(x \right)}{a^{2}}+\frac{b \ln \left(b x +a \right)}{a^{2}}-\frac{1}{a x}"," ",0,"-1/a^2*b*ln(x)+1/a^2*b*ln(b*x+a)-1/a/x","A"
309,1,41,40,0.048000," ","int(1/(b*x^4+a*x^3),x)","\frac{b^{2} \ln \left(x \right)}{a^{3}}-\frac{b^{2} \ln \left(b x +a \right)}{a^{3}}+\frac{b}{a^{2} x}-\frac{1}{2 a \,x^{2}}"," ",0,"1/a^3*b^2*ln(x)-1/a^3*b^2*ln(b*x+a)+1/a^2*b/x-1/2/a/x^2","A"
310,1,120,92,0.047000," ","int(x^4/(b*x^4+a*x^3)^(1/2),x)","\frac{\sqrt{\left(b x +a \right) x}\, \left(16 \sqrt{b \,x^{2}+a x}\, b^{\frac{7}{2}} x^{2}-15 a^{3} b \ln \left(\frac{2 b x +a +2 \sqrt{b \,x^{2}+a x}\, \sqrt{b}}{2 \sqrt{b}}\right)-20 \sqrt{b \,x^{2}+a x}\, a \,b^{\frac{5}{2}} x +30 \sqrt{b \,x^{2}+a x}\, a^{2} b^{\frac{3}{2}}\right) x}{48 \sqrt{b \,x^{4}+a \,x^{3}}\, b^{\frac{9}{2}}}"," ",0,"1/48*x*((b*x+a)*x)^(1/2)*(16*x^2*(b*x^2+a*x)^(1/2)*b^(7/2)-20*(b*x^2+a*x)^(1/2)*b^(5/2)*x*a+30*(b*x^2+a*x)^(1/2)*b^(3/2)*a^2-15*ln(1/2*(2*b*x+a+2*(b*x^2+a*x)^(1/2)*b^(1/2))/b^(1/2))*a^3*b)/(b*x^4+a*x^3)^(1/2)/b^(9/2)","A"
311,1,98,70,0.053000," ","int(x^3/(b*x^4+a*x^3)^(1/2),x)","\frac{\sqrt{\left(b x +a \right) x}\, \left(3 a^{2} b \ln \left(\frac{2 b x +a +2 \sqrt{b \,x^{2}+a x}\, \sqrt{b}}{2 \sqrt{b}}\right)+4 \sqrt{b \,x^{2}+a x}\, b^{\frac{5}{2}} x -6 \sqrt{b \,x^{2}+a x}\, a \,b^{\frac{3}{2}}\right) x}{8 \sqrt{b \,x^{4}+a \,x^{3}}\, b^{\frac{7}{2}}}"," ",0,"1/8*x*((b*x+a)*x)^(1/2)*(4*x*(b*x^2+a*x)^(1/2)*b^(5/2)-6*(b*x^2+a*x)^(1/2)*b^(3/2)*a+3*ln(1/2*(2*b*x+a+2*(b*x^2+a*x)^(1/2)*b^(1/2))/b^(1/2))*a^2*b)/(b*x^4+a*x^3)^(1/2)/b^(7/2)","A"
312,1,78,48,0.049000," ","int(x^2/(b*x^4+a*x^3)^(1/2),x)","\frac{\sqrt{\left(b x +a \right) x}\, \left(-a b \ln \left(\frac{2 b x +a +2 \sqrt{b \,x^{2}+a x}\, \sqrt{b}}{2 \sqrt{b}}\right)+2 \sqrt{b \,x^{2}+a x}\, b^{\frac{3}{2}}\right) x}{2 \sqrt{b \,x^{4}+a \,x^{3}}\, b^{\frac{5}{2}}}"," ",0,"1/2*x*((b*x+a)*x)^(1/2)*(2*(b*x^2+a*x)^(1/2)*b^(3/2)-a*ln(1/2*(2*b*x+a+2*(b*x^2+a*x)^(1/2)*b^(1/2))/b^(1/2))*b)/(b*x^4+a*x^3)^(1/2)/b^(5/2)","A"
313,1,56,26,0.051000," ","int(x/(b*x^4+a*x^3)^(1/2),x)","\frac{\sqrt{\left(b x +a \right) x}\, x \ln \left(\frac{2 b x +a +2 \sqrt{b \,x^{2}+a x}\, \sqrt{b}}{2 \sqrt{b}}\right)}{\sqrt{b \,x^{4}+a \,x^{3}}\, \sqrt{b}}"," ",0,"1/(b*x^4+a*x^3)^(1/2)*x*((b*x+a)*x)^(1/2)*ln(1/2*(2*b*x+a+2*(b*x^2+a*x)^(1/2)*b^(1/2))/b^(1/2))/b^(1/2)","B"
314,1,25,21,0.048000," ","int(1/(b*x^4+a*x^3)^(1/2),x)","-\frac{2 \left(b x +a \right) x}{\sqrt{b \,x^{4}+a \,x^{3}}\, a}"," ",0,"-2*(b*x+a)*x/a/(b*x^4+a*x^3)^(1/2)","A"
315,1,30,44,0.054000," ","int(1/x/(b*x^4+a*x^3)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(-2 b x +a \right)}{3 \sqrt{b \,x^{4}+a \,x^{3}}\, a^{2}}"," ",0,"-2/3*(b*x+a)*(-2*b*x+a)/a^2/(b*x^4+a*x^3)^(1/2)","A"
316,1,46,68,0.044000," ","int(1/x^2/(b*x^4+a*x^3)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(8 b^{2} x^{2}-4 a b x +3 a^{2}\right)}{15 \sqrt{b \,x^{4}+a \,x^{3}}\, a^{3} x}"," ",0,"-2/15*(b*x+a)*(8*b^2*x^2-4*a*b*x+3*a^2)/x/a^3/(b*x^4+a*x^3)^(1/2)","A"
317,1,57,92,0.046000," ","int(1/x^3/(b*x^4+a*x^3)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(-16 b^{3} x^{3}+8 a \,b^{2} x^{2}-6 a^{2} b x +5 a^{3}\right)}{35 \sqrt{b \,x^{4}+a \,x^{3}}\, a^{4} x^{2}}"," ",0,"-2/35*(b*x+a)*(-16*b^3*x^3+8*a*b^2*x^2-6*a^2*b*x+5*a^3)/x^2/a^4/(b*x^4+a*x^3)^(1/2)","A"
318,1,68,116,0.046000," ","int(1/x^4/(b*x^4+a*x^3)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(128 b^{4} x^{4}-64 a \,b^{3} x^{3}+48 b^{2} x^{2} a^{2}-40 b x \,a^{3}+35 a^{4}\right)}{315 \sqrt{b \,x^{4}+a \,x^{3}}\, a^{5} x^{3}}"," ",0,"-2/315*(b*x+a)*(128*b^4*x^4-64*a*b^3*x^3+48*a^2*b^2*x^2-40*a^3*b*x+35*a^4)/x^3/a^5/(b*x^4+a*x^3)^(1/2)","A"
319,1,23,22,0.045000," ","int(1/(b*x^5+x^3),x)","-b \ln \left(x \right)+\frac{b \ln \left(b \,x^{2}+1\right)}{2}-\frac{1}{2 x^{2}}"," ",0,"-1/2/x^2-b*ln(x)+1/2*b*ln(b*x^2+1)","A"
320,1,23,23,0.050000," ","int(1/(b*x^5-x^3),x)","-b \ln \left(x \right)+\frac{b \ln \left(b \,x^{2}-1\right)}{2}+\frac{1}{2 x^{2}}"," ",0,"1/2*b*ln(b*x^2-1)+1/2/x^2-b*ln(x)","A"
321,1,9,8,0.043000," ","int(1/(a*x+b*x),x)","\frac{\ln \left(x \right)}{a +b}"," ",0,"ln(x)/(a+b)","A"
322,1,11,10,0.034000," ","int(1/(a*x+b*x)^2,x)","-\frac{1}{\left(a +b \right)^{2} x}"," ",0,"-1/(a+b)^2/x","A"
323,1,11,10,0.046000," ","int(1/(a*x+b*x)^3,x)","-\frac{1}{2 \left(a +b \right)^{3} x^{2}}"," ",0,"-1/2/(a+b)^3/x^2","A"
324,1,11,10,0.043000," ","int(1/(a*x^2+b*x^2),x)","-\frac{1}{\left(a +b \right) x}"," ",0,"-1/(a+b)/x","A"
325,1,19,20,0.045000," ","int(1/(a*x^n+b*x^n),x)","-\frac{x \,x^{-n}}{\left(n -1\right) \left(a +b \right)}"," ",0,"-x/(n-1)/(x^n)/(a+b)","A"
326,1,21,20,0.043000," ","int(1/(a*x^n+b*x^n)^2,x)","-\frac{x \,x^{-2 n}}{\left(2 n -1\right) \left(a +b \right)^{2}}"," ",0,"-x/(2*n-1)/(x^n)^2/(a+b)^2","A"
327,1,21,20,0.041000," ","int(1/(a*x^n+b*x^n)^3,x)","-\frac{x \,x^{-3 n}}{\left(3 n -1\right) \left(a +b \right)^{3}}"," ",0,"-x/(3*n-1)/(x^n)^3/(a+b)^3","A"
328,1,135,14,0.048000," ","int((b*x^14+a*x)^12,x)","\frac{1}{169} b^{12} x^{169}+\frac{1}{13} a \,b^{11} x^{156}+\frac{6}{13} a^{2} b^{10} x^{143}+\frac{22}{13} a^{3} b^{9} x^{130}+\frac{55}{13} a^{4} b^{8} x^{117}+\frac{99}{13} a^{5} b^{7} x^{104}+\frac{132}{13} a^{6} b^{6} x^{91}+\frac{132}{13} a^{7} b^{5} x^{78}+\frac{99}{13} a^{8} b^{4} x^{65}+\frac{55}{13} a^{9} b^{3} x^{52}+\frac{22}{13} a^{10} b^{2} x^{39}+\frac{6}{13} a^{11} b \,x^{26}+\frac{1}{13} a^{12} x^{13}"," ",0,"1/169*b^12*x^169+1/13*a*b^11*x^156+6/13*a^2*b^10*x^143+22/13*a^3*b^9*x^130+55/13*a^4*b^8*x^117+99/13*a^5*b^7*x^104+132/13*a^6*b^6*x^91+132/13*a^7*b^5*x^78+99/13*a^8*b^4*x^65+55/13*a^9*b^3*x^52+22/13*a^10*b^2*x^39+6/13*a^11*b*x^26+1/13*a^12*x^13","B"
329,1,135,14,0.039000," ","int(x^12*(b*x^26+a*x)^12,x)","\frac{1}{325} b^{12} x^{325}+\frac{1}{25} a \,b^{11} x^{300}+\frac{6}{25} a^{2} b^{10} x^{275}+\frac{22}{25} a^{3} b^{9} x^{250}+\frac{11}{5} a^{4} b^{8} x^{225}+\frac{99}{25} a^{5} b^{7} x^{200}+\frac{132}{25} a^{6} b^{6} x^{175}+\frac{132}{25} a^{7} b^{5} x^{150}+\frac{99}{25} a^{8} b^{4} x^{125}+\frac{11}{5} a^{9} b^{3} x^{100}+\frac{22}{25} a^{10} b^{2} x^{75}+\frac{6}{25} a^{11} b \,x^{50}+\frac{1}{25} a^{12} x^{25}"," ",0,"1/325*b^12*x^325+1/25*a*b^11*x^300+6/25*a^2*b^10*x^275+22/25*a^3*b^9*x^250+11/5*a^4*b^8*x^225+99/25*a^5*b^7*x^200+132/25*a^6*b^6*x^175+132/25*a^7*b^5*x^150+99/25*a^8*b^4*x^125+11/5*a^9*b^3*x^100+22/25*a^10*b^2*x^75+6/25*a^11*b*x^50+1/25*a^12*x^25","B"
330,1,135,14,0.037000," ","int(x^24*(b*x^38+a*x)^12,x)","\frac{1}{481} b^{12} x^{481}+\frac{1}{37} a \,b^{11} x^{444}+\frac{6}{37} a^{2} b^{10} x^{407}+\frac{22}{37} a^{3} b^{9} x^{370}+\frac{55}{37} a^{4} b^{8} x^{333}+\frac{99}{37} a^{5} b^{7} x^{296}+\frac{132}{37} a^{6} b^{6} x^{259}+\frac{132}{37} a^{7} b^{5} x^{222}+\frac{99}{37} a^{8} b^{4} x^{185}+\frac{55}{37} a^{9} b^{3} x^{148}+\frac{22}{37} a^{10} b^{2} x^{111}+\frac{6}{37} a^{11} b \,x^{74}+\frac{1}{37} a^{12} x^{37}"," ",0,"1/481*b^12*x^481+1/37*a*b^11*x^444+6/37*a^2*b^10*x^407+22/37*a^3*b^9*x^370+55/37*a^4*b^8*x^333+99/37*a^5*b^7*x^296+132/37*a^6*b^6*x^259+132/37*a^7*b^5*x^222+99/37*a^8*b^4*x^185+55/37*a^9*b^3*x^148+22/37*a^10*b^2*x^111+6/37*a^11*b*x^74+1/37*a^12*x^37","B"
331,1,339,25,0.108000," ","int(x^(12*m-12)*(a*x+b*x^(2+12*m))^12,x)","\frac{a^{12} x^{12 m +2}}{\left(12 m +1\right) x}+\frac{6 a^{11} b \,x^{24 m +4}}{\left(12 m +1\right) x^{2}}+\frac{22 a^{10} b^{2} x^{36 m +6}}{\left(12 m +1\right) x^{3}}+\frac{55 a^{9} b^{3} x^{48 m +8}}{\left(12 m +1\right) x^{4}}+\frac{99 a^{8} b^{4} x^{60 m +10}}{\left(12 m +1\right) x^{5}}+\frac{132 a^{7} b^{5} x^{72 m +12}}{\left(12 m +1\right) x^{6}}+\frac{132 a^{6} b^{6} x^{84 m +14}}{\left(12 m +1\right) x^{7}}+\frac{99 a^{5} b^{7} x^{96 m +16}}{\left(12 m +1\right) x^{8}}+\frac{55 a^{4} b^{8} x^{108 m +18}}{\left(12 m +1\right) x^{9}}+\frac{22 a^{3} b^{9} x^{120 m +20}}{\left(12 m +1\right) x^{10}}+\frac{6 a^{2} b^{10} x^{132 m +22}}{\left(12 m +1\right) x^{11}}+\frac{a \,b^{11} x^{144 m +24}}{\left(12 m +1\right) x^{12}}+\frac{b^{12} x^{156 m +26}}{13 \left(12 m +1\right) x^{13}}"," ",0,"1/13/(12*m+1)*b^12/x^13*(x^(2+12*m))^13+1/(12*m+1)*a*b^11/x^12*(x^(2+12*m))^12+6/(12*m+1)*a^2*b^10/x^11*(x^(2+12*m))^11+22/(12*m+1)*a^3*b^9/x^10*(x^(2+12*m))^10+55/(12*m+1)*a^4*b^8/x^9*(x^(2+12*m))^9+99/(12*m+1)*a^5*b^7/x^8*(x^(2+12*m))^8+132/(12*m+1)*a^6*b^6/x^7*(x^(2+12*m))^7+132/(12*m+1)*a^7*b^5/x^6*(x^(2+12*m))^6+99/(12*m+1)*a^8*b^4/x^5*(x^(2+12*m))^5+55/(12*m+1)*a^9*b^3/x^4*(x^(2+12*m))^4+22/(12*m+1)*a^10*b^2/x^3*(x^(2+12*m))^3+6/(12*m+1)*a^11*b/x^2*(x^(2+12*m))^2+1/(12*m+1)*a^12/x*x^(2+12*m)","B"
332,1,135,14,0.047000," ","int((b*x^14+a*x)^12,x)","\frac{1}{169} b^{12} x^{169}+\frac{1}{13} a \,b^{11} x^{156}+\frac{6}{13} a^{2} b^{10} x^{143}+\frac{22}{13} a^{3} b^{9} x^{130}+\frac{55}{13} a^{4} b^{8} x^{117}+\frac{99}{13} a^{5} b^{7} x^{104}+\frac{132}{13} a^{6} b^{6} x^{91}+\frac{132}{13} a^{7} b^{5} x^{78}+\frac{99}{13} a^{8} b^{4} x^{65}+\frac{55}{13} a^{9} b^{3} x^{52}+\frac{22}{13} a^{10} b^{2} x^{39}+\frac{6}{13} a^{11} b \,x^{26}+\frac{1}{13} a^{12} x^{13}"," ",0,"1/169*b^12*x^169+1/13*a*b^11*x^156+6/13*a^2*b^10*x^143+22/13*a^3*b^9*x^130+55/13*a^4*b^8*x^117+99/13*a^5*b^7*x^104+132/13*a^6*b^6*x^91+132/13*a^7*b^5*x^78+99/13*a^8*b^4*x^65+55/13*a^9*b^3*x^52+22/13*a^10*b^2*x^39+6/13*a^11*b*x^26+1/13*a^12*x^13","B"
333,1,135,14,0.043000," ","int((b*x^27+a*x^2)^12,x)","\frac{1}{325} b^{12} x^{325}+\frac{1}{25} a \,b^{11} x^{300}+\frac{6}{25} a^{2} b^{10} x^{275}+\frac{22}{25} a^{3} b^{9} x^{250}+\frac{11}{5} a^{4} b^{8} x^{225}+\frac{99}{25} a^{5} b^{7} x^{200}+\frac{132}{25} a^{6} b^{6} x^{175}+\frac{132}{25} a^{7} b^{5} x^{150}+\frac{99}{25} a^{8} b^{4} x^{125}+\frac{11}{5} a^{9} b^{3} x^{100}+\frac{22}{25} a^{10} b^{2} x^{75}+\frac{6}{25} a^{11} b \,x^{50}+\frac{1}{25} a^{12} x^{25}"," ",0,"1/325*b^12*x^325+1/25*a*b^11*x^300+6/25*a^2*b^10*x^275+22/25*a^3*b^9*x^250+11/5*a^4*b^8*x^225+99/25*a^5*b^7*x^200+132/25*a^6*b^6*x^175+132/25*a^7*b^5*x^150+99/25*a^8*b^4*x^125+11/5*a^9*b^3*x^100+22/25*a^10*b^2*x^75+6/25*a^11*b*x^50+1/25*a^12*x^25","B"
334,1,135,14,0.043000," ","int((b*x^40+a*x^3)^12,x)","\frac{1}{481} b^{12} x^{481}+\frac{1}{37} a \,b^{11} x^{444}+\frac{6}{37} a^{2} b^{10} x^{407}+\frac{22}{37} a^{3} b^{9} x^{370}+\frac{55}{37} a^{4} b^{8} x^{333}+\frac{99}{37} a^{5} b^{7} x^{296}+\frac{132}{37} a^{6} b^{6} x^{259}+\frac{132}{37} a^{7} b^{5} x^{222}+\frac{99}{37} a^{8} b^{4} x^{185}+\frac{55}{37} a^{9} b^{3} x^{148}+\frac{22}{37} a^{10} b^{2} x^{111}+\frac{6}{37} a^{11} b \,x^{74}+\frac{1}{37} a^{12} x^{37}"," ",0,"1/481*b^12*x^481+1/37*a*b^11*x^444+6/37*a^2*b^10*x^407+22/37*a^3*b^9*x^370+55/37*a^4*b^8*x^333+99/37*a^5*b^7*x^296+132/37*a^6*b^6*x^259+132/37*a^7*b^5*x^222+99/37*a^8*b^4*x^185+55/37*a^9*b^3*x^148+22/37*a^10*b^2*x^111+6/37*a^11*b*x^74+1/37*a^12*x^37","B"
335,1,287,25,0.085000," ","int((a*x^m+b*x^(1+13*m))^12,x)","\frac{b^{12} x^{13} x^{156 m}}{13+156 m}+\frac{a \,b^{11} x^{12} x^{144 m}}{12 m +1}+\frac{6 a^{2} b^{10} x^{11} x^{132 m}}{12 m +1}+\frac{22 a^{3} b^{9} x^{10} x^{120 m}}{12 m +1}+\frac{55 a^{4} b^{8} x^{9} x^{108 m}}{12 m +1}+\frac{99 a^{5} b^{7} x^{8} x^{96 m}}{12 m +1}+\frac{132 a^{6} b^{6} x^{7} x^{84 m}}{12 m +1}+\frac{132 a^{7} b^{5} x^{6} x^{72 m}}{12 m +1}+\frac{99 a^{8} b^{4} x^{5} x^{60 m}}{12 m +1}+\frac{55 a^{9} b^{3} x^{4} x^{48 m}}{12 m +1}+\frac{22 a^{10} b^{2} x^{3} x^{36 m}}{12 m +1}+\frac{6 a^{11} b \,x^{2} x^{24 m}}{12 m +1}+\frac{a^{12} x \,x^{12 m}}{12 m +1}"," ",0,"1/13*b^12*x^13/(12*m+1)*(x^m)^156+a*b^11*x^12/(12*m+1)*(x^m)^144+6*a^2*b^10*x^11/(12*m+1)*(x^m)^132+22*a^3*b^9*x^10/(12*m+1)*(x^m)^120+55*a^4*b^8*x^9/(12*m+1)*(x^m)^108+99*a^5*b^7*x^8/(12*m+1)*(x^m)^96+132*a^6*b^6*x^7/(12*m+1)*(x^m)^84+132*a^7*b^5*x^6/(12*m+1)*(x^m)^72+99*a^8*b^4*x^5/(12*m+1)*(x^m)^60+55*a^9*b^3*x^4/(12*m+1)*(x^m)^48+22*a^10*b^2*x^3/(12*m+1)*(x^m)^36+6*a^11*b*x^2/(12*m+1)*(x^m)^24+a^12/(12*m+1)*x*(x^m)^12","B"
336,1,126,25,0.064000," ","int((a*x^m+b*x^(1+6*m))^5,x)","\frac{b^{5} x^{6} x^{30 m}}{6+30 m}+\frac{a \,b^{4} x^{5} x^{25 m}}{5 m +1}+\frac{5 a^{2} b^{3} x^{4} x^{20 m}}{2 \left(5 m +1\right)}+\frac{10 a^{3} b^{2} x^{3} x^{15 m}}{3 \left(5 m +1\right)}+\frac{5 a^{4} b \,x^{2} x^{10 m}}{2 \left(5 m +1\right)}+\frac{a^{5} x \,x^{5 m}}{5 m +1}"," ",0,"1/6*b^5*x^6/(1+5*m)*(x^m)^30+a*b^4*x^5/(1+5*m)*(x^m)^25+5/2*a^2*b^3*x^4/(1+5*m)*(x^m)^20+10/3*a^3*b^2*x^3/(1+5*m)*(x^m)^15+5/2*a^4*b*x^2/(1+5*m)*(x^m)^10+a^5/(1+5*m)*x*(x^m)^5","B"
337,1,39,25,0.068000," ","int(1/(b*x^(1-2*m)+a*x^m)^3,x)","-\frac{\left(2 a \,x^{3 m}+b x \right) x}{2 \left(3 m -1\right) \left(a \,x^{3 m}+b x \right)^{2} a^{2}}"," ",0,"-1/2*x*(2*a*(x^m)^3+b*x)/(-1+3*m)/a^2/(a*(x^m)^3+b*x)^2","A"
338,1,14,13,0.039000," ","int(1/(b/x+a*x),x)","\frac{\ln \left(a \,x^{2}+b \right)}{2 a}"," ",0,"1/2/a*ln(a*x^2+b)","A"
339,1,14,13,0.041000," ","int(1/(b/x^2+a*x),x)","\frac{\ln \left(a \,x^{3}+b \right)}{3 a}"," ",0,"1/3/a*ln(a*x^3+b)","A"
340,1,14,13,0.036000," ","int(1/(b/x^3+a*x),x)","\frac{\ln \left(a \,x^{4}+b \right)}{4 a}"," ",0,"1/4*ln(a*x^4+b)/a","A"
341,1,31,17,0.049000," ","int(1/(b/x+a*x)^3,x)","\frac{b}{4 \left(a \,x^{2}+b \right)^{2} a^{2}}-\frac{1}{2 \left(a \,x^{2}+b \right) a^{2}}"," ",0,"-1/2/a^2/(a*x^2+b)+1/4/a^2*b/(a*x^2+b)^2","A"
342,1,31,17,0.051000," ","int(1/(b/x^3+a*x^2)^3,x)","\frac{b}{10 \left(a \,x^{5}+b \right)^{2} a^{2}}-\frac{1}{5 \left(a \,x^{5}+b \right) a^{2}}"," ",0,"-1/5/a^2/(a*x^5+b)+1/10/a^2*b/(a*x^5+b)^2","A"
343,1,31,17,0.055000," ","int(1/(b/x^5+a*x^3)^3,x)","\frac{b}{16 \left(a \,x^{8}+b \right)^{2} a^{2}}-\frac{1}{8 \left(a \,x^{8}+b \right) a^{2}}"," ",0,"-1/8/a^2/(a*x^8+b)+1/16/a^2*b/(a*x^8+b)^2","A"
344,1,23,22,0.043000," ","int((a/x+b*x)^2,x)","\frac{b^{2} x^{3}}{3}+2 a b x -\frac{a^{2}}{x}"," ",0,"-a^2/x+2*a*b*x+1/3*b^2*x^3","A"
345,1,35,34,0.044000," ","int((a/x+b*x)^3,x)","\frac{b^{3} x^{4}}{4}+\frac{3 a \,b^{2} x^{2}}{2}+3 a^{2} b \ln \left(x \right)-\frac{a^{3}}{2 x^{2}}"," ",0,"-1/2*a^3/x^2+3/2*a*b^2*x^2+1/4*b^3*x^4+3*a^2*b*ln(x)","A"
346,1,45,44,0.048000," ","int((a/x+b*x)^4,x)","\frac{b^{4} x^{5}}{5}+\frac{4 a \,b^{3} x^{3}}{3}+6 a^{2} b^{2} x -\frac{4 a^{3} b}{x}-\frac{a^{4}}{3 x^{3}}"," ",0,"-1/3*a^4/x^3-4*a^3*b/x+6*a^2*b^2*x+4/3*a*b^3*x^3+1/5*b^4*x^5","A"
347,1,156,126,0.108000," ","int(1/(1/x^2+x^3),x)","\frac{2 \sqrt{5}\, \arctan \left(\frac{4 x -\sqrt{5}-1}{\sqrt{10-2 \sqrt{5}}}\right)}{5 \sqrt{10-2 \sqrt{5}}}-\frac{2 \sqrt{5}\, \arctan \left(\frac{4 x +\sqrt{5}-1}{\sqrt{10+2 \sqrt{5}}}\right)}{5 \sqrt{10+2 \sqrt{5}}}+\frac{\ln \left(x +1\right)}{5}+\frac{\sqrt{5}\, \ln \left(2 x^{2}-\sqrt{5}\, x -x +2\right)}{20}-\frac{\ln \left(2 x^{2}-\sqrt{5}\, x -x +2\right)}{20}-\frac{\sqrt{5}\, \ln \left(2 x^{2}+\sqrt{5}\, x -x +2\right)}{20}-\frac{\ln \left(2 x^{2}+\sqrt{5}\, x -x +2\right)}{20}"," ",0,"-1/20*ln(2*x^2+5^(1/2)*x-x+2)*5^(1/2)-1/20*ln(2*x^2+5^(1/2)*x-x+2)-2/5/(10+2*5^(1/2))^(1/2)*arctan((4*x+5^(1/2)-1)/(10+2*5^(1/2))^(1/2))*5^(1/2)+1/20*ln(2*x^2-5^(1/2)*x-x+2)*5^(1/2)-1/20*ln(2*x^2-5^(1/2)*x-x+2)+2/5/(10-2*5^(1/2))^(1/2)*arctan((4*x-5^(1/2)-1)/(10-2*5^(1/2))^(1/2))*5^(1/2)+1/5*ln(x+1)","A"
348,1,363,27,0.211000," ","int(x^p*(a*x^n+b*x^(1+13*n+p))^12,x)","\frac{b^{12} x^{13} x^{156 n} x^{13 p}}{13+156 n +13 p}+\frac{a \,b^{11} x^{12} x^{144 n} x^{12 p}}{12 n +p +1}+\frac{6 a^{2} b^{10} x^{11} x^{132 n} x^{11 p}}{12 n +p +1}+\frac{22 a^{3} b^{9} x^{10} x^{120 n} x^{10 p}}{12 n +p +1}+\frac{55 a^{4} b^{8} x^{9} x^{108 n} x^{9 p}}{12 n +p +1}+\frac{99 a^{5} b^{7} x^{8} x^{96 n} x^{8 p}}{12 n +p +1}+\frac{132 a^{6} b^{6} x^{7} x^{84 n} x^{7 p}}{12 n +p +1}+\frac{132 a^{7} b^{5} x^{6} x^{72 n} x^{6 p}}{12 n +p +1}+\frac{99 a^{8} b^{4} x^{5} x^{60 n} x^{5 p}}{12 n +p +1}+\frac{55 a^{9} b^{3} x^{4} x^{48 n} x^{4 p}}{12 n +p +1}+\frac{22 a^{10} b^{2} x^{3} x^{36 n} x^{3 p}}{12 n +p +1}+\frac{6 a^{11} b \,x^{2} x^{24 n} x^{2 p}}{12 n +p +1}+\frac{a^{12} x \,x^{p} x^{12 n}}{12 n +p +1}"," ",0,"1/13*b^12*x^13*(x^n)^156/(1+12*n+p)*(x^p)^13+a*b^11*x^12*(x^n)^144/(1+12*n+p)*(x^p)^12+6*a^2*b^10*x^11*(x^n)^132/(1+12*n+p)*(x^p)^11+22*a^3*b^9*x^10*(x^n)^120/(1+12*n+p)*(x^p)^10+55*a^4*b^8*x^9*(x^n)^108/(1+12*n+p)*(x^p)^9+99*a^5*b^7*x^8*(x^n)^96/(1+12*n+p)*(x^p)^8+132*a^6*b^6*x^7*(x^n)^84/(1+12*n+p)*(x^p)^7+132*a^7*b^5*x^6*(x^n)^72/(1+12*n+p)*(x^p)^6+99*a^8*b^4*x^5*(x^n)^60/(1+12*n+p)*(x^p)^5+55*a^9*b^3*x^4*(x^n)^48/(1+12*n+p)*(x^p)^4+22*a^10*b^2*x^3*(x^n)^36/(1+12*n+p)*(x^p)^3+6*a^11*b*x^2*(x^n)^24/(1+12*n+p)*(x^p)^2+a^12/(1+12*n+p)*x*(x^n)^12*x^p","B"
349,1,135,14,0.043000," ","int(x^12*(b*x^13+a)^12,x)","\frac{1}{169} b^{12} x^{169}+\frac{1}{13} a \,b^{11} x^{156}+\frac{6}{13} a^{2} b^{10} x^{143}+\frac{22}{13} a^{3} b^{9} x^{130}+\frac{55}{13} a^{4} b^{8} x^{117}+\frac{99}{13} a^{5} b^{7} x^{104}+\frac{132}{13} a^{6} b^{6} x^{91}+\frac{132}{13} a^{7} b^{5} x^{78}+\frac{99}{13} a^{8} b^{4} x^{65}+\frac{55}{13} a^{9} b^{3} x^{52}+\frac{22}{13} a^{10} b^{2} x^{39}+\frac{6}{13} a^{11} b \,x^{26}+\frac{1}{13} a^{12} x^{13}"," ",0,"1/169*b^12*x^169+1/13*a*b^11*x^156+6/13*a^2*b^10*x^143+22/13*a^3*b^9*x^130+55/13*a^4*b^8*x^117+99/13*a^5*b^7*x^104+132/13*a^6*b^6*x^91+132/13*a^7*b^5*x^78+99/13*a^8*b^4*x^65+55/13*a^9*b^3*x^52+22/13*a^10*b^2*x^39+6/13*a^11*b*x^26+1/13*a^12*x^13","B"
350,1,135,14,0.044000," ","int(x^12*(b*x^26+a*x)^12,x)","\frac{1}{325} b^{12} x^{325}+\frac{1}{25} a \,b^{11} x^{300}+\frac{6}{25} a^{2} b^{10} x^{275}+\frac{22}{25} a^{3} b^{9} x^{250}+\frac{11}{5} a^{4} b^{8} x^{225}+\frac{99}{25} a^{5} b^{7} x^{200}+\frac{132}{25} a^{6} b^{6} x^{175}+\frac{132}{25} a^{7} b^{5} x^{150}+\frac{99}{25} a^{8} b^{4} x^{125}+\frac{11}{5} a^{9} b^{3} x^{100}+\frac{22}{25} a^{10} b^{2} x^{75}+\frac{6}{25} a^{11} b \,x^{50}+\frac{1}{25} a^{12} x^{25}"," ",0,"1/325*b^12*x^325+1/25*a*b^11*x^300+6/25*a^2*b^10*x^275+22/25*a^3*b^9*x^250+11/5*a^4*b^8*x^225+99/25*a^5*b^7*x^200+132/25*a^6*b^6*x^175+132/25*a^7*b^5*x^150+99/25*a^8*b^4*x^125+11/5*a^9*b^3*x^100+22/25*a^10*b^2*x^75+6/25*a^11*b*x^50+1/25*a^12*x^25","B"
351,1,135,14,0.039000," ","int(x^12*(b*x^39+a*x^2)^12,x)","\frac{1}{481} b^{12} x^{481}+\frac{1}{37} a \,b^{11} x^{444}+\frac{6}{37} a^{2} b^{10} x^{407}+\frac{22}{37} a^{3} b^{9} x^{370}+\frac{55}{37} a^{4} b^{8} x^{333}+\frac{99}{37} a^{5} b^{7} x^{296}+\frac{132}{37} a^{6} b^{6} x^{259}+\frac{132}{37} a^{7} b^{5} x^{222}+\frac{99}{37} a^{8} b^{4} x^{185}+\frac{55}{37} a^{9} b^{3} x^{148}+\frac{22}{37} a^{10} b^{2} x^{111}+\frac{6}{37} a^{11} b \,x^{74}+\frac{1}{37} a^{12} x^{37}"," ",0,"1/481*b^12*x^481+1/37*a*b^11*x^444+6/37*a^2*b^10*x^407+22/37*a^3*b^9*x^370+55/37*a^4*b^8*x^333+99/37*a^5*b^7*x^296+132/37*a^6*b^6*x^259+132/37*a^7*b^5*x^222+99/37*a^8*b^4*x^185+55/37*a^9*b^3*x^148+22/37*a^10*b^2*x^111+6/37*a^11*b*x^74+1/37*a^12*x^37","B"
352,1,135,14,0.039000," ","int(x^24*(b*x^25+a)^12,x)","\frac{1}{325} b^{12} x^{325}+\frac{1}{25} a \,b^{11} x^{300}+\frac{6}{25} a^{2} b^{10} x^{275}+\frac{22}{25} a^{3} b^{9} x^{250}+\frac{11}{5} a^{4} b^{8} x^{225}+\frac{99}{25} a^{5} b^{7} x^{200}+\frac{132}{25} a^{6} b^{6} x^{175}+\frac{132}{25} a^{7} b^{5} x^{150}+\frac{99}{25} a^{8} b^{4} x^{125}+\frac{11}{5} a^{9} b^{3} x^{100}+\frac{22}{25} a^{10} b^{2} x^{75}+\frac{6}{25} a^{11} b \,x^{50}+\frac{1}{25} a^{12} x^{25}"," ",0,"1/325*b^12*x^325+1/25*a*b^11*x^300+6/25*a^2*b^10*x^275+22/25*a^3*b^9*x^250+11/5*a^4*b^8*x^225+99/25*a^5*b^7*x^200+132/25*a^6*b^6*x^175+132/25*a^7*b^5*x^150+99/25*a^8*b^4*x^125+11/5*a^9*b^3*x^100+22/25*a^10*b^2*x^75+6/25*a^11*b*x^50+1/25*a^12*x^25","B"
353,1,135,14,0.042000," ","int(x^24*(b*x^38+a*x)^12,x)","\frac{1}{481} b^{12} x^{481}+\frac{1}{37} a \,b^{11} x^{444}+\frac{6}{37} a^{2} b^{10} x^{407}+\frac{22}{37} a^{3} b^{9} x^{370}+\frac{55}{37} a^{4} b^{8} x^{333}+\frac{99}{37} a^{5} b^{7} x^{296}+\frac{132}{37} a^{6} b^{6} x^{259}+\frac{132}{37} a^{7} b^{5} x^{222}+\frac{99}{37} a^{8} b^{4} x^{185}+\frac{55}{37} a^{9} b^{3} x^{148}+\frac{22}{37} a^{10} b^{2} x^{111}+\frac{6}{37} a^{11} b \,x^{74}+\frac{1}{37} a^{12} x^{37}"," ",0,"1/481*b^12*x^481+1/37*a*b^11*x^444+6/37*a^2*b^10*x^407+22/37*a^3*b^9*x^370+55/37*a^4*b^8*x^333+99/37*a^5*b^7*x^296+132/37*a^6*b^6*x^259+132/37*a^7*b^5*x^222+99/37*a^8*b^4*x^185+55/37*a^9*b^3*x^148+22/37*a^10*b^2*x^111+6/37*a^11*b*x^74+1/37*a^12*x^37","B"
354,1,135,14,0.043000," ","int(x^36*(b*x^37+a)^12,x)","\frac{1}{481} b^{12} x^{481}+\frac{1}{37} a \,b^{11} x^{444}+\frac{6}{37} a^{2} b^{10} x^{407}+\frac{22}{37} a^{3} b^{9} x^{370}+\frac{55}{37} a^{4} b^{8} x^{333}+\frac{99}{37} a^{5} b^{7} x^{296}+\frac{132}{37} a^{6} b^{6} x^{259}+\frac{132}{37} a^{7} b^{5} x^{222}+\frac{99}{37} a^{8} b^{4} x^{185}+\frac{55}{37} a^{9} b^{3} x^{148}+\frac{22}{37} a^{10} b^{2} x^{111}+\frac{6}{37} a^{11} b \,x^{74}+\frac{1}{37} a^{12} x^{37}"," ",0,"1/481*b^12*x^481+1/37*a*b^11*x^444+6/37*a^2*b^10*x^407+22/37*a^3*b^9*x^370+55/37*a^4*b^8*x^333+99/37*a^5*b^7*x^296+132/37*a^6*b^6*x^259+132/37*a^7*b^5*x^222+99/37*a^8*b^4*x^185+55/37*a^9*b^3*x^148+22/37*a^10*b^2*x^111+6/37*a^11*b*x^74+1/37*a^12*x^37","B"
355,1,36,23,0.051000," ","int(1/(a*x+b*x^n),x)","\frac{n \ln \left(x \right)}{\left(n -1\right) a}-\frac{\ln \left(a x +b \,{\mathrm e}^{n \ln \left(x \right)}\right)}{\left(n -1\right) a}"," ",0,"n/a/(n-1)*ln(x)-1/a/(n-1)*ln(a*x+b*exp(n*ln(x)))","A"
356,1,39,23,0.053000," ","int(1/(a*x+b*x^(n+1)),x)","\frac{\ln \left(x \right)}{a}+\frac{\ln \left(x \right)}{a n}-\frac{\ln \left(a x +b \,{\mathrm e}^{\left(n +1\right) \ln \left(x \right)}\right)}{a n}"," ",0,"1/a*ln(x)+1/a/n*ln(x)-1/a/n*ln(a*x+b*exp((n+1)*ln(x)))","A"
357,1,41,15,0.056000," ","int(1/(a*x+b*x^(-n+1)),x)","\frac{\ln \left(x \right)}{a}-\frac{\ln \left(x \right)}{a n}+\frac{\ln \left(a x +b \,{\mathrm e}^{\left(-n +1\right) \ln \left(x \right)}\right)}{a n}"," ",0,"1/a*ln(x)-1/a/n*ln(x)+1/a/n*ln(a*x+b*exp((-n+1)*ln(x)))","B"
358,1,32,18,0.051000," ","int(1/(2*x+3*x^(n+1)),x)","\frac{\ln \left(x \right)}{2}+\frac{\ln \left(x \right)}{2 n}-\frac{\ln \left(2 x +3 \,{\mathrm e}^{\left(n +1\right) \ln \left(x \right)}\right)}{2 n}"," ",0,"1/2*ln(x)+1/2/n*ln(x)-1/2/n*ln(2*x+3*exp((n+1)*ln(x)))","A"
359,1,34,13,0.050000," ","int(1/(2*x+3*x^(-n+1)),x)","\frac{\ln \left(x \right)}{2}-\frac{\ln \left(x \right)}{2 n}+\frac{\ln \left(2 x +3 \,{\mathrm e}^{\left(-n +1\right) \ln \left(x \right)}\right)}{2 n}"," ",0,"1/2*ln(x)-1/2/n*ln(x)+1/2/n*ln(2*x+3*exp((-n+1)*ln(x)))","B"
360,1,12,10,0.046000," ","int(1/(x-x^(1/2)),x)","-2 \arctanh \left(\sqrt{x}\right)+\ln \left(x -1\right)"," ",0,"ln(x-1)-2*arctanh(x^(1/2))","A"
361,1,116,10,0.436000," ","int(1/(-x^(3/5)+x),x)","2 \ln \left(x^{\frac{1}{5}}+1\right)+\frac{\ln \left(x -1\right)}{2}+\frac{\ln \left(x +1\right)}{2}+2 \ln \left(x^{\frac{1}{5}}-1\right)-\frac{\ln \left(2 x^{\frac{2}{5}}-\sqrt{5}\, x^{\frac{1}{5}}-x^{\frac{1}{5}}+2\right)}{2}-\frac{\ln \left(2 x^{\frac{2}{5}}-\sqrt{5}\, x^{\frac{1}{5}}+x^{\frac{1}{5}}+2\right)}{2}-\frac{\ln \left(2 x^{\frac{2}{5}}+\sqrt{5}\, x^{\frac{1}{5}}-x^{\frac{1}{5}}+2\right)}{2}-\frac{\ln \left(2 x^{\frac{2}{5}}+\sqrt{5}\, x^{\frac{1}{5}}+x^{\frac{1}{5}}+2\right)}{2}"," ",0,"1/2*ln(x+1)+1/2*ln(x-1)+2*ln(x^(1/5)-1)-1/2*ln(-5^(1/2)*x^(1/5)+2*x^(2/5)+x^(1/5)+2)-1/2*ln(5^(1/2)*x^(1/5)+2*x^(2/5)+x^(1/5)+2)-1/2*ln(2*x^(2/5)-5^(1/2)*x^(1/5)-x^(1/5)+2)-1/2*ln(2*x^(2/5)+5^(1/2)*x^(1/5)-x^(1/5)+2)+2*ln(x^(1/5)+1)","B"
362,1,9,8,0.044000," ","int(1/(1/x^(1/3)+x),x)","\frac{3 \ln \left(x^{\frac{4}{3}}+1\right)}{4}"," ",0,"3/4*ln(1+x^(4/3))","A"
363,1,39,20,0.162000," ","int(1/(x+x^(2^(1/2))),x)","\sqrt{2}\, \ln \left(x \right)+2 \ln \left(x \right)-\sqrt{2}\, \ln \left(x +{\mathrm e}^{\sqrt{2}\, \ln \left(x \right)}\right)-\ln \left(x +{\mathrm e}^{\sqrt{2}\, \ln \left(x \right)}\right)"," ",0,"2^(1/2)*ln(x)+2*ln(x)-ln(x+exp(2^(1/2)*ln(x)))*2^(1/2)-ln(x+exp(2^(1/2)*ln(x)))","A"
364,0,0,65,0.866000," ","int(x^(-1-1/2*j)*(a*x^j+b*x^n)^(1/2),x)","\int \sqrt{a \,x^{j}+b \,x^{n}}\, x^{-\frac{j}{2}-1}\, dx"," ",0,"int(x^(-1-1/2*j)*(a*x^j+b*x^n)^(1/2),x)","F"
365,0,0,87,0.950000," ","int((c*x)^(-1/2*j-1)*(a*x^j+b*x^n)^(1/2),x)","\int \sqrt{a \,x^{j}+b \,x^{n}}\, \left(c x \right)^{-\frac{j}{2}-1}\, dx"," ",0,"int((c*x)^(-1/2*j-1)*(a*x^j+b*x^n)^(1/2),x)","F"
366,0,0,75,0.761000," ","int((a*x^3+b*x^n)^(1/2)/(c*x)^(5/2),x)","\int \frac{\sqrt{a \,x^{3}+b \,x^{n}}}{\left(c x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a*x^3+b*x^n)^(1/2)/(c*x)^(5/2),x)","F"
367,0,0,63,0.723000," ","int((a*x^2+b*x^n)^(1/2)/c^2/x^2,x)","\int \frac{\sqrt{a \,x^{2}+b \,x^{n}}}{c^{2} x^{2}}\, dx"," ",0,"int((a*x^2+b*x^n)^(1/2)/c^2/x^2,x)","F"
368,0,0,71,0.971000," ","int((a*x+b*x^n)^(1/2)/(c*x)^(3/2),x)","\int \frac{\sqrt{a x +b \,x^{n}}}{\left(c x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*x+b*x^n)^(1/2)/(c*x)^(3/2),x)","F"
369,1,39,43,0.044000," ","int((b*x^n+a)^(1/2)/c/x,x)","\frac{-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b \,x^{n}+a}}{\sqrt{a}}\right)+2 \sqrt{b \,x^{n}+a}}{c n}"," ",0,"1/c/n*(2*(b*x^n+a)^(1/2)-2*a^(1/2)*arctanh((b*x^n+a)^(1/2)/a^(1/2)))","A"
370,0,0,68,0.715000," ","int((a/x+b*x^n)^(1/2)/(c*x)^(1/2),x)","\int \frac{\sqrt{b \,x^{n}+\frac{a}{x}}}{\sqrt{c x}}\, dx"," ",0,"int((a/x+b*x^n)^(1/2)/(c*x)^(1/2),x)","F"
371,0,0,53,0.716000," ","int((a/x^2+b*x^n)^(1/2),x)","\int \sqrt{b \,x^{n}+\frac{a}{x^{2}}}\, dx"," ",0,"int((a/x^2+b*x^n)^(1/2),x)","F"
372,0,0,69,0.739000," ","int((c*x)^(1/2)*(a/x^3+b*x^n)^(1/2),x)","\int \sqrt{c x}\, \sqrt{b \,x^{n}+\frac{a}{x^{3}}}\, dx"," ",0,"int((c*x)^(1/2)*(a/x^3+b*x^n)^(1/2),x)","F"
373,0,0,125,0.868000," ","int((c*x)^(-1-3/2*j)*(a*x^j+b*x^n)^(3/2),x)","\int \left(a \,x^{j}+b \,x^{n}\right)^{\frac{3}{2}} \left(c x \right)^{-\frac{3 j}{2}-1}\, dx"," ",0,"int((c*x)^(-1-3/2*j)*(a*x^j+b*x^n)^(3/2),x)","F"
374,0,0,106,0.710000," ","int((a*x^3+b*x^n)^(3/2)/(c*x)^(11/2),x)","\int \frac{\left(a \,x^{3}+b \,x^{n}\right)^{\frac{3}{2}}}{\left(c x \right)^{\frac{11}{2}}}\, dx"," ",0,"int((a*x^3+b*x^n)^(3/2)/(c*x)^(11/2),x)","F"
375,0,0,92,0.709000," ","int((a*x^2+b*x^n)^(3/2)/c^4/x^4,x)","\int \frac{\left(a \,x^{2}+b \,x^{n}\right)^{\frac{3}{2}}}{c^{4} x^{4}}\, dx"," ",0,"int((a*x^2+b*x^n)^(3/2)/c^4/x^4,x)","F"
376,0,0,100,0.687000," ","int((a*x+b*x^n)^(3/2)/(c*x)^(5/2),x)","\int \frac{\left(a x +b \,x^{n}\right)^{\frac{3}{2}}}{\left(c x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a*x+b*x^n)^(3/2)/(c*x)^(5/2),x)","F"
377,1,51,61,0.049000," ","int((b*x^n+a)^(3/2)/c/x,x)","\frac{-2 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{b \,x^{n}+a}}{\sqrt{a}}\right)+2 \sqrt{b \,x^{n}+a}\, a +\frac{2 \left(b \,x^{n}+a \right)^{\frac{3}{2}}}{3}}{c n}"," ",0,"1/c/n*(2/3*(b*x^n+a)^(3/2)+2*(b*x^n+a)^(1/2)*a-2*a^(3/2)*arctanh((b*x^n+a)^(1/2)/a^(1/2)))","A"
378,0,0,95,0.668000," ","int((c*x)^(1/2)*(b*x^n+a/x)^(3/2),x)","\int \sqrt{c x}\, \left(b \,x^{n}+\frac{a}{x}\right)^{\frac{3}{2}}\, dx"," ",0,"int((c*x)^(1/2)*(b*x^n+a/x)^(3/2),x)","F"
379,0,0,86,0.696000," ","int(c^2*x^2*(b*x^n+a/x^2)^(3/2),x)","\int \left(b \,x^{n}+\frac{a}{x^{2}}\right)^{\frac{3}{2}} c^{2} x^{2}\, dx"," ",0,"int(c^2*x^2*(b*x^n+a/x^2)^(3/2),x)","F"
380,0,0,100,0.708000," ","int((c*x)^(7/2)*(b*x^n+a/x^3)^(3/2),x)","\int \left(c x \right)^{\frac{7}{2}} \left(b \,x^{n}+\frac{a}{x^{3}}\right)^{\frac{3}{2}}\, dx"," ",0,"int((c*x)^(7/2)*(b*x^n+a/x^3)^(3/2),x)","F"
381,0,0,88,0.727000," ","int(c^5*x^5*(a/x^4+b*x^n)^(3/2),x)","\int \left(b \,x^{n}+\frac{a}{x^{4}}\right)^{\frac{3}{2}} c^{5} x^{5}\, dx"," ",0,"int(c^5*x^5*(a/x^4+b*x^n)^(3/2),x)","F"
382,1,47,43,0.076000," ","int(((b*x+a)/x^2)^(1/2),x)","\frac{2 \sqrt{\frac{b x +a}{x^{2}}}\, \left(-\sqrt{a}\, \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+\sqrt{b x +a}\right) x}{\sqrt{b x +a}}"," ",0,"2*((b*x+a)/x^2)^(1/2)*x*(-a^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2))+(b*x+a)^(1/2))/(b*x+a)^(1/2)","A"
383,1,61,34,0.076000," ","int(((b*x^2+a)/x^2)^(1/2),x)","\frac{\sqrt{\frac{b \,x^{2}+a}{x^{2}}}\, \left(-\sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)+\sqrt{b \,x^{2}+a}\right) x}{\sqrt{b \,x^{2}+a}}"," ",0,"((b*x^2+a)/x^2)^(1/2)*x/(b*x^2+a)^(1/2)*((b*x^2+a)^(1/2)-a^(1/2)*ln(2*(a+(b*x^2+a)^(1/2)*a^(1/2))/x))","A"
384,1,55,39,0.080000," ","int(((b*x^3+a)/x^2)^(1/2),x)","\frac{2 \sqrt{\frac{b \,x^{3}+a}{x^{2}}}\, \left(-\sqrt{a}\, \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)+\sqrt{b \,x^{3}+a}\right) x}{3 \sqrt{b \,x^{3}+a}}"," ",0,"2/3*((b*x^3+a)/x^2)^(1/2)*x*(-arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2)+(b*x^3+a)^(1/2))/(b*x^3+a)^(1/2)","A"
385,1,74,53,1.870000," ","int(((b*x^n+a)/x^2)^(1/2),x)","-\frac{2 \sqrt{\frac{b \,{\mathrm e}^{n \ln \left(x \right)}+a}{x^{2}}}\, \sqrt{a}\, x \arctanh \left(\frac{\sqrt{b \,{\mathrm e}^{n \ln \left(x \right)}+a}}{\sqrt{a}}\right)}{\sqrt{b \,{\mathrm e}^{n \ln \left(x \right)}+a}\, n}+\frac{2 \sqrt{\frac{b \,{\mathrm e}^{n \ln \left(x \right)}+a}{x^{2}}}\, x}{n}"," ",0,"2/n*((b*exp(n*ln(x))+a)/x^2)^(1/2)*x-2*a^(1/2)/n*arctanh((b*exp(n*ln(x))+a)^(1/2)/a^(1/2))*((b*exp(n*ln(x))+a)/x^2)^(1/2)/(b*exp(n*ln(x))+a)^(1/2)*x","A"
386,1,55,45,0.085000," ","int(((b*x-a)/x^2)^(1/2),x)","\frac{2 \sqrt{\frac{b x -a}{x^{2}}}\, \left(-\sqrt{a}\, \arctan \left(\frac{\sqrt{b x -a}}{\sqrt{a}}\right)+\sqrt{b x -a}\right) x}{\sqrt{b x -a}}"," ",0,"2*((b*x-a)/x^2)^(1/2)*x*(-a^(1/2)*arctan((b*x-a)^(1/2)/a^(1/2))+(b*x-a)^(1/2))/(b*x-a)^(1/2)","A"
387,1,81,35,0.087000," ","int(((b*x^2-a)/x^2)^(1/2),x)","\frac{\sqrt{\frac{b \,x^{2}-a}{x^{2}}}\, \left(a \ln \left(\frac{-2 a +2 \sqrt{-a}\, \sqrt{b \,x^{2}-a}}{x}\right)+\sqrt{-a}\, \sqrt{b \,x^{2}-a}\right) x}{\sqrt{-a}\, \sqrt{b \,x^{2}-a}}"," ",0,"((b*x^2-a)/x^2)^(1/2)*x*((-a)^(1/2)*(b*x^2-a)^(1/2)+a*ln(2*((-a)^(1/2)*(b*x^2-a)^(1/2)-a)/x))/(-a)^(1/2)/(b*x^2-a)^(1/2)","B"
388,1,73,41,0.110000," ","int(((b*x^3-a)/x^2)^(1/2),x)","\frac{2 \sqrt{\frac{b \,x^{3}-a}{x^{2}}}\, \left(a \arctanh \left(\frac{\sqrt{b \,x^{3}-a}}{\sqrt{-a}}\right)+\sqrt{b \,x^{3}-a}\, \sqrt{-a}\right) x}{3 \sqrt{b \,x^{3}-a}\, \sqrt{-a}}"," ",0,"2/3*((b*x^3-a)/x^2)^(1/2)*x*((b*x^3-a)^(1/2)*(-a)^(1/2)+a*arctanh((b*x^3-a)^(1/2)/(-a)^(1/2)))/(b*x^3-a)^(1/2)/(-a)^(1/2)","A"
389,1,105,55,1.987000," ","int(((b*x^n-a)/x^2)^(1/2),x)","-\frac{2 \sqrt{\frac{b \,{\mathrm e}^{n \ln \left(x \right)}-a}{x^{2}}}\, \sqrt{a}\, x \arctan \left(\frac{\sqrt{b \,{\mathrm e}^{n \ln \left(x \right)}-a}}{\sqrt{a}}\right)}{\sqrt{b \,{\mathrm e}^{n \ln \left(x \right)}-a}\, n}-\frac{2 \left(-b \,{\mathrm e}^{n \ln \left(x \right)}+a \right) \sqrt{\frac{b \,{\mathrm e}^{n \ln \left(x \right)}-a}{x^{2}}}\, x}{\left(b \,{\mathrm e}^{n \ln \left(x \right)}-a \right) n}"," ",0,"-2*(a-b*exp(n*ln(x)))/n/(b*exp(n*ln(x))-a)*((b*exp(n*ln(x))-a)/x^2)^(1/2)*x-2*a^(1/2)/n*arctan((b*exp(n*ln(x))-a)^(1/2)/a^(1/2))*((b*exp(n*ln(x))-a)/x^2)^(1/2)/(b*exp(n*ln(x))-a)^(1/2)*x","A"
390,0,0,52,0.792000," ","int((c*x)^(-1+1/2*j)/(a*x^j+b*x^n)^(1/2),x)","\int \frac{\left(c x \right)^{\frac{j}{2}-1}}{\sqrt{a \,x^{j}+b \,x^{n}}}\, dx"," ",0,"int((c*x)^(-1+1/2*j)/(a*x^j+b*x^n)^(1/2),x)","F"
391,0,0,41,0.729000," ","int((c*x)^(1/2)/(a*x^3+b*x^n)^(1/2),x)","\int \frac{\sqrt{c x}}{\sqrt{a \,x^{3}+b \,x^{n}}}\, dx"," ",0,"int((c*x)^(1/2)/(a*x^3+b*x^n)^(1/2),x)","F"
392,0,0,31,0.709000," ","int(1/(a*x^2+b*x^n)^(1/2),x)","\int \frac{1}{\sqrt{a \,x^{2}+b \,x^{n}}}\, dx"," ",0,"int(1/(a*x^2+b*x^n)^(1/2),x)","F"
393,0,0,39,0.715000," ","int(1/(c*x)^(1/2)/(a*x+b*x^n)^(1/2),x)","\int \frac{1}{\sqrt{c x}\, \sqrt{a x +b \,x^{n}}}\, dx"," ",0,"int(1/(c*x)^(1/2)/(a*x+b*x^n)^(1/2),x)","F"
394,1,26,25,0.050000," ","int(1/c/x/(b*x^n+a)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{b \,x^{n}+a}}{\sqrt{a}}\right)}{\sqrt{a}\, c n}"," ",0,"-2*arctanh((b*x^n+a)^(1/2)/a^(1/2))/c/n/a^(1/2)","A"
395,0,0,42,0.724000," ","int(1/(c*x)^(3/2)/(b*x^n+a/x)^(1/2),x)","\int \frac{1}{\left(c x \right)^{\frac{3}{2}} \sqrt{b \,x^{n}+\frac{a}{x}}}\, dx"," ",0,"int(1/(c*x)^(3/2)/(b*x^n+a/x)^(1/2),x)","F"
396,0,0,34,0.704000," ","int(1/c^2/x^2/(b*x^n+a/x^2)^(1/2),x)","\int \frac{1}{\sqrt{b \,x^{n}+\frac{a}{x^{2}}}\, c^{2} x^{2}}\, dx"," ",0,"int(1/c^2/x^2/(b*x^n+a/x^2)^(1/2),x)","F"
397,0,0,42,0.723000," ","int(1/(c*x)^(5/2)/(b*x^n+a/x^3)^(1/2),x)","\int \frac{1}{\left(c x \right)^{\frac{5}{2}} \sqrt{b \,x^{n}+\frac{a}{x^{3}}}}\, dx"," ",0,"int(1/(c*x)^(5/2)/(b*x^n+a/x^3)^(1/2),x)","F"
398,0,0,93,0.832000," ","int((c*x)^(-1+3/2*j)/(a*x^j+b*x^n)^(3/2),x)","\int \frac{\left(c x \right)^{\frac{3 j}{2}-1}}{\left(a \,x^{j}+b \,x^{n}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*x)^(-1+3/2*j)/(a*x^j+b*x^n)^(3/2),x)","F"
399,0,0,78,0.731000," ","int((c*x)^(7/2)/(a*x^3+b*x^n)^(3/2),x)","\int \frac{\left(c x \right)^{\frac{7}{2}}}{\left(a \,x^{3}+b \,x^{n}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*x)^(7/2)/(a*x^3+b*x^n)^(3/2),x)","F"
400,0,0,64,0.702000," ","int(c^2*x^2/(a*x^2+b*x^n)^(3/2),x)","\int \frac{c^{2} x^{2}}{\left(a \,x^{2}+b \,x^{n}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(c^2*x^2/(a*x^2+b*x^n)^(3/2),x)","F"
401,0,0,69,0.738000," ","int((c*x)^(1/2)/(a*x+b*x^n)^(3/2),x)","\int \frac{\sqrt{c x}}{\left(a x +b \,x^{n}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*x)^(1/2)/(a*x+b*x^n)^(3/2),x)","F"
402,1,42,46,0.051000," ","int(1/c/x/(b*x^n+a)^(3/2),x)","\frac{-\frac{2 \arctanh \left(\frac{\sqrt{b \,x^{n}+a}}{\sqrt{a}}\right)}{a^{\frac{3}{2}}}+\frac{2}{\sqrt{b \,x^{n}+a}\, a}}{c n}"," ",0,"1/c/n*(-2/a^(3/2)*arctanh((b*x^n+a)^(1/2)/a^(1/2))+2/(b*x^n+a)^(1/2)/a)","A"
403,0,0,74,0.681000," ","int(1/(c*x)^(5/2)/(b*x^n+a/x)^(3/2),x)","\int \frac{1}{\left(c x \right)^{\frac{5}{2}} \left(b \,x^{n}+\frac{a}{x}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(c*x)^(5/2)/(b*x^n+a/x)^(3/2),x)","F"
404,0,0,64,0.720000," ","int(1/c^4/x^4/(b*x^n+a/x^2)^(3/2),x)","\int \frac{1}{\left(b \,x^{n}+\frac{a}{x^{2}}\right)^{\frac{3}{2}} c^{4} x^{4}}\, dx"," ",0,"int(1/c^4/x^4/(b*x^n+a/x^2)^(3/2),x)","F"
405,0,0,74,0.694000," ","int(1/(c*x)^(11/2)/(b*x^n+a/x^3)^(3/2),x)","\int \frac{1}{\left(c x \right)^{\frac{11}{2}} \left(b \,x^{n}+\frac{a}{x^{3}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(c*x)^(11/2)/(b*x^n+a/x^3)^(3/2),x)","F"
406,0,0,64,0.730000," ","int(1/c^7/x^7/(b*x^n+a/x^4)^(3/2),x)","\int \frac{1}{\left(b \,x^{n}+\frac{a}{x^{4}}\right)^{\frac{3}{2}} c^{7} x^{7}}\, dx"," ",0,"int(1/c^7/x^7/(b*x^n+a/x^4)^(3/2),x)","F"
407,1,477,24,0.570000," ","int(1/((b*x^3+a)/x)^(1/2),x)","-\frac{4 \left(b \,x^{3}+a \right) \left(i \sqrt{3}-1\right) \sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)^{2} \sqrt{\frac{2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(\EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)-\EllipticPi \left(\sqrt{-\frac{\left(i \sqrt{3}-3\right) b x}{\left(i \sqrt{3}-1\right) \left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \frac{i \sqrt{3}-1}{i \sqrt{3}-3}, \sqrt{\frac{\left(i \sqrt{3}+3\right) \left(i \sqrt{3}-1\right)}{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}}\right)\right)}{\sqrt{\frac{b \,x^{3}+a}{x}}\, \sqrt{\left(b \,x^{3}+a \right) x}\, \left(i \sqrt{3}-3\right) \sqrt{\frac{\left(-b x +\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}-\left(-a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, b^{2}}"," ",0,"-4*(b*x^3+a)*(I*3^(1/2)-1)*(-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2)*(-b*x+(-a*b^2)^(1/3))^2*((2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(-a*b^2)^(1/3)))^(1/2)*((-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3)))^(1/2)/b^2*(EllipticF((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2))-EllipticPi((-(I*3^(1/2)-3)/(I*3^(1/2)-1)/(-b*x+(-a*b^2)^(1/3))*b*x)^(1/2),(I*3^(1/2)-1)/(I*3^(1/2)-3),((I*3^(1/2)+3)*(I*3^(1/2)-1)/(1+I*3^(1/2))/(I*3^(1/2)-3))^(1/2)))/((b*x^3+a)/x)^(1/2)/((b*x^3+a)*x)^(1/2)/(I*3^(1/2)-3)/((-b*x+(-a*b^2)^(1/3))*(2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3))*(-2*b*x+I*3^(1/2)*(-a*b^2)^(1/3)-(-a*b^2)^(1/3))/b^2*x)^(1/2)","C"
408,1,49,24,0.194000," ","int(1/((b*x^4+a)/x^2)^(1/2),x)","\frac{\sqrt{b \,x^{4}+a}\, \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 \sqrt{\frac{b \,x^{4}+a}{x^{2}}}\, \sqrt{b}\, x}"," ",0,"1/2/((b*x^4+a)/x^2)^(1/2)/x*(b*x^4+a)^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))/b^(1/2)","A"
409,0,0,24,0.115000," ","int(1/((b*x^5+a)/x^3)^(1/2),x)","\int \frac{1}{\sqrt{\frac{b \,x^{5}+a}{x^{3}}}}\, dx"," ",0,"int(1/((b*x^5+a)/x^3)^(1/2),x)","F"
410,0,0,31,0.732000," ","int(1/(x^(2-n)*(b*x^n+a))^(1/2),x)","\int \frac{1}{\sqrt{\left(b \,x^{n}+a \right) x^{-n +2}}}\, dx"," ",0,"int(1/(x^(2-n)*(b*x^n+a))^(1/2),x)","F"
411,1,471,25,6.219000," ","int(1/((-b*x^3+a)/x)^(1/2),x)","\frac{4 \left(b \,x^{3}-a \right) \left(1+i \sqrt{3}\right) \sqrt{-\frac{\left(i \sqrt{3}+3\right) b x}{\left(1+i \sqrt{3}\right) \left(-b x +\left(a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(-b x +\left(a \,b^{2}\right)^{\frac{1}{3}}\right)^{2} \sqrt{\frac{-2 b x +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}-\left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(i \sqrt{3}-1\right) \left(-b x +\left(a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \sqrt{\frac{2 b x +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(1+i \sqrt{3}\right) \left(-b x +\left(a \,b^{2}\right)^{\frac{1}{3}}\right)}}\, \left(\EllipticF \left(\sqrt{-\frac{\left(i \sqrt{3}+3\right) b x}{\left(1+i \sqrt{3}\right) \left(-b x +\left(a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(i \sqrt{3}-3\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(i \sqrt{3}+3\right)}}\right)-\EllipticPi \left(\sqrt{-\frac{\left(i \sqrt{3}+3\right) b x}{\left(1+i \sqrt{3}\right) \left(-b x +\left(a \,b^{2}\right)^{\frac{1}{3}}\right)}}, \frac{1+i \sqrt{3}}{i \sqrt{3}+3}, \sqrt{\frac{\left(i \sqrt{3}-3\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(i \sqrt{3}+3\right)}}\right)\right)}{\sqrt{-\frac{b \,x^{3}-a}{x}}\, \sqrt{-\left(b \,x^{3}-a \right) x}\, \left(i \sqrt{3}+3\right) \sqrt{-\frac{\left(-b x +\left(a \,b^{2}\right)^{\frac{1}{3}}\right) \left(-2 b x +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}-\left(a \,b^{2}\right)^{\frac{1}{3}}\right) \left(2 b x +i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}+\left(a \,b^{2}\right)^{\frac{1}{3}}\right) x}{b^{2}}}\, b^{2}}"," ",0,"4*(b*x^3-a)*(1+I*3^(1/2))*(-(I*3^(1/2)+3)*x*b/(1+I*3^(1/2))/(-b*x+(a*b^2)^(1/3)))^(1/2)*(-b*x+(a*b^2)^(1/3))^2*((I*3^(1/2)*(a*b^2)^(1/3)-2*b*x-(a*b^2)^(1/3))/(I*3^(1/2)-1)/(-b*x+(a*b^2)^(1/3)))^(1/2)*((I*3^(1/2)*(a*b^2)^(1/3)+2*b*x+(a*b^2)^(1/3))/(1+I*3^(1/2))/(-b*x+(a*b^2)^(1/3)))^(1/2)/b^2*(EllipticF((-(I*3^(1/2)+3)*x*b/(1+I*3^(1/2))/(-b*x+(a*b^2)^(1/3)))^(1/2),((I*3^(1/2)-3)*(1+I*3^(1/2))/(I*3^(1/2)-1)/(I*3^(1/2)+3))^(1/2))-EllipticPi((-(I*3^(1/2)+3)*x*b/(1+I*3^(1/2))/(-b*x+(a*b^2)^(1/3)))^(1/2),(1+I*3^(1/2))/(I*3^(1/2)+3),((I*3^(1/2)-3)*(1+I*3^(1/2))/(I*3^(1/2)-1)/(I*3^(1/2)+3))^(1/2)))/(-(b*x^3-a)/x)^(1/2)/(-(b*x^3-a)*x)^(1/2)/(I*3^(1/2)+3)/(-1/b^2*x*(-b*x+(a*b^2)^(1/3))*(I*3^(1/2)*(a*b^2)^(1/3)-2*b*x-(a*b^2)^(1/3))*(I*3^(1/2)*(a*b^2)^(1/3)+2*b*x+(a*b^2)^(1/3)))^(1/2)","C"
412,1,53,25,0.190000," ","int(1/((-b*x^4+a)/x^2)^(1/2),x)","\frac{\sqrt{-b \,x^{4}+a}\, \arctan \left(\frac{\sqrt{b}\, x^{2}}{\sqrt{-b \,x^{4}+a}}\right)}{2 \sqrt{-\frac{b \,x^{4}-a}{x^{2}}}\, \sqrt{b}\, x}"," ",0,"1/2/(-(b*x^4-a)/x^2)^(1/2)/x*(-b*x^4+a)^(1/2)/b^(1/2)*arctan(1/(-b*x^4+a)^(1/2)*b^(1/2)*x^2)","B"
413,0,0,25,0.157000," ","int(1/((-b*x^5+a)/x^3)^(1/2),x)","\int \frac{1}{\sqrt{\frac{-b \,x^{5}+a}{x^{3}}}}\, dx"," ",0,"int(1/((-b*x^5+a)/x^3)^(1/2),x)","F"
414,0,0,32,1.377000," ","int(1/(x^(-n+2)*(-b*x^n+a))^(1/2),x)","\int \frac{1}{\sqrt{\left(-b \,x^{n}+a \right) x^{-n +2}}}\, dx"," ",0,"int(1/(x^(-n+2)*(-b*x^n+a))^(1/2),x)","F"
415,0,0,31,0.760000," ","int(1/(x^n*(a+b*x^(-n+2)))^(1/2),x)","\int \frac{1}{\sqrt{\left(b \,x^{-n +2}+a \right) x^{n}}}\, dx"," ",0,"int(1/(x^n*(a+b*x^(-n+2)))^(1/2),x)","F"
416,0,0,31,2.102000," ","int(1/(x^2*(b+a*x^(n-2)))^(1/2),x)","\int \frac{1}{\sqrt{\left(a \,x^{n -2}+b \right) x^{2}}}\, dx"," ",0,"int(1/(x^2*(b+a*x^(n-2)))^(1/2),x)","F"
417,0,0,31,0.720000," ","int(1/(x*(b*x+a*x^(n-1)))^(1/2),x)","\int \frac{1}{\sqrt{\left(a \,x^{n -1}+b x \right) x}}\, dx"," ",0,"int(1/(x*(b*x+a*x^(n-1)))^(1/2),x)","F"
418,0,0,32,0.696000," ","int(1/(x^n*(a-b*x^(-n+2)))^(1/2),x)","\int \frac{1}{\sqrt{\left(-b \,x^{-n +2}+a \right) x^{n}}}\, dx"," ",0,"int(1/(x^n*(a-b*x^(-n+2)))^(1/2),x)","F"
419,0,0,32,2.152000," ","int(1/(x^2*(-b+a*x^(n-2)))^(1/2),x)","\int \frac{1}{\sqrt{\left(a \,x^{n -2}-b \right) x^{2}}}\, dx"," ",0,"int(1/(x^2*(-b+a*x^(n-2)))^(1/2),x)","F"
420,0,0,32,0.694000," ","int(1/(x*(-b*x+a*x^(n-1)))^(1/2),x)","\int \frac{1}{\sqrt{\left(a \,x^{n -1}-b x \right) x}}\, dx"," ",0,"int(1/(x*(-b*x+a*x^(n-1)))^(1/2),x)","F"
421,0,0,99,0.884000," ","int((c*x)^m*(a*x^j+b*x^n)^(3/2),x)","\int \left(a \,x^{j}+b \,x^{n}\right)^{\frac{3}{2}} \left(c x \right)^{m}\, dx"," ",0,"int((c*x)^m*(a*x^j+b*x^n)^(3/2),x)","F"
422,0,0,94,0.839000," ","int((c*x)^m*(a*x^j+b*x^n)^(1/2),x)","\int \sqrt{a \,x^{j}+b \,x^{n}}\, \left(c x \right)^{m}\, dx"," ",0,"int((c*x)^m*(a*x^j+b*x^n)^(1/2),x)","F"
423,0,0,94,0.820000," ","int((c*x)^m/(a*x^j+b*x^n)^(1/2),x)","\int \frac{\left(c x \right)^{m}}{\sqrt{a \,x^{j}+b \,x^{n}}}\, dx"," ",0,"int((c*x)^m/(a*x^j+b*x^n)^(1/2),x)","F"
424,0,0,103,0.793000," ","int((c*x)^m/(a*x^j+b*x^n)^(3/2),x)","\int \frac{\left(c x \right)^{m}}{\left(a \,x^{j}+b \,x^{n}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*x)^m/(a*x^j+b*x^n)^(3/2),x)","F"
425,0,0,103,0.807000," ","int((c*x)^m/(a*x^j+b*x^n)^(5/2),x)","\int \frac{\left(c x \right)^{m}}{\left(a \,x^{j}+b \,x^{n}\right)^{\frac{5}{2}}}\, dx"," ",0,"int((c*x)^m/(a*x^j+b*x^n)^(5/2),x)","F"
426,0,0,89,0.806000," ","int((a*x^j+b*x^n)^(3/2),x)","\int \left(a \,x^{j}+b \,x^{n}\right)^{\frac{3}{2}}\, dx"," ",0,"int((a*x^j+b*x^n)^(3/2),x)","F"
427,0,0,81,0.847000," ","int((a*x^j+b*x^n)^(1/2),x)","\int \sqrt{a \,x^{j}+b \,x^{n}}\, dx"," ",0,"int((a*x^j+b*x^n)^(1/2),x)","F"
428,0,0,86,0.783000," ","int(1/(a*x^j+b*x^n)^(1/2),x)","\int \frac{1}{\sqrt{a \,x^{j}+b \,x^{n}}}\, dx"," ",0,"int(1/(a*x^j+b*x^n)^(1/2),x)","F"
429,0,0,95,0.773000," ","int(1/(a*x^j+b*x^n)^(3/2),x)","\int \frac{1}{\left(a \,x^{j}+b \,x^{n}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a*x^j+b*x^n)^(3/2),x)","F"
430,0,0,95,0.796000," ","int(1/(a*x^j+b*x^n)^(5/2),x)","\int \frac{1}{\left(a \,x^{j}+b \,x^{n}\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a*x^j+b*x^n)^(5/2),x)","F"
431,1,16,14,0.047000," ","int(((x+1)/x^5)^(1/2),x)","-\frac{2 \left(x +1\right) \sqrt{\frac{x +1}{x^{5}}}\, x}{3}"," ",0,"-2/3*x*(x+1)*((x+1)/x^5)^(1/2)","A"
432,1,18,12,0.054000," ","int((x+x^(5/2))^(1/2),x)","\frac{4 \sqrt{x^{\frac{5}{2}}+x}\, \left(x^{\frac{3}{2}}+1\right)}{9 \sqrt{x}}"," ",0,"4/9*(x+x^(5/2))^(1/2)/x^(1/2)*(x^(3/2)+1)","A"
433,1,7,6,0.044000," ","int(1/(x^(3/2)+x^(1/2)),x)","2 \arctan \left(\sqrt{x}\right)"," ",0,"2*arctan(x^(1/2))","A"
434,1,29,21,0.050000," ","int(x*(x^2*(b*x^3+a))^(1/2),x)","\frac{2 \left(b \,x^{3}+a \right) \sqrt{\left(b \,x^{3}+a \right) x^{2}}}{9 b x}"," ",0,"2/9*(b*x^3+a)*(x^2*(b*x^3+a))^(1/2)/b/x","A"
435,1,29,21,0.044000," ","int(x*(b*x^5+a*x^2)^(1/2),x)","\frac{2 \left(b \,x^{3}+a \right) \sqrt{b \,x^{5}+a \,x^{2}}}{9 b x}"," ",0,"2/9*(b*x^3+a)*(b*x^5+a*x^2)^(1/2)/b/x","A"
436,1,29,21,0.053000," ","int((x^4*(b*x^3+a))^(1/2),x)","\frac{2 \left(b \,x^{3}+a \right) \sqrt{\left(b \,x^{3}+a \right) x^{4}}}{9 b \,x^{2}}"," ",0,"2/9*(b*x^3+a)*(x^4*(b*x^3+a))^(1/2)/b/x^2","A"
437,0,0,738,0.542000," ","int(1/(a*x^(1/3)+b*x^(2/3))^(1/3),x)","\int \frac{1}{\left(b \,x^{\frac{2}{3}}+a \,x^{\frac{1}{3}}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(a*x^(1/3)+b*x^(2/3))^(1/3),x)","F"
438,0,0,362,0.480000," ","int(1/(b*x^(2/3)+a*x^(1/3))^(2/3),x)","\int \frac{1}{\left(b \,x^{\frac{2}{3}}+a \,x^{\frac{1}{3}}\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(b*x^(2/3)+a*x^(1/3))^(2/3),x)","F"
439,0,0,91,0.744000," ","int(x^m*(a*x^j+b*x^n)^p,x)","\int x^{m} \left(a \,x^{j}+b \,x^{n}\right)^{p}\, dx"," ",0,"int(x^m*(a*x^j+b*x^n)^p,x)","F"
440,0,0,72,0.809000," ","int(x^(-p*q-1)*(b*x^n+a*x^q)^p,x)","\int x^{-p q -1} \left(a \,x^{q}+b \,x^{n}\right)^{p}\, dx"," ",0,"int(x^(-p*q-1)*(b*x^n+a*x^q)^p,x)","F"
441,0,0,69,0.760000," ","int(x^(-n*p-1)*(a*x^q+b*x^n)^p,x)","\int x^{-n p -1} \left(a \,x^{q}+b \,x^{n}\right)^{p}\, dx"," ",0,"int(x^(-n*p-1)*(a*x^q+b*x^n)^p,x)","F"
442,0,0,72,0.786000," ","int(x^(-1-n-(p-1)*q)*(a*x^q+b*x^n)^p,x)","\int x^{-n -\left(p -1\right) q -1} \left(a \,x^{q}+b \,x^{n}\right)^{p}\, dx"," ",0,"int(x^(-1-n-(p-1)*q)*(a*x^q+b*x^n)^p,x)","F"
443,0,0,86,0.804000," ","int(x^(-1-n*(p-1)-q)*(a*x^q+b*x^n)^p,x)","\int x^{-\left(p -1\right) n -q -1} \left(a \,x^{q}+b \,x^{n}\right)^{p}\, dx"," ",0,"int(x^(-1-n*(p-1)-q)*(a*x^q+b*x^n)^p,x)","F"
444,0,0,45,0.856000," ","int((a*x^m+b*x^(m*p+m+1))^p,x)","\int \left(a \,x^{m}+b \,x^{m p +m +1}\right)^{p}\, dx"," ",0,"int((a*x^m+b*x^(m*p+m+1))^p,x)","F"
445,0,0,45,0.848000," ","int((x^m*(a+b*x^(m*p+1)))^p,x)","\int \left(\left(b \,x^{m p +1}+a \right) x^{m}\right)^{p}\, dx"," ",0,"int((x^m*(a+b*x^(m*p+1)))^p,x)","F"
446,0,0,47,0.908000," ","int(x^n*(x^m*(a+b*x^(m*p+n+1)))^p,x)","\int x^{n} \left(\left(b \,x^{m p +n +1}+a \right) x^{m}\right)^{p}\, dx"," ",0,"int(x^n*(x^m*(a+b*x^(m*p+n+1)))^p,x)","F"
447,0,0,47,0.882000," ","int(x^n*(a*x^m+b*x^(m*p+m+n+1))^p,x)","\int x^{n} \left(a \,x^{m}+b \,x^{m p +m +n +1}\right)^{p}\, dx"," ",0,"int(x^n*(a*x^m+b*x^(m*p+m+n+1))^p,x)","F"
448,1,40,38,0.188000," ","int((x^(2*n-2)*(b*x^n+a))^(1/2),x)","\frac{2 \sqrt{\frac{\left(b \,x^{n}+a \right) x^{2 n}}{x^{2}}}\, \left(b \,x^{n}+a \right) x \,x^{-n}}{3 b n}"," ",0,"2/3*(1/x^2*(x^n)^2*(b*x^n+a))^(1/2)*(b*x^n+a)/(x^n)*x/b/n","A"
449,1,40,38,0.079000," ","int((x^(3*n-3)*(b*x^n+a))^(1/3),x)","\frac{3 \left(\frac{\left(b \,x^{n}+a \right) x^{3 n}}{x^{3}}\right)^{\frac{1}{3}} \left(b \,x^{n}+a \right) x \,x^{-n}}{4 b n}"," ",0,"3/4*(1/x^3*(x^n)^3*(b*x^n+a))^(1/3)*x/(x^n)*(b*x^n+a)/b/n","A"
450,1,40,38,0.069000," ","int((x^(4*n-4)*(b*x^n+a))^(1/4),x)","\frac{4 \left(\frac{\left(b \,x^{n}+a \right) x^{4 n}}{x^{4}}\right)^{\frac{1}{4}} \left(b \,x^{n}+a \right) x \,x^{-n}}{5 b n}"," ",0,"4/5*(1/x^4*(x^n)^4*(b*x^n+a))^(1/4)*x/(x^n)*(b*x^n+a)/b/n","A"
451,0,0,58,0.720000," ","int((x^((n-1)*p)*(b*x^n+a))^(1/p),x)","\int \left(\left(b \,x^{n}+a \right) x^{\left(n -1\right) p}\right)^{\frac{1}{p}}\, dx"," ",0,"int((x^((n-1)*p)*(b*x^n+a))^(1/p),x)","F"
452,0,0,59,0.726000," ","int((x^((n-1)/p)*(b*x^n+a))^p,x)","\int \left(\left(b \,x^{n}+a \right) x^{\frac{n -1}{p}}\right)^{p}\, dx"," ",0,"int((x^((n-1)/p)*(b*x^n+a))^p,x)","F"
453,0,0,40,1.269000," ","int(x^(-1+n-p*(1+q))*(a*x^n+b*x^p)^q,x)","\int x^{n -\left(q +1\right) p -1} \left(a \,x^{n}+b \,x^{p}\right)^{q}\, dx"," ",0,"int(x^(-1+n-p*(1+q))*(a*x^n+b*x^p)^q,x)","F"
454,0,0,41,0.869000," ","int(x^(-1-n*q-(q+1)*p)*(x^n*(a+b*x^p))^q,x)","\int x^{-n q -\left(q +1\right) p -1} \left(\left(b \,x^{p}+a \right) x^{n}\right)^{q}\, dx"," ",0,"int(x^(-1-n*q-(q+1)*p)*(x^n*(a+b*x^p))^q,x)","F"