1,1,206,0,0.912928," ","integrate(x^3*(B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, B a^{3} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(40 \, B b^{3} x^{5} + 48 \, A b^{3} x^{4} + 10 \, B a b^{2} x^{3} + 16 \, A a b^{2} x^{2} - 15 \, B a^{2} b x - 32 \, A a^{2} b\right)} \sqrt{b x^{2} + a}}{480 \, b^{3}}, -\frac{15 \, B a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(40 \, B b^{3} x^{5} + 48 \, A b^{3} x^{4} + 10 \, B a b^{2} x^{3} + 16 \, A a b^{2} x^{2} - 15 \, B a^{2} b x - 32 \, A a^{2} b\right)} \sqrt{b x^{2} + a}}{240 \, b^{3}}\right]"," ",0,"[1/480*(15*B*a^3*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(40*B*b^3*x^5 + 48*A*b^3*x^4 + 10*B*a*b^2*x^3 + 16*A*a*b^2*x^2 - 15*B*a^2*b*x - 32*A*a^2*b)*sqrt(b*x^2 + a))/b^3, -1/240*(15*B*a^3*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (40*B*b^3*x^5 + 48*A*b^3*x^4 + 10*B*a*b^2*x^3 + 16*A*a*b^2*x^2 - 15*B*a^2*b*x - 32*A*a^2*b)*sqrt(b*x^2 + a))/b^3]","A",0
2,1,175,0,0.996945," ","integrate(x^2*(B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, A a^{2} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(24 \, B b^{2} x^{4} + 30 \, A b^{2} x^{3} + 8 \, B a b x^{2} + 15 \, A a b x - 16 \, B a^{2}\right)} \sqrt{b x^{2} + a}}{240 \, b^{2}}, \frac{15 \, A a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(24 \, B b^{2} x^{4} + 30 \, A b^{2} x^{3} + 8 \, B a b x^{2} + 15 \, A a b x - 16 \, B a^{2}\right)} \sqrt{b x^{2} + a}}{120 \, b^{2}}\right]"," ",0,"[1/240*(15*A*a^2*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(24*B*b^2*x^4 + 30*A*b^2*x^3 + 8*B*a*b*x^2 + 15*A*a*b*x - 16*B*a^2)*sqrt(b*x^2 + a))/b^2, 1/120*(15*A*a^2*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (24*B*b^2*x^4 + 30*A*b^2*x^3 + 8*B*a*b*x^2 + 15*A*a*b*x - 16*B*a^2)*sqrt(b*x^2 + a))/b^2]","A",0
3,1,157,0,0.664386," ","integrate(x*(B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, B a^{2} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(6 \, B b^{2} x^{3} + 8 \, A b^{2} x^{2} + 3 \, B a b x + 8 \, A a b\right)} \sqrt{b x^{2} + a}}{48 \, b^{2}}, \frac{3 \, B a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(6 \, B b^{2} x^{3} + 8 \, A b^{2} x^{2} + 3 \, B a b x + 8 \, A a b\right)} \sqrt{b x^{2} + a}}{24 \, b^{2}}\right]"," ",0,"[1/48*(3*B*a^2*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(6*B*b^2*x^3 + 8*A*b^2*x^2 + 3*B*a*b*x + 8*A*a*b)*sqrt(b*x^2 + a))/b^2, 1/24*(3*B*a^2*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (6*B*b^2*x^3 + 8*A*b^2*x^2 + 3*B*a*b*x + 8*A*a*b)*sqrt(b*x^2 + a))/b^2]","A",0
4,1,128,0,0.735185," ","integrate((B*x+A)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, A a \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(2 \, B b x^{2} + 3 \, A b x + 2 \, B a\right)} \sqrt{b x^{2} + a}}{12 \, b}, -\frac{3 \, A a \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, B b x^{2} + 3 \, A b x + 2 \, B a\right)} \sqrt{b x^{2} + a}}{6 \, b}\right]"," ",0,"[1/12*(3*A*a*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(2*B*b*x^2 + 3*A*b*x + 2*B*a)*sqrt(b*x^2 + a))/b, -1/6*(3*A*a*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*B*b*x^2 + 3*A*b*x + 2*B*a)*sqrt(b*x^2 + a))/b]","A",0
5,1,341,0,1.017155," ","integrate((B*x+A)*(b*x^2+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{B a \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, A \sqrt{a} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(B b x + 2 \, A b\right)} \sqrt{b x^{2} + a}}{4 \, b}, -\frac{B a \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - A \sqrt{a} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(B b x + 2 \, A b\right)} \sqrt{b x^{2} + a}}{2 \, b}, \frac{4 \, A \sqrt{-a} b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + B a \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(B b x + 2 \, A b\right)} \sqrt{b x^{2} + a}}{4 \, b}, -\frac{B a \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 2 \, A \sqrt{-a} b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(B b x + 2 \, A b\right)} \sqrt{b x^{2} + a}}{2 \, b}\right]"," ",0,"[1/4*(B*a*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*A*sqrt(a)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(B*b*x + 2*A*b)*sqrt(b*x^2 + a))/b, -1/2*(B*a*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - A*sqrt(a)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - (B*b*x + 2*A*b)*sqrt(b*x^2 + a))/b, 1/4*(4*A*sqrt(-a)*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + B*a*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(B*b*x + 2*A*b)*sqrt(b*x^2 + a))/b, -1/2*(B*a*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 2*A*sqrt(-a)*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (B*b*x + 2*A*b)*sqrt(b*x^2 + a))/b]","A",0
6,1,333,0,0.927084," ","integrate((B*x+A)*(b*x^2+a)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{A \sqrt{b} x \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + B \sqrt{a} x \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, \sqrt{b x^{2} + a} {\left(B x - A\right)}}{2 \, x}, -\frac{2 \, A \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - B \sqrt{a} x \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, \sqrt{b x^{2} + a} {\left(B x - A\right)}}{2 \, x}, \frac{2 \, B \sqrt{-a} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + A \sqrt{b} x \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, \sqrt{b x^{2} + a} {\left(B x - A\right)}}{2 \, x}, -\frac{A \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - B \sqrt{-a} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - \sqrt{b x^{2} + a} {\left(B x - A\right)}}{x}\right]"," ",0,"[1/2*(A*sqrt(b)*x*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + B*sqrt(a)*x*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*sqrt(b*x^2 + a)*(B*x - A))/x, -1/2*(2*A*sqrt(-b)*x*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - B*sqrt(a)*x*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*sqrt(b*x^2 + a)*(B*x - A))/x, 1/2*(2*B*sqrt(-a)*x*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + A*sqrt(b)*x*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*sqrt(b*x^2 + a)*(B*x - A))/x, -(A*sqrt(-b)*x*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - B*sqrt(-a)*x*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - sqrt(b*x^2 + a)*(B*x - A))/x]","A",0
7,1,377,0,0.708040," ","integrate((B*x+A)*(b*x^2+a)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{2 \, B a \sqrt{b} x^{2} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + A \sqrt{a} b x^{2} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(2 \, B a x + A a\right)} \sqrt{b x^{2} + a}}{4 \, a x^{2}}, -\frac{4 \, B a \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - A \sqrt{a} b x^{2} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, B a x + A a\right)} \sqrt{b x^{2} + a}}{4 \, a x^{2}}, \frac{A \sqrt{-a} b x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + B a \sqrt{b} x^{2} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - {\left(2 \, B a x + A a\right)} \sqrt{b x^{2} + a}}{2 \, a x^{2}}, -\frac{2 \, B a \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - A \sqrt{-a} b x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(2 \, B a x + A a\right)} \sqrt{b x^{2} + a}}{2 \, a x^{2}}\right]"," ",0,"[1/4*(2*B*a*sqrt(b)*x^2*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + A*sqrt(a)*b*x^2*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(2*B*a*x + A*a)*sqrt(b*x^2 + a))/(a*x^2), -1/4*(4*B*a*sqrt(-b)*x^2*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - A*sqrt(a)*b*x^2*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*B*a*x + A*a)*sqrt(b*x^2 + a))/(a*x^2), 1/2*(A*sqrt(-a)*b*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + B*a*sqrt(b)*x^2*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - (2*B*a*x + A*a)*sqrt(b*x^2 + a))/(a*x^2), -1/2*(2*B*a*sqrt(-b)*x^2*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - A*sqrt(-a)*b*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (2*B*a*x + A*a)*sqrt(b*x^2 + a))/(a*x^2)]","A",0
8,1,254,0,0.732410," ","integrate(x^3*(B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, B a^{4} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(560 \, B b^{4} x^{7} + 640 \, A b^{4} x^{6} + 840 \, B a b^{3} x^{5} + 1024 \, A a b^{3} x^{4} + 70 \, B a^{2} b^{2} x^{3} + 128 \, A a^{2} b^{2} x^{2} - 105 \, B a^{3} b x - 256 \, A a^{3} b\right)} \sqrt{b x^{2} + a}}{8960 \, b^{3}}, -\frac{105 \, B a^{4} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(560 \, B b^{4} x^{7} + 640 \, A b^{4} x^{6} + 840 \, B a b^{3} x^{5} + 1024 \, A a b^{3} x^{4} + 70 \, B a^{2} b^{2} x^{3} + 128 \, A a^{2} b^{2} x^{2} - 105 \, B a^{3} b x - 256 \, A a^{3} b\right)} \sqrt{b x^{2} + a}}{4480 \, b^{3}}\right]"," ",0,"[1/8960*(105*B*a^4*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(560*B*b^4*x^7 + 640*A*b^4*x^6 + 840*B*a*b^3*x^5 + 1024*A*a*b^3*x^4 + 70*B*a^2*b^2*x^3 + 128*A*a^2*b^2*x^2 - 105*B*a^3*b*x - 256*A*a^3*b)*sqrt(b*x^2 + a))/b^3, -1/4480*(105*B*a^4*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (560*B*b^4*x^7 + 640*A*b^4*x^6 + 840*B*a*b^3*x^5 + 1024*A*a*b^3*x^4 + 70*B*a^2*b^2*x^3 + 128*A*a^2*b^2*x^2 - 105*B*a^3*b*x - 256*A*a^3*b)*sqrt(b*x^2 + a))/b^3]","A",0
9,1,223,0,0.910331," ","integrate(x^2*(B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, A a^{3} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(240 \, B b^{3} x^{6} + 280 \, A b^{3} x^{5} + 384 \, B a b^{2} x^{4} + 490 \, A a b^{2} x^{3} + 48 \, B a^{2} b x^{2} + 105 \, A a^{2} b x - 96 \, B a^{3}\right)} \sqrt{b x^{2} + a}}{3360 \, b^{2}}, \frac{105 \, A a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(240 \, B b^{3} x^{6} + 280 \, A b^{3} x^{5} + 384 \, B a b^{2} x^{4} + 490 \, A a b^{2} x^{3} + 48 \, B a^{2} b x^{2} + 105 \, A a^{2} b x - 96 \, B a^{3}\right)} \sqrt{b x^{2} + a}}{1680 \, b^{2}}\right]"," ",0,"[1/3360*(105*A*a^3*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(240*B*b^3*x^6 + 280*A*b^3*x^5 + 384*B*a*b^2*x^4 + 490*A*a*b^2*x^3 + 48*B*a^2*b*x^2 + 105*A*a^2*b*x - 96*B*a^3)*sqrt(b*x^2 + a))/b^2, 1/1680*(105*A*a^3*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (240*B*b^3*x^6 + 280*A*b^3*x^5 + 384*B*a*b^2*x^4 + 490*A*a*b^2*x^3 + 48*B*a^2*b*x^2 + 105*A*a^2*b*x - 96*B*a^3)*sqrt(b*x^2 + a))/b^2]","A",0
10,1,205,0,0.992665," ","integrate(x*(B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, B a^{3} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(40 \, B b^{3} x^{5} + 48 \, A b^{3} x^{4} + 70 \, B a b^{2} x^{3} + 96 \, A a b^{2} x^{2} + 15 \, B a^{2} b x + 48 \, A a^{2} b\right)} \sqrt{b x^{2} + a}}{480 \, b^{2}}, \frac{15 \, B a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(40 \, B b^{3} x^{5} + 48 \, A b^{3} x^{4} + 70 \, B a b^{2} x^{3} + 96 \, A a b^{2} x^{2} + 15 \, B a^{2} b x + 48 \, A a^{2} b\right)} \sqrt{b x^{2} + a}}{240 \, b^{2}}\right]"," ",0,"[1/480*(15*B*a^3*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(40*B*b^3*x^5 + 48*A*b^3*x^4 + 70*B*a*b^2*x^3 + 96*A*a*b^2*x^2 + 15*B*a^2*b*x + 48*A*a^2*b)*sqrt(b*x^2 + a))/b^2, 1/240*(15*B*a^3*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (40*B*b^3*x^5 + 48*A*b^3*x^4 + 70*B*a*b^2*x^3 + 96*A*a*b^2*x^2 + 15*B*a^2*b*x + 48*A*a^2*b)*sqrt(b*x^2 + a))/b^2]","A",0
11,1,176,0,0.924732," ","integrate((B*x+A)*(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, A a^{2} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(8 \, B b^{2} x^{4} + 10 \, A b^{2} x^{3} + 16 \, B a b x^{2} + 25 \, A a b x + 8 \, B a^{2}\right)} \sqrt{b x^{2} + a}}{80 \, b}, -\frac{15 \, A a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, B b^{2} x^{4} + 10 \, A b^{2} x^{3} + 16 \, B a b x^{2} + 25 \, A a b x + 8 \, B a^{2}\right)} \sqrt{b x^{2} + a}}{40 \, b}\right]"," ",0,"[1/80*(15*A*a^2*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(8*B*b^2*x^4 + 10*A*b^2*x^3 + 16*B*a*b*x^2 + 25*A*a*b*x + 8*B*a^2)*sqrt(b*x^2 + a))/b, -1/40*(15*A*a^2*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8*B*b^2*x^4 + 10*A*b^2*x^3 + 16*B*a*b*x^2 + 25*A*a*b*x + 8*B*a^2)*sqrt(b*x^2 + a))/b]","A",0
12,1,439,0,0.887955," ","integrate((B*x+A)*(b*x^2+a)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{9 \, B a^{2} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 24 \, A a^{\frac{3}{2}} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(6 \, B b^{2} x^{3} + 8 \, A b^{2} x^{2} + 15 \, B a b x + 32 \, A a b\right)} \sqrt{b x^{2} + a}}{48 \, b}, -\frac{9 \, B a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 12 \, A a^{\frac{3}{2}} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(6 \, B b^{2} x^{3} + 8 \, A b^{2} x^{2} + 15 \, B a b x + 32 \, A a b\right)} \sqrt{b x^{2} + a}}{24 \, b}, \frac{48 \, A \sqrt{-a} a b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + 9 \, B a^{2} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(6 \, B b^{2} x^{3} + 8 \, A b^{2} x^{2} + 15 \, B a b x + 32 \, A a b\right)} \sqrt{b x^{2} + a}}{48 \, b}, -\frac{9 \, B a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 24 \, A \sqrt{-a} a b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(6 \, B b^{2} x^{3} + 8 \, A b^{2} x^{2} + 15 \, B a b x + 32 \, A a b\right)} \sqrt{b x^{2} + a}}{24 \, b}\right]"," ",0,"[1/48*(9*B*a^2*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 24*A*a^(3/2)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(6*B*b^2*x^3 + 8*A*b^2*x^2 + 15*B*a*b*x + 32*A*a*b)*sqrt(b*x^2 + a))/b, -1/24*(9*B*a^2*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 12*A*a^(3/2)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - (6*B*b^2*x^3 + 8*A*b^2*x^2 + 15*B*a*b*x + 32*A*a*b)*sqrt(b*x^2 + a))/b, 1/48*(48*A*sqrt(-a)*a*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + 9*B*a^2*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(6*B*b^2*x^3 + 8*A*b^2*x^2 + 15*B*a*b*x + 32*A*a*b)*sqrt(b*x^2 + a))/b, -1/24*(9*B*a^2*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 24*A*sqrt(-a)*a*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (6*B*b^2*x^3 + 8*A*b^2*x^2 + 15*B*a*b*x + 32*A*a*b)*sqrt(b*x^2 + a))/b]","A",0
13,1,411,0,0.848785," ","integrate((B*x+A)*(b*x^2+a)^(3/2)/x^2,x, algorithm=""fricas"")","\left[\frac{9 \, A a \sqrt{b} x \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 6 \, B a^{\frac{3}{2}} x \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, B b x^{3} + 3 \, A b x^{2} + 8 \, B a x - 6 \, A a\right)} \sqrt{b x^{2} + a}}{12 \, x}, -\frac{9 \, A a \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 3 \, B a^{\frac{3}{2}} x \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(2 \, B b x^{3} + 3 \, A b x^{2} + 8 \, B a x - 6 \, A a\right)} \sqrt{b x^{2} + a}}{6 \, x}, \frac{12 \, B \sqrt{-a} a x \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + 9 \, A a \sqrt{b} x \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(2 \, B b x^{3} + 3 \, A b x^{2} + 8 \, B a x - 6 \, A a\right)} \sqrt{b x^{2} + a}}{12 \, x}, -\frac{9 \, A a \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 6 \, B \sqrt{-a} a x \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, B b x^{3} + 3 \, A b x^{2} + 8 \, B a x - 6 \, A a\right)} \sqrt{b x^{2} + a}}{6 \, x}\right]"," ",0,"[1/12*(9*A*a*sqrt(b)*x*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 6*B*a^(3/2)*x*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*B*b*x^3 + 3*A*b*x^2 + 8*B*a*x - 6*A*a)*sqrt(b*x^2 + a))/x, -1/6*(9*A*a*sqrt(-b)*x*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 3*B*a^(3/2)*x*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - (2*B*b*x^3 + 3*A*b*x^2 + 8*B*a*x - 6*A*a)*sqrt(b*x^2 + a))/x, 1/12*(12*B*sqrt(-a)*a*x*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + 9*A*a*sqrt(b)*x*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(2*B*b*x^3 + 3*A*b*x^2 + 8*B*a*x - 6*A*a)*sqrt(b*x^2 + a))/x, -1/6*(9*A*a*sqrt(-b)*x*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 6*B*sqrt(-a)*a*x*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (2*B*b*x^3 + 3*A*b*x^2 + 8*B*a*x - 6*A*a)*sqrt(b*x^2 + a))/x]","A",0
14,1,425,0,0.978484," ","integrate((B*x+A)*(b*x^2+a)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, B a \sqrt{b} x^{2} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 3 \, A \sqrt{a} b x^{2} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(B b x^{3} + 2 \, A b x^{2} - 2 \, B a x - A a\right)} \sqrt{b x^{2} + a}}{4 \, x^{2}}, -\frac{6 \, B a \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 3 \, A \sqrt{a} b x^{2} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(B b x^{3} + 2 \, A b x^{2} - 2 \, B a x - A a\right)} \sqrt{b x^{2} + a}}{4 \, x^{2}}, \frac{6 \, A \sqrt{-a} b x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + 3 \, B a \sqrt{b} x^{2} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(B b x^{3} + 2 \, A b x^{2} - 2 \, B a x - A a\right)} \sqrt{b x^{2} + a}}{4 \, x^{2}}, -\frac{3 \, B a \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 3 \, A \sqrt{-a} b x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(B b x^{3} + 2 \, A b x^{2} - 2 \, B a x - A a\right)} \sqrt{b x^{2} + a}}{2 \, x^{2}}\right]"," ",0,"[1/4*(3*B*a*sqrt(b)*x^2*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 3*A*sqrt(a)*b*x^2*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(B*b*x^3 + 2*A*b*x^2 - 2*B*a*x - A*a)*sqrt(b*x^2 + a))/x^2, -1/4*(6*B*a*sqrt(-b)*x^2*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 3*A*sqrt(a)*b*x^2*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(B*b*x^3 + 2*A*b*x^2 - 2*B*a*x - A*a)*sqrt(b*x^2 + a))/x^2, 1/4*(6*A*sqrt(-a)*b*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + 3*B*a*sqrt(b)*x^2*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(B*b*x^3 + 2*A*b*x^2 - 2*B*a*x - A*a)*sqrt(b*x^2 + a))/x^2, -1/2*(3*B*a*sqrt(-b)*x^2*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 3*A*sqrt(-a)*b*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (B*b*x^3 + 2*A*b*x^2 - 2*B*a*x - A*a)*sqrt(b*x^2 + a))/x^2]","A",0
15,1,302,0,1.017850," ","integrate(x^3*(B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{945 \, B a^{5} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(8064 \, B b^{5} x^{9} + 8960 \, A b^{5} x^{8} + 21168 \, B a b^{4} x^{7} + 24320 \, A a b^{4} x^{6} + 15624 \, B a^{2} b^{3} x^{5} + 19200 \, A a^{2} b^{3} x^{4} + 630 \, B a^{3} b^{2} x^{3} + 1280 \, A a^{3} b^{2} x^{2} - 945 \, B a^{4} b x - 2560 \, A a^{4} b\right)} \sqrt{b x^{2} + a}}{161280 \, b^{3}}, -\frac{945 \, B a^{5} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8064 \, B b^{5} x^{9} + 8960 \, A b^{5} x^{8} + 21168 \, B a b^{4} x^{7} + 24320 \, A a b^{4} x^{6} + 15624 \, B a^{2} b^{3} x^{5} + 19200 \, A a^{2} b^{3} x^{4} + 630 \, B a^{3} b^{2} x^{3} + 1280 \, A a^{3} b^{2} x^{2} - 945 \, B a^{4} b x - 2560 \, A a^{4} b\right)} \sqrt{b x^{2} + a}}{80640 \, b^{3}}\right]"," ",0,"[1/161280*(945*B*a^5*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(8064*B*b^5*x^9 + 8960*A*b^5*x^8 + 21168*B*a*b^4*x^7 + 24320*A*a*b^4*x^6 + 15624*B*a^2*b^3*x^5 + 19200*A*a^2*b^3*x^4 + 630*B*a^3*b^2*x^3 + 1280*A*a^3*b^2*x^2 - 945*B*a^4*b*x - 2560*A*a^4*b)*sqrt(b*x^2 + a))/b^3, -1/80640*(945*B*a^5*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8064*B*b^5*x^9 + 8960*A*b^5*x^8 + 21168*B*a*b^4*x^7 + 24320*A*a*b^4*x^6 + 15624*B*a^2*b^3*x^5 + 19200*A*a^2*b^3*x^4 + 630*B*a^3*b^2*x^3 + 1280*A*a^3*b^2*x^2 - 945*B*a^4*b*x - 2560*A*a^4*b)*sqrt(b*x^2 + a))/b^3]","A",0
16,1,271,0,0.801213," ","integrate(x^2*(B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, A a^{4} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(896 \, B b^{4} x^{8} + 1008 \, A b^{4} x^{7} + 2432 \, B a b^{3} x^{6} + 2856 \, A a b^{3} x^{5} + 1920 \, B a^{2} b^{2} x^{4} + 2478 \, A a^{2} b^{2} x^{3} + 128 \, B a^{3} b x^{2} + 315 \, A a^{3} b x - 256 \, B a^{4}\right)} \sqrt{b x^{2} + a}}{16128 \, b^{2}}, \frac{315 \, A a^{4} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(896 \, B b^{4} x^{8} + 1008 \, A b^{4} x^{7} + 2432 \, B a b^{3} x^{6} + 2856 \, A a b^{3} x^{5} + 1920 \, B a^{2} b^{2} x^{4} + 2478 \, A a^{2} b^{2} x^{3} + 128 \, B a^{3} b x^{2} + 315 \, A a^{3} b x - 256 \, B a^{4}\right)} \sqrt{b x^{2} + a}}{8064 \, b^{2}}\right]"," ",0,"[1/16128*(315*A*a^4*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(896*B*b^4*x^8 + 1008*A*b^4*x^7 + 2432*B*a*b^3*x^6 + 2856*A*a*b^3*x^5 + 1920*B*a^2*b^2*x^4 + 2478*A*a^2*b^2*x^3 + 128*B*a^3*b*x^2 + 315*A*a^3*b*x - 256*B*a^4)*sqrt(b*x^2 + a))/b^2, 1/8064*(315*A*a^4*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (896*B*b^4*x^8 + 1008*A*b^4*x^7 + 2432*B*a*b^3*x^6 + 2856*A*a*b^3*x^5 + 1920*B*a^2*b^2*x^4 + 2478*A*a^2*b^2*x^3 + 128*B*a^3*b*x^2 + 315*A*a^3*b*x - 256*B*a^4)*sqrt(b*x^2 + a))/b^2]","A",0
17,1,253,0,1.017987," ","integrate(x*(B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, B a^{4} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(336 \, B b^{4} x^{7} + 384 \, A b^{4} x^{6} + 952 \, B a b^{3} x^{5} + 1152 \, A a b^{3} x^{4} + 826 \, B a^{2} b^{2} x^{3} + 1152 \, A a^{2} b^{2} x^{2} + 105 \, B a^{3} b x + 384 \, A a^{3} b\right)} \sqrt{b x^{2} + a}}{5376 \, b^{2}}, \frac{105 \, B a^{4} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(336 \, B b^{4} x^{7} + 384 \, A b^{4} x^{6} + 952 \, B a b^{3} x^{5} + 1152 \, A a b^{3} x^{4} + 826 \, B a^{2} b^{2} x^{3} + 1152 \, A a^{2} b^{2} x^{2} + 105 \, B a^{3} b x + 384 \, A a^{3} b\right)} \sqrt{b x^{2} + a}}{2688 \, b^{2}}\right]"," ",0,"[1/5376*(105*B*a^4*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(336*B*b^4*x^7 + 384*A*b^4*x^6 + 952*B*a*b^3*x^5 + 1152*A*a*b^3*x^4 + 826*B*a^2*b^2*x^3 + 1152*A*a^2*b^2*x^2 + 105*B*a^3*b*x + 384*A*a^3*b)*sqrt(b*x^2 + a))/b^2, 1/2688*(105*B*a^4*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (336*B*b^4*x^7 + 384*A*b^4*x^6 + 952*B*a*b^3*x^5 + 1152*A*a*b^3*x^4 + 826*B*a^2*b^2*x^3 + 1152*A*a^2*b^2*x^2 + 105*B*a^3*b*x + 384*A*a^3*b)*sqrt(b*x^2 + a))/b^2]","A",0
18,1,224,0,0.563983," ","integrate((B*x+A)*(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, A a^{3} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(48 \, B b^{3} x^{6} + 56 \, A b^{3} x^{5} + 144 \, B a b^{2} x^{4} + 182 \, A a b^{2} x^{3} + 144 \, B a^{2} b x^{2} + 231 \, A a^{2} b x + 48 \, B a^{3}\right)} \sqrt{b x^{2} + a}}{672 \, b}, -\frac{105 \, A a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(48 \, B b^{3} x^{6} + 56 \, A b^{3} x^{5} + 144 \, B a b^{2} x^{4} + 182 \, A a b^{2} x^{3} + 144 \, B a^{2} b x^{2} + 231 \, A a^{2} b x + 48 \, B a^{3}\right)} \sqrt{b x^{2} + a}}{336 \, b}\right]"," ",0,"[1/672*(105*A*a^3*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(48*B*b^3*x^6 + 56*A*b^3*x^5 + 144*B*a*b^2*x^4 + 182*A*a*b^2*x^3 + 144*B*a^2*b*x^2 + 231*A*a^2*b*x + 48*B*a^3)*sqrt(b*x^2 + a))/b, -1/336*(105*A*a^3*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (48*B*b^3*x^6 + 56*A*b^3*x^5 + 144*B*a*b^2*x^4 + 182*A*a*b^2*x^3 + 144*B*a^2*b*x^2 + 231*A*a^2*b*x + 48*B*a^3)*sqrt(b*x^2 + a))/b]","A",0
19,1,539,0,0.926661," ","integrate((B*x+A)*(b*x^2+a)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{75 \, B a^{3} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 240 \, A a^{\frac{5}{2}} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(40 \, B b^{3} x^{5} + 48 \, A b^{3} x^{4} + 130 \, B a b^{2} x^{3} + 176 \, A a b^{2} x^{2} + 165 \, B a^{2} b x + 368 \, A a^{2} b\right)} \sqrt{b x^{2} + a}}{480 \, b}, -\frac{75 \, B a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 120 \, A a^{\frac{5}{2}} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(40 \, B b^{3} x^{5} + 48 \, A b^{3} x^{4} + 130 \, B a b^{2} x^{3} + 176 \, A a b^{2} x^{2} + 165 \, B a^{2} b x + 368 \, A a^{2} b\right)} \sqrt{b x^{2} + a}}{240 \, b}, \frac{480 \, A \sqrt{-a} a^{2} b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + 75 \, B a^{3} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(40 \, B b^{3} x^{5} + 48 \, A b^{3} x^{4} + 130 \, B a b^{2} x^{3} + 176 \, A a b^{2} x^{2} + 165 \, B a^{2} b x + 368 \, A a^{2} b\right)} \sqrt{b x^{2} + a}}{480 \, b}, -\frac{75 \, B a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 240 \, A \sqrt{-a} a^{2} b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(40 \, B b^{3} x^{5} + 48 \, A b^{3} x^{4} + 130 \, B a b^{2} x^{3} + 176 \, A a b^{2} x^{2} + 165 \, B a^{2} b x + 368 \, A a^{2} b\right)} \sqrt{b x^{2} + a}}{240 \, b}\right]"," ",0,"[1/480*(75*B*a^3*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 240*A*a^(5/2)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(40*B*b^3*x^5 + 48*A*b^3*x^4 + 130*B*a*b^2*x^3 + 176*A*a*b^2*x^2 + 165*B*a^2*b*x + 368*A*a^2*b)*sqrt(b*x^2 + a))/b, -1/240*(75*B*a^3*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 120*A*a^(5/2)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - (40*B*b^3*x^5 + 48*A*b^3*x^4 + 130*B*a*b^2*x^3 + 176*A*a*b^2*x^2 + 165*B*a^2*b*x + 368*A*a^2*b)*sqrt(b*x^2 + a))/b, 1/480*(480*A*sqrt(-a)*a^2*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + 75*B*a^3*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(40*B*b^3*x^5 + 48*A*b^3*x^4 + 130*B*a*b^2*x^3 + 176*A*a*b^2*x^2 + 165*B*a^2*b*x + 368*A*a^2*b)*sqrt(b*x^2 + a))/b, -1/240*(75*B*a^3*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 240*A*sqrt(-a)*a^2*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (40*B*b^3*x^5 + 48*A*b^3*x^4 + 130*B*a*b^2*x^3 + 176*A*a*b^2*x^2 + 165*B*a^2*b*x + 368*A*a^2*b)*sqrt(b*x^2 + a))/b]","A",0
20,1,519,0,0.946494," ","integrate((B*x+A)*(b*x^2+a)^(5/2)/x^2,x, algorithm=""fricas"")","\left[\frac{225 \, A a^{2} \sqrt{b} x \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 120 \, B a^{\frac{5}{2}} x \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(24 \, B b^{2} x^{5} + 30 \, A b^{2} x^{4} + 88 \, B a b x^{3} + 135 \, A a b x^{2} + 184 \, B a^{2} x - 120 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{240 \, x}, -\frac{225 \, A a^{2} \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 60 \, B a^{\frac{5}{2}} x \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(24 \, B b^{2} x^{5} + 30 \, A b^{2} x^{4} + 88 \, B a b x^{3} + 135 \, A a b x^{2} + 184 \, B a^{2} x - 120 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{120 \, x}, \frac{240 \, B \sqrt{-a} a^{2} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + 225 \, A a^{2} \sqrt{b} x \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(24 \, B b^{2} x^{5} + 30 \, A b^{2} x^{4} + 88 \, B a b x^{3} + 135 \, A a b x^{2} + 184 \, B a^{2} x - 120 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{240 \, x}, -\frac{225 \, A a^{2} \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 120 \, B \sqrt{-a} a^{2} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(24 \, B b^{2} x^{5} + 30 \, A b^{2} x^{4} + 88 \, B a b x^{3} + 135 \, A a b x^{2} + 184 \, B a^{2} x - 120 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{120 \, x}\right]"," ",0,"[1/240*(225*A*a^2*sqrt(b)*x*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 120*B*a^(5/2)*x*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(24*B*b^2*x^5 + 30*A*b^2*x^4 + 88*B*a*b*x^3 + 135*A*a*b*x^2 + 184*B*a^2*x - 120*A*a^2)*sqrt(b*x^2 + a))/x, -1/120*(225*A*a^2*sqrt(-b)*x*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 60*B*a^(5/2)*x*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - (24*B*b^2*x^5 + 30*A*b^2*x^4 + 88*B*a*b*x^3 + 135*A*a*b*x^2 + 184*B*a^2*x - 120*A*a^2)*sqrt(b*x^2 + a))/x, 1/240*(240*B*sqrt(-a)*a^2*x*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + 225*A*a^2*sqrt(b)*x*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(24*B*b^2*x^5 + 30*A*b^2*x^4 + 88*B*a*b*x^3 + 135*A*a*b*x^2 + 184*B*a^2*x - 120*A*a^2)*sqrt(b*x^2 + a))/x, -1/120*(225*A*a^2*sqrt(-b)*x*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 120*B*sqrt(-a)*a^2*x*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (24*B*b^2*x^5 + 30*A*b^2*x^4 + 88*B*a*b*x^3 + 135*A*a*b*x^2 + 184*B*a^2*x - 120*A*a^2)*sqrt(b*x^2 + a))/x]","A",0
21,1,535,0,0.580769," ","integrate((B*x+A)*(b*x^2+a)^(5/2)/x^3,x, algorithm=""fricas"")","\left[\frac{45 \, B a^{2} \sqrt{b} x^{2} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 60 \, A a^{\frac{3}{2}} b x^{2} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(6 \, B b^{2} x^{5} + 8 \, A b^{2} x^{4} + 27 \, B a b x^{3} + 56 \, A a b x^{2} - 24 \, B a^{2} x - 12 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{48 \, x^{2}}, -\frac{45 \, B a^{2} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 30 \, A a^{\frac{3}{2}} b x^{2} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - {\left(6 \, B b^{2} x^{5} + 8 \, A b^{2} x^{4} + 27 \, B a b x^{3} + 56 \, A a b x^{2} - 24 \, B a^{2} x - 12 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{24 \, x^{2}}, \frac{120 \, A \sqrt{-a} a b x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + 45 \, B a^{2} \sqrt{b} x^{2} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(6 \, B b^{2} x^{5} + 8 \, A b^{2} x^{4} + 27 \, B a b x^{3} + 56 \, A a b x^{2} - 24 \, B a^{2} x - 12 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{48 \, x^{2}}, -\frac{45 \, B a^{2} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - 60 \, A \sqrt{-a} a b x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(6 \, B b^{2} x^{5} + 8 \, A b^{2} x^{4} + 27 \, B a b x^{3} + 56 \, A a b x^{2} - 24 \, B a^{2} x - 12 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{24 \, x^{2}}\right]"," ",0,"[1/48*(45*B*a^2*sqrt(b)*x^2*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 60*A*a^(3/2)*b*x^2*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(6*B*b^2*x^5 + 8*A*b^2*x^4 + 27*B*a*b*x^3 + 56*A*a*b*x^2 - 24*B*a^2*x - 12*A*a^2)*sqrt(b*x^2 + a))/x^2, -1/24*(45*B*a^2*sqrt(-b)*x^2*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 30*A*a^(3/2)*b*x^2*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - (6*B*b^2*x^5 + 8*A*b^2*x^4 + 27*B*a*b*x^3 + 56*A*a*b*x^2 - 24*B*a^2*x - 12*A*a^2)*sqrt(b*x^2 + a))/x^2, 1/48*(120*A*sqrt(-a)*a*b*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + 45*B*a^2*sqrt(b)*x^2*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(6*B*b^2*x^5 + 8*A*b^2*x^4 + 27*B*a*b*x^3 + 56*A*a*b*x^2 - 24*B*a^2*x - 12*A*a^2)*sqrt(b*x^2 + a))/x^2, -1/24*(45*B*a^2*sqrt(-b)*x^2*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - 60*A*sqrt(-a)*a*b*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (6*B*b^2*x^5 + 8*A*b^2*x^4 + 27*B*a*b*x^3 + 56*A*a*b*x^2 - 24*B*a^2*x - 12*A*a^2)*sqrt(b*x^2 + a))/x^2]","A",0
22,1,158,0,0.758399," ","integrate(x^3*(B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{9 \, B a^{2} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(6 \, B b^{2} x^{3} + 8 \, A b^{2} x^{2} - 9 \, B a b x - 16 \, A a b\right)} \sqrt{b x^{2} + a}}{48 \, b^{3}}, -\frac{9 \, B a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(6 \, B b^{2} x^{3} + 8 \, A b^{2} x^{2} - 9 \, B a b x - 16 \, A a b\right)} \sqrt{b x^{2} + a}}{24 \, b^{3}}\right]"," ",0,"[1/48*(9*B*a^2*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(6*B*b^2*x^3 + 8*A*b^2*x^2 - 9*B*a*b*x - 16*A*a*b)*sqrt(b*x^2 + a))/b^3, -1/24*(9*B*a^2*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (6*B*b^2*x^3 + 8*A*b^2*x^2 - 9*B*a*b*x - 16*A*a*b)*sqrt(b*x^2 + a))/b^3]","A",0
23,1,127,0,0.901676," ","integrate(x^2*(B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, A a \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(2 \, B b x^{2} + 3 \, A b x - 4 \, B a\right)} \sqrt{b x^{2} + a}}{12 \, b^{2}}, \frac{3 \, A a \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(2 \, B b x^{2} + 3 \, A b x - 4 \, B a\right)} \sqrt{b x^{2} + a}}{6 \, b^{2}}\right]"," ",0,"[1/12*(3*A*a*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(2*B*b*x^2 + 3*A*b*x - 4*B*a)*sqrt(b*x^2 + a))/b^2, 1/6*(3*A*a*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (2*B*b*x^2 + 3*A*b*x - 4*B*a)*sqrt(b*x^2 + a))/b^2]","A",0
24,1,109,0,0.677117," ","integrate(x*(B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{B a \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(B b x + 2 \, A b\right)} \sqrt{b x^{2} + a}}{4 \, b^{2}}, \frac{B a \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(B b x + 2 \, A b\right)} \sqrt{b x^{2} + a}}{2 \, b^{2}}\right]"," ",0,"[1/4*(B*a*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(B*b*x + 2*A*b)*sqrt(b*x^2 + a))/b^2, 1/2*(B*a*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (B*b*x + 2*A*b)*sqrt(b*x^2 + a))/b^2]","A",0
25,1,92,0,1.163561," ","integrate((B*x+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, \sqrt{b x^{2} + a} B}{2 \, b}, -\frac{A \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - \sqrt{b x^{2} + a} B}{b}\right]"," ",0,"[1/2*(A*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*sqrt(b*x^2 + a)*B)/b, -(A*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - sqrt(b*x^2 + a)*B)/b]","A",0
26,1,273,0,1.287534," ","integrate((B*x+A)/x/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{B a \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + A \sqrt{a} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right)}{2 \, a b}, -\frac{2 \, B a \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - A \sqrt{a} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right)}{2 \, a b}, \frac{2 \, A \sqrt{-a} b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + B a \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{2 \, a b}, -\frac{B a \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - A \sqrt{-a} b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right)}{a b}\right]"," ",0,"[1/2*(B*a*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + A*sqrt(a)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2))/(a*b), -1/2*(2*B*a*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - A*sqrt(a)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2))/(a*b), 1/2*(2*A*sqrt(-a)*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + B*a*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a))/(a*b), -(B*a*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - A*sqrt(-a)*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)))/(a*b)]","A",0
27,1,101,0,0.803801," ","integrate((B*x+A)/x^2/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{B \sqrt{a} x \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, \sqrt{b x^{2} + a} A}{2 \, a x}, \frac{B \sqrt{-a} x \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - \sqrt{b x^{2} + a} A}{a x}\right]"," ",0,"[1/2*(B*sqrt(a)*x*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*sqrt(b*x^2 + a)*A)/(a*x), (B*sqrt(-a)*x*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - sqrt(b*x^2 + a)*A)/(a*x)]","A",0
28,1,123,0,0.751580," ","integrate((B*x+A)/x^3/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{a} b x^{2} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(2 \, B a x + A a\right)} \sqrt{b x^{2} + a}}{4 \, a^{2} x^{2}}, -\frac{A \sqrt{-a} b x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(2 \, B a x + A a\right)} \sqrt{b x^{2} + a}}{2 \, a^{2} x^{2}}\right]"," ",0,"[1/4*(A*sqrt(a)*b*x^2*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(2*B*a*x + A*a)*sqrt(b*x^2 + a))/(a^2*x^2), -1/2*(A*sqrt(-a)*b*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (2*B*a*x + A*a)*sqrt(b*x^2 + a))/(a^2*x^2)]","A",0
29,1,197,0,0.894431," ","integrate(x^3*(B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a b x^{2} + B a^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(B b^{2} x^{3} + 2 \, A b^{2} x^{2} + 3 \, B a b x + 4 \, A a b\right)} \sqrt{b x^{2} + a}}{4 \, {\left(b^{4} x^{2} + a b^{3}\right)}}, \frac{3 \, {\left(B a b x^{2} + B a^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(B b^{2} x^{3} + 2 \, A b^{2} x^{2} + 3 \, B a b x + 4 \, A a b\right)} \sqrt{b x^{2} + a}}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}}\right]"," ",0,"[1/4*(3*(B*a*b*x^2 + B*a^2)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(B*b^2*x^3 + 2*A*b^2*x^2 + 3*B*a*b*x + 4*A*a*b)*sqrt(b*x^2 + a))/(b^4*x^2 + a*b^3), 1/2*(3*(B*a*b*x^2 + B*a^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (B*b^2*x^3 + 2*A*b^2*x^2 + 3*B*a*b*x + 4*A*a*b)*sqrt(b*x^2 + a))/(b^4*x^2 + a*b^3)]","A",0
30,1,164,0,1.046855," ","integrate(x^2*(B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(A b x^{2} + A a\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(B b x^{2} - A b x + 2 \, B a\right)} \sqrt{b x^{2} + a}}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}}, -\frac{{\left(A b x^{2} + A a\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(B b x^{2} - A b x + 2 \, B a\right)} \sqrt{b x^{2} + a}}{b^{3} x^{2} + a b^{2}}\right]"," ",0,"[1/2*((A*b*x^2 + A*a)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(B*b*x^2 - A*b*x + 2*B*a)*sqrt(b*x^2 + a))/(b^3*x^2 + a*b^2), -((A*b*x^2 + A*a)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (B*b*x^2 - A*b*x + 2*B*a)*sqrt(b*x^2 + a))/(b^3*x^2 + a*b^2)]","A",0
31,1,147,0,0.907890," ","integrate(x*(B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(B b x^{2} + B a\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(B b x + A b\right)} \sqrt{b x^{2} + a}}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}}, -\frac{{\left(B b x^{2} + B a\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(B b x + A b\right)} \sqrt{b x^{2} + a}}{b^{3} x^{2} + a b^{2}}\right]"," ",0,"[1/2*((B*b*x^2 + B*a)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(B*b*x + A*b)*sqrt(b*x^2 + a))/(b^3*x^2 + a*b^2), -((B*b*x^2 + B*a)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (B*b*x + A*b)*sqrt(b*x^2 + a))/(b^3*x^2 + a*b^2)]","A",0
32,1,35,0,0.847812," ","integrate((B*x+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(A b x - B a\right)} \sqrt{b x^{2} + a}}{a b^{2} x^{2} + a^{2} b}"," ",0,"(A*b*x - B*a)*sqrt(b*x^2 + a)/(a*b^2*x^2 + a^2*b)","A",0
33,1,146,0,1.001970," ","integrate((B*x+A)/x/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(A b x^{2} + A a\right)} \sqrt{a} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(B a x + A a\right)} \sqrt{b x^{2} + a}}{2 \, {\left(a^{2} b x^{2} + a^{3}\right)}}, \frac{{\left(A b x^{2} + A a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(B a x + A a\right)} \sqrt{b x^{2} + a}}{a^{2} b x^{2} + a^{3}}\right]"," ",0,"[1/2*((A*b*x^2 + A*a)*sqrt(a)*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(B*a*x + A*a)*sqrt(b*x^2 + a))/(a^2*b*x^2 + a^3), ((A*b*x^2 + A*a)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (B*a*x + A*a)*sqrt(b*x^2 + a))/(a^2*b*x^2 + a^3)]","A",0
34,1,169,0,0.876167," ","integrate((B*x+A)/x^2/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(B b x^{3} + B a x\right)} \sqrt{a} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(2 \, A b x^{2} - B a x + A a\right)} \sqrt{b x^{2} + a}}{2 \, {\left(a^{2} b x^{3} + a^{3} x\right)}}, \frac{{\left(B b x^{3} + B a x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, A b x^{2} - B a x + A a\right)} \sqrt{b x^{2} + a}}{a^{2} b x^{3} + a^{3} x}\right]"," ",0,"[1/2*((B*b*x^3 + B*a*x)*sqrt(a)*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(2*A*b*x^2 - B*a*x + A*a)*sqrt(b*x^2 + a))/(a^2*b*x^3 + a^3*x), ((B*b*x^3 + B*a*x)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (2*A*b*x^2 - B*a*x + A*a)*sqrt(b*x^2 + a))/(a^2*b*x^3 + a^3*x)]","A",0
35,1,211,0,0.899404," ","integrate((B*x+A)/x^3/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A b^{2} x^{4} + A a b x^{2}\right)} \sqrt{a} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(4 \, B a b x^{3} + 3 \, A a b x^{2} + 2 \, B a^{2} x + A a^{2}\right)} \sqrt{b x^{2} + a}}{4 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}, -\frac{3 \, {\left(A b^{2} x^{4} + A a b x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(4 \, B a b x^{3} + 3 \, A a b x^{2} + 2 \, B a^{2} x + A a^{2}\right)} \sqrt{b x^{2} + a}}{2 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}\right]"," ",0,"[1/4*(3*(A*b^2*x^4 + A*a*b*x^2)*sqrt(a)*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(4*B*a*b*x^3 + 3*A*a*b*x^2 + 2*B*a^2*x + A*a^2)*sqrt(b*x^2 + a))/(a^3*b*x^4 + a^4*x^2), -1/2*(3*(A*b^2*x^4 + A*a*b*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (4*B*a*b*x^3 + 3*A*a*b*x^2 + 2*B*a^2*x + A*a^2)*sqrt(b*x^2 + a))/(a^3*b*x^4 + a^4*x^2)]","A",0
36,1,239,0,0.821551," ","integrate(x^3*(B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B b^{2} x^{4} + 2 \, B a b x^{2} + B a^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(4 \, B b^{2} x^{3} + 3 \, A b^{2} x^{2} + 3 \, B a b x + 2 \, A a b\right)} \sqrt{b x^{2} + a}}{6 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}}, -\frac{3 \, {\left(B b^{2} x^{4} + 2 \, B a b x^{2} + B a^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(4 \, B b^{2} x^{3} + 3 \, A b^{2} x^{2} + 3 \, B a b x + 2 \, A a b\right)} \sqrt{b x^{2} + a}}{3 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}}\right]"," ",0,"[1/6*(3*(B*b^2*x^4 + 2*B*a*b*x^2 + B*a^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(4*B*b^2*x^3 + 3*A*b^2*x^2 + 3*B*a*b*x + 2*A*a*b)*sqrt(b*x^2 + a))/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3), -1/3*(3*(B*b^2*x^4 + 2*B*a*b*x^2 + B*a^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (4*B*b^2*x^3 + 3*A*b^2*x^2 + 3*B*a*b*x + 2*A*a*b)*sqrt(b*x^2 + a))/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)]","A",0
37,1,63,0,0.981011," ","integrate(x^2*(B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(A b^{2} x^{3} - 3 \, B a b x^{2} - 2 \, B a^{2}\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}"," ",0,"1/3*(A*b^2*x^3 - 3*B*a*b*x^2 - 2*B*a^2)*sqrt(b*x^2 + a)/(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)","A",0
38,1,49,0,0.924474," ","integrate(x*(B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(B b x^{3} - A a\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{2} + a^{3} b\right)}}"," ",0,"1/3*(B*b*x^3 - A*a)*sqrt(b*x^2 + a)/(a*b^3*x^4 + 2*a^2*b^2*x^2 + a^3*b)","A",0
39,1,62,0,0.878038," ","integrate((B*x+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, A b^{2} x^{3} + 3 \, A a b x - B a^{2}\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}}"," ",0,"1/3*(2*A*b^2*x^3 + 3*A*a*b*x - B*a^2)*sqrt(b*x^2 + a)/(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b)","A",0
40,1,239,0,0.753169," ","integrate((B*x+A)/x/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A b^{2} x^{4} + 2 \, A a b x^{2} + A a^{2}\right)} \sqrt{a} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, B a b x^{3} + 3 \, A a b x^{2} + 3 \, B a^{2} x + 4 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{6 \, {\left(a^{3} b^{2} x^{4} + 2 \, a^{4} b x^{2} + a^{5}\right)}}, \frac{3 \, {\left(A b^{2} x^{4} + 2 \, A a b x^{2} + A a^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(2 \, B a b x^{3} + 3 \, A a b x^{2} + 3 \, B a^{2} x + 4 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a^{3} b^{2} x^{4} + 2 \, a^{4} b x^{2} + a^{5}\right)}}\right]"," ",0,"[1/6*(3*(A*b^2*x^4 + 2*A*a*b*x^2 + A*a^2)*sqrt(a)*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*B*a*b*x^3 + 3*A*a*b*x^2 + 3*B*a^2*x + 4*A*a^2)*sqrt(b*x^2 + a))/(a^3*b^2*x^4 + 2*a^4*b*x^2 + a^5), 1/3*(3*(A*b^2*x^4 + 2*A*a*b*x^2 + A*a^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (2*B*a*b*x^3 + 3*A*a*b*x^2 + 3*B*a^2*x + 4*A*a^2)*sqrt(b*x^2 + a))/(a^3*b^2*x^4 + 2*a^4*b*x^2 + a^5)]","A",0
41,1,264,0,1.042123," ","integrate((B*x+A)/x^2/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B b^{2} x^{5} + 2 \, B a b x^{3} + B a^{2} x\right)} \sqrt{a} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(8 \, A b^{2} x^{4} - 3 \, B a b x^{3} + 12 \, A a b x^{2} - 4 \, B a^{2} x + 3 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{6 \, {\left(a^{3} b^{2} x^{5} + 2 \, a^{4} b x^{3} + a^{5} x\right)}}, \frac{3 \, {\left(B b^{2} x^{5} + 2 \, B a b x^{3} + B a^{2} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, A b^{2} x^{4} - 3 \, B a b x^{3} + 12 \, A a b x^{2} - 4 \, B a^{2} x + 3 \, A a^{2}\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a^{3} b^{2} x^{5} + 2 \, a^{4} b x^{3} + a^{5} x\right)}}\right]"," ",0,"[1/6*(3*(B*b^2*x^5 + 2*B*a*b*x^3 + B*a^2*x)*sqrt(a)*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(8*A*b^2*x^4 - 3*B*a*b*x^3 + 12*A*a*b*x^2 - 4*B*a^2*x + 3*A*a^2)*sqrt(b*x^2 + a))/(a^3*b^2*x^5 + 2*a^4*b*x^3 + a^5*x), 1/3*(3*(B*b^2*x^5 + 2*B*a*b*x^3 + B*a^2*x)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (8*A*b^2*x^4 - 3*B*a*b*x^3 + 12*A*a*b*x^2 - 4*B*a^2*x + 3*A*a^2)*sqrt(b*x^2 + a))/(a^3*b^2*x^5 + 2*a^4*b*x^3 + a^5*x)]","A",0
42,1,307,0,0.787437," ","integrate((B*x+A)/x^3/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(A b^{3} x^{6} + 2 \, A a b^{2} x^{4} + A a^{2} b x^{2}\right)} \sqrt{a} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(16 \, B a b^{2} x^{5} + 15 \, A a b^{2} x^{4} + 24 \, B a^{2} b x^{3} + 20 \, A a^{2} b x^{2} + 6 \, B a^{3} x + 3 \, A a^{3}\right)} \sqrt{b x^{2} + a}}{12 \, {\left(a^{4} b^{2} x^{6} + 2 \, a^{5} b x^{4} + a^{6} x^{2}\right)}}, -\frac{15 \, {\left(A b^{3} x^{6} + 2 \, A a b^{2} x^{4} + A a^{2} b x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(16 \, B a b^{2} x^{5} + 15 \, A a b^{2} x^{4} + 24 \, B a^{2} b x^{3} + 20 \, A a^{2} b x^{2} + 6 \, B a^{3} x + 3 \, A a^{3}\right)} \sqrt{b x^{2} + a}}{6 \, {\left(a^{4} b^{2} x^{6} + 2 \, a^{5} b x^{4} + a^{6} x^{2}\right)}}\right]"," ",0,"[1/12*(15*(A*b^3*x^6 + 2*A*a*b^2*x^4 + A*a^2*b*x^2)*sqrt(a)*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(16*B*a*b^2*x^5 + 15*A*a*b^2*x^4 + 24*B*a^2*b*x^3 + 20*A*a^2*b*x^2 + 6*B*a^3*x + 3*A*a^3)*sqrt(b*x^2 + a))/(a^4*b^2*x^6 + 2*a^5*b*x^4 + a^6*x^2), -1/6*(15*(A*b^3*x^6 + 2*A*a*b^2*x^4 + A*a^2*b*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (16*B*a*b^2*x^5 + 15*A*a*b^2*x^4 + 24*B*a^2*b*x^3 + 20*A*a^2*b*x^2 + 6*B*a^3*x + 3*A*a^3)*sqrt(b*x^2 + a))/(a^4*b^2*x^6 + 2*a^5*b*x^4 + a^6*x^2)]","A",0
43,1,31,0,0.602448," ","integrate((1-x)*x/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} {\left(x - 2\right)} + \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"1/2*sqrt(-x^2 + 1)*(x - 2) + arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
44,1,31,0,0.623793," ","integrate((-x^2+x)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} {\left(x - 2\right)} + \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"1/2*sqrt(-x^2 + 1)*(x - 2) + arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
45,1,26,0,0.868759," ","integrate((x^2+3)/(x^2-3),x, algorithm=""fricas"")","\sqrt{3} \log\left(\frac{x^{2} - 2 \, \sqrt{3} x + 3}{x^{2} - 3}\right) + x"," ",0,"sqrt(3)*log((x^2 - 2*sqrt(3)*x + 3)/(x^2 - 3)) + x","A",0
46,1,6,0,1.003130," ","integrate((x^2-1)/(x^2+1),x, algorithm=""fricas"")","x - 2 \, \arctan\left(x\right)"," ",0,"x - 2*arctan(x)","A",0
47,1,522,0,0.859679," ","integrate(x^7*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(B b^{4} x^{8} + 4 \, B a b^{3} x^{6} + 6 \, B a^{2} b^{2} x^{4} + 4 \, B a^{3} b x^{2} + B a^{4}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(105 \, C b^{4} x^{8} - 176 \, B b^{4} x^{7} - 406 \, B a b^{3} x^{5} - 350 \, B a^{2} b^{2} x^{3} + 105 \, {\left(8 \, C a b^{3} - A b^{4}\right)} x^{6} - 105 \, B a^{3} b x + 384 \, C a^{4} - 48 \, A a^{3} b + 210 \, {\left(8 \, C a^{2} b^{2} - A a b^{3}\right)} x^{4} + 168 \, {\left(8 \, C a^{3} b - A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{210 \, {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}}, -\frac{105 \, {\left(B b^{4} x^{8} + 4 \, B a b^{3} x^{6} + 6 \, B a^{2} b^{2} x^{4} + 4 \, B a^{3} b x^{2} + B a^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(105 \, C b^{4} x^{8} - 176 \, B b^{4} x^{7} - 406 \, B a b^{3} x^{5} - 350 \, B a^{2} b^{2} x^{3} + 105 \, {\left(8 \, C a b^{3} - A b^{4}\right)} x^{6} - 105 \, B a^{3} b x + 384 \, C a^{4} - 48 \, A a^{3} b + 210 \, {\left(8 \, C a^{2} b^{2} - A a b^{3}\right)} x^{4} + 168 \, {\left(8 \, C a^{3} b - A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(b^{9} x^{8} + 4 \, a b^{8} x^{6} + 6 \, a^{2} b^{7} x^{4} + 4 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}}\right]"," ",0,"[1/210*(105*(B*b^4*x^8 + 4*B*a*b^3*x^6 + 6*B*a^2*b^2*x^4 + 4*B*a^3*b*x^2 + B*a^4)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(105*C*b^4*x^8 - 176*B*b^4*x^7 - 406*B*a*b^3*x^5 - 350*B*a^2*b^2*x^3 + 105*(8*C*a*b^3 - A*b^4)*x^6 - 105*B*a^3*b*x + 384*C*a^4 - 48*A*a^3*b + 210*(8*C*a^2*b^2 - A*a*b^3)*x^4 + 168*(8*C*a^3*b - A*a^2*b^2)*x^2)*sqrt(b*x^2 + a))/(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5), -1/105*(105*(B*b^4*x^8 + 4*B*a*b^3*x^6 + 6*B*a^2*b^2*x^4 + 4*B*a^3*b*x^2 + B*a^4)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (105*C*b^4*x^8 - 176*B*b^4*x^7 - 406*B*a*b^3*x^5 - 350*B*a^2*b^2*x^3 + 105*(8*C*a*b^3 - A*b^4)*x^6 - 105*B*a^3*b*x + 384*C*a^4 - 48*A*a^3*b + 210*(8*C*a^2*b^2 - A*a*b^3)*x^4 + 168*(8*C*a^3*b - A*a^2*b^2)*x^2)*sqrt(b*x^2 + a))/(b^9*x^8 + 4*a*b^8*x^6 + 6*a^2*b^7*x^4 + 4*a^3*b^6*x^2 + a^4*b^5)]","A",0
48,1,467,0,1.105377," ","integrate(x^6*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(C a b^{4} x^{8} + 4 \, C a^{2} b^{3} x^{6} + 6 \, C a^{3} b^{2} x^{4} + 4 \, C a^{4} b x^{2} + C a^{5}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(105 \, B a b^{4} x^{6} + 406 \, C a^{2} b^{3} x^{5} + 210 \, B a^{2} b^{3} x^{4} + 350 \, C a^{3} b^{2} x^{3} + 168 \, B a^{3} b^{2} x^{2} + {\left(176 \, C a b^{4} - 15 \, A b^{5}\right)} x^{7} + 105 \, C a^{4} b x + 48 \, B a^{4} b\right)} \sqrt{b x^{2} + a}}{210 \, {\left(a b^{9} x^{8} + 4 \, a^{2} b^{8} x^{6} + 6 \, a^{3} b^{7} x^{4} + 4 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)}}, -\frac{105 \, {\left(C a b^{4} x^{8} + 4 \, C a^{2} b^{3} x^{6} + 6 \, C a^{3} b^{2} x^{4} + 4 \, C a^{4} b x^{2} + C a^{5}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(105 \, B a b^{4} x^{6} + 406 \, C a^{2} b^{3} x^{5} + 210 \, B a^{2} b^{3} x^{4} + 350 \, C a^{3} b^{2} x^{3} + 168 \, B a^{3} b^{2} x^{2} + {\left(176 \, C a b^{4} - 15 \, A b^{5}\right)} x^{7} + 105 \, C a^{4} b x + 48 \, B a^{4} b\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a b^{9} x^{8} + 4 \, a^{2} b^{8} x^{6} + 6 \, a^{3} b^{7} x^{4} + 4 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right)}}\right]"," ",0,"[1/210*(105*(C*a*b^4*x^8 + 4*C*a^2*b^3*x^6 + 6*C*a^3*b^2*x^4 + 4*C*a^4*b*x^2 + C*a^5)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(105*B*a*b^4*x^6 + 406*C*a^2*b^3*x^5 + 210*B*a^2*b^3*x^4 + 350*C*a^3*b^2*x^3 + 168*B*a^3*b^2*x^2 + (176*C*a*b^4 - 15*A*b^5)*x^7 + 105*C*a^4*b*x + 48*B*a^4*b)*sqrt(b*x^2 + a))/(a*b^9*x^8 + 4*a^2*b^8*x^6 + 6*a^3*b^7*x^4 + 4*a^4*b^6*x^2 + a^5*b^5), -1/105*(105*(C*a*b^4*x^8 + 4*C*a^2*b^3*x^6 + 6*C*a^3*b^2*x^4 + 4*C*a^4*b*x^2 + C*a^5)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (105*B*a*b^4*x^6 + 406*C*a^2*b^3*x^5 + 210*B*a^2*b^3*x^4 + 350*C*a^3*b^2*x^3 + 168*B*a^3*b^2*x^2 + (176*C*a*b^4 - 15*A*b^5)*x^7 + 105*C*a^4*b*x + 48*B*a^4*b)*sqrt(b*x^2 + a))/(a*b^9*x^8 + 4*a^2*b^8*x^6 + 6*a^3*b^7*x^4 + 4*a^4*b^6*x^2 + a^5*b^5)]","A",0
49,1,137,0,0.676237," ","integrate(x^5*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(15 \, B b^{4} x^{7} - 105 \, C a b^{3} x^{6} - 48 \, C a^{4} - 8 \, A a^{3} b - 35 \, {\left(6 \, C a^{2} b^{2} + A a b^{3}\right)} x^{4} - 28 \, {\left(6 \, C a^{3} b + A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a b^{8} x^{8} + 4 \, a^{2} b^{7} x^{6} + 6 \, a^{3} b^{6} x^{4} + 4 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)}}"," ",0,"1/105*(15*B*b^4*x^7 - 105*C*a*b^3*x^6 - 48*C*a^4 - 8*A*a^3*b - 35*(6*C*a^2*b^2 + A*a*b^3)*x^4 - 28*(6*C*a^3*b + A*a^2*b^2)*x^2)*sqrt(b*x^2 + a)/(a*b^8*x^8 + 4*a^2*b^7*x^6 + 6*a^3*b^6*x^4 + 4*a^4*b^5*x^2 + a^5*b^4)","A",0
50,1,122,0,0.925339," ","integrate(x^4*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(21 \, A a b^{3} x^{5} - 35 \, B a^{2} b^{2} x^{4} + 3 \, {\left(5 \, C a b^{3} + 2 \, A b^{4}\right)} x^{7} - 28 \, B a^{3} b x^{2} - 8 \, B a^{4}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{2} b^{7} x^{8} + 4 \, a^{3} b^{6} x^{6} + 6 \, a^{4} b^{5} x^{4} + 4 \, a^{5} b^{4} x^{2} + a^{6} b^{3}\right)}}"," ",0,"1/105*(21*A*a*b^3*x^5 - 35*B*a^2*b^2*x^4 + 3*(5*C*a*b^3 + 2*A*b^4)*x^7 - 28*B*a^3*b*x^2 - 8*B*a^4)*sqrt(b*x^2 + a)/(a^2*b^7*x^8 + 4*a^3*b^6*x^6 + 6*a^4*b^5*x^4 + 4*a^5*b^4*x^2 + a^6*b^3)","A",0
51,1,131,0,1.008042," ","integrate(x^3*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(6 \, B b^{4} x^{7} + 21 \, B a b^{3} x^{5} - 35 \, C a^{2} b^{2} x^{4} - 8 \, C a^{4} - 6 \, A a^{3} b - 7 \, {\left(4 \, C a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{2} b^{7} x^{8} + 4 \, a^{3} b^{6} x^{6} + 6 \, a^{4} b^{5} x^{4} + 4 \, a^{5} b^{4} x^{2} + a^{6} b^{3}\right)}}"," ",0,"1/105*(6*B*b^4*x^7 + 21*B*a*b^3*x^5 - 35*C*a^2*b^2*x^4 - 8*C*a^4 - 6*A*a^3*b - 7*(4*C*a^3*b + 3*A*a^2*b^2)*x^2)*sqrt(b*x^2 + a)/(a^2*b^7*x^8 + 4*a^3*b^6*x^6 + 6*a^4*b^5*x^4 + 4*a^5*b^4*x^2 + a^6*b^3)","A",0
52,1,134,0,0.987409," ","integrate(x^2*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(35 \, A a^{2} b^{2} x^{3} + 2 \, {\left(3 \, C a b^{3} + 4 \, A b^{4}\right)} x^{7} - 21 \, B a^{3} b x^{2} + 7 \, {\left(3 \, C a^{2} b^{2} + 4 \, A a b^{3}\right)} x^{5} - 6 \, B a^{4}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{3} b^{6} x^{8} + 4 \, a^{4} b^{5} x^{6} + 6 \, a^{5} b^{4} x^{4} + 4 \, a^{6} b^{3} x^{2} + a^{7} b^{2}\right)}}"," ",0,"1/105*(35*A*a^2*b^2*x^3 + 2*(3*C*a*b^3 + 4*A*b^4)*x^7 - 21*B*a^3*b*x^2 + 7*(3*C*a^2*b^2 + 4*A*a*b^3)*x^5 - 6*B*a^4)*sqrt(b*x^2 + a)/(a^3*b^6*x^8 + 4*a^4*b^5*x^6 + 6*a^5*b^4*x^4 + 4*a^6*b^3*x^2 + a^7*b^2)","A",0
53,1,119,0,0.772486," ","integrate(x*(C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(8 \, B b^{4} x^{7} + 28 \, B a b^{3} x^{5} + 35 \, B a^{2} b^{2} x^{3} - 21 \, C a^{3} b x^{2} - 6 \, C a^{4} - 15 \, A a^{3} b\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{3} b^{6} x^{8} + 4 \, a^{4} b^{5} x^{6} + 6 \, a^{5} b^{4} x^{4} + 4 \, a^{6} b^{3} x^{2} + a^{7} b^{2}\right)}}"," ",0,"1/105*(8*B*b^4*x^7 + 28*B*a*b^3*x^5 + 35*B*a^2*b^2*x^3 - 21*C*a^3*b*x^2 - 6*C*a^4 - 15*A*a^3*b)*sqrt(b*x^2 + a)/(a^3*b^6*x^8 + 4*a^4*b^5*x^6 + 6*a^5*b^4*x^4 + 4*a^6*b^3*x^2 + a^7*b^2)","A",0
54,1,137,0,0.602746," ","integrate((C*x^2+B*x+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(C a b^{3} + 6 \, A b^{4}\right)} x^{7} + 105 \, A a^{3} b x + 28 \, {\left(C a^{2} b^{2} + 6 \, A a b^{3}\right)} x^{5} - 15 \, B a^{4} + 35 \, {\left(C a^{3} b + 6 \, A a^{2} b^{2}\right)} x^{3}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{4} b^{5} x^{8} + 4 \, a^{5} b^{4} x^{6} + 6 \, a^{6} b^{3} x^{4} + 4 \, a^{7} b^{2} x^{2} + a^{8} b\right)}}"," ",0,"1/105*(8*(C*a*b^3 + 6*A*b^4)*x^7 + 105*A*a^3*b*x + 28*(C*a^2*b^2 + 6*A*a*b^3)*x^5 - 15*B*a^4 + 35*(C*a^3*b + 6*A*a^2*b^2)*x^3)*sqrt(b*x^2 + a)/(a^4*b^5*x^8 + 4*a^5*b^4*x^6 + 6*a^6*b^3*x^4 + 4*a^7*b^2*x^2 + a^8*b)","A",0
55,1,465,0,0.806430," ","integrate((C*x^2+B*x+A)/x/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(A b^{5} x^{8} + 4 \, A a b^{4} x^{6} + 6 \, A a^{2} b^{3} x^{4} + 4 \, A a^{3} b^{2} x^{2} + A a^{4} b\right)} \sqrt{a} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(48 \, B a b^{4} x^{7} + 105 \, A a b^{4} x^{6} + 168 \, B a^{2} b^{3} x^{5} + 350 \, A a^{2} b^{3} x^{4} + 210 \, B a^{3} b^{2} x^{3} + 406 \, A a^{3} b^{2} x^{2} + 105 \, B a^{4} b x - 15 \, C a^{5} + 176 \, A a^{4} b\right)} \sqrt{b x^{2} + a}}{210 \, {\left(a^{5} b^{5} x^{8} + 4 \, a^{6} b^{4} x^{6} + 6 \, a^{7} b^{3} x^{4} + 4 \, a^{8} b^{2} x^{2} + a^{9} b\right)}}, \frac{105 \, {\left(A b^{5} x^{8} + 4 \, A a b^{4} x^{6} + 6 \, A a^{2} b^{3} x^{4} + 4 \, A a^{3} b^{2} x^{2} + A a^{4} b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(48 \, B a b^{4} x^{7} + 105 \, A a b^{4} x^{6} + 168 \, B a^{2} b^{3} x^{5} + 350 \, A a^{2} b^{3} x^{4} + 210 \, B a^{3} b^{2} x^{3} + 406 \, A a^{3} b^{2} x^{2} + 105 \, B a^{4} b x - 15 \, C a^{5} + 176 \, A a^{4} b\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{5} b^{5} x^{8} + 4 \, a^{6} b^{4} x^{6} + 6 \, a^{7} b^{3} x^{4} + 4 \, a^{8} b^{2} x^{2} + a^{9} b\right)}}\right]"," ",0,"[1/210*(105*(A*b^5*x^8 + 4*A*a*b^4*x^6 + 6*A*a^2*b^3*x^4 + 4*A*a^3*b^2*x^2 + A*a^4*b)*sqrt(a)*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(48*B*a*b^4*x^7 + 105*A*a*b^4*x^6 + 168*B*a^2*b^3*x^5 + 350*A*a^2*b^3*x^4 + 210*B*a^3*b^2*x^3 + 406*A*a^3*b^2*x^2 + 105*B*a^4*b*x - 15*C*a^5 + 176*A*a^4*b)*sqrt(b*x^2 + a))/(a^5*b^5*x^8 + 4*a^6*b^4*x^6 + 6*a^7*b^3*x^4 + 4*a^8*b^2*x^2 + a^9*b), 1/105*(105*(A*b^5*x^8 + 4*A*a*b^4*x^6 + 6*A*a^2*b^3*x^4 + 4*A*a^3*b^2*x^2 + A*a^4*b)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (48*B*a*b^4*x^7 + 105*A*a*b^4*x^6 + 168*B*a^2*b^3*x^5 + 350*A*a^2*b^3*x^4 + 210*B*a^3*b^2*x^3 + 406*A*a^3*b^2*x^2 + 105*B*a^4*b*x - 15*C*a^5 + 176*A*a^4*b)*sqrt(b*x^2 + a))/(a^5*b^5*x^8 + 4*a^6*b^4*x^6 + 6*a^7*b^3*x^4 + 4*a^8*b^2*x^2 + a^9*b)]","A",0
56,1,525,0,0.707810," ","integrate((C*x^2+B*x+A)/x^2/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(B b^{4} x^{9} + 4 \, B a b^{3} x^{7} + 6 \, B a^{2} b^{2} x^{5} + 4 \, B a^{3} b x^{3} + B a^{4} x\right)} \sqrt{a} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(105 \, B a b^{3} x^{7} + 350 \, B a^{2} b^{2} x^{5} + 48 \, {\left(C a b^{3} - 8 \, A b^{4}\right)} x^{8} + 406 \, B a^{3} b x^{3} + 168 \, {\left(C a^{2} b^{2} - 8 \, A a b^{3}\right)} x^{6} + 176 \, B a^{4} x - 105 \, A a^{4} + 210 \, {\left(C a^{3} b - 8 \, A a^{2} b^{2}\right)} x^{4} + 105 \, {\left(C a^{4} - 8 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{210 \, {\left(a^{5} b^{4} x^{9} + 4 \, a^{6} b^{3} x^{7} + 6 \, a^{7} b^{2} x^{5} + 4 \, a^{8} b x^{3} + a^{9} x\right)}}, \frac{105 \, {\left(B b^{4} x^{9} + 4 \, B a b^{3} x^{7} + 6 \, B a^{2} b^{2} x^{5} + 4 \, B a^{3} b x^{3} + B a^{4} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(105 \, B a b^{3} x^{7} + 350 \, B a^{2} b^{2} x^{5} + 48 \, {\left(C a b^{3} - 8 \, A b^{4}\right)} x^{8} + 406 \, B a^{3} b x^{3} + 168 \, {\left(C a^{2} b^{2} - 8 \, A a b^{3}\right)} x^{6} + 176 \, B a^{4} x - 105 \, A a^{4} + 210 \, {\left(C a^{3} b - 8 \, A a^{2} b^{2}\right)} x^{4} + 105 \, {\left(C a^{4} - 8 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{5} b^{4} x^{9} + 4 \, a^{6} b^{3} x^{7} + 6 \, a^{7} b^{2} x^{5} + 4 \, a^{8} b x^{3} + a^{9} x\right)}}\right]"," ",0,"[1/210*(105*(B*b^4*x^9 + 4*B*a*b^3*x^7 + 6*B*a^2*b^2*x^5 + 4*B*a^3*b*x^3 + B*a^4*x)*sqrt(a)*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(105*B*a*b^3*x^7 + 350*B*a^2*b^2*x^5 + 48*(C*a*b^3 - 8*A*b^4)*x^8 + 406*B*a^3*b*x^3 + 168*(C*a^2*b^2 - 8*A*a*b^3)*x^6 + 176*B*a^4*x - 105*A*a^4 + 210*(C*a^3*b - 8*A*a^2*b^2)*x^4 + 105*(C*a^4 - 8*A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^5*b^4*x^9 + 4*a^6*b^3*x^7 + 6*a^7*b^2*x^5 + 4*a^8*b*x^3 + a^9*x), 1/105*(105*(B*b^4*x^9 + 4*B*a*b^3*x^7 + 6*B*a^2*b^2*x^5 + 4*B*a^3*b*x^3 + B*a^4*x)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (105*B*a*b^3*x^7 + 350*B*a^2*b^2*x^5 + 48*(C*a*b^3 - 8*A*b^4)*x^8 + 406*B*a^3*b*x^3 + 168*(C*a^2*b^2 - 8*A*a*b^3)*x^6 + 176*B*a^4*x - 105*A*a^4 + 210*(C*a^3*b - 8*A*a^2*b^2)*x^4 + 105*(C*a^4 - 8*A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^5*b^4*x^9 + 4*a^6*b^3*x^7 + 6*a^7*b^2*x^5 + 4*a^8*b*x^3 + a^9*x)]","A",0
57,1,688,0,1.170595," ","integrate((C*x^2+B*x+A)/x^3/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(2 \, C a b^{4} - 9 \, A b^{5}\right)} x^{10} + 4 \, {\left(2 \, C a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{8} + 6 \, {\left(2 \, C a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} x^{6} + 4 \, {\left(2 \, C a^{4} b - 9 \, A a^{3} b^{2}\right)} x^{4} + {\left(2 \, C a^{5} - 9 \, A a^{4} b\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(768 \, B a b^{4} x^{9} + 2688 \, B a^{2} b^{3} x^{7} + 3360 \, B a^{3} b^{2} x^{5} + 1680 \, B a^{4} b x^{3} - 105 \, {\left(2 \, C a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{8} + 210 \, B a^{5} x - 350 \, {\left(2 \, C a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} x^{6} + 105 \, A a^{5} - 406 \, {\left(2 \, C a^{4} b - 9 \, A a^{3} b^{2}\right)} x^{4} - 176 \, {\left(2 \, C a^{5} - 9 \, A a^{4} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{420 \, {\left(a^{6} b^{4} x^{10} + 4 \, a^{7} b^{3} x^{8} + 6 \, a^{8} b^{2} x^{6} + 4 \, a^{9} b x^{4} + a^{10} x^{2}\right)}}, \frac{105 \, {\left({\left(2 \, C a b^{4} - 9 \, A b^{5}\right)} x^{10} + 4 \, {\left(2 \, C a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{8} + 6 \, {\left(2 \, C a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} x^{6} + 4 \, {\left(2 \, C a^{4} b - 9 \, A a^{3} b^{2}\right)} x^{4} + {\left(2 \, C a^{5} - 9 \, A a^{4} b\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(768 \, B a b^{4} x^{9} + 2688 \, B a^{2} b^{3} x^{7} + 3360 \, B a^{3} b^{2} x^{5} + 1680 \, B a^{4} b x^{3} - 105 \, {\left(2 \, C a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{8} + 210 \, B a^{5} x - 350 \, {\left(2 \, C a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} x^{6} + 105 \, A a^{5} - 406 \, {\left(2 \, C a^{4} b - 9 \, A a^{3} b^{2}\right)} x^{4} - 176 \, {\left(2 \, C a^{5} - 9 \, A a^{4} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{210 \, {\left(a^{6} b^{4} x^{10} + 4 \, a^{7} b^{3} x^{8} + 6 \, a^{8} b^{2} x^{6} + 4 \, a^{9} b x^{4} + a^{10} x^{2}\right)}}\right]"," ",0,"[-1/420*(105*((2*C*a*b^4 - 9*A*b^5)*x^10 + 4*(2*C*a^2*b^3 - 9*A*a*b^4)*x^8 + 6*(2*C*a^3*b^2 - 9*A*a^2*b^3)*x^6 + 4*(2*C*a^4*b - 9*A*a^3*b^2)*x^4 + (2*C*a^5 - 9*A*a^4*b)*x^2)*sqrt(a)*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(768*B*a*b^4*x^9 + 2688*B*a^2*b^3*x^7 + 3360*B*a^3*b^2*x^5 + 1680*B*a^4*b*x^3 - 105*(2*C*a^2*b^3 - 9*A*a*b^4)*x^8 + 210*B*a^5*x - 350*(2*C*a^3*b^2 - 9*A*a^2*b^3)*x^6 + 105*A*a^5 - 406*(2*C*a^4*b - 9*A*a^3*b^2)*x^4 - 176*(2*C*a^5 - 9*A*a^4*b)*x^2)*sqrt(b*x^2 + a))/(a^6*b^4*x^10 + 4*a^7*b^3*x^8 + 6*a^8*b^2*x^6 + 4*a^9*b*x^4 + a^10*x^2), 1/210*(105*((2*C*a*b^4 - 9*A*b^5)*x^10 + 4*(2*C*a^2*b^3 - 9*A*a*b^4)*x^8 + 6*(2*C*a^3*b^2 - 9*A*a^2*b^3)*x^6 + 4*(2*C*a^4*b - 9*A*a^3*b^2)*x^4 + (2*C*a^5 - 9*A*a^4*b)*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (768*B*a*b^4*x^9 + 2688*B*a^2*b^3*x^7 + 3360*B*a^3*b^2*x^5 + 1680*B*a^4*b*x^3 - 105*(2*C*a^2*b^3 - 9*A*a*b^4)*x^8 + 210*B*a^5*x - 350*(2*C*a^3*b^2 - 9*A*a^2*b^3)*x^6 + 105*A*a^5 - 406*(2*C*a^4*b - 9*A*a^3*b^2)*x^4 - 176*(2*C*a^5 - 9*A*a^4*b)*x^2)*sqrt(b*x^2 + a))/(a^6*b^4*x^10 + 4*a^7*b^3*x^8 + 6*a^8*b^2*x^6 + 4*a^9*b*x^4 + a^10*x^2)]","A",0
58,0,0,0,0.905478," ","integrate(A*(c*x)^m/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c x\right)^{m} A}{b x^{2} + a}, x\right)"," ",0,"integral((c*x)^m*A/(b*x^2 + a), x)","F",0
59,0,0,0,0.912092," ","integrate((c*x)^m*(B*x+A)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} \left(c x\right)^{m}}{b x^{2} + a}, x\right)"," ",0,"integral((B*x + A)*(c*x)^m/(b*x^2 + a), x)","F",0
60,0,0,0,0.761344," ","integrate((c*x)^m*(C*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + A\right)} \left(c x\right)^{m}}{b x^{2} + a}, x\right)"," ",0,"integral((C*x^2 + A)*(c*x)^m/(b*x^2 + a), x)","F",0
61,0,0,0,0.968684," ","integrate((c*x)^m*(C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C x^{2} + B x + A\right)} \left(c x\right)^{m}}{b x^{2} + a}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*(c*x)^m/(b*x^2 + a), x)","F",0
62,-2,0,0,0.000000," ","integrate(x^3*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
63,-2,0,0,0.000000," ","integrate(x^2*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
64,-2,0,0,0.000000," ","integrate(x*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
65,-2,0,0,0.000000," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
66,1,48,0,0.824508," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x,x, algorithm=""fricas"")","\frac{1}{5} \, D b x^{5} + \frac{1}{4} \, C b x^{4} + \frac{1}{3} \, {\left(D a + B b\right)} x^{3} + B a x + \frac{1}{2} \, {\left(C a + A b\right)} x^{2} + A a \log\left(x\right)"," ",0,"1/5*D*b*x^5 + 1/4*C*b*x^4 + 1/3*(D*a + B*b)*x^3 + B*a*x + 1/2*(C*a + A*b)*x^2 + A*a*log(x)","A",0
67,1,55,0,0.814529," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x^2,x, algorithm=""fricas"")","\frac{3 \, D b x^{5} + 4 \, C b x^{4} + 6 \, {\left(D a + B b\right)} x^{3} + 12 \, B a x \log\left(x\right) + 12 \, {\left(C a + A b\right)} x^{2} - 12 \, A a}{12 \, x}"," ",0,"1/12*(3*D*b*x^5 + 4*C*b*x^4 + 6*(D*a + B*b)*x^3 + 12*B*a*x*log(x) + 12*(C*a + A*b)*x^2 - 12*A*a)/x","A",0
68,1,55,0,0.616077," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x^3,x, algorithm=""fricas"")","\frac{2 \, D b x^{5} + 3 \, C b x^{4} + 6 \, {\left(D a + B b\right)} x^{3} + 6 \, {\left(C a + A b\right)} x^{2} \log\left(x\right) - 6 \, B a x - 3 \, A a}{6 \, x^{2}}"," ",0,"1/6*(2*D*b*x^5 + 3*C*b*x^4 + 6*(D*a + B*b)*x^3 + 6*(C*a + A*b)*x^2*log(x) - 6*B*a*x - 3*A*a)/x^2","A",0
69,1,55,0,0.752453," ","integrate((b*x^2+a)*(D*x^3+C*x^2+B*x+A)/x^4,x, algorithm=""fricas"")","\frac{3 \, D b x^{5} + 6 \, C b x^{4} + 6 \, {\left(D a + B b\right)} x^{3} \log\left(x\right) - 3 \, B a x - 6 \, {\left(C a + A b\right)} x^{2} - 2 \, A a}{6 \, x^{3}}"," ",0,"1/6*(3*D*b*x^5 + 6*C*b*x^4 + 6*(D*a + B*b)*x^3*log(x) - 3*B*a*x - 6*(C*a + A*b)*x^2 - 2*A*a)/x^3","A",0
70,-2,0,0,0.000000," ","integrate(x^3*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
71,-2,0,0,0.000000," ","integrate(x^2*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
72,-2,0,0,0.000000," ","integrate(x*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
73,-2,0,0,0.000000," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
74,1,96,0,0.801899," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x,x, algorithm=""fricas"")","\frac{1}{7} \, D b^{2} x^{7} + \frac{1}{6} \, C b^{2} x^{6} + \frac{1}{5} \, {\left(2 \, D a b + B b^{2}\right)} x^{5} + \frac{1}{4} \, {\left(2 \, C a b + A b^{2}\right)} x^{4} + B a^{2} x + \frac{1}{3} \, {\left(D a^{2} + 2 \, B a b\right)} x^{3} + A a^{2} \log\left(x\right) + \frac{1}{2} \, {\left(C a^{2} + 2 \, A a b\right)} x^{2}"," ",0,"1/7*D*b^2*x^7 + 1/6*C*b^2*x^6 + 1/5*(2*D*a*b + B*b^2)*x^5 + 1/4*(2*C*a*b + A*b^2)*x^4 + B*a^2*x + 1/3*(D*a^2 + 2*B*a*b)*x^3 + A*a^2*log(x) + 1/2*(C*a^2 + 2*A*a*b)*x^2","A",0
75,1,103,0,0.513574," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x^2,x, algorithm=""fricas"")","\frac{10 \, D b^{2} x^{7} + 12 \, C b^{2} x^{6} + 15 \, {\left(2 \, D a b + B b^{2}\right)} x^{5} + 20 \, {\left(2 \, C a b + A b^{2}\right)} x^{4} + 60 \, B a^{2} x \log\left(x\right) + 30 \, {\left(D a^{2} + 2 \, B a b\right)} x^{3} - 60 \, A a^{2} + 60 \, {\left(C a^{2} + 2 \, A a b\right)} x^{2}}{60 \, x}"," ",0,"1/60*(10*D*b^2*x^7 + 12*C*b^2*x^6 + 15*(2*D*a*b + B*b^2)*x^5 + 20*(2*C*a*b + A*b^2)*x^4 + 60*B*a^2*x*log(x) + 30*(D*a^2 + 2*B*a*b)*x^3 - 60*A*a^2 + 60*(C*a^2 + 2*A*a*b)*x^2)/x","A",0
76,1,103,0,0.660130," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x^3,x, algorithm=""fricas"")","\frac{12 \, D b^{2} x^{7} + 15 \, C b^{2} x^{6} + 20 \, {\left(2 \, D a b + B b^{2}\right)} x^{5} + 30 \, {\left(2 \, C a b + A b^{2}\right)} x^{4} - 60 \, B a^{2} x + 60 \, {\left(D a^{2} + 2 \, B a b\right)} x^{3} + 60 \, {\left(C a^{2} + 2 \, A a b\right)} x^{2} \log\left(x\right) - 30 \, A a^{2}}{60 \, x^{2}}"," ",0,"1/60*(12*D*b^2*x^7 + 15*C*b^2*x^6 + 20*(2*D*a*b + B*b^2)*x^5 + 30*(2*C*a*b + A*b^2)*x^4 - 60*B*a^2*x + 60*(D*a^2 + 2*B*a*b)*x^3 + 60*(C*a^2 + 2*A*a*b)*x^2*log(x) - 30*A*a^2)/x^2","A",0
77,1,103,0,0.880729," ","integrate((b*x^2+a)^2*(D*x^3+C*x^2+B*x+A)/x^4,x, algorithm=""fricas"")","\frac{3 \, D b^{2} x^{7} + 4 \, C b^{2} x^{6} + 6 \, {\left(2 \, D a b + B b^{2}\right)} x^{5} + 12 \, {\left(2 \, C a b + A b^{2}\right)} x^{4} + 12 \, {\left(D a^{2} + 2 \, B a b\right)} x^{3} \log\left(x\right) - 6 \, B a^{2} x - 4 \, A a^{2} - 12 \, {\left(C a^{2} + 2 \, A a b\right)} x^{2}}{12 \, x^{3}}"," ",0,"1/12*(3*D*b^2*x^7 + 4*C*b^2*x^6 + 6*(2*D*a*b + B*b^2)*x^5 + 12*(2*C*a*b + A*b^2)*x^4 + 12*(D*a^2 + 2*B*a*b)*x^3*log(x) - 6*B*a^2*x - 4*A*a^2 - 12*(C*a^2 + 2*A*a*b)*x^2)/x^3","A",0
78,-2,0,0,0.000000," ","integrate(x^3*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
79,-2,0,0,0.000000," ","integrate(x^2*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
80,-2,0,0,0.000000," ","integrate(x*(b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
81,-2,0,0,0.000000," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> keys do not match self's parent","F(-2)",0
82,1,140,0,0.737071," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x,x, algorithm=""fricas"")","\frac{1}{9} \, D b^{3} x^{9} + \frac{1}{8} \, C b^{3} x^{8} + \frac{1}{7} \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{7} + \frac{1}{6} \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{6} + \frac{3}{5} \, {\left(D a^{2} b + B a b^{2}\right)} x^{5} + B a^{3} x + \frac{3}{4} \, {\left(C a^{2} b + A a b^{2}\right)} x^{4} + A a^{3} \log\left(x\right) + \frac{1}{3} \, {\left(D a^{3} + 3 \, B a^{2} b\right)} x^{3} + \frac{1}{2} \, {\left(C a^{3} + 3 \, A a^{2} b\right)} x^{2}"," ",0,"1/9*D*b^3*x^9 + 1/8*C*b^3*x^8 + 1/7*(3*D*a*b^2 + B*b^3)*x^7 + 1/6*(3*C*a*b^2 + A*b^3)*x^6 + 3/5*(D*a^2*b + B*a*b^2)*x^5 + B*a^3*x + 3/4*(C*a^2*b + A*a*b^2)*x^4 + A*a^3*log(x) + 1/3*(D*a^3 + 3*B*a^2*b)*x^3 + 1/2*(C*a^3 + 3*A*a^2*b)*x^2","A",0
83,1,147,0,0.814753," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x^2,x, algorithm=""fricas"")","\frac{105 \, D b^{3} x^{9} + 120 \, C b^{3} x^{8} + 140 \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{7} + 168 \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{6} + 630 \, {\left(D a^{2} b + B a b^{2}\right)} x^{5} + 840 \, B a^{3} x \log\left(x\right) + 840 \, {\left(C a^{2} b + A a b^{2}\right)} x^{4} - 840 \, A a^{3} + 420 \, {\left(D a^{3} + 3 \, B a^{2} b\right)} x^{3} + 840 \, {\left(C a^{3} + 3 \, A a^{2} b\right)} x^{2}}{840 \, x}"," ",0,"1/840*(105*D*b^3*x^9 + 120*C*b^3*x^8 + 140*(3*D*a*b^2 + B*b^3)*x^7 + 168*(3*C*a*b^2 + A*b^3)*x^6 + 630*(D*a^2*b + B*a*b^2)*x^5 + 840*B*a^3*x*log(x) + 840*(C*a^2*b + A*a*b^2)*x^4 - 840*A*a^3 + 420*(D*a^3 + 3*B*a^2*b)*x^3 + 840*(C*a^3 + 3*A*a^2*b)*x^2)/x","A",0
84,1,147,0,0.842154," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x^3,x, algorithm=""fricas"")","\frac{60 \, D b^{3} x^{9} + 70 \, C b^{3} x^{8} + 84 \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{7} + 105 \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{6} + 420 \, {\left(D a^{2} b + B a b^{2}\right)} x^{5} - 420 \, B a^{3} x + 630 \, {\left(C a^{2} b + A a b^{2}\right)} x^{4} - 210 \, A a^{3} + 420 \, {\left(D a^{3} + 3 \, B a^{2} b\right)} x^{3} + 420 \, {\left(C a^{3} + 3 \, A a^{2} b\right)} x^{2} \log\left(x\right)}{420 \, x^{2}}"," ",0,"1/420*(60*D*b^3*x^9 + 70*C*b^3*x^8 + 84*(3*D*a*b^2 + B*b^3)*x^7 + 105*(3*C*a*b^2 + A*b^3)*x^6 + 420*(D*a^2*b + B*a*b^2)*x^5 - 420*B*a^3*x + 630*(C*a^2*b + A*a*b^2)*x^4 - 210*A*a^3 + 420*(D*a^3 + 3*B*a^2*b)*x^3 + 420*(C*a^3 + 3*A*a^2*b)*x^2*log(x))/x^2","A",0
85,1,147,0,0.773533," ","integrate((b*x^2+a)^3*(D*x^3+C*x^2+B*x+A)/x^4,x, algorithm=""fricas"")","\frac{10 \, D b^{3} x^{9} + 12 \, C b^{3} x^{8} + 15 \, {\left(3 \, D a b^{2} + B b^{3}\right)} x^{7} + 20 \, {\left(3 \, C a b^{2} + A b^{3}\right)} x^{6} + 90 \, {\left(D a^{2} b + B a b^{2}\right)} x^{5} - 30 \, B a^{3} x + 180 \, {\left(C a^{2} b + A a b^{2}\right)} x^{4} + 60 \, {\left(D a^{3} + 3 \, B a^{2} b\right)} x^{3} \log\left(x\right) - 20 \, A a^{3} - 60 \, {\left(C a^{3} + 3 \, A a^{2} b\right)} x^{2}}{60 \, x^{3}}"," ",0,"1/60*(10*D*b^3*x^9 + 12*C*b^3*x^8 + 15*(3*D*a*b^2 + B*b^3)*x^7 + 20*(3*C*a*b^2 + A*b^3)*x^6 + 90*(D*a^2*b + B*a*b^2)*x^5 - 30*B*a^3*x + 180*(C*a^2*b + A*a*b^2)*x^4 + 60*(D*a^3 + 3*B*a^2*b)*x^3*log(x) - 20*A*a^3 - 60*(C*a^3 + 3*A*a^2*b)*x^2)/x^3","A",0
86,1,332,0,0.964864," ","integrate(x^4*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{10 \, D b^{3} x^{6} + 12 \, C b^{3} x^{5} - 15 \, {\left(D a b^{2} - B b^{3}\right)} x^{4} - 20 \, {\left(C a b^{2} - A b^{3}\right)} x^{3} + 30 \, {\left(D a^{2} b - B a b^{2}\right)} x^{2} - 30 \, {\left(C a^{2} b - A a b^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 60 \, {\left(C a^{2} b - A a b^{2}\right)} x - 30 \, {\left(D a^{3} - B a^{2} b\right)} \log\left(b x^{2} + a\right)}{60 \, b^{4}}, \frac{10 \, D b^{3} x^{6} + 12 \, C b^{3} x^{5} - 15 \, {\left(D a b^{2} - B b^{3}\right)} x^{4} - 20 \, {\left(C a b^{2} - A b^{3}\right)} x^{3} + 30 \, {\left(D a^{2} b - B a b^{2}\right)} x^{2} - 60 \, {\left(C a^{2} b - A a b^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 60 \, {\left(C a^{2} b - A a b^{2}\right)} x - 30 \, {\left(D a^{3} - B a^{2} b\right)} \log\left(b x^{2} + a\right)}{60 \, b^{4}}\right]"," ",0,"[1/60*(10*D*b^3*x^6 + 12*C*b^3*x^5 - 15*(D*a*b^2 - B*b^3)*x^4 - 20*(C*a*b^2 - A*b^3)*x^3 + 30*(D*a^2*b - B*a*b^2)*x^2 - 30*(C*a^2*b - A*a*b^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 60*(C*a^2*b - A*a*b^2)*x - 30*(D*a^3 - B*a^2*b)*log(b*x^2 + a))/b^4, 1/60*(10*D*b^3*x^6 + 12*C*b^3*x^5 - 15*(D*a*b^2 - B*b^3)*x^4 - 20*(C*a*b^2 - A*b^3)*x^3 + 30*(D*a^2*b - B*a*b^2)*x^2 - 60*(C*a^2*b - A*a*b^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 60*(C*a^2*b - A*a*b^2)*x - 30*(D*a^3 - B*a^2*b)*log(b*x^2 + a))/b^4]","A",0
87,1,270,0,0.940802," ","integrate(x^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{12 \, D b^{2} x^{5} + 15 \, C b^{2} x^{4} - 20 \, {\left(D a b - B b^{2}\right)} x^{3} - 30 \, {\left(C a b - A b^{2}\right)} x^{2} + 30 \, {\left(D a^{2} - B a b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 60 \, {\left(D a^{2} - B a b\right)} x + 30 \, {\left(C a^{2} - A a b\right)} \log\left(b x^{2} + a\right)}{60 \, b^{3}}, \frac{12 \, D b^{2} x^{5} + 15 \, C b^{2} x^{4} - 20 \, {\left(D a b - B b^{2}\right)} x^{3} - 30 \, {\left(C a b - A b^{2}\right)} x^{2} - 60 \, {\left(D a^{2} - B a b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 60 \, {\left(D a^{2} - B a b\right)} x + 30 \, {\left(C a^{2} - A a b\right)} \log\left(b x^{2} + a\right)}{60 \, b^{3}}\right]"," ",0,"[1/60*(12*D*b^2*x^5 + 15*C*b^2*x^4 - 20*(D*a*b - B*b^2)*x^3 - 30*(C*a*b - A*b^2)*x^2 + 30*(D*a^2 - B*a*b)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 60*(D*a^2 - B*a*b)*x + 30*(C*a^2 - A*a*b)*log(b*x^2 + a))/b^3, 1/60*(12*D*b^2*x^5 + 15*C*b^2*x^4 - 20*(D*a*b - B*b^2)*x^3 - 30*(C*a*b - A*b^2)*x^2 - 60*(D*a^2 - B*a*b)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 60*(D*a^2 - B*a*b)*x + 30*(C*a^2 - A*a*b)*log(b*x^2 + a))/b^3]","A",0
88,1,238,0,0.923314," ","integrate(x^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{3 \, D b^{2} x^{4} + 4 \, C b^{2} x^{3} - 6 \, {\left(D a b - B b^{2}\right)} x^{2} - 6 \, {\left(C a b - A b^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 12 \, {\left(C a b - A b^{2}\right)} x + 6 \, {\left(D a^{2} - B a b\right)} \log\left(b x^{2} + a\right)}{12 \, b^{3}}, \frac{3 \, D b^{2} x^{4} + 4 \, C b^{2} x^{3} - 6 \, {\left(D a b - B b^{2}\right)} x^{2} + 12 \, {\left(C a b - A b^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 12 \, {\left(C a b - A b^{2}\right)} x + 6 \, {\left(D a^{2} - B a b\right)} \log\left(b x^{2} + a\right)}{12 \, b^{3}}\right]"," ",0,"[1/12*(3*D*b^2*x^4 + 4*C*b^2*x^3 - 6*(D*a*b - B*b^2)*x^2 - 6*(C*a*b - A*b^2)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 12*(C*a*b - A*b^2)*x + 6*(D*a^2 - B*a*b)*log(b*x^2 + a))/b^3, 1/12*(3*D*b^2*x^4 + 4*C*b^2*x^3 - 6*(D*a*b - B*b^2)*x^2 + 12*(C*a*b - A*b^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 12*(C*a*b - A*b^2)*x + 6*(D*a^2 - B*a*b)*log(b*x^2 + a))/b^3]","A",0
89,1,180,0,0.984010," ","integrate(x*(D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, D b x^{3} + 3 \, C b x^{2} + 3 \, {\left(D a - B b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 6 \, {\left(D a - B b\right)} x - 3 \, {\left(C a - A b\right)} \log\left(b x^{2} + a\right)}{6 \, b^{2}}, \frac{2 \, D b x^{3} + 3 \, C b x^{2} + 6 \, {\left(D a - B b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 6 \, {\left(D a - B b\right)} x - 3 \, {\left(C a - A b\right)} \log\left(b x^{2} + a\right)}{6 \, b^{2}}\right]"," ",0,"[1/6*(2*D*b*x^3 + 3*C*b*x^2 + 3*(D*a - B*b)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 6*(D*a - B*b)*x - 3*(C*a - A*b)*log(b*x^2 + a))/b^2, 1/6*(2*D*b*x^3 + 3*C*b*x^2 + 6*(D*a - B*b)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 6*(D*a - B*b)*x - 3*(C*a - A*b)*log(b*x^2 + a))/b^2]","A",0
90,1,157,0,0.760067," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{D a b x^{2} + 2 \, C a b x + {\left(C a - A b\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - {\left(D a^{2} - B a b\right)} \log\left(b x^{2} + a\right)}{2 \, a b^{2}}, \frac{D a b x^{2} + 2 \, C a b x - 2 \, {\left(C a - A b\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - {\left(D a^{2} - B a b\right)} \log\left(b x^{2} + a\right)}{2 \, a b^{2}}\right]"," ",0,"[1/2*(D*a*b*x^2 + 2*C*a*b*x + (C*a - A*b)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - (D*a^2 - B*a*b)*log(b*x^2 + a))/(a*b^2), 1/2*(D*a*b*x^2 + 2*C*a*b*x - 2*(C*a - A*b)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - (D*a^2 - B*a*b)*log(b*x^2 + a))/(a*b^2)]","A",0
91,1,158,0,0.920128," ","integrate((D*x^3+C*x^2+B*x+A)/x/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, D a b x + 2 \, A b^{2} \log\left(x\right) - {\left(D a - B b\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + {\left(C a b - A b^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, a b^{2}}, \frac{2 \, D a b x + 2 \, A b^{2} \log\left(x\right) - 2 \, {\left(D a - B b\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(C a b - A b^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, a b^{2}}\right]"," ",0,"[1/2*(2*D*a*b*x + 2*A*b^2*log(x) - (D*a - B*b)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + (C*a*b - A*b^2)*log(b*x^2 + a))/(a*b^2), 1/2*(2*D*a*b*x + 2*A*b^2*log(x) - 2*(D*a - B*b)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (C*a*b - A*b^2)*log(b*x^2 + a))/(a*b^2)]","A",0
92,1,165,0,0.768027," ","integrate((D*x^3+C*x^2+B*x+A)/x^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, B a b x \log\left(x\right) + {\left(C a - A b\right)} \sqrt{-a b} x \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, A a b + {\left(D a^{2} - B a b\right)} x \log\left(b x^{2} + a\right)}{2 \, a^{2} b x}, \frac{2 \, B a b x \log\left(x\right) + 2 \, {\left(C a - A b\right)} \sqrt{a b} x \arctan\left(\frac{\sqrt{a b} x}{a}\right) - 2 \, A a b + {\left(D a^{2} - B a b\right)} x \log\left(b x^{2} + a\right)}{2 \, a^{2} b x}\right]"," ",0,"[1/2*(2*B*a*b*x*log(x) + (C*a - A*b)*sqrt(-a*b)*x*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*A*a*b + (D*a^2 - B*a*b)*x*log(b*x^2 + a))/(a^2*b*x), 1/2*(2*B*a*b*x*log(x) + 2*(C*a - A*b)*sqrt(a*b)*x*arctan(sqrt(a*b)*x/a) - 2*A*a*b + (D*a^2 - B*a*b)*x*log(b*x^2 + a))/(a^2*b*x)]","A",0
93,1,205,0,1.043570," ","integrate((D*x^3+C*x^2+B*x+A)/x^3/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{{\left(D a - B b\right)} \sqrt{-a b} x^{2} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, B a b x + {\left(C a b - A b^{2}\right)} x^{2} \log\left(b x^{2} + a\right) - 2 \, {\left(C a b - A b^{2}\right)} x^{2} \log\left(x\right) + A a b}{2 \, a^{2} b x^{2}}, \frac{2 \, {\left(D a - B b\right)} \sqrt{a b} x^{2} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - 2 \, B a b x - {\left(C a b - A b^{2}\right)} x^{2} \log\left(b x^{2} + a\right) + 2 \, {\left(C a b - A b^{2}\right)} x^{2} \log\left(x\right) - A a b}{2 \, a^{2} b x^{2}}\right]"," ",0,"[-1/2*((D*a - B*b)*sqrt(-a*b)*x^2*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*B*a*b*x + (C*a*b - A*b^2)*x^2*log(b*x^2 + a) - 2*(C*a*b - A*b^2)*x^2*log(x) + A*a*b)/(a^2*b*x^2), 1/2*(2*(D*a - B*b)*sqrt(a*b)*x^2*arctan(sqrt(a*b)*x/a) - 2*B*a*b*x - (C*a*b - A*b^2)*x^2*log(b*x^2 + a) + 2*(C*a*b - A*b^2)*x^2*log(x) - A*a*b)/(a^2*b*x^2)]","A",0
94,1,468,0,0.583613," ","integrate(x^4*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{3 \, D b^{3} x^{6} + 4 \, C b^{3} x^{5} - 3 \, {\left(3 \, D a b^{2} - 2 \, B b^{3}\right)} x^{4} + 6 \, D a^{3} - 6 \, B a^{2} b - 4 \, {\left(5 \, C a b^{2} - 3 \, A b^{3}\right)} x^{3} - 6 \, {\left(2 \, D a^{2} b - B a b^{2}\right)} x^{2} - 3 \, {\left(5 \, C a^{2} b - 3 \, A a b^{2} + {\left(5 \, C a b^{2} - 3 \, A b^{3}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 6 \, {\left(5 \, C a^{2} b - 3 \, A a b^{2}\right)} x + 6 \, {\left(3 \, D a^{3} - 2 \, B a^{2} b + {\left(3 \, D a^{2} b - 2 \, B a b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{12 \, {\left(b^{5} x^{2} + a b^{4}\right)}}, \frac{3 \, D b^{3} x^{6} + 4 \, C b^{3} x^{5} - 3 \, {\left(3 \, D a b^{2} - 2 \, B b^{3}\right)} x^{4} + 6 \, D a^{3} - 6 \, B a^{2} b - 4 \, {\left(5 \, C a b^{2} - 3 \, A b^{3}\right)} x^{3} - 6 \, {\left(2 \, D a^{2} b - B a b^{2}\right)} x^{2} + 6 \, {\left(5 \, C a^{2} b - 3 \, A a b^{2} + {\left(5 \, C a b^{2} - 3 \, A b^{3}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 6 \, {\left(5 \, C a^{2} b - 3 \, A a b^{2}\right)} x + 6 \, {\left(3 \, D a^{3} - 2 \, B a^{2} b + {\left(3 \, D a^{2} b - 2 \, B a b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{12 \, {\left(b^{5} x^{2} + a b^{4}\right)}}\right]"," ",0,"[1/12*(3*D*b^3*x^6 + 4*C*b^3*x^5 - 3*(3*D*a*b^2 - 2*B*b^3)*x^4 + 6*D*a^3 - 6*B*a^2*b - 4*(5*C*a*b^2 - 3*A*b^3)*x^3 - 6*(2*D*a^2*b - B*a*b^2)*x^2 - 3*(5*C*a^2*b - 3*A*a*b^2 + (5*C*a*b^2 - 3*A*b^3)*x^2)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 6*(5*C*a^2*b - 3*A*a*b^2)*x + 6*(3*D*a^3 - 2*B*a^2*b + (3*D*a^2*b - 2*B*a*b^2)*x^2)*log(b*x^2 + a))/(b^5*x^2 + a*b^4), 1/12*(3*D*b^3*x^6 + 4*C*b^3*x^5 - 3*(3*D*a*b^2 - 2*B*b^3)*x^4 + 6*D*a^3 - 6*B*a^2*b - 4*(5*C*a*b^2 - 3*A*b^3)*x^3 - 6*(2*D*a^2*b - B*a*b^2)*x^2 + 6*(5*C*a^2*b - 3*A*a*b^2 + (5*C*a*b^2 - 3*A*b^3)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 6*(5*C*a^2*b - 3*A*a*b^2)*x + 6*(3*D*a^3 - 2*B*a^2*b + (3*D*a^2*b - 2*B*a*b^2)*x^2)*log(b*x^2 + a))/(b^5*x^2 + a*b^4)]","A",0
95,1,372,0,0.855122," ","integrate(x^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, D b^{2} x^{5} + 6 \, C b^{2} x^{4} + 6 \, C a b x^{2} - 4 \, {\left(5 \, D a b - 3 \, B b^{2}\right)} x^{3} - 6 \, C a^{2} + 6 \, A a b + 3 \, {\left(5 \, D a^{2} - 3 \, B a b + {\left(5 \, D a b - 3 \, B b^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 6 \, {\left(5 \, D a^{2} - 3 \, B a b\right)} x - 6 \, {\left(2 \, C a^{2} - A a b + {\left(2 \, C a b - A b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{12 \, {\left(b^{4} x^{2} + a b^{3}\right)}}, \frac{2 \, D b^{2} x^{5} + 3 \, C b^{2} x^{4} + 3 \, C a b x^{2} - 2 \, {\left(5 \, D a b - 3 \, B b^{2}\right)} x^{3} - 3 \, C a^{2} + 3 \, A a b + 3 \, {\left(5 \, D a^{2} - 3 \, B a b + {\left(5 \, D a b - 3 \, B b^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 3 \, {\left(5 \, D a^{2} - 3 \, B a b\right)} x - 3 \, {\left(2 \, C a^{2} - A a b + {\left(2 \, C a b - A b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{6 \, {\left(b^{4} x^{2} + a b^{3}\right)}}\right]"," ",0,"[1/12*(4*D*b^2*x^5 + 6*C*b^2*x^4 + 6*C*a*b*x^2 - 4*(5*D*a*b - 3*B*b^2)*x^3 - 6*C*a^2 + 6*A*a*b + 3*(5*D*a^2 - 3*B*a*b + (5*D*a*b - 3*B*b^2)*x^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 6*(5*D*a^2 - 3*B*a*b)*x - 6*(2*C*a^2 - A*a*b + (2*C*a*b - A*b^2)*x^2)*log(b*x^2 + a))/(b^4*x^2 + a*b^3), 1/6*(2*D*b^2*x^5 + 3*C*b^2*x^4 + 3*C*a*b*x^2 - 2*(5*D*a*b - 3*B*b^2)*x^3 - 3*C*a^2 + 3*A*a*b + 3*(5*D*a^2 - 3*B*a*b + (5*D*a*b - 3*B*b^2)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 3*(5*D*a^2 - 3*B*a*b)*x - 3*(2*C*a^2 - A*a*b + (2*C*a*b - A*b^2)*x^2)*log(b*x^2 + a))/(b^4*x^2 + a*b^3)]","A",0
96,1,357,0,0.875041," ","integrate(x^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, D a b^{2} x^{4} + 4 \, C a b^{2} x^{3} + 2 \, D a^{2} b x^{2} - 2 \, D a^{3} + 2 \, B a^{2} b + {\left(3 \, C a^{2} - A a b + {\left(3 \, C a b - A b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(3 \, C a^{2} b - A a b^{2}\right)} x - 2 \, {\left(2 \, D a^{3} - B a^{2} b + {\left(2 \, D a^{2} b - B a b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}, \frac{D a b^{2} x^{4} + 2 \, C a b^{2} x^{3} + D a^{2} b x^{2} - D a^{3} + B a^{2} b - {\left(3 \, C a^{2} - A a b + {\left(3 \, C a b - A b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(3 \, C a^{2} b - A a b^{2}\right)} x - {\left(2 \, D a^{3} - B a^{2} b + {\left(2 \, D a^{2} b - B a b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}\right]"," ",0,"[1/4*(2*D*a*b^2*x^4 + 4*C*a*b^2*x^3 + 2*D*a^2*b*x^2 - 2*D*a^3 + 2*B*a^2*b + (3*C*a^2 - A*a*b + (3*C*a*b - A*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(3*C*a^2*b - A*a*b^2)*x - 2*(2*D*a^3 - B*a^2*b + (2*D*a^2*b - B*a*b^2)*x^2)*log(b*x^2 + a))/(a*b^4*x^2 + a^2*b^3), 1/2*(D*a*b^2*x^4 + 2*C*a*b^2*x^3 + D*a^2*b*x^2 - D*a^3 + B*a^2*b - (3*C*a^2 - A*a*b + (3*C*a*b - A*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (3*C*a^2*b - A*a*b^2)*x - (2*D*a^3 - B*a^2*b + (2*D*a^2*b - B*a*b^2)*x^2)*log(b*x^2 + a))/(a*b^4*x^2 + a^2*b^3)]","A",0
97,1,287,0,0.811999," ","integrate(x*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, D a b^{2} x^{3} + 2 \, C a^{2} b - 2 \, A a b^{2} - {\left(3 \, D a^{2} - B a b + {\left(3 \, D a b - B b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(3 \, D a^{2} b - B a b^{2}\right)} x + 2 \, {\left(C a b^{2} x^{2} + C a^{2} b\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}, \frac{2 \, D a b^{2} x^{3} + C a^{2} b - A a b^{2} - {\left(3 \, D a^{2} - B a b + {\left(3 \, D a b - B b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(3 \, D a^{2} b - B a b^{2}\right)} x + {\left(C a b^{2} x^{2} + C a^{2} b\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}\right]"," ",0,"[1/4*(4*D*a*b^2*x^3 + 2*C*a^2*b - 2*A*a*b^2 - (3*D*a^2 - B*a*b + (3*D*a*b - B*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(3*D*a^2*b - B*a*b^2)*x + 2*(C*a*b^2*x^2 + C*a^2*b)*log(b*x^2 + a))/(a*b^4*x^2 + a^2*b^3), 1/2*(2*D*a*b^2*x^3 + C*a^2*b - A*a*b^2 - (3*D*a^2 - B*a*b + (3*D*a*b - B*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (3*D*a^2*b - B*a*b^2)*x + (C*a*b^2*x^2 + C*a^2*b)*log(b*x^2 + a))/(a*b^4*x^2 + a^2*b^3)]","A",0
98,1,257,0,0.845346," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, D a^{3} - 2 \, B a^{2} b - {\left(C a^{2} + A a b + {\left(C a b + A b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, {\left(C a^{2} b - A a b^{2}\right)} x + 2 \, {\left(D a^{2} b x^{2} + D a^{3}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}, \frac{D a^{3} - B a^{2} b + {\left(C a^{2} + A a b + {\left(C a b + A b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - {\left(C a^{2} b - A a b^{2}\right)} x + {\left(D a^{2} b x^{2} + D a^{3}\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}\right]"," ",0,"[1/4*(2*D*a^3 - 2*B*a^2*b - (C*a^2 + A*a*b + (C*a*b + A*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*(C*a^2*b - A*a*b^2)*x + 2*(D*a^2*b*x^2 + D*a^3)*log(b*x^2 + a))/(a^2*b^3*x^2 + a^3*b^2), 1/2*(D*a^3 - B*a^2*b + (C*a^2 + A*a*b + (C*a*b + A*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - (C*a^2*b - A*a*b^2)*x + (D*a^2*b*x^2 + D*a^3)*log(b*x^2 + a))/(a^2*b^3*x^2 + a^3*b^2)]","A",0
99,1,296,0,0.874115," ","integrate((D*x^3+C*x^2+B*x+A)/x/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, C a^{2} b - 2 \, A a b^{2} + {\left(D a^{2} + B a b + {\left(D a b + B b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(D a^{2} b - B a b^{2}\right)} x + 2 \, {\left(A b^{3} x^{2} + A a b^{2}\right)} \log\left(b x^{2} + a\right) - 4 \, {\left(A b^{3} x^{2} + A a b^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}, -\frac{C a^{2} b - A a b^{2} - {\left(D a^{2} + B a b + {\left(D a b + B b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(D a^{2} b - B a b^{2}\right)} x + {\left(A b^{3} x^{2} + A a b^{2}\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(A b^{3} x^{2} + A a b^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}\right]"," ",0,"[-1/4*(2*C*a^2*b - 2*A*a*b^2 + (D*a^2 + B*a*b + (D*a*b + B*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(D*a^2*b - B*a*b^2)*x + 2*(A*b^3*x^2 + A*a*b^2)*log(b*x^2 + a) - 4*(A*b^3*x^2 + A*a*b^2)*log(x))/(a^2*b^3*x^2 + a^3*b^2), -1/2*(C*a^2*b - A*a*b^2 - (D*a^2 + B*a*b + (D*a*b + B*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (D*a^2*b - B*a*b^2)*x + (A*b^3*x^2 + A*a*b^2)*log(b*x^2 + a) - 2*(A*b^3*x^2 + A*a*b^2)*log(x))/(a^2*b^3*x^2 + a^3*b^2)]","A",0
100,1,336,0,0.876414," ","integrate((D*x^3+C*x^2+B*x+A)/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, A a^{2} b - 2 \, {\left(C a^{2} b - 3 \, A a b^{2}\right)} x^{2} - {\left({\left(C a b - 3 \, A b^{2}\right)} x^{3} + {\left(C a^{2} - 3 \, A a b\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(D a^{3} - B a^{2} b\right)} x + 2 \, {\left(B a b^{2} x^{3} + B a^{2} b x\right)} \log\left(b x^{2} + a\right) - 4 \, {\left(B a b^{2} x^{3} + B a^{2} b x\right)} \log\left(x\right)}{4 \, {\left(a^{3} b^{2} x^{3} + a^{4} b x\right)}}, -\frac{2 \, A a^{2} b - {\left(C a^{2} b - 3 \, A a b^{2}\right)} x^{2} - {\left({\left(C a b - 3 \, A b^{2}\right)} x^{3} + {\left(C a^{2} - 3 \, A a b\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(D a^{3} - B a^{2} b\right)} x + {\left(B a b^{2} x^{3} + B a^{2} b x\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(B a b^{2} x^{3} + B a^{2} b x\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{2} x^{3} + a^{4} b x\right)}}\right]"," ",0,"[-1/4*(4*A*a^2*b - 2*(C*a^2*b - 3*A*a*b^2)*x^2 - ((C*a*b - 3*A*b^2)*x^3 + (C*a^2 - 3*A*a*b)*x)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(D*a^3 - B*a^2*b)*x + 2*(B*a*b^2*x^3 + B*a^2*b*x)*log(b*x^2 + a) - 4*(B*a*b^2*x^3 + B*a^2*b*x)*log(x))/(a^3*b^2*x^3 + a^4*b*x), -1/2*(2*A*a^2*b - (C*a^2*b - 3*A*a*b^2)*x^2 - ((C*a*b - 3*A*b^2)*x^3 + (C*a^2 - 3*A*a*b)*x)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (D*a^3 - B*a^2*b)*x + (B*a*b^2*x^3 + B*a^2*b*x)*log(b*x^2 + a) - 2*(B*a*b^2*x^3 + B*a^2*b*x)*log(x))/(a^3*b^2*x^3 + a^4*b*x)]","A",0
101,1,441,0,1.018787," ","integrate((D*x^3+C*x^2+B*x+A)/x^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, B a^{2} b x + 2 \, A a^{2} b - 2 \, {\left(D a^{2} b - 3 \, B a b^{2}\right)} x^{3} - 2 \, {\left(C a^{2} b - 2 \, A a b^{2}\right)} x^{2} + {\left({\left(D a b - 3 \, B b^{2}\right)} x^{4} + {\left(D a^{2} - 3 \, B a b\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left({\left(C a b^{2} - 2 \, A b^{3}\right)} x^{4} + {\left(C a^{2} b - 2 \, A a b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - 4 \, {\left({\left(C a b^{2} - 2 \, A b^{3}\right)} x^{4} + {\left(C a^{2} b - 2 \, A a b^{2}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{3} b^{2} x^{4} + a^{4} b x^{2}\right)}}, -\frac{2 \, B a^{2} b x + A a^{2} b - {\left(D a^{2} b - 3 \, B a b^{2}\right)} x^{3} - {\left(C a^{2} b - 2 \, A a b^{2}\right)} x^{2} - {\left({\left(D a b - 3 \, B b^{2}\right)} x^{4} + {\left(D a^{2} - 3 \, B a b\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left({\left(C a b^{2} - 2 \, A b^{3}\right)} x^{4} + {\left(C a^{2} b - 2 \, A a b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - 2 \, {\left({\left(C a b^{2} - 2 \, A b^{3}\right)} x^{4} + {\left(C a^{2} b - 2 \, A a b^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{2} x^{4} + a^{4} b x^{2}\right)}}\right]"," ",0,"[-1/4*(4*B*a^2*b*x + 2*A*a^2*b - 2*(D*a^2*b - 3*B*a*b^2)*x^3 - 2*(C*a^2*b - 2*A*a*b^2)*x^2 + ((D*a*b - 3*B*b^2)*x^4 + (D*a^2 - 3*B*a*b)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*((C*a*b^2 - 2*A*b^3)*x^4 + (C*a^2*b - 2*A*a*b^2)*x^2)*log(b*x^2 + a) - 4*((C*a*b^2 - 2*A*b^3)*x^4 + (C*a^2*b - 2*A*a*b^2)*x^2)*log(x))/(a^3*b^2*x^4 + a^4*b*x^2), -1/2*(2*B*a^2*b*x + A*a^2*b - (D*a^2*b - 3*B*a*b^2)*x^3 - (C*a^2*b - 2*A*a*b^2)*x^2 - ((D*a*b - 3*B*b^2)*x^4 + (D*a^2 - 3*B*a*b)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + ((C*a*b^2 - 2*A*b^3)*x^4 + (C*a^2*b - 2*A*a*b^2)*x^2)*log(b*x^2 + a) - 2*((C*a*b^2 - 2*A*b^3)*x^4 + (C*a^2*b - 2*A*a*b^2)*x^2)*log(x))/(a^3*b^2*x^4 + a^4*b*x^2)]","A",0
102,1,574,0,0.837944," ","integrate(x^4*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{8 \, D a b^{3} x^{6} + 16 \, C a b^{3} x^{5} + 16 \, D a^{2} b^{2} x^{4} - 20 \, D a^{4} + 12 \, B a^{3} b + 10 \, {\left(5 \, C a^{2} b^{2} - A a b^{3}\right)} x^{3} - 16 \, {\left(D a^{3} b - B a^{2} b^{2}\right)} x^{2} + 3 \, {\left({\left(5 \, C a b^{2} - A b^{3}\right)} x^{4} + 5 \, C a^{3} - A a^{2} b + 2 \, {\left(5 \, C a^{2} b - A a b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(5 \, C a^{3} b - A a^{2} b^{2}\right)} x - 8 \, {\left(3 \, D a^{4} - B a^{3} b + {\left(3 \, D a^{2} b^{2} - B a b^{3}\right)} x^{4} + 2 \, {\left(3 \, D a^{3} b - B a^{2} b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{16 \, {\left(a b^{6} x^{4} + 2 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}, \frac{4 \, D a b^{3} x^{6} + 8 \, C a b^{3} x^{5} + 8 \, D a^{2} b^{2} x^{4} - 10 \, D a^{4} + 6 \, B a^{3} b + 5 \, {\left(5 \, C a^{2} b^{2} - A a b^{3}\right)} x^{3} - 8 \, {\left(D a^{3} b - B a^{2} b^{2}\right)} x^{2} - 3 \, {\left({\left(5 \, C a b^{2} - A b^{3}\right)} x^{4} + 5 \, C a^{3} - A a^{2} b + 2 \, {\left(5 \, C a^{2} b - A a b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(5 \, C a^{3} b - A a^{2} b^{2}\right)} x - 4 \, {\left(3 \, D a^{4} - B a^{3} b + {\left(3 \, D a^{2} b^{2} - B a b^{3}\right)} x^{4} + 2 \, {\left(3 \, D a^{3} b - B a^{2} b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{8 \, {\left(a b^{6} x^{4} + 2 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}\right]"," ",0,"[1/16*(8*D*a*b^3*x^6 + 16*C*a*b^3*x^5 + 16*D*a^2*b^2*x^4 - 20*D*a^4 + 12*B*a^3*b + 10*(5*C*a^2*b^2 - A*a*b^3)*x^3 - 16*(D*a^3*b - B*a^2*b^2)*x^2 + 3*((5*C*a*b^2 - A*b^3)*x^4 + 5*C*a^3 - A*a^2*b + 2*(5*C*a^2*b - A*a*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(5*C*a^3*b - A*a^2*b^2)*x - 8*(3*D*a^4 - B*a^3*b + (3*D*a^2*b^2 - B*a*b^3)*x^4 + 2*(3*D*a^3*b - B*a^2*b^2)*x^2)*log(b*x^2 + a))/(a*b^6*x^4 + 2*a^2*b^5*x^2 + a^3*b^4), 1/8*(4*D*a*b^3*x^6 + 8*C*a*b^3*x^5 + 8*D*a^2*b^2*x^4 - 10*D*a^4 + 6*B*a^3*b + 5*(5*C*a^2*b^2 - A*a*b^3)*x^3 - 8*(D*a^3*b - B*a^2*b^2)*x^2 - 3*((5*C*a*b^2 - A*b^3)*x^4 + 5*C*a^3 - A*a^2*b + 2*(5*C*a^2*b - A*a*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 3*(5*C*a^3*b - A*a^2*b^2)*x - 4*(3*D*a^4 - B*a^3*b + (3*D*a^2*b^2 - B*a*b^3)*x^4 + 2*(3*D*a^3*b - B*a^2*b^2)*x^2)*log(b*x^2 + a))/(a*b^6*x^4 + 2*a^2*b^5*x^2 + a^3*b^4)]","A",0
103,1,480,0,0.932588," ","integrate(x^3*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{16 \, D a b^{3} x^{5} + 12 \, C a^{3} b - 4 \, A a^{2} b^{2} + 10 \, {\left(5 \, D a^{2} b^{2} - B a b^{3}\right)} x^{3} + 8 \, {\left(2 \, C a^{2} b^{2} - A a b^{3}\right)} x^{2} - 3 \, {\left({\left(5 \, D a b^{2} - B b^{3}\right)} x^{4} + 5 \, D a^{3} - B a^{2} b + 2 \, {\left(5 \, D a^{2} b - B a b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(5 \, D a^{3} b - B a^{2} b^{2}\right)} x + 8 \, {\left(C a b^{3} x^{4} + 2 \, C a^{2} b^{2} x^{2} + C a^{3} b\right)} \log\left(b x^{2} + a\right)}{16 \, {\left(a b^{6} x^{4} + 2 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}, \frac{8 \, D a b^{3} x^{5} + 6 \, C a^{3} b - 2 \, A a^{2} b^{2} + 5 \, {\left(5 \, D a^{2} b^{2} - B a b^{3}\right)} x^{3} + 4 \, {\left(2 \, C a^{2} b^{2} - A a b^{3}\right)} x^{2} - 3 \, {\left({\left(5 \, D a b^{2} - B b^{3}\right)} x^{4} + 5 \, D a^{3} - B a^{2} b + 2 \, {\left(5 \, D a^{2} b - B a b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(5 \, D a^{3} b - B a^{2} b^{2}\right)} x + 4 \, {\left(C a b^{3} x^{4} + 2 \, C a^{2} b^{2} x^{2} + C a^{3} b\right)} \log\left(b x^{2} + a\right)}{8 \, {\left(a b^{6} x^{4} + 2 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}\right]"," ",0,"[1/16*(16*D*a*b^3*x^5 + 12*C*a^3*b - 4*A*a^2*b^2 + 10*(5*D*a^2*b^2 - B*a*b^3)*x^3 + 8*(2*C*a^2*b^2 - A*a*b^3)*x^2 - 3*((5*D*a*b^2 - B*b^3)*x^4 + 5*D*a^3 - B*a^2*b + 2*(5*D*a^2*b - B*a*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(5*D*a^3*b - B*a^2*b^2)*x + 8*(C*a*b^3*x^4 + 2*C*a^2*b^2*x^2 + C*a^3*b)*log(b*x^2 + a))/(a*b^6*x^4 + 2*a^2*b^5*x^2 + a^3*b^4), 1/8*(8*D*a*b^3*x^5 + 6*C*a^3*b - 2*A*a^2*b^2 + 5*(5*D*a^2*b^2 - B*a*b^3)*x^3 + 4*(2*C*a^2*b^2 - A*a*b^3)*x^2 - 3*((5*D*a*b^2 - B*b^3)*x^4 + 5*D*a^3 - B*a^2*b + 2*(5*D*a^2*b - B*a*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 3*(5*D*a^3*b - B*a^2*b^2)*x + 4*(C*a*b^3*x^4 + 2*C*a^2*b^2*x^2 + C*a^3*b)*log(b*x^2 + a))/(a*b^6*x^4 + 2*a^2*b^5*x^2 + a^3*b^4)]","A",0
104,1,447,0,0.864607," ","integrate(x^2*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{12 \, D a^{4} - 4 \, B a^{3} b - 2 \, {\left(5 \, C a^{2} b^{2} - A a b^{3}\right)} x^{3} + 8 \, {\left(2 \, D a^{3} b - B a^{2} b^{2}\right)} x^{2} - {\left({\left(3 \, C a b^{2} + A b^{3}\right)} x^{4} + 3 \, C a^{3} + A a^{2} b + 2 \, {\left(3 \, C a^{2} b + A a b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, {\left(3 \, C a^{3} b + A a^{2} b^{2}\right)} x + 8 \, {\left(D a^{2} b^{2} x^{4} + 2 \, D a^{3} b x^{2} + D a^{4}\right)} \log\left(b x^{2} + a\right)}{16 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}, \frac{6 \, D a^{4} - 2 \, B a^{3} b - {\left(5 \, C a^{2} b^{2} - A a b^{3}\right)} x^{3} + 4 \, {\left(2 \, D a^{3} b - B a^{2} b^{2}\right)} x^{2} + {\left({\left(3 \, C a b^{2} + A b^{3}\right)} x^{4} + 3 \, C a^{3} + A a^{2} b + 2 \, {\left(3 \, C a^{2} b + A a b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - {\left(3 \, C a^{3} b + A a^{2} b^{2}\right)} x + 4 \, {\left(D a^{2} b^{2} x^{4} + 2 \, D a^{3} b x^{2} + D a^{4}\right)} \log\left(b x^{2} + a\right)}{8 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}\right]"," ",0,"[1/16*(12*D*a^4 - 4*B*a^3*b - 2*(5*C*a^2*b^2 - A*a*b^3)*x^3 + 8*(2*D*a^3*b - B*a^2*b^2)*x^2 - ((3*C*a*b^2 + A*b^3)*x^4 + 3*C*a^3 + A*a^2*b + 2*(3*C*a^2*b + A*a*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*(3*C*a^3*b + A*a^2*b^2)*x + 8*(D*a^2*b^2*x^4 + 2*D*a^3*b*x^2 + D*a^4)*log(b*x^2 + a))/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3), 1/8*(6*D*a^4 - 2*B*a^3*b - (5*C*a^2*b^2 - A*a*b^3)*x^3 + 4*(2*D*a^3*b - B*a^2*b^2)*x^2 + ((3*C*a*b^2 + A*b^3)*x^4 + 3*C*a^3 + A*a^2*b + 2*(3*C*a^2*b + A*a*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - (3*C*a^3*b + A*a^2*b^2)*x + 4*(D*a^2*b^2*x^4 + 2*D*a^3*b*x^2 + D*a^4)*log(b*x^2 + a))/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3)]","A",0
105,1,357,0,0.768405," ","integrate(x*(D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{8 \, C a^{2} b^{2} x^{2} + 4 \, C a^{3} b + 4 \, A a^{2} b^{2} + 2 \, {\left(5 \, D a^{2} b^{2} - B a b^{3}\right)} x^{3} + {\left({\left(3 \, D a b^{2} + B b^{3}\right)} x^{4} + 3 \, D a^{3} + B a^{2} b + 2 \, {\left(3 \, D a^{2} b + B a b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(3 \, D a^{3} b + B a^{2} b^{2}\right)} x}{16 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}, -\frac{4 \, C a^{2} b^{2} x^{2} + 2 \, C a^{3} b + 2 \, A a^{2} b^{2} + {\left(5 \, D a^{2} b^{2} - B a b^{3}\right)} x^{3} - {\left({\left(3 \, D a b^{2} + B b^{3}\right)} x^{4} + 3 \, D a^{3} + B a^{2} b + 2 \, {\left(3 \, D a^{2} b + B a b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(3 \, D a^{3} b + B a^{2} b^{2}\right)} x}{8 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}\right]"," ",0,"[-1/16*(8*C*a^2*b^2*x^2 + 4*C*a^3*b + 4*A*a^2*b^2 + 2*(5*D*a^2*b^2 - B*a*b^3)*x^3 + ((3*D*a*b^2 + B*b^3)*x^4 + 3*D*a^3 + B*a^2*b + 2*(3*D*a^2*b + B*a*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(3*D*a^3*b + B*a^2*b^2)*x)/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3), -1/8*(4*C*a^2*b^2*x^2 + 2*C*a^3*b + 2*A*a^2*b^2 + (5*D*a^2*b^2 - B*a*b^3)*x^3 - ((3*D*a*b^2 + B*b^3)*x^4 + 3*D*a^3 + B*a^2*b + 2*(3*D*a^2*b + B*a*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (3*D*a^3*b + B*a^2*b^2)*x)/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3)]","A",0
106,1,346,0,0.880141," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{8 \, D a^{3} b x^{2} + 4 \, D a^{4} + 4 \, B a^{3} b - 2 \, {\left(C a^{2} b^{2} + 3 \, A a b^{3}\right)} x^{3} + {\left({\left(C a b^{2} + 3 \, A b^{3}\right)} x^{4} + C a^{3} + 3 \, A a^{2} b + 2 \, {\left(C a^{2} b + 3 \, A a b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(C a^{3} b - 5 \, A a^{2} b^{2}\right)} x}{16 \, {\left(a^{3} b^{4} x^{4} + 2 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}, -\frac{4 \, D a^{3} b x^{2} + 2 \, D a^{4} + 2 \, B a^{3} b - {\left(C a^{2} b^{2} + 3 \, A a b^{3}\right)} x^{3} - {\left({\left(C a b^{2} + 3 \, A b^{3}\right)} x^{4} + C a^{3} + 3 \, A a^{2} b + 2 \, {\left(C a^{2} b + 3 \, A a b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(C a^{3} b - 5 \, A a^{2} b^{2}\right)} x}{8 \, {\left(a^{3} b^{4} x^{4} + 2 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}\right]"," ",0,"[-1/16*(8*D*a^3*b*x^2 + 4*D*a^4 + 4*B*a^3*b - 2*(C*a^2*b^2 + 3*A*a*b^3)*x^3 + ((C*a*b^2 + 3*A*b^3)*x^4 + C*a^3 + 3*A*a^2*b + 2*(C*a^2*b + 3*A*a*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(C*a^3*b - 5*A*a^2*b^2)*x)/(a^3*b^4*x^4 + 2*a^4*b^3*x^2 + a^5*b^2), -1/8*(4*D*a^3*b*x^2 + 2*D*a^4 + 2*B*a^3*b - (C*a^2*b^2 + 3*A*a*b^3)*x^3 - ((C*a*b^2 + 3*A*b^3)*x^4 + C*a^3 + 3*A*a^2*b + 2*(C*a^2*b + 3*A*a*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (C*a^3*b - 5*A*a^2*b^2)*x)/(a^3*b^4*x^4 + 2*a^4*b^3*x^2 + a^5*b^2)]","A",0
107,1,488,0,0.957172," ","integrate((D*x^3+C*x^2+B*x+A)/x/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{8 \, A a b^{3} x^{2} - 4 \, C a^{3} b + 12 \, A a^{2} b^{2} + 2 \, {\left(D a^{2} b^{2} + 3 \, B a b^{3}\right)} x^{3} - {\left({\left(D a b^{2} + 3 \, B b^{3}\right)} x^{4} + D a^{3} + 3 \, B a^{2} b + 2 \, {\left(D a^{2} b + 3 \, B a b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, {\left(D a^{3} b - 5 \, B a^{2} b^{2}\right)} x - 8 \, {\left(A b^{4} x^{4} + 2 \, A a b^{3} x^{2} + A a^{2} b^{2}\right)} \log\left(b x^{2} + a\right) + 16 \, {\left(A b^{4} x^{4} + 2 \, A a b^{3} x^{2} + A a^{2} b^{2}\right)} \log\left(x\right)}{16 \, {\left(a^{3} b^{4} x^{4} + 2 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}, \frac{4 \, A a b^{3} x^{2} - 2 \, C a^{3} b + 6 \, A a^{2} b^{2} + {\left(D a^{2} b^{2} + 3 \, B a b^{3}\right)} x^{3} + {\left({\left(D a b^{2} + 3 \, B b^{3}\right)} x^{4} + D a^{3} + 3 \, B a^{2} b + 2 \, {\left(D a^{2} b + 3 \, B a b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - {\left(D a^{3} b - 5 \, B a^{2} b^{2}\right)} x - 4 \, {\left(A b^{4} x^{4} + 2 \, A a b^{3} x^{2} + A a^{2} b^{2}\right)} \log\left(b x^{2} + a\right) + 8 \, {\left(A b^{4} x^{4} + 2 \, A a b^{3} x^{2} + A a^{2} b^{2}\right)} \log\left(x\right)}{8 \, {\left(a^{3} b^{4} x^{4} + 2 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}\right]"," ",0,"[1/16*(8*A*a*b^3*x^2 - 4*C*a^3*b + 12*A*a^2*b^2 + 2*(D*a^2*b^2 + 3*B*a*b^3)*x^3 - ((D*a*b^2 + 3*B*b^3)*x^4 + D*a^3 + 3*B*a^2*b + 2*(D*a^2*b + 3*B*a*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*(D*a^3*b - 5*B*a^2*b^2)*x - 8*(A*b^4*x^4 + 2*A*a*b^3*x^2 + A*a^2*b^2)*log(b*x^2 + a) + 16*(A*b^4*x^4 + 2*A*a*b^3*x^2 + A*a^2*b^2)*log(x))/(a^3*b^4*x^4 + 2*a^4*b^3*x^2 + a^5*b^2), 1/8*(4*A*a*b^3*x^2 - 2*C*a^3*b + 6*A*a^2*b^2 + (D*a^2*b^2 + 3*B*a*b^3)*x^3 + ((D*a*b^2 + 3*B*b^3)*x^4 + D*a^3 + 3*B*a^2*b + 2*(D*a^2*b + 3*B*a*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - (D*a^3*b - 5*B*a^2*b^2)*x - 4*(A*b^4*x^4 + 2*A*a*b^3*x^2 + A*a^2*b^2)*log(b*x^2 + a) + 8*(A*b^4*x^4 + 2*A*a*b^3*x^2 + A*a^2*b^2)*log(x))/(a^3*b^4*x^4 + 2*a^4*b^3*x^2 + a^5*b^2)]","B",0
108,1,524,0,0.902892," ","integrate((D*x^3+C*x^2+B*x+A)/x^2/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{8 \, B a^{2} b^{2} x^{3} - 16 \, A a^{3} b + 6 \, {\left(C a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{4} + 10 \, {\left(C a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{2} + 3 \, {\left({\left(C a b^{2} - 5 \, A b^{3}\right)} x^{5} + 2 \, {\left(C a^{2} b - 5 \, A a b^{2}\right)} x^{3} + {\left(C a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 4 \, {\left(D a^{4} - 3 \, B a^{3} b\right)} x - 8 \, {\left(B a b^{3} x^{5} + 2 \, B a^{2} b^{2} x^{3} + B a^{3} b x\right)} \log\left(b x^{2} + a\right) + 16 \, {\left(B a b^{3} x^{5} + 2 \, B a^{2} b^{2} x^{3} + B a^{3} b x\right)} \log\left(x\right)}{16 \, {\left(a^{4} b^{3} x^{5} + 2 \, a^{5} b^{2} x^{3} + a^{6} b x\right)}}, \frac{4 \, B a^{2} b^{2} x^{3} - 8 \, A a^{3} b + 3 \, {\left(C a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{4} + 5 \, {\left(C a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{2} + 3 \, {\left({\left(C a b^{2} - 5 \, A b^{3}\right)} x^{5} + 2 \, {\left(C a^{2} b - 5 \, A a b^{2}\right)} x^{3} + {\left(C a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - 2 \, {\left(D a^{4} - 3 \, B a^{3} b\right)} x - 4 \, {\left(B a b^{3} x^{5} + 2 \, B a^{2} b^{2} x^{3} + B a^{3} b x\right)} \log\left(b x^{2} + a\right) + 8 \, {\left(B a b^{3} x^{5} + 2 \, B a^{2} b^{2} x^{3} + B a^{3} b x\right)} \log\left(x\right)}{8 \, {\left(a^{4} b^{3} x^{5} + 2 \, a^{5} b^{2} x^{3} + a^{6} b x\right)}}\right]"," ",0,"[1/16*(8*B*a^2*b^2*x^3 - 16*A*a^3*b + 6*(C*a^2*b^2 - 5*A*a*b^3)*x^4 + 10*(C*a^3*b - 5*A*a^2*b^2)*x^2 + 3*((C*a*b^2 - 5*A*b^3)*x^5 + 2*(C*a^2*b - 5*A*a*b^2)*x^3 + (C*a^3 - 5*A*a^2*b)*x)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 4*(D*a^4 - 3*B*a^3*b)*x - 8*(B*a*b^3*x^5 + 2*B*a^2*b^2*x^3 + B*a^3*b*x)*log(b*x^2 + a) + 16*(B*a*b^3*x^5 + 2*B*a^2*b^2*x^3 + B*a^3*b*x)*log(x))/(a^4*b^3*x^5 + 2*a^5*b^2*x^3 + a^6*b*x), 1/8*(4*B*a^2*b^2*x^3 - 8*A*a^3*b + 3*(C*a^2*b^2 - 5*A*a*b^3)*x^4 + 5*(C*a^3*b - 5*A*a^2*b^2)*x^2 + 3*((C*a*b^2 - 5*A*b^3)*x^5 + 2*(C*a^2*b - 5*A*a*b^2)*x^3 + (C*a^3 - 5*A*a^2*b)*x)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - 2*(D*a^4 - 3*B*a^3*b)*x - 4*(B*a*b^3*x^5 + 2*B*a^2*b^2*x^3 + B*a^3*b*x)*log(b*x^2 + a) + 8*(B*a*b^3*x^5 + 2*B*a^2*b^2*x^3 + B*a^3*b*x)*log(x))/(a^4*b^3*x^5 + 2*a^5*b^2*x^3 + a^6*b*x)]","B",0
109,1,696,0,0.826804," ","integrate((D*x^3+C*x^2+B*x+A)/x^3/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, B a^{3} b x - 6 \, {\left(D a^{2} b^{2} - 5 \, B a b^{3}\right)} x^{5} + 8 \, A a^{3} b - 8 \, {\left(C a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{4} - 10 \, {\left(D a^{3} b - 5 \, B a^{2} b^{2}\right)} x^{3} - 12 \, {\left(C a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{2} + 3 \, {\left({\left(D a b^{2} - 5 \, B b^{3}\right)} x^{6} + 2 \, {\left(D a^{2} b - 5 \, B a b^{2}\right)} x^{4} + {\left(D a^{3} - 5 \, B a^{2} b\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 8 \, {\left({\left(C a b^{3} - 3 \, A b^{4}\right)} x^{6} + 2 \, {\left(C a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{4} + {\left(C a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - 16 \, {\left({\left(C a b^{3} - 3 \, A b^{4}\right)} x^{6} + 2 \, {\left(C a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{4} + {\left(C a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{2}\right)} \log\left(x\right)}{16 \, {\left(a^{4} b^{3} x^{6} + 2 \, a^{5} b^{2} x^{4} + a^{6} b x^{2}\right)}}, -\frac{8 \, B a^{3} b x - 3 \, {\left(D a^{2} b^{2} - 5 \, B a b^{3}\right)} x^{5} + 4 \, A a^{3} b - 4 \, {\left(C a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{4} - 5 \, {\left(D a^{3} b - 5 \, B a^{2} b^{2}\right)} x^{3} - 6 \, {\left(C a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{2} - 3 \, {\left({\left(D a b^{2} - 5 \, B b^{3}\right)} x^{6} + 2 \, {\left(D a^{2} b - 5 \, B a b^{2}\right)} x^{4} + {\left(D a^{3} - 5 \, B a^{2} b\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 4 \, {\left({\left(C a b^{3} - 3 \, A b^{4}\right)} x^{6} + 2 \, {\left(C a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{4} + {\left(C a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - 8 \, {\left({\left(C a b^{3} - 3 \, A b^{4}\right)} x^{6} + 2 \, {\left(C a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{4} + {\left(C a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{2}\right)} \log\left(x\right)}{8 \, {\left(a^{4} b^{3} x^{6} + 2 \, a^{5} b^{2} x^{4} + a^{6} b x^{2}\right)}}\right]"," ",0,"[-1/16*(16*B*a^3*b*x - 6*(D*a^2*b^2 - 5*B*a*b^3)*x^5 + 8*A*a^3*b - 8*(C*a^2*b^2 - 3*A*a*b^3)*x^4 - 10*(D*a^3*b - 5*B*a^2*b^2)*x^3 - 12*(C*a^3*b - 3*A*a^2*b^2)*x^2 + 3*((D*a*b^2 - 5*B*b^3)*x^6 + 2*(D*a^2*b - 5*B*a*b^2)*x^4 + (D*a^3 - 5*B*a^2*b)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 8*((C*a*b^3 - 3*A*b^4)*x^6 + 2*(C*a^2*b^2 - 3*A*a*b^3)*x^4 + (C*a^3*b - 3*A*a^2*b^2)*x^2)*log(b*x^2 + a) - 16*((C*a*b^3 - 3*A*b^4)*x^6 + 2*(C*a^2*b^2 - 3*A*a*b^3)*x^4 + (C*a^3*b - 3*A*a^2*b^2)*x^2)*log(x))/(a^4*b^3*x^6 + 2*a^5*b^2*x^4 + a^6*b*x^2), -1/8*(8*B*a^3*b*x - 3*(D*a^2*b^2 - 5*B*a*b^3)*x^5 + 4*A*a^3*b - 4*(C*a^2*b^2 - 3*A*a*b^3)*x^4 - 5*(D*a^3*b - 5*B*a^2*b^2)*x^3 - 6*(C*a^3*b - 3*A*a^2*b^2)*x^2 - 3*((D*a*b^2 - 5*B*b^3)*x^6 + 2*(D*a^2*b - 5*B*a*b^2)*x^4 + (D*a^3 - 5*B*a^2*b)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 4*((C*a*b^3 - 3*A*b^4)*x^6 + 2*(C*a^2*b^2 - 3*A*a*b^3)*x^4 + (C*a^3*b - 3*A*a^2*b^2)*x^2)*log(b*x^2 + a) - 8*((C*a*b^3 - 3*A*b^4)*x^6 + 2*(C*a^2*b^2 - 3*A*a*b^3)*x^4 + (C*a^3*b - 3*A*a^2*b^2)*x^2)*log(x))/(a^4*b^3*x^6 + 2*a^5*b^2*x^4 + a^6*b*x^2)]","B",0
110,1,24,0,0.804242," ","integrate((4*x^3-x)/(x^2+5)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(x^{2} + 5\right)} \log\left(x^{2} + 5\right) + 21}{2 \, {\left(x^{2} + 5\right)}}"," ",0,"1/2*(4*(x^2 + 5)*log(x^2 + 5) + 21)/(x^2 + 5)","A",0
111,1,14,0,0.816210," ","integrate((x^3-x)/(x^2-2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(x^{2} + 1\right)} \sqrt{x^{2} - 2}"," ",0,"1/3*(x^2 + 1)*sqrt(x^2 - 2)","A",0
112,1,20,0,0.740547," ","integrate((2*x^4-x^2)/(2*x^2+1),x, algorithm=""fricas"")","\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
113,1,24,0,0.828973," ","integrate((x^4+x^3)/(x^2+1),x, algorithm=""fricas"")","\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
114,1,452,0,0.858986," ","integrate(x^6*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{630 \, b^{5} f x^{11} + 770 \, {\left(b^{5} e - a b^{4} f\right)} x^{9} + 990 \, {\left(b^{5} d - a b^{4} e + a^{2} b^{3} f\right)} x^{7} + 1386 \, {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} x^{5} - 2310 \, {\left(a b^{4} c - a^{2} b^{3} d + a^{3} b^{2} e - a^{4} b f\right)} x^{3} - 3465 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 6930 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} x}{6930 \, b^{6}}, \frac{315 \, b^{5} f x^{11} + 385 \, {\left(b^{5} e - a b^{4} f\right)} x^{9} + 495 \, {\left(b^{5} d - a b^{4} e + a^{2} b^{3} f\right)} x^{7} + 693 \, {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} x^{5} - 1155 \, {\left(a b^{4} c - a^{2} b^{3} d + a^{3} b^{2} e - a^{4} b f\right)} x^{3} - 3465 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 3465 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} x}{3465 \, b^{6}}\right]"," ",0,"[1/6930*(630*b^5*f*x^11 + 770*(b^5*e - a*b^4*f)*x^9 + 990*(b^5*d - a*b^4*e + a^2*b^3*f)*x^7 + 1386*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*x^5 - 2310*(a*b^4*c - a^2*b^3*d + a^3*b^2*e - a^4*b*f)*x^3 - 3465*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 6930*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*x)/b^6, 1/3465*(315*b^5*f*x^11 + 385*(b^5*e - a*b^4*f)*x^9 + 495*(b^5*d - a*b^4*e + a^2*b^3*f)*x^7 + 693*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*x^5 - 1155*(a*b^4*c - a^2*b^3*d + a^3*b^2*e - a^4*b*f)*x^3 - 3465*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 3465*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*x)/b^6]","A",0
115,1,368,0,0.668154," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{70 \, b^{4} f x^{9} + 90 \, {\left(b^{4} e - a b^{3} f\right)} x^{7} + 126 \, {\left(b^{4} d - a b^{3} e + a^{2} b^{2} f\right)} x^{5} + 210 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{3} - 315 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 630 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x}{630 \, b^{5}}, \frac{35 \, b^{4} f x^{9} + 45 \, {\left(b^{4} e - a b^{3} f\right)} x^{7} + 63 \, {\left(b^{4} d - a b^{3} e + a^{2} b^{2} f\right)} x^{5} + 105 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{3} + 315 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 315 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x}{315 \, b^{5}}\right]"," ",0,"[1/630*(70*b^4*f*x^9 + 90*(b^4*e - a*b^3*f)*x^7 + 126*(b^4*d - a*b^3*e + a^2*b^2*f)*x^5 + 210*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^3 - 315*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 630*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x)/b^5, 1/315*(35*b^4*f*x^9 + 45*(b^4*e - a*b^3*f)*x^7 + 63*(b^4*d - a*b^3*e + a^2*b^2*f)*x^5 + 105*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^3 + 315*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 315*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x)/b^5]","A",0
116,1,286,0,0.791477," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{30 \, b^{3} f x^{7} + 42 \, {\left(b^{3} e - a b^{2} f\right)} x^{5} + 70 \, {\left(b^{3} d - a b^{2} e + a^{2} b f\right)} x^{3} - 105 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 210 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x}{210 \, b^{4}}, \frac{15 \, b^{3} f x^{7} + 21 \, {\left(b^{3} e - a b^{2} f\right)} x^{5} + 35 \, {\left(b^{3} d - a b^{2} e + a^{2} b f\right)} x^{3} - 105 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 105 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x}{105 \, b^{4}}\right]"," ",0,"[1/210*(30*b^3*f*x^7 + 42*(b^3*e - a*b^2*f)*x^5 + 70*(b^3*d - a*b^2*e + a^2*b*f)*x^3 - 105*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 210*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^4, 1/105*(15*b^3*f*x^7 + 21*(b^3*e - a*b^2*f)*x^5 + 35*(b^3*d - a*b^2*e + a^2*b*f)*x^3 - 105*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 105*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^4]","A",0
117,1,236,0,1.139602," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{6 \, a b^{3} f x^{5} + 10 \, {\left(a b^{3} e - a^{2} b^{2} f\right)} x^{3} + 15 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 30 \, {\left(a b^{3} d - a^{2} b^{2} e + a^{3} b f\right)} x}{30 \, a b^{4}}, \frac{3 \, a b^{3} f x^{5} + 5 \, {\left(a b^{3} e - a^{2} b^{2} f\right)} x^{3} + 15 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 15 \, {\left(a b^{3} d - a^{2} b^{2} e + a^{3} b f\right)} x}{15 \, a b^{4}}\right]"," ",0,"[1/30*(6*a*b^3*f*x^5 + 10*(a*b^3*e - a^2*b^2*f)*x^3 + 15*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 30*(a*b^3*d - a^2*b^2*e + a^3*b*f)*x)/(a*b^4), 1/15*(3*a*b^3*f*x^5 + 5*(a*b^3*e - a^2*b^2*f)*x^3 + 15*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 15*(a*b^3*d - a^2*b^2*e + a^3*b*f)*x)/(a*b^4)]","A",0
118,1,211,0,1.252164," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} b^{2} f x^{4} - 6 \, a b^{3} c + 3 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \sqrt{-a b} x \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(a^{2} b^{2} e - a^{3} b f\right)} x^{2}}{6 \, a^{2} b^{3} x}, \frac{a^{2} b^{2} f x^{4} - 3 \, a b^{3} c - 3 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \sqrt{a b} x \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(a^{2} b^{2} e - a^{3} b f\right)} x^{2}}{3 \, a^{2} b^{3} x}\right]"," ",0,"[1/6*(2*a^2*b^2*f*x^4 - 6*a*b^3*c + 3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*sqrt(-a*b)*x*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(a^2*b^2*e - a^3*b*f)*x^2)/(a^2*b^3*x), 1/3*(a^2*b^2*f*x^4 - 3*a*b^3*c - 3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*sqrt(a*b)*x*arctan(sqrt(a*b)*x/a) + 3*(a^2*b^2*e - a^3*b*f)*x^2)/(a^2*b^3*x)]","A",0
119,1,216,0,1.153099," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{6 \, a^{3} b f x^{4} + 3 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \sqrt{-a b} x^{3} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, a^{2} b^{2} c + 6 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} x^{2}}{6 \, a^{3} b^{2} x^{3}}, \frac{3 \, a^{3} b f x^{4} + 3 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \sqrt{a b} x^{3} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - a^{2} b^{2} c + 3 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} x^{2}}{3 \, a^{3} b^{2} x^{3}}\right]"," ",0,"[1/6*(6*a^3*b*f*x^4 + 3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*sqrt(-a*b)*x^3*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*a^2*b^2*c + 6*(a*b^3*c - a^2*b^2*d)*x^2)/(a^3*b^2*x^3), 1/3*(3*a^3*b*f*x^4 + 3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*sqrt(a*b)*x^3*arctan(sqrt(a*b)*x/a) - a^2*b^2*c + 3*(a*b^3*c - a^2*b^2*d)*x^2)/(a^3*b^2*x^3)]","A",0
120,1,246,0,1.200585," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \sqrt{-a b} x^{5} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 6 \, a^{3} b c - 30 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e\right)} x^{4} + 10 \, {\left(a^{2} b^{2} c - a^{3} b d\right)} x^{2}}{30 \, a^{4} b x^{5}}, -\frac{15 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} \sqrt{a b} x^{5} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, a^{3} b c + 15 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e\right)} x^{4} - 5 \, {\left(a^{2} b^{2} c - a^{3} b d\right)} x^{2}}{15 \, a^{4} b x^{5}}\right]"," ",0,"[1/30*(15*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*sqrt(-a*b)*x^5*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 6*a^3*b*c - 30*(a*b^3*c - a^2*b^2*d + a^3*b*e)*x^4 + 10*(a^2*b^2*c - a^3*b*d)*x^2)/(a^4*b*x^5), -1/15*(15*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*sqrt(a*b)*x^5*arctan(sqrt(a*b)*x/a) + 3*a^3*b*c + 15*(a*b^3*c - a^2*b^2*d + a^3*b*e)*x^4 - 5*(a^2*b^2*c - a^3*b*d)*x^2)/(a^4*b*x^5)]","A",0
121,1,292,0,0.848903," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{7} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 210 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{6} + 70 \, {\left(a b^{2} c - a^{2} b d + a^{3} e\right)} x^{4} + 30 \, a^{3} c - 42 \, {\left(a^{2} b c - a^{3} d\right)} x^{2}}{210 \, a^{4} x^{7}}, \frac{105 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{7} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 105 \, {\left(b^{3} c - a b^{2} d + a^{2} b e - a^{3} f\right)} x^{6} - 35 \, {\left(a b^{2} c - a^{2} b d + a^{3} e\right)} x^{4} - 15 \, a^{3} c + 21 \, {\left(a^{2} b c - a^{3} d\right)} x^{2}}{105 \, a^{4} x^{7}}\right]"," ",0,"[-1/210*(105*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^7*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 210*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^6 + 70*(a*b^2*c - a^2*b*d + a^3*e)*x^4 + 30*a^3*c - 42*(a^2*b*c - a^3*d)*x^2)/(a^4*x^7), 1/105*(105*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^7*sqrt(b/a)*arctan(x*sqrt(b/a)) + 105*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^6 - 35*(a*b^2*c - a^2*b*d + a^3*e)*x^4 - 15*a^3*c + 21*(a^2*b*c - a^3*d)*x^2)/(a^4*x^7)]","A",0
122,1,374,0,0.953609," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{9} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 630 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{8} - 210 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x^{6} + 70 \, a^{4} c + 126 \, {\left(a^{2} b^{2} c - a^{3} b d + a^{4} e\right)} x^{4} - 90 \, {\left(a^{3} b c - a^{4} d\right)} x^{2}}{630 \, a^{5} x^{9}}, -\frac{315 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{9} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 315 \, {\left(b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right)} x^{8} - 105 \, {\left(a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right)} x^{6} + 35 \, a^{4} c + 63 \, {\left(a^{2} b^{2} c - a^{3} b d + a^{4} e\right)} x^{4} - 45 \, {\left(a^{3} b c - a^{4} d\right)} x^{2}}{315 \, a^{5} x^{9}}\right]"," ",0,"[-1/630*(315*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^9*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 630*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^8 - 210*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x^6 + 70*a^4*c + 126*(a^2*b^2*c - a^3*b*d + a^4*e)*x^4 - 90*(a^3*b*c - a^4*d)*x^2)/(a^5*x^9), -1/315*(315*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^9*sqrt(b/a)*arctan(x*sqrt(b/a)) + 315*(b^4*c - a*b^3*d + a^2*b^2*e - a^3*b*f)*x^8 - 105*(a*b^3*c - a^2*b^2*d + a^3*b*e - a^4*f)*x^6 + 35*a^4*c + 63*(a^2*b^2*c - a^3*b*d + a^4*e)*x^4 - 45*(a^3*b*c - a^4*d)*x^2)/(a^5*x^9)]","A",0
123,1,458,0,1.083494," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^12/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{3465 \, {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} x^{11} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 6930 \, {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} x^{10} + 2310 \, {\left(a b^{4} c - a^{2} b^{3} d + a^{3} b^{2} e - a^{4} b f\right)} x^{8} - 1386 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} x^{6} + 630 \, a^{5} c + 990 \, {\left(a^{3} b^{2} c - a^{4} b d + a^{5} e\right)} x^{4} - 770 \, {\left(a^{4} b c - a^{5} d\right)} x^{2}}{6930 \, a^{6} x^{11}}, \frac{3465 \, {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} x^{11} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 3465 \, {\left(b^{5} c - a b^{4} d + a^{2} b^{3} e - a^{3} b^{2} f\right)} x^{10} - 1155 \, {\left(a b^{4} c - a^{2} b^{3} d + a^{3} b^{2} e - a^{4} b f\right)} x^{8} + 693 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right)} x^{6} - 315 \, a^{5} c - 495 \, {\left(a^{3} b^{2} c - a^{4} b d + a^{5} e\right)} x^{4} + 385 \, {\left(a^{4} b c - a^{5} d\right)} x^{2}}{3465 \, a^{6} x^{11}}\right]"," ",0,"[-1/6930*(3465*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*x^11*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 6930*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*x^10 + 2310*(a*b^4*c - a^2*b^3*d + a^3*b^2*e - a^4*b*f)*x^8 - 1386*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*x^6 + 630*a^5*c + 990*(a^3*b^2*c - a^4*b*d + a^5*e)*x^4 - 770*(a^4*b*c - a^5*d)*x^2)/(a^6*x^11), 1/3465*(3465*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*x^11*sqrt(b/a)*arctan(x*sqrt(b/a)) + 3465*(b^5*c - a*b^4*d + a^2*b^3*e - a^3*b^2*f)*x^10 - 1155*(a*b^4*c - a^2*b^3*d + a^3*b^2*e - a^4*b*f)*x^8 + 693*(a^2*b^3*c - a^3*b^2*d + a^4*b*e - a^5*f)*x^6 - 315*a^5*c - 495*(a^3*b^2*c - a^4*b*d + a^5*e)*x^4 + 385*(a^4*b*c - a^5*d)*x^2)/(a^6*x^11)]","A",0
124,1,572,0,0.874595," ","integrate(x^6*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{140 \, b^{5} f x^{11} + 20 \, {\left(9 \, b^{5} e - 11 \, a b^{4} f\right)} x^{9} + 36 \, {\left(7 \, b^{5} d - 9 \, a b^{4} e + 11 \, a^{2} b^{3} f\right)} x^{7} + 84 \, {\left(5 \, b^{5} c - 7 \, a b^{4} d + 9 \, a^{2} b^{3} e - 11 \, a^{3} b^{2} f\right)} x^{5} - 420 \, {\left(5 \, a b^{4} c - 7 \, a^{2} b^{3} d + 9 \, a^{3} b^{2} e - 11 \, a^{4} b f\right)} x^{3} - 315 \, {\left(5 \, a^{2} b^{3} c - 7 \, a^{3} b^{2} d + 9 \, a^{4} b e - 11 \, a^{5} f + {\left(5 \, a b^{4} c - 7 \, a^{2} b^{3} d + 9 \, a^{3} b^{2} e - 11 \, a^{4} b f\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 630 \, {\left(5 \, a^{2} b^{3} c - 7 \, a^{3} b^{2} d + 9 \, a^{4} b e - 11 \, a^{5} f\right)} x}{1260 \, {\left(b^{7} x^{2} + a b^{6}\right)}}, \frac{70 \, b^{5} f x^{11} + 10 \, {\left(9 \, b^{5} e - 11 \, a b^{4} f\right)} x^{9} + 18 \, {\left(7 \, b^{5} d - 9 \, a b^{4} e + 11 \, a^{2} b^{3} f\right)} x^{7} + 42 \, {\left(5 \, b^{5} c - 7 \, a b^{4} d + 9 \, a^{2} b^{3} e - 11 \, a^{3} b^{2} f\right)} x^{5} - 210 \, {\left(5 \, a b^{4} c - 7 \, a^{2} b^{3} d + 9 \, a^{3} b^{2} e - 11 \, a^{4} b f\right)} x^{3} + 315 \, {\left(5 \, a^{2} b^{3} c - 7 \, a^{3} b^{2} d + 9 \, a^{4} b e - 11 \, a^{5} f + {\left(5 \, a b^{4} c - 7 \, a^{2} b^{3} d + 9 \, a^{3} b^{2} e - 11 \, a^{4} b f\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 315 \, {\left(5 \, a^{2} b^{3} c - 7 \, a^{3} b^{2} d + 9 \, a^{4} b e - 11 \, a^{5} f\right)} x}{630 \, {\left(b^{7} x^{2} + a b^{6}\right)}}\right]"," ",0,"[1/1260*(140*b^5*f*x^11 + 20*(9*b^5*e - 11*a*b^4*f)*x^9 + 36*(7*b^5*d - 9*a*b^4*e + 11*a^2*b^3*f)*x^7 + 84*(5*b^5*c - 7*a*b^4*d + 9*a^2*b^3*e - 11*a^3*b^2*f)*x^5 - 420*(5*a*b^4*c - 7*a^2*b^3*d + 9*a^3*b^2*e - 11*a^4*b*f)*x^3 - 315*(5*a^2*b^3*c - 7*a^3*b^2*d + 9*a^4*b*e - 11*a^5*f + (5*a*b^4*c - 7*a^2*b^3*d + 9*a^3*b^2*e - 11*a^4*b*f)*x^2)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 630*(5*a^2*b^3*c - 7*a^3*b^2*d + 9*a^4*b*e - 11*a^5*f)*x)/(b^7*x^2 + a*b^6), 1/630*(70*b^5*f*x^11 + 10*(9*b^5*e - 11*a*b^4*f)*x^9 + 18*(7*b^5*d - 9*a*b^4*e + 11*a^2*b^3*f)*x^7 + 42*(5*b^5*c - 7*a*b^4*d + 9*a^2*b^3*e - 11*a^3*b^2*f)*x^5 - 210*(5*a*b^4*c - 7*a^2*b^3*d + 9*a^3*b^2*e - 11*a^4*b*f)*x^3 + 315*(5*a^2*b^3*c - 7*a^3*b^2*d + 9*a^4*b*e - 11*a^5*f + (5*a*b^4*c - 7*a^2*b^3*d + 9*a^3*b^2*e - 11*a^4*b*f)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 315*(5*a^2*b^3*c - 7*a^3*b^2*d + 9*a^4*b*e - 11*a^5*f)*x)/(b^7*x^2 + a*b^6)]","A",0
125,1,478,0,1.171383," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{60 \, b^{4} f x^{9} + 12 \, {\left(7 \, b^{4} e - 9 \, a b^{3} f\right)} x^{7} + 28 \, {\left(5 \, b^{4} d - 7 \, a b^{3} e + 9 \, a^{2} b^{2} f\right)} x^{5} + 140 \, {\left(3 \, b^{4} c - 5 \, a b^{3} d + 7 \, a^{2} b^{2} e - 9 \, a^{3} b f\right)} x^{3} - 105 \, {\left(3 \, a b^{3} c - 5 \, a^{2} b^{2} d + 7 \, a^{3} b e - 9 \, a^{4} f + {\left(3 \, b^{4} c - 5 \, a b^{3} d + 7 \, a^{2} b^{2} e - 9 \, a^{3} b f\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 210 \, {\left(3 \, a b^{3} c - 5 \, a^{2} b^{2} d + 7 \, a^{3} b e - 9 \, a^{4} f\right)} x}{420 \, {\left(b^{6} x^{2} + a b^{5}\right)}}, \frac{30 \, b^{4} f x^{9} + 6 \, {\left(7 \, b^{4} e - 9 \, a b^{3} f\right)} x^{7} + 14 \, {\left(5 \, b^{4} d - 7 \, a b^{3} e + 9 \, a^{2} b^{2} f\right)} x^{5} + 70 \, {\left(3 \, b^{4} c - 5 \, a b^{3} d + 7 \, a^{2} b^{2} e - 9 \, a^{3} b f\right)} x^{3} - 105 \, {\left(3 \, a b^{3} c - 5 \, a^{2} b^{2} d + 7 \, a^{3} b e - 9 \, a^{4} f + {\left(3 \, b^{4} c - 5 \, a b^{3} d + 7 \, a^{2} b^{2} e - 9 \, a^{3} b f\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 105 \, {\left(3 \, a b^{3} c - 5 \, a^{2} b^{2} d + 7 \, a^{3} b e - 9 \, a^{4} f\right)} x}{210 \, {\left(b^{6} x^{2} + a b^{5}\right)}}\right]"," ",0,"[1/420*(60*b^4*f*x^9 + 12*(7*b^4*e - 9*a*b^3*f)*x^7 + 28*(5*b^4*d - 7*a*b^3*e + 9*a^2*b^2*f)*x^5 + 140*(3*b^4*c - 5*a*b^3*d + 7*a^2*b^2*e - 9*a^3*b*f)*x^3 - 105*(3*a*b^3*c - 5*a^2*b^2*d + 7*a^3*b*e - 9*a^4*f + (3*b^4*c - 5*a*b^3*d + 7*a^2*b^2*e - 9*a^3*b*f)*x^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 210*(3*a*b^3*c - 5*a^2*b^2*d + 7*a^3*b*e - 9*a^4*f)*x)/(b^6*x^2 + a*b^5), 1/210*(30*b^4*f*x^9 + 6*(7*b^4*e - 9*a*b^3*f)*x^7 + 14*(5*b^4*d - 7*a*b^3*e + 9*a^2*b^2*f)*x^5 + 70*(3*b^4*c - 5*a*b^3*d + 7*a^2*b^2*e - 9*a^3*b*f)*x^3 - 105*(3*a*b^3*c - 5*a^2*b^2*d + 7*a^3*b*e - 9*a^4*f + (3*b^4*c - 5*a*b^3*d + 7*a^2*b^2*e - 9*a^3*b*f)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 105*(3*a*b^3*c - 5*a^2*b^2*d + 7*a^3*b*e - 9*a^4*f)*x)/(b^6*x^2 + a*b^5)]","A",0
126,1,418,0,1.170272," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{12 \, a b^{4} f x^{7} + 4 \, {\left(5 \, a b^{4} e - 7 \, a^{2} b^{3} f\right)} x^{5} + 20 \, {\left(3 \, a b^{4} d - 5 \, a^{2} b^{3} e + 7 \, a^{3} b^{2} f\right)} x^{3} + 15 \, {\left(a b^{3} c - 3 \, a^{2} b^{2} d + 5 \, a^{3} b e - 7 \, a^{4} f + {\left(b^{4} c - 3 \, a b^{3} d + 5 \, a^{2} b^{2} e - 7 \, a^{3} b f\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 30 \, {\left(a b^{4} c - 3 \, a^{2} b^{3} d + 5 \, a^{3} b^{2} e - 7 \, a^{4} b f\right)} x}{60 \, {\left(a b^{6} x^{2} + a^{2} b^{5}\right)}}, \frac{6 \, a b^{4} f x^{7} + 2 \, {\left(5 \, a b^{4} e - 7 \, a^{2} b^{3} f\right)} x^{5} + 10 \, {\left(3 \, a b^{4} d - 5 \, a^{2} b^{3} e + 7 \, a^{3} b^{2} f\right)} x^{3} + 15 \, {\left(a b^{3} c - 3 \, a^{2} b^{2} d + 5 \, a^{3} b e - 7 \, a^{4} f + {\left(b^{4} c - 3 \, a b^{3} d + 5 \, a^{2} b^{2} e - 7 \, a^{3} b f\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - 15 \, {\left(a b^{4} c - 3 \, a^{2} b^{3} d + 5 \, a^{3} b^{2} e - 7 \, a^{4} b f\right)} x}{30 \, {\left(a b^{6} x^{2} + a^{2} b^{5}\right)}}\right]"," ",0,"[1/60*(12*a*b^4*f*x^7 + 4*(5*a*b^4*e - 7*a^2*b^3*f)*x^5 + 20*(3*a*b^4*d - 5*a^2*b^3*e + 7*a^3*b^2*f)*x^3 + 15*(a*b^3*c - 3*a^2*b^2*d + 5*a^3*b*e - 7*a^4*f + (b^4*c - 3*a*b^3*d + 5*a^2*b^2*e - 7*a^3*b*f)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 30*(a*b^4*c - 3*a^2*b^3*d + 5*a^3*b^2*e - 7*a^4*b*f)*x)/(a*b^6*x^2 + a^2*b^5), 1/30*(6*a*b^4*f*x^7 + 2*(5*a*b^4*e - 7*a^2*b^3*f)*x^5 + 10*(3*a*b^4*d - 5*a^2*b^3*e + 7*a^3*b^2*f)*x^3 + 15*(a*b^3*c - 3*a^2*b^2*d + 5*a^3*b*e - 7*a^4*f + (b^4*c - 3*a*b^3*d + 5*a^2*b^2*e - 7*a^3*b*f)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - 15*(a*b^4*c - 3*a^2*b^3*d + 5*a^3*b^2*e - 7*a^4*b*f)*x)/(a*b^6*x^2 + a^2*b^5)]","A",0
127,1,364,0,1.043905," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} b^{3} f x^{5} + 4 \, {\left(3 \, a^{2} b^{3} e - 5 \, a^{3} b^{2} f\right)} x^{3} - 3 \, {\left(a b^{3} c + a^{2} b^{2} d - 3 \, a^{3} b e + 5 \, a^{4} f + {\left(b^{4} c + a b^{3} d - 3 \, a^{2} b^{2} e + 5 \, a^{3} b f\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(a b^{4} c - a^{2} b^{3} d + 3 \, a^{3} b^{2} e - 5 \, a^{4} b f\right)} x}{12 \, {\left(a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}, \frac{2 \, a^{2} b^{3} f x^{5} + 2 \, {\left(3 \, a^{2} b^{3} e - 5 \, a^{3} b^{2} f\right)} x^{3} + 3 \, {\left(a b^{3} c + a^{2} b^{2} d - 3 \, a^{3} b e + 5 \, a^{4} f + {\left(b^{4} c + a b^{3} d - 3 \, a^{2} b^{2} e + 5 \, a^{3} b f\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(a b^{4} c - a^{2} b^{3} d + 3 \, a^{3} b^{2} e - 5 \, a^{4} b f\right)} x}{6 \, {\left(a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}\right]"," ",0,"[1/12*(4*a^2*b^3*f*x^5 + 4*(3*a^2*b^3*e - 5*a^3*b^2*f)*x^3 - 3*(a*b^3*c + a^2*b^2*d - 3*a^3*b*e + 5*a^4*f + (b^4*c + a*b^3*d - 3*a^2*b^2*e + 5*a^3*b*f)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(a*b^4*c - a^2*b^3*d + 3*a^3*b^2*e - 5*a^4*b*f)*x)/(a^2*b^5*x^2 + a^3*b^4), 1/6*(2*a^2*b^3*f*x^5 + 2*(3*a^2*b^3*e - 5*a^3*b^2*f)*x^3 + 3*(a*b^3*c + a^2*b^2*d - 3*a^3*b*e + 5*a^4*f + (b^4*c + a*b^3*d - 3*a^2*b^2*e + 5*a^3*b*f)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 3*(a*b^4*c - a^2*b^3*d + 3*a^3*b^2*e - 5*a^4*b*f)*x)/(a^2*b^5*x^2 + a^3*b^4)]","A",0
128,1,354,0,1.018083," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{3} b^{2} f x^{4} - 4 \, a^{2} b^{3} c - 2 \, {\left(3 \, a b^{4} c - a^{2} b^{3} d + a^{3} b^{2} e - 3 \, a^{4} b f\right)} x^{2} - {\left({\left(3 \, b^{4} c - a b^{3} d - a^{2} b^{2} e + 3 \, a^{3} b f\right)} x^{3} + {\left(3 \, a b^{3} c - a^{2} b^{2} d - a^{3} b e + 3 \, a^{4} f\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{4 \, {\left(a^{3} b^{4} x^{3} + a^{4} b^{3} x\right)}}, \frac{2 \, a^{3} b^{2} f x^{4} - 2 \, a^{2} b^{3} c - {\left(3 \, a b^{4} c - a^{2} b^{3} d + a^{3} b^{2} e - 3 \, a^{4} b f\right)} x^{2} - {\left({\left(3 \, b^{4} c - a b^{3} d - a^{2} b^{2} e + 3 \, a^{3} b f\right)} x^{3} + {\left(3 \, a b^{3} c - a^{2} b^{2} d - a^{3} b e + 3 \, a^{4} f\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{2 \, {\left(a^{3} b^{4} x^{3} + a^{4} b^{3} x\right)}}\right]"," ",0,"[1/4*(4*a^3*b^2*f*x^4 - 4*a^2*b^3*c - 2*(3*a*b^4*c - a^2*b^3*d + a^3*b^2*e - 3*a^4*b*f)*x^2 - ((3*b^4*c - a*b^3*d - a^2*b^2*e + 3*a^3*b*f)*x^3 + (3*a*b^3*c - a^2*b^2*d - a^3*b*e + 3*a^4*f)*x)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^3*b^4*x^3 + a^4*b^3*x), 1/2*(2*a^3*b^2*f*x^4 - 2*a^2*b^3*c - (3*a*b^4*c - a^2*b^3*d + a^3*b^2*e - 3*a^4*b*f)*x^2 - ((3*b^4*c - a*b^3*d - a^2*b^2*e + 3*a^3*b*f)*x^3 + (3*a*b^3*c - a^2*b^2*d - a^3*b*e + 3*a^4*f)*x)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^3*b^4*x^3 + a^4*b^3*x)]","A",0
129,1,378,0,1.018714," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{3} b^{2} c - 6 \, {\left(5 \, a b^{4} c - 3 \, a^{2} b^{3} d + a^{3} b^{2} e - a^{4} b f\right)} x^{4} - 4 \, {\left(5 \, a^{2} b^{3} c - 3 \, a^{3} b^{2} d\right)} x^{2} + 3 \, {\left({\left(5 \, b^{4} c - 3 \, a b^{3} d + a^{2} b^{2} e + a^{3} b f\right)} x^{5} + {\left(5 \, a b^{3} c - 3 \, a^{2} b^{2} d + a^{3} b e + a^{4} f\right)} x^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{12 \, {\left(a^{4} b^{3} x^{5} + a^{5} b^{2} x^{3}\right)}}, -\frac{2 \, a^{3} b^{2} c - 3 \, {\left(5 \, a b^{4} c - 3 \, a^{2} b^{3} d + a^{3} b^{2} e - a^{4} b f\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{3} c - 3 \, a^{3} b^{2} d\right)} x^{2} - 3 \, {\left({\left(5 \, b^{4} c - 3 \, a b^{3} d + a^{2} b^{2} e + a^{3} b f\right)} x^{5} + {\left(5 \, a b^{3} c - 3 \, a^{2} b^{2} d + a^{3} b e + a^{4} f\right)} x^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{6 \, {\left(a^{4} b^{3} x^{5} + a^{5} b^{2} x^{3}\right)}}\right]"," ",0,"[-1/12*(4*a^3*b^2*c - 6*(5*a*b^4*c - 3*a^2*b^3*d + a^3*b^2*e - a^4*b*f)*x^4 - 4*(5*a^2*b^3*c - 3*a^3*b^2*d)*x^2 + 3*((5*b^4*c - 3*a*b^3*d + a^2*b^2*e + a^3*b*f)*x^5 + (5*a*b^3*c - 3*a^2*b^2*d + a^3*b*e + a^4*f)*x^3)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^4*b^3*x^5 + a^5*b^2*x^3), -1/6*(2*a^3*b^2*c - 3*(5*a*b^4*c - 3*a^2*b^3*d + a^3*b^2*e - a^4*b*f)*x^4 - 2*(5*a^2*b^3*c - 3*a^3*b^2*d)*x^2 - 3*((5*b^4*c - 3*a*b^3*d + a^2*b^2*e + a^3*b*f)*x^5 + (5*a*b^3*c - 3*a^2*b^2*d + a^3*b*e + a^4*f)*x^3)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^4*b^3*x^5 + a^5*b^2*x^3)]","A",0
130,1,438,0,0.962037," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{30 \, {\left(7 \, a b^{4} c - 5 \, a^{2} b^{3} d + 3 \, a^{3} b^{2} e - a^{4} b f\right)} x^{6} + 12 \, a^{4} b c + 20 \, {\left(7 \, a^{2} b^{3} c - 5 \, a^{3} b^{2} d + 3 \, a^{4} b e\right)} x^{4} - 4 \, {\left(7 \, a^{3} b^{2} c - 5 \, a^{4} b d\right)} x^{2} - 15 \, {\left({\left(7 \, b^{4} c - 5 \, a b^{3} d + 3 \, a^{2} b^{2} e - a^{3} b f\right)} x^{7} + {\left(7 \, a b^{3} c - 5 \, a^{2} b^{2} d + 3 \, a^{3} b e - a^{4} f\right)} x^{5}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{60 \, {\left(a^{5} b^{2} x^{7} + a^{6} b x^{5}\right)}}, -\frac{15 \, {\left(7 \, a b^{4} c - 5 \, a^{2} b^{3} d + 3 \, a^{3} b^{2} e - a^{4} b f\right)} x^{6} + 6 \, a^{4} b c + 10 \, {\left(7 \, a^{2} b^{3} c - 5 \, a^{3} b^{2} d + 3 \, a^{4} b e\right)} x^{4} - 2 \, {\left(7 \, a^{3} b^{2} c - 5 \, a^{4} b d\right)} x^{2} + 15 \, {\left({\left(7 \, b^{4} c - 5 \, a b^{3} d + 3 \, a^{2} b^{2} e - a^{3} b f\right)} x^{7} + {\left(7 \, a b^{3} c - 5 \, a^{2} b^{2} d + 3 \, a^{3} b e - a^{4} f\right)} x^{5}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{30 \, {\left(a^{5} b^{2} x^{7} + a^{6} b x^{5}\right)}}\right]"," ",0,"[-1/60*(30*(7*a*b^4*c - 5*a^2*b^3*d + 3*a^3*b^2*e - a^4*b*f)*x^6 + 12*a^4*b*c + 20*(7*a^2*b^3*c - 5*a^3*b^2*d + 3*a^4*b*e)*x^4 - 4*(7*a^3*b^2*c - 5*a^4*b*d)*x^2 - 15*((7*b^4*c - 5*a*b^3*d + 3*a^2*b^2*e - a^3*b*f)*x^7 + (7*a*b^3*c - 5*a^2*b^2*d + 3*a^3*b*e - a^4*f)*x^5)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^5*b^2*x^7 + a^6*b*x^5), -1/30*(15*(7*a*b^4*c - 5*a^2*b^3*d + 3*a^3*b^2*e - a^4*b*f)*x^6 + 6*a^4*b*c + 10*(7*a^2*b^3*c - 5*a^3*b^2*d + 3*a^4*b*e)*x^4 - 2*(7*a^3*b^2*c - 5*a^4*b*d)*x^2 + 15*((7*b^4*c - 5*a*b^3*d + 3*a^2*b^2*e - a^3*b*f)*x^7 + (7*a*b^3*c - 5*a^2*b^2*d + 3*a^3*b*e - a^4*f)*x^5)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^5*b^2*x^7 + a^6*b*x^5)]","A",0
131,1,488,0,1.016495," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{210 \, {\left(9 \, b^{4} c - 7 \, a b^{3} d + 5 \, a^{2} b^{2} e - 3 \, a^{3} b f\right)} x^{8} + 140 \, {\left(9 \, a b^{3} c - 7 \, a^{2} b^{2} d + 5 \, a^{3} b e - 3 \, a^{4} f\right)} x^{6} - 60 \, a^{4} c - 28 \, {\left(9 \, a^{2} b^{2} c - 7 \, a^{3} b d + 5 \, a^{4} e\right)} x^{4} + 12 \, {\left(9 \, a^{3} b c - 7 \, a^{4} d\right)} x^{2} - 105 \, {\left({\left(9 \, b^{4} c - 7 \, a b^{3} d + 5 \, a^{2} b^{2} e - 3 \, a^{3} b f\right)} x^{9} + {\left(9 \, a b^{3} c - 7 \, a^{2} b^{2} d + 5 \, a^{3} b e - 3 \, a^{4} f\right)} x^{7}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{420 \, {\left(a^{5} b x^{9} + a^{6} x^{7}\right)}}, \frac{105 \, {\left(9 \, b^{4} c - 7 \, a b^{3} d + 5 \, a^{2} b^{2} e - 3 \, a^{3} b f\right)} x^{8} + 70 \, {\left(9 \, a b^{3} c - 7 \, a^{2} b^{2} d + 5 \, a^{3} b e - 3 \, a^{4} f\right)} x^{6} - 30 \, a^{4} c - 14 \, {\left(9 \, a^{2} b^{2} c - 7 \, a^{3} b d + 5 \, a^{4} e\right)} x^{4} + 6 \, {\left(9 \, a^{3} b c - 7 \, a^{4} d\right)} x^{2} + 105 \, {\left({\left(9 \, b^{4} c - 7 \, a b^{3} d + 5 \, a^{2} b^{2} e - 3 \, a^{3} b f\right)} x^{9} + {\left(9 \, a b^{3} c - 7 \, a^{2} b^{2} d + 5 \, a^{3} b e - 3 \, a^{4} f\right)} x^{7}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{210 \, {\left(a^{5} b x^{9} + a^{6} x^{7}\right)}}\right]"," ",0,"[1/420*(210*(9*b^4*c - 7*a*b^3*d + 5*a^2*b^2*e - 3*a^3*b*f)*x^8 + 140*(9*a*b^3*c - 7*a^2*b^2*d + 5*a^3*b*e - 3*a^4*f)*x^6 - 60*a^4*c - 28*(9*a^2*b^2*c - 7*a^3*b*d + 5*a^4*e)*x^4 + 12*(9*a^3*b*c - 7*a^4*d)*x^2 - 105*((9*b^4*c - 7*a*b^3*d + 5*a^2*b^2*e - 3*a^3*b*f)*x^9 + (9*a*b^3*c - 7*a^2*b^2*d + 5*a^3*b*e - 3*a^4*f)*x^7)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^5*b*x^9 + a^6*x^7), 1/210*(105*(9*b^4*c - 7*a*b^3*d + 5*a^2*b^2*e - 3*a^3*b*f)*x^8 + 70*(9*a*b^3*c - 7*a^2*b^2*d + 5*a^3*b*e - 3*a^4*f)*x^6 - 30*a^4*c - 14*(9*a^2*b^2*c - 7*a^3*b*d + 5*a^4*e)*x^4 + 6*(9*a^3*b*c - 7*a^4*d)*x^2 + 105*((9*b^4*c - 7*a*b^3*d + 5*a^2*b^2*e - 3*a^3*b*f)*x^9 + (9*a*b^3*c - 7*a^2*b^2*d + 5*a^3*b*e - 3*a^4*f)*x^7)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^5*b*x^9 + a^6*x^7)]","A",0
132,1,582,0,0.871718," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{630 \, {\left(11 \, b^{5} c - 9 \, a b^{4} d + 7 \, a^{2} b^{3} e - 5 \, a^{3} b^{2} f\right)} x^{10} + 420 \, {\left(11 \, a b^{4} c - 9 \, a^{2} b^{3} d + 7 \, a^{3} b^{2} e - 5 \, a^{4} b f\right)} x^{8} - 84 \, {\left(11 \, a^{2} b^{3} c - 9 \, a^{3} b^{2} d + 7 \, a^{4} b e - 5 \, a^{5} f\right)} x^{6} + 140 \, a^{5} c + 36 \, {\left(11 \, a^{3} b^{2} c - 9 \, a^{4} b d + 7 \, a^{5} e\right)} x^{4} - 20 \, {\left(11 \, a^{4} b c - 9 \, a^{5} d\right)} x^{2} + 315 \, {\left({\left(11 \, b^{5} c - 9 \, a b^{4} d + 7 \, a^{2} b^{3} e - 5 \, a^{3} b^{2} f\right)} x^{11} + {\left(11 \, a b^{4} c - 9 \, a^{2} b^{3} d + 7 \, a^{3} b^{2} e - 5 \, a^{4} b f\right)} x^{9}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{1260 \, {\left(a^{6} b x^{11} + a^{7} x^{9}\right)}}, -\frac{315 \, {\left(11 \, b^{5} c - 9 \, a b^{4} d + 7 \, a^{2} b^{3} e - 5 \, a^{3} b^{2} f\right)} x^{10} + 210 \, {\left(11 \, a b^{4} c - 9 \, a^{2} b^{3} d + 7 \, a^{3} b^{2} e - 5 \, a^{4} b f\right)} x^{8} - 42 \, {\left(11 \, a^{2} b^{3} c - 9 \, a^{3} b^{2} d + 7 \, a^{4} b e - 5 \, a^{5} f\right)} x^{6} + 70 \, a^{5} c + 18 \, {\left(11 \, a^{3} b^{2} c - 9 \, a^{4} b d + 7 \, a^{5} e\right)} x^{4} - 10 \, {\left(11 \, a^{4} b c - 9 \, a^{5} d\right)} x^{2} + 315 \, {\left({\left(11 \, b^{5} c - 9 \, a b^{4} d + 7 \, a^{2} b^{3} e - 5 \, a^{3} b^{2} f\right)} x^{11} + {\left(11 \, a b^{4} c - 9 \, a^{2} b^{3} d + 7 \, a^{3} b^{2} e - 5 \, a^{4} b f\right)} x^{9}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{630 \, {\left(a^{6} b x^{11} + a^{7} x^{9}\right)}}\right]"," ",0,"[-1/1260*(630*(11*b^5*c - 9*a*b^4*d + 7*a^2*b^3*e - 5*a^3*b^2*f)*x^10 + 420*(11*a*b^4*c - 9*a^2*b^3*d + 7*a^3*b^2*e - 5*a^4*b*f)*x^8 - 84*(11*a^2*b^3*c - 9*a^3*b^2*d + 7*a^4*b*e - 5*a^5*f)*x^6 + 140*a^5*c + 36*(11*a^3*b^2*c - 9*a^4*b*d + 7*a^5*e)*x^4 - 20*(11*a^4*b*c - 9*a^5*d)*x^2 + 315*((11*b^5*c - 9*a*b^4*d + 7*a^2*b^3*e - 5*a^3*b^2*f)*x^11 + (11*a*b^4*c - 9*a^2*b^3*d + 7*a^3*b^2*e - 5*a^4*b*f)*x^9)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^6*b*x^11 + a^7*x^9), -1/630*(315*(11*b^5*c - 9*a*b^4*d + 7*a^2*b^3*e - 5*a^3*b^2*f)*x^10 + 210*(11*a*b^4*c - 9*a^2*b^3*d + 7*a^3*b^2*e - 5*a^4*b*f)*x^8 - 42*(11*a^2*b^3*c - 9*a^3*b^2*d + 7*a^4*b*e - 5*a^5*f)*x^6 + 70*a^5*c + 18*(11*a^3*b^2*c - 9*a^4*b*d + 7*a^5*e)*x^4 - 10*(11*a^4*b*c - 9*a^5*d)*x^2 + 315*((11*b^5*c - 9*a*b^4*d + 7*a^2*b^3*e - 5*a^3*b^2*f)*x^11 + (11*a*b^4*c - 9*a^2*b^3*d + 7*a^3*b^2*e - 5*a^4*b*f)*x^9)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^6*b*x^11 + a^7*x^9)]","A",0
133,1,762,0,1.079395," ","integrate(x^8*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{560 \, b^{6} f x^{13} + 80 \, {\left(9 \, b^{6} e - 13 \, a b^{5} f\right)} x^{11} + 16 \, {\left(63 \, b^{6} d - 99 \, a b^{5} e + 143 \, a^{2} b^{4} f\right)} x^{9} + 48 \, {\left(35 \, b^{6} c - 63 \, a b^{5} d + 99 \, a^{2} b^{4} e - 143 \, a^{3} b^{3} f\right)} x^{7} - 336 \, {\left(35 \, a b^{5} c - 63 \, a^{2} b^{4} d + 99 \, a^{3} b^{3} e - 143 \, a^{4} b^{2} f\right)} x^{5} - 1050 \, {\left(35 \, a^{2} b^{4} c - 63 \, a^{3} b^{3} d + 99 \, a^{4} b^{2} e - 143 \, a^{5} b f\right)} x^{3} - 315 \, {\left(35 \, a^{3} b^{3} c - 63 \, a^{4} b^{2} d + 99 \, a^{5} b e - 143 \, a^{6} f + {\left(35 \, a b^{5} c - 63 \, a^{2} b^{4} d + 99 \, a^{3} b^{3} e - 143 \, a^{4} b^{2} f\right)} x^{4} + 2 \, {\left(35 \, a^{2} b^{4} c - 63 \, a^{3} b^{3} d + 99 \, a^{4} b^{2} e - 143 \, a^{5} b f\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 630 \, {\left(35 \, a^{3} b^{3} c - 63 \, a^{4} b^{2} d + 99 \, a^{5} b e - 143 \, a^{6} f\right)} x}{5040 \, {\left(b^{9} x^{4} + 2 \, a b^{8} x^{2} + a^{2} b^{7}\right)}}, \frac{280 \, b^{6} f x^{13} + 40 \, {\left(9 \, b^{6} e - 13 \, a b^{5} f\right)} x^{11} + 8 \, {\left(63 \, b^{6} d - 99 \, a b^{5} e + 143 \, a^{2} b^{4} f\right)} x^{9} + 24 \, {\left(35 \, b^{6} c - 63 \, a b^{5} d + 99 \, a^{2} b^{4} e - 143 \, a^{3} b^{3} f\right)} x^{7} - 168 \, {\left(35 \, a b^{5} c - 63 \, a^{2} b^{4} d + 99 \, a^{3} b^{3} e - 143 \, a^{4} b^{2} f\right)} x^{5} - 525 \, {\left(35 \, a^{2} b^{4} c - 63 \, a^{3} b^{3} d + 99 \, a^{4} b^{2} e - 143 \, a^{5} b f\right)} x^{3} + 315 \, {\left(35 \, a^{3} b^{3} c - 63 \, a^{4} b^{2} d + 99 \, a^{5} b e - 143 \, a^{6} f + {\left(35 \, a b^{5} c - 63 \, a^{2} b^{4} d + 99 \, a^{3} b^{3} e - 143 \, a^{4} b^{2} f\right)} x^{4} + 2 \, {\left(35 \, a^{2} b^{4} c - 63 \, a^{3} b^{3} d + 99 \, a^{4} b^{2} e - 143 \, a^{5} b f\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 315 \, {\left(35 \, a^{3} b^{3} c - 63 \, a^{4} b^{2} d + 99 \, a^{5} b e - 143 \, a^{6} f\right)} x}{2520 \, {\left(b^{9} x^{4} + 2 \, a b^{8} x^{2} + a^{2} b^{7}\right)}}\right]"," ",0,"[1/5040*(560*b^6*f*x^13 + 80*(9*b^6*e - 13*a*b^5*f)*x^11 + 16*(63*b^6*d - 99*a*b^5*e + 143*a^2*b^4*f)*x^9 + 48*(35*b^6*c - 63*a*b^5*d + 99*a^2*b^4*e - 143*a^3*b^3*f)*x^7 - 336*(35*a*b^5*c - 63*a^2*b^4*d + 99*a^3*b^3*e - 143*a^4*b^2*f)*x^5 - 1050*(35*a^2*b^4*c - 63*a^3*b^3*d + 99*a^4*b^2*e - 143*a^5*b*f)*x^3 - 315*(35*a^3*b^3*c - 63*a^4*b^2*d + 99*a^5*b*e - 143*a^6*f + (35*a*b^5*c - 63*a^2*b^4*d + 99*a^3*b^3*e - 143*a^4*b^2*f)*x^4 + 2*(35*a^2*b^4*c - 63*a^3*b^3*d + 99*a^4*b^2*e - 143*a^5*b*f)*x^2)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 630*(35*a^3*b^3*c - 63*a^4*b^2*d + 99*a^5*b*e - 143*a^6*f)*x)/(b^9*x^4 + 2*a*b^8*x^2 + a^2*b^7), 1/2520*(280*b^6*f*x^13 + 40*(9*b^6*e - 13*a*b^5*f)*x^11 + 8*(63*b^6*d - 99*a*b^5*e + 143*a^2*b^4*f)*x^9 + 24*(35*b^6*c - 63*a*b^5*d + 99*a^2*b^4*e - 143*a^3*b^3*f)*x^7 - 168*(35*a*b^5*c - 63*a^2*b^4*d + 99*a^3*b^3*e - 143*a^4*b^2*f)*x^5 - 525*(35*a^2*b^4*c - 63*a^3*b^3*d + 99*a^4*b^2*e - 143*a^5*b*f)*x^3 + 315*(35*a^3*b^3*c - 63*a^4*b^2*d + 99*a^5*b*e - 143*a^6*f + (35*a*b^5*c - 63*a^2*b^4*d + 99*a^3*b^3*e - 143*a^4*b^2*f)*x^4 + 2*(35*a^2*b^4*c - 63*a^3*b^3*d + 99*a^4*b^2*e - 143*a^5*b*f)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 315*(35*a^3*b^3*c - 63*a^4*b^2*d + 99*a^5*b*e - 143*a^6*f)*x)/(b^9*x^4 + 2*a*b^8*x^2 + a^2*b^7)]","A",0
134,1,668,0,1.142455," ","integrate(x^6*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{240 \, b^{5} f x^{11} + 48 \, {\left(7 \, b^{5} e - 11 \, a b^{4} f\right)} x^{9} + 16 \, {\left(35 \, b^{5} d - 63 \, a b^{4} e + 99 \, a^{2} b^{3} f\right)} x^{7} + 112 \, {\left(15 \, b^{5} c - 35 \, a b^{4} d + 63 \, a^{2} b^{3} e - 99 \, a^{3} b^{2} f\right)} x^{5} + 350 \, {\left(15 \, a b^{4} c - 35 \, a^{2} b^{3} d + 63 \, a^{3} b^{2} e - 99 \, a^{4} b f\right)} x^{3} - 105 \, {\left(15 \, a^{2} b^{3} c - 35 \, a^{3} b^{2} d + 63 \, a^{4} b e - 99 \, a^{5} f + {\left(15 \, b^{5} c - 35 \, a b^{4} d + 63 \, a^{2} b^{3} e - 99 \, a^{3} b^{2} f\right)} x^{4} + 2 \, {\left(15 \, a b^{4} c - 35 \, a^{2} b^{3} d + 63 \, a^{3} b^{2} e - 99 \, a^{4} b f\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 210 \, {\left(15 \, a^{2} b^{3} c - 35 \, a^{3} b^{2} d + 63 \, a^{4} b e - 99 \, a^{5} f\right)} x}{1680 \, {\left(b^{8} x^{4} + 2 \, a b^{7} x^{2} + a^{2} b^{6}\right)}}, \frac{120 \, b^{5} f x^{11} + 24 \, {\left(7 \, b^{5} e - 11 \, a b^{4} f\right)} x^{9} + 8 \, {\left(35 \, b^{5} d - 63 \, a b^{4} e + 99 \, a^{2} b^{3} f\right)} x^{7} + 56 \, {\left(15 \, b^{5} c - 35 \, a b^{4} d + 63 \, a^{2} b^{3} e - 99 \, a^{3} b^{2} f\right)} x^{5} + 175 \, {\left(15 \, a b^{4} c - 35 \, a^{2} b^{3} d + 63 \, a^{3} b^{2} e - 99 \, a^{4} b f\right)} x^{3} - 105 \, {\left(15 \, a^{2} b^{3} c - 35 \, a^{3} b^{2} d + 63 \, a^{4} b e - 99 \, a^{5} f + {\left(15 \, b^{5} c - 35 \, a b^{4} d + 63 \, a^{2} b^{3} e - 99 \, a^{3} b^{2} f\right)} x^{4} + 2 \, {\left(15 \, a b^{4} c - 35 \, a^{2} b^{3} d + 63 \, a^{3} b^{2} e - 99 \, a^{4} b f\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 105 \, {\left(15 \, a^{2} b^{3} c - 35 \, a^{3} b^{2} d + 63 \, a^{4} b e - 99 \, a^{5} f\right)} x}{840 \, {\left(b^{8} x^{4} + 2 \, a b^{7} x^{2} + a^{2} b^{6}\right)}}\right]"," ",0,"[1/1680*(240*b^5*f*x^11 + 48*(7*b^5*e - 11*a*b^4*f)*x^9 + 16*(35*b^5*d - 63*a*b^4*e + 99*a^2*b^3*f)*x^7 + 112*(15*b^5*c - 35*a*b^4*d + 63*a^2*b^3*e - 99*a^3*b^2*f)*x^5 + 350*(15*a*b^4*c - 35*a^2*b^3*d + 63*a^3*b^2*e - 99*a^4*b*f)*x^3 - 105*(15*a^2*b^3*c - 35*a^3*b^2*d + 63*a^4*b*e - 99*a^5*f + (15*b^5*c - 35*a*b^4*d + 63*a^2*b^3*e - 99*a^3*b^2*f)*x^4 + 2*(15*a*b^4*c - 35*a^2*b^3*d + 63*a^3*b^2*e - 99*a^4*b*f)*x^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 210*(15*a^2*b^3*c - 35*a^3*b^2*d + 63*a^4*b*e - 99*a^5*f)*x)/(b^8*x^4 + 2*a*b^7*x^2 + a^2*b^6), 1/840*(120*b^5*f*x^11 + 24*(7*b^5*e - 11*a*b^4*f)*x^9 + 8*(35*b^5*d - 63*a*b^4*e + 99*a^2*b^3*f)*x^7 + 56*(15*b^5*c - 35*a*b^4*d + 63*a^2*b^3*e - 99*a^3*b^2*f)*x^5 + 175*(15*a*b^4*c - 35*a^2*b^3*d + 63*a^3*b^2*e - 99*a^4*b*f)*x^3 - 105*(15*a^2*b^3*c - 35*a^3*b^2*d + 63*a^4*b*e - 99*a^5*f + (15*b^5*c - 35*a*b^4*d + 63*a^2*b^3*e - 99*a^3*b^2*f)*x^4 + 2*(15*a*b^4*c - 35*a^2*b^3*d + 63*a^3*b^2*e - 99*a^4*b*f)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 105*(15*a^2*b^3*c - 35*a^3*b^2*d + 63*a^4*b*e - 99*a^5*f)*x)/(b^8*x^4 + 2*a*b^7*x^2 + a^2*b^6)]","A",0
135,1,614,0,0.935247," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{48 \, a b^{5} f x^{9} + 16 \, {\left(5 \, a b^{5} e - 9 \, a^{2} b^{4} f\right)} x^{7} + 16 \, {\left(15 \, a b^{5} d - 35 \, a^{2} b^{4} e + 63 \, a^{3} b^{3} f\right)} x^{5} - 50 \, {\left(3 \, a b^{5} c - 15 \, a^{2} b^{4} d + 35 \, a^{3} b^{3} e - 63 \, a^{4} b^{2} f\right)} x^{3} + 15 \, {\left(3 \, a^{2} b^{3} c - 15 \, a^{3} b^{2} d + 35 \, a^{4} b e - 63 \, a^{5} f + {\left(3 \, b^{5} c - 15 \, a b^{4} d + 35 \, a^{2} b^{3} e - 63 \, a^{3} b^{2} f\right)} x^{4} + 2 \, {\left(3 \, a b^{4} c - 15 \, a^{2} b^{3} d + 35 \, a^{3} b^{2} e - 63 \, a^{4} b f\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 30 \, {\left(3 \, a^{2} b^{4} c - 15 \, a^{3} b^{3} d + 35 \, a^{4} b^{2} e - 63 \, a^{5} b f\right)} x}{240 \, {\left(a b^{8} x^{4} + 2 \, a^{2} b^{7} x^{2} + a^{3} b^{6}\right)}}, \frac{24 \, a b^{5} f x^{9} + 8 \, {\left(5 \, a b^{5} e - 9 \, a^{2} b^{4} f\right)} x^{7} + 8 \, {\left(15 \, a b^{5} d - 35 \, a^{2} b^{4} e + 63 \, a^{3} b^{3} f\right)} x^{5} - 25 \, {\left(3 \, a b^{5} c - 15 \, a^{2} b^{4} d + 35 \, a^{3} b^{3} e - 63 \, a^{4} b^{2} f\right)} x^{3} + 15 \, {\left(3 \, a^{2} b^{3} c - 15 \, a^{3} b^{2} d + 35 \, a^{4} b e - 63 \, a^{5} f + {\left(3 \, b^{5} c - 15 \, a b^{4} d + 35 \, a^{2} b^{3} e - 63 \, a^{3} b^{2} f\right)} x^{4} + 2 \, {\left(3 \, a b^{4} c - 15 \, a^{2} b^{3} d + 35 \, a^{3} b^{2} e - 63 \, a^{4} b f\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - 15 \, {\left(3 \, a^{2} b^{4} c - 15 \, a^{3} b^{3} d + 35 \, a^{4} b^{2} e - 63 \, a^{5} b f\right)} x}{120 \, {\left(a b^{8} x^{4} + 2 \, a^{2} b^{7} x^{2} + a^{3} b^{6}\right)}}\right]"," ",0,"[1/240*(48*a*b^5*f*x^9 + 16*(5*a*b^5*e - 9*a^2*b^4*f)*x^7 + 16*(15*a*b^5*d - 35*a^2*b^4*e + 63*a^3*b^3*f)*x^5 - 50*(3*a*b^5*c - 15*a^2*b^4*d + 35*a^3*b^3*e - 63*a^4*b^2*f)*x^3 + 15*(3*a^2*b^3*c - 15*a^3*b^2*d + 35*a^4*b*e - 63*a^5*f + (3*b^5*c - 15*a*b^4*d + 35*a^2*b^3*e - 63*a^3*b^2*f)*x^4 + 2*(3*a*b^4*c - 15*a^2*b^3*d + 35*a^3*b^2*e - 63*a^4*b*f)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 30*(3*a^2*b^4*c - 15*a^3*b^3*d + 35*a^4*b^2*e - 63*a^5*b*f)*x)/(a*b^8*x^4 + 2*a^2*b^7*x^2 + a^3*b^6), 1/120*(24*a*b^5*f*x^9 + 8*(5*a*b^5*e - 9*a^2*b^4*f)*x^7 + 8*(15*a*b^5*d - 35*a^2*b^4*e + 63*a^3*b^3*f)*x^5 - 25*(3*a*b^5*c - 15*a^2*b^4*d + 35*a^3*b^3*e - 63*a^4*b^2*f)*x^3 + 15*(3*a^2*b^3*c - 15*a^3*b^2*d + 35*a^4*b*e - 63*a^5*f + (3*b^5*c - 15*a*b^4*d + 35*a^2*b^3*e - 63*a^3*b^2*f)*x^4 + 2*(3*a*b^4*c - 15*a^2*b^3*d + 35*a^3*b^2*e - 63*a^4*b*f)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - 15*(3*a^2*b^4*c - 15*a^3*b^3*d + 35*a^4*b^2*e - 63*a^5*b*f)*x)/(a*b^8*x^4 + 2*a^2*b^7*x^2 + a^3*b^6)]","A",0
136,1,555,0,0.970873," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{16 \, a^{2} b^{4} f x^{7} + 16 \, {\left(3 \, a^{2} b^{4} e - 7 \, a^{3} b^{3} f\right)} x^{5} + 2 \, {\left(3 \, a b^{5} c - 15 \, a^{2} b^{4} d + 75 \, a^{3} b^{3} e - 175 \, a^{4} b^{2} f\right)} x^{3} - 3 \, {\left(a^{2} b^{3} c + 3 \, a^{3} b^{2} d - 15 \, a^{4} b e + 35 \, a^{5} f + {\left(b^{5} c + 3 \, a b^{4} d - 15 \, a^{2} b^{3} e + 35 \, a^{3} b^{2} f\right)} x^{4} + 2 \, {\left(a b^{4} c + 3 \, a^{2} b^{3} d - 15 \, a^{3} b^{2} e + 35 \, a^{4} b f\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 6 \, {\left(a^{2} b^{4} c + 3 \, a^{3} b^{3} d - 15 \, a^{4} b^{2} e + 35 \, a^{5} b f\right)} x}{48 \, {\left(a^{2} b^{7} x^{4} + 2 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}}, \frac{8 \, a^{2} b^{4} f x^{7} + 8 \, {\left(3 \, a^{2} b^{4} e - 7 \, a^{3} b^{3} f\right)} x^{5} + {\left(3 \, a b^{5} c - 15 \, a^{2} b^{4} d + 75 \, a^{3} b^{3} e - 175 \, a^{4} b^{2} f\right)} x^{3} + 3 \, {\left(a^{2} b^{3} c + 3 \, a^{3} b^{2} d - 15 \, a^{4} b e + 35 \, a^{5} f + {\left(b^{5} c + 3 \, a b^{4} d - 15 \, a^{2} b^{3} e + 35 \, a^{3} b^{2} f\right)} x^{4} + 2 \, {\left(a b^{4} c + 3 \, a^{2} b^{3} d - 15 \, a^{3} b^{2} e + 35 \, a^{4} b f\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - 3 \, {\left(a^{2} b^{4} c + 3 \, a^{3} b^{3} d - 15 \, a^{4} b^{2} e + 35 \, a^{5} b f\right)} x}{24 \, {\left(a^{2} b^{7} x^{4} + 2 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}}\right]"," ",0,"[1/48*(16*a^2*b^4*f*x^7 + 16*(3*a^2*b^4*e - 7*a^3*b^3*f)*x^5 + 2*(3*a*b^5*c - 15*a^2*b^4*d + 75*a^3*b^3*e - 175*a^4*b^2*f)*x^3 - 3*(a^2*b^3*c + 3*a^3*b^2*d - 15*a^4*b*e + 35*a^5*f + (b^5*c + 3*a*b^4*d - 15*a^2*b^3*e + 35*a^3*b^2*f)*x^4 + 2*(a*b^4*c + 3*a^2*b^3*d - 15*a^3*b^2*e + 35*a^4*b*f)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 6*(a^2*b^4*c + 3*a^3*b^3*d - 15*a^4*b^2*e + 35*a^5*b*f)*x)/(a^2*b^7*x^4 + 2*a^3*b^6*x^2 + a^4*b^5), 1/24*(8*a^2*b^4*f*x^7 + 8*(3*a^2*b^4*e - 7*a^3*b^3*f)*x^5 + (3*a*b^5*c - 15*a^2*b^4*d + 75*a^3*b^3*e - 175*a^4*b^2*f)*x^3 + 3*(a^2*b^3*c + 3*a^3*b^2*d - 15*a^4*b*e + 35*a^5*f + (b^5*c + 3*a*b^4*d - 15*a^2*b^3*e + 35*a^3*b^2*f)*x^4 + 2*(a*b^4*c + 3*a^2*b^3*d - 15*a^3*b^2*e + 35*a^4*b*f)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - 3*(a^2*b^4*c + 3*a^3*b^3*d - 15*a^4*b^2*e + 35*a^5*b*f)*x)/(a^2*b^7*x^4 + 2*a^3*b^6*x^2 + a^4*b^5)]","A",0
137,1,504,0,1.171142," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{16 \, a^{3} b^{3} f x^{5} + 2 \, {\left(3 \, a b^{5} c + a^{2} b^{4} d - 5 \, a^{3} b^{3} e + 25 \, a^{4} b^{2} f\right)} x^{3} + {\left(3 \, a^{2} b^{3} c + a^{3} b^{2} d + 3 \, a^{4} b e - 15 \, a^{5} f + {\left(3 \, b^{5} c + a b^{4} d + 3 \, a^{2} b^{3} e - 15 \, a^{3} b^{2} f\right)} x^{4} + 2 \, {\left(3 \, a b^{4} c + a^{2} b^{3} d + 3 \, a^{3} b^{2} e - 15 \, a^{4} b f\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(5 \, a^{2} b^{4} c - a^{3} b^{3} d - 3 \, a^{4} b^{2} e + 15 \, a^{5} b f\right)} x}{16 \, {\left(a^{3} b^{6} x^{4} + 2 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)}}, \frac{8 \, a^{3} b^{3} f x^{5} + {\left(3 \, a b^{5} c + a^{2} b^{4} d - 5 \, a^{3} b^{3} e + 25 \, a^{4} b^{2} f\right)} x^{3} + {\left(3 \, a^{2} b^{3} c + a^{3} b^{2} d + 3 \, a^{4} b e - 15 \, a^{5} f + {\left(3 \, b^{5} c + a b^{4} d + 3 \, a^{2} b^{3} e - 15 \, a^{3} b^{2} f\right)} x^{4} + 2 \, {\left(3 \, a b^{4} c + a^{2} b^{3} d + 3 \, a^{3} b^{2} e - 15 \, a^{4} b f\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(5 \, a^{2} b^{4} c - a^{3} b^{3} d - 3 \, a^{4} b^{2} e + 15 \, a^{5} b f\right)} x}{8 \, {\left(a^{3} b^{6} x^{4} + 2 \, a^{4} b^{5} x^{2} + a^{5} b^{4}\right)}}\right]"," ",0,"[1/16*(16*a^3*b^3*f*x^5 + 2*(3*a*b^5*c + a^2*b^4*d - 5*a^3*b^3*e + 25*a^4*b^2*f)*x^3 + (3*a^2*b^3*c + a^3*b^2*d + 3*a^4*b*e - 15*a^5*f + (3*b^5*c + a*b^4*d + 3*a^2*b^3*e - 15*a^3*b^2*f)*x^4 + 2*(3*a*b^4*c + a^2*b^3*d + 3*a^3*b^2*e - 15*a^4*b*f)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(5*a^2*b^4*c - a^3*b^3*d - 3*a^4*b^2*e + 15*a^5*b*f)*x)/(a^3*b^6*x^4 + 2*a^4*b^5*x^2 + a^5*b^4), 1/8*(8*a^3*b^3*f*x^5 + (3*a*b^5*c + a^2*b^4*d - 5*a^3*b^3*e + 25*a^4*b^2*f)*x^3 + (3*a^2*b^3*c + a^3*b^2*d + 3*a^4*b*e - 15*a^5*f + (3*b^5*c + a*b^4*d + 3*a^2*b^3*e - 15*a^3*b^2*f)*x^4 + 2*(3*a*b^4*c + a^2*b^3*d + 3*a^3*b^2*e - 15*a^4*b*f)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (5*a^2*b^4*c - a^3*b^3*d - 3*a^4*b^2*e + 15*a^5*b*f)*x)/(a^3*b^6*x^4 + 2*a^4*b^5*x^2 + a^5*b^4)]","A",0
138,1,517,0,1.173532," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, a^{3} b^{3} c + 2 \, {\left(15 \, a b^{5} c - 3 \, a^{2} b^{4} d - a^{3} b^{3} e + 5 \, a^{4} b^{2} f\right)} x^{4} + 2 \, {\left(25 \, a^{2} b^{4} c - 5 \, a^{3} b^{3} d + a^{4} b^{2} e + 3 \, a^{5} b f\right)} x^{2} - {\left({\left(15 \, b^{5} c - 3 \, a b^{4} d - a^{2} b^{3} e - 3 \, a^{3} b^{2} f\right)} x^{5} + 2 \, {\left(15 \, a b^{4} c - 3 \, a^{2} b^{3} d - a^{3} b^{2} e - 3 \, a^{4} b f\right)} x^{3} + {\left(15 \, a^{2} b^{3} c - 3 \, a^{3} b^{2} d - a^{4} b e - 3 \, a^{5} f\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{16 \, {\left(a^{4} b^{5} x^{5} + 2 \, a^{5} b^{4} x^{3} + a^{6} b^{3} x\right)}}, -\frac{8 \, a^{3} b^{3} c + {\left(15 \, a b^{5} c - 3 \, a^{2} b^{4} d - a^{3} b^{3} e + 5 \, a^{4} b^{2} f\right)} x^{4} + {\left(25 \, a^{2} b^{4} c - 5 \, a^{3} b^{3} d + a^{4} b^{2} e + 3 \, a^{5} b f\right)} x^{2} + {\left({\left(15 \, b^{5} c - 3 \, a b^{4} d - a^{2} b^{3} e - 3 \, a^{3} b^{2} f\right)} x^{5} + 2 \, {\left(15 \, a b^{4} c - 3 \, a^{2} b^{3} d - a^{3} b^{2} e - 3 \, a^{4} b f\right)} x^{3} + {\left(15 \, a^{2} b^{3} c - 3 \, a^{3} b^{2} d - a^{4} b e - 3 \, a^{5} f\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{8 \, {\left(a^{4} b^{5} x^{5} + 2 \, a^{5} b^{4} x^{3} + a^{6} b^{3} x\right)}}\right]"," ",0,"[-1/16*(16*a^3*b^3*c + 2*(15*a*b^5*c - 3*a^2*b^4*d - a^3*b^3*e + 5*a^4*b^2*f)*x^4 + 2*(25*a^2*b^4*c - 5*a^3*b^3*d + a^4*b^2*e + 3*a^5*b*f)*x^2 - ((15*b^5*c - 3*a*b^4*d - a^2*b^3*e - 3*a^3*b^2*f)*x^5 + 2*(15*a*b^4*c - 3*a^2*b^3*d - a^3*b^2*e - 3*a^4*b*f)*x^3 + (15*a^2*b^3*c - 3*a^3*b^2*d - a^4*b*e - 3*a^5*f)*x)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^4*b^5*x^5 + 2*a^5*b^4*x^3 + a^6*b^3*x), -1/8*(8*a^3*b^3*c + (15*a*b^5*c - 3*a^2*b^4*d - a^3*b^3*e + 5*a^4*b^2*f)*x^4 + (25*a^2*b^4*c - 5*a^3*b^3*d + a^4*b^2*e + 3*a^5*b*f)*x^2 + ((15*b^5*c - 3*a*b^4*d - a^2*b^3*e - 3*a^3*b^2*f)*x^5 + 2*(15*a*b^4*c - 3*a^2*b^3*d - a^3*b^2*e - 3*a^4*b*f)*x^3 + (15*a^2*b^3*c - 3*a^3*b^2*d - a^4*b*e - 3*a^5*f)*x)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^4*b^5*x^5 + 2*a^5*b^4*x^3 + a^6*b^3*x)]","A",0
139,1,570,0,0.867168," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, a^{4} b^{2} c - 6 \, {\left(35 \, a b^{5} c - 15 \, a^{2} b^{4} d + 3 \, a^{3} b^{3} e + a^{4} b^{2} f\right)} x^{6} - 2 \, {\left(175 \, a^{2} b^{4} c - 75 \, a^{3} b^{3} d + 15 \, a^{4} b^{2} e - 3 \, a^{5} b f\right)} x^{4} - 16 \, {\left(7 \, a^{3} b^{3} c - 3 \, a^{4} b^{2} d\right)} x^{2} + 3 \, {\left({\left(35 \, b^{5} c - 15 \, a b^{4} d + 3 \, a^{2} b^{3} e + a^{3} b^{2} f\right)} x^{7} + 2 \, {\left(35 \, a b^{4} c - 15 \, a^{2} b^{3} d + 3 \, a^{3} b^{2} e + a^{4} b f\right)} x^{5} + {\left(35 \, a^{2} b^{3} c - 15 \, a^{3} b^{2} d + 3 \, a^{4} b e + a^{5} f\right)} x^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{48 \, {\left(a^{5} b^{4} x^{7} + 2 \, a^{6} b^{3} x^{5} + a^{7} b^{2} x^{3}\right)}}, -\frac{8 \, a^{4} b^{2} c - 3 \, {\left(35 \, a b^{5} c - 15 \, a^{2} b^{4} d + 3 \, a^{3} b^{3} e + a^{4} b^{2} f\right)} x^{6} - {\left(175 \, a^{2} b^{4} c - 75 \, a^{3} b^{3} d + 15 \, a^{4} b^{2} e - 3 \, a^{5} b f\right)} x^{4} - 8 \, {\left(7 \, a^{3} b^{3} c - 3 \, a^{4} b^{2} d\right)} x^{2} - 3 \, {\left({\left(35 \, b^{5} c - 15 \, a b^{4} d + 3 \, a^{2} b^{3} e + a^{3} b^{2} f\right)} x^{7} + 2 \, {\left(35 \, a b^{4} c - 15 \, a^{2} b^{3} d + 3 \, a^{3} b^{2} e + a^{4} b f\right)} x^{5} + {\left(35 \, a^{2} b^{3} c - 15 \, a^{3} b^{2} d + 3 \, a^{4} b e + a^{5} f\right)} x^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{24 \, {\left(a^{5} b^{4} x^{7} + 2 \, a^{6} b^{3} x^{5} + a^{7} b^{2} x^{3}\right)}}\right]"," ",0,"[-1/48*(16*a^4*b^2*c - 6*(35*a*b^5*c - 15*a^2*b^4*d + 3*a^3*b^3*e + a^4*b^2*f)*x^6 - 2*(175*a^2*b^4*c - 75*a^3*b^3*d + 15*a^4*b^2*e - 3*a^5*b*f)*x^4 - 16*(7*a^3*b^3*c - 3*a^4*b^2*d)*x^2 + 3*((35*b^5*c - 15*a*b^4*d + 3*a^2*b^3*e + a^3*b^2*f)*x^7 + 2*(35*a*b^4*c - 15*a^2*b^3*d + 3*a^3*b^2*e + a^4*b*f)*x^5 + (35*a^2*b^3*c - 15*a^3*b^2*d + 3*a^4*b*e + a^5*f)*x^3)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^5*b^4*x^7 + 2*a^6*b^3*x^5 + a^7*b^2*x^3), -1/24*(8*a^4*b^2*c - 3*(35*a*b^5*c - 15*a^2*b^4*d + 3*a^3*b^3*e + a^4*b^2*f)*x^6 - (175*a^2*b^4*c - 75*a^3*b^3*d + 15*a^4*b^2*e - 3*a^5*b*f)*x^4 - 8*(7*a^3*b^3*c - 3*a^4*b^2*d)*x^2 - 3*((35*b^5*c - 15*a*b^4*d + 3*a^2*b^3*e + a^3*b^2*f)*x^7 + 2*(35*a*b^4*c - 15*a^2*b^3*d + 3*a^3*b^2*e + a^4*b*f)*x^5 + (35*a^2*b^3*c - 15*a^3*b^2*d + 3*a^4*b*e + a^5*f)*x^3)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^5*b^4*x^7 + 2*a^6*b^3*x^5 + a^7*b^2*x^3)]","A",0
140,1,628,0,1.163290," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{30 \, {\left(63 \, a b^{5} c - 35 \, a^{2} b^{4} d + 15 \, a^{3} b^{3} e - 3 \, a^{4} b^{2} f\right)} x^{8} + 48 \, a^{5} b c + 50 \, {\left(63 \, a^{2} b^{4} c - 35 \, a^{3} b^{3} d + 15 \, a^{4} b^{2} e - 3 \, a^{5} b f\right)} x^{6} + 16 \, {\left(63 \, a^{3} b^{3} c - 35 \, a^{4} b^{2} d + 15 \, a^{5} b e\right)} x^{4} - 16 \, {\left(9 \, a^{4} b^{2} c - 5 \, a^{5} b d\right)} x^{2} - 15 \, {\left({\left(63 \, b^{5} c - 35 \, a b^{4} d + 15 \, a^{2} b^{3} e - 3 \, a^{3} b^{2} f\right)} x^{9} + 2 \, {\left(63 \, a b^{4} c - 35 \, a^{2} b^{3} d + 15 \, a^{3} b^{2} e - 3 \, a^{4} b f\right)} x^{7} + {\left(63 \, a^{2} b^{3} c - 35 \, a^{3} b^{2} d + 15 \, a^{4} b e - 3 \, a^{5} f\right)} x^{5}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{240 \, {\left(a^{6} b^{3} x^{9} + 2 \, a^{7} b^{2} x^{7} + a^{8} b x^{5}\right)}}, -\frac{15 \, {\left(63 \, a b^{5} c - 35 \, a^{2} b^{4} d + 15 \, a^{3} b^{3} e - 3 \, a^{4} b^{2} f\right)} x^{8} + 24 \, a^{5} b c + 25 \, {\left(63 \, a^{2} b^{4} c - 35 \, a^{3} b^{3} d + 15 \, a^{4} b^{2} e - 3 \, a^{5} b f\right)} x^{6} + 8 \, {\left(63 \, a^{3} b^{3} c - 35 \, a^{4} b^{2} d + 15 \, a^{5} b e\right)} x^{4} - 8 \, {\left(9 \, a^{4} b^{2} c - 5 \, a^{5} b d\right)} x^{2} + 15 \, {\left({\left(63 \, b^{5} c - 35 \, a b^{4} d + 15 \, a^{2} b^{3} e - 3 \, a^{3} b^{2} f\right)} x^{9} + 2 \, {\left(63 \, a b^{4} c - 35 \, a^{2} b^{3} d + 15 \, a^{3} b^{2} e - 3 \, a^{4} b f\right)} x^{7} + {\left(63 \, a^{2} b^{3} c - 35 \, a^{3} b^{2} d + 15 \, a^{4} b e - 3 \, a^{5} f\right)} x^{5}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{120 \, {\left(a^{6} b^{3} x^{9} + 2 \, a^{7} b^{2} x^{7} + a^{8} b x^{5}\right)}}\right]"," ",0,"[-1/240*(30*(63*a*b^5*c - 35*a^2*b^4*d + 15*a^3*b^3*e - 3*a^4*b^2*f)*x^8 + 48*a^5*b*c + 50*(63*a^2*b^4*c - 35*a^3*b^3*d + 15*a^4*b^2*e - 3*a^5*b*f)*x^6 + 16*(63*a^3*b^3*c - 35*a^4*b^2*d + 15*a^5*b*e)*x^4 - 16*(9*a^4*b^2*c - 5*a^5*b*d)*x^2 - 15*((63*b^5*c - 35*a*b^4*d + 15*a^2*b^3*e - 3*a^3*b^2*f)*x^9 + 2*(63*a*b^4*c - 35*a^2*b^3*d + 15*a^3*b^2*e - 3*a^4*b*f)*x^7 + (63*a^2*b^3*c - 35*a^3*b^2*d + 15*a^4*b*e - 3*a^5*f)*x^5)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^6*b^3*x^9 + 2*a^7*b^2*x^7 + a^8*b*x^5), -1/120*(15*(63*a*b^5*c - 35*a^2*b^4*d + 15*a^3*b^3*e - 3*a^4*b^2*f)*x^8 + 24*a^5*b*c + 25*(63*a^2*b^4*c - 35*a^3*b^3*d + 15*a^4*b^2*e - 3*a^5*b*f)*x^6 + 8*(63*a^3*b^3*c - 35*a^4*b^2*d + 15*a^5*b*e)*x^4 - 8*(9*a^4*b^2*c - 5*a^5*b*d)*x^2 + 15*((63*b^5*c - 35*a*b^4*d + 15*a^2*b^3*e - 3*a^3*b^2*f)*x^9 + 2*(63*a*b^4*c - 35*a^2*b^3*d + 15*a^3*b^2*e - 3*a^4*b*f)*x^7 + (63*a^2*b^3*c - 35*a^3*b^2*d + 15*a^4*b*e - 3*a^5*f)*x^5)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^6*b^3*x^9 + 2*a^7*b^2*x^7 + a^8*b*x^5)]","A",0
141,1,678,0,1.079721," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{210 \, {\left(99 \, b^{5} c - 63 \, a b^{4} d + 35 \, a^{2} b^{3} e - 15 \, a^{3} b^{2} f\right)} x^{10} + 350 \, {\left(99 \, a b^{4} c - 63 \, a^{2} b^{3} d + 35 \, a^{3} b^{2} e - 15 \, a^{4} b f\right)} x^{8} + 112 \, {\left(99 \, a^{2} b^{3} c - 63 \, a^{3} b^{2} d + 35 \, a^{4} b e - 15 \, a^{5} f\right)} x^{6} - 240 \, a^{5} c - 16 \, {\left(99 \, a^{3} b^{2} c - 63 \, a^{4} b d + 35 \, a^{5} e\right)} x^{4} + 48 \, {\left(11 \, a^{4} b c - 7 \, a^{5} d\right)} x^{2} - 105 \, {\left({\left(99 \, b^{5} c - 63 \, a b^{4} d + 35 \, a^{2} b^{3} e - 15 \, a^{3} b^{2} f\right)} x^{11} + 2 \, {\left(99 \, a b^{4} c - 63 \, a^{2} b^{3} d + 35 \, a^{3} b^{2} e - 15 \, a^{4} b f\right)} x^{9} + {\left(99 \, a^{2} b^{3} c - 63 \, a^{3} b^{2} d + 35 \, a^{4} b e - 15 \, a^{5} f\right)} x^{7}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{1680 \, {\left(a^{6} b^{2} x^{11} + 2 \, a^{7} b x^{9} + a^{8} x^{7}\right)}}, \frac{105 \, {\left(99 \, b^{5} c - 63 \, a b^{4} d + 35 \, a^{2} b^{3} e - 15 \, a^{3} b^{2} f\right)} x^{10} + 175 \, {\left(99 \, a b^{4} c - 63 \, a^{2} b^{3} d + 35 \, a^{3} b^{2} e - 15 \, a^{4} b f\right)} x^{8} + 56 \, {\left(99 \, a^{2} b^{3} c - 63 \, a^{3} b^{2} d + 35 \, a^{4} b e - 15 \, a^{5} f\right)} x^{6} - 120 \, a^{5} c - 8 \, {\left(99 \, a^{3} b^{2} c - 63 \, a^{4} b d + 35 \, a^{5} e\right)} x^{4} + 24 \, {\left(11 \, a^{4} b c - 7 \, a^{5} d\right)} x^{2} + 105 \, {\left({\left(99 \, b^{5} c - 63 \, a b^{4} d + 35 \, a^{2} b^{3} e - 15 \, a^{3} b^{2} f\right)} x^{11} + 2 \, {\left(99 \, a b^{4} c - 63 \, a^{2} b^{3} d + 35 \, a^{3} b^{2} e - 15 \, a^{4} b f\right)} x^{9} + {\left(99 \, a^{2} b^{3} c - 63 \, a^{3} b^{2} d + 35 \, a^{4} b e - 15 \, a^{5} f\right)} x^{7}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{840 \, {\left(a^{6} b^{2} x^{11} + 2 \, a^{7} b x^{9} + a^{8} x^{7}\right)}}\right]"," ",0,"[1/1680*(210*(99*b^5*c - 63*a*b^4*d + 35*a^2*b^3*e - 15*a^3*b^2*f)*x^10 + 350*(99*a*b^4*c - 63*a^2*b^3*d + 35*a^3*b^2*e - 15*a^4*b*f)*x^8 + 112*(99*a^2*b^3*c - 63*a^3*b^2*d + 35*a^4*b*e - 15*a^5*f)*x^6 - 240*a^5*c - 16*(99*a^3*b^2*c - 63*a^4*b*d + 35*a^5*e)*x^4 + 48*(11*a^4*b*c - 7*a^5*d)*x^2 - 105*((99*b^5*c - 63*a*b^4*d + 35*a^2*b^3*e - 15*a^3*b^2*f)*x^11 + 2*(99*a*b^4*c - 63*a^2*b^3*d + 35*a^3*b^2*e - 15*a^4*b*f)*x^9 + (99*a^2*b^3*c - 63*a^3*b^2*d + 35*a^4*b*e - 15*a^5*f)*x^7)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^6*b^2*x^11 + 2*a^7*b*x^9 + a^8*x^7), 1/840*(105*(99*b^5*c - 63*a*b^4*d + 35*a^2*b^3*e - 15*a^3*b^2*f)*x^10 + 175*(99*a*b^4*c - 63*a^2*b^3*d + 35*a^3*b^2*e - 15*a^4*b*f)*x^8 + 56*(99*a^2*b^3*c - 63*a^3*b^2*d + 35*a^4*b*e - 15*a^5*f)*x^6 - 120*a^5*c - 8*(99*a^3*b^2*c - 63*a^4*b*d + 35*a^5*e)*x^4 + 24*(11*a^4*b*c - 7*a^5*d)*x^2 + 105*((99*b^5*c - 63*a*b^4*d + 35*a^2*b^3*e - 15*a^3*b^2*f)*x^11 + 2*(99*a*b^4*c - 63*a^2*b^3*d + 35*a^3*b^2*e - 15*a^4*b*f)*x^9 + (99*a^2*b^3*c - 63*a^3*b^2*d + 35*a^4*b*e - 15*a^5*f)*x^7)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^6*b^2*x^11 + 2*a^7*b*x^9 + a^8*x^7)]","A",0
142,1,772,0,0.745391," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{630 \, {\left(143 \, b^{6} c - 99 \, a b^{5} d + 63 \, a^{2} b^{4} e - 35 \, a^{3} b^{3} f\right)} x^{12} + 1050 \, {\left(143 \, a b^{5} c - 99 \, a^{2} b^{4} d + 63 \, a^{3} b^{3} e - 35 \, a^{4} b^{2} f\right)} x^{10} + 336 \, {\left(143 \, a^{2} b^{4} c - 99 \, a^{3} b^{3} d + 63 \, a^{4} b^{2} e - 35 \, a^{5} b f\right)} x^{8} + 560 \, a^{6} c - 48 \, {\left(143 \, a^{3} b^{3} c - 99 \, a^{4} b^{2} d + 63 \, a^{5} b e - 35 \, a^{6} f\right)} x^{6} + 16 \, {\left(143 \, a^{4} b^{2} c - 99 \, a^{5} b d + 63 \, a^{6} e\right)} x^{4} - 80 \, {\left(13 \, a^{5} b c - 9 \, a^{6} d\right)} x^{2} + 315 \, {\left({\left(143 \, b^{6} c - 99 \, a b^{5} d + 63 \, a^{2} b^{4} e - 35 \, a^{3} b^{3} f\right)} x^{13} + 2 \, {\left(143 \, a b^{5} c - 99 \, a^{2} b^{4} d + 63 \, a^{3} b^{3} e - 35 \, a^{4} b^{2} f\right)} x^{11} + {\left(143 \, a^{2} b^{4} c - 99 \, a^{3} b^{3} d + 63 \, a^{4} b^{2} e - 35 \, a^{5} b f\right)} x^{9}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{5040 \, {\left(a^{7} b^{2} x^{13} + 2 \, a^{8} b x^{11} + a^{9} x^{9}\right)}}, -\frac{315 \, {\left(143 \, b^{6} c - 99 \, a b^{5} d + 63 \, a^{2} b^{4} e - 35 \, a^{3} b^{3} f\right)} x^{12} + 525 \, {\left(143 \, a b^{5} c - 99 \, a^{2} b^{4} d + 63 \, a^{3} b^{3} e - 35 \, a^{4} b^{2} f\right)} x^{10} + 168 \, {\left(143 \, a^{2} b^{4} c - 99 \, a^{3} b^{3} d + 63 \, a^{4} b^{2} e - 35 \, a^{5} b f\right)} x^{8} + 280 \, a^{6} c - 24 \, {\left(143 \, a^{3} b^{3} c - 99 \, a^{4} b^{2} d + 63 \, a^{5} b e - 35 \, a^{6} f\right)} x^{6} + 8 \, {\left(143 \, a^{4} b^{2} c - 99 \, a^{5} b d + 63 \, a^{6} e\right)} x^{4} - 40 \, {\left(13 \, a^{5} b c - 9 \, a^{6} d\right)} x^{2} + 315 \, {\left({\left(143 \, b^{6} c - 99 \, a b^{5} d + 63 \, a^{2} b^{4} e - 35 \, a^{3} b^{3} f\right)} x^{13} + 2 \, {\left(143 \, a b^{5} c - 99 \, a^{2} b^{4} d + 63 \, a^{3} b^{3} e - 35 \, a^{4} b^{2} f\right)} x^{11} + {\left(143 \, a^{2} b^{4} c - 99 \, a^{3} b^{3} d + 63 \, a^{4} b^{2} e - 35 \, a^{5} b f\right)} x^{9}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{2520 \, {\left(a^{7} b^{2} x^{13} + 2 \, a^{8} b x^{11} + a^{9} x^{9}\right)}}\right]"," ",0,"[-1/5040*(630*(143*b^6*c - 99*a*b^5*d + 63*a^2*b^4*e - 35*a^3*b^3*f)*x^12 + 1050*(143*a*b^5*c - 99*a^2*b^4*d + 63*a^3*b^3*e - 35*a^4*b^2*f)*x^10 + 336*(143*a^2*b^4*c - 99*a^3*b^3*d + 63*a^4*b^2*e - 35*a^5*b*f)*x^8 + 560*a^6*c - 48*(143*a^3*b^3*c - 99*a^4*b^2*d + 63*a^5*b*e - 35*a^6*f)*x^6 + 16*(143*a^4*b^2*c - 99*a^5*b*d + 63*a^6*e)*x^4 - 80*(13*a^5*b*c - 9*a^6*d)*x^2 + 315*((143*b^6*c - 99*a*b^5*d + 63*a^2*b^4*e - 35*a^3*b^3*f)*x^13 + 2*(143*a*b^5*c - 99*a^2*b^4*d + 63*a^3*b^3*e - 35*a^4*b^2*f)*x^11 + (143*a^2*b^4*c - 99*a^3*b^3*d + 63*a^4*b^2*e - 35*a^5*b*f)*x^9)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^7*b^2*x^13 + 2*a^8*b*x^11 + a^9*x^9), -1/2520*(315*(143*b^6*c - 99*a*b^5*d + 63*a^2*b^4*e - 35*a^3*b^3*f)*x^12 + 525*(143*a*b^5*c - 99*a^2*b^4*d + 63*a^3*b^3*e - 35*a^4*b^2*f)*x^10 + 168*(143*a^2*b^4*c - 99*a^3*b^3*d + 63*a^4*b^2*e - 35*a^5*b*f)*x^8 + 280*a^6*c - 24*(143*a^3*b^3*c - 99*a^4*b^2*d + 63*a^5*b*e - 35*a^6*f)*x^6 + 8*(143*a^4*b^2*c - 99*a^5*b*d + 63*a^6*e)*x^4 - 40*(13*a^5*b*c - 9*a^6*d)*x^2 + 315*((143*b^6*c - 99*a*b^5*d + 63*a^2*b^4*e - 35*a^3*b^3*f)*x^13 + 2*(143*a*b^5*c - 99*a^2*b^4*d + 63*a^3*b^3*e - 35*a^4*b^2*f)*x^11 + (143*a^2*b^4*c - 99*a^3*b^3*d + 63*a^4*b^2*e - 35*a^5*b*f)*x^9)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^7*b^2*x^13 + 2*a^8*b*x^11 + a^9*x^9)]","A",0
143,1,177,0,1.030342," ","integrate(x^5*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(315 \, b^{5} f x^{10} + 35 \, {\left(11 \, b^{5} e - 10 \, a b^{4} f\right)} x^{8} + 5 \, {\left(99 \, b^{5} d - 88 \, a b^{4} e + 80 \, a^{2} b^{3} f\right)} x^{6} + 1848 \, a^{2} b^{3} c - 1584 \, a^{3} b^{2} d + 1408 \, a^{4} b e - 1280 \, a^{5} f + 3 \, {\left(231 \, b^{5} c - 198 \, a b^{4} d + 176 \, a^{2} b^{3} e - 160 \, a^{3} b^{2} f\right)} x^{4} - 4 \, {\left(231 \, a b^{4} c - 198 \, a^{2} b^{3} d + 176 \, a^{3} b^{2} e - 160 \, a^{4} b f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{3465 \, b^{6}}"," ",0,"1/3465*(315*b^5*f*x^10 + 35*(11*b^5*e - 10*a*b^4*f)*x^8 + 5*(99*b^5*d - 88*a*b^4*e + 80*a^2*b^3*f)*x^6 + 1848*a^2*b^3*c - 1584*a^3*b^2*d + 1408*a^4*b*e - 1280*a^5*f + 3*(231*b^5*c - 198*a*b^4*d + 176*a^2*b^3*e - 160*a^3*b^2*f)*x^4 - 4*(231*a*b^4*c - 198*a^2*b^3*d + 176*a^3*b^2*e - 160*a^4*b*f)*x^2)*sqrt(b*x^2 + a)/b^6","A",0
144,1,134,0,1.104450," ","integrate(x^3*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(35 \, b^{4} f x^{8} + 5 \, {\left(9 \, b^{4} e - 8 \, a b^{3} f\right)} x^{6} - 210 \, a b^{3} c + 168 \, a^{2} b^{2} d - 144 \, a^{3} b e + 128 \, a^{4} f + 3 \, {\left(21 \, b^{4} d - 18 \, a b^{3} e + 16 \, a^{2} b^{2} f\right)} x^{4} + {\left(105 \, b^{4} c - 84 \, a b^{3} d + 72 \, a^{2} b^{2} e - 64 \, a^{3} b f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{315 \, b^{5}}"," ",0,"1/315*(35*b^4*f*x^8 + 5*(9*b^4*e - 8*a*b^3*f)*x^6 - 210*a*b^3*c + 168*a^2*b^2*d - 144*a^3*b*e + 128*a^4*f + 3*(21*b^4*d - 18*a*b^3*e + 16*a^2*b^2*f)*x^4 + (105*b^4*c - 84*a*b^3*d + 72*a^2*b^2*e - 64*a^3*b*f)*x^2)*sqrt(b*x^2 + a)/b^5","A",0
145,1,94,0,0.975575," ","integrate(x*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, b^{3} f x^{6} + 3 \, {\left(7 \, b^{3} e - 6 \, a b^{2} f\right)} x^{4} + 105 \, b^{3} c - 70 \, a b^{2} d + 56 \, a^{2} b e - 48 \, a^{3} f + {\left(35 \, b^{3} d - 28 \, a b^{2} e + 24 \, a^{2} b f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, b^{4}}"," ",0,"1/105*(15*b^3*f*x^6 + 3*(7*b^3*e - 6*a*b^2*f)*x^4 + 105*b^3*c - 70*a*b^2*d + 56*a^2*b*e - 48*a^3*f + (35*b^3*d - 28*a*b^2*e + 24*a^2*b*f)*x^2)*sqrt(b*x^2 + a)/b^4","A",0
146,1,205,0,1.033846," ","integrate((f*x^6+e*x^4+d*x^2+c)/x/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{3} c \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(3 \, a b^{2} f x^{4} + 15 \, a b^{2} d - 10 \, a^{2} b e + 8 \, a^{3} f + {\left(5 \, a b^{2} e - 4 \, a^{2} b f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{30 \, a b^{3}}, \frac{15 \, \sqrt{-a} b^{3} c \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, a b^{2} f x^{4} + 15 \, a b^{2} d - 10 \, a^{2} b e + 8 \, a^{3} f + {\left(5 \, a b^{2} e - 4 \, a^{2} b f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, a b^{3}}\right]"," ",0,"[1/30*(15*sqrt(a)*b^3*c*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*a*b^2*f*x^4 + 15*a*b^2*d - 10*a^2*b*e + 8*a^3*f + (5*a*b^2*e - 4*a^2*b*f)*x^2)*sqrt(b*x^2 + a))/(a*b^3), 1/15*(15*sqrt(-a)*b^3*c*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*a*b^2*f*x^4 + 15*a*b^2*d - 10*a^2*b*e + 8*a^3*f + (5*a*b^2*e - 4*a^2*b*f)*x^2)*sqrt(b*x^2 + a))/(a*b^3)]","A",0
147,1,210,0,0.930680," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^3/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c - 2 \, a b^{2} d\right)} \sqrt{a} x^{2} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(2 \, a^{2} b f x^{4} - 3 \, a b^{2} c + 2 \, {\left(3 \, a^{2} b e - 2 \, a^{3} f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{12 \, a^{2} b^{2} x^{2}}, -\frac{3 \, {\left(b^{3} c - 2 \, a b^{2} d\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, a^{2} b f x^{4} - 3 \, a b^{2} c + 2 \, {\left(3 \, a^{2} b e - 2 \, a^{3} f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{6 \, a^{2} b^{2} x^{2}}\right]"," ",0,"[-1/12*(3*(b^3*c - 2*a*b^2*d)*sqrt(a)*x^2*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(2*a^2*b*f*x^4 - 3*a*b^2*c + 2*(3*a^2*b*e - 2*a^3*f)*x^2)*sqrt(b*x^2 + a))/(a^2*b^2*x^2), -1/6*(3*(b^3*c - 2*a*b^2*d)*sqrt(-a)*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (2*a^2*b*f*x^4 - 3*a*b^2*c + 2*(3*a^2*b*e - 2*a^3*f)*x^2)*sqrt(b*x^2 + a))/(a^2*b^2*x^2)]","A",0
148,1,221,0,1.079924," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^5/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{3} c - 4 \, a b^{2} d + 8 \, a^{2} b e\right)} \sqrt{a} x^{4} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(8 \, a^{3} f x^{4} - 2 \, a^{2} b c + {\left(3 \, a b^{2} c - 4 \, a^{2} b d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{16 \, a^{3} b x^{4}}, \frac{{\left(3 \, b^{3} c - 4 \, a b^{2} d + 8 \, a^{2} b e\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(8 \, a^{3} f x^{4} - 2 \, a^{2} b c + {\left(3 \, a b^{2} c - 4 \, a^{2} b d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{8 \, a^{3} b x^{4}}\right]"," ",0,"[1/16*((3*b^3*c - 4*a*b^2*d + 8*a^2*b*e)*sqrt(a)*x^4*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(8*a^3*f*x^4 - 2*a^2*b*c + (3*a*b^2*c - 4*a^2*b*d)*x^2)*sqrt(b*x^2 + a))/(a^3*b*x^4), 1/8*((3*b^3*c - 4*a*b^2*d + 8*a^2*b*e)*sqrt(-a)*x^4*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (8*a^3*f*x^4 - 2*a^2*b*c + (3*a*b^2*c - 4*a^2*b*d)*x^2)*sqrt(b*x^2 + a))/(a^3*b*x^4)]","A",0
149,1,261,0,1.151391," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^7/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} c - 6 \, a b^{2} d + 8 \, a^{2} b e - 16 \, a^{3} f\right)} \sqrt{a} x^{6} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(3 \, {\left(5 \, a b^{2} c - 6 \, a^{2} b d + 8 \, a^{3} e\right)} x^{4} + 8 \, a^{3} c - 2 \, {\left(5 \, a^{2} b c - 6 \, a^{3} d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{96 \, a^{4} x^{6}}, -\frac{3 \, {\left(5 \, b^{3} c - 6 \, a b^{2} d + 8 \, a^{2} b e - 16 \, a^{3} f\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, {\left(5 \, a b^{2} c - 6 \, a^{2} b d + 8 \, a^{3} e\right)} x^{4} + 8 \, a^{3} c - 2 \, {\left(5 \, a^{2} b c - 6 \, a^{3} d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{48 \, a^{4} x^{6}}\right]"," ",0,"[-1/96*(3*(5*b^3*c - 6*a*b^2*d + 8*a^2*b*e - 16*a^3*f)*sqrt(a)*x^6*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*(5*a*b^2*c - 6*a^2*b*d + 8*a^3*e)*x^4 + 8*a^3*c - 2*(5*a^2*b*c - 6*a^3*d)*x^2)*sqrt(b*x^2 + a))/(a^4*x^6), -1/48*(3*(5*b^3*c - 6*a*b^2*d + 8*a^2*b*e - 16*a^3*f)*sqrt(-a)*x^6*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*(5*a*b^2*c - 6*a^2*b*d + 8*a^3*e)*x^4 + 8*a^3*c - 2*(5*a^2*b*c - 6*a^3*d)*x^2)*sqrt(b*x^2 + a))/(a^4*x^6)]","A",0
150,1,341,0,1.402973," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^9/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(35 \, b^{4} c - 40 \, a b^{3} d + 48 \, a^{2} b^{2} e - 64 \, a^{3} b f\right)} \sqrt{a} x^{8} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(3 \, {\left(35 \, a b^{3} c - 40 \, a^{2} b^{2} d + 48 \, a^{3} b e - 64 \, a^{4} f\right)} x^{6} - 48 \, a^{4} c - 2 \, {\left(35 \, a^{2} b^{2} c - 40 \, a^{3} b d + 48 \, a^{4} e\right)} x^{4} + 8 \, {\left(7 \, a^{3} b c - 8 \, a^{4} d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{768 \, a^{5} x^{8}}, \frac{3 \, {\left(35 \, b^{4} c - 40 \, a b^{3} d + 48 \, a^{2} b^{2} e - 64 \, a^{3} b f\right)} \sqrt{-a} x^{8} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, {\left(35 \, a b^{3} c - 40 \, a^{2} b^{2} d + 48 \, a^{3} b e - 64 \, a^{4} f\right)} x^{6} - 48 \, a^{4} c - 2 \, {\left(35 \, a^{2} b^{2} c - 40 \, a^{3} b d + 48 \, a^{4} e\right)} x^{4} + 8 \, {\left(7 \, a^{3} b c - 8 \, a^{4} d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{384 \, a^{5} x^{8}}\right]"," ",0,"[-1/768*(3*(35*b^4*c - 40*a*b^3*d + 48*a^2*b^2*e - 64*a^3*b*f)*sqrt(a)*x^8*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(3*(35*a*b^3*c - 40*a^2*b^2*d + 48*a^3*b*e - 64*a^4*f)*x^6 - 48*a^4*c - 2*(35*a^2*b^2*c - 40*a^3*b*d + 48*a^4*e)*x^4 + 8*(7*a^3*b*c - 8*a^4*d)*x^2)*sqrt(b*x^2 + a))/(a^5*x^8), 1/384*(3*(35*b^4*c - 40*a*b^3*d + 48*a^2*b^2*e - 64*a^3*b*f)*sqrt(-a)*x^8*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*(35*a*b^3*c - 40*a^2*b^2*d + 48*a^3*b*e - 64*a^4*f)*x^6 - 48*a^4*c - 2*(35*a^2*b^2*c - 40*a^3*b*d + 48*a^4*e)*x^4 + 8*(7*a^3*b*c - 8*a^4*d)*x^2)*sqrt(b*x^2 + a))/(a^5*x^8)]","A",0
151,1,414,0,1.437115," ","integrate(x^4*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(96 \, a^{2} b^{3} c - 80 \, a^{3} b^{2} d + 70 \, a^{4} b e - 63 \, a^{5} f\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(384 \, b^{5} f x^{9} + 48 \, {\left(10 \, b^{5} e - 9 \, a b^{4} f\right)} x^{7} + 8 \, {\left(80 \, b^{5} d - 70 \, a b^{4} e + 63 \, a^{2} b^{3} f\right)} x^{5} + 10 \, {\left(96 \, b^{5} c - 80 \, a b^{4} d + 70 \, a^{2} b^{3} e - 63 \, a^{3} b^{2} f\right)} x^{3} - 15 \, {\left(96 \, a b^{4} c - 80 \, a^{2} b^{3} d + 70 \, a^{3} b^{2} e - 63 \, a^{4} b f\right)} x\right)} \sqrt{b x^{2} + a}}{7680 \, b^{6}}, -\frac{15 \, {\left(96 \, a^{2} b^{3} c - 80 \, a^{3} b^{2} d + 70 \, a^{4} b e - 63 \, a^{5} f\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(384 \, b^{5} f x^{9} + 48 \, {\left(10 \, b^{5} e - 9 \, a b^{4} f\right)} x^{7} + 8 \, {\left(80 \, b^{5} d - 70 \, a b^{4} e + 63 \, a^{2} b^{3} f\right)} x^{5} + 10 \, {\left(96 \, b^{5} c - 80 \, a b^{4} d + 70 \, a^{2} b^{3} e - 63 \, a^{3} b^{2} f\right)} x^{3} - 15 \, {\left(96 \, a b^{4} c - 80 \, a^{2} b^{3} d + 70 \, a^{3} b^{2} e - 63 \, a^{4} b f\right)} x\right)} \sqrt{b x^{2} + a}}{3840 \, b^{6}}\right]"," ",0,"[-1/7680*(15*(96*a^2*b^3*c - 80*a^3*b^2*d + 70*a^4*b*e - 63*a^5*f)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(384*b^5*f*x^9 + 48*(10*b^5*e - 9*a*b^4*f)*x^7 + 8*(80*b^5*d - 70*a*b^4*e + 63*a^2*b^3*f)*x^5 + 10*(96*b^5*c - 80*a*b^4*d + 70*a^2*b^3*e - 63*a^3*b^2*f)*x^3 - 15*(96*a*b^4*c - 80*a^2*b^3*d + 70*a^3*b^2*e - 63*a^4*b*f)*x)*sqrt(b*x^2 + a))/b^6, -1/3840*(15*(96*a^2*b^3*c - 80*a^3*b^2*d + 70*a^4*b*e - 63*a^5*f)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (384*b^5*f*x^9 + 48*(10*b^5*e - 9*a*b^4*f)*x^7 + 8*(80*b^5*d - 70*a*b^4*e + 63*a^2*b^3*f)*x^5 + 10*(96*b^5*c - 80*a*b^4*d + 70*a^2*b^3*e - 63*a^3*b^2*f)*x^3 - 15*(96*a*b^4*c - 80*a^2*b^3*d + 70*a^3*b^2*e - 63*a^4*b*f)*x)*sqrt(b*x^2 + a))/b^6]","A",0
152,1,329,0,1.067959," ","integrate(x^2*(f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(64 \, a b^{3} c - 48 \, a^{2} b^{2} d + 40 \, a^{3} b e - 35 \, a^{4} f\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(48 \, b^{4} f x^{7} + 8 \, {\left(8 \, b^{4} e - 7 \, a b^{3} f\right)} x^{5} + 2 \, {\left(48 \, b^{4} d - 40 \, a b^{3} e + 35 \, a^{2} b^{2} f\right)} x^{3} + 3 \, {\left(64 \, b^{4} c - 48 \, a b^{3} d + 40 \, a^{2} b^{2} e - 35 \, a^{3} b f\right)} x\right)} \sqrt{b x^{2} + a}}{768 \, b^{5}}, \frac{3 \, {\left(64 \, a b^{3} c - 48 \, a^{2} b^{2} d + 40 \, a^{3} b e - 35 \, a^{4} f\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(48 \, b^{4} f x^{7} + 8 \, {\left(8 \, b^{4} e - 7 \, a b^{3} f\right)} x^{5} + 2 \, {\left(48 \, b^{4} d - 40 \, a b^{3} e + 35 \, a^{2} b^{2} f\right)} x^{3} + 3 \, {\left(64 \, b^{4} c - 48 \, a b^{3} d + 40 \, a^{2} b^{2} e - 35 \, a^{3} b f\right)} x\right)} \sqrt{b x^{2} + a}}{384 \, b^{5}}\right]"," ",0,"[-1/768*(3*(64*a*b^3*c - 48*a^2*b^2*d + 40*a^3*b*e - 35*a^4*f)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(48*b^4*f*x^7 + 8*(8*b^4*e - 7*a*b^3*f)*x^5 + 2*(48*b^4*d - 40*a*b^3*e + 35*a^2*b^2*f)*x^3 + 3*(64*b^4*c - 48*a*b^3*d + 40*a^2*b^2*e - 35*a^3*b*f)*x)*sqrt(b*x^2 + a))/b^5, 1/384*(3*(64*a*b^3*c - 48*a^2*b^2*d + 40*a^3*b*e - 35*a^4*f)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (48*b^4*f*x^7 + 8*(8*b^4*e - 7*a*b^3*f)*x^5 + 2*(48*b^4*d - 40*a*b^3*e + 35*a^2*b^2*f)*x^3 + 3*(64*b^4*c - 48*a*b^3*d + 40*a^2*b^2*e - 35*a^3*b*f)*x)*sqrt(b*x^2 + a))/b^5]","A",0
153,1,250,0,1.009466," ","integrate((f*x^6+e*x^4+d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(16 \, b^{3} c - 8 \, a b^{2} d + 6 \, a^{2} b e - 5 \, a^{3} f\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(8 \, b^{3} f x^{5} + 2 \, {\left(6 \, b^{3} e - 5 \, a b^{2} f\right)} x^{3} + 3 \, {\left(8 \, b^{3} d - 6 \, a b^{2} e + 5 \, a^{2} b f\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, b^{4}}, -\frac{3 \, {\left(16 \, b^{3} c - 8 \, a b^{2} d + 6 \, a^{2} b e - 5 \, a^{3} f\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, b^{3} f x^{5} + 2 \, {\left(6 \, b^{3} e - 5 \, a b^{2} f\right)} x^{3} + 3 \, {\left(8 \, b^{3} d - 6 \, a b^{2} e + 5 \, a^{2} b f\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, b^{4}}\right]"," ",0,"[-1/96*(3*(16*b^3*c - 8*a*b^2*d + 6*a^2*b*e - 5*a^3*f)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(8*b^3*f*x^5 + 2*(6*b^3*e - 5*a*b^2*f)*x^3 + 3*(8*b^3*d - 6*a*b^2*e + 5*a^2*b*f)*x)*sqrt(b*x^2 + a))/b^4, -1/48*(3*(16*b^3*c - 8*a*b^2*d + 6*a^2*b*e - 5*a^3*f)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8*b^3*f*x^5 + 2*(6*b^3*e - 5*a*b^2*f)*x^3 + 3*(8*b^3*d - 6*a*b^2*e + 5*a^2*b*f)*x)*sqrt(b*x^2 + a))/b^4]","A",0
154,1,216,0,0.876678," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^2/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(8 \, a b^{2} d - 4 \, a^{2} b e + 3 \, a^{3} f\right)} \sqrt{b} x \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(2 \, a b^{2} f x^{4} - 8 \, b^{3} c + {\left(4 \, a b^{2} e - 3 \, a^{2} b f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{16 \, a b^{3} x}, -\frac{{\left(8 \, a b^{2} d - 4 \, a^{2} b e + 3 \, a^{3} f\right)} \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, a b^{2} f x^{4} - 8 \, b^{3} c + {\left(4 \, a b^{2} e - 3 \, a^{2} b f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{8 \, a b^{3} x}\right]"," ",0,"[1/16*((8*a*b^2*d - 4*a^2*b*e + 3*a^3*f)*sqrt(b)*x*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(2*a*b^2*f*x^4 - 8*b^3*c + (4*a*b^2*e - 3*a^2*b*f)*x^2)*sqrt(b*x^2 + a))/(a*b^3*x), -1/8*((8*a*b^2*d - 4*a^2*b*e + 3*a^3*f)*sqrt(-b)*x*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*a*b^2*f*x^4 - 8*b^3*c + (4*a*b^2*e - 3*a^2*b*f)*x^2)*sqrt(b*x^2 + a))/(a*b^3*x)]","A",0
155,1,210,0,0.737862," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^4/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, a^{2} b e - a^{3} f\right)} \sqrt{b} x^{3} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(3 \, a^{2} b f x^{4} - 2 \, a b^{2} c + 2 \, {\left(2 \, b^{3} c - 3 \, a b^{2} d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{12 \, a^{2} b^{2} x^{3}}, -\frac{3 \, {\left(2 \, a^{2} b e - a^{3} f\right)} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(3 \, a^{2} b f x^{4} - 2 \, a b^{2} c + 2 \, {\left(2 \, b^{3} c - 3 \, a b^{2} d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{6 \, a^{2} b^{2} x^{3}}\right]"," ",0,"[-1/12*(3*(2*a^2*b*e - a^3*f)*sqrt(b)*x^3*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(3*a^2*b*f*x^4 - 2*a*b^2*c + 2*(2*b^3*c - 3*a*b^2*d)*x^2)*sqrt(b*x^2 + a))/(a^2*b^2*x^3), -1/6*(3*(2*a^2*b*e - a^3*f)*sqrt(-b)*x^3*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (3*a^2*b*f*x^4 - 2*a*b^2*c + 2*(2*b^3*c - 3*a*b^2*d)*x^2)*sqrt(b*x^2 + a))/(a^2*b^2*x^3)]","A",0
156,1,221,0,1.023879," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^6/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{3} \sqrt{b} f x^{5} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left({\left(8 \, b^{3} c - 10 \, a b^{2} d + 15 \, a^{2} b e\right)} x^{4} + 3 \, a^{2} b c - {\left(4 \, a b^{2} c - 5 \, a^{2} b d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{30 \, a^{3} b x^{5}}, -\frac{15 \, a^{3} \sqrt{-b} f x^{5} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left({\left(8 \, b^{3} c - 10 \, a b^{2} d + 15 \, a^{2} b e\right)} x^{4} + 3 \, a^{2} b c - {\left(4 \, a b^{2} c - 5 \, a^{2} b d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, a^{3} b x^{5}}\right]"," ",0,"[1/30*(15*a^3*sqrt(b)*f*x^5*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*((8*b^3*c - 10*a*b^2*d + 15*a^2*b*e)*x^4 + 3*a^2*b*c - (4*a*b^2*c - 5*a^2*b*d)*x^2)*sqrt(b*x^2 + a))/(a^3*b*x^5), -1/15*(15*a^3*sqrt(-b)*f*x^5*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + ((8*b^3*c - 10*a*b^2*d + 15*a^2*b*e)*x^4 + 3*a^2*b*c - (4*a*b^2*c - 5*a^2*b*d)*x^2)*sqrt(b*x^2 + a))/(a^3*b*x^5)]","A",0
157,1,100,0,1.208462," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^8/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(48 \, b^{3} c - 56 \, a b^{2} d + 70 \, a^{2} b e - 105 \, a^{3} f\right)} x^{6} - {\left(24 \, a b^{2} c - 28 \, a^{2} b d + 35 \, a^{3} e\right)} x^{4} - 15 \, a^{3} c + 3 \, {\left(6 \, a^{2} b c - 7 \, a^{3} d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, a^{4} x^{7}}"," ",0,"1/105*((48*b^3*c - 56*a*b^2*d + 70*a^2*b*e - 105*a^3*f)*x^6 - (24*a*b^2*c - 28*a^2*b*d + 35*a^3*e)*x^4 - 15*a^3*c + 3*(6*a^2*b*c - 7*a^3*d)*x^2)*sqrt(b*x^2 + a)/(a^4*x^7)","A",0
158,1,141,0,1.601524," ","integrate((f*x^6+e*x^4+d*x^2+c)/x^10/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(64 \, b^{4} c - 72 \, a b^{3} d + 84 \, a^{2} b^{2} e - 105 \, a^{3} b f\right)} x^{8} - {\left(64 \, a b^{3} c - 72 \, a^{2} b^{2} d + 84 \, a^{3} b e - 105 \, a^{4} f\right)} x^{6} + 35 \, a^{4} c + 3 \, {\left(16 \, a^{2} b^{2} c - 18 \, a^{3} b d + 21 \, a^{4} e\right)} x^{4} - 5 \, {\left(8 \, a^{3} b c - 9 \, a^{4} d\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{315 \, a^{5} x^{9}}"," ",0,"-1/315*(2*(64*b^4*c - 72*a*b^3*d + 84*a^2*b^2*e - 105*a^3*b*f)*x^8 - (64*a*b^3*c - 72*a^2*b^2*d + 84*a^3*b*e - 105*a^4*f)*x^6 + 35*a^4*c + 3*(16*a^2*b^2*c - 18*a^3*b*d + 21*a^4*e)*x^4 - 5*(8*a^3*b*c - 9*a^4*d)*x^2)*sqrt(b*x^2 + a)/(a^5*x^9)","A",0
159,1,987,0,1.769213," ","integrate(x^8*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left({\left(429 \, D a^{3} b^{4} - 198 \, C a^{2} b^{5} + 72 \, B a b^{6} - 16 \, A b^{7}\right)} x^{8} + 429 \, D a^{7} - 198 \, C a^{6} b + 72 \, B a^{5} b^{2} - 16 \, A a^{4} b^{3} + 4 \, {\left(429 \, D a^{4} b^{3} - 198 \, C a^{3} b^{4} + 72 \, B a^{2} b^{5} - 16 \, A a b^{6}\right)} x^{6} + 6 \, {\left(429 \, D a^{5} b^{2} - 198 \, C a^{4} b^{3} + 72 \, B a^{3} b^{4} - 16 \, A a^{2} b^{5}\right)} x^{4} + 4 \, {\left(429 \, D a^{6} b - 198 \, C a^{5} b^{2} + 72 \, B a^{4} b^{3} - 16 \, A a^{3} b^{4}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(280 \, D b^{7} x^{13} - 70 \, {\left(13 \, D a b^{6} - 6 \, C b^{7}\right)} x^{11} + 35 \, {\left(143 \, D a^{2} b^{5} - 66 \, C a b^{6} + 24 \, B b^{7}\right)} x^{9} + 176 \, {\left(429 \, D a^{3} b^{4} - 198 \, C a^{2} b^{5} + 72 \, B a b^{6} - 16 \, A b^{7}\right)} x^{7} + 406 \, {\left(429 \, D a^{4} b^{3} - 198 \, C a^{3} b^{4} + 72 \, B a^{2} b^{5} - 16 \, A a b^{6}\right)} x^{5} + 350 \, {\left(429 \, D a^{5} b^{2} - 198 \, C a^{4} b^{3} + 72 \, B a^{3} b^{4} - 16 \, A a^{2} b^{5}\right)} x^{3} + 105 \, {\left(429 \, D a^{6} b - 198 \, C a^{5} b^{2} + 72 \, B a^{4} b^{3} - 16 \, A a^{3} b^{4}\right)} x\right)} \sqrt{b x^{2} + a}}{3360 \, {\left(b^{12} x^{8} + 4 \, a b^{11} x^{6} + 6 \, a^{2} b^{10} x^{4} + 4 \, a^{3} b^{9} x^{2} + a^{4} b^{8}\right)}}, \frac{105 \, {\left({\left(429 \, D a^{3} b^{4} - 198 \, C a^{2} b^{5} + 72 \, B a b^{6} - 16 \, A b^{7}\right)} x^{8} + 429 \, D a^{7} - 198 \, C a^{6} b + 72 \, B a^{5} b^{2} - 16 \, A a^{4} b^{3} + 4 \, {\left(429 \, D a^{4} b^{3} - 198 \, C a^{3} b^{4} + 72 \, B a^{2} b^{5} - 16 \, A a b^{6}\right)} x^{6} + 6 \, {\left(429 \, D a^{5} b^{2} - 198 \, C a^{4} b^{3} + 72 \, B a^{3} b^{4} - 16 \, A a^{2} b^{5}\right)} x^{4} + 4 \, {\left(429 \, D a^{6} b - 198 \, C a^{5} b^{2} + 72 \, B a^{4} b^{3} - 16 \, A a^{3} b^{4}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(280 \, D b^{7} x^{13} - 70 \, {\left(13 \, D a b^{6} - 6 \, C b^{7}\right)} x^{11} + 35 \, {\left(143 \, D a^{2} b^{5} - 66 \, C a b^{6} + 24 \, B b^{7}\right)} x^{9} + 176 \, {\left(429 \, D a^{3} b^{4} - 198 \, C a^{2} b^{5} + 72 \, B a b^{6} - 16 \, A b^{7}\right)} x^{7} + 406 \, {\left(429 \, D a^{4} b^{3} - 198 \, C a^{3} b^{4} + 72 \, B a^{2} b^{5} - 16 \, A a b^{6}\right)} x^{5} + 350 \, {\left(429 \, D a^{5} b^{2} - 198 \, C a^{4} b^{3} + 72 \, B a^{3} b^{4} - 16 \, A a^{2} b^{5}\right)} x^{3} + 105 \, {\left(429 \, D a^{6} b - 198 \, C a^{5} b^{2} + 72 \, B a^{4} b^{3} - 16 \, A a^{3} b^{4}\right)} x\right)} \sqrt{b x^{2} + a}}{1680 \, {\left(b^{12} x^{8} + 4 \, a b^{11} x^{6} + 6 \, a^{2} b^{10} x^{4} + 4 \, a^{3} b^{9} x^{2} + a^{4} b^{8}\right)}}\right]"," ",0,"[1/3360*(105*((429*D*a^3*b^4 - 198*C*a^2*b^5 + 72*B*a*b^6 - 16*A*b^7)*x^8 + 429*D*a^7 - 198*C*a^6*b + 72*B*a^5*b^2 - 16*A*a^4*b^3 + 4*(429*D*a^4*b^3 - 198*C*a^3*b^4 + 72*B*a^2*b^5 - 16*A*a*b^6)*x^6 + 6*(429*D*a^5*b^2 - 198*C*a^4*b^3 + 72*B*a^3*b^4 - 16*A*a^2*b^5)*x^4 + 4*(429*D*a^6*b - 198*C*a^5*b^2 + 72*B*a^4*b^3 - 16*A*a^3*b^4)*x^2)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(280*D*b^7*x^13 - 70*(13*D*a*b^6 - 6*C*b^7)*x^11 + 35*(143*D*a^2*b^5 - 66*C*a*b^6 + 24*B*b^7)*x^9 + 176*(429*D*a^3*b^4 - 198*C*a^2*b^5 + 72*B*a*b^6 - 16*A*b^7)*x^7 + 406*(429*D*a^4*b^3 - 198*C*a^3*b^4 + 72*B*a^2*b^5 - 16*A*a*b^6)*x^5 + 350*(429*D*a^5*b^2 - 198*C*a^4*b^3 + 72*B*a^3*b^4 - 16*A*a^2*b^5)*x^3 + 105*(429*D*a^6*b - 198*C*a^5*b^2 + 72*B*a^4*b^3 - 16*A*a^3*b^4)*x)*sqrt(b*x^2 + a))/(b^12*x^8 + 4*a*b^11*x^6 + 6*a^2*b^10*x^4 + 4*a^3*b^9*x^2 + a^4*b^8), 1/1680*(105*((429*D*a^3*b^4 - 198*C*a^2*b^5 + 72*B*a*b^6 - 16*A*b^7)*x^8 + 429*D*a^7 - 198*C*a^6*b + 72*B*a^5*b^2 - 16*A*a^4*b^3 + 4*(429*D*a^4*b^3 - 198*C*a^3*b^4 + 72*B*a^2*b^5 - 16*A*a*b^6)*x^6 + 6*(429*D*a^5*b^2 - 198*C*a^4*b^3 + 72*B*a^3*b^4 - 16*A*a^2*b^5)*x^4 + 4*(429*D*a^6*b - 198*C*a^5*b^2 + 72*B*a^4*b^3 - 16*A*a^3*b^4)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (280*D*b^7*x^13 - 70*(13*D*a*b^6 - 6*C*b^7)*x^11 + 35*(143*D*a^2*b^5 - 66*C*a*b^6 + 24*B*b^7)*x^9 + 176*(429*D*a^3*b^4 - 198*C*a^2*b^5 + 72*B*a*b^6 - 16*A*b^7)*x^7 + 406*(429*D*a^4*b^3 - 198*C*a^3*b^4 + 72*B*a^2*b^5 - 16*A*a*b^6)*x^5 + 350*(429*D*a^5*b^2 - 198*C*a^4*b^3 + 72*B*a^3*b^4 - 16*A*a^2*b^5)*x^3 + 105*(429*D*a^6*b - 198*C*a^5*b^2 + 72*B*a^4*b^3 - 16*A*a^3*b^4)*x)*sqrt(b*x^2 + a))/(b^12*x^8 + 4*a*b^11*x^6 + 6*a^2*b^10*x^4 + 4*a^3*b^9*x^2 + a^4*b^8)]","A",0
160,1,816,0,1.545526," ","integrate(x^6*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left({\left(99 \, D a^{3} b^{4} - 36 \, C a^{2} b^{5} + 8 \, B a b^{6}\right)} x^{8} + 99 \, D a^{7} - 36 \, C a^{6} b + 8 \, B a^{5} b^{2} + 4 \, {\left(99 \, D a^{4} b^{3} - 36 \, C a^{3} b^{4} + 8 \, B a^{2} b^{5}\right)} x^{6} + 6 \, {\left(99 \, D a^{5} b^{2} - 36 \, C a^{4} b^{3} + 8 \, B a^{3} b^{4}\right)} x^{4} + 4 \, {\left(99 \, D a^{6} b - 36 \, C a^{5} b^{2} + 8 \, B a^{4} b^{3}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(210 \, D a b^{6} x^{11} - 105 \, {\left(11 \, D a^{2} b^{5} - 4 \, C a b^{6}\right)} x^{9} - 8 \, {\left(2178 \, D a^{3} b^{4} - 792 \, C a^{2} b^{5} + 176 \, B a b^{6} - 15 \, A b^{7}\right)} x^{7} - 406 \, {\left(99 \, D a^{4} b^{3} - 36 \, C a^{3} b^{4} + 8 \, B a^{2} b^{5}\right)} x^{5} - 350 \, {\left(99 \, D a^{5} b^{2} - 36 \, C a^{4} b^{3} + 8 \, B a^{3} b^{4}\right)} x^{3} - 105 \, {\left(99 \, D a^{6} b - 36 \, C a^{5} b^{2} + 8 \, B a^{4} b^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{1680 \, {\left(a b^{11} x^{8} + 4 \, a^{2} b^{10} x^{6} + 6 \, a^{3} b^{9} x^{4} + 4 \, a^{4} b^{8} x^{2} + a^{5} b^{7}\right)}}, -\frac{105 \, {\left({\left(99 \, D a^{3} b^{4} - 36 \, C a^{2} b^{5} + 8 \, B a b^{6}\right)} x^{8} + 99 \, D a^{7} - 36 \, C a^{6} b + 8 \, B a^{5} b^{2} + 4 \, {\left(99 \, D a^{4} b^{3} - 36 \, C a^{3} b^{4} + 8 \, B a^{2} b^{5}\right)} x^{6} + 6 \, {\left(99 \, D a^{5} b^{2} - 36 \, C a^{4} b^{3} + 8 \, B a^{3} b^{4}\right)} x^{4} + 4 \, {\left(99 \, D a^{6} b - 36 \, C a^{5} b^{2} + 8 \, B a^{4} b^{3}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(210 \, D a b^{6} x^{11} - 105 \, {\left(11 \, D a^{2} b^{5} - 4 \, C a b^{6}\right)} x^{9} - 8 \, {\left(2178 \, D a^{3} b^{4} - 792 \, C a^{2} b^{5} + 176 \, B a b^{6} - 15 \, A b^{7}\right)} x^{7} - 406 \, {\left(99 \, D a^{4} b^{3} - 36 \, C a^{3} b^{4} + 8 \, B a^{2} b^{5}\right)} x^{5} - 350 \, {\left(99 \, D a^{5} b^{2} - 36 \, C a^{4} b^{3} + 8 \, B a^{3} b^{4}\right)} x^{3} - 105 \, {\left(99 \, D a^{6} b - 36 \, C a^{5} b^{2} + 8 \, B a^{4} b^{3}\right)} x\right)} \sqrt{b x^{2} + a}}{840 \, {\left(a b^{11} x^{8} + 4 \, a^{2} b^{10} x^{6} + 6 \, a^{3} b^{9} x^{4} + 4 \, a^{4} b^{8} x^{2} + a^{5} b^{7}\right)}}\right]"," ",0,"[1/1680*(105*((99*D*a^3*b^4 - 36*C*a^2*b^5 + 8*B*a*b^6)*x^8 + 99*D*a^7 - 36*C*a^6*b + 8*B*a^5*b^2 + 4*(99*D*a^4*b^3 - 36*C*a^3*b^4 + 8*B*a^2*b^5)*x^6 + 6*(99*D*a^5*b^2 - 36*C*a^4*b^3 + 8*B*a^3*b^4)*x^4 + 4*(99*D*a^6*b - 36*C*a^5*b^2 + 8*B*a^4*b^3)*x^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(210*D*a*b^6*x^11 - 105*(11*D*a^2*b^5 - 4*C*a*b^6)*x^9 - 8*(2178*D*a^3*b^4 - 792*C*a^2*b^5 + 176*B*a*b^6 - 15*A*b^7)*x^7 - 406*(99*D*a^4*b^3 - 36*C*a^3*b^4 + 8*B*a^2*b^5)*x^5 - 350*(99*D*a^5*b^2 - 36*C*a^4*b^3 + 8*B*a^3*b^4)*x^3 - 105*(99*D*a^6*b - 36*C*a^5*b^2 + 8*B*a^4*b^3)*x)*sqrt(b*x^2 + a))/(a*b^11*x^8 + 4*a^2*b^10*x^6 + 6*a^3*b^9*x^4 + 4*a^4*b^8*x^2 + a^5*b^7), -1/840*(105*((99*D*a^3*b^4 - 36*C*a^2*b^5 + 8*B*a*b^6)*x^8 + 99*D*a^7 - 36*C*a^6*b + 8*B*a^5*b^2 + 4*(99*D*a^4*b^3 - 36*C*a^3*b^4 + 8*B*a^2*b^5)*x^6 + 6*(99*D*a^5*b^2 - 36*C*a^4*b^3 + 8*B*a^3*b^4)*x^4 + 4*(99*D*a^6*b - 36*C*a^5*b^2 + 8*B*a^4*b^3)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (210*D*a*b^6*x^11 - 105*(11*D*a^2*b^5 - 4*C*a*b^6)*x^9 - 8*(2178*D*a^3*b^4 - 792*C*a^2*b^5 + 176*B*a*b^6 - 15*A*b^7)*x^7 - 406*(99*D*a^4*b^3 - 36*C*a^3*b^4 + 8*B*a^2*b^5)*x^5 - 350*(99*D*a^5*b^2 - 36*C*a^4*b^3 + 8*B*a^3*b^4)*x^3 - 105*(99*D*a^6*b - 36*C*a^5*b^2 + 8*B*a^4*b^3)*x)*sqrt(b*x^2 + a))/(a*b^11*x^8 + 4*a^2*b^10*x^6 + 6*a^3*b^9*x^4 + 4*a^4*b^8*x^2 + a^5*b^7)]","A",0
161,1,653,0,1.091153," ","integrate(x^4*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left({\left(9 \, D a^{3} b^{4} - 2 \, C a^{2} b^{5}\right)} x^{8} + 9 \, D a^{7} - 2 \, C a^{6} b + 4 \, {\left(9 \, D a^{4} b^{3} - 2 \, C a^{3} b^{4}\right)} x^{6} + 6 \, {\left(9 \, D a^{5} b^{2} - 2 \, C a^{4} b^{3}\right)} x^{4} + 4 \, {\left(9 \, D a^{6} b - 2 \, C a^{5} b^{2}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(105 \, D a^{2} b^{5} x^{9} + 2 \, {\left(792 \, D a^{3} b^{4} - 176 \, C a^{2} b^{5} + 15 \, B a b^{6} + 6 \, A b^{7}\right)} x^{7} + 14 \, {\left(261 \, D a^{4} b^{3} - 58 \, C a^{3} b^{4} + 3 \, A a b^{6}\right)} x^{5} + 350 \, {\left(9 \, D a^{5} b^{2} - 2 \, C a^{4} b^{3}\right)} x^{3} + 105 \, {\left(9 \, D a^{6} b - 2 \, C a^{5} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{420 \, {\left(a^{2} b^{10} x^{8} + 4 \, a^{3} b^{9} x^{6} + 6 \, a^{4} b^{8} x^{4} + 4 \, a^{5} b^{7} x^{2} + a^{6} b^{6}\right)}}, \frac{105 \, {\left({\left(9 \, D a^{3} b^{4} - 2 \, C a^{2} b^{5}\right)} x^{8} + 9 \, D a^{7} - 2 \, C a^{6} b + 4 \, {\left(9 \, D a^{4} b^{3} - 2 \, C a^{3} b^{4}\right)} x^{6} + 6 \, {\left(9 \, D a^{5} b^{2} - 2 \, C a^{4} b^{3}\right)} x^{4} + 4 \, {\left(9 \, D a^{6} b - 2 \, C a^{5} b^{2}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(105 \, D a^{2} b^{5} x^{9} + 2 \, {\left(792 \, D a^{3} b^{4} - 176 \, C a^{2} b^{5} + 15 \, B a b^{6} + 6 \, A b^{7}\right)} x^{7} + 14 \, {\left(261 \, D a^{4} b^{3} - 58 \, C a^{3} b^{4} + 3 \, A a b^{6}\right)} x^{5} + 350 \, {\left(9 \, D a^{5} b^{2} - 2 \, C a^{4} b^{3}\right)} x^{3} + 105 \, {\left(9 \, D a^{6} b - 2 \, C a^{5} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{210 \, {\left(a^{2} b^{10} x^{8} + 4 \, a^{3} b^{9} x^{6} + 6 \, a^{4} b^{8} x^{4} + 4 \, a^{5} b^{7} x^{2} + a^{6} b^{6}\right)}}\right]"," ",0,"[1/420*(105*((9*D*a^3*b^4 - 2*C*a^2*b^5)*x^8 + 9*D*a^7 - 2*C*a^6*b + 4*(9*D*a^4*b^3 - 2*C*a^3*b^4)*x^6 + 6*(9*D*a^5*b^2 - 2*C*a^4*b^3)*x^4 + 4*(9*D*a^6*b - 2*C*a^5*b^2)*x^2)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(105*D*a^2*b^5*x^9 + 2*(792*D*a^3*b^4 - 176*C*a^2*b^5 + 15*B*a*b^6 + 6*A*b^7)*x^7 + 14*(261*D*a^4*b^3 - 58*C*a^3*b^4 + 3*A*a*b^6)*x^5 + 350*(9*D*a^5*b^2 - 2*C*a^4*b^3)*x^3 + 105*(9*D*a^6*b - 2*C*a^5*b^2)*x)*sqrt(b*x^2 + a))/(a^2*b^10*x^8 + 4*a^3*b^9*x^6 + 6*a^4*b^8*x^4 + 4*a^5*b^7*x^2 + a^6*b^6), 1/210*(105*((9*D*a^3*b^4 - 2*C*a^2*b^5)*x^8 + 9*D*a^7 - 2*C*a^6*b + 4*(9*D*a^4*b^3 - 2*C*a^3*b^4)*x^6 + 6*(9*D*a^5*b^2 - 2*C*a^4*b^3)*x^4 + 4*(9*D*a^6*b - 2*C*a^5*b^2)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (105*D*a^2*b^5*x^9 + 2*(792*D*a^3*b^4 - 176*C*a^2*b^5 + 15*B*a*b^6 + 6*A*b^7)*x^7 + 14*(261*D*a^4*b^3 - 58*C*a^3*b^4 + 3*A*a*b^6)*x^5 + 350*(9*D*a^5*b^2 - 2*C*a^4*b^3)*x^3 + 105*(9*D*a^6*b - 2*C*a^5*b^2)*x)*sqrt(b*x^2 + a))/(a^2*b^10*x^8 + 4*a^3*b^9*x^6 + 6*a^4*b^8*x^4 + 4*a^5*b^7*x^2 + a^6*b^6)]","A",0
162,1,491,0,1.425370," ","integrate(x^2*(D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(D a^{3} b^{4} x^{8} + 4 \, D a^{4} b^{3} x^{6} + 6 \, D a^{5} b^{2} x^{4} + 4 \, D a^{6} b x^{2} + D a^{7}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(105 \, D a^{6} b x + {\left(176 \, D a^{3} b^{4} - 15 \, C a^{2} b^{5} - 6 \, B a b^{6} - 8 \, A b^{7}\right)} x^{7} + 7 \, {\left(58 \, D a^{4} b^{3} - 3 \, B a^{2} b^{5} - 4 \, A a b^{6}\right)} x^{5} + 35 \, {\left(10 \, D a^{5} b^{2} - A a^{2} b^{5}\right)} x^{3}\right)} \sqrt{b x^{2} + a}}{210 \, {\left(a^{3} b^{9} x^{8} + 4 \, a^{4} b^{8} x^{6} + 6 \, a^{5} b^{7} x^{4} + 4 \, a^{6} b^{6} x^{2} + a^{7} b^{5}\right)}}, -\frac{105 \, {\left(D a^{3} b^{4} x^{8} + 4 \, D a^{4} b^{3} x^{6} + 6 \, D a^{5} b^{2} x^{4} + 4 \, D a^{6} b x^{2} + D a^{7}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(105 \, D a^{6} b x + {\left(176 \, D a^{3} b^{4} - 15 \, C a^{2} b^{5} - 6 \, B a b^{6} - 8 \, A b^{7}\right)} x^{7} + 7 \, {\left(58 \, D a^{4} b^{3} - 3 \, B a^{2} b^{5} - 4 \, A a b^{6}\right)} x^{5} + 35 \, {\left(10 \, D a^{5} b^{2} - A a^{2} b^{5}\right)} x^{3}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{3} b^{9} x^{8} + 4 \, a^{4} b^{8} x^{6} + 6 \, a^{5} b^{7} x^{4} + 4 \, a^{6} b^{6} x^{2} + a^{7} b^{5}\right)}}\right]"," ",0,"[1/210*(105*(D*a^3*b^4*x^8 + 4*D*a^4*b^3*x^6 + 6*D*a^5*b^2*x^4 + 4*D*a^6*b*x^2 + D*a^7)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(105*D*a^6*b*x + (176*D*a^3*b^4 - 15*C*a^2*b^5 - 6*B*a*b^6 - 8*A*b^7)*x^7 + 7*(58*D*a^4*b^3 - 3*B*a^2*b^5 - 4*A*a*b^6)*x^5 + 35*(10*D*a^5*b^2 - A*a^2*b^5)*x^3)*sqrt(b*x^2 + a))/(a^3*b^9*x^8 + 4*a^4*b^8*x^6 + 6*a^5*b^7*x^4 + 4*a^6*b^6*x^2 + a^7*b^5), -1/105*(105*(D*a^3*b^4*x^8 + 4*D*a^4*b^3*x^6 + 6*D*a^5*b^2*x^4 + 4*D*a^6*b*x^2 + D*a^7)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (105*D*a^6*b*x + (176*D*a^3*b^4 - 15*C*a^2*b^5 - 6*B*a*b^6 - 8*A*b^7)*x^7 + 7*(58*D*a^4*b^3 - 3*B*a^2*b^5 - 4*A*a*b^6)*x^5 + 35*(10*D*a^5*b^2 - A*a^2*b^5)*x^3)*sqrt(b*x^2 + a))/(a^3*b^9*x^8 + 4*a^4*b^8*x^6 + 6*a^5*b^7*x^4 + 4*a^6*b^6*x^2 + a^7*b^5)]","A",0
163,1,141,0,1.012656," ","integrate((D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left({\left(15 \, D a^{3} + 6 \, C a^{2} b + 8 \, B a b^{2} + 48 \, A b^{3}\right)} x^{7} + 7 \, {\left(3 \, C a^{3} + 4 \, B a^{2} b + 24 \, A a b^{2}\right)} x^{5} + 105 \, A a^{3} x + 35 \, {\left(B a^{3} + 6 \, A a^{2} b\right)} x^{3}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{4} b^{4} x^{8} + 4 \, a^{5} b^{3} x^{6} + 6 \, a^{6} b^{2} x^{4} + 4 \, a^{7} b x^{2} + a^{8}\right)}}"," ",0,"1/105*((15*D*a^3 + 6*C*a^2*b + 8*B*a*b^2 + 48*A*b^3)*x^7 + 7*(3*C*a^3 + 4*B*a^2*b + 24*A*a*b^2)*x^5 + 105*A*a^3*x + 35*(B*a^3 + 6*A*a^2*b)*x^3)*sqrt(b*x^2 + a)/(a^4*b^4*x^8 + 4*a^5*b^3*x^6 + 6*a^6*b^2*x^4 + 4*a^7*b*x^2 + a^8)","A",0
164,1,182,0,0.928119," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^2/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(3 \, D a^{3} b + 4 \, C a^{2} b^{2} + 24 \, B a b^{3} - 192 \, A b^{4}\right)} x^{8} + 7 \, {\left(3 \, D a^{4} + 4 \, C a^{3} b + 24 \, B a^{2} b^{2} - 192 \, A a b^{3}\right)} x^{6} - 105 \, A a^{4} + 35 \, {\left(C a^{4} + 6 \, B a^{3} b - 48 \, A a^{2} b^{2}\right)} x^{4} + 105 \, {\left(B a^{4} - 8 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{5} b^{4} x^{9} + 4 \, a^{6} b^{3} x^{7} + 6 \, a^{7} b^{2} x^{5} + 4 \, a^{8} b x^{3} + a^{9} x\right)}}"," ",0,"1/105*(2*(3*D*a^3*b + 4*C*a^2*b^2 + 24*B*a*b^3 - 192*A*b^4)*x^8 + 7*(3*D*a^4 + 4*C*a^3*b + 24*B*a^2*b^2 - 192*A*a*b^3)*x^6 - 105*A*a^4 + 35*(C*a^4 + 6*B*a^3*b - 48*A*a^2*b^2)*x^4 + 105*(B*a^4 - 8*A*a^3*b)*x^2)*sqrt(b*x^2 + a)/(a^5*b^4*x^9 + 4*a^6*b^3*x^7 + 6*a^7*b^2*x^5 + 4*a^8*b*x^3 + a^9*x)","A",0
165,1,225,0,1.469529," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^4/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(D a^{3} b^{2} + 6 \, C a^{2} b^{3} - 48 \, B a b^{4} + 160 \, A b^{5}\right)} x^{10} + 28 \, {\left(D a^{4} b + 6 \, C a^{3} b^{2} - 48 \, B a^{2} b^{3} + 160 \, A a b^{4}\right)} x^{8} + 35 \, {\left(D a^{5} + 6 \, C a^{4} b - 48 \, B a^{3} b^{2} + 160 \, A a^{2} b^{3}\right)} x^{6} - 35 \, A a^{5} + 35 \, {\left(3 \, C a^{5} - 24 \, B a^{4} b + 80 \, A a^{3} b^{2}\right)} x^{4} - 35 \, {\left(3 \, B a^{5} - 10 \, A a^{4} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{6} b^{4} x^{11} + 4 \, a^{7} b^{3} x^{9} + 6 \, a^{8} b^{2} x^{7} + 4 \, a^{9} b x^{5} + a^{10} x^{3}\right)}}"," ",0,"1/105*(8*(D*a^3*b^2 + 6*C*a^2*b^3 - 48*B*a*b^4 + 160*A*b^5)*x^10 + 28*(D*a^4*b + 6*C*a^3*b^2 - 48*B*a^2*b^3 + 160*A*a*b^4)*x^8 + 35*(D*a^5 + 6*C*a^4*b - 48*B*a^3*b^2 + 160*A*a^2*b^3)*x^6 - 35*A*a^5 + 35*(3*C*a^5 - 24*B*a^4*b + 80*A*a^3*b^2)*x^4 - 35*(3*B*a^5 - 10*A*a^4*b)*x^2)*sqrt(b*x^2 + a)/(a^6*b^4*x^11 + 4*a^7*b^3*x^9 + 6*a^8*b^2*x^7 + 4*a^9*b*x^5 + a^10*x^3)","A",0
166,1,270,0,1.829333," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^6/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(16 \, {\left(3 \, D a^{3} b^{3} - 24 \, C a^{2} b^{4} + 80 \, B a b^{5} - 192 \, A b^{6}\right)} x^{12} + 56 \, {\left(3 \, D a^{4} b^{2} - 24 \, C a^{3} b^{3} + 80 \, B a^{2} b^{4} - 192 \, A a b^{5}\right)} x^{10} + 70 \, {\left(3 \, D a^{5} b - 24 \, C a^{4} b^{2} + 80 \, B a^{3} b^{3} - 192 \, A a^{2} b^{4}\right)} x^{8} - 21 \, A a^{6} + 35 \, {\left(3 \, D a^{6} - 24 \, C a^{5} b + 80 \, B a^{4} b^{2} - 192 \, A a^{3} b^{3}\right)} x^{6} - 35 \, {\left(3 \, C a^{6} - 10 \, B a^{5} b + 24 \, A a^{4} b^{2}\right)} x^{4} - 7 \, {\left(5 \, B a^{6} - 12 \, A a^{5} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{7} b^{4} x^{13} + 4 \, a^{8} b^{3} x^{11} + 6 \, a^{9} b^{2} x^{9} + 4 \, a^{10} b x^{7} + a^{11} x^{5}\right)}}"," ",0,"1/105*(16*(3*D*a^3*b^3 - 24*C*a^2*b^4 + 80*B*a*b^5 - 192*A*b^6)*x^12 + 56*(3*D*a^4*b^2 - 24*C*a^3*b^3 + 80*B*a^2*b^4 - 192*A*a*b^5)*x^10 + 70*(3*D*a^5*b - 24*C*a^4*b^2 + 80*B*a^3*b^3 - 192*A*a^2*b^4)*x^8 - 21*A*a^6 + 35*(3*D*a^6 - 24*C*a^5*b + 80*B*a^4*b^2 - 192*A*a^3*b^3)*x^6 - 35*(3*C*a^6 - 10*B*a^5*b + 24*A*a^4*b^2)*x^4 - 7*(5*B*a^6 - 12*A*a^5*b)*x^2)*sqrt(b*x^2 + a)/(a^7*b^4*x^13 + 4*a^8*b^3*x^11 + 6*a^9*b^2*x^9 + 4*a^10*b*x^7 + a^11*x^5)","A",0
167,1,311,0,2.896302," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^8/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","-\frac{{\left(128 \, {\left(3 \, D a^{3} b^{4} - 10 \, C a^{2} b^{5} + 24 \, B a b^{6} - 48 \, A b^{7}\right)} x^{14} + 448 \, {\left(3 \, D a^{4} b^{3} - 10 \, C a^{3} b^{4} + 24 \, B a^{2} b^{5} - 48 \, A a b^{6}\right)} x^{12} + 560 \, {\left(3 \, D a^{5} b^{2} - 10 \, C a^{4} b^{3} + 24 \, B a^{3} b^{4} - 48 \, A a^{2} b^{5}\right)} x^{10} + 280 \, {\left(3 \, D a^{6} b - 10 \, C a^{5} b^{2} + 24 \, B a^{4} b^{3} - 48 \, A a^{3} b^{4}\right)} x^{8} + 15 \, A a^{7} + 35 \, {\left(3 \, D a^{7} - 10 \, C a^{6} b + 24 \, B a^{5} b^{2} - 48 \, A a^{4} b^{3}\right)} x^{6} + 7 \, {\left(5 \, C a^{7} - 12 \, B a^{6} b + 24 \, A a^{5} b^{2}\right)} x^{4} + 21 \, {\left(B a^{7} - 2 \, A a^{6} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{8} b^{4} x^{15} + 4 \, a^{9} b^{3} x^{13} + 6 \, a^{10} b^{2} x^{11} + 4 \, a^{11} b x^{9} + a^{12} x^{7}\right)}}"," ",0,"-1/105*(128*(3*D*a^3*b^4 - 10*C*a^2*b^5 + 24*B*a*b^6 - 48*A*b^7)*x^14 + 448*(3*D*a^4*b^3 - 10*C*a^3*b^4 + 24*B*a^2*b^5 - 48*A*a*b^6)*x^12 + 560*(3*D*a^5*b^2 - 10*C*a^4*b^3 + 24*B*a^3*b^4 - 48*A*a^2*b^5)*x^10 + 280*(3*D*a^6*b - 10*C*a^5*b^2 + 24*B*a^4*b^3 - 48*A*a^3*b^4)*x^8 + 15*A*a^7 + 35*(3*D*a^7 - 10*C*a^6*b + 24*B*a^5*b^2 - 48*A*a^4*b^3)*x^6 + 7*(5*C*a^7 - 12*B*a^6*b + 24*A*a^5*b^2)*x^4 + 21*(B*a^7 - 2*A*a^6*b)*x^2)*sqrt(b*x^2 + a)/(a^8*b^4*x^15 + 4*a^9*b^3*x^13 + 6*a^10*b^2*x^11 + 4*a^11*b*x^9 + a^12*x^7)","A",0
168,1,354,0,3.809787," ","integrate((D*x^6+C*x^4+B*x^2+A)/x^10/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left(256 \, {\left(15 \, D a^{3} b^{5} - 36 \, C a^{2} b^{6} + 72 \, B a b^{7} - 128 \, A b^{8}\right)} x^{16} + 896 \, {\left(15 \, D a^{4} b^{4} - 36 \, C a^{3} b^{5} + 72 \, B a^{2} b^{6} - 128 \, A a b^{7}\right)} x^{14} + 1120 \, {\left(15 \, D a^{5} b^{3} - 36 \, C a^{4} b^{4} + 72 \, B a^{3} b^{5} - 128 \, A a^{2} b^{6}\right)} x^{12} + 560 \, {\left(15 \, D a^{6} b^{2} - 36 \, C a^{5} b^{3} + 72 \, B a^{4} b^{4} - 128 \, A a^{3} b^{5}\right)} x^{10} - 35 \, A a^{8} + 70 \, {\left(15 \, D a^{7} b - 36 \, C a^{6} b^{2} + 72 \, B a^{5} b^{3} - 128 \, A a^{4} b^{4}\right)} x^{8} - 7 \, {\left(15 \, D a^{8} - 36 \, C a^{7} b + 72 \, B a^{6} b^{2} - 128 \, A a^{5} b^{3}\right)} x^{6} - 7 \, {\left(9 \, C a^{8} - 18 \, B a^{7} b + 32 \, A a^{6} b^{2}\right)} x^{4} - 5 \, {\left(9 \, B a^{8} - 16 \, A a^{7} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{315 \, {\left(a^{9} b^{4} x^{17} + 4 \, a^{10} b^{3} x^{15} + 6 \, a^{11} b^{2} x^{13} + 4 \, a^{12} b x^{11} + a^{13} x^{9}\right)}}"," ",0,"1/315*(256*(15*D*a^3*b^5 - 36*C*a^2*b^6 + 72*B*a*b^7 - 128*A*b^8)*x^16 + 896*(15*D*a^4*b^4 - 36*C*a^3*b^5 + 72*B*a^2*b^6 - 128*A*a*b^7)*x^14 + 1120*(15*D*a^5*b^3 - 36*C*a^4*b^4 + 72*B*a^3*b^5 - 128*A*a^2*b^6)*x^12 + 560*(15*D*a^6*b^2 - 36*C*a^5*b^3 + 72*B*a^4*b^4 - 128*A*a^3*b^5)*x^10 - 35*A*a^8 + 70*(15*D*a^7*b - 36*C*a^6*b^2 + 72*B*a^5*b^3 - 128*A*a^4*b^4)*x^8 - 7*(15*D*a^8 - 36*C*a^7*b + 72*B*a^6*b^2 - 128*A*a^5*b^3)*x^6 - 7*(9*C*a^8 - 18*B*a^7*b + 32*A*a^6*b^2)*x^4 - 5*(9*B*a^8 - 16*A*a^7*b)*x^2)*sqrt(b*x^2 + a)/(a^9*b^4*x^17 + 4*a^10*b^3*x^15 + 6*a^11*b^2*x^13 + 4*a^12*b*x^11 + a^13*x^9)","A",0
169,1,177,0,0.956168," ","integrate((f*x^11+e*x^9+d*x^7+c*x^5)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(315 \, b^{5} f x^{10} + 35 \, {\left(11 \, b^{5} e - 10 \, a b^{4} f\right)} x^{8} + 5 \, {\left(99 \, b^{5} d - 88 \, a b^{4} e + 80 \, a^{2} b^{3} f\right)} x^{6} + 1848 \, a^{2} b^{3} c - 1584 \, a^{3} b^{2} d + 1408 \, a^{4} b e - 1280 \, a^{5} f + 3 \, {\left(231 \, b^{5} c - 198 \, a b^{4} d + 176 \, a^{2} b^{3} e - 160 \, a^{3} b^{2} f\right)} x^{4} - 4 \, {\left(231 \, a b^{4} c - 198 \, a^{2} b^{3} d + 176 \, a^{3} b^{2} e - 160 \, a^{4} b f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{3465 \, b^{6}}"," ",0,"1/3465*(315*b^5*f*x^10 + 35*(11*b^5*e - 10*a*b^4*f)*x^8 + 5*(99*b^5*d - 88*a*b^4*e + 80*a^2*b^3*f)*x^6 + 1848*a^2*b^3*c - 1584*a^3*b^2*d + 1408*a^4*b*e - 1280*a^5*f + 3*(231*b^5*c - 198*a*b^4*d + 176*a^2*b^3*e - 160*a^3*b^2*f)*x^4 - 4*(231*a*b^4*c - 198*a^2*b^3*d + 176*a^3*b^2*e - 160*a^4*b*f)*x^2)*sqrt(b*x^2 + a)/b^6","A",0
170,1,134,0,1.107747," ","integrate((f*x^9+e*x^7+d*x^5+c*x^3)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(35 \, b^{4} f x^{8} + 5 \, {\left(9 \, b^{4} e - 8 \, a b^{3} f\right)} x^{6} - 210 \, a b^{3} c + 168 \, a^{2} b^{2} d - 144 \, a^{3} b e + 128 \, a^{4} f + 3 \, {\left(21 \, b^{4} d - 18 \, a b^{3} e + 16 \, a^{2} b^{2} f\right)} x^{4} + {\left(105 \, b^{4} c - 84 \, a b^{3} d + 72 \, a^{2} b^{2} e - 64 \, a^{3} b f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{315 \, b^{5}}"," ",0,"1/315*(35*b^4*f*x^8 + 5*(9*b^4*e - 8*a*b^3*f)*x^6 - 210*a*b^3*c + 168*a^2*b^2*d - 144*a^3*b*e + 128*a^4*f + 3*(21*b^4*d - 18*a*b^3*e + 16*a^2*b^2*f)*x^4 + (105*b^4*c - 84*a*b^3*d + 72*a^2*b^2*e - 64*a^3*b*f)*x^2)*sqrt(b*x^2 + a)/b^5","A",0
171,1,94,0,0.712142," ","integrate((f*x^7+e*x^5+d*x^3+c*x)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, b^{3} f x^{6} + 3 \, {\left(7 \, b^{3} e - 6 \, a b^{2} f\right)} x^{4} + 105 \, b^{3} c - 70 \, a b^{2} d + 56 \, a^{2} b e - 48 \, a^{3} f + {\left(35 \, b^{3} d - 28 \, a b^{2} e + 24 \, a^{2} b f\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, b^{4}}"," ",0,"1/105*(15*b^3*f*x^6 + 3*(7*b^3*e - 6*a*b^2*f)*x^4 + 105*b^3*c - 70*a*b^2*d + 56*a^2*b*e - 48*a^3*f + (35*b^3*d - 28*a*b^2*e + 24*a^2*b*f)*x^2)*sqrt(b*x^2 + a)/b^4","A",0
172,1,705,0,1.520808," ","integrate(x^2*(F*x^8+D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, F a^{8} - 2 \, D a^{7} b + {\left(9 \, F a^{4} b^{4} - 2 \, D a^{3} b^{5}\right)} x^{8} + 4 \, {\left(9 \, F a^{5} b^{3} - 2 \, D a^{4} b^{4}\right)} x^{6} + 6 \, {\left(9 \, F a^{6} b^{2} - 2 \, D a^{5} b^{3}\right)} x^{4} + 4 \, {\left(9 \, F a^{7} b - 2 \, D a^{6} b^{2}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(105 \, F a^{3} b^{5} x^{9} + 2 \, {\left(792 \, F a^{4} b^{4} - 176 \, D a^{3} b^{5} + 15 \, C a^{2} b^{6} + 6 \, B a b^{7} + 8 \, A b^{8}\right)} x^{7} + 14 \, {\left(261 \, F a^{5} b^{3} - 58 \, D a^{4} b^{4} + 3 \, B a^{2} b^{6} + 4 \, A a b^{7}\right)} x^{5} + 70 \, {\left(45 \, F a^{6} b^{2} - 10 \, D a^{5} b^{3} + A a^{2} b^{6}\right)} x^{3} + 105 \, {\left(9 \, F a^{7} b - 2 \, D a^{6} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{420 \, {\left(a^{3} b^{10} x^{8} + 4 \, a^{4} b^{9} x^{6} + 6 \, a^{5} b^{8} x^{4} + 4 \, a^{6} b^{7} x^{2} + a^{7} b^{6}\right)}}, \frac{105 \, {\left(9 \, F a^{8} - 2 \, D a^{7} b + {\left(9 \, F a^{4} b^{4} - 2 \, D a^{3} b^{5}\right)} x^{8} + 4 \, {\left(9 \, F a^{5} b^{3} - 2 \, D a^{4} b^{4}\right)} x^{6} + 6 \, {\left(9 \, F a^{6} b^{2} - 2 \, D a^{5} b^{3}\right)} x^{4} + 4 \, {\left(9 \, F a^{7} b - 2 \, D a^{6} b^{2}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(105 \, F a^{3} b^{5} x^{9} + 2 \, {\left(792 \, F a^{4} b^{4} - 176 \, D a^{3} b^{5} + 15 \, C a^{2} b^{6} + 6 \, B a b^{7} + 8 \, A b^{8}\right)} x^{7} + 14 \, {\left(261 \, F a^{5} b^{3} - 58 \, D a^{4} b^{4} + 3 \, B a^{2} b^{6} + 4 \, A a b^{7}\right)} x^{5} + 70 \, {\left(45 \, F a^{6} b^{2} - 10 \, D a^{5} b^{3} + A a^{2} b^{6}\right)} x^{3} + 105 \, {\left(9 \, F a^{7} b - 2 \, D a^{6} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{210 \, {\left(a^{3} b^{10} x^{8} + 4 \, a^{4} b^{9} x^{6} + 6 \, a^{5} b^{8} x^{4} + 4 \, a^{6} b^{7} x^{2} + a^{7} b^{6}\right)}}\right]"," ",0,"[-1/420*(105*(9*F*a^8 - 2*D*a^7*b + (9*F*a^4*b^4 - 2*D*a^3*b^5)*x^8 + 4*(9*F*a^5*b^3 - 2*D*a^4*b^4)*x^6 + 6*(9*F*a^6*b^2 - 2*D*a^5*b^3)*x^4 + 4*(9*F*a^7*b - 2*D*a^6*b^2)*x^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(105*F*a^3*b^5*x^9 + 2*(792*F*a^4*b^4 - 176*D*a^3*b^5 + 15*C*a^2*b^6 + 6*B*a*b^7 + 8*A*b^8)*x^7 + 14*(261*F*a^5*b^3 - 58*D*a^4*b^4 + 3*B*a^2*b^6 + 4*A*a*b^7)*x^5 + 70*(45*F*a^6*b^2 - 10*D*a^5*b^3 + A*a^2*b^6)*x^3 + 105*(9*F*a^7*b - 2*D*a^6*b^2)*x)*sqrt(b*x^2 + a))/(a^3*b^10*x^8 + 4*a^4*b^9*x^6 + 6*a^5*b^8*x^4 + 4*a^6*b^7*x^2 + a^7*b^6), 1/210*(105*(9*F*a^8 - 2*D*a^7*b + (9*F*a^4*b^4 - 2*D*a^3*b^5)*x^8 + 4*(9*F*a^5*b^3 - 2*D*a^4*b^4)*x^6 + 6*(9*F*a^6*b^2 - 2*D*a^5*b^3)*x^4 + 4*(9*F*a^7*b - 2*D*a^6*b^2)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (105*F*a^3*b^5*x^9 + 2*(792*F*a^4*b^4 - 176*D*a^3*b^5 + 15*C*a^2*b^6 + 6*B*a*b^7 + 8*A*b^8)*x^7 + 14*(261*F*a^5*b^3 - 58*D*a^4*b^4 + 3*B*a^2*b^6 + 4*A*a*b^7)*x^5 + 70*(45*F*a^6*b^2 - 10*D*a^5*b^3 + A*a^2*b^6)*x^3 + 105*(9*F*a^7*b - 2*D*a^6*b^2)*x)*sqrt(b*x^2 + a))/(a^3*b^10*x^8 + 4*a^4*b^9*x^6 + 6*a^5*b^8*x^4 + 4*a^6*b^7*x^2 + a^7*b^6)]","A",0
173,1,567,0,1.421018," ","integrate((F*x^8+D*x^6+C*x^4+B*x^2+A)/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(F a^{4} b^{4} x^{8} + 4 \, F a^{5} b^{3} x^{6} + 6 \, F a^{6} b^{2} x^{4} + 4 \, F a^{7} b x^{2} + F a^{8}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left({\left(176 \, F a^{4} b^{4} - 15 \, D a^{3} b^{5} - 6 \, C a^{2} b^{6} - 8 \, B a b^{7} - 48 \, A b^{8}\right)} x^{7} + 7 \, {\left(58 \, F a^{5} b^{3} - 3 \, C a^{3} b^{5} - 4 \, B a^{2} b^{6} - 24 \, A a b^{7}\right)} x^{5} + 35 \, {\left(10 \, F a^{6} b^{2} - B a^{3} b^{5} - 6 \, A a^{2} b^{6}\right)} x^{3} + 105 \, {\left(F a^{7} b - A a^{3} b^{5}\right)} x\right)} \sqrt{b x^{2} + a}}{210 \, {\left(a^{4} b^{9} x^{8} + 4 \, a^{5} b^{8} x^{6} + 6 \, a^{6} b^{7} x^{4} + 4 \, a^{7} b^{6} x^{2} + a^{8} b^{5}\right)}}, -\frac{105 \, {\left(F a^{4} b^{4} x^{8} + 4 \, F a^{5} b^{3} x^{6} + 6 \, F a^{6} b^{2} x^{4} + 4 \, F a^{7} b x^{2} + F a^{8}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left({\left(176 \, F a^{4} b^{4} - 15 \, D a^{3} b^{5} - 6 \, C a^{2} b^{6} - 8 \, B a b^{7} - 48 \, A b^{8}\right)} x^{7} + 7 \, {\left(58 \, F a^{5} b^{3} - 3 \, C a^{3} b^{5} - 4 \, B a^{2} b^{6} - 24 \, A a b^{7}\right)} x^{5} + 35 \, {\left(10 \, F a^{6} b^{2} - B a^{3} b^{5} - 6 \, A a^{2} b^{6}\right)} x^{3} + 105 \, {\left(F a^{7} b - A a^{3} b^{5}\right)} x\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{4} b^{9} x^{8} + 4 \, a^{5} b^{8} x^{6} + 6 \, a^{6} b^{7} x^{4} + 4 \, a^{7} b^{6} x^{2} + a^{8} b^{5}\right)}}\right]"," ",0,"[1/210*(105*(F*a^4*b^4*x^8 + 4*F*a^5*b^3*x^6 + 6*F*a^6*b^2*x^4 + 4*F*a^7*b*x^2 + F*a^8)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*((176*F*a^4*b^4 - 15*D*a^3*b^5 - 6*C*a^2*b^6 - 8*B*a*b^7 - 48*A*b^8)*x^7 + 7*(58*F*a^5*b^3 - 3*C*a^3*b^5 - 4*B*a^2*b^6 - 24*A*a*b^7)*x^5 + 35*(10*F*a^6*b^2 - B*a^3*b^5 - 6*A*a^2*b^6)*x^3 + 105*(F*a^7*b - A*a^3*b^5)*x)*sqrt(b*x^2 + a))/(a^4*b^9*x^8 + 4*a^5*b^8*x^6 + 6*a^6*b^7*x^4 + 4*a^7*b^6*x^2 + a^8*b^5), -1/105*(105*(F*a^4*b^4*x^8 + 4*F*a^5*b^3*x^6 + 6*F*a^6*b^2*x^4 + 4*F*a^7*b*x^2 + F*a^8)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + ((176*F*a^4*b^4 - 15*D*a^3*b^5 - 6*C*a^2*b^6 - 8*B*a*b^7 - 48*A*b^8)*x^7 + 7*(58*F*a^5*b^3 - 3*C*a^3*b^5 - 4*B*a^2*b^6 - 24*A*a*b^7)*x^5 + 35*(10*F*a^6*b^2 - B*a^3*b^5 - 6*A*a^2*b^6)*x^3 + 105*(F*a^7*b - A*a^3*b^5)*x)*sqrt(b*x^2 + a))/(a^4*b^9*x^8 + 4*a^5*b^8*x^6 + 6*a^6*b^7*x^4 + 4*a^7*b^6*x^2 + a^8*b^5)]","A",0
174,1,187,0,0.924977," ","integrate((F*x^8+D*x^6+C*x^4+B*x^2+A)/x^2/(b*x^2+a)^(9/2),x, algorithm=""fricas"")","\frac{{\left({\left(15 \, F a^{4} + 6 \, D a^{3} b + 8 \, C a^{2} b^{2} + 48 \, B a b^{3} - 384 \, A b^{4}\right)} x^{8} + 7 \, {\left(3 \, D a^{4} + 4 \, C a^{3} b + 24 \, B a^{2} b^{2} - 192 \, A a b^{3}\right)} x^{6} - 105 \, A a^{4} + 35 \, {\left(C a^{4} + 6 \, B a^{3} b - 48 \, A a^{2} b^{2}\right)} x^{4} + 105 \, {\left(B a^{4} - 8 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, {\left(a^{5} b^{4} x^{9} + 4 \, a^{6} b^{3} x^{7} + 6 \, a^{7} b^{2} x^{5} + 4 \, a^{8} b x^{3} + a^{9} x\right)}}"," ",0,"1/105*((15*F*a^4 + 6*D*a^3*b + 8*C*a^2*b^2 + 48*B*a*b^3 - 384*A*b^4)*x^8 + 7*(3*D*a^4 + 4*C*a^3*b + 24*B*a^2*b^2 - 192*A*a*b^3)*x^6 - 105*A*a^4 + 35*(C*a^4 + 6*B*a^3*b - 48*A*a^2*b^2)*x^4 + 105*(B*a^4 - 8*A*a^3*b)*x^2)*sqrt(b*x^2 + a)/(a^5*b^4*x^9 + 4*a^6*b^3*x^7 + 6*a^7*b^2*x^5 + 4*a^8*b*x^3 + a^9*x)","A",0
