1,1,93,0,0.509452," ","integrate(x^3*(B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{B a^{3} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{5}{2}}} + \frac{1}{240} \, \sqrt{b x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, B x + 6 \, A\right)} x + \frac{5 \, B a}{b}\right)} x + \frac{8 \, A a}{b}\right)} x - \frac{15 \, B a^{2}}{b^{2}}\right)} x - \frac{32 \, A a^{2}}{b^{2}}\right)}"," ",0,"-1/16*B*a^3*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2) + 1/240*sqrt(b*x^2 + a)*((2*((4*(5*B*x + 6*A)*x + 5*B*a/b)*x + 8*A*a/b)*x - 15*B*a^2/b^2)*x - 32*A*a^2/b^2)","A",0
2,1,81,0,0.470567," ","integrate(x^2*(B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{A a^{2} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{3}{2}}} + \frac{1}{120} \, \sqrt{b x^{2} + a} {\left({\left(2 \, {\left(3 \, {\left(4 \, B x + 5 \, A\right)} x + \frac{4 \, B a}{b}\right)} x + \frac{15 \, A a}{b}\right)} x - \frac{16 \, B a^{2}}{b^{2}}\right)}"," ",0,"1/8*A*a^2*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2) + 1/120*sqrt(b*x^2 + a)*((2*(3*(4*B*x + 5*A)*x + 4*B*a/b)*x + 15*A*a/b)*x - 16*B*a^2/b^2)","A",0
3,1,68,0,0.440495," ","integrate(x*(B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{B a^{2} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{3}{2}}} + \frac{1}{24} \, \sqrt{b x^{2} + a} {\left({\left(2 \, {\left(3 \, B x + 4 \, A\right)} x + \frac{3 \, B a}{b}\right)} x + \frac{8 \, A a}{b}\right)}"," ",0,"1/8*B*a^2*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2) + 1/24*sqrt(b*x^2 + a)*((2*(3*B*x + 4*A)*x + 3*B*a/b)*x + 8*A*a/b)","A",0
4,1,55,0,0.413834," ","integrate((B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{A a \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, \sqrt{b}} + \frac{1}{6} \, \sqrt{b x^{2} + a} {\left({\left(2 \, B x + 3 \, A\right)} x + \frac{2 \, B a}{b}\right)}"," ",0,"-1/2*A*a*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b) + 1/6*sqrt(b*x^2 + a)*((2*B*x + 3*A)*x + 2*B*a/b)","A",0
5,1,78,0,0.452373," ","integrate((B*x+A)*(b*x^2+a)^(1/2)/x,x, algorithm=""giac"")","\frac{2 \, A a \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{B a \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, \sqrt{b}} + \frac{1}{2} \, \sqrt{b x^{2} + a} {\left(B x + 2 \, A\right)}"," ",0,"2*A*a*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/sqrt(-a) - 1/2*B*a*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b) + 1/2*sqrt(b*x^2 + a)*(B*x + 2*A)","A",0
6,1,102,0,0.474490," ","integrate((B*x+A)*(b*x^2+a)^(1/2)/x^2,x, algorithm=""giac"")","\frac{2 \, B a \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - A \sqrt{b} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right) + \sqrt{b x^{2} + a} B + \frac{2 \, A a \sqrt{b}}{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a}"," ",0,"2*B*a*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/sqrt(-a) - A*sqrt(b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a))) + sqrt(b*x^2 + a)*B + 2*A*a*sqrt(b)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)","A",0
7,1,163,0,0.481540," ","integrate((B*x+A)*(b*x^2+a)^(1/2)/x^3,x, algorithm=""giac"")","\frac{A b \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - B \sqrt{b} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right) + \frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{3} A b + 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a \sqrt{b} + {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)} A a b - 2 \, B a^{2} \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{2}}"," ",0,"A*b*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/sqrt(-a) - B*sqrt(b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a))) + ((sqrt(b)*x - sqrt(b*x^2 + a))^3*A*b + 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a*sqrt(b) + (sqrt(b)*x - sqrt(b*x^2 + a))*A*a*b - 2*B*a^2*sqrt(b))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^2","B",0
8,1,115,0,0.440018," ","integrate(x^3*(B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{3 \, B a^{4} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{128 \, b^{\frac{5}{2}}} - \frac{1}{4480} \, \sqrt{b x^{2} + a} {\left(\frac{256 \, A a^{3}}{b^{2}} + {\left(\frac{105 \, B a^{3}}{b^{2}} - 2 \, {\left(\frac{64 \, A a^{2}}{b} + {\left(\frac{35 \, B a^{2}}{b} + 4 \, {\left(128 \, A a + 5 \, {\left(21 \, B a + 2 \, {\left(7 \, B b x + 8 \, A b\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"-3/128*B*a^4*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2) - 1/4480*sqrt(b*x^2 + a)*(256*A*a^3/b^2 + (105*B*a^3/b^2 - 2*(64*A*a^2/b + (35*B*a^2/b + 4*(128*A*a + 5*(21*B*a + 2*(7*B*b*x + 8*A*b)*x)*x)*x)*x)*x)*x)","A",0
9,1,103,0,0.506373," ","integrate(x^2*(B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{A a^{3} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{3}{2}}} - \frac{1}{1680} \, \sqrt{b x^{2} + a} {\left(\frac{96 \, B a^{3}}{b^{2}} - {\left(\frac{105 \, A a^{2}}{b} + 2 \, {\left(\frac{24 \, B a^{2}}{b} + {\left(245 \, A a + 4 \, {\left(48 \, B a + 5 \, {\left(6 \, B b x + 7 \, A b\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"1/16*A*a^3*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2) - 1/1680*sqrt(b*x^2 + a)*(96*B*a^3/b^2 - (105*A*a^2/b + 2*(24*B*a^2/b + (245*A*a + 4*(48*B*a + 5*(6*B*b*x + 7*A*b)*x)*x)*x)*x)*x)","A",0
10,1,89,0,0.472573," ","integrate(x*(B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{B a^{3} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{3}{2}}} + \frac{1}{240} \, \sqrt{b x^{2} + a} {\left(\frac{48 \, A a^{2}}{b} + {\left(\frac{15 \, B a^{2}}{b} + 2 \, {\left(48 \, A a + {\left(35 \, B a + 4 \, {\left(5 \, B b x + 6 \, A b\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"1/16*B*a^3*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2) + 1/240*sqrt(b*x^2 + a)*(48*A*a^2/b + (15*B*a^2/b + 2*(48*A*a + (35*B*a + 4*(5*B*b*x + 6*A*b)*x)*x)*x)*x)","A",0
11,1,76,0,0.439794," ","integrate((B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{3 \, A a^{2} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, \sqrt{b}} + \frac{1}{40} \, \sqrt{b x^{2} + a} {\left(\frac{8 \, B a^{2}}{b} + {\left(25 \, A a + 2 \, {\left(8 \, B a + {\left(4 \, B b x + 5 \, A b\right)} x\right)} x\right)} x\right)}"," ",0,"-3/8*A*a^2*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b) + 1/40*sqrt(b*x^2 + a)*(8*B*a^2/b + (25*A*a + 2*(8*B*a + (4*B*b*x + 5*A*b)*x)*x)*x)","A",0
12,1,100,0,0.538884," ","integrate((B*x+A)*(b*x^2+a)^(3/2)/x,x, algorithm=""giac"")","\frac{2 \, A a^{2} \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{3 \, B a^{2} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, \sqrt{b}} + \frac{1}{24} \, \sqrt{b x^{2} + a} {\left(32 \, A a + {\left(15 \, B a + 2 \, {\left(3 \, B b x + 4 \, A b\right)} x\right)} x\right)}"," ",0,"2*A*a^2*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/sqrt(-a) - 3/8*B*a^2*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b) + 1/24*sqrt(b*x^2 + a)*(32*A*a + (15*B*a + 2*(3*B*b*x + 4*A*b)*x)*x)","A",0
13,1,124,0,0.601565," ","integrate((B*x+A)*(b*x^2+a)^(3/2)/x^2,x, algorithm=""giac"")","\frac{2 \, B a^{2} \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{3}{2} \, A a \sqrt{b} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right) + \frac{2 \, A a^{2} \sqrt{b}}{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a} + \frac{1}{6} \, \sqrt{b x^{2} + a} {\left(8 \, B a + {\left(2 \, B b x + 3 \, A b\right)} x\right)}"," ",0,"2*B*a^2*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/sqrt(-a) - 3/2*A*a*sqrt(b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a))) + 2*A*a^2*sqrt(b)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a) + 1/6*sqrt(b*x^2 + a)*(8*B*a + (2*B*b*x + 3*A*b)*x)","A",0
14,1,191,0,0.550231," ","integrate((B*x+A)*(b*x^2+a)^(3/2)/x^3,x, algorithm=""giac"")","\frac{3 \, A a b \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{3}{2} \, B a \sqrt{b} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right) + \frac{1}{2} \, {\left(B b x + 2 \, A b\right)} \sqrt{b x^{2} + a} + \frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{3} A a b + 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{2} \sqrt{b} + {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)} A a^{2} b - 2 \, B a^{3} \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{2}}"," ",0,"3*A*a*b*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/sqrt(-a) - 3/2*B*a*sqrt(b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a))) + 1/2*(B*b*x + 2*A*b)*sqrt(b*x^2 + a) + ((sqrt(b)*x - sqrt(b*x^2 + a))^3*A*a*b + 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^2*sqrt(b) + (sqrt(b)*x - sqrt(b*x^2 + a))*A*a^2*b - 2*B*a^3*sqrt(b))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^2","B",0
15,1,140,0,0.529416," ","integrate(x^3*(B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{3 \, B a^{5} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{256 \, b^{\frac{5}{2}}} - \frac{1}{80640} \, {\left(\frac{2560 \, A a^{4}}{b^{2}} + {\left(\frac{945 \, B a^{4}}{b^{2}} - 2 \, {\left(\frac{640 \, A a^{3}}{b} + {\left(\frac{315 \, B a^{3}}{b} + 4 \, {\left(2400 \, A a^{2} + {\left(1953 \, B a^{2} + 2 \, {\left(1520 \, A a b + 7 \, {\left(189 \, B a b + 8 \, {\left(9 \, B b^{2} x + 10 \, A b^{2}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{b x^{2} + a}"," ",0,"-3/256*B*a^5*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2) - 1/80640*(2560*A*a^4/b^2 + (945*B*a^4/b^2 - 2*(640*A*a^3/b + (315*B*a^3/b + 4*(2400*A*a^2 + (1953*B*a^2 + 2*(1520*A*a*b + 7*(189*B*a*b + 8*(9*B*b^2*x + 10*A*b^2)*x)*x)*x)*x)*x)*x)*x)*x)*sqrt(b*x^2 + a)","A",0
16,1,128,0,0.460468," ","integrate(x^2*(B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{5 \, A a^{4} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{128 \, b^{\frac{3}{2}}} - \frac{1}{8064} \, {\left(\frac{256 \, B a^{4}}{b^{2}} - {\left(\frac{315 \, A a^{3}}{b} + 2 \, {\left(\frac{64 \, B a^{3}}{b} + {\left(1239 \, A a^{2} + 4 \, {\left(240 \, B a^{2} + {\left(357 \, A a b + 2 \, {\left(152 \, B a b + 7 \, {\left(8 \, B b^{2} x + 9 \, A b^{2}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{b x^{2} + a}"," ",0,"5/128*A*a^4*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2) - 1/8064*(256*B*a^4/b^2 - (315*A*a^3/b + 2*(64*B*a^3/b + (1239*A*a^2 + 4*(240*B*a^2 + (357*A*a*b + 2*(152*B*a*b + 7*(8*B*b^2*x + 9*A*b^2)*x)*x)*x)*x)*x)*x)*x)*sqrt(b*x^2 + a)","A",0
17,1,114,0,0.498974," ","integrate(x*(B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{5 \, B a^{4} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{128 \, b^{\frac{3}{2}}} + \frac{1}{2688} \, {\left(\frac{384 \, A a^{3}}{b} + {\left(\frac{105 \, B a^{3}}{b} + 2 \, {\left(576 \, A a^{2} + {\left(413 \, B a^{2} + 4 \, {\left(144 \, A a b + {\left(119 \, B a b + 6 \, {\left(7 \, B b^{2} x + 8 \, A b^{2}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{b x^{2} + a}"," ",0,"5/128*B*a^4*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2) + 1/2688*(384*A*a^3/b + (105*B*a^3/b + 2*(576*A*a^2 + (413*B*a^2 + 4*(144*A*a*b + (119*B*a*b + 6*(7*B*b^2*x + 8*A*b^2)*x)*x)*x)*x)*x)*x)*sqrt(b*x^2 + a)","A",0
18,1,101,0,0.607702," ","integrate((B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{5 \, A a^{3} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, \sqrt{b}} + \frac{1}{336} \, {\left(\frac{48 \, B a^{3}}{b} + {\left(231 \, A a^{2} + 2 \, {\left(72 \, B a^{2} + {\left(91 \, A a b + 4 \, {\left(18 \, B a b + {\left(6 \, B b^{2} x + 7 \, A b^{2}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{b x^{2} + a}"," ",0,"-5/16*A*a^3*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b) + 1/336*(48*B*a^3/b + (231*A*a^2 + 2*(72*B*a^2 + (91*A*a*b + 4*(18*B*a*b + (6*B*b^2*x + 7*A*b^2)*x)*x)*x)*x)*x)*sqrt(b*x^2 + a)","A",0
19,1,125,0,0.584973," ","integrate((B*x+A)*(b*x^2+a)^(5/2)/x,x, algorithm=""giac"")","\frac{2 \, A a^{3} \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{5 \, B a^{3} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, \sqrt{b}} + \frac{1}{240} \, {\left(368 \, A a^{2} + {\left(165 \, B a^{2} + 2 \, {\left(88 \, A a b + {\left(65 \, B a b + 4 \, {\left(5 \, B b^{2} x + 6 \, A b^{2}\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{b x^{2} + a}"," ",0,"2*A*a^3*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/sqrt(-a) - 5/16*B*a^3*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b) + 1/240*(368*A*a^2 + (165*B*a^2 + 2*(88*A*a*b + (65*B*a*b + 4*(5*B*b^2*x + 6*A*b^2)*x)*x)*x)*x)*sqrt(b*x^2 + a)","A",0
20,1,150,0,0.499177," ","integrate((B*x+A)*(b*x^2+a)^(5/2)/x^2,x, algorithm=""giac"")","\frac{2 \, B a^{3} \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{15}{8} \, A a^{2} \sqrt{b} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right) + \frac{2 \, A a^{3} \sqrt{b}}{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a} + \frac{1}{120} \, {\left(184 \, B a^{2} + {\left(135 \, A a b + 2 \, {\left(44 \, B a b + 3 \, {\left(4 \, B b^{2} x + 5 \, A b^{2}\right)} x\right)} x\right)} x\right)} \sqrt{b x^{2} + a}"," ",0,"2*B*a^3*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/sqrt(-a) - 15/8*A*a^2*sqrt(b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a))) + 2*A*a^3*sqrt(b)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a) + 1/120*(184*B*a^2 + (135*A*a*b + 2*(44*B*a*b + 3*(4*B*b^2*x + 5*A*b^2)*x)*x)*x)*sqrt(b*x^2 + a)","A",0
21,1,219,0,0.569429," ","integrate((B*x+A)*(b*x^2+a)^(5/2)/x^3,x, algorithm=""giac"")","\frac{5 \, A a^{2} b \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{15}{8} \, B a^{2} \sqrt{b} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right) + \frac{1}{24} \, {\left(56 \, A a b + {\left(27 \, B a b + 2 \, {\left(3 \, B b^{2} x + 4 \, A b^{2}\right)} x\right)} x\right)} \sqrt{b x^{2} + a} + \frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{3} A a^{2} b + 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{3} \sqrt{b} + {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)} A a^{3} b - 2 \, B a^{4} \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{2}}"," ",0,"5*A*a^2*b*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/sqrt(-a) - 15/8*B*a^2*sqrt(b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a))) + 1/24*(56*A*a*b + (27*B*a*b + 2*(3*B*b^2*x + 4*A*b^2)*x)*x)*sqrt(b*x^2 + a) + ((sqrt(b)*x - sqrt(b*x^2 + a))^3*A*a^2*b + 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^3*sqrt(b) + (sqrt(b)*x - sqrt(b*x^2 + a))*A*a^3*b - 2*B*a^4*sqrt(b))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^2","A",0
22,1,74,0,0.498113," ","integrate(x^3*(B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{b x^{2} + a} {\left({\left(2 \, {\left(\frac{3 \, B x}{b} + \frac{4 \, A}{b}\right)} x - \frac{9 \, B a}{b^{2}}\right)} x - \frac{16 \, A a}{b^{2}}\right)} - \frac{3 \, B a^{2} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{5}{2}}}"," ",0,"1/24*sqrt(b*x^2 + a)*((2*(3*B*x/b + 4*A/b)*x - 9*B*a/b^2)*x - 16*A*a/b^2) - 3/8*B*a^2*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
23,1,61,0,0.523602," ","integrate(x^2*(B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{b x^{2} + a} {\left({\left(\frac{2 \, B x}{b} + \frac{3 \, A}{b}\right)} x - \frac{4 \, B a}{b^{2}}\right)} + \frac{A a \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{3}{2}}}"," ",0,"1/6*sqrt(b*x^2 + a)*((2*B*x/b + 3*A/b)*x - 4*B*a/b^2) + 1/2*A*a*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
24,1,50,0,0.479072," ","integrate(x*(B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{b x^{2} + a} {\left(\frac{B x}{b} + \frac{2 \, A}{b}\right)} + \frac{B a \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{3}{2}}}"," ",0,"1/2*sqrt(b*x^2 + a)*(B*x/b + 2*A/b) + 1/2*B*a*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
25,1,39,0,0.546913," ","integrate((B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{A \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{\sqrt{b}} + \frac{\sqrt{b x^{2} + a} B}{b}"," ",0,"-A*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b) + sqrt(b*x^2 + a)*B/b","A",0
26,1,58,0,0.499410," ","integrate((B*x+A)/x/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, A \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{B \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{\sqrt{b}}"," ",0,"2*A*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/sqrt(-a) - B*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b)","A",0
27,1,65,0,0.510532," ","integrate((B*x+A)/x^2/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, B \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + \frac{2 \, A \sqrt{b}}{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a}"," ",0,"2*B*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/sqrt(-a) + 2*A*sqrt(b)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)","A",0
28,1,146,0,0.430907," ","integrate((B*x+A)/x^3/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{A b \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{3} A b + 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a \sqrt{b} + {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)} A a b - 2 \, B a^{2} \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{2} a}"," ",0,"-A*b*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + ((sqrt(b)*x - sqrt(b*x^2 + a))^3*A*b + 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a*sqrt(b) + (sqrt(b)*x - sqrt(b*x^2 + a))*A*a*b - 2*B*a^2*sqrt(b))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^2*a)","B",0
29,1,70,0,0.511579," ","integrate(x^3*(B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{B x}{b} + \frac{2 \, A}{b}\right)} x + \frac{3 \, B a}{b^{2}}\right)} x + \frac{4 \, A a}{b^{2}}}{2 \, \sqrt{b x^{2} + a}} + \frac{3 \, B a \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{5}{2}}}"," ",0,"1/2*(((B*x/b + 2*A/b)*x + 3*B*a/b^2)*x + 4*A*a/b^2)/sqrt(b*x^2 + a) + 3/2*B*a*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
30,1,58,0,0.547271," ","integrate(x^2*(B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{B x}{b} - \frac{A}{b}\right)} x + \frac{2 \, B a}{b^{2}}}{\sqrt{b x^{2} + a}} - \frac{A \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{b^{\frac{3}{2}}}"," ",0,"((B*x/b - A/b)*x + 2*B*a/b^2)/sqrt(b*x^2 + a) - A*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
31,1,48,0,0.498456," ","integrate(x*(B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{B x}{b} + \frac{A}{b}}{\sqrt{b x^{2} + a}} - \frac{B \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{b^{\frac{3}{2}}}"," ",0,"-(B*x/b + A/b)/sqrt(b*x^2 + a) - B*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
32,1,23,0,0.443432," ","integrate((B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{A x}{a} - \frac{B}{b}}{\sqrt{b x^{2} + a}}"," ",0,"(A*x/a - B/b)/sqrt(b*x^2 + a)","A",0
33,1,59,0,0.444821," ","integrate((B*x+A)/x/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{B x}{a} + \frac{A}{a}}{\sqrt{b x^{2} + a}} + \frac{2 \, A \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a}"," ",0,"(B*x/a + A/a)/sqrt(b*x^2 + a) + 2*A*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a)","A",0
34,1,96,0,0.501596," ","integrate((B*x+A)/x^2/(b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{A b x}{a^{2}} - \frac{B}{a}}{\sqrt{b x^{2} + a}} + \frac{2 \, B \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{2 \, A \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)} a}"," ",0,"-(A*b*x/a^2 - B/a)/sqrt(b*x^2 + a) + 2*B*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 2*A*sqrt(b)/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)*a)","A",0
35,1,171,0,0.496921," ","integrate((B*x+A)/x^3/(b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{B b x}{a^{2}} + \frac{A b}{a^{2}}}{\sqrt{b x^{2} + a}} - \frac{3 \, A b \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{3} A b + 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a \sqrt{b} + {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)} A a b - 2 \, B a^{2} \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{2} a^{2}}"," ",0,"-(B*b*x/a^2 + A*b/a^2)/sqrt(b*x^2 + a) - 3*A*b*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) + ((sqrt(b)*x - sqrt(b*x^2 + a))^3*A*b + 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a*sqrt(b) + (sqrt(b)*x - sqrt(b*x^2 + a))*A*a*b - 2*B*a^2*sqrt(b))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^2*a^2)","B",0
36,1,70,0,0.481885," ","integrate(x^3*(B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{{\left({\left(\frac{4 \, B x}{b} + \frac{3 \, A}{b}\right)} x + \frac{3 \, B a}{b^{2}}\right)} x + \frac{2 \, A a}{b^{2}}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} - \frac{B \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{b^{\frac{5}{2}}}"," ",0,"-1/3*(((4*B*x/b + 3*A/b)*x + 3*B*a/b^2)*x + 2*A*a/b^2)/(b*x^2 + a)^(3/2) - B*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
37,1,36,0,0.482423," ","integrate(x^2*(B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left(\frac{A x}{a} - \frac{3 \, B}{b}\right)} x^{2} - \frac{2 \, B a}{b^{2}}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*((A*x/a - 3*B/b)*x^2 - 2*B*a/b^2)/(b*x^2 + a)^(3/2)","A",0
38,1,26,0,0.517530," ","integrate(x*(B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{\frac{B x^{3}}{a} - \frac{A}{b}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*(B*x^3/a - A/b)/(b*x^2 + a)^(3/2)","A",0
39,1,37,0,0.477566," ","integrate((B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left(\frac{2 \, A b x^{2}}{a^{2}} + \frac{3 \, A}{a}\right)} x - \frac{B}{b}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*((2*A*b*x^2/a^2 + 3*A/a)*x - B/b)/(b*x^2 + a)^(3/2)","A",0
40,1,82,0,0.539868," ","integrate((B*x+A)/x/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, B b x}{a^{2}} + \frac{3 \, A b}{a^{2}}\right)} x + \frac{3 \, B}{a}\right)} x + \frac{4 \, A}{a}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} + \frac{2 \, A \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}}"," ",0,"1/3*(((2*B*b*x/a^2 + 3*A*b/a^2)*x + 3*B/a)*x + 4*A/a)/(b*x^2 + a)^(3/2) + 2*A*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2)","A",0
41,1,119,0,0.552870," ","integrate((B*x+A)/x^2/(b*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{{\left({\left(\frac{5 \, A b^{2} x}{a^{3}} - \frac{3 \, B b}{a^{2}}\right)} x + \frac{6 \, A b}{a^{2}}\right)} x - \frac{4 \, B}{a}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} + \frac{2 \, B \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{2 \, A \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)} a^{2}}"," ",0,"-1/3*(((5*A*b^2*x/a^3 - 3*B*b/a^2)*x + 6*A*b/a^2)*x - 4*B/a)/(b*x^2 + a)^(3/2) + 2*B*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) + 2*A*sqrt(b)/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)*a^2)","A",0
42,1,197,0,0.533639," ","integrate((B*x+A)/x^3/(b*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{{\left({\left(\frac{5 \, B b^{2} x}{a^{3}} + \frac{6 \, A b^{2}}{a^{3}}\right)} x + \frac{6 \, B b}{a^{2}}\right)} x + \frac{7 \, A b}{a^{2}}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} - \frac{5 \, A b \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} + \frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{3} A b + 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a \sqrt{b} + {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)} A a b - 2 \, B a^{2} \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{2} a^{3}}"," ",0,"-1/3*(((5*B*b^2*x/a^3 + 6*A*b^2/a^3)*x + 6*B*b/a^2)*x + 7*A*b/a^2)/(b*x^2 + a)^(3/2) - 5*A*b*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^3) + ((sqrt(b)*x - sqrt(b*x^2 + a))^3*A*b + 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a*sqrt(b) + (sqrt(b)*x - sqrt(b*x^2 + a))*A*a*b - 2*B*a^2*sqrt(b))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^2*a^3)","A",0
43,1,19,0,0.471139," ","integrate((1-x)*x/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} {\left(x - 2\right)} - \frac{1}{2} \, \arcsin\left(x\right)"," ",0,"1/2*sqrt(-x^2 + 1)*(x - 2) - 1/2*arcsin(x)","A",0
44,1,19,0,0.416745," ","integrate((-x^2+x)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} {\left(x - 2\right)} - \frac{1}{2} \, \arcsin\left(x\right)"," ",0,"1/2*sqrt(-x^2 + 1)*(x - 2) - 1/2*arcsin(x)","A",0
45,1,30,0,0.409538," ","integrate((x^2+3)/(x^2-3),x, algorithm=""giac"")","\sqrt{3} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{3} \right|}}{{\left| 2 \, x + 2 \, \sqrt{3} \right|}}\right) + x"," ",0,"sqrt(3)*log(abs(2*x - 2*sqrt(3))/abs(2*x + 2*sqrt(3))) + x","B",0
46,1,6,0,0.458439," ","integrate((x^2-1)/(x^2+1),x, algorithm=""giac"")","x - 2 \, \arctan\left(x\right)"," ",0,"x - 2*arctan(x)","A",0
47,1,204,0,0.539181," ","integrate(x^7*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left({\left({\left({\left({\left({\left(\frac{105 \, C x}{b} - \frac{176 \, B}{b}\right)} x + \frac{105 \, {\left(8 \, C a^{4} b^{7} - A a^{3} b^{8}\right)}}{a^{3} b^{9}}\right)} x - \frac{406 \, B a}{b^{2}}\right)} x + \frac{210 \, {\left(8 \, C a^{5} b^{6} - A a^{4} b^{7}\right)}}{a^{3} b^{9}}\right)} x - \frac{350 \, B a^{2}}{b^{3}}\right)} x + \frac{168 \, {\left(8 \, C a^{6} b^{5} - A a^{5} b^{6}\right)}}{a^{3} b^{9}}\right)} x - \frac{105 \, B a^{3}}{b^{4}}\right)} x + \frac{48 \, {\left(8 \, C a^{7} b^{4} - A a^{6} b^{5}\right)}}{a^{3} b^{9}}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} - \frac{B \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{b^{\frac{9}{2}}}"," ",0,"1/105*((((((((105*C*x/b - 176*B/b)*x + 105*(8*C*a^4*b^7 - A*a^3*b^8)/(a^3*b^9))*x - 406*B*a/b^2)*x + 210*(8*C*a^5*b^6 - A*a^4*b^7)/(a^3*b^9))*x - 350*B*a^2/b^3)*x + 168*(8*C*a^6*b^5 - A*a^5*b^6)/(a^3*b^9))*x - 105*B*a^3/b^4)*x + 48*(8*C*a^7*b^4 - A*a^6*b^5)/(a^3*b^9))/(b*x^2 + a)^(7/2) - B*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(9/2)","A",0
48,1,138,0,0.526720," ","integrate(x^6*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","-\frac{{\left({\left({\left({\left({\left(x {\left(\frac{105 \, B}{b} + \frac{{\left(176 \, C a^{3} b^{7} - 15 \, A a^{2} b^{8}\right)} x}{a^{3} b^{8}}\right)} + \frac{406 \, C a}{b^{2}}\right)} x + \frac{210 \, B a}{b^{2}}\right)} x + \frac{350 \, C a^{2}}{b^{3}}\right)} x + \frac{168 \, B a^{2}}{b^{3}}\right)} x + \frac{105 \, C a^{3}}{b^{4}}\right)} x + \frac{48 \, B a^{3}}{b^{4}}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} - \frac{C \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{b^{\frac{9}{2}}}"," ",0,"-1/105*((((((x*(105*B/b + (176*C*a^3*b^7 - 15*A*a^2*b^8)*x/(a^3*b^8)) + 406*C*a/b^2)*x + 210*B*a/b^2)*x + 350*C*a^2/b^3)*x + 168*B*a^2/b^3)*x + 105*C*a^3/b^4)*x + 48*B*a^3/b^4)/(b*x^2 + a)^(7/2) - C*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(9/2)","A",0
49,1,112,0,0.624172," ","integrate(x^5*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left(5 \, {\left(3 \, {\left(\frac{B x}{a} - \frac{7 \, C}{b}\right)} x^{2} - \frac{7 \, {\left(6 \, C a^{4} b^{2} + A a^{3} b^{3}\right)}}{a^{3} b^{4}}\right)} x^{2} - \frac{28 \, {\left(6 \, C a^{5} b + A a^{4} b^{2}\right)}}{a^{3} b^{4}}\right)} x^{2} - \frac{8 \, {\left(6 \, C a^{6} + A a^{5} b\right)}}{a^{3} b^{4}}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}}"," ",0,"1/105*((5*(3*(B*x/a - 7*C/b)*x^2 - 7*(6*C*a^4*b^2 + A*a^3*b^3)/(a^3*b^4))*x^2 - 28*(6*C*a^5*b + A*a^4*b^2)/(a^3*b^4))*x^2 - 8*(6*C*a^6 + A*a^5*b)/(a^3*b^4))/(b*x^2 + a)^(7/2)","A",0
50,1,81,0,0.580129," ","integrate(x^4*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(3 \, x {\left(\frac{7 \, A}{a} + \frac{{\left(5 \, C a^{2} b^{3} + 2 \, A a b^{4}\right)} x^{2}}{a^{3} b^{3}}\right)} - \frac{35 \, B}{b}\right)} x^{2} - \frac{28 \, B a}{b^{2}}\right)} x^{2} - \frac{8 \, B a^{2}}{b^{3}}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}}"," ",0,"1/105*(((3*x*(7*A/a + (5*C*a^2*b^3 + 2*A*a*b^4)*x^2/(a^3*b^3)) - 35*B/b)*x^2 - 28*B*a/b^2)*x^2 - 8*B*a^2/b^3)/(b*x^2 + a)^(7/2)","A",0
51,1,95,0,0.586169," ","integrate(x^3*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(3 \, {\left(\frac{2 \, B b x^{2}}{a^{2}} + \frac{7 \, B}{a}\right)} x - \frac{35 \, C}{b}\right)} x^{2} - \frac{7 \, {\left(4 \, C a^{4} b + 3 \, A a^{3} b^{2}\right)}}{a^{3} b^{3}}\right)} x^{2} - \frac{2 \, {\left(4 \, C a^{5} + 3 \, A a^{4} b\right)}}{a^{3} b^{3}}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}}"," ",0,"1/105*(((3*(2*B*b*x^2/a^2 + 7*B/a)*x - 35*C/b)*x^2 - 7*(4*C*a^4*b + 3*A*a^3*b^2)/(a^3*b^3))*x^2 - 2*(4*C*a^5 + 3*A*a^4*b)/(a^3*b^3))/(b*x^2 + a)^(7/2)","A",0
52,1,94,0,0.518255," ","integrate(x^2*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(x^{2} {\left(\frac{2 \, {\left(3 \, C a b^{4} + 4 \, A b^{5}\right)} x^{2}}{a^{3} b^{3}} + \frac{7 \, {\left(3 \, C a^{2} b^{3} + 4 \, A a b^{4}\right)}}{a^{3} b^{3}}\right)} + \frac{35 \, A}{a}\right)} x - \frac{21 \, B}{b}\right)} x^{2} - \frac{6 \, B a}{b^{2}}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}}"," ",0,"1/105*(((x^2*(2*(3*C*a*b^4 + 4*A*b^5)*x^2/(a^3*b^3) + 7*(3*C*a^2*b^3 + 4*A*a*b^4)/(a^3*b^3)) + 35*A/a)*x - 21*B/b)*x^2 - 6*B*a/b^2)/(b*x^2 + a)^(7/2)","A",0
53,1,82,0,0.603541," ","integrate(x*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(4 \, {\left(\frac{2 \, B b^{2} x^{2}}{a^{3}} + \frac{7 \, B b}{a^{2}}\right)} x^{2} + \frac{35 \, B}{a}\right)} x - \frac{21 \, C}{b}\right)} x^{2} - \frac{3 \, {\left(2 \, C a^{4} b + 5 \, A a^{3} b^{2}\right)}}{a^{3} b^{3}}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}}"," ",0,"1/105*(((4*(2*B*b^2*x^2/a^3 + 7*B*b/a^2)*x^2 + 35*B/a)*x - 21*C/b)*x^2 - 3*(2*C*a^4*b + 5*A*a^3*b^2)/(a^3*b^3))/(b*x^2 + a)^(7/2)","A",0
54,1,112,0,0.503689," ","integrate((C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(4 \, x^{2} {\left(\frac{2 \, {\left(C a b^{5} + 6 \, A b^{6}\right)} x^{2}}{a^{4} b^{3}} + \frac{7 \, {\left(C a^{2} b^{4} + 6 \, A a b^{5}\right)}}{a^{4} b^{3}}\right)} + \frac{35 \, {\left(C a^{3} b^{3} + 6 \, A a^{2} b^{4}\right)}}{a^{4} b^{3}}\right)} x^{2} + \frac{105 \, A}{a}\right)} x - \frac{15 \, B}{b}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}}"," ",0,"1/105*(((4*x^2*(2*(C*a*b^5 + 6*A*b^6)*x^2/(a^4*b^3) + 7*(C*a^2*b^4 + 6*A*a*b^5)/(a^4*b^3)) + 35*(C*a^3*b^3 + 6*A*a^2*b^4)/(a^4*b^3))*x^2 + 105*A/a)*x - 15*B/b)/(b*x^2 + a)^(7/2)","A",0
55,1,152,0,0.572942," ","integrate((C*x^2+B*x+A)/x/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left({\left({\left(3 \, {\left({\left(\frac{16 \, B b^{3} x}{a^{4}} + \frac{35 \, A b^{3}}{a^{4}}\right)} x + \frac{56 \, B b^{2}}{a^{3}}\right)} x + \frac{350 \, A b^{2}}{a^{3}}\right)} x + \frac{210 \, B b}{a^{2}}\right)} x + \frac{406 \, A b}{a^{2}}\right)} x + \frac{105 \, B}{a}\right)} x - \frac{15 \, C a^{14} b^{2} - 176 \, A a^{13} b^{3}}{a^{14} b^{3}}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} + \frac{2 \, A \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{4}}"," ",0,"1/105*(((((3*((16*B*b^3*x/a^4 + 35*A*b^3/a^4)*x + 56*B*b^2/a^3)*x + 350*A*b^2/a^3)*x + 210*B*b/a^2)*x + 406*A*b/a^2)*x + 105*B/a)*x - (15*C*a^14*b^2 - 176*A*a^13*b^3)/(a^14*b^3))/(b*x^2 + a)^(7/2) + 2*A*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^4)","A",0
56,1,239,0,0.510840," ","integrate((C*x^2+B*x+A)/x^2/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left({\left({\left(3 \, {\left(x {\left(\frac{35 \, B b^{3}}{a^{4}} + \frac{{\left(16 \, C a^{20} b^{6} - 93 \, A a^{19} b^{7}\right)} x}{a^{24} b^{3}}\right)} + \frac{28 \, {\left(2 \, C a^{21} b^{5} - 11 \, A a^{20} b^{6}\right)}}{a^{24} b^{3}}\right)} x + \frac{350 \, B b^{2}}{a^{3}}\right)} x + \frac{210 \, {\left(C a^{22} b^{4} - 5 \, A a^{21} b^{5}\right)}}{a^{24} b^{3}}\right)} x + \frac{406 \, B b}{a^{2}}\right)} x + \frac{105 \, {\left(C a^{23} b^{3} - 4 \, A a^{22} b^{4}\right)}}{a^{24} b^{3}}\right)} x + \frac{176 \, B}{a}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} + \frac{2 \, B \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{4}} + \frac{2 \, A \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)} a^{4}}"," ",0,"1/105*(((((3*(x*(35*B*b^3/a^4 + (16*C*a^20*b^6 - 93*A*a^19*b^7)*x/(a^24*b^3)) + 28*(2*C*a^21*b^5 - 11*A*a^20*b^6)/(a^24*b^3))*x + 350*B*b^2/a^3)*x + 210*(C*a^22*b^4 - 5*A*a^21*b^5)/(a^24*b^3))*x + 406*B*b/a^2)*x + 105*(C*a^23*b^3 - 4*A*a^22*b^4)/(a^24*b^3))*x + 176*B/a)/(b*x^2 + a)^(7/2) + 2*B*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^4) + 2*A*sqrt(b)/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)*a^4)","A",0
57,1,325,0,0.483512," ","integrate((C*x^2+B*x+A)/x^3/(b*x^2+a)^(9/2),x, algorithm=""giac"")","-\frac{{\left({\left({\left({\left(3 \, {\left({\left(\frac{93 \, B b^{4} x}{a^{5}} - \frac{35 \, {\left(C a^{24} b^{6} - 4 \, A a^{23} b^{7}\right)}}{a^{28} b^{3}}\right)} x + \frac{308 \, B b^{3}}{a^{4}}\right)} x - \frac{35 \, {\left(10 \, C a^{25} b^{5} - 39 \, A a^{24} b^{6}\right)}}{a^{28} b^{3}}\right)} x + \frac{1050 \, B b^{2}}{a^{3}}\right)} x - \frac{14 \, {\left(29 \, C a^{26} b^{4} - 108 \, A a^{25} b^{5}\right)}}{a^{28} b^{3}}\right)} x + \frac{420 \, B b}{a^{2}}\right)} x - \frac{2 \, {\left(88 \, C a^{27} b^{3} - 291 \, A a^{26} b^{4}\right)}}{a^{28} b^{3}}}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} + \frac{{\left(2 \, C a - 9 \, A b\right)} \arctan\left(-\frac{\sqrt{b} x - \sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{5}} + \frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{3} A b + 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a \sqrt{b} + {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)} A a b - 2 \, B a^{2} \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{2} a^{5}}"," ",0,"-1/105*(((((3*((93*B*b^4*x/a^5 - 35*(C*a^24*b^6 - 4*A*a^23*b^7)/(a^28*b^3))*x + 308*B*b^3/a^4)*x - 35*(10*C*a^25*b^5 - 39*A*a^24*b^6)/(a^28*b^3))*x + 1050*B*b^2/a^3)*x - 14*(29*C*a^26*b^4 - 108*A*a^25*b^5)/(a^28*b^3))*x + 420*B*b/a^2)*x - 2*(88*C*a^27*b^3 - 291*A*a^26*b^4)/(a^28*b^3))/(b*x^2 + a)^(7/2) + (2*C*a - 9*A*b)*arctan(-(sqrt(b)*x - sqrt(b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^5) + ((sqrt(b)*x - sqrt(b*x^2 + a))^3*A*b + 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a*sqrt(b) + (sqrt(b)*x - sqrt(b*x^2 + a))*A*a*b - 2*B*a^2*sqrt(b))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^2*a^5)","A",0
58,0,0,0,0.000000," ","integrate(A*(c*x)^m/(b*x^2+a),x, algorithm=""giac"")","\int \frac{\left(c x\right)^{m} A}{b x^{2} + a}\,{d x}"," ",0,"integrate((c*x)^m*A/(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=""giac"")","\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=""giac"")","\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=""giac"")","\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
62,1,57,0,0.368505," ","integrate(x^3*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{9} \, D b x^{9} + \frac{1}{8} \, C b x^{8} + \frac{1}{7} \, D a x^{7} + \frac{1}{7} \, B b x^{7} + \frac{1}{6} \, C a x^{6} + \frac{1}{6} \, A b x^{6} + \frac{1}{5} \, B a x^{5} + \frac{1}{4} \, A a x^{4}"," ",0,"1/9*D*b*x^9 + 1/8*C*b*x^8 + 1/7*D*a*x^7 + 1/7*B*b*x^7 + 1/6*C*a*x^6 + 1/6*A*b*x^6 + 1/5*B*a*x^5 + 1/4*A*a*x^4","A",0
63,1,57,0,0.378982," ","integrate(x^2*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{8} \, D b x^{8} + \frac{1}{7} \, C b x^{7} + \frac{1}{6} \, D a x^{6} + \frac{1}{6} \, B b x^{6} + \frac{1}{5} \, C a x^{5} + \frac{1}{5} \, A b x^{5} + \frac{1}{4} \, B a x^{4} + \frac{1}{3} \, A a x^{3}"," ",0,"1/8*D*b*x^8 + 1/7*C*b*x^7 + 1/6*D*a*x^6 + 1/6*B*b*x^6 + 1/5*C*a*x^5 + 1/5*A*b*x^5 + 1/4*B*a*x^4 + 1/3*A*a*x^3","A",0
64,1,57,0,0.317584," ","integrate(x*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{7} \, D b x^{7} + \frac{1}{6} \, C b x^{6} + \frac{1}{5} \, D a x^{5} + \frac{1}{5} \, B b x^{5} + \frac{1}{4} \, C a x^{4} + \frac{1}{4} \, A b x^{4} + \frac{1}{3} \, B a x^{3} + \frac{1}{2} \, A a x^{2}"," ",0,"1/7*D*b*x^7 + 1/6*C*b*x^6 + 1/5*D*a*x^5 + 1/5*B*b*x^5 + 1/4*C*a*x^4 + 1/4*A*b*x^4 + 1/3*B*a*x^3 + 1/2*A*a*x^2","A",0
65,1,54,0,0.360816," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{6} \, D b x^{6} + \frac{1}{5} \, C b x^{5} + \frac{1}{4} \, D a x^{4} + \frac{1}{4} \, B b x^{4} + \frac{1}{3} \, C a x^{3} + \frac{1}{3} \, A b x^{3} + \frac{1}{2} \, B a x^{2} + A a x"," ",0,"1/6*D*b*x^6 + 1/5*C*b*x^5 + 1/4*D*a*x^4 + 1/4*B*b*x^4 + 1/3*C*a*x^3 + 1/3*A*b*x^3 + 1/2*B*a*x^2 + A*a*x","A",0
66,1,53,0,0.409915," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x,x, algorithm=""giac"")","\frac{1}{5} \, D b x^{5} + \frac{1}{4} \, C b x^{4} + \frac{1}{3} \, D a x^{3} + \frac{1}{3} \, B b x^{3} + \frac{1}{2} \, C a x^{2} + \frac{1}{2} \, A b x^{2} + B a x + A a \log\left({\left| x \right|}\right)"," ",0,"1/5*D*b*x^5 + 1/4*C*b*x^4 + 1/3*D*a*x^3 + 1/3*B*b*x^3 + 1/2*C*a*x^2 + 1/2*A*b*x^2 + B*a*x + A*a*log(abs(x))","A",0
67,1,50,0,0.385910," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x^2,x, algorithm=""giac"")","\frac{1}{4} \, D b x^{4} + \frac{1}{3} \, C b x^{3} + \frac{1}{2} \, D a x^{2} + \frac{1}{2} \, B b x^{2} + C a x + A b x + B a \log\left({\left| x \right|}\right) - \frac{A a}{x}"," ",0,"1/4*D*b*x^4 + 1/3*C*b*x^3 + 1/2*D*a*x^2 + 1/2*B*b*x^2 + C*a*x + A*b*x + B*a*log(abs(x)) - A*a/x","A",0
68,1,48,0,0.375101," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x^3,x, algorithm=""giac"")","\frac{1}{3} \, D b x^{3} + \frac{1}{2} \, C b x^{2} + D a x + B b x + {\left(C a + A b\right)} \log\left({\left| x \right|}\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*x + B*b*x + (C*a + A*b)*log(abs(x)) - 1/2*(2*B*a*x + A*a)/x^2","A",0
69,1,50,0,0.431672," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x^4,x, algorithm=""giac"")","\frac{1}{2} \, D b x^{2} + C b x + {\left(D a + B b\right)} \log\left({\left| x \right|}\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(abs(x)) - 1/6*(3*B*a*x + 6*(C*a + A*b)*x^2 + 2*A*a)/x^3","A",0
70,1,105,0,0.350416," ","integrate(x^3*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{11} \, D b^{2} x^{11} + \frac{1}{10} \, C b^{2} x^{10} + \frac{2}{9} \, D a b x^{9} + \frac{1}{9} \, B b^{2} x^{9} + \frac{1}{4} \, C a b x^{8} + \frac{1}{8} \, A b^{2} x^{8} + \frac{1}{7} \, D a^{2} x^{7} + \frac{2}{7} \, B a b x^{7} + \frac{1}{6} \, C a^{2} x^{6} + \frac{1}{3} \, A a b x^{6} + \frac{1}{5} \, B a^{2} x^{5} + \frac{1}{4} \, A a^{2} x^{4}"," ",0,"1/11*D*b^2*x^11 + 1/10*C*b^2*x^10 + 2/9*D*a*b*x^9 + 1/9*B*b^2*x^9 + 1/4*C*a*b*x^8 + 1/8*A*b^2*x^8 + 1/7*D*a^2*x^7 + 2/7*B*a*b*x^7 + 1/6*C*a^2*x^6 + 1/3*A*a*b*x^6 + 1/5*B*a^2*x^5 + 1/4*A*a^2*x^4","A",0
71,1,105,0,0.369253," ","integrate(x^2*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{10} \, D b^{2} x^{10} + \frac{1}{9} \, C b^{2} x^{9} + \frac{1}{4} \, D a b x^{8} + \frac{1}{8} \, B b^{2} x^{8} + \frac{2}{7} \, C a b x^{7} + \frac{1}{7} \, A b^{2} x^{7} + \frac{1}{6} \, D a^{2} x^{6} + \frac{1}{3} \, B a b x^{6} + \frac{1}{5} \, C a^{2} x^{5} + \frac{2}{5} \, A a b x^{5} + \frac{1}{4} \, B a^{2} x^{4} + \frac{1}{3} \, A a^{2} x^{3}"," ",0,"1/10*D*b^2*x^10 + 1/9*C*b^2*x^9 + 1/4*D*a*b*x^8 + 1/8*B*b^2*x^8 + 2/7*C*a*b*x^7 + 1/7*A*b^2*x^7 + 1/6*D*a^2*x^6 + 1/3*B*a*b*x^6 + 1/5*C*a^2*x^5 + 2/5*A*a*b*x^5 + 1/4*B*a^2*x^4 + 1/3*A*a^2*x^3","A",0
72,1,105,0,0.360123," ","integrate(x*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{9} \, D b^{2} x^{9} + \frac{1}{8} \, C b^{2} x^{8} + \frac{2}{7} \, D a b x^{7} + \frac{1}{7} \, B b^{2} x^{7} + \frac{1}{3} \, C a b x^{6} + \frac{1}{6} \, A b^{2} x^{6} + \frac{1}{5} \, D a^{2} x^{5} + \frac{2}{5} \, B a b x^{5} + \frac{1}{4} \, C a^{2} x^{4} + \frac{1}{2} \, A a b x^{4} + \frac{1}{3} \, B a^{2} x^{3} + \frac{1}{2} \, A a^{2} x^{2}"," ",0,"1/9*D*b^2*x^9 + 1/8*C*b^2*x^8 + 2/7*D*a*b*x^7 + 1/7*B*b^2*x^7 + 1/3*C*a*b*x^6 + 1/6*A*b^2*x^6 + 1/5*D*a^2*x^5 + 2/5*B*a*b*x^5 + 1/4*C*a^2*x^4 + 1/2*A*a*b*x^4 + 1/3*B*a^2*x^3 + 1/2*A*a^2*x^2","A",0
73,1,102,0,0.378766," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{8} \, D b^{2} x^{8} + \frac{1}{7} \, C b^{2} x^{7} + \frac{1}{3} \, D a b x^{6} + \frac{1}{6} \, B b^{2} x^{6} + \frac{2}{5} \, C a b x^{5} + \frac{1}{5} \, A b^{2} x^{5} + \frac{1}{4} \, D a^{2} x^{4} + \frac{1}{2} \, B a b x^{4} + \frac{1}{3} \, C a^{2} x^{3} + \frac{2}{3} \, A a b x^{3} + \frac{1}{2} \, B a^{2} x^{2} + A a^{2} x"," ",0,"1/8*D*b^2*x^8 + 1/7*C*b^2*x^7 + 1/3*D*a*b*x^6 + 1/6*B*b^2*x^6 + 2/5*C*a*b*x^5 + 1/5*A*b^2*x^5 + 1/4*D*a^2*x^4 + 1/2*B*a*b*x^4 + 1/3*C*a^2*x^3 + 2/3*A*a*b*x^3 + 1/2*B*a^2*x^2 + A*a^2*x","A",0
74,1,100,0,0.464060," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x,x, algorithm=""giac"")","\frac{1}{7} \, D b^{2} x^{7} + \frac{1}{6} \, C b^{2} x^{6} + \frac{2}{5} \, D a b x^{5} + \frac{1}{5} \, B b^{2} x^{5} + \frac{1}{2} \, C a b x^{4} + \frac{1}{4} \, A b^{2} x^{4} + \frac{1}{3} \, D a^{2} x^{3} + \frac{2}{3} \, B a b x^{3} + \frac{1}{2} \, C a^{2} x^{2} + A a b x^{2} + B a^{2} x + A a^{2} \log\left({\left| x \right|}\right)"," ",0,"1/7*D*b^2*x^7 + 1/6*C*b^2*x^6 + 2/5*D*a*b*x^5 + 1/5*B*b^2*x^5 + 1/2*C*a*b*x^4 + 1/4*A*b^2*x^4 + 1/3*D*a^2*x^3 + 2/3*B*a*b*x^3 + 1/2*C*a^2*x^2 + A*a*b*x^2 + B*a^2*x + A*a^2*log(abs(x))","A",0
75,1,98,0,0.378458," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x^2,x, algorithm=""giac"")","\frac{1}{6} \, D b^{2} x^{6} + \frac{1}{5} \, C b^{2} x^{5} + \frac{1}{2} \, D a b x^{4} + \frac{1}{4} \, B b^{2} x^{4} + \frac{2}{3} \, C a b x^{3} + \frac{1}{3} \, A b^{2} x^{3} + \frac{1}{2} \, D a^{2} x^{2} + B a b x^{2} + C a^{2} x + 2 \, A a b x + B a^{2} \log\left({\left| x \right|}\right) - \frac{A a^{2}}{x}"," ",0,"1/6*D*b^2*x^6 + 1/5*C*b^2*x^5 + 1/2*D*a*b*x^4 + 1/4*B*b^2*x^4 + 2/3*C*a*b*x^3 + 1/3*A*b^2*x^3 + 1/2*D*a^2*x^2 + B*a*b*x^2 + C*a^2*x + 2*A*a*b*x + B*a^2*log(abs(x)) - A*a^2/x","A",0
76,1,97,0,0.335355," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x^3,x, algorithm=""giac"")","\frac{1}{5} \, D b^{2} x^{5} + \frac{1}{4} \, C b^{2} x^{4} + \frac{2}{3} \, D a b x^{3} + \frac{1}{3} \, B b^{2} x^{3} + C a b x^{2} + \frac{1}{2} \, A b^{2} x^{2} + D a^{2} x + 2 \, B a b x + {\left(C a^{2} + 2 \, A a b\right)} \log\left({\left| x \right|}\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 + 2/3*D*a*b*x^3 + 1/3*B*b^2*x^3 + C*a*b*x^2 + 1/2*A*b^2*x^2 + D*a^2*x + 2*B*a*b*x + (C*a^2 + 2*A*a*b)*log(abs(x)) - 1/2*(2*B*a^2*x + A*a^2)/x^2","A",0
77,1,97,0,0.429760," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x^4,x, algorithm=""giac"")","\frac{1}{4} \, D b^{2} x^{4} + \frac{1}{3} \, C b^{2} x^{3} + D a b x^{2} + \frac{1}{2} \, B b^{2} x^{2} + 2 \, C a b x + A b^{2} x + {\left(D a^{2} + 2 \, B a b\right)} \log\left({\left| x \right|}\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 + D*a*b*x^2 + 1/2*B*b^2*x^2 + 2*C*a*b*x + A*b^2*x + (D*a^2 + 2*B*a*b)*log(abs(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
78,1,153,0,0.459141," ","integrate(x^3*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{13} \, D b^{3} x^{13} + \frac{1}{12} \, C b^{3} x^{12} + \frac{3}{11} \, D a b^{2} x^{11} + \frac{1}{11} \, B b^{3} x^{11} + \frac{3}{10} \, C a b^{2} x^{10} + \frac{1}{10} \, A b^{3} x^{10} + \frac{1}{3} \, D a^{2} b x^{9} + \frac{1}{3} \, B a b^{2} x^{9} + \frac{3}{8} \, C a^{2} b x^{8} + \frac{3}{8} \, A a b^{2} x^{8} + \frac{1}{7} \, D a^{3} x^{7} + \frac{3}{7} \, B a^{2} b x^{7} + \frac{1}{6} \, C a^{3} x^{6} + \frac{1}{2} \, A a^{2} b x^{6} + \frac{1}{5} \, B a^{3} x^{5} + \frac{1}{4} \, A a^{3} x^{4}"," ",0,"1/13*D*b^3*x^13 + 1/12*C*b^3*x^12 + 3/11*D*a*b^2*x^11 + 1/11*B*b^3*x^11 + 3/10*C*a*b^2*x^10 + 1/10*A*b^3*x^10 + 1/3*D*a^2*b*x^9 + 1/3*B*a*b^2*x^9 + 3/8*C*a^2*b*x^8 + 3/8*A*a*b^2*x^8 + 1/7*D*a^3*x^7 + 3/7*B*a^2*b*x^7 + 1/6*C*a^3*x^6 + 1/2*A*a^2*b*x^6 + 1/5*B*a^3*x^5 + 1/4*A*a^3*x^4","A",0
79,1,153,0,0.461093," ","integrate(x^2*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{12} \, D b^{3} x^{12} + \frac{1}{11} \, C b^{3} x^{11} + \frac{3}{10} \, D a b^{2} x^{10} + \frac{1}{10} \, B b^{3} x^{10} + \frac{1}{3} \, C a b^{2} x^{9} + \frac{1}{9} \, A b^{3} x^{9} + \frac{3}{8} \, D a^{2} b x^{8} + \frac{3}{8} \, B a b^{2} x^{8} + \frac{3}{7} \, C a^{2} b x^{7} + \frac{3}{7} \, A a b^{2} x^{7} + \frac{1}{6} \, D a^{3} x^{6} + \frac{1}{2} \, B a^{2} b x^{6} + \frac{1}{5} \, C a^{3} x^{5} + \frac{3}{5} \, A a^{2} b x^{5} + \frac{1}{4} \, B a^{3} x^{4} + \frac{1}{3} \, A a^{3} x^{3}"," ",0,"1/12*D*b^3*x^12 + 1/11*C*b^3*x^11 + 3/10*D*a*b^2*x^10 + 1/10*B*b^3*x^10 + 1/3*C*a*b^2*x^9 + 1/9*A*b^3*x^9 + 3/8*D*a^2*b*x^8 + 3/8*B*a*b^2*x^8 + 3/7*C*a^2*b*x^7 + 3/7*A*a*b^2*x^7 + 1/6*D*a^3*x^6 + 1/2*B*a^2*b*x^6 + 1/5*C*a^3*x^5 + 3/5*A*a^2*b*x^5 + 1/4*B*a^3*x^4 + 1/3*A*a^3*x^3","A",0
80,1,153,0,0.361659," ","integrate(x*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{11} \, D b^{3} x^{11} + \frac{1}{10} \, C b^{3} x^{10} + \frac{1}{3} \, D a b^{2} x^{9} + \frac{1}{9} \, B b^{3} x^{9} + \frac{3}{8} \, C a b^{2} x^{8} + \frac{1}{8} \, A b^{3} x^{8} + \frac{3}{7} \, D a^{2} b x^{7} + \frac{3}{7} \, B a b^{2} x^{7} + \frac{1}{2} \, C a^{2} b x^{6} + \frac{1}{2} \, A a b^{2} x^{6} + \frac{1}{5} \, D a^{3} x^{5} + \frac{3}{5} \, B a^{2} b x^{5} + \frac{1}{4} \, C a^{3} x^{4} + \frac{3}{4} \, A a^{2} b x^{4} + \frac{1}{3} \, B a^{3} x^{3} + \frac{1}{2} \, A a^{3} x^{2}"," ",0,"1/11*D*b^3*x^11 + 1/10*C*b^3*x^10 + 1/3*D*a*b^2*x^9 + 1/9*B*b^3*x^9 + 3/8*C*a*b^2*x^8 + 1/8*A*b^3*x^8 + 3/7*D*a^2*b*x^7 + 3/7*B*a*b^2*x^7 + 1/2*C*a^2*b*x^6 + 1/2*A*a*b^2*x^6 + 1/5*D*a^3*x^5 + 3/5*B*a^2*b*x^5 + 1/4*C*a^3*x^4 + 3/4*A*a^2*b*x^4 + 1/3*B*a^3*x^3 + 1/2*A*a^3*x^2","A",0
81,1,149,0,0.400559," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""giac"")","\frac{1}{10} \, D b^{3} x^{10} + \frac{1}{9} \, C b^{3} x^{9} + \frac{3}{8} \, D a b^{2} x^{8} + \frac{1}{8} \, B b^{3} x^{8} + \frac{3}{7} \, C a b^{2} x^{7} + \frac{1}{7} \, A b^{3} x^{7} + \frac{1}{2} \, D a^{2} b x^{6} + \frac{1}{2} \, B a b^{2} x^{6} + \frac{3}{5} \, C a^{2} b x^{5} + \frac{3}{5} \, A a b^{2} x^{5} + \frac{1}{4} \, D a^{3} x^{4} + \frac{3}{4} \, B a^{2} b x^{4} + \frac{1}{3} \, C a^{3} x^{3} + A a^{2} b x^{3} + \frac{1}{2} \, B a^{3} x^{2} + A a^{3} x"," ",0,"1/10*D*b^3*x^10 + 1/9*C*b^3*x^9 + 3/8*D*a*b^2*x^8 + 1/8*B*b^3*x^8 + 3/7*C*a*b^2*x^7 + 1/7*A*b^3*x^7 + 1/2*D*a^2*b*x^6 + 1/2*B*a*b^2*x^6 + 3/5*C*a^2*b*x^5 + 3/5*A*a*b^2*x^5 + 1/4*D*a^3*x^4 + 3/4*B*a^2*b*x^4 + 1/3*C*a^3*x^3 + A*a^2*b*x^3 + 1/2*B*a^3*x^2 + A*a^3*x","A",0
82,1,148,0,0.327238," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x,x, algorithm=""giac"")","\frac{1}{9} \, D b^{3} x^{9} + \frac{1}{8} \, C b^{3} x^{8} + \frac{3}{7} \, D a b^{2} x^{7} + \frac{1}{7} \, B b^{3} x^{7} + \frac{1}{2} \, C a b^{2} x^{6} + \frac{1}{6} \, A b^{3} x^{6} + \frac{3}{5} \, D a^{2} b x^{5} + \frac{3}{5} \, B a b^{2} x^{5} + \frac{3}{4} \, C a^{2} b x^{4} + \frac{3}{4} \, A a b^{2} x^{4} + \frac{1}{3} \, D a^{3} x^{3} + B a^{2} b x^{3} + \frac{1}{2} \, C a^{3} x^{2} + \frac{3}{2} \, A a^{2} b x^{2} + B a^{3} x + A a^{3} \log\left({\left| x \right|}\right)"," ",0,"1/9*D*b^3*x^9 + 1/8*C*b^3*x^8 + 3/7*D*a*b^2*x^7 + 1/7*B*b^3*x^7 + 1/2*C*a*b^2*x^6 + 1/6*A*b^3*x^6 + 3/5*D*a^2*b*x^5 + 3/5*B*a*b^2*x^5 + 3/4*C*a^2*b*x^4 + 3/4*A*a*b^2*x^4 + 1/3*D*a^3*x^3 + B*a^2*b*x^3 + 1/2*C*a^3*x^2 + 3/2*A*a^2*b*x^2 + B*a^3*x + A*a^3*log(abs(x))","A",0
83,1,145,0,0.406044," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x^2,x, algorithm=""giac"")","\frac{1}{8} \, D b^{3} x^{8} + \frac{1}{7} \, C b^{3} x^{7} + \frac{1}{2} \, D a b^{2} x^{6} + \frac{1}{6} \, B b^{3} x^{6} + \frac{3}{5} \, C a b^{2} x^{5} + \frac{1}{5} \, A b^{3} x^{5} + \frac{3}{4} \, D a^{2} b x^{4} + \frac{3}{4} \, B a b^{2} x^{4} + C a^{2} b x^{3} + A a b^{2} x^{3} + \frac{1}{2} \, D a^{3} x^{2} + \frac{3}{2} \, B a^{2} b x^{2} + C a^{3} x + 3 \, A a^{2} b x + B a^{3} \log\left({\left| x \right|}\right) - \frac{A a^{3}}{x}"," ",0,"1/8*D*b^3*x^8 + 1/7*C*b^3*x^7 + 1/2*D*a*b^2*x^6 + 1/6*B*b^3*x^6 + 3/5*C*a*b^2*x^5 + 1/5*A*b^3*x^5 + 3/4*D*a^2*b*x^4 + 3/4*B*a*b^2*x^4 + C*a^2*b*x^3 + A*a*b^2*x^3 + 1/2*D*a^3*x^2 + 3/2*B*a^2*b*x^2 + C*a^3*x + 3*A*a^2*b*x + B*a^3*log(abs(x)) - A*a^3/x","A",0
84,1,144,0,0.408706," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x^3,x, algorithm=""giac"")","\frac{1}{7} \, D b^{3} x^{7} + \frac{1}{6} \, C b^{3} x^{6} + \frac{3}{5} \, D a b^{2} x^{5} + \frac{1}{5} \, B b^{3} x^{5} + \frac{3}{4} \, C a b^{2} x^{4} + \frac{1}{4} \, A b^{3} x^{4} + D a^{2} b x^{3} + B a b^{2} x^{3} + \frac{3}{2} \, C a^{2} b x^{2} + \frac{3}{2} \, A a b^{2} x^{2} + D a^{3} x + 3 \, B a^{2} b x + {\left(C a^{3} + 3 \, A a^{2} b\right)} \log\left({\left| x \right|}\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 + 3/5*D*a*b^2*x^5 + 1/5*B*b^3*x^5 + 3/4*C*a*b^2*x^4 + 1/4*A*b^3*x^4 + D*a^2*b*x^3 + B*a*b^2*x^3 + 3/2*C*a^2*b*x^2 + 3/2*A*a*b^2*x^2 + D*a^3*x + 3*B*a^2*b*x + (C*a^3 + 3*A*a^2*b)*log(abs(x)) - 1/2*(2*B*a^3*x + A*a^3)/x^2","A",0
85,1,146,0,0.395993," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x^4,x, algorithm=""giac"")","\frac{1}{6} \, D b^{3} x^{6} + \frac{1}{5} \, C b^{3} x^{5} + \frac{3}{4} \, D a b^{2} x^{4} + \frac{1}{4} \, B b^{3} x^{4} + C a b^{2} x^{3} + \frac{1}{3} \, A b^{3} x^{3} + \frac{3}{2} \, D a^{2} b x^{2} + \frac{3}{2} \, B a b^{2} x^{2} + 3 \, C a^{2} b x + 3 \, A a b^{2} x + {\left(D a^{3} + 3 \, B a^{2} b\right)} \log\left({\left| x \right|}\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 + 3/4*D*a*b^2*x^4 + 1/4*B*b^3*x^4 + C*a*b^2*x^3 + 1/3*A*b^3*x^3 + 3/2*D*a^2*b*x^2 + 3/2*B*a*b^2*x^2 + 3*C*a^2*b*x + 3*A*a*b^2*x + (D*a^3 + 3*B*a^2*b)*log(abs(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
86,1,161,0,0.431330," ","integrate(x^4*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""giac"")","-\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{{\left(D a^{3} - B a^{2} b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}} + \frac{10 \, D b^{5} x^{6} + 12 \, C b^{5} x^{5} - 15 \, D a b^{4} x^{4} + 15 \, B b^{5} x^{4} - 20 \, C a b^{4} x^{3} + 20 \, A b^{5} x^{3} + 30 \, D a^{2} b^{3} x^{2} - 30 \, B a b^{4} x^{2} + 60 \, C a^{2} b^{3} x - 60 \, A a b^{4} x}{60 \, b^{6}}"," ",0,"-(C*a^3 - A*a^2*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) - 1/2*(D*a^3 - B*a^2*b)*log(b*x^2 + a)/b^4 + 1/60*(10*D*b^5*x^6 + 12*C*b^5*x^5 - 15*D*a*b^4*x^4 + 15*B*b^5*x^4 - 20*C*a*b^4*x^3 + 20*A*b^5*x^3 + 30*D*a^2*b^3*x^2 - 30*B*a*b^4*x^2 + 60*C*a^2*b^3*x - 60*A*a*b^4*x)/b^6","A",0
87,1,137,0,0.350490," ","integrate(x^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""giac"")","\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^{4} x^{5} + 15 \, C b^{4} x^{4} - 20 \, D a b^{3} x^{3} + 20 \, B b^{4} x^{3} - 30 \, C a b^{3} x^{2} + 30 \, A b^{4} x^{2} + 60 \, D a^{2} b^{2} x - 60 \, B a b^{3} x}{60 \, b^{5}}"," ",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^4*x^5 + 15*C*b^4*x^4 - 20*D*a*b^3*x^3 + 20*B*b^4*x^3 - 30*C*a*b^3*x^2 + 30*A*b^4*x^2 + 60*D*a^2*b^2*x - 60*B*a*b^3*x)/b^5","A",0
88,1,112,0,0.399120," ","integrate(x^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(C a^{2} - A a b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{{\left(D a^{2} - B a b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{3}} + \frac{3 \, D b^{3} x^{4} + 4 \, C b^{3} x^{3} - 6 \, D a b^{2} x^{2} + 6 \, B b^{3} x^{2} - 12 \, C a b^{2} x + 12 \, A b^{3} x}{12 \, b^{4}}"," ",0,"(C*a^2 - A*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/2*(D*a^2 - B*a*b)*log(b*x^2 + a)/b^3 + 1/12*(3*D*b^3*x^4 + 4*C*b^3*x^3 - 6*D*a*b^2*x^2 + 6*B*b^3*x^2 - 12*C*a*b^2*x + 12*A*b^3*x)/b^4","A",0
89,1,88,0,0.423177," ","integrate(x*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""giac"")","-\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^{2} x^{3} + 3 \, C b^{2} x^{2} - 6 \, D a b x + 6 \, B b^{2} x}{6 \, b^{3}}"," ",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^2*x^3 + 3*C*b^2*x^2 - 6*D*a*b*x + 6*B*b^2*x)/b^3","A",0
90,1,66,0,0.460393," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(C a - A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b} - \frac{{\left(D a - B b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{2}} + \frac{D b x^{2} + 2 \, C b x}{2 \, b^{2}}"," ",0,"-(C*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b) - 1/2*(D*a - B*b)*log(b*x^2 + a)/b^2 + 1/2*(D*b*x^2 + 2*C*b*x)/b^2","A",0
91,1,66,0,0.450632," ","integrate((D*x^3+C*x^2+B*x+A)/x/(b*x^2+a),x, algorithm=""giac"")","\frac{D x}{b} + \frac{A \log\left({\left| x \right|}\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(abs(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
92,1,68,0,0.383449," ","integrate((D*x^3+C*x^2+B*x+A)/x^2/(b*x^2+a),x, algorithm=""giac"")","\frac{B \log\left({\left| x \right|}\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(abs(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
93,1,80,0,0.386370," ","integrate((D*x^3+C*x^2+B*x+A)/x^3/(b*x^2+a),x, algorithm=""giac"")","\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({\left| x \right|}\right)}{a^{2}} - \frac{2 \, B a x + A a}{2 \, a^{2} 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(abs(x))/a^2 - 1/2*(2*B*a*x + A*a)/(a^2*x^2)","A",0
94,1,159,0,0.432466," ","integrate(x^4*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\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{{\left(3 \, D a^{2} - 2 \, B a b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}} + \frac{D a^{3} - B a^{2} b - {\left(C a^{2} b - A a b^{2}\right)} x}{2 \, {\left(b x^{2} + a\right)} b^{4}} + \frac{3 \, D b^{6} x^{4} + 4 \, C b^{6} x^{3} - 12 \, D a b^{5} x^{2} + 6 \, B b^{6} x^{2} - 24 \, C a b^{5} x + 12 \, A b^{6} x}{12 \, b^{8}}"," ",0,"1/2*(5*C*a^2 - 3*A*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/2*(3*D*a^2 - 2*B*a*b)*log(b*x^2 + a)/b^4 + 1/2*(D*a^3 - B*a^2*b - (C*a^2*b - A*a*b^2)*x)/((b*x^2 + a)*b^4) + 1/12*(3*D*b^6*x^4 + 4*C*b^6*x^3 - 12*D*a*b^5*x^2 + 6*B*b^6*x^2 - 24*C*a*b^5*x + 12*A*b^6*x)/b^8","A",0
95,1,131,0,0.377033," ","integrate(x^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""giac"")","-\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{C a^{2} - A a b + {\left(D a^{2} - B a b\right)} x}{2 \, {\left(b x^{2} + a\right)} b^{3}} + \frac{2 \, D b^{4} x^{3} + 3 \, C b^{4} x^{2} - 12 \, D a b^{3} x + 6 \, B b^{4} x}{6 \, b^{6}}"," ",0,"-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) - 1/2*(C*a^2 - A*a*b + (D*a^2 - B*a*b)*x)/((b*x^2 + a)*b^3) + 1/6*(2*D*b^4*x^3 + 3*C*b^4*x^2 - 12*D*a*b^3*x + 6*B*b^4*x)/b^6","A",0
96,1,111,0,0.390493," ","integrate(x^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, C a - A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{2}} - \frac{{\left(2 \, D a - B b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{3}} + \frac{D b^{2} x^{2} + 2 \, C b^{2} x}{2 \, b^{4}} - \frac{D a^{2} - B a b - {\left(C a b - A b^{2}\right)} x}{2 \, {\left(b x^{2} + a\right)} b^{3}}"," ",0,"-1/2*(3*C*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) - 1/2*(2*D*a - B*b)*log(b*x^2 + a)/b^3 + 1/2*(D*b^2*x^2 + 2*C*b^2*x)/b^4 - 1/2*(D*a^2 - B*a*b - (C*a*b - A*b^2)*x)/((b*x^2 + a)*b^3)","A",0
97,1,81,0,0.431096," ","integrate(x*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\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}} + \frac{C a - A b + {\left(D a - B b\right)} x}{2 \, {\left(b x^{2} + a\right)} b^{2}}"," ",0,"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) + 1/2*(C*a - A*b + (D*a - B*b)*x)/((b*x^2 + a)*b^2)","A",0
98,1,88,0,0.375046," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\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} - \frac{{\left(C a - A b\right)} x - \frac{D a^{2} - B a b}{b}}{2 \, {\left(b x^{2} + a\right)} a b}"," ",0,"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) - 1/2*((C*a - A*b)*x - (D*a^2 - B*a*b)/b)/((b*x^2 + a)*a*b)","A",0
99,1,93,0,0.347681," ","integrate((D*x^3+C*x^2+B*x+A)/x/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{A \log\left(b x^{2} + a\right)}{2 \, a^{2}} + \frac{A \log\left({\left| x \right|}\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} - \frac{C a^{2} - A a b + {\left(D a^{2} - B a b\right)} x}{2 \, {\left(b x^{2} + a\right)} a^{2} b}"," ",0,"-1/2*A*log(b*x^2 + a)/a^2 + A*log(abs(x))/a^2 + 1/2*(D*a + B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b) - 1/2*(C*a^2 - A*a*b + (D*a^2 - B*a*b)*x)/((b*x^2 + a)*a^2*b)","A",0
100,1,103,0,0.342301," ","integrate((D*x^3+C*x^2+B*x+A)/x^2/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{B \log\left(b x^{2} + a\right)}{2 \, a^{2}} + \frac{B \log\left({\left| x \right|}\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}} + \frac{C a b x^{2} - 3 \, A b^{2} x^{2} - D a^{2} x + B a b x - 2 \, A a b}{2 \, {\left(b x^{3} + a x\right)} a^{2} b}"," ",0,"-1/2*B*log(b*x^2 + a)/a^2 + B*log(abs(x))/a^2 + 1/2*(C*a - 3*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) + 1/2*(C*a*b*x^2 - 3*A*b^2*x^2 - D*a^2*x + B*a*b*x - 2*A*a*b)/((b*x^3 + a*x)*a^2*b)","A",0
101,1,126,0,0.422411," ","integrate((D*x^3+C*x^2+B*x+A)/x^3/(b*x^2+a)^2,x, algorithm=""giac"")","\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({\left| x \right|}\right)}{a^{3}} - \frac{2 \, B a^{2} x - {\left(D a^{2} - 3 \, B a b\right)} x^{3} + A a^{2} - {\left(C a^{2} - 2 \, A a b\right)} x^{2}}{2 \, {\left(b x^{2} + a\right)} a^{3} x^{2}}"," ",0,"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(abs(x))/a^3 - 1/2*(2*B*a^2*x - (D*a^2 - 3*B*a*b)*x^3 + A*a^2 - (C*a^2 - 2*A*a*b)*x^2)/((b*x^2 + a)*a^3*x^2)","A",0
102,1,157,0,0.410045," ","integrate(x^4*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""giac"")","-\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{{\left(3 \, D a - B b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}} + \frac{D b^{3} x^{2} + 2 \, C b^{3} x}{2 \, b^{6}} - \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 x^{2} + a\right)}^{2} b^{4}}"," ",0,"-3/8*(5*C*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) - 1/2*(3*D*a - B*b)*log(b*x^2 + a)/b^4 + 1/2*(D*b^3*x^2 + 2*C*b^3*x)/b^6 - 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*x^2 + a)^2*b^4)","A",0
103,1,122,0,0.384967," ","integrate(x^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\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}} + \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 x^{2} + a\right)}^{2} b^{3}}"," ",0,"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) + 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*x^2 + a)^2*b^3)","A",0
104,1,128,0,0.422216," ","integrate(x^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\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}} - \frac{{\left(5 \, C a b - A b^{2}\right)} x^{3} - 4 \, {\left(2 \, D a^{2} - B a b\right)} x^{2} + {\left(3 \, C a^{2} + A a b\right)} x - \frac{2 \, {\left(3 \, D a^{3} - B a^{2} b\right)}}{b}}{8 \, {\left(b x^{2} + a\right)}^{2} a b^{2}}"," ",0,"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) - 1/8*((5*C*a*b - A*b^2)*x^3 - 4*(2*D*a^2 - B*a*b)*x^2 + (3*C*a^2 + A*a*b)*x - 2*(3*D*a^3 - B*a^2*b)/b)/((b*x^2 + a)^2*a*b^2)","A",0
105,1,97,0,0.391477," ","integrate(x*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, D a + B b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a b^{2}} - \frac{5 \, D a b x^{3} - B b^{2} x^{3} + 4 \, C a b x^{2} + 3 \, D a^{2} x + B a b x + 2 \, C a^{2} + 2 \, A a b}{8 \, {\left(b x^{2} + a\right)}^{2} a b^{2}}"," ",0,"1/8*(3*D*a + B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2) - 1/8*(5*D*a*b*x^3 - B*b^2*x^3 + 4*C*a*b*x^2 + 3*D*a^2*x + B*a*b*x + 2*C*a^2 + 2*A*a*b)/((b*x^2 + a)^2*a*b^2)","A",0
106,1,106,0,0.385622," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(C a + 3 \, A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b} + \frac{C a b^{2} x^{3} + 3 \, A b^{3} x^{3} - 4 \, D a^{2} b x^{2} - C a^{2} b x + 5 \, A a b^{2} x - 2 \, D a^{3} - 2 \, B a^{2} b}{8 \, {\left(b x^{2} + a\right)}^{2} a^{2} b^{2}}"," ",0,"1/8*(C*a + 3*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b) + 1/8*(C*a*b^2*x^3 + 3*A*b^3*x^3 - 4*D*a^2*b*x^2 - C*a^2*b*x + 5*A*a*b^2*x - 2*D*a^3 - 2*B*a^2*b)/((b*x^2 + a)^2*a^2*b^2)","A",0
107,1,128,0,0.479198," ","integrate((D*x^3+C*x^2+B*x+A)/x/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{A \log\left(b x^{2} + a\right)}{2 \, a^{3}} + \frac{A \log\left({\left| x \right|}\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} + \frac{4 \, A a b^{2} x^{2} - 2 \, C a^{3} + 6 \, A a^{2} b + {\left(D a^{2} b + 3 \, B a b^{2}\right)} x^{3} - {\left(D a^{3} - 5 \, B a^{2} b\right)} x}{8 \, {\left(b x^{2} + a\right)}^{2} a^{3} b}"," ",0,"-1/2*A*log(b*x^2 + a)/a^3 + A*log(abs(x))/a^3 + 1/8*(D*a + 3*B*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b) + 1/8*(4*A*a*b^2*x^2 - 2*C*a^3 + 6*A*a^2*b + (D*a^2*b + 3*B*a*b^2)*x^3 - (D*a^3 - 5*B*a^2*b)*x)/((b*x^2 + a)^2*a^3*b)","A",0
108,1,141,0,0.490037," ","integrate((D*x^3+C*x^2+B*x+A)/x^2/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{B \log\left(b x^{2} + a\right)}{2 \, a^{3}} + \frac{B \log\left({\left| x \right|}\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}} + \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(b x^{2} + a\right)}^{2} a^{3} b x}"," ",0,"-1/2*B*log(b*x^2 + a)/a^3 + B*log(abs(x))/a^3 + 3/8*(C*a - 5*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3) + 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)/((b*x^2 + a)^2*a^3*b*x)","A",0
109,1,162,0,0.379988," ","integrate((D*x^3+C*x^2+B*x+A)/x^3/(b*x^2+a)^3,x, algorithm=""giac"")","\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({\left| x \right|}\right)}{a^{4}} + \frac{3 \, D a b x^{5} - 15 \, B b^{2} x^{5} + 4 \, C a b x^{4} - 12 \, A b^{2} x^{4} + 5 \, D a^{2} x^{3} - 25 \, B a b x^{3} + 6 \, C a^{2} x^{2} - 18 \, A a b x^{2} - 8 \, B a^{2} x - 4 \, A a^{2}}{8 \, {\left(b x^{3} + a x\right)}^{2} a^{3}}"," ",0,"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(abs(x))/a^4 + 1/8*(3*D*a*b*x^5 - 15*B*b^2*x^5 + 4*C*a*b*x^4 - 12*A*b^2*x^4 + 5*D*a^2*x^3 - 25*B*a*b*x^3 + 6*C*a^2*x^2 - 18*A*a*b*x^2 - 8*B*a^2*x - 4*A*a^2)/((b*x^3 + a*x)^2*a^3)","A",0
110,1,25,0,0.316673," ","integrate((4*x^3-x)/(x^2+5)^2,x, algorithm=""giac"")","-\frac{4 \, x^{2} - 1}{2 \, {\left(x^{2} + 5\right)}} + 2 \, \log\left(x^{2} + 5\right)"," ",0,"-1/2*(4*x^2 - 1)/(x^2 + 5) + 2*log(x^2 + 5)","A",0
111,1,17,0,0.400532," ","integrate((x^3-x)/(x^2-2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(x^{2} - 2\right)}^{\frac{3}{2}} + \sqrt{x^{2} - 2}"," ",0,"1/3*(x^2 - 2)^(3/2) + sqrt(x^2 - 2)","A",0
112,1,20,0,0.354818," ","integrate((2*x^4-x^2)/(2*x^2+1),x, algorithm=""giac"")","\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
113,1,24,0,0.388674," ","integrate((x^4+x^3)/(x^2+1),x, algorithm=""giac"")","\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
114,1,250,0,0.457272," ","integrate(x^6*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(a^{3} b^{3} c - a^{4} b^{2} d - a^{6} f + a^{5} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{6}} + \frac{315 \, b^{10} f x^{11} - 385 \, a b^{9} f x^{9} + 385 \, b^{10} x^{9} e + 495 \, b^{10} d x^{7} + 495 \, a^{2} b^{8} f x^{7} - 495 \, a b^{9} x^{7} e + 693 \, b^{10} c x^{5} - 693 \, a b^{9} d x^{5} - 693 \, a^{3} b^{7} f x^{5} + 693 \, a^{2} b^{8} x^{5} e - 1155 \, a b^{9} c x^{3} + 1155 \, a^{2} b^{8} d x^{3} + 1155 \, a^{4} b^{6} f x^{3} - 1155 \, a^{3} b^{7} x^{3} e + 3465 \, a^{2} b^{8} c x - 3465 \, a^{3} b^{7} d x - 3465 \, a^{5} b^{5} f x + 3465 \, a^{4} b^{6} x e}{3465 \, b^{11}}"," ",0,"-(a^3*b^3*c - a^4*b^2*d - a^6*f + a^5*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) + 1/3465*(315*b^10*f*x^11 - 385*a*b^9*f*x^9 + 385*b^10*x^9*e + 495*b^10*d*x^7 + 495*a^2*b^8*f*x^7 - 495*a*b^9*x^7*e + 693*b^10*c*x^5 - 693*a*b^9*d*x^5 - 693*a^3*b^7*f*x^5 + 693*a^2*b^8*x^5*e - 1155*a*b^9*c*x^3 + 1155*a^2*b^8*d*x^3 + 1155*a^4*b^6*f*x^3 - 1155*a^3*b^7*x^3*e + 3465*a^2*b^8*c*x - 3465*a^3*b^7*d*x - 3465*a^5*b^5*f*x + 3465*a^4*b^6*x*e)/b^11","A",0
115,1,200,0,0.367763," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d - a^{5} f + a^{4} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{5}} + \frac{35 \, b^{8} f x^{9} - 45 \, a b^{7} f x^{7} + 45 \, b^{8} x^{7} e + 63 \, b^{8} d x^{5} + 63 \, a^{2} b^{6} f x^{5} - 63 \, a b^{7} x^{5} e + 105 \, b^{8} c x^{3} - 105 \, a b^{7} d x^{3} - 105 \, a^{3} b^{5} f x^{3} + 105 \, a^{2} b^{6} x^{3} e - 315 \, a b^{7} c x + 315 \, a^{2} b^{6} d x + 315 \, a^{4} b^{4} f x - 315 \, a^{3} b^{5} x e}{315 \, b^{9}}"," ",0,"(a^2*b^3*c - a^3*b^2*d - a^5*f + a^4*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/315*(35*b^8*f*x^9 - 45*a*b^7*f*x^7 + 45*b^8*x^7*e + 63*b^8*d*x^5 + 63*a^2*b^6*f*x^5 - 63*a*b^7*x^5*e + 105*b^8*c*x^3 - 105*a*b^7*d*x^3 - 105*a^3*b^5*f*x^3 + 105*a^2*b^6*x^3*e - 315*a*b^7*c*x + 315*a^2*b^6*d*x + 315*a^4*b^4*f*x - 315*a^3*b^5*x*e)/b^9","A",0
116,1,152,0,0.415615," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(a b^{3} c - a^{2} b^{2} d - a^{4} f + a^{3} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{4}} + \frac{15 \, b^{6} f x^{7} - 21 \, a b^{5} f x^{5} + 21 \, b^{6} x^{5} e + 35 \, b^{6} d x^{3} + 35 \, a^{2} b^{4} f x^{3} - 35 \, a b^{5} x^{3} e + 105 \, b^{6} c x - 105 \, a b^{5} d x - 105 \, a^{3} b^{3} f x + 105 \, a^{2} b^{4} x e}{105 \, b^{7}}"," ",0,"-(a*b^3*c - a^2*b^2*d - a^4*f + a^3*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/105*(15*b^6*f*x^7 - 21*a*b^5*f*x^5 + 21*b^6*x^5*e + 35*b^6*d*x^3 + 35*a^2*b^4*f*x^3 - 35*a*b^5*x^3*e + 105*b^6*c*x - 105*a*b^5*d*x - 105*a^3*b^3*f*x + 105*a^2*b^4*x*e)/b^7","A",0
117,1,106,0,0.447628," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{3 \, b^{4} f x^{5} - 5 \, a b^{3} f x^{3} + 5 \, b^{4} x^{3} e + 15 \, b^{4} d x + 15 \, a^{2} b^{2} f x - 15 \, a b^{3} x e}{15 \, b^{5}}"," ",0,"(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/15*(3*b^4*f*x^5 - 5*a*b^3*f*x^3 + 5*b^4*x^3*e + 15*b^4*d*x + 15*a^2*b^2*f*x - 15*a*b^3*x*e)/b^5","A",0
118,1,86,0,0.336907," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a),x, algorithm=""giac"")","-\frac{c}{a x} - \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a b^{2}} + \frac{b^{2} f x^{3} - 3 \, a b f x + 3 \, b^{2} x e}{3 \, b^{3}}"," ",0,"-c/(a*x) - (b^3*c - a*b^2*d - a^3*f + a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2) + 1/3*(b^2*f*x^3 - 3*a*b*f*x + 3*b^2*x*e)/b^3","A",0
119,1,81,0,0.355078," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a),x, algorithm=""giac"")","\frac{f x}{b} + \frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2} b} + \frac{3 \, b c x^{2} - 3 \, a d x^{2} - a c}{3 \, a^{2} x^{3}}"," ",0,"f*x/b + (b^3*c - a*b^2*d - a^3*f + a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b) + 1/3*(3*b*c*x^2 - 3*a*d*x^2 - a*c)/(a^2*x^3)","A",0
120,1,105,0,0.366868," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} - \frac{15 \, b^{2} c x^{4} - 15 \, a b d x^{4} + 15 \, a^{2} x^{4} e - 5 \, a b c x^{2} + 5 \, a^{2} d x^{2} + 3 \, a^{2} c}{15 \, a^{3} x^{5}}"," ",0,"-(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3) - 1/15*(15*b^2*c*x^4 - 15*a*b*d*x^4 + 15*a^2*x^4*e - 5*a*b*c*x^2 + 5*a^2*d*x^2 + 3*a^2*c)/(a^3*x^5)","A",0
121,1,151,0,0.455192," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{4} c - a b^{3} d - a^{3} b f + a^{2} b^{2} e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}} + \frac{105 \, b^{3} c x^{6} - 105 \, a b^{2} d x^{6} - 105 \, a^{3} f x^{6} + 105 \, a^{2} b x^{6} e - 35 \, a b^{2} c x^{4} + 35 \, a^{2} b d x^{4} - 35 \, a^{3} x^{4} e + 21 \, a^{2} b c x^{2} - 21 \, a^{3} d x^{2} - 15 \, a^{3} c}{105 \, a^{4} x^{7}}"," ",0,"(b^4*c - a*b^3*d - a^3*b*f + a^2*b^2*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4) + 1/105*(105*b^3*c*x^6 - 105*a*b^2*d*x^6 - 105*a^3*f*x^6 + 105*a^2*b*x^6*e - 35*a*b^2*c*x^4 + 35*a^2*b*d*x^4 - 35*a^3*x^4*e + 21*a^2*b*c*x^2 - 21*a^3*d*x^2 - 15*a^3*c)/(a^4*x^7)","A",0
122,1,201,0,0.422819," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b^{5} c - a b^{4} d - a^{3} b^{2} f + a^{2} b^{3} e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{5}} - \frac{315 \, b^{4} c x^{8} - 315 \, a b^{3} d x^{8} - 315 \, a^{3} b f x^{8} + 315 \, a^{2} b^{2} x^{8} e - 105 \, a b^{3} c x^{6} + 105 \, a^{2} b^{2} d x^{6} + 105 \, a^{4} f x^{6} - 105 \, a^{3} b x^{6} e + 63 \, a^{2} b^{2} c x^{4} - 63 \, a^{3} b d x^{4} + 63 \, a^{4} x^{4} e - 45 \, a^{3} b c x^{2} + 45 \, a^{4} d x^{2} + 35 \, a^{4} c}{315 \, a^{5} x^{9}}"," ",0,"-(b^5*c - a*b^4*d - a^3*b^2*f + a^2*b^3*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5) - 1/315*(315*b^4*c*x^8 - 315*a*b^3*d*x^8 - 315*a^3*b*f*x^8 + 315*a^2*b^2*x^8*e - 105*a*b^3*c*x^6 + 105*a^2*b^2*d*x^6 + 105*a^4*f*x^6 - 105*a^3*b*x^6*e + 63*a^2*b^2*c*x^4 - 63*a^3*b*d*x^4 + 63*a^4*x^4*e - 45*a^3*b*c*x^2 + 45*a^4*d*x^2 + 35*a^4*c)/(a^5*x^9)","A",0
123,1,249,0,0.355532," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^12/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{6} c - a b^{5} d - a^{3} b^{3} f + a^{2} b^{4} e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{6}} + \frac{3465 \, b^{5} c x^{10} - 3465 \, a b^{4} d x^{10} - 3465 \, a^{3} b^{2} f x^{10} + 3465 \, a^{2} b^{3} x^{10} e - 1155 \, a b^{4} c x^{8} + 1155 \, a^{2} b^{3} d x^{8} + 1155 \, a^{4} b f x^{8} - 1155 \, a^{3} b^{2} x^{8} e + 693 \, a^{2} b^{3} c x^{6} - 693 \, a^{3} b^{2} d x^{6} - 693 \, a^{5} f x^{6} + 693 \, a^{4} b x^{6} e - 495 \, a^{3} b^{2} c x^{4} + 495 \, a^{4} b d x^{4} - 495 \, a^{5} x^{4} e + 385 \, a^{4} b c x^{2} - 385 \, a^{5} d x^{2} - 315 \, a^{5} c}{3465 \, a^{6} x^{11}}"," ",0,"(b^6*c - a*b^5*d - a^3*b^3*f + a^2*b^4*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^6) + 1/3465*(3465*b^5*c*x^10 - 3465*a*b^4*d*x^10 - 3465*a^3*b^2*f*x^10 + 3465*a^2*b^3*x^10*e - 1155*a*b^4*c*x^8 + 1155*a^2*b^3*d*x^8 + 1155*a^4*b*f*x^8 - 1155*a^3*b^2*x^8*e + 693*a^2*b^3*c*x^6 - 693*a^3*b^2*d*x^6 - 693*a^5*f*x^6 + 693*a^4*b*x^6*e - 495*a^3*b^2*c*x^4 + 495*a^4*b*d*x^4 - 495*a^5*x^4*e + 385*a^4*b*c*x^2 - 385*a^5*d*x^2 - 315*a^5*c)/(a^6*x^11)","A",0
124,1,252,0,0.386744," ","integrate(x^6*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(5 \, a^{2} b^{3} c - 7 \, a^{3} b^{2} d - 11 \, a^{5} f + 9 \, a^{4} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{6}} - \frac{a^{2} b^{3} c x - a^{3} b^{2} d x - a^{5} f x + a^{4} b x e}{2 \, {\left(b x^{2} + a\right)} b^{6}} + \frac{35 \, b^{16} f x^{9} - 90 \, a b^{15} f x^{7} + 45 \, b^{16} x^{7} e + 63 \, b^{16} d x^{5} + 189 \, a^{2} b^{14} f x^{5} - 126 \, a b^{15} x^{5} e + 105 \, b^{16} c x^{3} - 210 \, a b^{15} d x^{3} - 420 \, a^{3} b^{13} f x^{3} + 315 \, a^{2} b^{14} x^{3} e - 630 \, a b^{15} c x + 945 \, a^{2} b^{14} d x + 1575 \, a^{4} b^{12} f x - 1260 \, a^{3} b^{13} x e}{315 \, b^{18}}"," ",0,"1/2*(5*a^2*b^3*c - 7*a^3*b^2*d - 11*a^5*f + 9*a^4*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) - 1/2*(a^2*b^3*c*x - a^3*b^2*d*x - a^5*f*x + a^4*b*x*e)/((b*x^2 + a)*b^6) + 1/315*(35*b^16*f*x^9 - 90*a*b^15*f*x^7 + 45*b^16*x^7*e + 63*b^16*d*x^5 + 189*a^2*b^14*f*x^5 - 126*a*b^15*x^5*e + 105*b^16*c*x^3 - 210*a*b^15*d*x^3 - 420*a^3*b^13*f*x^3 + 315*a^2*b^14*x^3*e - 630*a*b^15*c*x + 945*a^2*b^14*d*x + 1575*a^4*b^12*f*x - 1260*a^3*b^13*x*e)/b^18","A",0
125,1,201,0,0.416821," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, a b^{3} c - 5 \, a^{2} b^{2} d - 9 \, a^{4} f + 7 \, a^{3} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{5}} + \frac{a b^{3} c x - a^{2} b^{2} d x - a^{4} f x + a^{3} b x e}{2 \, {\left(b x^{2} + a\right)} b^{5}} + \frac{15 \, b^{12} f x^{7} - 42 \, a b^{11} f x^{5} + 21 \, b^{12} x^{5} e + 35 \, b^{12} d x^{3} + 105 \, a^{2} b^{10} f x^{3} - 70 \, a b^{11} x^{3} e + 105 \, b^{12} c x - 210 \, a b^{11} d x - 420 \, a^{3} b^{9} f x + 315 \, a^{2} b^{10} x e}{105 \, b^{14}}"," ",0,"-1/2*(3*a*b^3*c - 5*a^2*b^2*d - 9*a^4*f + 7*a^3*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/2*(a*b^3*c*x - a^2*b^2*d*x - a^4*f*x + a^3*b*x*e)/((b*x^2 + a)*b^5) + 1/105*(15*b^12*f*x^7 - 42*a*b^11*f*x^5 + 21*b^12*x^5*e + 35*b^12*d*x^3 + 105*a^2*b^10*f*x^3 - 70*a*b^11*x^3*e + 105*b^12*c*x - 210*a*b^11*d*x - 420*a^3*b^9*f*x + 315*a^2*b^10*x*e)/b^14","A",0
126,1,152,0,0.373243," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b^{3} c - 3 \, a b^{2} d - 7 \, a^{3} f + 5 \, a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{4}} - \frac{b^{3} c x - a b^{2} d x - a^{3} f x + a^{2} b x e}{2 \, {\left(b x^{2} + a\right)} b^{4}} + \frac{3 \, b^{8} f x^{5} - 10 \, a b^{7} f x^{3} + 5 \, b^{8} x^{3} e + 15 \, b^{8} d x + 45 \, a^{2} b^{6} f x - 30 \, a b^{7} x e}{15 \, b^{10}}"," ",0,"1/2*(b^3*c - 3*a*b^2*d - 7*a^3*f + 5*a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) - 1/2*(b^3*c*x - a*b^2*d*x - a^3*f*x + a^2*b*x*e)/((b*x^2 + a)*b^4) + 1/15*(3*b^8*f*x^5 - 10*a*b^7*f*x^3 + 5*b^8*x^3*e + 15*b^8*d*x + 45*a^2*b^6*f*x - 30*a*b^7*x*e)/b^10","A",0
127,1,126,0,0.402809," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b^{3} c + a b^{2} d + 5 \, a^{3} f - 3 \, a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{3}} + \frac{b^{3} c x - a b^{2} d x - a^{3} f x + a^{2} b x e}{2 \, {\left(b x^{2} + a\right)} a b^{3}} + \frac{b^{4} f x^{3} - 6 \, a b^{3} f x + 3 \, b^{4} x e}{3 \, b^{6}}"," ",0,"1/2*(b^3*c + a*b^2*d + 5*a^3*f - 3*a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^3) + 1/2*(b^3*c*x - a*b^2*d*x - a^3*f*x + a^2*b*x*e)/((b*x^2 + a)*a*b^3) + 1/3*(b^4*f*x^3 - 6*a*b^3*f*x + 3*b^4*x*e)/b^6","A",0
128,1,122,0,0.360306," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{f x}{b^{2}} - \frac{{\left(3 \, b^{3} c - a b^{2} d + 3 \, a^{3} f - a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2} b^{2}} - \frac{3 \, b^{3} c x^{2} - a b^{2} d x^{2} - a^{3} f x^{2} + a^{2} b x^{2} e + 2 \, a b^{2} c}{2 \, {\left(b x^{3} + a x\right)} a^{2} b^{2}}"," ",0,"f*x/b^2 - 1/2*(3*b^3*c - a*b^2*d + 3*a^3*f - a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^2) - 1/2*(3*b^3*c*x^2 - a*b^2*d*x^2 - a^3*f*x^2 + a^2*b*x^2*e + 2*a*b^2*c)/((b*x^3 + a*x)*a^2*b^2)","A",0
129,1,123,0,0.482818," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(5 \, b^{3} c - 3 \, a b^{2} d + a^{3} f + a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{3} b} + \frac{b^{3} c x - a b^{2} d x - a^{3} f x + a^{2} b x e}{2 \, {\left(b x^{2} + a\right)} a^{3} b} + \frac{6 \, b c x^{2} - 3 \, a d x^{2} - a c}{3 \, a^{3} x^{3}}"," ",0,"1/2*(5*b^3*c - 3*a*b^2*d + a^3*f + a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3*b) + 1/2*(b^3*c*x - a*b^2*d*x - a^3*f*x + a^2*b*x*e)/((b*x^2 + a)*a^3*b) + 1/3*(6*b*c*x^2 - 3*a*d*x^2 - a*c)/(a^3*x^3)","A",0
130,1,151,0,0.489552," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(7 \, b^{3} c - 5 \, a b^{2} d - a^{3} f + 3 \, a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{4}} - \frac{b^{3} c x - a b^{2} d x - a^{3} f x + a^{2} b x e}{2 \, {\left(b x^{2} + a\right)} a^{4}} - \frac{45 \, b^{2} c x^{4} - 30 \, a b d x^{4} + 15 \, a^{2} x^{4} e - 10 \, a b c x^{2} + 5 \, a^{2} d x^{2} + 3 \, a^{2} c}{15 \, a^{4} x^{5}}"," ",0,"-1/2*(7*b^3*c - 5*a*b^2*d - a^3*f + 3*a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4) - 1/2*(b^3*c*x - a*b^2*d*x - a^3*f*x + a^2*b*x*e)/((b*x^2 + a)*a^4) - 1/15*(45*b^2*c*x^4 - 30*a*b*d*x^4 + 15*a^2*x^4*e - 10*a*b*c*x^2 + 5*a^2*d*x^2 + 3*a^2*c)/(a^4*x^5)","A",0
131,1,201,0,0.432861," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(9 \, b^{4} c - 7 \, a b^{3} d - 3 \, a^{3} b f + 5 \, a^{2} b^{2} e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{5}} + \frac{b^{4} c x - a b^{3} d x - a^{3} b f x + a^{2} b^{2} x e}{2 \, {\left(b x^{2} + a\right)} a^{5}} + \frac{420 \, b^{3} c x^{6} - 315 \, a b^{2} d x^{6} - 105 \, a^{3} f x^{6} + 210 \, a^{2} b x^{6} e - 105 \, a b^{2} c x^{4} + 70 \, a^{2} b d x^{4} - 35 \, a^{3} x^{4} e + 42 \, a^{2} b c x^{2} - 21 \, a^{3} d x^{2} - 15 \, a^{3} c}{105 \, a^{5} x^{7}}"," ",0,"1/2*(9*b^4*c - 7*a*b^3*d - 3*a^3*b*f + 5*a^2*b^2*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5) + 1/2*(b^4*c*x - a*b^3*d*x - a^3*b*f*x + a^2*b^2*x*e)/((b*x^2 + a)*a^5) + 1/105*(420*b^3*c*x^6 - 315*a*b^2*d*x^6 - 105*a^3*f*x^6 + 210*a^2*b*x^6*e - 105*a*b^2*c*x^4 + 70*a^2*b*d*x^4 - 35*a^3*x^4*e + 42*a^2*b*c*x^2 - 21*a^3*d*x^2 - 15*a^3*c)/(a^5*x^7)","A",0
132,1,252,0,0.377728," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(11 \, b^{5} c - 9 \, a b^{4} d - 5 \, a^{3} b^{2} f + 7 \, a^{2} b^{3} e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{6}} - \frac{b^{5} c x - a b^{4} d x - a^{3} b^{2} f x + a^{2} b^{3} x e}{2 \, {\left(b x^{2} + a\right)} a^{6}} - \frac{1575 \, b^{4} c x^{8} - 1260 \, a b^{3} d x^{8} - 630 \, a^{3} b f x^{8} + 945 \, a^{2} b^{2} x^{8} e - 420 \, a b^{3} c x^{6} + 315 \, a^{2} b^{2} d x^{6} + 105 \, a^{4} f x^{6} - 210 \, a^{3} b x^{6} e + 189 \, a^{2} b^{2} c x^{4} - 126 \, a^{3} b d x^{4} + 63 \, a^{4} x^{4} e - 90 \, a^{3} b c x^{2} + 45 \, a^{4} d x^{2} + 35 \, a^{4} c}{315 \, a^{6} x^{9}}"," ",0,"-1/2*(11*b^5*c - 9*a*b^4*d - 5*a^3*b^2*f + 7*a^2*b^3*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^6) - 1/2*(b^5*c*x - a*b^4*d*x - a^3*b^2*f*x + a^2*b^3*x*e)/((b*x^2 + a)*a^6) - 1/315*(1575*b^4*c*x^8 - 1260*a*b^3*d*x^8 - 630*a^3*b*f*x^8 + 945*a^2*b^2*x^8*e - 420*a*b^3*c*x^6 + 315*a^2*b^2*d*x^6 + 105*a^4*f*x^6 - 210*a^3*b*x^6*e + 189*a^2*b^2*c*x^4 - 126*a^3*b*d*x^4 + 63*a^4*x^4*e - 90*a^3*b*c*x^2 + 45*a^4*d*x^2 + 35*a^4*c)/(a^6*x^9)","A",0
133,1,301,0,0.400356," ","integrate(x^8*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(35 \, a^{2} b^{3} c - 63 \, a^{3} b^{2} d - 143 \, a^{5} f + 99 \, a^{4} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{7}} - \frac{13 \, a^{2} b^{4} c x^{3} - 17 \, a^{3} b^{3} d x^{3} - 25 \, a^{5} b f x^{3} + 21 \, a^{4} b^{2} x^{3} e + 11 \, a^{3} b^{3} c x - 15 \, a^{4} b^{2} d x - 23 \, a^{6} f x + 19 \, a^{5} b x e}{8 \, {\left(b x^{2} + a\right)}^{2} b^{7}} + \frac{35 \, b^{24} f x^{9} - 135 \, a b^{23} f x^{7} + 45 \, b^{24} x^{7} e + 63 \, b^{24} d x^{5} + 378 \, a^{2} b^{22} f x^{5} - 189 \, a b^{23} x^{5} e + 105 \, b^{24} c x^{3} - 315 \, a b^{23} d x^{3} - 1050 \, a^{3} b^{21} f x^{3} + 630 \, a^{2} b^{22} x^{3} e - 945 \, a b^{23} c x + 1890 \, a^{2} b^{22} d x + 4725 \, a^{4} b^{20} f x - 3150 \, a^{3} b^{21} x e}{315 \, b^{27}}"," ",0,"1/8*(35*a^2*b^3*c - 63*a^3*b^2*d - 143*a^5*f + 99*a^4*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^7) - 1/8*(13*a^2*b^4*c*x^3 - 17*a^3*b^3*d*x^3 - 25*a^5*b*f*x^3 + 21*a^4*b^2*x^3*e + 11*a^3*b^3*c*x - 15*a^4*b^2*d*x - 23*a^6*f*x + 19*a^5*b*x*e)/((b*x^2 + a)^2*b^7) + 1/315*(35*b^24*f*x^9 - 135*a*b^23*f*x^7 + 45*b^24*x^7*e + 63*b^24*d*x^5 + 378*a^2*b^22*f*x^5 - 189*a*b^23*x^5*e + 105*b^24*c*x^3 - 315*a*b^23*d*x^3 - 1050*a^3*b^21*f*x^3 + 630*a^2*b^22*x^3*e - 945*a*b^23*c*x + 1890*a^2*b^22*d*x + 4725*a^4*b^20*f*x - 3150*a^3*b^21*x*e)/b^27","A",0
134,1,250,0,0.470292," ","integrate(x^6*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(15 \, a b^{3} c - 35 \, a^{2} b^{2} d - 99 \, a^{4} f + 63 \, a^{3} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{6}} + \frac{9 \, a b^{4} c x^{3} - 13 \, a^{2} b^{3} d x^{3} - 21 \, a^{4} b f x^{3} + 17 \, a^{3} b^{2} x^{3} e + 7 \, a^{2} b^{3} c x - 11 \, a^{3} b^{2} d x - 19 \, a^{5} f x + 15 \, a^{4} b x e}{8 \, {\left(b x^{2} + a\right)}^{2} b^{6}} + \frac{15 \, b^{18} f x^{7} - 63 \, a b^{17} f x^{5} + 21 \, b^{18} x^{5} e + 35 \, b^{18} d x^{3} + 210 \, a^{2} b^{16} f x^{3} - 105 \, a b^{17} x^{3} e + 105 \, b^{18} c x - 315 \, a b^{17} d x - 1050 \, a^{3} b^{15} f x + 630 \, a^{2} b^{16} x e}{105 \, b^{21}}"," ",0,"-1/8*(15*a*b^3*c - 35*a^2*b^2*d - 99*a^4*f + 63*a^3*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) + 1/8*(9*a*b^4*c*x^3 - 13*a^2*b^3*d*x^3 - 21*a^4*b*f*x^3 + 17*a^3*b^2*x^3*e + 7*a^2*b^3*c*x - 11*a^3*b^2*d*x - 19*a^5*f*x + 15*a^4*b*x*e)/((b*x^2 + a)^2*b^6) + 1/105*(15*b^18*f*x^7 - 63*a*b^17*f*x^5 + 21*b^18*x^5*e + 35*b^18*d*x^3 + 210*a^2*b^16*f*x^3 - 105*a*b^17*x^3*e + 105*b^18*c*x - 315*a*b^17*d*x - 1050*a^3*b^15*f*x + 630*a^2*b^16*x*e)/b^21","A",0
135,1,200,0,0.509126," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, b^{3} c - 15 \, a b^{2} d - 63 \, a^{3} f + 35 \, a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{5}} - \frac{5 \, b^{4} c x^{3} - 9 \, a b^{3} d x^{3} - 17 \, a^{3} b f x^{3} + 13 \, a^{2} b^{2} x^{3} e + 3 \, a b^{3} c x - 7 \, a^{2} b^{2} d x - 15 \, a^{4} f x + 11 \, a^{3} b x e}{8 \, {\left(b x^{2} + a\right)}^{2} b^{5}} + \frac{3 \, b^{12} f x^{5} - 15 \, a b^{11} f x^{3} + 5 \, b^{12} x^{3} e + 15 \, b^{12} d x + 90 \, a^{2} b^{10} f x - 45 \, a b^{11} x e}{15 \, b^{15}}"," ",0,"1/8*(3*b^3*c - 15*a*b^2*d - 63*a^3*f + 35*a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) - 1/8*(5*b^4*c*x^3 - 9*a*b^3*d*x^3 - 17*a^3*b*f*x^3 + 13*a^2*b^2*x^3*e + 3*a*b^3*c*x - 7*a^2*b^2*d*x - 15*a^4*f*x + 11*a^3*b*x*e)/((b*x^2 + a)^2*b^5) + 1/15*(3*b^12*f*x^5 - 15*a*b^11*f*x^3 + 5*b^12*x^3*e + 15*b^12*d*x + 90*a^2*b^10*f*x - 45*a*b^11*x*e)/b^15","A",0
136,1,173,0,0.448205," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(b^{3} c + 3 \, a b^{2} d + 35 \, a^{3} f - 15 \, a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a b^{4}} + \frac{b^{4} c x^{3} - 5 \, a b^{3} d x^{3} - 13 \, a^{3} b f x^{3} + 9 \, a^{2} b^{2} x^{3} e - a b^{3} c x - 3 \, a^{2} b^{2} d x - 11 \, a^{4} f x + 7 \, a^{3} b x e}{8 \, {\left(b x^{2} + a\right)}^{2} a b^{4}} + \frac{b^{6} f x^{3} - 9 \, a b^{5} f x + 3 \, b^{6} x e}{3 \, b^{9}}"," ",0,"1/8*(b^3*c + 3*a*b^2*d + 35*a^3*f - 15*a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^4) + 1/8*(b^4*c*x^3 - 5*a*b^3*d*x^3 - 13*a^3*b*f*x^3 + 9*a^2*b^2*x^3*e - a*b^3*c*x - 3*a^2*b^2*d*x - 11*a^4*f*x + 7*a^3*b*x*e)/((b*x^2 + a)^2*a*b^4) + 1/3*(b^6*f*x^3 - 9*a*b^5*f*x + 3*b^6*x*e)/b^9","A",0
137,1,149,0,0.456609," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{f x}{b^{3}} + \frac{{\left(3 \, b^{3} c + a b^{2} d - 15 \, a^{3} f + 3 \, a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b^{3}} + \frac{3 \, b^{4} c x^{3} + a b^{3} d x^{3} + 9 \, a^{3} b f x^{3} - 5 \, a^{2} b^{2} x^{3} e + 5 \, a b^{3} c x - a^{2} b^{2} d x + 7 \, a^{4} f x - 3 \, a^{3} b x e}{8 \, {\left(b x^{2} + a\right)}^{2} a^{2} b^{3}}"," ",0,"f*x/b^3 + 1/8*(3*b^3*c + a*b^2*d - 15*a^3*f + 3*a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^3) + 1/8*(3*b^4*c*x^3 + a*b^3*d*x^3 + 9*a^3*b*f*x^3 - 5*a^2*b^2*x^3*e + 5*a*b^3*c*x - a^2*b^2*d*x + 7*a^4*f*x - 3*a^3*b*x*e)/((b*x^2 + a)^2*a^2*b^3)","A",0
138,1,153,0,0.449085," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{c}{a^{3} x} - \frac{{\left(15 \, b^{3} c - 3 \, a b^{2} d - 3 \, a^{3} f - a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{3} b^{2}} - \frac{7 \, b^{4} c x^{3} - 3 \, a b^{3} d x^{3} + 5 \, a^{3} b f x^{3} - a^{2} b^{2} x^{3} e + 9 \, a b^{3} c x - 5 \, a^{2} b^{2} d x + 3 \, a^{4} f x + a^{3} b x e}{8 \, {\left(b x^{2} + a\right)}^{2} a^{3} b^{2}}"," ",0,"-c/(a^3*x) - 1/8*(15*b^3*c - 3*a*b^2*d - 3*a^3*f - a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3*b^2) - 1/8*(7*b^4*c*x^3 - 3*a*b^3*d*x^3 + 5*a^3*b*f*x^3 - a^2*b^2*x^3*e + 9*a*b^3*c*x - 5*a^2*b^2*d*x + 3*a^4*f*x + a^3*b*x*e)/((b*x^2 + a)^2*a^3*b^2)","A",0
139,1,170,0,0.448711," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(35 \, b^{3} c - 15 \, a b^{2} d + a^{3} f + 3 \, a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{4} b} + \frac{11 \, b^{4} c x^{3} - 7 \, a b^{3} d x^{3} + a^{3} b f x^{3} + 3 \, a^{2} b^{2} x^{3} e + 13 \, a b^{3} c x - 9 \, a^{2} b^{2} d x - a^{4} f x + 5 \, a^{3} b x e}{8 \, {\left(b x^{2} + a\right)}^{2} a^{4} b} + \frac{9 \, b c x^{2} - 3 \, a d x^{2} - a c}{3 \, a^{4} x^{3}}"," ",0,"1/8*(35*b^3*c - 15*a*b^2*d + a^3*f + 3*a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4*b) + 1/8*(11*b^4*c*x^3 - 7*a*b^3*d*x^3 + a^3*b*f*x^3 + 3*a^2*b^2*x^3*e + 13*a*b^3*c*x - 9*a^2*b^2*d*x - a^4*f*x + 5*a^3*b*x*e)/((b*x^2 + a)^2*a^4*b) + 1/3*(9*b*c*x^2 - 3*a*d*x^2 - a*c)/(a^4*x^3)","A",0
140,1,198,0,0.439104," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(63 \, b^{3} c - 35 \, a b^{2} d - 3 \, a^{3} f + 15 \, a^{2} b e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{5}} - \frac{15 \, b^{4} c x^{3} - 11 \, a b^{3} d x^{3} - 3 \, a^{3} b f x^{3} + 7 \, a^{2} b^{2} x^{3} e + 17 \, a b^{3} c x - 13 \, a^{2} b^{2} d x - 5 \, a^{4} f x + 9 \, a^{3} b x e}{8 \, {\left(b x^{2} + a\right)}^{2} a^{5}} - \frac{90 \, b^{2} c x^{4} - 45 \, a b d x^{4} + 15 \, a^{2} x^{4} e - 15 \, a b c x^{2} + 5 \, a^{2} d x^{2} + 3 \, a^{2} c}{15 \, a^{5} x^{5}}"," ",0,"-1/8*(63*b^3*c - 35*a*b^2*d - 3*a^3*f + 15*a^2*b*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5) - 1/8*(15*b^4*c*x^3 - 11*a*b^3*d*x^3 - 3*a^3*b*f*x^3 + 7*a^2*b^2*x^3*e + 17*a*b^3*c*x - 13*a^2*b^2*d*x - 5*a^4*f*x + 9*a^3*b*x*e)/((b*x^2 + a)^2*a^5) - 1/15*(90*b^2*c*x^4 - 45*a*b*d*x^4 + 15*a^2*x^4*e - 15*a*b*c*x^2 + 5*a^2*d*x^2 + 3*a^2*c)/(a^5*x^5)","A",0
141,1,250,0,0.466133," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(99 \, b^{4} c - 63 \, a b^{3} d - 15 \, a^{3} b f + 35 \, a^{2} b^{2} e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{6}} + \frac{19 \, b^{5} c x^{3} - 15 \, a b^{4} d x^{3} - 7 \, a^{3} b^{2} f x^{3} + 11 \, a^{2} b^{3} x^{3} e + 21 \, a b^{4} c x - 17 \, a^{2} b^{3} d x - 9 \, a^{4} b f x + 13 \, a^{3} b^{2} x e}{8 \, {\left(b x^{2} + a\right)}^{2} a^{6}} + \frac{1050 \, b^{3} c x^{6} - 630 \, a b^{2} d x^{6} - 105 \, a^{3} f x^{6} + 315 \, a^{2} b x^{6} e - 210 \, a b^{2} c x^{4} + 105 \, a^{2} b d x^{4} - 35 \, a^{3} x^{4} e + 63 \, a^{2} b c x^{2} - 21 \, a^{3} d x^{2} - 15 \, a^{3} c}{105 \, a^{6} x^{7}}"," ",0,"1/8*(99*b^4*c - 63*a*b^3*d - 15*a^3*b*f + 35*a^2*b^2*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^6) + 1/8*(19*b^5*c*x^3 - 15*a*b^4*d*x^3 - 7*a^3*b^2*f*x^3 + 11*a^2*b^3*x^3*e + 21*a*b^4*c*x - 17*a^2*b^3*d*x - 9*a^4*b*f*x + 13*a^3*b^2*x*e)/((b*x^2 + a)^2*a^6) + 1/105*(1050*b^3*c*x^6 - 630*a*b^2*d*x^6 - 105*a^3*f*x^6 + 315*a^2*b*x^6*e - 210*a*b^2*c*x^4 + 105*a^2*b*d*x^4 - 35*a^3*x^4*e + 63*a^2*b*c*x^2 - 21*a^3*d*x^2 - 15*a^3*c)/(a^6*x^7)","A",0
142,1,301,0,0.403174," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(143 \, b^{5} c - 99 \, a b^{4} d - 35 \, a^{3} b^{2} f + 63 \, a^{2} b^{3} e\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{7}} - \frac{23 \, b^{6} c x^{3} - 19 \, a b^{5} d x^{3} - 11 \, a^{3} b^{3} f x^{3} + 15 \, a^{2} b^{4} x^{3} e + 25 \, a b^{5} c x - 21 \, a^{2} b^{4} d x - 13 \, a^{4} b^{2} f x + 17 \, a^{3} b^{3} x e}{8 \, {\left(b x^{2} + a\right)}^{2} a^{7}} - \frac{4725 \, b^{4} c x^{8} - 3150 \, a b^{3} d x^{8} - 945 \, a^{3} b f x^{8} + 1890 \, a^{2} b^{2} x^{8} e - 1050 \, a b^{3} c x^{6} + 630 \, a^{2} b^{2} d x^{6} + 105 \, a^{4} f x^{6} - 315 \, a^{3} b x^{6} e + 378 \, a^{2} b^{2} c x^{4} - 189 \, a^{3} b d x^{4} + 63 \, a^{4} x^{4} e - 135 \, a^{3} b c x^{2} + 45 \, a^{4} d x^{2} + 35 \, a^{4} c}{315 \, a^{7} x^{9}}"," ",0,"-1/8*(143*b^5*c - 99*a*b^4*d - 35*a^3*b^2*f + 63*a^2*b^3*e)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^7) - 1/8*(23*b^6*c*x^3 - 19*a*b^5*d*x^3 - 11*a^3*b^3*f*x^3 + 15*a^2*b^4*x^3*e + 25*a*b^5*c*x - 21*a^2*b^4*d*x - 13*a^4*b^2*f*x + 17*a^3*b^3*x*e)/((b*x^2 + a)^2*a^7) - 1/315*(4725*b^4*c*x^8 - 3150*a*b^3*d*x^8 - 945*a^3*b*f*x^8 + 1890*a^2*b^2*x^8*e - 1050*a*b^3*c*x^6 + 630*a^2*b^2*d*x^6 + 105*a^4*f*x^6 - 315*a^3*b*x^6*e + 378*a^2*b^2*c*x^4 - 189*a^3*b*d*x^4 + 63*a^4*x^4*e - 135*a^3*b*c*x^2 + 45*a^4*d*x^2 + 35*a^4*c)/(a^7*x^9)","A",0
143,1,264,0,0.448781," ","integrate(x^5*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d - a^{5} f + a^{4} b e\right)} \sqrt{b x^{2} + a}}{b^{6}} + \frac{693 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3} c - 2310 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{3} c + 495 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2} d - 2079 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b^{2} d + 3465 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b^{2} d + 315 \, {\left(b x^{2} + a\right)}^{\frac{11}{2}} f - 1925 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} a f + 4950 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} f - 6930 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3} f + 5775 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4} f + 385 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} b e - 1980 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a b e + 4158 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2} b e - 4620 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3} b e}{3465 \, b^{6}}"," ",0,"(a^2*b^3*c - a^3*b^2*d - a^5*f + a^4*b*e)*sqrt(b*x^2 + a)/b^6 + 1/3465*(693*(b*x^2 + a)^(5/2)*b^3*c - 2310*(b*x^2 + a)^(3/2)*a*b^3*c + 495*(b*x^2 + a)^(7/2)*b^2*d - 2079*(b*x^2 + a)^(5/2)*a*b^2*d + 3465*(b*x^2 + a)^(3/2)*a^2*b^2*d + 315*(b*x^2 + a)^(11/2)*f - 1925*(b*x^2 + a)^(9/2)*a*f + 4950*(b*x^2 + a)^(7/2)*a^2*f - 6930*(b*x^2 + a)^(5/2)*a^3*f + 5775*(b*x^2 + a)^(3/2)*a^4*f + 385*(b*x^2 + a)^(9/2)*b*e - 1980*(b*x^2 + a)^(7/2)*a*b*e + 4158*(b*x^2 + a)^(5/2)*a^2*b*e - 4620*(b*x^2 + a)^(3/2)*a^3*b*e)/b^6","A",0
144,1,197,0,0.507502," ","integrate(x^3*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(a b^{3} c - a^{2} b^{2} d - a^{4} f + a^{3} b e\right)} \sqrt{b x^{2} + a}}{b^{5}} + \frac{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3} c + 63 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2} d - 210 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2} d + 35 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} f - 180 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a f + 378 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2} f - 420 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3} f + 45 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b e - 189 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b e + 315 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b e}{315 \, b^{5}}"," ",0,"-(a*b^3*c - a^2*b^2*d - a^4*f + a^3*b*e)*sqrt(b*x^2 + a)/b^5 + 1/315*(105*(b*x^2 + a)^(3/2)*b^3*c + 63*(b*x^2 + a)^(5/2)*b^2*d - 210*(b*x^2 + a)^(3/2)*a*b^2*d + 35*(b*x^2 + a)^(9/2)*f - 180*(b*x^2 + a)^(7/2)*a*f + 378*(b*x^2 + a)^(5/2)*a^2*f - 420*(b*x^2 + a)^(3/2)*a^3*f + 45*(b*x^2 + a)^(7/2)*b*e - 189*(b*x^2 + a)^(5/2)*a*b*e + 315*(b*x^2 + a)^(3/2)*a^2*b*e)/b^5","A",0
145,1,130,0,0.407342," ","integrate(x*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \sqrt{b x^{2} + a}}{b^{4}} + \frac{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2} d + 15 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} f - 63 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a f + 105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} f + 21 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b e - 70 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b e}{105 \, b^{4}}"," ",0,"(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*sqrt(b*x^2 + a)/b^4 + 1/105*(35*(b*x^2 + a)^(3/2)*b^2*d + 15*(b*x^2 + a)^(7/2)*f - 63*(b*x^2 + a)^(5/2)*a*f + 105*(b*x^2 + a)^(3/2)*a^2*f + 21*(b*x^2 + a)^(5/2)*b*e - 70*(b*x^2 + a)^(3/2)*a*b*e)/b^4","A",0
146,1,127,0,0.397717," ","integrate((f*x^6+e*x^4+d*x^2+c)/x/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{c \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + \frac{15 \, \sqrt{b x^{2} + a} b^{14} d + 3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{12} f - 10 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{12} f + 15 \, \sqrt{b x^{2} + a} a^{2} b^{12} f + 5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{13} e - 15 \, \sqrt{b x^{2} + a} a b^{13} e}{15 \, b^{15}}"," ",0,"c*arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a) + 1/15*(15*sqrt(b*x^2 + a)*b^14*d + 3*(b*x^2 + a)^(5/2)*b^12*f - 10*(b*x^2 + a)^(3/2)*a*b^12*f + 15*sqrt(b*x^2 + a)*a^2*b^12*f + 5*(b*x^2 + a)^(3/2)*b^13*e - 15*sqrt(b*x^2 + a)*a*b^13*e)/b^15","A",0
147,1,114,0,0.554483," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^3/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(b^{2} c - 2 \, a b d\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{3 \, \sqrt{b x^{2} + a} b c}{a x^{2}} - \frac{2 \, {\left({\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2} f - 3 \, \sqrt{b x^{2} + a} a b^{2} f + 3 \, \sqrt{b x^{2} + a} b^{3} e\right)}}{b^{3}}}{6 \, b}"," ",0,"-1/6*(3*(b^2*c - 2*a*b*d)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a) + 3*sqrt(b*x^2 + a)*b*c/(a*x^2) - 2*((b*x^2 + a)^(3/2)*b^2*f - 3*sqrt(b*x^2 + a)*a*b^2*f + 3*sqrt(b*x^2 + a)*b^3*e)/b^3)/b","A",0
148,1,141,0,0.396613," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^5/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{8 \, \sqrt{b x^{2} + a} f + \frac{{\left(3 \, b^{3} c - 4 \, a b^{2} d + 8 \, a^{2} b e\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3} c - 5 \, \sqrt{b x^{2} + a} a b^{3} c - 4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2} d + 4 \, \sqrt{b x^{2} + a} a^{2} b^{2} d}{a^{2} b^{2} x^{4}}}{8 \, b}"," ",0,"1/8*(8*sqrt(b*x^2 + a)*f + (3*b^3*c - 4*a*b^2*d + 8*a^2*b*e)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^2) + (3*(b*x^2 + a)^(3/2)*b^3*c - 5*sqrt(b*x^2 + a)*a*b^3*c - 4*(b*x^2 + a)^(3/2)*a*b^2*d + 4*sqrt(b*x^2 + a)*a^2*b^2*d)/(a^2*b^2*x^4))/b","A",0
149,1,232,0,0.391282," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^7/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(5 \, b^{4} c - 6 \, a b^{3} d - 16 \, a^{3} b f + 8 \, a^{2} b^{2} e\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} + \frac{15 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{4} c - 40 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{4} c + 33 \, \sqrt{b x^{2} + a} a^{2} b^{4} c - 18 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b^{3} d + 48 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b^{3} d - 30 \, \sqrt{b x^{2} + a} a^{3} b^{3} d + 24 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2} b^{2} e - 48 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3} b^{2} e + 24 \, \sqrt{b x^{2} + a} a^{4} b^{2} e}{a^{3} b^{3} x^{6}}}{48 \, b}"," ",0,"-1/48*(3*(5*b^4*c - 6*a*b^3*d - 16*a^3*b*f + 8*a^2*b^2*e)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^3) + (15*(b*x^2 + a)^(5/2)*b^4*c - 40*(b*x^2 + a)^(3/2)*a*b^4*c + 33*sqrt(b*x^2 + a)*a^2*b^4*c - 18*(b*x^2 + a)^(5/2)*a*b^3*d + 48*(b*x^2 + a)^(3/2)*a^2*b^3*d - 30*sqrt(b*x^2 + a)*a^3*b^3*d + 24*(b*x^2 + a)^(5/2)*a^2*b^2*e - 48*(b*x^2 + a)^(3/2)*a^3*b^2*e + 24*sqrt(b*x^2 + a)*a^4*b^2*e)/(a^3*b^3*x^6))/b","A",0
150,1,361,0,0.396740," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^9/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(35 \, b^{5} c - 40 \, a b^{4} d - 64 \, a^{3} b^{2} f + 48 \, a^{2} b^{3} e\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{4}} + \frac{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{5} c - 385 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b^{5} c + 511 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b^{5} c - 279 \, \sqrt{b x^{2} + a} a^{3} b^{5} c - 120 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a b^{4} d + 440 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2} b^{4} d - 584 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3} b^{4} d + 264 \, \sqrt{b x^{2} + a} a^{4} b^{4} d - 192 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{3} b^{2} f + 576 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{4} b^{2} f - 576 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{5} b^{2} f + 192 \, \sqrt{b x^{2} + a} a^{6} b^{2} f + 144 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} b^{3} e - 528 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3} b^{3} e + 624 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4} b^{3} e - 240 \, \sqrt{b x^{2} + a} a^{5} b^{3} e}{a^{4} b^{4} x^{8}}}{384 \, b}"," ",0,"1/384*(3*(35*b^5*c - 40*a*b^4*d - 64*a^3*b^2*f + 48*a^2*b^3*e)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^4) + (105*(b*x^2 + a)^(7/2)*b^5*c - 385*(b*x^2 + a)^(5/2)*a*b^5*c + 511*(b*x^2 + a)^(3/2)*a^2*b^5*c - 279*sqrt(b*x^2 + a)*a^3*b^5*c - 120*(b*x^2 + a)^(7/2)*a*b^4*d + 440*(b*x^2 + a)^(5/2)*a^2*b^4*d - 584*(b*x^2 + a)^(3/2)*a^3*b^4*d + 264*sqrt(b*x^2 + a)*a^4*b^4*d - 192*(b*x^2 + a)^(7/2)*a^3*b^2*f + 576*(b*x^2 + a)^(5/2)*a^4*b^2*f - 576*(b*x^2 + a)^(3/2)*a^5*b^2*f + 192*sqrt(b*x^2 + a)*a^6*b^2*f + 144*(b*x^2 + a)^(7/2)*a^2*b^3*e - 528*(b*x^2 + a)^(5/2)*a^3*b^3*e + 624*(b*x^2 + a)^(3/2)*a^4*b^3*e - 240*sqrt(b*x^2 + a)*a^5*b^3*e)/(a^4*b^4*x^8))/b","B",0
151,1,224,0,0.526817," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{3840} \, {\left(2 \, {\left(4 \, {\left(6 \, {\left(\frac{8 \, f x^{2}}{b} - \frac{9 \, a b^{7} f - 10 \, b^{8} e}{b^{9}}\right)} x^{2} + \frac{80 \, b^{8} d + 63 \, a^{2} b^{6} f - 70 \, a b^{7} e}{b^{9}}\right)} x^{2} + \frac{5 \, {\left(96 \, b^{8} c - 80 \, a b^{7} d - 63 \, a^{3} b^{5} f + 70 \, a^{2} b^{6} e\right)}}{b^{9}}\right)} x^{2} - \frac{15 \, {\left(96 \, a b^{7} c - 80 \, a^{2} b^{6} d - 63 \, a^{4} b^{4} f + 70 \, a^{3} b^{5} e\right)}}{b^{9}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(96 \, a^{2} b^{3} c - 80 \, a^{3} b^{2} d - 63 \, a^{5} f + 70 \, a^{4} b e\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{256 \, b^{\frac{11}{2}}}"," ",0,"1/3840*(2*(4*(6*(8*f*x^2/b - (9*a*b^7*f - 10*b^8*e)/b^9)*x^2 + (80*b^8*d + 63*a^2*b^6*f - 70*a*b^7*e)/b^9)*x^2 + 5*(96*b^8*c - 80*a*b^7*d - 63*a^3*b^5*f + 70*a^2*b^6*e)/b^9)*x^2 - 15*(96*a*b^7*c - 80*a^2*b^6*d - 63*a^4*b^4*f + 70*a^3*b^5*e)/b^9)*sqrt(b*x^2 + a)*x - 1/256*(96*a^2*b^3*c - 80*a^3*b^2*d - 63*a^5*f + 70*a^4*b*e)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(11/2)","A",0
152,1,175,0,0.537260," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(\frac{6 \, f x^{2}}{b} - \frac{7 \, a b^{5} f - 8 \, b^{6} e}{b^{7}}\right)} x^{2} + \frac{48 \, b^{6} d + 35 \, a^{2} b^{4} f - 40 \, a b^{5} e}{b^{7}}\right)} x^{2} + \frac{3 \, {\left(64 \, b^{6} c - 48 \, a b^{5} d - 35 \, a^{3} b^{3} f + 40 \, a^{2} b^{4} e\right)}}{b^{7}}\right)} \sqrt{b x^{2} + a} x + \frac{{\left(64 \, a b^{3} c - 48 \, a^{2} b^{2} d - 35 \, a^{4} f + 40 \, a^{3} b e\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{128 \, b^{\frac{9}{2}}}"," ",0,"1/384*(2*(4*(6*f*x^2/b - (7*a*b^5*f - 8*b^6*e)/b^7)*x^2 + (48*b^6*d + 35*a^2*b^4*f - 40*a*b^5*e)/b^7)*x^2 + 3*(64*b^6*c - 48*a*b^5*d - 35*a^3*b^3*f + 40*a^2*b^4*e)/b^7)*sqrt(b*x^2 + a)*x + 1/128*(64*a*b^3*c - 48*a^2*b^2*d - 35*a^4*f + 40*a^3*b*e)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(9/2)","A",0
153,1,129,0,0.564432," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(\frac{4 \, f x^{2}}{b} - \frac{5 \, a b^{3} f - 6 \, b^{4} e}{b^{5}}\right)} x^{2} + \frac{3 \, {\left(8 \, b^{4} d + 5 \, a^{2} b^{2} f - 6 \, a b^{3} e\right)}}{b^{5}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(16 \, b^{3} c - 8 \, a b^{2} d - 5 \, a^{3} f + 6 \, a^{2} b e\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{7}{2}}}"," ",0,"1/48*(2*(4*f*x^2/b - (5*a*b^3*f - 6*b^4*e)/b^5)*x^2 + 3*(8*b^4*d + 5*a^2*b^2*f - 6*a*b^3*e)/b^5)*sqrt(b*x^2 + a)*x - 1/16*(16*b^3*c - 8*a*b^2*d - 5*a^3*f + 6*a^2*b*e)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
154,1,121,0,0.522405," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{b x^{2} + a} {\left(\frac{2 \, f x^{2}}{b} - \frac{3 \, a b f - 4 \, b^{2} e}{b^{3}}\right)} x + \frac{2 \, \sqrt{b} c}{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a} - \frac{{\left(8 \, b^{\frac{5}{2}} d + 3 \, a^{2} \sqrt{b} f - 4 \, a b^{\frac{3}{2}} e\right)} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right)}{16 \, b^{3}}"," ",0,"1/8*sqrt(b*x^2 + a)*(2*f*x^2/b - (3*a*b*f - 4*b^2*e)/b^3)*x + 2*sqrt(b)*c/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a) - 1/16*(8*b^(5/2)*d + 3*a^2*sqrt(b)*f - 4*a*b^(3/2)*e)*log((sqrt(b)*x - sqrt(b*x^2 + a))^2)/b^3","A",0
155,1,176,0,0.559207," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2} + a} f x}{2 \, b} + \frac{{\left(a \sqrt{b} f - 2 \, b^{\frac{3}{2}} e\right)} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right)}{4 \, b^{2}} + \frac{2 \, {\left(3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} \sqrt{b} d + 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b^{\frac{3}{2}} c - 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a \sqrt{b} d - 2 \, a b^{\frac{3}{2}} c + 3 \, a^{2} \sqrt{b} d\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"1/2*sqrt(b*x^2 + a)*f*x/b + 1/4*(a*sqrt(b)*f - 2*b^(3/2)*e)*log((sqrt(b)*x - sqrt(b*x^2 + a))^2)/b^2 + 2/3*(3*(sqrt(b)*x - sqrt(b*x^2 + a))^4*sqrt(b)*d + 6*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b^(3/2)*c - 6*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*sqrt(b)*d - 2*a*b^(3/2)*c + 3*a^2*sqrt(b)*d)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^3","A",0
156,1,324,0,0.597026," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{f \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right)}{2 \, \sqrt{b}} + \frac{2 \, {\left(15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} \sqrt{b} e + 30 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} b^{\frac{3}{2}} d - 60 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a \sqrt{b} e + 80 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} b^{\frac{5}{2}} c - 70 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a b^{\frac{3}{2}} d + 90 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} \sqrt{b} e - 40 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a b^{\frac{5}{2}} c + 50 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{2} b^{\frac{3}{2}} d - 60 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{3} \sqrt{b} e + 8 \, a^{2} b^{\frac{5}{2}} c - 10 \, a^{3} b^{\frac{3}{2}} d + 15 \, a^{4} \sqrt{b} e\right)}}{15 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{5}}"," ",0,"-1/2*f*log((sqrt(b)*x - sqrt(b*x^2 + a))^2)/sqrt(b) + 2/15*(15*(sqrt(b)*x - sqrt(b*x^2 + a))^8*sqrt(b)*e + 30*(sqrt(b)*x - sqrt(b*x^2 + a))^6*b^(3/2)*d - 60*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a*sqrt(b)*e + 80*(sqrt(b)*x - sqrt(b*x^2 + a))^4*b^(5/2)*c - 70*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a*b^(3/2)*d + 90*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*sqrt(b)*e - 40*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*b^(5/2)*c + 50*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^2*b^(3/2)*d - 60*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^3*sqrt(b)*e + 8*a^2*b^(5/2)*c - 10*a^3*b^(3/2)*d + 15*a^4*sqrt(b)*e)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^5","B",0
157,1,554,0,0.570837," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(105 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} \sqrt{b} f - 630 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a \sqrt{b} f + 210 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} b^{\frac{3}{2}} e + 560 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} b^{\frac{5}{2}} d + 1575 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{2} \sqrt{b} f - 910 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a b^{\frac{3}{2}} e + 1680 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} b^{\frac{7}{2}} c - 1400 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a b^{\frac{5}{2}} d - 2100 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{3} \sqrt{b} f + 1540 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} b^{\frac{3}{2}} e - 1008 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a b^{\frac{7}{2}} c + 1176 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} b^{\frac{5}{2}} d + 1575 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{4} \sqrt{b} f - 1260 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{3} b^{\frac{3}{2}} e + 336 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{2} b^{\frac{7}{2}} c - 392 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{3} b^{\frac{5}{2}} d - 630 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{5} \sqrt{b} f + 490 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{4} b^{\frac{3}{2}} e - 48 \, a^{3} b^{\frac{7}{2}} c + 56 \, a^{4} b^{\frac{5}{2}} d + 105 \, a^{6} \sqrt{b} f - 70 \, a^{5} b^{\frac{3}{2}} e\right)}}{105 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{7}}"," ",0,"2/105*(105*(sqrt(b)*x - sqrt(b*x^2 + a))^12*sqrt(b)*f - 630*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a*sqrt(b)*f + 210*(sqrt(b)*x - sqrt(b*x^2 + a))^10*b^(3/2)*e + 560*(sqrt(b)*x - sqrt(b*x^2 + a))^8*b^(5/2)*d + 1575*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^2*sqrt(b)*f - 910*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a*b^(3/2)*e + 1680*(sqrt(b)*x - sqrt(b*x^2 + a))^6*b^(7/2)*c - 1400*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a*b^(5/2)*d - 2100*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^3*sqrt(b)*f + 1540*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*b^(3/2)*e - 1008*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a*b^(7/2)*c + 1176*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*b^(5/2)*d + 1575*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^4*sqrt(b)*f - 1260*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^3*b^(3/2)*e + 336*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^2*b^(7/2)*c - 392*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^3*b^(5/2)*d - 630*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^5*sqrt(b)*f + 490*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^4*b^(3/2)*e - 48*a^3*b^(7/2)*c + 56*a^4*b^(5/2)*d + 105*a^6*sqrt(b)*f - 70*a^5*b^(3/2)*e)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^7","B",0
158,1,667,0,0.603220," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(315 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} b^{\frac{3}{2}} f - 1995 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} a b^{\frac{3}{2}} f + 840 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} b^{\frac{5}{2}} e + 2520 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} b^{\frac{7}{2}} d + 5355 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{2} b^{\frac{3}{2}} f - 3780 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a b^{\frac{5}{2}} e + 8064 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} b^{\frac{9}{2}} c - 6552 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a b^{\frac{7}{2}} d - 7875 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{3} b^{\frac{3}{2}} f + 6804 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{2} b^{\frac{5}{2}} e - 5376 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a b^{\frac{9}{2}} c + 6048 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} b^{\frac{7}{2}} d + 6825 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{4} b^{\frac{3}{2}} f - 6216 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{3} b^{\frac{5}{2}} e + 2304 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} b^{\frac{9}{2}} c - 2592 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{3} b^{\frac{7}{2}} d - 3465 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{5} b^{\frac{3}{2}} f + 3024 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{4} b^{\frac{5}{2}} e - 576 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{3} b^{\frac{9}{2}} c + 648 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{4} b^{\frac{7}{2}} d + 945 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{6} b^{\frac{3}{2}} f - 756 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{5} b^{\frac{5}{2}} e + 64 \, a^{4} b^{\frac{9}{2}} c - 72 \, a^{5} b^{\frac{7}{2}} d - 105 \, a^{7} b^{\frac{3}{2}} f + 84 \, a^{6} b^{\frac{5}{2}} e\right)}}{315 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{9}}"," ",0,"4/315*(315*(sqrt(b)*x - sqrt(b*x^2 + a))^14*b^(3/2)*f - 1995*(sqrt(b)*x - sqrt(b*x^2 + a))^12*a*b^(3/2)*f + 840*(sqrt(b)*x - sqrt(b*x^2 + a))^12*b^(5/2)*e + 2520*(sqrt(b)*x - sqrt(b*x^2 + a))^10*b^(7/2)*d + 5355*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^2*b^(3/2)*f - 3780*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a*b^(5/2)*e + 8064*(sqrt(b)*x - sqrt(b*x^2 + a))^8*b^(9/2)*c - 6552*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a*b^(7/2)*d - 7875*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^3*b^(3/2)*f + 6804*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^2*b^(5/2)*e - 5376*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a*b^(9/2)*c + 6048*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*b^(7/2)*d + 6825*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^4*b^(3/2)*f - 6216*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^3*b^(5/2)*e + 2304*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*b^(9/2)*c - 2592*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^3*b^(7/2)*d - 3465*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^5*b^(3/2)*f + 3024*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^4*b^(5/2)*e - 576*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^3*b^(9/2)*c + 648*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^4*b^(7/2)*d + 945*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^6*b^(3/2)*f - 756*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^5*b^(5/2)*e + 64*a^4*b^(9/2)*c - 72*a^5*b^(7/2)*d - 105*a^7*b^(3/2)*f + 84*a^6*b^(5/2)*e)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^9","B",0
159,1,342,0,0.641845," ","integrate(x^8*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left({\left({\left(35 \, {\left(2 \, {\left(\frac{4 \, D x^{2}}{b} - \frac{13 \, D a^{4} b^{11} - 6 \, C a^{3} b^{12}}{a^{3} b^{13}}\right)} x^{2} + \frac{143 \, D a^{5} b^{10} - 66 \, C a^{4} b^{11} + 24 \, B a^{3} b^{12}}{a^{3} b^{13}}\right)} x^{2} + \frac{176 \, {\left(429 \, D a^{6} b^{9} - 198 \, C a^{5} b^{10} + 72 \, B a^{4} b^{11} - 16 \, A a^{3} b^{12}\right)}}{a^{3} b^{13}}\right)} x^{2} + \frac{406 \, {\left(429 \, D a^{7} b^{8} - 198 \, C a^{6} b^{9} + 72 \, B a^{5} b^{10} - 16 \, A a^{4} b^{11}\right)}}{a^{3} b^{13}}\right)} x^{2} + \frac{350 \, {\left(429 \, D a^{8} b^{7} - 198 \, C a^{7} b^{8} + 72 \, B a^{6} b^{9} - 16 \, A a^{5} b^{10}\right)}}{a^{3} b^{13}}\right)} x^{2} + \frac{105 \, {\left(429 \, D a^{9} b^{6} - 198 \, C a^{8} b^{7} + 72 \, B a^{7} b^{8} - 16 \, A a^{6} b^{9}\right)}}{a^{3} b^{13}}\right)} x}{1680 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} + \frac{{\left(429 \, D a^{3} - 198 \, C a^{2} b + 72 \, B a b^{2} - 16 \, A b^{3}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{15}{2}}}"," ",0,"1/1680*((((35*(2*(4*D*x^2/b - (13*D*a^4*b^11 - 6*C*a^3*b^12)/(a^3*b^13))*x^2 + (143*D*a^5*b^10 - 66*C*a^4*b^11 + 24*B*a^3*b^12)/(a^3*b^13))*x^2 + 176*(429*D*a^6*b^9 - 198*C*a^5*b^10 + 72*B*a^4*b^11 - 16*A*a^3*b^12)/(a^3*b^13))*x^2 + 406*(429*D*a^7*b^8 - 198*C*a^6*b^9 + 72*B*a^5*b^10 - 16*A*a^4*b^11)/(a^3*b^13))*x^2 + 350*(429*D*a^8*b^7 - 198*C*a^7*b^8 + 72*B*a^6*b^9 - 16*A*a^5*b^10)/(a^3*b^13))*x^2 + 105*(429*D*a^9*b^6 - 198*C*a^8*b^7 + 72*B*a^7*b^8 - 16*A*a^6*b^9)/(a^3*b^13))*x/(b*x^2 + a)^(7/2) + 1/16*(429*D*a^3 - 198*C*a^2*b + 72*B*a*b^2 - 16*A*b^3)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(15/2)","A",0
160,1,265,0,0.593042," ","integrate(x^6*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left({\left({\left(105 \, {\left(\frac{2 \, D x^{2}}{b} - \frac{11 \, D a^{4} b^{9} - 4 \, C a^{3} b^{10}}{a^{3} b^{11}}\right)} x^{2} - \frac{8 \, {\left(2178 \, D a^{5} b^{8} - 792 \, C a^{4} b^{9} + 176 \, B a^{3} b^{10} - 15 \, A a^{2} b^{11}\right)}}{a^{3} b^{11}}\right)} x^{2} - \frac{406 \, {\left(99 \, D a^{6} b^{7} - 36 \, C a^{5} b^{8} + 8 \, B a^{4} b^{9}\right)}}{a^{3} b^{11}}\right)} x^{2} - \frac{350 \, {\left(99 \, D a^{7} b^{6} - 36 \, C a^{6} b^{7} + 8 \, B a^{5} b^{8}\right)}}{a^{3} b^{11}}\right)} x^{2} - \frac{105 \, {\left(99 \, D a^{8} b^{5} - 36 \, C a^{7} b^{6} + 8 \, B a^{6} b^{7}\right)}}{a^{3} b^{11}}\right)} x}{840 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} - \frac{{\left(99 \, D a^{2} - 36 \, C a b + 8 \, B b^{2}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{13}{2}}}"," ",0,"1/840*((((105*(2*D*x^2/b - (11*D*a^4*b^9 - 4*C*a^3*b^10)/(a^3*b^11))*x^2 - 8*(2178*D*a^5*b^8 - 792*C*a^4*b^9 + 176*B*a^3*b^10 - 15*A*a^2*b^11)/(a^3*b^11))*x^2 - 406*(99*D*a^6*b^7 - 36*C*a^5*b^8 + 8*B*a^4*b^9)/(a^3*b^11))*x^2 - 350*(99*D*a^7*b^6 - 36*C*a^6*b^7 + 8*B*a^5*b^8)/(a^3*b^11))*x^2 - 105*(99*D*a^8*b^5 - 36*C*a^7*b^6 + 8*B*a^6*b^7)/(a^3*b^11))*x/(b*x^2 + a)^(7/2) - 1/8*(99*D*a^2 - 36*C*a*b + 8*B*b^2)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(13/2)","A",0
161,1,203,0,0.597747," ","integrate(x^4*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left({\left({\left(\frac{105 \, D x^{2}}{b} + \frac{2 \, {\left(792 \, D a^{4} b^{7} - 176 \, C a^{3} b^{8} + 15 \, B a^{2} b^{9} + 6 \, A a b^{10}\right)}}{a^{3} b^{9}}\right)} x^{2} + \frac{14 \, {\left(261 \, D a^{5} b^{6} - 58 \, C a^{4} b^{7} + 3 \, A a^{2} b^{9}\right)}}{a^{3} b^{9}}\right)} x^{2} + \frac{350 \, {\left(9 \, D a^{6} b^{5} - 2 \, C a^{5} b^{6}\right)}}{a^{3} b^{9}}\right)} x^{2} + \frac{105 \, {\left(9 \, D a^{7} b^{4} - 2 \, C a^{6} b^{5}\right)}}{a^{3} b^{9}}\right)} x}{210 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} + \frac{{\left(9 \, D a - 2 \, C b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{11}{2}}}"," ",0,"1/210*((((105*D*x^2/b + 2*(792*D*a^4*b^7 - 176*C*a^3*b^8 + 15*B*a^2*b^9 + 6*A*a*b^10)/(a^3*b^9))*x^2 + 14*(261*D*a^5*b^6 - 58*C*a^4*b^7 + 3*A*a^2*b^9)/(a^3*b^9))*x^2 + 350*(9*D*a^6*b^5 - 2*C*a^5*b^6)/(a^3*b^9))*x^2 + 105*(9*D*a^7*b^4 - 2*C*a^6*b^5)/(a^3*b^9))*x/(b*x^2 + a)^(7/2) + 1/2*(9*D*a - 2*C*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(11/2)","A",0
162,1,160,0,0.550019," ","integrate(x^2*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","-\frac{{\left({\left(x^{2} {\left(\frac{{\left(176 \, D a^{3} b^{6} - 15 \, C a^{2} b^{7} - 6 \, B a b^{8} - 8 \, A b^{9}\right)} x^{2}}{a^{3} b^{7}} + \frac{7 \, {\left(58 \, D a^{4} b^{5} - 3 \, B a^{2} b^{7} - 4 \, A a b^{8}\right)}}{a^{3} b^{7}}\right)} + \frac{35 \, {\left(10 \, D a^{5} b^{4} - A a^{2} b^{7}\right)}}{a^{3} b^{7}}\right)} x^{2} + \frac{105 \, D a^{3}}{b^{4}}\right)} x}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} - \frac{D \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{b^{\frac{9}{2}}}"," ",0,"-1/105*((x^2*((176*D*a^3*b^6 - 15*C*a^2*b^7 - 6*B*a*b^8 - 8*A*b^9)*x^2/(a^3*b^7) + 7*(58*D*a^4*b^5 - 3*B*a^2*b^7 - 4*A*a*b^8)/(a^3*b^7)) + 35*(10*D*a^5*b^4 - A*a^2*b^7)/(a^3*b^7))*x^2 + 105*D*a^3/b^4)*x/(b*x^2 + a)^(7/2) - D*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(9/2)","A",0
163,1,131,0,0.534284," ","integrate((D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(x^{2} {\left(\frac{{\left(15 \, D a^{3} b^{3} + 6 \, C a^{2} b^{4} + 8 \, B a b^{5} + 48 \, A b^{6}\right)} x^{2}}{a^{4} b^{3}} + \frac{7 \, {\left(3 \, C a^{3} b^{3} + 4 \, B a^{2} b^{4} + 24 \, A a b^{5}\right)}}{a^{4} b^{3}}\right)} + \frac{35 \, {\left(B a^{3} b^{3} + 6 \, A a^{2} b^{4}\right)}}{a^{4} b^{3}}\right)} x^{2} + \frac{105 \, A}{a}\right)} x}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}}"," ",0,"1/105*((x^2*((15*D*a^3*b^3 + 6*C*a^2*b^4 + 8*B*a*b^5 + 48*A*b^6)*x^2/(a^4*b^3) + 7*(3*C*a^3*b^3 + 4*B*a^2*b^4 + 24*A*a*b^5)/(a^4*b^3)) + 35*(B*a^3*b^3 + 6*A*a^2*b^4)/(a^4*b^3))*x^2 + 105*A/a)*x/(b*x^2 + a)^(7/2)","A",0
164,1,211,0,0.575095," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^2/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(x^{2} {\left(\frac{{\left(6 \, D a^{12} b^{4} + 8 \, C a^{11} b^{5} + 48 \, B a^{10} b^{6} - 279 \, A a^{9} b^{7}\right)} x^{2}}{a^{14} b^{3}} + \frac{7 \, {\left(3 \, D a^{13} b^{3} + 4 \, C a^{12} b^{4} + 24 \, B a^{11} b^{5} - 132 \, A a^{10} b^{6}\right)}}{a^{14} b^{3}}\right)} + \frac{35 \, {\left(C a^{13} b^{3} + 6 \, B a^{12} b^{4} - 30 \, A a^{11} b^{5}\right)}}{a^{14} b^{3}}\right)} x^{2} + \frac{105 \, {\left(B a^{13} b^{3} - 4 \, A a^{12} b^{4}\right)}}{a^{14} b^{3}}\right)} x}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} + \frac{2 \, A \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)} a^{4}}"," ",0,"1/105*((x^2*((6*D*a^12*b^4 + 8*C*a^11*b^5 + 48*B*a^10*b^6 - 279*A*a^9*b^7)*x^2/(a^14*b^3) + 7*(3*D*a^13*b^3 + 4*C*a^12*b^4 + 24*B*a^11*b^5 - 132*A*a^10*b^6)/(a^14*b^3)) + 35*(C*a^13*b^3 + 6*B*a^12*b^4 - 30*A*a^11*b^5)/(a^14*b^3))*x^2 + 105*(B*a^13*b^3 - 4*A*a^12*b^4)/(a^14*b^3))*x/(b*x^2 + a)^(7/2) + 2*A*sqrt(b)/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)*a^4)","A",0
165,1,349,0,0.556757," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^4/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(x^{2} {\left(\frac{{\left(8 \, D a^{15} b^{5} + 48 \, C a^{14} b^{6} - 279 \, B a^{13} b^{7} + 790 \, A a^{12} b^{8}\right)} x^{2}}{a^{18} b^{3}} + \frac{7 \, {\left(4 \, D a^{16} b^{4} + 24 \, C a^{15} b^{5} - 132 \, B a^{14} b^{6} + 365 \, A a^{13} b^{7}\right)}}{a^{18} b^{3}}\right)} + \frac{35 \, {\left(D a^{17} b^{3} + 6 \, C a^{16} b^{4} - 30 \, B a^{15} b^{5} + 80 \, A a^{14} b^{6}\right)}}{a^{18} b^{3}}\right)} x^{2} + \frac{105 \, {\left(C a^{17} b^{3} - 4 \, B a^{16} b^{4} + 10 \, A a^{15} b^{5}\right)}}{a^{18} b^{3}}\right)} x}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} + \frac{2 \, {\left(3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a \sqrt{b} - 12 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A b^{\frac{3}{2}} - 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{2} \sqrt{b} + 30 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a b^{\frac{3}{2}} + 3 \, B a^{3} \sqrt{b} - 14 \, A a^{2} b^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{3} a^{5}}"," ",0,"1/105*((x^2*((8*D*a^15*b^5 + 48*C*a^14*b^6 - 279*B*a^13*b^7 + 790*A*a^12*b^8)*x^2/(a^18*b^3) + 7*(4*D*a^16*b^4 + 24*C*a^15*b^5 - 132*B*a^14*b^6 + 365*A*a^13*b^7)/(a^18*b^3)) + 35*(D*a^17*b^3 + 6*C*a^16*b^4 - 30*B*a^15*b^5 + 80*A*a^14*b^6)/(a^18*b^3))*x^2 + 105*(C*a^17*b^3 - 4*B*a^16*b^4 + 10*A*a^15*b^5)/(a^18*b^3))*x/(b*x^2 + a)^(7/2) + 2/3*(3*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a*sqrt(b) - 12*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*b^(3/2) - 6*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^2*sqrt(b) + 30*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a*b^(3/2) + 3*B*a^3*sqrt(b) - 14*A*a^2*b^(3/2))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^3*a^5)","A",0
166,1,592,0,0.632158," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^6/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(x^{2} {\left(\frac{{\left(48 \, D a^{18} b^{6} - 279 \, C a^{17} b^{7} + 790 \, B a^{16} b^{8} - 1686 \, A a^{15} b^{9}\right)} x^{2}}{a^{22} b^{3}} + \frac{7 \, {\left(24 \, D a^{19} b^{5} - 132 \, C a^{18} b^{6} + 365 \, B a^{17} b^{7} - 768 \, A a^{16} b^{8}\right)}}{a^{22} b^{3}}\right)} + \frac{35 \, {\left(6 \, D a^{20} b^{4} - 30 \, C a^{19} b^{5} + 80 \, B a^{18} b^{6} - 165 \, A a^{17} b^{7}\right)}}{a^{22} b^{3}}\right)} x^{2} + \frac{105 \, {\left(D a^{21} b^{3} - 4 \, C a^{20} b^{4} + 10 \, B a^{19} b^{5} - 20 \, A a^{18} b^{6}\right)}}{a^{22} b^{3}}\right)} x}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} + \frac{2 \, {\left(15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} C a^{2} \sqrt{b} - 60 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a b^{\frac{3}{2}} + 150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A b^{\frac{5}{2}} - 60 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} C a^{3} \sqrt{b} + 270 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{2} b^{\frac{3}{2}} - 720 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a b^{\frac{5}{2}} + 90 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} C a^{4} \sqrt{b} - 430 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{3} b^{\frac{3}{2}} + 1260 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{2} b^{\frac{5}{2}} - 60 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} C a^{5} \sqrt{b} + 290 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{4} b^{\frac{3}{2}} - 840 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{3} b^{\frac{5}{2}} + 15 \, C a^{6} \sqrt{b} - 70 \, B a^{5} b^{\frac{3}{2}} + 198 \, A a^{4} b^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{5} a^{6}}"," ",0,"1/105*((x^2*((48*D*a^18*b^6 - 279*C*a^17*b^7 + 790*B*a^16*b^8 - 1686*A*a^15*b^9)*x^2/(a^22*b^3) + 7*(24*D*a^19*b^5 - 132*C*a^18*b^6 + 365*B*a^17*b^7 - 768*A*a^16*b^8)/(a^22*b^3)) + 35*(6*D*a^20*b^4 - 30*C*a^19*b^5 + 80*B*a^18*b^6 - 165*A*a^17*b^7)/(a^22*b^3))*x^2 + 105*(D*a^21*b^3 - 4*C*a^20*b^4 + 10*B*a^19*b^5 - 20*A*a^18*b^6)/(a^22*b^3))*x/(b*x^2 + a)^(7/2) + 2/15*(15*(sqrt(b)*x - sqrt(b*x^2 + a))^8*C*a^2*sqrt(b) - 60*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a*b^(3/2) + 150*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*b^(5/2) - 60*(sqrt(b)*x - sqrt(b*x^2 + a))^6*C*a^3*sqrt(b) + 270*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^2*b^(3/2) - 720*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a*b^(5/2) + 90*(sqrt(b)*x - sqrt(b*x^2 + a))^4*C*a^4*sqrt(b) - 430*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^3*b^(3/2) + 1260*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^2*b^(5/2) - 60*(sqrt(b)*x - sqrt(b*x^2 + a))^2*C*a^5*sqrt(b) + 290*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^4*b^(3/2) - 840*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^3*b^(5/2) + 15*C*a^6*sqrt(b) - 70*B*a^5*b^(3/2) + 198*A*a^4*b^(5/2))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^5*a^6)","B",0
167,1,938,0,0.711587," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^8/(b*x^2+a)^(9/2),x, algorithm=""giac"")","-\frac{{\left({\left(x^{2} {\left(\frac{{\left(279 \, D a^{21} b^{7} - 790 \, C a^{20} b^{8} + 1686 \, B a^{19} b^{9} - 3072 \, A a^{18} b^{10}\right)} x^{2}}{a^{26} b^{3}} + \frac{7 \, {\left(132 \, D a^{22} b^{6} - 365 \, C a^{21} b^{7} + 768 \, B a^{20} b^{8} - 1386 \, A a^{19} b^{9}\right)}}{a^{26} b^{3}}\right)} + \frac{35 \, {\left(30 \, D a^{23} b^{5} - 80 \, C a^{22} b^{6} + 165 \, B a^{21} b^{7} - 294 \, A a^{20} b^{8}\right)}}{a^{26} b^{3}}\right)} x^{2} + \frac{105 \, {\left(4 \, D a^{24} b^{4} - 10 \, C a^{23} b^{5} + 20 \, B a^{22} b^{6} - 35 \, A a^{21} b^{7}\right)}}{a^{26} b^{3}}\right)} x}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} + \frac{2 \, {\left(105 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} D a^{3} \sqrt{b} - 420 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} C a^{2} b^{\frac{3}{2}} + 1050 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} B a b^{\frac{5}{2}} - 2100 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} A b^{\frac{7}{2}} - 630 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} D a^{4} \sqrt{b} + 2730 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} C a^{3} b^{\frac{3}{2}} - 7140 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} B a^{2} b^{\frac{5}{2}} + 14700 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} A a b^{\frac{7}{2}} + 1575 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} D a^{5} \sqrt{b} - 7210 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} C a^{4} b^{\frac{3}{2}} + 19950 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a^{3} b^{\frac{5}{2}} - 42840 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A a^{2} b^{\frac{7}{2}} - 2100 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} D a^{6} \sqrt{b} + 9940 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} C a^{5} b^{\frac{3}{2}} - 28560 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{4} b^{\frac{5}{2}} + 64680 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a^{3} b^{\frac{7}{2}} + 1575 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} D a^{7} \sqrt{b} - 7560 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} C a^{6} b^{\frac{3}{2}} + 21966 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{5} b^{\frac{5}{2}} - 49812 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{4} b^{\frac{7}{2}} - 630 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} D a^{8} \sqrt{b} + 3010 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} C a^{7} b^{\frac{3}{2}} - 8652 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{6} b^{\frac{5}{2}} + 19404 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{5} b^{\frac{7}{2}} + 105 \, D a^{9} \sqrt{b} - 490 \, C a^{8} b^{\frac{3}{2}} + 1386 \, B a^{7} b^{\frac{5}{2}} - 3072 \, A a^{6} b^{\frac{7}{2}}\right)}}{105 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{7} a^{7}}"," ",0,"-1/105*((x^2*((279*D*a^21*b^7 - 790*C*a^20*b^8 + 1686*B*a^19*b^9 - 3072*A*a^18*b^10)*x^2/(a^26*b^3) + 7*(132*D*a^22*b^6 - 365*C*a^21*b^7 + 768*B*a^20*b^8 - 1386*A*a^19*b^9)/(a^26*b^3)) + 35*(30*D*a^23*b^5 - 80*C*a^22*b^6 + 165*B*a^21*b^7 - 294*A*a^20*b^8)/(a^26*b^3))*x^2 + 105*(4*D*a^24*b^4 - 10*C*a^23*b^5 + 20*B*a^22*b^6 - 35*A*a^21*b^7)/(a^26*b^3))*x/(b*x^2 + a)^(7/2) + 2/105*(105*(sqrt(b)*x - sqrt(b*x^2 + a))^12*D*a^3*sqrt(b) - 420*(sqrt(b)*x - sqrt(b*x^2 + a))^12*C*a^2*b^(3/2) + 1050*(sqrt(b)*x - sqrt(b*x^2 + a))^12*B*a*b^(5/2) - 2100*(sqrt(b)*x - sqrt(b*x^2 + a))^12*A*b^(7/2) - 630*(sqrt(b)*x - sqrt(b*x^2 + a))^10*D*a^4*sqrt(b) + 2730*(sqrt(b)*x - sqrt(b*x^2 + a))^10*C*a^3*b^(3/2) - 7140*(sqrt(b)*x - sqrt(b*x^2 + a))^10*B*a^2*b^(5/2) + 14700*(sqrt(b)*x - sqrt(b*x^2 + a))^10*A*a*b^(7/2) + 1575*(sqrt(b)*x - sqrt(b*x^2 + a))^8*D*a^5*sqrt(b) - 7210*(sqrt(b)*x - sqrt(b*x^2 + a))^8*C*a^4*b^(3/2) + 19950*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a^3*b^(5/2) - 42840*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*a^2*b^(7/2) - 2100*(sqrt(b)*x - sqrt(b*x^2 + a))^6*D*a^6*sqrt(b) + 9940*(sqrt(b)*x - sqrt(b*x^2 + a))^6*C*a^5*b^(3/2) - 28560*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^4*b^(5/2) + 64680*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a^3*b^(7/2) + 1575*(sqrt(b)*x - sqrt(b*x^2 + a))^4*D*a^7*sqrt(b) - 7560*(sqrt(b)*x - sqrt(b*x^2 + a))^4*C*a^6*b^(3/2) + 21966*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^5*b^(5/2) - 49812*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^4*b^(7/2) - 630*(sqrt(b)*x - sqrt(b*x^2 + a))^2*D*a^8*sqrt(b) + 3010*(sqrt(b)*x - sqrt(b*x^2 + a))^2*C*a^7*b^(3/2) - 8652*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^6*b^(5/2) + 19404*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^5*b^(7/2) + 105*D*a^9*sqrt(b) - 490*C*a^8*b^(3/2) + 1386*B*a^7*b^(5/2) - 3072*A*a^6*b^(7/2))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^7*a^7)","B",0
168,1,1162,0,0.735994," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^10/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(x^{2} {\left(\frac{{\left(790 \, D a^{24} b^{8} - 1686 \, C a^{23} b^{9} + 3072 \, B a^{22} b^{10} - 5053 \, A a^{21} b^{11}\right)} x^{2}}{a^{30} b^{3}} + \frac{7 \, {\left(365 \, D a^{25} b^{7} - 768 \, C a^{24} b^{8} + 1386 \, B a^{23} b^{9} - 2264 \, A a^{22} b^{10}\right)}}{a^{30} b^{3}}\right)} + \frac{35 \, {\left(80 \, D a^{26} b^{6} - 165 \, C a^{25} b^{7} + 294 \, B a^{24} b^{8} - 476 \, A a^{23} b^{9}\right)}}{a^{30} b^{3}}\right)} x^{2} + \frac{105 \, {\left(10 \, D a^{27} b^{5} - 20 \, C a^{26} b^{6} + 35 \, B a^{25} b^{7} - 56 \, A a^{24} b^{8}\right)}}{a^{30} b^{3}}\right)} x}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} - \frac{2 \, {\left(1260 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{16} D a^{3} b^{\frac{3}{2}} - 3150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{16} C a^{2} b^{\frac{5}{2}} + 6300 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{16} B a b^{\frac{7}{2}} - 11025 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{16} A b^{\frac{9}{2}} - 10710 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} D a^{4} b^{\frac{3}{2}} + 27720 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} C a^{3} b^{\frac{5}{2}} - 56700 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} B a^{2} b^{\frac{7}{2}} + 100800 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} A a b^{\frac{9}{2}} + 39270 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} D a^{5} b^{\frac{3}{2}} - 105840 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} C a^{4} b^{\frac{5}{2}} + 223020 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} B a^{3} b^{\frac{7}{2}} - 405300 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} A a^{2} b^{\frac{9}{2}} - 81270 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} D a^{6} b^{\frac{3}{2}} + 226800 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} C a^{5} b^{\frac{5}{2}} - 495180 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} B a^{4} b^{\frac{7}{2}} + 927360 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} A a^{3} b^{\frac{9}{2}} + 103950 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} D a^{7} b^{\frac{3}{2}} - 297108 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} C a^{6} b^{\frac{5}{2}} + 666036 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a^{5} b^{\frac{7}{2}} - 1291374 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A a^{4} b^{\frac{9}{2}} - 84210 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} D a^{8} b^{\frac{3}{2}} + 243432 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} C a^{7} b^{\frac{5}{2}} - 551124 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{6} b^{\frac{7}{2}} + 1073856 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a^{5} b^{\frac{9}{2}} + 42210 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} D a^{9} b^{\frac{3}{2}} - 121968 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} C a^{8} b^{\frac{5}{2}} + 275076 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{7} b^{\frac{7}{2}} - 533124 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{6} b^{\frac{9}{2}} - 11970 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} D a^{10} b^{\frac{3}{2}} + 34272 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} C a^{9} b^{\frac{5}{2}} - 76644 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{8} b^{\frac{7}{2}} + 147456 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{7} b^{\frac{9}{2}} + 1470 \, D a^{11} b^{\frac{3}{2}} - 4158 \, C a^{10} b^{\frac{5}{2}} + 9216 \, B a^{9} b^{\frac{7}{2}} - 17609 \, A a^{8} b^{\frac{9}{2}}\right)}}{315 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{9} a^{8}}"," ",0,"1/105*((x^2*((790*D*a^24*b^8 - 1686*C*a^23*b^9 + 3072*B*a^22*b^10 - 5053*A*a^21*b^11)*x^2/(a^30*b^3) + 7*(365*D*a^25*b^7 - 768*C*a^24*b^8 + 1386*B*a^23*b^9 - 2264*A*a^22*b^10)/(a^30*b^3)) + 35*(80*D*a^26*b^6 - 165*C*a^25*b^7 + 294*B*a^24*b^8 - 476*A*a^23*b^9)/(a^30*b^3))*x^2 + 105*(10*D*a^27*b^5 - 20*C*a^26*b^6 + 35*B*a^25*b^7 - 56*A*a^24*b^8)/(a^30*b^3))*x/(b*x^2 + a)^(7/2) - 2/315*(1260*(sqrt(b)*x - sqrt(b*x^2 + a))^16*D*a^3*b^(3/2) - 3150*(sqrt(b)*x - sqrt(b*x^2 + a))^16*C*a^2*b^(5/2) + 6300*(sqrt(b)*x - sqrt(b*x^2 + a))^16*B*a*b^(7/2) - 11025*(sqrt(b)*x - sqrt(b*x^2 + a))^16*A*b^(9/2) - 10710*(sqrt(b)*x - sqrt(b*x^2 + a))^14*D*a^4*b^(3/2) + 27720*(sqrt(b)*x - sqrt(b*x^2 + a))^14*C*a^3*b^(5/2) - 56700*(sqrt(b)*x - sqrt(b*x^2 + a))^14*B*a^2*b^(7/2) + 100800*(sqrt(b)*x - sqrt(b*x^2 + a))^14*A*a*b^(9/2) + 39270*(sqrt(b)*x - sqrt(b*x^2 + a))^12*D*a^5*b^(3/2) - 105840*(sqrt(b)*x - sqrt(b*x^2 + a))^12*C*a^4*b^(5/2) + 223020*(sqrt(b)*x - sqrt(b*x^2 + a))^12*B*a^3*b^(7/2) - 405300*(sqrt(b)*x - sqrt(b*x^2 + a))^12*A*a^2*b^(9/2) - 81270*(sqrt(b)*x - sqrt(b*x^2 + a))^10*D*a^6*b^(3/2) + 226800*(sqrt(b)*x - sqrt(b*x^2 + a))^10*C*a^5*b^(5/2) - 495180*(sqrt(b)*x - sqrt(b*x^2 + a))^10*B*a^4*b^(7/2) + 927360*(sqrt(b)*x - sqrt(b*x^2 + a))^10*A*a^3*b^(9/2) + 103950*(sqrt(b)*x - sqrt(b*x^2 + a))^8*D*a^7*b^(3/2) - 297108*(sqrt(b)*x - sqrt(b*x^2 + a))^8*C*a^6*b^(5/2) + 666036*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a^5*b^(7/2) - 1291374*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*a^4*b^(9/2) - 84210*(sqrt(b)*x - sqrt(b*x^2 + a))^6*D*a^8*b^(3/2) + 243432*(sqrt(b)*x - sqrt(b*x^2 + a))^6*C*a^7*b^(5/2) - 551124*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^6*b^(7/2) + 1073856*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a^5*b^(9/2) + 42210*(sqrt(b)*x - sqrt(b*x^2 + a))^4*D*a^9*b^(3/2) - 121968*(sqrt(b)*x - sqrt(b*x^2 + a))^4*C*a^8*b^(5/2) + 275076*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^7*b^(7/2) - 533124*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^6*b^(9/2) - 11970*(sqrt(b)*x - sqrt(b*x^2 + a))^2*D*a^10*b^(3/2) + 34272*(sqrt(b)*x - sqrt(b*x^2 + a))^2*C*a^9*b^(5/2) - 76644*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^8*b^(7/2) + 147456*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^7*b^(9/2) + 1470*D*a^11*b^(3/2) - 4158*C*a^10*b^(5/2) + 9216*B*a^9*b^(7/2) - 17609*A*a^8*b^(9/2))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^9*a^8)","B",0
169,1,264,0,0.453961," ","integrate((f*x^11+e*x^9+d*x^7+c*x^5)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(a^{2} b^{3} c - a^{3} b^{2} d - a^{5} f + a^{4} b e\right)} \sqrt{b x^{2} + a}}{b^{6}} + \frac{693 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{3} c - 2310 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{3} c + 495 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b^{2} d - 2079 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b^{2} d + 3465 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b^{2} d + 315 \, {\left(b x^{2} + a\right)}^{\frac{11}{2}} f - 1925 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} a f + 4950 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} f - 6930 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3} f + 5775 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4} f + 385 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} b e - 1980 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a b e + 4158 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2} b e - 4620 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3} b e}{3465 \, b^{6}}"," ",0,"(a^2*b^3*c - a^3*b^2*d - a^5*f + a^4*b*e)*sqrt(b*x^2 + a)/b^6 + 1/3465*(693*(b*x^2 + a)^(5/2)*b^3*c - 2310*(b*x^2 + a)^(3/2)*a*b^3*c + 495*(b*x^2 + a)^(7/2)*b^2*d - 2079*(b*x^2 + a)^(5/2)*a*b^2*d + 3465*(b*x^2 + a)^(3/2)*a^2*b^2*d + 315*(b*x^2 + a)^(11/2)*f - 1925*(b*x^2 + a)^(9/2)*a*f + 4950*(b*x^2 + a)^(7/2)*a^2*f - 6930*(b*x^2 + a)^(5/2)*a^3*f + 5775*(b*x^2 + a)^(3/2)*a^4*f + 385*(b*x^2 + a)^(9/2)*b*e - 1980*(b*x^2 + a)^(7/2)*a*b*e + 4158*(b*x^2 + a)^(5/2)*a^2*b*e - 4620*(b*x^2 + a)^(3/2)*a^3*b*e)/b^6","A",0
170,1,197,0,0.498493," ","integrate((f*x^9+e*x^7+d*x^5+c*x^3)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(a b^{3} c - a^{2} b^{2} d - a^{4} f + a^{3} b e\right)} \sqrt{b x^{2} + a}}{b^{5}} + \frac{105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3} c + 63 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b^{2} d - 210 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b^{2} d + 35 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} f - 180 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a f + 378 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2} f - 420 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3} f + 45 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} b e - 189 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a b e + 315 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b e}{315 \, b^{5}}"," ",0,"-(a*b^3*c - a^2*b^2*d - a^4*f + a^3*b*e)*sqrt(b*x^2 + a)/b^5 + 1/315*(105*(b*x^2 + a)^(3/2)*b^3*c + 63*(b*x^2 + a)^(5/2)*b^2*d - 210*(b*x^2 + a)^(3/2)*a*b^2*d + 35*(b*x^2 + a)^(9/2)*f - 180*(b*x^2 + a)^(7/2)*a*f + 378*(b*x^2 + a)^(5/2)*a^2*f - 420*(b*x^2 + a)^(3/2)*a^3*f + 45*(b*x^2 + a)^(7/2)*b*e - 189*(b*x^2 + a)^(5/2)*a*b*e + 315*(b*x^2 + a)^(3/2)*a^2*b*e)/b^5","A",0
171,1,130,0,0.397650," ","integrate((f*x^7+e*x^5+d*x^3+c*x)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(b^{3} c - a b^{2} d - a^{3} f + a^{2} b e\right)} \sqrt{b x^{2} + a}}{b^{4}} + \frac{35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2} d + 15 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} f - 63 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a f + 105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} f + 21 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} b e - 70 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a b e}{105 \, b^{4}}"," ",0,"(b^3*c - a*b^2*d - a^3*f + a^2*b*e)*sqrt(b*x^2 + a)/b^4 + 1/105*(35*(b*x^2 + a)^(3/2)*b^2*d + 15*(b*x^2 + a)^(7/2)*f - 63*(b*x^2 + a)^(5/2)*a*f + 105*(b*x^2 + a)^(3/2)*a^2*f + 21*(b*x^2 + a)^(5/2)*b*e - 70*(b*x^2 + a)^(3/2)*a*b*e)/b^4","A",0
172,1,224,0,0.558621," ","integrate(x^2*(F*x^8+D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left({\left({\left(\frac{105 \, F x^{2}}{b} + \frac{2 \, {\left(792 \, F a^{4} b^{7} - 176 \, D a^{3} b^{8} + 15 \, C a^{2} b^{9} + 6 \, B a b^{10} + 8 \, A b^{11}\right)}}{a^{3} b^{9}}\right)} x^{2} + \frac{14 \, {\left(261 \, F a^{5} b^{6} - 58 \, D a^{4} b^{7} + 3 \, B a^{2} b^{9} + 4 \, A a b^{10}\right)}}{a^{3} b^{9}}\right)} x^{2} + \frac{70 \, {\left(45 \, F a^{6} b^{5} - 10 \, D a^{5} b^{6} + A a^{2} b^{9}\right)}}{a^{3} b^{9}}\right)} x^{2} + \frac{105 \, {\left(9 \, F a^{7} b^{4} - 2 \, D a^{6} b^{5}\right)}}{a^{3} b^{9}}\right)} x}{210 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} + \frac{{\left(9 \, F a - 2 \, D b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{11}{2}}}"," ",0,"1/210*((((105*F*x^2/b + 2*(792*F*a^4*b^7 - 176*D*a^3*b^8 + 15*C*a^2*b^9 + 6*B*a*b^10 + 8*A*b^11)/(a^3*b^9))*x^2 + 14*(261*F*a^5*b^6 - 58*D*a^4*b^7 + 3*B*a^2*b^9 + 4*A*a*b^10)/(a^3*b^9))*x^2 + 70*(45*F*a^6*b^5 - 10*D*a^5*b^6 + A*a^2*b^9)/(a^3*b^9))*x^2 + 105*(9*F*a^7*b^4 - 2*D*a^6*b^5)/(a^3*b^9))*x/(b*x^2 + a)^(7/2) + 1/2*(9*F*a - 2*D*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(11/2)","A",0
173,1,204,0,0.589513," ","integrate((F*x^8+D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""giac"")","-\frac{{\left({\left(x^{2} {\left(\frac{{\left(176 \, F a^{4} b^{6} - 15 \, D a^{3} b^{7} - 6 \, C a^{2} b^{8} - 8 \, B a b^{9} - 48 \, A b^{10}\right)} x^{2}}{a^{4} b^{7}} + \frac{7 \, {\left(58 \, F a^{5} b^{5} - 3 \, C a^{3} b^{7} - 4 \, B a^{2} b^{8} - 24 \, A a b^{9}\right)}}{a^{4} b^{7}}\right)} + \frac{35 \, {\left(10 \, F a^{6} b^{4} - B a^{3} b^{7} - 6 \, A a^{2} b^{8}\right)}}{a^{4} b^{7}}\right)} x^{2} + \frac{105 \, {\left(F a^{7} b^{3} - A a^{3} b^{7}\right)}}{a^{4} b^{7}}\right)} x}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} - \frac{F \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{b^{\frac{9}{2}}}"," ",0,"-1/105*((x^2*((176*F*a^4*b^6 - 15*D*a^3*b^7 - 6*C*a^2*b^8 - 8*B*a*b^9 - 48*A*b^10)*x^2/(a^4*b^7) + 7*(58*F*a^5*b^5 - 3*C*a^3*b^7 - 4*B*a^2*b^8 - 24*A*a*b^9)/(a^4*b^7)) + 35*(10*F*a^6*b^4 - B*a^3*b^7 - 6*A*a^2*b^8)/(a^4*b^7))*x^2 + 105*(F*a^7*b^3 - A*a^3*b^7)/(a^4*b^7))*x/(b*x^2 + a)^(7/2) - F*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(9/2)","A",0
174,1,220,0,0.602135," ","integrate((F*x^8+D*x^6+C*x^4+B*x^2+A)/x^2/(b*x^2+a)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(x^{2} {\left(\frac{{\left(15 \, F a^{13} b^{3} + 6 \, D a^{12} b^{4} + 8 \, C a^{11} b^{5} + 48 \, B a^{10} b^{6} - 279 \, A a^{9} b^{7}\right)} x^{2}}{a^{14} b^{3}} + \frac{7 \, {\left(3 \, D a^{13} b^{3} + 4 \, C a^{12} b^{4} + 24 \, B a^{11} b^{5} - 132 \, A a^{10} b^{6}\right)}}{a^{14} b^{3}}\right)} + \frac{35 \, {\left(C a^{13} b^{3} + 6 \, B a^{12} b^{4} - 30 \, A a^{11} b^{5}\right)}}{a^{14} b^{3}}\right)} x^{2} + \frac{105 \, {\left(B a^{13} b^{3} - 4 \, A a^{12} b^{4}\right)}}{a^{14} b^{3}}\right)} x}{105 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}}} + \frac{2 \, A \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)} a^{4}}"," ",0,"1/105*((x^2*((15*F*a^13*b^3 + 6*D*a^12*b^4 + 8*C*a^11*b^5 + 48*B*a^10*b^6 - 279*A*a^9*b^7)*x^2/(a^14*b^3) + 7*(3*D*a^13*b^3 + 4*C*a^12*b^4 + 24*B*a^11*b^5 - 132*A*a^10*b^6)/(a^14*b^3)) + 35*(C*a^13*b^3 + 6*B*a^12*b^4 - 30*A*a^11*b^5)/(a^14*b^3))*x^2 + 105*(B*a^13*b^3 - 4*A*a^12*b^4)/(a^14*b^3))*x/(b*x^2 + a)^(7/2) + 2*A*sqrt(b)/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)*a^4)","A",0
