1,1,97,0,0.172978," ","integrate((b*x^3+a)*(d*x^3+c)^4,x, algorithm=""giac"")","\frac{1}{16} \, b d^{4} x^{16} + \frac{4}{13} \, b c d^{3} x^{13} + \frac{1}{13} \, a d^{4} x^{13} + \frac{3}{5} \, b c^{2} d^{2} x^{10} + \frac{2}{5} \, a c d^{3} x^{10} + \frac{4}{7} \, b c^{3} d x^{7} + \frac{6}{7} \, a c^{2} d^{2} x^{7} + \frac{1}{4} \, b c^{4} x^{4} + a c^{3} d x^{4} + a c^{4} x"," ",0,"1/16*b*d^4*x^16 + 4/13*b*c*d^3*x^13 + 1/13*a*d^4*x^13 + 3/5*b*c^2*d^2*x^10 + 2/5*a*c*d^3*x^10 + 4/7*b*c^3*d*x^7 + 6/7*a*c^2*d^2*x^7 + 1/4*b*c^4*x^4 + a*c^3*d*x^4 + a*c^4*x","A",0
2,1,74,0,0.147829," ","integrate((b*x^3+a)*(d*x^3+c)^3,x, algorithm=""giac"")","\frac{1}{13} \, b d^{3} x^{13} + \frac{3}{10} \, b c d^{2} x^{10} + \frac{1}{10} \, a d^{3} x^{10} + \frac{3}{7} \, b c^{2} d x^{7} + \frac{3}{7} \, a c d^{2} x^{7} + \frac{1}{4} \, b c^{3} x^{4} + \frac{3}{4} \, a c^{2} d x^{4} + a c^{3} x"," ",0,"1/13*b*d^3*x^13 + 3/10*b*c*d^2*x^10 + 1/10*a*d^3*x^10 + 3/7*b*c^2*d*x^7 + 3/7*a*c*d^2*x^7 + 1/4*b*c^3*x^4 + 3/4*a*c^2*d*x^4 + a*c^3*x","A",0
3,1,50,0,0.188761," ","integrate((b*x^3+a)*(d*x^3+c)^2,x, algorithm=""giac"")","\frac{1}{10} \, b d^{2} x^{10} + \frac{2}{7} \, b c d x^{7} + \frac{1}{7} \, a d^{2} x^{7} + \frac{1}{4} \, b c^{2} x^{4} + \frac{1}{2} \, a c d x^{4} + a c^{2} x"," ",0,"1/10*b*d^2*x^10 + 2/7*b*c*d*x^7 + 1/7*a*d^2*x^7 + 1/4*b*c^2*x^4 + 1/2*a*c*d*x^4 + a*c^2*x","A",0
4,1,26,0,0.149344," ","integrate((b*x^3+a)*(d*x^3+c),x, algorithm=""giac"")","\frac{1}{7} \, b d x^{7} + \frac{1}{4} \, b c x^{4} + \frac{1}{4} \, a d x^{4} + a c x"," ",0,"1/7*b*d*x^7 + 1/4*b*c*x^4 + 1/4*a*d*x^4 + a*c*x","A",0
5,1,133,0,0.202068," ","integrate((b*x^3+a)/(d*x^3+c),x, algorithm=""giac"")","\frac{\sqrt{3} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-c d^{2}\right)^{\frac{2}{3}}} + \frac{{\left(b c - a d\right)} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, \left(-c d^{2}\right)^{\frac{2}{3}}} + \frac{b x}{d} + \frac{{\left(b c - a d\right)} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{3 \, c d}"," ",0,"1/3*sqrt(3)*(b*c - a*d)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/(-c*d^2)^(2/3) + 1/6*(b*c - a*d)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/(-c*d^2)^(2/3) + b*x/d + 1/3*(b*c - a*d)*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(c*d)","A",0
6,1,160,0,0.190536," ","integrate((b*x^3+a)/(d*x^3+c)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b c + 2 \, a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-c d^{2}\right)^{\frac{2}{3}} c} - \frac{{\left(b c + 2 \, a d\right)} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{18 \, \left(-c d^{2}\right)^{\frac{2}{3}} c} - \frac{{\left(b c + 2 \, a d\right)} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{9 \, c^{2} d} - \frac{b c x - a d x}{3 \, {\left(d x^{3} + c\right)} c d}"," ",0,"-1/9*sqrt(3)*(b*c + 2*a*d)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/((-c*d^2)^(2/3)*c) - 1/18*(b*c + 2*a*d)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/((-c*d^2)^(2/3)*c) - 1/9*(b*c + 2*a*d)*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(c^2*d) - 1/3*(b*c*x - a*d*x)/((d*x^3 + c)*c*d)","A",0
7,1,180,0,0.191060," ","integrate((b*x^3+a)/(d*x^3+c)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b c + 5 \, a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-c d^{2}\right)^{\frac{2}{3}} c^{2}} - \frac{{\left(b c + 5 \, a d\right)} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{54 \, \left(-c d^{2}\right)^{\frac{2}{3}} c^{2}} - \frac{{\left(b c + 5 \, a d\right)} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{27 \, c^{3} d} + \frac{b c d x^{4} + 5 \, a d^{2} x^{4} - 2 \, b c^{2} x + 8 \, a c d x}{18 \, {\left(d x^{3} + c\right)}^{2} c^{2} d}"," ",0,"-1/27*sqrt(3)*(b*c + 5*a*d)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/((-c*d^2)^(2/3)*c^2) - 1/54*(b*c + 5*a*d)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/((-c*d^2)^(2/3)*c^2) - 1/27*(b*c + 5*a*d)*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(c^3*d) + 1/18*(b*c*d*x^4 + 5*a*d^2*x^4 - 2*b*c^2*x + 8*a*c*d*x)/((d*x^3 + c)^2*c^2*d)","A",0
8,1,132,0,0.159334," ","integrate((b*x^3+a)^2*(d*x^3+c)^3,x, algorithm=""giac"")","\frac{1}{16} \, b^{2} d^{3} x^{16} + \frac{3}{13} \, b^{2} c d^{2} x^{13} + \frac{2}{13} \, a b d^{3} x^{13} + \frac{3}{10} \, b^{2} c^{2} d x^{10} + \frac{3}{5} \, a b c d^{2} x^{10} + \frac{1}{10} \, a^{2} d^{3} x^{10} + \frac{1}{7} \, b^{2} c^{3} x^{7} + \frac{6}{7} \, a b c^{2} d x^{7} + \frac{3}{7} \, a^{2} c d^{2} x^{7} + \frac{1}{2} \, a b c^{3} x^{4} + \frac{3}{4} \, a^{2} c^{2} d x^{4} + a^{2} c^{3} x"," ",0,"1/16*b^2*d^3*x^16 + 3/13*b^2*c*d^2*x^13 + 2/13*a*b*d^3*x^13 + 3/10*b^2*c^2*d*x^10 + 3/5*a*b*c*d^2*x^10 + 1/10*a^2*d^3*x^10 + 1/7*b^2*c^3*x^7 + 6/7*a*b*c^2*d*x^7 + 3/7*a^2*c*d^2*x^7 + 1/2*a*b*c^3*x^4 + 3/4*a^2*c^2*d*x^4 + a^2*c^3*x","A",0
9,1,91,0,0.208398," ","integrate((b*x^3+a)^2*(d*x^3+c)^2,x, algorithm=""giac"")","\frac{1}{13} \, b^{2} d^{2} x^{13} + \frac{1}{5} \, b^{2} c d x^{10} + \frac{1}{5} \, a b d^{2} x^{10} + \frac{1}{7} \, b^{2} c^{2} x^{7} + \frac{4}{7} \, a b c d x^{7} + \frac{1}{7} \, a^{2} d^{2} x^{7} + \frac{1}{2} \, a b c^{2} x^{4} + \frac{1}{2} \, a^{2} c d x^{4} + a^{2} c^{2} x"," ",0,"1/13*b^2*d^2*x^13 + 1/5*b^2*c*d*x^10 + 1/5*a*b*d^2*x^10 + 1/7*b^2*c^2*x^7 + 4/7*a*b*c*d*x^7 + 1/7*a^2*d^2*x^7 + 1/2*a*b*c^2*x^4 + 1/2*a^2*c*d*x^4 + a^2*c^2*x","A",0
10,1,50,0,0.158515," ","integrate((b*x^3+a)^2*(d*x^3+c),x, algorithm=""giac"")","\frac{1}{10} \, b^{2} d x^{10} + \frac{1}{7} \, b^{2} c x^{7} + \frac{2}{7} \, a b d x^{7} + \frac{1}{2} \, a b c x^{4} + \frac{1}{4} \, a^{2} d x^{4} + a^{2} c x"," ",0,"1/10*b^2*d*x^10 + 1/7*b^2*c*x^7 + 2/7*a*b*d*x^7 + 1/2*a*b*c*x^4 + 1/4*a^2*d*x^4 + a^2*c*x","A",0
11,1,211,0,0.194459," ","integrate((b*x^3+a)^2/(d*x^3+c),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-c d^{2}\right)^{\frac{2}{3}} d} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, \left(-c d^{2}\right)^{\frac{2}{3}} d} - \frac{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{3 \, c d^{4}} + \frac{b^{2} d^{3} x^{4} - 4 \, b^{2} c d^{2} x + 8 \, a b d^{3} x}{4 \, d^{4}}"," ",0,"-1/3*sqrt(3)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/((-c*d^2)^(2/3)*d) - 1/6*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/((-c*d^2)^(2/3)*d) - 1/3*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(c*d^4) + 1/4*(b^2*d^3*x^4 - 4*b^2*c*d^2*x + 8*a*b*d^3*x)/d^4","A",0
12,1,233,0,0.190217," ","integrate((b*x^3+a)^2/(d*x^3+c)^2,x, algorithm=""giac"")","\frac{b^{2} x}{d^{2}} + \frac{2 \, \sqrt{3} {\left(2 \, b^{2} c^{2} - a b c d - a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-c d^{2}\right)^{\frac{2}{3}} c d} + \frac{{\left(2 \, b^{2} c^{2} - a b c d - a^{2} d^{2}\right)} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{9 \, \left(-c d^{2}\right)^{\frac{2}{3}} c d} + \frac{2 \, {\left(2 \, b^{2} c^{2} - a b c d - a^{2} d^{2}\right)} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{9 \, c^{2} d^{2}} + \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{3 \, {\left(d x^{3} + c\right)} c d^{2}}"," ",0,"b^2*x/d^2 + 2/9*sqrt(3)*(2*b^2*c^2 - a*b*c*d - a^2*d^2)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/((-c*d^2)^(2/3)*c*d) + 1/9*(2*b^2*c^2 - a*b*c*d - a^2*d^2)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/((-c*d^2)^(2/3)*c*d) + 2/9*(2*b^2*c^2 - a*b*c*d - a^2*d^2)*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(c^2*d^2) + 1/3*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((d*x^3 + c)*c*d^2)","A",0
13,1,264,0,0.196517," ","integrate((b*x^3+a)^2/(d*x^3+c)^3,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{27 \, \left(-c d^{2}\right)^{\frac{2}{3}} c^{2} d} - \frac{{\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{54 \, \left(-c d^{2}\right)^{\frac{2}{3}} c^{2} d} - \frac{{\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{27 \, c^{3} d^{2}} - \frac{7 \, b^{2} c^{2} d x^{4} - 2 \, a b c d^{2} x^{4} - 5 \, a^{2} d^{3} x^{4} + 4 \, b^{2} c^{3} x + 4 \, a b c^{2} d x - 8 \, a^{2} c d^{2} x}{18 \, {\left(d x^{3} + c\right)}^{2} c^{2} d^{2}}"," ",0,"-1/27*sqrt(3)*(2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/((-c*d^2)^(2/3)*c^2*d) - 1/54*(2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/((-c*d^2)^(2/3)*c^2*d) - 1/27*(2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(c^3*d^2) - 1/18*(7*b^2*c^2*d*x^4 - 2*a*b*c*d^2*x^4 - 5*a^2*d^3*x^4 + 4*b^2*c^3*x + 4*a*b*c^2*d*x - 8*a^2*c*d^2*x)/((d*x^3 + c)^2*c^2*d^2)","A",0
14,1,391,0,0.200844," ","integrate((d*x^3+c)^4/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3}} - \frac{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{3}} - \frac{{\left(b^{10} c^{4} - 4 \, a b^{9} c^{3} d + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{3} b^{7} c d^{3} + a^{4} b^{6} d^{4}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{10}} + \frac{14 \, b^{9} d^{4} x^{10} + 80 \, b^{9} c d^{3} x^{7} - 20 \, a b^{8} d^{4} x^{7} + 210 \, b^{9} c^{2} d^{2} x^{4} - 140 \, a b^{8} c d^{3} x^{4} + 35 \, a^{2} b^{7} d^{4} x^{4} + 560 \, b^{9} c^{3} d x - 840 \, a b^{8} c^{2} d^{2} x + 560 \, a^{2} b^{7} c d^{3} x - 140 \, a^{3} b^{6} d^{4} x}{140 \, b^{10}}"," ",0,"-1/3*sqrt(3)*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b^3) - 1/6*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b^3) - 1/3*(b^10*c^4 - 4*a*b^9*c^3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^10) + 1/140*(14*b^9*d^4*x^10 + 80*b^9*c*d^3*x^7 - 20*a*b^8*d^4*x^7 + 210*b^9*c^2*d^2*x^4 - 140*a*b^8*c*d^3*x^4 + 35*a^2*b^7*d^4*x^4 + 560*b^9*c^3*d*x - 840*a*b^8*c^2*d^2*x + 560*a^2*b^7*c*d^3*x - 140*a^3*b^6*d^4*x)/b^10","A",0
15,1,296,0,0.184862," ","integrate((d*x^3+c)^3/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{2}} - \frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} b^{2}} - \frac{{\left(b^{7} c^{3} - 3 \, a b^{6} c^{2} d + 3 \, a^{2} b^{5} c d^{2} - a^{3} b^{4} d^{3}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{7}} + \frac{4 \, b^{6} d^{3} x^{7} + 21 \, b^{6} c d^{2} x^{4} - 7 \, a b^{5} d^{3} x^{4} + 84 \, b^{6} c^{2} d x - 84 \, a b^{5} c d^{2} x + 28 \, a^{2} b^{4} d^{3} x}{28 \, b^{7}}"," ",0,"-1/3*sqrt(3)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b^2) - 1/6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b^2) - 1/3*(b^7*c^3 - 3*a*b^6*c^2*d + 3*a^2*b^5*c*d^2 - a^3*b^4*d^3)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^7) + 1/28*(4*b^6*d^3*x^7 + 21*b^6*c*d^2*x^4 - 7*a*b^5*d^3*x^4 + 84*b^6*c^2*d*x - 84*a*b^5*c*d^2*x + 28*a^2*b^4*d^3*x)/b^7","A",0
16,1,211,0,0.323531," ","integrate((d*x^3+c)^2/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}} b} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}} b} - \frac{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b^{4}} + \frac{b^{3} d^{2} x^{4} + 8 \, b^{3} c d x - 4 \, a b^{2} d^{2} x}{4 \, b^{4}}"," ",0,"-1/3*sqrt(3)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*b) - 1/6*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*b) - 1/3*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^4) + 1/4*(b^3*d^2*x^4 + 8*b^3*c*d*x - 4*a*b^2*d^2*x)/b^4","A",0
17,1,133,0,0.191493," ","integrate((d*x^3+c)/(b*x^3+a),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-a b^{2}\right)^{\frac{2}{3}}} - \frac{{\left(b c - a d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, \left(-a b^{2}\right)^{\frac{2}{3}}} + \frac{d x}{b} - \frac{{\left(b c - a d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, a b}"," ",0,"-1/3*sqrt(3)*(b*c - a*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(-a*b^2)^(2/3) - 1/6*(b*c - a*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(-a*b^2)^(2/3) + d*x/b - 1/3*(b*c - a*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b)","A",0
18,1,278,0,0.265762," ","integrate(1/(b*x^3+a)/(d*x^3+c),x, algorithm=""giac"")","-\frac{b \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, {\left(a b c - a^{2} d\right)}} + \frac{d \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{3 \, {\left(b c^{2} - a c d\right)}} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{\sqrt{3} a b c - \sqrt{3} a^{2} d} - \frac{\left(-c d^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{\sqrt{3} b c^{2} - \sqrt{3} a c d} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, {\left(a b c - a^{2} d\right)}} - \frac{\left(-c d^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, {\left(b c^{2} - a c d\right)}}"," ",0,"-1/3*b*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b*c - a^2*d) + 1/3*d*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(b*c^2 - a*c*d) + (-a*b^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(sqrt(3)*a*b*c - sqrt(3)*a^2*d) - (-c*d^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/(sqrt(3)*b*c^2 - sqrt(3)*a*c*d) + 1/6*(-a*b^2)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b*c - a^2*d) - 1/6*(-c*d^2)^(1/3)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/(b*c^2 - a*c*d)","A",0
19,1,443,0,0.203215," ","integrate(1/(b*x^3+a)/(d*x^3+c)^2,x, algorithm=""giac"")","-\frac{b^{2} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{3 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} b \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{\sqrt{3} a b^{2} c^{2} - 2 \, \sqrt{3} a^{2} b c d + \sqrt{3} a^{3} d^{2}} + \frac{\left(-a b^{2}\right)^{\frac{1}{3}} b \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}} + \frac{{\left(5 \, b c d - 2 \, a d^{2}\right)} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{9 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)}} - \frac{{\left(5 \, \left(-c d^{2}\right)^{\frac{1}{3}} b c - 2 \, \left(-c d^{2}\right)^{\frac{1}{3}} a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{3 \, {\left(\sqrt{3} b^{2} c^{4} - 2 \, \sqrt{3} a b c^{3} d + \sqrt{3} a^{2} c^{2} d^{2}\right)}} - \frac{{\left(5 \, \left(-c d^{2}\right)^{\frac{1}{3}} b c - 2 \, \left(-c d^{2}\right)^{\frac{1}{3}} a d\right)} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{18 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)}} - \frac{d x}{3 \, {\left(d x^{3} + c\right)} {\left(b c^{2} - a c d\right)}}"," ",0,"-1/3*b^2*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2) + (-a*b^2)^(1/3)*b*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(sqrt(3)*a*b^2*c^2 - 2*sqrt(3)*a^2*b*c*d + sqrt(3)*a^3*d^2) + 1/6*(-a*b^2)^(1/3)*b*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2) + 1/9*(5*b*c*d - 2*a*d^2)*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2) - 1/3*(5*(-c*d^2)^(1/3)*b*c - 2*(-c*d^2)^(1/3)*a*d)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/(sqrt(3)*b^2*c^4 - 2*sqrt(3)*a*b*c^3*d + sqrt(3)*a^2*c^2*d^2) - 1/18*(5*(-c*d^2)^(1/3)*b*c - 2*(-c*d^2)^(1/3)*a*d)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2) - 1/3*d*x/((d*x^3 + c)*(b*c^2 - a*c*d))","A",0
20,1,529,0,0.189581," ","integrate((d*x^3+c)^5/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 40 \, a^{2} b^{3} c^{3} d^{2} + 70 \, a^{3} b^{2} c^{2} d^{3} - 50 \, a^{4} b c d^{4} + 13 \, a^{5} d^{5}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{4}} - \frac{{\left(2 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 40 \, a^{2} b^{3} c^{3} d^{2} + 70 \, a^{3} b^{2} c^{2} d^{3} - 50 \, a^{4} b c d^{4} + 13 \, a^{5} d^{5}\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{4}} - \frac{{\left(2 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 40 \, a^{2} b^{3} c^{3} d^{2} + 70 \, a^{3} b^{2} c^{2} d^{3} - 50 \, a^{4} b c d^{4} + 13 \, a^{5} d^{5}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2} b^{5}} + \frac{b^{5} c^{5} x - 5 \, a b^{4} c^{4} d x + 10 \, a^{2} b^{3} c^{3} d^{2} x - 10 \, a^{3} b^{2} c^{2} d^{3} x + 5 \, a^{4} b c d^{4} x - a^{5} d^{5} x}{3 \, {\left(b x^{3} + a\right)} a b^{5}} + \frac{14 \, b^{18} d^{5} x^{10} + 100 \, b^{18} c d^{4} x^{7} - 40 \, a b^{17} d^{5} x^{7} + 350 \, b^{18} c^{2} d^{3} x^{4} - 350 \, a b^{17} c d^{4} x^{4} + 105 \, a^{2} b^{16} d^{5} x^{4} + 1400 \, b^{18} c^{3} d^{2} x - 2800 \, a b^{17} c^{2} d^{3} x + 2100 \, a^{2} b^{16} c d^{4} x - 560 \, a^{3} b^{15} d^{5} x}{140 \, b^{20}}"," ",0,"-1/9*sqrt(3)*(2*b^5*c^5 + 5*a*b^4*c^4*d - 40*a^2*b^3*c^3*d^2 + 70*a^3*b^2*c^2*d^3 - 50*a^4*b*c*d^4 + 13*a^5*d^5)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b^4) - 1/18*(2*b^5*c^5 + 5*a*b^4*c^4*d - 40*a^2*b^3*c^3*d^2 + 70*a^3*b^2*c^2*d^3 - 50*a^4*b*c*d^4 + 13*a^5*d^5)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b^4) - 1/9*(2*b^5*c^5 + 5*a*b^4*c^4*d - 40*a^2*b^3*c^3*d^2 + 70*a^3*b^2*c^2*d^3 - 50*a^4*b*c*d^4 + 13*a^5*d^5)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^5) + 1/3*(b^5*c^5*x - 5*a*b^4*c^4*d*x + 10*a^2*b^3*c^3*d^2*x - 10*a^3*b^2*c^2*d^3*x + 5*a^4*b*c*d^4*x - a^5*d^5*x)/((b*x^3 + a)*a*b^5) + 1/140*(14*b^18*d^5*x^10 + 100*b^18*c*d^4*x^7 - 40*a*b^17*d^5*x^7 + 350*b^18*c^2*d^3*x^4 - 350*a*b^17*c*d^4*x^4 + 105*a^2*b^16*d^5*x^4 + 1400*b^18*c^3*d^2*x - 2800*a*b^17*c^2*d^3*x + 2100*a^2*b^16*c*d^4*x - 560*a^3*b^15*d^5*x)/b^20","A",0
21,1,412,0,0.190191," ","integrate((d*x^3+c)^4/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{2 \, \sqrt{3} {\left(b^{4} c^{4} + 2 \, a b^{3} c^{3} d - 12 \, a^{2} b^{2} c^{2} d^{2} + 14 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{3}} - \frac{{\left(b^{4} c^{4} + 2 \, a b^{3} c^{3} d - 12 \, a^{2} b^{2} c^{2} d^{2} + 14 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{3}} - \frac{2 \, {\left(b^{4} c^{4} + 2 \, a b^{3} c^{3} d - 12 \, a^{2} b^{2} c^{2} d^{2} + 14 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2} b^{4}} + \frac{b^{4} c^{4} x - 4 \, a b^{3} c^{3} d x + 6 \, a^{2} b^{2} c^{2} d^{2} x - 4 \, a^{3} b c d^{3} x + a^{4} d^{4} x}{3 \, {\left(b x^{3} + a\right)} a b^{4}} + \frac{2 \, b^{12} d^{4} x^{7} + 14 \, b^{12} c d^{3} x^{4} - 7 \, a b^{11} d^{4} x^{4} + 84 \, b^{12} c^{2} d^{2} x - 112 \, a b^{11} c d^{3} x + 42 \, a^{2} b^{10} d^{4} x}{14 \, b^{14}}"," ",0,"-2/9*sqrt(3)*(b^4*c^4 + 2*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 14*a^3*b*c*d^3 - 5*a^4*d^4)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b^3) - 1/9*(b^4*c^4 + 2*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 14*a^3*b*c*d^3 - 5*a^4*d^4)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b^3) - 2/9*(b^4*c^4 + 2*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 14*a^3*b*c*d^3 - 5*a^4*d^4)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^4) + 1/3*(b^4*c^4*x - 4*a*b^3*c^3*d*x + 6*a^2*b^2*c^2*d^2*x - 4*a^3*b*c*d^3*x + a^4*d^4*x)/((b*x^3 + a)*a*b^4) + 1/14*(2*b^12*d^4*x^7 + 14*b^12*c*d^3*x^4 - 7*a*b^11*d^4*x^4 + 84*b^12*c^2*d^2*x - 112*a*b^11*c*d^3*x + 42*a^2*b^10*d^4*x)/b^14","A",0
22,1,319,0,0.200461," ","integrate((d*x^3+c)^3/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 12 \, a^{2} b c d^{2} + 7 \, a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2}} - \frac{{\left(2 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 12 \, a^{2} b c d^{2} + 7 \, a^{3} d^{3}\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b^{2}} - \frac{{\left(2 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 12 \, a^{2} b c d^{2} + 7 \, a^{3} d^{3}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2} b^{3}} + \frac{b^{3} c^{3} x - 3 \, a b^{2} c^{2} d x + 3 \, a^{2} b c d^{2} x - a^{3} d^{3} x}{3 \, {\left(b x^{3} + a\right)} a b^{3}} + \frac{b^{6} d^{3} x^{4} + 12 \, b^{6} c d^{2} x - 8 \, a b^{5} d^{3} x}{4 \, b^{8}}"," ",0,"-1/9*sqrt(3)*(2*b^3*c^3 + 3*a*b^2*c^2*d - 12*a^2*b*c*d^2 + 7*a^3*d^3)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b^2) - 1/18*(2*b^3*c^3 + 3*a*b^2*c^2*d - 12*a^2*b*c*d^2 + 7*a^3*d^3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b^2) - 1/9*(2*b^3*c^3 + 3*a*b^2*c^2*d - 12*a^2*b*c*d^2 + 7*a^3*d^3)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^3) + 1/3*(b^3*c^3*x - 3*a*b^2*c^2*d*x + 3*a^2*b*c*d^2*x - a^3*d^3*x)/((b*x^3 + a)*a*b^3) + 1/4*(b^6*d^3*x^4 + 12*b^6*c*d^2*x - 8*a*b^5*d^3*x)/b^8","A",0
23,1,227,0,0.213035," ","integrate((d*x^3+c)^2/(b*x^3+a)^2,x, algorithm=""giac"")","\frac{d^{2} x}{b^{2}} - \frac{2 \, \sqrt{3} {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} - \frac{{\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a b} - \frac{2 \, {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2} b^{2}} + \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{3 \, {\left(b x^{3} + a\right)} a b^{2}}"," ",0,"d^2*x/b^2 - 2/9*sqrt(3)*(b^2*c^2 + a*b*c*d - 2*a^2*d^2)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a*b) - 1/9*(b^2*c^2 + a*b*c*d - 2*a^2*d^2)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a*b) - 2/9*(b^2*c^2 + a*b*c*d - 2*a^2*d^2)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^2) + 1/3*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((b*x^3 + a)*a*b^2)","A",0
24,1,160,0,0.170904," ","integrate((d*x^3+c)/(b*x^3+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(2 \, b c + a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(2 \, b c + a d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, \left(-a b^{2}\right)^{\frac{2}{3}} a} - \frac{{\left(2 \, b c + a d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, a^{2} b} + \frac{b c x - a d x}{3 \, {\left(b x^{3} + a\right)} a b}"," ",0,"-1/9*sqrt(3)*(2*b*c + a*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/((-a*b^2)^(2/3)*a) - 1/18*(2*b*c + a*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/((-a*b^2)^(2/3)*a) - 1/9*(2*b*c + a*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b) + 1/3*(b*c*x - a*d*x)/((b*x^3 + a)*a*b)","A",0
25,1,443,0,0.200644," ","integrate(1/(b*x^3+a)^2/(d*x^3+c),x, algorithm=""giac"")","-\frac{d^{2} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{3 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}} + \frac{\left(-c d^{2}\right)^{\frac{1}{3}} d \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{\sqrt{3} b^{2} c^{3} - 2 \, \sqrt{3} a b c^{2} d + \sqrt{3} a^{2} c d^{2}} + \frac{\left(-c d^{2}\right)^{\frac{1}{3}} d \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}} - \frac{{\left(2 \, b^{2} c - 5 \, a b d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)}} + \frac{{\left(2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, {\left(\sqrt{3} a^{2} b^{2} c^{2} - 2 \, \sqrt{3} a^{3} b c d + \sqrt{3} a^{4} d^{2}\right)}} + \frac{{\left(2 \, \left(-a b^{2}\right)^{\frac{1}{3}} b c - 5 \, \left(-a b^{2}\right)^{\frac{1}{3}} a d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)}} + \frac{b x}{3 \, {\left(b x^{3} + a\right)} {\left(a b c - a^{2} d\right)}}"," ",0,"-1/3*d^2*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2) + (-c*d^2)^(1/3)*d*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/(sqrt(3)*b^2*c^3 - 2*sqrt(3)*a*b*c^2*d + sqrt(3)*a^2*c*d^2) + 1/6*(-c*d^2)^(1/3)*d*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2) - 1/9*(2*b^2*c - 5*a*b*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2) + 1/3*(2*(-a*b^2)^(1/3)*b*c - 5*(-a*b^2)^(1/3)*a*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(sqrt(3)*a^2*b^2*c^2 - 2*sqrt(3)*a^3*b*c*d + sqrt(3)*a^4*d^2) + 1/18*(2*(-a*b^2)^(1/3)*b*c - 5*(-a*b^2)^(1/3)*a*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2) + 1/3*b*x/((b*x^3 + a)*(a*b*c - a^2*d))","A",0
26,1,664,0,0.222381," ","integrate(1/(b*x^3+a)^2/(d*x^3+c)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(b^{3} c - 4 \, a b^{2} d\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \right|}\right)}{9 \, {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)}} - \frac{2 \, {\left(4 \, b c d^{2} - a d^{3}\right)} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \right|}\right)}{9 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)}} + \frac{2 \, {\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{2} c - 4 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{3 \, {\left(\sqrt{3} a^{2} b^{3} c^{3} - 3 \, \sqrt{3} a^{3} b^{2} c^{2} d + 3 \, \sqrt{3} a^{4} b c d^{2} - \sqrt{3} a^{5} d^{3}\right)}} + \frac{2 \, {\left(4 \, \left(-c d^{2}\right)^{\frac{1}{3}} b c d - \left(-c d^{2}\right)^{\frac{1}{3}} a d^{2}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}}}\right)}{3 \, {\left(\sqrt{3} b^{3} c^{5} - 3 \, \sqrt{3} a b^{2} c^{4} d + 3 \, \sqrt{3} a^{2} b c^{3} d^{2} - \sqrt{3} a^{3} c^{2} d^{3}\right)}} + \frac{{\left(\left(-a b^{2}\right)^{\frac{1}{3}} b^{2} c - 4 \, \left(-a b^{2}\right)^{\frac{1}{3}} a b d\right)} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \, {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)}} + \frac{{\left(4 \, \left(-c d^{2}\right)^{\frac{1}{3}} b c d - \left(-c d^{2}\right)^{\frac{1}{3}} a d^{2}\right)} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right)}{9 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)}} + \frac{b^{2} c d x^{4} + a b d^{2} x^{4} + b^{2} c^{2} x + a^{2} d^{2} x}{3 \, {\left(b d x^{6} + b c x^{3} + a d x^{3} + a c\right)} {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)}}"," ",0,"-2/9*(b^3*c - 4*a*b^2*d)*(-a/b)^(1/3)*log(abs(x - (-a/b)^(1/3)))/(a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3) - 2/9*(4*b*c*d^2 - a*d^3)*(-c/d)^(1/3)*log(abs(x - (-c/d)^(1/3)))/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3) + 2/3*((-a*b^2)^(1/3)*b^2*c - 4*(-a*b^2)^(1/3)*a*b*d)*arctan(1/3*sqrt(3)*(2*x + (-a/b)^(1/3))/(-a/b)^(1/3))/(sqrt(3)*a^2*b^3*c^3 - 3*sqrt(3)*a^3*b^2*c^2*d + 3*sqrt(3)*a^4*b*c*d^2 - sqrt(3)*a^5*d^3) + 2/3*(4*(-c*d^2)^(1/3)*b*c*d - (-c*d^2)^(1/3)*a*d^2)*arctan(1/3*sqrt(3)*(2*x + (-c/d)^(1/3))/(-c/d)^(1/3))/(sqrt(3)*b^3*c^5 - 3*sqrt(3)*a*b^2*c^4*d + 3*sqrt(3)*a^2*b*c^3*d^2 - sqrt(3)*a^3*c^2*d^3) + 1/9*((-a*b^2)^(1/3)*b^2*c - 4*(-a*b^2)^(1/3)*a*b*d)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3))/(a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3) + 1/9*(4*(-c*d^2)^(1/3)*b*c*d - (-c*d^2)^(1/3)*a*d^2)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3))/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3) + 1/3*(b^2*c*d*x^4 + a*b*d^2*x^4 + b^2*c^2*x + a^2*d^2*x)/((b*d*x^6 + b*c*x^3 + a*d*x^3 + a*c)*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2))","A",0
27,0,0,0,0.000000," ","integrate((-b*x^3+a)*(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int -{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b x^{3} - a\right)}\,{d x}"," ",0,"integrate(-(b*x^3 + a)^(2/3)*(b*x^3 - a), x)","F",0
28,0,0,0,0.000000," ","integrate((-b*x^3+a)/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int -\frac{b x^{3} - a}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(b*x^3 - a)/(b*x^3 + a)^(1/3), x)","F",0
29,0,0,0,0.000000," ","integrate((-b*x^3+a)/(b*x^3+a)^(4/3),x, algorithm=""giac"")","\int -\frac{b x^{3} - a}{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(-(b*x^3 - a)/(b*x^3 + a)^(4/3), x)","F",0
30,0,0,0,0.000000," ","integrate((-b*x^3+a)/(b*x^3+a)^(7/3),x, algorithm=""giac"")","\int -\frac{b x^{3} - a}{{\left(b x^{3} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(-(b*x^3 - a)/(b*x^3 + a)^(7/3), x)","F",0
31,0,0,0,0.000000," ","integrate((-b*x^3+a)/(b*x^3+a)^(10/3),x, algorithm=""giac"")","\int -\frac{b x^{3} - a}{{\left(b x^{3} + a\right)}^{\frac{10}{3}}}\,{d x}"," ",0,"integrate(-(b*x^3 - a)/(b*x^3 + a)^(10/3), x)","F",0
32,0,0,0,0.000000," ","integrate((-b*x^3+a)/(b*x^3+a)^(13/3),x, algorithm=""giac"")","\int -\frac{b x^{3} - a}{{\left(b x^{3} + a\right)}^{\frac{13}{3}}}\,{d x}"," ",0,"integrate(-(b*x^3 - a)/(b*x^3 + a)^(13/3), x)","F",0
33,0,0,0,0.000000," ","integrate((-b*x^3+a)/(b*x^3+a)^(16/3),x, algorithm=""giac"")","\int -\frac{b x^{3} - a}{{\left(b x^{3} + a\right)}^{\frac{16}{3}}}\,{d x}"," ",0,"integrate(-(b*x^3 - a)/(b*x^3 + a)^(16/3), x)","F",0
34,0,0,0,0.000000," ","integrate((b*x^3+a)^(7/3)/(-b*x^3+a),x, algorithm=""giac"")","\int -\frac{{\left(b x^{3} + a\right)}^{\frac{7}{3}}}{b x^{3} - a}\,{d x}"," ",0,"integrate(-(b*x^3 + a)^(7/3)/(b*x^3 - a), x)","F",0
35,0,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/(-b*x^3+a),x, algorithm=""giac"")","\int -\frac{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}{b x^{3} - a}\,{d x}"," ",0,"integrate(-(b*x^3 + a)^(4/3)/(b*x^3 - a), x)","F",0
36,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(-b*x^3+a),x, algorithm=""giac"")","\int -\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b x^{3} - a}\,{d x}"," ",0,"integrate(-(b*x^3 + a)^(1/3)/(b*x^3 - a), x)","F",0
37,0,0,0,0.000000," ","integrate(1/(-b*x^3+a)/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b x^{3} - a\right)}}\,{d x}"," ",0,"integrate(-1/((b*x^3 + a)^(2/3)*(b*x^3 - a)), x)","F",0
38,0,0,0,0.000000," ","integrate(1/(-b*x^3+a)/(b*x^3+a)^(5/3),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{3} + a\right)}^{\frac{5}{3}} {\left(b x^{3} - a\right)}}\,{d x}"," ",0,"integrate(-1/((b*x^3 + a)^(5/3)*(b*x^3 - a)), x)","F",0
39,0,0,0,0.000000," ","integrate(1/(-b*x^3+a)/(b*x^3+a)^(8/3),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{3} + a\right)}^{\frac{8}{3}} {\left(b x^{3} - a\right)}}\,{d x}"," ",0,"integrate(-1/((b*x^3 + a)^(8/3)*(b*x^3 - a)), x)","F",0
40,0,0,0,0.000000," ","integrate((-b*x^3+a)^2*(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b x^{3} - a\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)*(b*x^3 - a)^2, x)","F",0
41,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(1/3), x)","F",0
42,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(4/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(4/3), x)","F",0
43,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(7/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(7/3), x)","F",0
44,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(10/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{10}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(10/3), x)","F",0
45,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(13/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{13}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(13/3), x)","F",0
46,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(16/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{16}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(16/3), x)","F",0
47,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(19/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{19}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(19/3), x)","F",0
48,0,0,0,0.000000," ","integrate((-b*x^3+a)^2*(b*x^3+a)^(4/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{4}{3}} {\left(b x^{3} - a\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(4/3)*(b*x^3 - a)^2, x)","F",0
49,0,0,0,0.000000," ","integrate((-b*x^3+a)^2*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b x^{3} - a\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*(b*x^3 - a)^2, x)","F",0
50,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(2/3), x)","F",0
51,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(5/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(5/3), x)","F",0
52,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(8/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{8}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(8/3), x)","F",0
53,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(11/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{11}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(11/3), x)","F",0
54,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(14/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{14}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(14/3), x)","F",0
55,0,0,0,0.000000," ","integrate((-b*x^3+a)^2/(b*x^3+a)^(17/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} - a\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{17}{3}}}\,{d x}"," ",0,"integrate((b*x^3 - a)^2/(b*x^3 + a)^(17/3), x)","F",0
56,0,0,0,0.000000," ","integrate((b*x^3+a)^(5/3)*(d*x^3+c),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{5}{3}} {\left(d x^{3} + c\right)}\,{d x}"," ",0,"integrate((b*x^3 + a)^(5/3)*(d*x^3 + c), x)","F",0
57,0,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)*(d*x^3+c),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(d x^{3} + c\right)}\,{d x}"," ",0,"integrate((b*x^3 + a)^(2/3)*(d*x^3 + c), x)","F",0
58,0,0,0,0.000000," ","integrate((d*x^3+c)/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{d x^{3} + c}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)/(b*x^3 + a)^(1/3), x)","F",0
59,0,0,0,0.000000," ","integrate((d*x^3+c)/(b*x^3+a)^(4/3),x, algorithm=""giac"")","\int \frac{d x^{3} + c}{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)/(b*x^3 + a)^(4/3), x)","F",0
60,0,0,0,0.000000," ","integrate((d*x^3+c)/(b*x^3+a)^(7/3),x, algorithm=""giac"")","\int \frac{d x^{3} + c}{{\left(b x^{3} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)/(b*x^3 + a)^(7/3), x)","F",0
61,0,0,0,0.000000," ","integrate((d*x^3+c)/(b*x^3+a)^(10/3),x, algorithm=""giac"")","\int \frac{d x^{3} + c}{{\left(b x^{3} + a\right)}^{\frac{10}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)/(b*x^3 + a)^(10/3), x)","F",0
62,0,0,0,0.000000," ","integrate((d*x^3+c)/(b*x^3+a)^(13/3),x, algorithm=""giac"")","\int \frac{d x^{3} + c}{{\left(b x^{3} + a\right)}^{\frac{13}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)/(b*x^3 + a)^(13/3), x)","F",0
63,0,0,0,0.000000," ","integrate((d*x^3+c)/(b*x^3+a)^(16/3),x, algorithm=""giac"")","\int \frac{d x^{3} + c}{{\left(b x^{3} + a\right)}^{\frac{16}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)/(b*x^3 + a)^(16/3), x)","F",0
64,0,0,0,0.000000," ","integrate((b*x^3+a)^(7/3)*(d*x^3+c),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{7}{3}} {\left(d x^{3} + c\right)}\,{d x}"," ",0,"integrate((b*x^3 + a)^(7/3)*(d*x^3 + c), x)","F",0
65,0,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)*(d*x^3+c),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{4}{3}} {\left(d x^{3} + c\right)}\,{d x}"," ",0,"integrate((b*x^3 + a)^(4/3)*(d*x^3 + c), x)","F",0
66,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)*(d*x^3+c),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x^{3} + c\right)}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*(d*x^3 + c), x)","F",0
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69,0,0,0,0.000000," ","integrate((d*x^3+c)/(b*x^3+a)^(8/3),x, algorithm=""giac"")","\int \frac{d x^{3} + c}{{\left(b x^{3} + a\right)}^{\frac{8}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)/(b*x^3 + a)^(8/3), x)","F",0
70,0,0,0,0.000000," ","integrate((b*x^3+a)^(5/3)*(d*x^3+c)^2,x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{5}{3}} {\left(d x^{3} + c\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(5/3)*(d*x^3 + c)^2, x)","F",0
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72,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(1/3), x)","F",0
73,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(4/3),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(4/3), x)","F",0
74,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(7/3),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(7/3), x)","F",0
75,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(10/3),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{10}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(10/3), x)","F",0
76,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(13/3),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{13}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(13/3), x)","F",0
77,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(16/3),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{16}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(16/3), x)","F",0
78,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(19/3),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{19}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(19/3), x)","F",0
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80,0,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)*(d*x^3+c)^2,x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{4}{3}} {\left(d x^{3} + c\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(4/3)*(d*x^3 + c)^2, x)","F",0
81,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)*(d*x^3+c)^2,x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x^{3} + c\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*(d*x^3 + c)^2, x)","F",0
82,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(2/3), x)","F",0
83,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(5/3),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(5/3), x)","F",0
84,0,0,0,0.000000," ","integrate((d*x^3+c)^2/(b*x^3+a)^(8/3),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{8}{3}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^2/(b*x^3 + a)^(8/3), x)","F",0
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121,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(8/3)/(d*x^3+c)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{8}{3}} {\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(8/3)*(d*x^3 + c)^3), x)","F",0
122,0,0,0,0.000000," ","integrate((b*x^3+a)^(7/4)/(d*x^3+c)^(37/12),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{7}{4}}}{{\left(d x^{3} + c\right)}^{\frac{37}{12}}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(7/4)/(d*x^3 + c)^(37/12), x)","F",0
123,0,0,0,0.000000," ","integrate((b*x^3+a)^(5/4)/(d*x^3+c)^(31/12),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{5}{4}}}{{\left(d x^{3} + c\right)}^{\frac{31}{12}}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(5/4)/(d*x^3 + c)^(31/12), x)","F",0
124,0,0,0,0.000000," ","integrate((b*x^3+a)^(3/4)/(d*x^3+c)^(25/12),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{3}{4}}}{{\left(d x^{3} + c\right)}^{\frac{25}{12}}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(3/4)/(d*x^3 + c)^(25/12), x)","F",0
125,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/4)/(d*x^3+c)^(19/12),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{4}}}{{\left(d x^{3} + c\right)}^{\frac{19}{12}}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/4)/(d*x^3 + c)^(19/12), x)","F",0
126,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(1/4)/(d*x^3+c)^(13/12),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{4}} {\left(d x^{3} + c\right)}^{\frac{13}{12}}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/4)*(d*x^3 + c)^(13/12)), x)","F",0
127,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(3/4)/(d*x^3+c)^(7/12),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{3}{4}} {\left(d x^{3} + c\right)}^{\frac{7}{12}}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(3/4)*(d*x^3 + c)^(7/12)), x)","F",0
128,0,0,0,0.000000," ","integrate(1/(b*x^3+a)^(5/4)/(d*x^3+c)^(1/12),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{5}{4}} {\left(d x^{3} + c\right)}^{\frac{1}{12}}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(5/4)*(d*x^3 + c)^(1/12)), x)","F",0
129,0,0,0,0.000000," ","integrate((d*x^3+c)^(5/12)/(b*x^3+a)^(7/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{\frac{5}{12}}}{{\left(b x^{3} + a\right)}^{\frac{7}{4}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^(5/12)/(b*x^3 + a)^(7/4), x)","F",0
130,0,0,0,0.000000," ","integrate((d*x^3+c)^(11/12)/(b*x^3+a)^(9/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{\frac{11}{12}}}{{\left(b x^{3} + a\right)}^{\frac{9}{4}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^(11/12)/(b*x^3 + a)^(9/4), x)","F",0
131,0,0,0,0.000000," ","integrate((d*x^3+c)^(17/12)/(b*x^3+a)^(11/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{\frac{17}{12}}}{{\left(b x^{3} + a\right)}^{\frac{11}{4}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^(17/12)/(b*x^3 + a)^(11/4), x)","F",0
132,0,0,0,0.000000," ","integrate((d*x^3+c)^(23/12)/(b*x^3+a)^(13/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{\frac{23}{12}}}{{\left(b x^{3} + a\right)}^{\frac{13}{4}}}\,{d x}"," ",0,"integrate((d*x^3 + c)^(23/12)/(b*x^3 + a)^(13/4), x)","F",0
133,0,0,0,0.000000," ","integrate((b*x^3+a)^m*(d*x^3+c)^p,x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{m} {\left(d x^{3} + c\right)}^{p}\,{d x}"," ",0,"integrate((b*x^3 + a)^m*(d*x^3 + c)^p, x)","F",0
134,0,0,0,0.000000," ","integrate((b*x^3+a)^2*(d*x^3+c)^q,x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{2} {\left(d x^{3} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^3 + a)^2*(d*x^3 + c)^q, x)","F",0
135,0,0,0,0.000000," ","integrate((b*x^3+a)*(d*x^3+c)^q,x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)} {\left(d x^{3} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^3 + a)*(d*x^3 + c)^q, x)","F",0
136,0,0,0,0.000000," ","integrate((d*x^3+c)^q/(b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{q}}{b x^{3} + a}\,{d x}"," ",0,"integrate((d*x^3 + c)^q/(b*x^3 + a), x)","F",0
137,0,0,0,0.000000," ","integrate((d*x^3+c)^q/(b*x^3+a)^2,x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{q}}{{\left(b x^{3} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^3 + c)^q/(b*x^3 + a)^2, x)","F",0
138,0,0,0,0.000000," ","integrate((b*x^3+a)^m*(d*x^3+c)^3,x, algorithm=""giac"")","\int {\left(d x^{3} + c\right)}^{3} {\left(b x^{3} + a\right)}^{m}\,{d x}"," ",0,"integrate((d*x^3 + c)^3*(b*x^3 + a)^m, x)","F",0
139,0,0,0,0.000000," ","integrate((b*x^3+a)^m*(d*x^3+c)^2,x, algorithm=""giac"")","\int {\left(d x^{3} + c\right)}^{2} {\left(b x^{3} + a\right)}^{m}\,{d x}"," ",0,"integrate((d*x^3 + c)^2*(b*x^3 + a)^m, x)","F",0
140,0,0,0,0.000000," ","integrate((b*x^3+a)^m*(d*x^3+c),x, algorithm=""giac"")","\int {\left(d x^{3} + c\right)} {\left(b x^{3} + a\right)}^{m}\,{d x}"," ",0,"integrate((d*x^3 + c)*(b*x^3 + a)^m, x)","F",0
141,0,0,0,0.000000," ","integrate((b*x^3+a)^m,x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{m}\,{d x}"," ",0,"integrate((b*x^3 + a)^m, x)","F",0
142,0,0,0,0.000000," ","integrate((b*x^3+a)^m/(d*x^3+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{m}}{d x^{3} + c}\,{d x}"," ",0,"integrate((b*x^3 + a)^m/(d*x^3 + c), x)","F",0
143,0,0,0,0.000000," ","integrate((b*x^3+a)^m/(d*x^3+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{m}}{{\left(d x^{3} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^m/(d*x^3 + c)^2, x)","F",0
144,0,0,0,0.000000," ","integrate((b*x^3+a)^m/(d*x^3+c)^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{m}}{{\left(d x^{3} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^3 + a)^m/(d*x^3 + c)^3, x)","F",0
145,0,0,0,0.000000," ","integrate((b*x^3+a)^(-1-b*c/(-3*a*d+3*b*c))*(d*x^3+c)^(-1+a*d/(-3*a*d+3*b*c)),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{-\frac{b c}{3 \, {\left(b c - a d\right)}} - 1} {\left(d x^{3} + c\right)}^{\frac{a d}{3 \, {\left(b c - a d\right)}} - 1}\,{d x}"," ",0,"integrate((b*x^3 + a)^(-1/3*b*c/(b*c - a*d) - 1)*(d*x^3 + c)^(1/3*a*d/(b*c - a*d) - 1), x)","F",0
146,1,98,0,0.155816," ","integrate((b*x^4+a)*(d*x^4+c)^4,x, algorithm=""giac"")","\frac{1}{21} \, b d^{4} x^{21} + \frac{4}{17} \, b c d^{3} x^{17} + \frac{1}{17} \, a d^{4} x^{17} + \frac{6}{13} \, b c^{2} d^{2} x^{13} + \frac{4}{13} \, a c d^{3} x^{13} + \frac{4}{9} \, b c^{3} d x^{9} + \frac{2}{3} \, a c^{2} d^{2} x^{9} + \frac{1}{5} \, b c^{4} x^{5} + \frac{4}{5} \, a c^{3} d x^{5} + a c^{4} x"," ",0,"1/21*b*d^4*x^21 + 4/17*b*c*d^3*x^17 + 1/17*a*d^4*x^17 + 6/13*b*c^2*d^2*x^13 + 4/13*a*c*d^3*x^13 + 4/9*b*c^3*d*x^9 + 2/3*a*c^2*d^2*x^9 + 1/5*b*c^4*x^5 + 4/5*a*c^3*d*x^5 + a*c^4*x","A",0
147,1,74,0,0.150167," ","integrate((b*x^4+a)*(d*x^4+c)^3,x, algorithm=""giac"")","\frac{1}{17} \, b d^{3} x^{17} + \frac{3}{13} \, b c d^{2} x^{13} + \frac{1}{13} \, a d^{3} x^{13} + \frac{1}{3} \, b c^{2} d x^{9} + \frac{1}{3} \, a c d^{2} x^{9} + \frac{1}{5} \, b c^{3} x^{5} + \frac{3}{5} \, a c^{2} d x^{5} + a c^{3} x"," ",0,"1/17*b*d^3*x^17 + 3/13*b*c*d^2*x^13 + 1/13*a*d^3*x^13 + 1/3*b*c^2*d*x^9 + 1/3*a*c*d^2*x^9 + 1/5*b*c^3*x^5 + 3/5*a*c^2*d*x^5 + a*c^3*x","A",0
148,1,50,0,0.161085," ","integrate((b*x^4+a)*(d*x^4+c)^2,x, algorithm=""giac"")","\frac{1}{13} \, b d^{2} x^{13} + \frac{2}{9} \, b c d x^{9} + \frac{1}{9} \, a d^{2} x^{9} + \frac{1}{5} \, b c^{2} x^{5} + \frac{2}{5} \, a c d x^{5} + a c^{2} x"," ",0,"1/13*b*d^2*x^13 + 2/9*b*c*d*x^9 + 1/9*a*d^2*x^9 + 1/5*b*c^2*x^5 + 2/5*a*c*d*x^5 + a*c^2*x","A",0
149,1,26,0,0.149500," ","integrate((b*x^4+a)*(d*x^4+c),x, algorithm=""giac"")","\frac{1}{9} \, b d x^{9} + \frac{1}{5} \, b c x^{5} + \frac{1}{5} \, a d x^{5} + a c x"," ",0,"1/9*b*d*x^9 + 1/5*b*c*x^5 + 1/5*a*d*x^5 + a*c*x","A",0
150,1,245,0,0.164881," ","integrate((b*x^4+a)/(d*x^4+c),x, algorithm=""giac"")","\frac{b x}{d} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c - \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, c d^{2}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c - \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, c d^{2}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c - \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{8 \, c d^{2}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c - \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{8 \, c d^{2}}"," ",0,"b*x/d - 1/4*sqrt(2)*((c*d^3)^(1/4)*b*c - (c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c*d^2) - 1/4*sqrt(2)*((c*d^3)^(1/4)*b*c - (c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c*d^2) - 1/8*sqrt(2)*((c*d^3)^(1/4)*b*c - (c*d^3)^(1/4)*a*d)*log(x^2 + sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c*d^2) + 1/8*sqrt(2)*((c*d^3)^(1/4)*b*c - (c*d^3)^(1/4)*a*d)*log(x^2 - sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c*d^2)","A",0
151,1,266,0,0.168769," ","integrate((b*x^4+a)/(d*x^4+c)^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{16 \, c^{2} d^{2}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{16 \, c^{2} d^{2}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{32 \, c^{2} d^{2}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{32 \, c^{2} d^{2}} - \frac{b c x - a d x}{4 \, {\left(d x^{4} + c\right)} c d}"," ",0,"1/16*sqrt(2)*((c*d^3)^(1/4)*b*c + 3*(c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c^2*d^2) + 1/16*sqrt(2)*((c*d^3)^(1/4)*b*c + 3*(c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c^2*d^2) + 1/32*sqrt(2)*((c*d^3)^(1/4)*b*c + 3*(c*d^3)^(1/4)*a*d)*log(x^2 + sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c^2*d^2) - 1/32*sqrt(2)*((c*d^3)^(1/4)*b*c + 3*(c*d^3)^(1/4)*a*d)*log(x^2 - sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c^2*d^2) - 1/4*(b*c*x - a*d*x)/((d*x^4 + c)*c*d)","A",0
152,1,286,0,0.193641," ","integrate((b*x^4+a)/(d*x^4+c)^3,x, algorithm=""giac"")","\frac{3 \, \sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{128 \, c^{3} d^{2}} + \frac{3 \, \sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{128 \, c^{3} d^{2}} + \frac{3 \, \sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{256 \, c^{3} d^{2}} - \frac{3 \, \sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{256 \, c^{3} d^{2}} + \frac{b c d x^{5} + 7 \, a d^{2} x^{5} - 3 \, b c^{2} x + 11 \, a c d x}{32 \, {\left(d x^{4} + c\right)}^{2} c^{2} d}"," ",0,"3/128*sqrt(2)*((c*d^3)^(1/4)*b*c + 7*(c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c^3*d^2) + 3/128*sqrt(2)*((c*d^3)^(1/4)*b*c + 7*(c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c^3*d^2) + 3/256*sqrt(2)*((c*d^3)^(1/4)*b*c + 7*(c*d^3)^(1/4)*a*d)*log(x^2 + sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c^3*d^2) - 3/256*sqrt(2)*((c*d^3)^(1/4)*b*c + 7*(c*d^3)^(1/4)*a*d)*log(x^2 - sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c^3*d^2) + 1/32*(b*c*d*x^5 + 7*a*d^2*x^5 - 3*b*c^2*x + 11*a*c*d*x)/((d*x^4 + c)^2*c^2*d)","A",0
153,1,173,0,0.150120," ","integrate((b*x^4+a)^2*(d*x^4+c)^4,x, algorithm=""giac"")","\frac{1}{25} \, b^{2} d^{4} x^{25} + \frac{4}{21} \, b^{2} c d^{3} x^{21} + \frac{2}{21} \, a b d^{4} x^{21} + \frac{6}{17} \, b^{2} c^{2} d^{2} x^{17} + \frac{8}{17} \, a b c d^{3} x^{17} + \frac{1}{17} \, a^{2} d^{4} x^{17} + \frac{4}{13} \, b^{2} c^{3} d x^{13} + \frac{12}{13} \, a b c^{2} d^{2} x^{13} + \frac{4}{13} \, a^{2} c d^{3} x^{13} + \frac{1}{9} \, b^{2} c^{4} x^{9} + \frac{8}{9} \, a b c^{3} d x^{9} + \frac{2}{3} \, a^{2} c^{2} d^{2} x^{9} + \frac{2}{5} \, a b c^{4} x^{5} + \frac{4}{5} \, a^{2} c^{3} d x^{5} + a^{2} c^{4} x"," ",0,"1/25*b^2*d^4*x^25 + 4/21*b^2*c*d^3*x^21 + 2/21*a*b*d^4*x^21 + 6/17*b^2*c^2*d^2*x^17 + 8/17*a*b*c*d^3*x^17 + 1/17*a^2*d^4*x^17 + 4/13*b^2*c^3*d*x^13 + 12/13*a*b*c^2*d^2*x^13 + 4/13*a^2*c*d^3*x^13 + 1/9*b^2*c^4*x^9 + 8/9*a*b*c^3*d*x^9 + 2/3*a^2*c^2*d^2*x^9 + 2/5*a*b*c^4*x^5 + 4/5*a^2*c^3*d*x^5 + a^2*c^4*x","A",0
154,1,132,0,0.151187," ","integrate((b*x^4+a)^2*(d*x^4+c)^3,x, algorithm=""giac"")","\frac{1}{21} \, b^{2} d^{3} x^{21} + \frac{3}{17} \, b^{2} c d^{2} x^{17} + \frac{2}{17} \, a b d^{3} x^{17} + \frac{3}{13} \, b^{2} c^{2} d x^{13} + \frac{6}{13} \, a b c d^{2} x^{13} + \frac{1}{13} \, a^{2} d^{3} x^{13} + \frac{1}{9} \, b^{2} c^{3} x^{9} + \frac{2}{3} \, a b c^{2} d x^{9} + \frac{1}{3} \, a^{2} c d^{2} x^{9} + \frac{2}{5} \, a b c^{3} x^{5} + \frac{3}{5} \, a^{2} c^{2} d x^{5} + a^{2} c^{3} x"," ",0,"1/21*b^2*d^3*x^21 + 3/17*b^2*c*d^2*x^17 + 2/17*a*b*d^3*x^17 + 3/13*b^2*c^2*d*x^13 + 6/13*a*b*c*d^2*x^13 + 1/13*a^2*d^3*x^13 + 1/9*b^2*c^3*x^9 + 2/3*a*b*c^2*d*x^9 + 1/3*a^2*c*d^2*x^9 + 2/5*a*b*c^3*x^5 + 3/5*a^2*c^2*d*x^5 + a^2*c^3*x","A",0
155,1,91,0,0.166123," ","integrate((b*x^4+a)^2*(d*x^4+c)^2,x, algorithm=""giac"")","\frac{1}{17} \, b^{2} d^{2} x^{17} + \frac{2}{13} \, b^{2} c d x^{13} + \frac{2}{13} \, a b d^{2} x^{13} + \frac{1}{9} \, b^{2} c^{2} x^{9} + \frac{4}{9} \, a b c d x^{9} + \frac{1}{9} \, a^{2} d^{2} x^{9} + \frac{2}{5} \, a b c^{2} x^{5} + \frac{2}{5} \, a^{2} c d x^{5} + a^{2} c^{2} x"," ",0,"1/17*b^2*d^2*x^17 + 2/13*b^2*c*d*x^13 + 2/13*a*b*d^2*x^13 + 1/9*b^2*c^2*x^9 + 4/9*a*b*c*d*x^9 + 1/9*a^2*d^2*x^9 + 2/5*a*b*c^2*x^5 + 2/5*a^2*c*d*x^5 + a^2*c^2*x","A",0
156,1,50,0,0.148796," ","integrate((b*x^4+a)^2*(d*x^4+c),x, algorithm=""giac"")","\frac{1}{13} \, b^{2} d x^{13} + \frac{1}{9} \, b^{2} c x^{9} + \frac{2}{9} \, a b d x^{9} + \frac{2}{5} \, a b c x^{5} + \frac{1}{5} \, a^{2} d x^{5} + a^{2} c x"," ",0,"1/13*b^2*d*x^13 + 1/9*b^2*c*x^9 + 2/9*a*b*d*x^9 + 2/5*a*b*c*x^5 + 1/5*a^2*d*x^5 + a^2*c*x","A",0
157,1,353,0,0.197892," ","integrate((b*x^4+a)^2/(d*x^4+c),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, c d^{3}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, c d^{3}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{8 \, c d^{3}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{8 \, c d^{3}} + \frac{b^{2} d^{4} x^{5} - 5 \, b^{2} c d^{3} x + 10 \, a b d^{4} x}{5 \, d^{5}}"," ",0,"1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c*d^3) + 1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c*d^3) + 1/8*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(x^2 + sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c*d^3) - 1/8*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(x^2 - sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c*d^3) + 1/5*(b^2*d^4*x^5 - 5*b^2*c*d^3*x + 10*a*b*d^4*x)/d^5","A",0
158,1,376,0,0.174084," ","integrate((b*x^4+a)^2/(d*x^4+c)^2,x, algorithm=""giac"")","\frac{b^{2} x}{d^{2}} - \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{16 \, c^{2} d^{3}} - \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{16 \, c^{2} d^{3}} - \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{32 \, c^{2} d^{3}} + \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{32 \, c^{2} d^{3}} + \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{4 \, {\left(d x^{4} + c\right)} c d^{2}}"," ",0,"b^2*x/d^2 - 1/16*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c^2*d^3) - 1/16*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c^2*d^3) - 1/32*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(x^2 + sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c^2*d^3) + 1/32*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(x^2 - sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c^2*d^3) + 1/4*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((d*x^4 + c)*c*d^2)","A",0
159,1,407,0,0.211511," ","integrate((b*x^4+a)^2/(d*x^4+c)^3,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{128 \, c^{3} d^{3}} + \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{128 \, c^{3} d^{3}} + \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{256 \, c^{3} d^{3}} - \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{256 \, c^{3} d^{3}} - \frac{9 \, b^{2} c^{2} d x^{5} - 2 \, a b c d^{2} x^{5} - 7 \, a^{2} d^{3} x^{5} + 5 \, b^{2} c^{3} x + 6 \, a b c^{2} d x - 11 \, a^{2} c d^{2} x}{32 \, {\left(d x^{4} + c\right)}^{2} c^{2} d^{2}}"," ",0,"1/128*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c^3*d^3) + 1/128*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(c^3*d^3) + 1/256*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*log(x^2 + sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c^3*d^3) - 1/256*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*log(x^2 - sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(c^3*d^3) - 1/32*(9*b^2*c^2*d*x^5 - 2*a*b*c*d^2*x^5 - 7*a^2*d^3*x^5 + 5*b^2*c^3*x + 6*a*b*c^2*d*x - 11*a^2*c*d^2*x)/((d*x^4 + c)^2*c^2*d^2)","A",0
160,1,617,0,0.483731," ","integrate((d*x^4+c)^4/(b*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{4} c^{4} - 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} c^{3} d + 6 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{2} c^{2} d^{2} - 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b c d^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a^{4} d^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{5}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{4} c^{4} - 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} c^{3} d + 6 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{2} c^{2} d^{2} - 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b c d^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a^{4} d^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{5}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{4} c^{4} - 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} c^{3} d + 6 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{2} c^{2} d^{2} - 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b c d^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a^{4} d^{4}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{5}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{4} c^{4} - 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} c^{3} d + 6 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{2} c^{2} d^{2} - 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b c d^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a^{4} d^{4}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{5}} + \frac{45 \, b^{12} d^{4} x^{13} + 260 \, b^{12} c d^{3} x^{9} - 65 \, a b^{11} d^{4} x^{9} + 702 \, b^{12} c^{2} d^{2} x^{5} - 468 \, a b^{11} c d^{3} x^{5} + 117 \, a^{2} b^{10} d^{4} x^{5} + 2340 \, b^{12} c^{3} d x - 3510 \, a b^{11} c^{2} d^{2} x + 2340 \, a^{2} b^{10} c d^{3} x - 585 \, a^{3} b^{9} d^{4} x}{585 \, b^{13}}"," ",0,"1/4*sqrt(2)*((a*b^3)^(1/4)*b^4*c^4 - 4*(a*b^3)^(1/4)*a*b^3*c^3*d + 6*(a*b^3)^(1/4)*a^2*b^2*c^2*d^2 - 4*(a*b^3)^(1/4)*a^3*b*c*d^3 + (a*b^3)^(1/4)*a^4*d^4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^5) + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^4*c^4 - 4*(a*b^3)^(1/4)*a*b^3*c^3*d + 6*(a*b^3)^(1/4)*a^2*b^2*c^2*d^2 - 4*(a*b^3)^(1/4)*a^3*b*c*d^3 + (a*b^3)^(1/4)*a^4*d^4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^5) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^4*c^4 - 4*(a*b^3)^(1/4)*a*b^3*c^3*d + 6*(a*b^3)^(1/4)*a^2*b^2*c^2*d^2 - 4*(a*b^3)^(1/4)*a^3*b*c*d^3 + (a*b^3)^(1/4)*a^4*d^4)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^5) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^4*c^4 - 4*(a*b^3)^(1/4)*a*b^3*c^3*d + 6*(a*b^3)^(1/4)*a^2*b^2*c^2*d^2 - 4*(a*b^3)^(1/4)*a^3*b*c*d^3 + (a*b^3)^(1/4)*a^4*d^4)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^5) + 1/585*(45*b^12*d^4*x^13 + 260*b^12*c*d^3*x^9 - 65*a*b^11*d^4*x^9 + 702*b^12*c^2*d^2*x^5 - 468*a*b^11*c*d^3*x^5 + 117*a^2*b^10*d^4*x^5 + 2340*b^12*c^3*d*x - 3510*a*b^11*c^2*d^2*x + 2340*a^2*b^10*c*d^3*x - 585*a^3*b^9*d^4*x)/b^13","B",0
161,1,481,0,0.173170," ","integrate((d*x^4+c)^3/(b*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{4}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{4}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{4}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{4}} + \frac{5 \, b^{8} d^{3} x^{9} + 27 \, b^{8} c d^{2} x^{5} - 9 \, a b^{7} d^{3} x^{5} + 135 \, b^{8} c^{2} d x - 135 \, a b^{7} c d^{2} x + 45 \, a^{2} b^{6} d^{3} x}{45 \, b^{9}}"," ",0,"1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^4) + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^4) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^4) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^4) + 1/45*(5*b^8*d^3*x^9 + 27*b^8*c*d^2*x^5 - 9*a*b^7*d^3*x^5 + 135*b^8*c^2*d*x - 135*a*b^7*c*d^2*x + 45*a^2*b^6*d^3*x)/b^9","B",0
162,1,353,0,0.176794," ","integrate((d*x^4+c)^2/(b*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(a b^{3}\right)^{\frac{1}{4}} a b c d + \left(a b^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(a b^{3}\right)^{\frac{1}{4}} a b c d + \left(a b^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(a b^{3}\right)^{\frac{1}{4}} a b c d + \left(a b^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(a b^{3}\right)^{\frac{1}{4}} a b c d + \left(a b^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} + \frac{b^{4} d^{2} x^{5} + 10 \, b^{4} c d x - 5 \, a b^{3} d^{2} x}{5 \, b^{5}}"," ",0,"1/4*sqrt(2)*((a*b^3)^(1/4)*b^2*c^2 - 2*(a*b^3)^(1/4)*a*b*c*d + (a*b^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^2*c^2 - 2*(a*b^3)^(1/4)*a*b*c*d + (a*b^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c^2 - 2*(a*b^3)^(1/4)*a*b*c*d + (a*b^3)^(1/4)*a^2*d^2)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c^2 - 2*(a*b^3)^(1/4)*a*b*c*d + (a*b^3)^(1/4)*a^2*d^2)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) + 1/5*(b^4*d^2*x^5 + 10*b^4*c*d*x - 5*a*b^3*d^2*x)/b^5","A",0
163,1,245,0,0.165324," ","integrate((d*x^4+c)/(b*x^4+a),x, algorithm=""giac"")","\frac{d x}{b} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b c - \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b c - \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b c - \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{2}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b c - \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{2}}"," ",0,"d*x/b + 1/4*sqrt(2)*((a*b^3)^(1/4)*b*c - (a*b^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^2) + 1/4*sqrt(2)*((a*b^3)^(1/4)*b*c - (a*b^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^2) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b*c - (a*b^3)^(1/4)*a*d)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^2) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b*c - (a*b^3)^(1/4)*a*d)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^2)","A",0
164,1,437,0,0.209008," ","integrate(1/(b*x^4+a)/(d*x^4+c),x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a b c - \sqrt{2} a^{2} d\right)}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a b c - \sqrt{2} a^{2} d\right)}} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} b c^{2} - \sqrt{2} a c d\right)}} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} b c^{2} - \sqrt{2} a c d\right)}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{4 \, {\left(\sqrt{2} a b c - \sqrt{2} a^{2} d\right)}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{4 \, {\left(\sqrt{2} a b c - \sqrt{2} a^{2} d\right)}} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{4 \, {\left(\sqrt{2} b c^{2} - \sqrt{2} a c d\right)}} + \frac{\left(c d^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{4 \, {\left(\sqrt{2} b c^{2} - \sqrt{2} a c d\right)}}"," ",0,"1/2*(a*b^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(sqrt(2)*a*b*c - sqrt(2)*a^2*d) + 1/2*(a*b^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(sqrt(2)*a*b*c - sqrt(2)*a^2*d) - 1/2*(c*d^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(sqrt(2)*b*c^2 - sqrt(2)*a*c*d) - 1/2*(c*d^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(sqrt(2)*b*c^2 - sqrt(2)*a*c*d) + 1/4*(a*b^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(sqrt(2)*a*b*c - sqrt(2)*a^2*d) - 1/4*(a*b^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(sqrt(2)*a*b*c - sqrt(2)*a^2*d) - 1/4*(c*d^3)^(1/4)*log(x^2 + sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(sqrt(2)*b*c^2 - sqrt(2)*a*c*d) + 1/4*(c*d^3)^(1/4)*log(x^2 - sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(sqrt(2)*b*c^2 - sqrt(2)*a*c*d)","A",0
165,1,667,0,0.194852," ","integrate(1/(b*x^4+a)/(d*x^4+c)^2,x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{1}{4}} b \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a b^{2} c^{2} - 2 \, \sqrt{2} a^{2} b c d + \sqrt{2} a^{3} d^{2}\right)}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a b^{2} c^{2} - 2 \, \sqrt{2} a^{2} b c d + \sqrt{2} a^{3} d^{2}\right)}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{4 \, {\left(\sqrt{2} a b^{2} c^{2} - 2 \, \sqrt{2} a^{2} b c d + \sqrt{2} a^{3} d^{2}\right)}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{4 \, {\left(\sqrt{2} a b^{2} c^{2} - 2 \, \sqrt{2} a^{2} b c d + \sqrt{2} a^{3} d^{2}\right)}} - \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{4} - 2 \, \sqrt{2} a b c^{3} d + \sqrt{2} a^{2} c^{2} d^{2}\right)}} - \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{4} - 2 \, \sqrt{2} a b c^{3} d + \sqrt{2} a^{2} c^{2} d^{2}\right)}} - \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{16 \, {\left(\sqrt{2} b^{2} c^{4} - 2 \, \sqrt{2} a b c^{3} d + \sqrt{2} a^{2} c^{2} d^{2}\right)}} + \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{16 \, {\left(\sqrt{2} b^{2} c^{4} - 2 \, \sqrt{2} a b c^{3} d + \sqrt{2} a^{2} c^{2} d^{2}\right)}} - \frac{d x}{4 \, {\left(d x^{4} + c\right)} {\left(b c^{2} - a c d\right)}}"," ",0,"1/2*(a*b^3)^(1/4)*b*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(sqrt(2)*a*b^2*c^2 - 2*sqrt(2)*a^2*b*c*d + sqrt(2)*a^3*d^2) + 1/2*(a*b^3)^(1/4)*b*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(sqrt(2)*a*b^2*c^2 - 2*sqrt(2)*a^2*b*c*d + sqrt(2)*a^3*d^2) + 1/4*(a*b^3)^(1/4)*b*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(sqrt(2)*a*b^2*c^2 - 2*sqrt(2)*a^2*b*c*d + sqrt(2)*a^3*d^2) - 1/4*(a*b^3)^(1/4)*b*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(sqrt(2)*a*b^2*c^2 - 2*sqrt(2)*a^2*b*c*d + sqrt(2)*a^3*d^2) - 1/8*(7*(c*d^3)^(1/4)*b*c - 3*(c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(sqrt(2)*b^2*c^4 - 2*sqrt(2)*a*b*c^3*d + sqrt(2)*a^2*c^2*d^2) - 1/8*(7*(c*d^3)^(1/4)*b*c - 3*(c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(sqrt(2)*b^2*c^4 - 2*sqrt(2)*a*b*c^3*d + sqrt(2)*a^2*c^2*d^2) - 1/16*(7*(c*d^3)^(1/4)*b*c - 3*(c*d^3)^(1/4)*a*d)*log(x^2 + sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(sqrt(2)*b^2*c^4 - 2*sqrt(2)*a*b*c^3*d + sqrt(2)*a^2*c^2*d^2) + 1/16*(7*(c*d^3)^(1/4)*b*c - 3*(c*d^3)^(1/4)*a*d)*log(x^2 - sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(sqrt(2)*b^2*c^4 - 2*sqrt(2)*a*b*c^3*d + sqrt(2)*a^2*c^2*d^2) - 1/4*d*x/((d*x^4 + c)*(b*c^2 - a*c*d))","A",0
166,1,798,0,0.179310," ","integrate((d*x^4+c)^5/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{5} c^{5} + 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{4} c^{4} d - 50 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{3} c^{3} d^{2} + 90 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b^{2} c^{2} d^{3} - 65 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{4} b c d^{4} + 17 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{5} d^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{6}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{5} c^{5} + 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{4} c^{4} d - 50 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{3} c^{3} d^{2} + 90 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b^{2} c^{2} d^{3} - 65 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{4} b c d^{4} + 17 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{5} d^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{6}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{5} c^{5} + 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{4} c^{4} d - 50 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{3} c^{3} d^{2} + 90 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b^{2} c^{2} d^{3} - 65 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{4} b c d^{4} + 17 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{5} d^{5}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{6}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{5} c^{5} + 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{4} c^{4} d - 50 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{3} c^{3} d^{2} + 90 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b^{2} c^{2} d^{3} - 65 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{4} b c d^{4} + 17 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{5} d^{5}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{6}} + \frac{b^{5} c^{5} x - 5 \, a b^{4} c^{4} d x + 10 \, a^{2} b^{3} c^{3} d^{2} x - 10 \, a^{3} b^{2} c^{2} d^{3} x + 5 \, a^{4} b c d^{4} x - a^{5} d^{5} x}{4 \, {\left(b x^{4} + a\right)} a b^{5}} + \frac{45 \, b^{24} d^{5} x^{13} + 325 \, b^{24} c d^{4} x^{9} - 130 \, a b^{23} d^{5} x^{9} + 1170 \, b^{24} c^{2} d^{3} x^{5} - 1170 \, a b^{23} c d^{4} x^{5} + 351 \, a^{2} b^{22} d^{5} x^{5} + 5850 \, b^{24} c^{3} d^{2} x - 11700 \, a b^{23} c^{2} d^{3} x + 8775 \, a^{2} b^{22} c d^{4} x - 2340 \, a^{3} b^{21} d^{5} x}{585 \, b^{26}}"," ",0,"1/16*sqrt(2)*(3*(a*b^3)^(1/4)*b^5*c^5 + 5*(a*b^3)^(1/4)*a*b^4*c^4*d - 50*(a*b^3)^(1/4)*a^2*b^3*c^3*d^2 + 90*(a*b^3)^(1/4)*a^3*b^2*c^2*d^3 - 65*(a*b^3)^(1/4)*a^4*b*c*d^4 + 17*(a*b^3)^(1/4)*a^5*d^5)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^6) + 1/16*sqrt(2)*(3*(a*b^3)^(1/4)*b^5*c^5 + 5*(a*b^3)^(1/4)*a*b^4*c^4*d - 50*(a*b^3)^(1/4)*a^2*b^3*c^3*d^2 + 90*(a*b^3)^(1/4)*a^3*b^2*c^2*d^3 - 65*(a*b^3)^(1/4)*a^4*b*c*d^4 + 17*(a*b^3)^(1/4)*a^5*d^5)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^6) + 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^5*c^5 + 5*(a*b^3)^(1/4)*a*b^4*c^4*d - 50*(a*b^3)^(1/4)*a^2*b^3*c^3*d^2 + 90*(a*b^3)^(1/4)*a^3*b^2*c^2*d^3 - 65*(a*b^3)^(1/4)*a^4*b*c*d^4 + 17*(a*b^3)^(1/4)*a^5*d^5)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^6) - 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^5*c^5 + 5*(a*b^3)^(1/4)*a*b^4*c^4*d - 50*(a*b^3)^(1/4)*a^2*b^3*c^3*d^2 + 90*(a*b^3)^(1/4)*a^3*b^2*c^2*d^3 - 65*(a*b^3)^(1/4)*a^4*b*c*d^4 + 17*(a*b^3)^(1/4)*a^5*d^5)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^6) + 1/4*(b^5*c^5*x - 5*a*b^4*c^4*d*x + 10*a^2*b^3*c^3*d^2*x - 10*a^3*b^2*c^2*d^3*x + 5*a^4*b*c*d^4*x - a^5*d^5*x)/((b*x^4 + a)*a*b^5) + 1/585*(45*b^24*d^5*x^13 + 325*b^24*c*d^4*x^9 - 130*a*b^23*d^5*x^9 + 1170*b^24*c^2*d^3*x^5 - 1170*a*b^23*c*d^4*x^5 + 351*a^2*b^22*d^5*x^5 + 5850*b^24*c^3*d^2*x - 11700*a*b^23*c^2*d^3*x + 8775*a^2*b^22*c*d^4*x - 2340*a^3*b^21*d^5*x)/b^26","B",0
167,1,642,0,0.173745," ","integrate((d*x^4+c)^4/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{4} c^{4} + 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} c^{3} d - 30 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{2} c^{2} d^{2} + 36 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b c d^{3} - 13 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{4} d^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{5}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{4} c^{4} + 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} c^{3} d - 30 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{2} c^{2} d^{2} + 36 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b c d^{3} - 13 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{4} d^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{5}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{4} c^{4} + 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} c^{3} d - 30 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{2} c^{2} d^{2} + 36 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b c d^{3} - 13 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{4} d^{4}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{5}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{4} c^{4} + 4 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} c^{3} d - 30 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b^{2} c^{2} d^{2} + 36 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} b c d^{3} - 13 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{4} d^{4}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{5}} + \frac{b^{4} c^{4} x - 4 \, a b^{3} c^{3} d x + 6 \, a^{2} b^{2} c^{2} d^{2} x - 4 \, a^{3} b c d^{3} x + a^{4} d^{4} x}{4 \, {\left(b x^{4} + a\right)} a b^{4}} + \frac{5 \, b^{16} d^{4} x^{9} + 36 \, b^{16} c d^{3} x^{5} - 18 \, a b^{15} d^{4} x^{5} + 270 \, b^{16} c^{2} d^{2} x - 360 \, a b^{15} c d^{3} x + 135 \, a^{2} b^{14} d^{4} x}{45 \, b^{18}}"," ",0,"1/16*sqrt(2)*(3*(a*b^3)^(1/4)*b^4*c^4 + 4*(a*b^3)^(1/4)*a*b^3*c^3*d - 30*(a*b^3)^(1/4)*a^2*b^2*c^2*d^2 + 36*(a*b^3)^(1/4)*a^3*b*c*d^3 - 13*(a*b^3)^(1/4)*a^4*d^4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^5) + 1/16*sqrt(2)*(3*(a*b^3)^(1/4)*b^4*c^4 + 4*(a*b^3)^(1/4)*a*b^3*c^3*d - 30*(a*b^3)^(1/4)*a^2*b^2*c^2*d^2 + 36*(a*b^3)^(1/4)*a^3*b*c*d^3 - 13*(a*b^3)^(1/4)*a^4*d^4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^5) + 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^4*c^4 + 4*(a*b^3)^(1/4)*a*b^3*c^3*d - 30*(a*b^3)^(1/4)*a^2*b^2*c^2*d^2 + 36*(a*b^3)^(1/4)*a^3*b*c*d^3 - 13*(a*b^3)^(1/4)*a^4*d^4)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^5) - 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^4*c^4 + 4*(a*b^3)^(1/4)*a*b^3*c^3*d - 30*(a*b^3)^(1/4)*a^2*b^2*c^2*d^2 + 36*(a*b^3)^(1/4)*a^3*b*c*d^3 - 13*(a*b^3)^(1/4)*a^4*d^4)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^5) + 1/4*(b^4*c^4*x - 4*a*b^3*c^3*d*x + 6*a^2*b^2*c^2*d^2*x - 4*a^3*b*c*d^3*x + a^4*d^4*x)/((b*x^4 + a)*a*b^4) + 1/45*(5*b^16*d^4*x^9 + 36*b^16*c*d^3*x^5 - 18*a*b^15*d^4*x^5 + 270*b^16*c^2*d^2*x - 360*a*b^15*c*d^3*x + 135*a^2*b^14*d^4*x)/b^18","B",0
168,1,496,0,0.178982," ","integrate((d*x^4+c)^3/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{4}} + \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{4}} + \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{4}} - \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{4}} + \frac{b^{3} c^{3} x - 3 \, a b^{2} c^{2} d x + 3 \, a^{2} b c d^{2} x - a^{3} d^{3} x}{4 \, {\left(b x^{4} + a\right)} a b^{3}} + \frac{b^{8} d^{3} x^{5} + 15 \, b^{8} c d^{2} x - 10 \, a b^{7} d^{3} x}{5 \, b^{10}}"," ",0,"3/16*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 + (a*b^3)^(1/4)*a*b^2*c^2*d - 5*(a*b^3)^(1/4)*a^2*b*c*d^2 + 3*(a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^4) + 3/16*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 + (a*b^3)^(1/4)*a*b^2*c^2*d - 5*(a*b^3)^(1/4)*a^2*b*c*d^2 + 3*(a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^4) + 3/32*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 + (a*b^3)^(1/4)*a*b^2*c^2*d - 5*(a*b^3)^(1/4)*a^2*b*c*d^2 + 3*(a*b^3)^(1/4)*a^3*d^3)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^4) - 3/32*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 + (a*b^3)^(1/4)*a*b^2*c^2*d - 5*(a*b^3)^(1/4)*a^2*b*c*d^2 + 3*(a*b^3)^(1/4)*a^3*d^3)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^4) + 1/4*(b^3*c^3*x - 3*a*b^2*c^2*d*x + 3*a^2*b*c*d^2*x - a^3*d^3*x)/((b*x^4 + a)*a*b^3) + 1/5*(b^8*d^3*x^5 + 15*b^8*c*d^2*x - 10*a*b^7*d^3*x)/b^10","A",0
169,1,376,0,0.168289," ","integrate((d*x^4+c)^2/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{d^{2} x}{b^{2}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 2 \, \left(a b^{3}\right)^{\frac{1}{4}} a b c d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 2 \, \left(a b^{3}\right)^{\frac{1}{4}} a b c d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 2 \, \left(a b^{3}\right)^{\frac{1}{4}} a b c d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 2 \, \left(a b^{3}\right)^{\frac{1}{4}} a b c d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{3}} + \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{4 \, {\left(b x^{4} + a\right)} a b^{2}}"," ",0,"d^2*x/b^2 + 1/16*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c^2 + 2*(a*b^3)^(1/4)*a*b*c*d - 5*(a*b^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/16*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c^2 + 2*(a*b^3)^(1/4)*a*b*c*d - 5*(a*b^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^3) + 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c^2 + 2*(a*b^3)^(1/4)*a*b*c*d - 5*(a*b^3)^(1/4)*a^2*d^2)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3) - 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b^2*c^2 + 2*(a*b^3)^(1/4)*a*b*c*d - 5*(a*b^3)^(1/4)*a^2*d^2)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^3) + 1/4*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((b*x^4 + a)*a*b^2)","A",0
170,1,266,0,0.165727," ","integrate((d*x^4+c)/(b*x^4+a)^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{2}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} b^{2}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{2}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{32 \, a^{2} b^{2}} + \frac{b c x - a d x}{4 \, {\left(b x^{4} + a\right)} a b}"," ",0,"1/16*sqrt(2)*(3*(a*b^3)^(1/4)*b*c + (a*b^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^2) + 1/16*sqrt(2)*(3*(a*b^3)^(1/4)*b*c + (a*b^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a^2*b^2) + 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b*c + (a*b^3)^(1/4)*a*d)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^2) - 1/32*sqrt(2)*(3*(a*b^3)^(1/4)*b*c + (a*b^3)^(1/4)*a*d)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a^2*b^2) + 1/4*(b*c*x - a*d*x)/((b*x^4 + a)*a*b)","A",0
171,1,667,0,0.216815," ","integrate(1/(b*x^4+a)^2/(d*x^4+c),x, algorithm=""giac"")","\frac{\left(c d^{3}\right)^{\frac{1}{4}} d \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} b^{2} c^{3} - 2 \, \sqrt{2} a b c^{2} d + \sqrt{2} a^{2} c d^{2}\right)}} + \frac{\left(c d^{3}\right)^{\frac{1}{4}} d \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} b^{2} c^{3} - 2 \, \sqrt{2} a b c^{2} d + \sqrt{2} a^{2} c d^{2}\right)}} + \frac{\left(c d^{3}\right)^{\frac{1}{4}} d \log\left(x^{2} + \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{3} - 2 \, \sqrt{2} a b c^{2} d + \sqrt{2} a^{2} c d^{2}\right)}} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} d \log\left(x^{2} - \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{3} - 2 \, \sqrt{2} a b c^{2} d + \sqrt{2} a^{2} c d^{2}\right)}} + \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b c - 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}\right)}} + \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b c - 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}\right)}} + \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b c - 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, {\left(\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}\right)}} - \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b c - 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, {\left(\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}\right)}} + \frac{b x}{4 \, {\left(b x^{4} + a\right)} {\left(a b c - a^{2} d\right)}}"," ",0,"1/2*(c*d^3)^(1/4)*d*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(sqrt(2)*b^2*c^3 - 2*sqrt(2)*a*b*c^2*d + sqrt(2)*a^2*c*d^2) + 1/2*(c*d^3)^(1/4)*d*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(sqrt(2)*b^2*c^3 - 2*sqrt(2)*a*b*c^2*d + sqrt(2)*a^2*c*d^2) + 1/4*(c*d^3)^(1/4)*d*log(x^2 + sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(sqrt(2)*b^2*c^3 - 2*sqrt(2)*a*b*c^2*d + sqrt(2)*a^2*c*d^2) - 1/4*(c*d^3)^(1/4)*d*log(x^2 - sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(sqrt(2)*b^2*c^3 - 2*sqrt(2)*a*b*c^2*d + sqrt(2)*a^2*c*d^2) + 1/8*(3*(a*b^3)^(1/4)*b*c - 7*(a*b^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) + 1/8*(3*(a*b^3)^(1/4)*b*c - 7*(a*b^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) + 1/16*(3*(a*b^3)^(1/4)*b*c - 7*(a*b^3)^(1/4)*a*d)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) - 1/16*(3*(a*b^3)^(1/4)*b*c - 7*(a*b^3)^(1/4)*a*d)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) + 1/4*b*x/((b*x^4 + a)*(a*b*c - a^2*d))","A",0
172,1,967,0,0.218333," ","integrate(1/(b*x^4+a)^2/(d*x^4+c)^2,x, algorithm=""giac"")","\frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} + \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} + \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{5} - 3 \, \sqrt{2} a b^{2} c^{4} d + 3 \, \sqrt{2} a^{2} b c^{3} d^{2} - \sqrt{2} a^{3} c^{2} d^{3}\right)}} + \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{5} - 3 \, \sqrt{2} a b^{2} c^{4} d + 3 \, \sqrt{2} a^{2} b c^{3} d^{2} - \sqrt{2} a^{3} c^{2} d^{3}\right)}} + \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} - \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{16 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} + \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{16 \, {\left(\sqrt{2} b^{3} c^{5} - 3 \, \sqrt{2} a b^{2} c^{4} d + 3 \, \sqrt{2} a^{2} b c^{3} d^{2} - \sqrt{2} a^{3} c^{2} d^{3}\right)}} - \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{c}{d}\right)^{\frac{1}{4}} + \sqrt{\frac{c}{d}}\right)}{16 \, {\left(\sqrt{2} b^{3} c^{5} - 3 \, \sqrt{2} a b^{2} c^{4} d + 3 \, \sqrt{2} a^{2} b c^{3} d^{2} - \sqrt{2} a^{3} c^{2} d^{3}\right)}} + \frac{b^{2} c d x^{5} + a b d^{2} x^{5} + b^{2} c^{2} x + a^{2} d^{2} x}{4 \, {\left(b d x^{8} + b c x^{4} + a d x^{4} + a c\right)} {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)}}"," ",0,"1/8*(3*(a*b^3)^(1/4)*b^2*c - 11*(a*b^3)^(1/4)*a*b*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) + 1/8*(3*(a*b^3)^(1/4)*b^2*c - 11*(a*b^3)^(1/4)*a*b*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) + 1/8*(11*(c*d^3)^(1/4)*b*c*d - 3*(c*d^3)^(1/4)*a*d^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(sqrt(2)*b^3*c^5 - 3*sqrt(2)*a*b^2*c^4*d + 3*sqrt(2)*a^2*b*c^3*d^2 - sqrt(2)*a^3*c^2*d^3) + 1/8*(11*(c*d^3)^(1/4)*b*c*d - 3*(c*d^3)^(1/4)*a*d^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(c/d)^(1/4))/(c/d)^(1/4))/(sqrt(2)*b^3*c^5 - 3*sqrt(2)*a*b^2*c^4*d + 3*sqrt(2)*a^2*b*c^3*d^2 - sqrt(2)*a^3*c^2*d^3) + 1/16*(3*(a*b^3)^(1/4)*b^2*c - 11*(a*b^3)^(1/4)*a*b*d)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) - 1/16*(3*(a*b^3)^(1/4)*b^2*c - 11*(a*b^3)^(1/4)*a*b*d)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) + 1/16*(11*(c*d^3)^(1/4)*b*c*d - 3*(c*d^3)^(1/4)*a*d^2)*log(x^2 + sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(sqrt(2)*b^3*c^5 - 3*sqrt(2)*a*b^2*c^4*d + 3*sqrt(2)*a^2*b*c^3*d^2 - sqrt(2)*a^3*c^2*d^3) - 1/16*(11*(c*d^3)^(1/4)*b*c*d - 3*(c*d^3)^(1/4)*a*d^2)*log(x^2 - sqrt(2)*x*(c/d)^(1/4) + sqrt(c/d))/(sqrt(2)*b^3*c^5 - 3*sqrt(2)*a*b^2*c^4*d + 3*sqrt(2)*a^2*b*c^3*d^2 - sqrt(2)*a^3*c^2*d^3) + 1/4*(b^2*c*d*x^5 + a*b*d^2*x^5 + b^2*c^2*x + a^2*d^2*x)/((b*d*x^8 + b*c*x^4 + a*d*x^4 + a*c)*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2))","B",0
173,0,0,0,0.000000," ","integrate((-b*x^4+a)^(5/2)/(-d*x^4+c),x, algorithm=""giac"")","\int -\frac{{\left(-b x^{4} + a\right)}^{\frac{5}{2}}}{d x^{4} - c}\,{d x}"," ",0,"integrate(-(-b*x^4 + a)^(5/2)/(d*x^4 - c), x)","F",0
174,0,0,0,0.000000," ","integrate((-b*x^4+a)^(3/2)/(-d*x^4+c),x, algorithm=""giac"")","\int -\frac{{\left(-b x^{4} + a\right)}^{\frac{3}{2}}}{d x^{4} - c}\,{d x}"," ",0,"integrate(-(-b*x^4 + a)^(3/2)/(d*x^4 - c), x)","F",0
175,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/2)/(-d*x^4+c),x, algorithm=""giac"")","\int -\frac{\sqrt{-b x^{4} + a}}{d x^{4} - c}\,{d x}"," ",0,"integrate(-sqrt(-b*x^4 + a)/(d*x^4 - c), x)","F",0
176,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(1/2)/(-d*x^4+c),x, algorithm=""giac"")","\int -\frac{1}{\sqrt{-b x^{4} + a} {\left(d x^{4} - c\right)}}\,{d x}"," ",0,"integrate(-1/(sqrt(-b*x^4 + a)*(d*x^4 - c)), x)","F",0
177,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(3/2)/(-d*x^4+c),x, algorithm=""giac"")","\int -\frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{2}} {\left(d x^{4} - c\right)}}\,{d x}"," ",0,"integrate(-1/((-b*x^4 + a)^(3/2)*(d*x^4 - c)), x)","F",0
178,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(5/2)/(-d*x^4+c),x, algorithm=""giac"")","\int -\frac{1}{{\left(-b x^{4} + a\right)}^{\frac{5}{2}} {\left(d x^{4} - c\right)}}\,{d x}"," ",0,"integrate(-1/((-b*x^4 + a)^(5/2)*(d*x^4 - c)), x)","F",0
179,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/2)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{2}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/2)/(d*x^4 + c), x)","F",0
180,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/2)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{4} + a}}{d x^{4} + c}\,{d x}"," ",0,"integrate(sqrt(b*x^4 + a)/(d*x^4 + c), x)","F",0
181,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(1/2)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{4} + a} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^4 + a)*(d*x^4 + c)), x)","F",0
182,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(3/2)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{2}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/2)*(d*x^4 + c)), x)","F",0
183,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(5/2)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{2}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/2)*(d*x^4 + c)), x)","F",0
184,0,0,0,0.000000," ","integrate((-b*x^4+a)^(7/2)/(-d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{7}{2}}}{{\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(7/2)/(d*x^4 - c)^2, x)","F",0
185,0,0,0,0.000000," ","integrate((-b*x^4+a)^(5/2)/(-d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{5}{2}}}{{\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(5/2)/(d*x^4 - c)^2, x)","F",0
186,0,0,0,0.000000," ","integrate((-b*x^4+a)^(3/2)/(-d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{{\left(-b x^{4} + a\right)}^{\frac{3}{2}}}{{\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate((-b*x^4 + a)^(3/2)/(d*x^4 - c)^2, x)","F",0
187,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/2)/(-d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{4} + a}}{{\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-b*x^4 + a)/(d*x^4 - c)^2, x)","F",0
188,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(1/2)/(-d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b x^{4} + a} {\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-b*x^4 + a)*(d*x^4 - c)^2), x)","F",0
189,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(3/2)/(-d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{3}{2}} {\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(3/2)*(d*x^4 - c)^2), x)","F",0
190,0,0,0,0.000000," ","integrate(1/(-b*x^4+a)^(5/2)/(-d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{4} + a\right)}^{\frac{5}{2}} {\left(d x^{4} - c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((-b*x^4 + a)^(5/2)*(d*x^4 - c)^2), x)","F",0
191,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/2)/(-b*c*x^4+a*c),x, algorithm=""giac"")","\int -\frac{\sqrt{b x^{4} + a}}{b c x^{4} - a c}\,{d x}"," ",0,"integrate(-sqrt(b*x^4 + a)/(b*c*x^4 - a*c), x)","F",0
192,0,0,0,0.000000," ","integrate((-b*x^4+a)^(1/2)/(b*c*x^4+a*c),x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{4} + a}}{b c x^{4} + a c}\,{d x}"," ",0,"integrate(sqrt(-b*x^4 + a)/(b*c*x^4 + a*c), x)","F",0
193,0,0,0,0.000000," ","integrate((b*x^4+a)^(7/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{7}{4}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(7/4)/(d*x^4 + c), x)","F",0
194,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/(d*x^4 + c), x)","F",0
195,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(1/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*(d*x^4 + c)), x)","F",0
196,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(5/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*(d*x^4 + c)), x)","F",0
197,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(9/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{9}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(9/4)*(d*x^4 + c)), x)","F",0
198,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(13/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{13}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(13/4)*(d*x^4 + c)), x)","F",0
199,0,0,0,0.000000," ","integrate((b*x^4+a)^(9/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{9}{4}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(9/4)/(d*x^4 + c), x)","F",0
200,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/(d*x^4 + c), x)","F",0
201,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{d x^{4} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/(d*x^4 + c), x)","F",0
202,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(3/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*(d*x^4 + c)), x)","F",0
203,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(7/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{7}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(7/4)*(d*x^4 + c)), x)","F",0
204,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(11/4)/(d*x^4+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{11}{4}} {\left(d x^{4} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(11/4)*(d*x^4 + c)), x)","F",0
205,0,0,0,0.000000," ","integrate((b*x^4+a)^(11/4)/(d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{11}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(11/4)/(d*x^4 + c)^2, x)","F",0
206,0,0,0,0.000000," ","integrate((b*x^4+a)^(7/4)/(d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{7}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(7/4)/(d*x^4 + c)^2, x)","F",0
207,0,0,0,0.000000," ","integrate((b*x^4+a)^(3/4)/(d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{3}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(3/4)/(d*x^4 + c)^2, x)","F",0
208,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(1/4)/(d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{1}{4}} {\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(1/4)*(d*x^4 + c)^2), x)","F",0
209,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(5/4)/(d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{5}{4}} {\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(5/4)*(d*x^4 + c)^2), x)","F",0
210,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(9/4)/(d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{9}{4}} {\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(9/4)*(d*x^4 + c)^2), x)","F",0
211,0,0,0,0.000000," ","integrate((b*x^4+a)^(9/4)/(d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{9}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(9/4)/(d*x^4 + c)^2, x)","F",0
212,0,0,0,0.000000," ","integrate((b*x^4+a)^(5/4)/(d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{5}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(5/4)/(d*x^4 + c)^2, x)","F",0
213,0,0,0,0.000000," ","integrate((b*x^4+a)^(1/4)/(d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{\frac{1}{4}}}{{\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^(1/4)/(d*x^4 + c)^2, x)","F",0
214,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(3/4)/(d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{3}{4}} {\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(3/4)*(d*x^4 + c)^2), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(b*x^4+a)^(7/4)/(d*x^4+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)}^{\frac{7}{4}} {\left(d x^{4} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)^(7/4)*(d*x^4 + c)^2), x)","F",0
216,0,0,0,0.000000," ","integrate(1/(x^4+1)^(1/4)/(x^4+2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 2\right)} {\left(x^{4} + 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((x^4 + 2)*(x^4 + 1)^(1/4)), x)","F",0
217,0,0,0,0.000000," ","integrate(1/(a-(a-b)*x^4)/(b*x^4+a)^(1/4),x, algorithm=""giac"")","\int -\frac{1}{{\left({\left(a - b\right)} x^{4} - a\right)} {\left(b x^{4} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-1/(((a - b)*x^4 - a)*(b*x^4 + a)^(1/4)), x)","F",0
218,0,0,0,0.000000," ","integrate((b*x^4+a)^p*(d*x^4+c)^q,x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{p} {\left(d x^{4} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^4 + a)^p*(d*x^4 + c)^q, x)","F",0
219,0,0,0,0.000000," ","integrate((b*x^4+a)^2*(d*x^4+c)^q,x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{2} {\left(d x^{4} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^4 + a)^2*(d*x^4 + c)^q, x)","F",0
220,0,0,0,0.000000," ","integrate((b*x^4+a)*(d*x^4+c)^q,x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)} {\left(d x^{4} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^4 + a)*(d*x^4 + c)^q, x)","F",0
221,0,0,0,0.000000," ","integrate((d*x^4+c)^q/(b*x^4+a),x, algorithm=""giac"")","\int \frac{{\left(d x^{4} + c\right)}^{q}}{b x^{4} + a}\,{d x}"," ",0,"integrate((d*x^4 + c)^q/(b*x^4 + a), x)","F",0
222,0,0,0,0.000000," ","integrate((d*x^4+c)^q/(b*x^4+a)^2,x, algorithm=""giac"")","\int \frac{{\left(d x^{4} + c\right)}^{q}}{{\left(b x^{4} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^4 + c)^q/(b*x^4 + a)^2, x)","F",0
223,0,0,0,0.000000," ","integrate(1/(b*x^5+a)^(1/5)/(d*x^5+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{5} + a\right)}^{\frac{1}{5}} {\left(d x^{5} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^5 + a)^(1/5)*(d*x^5 + c)), x)","F",0
224,-2,0,0,0.000000," ","integrate((c+d/x)^3*(a+b/x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [-89,63,-49]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [61.7937478349,-30,70]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [73.519035968,-9,-13]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [18,15.451549686,-33]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
225,-2,0,0,0.000000," ","integrate((c+d/x)^2*(a+b/x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [-89,63,-49]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [61.7937478349,-30,70]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [73.519035968,-9,-13]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [18,15.451549686,-33]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
226,-2,0,0,0.000000," ","integrate((c+d/x)*(a+b/x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [-89,63,-49]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [61.7937478349,-30,70]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [73.519035968,-9,-13]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [18,15.451549686,-33]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
227,1,64,0,0.199980," ","integrate((a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{b \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right) \mathrm{sgn}\left(x\right)}{2 \, \sqrt{a}} + \frac{b \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{2 \, \sqrt{a}} + \sqrt{a x^{2} + b x} \mathrm{sgn}\left(x\right)"," ",0,"-1/2*b*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))*sgn(x)/sqrt(a) + 1/2*b*log(abs(b))*sgn(x)/sqrt(a) + sqrt(a*x^2 + b*x)*sgn(x)","B",0
228,-2,0,0,0.000000," ","integrate((a+b/x)^(1/2)/(c+d/x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Error: Bad Argument Type","F(-2)",0
229,-2,0,0,0.000000," ","integrate((a+b/x)^(1/2)/(c+d/x)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Unable to divide, perhaps due to rounding error%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,6,4,0]%%%}+%%%{%%%{8,[1]%%%},[3,5,4,1]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,5,5,1]%%%}+%%%{%%{[%%%{-8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,4,4,2]%%%}+%%%{%%%{8,[1]%%%},[1,4,5,2]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,4,6,2]%%%} / %%%{%%%{1,[1]%%%},[4,2,0,0]%%%}+%%%{%%{poly1[%%%{-4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,1]%%%}+%%%{%%%{2,[1]%%%},[2,1,1,1]%%%}+%%%{%%%{4,[2]%%%},[2,0,0,2]%%%}+%%%{%%{poly1[%%%{-4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,1,2]%%%}+%%%{%%%{1,[1]%%%},[0,0,2,2]%%%} Error: Bad Argument Value","F(-2)",0
230,1,820,0,0.411513," ","integrate((a+b/x)^(1/2)/(c+d/x)^3,x, algorithm=""giac"")","-\frac{{\left(15 \, \sqrt{a} b^{2} c^{2} d \arctan\left(\frac{\sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right) - 40 \, a^{\frac{3}{2}} b c d^{2} \arctan\left(\frac{\sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right) + 24 \, a^{\frac{5}{2}} d^{3} \arctan\left(\frac{\sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right) - 2 \, \sqrt{b c d - a d^{2}} b^{2} c^{2} \log\left({\left| b \right|}\right) + 14 \, \sqrt{b c d - a d^{2}} a b c d \log\left({\left| b \right|}\right) - 12 \, \sqrt{b c d - a d^{2}} a^{2} d^{2} \log\left({\left| b \right|}\right) + 9 \, \sqrt{b c d - a d^{2}} a b c d - 10 \, \sqrt{b c d - a d^{2}} a^{2} d^{2}\right)} \mathrm{sgn}\left(x\right)}{4 \, {\left(\sqrt{b c d - a d^{2}} \sqrt{a} b c^{5} - \sqrt{b c d - a d^{2}} a^{\frac{3}{2}} c^{4} d\right)}} - \frac{{\left(15 \, b^{2} c^{2} d \mathrm{sgn}\left(x\right) - 40 \, a b c d^{2} \mathrm{sgn}\left(x\right) + 24 \, a^{2} d^{3} \mathrm{sgn}\left(x\right)\right)} \arctan\left(-\frac{{\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} c + \sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right)}{4 \, {\left(b c^{5} - a c^{4} d\right)} \sqrt{b c d - a d^{2}}} + \frac{\sqrt{a x^{2} + b x} \mathrm{sgn}\left(x\right)}{c^{3}} - \frac{9 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} \sqrt{a} b^{2} c^{3} d \mathrm{sgn}\left(x\right) - 32 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b c^{2} d^{2} \mathrm{sgn}\left(x\right) + 24 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{5}{2}} c d^{3} \mathrm{sgn}\left(x\right) + 3 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{2} c^{2} d^{2} \mathrm{sgn}\left(x\right) - 40 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a^{2} b c d^{3} \mathrm{sgn}\left(x\right) + 40 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a^{3} d^{4} \mathrm{sgn}\left(x\right) + 7 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{3} c^{2} d^{2} \mathrm{sgn}\left(x\right) - 44 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} a^{\frac{3}{2}} b^{2} c d^{3} \mathrm{sgn}\left(x\right) + 40 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} a^{\frac{5}{2}} b d^{4} \mathrm{sgn}\left(x\right) - 9 \, a b^{3} c d^{3} \mathrm{sgn}\left(x\right) + 10 \, a^{2} b^{2} d^{4} \mathrm{sgn}\left(x\right)}{4 \, {\left(\sqrt{a} b c^{5} - a^{\frac{3}{2}} c^{4} d\right)} {\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} c + 2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} d + b d\right)}^{2}} - \frac{{\left(b c \mathrm{sgn}\left(x\right) - 6 \, a d \mathrm{sgn}\left(x\right)\right)} \log\left({\left| 2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} + b \right|}\right)}{2 \, \sqrt{a} c^{4}}"," ",0,"-1/4*(15*sqrt(a)*b^2*c^2*d*arctan(sqrt(a)*d/sqrt(b*c*d - a*d^2)) - 40*a^(3/2)*b*c*d^2*arctan(sqrt(a)*d/sqrt(b*c*d - a*d^2)) + 24*a^(5/2)*d^3*arctan(sqrt(a)*d/sqrt(b*c*d - a*d^2)) - 2*sqrt(b*c*d - a*d^2)*b^2*c^2*log(abs(b)) + 14*sqrt(b*c*d - a*d^2)*a*b*c*d*log(abs(b)) - 12*sqrt(b*c*d - a*d^2)*a^2*d^2*log(abs(b)) + 9*sqrt(b*c*d - a*d^2)*a*b*c*d - 10*sqrt(b*c*d - a*d^2)*a^2*d^2)*sgn(x)/(sqrt(b*c*d - a*d^2)*sqrt(a)*b*c^5 - sqrt(b*c*d - a*d^2)*a^(3/2)*c^4*d) - 1/4*(15*b^2*c^2*d*sgn(x) - 40*a*b*c*d^2*sgn(x) + 24*a^2*d^3*sgn(x))*arctan(-((sqrt(a)*x - sqrt(a*x^2 + b*x))*c + sqrt(a)*d)/sqrt(b*c*d - a*d^2))/((b*c^5 - a*c^4*d)*sqrt(b*c*d - a*d^2)) + sqrt(a*x^2 + b*x)*sgn(x)/c^3 - 1/4*(9*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*sqrt(a)*b^2*c^3*d*sgn(x) - 32*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b*c^2*d^2*sgn(x) + 24*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(5/2)*c*d^3*sgn(x) + 3*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^2*c^2*d^2*sgn(x) - 40*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a^2*b*c*d^3*sgn(x) + 40*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a^3*d^4*sgn(x) + 7*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^3*c^2*d^2*sgn(x) - 44*(sqrt(a)*x - sqrt(a*x^2 + b*x))*a^(3/2)*b^2*c*d^3*sgn(x) + 40*(sqrt(a)*x - sqrt(a*x^2 + b*x))*a^(5/2)*b*d^4*sgn(x) - 9*a*b^3*c*d^3*sgn(x) + 10*a^2*b^2*d^4*sgn(x))/((sqrt(a)*b*c^5 - a^(3/2)*c^4*d)*((sqrt(a)*x - sqrt(a*x^2 + b*x))^2*c + 2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*d + b*d)^2) - 1/2*(b*c*sgn(x) - 6*a*d*sgn(x))*log(abs(2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) + b))/(sqrt(a)*c^4)","B",0
231,-2,0,0,0.000000," ","integrate((a+b/x)^(3/2)*(c+d/x)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [18.6420984049,-49,-86]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [78.6493344628,22,42]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [-13,74.7709350525,24]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Evaluation time: 0.8Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
232,-2,0,0,0.000000," ","integrate((a+b/x)^(3/2)*(c+d/x)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [18.6420984049,-49,-86]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [78.6493344628,22,42]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [-13,74.7709350525,24]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Evaluation time: 0.43Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
233,-2,0,0,0.000000," ","integrate((a+b/x)^(3/2)*(c+d/x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [18.6420984049,-49,-86]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [78.6493344628,22,42]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [-13,74.7709350525,24]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
234,-2,0,0,0.000000," ","integrate((a+b/x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [82.1195442914,26,-89]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [85.3561567818,-64,-30]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [42,43.9628838282,-9]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
235,-2,0,0,0.000000," ","integrate((a+b/x)^(3/2)/(c+d/x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Error: Bad Argument Type","F(-2)",0
236,-2,0,0,0.000000," ","integrate((a+b/x)^(3/2)/(c+d/x)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Unable to divide, perhaps due to rounding error%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,6,4,0]%%%}+%%%{%%%{8,[1]%%%},[3,5,4,1]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,5,5,1]%%%}+%%%{%%{[%%%{-8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,4,4,2]%%%}+%%%{%%%{8,[1]%%%},[1,4,5,2]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,4,6,2]%%%} / %%%{%%%{1,[1]%%%},[4,2,0,0]%%%}+%%%{%%{poly1[%%%{-4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,1]%%%}+%%%{%%%{2,[1]%%%},[2,1,1,1]%%%}+%%%{%%%{4,[2]%%%},[2,0,0,2]%%%}+%%%{%%{poly1[%%%{-4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,1,2]%%%}+%%%{%%%{1,[1]%%%},[0,0,2,2]%%%} Error: Bad Argument Value","F(-2)",0
237,1,727,0,0.611319," ","integrate((a+b/x)^(3/2)/(c+d/x)^3,x, algorithm=""giac"")","\frac{\sqrt{a x^{2} + b x} a \mathrm{sgn}\left(x\right)}{c^{3}} + \frac{3 \, {\left(b^{2} c^{2} \mathrm{sgn}\left(x\right) - 8 \, a b c d \mathrm{sgn}\left(x\right) + 8 \, a^{2} d^{2} \mathrm{sgn}\left(x\right)\right)} \arctan\left(-\frac{{\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} c + \sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right)}{4 \, \sqrt{b c d - a d^{2}} c^{4}} - \frac{3 \, {\left(a b c \mathrm{sgn}\left(x\right) - 2 \, a^{2} d \mathrm{sgn}\left(x\right)\right)} \log\left({\left| 2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} + b \right|}\right)}{2 \, \sqrt{a} c^{4}} + \frac{{\left(3 \, \sqrt{a} b^{2} c^{2} \arctan\left(\frac{\sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right) - 24 \, a^{\frac{3}{2}} b c d \arctan\left(\frac{\sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right) + 24 \, a^{\frac{5}{2}} d^{2} \arctan\left(\frac{\sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right) + 6 \, \sqrt{b c d - a d^{2}} a b c \log\left({\left| b \right|}\right) - 12 \, \sqrt{b c d - a d^{2}} a^{2} d \log\left({\left| b \right|}\right) + 5 \, \sqrt{b c d - a d^{2}} a b c - 10 \, \sqrt{b c d - a d^{2}} a^{2} d\right)} \mathrm{sgn}\left(x\right)}{4 \, \sqrt{b c d - a d^{2}} \sqrt{a} c^{4}} + \frac{5 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} \sqrt{a} b^{2} c^{3} \mathrm{sgn}\left(x\right) - 24 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b c^{2} d \mathrm{sgn}\left(x\right) + 24 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{5}{2}} c d^{2} \mathrm{sgn}\left(x\right) - {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{2} c^{2} d \mathrm{sgn}\left(x\right) - 24 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a^{2} b c d^{2} \mathrm{sgn}\left(x\right) + 40 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a^{3} d^{3} \mathrm{sgn}\left(x\right) + 3 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{3} c^{2} d \mathrm{sgn}\left(x\right) - 28 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} a^{\frac{3}{2}} b^{2} c d^{2} \mathrm{sgn}\left(x\right) + 40 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} a^{\frac{5}{2}} b d^{3} \mathrm{sgn}\left(x\right) - 5 \, a b^{3} c d^{2} \mathrm{sgn}\left(x\right) + 10 \, a^{2} b^{2} d^{3} \mathrm{sgn}\left(x\right)}{4 \, {\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} c + 2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} d + b d\right)}^{2} \sqrt{a} c^{4}}"," ",0,"sqrt(a*x^2 + b*x)*a*sgn(x)/c^3 + 3/4*(b^2*c^2*sgn(x) - 8*a*b*c*d*sgn(x) + 8*a^2*d^2*sgn(x))*arctan(-((sqrt(a)*x - sqrt(a*x^2 + b*x))*c + sqrt(a)*d)/sqrt(b*c*d - a*d^2))/(sqrt(b*c*d - a*d^2)*c^4) - 3/2*(a*b*c*sgn(x) - 2*a^2*d*sgn(x))*log(abs(2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) + b))/(sqrt(a)*c^4) + 1/4*(3*sqrt(a)*b^2*c^2*arctan(sqrt(a)*d/sqrt(b*c*d - a*d^2)) - 24*a^(3/2)*b*c*d*arctan(sqrt(a)*d/sqrt(b*c*d - a*d^2)) + 24*a^(5/2)*d^2*arctan(sqrt(a)*d/sqrt(b*c*d - a*d^2)) + 6*sqrt(b*c*d - a*d^2)*a*b*c*log(abs(b)) - 12*sqrt(b*c*d - a*d^2)*a^2*d*log(abs(b)) + 5*sqrt(b*c*d - a*d^2)*a*b*c - 10*sqrt(b*c*d - a*d^2)*a^2*d)*sgn(x)/(sqrt(b*c*d - a*d^2)*sqrt(a)*c^4) + 1/4*(5*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*sqrt(a)*b^2*c^3*sgn(x) - 24*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b*c^2*d*sgn(x) + 24*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(5/2)*c*d^2*sgn(x) - (sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^2*c^2*d*sgn(x) - 24*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a^2*b*c*d^2*sgn(x) + 40*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a^3*d^3*sgn(x) + 3*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^3*c^2*d*sgn(x) - 28*(sqrt(a)*x - sqrt(a*x^2 + b*x))*a^(3/2)*b^2*c*d^2*sgn(x) + 40*(sqrt(a)*x - sqrt(a*x^2 + b*x))*a^(5/2)*b*d^3*sgn(x) - 5*a*b^3*c*d^2*sgn(x) + 10*a^2*b^2*d^3*sgn(x))/(((sqrt(a)*x - sqrt(a*x^2 + b*x))^2*c + 2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*d + b*d)^2*sqrt(a)*c^4)","B",0
238,-2,0,0,0.000000," ","integrate((a+b/x)^(5/2)*(c+d/x)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [18.6420984049,-49,-86]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [78.6493344628,22,42]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [-13,74.7709350525,24]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Evaluation time: 1.79Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
239,-2,0,0,0.000000," ","integrate((a+b/x)^(5/2)*(c+d/x)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [18.6420984049,-49,-86]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [78.6493344628,22,42]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [-13,74.7709350525,24]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Evaluation time: 0.81Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
240,-2,0,0,0.000000," ","integrate((a+b/x)^(5/2)*(c+d/x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [7,-27,26]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [18.6420984049,-49,-86]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [78.6493344628,22,42]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [-13,74.7709350525,24]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
241,-2,0,0,0.000000," ","integrate((a+b/x)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{2,[1,3,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{1,[0,2,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [82.1195442914,26,-89]Warning, choosing root of [1,0,%%%{-4,[1,0,0]%%%}+%%%{-2,[0,1,1]%%%},0,%%%{1,[0,2,2]%%%}] at parameters values [85.3561567818,-64,-30]Warning, choosing root of [1,0,%%%{-2,[1,0,1]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,2]%%%}] at parameters values [42,43.9628838282,-9]Sign error (%%%{-b,0%%%}+%%%{2*sqrt(a)*sqrt(b),1/2%%%}+%%%{-2*a,1%%%}+%%%{a*sqrt(a)*sqrt(b)/b,3/2%%%}+%%%{-a^2*sqrt(a)*sqrt(b)/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
242,-2,0,0,0.000000," ","integrate((a+b/x)^(5/2)/(c+d/x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Error: Bad Argument Type","F(-2)",0
243,-2,0,0,0.000000," ","integrate((a+b/x)^(5/2)/(c+d/x)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Unable to divide, perhaps due to rounding error%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,6,4,0]%%%}+%%%{%%%{8,[1]%%%},[3,5,4,1]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,5,5,1]%%%}+%%%{%%{[%%%{-8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,4,4,2]%%%}+%%%{%%%{8,[1]%%%},[1,4,5,2]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,4,6,2]%%%} / %%%{%%%{1,[1]%%%},[4,2,0,0]%%%}+%%%{%%{poly1[%%%{-4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,1]%%%}+%%%{%%%{2,[1]%%%},[2,1,1,1]%%%}+%%%{%%%{4,[2]%%%},[2,0,0,2]%%%}+%%%{%%{poly1[%%%{-4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,1,2]%%%}+%%%{%%%{1,[1]%%%},[0,0,2,2]%%%} Error: Bad Argument Value","F(-2)",0
244,1,945,0,0.489399," ","integrate((a+b/x)^(5/2)/(c+d/x)^3,x, algorithm=""giac"")","\frac{\sqrt{a x^{2} + b x} a^{2} \mathrm{sgn}\left(x\right)}{c^{3}} - \frac{{\left(5 \, a^{2} b c \mathrm{sgn}\left(x\right) - 6 \, a^{3} d \mathrm{sgn}\left(x\right)\right)} \log\left({\left| 2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} + b \right|}\right)}{2 \, \sqrt{a} c^{4}} + \frac{{\left(b^{3} c^{3} \mathrm{sgn}\left(x\right) + 7 \, a b^{2} c^{2} d \mathrm{sgn}\left(x\right) - 32 \, a^{2} b c d^{2} \mathrm{sgn}\left(x\right) + 24 \, a^{3} d^{3} \mathrm{sgn}\left(x\right)\right)} \arctan\left(-\frac{{\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} c + \sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right)}{4 \, \sqrt{b c d - a d^{2}} c^{4} d} + \frac{{\left(\sqrt{a} b^{3} c^{3} \arctan\left(\frac{\sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right) + 7 \, a^{\frac{3}{2}} b^{2} c^{2} d \arctan\left(\frac{\sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right) - 32 \, a^{\frac{5}{2}} b c d^{2} \arctan\left(\frac{\sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right) + 24 \, a^{\frac{7}{2}} d^{3} \arctan\left(\frac{\sqrt{a} d}{\sqrt{b c d - a d^{2}}}\right) + 10 \, \sqrt{b c d - a d^{2}} a^{2} b c d \log\left({\left| b \right|}\right) - 12 \, \sqrt{b c d - a d^{2}} a^{3} d^{2} \log\left({\left| b \right|}\right) - \sqrt{b c d - a d^{2}} a b^{2} c^{2} + 11 \, \sqrt{b c d - a d^{2}} a^{2} b c d - 10 \, \sqrt{b c d - a d^{2}} a^{3} d^{2}\right)} \mathrm{sgn}\left(x\right)}{4 \, \sqrt{b c d - a d^{2}} \sqrt{a} c^{4} d} - \frac{{\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} \sqrt{a} b^{3} c^{4} \mathrm{sgn}\left(x\right) - 17 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{3}{2}} b^{2} c^{3} d \mathrm{sgn}\left(x\right) + 40 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{5}{2}} b c^{2} d^{2} \mathrm{sgn}\left(x\right) - 24 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{3} a^{\frac{7}{2}} c d^{3} \mathrm{sgn}\left(x\right) - 5 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a b^{3} c^{3} d \mathrm{sgn}\left(x\right) - 3 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a^{2} b^{2} c^{2} d^{2} \mathrm{sgn}\left(x\right) + 48 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a^{3} b c d^{3} \mathrm{sgn}\left(x\right) - 40 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} a^{4} d^{4} \mathrm{sgn}\left(x\right) - {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} b^{4} c^{3} d \mathrm{sgn}\left(x\right) - 11 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} a^{\frac{3}{2}} b^{3} c^{2} d^{2} \mathrm{sgn}\left(x\right) + 52 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} a^{\frac{5}{2}} b^{2} c d^{3} \mathrm{sgn}\left(x\right) - 40 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} a^{\frac{7}{2}} b d^{4} \mathrm{sgn}\left(x\right) - a b^{4} c^{2} d^{2} \mathrm{sgn}\left(x\right) + 11 \, a^{2} b^{3} c d^{3} \mathrm{sgn}\left(x\right) - 10 \, a^{3} b^{2} d^{4} \mathrm{sgn}\left(x\right)}{4 \, {\left({\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)}^{2} c + 2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} d + b d\right)}^{2} \sqrt{a} c^{4} d}"," ",0,"sqrt(a*x^2 + b*x)*a^2*sgn(x)/c^3 - 1/2*(5*a^2*b*c*sgn(x) - 6*a^3*d*sgn(x))*log(abs(2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) + b))/(sqrt(a)*c^4) + 1/4*(b^3*c^3*sgn(x) + 7*a*b^2*c^2*d*sgn(x) - 32*a^2*b*c*d^2*sgn(x) + 24*a^3*d^3*sgn(x))*arctan(-((sqrt(a)*x - sqrt(a*x^2 + b*x))*c + sqrt(a)*d)/sqrt(b*c*d - a*d^2))/(sqrt(b*c*d - a*d^2)*c^4*d) + 1/4*(sqrt(a)*b^3*c^3*arctan(sqrt(a)*d/sqrt(b*c*d - a*d^2)) + 7*a^(3/2)*b^2*c^2*d*arctan(sqrt(a)*d/sqrt(b*c*d - a*d^2)) - 32*a^(5/2)*b*c*d^2*arctan(sqrt(a)*d/sqrt(b*c*d - a*d^2)) + 24*a^(7/2)*d^3*arctan(sqrt(a)*d/sqrt(b*c*d - a*d^2)) + 10*sqrt(b*c*d - a*d^2)*a^2*b*c*d*log(abs(b)) - 12*sqrt(b*c*d - a*d^2)*a^3*d^2*log(abs(b)) - sqrt(b*c*d - a*d^2)*a*b^2*c^2 + 11*sqrt(b*c*d - a*d^2)*a^2*b*c*d - 10*sqrt(b*c*d - a*d^2)*a^3*d^2)*sgn(x)/(sqrt(b*c*d - a*d^2)*sqrt(a)*c^4*d) - 1/4*((sqrt(a)*x - sqrt(a*x^2 + b*x))^3*sqrt(a)*b^3*c^4*sgn(x) - 17*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^2*c^3*d*sgn(x) + 40*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(5/2)*b*c^2*d^2*sgn(x) - 24*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(7/2)*c*d^3*sgn(x) - 5*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^3*c^3*d*sgn(x) - 3*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a^2*b^2*c^2*d^2*sgn(x) + 48*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a^3*b*c*d^3*sgn(x) - 40*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a^4*d^4*sgn(x) - (sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^4*c^3*d*sgn(x) - 11*(sqrt(a)*x - sqrt(a*x^2 + b*x))*a^(3/2)*b^3*c^2*d^2*sgn(x) + 52*(sqrt(a)*x - sqrt(a*x^2 + b*x))*a^(5/2)*b^2*c*d^3*sgn(x) - 40*(sqrt(a)*x - sqrt(a*x^2 + b*x))*a^(7/2)*b*d^4*sgn(x) - a*b^4*c^2*d^2*sgn(x) + 11*a^2*b^3*c*d^3*sgn(x) - 10*a^3*b^2*d^4*sgn(x))/(((sqrt(a)*x - sqrt(a*x^2 + b*x))^2*c + 2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*d + b*d)^2*sqrt(a)*c^4*d)","B",0
245,1,158,0,0.204472," ","integrate((c+d/x)^3/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{\frac{3 \, b^{2} c^{3} \sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a} - \frac{3 \, {\left(b^{2} c^{3} - 6 \, a b c^{2} d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a} + \frac{2 \, {\left(9 \, b^{3} c d^{2} \sqrt{\frac{a x + b}{x}} - 3 \, a b^{2} d^{3} \sqrt{\frac{a x + b}{x}} + \frac{{\left(a x + b\right)} b^{2} d^{3} \sqrt{\frac{a x + b}{x}}}{x}\right)}}{b^{3}}}{3 \, b}"," ",0,"-1/3*(3*b^2*c^3*sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a) - 3*(b^2*c^3 - 6*a*b*c^2*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a) + 2*(9*b^3*c*d^2*sqrt((a*x + b)/x) - 3*a*b^2*d^3*sqrt((a*x + b)/x) + (a*x + b)*b^2*d^3*sqrt((a*x + b)/x)/x)/b^3)/b","A",0
246,1,99,0,0.183002," ","integrate((c+d/x)^2/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{\frac{b^{2} c^{2} \sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a} + 2 \, d^{2} \sqrt{\frac{a x + b}{x}} - \frac{{\left(b^{2} c^{2} - 4 \, a b c d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a}}{b}"," ",0,"-(b^2*c^2*sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a) + 2*d^2*sqrt((a*x + b)/x) - (b^2*c^2 - 4*a*b*c*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a))/b","A",0
247,1,78,0,0.197016," ","integrate((c+d/x)/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{\frac{b^{2} c \sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a} - \frac{{\left(b^{2} c - 2 \, a b d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a}}{b}"," ",0,"-(b^2*c*sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a) - (b^2*c - 2*a*b*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a))/b","A",0
248,1,71,0,0.238827," ","integrate(1/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{b \log\left({\left| b \right|}\right) \mathrm{sgn}\left(x\right)}{2 \, a^{\frac{3}{2}}} + \frac{b \log\left({\left| -2 \, {\left(\sqrt{a} x - \sqrt{a x^{2} + b x}\right)} \sqrt{a} - b \right|}\right)}{2 \, a^{\frac{3}{2}} \mathrm{sgn}\left(x\right)} + \frac{\sqrt{a x^{2} + b x}}{a \mathrm{sgn}\left(x\right)}"," ",0,"-1/2*b*log(abs(b))*sgn(x)/a^(3/2) + 1/2*b*log(abs(-2*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a) - b))/(a^(3/2)*sgn(x)) + sqrt(a*x^2 + b*x)/(a*sgn(x))","B",0
249,1,134,0,0.181441," ","integrate(1/(c+d/x)/(a+b/x)^(1/2),x, algorithm=""giac"")","-b^{2} {\left(\frac{2 \, d^{2} \arctan\left(\frac{d \sqrt{\frac{a x + b}{x}}}{\sqrt{b c d - a d^{2}}}\right)}{\sqrt{b c d - a d^{2}} b^{2} c^{2}} + \frac{\sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a b c} - \frac{{\left(b c + 2 \, a d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a b^{2} c^{2}}\right)}"," ",0,"-b^2*(2*d^2*arctan(d*sqrt((a*x + b)/x)/sqrt(b*c*d - a*d^2))/(sqrt(b*c*d - a*d^2)*b^2*c^2) + sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a*b*c) - (b*c + 2*a*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a*b^2*c^2))","A",0
250,1,300,0,0.219526," ","integrate(1/(c+d/x)^2/(a+b/x)^(1/2),x, algorithm=""giac"")","-b^{3} {\left(\frac{{\left(5 \, b c d^{2} - 4 \, a d^{3}\right)} \arctan\left(\frac{d \sqrt{\frac{a x + b}{x}}}{\sqrt{b c d - a d^{2}}}\right)}{{\left(b^{4} c^{4} - a b^{3} c^{3} d\right)} \sqrt{b c d - a d^{2}}} + \frac{b^{2} c^{2} \sqrt{\frac{a x + b}{x}} - 2 \, a b c d \sqrt{\frac{a x + b}{x}} + 2 \, a^{2} d^{2} \sqrt{\frac{a x + b}{x}} + \frac{{\left(a x + b\right)} b c d \sqrt{\frac{a x + b}{x}}}{x} - \frac{2 \, {\left(a x + b\right)} a d^{2} \sqrt{\frac{a x + b}{x}}}{x}}{{\left(a b^{3} c^{3} - a^{2} b^{2} c^{2} d\right)} {\left(a b c - a^{2} d - \frac{{\left(a x + b\right)} b c}{x} + \frac{2 \, {\left(a x + b\right)} a d}{x} - \frac{{\left(a x + b\right)}^{2} d}{x^{2}}\right)}} - \frac{{\left(b c + 4 \, a d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a b^{3} c^{3}}\right)}"," ",0,"-b^3*((5*b*c*d^2 - 4*a*d^3)*arctan(d*sqrt((a*x + b)/x)/sqrt(b*c*d - a*d^2))/((b^4*c^4 - a*b^3*c^3*d)*sqrt(b*c*d - a*d^2)) + (b^2*c^2*sqrt((a*x + b)/x) - 2*a*b*c*d*sqrt((a*x + b)/x) + 2*a^2*d^2*sqrt((a*x + b)/x) + (a*x + b)*b*c*d*sqrt((a*x + b)/x)/x - 2*(a*x + b)*a*d^2*sqrt((a*x + b)/x)/x)/((a*b^3*c^3 - a^2*b^2*c^2*d)*(a*b*c - a^2*d - (a*x + b)*b*c/x + 2*(a*x + b)*a*d/x - (a*x + b)^2*d/x^2)) - (b*c + 4*a*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a*b^3*c^3))","A",0
251,1,352,0,0.288298," ","integrate(1/(c+d/x)^3/(a+b/x)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, b^{4} {\left(\frac{{\left(35 \, b^{2} c^{2} d^{2} - 56 \, a b c d^{3} + 24 \, a^{2} d^{4}\right)} \arctan\left(\frac{d \sqrt{\frac{a x + b}{x}}}{\sqrt{b c d - a d^{2}}}\right)}{{\left(b^{6} c^{6} - 2 \, a b^{5} c^{5} d + a^{2} b^{4} c^{4} d^{2}\right)} \sqrt{b c d - a d^{2}}} + \frac{13 \, b^{2} c^{2} d^{2} \sqrt{\frac{a x + b}{x}} - 21 \, a b c d^{3} \sqrt{\frac{a x + b}{x}} + 8 \, a^{2} d^{4} \sqrt{\frac{a x + b}{x}} + \frac{11 \, {\left(a x + b\right)} b c d^{3} \sqrt{\frac{a x + b}{x}}}{x} - \frac{8 \, {\left(a x + b\right)} a d^{4} \sqrt{\frac{a x + b}{x}}}{x}}{{\left(b^{5} c^{5} - 2 \, a b^{4} c^{4} d + a^{2} b^{3} c^{3} d^{2}\right)} {\left(b c - a d + \frac{{\left(a x + b\right)} d}{x}\right)}^{2}} + \frac{4 \, \sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a b^{3} c^{3}} - \frac{4 \, {\left(b c + 6 \, a d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a b^{4} c^{4}}\right)}"," ",0,"-1/4*b^4*((35*b^2*c^2*d^2 - 56*a*b*c*d^3 + 24*a^2*d^4)*arctan(d*sqrt((a*x + b)/x)/sqrt(b*c*d - a*d^2))/((b^6*c^6 - 2*a*b^5*c^5*d + a^2*b^4*c^4*d^2)*sqrt(b*c*d - a*d^2)) + (13*b^2*c^2*d^2*sqrt((a*x + b)/x) - 21*a*b*c*d^3*sqrt((a*x + b)/x) + 8*a^2*d^4*sqrt((a*x + b)/x) + 11*(a*x + b)*b*c*d^3*sqrt((a*x + b)/x)/x - 8*(a*x + b)*a*d^4*sqrt((a*x + b)/x)/x)/((b^5*c^5 - 2*a*b^4*c^4*d + a^2*b^3*c^3*d^2)*(b*c - a*d + (a*x + b)*d/x)^2) + 4*sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a*b^3*c^3) - 4*(b*c + 6*a*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a*b^4*c^4))","A",0
252,1,222,0,0.209243," ","integrate((c+d/x)^3/(a+b/x)^(3/2),x, algorithm=""giac"")","-\frac{\frac{2 \, d^{3} \sqrt{\frac{a x + b}{x}}}{b} - \frac{3 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} - \frac{2 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d + 6 \, a^{3} b c d^{2} - 2 \, a^{4} d^{3} - \frac{3 \, {\left(a x + b\right)} b^{3} c^{3}}{x} + \frac{6 \, {\left(a x + b\right)} a b^{2} c^{2} d}{x} - \frac{6 \, {\left(a x + b\right)} a^{2} b c d^{2}}{x} + \frac{2 \, {\left(a x + b\right)} a^{3} d^{3}}{x}}{{\left(a \sqrt{\frac{a x + b}{x}} - \frac{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)} a^{2} b}}{b}"," ",0,"-(2*d^3*sqrt((a*x + b)/x)/b - 3*(b^2*c^3 - 2*a*b*c^2*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^2) - (2*a*b^3*c^3 - 6*a^2*b^2*c^2*d + 6*a^3*b*c*d^2 - 2*a^4*d^3 - 3*(a*x + b)*b^3*c^3/x + 6*(a*x + b)*a*b^2*c^2*d/x - 6*(a*x + b)*a^2*b*c*d^2/x + 2*(a*x + b)*a^3*d^3/x)/((a*sqrt((a*x + b)/x) - (a*x + b)*sqrt((a*x + b)/x)/x)*a^2*b))/b","A",0
253,1,160,0,0.226341," ","integrate((c+d/x)^2/(a+b/x)^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(3 \, b^{2} c^{2} - 4 \, a b c d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{2 \, a b^{2} c^{2} - 4 \, a^{2} b c d + 2 \, a^{3} d^{2} - \frac{3 \, {\left(a x + b\right)} b^{2} c^{2}}{x} + \frac{4 \, {\left(a x + b\right)} a b c d}{x} - \frac{2 \, {\left(a x + b\right)} a^{2} d^{2}}{x}}{{\left(a \sqrt{\frac{a x + b}{x}} - \frac{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)} a^{2}}}{b}"," ",0,"((3*b^2*c^2 - 4*a*b*c*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^2) + (2*a*b^2*c^2 - 4*a^2*b*c*d + 2*a^3*d^2 - 3*(a*x + b)*b^2*c^2/x + 4*(a*x + b)*a*b*c*d/x - 2*(a*x + b)*a^2*d^2/x)/((a*sqrt((a*x + b)/x) - (a*x + b)*sqrt((a*x + b)/x)/x)*a^2))/b","A",0
254,1,127,0,0.195523," ","integrate((c+d/x)/(a+b/x)^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(3 \, b^{2} c - 2 \, a b d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{2 \, a b^{2} c - 2 \, a^{2} b d - \frac{3 \, {\left(a x + b\right)} b^{2} c}{x} + \frac{2 \, {\left(a x + b\right)} a b d}{x}}{{\left(a \sqrt{\frac{a x + b}{x}} - \frac{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)} a^{2}}}{b}"," ",0,"((3*b^2*c - 2*a*b*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^2) + (2*a*b^2*c - 2*a^2*b*d - 3*(a*x + b)*b^2*c/x + 2*(a*x + b)*a*b*d/x)/((a*sqrt((a*x + b)/x) - (a*x + b)*sqrt((a*x + b)/x)/x)*a^2))/b","A",0
255,1,86,0,0.164769," ","integrate(1/(a+b/x)^(3/2),x, algorithm=""giac"")","b {\left(\frac{3 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{2 \, a - \frac{3 \, {\left(a x + b\right)}}{x}}{{\left(a \sqrt{\frac{a x + b}{x}} - \frac{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)} a^{2}}\right)}"," ",0,"b*(3*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^2) + (2*a - 3*(a*x + b)/x)/((a*sqrt((a*x + b)/x) - (a*x + b)*sqrt((a*x + b)/x)/x)*a^2))","A",0
256,1,200,0,0.206492," ","integrate(1/(a+b/x)^(3/2)/(c+d/x),x, algorithm=""giac"")","{\left(\frac{2 \, d^{3} \arctan\left(\frac{d \sqrt{\frac{a x + b}{x}}}{\sqrt{b c d - a d^{2}}}\right)}{{\left(b^{3} c^{3} - a b^{2} c^{2} d\right)} \sqrt{b c d - a d^{2}}} + \frac{2 \, a b c - \frac{3 \, {\left(a x + b\right)} b c}{x} + \frac{{\left(a x + b\right)} a d}{x}}{{\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} {\left(a \sqrt{\frac{a x + b}{x}} - \frac{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)}} + \frac{{\left(3 \, b c + 2 \, a d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} b^{2} c^{2}}\right)} b^{2}"," ",0,"(2*d^3*arctan(d*sqrt((a*x + b)/x)/sqrt(b*c*d - a*d^2))/((b^3*c^3 - a*b^2*c^2*d)*sqrt(b*c*d - a*d^2)) + (2*a*b*c - 3*(a*x + b)*b*c/x + (a*x + b)*a*d/x)/((a^2*b^2*c^2 - a^3*b*c*d)*(a*sqrt((a*x + b)/x) - (a*x + b)*sqrt((a*x + b)/x)/x)) + (3*b*c + 2*a*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^2*b^2*c^2))*b^2","A",0
257,1,424,0,0.256482," ","integrate(1/(a+b/x)^(3/2)/(c+d/x)^2,x, algorithm=""giac"")","b^{3} {\left(\frac{{\left(7 \, b c d^{3} - 4 \, a d^{4}\right)} \arctan\left(\frac{d \sqrt{\frac{a x + b}{x}}}{\sqrt{b c d - a d^{2}}}\right)}{{\left(b^{5} c^{5} - 2 \, a b^{4} c^{4} d + a^{2} b^{3} c^{3} d^{2}\right)} \sqrt{b c d - a d^{2}}} + \frac{2 \, a b^{3} c^{3} - 2 \, a^{2} b^{2} c^{2} d - \frac{3 \, {\left(a x + b\right)} b^{3} c^{3}}{x} + \frac{7 \, {\left(a x + b\right)} a b^{2} c^{2} d}{x} - \frac{3 \, {\left(a x + b\right)} a^{2} b c d^{2}}{x} + \frac{2 \, {\left(a x + b\right)} a^{3} d^{3}}{x} - \frac{3 \, {\left(a x + b\right)}^{2} b^{2} c^{2} d}{x^{2}} + \frac{2 \, {\left(a x + b\right)}^{2} a b c d^{2}}{x^{2}} - \frac{2 \, {\left(a x + b\right)}^{2} a^{2} d^{3}}{x^{2}}}{{\left(a^{2} b^{4} c^{4} - 2 \, a^{3} b^{3} c^{3} d + a^{4} b^{2} c^{2} d^{2}\right)} {\left(a b c \sqrt{\frac{a x + b}{x}} - a^{2} d \sqrt{\frac{a x + b}{x}} - \frac{{\left(a x + b\right)} b c \sqrt{\frac{a x + b}{x}}}{x} + \frac{2 \, {\left(a x + b\right)} a d \sqrt{\frac{a x + b}{x}}}{x} - \frac{{\left(a x + b\right)}^{2} d \sqrt{\frac{a x + b}{x}}}{x^{2}}\right)}} + \frac{{\left(3 \, b c + 4 \, a d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} b^{3} c^{3}}\right)}"," ",0,"b^3*((7*b*c*d^3 - 4*a*d^4)*arctan(d*sqrt((a*x + b)/x)/sqrt(b*c*d - a*d^2))/((b^5*c^5 - 2*a*b^4*c^4*d + a^2*b^3*c^3*d^2)*sqrt(b*c*d - a*d^2)) + (2*a*b^3*c^3 - 2*a^2*b^2*c^2*d - 3*(a*x + b)*b^3*c^3/x + 7*(a*x + b)*a*b^2*c^2*d/x - 3*(a*x + b)*a^2*b*c*d^2/x + 2*(a*x + b)*a^3*d^3/x - 3*(a*x + b)^2*b^2*c^2*d/x^2 + 2*(a*x + b)^2*a*b*c*d^2/x^2 - 2*(a*x + b)^2*a^2*d^3/x^2)/((a^2*b^4*c^4 - 2*a^3*b^3*c^3*d + a^4*b^2*c^2*d^2)*(a*b*c*sqrt((a*x + b)/x) - a^2*d*sqrt((a*x + b)/x) - (a*x + b)*b*c*sqrt((a*x + b)/x)/x + 2*(a*x + b)*a*d*sqrt((a*x + b)/x)/x - (a*x + b)^2*d*sqrt((a*x + b)/x)/x^2)) + (3*b*c + 4*a*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^2*b^3*c^3))","B",0
258,1,516,0,0.308656," ","integrate(1/(a+b/x)^(3/2)/(c+d/x)^3,x, algorithm=""giac"")","\frac{1}{4} \, b^{4} {\left(\frac{3 \, {\left(21 \, b^{2} c^{2} d^{3} - 24 \, a b c d^{4} + 8 \, a^{2} d^{5}\right)} \arctan\left(\frac{d \sqrt{\frac{a x + b}{x}}}{\sqrt{b c d - a d^{2}}}\right)}{{\left(b^{7} c^{7} - 3 \, a b^{6} c^{6} d + 3 \, a^{2} b^{5} c^{5} d^{2} - a^{3} b^{4} c^{4} d^{3}\right)} \sqrt{b c d - a d^{2}}} + \frac{4 \, {\left(2 \, a b^{3} c^{3} - \frac{3 \, {\left(a x + b\right)} b^{3} c^{3}}{x} + \frac{3 \, {\left(a x + b\right)} a b^{2} c^{2} d}{x} - \frac{3 \, {\left(a x + b\right)} a^{2} b c d^{2}}{x} + \frac{{\left(a x + b\right)} a^{3} d^{3}}{x}\right)}}{{\left(a^{2} b^{6} c^{6} - 3 \, a^{3} b^{5} c^{5} d + 3 \, a^{4} b^{4} c^{4} d^{2} - a^{5} b^{3} c^{3} d^{3}\right)} {\left(a \sqrt{\frac{a x + b}{x}} - \frac{{\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}}{x}\right)}} + \frac{17 \, b^{2} c^{2} d^{3} \sqrt{\frac{a x + b}{x}} - 25 \, a b c d^{4} \sqrt{\frac{a x + b}{x}} + 8 \, a^{2} d^{5} \sqrt{\frac{a x + b}{x}} + \frac{15 \, {\left(a x + b\right)} b c d^{4} \sqrt{\frac{a x + b}{x}}}{x} - \frac{8 \, {\left(a x + b\right)} a d^{5} \sqrt{\frac{a x + b}{x}}}{x}}{{\left(b^{6} c^{6} - 3 \, a b^{5} c^{5} d + 3 \, a^{2} b^{4} c^{4} d^{2} - a^{3} b^{3} c^{3} d^{3}\right)} {\left(b c - a d + \frac{{\left(a x + b\right)} d}{x}\right)}^{2}} + \frac{12 \, {\left(b c + 2 \, a d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} b^{4} c^{4}}\right)}"," ",0,"1/4*b^4*(3*(21*b^2*c^2*d^3 - 24*a*b*c*d^4 + 8*a^2*d^5)*arctan(d*sqrt((a*x + b)/x)/sqrt(b*c*d - a*d^2))/((b^7*c^7 - 3*a*b^6*c^6*d + 3*a^2*b^5*c^5*d^2 - a^3*b^4*c^4*d^3)*sqrt(b*c*d - a*d^2)) + 4*(2*a*b^3*c^3 - 3*(a*x + b)*b^3*c^3/x + 3*(a*x + b)*a*b^2*c^2*d/x - 3*(a*x + b)*a^2*b*c*d^2/x + (a*x + b)*a^3*d^3/x)/((a^2*b^6*c^6 - 3*a^3*b^5*c^5*d + 3*a^4*b^4*c^4*d^2 - a^5*b^3*c^3*d^3)*(a*sqrt((a*x + b)/x) - (a*x + b)*sqrt((a*x + b)/x)/x)) + (17*b^2*c^2*d^3*sqrt((a*x + b)/x) - 25*a*b*c*d^4*sqrt((a*x + b)/x) + 8*a^2*d^5*sqrt((a*x + b)/x) + 15*(a*x + b)*b*c*d^4*sqrt((a*x + b)/x)/x - 8*(a*x + b)*a*d^5*sqrt((a*x + b)/x)/x)/((b^6*c^6 - 3*a*b^5*c^5*d + 3*a^2*b^4*c^4*d^2 - a^3*b^3*c^3*d^3)*(b*c - a*d + (a*x + b)*d/x)^2) + 12*(b*c + 2*a*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^2*b^4*c^4))","A",0
259,1,203,0,0.256061," ","integrate((c+d/x)^3/(a+b/x)^(5/2),x, algorithm=""giac"")","-\frac{\frac{3 \, b^{2} c^{3} \sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a^{3}} - \frac{3 \, {\left(5 \, b^{2} c^{3} - 6 \, a b c^{2} d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} - \frac{2 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3} + \frac{6 \, {\left(a x + b\right)} b^{3} c^{3}}{x} - \frac{9 \, {\left(a x + b\right)} a b^{2} c^{2} d}{x} + \frac{3 \, {\left(a x + b\right)} a^{3} d^{3}}{x}\right)} x}{{\left(a x + b\right)} a^{3} b \sqrt{\frac{a x + b}{x}}}}{3 \, b}"," ",0,"-1/3*(3*b^2*c^3*sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a^3) - 3*(5*b^2*c^3 - 6*a*b*c^2*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^3) - 2*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3 + 6*(a*x + b)*b^3*c^3/x - 9*(a*x + b)*a*b^2*c^2*d/x + 3*(a*x + b)*a^3*d^3/x)*x/((a*x + b)*a^3*b*sqrt((a*x + b)/x)))/b","A",0
260,1,163,0,0.205396," ","integrate((c+d/x)^2/(a+b/x)^(5/2),x, algorithm=""giac"")","-\frac{\frac{3 \, b^{2} c^{2} \sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a^{3}} - \frac{3 \, {\left(5 \, b^{2} c^{2} - 4 \, a b c d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} - \frac{2 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2} + \frac{6 \, {\left(a x + b\right)} b^{2} c^{2}}{x} - \frac{6 \, {\left(a x + b\right)} a b c d}{x}\right)} x}{{\left(a x + b\right)} a^{3} \sqrt{\frac{a x + b}{x}}}}{3 \, b}"," ",0,"-1/3*(3*b^2*c^2*sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a^3) - 3*(5*b^2*c^2 - 4*a*b*c*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^3) - 2*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2 + 6*(a*x + b)*b^2*c^2/x - 6*(a*x + b)*a*b*c*d/x)*x/((a*x + b)*a^3*sqrt((a*x + b)/x)))/b","A",0
261,1,145,0,0.219883," ","integrate((c+d/x)/(a+b/x)^(5/2),x, algorithm=""giac"")","-\frac{\frac{3 \, b^{2} c \sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a^{3}} - \frac{3 \, {\left(5 \, b^{2} c - 2 \, a b d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} - \frac{2 \, {\left(a b^{2} c - a^{2} b d + \frac{6 \, {\left(a x + b\right)} b^{2} c}{x} - \frac{3 \, {\left(a x + b\right)} a b d}{x}\right)} x}{{\left(a x + b\right)} a^{3} \sqrt{\frac{a x + b}{x}}}}{3 \, b}"," ",0,"-1/3*(3*b^2*c*sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a^3) - 3*(5*b^2*c - 2*a*b*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^3) - 2*(a*b^2*c - a^2*b*d + 6*(a*x + b)*b^2*c/x - 3*(a*x + b)*a*b*d/x)*x/((a*x + b)*a^3*sqrt((a*x + b)/x)))/b","A",0
262,1,98,0,0.238604," ","integrate(1/(a+b/x)^(5/2),x, algorithm=""giac"")","\frac{1}{3} \, b {\left(\frac{2 \, {\left(a + \frac{6 \, {\left(a x + b\right)}}{x}\right)} x}{{\left(a x + b\right)} a^{3} \sqrt{\frac{a x + b}{x}}} + \frac{15 \, \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} - \frac{3 \, \sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a^{3}}\right)}"," ",0,"1/3*b*(2*(a + 6*(a*x + b)/x)*x/((a*x + b)*a^3*sqrt((a*x + b)/x)) + 15*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^3) - 3*sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a^3))","A",0
263,1,247,0,0.219499," ","integrate(1/(a+b/x)^(5/2)/(c+d/x),x, algorithm=""giac"")","-\frac{1}{3} \, {\left(\frac{6 \, d^{4} \arctan\left(\frac{d \sqrt{\frac{a x + b}{x}}}{\sqrt{b c d - a d^{2}}}\right)}{{\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + a^{2} b^{2} c^{2} d^{2}\right)} \sqrt{b c d - a d^{2}}} - \frac{2 \, {\left(a b c - a^{2} d + \frac{6 \, {\left(a x + b\right)} b c}{x} - \frac{9 \, {\left(a x + b\right)} a d}{x}\right)} x}{{\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2}\right)} {\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}} + \frac{3 \, \sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a^{3} b c} - \frac{3 \, {\left(5 \, b c + 2 \, a d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3} b^{2} c^{2}}\right)} b^{2}"," ",0,"-1/3*(6*d^4*arctan(d*sqrt((a*x + b)/x)/sqrt(b*c*d - a*d^2))/((b^4*c^4 - 2*a*b^3*c^3*d + a^2*b^2*c^2*d^2)*sqrt(b*c*d - a*d^2)) - 2*(a*b*c - a^2*d + 6*(a*x + b)*b*c/x - 9*(a*x + b)*a*d/x)*x/((a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2)*(a*x + b)*sqrt((a*x + b)/x)) + 3*sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a^3*b*c) - 3*(5*b*c + 2*a*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^3*b^2*c^2))*b^2","A",0
264,1,576,0,0.325595," ","integrate(1/(a+b/x)^(5/2)/(c+d/x)^2,x, algorithm=""giac"")","-\frac{1}{3} \, b^{3} {\left(\frac{3 \, {\left(9 \, b c d^{4} - 4 \, a d^{5}\right)} \arctan\left(\frac{d \sqrt{\frac{a x + b}{x}}}{\sqrt{b c d - a d^{2}}}\right)}{{\left(b^{6} c^{6} - 3 \, a b^{5} c^{5} d + 3 \, a^{2} b^{4} c^{4} d^{2} - a^{3} b^{3} c^{3} d^{3}\right)} \sqrt{b c d - a d^{2}}} - \frac{2 \, {\left(a b c - a^{2} d + \frac{6 \, {\left(a x + b\right)} b c}{x} - \frac{12 \, {\left(a x + b\right)} a d}{x}\right)} x}{{\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} {\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}} + \frac{3 \, {\left(b^{4} c^{4} \sqrt{\frac{a x + b}{x}} - 4 \, a b^{3} c^{3} d \sqrt{\frac{a x + b}{x}} + 6 \, a^{2} b^{2} c^{2} d^{2} \sqrt{\frac{a x + b}{x}} - 4 \, a^{3} b c d^{3} \sqrt{\frac{a x + b}{x}} + 2 \, a^{4} d^{4} \sqrt{\frac{a x + b}{x}} + \frac{{\left(a x + b\right)} b^{3} c^{3} d \sqrt{\frac{a x + b}{x}}}{x} - \frac{3 \, {\left(a x + b\right)} a b^{2} c^{2} d^{2} \sqrt{\frac{a x + b}{x}}}{x} + \frac{3 \, {\left(a x + b\right)} a^{2} b c d^{3} \sqrt{\frac{a x + b}{x}}}{x} - \frac{2 \, {\left(a x + b\right)} a^{3} d^{4} \sqrt{\frac{a x + b}{x}}}{x}\right)}}{{\left(a^{3} b^{5} c^{5} - 3 \, a^{4} b^{4} c^{4} d + 3 \, a^{5} b^{3} c^{3} d^{2} - a^{6} b^{2} c^{2} d^{3}\right)} {\left(a b c - a^{2} d - \frac{{\left(a x + b\right)} b c}{x} + \frac{2 \, {\left(a x + b\right)} a d}{x} - \frac{{\left(a x + b\right)}^{2} d}{x^{2}}\right)}} - \frac{3 \, {\left(5 \, b c + 4 \, a d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3} b^{3} c^{3}}\right)}"," ",0,"-1/3*b^3*(3*(9*b*c*d^4 - 4*a*d^5)*arctan(d*sqrt((a*x + b)/x)/sqrt(b*c*d - a*d^2))/((b^6*c^6 - 3*a*b^5*c^5*d + 3*a^2*b^4*c^4*d^2 - a^3*b^3*c^3*d^3)*sqrt(b*c*d - a*d^2)) - 2*(a*b*c - a^2*d + 6*(a*x + b)*b*c/x - 12*(a*x + b)*a*d/x)*x/((a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*(a*x + b)*sqrt((a*x + b)/x)) + 3*(b^4*c^4*sqrt((a*x + b)/x) - 4*a*b^3*c^3*d*sqrt((a*x + b)/x) + 6*a^2*b^2*c^2*d^2*sqrt((a*x + b)/x) - 4*a^3*b*c*d^3*sqrt((a*x + b)/x) + 2*a^4*d^4*sqrt((a*x + b)/x) + (a*x + b)*b^3*c^3*d*sqrt((a*x + b)/x)/x - 3*(a*x + b)*a*b^2*c^2*d^2*sqrt((a*x + b)/x)/x + 3*(a*x + b)*a^2*b*c*d^3*sqrt((a*x + b)/x)/x - 2*(a*x + b)*a^3*d^4*sqrt((a*x + b)/x)/x)/((a^3*b^5*c^5 - 3*a^4*b^4*c^4*d + 3*a^5*b^3*c^3*d^2 - a^6*b^2*c^2*d^3)*(a*b*c - a^2*d - (a*x + b)*b*c/x + 2*(a*x + b)*a*d/x - (a*x + b)^2*d/x^2)) - 3*(5*b*c + 4*a*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^3*b^3*c^3))","B",0
265,1,523,0,0.285366," ","integrate(1/(a+b/x)^(5/2)/(c+d/x)^3,x, algorithm=""giac"")","-\frac{1}{12} \, b^{4} {\left(\frac{3 \, {\left(99 \, b^{2} c^{2} d^{4} - 88 \, a b c d^{5} + 24 \, a^{2} d^{6}\right)} \arctan\left(\frac{d \sqrt{\frac{a x + b}{x}}}{\sqrt{b c d - a d^{2}}}\right)}{{\left(b^{8} c^{8} - 4 \, a b^{7} c^{7} d + 6 \, a^{2} b^{6} c^{6} d^{2} - 4 \, a^{3} b^{5} c^{5} d^{3} + a^{4} b^{4} c^{4} d^{4}\right)} \sqrt{b c d - a d^{2}}} - \frac{8 \, {\left(a b c - a^{2} d + \frac{6 \, {\left(a x + b\right)} b c}{x} - \frac{15 \, {\left(a x + b\right)} a d}{x}\right)} x}{{\left(a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}\right)} {\left(a x + b\right)} \sqrt{\frac{a x + b}{x}}} + \frac{3 \, {\left(21 \, b^{2} c^{2} d^{4} \sqrt{\frac{a x + b}{x}} - 29 \, a b c d^{5} \sqrt{\frac{a x + b}{x}} + 8 \, a^{2} d^{6} \sqrt{\frac{a x + b}{x}} + \frac{19 \, {\left(a x + b\right)} b c d^{5} \sqrt{\frac{a x + b}{x}}}{x} - \frac{8 \, {\left(a x + b\right)} a d^{6} \sqrt{\frac{a x + b}{x}}}{x}\right)}}{{\left(b^{7} c^{7} - 4 \, a b^{6} c^{6} d + 6 \, a^{2} b^{5} c^{5} d^{2} - 4 \, a^{3} b^{4} c^{4} d^{3} + a^{4} b^{3} c^{3} d^{4}\right)} {\left(b c - a d + \frac{{\left(a x + b\right)} d}{x}\right)}^{2}} + \frac{12 \, \sqrt{\frac{a x + b}{x}}}{{\left(a - \frac{a x + b}{x}\right)} a^{3} b^{3} c^{3}} - \frac{12 \, {\left(5 \, b c + 6 \, a d\right)} \arctan\left(\frac{\sqrt{\frac{a x + b}{x}}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3} b^{4} c^{4}}\right)}"," ",0,"-1/12*b^4*(3*(99*b^2*c^2*d^4 - 88*a*b*c*d^5 + 24*a^2*d^6)*arctan(d*sqrt((a*x + b)/x)/sqrt(b*c*d - a*d^2))/((b^8*c^8 - 4*a*b^7*c^7*d + 6*a^2*b^6*c^6*d^2 - 4*a^3*b^5*c^5*d^3 + a^4*b^4*c^4*d^4)*sqrt(b*c*d - a*d^2)) - 8*(a*b*c - a^2*d + 6*(a*x + b)*b*c/x - 15*(a*x + b)*a*d/x)*x/((a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4)*(a*x + b)*sqrt((a*x + b)/x)) + 3*(21*b^2*c^2*d^4*sqrt((a*x + b)/x) - 29*a*b*c*d^5*sqrt((a*x + b)/x) + 8*a^2*d^6*sqrt((a*x + b)/x) + 19*(a*x + b)*b*c*d^5*sqrt((a*x + b)/x)/x - 8*(a*x + b)*a*d^6*sqrt((a*x + b)/x)/x)/((b^7*c^7 - 4*a*b^6*c^6*d + 6*a^2*b^5*c^5*d^2 - 4*a^3*b^4*c^4*d^3 + a^4*b^3*c^3*d^4)*(b*c - a*d + (a*x + b)*d/x)^2) + 12*sqrt((a*x + b)/x)/((a - (a*x + b)/x)*a^3*b^3*c^3) - 12*(5*b*c + 6*a*d)*arctan(sqrt((a*x + b)/x)/sqrt(-a))/(sqrt(-a)*a^3*b^4*c^4))","A",0
266,0,0,0,0.000000," ","integrate((c+d/x)^(1/2)*(a+b/x)^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{x}} \sqrt{c + \frac{d}{x}}\,{d x}"," ",0,"integrate(sqrt(a + b/x)*sqrt(c + d/x), x)","F",0
267,0,0,0,0.000000," ","integrate((a+b/x)^(1/2)/(c+d/x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{x}}}{\sqrt{c + \frac{d}{x}}}\,{d x}"," ",0,"integrate(sqrt(a + b/x)/sqrt(c + d/x), x)","F",0
268,-2,0,0,0.000000," ","integrate((a+b/x)^(1/2)/(c+d/x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Unable to divide, perhaps due to rounding error%%%{%%%{1,[1]%%%},[2,1,2]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,3]%%%}+%%%{1,[0,1,4]%%%} / %%%{%%%{1,[2]%%%},[2,0,0]%%%}+%%%{%%{[%%%{-2,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,1]%%%}+%%%{%%%{1,[1]%%%},[0,0,2]%%%} Error: Bad Argument Value","F(-2)",0
269,0,0,0,0.000000," ","integrate((a+b/x)^p*(c+d/x)^q,x, algorithm=""giac"")","\int {\left(a + \frac{b}{x}\right)}^{p} {\left(c + \frac{d}{x}\right)}^{q}\,{d x}"," ",0,"integrate((a + b/x)^p*(c + d/x)^q, x)","F",0
270,1,33,0,0.153304," ","integrate((a+b/x^2)/(c+d/x^2),x, algorithm=""giac"")","\frac{a x}{c} + \frac{{\left(b c - a d\right)} \arctan\left(\frac{c x}{\sqrt{c d}}\right)}{\sqrt{c d} c}"," ",0,"a*x/c + (b*c - a*d)*arctan(c*x/sqrt(c*d))/(sqrt(c*d)*c)","A",0
271,0,0,0,0.000000," ","integrate((c+d/x^2)^(1/2)*(a+b/x^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{x^{2}}} \sqrt{c + \frac{d}{x^{2}}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^2)*sqrt(c + d/x^2), x)","F",0
272,0,0,0,0.000000," ","integrate((a+b/x^2)^(1/2)/(c+d/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{x^{2}}}}{\sqrt{c + \frac{d}{x^{2}}}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^2)/sqrt(c + d/x^2), x)","F",0
273,0,0,0,0.000000," ","integrate((a+b/x^2)^(1/2)/(c+d/x^2)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{x^{2}}}}{{\left(c + \frac{d}{x^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(a + b/x^2)/(c + d/x^2)^(3/2), x)","F",0
274,0,0,0,0.000000," ","integrate((a+b/x^2)^p*(c+d/x^2)^q,x, algorithm=""giac"")","\int {\left(a + \frac{b}{x^{2}}\right)}^{p} {\left(c + \frac{d}{x^{2}}\right)}^{q}\,{d x}"," ",0,"integrate((a + b/x^2)^p*(c + d/x^2)^q, x)","F",0
275,1,133,0,0.222117," ","integrate((a+b/x^3)/(c+d/x^3),x, algorithm=""giac"")","-\frac{\sqrt{3} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{d}{c}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{d}{c}\right)^{\frac{1}{3}}}\right)}{3 \, \left(-c^{2} d\right)^{\frac{2}{3}}} - \frac{{\left(b c - a d\right)} \log\left(x^{2} + x \left(-\frac{d}{c}\right)^{\frac{1}{3}} + \left(-\frac{d}{c}\right)^{\frac{2}{3}}\right)}{6 \, \left(-c^{2} d\right)^{\frac{2}{3}}} + \frac{a x}{c} - \frac{{\left(b c - a d\right)} \left(-\frac{d}{c}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{d}{c}\right)^{\frac{1}{3}} \right|}\right)}{3 \, c d}"," ",0,"-1/3*sqrt(3)*(b*c - a*d)*arctan(1/3*sqrt(3)*(2*x + (-d/c)^(1/3))/(-d/c)^(1/3))/(-c^2*d)^(2/3) - 1/6*(b*c - a*d)*log(x^2 + x*(-d/c)^(1/3) + (-d/c)^(2/3))/(-c^2*d)^(2/3) + a*x/c - 1/3*(b*c - a*d)*(-d/c)^(1/3)*log(abs(x - (-d/c)^(1/3)))/(c*d)","A",0
276,1,49,0,0.194640," ","integrate((a+b*x^(1/2))/(c+d*x^(1/2)),x, algorithm=""giac"")","\frac{b d x - 2 \, b c \sqrt{x} + 2 \, a d \sqrt{x}}{d^{2}} + \frac{2 \, {\left(b c^{2} - a c d\right)} \log\left({\left| d \sqrt{x} + c \right|}\right)}{d^{3}}"," ",0,"(b*d*x - 2*b*c*sqrt(x) + 2*a*d*sqrt(x))/d^2 + 2*(b*c^2 - a*c*d)*log(abs(d*sqrt(x) + c))/d^3","A",0
277,1,20,0,0.204570," ","integrate((-1+x^(1/3))/(1+x^(1/3)),x, algorithm=""giac"")","x - 3 \, x^{\frac{2}{3}} + 6 \, x^{\frac{1}{3}} - 6 \, \log\left(x^{\frac{1}{3}} + 1\right)"," ",0,"x - 3*x^(2/3) + 6*x^(1/3) - 6*log(x^(1/3) + 1)","A",0
278,1,24,0,0.182479," ","integrate((1+x^(2/3))/(-1+x^(2/3)),x, algorithm=""giac"")","x + 6 \, x^{\frac{1}{3}} - 3 \, \log\left(x^{\frac{1}{3}} + 1\right) + 3 \, \log\left({\left| x^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"x + 6*x^(1/3) - 3*log(x^(1/3) + 1) + 3*log(abs(x^(1/3) - 1))","A",0
279,1,71,0,0.165941," ","integrate((-16+x^(3/4))/(16+x^(3/4)),x, algorithm=""giac"")","\frac{256}{3} \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(-\frac{1}{6} \, \sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} - x^{\frac{1}{4}}\right)}\right) - \frac{128}{3} \cdot 2^{\frac{1}{3}} \log\left(4 \cdot 2^{\frac{2}{3}} - 2 \cdot 2^{\frac{1}{3}} x^{\frac{1}{4}} + \sqrt{x}\right) + \frac{256}{3} \cdot 2^{\frac{1}{3}} \log\left(2 \cdot 2^{\frac{1}{3}} + x^{\frac{1}{4}}\right) + x - 128 \, x^{\frac{1}{4}}"," ",0,"256/3*sqrt(3)*2^(1/3)*arctan(-1/6*sqrt(3)*2^(2/3)*(2^(1/3) - x^(1/4))) - 128/3*2^(1/3)*log(4*2^(2/3) - 2*2^(1/3)*x^(1/4) + sqrt(x)) + 256/3*2^(1/3)*log(2*2^(1/3) + x^(1/4)) + x - 128*x^(1/4)","A",0
280,1,23,0,0.151901," ","integrate((1+1/x^(1/3))/(-1+1/x^(1/3)),x, algorithm=""giac"")","-x - 3 \, x^{\frac{2}{3}} - 6 \, x^{\frac{1}{3}} - 6 \, \log\left({\left| x^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-x - 3*x^(2/3) - 6*x^(1/3) - 6*log(abs(x^(1/3) - 1))","A",0
281,0,0,0,0.000000," ","integrate((a-b*x^n)^(3/2)*(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{\frac{3}{2}} {\left(-b x^{n} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^(3/2)*(-b*x^n + a)^(3/2), x)","F",0
282,0,0,0,0.000000," ","integrate((a-b*x^n)^(1/2)*(a+b*x^n)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{n} + a} \sqrt{-b x^{n} + a}\,{d x}"," ",0,"integrate(sqrt(b*x^n + a)*sqrt(-b*x^n + a), x)","F",0
283,0,0,0,0.000000," ","integrate((a-b*x^n)^p*(a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} {\left(-b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(-b*x^n + a)^p, x)","F",0
284,1,740,0,0.215803," ","integrate((a+b*x^n)*(c+d*x^n)^4,x, algorithm=""giac"")","\frac{120 \, a c^{4} n^{5} x + 24 \, b d^{4} n^{4} x x^{5 \, n} + 120 \, b c d^{3} n^{4} x x^{4 \, n} + 30 \, a d^{4} n^{4} x x^{4 \, n} + 240 \, b c^{2} d^{2} n^{4} x x^{3 \, n} + 160 \, a c d^{3} n^{4} x x^{3 \, n} + 240 \, b c^{3} d n^{4} x x^{2 \, n} + 360 \, a c^{2} d^{2} n^{4} x x^{2 \, n} + 120 \, b c^{4} n^{4} x x^{n} + 480 \, a c^{3} d n^{4} x x^{n} + 274 \, a c^{4} n^{4} x + 50 \, b d^{4} n^{3} x x^{5 \, n} + 244 \, b c d^{3} n^{3} x x^{4 \, n} + 61 \, a d^{4} n^{3} x x^{4 \, n} + 468 \, b c^{2} d^{2} n^{3} x x^{3 \, n} + 312 \, a c d^{3} n^{3} x x^{3 \, n} + 428 \, b c^{3} d n^{3} x x^{2 \, n} + 642 \, a c^{2} d^{2} n^{3} x x^{2 \, n} + 154 \, b c^{4} n^{3} x x^{n} + 616 \, a c^{3} d n^{3} x x^{n} + 225 \, a c^{4} n^{3} x + 35 \, b d^{4} n^{2} x x^{5 \, n} + 164 \, b c d^{3} n^{2} x x^{4 \, n} + 41 \, a d^{4} n^{2} x x^{4 \, n} + 294 \, b c^{2} d^{2} n^{2} x x^{3 \, n} + 196 \, a c d^{3} n^{2} x x^{3 \, n} + 236 \, b c^{3} d n^{2} x x^{2 \, n} + 354 \, a c^{2} d^{2} n^{2} x x^{2 \, n} + 71 \, b c^{4} n^{2} x x^{n} + 284 \, a c^{3} d n^{2} x x^{n} + 85 \, a c^{4} n^{2} x + 10 \, b d^{4} n x x^{5 \, n} + 44 \, b c d^{3} n x x^{4 \, n} + 11 \, a d^{4} n x x^{4 \, n} + 72 \, b c^{2} d^{2} n x x^{3 \, n} + 48 \, a c d^{3} n x x^{3 \, n} + 52 \, b c^{3} d n x x^{2 \, n} + 78 \, a c^{2} d^{2} n x x^{2 \, n} + 14 \, b c^{4} n x x^{n} + 56 \, a c^{3} d n x x^{n} + 15 \, a c^{4} n x + b d^{4} x x^{5 \, n} + 4 \, b c d^{3} x x^{4 \, n} + a d^{4} x x^{4 \, n} + 6 \, b c^{2} d^{2} x x^{3 \, n} + 4 \, a c d^{3} x x^{3 \, n} + 4 \, b c^{3} d x x^{2 \, n} + 6 \, a c^{2} d^{2} x x^{2 \, n} + b c^{4} x x^{n} + 4 \, a c^{3} d x x^{n} + a c^{4} x}{120 \, n^{5} + 274 \, n^{4} + 225 \, n^{3} + 85 \, n^{2} + 15 \, n + 1}"," ",0,"(120*a*c^4*n^5*x + 24*b*d^4*n^4*x*x^(5*n) + 120*b*c*d^3*n^4*x*x^(4*n) + 30*a*d^4*n^4*x*x^(4*n) + 240*b*c^2*d^2*n^4*x*x^(3*n) + 160*a*c*d^3*n^4*x*x^(3*n) + 240*b*c^3*d*n^4*x*x^(2*n) + 360*a*c^2*d^2*n^4*x*x^(2*n) + 120*b*c^4*n^4*x*x^n + 480*a*c^3*d*n^4*x*x^n + 274*a*c^4*n^4*x + 50*b*d^4*n^3*x*x^(5*n) + 244*b*c*d^3*n^3*x*x^(4*n) + 61*a*d^4*n^3*x*x^(4*n) + 468*b*c^2*d^2*n^3*x*x^(3*n) + 312*a*c*d^3*n^3*x*x^(3*n) + 428*b*c^3*d*n^3*x*x^(2*n) + 642*a*c^2*d^2*n^3*x*x^(2*n) + 154*b*c^4*n^3*x*x^n + 616*a*c^3*d*n^3*x*x^n + 225*a*c^4*n^3*x + 35*b*d^4*n^2*x*x^(5*n) + 164*b*c*d^3*n^2*x*x^(4*n) + 41*a*d^4*n^2*x*x^(4*n) + 294*b*c^2*d^2*n^2*x*x^(3*n) + 196*a*c*d^3*n^2*x*x^(3*n) + 236*b*c^3*d*n^2*x*x^(2*n) + 354*a*c^2*d^2*n^2*x*x^(2*n) + 71*b*c^4*n^2*x*x^n + 284*a*c^3*d*n^2*x*x^n + 85*a*c^4*n^2*x + 10*b*d^4*n*x*x^(5*n) + 44*b*c*d^3*n*x*x^(4*n) + 11*a*d^4*n*x*x^(4*n) + 72*b*c^2*d^2*n*x*x^(3*n) + 48*a*c*d^3*n*x*x^(3*n) + 52*b*c^3*d*n*x*x^(2*n) + 78*a*c^2*d^2*n*x*x^(2*n) + 14*b*c^4*n*x*x^n + 56*a*c^3*d*n*x*x^n + 15*a*c^4*n*x + b*d^4*x*x^(5*n) + 4*b*c*d^3*x*x^(4*n) + a*d^4*x*x^(4*n) + 6*b*c^2*d^2*x*x^(3*n) + 4*a*c*d^3*x*x^(3*n) + 4*b*c^3*d*x*x^(2*n) + 6*a*c^2*d^2*x*x^(2*n) + b*c^4*x*x^n + 4*a*c^3*d*x*x^n + a*c^4*x)/(120*n^5 + 274*n^4 + 225*n^3 + 85*n^2 + 15*n + 1)","B",0
285,1,450,0,0.193476," ","integrate((a+b*x^n)*(c+d*x^n)^3,x, algorithm=""giac"")","\frac{24 \, a c^{3} n^{4} x + 6 \, b d^{3} n^{3} x x^{4 \, n} + 24 \, b c d^{2} n^{3} x x^{3 \, n} + 8 \, a d^{3} n^{3} x x^{3 \, n} + 36 \, b c^{2} d n^{3} x x^{2 \, n} + 36 \, a c d^{2} n^{3} x x^{2 \, n} + 24 \, b c^{3} n^{3} x x^{n} + 72 \, a c^{2} d n^{3} x x^{n} + 50 \, a c^{3} n^{3} x + 11 \, b d^{3} n^{2} x x^{4 \, n} + 42 \, b c d^{2} n^{2} x x^{3 \, n} + 14 \, a d^{3} n^{2} x x^{3 \, n} + 57 \, b c^{2} d n^{2} x x^{2 \, n} + 57 \, a c d^{2} n^{2} x x^{2 \, n} + 26 \, b c^{3} n^{2} x x^{n} + 78 \, a c^{2} d n^{2} x x^{n} + 35 \, a c^{3} n^{2} x + 6 \, b d^{3} n x x^{4 \, n} + 21 \, b c d^{2} n x x^{3 \, n} + 7 \, a d^{3} n x x^{3 \, n} + 24 \, b c^{2} d n x x^{2 \, n} + 24 \, a c d^{2} n x x^{2 \, n} + 9 \, b c^{3} n x x^{n} + 27 \, a c^{2} d n x x^{n} + 10 \, a c^{3} n x + b d^{3} x x^{4 \, n} + 3 \, b c d^{2} x x^{3 \, n} + a d^{3} x x^{3 \, n} + 3 \, b c^{2} d x x^{2 \, n} + 3 \, a c d^{2} x x^{2 \, n} + b c^{3} x x^{n} + 3 \, a c^{2} d x x^{n} + a c^{3} x}{24 \, n^{4} + 50 \, n^{3} + 35 \, n^{2} + 10 \, n + 1}"," ",0,"(24*a*c^3*n^4*x + 6*b*d^3*n^3*x*x^(4*n) + 24*b*c*d^2*n^3*x*x^(3*n) + 8*a*d^3*n^3*x*x^(3*n) + 36*b*c^2*d*n^3*x*x^(2*n) + 36*a*c*d^2*n^3*x*x^(2*n) + 24*b*c^3*n^3*x*x^n + 72*a*c^2*d*n^3*x*x^n + 50*a*c^3*n^3*x + 11*b*d^3*n^2*x*x^(4*n) + 42*b*c*d^2*n^2*x*x^(3*n) + 14*a*d^3*n^2*x*x^(3*n) + 57*b*c^2*d*n^2*x*x^(2*n) + 57*a*c*d^2*n^2*x*x^(2*n) + 26*b*c^3*n^2*x*x^n + 78*a*c^2*d*n^2*x*x^n + 35*a*c^3*n^2*x + 6*b*d^3*n*x*x^(4*n) + 21*b*c*d^2*n*x*x^(3*n) + 7*a*d^3*n*x*x^(3*n) + 24*b*c^2*d*n*x*x^(2*n) + 24*a*c*d^2*n*x*x^(2*n) + 9*b*c^3*n*x*x^n + 27*a*c^2*d*n*x*x^n + 10*a*c^3*n*x + b*d^3*x*x^(4*n) + 3*b*c*d^2*x*x^(3*n) + a*d^3*x*x^(3*n) + 3*b*c^2*d*x*x^(2*n) + 3*a*c*d^2*x*x^(2*n) + b*c^3*x*x^n + 3*a*c^2*d*x*x^n + a*c^3*x)/(24*n^4 + 50*n^3 + 35*n^2 + 10*n + 1)","B",0
286,1,232,0,0.187810," ","integrate((a+b*x^n)*(c+d*x^n)^2,x, algorithm=""giac"")","\frac{6 \, a c^{2} n^{3} x + 2 \, b d^{2} n^{2} x x^{3 \, n} + 6 \, b c d n^{2} x x^{2 \, n} + 3 \, a d^{2} n^{2} x x^{2 \, n} + 6 \, b c^{2} n^{2} x x^{n} + 12 \, a c d n^{2} x x^{n} + 11 \, a c^{2} n^{2} x + 3 \, b d^{2} n x x^{3 \, n} + 8 \, b c d n x x^{2 \, n} + 4 \, a d^{2} n x x^{2 \, n} + 5 \, b c^{2} n x x^{n} + 10 \, a c d n x x^{n} + 6 \, a c^{2} n x + b d^{2} x x^{3 \, n} + 2 \, b c d x x^{2 \, n} + a d^{2} x x^{2 \, n} + b c^{2} x x^{n} + 2 \, a c d x x^{n} + a c^{2} x}{6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1}"," ",0,"(6*a*c^2*n^3*x + 2*b*d^2*n^2*x*x^(3*n) + 6*b*c*d*n^2*x*x^(2*n) + 3*a*d^2*n^2*x*x^(2*n) + 6*b*c^2*n^2*x*x^n + 12*a*c*d*n^2*x*x^n + 11*a*c^2*n^2*x + 3*b*d^2*n*x*x^(3*n) + 8*b*c*d*n*x*x^(2*n) + 4*a*d^2*n*x*x^(2*n) + 5*b*c^2*n*x*x^n + 10*a*c*d*n*x*x^n + 6*a*c^2*n*x + b*d^2*x*x^(3*n) + 2*b*c*d*x*x^(2*n) + a*d^2*x*x^(2*n) + b*c^2*x*x^n + 2*a*c*d*x*x^n + a*c^2*x)/(6*n^3 + 11*n^2 + 6*n + 1)","B",0
287,1,83,0,0.168710," ","integrate((a+b*x^n)*(c+d*x^n),x, algorithm=""giac"")","\frac{2 \, a c n^{2} x + b d n x x^{2 \, n} + 2 \, b c n x x^{n} + 2 \, a d n x x^{n} + 3 \, a c n x + b d x x^{2 \, n} + b c x x^{n} + a d x x^{n} + a c x}{2 \, n^{2} + 3 \, n + 1}"," ",0,"(2*a*c*n^2*x + b*d*n*x*x^(2*n) + 2*b*c*n*x*x^n + 2*a*d*n*x*x^n + 3*a*c*n*x + b*d*x*x^(2*n) + b*c*x*x^n + a*d*x*x^n + a*c*x)/(2*n^2 + 3*n + 1)","B",0
288,0,0,0,0.000000," ","integrate((a+b*x^n)/(c+d*x^n),x, algorithm=""giac"")","\int \frac{b x^{n} + a}{d x^{n} + c}\,{d x}"," ",0,"integrate((b*x^n + a)/(d*x^n + c), x)","F",0
289,0,0,0,0.000000," ","integrate((a+b*x^n)/(c+d*x^n)^2,x, algorithm=""giac"")","\int \frac{b x^{n} + a}{{\left(d x^{n} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^n + a)/(d*x^n + c)^2, x)","F",0
290,0,0,0,0.000000," ","integrate((a+b*x^n)/(c+d*x^n)^3,x, algorithm=""giac"")","\int \frac{b x^{n} + a}{{\left(d x^{n} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^n + a)/(d*x^n + c)^3, x)","F",0
291,0,0,0,0.000000," ","integrate((a+b*x^n)/(c+d*x^n)^4,x, algorithm=""giac"")","\int \frac{b x^{n} + a}{{\left(d x^{n} + c\right)}^{4}}\,{d x}"," ",0,"integrate((b*x^n + a)/(d*x^n + c)^4, x)","F",0
292,1,947,0,0.242707," ","integrate((a+b*x^n)^2*(d+e*x^n)^3,x, algorithm=""giac"")","\frac{120 \, a^{2} d^{3} n^{5} x + 60 \, b^{2} d^{3} n^{4} x x^{2 \, n} + 240 \, a b d^{3} n^{4} x x^{n} + 120 \, b^{2} d^{2} n^{4} x x^{3 \, n} e + 360 \, a b d^{2} n^{4} x x^{2 \, n} e + 360 \, a^{2} d^{2} n^{4} x x^{n} e + 274 \, a^{2} d^{3} n^{4} x + 107 \, b^{2} d^{3} n^{3} x x^{2 \, n} + 308 \, a b d^{3} n^{3} x x^{n} + 90 \, b^{2} d n^{4} x x^{4 \, n} e^{2} + 240 \, a b d n^{4} x x^{3 \, n} e^{2} + 180 \, a^{2} d n^{4} x x^{2 \, n} e^{2} + 234 \, b^{2} d^{2} n^{3} x x^{3 \, n} e + 642 \, a b d^{2} n^{3} x x^{2 \, n} e + 462 \, a^{2} d^{2} n^{3} x x^{n} e + 225 \, a^{2} d^{3} n^{3} x + 59 \, b^{2} d^{3} n^{2} x x^{2 \, n} + 142 \, a b d^{3} n^{2} x x^{n} + 24 \, b^{2} n^{4} x x^{5 \, n} e^{3} + 60 \, a b n^{4} x x^{4 \, n} e^{3} + 40 \, a^{2} n^{4} x x^{3 \, n} e^{3} + 183 \, b^{2} d n^{3} x x^{4 \, n} e^{2} + 468 \, a b d n^{3} x x^{3 \, n} e^{2} + 321 \, a^{2} d n^{3} x x^{2 \, n} e^{2} + 147 \, b^{2} d^{2} n^{2} x x^{3 \, n} e + 354 \, a b d^{2} n^{2} x x^{2 \, n} e + 213 \, a^{2} d^{2} n^{2} x x^{n} e + 85 \, a^{2} d^{3} n^{2} x + 13 \, b^{2} d^{3} n x x^{2 \, n} + 28 \, a b d^{3} n x x^{n} + 50 \, b^{2} n^{3} x x^{5 \, n} e^{3} + 122 \, a b n^{3} x x^{4 \, n} e^{3} + 78 \, a^{2} n^{3} x x^{3 \, n} e^{3} + 123 \, b^{2} d n^{2} x x^{4 \, n} e^{2} + 294 \, a b d n^{2} x x^{3 \, n} e^{2} + 177 \, a^{2} d n^{2} x x^{2 \, n} e^{2} + 36 \, b^{2} d^{2} n x x^{3 \, n} e + 78 \, a b d^{2} n x x^{2 \, n} e + 42 \, a^{2} d^{2} n x x^{n} e + 15 \, a^{2} d^{3} n x + b^{2} d^{3} x x^{2 \, n} + 2 \, a b d^{3} x x^{n} + 35 \, b^{2} n^{2} x x^{5 \, n} e^{3} + 82 \, a b n^{2} x x^{4 \, n} e^{3} + 49 \, a^{2} n^{2} x x^{3 \, n} e^{3} + 33 \, b^{2} d n x x^{4 \, n} e^{2} + 72 \, a b d n x x^{3 \, n} e^{2} + 39 \, a^{2} d n x x^{2 \, n} e^{2} + 3 \, b^{2} d^{2} x x^{3 \, n} e + 6 \, a b d^{2} x x^{2 \, n} e + 3 \, a^{2} d^{2} x x^{n} e + a^{2} d^{3} x + 10 \, b^{2} n x x^{5 \, n} e^{3} + 22 \, a b n x x^{4 \, n} e^{3} + 12 \, a^{2} n x x^{3 \, n} e^{3} + 3 \, b^{2} d x x^{4 \, n} e^{2} + 6 \, a b d x x^{3 \, n} e^{2} + 3 \, a^{2} d x x^{2 \, n} e^{2} + b^{2} x x^{5 \, n} e^{3} + 2 \, a b x x^{4 \, n} e^{3} + a^{2} x x^{3 \, n} e^{3}}{120 \, n^{5} + 274 \, n^{4} + 225 \, n^{3} + 85 \, n^{2} + 15 \, n + 1}"," ",0,"(120*a^2*d^3*n^5*x + 60*b^2*d^3*n^4*x*x^(2*n) + 240*a*b*d^3*n^4*x*x^n + 120*b^2*d^2*n^4*x*x^(3*n)*e + 360*a*b*d^2*n^4*x*x^(2*n)*e + 360*a^2*d^2*n^4*x*x^n*e + 274*a^2*d^3*n^4*x + 107*b^2*d^3*n^3*x*x^(2*n) + 308*a*b*d^3*n^3*x*x^n + 90*b^2*d*n^4*x*x^(4*n)*e^2 + 240*a*b*d*n^4*x*x^(3*n)*e^2 + 180*a^2*d*n^4*x*x^(2*n)*e^2 + 234*b^2*d^2*n^3*x*x^(3*n)*e + 642*a*b*d^2*n^3*x*x^(2*n)*e + 462*a^2*d^2*n^3*x*x^n*e + 225*a^2*d^3*n^3*x + 59*b^2*d^3*n^2*x*x^(2*n) + 142*a*b*d^3*n^2*x*x^n + 24*b^2*n^4*x*x^(5*n)*e^3 + 60*a*b*n^4*x*x^(4*n)*e^3 + 40*a^2*n^4*x*x^(3*n)*e^3 + 183*b^2*d*n^3*x*x^(4*n)*e^2 + 468*a*b*d*n^3*x*x^(3*n)*e^2 + 321*a^2*d*n^3*x*x^(2*n)*e^2 + 147*b^2*d^2*n^2*x*x^(3*n)*e + 354*a*b*d^2*n^2*x*x^(2*n)*e + 213*a^2*d^2*n^2*x*x^n*e + 85*a^2*d^3*n^2*x + 13*b^2*d^3*n*x*x^(2*n) + 28*a*b*d^3*n*x*x^n + 50*b^2*n^3*x*x^(5*n)*e^3 + 122*a*b*n^3*x*x^(4*n)*e^3 + 78*a^2*n^3*x*x^(3*n)*e^3 + 123*b^2*d*n^2*x*x^(4*n)*e^2 + 294*a*b*d*n^2*x*x^(3*n)*e^2 + 177*a^2*d*n^2*x*x^(2*n)*e^2 + 36*b^2*d^2*n*x*x^(3*n)*e + 78*a*b*d^2*n*x*x^(2*n)*e + 42*a^2*d^2*n*x*x^n*e + 15*a^2*d^3*n*x + b^2*d^3*x*x^(2*n) + 2*a*b*d^3*x*x^n + 35*b^2*n^2*x*x^(5*n)*e^3 + 82*a*b*n^2*x*x^(4*n)*e^3 + 49*a^2*n^2*x*x^(3*n)*e^3 + 33*b^2*d*n*x*x^(4*n)*e^2 + 72*a*b*d*n*x*x^(3*n)*e^2 + 39*a^2*d*n*x*x^(2*n)*e^2 + 3*b^2*d^2*x*x^(3*n)*e + 6*a*b*d^2*x*x^(2*n)*e + 3*a^2*d^2*x*x^n*e + a^2*d^3*x + 10*b^2*n*x*x^(5*n)*e^3 + 22*a*b*n*x*x^(4*n)*e^3 + 12*a^2*n*x*x^(3*n)*e^3 + 3*b^2*d*x*x^(4*n)*e^2 + 6*a*b*d*x*x^(3*n)*e^2 + 3*a^2*d*x*x^(2*n)*e^2 + b^2*x*x^(5*n)*e^3 + 2*a*b*x*x^(4*n)*e^3 + a^2*x*x^(3*n)*e^3)/(120*n^5 + 274*n^4 + 225*n^3 + 85*n^2 + 15*n + 1)","B",0
293,1,539,0,0.224633," ","integrate((a+b*x^n)^2*(d+e*x^n)^2,x, algorithm=""giac"")","\frac{24 \, a^{2} d^{2} n^{4} x + 12 \, b^{2} d^{2} n^{3} x x^{2 \, n} + 48 \, a b d^{2} n^{3} x x^{n} + 16 \, b^{2} d n^{3} x x^{3 \, n} e + 48 \, a b d n^{3} x x^{2 \, n} e + 48 \, a^{2} d n^{3} x x^{n} e + 50 \, a^{2} d^{2} n^{3} x + 19 \, b^{2} d^{2} n^{2} x x^{2 \, n} + 52 \, a b d^{2} n^{2} x x^{n} + 6 \, b^{2} n^{3} x x^{4 \, n} e^{2} + 16 \, a b n^{3} x x^{3 \, n} e^{2} + 12 \, a^{2} n^{3} x x^{2 \, n} e^{2} + 28 \, b^{2} d n^{2} x x^{3 \, n} e + 76 \, a b d n^{2} x x^{2 \, n} e + 52 \, a^{2} d n^{2} x x^{n} e + 35 \, a^{2} d^{2} n^{2} x + 8 \, b^{2} d^{2} n x x^{2 \, n} + 18 \, a b d^{2} n x x^{n} + 11 \, b^{2} n^{2} x x^{4 \, n} e^{2} + 28 \, a b n^{2} x x^{3 \, n} e^{2} + 19 \, a^{2} n^{2} x x^{2 \, n} e^{2} + 14 \, b^{2} d n x x^{3 \, n} e + 32 \, a b d n x x^{2 \, n} e + 18 \, a^{2} d n x x^{n} e + 10 \, a^{2} d^{2} n x + b^{2} d^{2} x x^{2 \, n} + 2 \, a b d^{2} x x^{n} + 6 \, b^{2} n x x^{4 \, n} e^{2} + 14 \, a b n x x^{3 \, n} e^{2} + 8 \, a^{2} n x x^{2 \, n} e^{2} + 2 \, b^{2} d x x^{3 \, n} e + 4 \, a b d x x^{2 \, n} e + 2 \, a^{2} d x x^{n} e + a^{2} d^{2} x + b^{2} x x^{4 \, n} e^{2} + 2 \, a b x x^{3 \, n} e^{2} + a^{2} x x^{2 \, n} e^{2}}{24 \, n^{4} + 50 \, n^{3} + 35 \, n^{2} + 10 \, n + 1}"," ",0,"(24*a^2*d^2*n^4*x + 12*b^2*d^2*n^3*x*x^(2*n) + 48*a*b*d^2*n^3*x*x^n + 16*b^2*d*n^3*x*x^(3*n)*e + 48*a*b*d*n^3*x*x^(2*n)*e + 48*a^2*d*n^3*x*x^n*e + 50*a^2*d^2*n^3*x + 19*b^2*d^2*n^2*x*x^(2*n) + 52*a*b*d^2*n^2*x*x^n + 6*b^2*n^3*x*x^(4*n)*e^2 + 16*a*b*n^3*x*x^(3*n)*e^2 + 12*a^2*n^3*x*x^(2*n)*e^2 + 28*b^2*d*n^2*x*x^(3*n)*e + 76*a*b*d*n^2*x*x^(2*n)*e + 52*a^2*d*n^2*x*x^n*e + 35*a^2*d^2*n^2*x + 8*b^2*d^2*n*x*x^(2*n) + 18*a*b*d^2*n*x*x^n + 11*b^2*n^2*x*x^(4*n)*e^2 + 28*a*b*n^2*x*x^(3*n)*e^2 + 19*a^2*n^2*x*x^(2*n)*e^2 + 14*b^2*d*n*x*x^(3*n)*e + 32*a*b*d*n*x*x^(2*n)*e + 18*a^2*d*n*x*x^n*e + 10*a^2*d^2*n*x + b^2*d^2*x*x^(2*n) + 2*a*b*d^2*x*x^n + 6*b^2*n*x*x^(4*n)*e^2 + 14*a*b*n*x*x^(3*n)*e^2 + 8*a^2*n*x*x^(2*n)*e^2 + 2*b^2*d*x*x^(3*n)*e + 4*a*b*d*x*x^(2*n)*e + 2*a^2*d*x*x^n*e + a^2*d^2*x + b^2*x*x^(4*n)*e^2 + 2*a*b*x*x^(3*n)*e^2 + a^2*x*x^(2*n)*e^2)/(24*n^4 + 50*n^3 + 35*n^2 + 10*n + 1)","B",0
294,1,232,0,0.271519," ","integrate((a+b*x^n)^2*(c+d*x^n),x, algorithm=""giac"")","\frac{6 \, a^{2} c n^{3} x + 2 \, b^{2} d n^{2} x x^{3 \, n} + 3 \, b^{2} c n^{2} x x^{2 \, n} + 6 \, a b d n^{2} x x^{2 \, n} + 12 \, a b c n^{2} x x^{n} + 6 \, a^{2} d n^{2} x x^{n} + 11 \, a^{2} c n^{2} x + 3 \, b^{2} d n x x^{3 \, n} + 4 \, b^{2} c n x x^{2 \, n} + 8 \, a b d n x x^{2 \, n} + 10 \, a b c n x x^{n} + 5 \, a^{2} d n x x^{n} + 6 \, a^{2} c n x + b^{2} d x x^{3 \, n} + b^{2} c x x^{2 \, n} + 2 \, a b d x x^{2 \, n} + 2 \, a b c x x^{n} + a^{2} d x x^{n} + a^{2} c x}{6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1}"," ",0,"(6*a^2*c*n^3*x + 2*b^2*d*n^2*x*x^(3*n) + 3*b^2*c*n^2*x*x^(2*n) + 6*a*b*d*n^2*x*x^(2*n) + 12*a*b*c*n^2*x*x^n + 6*a^2*d*n^2*x*x^n + 11*a^2*c*n^2*x + 3*b^2*d*n*x*x^(3*n) + 4*b^2*c*n*x*x^(2*n) + 8*a*b*d*n*x*x^(2*n) + 10*a*b*c*n*x*x^n + 5*a^2*d*n*x*x^n + 6*a^2*c*n*x + b^2*d*x*x^(3*n) + b^2*c*x*x^(2*n) + 2*a*b*d*x*x^(2*n) + 2*a*b*c*x*x^n + a^2*d*x*x^n + a^2*c*x)/(6*n^3 + 11*n^2 + 6*n + 1)","B",0
295,0,0,0,0.000000," ","integrate((a+b*x^n)^2/(c+d*x^n),x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{2}}{d x^{n} + c}\,{d x}"," ",0,"integrate((b*x^n + a)^2/(d*x^n + c), x)","F",0
296,0,0,0,0.000000," ","integrate((a+b*x^n)^2/(c+d*x^n)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{2}}{{\left(d x^{n} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^2/(d*x^n + c)^2, x)","F",0
297,0,0,0,0.000000," ","integrate((a+b*x^n)^2/(c+d*x^n)^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{2}}{{\left(d x^{n} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^n + a)^2/(d*x^n + c)^3, x)","F",0
298,0,0,0,0.000000," ","integrate((c+d*x^n)^4/(a+b*x^n),x, algorithm=""giac"")","\int \frac{{\left(d x^{n} + c\right)}^{4}}{b x^{n} + a}\,{d x}"," ",0,"integrate((d*x^n + c)^4/(b*x^n + a), x)","F",0
299,0,0,0,0.000000," ","integrate((c+d*x^n)^3/(a+b*x^n),x, algorithm=""giac"")","\int \frac{{\left(d x^{n} + c\right)}^{3}}{b x^{n} + a}\,{d x}"," ",0,"integrate((d*x^n + c)^3/(b*x^n + a), x)","F",0
300,0,0,0,0.000000," ","integrate((c+d*x^n)^2/(a+b*x^n),x, algorithm=""giac"")","\int \frac{{\left(d x^{n} + c\right)}^{2}}{b x^{n} + a}\,{d x}"," ",0,"integrate((d*x^n + c)^2/(b*x^n + a), x)","F",0
301,0,0,0,0.000000," ","integrate((c+d*x^n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{d x^{n} + c}{b x^{n} + a}\,{d x}"," ",0,"integrate((d*x^n + c)/(b*x^n + a), x)","F",0
302,0,0,0,0.000000," ","integrate(1/(a+b*x^n)/(c+d*x^n),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)} {\left(d x^{n} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*(d*x^n + c)), x)","F",0
303,0,0,0,0.000000," ","integrate(1/(a+b*x^n)/(c+d*x^n)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)} {\left(d x^{n} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*(d*x^n + c)^2), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(a+b*x^n)/(c+d*x^n)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)} {\left(d x^{n} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*(d*x^n + c)^3), x)","F",0
305,0,0,0,0.000000," ","integrate((c+d*x^n)^4/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{{\left(d x^{n} + c\right)}^{4}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^n + c)^4/(b*x^n + a)^2, x)","F",0
306,0,0,0,0.000000," ","integrate((c+d*x^n)^3/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{{\left(d x^{n} + c\right)}^{3}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^n + c)^3/(b*x^n + a)^2, x)","F",0
307,0,0,0,0.000000," ","integrate((c+d*x^n)^2/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{{\left(d x^{n} + c\right)}^{2}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^n + c)^2/(b*x^n + a)^2, x)","F",0
308,0,0,0,0.000000," ","integrate((c+d*x^n)/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{d x^{n} + c}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^n + c)/(b*x^n + a)^2, x)","F",0
309,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{2} {\left(d x^{n} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^2*(d*x^n + c)), x)","F",0
310,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^2/(c+d*x^n)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{2} {\left(d x^{n} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^2*(d*x^n + c)^2), x)","F",0
311,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^2/(c+d*x^n)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{2} {\left(d x^{n} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^2*(d*x^n + c)^3), x)","F",0
312,0,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n)^q,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(d*x^n + c)^q, x)","F",0
313,-2,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2,0,6,4,2,4,4,3,0]%%%}+%%%{4,[2,0,6,4,2,3,4,3,0]%%%}+%%%{6,[2,0,6,4,2,2,4,3,0]%%%}+%%%{4,[2,0,6,4,2,1,4,3,0]%%%}+%%%{1,[2,0,6,4,2,0,4,3,0]%%%}+%%%{3,[1,0,6,4,2,4,4,2,1]%%%}+%%%{12,[1,0,6,4,2,3,4,2,1]%%%}+%%%{18,[1,0,6,4,2,2,4,2,1]%%%}+%%%{12,[1,0,6,4,2,1,4,2,1]%%%}+%%%{3,[1,0,6,4,2,0,4,2,1]%%%}+%%%{-1,[1,0,6,4,1,4,5,3,0]%%%}+%%%{-4,[1,0,6,4,1,3,5,3,0]%%%}+%%%{-6,[1,0,6,4,1,2,5,3,0]%%%}+%%%{-4,[1,0,6,4,1,1,5,3,0]%%%}+%%%{-1,[1,0,6,4,1,0,5,3,0]%%%}+%%%{1,[0,0,6,4,3,4,3,0,3]%%%}+%%%{4,[0,0,6,4,3,3,3,0,3]%%%}+%%%{6,[0,0,6,4,3,2,3,0,3]%%%}+%%%{4,[0,0,6,4,3,1,3,0,3]%%%}+%%%{1,[0,0,6,4,3,0,3,0,3]%%%}+%%%{1,[0,0,6,3,3,3,3,0,3]%%%}+%%%{3,[0,0,6,3,3,2,3,0,3]%%%}+%%%{3,[0,0,6,3,3,1,3,0,3]%%%}+%%%{1,[0,0,6,3,3,0,3,0,3]%%%}+%%%{-3,[0,0,6,3,2,3,4,1,2]%%%}+%%%{-9,[0,0,6,3,2,2,4,1,2]%%%}+%%%{-9,[0,0,6,3,2,1,4,1,2]%%%}+%%%{-3,[0,0,6,3,2,0,4,1,2]%%%}+%%%{3,[0,0,6,3,1,3,5,2,1]%%%}+%%%{9,[0,0,6,3,1,2,5,2,1]%%%}+%%%{9,[0,0,6,3,1,1,5,2,1]%%%}+%%%{3,[0,0,6,3,1,0,5,2,1]%%%}+%%%{-1,[0,0,6,3,0,3,6,3,0]%%%}+%%%{-3,[0,0,6,3,0,2,6,3,0]%%%}+%%%{-3,[0,0,6,3,0,1,6,3,0]%%%}+%%%{-1,[0,0,6,3,0,0,6,3,0]%%%} / %%%{1,[0,0,7,4,3,4,4,0,0]%%%}+%%%{4,[0,0,7,4,3,3,4,0,0]%%%}+%%%{6,[0,0,7,4,3,2,4,0,0]%%%}+%%%{4,[0,0,7,4,3,1,4,0,0]%%%}+%%%{1,[0,0,7,4,3,0,4,0,0]%%%} Error: Bad Argument Value","F(-2)",0
314,-2,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{-1,[1,0,4,3,1,3,3,2,0]%%%}+%%%{-3,[1,0,4,3,1,2,3,2,0]%%%}+%%%{-3,[1,0,4,3,1,1,3,2,0]%%%}+%%%{-1,[1,0,4,3,1,0,3,2,0]%%%}+%%%{-1,[0,0,4,3,2,3,2,0,2]%%%}+%%%{-3,[0,0,4,3,2,2,2,0,2]%%%}+%%%{-3,[0,0,4,3,2,1,2,0,2]%%%}+%%%{-1,[0,0,4,3,2,0,2,0,2]%%%}+%%%{-1,[0,0,4,2,2,2,2,0,2]%%%}+%%%{-2,[0,0,4,2,2,1,2,0,2]%%%}+%%%{-1,[0,0,4,2,2,0,2,0,2]%%%}+%%%{2,[0,0,4,2,1,2,3,1,1]%%%}+%%%{4,[0,0,4,2,1,1,3,1,1]%%%}+%%%{2,[0,0,4,2,1,0,3,1,1]%%%}+%%%{-1,[0,0,4,2,0,2,4,2,0]%%%}+%%%{-2,[0,0,4,2,0,1,4,2,0]%%%}+%%%{-1,[0,0,4,2,0,0,4,2,0]%%%} / %%%{-1,[0,0,5,3,2,3,3,0,0]%%%}+%%%{-3,[0,0,5,3,2,2,3,0,0]%%%}+%%%{-3,[0,0,5,3,2,1,3,0,0]%%%}+%%%{-1,[0,0,5,3,2,0,3,0,0]%%%} Error: Bad Argument Value","F(-2)",0
315,-2,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[0,0,2,2,1,2,1,0,1]%%%}+%%%{2,[0,0,2,2,1,1,1,0,1]%%%}+%%%{1,[0,0,2,2,1,0,1,0,1]%%%}+%%%{1,[0,0,2,1,1,1,1,0,1]%%%}+%%%{1,[0,0,2,1,1,0,1,0,1]%%%}+%%%{-1,[0,0,2,1,0,1,2,1,0]%%%}+%%%{-1,[0,0,2,1,0,0,2,1,0]%%%} / %%%{1,[0,0,3,2,1,2,2,0,0]%%%}+%%%{2,[0,0,3,2,1,1,2,0,0]%%%}+%%%{1,[0,0,3,2,1,0,2,0,0]%%%} Error: Bad Argument Value","F(-2)",0
316,0,0,0,0.000000," ","integrate((a+b*x^n)^p,x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*x^n + a)^p, x)","F",0
317,0,0,0,0.000000," ","integrate((a+b*x^n)^p/(c+d*x^n),x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{p}}{d x^{n} + c}\,{d x}"," ",0,"integrate((b*x^n + a)^p/(d*x^n + c), x)","F",0
318,0,0,0,0.000000," ","integrate((a+b*x^n)^p/(c+d*x^n)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{p}}{{\left(d x^{n} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^n + a)^p/(d*x^n + c)^2, x)","F",0
319,0,0,0,0.000000," ","integrate((a+b*x^n)^p/(c+d*x^n)^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{n} + a\right)}^{p}}{{\left(d x^{n} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^n + a)^p/(d*x^n + c)^3, x)","F",0
320,0,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n)^(-1-1/n-p),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{-p - \frac{1}{n} - 1}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(d*x^n + c)^(-p - 1/n - 1), x)","F",0
321,-2,0,0,0.000000," ","integrate((a+b*x^n)^3*(c+d*x^n)^(-4-1/n),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{81,[2,0,6,4,2,4,3,0]%%%}+%%%{108,[2,0,6,3,2,4,3,0]%%%}+%%%{54,[2,0,6,2,2,4,3,0]%%%}+%%%{12,[2,0,6,1,2,4,3,0]%%%}+%%%{1,[2,0,6,0,2,4,3,0]%%%}+%%%{243,[1,0,6,4,2,4,2,1]%%%}+%%%{-81,[1,0,6,4,1,5,3,0]%%%}+%%%{324,[1,0,6,3,2,4,2,1]%%%}+%%%{-108,[1,0,6,3,1,5,3,0]%%%}+%%%{162,[1,0,6,2,2,4,2,1]%%%}+%%%{-54,[1,0,6,2,1,5,3,0]%%%}+%%%{36,[1,0,6,1,2,4,2,1]%%%}+%%%{-12,[1,0,6,1,1,5,3,0]%%%}+%%%{3,[1,0,6,0,2,4,2,1]%%%}+%%%{-1,[1,0,6,0,1,5,3,0]%%%}+%%%{81,[0,0,6,4,3,3,0,3]%%%}+%%%{81,[0,0,6,3,3,3,0,3]%%%}+%%%{81,[0,0,6,3,2,4,1,2]%%%}+%%%{-81,[0,0,6,3,1,5,2,1]%%%}+%%%{27,[0,0,6,3,0,6,3,0]%%%}+%%%{27,[0,0,6,2,3,3,0,3]%%%}+%%%{81,[0,0,6,2,2,4,1,2]%%%}+%%%{-81,[0,0,6,2,1,5,2,1]%%%}+%%%{27,[0,0,6,2,0,6,3,0]%%%}+%%%{3,[0,0,6,1,3,3,0,3]%%%}+%%%{27,[0,0,6,1,2,4,1,2]%%%}+%%%{-27,[0,0,6,1,1,5,2,1]%%%}+%%%{9,[0,0,6,1,0,6,3,0]%%%}+%%%{3,[0,0,6,0,2,4,1,2]%%%}+%%%{-3,[0,0,6,0,1,5,2,1]%%%}+%%%{1,[0,0,6,0,0,6,3,0]%%%} / %%%{81,[0,0,7,4,3,4,0,0]%%%}+%%%{108,[0,0,7,3,3,4,0,0]%%%}+%%%{54,[0,0,7,2,3,4,0,0]%%%}+%%%{12,[0,0,7,1,3,4,0,0]%%%}+%%%{1,[0,0,7,0,3,4,0,0]%%%} Error: Bad Argument Value","F(-2)",0
322,-2,0,0,0.000000," ","integrate((a+b*x^n)^2*(c+d*x^n)^(-3-1/n),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{8,[1,0,4,3,1,3,2,0]%%%}+%%%{12,[1,0,4,2,1,3,2,0]%%%}+%%%{6,[1,0,4,1,1,3,2,0]%%%}+%%%{1,[1,0,4,0,1,3,2,0]%%%}+%%%{8,[0,0,4,3,2,2,0,2]%%%}+%%%{8,[0,0,4,2,2,2,0,2]%%%}+%%%{8,[0,0,4,2,1,3,1,1]%%%}+%%%{-4,[0,0,4,2,0,4,2,0]%%%}+%%%{2,[0,0,4,1,2,2,0,2]%%%}+%%%{8,[0,0,4,1,1,3,1,1]%%%}+%%%{-4,[0,0,4,1,0,4,2,0]%%%}+%%%{2,[0,0,4,0,1,3,1,1]%%%}+%%%{-1,[0,0,4,0,0,4,2,0]%%%} / %%%{8,[0,0,5,3,2,3,0,0]%%%}+%%%{12,[0,0,5,2,2,3,0,0]%%%}+%%%{6,[0,0,5,1,2,3,0,0]%%%}+%%%{1,[0,0,5,0,2,3,0,0]%%%} Error: Bad Argument Value","F(-2)",0
323,-2,0,0,0.000000," ","integrate((a+b*x^n)*(c+d*x^n)^(-2-1/n),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[0,0,2,2,1,1,0,1]%%%}+%%%{1,[0,0,2,1,1,1,0,1]%%%}+%%%{1,[0,0,2,1,0,2,1,0]%%%}+%%%{1,[0,0,2,0,0,2,1,0]%%%} / %%%{1,[0,0,3,2,1,2,0,0]%%%}+%%%{2,[0,0,3,1,1,2,0,0]%%%}+%%%{1,[0,0,3,0,1,2,0,0]%%%} Error: Bad Argument Value","F(-2)",0
324,0,0,0,0.000000," ","integrate((c+d*x^n)^(-1-1/n),x, algorithm=""giac"")","\int {\left(d x^{n} + c\right)}^{-\frac{1}{n} - 1}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n - 1), x)","F",0
325,0,0,0,0.000000," ","integrate(1/(a+b*x^n)/((c+d*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)} {\left(d x^{n} + c\right)}^{\left(\frac{1}{n}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)*(d*x^n + c)^(1/n)), x)","F",0
326,0,0,0,0.000000," ","integrate((c+d*x^n)^(1-1/n)/(a+b*x^n)^2,x, algorithm=""giac"")","\int \frac{{\left(d x^{n} + c\right)}^{-\frac{1}{n} + 1}}{{\left(b x^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n + 1)/(b*x^n + a)^2, x)","F",0
327,0,0,0,0.000000," ","integrate((c+d*x^n)^(2-1/n)/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{{\left(d x^{n} + c\right)}^{-\frac{1}{n} + 2}}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n + 2)/(b*x^n + a)^3, x)","F",0
328,0,0,0,0.000000," ","integrate((a+b*x^n)^p*(c+d*x^n)^(-2-1/n-p),x, algorithm=""giac"")","\int {\left(b x^{n} + a\right)}^{p} {\left(d x^{n} + c\right)}^{-p - \frac{1}{n} - 2}\,{d x}"," ",0,"integrate((b*x^n + a)^p*(d*x^n + c)^(-p - 1/n - 2), x)","F",0
329,0,0,0,0.000000," ","integrate((a+b*x^n)^((a*d*n-b*c*(1+n))/(-a*d+b*c)/n)*(c+d*x^n)^((a*d*n-b*c*n+a*d)/(-a*d*n+b*c*n)),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{\frac{b c {\left(n + 1\right)} - a d n}{{\left(b c - a d\right)} n}} {\left(d x^{n} + c\right)}^{\frac{b c n - a d n - a d}{b c n - a d n}}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^((b*c*(n + 1) - a*d*n)/((b*c - a*d)*n))*(d*x^n + c)^((b*c*n - a*d*n - a*d)/(b*c*n - a*d*n))), x)","F",0
330,-2,0,0,0.000000," ","integrate((a+b*x^n)^2*(c+d*x^n)^(-4-1/n),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{27,[1,0,4,3,1,3,2,0]%%%}+%%%{27,[1,0,4,2,1,3,2,0]%%%}+%%%{9,[1,0,4,1,1,3,2,0]%%%}+%%%{1,[1,0,4,0,1,3,2,0]%%%}+%%%{27,[0,0,4,3,2,2,0,2]%%%}+%%%{18,[0,0,4,2,2,2,0,2]%%%}+%%%{18,[0,0,4,2,1,3,1,1]%%%}+%%%{-9,[0,0,4,2,0,4,2,0]%%%}+%%%{3,[0,0,4,1,2,2,0,2]%%%}+%%%{12,[0,0,4,1,1,3,1,1]%%%}+%%%{-6,[0,0,4,1,0,4,2,0]%%%}+%%%{2,[0,0,4,0,1,3,1,1]%%%}+%%%{-1,[0,0,4,0,0,4,2,0]%%%} / %%%{27,[0,0,5,3,2,3,0,0]%%%}+%%%{27,[0,0,5,2,2,3,0,0]%%%}+%%%{9,[0,0,5,1,2,3,0,0]%%%}+%%%{1,[0,0,5,0,2,3,0,0]%%%} Error: Bad Argument Value","F(-2)",0
331,-2,0,0,0.000000," ","integrate((a+b*x^n)*(c+d*x^n)^(-3-1/n),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{4,[0,0,2,2,1,1,0,1]%%%}+%%%{2,[0,0,2,1,1,1,0,1]%%%}+%%%{2,[0,0,2,1,0,2,1,0]%%%}+%%%{1,[0,0,2,0,0,2,1,0]%%%} / %%%{4,[0,0,3,2,1,2,0,0]%%%}+%%%{4,[0,0,3,1,1,2,0,0]%%%}+%%%{1,[0,0,3,0,1,2,0,0]%%%} Error: Bad Argument Value","F(-2)",0
332,0,0,0,0.000000," ","integrate((c+d*x^n)^(-2-1/n),x, algorithm=""giac"")","\int {\left(d x^{n} + c\right)}^{-\frac{1}{n} - 2}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n - 2), x)","F",0
333,0,0,0,0.000000," ","integrate((c+d*x^n)^(-1-1/n)/(a+b*x^n),x, algorithm=""giac"")","\int \frac{{\left(d x^{n} + c\right)}^{-\frac{1}{n} - 1}}{b x^{n} + a}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n - 1)/(b*x^n + a), x)","F",0
334,0,0,0,0.000000," ","integrate(1/(a+b*x^n)^2/((c+d*x^n)^(1/n)),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{n} + a\right)}^{2} {\left(d x^{n} + c\right)}^{\left(\frac{1}{n}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^n + a)^2*(d*x^n + c)^(1/n)), x)","F",0
335,0,0,0,0.000000," ","integrate((c+d*x^n)^(1-1/n)/(a+b*x^n)^3,x, algorithm=""giac"")","\int \frac{{\left(d x^{n} + c\right)}^{-\frac{1}{n} + 1}}{{\left(b x^{n} + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n + 1)/(b*x^n + a)^3, x)","F",0
336,0,0,0,0.000000," ","integrate((c+d*x^n)^(2-1/n)/(a+b*x^n)^4,x, algorithm=""giac"")","\int \frac{{\left(d x^{n} + c\right)}^{-\frac{1}{n} + 2}}{{\left(b x^{n} + a\right)}^{4}}\,{d x}"," ",0,"integrate((d*x^n + c)^(-1/n + 2)/(b*x^n + a)^4, x)","F",0
337,1,621,0,0.759851," ","integrate(x^5*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{168 \, {\left({\left({\left(2 \, {\left({\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{5 \, {\left(d x + c\right)}}{d^{5}} - \frac{31 \, c}{d^{5}}\right)} + \frac{321 \, c^{2}}{d^{5}}\right)} - \frac{451 \, c^{3}}{d^{5}}\right)} {\left(d x + c\right)} + \frac{745 \, c^{4}}{d^{5}}\right)} {\left(d x + c\right)} - \frac{405 \, c^{5}}{d^{5}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{150 \, c^{6} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{5}}\right)} a c + 3 \, {\left({\left({\left(2 \, {\left({\left(4 \, {\left(5 \, {\left(d x + c\right)} {\left(6 \, {\left(d x + c\right)} {\left(\frac{7 \, {\left(d x + c\right)}}{d^{7}} - \frac{57 \, c}{d^{7}}\right)} + \frac{1219 \, c^{2}}{d^{7}}\right)} - \frac{12463 \, c^{3}}{d^{7}}\right)} {\left(d x + c\right)} + \frac{64233 \, c^{4}}{d^{7}}\right)} {\left(d x + c\right)} - \frac{53963 \, c^{5}}{d^{7}}\right)} {\left(d x + c\right)} + \frac{59465 \, c^{6}}{d^{7}}\right)} {\left(d x + c\right)} - \frac{23205 \, c^{7}}{d^{7}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{7350 \, c^{8} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{7}}\right)} b c + 24 \, {\left({\left({\left(2 \, {\left({\left(4 \, {\left(d x + c\right)} {\left(5 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{6}} - \frac{43 \, c}{d^{6}}\right)} + \frac{661 \, c^{2}}{d^{6}}\right)} - \frac{4551 \, c^{3}}{d^{6}}\right)} {\left(d x + c\right)} + \frac{4781 \, c^{4}}{d^{6}}\right)} {\left(d x + c\right)} - \frac{6335 \, c^{5}}{d^{6}}\right)} {\left(d x + c\right)} + \frac{2835 \, c^{6}}{d^{6}}\right)} \sqrt{d x + c} \sqrt{d x - c} + \frac{1050 \, c^{7} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{6}}\right)} a d + {\left({\left({\left(2 \, {\left({\left(4 \, {\left(5 \, {\left(2 \, {\left(d x + c\right)} {\left(7 \, {\left(d x + c\right)} {\left(\frac{8 \, {\left(d x + c\right)}}{d^{8}} - \frac{73 \, c}{d^{8}}\right)} + \frac{2073 \, c^{2}}{d^{8}}\right)} - \frac{9833 \, c^{3}}{d^{8}}\right)} {\left(d x + c\right)} + \frac{75293 \, c^{4}}{d^{8}}\right)} {\left(d x + c\right)} - \frac{310203 \, c^{5}}{d^{8}}\right)} {\left(d x + c\right)} + \frac{216993 \, c^{6}}{d^{8}}\right)} {\left(d x + c\right)} - \frac{205275 \, c^{7}}{d^{8}}\right)} {\left(d x + c\right)} + \frac{69615 \, c^{8}}{d^{8}}\right)} \sqrt{d x + c} \sqrt{d x - c} + \frac{22050 \, c^{9} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{8}}\right)} b d}{40320 \, d}"," ",0,"1/40320*(168*(((2*((d*x + c)*(4*(d*x + c)*(5*(d*x + c)/d^5 - 31*c/d^5) + 321*c^2/d^5) - 451*c^3/d^5)*(d*x + c) + 745*c^4/d^5)*(d*x + c) - 405*c^5/d^5)*sqrt(d*x + c)*sqrt(d*x - c) - 150*c^6*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^5)*a*c + 3*(((2*((4*(5*(d*x + c)*(6*(d*x + c)*(7*(d*x + c)/d^7 - 57*c/d^7) + 1219*c^2/d^7) - 12463*c^3/d^7)*(d*x + c) + 64233*c^4/d^7)*(d*x + c) - 53963*c^5/d^7)*(d*x + c) + 59465*c^6/d^7)*(d*x + c) - 23205*c^7/d^7)*sqrt(d*x + c)*sqrt(d*x - c) - 7350*c^8*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^7)*b*c + 24*(((2*((4*(d*x + c)*(5*(d*x + c)*(6*(d*x + c)/d^6 - 43*c/d^6) + 661*c^2/d^6) - 4551*c^3/d^6)*(d*x + c) + 4781*c^4/d^6)*(d*x + c) - 6335*c^5/d^6)*(d*x + c) + 2835*c^6/d^6)*sqrt(d*x + c)*sqrt(d*x - c) + 1050*c^7*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^6)*a*d + (((2*((4*(5*(2*(d*x + c)*(7*(d*x + c)*(8*(d*x + c)/d^8 - 73*c/d^8) + 2073*c^2/d^8) - 9833*c^3/d^8)*(d*x + c) + 75293*c^4/d^8)*(d*x + c) - 310203*c^5/d^8)*(d*x + c) + 216993*c^6/d^8)*(d*x + c) - 205275*c^7/d^8)*(d*x + c) + 69615*c^8/d^8)*sqrt(d*x + c)*sqrt(d*x - c) + 22050*c^9*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^8)*b*d)/d","B",0
338,1,495,0,0.748309," ","integrate(x^3*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{70 \, {\left({\left({\left(d x + c\right)} {\left(2 \, {\left(d x + c\right)} {\left(\frac{3 \, {\left(d x + c\right)}}{d^{3}} - \frac{13 \, c}{d^{3}}\right)} + \frac{43 \, c^{2}}{d^{3}}\right)} - \frac{39 \, c^{3}}{d^{3}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{18 \, c^{4} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{3}}\right)} a c + 7 \, {\left({\left({\left(2 \, {\left({\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{5 \, {\left(d x + c\right)}}{d^{5}} - \frac{31 \, c}{d^{5}}\right)} + \frac{321 \, c^{2}}{d^{5}}\right)} - \frac{451 \, c^{3}}{d^{5}}\right)} {\left(d x + c\right)} + \frac{745 \, c^{4}}{d^{5}}\right)} {\left(d x + c\right)} - \frac{405 \, c^{5}}{d^{5}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{150 \, c^{6} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{5}}\right)} b c + 14 \, {\left({\left({\left(2 \, {\left(d x + c\right)} {\left(3 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{4}} - \frac{21 \, c}{d^{4}}\right)} + \frac{133 \, c^{2}}{d^{4}}\right)} - \frac{295 \, c^{3}}{d^{4}}\right)} {\left(d x + c\right)} + \frac{195 \, c^{4}}{d^{4}}\right)} \sqrt{d x + c} \sqrt{d x - c} + \frac{90 \, c^{5} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{4}}\right)} a d + {\left({\left({\left(2 \, {\left({\left(4 \, {\left(d x + c\right)} {\left(5 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{6}} - \frac{43 \, c}{d^{6}}\right)} + \frac{661 \, c^{2}}{d^{6}}\right)} - \frac{4551 \, c^{3}}{d^{6}}\right)} {\left(d x + c\right)} + \frac{4781 \, c^{4}}{d^{6}}\right)} {\left(d x + c\right)} - \frac{6335 \, c^{5}}{d^{6}}\right)} {\left(d x + c\right)} + \frac{2835 \, c^{6}}{d^{6}}\right)} \sqrt{d x + c} \sqrt{d x - c} + \frac{1050 \, c^{7} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{6}}\right)} b d}{1680 \, d}"," ",0,"1/1680*(70*(((d*x + c)*(2*(d*x + c)*(3*(d*x + c)/d^3 - 13*c/d^3) + 43*c^2/d^3) - 39*c^3/d^3)*sqrt(d*x + c)*sqrt(d*x - c) - 18*c^4*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^3)*a*c + 7*(((2*((d*x + c)*(4*(d*x + c)*(5*(d*x + c)/d^5 - 31*c/d^5) + 321*c^2/d^5) - 451*c^3/d^5)*(d*x + c) + 745*c^4/d^5)*(d*x + c) - 405*c^5/d^5)*sqrt(d*x + c)*sqrt(d*x - c) - 150*c^6*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^5)*b*c + 14*(((2*(d*x + c)*(3*(d*x + c)*(4*(d*x + c)/d^4 - 21*c/d^4) + 133*c^2/d^4) - 295*c^3/d^4)*(d*x + c) + 195*c^4/d^4)*sqrt(d*x + c)*sqrt(d*x - c) + 90*c^5*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^4)*a*d + (((2*((4*(d*x + c)*(5*(d*x + c)*(6*(d*x + c)/d^6 - 43*c/d^6) + 661*c^2/d^6) - 4551*c^3/d^6)*(d*x + c) + 4781*c^4/d^6)*(d*x + c) - 6335*c^5/d^6)*(d*x + c) + 2835*c^6/d^6)*sqrt(d*x + c)*sqrt(d*x - c) + 1050*c^7*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^6)*b*d)/d","B",0
339,1,361,0,0.370973," ","integrate(x*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{5 \, {\left({\left({\left(d x + c\right)} {\left(2 \, {\left(d x + c\right)} {\left(\frac{3 \, {\left(d x + c\right)}}{d^{3}} - \frac{13 \, c}{d^{3}}\right)} + \frac{43 \, c^{2}}{d^{3}}\right)} - \frac{39 \, c^{3}}{d^{3}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{18 \, c^{4} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{3}}\right)} b c + 20 \, {\left(\sqrt{d x + c} \sqrt{d x - c} {\left({\left(d x + c\right)} {\left(\frac{2 \, {\left(d x + c\right)}}{d^{2}} - \frac{7 \, c}{d^{2}}\right)} + \frac{9 \, c^{2}}{d^{2}}\right)} + \frac{6 \, c^{3} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{2}}\right)} a d + {\left({\left({\left(2 \, {\left(d x + c\right)} {\left(3 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{4}} - \frac{21 \, c}{d^{4}}\right)} + \frac{133 \, c^{2}}{d^{4}}\right)} - \frac{295 \, c^{3}}{d^{4}}\right)} {\left(d x + c\right)} + \frac{195 \, c^{4}}{d^{4}}\right)} \sqrt{d x + c} \sqrt{d x - c} + \frac{90 \, c^{5} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{4}}\right)} b d - \frac{60 \, {\left(2 \, c^{2} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right) - \sqrt{d x + c} \sqrt{d x - c} {\left(d x - 2 \, c\right)}\right)} a c}{d}}{120 \, d}"," ",0,"1/120*(5*(((d*x + c)*(2*(d*x + c)*(3*(d*x + c)/d^3 - 13*c/d^3) + 43*c^2/d^3) - 39*c^3/d^3)*sqrt(d*x + c)*sqrt(d*x - c) - 18*c^4*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^3)*b*c + 20*(sqrt(d*x + c)*sqrt(d*x - c)*((d*x + c)*(2*(d*x + c)/d^2 - 7*c/d^2) + 9*c^2/d^2) + 6*c^3*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^2)*a*d + (((2*(d*x + c)*(3*(d*x + c)*(4*(d*x + c)/d^4 - 21*c/d^4) + 133*c^2/d^4) - 295*c^3/d^4)*(d*x + c) + 195*c^4/d^4)*sqrt(d*x + c)*sqrt(d*x - c) + 90*c^5*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^4)*b*d - 60*(2*c^2*log(abs(-sqrt(d*x + c) + sqrt(d*x - c))) - sqrt(d*x + c)*sqrt(d*x - c)*(d*x - 2*c))*a*c/d)/d","B",0
340,1,78,0,0.319925," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x,x, algorithm=""giac"")","2 \, a c \arctan\left(\frac{{\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}}{2 \, c}\right) + \frac{1}{3} \, \sqrt{d x + c} \sqrt{d x - c} {\left({\left(d x + c\right)} {\left(\frac{{\left(d x + c\right)} b}{d^{2}} - \frac{2 \, b c}{d^{2}}\right)} + 3 \, a\right)}"," ",0,"2*a*c*arctan(1/2*(sqrt(d*x + c) - sqrt(d*x - c))^2/c) + 1/3*sqrt(d*x + c)*sqrt(d*x - c)*((d*x + c)*((d*x + c)*b/d^2 - 2*b*c/d^2) + 3*a)","A",0
341,1,157,0,0.421218," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^3,x, algorithm=""giac"")","\frac{\sqrt{d x + c} \sqrt{d x - c} b d + \frac{{\left(2 \, b c^{2} d - a d^{3}\right)} \arctan\left(\frac{{\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}}{2 \, c}\right)}{c} + \frac{2 \, {\left(a d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{6} - 4 \, a c^{2} d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2}\right)}^{2}}}{d}"," ",0,"(sqrt(d*x + c)*sqrt(d*x - c)*b*d + (2*b*c^2*d - a*d^3)*arctan(1/2*(sqrt(d*x + c) - sqrt(d*x - c))^2/c)/c + 2*(a*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^6 - 4*a*c^2*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^2)/((sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2)^2)/d","A",0
342,1,324,0,0.454645," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^5,x, algorithm=""giac"")","-\frac{\frac{{\left(4 \, b c^{2} d^{3} + a d^{5}\right)} \arctan\left(\frac{{\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}}{2 \, c}\right)}{c^{3}} - \frac{2 \, {\left(4 \, b c^{2} d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{14} - a d^{5} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{14} + 16 \, b c^{4} d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{10} + 28 \, a c^{2} d^{5} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{10} - 64 \, b c^{6} d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{6} - 112 \, a c^{4} d^{5} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{6} - 256 \, b c^{8} d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 64 \, a c^{6} d^{5} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2}\right)}^{4} c^{2}}}{4 \, d}"," ",0,"-1/4*((4*b*c^2*d^3 + a*d^5)*arctan(1/2*(sqrt(d*x + c) - sqrt(d*x - c))^2/c)/c^3 - 2*(4*b*c^2*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^14 - a*d^5*(sqrt(d*x + c) - sqrt(d*x - c))^14 + 16*b*c^4*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^10 + 28*a*c^2*d^5*(sqrt(d*x + c) - sqrt(d*x - c))^10 - 64*b*c^6*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^6 - 112*a*c^4*d^5*(sqrt(d*x + c) - sqrt(d*x - c))^6 - 256*b*c^8*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^2 + 64*a*c^6*d^5*(sqrt(d*x + c) - sqrt(d*x - c))^2)/(((sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2)^4*c^2))/d","B",0
343,1,558,0,0.626783," ","integrate(x^4*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{112 \, {\left({\left({\left(2 \, {\left(d x + c\right)} {\left(3 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{4}} - \frac{21 \, c}{d^{4}}\right)} + \frac{133 \, c^{2}}{d^{4}}\right)} - \frac{295 \, c^{3}}{d^{4}}\right)} {\left(d x + c\right)} + \frac{195 \, c^{4}}{d^{4}}\right)} \sqrt{d x + c} \sqrt{d x - c} + \frac{90 \, c^{5} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{4}}\right)} a c + 8 \, {\left({\left({\left(2 \, {\left({\left(4 \, {\left(d x + c\right)} {\left(5 \, {\left(d x + c\right)} {\left(\frac{6 \, {\left(d x + c\right)}}{d^{6}} - \frac{43 \, c}{d^{6}}\right)} + \frac{661 \, c^{2}}{d^{6}}\right)} - \frac{4551 \, c^{3}}{d^{6}}\right)} {\left(d x + c\right)} + \frac{4781 \, c^{4}}{d^{6}}\right)} {\left(d x + c\right)} - \frac{6335 \, c^{5}}{d^{6}}\right)} {\left(d x + c\right)} + \frac{2835 \, c^{6}}{d^{6}}\right)} \sqrt{d x + c} \sqrt{d x - c} + \frac{1050 \, c^{7} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{6}}\right)} b c + 56 \, {\left({\left({\left(2 \, {\left({\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{5 \, {\left(d x + c\right)}}{d^{5}} - \frac{31 \, c}{d^{5}}\right)} + \frac{321 \, c^{2}}{d^{5}}\right)} - \frac{451 \, c^{3}}{d^{5}}\right)} {\left(d x + c\right)} + \frac{745 \, c^{4}}{d^{5}}\right)} {\left(d x + c\right)} - \frac{405 \, c^{5}}{d^{5}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{150 \, c^{6} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{5}}\right)} a d + {\left({\left({\left(2 \, {\left({\left(4 \, {\left(5 \, {\left(d x + c\right)} {\left(6 \, {\left(d x + c\right)} {\left(\frac{7 \, {\left(d x + c\right)}}{d^{7}} - \frac{57 \, c}{d^{7}}\right)} + \frac{1219 \, c^{2}}{d^{7}}\right)} - \frac{12463 \, c^{3}}{d^{7}}\right)} {\left(d x + c\right)} + \frac{64233 \, c^{4}}{d^{7}}\right)} {\left(d x + c\right)} - \frac{53963 \, c^{5}}{d^{7}}\right)} {\left(d x + c\right)} + \frac{59465 \, c^{6}}{d^{7}}\right)} {\left(d x + c\right)} - \frac{23205 \, c^{7}}{d^{7}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{7350 \, c^{8} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{7}}\right)} b d}{13440 \, d}"," ",0,"1/13440*(112*(((2*(d*x + c)*(3*(d*x + c)*(4*(d*x + c)/d^4 - 21*c/d^4) + 133*c^2/d^4) - 295*c^3/d^4)*(d*x + c) + 195*c^4/d^4)*sqrt(d*x + c)*sqrt(d*x - c) + 90*c^5*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^4)*a*c + 8*(((2*((4*(d*x + c)*(5*(d*x + c)*(6*(d*x + c)/d^6 - 43*c/d^6) + 661*c^2/d^6) - 4551*c^3/d^6)*(d*x + c) + 4781*c^4/d^6)*(d*x + c) - 6335*c^5/d^6)*(d*x + c) + 2835*c^6/d^6)*sqrt(d*x + c)*sqrt(d*x - c) + 1050*c^7*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^6)*b*c + 56*(((2*((d*x + c)*(4*(d*x + c)*(5*(d*x + c)/d^5 - 31*c/d^5) + 321*c^2/d^5) - 451*c^3/d^5)*(d*x + c) + 745*c^4/d^5)*(d*x + c) - 405*c^5/d^5)*sqrt(d*x + c)*sqrt(d*x - c) - 150*c^6*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^5)*a*d + (((2*((4*(5*(d*x + c)*(6*(d*x + c)*(7*(d*x + c)/d^7 - 57*c/d^7) + 1219*c^2/d^7) - 12463*c^3/d^7)*(d*x + c) + 64233*c^4/d^7)*(d*x + c) - 53963*c^5/d^7)*(d*x + c) + 59465*c^6/d^7)*(d*x + c) - 23205*c^7/d^7)*sqrt(d*x + c)*sqrt(d*x - c) - 7350*c^8*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^7)*b*d)/d","B",0
344,1,432,0,0.457767," ","integrate(x^2*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{40 \, {\left(\sqrt{d x + c} \sqrt{d x - c} {\left({\left(d x + c\right)} {\left(\frac{2 \, {\left(d x + c\right)}}{d^{2}} - \frac{7 \, c}{d^{2}}\right)} + \frac{9 \, c^{2}}{d^{2}}\right)} + \frac{6 \, c^{3} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{2}}\right)} a c + 2 \, {\left({\left({\left(2 \, {\left(d x + c\right)} {\left(3 \, {\left(d x + c\right)} {\left(\frac{4 \, {\left(d x + c\right)}}{d^{4}} - \frac{21 \, c}{d^{4}}\right)} + \frac{133 \, c^{2}}{d^{4}}\right)} - \frac{295 \, c^{3}}{d^{4}}\right)} {\left(d x + c\right)} + \frac{195 \, c^{4}}{d^{4}}\right)} \sqrt{d x + c} \sqrt{d x - c} + \frac{90 \, c^{5} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{4}}\right)} b c + 10 \, {\left({\left({\left(d x + c\right)} {\left(2 \, {\left(d x + c\right)} {\left(\frac{3 \, {\left(d x + c\right)}}{d^{3}} - \frac{13 \, c}{d^{3}}\right)} + \frac{43 \, c^{2}}{d^{3}}\right)} - \frac{39 \, c^{3}}{d^{3}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{18 \, c^{4} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{3}}\right)} a d + {\left({\left({\left(2 \, {\left({\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{5 \, {\left(d x + c\right)}}{d^{5}} - \frac{31 \, c}{d^{5}}\right)} + \frac{321 \, c^{2}}{d^{5}}\right)} - \frac{451 \, c^{3}}{d^{5}}\right)} {\left(d x + c\right)} + \frac{745 \, c^{4}}{d^{5}}\right)} {\left(d x + c\right)} - \frac{405 \, c^{5}}{d^{5}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{150 \, c^{6} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{5}}\right)} b d}{240 \, d}"," ",0,"1/240*(40*(sqrt(d*x + c)*sqrt(d*x - c)*((d*x + c)*(2*(d*x + c)/d^2 - 7*c/d^2) + 9*c^2/d^2) + 6*c^3*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^2)*a*c + 2*(((2*(d*x + c)*(3*(d*x + c)*(4*(d*x + c)/d^4 - 21*c/d^4) + 133*c^2/d^4) - 295*c^3/d^4)*(d*x + c) + 195*c^4/d^4)*sqrt(d*x + c)*sqrt(d*x - c) + 90*c^5*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^4)*b*c + 10*(((d*x + c)*(2*(d*x + c)*(3*(d*x + c)/d^3 - 13*c/d^3) + 43*c^2/d^3) - 39*c^3/d^3)*sqrt(d*x + c)*sqrt(d*x - c) - 18*c^4*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^3)*a*d + (((2*((d*x + c)*(4*(d*x + c)*(5*(d*x + c)/d^5 - 31*c/d^5) + 321*c^2/d^5) - 451*c^3/d^5)*(d*x + c) + 745*c^4/d^5)*(d*x + c) - 405*c^5/d^5)*sqrt(d*x + c)*sqrt(d*x - c) - 150*c^6*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^5)*b*d)/d","B",0
345,1,288,0,0.350363," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{24 \, {\left(2 \, c \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right) + \sqrt{d x + c} \sqrt{d x - c}\right)} a c + 4 \, {\left(\sqrt{d x + c} \sqrt{d x - c} {\left({\left(d x + c\right)} {\left(\frac{2 \, {\left(d x + c\right)}}{d^{2}} - \frac{7 \, c}{d^{2}}\right)} + \frac{9 \, c^{2}}{d^{2}}\right)} + \frac{6 \, c^{3} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{2}}\right)} b c + {\left({\left({\left(d x + c\right)} {\left(2 \, {\left(d x + c\right)} {\left(\frac{3 \, {\left(d x + c\right)}}{d^{3}} - \frac{13 \, c}{d^{3}}\right)} + \frac{43 \, c^{2}}{d^{3}}\right)} - \frac{39 \, c^{3}}{d^{3}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{18 \, c^{4} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{3}}\right)} b d - 12 \, {\left(2 \, c^{2} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right) - \sqrt{d x + c} \sqrt{d x - c} {\left(d x - 2 \, c\right)}\right)} a}{24 \, d}"," ",0,"1/24*(24*(2*c*log(abs(-sqrt(d*x + c) + sqrt(d*x - c))) + sqrt(d*x + c)*sqrt(d*x - c))*a*c + 4*(sqrt(d*x + c)*sqrt(d*x - c)*((d*x + c)*(2*(d*x + c)/d^2 - 7*c/d^2) + 9*c^2/d^2) + 6*c^3*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^2)*b*c + (((d*x + c)*(2*(d*x + c)*(3*(d*x + c)/d^3 - 13*c/d^3) + 43*c^2/d^3) - 39*c^3/d^3)*sqrt(d*x + c)*sqrt(d*x - c) - 18*c^4*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^3)*b*d - 12*(2*c^2*log(abs(-sqrt(d*x + c) + sqrt(d*x - c))) - sqrt(d*x + c)*sqrt(d*x - c)*(d*x - 2*c))*a)/d","B",0
346,1,110,0,0.395413," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^2,x, algorithm=""giac"")","-\frac{\frac{32 \, a c^{2} d^{2}}{{\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2}} - 2 \, {\left({\left(d x + c\right)} b - b c\right)} \sqrt{d x + c} \sqrt{d x - c} - {\left(b c^{2} - 2 \, a d^{2}\right)} \log\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4}\right)}{4 \, d}"," ",0,"-1/4*(32*a*c^2*d^2/((sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2) - 2*((d*x + c)*b - b*c)*sqrt(d*x + c)*sqrt(d*x - c) - (b*c^2 - 2*a*d^2)*log((sqrt(d*x + c) - sqrt(d*x - c))^4))/d","A",0
347,1,171,0,0.382530," ","integrate((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{3 \, b d^{2} \log\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4}\right) + \frac{16 \, {\left(3 \, b c^{2} d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{8} - 3 \, a d^{4} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{8} + 24 \, b c^{4} d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 48 \, b c^{6} d^{2} - 16 \, a c^{4} d^{4}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2}\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3*b*d^2*log((sqrt(d*x + c) - sqrt(d*x - c))^4) + 16*(3*b*c^2*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^8 - 3*a*d^4*(sqrt(d*x + c) - sqrt(d*x - c))^8 + 24*b*c^4*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^4 + 48*b*c^6*d^2 - 16*a*c^4*d^4)/((sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2)^3)/d","B",0
348,1,172,0,0.230717," ","integrate(x^4*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""giac"")","\frac{{\left({\left(2 \, {\left({\left(c x + 1\right)} {\left(4 \, {\left(c x + 1\right)} {\left(\frac{{\left(c x + 1\right)} b}{c^{6}} - \frac{5 \, b}{c^{6}}\right)} + \frac{3 \, {\left(2 \, a c^{38} + 15 \, b c^{36}\right)}}{c^{42}}\right)} - \frac{18 \, a c^{38} + 55 \, b c^{36}}{c^{42}}\right)} {\left(c x + 1\right)} + \frac{54 \, a c^{38} + 85 \, b c^{36}}{c^{42}}\right)} {\left(c x + 1\right)} - \frac{3 \, {\left(10 \, a c^{38} + 11 \, b c^{36}\right)}}{c^{42}}\right)} \sqrt{c x + 1} \sqrt{c x - 1} - \frac{6 \, {\left(6 \, a c^{2} + 5 \, b\right)} \log\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}{c^{6}}}{48 \, c}"," ",0,"1/48*(((2*((c*x + 1)*(4*(c*x + 1)*((c*x + 1)*b/c^6 - 5*b/c^6) + 3*(2*a*c^38 + 15*b*c^36)/c^42) - (18*a*c^38 + 55*b*c^36)/c^42)*(c*x + 1) + (54*a*c^38 + 85*b*c^36)/c^42)*(c*x + 1) - 3*(10*a*c^38 + 11*b*c^36)/c^42)*sqrt(c*x + 1)*sqrt(c*x - 1) - 6*(6*a*c^2 + 5*b)*log(sqrt(c*x + 1) - sqrt(c*x - 1))/c^6)/c","A",0
349,1,108,0,0.222850," ","integrate(x^3*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(c x + 1\right)} {\left(3 \, {\left(c x + 1\right)} {\left(\frac{{\left(c x + 1\right)} b}{c^{5}} - \frac{4 \, b}{c^{5}}\right)} + \frac{5 \, a c^{27} + 22 \, b c^{25}}{c^{30}}\right)} - \frac{10 \, {\left(a c^{27} + 2 \, b c^{25}\right)}}{c^{30}}\right)} {\left(c x + 1\right)} + \frac{15 \, {\left(a c^{27} + b c^{25}\right)}}{c^{30}}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{15 \, c}"," ",0,"1/15*(((c*x + 1)*(3*(c*x + 1)*((c*x + 1)*b/c^5 - 4*b/c^5) + (5*a*c^27 + 22*b*c^25)/c^30) - 10*(a*c^27 + 2*b*c^25)/c^30)*(c*x + 1) + 15*(a*c^27 + b*c^25)/c^30)*sqrt(c*x + 1)*sqrt(c*x - 1)/c","A",0
350,1,121,0,0.372966," ","integrate(x^2*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""giac"")","\frac{{\left({\left(c x + 1\right)} {\left(2 \, {\left(c x + 1\right)} {\left(\frac{{\left(c x + 1\right)} b}{c^{4}} - \frac{3 \, b}{c^{4}}\right)} + \frac{4 \, a c^{18} + 9 \, b c^{16}}{c^{20}}\right)} - \frac{4 \, a c^{18} + 5 \, b c^{16}}{c^{20}}\right)} \sqrt{c x + 1} \sqrt{c x - 1} - \frac{2 \, {\left(4 \, a c^{2} + 3 \, b\right)} \log\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}{c^{4}}}{8 \, c}"," ",0,"1/8*(((c*x + 1)*(2*(c*x + 1)*((c*x + 1)*b/c^4 - 3*b/c^4) + (4*a*c^18 + 9*b*c^16)/c^20) - (4*a*c^18 + 5*b*c^16)/c^20)*sqrt(c*x + 1)*sqrt(c*x - 1) - 2*(4*a*c^2 + 3*b)*log(sqrt(c*x + 1) - sqrt(c*x - 1))/c^4)/c","A",0
351,1,59,0,0.221684," ","integrate(x*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x + 1} \sqrt{c x - 1} {\left({\left(c x + 1\right)} {\left(\frac{{\left(c x + 1\right)} b}{c^{3}} - \frac{2 \, b}{c^{3}}\right)} + \frac{3 \, {\left(a c^{11} + b c^{9}\right)}}{c^{12}}\right)}}{3 \, c}"," ",0,"1/3*sqrt(c*x + 1)*sqrt(c*x - 1)*((c*x + 1)*((c*x + 1)*b/c^3 - 2*b/c^3) + 3*(a*c^11 + b*c^9)/c^12)/c","A",0
352,1,69,0,0.175571," ","integrate((b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x + 1} \sqrt{c x - 1} {\left(\frac{{\left(c x + 1\right)} b}{c^{2}} - \frac{b}{c^{2}}\right)} - \frac{2 \, {\left(2 \, a c^{2} + b\right)} \log\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}{c^{2}}}{2 \, c}"," ",0,"1/2*(sqrt(c*x + 1)*sqrt(c*x - 1)*((c*x + 1)*b/c^2 - b/c^2) - 2*(2*a*c^2 + b)*log(sqrt(c*x + 1) - sqrt(c*x - 1))/c^2)/c","A",0
353,1,45,0,0.223654," ","integrate((b*x^2+a)/x/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""giac"")","-2 \, a \arctan\left(\frac{1}{2} \, {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{2}\right) + \frac{\sqrt{c x + 1} \sqrt{c x - 1} b}{c^{2}}"," ",0,"-2*a*arctan(1/2*(sqrt(c*x + 1) - sqrt(c*x - 1))^2) + sqrt(c*x + 1)*sqrt(c*x - 1)*b/c^2","A",0
354,1,58,0,0.216172," ","integrate((b*x^2+a)/x^2/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""giac"")","\frac{\frac{16 \, a c^{2}}{{\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{4} + 4} - b \log\left({\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{4}\right)}{2 \, c}"," ",0,"1/2*(16*a*c^2/((sqrt(c*x + 1) - sqrt(c*x - 1))^4 + 4) - b*log((sqrt(c*x + 1) - sqrt(c*x - 1))^4))/c","A",0
355,1,114,0,0.212511," ","integrate((b*x^2+a)/x^3/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""giac"")","-\frac{{\left(a c^{3} + 2 \, b c\right)} \arctan\left(\frac{1}{2} \, {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{2}\right) + \frac{2 \, {\left(a c^{3} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{6} - 4 \, a c^{3} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{2}\right)}}{{\left({\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{4} + 4\right)}^{2}}}{c}"," ",0,"-((a*c^3 + 2*b*c)*arctan(1/2*(sqrt(c*x + 1) - sqrt(c*x - 1))^2) + 2*(a*c^3*(sqrt(c*x + 1) - sqrt(c*x - 1))^6 - 4*a*c^3*(sqrt(c*x + 1) - sqrt(c*x - 1))^2)/((sqrt(c*x + 1) - sqrt(c*x - 1))^4 + 4)^2)/c","B",0
356,1,116,0,0.205735," ","integrate((b*x^2+a)/x^4/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""giac"")","\frac{8 \, {\left(3 \, b c^{2} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{8} + 24 \, a c^{4} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{4} + 24 \, b c^{2} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{4} + 32 \, a c^{4} + 48 \, b c^{2}\right)}}{3 \, {\left({\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{4} + 4\right)}^{3} c}"," ",0,"8/3*(3*b*c^2*(sqrt(c*x + 1) - sqrt(c*x - 1))^8 + 24*a*c^4*(sqrt(c*x + 1) - sqrt(c*x - 1))^4 + 24*b*c^2*(sqrt(c*x + 1) - sqrt(c*x - 1))^4 + 32*a*c^4 + 48*b*c^2)/(((sqrt(c*x + 1) - sqrt(c*x - 1))^4 + 4)^3*c)","B",0
357,1,268,0,0.220773," ","integrate((b*x^2+a)/x^5/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""giac"")","-\frac{{\left(3 \, a c^{5} + 4 \, b c^{3}\right)} \arctan\left(\frac{1}{2} \, {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{2}\right) + \frac{2 \, {\left(3 \, a c^{5} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{14} + 4 \, b c^{3} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{14} + 44 \, a c^{5} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{10} + 16 \, b c^{3} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{10} - 176 \, a c^{5} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{6} - 64 \, b c^{3} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{6} - 192 \, a c^{5} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{2} - 256 \, b c^{3} {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{2}\right)}}{{\left({\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{4} + 4\right)}^{4}}}{4 \, c}"," ",0,"-1/4*((3*a*c^5 + 4*b*c^3)*arctan(1/2*(sqrt(c*x + 1) - sqrt(c*x - 1))^2) + 2*(3*a*c^5*(sqrt(c*x + 1) - sqrt(c*x - 1))^14 + 4*b*c^3*(sqrt(c*x + 1) - sqrt(c*x - 1))^14 + 44*a*c^5*(sqrt(c*x + 1) - sqrt(c*x - 1))^10 + 16*b*c^3*(sqrt(c*x + 1) - sqrt(c*x - 1))^10 - 176*a*c^5*(sqrt(c*x + 1) - sqrt(c*x - 1))^6 - 64*b*c^3*(sqrt(c*x + 1) - sqrt(c*x - 1))^6 - 192*a*c^5*(sqrt(c*x + 1) - sqrt(c*x - 1))^2 - 256*b*c^3*(sqrt(c*x + 1) - sqrt(c*x - 1))^2)/((sqrt(c*x + 1) - sqrt(c*x - 1))^4 + 4)^4)/c","B",0
358,1,203,0,0.279508," ","integrate(x^4*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{{\left({\left(2 \, {\left({\left(d x + c\right)} {\left(4 \, {\left(d x + c\right)} {\left(\frac{{\left(d x + c\right)} b}{d^{6}} - \frac{5 \, b c}{d^{6}}\right)} + \frac{3 \, {\left(15 \, b c^{2} d^{36} + 2 \, a d^{38}\right)}}{d^{42}}\right)} - \frac{55 \, b c^{3} d^{36} + 18 \, a c d^{38}}{d^{42}}\right)} {\left(d x + c\right)} + \frac{85 \, b c^{4} d^{36} + 54 \, a c^{2} d^{38}}{d^{42}}\right)} {\left(d x + c\right)} - \frac{3 \, {\left(11 \, b c^{5} d^{36} + 10 \, a c^{3} d^{38}\right)}}{d^{42}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{6 \, {\left(5 \, b c^{6} + 6 \, a c^{4} d^{2}\right)} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{6}}}{48 \, d}"," ",0,"1/48*(((2*((d*x + c)*(4*(d*x + c)*((d*x + c)*b/d^6 - 5*b*c/d^6) + 3*(15*b*c^2*d^36 + 2*a*d^38)/d^42) - (55*b*c^3*d^36 + 18*a*c*d^38)/d^42)*(d*x + c) + (85*b*c^4*d^36 + 54*a*c^2*d^38)/d^42)*(d*x + c) - 3*(11*b*c^5*d^36 + 10*a*c^3*d^38)/d^42)*sqrt(d*x + c)*sqrt(d*x - c) - 6*(5*b*c^6 + 6*a*c^4*d^2)*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^6)/d","A",0
359,1,124,0,0.251245," ","integrate(x^3*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(d x + c\right)} {\left(3 \, {\left(d x + c\right)} {\left(\frac{{\left(d x + c\right)} b}{d^{5}} - \frac{4 \, b c}{d^{5}}\right)} + \frac{22 \, b c^{2} d^{25} + 5 \, a d^{27}}{d^{30}}\right)} - \frac{10 \, {\left(2 \, b c^{3} d^{25} + a c d^{27}\right)}}{d^{30}}\right)} {\left(d x + c\right)} + \frac{15 \, {\left(b c^{4} d^{25} + a c^{2} d^{27}\right)}}{d^{30}}\right)} \sqrt{d x + c} \sqrt{d x - c}}{15 \, d}"," ",0,"1/15*(((d*x + c)*(3*(d*x + c)*((d*x + c)*b/d^5 - 4*b*c/d^5) + (22*b*c^2*d^25 + 5*a*d^27)/d^30) - 10*(2*b*c^3*d^25 + a*c*d^27)/d^30)*(d*x + c) + 15*(b*c^4*d^25 + a*c^2*d^27)/d^30)*sqrt(d*x + c)*sqrt(d*x - c)/d","A",0
360,1,140,0,0.232882," ","integrate(x^2*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)} {\left(2 \, {\left(d x + c\right)} {\left(\frac{{\left(d x + c\right)} b}{d^{4}} - \frac{3 \, b c}{d^{4}}\right)} + \frac{9 \, b c^{2} d^{16} + 4 \, a d^{18}}{d^{20}}\right)} - \frac{5 \, b c^{3} d^{16} + 4 \, a c d^{18}}{d^{20}}\right)} \sqrt{d x + c} \sqrt{d x - c} - \frac{2 \, {\left(3 \, b c^{4} + 4 \, a c^{2} d^{2}\right)} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{4}}}{8 \, d}"," ",0,"1/8*(((d*x + c)*(2*(d*x + c)*((d*x + c)*b/d^4 - 3*b*c/d^4) + (9*b*c^2*d^16 + 4*a*d^18)/d^20) - (5*b*c^3*d^16 + 4*a*c*d^18)/d^20)*sqrt(d*x + c)*sqrt(d*x - c) - 2*(3*b*c^4 + 4*a*c^2*d^2)*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^4)/d","A",0
361,1,65,0,0.198410," ","integrate(x*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{d x + c} \sqrt{d x - c} {\left({\left(d x + c\right)} {\left(\frac{{\left(d x + c\right)} b}{d^{3}} - \frac{2 \, b c}{d^{3}}\right)} + \frac{3 \, {\left(b c^{2} d^{9} + a d^{11}\right)}}{d^{12}}\right)}}{3 \, d}"," ",0,"1/3*sqrt(d*x + c)*sqrt(d*x - c)*((d*x + c)*((d*x + c)*b/d^3 - 2*b*c/d^3) + 3*(b*c^2*d^9 + a*d^11)/d^12)/d","A",0
362,1,79,0,0.264971," ","integrate((b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{d x + c} \sqrt{d x - c} {\left(\frac{{\left(d x + c\right)} b}{d^{2}} - \frac{b c}{d^{2}}\right)} - \frac{2 \, {\left(b c^{2} + 2 \, a d^{2}\right)} \log\left({\left| -\sqrt{d x + c} + \sqrt{d x - c} \right|}\right)}{d^{2}}}{2 \, d}"," ",0,"1/2*(sqrt(d*x + c)*sqrt(d*x - c)*((d*x + c)*b/d^2 - b*c/d^2) - 2*(b*c^2 + 2*a*d^2)*log(abs(-sqrt(d*x + c) + sqrt(d*x - c)))/d^2)/d","A",0
363,1,55,0,0.209421," ","integrate((b*x^2+a)/x/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, a \arctan\left(\frac{{\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}}{2 \, c}\right)}{c} + \frac{\sqrt{d x + c} \sqrt{d x - c} b}{d^{2}}"," ",0,"-2*a*arctan(1/2*(sqrt(d*x + c) - sqrt(d*x - c))^2/c)/c + sqrt(d*x + c)*sqrt(d*x - c)*b/d^2","A",0
364,1,66,0,0.217387," ","integrate((b*x^2+a)/x^2/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{\frac{16 \, a d^{2}}{{\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2}} - b \log\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4}\right)}{2 \, d}"," ",0,"1/2*(16*a*d^2/((sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2) - b*log((sqrt(d*x + c) - sqrt(d*x - c))^4))/d","A",0
365,1,141,0,0.494288," ","integrate((b*x^2+a)/x^3/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, b c^{2} d + a d^{3}\right)} \arctan\left(\frac{{\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}}{2 \, c}\right)}{c^{3}} + \frac{2 \, {\left(a d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{6} - 4 \, a c^{2} d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2}\right)}^{2} c^{2}}}{d}"," ",0,"-((2*b*c^2*d + a*d^3)*arctan(1/2*(sqrt(d*x + c) - sqrt(d*x - c))^2/c)/c^3 + 2*(a*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^6 - 4*a*c^2*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^2)/(((sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2)^2*c^2))/d","B",0
366,1,137,0,0.243797," ","integrate((b*x^2+a)/x^4/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""giac"")","\frac{8 \, {\left(3 \, b d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{8} + 24 \, b c^{2} d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 24 \, a d^{4} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 48 \, b c^{4} d^{2} + 32 \, a c^{2} d^{4}\right)}}{3 \, {\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2}\right)}^{3} d}"," ",0,"8/3*(3*b*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^8 + 24*b*c^2*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^4 + 24*a*d^4*(sqrt(d*x + c) - sqrt(d*x - c))^4 + 48*b*c^4*d^2 + 32*a*c^2*d^4)/(((sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2)^3*d)","B",0
367,1,325,0,0.270777," ","integrate((b*x^2+a)/x^5/(d*x-c)^(1/2)/(d*x+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{{\left(4 \, b c^{2} d^{3} + 3 \, a d^{5}\right)} \arctan\left(\frac{{\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}}{2 \, c}\right)}{c^{5}} + \frac{2 \, {\left(4 \, b c^{2} d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{14} + 3 \, a d^{5} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{14} + 16 \, b c^{4} d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{10} + 44 \, a c^{2} d^{5} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{10} - 64 \, b c^{6} d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{6} - 176 \, a c^{4} d^{5} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{6} - 256 \, b c^{8} d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} - 192 \, a c^{6} d^{5} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2}\right)}^{4} c^{4}}}{4 \, d}"," ",0,"-1/4*((4*b*c^2*d^3 + 3*a*d^5)*arctan(1/2*(sqrt(d*x + c) - sqrt(d*x - c))^2/c)/c^5 + 2*(4*b*c^2*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^14 + 3*a*d^5*(sqrt(d*x + c) - sqrt(d*x - c))^14 + 16*b*c^4*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^10 + 44*a*c^2*d^5*(sqrt(d*x + c) - sqrt(d*x - c))^10 - 64*b*c^6*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^6 - 176*a*c^4*d^5*(sqrt(d*x + c) - sqrt(d*x - c))^6 - 256*b*c^8*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^2 - 192*a*c^6*d^5*(sqrt(d*x + c) - sqrt(d*x - c))^2)/(((sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2)^4*c^4))/d","B",0
368,1,214,0,0.398141," ","integrate(x^4*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(d x + c\right)} {\left(2 \, {\left(d x + c\right)} {\left(\frac{{\left(d x + c\right)} b}{d^{7}} - \frac{5 \, b c}{d^{7}}\right)} + \frac{25 \, b c^{2} d^{35} + 4 \, a d^{37}}{d^{42}}\right)} - \frac{35 \, b c^{3} d^{35} + 12 \, a c d^{37}}{d^{42}}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(7 \, b c^{4} d^{35} + 2 \, a c^{2} d^{37}\right)}}{d^{42}}\right)} \sqrt{d x + c}}{8 \, \sqrt{d x - c}} - \frac{3 \, {\left(5 \, b c^{4} + 4 \, a c^{2} d^{2}\right)} \log\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}\right)}{8 \, d^{7}} - \frac{2 \, {\left(b c^{5} + a c^{3} d^{2}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 2 \, c\right)} d^{7}}"," ",0,"1/8*(((d*x + c)*(2*(d*x + c)*((d*x + c)*b/d^7 - 5*b*c/d^7) + (25*b*c^2*d^35 + 4*a*d^37)/d^42) - (35*b*c^3*d^35 + 12*a*c*d^37)/d^42)*(d*x + c) + 2*(7*b*c^4*d^35 + 2*a*c^2*d^37)/d^42)*sqrt(d*x + c)/sqrt(d*x - c) - 3/8*(5*b*c^4 + 4*a*c^2*d^2)*log((sqrt(d*x + c) - sqrt(d*x - c))^2)/d^7 - 2*(b*c^5 + a*c^3*d^2)/(((sqrt(d*x + c) - sqrt(d*x - c))^2 + 2*c)*d^7)","A",0
369,1,200,0,0.434910," ","integrate(x^3*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(2 \, {\left(d x + c\right)} {\left({\left(d x + c\right)} {\left(\frac{{\left(d x + c\right)} b}{d^{6}} - \frac{4 \, b c}{d^{6}}\right)} + \frac{10 \, b c^{2} d^{24} + 3 \, a d^{26}}{d^{30}}\right)} - \frac{3 \, {\left(9 \, b c^{3} d^{24} + 5 \, a c d^{26}\right)}}{d^{30}}\right)} \sqrt{d x + c}}{6 \, \sqrt{d x - c}} + \frac{2 \, {\left(b^{2} c^{8} + 2 \, a b c^{6} d^{2} + a^{2} c^{4} d^{4}\right)}}{{\left(b c^{4} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + a c^{2} d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 2 \, b c^{5} + 2 \, a c^{3} d^{2}\right)} d^{6}}"," ",0,"1/6*(2*(d*x + c)*((d*x + c)*((d*x + c)*b/d^6 - 4*b*c/d^6) + (10*b*c^2*d^24 + 3*a*d^26)/d^30) - 3*(9*b*c^3*d^24 + 5*a*c*d^26)/d^30)*sqrt(d*x + c)/sqrt(d*x - c) + 2*(b^2*c^8 + 2*a*b*c^6*d^2 + a^2*c^4*d^4)/((b*c^4*(sqrt(d*x + c) - sqrt(d*x - c))^2 + a*c^2*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^2 + 2*b*c^5 + 2*a*c^3*d^2)*d^6)","B",0
370,1,147,0,0.321136," ","integrate(x^2*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""giac"")","\frac{\sqrt{d x + c} {\left({\left(d x + c\right)} {\left(\frac{{\left(d x + c\right)} b}{d^{5}} - \frac{3 \, b c}{d^{5}}\right)} + \frac{b c^{2} d^{15} - a d^{17}}{d^{20}}\right)}}{2 \, \sqrt{d x - c}} - \frac{{\left(3 \, b c^{2} + 2 \, a d^{2}\right)} \log\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}\right)}{2 \, d^{5}} - \frac{2 \, {\left(b c^{3} + a c d^{2}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 2 \, c\right)} d^{5}}"," ",0,"1/2*sqrt(d*x + c)*((d*x + c)*((d*x + c)*b/d^5 - 3*b*c/d^5) + (b*c^2*d^15 - a*d^17)/d^20)/sqrt(d*x - c) - 1/2*(3*b*c^2 + 2*a*d^2)*log((sqrt(d*x + c) - sqrt(d*x - c))^2)/d^5 - 2*(b*c^3 + a*c*d^2)/(((sqrt(d*x + c) - sqrt(d*x - c))^2 + 2*c)*d^5)","A",0
371,1,152,0,0.279573," ","integrate(x*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""giac"")","\frac{\sqrt{d x + c} {\left(\frac{2 \, {\left(d x + c\right)} b}{d^{4}} - \frac{5 \, b c^{2} d^{8} + a d^{10}}{c d^{12}}\right)}}{2 \, \sqrt{d x - c}} + \frac{2 \, {\left(b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}\right)}}{{\left(b c^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + a d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 2 \, b c^{3} + 2 \, a c d^{2}\right)} d^{4}}"," ",0,"1/2*sqrt(d*x + c)*(2*(d*x + c)*b/d^4 - (5*b*c^2*d^8 + a*d^10)/(c*d^12))/sqrt(d*x - c) + 2*(b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/((b*c^2*(sqrt(d*x + c) - sqrt(d*x - c))^2 + a*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^2 + 2*b*c^3 + 2*a*c*d^2)*d^4)","B",0
372,1,113,0,0.280453," ","integrate((b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""giac"")","-\frac{b \log\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}\right)}{d^{3}} - \frac{2 \, {\left(b c^{2} + a d^{2}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 2 \, c\right)} c d^{3}} - \frac{{\left(b c^{2} d^{3} + a d^{5}\right)} \sqrt{d x + c}}{2 \, \sqrt{d x - c} c^{2} d^{6}}"," ",0,"-b*log((sqrt(d*x + c) - sqrt(d*x - c))^2)/d^3 - 2*(b*c^2 + a*d^2)/(((sqrt(d*x + c) - sqrt(d*x - c))^2 + 2*c)*c*d^3) - 1/2*(b*c^2*d^3 + a*d^5)*sqrt(d*x + c)/(sqrt(d*x - c)*c^2*d^6)","B",0
373,1,115,0,0.362211," ","integrate((b*x^2+a)/x/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""giac"")","\frac{2 \, a \arctan\left(\frac{{\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}}{2 \, c}\right)}{c^{3}} - \frac{{\left(b c^{2} + a d^{2}\right)} \sqrt{d x + c}}{2 \, \sqrt{d x - c} c^{3} d^{2}} + \frac{2 \, {\left(b c^{2} + a d^{2}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 2 \, c\right)} c^{2} d^{2}}"," ",0,"2*a*arctan(1/2*(sqrt(d*x + c) - sqrt(d*x - c))^2/c)/c^3 - 1/2*(b*c^2 + a*d^2)*sqrt(d*x + c)/(sqrt(d*x - c)*c^3*d^2) + 2*(b*c^2 + a*d^2)/(((sqrt(d*x + c) - sqrt(d*x - c))^2 + 2*c)*c^2*d^2)","B",0
374,1,219,0,0.458830," ","integrate((b*x^2+a)/x^2/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""giac"")","-\frac{{\left(b c^{2} + a d^{2}\right)} \sqrt{d x + c}}{2 \, \sqrt{d x - c} c^{4} d} - \frac{2 \, {\left(b c^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + a d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, a c d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 4 \, b c^{4} + 12 \, a c^{2} d^{2}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{6} + 2 \, c {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 8 \, c^{3}\right)} c^{3} d}"," ",0,"-1/2*(b*c^2 + a*d^2)*sqrt(d*x + c)/(sqrt(d*x - c)*c^4*d) - 2*(b*c^2*(sqrt(d*x + c) - sqrt(d*x - c))^4 + a*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*a*c*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^2 + 4*b*c^4 + 12*a*c^2*d^2)/(((sqrt(d*x + c) - sqrt(d*x - c))^6 + 2*c*(sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2*(sqrt(d*x + c) - sqrt(d*x - c))^2 + 8*c^3)*c^3*d)","B",0
375,1,211,0,0.542027," ","integrate((b*x^2+a)/x^3/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(2 \, b c^{2} + 3 \, a d^{2}\right)} \arctan\left(\frac{{\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}}{2 \, c}\right)}{c^{5}} - \frac{{\left(b c^{2} + a d^{2}\right)} \sqrt{d x + c}}{2 \, \sqrt{d x - c} c^{5}} + \frac{2 \, {\left(b c^{2} + a d^{2}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 2 \, c\right)} c^{4}} + \frac{2 \, {\left(a d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{6} - 4 \, a c^{2} d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2}\right)}^{2} c^{4}}"," ",0,"(2*b*c^2 + 3*a*d^2)*arctan(1/2*(sqrt(d*x + c) - sqrt(d*x - c))^2/c)/c^5 - 1/2*(b*c^2 + a*d^2)*sqrt(d*x + c)/(sqrt(d*x - c)*c^5) + 2*(b*c^2 + a*d^2)/(((sqrt(d*x + c) - sqrt(d*x - c))^2 + 2*c)*c^4) + 2*(a*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^6 - 4*a*c^2*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^2)/(((sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2)^2*c^4)","B",0
376,1,242,0,0.727672," ","integrate((b*x^2+a)/x^4/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""giac"")","-\frac{{\left(b c^{2} d + a d^{3}\right)} \sqrt{d x + c}}{2 \, \sqrt{d x - c} c^{6}} - \frac{2 \, {\left(b c^{2} d + a d^{3}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 2 \, c\right)} c^{5}} - \frac{8 \, {\left(3 \, b c^{2} d {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{8} + 3 \, a d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{8} + 24 \, b c^{4} d {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 48 \, a c^{2} d^{3} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 48 \, b c^{6} d + 80 \, a c^{4} d^{3}\right)}}{3 \, {\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2}\right)}^{3} c^{4}}"," ",0,"-1/2*(b*c^2*d + a*d^3)*sqrt(d*x + c)/(sqrt(d*x - c)*c^6) - 2*(b*c^2*d + a*d^3)/(((sqrt(d*x + c) - sqrt(d*x - c))^2 + 2*c)*c^5) - 8/3*(3*b*c^2*d*(sqrt(d*x + c) - sqrt(d*x - c))^8 + 3*a*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^8 + 24*b*c^4*d*(sqrt(d*x + c) - sqrt(d*x - c))^4 + 48*a*c^2*d^3*(sqrt(d*x + c) - sqrt(d*x - c))^4 + 48*b*c^6*d + 80*a*c^4*d^3)/(((sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2)^3*c^4)","B",0
377,1,402,0,0.794324," ","integrate((b*x^2+a)/x^5/(d*x-c)^(3/2)/(d*x+c)^(3/2),x, algorithm=""giac"")","\frac{3 \, {\left(4 \, b c^{2} d^{2} + 5 \, a d^{4}\right)} \arctan\left(\frac{{\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}}{2 \, c}\right)}{4 \, c^{7}} - \frac{{\left(b c^{2} d^{2} + a d^{4}\right)} \sqrt{d x + c}}{2 \, \sqrt{d x - c} c^{7}} + \frac{2 \, {\left(b c^{2} d^{2} + a d^{4}\right)}}{{\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} + 2 \, c\right)} c^{6}} + \frac{4 \, b c^{2} d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{14} + 7 \, a d^{4} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{14} + 16 \, b c^{4} d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{10} + 60 \, a c^{2} d^{4} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{10} - 64 \, b c^{6} d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{6} - 240 \, a c^{4} d^{4} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{6} - 256 \, b c^{8} d^{2} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2} - 448 \, a c^{6} d^{4} {\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{2}}{2 \, {\left({\left(\sqrt{d x + c} - \sqrt{d x - c}\right)}^{4} + 4 \, c^{2}\right)}^{4} c^{6}}"," ",0,"3/4*(4*b*c^2*d^2 + 5*a*d^4)*arctan(1/2*(sqrt(d*x + c) - sqrt(d*x - c))^2/c)/c^7 - 1/2*(b*c^2*d^2 + a*d^4)*sqrt(d*x + c)/(sqrt(d*x - c)*c^7) + 2*(b*c^2*d^2 + a*d^4)/(((sqrt(d*x + c) - sqrt(d*x - c))^2 + 2*c)*c^6) + 1/2*(4*b*c^2*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^14 + 7*a*d^4*(sqrt(d*x + c) - sqrt(d*x - c))^14 + 16*b*c^4*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^10 + 60*a*c^2*d^4*(sqrt(d*x + c) - sqrt(d*x - c))^10 - 64*b*c^6*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^6 - 240*a*c^4*d^4*(sqrt(d*x + c) - sqrt(d*x - c))^6 - 256*b*c^8*d^2*(sqrt(d*x + c) - sqrt(d*x - c))^2 - 448*a*c^6*d^4*(sqrt(d*x + c) - sqrt(d*x - c))^2)/(((sqrt(d*x + c) - sqrt(d*x - c))^4 + 4*c^2)^4*c^6)","B",0
378,1,40,0,0.170539," ","integrate((c^2*x^2+1)/x/(c*x-1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""giac"")","\sqrt{c x + 1} \sqrt{c x - 1} - 2 \, \arctan\left(\frac{1}{2} \, {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{2}\right)"," ",0,"sqrt(c*x + 1)*sqrt(c*x - 1) - 2*arctan(1/2*(sqrt(c*x + 1) - sqrt(c*x - 1))^2)","A",0
379,0,0,0,0.000000," ","integrate((d*x^2+c)/(x^((a^2*d+2*b^2*c)/(a^2*d+b^2*c)))/(b*x-a)^(1/2)/(b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{\sqrt{b x + a} \sqrt{b x - a} x^{\frac{2 \, b^{2} c + a^{2} d}{b^{2} c + a^{2} d}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/(sqrt(b*x + a)*sqrt(b*x - a)*x^((2*b^2*c + a^2*d)/(b^2*c + a^2*d))), x)","F",0
380,0,0,0,0.000000," ","integrate(1/(1+x)^(1/2)/(-1-x^(1/2))^(1/2)/(-1+x^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x + 1} \sqrt{\sqrt{x} - 1} \sqrt{-\sqrt{x} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(x + 1)*sqrt(sqrt(x) - 1)*sqrt(-sqrt(x) - 1)), x)","F",0
381,0,0,0,0.000000," ","integrate(1/(b^2*x+a^2)^(1/2)/(a-b*x^(1/2))^(1/2)/(a+b*x^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b^{2} x + a^{2}} \sqrt{b \sqrt{x} + a} \sqrt{-b \sqrt{x} + a}}\,{d x}"," ",0,"integrate(1/(sqrt(b^2*x + a^2)*sqrt(b*sqrt(x) + a)*sqrt(-b*sqrt(x) + a)), x)","F",0
382,0,0,0,0.000000," ","integrate((a-b*x^n)^p*(a+b*x^n)^p*(c+d*x^(2*n))^q,x, algorithm=""giac"")","\int {\left(d x^{2 \, n} + c\right)}^{q} {\left(b x^{n} + a\right)}^{p} {\left(-b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x^(2*n) + c)^q*(b*x^n + a)^p*(-b*x^n + a)^p, x)","F",0
383,0,0,0,0.000000," ","integrate((a-b*x^n)^p*(a+b*x^n)^p*(a^2+b^2*x^(2*n))^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{2 \, n} + a^{2}\right)}^{p} {\left(b x^{n} + a\right)}^{p} {\left(-b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((b^2*x^(2*n) + a^2)^p*(b*x^n + a)^p*(-b*x^n + a)^p, x)","F",0
384,0,0,0,0.000000," ","integrate((c+d*x^(2*n))^p/(a-b*x^n)/(a+b*x^n),x, algorithm=""giac"")","\int -\frac{{\left(d x^{2 \, n} + c\right)}^{p}}{{\left(b x^{n} + a\right)} {\left(b x^{n} - a\right)}}\,{d x}"," ",0,"integrate(-(d*x^(2*n) + c)^p/((b*x^n + a)*(b*x^n - a)), x)","F",0
385,0,0,0,0.000000," ","integrate((a-b*x^(1/2*n))^p*(a+b*x^(1/2*n))^p*(a^2*d*(1+p)/b^2/(1+(-n*p-2*n-1)/n)+d*x^n)^((-n*p-2*n-1)/n),x, algorithm=""giac"")","\int \frac{{\left(b x^{\frac{1}{2} \, n} + a\right)}^{p} {\left(-b x^{\frac{1}{2} \, n} + a\right)}^{p}}{{\left(d x^{n} - \frac{a^{2} d {\left(p + 1\right)}}{b^{2} {\left(\frac{n p + 2 \, n + 1}{n} - 1\right)}}\right)}^{\frac{n p + 2 \, n + 1}{n}}}\,{d x}"," ",0,"integrate((b*x^(1/2*n) + a)^p*(-b*x^(1/2*n) + a)^p/(d*x^n - a^2*d*(p + 1)/(b^2*((n*p + 2*n + 1)/n - 1)))^((n*p + 2*n + 1)/n), x)","F",0
