1,1,107,0,1.407254," ","integrate(x^3*(B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B x^{3}}{6 \, b} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A x^{2}}{5 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B a x}{8 \, b^{2}} + \frac{\sqrt{b x^{2} + a} B a^{2} x}{16 \, b^{2}} + \frac{B a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{5}{2}}} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a}{15 \, b^{2}}"," ",0,"1/6*(b*x^2 + a)^(3/2)*B*x^3/b + 1/5*(b*x^2 + a)^(3/2)*A*x^2/b - 1/8*(b*x^2 + a)^(3/2)*B*a*x/b^2 + 1/16*sqrt(b*x^2 + a)*B*a^2*x/b^2 + 1/16*B*a^3*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 2/15*(b*x^2 + a)^(3/2)*A*a/b^2","A",0
2,1,86,0,1.362631," ","integrate(x^2*(B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B x^{2}}{5 \, b} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A x}{4 \, b} - \frac{\sqrt{b x^{2} + a} A a x}{8 \, b} - \frac{A a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{3}{2}}} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a}{15 \, b^{2}}"," ",0,"1/5*(b*x^2 + a)^(3/2)*B*x^2/b + 1/4*(b*x^2 + a)^(3/2)*A*x/b - 1/8*sqrt(b*x^2 + a)*A*a*x/b - 1/8*A*a^2*arcsinh(b*x/sqrt(a*b))/b^(3/2) - 2/15*(b*x^2 + a)^(3/2)*B*a/b^2","A",0
3,1,67,0,1.318746," ","integrate(x*(B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B x}{4 \, b} - \frac{\sqrt{b x^{2} + a} B a x}{8 \, b} - \frac{B a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{3}{2}}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{3 \, b}"," ",0,"1/4*(b*x^2 + a)^(3/2)*B*x/b - 1/8*sqrt(b*x^2 + a)*B*a*x/b - 1/8*B*a^2*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 1/3*(b*x^2 + a)^(3/2)*A/b","A",0
4,1,45,0,1.317990," ","integrate((B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{b x^{2} + a} A x + \frac{A a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{b}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{3 \, b}"," ",0,"1/2*sqrt(b*x^2 + a)*A*x + 1/2*A*a*arcsinh(b*x/sqrt(a*b))/sqrt(b) + 1/3*(b*x^2 + a)^(3/2)*B/b","A",0
5,1,59,0,1.360450," ","integrate((B*x+A)*(b*x^2+a)^(1/2)/x,x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{b x^{2} + a} B x + \frac{B a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{b}} - A \sqrt{a} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \sqrt{b x^{2} + a} A"," ",0,"1/2*sqrt(b*x^2 + a)*B*x + 1/2*B*a*arcsinh(b*x/sqrt(a*b))/sqrt(b) - A*sqrt(a)*arcsinh(a/(sqrt(a*b)*abs(x))) + sqrt(b*x^2 + a)*A","A",0
6,1,59,0,1.385726," ","integrate((B*x+A)*(b*x^2+a)^(1/2)/x^2,x, algorithm=""maxima"")","A \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - B \sqrt{a} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \sqrt{b x^{2} + a} B - \frac{\sqrt{b x^{2} + a} A}{x}"," ",0,"A*sqrt(b)*arcsinh(b*x/sqrt(a*b)) - B*sqrt(a)*arcsinh(a/(sqrt(a*b)*abs(x))) + sqrt(b*x^2 + a)*B - sqrt(b*x^2 + a)*A/x","A",0
7,1,83,0,1.361844," ","integrate((B*x+A)*(b*x^2+a)^(1/2)/x^3,x, algorithm=""maxima"")","B \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{A b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, \sqrt{a}} + \frac{\sqrt{b x^{2} + a} A b}{2 \, a} - \frac{\sqrt{b x^{2} + a} B}{x} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{2 \, a x^{2}}"," ",0,"B*sqrt(b)*arcsinh(b*x/sqrt(a*b)) - 1/2*A*b*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + 1/2*sqrt(b*x^2 + a)*A*b/a - sqrt(b*x^2 + a)*B/x - 1/2*(b*x^2 + a)^(3/2)*A/(a*x^2)","A",0
8,1,126,0,1.390095," ","integrate(x^3*(B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B x^{3}}{8 \, b} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A x^{2}}{7 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B a x}{16 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} x}{64 \, b^{2}} + \frac{3 \, \sqrt{b x^{2} + a} B a^{3} x}{128 \, b^{2}} + \frac{3 \, B a^{4} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{5}{2}}} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a}{35 \, b^{2}}"," ",0,"1/8*(b*x^2 + a)^(5/2)*B*x^3/b + 1/7*(b*x^2 + a)^(5/2)*A*x^2/b - 1/16*(b*x^2 + a)^(5/2)*B*a*x/b^2 + 1/64*(b*x^2 + a)^(3/2)*B*a^2*x/b^2 + 3/128*sqrt(b*x^2 + a)*B*a^3*x/b^2 + 3/128*B*a^4*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 2/35*(b*x^2 + a)^(5/2)*A*a/b^2","A",0
9,1,105,0,1.373992," ","integrate(x^2*(B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B x^{2}}{7 \, b} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A x}{6 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A a x}{24 \, b} - \frac{\sqrt{b x^{2} + a} A a^{2} x}{16 \, b} - \frac{A a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{3}{2}}} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a}{35 \, b^{2}}"," ",0,"1/7*(b*x^2 + a)^(5/2)*B*x^2/b + 1/6*(b*x^2 + a)^(5/2)*A*x/b - 1/24*(b*x^2 + a)^(3/2)*A*a*x/b - 1/16*sqrt(b*x^2 + a)*A*a^2*x/b - 1/16*A*a^3*arcsinh(b*x/sqrt(a*b))/b^(3/2) - 2/35*(b*x^2 + a)^(5/2)*B*a/b^2","A",0
10,1,86,0,1.350747," ","integrate(x*(B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B x}{6 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B a x}{24 \, b} - \frac{\sqrt{b x^{2} + a} B a^{2} x}{16 \, b} - \frac{B a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{3}{2}}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{5 \, b}"," ",0,"1/6*(b*x^2 + a)^(5/2)*B*x/b - 1/24*(b*x^2 + a)^(3/2)*B*a*x/b - 1/16*sqrt(b*x^2 + a)*B*a^2*x/b - 1/16*B*a^3*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 1/5*(b*x^2 + a)^(5/2)*A/b","A",0
11,1,61,0,1.411538," ","integrate((B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A x + \frac{3}{8} \, \sqrt{b x^{2} + a} A a x + \frac{3 \, A a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{b}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B}{5 \, b}"," ",0,"1/4*(b*x^2 + a)^(3/2)*A*x + 3/8*sqrt(b*x^2 + a)*A*a*x + 3/8*A*a^2*arcsinh(b*x/sqrt(a*b))/sqrt(b) + 1/5*(b*x^2 + a)^(5/2)*B/b","A",0
12,1,88,0,1.319126," ","integrate((B*x+A)*(b*x^2+a)^(3/2)/x,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B x + \frac{3}{8} \, \sqrt{b x^{2} + a} B a x + \frac{3 \, B a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{b}} - A a^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \frac{1}{3} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A + \sqrt{b x^{2} + a} A a"," ",0,"1/4*(b*x^2 + a)^(3/2)*B*x + 3/8*sqrt(b*x^2 + a)*B*a*x + 3/8*B*a^2*arcsinh(b*x/sqrt(a*b))/sqrt(b) - A*a^(3/2)*arcsinh(a/(sqrt(a*b)*abs(x))) + 1/3*(b*x^2 + a)^(3/2)*A + sqrt(b*x^2 + a)*A*a","A",0
13,1,88,0,1.386393," ","integrate((B*x+A)*(b*x^2+a)^(3/2)/x^2,x, algorithm=""maxima"")","\frac{3}{2} \, \sqrt{b x^{2} + a} A b x + \frac{3}{2} \, A a \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - B a^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \frac{1}{3} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B + \sqrt{b x^{2} + a} B a - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{x}"," ",0,"3/2*sqrt(b*x^2 + a)*A*b*x + 3/2*A*a*sqrt(b)*arcsinh(b*x/sqrt(a*b)) - B*a^(3/2)*arcsinh(a/(sqrt(a*b)*abs(x))) + 1/3*(b*x^2 + a)^(3/2)*B + sqrt(b*x^2 + a)*B*a - (b*x^2 + a)^(3/2)*A/x","A",0
14,1,112,0,1.279341," ","integrate((B*x+A)*(b*x^2+a)^(3/2)/x^3,x, algorithm=""maxima"")","\frac{3}{2} \, \sqrt{b x^{2} + a} B b x + \frac{3}{2} \, B a \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{3}{2} \, A \sqrt{a} b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \frac{3}{2} \, \sqrt{b x^{2} + a} A b + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{2 \, a} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{x} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{2 \, a x^{2}}"," ",0,"3/2*sqrt(b*x^2 + a)*B*b*x + 3/2*B*a*sqrt(b)*arcsinh(b*x/sqrt(a*b)) - 3/2*A*sqrt(a)*b*arcsinh(a/(sqrt(a*b)*abs(x))) + 3/2*sqrt(b*x^2 + a)*A*b + 1/2*(b*x^2 + a)^(3/2)*A*b/a - (b*x^2 + a)^(3/2)*B/x - 1/2*(b*x^2 + a)^(5/2)*A/(a*x^2)","A",0
15,1,145,0,1.358179," ","integrate(x^3*(B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B x^{3}}{10 \, b} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A x^{2}}{9 \, b} - \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a x}{80 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{2} x}{160 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{3} x}{128 \, b^{2}} + \frac{3 \, \sqrt{b x^{2} + a} B a^{4} x}{256 \, b^{2}} + \frac{3 \, B a^{5} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, b^{\frac{5}{2}}} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A a}{63 \, b^{2}}"," ",0,"1/10*(b*x^2 + a)^(7/2)*B*x^3/b + 1/9*(b*x^2 + a)^(7/2)*A*x^2/b - 3/80*(b*x^2 + a)^(7/2)*B*a*x/b^2 + 1/160*(b*x^2 + a)^(5/2)*B*a^2*x/b^2 + 1/128*(b*x^2 + a)^(3/2)*B*a^3*x/b^2 + 3/256*sqrt(b*x^2 + a)*B*a^4*x/b^2 + 3/256*B*a^5*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 2/63*(b*x^2 + a)^(7/2)*A*a/b^2","A",0
16,1,124,0,1.373253," ","integrate(x^2*(B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B x^{2}}{9 \, b} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A x}{8 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A a x}{48 \, b} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{2} x}{192 \, b} - \frac{5 \, \sqrt{b x^{2} + a} A a^{3} x}{128 \, b} - \frac{5 \, A a^{4} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{3}{2}}} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a}{63 \, b^{2}}"," ",0,"1/9*(b*x^2 + a)^(7/2)*B*x^2/b + 1/8*(b*x^2 + a)^(7/2)*A*x/b - 1/48*(b*x^2 + a)^(5/2)*A*a*x/b - 5/192*(b*x^2 + a)^(3/2)*A*a^2*x/b - 5/128*sqrt(b*x^2 + a)*A*a^3*x/b - 5/128*A*a^4*arcsinh(b*x/sqrt(a*b))/b^(3/2) - 2/63*(b*x^2 + a)^(7/2)*B*a/b^2","A",0
17,1,105,0,1.443523," ","integrate(x*(B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B x}{8 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B a x}{48 \, b} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} x}{192 \, b} - \frac{5 \, \sqrt{b x^{2} + a} B a^{3} x}{128 \, b} - \frac{5 \, B a^{4} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{3}{2}}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{7 \, b}"," ",0,"1/8*(b*x^2 + a)^(7/2)*B*x/b - 1/48*(b*x^2 + a)^(5/2)*B*a*x/b - 5/192*(b*x^2 + a)^(3/2)*B*a^2*x/b - 5/128*sqrt(b*x^2 + a)*B*a^3*x/b - 5/128*B*a^4*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 1/7*(b*x^2 + a)^(7/2)*A/b","A",0
18,1,77,0,1.396616," ","integrate((B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A x + \frac{5}{24} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a x + \frac{5}{16} \, \sqrt{b x^{2} + a} A a^{2} x + \frac{5 \, A a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{b}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B}{7 \, b}"," ",0,"1/6*(b*x^2 + a)^(5/2)*A*x + 5/24*(b*x^2 + a)^(3/2)*A*a*x + 5/16*sqrt(b*x^2 + a)*A*a^2*x + 5/16*A*a^3*arcsinh(b*x/sqrt(a*b))/sqrt(b) + 1/7*(b*x^2 + a)^(7/2)*B/b","A",0
19,1,119,0,1.377858," ","integrate((B*x+A)*(b*x^2+a)^(5/2)/x,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B x + \frac{5}{24} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a x + \frac{5}{16} \, \sqrt{b x^{2} + a} B a^{2} x + \frac{5 \, B a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{b}} - A a^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \frac{1}{5} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A + \frac{1}{3} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a + \sqrt{b x^{2} + a} A a^{2}"," ",0,"1/6*(b*x^2 + a)^(5/2)*B*x + 5/24*(b*x^2 + a)^(3/2)*B*a*x + 5/16*sqrt(b*x^2 + a)*B*a^2*x + 5/16*B*a^3*arcsinh(b*x/sqrt(a*b))/sqrt(b) - A*a^(5/2)*arcsinh(a/(sqrt(a*b)*abs(x))) + 1/5*(b*x^2 + a)^(5/2)*A + 1/3*(b*x^2 + a)^(3/2)*A*a + sqrt(b*x^2 + a)*A*a^2","A",0
20,1,120,0,1.403450," ","integrate((B*x+A)*(b*x^2+a)^(5/2)/x^2,x, algorithm=""maxima"")","\frac{5}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b x + \frac{15}{8} \, \sqrt{b x^{2} + a} A a b x + \frac{15}{8} \, A a^{2} \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - B a^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \frac{1}{5} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B + \frac{1}{3} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a + \sqrt{b x^{2} + a} B a^{2} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{x}"," ",0,"5/4*(b*x^2 + a)^(3/2)*A*b*x + 15/8*sqrt(b*x^2 + a)*A*a*b*x + 15/8*A*a^2*sqrt(b)*arcsinh(b*x/sqrt(a*b)) - B*a^(5/2)*arcsinh(a/(sqrt(a*b)*abs(x))) + 1/5*(b*x^2 + a)^(5/2)*B + 1/3*(b*x^2 + a)^(3/2)*B*a + sqrt(b*x^2 + a)*B*a^2 - (b*x^2 + a)^(5/2)*A/x","A",0
21,1,143,0,1.382048," ","integrate((B*x+A)*(b*x^2+a)^(5/2)/x^3,x, algorithm=""maxima"")","\frac{5}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b x + \frac{15}{8} \, \sqrt{b x^{2} + a} B a b x + \frac{15}{8} \, B a^{2} \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{5}{2} \, A a^{\frac{3}{2}} b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \frac{5}{6} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b}{2 \, a} + \frac{5}{2} \, \sqrt{b x^{2} + a} A a b - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B}{x} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{2 \, a x^{2}}"," ",0,"5/4*(b*x^2 + a)^(3/2)*B*b*x + 15/8*sqrt(b*x^2 + a)*B*a*b*x + 15/8*B*a^2*sqrt(b)*arcsinh(b*x/sqrt(a*b)) - 5/2*A*a^(3/2)*b*arcsinh(a/(sqrt(a*b)*abs(x))) + 5/6*(b*x^2 + a)^(3/2)*A*b + 1/2*(b*x^2 + a)^(5/2)*A*b/a + 5/2*sqrt(b*x^2 + a)*A*a*b - (b*x^2 + a)^(5/2)*B/x - 1/2*(b*x^2 + a)^(7/2)*A/(a*x^2)","A",0
22,1,88,0,1.361022," ","integrate(x^3*(B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} B x^{3}}{4 \, b} + \frac{\sqrt{b x^{2} + a} A x^{2}}{3 \, b} - \frac{3 \, \sqrt{b x^{2} + a} B a x}{8 \, b^{2}} + \frac{3 \, B a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{5}{2}}} - \frac{2 \, \sqrt{b x^{2} + a} A a}{3 \, b^{2}}"," ",0,"1/4*sqrt(b*x^2 + a)*B*x^3/b + 1/3*sqrt(b*x^2 + a)*A*x^2/b - 3/8*sqrt(b*x^2 + a)*B*a*x/b^2 + 3/8*B*a^2*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 2/3*sqrt(b*x^2 + a)*A*a/b^2","A",0
23,1,67,0,1.293048," ","integrate(x^2*(B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} B x^{2}}{3 \, b} + \frac{\sqrt{b x^{2} + a} A x}{2 \, b} - \frac{A a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{3}{2}}} - \frac{2 \, \sqrt{b x^{2} + a} B a}{3 \, b^{2}}"," ",0,"1/3*sqrt(b*x^2 + a)*B*x^2/b + 1/2*sqrt(b*x^2 + a)*A*x/b - 1/2*A*a*arcsinh(b*x/sqrt(a*b))/b^(3/2) - 2/3*sqrt(b*x^2 + a)*B*a/b^2","A",0
24,1,47,0,1.326073," ","integrate(x*(B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} B x}{2 \, b} - \frac{B a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{3}{2}}} + \frac{\sqrt{b x^{2} + a} A}{b}"," ",0,"1/2*sqrt(b*x^2 + a)*B*x/b - 1/2*B*a*arcsinh(b*x/sqrt(a*b))/b^(3/2) + sqrt(b*x^2 + a)*A/b","A",0
25,1,29,0,1.355443," ","integrate((B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{A \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}} + \frac{\sqrt{b x^{2} + a} B}{b}"," ",0,"A*arcsinh(b*x/sqrt(a*b))/sqrt(b) + sqrt(b*x^2 + a)*B/b","A",0
26,1,33,0,1.376859," ","integrate((B*x+A)/x/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{B \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}} - \frac{A \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{\sqrt{a}}"," ",0,"B*arcsinh(b*x/sqrt(a*b))/sqrt(b) - A*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a)","A",0
27,1,37,0,1.306254," ","integrate((B*x+A)/x^2/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{B \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{\sqrt{a}} - \frac{\sqrt{b x^{2} + a} A}{a x}"," ",0,"-B*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) - sqrt(b*x^2 + a)*A/(a*x)","A",0
28,1,56,0,1.314531," ","integrate((B*x+A)/x^3/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{A b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{3}{2}}} - \frac{\sqrt{b x^{2} + a} B}{a x} - \frac{\sqrt{b x^{2} + a} A}{2 \, a x^{2}}"," ",0,"1/2*A*b*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) - sqrt(b*x^2 + a)*B/(a*x) - 1/2*sqrt(b*x^2 + a)*A/(a*x^2)","A",0
29,1,85,0,1.352306," ","integrate(x^3*(B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{B x^{3}}{2 \, \sqrt{b x^{2} + a} b} + \frac{A x^{2}}{\sqrt{b x^{2} + a} b} + \frac{3 \, B a x}{2 \, \sqrt{b x^{2} + a} b^{2}} - \frac{3 \, B a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{5}{2}}} + \frac{2 \, A a}{\sqrt{b x^{2} + a} b^{2}}"," ",0,"1/2*B*x^3/(sqrt(b*x^2 + a)*b) + A*x^2/(sqrt(b*x^2 + a)*b) + 3/2*B*a*x/(sqrt(b*x^2 + a)*b^2) - 3/2*B*a*arcsinh(b*x/sqrt(a*b))/b^(5/2) + 2*A*a/(sqrt(b*x^2 + a)*b^2)","A",0
30,1,64,0,1.295563," ","integrate(x^2*(B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{B x^{2}}{\sqrt{b x^{2} + a} b} - \frac{A x}{\sqrt{b x^{2} + a} b} + \frac{A \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}} + \frac{2 \, B a}{\sqrt{b x^{2} + a} b^{2}}"," ",0,"B*x^2/(sqrt(b*x^2 + a)*b) - A*x/(sqrt(b*x^2 + a)*b) + A*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 2*B*a/(sqrt(b*x^2 + a)*b^2)","A",0
31,1,46,0,1.308710," ","integrate(x*(B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","-\frac{B x}{\sqrt{b x^{2} + a} b} + \frac{B \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}} - \frac{A}{\sqrt{b x^{2} + a} b}"," ",0,"-B*x/(sqrt(b*x^2 + a)*b) + B*arcsinh(b*x/sqrt(a*b))/b^(3/2) - A/(sqrt(b*x^2 + a)*b)","A",0
32,1,31,0,1.366485," ","integrate((B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{A x}{\sqrt{b x^{2} + a} a} - \frac{B}{\sqrt{b x^{2} + a} b}"," ",0,"A*x/(sqrt(b*x^2 + a)*a) - B/(sqrt(b*x^2 + a)*b)","A",0
33,1,48,0,1.299137," ","integrate((B*x+A)/x/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{B x}{\sqrt{b x^{2} + a} a} - \frac{A \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{a^{\frac{3}{2}}} + \frac{A}{\sqrt{b x^{2} + a} a}"," ",0,"B*x/(sqrt(b*x^2 + a)*a) - A*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) + A/(sqrt(b*x^2 + a)*a)","A",0
34,1,68,0,1.319115," ","integrate((B*x+A)/x^2/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, A b x}{\sqrt{b x^{2} + a} a^{2}} - \frac{B \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{a^{\frac{3}{2}}} + \frac{B}{\sqrt{b x^{2} + a} a} - \frac{A}{\sqrt{b x^{2} + a} a x}"," ",0,"-2*A*b*x/(sqrt(b*x^2 + a)*a^2) - B*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) + B/(sqrt(b*x^2 + a)*a) - A/(sqrt(b*x^2 + a)*a*x)","A",0
35,1,89,0,1.353415," ","integrate((B*x+A)/x^3/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, B b x}{\sqrt{b x^{2} + a} a^{2}} + \frac{3 \, A b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{5}{2}}} - \frac{3 \, A b}{2 \, \sqrt{b x^{2} + a} a^{2}} - \frac{B}{\sqrt{b x^{2} + a} a x} - \frac{A}{2 \, \sqrt{b x^{2} + a} a x^{2}}"," ",0,"-2*B*b*x/(sqrt(b*x^2 + a)*a^2) + 3/2*A*b*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) - 3/2*A*b/(sqrt(b*x^2 + a)*a^2) - B/(sqrt(b*x^2 + a)*a*x) - 1/2*A/(sqrt(b*x^2 + a)*a*x^2)","A",0
36,1,102,0,1.408551," ","integrate(x^3*(B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, B x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)} - \frac{A x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} - \frac{B x}{3 \, \sqrt{b x^{2} + a} b^{2}} + \frac{B \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{5}{2}}} - \frac{2 \, A a}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}"," ",0,"-1/3*B*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2)) - A*x^2/((b*x^2 + a)^(3/2)*b) - 1/3*B*x/(sqrt(b*x^2 + a)*b^2) + B*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 2/3*A*a/((b*x^2 + a)^(3/2)*b^2)","A",0
37,1,70,0,1.359563," ","integrate(x^2*(B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","-\frac{B x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} - \frac{A x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{A x}{3 \, \sqrt{b x^{2} + a} a b} - \frac{2 \, B a}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}"," ",0,"-B*x^2/((b*x^2 + a)^(3/2)*b) - 1/3*A*x/((b*x^2 + a)^(3/2)*b) + 1/3*A*x/(sqrt(b*x^2 + a)*a*b) - 2/3*B*a/((b*x^2 + a)^(3/2)*b^2)","A",0
38,1,51,0,1.311031," ","integrate(x*(B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","-\frac{B x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{B x}{3 \, \sqrt{b x^{2} + a} a b} - \frac{A}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b}"," ",0,"-1/3*B*x/((b*x^2 + a)^(3/2)*b) + 1/3*B*x/(sqrt(b*x^2 + a)*a*b) - 1/3*A/((b*x^2 + a)^(3/2)*b)","A",0
39,1,48,0,1.367177," ","integrate((B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{2 \, A x}{3 \, \sqrt{b x^{2} + a} a^{2}} + \frac{A x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{B}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b}"," ",0,"2/3*A*x/(sqrt(b*x^2 + a)*a^2) + 1/3*A*x/((b*x^2 + a)^(3/2)*a) - 1/3*B/((b*x^2 + a)^(3/2)*b)","A",0
40,1,80,0,1.366660," ","integrate((B*x+A)/x/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{2 \, B x}{3 \, \sqrt{b x^{2} + a} a^{2}} + \frac{B x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{A \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{a^{\frac{5}{2}}} + \frac{A}{\sqrt{b x^{2} + a} a^{2}} + \frac{A}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a}"," ",0,"2/3*B*x/(sqrt(b*x^2 + a)*a^2) + 1/3*B*x/((b*x^2 + a)^(3/2)*a) - A*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) + A/(sqrt(b*x^2 + a)*a^2) + 1/3*A/((b*x^2 + a)^(3/2)*a)","A",0
41,1,100,0,1.341606," ","integrate((B*x+A)/x^2/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","-\frac{8 \, A b x}{3 \, \sqrt{b x^{2} + a} a^{3}} - \frac{4 \, A b x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2}} - \frac{B \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{a^{\frac{5}{2}}} + \frac{B}{\sqrt{b x^{2} + a} a^{2}} + \frac{B}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{A}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a x}"," ",0,"-8/3*A*b*x/(sqrt(b*x^2 + a)*a^3) - 4/3*A*b*x/((b*x^2 + a)^(3/2)*a^2) - B*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) + B/(sqrt(b*x^2 + a)*a^2) + 1/3*B/((b*x^2 + a)^(3/2)*a) - A/((b*x^2 + a)^(3/2)*a*x)","A",0
42,1,122,0,1.341613," ","integrate((B*x+A)/x^3/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","-\frac{8 \, B b x}{3 \, \sqrt{b x^{2} + a} a^{3}} - \frac{4 \, B b x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2}} + \frac{5 \, A b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{7}{2}}} - \frac{5 \, A b}{2 \, \sqrt{b x^{2} + a} a^{3}} - \frac{5 \, A b}{6 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2}} - \frac{B}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a x} - \frac{A}{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a x^{2}}"," ",0,"-8/3*B*b*x/(sqrt(b*x^2 + a)*a^3) - 4/3*B*b*x/((b*x^2 + a)^(3/2)*a^2) + 5/2*A*b*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(7/2) - 5/2*A*b/(sqrt(b*x^2 + a)*a^3) - 5/6*A*b/((b*x^2 + a)^(3/2)*a^2) - B/((b*x^2 + a)^(3/2)*a*x) - 1/2*A/((b*x^2 + a)^(3/2)*a*x^2)","A",0
43,1,28,0,2.969461," ","integrate((1-x)*x/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} x - \sqrt{-x^{2} + 1} - \frac{1}{2} \, \arcsin\left(x\right)"," ",0,"1/2*sqrt(-x^2 + 1)*x - sqrt(-x^2 + 1) - 1/2*arcsin(x)","A",0
44,1,28,0,2.888524," ","integrate((-x^2+x)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} x - \sqrt{-x^{2} + 1} - \frac{1}{2} \, \arcsin\left(x\right)"," ",0,"1/2*sqrt(-x^2 + 1)*x - sqrt(-x^2 + 1) - 1/2*arcsin(x)","A",0
45,1,22,0,2.876283," ","integrate((x^2+3)/(x^2-3),x, algorithm=""maxima"")","\sqrt{3} \log\left(\frac{x - \sqrt{3}}{x + \sqrt{3}}\right) + x"," ",0,"sqrt(3)*log((x - sqrt(3))/(x + sqrt(3))) + x","A",0
46,1,6,0,2.972217," ","integrate((x^2-1)/(x^2+1),x, algorithm=""maxima"")","x - 2 \, \arctan\left(x\right)"," ",0,"x - 2*arctan(x)","A",0
47,1,435,0,1.679938," ","integrate(x^7*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{C x^{8}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{1}{35} \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} B x + \frac{8 \, C a x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{A x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{B x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{15 \, b} - \frac{B x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{3 \, b^{2}} + \frac{16 \, C a^{2} x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} - \frac{2 \, A a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{B a x^{3}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} + \frac{64 \, C a^{3} x^{2}}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}} - \frac{8 \, A a^{2} x^{2}}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{139 \, B x}{105 \, \sqrt{b x^{2} + a} b^{4}} + \frac{17 \, B a x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}} - \frac{29 \, B a^{2} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} + \frac{B \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{9}{2}}} + \frac{128 \, C a^{4}}{35 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{5}} - \frac{16 \, A a^{3}}{35 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}"," ",0,"C*x^8/((b*x^2 + a)^(7/2)*b) - 1/35*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*B*x + 8*C*a*x^6/((b*x^2 + a)^(7/2)*b^2) - A*x^6/((b*x^2 + a)^(7/2)*b) - 1/15*B*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b - 1/3*B*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^2 + 16*C*a^2*x^4/((b*x^2 + a)^(7/2)*b^3) - 2*A*a*x^4/((b*x^2 + a)^(7/2)*b^2) - B*a*x^3/((b*x^2 + a)^(5/2)*b^3) + 64/5*C*a^3*x^2/((b*x^2 + a)^(7/2)*b^4) - 8/5*A*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 139/105*B*x/(sqrt(b*x^2 + a)*b^4) + 17/105*B*a*x/((b*x^2 + a)^(3/2)*b^4) - 29/35*B*a^2*x/((b*x^2 + a)^(5/2)*b^4) + B*arcsinh(b*x/sqrt(a*b))/b^(9/2) + 128/35*C*a^4/((b*x^2 + a)^(7/2)*b^5) - 16/35*A*a^3/((b*x^2 + a)^(7/2)*b^4)","B",0
48,1,447,0,1.634518," ","integrate(x^6*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{1}{35} \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} C x - \frac{B x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{C x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{15 \, b} - \frac{A x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{C x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{3 \, b^{2}} - \frac{2 \, B a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{C a x^{3}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{5 \, A a x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{8 \, B a^{2} x^{2}}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{139 \, C x}{105 \, \sqrt{b x^{2} + a} b^{4}} + \frac{17 \, C a x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}} - \frac{29 \, C a^{2} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} + \frac{A x}{14 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{A x}{7 \, \sqrt{b x^{2} + a} a b^{3}} + \frac{3 \, A a x}{56 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{15 \, A a^{2} x}{56 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{C \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{9}{2}}} - \frac{16 \, B a^{3}}{35 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}"," ",0,"-1/35*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*C*x - B*x^6/((b*x^2 + a)^(7/2)*b) - 1/15*C*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b - 1/2*A*x^5/((b*x^2 + a)^(7/2)*b) - 1/3*C*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^2 - 2*B*a*x^4/((b*x^2 + a)^(7/2)*b^2) - C*a*x^3/((b*x^2 + a)^(5/2)*b^3) - 5/8*A*a*x^3/((b*x^2 + a)^(7/2)*b^2) - 8/5*B*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 139/105*C*x/(sqrt(b*x^2 + a)*b^4) + 17/105*C*a*x/((b*x^2 + a)^(3/2)*b^4) - 29/35*C*a^2*x/((b*x^2 + a)^(5/2)*b^4) + 1/14*A*x/((b*x^2 + a)^(3/2)*b^3) + 1/7*A*x/(sqrt(b*x^2 + a)*a*b^3) + 3/56*A*a*x/((b*x^2 + a)^(5/2)*b^3) - 15/56*A*a^2*x/((b*x^2 + a)^(7/2)*b^3) + C*arcsinh(b*x/sqrt(a*b))/b^(9/2) - 16/35*B*a^3/((b*x^2 + a)^(7/2)*b^4)","B",0
49,1,240,0,1.442788," ","integrate(x^5*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{C x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{B x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{2 \, C a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{A x^{4}}{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{5 \, B a x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{8 \, C a^{2} x^{2}}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} - \frac{4 \, A a x^{2}}{15 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{B x}{14 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{B x}{7 \, \sqrt{b x^{2} + a} a b^{3}} + \frac{3 \, B a x}{56 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{15 \, B a^{2} x}{56 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} - \frac{16 \, C a^{3}}{35 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}} - \frac{8 \, A a^{2}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}}"," ",0,"-C*x^6/((b*x^2 + a)^(7/2)*b) - 1/2*B*x^5/((b*x^2 + a)^(7/2)*b) - 2*C*a*x^4/((b*x^2 + a)^(7/2)*b^2) - 1/3*A*x^4/((b*x^2 + a)^(7/2)*b) - 5/8*B*a*x^3/((b*x^2 + a)^(7/2)*b^2) - 8/5*C*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) - 4/15*A*a*x^2/((b*x^2 + a)^(7/2)*b^2) + 1/14*B*x/((b*x^2 + a)^(3/2)*b^3) + 1/7*B*x/(sqrt(b*x^2 + a)*a*b^3) + 3/56*B*a*x/((b*x^2 + a)^(5/2)*b^3) - 15/56*B*a^2*x/((b*x^2 + a)^(7/2)*b^3) - 16/35*C*a^3/((b*x^2 + a)^(7/2)*b^4) - 8/105*A*a^2/((b*x^2 + a)^(7/2)*b^3)","B",0
50,1,253,0,1.417765," ","integrate(x^4*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{C x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{B x^{4}}{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{5 \, C a x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{A x^{3}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{4 \, B a x^{2}}{15 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{C x}{14 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{C x}{7 \, \sqrt{b x^{2} + a} a b^{3}} + \frac{3 \, C a x}{56 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{15 \, C a^{2} x}{56 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{3 \, A x}{140 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{2 \, A x}{35 \, \sqrt{b x^{2} + a} a^{2} b^{2}} + \frac{A x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2}} - \frac{3 \, A a x}{28 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{8 \, B a^{2}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}}"," ",0,"-1/2*C*x^5/((b*x^2 + a)^(7/2)*b) - 1/3*B*x^4/((b*x^2 + a)^(7/2)*b) - 5/8*C*a*x^3/((b*x^2 + a)^(7/2)*b^2) - 1/4*A*x^3/((b*x^2 + a)^(7/2)*b) - 4/15*B*a*x^2/((b*x^2 + a)^(7/2)*b^2) + 1/14*C*x/((b*x^2 + a)^(3/2)*b^3) + 1/7*C*x/(sqrt(b*x^2 + a)*a*b^3) + 3/56*C*a*x/((b*x^2 + a)^(5/2)*b^3) - 15/56*C*a^2*x/((b*x^2 + a)^(7/2)*b^3) + 3/140*A*x/((b*x^2 + a)^(5/2)*b^2) + 2/35*A*x/(sqrt(b*x^2 + a)*a^2*b^2) + 1/35*A*x/((b*x^2 + a)^(3/2)*a*b^2) - 3/28*A*a*x/((b*x^2 + a)^(7/2)*b^2) - 8/105*B*a^2/((b*x^2 + a)^(7/2)*b^3)","A",0
51,1,179,0,1.380114," ","integrate(x^3*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{C x^{4}}{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{B x^{3}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{4 \, C a x^{2}}{15 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{A x^{2}}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{3 \, B x}{140 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{2 \, B x}{35 \, \sqrt{b x^{2} + a} a^{2} b^{2}} + \frac{B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2}} - \frac{3 \, B a x}{28 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{8 \, C a^{2}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} - \frac{2 \, A a}{35 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}}"," ",0,"-1/3*C*x^4/((b*x^2 + a)^(7/2)*b) - 1/4*B*x^3/((b*x^2 + a)^(7/2)*b) - 4/15*C*a*x^2/((b*x^2 + a)^(7/2)*b^2) - 1/5*A*x^2/((b*x^2 + a)^(7/2)*b) + 3/140*B*x/((b*x^2 + a)^(5/2)*b^2) + 2/35*B*x/(sqrt(b*x^2 + a)*a^2*b^2) + 1/35*B*x/((b*x^2 + a)^(3/2)*a*b^2) - 3/28*B*a*x/((b*x^2 + a)^(7/2)*b^2) - 8/105*C*a^2/((b*x^2 + a)^(7/2)*b^3) - 2/35*A*a/((b*x^2 + a)^(7/2)*b^2)","A",0
52,1,197,0,1.419514," ","integrate(x^2*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{C x^{3}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{B x^{2}}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{3 \, C x}{140 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{2 \, C x}{35 \, \sqrt{b x^{2} + a} a^{2} b^{2}} + \frac{C x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2}} - \frac{3 \, C a x}{28 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{A x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{8 \, A x}{105 \, \sqrt{b x^{2} + a} a^{3} b} + \frac{4 \, A x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b} + \frac{A x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b} - \frac{2 \, B a}{35 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}}"," ",0,"-1/4*C*x^3/((b*x^2 + a)^(7/2)*b) - 1/5*B*x^2/((b*x^2 + a)^(7/2)*b) + 3/140*C*x/((b*x^2 + a)^(5/2)*b^2) + 2/35*C*x/(sqrt(b*x^2 + a)*a^2*b^2) + 1/35*C*x/((b*x^2 + a)^(3/2)*a*b^2) - 3/28*C*a*x/((b*x^2 + a)^(7/2)*b^2) - 1/7*A*x/((b*x^2 + a)^(7/2)*b) + 8/105*A*x/(sqrt(b*x^2 + a)*a^3*b) + 4/105*A*x/((b*x^2 + a)^(3/2)*a^2*b) + 1/35*A*x/((b*x^2 + a)^(5/2)*a*b) - 2/35*B*a/((b*x^2 + a)^(7/2)*b^2)","A",0
53,1,123,0,1.340934," ","integrate(x*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{C x^{2}}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{B x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{8 \, B x}{105 \, \sqrt{b x^{2} + a} a^{3} b} + \frac{4 \, B x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b} + \frac{B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b} - \frac{2 \, C a}{35 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{A}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b}"," ",0,"-1/5*C*x^2/((b*x^2 + a)^(7/2)*b) - 1/7*B*x/((b*x^2 + a)^(7/2)*b) + 8/105*B*x/(sqrt(b*x^2 + a)*a^3*b) + 4/105*B*x/((b*x^2 + a)^(3/2)*a^2*b) + 1/35*B*x/((b*x^2 + a)^(5/2)*a*b) - 2/35*C*a/((b*x^2 + a)^(7/2)*b^2) - 1/7*A/((b*x^2 + a)^(7/2)*b)","A",0
54,1,153,0,1.334069," ","integrate((C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{16 \, A x}{35 \, \sqrt{b x^{2} + a} a^{4}} + \frac{8 \, A x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{6 \, A x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{A x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} - \frac{C x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{8 \, C x}{105 \, \sqrt{b x^{2} + a} a^{3} b} + \frac{4 \, C x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b} + \frac{C x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b} - \frac{B}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b}"," ",0,"16/35*A*x/(sqrt(b*x^2 + a)*a^4) + 8/35*A*x/((b*x^2 + a)^(3/2)*a^3) + 6/35*A*x/((b*x^2 + a)^(5/2)*a^2) + 1/7*A*x/((b*x^2 + a)^(7/2)*a) - 1/7*C*x/((b*x^2 + a)^(7/2)*b) + 8/105*C*x/(sqrt(b*x^2 + a)*a^3*b) + 4/105*C*x/((b*x^2 + a)^(3/2)*a^2*b) + 1/35*C*x/((b*x^2 + a)^(5/2)*a*b) - 1/7*B/((b*x^2 + a)^(7/2)*b)","A",0
55,1,157,0,1.448071," ","integrate((C*x^2+B*x+A)/x/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{16 \, B x}{35 \, \sqrt{b x^{2} + a} a^{4}} + \frac{8 \, B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{6 \, B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{B x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} - \frac{A \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{a^{\frac{9}{2}}} + \frac{A}{\sqrt{b x^{2} + a} a^{4}} + \frac{A}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{A}{5 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{A}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} - \frac{C}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b}"," ",0,"16/35*B*x/(sqrt(b*x^2 + a)*a^4) + 8/35*B*x/((b*x^2 + a)^(3/2)*a^3) + 6/35*B*x/((b*x^2 + a)^(5/2)*a^2) + 1/7*B*x/((b*x^2 + a)^(7/2)*a) - A*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(9/2) + A/(sqrt(b*x^2 + a)*a^4) + 1/3*A/((b*x^2 + a)^(3/2)*a^3) + 1/5*A/((b*x^2 + a)^(5/2)*a^2) + 1/7*A/((b*x^2 + a)^(7/2)*a) - 1/7*C/((b*x^2 + a)^(7/2)*b)","A",0
56,1,228,0,1.411892," ","integrate((C*x^2+B*x+A)/x^2/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{16 \, C x}{35 \, \sqrt{b x^{2} + a} a^{4}} + \frac{8 \, C x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{6 \, C x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{C x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} - \frac{128 \, A b x}{35 \, \sqrt{b x^{2} + a} a^{5}} - \frac{64 \, A b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4}} - \frac{48 \, A b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3}} - \frac{8 \, A b x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2}} - \frac{B \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{a^{\frac{9}{2}}} + \frac{B}{\sqrt{b x^{2} + a} a^{4}} + \frac{B}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{B}{5 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{B}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} - \frac{A}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a x}"," ",0,"16/35*C*x/(sqrt(b*x^2 + a)*a^4) + 8/35*C*x/((b*x^2 + a)^(3/2)*a^3) + 6/35*C*x/((b*x^2 + a)^(5/2)*a^2) + 1/7*C*x/((b*x^2 + a)^(7/2)*a) - 128/35*A*b*x/(sqrt(b*x^2 + a)*a^5) - 64/35*A*b*x/((b*x^2 + a)^(3/2)*a^4) - 48/35*A*b*x/((b*x^2 + a)^(5/2)*a^3) - 8/7*A*b*x/((b*x^2 + a)^(7/2)*a^2) - B*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(9/2) + B/(sqrt(b*x^2 + a)*a^4) + 1/3*B/((b*x^2 + a)^(3/2)*a^3) + 1/5*B/((b*x^2 + a)^(5/2)*a^2) + 1/7*B/((b*x^2 + a)^(7/2)*a) - A/((b*x^2 + a)^(7/2)*a*x)","A",0
57,1,265,0,1.494929," ","integrate((C*x^2+B*x+A)/x^3/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{128 \, B b x}{35 \, \sqrt{b x^{2} + a} a^{5}} - \frac{64 \, B b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4}} - \frac{48 \, B b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3}} - \frac{8 \, B b x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2}} - \frac{C \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{a^{\frac{9}{2}}} + \frac{9 \, A b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{11}{2}}} + \frac{C}{\sqrt{b x^{2} + a} a^{4}} + \frac{C}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{C}{5 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{C}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} - \frac{9 \, A b}{2 \, \sqrt{b x^{2} + a} a^{5}} - \frac{3 \, A b}{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4}} - \frac{9 \, A b}{10 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3}} - \frac{9 \, A b}{14 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2}} - \frac{B}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a x} - \frac{A}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a x^{2}}"," ",0,"-128/35*B*b*x/(sqrt(b*x^2 + a)*a^5) - 64/35*B*b*x/((b*x^2 + a)^(3/2)*a^4) - 48/35*B*b*x/((b*x^2 + a)^(5/2)*a^3) - 8/7*B*b*x/((b*x^2 + a)^(7/2)*a^2) - C*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(9/2) + 9/2*A*b*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(11/2) + C/(sqrt(b*x^2 + a)*a^4) + 1/3*C/((b*x^2 + a)^(3/2)*a^3) + 1/5*C/((b*x^2 + a)^(5/2)*a^2) + 1/7*C/((b*x^2 + a)^(7/2)*a) - 9/2*A*b/(sqrt(b*x^2 + a)*a^5) - 3/2*A*b/((b*x^2 + a)^(3/2)*a^4) - 9/10*A*b/((b*x^2 + a)^(5/2)*a^3) - 9/14*A*b/((b*x^2 + a)^(7/2)*a^2) - B/((b*x^2 + a)^(7/2)*a*x) - 1/2*A/((b*x^2 + a)^(7/2)*a*x^2)","A",0
58,0,0,0,0.000000," ","integrate(A*(c*x)^m/(b*x^2+a),x, algorithm=""maxima"")","A \int \frac{\left(c x\right)^{m}}{b x^{2} + a}\,{d x}"," ",0,"A*integrate((c*x)^m/(b*x^2 + a), x)","F",0
59,0,0,0,0.000000," ","integrate((c*x)^m*(B*x+A)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(B x + A\right)} \left(c x\right)^{m}}{b x^{2} + a}\,{d x}"," ",0,"integrate((B*x + A)*(c*x)^m/(b*x^2 + a), x)","F",0
60,0,0,0,0.000000," ","integrate((c*x)^m*(C*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + A\right)} \left(c x\right)^{m}}{b x^{2} + a}\,{d x}"," ",0,"integrate((C*x^2 + A)*(c*x)^m/(b*x^2 + a), x)","F",0
61,0,0,0,0.000000," ","integrate((c*x)^m*(C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} \left(c x\right)^{m}}{b x^{2} + a}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*(c*x)^m/(b*x^2 + a), x)","F",0
62,1,53,0,1.341456," ","integrate(x^3*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{9} \, D b x^{9} + \frac{1}{8} \, C b x^{8} + \frac{1}{7} \, {\left(D a + B b\right)} x^{7} + \frac{1}{5} \, B a x^{5} + \frac{1}{6} \, {\left(C a + A b\right)} x^{6} + \frac{1}{4} \, A a x^{4}"," ",0,"1/9*D*b*x^9 + 1/8*C*b*x^8 + 1/7*(D*a + B*b)*x^7 + 1/5*B*a*x^5 + 1/6*(C*a + A*b)*x^6 + 1/4*A*a*x^4","A",0
63,1,53,0,1.325445," ","integrate(x^2*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{8} \, D b x^{8} + \frac{1}{7} \, C b x^{7} + \frac{1}{6} \, {\left(D a + B b\right)} x^{6} + \frac{1}{4} \, B a x^{4} + \frac{1}{5} \, {\left(C a + A b\right)} x^{5} + \frac{1}{3} \, A a x^{3}"," ",0,"1/8*D*b*x^8 + 1/7*C*b*x^7 + 1/6*(D*a + B*b)*x^6 + 1/4*B*a*x^4 + 1/5*(C*a + A*b)*x^5 + 1/3*A*a*x^3","A",0
64,1,53,0,1.311504," ","integrate(x*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{7} \, D b x^{7} + \frac{1}{6} \, C b x^{6} + \frac{1}{5} \, {\left(D a + B b\right)} x^{5} + \frac{1}{3} \, B a x^{3} + \frac{1}{4} \, {\left(C a + A b\right)} x^{4} + \frac{1}{2} \, A a x^{2}"," ",0,"1/7*D*b*x^7 + 1/6*C*b*x^6 + 1/5*(D*a + B*b)*x^5 + 1/3*B*a*x^3 + 1/4*(C*a + A*b)*x^4 + 1/2*A*a*x^2","A",0
65,1,50,0,1.321816," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{6} \, D b x^{6} + \frac{1}{5} \, C b x^{5} + \frac{1}{4} \, {\left(D a + B b\right)} x^{4} + \frac{1}{2} \, B a x^{2} + \frac{1}{3} \, {\left(C a + A b\right)} x^{3} + A a x"," ",0,"1/6*D*b*x^6 + 1/5*C*b*x^5 + 1/4*(D*a + B*b)*x^4 + 1/2*B*a*x^2 + 1/3*(C*a + A*b)*x^3 + A*a*x","A",0
66,1,48,0,1.354124," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x,x, algorithm=""maxima"")","\frac{1}{5} \, D b x^{5} + \frac{1}{4} \, C b x^{4} + \frac{1}{3} \, {\left(D a + B b\right)} x^{3} + B a x + \frac{1}{2} \, {\left(C a + A b\right)} x^{2} + A a \log\left(x\right)"," ",0,"1/5*D*b*x^5 + 1/4*C*b*x^4 + 1/3*(D*a + B*b)*x^3 + B*a*x + 1/2*(C*a + A*b)*x^2 + A*a*log(x)","A",0
67,1,48,0,1.343403," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, D b x^{4} + \frac{1}{3} \, C b x^{3} + \frac{1}{2} \, {\left(D a + B b\right)} x^{2} + B a \log\left(x\right) + {\left(C a + A b\right)} x - \frac{A a}{x}"," ",0,"1/4*D*b*x^4 + 1/3*C*b*x^3 + 1/2*(D*a + B*b)*x^2 + B*a*log(x) + (C*a + A*b)*x - A*a/x","A",0
68,1,48,0,1.315678," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x^3,x, algorithm=""maxima"")","\frac{1}{3} \, D b x^{3} + \frac{1}{2} \, C b x^{2} + {\left(D a + B b\right)} x + {\left(C a + A b\right)} \log\left(x\right) - \frac{2 \, B a x + A a}{2 \, x^{2}}"," ",0,"1/3*D*b*x^3 + 1/2*C*b*x^2 + (D*a + B*b)*x + (C*a + A*b)*log(x) - 1/2*(2*B*a*x + A*a)/x^2","A",0
69,1,49,0,1.328417," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x^4,x, algorithm=""maxima"")","\frac{1}{2} \, D b x^{2} + C b x + {\left(D a + B b\right)} \log\left(x\right) - \frac{3 \, B a x + 6 \, {\left(C a + A b\right)} x^{2} + 2 \, A a}{6 \, x^{3}}"," ",0,"1/2*D*b*x^2 + C*b*x + (D*a + B*b)*log(x) - 1/6*(3*B*a*x + 6*(C*a + A*b)*x^2 + 2*A*a)/x^3","A",0
70,1,101,0,1.364627," ","integrate(x^3*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{11} \, D b^{2} x^{11} + \frac{1}{10} \, C b^{2} x^{10} + \frac{1}{9} \, {\left(2 \, D a b + B b^{2}\right)} x^{9} + \frac{1}{8} \, {\left(2 \, C a b + A b^{2}\right)} x^{8} + \frac{1}{5} \, B a^{2} x^{5} + \frac{1}{7} \, {\left(D a^{2} + 2 \, B a b\right)} x^{7} + \frac{1}{4} \, A a^{2} x^{4} + \frac{1}{6} \, {\left(C a^{2} + 2 \, A a b\right)} x^{6}"," ",0,"1/11*D*b^2*x^11 + 1/10*C*b^2*x^10 + 1/9*(2*D*a*b + B*b^2)*x^9 + 1/8*(2*C*a*b + A*b^2)*x^8 + 1/5*B*a^2*x^5 + 1/7*(D*a^2 + 2*B*a*b)*x^7 + 1/4*A*a^2*x^4 + 1/6*(C*a^2 + 2*A*a*b)*x^6","A",0
71,1,101,0,1.304873," ","integrate(x^2*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{10} \, D b^{2} x^{10} + \frac{1}{9} \, C b^{2} x^{9} + \frac{1}{8} \, {\left(2 \, D a b + B b^{2}\right)} x^{8} + \frac{1}{7} \, {\left(2 \, C a b + A b^{2}\right)} x^{7} + \frac{1}{4} \, B a^{2} x^{4} + \frac{1}{6} \, {\left(D a^{2} + 2 \, B a b\right)} x^{6} + \frac{1}{3} \, A a^{2} x^{3} + \frac{1}{5} \, {\left(C a^{2} + 2 \, A a b\right)} x^{5}"," ",0,"1/10*D*b^2*x^10 + 1/9*C*b^2*x^9 + 1/8*(2*D*a*b + B*b^2)*x^8 + 1/7*(2*C*a*b + A*b^2)*x^7 + 1/4*B*a^2*x^4 + 1/6*(D*a^2 + 2*B*a*b)*x^6 + 1/3*A*a^2*x^3 + 1/5*(C*a^2 + 2*A*a*b)*x^5","A",0
72,1,101,0,1.389012," ","integrate(x*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{9} \, D b^{2} x^{9} + \frac{1}{8} \, C b^{2} x^{8} + \frac{1}{7} \, {\left(2 \, D a b + B b^{2}\right)} x^{7} + \frac{1}{6} \, {\left(2 \, C a b + A b^{2}\right)} x^{6} + \frac{1}{3} \, B a^{2} x^{3} + \frac{1}{5} \, {\left(D a^{2} + 2 \, B a b\right)} x^{5} + \frac{1}{2} \, A a^{2} x^{2} + \frac{1}{4} \, {\left(C a^{2} + 2 \, A a b\right)} x^{4}"," ",0,"1/9*D*b^2*x^9 + 1/8*C*b^2*x^8 + 1/7*(2*D*a*b + B*b^2)*x^7 + 1/6*(2*C*a*b + A*b^2)*x^6 + 1/3*B*a^2*x^3 + 1/5*(D*a^2 + 2*B*a*b)*x^5 + 1/2*A*a^2*x^2 + 1/4*(C*a^2 + 2*A*a*b)*x^4","A",0
73,1,98,0,1.347787," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{8} \, D b^{2} x^{8} + \frac{1}{7} \, C b^{2} x^{7} + \frac{1}{6} \, {\left(2 \, D a b + B b^{2}\right)} x^{6} + \frac{1}{5} \, {\left(2 \, C a b + A b^{2}\right)} x^{5} + \frac{1}{2} \, B a^{2} x^{2} + \frac{1}{4} \, {\left(D a^{2} + 2 \, B a b\right)} x^{4} + A a^{2} x + \frac{1}{3} \, {\left(C a^{2} + 2 \, A a b\right)} x^{3}"," ",0,"1/8*D*b^2*x^8 + 1/7*C*b^2*x^7 + 1/6*(2*D*a*b + B*b^2)*x^6 + 1/5*(2*C*a*b + A*b^2)*x^5 + 1/2*B*a^2*x^2 + 1/4*(D*a^2 + 2*B*a*b)*x^4 + A*a^2*x + 1/3*(C*a^2 + 2*A*a*b)*x^3","A",0
74,1,96,0,1.383872," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x,x, algorithm=""maxima"")","\frac{1}{7} \, D b^{2} x^{7} + \frac{1}{6} \, C b^{2} x^{6} + \frac{1}{5} \, {\left(2 \, D a b + B b^{2}\right)} x^{5} + \frac{1}{4} \, {\left(2 \, C a b + A b^{2}\right)} x^{4} + B a^{2} x + \frac{1}{3} \, {\left(D a^{2} + 2 \, B a b\right)} x^{3} + A a^{2} \log\left(x\right) + \frac{1}{2} \, {\left(C a^{2} + 2 \, A a b\right)} x^{2}"," ",0,"1/7*D*b^2*x^7 + 1/6*C*b^2*x^6 + 1/5*(2*D*a*b + B*b^2)*x^5 + 1/4*(2*C*a*b + A*b^2)*x^4 + B*a^2*x + 1/3*(D*a^2 + 2*B*a*b)*x^3 + A*a^2*log(x) + 1/2*(C*a^2 + 2*A*a*b)*x^2","A",0
75,1,96,0,1.315427," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x^2,x, algorithm=""maxima"")","\frac{1}{6} \, D b^{2} x^{6} + \frac{1}{5} \, C b^{2} x^{5} + \frac{1}{4} \, {\left(2 \, D a b + B b^{2}\right)} x^{4} + \frac{1}{3} \, {\left(2 \, C a b + A b^{2}\right)} x^{3} + B a^{2} \log\left(x\right) + \frac{1}{2} \, {\left(D a^{2} + 2 \, B a b\right)} x^{2} - \frac{A a^{2}}{x} + {\left(C a^{2} + 2 \, A a b\right)} x"," ",0,"1/6*D*b^2*x^6 + 1/5*C*b^2*x^5 + 1/4*(2*D*a*b + B*b^2)*x^4 + 1/3*(2*C*a*b + A*b^2)*x^3 + B*a^2*log(x) + 1/2*(D*a^2 + 2*B*a*b)*x^2 - A*a^2/x + (C*a^2 + 2*A*a*b)*x","A",0
76,1,96,0,1.324959," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x^3,x, algorithm=""maxima"")","\frac{1}{5} \, D b^{2} x^{5} + \frac{1}{4} \, C b^{2} x^{4} + \frac{1}{3} \, {\left(2 \, D a b + B b^{2}\right)} x^{3} + \frac{1}{2} \, {\left(2 \, C a b + A b^{2}\right)} x^{2} + {\left(D a^{2} + 2 \, B a b\right)} x + {\left(C a^{2} + 2 \, A a b\right)} \log\left(x\right) - \frac{2 \, B a^{2} x + A a^{2}}{2 \, x^{2}}"," ",0,"1/5*D*b^2*x^5 + 1/4*C*b^2*x^4 + 1/3*(2*D*a*b + B*b^2)*x^3 + 1/2*(2*C*a*b + A*b^2)*x^2 + (D*a^2 + 2*B*a*b)*x + (C*a^2 + 2*A*a*b)*log(x) - 1/2*(2*B*a^2*x + A*a^2)/x^2","A",0
77,1,97,0,1.370286," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x^4,x, algorithm=""maxima"")","\frac{1}{4} \, D b^{2} x^{4} + \frac{1}{3} \, C b^{2} x^{3} + \frac{1}{2} \, {\left(2 \, D a b + B b^{2}\right)} x^{2} + {\left(2 \, C a b + A b^{2}\right)} x + {\left(D a^{2} + 2 \, B a b\right)} \log\left(x\right) - \frac{3 \, B a^{2} x + 2 \, A a^{2} + 6 \, {\left(C a^{2} + 2 \, A a b\right)} x^{2}}{6 \, x^{3}}"," ",0,"1/4*D*b^2*x^4 + 1/3*C*b^2*x^3 + 1/2*(2*D*a*b + B*b^2)*x^2 + (2*C*a*b + A*b^2)*x + (D*a^2 + 2*B*a*b)*log(x) - 1/6*(3*B*a^2*x + 2*A*a^2 + 6*(C*a^2 + 2*A*a*b)*x^2)/x^3","A",0
78,1,145,0,1.327808," ","integrate(x^3*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{13} \, D b^{3} x^{13} + \frac{1}{12} \, C b^{3} x^{12} + \frac{1}{11} \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{11} + \frac{1}{10} \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{10} + \frac{1}{3} \, {\left(D a^{2} b + B a b^{2}\right)} x^{9} + \frac{1}{5} \, B a^{3} x^{5} + \frac{3}{8} \, {\left(C a^{2} b + A a b^{2}\right)} x^{8} + \frac{1}{4} \, A a^{3} x^{4} + \frac{1}{7} \, {\left(D a^{3} + 3 \, B a^{2} b\right)} x^{7} + \frac{1}{6} \, {\left(C a^{3} + 3 \, A a^{2} b\right)} x^{6}"," ",0,"1/13*D*b^3*x^13 + 1/12*C*b^3*x^12 + 1/11*(3*D*a*b^2 + B*b^3)*x^11 + 1/10*(3*C*a*b^2 + A*b^3)*x^10 + 1/3*(D*a^2*b + B*a*b^2)*x^9 + 1/5*B*a^3*x^5 + 3/8*(C*a^2*b + A*a*b^2)*x^8 + 1/4*A*a^3*x^4 + 1/7*(D*a^3 + 3*B*a^2*b)*x^7 + 1/6*(C*a^3 + 3*A*a^2*b)*x^6","A",0
79,1,145,0,1.361181," ","integrate(x^2*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{12} \, D b^{3} x^{12} + \frac{1}{11} \, C b^{3} x^{11} + \frac{1}{10} \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{10} + \frac{1}{9} \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{9} + \frac{3}{8} \, {\left(D a^{2} b + B a b^{2}\right)} x^{8} + \frac{1}{4} \, B a^{3} x^{4} + \frac{3}{7} \, {\left(C a^{2} b + A a b^{2}\right)} x^{7} + \frac{1}{3} \, A a^{3} x^{3} + \frac{1}{6} \, {\left(D a^{3} + 3 \, B a^{2} b\right)} x^{6} + \frac{1}{5} \, {\left(C a^{3} + 3 \, A a^{2} b\right)} x^{5}"," ",0,"1/12*D*b^3*x^12 + 1/11*C*b^3*x^11 + 1/10*(3*D*a*b^2 + B*b^3)*x^10 + 1/9*(3*C*a*b^2 + A*b^3)*x^9 + 3/8*(D*a^2*b + B*a*b^2)*x^8 + 1/4*B*a^3*x^4 + 3/7*(C*a^2*b + A*a*b^2)*x^7 + 1/3*A*a^3*x^3 + 1/6*(D*a^3 + 3*B*a^2*b)*x^6 + 1/5*(C*a^3 + 3*A*a^2*b)*x^5","A",0
80,1,145,0,1.335547," ","integrate(x*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{11} \, D b^{3} x^{11} + \frac{1}{10} \, C b^{3} x^{10} + \frac{1}{9} \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{9} + \frac{1}{8} \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{8} + \frac{3}{7} \, {\left(D a^{2} b + B a b^{2}\right)} x^{7} + \frac{1}{3} \, B a^{3} x^{3} + \frac{1}{2} \, {\left(C a^{2} b + A a b^{2}\right)} x^{6} + \frac{1}{2} \, A a^{3} x^{2} + \frac{1}{5} \, {\left(D a^{3} + 3 \, B a^{2} b\right)} x^{5} + \frac{1}{4} \, {\left(C a^{3} + 3 \, A a^{2} b\right)} x^{4}"," ",0,"1/11*D*b^3*x^11 + 1/10*C*b^3*x^10 + 1/9*(3*D*a*b^2 + B*b^3)*x^9 + 1/8*(3*C*a*b^2 + A*b^3)*x^8 + 3/7*(D*a^2*b + B*a*b^2)*x^7 + 1/3*B*a^3*x^3 + 1/2*(C*a^2*b + A*a*b^2)*x^6 + 1/2*A*a^3*x^2 + 1/5*(D*a^3 + 3*B*a^2*b)*x^5 + 1/4*(C*a^3 + 3*A*a^2*b)*x^4","A",0
81,1,142,0,1.341164," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""maxima"")","\frac{1}{10} \, D b^{3} x^{10} + \frac{1}{9} \, C b^{3} x^{9} + \frac{1}{8} \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{8} + \frac{1}{7} \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{7} + \frac{1}{2} \, {\left(D a^{2} b + B a b^{2}\right)} x^{6} + \frac{1}{2} \, B a^{3} x^{2} + \frac{3}{5} \, {\left(C a^{2} b + A a b^{2}\right)} x^{5} + A a^{3} x + \frac{1}{4} \, {\left(D a^{3} + 3 \, B a^{2} b\right)} x^{4} + \frac{1}{3} \, {\left(C a^{3} + 3 \, A a^{2} b\right)} x^{3}"," ",0,"1/10*D*b^3*x^10 + 1/9*C*b^3*x^9 + 1/8*(3*D*a*b^2 + B*b^3)*x^8 + 1/7*(3*C*a*b^2 + A*b^3)*x^7 + 1/2*(D*a^2*b + B*a*b^2)*x^6 + 1/2*B*a^3*x^2 + 3/5*(C*a^2*b + A*a*b^2)*x^5 + A*a^3*x + 1/4*(D*a^3 + 3*B*a^2*b)*x^4 + 1/3*(C*a^3 + 3*A*a^2*b)*x^3","A",0
82,1,140,0,1.320726," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x,x, algorithm=""maxima"")","\frac{1}{9} \, D b^{3} x^{9} + \frac{1}{8} \, C b^{3} x^{8} + \frac{1}{7} \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{7} + \frac{1}{6} \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{6} + \frac{3}{5} \, {\left(D a^{2} b + B a b^{2}\right)} x^{5} + B a^{3} x + \frac{3}{4} \, {\left(C a^{2} b + A a b^{2}\right)} x^{4} + A a^{3} \log\left(x\right) + \frac{1}{3} \, {\left(D a^{3} + 3 \, B a^{2} b\right)} x^{3} + \frac{1}{2} \, {\left(C a^{3} + 3 \, A a^{2} b\right)} x^{2}"," ",0,"1/9*D*b^3*x^9 + 1/8*C*b^3*x^8 + 1/7*(3*D*a*b^2 + B*b^3)*x^7 + 1/6*(3*C*a*b^2 + A*b^3)*x^6 + 3/5*(D*a^2*b + B*a*b^2)*x^5 + B*a^3*x + 3/4*(C*a^2*b + A*a*b^2)*x^4 + A*a^3*log(x) + 1/3*(D*a^3 + 3*B*a^2*b)*x^3 + 1/2*(C*a^3 + 3*A*a^2*b)*x^2","A",0
83,1,139,0,1.348488," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x^2,x, algorithm=""maxima"")","\frac{1}{8} \, D b^{3} x^{8} + \frac{1}{7} \, C b^{3} x^{7} + \frac{1}{6} \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{6} + \frac{1}{5} \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{5} + \frac{3}{4} \, {\left(D a^{2} b + B a b^{2}\right)} x^{4} + B a^{3} \log\left(x\right) + {\left(C a^{2} b + A a b^{2}\right)} x^{3} - \frac{A a^{3}}{x} + \frac{1}{2} \, {\left(D a^{3} + 3 \, B a^{2} b\right)} x^{2} + {\left(C a^{3} + 3 \, A a^{2} b\right)} x"," ",0,"1/8*D*b^3*x^8 + 1/7*C*b^3*x^7 + 1/6*(3*D*a*b^2 + B*b^3)*x^6 + 1/5*(3*C*a*b^2 + A*b^3)*x^5 + 3/4*(D*a^2*b + B*a*b^2)*x^4 + B*a^3*log(x) + (C*a^2*b + A*a*b^2)*x^3 - A*a^3/x + 1/2*(D*a^3 + 3*B*a^2*b)*x^2 + (C*a^3 + 3*A*a^2*b)*x","A",0
84,1,139,0,1.357208," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x^3,x, algorithm=""maxima"")","\frac{1}{7} \, D b^{3} x^{7} + \frac{1}{6} \, C b^{3} x^{6} + \frac{1}{5} \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{5} + \frac{1}{4} \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{4} + {\left(D a^{2} b + B a b^{2}\right)} x^{3} + \frac{3}{2} \, {\left(C a^{2} b + A a b^{2}\right)} x^{2} + {\left(D a^{3} + 3 \, B a^{2} b\right)} x + {\left(C a^{3} + 3 \, A a^{2} b\right)} \log\left(x\right) - \frac{2 \, B a^{3} x + A a^{3}}{2 \, x^{2}}"," ",0,"1/7*D*b^3*x^7 + 1/6*C*b^3*x^6 + 1/5*(3*D*a*b^2 + B*b^3)*x^5 + 1/4*(3*C*a*b^2 + A*b^3)*x^4 + (D*a^2*b + B*a*b^2)*x^3 + 3/2*(C*a^2*b + A*a*b^2)*x^2 + (D*a^3 + 3*B*a^2*b)*x + (C*a^3 + 3*A*a^2*b)*log(x) - 1/2*(2*B*a^3*x + A*a^3)/x^2","A",0
85,1,142,0,1.317493," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, D b^{3} x^{6} + \frac{1}{5} \, C b^{3} x^{5} + \frac{1}{4} \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{4} + \frac{1}{3} \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{3} + \frac{3}{2} \, {\left(D a^{2} b + B a b^{2}\right)} x^{2} + 3 \, {\left(C a^{2} b + A a b^{2}\right)} x + {\left(D a^{3} + 3 \, B a^{2} b\right)} \log\left(x\right) - \frac{3 \, B a^{3} x + 2 \, A a^{3} + 6 \, {\left(C a^{3} + 3 \, A a^{2} b\right)} x^{2}}{6 \, x^{3}}"," ",0,"1/6*D*b^3*x^6 + 1/5*C*b^3*x^5 + 1/4*(3*D*a*b^2 + B*b^3)*x^4 + 1/3*(3*C*a*b^2 + A*b^3)*x^3 + 3/2*(D*a^2*b + B*a*b^2)*x^2 + 3*(C*a^2*b + A*a*b^2)*x + (D*a^3 + 3*B*a^2*b)*log(x) - 1/6*(3*B*a^3*x + 2*A*a^3 + 6*(C*a^3 + 3*A*a^2*b)*x^2)/x^3","A",0
86,1,145,0,2.962065," ","integrate(x^4*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(C a^{3} - A a^{2} b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{10 \, D b^{2} x^{6} + 12 \, C b^{2} x^{5} - 15 \, {\left(D a b - B b^{2}\right)} x^{4} - 20 \, {\left(C a b - A b^{2}\right)} x^{3} + 30 \, {\left(D a^{2} - B a b\right)} x^{2} + 60 \, {\left(C a^{2} - A a b\right)} x}{60 \, b^{3}} - \frac{{\left(D a^{3} - B a^{2} b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"-(C*a^3 - A*a^2*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/60*(10*D*b^2*x^6 + 12*C*b^2*x^5 - 15*(D*a*b - B*b^2)*x^4 - 20*(C*a*b - A*b^2)*x^3 + 30*(D*a^2 - B*a*b)*x^2 + 60*(C*a^2 - A*a*b)*x)/b^3 - 1/2*(D*a^3 - B*a^2*b)*log(b*x^2 + a)/b^4","A",0
87,1,127,0,2.931869," ","integrate(x^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(C a^{2} - A a b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{3}} - \frac{{\left(D a^{3} - B a^{2} b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{12 \, D b^{2} x^{5} + 15 \, C b^{2} x^{4} - 20 \, {\left(D a b - B b^{2}\right)} x^{3} - 30 \, {\left(C a b - A b^{2}\right)} x^{2} + 60 \, {\left(D a^{2} - B a b\right)} x}{60 \, b^{3}}"," ",0,"1/2*(C*a^2 - A*a*b)*log(b*x^2 + a)/b^3 - (D*a^3 - B*a^2*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/60*(12*D*b^2*x^5 + 15*C*b^2*x^4 - 20*(D*a*b - B*b^2)*x^3 - 30*(C*a*b - A*b^2)*x^2 + 60*(D*a^2 - B*a*b)*x)/b^3","A",0
88,1,98,0,3.001632," ","integrate(x^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(C a^{2} - A a b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{3 \, D b x^{4} + 4 \, C b x^{3} - 6 \, {\left(D a - B b\right)} x^{2} - 12 \, {\left(C a - A b\right)} x}{12 \, b^{2}} + \frac{{\left(D a^{2} - B a b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{3}}"," ",0,"(C*a^2 - A*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/12*(3*D*b*x^4 + 4*C*b*x^3 - 6*(D*a - B*b)*x^2 - 12*(C*a - A*b)*x)/b^2 + 1/2*(D*a^2 - B*a*b)*log(b*x^2 + a)/b^3","A",0
89,1,82,0,3.007282," ","integrate(x*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(C a - A b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{2}} + \frac{{\left(D a^{2} - B a b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{2 \, D b x^{3} + 3 \, C b x^{2} - 6 \, {\left(D a - B b\right)} x}{6 \, b^{2}}"," ",0,"-1/2*(C*a - A*b)*log(b*x^2 + a)/b^2 + (D*a^2 - B*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/6*(2*D*b*x^3 + 3*C*b*x^2 - 6*(D*a - B*b)*x)/b^2","A",0
90,1,64,0,2.928532," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(C a - A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b} + \frac{D x^{2} + 2 \, C x}{2 \, b} - \frac{{\left(D a - B b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"-(C*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b) + 1/2*(D*x^2 + 2*C*x)/b - 1/2*(D*a - B*b)*log(b*x^2 + a)/b^2","A",0
91,1,65,0,2.930721," ","integrate((D*x^3+C*x^2+B*x+A)/x/(b*x^2+a),x, algorithm=""maxima"")","\frac{D x}{b} + \frac{A \log\left(x\right)}{a} - \frac{{\left(D a - B b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b} + \frac{{\left(C a - A b\right)} \log\left(b x^{2} + a\right)}{2 \, a b}"," ",0,"D*x/b + A*log(x)/a - (D*a - B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b) + 1/2*(C*a - A*b)*log(b*x^2 + a)/(a*b)","A",0
92,1,67,0,3.001090," ","integrate((D*x^3+C*x^2+B*x+A)/x^2/(b*x^2+a),x, algorithm=""maxima"")","\frac{B \log\left(x\right)}{a} + \frac{{\left(C a - A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a} + \frac{{\left(D a - B b\right)} \log\left(b x^{2} + a\right)}{2 \, a b} - \frac{A}{a x}"," ",0,"B*log(x)/a + (C*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a) + 1/2*(D*a - B*b)*log(b*x^2 + a)/(a*b) - A/(a*x)","A",0
93,1,76,0,3.051530," ","integrate((D*x^3+C*x^2+B*x+A)/x^3/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(D a - B b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a} - \frac{{\left(C a - A b\right)} \log\left(b x^{2} + a\right)}{2 \, a^{2}} + \frac{{\left(C a - A b\right)} \log\left(x\right)}{a^{2}} - \frac{2 \, B x + A}{2 \, a x^{2}}"," ",0,"(D*a - B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a) - 1/2*(C*a - A*b)*log(b*x^2 + a)/a^2 + (C*a - A*b)*log(x)/a^2 - 1/2*(2*B*x + A)/(a*x^2)","A",0
94,1,150,0,2.834833," ","integrate(x^4*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{D a^{3} - B a^{2} b - {\left(C a^{2} b - A a b^{2}\right)} x}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} + \frac{{\left(5 \, C a^{2} - 3 \, A a b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{3}} + \frac{3 \, D b x^{4} + 4 \, C b x^{3} - 6 \, {\left(2 \, D a - B b\right)} x^{2} - 12 \, {\left(2 \, C a - A b\right)} x}{12 \, b^{3}} + \frac{{\left(3 \, D a^{2} - 2 \, B a b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"1/2*(D*a^3 - B*a^2*b - (C*a^2*b - A*a*b^2)*x)/(b^5*x^2 + a*b^4) + 1/2*(5*C*a^2 - 3*A*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/12*(3*D*b*x^4 + 4*C*b*x^3 - 6*(2*D*a - B*b)*x^2 - 12*(2*C*a - A*b)*x)/b^3 + 1/2*(3*D*a^2 - 2*B*a*b)*log(b*x^2 + a)/b^4","A",0
95,1,127,0,2.998748," ","integrate(x^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{C a^{2} - A a b + {\left(D a^{2} - B a b\right)} x}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}} - \frac{{\left(2 \, C a - A b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{3}} + \frac{{\left(5 \, D a^{2} - 3 \, B a b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{3}} + \frac{2 \, D b x^{3} + 3 \, C b x^{2} - 6 \, {\left(2 \, D a - B b\right)} x}{6 \, b^{3}}"," ",0,"-1/2*(C*a^2 - A*a*b + (D*a^2 - B*a*b)*x)/(b^4*x^2 + a*b^3) - 1/2*(2*C*a - A*b)*log(b*x^2 + a)/b^3 + 1/2*(5*D*a^2 - 3*B*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/6*(2*D*b*x^3 + 3*C*b*x^2 - 6*(2*D*a - B*b)*x)/b^3","A",0
96,1,108,0,2.963262," ","integrate(x^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{D a^{2} - B a b - {\left(C a b - A b^{2}\right)} x}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}} - \frac{{\left(3 \, C a - A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{2}} + \frac{D x^{2} + 2 \, C x}{2 \, b^{2}} - \frac{{\left(2 \, D a - B b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{3}}"," ",0,"-1/2*(D*a^2 - B*a*b - (C*a*b - A*b^2)*x)/(b^4*x^2 + a*b^3) - 1/2*(3*C*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/2*(D*x^2 + 2*C*x)/b^2 - 1/2*(2*D*a - B*b)*log(b*x^2 + a)/b^3","A",0
97,1,84,0,3.015881," ","integrate(x*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{C a - A b + {\left(D a - B b\right)} x}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}} + \frac{D x}{b^{2}} + \frac{C \log\left(b x^{2} + a\right)}{2 \, b^{2}} - \frac{{\left(3 \, D a - B b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{2}}"," ",0,"1/2*(C*a - A*b + (D*a - B*b)*x)/(b^3*x^2 + a*b^2) + D*x/b^2 + 1/2*C*log(b*x^2 + a)/b^2 - 1/2*(3*D*a - B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2)","A",0
98,1,89,0,2.944834," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{D a^{2} - B a b - {\left(C a b - A b^{2}\right)} x}{2 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}} + \frac{D \log\left(b x^{2} + a\right)}{2 \, b^{2}} + \frac{{\left(C a + A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b}"," ",0,"1/2*(D*a^2 - B*a*b - (C*a*b - A*b^2)*x)/(a*b^3*x^2 + a^2*b^2) + 1/2*D*log(b*x^2 + a)/b^2 + 1/2*(C*a + A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b)","A",0
99,1,87,0,2.914220," ","integrate((D*x^3+C*x^2+B*x+A)/x/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{C a - A b + {\left(D a - B b\right)} x}{2 \, {\left(a b^{2} x^{2} + a^{2} b\right)}} - \frac{A \log\left(b x^{2} + a\right)}{2 \, a^{2}} + \frac{A \log\left(x\right)}{a^{2}} + \frac{{\left(D a + B b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b}"," ",0,"-1/2*(C*a - A*b + (D*a - B*b)*x)/(a*b^2*x^2 + a^2*b) - 1/2*A*log(b*x^2 + a)/a^2 + A*log(x)/a^2 + 1/2*(D*a + B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b)","A",0
100,1,105,0,2.984521," ","integrate((D*x^3+C*x^2+B*x+A)/x^2/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{2 \, A a b - {\left(C a b - 3 \, A b^{2}\right)} x^{2} + {\left(D a^{2} - B a b\right)} x}{2 \, {\left(a^{2} b^{2} x^{3} + a^{3} b x\right)}} - \frac{B \log\left(b x^{2} + a\right)}{2 \, a^{2}} + \frac{B \log\left(x\right)}{a^{2}} + \frac{{\left(C a - 3 \, A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2}}"," ",0,"-1/2*(2*A*a*b - (C*a*b - 3*A*b^2)*x^2 + (D*a^2 - B*a*b)*x)/(a^2*b^2*x^3 + a^3*b*x) - 1/2*B*log(b*x^2 + a)/a^2 + B*log(x)/a^2 + 1/2*(C*a - 3*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2)","A",0
101,1,117,0,2.944506," ","integrate((D*x^3+C*x^2+B*x+A)/x^3/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(D a - 3 \, B b\right)} x^{3} - 2 \, B a x + {\left(C a - 2 \, A b\right)} x^{2} - A a}{2 \, {\left(a^{2} b x^{4} + a^{3} x^{2}\right)}} + \frac{{\left(D a - 3 \, B b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2}} - \frac{{\left(C a - 2 \, A b\right)} \log\left(b x^{2} + a\right)}{2 \, a^{3}} + \frac{{\left(C a - 2 \, A b\right)} \log\left(x\right)}{a^{3}}"," ",0,"1/2*((D*a - 3*B*b)*x^3 - 2*B*a*x + (C*a - 2*A*b)*x^2 - A*a)/(a^2*b*x^4 + a^3*x^2) + 1/2*(D*a - 3*B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) - 1/2*(C*a - 2*A*b)*log(b*x^2 + a)/a^3 + (C*a - 2*A*b)*log(x)/a^3","A",0
102,1,165,0,3.074686," ","integrate(x^4*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{10 \, D a^{3} - 6 \, B a^{2} b - {\left(9 \, C a b^{2} - 5 \, A b^{3}\right)} x^{3} + 4 \, {\left(3 \, D a^{2} b - 2 \, B a b^{2}\right)} x^{2} - {\left(7 \, C a^{2} b - 3 \, A a b^{2}\right)} x}{8 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}} - \frac{3 \, {\left(5 \, C a - A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{3}} + \frac{D x^{2} + 2 \, C x}{2 \, b^{3}} - \frac{{\left(3 \, D a - B b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"-1/8*(10*D*a^3 - 6*B*a^2*b - (9*C*a*b^2 - 5*A*b^3)*x^3 + 4*(3*D*a^2*b - 2*B*a*b^2)*x^2 - (7*C*a^2*b - 3*A*a*b^2)*x)/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4) - 3/8*(5*C*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/2*(D*x^2 + 2*C*x)/b^3 - 1/2*(3*D*a - B*b)*log(b*x^2 + a)/b^4","A",0
103,1,136,0,2.984122," ","integrate(x^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(9 \, D a b - 5 \, B b^{2}\right)} x^{3} + 6 \, C a^{2} - 2 \, A a b + 4 \, {\left(2 \, C a b - A b^{2}\right)} x^{2} + {\left(7 \, D a^{2} - 3 \, B a b\right)} x}{8 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}} + \frac{D x}{b^{3}} + \frac{C \log\left(b x^{2} + a\right)}{2 \, b^{3}} - \frac{3 \, {\left(5 \, D a - B b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{3}}"," ",0,"1/8*((9*D*a*b - 5*B*b^2)*x^3 + 6*C*a^2 - 2*A*a*b + 4*(2*C*a*b - A*b^2)*x^2 + (7*D*a^2 - 3*B*a*b)*x)/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3) + D*x/b^3 + 1/2*C*log(b*x^2 + a)/b^3 - 3/8*(5*D*a - B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3)","A",0
104,1,146,0,2.976632," ","integrate(x^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{6 \, D a^{3} - 2 \, B a^{2} b - {\left(5 \, C a b^{2} - A b^{3}\right)} x^{3} + 4 \, {\left(2 \, D a^{2} b - B a b^{2}\right)} x^{2} - {\left(3 \, C a^{2} b + A a b^{2}\right)} x}{8 \, {\left(a b^{5} x^{4} + 2 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}} + \frac{D \log\left(b x^{2} + a\right)}{2 \, b^{3}} + \frac{{\left(3 \, C a + A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a b^{2}}"," ",0,"1/8*(6*D*a^3 - 2*B*a^2*b - (5*C*a*b^2 - A*b^3)*x^3 + 4*(2*D*a^2*b - B*a*b^2)*x^2 - (3*C*a^2*b + A*a*b^2)*x)/(a*b^5*x^4 + 2*a^2*b^4*x^2 + a^3*b^3) + 1/2*D*log(b*x^2 + a)/b^3 + 1/8*(3*C*a + A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2)","A",0
105,1,111,0,2.992742," ","integrate(x*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{4 \, C a b x^{2} + {\left(5 \, D a b - B b^{2}\right)} x^{3} + 2 \, C a^{2} + 2 \, A a b + {\left(3 \, D a^{2} + B a b\right)} x}{8 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}} + \frac{{\left(3 \, D a + B b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a b^{2}}"," ",0,"-1/8*(4*C*a*b*x^2 + (5*D*a*b - B*b^2)*x^3 + 2*C*a^2 + 2*A*a*b + (3*D*a^2 + B*a*b)*x)/(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2) + 1/8*(3*D*a + B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2)","A",0
106,1,122,0,2.998317," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{4 \, D a^{2} b x^{2} + 2 \, D a^{3} + 2 \, B a^{2} b - {\left(C a b^{2} + 3 \, A b^{3}\right)} x^{3} + {\left(C a^{2} b - 5 \, A a b^{2}\right)} x}{8 \, {\left(a^{2} b^{4} x^{4} + 2 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)}} + \frac{{\left(C a + 3 \, A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b}"," ",0,"-1/8*(4*D*a^2*b*x^2 + 2*D*a^3 + 2*B*a^2*b - (C*a*b^2 + 3*A*b^3)*x^3 + (C*a^2*b - 5*A*a*b^2)*x)/(a^2*b^4*x^4 + 2*a^3*b^3*x^2 + a^4*b^2) + 1/8*(C*a + 3*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b)","A",0
107,1,133,0,2.903594," ","integrate((D*x^3+C*x^2+B*x+A)/x/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{4 \, A b^{2} x^{2} + {\left(D a b + 3 \, B b^{2}\right)} x^{3} - 2 \, C a^{2} + 6 \, A a b - {\left(D a^{2} - 5 \, B a b\right)} x}{8 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}} - \frac{A \log\left(b x^{2} + a\right)}{2 \, a^{3}} + \frac{A \log\left(x\right)}{a^{3}} + \frac{{\left(D a + 3 \, B b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b}"," ",0,"1/8*(4*A*b^2*x^2 + (D*a*b + 3*B*b^2)*x^3 - 2*C*a^2 + 6*A*a*b - (D*a^2 - 5*B*a*b)*x)/(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b) - 1/2*A*log(b*x^2 + a)/a^3 + A*log(x)/a^3 + 1/8*(D*a + 3*B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b)","A",0
108,1,152,0,2.985695," ","integrate((D*x^3+C*x^2+B*x+A)/x^2/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{4 \, B a b^{2} x^{3} + 3 \, {\left(C a b^{2} - 5 \, A b^{3}\right)} x^{4} - 8 \, A a^{2} b + 5 \, {\left(C a^{2} b - 5 \, A a b^{2}\right)} x^{2} - 2 \, {\left(D a^{3} - 3 \, B a^{2} b\right)} x}{8 \, {\left(a^{3} b^{3} x^{5} + 2 \, a^{4} b^{2} x^{3} + a^{5} b x\right)}} - \frac{B \log\left(b x^{2} + a\right)}{2 \, a^{3}} + \frac{B \log\left(x\right)}{a^{3}} + \frac{3 \, {\left(C a - 5 \, A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{3}}"," ",0,"1/8*(4*B*a*b^2*x^3 + 3*(C*a*b^2 - 5*A*b^3)*x^4 - 8*A*a^2*b + 5*(C*a^2*b - 5*A*a*b^2)*x^2 - 2*(D*a^3 - 3*B*a^2*b)*x)/(a^3*b^3*x^5 + 2*a^4*b^2*x^3 + a^5*b*x) - 1/2*B*log(b*x^2 + a)/a^3 + B*log(x)/a^3 + 3/8*(C*a - 5*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3)","A",0
109,1,172,0,2.991042," ","integrate((D*x^3+C*x^2+B*x+A)/x^3/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(D a b - 5 \, B b^{2}\right)} x^{5} + 4 \, {\left(C a b - 3 \, A b^{2}\right)} x^{4} - 8 \, B a^{2} x + 5 \, {\left(D a^{2} - 5 \, B a b\right)} x^{3} - 4 \, A a^{2} + 6 \, {\left(C a^{2} - 3 \, A a b\right)} x^{2}}{8 \, {\left(a^{3} b^{2} x^{6} + 2 \, a^{4} b x^{4} + a^{5} x^{2}\right)}} + \frac{3 \, {\left(D a - 5 \, B b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{3}} - \frac{{\left(C a - 3 \, A b\right)} \log\left(b x^{2} + a\right)}{2 \, a^{4}} + \frac{{\left(C a - 3 \, A b\right)} \log\left(x\right)}{a^{4}}"," ",0,"1/8*(3*(D*a*b - 5*B*b^2)*x^5 + 4*(C*a*b - 3*A*b^2)*x^4 - 8*B*a^2*x + 5*(D*a^2 - 5*B*a*b)*x^3 - 4*A*a^2 + 6*(C*a^2 - 3*A*a*b)*x^2)/(a^3*b^2*x^6 + 2*a^4*b*x^4 + a^5*x^2) + 3/8*(D*a - 5*B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3) - 1/2*(C*a - 3*A*b)*log(b*x^2 + a)/a^4 + (C*a - 3*A*b)*log(x)/a^4","A",0
110,1,18,0,1.338632," ","integrate((4*x^3-x)/(x^2+5)^2,x, algorithm=""maxima"")","\frac{21}{2 \, {\left(x^{2} + 5\right)}} + 2 \, \log\left(x^{2} + 5\right)"," ",0,"21/2/(x^2 + 5) + 2*log(x^2 + 5)","A",0
111,1,22,0,1.344229," ","integrate((x^3-x)/(x^2-2)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{x^{2} - 2} x^{2} + \frac{1}{3} \, \sqrt{x^{2} - 2}"," ",0,"1/3*sqrt(x^2 - 2)*x^2 + 1/3*sqrt(x^2 - 2)","A",0
112,1,20,0,2.920151," ","integrate((2*x^4-x^2)/(2*x^2+1),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} + \frac{1}{2} \, \sqrt{2} \arctan\left(\sqrt{2} x\right) - x"," ",0,"1/3*x^3 + 1/2*sqrt(2)*arctan(sqrt(2)*x) - x","A",0
113,1,24,0,2.899052," ","integrate((x^4+x^3)/(x^2+1),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} - x + \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"1/3*x^3 + 1/2*x^2 - x + arctan(x) - 1/2*log(x^2 + 1)","A",0
114,1,213,0,2.897340," ","integrate(x^6*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(a^{3} b^{3} c - a^{4} b^{2} d + a^{5} b e - a^{6} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{6}} + \frac{315 \, b^{5} f x^{11} + 385 \, {\left(b^{5} e - a b^{4} f\right)} x^{9} + 495 \, {\left(b^{5} d - a b^{4} e + a^{2} b^{3} f\right)} x^{7} + 693 \, {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} x^{5} - 1155 \, {\left(a b^{4} c - a^{2} b^{3} d + a^{3} b^{2} e - a^{4} b f\right)} x^{3} + 3465 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} x}{3465 \, b^{6}}"," ",0,"-(a^3*b^3*c - a^4*b^2*d + a^5*b*e - a^6*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) + 1/3465*(315*b^5*f*x^11 + 385*(b^5*e - a*b^4*f)*x^9 + 495*(b^5*d - a*b^4*e + a^2*b^3*f)*x^7 + 693*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*x^5 - 1155*(a*b^4*c - a^2*b^3*d + a^3*b^2*e - a^4*b*f)*x^3 + 3465*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*x)/b^6","A",0
115,1,172,0,2.930123," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{5}} + \frac{35 \, b^{4} f x^{9} + 45 \, {\left(b^{4} e - a b^{3} f\right)} x^{7} + 63 \, {\left(b^{4} d - a b^{3} e + a^{2} b^{2} f\right)} x^{5} + 105 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{3} - 315 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x}{315 \, b^{5}}"," ",0,"(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/315*(35*b^4*f*x^9 + 45*(b^4*e - a*b^3*f)*x^7 + 63*(b^4*d - a*b^3*e + a^2*b^2*f)*x^5 + 105*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^3 - 315*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x)/b^5","A",0
116,1,133,0,2.963899," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{4}} + \frac{15 \, b^{3} f x^{7} + 21 \, {\left(b^{3} e - a b^{2} f\right)} x^{5} + 35 \, {\left(b^{3} d - a b^{2} e + a^{2} b f\right)} x^{3} + 105 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x}{105 \, b^{4}}"," ",0,"-(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/105*(15*b^3*f*x^7 + 21*(b^3*e - a*b^2*f)*x^5 + 35*(b^3*d - a*b^2*e + a^2*b*f)*x^3 + 105*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^4","A",0
117,1,94,0,2.971623," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{3 \, b^{2} f x^{5} + 5 \, {\left(b^{2} e - a b f\right)} x^{3} + 15 \, {\left(b^{2} d - a b e + a^{2} f\right)} x}{15 \, b^{3}}"," ",0,"(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/15*(3*b^2*f*x^5 + 5*(b^2*e - a*b*f)*x^3 + 15*(b^2*d - a*b*e + a^2*f)*x)/b^3","A",0
118,1,80,0,2.928876," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a),x, algorithm=""maxima"")","\frac{b f x^{3} + 3 \, {\left(b e - a f\right)} x}{3 \, b^{2}} - \frac{c}{a x} - \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a b^{2}}"," ",0,"1/3*(b*f*x^3 + 3*(b*e - a*f)*x)/b^2 - c/(a*x) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2)","A",0
119,1,79,0,2.938282," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a),x, algorithm=""maxima"")","\frac{f x}{b} + \frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2} b} + \frac{3 \, {\left(b c - a d\right)} x^{2} - a c}{3 \, a^{2} x^{3}}"," ",0,"f*x/b + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b) + 1/3*(3*(b*c - a*d)*x^2 - a*c)/(a^2*x^3)","A",0
120,1,97,0,3.089629," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} - \frac{15 \, {\left(b^{2} c - a b d + a^{2} e\right)} x^{4} + 3 \, a^{2} c - 5 \, {\left(a b c - a^{2} d\right)} x^{2}}{15 \, a^{3} x^{5}}"," ",0,"-(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3) - 1/15*(15*(b^2*c - a*b*d + a^2*e)*x^4 + 3*a^2*c - 5*(a*b*c - a^2*d)*x^2)/(a^3*x^5)","A",0
121,1,134,0,3.030923," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}} + \frac{105 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{6} - 35 \, {\left(a b^{2} c - a^{2} b d + a^{3} e\right)} x^{4} - 15 \, a^{3} c + 21 \, {\left(a^{2} b c - a^{3} d\right)} x^{2}}{105 \, a^{4} x^{7}}"," ",0,"(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4) + 1/105*(105*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^6 - 35*(a*b^2*c - a^2*b*d + a^3*e)*x^4 - 15*a^3*c + 21*(a^2*b*c - a^3*d)*x^2)/(a^4*x^7)","A",0
122,1,175,0,3.005674," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{5}} - \frac{315 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{8} - 105 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x^{6} + 35 \, a^{4} c + 63 \, {\left(a^{2} b^{2} c - a^{3} b d + a^{4} e\right)} x^{4} - 45 \, {\left(a^{3} b c - a^{4} d\right)} x^{2}}{315 \, a^{5} x^{9}}"," ",0,"-(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5) - 1/315*(315*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^8 - 105*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x^6 + 35*a^4*c + 63*(a^2*b^2*c - a^3*b*d + a^4*e)*x^4 - 45*(a^3*b*c - a^4*d)*x^2)/(a^5*x^9)","A",0
123,1,214,0,2.952489," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^12/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(b^{6} c - a b^{5} d + a^{2} b^{4} e - a^{3} b^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{6}} + \frac{3465 \, {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} x^{10} - 1155 \, {\left(a b^{4} c - a^{2} b^{3} d + a^{3} b^{2} e - a^{4} b f\right)} x^{8} + 693 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} x^{6} - 315 \, a^{5} c - 495 \, {\left(a^{3} b^{2} c - a^{4} b d + a^{5} e\right)} x^{4} + 385 \, {\left(a^{4} b c - a^{5} d\right)} x^{2}}{3465 \, a^{6} x^{11}}"," ",0,"(b^6*c - a*b^5*d + a^2*b^4*e - a^3*b^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^6) + 1/3465*(3465*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*x^10 - 1155*(a*b^4*c - a^2*b^3*d + a^3*b^2*e - a^4*b*f)*x^8 + 693*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*x^6 - 315*a^5*c - 495*(a^3*b^2*c - a^4*b*d + a^5*e)*x^4 + 385*(a^4*b*c - a^5*d)*x^2)/(a^6*x^11)","A",0
124,1,227,0,3.007263," ","integrate(x^6*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} x}{2 \, {\left(b^{7} x^{2} + a b^{6}\right)}} + \frac{{\left(5 \, a^{2} b^{3} c - 7 \, a^{3} b^{2} d + 9 \, a^{4} b e - 11 \, a^{5} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{6}} + \frac{35 \, b^{4} f x^{9} + 45 \, {\left(b^{4} e - 2 \, a b^{3} f\right)} x^{7} + 63 \, {\left(b^{4} d - 2 \, a b^{3} e + 3 \, a^{2} b^{2} f\right)} x^{5} + 105 \, {\left(b^{4} c - 2 \, a b^{3} d + 3 \, a^{2} b^{2} e - 4 \, a^{3} b f\right)} x^{3} - 315 \, {\left(2 \, a b^{3} c - 3 \, a^{2} b^{2} d + 4 \, a^{3} b e - 5 \, a^{4} f\right)} x}{315 \, b^{6}}"," ",0,"-1/2*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*x/(b^7*x^2 + a*b^6) + 1/2*(5*a^2*b^3*c - 7*a^3*b^2*d + 9*a^4*b*e - 11*a^5*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) + 1/315*(35*b^4*f*x^9 + 45*(b^4*e - 2*a*b^3*f)*x^7 + 63*(b^4*d - 2*a*b^3*e + 3*a^2*b^2*f)*x^5 + 105*(b^4*c - 2*a*b^3*d + 3*a^2*b^2*e - 4*a^3*b*f)*x^3 - 315*(2*a*b^3*c - 3*a^2*b^2*d + 4*a^3*b*e - 5*a^4*f)*x)/b^6","A",0
125,1,183,0,3.006300," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x}{2 \, {\left(b^{6} x^{2} + a b^{5}\right)}} - \frac{{\left(3 \, a b^{3} c - 5 \, a^{2} b^{2} d + 7 \, a^{3} b e - 9 \, a^{4} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{5}} + \frac{15 \, b^{3} f x^{7} + 21 \, {\left(b^{3} e - 2 \, a b^{2} f\right)} x^{5} + 35 \, {\left(b^{3} d - 2 \, a b^{2} e + 3 \, a^{2} b f\right)} x^{3} + 105 \, {\left(b^{3} c - 2 \, a b^{2} d + 3 \, a^{2} b e - 4 \, a^{3} f\right)} x}{105 \, b^{5}}"," ",0,"1/2*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x/(b^6*x^2 + a*b^5) - 1/2*(3*a*b^3*c - 5*a^2*b^2*d + 7*a^3*b*e - 9*a^4*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/105*(15*b^3*f*x^7 + 21*(b^3*e - 2*a*b^2*f)*x^5 + 35*(b^3*d - 2*a*b^2*e + 3*a^2*b*f)*x^3 + 105*(b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x)/b^5","A",0
126,1,140,0,2.956533," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} + \frac{{\left(b^{3} c - 3 \, a b^{2} d + 5 \, a^{2} b e - 7 \, a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{4}} + \frac{3 \, b^{2} f x^{5} + 5 \, {\left(b^{2} e - 2 \, a b f\right)} x^{3} + 15 \, {\left(b^{2} d - 2 \, a b e + 3 \, a^{2} f\right)} x}{15 \, b^{4}}"," ",0,"-1/2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x/(b^5*x^2 + a*b^4) + 1/2*(b^3*c - 3*a*b^2*d + 5*a^2*b*e - 7*a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/15*(3*b^2*f*x^5 + 5*(b^2*e - 2*a*b*f)*x^3 + 15*(b^2*d - 2*a*b*e + 3*a^2*f)*x)/b^4","A",0
127,1,117,0,2.966787," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}} + \frac{b f x^{3} + 3 \, {\left(b e - 2 \, a f\right)} x}{3 \, b^{3}} + \frac{{\left(b^{3} c + a b^{2} d - 3 \, a^{2} b e + 5 \, a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{3}}"," ",0,"1/2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x/(a*b^4*x^2 + a^2*b^3) + 1/3*(b*f*x^3 + 3*(b*e - 2*a*f)*x)/b^3 + 1/2*(b^3*c + a*b^2*d - 3*a^2*b*e + 5*a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^3)","A",0
128,1,117,0,2.992249," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{2 \, a b^{2} c + {\left(3 \, b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{2}}{2 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2} x\right)}} + \frac{f x}{b^{2}} - \frac{{\left(3 \, b^{3} c - a b^{2} d - a^{2} b e + 3 \, a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2} b^{2}}"," ",0,"-1/2*(2*a*b^2*c + (3*b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(a^2*b^3*x^3 + a^3*b^2*x) + f*x/b^2 - 1/2*(3*b^3*c - a*b^2*d - a^2*b*e + 3*a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^2)","A",0
129,1,130,0,3.023308," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, b^{3} c - 3 \, a b^{2} d + a^{2} b e - a^{3} f\right)} x^{4} - 2 \, a^{2} b c + 2 \, {\left(5 \, a b^{2} c - 3 \, a^{2} b d\right)} x^{2}}{6 \, {\left(a^{3} b^{2} x^{5} + a^{4} b x^{3}\right)}} + \frac{{\left(5 \, b^{3} c - 3 \, a b^{2} d + a^{2} b e + a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{3} b}"," ",0,"1/6*(3*(5*b^3*c - 3*a*b^2*d + a^2*b*e - a^3*f)*x^4 - 2*a^2*b*c + 2*(5*a*b^2*c - 3*a^2*b*d)*x^2)/(a^3*b^2*x^5 + a^4*b*x^3) + 1/2*(5*b^3*c - 3*a*b^2*d + a^2*b*e + a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3*b)","A",0
130,1,151,0,2.989363," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{15 \, {\left(7 \, b^{3} c - 5 \, a b^{2} d + 3 \, a^{2} b e - a^{3} f\right)} x^{6} + 10 \, {\left(7 \, a b^{2} c - 5 \, a^{2} b d + 3 \, a^{3} e\right)} x^{4} + 6 \, a^{3} c - 2 \, {\left(7 \, a^{2} b c - 5 \, a^{3} d\right)} x^{2}}{30 \, {\left(a^{4} b x^{7} + a^{5} x^{5}\right)}} - \frac{{\left(7 \, b^{3} c - 5 \, a b^{2} d + 3 \, a^{2} b e - a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{4}}"," ",0,"-1/30*(15*(7*b^3*c - 5*a*b^2*d + 3*a^2*b*e - a^3*f)*x^6 + 10*(7*a*b^2*c - 5*a^2*b*d + 3*a^3*e)*x^4 + 6*a^3*c - 2*(7*a^2*b*c - 5*a^3*d)*x^2)/(a^4*b*x^7 + a^5*x^5) - 1/2*(7*b^3*c - 5*a*b^2*d + 3*a^2*b*e - a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4)","A",0
131,1,194,0,3.047202," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{105 \, {\left(9 \, b^{4} c - 7 \, a b^{3} d + 5 \, a^{2} b^{2} e - 3 \, a^{3} b f\right)} x^{8} + 70 \, {\left(9 \, a b^{3} c - 7 \, a^{2} b^{2} d + 5 \, a^{3} b e - 3 \, a^{4} f\right)} x^{6} - 30 \, a^{4} c - 14 \, {\left(9 \, a^{2} b^{2} c - 7 \, a^{3} b d + 5 \, a^{4} e\right)} x^{4} + 6 \, {\left(9 \, a^{3} b c - 7 \, a^{4} d\right)} x^{2}}{210 \, {\left(a^{5} b x^{9} + a^{6} x^{7}\right)}} + \frac{{\left(9 \, b^{4} c - 7 \, a b^{3} d + 5 \, a^{2} b^{2} e - 3 \, a^{3} b f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{5}}"," ",0,"1/210*(105*(9*b^4*c - 7*a*b^3*d + 5*a^2*b^2*e - 3*a^3*b*f)*x^8 + 70*(9*a*b^3*c - 7*a^2*b^2*d + 5*a^3*b*e - 3*a^4*f)*x^6 - 30*a^4*c - 14*(9*a^2*b^2*c - 7*a^3*b*d + 5*a^4*e)*x^4 + 6*(9*a^3*b*c - 7*a^4*d)*x^2)/(a^5*b*x^9 + a^6*x^7) + 1/2*(9*b^4*c - 7*a*b^3*d + 5*a^2*b^2*e - 3*a^3*b*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5)","A",0
132,1,238,0,2.985065," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{315 \, {\left(11 \, b^{5} c - 9 \, a b^{4} d + 7 \, a^{2} b^{3} e - 5 \, a^{3} b^{2} f\right)} x^{10} + 210 \, {\left(11 \, a b^{4} c - 9 \, a^{2} b^{3} d + 7 \, a^{3} b^{2} e - 5 \, a^{4} b f\right)} x^{8} - 42 \, {\left(11 \, a^{2} b^{3} c - 9 \, a^{3} b^{2} d + 7 \, a^{4} b e - 5 \, a^{5} f\right)} x^{6} + 70 \, a^{5} c + 18 \, {\left(11 \, a^{3} b^{2} c - 9 \, a^{4} b d + 7 \, a^{5} e\right)} x^{4} - 10 \, {\left(11 \, a^{4} b c - 9 \, a^{5} d\right)} x^{2}}{630 \, {\left(a^{6} b x^{11} + a^{7} x^{9}\right)}} - \frac{{\left(11 \, b^{5} c - 9 \, a b^{4} d + 7 \, a^{2} b^{3} e - 5 \, a^{3} b^{2} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{6}}"," ",0,"-1/630*(315*(11*b^5*c - 9*a*b^4*d + 7*a^2*b^3*e - 5*a^3*b^2*f)*x^10 + 210*(11*a*b^4*c - 9*a^2*b^3*d + 7*a^3*b^2*e - 5*a^4*b*f)*x^8 - 42*(11*a^2*b^3*c - 9*a^3*b^2*d + 7*a^4*b*e - 5*a^5*f)*x^6 + 70*a^5*c + 18*(11*a^3*b^2*c - 9*a^4*b*d + 7*a^5*e)*x^4 - 10*(11*a^4*b*c - 9*a^5*d)*x^2)/(a^6*b*x^11 + a^7*x^9) - 1/2*(11*b^5*c - 9*a*b^4*d + 7*a^2*b^3*e - 5*a^3*b^2*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^6)","A",0
133,1,281,0,3.104145," ","integrate(x^8*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(13 \, a^{2} b^{4} c - 17 \, a^{3} b^{3} d + 21 \, a^{4} b^{2} e - 25 \, a^{5} b f\right)} x^{3} + {\left(11 \, a^{3} b^{3} c - 15 \, a^{4} b^{2} d + 19 \, a^{5} b e - 23 \, a^{6} f\right)} x}{8 \, {\left(b^{9} x^{4} + 2 \, a b^{8} x^{2} + a^{2} b^{7}\right)}} + \frac{{\left(35 \, a^{2} b^{3} c - 63 \, a^{3} b^{2} d + 99 \, a^{4} b e - 143 \, a^{5} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{7}} + \frac{35 \, b^{4} f x^{9} + 45 \, {\left(b^{4} e - 3 \, a b^{3} f\right)} x^{7} + 63 \, {\left(b^{4} d - 3 \, a b^{3} e + 6 \, a^{2} b^{2} f\right)} x^{5} + 105 \, {\left(b^{4} c - 3 \, a b^{3} d + 6 \, a^{2} b^{2} e - 10 \, a^{3} b f\right)} x^{3} - 315 \, {\left(3 \, a b^{3} c - 6 \, a^{2} b^{2} d + 10 \, a^{3} b e - 15 \, a^{4} f\right)} x}{315 \, b^{7}}"," ",0,"-1/8*((13*a^2*b^4*c - 17*a^3*b^3*d + 21*a^4*b^2*e - 25*a^5*b*f)*x^3 + (11*a^3*b^3*c - 15*a^4*b^2*d + 19*a^5*b*e - 23*a^6*f)*x)/(b^9*x^4 + 2*a*b^8*x^2 + a^2*b^7) + 1/8*(35*a^2*b^3*c - 63*a^3*b^2*d + 99*a^4*b*e - 143*a^5*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^7) + 1/315*(35*b^4*f*x^9 + 45*(b^4*e - 3*a*b^3*f)*x^7 + 63*(b^4*d - 3*a*b^3*e + 6*a^2*b^2*f)*x^5 + 105*(b^4*c - 3*a*b^3*d + 6*a^2*b^2*e - 10*a^3*b*f)*x^3 - 315*(3*a*b^3*c - 6*a^2*b^2*d + 10*a^3*b*e - 15*a^4*f)*x)/b^7","A",0
134,1,237,0,2.991019," ","integrate(x^6*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(9 \, a b^{4} c - 13 \, a^{2} b^{3} d + 17 \, a^{3} b^{2} e - 21 \, a^{4} b f\right)} x^{3} + {\left(7 \, a^{2} b^{3} c - 11 \, a^{3} b^{2} d + 15 \, a^{4} b e - 19 \, a^{5} f\right)} x}{8 \, {\left(b^{8} x^{4} + 2 \, a b^{7} x^{2} + a^{2} b^{6}\right)}} - \frac{{\left(15 \, a b^{3} c - 35 \, a^{2} b^{2} d + 63 \, a^{3} b e - 99 \, a^{4} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{6}} + \frac{15 \, b^{3} f x^{7} + 21 \, {\left(b^{3} e - 3 \, a b^{2} f\right)} x^{5} + 35 \, {\left(b^{3} d - 3 \, a b^{2} e + 6 \, a^{2} b f\right)} x^{3} + 105 \, {\left(b^{3} c - 3 \, a b^{2} d + 6 \, a^{2} b e - 10 \, a^{3} f\right)} x}{105 \, b^{6}}"," ",0,"1/8*((9*a*b^4*c - 13*a^2*b^3*d + 17*a^3*b^2*e - 21*a^4*b*f)*x^3 + (7*a^2*b^3*c - 11*a^3*b^2*d + 15*a^4*b*e - 19*a^5*f)*x)/(b^8*x^4 + 2*a*b^7*x^2 + a^2*b^6) - 1/8*(15*a*b^3*c - 35*a^2*b^2*d + 63*a^3*b*e - 99*a^4*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) + 1/105*(15*b^3*f*x^7 + 21*(b^3*e - 3*a*b^2*f)*x^5 + 35*(b^3*d - 3*a*b^2*e + 6*a^2*b*f)*x^3 + 105*(b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x)/b^6","A",0
135,1,193,0,3.038293," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(5 \, b^{4} c - 9 \, a b^{3} d + 13 \, a^{2} b^{2} e - 17 \, a^{3} b f\right)} x^{3} + {\left(3 \, a b^{3} c - 7 \, a^{2} b^{2} d + 11 \, a^{3} b e - 15 \, a^{4} f\right)} x}{8 \, {\left(b^{7} x^{4} + 2 \, a b^{6} x^{2} + a^{2} b^{5}\right)}} + \frac{{\left(3 \, b^{3} c - 15 \, a b^{2} d + 35 \, a^{2} b e - 63 \, a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{5}} + \frac{3 \, b^{2} f x^{5} + 5 \, {\left(b^{2} e - 3 \, a b f\right)} x^{3} + 15 \, {\left(b^{2} d - 3 \, a b e + 6 \, a^{2} f\right)} x}{15 \, b^{5}}"," ",0,"-1/8*((5*b^4*c - 9*a*b^3*d + 13*a^2*b^2*e - 17*a^3*b*f)*x^3 + (3*a*b^3*c - 7*a^2*b^2*d + 11*a^3*b*e - 15*a^4*f)*x)/(b^7*x^4 + 2*a*b^6*x^2 + a^2*b^5) + 1/8*(3*b^3*c - 15*a*b^2*d + 35*a^2*b*e - 63*a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/15*(3*b^2*f*x^5 + 5*(b^2*e - 3*a*b*f)*x^3 + 15*(b^2*d - 3*a*b*e + 6*a^2*f)*x)/b^5","A",0
136,1,169,0,3.021313," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(b^{4} c - 5 \, a b^{3} d + 9 \, a^{2} b^{2} e - 13 \, a^{3} b f\right)} x^{3} - {\left(a b^{3} c + 3 \, a^{2} b^{2} d - 7 \, a^{3} b e + 11 \, a^{4} f\right)} x}{8 \, {\left(a b^{6} x^{4} + 2 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}} + \frac{b f x^{3} + 3 \, {\left(b e - 3 \, a f\right)} x}{3 \, b^{4}} + \frac{{\left(b^{3} c + 3 \, a b^{2} d - 15 \, a^{2} b e + 35 \, a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a b^{4}}"," ",0,"1/8*((b^4*c - 5*a*b^3*d + 9*a^2*b^2*e - 13*a^3*b*f)*x^3 - (a*b^3*c + 3*a^2*b^2*d - 7*a^3*b*e + 11*a^4*f)*x)/(a*b^6*x^4 + 2*a^2*b^5*x^2 + a^3*b^4) + 1/3*(b*f*x^3 + 3*(b*e - 3*a*f)*x)/b^4 + 1/8*(b^3*c + 3*a*b^2*d - 15*a^2*b*e + 35*a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^4)","A",0
137,1,154,0,2.996105," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(3 \, b^{4} c + a b^{3} d - 5 \, a^{2} b^{2} e + 9 \, a^{3} b f\right)} x^{3} + {\left(5 \, a b^{3} c - a^{2} b^{2} d - 3 \, a^{3} b e + 7 \, a^{4} f\right)} x}{8 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}} + \frac{f x}{b^{3}} + \frac{{\left(3 \, b^{3} c + a b^{2} d + 3 \, a^{2} b e - 15 \, a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b^{3}}"," ",0,"1/8*((3*b^4*c + a*b^3*d - 5*a^2*b^2*e + 9*a^3*b*f)*x^3 + (5*a*b^3*c - a^2*b^2*d - 3*a^3*b*e + 7*a^4*f)*x)/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3) + f*x/b^3 + 1/8*(3*b^3*c + a*b^2*d + 3*a^2*b*e - 15*a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^3)","A",0
138,1,161,0,2.991999," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{8 \, a^{2} b^{2} c + {\left(15 \, b^{4} c - 3 \, a b^{3} d - a^{2} b^{2} e + 5 \, a^{3} b f\right)} x^{4} + {\left(25 \, a b^{3} c - 5 \, a^{2} b^{2} d + a^{3} b e + 3 \, a^{4} f\right)} x^{2}}{8 \, {\left(a^{3} b^{4} x^{5} + 2 \, a^{4} b^{3} x^{3} + a^{5} b^{2} x\right)}} - \frac{{\left(15 \, b^{3} c - 3 \, a b^{2} d - a^{2} b e - 3 \, a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{3} b^{2}}"," ",0,"-1/8*(8*a^2*b^2*c + (15*b^4*c - 3*a*b^3*d - a^2*b^2*e + 5*a^3*b*f)*x^4 + (25*a*b^3*c - 5*a^2*b^2*d + a^3*b*e + 3*a^4*f)*x^2)/(a^3*b^4*x^5 + 2*a^4*b^3*x^3 + a^5*b^2*x) - 1/8*(15*b^3*c - 3*a*b^2*d - a^2*b*e - 3*a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3*b^2)","A",0
139,1,181,0,3.073400," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(35 \, b^{4} c - 15 \, a b^{3} d + 3 \, a^{2} b^{2} e + a^{3} b f\right)} x^{6} - 8 \, a^{3} b c + {\left(175 \, a b^{3} c - 75 \, a^{2} b^{2} d + 15 \, a^{3} b e - 3 \, a^{4} f\right)} x^{4} + 8 \, {\left(7 \, a^{2} b^{2} c - 3 \, a^{3} b d\right)} x^{2}}{24 \, {\left(a^{4} b^{3} x^{7} + 2 \, a^{5} b^{2} x^{5} + a^{6} b x^{3}\right)}} + \frac{{\left(35 \, b^{3} c - 15 \, a b^{2} d + 3 \, a^{2} b e + a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{4} b}"," ",0,"1/24*(3*(35*b^4*c - 15*a*b^3*d + 3*a^2*b^2*e + a^3*b*f)*x^6 - 8*a^3*b*c + (175*a*b^3*c - 75*a^2*b^2*d + 15*a^3*b*e - 3*a^4*f)*x^4 + 8*(7*a^2*b^2*c - 3*a^3*b*d)*x^2)/(a^4*b^3*x^7 + 2*a^5*b^2*x^5 + a^6*b*x^3) + 1/8*(35*b^3*c - 15*a*b^2*d + 3*a^2*b*e + a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4*b)","A",0
140,1,202,0,2.977667," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{15 \, {\left(63 \, b^{4} c - 35 \, a b^{3} d + 15 \, a^{2} b^{2} e - 3 \, a^{3} b f\right)} x^{8} + 25 \, {\left(63 \, a b^{3} c - 35 \, a^{2} b^{2} d + 15 \, a^{3} b e - 3 \, a^{4} f\right)} x^{6} + 24 \, a^{4} c + 8 \, {\left(63 \, a^{2} b^{2} c - 35 \, a^{3} b d + 15 \, a^{4} e\right)} x^{4} - 8 \, {\left(9 \, a^{3} b c - 5 \, a^{4} d\right)} x^{2}}{120 \, {\left(a^{5} b^{2} x^{9} + 2 \, a^{6} b x^{7} + a^{7} x^{5}\right)}} - \frac{{\left(63 \, b^{3} c - 35 \, a b^{2} d + 15 \, a^{2} b e - 3 \, a^{3} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{5}}"," ",0,"-1/120*(15*(63*b^4*c - 35*a*b^3*d + 15*a^2*b^2*e - 3*a^3*b*f)*x^8 + 25*(63*a*b^3*c - 35*a^2*b^2*d + 15*a^3*b*e - 3*a^4*f)*x^6 + 24*a^4*c + 8*(63*a^2*b^2*c - 35*a^3*b*d + 15*a^4*e)*x^4 - 8*(9*a^3*b*c - 5*a^4*d)*x^2)/(a^5*b^2*x^9 + 2*a^6*b*x^7 + a^7*x^5) - 1/8*(63*b^3*c - 35*a*b^2*d + 15*a^2*b*e - 3*a^3*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5)","A",0
141,1,247,0,3.026442," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{105 \, {\left(99 \, b^{5} c - 63 \, a b^{4} d + 35 \, a^{2} b^{3} e - 15 \, a^{3} b^{2} f\right)} x^{10} + 175 \, {\left(99 \, a b^{4} c - 63 \, a^{2} b^{3} d + 35 \, a^{3} b^{2} e - 15 \, a^{4} b f\right)} x^{8} + 56 \, {\left(99 \, a^{2} b^{3} c - 63 \, a^{3} b^{2} d + 35 \, a^{4} b e - 15 \, a^{5} f\right)} x^{6} - 120 \, a^{5} c - 8 \, {\left(99 \, a^{3} b^{2} c - 63 \, a^{4} b d + 35 \, a^{5} e\right)} x^{4} + 24 \, {\left(11 \, a^{4} b c - 7 \, a^{5} d\right)} x^{2}}{840 \, {\left(a^{6} b^{2} x^{11} + 2 \, a^{7} b x^{9} + a^{8} x^{7}\right)}} + \frac{{\left(99 \, b^{4} c - 63 \, a b^{3} d + 35 \, a^{2} b^{2} e - 15 \, a^{3} b f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{6}}"," ",0,"1/840*(105*(99*b^5*c - 63*a*b^4*d + 35*a^2*b^3*e - 15*a^3*b^2*f)*x^10 + 175*(99*a*b^4*c - 63*a^2*b^3*d + 35*a^3*b^2*e - 15*a^4*b*f)*x^8 + 56*(99*a^2*b^3*c - 63*a^3*b^2*d + 35*a^4*b*e - 15*a^5*f)*x^6 - 120*a^5*c - 8*(99*a^3*b^2*c - 63*a^4*b*d + 35*a^5*e)*x^4 + 24*(11*a^4*b*c - 7*a^5*d)*x^2)/(a^6*b^2*x^11 + 2*a^7*b*x^9 + a^8*x^7) + 1/8*(99*b^4*c - 63*a*b^3*d + 35*a^2*b^2*e - 15*a^3*b*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^6)","A",0
142,1,291,0,3.090206," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{315 \, {\left(143 \, b^{6} c - 99 \, a b^{5} d + 63 \, a^{2} b^{4} e - 35 \, a^{3} b^{3} f\right)} x^{12} + 525 \, {\left(143 \, a b^{5} c - 99 \, a^{2} b^{4} d + 63 \, a^{3} b^{3} e - 35 \, a^{4} b^{2} f\right)} x^{10} + 168 \, {\left(143 \, a^{2} b^{4} c - 99 \, a^{3} b^{3} d + 63 \, a^{4} b^{2} e - 35 \, a^{5} b f\right)} x^{8} + 280 \, a^{6} c - 24 \, {\left(143 \, a^{3} b^{3} c - 99 \, a^{4} b^{2} d + 63 \, a^{5} b e - 35 \, a^{6} f\right)} x^{6} + 8 \, {\left(143 \, a^{4} b^{2} c - 99 \, a^{5} b d + 63 \, a^{6} e\right)} x^{4} - 40 \, {\left(13 \, a^{5} b c - 9 \, a^{6} d\right)} x^{2}}{2520 \, {\left(a^{7} b^{2} x^{13} + 2 \, a^{8} b x^{11} + a^{9} x^{9}\right)}} - \frac{{\left(143 \, b^{5} c - 99 \, a b^{4} d + 63 \, a^{2} b^{3} e - 35 \, a^{3} b^{2} f\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{7}}"," ",0,"-1/2520*(315*(143*b^6*c - 99*a*b^5*d + 63*a^2*b^4*e - 35*a^3*b^3*f)*x^12 + 525*(143*a*b^5*c - 99*a^2*b^4*d + 63*a^3*b^3*e - 35*a^4*b^2*f)*x^10 + 168*(143*a^2*b^4*c - 99*a^3*b^3*d + 63*a^4*b^2*e - 35*a^5*b*f)*x^8 + 280*a^6*c - 24*(143*a^3*b^3*c - 99*a^4*b^2*d + 63*a^5*b*e - 35*a^6*f)*x^6 + 8*(143*a^4*b^2*c - 99*a^5*b*d + 63*a^6*e)*x^4 - 40*(13*a^5*b*c - 9*a^6*d)*x^2)/(a^7*b^2*x^13 + 2*a^8*b*x^11 + a^9*x^9) - 1/8*(143*b^5*c - 99*a*b^4*d + 63*a^2*b^3*e - 35*a^3*b^2*f)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^7)","A",0
143,1,347,0,1.400716," ","integrate(x^5*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{10}}{11 \, b} + \frac{\sqrt{b x^{2} + a} e x^{8}}{9 \, b} - \frac{10 \, \sqrt{b x^{2} + a} a f x^{8}}{99 \, b^{2}} + \frac{\sqrt{b x^{2} + a} d x^{6}}{7 \, b} - \frac{8 \, \sqrt{b x^{2} + a} a e x^{6}}{63 \, b^{2}} + \frac{80 \, \sqrt{b x^{2} + a} a^{2} f x^{6}}{693 \, b^{3}} + \frac{\sqrt{b x^{2} + a} c x^{4}}{5 \, b} - \frac{6 \, \sqrt{b x^{2} + a} a d x^{4}}{35 \, b^{2}} + \frac{16 \, \sqrt{b x^{2} + a} a^{2} e x^{4}}{105 \, b^{3}} - \frac{32 \, \sqrt{b x^{2} + a} a^{3} f x^{4}}{231 \, b^{4}} - \frac{4 \, \sqrt{b x^{2} + a} a c x^{2}}{15 \, b^{2}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} d x^{2}}{35 \, b^{3}} - \frac{64 \, \sqrt{b x^{2} + a} a^{3} e x^{2}}{315 \, b^{4}} + \frac{128 \, \sqrt{b x^{2} + a} a^{4} f x^{2}}{693 \, b^{5}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} c}{15 \, b^{3}} - \frac{16 \, \sqrt{b x^{2} + a} a^{3} d}{35 \, b^{4}} + \frac{128 \, \sqrt{b x^{2} + a} a^{4} e}{315 \, b^{5}} - \frac{256 \, \sqrt{b x^{2} + a} a^{5} f}{693 \, b^{6}}"," ",0,"1/11*sqrt(b*x^2 + a)*f*x^10/b + 1/9*sqrt(b*x^2 + a)*e*x^8/b - 10/99*sqrt(b*x^2 + a)*a*f*x^8/b^2 + 1/7*sqrt(b*x^2 + a)*d*x^6/b - 8/63*sqrt(b*x^2 + a)*a*e*x^6/b^2 + 80/693*sqrt(b*x^2 + a)*a^2*f*x^6/b^3 + 1/5*sqrt(b*x^2 + a)*c*x^4/b - 6/35*sqrt(b*x^2 + a)*a*d*x^4/b^2 + 16/105*sqrt(b*x^2 + a)*a^2*e*x^4/b^3 - 32/231*sqrt(b*x^2 + a)*a^3*f*x^4/b^4 - 4/15*sqrt(b*x^2 + a)*a*c*x^2/b^2 + 8/35*sqrt(b*x^2 + a)*a^2*d*x^2/b^3 - 64/315*sqrt(b*x^2 + a)*a^3*e*x^2/b^4 + 128/693*sqrt(b*x^2 + a)*a^4*f*x^2/b^5 + 8/15*sqrt(b*x^2 + a)*a^2*c/b^3 - 16/35*sqrt(b*x^2 + a)*a^3*d/b^4 + 128/315*sqrt(b*x^2 + a)*a^4*e/b^5 - 256/693*sqrt(b*x^2 + a)*a^5*f/b^6","A",0
144,1,263,0,1.448910," ","integrate(x^3*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{8}}{9 \, b} + \frac{\sqrt{b x^{2} + a} e x^{6}}{7 \, b} - \frac{8 \, \sqrt{b x^{2} + a} a f x^{6}}{63 \, b^{2}} + \frac{\sqrt{b x^{2} + a} d x^{4}}{5 \, b} - \frac{6 \, \sqrt{b x^{2} + a} a e x^{4}}{35 \, b^{2}} + \frac{16 \, \sqrt{b x^{2} + a} a^{2} f x^{4}}{105 \, b^{3}} + \frac{\sqrt{b x^{2} + a} c x^{2}}{3 \, b} - \frac{4 \, \sqrt{b x^{2} + a} a d x^{2}}{15 \, b^{2}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} e x^{2}}{35 \, b^{3}} - \frac{64 \, \sqrt{b x^{2} + a} a^{3} f x^{2}}{315 \, b^{4}} - \frac{2 \, \sqrt{b x^{2} + a} a c}{3 \, b^{2}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} d}{15 \, b^{3}} - \frac{16 \, \sqrt{b x^{2} + a} a^{3} e}{35 \, b^{4}} + \frac{128 \, \sqrt{b x^{2} + a} a^{4} f}{315 \, b^{5}}"," ",0,"1/9*sqrt(b*x^2 + a)*f*x^8/b + 1/7*sqrt(b*x^2 + a)*e*x^6/b - 8/63*sqrt(b*x^2 + a)*a*f*x^6/b^2 + 1/5*sqrt(b*x^2 + a)*d*x^4/b - 6/35*sqrt(b*x^2 + a)*a*e*x^4/b^2 + 16/105*sqrt(b*x^2 + a)*a^2*f*x^4/b^3 + 1/3*sqrt(b*x^2 + a)*c*x^2/b - 4/15*sqrt(b*x^2 + a)*a*d*x^2/b^2 + 8/35*sqrt(b*x^2 + a)*a^2*e*x^2/b^3 - 64/315*sqrt(b*x^2 + a)*a^3*f*x^2/b^4 - 2/3*sqrt(b*x^2 + a)*a*c/b^2 + 8/15*sqrt(b*x^2 + a)*a^2*d/b^3 - 16/35*sqrt(b*x^2 + a)*a^3*e/b^4 + 128/315*sqrt(b*x^2 + a)*a^4*f/b^5","A",0
145,1,180,0,1.348724," ","integrate(x*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{6}}{7 \, b} + \frac{\sqrt{b x^{2} + a} e x^{4}}{5 \, b} - \frac{6 \, \sqrt{b x^{2} + a} a f x^{4}}{35 \, b^{2}} + \frac{\sqrt{b x^{2} + a} d x^{2}}{3 \, b} - \frac{4 \, \sqrt{b x^{2} + a} a e x^{2}}{15 \, b^{2}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} f x^{2}}{35 \, b^{3}} + \frac{\sqrt{b x^{2} + a} c}{b} - \frac{2 \, \sqrt{b x^{2} + a} a d}{3 \, b^{2}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} e}{15 \, b^{3}} - \frac{16 \, \sqrt{b x^{2} + a} a^{3} f}{35 \, b^{4}}"," ",0,"1/7*sqrt(b*x^2 + a)*f*x^6/b + 1/5*sqrt(b*x^2 + a)*e*x^4/b - 6/35*sqrt(b*x^2 + a)*a*f*x^4/b^2 + 1/3*sqrt(b*x^2 + a)*d*x^2/b - 4/15*sqrt(b*x^2 + a)*a*e*x^2/b^2 + 8/35*sqrt(b*x^2 + a)*a^2*f*x^2/b^3 + sqrt(b*x^2 + a)*c/b - 2/3*sqrt(b*x^2 + a)*a*d/b^2 + 8/15*sqrt(b*x^2 + a)*a^2*e/b^3 - 16/35*sqrt(b*x^2 + a)*a^3*f/b^4","A",0
146,1,122,0,1.346010," ","integrate((f*x^6+e*x^4+d*x^2+c)/x/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{4}}{5 \, b} + \frac{\sqrt{b x^{2} + a} e x^{2}}{3 \, b} - \frac{4 \, \sqrt{b x^{2} + a} a f x^{2}}{15 \, b^{2}} - \frac{c \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{\sqrt{a}} + \frac{\sqrt{b x^{2} + a} d}{b} - \frac{2 \, \sqrt{b x^{2} + a} a e}{3 \, b^{2}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} f}{15 \, b^{3}}"," ",0,"1/5*sqrt(b*x^2 + a)*f*x^4/b + 1/3*sqrt(b*x^2 + a)*e*x^2/b - 4/15*sqrt(b*x^2 + a)*a*f*x^2/b^2 - c*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + sqrt(b*x^2 + a)*d/b - 2/3*sqrt(b*x^2 + a)*a*e/b^2 + 8/15*sqrt(b*x^2 + a)*a^2*f/b^3","A",0
147,1,104,0,1.327354," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^3/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{2}}{3 \, b} + \frac{b c \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{3}{2}}} - \frac{d \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{\sqrt{a}} + \frac{\sqrt{b x^{2} + a} e}{b} - \frac{2 \, \sqrt{b x^{2} + a} a f}{3 \, b^{2}} - \frac{\sqrt{b x^{2} + a} c}{2 \, a x^{2}}"," ",0,"1/3*sqrt(b*x^2 + a)*f*x^2/b + 1/2*b*c*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) - d*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + sqrt(b*x^2 + a)*e/b - 2/3*sqrt(b*x^2 + a)*a*f/b^2 - 1/2*sqrt(b*x^2 + a)*c/(a*x^2)","A",0
148,1,128,0,1.379332," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^5/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{3 \, b^{2} c \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, a^{\frac{5}{2}}} + \frac{b d \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{3}{2}}} - \frac{e \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{\sqrt{a}} + \frac{\sqrt{b x^{2} + a} f}{b} + \frac{3 \, \sqrt{b x^{2} + a} b c}{8 \, a^{2} x^{2}} - \frac{\sqrt{b x^{2} + a} d}{2 \, a x^{2}} - \frac{\sqrt{b x^{2} + a} c}{4 \, a x^{4}}"," ",0,"-3/8*b^2*c*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) + 1/2*b*d*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) - e*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + sqrt(b*x^2 + a)*f/b + 3/8*sqrt(b*x^2 + a)*b*c/(a^2*x^2) - 1/2*sqrt(b*x^2 + a)*d/(a*x^2) - 1/4*sqrt(b*x^2 + a)*c/(a*x^4)","A",0
149,1,193,0,1.388398," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^7/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{5 \, b^{3} c \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{16 \, a^{\frac{7}{2}}} - \frac{3 \, b^{2} d \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, a^{\frac{5}{2}}} + \frac{b e \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{3}{2}}} - \frac{f \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{\sqrt{a}} - \frac{5 \, \sqrt{b x^{2} + a} b^{2} c}{16 \, a^{3} x^{2}} + \frac{3 \, \sqrt{b x^{2} + a} b d}{8 \, a^{2} x^{2}} - \frac{\sqrt{b x^{2} + a} e}{2 \, a x^{2}} + \frac{5 \, \sqrt{b x^{2} + a} b c}{24 \, a^{2} x^{4}} - \frac{\sqrt{b x^{2} + a} d}{4 \, a x^{4}} - \frac{\sqrt{b x^{2} + a} c}{6 \, a x^{6}}"," ",0,"5/16*b^3*c*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(7/2) - 3/8*b^2*d*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) + 1/2*b*e*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) - f*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) - 5/16*sqrt(b*x^2 + a)*b^2*c/(a^3*x^2) + 3/8*sqrt(b*x^2 + a)*b*d/(a^2*x^2) - 1/2*sqrt(b*x^2 + a)*e/(a*x^2) + 5/24*sqrt(b*x^2 + a)*b*c/(a^2*x^4) - 1/4*sqrt(b*x^2 + a)*d/(a*x^4) - 1/6*sqrt(b*x^2 + a)*c/(a*x^6)","A",0
150,1,275,0,1.345548," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^9/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{35 \, b^{4} c \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{128 \, a^{\frac{9}{2}}} + \frac{5 \, b^{3} d \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{16 \, a^{\frac{7}{2}}} - \frac{3 \, b^{2} e \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, a^{\frac{5}{2}}} + \frac{b f \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{3}{2}}} + \frac{35 \, \sqrt{b x^{2} + a} b^{3} c}{128 \, a^{4} x^{2}} - \frac{5 \, \sqrt{b x^{2} + a} b^{2} d}{16 \, a^{3} x^{2}} + \frac{3 \, \sqrt{b x^{2} + a} b e}{8 \, a^{2} x^{2}} - \frac{\sqrt{b x^{2} + a} f}{2 \, a x^{2}} - \frac{35 \, \sqrt{b x^{2} + a} b^{2} c}{192 \, a^{3} x^{4}} + \frac{5 \, \sqrt{b x^{2} + a} b d}{24 \, a^{2} x^{4}} - \frac{\sqrt{b x^{2} + a} e}{4 \, a x^{4}} + \frac{7 \, \sqrt{b x^{2} + a} b c}{48 \, a^{2} x^{6}} - \frac{\sqrt{b x^{2} + a} d}{6 \, a x^{6}} - \frac{\sqrt{b x^{2} + a} c}{8 \, a x^{8}}"," ",0,"-35/128*b^4*c*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(9/2) + 5/16*b^3*d*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(7/2) - 3/8*b^2*e*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) + 1/2*b*f*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) + 35/128*sqrt(b*x^2 + a)*b^3*c/(a^4*x^2) - 5/16*sqrt(b*x^2 + a)*b^2*d/(a^3*x^2) + 3/8*sqrt(b*x^2 + a)*b*e/(a^2*x^2) - 1/2*sqrt(b*x^2 + a)*f/(a*x^2) - 35/192*sqrt(b*x^2 + a)*b^2*c/(a^3*x^4) + 5/24*sqrt(b*x^2 + a)*b*d/(a^2*x^4) - 1/4*sqrt(b*x^2 + a)*e/(a*x^4) + 7/48*sqrt(b*x^2 + a)*b*c/(a^2*x^6) - 1/6*sqrt(b*x^2 + a)*d/(a*x^6) - 1/8*sqrt(b*x^2 + a)*c/(a*x^8)","A",0
151,1,339,0,1.458696," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{9}}{10 \, b} + \frac{\sqrt{b x^{2} + a} e x^{7}}{8 \, b} - \frac{9 \, \sqrt{b x^{2} + a} a f x^{7}}{80 \, b^{2}} + \frac{\sqrt{b x^{2} + a} d x^{5}}{6 \, b} - \frac{7 \, \sqrt{b x^{2} + a} a e x^{5}}{48 \, b^{2}} + \frac{21 \, \sqrt{b x^{2} + a} a^{2} f x^{5}}{160 \, b^{3}} + \frac{\sqrt{b x^{2} + a} c x^{3}}{4 \, b} - \frac{5 \, \sqrt{b x^{2} + a} a d x^{3}}{24 \, b^{2}} + \frac{35 \, \sqrt{b x^{2} + a} a^{2} e x^{3}}{192 \, b^{3}} - \frac{21 \, \sqrt{b x^{2} + a} a^{3} f x^{3}}{128 \, b^{4}} - \frac{3 \, \sqrt{b x^{2} + a} a c x}{8 \, b^{2}} + \frac{5 \, \sqrt{b x^{2} + a} a^{2} d x}{16 \, b^{3}} - \frac{35 \, \sqrt{b x^{2} + a} a^{3} e x}{128 \, b^{4}} + \frac{63 \, \sqrt{b x^{2} + a} a^{4} f x}{256 \, b^{5}} + \frac{3 \, a^{2} c \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{5}{2}}} - \frac{5 \, a^{3} d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{7}{2}}} + \frac{35 \, a^{4} e \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{9}{2}}} - \frac{63 \, a^{5} f \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, b^{\frac{11}{2}}}"," ",0,"1/10*sqrt(b*x^2 + a)*f*x^9/b + 1/8*sqrt(b*x^2 + a)*e*x^7/b - 9/80*sqrt(b*x^2 + a)*a*f*x^7/b^2 + 1/6*sqrt(b*x^2 + a)*d*x^5/b - 7/48*sqrt(b*x^2 + a)*a*e*x^5/b^2 + 21/160*sqrt(b*x^2 + a)*a^2*f*x^5/b^3 + 1/4*sqrt(b*x^2 + a)*c*x^3/b - 5/24*sqrt(b*x^2 + a)*a*d*x^3/b^2 + 35/192*sqrt(b*x^2 + a)*a^2*e*x^3/b^3 - 21/128*sqrt(b*x^2 + a)*a^3*f*x^3/b^4 - 3/8*sqrt(b*x^2 + a)*a*c*x/b^2 + 5/16*sqrt(b*x^2 + a)*a^2*d*x/b^3 - 35/128*sqrt(b*x^2 + a)*a^3*e*x/b^4 + 63/256*sqrt(b*x^2 + a)*a^4*f*x/b^5 + 3/8*a^2*c*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 5/16*a^3*d*arcsinh(b*x/sqrt(a*b))/b^(7/2) + 35/128*a^4*e*arcsinh(b*x/sqrt(a*b))/b^(9/2) - 63/256*a^5*f*arcsinh(b*x/sqrt(a*b))/b^(11/2)","A",0
152,1,255,0,1.386717," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{7}}{8 \, b} + \frac{\sqrt{b x^{2} + a} e x^{5}}{6 \, b} - \frac{7 \, \sqrt{b x^{2} + a} a f x^{5}}{48 \, b^{2}} + \frac{\sqrt{b x^{2} + a} d x^{3}}{4 \, b} - \frac{5 \, \sqrt{b x^{2} + a} a e x^{3}}{24 \, b^{2}} + \frac{35 \, \sqrt{b x^{2} + a} a^{2} f x^{3}}{192 \, b^{3}} + \frac{\sqrt{b x^{2} + a} c x}{2 \, b} - \frac{3 \, \sqrt{b x^{2} + a} a d x}{8 \, b^{2}} + \frac{5 \, \sqrt{b x^{2} + a} a^{2} e x}{16 \, b^{3}} - \frac{35 \, \sqrt{b x^{2} + a} a^{3} f x}{128 \, b^{4}} - \frac{a c \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{3}{2}}} + \frac{3 \, a^{2} d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{5}{2}}} - \frac{5 \, a^{3} e \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{7}{2}}} + \frac{35 \, a^{4} f \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{9}{2}}}"," ",0,"1/8*sqrt(b*x^2 + a)*f*x^7/b + 1/6*sqrt(b*x^2 + a)*e*x^5/b - 7/48*sqrt(b*x^2 + a)*a*f*x^5/b^2 + 1/4*sqrt(b*x^2 + a)*d*x^3/b - 5/24*sqrt(b*x^2 + a)*a*e*x^3/b^2 + 35/192*sqrt(b*x^2 + a)*a^2*f*x^3/b^3 + 1/2*sqrt(b*x^2 + a)*c*x/b - 3/8*sqrt(b*x^2 + a)*a*d*x/b^2 + 5/16*sqrt(b*x^2 + a)*a^2*e*x/b^3 - 35/128*sqrt(b*x^2 + a)*a^3*f*x/b^4 - 1/2*a*c*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 3/8*a^2*d*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 5/16*a^3*e*arcsinh(b*x/sqrt(a*b))/b^(7/2) + 35/128*a^4*f*arcsinh(b*x/sqrt(a*b))/b^(9/2)","A",0
153,1,174,0,1.349545," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{5}}{6 \, b} + \frac{\sqrt{b x^{2} + a} e x^{3}}{4 \, b} - \frac{5 \, \sqrt{b x^{2} + a} a f x^{3}}{24 \, b^{2}} + \frac{\sqrt{b x^{2} + a} d x}{2 \, b} - \frac{3 \, \sqrt{b x^{2} + a} a e x}{8 \, b^{2}} + \frac{5 \, \sqrt{b x^{2} + a} a^{2} f x}{16 \, b^{3}} + \frac{c \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}} - \frac{a d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{3}{2}}} + \frac{3 \, a^{2} e \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{5}{2}}} - \frac{5 \, a^{3} f \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{7}{2}}}"," ",0,"1/6*sqrt(b*x^2 + a)*f*x^5/b + 1/4*sqrt(b*x^2 + a)*e*x^3/b - 5/24*sqrt(b*x^2 + a)*a*f*x^3/b^2 + 1/2*sqrt(b*x^2 + a)*d*x/b - 3/8*sqrt(b*x^2 + a)*a*e*x/b^2 + 5/16*sqrt(b*x^2 + a)*a^2*f*x/b^3 + c*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 1/2*a*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 3/8*a^2*e*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 5/16*a^3*f*arcsinh(b*x/sqrt(a*b))/b^(7/2)","A",0
154,1,118,0,1.258845," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{3}}{4 \, b} + \frac{\sqrt{b x^{2} + a} e x}{2 \, b} - \frac{3 \, \sqrt{b x^{2} + a} a f x}{8 \, b^{2}} + \frac{d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}} - \frac{a e \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{3}{2}}} + \frac{3 \, a^{2} f \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{5}{2}}} - \frac{\sqrt{b x^{2} + a} c}{a x}"," ",0,"1/4*sqrt(b*x^2 + a)*f*x^3/b + 1/2*sqrt(b*x^2 + a)*e*x/b - 3/8*sqrt(b*x^2 + a)*a*f*x/b^2 + d*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 1/2*a*e*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 3/8*a^2*f*arcsinh(b*x/sqrt(a*b))/b^(5/2) - sqrt(b*x^2 + a)*c/(a*x)","A",0
155,1,102,0,1.332592," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x}{2 \, b} + \frac{e \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}} - \frac{a f \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{3}{2}}} + \frac{2 \, \sqrt{b x^{2} + a} b c}{3 \, a^{2} x} - \frac{\sqrt{b x^{2} + a} d}{a x} - \frac{\sqrt{b x^{2} + a} c}{3 \, a x^{3}}"," ",0,"1/2*sqrt(b*x^2 + a)*f*x/b + e*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 1/2*a*f*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 2/3*sqrt(b*x^2 + a)*b*c/(a^2*x) - sqrt(b*x^2 + a)*d/(a*x) - 1/3*sqrt(b*x^2 + a)*c/(a*x^3)","A",0
156,1,128,0,1.326984," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{f \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}} - \frac{8 \, \sqrt{b x^{2} + a} b^{2} c}{15 \, a^{3} x} + \frac{2 \, \sqrt{b x^{2} + a} b d}{3 \, a^{2} x} - \frac{\sqrt{b x^{2} + a} e}{a x} + \frac{4 \, \sqrt{b x^{2} + a} b c}{15 \, a^{2} x^{3}} - \frac{\sqrt{b x^{2} + a} d}{3 \, a x^{3}} - \frac{\sqrt{b x^{2} + a} c}{5 \, a x^{5}}"," ",0,"f*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 8/15*sqrt(b*x^2 + a)*b^2*c/(a^3*x) + 2/3*sqrt(b*x^2 + a)*b*d/(a^2*x) - sqrt(b*x^2 + a)*e/(a*x) + 4/15*sqrt(b*x^2 + a)*b*c/(a^2*x^3) - 1/3*sqrt(b*x^2 + a)*d/(a*x^3) - 1/5*sqrt(b*x^2 + a)*c/(a*x^5)","A",0
157,1,193,0,1.402833," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{16 \, \sqrt{b x^{2} + a} b^{3} c}{35 \, a^{4} x} - \frac{8 \, \sqrt{b x^{2} + a} b^{2} d}{15 \, a^{3} x} + \frac{2 \, \sqrt{b x^{2} + a} b e}{3 \, a^{2} x} - \frac{\sqrt{b x^{2} + a} f}{a x} - \frac{8 \, \sqrt{b x^{2} + a} b^{2} c}{35 \, a^{3} x^{3}} + \frac{4 \, \sqrt{b x^{2} + a} b d}{15 \, a^{2} x^{3}} - \frac{\sqrt{b x^{2} + a} e}{3 \, a x^{3}} + \frac{6 \, \sqrt{b x^{2} + a} b c}{35 \, a^{2} x^{5}} - \frac{\sqrt{b x^{2} + a} d}{5 \, a x^{5}} - \frac{\sqrt{b x^{2} + a} c}{7 \, a x^{7}}"," ",0,"16/35*sqrt(b*x^2 + a)*b^3*c/(a^4*x) - 8/15*sqrt(b*x^2 + a)*b^2*d/(a^3*x) + 2/3*sqrt(b*x^2 + a)*b*e/(a^2*x) - sqrt(b*x^2 + a)*f/(a*x) - 8/35*sqrt(b*x^2 + a)*b^2*c/(a^3*x^3) + 4/15*sqrt(b*x^2 + a)*b*d/(a^2*x^3) - 1/3*sqrt(b*x^2 + a)*e/(a*x^3) + 6/35*sqrt(b*x^2 + a)*b*c/(a^2*x^5) - 1/5*sqrt(b*x^2 + a)*d/(a*x^5) - 1/7*sqrt(b*x^2 + a)*c/(a*x^7)","A",0
158,1,275,0,1.386186," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{128 \, \sqrt{b x^{2} + a} b^{4} c}{315 \, a^{5} x} + \frac{16 \, \sqrt{b x^{2} + a} b^{3} d}{35 \, a^{4} x} - \frac{8 \, \sqrt{b x^{2} + a} b^{2} e}{15 \, a^{3} x} + \frac{2 \, \sqrt{b x^{2} + a} b f}{3 \, a^{2} x} + \frac{64 \, \sqrt{b x^{2} + a} b^{3} c}{315 \, a^{4} x^{3}} - \frac{8 \, \sqrt{b x^{2} + a} b^{2} d}{35 \, a^{3} x^{3}} + \frac{4 \, \sqrt{b x^{2} + a} b e}{15 \, a^{2} x^{3}} - \frac{\sqrt{b x^{2} + a} f}{3 \, a x^{3}} - \frac{16 \, \sqrt{b x^{2} + a} b^{2} c}{105 \, a^{3} x^{5}} + \frac{6 \, \sqrt{b x^{2} + a} b d}{35 \, a^{2} x^{5}} - \frac{\sqrt{b x^{2} + a} e}{5 \, a x^{5}} + \frac{8 \, \sqrt{b x^{2} + a} b c}{63 \, a^{2} x^{7}} - \frac{\sqrt{b x^{2} + a} d}{7 \, a x^{7}} - \frac{\sqrt{b x^{2} + a} c}{9 \, a x^{9}}"," ",0,"-128/315*sqrt(b*x^2 + a)*b^4*c/(a^5*x) + 16/35*sqrt(b*x^2 + a)*b^3*d/(a^4*x) - 8/15*sqrt(b*x^2 + a)*b^2*e/(a^3*x) + 2/3*sqrt(b*x^2 + a)*b*f/(a^2*x) + 64/315*sqrt(b*x^2 + a)*b^3*c/(a^4*x^3) - 8/35*sqrt(b*x^2 + a)*b^2*d/(a^3*x^3) + 4/15*sqrt(b*x^2 + a)*b*e/(a^2*x^3) - 1/3*sqrt(b*x^2 + a)*f/(a*x^3) - 16/105*sqrt(b*x^2 + a)*b^2*c/(a^3*x^5) + 6/35*sqrt(b*x^2 + a)*b*d/(a^2*x^5) - 1/5*sqrt(b*x^2 + a)*e/(a*x^5) + 8/63*sqrt(b*x^2 + a)*b*c/(a^2*x^7) - 1/7*sqrt(b*x^2 + a)*d/(a*x^7) - 1/9*sqrt(b*x^2 + a)*c/(a*x^9)","A",0
159,1,1221,0,1.887940," ","integrate(x^8*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{D x^{13}}{6 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{13 \, D a x^{11}}{24 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{C x^{11}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{143 \, D a^{2} x^{9}}{48 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} - \frac{11 \, C a x^{9}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{B x^{9}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{1}{35} \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} A x + \frac{429 \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} D a^{3} x}{560 \, b^{3}} - \frac{99 \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} C a^{2} x}{280 \, b^{2}} + \frac{9 \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} B a x}{70 \, b} + \frac{143 \, D a^{3} x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{80 \, b^{4}} - \frac{33 \, C a^{2} x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{40 \, b^{3}} + \frac{3 \, B a x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{10 \, b^{2}} - \frac{A x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{15 \, b} + \frac{143 \, D a^{3} x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{16 \, b^{5}} - \frac{33 \, C a^{2} x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{8 \, b^{4}} + \frac{3 \, B a x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{2 \, b^{3}} - \frac{A x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{3 \, b^{2}} + \frac{429 \, D a^{4} x^{3}}{16 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{6}} - \frac{99 \, C a^{3} x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{5}} + \frac{9 \, B a^{2} x^{3}}{2 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} - \frac{A a x^{3}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{19877 \, D a^{3} x}{560 \, \sqrt{b x^{2} + a} b^{7}} - \frac{2431 \, D a^{4} x}{560 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{7}} + \frac{12441 \, D a^{5} x}{560 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{7}} + \frac{4587 \, C a^{2} x}{280 \, \sqrt{b x^{2} + a} b^{6}} + \frac{561 \, C a^{3} x}{280 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{6}} - \frac{2871 \, C a^{4} x}{280 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{6}} - \frac{417 \, B a x}{70 \, \sqrt{b x^{2} + a} b^{5}} - \frac{51 \, B a^{2} x}{70 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{5}} + \frac{261 \, B a^{3} x}{70 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{5}} + \frac{139 \, A x}{105 \, \sqrt{b x^{2} + a} b^{4}} + \frac{17 \, A a x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}} - \frac{29 \, A a^{2} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} - \frac{429 \, D a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{15}{2}}} + \frac{99 \, C a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{13}{2}}} - \frac{9 \, B a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{11}{2}}} + \frac{A \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{9}{2}}}"," ",0,"1/6*D*x^13/((b*x^2 + a)^(7/2)*b) - 13/24*D*a*x^11/((b*x^2 + a)^(7/2)*b^2) + 1/4*C*x^11/((b*x^2 + a)^(7/2)*b) + 143/48*D*a^2*x^9/((b*x^2 + a)^(7/2)*b^3) - 11/8*C*a*x^9/((b*x^2 + a)^(7/2)*b^2) + 1/2*B*x^9/((b*x^2 + a)^(7/2)*b) - 1/35*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*A*x + 429/560*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*D*a^3*x/b^3 - 99/280*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*C*a^2*x/b^2 + 9/70*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*B*a*x/b + 143/80*D*a^3*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b^4 - 33/40*C*a^2*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b^3 + 3/10*B*a*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b^2 - 1/15*A*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b + 143/16*D*a^3*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^5 - 33/8*C*a^2*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^4 + 3/2*B*a*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^3 - 1/3*A*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^2 + 429/16*D*a^4*x^3/((b*x^2 + a)^(5/2)*b^6) - 99/8*C*a^3*x^3/((b*x^2 + a)^(5/2)*b^5) + 9/2*B*a^2*x^3/((b*x^2 + a)^(5/2)*b^4) - A*a*x^3/((b*x^2 + a)^(5/2)*b^3) - 19877/560*D*a^3*x/(sqrt(b*x^2 + a)*b^7) - 2431/560*D*a^4*x/((b*x^2 + a)^(3/2)*b^7) + 12441/560*D*a^5*x/((b*x^2 + a)^(5/2)*b^7) + 4587/280*C*a^2*x/(sqrt(b*x^2 + a)*b^6) + 561/280*C*a^3*x/((b*x^2 + a)^(3/2)*b^6) - 2871/280*C*a^4*x/((b*x^2 + a)^(5/2)*b^6) - 417/70*B*a*x/(sqrt(b*x^2 + a)*b^5) - 51/70*B*a^2*x/((b*x^2 + a)^(3/2)*b^5) + 261/70*B*a^3*x/((b*x^2 + a)^(5/2)*b^5) + 139/105*A*x/(sqrt(b*x^2 + a)*b^4) + 17/105*A*a*x/((b*x^2 + a)^(3/2)*b^4) - 29/35*A*a^2*x/((b*x^2 + a)^(5/2)*b^4) - 429/16*D*a^3*arcsinh(b*x/sqrt(a*b))/b^(15/2) + 99/8*C*a^2*arcsinh(b*x/sqrt(a*b))/b^(13/2) - 9/2*B*a*arcsinh(b*x/sqrt(a*b))/b^(11/2) + A*arcsinh(b*x/sqrt(a*b))/b^(9/2)","B",0
160,1,986,0,1.786588," ","integrate(x^6*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{D x^{11}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{11 \, D a x^{9}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{C x^{9}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{1}{35} \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} B x - \frac{99 \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} D a^{2} x}{280 \, b^{2}} + \frac{9 \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} C a x}{70 \, b} - \frac{33 \, D a^{2} x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{40 \, b^{3}} + \frac{3 \, C a x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{10 \, b^{2}} - \frac{B x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{15 \, b} - \frac{A x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{33 \, D a^{2} x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{8 \, b^{4}} + \frac{3 \, C a x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{2 \, b^{3}} - \frac{B x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{3 \, b^{2}} - \frac{99 \, D a^{3} x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{5}} + \frac{9 \, C a^{2} x^{3}}{2 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} - \frac{B a x^{3}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{5 \, A a x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{4587 \, D a^{2} x}{280 \, \sqrt{b x^{2} + a} b^{6}} + \frac{561 \, D a^{3} x}{280 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{6}} - \frac{2871 \, D a^{4} x}{280 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{6}} - \frac{417 \, C a x}{70 \, \sqrt{b x^{2} + a} b^{5}} - \frac{51 \, C a^{2} x}{70 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{5}} + \frac{261 \, C a^{3} x}{70 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{5}} + \frac{139 \, B x}{105 \, \sqrt{b x^{2} + a} b^{4}} + \frac{17 \, B a x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}} - \frac{29 \, B a^{2} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} + \frac{A x}{14 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{A x}{7 \, \sqrt{b x^{2} + a} a b^{3}} + \frac{3 \, A a x}{56 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{15 \, A a^{2} x}{56 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{99 \, D a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{13}{2}}} - \frac{9 \, C a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{11}{2}}} + \frac{B \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{9}{2}}}"," ",0,"1/4*D*x^11/((b*x^2 + a)^(7/2)*b) - 11/8*D*a*x^9/((b*x^2 + a)^(7/2)*b^2) + 1/2*C*x^9/((b*x^2 + a)^(7/2)*b) - 1/35*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*B*x - 99/280*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*D*a^2*x/b^2 + 9/70*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*C*a*x/b - 33/40*D*a^2*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b^3 + 3/10*C*a*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b^2 - 1/15*B*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b - 1/2*A*x^5/((b*x^2 + a)^(7/2)*b) - 33/8*D*a^2*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^4 + 3/2*C*a*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^3 - 1/3*B*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^2 - 99/8*D*a^3*x^3/((b*x^2 + a)^(5/2)*b^5) + 9/2*C*a^2*x^3/((b*x^2 + a)^(5/2)*b^4) - B*a*x^3/((b*x^2 + a)^(5/2)*b^3) - 5/8*A*a*x^3/((b*x^2 + a)^(7/2)*b^2) + 4587/280*D*a^2*x/(sqrt(b*x^2 + a)*b^6) + 561/280*D*a^3*x/((b*x^2 + a)^(3/2)*b^6) - 2871/280*D*a^4*x/((b*x^2 + a)^(5/2)*b^6) - 417/70*C*a*x/(sqrt(b*x^2 + a)*b^5) - 51/70*C*a^2*x/((b*x^2 + a)^(3/2)*b^5) + 261/70*C*a^3*x/((b*x^2 + a)^(5/2)*b^5) + 139/105*B*x/(sqrt(b*x^2 + a)*b^4) + 17/105*B*a*x/((b*x^2 + a)^(3/2)*b^4) - 29/35*B*a^2*x/((b*x^2 + a)^(5/2)*b^4) + 1/14*A*x/((b*x^2 + a)^(3/2)*b^3) + 1/7*A*x/(sqrt(b*x^2 + a)*a*b^3) + 3/56*A*a*x/((b*x^2 + a)^(5/2)*b^3) - 15/56*A*a^2*x/((b*x^2 + a)^(7/2)*b^3) + 99/8*D*a^2*arcsinh(b*x/sqrt(a*b))/b^(13/2) - 9/2*C*a*arcsinh(b*x/sqrt(a*b))/b^(11/2) + B*arcsinh(b*x/sqrt(a*b))/b^(9/2)","B",0
161,1,753,0,1.685987," ","integrate(x^4*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{D x^{9}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{1}{35} \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} C x + \frac{9 \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} D a x}{70 \, b} + \frac{3 \, D a x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{10 \, b^{2}} - \frac{C x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{15 \, b} - \frac{B x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{3 \, D a x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{2 \, b^{3}} - \frac{C x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{3 \, b^{2}} + \frac{9 \, D a^{2} x^{3}}{2 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} - \frac{C a x^{3}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{5 \, B a x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{A x^{3}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{417 \, D a x}{70 \, \sqrt{b x^{2} + a} b^{5}} - \frac{51 \, D a^{2} x}{70 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{5}} + \frac{261 \, D a^{3} x}{70 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{5}} + \frac{139 \, C x}{105 \, \sqrt{b x^{2} + a} b^{4}} + \frac{17 \, C a x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}} - \frac{29 \, C a^{2} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} + \frac{B x}{14 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{B x}{7 \, \sqrt{b x^{2} + a} a b^{3}} + \frac{3 \, B a x}{56 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{15 \, B a^{2} x}{56 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{3 \, A x}{140 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{2 \, A x}{35 \, \sqrt{b x^{2} + a} a^{2} b^{2}} + \frac{A x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2}} - \frac{3 \, A a x}{28 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{9 \, D a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{11}{2}}} + \frac{C \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{9}{2}}}"," ",0,"1/2*D*x^9/((b*x^2 + a)^(7/2)*b) - 1/35*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*C*x + 9/70*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*D*a*x/b + 3/10*D*a*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b^2 - 1/15*C*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b - 1/2*B*x^5/((b*x^2 + a)^(7/2)*b) + 3/2*D*a*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^3 - 1/3*C*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^2 + 9/2*D*a^2*x^3/((b*x^2 + a)^(5/2)*b^4) - C*a*x^3/((b*x^2 + a)^(5/2)*b^3) - 5/8*B*a*x^3/((b*x^2 + a)^(7/2)*b^2) - 1/4*A*x^3/((b*x^2 + a)^(7/2)*b) - 417/70*D*a*x/(sqrt(b*x^2 + a)*b^5) - 51/70*D*a^2*x/((b*x^2 + a)^(3/2)*b^5) + 261/70*D*a^3*x/((b*x^2 + a)^(5/2)*b^5) + 139/105*C*x/(sqrt(b*x^2 + a)*b^4) + 17/105*C*a*x/((b*x^2 + a)^(3/2)*b^4) - 29/35*C*a^2*x/((b*x^2 + a)^(5/2)*b^4) + 1/14*B*x/((b*x^2 + a)^(3/2)*b^3) + 1/7*B*x/(sqrt(b*x^2 + a)*a*b^3) + 3/56*B*a*x/((b*x^2 + a)^(5/2)*b^3) - 15/56*B*a^2*x/((b*x^2 + a)^(7/2)*b^3) + 3/140*A*x/((b*x^2 + a)^(5/2)*b^2) + 2/35*A*x/(sqrt(b*x^2 + a)*a^2*b^2) + 1/35*A*x/((b*x^2 + a)^(3/2)*a*b^2) - 3/28*A*a*x/((b*x^2 + a)^(7/2)*b^2) - 9/2*D*a*arcsinh(b*x/sqrt(a*b))/b^(11/2) + C*arcsinh(b*x/sqrt(a*b))/b^(9/2)","B",0
162,1,533,0,1.661289," ","integrate(x^2*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{1}{35} \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} D x - \frac{D x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{15 \, b} - \frac{C x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{D x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{3 \, b^{2}} - \frac{D a x^{3}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{5 \, C a x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{B x^{3}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{139 \, D x}{105 \, \sqrt{b x^{2} + a} b^{4}} + \frac{17 \, D a x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}} - \frac{29 \, D a^{2} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} + \frac{C x}{14 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{C x}{7 \, \sqrt{b x^{2} + a} a b^{3}} + \frac{3 \, C a x}{56 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{15 \, C a^{2} x}{56 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{3 \, B x}{140 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{2 \, B x}{35 \, \sqrt{b x^{2} + a} a^{2} b^{2}} + \frac{B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2}} - \frac{3 \, B a x}{28 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{A x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{8 \, A x}{105 \, \sqrt{b x^{2} + a} a^{3} b} + \frac{4 \, A x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b} + \frac{A x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b} + \frac{D \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{9}{2}}}"," ",0,"-1/35*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*D*x - 1/15*D*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b - 1/2*C*x^5/((b*x^2 + a)^(7/2)*b) - 1/3*D*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^2 - D*a*x^3/((b*x^2 + a)^(5/2)*b^3) - 5/8*C*a*x^3/((b*x^2 + a)^(7/2)*b^2) - 1/4*B*x^3/((b*x^2 + a)^(7/2)*b) + 139/105*D*x/(sqrt(b*x^2 + a)*b^4) + 17/105*D*a*x/((b*x^2 + a)^(3/2)*b^4) - 29/35*D*a^2*x/((b*x^2 + a)^(5/2)*b^4) + 1/14*C*x/((b*x^2 + a)^(3/2)*b^3) + 1/7*C*x/(sqrt(b*x^2 + a)*a*b^3) + 3/56*C*a*x/((b*x^2 + a)^(5/2)*b^3) - 15/56*C*a^2*x/((b*x^2 + a)^(7/2)*b^3) + 3/140*B*x/((b*x^2 + a)^(5/2)*b^2) + 2/35*B*x/(sqrt(b*x^2 + a)*a^2*b^2) + 1/35*B*x/((b*x^2 + a)^(3/2)*a*b^2) - 3/28*B*a*x/((b*x^2 + a)^(7/2)*b^2) - 1/7*A*x/((b*x^2 + a)^(7/2)*b) + 8/105*A*x/(sqrt(b*x^2 + a)*a^3*b) + 4/105*A*x/((b*x^2 + a)^(3/2)*a^2*b) + 1/35*A*x/((b*x^2 + a)^(5/2)*a*b) + D*arcsinh(b*x/sqrt(a*b))/b^(9/2)","B",0
163,1,335,0,1.422770," ","integrate((D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{D x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{5 \, D a x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{C x^{3}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{16 \, A x}{35 \, \sqrt{b x^{2} + a} a^{4}} + \frac{8 \, A x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{6 \, A x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{A x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} + \frac{D x}{14 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{D x}{7 \, \sqrt{b x^{2} + a} a b^{3}} + \frac{3 \, D a x}{56 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{15 \, D a^{2} x}{56 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{3 \, C x}{140 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{2 \, C x}{35 \, \sqrt{b x^{2} + a} a^{2} b^{2}} + \frac{C x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2}} - \frac{3 \, C a x}{28 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{B x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{8 \, B x}{105 \, \sqrt{b x^{2} + a} a^{3} b} + \frac{4 \, B x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b} + \frac{B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b}"," ",0,"-1/2*D*x^5/((b*x^2 + a)^(7/2)*b) - 5/8*D*a*x^3/((b*x^2 + a)^(7/2)*b^2) - 1/4*C*x^3/((b*x^2 + a)^(7/2)*b) + 16/35*A*x/(sqrt(b*x^2 + a)*a^4) + 8/35*A*x/((b*x^2 + a)^(3/2)*a^3) + 6/35*A*x/((b*x^2 + a)^(5/2)*a^2) + 1/7*A*x/((b*x^2 + a)^(7/2)*a) + 1/14*D*x/((b*x^2 + a)^(3/2)*b^3) + 1/7*D*x/(sqrt(b*x^2 + a)*a*b^3) + 3/56*D*a*x/((b*x^2 + a)^(5/2)*b^3) - 15/56*D*a^2*x/((b*x^2 + a)^(7/2)*b^3) + 3/140*C*x/((b*x^2 + a)^(5/2)*b^2) + 2/35*C*x/(sqrt(b*x^2 + a)*a^2*b^2) + 1/35*C*x/((b*x^2 + a)^(3/2)*a*b^2) - 3/28*C*a*x/((b*x^2 + a)^(7/2)*b^2) - 1/7*B*x/((b*x^2 + a)^(7/2)*b) + 8/105*B*x/(sqrt(b*x^2 + a)*a^3*b) + 4/105*B*x/((b*x^2 + a)^(3/2)*a^2*b) + 1/35*B*x/((b*x^2 + a)^(5/2)*a*b)","B",0
164,1,313,0,1.471478," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^2/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{D x^{3}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{16 \, B x}{35 \, \sqrt{b x^{2} + a} a^{4}} + \frac{8 \, B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{6 \, B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{B x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} + \frac{3 \, D x}{140 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{2 \, D x}{35 \, \sqrt{b x^{2} + a} a^{2} b^{2}} + \frac{D x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2}} - \frac{3 \, D a x}{28 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{C x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{8 \, C x}{105 \, \sqrt{b x^{2} + a} a^{3} b} + \frac{4 \, C x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b} + \frac{C x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b} - \frac{128 \, A b x}{35 \, \sqrt{b x^{2} + a} a^{5}} - \frac{64 \, A b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4}} - \frac{48 \, A b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3}} - \frac{8 \, A b x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2}} - \frac{A}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a x}"," ",0,"-1/4*D*x^3/((b*x^2 + a)^(7/2)*b) + 16/35*B*x/(sqrt(b*x^2 + a)*a^4) + 8/35*B*x/((b*x^2 + a)^(3/2)*a^3) + 6/35*B*x/((b*x^2 + a)^(5/2)*a^2) + 1/7*B*x/((b*x^2 + a)^(7/2)*a) + 3/140*D*x/((b*x^2 + a)^(5/2)*b^2) + 2/35*D*x/(sqrt(b*x^2 + a)*a^2*b^2) + 1/35*D*x/((b*x^2 + a)^(3/2)*a*b^2) - 3/28*D*a*x/((b*x^2 + a)^(7/2)*b^2) - 1/7*C*x/((b*x^2 + a)^(7/2)*b) + 8/105*C*x/(sqrt(b*x^2 + a)*a^3*b) + 4/105*C*x/((b*x^2 + a)^(3/2)*a^2*b) + 1/35*C*x/((b*x^2 + a)^(5/2)*a*b) - 128/35*A*b*x/(sqrt(b*x^2 + a)*a^5) - 64/35*A*b*x/((b*x^2 + a)^(3/2)*a^4) - 48/35*A*b*x/((b*x^2 + a)^(5/2)*a^3) - 8/7*A*b*x/((b*x^2 + a)^(7/2)*a^2) - A/((b*x^2 + a)^(7/2)*a*x)","A",0
165,1,337,0,1.467601," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^4/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{16 \, C x}{35 \, \sqrt{b x^{2} + a} a^{4}} + \frac{8 \, C x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{6 \, C x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{C x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} - \frac{D x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{8 \, D x}{105 \, \sqrt{b x^{2} + a} a^{3} b} + \frac{4 \, D x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b} + \frac{D x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b} - \frac{128 \, B b x}{35 \, \sqrt{b x^{2} + a} a^{5}} - \frac{64 \, B b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4}} - \frac{48 \, B b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3}} - \frac{8 \, B b x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2}} + \frac{256 \, A b^{2} x}{21 \, \sqrt{b x^{2} + a} a^{6}} + \frac{128 \, A b^{2} x}{21 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{5}} + \frac{32 \, A b^{2} x}{7 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{4}} + \frac{80 \, A b^{2} x}{21 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{3}} - \frac{B}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a x} + \frac{10 \, A b}{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} x} - \frac{A}{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a x^{3}}"," ",0,"16/35*C*x/(sqrt(b*x^2 + a)*a^4) + 8/35*C*x/((b*x^2 + a)^(3/2)*a^3) + 6/35*C*x/((b*x^2 + a)^(5/2)*a^2) + 1/7*C*x/((b*x^2 + a)^(7/2)*a) - 1/7*D*x/((b*x^2 + a)^(7/2)*b) + 8/105*D*x/(sqrt(b*x^2 + a)*a^3*b) + 4/105*D*x/((b*x^2 + a)^(3/2)*a^2*b) + 1/35*D*x/((b*x^2 + a)^(5/2)*a*b) - 128/35*B*b*x/(sqrt(b*x^2 + a)*a^5) - 64/35*B*b*x/((b*x^2 + a)^(3/2)*a^4) - 48/35*B*b*x/((b*x^2 + a)^(5/2)*a^3) - 8/7*B*b*x/((b*x^2 + a)^(7/2)*a^2) + 256/21*A*b^2*x/(sqrt(b*x^2 + a)*a^6) + 128/21*A*b^2*x/((b*x^2 + a)^(3/2)*a^5) + 32/7*A*b^2*x/((b*x^2 + a)^(5/2)*a^4) + 80/21*A*b^2*x/((b*x^2 + a)^(7/2)*a^3) - B/((b*x^2 + a)^(7/2)*a*x) + 10/3*A*b/((b*x^2 + a)^(7/2)*a^2*x) - 1/3*A/((b*x^2 + a)^(7/2)*a*x^3)","A",0
166,1,398,0,1.545187," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^6/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{16 \, D x}{35 \, \sqrt{b x^{2} + a} a^{4}} + \frac{8 \, D x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{6 \, D x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{D x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} - \frac{128 \, C b x}{35 \, \sqrt{b x^{2} + a} a^{5}} - \frac{64 \, C b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4}} - \frac{48 \, C b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3}} - \frac{8 \, C b x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2}} + \frac{256 \, B b^{2} x}{21 \, \sqrt{b x^{2} + a} a^{6}} + \frac{128 \, B b^{2} x}{21 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{5}} + \frac{32 \, B b^{2} x}{7 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{4}} + \frac{80 \, B b^{2} x}{21 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{3}} - \frac{1024 \, A b^{3} x}{35 \, \sqrt{b x^{2} + a} a^{7}} - \frac{512 \, A b^{3} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{6}} - \frac{384 \, A b^{3} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{5}} - \frac{64 \, A b^{3} x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{4}} - \frac{C}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a x} + \frac{10 \, B b}{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} x} - \frac{8 \, A b^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{3} x} - \frac{B}{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a x^{3}} + \frac{4 \, A b}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} x^{3}} - \frac{A}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a x^{5}}"," ",0,"16/35*D*x/(sqrt(b*x^2 + a)*a^4) + 8/35*D*x/((b*x^2 + a)^(3/2)*a^3) + 6/35*D*x/((b*x^2 + a)^(5/2)*a^2) + 1/7*D*x/((b*x^2 + a)^(7/2)*a) - 128/35*C*b*x/(sqrt(b*x^2 + a)*a^5) - 64/35*C*b*x/((b*x^2 + a)^(3/2)*a^4) - 48/35*C*b*x/((b*x^2 + a)^(5/2)*a^3) - 8/7*C*b*x/((b*x^2 + a)^(7/2)*a^2) + 256/21*B*b^2*x/(sqrt(b*x^2 + a)*a^6) + 128/21*B*b^2*x/((b*x^2 + a)^(3/2)*a^5) + 32/7*B*b^2*x/((b*x^2 + a)^(5/2)*a^4) + 80/21*B*b^2*x/((b*x^2 + a)^(7/2)*a^3) - 1024/35*A*b^3*x/(sqrt(b*x^2 + a)*a^7) - 512/35*A*b^3*x/((b*x^2 + a)^(3/2)*a^6) - 384/35*A*b^3*x/((b*x^2 + a)^(5/2)*a^5) - 64/7*A*b^3*x/((b*x^2 + a)^(7/2)*a^4) - C/((b*x^2 + a)^(7/2)*a*x) + 10/3*B*b/((b*x^2 + a)^(7/2)*a^2*x) - 8*A*b^2/((b*x^2 + a)^(7/2)*a^3*x) - 1/3*B/((b*x^2 + a)^(7/2)*a*x^3) + 4/5*A*b/((b*x^2 + a)^(7/2)*a^2*x^3) - 1/5*A/((b*x^2 + a)^(7/2)*a*x^5)","A",0
167,1,489,0,1.517912," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^8/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{128 \, D b x}{35 \, \sqrt{b x^{2} + a} a^{5}} - \frac{64 \, D b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4}} - \frac{48 \, D b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3}} - \frac{8 \, D b x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2}} + \frac{256 \, C b^{2} x}{21 \, \sqrt{b x^{2} + a} a^{6}} + \frac{128 \, C b^{2} x}{21 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{5}} + \frac{32 \, C b^{2} x}{7 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{4}} + \frac{80 \, C b^{2} x}{21 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{3}} - \frac{1024 \, B b^{3} x}{35 \, \sqrt{b x^{2} + a} a^{7}} - \frac{512 \, B b^{3} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{6}} - \frac{384 \, B b^{3} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{5}} - \frac{64 \, B b^{3} x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{4}} + \frac{2048 \, A b^{4} x}{35 \, \sqrt{b x^{2} + a} a^{8}} + \frac{1024 \, A b^{4} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{7}} + \frac{768 \, A b^{4} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{6}} + \frac{128 \, A b^{4} x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{5}} - \frac{D}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a x} + \frac{10 \, C b}{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} x} - \frac{8 \, B b^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{3} x} + \frac{16 \, A b^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{4} x} - \frac{C}{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a x^{3}} + \frac{4 \, B b}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} x^{3}} - \frac{8 \, A b^{2}}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{3} x^{3}} - \frac{B}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a x^{5}} + \frac{2 \, A b}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} x^{5}} - \frac{A}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a x^{7}}"," ",0,"-128/35*D*b*x/(sqrt(b*x^2 + a)*a^5) - 64/35*D*b*x/((b*x^2 + a)^(3/2)*a^4) - 48/35*D*b*x/((b*x^2 + a)^(5/2)*a^3) - 8/7*D*b*x/((b*x^2 + a)^(7/2)*a^2) + 256/21*C*b^2*x/(sqrt(b*x^2 + a)*a^6) + 128/21*C*b^2*x/((b*x^2 + a)^(3/2)*a^5) + 32/7*C*b^2*x/((b*x^2 + a)^(5/2)*a^4) + 80/21*C*b^2*x/((b*x^2 + a)^(7/2)*a^3) - 1024/35*B*b^3*x/(sqrt(b*x^2 + a)*a^7) - 512/35*B*b^3*x/((b*x^2 + a)^(3/2)*a^6) - 384/35*B*b^3*x/((b*x^2 + a)^(5/2)*a^5) - 64/7*B*b^3*x/((b*x^2 + a)^(7/2)*a^4) + 2048/35*A*b^4*x/(sqrt(b*x^2 + a)*a^8) + 1024/35*A*b^4*x/((b*x^2 + a)^(3/2)*a^7) + 768/35*A*b^4*x/((b*x^2 + a)^(5/2)*a^6) + 128/7*A*b^4*x/((b*x^2 + a)^(7/2)*a^5) - D/((b*x^2 + a)^(7/2)*a*x) + 10/3*C*b/((b*x^2 + a)^(7/2)*a^2*x) - 8*B*b^2/((b*x^2 + a)^(7/2)*a^3*x) + 16*A*b^3/((b*x^2 + a)^(7/2)*a^4*x) - 1/3*C/((b*x^2 + a)^(7/2)*a*x^3) + 4/5*B*b/((b*x^2 + a)^(7/2)*a^2*x^3) - 8/5*A*b^2/((b*x^2 + a)^(7/2)*a^3*x^3) - 1/5*B/((b*x^2 + a)^(7/2)*a*x^5) + 2/5*A*b/((b*x^2 + a)^(7/2)*a^2*x^5) - 1/7*A/((b*x^2 + a)^(7/2)*a*x^7)","A",0
168,1,579,0,1.573853," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^10/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{256 \, D b^{2} x}{21 \, \sqrt{b x^{2} + a} a^{6}} + \frac{128 \, D b^{2} x}{21 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{5}} + \frac{32 \, D b^{2} x}{7 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{4}} + \frac{80 \, D b^{2} x}{21 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{3}} - \frac{1024 \, C b^{3} x}{35 \, \sqrt{b x^{2} + a} a^{7}} - \frac{512 \, C b^{3} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{6}} - \frac{384 \, C b^{3} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{5}} - \frac{64 \, C b^{3} x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{4}} + \frac{2048 \, B b^{4} x}{35 \, \sqrt{b x^{2} + a} a^{8}} + \frac{1024 \, B b^{4} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{7}} + \frac{768 \, B b^{4} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{6}} + \frac{128 \, B b^{4} x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{5}} - \frac{32768 \, A b^{5} x}{315 \, \sqrt{b x^{2} + a} a^{9}} - \frac{16384 \, A b^{5} x}{315 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{8}} - \frac{4096 \, A b^{5} x}{105 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{7}} - \frac{2048 \, A b^{5} x}{63 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{6}} + \frac{10 \, D b}{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} x} - \frac{8 \, C b^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{3} x} + \frac{16 \, B b^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{4} x} - \frac{256 \, A b^{4}}{9 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{5} x} - \frac{D}{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a x^{3}} + \frac{4 \, C b}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} x^{3}} - \frac{8 \, B b^{2}}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{3} x^{3}} + \frac{128 \, A b^{3}}{45 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{4} x^{3}} - \frac{C}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a x^{5}} + \frac{2 \, B b}{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} x^{5}} - \frac{32 \, A b^{2}}{45 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{3} x^{5}} - \frac{B}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a x^{7}} + \frac{16 \, A b}{63 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} x^{7}} - \frac{A}{9 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a x^{9}}"," ",0,"256/21*D*b^2*x/(sqrt(b*x^2 + a)*a^6) + 128/21*D*b^2*x/((b*x^2 + a)^(3/2)*a^5) + 32/7*D*b^2*x/((b*x^2 + a)^(5/2)*a^4) + 80/21*D*b^2*x/((b*x^2 + a)^(7/2)*a^3) - 1024/35*C*b^3*x/(sqrt(b*x^2 + a)*a^7) - 512/35*C*b^3*x/((b*x^2 + a)^(3/2)*a^6) - 384/35*C*b^3*x/((b*x^2 + a)^(5/2)*a^5) - 64/7*C*b^3*x/((b*x^2 + a)^(7/2)*a^4) + 2048/35*B*b^4*x/(sqrt(b*x^2 + a)*a^8) + 1024/35*B*b^4*x/((b*x^2 + a)^(3/2)*a^7) + 768/35*B*b^4*x/((b*x^2 + a)^(5/2)*a^6) + 128/7*B*b^4*x/((b*x^2 + a)^(7/2)*a^5) - 32768/315*A*b^5*x/(sqrt(b*x^2 + a)*a^9) - 16384/315*A*b^5*x/((b*x^2 + a)^(3/2)*a^8) - 4096/105*A*b^5*x/((b*x^2 + a)^(5/2)*a^7) - 2048/63*A*b^5*x/((b*x^2 + a)^(7/2)*a^6) + 10/3*D*b/((b*x^2 + a)^(7/2)*a^2*x) - 8*C*b^2/((b*x^2 + a)^(7/2)*a^3*x) + 16*B*b^3/((b*x^2 + a)^(7/2)*a^4*x) - 256/9*A*b^4/((b*x^2 + a)^(7/2)*a^5*x) - 1/3*D/((b*x^2 + a)^(7/2)*a*x^3) + 4/5*C*b/((b*x^2 + a)^(7/2)*a^2*x^3) - 8/5*B*b^2/((b*x^2 + a)^(7/2)*a^3*x^3) + 128/45*A*b^3/((b*x^2 + a)^(7/2)*a^4*x^3) - 1/5*C/((b*x^2 + a)^(7/2)*a*x^5) + 2/5*B*b/((b*x^2 + a)^(7/2)*a^2*x^5) - 32/45*A*b^2/((b*x^2 + a)^(7/2)*a^3*x^5) - 1/7*B/((b*x^2 + a)^(7/2)*a*x^7) + 16/63*A*b/((b*x^2 + a)^(7/2)*a^2*x^7) - 1/9*A/((b*x^2 + a)^(7/2)*a*x^9)","A",0
169,1,347,0,1.434962," ","integrate((f*x^11+e*x^9+d*x^7+c*x^5)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{10}}{11 \, b} + \frac{\sqrt{b x^{2} + a} e x^{8}}{9 \, b} - \frac{10 \, \sqrt{b x^{2} + a} a f x^{8}}{99 \, b^{2}} + \frac{\sqrt{b x^{2} + a} d x^{6}}{7 \, b} - \frac{8 \, \sqrt{b x^{2} + a} a e x^{6}}{63 \, b^{2}} + \frac{80 \, \sqrt{b x^{2} + a} a^{2} f x^{6}}{693 \, b^{3}} + \frac{\sqrt{b x^{2} + a} c x^{4}}{5 \, b} - \frac{6 \, \sqrt{b x^{2} + a} a d x^{4}}{35 \, b^{2}} + \frac{16 \, \sqrt{b x^{2} + a} a^{2} e x^{4}}{105 \, b^{3}} - \frac{32 \, \sqrt{b x^{2} + a} a^{3} f x^{4}}{231 \, b^{4}} - \frac{4 \, \sqrt{b x^{2} + a} a c x^{2}}{15 \, b^{2}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} d x^{2}}{35 \, b^{3}} - \frac{64 \, \sqrt{b x^{2} + a} a^{3} e x^{2}}{315 \, b^{4}} + \frac{128 \, \sqrt{b x^{2} + a} a^{4} f x^{2}}{693 \, b^{5}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} c}{15 \, b^{3}} - \frac{16 \, \sqrt{b x^{2} + a} a^{3} d}{35 \, b^{4}} + \frac{128 \, \sqrt{b x^{2} + a} a^{4} e}{315 \, b^{5}} - \frac{256 \, \sqrt{b x^{2} + a} a^{5} f}{693 \, b^{6}}"," ",0,"1/11*sqrt(b*x^2 + a)*f*x^10/b + 1/9*sqrt(b*x^2 + a)*e*x^8/b - 10/99*sqrt(b*x^2 + a)*a*f*x^8/b^2 + 1/7*sqrt(b*x^2 + a)*d*x^6/b - 8/63*sqrt(b*x^2 + a)*a*e*x^6/b^2 + 80/693*sqrt(b*x^2 + a)*a^2*f*x^6/b^3 + 1/5*sqrt(b*x^2 + a)*c*x^4/b - 6/35*sqrt(b*x^2 + a)*a*d*x^4/b^2 + 16/105*sqrt(b*x^2 + a)*a^2*e*x^4/b^3 - 32/231*sqrt(b*x^2 + a)*a^3*f*x^4/b^4 - 4/15*sqrt(b*x^2 + a)*a*c*x^2/b^2 + 8/35*sqrt(b*x^2 + a)*a^2*d*x^2/b^3 - 64/315*sqrt(b*x^2 + a)*a^3*e*x^2/b^4 + 128/693*sqrt(b*x^2 + a)*a^4*f*x^2/b^5 + 8/15*sqrt(b*x^2 + a)*a^2*c/b^3 - 16/35*sqrt(b*x^2 + a)*a^3*d/b^4 + 128/315*sqrt(b*x^2 + a)*a^4*e/b^5 - 256/693*sqrt(b*x^2 + a)*a^5*f/b^6","A",0
170,1,263,0,1.367174," ","integrate((f*x^9+e*x^7+d*x^5+c*x^3)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{8}}{9 \, b} + \frac{\sqrt{b x^{2} + a} e x^{6}}{7 \, b} - \frac{8 \, \sqrt{b x^{2} + a} a f x^{6}}{63 \, b^{2}} + \frac{\sqrt{b x^{2} + a} d x^{4}}{5 \, b} - \frac{6 \, \sqrt{b x^{2} + a} a e x^{4}}{35 \, b^{2}} + \frac{16 \, \sqrt{b x^{2} + a} a^{2} f x^{4}}{105 \, b^{3}} + \frac{\sqrt{b x^{2} + a} c x^{2}}{3 \, b} - \frac{4 \, \sqrt{b x^{2} + a} a d x^{2}}{15 \, b^{2}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} e x^{2}}{35 \, b^{3}} - \frac{64 \, \sqrt{b x^{2} + a} a^{3} f x^{2}}{315 \, b^{4}} - \frac{2 \, \sqrt{b x^{2} + a} a c}{3 \, b^{2}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} d}{15 \, b^{3}} - \frac{16 \, \sqrt{b x^{2} + a} a^{3} e}{35 \, b^{4}} + \frac{128 \, \sqrt{b x^{2} + a} a^{4} f}{315 \, b^{5}}"," ",0,"1/9*sqrt(b*x^2 + a)*f*x^8/b + 1/7*sqrt(b*x^2 + a)*e*x^6/b - 8/63*sqrt(b*x^2 + a)*a*f*x^6/b^2 + 1/5*sqrt(b*x^2 + a)*d*x^4/b - 6/35*sqrt(b*x^2 + a)*a*e*x^4/b^2 + 16/105*sqrt(b*x^2 + a)*a^2*f*x^4/b^3 + 1/3*sqrt(b*x^2 + a)*c*x^2/b - 4/15*sqrt(b*x^2 + a)*a*d*x^2/b^2 + 8/35*sqrt(b*x^2 + a)*a^2*e*x^2/b^3 - 64/315*sqrt(b*x^2 + a)*a^3*f*x^2/b^4 - 2/3*sqrt(b*x^2 + a)*a*c/b^2 + 8/15*sqrt(b*x^2 + a)*a^2*d/b^3 - 16/35*sqrt(b*x^2 + a)*a^3*e/b^4 + 128/315*sqrt(b*x^2 + a)*a^4*f/b^5","A",0
171,1,180,0,1.355264," ","integrate((f*x^7+e*x^5+d*x^3+c*x)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} f x^{6}}{7 \, b} + \frac{\sqrt{b x^{2} + a} e x^{4}}{5 \, b} - \frac{6 \, \sqrt{b x^{2} + a} a f x^{4}}{35 \, b^{2}} + \frac{\sqrt{b x^{2} + a} d x^{2}}{3 \, b} - \frac{4 \, \sqrt{b x^{2} + a} a e x^{2}}{15 \, b^{2}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} f x^{2}}{35 \, b^{3}} + \frac{\sqrt{b x^{2} + a} c}{b} - \frac{2 \, \sqrt{b x^{2} + a} a d}{3 \, b^{2}} + \frac{8 \, \sqrt{b x^{2} + a} a^{2} e}{15 \, b^{3}} - \frac{16 \, \sqrt{b x^{2} + a} a^{3} f}{35 \, b^{4}}"," ",0,"1/7*sqrt(b*x^2 + a)*f*x^6/b + 1/5*sqrt(b*x^2 + a)*e*x^4/b - 6/35*sqrt(b*x^2 + a)*a*f*x^4/b^2 + 1/3*sqrt(b*x^2 + a)*d*x^2/b - 4/15*sqrt(b*x^2 + a)*a*e*x^2/b^2 + 8/35*sqrt(b*x^2 + a)*a^2*f*x^2/b^3 + sqrt(b*x^2 + a)*c/b - 2/3*sqrt(b*x^2 + a)*a*d/b^2 + 8/15*sqrt(b*x^2 + a)*a^2*e/b^3 - 16/35*sqrt(b*x^2 + a)*a^3*f/b^4","A",0
172,1,826,0,1.747205," ","integrate(x^2*(F*x^8+D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","\frac{F x^{9}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{1}{35} \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} D x + \frac{9 \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} F a x}{70 \, b} + \frac{3 \, F a x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{10 \, b^{2}} - \frac{D x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{15 \, b} - \frac{C x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{3 \, F a x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{2 \, b^{3}} - \frac{D x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{3 \, b^{2}} + \frac{9 \, F a^{2} x^{3}}{2 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} - \frac{D a x^{3}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{5 \, C a x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{B x^{3}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{417 \, F a x}{70 \, \sqrt{b x^{2} + a} b^{5}} - \frac{51 \, F a^{2} x}{70 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{5}} + \frac{261 \, F a^{3} x}{70 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{5}} + \frac{139 \, D x}{105 \, \sqrt{b x^{2} + a} b^{4}} + \frac{17 \, D a x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}} - \frac{29 \, D a^{2} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} + \frac{C x}{14 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{C x}{7 \, \sqrt{b x^{2} + a} a b^{3}} + \frac{3 \, C a x}{56 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{15 \, C a^{2} x}{56 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{3 \, B x}{140 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{2 \, B x}{35 \, \sqrt{b x^{2} + a} a^{2} b^{2}} + \frac{B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2}} - \frac{3 \, B a x}{28 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{A x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{8 \, A x}{105 \, \sqrt{b x^{2} + a} a^{3} b} + \frac{4 \, A x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b} + \frac{A x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b} - \frac{9 \, F a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{11}{2}}} + \frac{D \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{9}{2}}}"," ",0,"1/2*F*x^9/((b*x^2 + a)^(7/2)*b) - 1/35*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*D*x + 9/70*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*F*a*x/b + 3/10*F*a*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b^2 - 1/15*D*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b - 1/2*C*x^5/((b*x^2 + a)^(7/2)*b) + 3/2*F*a*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^3 - 1/3*D*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^2 + 9/2*F*a^2*x^3/((b*x^2 + a)^(5/2)*b^4) - D*a*x^3/((b*x^2 + a)^(5/2)*b^3) - 5/8*C*a*x^3/((b*x^2 + a)^(7/2)*b^2) - 1/4*B*x^3/((b*x^2 + a)^(7/2)*b) - 417/70*F*a*x/(sqrt(b*x^2 + a)*b^5) - 51/70*F*a^2*x/((b*x^2 + a)^(3/2)*b^5) + 261/70*F*a^3*x/((b*x^2 + a)^(5/2)*b^5) + 139/105*D*x/(sqrt(b*x^2 + a)*b^4) + 17/105*D*a*x/((b*x^2 + a)^(3/2)*b^4) - 29/35*D*a^2*x/((b*x^2 + a)^(5/2)*b^4) + 1/14*C*x/((b*x^2 + a)^(3/2)*b^3) + 1/7*C*x/(sqrt(b*x^2 + a)*a*b^3) + 3/56*C*a*x/((b*x^2 + a)^(5/2)*b^3) - 15/56*C*a^2*x/((b*x^2 + a)^(7/2)*b^3) + 3/140*B*x/((b*x^2 + a)^(5/2)*b^2) + 2/35*B*x/(sqrt(b*x^2 + a)*a^2*b^2) + 1/35*B*x/((b*x^2 + a)^(3/2)*a*b^2) - 3/28*B*a*x/((b*x^2 + a)^(7/2)*b^2) - 1/7*A*x/((b*x^2 + a)^(7/2)*b) + 8/105*A*x/(sqrt(b*x^2 + a)*a^3*b) + 4/105*A*x/((b*x^2 + a)^(3/2)*a^2*b) + 1/35*A*x/((b*x^2 + a)^(5/2)*a*b) - 9/2*F*a*arcsinh(b*x/sqrt(a*b))/b^(11/2) + D*arcsinh(b*x/sqrt(a*b))/b^(9/2)","B",0
173,1,597,0,1.742680," ","integrate((F*x^8+D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{1}{35} \, {\left(\frac{35 \, x^{6}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{70 \, a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} + \frac{56 \, a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{16 \, a^{3}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{4}}\right)} F x - \frac{F x {\left(\frac{15 \, x^{4}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b} + \frac{20 \, a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{8 \, a^{2}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}}\right)}}{15 \, b} - \frac{D x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{F x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{3 \, b^{2}} - \frac{F a x^{3}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{5 \, D a x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{C x^{3}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{16 \, A x}{35 \, \sqrt{b x^{2} + a} a^{4}} + \frac{8 \, A x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{6 \, A x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{A x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} + \frac{139 \, F x}{105 \, \sqrt{b x^{2} + a} b^{4}} + \frac{17 \, F a x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}} - \frac{29 \, F a^{2} x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4}} + \frac{D x}{14 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{D x}{7 \, \sqrt{b x^{2} + a} a b^{3}} + \frac{3 \, D a x}{56 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{15 \, D a^{2} x}{56 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{3 \, C x}{140 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{2 \, C x}{35 \, \sqrt{b x^{2} + a} a^{2} b^{2}} + \frac{C x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2}} - \frac{3 \, C a x}{28 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{B x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{8 \, B x}{105 \, \sqrt{b x^{2} + a} a^{3} b} + \frac{4 \, B x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b} + \frac{B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b} + \frac{F \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{9}{2}}}"," ",0,"-1/35*(35*x^6/((b*x^2 + a)^(7/2)*b) + 70*a*x^4/((b*x^2 + a)^(7/2)*b^2) + 56*a^2*x^2/((b*x^2 + a)^(7/2)*b^3) + 16*a^3/((b*x^2 + a)^(7/2)*b^4))*F*x - 1/15*F*x*(15*x^4/((b*x^2 + a)^(5/2)*b) + 20*a*x^2/((b*x^2 + a)^(5/2)*b^2) + 8*a^2/((b*x^2 + a)^(5/2)*b^3))/b - 1/2*D*x^5/((b*x^2 + a)^(7/2)*b) - 1/3*F*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^2 - F*a*x^3/((b*x^2 + a)^(5/2)*b^3) - 5/8*D*a*x^3/((b*x^2 + a)^(7/2)*b^2) - 1/4*C*x^3/((b*x^2 + a)^(7/2)*b) + 16/35*A*x/(sqrt(b*x^2 + a)*a^4) + 8/35*A*x/((b*x^2 + a)^(3/2)*a^3) + 6/35*A*x/((b*x^2 + a)^(5/2)*a^2) + 1/7*A*x/((b*x^2 + a)^(7/2)*a) + 139/105*F*x/(sqrt(b*x^2 + a)*b^4) + 17/105*F*a*x/((b*x^2 + a)^(3/2)*b^4) - 29/35*F*a^2*x/((b*x^2 + a)^(5/2)*b^4) + 1/14*D*x/((b*x^2 + a)^(3/2)*b^3) + 1/7*D*x/(sqrt(b*x^2 + a)*a*b^3) + 3/56*D*a*x/((b*x^2 + a)^(5/2)*b^3) - 15/56*D*a^2*x/((b*x^2 + a)^(7/2)*b^3) + 3/140*C*x/((b*x^2 + a)^(5/2)*b^2) + 2/35*C*x/(sqrt(b*x^2 + a)*a^2*b^2) + 1/35*C*x/((b*x^2 + a)^(3/2)*a*b^2) - 3/28*C*a*x/((b*x^2 + a)^(7/2)*b^2) - 1/7*B*x/((b*x^2 + a)^(7/2)*b) + 8/105*B*x/(sqrt(b*x^2 + a)*a^3*b) + 4/105*B*x/((b*x^2 + a)^(3/2)*a^2*b) + 1/35*B*x/((b*x^2 + a)^(5/2)*a*b) + F*arcsinh(b*x/sqrt(a*b))/b^(9/2)","B",0
174,1,421,0,1.539543," ","integrate((F*x^8+D*x^6+C*x^4+B*x^2+A)/x^2/(b*x^2+a)^(9/2),x, algorithm=""maxima"")","-\frac{F x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} - \frac{5 \, F a x^{3}}{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{D x^{3}}{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{16 \, B x}{35 \, \sqrt{b x^{2} + a} a^{4}} + \frac{8 \, B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{6 \, B x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2}} + \frac{B x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a} + \frac{F x}{14 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{F x}{7 \, \sqrt{b x^{2} + a} a b^{3}} + \frac{3 \, F a x}{56 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3}} - \frac{15 \, F a^{2} x}{56 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{3}} + \frac{3 \, D x}{140 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2}} + \frac{2 \, D x}{35 \, \sqrt{b x^{2} + a} a^{2} b^{2}} + \frac{D x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2}} - \frac{3 \, D a x}{28 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2}} - \frac{C x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b} + \frac{8 \, C x}{105 \, \sqrt{b x^{2} + a} a^{3} b} + \frac{4 \, C x}{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b} + \frac{C x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b} - \frac{128 \, A b x}{35 \, \sqrt{b x^{2} + a} a^{5}} - \frac{64 \, A b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4}} - \frac{48 \, A b x}{35 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3}} - \frac{8 \, A b x}{7 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2}} - \frac{A}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a x}"," ",0,"-1/2*F*x^5/((b*x^2 + a)^(7/2)*b) - 5/8*F*a*x^3/((b*x^2 + a)^(7/2)*b^2) - 1/4*D*x^3/((b*x^2 + a)^(7/2)*b) + 16/35*B*x/(sqrt(b*x^2 + a)*a^4) + 8/35*B*x/((b*x^2 + a)^(3/2)*a^3) + 6/35*B*x/((b*x^2 + a)^(5/2)*a^2) + 1/7*B*x/((b*x^2 + a)^(7/2)*a) + 1/14*F*x/((b*x^2 + a)^(3/2)*b^3) + 1/7*F*x/(sqrt(b*x^2 + a)*a*b^3) + 3/56*F*a*x/((b*x^2 + a)^(5/2)*b^3) - 15/56*F*a^2*x/((b*x^2 + a)^(7/2)*b^3) + 3/140*D*x/((b*x^2 + a)^(5/2)*b^2) + 2/35*D*x/(sqrt(b*x^2 + a)*a^2*b^2) + 1/35*D*x/((b*x^2 + a)^(3/2)*a*b^2) - 3/28*D*a*x/((b*x^2 + a)^(7/2)*b^2) - 1/7*C*x/((b*x^2 + a)^(7/2)*b) + 8/105*C*x/(sqrt(b*x^2 + a)*a^3*b) + 4/105*C*x/((b*x^2 + a)^(3/2)*a^2*b) + 1/35*C*x/((b*x^2 + a)^(5/2)*a*b) - 128/35*A*b*x/(sqrt(b*x^2 + a)*a^5) - 64/35*A*b*x/((b*x^2 + a)^(3/2)*a^4) - 48/35*A*b*x/((b*x^2 + a)^(5/2)*a^3) - 8/7*A*b*x/((b*x^2 + a)^(7/2)*a^2) - A/((b*x^2 + a)^(7/2)*a*x)","B",0
